%comment; # The Reflective Lorentzian Lattices of Rank 3
%comment; # Daniel Allcock
%comment; #
%comment; # The arcane comment syntax here makes this file readable by both TeX and Perl
%comment; # Arcane header of header/footer pair for wrapping a tex file to make it into a perl script.
%comment; # The purpose of the unused perl hash variable "%comment" is to make all this invisible to TeX.
%comment; # Daniel Allcock 2010

%comment; # Open the very file perl is parsing (ie this file), and extract lines with certain prefixes
%comment; open(FILE, $0) or die("Could not open $0");
%comment; if ($#ARGV==0 && $ARGV[0]=~/explicit/) { while (<FILE>)  { if (s/^%EXPLICIT%//) { print ; } } exit; }
%comment; if ($#ARGV==0 && $ARGV[0]=~/implicit/) { while (<FILE>)  { if (s/^%IMPLICIT%//) { print ; } } exit; }
%comment; if ($#ARGV==0 && $ARGV[0]=~/duality/) { while (<FILE>)  { if (s/^%DUALITY%//) { print ; } } exit; }
%comment; if ($#ARGV==0 && $ARGV[0]=~/all/) { while (<FILE>)  { if (s/^%(IMPLICIT|EXPLICIT|DUALITY)%//) { print ; } } exit; }

%comment; # If none of the above applied, print a usage message
%comment; print "usage:\nperl $0 all\nperl $0 explicit\nperl $0 implicit\nperl $0 duality\n";
%comment; print "Print the reflective rank 3 Lorentzian lattices in PARI-readable format.\n";
%comment; print "(All of them, or those printed explicitly in the paper, or those printed\n";
%comment; print "implicitly in terms of filling and mainification operations, or those obtained\n";
%comment; print "from the explicity/implicitly listed lattices by duality operations.)\n";
%comment; print "The format of each output line is [IP,EDs,roots,W,L].  IP is the\n";
%comment; print "inner product matrix.  EDs are the elementary divisors [a,b,c]\n";
%comment; print "of the lattice inside its dual, with c|b|a, in the sense that the dual\n";
%comment; print "lattice is spanned by (1/a,0,0), (0,1/b,0), (0,0,1/c). The columns of\n";
%comment; print "\"roots\" are the simple roots, W is the number of the Weyl group,\n";
%comment; print "and L is the number of the lattice among all those with that Weyl group.\n";
%comment; print "In this numbering, the explictly printed lattices come first,\n";
%comment; print "in the order printed in the paper, then the implicitly\n";
%comment; print "printed lattices, in some unspecified order, and then the\n";
%comment; print "ones obtained by duality, again in some unspecified order.\n";
%comment; print "Probably you want to redirect all this data to a file, say foo,  by\n";
%comment; print "appending \"> foo\" at the end of one of the command lines above.\n";
%comment; exit;

%comment; # Make Perl ignore the TeX code,  using Perl's slightly obscure "here document" feature.
%comment; # This is needed despite the "exit" command above.
%comment; # The single quotes are essential to stop Perl from parsing the TeX
%comment; # and trying to substitute in values of variables. 
%comment; $variable_to_hold_and_ignore_whole_tex_file = << 'IGNORE_EVERYTHING_HERE';

% CHECKLIST:
%
% cross-references to lemmas, etc. refer to lem-...
% declarations of lemmas, etc. refer to lem-...
% cross-references correct
% parenthesis balance
% spell-checking
% \cite's without arguments.  (LaTeX doesn't complain!)
% consistent use of sets: {:} vs {|} 
% hyphens in Jordan constituents

\documentclass[12pt]{amsart}
\usepackage{amssymb}
\usepackage{graphics}  % pdf file inclusion

% generated by rk3_find_reflectives
\def\SENOCNumNarrowMatrices{416}
\def\SENOCNumNarrowMatricesRejectedRankTwo{1}
\def\SENOCNumNarrowMatricesRejectedPositiveDefinite{0}
\def\SENOCNumNarrowMatricesRejectedImprimitiveRoot{0}
\def\SENOCNumNarrowMatricesRemaining{415}
\def\SENOCNumEnlargements{8348}
\def\SENOCNumEnlargementsRejectedImprimitiveRoot{3727}
\def\SENOCNumEnlargementsRemaining{4621}
\def\SEOCNumNarrowMatrices{3030}
\def\SEOCNumNarrowMatricesRejectedRankTwo{8}
\def\SEOCNumNarrowMatricesRejectedPositiveDefinite{5}
\def\SEOCNumNarrowMatricesRejectedImprimitiveRoot{0}
\def\SEOCNumNarrowMatricesRemaining{3017}
\def\SEOCNumEnlargements{34894}
\def\SEOCNumEnlargementsRejectedImprimitiveRoot{17036}
\def\SEOCNumEnlargementsRemaining{17858}
\def\SPNOCNumNarrowMatrices{9150}
\def\SPNOCNumNarrowMatricesRejectedRankTwo{0}
\def\SPNOCNumNarrowMatricesRejectedPositiveDefinite{0}
\def\SPNOCNumNarrowMatricesRejectedImprimitiveRoot{4153}
\def\SPNOCNumNarrowMatricesRemaining{4997}
\def\SPNOCNumEnlargements{22954}
\def\SPNOCNumEnlargementsRejectedImprimitiveRoot{12392}
\def\SPNOCNumEnlargementsRemaining{10562}
\def\SPOCNumNarrowMatrices{168075}
\def\SPOCNumNarrowMatricesRejectedRankTwo{0}
\def\SPOCNumNarrowMatricesRejectedPositiveDefinite{0}
\def\SPOCNumNarrowMatricesRejectedImprimitiveRoot{84357}
\def\SPOCNumNarrowMatricesRemaining{83718}
\def\SPOCNumEnlargements{311829}
\def\SPOCNumEnlargementsRejectedImprimitiveRoot{181934}
\def\SPOCNumEnlargementsRemaining{129895}
\def\CPNumNarrowMatrices{137235}
\def\CPNumNarrowMatricesRejectedRankTwo{0}
\def\CPNumNarrowMatricesRejectedPositiveDefinite{0}
\def\CPNumNarrowMatricesRejectedImprimitiveRoot{101189}
\def\CPNumNarrowMatricesRemaining{36046}
\def\CPNumEnlargements{134182}
\def\CPNumEnlargementsRejectedImprimitiveRoot{82190}
\def\CPNumEnlargementsRemaining{51992}
\def\TotalNumEnlargements{512207}
\def\TotalNumNarrowMatricesRemaining{128193}
\def\NumCandidates{214928}
% generated by rk3_statistify_candidates
\def\NumCandidatesFailRootSimplicity{10408}
\def\NumRemainingCandidates{204520}
\def\NumCandidatesSSF{2497}
\def\NumCandidatesDistinctSSF{857}
\def\NumCandidatesNonSSF{202023}
% generated by tex_reflectives
% for uniform layout of super- and sub-scripts in corner symbols and genus symbols:
% (#1=dimen to lower superscript, #2=pts to raise subscript, #3=superscript, #4=subscript
\def\above#1#2#3#4{\genfrac{}{}{0pt}{}{\lower#1\hbox{\smash{$\scriptstyle #3$}}}{\raise#2\hbox{\smash{$\scriptstyle #4$}}}}

% 2's, 3's and \infty's with vertical lines through them, for weyl groups with dihedral diagram automorphism groups:
\newdimen{\twowidth}\settowidth{\twowidth}{2}
\newdimen{\halftwo}\setlength{\halftwo}{0.5\twowidth}
\def\slashtwo{2\llap{\hbox to 0pt{\hss$|$\hss}\kern\halftwo}}
\newdimen{\threewidth}\settowidth{\threewidth}{3}
\newdimen{\halfthree}\setlength{\halfthree}{0.5\threewidth}
\def\slashthree{3\llap{\hbox to 0pt{\hss$|$\hss}\kern\halfthree}}
\newdimen{\inftywidth}\settowidth{\inftywidth}{$\infty$}
\newdimen{\halfinfty}\setlength{\halfinfty}{0.5\inftywidth}
\def\slashinfty{\infty\llap{\hbox to 0pt{\hss$|$\hss}\kern\halfinfty}}

% these interact delicately to enable the same tex code to lay out several different cases in the table.
% don't tweak carelessly.  Typesetting goals (last most preferable; 2nd matrix may be absent):
%
% [xxxxxxxxxx].......
% [xxxxxxxxxx][xxxxxx
% ...xxxxxxxxxxxxxxx]
% or
% [xxxxxxxxxx].......
% [xxxxxxxxxx].......
% ......[xxxxxxxxxxx]
% or
% [xxxxxxx][xxxx][xxx
% ..xxxxxxxxxxxxxxxx]
% or
% [xxxxx][xxx].......
% ......[xxxxxxxxxxx]
% or
% [xxxxx][xxx]...[xx]
%
\def\BreakWithGlue#1#2#3{\nolinebreak\hskip #1\hbox{}\penalty #2\hbox{}\nolinebreak\hskip #3}
\def\EasyButWeakLineBreak{\BreakWithGlue{0pt plus 1 fill}{500}{0pt plus 1 fill}}
\def\HardButStrongLineBreak{\BreakWithGlue{0pt plus 1 filll}{600}{0pt plus -1 filll}}
%
% #1 is header material put before the "tabular", #2--#4 are column entries
\def\OneColumnOfMatrix#1#2#3#4{\begingroup #1\begin{tabular}{@{}c@{}}#2\\#3\\#4\end{tabular}\endgroup}

% other macros for the table
\newcommand\spacer{\ }
\def\instructions#1{$\langle #1\rangle$}
\def\pdualwitharg#1{\mathop{\hbox{$#1$-dual}}\nolimits}
\def\pfillwitharg#1{\mathop{\hbox{$#1$-fill}}\nolimits}
\def\main{\mathop{\rm main}\nolimits}
\def\iso{\cong}

\long\def\GramMatrix#1{#1} % This line second ==> prints Gram Matrices
\long\def\GramMatrix#1{}   % This line second ==> doesn't.
% computer-computed values for use in the paper
\def\NumLattices{8595}
\def\NumPrintedExplicitly{704}
\def\NumPrintedImplicitly{715}
\def\NumGotByDuality{7176}
\def\NumMainLattices{122}
\def\NumSSFbutNotMain{38}
\def\NumTriangles{46}
\def\NumWeylGroups{374}
\def\LargestArea{$12\pi$}
\def\SmallestArea{$\pi/12$}
\def\WeylsWithLargestArea{$W_{329}$, $W_{365}$ and $W_{371}$}
\def\WeylsWithSmallestArea{$W_{3}$}
\def\MostLatticesInWeyl{176}
\def\LeastLatticesInWeyl{1}
\def\WeylsWithMostLattices{$W_{68}$}
\def\WeylsWithLeastLattices{$W_{286}$}
\def\MostEdges{28}
\def\WeylsWithMostEdges{$W_{365}$}
\def\LargestCyclic{3}
\def\WeylsWithLargestCyclic{$W_{174}$}
\def\WeylsWithDihedralEight{$W_{182}$, $W_{184}$, $W_{238}$, $W_{285}$, $W_{286}$, $W_{307}$, $W_{324}$, $W_{349}$, $W_{359}$ and $W_{365}$}
\def\WeylsWithDihedralTwelve{$W_{234}$, $W_{320}$ and $W_{350}$}
\def\NumRegularWeyl{2}
\def\RegularWeyls{$W_{234}$ and $W_{286}$}
\def\NumIdealWeyl{3}
\def\IdealWeyls{$W_{247}$, $W_{285}$ and $W_{286}$}
\def\NumRightAngledWeyl{163}
\def\RightAngledWeyls{$W_{14}$, $W_{17}$, $W_{25}$, $W_{35}$, $W_{38}$, $W_{42}$, $W_{43}$, $W_{45}$, $W_{47}$, $W_{50}$, $W_{56}$, $W_{57}$, $W_{60}$, $W_{66}$, $W_{68}$, $W_{69}$, $W_{70}$, $W_{72}$, $W_{75}$, $W_{76}$, $W_{79}$, $W_{80}$, $W_{81}$, $W_{82}$, $W_{84}$, $W_{87}$, $W_{88}$, $W_{91}$, $W_{95}$, $W_{97}$, $W_{98}$, $W_{100}$, $W_{102}$, $W_{103}$, $W_{104}$, $W_{105}$, $W_{107}$, $W_{110}$, $W_{111}$, $W_{115}$, $W_{118}$, $W_{121}$, $W_{122}$, $W_{124}$, $W_{128}$, $W_{129}$, $W_{130}$, $W_{131}$, $W_{132}$, $W_{135}$, $W_{136}$, $W_{137}$, $W_{138}$, $W_{139}$, $W_{151}$, $W_{165}$, $W_{166}$, $W_{172}$, $W_{175}$, $W_{177}$, $W_{193}$, $W_{196}$, $W_{199}$, $W_{204}$, $W_{205}$, $W_{207}$, $W_{208}$, $W_{210}$, $W_{211}$, $W_{212}$, $W_{213}$, $W_{214}$, $W_{219}$, $W_{223}$, $W_{224}$, $W_{225}$, $W_{229}$, $W_{230}$, $W_{232}$, $W_{234}$, $W_{235}$, $W_{236}$, $W_{238}$, $W_{241}$, $W_{242}$, $W_{243}$, $W_{244}$, $W_{245}$, $W_{249}$, $W_{252}$, $W_{254}$, $W_{256}$, $W_{257}$, $W_{260}$, $W_{261}$, $W_{262}$, $W_{264}$, $W_{269}$, $W_{270}$, $W_{271}$, $W_{272}$, $W_{273}$, $W_{276}$, $W_{277}$, $W_{281}$, $W_{282}$, $W_{289}$, $W_{290}$, $W_{292}$, $W_{293}$, $W_{295}$, $W_{296}$, $W_{297}$, $W_{301}$, $W_{303}$, $W_{304}$, $W_{305}$, $W_{307}$, $W_{309}$, $W_{310}$, $W_{311}$, $W_{312}$, $W_{313}$, $W_{314}$, $W_{315}$, $W_{316}$, $W_{317}$, $W_{318}$, $W_{319}$, $W_{320}$, $W_{321}$, $W_{322}$, $W_{323}$, $W_{324}$, $W_{325}$, $W_{327}$, $W_{328}$, $W_{333}$, $W_{336}$, $W_{337}$, $W_{338}$, $W_{339}$, $W_{340}$, $W_{345}$, $W_{346}$, $W_{347}$, $W_{349}$, $W_{350}$, $W_{351}$, $W_{352}$, $W_{353}$, $W_{354}$, $W_{357}$, $W_{359}$, $W_{360}$, $W_{363}$, $W_{365}$, $W_{367}$, $W_{368}$, $W_{369}$, $W_{370}$, $W_{372}$ and $W_{373}$}
\def\NumCompactChambers{269}
\def\NumTriangularWeyls{7}
\def\TriangularWeyls{$W_{1}$, $W_{2}$, $W_{3}$, $W_{7}$, $W_{140}$, $W_{145}$ and $W_{155}$}
\def\NumCommClasses{39}
\def\NumGenera{8488}
\def\MostReflectivesInGenus{2}
\def\NumGeneraWithMostLattices{107}
\def\GeneraWithMostLattices{558, 881, 918, 1282, 1388, 1390, 1420, 1918, 1954, 2068, 2074, 2219, 2374, 2717, 2721, 2887, 2888, 2892, 2932, 2935, 3040, 3043, 3330, 3610, 3665, 3771, 3802, 3948, 3967, 3970, 4001, 4002, 4069, 4274, 4279, 4441, 4578, 4581, 4586, 4761, 4762, 4763, 4764, 4766, 4812, 4814, 4880, 4899, 4924, 4926, 5112, 5207, 5483, 5536, 5784, 5847, 5863, 5970, 5971, 5986, 6102, 6226, 6345, 6348, 6349, 6449, 6478, 6479, 6625, 6713, 6714, 6726, 6727, 6942, 6979, 6999, 7080, 7091, 7111, 7169, 7210, 7213, 7233, 7248, 7274, 7305, 7306, 7382, 7407, 7463, 7512, 7529, 7594, 7618, 7678, 7710, 7754, 8021, 8074, 8230, 8253, 8254, 8301, 8308, 8316, 8342 and 8449}
\def\GenusWithTwoWeyls{{$1\above{1pt}{1pt}{1}{7}8\above{1pt}{1pt}{1}{1}256\above{1pt}{1pt}{1}{1}$}}
\def\GenusWithTwoWeylsFirstLattice{{L_{341.1}}}
\def\GenusWithTwoWeylsSecondLattice{{L_{342.1}}}
\def\GenusWithTwoWeylsFirstCornerSymbols{{${256}\above{1pt}{1pt}{*}{2}{32}\above{1pt}{1pt}{32,17}{\infty z}{8}\above{1pt}{1pt}{32,9}{\infty}{32}\above{1pt}{1pt}{s}{2}$}\relax$\,(\times2)$%
}
\def\GenusWithTwoWeylsSecondCornerSymbols{{${256}\above{1pt}{1pt}{r}{2}{4}\above{1pt}{1pt}{b}{2}{256}\above{1pt}{1pt}{l}{2}{8}\above{1pt}{1pt}{32,17}{\infty}{32}\above{1pt}{1pt}{32,25}{\infty z}{8}\above{1pt}{1pt}{}{2}$}%
}
\def\GenusWithTwoWeylsFirstWeyl{$W_{341}$}
\def\GenusWithTwoWeylsSecondWeyl{$W_{342}$}
\def\MostNegativeDet{$-29811600$}
\def\MostNegativeDetOfMinimalInDualityClass{$-108000$}
\def\LargestPrimeInDet{97}
\def\LargestRootNorm{14400}
\def\LargestRootNormofMinimalInDualityClass{7200}
\def\NumDualityClasses{1419}
\def\NumEssentialDualityClasses{704}
\def\ImplicitGeneraTable{%
\begingroup
\parindent=0pt
\parskip=0pt\small
\raggedbottom
%
% LATTICE L10.4
%
\leavevmode%
$\pfillwitharg{2}({L_{10.1}})$%
\ shares genus with 5-dual\nopagebreak\par%
\nopagebreak\par%
{$1\above{1pt}{1pt}{-2}{{\rm II}}2\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{-}{}5\above{1pt}{1pt}{-}{}25\above{1pt}{1pt}{-}{}$}%
% END OF LATTICE L10.4
%
\hbox{}\par\smallskip%
%
% LATTICE L248.5
%
\leavevmode%
$\main({L_{248.2}})$%
\ shares genus with {$ {L_{248.1}}$}%
\nopagebreak\par%
\nopagebreak\par%
{$[1\above{1pt}{1pt}{1}{}2\above{1pt}{1pt}{1}{}]\above{1pt}{1pt}{}{0}128\above{1pt}{1pt}{1}{1}$}%
% END OF LATTICE L248.5
%
\hbox{}\par\smallskip%
%
% LATTICE L194.4
%
\leavevmode%
$\pfillwitharg{2}({L_{194.1}})$%
\ shares genus with 5-dual\nopagebreak\par%
\nopagebreak\par%
{$1\above{1pt}{1pt}{-2}{{\rm II}}2\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{2}{}9\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-}{}5\above{1pt}{1pt}{-}{}25\above{1pt}{1pt}{-}{}$}%
% END OF LATTICE L194.4
%
\hbox{}\par\smallskip%
%
% LATTICE L195.4
%
\leavevmode%
$\pfillwitharg{2}({L_{195.1}})$%
\ shares genus with 5-dual\nopagebreak\par%
\nopagebreak\par%
{$1\above{1pt}{1pt}{-2}{{\rm II}}2\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{-2}{}9\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{-}{}5\above{1pt}{1pt}{-}{}25\above{1pt}{1pt}{-}{}$}%
% END OF LATTICE L195.4
%
\hbox{}\par\smallskip%
%
% LATTICE L73.4
%
\leavevmode%
$\pfillwitharg{2}({L_{73.1}})$%
\ shares genus with 5-dual\nopagebreak\par%
\nopagebreak\par%
{$1\above{1pt}{1pt}{2}{{\rm II}}2\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{-}{}5\above{1pt}{1pt}{-}{}25\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}11\above{1pt}{1pt}{-}{}$}%
% END OF LATTICE L73.4
%
\hbox{}\par\smallskip%
%
% LATTICE L366.2
%
\leavevmode%
$\pfillwitharg{2}({L_{366.1}})$%
\ shares genus with 13-dual\nopagebreak\par%
\nopagebreak\par%
{$1\above{1pt}{1pt}{-2}{{\rm II}}2\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{-}{}13\above{1pt}{1pt}{-}{}169\above{1pt}{1pt}{-}{}$}%
% END OF LATTICE L366.2
%
\hbox{}\par\smallskip%
%
% LATTICE L345.4
%
\leavevmode%
$\pfillwitharg{2}({L_{345.1}})$%
\ shares genus with 3-dual; isometric to own %
7-dual\nopagebreak\par%
\nopagebreak\par%
{$1\above{1pt}{1pt}{-2}{{\rm II}}2\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{1}{}9\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{1}{}7\above{1pt}{1pt}{1}{}49\above{1pt}{1pt}{1}{}$}%
% END OF LATTICE L345.4
%
\hbox{}\par\smallskip%
\endgroup
}%

\hyphenation{Lor-entz-ian}
\hyphenation{or-thog-o-nal}
\raggedbottom
\overfullrule=10pt
\allowdisplaybreaks

\def\rh{{\rm rh}} % reflective hull
\def\pdual{\mathop{\hbox{\rm $p$-dual}}\nolimits}
\def\pfill{\mathop{\hbox{\rm $p$-fill}}\nolimits}
\def\diag{\mathop{\hbox{diag}}\nolimits}
\def\II{{\rm II}}
\def\I{{\rm I}}

% SPECIFIC SYMBOLS
\def\Z{\mathbb{Z}} % the integers
\def\Q{\mathbb{Q}} % the rational numbers
\def\R{\mathbb{R}} % the real numbers
\def\rp{\R P} % real projective space
\def\D{\Delta} % discriminant group
\def\O{{\rm O}} % orthogonal group

% corner symbols
\def\corner#1#2{^{#1}_{#2}}
\def\gluez{z}
\def\gluea{a}
\def\glueboth{b}

% GENERIC SYMBOLS
\def\a{\alpha}
\def\b{\beta}
\def\c{\gamma}
\def\e{\varepsilon}
\def\ahat{\hat{a}}
\def\bhat{\hat{b}}
\def\rhat{\hat{r}}
\def\shat{\hat{s}}
\def\that{\hat{t}}
\def\Ctilde{\tilde{C}}
\def\DD{\mathcal{D}}
\def\FF{\mathcal{F}}

% OPERATORS
\def\del{\partial} % boundary of polygon
\def\tensor{\otimes}
\let\iso=\cong
\let\cong=\equiv
\def\sset{\subseteq}
\def\sat{{\rm\scriptstyle sat}} % saturation
\def\aut{\mathop{\rm Aut}\nolimits}
\def\notperp{\not\perp}
\def\legendre#1#2{\left(\frac{#1}{#2}\right)}

% COMPOSITES, LAYOUT
\def\set#1#2{\{#1\,:\,#2\}}
\def\bigset#1#2{\bigl\{#1\,:\,#2\bigr\}}
\def\varset#1#2{\left\{#1\,:\,#2\right\}}
\def\spanof#1{\langle#1\rangle}
\def\bigspanof#1{\bigl\langle#1\bigr\rangle}
\def\textmatrix#1#2#3#4{\bigl(\begin{smallmatrix}#1&#2\\#3&#4\end{smallmatrix}\bigr)}
\def\centeroverfull#1{\setbox0=\hbox{#1}\newdimen\foo\foo=\wd0\advance\foo by -\hsize\divide\foo by 2\advance\foo by\hsize\rlap{\kern\foo\llap{\box0}}}
% a vcenter that works; from the web
\newcommand{\myvcenter}[1]{\ensuremath{\vcenter{\hbox{#1}}}}
\newcommand\breakok{\discretionary{}{}{}}

% MARGINALIA
% #1=what will appear in text, #2=in margin, #3=in index
\def\Xdefinition#1#2#3{#1\marginpar{\rm\scriptsize #2}\index{#3}}
\def\Xdefinition#1#2#3{#1} % no marginal defintions

\def\defn#1{\Xdefinition{#1}{#1}{#1}}
%\def\defn#1{\marginpar{\rm\scriptsize #1}#1}
\def\bfdefn#1{\marginpar{\rm\scriptsize #1}{\bf #1}}
\def\bfdefn#1{{\bf #1}}
\def\notation#1{\marginpar{#1}#1}
\def\notation#1{#1} % no marginal notation notes

% ENVIRONMENTS
\newtheorem{theorem}{Theorem}
\newtheorem{thmdef}[theorem]{Theorem (and Definition)}
\newtheorem{lemma}[theorem]{Lemma}
\theoremstyle{remark}
\newtheorem*{example}{Example}
\newtheorem*{remark}{Remark}
\newtheorem*{remarks}{Remarks}
\newtheorem*{definition}{Definition}
\renewcommand\theenumi{\roman{enumi}}

\begin{document}

\title[Reflective Lorentzian lattices]{The reflective Lorentzian lattices of rank 3}
%
\author{Daniel Allcock}
\address{Department of Mathematics\\U.T. Austin}
\email{allcock@math.utexas.edu}
\urladdr{http://www.math.utexas.edu/\textasciitilde allcock}
%
\thanks{Partly supported by NSF grant DMS-0600112.}
\subjclass[2000]{11H56 (20F55, 22E40)}
\keywords{Lorentzian lattice, Weyl group, Coxeter group, Vinberg's algorithm}
\date{November 19, 2010}
%\date{November 18, 2010}
%\date{November 13, 2010}
%\date{August 29, 2010}
%\date{August 20, 2010}
%\date{August 2, 2010}
%\date{July 4, 2010}
%\date{May 8, 2009}
%\date{May 5, 2009}
%\date{April 26, 2009}
%\date{March 26, 2009}
%\date{February 6, 2009}
%\date{January 28, 2009}
%\date{January 24, 2009}
%\date{December 7, 2008}
%\date{October 21, 2008}
%\date{October 19, 2008}
%\date{October 14, 2008}
%\date{October 5, 2008}
%\date{September 20, 2008}

\begin{abstract}
We classify all the symmetric integer bilinear forms of signature
$(2,1)$ whose isometry groups are generated up to finite index by
reflections.  There \NumLattices{} of them up to scale, whose
\NumWeylGroups{} distinct Weyl groups fall into \NumCommClasses{}
commensurability classes.  This extends Nikulin's enumeration of the
strongly square-free cases.  Our technique is an analysis of the shape
of the Weyl chamber, followed by computer work using Vinberg's
algorithm and our ``method of bijections''.  We also correct a minor
error in Conway and Sloane's definition of their canonical $2$-adic
symbol.
\end{abstract}

\maketitle

\section{Introduction}
\label{sec-intro}

Lorentzian lattices, that is, integral symmetric bilinear forms of
signature $(n,1)$, play a major role in K3 surface theory and the
structure theory of hyperbolic Kac-Moody algebras.  In both cases, the
lattices which are reflective, meaning that their isometry groups are
generated by reflections up to finite index, play a special role.  In
the KM case they provide candidates for root lattices of KMA's with
hyperbolic Weyl groups that are large enough to be interesting.  For
K3's they are important because a K3 surface has finite automorphism
group if and only if its Picard group is ``2-reflective'', meaning
that its isometry group is generated up to finite index by reflections
in classes with self-intersection $-2$
(see \cite{Piatetski-Shapiro-Shafarevich}).  If the Picard group is
not 2-reflective but is still reflective, then one can often describe
the automorphism group of the surface very
explicitly \cite{Vinberg-most-algebraic}\cite{Borcherds-Coxeter-groups-Lorentzian-lattices-and-K3s}\cite{Nikulin-K3s-with-interesting-symmetry-groups}.
The problem of classifying all reflective lattices of given rank, here
$n+1$, is also of interest in its own right from the perspectives of
Coxeter groups and arithmetic subgroups of $\O(n,1)$.  

In this paper we give the classification of reflective Lorentzian
lattices of rank~$3$.  There are \NumLattices{} of them up to scale,
but this large number makes the result seem more complicated than it
is.  For example,
\MostLatticesInWeyl{} lattices
share a single Weyl group (\WeylsWithMostLattices{} in the table).

Our work is logically independent of Nikulin's monumental paper
\cite{Nikulin-rk3}, but follows it conceptually.  His work had
the same motivations as ours, and solves a problem both more general
and more specific.  He considered Lorentzian lattices that satisfy the
more general condition of being ``almost reflective'', meaning that
the Weyl chamber is small enough that its isometry group is $\Z^l$ by
finite.  This is a very natural class of lattices from both the K3 and
KM perspectives.  He also restricts attention to lattices that are
strongly square-free (SSF), which in rank~$3$ means they have
square-free determinant.  The full classification is desirable from
the KM perspective, because for example the root lattice even of a
finite-dimensional simple Lie algebra need not be SSF.  On the other
hand, every lattice canonically determines a SSF lattice, so that his
classification does yield all lattices whose reflection groups are
maximal under inclusion.  The SSF condition  also enabled Nikulin to
use some tools from the theory of quadratic forms that we avoid.
There are 1097 lattices in Nikulin's 160 SSF lattices' duality classes
(defined in section~\ref{sec-background}), while our
\NumLattices\ lattices fall into \NumDualityClasses\ duality classes.
Most of our techniques run parallel to or are refinements of Nikulin's
methods.

We have strived to keep the table of lattices to a manageable size,
while remaining complete in the sense that the full classification can
be mechanically recovered from the information we give.  So we have
printed only \NumPrintedExplicitly\ of them and given operations to
obtain the others.  Even after this reduction, the table is still
large.  The unabridged list of lattices is available separately
as \cite{Allcock-full-tables-rk3}, including the Gram matrices if
desired.  Anyone wanting to work seriously with the lattices will need
computer-readable data, which is very easy to extract from the TeX
source file of this paper.  Namely, by arcane computer tricks we have
arranged for the TeX source to be simultaneously a Perl script that
prints out all \NumLattices\ lattices (or optionally just some of
them) in computer-readable format.  If the file is saved as say {\tt
file.tex} then simply enter {\tt perl file.tex} at the unix command
line.

For each reflective lattice $L$, we worked out the conjugacy class
of its Weyl group $W(L)$ in $\O(2,1)$, the normalizers of $W(L)$ in
$\aut L$ and $\O(2,1)$, the area of its Weyl chamber, its genus as a
bilinear form over $\Z$, one construction of $L$ for each corner of
its chamber, and the relations among the lattices under $p$-duality
and $p$-filling (defined in section~\ref{sec-background}).  Some
summary information appears in section~\ref{sec-how-to-read}, for example
largest and smallest Weyl chambers, most and fewest lattices with
given Weyl group, most edges (\MostEdges), numbers of chambers with
interesting properties like regularity or compactness, genera
containing multiple reflective lattices, and the most-negative
determinants and largest root norms.

Here is a brief survey of related work.  Analogues of Nikulin's work
have been done for ranks $4$ and~$5$ by R.\ Scharlau \cite{Scharlau}
and C.\ Walhorn \cite{Walhorn} respectively; see also
\cite{Scharlau-Walhorn}.  In rank${}\geq21$, Esselmann
\cite{Esselmann} proved there are only $2$ reflective lattices, both
in rank~$22$---the even sublattice of $\Z^{21,1}$ (recognized as
reflective by Borcherds \cite{Borcherds-I21-1}) and its dual lattice.
Also, Nikulin \cite{Nikulin-finiteness} proved that there are only finitely many
reflective lattices in each rank, so that a classification is
possible.  The lattices of most interest for K3 surfaces are 
the 2-reflective ones, and these have been completely classified by
Nikulin \cite{Nikulin-2-reflective-rank-5+}\cite{Nikulin-2-reflective-rank-3}
and Vinberg \cite{Vinberg-2-reflective-rank-4}.

Beyond these results, the field is mostly a long list of examples found by various authors,
with only glimmers of a general theory, like Borcherds' suggested
almost-bijection between ``good'' reflection groups and ``good''
automorphic forms \cite[\S12]{Borcherds-almost-bijection}.  To choose a few
highlights, we mention Coxeter and Whitrow's analysis \cite{Coxeter-Whitrow} of
$\Z^{3,1}$, Vinberg's famous paper \cite{Vinberg} treating $\Z^{n,1}$ for
$n\leq17$, its sequel with Kaplinskaja \cite{Vinberg-Kaplinskaja} extending this to
$n\leq19$, Conway's analysis \cite{Conway-II25-1} of the even unimodular Lorentzian
lattice of rank~$26$, and Borcherds' method of deducing
reflectivity of a lattice from the existence of a suitable automorphic
form \cite{Borcherds-reflection-groups-of-Lorentzian-lattices}.  Before this, Vinberg's algorithm \cite{Vinberg} was the only
systematic way to prove a given lattice reflective.

Here is an overview of the paper.  After providing background material
in section~\ref{sec-background}, we consider the shape of a hyperbolic
polygon $P$ in section~\ref{sec-shape-of-polygon}.  The main result is
the existence of $3$, $4$ or $5$ consecutive edges such that the lines
in the hyperbolic plane $H^2$ containing them are ``not too far
apart''.  This is our version of Nikulin's method of narrow parts of
polyhedra \cite[\S4]{Nikulin-rk3}\cite{Nikulin-finiteness}, and some of the same
constants appear.  Our technique is based the bisectors of angles and edges of $P$, while his is based on
choosing a suitable point $p$ of $P$'s interior and considering how
the family of lines through $p$ meet $\del P$.  Our method is simpler
and improves certain bounds, but has no extension to
higher-dimensional hyperbolic spaces, while his method works in
arbitrary dimensions.  For a more detailed comparison, please see the
end of section~\ref{sec-shape-of-polygon}.

In section~\ref{sec-shape-of-2-dimensional-Weyl-chamber} we convert
these bounds on the shape of the Weyl chamber into an enumeration of
inner product matrices of $3$, $4$ or $5$ consecutive simple roots of
$W(L)$.  This is mostly a matter of organizing the parameters and
calculations, since the computations themselves are just arithmetic.
In section~\ref{sec-corner-symbols} we introduce ``corner symbols''.
Essentially, given $L$ and two consecutive simple roots $r$ and $s$,
we define a symbol like ${2}\above{1pt}{1pt}{*}{4}{4}$ or
${26}\above{1pt}{1pt}{4,3}{\infty b}{104}$ displaying their norms,
with the super- and subscripts giving enough information to recover
the inclusion $\spanof{r,s}\to L$.  So two lattices, each with a
chamber and a pair of consecutive simple roots, are isometric by an
isometry identifying these data if and only if the corner symbols and
lattice determinants coincide.  Some device of this sort is required,
even for sorting the reflective lattices into isometry classes,
because the genus of a lattice is not a strong enough invariant to
distinguish it.  In one case (see section~\ref{sec-how-to-read}), two
lattices with the same genus even have different Weyl groups.  We also
use corner symbols in the proof of the main theorem
(theorem~\ref{thm-main-thm} in section~\ref{sec-rank-3}) and for
tabulating our results.

Besides the proof of the main theorem, section~\ref{sec-rank-3} also
introduces what we call the ``method of bijections'', which is a
general algorithm for determining whether a finite-index subgroup of a
Coxeter group is generated by reflections up to finite index.
Section~\ref{sec-how-to-read} explains how to read the table at the
end of the paper.  That table displays \NumPrintedExplicitly{}
lattices explicitly, together with operations to apply to obtain the
full list of lattices.  Finally, in section~\ref{sec-Conway-Sloane} we
discuss the effects of various ``moves'' between lattices on the
Conway-Sloane genus symbol \cite[ch.~15]{SPLAG}.  We also resolve a
small error in their definition of the canonical $2$-adic symbol.

Computer calculations were important at every stage of this project,
as explained in detail in section~\ref{sec-rank-3}.  We wrote our programs in
C++, using the PARI software library \cite{PARI}, and the full
classification runs in around an hour on the author's laptop computer.  The source code is available
on request.  Although there is no a posteriori check, like the mass formula used when enumerating
unimodular lattices \cite{Conway-Sloane-unimodular-enumeration},  we can offer several remarks in favor of
the reliability of our results.  First, in the SSF case we recovered
Nikulin's results exactly; second, many steps of the calculation
provided proofs of their results (e.g., that a lattice is reflective
or not); and third, our list of lattices is closed under the
operations of $p$-duality and $p$-filling (see section~\ref{sec-background}) and
``mainification'' (section~\ref{sec-how-to-read}).  
This is a meaningful check because our enumeration methods have
nothing to do with these relations among lattices.
%This closedness didn't require
%any tweaking of the code---once we got our list of lattices, it was
%already closed (and agreed with Nikulin's results).

I am grateful to the Max Planck Institute in Bonn, where some of this
work was carried out.

\section{Background}
\label{sec-background}

For experts, the key points in this section are (i) lattices need not
be integral and (ii) the definition of ``reflective hull''.
The notation $\spanof{x,\dots,z}$ indicates the $\Z$-span of some
vectors.

{\it Lattices:\/} A lattice means a free abelian group $L$ equipped
with a $\Q$-valued symmetric bilinear form, called the inner product.
If $L$ has signature $(n,1)$ then we call it Lorentzian.  If the inner
product is $\Z$-valued then $L$ is called integral.  In this case we
call the gcd of $L$'s inner products the scale of $L$.  We call $L$
unscaled if it is integral and its scale is~$1$.  The norm $r^2$ of a
vector means its inner product with itself, and $r$ is called
primitive if $L$ contains none of the elements $r/n$, $n>1$.  $L$ is
called \defn{even} if all its vectors have even norm, and
\defn{odd} otherwise.  If $L$ is nondegenerate then its \defn{dual}, written \notation{$L^*$},
means the set of vectors in $L\tensor\Q$ having integer inner products
with all of $L$.  So $L$ is integral just if $L\sset L^*$.  In this
case $L$'s
\defn{discriminant group} is defined as \notation{$\D(L)$}$:=L^*/L$, a
finite abelian group.   The determinant $\det L$ is the determinant
of any inner product matrix, and when $L$ is integral we have $|\det
L|=|\D(L)|$. 

{\it Roots:\/} A root means a primitive lattice vector $r$ of positive
norm, such that reflection in $r$, given by 
$$
x\mapsto x-2\frac{x\cdot r}{r^2}r
$$ 
preserves $L$.  Under the primitivity hypothesis, this
condition on the reflection is
equivalent to $L\cdot r\sset\frac{1}{2}r^2\Z$.  Now suppose
$r_1,\dots,r_n$ are roots in a lattice $L$, whose span is
nondegenerate.  Then their reflective hull
$\spanof{r_1,\dots,r_n}^{\rh}$ means 
$$
\spanof{r_1,\dots,r_n}^\rh:=\set{v\in
\spanof{r_1,\dots,r_n}\tensor\Q}{\textstyle\hbox{$v\cdot r_i\in\frac{1}{2}r_i^2\Z$ for
    all $i$}}.
$$ The key property of the reflective hull is that it contains the
projection of $L$ to $\spanof{r_1,\dots,r_n}\tensor\Q$.  In the special
case that $r_1,\dots,r_n$ generate $L$ up to finite index, we have
$$
\spanof{r_1,\dots,r_n}\sset L\sset\spanof{r_1,\dots,r_n}^\rh.
$$
Then there are only finitely many possibilities for $L$, giving us
some control over a lattice when all we know is some of its roots.  As
far as I know, the reflective hull was first introduced
in \cite{Scharlau-positive-definite-reflective-lattices}, in terms of
the ``reduced discriminant group''.  For use in the proof of
theorem~\ref{thmdef-finite-corner-symbols}, we mention that if $r$ and
$s$ are simple roots for an $A_1^2$, $A_2$, $B_2$ or $G_2$ root
system, then $\spanof{r,s}^\rh/\spanof{r,s}$ is $(\Z/2)^2$, $\Z/3$,
$\Z/2$ or trivial, respectively.

{\it Weyl Group:\/} We write $W(L)$ for the Weyl group of $L$, meaning
the subgroup of $O(L)$ generated by reflections in roots.  When $L$ is
Lorentzian, $O(L)$ acts on hyperbolic space $H^n$, which is defined as
the image of the negative-norm vectors of $L\tensor\R$ in
$P(L\tensor\R)$.  For $r$ a root, we refer to $r^\perp\sset
L\tensor\R$ and the corresponding subset of $H^n$ as $r$'s mirror.
The mirrors form a locally finite hyperplane arrangement in $H^n$, and
a Weyl chamber (or just chamber) means the closure in $H^n$ of a
component of the complement of the arrangement.  Often one chooses a
chamber $C$ and calls it ``the'' Weyl chamber.  The general theory of
Coxeter groups (see e.g. \cite{Vinberg-general-theory}) implies that
$C$ is a fundamental domain for $W(L)$.  Note that $C$ may have
infinitely many sides, or even be all of $H^n$ (if $L$ has no roots).
A Lorentzian lattice $L$ is called reflective if $C$ has finite
volume.  The purpose of this paper is to classify all reflective
lattices of signature $(2,1)$.  For a discrete group $\Gamma$ of
isometries of $H^n$, not necessarily generated by reflections, its
reflection subgroup means the group generated by its reflections, and
the Weyl chamber of $\Gamma$ means the Weyl chamber of this subgroup.

{\it Simple roots:\/}
The preimage of $C$ in $\R^{2,1}-\{0\}$ has two components; choose one and
call it $\Ctilde$.  For every facet of $\Ctilde$, there is a unique
outward-pointing root $r$ orthogonal to that facet (outward-pointing means
that $r^\perp$ separates $r$ from $\Ctilde$).  These are called the
simple roots, and their pairwise inner products are${}\leq0$.
Changing the choice of component simply negates to simple roots, so
the choice of component will never matter to us.   These
considerations also apply to subgroups of $W(L)$ that are generated by
reflections.

{\it Vinberg's algorithm:\/}
Given a Lorentzian lattice $L$, a negative-norm vector $k$ (called the
controlling vector) and a set of simple roots for the stabilizer of
$k$ in $W(L)$, there is a unique extension of these roots to a set of
simple roots for $W(L)$.  Vinberg's algorithm \cite{Vinberg} finds this
extension, by iteratively adjoining batches of new simple roots.  If
$L$ is reflective then there are only finitely many simple roots, so
after some number of iterations the algorithm will have found them
all.  One can recognize when this happens because the polygon defined
by the so-far-found simple roots has finite area.  Then the algorithm
terminates.  On the other hand, if $C$ has infinite area then the
algorithm will still find all the simple roots, but must run forever
to get them.  In this case one must recognize $L$ as
non-reflective, which one does by looking for automorphisms of $L$
preserving $C$.  See section~\ref{sec-rank-3} for the details of the method we
used.  There is a variation on Vinberg's algorithm using a null
vector as controlling vector \cite{Conway-II25-1}, but the original algorithm was sufficient
for our purposes.

{\it $p$-duality:\/}
For $p$ a prime, the $p$-dual of a nondegenerate lattice $L$ is the
lattice in $L\tensor\Q$ characterized by
$$
\pdual(L)\tensor\Z_q=
\begin{cases}
L^*\tensor\Z_q&\hbox{if $q=p$}\\
L\tensor\Z_q&\hbox{if $q\neq p$}
\end{cases}
$$
for all primes $q$, where $\Z_q$ is the ring of $q$-adic integers.
Applying $p$-duality twice recovers $L$, so $L$ and its $p$-dual have
the same automorphism group.  When $L$ is integral one can be  much
more concrete: $\pdual(L)$ is the sublattice of $L^*$ corresponding to
the $p$-power part of $\D(L)$.  The effect of $p$-duality on the
Conway-Sloane genus symbol is explained in section~\ref{sec-Conway-Sloane}.

In our applications $L$ will be  unscaled, so the
$p$-power part of $\D(L)$ has the form $\oplus_{i=1}^n\Z/p^{a_i}$
where $n=\dim L$ and at least one of the $a_i$'s is $0$.  In this case
we define the ``rescaled $p$-dual'' of $L$ as $\pdual(L)$ with all
inner products multiplied by $p^a$, where $a=\max\{a_1,\dots,a_n\}$.
This lattice is also unscaled, and the $p$-power part of
its discriminant group is $\oplus_{i=1}^n\Z/p^{a-a_i}$.  Repeating the
operation recovers $L$.  We say that unscaled lattices are in
the same duality class if they are related by a chain of
rescaled $p$-dualities.  Our main interest in rescaled $p$-duality is that all
the lattices in a duality class have the same isometry group, so we
may usually replace any one of them by a member of the class with
smallest $|\det|$.

{\it $p$-filling:\/} Suppose $L$ is an integral lattice, $p$ is a
prime, and $\D(L)$ has some elements of order $p^2$.  Then we define
the $p$-filling of $L$ as the sublattice of $L^*$ corresponding to
$p^{n-1}A\sset\D(L)$, where $A$ is the $p$-power part of $\D(L)$ and
$p^n$ is the largest power of $p$ among the orders of elements of
$\D(L)$.  One can check that $\pfill(L)$ is integral, and obviously
its determinant is smaller in absolute value.  The operation is not
reversible, but we do have the inclusion $\aut L\sset\aut(\pfill(L))$.
As for $p$-duality, the effect of $p$-filling on the Conway-Sloane
genus symbol is explained in section~\ref{sec-Conway-Sloane}.

{\it SSF lattices:\/}
Given any integral lattice $L$, one can apply $p$-filling operations
until no more are possible, arriving at a lattice whose discriminant
group is a sum of cyclic groups of prime order.  Then applying
rescaled $p$-duality for some primes $p$ leaves a lattice whose discriminant
group has rank (i.e., cardinality of its smallest generating set) at
most $\frac{1}{2}\dim L$.  Such a lattice is called strongly square-free
(SSF).  For rank~$3$ lattices this is equivalent to $|\D(L)|$ being
square-free.  Nikulin's paper \cite{Nikulin-rk3} classified the SSF reflective
Lorentzian lattices of rank~$3$.
Watson \cite{Watson-I}\cite{Watson-II} introduced
operations leading from any lattice to a SSF one, and our operations
are presumably special cases of his.

\section{The shape of a hyperbolic polygon}
\label{sec-shape-of-polygon}

In this section we develop our version of Nikulin's method of narrow
parts of polyhedra \cite{Nikulin-finiteness}\cite{Nikulin-rk3}.  We will prove the following theorem,
asserting that any finite-sided finite-area polygon $P$ in $H^2$ has
one of three geometric properties, and then give numerical
consequences of them.  These consequences have the general form: $P$
has several consecutive edges, such that the distances between the lines
containing them are less than some a priori bounds.  See the remark at
the end of the section for a detailed comparison of our method with
Nikulin's.  

\begin{thmdef}
\label{thmdef-shape-of-polygons}
Suppose $P$ is a finite-sided finite-area polygon in $H^2$.  Then one
of its edges is \bfdefn{short}, meaning that the angle bisectors based
at its endpoints cross.  
Furthermore, one of the following holds:
\begin{enumerate}
\item
\label{case-there-exists-short-edge}
$P$ has a short edge
orthogonal to at most one of its neighbors, with its neighbors  not
orthogonal to each other.
\item
\label{case-there-exists-short-pair}
$P$ has at least $5$ edges and a \bfdefn{short pair} $(S,T)$, meaning:
$S$ is a short edge orthogonal to its neighbors, $T$ is one of these
neighbors, and the perpendicular bisector of $S$ meets the angle
bisector based at the far vertex of $T$.
\item
\label{case-there-exists-close-pair}
$P$ has at least $6$ edges and a \bfdefn{close pair} of short edges
$\{S,S'\}$, meaning: $S$ and $S'$ are short edges orthogonal to their
neighbors, their perpendicular bisectors cross, and some \bfdefn{long}
(i.e., not short) edge is adjacent to both of them.
\end{enumerate}
\end{thmdef}

For our purposes, the perpendicular bisector of a finite-length edge
of a  polygon $P$  means the ray departing from the midpoint of
that edge, into the interior of $P$.  
The angle bisector at
a finite vertex is a ray defined in the usual way, and the angle
bisector at an ideal vertex means the set of points equidistant from
(the lines containing) the two edges meeting there.  We think of it as a ray based at the ideal vertex.

\begin{lemma}
\label{lem-rays-into-interior-of-P}
Suppose $P$ is a convex polygon in $H^2\cup\partial H^2$ and $x_1,\dots,x_{n\geq2}$
are distinct points of $\del P$, numbered consecutively in the
positive direction around $\del P$, with subscripts read modulo~$n$.
Suppose a ray $b_i$ departs from each $x_i$, into the interior of $P$.
Then for some neighboring pair $b_i,b_{i+1}$ of these rays, either
they meet or one of them meets the open arc $(x_i,x_{i+1})$ of $\del
P$.
\end{lemma}

\begin{remarks}
 When speaking of arcs of $\del P$, we always mean those traversed in
 the positive direction.  Also,  the proof works for the
 closure of any open convex subset of $H^2$;  one should interpret
 $\del P$ as the topological boundary of $P$ in $\rp^2$.
\end{remarks}

\begin{proof}
By convexity of $P$ and the fact that $b_i$ enters the
interior of $P$, 
its closure $\bar b_i$ meets $\del P$ at one other point $y_i$.  (We
refer to $\bar b_i$ rather than $b_i$ because $y_i$ might lie in $\del
H^2$.)  Now, $y_i$ lies in exactly one arc of $\del P$ of the form
$(x_j,x_{j+1}]$, and we define $s_i$ as the number of steps from $x_i$
 to $x_j$.  Formally: $s_i$ is the number in $\{0,\dots,n-1\}$ such
 that $i+s_i\cong j$ mod $n$.

Now choose $i$ with $s_i$ minimal.  If $s_i=0$ then $b_i$ meets
$(x_i,x_{i+1})$ or contains $x_{i+1}\in b_{i+1}$ and we're done, so suppose
$s_i>0$.  Now, either $b_{i+1}$ meets $(x_i,x_{i+1})$, so we're done,
or it meets $b_i$, so we're done, or else $y_{i+1}$ lies in
$(x_{i+1},y_i]\sset(x_{i+1},x_{j+1}]$.  In the last case $s_{i+1}<s_i$, so
   we have a contradiction of minimality.
\end{proof}

\begin{proof}[Proof of theorem~\ref{thmdef-shape-of-polygons}.]
To find a short edge, apply
lemma~\ref{lem-rays-into-interior-of-P} with $x_1,\dots,\breakok x_n$ the
vertices of $P$ and $b_i$ the angle bisector at $x_i$.   No
$b_i$ can meet $[x_{i-1},x_i)$ or $(x_i,x_{i+1}]$, so some neighboring
pair of bisectors must cross, yielding a short edge.

Suppose for the moment that some short edge is non-orthogonal to at
least one of its neighbors.  Then conclusion~\eqref{case-there-exists-short-edge} applies, except if
its neighbors, call them $T$ and $T'$, are orthogonal to each other.
This can only happen if $P$ is a triangle.  In a triangle all
edges are short and at most one angle equals $\pi/2$.  Therefore
conclusion~\eqref{case-there-exists-short-edge} applies with $T$ or $T'$ taken as the short edge.

We suppose for the rest of the proof that every short edge of $P$ is
orthogonal to its neighbors, because this is the only case where
anything remains to prove.  

Next we show that $P$ has${}\geq5$ sides; suppose otherwise.  We
already treated triangles, so suppose $P$ is a quadrilateral.  Because
$H^2$ has negative curvature, $P$ has a vertex with
angle${}\neq\pi/2$; write $E$ and $F$ for the edges incident there.
The angle bisector based there meets one of the other two edges
(perhaps at infinity), say the one next to $E$.  Drawing a picture
shows that $E$ is short.  So $P$ has a short edge involved in an
angle${}\neq\pi/2$, a contradiction.

Next we claim that if $S$ and $S'$ are adjacent short edges, say with $S'$ at
least as long as $S$, then $(S,S')$ is a short pair.  Write $b,b'$ for
the perpendicular bisectors of $S$, $S'$,  write $\c$ for the angle
bisector at $S\cap S'$, and write $\a$ (resp. $\a'$) for the angle bisector
at the other vertex of $S$ (resp. $S'$).  We hope the left half of
figure~\ref{fig-shape-of-polygon} will help the reader.  Now, $\a$
meets $\c$ because $S$ is short, and $b$ passes though $\a\cap\c$
because it is the perpendicular bisector of an edge whose two angles
are equal.  The same conclusions apply with $\a',b',S'$ in place of
$\a,b,S$.  Furthermore, the intersection point $\a'\cap b'\cap\c$ is
at least as far away from $S\cap S'$ as $\a\cap b\cap\c$ is, because
$S'$ is at least as long as $S$.  If $S'$ is strictly longer than $S$,
then $b$ enters the interior of the triangle bounded by $\c$, $\a'$
and $S'$ by passing through $\c$.  Since $b$ cannot meet $S'$, it must
meet $\a'$ as it exits the triangle.  So $(S,S')$ is a short pair.
(In the limiting case where $S$ and $S'$ have the same length, $\a$,
$b$, $\c$, $b'$ and $\a'$ all meet at a single point.)

\begin{figure}
\scalebox{.45}{\includegraphics{shape_of_polygon.pdf}}
\caption{See the proof of theorem~\ref{thmdef-shape-of-polygons}.}
\label{fig-shape-of-polygon}
\end{figure}

Now an argument similar to the one used for quadrilaterals shows that
a pentagon has a
short pair.  Namely, suppose $S$ is a short edge, and write $T,T'$ for
its neighbors and $U,U'$ for their other neighbors.  The perpendicular
bisector of $S$ cannot meet $T$ or $T'$ (since $S\perp T,T'$), so it
meets $U$ or $U'$ (perhaps at infinity), say $U$.
Then the angle bisector at $T\cap U$ either meets $b$, so $(S,T)$ is a
short pair, or it meets $S$.  In the latter case, $T$ is also short,
and the previous paragraph assures us that either $(S,T)$ or $(T,S)$
is a short pair.  This finishes the treatment of a pentagon, so we
take $P$ to have${}\geq6$ edges in the rest of the proof.

At this point it suffices to prove that $P$ has a short pair, or a close pair of
short edges.  
We apply lemma~\ref{lem-rays-into-interior-of-P} again.
Let $x_1,\dots,x_n$ be the midpoints of the short edges and the
vertices not on short edges, in whatever order they occur around $\del
P$.  If $x_i$ is the midpoint of an edge, let $b_i$ be the
perpendicular bisector of that edge.  If $x_i$ is a vertex not on a
short edge, let $b_i$ be the angle bisector there.
Lemma~\ref{lem-rays-into-interior-of-P} now gives us some $i$ such
that either $b_i$ and $b_{i+1}$ meet, or one of them meets
$(x_i,x_{i+1})$.  We now consider the various possibilities:

If both are angle bisectors then $x_i$ and $x_{i+1}$ must be the
endpoints of one edge, or else there would be some other $x_j$ between
them.  The angle bisector based at an endpoint of the edge cannot
cross the interior of the edge, so $b_i$ and $b_{i+1}$ must cross, so
the edge must be short.  But this is impossible because then $b_i$ and
$b_{i+1}$ would not be among $b_1,\dots,b_n$.  So this case cannot
occur.

If one, say $b_i$, is the perpendicular bisector of a short edge $S$,
and the other is an angle bisector, then we may suppose the following holds: the edge $T$ after $S$ is long, and  $b_{i+1}$ is the angle bisector based
at the endpoint of $T$ away from $S$.  Otherwise, some other $x_j$
would come between $x_i$ and $x_{i+1}$.  If $b_i$ and $b_{i+1}$ meet
then $(S,T)$ is a short pair.  Also, $b_i$ cannot meet
$(x_i,x_{i+1})$ since $S\perp T$.  The only other possibility is that
$b_{i+1}$ crosses $S$ between $x_i$ and $S\cap T$.  But in this case
the angle bisectors based at the endpoints of $T$ would cross, so $T$
would also be short, a contradiction.

Finally, suppose $b_i$ and $b_{i+1}$ are the perpendicular bisectors
of short edges $S,S'$.  
If $S,S'$ are adjacent then one of the pairs $(S,S')$, $(S',S)$ is a
short pair; so we suppose they are not adjacent.  There
must be exactly one edge between them, which must be long, for otherwise some other $x_j$
would come between $x_i$ and $x_{i+1}$.  
If $b_i$ and $b_{i+1}$ cross then $S$ and $S'$ forms a close pair of
short edges and we are done.  The only other possibility (up to
exchanging $b_i\leftrightarrow b_{i+1}$, $S\leftrightarrow S'$) is
pictured in the right half of figure~\ref{fig-shape-of-polygon}.
Namely, $b_{i+1}$ meets $S$ between $S\cap T$ and the midpoint of $S$.
In this case, the angle bisector based at $S\cap T$ either meets
$b_{i+1}$, so $(S',T)$ is a short pair, or it meets $S'$, which
implies that $T$ is short, a contradiction.
\end{proof}

In lemmas~\ref{lem-numerical-consequences-of-short-edge}--\ref{lem-numerical-consequences-of-close-short-edges} we give numerical inequalities expressing the
geometric configurations from theorem~\ref{thmdef-shape-of-polygons}.  We
have tried to formulate the results as uniformly as possible.  In each
of the cases (short edge, short pair, close pair of short edges), we
consider three edges $R,T,R'$ of a convex polygon in $H^2$, consecutive
except that there might be a short edge $S$ (resp. $S'$) between $R$
(resp. $R'$) and $T$.  We write $\rhat,\that,\rhat'$ for the
corresponding outward-pointing unit vectors in $\R^{2,1}$ (and $\shat,\shat'$ when
$S,S'$ are present).  We define $\mu=-\rhat\cdot\that$ and
$\mu'=-\rhat'\cdot\that$, and the hypotheses of the lemmas always
give upper bounds on them (e.g., if $R,T$ are adjacent then
$\mu\leq1$).  The main assertion of each lemma is a constraint on
$\lambda:=-\rhat\cdot\rhat'$, namely
\begin{equation}
\label{eq-BASIC-INEQUALITY}
\begin{split}
\lambda<K:={}&1+\mu+\mu'+2\sqrt{1+\mu}\sqrt{1+\mu'}\\
={}&\bigl(\sqrt{1+\mu}+\sqrt{1+\mu'}\,\bigr)^2-1.
\end{split}
\end{equation}
This may be regarded as giving an upper bound on the hyperbolic
distance between (the lines containing) $R$ and $R'$.  The bound
\eqref{eq-BASIC-INEQUALITY} plays a crucial role in section~\ref{sec-shape-of-2-dimensional-Weyl-chamber}.

\begin{lemma}
\label{lem-numerical-consequences-of-short-edge}
Suppose $R,T,R'$ are consecutive edges of a polygon in $H^2$.  Then
$K\leq7$, and $T$ is short if and only if $\lambda<K$.
\end{lemma}

\begin{proof}
Observe that $\rhat-\that$ and $\rhat'-\that$ are vectors orthogonal
to the angle bisectors based at $R\cap T$ and $R'\cap T$; in fact they
point outward from the region bounded by $T$ and these two bisectors.
The  bisectors intersect if and only if
$$
\bigl(\rhat-\that\,\bigr)\cdot\bigl(\rhat'-\that\,\bigr)
<-\sqrt{\bigl(\rhat-\that\,\bigr)^2}\sqrt{\bigl(\rhat'-\that\,\bigr)^2}.
$$ 
(This is the condition that $\rhat-\that$ and $\rhat'-\that$ have
positive-definite inner product matrix.)
Using $\rhat^2=\rhat'^{\,2}=\that^2=1$ and the definitions of $\mu$ and
$\mu'$, then rearranging, yields $\lambda<K$.  And $K$ is largest when
$\mu$ and $\mu'$ are, namely when $T$ is parallel to $R,R'$, yielding
$\mu=\mu'=1$ and 
$K= 7$.
\end{proof}

If a short edge is orthogonal to its neighbors, then its neighbors'
unit vectors' inner product lies in $(-3,-1)$.  This is because $K=3$
when $\mu=\mu'=0$ in lemma~\ref{lem-numerical-consequences-of-short-edge}.  We will use this in the next two lemmas.

\begin{lemma}
\label{lem-numerical-consequences-of-short-pair}
Suppose $R,S,T,R'$ are distinct consecutive edges of a polygon in
$H^2$, with $S$ short and orthogonal to $R$ and $T$.  Then
$\mu\in(1,3)$ and $K<5+4\sqrt2\approx10.657...$, and a necessary
condition for $(S,T)$ to be a short pair is $\lambda<K$.  Furthermore,
the projection $s_0$ of $\rhat'$ to the $\Q$-span of $\shat$ satisfies
\begin{equation}
\label{eq-properties-of-s0}
s_0^2=s_0\cdot\rhat'
=1+\frac{\lambda^2+2\lambda\mu\mu'+\mu'^{\,2}}{\mu^2-1}.
\end{equation}
\end{lemma}

\begin{remark}
In this lemma, $\lambda<K$ is necessary but not sufficient, while in
lemma~\ref{lem-numerical-consequences-of-short-edge} it was both.  The
reason for the difference is that here, if $T$ is short enough then
the angle bisector at $T\cap R'$ will exit $P$ before it can cross the
perpendicular bisector of $S$.  A similar phenomenon occurs in the
next lemma also.
\end{remark}

\begin{proof}
First we note that $\mu>1$ since $R$ and $T$ are ultraparallel.  Also,
$\mu<3$ by the remark before the lemma.  The proof that $\lambda<K$ is exactly
the same as in the previous proof, using the fact that $\rhat-\that$
is orthogonal to the perpendicular bisector of $S$.  (Lemmas \ref{lem-numerical-consequences-of-short-edge}--\ref{lem-numerical-consequences-of-close-short-edges}
acquire a certain unity when the perpendicular bisector of $S$ is
regarded as the ``angle bisector'' of the ultraparallel edges $R$ and
$T$.)  The inequality $K<5+4\sqrt2$ follows from $\mu<3,\mu'\leq1$.

Next, the $\Q$-span of $\shat$ is $\spanof{\rhat,\that\,}^\perp$, so $s_0$ is got
from $\rhat'$ by adding suitable multiples of $\rhat$ and $\that$.
Computation reveals
$$
s_0=\rhat'
+\frac{\lambda+\mu\mu'}{1-\mu^2}\rhat
+\frac{\lambda\mu+\mu'}{1-\mu^2}\that,
$$ 
and then one can work out $s_0\cdot\rhat'$.  Finally,
$s_0^2=s_0\cdot\rhat'$ because $s_0$ was defined as an orthogonal
projection of $\rhat'$. 
\end{proof}

\begin{lemma}
\label{lem-numerical-consequences-of-close-short-edges}
Suppose $R,S,T,S',R'$ are distinct consecutive edges of a polygon in
$H^2$, and assume $S$ and $S'$ are short and orthogonal to their
neighbors.  Then $\mu,\mu'\in(1,3)$, $K<15$, and a necessary condition
for $(S,S')$ to be a close pair of short edges is $\lambda<K$.
Furthermore, the projection $s_0$ of $\rhat'$ to the $\Q$-span of ${\shat}$
satisfies \eqref{eq-properties-of-s0}, and similarly with primed and
unprimed letters exchanged.  Finally,
\begin{equation}
\label{eq-s0-dot-s0prime}
s_0\cdot s_0'=
\lambda+\mu\mu'-\frac{(\lambda+\mu\mu')^3}{(\mu^2-1)(\mu'^{\,2}-1)}.
\end{equation}
\end{lemma}

\begin{proof}
Essentially the same as the previous one.  The computation of
$s_0\cdot s_0'$ is tedious but mechanical.
\end{proof}

\begin{remarks}
The constants $7$, $5+4\sqrt2$ and $15$ appearing in lemmas
\ref{lem-numerical-consequences-of-short-edge}--\ref{lem-numerical-consequences-of-close-short-edges} are essentially the same as the constants $14$,
$10+8\sqrt2$ and $30$ in Nikulin's (4.1.53), (4.1.55) and (4.1.58)
in \cite[Theorem~4.1.8]{Nikulin-rk3}.  The factor of $2$ comes from
the fact that he uses norm~$2$ vectors where we use unit vectors.  And
our short edge, short pair, close pair cases in
theorem~\ref{thmdef-shape-of-polygons} correspond to his type I, II
and III narrow parts of polygons.  In the short edge case, our
condition that the short edge be non-orthogonal to one of its
neighbors corresponds to Nikulin's
condition \cite[Theorem~4.1.4]{Nikulin-rk3} that the Dynkin diagram of
the $3$ roots be connected.

Our results simplify his slightly in that we can suppose $P$
has${}\geq5$ (resp.~$6$) edges in the short pair (resp. close pair)
cases.  More important is our bound on $\rhat\cdot\rhat'$ in terms of
$\rhat\cdot\that$ and $\rhat'\cdot\that$, which we believe is optimal.
The analogous bounds in Nikulin's paper are the second part of
(4.1.4), formula (4.1.10) or (4.1.55), and formula (4.1.13).  Our
bounds are better and simpler in the short pair and close pair cases.
They limit the size of the enumeration in the next section enough that
we can avoid considering class numbers of imaginary quadratic fields,
which Nikulin uses in his section~3.2.
\end{remarks}

\section{The shape of a 2-dimensional Weyl chamber}
\label{sec-shape-of-2-dimensional-Weyl-chamber}

In this section we consider a Lorentzian lattice $L$ of rank~3, and
assume that its Weyl chamber $C$ possesses one of the features
\eqref{case-there-exists-short-edge}--\eqref{case-there-exists-close-pair}
from theorem~\ref{thmdef-shape-of-polygons}.  This always holds if $C$
has finite area.  The goal is to restrict $L$ to one of finitely many
possibilities (up to scale).  This is achieved in
section~\ref{sec-rank-3}, but we do most of the work here, by showing
that the simple roots corresponding to 3, 4 or 5 suitable consecutive
edges have one of finitely many inner product matrices (up to scale).
The point is not really this finiteness, which was already known by Nikulin's
finiteness theorem \cite{Nikulin-finiteness}.  What is important is that all
possibilities are worked out explicitly.  The main tool is
lemma~\ref{lem-integerization-of-inner-products} below, which allows
one to obtain information about two roots of $L$, given information
about the corresponding unit vectors.

In fact we will work with ``quasiroots'' of $L$ rather than roots; the
point is that the methods of this section can be used to gain control
of the 3-dimensional lattice associated to any finite-area
2-dimensional face of any Weyl chamber.  
The author intends to use this in higher-dimensional analogues of this paper.  For
purposes of classifying rank~3 reflective lattices, we will not need
this generalization, so the reader may read ``root'' in place of
``quasiroot'' and assume that $\rho$, $\sigma$, $\tau$, $\sigma'$ and
$\rho'$ are always $2$.  For use in the general case, here is the
definition.  If $L$ is any lattice then we say that $a\in L$ is a
\defn{quasiroot} of $L$ of \defn{weight} $\a\in\{1,2,\dots\}$ if $a$
is primitive, $a^2>0$, and $L\cdot a\sset\frac{1}{\a}a^2\Z$.  
Notice that scaling a lattice up or down doesn't affect the quasiroot
weights.

When a
roman letter represents a quasiroot we will
use the corresponding greek letter for its weight.  A quasiroot of weight~2 is the same thing as a root,
and quasiroot of weight~1 is the same thing as a generator of a
1-dimensional positive-definite summand of $L$.  Of course, every primitive
positive-norm vector of $L$ is a quasiroot of weight equal to its norm.
But sometimes one has an a priori bound on the
weights of quasiroots involved, independent of their norms.

\begin{lemma}
\label{lem-integerization-of-inner-products}
Suppose $a,b$ are quasiroots of weights $\a$, $\b$ in a lattice $L$,
whose associated unit vectors satisfy $\ahat\cdot\bhat=-K$ for some $K>0$.  Then the inner product
matrix of $a$ and $b$ is a rational number times
\begin{equation}
\label{eq-integerization-of-inner-products}
\begin{pmatrix}
\a u&-uv\\
-uv&\b v
\end{pmatrix},
\end{equation}
for some positive integers $u,v$ satisfying $uv=K^2\a\b$.
\end{lemma}

We will also use versions of this lemma with both $=$ signs replaced
by $\leq$ or both by $<$.  These are formal consequences of this
version. 

\begin{proof}
We know $a\cdot b\in\frac{1}{\a}a^2\Z$ and $a\cdot
b\in\frac{1}{\b}b^2\Z$, so
\begin{equation}
\label{eq-foo}
a\cdot b=-va^2/\a
\qquad\hbox{and}\qquad
a\cdot b=-ub^2/\b
\end{equation}
for some positive integers $u,v$.  This gives
$$
-a\cdot b
=
\sqrt{(-a\cdot b)^2}
=
\sqrt{(va^2/\a)(ub^2/\b)}
=
\sqrt{a^2}\sqrt{b^2}\sqrt{uv/\a\b}.
$$
Rewriting $-\ahat\cdot\bhat=K$ as $-a\cdot b=K\sqrt{a^2}\sqrt{b^2}$
yields $uv=K^2\a\b$.  For convenience we scale the inner products so
that $a\cdot b=-uv$, and then \eqref{eq-foo} gives $a^2=\a u$ and
$b^2=\b v$.
\end{proof}

The hypothesis $a\cdot b\neq0$ in the lemma is essential and annoying:
when two quasiroots are orthogonal, their norms need not satisfy any
relation at all.  For example, in the proof of
lemma~\ref{lem-shape-of-2d-SE-integral-polygon}, the hypothesis
$R\notperp T,R'$ will be used to relate the norms of $r$, $t$ and
$r'$, an essential part of the proof.  If we could do away with the
non-orthogonality hypothesis in lemma~\ref{lem-integerization-of-inner-products} then we could carry out
our enumeration of lattices using only the existence of a short edge.
The possibility of orthogonality is what forces us to consider the
more-complicated configurations of theorem~\ref{thmdef-shape-of-polygons}.

The setup for
lemmas~\ref{lem-shape-of-2d-SE-integral-polygon}--\ref{lem-shape-of-2D-CP-integral-polygon}
below is similar to that for
lemmas~\ref{lem-numerical-consequences-of-short-edge}--\ref{lem-numerical-consequences-of-close-short-edges}.
Their hypotheses are exactly the ``outputs'' of the short edge, short
pair and close pair cases of theorem~\ref{thmdef-shape-of-polygons}.
$P$ is a finite-sided finite-area polygon in $H^2$, with angles at
most $\pi/2$, whose edges are the orthogonal complements of quasiroots
of a rank~3 Lorentzian lattice $L$.  $R$, $T$ and $R'$ are distinct
edges of $P$, consecutive except that there might be a short edge $S$
(resp. $S'$) between $R$ (resp. $R'$) and $T$.  We write $r,t,r'$ (and
$s,s'$ when $S,S'$ are present) for the outward-pointing quasiroots of
$L$ orthogonal to $R,\dots,R'$.  We suppose that $r$, $t$ and $r'$
(and $s$ and $s'$ if present) are quasiroots of weights $\rho$, $\tau$
and $\rho'$ (and $\sigma$ and $\sigma'$ if relevant).  As usual, we use hats to
indicate the corresponding unit vectors.  As in section~\ref{sec-shape-of-polygon} we define
$\mu=-\rhat\cdot\that$, $\mu'=-\rhat'\cdot\that$,
$$
K=1+\mu+\mu'+2\sqrt{1+\mu}\sqrt{1+\mu'},
$$
and $\lambda=-\rhat\cdot\rhat'$.  In
lemmas~\ref{lem-shape-of-2d-SE-integral-polygon}--\ref{lem-shape-of-2D-CP-integral-polygon}
$\mu$, $\mu'$ and $\lambda$ will be given by the formulas
$\mu=\sqrt{AB/\rho\tau}$, $\mu'=\sqrt{A'B'/\rho'\tau}$ and
$\lambda=\sqrt{CC'/\rho\rho'}$, where $A,B,A',B',C,C'$ are
non-negative integers described in the lemmas.  In particular, $K$ is
a function of $A,B,A',B'$.  We have tried to make the treatment as
uniform as possible, but the essential difference between orthogonal
and non-orthogonal quasiroots forces separate treatment of the cases
$T\perp R'$, $T\notperp R'$ in each of
lemmas \ref{lem-shape-of-2d-SE-integral-polygon}
and~\ref{lem-shape-of-2d-SP-integral-polygon}.

\begin{lemma}
\label{lem-shape-of-2d-SE-integral-polygon}
Suppose $R,T,R'$ are consecutive edges of $P$, $T$ is short, and
$R\notperp T,R'$.  Then the inner product matrix of $r,t,r'$ is one of
finitely many possibilities, up to scale.

More precisely, let $(A,B)$ vary over all pairs of positive integers
satisfying $AB\leq\rho\tau$ and let $(A',B')$ vary over $(0,0)$ and
all pairs of positive integers satisfying $A'B'\leq\rho'\tau$.  For
fixed such $A,B,A',B'$, let $(C,C')$ vary over all pairs of positive
integers satisfying
\begin{displaymath}
CC' < K^2\rho\rho'
\end{displaymath}
and
\begin{equation}
\label{eq-def-of-beta-short-side-case}
AB'C' = A'BC\hbox{; call the common value $\b$.}
\end{equation}
Then
for some such $A,B,A',B',C,C'$,
the inner product matrix of
$r,t,r'$ is a rational multiple of
\begin{gather}
\label{eq-shape-of-2d-SE-integral-polygon-NONorthogonality-case}
\begin{pmatrix}
\rho AB'&   -ABB'   &    -\b   \\
-ABB'   & \tau BB'  &  -A'B'B  \\
-\b     &  -A'B'B   & \rho'A'B
\end{pmatrix}
\hbox{ if $A',B'\neq0$}\\
%
\label{eq-shape-of-2d-SE-integral-polygon-orthogonality-case}
\begin{pmatrix}
\rho AC &   -ABC   &   -ACC'   \\
-ABC    & \tau BC  &     0     \\
-ACC'   &     0    & \rho'AC'
\end{pmatrix}
\hbox{ if $A',B'=0$.}
\end{gather}
\end{lemma}

\begin{proof}
We have $\mu\in(0,1]$ by hypothesis, so lemma~\ref{lem-integerization-of-inner-products} says there exist
positive integers $A,B$ with $AB\leq\rho\tau$, such that $r,t$ have
inner product matrix a rational multiple of
\begin{equation}
\label{eq-r-t-inner-product-matrix}
\begin{pmatrix}
\rho A& -AB\\
-AB&\tau B
\end{pmatrix}.
\end{equation}

Now suppose $T\notperp R'$.  Then the argument of the previous
paragraph applies with primed and unprimed symbols exchanged.  And by
shortness of $T$, $\lambda<K$ (lemma~\ref{lem-numerical-consequences-of-short-edge}).  Then another
application of lemma~\ref{lem-integerization-of-inner-products} (using the hypothesis $R\notperp R'$)
shows there exist positive integers $C,C'$ with $CC'<K^2\rho\rho'$, such
that $r,r'$ have inner product matrix a rational multiple of
\begin{equation}
\label{eq-r-rprime-inner-product-matrix}
\begin{pmatrix}
\rho C &-CC'\\
-CC'&\rho'C'
\end{pmatrix}.
\end{equation}
Now we see
$$
\frac{\rho'C'}{\rho C}
=
\frac{r'^{\,2}}{r^2}
=
\frac{r'^{\,2}}{t^2}\frac{t^2}{r^2}
=
\frac{\rho'A'}{\tau B'}\frac{\tau B}{\rho A},
$$
so $AB'C'=A'BC$.  This establishes \eqref{eq-def-of-beta-short-side-case}.  Now we put all three
$2\times2$ matrices together by choosing the scale at which $t^2=\tau
BB'$, leading to \eqref{eq-shape-of-2d-SE-integral-polygon-NONorthogonality-case}.

It remains to consider the case $T\perp R'$.  Then we take $A'=B'=0$
and note that $\sqrt{A'B'/\rho'\tau}$ is indeed equal to
$\mu'=-\rhat'\cdot\that=0$, so this is consistent with the definition
of $\mu'$.  The same argument as before shows that
$r,r'$ have inner product matrix a rational multiple of
\eqref{eq-r-rprime-inner-product-matrix}.  This time
\eqref{eq-def-of-beta-short-side-case} is trivially true because both
sides vanish.  Now we put together \eqref{eq-r-t-inner-product-matrix}
and \eqref{eq-r-rprime-inner-product-matrix} by choosing the scale at
which $r^2=\rho AC$.  Finally, using $r'\cdot t=0$, the resulting
inner product matrix is
\eqref{eq-shape-of-2d-SE-integral-polygon-orthogonality-case}.
\end{proof}

\begin{lemma}
\label{lem-shape-of-2d-SP-integral-polygon}
Suppose $P$ has at least $5$ edges, and $R,S,T,R'$ are consecutive
edges with $(S,T)$ a short pair.  Then the inner product matrix of
$r,s,t,r'$ is one of finitely many possibilities, up to scale. 

More precisely, let $(A,B)$ vary over all pairs of positive integers
with $\rho\tau<AB<9\rho\tau$ and let $(A',B')$ vary over $(0,0)$ and
all pairs of positive integers with $A'B'\leq\rho'\tau$.  For fixed
such $A,B,A',B'$, let $(C,C')$ vary over all pairs of positive
integers satisfying
\begin{gather}
\label{eq-constraint-on-CCprime-SP-case}
\rho\rho'<CC'<K^2\rho\rho'
\\
\label{eq-def-of-beta-short-pair-case}
AB'C' {}= A'BC\hbox{; call the common value $\b$, and}
\\
\label{eq-def-of-N-short-pair-case}
N:=\rho'\sigma+\sigma
\frac{CC'\tau+2\b+A'B'\rho}{AB-\rho\tau}
\hbox{ is an integer}.
\end{gather}
For fixed such $A,B,A',B',C,C'$, let $k$ vary over all positive
integers dividing $N$.  Then for some such $A,B,A',B',C,C',k$, the
inner product matrix of $r,s,t,r'$ is a rational multiple of
\begin{gather}
\label{eq-shape-of-2d-SP-integral-polygon-NONorthogonality-case}
\begin{pmatrix}
\rho AB'&        0      &    -ABB'    &     -\b         \\
0       &\sigma A'BN/k^2&      0      &   -A'BN/k   \\
-ABB'   &        0      & \tau BB'   &    -A'B'B       \\
-\b     &  -A'BN/k      &    -A'B'B   &   \rho'A'B
\end{pmatrix}
\hbox{ if $A',B'\neq0$}\\
%
\label{eq-shape-of-2d-SP-integral-polygon-orthogonality-case}
\begin{pmatrix}
\rho AC &   0             &  -ABC   &   -ACC' \\
0       & \sigma AC'N/k^2 &    0    & -AC'N/k \\
-ABC    &   0             & \tau BC &     0   \\
-ACC'   & -AC'N/k         &    0    & \rho'AC'
\end{pmatrix}
\hbox{ if $A',B'=0$.}
\end{gather}
\end{lemma}

\begin{proof}
Lemma~\ref{lem-numerical-consequences-of-short-edge} says that $1<\mu<3$.  So apply the previous proof with
this inequality in place of $0<\mu\leq1$.  The result is that $r,t,r'$
have inner products (up to scale) as in \eqref{eq-shape-of-2d-SP-integral-polygon-NONorthogonality-case} or \eqref{eq-shape-of-2d-SP-integral-polygon-orthogonality-case}, where
$A,B,A',B',C,C'$ have the stated properties up to and including
\eqref{eq-def-of-beta-short-pair-case}.  For the treatment of the inner product matrix of $r,r'$
in that argument, note that $R\notperp R'$ by the fact that $P$ has at
least $5$ edges.  Indeed $R$ and $R'$ are not even adjacent.  Since $P$
has all angles${}\leq\pi/2$, this says that the lines containing
$R$ and $R'$ are ultraparallel.  This gives $\lambda>1$, which
proves the $CC'>\rho\rho'$ inequality in \eqref{eq-constraint-on-CCprime-SP-case}.

Now we consider $s$.  As in lemma~\ref{lem-numerical-consequences-of-short-pair}, let $s_0$ be the projection
of $\rhat'$ to $\Q\cdot{s}$, so the projection of $r'$ is
$\sqrt{r'^{\,2}}s_0$, which lies in $\frac{1}{\sigma}s\Z$ since 
$s$ is a quasiroot of weight $\sigma$.
Therefore there is a
positive integer $k$ such that $\sqrt{r'^{\,2}}s_0=-ks/\sigma$, i.e.,
\begin{equation}
\label{eq-formula-for-s}
s=-\sigma\sqrt{r'^{\,2}}s_0/k.
\end{equation}
On the other hand, $r'$ is a quasiroot of weight $\rho'$, so $s\cdot
r'\in\frac{1}{\rho'}r'^{\,2}\Z$.  To work with this condition we define
the integer
\begin{equation}
\begin{split}
\label{eq-formula-for-M}
M:&{}=\rho'\frac{s\cdot r'}{r'^{\,2}}
=\rho'\frac{s\cdot\sqrt{r'^{\,2}}s_0}{r'^{\,2}}
=\rho'\frac{-\sigma\sqrt{r'^{\,2}}\sqrt{r'^{\,2}}}{k r'^{\,2}}s_0^2
=-\frac{\rho'\sigma}{k}s_0^2\\
%
&{}=-\frac{\rho'\sigma}{k}
\Bigl(1+\frac{\lambda^2+2\lambda\mu\mu'+2\mu'^{\,2}}{\mu^2-1}\Bigr),
\end{split}
\end{equation}
where the last step uses \eqref{lem-numerical-consequences-of-short-pair}.  A calculation shows $M=-N/k$ where
$N$ is defined in \eqref{eq-def-of-N-short-pair-case}.  Since $M$ is
an integer we must have
$N\in\Z$ and $k|N$.

We have shown that $A,B,A',B',C,C',k$ have all the properties claimed,
and all that remains is to work out the remaining entries in the inner
product matrix.  We have $s\cdot r=s\cdot t=0$ by the short pair
hypothesis.  Referring to \eqref{eq-formula-for-M} gives
$$
s\cdot r'=Mr'^{\,2}/\rho'=-Nr'^{\,2}/k\rho'
$$
and referring to \eqref{eq-formula-for-s} and \eqref{eq-formula-for-M} gives
$$
s^2=\frac{\sigma^2}{k^2}r'^{\,2}s_0^2
=\frac{\sigma^2}{k^2}r'^{\,2}\Bigl(-\frac{Mk}{\rho'\sigma}\Bigr)
=\frac{\sigma}{k}r'^{\,2}\Bigl(-\frac{-N/k}{\rho'}\Bigr)
=N\sigma r'^{\,2}/\rho'k^2.
$$
This allows one to fill in the missing entries of \eqref{eq-shape-of-2d-SP-integral-polygon-NONorthogonality-case} and
\eqref{eq-shape-of-2d-SP-integral-polygon-orthogonality-case}, using the values for $r'^{\,2}$ given there.
\end{proof}

\begin{lemma}
\label{lem-shape-of-2D-CP-integral-polygon}
Suppose $P$ has at least $6$ edges and $R,S,T,S',R'$ are consecutive
edges, with $S$ and $S'$ forming a close pair of short edges.  Then
the inner product matrix for $r,s,t,s',r'$ is one of finitely many
possibilities, up to scale.

More precisely,  let $(A,B)$ vary over all pairs of positive integers
satisfying $\rho\tau<AB<9\rho\tau$, and let $(A',B')$ vary over all
pairs of positive integers satisfying $\rho'\tau<A'B'<9\rho'\tau$.
For fixed such $A,B,A',B'$, let $(C,C')$ vary over all pairs of
positive integers satisfying
\begin{gather}
\rho\rho'<CC'<K^2\rho\rho'
\\
\label{eq-def-of-beta-close-pair-case}
AB'C'= A'BC\hbox{; call the common value $\b$, and}
\\
\label{eq-N-and-Nprime-in-Z}
\hbox{$N$ and $N'$ are integers,}
\end{gather}
where $N$ is defined as in \eqref{eq-def-of-N-short-pair-case} and $N'$ similarly, with primed
and unprimed letters exchanged.
For fixed such $A,B,A',B',C,C'$, let $(k,k')$ 
vary over all pairs of positive integers with $k|N$ and $k'|N'$, such that
\begin{equation}
\label{eq-integrality-conditions-for-s-and-sprime}
{\c k^2}/{A'BN}
\hbox{ and }
{\c k'^{\,2}}/{AB'N'}
\hbox{ are integers,}
\end{equation}
where
\begin{equation}
\label{eq-def-of-gamma}
\c=
\frac{\sigma\sigma'\b}{kk'\tau}
\Biggl(\tau+\frac{\b}{CC'}-
\frac{(\tau CC'+\b)^3}{(AB-\rho\tau)(A'B'-\rho'\tau)C^2C'^{\,2}}
\Biggr).
\end{equation}
Then for some such $A,B,A',B',C,C',k,k'$, the inner product matrix of
$r,s,t,s',r'$ is a rational multiple of
\begin{equation}
\label{eq-shape-of-2d-CP-integral-polygon}
\begin{pmatrix}
\rho AB' &       0         &  -ABB'   &  -AB'N'/k'        &     -\b    \\
     0   & \sigma A'BN/k^2 &    0     &       \c          & -A'BN/k \\
   -ABB' &       0         & \tau BB' &        0          &    -A'B'B   \\
-AB'N'/k' &      \c         &    0     & \sigma'AB'N'/k'^{\,2} &       0   \\
   -\b   &  -A'BN/k        & -A'B'B   &        0          & \rho'A'B
\end{pmatrix}.
\end{equation}
\end{lemma}

\begin{proof}
 Mostly this is a repeat of the $\mu'\neq0$ cases of the previous
 proofs.  Follow the proof of
 lemma~\ref{lem-shape-of-2d-SE-integral-polygon}, using
 $\mu,\mu'\in(1,3)$ from
 lemma~\ref{lem-numerical-consequences-of-short-edge} and
 $\lambda\in(1,K)$ from
 lemma~\ref{lem-numerical-consequences-of-close-short-edges}.  The
 result is that after rescaling, $r,t,r'$ have inner products as in
\eqref{eq-shape-of-2d-SE-integral-polygon-NONorthogonality-case}, where $A,B,A',B',C,C'$ satisfy the conditions up to and
 including \eqref{eq-def-of-beta-close-pair-case}.  Then lemma~\ref{lem-shape-of-2d-SP-integral-polygon}'s analysis of $N$ and $k$
 applies, and also applies with primed and unprimed symbols
 exchanged.  This shows that $N,N',k,k'$ have all the properties
 claimed except \eqref{eq-integrality-conditions-for-s-and-sprime}, and justifies all
 entries in \eqref{eq-shape-of-2d-CP-integral-polygon} except the $s\cdot s'$ entry.  To work this out
 we use $s=-\sigma\sqrt{r'^{\,2}}s_0/k$ by \eqref{eq-formula-for-s},
 $s'=-\sigma'\sqrt{r^2}s_0'/k'$ similarly, and formula \eqref{eq-s0-dot-s0prime} for
 $s_0\cdot s_0'$.  The result is
\begin{align*}
s\cdot s'
&{}=\frac{\sigma\sigma'}{kk'}\sqrt{r^2\,r'^{\,2}}\,s_0\cdot s_0'\\
&{}=\frac{\sigma\sigma'}{kk'}\sqrt{r^2\,r'^{\,2}}
\Bigl(\lambda+\mu\mu'-\frac{(\lambda+\mu\mu')^3}{(\mu^2-1)(\mu'^{\,2}-1)}\Bigr).
\end{align*}
A calculation shows that this equals $\c$, defined in \eqref{eq-def-of-gamma}.  This
gives the last entry in the matrix.  Finally, \eqref{eq-integrality-conditions-for-s-and-sprime} is the
condition that $\c=s\cdot s'$ lies in $\frac{1}{\sigma}s^2\Z$ and in
$\frac{1}{\sigma'}s'^{\,2}\Z$, which holds because $s$ and $s'$ are
quasiroots.
\end{proof}

\section{Corner symbols}
\label{sec-corner-symbols}

In this section we introduce a compact notation called a corner symbol for describing
a corner in $H^2$ of the Weyl chamber of a lattice $L$ of signature
$(2,1)$.  It is a formalization of the ideas in
\cite[pp. 59--62]{Nikulin-rk3}, and is 
needed for the proof of our main theorem in section~\ref{sec-rank-3} and presenting our results in
the table.
But the reader should skip it until it is needed.

Throughout this section suppose $L$ is a 3-dimensional Lorentzian
lattice and $e,f$ are consecutive edges of some Weyl chamber.  We will
define the ``corner symbol'' $S(L,e,f)$, whose key property is that
together with $D:=\det L$ it characterizes $(L,e,f)$ up to isometry.
First, there is a unique chamber $C\sset H^2$ of which $e,f$ are
edges.  Choose a component $\Ctilde$ of its preimage in
$L\tensor\R-\{0\}$.  Take $x,y$ to be simple roots corresponding to
$e,f$; implicit in this definition is that they point away from
$\Ctilde$.  Define $z$ as the primitive lattice vector in
$\spanof{x,y}^\perp$ that lies in (the closure of) $\Ctilde$.  We will
define the corner symbol in terms of $x,y,z$, so strictly speaking we
should write $S(L,e,f,\Ctilde)$ or $S(L,x,y,z)$.  But in the end the
choice of $\Ctilde$ is irrelevant because changing it simply negates
$x,y,z$.  So $S(L,e,f)$ will be well-defined.  We will write $X$ and
$Y$ for $x^2$ and $y^2$.  First we will define corner symbols for
corners in $H^2$, and then for ideal vertices.

The definitions involve some standard lattice-theoretic terms, which
we define here for clarity.  If $L$ is a lattice and $M$ a sublattice,
then $M$'s saturation $M_\sat$ is defined as $L\cap(M\tensor\Q)$, and
$M$ is called saturated if $M=M_\sat$.  Now suppose $L$ is integral
and $M$ is saturated.  Then $L$ lies between $M\oplus
M^\perp$ and $(M\oplus M^\perp)^*$, so it corresponds to a subgroup of $\D(M)\oplus\D(M^\perp)$.
This subgroup is called the glue group of the inclusion $M\oplus
M^\perp\to L$.  Because of saturation, it meets the two summands $\D(M)$,
$\D(M^\perp)$ trivially.

\begin{thmdef}%[Finite corner symbols]
\label{thmdef-finite-corner-symbols}
 Suppose $L$, $x$, $y$ and $z$ are as stated, with $z$ defining a
 finite vertex of $L$'s Weyl chamber.  Then for exactly one row of
 table~\ref{tab-finite-corner-symbols} do they satisfy the conditions listed in the middle
 three columns.  We define their \bfdefn{corner symbol} as the entry in
 the first column.  The corner symbol and $D$ determine the quadruple
 up to isometry, and $z^2$ is given in the last column in terms of
 $D$, $X$, $Y$ and $M:=\min\{X,Y\}$.
\end{thmdef}

\begin{table}
\centeroverfull{%
\begin{tabular}{ccccc}%
{\bf Corner}
&
&$\spanof{x,y}\to\spanof{x,y}_\sat$
&$\spanof{x,y}_\sat\oplus\spanof{z}\to L$\\
%
{\bf symbol}
&{\bf Angle}  
&{\bf by adjoining}
&{\bf by adjoining}
&$z^2$\\
\hline
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\noalign{\smallskip}
$X_2Y$
&$\pi/2$
&nothing
&nothing
&$D/XY$\\
%
\noalign{\smallskip}
$X_2^sY$
&$\pi/2$
&$(x+y)/2$
&nothing
&$4D/XY$\\
%
\noalign{\smallskip}
$X_2^bY$
&$\pi/2$
&nothing
&$(x+y+z)/2$
&$4D/XY$\\
%
\noalign{\smallskip}
$X_2^lY$
&$\pi/2$
&nothing
&$(x+z)/2$
&$4D/XY$\\
%
\noalign{\smallskip}
$X_2^rY$
&$\pi/2$
&nothing
&$(y+z)/2$
&$4D/XY$\\
%
\noalign{\smallskip}
$X_2^*Y$
&$\pi/2$
&$(x+y)/2$
&$(x+z)/2$, $(y+z)/2$
&$16D/XY$\\
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\noalign{\smallskip}
\noalign{\hrule}
\noalign{\smallskip}
$X_3^\pm X$
&$\pi/3$
&nothing
&$(2x+y\pm z)/3$
&$12D/X^2$\\
%
\noalign{\smallskip}
$X_4Y$
&$\pi/4$
&nothing
&nothing
&$D/M^2$\\
%
\noalign{\smallskip}
$X_4^*Y$
&$\pi/4$
&nothing
&$(z+\hbox{longer of $x,y$})/2$
&$4D/M^2$\\
%
\noalign{\smallskip}
$X_6Y$
&$\pi/6$
&nothing
&nothing
&$4D/3M^2$\\
%
\end{tabular}%
}%end centeroverfull
\medskip
\caption{Corner symbols for finite vertices of the Weyl chamber of 
 a 3-dimensional Lorentzian lattice $L$;  see theorem~\ref{thmdef-finite-corner-symbols}.
Here $D=\det L$ and
 $M=\min\{X,Y\}$.   When the angle is $\pi/4$ (resp. $\pi/6$), one
 of $X$ and $Y$ is 2 (resp. 3) times the other.}
\label{tab-finite-corner-symbols}
\end{table}

Here are some mnemonics for the notation.  The subscript always gives
the angle at that corner.  The absence of a superscript indicates the
absence of saturation and glue, so that $\spanof{x,y}$ is a summand of
$L$.  An asterisk indicates the most complicated saturation and/or
glue possible.  The remaining superscripts are
$s$ (saturation but no glue), $l$ (glue involving
the left root), $r$ (glue involving the right root),  $b$ (glue
involving both roots) and  $\pm$ (self-explanatory).

\begin{proof}
 At a finite vertex of a Weyl chamber, the angle is $\pi/n$ for
 $n\in\{2,3,4,6\}$, with $x$ and $y$ being simple roots for an
 $A_1^2$, $A_2$, $B_2$ or $G_2$ root system.   The
 projection of $L$ to $\spanof{x,y}\tensor\Q$ lies in the reflective
 hull of $x$ and $y$ (see section~\ref{sec-background}), and $x$ and
 $y$ are primitive in $L$.  This
 constrains the possible enlargements
 $\spanof{x,y}\to\spanof{x,y}_\sat$ and
 $\spanof{x,y}_\sat\oplus\spanof{z}\to L$ so tightly that all
 possibilities are listed.  (In the $A_2$ case there
 must be trivial saturation and nontrivial glue because otherwise
 every element of $W(G_2)=\aut\spanof{x,y}$ would extend to $L$, so
 $x$ and $y$ would not be simple roots.  Similarly, most of the
 $A_1^2$ cases can only occur if $X\neq Y$.)  Also, $z^2$ is easy to work
 out in each case.  The table shows how to reconstruct $(L,x,y,z)$
 from knowledge of $D$ and the corner symbol.
\end{proof}

Corner symbols at ideal vertices are more complicated.  Most of
the information is contained in the structure of $x^\perp$, which we
encode as follows.

\begin{lemma}
 \label{lem-lemma-for-ideal-corner-symbols}
 Suppose $L$ is a $2$-dimensional integral Lorentzian lattice and
 $z\in L$ is primitive isotropic.  Then there is a unique primitive
 null vector $u\in L$ with $z\cdot u<0$, and we define $\lambda$ as
 $z\cdot u$ and $s$ as $[L:\spanof{z,u}]$.  There exists a unique
 $a\in L$ of the form $a=\frac{1}{s}(\sigma z+ u)$ with
 $\sigma\in\{0,\dots,s-1\}$.  The triple $(\lambda,s,\sigma)$
 characterizes $(L,z)$ up to isometry.  The triples that arise by
 this construction are exactly the triples of integers with
 $\lambda<0$, $s>0$, $s^2|2\lambda$, $0\leq\sigma<s$ and
 $(\sigma,s)=1$.
\end{lemma}

\begin{proof}
 The uniqueness of $u$ is clear, and $\lambda<0$ by construction.
 Since $[L:\spanof{z,u}]=s$, $L$ lies between $\frac{1}{s}\spanof{z,u}$ and
 $\spanof{z,u}$, so it corresponds to a subgroup of order $s$ in
 $\frac{1}{s}\spanof{z,u}/\spanof{z,u}\iso(\Z/s)^2$.  By the
 primitivity of $z$ and $u$, this subgroup meets the subgroups
 $\spanof{\frac{1}{s}z}/\spanof{z}$ and
 $\spanof{\frac{1}{s}u}/\spanof{u}$ trivially, so it must be the
 graph of an isomorphism between them.  The
 existence and uniqueness of $a$ follows, as does the condition
 $(\sigma,s)=1$.  The inner product matrix of $L$ with respect to the basis $z$, $a$ is
$$
\begin{pmatrix}0&\lambda/s\\ \lambda/s&2\lambda\sigma/s^2\\\end{pmatrix}
$$
so integrality forces $s^2|2\lambda\sigma$, hence $s^2|2\lambda$.  If
$s$ satisfies this, then the rest of the matrix is automatically
integral, which justifies our claim about which triples can arise.
That $(\lambda,s,\sigma)$ determines $(L,z)$ follows from the
intrinsic nature of our constructions.
\end{proof}

\begin{thmdef}
\label{thmdef-ideal-corner-symbols}
Suppose $(L,x,y,z)$ are as in theorem~\ref{thmdef-finite-corner-symbols}, except that
$z$ defines an ideal vertex of $L$'s Weyl chamber.  Suppose also that
$z$ and $a$ are the basis of $x^\perp$ associated to the pair
$(x^\perp,z)$ by lemma~\ref{lem-lemma-for-ideal-corner-symbols}.  Then for exactly one row of
table~\ref{tab-ideal-corner-symbols} do the conditions in the last two columns hold.  We
define the \bfdefn{corner symbol} of $(L,x,y,z)$ to be the entry in the first
column.  The quadruple can be recovered up to isometry from its symbol
and knowledge of $D=\det L$.
\end{thmdef}

\begin{table}
\begin{tabular}{ccc}%
{\bf Corner}
&{\bf invariants}
&{$\spanof{x}\oplus x^\perp\to L$}\\
%
{\bf symbol}
&{\bf of $(x^\perp,z)$}
&{\bf by adjoining}\\
\hline
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\noalign{\smallskip}
$X\corner{s,\sigma}{\infty}Y$
&$(-s\sqrt{-D/X},s,\sigma)$
&nothing
\\
\noalign{\smallskip}
$X\corner{s,\sigma}{\infty\gluez}Y$
&$(-2s\sqrt{-D/X},s,\sigma)$
&$(x+z)/2$
\\
\noalign{\smallskip}
$X\corner{s,\sigma}{\infty\gluea}Y$
&$(-2s\sqrt{-D/X},s,\sigma)$
&$(x+a)/2$
\\
\noalign{\smallskip}
$X\corner{s,\sigma}{\infty\glueboth}Y$
&$(-2s\sqrt{-D/X},s,\sigma)$
&$(x+z+a)/2$
\\
\end{tabular}
\medskip
\caption{Corner symbols for ideal vertices of the Weyl chamber of 
 a 3-dimensional Lorentzian lattice of determinant $D$; 
 see theorem~\ref{thmdef-ideal-corner-symbols}.
 Note that the values of $s$ and $\sigma$ appear, while the 
 letters $z,a,b$ appear literally when relevant, for example 
 ${26}\above{1pt}{1pt}{4,3}{\infty b}{104}$.}
\label{tab-ideal-corner-symbols}
\end{table}

\begin{proof}
Because $x$ is a root, the glue group of $\spanof{x}\oplus x^\perp\to L$ is trivial
 or $\Z/2$.
 The determinant of $x^\perp$ is $D/X$ or $4D/X$ in these two cases.
  If $(\lambda,s,\sigma)$ are the invariants of
 $(x^\perp,z)$, then $\det x^\perp=\lambda^2/s^2$ gives us an
 equation for $\lambda$ in terms of $D$, $X$ and $s$.  If
 $\lambda=-s\sqrt{-D/X}$ then there is no glue, so the conditions of
 the top row are satisfied.  If $\lambda=-2s\sqrt{-D/X}$ then there is
 $\Z/2$ glue, and the last three rows of the table list all the
 possible gluings of $\spanof{x}$ to $x^\perp$.  This shows that the
 conditions of exactly one row of the table are satisfied, so the
 corner symbol is defined.  

Now we show that it and $D$ determine $(L,x,y,z)$.  By referring to
 the table we see that they determine $(x^\perp,z)$ up to isometry.
 Since the norm of $x$ is part of the symbol, they determine
 $\bigl(\spanof{x}\oplus x^\perp,x,z\bigr)$ up to isometry.  Since the
 symbol also indicates the glue, they determine $(L,x,z)$ up to
 isometry.  These determine the Weyl chamber uniquely, since of all
 the Weyl chambers of $L$ incident at $z$, there is only one for which
 $x$ is a simple root.  This in turn determines $y$, because only one
 simple root of that chamber besides $x$ is orthogonal to $z$.
\end{proof}

\section{The classification theorem}
\label{sec-rank-3}

Here is the main theorem of the paper; the list of lattices appears at
the end of the paper.

\begin{theorem}
\label{thm-main-thm}
Up to scale, there are \NumLattices{} lattices of signature $(2,1)$
whose isometry groups are generated up to finite index by reflections.
\end{theorem}

\begin{proof}
Suppose $L$ is such a lattice, with Weyl group $W$.  Since its Weyl
chamber $C$ has finitely many edges, theorem~\ref{thmdef-shape-of-polygons} applies, so that
$C$ has one of the three features described there: a short edge that is
non-orthogonal to at least one of its neighbors (which are
non-orthogonal to each other), at least $5$ edges and a short pair, or
at least $6$ edges and a
close pair.  Depending on which of those conditions holds, one of
lemmas~\ref{lem-shape-of-2d-SE-integral-polygon}--\ref{lem-shape-of-2D-CP-integral-polygon} applies, with the quasiroot weights
$\rho,\dots,\rho'$ all $2$ because roots are quasiroots of weight~$2$.
The conclusion is that $L$ has $3$, $4$ or $5$ consecutive simple
roots $r,\dots,r'$ whose inner product matrix is one of finitely many
possibilities, up to scale.  These possibilities are listed explicitly
there, and we enumerated them using a computer: the
numbers of matrices of the forms
\eqref{eq-shape-of-2d-SE-integral-polygon-NONorthogonality-case},
\eqref{eq-shape-of-2d-SE-integral-polygon-orthogonality-case},
\eqref{eq-shape-of-2d-SP-integral-polygon-NONorthogonality-case},
\eqref{eq-shape-of-2d-SP-integral-polygon-orthogonality-case} and
\eqref{eq-shape-of-2d-CP-integral-polygon} are
\SENOCNumNarrowMatrices{}, \SEOCNumNarrowMatrices{},
\SPNOCNumNarrowMatrices{}, \SPOCNumNarrowMatrices{} and
\CPNumNarrowMatrices{} respectively.

Some of these matrices are not really possibilities: of those of
form \eqref{eq-shape-of-2d-SE-integral-polygon-NONorthogonality-case},
\SENOCNumNarrowMatricesRejectedRankTwo{} has only rank~$2$.  Of those
of form \eqref{eq-shape-of-2d-SE-integral-polygon-orthogonality-case},
\SEOCNumNarrowMatricesRejectedRankTwo{} have rank~$2$ and
\SEOCNumNarrowMatricesRejectedPositiveDefinite{} are
positive-definite.  Matrices of the form
\eqref{eq-shape-of-2d-SP-integral-polygon-NONorthogonality-case} are
$4\times4$, so the span of $r,\dots,r'$ is obtained by quotienting
$\Z^4$ by the kernel of the inner product.  After
quotienting, $r,\dots,r'$ may no longer be primitive vectors.  When
this happens we reject the matrix because roots are always primitive.
In this way we reject \SPNOCNumNarrowMatricesRejectedImprimitiveRoot{}
matrices, and similarly we reject
\SPOCNumNarrowMatricesRejectedImprimitiveRoot{} and
\CPNumNarrowMatricesRejectedImprimitiveRoot{} of the forms
\eqref{eq-shape-of-2d-SP-integral-polygon-orthogonality-case} and
\eqref{eq-shape-of-2d-CP-integral-polygon}.  This leaves
\TotalNumNarrowMatricesRemaining{} possible inner product matrices
for
$r,\dots,r'$, up to scale.

For $M$ any one of of these matrices, say size $n\times n$, we regard
$M$ as an inner product on $\Z^n$ and define $L_M$ as the quotient by
the kernel of the form, equipped with the induced inner product.  Then
$r,\dots,r'$ are the images in this quotient of the standard basis
vectors of $\Z^n$ and are roots of $L_M$.  Let $E$ vary over all lattices that lie between
the span of these roots and their reflective hull (defined in section~\ref{sec-background}).  There are only
finitely many such enlargements of $L_M$, because $E$ corresponds to a
subgroup of the finite abelian group
$\spanof{r,\dots,r'}^\rh/\spanof{r,\dots,r'}$.  We enumerated the
possible pairs $(M,E)$ with a computer: a total of
\TotalNumEnlargements{}.  Because $r,\dots,r'$ are roots of $L$, $L$
lies between their span and their reflective hull, so $(L,r,\dots,r')$
is isometric to one of our candidates $(E,r,\dots,r')$, up to scale.
Because roots are always primitive, we may discard any
$(E,r,\dots,r')$ for which $r,\dots,r'$ are not primitive, leaving a
total of \NumCandidates{} candidate tuples $(E,r,\dots,r')$ to consider.
We rescaled each candidate to make it unscaled.  

Vinberg's algorithm is the essential tool for determining whether a
given lattice is reflective.  But we are not ready to apply it,
because we need to choose a controlling vector $k$ and find a set of
simple roots for its stabilizer $W_k$ in $W$.  A natural choice is to
take $k$ to represent one of the $2$, $3$ or $4$ vertices of $C$
determined by consecutive pairs among $r,\dots,r'$, and one would
expect $W_k$ to be generated by the reflections in those two roots.
But for some of the candidates $(E,r,\dots,r')$, $W_k$ is actually
larger.  For example, the two roots might be simple roots for an $A_2$
root system, but their span might contain additional roots of $L$,
enlarging the $A_2$ to $G_2$.  We discard the candidate if this occurs
at one of the $2$, $3$ or $4$ vertices.  The reason is that
$r,\dots,r'$ are not simple roots of $E$, because some other mirror of
$E$ passes through the interior of the angle at that vertex.  Since we
started with the assumption that $r,\dots,r'$ are simple roots of $L$,
the candidate $(E,r,\dots,r')$ cannot be isometric to
$(L,r,\dots,r')$.  In this manner we discard
\NumCandidatesFailRootSimplicity{} candidates.  This does not much
reduce the number of cases that must be analyzed, but does allow us to
apply Vinberg's algorithm in the remaining cases.

In principle we could have applied Vinberg's algorithm to the
\NumRemainingCandidates{} remaining candidates $(E,r,\dots,r')$.  In
practice we considered the \NumCandidatesSSF{} SSF cases first.
Because SSF lattices may be distinguished by their genera, one can
immediately sort them into isometry classes and keep only one
candidate from each class.  There turn out to be
\NumCandidatesDistinctSSF{} distinct SSF lattices among our
candidates.  To these we applied Vinberg's algorithm, obtaining
Nikulin's 160 lattices \cite{Nikulin-rk3} and simple roots for them.  We checked
that our results agree with his.

We mentioned in section~\ref{sec-background} that the original form of Vinberg's
algorithm (i.e., with negative-norm controlling vector) was enough for
us.  This is because in every one of the SSF cases, at least one of
the $2$, $3$ or $4$ possible starting corners lies in $H^2$,
rather than being an ideal vertex.  In fact one can show a priori that
this must happen: the Weyl chamber of a $3$-dimensional SSF lattice
cannot have consecutive ideal vertices.  But this isn't really needed since
one can just look at the corners in the 
\NumCandidatesDistinctSSF{} cases.

When applying the algorithm to one of our candidates $(E,r,\dots,r')$,
we checked after each new batch of simple roots whether the polygon
defined by the so-far-found simple roots closed up.  If this happened
then $E$ is reflective and we had a complete set of simple roots.
Otherwise, we looked at the corner symbols of $E$ at the so-far-found
corners.  If some corner symbol appears twice then $E$ admits an
automorphism carrying one corner to the other and preserving the
chamber $C$ being studied.  (Note that each corner can give two corner
symbols since its incident edges can be taking in either order.)
If we find an infinite-order automorphism
this way, or finite-order automorphisms with distinct fixed points,
then $C$ has infinite area and $E$ is non-reflective.  Conversely, if
$E$ is non-reflective then eventually enough corners of $C$ will be
found to show this.  With these stopping conditions, the algorithm is
guaranteed to terminate, either proving non-reflectivity or finding a
set of simple roots.

We remark that a nontrivial automorphism of $E$ preserving $C$ must be
an involution, by the argument for \cite[Prop.~3.4]{Scharlau}.  When we found such an
involution before finishing the search for simple roots, we used it to
speed up the search.

To analyze reflectivity in the non-SSF cases, we sorted them in
increasing order of $|\det E\,|$ and proceeded inductively.  Suppose when
studying a particular case $E$ that we have found all
the reflective lattices of smaller $|\det|$ and obtained simple roots
for them.  Since $E$ is not SSF, its $|\det|$ may be reduced by
$p$-filling or (rescaled) $p$-duality, as explained in
section~\ref{sec-background}.  Write $F$ for the resulting lattice.  If
$F$ is not reflective then $E$ cannot be either, since $W(E)\sset
W(F)$.  And if $F$ is reflective then we can determine whether $E$ is
by a much faster method than Vinberg's algorithm (explained below).  

But it is a nontrivial problem to determine whether $F$ is on the list
of known reflective lattices.  We solved this as follows.  If say $x$
and $y$ are consecutive simple roots of $E$'s Weyl chamber, then they
(or scalar multiples of them) are certainly roots of $F$.  These two
roots might not be extendible to a set of simple roots for $F$,
because of phenomena like the $A_2\sset G_2$ inclusion encountered
above.  But we can look in their rational span to obtain a pair of
simple roots for $F$.  Then we have a corner of $F$'s Weyl chamber and
we compute its corner symbol, say $S$.  We compare this corner symbol
with all the corner symbols for all the reflective lattices of $F$'s
determinant.  If $S$ does not appear then $F$ is not reflective and we
are done.  If $S$ does appear then we obtain an isomorphism of $F$
with a known reflective lattice, extending the two known simple roots
to a full set of simple roots.

We have reduced to the case that applying $p$-filling or rescaled
$p$-duality to $E$ yields a reflective lattice $F$ with a known set of
simple roots.  In the $p$-duality case, the isometry groups of $E$ and
$F$ are equal, so $E$ is reflective and we can obtain simple roots for
it by rescaling $F$'s.  So we assume the $p$-filling case.  Then $E$
is a known sublattice of $F$, lying between $F$ and $pF$, and we must
determine whether $E$ is reflective and obtain simple roots for it
when it is.  We did this using what we call the ``method of
bijections'', which we explain in a more general context below.

In this manner we determined all reflective lattices and found simple
roots for them.  There might be some redundancy in the list, but this
can be easily removed using the lists of corner symbols: two
reflective lattices are isometric if and only if they have the same
determinant and share a corner symbol.
\end{proof}

We now explain the ``method of bijections'', referred to in the proof.
The general setup is that $W$ is a Coxeter group with chamber $C$, $X$
is a finite set on which it acts, $x\in X$ and we want to know whether
the stabilizer $W_x$ is generated up to finite index by reflections.
In the proof of the theorem we used the case that $F$ is a Lorentzian
lattice, $W$ its Weyl group, $X$ the set of subgroups of $F/pF$ for
some prime $p$, $x$ is the subgroup corresponding to the sublattice
$E$ of $F$, and $W_x$ is the subgroup of $W(F)$ preserving $E$.  It
contains $W(E)$ because $\aut E\sset\aut(\pfill(E))$.

The method is a minor variation on traditional coset-enumeration
algorithms.  The idea is to build up a
bijection between a set of chambers and the orbit of $x$ in $X$.
Then the union of the chambers is a fundamental domain for $W_x$.  I imagine a little man
walking from chamber to chamber, being careful never to cross a mirror
of $W_x$.  
For any
chamber $D$ we write $w_D$ for the element of $W$ that sends $D$ to $C$.  
Two chambers $D$, $D'$
are $W_x$-equivalent if and only
if $w_D(x)=w_{D'}(x)$.

During the algorithm we maintain a list $\DD$ of chambers, and also
the list $\FF$ of all pairs $(D,f)$ where $D\in\DD$ and $f$ is an facet of
$D$.  We mark each $(D,f)\in\FF$ by one of the following:
\begin{center}
\begin{tabular}{rl}
``unexplored'':& no assertions are made about $(D,f)$;\\

``mirror'':& the reflection $R_f$ across $f$ lies in $W_x$;\\

``interior'':& $R_f\notin W_x$ and $R_f(D)\in\DD$;\\

``matched'':& $R_f\notin W_x$ and $R_f(D)\notin\DD$ but\\
&$w_D\circ R_f(x)=w_{D'}(x)$ for some $D'\in\DD$.
\end{tabular}
\end{center}
In the initial state, $\DD=\{C\}$ and all pairs $(C,f)$ are marked
``unexplored''.

At each iteration of the algorithm we choose an ``unexplored'' pair
$(D,f)\in\FF$ if one exists.  If none does then the algorithm
terminates.  If $R_f\in W_x$ then we mark the pair ``mirror''.  Otherwise, if $R_f(D)\in\DD$ then
we mark the pair ``interior''.  Otherwise, if $w_D\circ
R_f(x)=w_{D'}(x)$ for some $D'\in\DD$ then we mark the pair
``matched''.  Otherwise we mark $(D,f)$ as ``interior'' and
add $D':=R_f(D)$ to $\DD$ and all pairs
$(D',\hbox{facet of $D'$})$ to $\FF$, and mark them 
``unexplored''.   Then we continue to the next iteration.

In the last case of this chain of otherwise's, note that $w_{D'}=w_D\circ R_f$, and by the
conditions under which this case applies, $w_{D'}$ lies in a coset of
$W_x$ not represented by any previous member of $\DD$.  Since there
are only finitely many cosets of $W_x$ in $W$, the algorithm must
terminate.  Furthermore, at termination $R_f(D)$ is $W_x$-equivalent
to some member of $\DD$, for every $(D,f)\in\FF$, or else $R_f(D)$
would get adjoined to $\DD$ and the algorithm would continue.  So
$\DD$ is a complete set of coset representatives for $W_x$ in $W$ and
the union $U=\cup_{D\in\DD}D$ is a fundamental domain for $W_x$.  
Also, whenever the algorithm
adjoins a chamber $D'=R_f(D)$ to $\DD$, it is already known that $R_f\notin
W_x$.  It follows that both $D$, $D'$ lie in one Weyl chamber of
$W_x$, and by induction that all of $U$ does.

At termination,
each $(D,f)$ is marked ``interior'', ``matched'' or ``mirror''.
Each facet marked ``interior'' really is in $U$'s interior, except perhaps
for its boundary.  
If $(D,f)$ is marked ``matched'', then there is a unique $D'\in\DD$
for which $w_D\circ R_f(x)=w_{D'}(x)$, and we define
$\c_{D,f}=w_{D'}^{-1}\circ w_D\circ R_f$.  This carries $R_f(D)$ to
$D'$, and lies in $W_x$ because it preserves $x\in X$.
Our main claim about the algorithm is the following:

\begin{theorem}
\label{thm-method-of-bijections}
$W_x$ is generated by the reflections across those facets $f$ for
which $(D,f)$ is marked ``mirror'' and the $\c_{D,f}$ for which
$(D,f)$ is marked ``matched''.  The latter generate the stabilizer in
$W_x$ of $W_x$'s Weyl chamber.  In particular, $W_x$ is generated by
reflections up to finite index if and only if the group $\Gamma$
generated by all the $\c_{D,f}$ is finite.
\end{theorem}

\begin{proof}
The algorithm only marks $(D,f)$ as ``mirror'' if $R_f\in W_x$, and
all the $\c_{D,f}$ lie in $W_x$ by construction.  So the supposed
generators do in fact lie in $W_x$.  Next we observe that $\c_{D,f}$
preserves the Weyl chamber of $W_x$ that contains $U$; this is just
the fact that $\c_{D,f}$ sends $R_f(D)$ to $D'$, and $R_f(D)$ lies in
the same Weyl chamber of $W_x$ as $D$ because $R_f\notin W_x$.  It
follows that $\Gamma$ preserves this chamber of $W_x$.  Now consider
the polytope $V$ which is the union of the $\Gamma$-translates of $U$;
it lies in this single chamber of $W_x$.  The reflection across any
one of its facets is a $\Gamma$-conjugate of one of the reflections in
our generating set, so lies in $W_x$.  It follows that $V$ is the
whole of the Weyl chamber for $W_x$ that contains it.  All our claims
follow from this.
\end{proof}

In our situation, checking whether $\Gamma$ is finite amounts to
checking whether the $\c_{D,f}$ have a common fixed point in
hyperbolic space, which is
just linear algebra.  When $\Gamma$ is finite, we take the
$\Gamma$-images of the facets marked ``mirror''.  They bound $W_x$'s
chamber, yielding simple roots for $W_x$, which in our case is $W(E)$.

\section{How to read the table}
\label{sec-how-to-read}

At the end of the paper we exhibit the \NumLattices{} unscaled
reflective Lorentzian lattices of rank~3.  Only
\NumPrintedExplicitly{} lattices are displayed explicitly, and the
rest are obtained by some simple operations.  They are grouped
according to the conjugacy classes of their Weyl groups in
$O(2,1;\R)$. The first \NumMainLattices{} correspond to the main
lattices in Nikulin \cite{Nikulin-rk3} and are listed in the same
order.  Then come the Weyl groups of the lattices of Nikulin's table~2
whose Weyl groups have not been listed yet.  The remainder are listed
in no particular order.  Though we do not give details here, we
classified the \NumWeylGroups{} Weyl groups up to commensurability;
they represent \NumCommClasses{} classes.

\def\GeneralInformation{General Information}
\def\ChamberAngles{Chamber Angles}
\def\ChamberIsometries{Chamber Isometries}
\def\Genus{Genus}
\def\Determinant{Discriminant group and determinant}
\def\ImplicitlyPrintedLattices{Implicitly printed lattices}
\def\CornerSymbols{Corner Symbols and description of the lattices}
\def\SharingGenus{Distinct reflective lattices sharing a genus}
\def\InnerProductMatrix{Inner product matrix}
\def\DiagramAutomorphism{Diagram automorphism}
\def\SimpleRoots{Simple roots}
\def\TableCompleteness{Completeness of the table}
\def\ApplyingOperations{Applying filling, duality and mainification}

{\it\GeneralInformation:\/} For each Weyl group, its Euler
characteristic is $-\chi/24$ and the area of its Weyl chamber is
$\pi\chi/12$, where $\chi$ is given in the table.  The largest area is
\LargestArea{} (\WeylsWithLargestArea) and the smallest is
\SmallestArea{} (\WeylsWithSmallestArea).  The number of lattices
having that Weyl group is listed; the largest number is
\MostLatticesInWeyl{} (\WeylsWithMostLattices) and the smallest is
\LeastLatticesInWeyl{} (\WeylsWithLeastLattices).  For each $W_n$ we
have numbered the printed lattices having that Weyl group as
$L_{n.1}, L_{n.2},\dots$

{\it\ChamberAngles:\/}
At the right side
of the page we give the list
of the chamber's angles $\pi/(\hbox{2, 3, 4, 6 or $\infty$})$ in cyclic order.
The largest number of edges is \MostEdges{} (\WeylsWithMostEdges).  Of
the \NumWeylGroups{} different Weyl chambers, \NumRegularWeyl{} are
regular (\RegularWeyls), \NumIdealWeyl{} have all ideal vertices
(\IdealWeyls), \NumRightAngledWeyl{} have all right angles, and
\NumCompactChambers{} are compact.

{\it\ChamberIsometries:\/}
If the chamber has nontrivial
isometry group then the list of angles is followed by
``$\rtimes C_n$'' or ``$\rtimes D_n$''.  The subscript $n$ gives the number of isometries and
we write $D$ (resp.~$C$) when there are (resp.\ are not) reflections in this
finite group.  
Note the distinction between $C_2$ and $D_2$.
The largest $C_n$ appearing is $C_{\LargestCyclic}$
(\WeylsWithLargestCyclic) and the maximal dihedral groups appearing
are $D_{12}$ (\WeylsWithDihedralTwelve) and $D_8$
(\WeylsWithDihedralEight).  It happens very often that the
chamber admits reflections, but in this case the reflections don't
preserve any of the lattices having that Weyl group.  In the dihedral
case, we have also indicated how the mirrors of the reflections meet
the boundary of the chamber.  A vertical line through a digit (i.e.,
$\slashtwo$, $\slashthree$, $\slashinfty$) means that a mirror passes through that vertex, and a vertical line between two digits
means that a mirror bisects the edge
joining the two corresponding vertices.

{\it\Genus:\/}
For each lattice $L$ listed explicitly we give its genus, in one
version of the notation of Conway and Sloane \cite[ch.~15]{SPLAG}.  That is, for
each prime $p$ dividing twice the determinant, we give the $p$-adic
symbol for $L\tensor\Z_p$.  
We have printed the symbol for the $p^0$ constituent
explicitly to allow easy application of $p$-duality and $p$-filling
(see section~\ref{sec-Conway-Sloane}).
For $p=2$ we give their canonical $2$-adic symbol
in the ``compartment'' notation, but see section~\ref{sec-Conway-Sloane} because there is a
minor error in their paper which requires adjusting the meaning of
``canonical''.  
We have also suppressed the initial $\I$ or $\II$ that they
use because it can be read from the displayed $2$-adic symbol, and we
have suppressed the signature because it is always $(2,1)$.  For
example, they would write $\II_{2,1}(2\above{1pt}{1pt}{1}{1})$ in
place of our $1\above{1pt}{1pt}{2}{\II}2\above{1pt}{1pt}{1}{1}$.

The \NumLattices{} reflective lattices represent \NumGenera{} genera,
the largest number of reflective lattices in a genus is
\MostReflectivesInGenus{}, and \NumGeneraWithMostLattices{} genera
contain this many.  When a listed lattice is not the only reflective
lattice in its genus, this is noted in the table and we give
additional information; see ``\SharingGenus''
below.

{\it\Determinant:\/} The structure of the discriminant group $\D(L)$,
and therefore the determinant of $L$, can be read from the genus
symbol.  To do this one simply reads each symbol $q^{\pm k}$ as the
group $(\Z/q)^k$, where $q$ is a prime power, and the string of
symbols as the direct sum of groups.  One ignores the sign, and when
$q$ is even one also ignores any subscripts.  For example, if $L$ has
genus $1_{\II}^{-2}4^{1}_{1}{\cdot}3^{2}{\cdot}5^{-}125^{1}$ then
discriminant group is $(\Z/4)\oplus(\Z/3)^2\oplus(\Z/5)\oplus(\Z/125)\iso(\Z/1500)\oplus(\Z/15)$.
The most-negative determinant among all reflective lattices is
\MostNegativeDet.  But a better measure of complexity considers only
lattices which are minimal in their duality class,
yielding \MostNegativeDetOfMinimalInDualityClass.  The largest prime
factor among the determinants of our lattices is
\LargestPrimeInDet.

{\it\ImplicitlyPrintedLattices:\/} For some $L$'s in the table,
\instructions{\ldots} appears after the genus;
it indicates how to construct some other lattices, not explicitly
printed, from $L$.  A digit indicates the operation of $p$-filling
(see section~\ref{sec-background}) and $m$ indicates the operation of
``mainification''.  This has meaning when $L$ is odd and the $2^0$
Jordan constituent of the $2$-adic lattice $L\tensor\Z_2$ has
dimension $1$ or~$2$.  It means passage to $L$'s even sublattice,
followed by multiplying inner products by $\frac{1}{4}$ or
$\frac{1}{2}$ to obtain an unscaled lattice.  Every automorphism of
$L$ preserves $L$'s mainification.  For rank $3$ lattices, not
admitting mainification is equivalent to being ``main'' in Nikulin's
terminology \cite{Nikulin-rk3}.  We dislike our name
for the operation, because the mainification of a lattice might not be
main.

A string of these symbols indicates that these operations should be
applied in order, but usually the order is not important because the
operations commute, except for mainification and $2$-filling.  Since
all the primes involved are less than~10, we have printed them without
spaces.  So for example \instructions{3,32,3m,m} indicates that $L$'s
line on the table implicitly represents $4$ additional lattices.  One
is obtained by $3$-filling, one by $3$-filling followed by
$2$-filling, one by $3$-filling followed by mainification, and one by
mainification.  A total of \NumPrintedImplicitly{} lattices are
implicitly printed in this way.  We only use this convention when each
lattice obtained by the stated operations has the same Weyl group as
$L$, so that simple roots for the derived lattices are scalar
multiples of $L$'s.  See ``\ApplyingOperations'' below for how to easily
construct the inner product matrix and simple roots for lattices
obtained in this way.

It turns out that all of Nikulin's lattices are implicitly printed in
this fashion.  We have indicated this by for example
%XX hardcoded numbers!  recheck before sending final version
\instructions{\hbox{$23\to N_4$},3,2} for $L_{4.1}$.  This means that the
lattice got by applying $2$-filling and then $3$-filling to $L_{4.1}$
is numbered $N=4$ in Nikulin's \cite[table~1]{Nikulin-rk3}.  We replace $N$
by $N'$ to indicate lattices in his table~2.  We prepared our tables
so that our simple roots come in the same order as his.  Also, some
implicitly printed lattices share their genera with other reflective
lattices; we indicate this with an asterisk ``$*$'' and provide some
additional information in ``\SharingGenus'' below.

{\it\CornerSymbols:\/}
At the right we give the corner symbols at all the corners of the
chamber in the same cyclic order used to list the angles of the Weyl
chamber.  When $\aut L$ contains a nontrivial isometry preserving the
chamber, this isometry is always an involution, and we have written
``$(\times2)$'' after the corner symbols.  The full sequence of corner
symbols is then got by concatenating two copies of the ones listed.
By giving the corner symbols we have given enough information to
reconstruct $L$ in several different ways.  For example, the genus
\GenusWithTwoWeyls{} mentioned below contains
%  XX to check before final version: the printed corner symbol really
%  is the one that the text refers to.
$\GenusWithTwoWeylsSecondLattice={}$\GenusWithTwoWeylsSecondCornerSymbols,
and to construct it we find a consecutive
pair of roots, say ${8}\above{1pt}{1pt}{}{2}{256}$ (the
last root followed by the first one).  So $L$ has roots of norms $8$
and~$256$; the subscript says they are orthogonal, and the absence of
a superscript says that $L$ is generated by them and their orthogonal
complement.  Since the determinant is $-8\cdot256$, a generator for
the complement has norm $-1$.  So $L$ has inner product matrix
$\diag[-1,8,256]$.  Refer to section~\ref{sec-corner-symbols} for full
instructions on constructing $L$ from one of its corner symbols.  The
largest root norm among all reflective lattices (resp. those minimal
in their duality classes) is
\LargestRootNorm{} (resp. \LargestRootNormofMinimalInDualityClass).

{\it\SharingGenus:\/}  When one of our listed lattices $L$ shares its
genus with another reflective lattice, we state what the other lattice
is, either as a lattice in $L$'s duality class or by describing it in
terms of another $L_{n.i}$.  We also give all chains of $p$-dualities
that carry $L$ to a lattice isometric to $L$.  This information is
required to reconstitute the full table from what we have printed.
See ``\TableCompleteness'' below.  A few implicitly-listed lattices
also share their genera with other reflective lattices.  The
corresponding information for these lattices is the following:
\par\smallskip
\ImplicitGeneraTable
\smallskip
% XX to check before final version: the two lattices listed here
% really are printed explicitly, so the numbering makes sense.
\noindent
Reflective lattices having the same genus usually have
the same Weyl group.  But the genus \GenusWithTwoWeyls{} contains the
reflective lattices  $\GenusWithTwoWeylsFirstLattice$ and
$\GenusWithTwoWeylsSecondLattice$, which have Weyl groups
\GenusWithTwoWeylsFirstWeyl{} and \GenusWithTwoWeylsSecondWeyl{}.
The only other genus with
this property is the $2$-dual of this one.  

{\it\InnerProductMatrix:\/} This is the first displayed matrix.  We
did not seek bases in which the matrix entries are small, or bases
related to the corners of the chamber.  Rather, they are in Smith
normal form relative to their duals, which is useful when applying
$p$-filling and $p$-duality.  Namely, let $a,b,c$ be the elementary
divisors of the inclusion $L\to L^*$, where $c|b|a$.  These can be
read from the structure of $\D(L)$, which can be read from the genus
as explained under ``\Determinant''.  With respect to
the basis having the displayed inner product matrix, $L^*$ has basis
$(1/a,0,0)$, $(0,1/b,0)$, $(0,0,1/c)$.  Our lattices are unscaled, so
$c$ is always~$1$.

{\it\DiagramAutomorphism:\/} If $L$ admits a diagram automorphism,
that is, an isometry preserving the Weyl chamber (other than
negation), then this is an involution and we display it right after
the inner product matrix.

{\it\SimpleRoots:\/} Next we list the simple roots of $L$.  If $L$
has no diagram automorphism then all the simple roots are listed, in
the order used for the corner symbols.  If $L$ has a diagram
automorphism then only the first half of the simple roots are
displayed and the rest are got by applying the diagram automorphism.

{\it\TableCompleteness:\/} The table of lattices is complete
in the following sense.  There are \NumDualityClasses{} duality
classes of reflective lattices, and each has exactly one member
appearing in the table,
\NumPrintedExplicitly{} explicitly and \NumPrintedImplicitly{}
implicitly.  
The lattices printed explicitly always have minimal (i.e., least negative)
determinant in their duality classes.
The full list of reflective lattices is obtained from
our explicitly printed lattices by applying the stated operations and
then applying all possible rescaled $p$-dualities.

As stated, this is not quite explicit, because some chains of
$p$-dualities may lead back to $L$.  A fancy way to say this is that
$L$'s duality class is a homogeneous space for $(\Z/2)^\Omega$ where
$\Omega$ is the set of primes dividing $\det L$.  To find the other
lattices in the duality class, without duplicates, one must find a
subgroup of $(\Z/2)^\Omega$ acting simply-transitively, i.e., a
complement to the subgroup $T\sset(\Z/2)^\Omega$ acting trivially.  So
one needs to know $T$ in order to reconstruct the full list of
lattices without duplication.  If $L$ is the unique reflective lattice
in its genus (which is almost always the case) then one can determine
whether a given sequence of rescaled $p$-dualities yields a lattice
isometric to $L$ by computing the genus of the result and comparing
that to $L$'s.  (See section~\ref{sec-Conway-Sloane} for the easy
computational details.)  Otherwise, there is no easy way to determine this, and
it is for this reason that we have listed the nontrivial elements of $T$
explicitly when $L$ shares its genus with another reflective lattice.
We say ``elements'' but it turns out that $T$ is never larger than $\Z/2$.

{\it\ApplyingOperations:\/} Because of our choice of basis for the
lattices (see ``\InnerProductMatrix''), applying $p$-filling is easy.
Let $p^k$ be the $p$-part of the first elementary divisor $a$, and
adjoin $(1/p,0,0)$ to $L$.  This has the effect of dividing the first
row and column of the inner product matrix by $p$, and multiplying the
first coordinate of all roots by $p$.  (If $p^k|b$ then we would treat
the second coordinate similarly, but this never happens because the
explicitly printed lattices are all minimal in their duality classes.)
The result is the inner product matrix for $\pfill(L)$, and the simple
roots of $L$ expressed in a basis for $\pfill(L)$.  It may be that
some of $L$'s roots are divisible by $p$ in $\pdual(L)$, so if
necessary we divide by $p$ to make them primitive.  They will be roots
of $\pfill(L)$ since $\aut L\sset\aut\pfill(L)$.  When the filling
operation is indicated in our tables, these roots are a set of simple roots for
$\pfill(L)$.  This is because we only indicate filling operations when
they don't change the Weyl group.  Similar but slightly more
complicated operations treat mainification and rescaled $p$-duality.

\section{The Conway-Sloane genus symbol}
\label{sec-Conway-Sloane}

Genera of integer bilinear forms present some complicated phenomena,
and Conway and Sloane introduced a notation for working with them that
is as simple as possible \cite[ch.~15]{SPLAG}.  In this section we
state how to apply our operations of filling, duality and
mainification in terms of their notation.  We also correct a minor
error in their formulation of the canonical $2$-adic symbol.

{\it $p$-filling:\/} This affects only the $p$-adic symbol.  One
simply takes the Jordan constituent of largest scale $p^{a+2}$ and
replaces $a+2$ by $a$.  (Recall that $p$-filling is only defined if
$a\geq0$.)  The scale of the resulting summand of
$\pfill(L)\tensor\Z_p$ may be the same as that of another constituent
of $L$.  In this case one takes the direct sum of these sublattices of
$\pfill(L)$ to obtain the $p^a$-constituent.  The direct sum is
computed as follows, where we write $q$ for $p^a$:
\begin{align*}
q^{\e_1n_1}\oplus q^{\e_2n_2}&{}= q^{(\e_1\e_2)(n_1+n_2)}\\
\noalign{\noindent if $q$ is odd, while}
q^{\e_1n_1}_{t_1}\oplus q^{\e_2n_2}_{t_2}&{}= q^{(\e_1\e_2)(n_1+n_2)}_{t_1+t_2}\\
q^{\e_1n_1}_{t_1}\oplus q^{\e_2n_2}_{\II}&{}= q^{(\e_1\e_2)(n_1+n_2)}_{t_1}\\
q^{\e_1n_1}_{\II}\oplus q^{\e_2n_2}_{\II}&{}= q^{(\e_1\e_2)(n_1+n_2)}_{\II}
\end{align*}
if $q$ is even.  
Here the $\e_i$ are signs, $n_i\geq0$ are the ranks and $t_i\in\Z/8$
are the oddities.
In short, signs multiply and  ranks and
subscripts add, subject to the special rules involving $\II$.  When
$p=2$, sometimes there is additional oddity fusion or opportunity for
sign walking.  Here are some
examples of $2$-filling:
\begin{align*}
% simplest possible 2-filling (L374.1)
1^1_18^1_7256^1_1{\cdot}1^29^1
&{}\to
1^1_18^1_764^1_1{\cdot}1^29^1
\\
% 2-filling where new constituent oddity-fuses with old (L1.2), and
% enables sign-walking
1^{-2}_28^-_3
&{} \to 
1^{-2}_22^-_3 
= 
[1^{-2}2^-]_5
=
[1^22^1]_1
\\ 
% 2-filling where new constituent joins two previously separate
% compartments (diagonal[-1,4,8])
1^1_{-1}[4^18^1]_2
&{}\to
1^1_{-1}[4^12^1]_2
=
[1^12^14^1]_1
\\
% 2-filling where new constituent has same scale as a constituent
% already present, both being odd (L146.4)
1^1_14^1_716^1_1
&{}\to
1^1_14^1_7\oplus4^1_1
=
1^1_14^2_0
\\
% 2-filling where new constituent has same scale as a constituent
% already present, one having type II (L1.1)
1^2_{\II}4^1_1
&{}\to
1^2_{\II}\oplus1^1_1
=
1^3_1.
\end{align*}


{\it Rescaling:\/} Multiplying all inner products by a rational number
$s$ has the following effect on the $l$-adic symbols for all primes
$l$ that divide neither the numerator nor denominator of $s$.  The
sign of a constituent $(\hbox{power of $l$})^{\pm n}$  is flipped just
if $n$ is odd and the Legendre symbol $\legendre{s}{l}$ is~$-1$.  If
$l=2$ we must supplement this rule by describing how to alter the
subscript.  A subscript $\II$ is left alone, while a subscript
$t\in\Z/8$ is multiplied by $s$.

{\it Rescaled $p$-duality:\/} Say $q=p^a$ is the largest scale
appearing in the $p$-adic symbol.  One obtains the rescaled $p$-dual
by an alteration that doesn't affect $L\tensor\Z_l$ for $l\neq p$,
followed by rescaling by $p^a$.  So for $l\neq p$ the effect of
rescaled $p$-duality is the same as that of rescaling.  The $p$-adic
symbol is altered by replacing the scale $p^{a_i}$ of each constituent
by $p^{a-a_i}$, leaving superscripts and subscripts alone.  Since one
usually writes the constituents in increasing order of scale, this
also reverses the order of the constituents.  A single example of
$2$-duality should illustrate the process:
$$
% diag[-1,30,1800]: reverse the 2's; sign change the 3's; leave 5s
% alone
1^1_{-1}2^1_{-1}8^1_1{\cdot}1^-3^19^-{\cdot}1^15^125^-
\to
1^1_14^1_{-1}8^1_{-1}{\cdot}1^13^-9^1{\cdot}1^15^125^-.
$$

{\it Mainification:\/}
This is an alteration of $L$ that doesn't affect $L\tensor\Z_l$ for
odd $l$, followed by rescaling by $\frac{1}{4}$ or $\frac{1}{2}$.  So
for odd $l$ mainification has the same effect as rescaling.  Recall
that the mainification is only defined if $L$ is odd with
$2^0$-constituent of rank~$1$ or~$2$.  Referring to (33)
and (34) of \cite[ch. 15]{SPLAG}, this means that the constituent is
one of $1^1_{\pm1}$, $1^{-1}_{\pm3}$, $1^2_{\pm2}$, 
$1^{-2}_{\pm2}$, $1^2_0$ or $1^{-2}_4$.  To find the $2$-adic symbol of
$\main(L)$, begin by altering the $2^0$-constituent as follows:
$$
1^{\pm1}_t{}\to 4^{\pm1}_t
\qquad
1^{\pm2}_{\pm2}{}\to 2^{\pm2}_{\pm2}
\qquad
1^2_0{}\to2^2_{\II}
\qquad
1^{-2}_4{}\to2^{-2}_{\II}.
$$
The scale of the result may be the same as that of another constituent
present, in which case one takes their direct sum as above.  Finally,
one divides every scale by the smallest scale present ($2$ or $4$),
leaving all superscripts and subscripts alone.  This scaling factor is also
the one to use to work out the effect on the odd $l$-adic symbols.
Here are some examples:
\begin{gather*}
% 2-diml 2^0-constituent, no other primes or small 2-constituents (L1.3)
1^2_28^1_7
\to
2^2_28^1_7
\to
1^2_24^1_7
\\
% 2-diml 2^0-constituent, changes signs at p=3 (L4.2)
1^2_68^-_5{\cdot}1^-3^-9^1
\to
2^2_68^-_5{\cdot}1^-3^-9^1
\to
1^2_64^-_5{\cdot}1^13^19^-
\\
% 1-diml 2^0-constituent, no 2^1-constituent, with compartment fusion
% (L374.1)
1^1_18^1_7256^1_1{\cdot}1^29^1
\to
4^1_18^1_7256^1_1{\cdot}1^29^1
=
[4^18^1]_0256^1_1{\cdot}1^29^1
\to
[1^12^1]_064^1_1{\cdot}1^29^1
\\
% 1,2,4-constituents, changes sign at p=3 (diag[-1,6,4])
[1^12^-4^1]_3{\cdot}1^{-2}3^-
\to
[2^-4^2]_3{\cdot}1^{-2}3^-
\to
[1^-2^2]_3{\cdot}1^{-2}3^1.
\end{gather*}


\medskip
{\it The canonical $2$-adic symbol:\/} There is an error in the
definition of the canonical $2$-adic symbol by
Conway-Sloane \cite[ch.~15]{SPLAG}.  Distinct $2$-adic symbols can
represent isometric $2$-adic lattices, and Conway and Sloane give a
calculus for reducing every $2$-adic symbol to a canonical form.
First one uses ``sign walking'' to change some of the signs (and
simultaneously some of the oddities), and then one uses ``oddity
fusion''.  ``Compartments'' and ``trains'' refer to subchains of the
$2$-adic symbol that govern these operations. (The compartments are
delimited by brackets $[\cdots]$.)  Conway and Sloane state that one
can use sign walking to convert any $2$-adic symbol into one which has
plus signs everywhere except perhaps the first positive-dimensional
constituent in each train.  This is not true: sign walking would
supposedly take the $2$-dimensional lattice $1^1_12^-_3$ with total
oddity $1+3=4$ to one of the form $1^-_{\cdots} 2^1_{\cdots}$ with
total oddity $0$.  But the oddity of the first (resp. second)
constituent must be $\pm3$ (resp. $\pm1$) by (33)
of \cite[ch.~15]{SPLAG}, so the total oddity cannot be $0$.

So the canonical form we use is slightly more complicated: minus signs
are allowed either on the first positive-dimensional constituent of a train, or on
the second constituent of a compartment of the form $q^1_{\cdots}
r^-_{\cdots}$ with total oddity~$4$ or $q^-_{\cdots} r^-_{\cdots}$
with total oddity~$0$.  Here $q$ and $r$ are consecutive powers of
$2$.  Oddity fusion remains unchanged.  
Note that the second form $[q^-r^-]_0$ can only occur if the
$q$-constituent is the first positive-dimensional constituent of its
train. 
Using \cite[ch.~15, thm.~10]{SPLAG} we checked
that two $2$-adic lattices are isomorphic if and only if their
canonical symbols (in our sense) are identical.

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\vfill\eject

\begin{center}
\bf Table of Rank 3 Reflective Lorentzian Lattices
\end{center}
\medskip
\begingroup
\parindent=0pt
\parskip=0pt\small
\raggedbottom
%------------------------------WEYL-GROUP-W1--------------------------------
%
\leavevmode\llap{}%
$W_{1\phantom{0}\phantom{0}}$%
\qquad\llap{11} lattices, $\chi=3$%
\hfill%
$\infty24$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L1.1
%
\leavevmode%
${L_{1.1}}$%
{} : {$1\above{1pt}{1pt}{2}{{\rm II}}4\above{1pt}{1pt}{1}{1}$}\spacer%
\instructions{2\rightarrow N_{1}}%
\EasyButWeakLineBreak%
{${4}\above{1pt}{1pt}{1,0}{\infty b}{4}\above{1pt}{1pt}{r}{2}{2}\above{1pt}{1pt}{*}{4}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4\\0\\0
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\-1
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\-1\\-2
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-2\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\0\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\2\\-1
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[4, 0, 0; 0, 0, -1; 0, -1, -2],[4, 1, 1],[-1, 1, 0; -2, 0, 2; 0, 0, -1],0,1]
%
% END OF LATTICE L1.1
%
\hbox{}\par\smallskip%
%
% LATTICE L1.2
%
\leavevmode%
${L_{1.2}}$%
{} : {$1\above{1pt}{1pt}{-2}{2}8\above{1pt}{1pt}{-}{3}$}\spacer%
\instructions{2\rightarrow N'_{1}}%
\EasyButWeakLineBreak%
{${2}\above{1pt}{1pt}{4,3}{\infty a}{8}\above{1pt}{1pt}{s}{2}{4}\above{1pt}{1pt}{*}{4}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-168\\16\\32
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
16\\-1\\-3
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
32\\-3\\-6
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\2\\-1
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-4\\-4
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\-2\\6
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-168, 16, 32; 16, -1, -3; 32, -3, -6],[8, 1, 1],[0, -1, 1; 2, -4, -2; -1, -4, 6],0,2]
%
% END OF LATTICE L1.2
%
\hbox{}\par\smallskip%
%
% LATTICE L1.3
%
\leavevmode%
${L_{1.3}}$%
{} : {$1\above{1pt}{1pt}{2}{2}8\above{1pt}{1pt}{1}{7}$}\spacer%
\instructions{m}%
\EasyButWeakLineBreak%
{${2}\above{1pt}{1pt}{4,3}{\infty b}{8}\above{1pt}{1pt}{l}{2}{1}\above{1pt}{1pt}{}{4}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-328\\32\\56
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
32\\-3\\-6
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
56\\-6\\-7
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\15\\3
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3\\-24\\-4
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-7\\-2
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-328, 32, 56; 32, -3, -6; 56, -6, -7],[8, 1, 1],[2, -3, -1; 15, -24, -7; 3, -4, -2],0,3]
%
% END OF LATTICE L1.3
%
%
% LATTICE L1.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[0, -1, 0; -1, 0, 0; 0, 0, 1],[1, 1, 1],[0, 0, -1; -1, 0, 1; -1, 1, 0],0,4]
%
% END OF LATTICE L1.4
%
%
% LATTICE L1.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[2, 0, -2; 0, 1, -1; -2, -1, 2],[2, 1, 1],[0, 1, 0; 0, 0, 1; 1, 0, 0],0,5]
%
% END OF LATTICE L1.5
%
%
% LATTICE L1.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-4, 4, 4; 4, -2, -3; 4, -3, -3],[4, 1, 1],[0, -1, 1; 1, -2, -1; -1, 0, 2],0,6]
%
% END OF LATTICE L1.6
%
%
% LATTICE L1.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[0, -2, -2; -2, -2, -2; -2, -2, -1],[2, 2, 1],[-1, 0, 1; 2, -1, -1; -2, 1, 0],0,7]
%
% END OF LATTICE L1.7
%
%
% LATTICE L1.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[4, -4, 0; -4, 8, 4; 0, 4, 3],[4, 4, 1],[1, 0, 0; 0, 1, 1; 0, -2, 0],0,8]
%
% END OF LATTICE L1.8
%
%
% LATTICE L1.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[8, -4, 0; -4, 0, 0; 0, 0, 1],[4, 4, 1],[0, 0, 1; 1, 0, 0; -2, 1, 0],0,9]
%
% END OF LATTICE L1.9
%
%
% LATTICE L1.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-48, -56, -8; -56, -56, -8; -8, -8, -1],[8, 8, 1],[-1, 1, 0; 0, -1, 1; 8, 2, -8],0,10]
%
% END OF LATTICE L1.10
%
%
% LATTICE L1.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-48, -24, 8; -24, -8, 8; 8, 8, 3],[8, 8, 1],[-5, 1, 3; 8, -1, -5; -8, 2, 4],0,11]
%
% END OF LATTICE L1.11
%

\medskip%
%------------------------------WEYL-GROUP-W2--------------------------------
%
\leavevmode\llap{}%
$W_{2\phantom{0}\phantom{0}}$%
\qquad\llap{4} lattices, $\chi=2$%
\hfill%
$\infty23$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L2.1
%
\leavevmode%
${L_{2.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}8\above{1pt}{1pt}{-}{5}$}\spacer%
\instructions{2\rightarrow N_{2}}%
\EasyButWeakLineBreak%
{${2}\above{1pt}{1pt}{4,1}{\infty b}{8}\above{1pt}{1pt}{b}{2}{2}\above{1pt}{1pt}{+}{3}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-24\\8\\16
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
8\\-2\\-5
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
16\\-5\\-10
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\2\\-1
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-4\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\-1\\2
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-24, 8, 16; 8, -2, -5; 16, -5, -10],[8, 1, 1],[0, -1, 1; 2, -4, -1; -1, 0, 2],1,1]
%
% END OF LATTICE L2.1
%
%
% LATTICE L2.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[2, 0, 0; 0, 0, -1; 0, -1, 0],[2, 1, 1],[-1, 1, 0; 0, 0, -1; -1, 0, 1],1,2]
%
% END OF LATTICE L2.2
%
%
% LATTICE L2.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-4, -2, -4; -2, 0, -2; -4, -2, -3],[2, 2, 1],[2, -1, -1; -1, 0, 2; -2, 1, 0],1,3]
%
% END OF LATTICE L2.3
%
%
% LATTICE L2.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-16, 24, -8; 24, -16, 8; -8, 8, -3],[8, 8, 1],[2, -1, -1; -1, 0, 2; -8, 2, 8],1,4]
%
% END OF LATTICE L2.4
%

\medskip%
%------------------------------WEYL-GROUP-W3--------------------------------
%
\leavevmode\llap{}%
$W_{3\phantom{0}\phantom{0}}$%
\qquad\llap{6} lattices, $\chi=1$%
\hfill%
$426$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L3.1
%
\leavevmode%
${L_{3.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{2\rightarrow N_{3}}%
\EasyButWeakLineBreak%
{${2}\above{1pt}{1pt}{*}{4}{4}\above{1pt}{1pt}{b}{2}{6}\above{1pt}{1pt}{}{6}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-516\\36\\72
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
36\\-2\\-5
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
72\\-5\\-10
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\2\\-1
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\-2\\8
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-3\\-6
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-516, 36, 72; 36, -2, -5; 72, -5, -10],[12, 1, 1],[0, 1, -1; 2, -2, -3; -1, 8, -6],2,1]
%
% END OF LATTICE L3.1
%
%
% LATTICE L3.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-3, 0, 0; 0, 1, 0; 0, 0, 1],[3, 1, 1],[0, 0, -1; -1, 1, 0; 1, 0, -3],2,2]
%
% END OF LATTICE L3.2
%
%
% LATTICE L3.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-30, -33, -6; -33, -33, -6; -6, -6, -1],[3, 3, 1],[-1, -2, 5; 2, -1, -1; -6, 12, -13],2,3]
%
% END OF LATTICE L3.3
%
%
% LATTICE L3.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-12, -12, -12; -12, -6, -9; -12, -9, -10],[12, 3, 1],[1, 1, -1; 2, -2, -1; -3, 0, 2],2,4]
%
% END OF LATTICE L3.4
%
%
% LATTICE L3.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[312, -156, 84; -156, 88, -40; 84, -40, 23],[12, 4, 1],[-1, 2, 8; 0, 1, 3; 4, -6, -24],2,5]
%
% END OF LATTICE L3.5
%
%
% LATTICE L3.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[24, -84, -24; -84, 696, 192; -24, 192, 53],[12, 12, 1],[1, 0, 0; 0, -5, -1; 0, 18, 4],2,6]
%
% END OF LATTICE L3.6
%

\medskip%
%------------------------------WEYL-GROUP-W4--------------------------------
%
\leavevmode\llap{}%
$W_{4\phantom{0}\phantom{0}}$%
\qquad\llap{44} lattices, $\chi=6$%
\hfill%
$\infty222$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L4.1
%
\leavevmode%
${L_{4.1}}$%
{} : {$1\above{1pt}{1pt}{2}{{\rm II}}4\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{1}{}3\above{1pt}{1pt}{1}{}9\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{23\rightarrow N_{4},3,2}%
\EasyButWeakLineBreak%
{${12}\above{1pt}{1pt}{3,2}{\infty b}{12}\above{1pt}{1pt}{r}{2}{18}\above{1pt}{1pt}{b}{2}{4}\above{1pt}{1pt}{*}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2124\\0\\-108
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\-6\\3
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-108\\3\\4
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-10\\-18
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\28\\60
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\9\\18
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-10\\-20
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[2124, 0, -108; 0, -6, 3; -108, 3, 4],[36, 3, 1],[-1, 3, 1, -1; -10, 28, 9, -10; -18, 60, 18, -20],3,1]
%
% END OF LATTICE L4.1
%
\hbox{}\par\smallskip%
%
% LATTICE L4.2
%
\leavevmode%
${L_{4.2}}$%
{} : {$1\above{1pt}{1pt}{2}{6}8\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{-}{}9\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{3m,3,2}%
\EasyButWeakLineBreak%
{${6}\above{1pt}{1pt}{12,5}{\infty a}{24}\above{1pt}{1pt}{s}{2}{36}\above{1pt}{1pt}{*}{2}{8}\above{1pt}{1pt}{b}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3096\\-1440\\432
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1440\\-669\\198
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
432\\198\\-49
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-15\\35\\9
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
17\\-40\\-12
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
31\\-72\\-18
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-5\\12\\4
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-3096, -1440, 432; -1440, -669, 198; 432, 198, -49],[72, 3, 1],[-15, 17, 31, -5; 35, -40, -72, 12; 9, -12, -18, 4],3,2]
%
% END OF LATTICE L4.2
%
\hbox{}\par\smallskip%
%
% LATTICE L4.3
%
\leavevmode%
${L_{4.3}}$%
{} : {$1\above{1pt}{1pt}{-2}{6}8\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{-}{}9\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{32\rightarrow N'_{2},3,m}%
\EasyButWeakLineBreak%
{${6}\above{1pt}{1pt}{12,5}{\infty b}{24}\above{1pt}{1pt}{l}{2}{9}\above{1pt}{1pt}{}{2}{8}\above{1pt}{1pt}{r}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-9144\\-1800\\-1080
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1800\\-354\\-213
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1080\\-213\\-127
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\-5\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\-8\\-12
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-4\\15\\9
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-5\\16\\16
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-9144, -1800, -1080; -1800, -354, -213; -1080, -213, -127],[72, 3, 1],[1, 3, -4, -5; -5, -8, 15, 16; 0, -12, 9, 16],3,3]
%
% END OF LATTICE L4.3
%
%
% LATTICE L4.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[3, 0, 0; 0, 0, -1; 0, -1, 0],[3, 1, 1],[-1, 1, 0, -1; 0, 0, -1, -1; -3, 0, 1, -1],3,4]
%
% END OF LATTICE L4.4
%
%
% LATTICE L4.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[42, 18, -12; 18, 8, -5; -12, -5, 3],[6, 1, 1],[-7, 1, 1, -3; 9, 0, -2, 2; -18, 6, 1, -12],3,5]
%
% END OF LATTICE L4.5
%
%
% LATTICE L4.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-60, 12, 12; 12, -2, -3; 12, -3, -1],[12, 1, 1],[-1, -1, 1, 1; -3, -6, 3, 4; -3, 0, 2, 0],3,6]
%
% END OF LATTICE L4.6
%
%
% LATTICE L4.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[12, 0, 0; 0, 0, 1; 0, 1, 2],[12, 1, 1],[1, -1, 0, 1; 6, 0, 0, 4; 0, 0, -1, -2],3,7]
%
% END OF LATTICE L4.7
%
%
% LATTICE L4.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-1560, 48, 72; 48, -1, -3; 72, -3, -2],[24, 1, 1],[1, 1, -1, -1; 18, 12, -18, -16; 9, 12, -10, -12],3,8]
%
% END OF LATTICE L4.8
%
%
% LATTICE L4.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-191352, -21120, 2592; -21120, -2331, 286; 2592, 286, -35],[24, 1, 1],[-8, 1, 3, 1; 81, -12, -30, -8; 69, -24, -23, 8],3,9]
%
% END OF LATTICE L4.9
%
%
% LATTICE L4.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[18, 0, -9; 0, -15, -3; -9, -3, 4],[9, 3, 1],[2, -3, -1, 2; -1, 1, 0, -1; 3, -6, 0, 4],3,10]
%
% END OF LATTICE L4.10
%
%
% LATTICE L4.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[954, -18, -90; -18, -3, 3; -90, 3, 8],[18, 3, 1],[-1, 3, 1, -1; -4, 10, 3, -4; -9, 30, 9, -10],3,11]
%
% END OF LATTICE L4.11
%
%
% LATTICE L4.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-1548, 108, -180; 108, -6, 15; -180, 15, -17],[36, 3, 1],[-2, 3, 4, -1; -14, 22, 27, -8; 9, -12, -18, 4],3,12]
%
% END OF LATTICE L4.12
%
%
% LATTICE L4.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-6, -9, -6; -9, -12, -9; -6, -9, -5],[3, 3, 1],[3, -1, -3, 4; -1, 0, 2, 0; -1, 1, 0, -3],3,13]
%
% END OF LATTICE L4.13
%
%
% LATTICE L4.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[48, -18, 24; -18, 6, -8; 24, -8, 11],[6, 2, 1],[-13, 2, 1, -4; 36, -6, -3, 11; 54, -9, -4, 17],3,14]
%
% END OF LATTICE L4.14
%
%
% LATTICE L4.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[126, 24, 54; 24, -6, 9; 54, 9, 23],[6, 3, 1],[-26, 9, 6, -49; -5, 2, 1, -10; 64, -22, -15, 120],3,15]
%
% END OF LATTICE L4.15
%
%
% LATTICE L4.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[9, 0, 0; 0, -6, -3; 0, -3, -1],[9, 3, 1],[0, 1, 0, -1; 1, -1, -1, 0; -3, 0, 2, 0],3,16]
%
% END OF LATTICE L4.16
%
%
% LATTICE L4.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[12, -24, 12; -24, -18, 15; 12, 15, -11],[12, 3, 1],[1, -1, -2, 1; 3, -2, -7, 0; 5, -4, -12, 0],3,17]
%
% END OF LATTICE L4.17
%
%
% LATTICE L4.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[18, 294, 120; 294, 4368, 1782; 120, 1782, 727],[6, 6, 1],[-6, 1, 1, -6; -43, 2, 22, -23; 106, -5, -54, 57],3,18]
%
% END OF LATTICE L4.18
%
%
% LATTICE L4.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[36, -12, 12; -12, -24, 9; 12, 9, -2],[12, 3, 1],[1, -3, -1, 3; -2, 8, 2, -8; -4, 16, 3, -18],3,19]
%
% END OF LATTICE L4.19
%
%
% LATTICE L4.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-24, 12, -12; 12, 0, 4; -12, 4, -5],[12, 4, 1],[-2, 1, 1, -1; 3, 0, -2, 0; 6, -3, -4, 2],3,20]
%
% END OF LATTICE L4.20
%
%
% LATTICE L4.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[12, -12, 0; -12, 8, 0; 0, 0, 1],[12, 4, 1],[1, 2, 0, 0; 0, 3, 1, 0; 0, -6, 0, 1],3,21]
%
% END OF LATTICE L4.21
%
%
% LATTICE L4.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[18, 0, 0; 0, -3, -3; 0, -3, -2],[18, 3, 1],[0, 1, 0, -1; 2, -2, -1, 0; -3, 0, 1, 0],3,22]
%
% END OF LATTICE L4.22
%
%
% LATTICE L4.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3720, -2064, 288; -2064, -1143, 159; 288, 159, -22],[24, 3, 1],[-2, 1, 5, 1; 6, -4, -14, 0; 17, -16, -36, 12],3,23]
%
% END OF LATTICE L4.23
%
%
% LATTICE L4.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-936, 96, 48; 96, -9, -6; 48, -6, -1],[24, 3, 1],[1, -1, -1, 1; 7, -8, -7, 8; 5, -4, -6, 0],3,24]
%
% END OF LATTICE L4.24
%
%
% LATTICE L4.25
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[198, 54, 90; 54, 12, 24; 90, 24, 41],[18, 6, 1],[0, -7, -1, 4; 1, 1, 0, 0; 0, 15, 2, -9],3,25]
%
% END OF LATTICE L4.25
%
%
% LATTICE L4.26
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[36, 0, 0; 0, -6, -3; 0, -3, -1],[36, 3, 1],[0, -1, 0, 1; 1, -2, -1, 0; -3, 0, 2, 0],3,26]
%
% END OF LATTICE L4.26
%
%
% LATTICE L4.27
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[6066, -990, 2610; -990, 156, -426; 2610, -426, 1123],[18, 6, 1],[26, 4, -31, -3; 1, 1, 0, 0; -60, -9, 72, 7],3,27]
%
% END OF LATTICE L4.27
%
%
% LATTICE L4.28
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-180, 36, 0; 36, -6, -3; 0, -3, 8],[36, 3, 1],[-3, 1, 1, -1; -16, 4, 5, -6; -6, 0, 2, 0],3,28]
%
% END OF LATTICE L4.28
%
%
% LATTICE L4.29
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[216, 804, 240; 804, 2976, 888; 240, 888, 265],[12, 12, 1],[0, -1, -3, -1; -3, 0, 8, 2; 10, 1, -24, -6],3,29]
%
% END OF LATTICE L4.29
%
%
% LATTICE L4.30
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[276, 132, 72; 132, 72, 36; 72, 36, 19],[12, 12, 1],[-1, 0, -2, -2; -2, 1, -3, -4; 8, -2, 12, 15],3,30]
%
% END OF LATTICE L4.30
%
%
% LATTICE L4.31
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-4200, 264, 384; 264, -16, -24; 384, -24, -35],[24, 8, 1],[2, -1, -1, 0; -3, 9, 1, -3; 24, -18, -12, 2],3,31]
%
% END OF LATTICE L4.31
%
%
% LATTICE L4.32
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-24, 552, -72; 552, -8400, 1096; -72, 1096, -143],[24, 8, 1],[2, -1, -1, 0; -3, 18, 1, -3; -24, 138, 8, -23],3,32]
%
% END OF LATTICE L4.32
%
%
% LATTICE L4.33
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2520, -1152, 72; -1152, -525, 33; 72, 33, -2],[72, 3, 1],[-1, 1, 1, 1; 2, -4, -2, 0; -3, -36, 2, 36],3,33]
%
% END OF LATTICE L4.33
%
%
% LATTICE L4.34
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-191736, 1296, 2592; 1296, -3, -18; 2592, -18, -35],[72, 3, 1],[3, -1, -1, 1; 17, -4, -6, 0; 213, -72, -71, 72],3,34]
%
% END OF LATTICE L4.34
%
%
% LATTICE L4.35
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1440, 828, 288; 828, 480, 168; 288, 168, 59],[36, 12, 1],[-4, -5, 1, 5; 13, 16, -3, -15; -18, -21, 4, 18],3,35]
%
% END OF LATTICE L4.35
%
%
% LATTICE L4.36
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[64224, 8244, -8496; 8244, 1056, -1092; -8496, -1092, 1123],[36, 12, 1],[-17, -6, 31, 3; 52, 19, -93, -9; -78, -27, 144, 14],3,36]
%
% END OF LATTICE L4.36
%
%
% LATTICE L4.37
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[828, -1152, -1008; -1152, 2028, 1704; -1008, 1704, 1441],[36, 12, 1],[-11, -15, -17, -4; 34, 47, 51, 12; -48, -66, -72, -17],3,37]
%
% END OF LATTICE L4.37
%
%
% LATTICE L4.38
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[252, -72, -108; -72, 12, 24; -108, 24, 41],[36, 12, 1],[0, -1, 1, 2; 1, 5, -3, -6; 0, -6, 4, 9],3,38]
%
% END OF LATTICE L4.38
%
%
% LATTICE L4.39
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-48, -24, 0; -24, 72, -24; 0, -24, 7],[24, 24, 1],[-1, 1, 1, -1; 2, -3, -3, 2; 8, -10, -12, 6],3,39]
%
% END OF LATTICE L4.39
%
%
% LATTICE L4.40
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-10032, 8616, 1032; 8616, -6984, -840; 1032, -840, -101],[24, 24, 1],[-1, 2, 1, -1; 18, -31, -19, 15; -160, 278, 168, -135],3,40]
%
% END OF LATTICE L4.40
%
%
% LATTICE L4.41
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-720, -360, 288; -360, -168, 144; 288, 144, -115],[72, 24, 1],[-1, 3, -1, -7; 2, -1, -1, 0; 0, 6, -4, -18],3,41]
%
% END OF LATTICE L4.41
%
%
% LATTICE L4.42
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-30096, 1080, -9360; 1080, -24, 336; -9360, 336, -2911],[72, 24, 1],[15, -28, -5, 14; 2, -1, -1, 0; -48, 90, 16, -45],3,42]
%
% END OF LATTICE L4.42
%
%
% LATTICE L4.43
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-144, 792, -72; 792, -4200, 384; -72, 384, -35],[72, 24, 1],[-1, 3, 1, -1; 2, -1, -3, 0; 24, -18, -36, 2],3,43]
%
% END OF LATTICE L4.43
%
%
% LATTICE L4.44
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-720720, 5112, 10152; 5112, -24, -72; 10152, -72, -143],[72, 24, 1],[-1, 6, 1, -1; 2, -1, -3, 0; -72, 426, 72, -71],3,44]
%
% END OF LATTICE L4.44
%

\medskip%
%------------------------------WEYL-GROUP-W5--------------------------------
%
\leavevmode\llap{}%
$W_{5\phantom{0}\phantom{0}}$%
\qquad\llap{22} lattices, $\chi=9$%
\hfill%
$\infty242$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L5.1
%
\leavevmode%
${L_{5.1}}$%
{} : {$1\above{1pt}{1pt}{2}{{\rm II}}4\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{2}{}5\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2\rightarrow N_{5}}%
\EasyButWeakLineBreak%
{${20}\above{1pt}{1pt}{1,0}{\infty b}{20}\above{1pt}{1pt}{r}{2}{2}\above{1pt}{1pt}{*}{4}{4}\above{1pt}{1pt}{*}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-15020\\360\\680
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
360\\-8\\-17
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
680\\-17\\-30
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3\\-50\\-40
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
13\\200\\180
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\32\\27
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3\\-46\\-42
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-15020, 360, 680; 360, -8, -17; 680, -17, -30],[20, 1, 1],[-3, 13, 2, -3; -50, 200, 32, -46; -40, 180, 27, -42],4,1]
%
% END OF LATTICE L5.1
%
\hbox{}\par\smallskip%
%
% LATTICE L5.2
%
\leavevmode%
${L_{5.2}}$%
{} : {$1\above{1pt}{1pt}{2}{2}8\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{2}{}5\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{2\rightarrow N'_{5}}%
\EasyButWeakLineBreak%
{${10}\above{1pt}{1pt}{4,3}{\infty a}{40}\above{1pt}{1pt}{l}{2}{1}\above{1pt}{1pt}{}{4}{2}\above{1pt}{1pt}{b}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-8360\\240\\360
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
240\\-6\\-11
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
360\\-11\\-15
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2\\-25\\-30
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
9\\100\\140
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\12\\15
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-11\\-16
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-8360, 240, 360; 240, -6, -11; 360, -11, -15],[40, 1, 1],[-2, 9, 1, -1; -25, 100, 12, -11; -30, 140, 15, -16],4,2]
%
% END OF LATTICE L5.2
%
\hbox{}\par\smallskip%
%
% LATTICE L5.3
%
\leavevmode%
${L_{5.3}}$%
{} : {$1\above{1pt}{1pt}{-2}{2}8\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{2}{}5\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{m}%
\EasyButWeakLineBreak%
{${10}\above{1pt}{1pt}{4,3}{\infty b}{40}\above{1pt}{1pt}{s}{2}{4}\above{1pt}{1pt}{*}{4}{2}\above{1pt}{1pt}{s}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-34760\\200\\1560
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
200\\-1\\-9
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1560\\-9\\-70
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2\\0\\-45
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-20\\-20
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\2\\22
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\6\\-1
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-34760, 200, 1560; 200, -1, -9; 1560, -9, -70],[40, 1, 1],[-2, -1, 1, 0; 0, -20, 2, 6; -45, -20, 22, -1],4,3]
%
% END OF LATTICE L5.3
%
%
% LATTICE L5.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[5, 0, 0; 0, 0, -1; 0, -1, 0],[5, 1, 1],[-1, 1, 0, -1; 0, 0, -1, -1; -5, 0, 1, -2],4,4]
%
% END OF LATTICE L5.4
%
%
% LATTICE L5.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[310, 180, 240; 180, 105, 139; 240, 139, 186],[10, 1, 1],[104, 141, -4, -2; -80, -110, 3, 2; -75, -100, 3, 1],4,5]
%
% END OF LATTICE L5.5
%
%
% LATTICE L5.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-180, -20, -80; -20, -2, -9; -80, -9, -35],[20, 1, 1],[2, 1, -1, 0; 0, -10, 1, 3; -5, 0, 2, -1],4,6]
%
% END OF LATTICE L5.6
%
%
% LATTICE L5.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-8530, 350, -4010; 350, -12, 164; -4010, 164, -1885],[10, 2, 1],[174, 43, -23, 24; -105, -35, 12, -11; -380, -95, 50, -52],4,7]
%
% END OF LATTICE L5.7
%
%
% LATTICE L5.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-65, -45, 20; -45, -20, 15; 20, 15, -6],[5, 5, 1],[-1, -7, -6, 5; -1, 0, 2, -1; -8, -27, -15, 15],4,8]
%
% END OF LATTICE L5.8
%
%
% LATTICE L5.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-12970, -1010, -5320; -1010, -75, -415; -5320, -415, -2182],[10, 5, 1],[58, 37, -34, 32; -22, -10, 15, -16; -137, -88, 80, -75],4,9]
%
% END OF LATTICE L5.9
%
%
% LATTICE L5.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1880, -100, 440; -100, 20, -24; 440, -24, 103],[20, 4, 1],[-23, -7, -1, -12; 5, 0, 0, 3; 100, 30, 4, 52],4,10]
%
% END OF LATTICE L5.10
%
%
% LATTICE L5.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[23920, -7500, 4300; -7500, 2360, -1348; 4300, -1348, 773],[20, 4, 1],[9, 33, 26, 5; 0, 5, 5, 1; -50, -175, -136, -26],4,11]
%
% END OF LATTICE L5.11
%
%
% LATTICE L5.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1860, -17310, -7720; -17310, 162250, 72360; -7720, 72360, 32271],[10, 10, 1],[-15, -10, 3, 1; 976, 663, -187, -98; -2192, -1489, 420, 220],4,12]
%
% END OF LATTICE L5.12
%
%
% LATTICE L5.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1020, 220, 120; 220, -40, -25; 120, -25, -14],[20, 5, 1],[1, 1, -2, -3; -2, 0, 4, 2; 12, 8, -25, -30],4,13]
%
% END OF LATTICE L5.13
%
%
% LATTICE L5.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2100, -840, 200; -840, -335, 80; 200, 80, -19],[20, 5, 1],[0, 1, -1, -2; 1, -2, -1, 4; 4, 2, -15, -5],4,14]
%
% END OF LATTICE L5.14
%
%
% LATTICE L5.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-200, 80, 40; 80, -30, -15; 40, -15, -7],[40, 5, 1],[0, 1, 0, -1; -1, 4, 2, -3; 2, -4, -5, 0],4,15]
%
% END OF LATTICE L5.15
%
%
% LATTICE L5.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-33000, 440, 1120; 440, -5, -15; 1120, -15, -38],[40, 5, 1],[0, -1, 1, 2; 2, -4, -2, 8; -1, -28, 30, 55],4,16]
%
% END OF LATTICE L5.16
%
%
% LATTICE L5.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1320, 280, 360; 280, -48, -80; 360, -80, -97],[40, 8, 1],[-14, 17, 7, -8; -15, 15, 7, -7; -40, 50, 20, -24],4,17]
%
% END OF LATTICE L5.17
%
%
% LATTICE L5.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-27480, 2000, 760; 2000, -120, -56; 760, -56, -21],[40, 8, 1],[-7, 11, 4, -5; -5, 10, 3, -5; -240, 370, 136, -168],4,18]
%
% END OF LATTICE L5.18
%
%
% LATTICE L5.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[100, -160, -40; -160, 1060, 200; -40, 200, 39],[20, 20, 1],[-3, -1, -5, -12; 4, 1, 7, 17; -24, -6, -40, -100],4,19]
%
% END OF LATTICE L5.19
%
%
% LATTICE L5.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[120, 580, 100; 580, 3040, 520; 100, 520, 89],[20, 20, 1],[0, 1, 5, 1; 1, 1, 6, 5; -6, -7, -40, -30],4,20]
%
% END OF LATTICE L5.20
%
%
% LATTICE L5.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-240, 440, 80; 440, -680, -120; 80, -120, -21],[40, 40, 1],[-1, 0, 2, 1; -2, -1, 5, 8; 8, 6, -20, -40],4,21]
%
% END OF LATTICE L5.21
%
%
% LATTICE L5.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-240, -4360, 280; -4360, -77880, 5000; 280, 5000, -321],[40, 40, 1],[1, 1, -2, -5; 2, -3, -5, 8; 32, -46, -80, 120],4,22]
%
% END OF LATTICE L5.22
%

\medskip%
%------------------------------WEYL-GROUP-W6--------------------------------
%
\leavevmode\llap{}%
$W_{6\phantom{0}\phantom{0}}$%
\qquad\llap{6} lattices, $\chi=2$%
\hfill%
$2223$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L6.1
%
\leavevmode%
${L_{6.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{2\rightarrow N_{6}}%
\EasyButWeakLineBreak%
{${2}\above{1pt}{1pt}{b}{2}{10}\above{1pt}{1pt}{l}{2}{4}\above{1pt}{1pt}{r}{2}{2}\above{1pt}{1pt}{+}{3}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1660\\80\\100
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
80\\-2\\-5
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
100\\-5\\-6
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-1\\-16
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2\\-5\\-30
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\0\\16
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\2\\15
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-1660, 80, 100; 80, -2, -5; 100, -5, -6],[20, 1, 1],[-1, -2, 1, 1; -1, -5, 0, 2; -16, -30, 16, 15],5,1]
%
% END OF LATTICE L6.1
%
%
% LATTICE L6.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[15, 0, -5; 0, -1, 0; -5, 0, 2],[5, 1, 1],[0, 2, 0, -1; 0, 0, -1, -1; 1, 5, -1, -3],5,2]
%
% END OF LATTICE L6.2
%
%
% LATTICE L6.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-10, -25, 15; -25, -30, 20; 15, 20, -13],[5, 5, 1],[-1, -1, 0, 2; -6, -2, 3, 5; -10, -4, 5, 10],5,3]
%
% END OF LATTICE L6.3
%
%
% LATTICE L6.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[8440, -220, 1540; -220, 8, -40; 1540, -40, 281],[20, 4, 1],[3, 11, 2, 0; 2, 0, 0, 1; -16, -60, -11, 0],5,4]
%
% END OF LATTICE L6.4
%
%
% LATTICE L6.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[20, 0, 0; 0, -10, -5; 0, -5, -2],[20, 5, 1],[-1, 0, 1, 0; -1, -1, 0, 2; 0, 2, 0, -5],5,5]
%
% END OF LATTICE L6.5
%
%
% LATTICE L6.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[40, 100, 20; 100, 280, 60; 20, 60, 13],[20, 20, 1],[2, 0, 0, 1; -1, -1, -1, 0; 0, 4, 5, 0],5,6]
%
% END OF LATTICE L6.6
%

\medskip%
%------------------------------WEYL-GROUP-W7--------------------------------
%
\leavevmode\llap{}%
$W_{7\phantom{0}\phantom{0}}$%
\qquad\llap{16} lattices, $\chi=4$%
\hfill%
$\infty26$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L7.1
%
\leavevmode%
${L_{7.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}8\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{1}{}3\above{1pt}{1pt}{-}{}9\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{23\rightarrow N_{7},3,2}%
\EasyButWeakLineBreak%
{${6}\above{1pt}{1pt}{12,7}{\infty a}{24}\above{1pt}{1pt}{b}{2}{18}\above{1pt}{1pt}{}{6}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1224\\360\\-144
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
360\\-102\\39
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-144\\39\\-14
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-7\\-9
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\20\\24
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-3\\0
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-1224, 360, -144; 360, -102, 39; -144, 39, -14],[72, 3, 1],[-1, 3, -1; -7, 20, -3; -9, 24, 0],6,1]
%
% END OF LATTICE L7.1
%
%
% LATTICE L7.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[6, 0, 0; 0, 0, -1; 0, -1, 0],[6, 1, 1],[-1, 1, 0; 0, 0, -1; -3, 0, 1],6,2]
%
% END OF LATTICE L7.2
%
%
% LATTICE L7.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-264, -24, 336; -24, -2, 39; 336, 39, -34],[24, 1, 1],[-17, 7, 11; 144, -60, -93; -3, 0, 2],6,3]
%
% END OF LATTICE L7.3
%
%
% LATTICE L7.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-90, 36, 36; 36, -12, -15; 36, -15, -14],[18, 3, 1],[2, -3, -1; 2, -2, -3; 3, -6, 0],6,4]
%
% END OF LATTICE L7.4
%
%
% LATTICE L7.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-60, 18, -18; 18, -4, 6; -18, 6, -5],[6, 2, 1],[5, -1, -2; 6, 0, -3; -12, 3, 4],6,5]
%
% END OF LATTICE L7.5
%
%
% LATTICE L7.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-6, -18, -6; -18, -12, -9; -6, -9, -4],[6, 3, 1],[-1, -1, 3; -1, 0, 2; 4, 2, -9],6,6]
%
% END OF LATTICE L7.6
%
%
% LATTICE L7.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[12, 90, 36; 90, 744, 300; 36, 300, 121],[6, 6, 1],[-2, 0, 1; 1, 2, 0; -2, -5, 0],6,7]
%
% END OF LATTICE L7.7
%
%
% LATTICE L7.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-18, 18, 18; 18, -12, -9; 18, -9, -4],[18, 3, 1],[2, -1, -1; 5, -2, -3; -3, 0, 2],6,8]
%
% END OF LATTICE L7.8
%
%
% LATTICE L7.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3672, 48, 192; 48, 6, -3; 192, -3, -10],[24, 3, 1],[-1, 3, 0; -1, 4, -1; -19, 56, 0],6,9]
%
% END OF LATTICE L7.9
%
%
% LATTICE L7.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[36, 18, 18; 18, 12, 12; 18, 12, 11],[18, 6, 1],[0, 1, -1; 1, 1, 0; 0, -3, 0],6,10]
%
% END OF LATTICE L7.10
%
%
% LATTICE L7.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1368, 342, 648; 342, 84, 162; 648, 162, 307],[18, 6, 1],[-3, 4, -1; 1, 1, 0; 6, -9, 2],6,11]
%
% END OF LATTICE L7.11
%
%
% LATTICE L7.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1200, -1704, 168; -1704, 2416, -240; 168, -240, 23],[24, 8, 1],[-25, -46, 22; -15, -27, 13; 24, 54, -24],6,12]
%
% END OF LATTICE L7.12
%
%
% LATTICE L7.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-72, 0, 72; 0, 6, 15; 72, 15, -34],[72, 3, 1],[-3, 1, 2; 8, -4, -5; -3, 0, 2],6,13]
%
% END OF LATTICE L7.13
%
%
% LATTICE L7.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-48, 24, -24; 24, 144, 0; -24, 0, -11],[24, 24, 1],[4, 1, -11; -1, 0, 2; -8, -2, 24],6,14]
%
% END OF LATTICE L7.14
%
%
% LATTICE L7.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-720, -72, 72; -72, 48, 48; 72, 48, 23],[72, 24, 1],[0, -1, 13; 1, 4, -54; 0, -6, 72],6,15]
%
% END OF LATTICE L7.15
%
%
% LATTICE L7.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[363600, 44136, -6120; 44136, 5232, -744; -6120, -744, 103],[72, 24, 1],[-21, -41, 19; 10, 19, -9; -1176, -2298, 1064],6,16]
%
% END OF LATTICE L7.16
%

\medskip%
%------------------------------WEYL-GROUP-W8--------------------------------
%
\leavevmode\llap{}%
$W_{8\phantom{0}\phantom{0}}$%
\qquad\llap{6} lattices, $\chi=6$%
\hfill%
$4242\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L8.1
%
\leavevmode%
${L_{8.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{2}{}7\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{2\rightarrow N_{8}}%
\EasyButWeakLineBreak%
{${2}\above{1pt}{1pt}{*}{4}{4}\above{1pt}{1pt}{b}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-308\\56\\28
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
56\\-10\\-5
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
28\\-5\\-2
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\0\\-28
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\-1\\5
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\1
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\1\\-3
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-6\\0
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-308, 56, 28; 56, -10, -5; 28, -5, -2],[28, 1, 1],[0, -1, 0, 1; 1, -6, -1, 6; -3, 0, 2, -2],7,1]
%
% END OF LATTICE L8.1
%
%
% LATTICE L8.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-7, 0, 0; 0, 1, 0; 0, 0, 1],[7, 1, 1],[0, 0, -1, -1; -1, 1, 0, -2; 1, 0, -3, -2],7,2]
%
% END OF LATTICE L8.2
%
%
% LATTICE L8.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-91, -49, -14; -49, -21, -7; -14, -7, -2],[7, 7, 1],[0, -2, -1, 1; 2, -1, -3, 0; -7, 14, 14, -7],7,3]
%
% END OF LATTICE L8.3
%
%
% LATTICE L8.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[952, 140, -252; 140, 24, -36; -252, -36, 67],[28, 4, 1],[-7, -3, 1, -3; 5, 2, 0, 3; -24, -10, 4, -10],7,4]
%
% END OF LATTICE L8.4
%
%
% LATTICE L8.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-364, -84, -28; -84, -14, -7; -28, -7, -2],[28, 7, 1],[-1, -1, 1, 1; 2, -2, -3, 0; 7, 14, -7, -14],7,5]
%
% END OF LATTICE L8.5
%
%
% LATTICE L8.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[56, -308, 84; -308, 3864, -1064; 84, -1064, 293],[28, 28, 1],[1, 1, 1, 1; 0, 27, 31, 4; 0, 98, 112, 14],7,6]
%
% END OF LATTICE L8.6
%

\medskip%
%------------------------------WEYL-GROUP-W9--------------------------------
%
\leavevmode\llap{}%
$W_{9\phantom{0}\phantom{0}}$%
\qquad\llap{22} lattices, $\chi=12$%
\hfill%
$\infty2222$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L9.1
%
\leavevmode%
${L_{9.1}}$%
{} : {$1\above{1pt}{1pt}{2}{{\rm II}}4\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{-2}{}7\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2\rightarrow N_{9}}%
\EasyButWeakLineBreak%
{${28}\above{1pt}{1pt}{1,0}{\infty b}{28}\above{1pt}{1pt}{r}{2}{2}\above{1pt}{1pt}{s}{2}{14}\above{1pt}{1pt}{b}{2}{4}\above{1pt}{1pt}{*}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-21252\\532\\1204
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
532\\-12\\-33
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1204\\-33\\-62
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-31\\-602\\-280
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\56\\28
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5\\98\\45
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\28\\7
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-9\\-172\\-82
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-21252, 532, 1204; 532, -12, -33; 1204, -33, -62],[28, 1, 1],[-31, 3, 5, 1, -9; -602, 56, 98, 28, -172; -280, 28, 45, 7, -82],8,1]
%
% END OF LATTICE L9.1
%
\hbox{}\par\smallskip%
%
% LATTICE L9.2
%
\leavevmode%
${L_{9.2}}$%
{} : {$1\above{1pt}{1pt}{2}{6}8\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{-2}{}7\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2\rightarrow N'_{7}}%
\EasyButWeakLineBreak%
{${14}\above{1pt}{1pt}{4,1}{\infty a}{56}\above{1pt}{1pt}{s}{2}{4}\above{1pt}{1pt}{l}{2}{7}\above{1pt}{1pt}{}{2}{8}\above{1pt}{1pt}{r}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-39928\\224\\1176
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
224\\-1\\-7
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1176\\-7\\-34
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\126\\77
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\28\\28
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-42\\-26
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-35\\-28
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\48\\24
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-39928, 224, 1176; 224, -1, -7; 1176, -7, -34],[56, 1, 1],[3, 1, -1, -1, 1; 126, 28, -42, -35, 48; 77, 28, -26, -28, 24],8,2]
%
% END OF LATTICE L9.2
%
\hbox{}\par\smallskip%
%
% LATTICE L9.3
%
\leavevmode%
${L_{9.3}}$%
{} : {$1\above{1pt}{1pt}{-2}{6}8\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{-2}{}7\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{m}%
\EasyButWeakLineBreak%
{${14}\above{1pt}{1pt}{4,1}{\infty b}{56}\above{1pt}{1pt}{l}{2}{1}\above{1pt}{1pt}{r}{2}{28}\above{1pt}{1pt}{*}{2}{8}\above{1pt}{1pt}{b}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-655704\\94472\\11312
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
94472\\-13611\\-1630
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
11312\\-1630\\-195
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
48\\287\\385
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-5\\-28\\-56
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-7\\-42\\-55
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\14\\56
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
29\\172\\244
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-655704, 94472, 11312; 94472, -13611, -1630; 11312, -1630, -195],[56, 1, 1],[48, -5, -7, 3, 29; 287, -28, -42, 14, 172; 385, -56, -55, 56, 244],8,3]
%
% END OF LATTICE L9.3
%
%
% LATTICE L9.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[7, 0, 0; 0, 0, -1; 0, -1, 0],[7, 1, 1],[-1, 1, 0, -4, -1; 0, 0, -1, -7, -1; -7, 0, 1, -7, -3],8,4]
%
% END OF LATTICE L9.4
%
%
% LATTICE L9.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[4830, 3374, 3108; 3374, 2357, 2171; 3108, 2171, 2000],[14, 1, 1],[51, -9, 2, 74, 37; -28, 0, -1, -35, -18; -49, 14, -2, -77, -38],8,5]
%
% END OF LATTICE L9.5
%
%
% LATTICE L9.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-364, 28, 112; 28, -2, -7; 112, -7, -17],[28, 1, 1],[3, 1, -1, -2, 1; 63, 14, -21, -35, 24; -7, 0, 2, 0, -4],8,6]
%
% END OF LATTICE L9.6
%
%
% LATTICE L9.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-41146, 1526, -19754; 1526, -48, 730; -19754, 730, -9483],[14, 2, 1],[466, -23, -75, -13, 68; -301, 14, 49, 14, -43; -994, 49, 160, 28, -145],8,7]
%
% END OF LATTICE L9.7
%
%
% LATTICE L9.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-14, -49, -14; -49, -168, -49; -14, -49, -13],[7, 7, 1],[4, -1, -7, 3, 12; -1, 0, 2, 0, -2; -1, 1, 0, -4, -7],8,8]
%
% END OF LATTICE L9.8
%
%
% LATTICE L9.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-89950, -4676, -39130; -4676, -217, -2037; -39130, -2037, -17022],[14, 7, 1],[160, -15, -182, -7, 321; -40, 4, 45, 1, -82; -363, 34, 413, 16, -728],8,9]
%
% END OF LATTICE L9.9
%
%
% LATTICE L9.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[60592, -33796, -19040; -33796, 18856, 10620; -19040, 10620, 5983],[28, 4, 1],[155, -11, 12, 438, 110; -14, 0, -1, -35, -9; 518, -35, 40, 1456, 366],8,10]
%
% END OF LATTICE L9.10
%
%
% LATTICE L9.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[3640, 1820, -952; 1820, 908, -476; -952, -476, 249],[28, 4, 1],[-18, 11, 1, -51, -7; 7, 0, 0, 14, 2; -56, 42, 4, -168, -23],8,11]
%
% END OF LATTICE L9.11
%
%
% LATTICE L9.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2324, -336, 252; -336, -42, 35; 252, 35, -27],[28, 7, 1],[1, -1, -2, 1, 7; 3, -2, -7, 1, 16; 13, -12, -28, 10, 84],8,12]
%
% END OF LATTICE L9.12
%
%
% LATTICE L9.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[28000, -482146, -222768; -482146, 8303414, 3836462; -222768, 3836462, 1772577],[14, 14, 1],[-7, 1, -2, -11, -19; 664, -54, 181, 953, 1671; -1438, 117, -392, -2064, -3619],8,13]
%
% END OF LATTICE L9.13
%
%
% LATTICE L9.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[420, 784, -140; 784, 1456, -259; -140, -259, 46],[28, 7, 1],[1, -3, -5, -1, 3; -2, 8, 14, 4, -4; -8, 36, 63, 19, -14],8,14]
%
% END OF LATTICE L9.14
%
%
% LATTICE L9.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-75208, -38920, 2016; -38920, -20139, 1043; 2016, 1043, -54],[56, 7, 1],[-2, 1, 5, 0, -9; 6, -4, -14, 1, 32; 41, -40, -84, 19, 280],8,15]
%
% END OF LATTICE L9.15
%
%
% LATTICE L9.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-11368, 504, 280; 504, -21, -14; 280, -14, -5],[56, 7, 1],[1, -1, -1, 1, 7; 15, -16, -15, 16, 108; 13, -12, -14, 10, 84],8,16]
%
% END OF LATTICE L9.16
%
%
% LATTICE L9.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-142072, 1512, 5264; 1512, -16, -56; 5264, -56, -195],[56, 8, 1],[2, -1, -1, -3, 0; -7, 49, 16, 7, -7; 56, -42, -32, -84, 2],8,17]
%
% END OF LATTICE L9.17
%
%
% LATTICE L9.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-168, 3080, -392; 3080, -48336, 6152; -392, 6152, -783],[56, 8, 1],[2, -1, -1, -3, 0; -7, 98, 30, 7, -7; -56, 770, 236, 56, -55],8,18]
%
% END OF LATTICE L9.18
%
%
% LATTICE L9.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[280, -1764, 476; -1764, 11088, -2996; 476, -2996, 809],[28, 28, 1],[-4, -1, 21, 17, 11; 1, -1, -12, -6, -2; 6, -3, -56, -32, -14],8,19]
%
% END OF LATTICE L9.19
%
%
% LATTICE L9.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[756, -2324, 700; -2324, 7336, -2212; 700, -2212, 667],[28, 28, 1],[-1, 0, -2, -4, -3; -10, -3, -9, -23, -20; -32, -10, -28, -72, -63],8,20]
%
% END OF LATTICE L9.20
%
%
% LATTICE L9.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-112, 168, -56; 168, 56, 0; -56, 0, -5],[56, 56, 1],[-1, 1, 4, 1, -1; 2, -5, -15, -3, 4; 8, -18, -56, -12, 14],8,21]
%
% END OF LATTICE L9.21
%
%
% LATTICE L9.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-100464, -38136, 4984; -38136, -14168, 1848; 4984, 1848, -241],[56, 56, 1],[-1, 2, 6, 1, -1; 34, -63, -195, -35, 31; 240, -442, -1372, -248, 217],8,22]
%
% END OF LATTICE L9.22
%

\medskip%
%------------------------------WEYL-GROUP-W10--------------------------------
%
\leavevmode\llap{}%
$W_{10\phantom{0}}$%
\qquad\llap{16} lattices, $\chi=6$%
\hfill%
$\infty222$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L10.1
%
\leavevmode%
${L_{10.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}8\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{-}{}5\above{1pt}{1pt}{-}{}25\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{25\rightarrow N_{10},5,2*}%
\EasyButWeakLineBreak%
{${10}\above{1pt}{1pt}{20,9}{\infty a}{40}\above{1pt}{1pt}{b}{2}{50}\above{1pt}{1pt}{l}{2}{8}\above{1pt}{1pt}{r}{2}$}%
\nopagebreak\par%
shares genus with 5-dual\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-95800\\1200\\-10800
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1200\\-10\\165
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-10800\\165\\-1042
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-14\\-443\\75
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
15\\476\\-80
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
28\\885\\-150
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3\\-96\\16
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-95800, 1200, -10800; 1200, -10, 165; -10800, 165, -1042],[200, 5, 1],[-14, 15, 28, -3; -443, 476, 885, -96; 75, -80, -150, 16],9,1]
%
% END OF LATTICE L10.1
%
%
% LATTICE L10.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[10, 0, 0; 0, 0, -1; 0, -1, 0],[10, 1, 1],[-1, 1, 0, -1; 0, 0, -1, -2; -5, 0, 1, -2],9,2]
%
% END OF LATTICE L10.2
%
%
% LATTICE L10.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-760, 40, 80; 40, -2, -5; 80, -5, -2],[40, 1, 1],[-2, -1, 1, 1; -30, -20, 15, 16; -5, 0, 2, 0],9,3]
%
% END OF LATTICE L10.3
%
%
% LATTICE L10.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-950, 200, 400; 200, -40, -85; 400, -85, -168],[50, 5, 1],[3, -5, -1, 3; 4, -4, -5, 2; 5, -10, 0, 6],9,4]
%
% END OF LATTICE L10.4
%
%
% LATTICE L10.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-580, 50, -230; 50, -4, 20; -230, 20, -91],[10, 2, 1],[9, -2, -2, 2; 10, 0, -5, -1; -20, 5, 4, -5],9,5]
%
% END OF LATTICE L10.5
%
%
% LATTICE L10.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[10, -50, 0; -50, -60, -25; 0, -25, -2],[10, 5, 1],[-3, -1, 10, 9; -1, 0, 2, 0; 8, 2, -25, -20],9,6]
%
% END OF LATTICE L10.6
%
%
% LATTICE L10.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[20, 450, 200; 450, 10120, 4500; 200, 4500, 2001],[10, 10, 1],[2, 0, 1, 5; -17, 4, 0, -38; 38, -9, 0, 85],9,7]
%
% END OF LATTICE L10.7
%
%
% LATTICE L10.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[40, -80, 40; -80, -30, 25; 40, 25, -18],[40, 5, 1],[1, -1, -2, 1; 5, -4, -11, 0; 9, -8, -20, 0],9,8]
%
% END OF LATTICE L10.8
%
%
% LATTICE L10.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[50, 0, 0; 0, -10, -5; 0, -5, -2],[50, 5, 1],[0, 1, 0, -1; 2, -2, -1, 0; -5, 0, 2, 0],9,9]
%
% END OF LATTICE L10.9
%
%
% LATTICE L10.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-80, 1560, -200; 1560, -24272, 3112; -200, 3112, -399],[40, 8, 1],[2, -1, -1, 0; -5, 50, 2, -5; -40, 390, 16, -39],9,10]
%
% END OF LATTICE L10.10
%
%
% LATTICE L10.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2600, 250, 1250; 250, 20, 120; 1250, 120, 601],[50, 10, 1],[0, -17, -1, 12; 1, 2, 0, 0; 0, 35, 2, -25],9,11]
%
% END OF LATTICE L10.11
%
%
% LATTICE L10.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[100, 50, 50; 50, 80, 40; 50, 40, 29],[50, 10, 1],[4, 2, -1, 1; 3, 1, 0, 1; -10, -5, 0, -3],9,12]
%
% END OF LATTICE L10.12
%
%
% LATTICE L10.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[200, 0, 0; 0, -10, -5; 0, -5, -2],[200, 5, 1],[0, -1, 0, 1; 2, -4, -1, 0; -5, 0, 2, 0],9,13]
%
% END OF LATTICE L10.13
%
%
% LATTICE L10.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-39440, -41320, 2640; -41320, -42000, 2680; 2640, 2680, -171],[40, 40, 1],[-1, 2, 2, -1; 26, -47, -53, 23; 392, -706, -800, 345],9,14]
%
% END OF LATTICE L10.14
%
%
% LATTICE L10.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1131600, 11000, -222200; 11000, -80, 2160; -222200, 2160, -43631],[200, 40, 1],[55, -108, -22, 54; 2, -1, -1, 0; -280, 550, 112, -275],9,15]
%
% END OF LATTICE L10.15
%
%
% LATTICE L10.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-15800400, 39800, 79400; 39800, -80, -200; 79400, -200, -399],[200, 40, 1],[-1, 10, 2, -1; 2, -1, -5, 0; -200, 1990, 400, -199],9,16]
%
% END OF LATTICE L10.16
%

\medskip%
%------------------------------WEYL-GROUP-W11--------------------------------
%
\leavevmode\llap{}%
$W_{11\phantom{0}}$%
\qquad\llap{6} lattices, $\chi=5$%
\hfill%
$4223$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L11.1
%
\leavevmode%
${L_{11.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{2}{}11\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{2\rightarrow N_{11}}%
\EasyButWeakLineBreak%
{${2}\above{1pt}{1pt}{*}{4}{4}\above{1pt}{1pt}{b}{2}{22}\above{1pt}{1pt}{s}{2}{2}\above{1pt}{1pt}{+}{3}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-33924\\748\\1012
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
748\\-14\\-23
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1012\\-23\\-30
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\16\\55
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\22\\84
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-4\\-33\\-110
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2\\-15\\-56
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-33924, 748, 1012; 748, -14, -23; 1012, -23, -30],[44, 1, 1],[2, 3, -4, -2; 16, 22, -33, -15; 55, 84, -110, -56],10,1]
%
% END OF LATTICE L11.1
%
%
% LATTICE L11.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-11, 0, 0; 0, 1, 0; 0, 0, 1],[11, 1, 1],[0, 0, -3, -1; -1, 1, 0, -2; 1, 0, -11, -3],10,2]
%
% END OF LATTICE L11.2
%
%
% LATTICE L11.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-154, -253, 121; -253, -330, 176; 121, 176, -89],[11, 11, 1],[-15, -14, 2, 16; -12, -6, 3, 11; -44, -33, 8, 44],10,3]
%
% END OF LATTICE L11.3
%
%
% LATTICE L11.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[682264, -19932, -188672; -19932, 584, 5512; -188672, 5512, 52175],[44, 4, 1],[-54, -37, -73, -11; 7, 2, 0, 2; -196, -134, -264, -40],10,4]
%
% END OF LATTICE L11.4
%
%
% LATTICE L11.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1804, 528, 264; 528, -154, -77; 264, -77, -38],[44, 11, 1],[0, 3, 0, -2; 5, 10, -1, -7; -11, 0, 2, 0],10,5]
%
% END OF LATTICE L11.5
%
%
% LATTICE L11.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1144, 1540, -396; 1540, 2200, -572; -396, -572, 149],[44, 44, 1],[7, 2, 0, 2; -39, -7, 1, -13; -132, -22, 4, -44],10,6]
%
% END OF LATTICE L11.6
%

\medskip%
%------------------------------WEYL-GROUP-W12--------------------------------
%
\leavevmode\llap{}%
$W_{12\phantom{0}}$%
\qquad\llap{22} lattices, $\chi=36$%
\hfill%
$\infty222\infty222\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L12.1
%
\leavevmode%
${L_{12.1}}$%
{} : {$1\above{1pt}{1pt}{2}{{\rm II}}4\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{-2}{}11\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2\rightarrow N_{12}}%
\EasyButWeakLineBreak%
{${44}\above{1pt}{1pt}{1,0}{\infty b}{44}\above{1pt}{1pt}{r}{2}{2}\above{1pt}{1pt}{b}{2}{4}\above{1pt}{1pt}{*}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2348148\\9768\\70268
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
9768\\-40\\-293
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
70268\\-293\\-2102
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
42041\\1285284\\1225224
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-154\\-4709\\-4488
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1281\\-39162\\-37333
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-63\\-1826\\-1848
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-157\\-4796\\-4576
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-16\\-500\\-465
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-33\\-1040\\-958
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-2348148, 9768, 70268; 9768, -40, -293; 70268, -293, -2102],[44, 1, 1],[-63, -157, -16, -33, -91, 3, 9, 5; -1826, -4796, -500, -1040, -2882, 88, 286, 184; -1848, -4576, -465, -958, -2640, 88, 261, 142],11,1]
%
% END OF LATTICE L12.1
%
\hbox{}\par\smallskip%
%
% LATTICE L12.2
%
\leavevmode%
${L_{12.2}}$%
{} : {$1\above{1pt}{1pt}{2}{6}8\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{-2}{}11\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{2\rightarrow N'_{8}}%
\EasyButWeakLineBreak%
{${22}\above{1pt}{1pt}{4,1}{\infty b}{88}\above{1pt}{1pt}{s}{2}{4}\above{1pt}{1pt}{*}{2}{8}\above{1pt}{1pt}{b}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-238040\\528\\4840
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
528\\-1\\-11
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4840\\-11\\-98
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\10032\\-1672
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\-31\\5
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\-192\\31
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5\\330\\209
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\44\\44
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-66\\-42
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3\\-160\\-132
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-238040, 528, 4840; 528, -1, -11; 4840, -11, -98],[88, 1, 1],[5, 1, -1, -3, -5, -1, 1, 3; 330, 44, -66, -160, -198, 220, 78, 208; 209, 44, -42, -132, -231, -88, 40, 124],11,2]
%
% END OF LATTICE L12.2
%
\hbox{}\par\smallskip%
%
% LATTICE L12.3
%
\leavevmode%
${L_{12.3}}$%
{} : {$1\above{1pt}{1pt}{-2}{6}8\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{-2}{}11\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{m}%
\EasyButWeakLineBreak%
{${22}\above{1pt}{1pt}{4,1}{\infty a}{88}\above{1pt}{1pt}{l}{2}{1}\above{1pt}{1pt}{}{2}{8}\above{1pt}{1pt}{r}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1848\\-1848\\968
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1848\\-1826\\945
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
968\\945\\-483
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
527\\-1320\\-1584
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
472\\-1181\\-1416
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-218\\545\\653
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-105\\209\\198
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-21\\44\\44
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
11\\-22\\-21
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
77\\-160\\-160
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-1848, -1848, 968; -1848, -1826, 945; 968, 945, -483],[88, 1, 1],[-105, -21, 11, 77, 149, 109, -9, -61; 209, 44, -22, -160, -319, -264, 17, 120; 198, 44, -21, -160, -330, -308, 15, 112],11,3]
%
% END OF LATTICE L12.3
%
%
% LATTICE L12.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[11, 0, 0; 0, 0, -1; 0, -1, 0],[11, 1, 1],[-1, 1, 0, -3, -21, -23, -2, -1; 0, 0, -1, -7, -44, -44, -3, -1; -11, 0, 1, -7, -55, -66, -7, -5],11,4]
%
% END OF LATTICE L12.4
%
%
% LATTICE L12.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[38918, 28094, 12386; 28094, 20281, 8941; 12386, 8941, 3942],[22, 1, 1],[-1558, -1753, -82, -103, -202, -7, 2, -217; 902, 1012, 47, 58, 110, 0, -1, 126; 2849, 3212, 151, 192, 385, 22, -4, 396],11,5]
%
% END OF LATTICE L12.5
%
%
% LATTICE L12.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-924, 44, 264; 44, -2, -11; 264, -11, -49],[44, 1, 1],[-5, -1, 1, 3, 5, 1, -1, -3; -99, 110, 39, 104, 165, 22, -33, -80; -11, -44, -4, -8, -11, 0, 2, 0],11,6]
%
% END OF LATTICE L12.6
%
%
% LATTICE L12.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1056594, 13090, -504724; 13090, -160, 6252; -504724, 6252, -241101],[22, 2, 1],[4458, 3216, 443, 383, 1922, -26, -153, 197; -4081, -2959, -410, -356, -1793, 22, 143, -178; -9438, -6809, -938, -811, -4070, 55, 324, -417],11,7]
%
% END OF LATTICE L12.7
%
%
% LATTICE L12.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-22, -121, -22; -121, -660, -121; -22, -121, -21],[11, 11, 1],[22, 29, 39, 30, 6, -1, -11, 26; -1, -2, -4, -4, -1, 0, 2, 0; -21, -23, -22, -11, -1, 1, 0, -33],11,8]
%
% END OF LATTICE L12.8
%
%
% LATTICE L12.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[12163536, -1404788, -3361556; -1404788, 162248, 388232; -3361556, 388232, 929011],[44, 4, 1],[29273, 16081, 2846, 1626, 2737, -76, 64, 4194; -440, -242, -43, -25, -44, 0, -1, -63; 106106, 58289, 10316, 5894, 9922, -275, 232, 15202],11,9]
%
% END OF LATTICE L12.9
%
%
% LATTICE L12.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[8888, 4444, -2288; 4444, 2220, -1144; -2288, -1144, 589],[44, 4, 1],[-412, -457, -41, -11, -28, 17, 1, -29; 99, 110, 10, 3, 11, 0, 0, 7; -1408, -1562, -140, -37, -88, 66, 4, -99],11,10]
%
% END OF LATTICE L12.10
%
%
% LATTICE L12.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1655170, -138578, -755832; -138578, -11561, -63283; -755832, -63283, -345150],[22, 11, 1],[2116, 3067, 2336, 4055, 928, -23, -814, 2033; -168, -242, -183, -316, -72, 2, 63, -164; -4603, -6672, -5082, -8822, -2019, 50, 1771, -4422],11,11]
%
% END OF LATTICE L12.11
%
%
% LATTICE L12.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-12980, -968, 748; -968, -66, 55; 748, 55, -43],[44, 11, 1],[7, 17, 10, 13, 1, -1, -2, 19; 11, 30, 21, 32, 3, -2, -7, 24; 133, 328, 198, 264, 21, -20, -44, 352],11,12]
%
% END OF LATTICE L12.12
%
%
% LATTICE L12.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[86724, -4675726, -2227126; -4675726, 252108758, 120083590; -2227126, 120083590, 57197809],[22, 22, 1],[259, 146, 151, 96, 35, 1, -4, 198; -32882, -18496, -19027, -11939, -4250, -70, 461, -25193; 69044, 38837, 39952, 25069, 8924, 147, -968, 52899],11,13]
%
% END OF LATTICE L12.13
%
%
% LATTICE L12.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[8932, 11660, -1188; 11660, 15224, -1551; -1188, -1551, 158],[44, 11, 1],[-27, -23, -4, 3, 1, -3, -9, -55; 94, 84, 20, 0, -2, 8, 26, 184; 716, 648, 165, 22, -12, 56, 187, 1386],11,14]
%
% END OF LATTICE L12.14
%
%
% LATTICE L12.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-892936, 3784, 20768; 3784, -16, -88; 20768, -88, -483],[88, 8, 1],[-46, -21, -1, 0, 2, -1, -1, -4; 1133, 440, 4, -11, -11, 121, 47, 113; -2200, -990, -44, 2, 88, -66, -52, -194],11,15]
%
% END OF LATTICE L12.15
%
%
% LATTICE L12.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-440, 7656, -968; 7656, -121040, 15304; -968, 15304, -1935],[88, 8, 1],[-46, -21, -1, 0, 2, -1, -1, -2; 2101, 803, 4, -11, -11, 242, 91, 106; 16632, 6358, 32, -87, -88, 1914, 720, 839],11,16]
%
% END OF LATTICE L12.16
%
%
% LATTICE L12.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-324104, -165440, 5280; -165440, -84447, 2695; 5280, 2695, -86],[88, 11, 1],[-4, -13, -11, -19, -2, 1, 5, -5; 22, 60, 42, 64, 6, -4, -14, 48; 441, 1076, 638, 836, 65, -64, -132, 1188],11,17]
%
% END OF LATTICE L12.17
%
%
% LATTICE L12.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-43560, 1232, 704; 1232, -33, -22; 704, -22, -9],[88, 11, 1],[7, 17, 5, 13, 1, -1, -1, 19; 167, 404, 118, 304, 23, -24, -23, 456; 133, 328, 99, 264, 21, -20, -22, 352],11,18]
%
% END OF LATTICE L12.18
%
%
% LATTICE L12.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[88, 220, -88; 220, -10208, 2992; -88, 2992, -871],[44, 44, 1],[260, 127, 175, 39, -8, -1, 77, 465; 287, 141, 198, 46, -9, -2, 80, 510; 954, 469, 660, 154, -30, -7, 264, 1694],11,19]
%
% END OF LATTICE L12.19
%
%
% LATTICE L12.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1364, -8228, 2288; -8228, 52360, -14564; 2288, -14564, 4051],[44, 44, 1],[-17, -18, -16, -4, -1, 0, -2, -14; -430, -463, -431, -120, -38, -5, -37, -348; -1536, -1654, -1540, -429, -136, -18, -132, -1243],11,20]
%
% END OF LATTICE L12.20
%
%
% LATTICE L12.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-176, 616, -176; 616, -1496, 440; -176, 440, -129],[88, 88, 1],[23, 10, 4, -1, -1, 1, 7, 23; -94, -39, -11, 6, 2, -7, -35, -98; -360, -150, -44, 22, 8, -26, -132, -374],11,21]
%
% END OF LATTICE L12.21
%
%
% LATTICE L12.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-363440, 3642584, -992728; 3642584, -36506888, 9949368; -992728, 9949368, -2711541],[88, 88, 1],[77, 34, 15, -1, -3, 3, 22, 38; 4922, 2085, 697, -141, -166, 293, 1681, 2519; 18032, 7638, 2552, -517, -608, 1074, 6160, 9229],11,22]
%
% END OF LATTICE L12.22
%

\medskip%
%------------------------------WEYL-GROUP-W13--------------------------------
%
\leavevmode\llap{}%
$W_{13\phantom{0}}$%
\qquad\llap{22} lattices, $\chi=42$%
\hfill%
$\infty242\infty242\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L13.1
%
\leavevmode%
${L_{13.1}}$%
{} : {$1\above{1pt}{1pt}{2}{{\rm II}}4\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{2}{}13\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2\rightarrow N_{13}}%
\EasyButWeakLineBreak%
{${52}\above{1pt}{1pt}{1,0}{\infty b}{52}\above{1pt}{1pt}{r}{2}{2}\above{1pt}{1pt}{*}{4}{4}\above{1pt}{1pt}{*}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-14425996\\261508\\523016
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
261508\\-4740\\-9481
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
523016\\-9481\\-18962
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
896635\\125112\\24667916
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-16383\\-2287\\-450723
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-32508\\-4536\\-894349
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1159\\-130\\-31902
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2351\\-312\\-64688
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-258\\-38\\-7097
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-31\\-10\\-850
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-14425996, 261508, 523016; 261508, -4740, -9481; 523016, -9481, -18962],[52, 1, 1],[-1159, -2351, -258, -31, 41, 115, 0, -55; -130, -312, -38, -10, -26, 0, 2, -2; -31902, -64688, -7097, -850, 1144, 3172, -1, -1516],12,1]
%
% END OF LATTICE L13.1
%
\hbox{}\par\smallskip%
%
% LATTICE L13.2
%
\leavevmode%
${L_{13.2}}$%
{} : {$1\above{1pt}{1pt}{-2}{2}8\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{2}{}13\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{2\rightarrow N'_{10}}%
\EasyButWeakLineBreak%
{${26}\above{1pt}{1pt}{4,3}{\infty b}{104}\above{1pt}{1pt}{s}{2}{4}\above{1pt}{1pt}{*}{4}{2}\above{1pt}{1pt}{s}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5304\\104\\2080
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
104\\-9\\-65
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2080\\-65\\-198
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-11233\\-527280\\54912
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
468\\21969\\-2288
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2196\\103090\\-10737
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-412\\-19344\\2015
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1893\\-88868\\9256
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-225\\-10562\\1100
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-26\\-1220\\127
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[5304, 104, 2080; 104, -9, -65; 2080, -65, -198],[104, 1, 1],[-412, -1893, -225, -26, -56, 21, 9, -10; -19344, -88868, -10562, -1220, -2626, 988, 422, -470; 2015, 9256, 1100, 127, 273, -104, -44, 49],12,2]
%
% END OF LATTICE L13.2
%
\hbox{}\par\smallskip%
%
% LATTICE L13.3
%
\leavevmode%
${L_{13.3}}$%
{} : {$1\above{1pt}{1pt}{2}{2}8\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{2}{}13\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{m}%
\EasyButWeakLineBreak%
{${26}\above{1pt}{1pt}{4,3}{\infty a}{104}\above{1pt}{1pt}{l}{2}{1}\above{1pt}{1pt}{}{4}{2}\above{1pt}{1pt}{b}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2600\\-2600\\1352
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2600\\-2574\\1325
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1352\\1325\\-675
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-17109\\33488\\31304
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-15463\\30267\\28294
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7191\\-14076\\-13159
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-150\\299\\286
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-25\\52\\52
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
13\\-26\\-25
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\-5\\-6
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-2600, -2600, 1352; -2600, -2574, 1325; 1352, 1325, -675],[104, 1, 1],[-150, -25, 13, 2, -461, -2419, -154, -49; 299, 52, -26, -5, 897, 4732, 302, 97; 286, 52, -25, -6, 832, 4420, 283, 92],12,3]
%
% END OF LATTICE L13.3
%
%
% LATTICE L13.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[13, 0, 0; 0, 0, -1; 0, -1, 0],[13, 1, 1],[-1, 1, 0, -1, -25, -53, -12, -1; 0, 0, -1, -2, -39, -78, -17, -1; -13, 0, 1, -3, -104, -234, -55, -6],12,4]
%
% END OF LATTICE L13.4
%
%
% LATTICE L13.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[246506, 0, 15002; 0, 1, -1; 15002, -1, 914],[26, 1, 1],[526, 1177, 138, 30, 72, 19, 0, 16; -8710, -19500, -2287, -498, -1196, -312, 1, -264; -8645, -19344, -2268, -493, -1183, -312, 0, -263],12,5]
%
% END OF LATTICE L13.5
%
%
% LATTICE L13.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-373204, 15860, 6188; 15860, -674, -263; 6188, -263, -99],[52, 1, 1],[-412, -1893, -225, -26, -56, 21, 9, -10; -9672, -44434, -5281, -610, -1313, 494, 211, -235; -65, -312, -38, -5, -13, 0, 2, -1],12,6]
%
% END OF LATTICE L13.6
%
%
% LATTICE L13.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-4032158, 276510, -1877824; 276510, -18960, 128774; -1877824, 128774, -874525],[26, 2, 1],[15676, 15887, 3485, 416, -570, -781, 1, 746; -65, -78, -19, -5, -13, 0, 1, -1; -33670, -34125, -7486, -894, 1222, 1677, -2, -1602],12,7]
%
% END OF LATTICE L13.7
%
%
% LATTICE L13.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-481, -325, 286; -325, -156, 195; 286, 195, -170],[13, 13, 1],[19, -3, -40, 39, 131, 303, 940, 111; -1, 0, 2, -1, -5, -12, -38, -5; 31, -5, -65, 65, 216, 499, 1547, 182],12,8]
%
% END OF LATTICE L13.8
%
%
% LATTICE L13.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[460824, 218244, 115648; 218244, 103396, 54772; 115648, 54772, 29023],[52, 4, 1],[8537, 19049, 4459, 479, 1122, 269, -1, 264; 1703, 3796, 888, 95, 221, 52, 0, 53; -37232, -83070, -19444, -2088, -4888, -1170, 4, -1152],12,9]
%
% END OF LATTICE L13.9
%
%
% LATTICE L13.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[68544528, 52, 15594384; 52, 8, 12; 15594384, 12, 3547837],[52, 4, 1],[-46381, -51891, -24336, -2645, -6347, -837, 0, -1411; -4355, -4875, -2287, -249, -598, -78, 1, -132; 203866, 228085, 106968, 11626, 27898, 3679, 0, 6202],12,10]
%
% END OF LATTICE L13.10
%
%
% LATTICE L13.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1581658, -441532, -763958; -441532, -123253, -213265; -763958, -213265, -369000],[26, 13, 1],[1189, 2423, 3468, 433, -35, -115, -6, 721; -136, -274, -389, -44, 6, 14, -1, -86; -2383, -4858, -6955, -871, 69, 230, 13, -1443],12,11]
%
% END OF LATTICE L13.11
%
%
% LATTICE L13.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-114452, -52988, 4212; -52988, -24531, 1950; 4212, 1950, -155],[52, 13, 1],[0, 1, -1, -6, -10, -41, -59, -4; 2, -2, -3, 12, 27, 118, 177, 17; 25, 2, -65, -13, 66, 362, 611, 104],12,12]
%
% END OF LATTICE L13.12
%
%
% LATTICE L13.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[23764, -779454, -374738; -779454, 25652874, 12333100; -374738, 12333100, 5929369],[26, 26, 1],[-665, -744, -2268, -493, -91, -12, 0, -263; 29374, 32874, 100231, 21810, 4028, 528, -25, 11592; -61140, -68425, -208624, -45396, -8384, -1099, 52, -24128],12,13]
%
% END OF LATTICE L13.13
%
%
% LATTICE L13.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-105820, -103324, 8268; -103324, -100880, 8073; 8268, 8073, -646],[52, 13, 1],[9, -5, -5, 65, 139, 301, 449, 83; -2, 0, 2, -2, -10, -24, -38, -10; 90, -64, -39, 806, 1652, 3548, 5265, 936],12,14]
%
% END OF LATTICE L13.14
%
%
% LATTICE L13.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-356720, -13624, 624; -13624, -520, 24; 624, 24, -1],[104, 8, 1],[-1, -6, -2, -1, 1, 6, 2, 1; 52, 169, 53, 24, -26, -143, -47, -22; 416, 130, -12, -48, 0, 286, 108, 80],12,15]
%
% END OF LATTICE L13.15
%
%
% LATTICE L13.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-486512, 19032, 18200; 19032, -728, -704; 18200, -704, -677],[104, 8, 1],[261, 240, 49, 1, -27, -6, 5, 17; -6760, -6227, -1273, -28, 702, 169, -125, -438; 14040, 12922, 2640, 56, -1456, -338, 264, 912],12,16]
%
% END OF LATTICE L13.16
%
%
% LATTICE L13.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1829672, 4992, 23816; 4992, -13, -65; 23816, -65, -310],[104, 13, 1],[0, -1, 1, 6, 10, 41, 59, 4; 4, -4, -6, 24, 54, 236, 354, 34; -1, -76, 78, 455, 755, 3092, 4446, 299],12,17]
%
% END OF LATTICE L13.17
%
%
% LATTICE L13.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-229320, 3224, 1664; 3224, -39, -26; 1664, -26, -11],[104, 13, 1],[12, 53, 40, 8, 1, -1, -1, 5; 379, 1672, 1261, 251, 31, -32, -31, 159; 911, 4028, 3042, 611, 77, -76, -78, 377],12,18]
%
% END OF LATTICE L13.18
%
%
% LATTICE L13.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[884, -5096, -1196; -5096, 93028, 21372; -1196, 21372, 4911],[52, 52, 1],[-24, -1, -13, -138, -289, -625, -1865, -175; 131, 5, 71, 757, 1584, 3425, 10219, 958; -576, -22, -312, -3328, -6964, -15058, -44928, -4212],12,19]
%
% END OF LATTICE L13.19
%
%
% LATTICE L13.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[104, 988, 208; 988, 334464, 74152; 208, 74152, 16441],[52, 52, 1],[-61, -1, 1, -287, -640, -700, -4207, -414; 123, 2, 0, 583, 1297, 1418, 8520, 837; -554, -9, 0, -2626, -5842, -6387, -38376, -3770],12,20]
%
% END OF LATTICE L13.20
%
%
% LATTICE L13.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-624, -20072, -9776; -20072, -614536, -299312; -9776, -299312, -145781],[104, 104, 1],[1, 0, -4, -11, -13, -12, -32, -1; 74, -75, -633, -962, -884, -735, -1797, 152; -152, 154, 1300, 1976, 1816, 1510, 3692, -312],12,21]
%
% END OF LATTICE L13.21
%
%
% LATTICE L13.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-65624, -72176, -33488; -72176, -79352, -36816; -33488, -36816, -17081],[104, 104, 1],[-3, 2, 21, 37, 37, 32, 81, -3; 25, -25, -212, -323, -297, -247, -604, 51; -48, 50, 416, 624, 568, 470, 1144, -104],12,22]
%
% END OF LATTICE L13.22
%

\medskip%
%------------------------------WEYL-GROUP-W14--------------------------------
%
\leavevmode\llap{}%
$W_{14\phantom{0}}$%
\qquad\llap{6} lattices, $\chi=12$%
\hfill%
$222222\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L14.1
%
\leavevmode%
${L_{14.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{-2}{}13\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{2\rightarrow N_{14}}%
\EasyButWeakLineBreak%
{${4}\above{1pt}{1pt}{r}{2}{2}\above{1pt}{1pt}{b}{2}{26}\above{1pt}{1pt}{l}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-572\\-260\\52
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-260\\-118\\25
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
52\\25\\6
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
103\\-208\\-104
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
49\\-99\\-49
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4\\-8\\-5
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
17\\-36\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7\\-15\\2
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-6\\13\\0
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-572, -260, 52; -260, -118, 25; 52, 25, 6],[52, 1, 1],[17, 7, -6, -13, -6, 19; -36, -15, 13, 28, 13, -39; 0, 2, 0, -4, -3, -13],13,1]
%
% END OF LATTICE L14.1
%
%
% LATTICE L14.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[78, -13, 0; -13, 2, 0; 0, 0, 1],[13, 1, 1],[0, 0, -10, -2, -1, -3; 0, 1, -65, -14, -8, -26; 1, 0, -26, -5, -2, 0],13,2]
%
% END OF LATTICE L14.2
%
%
% LATTICE L14.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-13, -26, 0; -26, 39, 13; 0, 13, 2],[13, 13, 1],[3, 3, -1, -5, -4, 0; -2, -3, -1, 0, 2, 0; 13, 13, -1, -13, -13, 1],13,3]
%
% END OF LATTICE L14.3
%
%
% LATTICE L14.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[240760, -10660, 60528; -10660, 472, -2680; 60528, -2680, 15217],[52, 4, 1],[25, -1, -25, 3, 29, 389; -43, 0, 26, -6, -49, -663; -107, 4, 104, -13, -124, -1664],13,4]
%
% END OF LATTICE L14.4
%
%
% LATTICE L14.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[52, 0, 0; 0, -26, 13; 0, 13, -6],[52, 13, 1],[-5, -1, 0, 1, 0, -1; -16, 1, 1, 0, -5, -5; -52, 0, 2, 0, -13, -15],13,5]
%
% END OF LATTICE L14.5
%
%
% LATTICE L14.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[312, -676, -156; -676, 1560, 364; -156, 364, 85],[52, 52, 1],[-5, -2, 0, 0, -3, -5; -11, -1, -1, -3, -13, -13; 39, 0, 4, 13, 52, 48],13,6]
%
% END OF LATTICE L14.6
%

\medskip%
%------------------------------WEYL-GROUP-W15--------------------------------
%
\leavevmode\llap{}%
$W_{15\phantom{0}}$%
\qquad\llap{8} lattices, $\chi=8$%
\hfill%
$\infty232$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L15.1
%
\leavevmode%
${L_{15.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}8\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{-2}{}7\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2\rightarrow N_{15}}%
\EasyButWeakLineBreak%
{${14}\above{1pt}{1pt}{4,3}{\infty a}{56}\above{1pt}{1pt}{b}{2}{2}\above{1pt}{1pt}{-}{3}{2}\above{1pt}{1pt}{b}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-25256\\392\\672
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
392\\-6\\-11
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
672\\-11\\-14
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2\\-105\\-14
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
11\\560\\84
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\52\\7
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-51\\-8
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-25256, 392, 672; 392, -6, -11; 672, -11, -14],[56, 1, 1],[-2, 11, 1, -1; -105, 560, 52, -51; -14, 84, 7, -8],14,1]
%
% END OF LATTICE L15.1
%
%
% LATTICE L15.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[14, 0, 0; 0, 0, -1; 0, -1, 0],[14, 1, 1],[-1, 1, 0, -1; 0, 0, -1, -2; -7, 0, 1, -3],14,2]
%
% END OF LATTICE L15.2
%
%
% LATTICE L15.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-10472, 378, -4956; 378, -12, 178; -4956, 178, -2345],[14, 2, 1],[38, -54, -19, 20; -49, 63, 24, -23; -84, 119, 42, -44],14,3]
%
% END OF LATTICE L15.3
%
%
% LATTICE L15.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-17318, -1428, -7546; -1428, -98, -623; -7546, -623, -3288],[14, 7, 1],[25, -65, -86, 83; -2, 6, 7, -8; -57, 148, 196, -189],14,4]
%
% END OF LATTICE L15.4
%
%
% LATTICE L15.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[532, -25214, -11648; -25214, 1206184, 557214; -11648, 557214, 257413],[14, 14, 1],[1, 2, 2, 1; -24, -127, -291, -194; 52, 275, 630, 420],14,5]
%
% END OF LATTICE L15.5
%
%
% LATTICE L15.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-280, 112, 56; 112, -42, -21; 56, -21, -10],[56, 7, 1],[0, 1, 0, -1; -1, 4, 3, -3; 2, -4, -7, 0],14,6]
%
% END OF LATTICE L15.6
%
%
% LATTICE L15.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-9968, -1512, 224; -1512, -112, 32; 224, 32, -5],[56, 8, 1],[-9, 8, 4, -3; -7, 7, 3, -3; -448, 406, 200, -152],14,7]
%
% END OF LATTICE L15.7
%
%
% LATTICE L15.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-336, 280, -56; 280, 112, 0; -56, 0, -3],[56, 56, 1],[-1, 1, 3, -3; 2, -3, -7, 8; 16, -22, -56, 56],14,8]
%
% END OF LATTICE L15.8
%

\medskip%
%------------------------------WEYL-GROUP-W16--------------------------------
%
\leavevmode\llap{}%
$W_{16\phantom{0}}$%
\qquad\llap{24} lattices, $\chi=4$%
\hfill%
$2262$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L16.1
%
\leavevmode%
${L_{16.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{-}{}9\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{23\rightarrow N_{16},3,2}%
\EasyButWeakLineBreak%
{${36}\above{1pt}{1pt}{*}{2}{20}\above{1pt}{1pt}{b}{2}{6}\above{1pt}{1pt}{}{6}{2}\above{1pt}{1pt}{b}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-324180\\-9360\\3600
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-9360\\-66\\69
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3600\\69\\-34
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-5\\-138\\-810
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
9\\250\\1460
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\83\\486
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-4\\-111\\-649
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-324180, -9360, 3600; -9360, -66, 69; 3600, 69, -34],[180, 3, 1],[-5, 9, 3, -4; -138, 250, 83, -111; -810, 1460, 486, -649],15,1]
%
% END OF LATTICE L16.1
%
%
% LATTICE L16.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-30, 15, 0; 15, -7, 0; 0, 0, 1],[15, 1, 1],[0, 2, -1, -3; 0, 5, -3, -8; 1, 0, -3, 0],15,2]
%
% END OF LATTICE L16.2
%
%
% LATTICE L16.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-19380, -7260, 900; -7260, -2694, 323; 900, 323, -34],[60, 1, 1],[11, -61, -20, 27; -38, 210, 69, -93; -70, 380, 126, -169],15,3]
%
% END OF LATTICE L16.3
%
%
% LATTICE L16.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-3555, -180, 540; -180, -3, 27; 540, 27, -82],[45, 3, 1],[-4, 3, 4, -3; -3, 0, 2, -1; -27, 20, 27, -20],15,4]
%
% END OF LATTICE L16.4
%
%
% LATTICE L16.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-96285, -12240, 33720; -12240, -1554, 4287; 33720, 4287, -11809],[15, 3, 1],[-27, 74, 29, -68; 14, -45, -16, 39; -72, 195, 77, -180],15,5]
%
% END OF LATTICE L16.5
%
%
% LATTICE L16.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-21435, -2970, 10065; -2970, -410, 1395; 10065, 1395, -4726],[15, 5, 1],[13, -9, -46, 38; -9, 4, 27, -20; 25, -18, -90, 75],15,6]
%
% END OF LATTICE L16.6
%
%
% LATTICE L16.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-9270, -315, 495; -315, -3, 15; 495, 15, -26],[45, 3, 1],[1, -2, -3, 2; 5, -15, -16, 12; 22, -45, -66, 45],15,7]
%
% END OF LATTICE L16.7
%
%
% LATTICE L16.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[13860, -60, -480; -60, -18, 9; -480, 9, 14],[60, 3, 1],[5, 1, -2, 1; 52, 10, -21, 10; 138, 30, -55, 27],15,8]
%
% END OF LATTICE L16.8
%
%
% LATTICE L16.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2415, -4590, 945; -4590, 8835, -1815; 945, -1815, 373],[15, 15, 1],[-9, -4, 0, -7; 20, 9, 1, 18; 120, 54, 5, 105],15,9]
%
% END OF LATTICE L16.9
%
%
% LATTICE L16.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[20078520, -449700, -5223720; -449700, 10072, 116996; -5223720, 116996, 1359027],[60, 4, 1],[-37, -51, 19, -41; -49, -70, 12, -65; -138, -190, 72, -152],15,10]
%
% END OF LATTICE L16.10
%
%
% LATTICE L16.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-55140, 16920, -900; 16920, -5190, 275; -900, 275, -14],[60, 5, 1],[-9, 5, 16, -10; -32, 18, 57, -36; -50, 32, 90, -65],15,11]
%
% END OF LATTICE L16.11
%
%
% LATTICE L16.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-16020, 360, 180; 360, 42, -3; 180, -3, -2],[180, 3, 1],[1, 1, -1, 1; -2, 0, 2, -3; 92, 90, -93, 90],15,12]
%
% END OF LATTICE L16.12
%
%
% LATTICE L16.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-14895, 2880, 855; 2880, -555, -165; 855, -165, -49],[45, 15, 1],[0, -1, -1, 2; 3, 3, -5, -3; -10, -27, 0, 45],15,13]
%
% END OF LATTICE L16.13
%
%
% LATTICE L16.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-899865, -4545, 26730; -4545, -15, 135; 26730, 135, -794],[45, 15, 1],[-4, 3, 4, -15; -3, 0, 2, -1; -135, 101, 135, -505],15,14]
%
% END OF LATTICE L16.14
%
%
% LATTICE L16.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[924840, -82020, -249240; -82020, 7272, 22104; -249240, 22104, 67169],[60, 12, 1],[-8, -137, -15, 68; 1, 5, 1, 1; -30, -510, -56, 252],15,15]
%
% END OF LATTICE L16.15
%
%
% LATTICE L16.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2580, 3180, -660; 3180, 3690, -735; -660, -735, 142],[60, 15, 1],[-35, -1, 14, -8; 72, 2, -29, 16; 210, 6, -85, 45],15,16]
%
% END OF LATTICE L16.16
%
%
% LATTICE L16.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[285960, 60060, 31560; 60060, 12680, 6580; 31560, 6580, 3519],[60, 20, 1],[24, -9, -335, -218; -67, 25, 933, 607; -90, 34, 1260, 820],15,17]
%
% END OF LATTICE L16.17
%
%
% LATTICE L16.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[944821080, -11048220, 230823540; -11048220, 129192, -2699124; 230823540, -2699124, 56391107],[180, 12, 1],[409, 193, -47, 169; 3, 0, -8, -5; -1674, -790, 192, -692],15,18]
%
% END OF LATTICE L16.18
%
%
% LATTICE L16.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[11022120, 16020, 2691540; 16020, 24, 3912; 2691540, 3912, 657259],[180, 12, 1],[21, -22, 0, 211; 0, 15, 1, -12; -86, 90, 0, -864],15,19]
%
% END OF LATTICE L16.19
%
%
% LATTICE L16.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2340, 720, -900; 720, 210, 285; -900, 285, -346],[180, 15, 1],[-39, -7, 41, -35; -2, 0, 2, -3; 100, 18, -105, 90],15,20]
%
% END OF LATTICE L16.20
%
%
% LATTICE L16.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-147780, -7560, 1440; -7560, -330, 75; 1440, 75, -14],[180, 15, 1],[-5, 1, 3, -2; 12, -2, -7, 4; -450, 92, 270, -185],15,21]
%
% END OF LATTICE L16.21
%
%
% LATTICE L16.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[69240, -336660, 87540; -336660, 1636920, -425640; 87540, -425640, 110677],[60, 60, 1],[1, -7, -1, 35; 8, -3, 5, 54; 30, -6, 20, 180],15,22]
%
% END OF LATTICE L16.22
%
%
% LATTICE L16.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[19587240, -48060, -4890060; -48060, 120, 12000; -4890060, 12000, 1220831],[180, 60, 1],[-57, 58, 0, -803; 171, -171, 1, 2397; -230, 234, 0, -3240],15,23]
%
% END OF LATTICE L16.23
%
%
% LATTICE L16.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[21886920, -183780, -5479200; -183780, 1560, 46020; -5479200, 46020, 1371679],[180, 60, 1],[22, -21, -381, -254; -63, 63, 1135, 757; 90, -86, -1560, -1040],15,24]
%
% END OF LATTICE L16.24
%

\medskip%
%------------------------------WEYL-GROUP-W17--------------------------------
%
\leavevmode\llap{}%
$W_{17\phantom{0}}$%
\qquad\llap{44} lattices, $\chi=6$%
\hfill%
$22222$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L17.1
%
\leavevmode%
${L_{17.1}}$%
{} : {$1\above{1pt}{1pt}{2}{{\rm II}}4\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2\rightarrow N_{17}}%
\EasyButWeakLineBreak%
{${4}\above{1pt}{1pt}{*}{2}{12}\above{1pt}{1pt}{*}{2}{20}\above{1pt}{1pt}{b}{2}{2}\above{1pt}{1pt}{s}{2}{30}\above{1pt}{1pt}{b}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-22020\\360\\240
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
360\\-4\\-5
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
240\\-5\\-2
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-28\\-50
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-30\\-48
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\80\\150
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\28\\49
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\30\\45
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-22020, 360, 240; 360, -4, -5; 240, -5, -2],[60, 1, 1],[-1, -1, 3, 1, 1; -28, -30, 80, 28, 30; -50, -48, 150, 49, 45],16,1]
%
% END OF LATTICE L17.1
%
\hbox{}\par\smallskip%
%
% LATTICE L17.2
%
\leavevmode%
${L_{17.2}}$%
{} : {$1\above{1pt}{1pt}{-2}{6}8\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{2\rightarrow N'_{13}}%
\EasyButWeakLineBreak%
{${8}\above{1pt}{1pt}{b}{2}{6}\above{1pt}{1pt}{l}{2}{40}\above{1pt}{1pt}{}{2}{1}\above{1pt}{1pt}{r}{2}{60}\above{1pt}{1pt}{*}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
9960\\3240\\-120
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3240\\1054\\-39
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-120\\-39\\1
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
9\\-28\\-8
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\3\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-13\\40\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\-1
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
29\\-90\\-30
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[9960, 3240, -120; 3240, 1054, -39; -120, -39, 1],[120, 1, 1],[9, -1, -13, 0, 29; -28, 3, 40, 0, -90; -8, 0, 0, -1, -30],16,2]
%
% END OF LATTICE L17.2
%
\hbox{}\par\smallskip%
%
% LATTICE L17.3
%
\leavevmode%
${L_{17.3}}$%
{} : {$1\above{1pt}{1pt}{2}{6}8\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{m}%
\EasyButWeakLineBreak%
{${8}\above{1pt}{1pt}{r}{2}{6}\above{1pt}{1pt}{b}{2}{40}\above{1pt}{1pt}{*}{2}{4}\above{1pt}{1pt}{l}{2}{15}\above{1pt}{1pt}{}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-126840\\-3360\\600
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3360\\-89\\16
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
600\\16\\-1
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3\\112\\-8
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2\\75\\-3
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7\\-260\\20
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\-112\\6
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\-75\\0
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-126840, -3360, 600; -3360, -89, 16; 600, 16, -1],[120, 1, 1],[-3, -2, 7, 3, 2; 112, 75, -260, -112, -75; -8, -3, 20, 6, 0],16,3]
%
% END OF LATTICE L17.3
%
%
% LATTICE L17.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[30, -15, 0; -15, 7, 0; 0, 0, 1],[15, 1, 1],[0, 1, -4, -3, -11; 0, 3, -10, -8, -30; 1, 0, -5, -2, 0],16,4]
%
% END OF LATTICE L17.4
%
%
% LATTICE L17.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[510, 240, 330; 240, 113, 155; 330, 155, 214],[30, 1, 1],[-1, -2, -11, -2, -7; 2, 0, 10, 3, 15; 0, 3, 10, 1, 0],16,5]
%
% END OF LATTICE L17.5
%
%
% LATTICE L17.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-780, -360, 60; -360, -166, 29; 60, 29, 7],[60, 1, 1],[-15, -7, 19, 8, -7; 32, 15, -40, -17, 15; -4, -3, 0, 2, 0],16,6]
%
% END OF LATTICE L17.6
%
%
% LATTICE L17.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[165, 15, -75; 15, -3, -6; -75, -6, 34],[15, 3, 1],[4, 1, -34, -18, -12; 1, 0, -5, -2, 0; 9, 2, -75, -39, -25],16,7]
%
% END OF LATTICE L17.7
%
%
% LATTICE L17.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-15270, 570, -7530; 570, -16, 280; -7530, 280, -3713],[30, 2, 1],[17, 32, -51, -33, -29; -7, -15, 20, 14, 15; -35, -66, 105, 68, 60],16,8]
%
% END OF LATTICE L17.8
%
%
% LATTICE L17.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[105, -90, -45; -90, 35, 35; -45, 35, 19],[15, 5, 1],[7, 5, -11, -29, -11; -2, -3, 4, 12, 6; 20, 15, -32, -85, -33],16,9]
%
% END OF LATTICE L17.9
%
%
% LATTICE L17.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-19830, 780, -6510; 780, -24, 255; -6510, 255, -2137],[30, 3, 1],[29, 9, -87, -28, -8; -14, -5, 40, 14, 5; -90, -28, 270, 87, 25],16,10]
%
% END OF LATTICE L17.10
%
%
% LATTICE L17.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-29130, 1200, -5730; 1200, -40, 235; -5730, 235, -1127],[30, 5, 1],[25, 23, -15, -24, -4; -14, -15, 8, 14, 3; -130, -120, 78, 125, 21],16,11]
%
% END OF LATTICE L17.11
%
%
% LATTICE L17.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2460, -120, -60; -120, 6, 3; -60, 3, 1],[60, 3, 1],[-1, 0, 1, 0, -1; -16, 0, 20, 1, -15; -12, -1, 0, 0, -10],16,12]
%
% END OF LATTICE L17.12
%
%
% LATTICE L17.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-6060, -180, 240; -180, 6, 3; 240, 3, -8],[60, 3, 1],[-1, 1, 7, 0, -2; -14, 12, 90, 1, -25; -36, 34, 240, 0, -70],16,13]
%
% END OF LATTICE L17.13
%
%
% LATTICE L17.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1790340, -34770, 858870; -34770, 678, -16680; 858870, -16680, 412021],[30, 6, 1],[36, 71, 511, 167, 168; 1, 0, 5, 3, 5; -75, -148, -1065, -348, -350],16,14]
%
% END OF LATTICE L17.14
%
%
% LATTICE L17.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[30, -30, -15; -30, 15, 15; -15, 15, 8],[15, 15, 1],[0, -2, 2, 11, 3; 1, 1, -3, -10, -2; 0, -5, 6, 30, 8],16,15]
%
% END OF LATTICE L17.15
%
%
% LATTICE L17.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[424920, -16020, -105780; -16020, 604, 3988; -105780, 3988, 26333],[60, 4, 1],[-4, -38, -33, 1, 31; -7, -57, -50, 0, 30; -15, -144, -125, 4, 120],16,16]
%
% END OF LATTICE L17.16
%
%
% LATTICE L17.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[526080, -21780, -141060; -21780, 904, 5840; -141060, 5840, 37823],[60, 4, 1],[-8, -37, -158, -46, -112; 1, 0, 5, 3, 15; -30, -138, -590, -172, -420],16,17]
%
% END OF LATTICE L17.17
%
%
% LATTICE L17.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2220, 600, -180; 600, 140, -45; -180, -45, 14],[60, 5, 1],[-3, -1, 1, 1, -1; -16, -6, 4, 4, -6; -90, -30, 26, 25, -33],16,18]
%
% END OF LATTICE L17.18
%
%
% LATTICE L17.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1579740, -42150, 751830; -42150, 1130, -20060; 751830, -20060, 357811],[30, 10, 1],[50, 257, 129, 219, 140; 1, 0, 1, 3, 3; -105, -540, -271, -460, -294],16,19]
%
% END OF LATTICE L17.19
%
%
% LATTICE L17.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[420, -120, 0; -120, 35, 0; 0, 0, -1],[60, 5, 1],[1, -1, -1, 0, 1; 4, -3, -4, -1, 3; 0, 0, -4, -5, -3],16,20]
%
% END OF LATTICE L17.20
%
%
% LATTICE L17.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-217320, 1200, 2040; 1200, -3, -12; 2040, -12, -19],[120, 3, 1],[1, 1, 7, -1, -1; 16, 19, 140, -18, -20; 96, 95, 660, -96, -95],16,21]
%
% END OF LATTICE L17.21
%
%
% LATTICE L17.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[120, 0, 120; 0, -6, -27; 120, -27, -1],[120, 3, 1],[1, -2, -9, 2, 9; 4, -9, -40, 9, 40; 0, 2, 0, -3, -10],16,22]
%
% END OF LATTICE L17.22
%
%
% LATTICE L17.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1564590, 51390, -456360; 51390, 1695, -14985; -456360, -14985, 133114],[30, 15, 1],[-75, -64, -193, -164, -35; 152, 128, 388, 331, 71; -240, -205, -618, -525, -112],16,23]
%
% END OF LATTICE L17.23
%
%
% LATTICE L17.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2040, 0, -120; 0, 5, 0; -120, 0, -7],[120, 5, 1],[1, -1, -1, 0, 1; 4, 3, 0, -1, 0; -20, 15, 16, 0, -18],16,24]
%
% END OF LATTICE L17.24
%
%
% LATTICE L17.25
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[8040, 2520, -240; 2520, 790, -75; -240, -75, 7],[120, 5, 1],[-5, -1, 1, 1, -1; 16, 3, -4, -4, 3; 0, 0, -8, -10, -3],16,25]
%
% END OF LATTICE L17.25
%
%
% LATTICE L17.26
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1560, 60, 420; 60, 228, -12; 420, -12, -113],[60, 12, 1],[12, 15, 4, -29, -11; -1, -1, 0, 2, 0; 45, 56, 15, -108, -40],16,26]
%
% END OF LATTICE L17.26
%
%
% LATTICE L17.27
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[269160, -22140, -72360; -22140, 1824, 5952; -72360, 5952, 19453],[60, 12, 1],[-5, -6, -121, -45, -43; -2, -1, 0, 2, 0; -18, -22, -450, -168, -160],16,27]
%
% END OF LATTICE L17.27
%
%
% LATTICE L17.28
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[60, -60, -60; -60, 30, 15; -60, 15, -7],[60, 15, 1],[-1, 2, 5, 0, -1; -4, 6, 16, 1, -3; 0, -5, -12, 0, 2],16,28]
%
% END OF LATTICE L17.28
%
%
% LATTICE L17.29
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2460, 1980, 360; 1980, -1560, -285; 360, -285, -52],[60, 15, 1],[3, -1, -1, 1, 1; -2, 6, 2, -7, -3; 30, -40, -18, 45, 23],16,29]
%
% END OF LATTICE L17.29
%
%
% LATTICE L17.30
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-4383660, -2611530, -1073790; -2611530, -1555770, -639690; -1073790, -639690, -263023],[30, 30, 1],[-7, -5, 4, 14, 1; 573, 362, -341, -1109, -65; -1365, -860, 813, 2640, 154],16,30]
%
% END OF LATTICE L17.30
%
%
% LATTICE L17.31
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-75480, -3600, 1200; -3600, -152, 56; 1200, 56, -19],[120, 8, 1],[-1, -1, 2, 2, 1; -5, -3, 10, 9, 0; -78, -72, 155, 152, 60],16,31]
%
% END OF LATTICE L17.31
%
%
% LATTICE L17.32
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[120, 0, 120; 0, -8, -40; 120, -40, -79],[120, 8, 1],[-1, -1, 9, 4, 1; -5, -3, 45, 19, 0; 1, 0, -10, -4, 0],16,32]
%
% END OF LATTICE L17.32
%
%
% LATTICE L17.33
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-840, -60, -180; -60, 140, -120; -180, -120, 41],[60, 20, 1],[4, 16, -5, -37, -19; -11, -45, 14, 104, 54; -15, -60, 19, 140, 72],16,33]
%
% END OF LATTICE L17.33
%
%
% LATTICE L17.34
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[152880, 8220, 34560; 8220, 440, 1860; 34560, 1860, 7811],[60, 20, 1],[8, 41, 6, -22, -20; -23, -132, -19, 73, 69; -30, -150, -22, 80, 72],16,34]
%
% END OF LATTICE L17.34
%
%
% LATTICE L17.35
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[120, 0, 120; 0, -15, -60; 120, -60, -119],[120, 15, 1],[1, 5, 11, -1, -1; 0, 19, 44, -2, -4; 0, -5, -12, 0, 1],16,35]
%
% END OF LATTICE L17.35
%
%
% LATTICE L17.36
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[6360, 3480, -360; 3480, 1695, -180; -360, -180, 19],[120, 15, 1],[1, -1, -1, 1, 1; 4, -7, -8, 6, 6; 60, -85, -96, 75, 76],16,36]
%
% END OF LATTICE L17.36
%
%
% LATTICE L17.37
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2760, 240, 1200; 240, -24, 48; 1200, 48, 451],[120, 24, 1],[1, 13, 29, -4, -13; 4, 51, 115, -15, -50; -3, -40, -90, 12, 40],16,37]
%
% END OF LATTICE L17.37
%
%
% LATTICE L17.38
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-216840, -32520, 1920; -32520, -4848, 288; 1920, 288, -17],[120, 24, 1],[0, 2, 2, -1, -3; -1, -1, 0, 1, 0; -18, 208, 225, -96, -340],16,38]
%
% END OF LATTICE L17.38
%
%
% LATTICE L17.39
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[4020, 7980, -2040; 7980, 15960, -4080; -2040, -4080, 1043],[60, 60, 1],[-1, -1, 0, 2, 0; 12, 21, 10, -1, 1; 45, 80, 39, 0, 4],16,39]
%
% END OF LATTICE L17.39
%
%
% LATTICE L17.40
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1680, 10260, -2760; 10260, 62880, -16920; -2760, -16920, 4553],[60, 60, 1],[17, 2, 1, 5, 7; -27, -3, -5, -17, -13; -90, -10, -18, -60, -44],16,40]
%
% END OF LATTICE L17.40
%
%
% LATTICE L17.41
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[240, -120, 0; -120, -4120, 360; 0, 360, -31],[120, 40, 1],[-3, -1, 1, 4, -1; -6, 0, 2, 7, -3; -70, 0, 23, 80, -36],16,41]
%
% END OF LATTICE L17.41
%
%
% LATTICE L17.42
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[240, -120, 0; -120, -520, 80; 0, 80, -11],[120, 40, 1],[-1, -1, 1, 2, -1; -2, 0, 2, 3, -3; -15, 0, 14, 20, -24],16,42]
%
% END OF LATTICE L17.42
%
%
% LATTICE L17.43
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[9960, 27600, -480; 27600, 75720, -1320; -480, -1320, 23],[120, 120, 1],[1, -1, -1, 0, 1; 2, -1, -1, 1, 2; 135, -80, -78, 60, 136],16,43]
%
% END OF LATTICE L17.43
%
%
% LATTICE L17.44
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-240, 14280, -360; 14280, -814440, 20520; -360, 20520, -517],[120, 120, 1],[9, -1, -1, 1, 4; 10, 2, -1, -3, 3; 390, 80, -39, -120, 116],16,44]
%
% END OF LATTICE L17.44
%

\medskip%
%------------------------------WEYL-GROUP-W18--------------------------------
%
\leavevmode\llap{}%
$W_{18\phantom{0}}$%
\qquad\llap{88} lattices, $\chi=18$%
\hfill%
$\infty22222$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L18.1
%
\leavevmode%
${L_{18.1}}$%
{} : {$1\above{1pt}{1pt}{2}{{\rm II}}4\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{1}{}3\above{1pt}{1pt}{-}{}9\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{2}{}5\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{23\rightarrow N_{18},3,2}%
\EasyButWeakLineBreak%
{${60}\above{1pt}{1pt}{3,2}{\infty b}{60}\above{1pt}{1pt}{r}{2}{18}\above{1pt}{1pt}{b}{2}{10}\above{1pt}{1pt}{s}{2}{6}\above{1pt}{1pt}{b}{2}{4}\above{1pt}{1pt}{*}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-18654660\\443520\\38700
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
443520\\-10542\\-921
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
38700\\-921\\-80
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-53\\-1750\\-5490
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\100\\300
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
13\\429\\1350
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\65\\220
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-10\\-331\\-1026
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-21\\-694\\-2168
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-18654660, 443520, 38700; 443520, -10542, -921; 38700, -921, -80],[180, 3, 1],[-53, 3, 13, 2, -10, -21; -1750, 100, 429, 65, -331, -694; -5490, 300, 1350, 220, -1026, -2168],17,1]
%
% END OF LATTICE L18.1
%
\hbox{}\par\smallskip%
%
% LATTICE L18.2
%
\leavevmode%
${L_{18.2}}$%
{} : {$1\above{1pt}{1pt}{2}{6}8\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{1}{}9\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{2}{}5\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{3m,3,2}%
\EasyButWeakLineBreak%
{${30}\above{1pt}{1pt}{12,5}{\infty b}{120}\above{1pt}{1pt}{s}{2}{36}\above{1pt}{1pt}{*}{2}{20}\above{1pt}{1pt}{l}{2}{3}\above{1pt}{1pt}{}{2}{8}\above{1pt}{1pt}{r}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-116280\\-4680\\-5040
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-4680\\-186\\-201
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-5040\\-201\\-217
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2\\-145\\180
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-40\\60
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\72\\-90
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\50\\-70
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\-10\\9
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-88\\104
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-116280, -4680, -5040; -4680, -186, -201; -5040, -201, -217],[360, 3, 1],[-2, -1, 1, 1, 0, -1; -145, -40, 72, 50, -10, -88; 180, 60, -90, -70, 9, 104],17,2]
%
% END OF LATTICE L18.2
%
\hbox{}\par\smallskip%
%
% LATTICE L18.3
%
\leavevmode%
${L_{18.3}}$%
{} : {$1\above{1pt}{1pt}{-2}{6}8\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{1}{}9\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{2}{}5\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{32\rightarrow N'_{12},3,m}%
\EasyButWeakLineBreak%
{${30}\above{1pt}{1pt}{12,5}{\infty a}{120}\above{1pt}{1pt}{l}{2}{9}\above{1pt}{1pt}{}{2}{5}\above{1pt}{1pt}{r}{2}{12}\above{1pt}{1pt}{*}{2}{8}\above{1pt}{1pt}{b}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1572120\\-310680\\109800
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-310680\\-61395\\21696
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
109800\\21696\\-7663
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-219\\1315\\585
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
43\\-260\\-120
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
44\\-264\\-117
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-14\\85\\40
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-113\\680\\306
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-195\\1172\\524
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-1572120, -310680, 109800; -310680, -61395, 21696; 109800, 21696, -7663],[360, 3, 1],[-219, 43, 44, -14, -113, -195; 1315, -260, -264, 85, 680, 1172; 585, -120, -117, 40, 306, 524],17,3]
%
% END OF LATTICE L18.3
%
%
% LATTICE L18.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[15, 0, 0; 0, 0, -1; 0, -1, 0],[15, 1, 1],[-1, 1, 0, -2, -2, -1; 0, 0, -1, -5, -3, -1; -15, 0, 1, -5, -9, -7],17,4]
%
% END OF LATTICE L18.4
%
%
% LATTICE L18.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[30, 0, 30; 0, 168, -2003; 30, -2003, 23911],[30, 1, 1],[179, 1, 1, 64, 74, 97; -2145, 0, -12, -775, -894, -1168; -180, 0, -1, -65, -75, -98],17,5]
%
% END OF LATTICE L18.5
%
%
% LATTICE L18.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-1740, 60, 480; 60, -2, -15; 480, -15, -97],[60, 1, 1],[7, 1, -1, -1, 2, 5; 315, 30, -45, -35, 99, 232; -15, 0, 2, 0, -6, -12],17,6]
%
% END OF LATTICE L18.6
%
%
% LATTICE L18.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-302340, 120180, 5040; 120180, -47762, -2003; 5040, -2003, -84],[60, 1, 1],[-1, 1, 0, -1, -1, -1; 180, 0, -13, -5, 33, 70; -4350, 60, 310, 60, -846, -1728],17,7]
%
% END OF LATTICE L18.7
%
%
% LATTICE L18.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-817080, 960, 12600; 960, -1, -15; 12600, -15, -194],[120, 1, 1],[7, 1, -1, -1, 1, 5; 630, 60, -90, -70, 99, 464; 405, 60, -58, -60, 57, 288],17,8]
%
% END OF LATTICE L18.8
%
%
% LATTICE L18.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-3480, -3480, 1800; -3480, -3450, 1769; 1800, 1769, -899],[120, 1, 1],[-203, -29, 15, 17, -55, -143; 405, 60, -30, -35, 108, 284; 390, 60, -29, -35, 102, 272],17,9]
%
% END OF LATTICE L18.9
%
%
% LATTICE L18.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-8460, -1305, -135; -1305, -201, -21; -135, -21, -2],[45, 3, 1],[-6, 1, 2, -2, -4, -3; 35, -5, -12, 10, 22, 17; 30, -15, -9, 25, 33, 20],17,10]
%
% END OF LATTICE L18.10
%
%
% LATTICE L18.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-765630, 63630, 11070; 63630, -5271, -921; 11070, -921, -160],[90, 3, 1],[-53, 3, 13, 2, -10, -21; -160, 10, 39, 5, -31, -64; -2745, 150, 675, 110, -513, -1084],17,11]
%
% END OF LATTICE L18.11
%
%
% LATTICE L18.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-58140, -2340, -2700; -2340, -93, -108; -2700, -108, -125],[180, 3, 1],[-2, -1, 1, 1, 0, -1; -55, -10, 27, 15, -11, -36; 90, 30, -45, -35, 9, 52],17,12]
%
% END OF LATTICE L18.12
%
%
% LATTICE L18.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2955, 135, 1320; 135, -6, -60; 1320, -60, -589],[15, 3, 1],[-7, 2, 2, -12, -6, -12; 40, -5, -15, 25, 23, 56; -20, 5, 6, -30, -16, -33],17,13]
%
% END OF LATTICE L18.13
%
%
% LATTICE L18.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-680340, 180270, -332610; 180270, -47762, 88132; -332610, 88132, -162609],[30, 2, 1],[2189, -22, -155, -16, 437, 439; 180, 0, -13, -5, 33, 35; -4380, 45, 310, 30, -876, -879],17,14]
%
% END OF LATTICE L18.14
%
%
% LATTICE L18.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1365, 900, 570; 900, -560, -375; 570, -375, -238],[15, 5, 1],[47, -5, -30, 8, 128, 107; -3, 0, 2, 0, -6, -6; 117, -12, -75, 19, 315, 265],17,15]
%
% END OF LATTICE L18.15
%
%
% LATTICE L18.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-806310, 240360, -262050; 240360, -71643, 78117; -262050, 78117, -85166],[30, 3, 1],[728, -13, -155, -21, 144, 873; 60, 0, -13, -5, 11, 70; -2185, 40, 465, 60, -433, -2622],17,16]
%
% END OF LATTICE L18.16
%
%
% LATTICE L18.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-585, -270, 540; -270, -93, 150; 540, 150, -187],[45, 3, 1],[16, -71, -37, -239, -13, 14; -95, 425, 221, 1425, 77, -84; -30, 135, 70, 450, 24, -27],17,17]
%
% END OF LATTICE L18.17
%
%
% LATTICE L18.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1088490, 360540, -211650; 360540, -119405, 70105; -211650, 70105, -41154],[30, 5, 1],[436, -7, -155, -5, 428, 869; 36, 0, -13, -1, 33, 70; -2181, 36, 775, 24, -2145, -4350],17,18]
%
% END OF LATTICE L18.18
%
%
% LATTICE L18.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-19380, 360, 780; 360, -6, -15; 780, -15, -31],[60, 3, 1],[2, 1, -1, -3, 0, 3; 30, 10, -15, -35, 3, 52; 35, 20, -18, -60, -2, 48],17,19]
%
% END OF LATTICE L18.19
%
%
% LATTICE L18.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[89749770, 300450, 43079850; 300450, 1008, 144216; 43079850, 144216, 20678309],[30, 6, 1],[-5676, -12, -95, -6103, -2351, -4619; -715, 0, -12, -775, -298, -584; 11830, 25, 198, 12720, 4900, 9627],17,20]
%
% END OF LATTICE L18.20
%
%
% LATTICE L18.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-4766220, 33900, 129420; 33900, -240, -921; 129420, -921, -3514],[60, 3, 1],[-53, 3, 13, 6, -10, -63; -770, 40, 190, 100, -142, -908; -1750, 100, 429, 195, -331, -2082],17,21]
%
% END OF LATTICE L18.21
%
%
% LATTICE L18.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[30, -225, 0; -225, 1905, -15; 0, -15, 1],[15, 15, 1],[7, 0, 1, 15, 29, 57; 1, 0, 0, 2, 4, 8; 14, 1, 0, 24, 50, 105],17,22]
%
% END OF LATTICE L18.22
%
%
% LATTICE L18.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[43032840, 120180, -11475480; 120180, 336, -32048; -11475480, -32048, 3060143],[60, 4, 1],[1342, 4, 15, 959, 1109, 727; -2145, 0, -24, -1550, -1788, -1168; 5010, 15, 56, 3580, 4140, 2714],17,23]
%
% END OF LATTICE L18.23
%
%
% LATTICE L18.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[16440, 8220, -4200; 8220, 4108, -2100; -4200, -2100, 1073],[60, 4, 1],[-38, 23, 1, -51, -55, -15; 15, 0, 0, 10, 12, 4; -120, 90, 4, -180, -192, -51],17,24]
%
% END OF LATTICE L18.24
%
%
% LATTICE L18.25
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-186930, -38340, 17370; -38340, -7863, 3561; 17370, 3561, -1610],[90, 3, 1],[32, -147, -38, -244, -13, 29; -190, 880, 227, 1455, 77, -174; -75, 360, 92, 585, 30, -72],17,25]
%
% END OF LATTICE L18.25
%
%
% LATTICE L18.26
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-780, -120, -120; -120, -10, -15; -120, -15, -17],[60, 5, 1],[-1, -1, 1, 1, 2, -1; -3, -6, 3, 5, 15, 4; 9, 12, -10, -12, -30, 0],17,26]
%
% END OF LATTICE L18.26
%
%
% LATTICE L18.27
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[105502710, 420630, 50239350; 420630, 1680, 200300; 50239350, 200300, 23923483],[30, 10, 1],[-4264, -10, -119, -1527, -8825, -5781; -429, 0, -12, -155, -894, -584; 8958, 21, 250, 3208, 18540, 12145],17,27]
%
% END OF LATTICE L18.27
%
%
% LATTICE L18.28
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2580, 3840, -7620; 3840, -5100, 9955; -7620, 9955, -19382],[60, 5, 1],[-199, 19, 98, 19, -161, -379; -1122, 108, 552, 106, -912, -2140; -498, 48, 245, 47, -405, -950],17,28]
%
% END OF LATTICE L18.28
%
%
% LATTICE L18.29
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-38760, 360, 1560; 360, -3, -15; 1560, -15, -62],[120, 3, 1],[2, 1, -1, -3, 0, 3; 60, 20, -30, -70, 3, 104; 35, 20, -18, -60, -1, 48],17,29]
%
% END OF LATTICE L18.29
%
%
% LATTICE L18.30
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-524040, -84840, 18720; -84840, -13725, 3039; 18720, 3039, -662],[120, 3, 1],[171, -37, -34, 38, 91, 463; -830, 180, 165, -185, -442, -2248; 1025, -220, -204, 225, 544, 2772],17,30]
%
% END OF LATTICE L18.30
%
%
% LATTICE L18.31
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[89952690, -475680, -28407480; -475680, 2520, 150225; -28407480, 150225, 8971217],[30, 15, 1],[1063, 5, 89, 1142, 2200, 8647; -2269, -10, -190, -2439, -4698, -18462; 3404, 16, 285, 3657, 7045, 27690],17,31]
%
% END OF LATTICE L18.31
%
%
% LATTICE L18.32
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[6246810, -562410, 3085380; -562410, 50640, -277782; 3085380, -277782, 1523909],[90, 6, 1],[-44, 1437, 713, 4903, 397, 92; 5, -250, -123, -840, -67, -15; 90, -2955, -1466, -10080, -816, -189],17,32]
%
% END OF LATTICE L18.32
%
%
% LATTICE L18.33
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1260, -360, 360; -360, -102, 105; 360, 105, -97],[180, 3, 1],[-14, 3, 2, -4, -7, -37; 35, -10, -5, 15, 19, 96; -15, 0, 2, 0, -6, -36],17,33]
%
% END OF LATTICE L18.33
%
%
% LATTICE L18.34
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[182214810, -731790, 89001630; -731790, 2940, -357438; 89001630, -357438, 43472263],[90, 6, 1],[-4954, 22, -299, -2179, -2307, -1431; -295, 5, -18, -135, -142, -87; 10140, -45, 612, 4460, 4722, 2929],17,34]
%
% END OF LATTICE L18.34
%
%
% LATTICE L18.35
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-6660, 360, -1080; 360, -12, 69; -1080, 69, -160],[180, 3, 1],[7, -57, -13, -74, -2, 13; 40, -340, -77, -435, -11, 78; -30, 240, 55, 315, 9, -54],17,35]
%
% END OF LATTICE L18.35
%
%
% LATTICE L18.36
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-10200, 240, 600; 240, -5, -15; 600, -15, -34],[120, 5, 1],[1, 1, -1, -1, -1, 1; 18, 12, -18, -14, -9, 32; 9, 12, -10, -12, -15, 0],17,36]
%
% END OF LATTICE L18.36
%
%
% LATTICE L18.37
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-52188600, -96360, 1354200; -96360, -175, 2500; 1354200, 2500, -35139],[120, 5, 1],[-80, 25, 27, -8, -233, -377; -393, 120, 133, -38, -1134, -1844; -3111, 972, 1050, -311, -9060, -14660],17,37]
%
% END OF LATTICE L18.37
%
%
% LATTICE L18.38
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[90, -45, 0; -45, -3705, 765; 0, 765, -157],[45, 15, 1],[3, -4, -1, 7, 35, 17; 5, -8, 0, 14, 68, 32; 24, -39, 0, 68, 330, 155],17,38]
%
% END OF LATTICE L18.38
%
%
% LATTICE L18.39
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[45, 0, 0; 0, -2130, -405; 0, -405, -77],[45, 15, 1],[0, 1, 2, 2, 0, -1; -4, 1, 13, 27, 17, 0; 21, -6, -70, -144, -90, 0],17,39]
%
% END OF LATTICE L18.39
%
%
% LATTICE L18.40
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[20532480, -2065740, -5522520; -2065740, 207864, 555612; -5522520, 555612, 1485365],[60, 12, 1],[2593, -39, 316, 7078, 2484, 4574; -25, 0, -3, -65, -23, -43; 9650, -145, 1176, 26340, 9244, 17022],17,40]
%
% END OF LATTICE L18.40
%
%
% LATTICE L18.41
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[40920, -7740, -11100; -7740, 1524, 2100; -11100, 2100, 3011],[60, 12, 1],[-151, -19, -13, -291, -111, -114; 5, 0, 0, 10, 4, 4; -560, -70, -48, -1080, -412, -423],17,41]
%
% END OF LATTICE L18.41
%
%
% LATTICE L18.42
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-38100, -1920, 1500; -1920, -90, 75; 1500, 75, -59],[60, 15, 1],[1, -1, -2, 2, 5, 19; 3, -2, -7, 3, 11, 48; 29, -28, -60, 54, 140, 540],17,42]
%
% END OF LATTICE L18.42
%
%
% LATTICE L18.43
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-181773330, -102407970, -42111690; -102407970, -57694860, -23724990; -42111690, -23724990, -9756071],[30, 30, 1],[12, 0, -13, -1, 11, 35; 5211, -44, -5553, -166, 5133, 15599; -12724, 107, 13560, 408, -12530, -38085],17,43]
%
% END OF LATTICE L18.43
%
%
% LATTICE L18.44
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[45540, 54120, -3900; 54120, 64320, -4635; -3900, -4635, 334],[60, 15, 1],[1, -3, -13, -6, -2, 3; -2, 8, 38, 20, 10, 4; -16, 76, 375, 207, 115, 90],17,44]
%
% END OF LATTICE L18.44
%
%
% LATTICE L18.45
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3129240, 7080, 53040; 7080, -16, -120; 53040, -120, -899],[120, 8, 1],[2, -1, -1, -3, -1, 0; -15, 225, 94, 165, 6, -15; 120, -90, -72, -200, -60, 2],17,45]
%
% END OF LATTICE L18.45
%
%
% LATTICE L18.46
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-840, 14280, -1800; 14280, -226512, 28552; -1800, 28552, -3599],[120, 8, 1],[2, -1, -1, -3, -1, 0; -15, 450, 184, 315, 6, -15; -120, 3570, 1460, 2500, 48, -119],17,46]
%
% END OF LATTICE L18.46
%
%
% LATTICE L18.47
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-6547320, 1971360, 35640; 1971360, -593565, -10731; 35640, -10731, -194],[360, 3, 1],[21, -7, -3, 11, 6, 59; 70, -20, -10, 30, 19, 192; -15, -180, 2, 360, 51, 216],17,47]
%
% END OF LATTICE L18.47
%
%
% LATTICE L18.48
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-117808920, -23529240, 325440; -23529240, -4699347, 64998; 325440, 64998, -899],[360, 3, 1],[-74, 3, 5, -2, -31, -181; 445, -20, -30, 15, 188, 1092; 5385, -360, -359, 360, 2370, 13428],17,48]
%
% END OF LATTICE L18.48
%
%
% LATTICE L18.49
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[13023840, 5914860, -1048920; 5914860, 2686280, -476380; -1048920, -476380, 84483],[60, 20, 1],[487, -2, 206, 536, 2590, 1514; -1416, 6, -599, -1559, -7533, -4403; -1938, 9, -820, -2136, -10320, -6030],17,49]
%
% END OF LATTICE L18.49
%
%
% LATTICE L18.50
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[18300, -2520, 6780; -2520, 380, -960; 6780, -960, 2533],[60, 20, 1],[-28, -11, -21, -25, -109, -35; 87, 33, 63, 77, 339, 109; 108, 42, 80, 96, 420, 135],17,50]
%
% END OF LATTICE L18.50
%
%
% LATTICE L18.51
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[260730, -108450, -19980; -108450, 45105, 8310; -19980, 8310, 1531],[90, 15, 1],[-1, 3, 13, 2, 2, -1; 7, -16, -60, -7, 2, 16; -51, 126, 495, 64, 15, -100],17,51]
%
% END OF LATTICE L18.51
%
%
% LATTICE L18.52
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[90, 0, 0; 0, -1785, -330; 0, -330, -61],[90, 15, 1],[0, 1, 1, 1, 0, -1; -5, 2, 9, 18, 11, 0; 27, -12, -50, -99, -60, 0],17,52]
%
% END OF LATTICE L18.52
%
%
% LATTICE L18.53
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-861000, -436920, 10080; -436920, -221715, 5115; 10080, 5115, -118],[120, 15, 1],[-2, 1, 5, -1, -3, -29; 6, -4, -14, 6, 11, 96; 89, -88, -180, 174, 220, 1680],17,53]
%
% END OF LATTICE L18.53
%
%
% LATTICE L18.54
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-109800, 2280, 1320; 2280, -45, -30; 1320, -30, -13],[120, 15, 1],[1, -1, -1, 1, 5, 19; 31, -32, -31, 32, 158, 596; 29, -28, -30, 27, 140, 540],17,54]
%
% END OF LATTICE L18.54
%
%
% LATTICE L18.55
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2852640, 138420, 705060; 138420, 6720, 34212; 705060, 34212, 174263],[180, 12, 1],[-22, 196, 205, 1463, 127, 31; -5, 10, 13, 105, 11, 3; 90, -795, -832, -5940, -516, -126],17,55]
%
% END OF LATTICE L18.55
%
%
% LATTICE L18.56
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[728859240, -16073460, 178003260; -16073460, 354480, -3925488; 178003260, -3925488, 43472263],[180, 12, 1],[-8967, 121, -1091, -8119, -8555, -5259; -295, 5, -36, -270, -284, -174; 36690, -495, 4464, 33220, 35004, 21518],17,56]
%
% END OF LATTICE L18.56
%
%
% LATTICE L18.57
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1232460, 42480, 301860; 42480, 1500, 10404; 301860, 10404, 73933],[180, 12, 1],[-574, -81, -53, -363, -415, -143; 25, 5, 3, 15, 17, 6; 2340, 330, 216, 1480, 1692, 583],17,57]
%
% END OF LATTICE L18.57
%
%
% LATTICE L18.58
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[158040, -8820, 39780; -8820, 492, -2220; 39780, -2220, 10013],[180, 12, 1],[-2, 7, -1, -47, -13, -8; -35, -10, 0, -30, -16, -21; 0, -30, 4, 180, 48, 27],17,58]
%
% END OF LATTICE L18.58
%
%
% LATTICE L18.59
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-72540, -183240, -31500; -183240, -459105, -78840; -31500, -78840, -13537],[180, 15, 1],[52, -51, -107, 33, 254, 325; -182, 178, 375, -115, -887, -1136; 939, -918, -1935, 593, 4575, 5860],17,59]
%
% END OF LATTICE L18.59
%
%
% LATTICE L18.60
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[482130, 29700, 235710; 29700, 1830, 14520; 235710, 14520, 115237],[90, 30, 1],[-3, -58, -124, -143, -30, 22; 1, 13, 29, 36, 11, 0; 6, 117, 250, 288, 60, -45],17,60]
%
% END OF LATTICE L18.60
%
%
% LATTICE L18.61
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-17100, 5220, -540; 5220, -1590, 165; -540, 165, -17],[180, 15, 1],[0, -1, 0, 2, 3, 7; 1, -2, -1, 3, 7, 24; 9, 12, -10, -36, -30, 0],17,61]
%
% END OF LATTICE L18.61
%
%
% LATTICE L18.62
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[3272490, 158400, 1598490; 158400, 7590, 77370; 1598490, 77370, 780803],[90, 30, 1],[371, 19, -2629, -778, -2001, -426; 25, 1, -180, -53, -136, -29; -762, -39, 5400, 1598, 4110, 875],17,62]
%
% END OF LATTICE L18.62
%
%
% LATTICE L18.63
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2794860, -383400, -72720; -383400, 52590, 9975; -72720, 9975, 1892],[180, 15, 1],[-1, 3, 13, 2, 2, -1; 28, -76, -315, -45, -31, 42; -186, 516, 2160, 314, 240, -260],17,63]
%
% END OF LATTICE L18.63
%
%
% LATTICE L18.64
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-37620, 65160, -10440; 65160, -112560, 18015; -10440, 18015, -2882],[180, 15, 1],[25, -27, -60, -101, -49, 29; 50, -56, -122, -204, -98, 60; 222, -252, -545, -909, -435, 270],17,64]
%
% END OF LATTICE L18.64
%
%
% LATTICE L18.65
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-85320, 83280, -30120; 83280, -81288, 29400; -30120, 29400, -10633],[120, 24, 1],[-19, 42, 67, 148, 9, -7; -5, 25, 34, 65, 2, -5; 40, -50, -96, -240, -20, 6],17,65]
%
% END OF LATTICE L18.65
%
%
% LATTICE L18.66
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-4213080, -1126200, 106200; -1126200, -298800, 28392; 106200, 28392, -2677],[120, 24, 1],[82, -791, -1015, -1829, -33, 79; -5, 50, 64, 115, 2, -5; 3200, -30850, -39588, -71340, -1288, 3081],17,66]
%
% END OF LATTICE L18.66
%
%
% LATTICE L18.67
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-360, 8220, -2220; 8220, -138480, 37140; -2220, 37140, -9959],[60, 60, 1],[-12, -1, 165, 149, 129, 83; -27, -3, 364, 334, 292, 190; -98, -11, 1320, 1212, 1060, 690],17,67]
%
% END OF LATTICE L18.67
%
%
% LATTICE L18.68
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2100, -19380, 5220; -19380, 190440, -51300; 5220, -51300, 13819],[60, 60, 1],[-1, 0, -2, -4, -6, -5; -82, -7, -81, -217, -367, -344; -304, -26, -300, -804, -1360, -1275],17,68]
%
% END OF LATTICE L18.68
%
%
% LATTICE L18.69
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-7800, 6960, -3360; 6960, -6200, 3000; -3360, 3000, -1447],[120, 40, 1],[-13, 26, 71, 32, 31, -7; -3, 9, 22, 9, 6, -3; 24, -42, -120, -56, -60, 10],17,69]
%
% END OF LATTICE L18.69
%
%
% LATTICE L18.70
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-948840, 329760, 39000; 329760, -111080, -13560; 39000, -13560, -1603],[120, 40, 1],[-77, 445, 993, 374, 155, -74; -3, 18, 40, 15, 6, -3; -1848, 10674, 23820, 8972, 3720, -1775],17,70]
%
% END OF LATTICE L18.70
%
%
% LATTICE L18.71
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2283480, -2359440, -394560; -2359440, -2436690, -407445; -394560, -407445, -68129],[360, 15, 1],[83, -83, -167, 55, 207, 525; -581, 580, 1170, -384, -1447, -3672; 2994, -2988, -6030, 1978, 7455, 18920],17,71]
%
% END OF LATTICE L18.71
%
%
% LATTICE L18.72
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-447480, -736920, -118080; -736920, -1213050, -194355; -118080, -194355, -31139],[360, 15, 1],[49, -45, -52, 14, 227, 297; -173, 160, 183, -50, -806, -1052; 894, -828, -945, 259, 4170, 5440],17,72]
%
% END OF LATTICE L18.72
%
%
% LATTICE L18.73
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-34200, -11880, -1080; -11880, -4125, -375; -1080, -375, -34],[360, 15, 1],[-1, 1, 1, -1, -2, -17; 2, -4, -2, 6, 7, 48; 9, 12, -10, -36, -15, 0],17,73]
%
% END OF LATTICE L18.73
%
%
% LATTICE L18.74
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1299960, 128520, 22680; 128520, -12675, -2235; 22680, -2235, -394],[360, 15, 1],[3, -1, -1, 1, 9, 43; 124, -44, -41, 45, 382, 1800; -531, 192, 175, -198, -1650, -7740],17,74]
%
% END OF LATTICE L18.74
%
%
% LATTICE L18.75
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-32815440, -5913720, -831960; -5913720, -1065720, -149928; -831960, -149928, -21091],[360, 24, 1],[-33, 344, 145, 766, 9, -73; 200, -2065, -871, -4605, -55, 438; -120, 1110, 472, 2520, 36, -234],17,75]
%
% END OF LATTICE L18.75
%
%
% LATTICE L18.76
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-87377040, -17531640, 6124320; -17531640, -3517608, 1228800; 6124320, 1228800, -429247],[360, 24, 1],[167, -1641, -701, -3784, -67, 164; -1000, 9845, 4205, 22695, 401, -984; -480, 4770, 2036, 10980, 192, -477],17,76]
%
% END OF LATTICE L18.76
%
%
% LATTICE L18.77
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-111381840, 18542520, -316440; 18542520, -3086904, 52680; -316440, 52680, -899],[360, 24, 1],[-7, 76, 97, 58, 3, -5; -40, 455, 579, 345, 17, -30; 120, -90, -216, -200, -60, 2],17,77]
%
% END OF LATTICE L18.77
%
%
% LATTICE L18.78
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-456117840, -91351800, 1281240; -91351800, -18296040, 256608; 1281240, 256608, -3599],[360, 24, 1],[7, -151, -187, -108, -3, 5; -40, 905, 1119, 645, 17, -30; -360, 10770, 13212, 7540, 144, -359],17,78]
%
% END OF LATTICE L18.78
%
%
% LATTICE L18.79
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[20473200, 1976940, -3489120; 1976940, 190920, -336900; -3489120, -336900, 594643],[180, 60, 1],[-49, -317, -1356, -1630, -460, -22; 158, 1022, 4371, 5253, 1481, 69; -198, -1281, -5480, -6588, -1860, -90],17,79]
%
% END OF LATTICE L18.79
%
%
% LATTICE L18.80
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[28461600, -1753020, -8238960; -1753020, 107760, 507300; -8238960, 507300, 2384867],[180, 60, 1],[-452, -30, 6319, 1885, 4871, 1041; 1375, 91, -19227, -5735, -14819, -3167; -1854, -123, 25920, 7732, 19980, 4270],17,80]
%
% END OF LATTICE L18.80
%
%
% LATTICE L18.81
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[280011960, -30969900, -90567900; -30969900, 3425340, 10017000; -90567900, 10017000, 29293553],[180, 60, 1],[-583, -49, -581, -517, -2619, -817; 1607, 136, 1590, 1420, 7202, 2249; -2352, -198, -2340, -2084, -10560, -3295],17,81]
%
% END OF LATTICE L18.81
%
%
% LATTICE L18.82
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[230220, -3240, -58860; -3240, 300, 1020; -58860, 1020, 15193],[180, 60, 1],[100, 25, 49, 247, 397, 386; -307, -77, -151, -759, -1219, -1185; 408, 102, 200, 1008, 1620, 1575],17,82]
%
% END OF LATTICE L18.82
%
%
% LATTICE L18.83
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-240, 1320, -360; 1320, -6120, 1680; -360, 1680, -461],[120, 120, 1],[-1, 1, 10, 5, 2, -1; 2, -9, -63, -25, -5, 8; 8, -34, -240, -96, -20, 30],17,83]
%
% END OF LATTICE L18.83
%
%
% LATTICE L18.84
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-891120, 12460440, -3321840; 12460440, -174231000, 46448400; -3321840, 46448400, -12382721],[120, 120, 1],[-3, 3, 31, 16, 7, -1; -286, 519, 4273, 1911, 587, -252; -1072, 1946, 16020, 7164, 2200, -945],17,84]
%
% END OF LATTICE L18.84
%
%
% LATTICE L18.85
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3600, -2520, 5400; -2520, 840, -3000; 5400, -3000, 9553],[360, 120, 1],[31, -25, -90, -139, -58, 29; -250, 203, 729, 1125, 469, -234; -96, 78, 280, 432, 180, -90],17,85]
%
% END OF LATTICE L18.85
%
%
% LATTICE L18.86
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2673360, -20480040, -854280; -20480040, -156877800, -6543840; -854280, -6543840, -272963],[360, 120, 1],[63, -124, -332, -437, -126, 62; 194, -379, -1017, -1341, -389, 189; -4848, 9474, 25420, 33516, 9720, -4725],17,86]
%
% END OF LATTICE L18.86
%
%
% LATTICE L18.87
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-720, 2520, -1080; 2520, -7800, 3360; -1080, 3360, -1447],[360, 120, 1],[-1, 3, 22, 3, 2, -1; 10, -17, -147, -23, -25, 4; 24, -42, -360, -56, -60, 10],17,87]
%
% END OF LATTICE L18.87
%
%
% LATTICE L18.88
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3603600, 1857240, 76320; 1857240, -948840, -39000; 76320, -39000, -1603],[360, 120, 1],[-1, 6, 40, 5, 2, -1; 74, -427, -2859, -359, -149, 71; -1848, 10674, 71460, 8972, 3720, -1775],17,88]
%
% END OF LATTICE L18.88
%

\medskip%
%------------------------------WEYL-GROUP-W19--------------------------------
%
\leavevmode\llap{}%
$W_{19\phantom{0}}$%
\qquad\llap{12} lattices, $\chi=3$%
\hfill%
$4222$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L19.1
%
\leavevmode%
${L_{19.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{2}{}5\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{2\rightarrow N_{19}}%
\EasyButWeakLineBreak%
{${2}\above{1pt}{1pt}{*}{4}{4}\above{1pt}{1pt}{b}{2}{10}\above{1pt}{1pt}{l}{2}{12}\above{1pt}{1pt}{r}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-27060\\300\\540
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
300\\-2\\-7
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
540\\-7\\-10
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\27\\35
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-26\\-36
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2\\-55\\-70
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\24\\36
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-27060, 300, 540; 300, -2, -7; 540, -7, -10],[60, 1, 1],[1, -1, -2, 1; 27, -26, -55, 24; 35, -36, -70, 36],18,1]
%
% END OF LATTICE L19.1
%
%
% LATTICE L19.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-15, 0, 0; 0, 1, 0; 0, 0, 1],[15, 1, 1],[0, 0, -1, -1; -1, 1, 0, -3; 1, 0, -5, -3],18,2]
%
% END OF LATTICE L19.2
%
%
% LATTICE L19.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3030, 255, 1065; 255, -21, -90; 1065, -90, -374],[15, 3, 1],[-4, 5, 7, -2; -10, 9, 20, -3; -9, 12, 15, -5],18,3]
%
% END OF LATTICE L19.3
%
%
% LATTICE L19.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-4665, -300, 1785; -300, -10, 115; 1785, 115, -683],[15, 5, 1],[-25, 23, 10, -23; 2, -1, -1, 0; -65, 60, 26, -60],18,4]
%
% END OF LATTICE L19.4
%
%
% LATTICE L19.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-11580, 360, -3180; 360, -6, 105; -3180, 105, -866],[60, 3, 1],[-14, 15, 28, -5; -53, 58, 105, -20; 45, -48, -90, 16],18,5]
%
% END OF LATTICE L19.5
%
%
% LATTICE L19.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[30, -150, -15; -150, 1005, 105; -15, 105, 11],[15, 15, 1],[1, 2, 0, 0; 0, 2, 1, 1; 0, -15, -9, -10],18,6]
%
% END OF LATTICE L19.6
%
%
% LATTICE L19.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[422760, -24300, -113640; -24300, 1400, 6532; -113640, 6532, 30547],[60, 4, 1],[-15, -23, -43, -25; 1, 2, 0, 0; -56, -86, -160, -93],18,7]
%
% END OF LATTICE L19.7
%
%
% LATTICE L19.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[60, 0, 0; 0, -10, -5; 0, -5, -2],[60, 5, 1],[0, -1, 0, 1; 2, -2, -1, 0; -5, 0, 2, 0],18,8]
%
% END OF LATTICE L19.8
%
%
% LATTICE L19.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1515720, 159660, -390180; 159660, 16824, -41100; -390180, -41100, 100441],[60, 12, 1],[-31, -45, -139, -26; 1, 2, 0, 0; -120, -174, -540, -101],18,9]
%
% END OF LATTICE L19.9
%
%
% LATTICE L19.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[6420, -300, 300; -300, -30, -15; 300, -15, 14],[60, 15, 1],[5, -3, -2, 1; 2, -2, -1, 0; -105, 60, 42, -20],18,10]
%
% END OF LATTICE L19.10
%
%
% LATTICE L19.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[600, -180, 300; -180, 40, -80; 300, -80, 143],[60, 20, 1],[0, 3, -1, -4; 1, -7, 3, 12; 0, -10, 4, 15],18,11]
%
% END OF LATTICE L19.11
%
%
% LATTICE L19.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[120, 7500, -1980; 7500, 400920, -105840; -1980, -105840, 27941],[60, 60, 1],[1, 2, 0, 0; 0, -103, 19, 33; 0, -390, 72, 125],18,12]
%
% END OF LATTICE L19.12
%

\medskip%
%------------------------------WEYL-GROUP-W20--------------------------------
%
\leavevmode\llap{}%
$W_{20\phantom{0}}$%
\qquad\llap{22} lattices, $\chi=27$%
\hfill%
$\infty222242$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L20.1
%
\leavevmode%
${L_{20.1}}$%
{} : {$1\above{1pt}{1pt}{2}{{\rm II}}4\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{2}{}17\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2\rightarrow N_{20}}%
\EasyButWeakLineBreak%
{${68}\above{1pt}{1pt}{1,0}{\infty b}{68}\above{1pt}{1pt}{r}{2}{2}\above{1pt}{1pt}{b}{2}{34}\above{1pt}{1pt}{l}{2}{4}\above{1pt}{1pt}{r}{2}{2}\above{1pt}{1pt}{*}{4}{4}\above{1pt}{1pt}{*}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-53788\\1156\\2652
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1156\\-24\\-59
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2652\\-59\\-126
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-7\\-170\\-68
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
75\\1768\\748
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
17\\402\\169
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
132\\3128\\1309
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
17\\404\\168
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4\\96\\39
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-5\\-118\\-50
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-53788, 1156, 2652; 1156, -24, -59; 2652, -59, -126],[68, 1, 1],[-7, 75, 17, 132, 17, 4, -5; -170, 1768, 402, 3128, 404, 96, -118; -68, 748, 169, 1309, 168, 39, -50],19,1]
%
% END OF LATTICE L20.1
%
\hbox{}\par\smallskip%
%
% LATTICE L20.2
%
\leavevmode%
${L_{20.2}}$%
{} : {$1\above{1pt}{1pt}{2}{2}8\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{2}{}17\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2\rightarrow N'_{15}}%
\EasyButWeakLineBreak%
{${34}\above{1pt}{1pt}{4,3}{\infty b}{136}\above{1pt}{1pt}{l}{2}{1}\above{1pt}{1pt}{}{2}{17}\above{1pt}{1pt}{r}{2}{8}\above{1pt}{1pt}{l}{2}{1}\above{1pt}{1pt}{}{4}{2}\above{1pt}{1pt}{s}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2045576\\8160\\11424
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
8160\\-30\\-47
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
11424\\-47\\-63
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-4\\-289\\-510
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
59\\4216\\7548
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7\\501\\895
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
56\\4012\\7157
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
15\\1076\\1916
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\144\\255
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2\\-143\\-256
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-2045576, 8160, 11424; 8160, -30, -47; 11424, -47, -63],[136, 1, 1],[-4, 59, 7, 56, 15, 2, -2; -289, 4216, 501, 4012, 1076, 144, -143; -510, 7548, 895, 7157, 1916, 255, -256],19,2]
%
% END OF LATTICE L20.2
%
\hbox{}\par\smallskip%
%
% LATTICE L20.3
%
\leavevmode%
${L_{20.3}}$%
{} : {$1\above{1pt}{1pt}{-2}{2}8\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{2}{}17\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{m}%
\EasyButWeakLineBreak%
{${34}\above{1pt}{1pt}{4,3}{\infty a}{136}\above{1pt}{1pt}{s}{2}{4}\above{1pt}{1pt}{*}{2}{68}\above{1pt}{1pt}{s}{2}{8}\above{1pt}{1pt}{s}{2}{4}\above{1pt}{1pt}{*}{4}{2}\above{1pt}{1pt}{b}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-62696\\-15640\\952
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-15640\\-3901\\237
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
952\\237\\-14
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-40\\170\\153
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-175\\748\\748
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-21\\90\\94
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-87\\374\\408
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\-4\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7\\-30\\-32
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\4\\-1
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-62696, -15640, 952; -15640, -3901, 237; 952, 237, -14],[136, 1, 1],[-40, -175, -21, -87, 1, 7, -1; 170, 748, 90, 374, -4, -30, 4; 153, 748, 94, 408, 0, -32, -1],19,3]
%
% END OF LATTICE L20.3
%
%
% LATTICE L20.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[17, 0, 0; 0, 0, -1; 0, -1, 0],[17, 1, 1],[-1, 1, 0, -6, -1, -2, -1; 0, 0, -1, -17, -2, -3, -1; -17, 0, 1, -17, -4, -11, -8],19,4]
%
% END OF LATTICE L20.4
%
%
% LATTICE L20.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[10846, 578, 9554; 578, 31, 509; 9554, 509, 8416],[34, 1, 1],[-15, -155, -33, -266, -37, -14, -1; 0, 102, 25, 221, 34, 15, 2; 17, 170, 36, 289, 40, 15, 1],19,5]
%
% END OF LATTICE L20.5
%
%
% LATTICE L20.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-31348, -15164, 476; -15164, -7335, 230; 476, 230, -7],[68, 1, 1],[-40, -175, -21, -87, 1, 7, -1; 85, 374, 45, 187, -2, -15, 2; 68, 374, 49, 221, 2, -17, -3],19,6]
%
% END OF LATTICE L20.6
%
%
% LATTICE L20.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-293930, 4522, -143922; 4522, -60, 2214; -143922, 2214, -70471],[34, 2, 1],[366, -1356, -643, -5141, -344, -183, 184; -17, 51, 25, 204, 14, 8, -7; -748, 2771, 1314, 10506, 703, 374, -376],19,7]
%
% END OF LATTICE L20.7
%
%
% LATTICE L20.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1089972, -21352, 266424; -21352, 420, -5220; 266424, -5220, 65123],[68, 4, 1],[590, 821, 165, 701, 7, 15, 91; -1275, -1785, -361, -1547, -17, -33, -196; -2516, -3502, -704, -2992, -30, -64, -388],19,8]
%
% END OF LATTICE L20.8
%
%
% LATTICE L20.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[276896, -64532, 62424; -64532, 15048, -14548; 62424, -14548, 14073],[68, 4, 1],[23, 303, 280, 2382, 88, 146, 7; 0, 34, 33, 289, 11, 19, 1; -102, -1309, -1208, -10268, -379, -628, -30],19,9]
%
% END OF LATTICE L20.9
%
%
% LATTICE L20.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-561, -289, -34; -289, -136, -17; -34, -17, -2],[17, 17, 1],[-1, -1, -2, 0, 1, 0, -3; -1, -2, -8, -2, 0, 2, -1; 22, 29, 85, 13, -17, -17, 51],19,10]
%
% END OF LATTICE L20.10
%
%
% LATTICE L20.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1150526, -35122, -542946; -35122, -1071, -16575; -542946, -16575, -256222],[34, 17, 1],[16, -107, -438, -208, -479, -132, 124; -14, 104, 419, 197, 448, 119, -120; -33, 220, 901, 428, 986, 272, -255],19,11]
%
% END OF LATTICE L20.11
%
%
% LATTICE L20.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-67320, 4216, -5576; 4216, -240, 360; -5576, 360, -457],[136, 8, 1],[30, -117, -55, -437, -29, -15, 16; 119, -476, -223, -1768, -117, -60, 65; -272, 1054, 496, 3944, 262, 136, -144],19,12]
%
% END OF LATTICE L20.12
%
%
% LATTICE L20.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-273904, -7208, 4760; -7208, -40, 96; 4760, 96, -77],[136, 8, 1],[-15, 67, 31, 244, 16, 8, -9; -238, 1071, 495, 3893, 255, 127, -144; -1224, 5474, 2532, 19924, 1306, 652, -736],19,13]
%
% END OF LATTICE L20.13
%
%
% LATTICE L20.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2244, 544, 68; 544, -119, -17; 68, -17, -2],[68, 17, 1],[0, -1, -3, -1, -1, 1, 1; -1, -4, -8, -2, 0, 2, -1; 5, -10, -51, -21, -34, 17, 34],19,14]
%
% END OF LATTICE L20.14
%
%
% LATTICE L20.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[286144, -1220770, -592178; -1220770, 5216926, 2530654; -592178, 2530654, 1227583],[34, 34, 1],[1, 5, 36, 17, 20, 15, 1; -480, -2579, -18777, -8941, -10625, -8111, -610; 990, 5319, 38726, 18440, 21913, 16728, 1258],19,15]
%
% END OF LATTICE L20.15
%
%
% LATTICE L20.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-284444, 10812, 8500; 10812, -408, -323; 8500, -323, -254],[68, 17, 1],[1, 3, 5, 0, -7, -8, -5; -2, 0, 10, 8, 28, 16, 2; 36, 100, 153, -11, -272, -289, -170],19,16]
%
% END OF LATTICE L20.16
%
%
% LATTICE L20.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-17000, 2040, 136; 2040, -238, -17; 136, -17, -1],[136, 17, 1],[0, -1, -3, -1, -1, 1, 1; -1, -8, -20, -6, -4, 6, 3; 10, -20, -102, -42, -68, 34, 68],19,17]
%
% END OF LATTICE L20.17
%
%
% LATTICE L20.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-136, -272, -136; -272, -510, -255; -136, -255, -127],[136, 17, 1],[0, 3, 5, 2, 7, 0, -2; -1, 0, 5, 4, 28, 8, 1; 2, -4, -17, -11, -68, -17, 0],19,18]
%
% END OF LATTICE L20.18
%
%
% LATTICE L20.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[136, -884, -204; -884, 20468, 4760; -204, 4760, 1107],[68, 68, 1],[2, 3, 11, 3, 1, 1, 5; 41, 62, 222, 56, 8, 0, 95; -176, -266, -952, -240, -34, 0, -408],19,19]
%
% END OF LATTICE L20.19
%
%
% LATTICE L20.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1224, 23596, 5508; 23596, 663136, 154768; 5508, 154768, 36121],[68, 68, 1],[0, 2, 33, 17, 11, 19, 1; 7, 171, 2792, 1438, 932, 1634, 119; -30, -733, -11968, -6164, -3995, -7004, -510],19,20]
%
% END OF LATTICE L20.20
%
%
% LATTICE L20.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-4080, 39032, -2312; 39032, -371960, 22032; -2312, 22032, -1305],[136, 136, 1],[-1, 0, 5, 4, 7, 8, 1; -2, 7, 57, 27, 31, 17, -16; -32, 118, 952, 448, 510, 272, -272],19,21]
%
% END OF LATTICE L20.21
%
%
% LATTICE L20.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-4080, -25432, -5848; -25432, -157352, -36176; -5848, -36176, -8317],[136, 136, 1],[1, 3, 15, 4, 0, -8, -9; -2, -23, -143, -53, -39, 17, 64; 8, 98, 612, 228, 170, -68, -272],19,22]
%
% END OF LATTICE L20.22
%

\medskip%
%------------------------------WEYL-GROUP-W21--------------------------------
%
\leavevmode\llap{}%
$W_{21\phantom{0}}$%
\qquad\llap{6} lattices, $\chi=18$%
\hfill%
$422422\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L21.1
%
\leavevmode%
${L_{21.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{2}{}19\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{2\rightarrow N_{21}}%
\EasyButWeakLineBreak%
{${2}\above{1pt}{1pt}{*}{4}{4}\above{1pt}{1pt}{b}{2}{38}\above{1pt}{1pt}{s}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-26372\\-18468\\1672
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-18468\\-12930\\1171
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1672\\1171\\-106
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3191\\-1368\\35112
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2233\\-958\\24563
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-203\\87\\-2234
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-4\\2\\-41
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7\\-2\\88
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
139\\-57\\1558
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-26372, -18468, 1672; -18468, -12930, 1171; 1672, 1171, -106],[76, 1, 1],[-4, 7, 139, 25, 7, -6; 2, -2, -57, -11, -4, 0; -41, 88, 1558, 272, 66, -95],20,1]
%
% END OF LATTICE L21.1
%
%
% LATTICE L21.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-19, 0, 0; 0, 1, 0; 0, 0, 1],[19, 1, 1],[0, 0, -13, -3, -1, -6; -1, 1, 0, -2, -2, -19; 1, 0, -57, -13, -4, -19],20,2]
%
% END OF LATTICE L21.2
%
%
% LATTICE L21.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[590824, 1900, -159904; 1900, 8, -516; -159904, -516, 43279],[76, 4, 1],[0, -53, -1607, -273, -38, -122; 1, -184, -5624, -958, -135, -437; 0, -198, -6004, -1020, -142, -456],20,3]
%
% END OF LATTICE L21.3
%
%
% LATTICE L21.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-646, -1007, 1216; -1007, -1349, 1710; 1216, 1710, -2133],[19, 19, 1],[-65, 66, -133, -715, -326, -127; -96, 95, -179, -975, -452, -178; -114, 114, -221, -1197, -551, -216],20,4]
%
% END OF LATTICE L21.4
%
%
% LATTICE L21.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3904652, -464360, 51604; -464360, -55214, 6137; 51604, 6137, -682],[76, 19, 1],[96, 5, -3, -3, 57, 34; -11, -4, 0, 2, -2, -3; 7163, 342, -227, -209, 4294, 2545],20,5]
%
% END OF LATTICE L21.5
%
%
% LATTICE L21.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[152, 14972, -3952; 14972, 34750696, -9170540; -3952, -9170540, 2420061],[76, 76, 1],[-625, -55, -1, 1, -153, -207; -24789, -2156, -38, 0, -6107, -8225; -93936, -8170, -144, 0, -23142, -31168],20,6]
%
% END OF LATTICE L21.6
%

\medskip%
%------------------------------WEYL-GROUP-W22--------------------------------
%
\leavevmode\llap{}%
$W_{22\phantom{0}}$%
\qquad\llap{12} lattices, $\chi=4$%
\hfill%
$2622$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L22.1
%
\leavevmode%
${L_{22.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}7\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{2\rightarrow N_{22}}%
\EasyButWeakLineBreak%
{${4}\above{1pt}{1pt}{r}{2}{6}\above{1pt}{1pt}{}{6}{2}\above{1pt}{1pt}{b}{2}{42}\above{1pt}{1pt}{l}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-25788\\588\\252
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
588\\-10\\-7
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
252\\-7\\-2
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-20\\-56
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-21\\-54
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\20\\55
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\42\\105
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-25788, 588, 252; 588, -10, -7; 252, -7, -2],[84, 1, 1],[-1, -1, 1, 2; -20, -21, 20, 42; -56, -54, 55, 105],21,1]
%
% END OF LATTICE L22.1
%
%
% LATTICE L22.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[42, 21, 0; 21, 10, 0; 0, 0, 1],[21, 1, 1],[0, -2, 3, 13; 0, 3, -5, -21; 1, 0, -2, 0],21,2]
%
% END OF LATTICE L22.2
%
%
% LATTICE L22.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-35763, 1218, -11739; 1218, -39, 399; -11739, 399, -3853],[21, 3, 1],[220, 6, -39, 389; -216, -7, 40, -378; -693, -19, 123, -1225],21,3]
%
% END OF LATTICE L22.3
%
%
% LATTICE L22.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-82110, -1323, -23856; -1323, -14, -385; -23856, -385, -6931],[21, 7, 1],[509, 49, -94, 382; -154, -12, 27, -117; -1743, -168, 322, -1308],21,4]
%
% END OF LATTICE L22.4
%
%
% LATTICE L22.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-38388, 588, 924; 588, -6, -15; 924, -15, -22],[84, 3, 1],[1, 1, -1, -2; 8, 10, -9, -21; 36, 35, -36, -70],21,5]
%
% END OF LATTICE L22.5
%
%
% LATTICE L22.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1586760, -29988, 376320; -29988, 568, -7112; 376320, -7112, 89249],[84, 4, 1],[5, 37, 38, 100; 1, 0, 3, 21; -21, -156, -160, -420],21,6]
%
% END OF LATTICE L22.6
%
%
% LATTICE L22.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[4326, -95403, -29379; -95403, 2113734, 650916; -29379, 650916, 200447],[21, 21, 1],[-28, 1, 2, -8; 5321, -56, -569, 1455; -17283, 182, 1848, -4726],21,7]
%
% END OF LATTICE L22.7
%
%
% LATTICE L22.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-11172, 924, -1260; 924, -70, 105; -1260, 105, -142],[84, 7, 1],[7, 5, -6, -1; 8, 3, -6, 0; -56, -42, 49, 9],21,8]
%
% END OF LATTICE L22.8
%
%
% LATTICE L22.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[634872, -28812, 150192; -28812, 1320, -6816; 150192, -6816, 35531],[84, 12, 1],[22, 36, 37, 53; 0, 1, 2, 0; -93, -152, -156, -224],21,9]
%
% END OF LATTICE L22.9
%
%
% LATTICE L22.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-588, 168, 84; 168, -42, -21; 84, -21, -10],[84, 21, 1],[1, 0, -1, 0; 4, 3, -5, -1; 0, -7, 0, 2],21,10]
%
% END OF LATTICE L22.10
%
%
% LATTICE L22.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[403368, -12012, -106344; -12012, 392, 3192; -106344, 3192, 28055],[84, 28, 1],[-22, -61, -88, -58; 67, 183, 267, 177; -91, -252, -364, -240],21,11]
%
% END OF LATTICE L22.11
%
%
% LATTICE L22.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1176, 2100, 504; 2100, 3864, 924; 504, 924, 221],[84, 84, 1],[0, 1, 2, 0; -5, 13, 39, -1; 21, -56, -168, 4],21,12]
%
% END OF LATTICE L22.12
%

\medskip%
%------------------------------WEYL-GROUP-W23--------------------------------
%
\leavevmode\llap{}%
$W_{23\phantom{0}}$%
\qquad\llap{88} lattices, $\chi=48$%
\hfill%
$\infty2222\infty2222\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L23.1
%
\leavevmode%
${L_{23.1}}$%
{} : {$1\above{1pt}{1pt}{2}{{\rm II}}4\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{1}{}3\above{1pt}{1pt}{1}{}9\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}7\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{23\rightarrow N_{23},3,2}%
\EasyButWeakLineBreak%
{${84}\above{1pt}{1pt}{3,2}{\infty b}{84}\above{1pt}{1pt}{r}{2}{18}\above{1pt}{1pt}{b}{2}{12}\above{1pt}{1pt}{*}{2}{4}\above{1pt}{1pt}{*}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-16363116\\948024\\53676
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
948024\\-54906\\-3111
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
53676\\-3111\\-176
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
505343\\4563888\\73432800
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-29696\\-268193\\-4315200
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1632\\-14739\\-237151
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-333\\-3010\\-48342
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-899\\-8120\\-130620
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-403\\-3639\\-58572
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-259\\-2338\\-37656
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-49\\-442\\-7130
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-16363116, 948024, 53676; 948024, -54906, -3111; 53676, -3111, -176],[252, 3, 1],[-333, -899, -403, -259, -49, -115, 3, 19, 3, -15; -3010, -8120, -3639, -2338, -442, -1036, 28, 171, 26, -136; -48342, -130620, -58572, -37656, -7130, -16758, 420, 2772, 456, -2170],22,1]
%
% END OF LATTICE L23.1
%
\hbox{}\par\smallskip%
%
% LATTICE L23.2
%
\leavevmode%
${L_{23.2}}$%
{} : {$1\above{1pt}{1pt}{-2}{2}8\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{-}{}9\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{-2}{}7\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{3m,3,2}%
\EasyButWeakLineBreak%
{${42}\above{1pt}{1pt}{12,11}{\infty b}{168}\above{1pt}{1pt}{s}{2}{36}\above{1pt}{1pt}{*}{2}{24}\above{1pt}{1pt}{b}{2}{2}\above{1pt}{1pt}{s}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-8168328\\-56448\\-59472
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-56448\\-390\\-411
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-59472\\-411\\-433
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
6299\\88200\\-945000
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
43\\601\\-6450
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
46\\644\\-6901
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-4\\-133\\672
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-27\\-448\\4116
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-13\\-156\\1926
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-9\\-68\\1296
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\1\\136
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-8168328, -56448, -59472; -56448, -390, -411; -59472, -411, -433],[504, 3, 1],[-4, -27, -13, -9, -1, -3, -1, 1, 1, 0; -133, -448, -156, -68, 1, 35, 56, -12, -44, -15; 672, 4116, 1926, 1296, 136, 378, 84, -126, -96, 14],22,2]
%
% END OF LATTICE L23.2
%
\hbox{}\par\smallskip%
%
% LATTICE L23.3
%
\leavevmode%
${L_{23.3}}$%
{} : {$1\above{1pt}{1pt}{2}{2}8\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{-}{}9\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{-2}{}7\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{32\rightarrow N'_{16},3,m}%
\EasyButWeakLineBreak%
{${42}\above{1pt}{1pt}{12,11}{\infty a}{168}\above{1pt}{1pt}{l}{2}{9}\above{1pt}{1pt}{}{2}{24}\above{1pt}{1pt}{r}{2}{2}\above{1pt}{1pt}{b}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-22810536\\3272976\\-990864
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3272976\\-469623\\142176
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-990864\\142176\\-43039
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-6504625\\-39054960\\20738592
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
932578\\5599369\\-2973324
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-283932\\-1704780\\905255
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2617\\-15715\\8337
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-13491\\-81004\\43008
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2972\\-17844\\9477
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3747\\-22496\\11952
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-338\\-2029\\1079
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-22810536, 3272976, -990864; 3272976, -469623, 142176; -990864, 142176, -43039],[504, 3, 1],[-2617, -13491, -2972, -3747, -338, -729, 107, 104, -77, -140; -15715, -81004, -17844, -22496, -2029, -4375, 644, 624, -464, -841; 8337, 43008, 9477, 11952, 1079, 2331, -336, -333, 240, 445],22,3]
%
% END OF LATTICE L23.3
%
%
% LATTICE L23.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[21, 0, 0; 0, 0, -1; 0, -1, 0],[21, 1, 1],[-1, 1, 0, -1, -1, -13, -29, -8, -7, -1; 0, 0, -1, -3, -2, -21, -42, -11, -9, -1; -21, 0, 1, -3, -5, -84, -210, -61, -57, -10],22,4]
%
% END OF LATTICE L23.4
%
%
% LATTICE L23.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[42, 0, 42; 0, 360, -6101; 42, -6101, 103437],[42, 1, 1],[1919, 4591, 655, 1199, 199, 377, 1, 1, 113, 129; -32739, -78288, -11167, -20436, -3389, -6405, 0, -17, -1932, -2203; -1932, -4620, -659, -1206, -200, -378, 0, -1, -114, -130],22,5]
%
% END OF LATTICE L23.5
%
%
% LATTICE L23.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-3444, 84, 924; 84, -2, -21; 924, -21, -199],[84, 1, 1],[25, 139, 21, 41, 4, 10, 1, -1, -1, 1; 1659, 9114, 1371, 2664, 257, 630, 42, -63, -48, 70; -63, -336, -50, -96, -9, -21, 0, 2, 0, -3],22,6]
%
% END OF LATTICE L23.6
%
%
% LATTICE L23.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-1269996, 512484, 15120; 512484, -206790, -6101; 15120, -6101, -180],[84, 1, 1],[-13, -29, -4, -7, -1, -1, 1, 0, -1, -1; 1092, 2940, 439, 846, 160, 378, 0, -19, -6, 50; -38094, -102060, -15212, -29256, -5506, -12894, 84, 644, 120, -1778],22,7]
%
% END OF LATTICE L23.7
%
%
% LATTICE L23.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-3125640, 1848, 35280; 1848, -1, -21; 35280, -21, -398],[168, 1, 1],[25, 139, 21, 41, 4, 10, 1, -1, -1, 1; 3318, 18228, 2742, 5328, 514, 1260, 84, -126, -96, 140; 2037, 11340, 1714, 3348, 327, 819, 84, -82, -84, 81],22,8]
%
% END OF LATTICE L23.8
%
%
% LATTICE L23.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-6888, -6888, 3528; -6888, -6846, 3485; 3528, 3485, -1763],[168, 1, 1],[-1004, -5615, -425, -1663, -163, -410, -41, 21, 47, -39; 1995, 11172, 846, 3312, 325, 819, 84, -42, -96, 77; 1932, 10836, 821, 3216, 316, 798, 84, -41, -96, 74],22,9]
%
% END OF LATTICE L23.9
%
%
% LATTICE L23.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[1638, -252, 63; -252, 21, -66; 63, -66, -176],[63, 3, 1],[-433, -1044, -895, -273, -45, -78, 22, 19, -19, -28; -2611, -6293, -5394, -1645, -271, -469, 133, 114, -115, -169; 819, 1974, 1692, 516, 85, 147, -42, -36, 36, 53],22,10]
%
% END OF LATTICE L23.10
%
%
% LATTICE L23.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-8181558, 474012, 53676; 474012, -27453, -3111; 53676, -3111, -352],[126, 3, 1],[-333, -899, -403, -259, -49, -115, 3, 19, 3, -15; -3010, -8120, -3639, -2338, -442, -1036, 28, 171, 26, -136; -24171, -65310, -29286, -18828, -3565, -8379, 210, 1386, 228, -1085],22,11]
%
% END OF LATTICE L23.11
%
%
% LATTICE L23.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-718452, -11844, -13104; -11844, -195, -216; -13104, -216, -239],[252, 3, 1],[-4, -27, -13, -9, -1, -3, -1, 1, 1, 0; -133, -658, -285, -176, -15, -28, 14, 9, -8, -8; 336, 2058, 963, 648, 68, 189, 42, -63, -48, 7],22,12]
%
% END OF LATTICE L23.12
%
%
% LATTICE L23.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-16401, 315, -4368; 315, -6, 84; -4368, 84, -1163],[21, 3, 1],[47, 114, 98, 30, 15, 9, -2, -2, 2, 9; 294, 749, 657, 206, 110, 77, -7, -21, 6, 49; -154, -371, -318, -97, -48, -28, 7, 6, -7, -30],22,13]
%
% END OF LATTICE L23.13
%
%
% LATTICE L23.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2857596, 768726, -1406118; 768726, -206790, 378262; -1406118, 378262, -691899],[42, 2, 1],[19307, 25805, 7686, 7384, 2773, 6467, -31, -322, -20, 909; 1092, 1470, 439, 423, 160, 378, 0, -19, -3, 50; -38640, -51639, -15380, -14775, -5548, -12936, 63, 644, 39, -1820],22,14]
%
% END OF LATTICE L23.14
%
%
% LATTICE L23.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3386754, 1024968, 1149078; 1024968, -310185, -347757; 1149078, -347757, -389866],[42, 3, 1],[-6414, -17155, -7666, -4911, -2768, -2154, 19, 322, 15, -904; 364, 980, 439, 282, 160, 126, 0, -19, -2, 50; -19229, -51436, -22986, -14726, -8301, -6461, 56, 966, 46, -2709],22,15]
%
% END OF LATTICE L23.15
%
%
% LATTICE L23.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-4389, 2646, -1218; 2646, -1540, 735; -1218, 735, -338],[21, 7, 1],[-239, -613, -1258, -1187, -213, -65, 5, 42, -29, -91; -9, -24, -50, -48, -9, -3, 0, 2, 0, -3; 843, 2160, 4431, 4179, 749, 228, -18, -147, 105, 322],22,16]
%
% END OF LATTICE L23.16
%
%
% LATTICE L23.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1197, -189, 0; -189, 21, -3; 0, -3, -1],[63, 3, 1],[-15, -20, -4, -2, 1, 1, -8, -4, -6, -7; -98, -133, -27, -14, 6, 7, -49, -25, -38, -45; 252, 336, 67, 33, -18, -21, 126, 65, 99, 117],22,17]
%
% END OF LATTICE L23.17
%
%
% LATTICE L23.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-239484, 1260, 3948; 1260, -6, -21; 3948, -21, -65],[84, 3, 1],[4, 27, 13, 9, 3, 3, 1, -1, -1, 0; 112, 686, 321, 216, 68, 63, 14, -21, -16, 7; 203, 1400, 678, 472, 159, 161, 56, -54, -56, -3],22,18]
%
% END OF LATTICE L23.18
%
%
% LATTICE L23.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[30418542, 256242, 13036464; 256242, 2160, 109818; 13036464, 109818, 5587033],[42, 6, 1],[-14734, -17623, -15085, -4602, -4582, -2892, -3, -23, -434, -2972; -10913, -13048, -11167, -3406, -3389, -2135, 0, -17, -322, -2203; 34594, 41377, 35418, 10805, 10758, 6790, 7, 54, 1019, 6978],22,19]
%
% END OF LATTICE L23.19
%
%
% LATTICE L23.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2862468, 38892, 228900; 38892, -528, -3111; 228900, -3111, -18302],[84, 3, 1],[-333, -899, -403, -259, -147, -115, 3, 19, 3, -45; -6790, -18368, -8240, -5300, -3014, -2366, 56, 392, 68, -910; -3010, -8120, -3639, -2338, -1326, -1036, 28, 171, 26, -408],22,20]
%
% END OF LATTICE L23.20
%
%
% LATTICE L23.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-52024854, -362082, -8308734; -362082, -2520, -57827; -8308734, -57827, -1326963],[42, 7, 1],[-143, -391, -411, -797, -153, -53, -1, 19, 13, -43; -2721, -7290, -7606, -14628, -2753, -921, 6, 322, 60, -889; 1014, 2766, 2905, 5628, 1078, 372, 6, -133, -84, 308],22,21]
%
% END OF LATTICE L23.21
%
%
% LATTICE L23.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[364911960, 512484, 86883720; 512484, 720, 122020; 86883720, 122020, 20686581],[84, 4, 1],[-18224, -21800, -12441, -11387, -1890, -3581, -5, -19, -1073, -1225; -32739, -39144, -22334, -20436, -3389, -6405, 0, -34, -1932, -2203; 76734, 91791, 52384, 47946, 7958, 15078, 21, 80, 4518, 5158],22,22]
%
% END OF LATTICE L23.22
%
%
% LATTICE L23.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[32088, 16044, 7896; 16044, 8020, 3948; 7896, 3948, 1943],[84, 4, 1],[382, 857, 237, 104, 30, 31, -31, -1, 14, 29; 105, 252, 72, 33, 11, 21, 0, 0, 3, 7; -1764, -3990, -1108, -489, -144, -168, 126, 4, -63, -132],22,23]
%
% END OF LATTICE L23.23
%
%
% LATTICE L23.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-633402, -291564, 24570; -291564, -134211, 11310; 24570, 11310, -953],[126, 3, 1],[-291, -395, -40, -41, 19, 25, -137, -36, -111, -133; 581, 784, 79, 80, -39, -49, 280, 73, 224, 267; -609, -882, -94, -108, 27, 63, -210, -62, -204, -261],22,24]
%
% END OF LATTICE L23.24
%
%
% LATTICE L23.25
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[42, 5733, 1764; 5733, 834141, 256641; 1764, 256641, 78961],[21, 21, 1],[51, 122, 731, 223, 111, 10, 0, 1, 21, 72; 303, 736, 4440, 1366, 697, 67, 4, 0, 114, 413; -986, -2395, -14448, -4445, -2268, -218, -13, 0, -371, -1344],22,25]
%
% END OF LATTICE L23.25
%
%
% LATTICE L23.26
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2722776, 3024, 18816; 3024, -3, -21; 18816, -21, -130],[168, 3, 1],[4, 27, 13, 9, 3, 3, 1, -1, -1, 0; 224, 1372, 642, 432, 136, 126, 28, -42, -32, 14; 539, 3668, 1770, 1228, 411, 413, 140, -138, -140, -3],22,26]
%
% END OF LATTICE L23.26
%
%
% LATTICE L23.27
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1968120, 232680, 50904; 232680, -27501, -6027; 50904, -6027, -1306],[168, 3, 1],[-1217, -6267, -1380, -1739, -470, -337, 51, 48, -37, -196; -8694, -44772, -9859, -12424, -3358, -2408, 364, 343, -264, -1400; -7315, -37660, -8292, -10448, -2823, -2023, 308, 288, -224, -1179],22,27]
%
% END OF LATTICE L23.27
%
%
% LATTICE L23.28
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-112812, 33852, -1680; 33852, -10157, 504; -1680, 504, -25],[84, 7, 1],[2, 5, 3, 1, -1, -1, -1, 1, 7, 2; 18, 66, 57, 84, 2, -3, -6, 3, 36, 13; 225, 978, 931, 1596, 105, 6, -54, -7, 252, 126],22,28]
%
% END OF LATTICE L23.28
%
%
% LATTICE L23.29
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[3683568, 2303826, 1773576; 2303826, 1448118, 1109248; 1773576, 1109248, 853947],[42, 14, 1],[176173, 210667, 420719, 384995, 127721, 34507, 13, 641, 36365, 82959; -276, -330, -659, -603, -200, -54, 0, -1, -57, -130; -365538, -437109, -872942, -798819, -265006, -71598, -27, -1330, -75453, -172130],22,29]
%
% END OF LATTICE L23.29
%
%
% LATTICE L23.30
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1128372, -35112, 276444; -35112, -1092, 8603; 276444, 8603, -67726],[84, 7, 1],[-223, -611, -642, -1243, -237, -79, 7, 38, 35, -65; 1074, 2916, 3054, 5892, 1114, 366, -36, -174, -132, 326; -774, -2124, -2233, -4326, -826, -276, 24, 133, 126, -224],22,30]
%
% END OF LATTICE L23.30
%
%
% LATTICE L23.31
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[85302, -3276, 42462; -3276, 2514, -2028; 42462, -2028, 21203],[126, 6, 1],[18967, 14313, 3200, 2086, 115, 227, 4881, 2284, 3398, 8111; -6419, -4844, -1083, -706, -39, -77, -1652, -773, -1150, -2745; -38598, -29127, -6512, -4245, -234, -462, -9933, -4648, -6915, -16506],22,31]
%
% END OF LATTICE L23.31
%
%
% LATTICE L23.32
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2772, 1008, 756; 1008, -366, -273; 756, -273, -199],[252, 3, 1],[20, -5, -2, 3, 13, 78, 397, 58, 109, 29; 70, -14, -7, 8, 42, 259, 1330, 195, 368, 99; -21, 0, 2, 0, -9, -63, -336, -50, -96, -27],22,32]
%
% END OF LATTICE L23.32
%
%
% LATTICE L23.33
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1570535694, -9491202, 772451820; -9491202, 57360, -4668150; 772451820, -4668150, 379922479],[126, 6, 1],[-136020, -161135, -137363, -41698, -13644, -25022, 93, -673, -4314, -9362; -5495, -6503, -5541, -1681, -549, -1001, 7, -27, -175, -379; 276486, 327537, 279216, 84759, 27734, 50862, -189, 1368, 8769, 19030],22,33]
%
% END OF LATTICE L23.33
%
%
% LATTICE L23.34
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-140364, -21168, -7056; -21168, -3192, -1065; -7056, -1065, -352],[252, 3, 1],[19, -131, -33, -99, -115, -243, -317, -31, -29, 19; -112, 784, 197, 590, 684, 1442, 1876, 183, 170, -114; -42, 252, 65, 198, 234, 504, 672, 67, 66, -36],22,34]
%
% END OF LATTICE L23.34
%
%
% LATTICE L23.35
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1481550, 1784580, -730674; 1784580, 2172177, -895923; -730674, -895923, 371408],[42, 21, 1],[47731, 114153, 341959, 208615, 103811, 9349, 7, 521, 19705, 67429; -95554, -228526, -684577, -417632, -207822, -18716, -14, -1043, -39448, -134988; -136597, -326684, -978621, -597016, -297087, -26755, -20, -1491, -56392, -192969],22,35]
%
% END OF LATTICE L23.35
%
%
% LATTICE L23.36
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2603328, -1533084, 595056; -1533084, 902952, -350424; 595056, -350424, 136015],[84, 12, 1],[-10715, -12692, -21638, -6568, -3223, -1969, 8, -106, -680, -2213; -301, -357, -609, -185, -91, -56, 0, -3, -19, -62; 46102, 54607, 93096, 28258, 13866, 8470, -35, 456, 2926, 9522],22,36]
%
% END OF LATTICE L23.36
%
%
% LATTICE L23.37
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[905352, -50652, 214704; -50652, 2892, -12012; 214704, -12012, 50917],[84, 12, 1],[3415, 8275, 7127, 1096, 1119, 764, 83, 37, 98, 672; 35, 84, 72, 11, 11, 7, 0, 0, 1, 7; -14392, -34874, -30036, -4619, -4716, -3220, -350, -156, -413, -2832],22,37]
%
% END OF LATTICE L23.37
%
%
% LATTICE L23.38
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1300152, 3360, 8064; 3360, -7, -21; 8064, -21, -50],[168, 7, 1],[1, 1, -1, -7, -2, -2, -5, -3, -1, 1; 18, 12, -18, -96, -22, -12, 12, 42, 144, 28; 153, 156, -154, -1092, -315, -321, -828, -518, -252, 147],22,38]
%
% END OF LATTICE L23.38
%
%
% LATTICE L23.39
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-717528, 13272, 214872; 13272, -245, -3976; 214872, -3976, -64341],[168, 7, 1],[44, -13, -15, 61, 73, 182, 917, 467, 1747, 153; 387, -120, -131, 576, 659, 1629, 8184, 4163, 15552, 1357; 123, -36, -42, 168, 203, 507, 2556, 1302, 4872, 427],22,39]
%
% END OF LATTICE L23.39
%
%
% LATTICE L23.40
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[126, -63, 0; -63, -11193, -1575; 0, -1575, -221],[63, 21, 1],[46, 102, 589, 171, 24, 3, -4, -1, 25, 25; 89, 196, 1128, 326, 45, 5, -8, 0, 50, 49; -636, -1401, -8064, -2331, -322, -36, 57, 0, -357, -350],22,40]
%
% END OF LATTICE L23.40
%
%
% LATTICE L23.41
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[63, 0, 0; 0, -4956, 735; 0, 735, -109],[63, 21, 1],[1, 1, 1, 0, -1, 0, 1, 3, 4, 4; 26, 43, 70, 47, 0, -4, 1, 18, 41, 66; 174, 288, 469, 315, 0, -27, 6, 119, 273, 441],22,41]
%
% END OF LATTICE L23.41
%
%
% LATTICE L23.42
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2680944, -63672, 1680; -63672, -1512, 40; 1680, 40, -1],[168, 8, 1],[13, 4, 0, -1, -1, 1, 10, 4, 5, 3; -504, -147, 3, 42, 40, -42, -399, -159, -198, -118; 1512, 714, 92, -18, -80, 0, 798, 340, 450, 296],22,42]
%
% END OF LATTICE L23.42
%
%
% LATTICE L23.43
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3245424, 77784, 75768; 77784, -1848, -1808; 75768, -1808, -1765],[168, 8, 1],[239, 206, 49, 17, 1, -43, -10, 7, 11, 27; -9996, -8631, -2055, -714, -44, 1806, 441, -285, -456, -1126; 20496, 17682, 4208, 1461, 88, -3696, -882, 592, 939, 2312],22,43]
%
% END OF LATTICE L23.43
%
%
% LATTICE L23.44
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-24518088, 8177904, 98784; 8177904, -2727705, -32949; 98784, -32949, -398],[504, 3, 1],[50, -9, -5, 5, 29, 181, 933, 137, 259, 70; 140, -28, -14, 16, 84, 518, 2660, 390, 736, 198; 819, 84, -82, -84, 243, 2037, 11340, 1714, 3348, 981],22,44]
%
% END OF LATTICE L23.44
%
%
% LATTICE L23.45
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-451391976, 64548288, 892080; 64548288, -9230295, -127566; 892080, -127566, -1763],[504, 3, 1],[146, -5, -7, 3, 67, 456, 2413, 179, 685, 191; 875, -28, -42, 16, 399, 2723, 14420, 1070, 4096, 1143; 10563, -504, -503, 360, 5031, 33705, 177576, 13151, 50232, 13941],22,45]
%
% END OF LATTICE L23.45
%
%
% LATTICE L23.46
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-116340, -3948, 3108; -3948, -126, 105; 3108, 105, -83],[84, 21, 1],[1, -1, -2, 5, 10, 7, 33, 98, 59, 14; 3, -2, -7, 8, 21, 16, 78, 235, 144, 36; 41, -40, -84, 196, 399, 281, 1328, 3948, 2380, 567],22,46]
%
% END OF LATTICE L23.46
%
%
% LATTICE L23.47
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-16375028124, 39767806806, 19326557838; 39767806806, -96578671266, -46935786156; 19326557838, -46935786156, -22810088327],[42, 42, 1],[-907, -1215, -7606, -2438, -2753, -307, 1, 322, 10, -889; 1448, 1518, 8523, 2381, 1724, -2, -72, 153, 511, 2614; -3748, -4153, -23982, -6965, -5880, -256, 149, -42, -1043, -6132],22,47]
%
% END OF LATTICE L23.47
%
%
% LATTICE L23.48
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[421092, 18816, 17388; 18816, 840, 777; 17388, 777, 718],[84, 21, 1],[1, -3, -19, -21, -27, -9, -13, -29, -11, 3; -2, 8, 56, 68, 98, 38, 64, 160, 76, 10; -22, 64, 399, 434, 546, 176, 244, 525, 182, -84],22,48]
%
% END OF LATTICE L23.48
%
%
% LATTICE L23.49
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[4293408, 1290156, -140700; 1290156, 387688, -42280; -140700, -42280, 4611],[84, 28, 1],[197, 227, 892, 800, 125, 29, -1, 12, 104, 101; -702, -810, -3185, -2859, -448, -105, 3, -43, -369, -359; -426, -501, -1988, -1806, -294, -78, -3, -28, -210, -210],22,49]
%
% END OF LATTICE L23.49
%
%
% LATTICE L23.50
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[408072, 14532, -86436; 14532, 700, -2940; -86436, -2940, 18413],[84, 28, 1],[1447, 3437, 6853, 3134, 1043, 298, 53, 127, 356, 702; -4587, -10896, -21726, -9936, -3307, -945, -168, -402, -1128, -2225; 6060, 14394, 28700, 13125, 4368, 1248, 222, 532, 1491, 2940],22,50]
%
% END OF LATTICE L23.50
%
%
% LATTICE L23.51
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[877590, 348264, -52920; 348264, 138201, -21000; -52920, -21000, 3191],[126, 21, 1],[-1, 3, 19, 21, 9, 9, 13, 29, 11, -1; 13, -34, -201, -206, -79, -65, -70, -111, -2, 27; 69, -174, -1008, -1008, -371, -279, -246, -252, 168, 161],22,51]
%
% END OF LATTICE L23.51
%
%
% LATTICE L23.52
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-630, -2394, -378; -2394, -7203, -1176; -378, -1176, -191],[126, 21, 1],[-4, 5, 15, 57, 82, 30, 47, 37, 47, -4; -7, 10, 28, 104, 147, 53, 82, 64, 80, -9; 51, -72, -203, -756, -1071, -387, -600, -469, -588, 63],22,52]
%
% END OF LATTICE L23.52
%
%
% LATTICE L23.53
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[8020656, -380268, -2015748; -380268, 18048, 95568; -2015748, 95568, 506597],[252, 12, 1],[32, 1048, 995, 1497, 1810, 4287, 3271, 1473, 971, 41; 7, 175, 165, 247, 297, 700, 532, 239, 157, 6; 126, 4137, 3928, 5910, 7146, 16926, 12915, 5816, 3834, 162],22,53]
%
% END OF LATTICE L23.53
%
%
% LATTICE L23.54
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[6282142776, -18982404, -1596167748; -18982404, 57360, 4823052; -1596167748, 4823052, 405554533],[252, 12, 1],[70233, 83201, 141853, 43061, 7045, 12920, -48, 695, 4455, 4834; -5495, -6503, -11082, -3362, -549, -1001, 7, -54, -350, -379; 276486, 327537, 558432, 169518, 27734, 50862, -189, 2736, 17538, 19030],22,54]
%
% END OF LATTICE L23.54
%
%
% LATTICE L23.55
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[4351284, 19152, -1104012; 19152, 228, -4860; -1104012, -4860, 280111],[252, 12, 1],[12552, 30421, 26203, 4030, 1372, 2813, 309, 137, 360, 823; 245, 595, 513, 79, 27, 56, 7, 3, 7, 16; 49476, 119910, 103284, 15885, 5408, 11088, 1218, 540, 1419, 3244],22,55]
%
% END OF LATTICE L23.55
%
%
% LATTICE L23.56
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[855288, 28476, -214452; 28476, 948, -7140; -214452, -7140, 53771],[252, 12, 1],[-3, -11, 1, 5, 25, 94, 193, 51, 21, 14; 91, 14, 0, 8, 63, 343, 854, 248, 116, 123; 0, -42, 4, 21, 108, 420, 882, 236, 99, 72],22,56]
%
% END OF LATTICE L23.56
%
%
% LATTICE L23.57
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-232680, -120288, 6216; -120288, -62181, 3213; 6216, 3213, -166],[168, 21, 1],[-2, 1, 5, -3, -11, -9, -45, -137, -85, -22; 6, -4, -14, 16, 42, 32, 156, 470, 288, 72; 41, -40, -84, 196, 399, 281, 1328, 3948, 2380, 567],22,57]
%
% END OF LATTICE L23.57
%
%
% LATTICE L23.58
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-936264, 8232, 4368; 8232, -63, -42; 4368, -42, -19],[168, 21, 1],[1, -1, -1, 5, 10, 7, 33, 49, 59, 14; 47, -48, -47, 240, 477, 333, 1568, 2327, 2800, 663; 125, -124, -126, 616, 1239, 869, 4100, 6090, 7336, 1743],22,58]
%
% END OF LATTICE L23.58
%
%
% LATTICE L23.59
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-78288, -18648, -6048; -18648, -4440, -1440; -6048, -1440, -467],[168, 24, 1],[-1, -3, -3, -1, -1, 1, 3, 3, 1, 1; -140, -91, -53, -8, 12, 14, -35, -55, -28, -66; 448, 322, 204, 38, -24, -56, 70, 132, 74, 192],22,59]
%
% END OF LATTICE L23.59
%
%
% LATTICE L23.60
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2844240, -347592, -154056; -347592, -42408, -18792; -154056, -18792, -8327],[168, 24, 1],[85, 73, 52, 6, 1, -15, -3, 8, 4, 29; -6776, -5803, -4127, -475, -72, 1190, 217, -661, -323, -2322; 13720, 11746, 8352, 961, 144, -2408, -434, 1344, 655, 4704],22,60]
%
% END OF LATTICE L23.60
%
%
% LATTICE L23.61
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-260316, 629496, -102816; 629496, -1515129, 247590; -102816, 247590, -40457],[252, 21, 1],[76, -75, -155, 369, 249, 525, 2479, 7367, 4439, 352; -266, 262, 543, -1288, -870, -1835, -8666, -25755, -15520, -1231; -1821, 1794, 3717, -8820, -5957, -12564, -59334, -176337, -106260, -8428],22,61]
%
% END OF LATTICE L23.61
%
%
% LATTICE L23.62
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[4777794, 189504, 2356074; 189504, 7518, 93450; 2356074, 93450, 1161851],[126, 42, 1],[-3, -82, -299, -490, -1313, -497, -418, -701, -510, -187; 1, 16, 54, 83, 207, 73, 58, 94, 65, 15; 6, 165, 602, 987, 2646, 1002, 843, 1414, 1029, 378],22,62]
%
% END OF LATTICE L23.62
%
%
% LATTICE L23.63
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-40572, -6804, 1008; -6804, -1113, 168; 1008, 168, -25],[252, 21, 1],[4, 17, 16, 27, 5, 0, -1, 0, 5, 7; 10, 46, 45, 80, 18, 1, -2, -1, 8, 15; 225, 978, 931, 1596, 315, 6, -54, -7, 252, 378],22,63]
%
% END OF LATTICE L23.63
%
%
% LATTICE L23.64
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[12636666, -760032, 6220620; -760032, 45570, -374136; 6220620, -374136, 3062209],[126, 42, 1],[707, 28, -7114, -6547, -8097, -11141, -10462, -55490, -14321, -2337; -31, -1, 315, 289, 357, 491, 461, 2445, 631, 103; -1440, -57, 14490, 13335, 16492, 22692, 21309, 113022, 29169, 4760],22,64]
%
% END OF LATTICE L23.64
%
%
% LATTICE L23.65
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1755180, 563472, -83664; 563472, 180894, -26859; -83664, -26859, 3988],[252, 21, 1],[-1, 3, 19, 21, 9, 9, 13, 29, 11, -1; 4, -4, -3, 22, 24, 46, 104, 303, 178, 26; 6, 36, 378, 588, 350, 498, 972, 2646, 1428, 154],22,65]
%
% END OF LATTICE L23.65
%
%
% LATTICE L23.66
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-105588, -180936, -30996; -180936, -308742, -52941; -30996, -52941, -9076],[252, 21, 1],[-259, -405, -318, -401, 41, 37, -39, -126, -487, -707; -520, -812, -637, -802, 84, 74, -80, -255, -982, -1422; 3918, 6120, 4802, 6048, -630, -558, 600, 1918, 7392, 10710],22,66]
%
% END OF LATTICE L23.66
%
%
% LATTICE L23.67
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1512, -18228, -4368; -18228, 447216, 107268; -4368, 107268, 25729],[84, 84, 1],[1, 0, -21, -19, -35, -16, -15, -159, -41, -10; -129, -6, 2578, 2380, 4421, 2029, 1906, 20222, 5220, 1279; 538, 25, -10752, -9926, -18438, -8462, -7949, -84336, -21770, -5334],22,67]
%
% END OF LATTICE L23.67
%
%
% LATTICE L23.68
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[3444, -49308, -11676; -49308, 753480, 178416; -11676, 178416, 42247],[84, 84, 1],[-1, 0, -2, -2, -11, -7, -16, -94, -14, -13; 160, 9, 159, 217, 1312, 887, 2085, 12405, 1877, 1829; -676, -38, -672, -917, -5544, -3748, -8810, -52416, -7931, -7728],22,68]
%
% END OF LATTICE L23.68
%
%
% LATTICE L23.69
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-162960, -38808, -16464; -38808, -9240, -3920; -16464, -3920, -1663],[168, 56, 1],[1, 1, 1, -1, -3, -5, -5, -9, -7, -1; 6, -27, -87, -120, -82, -60, -27, -21, 12, 28; -24, 54, 196, 294, 224, 192, 114, 140, 42, -56],22,69]
%
% END OF LATTICE L23.69
%
%
% LATTICE L23.70
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-670992, -242760, -115416; -242760, -87528, -41608; -115416, -41608, -19779],[168, 56, 1],[-7, -1, 10, 14, 33, 41, 35, 58, 20, 1; 510, 57, -773, -1047, -2434, -3000, -2547, -4207, -1443, -56; -1032, -114, 1568, 2121, 4928, 6072, 5154, 8512, 2919, 112],22,70]
%
% END OF LATTICE L23.70
%
%
% LATTICE L23.71
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-520632, 573048, -94752; 573048, -627690, 103845; -94752, 103845, -17179],[504, 21, 1],[35, -35, -71, 173, 116, 244, 1151, 3419, 2059, 163; -245, 244, 498, -1204, -809, -1703, -8036, -23874, -14380, -1139; -1674, 1668, 3402, -8232, -5530, -11640, -54924, -163170, -98280, -7784],22,71]
%
% END OF LATTICE L23.71
%
%
% LATTICE L23.72
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3647448, 5775336, -997416; 5775336, -9095898, 1572291; -997416, 1572291, -271741],[504, 21, 1],[813, -805, -820, 3997, 2682, 5645, 26637, 39568, 47667, 3776; -2561, 2536, 2583, -12592, -8449, -17783, -83912, -124647, -150160, -11895; -17802, 17628, 17955, -87528, -58730, -123612, -583284, -866439, -1043784, -82684],22,72]
%
% END OF LATTICE L23.72
%
%
% LATTICE L23.73
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-81144, -68544, 2016; -68544, -57855, 1701; 2016, 1701, -50],[504, 21, 1],[-1, 1, 1, -3, -8, -6, -29, -29, -53, -13; 2, -4, -2, 16, 30, 20, 92, 90, 160, 36; 27, -96, -28, 420, 693, 435, 1944, 1876, 3276, 693],22,73]
%
% END OF LATTICE L23.73
%
%
% LATTICE L23.74
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-4393368, -312480, 49392; -312480, -22197, 3507; 49392, 3507, -554],[504, 21, 1],[3, -1, -1, 5, 16, 13, 65, 33, 123, 32; -164, 52, 55, -256, -852, -698, -3500, -1779, -6640, -1734; -771, 240, 259, -1176, -3969, -3261, -16368, -8323, -31080, -8127],22,74]
%
% END OF LATTICE L23.74
%
%
% LATTICE L23.75
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-234864, 10584, 504; 10584, -456, -24; 504, -24, -1],[504, 24, 1],[-1, -3, -1, -1, -1, 1, 3, 1, 1, 1; -28, -49, -15, -14, -12, 14, 35, 11, 10, 6; 0, -462, -172, -186, -216, 168, 630, 220, 234, 288],22,75]
%
% END OF LATTICE L23.75
%
%
% LATTICE L23.76
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-32060952, -4050144, 237888; -4050144, -511512, 30048; 237888, 30048, -1765],[504, 24, 1],[253, 213, 50, 17, 1, -43, -3, 10, 13, 89; 1757, 1484, 349, 119, 9, -301, -28, 67, 89, 615; 64008, 53970, 12680, 4317, 288, -10920, -882, 2488, 3267, 22464],22,76]
%
% END OF LATTICE L23.76
%
%
% LATTICE L23.77
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-306899208, 47940480, 9269568; 47940480, -7488744, -1447992; 9269568, -1447992, -279977],[504, 24, 1],[2701, 1971, 1265, 243, -41, -321, 409, 775, 437, 381; 16219, 11830, 7590, 1457, -247, -1925, 2464, 4662, 2627, 2289; 5544, 4074, 2628, 510, -80, -672, 798, 1548, 882, 776],22,77]
%
% END OF LATTICE L23.77
%
%
% LATTICE L23.78
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1730736, -45864, 4032; -45864, -1176, 120; 4032, 120, -5],[504, 24, 1],[71, 66, 49, 6, 1, -15, -10, -1, 2, 7; -2114, -1967, -1461, -179, -30, 448, 301, 33, -59, -208; 6384, 5922, 4392, 537, 88, -1344, -882, -72, 183, 632],22,78]
%
% END OF LATTICE L23.78
%
%
% LATTICE L23.79
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[532252224, -20786220, 150518088; -20786220, 811776, -5878236; 150518088, -5878236, 42565715],[252, 84, 1],[2298, 1696, 5239, 3353, 32, 71, 673, 4237, 6123, 7075; -7241, -5342, -16497, -10553, -93, -224, -2123, -13363, -19307, -22302; -9126, -6735, -20804, -13314, -126, -282, -2673, -16828, -24318, -28098],22,79]
%
% END OF LATTICE L23.79
%
%
% LATTICE L23.80
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2178288, -30996, -530964; -30996, 2352, -9744; -530964, -9744, -127709],[252, 84, 1],[338, 13, -6809, -6263, -3872, -5327, -5002, -53059, -13693, -1117; -1039, -40, 20931, 19253, 11903, 16376, 15377, 163113, 42095, 3434; -1326, -51, 26712, 24570, 15190, 20898, 19623, 208152, 53718, 4382],22,80]
%
% END OF LATTICE L23.80
%
%
% LATTICE L23.81
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[9585451512, 355372668, 2158799580; 355372668, 13175148, 80035704; 2158799580, 80035704, 486196777],[252, 84, 1],[1271, 71, 1267, 1727, 3479, 7054, 16579, 98633, 14923, 4846; -3593, -202, -3558, -4867, -9813, -19907, -46798, -278442, -42133, -13687; -5052, -282, -5040, -6867, -13832, -28044, -65910, -392112, -59325, -19264],22,81]
%
% END OF LATTICE L23.81
%
%
% LATTICE L23.82
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[3165624, 41076, 773640; 41076, 588, 9996; 773640, 9996, 189101],[252, 84, 1],[809, 1937, 3875, 1779, 1795, 174, 29, 57, 187, 1154; -2453, -5872, -11746, -5392, -5439, -527, -88, -174, -568, -3501; -3180, -7614, -15232, -6993, -7056, -684, -114, -224, -735, -4536],22,82]
%
% END OF LATTICE L23.82
%
%
% LATTICE L23.83
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1008, -52584, -25872; -52584, -2619624, -1288896; -25872, -1288896, -634157],[168, 168, 1],[-7, -6, -30, -7, -1, 1, 0, -6, -5, -17; -976, -731, -3347, -668, 248, 122, -123, -1777, -1040, -2810; 1984, 1486, 6804, 1358, -504, -248, 250, 3612, 2114, 5712],22,83]
%
% END OF LATTICE L23.83
%
%
% LATTICE L23.84
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-284088, -301392, -143808; -301392, -319704, -152544; -143808, -152544, -72785],[168, 168, 1],[23, 18, 85, 9, -3, -3, 2, 35, 11, 63; -327, -245, -1122, -112, 83, 41, -41, -594, -174, -941; 640, 478, 2184, 217, -168, -80, 82, 1176, 343, 1848],22,84]
%
% END OF LATTICE L23.84
%
%
% LATTICE L23.85
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3881808, -584136, -82656; -584136, -87864, -12432; -82656, -12432, -1759],[504, 168, 1],[-7, -6, -10, -7, -1, 1, 0, -2, -5, -17; 298, 265, 451, 326, 78, -44, -11, 57, 182, 684; -1776, -1590, -2716, -1974, -504, 264, 78, -308, -1050, -4032],22,85]
%
% END OF LATTICE L23.85
%
%
% LATTICE L23.86
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1315944, -9828000, 182952; -9828000, -73398696, 1366344; 182952, 1366344, -25435],[504, 168, 1],[55, 42, 65, 20, -11, -7, 6, 31, 28, 155; -107, -77, -114, -32, 39, 13, -17, -74, -62, -321; -5352, -3834, -5656, -1575, 2016, 648, -870, -3752, -3129, -16128],22,86]
%
% END OF LATTICE L23.86
%
%
% LATTICE L23.87
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-7477848, -1104264, -3719016; -1104264, -162960, -549192; -3719016, -549192, -1849607],[504, 168, 1],[346, -27, -2131, -1650, -1782, -2100, -1727, -8393, -1858, 28; 1, 1, 3, -1, -3, -5, -5, -27, -7, -1; -696, 54, 4284, 3318, 3584, 4224, 3474, 16884, 3738, -56],22,87]
%
% END OF LATTICE L23.87
%
%
% LATTICE L23.88
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-809928, -72576, -29736; -72576, -6216, -2520; -29736, -2520, -1019],[504, 168, 1],[-3, -1, 8, 5, 13, 17, 15, 76, 9, 1; 181, 58, -501, -305, -787, -1025, -902, -4563, -539, -57; -360, -114, 1008, 609, 1568, 2040, 1794, 9072, 1071, 112],22,88]
%
% END OF LATTICE L23.88
%

\medskip%
%------------------------------WEYL-GROUP-W24--------------------------------
%
\leavevmode\llap{}%
$W_{24\phantom{0}}$%
\qquad\llap{44} lattices, $\chi=9$%
\hfill%
$22224$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L24.1
%
\leavevmode%
${L_{24.1}}$%
{} : {$1\above{1pt}{1pt}{2}{{\rm II}}4\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{2}{}7\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2\rightarrow N_{24}}%
\EasyButWeakLineBreak%
{${4}\above{1pt}{1pt}{*}{2}{28}\above{1pt}{1pt}{b}{2}{6}\above{1pt}{1pt}{b}{2}{14}\above{1pt}{1pt}{s}{2}{2}\above{1pt}{1pt}{*}{4}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-278796\\2436\\2856
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2436\\-20\\-27
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2856\\-27\\-26
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3\\-198\\-124
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3\\-196\\-126
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4\\264\\165
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
13\\854\\539
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\196\\125
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-278796, 2436, 2856; 2436, -20, -27; 2856, -27, -26],[84, 1, 1],[-3, -3, 4, 13, 3; -198, -196, 264, 854, 196; -124, -126, 165, 539, 125],23,1]
%
% END OF LATTICE L24.1
%
\hbox{}\par\smallskip%
%
% LATTICE L24.2
%
\leavevmode%
${L_{24.2}}$%
{} : {$1\above{1pt}{1pt}{2}{2}8\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{2}{}7\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2\rightarrow N'_{19}}%
\EasyButWeakLineBreak%
{${2}\above{1pt}{1pt}{b}{2}{56}\above{1pt}{1pt}{*}{2}{12}\above{1pt}{1pt}{*}{2}{28}\above{1pt}{1pt}{l}{2}{1}\above{1pt}{1pt}{}{4}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1129128\\-560616\\11088
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-560616\\-278347\\5504
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
11088\\5504\\-107
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
74\\-151\\-99
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
151\\-308\\-196
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-197\\402\\264
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-645\\1316\\854
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-75\\153\\98
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-1129128, -560616, 11088; -560616, -278347, 5504; 11088, 5504, -107],[168, 1, 1],[74, 151, -197, -645, -75; -151, -308, 402, 1316, 153; -99, -196, 264, 854, 98],23,2]
%
% END OF LATTICE L24.2
%
\hbox{}\par\smallskip%
%
% LATTICE L24.3
%
\leavevmode%
${L_{24.3}}$%
{} : {$1\above{1pt}{1pt}{-2}{2}8\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{2}{}7\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{m}%
\EasyButWeakLineBreak%
{${2}\above{1pt}{1pt}{l}{2}{56}\above{1pt}{1pt}{}{2}{3}\above{1pt}{1pt}{}{2}{7}\above{1pt}{1pt}{r}{2}{4}\above{1pt}{1pt}{*}{4}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-514248\\3024\\1848
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3024\\-17\\-12
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1848\\-12\\-5
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\119\\83
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
15\\1792\\1232
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\120\\81
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-119\\-84
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-120\\-82
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-514248, 3024, 1848; 3024, -17, -12; 1848, -12, -5],[168, 1, 1],[1, 15, 1, -1, -1; 119, 1792, 120, -119, -120; 83, 1232, 81, -84, -82],23,3]
%
% END OF LATTICE L24.3
%
%
% LATTICE L24.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-84, -21, 0; -21, -5, 0; 0, 0, 1],[21, 1, 1],[0, -2, 1, 15, 7; 0, 7, -3, -49, -23; 1, 0, -3, -7, -1],23,4]
%
% END OF LATTICE L24.4
%
%
% LATTICE L24.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[8778, 6888, -126; 6888, 5405, -99; -126, -99, 2],[42, 1, 1],[0, 571, 187, 167, -10; 0, -742, -243, -217, 13; 1, -756, -249, -224, 13],23,5]
%
% END OF LATTICE L24.5
%
%
% LATTICE L24.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-151284, 1260, 1932; 1260, -10, -17; 1932, -17, -23],[84, 1, 1],[1, 15, 2, -2, -1; 66, 980, 129, -133, -65; 35, 532, 72, -70, -36],23,6]
%
% END OF LATTICE L24.6
%
%
% LATTICE L24.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-76272, 1617, -24654; 1617, -30, 522; -24654, 522, -7969],[21, 3, 1],[-47, 328, 120, 550, 48; 24, -203, -69, -301, -23; 147, -1029, -376, -1722, -150],23,7]
%
% END OF LATTICE L24.7
%
%
% LATTICE L24.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-170310, 3738, -84000; 3738, -80, 1842; -84000, 1842, -41429],[42, 2, 1],[58, 810, 443, 267, -59; -99, -1309, -708, -413, 98; -122, -1701, -930, -560, 124],23,8]
%
% END OF LATTICE L24.8
%
%
% LATTICE L24.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-208866, 5040, 70686; 5040, -120, -1707; 70686, -1707, -23921],[42, 3, 1],[-43, -1215, -111, -202, 44; -99, -2618, -236, -413, 98; -120, -3402, -311, -567, 123],23,9]
%
% END OF LATTICE L24.9
%
%
% LATTICE L24.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-128667, -4620, -37212; -4620, -161, -1337; -37212, -1337, -10762],[21, 7, 1],[-62, 73, 526, 110, 60; 35, -34, -264, -58, -36; 210, -248, -1785, -373, -203],23,10]
%
% END OF LATTICE L24.10
%
%
% LATTICE L24.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-14028, 672, 2772; 672, -30, -141; 2772, -141, -517],[84, 3, 1],[8, 127, 6, -16, -9; 80, 1260, 59, -161, -89; 21, 336, 16, -42, -24],23,11]
%
% END OF LATTICE L24.11
%
%
% LATTICE L24.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-41412, 1680, 8820; 1680, -60, -387; 8820, -387, -1774],[84, 3, 1],[-43, -45, 19, 188, 44; -430, -448, 190, 1876, 438; -120, -126, 53, 525, 123],23,12]
%
% END OF LATTICE L24.12
%
%
% LATTICE L24.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[190092, -78498, 79086; -78498, 32430, -32658; 79086, -32658, 32903],[42, 6, 1],[5, -7029, -1537, -4126, 245; 0, -371, -81, -217, 13; -12, 16527, 3614, 9702, -576],23,13]
%
% END OF LATTICE L24.13
%
%
% LATTICE L24.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-416094, -7308, -60984; -7308, -91, -1071; -60984, -1071, -8938],[42, 7, 1],[120, 455, 862, 72, -119; 2, 0, -3, -1, -1; -819, -3104, -5880, -491, 812],23,14]
%
% END OF LATTICE L24.14
%
%
% LATTICE L24.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[6138384, -515172, 1453704; -515172, 43240, -122004; 1453704, -122004, 344269],[84, 4, 1],[9, 110, 194, 1044, 434; 0, 7, 9, 35, 13; -38, -462, -816, -4396, -1828],23,15]
%
% END OF LATTICE L24.15
%
%
% LATTICE L24.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1236984, -122052, 292656; -122052, 12052, -28876; 292656, -28876, 69239],[84, 4, 1],[115, 374, 205, 53, 39; 5, 14, 6, 0, 2; -484, -1575, -864, -224, -164],23,16]
%
% END OF LATTICE L24.16
%
%
% LATTICE L24.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[18690, -204351, -62958; -204351, 2237844, 689451; -62958, 689451, 212411],[21, 21, 1],[5, -30, -51, -23, 1; -653, 4052, 6862, 3072, -194; 2121, -13161, -22288, -9978, 630],23,17]
%
% END OF LATTICE L24.17
%
%
% LATTICE L24.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-216888, -105504, 16464; -105504, -51321, 8001; 16464, 8001, -1178],[168, 3, 1],[197, 375, -175, -1667, -187; -412, -784, 366, 3486, 391; -45, -84, 40, 378, 42],23,18]
%
% END OF LATTICE L24.18
%
%
% LATTICE L24.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-338520, 4200, -39144; 4200, -51, 504; -39144, 504, -4223],[168, 3, 1],[-26, -377, -8, 27, 25; -1341, -19432, -412, 1393, 1288; 81, 1176, 25, -84, -78],23,19]
%
% END OF LATTICE L24.19
%
%
% LATTICE L24.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1596, 336, 168; 336, -70, -35; 168, -35, -17],[84, 7, 1],[0, 1, 2, 0, -1; 3, 8, 9, -1, -5; -7, -8, 0, 2, 0],23,20]
%
% END OF LATTICE L24.20
%
%
% LATTICE L24.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-421428, 8904, 8904; 8904, -182, -189; 8904, -189, -188],[84, 7, 1],[-3, -3, 4, 7, 21; -16, -18, 21, 41, 125; -126, -124, 168, 290, 868],23,21]
%
% END OF LATTICE L24.21
%
%
% LATTICE L24.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[77959014, 44478, 37544010; 44478, 28, 21420; 37544010, 21420, 18080689],[42, 14, 1],[0, 8854, 40595, 5179, -2171; 1, -54, -249, -32, 13; 0, -18385, -84294, -10754, 4508],23,22]
%
% END OF LATTICE L24.22
%
%
% LATTICE L24.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[64220898, -49434, 22503726; -49434, 42, -17325; 22503726, -17325, 7885561],[42, 21, 1],[0, 14323, 10945, 4189, -1756; 1, -28754, -21973, -8410, 3525; 0, -40938, -31283, -11973, 5019],23,23]
%
% END OF LATTICE L24.23
%
%
% LATTICE L24.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[442848, 523236, 122892; 523236, 618216, 145200; 122892, 145200, 34103],[84, 12, 1],[-5, 50, 12, -18, -32; 0, 7, 3, 35, 13; 18, -210, -56, -84, 60],23,24]
%
% END OF LATTICE L24.24
%
%
% LATTICE L24.25
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[55608, 58548, 15204; 58548, 61644, 16008; 15204, 16008, 4157],[84, 12, 1],[21, 37, -1, -23, 11; 5, 14, 2, 0, 2; -96, -189, -4, 84, -48],23,25]
%
% END OF LATTICE L24.25
%
%
% LATTICE L24.26
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-182616, 33600, 4032; 33600, -6181, -742; 4032, -742, -89],[168, 7, 1],[-2, -1, 5, 3, 3; -5, -4, 12, 10, 12; -49, -12, 126, 52, 35],23,26]
%
% END OF LATTICE L24.26
%
%
% LATTICE L24.27
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-4998840, 14448, 28896; 14448, -35, -84; 28896, -84, -167],[168, 7, 1],[7, 9, 1, -1, -1; 83, 104, 9, -12, -10; 1169, 1504, 168, -167, -168],23,27]
%
% END OF LATTICE L24.27
%
%
% LATTICE L24.28
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-54768, -6888, 2352; -6888, -856, 296; 2352, 296, -101],[168, 8, 1],[-3, -3, 4, 19, 6; 2, 0, -3, -7, -1; -64, -70, 84, 420, 136],23,28]
%
% END OF LATTICE L24.28
%
%
% LATTICE L24.29
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3889200, 20664, 40656; 20664, -104, -216; 40656, -216, -425],[168, 8, 1],[-3, -3, 4, 31, 12; 2, 0, -3, -7, -1; -288, -287, 384, 2968, 1148],23,29]
%
% END OF LATTICE L24.29
%
%
% LATTICE L24.30
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-145572, 107940, 4872; 107940, -80031, -3612; 4872, -3612, -163],[84, 21, 1],[7, 11, 2, -2, -3; 17, 24, 3, -5, -5; -168, -204, -7, 51, 21],23,30]
%
% END OF LATTICE L24.30
%
%
% LATTICE L24.31
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-132636, 8652, 41328; 8652, -546, -2709; 41328, -2709, -12868],[84, 21, 1],[-45, -43, 20, 101, 301; -88, -86, 39, 201, 601; -126, -120, 56, 282, 840],23,31]
%
% END OF LATTICE L24.31
%
%
% LATTICE L24.32
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-124770702, 302327718, 146928936; 302327718, -732558876, -356017956; 146928936, -356017956, -173021977],[42, 42, 1],[2, 0, -1, -1, -1; 40865, 77525, 97928, 24549, -40538; -84084, -159519, -201502, -50514, 83412],23,32]
%
% END OF LATTICE L24.32
%
%
% LATTICE L24.33
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[8476944, 385812, -1733424; 385812, 17584, -78876; -1733424, -78876, 354475],[84, 28, 1],[-10, -9, -617, -601, -1805; 31, 27, 1857, 1811, 5441; -42, -38, -2604, -2536, -7616],23,33]
%
% END OF LATTICE L24.33
%
%
% LATTICE L24.34
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[924, -168, -336; -168, 364, 308; -336, 308, 305],[84, 28, 1],[-26, -9, -19, 1, -13; 83, 29, 63, -3, 41; -112, -39, -84, 4, -56],23,34]
%
% END OF LATTICE L24.34
%
%
% LATTICE L24.35
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-488712, -96096, 14112; -96096, -18879, 2772; 14112, 2772, -407],[168, 21, 1],[1, -1, -1, 1, 3; -39, 28, 38, -20, -83; -231, 156, 224, -102, -462],23,35]
%
% END OF LATTICE L24.35
%
%
% LATTICE L24.36
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1627752, 14280, 533064; 14280, -105, -4704; 533064, -4704, -174533],[168, 21, 1],[392, 505, 19, -56, -57; 1567, 2016, 75, -224, -226; 1155, 1488, 56, -165, -168],23,36]
%
% END OF LATTICE L24.36
%
%
% LATTICE L24.37
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-45248784, -342888, -791784; -342888, -2568, -6000; -791784, -6000, -13855],[168, 24, 1],[55, 61, -24, -363, -118; 2, 0, -1, -7, -1; -3144, -3486, 1372, 20748, 6744],23,37]
%
% END OF LATTICE L24.37
%
%
% LATTICE L24.38
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2005584, 25704, -651672; 25704, -312, 8352; -651672, 8352, -211747],[168, 24, 1],[117, 116, -52, -1201, -464; 2, 0, -1, -7, -1; -360, -357, 160, 3696, 1428],23,38]
%
% END OF LATTICE L24.38
%
%
% LATTICE L24.39
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1243536, 753396, 209076; 753396, 456456, 126672; 209076, 126672, 35153],[84, 84, 1],[1, 0, 2, 8, 26; 10, -5, -81, -203, -579; -42, 18, 280, 684, 1932],23,39]
%
% END OF LATTICE L24.39
%
%
% LATTICE L24.40
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[8148, 91392, 21924; 91392, 1048740, 251496; 21924, 251496, 60311],[84, 84, 1],[89, 41, 51, 3, 23; 516, 236, 291, 17, 139; -2184, -999, -1232, -72, -588],23,40]
%
% END OF LATTICE L24.40
%
%
% LATTICE L24.41
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-336, 13608, -504; 13608, -550312, 20384; -504, 20384, -755],[168, 56, 1],[-3, -3, 4, 13, 42; 2, 0, -3, -1, -1; 56, 2, -84, -36, -56],23,41]
%
% END OF LATTICE L24.41
%
%
% LATTICE L24.42
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-84982800, 253512, 506856; 253512, -728, -1512; 506856, -1512, -3023],[168, 56, 1],[-3, -3, 4, 25, 84; 2, 0, -3, -1, -1; -504, -503, 672, 4192, 14084],23,42]
%
% END OF LATTICE L24.42
%
%
% LATTICE L24.43
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1650936, 4200168, 74760; 4200168, -10684464, -190176; 74760, -190176, -3385],[168, 168, 1],[2, 0, -1, -1, -1; -65, -11, 32, 75, 182; 3696, 618, -1820, -4236, -10248],23,43]
%
% END OF LATTICE L24.43
%
%
% LATTICE L24.44
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2184, 252504, -85680; 252504, -28102704, 9535848; -85680, 9535848, -3235717],[168, 168, 1],[2, 0, -1, -1, -1; -171, -170, 76, 1417, 4760; -504, -501, 224, 4176, 14028],23,44]
%
% END OF LATTICE L24.44
%

\medskip%
%------------------------------WEYL-GROUP-W25--------------------------------
%
\leavevmode\llap{}%
$W_{25\phantom{0}}$%
\qquad\llap{24} lattices, $\chi=6$%
\hfill%
$22222$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L25.1
%
\leavevmode%
${L_{25.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{1}{}9\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{2}{}7\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{23\rightarrow N_{25},3,2}%
\EasyButWeakLineBreak%
{${12}\above{1pt}{1pt}{*}{2}{252}\above{1pt}{1pt}{b}{2}{2}\above{1pt}{1pt}{l}{2}{36}\above{1pt}{1pt}{r}{2}{14}\above{1pt}{1pt}{b}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1925028\\-70560\\2520
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-70560\\2586\\-93
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2520\\-93\\2
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-5\\-134\\72
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-47\\-1260\\630
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\-1
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
17\\456\\-216
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
6\\161\\-70
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[1925028, -70560, 2520; -70560, 2586, -93; 2520, -93, 2],[252, 3, 1],[-5, -47, 0, 17, 6; -134, -1260, 0, 456, 161; 72, 630, -1, -216, -70],24,1]
%
% END OF LATTICE L25.1
%
%
% LATTICE L25.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[210, 63, 0; 63, 19, 0; 0, 0, -1],[21, 1, 1],[-1, -2, 1, 3, 6; 3, 7, -3, -10, -21; 0, 0, -1, -3, -7],24,2]
%
% END OF LATTICE L25.2
%
%
% LATTICE L25.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[1092, 252, -84; 252, -2, -3; -84, -3, 2],[84, 1, 1],[1, 3, 0, -1, -1; 18, 56, 0, -20, -21; 72, 210, -1, -72, -70],24,3]
%
% END OF LATTICE L25.3
%
%
% LATTICE L25.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[63, 63, 0; 63, -15, -9; 0, -9, -1],[63, 3, 1],[-1, 1, 1, 2, -1; 1, 0, -1, -3, 0; -9, 0, 8, 18, -7],24,4]
%
% END OF LATTICE L25.4
%
%
% LATTICE L25.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2898, 273, -924; 273, -3, 81; -924, 81, -293],[21, 3, 1],[10, 19, -21, -22, 6; -9, -14, 20, 20, -7; -34, -63, 72, 75, -21],24,5]
%
% END OF LATTICE L25.5
%
%
% LATTICE L25.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2562, -651, -756; -651, 21, -196; -756, -196, -223],[21, 7, 1],[82, 6, -61, -61, 3; -6, -1, 3, 4, 0; -273, -20, 203, 203, -10],24,6]
%
% END OF LATTICE L25.6
%
%
% LATTICE L25.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-630, 63, 252; 63, -6, -21; 252, -21, -41],[63, 3, 1],[3, 6, -1, -1, 2; 41, 84, -12, -14, 21; -3, -7, 0, 1, 0],24,7]
%
% END OF LATTICE L25.7
%
%
% LATTICE L25.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-10836, 420, 168; 420, -6, -9; 168, -9, -2],[84, 3, 1],[-1, -3, 1, 3, 1; -10, -28, 10, 28, 7; -40, -126, 39, 120, 42],24,8]
%
% END OF LATTICE L25.8
%
%
% LATTICE L25.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1228584, -16884, 291648; -16884, 232, -4008; 291648, -4008, 69233],[84, 4, 1],[47, 30, -18, 5, 113; 0, 7, 3, 1, 0; -198, -126, 76, -21, -476],24,9]
%
% END OF LATTICE L25.9
%
%
% LATTICE L25.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[210, -19005, -5859; -19005, 1726326, 532203; -5859, 532203, 164071],[21, 21, 1],[0, -1, -2, 1, 1; -41, -234, -505, -123, 74; 133, 759, 1638, 399, -240],24,10]
%
% END OF LATTICE L25.10
%
%
% LATTICE L25.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-420, 84, 84; 84, -14, -7; 84, -7, 18],[84, 7, 1],[1, 3, 3, -1, -1; 6, 20, 20, -8, -7; 0, -6, -7, 0, 2],24,11]
%
% END OF LATTICE L25.11
%
%
% LATTICE L25.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[23940, 1008, -756; 1008, 30, -27; -756, -27, 22],[252, 3, 1],[-1, -1, 1, 1, 1; -26, -28, 24, 24, 21; -66, -70, 63, 64, 63],24,12]
%
% END OF LATTICE L25.12
%
%
% LATTICE L25.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[632184, -24276, 149688; -24276, 936, -5748; 149688, -5748, 35443],[84, 12, 1],[9, 50, 20, 32, 179; 0, 7, 3, 1, 0; -38, -210, -84, -135, -756],24,13]
%
% END OF LATTICE L25.13
%
%
% LATTICE L25.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[126, 315, -126; 315, 777, -315; -126, -315, 127],[63, 21, 1],[3, 1, -1, -2, -1; -1, 0, 0, -2, -3; 0, 1, 0, -7, -9],24,14]
%
% END OF LATTICE L25.14
%
%
% LATTICE L25.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1071, 2079, 315; 2079, -3633, -546; 315, -546, -82],[63, 21, 1],[1, -1, -1, 4, 1; 10, -6, -9, 21, 7; -63, 36, 56, -126, -43],24,15]
%
% END OF LATTICE L25.15
%
%
% LATTICE L25.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3276, 420, 1176; 420, 42, -147; 1176, -147, -422],[84, 21, 1],[5, 17, 0, -89, -18; 0, -2, -1, 8, 2; 14, 48, 0, -252, -51],24,16]
%
% END OF LATTICE L25.16
%
%
% LATTICE L25.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[840, 2100, 1344; 2100, 4872, 3080; 1344, 3080, 1943],[84, 28, 1],[31, -8, -54, -22, 1; -93, 25, 165, 67, -3; 126, -34, -224, -91, 4],24,17]
%
% END OF LATTICE L25.17
%
%
% LATTICE L25.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[5516280, -108612, -1402380; -108612, 2136, 27612; -1402380, 27612, 356521],[252, 12, 1],[-29, 82, 110, -15, -577; -1, 7, 9, 0, -21; -114, 322, 432, -59, -2268],24,18]
%
% END OF LATTICE L25.18
%
%
% LATTICE L25.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[21203784, 1589364, -5365332; 1589364, 119064, -402168; -5365332, -402168, 1357625],[252, 12, 1],[1443, 2144, -642, 368, 3463; -70, -105, 31, -18, -168; 5682, 8442, -2528, 1449, 13636],24,19]
%
% END OF LATTICE L25.19
%
%
% LATTICE L25.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[252, 0, 252; 0, -42, -105; 252, -105, -10],[252, 21, 1],[1, 17, 6, -5, -2; 2, 42, 15, -12, -5; 0, -18, -7, 0, 2],24,20]
%
% END OF LATTICE L25.20
%
%
% LATTICE L25.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1048068, 8064, 8064; 8064, -42, -63; 8064, -63, -62],[252, 21, 1],[-1, -1, 1, 7, 4; -4, -6, 3, 40, 24; -126, -124, 126, 868, 495],24,21]
%
% END OF LATTICE L25.21
%
%
% LATTICE L25.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[504, -5124, -1428; -5124, 54264, 15120; -1428, 15120, 4213],[84, 84, 1],[1, 0, -2, 0, 1; 4, -5, -47, -41, -20; -14, 18, 168, 147, 72],24,22]
%
% END OF LATTICE L25.22
%
%
% LATTICE L25.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[64980216, 1015812, 15737148; 1015812, 15960, 245952; 15737148, 245952, 3811327],[252, 84, 1],[32, 31, 1921, 884, 1738; -95, -93, -5763, -2651, -5211; -126, -122, -7560, -3479, -6840],24,23]
%
% END OF LATTICE L25.23
%
%
% LATTICE L25.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[199080, -66276, 99792; -66276, 22008, -33180; 99792, -33180, 49991],[252, 84, 1],[-53, 5, 57, 80, -1; 157, -12, -166, -234, 3; 210, -18, -224, -315, 4],24,24]
%
% END OF LATTICE L25.24
%

\medskip%
%------------------------------WEYL-GROUP-W26--------------------------------
%
\leavevmode\llap{}%
$W_{26\phantom{0}}$%
\qquad\llap{8} lattices, $\chi=24$%
\hfill%
$\infty22\infty22\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L26.1
%
\leavevmode%
${L_{26.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}8\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{-2}{}11\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{2\rightarrow N_{26}}%
\EasyButWeakLineBreak%
{${22}\above{1pt}{1pt}{4,3}{\infty b}{88}\above{1pt}{1pt}{b}{2}{2}\above{1pt}{1pt}{s}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-19976\\-9240\\-880
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-9240\\-4274\\-407
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-880\\-407\\-38
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4223\\-9152\\352
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1956\\-4239\\163
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
192\\-416\\15
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-25\\55\\-11
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
61\\-132\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5\\-11\\2
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-19976, -9240, -880; -9240, -4274, -407; -880, -407, -38],[88, 1, 1],[-25, 61, 5, -107, -589, -17; 55, -132, -11, 231, 1276, 37; -11, 0, 2, 0, -44, -3],25,1]
%
% END OF LATTICE L26.1
%
%
% LATTICE L26.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[22, 0, 0; 0, 0, -1; 0, -1, 0],[22, 1, 1],[-1, 1, 0, -10, -23, -1; 0, 0, -1, -33, -66, -2; -11, 0, 1, -33, -88, -5],25,2]
%
% END OF LATTICE L26.2
%
%
% LATTICE L26.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-14476, 242, -6578; 242, -4, 110; -6578, 110, -2989],[22, 2, 1],[100, 126, 13, 21, -5, -2; -33, 22, 13, 55, 0, -11; -220, -275, -28, -44, 11, 4],25,3]
%
% END OF LATTICE L26.3
%
%
% LATTICE L26.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[154, -242, 66; -242, -660, -121; 66, -121, 28],[22, 11, 1],[25, 3, -54, -24, -1, 55; 0, -2, -3, -1, 0, 2; -53, -2, 121, 53, 2, -121],25,4]
%
% END OF LATTICE L26.4
%
%
% LATTICE L26.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[44, 5082, 2420; 5082, 584056, 278124; 2420, 278124, 132441],[22, 22, 1],[33, 38, 37, 5, 0, 1; -326, -377, -367, -41, 10, 0; 684, 791, 770, 86, -21, 0],25,5]
%
% END OF LATTICE L26.5
%
%
% LATTICE L26.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-174064, -25256, -8272; -25256, -3664, -1200; -8272, -1200, -393],[88, 8, 1],[1, 5, 1, -1, -5, -1; 22, -99, -33, -165, -44, 20; -88, 198, 80, 528, 242, -40],25,6]
%
% END OF LATTICE L26.6
%
%
% LATTICE L26.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-96536, -2728, 2024; -2728, -66, 55; 2024, 55, -42],[88, 11, 1],[2, 13, 5, 1, -1, -2; 21, 148, 61, 13, -12, -27; 122, 812, 319, 65, -64, -132],25,7]
%
% END OF LATTICE L26.7
%
%
% LATTICE L26.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-528, -4664, -2112; -4664, -39248, -17776; -2112, -17776, -8051],[88, 88, 1],[1, 0, -4, -6, -5, -1; 18, -19, -119, -97, -60, 40; -40, 42, 264, 216, 134, -88],25,8]
%
% END OF LATTICE L26.8
%

\medskip%
%------------------------------WEYL-GROUP-W27--------------------------------
%
\leavevmode\llap{}%
$W_{27\phantom{0}}$%
\qquad\llap{6} lattices, $\chi=22$%
\hfill%
$423423\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L27.1
%
\leavevmode%
${L_{27.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{2}{}23\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{2\rightarrow N_{27}}%
\EasyButWeakLineBreak%
{${2}\above{1pt}{1pt}{*}{4}{4}\above{1pt}{1pt}{b}{2}{2}\above{1pt}{1pt}{-}{3}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-182068\\2024\\4048
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2024\\-22\\-45
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4048\\-45\\-90
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
17939\\-21528\\814476
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-185\\221\\-8399
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-400\\480\\-18161
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\2\\-1
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-2\\-44
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\-5\\92
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-182068, 2024, 4048; 2024, -22, -45; 4048, -45, -90],[92, 1, 1],[0, -1, 2, 30, 31, 3; 2, -2, -5, -38, -34, -1; -1, -44, 92, 1363, 1406, 135],26,1]
%
% END OF LATTICE L27.1
%
%
% LATTICE L27.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-23, 0, 0; 0, 1, 0; 0, 0, 1],[23, 1, 1],[0, 0, -1, -12, -6, -1; -1, 1, 0, -17, -10, -3; 1, 0, -5, -55, -27, -4],26,2]
%
% END OF LATTICE L27.2
%
%
% LATTICE L27.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1738984, 92, -455492; 92, 8, -24; -455492, -24, 119307],[92, 4, 1],[0, -11, -439, -5136, -2557, -417; 1, 0, 18, 221, 111, 19; 0, -42, -1676, -19608, -9762, -1592],26,3]
%
% END OF LATTICE L27.3
%
%
% LATTICE L27.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-47334, 5037, -4324; 5037, -506, 460; -4324, 460, -395],[23, 23, 1],[63, -154, -396, -2589, -1109, -25; -1, -3, -3, -5, 0, 2; -690, 1679, 4324, 28290, 12121, 276],26,4]
%
% END OF LATTICE L27.4
%
%
% LATTICE L27.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1932, 2944, 1012; 2944, -4462, -1541; 1012, -1541, -530],[92, 23, 1],[465, 459, 35, -9, -3, 41; -38, -34, -1, 2, -2, -5; 989, 966, 69, -23, 0, 92],26,5]
%
% END OF LATTICE L27.5
%
%
% LATTICE L27.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[184, -1196, 276; -1196, 34408, -8188; 276, -8188, 1949],[92, 92, 1],[629, 313, 51, 1, 2, 54; 2520, 1249, 199, 0, 11, 221; 10488, 5198, 828, 0, 46, 920],26,6]
%
% END OF LATTICE L27.6
%

\medskip%
%------------------------------WEYL-GROUP-W28--------------------------------
%
\leavevmode\llap{}%
$W_{28\phantom{0}}$%
\qquad\llap{8} lattices, $\chi=14$%
\hfill%
$\infty2322$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L28.1
%
\leavevmode%
${L_{28.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}8\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{2}{}13\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{2\rightarrow N_{28}}%
\EasyButWeakLineBreak%
{${26}\above{1pt}{1pt}{4,1}{\infty a}{104}\above{1pt}{1pt}{b}{2}{2}\above{1pt}{1pt}{+}{3}{2}\above{1pt}{1pt}{l}{2}{8}\above{1pt}{1pt}{r}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-255855288\\3601312\\-238784
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3601312\\-50690\\3357
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-238784\\3357\\-194
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1062\\-76154\\-10621
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
343\\24596\\3432
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
161\\11545\\1610
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-168\\-12047\\-1681
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-795\\-57008\\-7952
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-255855288, 3601312, -238784; 3601312, -50690, 3357; -238784, 3357, -194],[104, 1, 1],[-1062, 343, 161, -168, -795; -76154, 24596, 11545, -12047, -57008; -10621, 3432, 1610, -1681, -7952],27,1]
%
% END OF LATTICE L28.1
%
%
% LATTICE L28.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[26, 0, 0; 0, 0, -1; 0, -1, 0],[26, 1, 1],[-1, 1, 0, -1, -1; 0, 0, -1, -3, -2; -13, 0, 1, -4, -6],27,2]
%
% END OF LATTICE L28.2
%
%
% LATTICE L28.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-77532, 3406, -37726; 3406, -144, 1654; -37726, 1654, -18355],[26, 2, 1],[-539, 42, 82, -83, -100; 689, -52, -105, 104, 127; 1170, -91, -178, 180, 217],27,3]
%
% END OF LATTICE L28.3
%
%
% LATTICE L28.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-264342, -10738, -123214; -10738, -312, -5005; -123214, -5005, -57432],[26, 13, 1],[-364, 55, 721, -715, -1745; -1, 0, 2, -1, -4; 781, -118, -1547, 1534, 3744],27,4]
%
% END OF LATTICE L28.4
%
%
% LATTICE L28.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[52, 77714, 37310; 77714, 122558592, 58839612; 37310, 58839612, 28248529],[26, 26, 1],[3, 0, 1, 24, 13; -1013, -205, 0, -4631, -3027; 2110, 427, 0, 9646, 6305],27,5]
%
% END OF LATTICE L28.5
%
%
% LATTICE L28.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-39338000, 3890744, 842192; 3890744, -384784, -83216; 842192, -83216, -17823],[104, 8, 1],[7561, -966, -1010, 1933, 844; 83538, -10673, -11159, 21357, 9325; -32760, 4186, 4376, -8376, -3657],27,6]
%
% END OF LATTICE L28.6
%
%
% LATTICE L28.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-56472, -2704, -13312; -2704, -78, -637; -13312, -637, -3138],[104, 13, 1],[-20, -113, -49, 52, 49; -1, -4, -1, 2, 0; 85, 480, 208, -221, -208],27,7]
%
% END OF LATTICE L28.7
%
%
% LATTICE L28.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-624, -82472, 1144; -82472, -9994192, 138632; 1144, 138632, -1923],[104, 104, 1],[-1, -1, -1, 2, 0; 5, 26, 88, -13, -11; 360, 1874, 6344, -936, -793],27,8]
%
% END OF LATTICE L28.8
%

\medskip%
%------------------------------WEYL-GROUP-W29--------------------------------
%
\leavevmode\llap{}%
$W_{29\phantom{0}}$%
\qquad\llap{6} lattices, $\chi=28$%
\hfill%
$22232223\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L29.1
%
\leavevmode%
${L_{29.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{-2}{}29\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{2\rightarrow N_{29}}%
\EasyButWeakLineBreak%
{${2}\above{1pt}{1pt}{b}{2}{58}\above{1pt}{1pt}{l}{2}{4}\above{1pt}{1pt}{r}{2}{2}\above{1pt}{1pt}{-}{3}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-42108\\1508\\812
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1508\\-54\\-29
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
812\\-29\\-14
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3189\\90596\\-3828
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-115\\-3267\\138
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-65\\-1846\\77
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\56\\-1
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
133\\3770\\-145
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
31\\880\\-36
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
16\\455\\-20
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-42108, 1508, 812; 1508, -54, -29; 812, -29, -14],[116, 1, 1],[2, 133, 31, 16, 3, 12, -1, -1; 56, 3770, 880, 455, 86, 348, -28, -29; -1, -145, -36, -20, -5, -29, 0, 2],28,1]
%
% END OF LATTICE L29.1
%
%
% LATTICE L29.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[435, 0, -29; 0, -1, 0; -29, 0, 2],[29, 1, 1],[0, 2, 0, -1, -2, -60, -6, -5; 0, 0, -1, -5, -8, -232, -23, -19; 1, 29, -1, -17, -31, -899, -89, -73],28,2]
%
% END OF LATTICE L29.2
%
%
% LATTICE L29.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[73080, 13108, 18096; 13108, 2408, 3248; 18096, 3248, 4481],[116, 4, 1],[126, 7256, 416, 847, 156, 922, 7, -1; 21, 1189, 68, 138, 25, 145, 1, 0; -524, -30160, -1729, -3520, -648, -3828, -29, 4],28,3]
%
% END OF LATTICE L29.3
%
%
% LATTICE L29.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1653, -841, 1595; -841, -406, 812; 1595, 812, -1539],[29, 29, 1],[-29, -629, -2366, -2782, -861, -261, -304, 112; 2, 0, -2, -5, -4, -2, -4, -1; -29, -655, -2465, -2900, -899, -273, -319, 116],28,4]
%
% END OF LATTICE L29.4
%
%
% LATTICE L29.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[116, 0, 0; 0, -406, -29; 0, -29, -2],[116, 29, 1],[-2, -3, -19, -9, -1, 0, 1, 0; -1, -5, -36, -20, -5, -1, 0, 2; 0, 46, 348, 203, 58, 12, 0, -29],28,5]
%
% END OF LATTICE L29.5
%
%
% LATTICE L29.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[232, 3364, 812; 3364, 47560, 11484; 812, 11484, 2773],[116, 116, 1],[14, 24, 39, 77, 12, 2, 0, 1; 27, 31, 46, 78, -1, -5, -7, 0; -116, -136, -203, -348, 0, 20, 29, 0],28,6]
%
% END OF LATTICE L29.6
%

\medskip%
%------------------------------WEYL-GROUP-W30--------------------------------
%
\leavevmode\llap{}%
$W_{30\phantom{0}}$%
\qquad\llap{48} lattices, $\chi=24$%
\hfill%
$\infty22\infty22\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L30.1
%
\leavevmode%
${L_{30.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}8\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{1}{}3\above{1pt}{1pt}{1}{}9\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-}{}5\above{1pt}{1pt}{1}{}25\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{235\rightarrow N_{30},35,25,23,5,3,2}%
\EasyButWeakLineBreak%
{${30}\above{1pt}{1pt}{60,31}{\infty b}{120}\above{1pt}{1pt}{b}{2}{18}\above{1pt}{1pt}{b}{2}{30}\above{1pt}{1pt}{60,19}{\infty a}{120}\above{1pt}{1pt}{b}{2}{450}\above{1pt}{1pt}{b}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1348200\\21600\\-55800
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
21600\\-330\\915
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-55800\\915\\-2282
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-15\\-317\\240
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-131\\-2756\\2100
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-23\\-483\\369
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-14\\-293\\225
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
15\\316\\-240
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
28\\585\\-450
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-1348200, 21600, -55800; 21600, -330, 915; -55800, 915, -2282],[1800, 15, 1],[-15, -131, -23, -14, 15, 28; -317, -2756, -483, -293, 316, 585; 240, 2100, 369, 225, -240, -450],29,1]
%
% END OF LATTICE L30.1
%
%
% LATTICE L30.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[30, 0, 0; 0, 0, -1; 0, -1, 0],[30, 1, 1],[-1, 1, 0, -4, -11, -1; 0, 0, -1, -15, -30, -2; -15, 0, 1, -15, -60, -7],29,2]
%
% END OF LATTICE L30.2
%
%
% LATTICE L30.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-606120, -296640, -7080; -296640, -145178, -3465; -7080, -3465, -82],[120, 1, 1],[-154, 323, 22, -301, -2143, -113; 315, -660, -45, 615, 4380, 231; -15, 0, 2, 0, -60, -5],29,3]
%
% END OF LATTICE L30.3
%
%
% LATTICE L30.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-141570, -29880, -11250; -29880, -6306, -2373; -11250, -2373, -890],[90, 3, 1],[84, -29, -28, 86, 369, 130; -460, 160, 153, -475, -2030, -714; 165, -60, -54, 180, 750, 261],29,4]
%
% END OF LATTICE L30.4
%
%
% LATTICE L30.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-1072050, -121500, 30750; -121500, -13770, 3485; 30750, 3485, -882],[150, 5, 1],[2, 1, -2, -4, -5, 0; 9, -24, 5, 81, 204, 17; 105, -60, -50, 180, 630, 67],29,5]
%
% END OF LATTICE L30.5
%
%
% LATTICE L30.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-164520, -75960, 2880; -75960, -35070, 1329; 2880, 1329, -50],[360, 3, 1],[-41, -243, -34, -9, 43, 4; 95, 560, 78, 20, -100, -9; 165, 900, 117, 15, -180, -9],29,6]
%
% END OF LATTICE L30.6
%
%
% LATTICE L30.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-12445800, -6142200, 25800; -6142200, -3031230, 12755; 25800, 12755, -42],[600, 5, 1],[-1315, -7087, -304, -103, 1415, 102; 2643, 14244, 611, 207, -2844, -205; -5130, -27660, -1187, -405, 5520, 400],29,7]
%
% END OF LATTICE L30.7
%
%
% LATTICE L30.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-94050, 6300, 44100; 6300, -420, -2955; 44100, -2955, -20678],[450, 15, 1],[45, 121, 32, 8, -15, -1; 41, 124, 36, 14, -14, -15; 90, 240, 63, 15, -30, 0],29,8]
%
% END OF LATTICE L30.8
%
%
% LATTICE L30.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-50340, 450, -23490; 450, -4, 210; -23490, 210, -10961],[30, 2, 1],[56, 92, 19, 29, -7, -2; -15, 90, 33, 105, 0, -15; -120, -195, -40, -60, 15, 4],29,9]
%
% END OF LATTICE L30.9
%
%
% LATTICE L30.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-33510, 450, -10050; 450, -6, 135; -10050, 135, -3014],[30, 3, 1],[12, 43, 14, 8, -3, -2; -5, 60, 33, 35, 0, -15; -40, -140, -45, -25, 10, 6],29,10]
%
% END OF LATTICE L30.10
%
%
% LATTICE L30.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-20010, 450, -3330; 450, -10, 75; -3330, 75, -554],[30, 5, 1],[4, 17, 10, 4, -1, -2; -3, 36, 33, 21, 0, -15; -24, -96, -55, -21, 6, 10],29,11]
%
% END OF LATTICE L30.11
%
%
% LATTICE L30.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[19020, 2250, 9120; 2250, 672, 1080; 9120, 1080, 4373],[30, 6, 1],[1821, 2662, 1567, 829, -12, 23; 10, 15, 9, 5, 0, 0; -3800, -5555, -3270, -1730, 25, -48],29,12]
%
% END OF LATTICE L30.12
%
%
% LATTICE L30.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-26370, 5940, -1800; 5940, -1338, 405; -1800, 405, -112],[90, 3, 1],[-79, 9, 10, -26, -219, -31; -355, 40, 45, -115, -980, -139; -15, 0, 2, 0, -30, -5],29,13]
%
% END OF LATTICE L30.13
%
%
% LATTICE L30.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[13620, 3150, 6480; 3150, 1120, 1500; 6480, 1500, 3083],[30, 10, 1],[935, 1364, 1335, 419, -10, 19; 6, 9, 9, 3, 0, 0; -1968, -2871, -2810, -882, 21, -40],29,14]
%
% END OF LATTICE L30.14
%
%
% LATTICE L30.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-42360, -9120, 1080; -9120, -1962, 231; 1080, 231, -26],[120, 3, 1],[-2, 19, 1, -18, -99, -13; 10, -100, -5, 95, 520, 68; 5, -100, -3, 95, 500, 63],29,15]
%
% END OF LATTICE L30.15
%
%
% LATTICE L30.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[4050, -240, -1410; -240, 1680, 1125; -1410, 1125, 1142],[30, 15, 1],[-230, -671, -985, -103, 5, -14; 462, 1348, 1979, 207, -10, 28; -739, -2156, -3165, -331, 16, -45],29,16]
%
% END OF LATTICE L30.16
%
%
% LATTICE L30.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1440, -1710, 810; -1710, 37680, -3126; 810, -3126, 587],[90, 6, 1],[1898, 81, 97, 3957, 5774, 3416; -235, -10, -12, -490, -715, -423; -3870, -165, -198, -8070, -11775, -6966],29,17]
%
% END OF LATTICE L30.17
%
%
% LATTICE L30.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[696240, 115290, 348930; 115290, 19104, 57780; 348930, 57780, 174871],[90, 6, 1],[-853, -66, -1, -1457, -2244, -461; -115, -10, 0, -190, -295, -61; 1740, 135, 2, 2970, 4575, 940],29,18]
%
% END OF LATTICE L30.18
%
%
% LATTICE L30.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[30840, 3360, 0; 3360, 350, 15; 0, 15, -14],[120, 5, 1],[-16, -85, -18, -1, 17, 1; 147, 780, 165, 9, -156, -9; 156, 828, 175, 9, -168, -10],29,19]
%
% END OF LATTICE L30.19
%
%
% LATTICE L30.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2637000, -1593510, -656160; -1593510, -962940, -396510; -656160, -396510, -163271],[30, 30, 1],[-1, 6, 33, 7, 0, -15; 70, 30, -67, -47, -7, 136; -166, -97, 30, 86, 17, -270],29,20]
%
% END OF LATTICE L30.20
%
%
% LATTICE L30.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-856560, -24600, 1080; -24600, -688, 40; 1080, 40, 3],[120, 8, 1],[-31, -7, 7, 71, 47, 1; 990, 225, -223, -2265, -1500, -32; -2040, -450, 464, 4680, 3090, 64],29,21]
%
% END OF LATTICE L30.21
%
%
% LATTICE L30.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-127080, -24120, 3240; -24120, -4578, 615; 3240, 615, -82],[360, 3, 1],[-7, 19, 1, -18, -119, -6; 35, -100, -5, 95, 620, 31; -15, 0, 2, 0, -60, -5],29,22]
%
% END OF LATTICE L30.22
%
%
% LATTICE L30.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-18810, 29430, -4590; 29430, -45930, 7155; -4590, 7155, -1114],[90, 15, 1],[-32, -99, -146, -12, 11, 14; -64, -200, -297, -25, 22, 30; -279, -876, -1305, -111, 96, 135],29,23]
%
% END OF LATTICE L30.23
%
%
% LATTICE L30.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-16290, 9630, 1800; 9630, -5520, -1035; 1800, -1035, -194],[90, 15, 1],[3, 11, 6, 2, -1, -1; -41, -160, -90, -32, 14, 17; 246, 954, 535, 189, -84, -100],29,24]
%
% END OF LATTICE L30.24
%
%
% LATTICE L30.25
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1827600, -32250, 901650; -32250, 960, -15920; 901650, -15920, 444831],[150, 10, 1],[4111, 244, 419, 8503, 12370, 2439; -201, -12, -20, -414, -603, -119; -8340, -495, -850, -17250, -25095, -4948],29,25]
%
% END OF LATTICE L30.25
%
%
% LATTICE L30.26
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-220440, -4800, 3600; -4800, -90, 75; 3600, 75, -58],[120, 15, 1],[1, -1, -2, 1, 9, 8; 21, -20, -43, 19, 180, 163; 89, -88, -180, 86, 788, 705],29,26]
%
% END OF LATTICE L30.26
%
%
% LATTICE L30.27
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1222650, -33000, -415650; -33000, 1440, 11205; -415650, 11205, 141304],[150, 15, 1],[-918, -109, -281, -1899, -5525, -1634; -67, -8, -20, -138, -402, -119; -2695, -320, -825, -5575, -16220, -4797],29,27]
%
% END OF LATTICE L30.27
%
%
% LATTICE L30.28
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[3916260, -385290, 1901880; -385290, 37920, -187110; 1901880, -187110, 923623],[90, 30, 1],[718, 1089, 3325, 405, 34, 44; 101, 155, 477, 59, 5, 3; -1458, -2211, -6750, -822, -69, -90],29,28]
%
% END OF LATTICE L30.28
%
%
% LATTICE L30.29
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[8079840, 463410, 3948120; 463410, 26580, 226440; 3948120, 226440, 1929203],[90, 30, 1],[329, 520, 544, 210, 19, -5; 40, 58, 57, 19, 1, 2; -678, -1071, -1120, -432, -39, 10],29,29]
%
% END OF LATTICE L30.29
%
%
% LATTICE L30.30
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-39120, -8760, -2760; -8760, -1872, -576; -2760, -576, -175],[120, 24, 1],[-11, -2, 8, 26, 17, 1; 150, 25, -111, -355, -230, -12; -320, -50, 240, 760, 490, 24],29,30]
%
% END OF LATTICE L30.30
%
%
% LATTICE L30.31
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-341174700, 5309250, -163451550; 5309250, -82620, 2543580; -163451550, 2543580, -78307123],[150, 30, 1],[757, -242, -1006, 1476, 2475, 1541; 3, -4, 5, 27, 34, 17; -1580, 505, 2100, -3080, -5165, -3216],29,31]
%
% END OF LATTICE L30.31
%
%
% LATTICE L30.32
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-60720, -13080, -5040; -13080, -2640, -1000; -5040, -1000, -377],[120, 40, 1],[-7, -1, 9, 17, 11, 1; 162, 21, -211, -393, -252, -20; -336, -42, 440, 816, 522, 40],29,32]
%
% END OF LATTICE L30.32
%
%
% LATTICE L30.33
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-269640, -876240, -156600; -876240, -2717130, -483075; -156600, -483075, -85834],[360, 15, 1],[587, -581, -1187, 568, 5201, 4652; -1847, 1828, 3735, -1787, -16364, -14637; 9324, -9228, -18855, 9021, 82608, 73890],29,33]
%
% END OF LATTICE L30.33
%
%
% LATTICE L30.34
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-4680, 3240, -360; 3240, -1290, 135; -360, 135, -14],[360, 15, 1],[0, -1, 0, 1, 5, 1; 1, -20, -1, 19, 100, 21; 9, -168, -10, 156, 828, 175],29,34]
%
% END OF LATTICE L30.34
%
%
% LATTICE L30.35
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1053450, 22050, 423450; 22050, -420, -8865; 423450, -8865, -170212],[450, 15, 1],[435, 1583, 172, 284, -145, -141; 41, 154, 17, 29, -14, -15; 1080, 3930, 427, 705, -360, -350],29,35]
%
% END OF LATTICE L30.35
%
%
% LATTICE L30.36
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-117360, -52920, 10440; -52920, -22800, 4536; 10440, 4536, -901],[360, 24, 1],[76, 47, 1, -31, -2, 26; 755, 470, 12, -310, -25, 255; 4680, 2910, 72, -1920, -150, 1584],29,36]
%
% END OF LATTICE L30.36
%
%
% LATTICE L30.37
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2824560, -329400, -140400; -329400, -38352, -16344; -140400, -16344, -6965],[360, 24, 1],[21, 17, 1, -11, -7, 1; -1970, -1565, -87, 1015, 610, -104; 4200, 3330, 184, -2160, -1290, 224],29,37]
%
% END OF LATTICE L30.37
%
%
% LATTICE L30.38
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-449400, 631800, -151800; 631800, -863610, 205065; -151800, 205065, -48446],[600, 15, 1],[-703, -6435, -1151, -726, 719, 1468; -1717, -15716, -2811, -1773, 1756, 3585; -5065, -46360, -8292, -5230, 5180, 10575],29,38]
%
% END OF LATTICE L30.38
%
%
% LATTICE L30.39
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[900, 450, 450; 450, 2940, 420; 450, 420, 239],[450, 30, 1],[139, 216, 134, 84, 7, -1; 22, 34, 21, 13, 1, 0; -300, -465, -288, -180, -15, 0],29,39]
%
% END OF LATTICE L30.39
%
%
% LATTICE L30.40
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[24798600, -342450, 12115800; -342450, 4740, -167310; 12115800, -167310, 5919391],[450, 30, 1],[1979, 2734, 517, 777, 22, 171; 22, 34, 7, 13, 1, 0; -4050, -5595, -1058, -1590, -45, -350],29,40]
%
% END OF LATTICE L30.40
%
%
% LATTICE L30.41
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-947760, -974520, -476640; -974520, -1002000, -490080; -476640, -490080, -239699],[120, 120, 1],[-3, 2, 24, 10, 5, -3; 89, -89, -845, -311, -133, 179; -176, 178, 1680, 616, 262, -360],29,41]
%
% END OF LATTICE L30.41
%
%
% LATTICE L30.42
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-186387600, -11898600, 409800; -11898600, -759440, 26160; 409800, 26160, -901],[600, 40, 1],[-31, -1, 9, 77, 47, 1; -93, -6, 26, 228, 141, 5; -16800, -630, 4848, 41640, 25470, 600],29,42]
%
% END OF LATTICE L30.42
%
%
% LATTICE L30.43
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-412200, -225000, 27000; -225000, -117870, 13875; 27000, 13875, -1618],[1800, 15, 1],[99, 523, 22, 5, -107, -6; -581, -3068, -129, -29, 628, 35; -3330, -17580, -739, -165, 3600, 200],29,43]
%
% END OF LATTICE L30.43
%
%
% LATTICE L30.44
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-150480, -125640, 23400; -125640, -99600, 18600; 23400, 18600, -3473],[360, 120, 1],[-7, 6, 62, 24, 11, -11; -157, 137, 1401, 539, 245, -255; -888, 774, 7920, 3048, 1386, -1440],29,44]
%
% END OF LATTICE L30.44
%
%
% LATTICE L30.45
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2648880, -1059480, -519840; -1059480, -423600, -207840; -519840, -207840, -101977],[360, 120, 1],[7, 5, 1, -3, -1, 3; -830, -563, -81, 349, 82, -400; 1656, 1122, 160, -696, -162, 800],29,45]
%
% END OF LATTICE L30.45
%
%
% LATTICE L30.46
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2830800, -265800, -71400; -265800, -15120, -3840; -71400, -3840, -967],[600, 120, 1],[38, 17, -19, -11, 10, 20; -5229, -2338, 2620, 1514, -1377, -2753; 17960, 8030, -9000, -5200, 4730, 9456],29,46]
%
% END OF LATTICE L30.46
%
%
% LATTICE L30.47
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-867600, 5400, 3600; 5400, 4560, -720; 3600, -720, 91],[1800, 120, 1],[-11, -1, 3, 27, 17, 1; -328, -31, 89, 803, 506, 30; -2160, -210, 584, 5280, 3330, 200],29,47]
%
% END OF LATTICE L30.47
%
%
% LATTICE L30.48
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-31899600, 376200, -36000; 376200, -2640, 120; -36000, 120, 11],[1800, 120, 1],[-7, -2, 22, 16, 11, 1; -1363, -391, 4275, 3113, 2141, 195; -8040, -2310, 25200, 18360, 12630, 1152],29,48]
%
% END OF LATTICE L30.48
%

\medskip%
%------------------------------WEYL-GROUP-W31--------------------------------
%
\leavevmode\llap{}%
$W_{31\phantom{0}}$%
\qquad\llap{16} lattices, $\chi=4$%
\hfill%
$6222$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L31.1
%
\leavevmode%
${L_{31.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}8\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{2\rightarrow N_{31}}%
\EasyButWeakLineBreak%
{${2}\above{1pt}{1pt}{}{6}{6}\above{1pt}{1pt}{b}{2}{10}\above{1pt}{1pt}{l}{2}{24}\above{1pt}{1pt}{r}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-221160\\960\\1800
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
960\\-2\\-9
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1800\\-9\\-14
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\52\\95
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-51\\-96
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2\\-105\\-190
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\48\\96
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-221160, 960, 1800; 960, -2, -9; 1800, -9, -14],[120, 1, 1],[1, -1, -2, 1; 52, -51, -105, 48; 95, -96, -190, 96],30,1]
%
% END OF LATTICE L31.1
%
%
% LATTICE L31.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[510, 150, 30; 150, 44, 9; 30, 9, 2],[30, 1, 1],[1, -2, 6, 13; -3, 6, -20, -42; -1, 3, -5, -12],30,2]
%
% END OF LATTICE L31.2
%
%
% LATTICE L31.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-62880, 690, -30750; 690, -4, 336; -30750, 336, -15037],[30, 2, 1],[-63, 64, 126, -16; 52, -51, -105, 12; 130, -132, -260, 33],30,3]
%
% END OF LATTICE L31.3
%
%
% LATTICE L31.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-74670, 900, -24270; 900, -6, 291; -24270, 291, -7888],[30, 3, 1],[-53, 18, 106, -9; 52, -17, -105, 8; 165, -56, -330, 28],30,4]
%
% END OF LATTICE L31.4
%
%
% LATTICE L31.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-100770, 1320, -19590; 1320, -10, 255; -19590, 255, -3808],[30, 5, 1],[-45, 46, 18, -23; 52, -51, -21, 24; 235, -240, -94, 120],30,5]
%
% END OF LATTICE L31.5
%
%
% LATTICE L31.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[4882560, -187290, 2342190; -187290, 7188, -89844; 2342190, -89844, 1123561],[30, 6, 1],[190, 191, 331, 130; 1, 2, 0, 0; -396, -398, -690, -271],30,6]
%
% END OF LATTICE L31.6
%
%
% LATTICE L31.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[4215840, -224670, 2006310; -224670, 11980, -106920; 2006310, -106920, 954799],[30, 10, 1],[238, 757, 79, 464; 1, 6, 0, 0; -500, -1590, -166, -975],30,7]
%
% END OF LATTICE L31.7
%
%
% LATTICE L31.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-236280, 1560, 2280; 1560, -6, -15; 2280, -15, -22],[120, 3, 1],[-1, 1, 2, -1; 2, -1, -5, 0; -105, 104, 210, -104],30,8]
%
% END OF LATTICE L31.8
%
%
% LATTICE L31.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[4737810, 291720, -1296840; 291720, 17970, -79845; -1296840, -79845, 354976],[30, 15, 1],[-178, -189, -59, -231; 357, 380, 118, 462; -570, -605, -189, -740],30,9]
%
% END OF LATTICE L31.9
%
%
% LATTICE L31.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[120, 0, 0; 0, -10, -5; 0, -5, -2],[120, 5, 1],[0, -1, 0, 1; 2, -3, -1, 0; -5, 0, 2, 0],30,10]
%
% END OF LATTICE L31.10
%
%
% LATTICE L31.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-14856960, -8907510, -3662910; -8907510, -5340480, -2196090; -3662910, -2196090, -903067],[30, 30, 1],[52, -17, -21, 4; -2443, 822, 980, -202; 5730, -1930, -2298, 475],30,11]
%
% END OF LATTICE L31.11
%
%
% LATTICE L31.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-557520, -79080, -9360; -79080, -11216, -1328; -9360, -1328, -157],[120, 8, 1],[7, -8, -14, 1; -38, 45, 75, -6; -96, 96, 200, -9],30,12]
%
% END OF LATTICE L31.12
%
%
% LATTICE L31.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-110040, 2400, -43320; 2400, -30, 945; -43320, 945, -17054],[120, 15, 1],[65, -63, -26, 63; 2, -1, -1, 0; -165, 160, 66, -160],30,13]
%
% END OF LATTICE L31.13
%
%
% LATTICE L31.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-90846960, -74040, 883440; -74040, -48, 720; 883440, 720, -8591],[120, 24, 1],[7, -48, -14, 6; 2, -1, -5, 0; 720, -4936, -1440, 617],30,14]
%
% END OF LATTICE L31.14
%
%
% LATTICE L31.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[240, 360, 0; 360, -1040, -40; 0, -40, -1],[120, 40, 1],[-3, 5, 1, -1; 2, -3, -1, 0; -80, 120, 32, -15],30,15]
%
% END OF LATTICE L31.15
%
%
% LATTICE L31.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-240, -24600, 5640; -24600, -2005680, 459840; 5640, 459840, -105427],[120, 120, 1],[2, -1, -1, 0; 55, -376, -22, 47; 240, -1640, -96, 205],30,16]
%
% END OF LATTICE L31.16
%

\medskip%
%------------------------------WEYL-GROUP-W32--------------------------------
%
\leavevmode\llap{}%
$W_{32\phantom{0}}$%
\qquad\llap{24} lattices, $\chi=20$%
\hfill%
$226226\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L32.1
%
\leavevmode%
${L_{32.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{1}{}3\above{1pt}{1pt}{-}{}9\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{2}{}11\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{23\rightarrow N_{32},3,2}%
\EasyButWeakLineBreak%
{${18}\above{1pt}{1pt}{s}{2}{22}\above{1pt}{1pt}{b}{2}{6}\above{1pt}{1pt}{}{6}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1983564\\-559152\\9108
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-559152\\-157602\\2559
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
9108\\2559\\-38
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-99001\\364320\\803880
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-27675\\101843\\224721
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
350\\-1288\\-2843
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-322\\1185\\2619
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-278\\1023\\2255
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3\\11\\21
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-1983564, -559152, 9108; -559152, -157602, 2559; 9108, 2559, -38],[396, 3, 1],[-322, -278, -3, 97, 3, -72; 1185, 1023, 11, -357, -11, 265; 2619, 2255, 21, -792, -22, 588],31,1]
%
% END OF LATTICE L32.1
%
%
% LATTICE L32.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[231, -66, -33; -66, 18, 11; -33, 11, 2],[33, 1, 1],[0, 8, -2, -18, -74, -16; 0, 22, -6, -51, -209, -45; 1, 11, -3, -22, -88, -18],31,2]
%
% END OF LATTICE L32.2
%
%
% LATTICE L32.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-3144108, 1143384, 11880; 1143384, -415802, -4321; 11880, -4321, -42],[132, 1, 1],[649, 1885, 140, -136, -4, 373; 1780, 5170, 384, -373, -11, 1023; 445, 1287, 93, -94, 0, 258],31,3]
%
% END OF LATTICE L32.3
%
%
% LATTICE L32.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-247302, 27522, -4059; 27522, -2595, 336; -4059, 336, -38],[99, 3, 1],[103, 89, 1, -31, -1, 23; 2292, 1980, 22, -690, -22, 512; 9261, 7997, 87, -2790, -88, 2070],31,4]
%
% END OF LATTICE L32.4
%
%
% LATTICE L32.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-368379, 57651, 120120; 57651, -8553, -18849; 120120, -18849, -39163],[33, 3, 1],[-1116, 23134, 6812, 22701, 56011, 383; -349, 7205, 2123, 7078, 17468, 120; -3255, 67485, 19871, 66219, 163383, 1117],31,5]
%
% END OF LATTICE L32.5
%
%
% LATTICE L32.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1132857, -27225, 21087; -27225, -570, 477; 21087, 477, -382],[99, 3, 1],[46, 434, 16, -8, -16, 22; 1605, 15147, 559, -279, -561, 767; 4543, 42867, 1581, -790, -1584, 2172],31,6]
%
% END OF LATTICE L32.6
%
%
% LATTICE L32.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3871230, 46629, 1375902; 46629, -462, -16588; 1375902, -16588, -489017],[33, 11, 1],[-1737, 3259, 31691, 35220, 7902, 1792; -744, 1406, 13656, 15165, 3401, 765; -4862, 9122, 88704, 98582, 22118, 5016],31,7]
%
% END OF LATTICE L32.7
%
%
% LATTICE L32.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2140644, 17160, 11220; 17160, -126, -93; 11220, -93, -58],[132, 3, 1],[-4, -8, 3, 25, 85, 4; -144, -286, 108, 897, 3047, 143; -543, -1089, 407, 3396, 11550, 544],31,8]
%
% END OF LATTICE L32.8
%
%
% LATTICE L32.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[436211160, 10956660, 109743084; 10956660, 275208, 2756504; 109743084, 2756504, 27609437],[132, 4, 1],[3822, 14064, 2594, 63, 181, 1291; 5811, 21373, 3939, 96, 286, 1968; -15772, -58036, -10704, -260, -748, -5328],31,9]
%
% END OF LATTICE L32.9
%
%
% LATTICE L32.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[9032694, 4237167, 376365; 4237167, 1987623, 176550; 376365, 176550, 15682],[33, 33, 1],[1, -127, -345, -1006, -208, 10; -8, 1488, 4038, 11762, 2430, -120; 66, -13704, -37180, -108273, -22365, 1111],31,10]
%
% END OF LATTICE L32.10
%
%
% LATTICE L32.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-19036908, -111276, 86328; -111276, -570, 477; 86328, 477, -382],[396, 3, 1],[23, 217, 8, -4, -8, 11; 3123, 29469, 1087, -543, -1089, 1493; 9097, 85833, 3165, -1582, -3168, 4350],31,11]
%
% END OF LATTICE L32.11
%
%
% LATTICE L32.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-288420, 24552, 12276; 24552, -2090, -1045; 12276, -1045, -522],[132, 11, 1],[-4, 0, 11, 19, 5, 4; -47, -1, 129, 239, 65, 63; 0, 2, 0, -33, -13, -33],31,12]
%
% END OF LATTICE L32.12
%
%
% LATTICE L32.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[256394952, -6351972, 62097420; -6351972, 157368, -1538412; 62097420, -1538412, 15039647],[132, 12, 1],[218, 288, 502, 4849, 18291, 1187; 1, 11, 7, 50, 176, 10; -900, -1188, -2072, -20016, -75504, -4900],31,13]
%
% END OF LATTICE L32.13
%
%
% LATTICE L32.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-45243, 9306, 4653; 9306, -1914, -957; 4653, -957, -478],[99, 33, 1],[-8, 0, 6, 26, 2, 0; -39, -1, 29, 174, 16, 16; 0, 2, 0, -99, -13, -33],31,14]
%
% END OF LATTICE L32.14
%
%
% LATTICE L32.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-41778, -138798, 4653; -138798, -460185, 15444; 4653, 15444, -518],[99, 33, 1],[-31, -1, 85, 152, 122, 36; -8, 0, 22, 38, 30, 8; -517, -9, 1419, 2497, 1989, 561],31,15]
%
% END OF LATTICE L32.15
%
%
% LATTICE L32.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1695276, -147048, 16368; -147048, -12738, 1419; 16368, 1419, -158],[132, 33, 1],[13, 3, 0, -4, 0, 3; 115, 29, 5, -31, -1, 23; 2376, 570, 44, -693, -9, 517],31,16]
%
% END OF LATTICE L32.16
%
%
% LATTICE L32.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2732784120, -25054524, -687827844; -25054524, 229704, 6306096; -687827844, 6306096, 173122765],[396, 12, 1],[-8383, -10757, -2173, -491, -89, -785; -3135, -4015, -809, -186, -44, -298; -33192, -42592, -8604, -1944, -352, -3108],31,17]
%
% END OF LATTICE L32.17
%
%
% LATTICE L32.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[49516292232, -520313508, -12505391712; -520313508, 5467416, 131405724; -12505391712, 131405724, 3158249837],[396, 12, 1],[-9439, -101917, -6007, -99, -3001, -3531; -63, -627, -31, 0, -66, -32; -37372, -403524, -23784, -392, -11880, -13980],31,18]
%
% END OF LATTICE L32.18
%
%
% LATTICE L32.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[190344, 94380, 23232; 94380, 48312, 12628; 23232, 12628, 3647],[132, 44, 1],[-53, 1, -1081, -3445, -1167, -2417; 161, -3, 3285, 10468, 3546, 7344; -220, 4, -4488, -14300, -4844, -10032],31,19]
%
% END OF LATTICE L32.19
%
%
% LATTICE L32.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-473220, 30096, 15048; 30096, -1914, -957; 15048, -957, -478],[396, 33, 1],[-4, 0, 3, 13, 1, 0; -63, -1, 47, 252, 22, 16; 0, 2, 0, -99, -13, -33],31,20]
%
% END OF LATTICE L32.20
%
%
% LATTICE L32.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-23897412, 7632504, -111276; 7632504, -2437710, 35541; -111276, 35541, -518],[396, 33, 1],[27, 1, -74, -133, -107, -32; 77, 3, -211, -380, -306, -92; -517, -9, 1419, 2497, 1989, 561],31,21]
%
% END OF LATTICE L32.21
%
%
% LATTICE L32.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[57816, -1255452, -304128; -1255452, 27379704, 6632604; -304128, 6632604, 1606717],[132, 132, 1],[-150, -52, -38, -9, -1, -15; 13679, 4765, 3505, 799, 61, 1321; -56496, -19680, -14476, -3300, -252, -5456],31,22]
%
% END OF LATTICE L32.22
%
%
% LATTICE L32.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[414216, 169884, -23760; 169884, 81048, -18348; -23760, -18348, 7871],[396, 132, 1],[701, -1, 1135, 12718, 1492, 3338; -2097, 3, -3395, -38043, -4463, -9985; -2772, 4, -4488, -50292, -5900, -13200],31,23]
%
% END OF LATTICE L32.23
%
%
% LATTICE L32.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[529538328, -24809004, 152252892; -24809004, 1162920, -7133544; 152252892, -7133544, 43776103],[396, 132, 1],[-611, -409, -12731, -38082, -38284, -25962; 1810, 1212, 37714, 112811, 113409, 76907; 2420, 1620, 50424, 150832, 151632, 102828],31,24]
%
% END OF LATTICE L32.24
%

\medskip%
%------------------------------WEYL-GROUP-W33--------------------------------
%
\leavevmode\llap{}%
$W_{33\phantom{0}}$%
\qquad\llap{44} lattices, $\chi=15$%
\hfill%
$222224$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L33.1
%
\leavevmode%
${L_{33.1}}$%
{} : {$1\above{1pt}{1pt}{2}{{\rm II}}4\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{2}{}11\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{2\rightarrow N_{33}}%
\EasyButWeakLineBreak%
{${4}\above{1pt}{1pt}{*}{2}{12}\above{1pt}{1pt}{b}{2}{22}\above{1pt}{1pt}{l}{2}{4}\above{1pt}{1pt}{r}{2}{66}\above{1pt}{1pt}{b}{2}{2}\above{1pt}{1pt}{*}{4}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-292380\\1584\\1848
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1584\\-8\\-11
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1848\\-11\\-10
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-110\\-64
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-108\\-66
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4\\440\\253
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\328\\192
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
20\\2178\\1287
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\108\\65
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-292380, 1584, 1848; 1584, -8, -11; 1848, -11, -10],[132, 1, 1],[-1, -1, 4, 3, 20, 1; -110, -108, 440, 328, 2178, 108; -64, -66, 253, 192, 1287, 65],32,1]
%
% END OF LATTICE L33.1
%
\hbox{}\par\smallskip%
%
% LATTICE L33.2
%
\leavevmode%
${L_{33.2}}$%
{} : {$1\above{1pt}{1pt}{2}{2}8\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{2}{}11\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2\rightarrow N'_{22}}%
\EasyButWeakLineBreak%
{${2}\above{1pt}{1pt}{b}{2}{24}\above{1pt}{1pt}{*}{2}{44}\above{1pt}{1pt}{s}{2}{8}\above{1pt}{1pt}{l}{2}{33}\above{1pt}{1pt}{}{2}{1}\above{1pt}{1pt}{}{4}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1159752\\-577368\\7128
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-577368\\-287435\\3548
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7128\\3548\\-43
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
37\\-75\\-55
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
77\\-156\\-108
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-293\\594\\440
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-223\\452\\328
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-749\\1518\\1089
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-38\\77\\54
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-1159752, -577368, 7128; -577368, -287435, 3548; 7128, 3548, -43],[264, 1, 1],[37, 77, -293, -223, -749, -38; -75, -156, 594, 452, 1518, 77; -55, -108, 440, 328, 1089, 54],32,2]
%
% END OF LATTICE L33.2
%
\hbox{}\par\smallskip%
%
% LATTICE L33.3
%
\leavevmode%
${L_{33.3}}$%
{} : {$1\above{1pt}{1pt}{-2}{2}8\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{2}{}11\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{m}%
\EasyButWeakLineBreak%
{${2}\above{1pt}{1pt}{l}{2}{24}\above{1pt}{1pt}{}{2}{11}\above{1pt}{1pt}{r}{2}{8}\above{1pt}{1pt}{s}{2}{132}\above{1pt}{1pt}{*}{2}{4}\above{1pt}{1pt}{*}{4}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-24359016\\35904\\78936
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
35904\\-49\\-119
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
78936\\-119\\-254
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4\\640\\943
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
35\\5592\\8256
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
29\\4631\\6842
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
9\\1436\\2124
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-7\\-1122\\-1650
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-5\\-798\\-1180
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-24359016, 35904, 78936; 35904, -49, -119; 78936, -119, -254],[264, 1, 1],[4, 35, 29, 9, -7, -5; 640, 5592, 4631, 1436, -1122, -798; 943, 8256, 6842, 2124, -1650, -1180],32,3]
%
% END OF LATTICE L33.3
%
%
% LATTICE L33.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[264, -99, 0; -99, 37, 0; 0, 0, 1],[33, 1, 1],[0, 1, -12, -5, -82, -6; 0, 3, -33, -14, -231, -17; 1, 0, -11, -3, -33, -1],32,4]
%
% END OF LATTICE L33.4
%
%
% LATTICE L33.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[2706, 2244, -66; 2244, 1861, -55; -66, -55, 2],[66, 1, 1],[0, -5, -27, -13, -80, -4; 0, 6, 33, 16, 99, 5; 1, 0, 11, 8, 66, 5],32,5]
%
% END OF LATTICE L33.5
%
%
% LATTICE L33.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-2041908, 12012, 16104; 12012, -62, -95; 16104, -95, -127],[132, 1, 1],[4, 31, 49, 7, -8, -4; 16, 120, 187, 26, -33, -15; 495, 3840, 6072, 868, -990, -496],32,6]
%
% END OF LATTICE L33.6
%
%
% LATTICE L33.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-652971, 11748, 222915; 11748, -186, -4011; 222915, -4011, -76100],[33, 3, 1],[327, 423, 4014, 287, -218, -328; 16, 20, 187, 13, -11, -15; 957, 1238, 11748, 840, -638, -960],32,7]
%
% END OF LATTICE L33.7
%
%
% LATTICE L33.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-181302, 2442, -89892; 2442, -32, 1210; -89892, 1210, -44569],[66, 2, 1],[30, 16, -117, -45, -607, -31; -55, -27, 220, 82, 1089, 54; -62, -33, 242, 93, 1254, 64],32,8]
%
% END OF LATTICE L33.8
%
%
% LATTICE L33.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-223674, 3300, -73854; 3300, -48, 1089; -73854, 1089, -24385],[66, 3, 1],[19, 7, -73, -57, -129, -20; -55, -18, 220, 164, 363, 54; -60, -22, 231, 180, 407, 63],32,9]
%
% END OF LATTICE L33.9
%
%
% LATTICE L33.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1486452, -45606, 537471; -45606, -1397, 16489; 537471, 16489, -194338],[33, 11, 1],[152, 581, 166, 129, -28, -148; 231, 897, 258, 203, -42, -232; 440, 1683, 481, 374, -81, -429],32,10]
%
% END OF LATTICE L33.10
%
%
% LATTICE L33.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2646732, -220044, 10428; -220044, -18294, 867; 10428, 867, -41],[132, 3, 1],[1, -5, -38, -9, -1, 5; -11, 60, 451, 106, 11, -59; 21, -4, -132, -48, -22, 24],32,11]
%
% END OF LATTICE L33.11
%
%
% LATTICE L33.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-238260, 2772, 2772; 2772, -30, -33; 2772, -33, -32],[132, 3, 1],[-1, -1, 4, 5, 14, 3; -20, -22, 77, 104, 297, 65; -66, -64, 264, 324, 902, 192],32,12]
%
% END OF LATTICE L33.12
%
%
% LATTICE L33.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[4512684, -224202, 2214498; -224202, 11166, -110022; 2214498, -110022, 1086715],[66, 6, 1],[53, 135, 4957, 1265, 5486, 913; 0, 1, 33, 8, 33, 5; -108, -275, -10098, -2577, -11176, -1860],32,13]
%
% END OF LATTICE L33.13
%
%
% LATTICE L33.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[546702024, -522588, 132395736; -522588, 500, -126556; 132395736, -126556, 32062495],[132, 4, 1],[929, 1076, 5573, 325, 959, 31; 31, 33, 154, 6, 0, 2; -3836, -4443, -23012, -1342, -3960, -128],32,14]
%
% END OF LATTICE L33.14
%
%
% LATTICE L33.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[4935216, -270996, 1193940; -270996, 14888, -65560; 1193940, -65560, 288841],[132, 4, 1],[15, 80, 1194, 164, 4540, 278; 0, 3, 33, 4, 99, 5; -62, -330, -4928, -677, -18744, -1148],32,15]
%
% END OF LATTICE L33.15
%
%
% LATTICE L33.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-625614, -7260, 112794; -7260, -55, 1309; 112794, 1309, -20336],[66, 11, 1],[-121, -119, 44, 361, 218, 119; 2, 0, -1, -6, -3, -1; -671, -660, 244, 2002, 1209, 660],32,16]
%
% END OF LATTICE L33.16
%
%
% LATTICE L33.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-85272, 20328, 1056; 20328, -4845, -252; 1056, -252, -13],[264, 3, 1],[-2, -1, 13, 9, 9, 1; -7, -4, 44, 32, 33, 4; -27, -4, 198, 108, 88, 3],32,17]
%
% END OF LATTICE L33.17
%
%
% LATTICE L33.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1634424, 16104, 11616; 16104, -147, -117; 11616, -117, -82],[264, 3, 1],[-1, 5, 19, 9, 1, -5; -22, 120, 451, 212, 22, -118; -111, 536, 2046, 972, 110, -540],32,18]
%
% END OF LATTICE L33.18
%
%
% LATTICE L33.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[967065, 63129, 33363; 63129, 4125, 2178; 33363, 2178, 1151],[33, 33, 1],[31, 24, 17, 11, 1, 1; 31, 22, 14, 6, 0, 2; -957, -737, -519, -330, -29, -33],32,19]
%
% END OF LATTICE L33.19
%
%
% LATTICE L33.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3828, 660, -396; 660, -88, 77; -396, 77, -38],[132, 11, 1],[7, 11, -2, -21, -14, -9; 14, 24, -4, -44, -30, -20; -44, -66, 13, 132, 87, 55],32,20]
%
% END OF LATTICE L33.20
%
%
% LATTICE L33.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[22440462, 28314, 10688436; 28314, 44, 13486; 10688436, 13486, 5090923],[66, 22, 1],[0, -613, -603, -1598, -1789, -985; 1, 0, 1, 4, 6, 5; 0, 1287, 1266, 3355, 3756, 2068],32,21]
%
% END OF LATTICE L33.21
%
%
% LATTICE L33.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-199452, 49104, -5808; 49104, -12089, 1430; -5808, 1430, -169],[132, 11, 1],[-5, -1, 2, 9, 1, -5; -15, 12, 9, 34, 3, -19; 44, 132, 7, -22, -9, 11],32,22]
%
% END OF LATTICE L33.22
%
%
% LATTICE L33.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[69960, 20724, 16368; 20724, 20652, 4440; 16368, 4440, 3841],[132, 12, 1],[1730, 637, 9659, 551, 757, 189; -201, -74, -1122, -64, -88, -22; -7140, -2629, -39864, -2274, -3124, -780],32,23]
%
% END OF LATTICE L33.23
%
%
% LATTICE L33.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[5188920, -167508, 1255320; -167508, 5424, -40524; 1255320, -40524, 303691],[132, 12, 1],[16, 15, 1789, 281, 2769, 549; 1, 0, 22, 4, 44, 10; -66, -62, -7392, -1161, -11440, -2268],32,24]
%
% END OF LATTICE L33.24
%
%
% LATTICE L33.25
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1239216, -20856, 7128; -20856, -344, 120; 7128, 120, -41],[264, 8, 1],[-1, -1, 4, 2, 31, 2; 2, 0, -11, -3, -33, -1; -168, -174, 660, 338, 5280, 344],32,25]
%
% END OF LATTICE L33.25
%
%
% LATTICE L33.26
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1308912, 7656, 15048; 7656, -40, -88; 15048, -88, -173],[264, 8, 1],[-1, -1, 4, 3, 53, 4; 2, 0, -11, -3, -33, -1; -88, -87, 352, 262, 4620, 348],32,26]
%
% END OF LATTICE L33.26
%
%
% LATTICE L33.27
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[7630590, -20196, -2303796; -20196, 66, 6105; -2303796, 6105, 695557],[66, 33, 1],[0, 185, 273, 1447, 270, 446; 1, -370, -545, -2886, -538, -887; 0, 616, 909, 4818, 899, 1485],32,27]
%
% END OF LATTICE L33.27
%
%
% LATTICE L33.28
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-34584, -4224, -4488; -4224, -473, -506; -4488, -506, -541],[264, 11, 1],[-1, 1, 1, 5, 1, 0; -97, 132, 100, 472, 87, -12; 99, -132, -102, -484, -90, 11],32,28]
%
% END OF LATTICE L33.28
%
%
% LATTICE L33.29
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-17822904, 98472, 77616; 98472, -539, -429; 77616, -429, -338],[264, 11, 1],[-5, -1, 1, 9, 1, -5; -30, 24, 9, 68, 6, -38; -1111, -264, 218, 1980, 222, -1100],32,29]
%
% END OF LATTICE L33.29
%
%
% LATTICE L33.30
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-12540, -21120, 2508; -21120, -35376, 4191; 2508, 4191, -496],[132, 33, 1],[7, 13, -2, -49, -14, -37; -12, -26, 3, 92, 27, 73; -66, -154, 15, 528, 157, 429],32,30]
%
% END OF LATTICE L33.30
%
%
% LATTICE L33.31
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-34279014, -22877118, -10570560; -22877118, -15267648, -7054542; -10570560, -7054542, -3259609],[66, 66, 1],[2, 0, -1, -3, -1, -1; 3687, 615, -1332, -5500, -2221, -3658; -7986, -1331, 2886, 11913, 4810, 7920],32,31]
%
% END OF LATTICE L33.31
%
%
% LATTICE L33.32
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-132, -528, -264; -528, -2046, -1023; -264, -1023, -511],[132, 33, 1],[0, 5, 3, 7, 0, -4; 16, 20, 5, -2, -1, 1; -33, -44, -12, 0, 2, 0],32,32]
%
% END OF LATTICE L33.32
%
%
% LATTICE L33.33
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[101112, -22308, -41316; -22308, 8492, 11792; -41316, 11792, 18889],[132, 44, 1],[1402, 1501, 647, 305, 35, 107; -4321, -4626, -1994, -940, -108, -330; 5764, 6171, 2660, 1254, 144, 440],32,33]
%
% END OF LATTICE L33.33
%
%
% LATTICE L33.34
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[507408, -43692, -156684; -43692, 3784, 13508; -156684, 13508, 48395],[132, 44, 1],[-27, -16, -42, -78, -232, -194; 81, 51, 129, 238, 705, 587; -110, -66, -172, -319, -948, -792],32,34]
%
% END OF LATTICE L33.34
%
%
% LATTICE L33.35
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-528, 2904, -264; 2904, -15816, 1440; -264, 1440, -131],[264, 24, 1],[-1, -1, 4, 4, 25, 6; 2, 0, -11, -3, -11, -1; 24, 2, -132, -42, -176, -24],32,35]
%
% END OF LATTICE L33.35
%
%
% LATTICE L33.36
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-36451536, 69432, 138600; 69432, -120, -264; 138600, -264, -527],[264, 24, 1],[-1, -1, 4, 7, 47, 12; 2, 0, -11, -3, -11, -1; -264, -263, 1056, 1842, 12364, 3156],32,36]
%
% END OF LATTICE L33.36
%
%
% LATTICE L33.37
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-93192, 53064, 4488; 53064, -30030, -2541; 4488, -2541, -215],[264, 33, 1],[1, -1, -1, -3, 0, 1; -15, 28, 18, 28, -4, -29; 198, -352, -234, -396, 47, 363],32,37]
%
% END OF LATTICE L33.37
%
%
% LATTICE L33.38
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-17668200, 169224, 134376; 169224, -1617, -1287; 134376, -1287, -1022],[264, 33, 1],[-16, -15, -1, 9, 1, -5; 32, 40, 5, -4, -2, 2; -2145, -2024, -138, 1188, 134, -660],32,38]
%
% END OF LATTICE L33.38
%
%
% LATTICE L33.39
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2244, 3300, 792; 3300, 25080, 6204; 792, 6204, 1535],[132, 132, 1],[31, 11, 14, 6, 0, 2; -559, -200, -257, -115, -1, -33; 2244, 803, 1032, 462, 4, 132],32,39]
%
% END OF LATTICE L33.39
%
%
% LATTICE L33.40
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[70224, -555852, -135828; -555852, 4399824, 1075140; -135828, 1075140, 262721],[132, 132, 1],[1, -3, -31, -52, -45, -93; -16, 5, 43, 66, 51, 85; 66, -22, -192, -297, -232, -396],32,40]
%
% END OF LATTICE L33.40
%
%
% LATTICE L33.41
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2891856, 2854104, -795432; 2854104, -2816792, 785048; -795432, 785048, -218791],[264, 88, 1],[123, 118, -45, -360, -574, -473; 2, 0, -1, -3, -3, -1; -440, -429, 160, 1298, 2076, 1716],32,41]
%
% END OF LATTICE L33.41
%
%
% LATTICE L33.42
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-276975336, 248842704, -4341480; 248842704, -223567432, 3900512; -4341480, 3900512, -68051],[264, 88, 1],[835, 917, 184, 36, -79, -46; -1, -3, -1, -1, 0, 1; -53328, -58674, -11796, -2354, 5040, 2992],32,42]
%
% END OF LATTICE L33.42
%
%
% LATTICE L33.43
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-173976, 2252184, 18744; 2252184, -29119728, -242352; 18744, -242352, -2017],[264, 264, 1],[2, 0, -1, -3, -1, -1; -35, -13, 16, 86, 41, 90; 4224, 1562, -1932, -10362, -4936, -10824],32,43]
%
% END OF LATTICE L33.43
%
%
% LATTICE L33.44
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1320, 66792, -30624; 66792, -3066096, 1405800; -30624, 1405800, -644557],[264, 264, 1],[2, 0, -1, -3, -1, -1; -121, -116, 44, 817, 497, 1392; -264, -253, 96, 1782, 1084, 3036],32,44]
%
% END OF LATTICE L33.44
%

\medskip%
%------------------------------WEYL-GROUP-W34--------------------------------
%
\leavevmode\llap{}%
$W_{34\phantom{0}}$%
\qquad\llap{88} lattices, $\chi=72$%
\hfill%
$\infty222222\infty222222\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L34.1
%
\leavevmode%
${L_{34.1}}$%
{} : {$1\above{1pt}{1pt}{2}{{\rm II}}4\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{1}{}3\above{1pt}{1pt}{-}{}9\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}11\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{23\rightarrow N_{34},3,2}%
\EasyButWeakLineBreak%
{${132}\above{1pt}{1pt}{3,2}{\infty b}{132}\above{1pt}{1pt}{r}{2}{18}\above{1pt}{1pt}{l}{2}{4}\above{1pt}{1pt}{r}{2}{6}\above{1pt}{1pt}{b}{2}{396}\above{1pt}{1pt}{*}{2}{4}\above{1pt}{1pt}{*}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-6574916700\\52718688\\1769328
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
52718688\\-422706\\-14187
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1769328\\-14187\\-476
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4245449\\496887468\\971019324
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-34075\\-3988139\\-7793634
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1125\\-131670\\-257311
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-311\\-36388\\-71478
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\352\\660
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
31\\3627\\7128
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5\\584\\1180
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-41\\-4801\\-9306
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3505\\-410322\\-798732
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-209\\-24466\\-47662
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-6574916700, 52718688, 1769328; 52718688, -422706, -14187; 1769328, -14187, -476],[396, 3, 1],[-311, 3, 31, 5, -41, -3505, -209, -789, -553, -106, -55, -84, -3095, -141; -36388, 352, 3627, 584, -4801, -410322, -24466, -92356, -64724, -12405, -6436, -9829, -362142, -16498; -71478, 660, 7128, 1180, -9306, -798732, -47662, -180114, -126456, -24282, -12616, -19284, -710820, -32390],33,1]
%
% END OF LATTICE L34.1
%
\hbox{}\par\smallskip%
%
% LATTICE L34.2
%
\leavevmode%
${L_{34.2}}$%
{} : {$1\above{1pt}{1pt}{-2}{2}8\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{1}{}9\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{-2}{}11\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{3m,3,2}%
\EasyButWeakLineBreak%
{${66}\above{1pt}{1pt}{12,11}{\infty a}{264}\above{1pt}{1pt}{s}{2}{36}\above{1pt}{1pt}{s}{2}{8}\above{1pt}{1pt}{l}{2}{3}\above{1pt}{1pt}{}{2}{792}\above{1pt}{1pt}{r}{2}{2}\above{1pt}{1pt}{b}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2375208\\-49104\\-50688
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-49104\\-1014\\-1047
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-50688\\-1047\\-1081
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\92400\\-88704
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\1849\\-1776
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\1925\\-1849
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-5\\-781\\990
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-88\\132
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\156\\-198
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\104\\-148
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\53\\-99
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
83\\792\\-4752
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\-21\\-76
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-2375208, -49104, -50688; -49104, -1014, -1047; -50688, -1047, -1081],[792, 3, 1],[-5, -1, 1, 1, 1, 83, 2, 5, 1, -1, -1, -1, -83, -2; -781, -88, 156, 104, 53, 792, -21, -319, -1012, -306, -204, -178, -13992, -329; 990, 132, -198, -148, -99, -4752, -76, 66, 924, 342, 244, 219, 17424, 412],33,2]
%
% END OF LATTICE L34.2
%
\hbox{}\par\smallskip%
%
% LATTICE L34.3
%
\leavevmode%
${L_{34.3}}$%
{} : {$1\above{1pt}{1pt}{2}{2}8\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{1}{}9\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{-2}{}11\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{32\rightarrow N'_{21},3,m}%
\EasyButWeakLineBreak%
{${66}\above{1pt}{1pt}{12,11}{\infty b}{264}\above{1pt}{1pt}{l}{2}{9}\above{1pt}{1pt}{r}{2}{8}\above{1pt}{1pt}{s}{2}{12}\above{1pt}{1pt}{*}{2}{792}\above{1pt}{1pt}{b}{2}{2}\above{1pt}{1pt}{s}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-35211528\\6384312\\-1161864
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
6384312\\-1157559\\210660
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1161864\\210660\\-38335
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2299969\\-13817232\\-6220368
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
417252\\2506672\\1128477
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-76428\\-459147\\-206704
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1076\\6457\\2871
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-95\\-572\\-264
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-98\\-588\\-261
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
71\\428\\200
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
673\\4046\\1836
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
46759\\281028\\127116
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1336\\8029\\3629
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-35211528, 6384312, -1161864; 6384312, -1157559, 210660; -1161864, 210660, -38335],[792, 3, 1],[1076, -95, -98, 71, 673, 46759, 1336, 4732, 5903, 494, 457, 647, 22937, 512; 6457, -572, -588, 428, 4046, 281028, 8029, 28435, 35464, 2967, 2744, 3884, 137676, 3073; 2871, -264, -261, 200, 1836, 127116, 3629, 12837, 15972, 1332, 1228, 1734, 61380, 1369],33,3]
%
% END OF LATTICE L34.3
%
%
% LATTICE L34.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[33, 0, 0; 0, 0, -1; 0, -1, 0],[33, 1, 1],[-1, 1, 0, -1, -8, -79, -13, -43, -23, -2, -1, -2, -9, -1; 0, 0, -1, -4, -27, -253, -41, -132, -66, -5, -2, -3, -11, -1; -33, 0, 1, -4, -39, -407, -68, -231, -132, -13, -8, -21, -121, -16],33,4]
%
% END OF LATTICE L34.4
%
%
% LATTICE L34.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[66, 0, 66; 0, 960, -25889; 66, -25889, 698233],[66, 1, 1],[11111, 6049, 274, 303, 362, 3973, 511, 989, 1, 1, 247, 1013, 20227, 3339; -300795, -163746, -7416, -8198, -9789, -107382, -13807, -26697, 0, -27, -6688, -27426, -547602, -90395; -11154, -6072, -275, -304, -363, -3982, -512, -990, 0, -1, -248, -1017, -20306, -3352],33,5]
%
% END OF LATTICE L34.5
%
%
% LATTICE L34.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-8580, 132, 2244; 132, -2, -33; 2244, -33, -511],[132, 1, 1],[28, 43, 3, 5, 8, 101, 7, 16, 1, -1, -1, 2, 75, 7; 3300, 4818, 321, 518, 813, 10164, 701, 1584, 66, -99, -74, 297, 9372, 853; -99, -132, -8, -12, -18, -220, -15, -33, 0, 2, 0, -12, -308, -27],33,6]
%
% END OF LATTICE L34.6
%
%
% LATTICE L34.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-8363388, 3417348, 63360; 3417348, -1396334, -25889; 63360, -25889, -480],[132, 1, 1],[-43, -23, -1, -1, -1, -9, -1, -1, 1, 0, -1, -4, -79, -13; 2706, 1848, 115, 176, 267, 3278, 448, 990, 0, -31, -8, 153, 4114, 728; -151602, -102696, -6334, -9624, -14532, -177980, -24294, -53526, 132, 1672, 300, -8778, -232276, -40974],33,7]
%
% END OF LATTICE L34.7
%
%
% LATTICE L34.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-19009320, 4488, 139392; 4488, -1, -33; 139392, -33, -1022],[264, 1, 1],[28, 43, 3, 5, 4, 101, 7, 16, 1, -1, -1, 1, 75, 7; 6600, 9636, 642, 1036, 813, 20328, 1402, 3168, 132, -198, -148, 297, 18744, 1706; 3597, 5544, 388, 648, 519, 13112, 909, 2079, 132, -130, -132, 126, 9592, 897],33,8]
%
% END OF LATTICE L34.8
%
%
% LATTICE L34.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-17160, -17160, 8712; -17160, -17094, 8645; 8712, 8645, -4355],[264, 1, 1],[-1688, -2663, -95, -321, -517, -6543, -454, -1040, -65, 33, 73, -103, -4369, -414; 3333, 5280, 189, 640, 1032, 13068, 907, 2079, 132, -66, -148, 198, 8580, 815; 3234, 5148, 185, 628, 1014, 12848, 892, 2046, 132, -65, -148, 186, 8272, 788],33,9]
%
% END OF LATTICE L34.9
%
%
% LATTICE L34.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-117216, -9207, -495; -9207, -723, -39; -495, -39, -2],[99, 3, 1],[-76, -45, -14, -3, -8, -137, -6, -12, 1, 2, -1, -12, -391, -22; 869, 517, 162, 35, 94, 1617, 71, 143, -11, -24, 11, 136, 4455, 251; 1683, 957, 279, 55, 135, 2178, 92, 165, -33, -27, 29, 285, 8910, 496],33,10]
%
% END OF LATTICE L34.10
%
%
% LATTICE L34.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-728678610, 12410046, 832986; 12410046, -211353, -14187; 832986, -14187, -952],[198, 3, 1],[-789, -553, -106, -55, -84, -3095, -141, -311, 3, 31, 5, -41, -3505, -209; -40282, -28226, -5409, -2806, -4285, -157872, -7192, -15862, 154, 1581, 254, -2095, -178992, -10672; -90057, -63228, -12141, -6308, -9642, -355410, -16195, -35739, 330, 3564, 590, -4653, -399366, -23831],33,11]
%
% END OF LATTICE L34.11
%
%
% LATTICE L34.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-1187604, -24552, -26136; -24552, -507, -540; -26136, -540, -575],[396, 3, 1],[-5, -1, 1, 1, 2, 83, 2, 5, 1, -1, -1, -2, -83, -2; -286, -22, 57, 30, 7, -1584, -59, -286, -550, -135, -82, -137, -5280, -123; 495, 66, -99, -74, -99, -2376, -38, 33, 462, 171, 122, 219, 8712, 206],33,12]
%
% END OF LATTICE L34.12
%
%
% LATTICE L34.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-132033, 891, 48906; 891, -6, -330; 48906, -330, -18115],[33, 3, 1],[-205, -114, -32, -18, -14, -218, -27, -15, 4, 2, -12, -36, -1102, -183; 957, 583, 189, 127, 117, 2046, 272, 187, -11, -33, 29, 143, 4818, 820; -572, -319, -90, -51, -40, -627, -78, -44, 11, 6, -33, -100, -3069, -510],33,13]
%
% END OF LATTICE L34.13
%
%
% LATTICE L34.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-18817788, 5126022, -9313854; 5126022, -1396334, 2537122; -9313854, 2537122, -4609887],[66, 2, 1],[77177, 26042, 3199, 2422, 7298, 44639, 12179, 26795, -49, -836, -59, 4517, 59333, 20903; 2706, 924, 115, 88, 267, 1639, 448, 990, 0, -31, -4, 153, 2057, 728; -154440, -52107, -6400, -4845, -14598, -89287, -24360, -53592, 99, 1672, 117, -9042, -118745, -41832],33,14]
%
% END OF LATTICE L34.14
%
%
% LATTICE L34.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-22302522, 6834696, -7349694; 6834696, -2094501, 2252343; -7349694, 2252343, -2422058],[66, 3, 1],[25568, 17277, 3188, 4833, 2429, 89179, 12168, 8928, -29, -836, -129, 1491, 117797, 20760; 902, 616, 115, 176, 89, 3278, 448, 330, 0, -31, -8, 51, 4114, 728; -76747, -51854, -9567, -14502, -7288, -267564, -36507, -26785, 88, 2508, 384, -4477, -353628, -62319],33,15]
%
% END OF LATTICE L34.15
%
%
% LATTICE L34.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-363330, -30492, -14157; -30492, -2559, -1188; -14157, -1188, -544],[99, 3, 1],[-1000, -606, -65, -130, -119, -691, -275, -188, 12, 11, -32, -151, -1685, -859; 11957, 7249, 778, 1557, 1426, 8283, 3297, 2255, -143, -132, 381, 1804, 20141, 10269; -99, -66, -8, -18, -18, -110, -45, -33, 0, 2, 0, -12, -154, -81],33,16]
%
% END OF LATTICE L34.16
%
%
% LATTICE L34.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-19437, 10890, 7128; 10890, -5984, -3993; 7128, -3993, -2614],[33, 11, 1],[1001, 613, 734, 497, 1382, 735, 1077, 203, -11, -132, 105, 1628, 1673, 3137; -9, -6, -8, -6, -18, -10, -15, -3, 0, 2, 0, -12, -14, -27; 2742, 1680, 2013, 1364, 3795, 2019, 2959, 558, -30, -363, 286, 4455, 4581, 8591],33,17]
%
% END OF LATTICE L34.17
%
%
% LATTICE L34.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-395868, 1584, 8184; 1584, -6, -33; 8184, -33, -169],[132, 3, 1],[5, 1, -1, -3, -2, -83, -6, -5, -1, 1, 3, 2, 83, 6; 165, 22, -33, -74, -33, -792, -38, 11, 154, 57, 122, 73, 2904, 206; 209, 44, -42, -132, -92, -3960, -291, -253, -88, 36, 120, 82, 3432, 249],33,18]
%
% END OF LATTICE L34.18
%
%
% LATTICE L34.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2038702644, 1706496, 16948668; 1706496, -1428, -14187; 16948668, -14187, -140902],[132, 3, 1],[-311, 3, 31, 15, -41, -3505, -627, -789, -553, -106, -165, -84, -3095, -423; -10142, 88, 1012, 520, -1298, -112024, -20074, -25322, -17820, -3430, -5356, -2732, -100760, -13778; -36388, 352, 3627, 1752, -4801, -410322, -73398, -92356, -64724, -12405, -19308, -9829, -362142, -49494],33,19]
%
% END OF LATTICE L34.19
%
%
% LATTICE L34.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[12673841334, 8543370, 6221703840; 8543370, 5760, 4194018; 6221703840, 4194018, 3054290933],[66, 6, 1],[-797048, -216959, -58963, -32599, -25961, -427336, -109918, -70896, -27, -215, -26579, -72669, -2176496, -718574; -100265, -27291, -7416, -4099, -3263, -53691, -13807, -8899, 0, -27, -3344, -9142, -273801, -90395; 1623754, 441991, 120120, 66411, 52888, 870573, 223926, 144430, 55, 438, 54147, 148042, 4433979, 1463886],33,20]
%
% END OF LATTICE L34.20
%
%
% LATTICE L34.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[78936, 39468, 19536; 39468, 19732, 9768; 19536, 9768, 4835],[132, 4, 1],[1975, 1061, 93, 47, 95, 215, 48, 49, -49, -1, 45, 365, 1809, 596; 363, 198, 18, 10, 24, 66, 17, 33, 0, 0, 8, 66, 330, 109; -8712, -4686, -412, -210, -432, -1001, -228, -264, 198, 4, -198, -1608, -7975, -2628],33,21]
%
% END OF LATTICE L34.21
%
%
% LATTICE L34.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[6082971576, 3417348, 1474659648; 3417348, 1920, 828448; 1474659648, 828448, 357493217],[132, 4, 1],[-172199, -46874, -8493, -2348, -11221, -61577, -7920, -15329, -8, -31, -1914, -31399, -313479, -51748; -300795, -81873, -14832, -4099, -19578, -107382, -13807, -26697, 0, -54, -3344, -54852, -547602, -90395; 711018, 193545, 35068, 9695, 46332, 254254, 32702, 63294, 33, 128, 7903, 129648, 1294370, 213670],33,22]
%
% END OF LATTICE L34.22
%
%
% LATTICE L34.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-333745038, -32039172, 9040086; -32039172, -3075720, 867813; 9040086, 867813, -244769],[198, 3, 1],[59531, 40371, 2493, 11375, 5729, 70189, 28747, 21121, -45, -660, -377, 3436, 91115, 48239; -669713, -454168, -28046, -127968, -64451, -789624, -323403, -237611, 506, 7425, 4242, -38654, -1025024, -542679; -175758, -119196, -7361, -33588, -16917, -207262, -84888, -62370, 132, 1949, 1116, -10143, -268994, -142416],33,23]
%
% END OF LATTICE L34.23
%
%
% LATTICE L34.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-548017734, -2405634, 93741912; -2405634, -10560, 411499; 93741912, 411499, -16035149],[66, 11, 1],[449, 313, 219, 341, 523, 587, 885, 179, 1, -62, -27, 262, 669, 1313; -6891, -4668, -3167, -4812, -7266, -8090, -12147, -2433, 6, 836, 150, -4389, -10558, -20487; 2448, 1710, 1199, 1870, 2871, 3224, 4862, 984, 6, -341, -154, 1419, 3640, 7150],33,24]
%
% END OF LATTICE L34.24
%
%
% LATTICE L34.25
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-791736, 1584, 16368; 1584, -3, -33; 16368, -33, -338],[264, 3, 1],[5, 1, -1, -3, -1, -83, -6, -5, -1, 1, 3, 1, 83, 6; 330, 44, -66, -148, -33, -1584, -76, 22, 308, 114, 244, 73, 5808, 412; 209, 44, -42, -132, -46, -3960, -291, -253, -88, 36, 120, 41, 3432, 249],33,25]
%
% END OF LATTICE L34.25
%
%
% LATTICE L34.26
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-11737176, -1932480, 195624; -1932480, -318153, 32229; 195624, 32229, -3242],[264, 3, 1],[1795, -169, -163, 387, 1163, 80357, 6879, 8105, 10069, 838, 2313, 1087, 38443, 2571; -9812, 924, 891, -2116, -6358, -439296, -37606, -44308, -55044, -4581, -12644, -5942, -210144, -14054; 10769, -1012, -978, 2316, 6970, 481668, 41235, 48587, 60368, 5025, 13872, 6520, 230604, 15423],33,26]
%
% END OF LATTICE L34.26
%
%
% LATTICE L34.27
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[66, -1089, 0; -1089, 19041, -33; 0, -33, 1],[33, 33, 1],[180, 98, 293, 162, 129, 193, 273, 16, 0, 1, 132, 361, 983, 1785; 11, 6, 18, 10, 8, 12, 17, 1, 0, 0, 8, 22, 60, 109; 320, 175, 528, 297, 242, 369, 528, 32, 1, 0, 231, 638, 1743, 3168],33,27]
%
% END OF LATTICE L34.27
%
%
% LATTICE L34.28
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-7524, -2376, 1980; -2376, -750, 627; 1980, 627, -511],[396, 3, 1],[-64, 7, 4, -13, -41, -949, -244, -288, -359, -20, -83, -39, -459, -92; 176, -22, -11, 42, 121, 2772, 711, 836, 1034, 57, 234, 109, 1276, 255; -33, 0, 2, 0, -12, -308, -81, -99, -132, -8, -36, -18, -220, -45],33,28]
%
% END OF LATTICE L34.28
%
%
% LATTICE L34.29
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3642080508, -67173480, -1145530980; -67173480, -1238880, -21127893; -1145530980, -21127893, -360299842],[396, 3, 1],[-184075, 573, 5746, 2729, -30652, -807831, -427169, -526217, -355719, -21889, -99587, -50063, -612753, -250837; 580030, -1804, -18106, -8604, 96580, 2545400, 1345974, 1658074, 1120856, 68972, 313800, 157750, 1930808, 790398; 551232, -1716, -17207, -8172, 91791, 2419142, 1279206, 1575816, 1065240, 65549, 298224, 149919, 1834954, 751158],33,29]
%
% END OF LATTICE L34.29
%
%
% LATTICE L34.30
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[26491880646, -362445534, 13109774040; -362445534, 4958772, -179359824; 13109774040, -179359824, 6487503763],[198, 6, 1],[-4804960, -1302243, -351019, -63897, -150673, -2459596, -209826, -400680, 833, -3911, -54413, -440877, -13157324, -1446514; -55363, -15004, -4044, -736, -1735, -28314, -2415, -4609, 11, -45, -627, -5080, -151602, -16667; 9708204, 2631123, 709218, 129101, 304428, 4969503, 423944, 809556, -1683, 7902, 109939, 890772, 26583777, 2922616],33,30]
%
% END OF LATTICE L34.30
%
%
% LATTICE L34.31
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[209269820628, -14403708198, 104004768582; -14403708198, 991384278, -7158482448; 104004768582, -7158482448, 51689210873],[198, 6, 1],[-3140669, -854544, -77341, -128008, -101612, -555867, -428137, -274567, 735, -278, -104849, -286483, -2859369, -2831861; 214258, 58300, 5277, 8736, 6937, 37961, 29244, 18766, -44, 19, 7152, 19543, 195063, 193188; 6349068, 1727517, 156350, 258777, 205416, 1123727, 865512, 555060, -1485, 562, 211959, 579144, 5780401, 5724792],33,31]
%
% END OF LATTICE L34.31
%
%
% LATTICE L34.32
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-15180, -660, -792; -660, -22, -33; -792, -33, -41],[132, 11, 1],[17, 17, 7, 5, 2, -1, -2, -1, -1, 1, 11, 38, 65, 58; 99, 102, 45, 38, 27, 12, 2, -3, -6, 3, 58, 213, 372, 334; -417, -420, -176, -132, -66, 4, 33, 21, 24, -22, -264, -924, -1588, -1419],33,32]
%
% END OF LATTICE L34.32
%
%
% LATTICE L34.33
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-9141396, -205524, -2821500; -205524, -4620, -63437; -2821500, -63437, -870854],[132, 11, 1],[223, 251, 243, 447, 731, 829, 1255, 253, -13, -124, -209, -136, 123, 411; -1350, -1608, -1596, -2968, -4878, -5544, -8402, -1698, 84, 834, 1444, 1068, -552, -2266; -624, -696, -671, -1232, -2013, -2282, -3454, -696, 36, 341, 572, 363, -358, -1166],33,33]
%
% END OF LATTICE L34.33
%
%
% LATTICE L34.34
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[9319728, 11957814, 4437972; 11957814, 15361126, 5694194; 4437972, 5694194, 2113323],[66, 22, 1],[796465, 216793, 216016, 119409, 285209, 142231, 402367, 70747, 10, 787, 97394, 798806, 724981, 2632875; -1014, -276, -275, -152, -363, -181, -512, -90, 0, -1, -124, -1017, -923, -3352; -1669842, -454521, -452892, -250349, -597960, -298197, -843590, -148326, -21, -1650, -204193, -1674750, -1519971, -5519998],33,34]
%
% END OF LATTICE L34.34
%
%
% LATTICE L34.35
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1206744, -90684, 291588; -90684, 6924, -21912; 291588, -21912, 70457],[132, 12, 1],[1670, 101, 29, 1101, 2995, 44830, 14799, 16414, 8941, 2437, 1365, 1115, 9422, 2463; 11, 0, 0, 8, 22, 330, 109, 121, 66, 18, 10, 8, 66, 17; -6908, -418, -120, -4554, -12388, -185427, -61212, -67892, -36982, -10080, -5646, -4612, -38973, -10188],33,35]
%
% END OF LATTICE L34.35
%
%
% LATTICE L34.36
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[8836764288, -232049004, 2139876156; -232049004, 6093576, -56192076; 2139876156, -56192076, 518184011],[132, 12, 1],[-129775, 301, -2534, -52943, -285968, -8534156, -1407359, -1558285, -422316, -227656, -62152, -97682, -1594204, -203971; -154, 0, -3, -62, -335, -9999, -1649, -1826, -495, -267, -73, -115, -1881, -241; 535898, -1243, 10464, 218625, 1180888, 35241294, 5811606, 6434846, 1743929, 940092, 256653, 403372, 6583170, 842286],33,36]
%
% END OF LATTICE L34.36
%
%
% LATTICE L34.37
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2132427000, -60572160, 549261504; -60572160, -1720568, 15601920; 549261504, 15601920, -141476449],[264, 8, 1],[-14851, 17, 464, 43, -2425, -32121, -11335, -41953, -14218, -1755, -1334, -4030, -24683, -6739; -15807, 0, 495, 64, -2442, -32835, -11621, -43197, -14751, -1836, -1405, -4263, -26169, -7153; -59400, 66, 1856, 174, -9684, -128326, -45288, -167640, -56826, -7016, -5334, -16116, -98714, -26952],33,37]
%
% END OF LATTICE L34.37
%
%
% LATTICE L34.38
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-9072106032, 133284888, 70813776; 133284888, -1958152, -1040392; 70813776, -1040392, -552741],[264, 8, 1],[-15805, -1, 495, 65, -2434, -16378, -11595, -43111, -14728, -1834, -1404, -4261, -13080, -7151; -504768, -33, 15809, 2077, -77727, -523028, -370286, -1376760, -470349, -58571, -44839, -136083, -417736, -228382; -1074744, -66, 33660, 4418, -165528, -1113783, -788512, -2931720, -1001550, -124716, -95474, -289752, -889449, -486272],33,38]
%
% END OF LATTICE L34.38
%
%
% LATTICE L34.39
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[61172166, 37542186, 4173642; 37542186, 23041689, 2562351; 4173642, 2562351, 285320],[66, 33, 1],[-124483, -67767, -101286, -111977, -44576, -133377, -188659, -11057, -3, -369, -91333, -124849, -679863, -1234511; 248628, 135350, 202297, 223650, 89031, 266392, 376806, 22084, 6, 737, 182418, 249359, 1357880, 2465670; -411905, -224236, -335148, -370524, -147499, -441336, -624261, -36587, -10, -1221, -302214, -413116, -2249616, -4084905],33,39]
%
% END OF LATTICE L34.39
%
%
% LATTICE L34.40
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-157144680, -52368624, 400752; -52368624, -17451897, 133551; 400752, 133551, -1022],[792, 3, 1],[-112, 15, 7, -29, -40, -1823, -467, -548, -675, -37, -151, -35, -817, -163; 352, -44, -22, 84, 121, 5544, 1422, 1672, 2068, 114, 468, 109, 2552, 510; 2079, 132, -130, -396, 126, 9592, 2691, 3597, 5544, 388, 1944, 519, 13112, 2727],33,40]
%
% END OF LATTICE L34.40
%
%
% LATTICE L34.41
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2745549576, -499033656, 3457872; -499033656, -90704823, 628506; 3457872, 628506, -4355],[792, 3, 1],[-361, 7, 11, -13, -149, -3721, -973, -1179, -1547, -46, -407, -201, -2439, -497; 2167, -44, -66, 84, 902, 22484, 5877, 7117, 9328, 277, 2448, 1208, 14652, 2985; 26103, -792, -791, 1800, 11868, 290356, 75591, 90981, 117876, 3452, 30132, 14742, 177980, 36171],33,41]
%
% END OF LATTICE L34.41
%
%
% LATTICE L34.42
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2124408, 5280, 13200; 5280, -11, -33; 13200, -33, -82],[264, 11, 1],[1, 1, -1, -11, -19, -65, -58, -17, -17, -7, -5, -1, 1, 2; 18, 12, -18, -148, -243, -816, -724, -210, -204, -78, -44, 3, 48, 52; 153, 156, -154, -1716, -2970, -10168, -9075, -2661, -2664, -1100, -792, -165, 136, 297],33,42]
%
% END OF LATTICE L34.42
%
%
% LATTICE L34.43
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2602776, 31680, -798864; 31680, -385, 9724; -798864, 9724, -245193],[264, 11, 1],[-62, 19, 21, -153, -857, -1669, -1544, -482, -563, -157, -391, -503, -507, -360; -177, 48, 61, -368, -2184, -4300, -3989, -1251, -1476, -418, -1060, -1386, -1412, -1009; 195, -60, -66, 484, 2706, 5268, 4873, 1521, 1776, 495, 1232, 1584, 1596, 1133],33,43]
%
% END OF LATTICE L34.43
%
%
% LATTICE L34.44
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[198, -99, 0; -99, -41217, 3795; 0, 3795, -349],[99, 33, 1],[157, 84, 241, 40, 79, 95, 38, 3, -4, -1, 40, 321, 865, 522; 311, 166, 474, 78, 152, 180, 71, 5, -8, 0, 80, 638, 1716, 1035; 3378, 1803, 5148, 847, 1650, 1953, 770, 54, -87, 0, 869, 6930, 18639, 11242],33,44]
%
% END OF LATTICE L34.44
%
%
% LATTICE L34.45
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-198, -3366, -297; -3366, -56067, -4950; -297, -4950, -437],[99, 33, 1],[42, 23, 23, 37, 27, 12, 47, 2, -1, -1, 29, 83, 76, 415; 34, 17, 14, 15, 4, -1, -12, -2, -1, 2, 33, 76, 65, 348; -417, -210, -176, -198, -66, 2, 99, 21, 12, -22, -396, -924, -794, -4257],33,45]
%
% END OF LATTICE L34.45
%
%
% LATTICE L34.46
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-494868, -10164, 8052; -10164, -198, 165; 8052, 165, -131],[132, 33, 1],[1, -1, -2, 25, 37, 205, 187, 19, 21, 32, 35, 13, 35, 23; 3, -2, -7, 42, 69, 392, 360, 37, 42, 67, 78, 31, 88, 60; 65, -64, -132, 1584, 2354, 13056, 11913, 1211, 1340, 2046, 2244, 836, 2256, 1485],33,46]
%
% END OF LATTICE L34.46
%
%
% LATTICE L34.47
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2503908, 72732, 69300; 72732, 2112, 2013; 69300, 2013, 1918],[132, 33, 1],[1, -3, -31, -165, -169, -835, -1473, -141, -67, -74, -45, -6, -5, 3; -2, 8, 92, 520, 542, 2696, 4766, 458, 220, 250, 164, 28, 40, 22; -34, 100, 1023, 5412, 5533, 27318, 48180, 4610, 2188, 2409, 1452, 187, 138, -132],33,47]
%
% END OF LATTICE L34.47
%
%
% LATTICE L34.48
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-34354858956, -22514946498, -10395102630; -22514946498, -14755491102, -6812578674; -10395102630, -6812578674, -3145352999],[66, 66, 1],[-2297, -778, -3167, -2406, -2422, -4045, -12147, -811, 1, 836, 75, -1463, -5279, -20487; 69018, 23326, 94725, 71822, 72207, 120513, 361772, 24134, -38, -24861, -1958, 44233, 158943, 616324; -141896, -47951, -194700, -147609, -148390, -247653, -743424, -49592, 79, 51084, 3993, -90970, -326811, -1267200],33,48]
%
% END OF LATTICE L34.48
%
%
% LATTICE L34.49
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[24542100, 400752, -6195024; 400752, 6612, -101160; -6195024, -101160, 1563775],[396, 12, 1],[6195, 383, 109, 1357, 11073, 165743, 18238, 60685, 33057, 9011, 1683, 4127, 34897, 3042; 154, 11, 3, 33, 269, 4026, 443, 1474, 803, 219, 41, 101, 858, 75; 24552, 1518, 432, 5378, 43884, 656865, 72280, 240504, 131010, 35712, 6670, 16356, 138303, 12056],33,49]
%
% END OF LATTICE L34.49
%
%
% LATTICE L34.50
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[4039992, -96228, -1008612; -96228, 2292, 24024; -1008612, 24024, 251807],[396, 12, 1],[-5, -17, 1, 47, 119, 578, 568, 621, 325, 27, 37, 21, 38, 20; -209, -22, 0, -102, -286, -1441, -1431, -1595, -880, -82, -144, -124, -363, -291; 0, -66, 4, 198, 504, 2453, 2412, 2640, 1386, 116, 162, 96, 187, 108],33,50]
%
% END OF LATTICE L34.50
%
%
% LATTICE L34.51
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[105967522584, -1662977844, -26764213212; -1662977844, 26097648, 420018252; -26764213212, 420018252, 6759836329],[396, 12, 1],[434888, -975, 8491, 59113, 957895, 28586653, 1571401, 5219772, 1414640, 762599, 69402, 327255, 5341307, 227809; -4609, 11, -90, -627, -10160, -303204, -16667, -55363, -15004, -8088, -736, -3470, -56628, -2415; 1722138, -3861, 33624, 234085, 3793224, 113201946, 6222682, 20670078, 5601915, 3019860, 274829, 1295916, 21151350, 902114],33,51]
%
% END OF LATTICE L34.51
%
%
% LATTICE L34.52
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[31635263916432, -431868139164, -7943018067468; -431868139164, 5895638808, 108433943880; -7943018067468, 108433943880, 1994342016137],[396, 12, 1],[776433, -1649, 1572, 295519, 1615098, 16120958, 7983043, 8853803, 2409208, 436166, 361088, 573592, 3139514, 1209455; 8404, -11, 17, 3183, 17399, 173679, 86007, 95392, 25960, 4701, 3894, 6191, 33913, 13071; 3091902, -6567, 6260, 1176813, 6431628, 64196726, 31789998, 35257530, 9593925, 1736896, 1437921, 2284152, 12502138, 4816278],33,52]
%
% END OF LATTICE L34.52
%
%
% LATTICE L34.53
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[280236, -20592, -83292; -20592, 1628, 6204; -83292, 6204, 24817],[132, 44, 1],[2030, 1075, 1019, 531, 1223, 306, 869, 158, 19, 75, 563, 4247, 1882, 6789; -6057, -3207, -3039, -1583, -3645, -912, -2590, -471, -57, -225, -1681, -12675, -5616, -20258; 8328, 4410, 4180, 2178, 5016, 1255, 3564, 648, 78, 308, 2310, 17424, 7721, 27852],33,53]
%
% END OF LATTICE L34.53
%
%
% LATTICE L34.54
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[493976208, 82141884, -61123524; 82141884, 13659272, -10163956; -61123524, -10163956, 7563363],[132, 44, 1],[-126331, -33631, -64238, -16659, -74416, -35636, -49171, -8113, 20, -2984, -16952, -261694, -233252, -421383; 378531, 100770, 192479, 49916, 222975, 106777, 147332, 24309, -60, 8941, 50794, 784125, 698903, 1262608; -512262, -136371, -260480, -67551, -301752, -144502, -199386, -32898, 81, -12100, -68739, -1061148, -945818, -1708674],33,54]
%
% END OF LATTICE L34.54
%
%
% LATTICE L34.55
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-78316392, 84098520, 32038512; 84098520, -90307536, -34403928; 32038512, -34403928, -13106659],[264, 24, 1],[-8312, 9, 835, 297, -851, -39698, -14418, -18528, -6719, -2665, -2127, -2199, -40822, -11202; -1639, 0, 165, 64, -154, -7425, -2711, -3509, -1287, -516, -415, -431, -8019, -2203; -16016, 22, 1608, 558, -1676, -77550, -28128, -36080, -13046, -5160, -4110, -4244, -78738, -21600],33,55]
%
% END OF LATTICE L34.55
%
%
% LATTICE L34.56
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-6795580176, 66322344, 39389856; 66322344, -647256, -384432; 39389856, -384432, -228319],[264, 24, 1],[-1637, -1, 165, 67, -146, -3594, -2633, -3423, -1264, -510, -412, -429, -3996, -2197; -16060, -11, 1619, 661, -1423, -35123, -25742, -33484, -12375, -4997, -4039, -4207, -39193, -21550; -255376, -154, 25740, 10446, -22792, -560901, -410904, -534160, -197230, -79572, -64278, -66928, -623403, -342744],33,56]
%
% END OF LATTICE L34.56
%
%
% LATTICE L34.57
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[4679334, -2250468, -197208; -2250468, 1082301, 94842; -197208, 94842, 8311],[198, 33, 1],[-1, 3, 31, 55, 169, 835, 491, 141, 67, 74, 15, 6, 5, -1; 25, -70, -699, -1214, -3706, -18264, -10731, -3077, -1456, -1590, -312, -109, -48, 49; -309, 870, 8712, 15158, 46299, 228222, 134101, 38457, 18204, 19899, 3916, 1386, 666, -583],33,57]
%
% END OF LATTICE L34.57
%
%
% LATTICE L34.58
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-12858714, -872784, -33858; -872784, -58179, -2211; -33858, -2211, -82],[198, 33, 1],[-30, 1, 15, 95, 42, 31, 100, -2, -17, -23, -143, -82, -95, -436; 838, -28, -419, -2652, -1171, -862, -2772, 58, 476, 643, 3996, 2291, 2654, 12180; -10209, 342, 5104, 32274, 14223, 10426, 33363, -747, -5820, -7843, -48708, -27918, -32338, -148401],33,58]
%
% END OF LATTICE L34.58
%
%
% LATTICE L34.59
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-989736, -505032, 16104; -505032, -257697, 8217; 16104, 8217, -262],[264, 33, 1],[-18, -21, -35, -43, -9, -53, -37, -2, 1, 5, -17, -16, -187, -173; 74, 84, 134, 156, 31, 176, 120, 6, -4, -14, 84, 69, 784, 720; 1211, 1340, 2046, 2244, 418, 2256, 1485, 65, -64, -132, 1584, 1177, 13056, 11913],33,59]
%
% END OF LATTICE L34.59
%
%
% LATTICE L34.60
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3565320, 20064, 10824; 20064, -99, -66; 10824, -66, -31],[264, 33, 1],[19, 21, 16, 35, 13, 35, 23, 1, -1, -1, 25, 37, 205, 187; 1365, 1508, 1148, 2508, 930, 2500, 1641, 71, -72, -71, 1800, 2660, 14732, 13437; 3719, 4112, 3135, 6864, 2552, 6876, 4521, 197, -196, -198, 4884, 7238, 40116, 36597],33,60]
%
% END OF LATTICE L34.60
%
%
% LATTICE L34.61
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1250172, -5487768, -460152; -5487768, -24065349, -2017752; -460152, -2017752, -169177],[396, 33, 1],[124, -123, -251, 1017, 4528, 25105, 7635, 2328, 2575, 3929, 1435, 1602, 4319, 947; -434, 430, 879, -3554, -15827, -87756, -26689, -8138, -9002, -13737, -5018, -5603, -15108, -3313; 4839, -4794, -9801, 39622, 176451, 978372, 297550, 90729, 100362, 153153, 55946, 62469, 168444, 36938],33,61]
%
% END OF LATTICE L34.61
%
%
% LATTICE L34.62
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-187308, 60192, -2772; 60192, -19338, 891; -2772, 891, -41],[396, 33, 1],[0, -1, 0, 25, 33, 59, 160, 16, 17, 8, 23, 7, 5, 8; 1, -2, -1, 42, 61, 112, 306, 31, 34, 17, 54, 19, 16, 30; 21, 24, -22, -792, -924, -1588, -4257, -417, -420, -176, -396, -66, 4, 99],33,62]
%
% END OF LATTICE L34.62
%
%
% LATTICE L34.63
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[9358668, -3526776, -313236; -3526776, 1329042, 118041; -313236, 118041, 10484],[396, 33, 1],[-1, 3, 31, 55, 169, 835, 491, 141, 67, 74, 15, 6, 5, -1; 16, -40, -375, -624, -1879, -9210, -5402, -1544, -724, -771, -140, -31, 42, 54; -210, 540, 5148, 8668, 26202, 128628, 75482, 21594, 10152, 10890, 2024, 528, -324, -638],33,63]
%
% END OF LATTICE L34.63
%
%
% LATTICE L34.64
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-25717428, -19491120, 4732596; -19491120, -14772120, 3586737; 4732596, 3586737, -870854],[396, 33, 1],[1573, -57, -784, -4807, -1984, -1241, -3167, 311, 999, 1255, 7633, 4339, 5009, 22949; -3206, 116, 1598, 9804, 4052, 2544, 6534, -626, -2032, -2556, -15552, -8842, -10208, -46770; -4656, 168, 2321, 14256, 5907, 3734, 9702, -888, -2940, -3707, -22572, -12837, -14822, -67914],33,64]
%
% END OF LATTICE L34.64
%
%
% LATTICE L34.65
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[469425330, 12821292, 232327656; 12821292, 350130, 6345504; 232327656, 6345504, 114983441],[198, 66, 1],[1703, 46, -27316, -34534, -230147, -585320, -694575, -202739, -50305, -123461, -15725, -21148, -17788, -9051; 55, 1, -891, -1123, -7480, -19020, -22569, -6587, -1634, -4008, -510, -685, -576, -293; -3444, -93, 55242, 69839, 465432, 1183707, 1404656, 410004, 101733, 249678, 31801, 42768, 35973, 18304],33,65]
%
% END OF LATTICE L34.65
%
%
% LATTICE L34.66
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[40454590770, 1113520518, 20021771286; 1113520518, 30649872, 551103168; 20021771286, 551103168, 9909167731],[198, 66, 1],[-12310, 46, -2265, -77570, -199601, -177909, -1928420, -192714, -51302, -48991, -76198, -56679, -27115, -224332; 49, 1, 9, 279, 716, 638, 6915, 691, 184, 176, 276, 209, 102, 855; 24870, -93, 4576, 156717, 403260, 359435, 3896046, 389346, 103647, 98978, 153945, 114510, 54781, 453222],33,66]
%
% END OF LATTICE L34.66
%
%
% LATTICE L34.67
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[6996, -175692, -42504; -175692, 4681512, 1132560; -42504, 1132560, 273991],[132, 132, 1],[-1, 0, -2, -16, -40, -53, -191, -19, -10, -28, -14, -10, -7, -19; 448, 15, 447, 4997, 12889, 17253, 62359, 6236, 3327, 9579, 5029, 3821, 2799, 7823; -1852, -62, -1848, -20658, -53284, -71325, -257796, -25780, -13754, -39600, -20790, -15796, -11571, -32340],33,67]
%
% END OF LATTICE L34.67
%
%
% LATTICE L34.68
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-5544, -42900, -10428; -42900, 2095104, 509520; -10428, 509520, 123913],[132, 132, 1],[1, 0, -33, -62, -275, -699, -1244, -121, -30, -147, -28, -25, -21, -16; -303, -9, 9694, 18401, 81768, 207968, 370187, 36019, 8938, 43880, 8386, 7522, 6328, 4831; 1246, 37, -39864, -75669, -336248, -855210, -1522290, -148118, -36755, -180444, -34485, -30932, -26022, -19866],33,68]
%
% END OF LATTICE L34.68
%
%
% LATTICE L34.69
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-776677176, -63310896, 12199176; -63310896, -5160792, 994416; 12199176, 994416, -191609],[792, 24, 1],[1869, -16, -185, -8, 300, 12097, 1427, 5303, 1809, 674, 171, 515, 9419, 855; -24607, 209, 2436, 107, -3937, -158895, -18747, -69685, -23782, -8865, -2250, -6778, -123981, -11255; -8712, 66, 864, 46, -1332, -54450, -6440, -24024, -8250, -3096, -790, -2388, -43758, -3976],33,69]
%
% END OF LATTICE L34.69
%
%
% LATTICE L34.70
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-26217286128, 8814306600, 119875536; 8814306600, -2963388360, -40302408; 119875536, -40302408, -548117],[792, 24, 1],[-14435, -4, 1454, 192, -1325, -32240, -7859, -30577, -11249, -4523, -1215, -3790, -35278, -6463; -38390, -11, 3867, 511, -3521, -85701, -20892, -81290, -29909, -12027, -3231, -10079, -93819, -17188; -334224, -66, 33660, 4418, -30888, -749529, -182632, -710160, -261030, -104868, -28154, -87792, -817047, -149672],33,70]
%
% END OF LATTICE L34.70
%
%
% LATTICE L34.71
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-356916337272, 29938939272, -7106001408; 29938939272, -2511345072, 596067264; -7106001408, 596067264, -141476449],[792, 24, 1],[9582, -17, -299, -65, 1611, 21176, 22384, 27554, 9301, 1143, 2597, 2609, 15960, 13064; 100133, -187, -3124, -651, 16907, 221991, 234603, 288695, 97394, 11961, 27162, 27278, 166837, 136551; -59400, 66, 1856, 522, -9684, -128326, -135864, -167640, -56826, -7016, -16002, -16116, -98714, -80856],33,71]
%
% END OF LATTICE L34.71
%
%
% LATTICE L34.72
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3676593096, 318300048, -50394168; 318300048, -27556680, 4362840; -50394168, 4362840, -690733],[792, 24, 1],[-5267, -1, 165, 67, -806, -5433, -11543, -14313, -4894, -610, -1402, -1419, -4357, -7147; -109615, -22, 3434, 1398, -16765, -113025, -240141, -297781, -101827, -12693, -29175, -29530, -90673, -148737; -308088, -66, 9652, 3942, -47088, -317515, -674640, -836616, -286110, -35668, -81990, -82992, -254837, -418032],33,72]
%
% END OF LATTICE L34.72
%
%
% LATTICE L34.73
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-68645544, 138307488, -1634424; 138307488, -278662824, 3293048; -1634424, 3293048, -38915],[264, 88, 1],[-149, 1, 76, 97, 347, 199, 605, 121, -8, -83, -104, -382, -227, -703; -87, 0, 45, 64, 258, 165, 529, 123, 9, -36, -55, -213, -129, -403; -1104, -42, 616, 1342, 7260, 5606, 19360, 5328, 1098, 440, -286, -1980, -1382, -4576],33,73]
%
% END OF LATTICE L34.73
%
%
% LATTICE L34.74
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-230390160, 5988840, 5057712; 5988840, -155672, -131472; 5057712, -131472, -111031],[264, 88, 1],[-85, -1, 45, 75, 346, 122, 815, 209, 32, -14, -44, -191, -60, -381; -108, -3, 59, 117, 603, 227, 1554, 420, 81, 19, -39, -213, -71, -462; -3744, -42, 1980, 3278, 15048, 5289, 35288, 9024, 1362, -660, -1958, -8448, -2649, -16808],33,74]
%
% END OF LATTICE L34.74
%
%
% LATTICE L34.75
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2500344, -5243832, -437976; -5243832, -10986690, -917565; -437976, -917565, -76631],[792, 33, 1],[59, -59, -119, 489, 1087, 12049, 3664, 1117, 1235, 1883, 687, 383, 2063, 452; -413, 412, 834, -3412, -7588, -84120, -25581, -7799, -8624, -13152, -4800, -2677, -14424, -3161; 4608, -4596, -9306, 38060, 84645, 938376, 285362, 87000, 96204, 146718, 53548, 29865, 160920, 35266],33,75]
%
% END OF LATTICE L34.75
%
%
% LATTICE L34.76
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-12698136, -45140040, -3720816; -45140040, -160262850, -13208547; -3720816, -13208547, -1088609],[792, 33, 1],[1293, -1285, -1300, 10671, 47451, 263005, 79979, 24383, 26961, 20557, 15005, 16739, 45107, 9887; -4073, 4048, 4095, -33616, -149480, -828516, -251949, -76811, -84932, -64758, -47268, -52730, -142092, -31145; 45000, -44724, -45243, 371404, 1651518, 9153792, 2783638, 848640, 938364, 715473, 522236, 582582, 1569888, 344102],33,76]
%
% END OF LATTICE L34.76
%
%
% LATTICE L34.77
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-8842680, -4713984, 26928; -4713984, -2512983, 14355; 26928, 14355, -82],[792, 33, 1],[-15, -17, -9, -31, -6, -11, -22, -1, 1, 1, -17, -14, -53, -146; 62, 68, 34, 108, 19, 32, 60, 2, -4, -2, 84, 61, 224, 612; 5919, 6312, 2992, 8712, 1353, 1984, 3267, 21, -372, -22, 9108, 6072, 21776, 59103],33,77]
%
% END OF LATTICE L34.77
%
%
% LATTICE L34.78
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-11152152, 1155528, 99000; 1155528, -118965, -10197; 99000, -10197, -874],[792, 33, 1],[25, 29, 8, 59, 25, 25, 53, 3, -1, -1, 25, 45, 87, 241; -3116, -3620, -1001, -7404, -3146, -3152, -6690, -380, 124, 127, -3084, -5594, -10832, -30018; 39183, 45516, 12584, 93060, 39534, 39604, 84051, 4773, -1560, -1595, 38808, 70356, 136220, 377487],33,78]
%
% END OF LATTICE L34.78
%
%
% LATTICE L34.79
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[58269870648, -2156887260, 16367309640; -2156887260, 79838220, -605843832; 16367309640, -605843832, 4597381493],[396, 132, 1],[3383, 113, 3379, 12585, 97379, 130348, 157042, 47113, 25135, 72365, 12663, 28861, 21140, 19694; -10867, -362, -10884, -40474, -313138, -419139, -504969, -151489, -80816, -232650, -40704, -92752, -67929, -63277; -13476, -450, -13464, -50138, -387948, -519291, -625636, -187692, -100134, -288288, -50446, -114972, -84213, -78452],33,79]
%
% END OF LATTICE L34.79
%
%
% LATTICE L34.80
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[3150972, -42768, 827244; -42768, 1452, -11880; 827244, -11880, 217669],[396, 132, 1],[-530, -53, -211, -5447, -13859, -6163, -66763, -6666, -3545, -3387, -5347, -4131, -1033, -8795; 1571, 157, 625, 16143, 41075, 18266, 197874, 19757, 10507, 10039, 15849, 12245, 3062, 26070; 2100, 210, 836, 21582, 54912, 24419, 264528, 26412, 14046, 13420, 21186, 16368, 4093, 34848],33,80]
%
% END OF LATTICE L34.80
%
%
% LATTICE L34.81
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[211814064, -6045732, 58078548; -6045732, 172128, -1657392; 58078548, -1657392, 15924659],[396, 132, 1],[824, 22, -26441, -16712, -222745, -566491, -336115, -98108, -24343, -119485, -7609, -20465, -17213, -4379; -2429, -65, 77937, 49261, 656575, 1669821, 990752, 289189, 71755, 352203, 22429, 60325, 50739, 12908; -3258, -87, 104544, 66077, 880704, 2239830, 1328954, 387906, 96249, 472428, 30085, 80916, 68058, 17314],33,81]
%
% END OF LATTICE L34.81
%
%
% LATTICE L34.82
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[78346040256, 5915301876, 15215119524; 5915301876, 446618568, 1148775672; 15215119524, 1148775672, 2954838067],[396, 132, 1],[-1705, 13, -628, -10913, -56182, -50078, -271409, -27123, -7220, -13786, -10708, -15888, -7578, -31285; 5683, -41, 2093, 36315, 186949, 166637, 903126, 90253, 24025, 45875, 35637, 52891, 25235, 104202; 6570, -51, 2420, 42075, 216612, 193078, 1046430, 104574, 27837, 53152, 41283, 61248, 29210, 120582],33,82]
%
% END OF LATTICE L34.82
%
%
% LATTICE L34.83
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[33505296, 34045704, -261888; 34045704, 34594824, -266112; -261888, -266112, 2047],[264, 264, 1],[131, 33, 84, 35, 19, 21, 47, 1, 0, 15, 64, 146, 375, 1339; -184, -45, -107, -39, -17, -16, -30, 0, -1, -31, -99, -213, -536, -1902; -7168, -1630, -3168, -594, 220, 606, 2112, 128, -130, -2112, -4686, -9020, -21726, -76032],33,83]
%
% END OF LATTICE L34.83
%
%
% LATTICE L34.84
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[321140688, -1621224, -2457840; -1621224, 8184, 12408; -2457840, 12408, 18811],[264, 264, 1],[217, 56, 150, 68, 41, 24, 113, 3, -1, 15, 97, 234, 306, 2197; -184, -45, -107, -39, -17, -8, -30, 0, -1, -31, -99, -213, -268, -1902; 28472, 7346, 19668, 8910, 5368, 3141, 14784, 392, -130, 1980, 12738, 30712, 40155, 288288],33,84]
%
% END OF LATTICE L34.84
%
%
% LATTICE L34.85
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[103784472, 31883544, -10893960; 31883544, 9794928, -3346728; -10893960, -3346728, 1143509],[792, 264, 1],[0, -1, -31, -33, -213, -536, -634, -184, -45, -107, -13, -17, -16, -10; 41, -130, -3417, -3418, -21722, -54351, -64175, -18565, -4501, -10476, -1213, -1433, -1221, -659; 120, -390, -10296, -10318, -65604, -164178, -193864, -56088, -13602, -31680, -3674, -4356, -3726, -2024],33,85]
%
% END OF LATTICE L34.85
%
%
% LATTICE L34.86
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[24552, -889416, 20592; -889416, 32224368, -746064; 20592, -746064, 17273],[792, 264, 1],[0, -1, -31, -33, -213, -268, -634, -184, -45, -107, -13, -17, -8, -10; 5, -1, 45, 75, 526, 681, 1625, 479, 122, 318, 46, 79, 45, 69; 216, -42, 1980, 3278, 22968, 29727, 70928, 20904, 5322, 13860, 2002, 3432, 1953, 2992],33,86]
%
% END OF LATTICE L34.86
%
%
% LATTICE L34.87
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-16739640720, -1071961704, 25522992; -1071961704, -68645544, 1634424; 25522992, 1634424, -38915],[792, 264, 1],[41, 3, -12, -55, -71, -43, -403, -29, 0, 15, 64, 86, 55, 529; 2, 17, 47, 147, 169, 98, 900, 62, -1, -31, -99, -89, -34, -228; 26976, 2682, -5896, -29898, -39468, -24086, -226512, -16416, -42, 8536, 37818, 52668, 34646, 337392],33,87]
%
% END OF LATTICE L34.87
%
%
% LATTICE L34.88
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-158841072720, -42287057208, 241160832; -42287057208, -11257763352, 64202424; 241160832, 64202424, -366143],[792, 264, 1],[127, 26, 10, -22, -49, -17, -337, -27, -1, 15, 97, 174, 67, 1387; 2, 17, 47, 147, 169, 49, 900, 62, -1, -31, -99, -89, -17, -228; 84000, 20106, 14828, 11286, -2640, -2605, -64152, -6912, -834, 4444, 46530, 99000, 41149, 873576],33,88]
%
% END OF LATTICE L34.88
%

\medskip%
%------------------------------WEYL-GROUP-W35--------------------------------
%
\leavevmode\llap{}%
$W_{35\phantom{0}}$%
\qquad\llap{18} lattices, $\chi=12$%
\hfill%
$222222\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L35.1
%
\leavevmode%
${L_{35.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{1}{}9\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}11\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{23\rightarrow N_{35},3,2}%
\EasyButWeakLineBreak%
{${12}\above{1pt}{1pt}{*}{2}{396}\above{1pt}{1pt}{b}{2}{2}\above{1pt}{1pt}{b}{2}{12}\above{1pt}{1pt}{*}{2}{44}\above{1pt}{1pt}{b}{2}{18}\above{1pt}{1pt}{b}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-16236\\1584\\0
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1584\\-150\\-3
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\-3\\2
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\10\\18
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
13\\132\\198
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\-1
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-5\\-52\\-78
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-19\\-198\\-286
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2\\-21\\-27
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-16236, 1584, 0; 1584, -150, -3; 0, -3, 2],[396, 3, 1],[1, 13, 0, -5, -19, -2; 10, 132, 0, -52, -198, -21; 18, 198, -1, -78, -286, -27],34,1]
%
% END OF LATTICE L35.1
%
%
% LATTICE L35.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[462, -165, 0; -165, 59, 0; 0, 0, -1],[33, 1, 1],[1, 4, -1, -16, -59, -4; 3, 11, -3, -45, -165, -11; 0, 0, -1, -12, -44, -3],34,2]
%
% END OF LATTICE L35.2
%
%
% LATTICE L35.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[660, 132, 132; 132, 26, 23; 132, 23, -2],[132, 1, 1],[1, 27, 3, -1, -27, -3; -6, -154, -17, 6, 154, 17; -6, 0, 2, 0, -22, -3],34,3]
%
% END OF LATTICE L35.3
%
%
% LATTICE L35.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[99, 99, 0; 99, 21, -9; 0, -9, -1],[99, 3, 1],[-1, 1, 1, 3, 7, -1; 1, 0, -1, -4, -11, 0; -9, 0, 8, 24, 55, -9],34,4]
%
% END OF LATTICE L35.4
%
%
% LATTICE L35.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-41811, 1551, 14223; 1551, -57, -528; 14223, -528, -4838],[33, 3, 1],[-17, 37, 21, -89, -1203, -127; -36, 88, 43, -204, -2728, -283; -46, 99, 57, -239, -3234, -342],34,5]
%
% END OF LATTICE L35.5
%
%
% LATTICE L35.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-118767, -2904, 42735; -2904, -55, 1045; 42735, 1045, -15377],[33, 11, 1],[-487, 36, 194, -2756, -1117, -1275; 9, -1, -3, 69, 27, 29; -1353, 100, 539, -7656, -3103, -3542],34,6]
%
% END OF LATTICE L35.6
%
%
% LATTICE L35.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-8580, 264, 132; 264, 30, -3; 132, -3, -2],[132, 3, 1],[1, 1, -1, -1, -1, 1; -2, 0, 2, 0, -22, -3; 68, 66, -69, -74, -132, 66],34,7]
%
% END OF LATTICE L35.7
%
%
% LATTICE L35.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[210936, -10956, 53064; -10956, 568, -2756; 53064, -2756, 13349],[132, 4, 1],[109, 293, -1, -19, 37, 31; -81, -220, 0, 12, -33, -23; -450, -1210, 4, 78, -154, -128],34,8]
%
% END OF LATTICE L35.8
%
%
% LATTICE L35.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[66, -726, -33; -726, 12111, 561; -33, 561, 26],[33, 33, 1],[-4, 1, 4, -27, -32, -35; -9, 3, 8, -73, -85, -90; 187, -63, -165, 1529, 1779, 1881],34,9]
%
% END OF LATTICE L35.9
%
%
% LATTICE L35.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[10428, 3828, -528; 3828, 1342, -187; -528, -187, 26],[132, 11, 1],[-1, -1, -1, 1, 1, 1; -24, -14, -11, 6, 8, 8; -198, -122, -99, 66, 78, 77],34,10]
%
% END OF LATTICE L35.10
%
%
% LATTICE L35.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[3192024, 8580, 772332; 8580, 24, 2076; 772332, 2076, 186871],[132, 12, 1],[15, -16, 0, 136, 1677, 151; 0, 11, 1, -7, -88, -8; -62, 66, 0, -562, -6930, -624],34,11]
%
% END OF LATTICE L35.11
%
%
% LATTICE L35.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[198, 990, -99; 990, 4983, -495; -99, -495, 49],[99, 33, 1],[-5, -4, 0, 4, 1, -1; 1, 0, -1, -4, -1, 0; 0, -9, -11, -33, -8, 0],34,12]
%
% END OF LATTICE L35.12
%
%
% LATTICE L35.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-10956, 1056, -264; 1056, 66, -33; -264, -33, 14],[132, 33, 1],[-1, -1, 0, 3, 3, 1; -38, -38, -1, 106, 106, 35; -110, -108, 0, 308, 306, 99],34,13]
%
% END OF LATTICE L35.13
%
%
% LATTICE L35.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1339272, -36036, -339372; -36036, 984, 9132; -339372, 9132, 85997],[396, 12, 1],[-47, -250, -2, -150, -639, -191; 5, 33, 1, 19, 77, 21; -186, -990, -8, -594, -2530, -756],34,14]
%
% END OF LATTICE L35.14
%
%
% LATTICE L35.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2237928, 75636, -486816; 75636, 2552, -16456; -486816, -16456, 105895],[132, 44, 1],[206, 35, -53, -143, -14, 74; -573, -96, 152, 408, 41, -207; 858, 146, -220, -594, -58, 308],34,15]
%
% END OF LATTICE L35.15
%
%
% LATTICE L35.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-74052, -7128, 396; -7128, -462, 33; 396, 33, -2],[396, 33, 1],[1, 1, 0, -3, -1, -1; 8, 6, -1, -26, -8, -6; 330, 288, -22, -1056, -338, -297],34,16]
%
% END OF LATTICE L35.16
%
%
% LATTICE L35.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[223080, -616044, -149160; -616044, 1701480, 411972; -149160, 411972, 99749],[132, 132, 1],[1, 0, -2, 0, 1, 3; 27, 77, 223, 261, 211, 65; -110, -318, -924, -1078, -870, -264],34,17]
%
% END OF LATTICE L35.17
%
%
% LATTICE L35.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[50813928, 382932, 12543300; 382932, 2904, 94512; 12543300, 94512, 3096295],[396, 132, 1],[50, 341, 389, 1317, 342, 200; -149, -1029, -1175, -3973, -1031, -597; -198, -1350, -1540, -5214, -1354, -792],34,18]
%
% END OF LATTICE L35.18
%

\medskip%
%------------------------------WEYL-GROUP-W36--------------------------------
%
\leavevmode\llap{}%
$W_{36\phantom{0}}$%
\qquad\llap{8} lattices, $\chi=36$%
\hfill%
$\infty222\infty222\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L36.1
%
\leavevmode%
${L_{36.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}8\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{2}{}17\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2\rightarrow N_{36}}%
\EasyButWeakLineBreak%
{${34}\above{1pt}{1pt}{4,1}{\infty b}{136}\above{1pt}{1pt}{b}{2}{2}\above{1pt}{1pt}{b}{2}{8}\above{1pt}{1pt}{b}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-171224\\-40800\\-4352
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-40800\\-9722\\-1037
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-4352\\-1037\\-110
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
39167\\-164832\\4896
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
9336\\-39290\\1167
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
984\\-4141\\122
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-32\\136\\-17
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
81\\-340\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4\\-17\\2
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-41\\172\\0
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-171224, -40800, -4352; -40800, -9722, -1037; -4352, -1037, -110],[136, 1, 1],[-32, 81, 4, -41, -376, -1713, -76, -55; 136, -340, -17, 172, 1581, 7208, 320, 232; -17, 0, 2, 0, -34, -204, -11, -12],35,1]
%
% END OF LATTICE L36.1
%
%
% LATTICE L36.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[34, 0, 0; 0, 0, -1; 0, -1, 0],[34, 1, 1],[-1, 1, 0, -1, -16, -35, -3, -1; 0, 0, -1, -4, -51, -102, -8, -2; -17, 0, 1, -4, -85, -204, -19, -8],35,2]
%
% END OF LATTICE L36.2
%
%
% LATTICE L36.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-83164, 578, -39134; 578, -4, 272; -39134, 272, -18415],[34, 2, 1],[290, 331, 59, 11, 33, -8, -2, 8; 221, 357, 80, 23, 136, 0, -17, -2; -612, -697, -124, -23, -68, 17, 4, -17],35,3]
%
% END OF LATTICE L36.3
%
%
% LATTICE L36.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[442, -578, 204; -578, -2448, -289; 204, -289, 94],[34, 17, 1],[-88, -301, -589, -351, -63, -1, 136, 49; -2, -6, -11, -6, -1, 0, 2, 0; 189, 644, 1258, 748, 134, 2, -289, -102],35,4]
%
% END OF LATTICE L36.4
%
%
% LATTICE L36.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-5184592, 9112, 77384; 9112, -16, -136; 77384, -136, -1155],[136, 8, 1],[2, -1, -1, -1, -19, -16, -2, 0; -17, 289, 107, 57, 697, 391, 13, -17; 136, -102, -80, -74, -1360, -1122, -136, 2],35,5]
%
% END OF LATTICE L36.5
%
%
% LATTICE L36.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[68, 19074, 9248; 19074, 5336368, 2587332; 9248, 2587332, 1254465],[34, 34, 1],[67, 75, 224, 41, 8, 0, 1, 34; -776, -857, -2523, -437, -65, 16, 0, -404; 1600, 1767, 5202, 901, 134, -33, 0, 833],35,6]
%
% END OF LATTICE L36.6
%
%
% LATTICE L36.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[680, -680, 408; -680, -102, 85; 408, 85, -66],[136, 17, 1],[6, 29, 23, 19, 1, -1, -2, 9; 119, 580, 463, 388, 21, -20, -43, 172; 188, 916, 731, 612, 33, -32, -68, 272],35,7]
%
% END OF LATTICE L36.7
%
%
% LATTICE L36.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-272, 1768, 408; 1768, -10064, -2312; 408, -2312, -531],[136, 136, 1],[-1, 1, 11, 9, 9, 7, 13, -1; -2, 9, 65, 41, 35, 24, 34, -8; 8, -38, -272, -170, -144, -98, -136, 34],35,8]
%
% END OF LATTICE L36.8
%

\medskip%
%------------------------------WEYL-GROUP-W37--------------------------------
%
\leavevmode\llap{}%
$W_{37\phantom{0}}$%
\qquad\llap{12} lattices, $\chi=8$%
\hfill%
$22322$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L37.1
%
\leavevmode%
${L_{37.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{-2}{}7\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{2\rightarrow N_{37}}%
\EasyButWeakLineBreak%
{${4}\above{1pt}{1pt}{*}{2}{20}\above{1pt}{1pt}{b}{2}{2}\above{1pt}{1pt}{+}{3}{2}\above{1pt}{1pt}{s}{2}{70}\above{1pt}{1pt}{b}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-246820\\3080\\-3360
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3080\\-38\\39
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3360\\39\\-26
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3\\-286\\-42
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7\\670\\100
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\191\\28
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3\\-287\\-43
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-37\\-3535\\-525
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-246820, 3080, -3360; 3080, -38, 39; -3360, 39, -26],[140, 1, 1],[-3, 7, 2, -3, -37; -286, 670, 191, -287, -3535; -42, 100, 28, -43, -525],36,1]
%
% END OF LATTICE L37.1
%
%
% LATTICE L37.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[70, -35, 0; -35, 17, 0; 0, 0, 1],[35, 1, 1],[0, 2, -3, -5, -29; 0, 5, -7, -12, -70; 1, 0, -3, -2, 0],36,2]
%
% END OF LATTICE L37.2
%
%
% LATTICE L37.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1364195, 21175, 551600; 21175, -310, -8565; 551600, -8565, -223034],[35, 5, 1],[-403, -269, -472, 470, 202; -172, -111, -191, 192, 70; -990, -661, -1160, 1155, 497],36,3]
%
% END OF LATTICE L37.3
%
%
% LATTICE L37.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1633485, -38605, 696185; -38605, -882, 16450; 696185, 16450, -296711],[35, 7, 1],[-614, -1987, -685, 688, 182; -149, -500, -176, 175, 55; -1449, -4690, -1617, 1624, 430],36,4]
%
% END OF LATTICE L37.4
%
%
% LATTICE L37.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1935080, -518980, -503020; -518980, 139208, 134908; -503020, 134908, 130759],[140, 4, 1],[99, -13, 145, 257, 2301; -5, 0, -6, -11, -105; 386, -50, 564, 1000, 8960],36,5]
%
% END OF LATTICE L37.5
%
%
% LATTICE L37.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-89460, -4340, 1120; -4340, -190, 55; 1120, 55, -14],[140, 5, 1],[-3, 1, 2, -2, -6; 8, -2, -5, 4, 14; -210, 72, 140, -145, -427],36,6]
%
% END OF LATTICE L37.6
%
%
% LATTICE L37.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-5279260, -612360, 46760; -612360, -71022, 5425; 46760, 5425, -414],[140, 7, 1],[21, -51, -14, 22, 38; -118, 290, 79, -125, -215; 826, -1960, -546, 847, 1475],36,7]
%
% END OF LATTICE L37.7
%
%
% LATTICE L37.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[586390, 6030850, -2258235; 6030850, 62026405, -23225615; -2258235, -23225615, 8696767],[35, 35, 1],[-166, -39, 1, 30, -32; 25428, 5959, -236, -4603, 4905; 67865, 15904, -630, -12285, 13091],36,8]
%
% END OF LATTICE L37.8
%
%
% LATTICE L37.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[11457880, 56140, -2951200; 56140, 280, -14460; -2951200, -14460, 760139],[140, 20, 1],[-188, -17, -103, -206, -548; -5, 0, -6, -11, -21; -730, -66, -400, -800, -2128],36,9]
%
% END OF LATTICE L37.9
%
%
% LATTICE L37.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[165459560, 5408060, -42683060; 5408060, 176792, -1395100; -42683060, -1395100, 11010809],[140, 28, 1],[2209, 1027, 555, 1737, 4103; 149, 70, 36, 115, 275; 8582, 3990, 2156, 6748, 15940],36,10]
%
% END OF LATTICE L37.10
%
%
% LATTICE L37.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-38220, 45500, -11200; 45500, -54110, 13335; -11200, 13335, -3282],[140, 35, 1],[71, -27, -47, 56, 22; 8, -2, -5, 4, 2; -210, 84, 140, -175, -67],36,11]
%
% END OF LATTICE L37.11
%
%
% LATTICE L37.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1960, 147700, -37380; 147700, 11581080, -2931040; -37380, -2931040, 741813],[140, 140, 1],[-39, -2, -30, -59, -19; 656, 39, 461, 922, 308; 2590, 154, 1820, 3640, 1216],36,12]
%
% END OF LATTICE L37.12
%

\medskip%
%------------------------------WEYL-GROUP-W38--------------------------------
%
\leavevmode\llap{}%
$W_{38\phantom{0}}$%
\qquad\llap{44} lattices, $\chi=36$%
\hfill%
$2222222222\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L38.1
%
\leavevmode%
${L_{38.1}}$%
{} : {$1\above{1pt}{1pt}{2}{{\rm II}}4\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{2}{}7\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2\rightarrow N_{38}}%
\EasyButWeakLineBreak%
{${20}\above{1pt}{1pt}{*}{2}{28}\above{1pt}{1pt}{*}{2}{4}\above{1pt}{1pt}{b}{2}{2}\above{1pt}{1pt}{s}{2}{14}\above{1pt}{1pt}{b}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2380\\140\\-140
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
140\\-4\\-3
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-140\\-3\\6
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-71\\-700\\-1820
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-11\\-111\\-286
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7\\70\\181
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
23\\240\\610
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
29\\294\\756
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7\\68\\178
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\-2\\-3
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2\\-28\\-63
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[2380, 140, -140; 140, -4, -3; -140, -3, 6],[140, 1, 1],[23, 29, 7, 0, -2, -3, -1, 1, 1, 9; 240, 294, 68, -2, -28, -40, -14, 12, 12, 98; 610, 756, 178, -3, -63, -90, -28, 30, 29, 245],37,1]
%
% END OF LATTICE L38.1
%
\hbox{}\par\smallskip%
%
% LATTICE L38.2
%
\leavevmode%
${L_{38.2}}$%
{} : {$1\above{1pt}{1pt}{-2}{6}8\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{2}{}7\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2\rightarrow N'_{25}}%
\EasyButWeakLineBreak%
{${40}\above{1pt}{1pt}{b}{2}{14}\above{1pt}{1pt}{l}{2}{8}\above{1pt}{1pt}{}{2}{1}\above{1pt}{1pt}{r}{2}{28}\above{1pt}{1pt}{*}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-133560\\560\\840
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
560\\-2\\-5
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
840\\-5\\1
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2521\\-446040\\-110880
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
14\\2477\\616
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\177\\43
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-39\\-6900\\-1720
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-29\\-5131\\-1274
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-17\\-3008\\-744
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-177\\-43
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3\\-532\\-126
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-133560, 560, 840; 560, -2, -5; 840, -5, 1],[280, 1, 1],[-39, -29, -17, -1, -3, -1, 1, 1, 0, -11; -6900, -5131, -3008, -177, -532, -180, 175, 176, 0, -1946; -1720, -1274, -744, -43, -126, -40, 42, 40, -1, -490],37,2]
%
% END OF LATTICE L38.2
%
\hbox{}\par\smallskip%
%
% LATTICE L38.3
%
\leavevmode%
${L_{38.3}}$%
{} : {$1\above{1pt}{1pt}{2}{6}8\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{2}{}7\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{m}%
\EasyButWeakLineBreak%
{${40}\above{1pt}{1pt}{r}{2}{14}\above{1pt}{1pt}{b}{2}{8}\above{1pt}{1pt}{*}{2}{4}\above{1pt}{1pt}{l}{2}{7}\above{1pt}{1pt}{}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
264040\\-2240\\-840
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2240\\19\\7
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-840\\7\\-2
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-36961\\-4385920\\258720
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
309\\36667\\-2163
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-42\\-4984\\293
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
119\\14120\\-840
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
86\\10206\\-595
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
49\\5816\\-332
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5\\594\\-30
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\357\\-14
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[264040, -2240, -840; -2240, 19, 7; -840, 7, -2],[280, 1, 1],[119, 86, 49, 5, 3, 1, -2, -1, 1, 18; 14120, 10206, 5816, 594, 357, 120, -238, -120, 118, 2135; -840, -595, -332, -30, -14, 0, 7, -4, -12, -133],37,3]
%
% END OF LATTICE L38.3
%
%
% LATTICE L38.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[420, -175, 0; -175, 73, 0; 0, 0, -1],[35, 1, 1],[2, 3, -2, -7, -131, -202, -283, -78, -13, -9; 5, 7, -5, -17, -315, -485, -679, -187, -31, -21; 0, 0, -2, -5, -91, -140, -196, -54, -9, -7],37,4]
%
% END OF LATTICE L38.4
%
%
% LATTICE L38.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[2310, 210, 980; 210, 19, 89; 980, 89, 416],[70, 1, 1],[11, 3, -1, 0, 36, 129, 193, 57, 7, 13; -130, -70, 2, 5, -217, -830, -1274, -386, -53, -119; 0, 7, 2, -1, -42, -140, -203, -58, -6, -7],37,5]
%
% END OF LATTICE L38.5
%
%
% LATTICE L38.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[11620, 560, 0; 560, 27, 0; 0, 0, -1],[140, 1, 1],[39, 29, 17, 2, 3, 1, -1, -1, 0, 11; -860, -637, -372, -43, -63, -20, 21, 20, -1, -245; -280, -196, -108, -9, -7, 0, 0, -4, -5, -91],37,6]
%
% END OF LATTICE L38.6
%
%
% LATTICE L38.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[19530, 490, 9590; 490, -16, 242; 9590, 242, 4709],[70, 2, 1],[854, 820, -32, -63, 3239, 6126, 18724, 2824, 761, 1647; -80, -77, 3, 6, -301, -570, -1743, -263, -71, -154; -1735, -1666, 65, 128, -6580, -12445, -38038, -5737, -1546, -3346],37,7]
%
% END OF LATTICE L38.7
%
%
% LATTICE L38.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[12530, 875, -5005; 875, 60, -350; -5005, -350, 1999],[35, 5, 1],[-3, 15, 11, 5, -137, -53, -407, -123, -33, -59; 3, -14, -15, -16, -70, -11, -42, -1, 12, 42; -7, 35, 25, 10, -350, -133, -1015, -305, -80, -140],37,8]
%
% END OF LATTICE L38.8
%
%
% LATTICE L38.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[7735, 0, -3430; 0, -7, 0; -3430, 0, 1521],[35, 7, 1],[31, -4, -31, -34, -24, -151, -20, -17, 22, 12; 0, 0, -2, -5, -13, -140, -28, -54, -9, -1; 70, -9, -70, -77, -55, -350, -47, -42, 49, 27],37,9]
%
% END OF LATTICE L38.9
%
%
% LATTICE L38.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[18690, 910, -3850; 910, -40, -185; -3850, -185, 793],[70, 5, 1],[-239, -573, 45, 44, -2270, -1717, -13119, -3957, -533, -1153; -32, -77, 6, 6, -301, -228, -1743, -526, -71, -154; -1168, -2800, 220, 215, -11095, -8392, -64120, -19340, -2605, -5635],37,10]
%
% END OF LATTICE L38.10
%
%
% LATTICE L38.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[20230, 1190, -5880; 1190, -56, -343; -5880, -343, 1709],[70, 7, 1],[-2147, -147, 81, 79, -583, -15433, -3369, -7113, -958, -296; -160, -11, 6, 6, -43, -1140, -249, -526, -71, -22; -7420, -508, 280, 273, -2015, -53340, -11644, -24584, -3311, -1023],37,11]
%
% END OF LATTICE L38.11
%
%
% LATTICE L38.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[763280, -10780, -197120; -10780, 152, 2784; -197120, 2784, 50907],[140, 4, 1],[238, 355, 104, 24, 22, -18, -47, -16, -2, 132; 215, 308, 87, 17, 21, 5, 0, 1, 5, 133; 910, 1358, 398, 92, 84, -70, -182, -62, -8, 504],37,12]
%
% END OF LATTICE L38.12
%
%
% LATTICE L38.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[10220, -2240, -2520; -2240, 332, 560; -2520, 560, 621],[140, 4, 1],[-1757, -4880, -666, -207, -101, 27, 36, -26, -139, -2321; -345, -959, -131, -41, -21, 5, 7, -5, -27, -455; -6825, -18956, -2587, -804, -392, 105, 140, -101, -540, -9016],37,13]
%
% END OF LATTICE L38.13
%
%
% LATTICE L38.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-19460, 280, 280; 280, 30, -5; 280, -5, -4],[140, 5, 1],[-1, -1, 3, 3, 37, 21, 141, 37, 2, -2; -2, 0, 6, 5, 49, 26, 168, 42, 1, -7; -68, -70, 200, 200, 2450, 1388, 9310, 2440, 130, -140],37,14]
%
% END OF LATTICE L38.14
%
%
% LATTICE L38.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[3850560, -27090, 1832180; -27090, 190, -12890; 1832180, -12890, 871791],[70, 10, 1],[-110, -167, 69, -19, -4398, -1556, -23157, -3401, -814, -1433; -13, -70, 1, 5, -217, -83, -1274, -193, -53, -119; 231, 350, -145, 40, 9240, 3269, 48650, 7145, 1710, 3010],37,15]
%
% END OF LATTICE L38.15
%
%
% LATTICE L38.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-8540, -1260, -560; -1260, -185, -80; -560, -80, -29],[140, 5, 1],[-3, 1, 7, 4, 3, -5, -29, -23, -6, -17; 24, -7, -56, -33, -49, 24, 175, 152, 45, 133; -8, 0, 20, 15, 105, 48, 140, 60, -5, -35],37,16]
%
% END OF LATTICE L38.16
%
%
% LATTICE L38.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2262960, -24570, 1054760; -24570, 266, -11452; 1054760, -11452, 491621],[70, 14, 1],[-539, -29, 62, -13, -582, -7231, -3079, -3170, -764, -195; -65, -10, 1, 5, -31, -415, -182, -193, -53, -17; 1155, 62, -133, 28, 1248, 15505, 6602, 6797, 1638, 418],37,17]
%
% END OF LATTICE L38.17
%
%
% LATTICE L38.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1260, 140, 140; 140, -14, -7; 140, -7, 32],[140, 7, 1],[99, 17, 27, -1, -1, 1, 3, 13, 6, 6; 990, 168, 262, -13, -11, 10, 32, 138, 63, 61; -280, -50, -84, 0, 2, 0, -6, -28, -14, -16],37,18]
%
% END OF LATTICE L38.18
%
%
% LATTICE L38.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[140, 0, 0; 0, -14, -7; 0, -7, -3],[140, 7, 1],[-41, -4, -15, -1, 0, 1, 0, -1, -1, -2; 0, -1, -8, -3, -1, 0, 1, 8, 3, 1; -280, -25, -84, 0, 2, 0, -3, -28, -14, -16],37,19]
%
% END OF LATTICE L38.19
%
%
% LATTICE L38.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-35, 0, 0; 0, 80220, -30205; 0, -30205, 11373],[35, 35, 1],[0, 0, 2, 5, 13, 28, 28, 54, 9, 1; 29, 32, -145, -514, -1380, -2981, -2984, -5759, -962, -96; 77, 85, -385, -1365, -3665, -7917, -7925, -15295, -2555, -255],37,20]
%
% END OF LATTICE L38.20
%
%
% LATTICE L38.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[113960, 48440, -1400; 48440, 20590, -595; -1400, -595, 17],[280, 5, 1],[5, -3, -17, -6, -93, -45, -137, -63, 1, 23; -12, 7, 40, 14, 210, 100, 301, 136, -3, -56; -8, 0, 0, -5, -350, -232, -840, -480, -25, -70],37,21]
%
% END OF LATTICE L38.21
%
%
% LATTICE L38.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[3080, 280, 280; 280, 15, 55; 280, 55, -58],[280, 5, 1],[3, -12, -7, 7, 136, 181, 656, 375, 39, 25; -24, 98, 56, -58, -1113, -1480, -5362, -3064, -318, -203; -8, 35, 20, -20, -385, -512, -1855, -1060, -110, -70],37,22]
%
% END OF LATTICE L38.22
%
%
% LATTICE L38.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-117320, 840, 840; 840, 63, -7; 840, -7, -6],[280, 7, 1],[41, 3, 7, -1, -1, -1, 1, 9, 2, 3; 0, -2, -16, -3, -2, 0, 2, 16, 3, 2; 5460, 395, 896, -140, -138, -140, 137, 1232, 273, 404],37,23]
%
% END OF LATTICE L38.23
%
%
% LATTICE L38.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[280, 0, 0; 0, -7, -7; 0, -7, -6],[280, 7, 1],[-41, -4, -15, -1, 0, 1, 0, -1, -1, -1; 0, -2, -16, -6, -1, 0, 2, 16, 6, 1; -280, -25, -84, 0, 1, 0, -3, -28, -14, -8],37,24]
%
% END OF LATTICE L38.24
%
%
% LATTICE L38.25
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-37520, 4200, -1400; 4200, -376, 112; -1400, 112, -31],[280, 8, 1],[-3, -1, 1, 4, 51, 73, 197, 13, 3, -2; -90, -28, 30, 119, 1505, 2150, 5796, 382, 87, -63; -190, -56, 63, 248, 3108, 4430, 11928, 785, 176, -140],37,25]
%
% END OF LATTICE L38.25
%
%
% LATTICE L38.26
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-37520, -280, 840; -280, 24, -8; 840, -8, -11],[280, 8, 1],[-1, -1, 1, 2, 23, 16, 85, 11, 1, -2; -30, -28, 30, 59, 665, 460, 2436, 314, 27, -63; -55, -56, 54, 108, 1232, 855, 4536, 586, 52, -112],37,26]
%
% END OF LATTICE L38.26
%
%
% LATTICE L38.27
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[915110, -24710, 162050; -24710, 665, -4375; 162050, -4375, 28696],[70, 35, 1],[77, 9, -47, 6, 216, 1071, 1139, 2343, 281, 71; -180, -28, 96, -7, -463, -2308, -2460, -5072, -615, -159; -462, -55, 280, -35, -1290, -6398, -6805, -14000, -1680, -425],37,27]
%
% END OF LATTICE L38.27
%
%
% LATTICE L38.28
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[4102840, -17780, -1056860; -17780, 80, 4580; -1056860, 4580, 272239],[140, 20, 1],[-17, -18, -85, -237, -4905, -1539, -10874, -3027, -541, -541; 0, 7, 2, -2, -84, -28, -203, -58, -12, -14; -66, -70, -330, -920, -19040, -5974, -42210, -11750, -2100, -2100],37,28]
%
% END OF LATTICE L38.28
%
%
% LATTICE L38.29
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[13020, -10640, -3080; -10640, 9420, 2500; -3080, 2500, 729],[140, 20, 1],[-11, 72, -32, -287, -6637, -1055, -14996, -2100, -779, -825; -1, 7, -3, -27, -623, -99, -1407, -197, -73, -77; -43, 280, -125, -1120, -25900, -4117, -58520, -8195, -3040, -3220],37,29]
%
% END OF LATTICE L38.29
%
%
% LATTICE L38.30
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[10360, 980, -2660; 980, 84, -252; -2660, -252, 683],[140, 28, 1],[-159, -62, -58, -15, 1, 9, 2, -2, -15, -31; 70, 27, 25, 6, 0, 0, 1, 3, 8, 14; -595, -232, -217, -56, 4, 35, 8, -7, -56, -116],37,30]
%
% END OF LATTICE L38.30
%
%
% LATTICE L38.31
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[88760, 32620, -22400; 32620, 11984, -8232; -22400, -8232, 5653],[140, 28, 1],[-4273, -828, -1541, -193, 1, 53, -16, -147, -229, -423; 140, 27, 50, 6, 0, 0, 1, 6, 8, 14; -16730, -3242, -6034, -756, 4, 210, -62, -574, -896, -1656],37,31]
%
% END OF LATTICE L38.31
%
%
% LATTICE L38.32
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[205940, -868070, -424760; -868070, 3639090, 1780660; -424760, 1780660, 871303],[70, 70, 1],[-16, -11, 3, 6, -43, -114, -249, -263, -71, -22; -14626, -10014, 2758, 5379, -39723, -105150, -229538, -242310, -65267, -20165; 29883, 20460, -5635, -10990, 81160, 214837, 468980, 495075, 133350, 41200],37,32]
%
% END OF LATTICE L38.32
%
%
% LATTICE L38.33
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[140, 0, 0; 0, -595, 35; 0, 35, -2],[140, 35, 1],[-1, 0, 1, 0, -3, -15, -8, -33, -4, -1; -4, -1, 0, 2, 0, -4, -3, -16, -4, -2; -84, -20, 0, 35, -25, -196, -120, -560, -105, -45],37,33]
%
% END OF LATTICE L38.33
%
%
% LATTICE L38.34
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-9660, -2380, 140; -2380, -560, 35; 140, 35, -2],[140, 35, 1],[1, 1, 1, -1, -3, -13, -13, -25, -2, 0; -4, -2, 0, 2, 0, -4, -6, -16, -4, -2; -14, 30, 70, -35, -235, -1106, -1150, -2310, -245, -45],37,34]
%
% END OF LATTICE L38.34
%
%
% LATTICE L38.35
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[890680, 55720, -7840; 55720, 3465, -490; -7840, -490, 69],[280, 35, 1],[-97, -49, -191, -17, -1, 1, 1, -1, -7, -11; -392, -199, -780, -72, -5, 0, 3, -4, -26, -44; -13832, -6995, -27300, -2450, -150, 112, 135, -140, -980, -1565],37,35]
%
% END OF LATTICE L38.35
%
%
% LATTICE L38.36
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[280, 0, 0; 0, 35, 0; 0, 0, -1],[280, 35, 1],[-15, -8, -33, -2, -1, -1, 0, 1, 0, -3; -4, -3, -16, -2, -2, -4, -1, 0, 1, 0; -252, -135, -560, -35, -20, -28, -5, 0, 0, -50],37,36]
%
% END OF LATTICE L38.36
%
%
% LATTICE L38.37
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[560, -280, 0; -280, -6680, 360; 0, 360, -19],[280, 40, 1],[-1, -1, 2, 8, 107, 31, 421, 28, 7, -2; -2, 0, 4, 15, 189, 54, 728, 48, 11, -7; -38, 0, 75, 280, 3500, 998, 13440, 885, 200, -140],37,37]
%
% END OF LATTICE L38.37
%
%
% LATTICE L38.38
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[560, -280, 0; -280, 120, -40; 0, -40, -79],[280, 40, 1],[-1, -1, 9, 18, 247, 36, 981, 131, 17, -2; -2, 0, 18, 35, 469, 68, 1848, 246, 31, -7; 1, 0, -10, -20, -280, -41, -1120, -150, -20, 0],37,38]
%
% END OF LATTICE L38.38
%
%
% LATTICE L38.39
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[985040, 139160, -4760; 139160, 19544, -672; -4760, -672, 23],[280, 56, 1],[29, 9, 3, -2, -1, 1, 3, 3, 5, 4; 0, -2, -2, -3, -1, 0, 2, 2, 3, 1; 5950, 1784, 553, -504, -236, 210, 680, 679, 1120, 852],37,39]
%
% END OF LATTICE L38.39
%
%
% LATTICE L38.40
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-560, -840, -280; -840, -952, -336; -280, -336, -117],[280, 56, 1],[93, 77, 77, 16, 3, 2, -1, -1, 3, 16; 290, 242, 244, 53, 11, 10, -2, -4, 7, 49; -1085, -904, -910, -196, -40, -35, 8, 14, -28, -184],37,40]
%
% END OF LATTICE L38.40
%
%
% LATTICE L38.41
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[280, -4900, 1260; -4900, 83860, -21560; 1260, -21560, 5543],[140, 140, 1],[-4, -3, 0, 1, -25, -32, -69, -72, -37, -11; -2, 5, 9, 0, -58, -72, -153, -157, -74, -16; -7, 20, 35, 0, -220, -273, -580, -595, -280, -60],37,41]
%
% END OF LATTICE L38.41
%
%
% LATTICE L38.42
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[280, 4340, -1120; 4340, 217280, -56000; -1120, -56000, 14433],[140, 140, 1],[-9, -3, 1, 1, -31, -79, -85, -177, -45, -13; -256, -85, 18, 0, -958, -2412, -2583, -5354, -1334, -376; -994, -330, 70, 0, -3720, -9366, -10030, -20790, -5180, -1460],37,42]
%
% END OF LATTICE L38.42
%
%
% LATTICE L38.43
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-560, 1960, 840; 1960, 5320, 2240; 840, 2240, 943],[280, 280, 1],[-7, -29, -29, -6, -1, 0, 1, 1, -1, -6; 353, 1458, 1454, 297, 51, 3, -34, -30, 59, 305; -833, -3440, -3430, -700, -120, -7, 80, 70, -140, -720],37,43]
%
% END OF LATTICE L38.43
%
%
% LATTICE L38.44
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-16240, -12040, 5320; -12040, -7560, 3360; 5320, 3360, -1493],[280, 280, 1],[29, 61, 31, 14, 3, 1, -1, -1, 1, 12; 910, 1938, 997, 477, 111, 42, -34, -45, -1, 365; 2142, 4560, 2345, 1120, 260, 98, -80, -105, 0, 860],37,44]
%
% END OF LATTICE L38.44
%

\medskip%
%------------------------------WEYL-GROUP-W39--------------------------------
%
\leavevmode\llap{}%
$W_{39\phantom{0}}$%
\qquad\llap{12} lattices, $\chi=9$%
\hfill%
$42222$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L39.1
%
\leavevmode%
${L_{39.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{2}{}5\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{2}{}7\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2\rightarrow N_{39}}%
\EasyButWeakLineBreak%
{${2}\above{1pt}{1pt}{*}{4}{4}\above{1pt}{1pt}{b}{2}{14}\above{1pt}{1pt}{s}{2}{10}\above{1pt}{1pt}{l}{2}{28}\above{1pt}{1pt}{r}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-691460\\2240\\3640
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2240\\-6\\-13
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3640\\-13\\-18
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\115\\119
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-114\\-120
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2\\-231\\-238
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\225\\240
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
15\\1708\\1792
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-691460, 2240, 3640; 2240, -6, -13; 3640, -13, -18],[140, 1, 1],[1, -1, -2, 2, 15; 115, -114, -231, 225, 1708; 119, -120, -238, 240, 1792],38,1]
%
% END OF LATTICE L39.1
%
%
% LATTICE L39.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-35, 0, 0; 0, 1, 0; 0, 0, 1],[35, 1, 1],[0, 0, -1, -3, -5; -1, 1, 0, -10, -21; 1, 0, -7, -15, -21],38,2]
%
% END OF LATTICE L39.2
%
%
% LATTICE L39.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-44030, -2275, 18060; -2275, -30, 925; 18060, 925, -7407],[35, 5, 1],[-227, 75, 1674, 672, 4667; -52, 17, 385, 155, 1078; -560, 185, 4130, 1658, 11515],38,3]
%
% END OF LATTICE L39.3
%
%
% LATTICE L39.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-805, -1680, 665; -1680, -133, 735; 665, 735, -423],[35, 7, 1],[-198, 65, 209, 2941, 584; -91, 30, 96, 1350, 268; -469, 154, 495, 6965, 1383],38,4]
%
% END OF LATTICE L39.4
%
%
% LATTICE L39.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[28405160, -807380, -7311220; -807380, 22952, 207812; -7311220, 207812, 1881839],[140, 4, 1],[-177, -89, -209, -1333, -1450; 3, 2, 0, 10, 14; -688, -346, -812, -5180, -5635],38,5]
%
% END OF LATTICE L39.5
%
%
% LATTICE L39.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-62580, 1400, -9940; 1400, -30, 235; -9940, 235, -1458],[140, 5, 1],[-13, 15, 26, -6, -209; -333, 386, 665, -155, -5376; 35, -40, -70, 16, 560],38,6]
%
% END OF LATTICE L39.6
%
%
% LATTICE L39.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-7420, 560, 280; 560, -42, -21; 280, -21, -10],[140, 7, 1],[0, -1, 0, 2, 1; 3, -14, -1, 25, 16; -7, 0, 2, 0, -8],38,7]
%
% END OF LATTICE L39.7
%
%
% LATTICE L39.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[101710, 583800, -218505; 583800, 3350935, -1254190; -218505, -1254190, 469419],[35, 35, 1],[4, 0, -9, -33, -37; -171, 131, 170, 404, 377; -455, 350, 450, 1064, 990],38,8]
%
% END OF LATTICE L39.8
%
%
% LATTICE L39.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[3589320, 1969100, -907620; 1969100, 1080280, -497920; -907620, -497920, 229507],[140, 20, 1],[-209, -125, -177, -257, -1468; 3, 2, 0, 2, 14; -820, -490, -700, -1012, -5775],38,9]
%
% END OF LATTICE L39.9
%
%
% LATTICE L39.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[11480, 2100, -2940; 2100, 840, -532; -2940, -532, 753],[140, 28, 1],[-65, -47, 1, -181, -39; 3, 2, 0, 10, 2; -252, -182, 4, -700, -151],38,10]
%
% END OF LATTICE L39.10
%
%
% LATTICE L39.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-5740, -1540, 140; -1540, 70, 105; 140, 105, 6],[140, 35, 1],[-13, 13, 4, -4, -25; 29, -30, -9, 9, 56; -210, 210, 65, -63, -400],38,11]
%
% END OF LATTICE L39.11
%
%
% LATTICE L39.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[54040, 291340, -75600; 291340, 1571080, -407680; -75600, -407680, 105789],[140, 140, 1],[0, -1, 1, 5, 3; 109, 91, 5, 79, 76; 420, 350, 20, 308, 295],38,12]
%
% END OF LATTICE L39.12
%

\medskip%
%------------------------------WEYL-GROUP-W40--------------------------------
%
\leavevmode\llap{}%
$W_{40\phantom{0}}$%
\qquad\llap{8} lattices, $\chi=40$%
\hfill%
$\infty232\infty232\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L40.1
%
\leavevmode%
${L_{40.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}8\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{-2}{}19\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{2\rightarrow N_{40}}%
\EasyButWeakLineBreak%
{${38}\above{1pt}{1pt}{4,3}{\infty b}{152}\above{1pt}{1pt}{b}{2}{2}\above{1pt}{1pt}{+}{3}{2}\above{1pt}{1pt}{s}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1205512\\6080\\8968
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
6080\\-30\\-47
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
8968\\-47\\-62
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
67031\\8557752\\3202640
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-360\\-45961\\-17200
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-441\\-56301\\-21071
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
346\\44175\\16530
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
619\\79040\\29564
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\256\\95
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2\\-255\\-96
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-1205512, 6080, 8968; 6080, -30, -47; 8968, -47, -62],[152, 1, 1],[346, 619, 2, -2, -4, 65, 7, 74; 44175, 79040, 256, -255, -513, 8284, 893, 9447; 16530, 29564, 95, -96, -190, 3116, 335, 3536],39,1]
%
% END OF LATTICE L40.1
%
%
% LATTICE L40.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[38, 0, 0; 0, 0, -1; 0, -1, 0],[38, 1, 1],[-1, 1, 0, -7, -37, -39, -1, -1; 0, 0, -1, -30, -152, -152, -3, -2; -19, 0, 1, -31, -171, -190, -6, -9],39,2]
%
% END OF LATTICE L40.2
%
%
% LATTICE L40.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-477128, 5586, -234688; 5586, -60, 2746; -234688, 2746, -115437],[38, 2, 1],[28663, 12829, 168, -167, -353, 1326, 577, 6127; -18202, -8132, -103, 104, 190, -874, -371, -3896; -58710, -26277, -344, 342, 722, -2717, -1182, -12550],39,3]
%
% END OF LATTICE L40.3
%
%
% LATTICE L40.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2306182, -53048, -1094362; -53048, -1178, -25175; -1094362, -25175, -519312],[38, 19, 1],[9314, 8323, 1003, -1012, -98, 893, 3605, 37876; -853, -764, -96, 95, 11, -78, -325, -3463; -19586, -17502, -2109, 2128, 206, -1878, -7581, -79648],39,4]
%
% END OF LATTICE L40.4
%
%
% LATTICE L40.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-6927856, -42104, 98800; -42104, -240, 600; 98800, 600, -1409],[152, 8, 1],[30, -129, -55, -576, -2690, -1201, -15, 16; 57, -266, -112, -1161, -5415, -2413, -29, 33; 2128, -9158, -3904, -40880, -190912, -85234, -1064, 1136],39,5]
%
% END OF LATTICE L40.5
%
%
% LATTICE L40.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[200260, -8617222, -4192388; -8617222, 370832120, 180414538; -4192388, 180414538, 87773965],[38, 38, 1],[-352, -149, 1, 14, -16, -35, -185, -1486; 336753, 142446, -1442, -13551, 15425, 33643, 177531, 1422263; -692194, -292797, 2964, 27854, -31706, -69153, -364914, -2923454],39,6]
%
% END OF LATTICE L40.6
%
%
% LATTICE L40.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-31768, 4256, 2128; 4256, -570, -285; 2128, -285, -142],[152, 19, 1],[0, 3, 5, 42, 10, 17, 0, -2; -1, 24, 46, 455, 111, 196, 9, -15; 2, -4, -19, -304, -78, -148, -19, 0],39,7]
%
% END OF LATTICE L40.7
%
%
% LATTICE L40.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-4560, -108376, 1976; -108376, -2558768, 46664; 1976, 46664, -851],[152, 152, 1],[111, 49, 9, -15, -1, 6, 46, 455; 158, 71, 19, -16, -2, 7, 59, 640; 8928, 4010, 1064, -912, -112, 398, 3344, 36176],39,8]
%
% END OF LATTICE L40.8
%

\medskip%
%------------------------------WEYL-GROUP-W41--------------------------------
%
\leavevmode\llap{}%
$W_{41\phantom{0}}$%
\qquad\llap{12} lattices, $\chi=7$%
\hfill%
$2264$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L41.1
%
\leavevmode%
${L_{41.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{2}{}13\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2\rightarrow N_{41}}%
\EasyButWeakLineBreak%
{${4}\above{1pt}{1pt}{*}{2}{52}\above{1pt}{1pt}{b}{2}{6}\above{1pt}{1pt}{}{6}{2}\above{1pt}{1pt}{*}{4}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-235092\\2496\\4836
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2496\\-26\\-53
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4836\\-53\\-94
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3\\-178\\-54
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3\\-182\\-52
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4\\237\\72
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\120\\35
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-235092, 2496, 4836; 2496, -26, -53; 4836, -53, -94],[156, 1, 1],[-3, -3, 4, 2; -178, -182, 237, 120; -54, -52, 72, 35],40,1]
%
% END OF LATTICE L41.1
%
%
% LATTICE L41.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-390, -117, 0; -117, -35, 0; 0, 0, 1],[39, 1, 1],[0, -4, 1, 6; 0, 13, -3, -19; 1, 0, -3, -1],40,2]
%
% END OF LATTICE L41.2
%
%
% LATTICE L41.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-12207, 741, -3900; 741, -33, 237; -3900, 237, -1246],[39, 3, 1],[-24, 148, 49, 26; -1, -13, -1, 2; 75, -468, -154, -81],40,3]
%
% END OF LATTICE L41.3
%
%
% LATTICE L41.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1651260, 21996, 8892; 21996, -282, -123; 8892, -123, -46],[156, 3, 1],[-7, -11, 3, 6; -266, -416, 114, 227; -642, -1014, 275, 552],40,4]
%
% END OF LATTICE L41.4
%
%
% LATTICE L41.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-21567, -1404, -6786; -1404, -91, -442; -6786, -442, -2135],[39, 13, 1],[-9, 12, 103, 5; 12, -4, -63, -14; 26, -37, -312, -13],40,5]
%
% END OF LATTICE L41.5
%
%
% LATTICE L41.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2770872, -302484, -715572; -302484, 33032, 78116; -715572, 78116, 184795],[156, 4, 1],[-19, -47, -145, -338; 1, 0, 6, 17; -74, -182, -564, -1316],40,6]
%
% END OF LATTICE L41.6
%
%
% LATTICE L41.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[4251, -10686, -3432; -10686, 36582, 11739; -3432, 11739, 3767],[39, 39, 1],[4, -10, -25, 0; -512, 1317, 3276, -25; 1599, -4113, -10231, 78],40,7]
%
% END OF LATTICE L41.7
%
%
% LATTICE L41.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[216053448, -7188948, -55461432; -7188948, 239208, 1845420; -55461432, 1845420, 14237081],[156, 12, 1],[-97, -380, -236, -1521; 1, 13, 5, 22; -378, -1482, -920, -5928],40,8]
%
% END OF LATTICE L41.8
%
%
% LATTICE L41.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-839748, 17004, 10920; 17004, -338, -221; 10920, -221, -142],[156, 13, 1],[-3, 1, 4, -6; 2, -2, -3, 12; -234, 80, 312, -481],40,9]
%
% END OF LATTICE L41.9
%
%
% LATTICE L41.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-526188, -4778436, -368940; -4778436, -43362618, -3348033; -368940, -3348033, -258502],[156, 39, 1],[175, -27, -75, 163; 1402, -218, -601, 1316; -18408, 2862, 7891, -17277],40,10]
%
% END OF LATTICE L41.10
%
%
% LATTICE L41.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[13778232, -92196, 3608592; -92196, 728, -24232; 3608592, -24232, 945175],[156, 52, 1],[247, 19, 721, 2430; -740, -57, -2157, -7273; -962, -74, -2808, -9464],40,11]
%
% END OF LATTICE L41.11
%
%
% LATTICE L41.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[96073224, 1309261044, -335401092; 1309261044, 17842271304, -4570759440; -335401092, -4570759440, 1170918293],[156, 156, 1],[-324, -25, -315, -3185; -1315, -95, -1309, -13194; -5226, -378, -5200, -52416],40,12]
%
% END OF LATTICE L41.12
%

\medskip%
%------------------------------WEYL-GROUP-W42--------------------------------
%
\leavevmode\llap{}%
$W_{42\phantom{0}}$%
\qquad\llap{104} lattices, $\chi=36$%
\hfill%
$2222222222\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L42.1
%
\leavevmode%
${L_{42.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{6}8\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{-2}{}13\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2m\rightarrow N_{42},2\rightarrow N'_{26}}%
\EasyButWeakLineBreak%
{${1}\above{1pt}{1pt}{}{2}{13}\above{1pt}{1pt}{r}{2}{12}\above{1pt}{1pt}{*}{2}{8}\above{1pt}{1pt}{*}{2}{156}\above{1pt}{1pt}{l}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2834520\\5616\\5928
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5616\\-10\\-13
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5928\\-13\\-11
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4679\\1212120\\1085760
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-10\\-2591\\-2320
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-9\\-2331\\-2089
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\258\\233
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
9\\2327\\2093
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7\\1812\\1626
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
9\\2332\\2088
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
71\\18408\\16458
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-2834520, 5616, 5928; 5616, -10, -13; 5928, -13, -11],[312, 1, 1],[1, 9, 7, 9, 71, 2, 4, -1, -1, 7; 258, 2327, 1812, 2332, 18408, 519, 1040, -258, -260, 1794; 233, 2093, 1626, 2088, 16458, 463, 923, -234, -232, 1638],41,1]
%
% END OF LATTICE L42.1
%
\hbox{}\par\smallskip%
%
% LATTICE L42.2
%
\leavevmode%
${L_{42.2}}$%
{} : {$1\above{1pt}{1pt}{2}{0}8\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{-2}{}13\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{m}%
\EasyButWeakLineBreak%
{${1}\above{1pt}{1pt}{r}{2}{52}\above{1pt}{1pt}{*}{2}{12}\above{1pt}{1pt}{s}{2}{8}\above{1pt}{1pt}{s}{2}{156}\above{1pt}{1pt}{*}{2}{4}\above{1pt}{1pt}{l}{2}{13}\above{1pt}{1pt}{}{2}{3}\above{1pt}{1pt}{r}{2}{8}\above{1pt}{1pt}{l}{2}{39}\above{1pt}{1pt}{}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3004872\\12168\\6240
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
12168\\-49\\-26
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
6240\\-26\\-11
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\414\\155
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
31\\6422\\2392
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
11\\2280\\846
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
13\\2696\\996
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
97\\20124\\7410
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5\\1038\\380
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4\\832\\299
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-207\\-78
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-208\\-76
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
10\\2067\\780
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-3004872, 12168, 6240; 12168, -49, -26; 6240, -26, -11],[312, 1, 1],[2, 31, 11, 13, 97, 5, 4, -1, -1, 10; 414, 6422, 2280, 2696, 20124, 1038, 832, -207, -208, 2067; 155, 2392, 846, 996, 7410, 380, 299, -78, -76, 780],41,2]
%
% END OF LATTICE L42.2
%
\hbox{}\par\smallskip%
%
% LATTICE L42.3
%
\leavevmode%
${L_{42.3}}$%
{} : {$1\above{1pt}{1pt}{2}{6}8\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{-2}{}13\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{m}%
\EasyButWeakLineBreak%
{${4}\above{1pt}{1pt}{*}{2}{52}\above{1pt}{1pt}{l}{2}{3}\above{1pt}{1pt}{}{2}{8}\above{1pt}{1pt}{}{2}{39}\above{1pt}{1pt}{r}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-50843832\\-1271088\\49920
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1271088\\-31777\\1248
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
49920\\1248\\-49
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
47423\\-1873248\\592800
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1186\\-46848\\14825
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-46\\1817\\-576
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7\\-274\\152
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
49\\-1924\\910
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
8\\-315\\126
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
17\\-672\\200
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
58\\-2301\\468
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-50843832, -1271088, 49920; -1271088, -31777, 1248; 49920, 1248, -49],[312, 1, 1],[7, 49, 8, 17, 58, 5, 3, -2, -1, 20; -274, -1924, -315, -672, -2301, -200, -130, 78, 40, -780; 152, 910, 126, 200, 468, -2, -260, -51, 0, 507],41,3]
%
% END OF LATTICE L42.3
%
\hbox{}\par\smallskip%
%
% LATTICE L42.4
%
\leavevmode%
${L_{42.4}}$%
{} : {$[1\above{1pt}{1pt}{-}{}2\above{1pt}{1pt}{1}{}]\above{1pt}{1pt}{}{2}16\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{-2}{}13\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${16}\above{1pt}{1pt}{s}{2}{52}\above{1pt}{1pt}{*}{2}{48}\above{1pt}{1pt}{s}{2}{8}\above{1pt}{1pt}{*}{2}{624}\above{1pt}{1pt}{l}{2}{1}\above{1pt}{1pt}{}{2}{208}\above{1pt}{1pt}{}{2}{3}\above{1pt}{1pt}{r}{2}{8}\above{1pt}{1pt}{*}{2}{156}\above{1pt}{1pt}{s}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
341328\\169728\\-624
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
169728\\84398\\-310
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-624\\-310\\1
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
201\\-408\\-1016
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
333\\-676\\-1690
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
65\\-132\\-336
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\2\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-77\\156\\312
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\-1
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
205\\-416\\-1040
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
34\\-69\\-171
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
135\\-274\\-680
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1345\\-2730\\-6786
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[341328, 169728, -624; 169728, 84398, -310; -624, -310, 1],[624, 2, 1],[201, 333, 65, -1, -77, 0, 205, 34, 135, 1345; -408, -676, -132, 2, 156, 0, -416, -69, -274, -2730; -1016, -1690, -336, 0, 312, -1, -1040, -171, -680, -6786],41,4]
%
% END OF LATTICE L42.4
%
\hbox{}\par\smallskip%
%
% LATTICE L42.5
%
\leavevmode%
${L_{42.5}}$%
{} : {$[1\above{1pt}{1pt}{1}{}2\above{1pt}{1pt}{1}{}]\above{1pt}{1pt}{}{0}16\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{-2}{}13\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{m}%
\EasyButWeakLineBreak%
{${16}\above{1pt}{1pt}{*}{2}{52}\above{1pt}{1pt}{s}{2}{48}\above{1pt}{1pt}{l}{2}{2}\above{1pt}{1pt}{}{2}{624}\above{1pt}{1pt}{}{2}{1}\above{1pt}{1pt}{r}{2}{208}\above{1pt}{1pt}{*}{2}{12}\above{1pt}{1pt}{l}{2}{2}\above{1pt}{1pt}{}{2}{39}\above{1pt}{1pt}{r}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-7951632\\7488\\18096
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7488\\-2\\-18
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
18096\\-18\\-41
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-76\\-408
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3\\-234\\-1222
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\72\\408
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\229\\1222
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
167\\12792\\68016
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4\\307\\1629
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
71\\5460\\28912
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7\\540\\2850
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\155\\814
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7\\546\\2847
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-7951632, 7488, 18096; 7488, -2, -18; 18096, -18, -41],[624, 2, 1],[-1, -3, 1, 3, 167, 4, 71, 7, 2, 7; -76, -234, 72, 229, 12792, 307, 5460, 540, 155, 546; -408, -1222, 408, 1222, 68016, 1629, 28912, 2850, 814, 2847],41,5]
%
% END OF LATTICE L42.5
%
\hbox{}\par\smallskip%
%
% LATTICE L42.6
%
\leavevmode%
${L_{42.6}}$%
{} : {$[1\above{1pt}{1pt}{-}{}2\above{1pt}{1pt}{1}{}]\above{1pt}{1pt}{}{4}16\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{-2}{}13\above{1pt}{1pt}{1}{}$}\EasyButWeakLineBreak%
{${16}\above{1pt}{1pt}{l}{2}{13}\above{1pt}{1pt}{}{2}{48}\above{1pt}{1pt}{}{2}{2}\above{1pt}{1pt}{r}{2}{624}\above{1pt}{1pt}{s}{2}{4}\above{1pt}{1pt}{*}{2}{208}\above{1pt}{1pt}{l}{2}{3}\above{1pt}{1pt}{}{2}{2}\above{1pt}{1pt}{r}{2}{156}\above{1pt}{1pt}{*}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-501072\\1872\\2496
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1872\\-2\\-12
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2496\\-12\\-11
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-76\\-144
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-78\\-143
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\72\\144
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\151\\286
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
107\\8112\\15288
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5\\380\\714
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
43\\3276\\6136
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\153\\285
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\77\\142
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5\\390\\702
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-501072, 1872, 2496; 1872, -2, -12; 2496, -12, -11],[624, 2, 1],[-1, -1, 1, 2, 107, 5, 43, 2, 1, 5; -76, -78, 72, 151, 8112, 380, 3276, 153, 77, 390; -144, -143, 144, 286, 15288, 714, 6136, 285, 142, 702],41,6]
%
% END OF LATTICE L42.6
%
\hbox{}\par\smallskip%
%
% LATTICE L42.7
%
\leavevmode%
${L_{42.7}}$%
{} : {$[1\above{1pt}{1pt}{1}{}2\above{1pt}{1pt}{1}{}]\above{1pt}{1pt}{}{6}16\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{-2}{}13\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{m}%
\EasyButWeakLineBreak%
{${16}\above{1pt}{1pt}{}{2}{13}\above{1pt}{1pt}{r}{2}{48}\above{1pt}{1pt}{*}{2}{8}\above{1pt}{1pt}{s}{2}{624}\above{1pt}{1pt}{*}{2}{4}\above{1pt}{1pt}{s}{2}{208}\above{1pt}{1pt}{s}{2}{12}\above{1pt}{1pt}{*}{2}{8}\above{1pt}{1pt}{l}{2}{39}\above{1pt}{1pt}{}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
243984\\-1872\\1872
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1872\\14\\-12
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1872\\-12\\-1
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7\\1072\\160
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4\\611\\91
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-156\\-24
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-154\\-24
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\156\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\154\\22
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
23\\3536\\520
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5\\768\\114
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7\\1074\\160
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
29\\4446\\663
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[243984, -1872, 1872; -1872, 14, -12; 1872, -12, -1],[624, 2, 1],[7, 4, -1, -1, 1, 1, 23, 5, 7, 29; 1072, 611, -156, -154, 156, 154, 3536, 768, 1074, 4446; 160, 91, -24, -24, 0, 22, 520, 114, 160, 663],41,7]
%
% END OF LATTICE L42.7
%
%
% LATTICE L42.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[312, 117, -39; 117, 43, -13; -39, -13, 2],[39, 1, 1],[0, -8, 2, 13, 370, 36, 164, 34, 11, 98; 0, 26, -6, -41, -1170, -114, -520, -108, -35, -312; 1, 13, -3, -18, -507, -49, -221, -45, -14, -117],41,8]
%
% END OF LATTICE L42.8
%
%
% LATTICE L42.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[4602, 2262, 234; 2262, 1112, 117; 234, 117, 35],[78, 1, 1],[39, -1628, -1228, -2689, -27938, -2172, -7615, -905, -155, 209; -80, 3341, 2520, 5518, 57330, 4457, 15626, 1857, 318, -429; 7, -299, -225, -492, -5109, -397, -1391, -165, -28, 39],41,9]
%
% END OF LATTICE L42.9
%
%
% LATTICE L42.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-4361916, -109044, 4680; -109044, -2726, 117; 4680, 117, -5],[156, 1, 1],[4, 8, -1, -1, 7, 2, 18, 7, 9, 71; -161, -325, 39, 40, -273, -79, -715, -279, -360, -2847; -28, -130, -24, 0, 156, 22, 104, 18, -8, -234],41,10]
%
% END OF LATTICE L42.10
%
%
% LATTICE L42.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-4836, -2496, 156; -2496, -1286, 79; 156, 79, -4],[156, 1, 1],[10, 43, 7, -1, -55, -7, -30, -4, 5, 94; -21, -91, -15, 2, 117, 15, 65, 9, -10, -195; -28, -130, -24, 0, 156, 22, 104, 18, -8, -234],41,11]
%
% END OF LATTICE L42.11
%
%
% LATTICE L42.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[156, 0, 0; 0, 2, 0; 0, 0, -1],[156, 2, 1],[0, -3, -1, -2, -20, -3, -5, -1, 0, 1; -1, -26, -6, -9, -78, -10, -13, 0, 1, 0; -1, -52, -15, -28, -273, -40, -65, -12, 0, 0],41,12]
%
% END OF LATTICE L42.12
%
%
% LATTICE L42.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-250536, 2496, 936; 2496, -22, -12; 936, -12, -1],[312, 2, 1],[-1, -2, 1, 2, 107, 5, 43, 4, 1, 5; -72, -143, 72, 143, 7644, 357, 3068, 285, 71, 351; -76, -156, 72, 151, 8112, 380, 3276, 306, 77, 390],41,13]
%
% END OF LATTICE L42.13
%
%
% LATTICE L42.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[13416, 6240, 312; 6240, 2866, 176; 312, 176, -19],[312, 2, 1],[-32, -307, -28, 7, 289, 73, 173, 65, -1, -461; 65, 624, 57, -14, -585, -148, -351, -132, 2, 936; 76, 728, 66, -18, -702, -176, -416, -156, 2, 1092],41,14]
%
% END OF LATTICE L42.14
%
%
% LATTICE L42.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-29211, -156, -9516; -156, 6, -51; -9516, -51, -3100],[39, 3, 1],[172, 4650, 890, 2455, 15822, 3446, 11028, 316, -43, -144; -13, -377, -73, -203, -1313, -287, -923, -27, 3, 13; -528, -14274, -2732, -7536, -48568, -10578, -33852, -970, 132, 442],41,15]
%
% END OF LATTICE L42.15
%
%
% LATTICE L42.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3272880, 94458, -1640496; 94458, -2726, 47346; -1640496, 47346, -822281],[78, 2, 1],[-87, 2800, 2173, 2415, 50459, 3942, 13905, 1682, 155, -344; 77, -2327, -1821, -2033, -42549, -3329, -11765, -1431, -135, 273; 178, -5720, -4440, -4935, -103116, -8056, -28418, -3438, -317, 702],41,16]
%
% END OF LATTICE L42.16
%
%
% LATTICE L42.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-5230758, 146250, 1739400; 146250, -4089, -48633; 1739400, -48633, -578408],[78, 3, 1],[65, -2140, -552, -3675, -12790, -2996, -10561, -425, -233, 89; 77, -2327, -607, -4066, -14183, -3329, -11765, -477, -270, 91; 189, -6240, -1609, -10710, -37271, -8730, -30771, -1238, -678, 260],41,17]
%
% END OF LATTICE L42.17
%
%
% LATTICE L42.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[623298, -63414, 286026; -63414, 6672, -29094; 286026, -29094, 131255],[78, 6, 1],[-1327, 55319, 13911, 45696, 316523, 73825, 258839, 10255, 2636, -2365; -80, 3341, 840, 2759, 19110, 4457, 15626, 619, 159, -143; 2874, -119808, -30128, -98967, -685516, -159888, -560586, -22210, -5709, 5122],41,18]
%
% END OF LATTICE L42.18
%
%
% LATTICE L42.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-9204, 780, 468; 780, -66, -39; 468, -39, -19],[156, 3, 1],[6, 8, -1, -1, 11, 6, 44, 5, 17, 41; 73, 91, -13, -12, 143, 77, 559, 63, 212, 507; -6, 0, 2, 0, -26, -12, -78, -8, -24, -52],41,19]
%
% END OF LATTICE L42.19
%
%
% LATTICE L42.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1716, 780, -156; 780, 354, -75; -156, -75, -16],[156, 3, 1],[-4, 43, 7, -1, -79, -35, -212, -20, -51, -90; 9, -91, -15, 2, 169, 75, 455, 43, 110, 195; -6, 0, 2, 0, -26, -12, -78, -8, -24, -52],41,20]
%
% END OF LATTICE L42.20
%
%
% LATTICE L42.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-59592, -1989, -18291; -1989, -65, -611; -18291, -611, -5614],[39, 13, 1],[104, 224, 1682, 1553, 2314, 2188, 540, 610, -25, -22; -124, -258, -1926, -1771, -2634, -2486, -612, -684, 31, 24; -325, -701, -5265, -4862, -7245, -6851, -1691, -1911, 78, 69],41,21]
%
% END OF LATTICE L42.21
%
%
% LATTICE L42.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[316680, 8892, -81432; 8892, 2380, -2340; -81432, -2340, 20941],[156, 4, 1],[-5777, -16455, -797, 10, -8761, -1633, -15655, -6613, -2480, -87569; -566, -1612, -78, 1, -858, -160, -1534, -648, -243, -8580; -22528, -64168, -3108, 39, -34164, -6368, -61048, -25788, -9671, -341484],41,22]
%
% END OF LATTICE L42.22
%
%
% LATTICE L42.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2181192, -16692, -551460; -16692, 128, 4220; -551460, 4220, 139423],[156, 4, 1],[-67, -241, -37, -19, -401, -35, -201, -65, -49, -925; -166, -572, -78, -38, -858, -80, -494, -168, -126, -2340; -260, -936, -144, -74, -1560, -136, -780, -252, -190, -3588],41,23]
%
% END OF LATTICE L42.23
%
%
% LATTICE L42.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1235208, 6864, 6864; 6864, -33, -39; 6864, -39, -38],[312, 3, 1],[3, 22, 5, 17, 41, 3, 4, -1, -1, 11; 77, 559, 126, 424, 1014, 73, 91, -26, -24, 286; 462, 3393, 772, 2628, 6344, 465, 624, -154, -156, 1690],41,24]
%
% END OF LATTICE L42.24
%
%
% LATTICE L42.25
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-188760, 2496, 5928; 2496, -33, -78; 5928, -78, -155],[312, 3, 1],[6, 83, 9, 29, 67, 9, 4, -1, -1, 12; 467, 6448, 698, 2244, 5174, 692, 299, -78, -76, 936; -6, -78, -8, -24, -52, -6, 0, 1, 0, -13],41,25]
%
% END OF LATTICE L42.25
%
%
% LATTICE L42.26
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-76596, 6396, -936; 6396, -534, 78; -936, 78, -11],[156, 6, 1],[-1, -5, -1, 0, 9, 2, 23, 1, 2, 2; -12, -65, -14, -5, 78, 21, 260, 12, 25, 26; 0, -39, -16, -42, -260, -27, -156, -1, 6, 13],41,26]
%
% END OF LATTICE L42.26
%
%
% LATTICE L42.27
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-25896, -624, -3120; -624, -15, -78; -3120, -78, -155],[312, 3, 1],[23, 153, 8, 49, 54, 13, 3, -2, -1, 24; -898, -5980, -313, -1920, -2119, -512, -130, 78, 40, -936; -12, -78, -4, -24, -26, -6, 0, 1, 0, -13],41,27]
%
% END OF LATTICE L42.27
%
%
% LATTICE L42.28
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-34301670, 66924, -5337150; 66924, -130, 10413; -5337150, 10413, -830431],[78, 13, 1],[-180, 418, 4253, 9497, 7645, 7776, 2114, 3343, 631, -49; 11, -40, -387, -840, -669, -674, -181, -276, -44, 6; 1157, -2687, -27339, -61048, -49143, -49985, -13589, -21489, -4056, 315],41,28]
%
% END OF LATTICE L42.28
%
%
% LATTICE L42.29
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-376584, -312, 2184; -312, 20, -4; 2184, -4, -11],[312, 4, 1],[4, 4, -1, -1, 7, 1, 18, 7, 9, 71; 207, 208, -51, -52, 351, 51, 923, 360, 464, 3666; 716, 715, -180, -180, 1248, 179, 3224, 1254, 1612, 12714],41,29]
%
% END OF LATTICE L42.29
%
%
% LATTICE L42.30
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-7872072, 207168, 94848; 207168, -5452, -2496; 94848, -2496, -1141],[312, 4, 1],[18, 73, 11, -1, -71, -9, -34, -1, 13, 94; 697, 2834, 429, -38, -2769, -352, -1339, -42, 498, 3627; -28, -130, -24, 0, 156, 22, 104, 9, -8, -117],41,30]
%
% END OF LATTICE L42.30
%
%
% LATTICE L42.31
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[11193, -58578, -18759; -58578, 316524, 101361; -18759, 101361, 32459],[39, 39, 1],[-17, -35, -87, -240, -119, -337, -83, -31, 4, 1; 3906, 8272, 20662, 57194, 28402, 80556, 19882, 7492, -886, -248; -12207, -25851, -64571, -178737, -88759, -251745, -62133, -23413, 2769, 775],41,31]
%
% END OF LATTICE L42.31
%
%
% LATTICE L42.32
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[116376, 19812, -29328; 19812, 3396, -4992; -29328, -4992, 7391],[156, 12, 1],[-205, -485, 1, -10, -415, -167, -1127, -125, -114, -1197; 32, 78, 0, 1, 52, 22, 156, 18, 17, 182; -792, -1872, 4, -39, -1612, -648, -4368, -484, -441, -4628],41,32]
%
% END OF LATTICE L42.32
%
%
% LATTICE L42.33
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[17160, 2184, -312; 2184, 138, -30; -312, -30, 5],[312, 6, 1],[-1, -5, -1, 0, 9, 2, 23, 1, 1, 2; -8, -39, -8, -1, 52, 13, 156, 7, 7, 13; -108, -546, -112, -9, 832, 198, 2340, 104, 105, 208],41,33]
%
% END OF LATTICE L42.33
%
%
% LATTICE L42.34
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2019576, -89700, -503880; -89700, 3984, 22380; -503880, 22380, 125717],[156, 12, 1],[325, 837, 1, -17, 145, 107, 1035, 143, 305, 1727; 172, 442, 0, -12, 52, 50, 520, 74, 160, 910; 1272, 3276, 4, -66, 572, 420, 4056, 560, 1194, 6760],41,34]
%
% END OF LATTICE L42.34
%
%
% LATTICE L42.35
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-28289352, 2357472, -62712; 2357472, -196458, 5226; -62712, 5226, -139],[312, 6, 1],[-1, 29, 13, 37, 239, 26, 163, 2, -3, -9; -12, 377, 168, 476, 3068, 333, 2080, 25, -40, -117; 0, 1092, 452, 1206, 7540, 792, 4680, 38, -150, -338],41,35]
%
% END OF LATTICE L42.35
%
%
% LATTICE L42.36
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-18876, 4680, -312; 4680, -1157, 78; -312, 78, -5],[156, 13, 1],[-2, 0, 5, 15, 13, 14, 4, 7, 1, -1; -7, -1, 9, 36, 33, 37, 11, 21, 4, -3; 13, -19, -195, -416, -327, -325, -85, -117, 0, 15],41,36]
%
% END OF LATTICE L42.36
%
%
% LATTICE L42.37
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[109356, 53196, -936; 53196, 25870, -455; -936, -455, 8],[156, 13, 1],[-1, 0, 2, 5, 4, 4, 1, 1, -1, -1; 3, -1, -15, -34, -27, -27, -7, -9, 2, 3; 52, -58, -624, -1352, -1068, -1066, -280, -390, 0, 54],41,37]
%
% END OF LATTICE L42.37
%
%
% LATTICE L42.38
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[101109840, -179478, 49566270; -179478, 910, -87984; 49566270, -87984, 24298477],[78, 26, 1],[29430, -94507, -926720, -1014634, -1621810, -1639107, -442052, -682957, -58484, 12133; 7, -23, -225, -246, -393, -397, -107, -165, -14, 3; -60034, 192784, 1890408, 2069743, 3308316, 3343600, 901738, 1393158, 119301, -24750],41,38]
%
% END OF LATTICE L42.38
%
%
% LATTICE L42.39
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[85488, 312, -312; 312, -8, 0; -312, 0, 1],[312, 8, 1],[0, -3, -2, -1, -40, -3, -10, -1, 0, 1; 1, -91, -63, -32, -1287, -97, -325, -33, 0, 39; 4, -884, -600, -303, -12168, -916, -3068, -312, -1, 312],41,39]
%
% END OF LATTICE L42.39
%
%
% LATTICE L42.40
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-24024, 0, -11856; 0, 8, 0; -11856, 0, -5851],[312, 8, 1],[0, 257, 172, 173, 3470, 261, 874, 89, 1, -77; 1, 0, -3, -5, -117, -10, -39, -6, -1, 0; 0, -520, -348, -350, -7020, -528, -1768, -180, -2, 156],41,40]
%
% END OF LATTICE L42.40
%
%
% LATTICE L42.41
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[312, 0, 0; 0, 8, 0; 0, 0, -1],[312, 8, 1],[0, -3, -2, -2, -40, -3, -10, -1, 0, 1; 1, 0, -3, -5, -117, -10, -39, -6, -1, 0; 0, -52, -36, -38, -780, -60, -208, -24, -2, 0],41,41]
%
% END OF LATTICE L42.41
%
%
% LATTICE L42.42
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[85160946, 203502, 28992132; 203502, 1365, 68679; 28992132, 68679, 9870472],[78, 39, 1],[22973, -73772, -241132, -1584043, -421994, -1279484, -345065, -177705, -91305, 3157; -45939, 147521, 482189, 3167594, 843857, 2558571, 690023, 355355, 182582, -6313; -67158, 215661, 704912, 4630704, 1233634, 3740373, 1008744, 519493, 266916, -9229],41,42]
%
% END OF LATTICE L42.42
%
%
% LATTICE L42.43
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1620528, -6240, 4368; -6240, 6, 12; 4368, 12, -11],[624, 6, 1],[1, 23, 1, 1, 1, -1, -5, -1, 0, 9; 73, 1716, 76, 77, 78, -76, -390, -80, -5, 624; 471, 10920, 478, 480, 481, -480, -2418, -488, -12, 4160],41,43]
%
% END OF LATTICE L42.43
%
%
% LATTICE L42.44
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-8385936, -4196400, 15600; -4196400, -2099910, 7806; 15600, 7806, -29],[624, 6, 1],[-13, -289, -6, -21, -11, 19, 73, 13, -1, -121; 28, 624, 13, 46, 26, -40, -156, -28, 2, 260; 543, 12480, 271, 1080, 1066, -552, -2730, -544, 0, 4888],41,44]
%
% END OF LATTICE L42.44
%
%
% LATTICE L42.45
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[49296, -3744, 2496; -3744, -186, 96; 2496, 96, -47],[624, 6, 1],[5, 51, 1, 2, 5, -1, -3, -1, 1, 29; -666, -6812, -134, -269, -676, 132, 403, 136, -131, -3848; -1098, -11232, -221, -444, -1118, 216, 663, 224, -216, -6344],41,45]
%
% END OF LATTICE L42.45
%
%
% LATTICE L42.46
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-188760, 12792, -3432; 12792, -564, 132; -3432, 132, -29],[312, 12, 1],[3, 44, 5, 17, 41, 6, 4, -1, -1, 11; 230, 3367, 382, 1296, 3120, 455, 299, -77, -76, 845; 693, 10140, 1150, 3900, 9386, 1368, 897, -232, -228, 2548],41,46]
%
% END OF LATTICE L42.46
%
%
% LATTICE L42.47
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-6925776, -29952, 15600; -29952, -114, 66; 15600, 66, -35],[624, 6, 1],[3, 49, 3, 11, 14, 9, 4, -1, -1, 9; 154, 2496, 152, 554, 702, 448, 195, -52, -50, 468; 1626, 26520, 1622, 5940, 7553, 4848, 2145, -544, -540, 4888],41,47]
%
% END OF LATTICE L42.47
%
%
% LATTICE L42.48
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-31557864, 2629848, 1280448; 2629848, -219156, -106704; 1280448, -106704, -51947],[312, 12, 1],[-183, -1126, -54, -283, -259, -30, 203, 37, -1, -405; -2380, -14651, -703, -3688, -3380, -395, 2626, 481, -12, -5265; 378, 2340, 113, 600, 559, 72, -390, -76, 0, 832],41,48]
%
% END OF LATTICE L42.48
%
%
% LATTICE L42.49
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-312, 2496, -312; 2496, 1313, -182; -312, -182, 25],[312, 13, 1],[1, 0, -5, -15, -13, -7, -2, -7, -1, 1; 18, -1, -108, -308, -264, -141, -40, -138, -20, 18; 143, -8, -858, -2444, -2094, -1118, -317, -1092, -156, 144],41,49]
%
% END OF LATTICE L42.49
%
%
% LATTICE L42.50
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[9048, 5616, -624; 5616, 1703, -208; -624, -208, 25],[312, 13, 1],[2, 1, -1, -11, -11, -13, -2, -4, -1, 1; 30, 14, -24, -184, -180, -210, -32, -63, -16, 15; 299, 140, -234, -1820, -1782, -2080, -317, -624, -156, 150],41,50]
%
% END OF LATTICE L42.50
%
%
% LATTICE L42.51
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[156, -156, 0; -156, 182, 0; 0, 0, -1],[156, 26, 1],[0, -1, -4, -7, -5, -9, -1, -1, 1, 1; -1, -2, -6, -9, -6, -10, -1, 0, 1, 0; -13, -16, -39, -52, -33, -52, -5, 0, 0, -12],41,51]
%
% END OF LATTICE L42.51
%
%
% LATTICE L42.52
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-26520, -3432, 936; -3432, -442, 117; 936, 117, -25],[312, 13, 1],[-7, -1, 4, 31, 14, 31, 9, 8, 1, -2; 62, 8, -39, -288, -129, -284, -82, -72, -8, 18; 26, -2, -39, -208, -87, -182, -50, -39, 0, 9],41,52]
%
% END OF LATTICE L42.52
%
%
% LATTICE L42.53
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[341328, 624, -624; 624, -8, 0; -624, 0, 1],[624, 8, 1],[-3, -5, -1, 0, 1, 0, -3, -1, -2, -20; -204, -338, -66, 1, 78, 0, -208, -69, -137, -1365; -1832, -3042, -600, 4, 624, -1, -1872, -618, -1228, -12246],41,53]
%
% END OF LATTICE L42.53
%
%
% LATTICE L42.54
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-96720, 0, -48048; 0, 8, 0; -48048, 0, -23869],[624, 8, 1],[1, 517, 85, 338, 3373, 505, 840, 167, 0, -155; -1, -26, -3, -9, -78, -10, -13, 0, 1, 0; -2, -1040, -171, -680, -6786, -1016, -1690, -336, 0, 312],41,54]
%
% END OF LATTICE L42.54
%
%
% LATTICE L42.55
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[624, 0, 0; 0, 8, 0; 0, 0, -1],[624, 8, 1],[0, -3, -1, -2, -10, -3, -5, -1, 0, 1; -1, -26, -6, -9, -39, -10, -13, 0, 1, 0; -2, -104, -30, -56, -273, -80, -130, -24, 0, 0],41,55]
%
% END OF LATTICE L42.55
%
%
% LATTICE L42.56
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-96720, 6864, 3744; 6864, 232, 96; 3744, 96, 37],[624, 8, 1],[7, 4, -1, -1, 1, 1, 23, 5, 7, 58; -1162, -663, 168, 167, -156, -166, -3822, -831, -1163, -9633; 2304, 1313, -336, -332, 312, 330, 7592, 1650, 2308, 19110],41,56]
%
% END OF LATTICE L42.56
%
%
% LATTICE L42.57
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[156, 0, 0; 0, -1950, 117; 0, 117, -7],[156, 39, 1],[-5, -1, 0, 1, 0, -1, -1, -2, -9, -2; -17, -5, -3, 0, 1, 5, 1, -1, -16, -5; -312, -90, -52, 0, 16, 78, 12, -26, -312, -94],41,57]
%
% END OF LATTICE L42.57
%
%
% LATTICE L42.58
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[48516, 22776, -1248; 22776, 10686, -585; -1248, -585, 32],[156, 39, 1],[2, 1, 1, -1, -1, -5, -2, -2, -3, 0; -21, -7, -5, 2, 3, 15, 5, 3, -10, -5; -312, -90, -52, 0, 16, 78, 12, -26, -312, -94],41,58]
%
% END OF LATTICE L42.58
%
%
% LATTICE L42.59
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-35015081088, 86208554562, 42448017846; 86208554562, -212248969530, -104508747330; 42448017846, -104508747330, -51458804689],[78, 78, 1],[11, -40, -129, -420, -223, -674, -181, -92, -22, 2; -110183, 256431, 869439, 2911732, 1562519, 4767629, 1296051, 683043, 193232, -10037; 223782, -520824, -1765868, -5913843, -3173536, -9683232, -2632326, -1387282, -392457, 20386],41,59]
%
% END OF LATTICE L42.59
%
%
% LATTICE L42.60
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[29328, 312, -10296; 312, -24, -72; -10296, -72, 3563],[312, 24, 1],[4, -263, -62, -96, -1296, -295, -998, -35, -1, 35; 17, -1053, -249, -386, -5213, -1187, -4017, -141, -4, 143; 12, -780, -184, -285, -3848, -876, -2964, -104, -3, 104],41,60]
%
% END OF LATTICE L42.60
%
%
% LATTICE L42.61
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-7176, 0, 1248; 0, 24, 0; 1248, 0, -217],[312, 24, 1],[0, -107, -24, -73, -490, -111, -374, -13, -1, 9; 1, 0, -1, -5, -39, -10, -39, -2, -1, 0; 0, -624, -140, -426, -2860, -648, -2184, -76, -6, 52],41,61]
%
% END OF LATTICE L42.61
%
%
% LATTICE L42.62
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1114152, 0, 10608; 0, 24, 0; 10608, 0, 101],[312, 24, 1],[0, 43, 10, 32, 220, 51, 178, 7, 2, 1; 1, 0, -1, -5, -39, -10, -39, -2, -1, 0; 0, -4524, -1052, -3366, -23140, -5364, -18720, -736, -210, -104],41,62]
%
% END OF LATTICE L42.62
%
%
% LATTICE L42.63
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[213720, -12948, 64428; -12948, 988, -4056; 64428, -4056, 19537],[156, 52, 1],[-253, -337, -2317, -1022, -2993, -2783, -675, -719, 10, -43; 740, 986, 6780, 2991, 8760, 8146, 1976, 2106, -29, 126; 988, 1316, 9048, 3991, 11688, 10868, 2636, 2808, -39, 168],41,63]
%
% END OF LATTICE L42.63
%
%
% LATTICE L42.64
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[312, -4056, 312; -4056, -52234, 4108; 312, 4108, -323],[312, 26, 1],[38, 27, 37, 12, 8, -1, -1, 1, 13, 59; 257, 184, 255, 84, 57, -4, -7, 0, 86, 396; 3302, 2364, 3276, 1079, 732, -52, -90, 0, 1105, 5088],41,64]
%
% END OF LATTICE L42.64
%
%
% LATTICE L42.65
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-9048, -312, -312; -312, 442, -52; -312, -52, -7],[312, 26, 1],[85, 11, 29, -1, -5, -2, 5, 26, 55, 43; -208, -27, -72, 2, 12, 5, -12, -63, -134, -105; -2288, -296, -780, 26, 132, 52, -136, -702, -1482, -1158],41,65]
%
% END OF LATTICE L42.65
%
%
% LATTICE L42.66
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2788656, 36972, 685776; 36972, 416, 9152; 685776, 9152, 168595],[156, 52, 1],[-387, -271, -1201, -447, -197, 267, 231, 1081, 367, 77; 1219, 853, 3777, 1401, 609, -853, -731, -3411, -1157, -243; 1508, 1056, 4680, 1742, 768, -1040, -900, -4212, -1430, -300],41,66]
%
% END OF LATTICE L42.66
%
%
% LATTICE L42.67
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[19032, -32448, 2808; -32448, 42627, -3705; 2808, -3705, 322],[312, 39, 1],[-6, -2, -3, -1, 1, 3, 1, 1, -7, -3; 263, 85, 122, 40, -38, -113, -35, -22, 360, 138; 3081, 996, 1430, 468, -446, -1326, -411, -260, 4212, 1616],41,67]
%
% END OF LATTICE L42.67
%
%
% LATTICE L42.68
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[219336, -149448, 12792; -149448, 96915, -8307; 12792, -8307, 712],[312, 39, 1],[-9, -2, -2, -1, 1, 6, 5, 5, 5, -1; 514, 109, 105, 52, -51, -305, -250, -242, -180, 70; 6162, 1308, 1261, 624, -613, -3666, -3006, -2912, -2184, 836],41,68]
%
% END OF LATTICE L42.68
%
%
% LATTICE L42.69
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-9516, 0, 468; 0, 78, 0; 468, 0, -23],[156, 78, 1],[-37, -5, -5, 0, 1, 2, -1, -3, -22, -6; -10, -1, 0, 1, 0, -1, -2, -2, -9, -2; -780, -105, -104, 0, 20, 39, -24, -65, -468, -127],41,69]
%
% END OF LATTICE L42.69
%
%
% LATTICE L42.70
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[312, 0, 0; 0, -44499, 1248; 0, 1248, -35],[312, 39, 1],[-5, -1, 0, 1, 0, -1, -1, -1, -9, -1; -28, -10, -4, 0, 2, 22, 8, 3, -8, -3; -1014, -360, -143, 0, 71, 780, 282, 104, -312, -110],41,70]
%
% END OF LATTICE L42.70
%
%
% LATTICE L42.71
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-209040, 30576, -2496; 30576, -4440, 360; -2496, 360, -29],[624, 24, 1],[1, 23, 1, 2, 2, -1, -5, -1, 0, 9; 14, 312, 13, 23, 13, -20, -78, -14, 1, 130; 87, 1872, 74, 108, -26, -168, -546, -88, 12, 832],41,71]
%
% END OF LATTICE L42.71
%
%
% LATTICE L42.72
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-45863376, 3822000, -22464; 3822000, -318504, 1872; -22464, 1872, -11],[624, 24, 1],[2, 23, 1, 2, 1, -1, -5, -1, 0, 9; 21, 260, 12, 25, 13, -12, -65, -14, -5, 78; -522, -2808, -2, 168, 169, 0, -858, -344, -864, -5200],41,72]
%
% END OF LATTICE L42.72
%
%
% LATTICE L42.73
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[12250992, -1018368, 3744; -1018368, 84648, -312; 3744, -312, 1],[624, 24, 1],[14, 75, 0, -5, -11, -1, 21, 9, 23, 139; 165, 884, 0, -59, -130, -12, 247, 106, 271, 1638; -930, -4992, -1, 312, 650, 24, -1482, -608, -1536, -9256],41,73]
%
% END OF LATTICE L42.73
%
%
% LATTICE L42.74
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-10349040, -71760, -16848; -71760, -456, -96; -16848, -96, -17],[624, 24, 1],[3, 49, 3, 11, 28, 9, 4, -1, -1, 9; -814, -13286, -813, -2979, -7579, -2434, -1079, 272, 271, -2444; 1626, 26520, 1622, 5940, 15106, 4848, 2145, -544, -540, 4888],41,74]
%
% END OF LATTICE L42.74
%
%
% LATTICE L42.75
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[19344, -1872, 0; -1872, 182, 0; 0, 0, -1],[624, 26, 1],[-9, -1, -1, 1, 1, 0, -1, -2, -7, -5; -88, -10, -12, 10, 12, 1, -8, -18, -66, -48; -104, -10, 0, 0, -24, -13, -32, -39, -104, -66],41,75]
%
% END OF LATTICE L42.75
%
%
% LATTICE L42.76
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[248664, 36504, -2496; 36504, 5252, -364; -2496, -364, 25],[312, 52, 1],[-14, -2, -7, -1, 1, 1, 0, -5, -15, -13; -57, -8, -27, -4, 3, 3, -1, -24, -64, -54; -2236, -317, -1092, -156, 144, 143, -16, -858, -2444, -2094],41,76]
%
% END OF LATTICE L42.76
%
%
% LATTICE L42.77
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-7689552, 24336, 24336; 24336, -26, -78; 24336, -78, -77],[624, 26, 1],[-1, -1, 1, 13, 59, 19, 27, 37, 12, 4; -4, -6, 0, 73, 336, 109, 156, 216, 71, 24; -312, -310, 312, 4030, 18288, 5889, 8368, 11466, 3718, 1239],41,77]
%
% END OF LATTICE L42.77
%
%
% LATTICE L42.78
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[624, 0, 624; 0, -26, -156; 624, -156, -311],[624, 26, 1],[-1, -1, 1, 26, 119, 77, 55, 38, 25, 17; -4, -6, 0, 151, 696, 452, 324, 225, 149, 102; 0, 1, 0, -26, -120, -78, -56, -39, -26, -18],41,78]
%
% END OF LATTICE L42.78
%
%
% LATTICE L42.79
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[386256, 42432, -3120; 42432, 4550, -338; -3120, -338, 25],[624, 26, 1],[-29, -2, -13, -1, 1, 1, -1, -7, -17, -7; -408, -28, -180, -14, 12, 12, -16, -102, -242, -99; -9152, -629, -4056, -312, 288, 286, -344, -2262, -5408, -2217],41,79]
%
% END OF LATTICE L42.79
%
%
% LATTICE L42.80
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-702312, -351312, -173160; -351312, -175708, -86580; -173160, -86580, -42637],[312, 52, 1],[-1260, -331, -461, 1, 65, 63, -68, -368, -1597, -631; 3775, 992, 1383, -2, -195, -190, 203, 1101, 4782, 1890; -2548, -670, -936, 0, 132, 130, -136, -741, -3224, -1275],41,80]
%
% END OF LATTICE L42.80
%
%
% LATTICE L42.81
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1092, -18252, 4680; -18252, 304824, -78156; 4680, -78156, 20039],[156, 156, 1],[-86, -20, -6, 0, -2, -16, -14, -28, -34, -32; -5, 5, 13, 10, 5, -1, -7, -15, -12, -7; 0, 24, 52, 39, 20, 0, -24, -52, -39, -20],41,81]
%
% END OF LATTICE L42.81
%
%
% LATTICE L42.82
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-132600, -30576, -14040; -30576, -6162, -2808; -14040, -2808, -1279],[312, 78, 1],[26, 19, 9, 9, 2, -1, -1, -1, 8, 13; -2189, -1608, -767, -773, -173, 76, 87, 100, -661, -1088; 4524, 3324, 1586, 1599, 358, -156, -180, -208, 1365, 2248],41,82]
%
% END OF LATTICE L42.82
%
%
% LATTICE L42.83
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[7800, 15288, -312; 15288, 27066, -546; -312, -546, 11],[312, 78, 1],[7, 1, 1, -1, -1, -2, -1, 0, 3, 1; -48, -7, -8, 2, 4, 9, 4, -1, -22, -7; -2184, -318, -364, 78, 172, 390, 168, -52, -1014, -320],41,83]
%
% END OF LATTICE L42.83
%
%
% LATTICE L42.84
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[4992, -47580, 12168; -47580, 405912, -103740; 12168, -103740, 26513],[156, 156, 1],[94, 16, -6, -18, -2, 20, 22, 44, 94, 40; 1885, 327, -107, -341, -35, 401, 435, 869, 1865, 797; 7332, 1272, -416, -1326, -136, 1560, 1692, 3380, 7254, 3100],41,84]
%
% END OF LATTICE L42.84
%
%
% LATTICE L42.85
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-565968, -141960, 2496; -141960, -35048, 624; 2496, 624, -11],[312, 104, 1],[27, 10, 29, 5, 7, 0, -1, -2, 4, 20; 29, 11, 33, 6, 9, 1, -1, -3, 4, 21; 7748, 2884, 8424, 1469, 2088, 52, -284, -624, 1131, 5712],41,85]
%
% END OF LATTICE L42.85
%
%
% LATTICE L42.86
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1989624, 0, -986232; 0, 104, 0; -986232, 0, -488863],[312, 104, 1],[-3093, -1146, -3325, -1147, -803, 0, 115, 232, -915, -2290; -10, -3, -6, -1, 0, 1, 0, -3, -5, -9; 6240, 2312, 6708, 2314, 1620, 0, -232, -468, 1846, 4620],41,86]
%
% END OF LATTICE L42.86
%
%
% LATTICE L42.87
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-213096, 0, 2808; 0, 104, 0; 2808, 0, -37],[312, 104, 1],[27, 10, 29, 10, 7, 0, -1, -2, 8, 20; -10, -3, -6, -1, 0, 1, 0, -3, -5, -9; 2028, 752, 2184, 754, 528, 0, -76, -156, 598, 1500],41,87]
%
% END OF LATTICE L42.87
%
%
% LATTICE L42.88
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[112944, 53040, -2496; 53040, 24882, -1170; -2496, -1170, 55],[624, 78, 1],[7, 1, 1, -1, -1, -1, -1, 0, 3, 1; -88, -12, -12, 2, 4, 4, 0, -3, -50, -14; -1560, -210, -208, 0, 40, 39, -48, -65, -936, -254],41,88]
%
% END OF LATTICE L42.88
%
%
% LATTICE L42.89
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[219336, -1077960, 21216; -1077960, 5159388, -101556; 21216, -101556, 1999],[312, 156, 1],[-12, -2, -3, -1, 1, 3, 2, 1, -7, -3; 673, 109, 157, 52, -49, -146, -91, -30, 456, 176; 34320, 5559, 8008, 2652, -2500, -7449, -4644, -1534, 23244, 8974],41,89]
%
% END OF LATTICE L42.89
%
%
% LATTICE L42.90
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-265200, -127920, 2496; -127920, -59358, 1170; 2496, 1170, -23],[624, 78, 1],[-1, -1, -1, 8, 13, 13, 19, 9, 9, 1; -4, -6, -8, 43, 72, 73, 108, 52, 53, 6; -312, -414, -520, 3042, 5056, 5109, 7536, 3614, 3666, 413],41,90]
%
% END OF LATTICE L42.90
%
%
% LATTICE L42.91
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-4450992, -541632, 21216; -541632, -65442, 2574; 21216, 2574, -101],[624, 78, 1],[-1, -1, -1, 21, 33, 65, 47, 11, 22, 5; -4, -6, -8, 121, 192, 380, 276, 65, 131, 30; -312, -363, -416, 7488, 11816, 23322, 16896, 3965, 7956, 1814],41,91]
%
% END OF LATTICE L42.91
%
%
% LATTICE L42.92
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1691664, -127296, 6240; -127296, -9438, 468; 6240, 468, -23],[624, 78, 1],[-27, -2, -5, -1, 1, 3, 1, -1, -13, -2; -128, -9, -20, -2, 4, 10, 0, -8, -70, -10; -9984, -729, -1768, -312, 352, 1014, 264, -442, -4992, -751],41,92]
%
% END OF LATTICE L42.92
%
%
% LATTICE L42.93
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[312, 0, 0; 0, -3900, -1716; 0, -1716, -755],[312, 156, 1],[-5, -1, 0, 1, 0, -1, -1, -1, -9, -1; 139, 40, 23, 0, -7, -34, -5, 6, 140, 21; -312, -90, -52, 0, 16, 78, 12, -13, -312, -47],41,93]
%
% END OF LATTICE L42.93
%
%
% LATTICE L42.94
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[19344, -11232, 1872; -11232, 3848, -624; 1872, -624, 101],[624, 104, 1],[-9, -1, -1, 1, 1, 0, -1, -4, -7, -5; -448, -50, -54, 45, 42, -2, -52, -201, -349, -249; -2600, -290, -312, 260, 240, -13, -304, -1170, -2028, -1446],41,94]
%
% END OF LATTICE L42.94
%
%
% LATTICE L42.95
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[624, -624, 0; -624, 728, 0; 0, 0, -1],[624, 104, 1],[-9, -1, -1, 1, 1, 0, -1, -2, -7, -5; -10, -1, 0, 1, 0, -1, -2, -3, -9, -6; -104, -10, 0, 0, -24, -26, -32, -39, -104, -66],41,95]
%
% END OF LATTICE L42.95
%
%
% LATTICE L42.96
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[711984, -711984, 4992; -711984, 712088, -4992; 4992, -4992, 35],[624, 104, 1],[-51, -6, -11, 1, -1, -3, -7, -23, -39, -14; -10, -1, 0, 1, 0, -1, -2, -6, -9, -3; 5824, 710, 1560, 0, 144, 286, 712, 2418, 4264, 1563],41,96]
%
% END OF LATTICE L42.96
%
%
% LATTICE L42.97
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[15600, -49296, 624; -49296, 156104, -1976; 624, -1976, 25],[624, 104, 1],[-29, -2, -13, -1, 1, 1, -1, -7, -17, -14; -30, -2, -12, -1, 0, 0, -2, -9, -19, -15; -1664, -109, -624, -52, -24, -26, -136, -546, -1092, -846],41,97]
%
% END OF LATTICE L42.97
%
%
% LATTICE L42.98
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[49296, 287976, -1872; 287976, 1679496, -10920; -1872, -10920, 71],[312, 312, 1],[3, 2, 3, 2, 1, 0, -1, -2, -1, 0; 29, 11, 11, 6, 3, 1, -1, -1, 4, 7; 4524, 1740, 1768, 975, 488, 156, -180, -208, 585, 1072],41,98]
%
% END OF LATTICE L42.98
%
%
% LATTICE L42.99
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[312, 0, 0; 0, -3432, -1560; 0, -1560, -709],[312, 312, 1],[-10, -3, -2, -1, 0, 1, 0, -1, -5, -3; 3, -10, -23, -35, -9, 0, 11, 24, 37, 10; 0, 24, 52, 78, 20, 0, -24, -52, -78, -20],41,99]
%
% END OF LATTICE L42.99
%
%
% LATTICE L42.100
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-222456, 0, 1248; 0, 312, 0; 1248, 0, -7],[312, 312, 1],[3, 2, 3, 4, 1, 0, -1, -2, -2, 0; -10, -3, -2, -1, 0, 1, 0, -1, -5, -3; 468, 336, 520, 702, 176, 0, -180, -364, -390, -20],41,100]
%
% END OF LATTICE L42.100
%
%
% LATTICE L42.101
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[112944, 382512, -2496; 382512, 1290120, -8424; -2496, -8424, 55],[624, 312, 1],[-37, -5, -5, 0, 1, 1, -1, -3, -22, -6; -44, -6, -6, 1, 2, 2, 0, -3, -25, -7; -8424, -1146, -1144, 156, 352, 351, -48, -598, -4836, -1346],41,101]
%
% END OF LATTICE L42.101
%
%
% LATTICE L42.102
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-38064, 0, -18096; 0, 312, 0; -18096, 0, -8603],[624, 312, 1],[-37, 23, 31, 446, 121, 743, 100, 99, 0, -19; -1, -2, -1, -9, -2, -10, -1, 0, 1, 0; 78, -48, -65, -936, -254, -1560, -210, -208, 0, 40],41,102]
%
% END OF LATTICE L42.102
%
%
% LATTICE L42.103
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2861040, 0, 8112; 0, 312, 0; 8112, 0, -23],[624, 312, 1],[2, -1, -3, -22, -3, -37, -5, -5, 0, 1; -1, -2, -2, -9, -1, -10, -1, 0, 1, 0; 702, -360, -1066, -7800, -1063, -13104, -1770, -1768, 0, 352],41,103]
%
% END OF LATTICE L42.103
%
%
% LATTICE L42.104
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-38064, -184080, -91104; -184080, -889512, -440232; -91104, -440232, -217877],[624, 312, 1],[-27, -2, -5, -1, 1, 3, 1, -1, -13, -4; 1550, 91, 104, -77, -20, 38, 178, 219, 1161, 281; -3120, -183, -208, 156, 40, -78, -360, -442, -2340, -566],41,104]
%
% END OF LATTICE L42.104
%

\medskip%
%------------------------------WEYL-GROUP-W43--------------------------------
%
\leavevmode\llap{}%
$W_{43\phantom{0}}$%
\qquad\llap{24} lattices, $\chi=24$%
\hfill%
$22222222\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L43.1
%
\leavevmode%
${L_{43.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{1}{}9\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{-2}{}13\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{23\rightarrow N_{43},3,2}%
\EasyButWeakLineBreak%
{${12}\above{1pt}{1pt}{r}{2}{26}\above{1pt}{1pt}{b}{2}{36}\above{1pt}{1pt}{b}{2}{2}\above{1pt}{1pt}{l}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-805428\\2808\\4212
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2808\\-6\\-15
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4212\\-15\\-22
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1561\\-21840\\-285480
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7\\97\\1281
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
8\\112\\1463
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-9\\-128\\-1644
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-14\\-195\\-2561
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-5\\-66\\-918
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\1\\-1
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-805428, 2808, 4212; 2808, -6, -15; 4212, -15, -22],[468, 3, 1],[-9, -14, -5, 0, 1, 1, -1, -1; -128, -195, -66, 1, 16, 13, -18, -15; -1644, -2561, -918, -1, 180, 182, -180, -182],42,1]
%
% END OF LATTICE L43.1
%
%
% LATTICE L43.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-195, -78, -39; -78, -30, -13; -39, -13, -2],[39, 1, 1],[-1, 8, 1, -4, -31, -112, -9, -4; 3, -26, -3, 14, 105, 377, 30, 13; 0, 13, -1, -19, -108, -364, -26, -8],42,2]
%
% END OF LATTICE L43.2
%
%
% LATTICE L43.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-61620, -20280, 624; -20280, -6674, 205; 624, 205, -6],[156, 1, 1],[-19, -4, 7, 6, 11, -9, -9, -7; 60, 13, -22, -19, -36, 26, 28, 22; 72, 26, -24, -26, -96, -65, 18, 23],42,3]
%
% END OF LATTICE L43.3
%
%
% LATTICE L43.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[202995, -16848, 1053; -16848, 1398, -87; 1053, -87, 5],[117, 3, 1],[3, -1, -4, -1, 5, 27, 10, 3; 38, -13, -51, -13, 62, 338, 126, 38; 30, -13, -45, -17, 18, 169, 81, 29],42,4]
%
% END OF LATTICE L43.4
%
%
% LATTICE L43.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[12246, 234, 3939; 234, -15, 75; 3939, 75, 1267],[39, 3, 1],[-18, 25, 27, 29, -14, -337, -51, -53; -1, 0, 1, 0, -3, -39, -4, -3; 56, -78, -84, -90, 44, 1053, 159, 165],42,5]
%
% END OF LATTICE L43.5
%
%
% LATTICE L43.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[234, -117, 0; -117, 57, -3; 0, -3, -5],[117, 3, 1],[2, -1, -1, -5, -2, 1, 1, 5; 4, 0, -2, -12, -8, -39, 1, 9; -3, 0, 1, 0, -9, -117, -4, -9],42,6]
%
% END OF LATTICE L43.6
%
%
% LATTICE L43.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1092, 312, -156; 312, 18, -15; -156, -15, 10],[156, 3, 1],[1, 1, -1, -1, -1, -1, 1, 1; 16, 13, -18, -19, -24, -52, 12, 16; 40, 39, -42, -45, -56, -117, 30, 39],42,7]
%
% END OF LATTICE L43.7
%
%
% LATTICE L43.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[12090, 897, 3666; 897, 65, 273; 3666, 273, 1111],[39, 13, 1],[-14, 1, 9, 13, 10, -2, -10, -14; 30, -1, -15, -17, 18, 13, 27, 29; 39, -3, -26, -39, -39, 3, 26, 39],42,8]
%
% END OF LATTICE L43.8
%
%
% LATTICE L43.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[4509336, -47580, -1141140; -47580, 504, 12040; -1141140, 12040, 288779],[156, 4, 1],[-67, -227, -19, -155, -475, -3296, -252, -116; -90, -312, -26, -204, -624, -4329, -331, -153; -261, -884, -74, -604, -1851, -12844, -982, -452],42,9]
%
% END OF LATTICE L43.9
%
%
% LATTICE L43.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2290860, 2340, -10296; 2340, -6, -9; -10296, -9, 46],[468, 3, 1],[5, 38, 3, 4, 3, 1, -1, -1; 196, 1521, 122, 165, 124, 39, -42, -45; 1152, 8775, 694, 927, 696, 234, -232, -234],42,10]
%
% END OF LATTICE L43.10
%
%
% LATTICE L43.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[7566, -24921, -7995; -24921, 79131, 25389; -7995, 25389, 8146],[39, 39, 1],[1, 1, 0, -7, -13, -10, -9, -2; -129, -120, -25, 636, 1193, 918, 823, 162; 403, 375, 78, -1989, -3731, -2871, -2574, -507],42,11]
%
% END OF LATTICE L43.11
%
%
% LATTICE L43.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[824616, -29172, -212004; -29172, 1032, 7500; -212004, 7500, 54505],[156, 12, 1],[-9, -201, -17, -9, -1, 6, 2, -6; 0, -13, -1, 7, 8, 169, 13, 5; -35, -780, -66, -36, -5, 0, 6, -24],42,12]
%
% END OF LATTICE L43.12
%
%
% LATTICE L43.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[156, 0, 0; 0, -26, 13; 0, 13, -6],[156, 13, 1],[1, 0, -1, -2, -17, -2, -3, 0; 0, 1, 2, -7, -96, -13, -26, -5; 0, 2, 0, -26, -312, -41, -78, -13],42,13]
%
% END OF LATTICE L43.13
%
%
% LATTICE L43.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-6786, 6786, -117; 6786, -6747, 117; -117, 117, -2],[117, 39, 1],[1, 1, 0, -7, -13, -10, -3, -2; 1, 0, -1, -12, -17, -12, -3, 0; 0, -63, -65, -351, -312, -171, -13, 117],42,14]
%
% END OF LATTICE L43.14
%
%
% LATTICE L43.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[117, 0, 0; 0, -1950, 117; 0, 117, -7],[117, 39, 1],[-1, 0, 1, 0, -3, -1, -4, -1; 5, 1, 0, -3, -13, -3, -6, 1; 78, 16, 0, -52, -234, -55, -117, 13],42,15]
%
% END OF LATTICE L43.15
%
%
% LATTICE L43.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[113841000, -248508, 28211508; -248508, 552, -61584; 28211508, -61584, 6991235],[468, 12, 1],[2130, 14201, 3011, 341, 142, 567, 397, 795; 13, 91, 21, 3, 1, 0, 0, 4; -8595, -57304, -12150, -1376, -573, -2288, -1602, -3208],42,16]
%
% END OF LATTICE L43.16
%
%
% LATTICE L43.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[723987576, -3414996, 179422776; -3414996, 16104, -846324; 179422776, -846324, 44465587],[468, 12, 1],[-3156, -64253, -1535, -1249, 200, 6611, 57, -3185; 13, 273, 7, 9, 1, 0, 0, 12; 12735, 259272, 6194, 5040, -807, -26676, -230, 12852],42,17]
%
% END OF LATTICE L43.17
%
%
% LATTICE L43.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[468, 1248, -468; 1248, 702, -273; -468, -273, 106],[156, 39, 1],[-3, -1, -1, 1, 3, 1, 1, -1; -136, -47, -58, 29, 96, 32, 28, -44; -364, -126, -156, 78, 260, 87, 78, -117],42,18]
%
% END OF LATTICE L43.18
%
%
% LATTICE L43.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[27768, 2964, 4836; 2964, 312, 520; 4836, 520, 839],[156, 52, 1],[-10, -1, 7, 15, 14, 3, -5, -13; 30, 3, -23, -57, -72, -24, 2, 36; 39, 4, -26, -52, -39, -4, 26, 52],42,19]
%
% END OF LATTICE L43.19
%
%
% LATTICE L43.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-107172, 26676, -468; 26676, -6630, 117; -468, 117, -2],[468, 39, 1],[-9, -4, -3, -2, 1, 1, 1, -1; -44, -18, -12, -6, 4, 3, 2, -9; -624, -171, -26, 117, 0, -63, -130, -351],42,20]
%
% END OF LATTICE L43.20
%
%
% LATTICE L43.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[3872700, 58032, -18252; 58032, 858, -273; -18252, -273, 86],[468, 39, 1],[-3, 0, 5, 2, 11, 1, 1, -1; -44, -2, 36, 18, 100, 9, 6, -11; -780, -7, 1170, 481, 2652, 241, 234, -247],42,21]
%
% END OF LATTICE L43.21
%
%
% LATTICE L43.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[169416, -438204, 112476; -438204, 1133496, -290940; 112476, -290940, 74677],[156, 156, 1],[1, 4, 8, 8, 1, -1, -5, -5; -63, -97, -97, -77, -43, -62, -62, -82; -247, -384, -390, -312, -169, -240, -234, -312],42,22]
%
% END OF LATTICE L43.22
%
%
% LATTICE L43.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[142241112, 2004444, -33761052; 2004444, 27768, -476112; -33761052, -476112, 8012951],[468, 156, 1],[3953, 2844, 11888, 2616, -87, -911, -6089, -683; -11852, -8527, -35643, -7843, 262, 2732, 18258, 2048; 15951, 11476, 47970, 10556, -351, -3676, -24570, -2756],42,23]
%
% END OF LATTICE L43.23
%
%
% LATTICE L43.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[3286296, -55692, -856440; -55692, 1560, 14976; -856440, 14976, 223543],[468, 156, 1],[5211, 7184, 1708, -116, -29, 589, 883, 7889; -15770, -21741, -5169, 351, 88, -1782, -2672, -23874; 21021, 28980, 6890, -468, -117, 2376, 3562, 31824],42,24]
%
% END OF LATTICE L43.24
%

\medskip%
%------------------------------WEYL-GROUP-W44--------------------------------
%
\leavevmode\llap{}%
$W_{44\phantom{0}}$%
\qquad\llap{32} lattices, $\chi=16$%
\hfill%
$\infty2622$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L44.1
%
\leavevmode%
${L_{44.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}8\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{1}{}3\above{1pt}{1pt}{-}{}9\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}7\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{23\rightarrow N_{44},3,2}%
\EasyButWeakLineBreak%
{${42}\above{1pt}{1pt}{12,1}{\infty a}{168}\above{1pt}{1pt}{b}{2}{18}\above{1pt}{1pt}{}{6}{6}\above{1pt}{1pt}{l}{2}{72}\above{1pt}{1pt}{r}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1218168\\-337176\\-519624
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-337176\\-91686\\-159513
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-519624\\-159513\\-71678
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
42396\\-131908\\-13797
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-28393\\88340\\9240
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-12611\\39237\\4104
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
13671\\-42535\\-4449
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
131419\\-408888\\-42768
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-1218168, -337176, -519624; -337176, -91686, -159513; -519624, -159513, -71678],[504, 3, 1],[42396, -28393, -12611, 13671, 131419; -131908, 88340, 39237, -42535, -408888; -13797, 9240, 4104, -4449, -42768],43,1]
%
% END OF LATTICE L44.1
%
%
% LATTICE L44.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[42, 0, 0; 0, 0, -1; 0, -1, 0],[42, 1, 1],[-1, 1, 0, -1, -1; 0, 0, -1, -3, -2; -21, 0, 1, -6, -10],43,2]
%
% END OF LATTICE L44.2
%
%
% LATTICE L44.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-446287800, -7827456, 229488; -7827456, -137286, 4025; 229488, 4025, -118],[168, 1, 1],[16, 115, 7, -5, -3; -903, -6468, -393, 282, 168; 315, 3024, 208, -105, -104],43,3]
%
% END OF LATTICE L44.3
%
%
% LATTICE L44.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-8661366, -575946, -188622; -575946, -38298, -12543; -188622, -12543, -4106],[126, 3, 1],[-172, 53, 52, -52, -259; 2401, -742, -726, 727, 3618; 567, -168, -171, 168, 846],43,4]
%
% END OF LATTICE L44.4
%
%
% LATTICE L44.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-26001780, -1618302, -12960738; -1618302, -100720, -806652; -12960738, -806652, -6460355],[42, 2, 1],[-509, -1667, -508, 163, 61; -231, -630, -183, 72, 21; 1050, 3423, 1042, -336, -125],43,5]
%
% END OF LATTICE L44.5
%
%
% LATTICE L44.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-37334514, -2374974, 12484122; -2374974, -151080, 794157; 12484122, 794157, -4174510],[42, 3, 1],[143, 963, 443, -46, -107; -77, -420, -183, 24, 42; 413, 2800, 1290, -133, -312],43,6]
%
% END OF LATTICE L44.6
%
%
% LATTICE L44.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2130240, 147042, 902580; 147042, 10392, 62286; 902580, 62286, 382423],[42, 6, 1],[2853, 7537, 7385, -6, 140; -427, -1127, -1104, 1, -21; -6664, -17605, -17250, 14, -327],43,7]
%
% END OF LATTICE L44.7
%
%
% LATTICE L44.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-28714602, -157878, -3647574; -157878, -868, -20055; -3647574, -20055, -463346],[42, 7, 1],[17, 91, 92, -37, -21; 27, 222, 248, -63, -62; -135, -726, -735, 294, 168],43,8]
%
% END OF LATTICE L44.8
%
%
% LATTICE L44.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-476406, 3906, 7686; 3906, -30, -63; 7686, -63, -124],[126, 3, 1],[3, 25, 4, -1, -1; -7, -14, -1, 2, 0; 189, 1554, 248, -63, -62],43,9]
%
% END OF LATTICE L44.9
%
%
% LATTICE L44.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[216216, 44688, -9576; 44688, -6762, 933; -9576, 933, -106],[168, 3, 1],[-121, 81, 36, -39, -375; -3304, 2212, 983, -1065, -10240; -18151, 12152, 5400, -5851, -56256],43,10]
%
% END OF LATTICE L44.10
%
%
% LATTICE L44.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[5578104, 431298, 2682876; 431298, 35728, 207438; 2682876, 207438, 1290371],[42, 14, 1],[-6967, -18406, -42082, 101, -798; 9, 24, 55, 0, 1; 14484, 38265, 87486, -210, 1659],43,11]
%
% END OF LATTICE L44.11
%
%
% LATTICE L44.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[43725780, -5530266, 21647808; -5530266, 699528, -2737932; 21647808, -2737932, 10717421],[126, 6, 1],[20577, 3071, -62, 5247, 13627; -889, -133, 3, -226, -588; -41790, -6237, 126, -10656, -27675],43,12]
%
% END OF LATTICE L44.12
%
%
% LATTICE L44.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[18976860, 7686, 9332820; 7686, 12, 3780; 9332820, 3780, 4589881],[126, 6, 1],[1859, 4947, 1619, 0, 30; 7, 28, 10, 1, 0; -3780, -10059, -3292, 0, -61],43,13]
%
% END OF LATTICE L44.13
%
%
% LATTICE L44.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2818242, -367332, 1245762; -367332, 53592, -166383; 1245762, -166383, 553484],[42, 21, 1],[-1864, -9849, -33777, 27, -1281; 3731, 19714, 67609, -54, 2564; 5317, 28094, 96348, -77, 3654],43,14]
%
% END OF LATTICE L44.14
%
%
% LATTICE L44.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-45816456, 5079144, -768264; 5079144, -563066, 85169; -768264, 85169, -12882],[168, 7, 1],[-37, -349, -167, 86, 83; -297, -2796, -1337, 690, 664; 243, 2328, 1120, -567, -560],43,15]
%
% END OF LATTICE L44.15
%
%
% LATTICE L44.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-109990608, 18359544, -332808; 18359544, -3064560, 55552; -332808, 55552, -1007],[168, 8, 1],[16, 139, 49, -5, -3; 105, 966, 342, -33, -21; 504, 7350, 2672, -168, -167],43,16]
%
% END OF LATTICE L44.16
%
%
% LATTICE L44.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-22837752, 27720, 51912; 27720, -30, -63; 51912, -63, -118],[504, 3, 1],[3, 29, 2, -1, -1; -7, -28, -1, 2, 0; 1323, 12768, 880, -441, -440],43,17]
%
% END OF LATTICE L44.17
%
%
% LATTICE L44.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-7928894484, 19221780018, 9341858778; 19221780018, -46598782188, -22647186786; 9341858778, -22647186786, -11006619599],[42, 42, 1],[9, 37, 248, -21, -31; 1973, 5042, 30149, -4268, -3391; -4052, -10343, -61824, 8764, 6951],43,18]
%
% END OF LATTICE L44.18
%
%
% LATTICE L44.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-65127258, 65248092, -1867572; 65248092, -65369136, 1871037; -1867572, 1871037, -53554],[126, 21, 1],[23, 195, 219, -54, -55; -1, -2, -1, 2, 0; -837, -6870, -7672, 1953, 1918],43,19]
%
% END OF LATTICE L44.19
%
%
% LATTICE L44.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-80394426, 26747658, 1773198; 26747658, -8899086, -589953; 1773198, -589953, -39110],[126, 21, 1],[70, -53, -52, 370, 1213; 139, -106, -102, 739, 2418; 1077, -804, -819, 5628, 18522],43,20]
%
% END OF LATTICE L44.20
%
%
% LATTICE L44.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-6552, -22008, 840; -22008, -47334, 1995; 840, 1995, -82],[168, 21, 1],[-13, 3, 36, -9, -195; -17, 4, 47, -12, -256; -547, 128, 1512, -385, -8232],43,21]
%
% END OF LATTICE L44.21
%
%
% LATTICE L44.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-370660080, -27901944, -183022224; -27901944, -2100336, -13777248; -183022224, -13777248, -90371573],[168, 24, 1],[12969, -2855, -3105, 5716, 5841; -7, 0, 2, -1, -2; -26264, 5782, 6288, -11576, -11829],43,22]
%
% END OF LATTICE L44.22
%
%
% LATTICE L44.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[3096389772, -259686, 1524941586; -259686, 84, -127890; 1524941586, -127890, 751018771],[126, 42, 1],[8989, 23916, 54787, 0, 1017; 823, 2191, 5020, 1, 93; -18252, -48561, -111244, 0, -2065],43,23]
%
% END OF LATTICE L44.23
%
%
% LATTICE L44.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[673239420, -33981066, 330466752; -33981066, 1715448, -16679964; 330466752, -16679964, 162213131],[126, 42, 1],[-22979, -385, 62, -65795, -134347; -775, -13, 3, -2218, -4530; 46734, 783, -126, 133812, 273231],43,24]
%
% END OF LATTICE L44.24
%
%
% LATTICE L44.25
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1680, 83496, -24360; 83496, -3948112, 1151864; -24360, 1151864, -336057],[168, 56, 1],[-1, -1, -1, 2, 0; 63, 912, 2320, -147, -145; 216, 3126, 7952, -504, -497],43,25]
%
% END OF LATTICE L44.25
%
%
% LATTICE L44.26
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-5277384, 35280, -1498392; 35280, -210, 10017; -1498392, 10017, -425434],[504, 21, 1],[-69, -661, -318, 161, 159; -1, -4, -1, 2, 0; 243, 2328, 1120, -567, -560],43,26]
%
% END OF LATTICE L44.26
%
%
% LATTICE L44.27
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-59976, -252000, -29232; -252000, -531930, -53361; -29232, -53361, -5090],[504, 21, 1],[488, -107, -1358, 320, 7243; -967, 212, 2691, -634, -14352; 7335, -1608, -20412, 4809, 108864],43,27]
%
% END OF LATTICE L44.27
%
%
% LATTICE L44.28
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-6103888560, -984629016, -126012096; -984629016, -158832240, -20327232; -126012096, -20327232, -2601463],[504, 24, 1],[-3848, 839, 923, -1685, -1727; 26929, -5873, -6459, 11794, 12087; -24024, 5250, 5760, -10536, -10791],43,28]
%
% END OF LATTICE L44.28
%
%
% LATTICE L44.29
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-254779056, 253512, 506520; 253512, -240, -504; 506520, -504, -1007],[504, 24, 1],[3, 44, 16, -1, -1; -7, -7, -1, 2, 0; 1512, 22134, 8048, -504, -503],43,29]
%
% END OF LATTICE L44.29
%
%
% LATTICE L44.30
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-453757584, -590510088, -219855888; -590510088, -768476688, -286115592; -219855888, -286115592, -106525187],[168, 168, 1],[2703, -1127, -1305, 15820, 12528; -1, 0, 2, -1, -2; -5576, 2326, 2688, -32648, -25851],43,30]
%
% END OF LATTICE L44.30
%
%
% LATTICE L44.31
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2305430064, -236102328, 48489840; -236102328, -24179568, 4965912; 48489840, 4965912, -1019881],[504, 168, 1],[-1, 0, 2, -1, -2; -493, 191, 291, -2716, -2193; -2448, 930, 1512, -13272, -10773],43,31]
%
% END OF LATTICE L44.31
%
%
% LATTICE L44.32
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-35533008, 35282520, -15299928; 35282520, -35033712, 15192072; -15299928, 15192072, -6587897],[504, 168, 1],[-94, -1347, -3425, 219, 214; -1, -1, -1, 2, 0; 216, 3126, 7952, -504, -497],43,32]
%
% END OF LATTICE L44.32
%

\medskip%
%------------------------------WEYL-GROUP-W45--------------------------------
%
\leavevmode\llap{}%
$W_{45\phantom{0}}$%
\qquad\llap{24} lattices, $\chi=12$%
\hfill%
$222222\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L45.1
%
\leavevmode%
${L_{45.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}8\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{1}{}9\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{2}{}7\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{23\rightarrow N_{45},3,2}%
\EasyButWeakLineBreak%
{${72}\above{1pt}{1pt}{r}{2}{14}\above{1pt}{1pt}{b}{2}{18}\above{1pt}{1pt}{l}{2}{8}\above{1pt}{1pt}{r}{2}{126}\above{1pt}{1pt}{b}{2}{2}\above{1pt}{1pt}{l}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-20664\\3024\\0
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3024\\-438\\-3
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\-3\\2
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7\\48\\72
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\7\\14
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-4\\-27\\-36
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-13\\-88\\-128
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-31\\-210\\-315
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\-1
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-20664, 3024, 0; 3024, -438, -3; 0, -3, 2],[504, 3, 1],[7, 1, -4, -13, -31, 0; 48, 7, -27, -88, -210, 0; 72, 14, -36, -128, -315, -1],44,1]
%
% END OF LATTICE L45.1
%
%
% LATTICE L45.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[714, 336, -42; 336, 158, -21; -42, -21, -10],[42, 1, 1],[-1, 30, -8, -111, -226, -20; 2, -63, 17, 234, 476, 42; 0, 7, -3, -32, -63, -5],44,2]
%
% END OF LATTICE L45.2
%
%
% LATTICE L45.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[840, 336, -168; 336, 134, -71; -168, -71, -2],[168, 1, 1],[-27, -3, 8, 27, 3, -8; 64, 7, -19, -64, -7, 19; -8, 0, 2, 0, -7, -3],44,3]
%
% END OF LATTICE L45.3
%
%
% LATTICE L45.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[516474, -25452, 1386; -25452, 1254, -69; 1386, -69, 2],[126, 3, 1],[-13, -6, 8, 15, 74, 0; -258, -119, 159, 298, 1470, 0; 108, 56, -54, -112, -567, -1],44,4]
%
% END OF LATTICE L45.4
%
%
% LATTICE L45.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1344, -126, -630; -126, 16, -62; -630, -62, -295],[42, 2, 1],[12, -20, -22, -10, 27, 23; -2, 7, 5, 2, -7, -5; -25, 42, 46, 21, -56, -48],44,5]
%
% END OF LATTICE L45.5
%
%
% LATTICE L45.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-546, -168, 210; -168, 24, 57; 210, 57, -80],[42, 3, 1],[-19, 15, 17, 15, -22, -18; -4, 7, 5, 4, -7, -5; -54, 42, 48, 42, -63, -51],44,6]
%
% END OF LATTICE L45.6
%
%
% LATTICE L45.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[24780, -1218, 10374; -1218, 60, -510; 10374, -510, 4343],[42, 6, 1],[19, 71, 5, 1, -1, 5; 3, 14, 0, -5, -21, -1; -45, -168, -12, -3, 0, -12],44,7]
%
% END OF LATTICE L45.7
%
%
% LATTICE L45.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[7014, 42, 1092; 42, -14, 7; 1092, 7, 170],[42, 7, 1],[11, -2, -12, -11, 2, 12; -4, 0, 2, 0, -1, -3; -70, 13, 77, 70, -13, -77],44,8]
%
% END OF LATTICE L45.8
%
%
% LATTICE L45.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2856, -1176, 504; -1176, -438, 159; 504, 159, -38],[168, 3, 1],[-37, -5, 10, 29, -2, -11; 152, 21, -41, -120, 7, 45; 144, 21, -39, -120, 0, 42],44,9]
%
% END OF LATTICE L45.9
%
%
% LATTICE L45.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[516012, -4242, 248640; -4242, 28, -2044; 248640, -2044, 119807],[42, 14, 1],[-172, -106, 0, 226, 133, 27; 2, 1, 1, 2, 1, 1; 357, 220, 0, -469, -276, -56],44,10]
%
% END OF LATTICE L45.10
%
%
% LATTICE L45.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[4777416, 449694, 2358342; 449694, 42288, 221988; 2358342, 221988, 1164181],[126, 6, 1],[-527, -3727, -4969, -1769, -9238, 684; -18, -126, -168, -60, -315, 23; 1071, 7574, 10098, 3595, 18774, -1390],44,11]
%
% END OF LATTICE L45.11
%
%
% LATTICE L45.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[449778, 4830, 153846; 4830, 42, 1659; 153846, 1659, 52618],[42, 21, 1],[-279, -86, 0, 367, 108, 22; 562, 173, 1, -730, -215, -43; 798, 246, 0, -1050, -309, -63],44,12]
%
% END OF LATTICE L45.12
%
%
% LATTICE L45.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1848, -168, -168; -168, 14, 7; -168, 7, -38],[168, 7, 1],[-1, -1, 0, 25, 4, 3; -16, -13, 1, 328, 52, 38; 0, 2, 0, -56, -9, -7],44,13]
%
% END OF LATTICE L45.13
%
%
% LATTICE L45.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-97104, -10248, 1512; -10248, -976, 152; 1512, 152, -23],[168, 8, 1],[1, -1, -3, -1, 1, 3; 9, -7, -27, -10, 0, 26; 125, -112, -376, -133, 56, 368],44,14]
%
% END OF LATTICE L45.14
%
%
% LATTICE L45.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2172912, -5276670, -2564394; -5276670, 12813276, 6227088; -2564394, 6227088, 3026285],[42, 42, 1],[-2, 0, 2, 0, -1, -3; 1826, -659, -3959, -1786, 679, 3979; -3759, 1356, 8148, 3675, -1398, -8190],44,15]
%
% END OF LATTICE L45.15
%
%
% LATTICE L45.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-22554, -12600, 882; -12600, -6846, 483; 882, 483, -34],[126, 21, 1],[-1, -2, 0, 19, 2, 4; -6, -9, 1, 90, 9, 15; -112, -180, 14, 1764, 179, 315],44,16]
%
% END OF LATTICE L45.16
%
%
% LATTICE L45.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1084440, 403200, -19152; 403200, -149898, 7119; -19152, 7119, -338],[168, 21, 1],[131, 21, 16, -3, -5, 0; 552, 88, 66, -16, -21, 1; 4200, 663, 483, -168, -159, 21],44,17]
%
% END OF LATTICE L45.17
%
%
% LATTICE L45.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[336, -168, 0; -168, -2928, 2160; 0, 2160, -1549],[168, 24, 1],[-22, -55, 35, 14, -1, -43; -45, -119, 69, 28, 0, -86; -63, -168, 96, 39, 0, -120],44,18]
%
% END OF LATTICE L45.18
%
%
% LATTICE L45.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[12500712, -214830, 6148926; -214830, 3696, -105672; 6148926, -105672, 3024571],[126, 42, 1],[141, 115, 117, 1517, 285, 619; -10, -6, -4, -84, -17, -45; -287, -234, -238, -3087, -580, -1260],44,19]
%
% END OF LATTICE L45.19
%
%
% LATTICE L45.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-26544, -13272, 672; -13272, -6608, 336; 672, 336, -17],[168, 56, 1],[2, 3, 3, 0, -1, -1; 0, -1, -3, -1, 0, 2; 77, 96, 56, -21, -40, 0],44,20]
%
% END OF LATTICE L45.20
%
%
% LATTICE L45.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-471240, 56952, -4032; 56952, -6846, 483; -4032, 483, -34],[504, 21, 1],[-1, -1, 0, 19, 1, 2; -24, -21, 1, 408, 21, 39; -224, -180, 14, 3528, 179, 315],44,21]
%
% END OF LATTICE L45.21
%
%
% LATTICE L45.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-101808, 2520, 504; 2520, 2256, 240; 504, 240, 25],[504, 24, 1],[-1, -11, 1, 1, -1, -5; 49, 546, -48, -48, 49, 243; -451, -5040, 440, 441, -448, -2232],44,22]
%
% END OF LATTICE L45.22
%
%
% LATTICE L45.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-19824, -700056, -12264; -700056, -24617040, -431256; -12264, -431256, -7555],[168, 168, 1],[0, -1, -3, -1, 0, 2; -71, -87, -47, 21, 37, -3; 4053, 4968, 2688, -1197, -2112, 168],44,23]
%
% END OF LATTICE L45.23
%
%
% LATTICE L45.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1008, 5544, -504; 5544, -38640, -2184; -504, -2184, 247],[504, 168, 1],[314, 156, 458, -3, -163, -51; 6, 3, 9, 0, -3, -1; 693, 344, 1008, -7, -360, -112],44,24]
%
% END OF LATTICE L45.24
%

\medskip%
%------------------------------WEYL-GROUP-W46--------------------------------
%
\leavevmode\llap{}%
$W_{46\phantom{0}}$%
\qquad\llap{24} lattices, $\chi=16$%
\hfill%
$222262$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L46.1
%
\leavevmode%
${L_{46.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{-}{}9\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{-2}{}17\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{23\rightarrow N_{46},3,2}%
\EasyButWeakLineBreak%
{${36}\above{1pt}{1pt}{*}{2}{68}\above{1pt}{1pt}{b}{2}{6}\above{1pt}{1pt}{s}{2}{306}\above{1pt}{1pt}{b}{2}{2}\above{1pt}{1pt}{}{6}{6}\above{1pt}{1pt}{b}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-85866660\\-89964\\332928
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-89964\\-66\\333
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
332928\\333\\-1282
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
17\\2892\\5166
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-63\\-10710\\-19142
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-21\\-3571\\-6381
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-215\\-36567\\-65331
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-8\\-1361\\-2431
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7\\1190\\2127
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-85866660, -89964, 332928; -89964, -66, 333; 332928, 333, -1282],[612, 3, 1],[17, -63, -21, -215, -8, 7; 2892, -10710, -3571, -36567, -1361, 1190; 5166, -19142, -6381, -65331, -2431, 2127],45,1]
%
% END OF LATTICE L46.1
%
%
% LATTICE L46.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-714, 255, 0; 255, -91, 0; 0, 0, 1],[51, 1, 1],[0, 6, -1, -53, -17, -25; 0, 17, -3, -153, -49, -72; 1, 0, -3, -17, -3, 0],45,2]
%
% END OF LATTICE L46.2
%
%
% LATTICE L46.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-109956, -12444, 816; -12444, -1282, 95; 816, 95, -6],[204, 1, 1],[1, -63, -14, -32, -1, 7; -2, 136, 30, 68, 2, -15; 104, -6426, -1431, -3281, -105, 714],45,3]
%
% END OF LATTICE L46.3
%
%
% LATTICE L46.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-49266, -9027, 612; -9027, -1335, 126; 612, 126, -7],[153, 3, 1],[7, -40, -23, -215, -7, 8; -15, 85, 49, 459, 15, -17; 342, -1972, -1131, -10557, -343, 393],45,4]
%
% END OF LATTICE L46.4
%
%
% LATTICE L46.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-4128195, 140964, 1372512; 140964, -4806, -46869; 1372512, -46869, -456322],[51, 3, 1],[6895, 138233, 12866, 61198, -736, 94; 6275, 125817, 11711, 55709, -669, 85; 20094, 402849, 37495, 178347, -2145, 274],45,5]
%
% END OF LATTICE L46.5
%
%
% LATTICE L46.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1224459, 91341, -9639; 91341, -6753, 690; -9639, 690, -62],[153, 3, 1],[15, 587, 39, -1, -49, 1; 258, 10098, 671, -17, -843, 17; 539, 21114, 1404, -34, -1764, 33],45,6]
%
% END OF LATTICE L46.6
%
%
% LATTICE L46.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3567756, 27948, 18360; 27948, -198, -147; 18360, -147, -94],[204, 3, 1],[19, 179, 4, -10, -5, 5; 454, 4284, 96, -238, -120, 119; 3000, 28254, 631, -1581, -789, 790],45,7]
%
% END OF LATTICE L46.7
%
%
% LATTICE L46.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[653938728, 280092, -166821000; 280092, 120, -71452; -166821000, -71452, 42556351],[204, 4, 1],[-25, -1084, -404, -1214, -152, -101; 0, -425, -189, -663, -95, -48; -98, -4250, -1584, -4760, -596, -396],45,8]
%
% END OF LATTICE L46.8
%
%
% LATTICE L46.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-30725358, 68493, 10790427; 68493, -119, -24055; 10790427, -24055, -3789486],[51, 17, 1],[40999, 48356, 229549, 21411, -4371, 1666; 3349, 3949, 18744, 1748, -358, 138; 116722, 137667, 653514, 60956, -12444, 4743],45,9]
%
% END OF LATTICE L46.9
%
%
% LATTICE L46.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-10451491812, 104683824, 893520; 104683824, -1048530, -8949; 893520, -8949, -62],[612, 3, 1],[-243, -9511, -316, 8, 397, -8; -24270, -949926, -31561, 799, 39651, -799; 1078, 42228, 1404, -34, -1764, 33],45,10]
%
% END OF LATTICE L46.10
%
%
% LATTICE L46.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1205952120, -11047620, -307553256; -11047620, 101208, 2817468; -307553256, 2817468, 78435125],[204, 12, 1],[-2367, -19430, -714, -312, -254, -2137; 20, 187, 9, 17, 1, 16; -9282, -76194, -2800, -1224, -996, -8380],45,11]
%
% END OF LATTICE L46.11
%
%
% LATTICE L46.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[856341, 1600482, 50235; 1600482, 2991354, 93891; 50235, 93891, 2947],[51, 51, 1],[-102, -124, -199, -57, 7, 1; 1148, 1379, 2201, 625, -95, 0; -34833, -41817, -66725, -18939, 2907, -17],45,12]
%
% END OF LATTICE L46.12
%
%
% LATTICE L46.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-145860, 89352, -25500; 89352, -54638, 15623; -25500, 15623, -4458],[204, 17, 1],[-25, 71, 277, 39, 28, -134; -2, 8, 30, 4, 2, -15; 136, -378, -1479, -209, -153, 714],45,13]
%
% END OF LATTICE L46.13
%
%
% LATTICE L46.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[120506066856, -1340061516, 29926984824; -1340061516, 14901864, -332796528; 29926984824, -332796528, 7432193615],[612, 12, 1],[380, -25187, -11667, -128731, -6441, -3448; 3, 51, 19, 153, 5, 1; -1530, 101422, 46980, 518364, 25936, 13884],45,14]
%
% END OF LATTICE L46.14
%
%
% LATTICE L46.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[54810488664, 12713048460, 13655491740; 12713048460, 2948735256, 3167330424; 13655491740, 3167330424, 3402130855],[612, 12, 1],[84875, 1987777, 63211, -15217, 28111, 237075; 1141, 26724, 850, -204, 378, 3187; -341734, -8003430, -254508, 61268, -113184, -954540],45,15]
%
% END OF LATTICE L46.15
%
%
% LATTICE L46.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-31518, -26775, -36261; -26775, -22695, -30753; -36261, -30753, -41666],[153, 51, 1],[46, -4, -71, -49, -35, 29; 153, -17, -262, -174, -120, 104; -153, 16, 255, 171, 119, -102],45,16]
%
% END OF LATTICE L46.16
%
%
% LATTICE L46.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-227817, 33048, 16524; 33048, -4794, -2397; 16524, -2397, -1198],[153, 51, 1],[3, 7, 8, 0, -10, 0; 29, 57, 55, -1, -69, 25; -17, -18, 0, 2, 0, -51],45,17]
%
% END OF LATTICE L46.17
%
%
% LATTICE L46.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3056940, -523056, 34884; -523056, -89454, 5967; 34884, 5967, -398],[204, 51, 1],[9, 7, 4, 0, -5, 0; 104, 74, 39, -1, -49, 8; 2346, 1722, 935, -15, -1173, 119],45,18]
%
% END OF LATTICE L46.18
%
%
% LATTICE L46.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[128114040, -509796, 32774028; -509796, 2040, -130424; 32774028, -130424, 8384231],[204, 68, 1],[43, 482, 3508, 702, 1668, 877; -123, -1405, -10233, -2049, -4871, -2559; -170, -1906, -13872, -2776, -6596, -3468],45,19]
%
% END OF LATTICE L46.19
%
%
% LATTICE L46.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-9307908, -9191628, 507348; -9191628, -9076470, 500973; 507348, 500973, -27650],[612, 51, 1],[-323, 71, 401, 241, 152, -134; 648, -142, -803, -483, -305, 268; 5814, -1270, -7191, -4329, -2737, 2397],45,20]
%
% END OF LATTICE L46.20
%
%
% LATTICE L46.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-911268, 66096, 33048; 66096, -4794, -2397; 33048, -2397, -1198],[612, 51, 1],[3, 7, 4, 0, -5, 0; 58, 114, 55, -1, -69, 25; -34, -36, 0, 2, 0, -51],45,21]
%
% END OF LATTICE L46.21
%
%
% LATTICE L46.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[231336, -5430684, 1384752; -5430684, 127612200, -32539428; 1384752, -32539428, 8297125],[204, 204, 1],[-119, -57, -35, -1, -15, -109; -8822, -4199, -2533, -49, -1093, -8102; -34578, -16458, -9928, -192, -4284, -31756],45,22]
%
% END OF LATTICE L46.22
%
%
% LATTICE L46.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[16441085016, 458366580, -3746364732; 458366580, 12778968, -104446164; -3746364732, -104446164, 853669255],[612, 204, 1],[76, 1725, 12947, 7943, 6389, 3186; -225, -5004, -37552, -23034, -18524, -9235; 306, 6958, 52224, 32040, 25772, 12852],45,23]
%
% END OF LATTICE L46.23
%
%
% LATTICE L46.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[735624, 307836, 47124; 307836, 157080, 40800; 47124, 40800, 18743],[612, 204, 1],[-2539, -3577, -2075, 1, -911, -7035; 7634, 10755, 6239, -3, 2739, 21152; -10234, -14418, -8364, 4, -3672, -28356],45,24]
%
% END OF LATTICE L46.24
%

\medskip%
%------------------------------WEYL-GROUP-W47--------------------------------
%
\leavevmode\llap{}%
$W_{47\phantom{0}}$%
\qquad\llap{44} lattices, $\chi=48$%
\hfill%
$222222222222\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L47.1
%
\leavevmode%
${L_{47.1}}$%
{} : {$1\above{1pt}{1pt}{2}{{\rm II}}4\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{-2}{}17\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2\rightarrow N_{47}}%
\EasyButWeakLineBreak%
{${4}\above{1pt}{1pt}{*}{2}{12}\above{1pt}{1pt}{*}{2}{68}\above{1pt}{1pt}{b}{2}{2}\above{1pt}{1pt}{l}{2}{12}\above{1pt}{1pt}{r}{2}{34}\above{1pt}{1pt}{b}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1142196\\4488\\4080
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4488\\-16\\-17
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4080\\-17\\-14
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
10097\\1016532\\1703196
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-45\\-4531\\-7590
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-33\\-3322\\-5567
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
13\\1308\\2194
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
37\\3726\\6240
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
191\\19244\\32198
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7\\706\\1179
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7\\708\\1176
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5\\510\\833
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-1142196, 4488, 4080; 4488, -16, -17; 4080, -17, -14],[204, 1, 1],[13, 37, 191, 7, 7, 5, -1, -1, 13, 2, 11, 46; 1308, 3726, 19244, 706, 708, 510, -100, -102, 1292, 200, 1104, 4624; 2194, 6240, 32198, 1179, 1176, 833, -170, -168, 2210, 339, 1860, 7769],46,1]
%
% END OF LATTICE L47.1
%
\hbox{}\par\smallskip%
%
% LATTICE L47.2
%
\leavevmode%
${L_{47.2}}$%
{} : {$1\above{1pt}{1pt}{-2}{6}8\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}17\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2\rightarrow N'_{28}}%
\EasyButWeakLineBreak%
{${8}\above{1pt}{1pt}{r}{2}{6}\above{1pt}{1pt}{l}{2}{136}\above{1pt}{1pt}{}{2}{1}\above{1pt}{1pt}{r}{2}{24}\above{1pt}{1pt}{l}{2}{17}\above{1pt}{1pt}{}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2521848\\8568\\4488
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
8568\\-26\\-17
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4488\\-17\\-7
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
13871\\2115480\\3745440
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-52\\-7931\\-14040
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-22\\-3355\\-5941
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
17\\2592\\4592
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
25\\3813\\6750
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
263\\40120\\70992
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5\\763\\1349
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
11\\1680\\2964
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5\\765\\1343
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-2521848, 8568, 4488; 8568, -26, -17; 4488, -17, -7],[408, 1, 1],[17, 25, 263, 5, 11, 5, -1, -1, 9, 1, 13, 29; 2592, 3813, 40120, 763, 1680, 765, -152, -153, 1360, 152, 1980, 4420; 4592, 6750, 70992, 1349, 2964, 1343, -272, -270, 2448, 271, 3516, 7837],46,2]
%
% END OF LATTICE L47.2
%
\hbox{}\par\smallskip%
%
% LATTICE L47.3
%
\leavevmode%
${L_{47.3}}$%
{} : {$1\above{1pt}{1pt}{2}{6}8\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}17\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{m}%
\EasyButWeakLineBreak%
{${8}\above{1pt}{1pt}{b}{2}{6}\above{1pt}{1pt}{b}{2}{136}\above{1pt}{1pt}{*}{2}{4}\above{1pt}{1pt}{s}{2}{24}\above{1pt}{1pt}{s}{2}{68}\above{1pt}{1pt}{*}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-6404376\\3014712\\21624
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3014712\\-1419106\\-10179
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
21624\\-10179\\-73
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
281519\\599760\\-244800
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-132526\\-282339\\115240
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-943\\-2009\\819
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
201\\428\\-144
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
283\\603\\-258
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2903\\6188\\-2992
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
105\\224\\-134
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
101\\216\\-204
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
63\\136\\-306
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-6404376, 3014712, 21624; 3014712, -1419106, -10179; 21624, -10179, -73],[408, 1, 1],[201, 283, 2903, 105, 101, 63, -17, -7, 225, 33, 175, 719; 428, 603, 6188, 224, 216, 136, -36, -15, 476, 70, 372, 1530; -144, -258, -2992, -134, -204, -306, -16, 18, 272, 14, -36, -374],46,3]
%
% END OF LATTICE L47.3
%
%
% LATTICE L47.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[714, -255, 0; -255, 91, 0; 0, 0, 1],[51, 1, 1],[0, 1, -24, -7, -23, -213, -32, -97, -520, -41, -25, -59; 0, 3, -68, -20, -66, -612, -92, -279, -1496, -118, -72, -170; 1, 0, -17, -4, -9, -68, -9, -24, -119, -8, -3, 0],46,4]
%
% END OF LATTICE L47.4
%
%
% LATTICE L47.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[6630, 3264, 4386; 3264, 1607, 2159; 4386, 2159, 2902],[102, 1, 1],[-1, -2, -95, -11, -65, -293, -87, -262, -1401, -55, -67, -81; 2, 0, 102, 13, 84, 391, 118, 360, 1938, 77, 96, 119; 0, 3, 68, 7, 36, 153, 44, 129, 680, 26, 30, 34],46,5]
%
% END OF LATTICE L47.5
%
%
% LATTICE L47.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-455532, -225012, 2652; -225012, -111145, 1309; 2652, 1309, -14],[204, 1, 1],[-641, -913, -9431, -346, -347, -250, 49, 25, -633, -98, -541, -2266; 1308, 1863, 19244, 706, 708, 510, -100, -51, 1292, 200, 1104, 4624; 868, 1233, 12716, 465, 462, 323, -68, -33, 884, 135, 738, 3077],46,6]
%
% END OF LATTICE L47.6
%
%
% LATTICE L47.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-217668, 3111, 74817; 3111, -42, -1071; 74817, -1071, -25715],[51, 3, 1],[-1571, -134, 523, 140, -1163, -49412, -8829, -10266, -177323, -15740, -4037, -38988; -3056, -260, 1020, 271, -2265, -96203, -17188, -19984, -345168, -30637, -7857, -75871; -4443, -379, 1479, 396, -3289, -139740, -24969, -29033, -501483, -44514, -11417, -110262],46,7]
%
% END OF LATTICE L47.7
%
%
% LATTICE L47.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-762450, 7242, -379542; 7242, -64, 3604; -379542, 3604, -188933],[102, 2, 1],[59, 116, -767, -235, -644, -5377, -759, -4316, -11133, -815, -406, -573; -25, -51, 323, 100, 276, 2312, 327, 1863, 4811, 353, 177, 255; -119, -234, 1547, 474, 1299, 10846, 1531, 8706, 22457, 1644, 819, 1156],46,8]
%
% END OF LATTICE L47.8
%
%
% LATTICE L47.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-978078, 9996, -324462; 9996, -96, 3315; -324462, 3315, -107635],[102, 3, 1],[101, 33, -1313, -201, -367, -4595, -1297, -1229, -19019, -696, -231, -488; -50, -17, 646, 100, 184, 2312, 654, 621, 9622, 353, 118, 255; -306, -100, 3978, 609, 1112, 13923, 3930, 3724, 57630, 2109, 700, 1479],46,9]
%
% END OF LATTICE L47.9
%
%
% LATTICE L47.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-216852, -408, 2244; -408, 6, 3; 2244, 3, -23],[204, 3, 1],[7, 2, 41, 0, -1, -4, 1, 2, 95, 6, 5, 38; 124, 36, 748, 1, -18, -85, 12, 32, 1564, 101, 86, 663; 696, 199, 4080, 0, -100, -408, 96, 197, 9384, 594, 496, 3774],46,10]
%
% END OF LATTICE L47.10
%
%
% LATTICE L47.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1009596, -469404, 25296; -469404, -218244, 11763; 25296, 11763, -632],[204, 3, 1],[-499, -247, -2249, 27, 49, -359, -313, -565, -11555, -636, -455, -3092; 1018, 504, 4590, -55, -100, 731, 638, 1152, 23562, 1297, 928, 6307; -1026, -506, -4590, 57, 100, -765, -654, -1174, -23970, -1317, -940, -6375],46,11]
%
% END OF LATTICE L47.11
%
%
% LATTICE L47.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[282253380, -1649442, 139459806; -1649442, 9642, -814980; 139459806, -814980, 68906305],[102, 6, 1],[126, 251, 14792, 3353, 3228, 86535, 12788, 25577, 204746, 16018, 3229, 23234; 1, 0, 51, 13, 14, 391, 59, 120, 969, 77, 16, 119; -255, -508, -29937, -6786, -6533, -175134, -25881, -51764, -414375, -32418, -6535, -47022],46,12]
%
% END OF LATTICE L47.12
%
%
% LATTICE L47.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[231635676, -1725636, -58198752; -1725636, 12856, 433568; -58198752, 433568, 14622509],[204, 4, 1],[-1109, -6683, -17873, -2808, -1712, -4144, -13, -49, -1201, -558, -1654, -14930; -2189, -13182, -35241, -5533, -3369, -8143, -25, -102, -2397, -1109, -3273, -29495; -4349, -26208, -70091, -11012, -6714, -16252, -51, -192, -4709, -2188, -6486, -58548],46,13]
%
% END OF LATTICE L47.13
%
%
% LATTICE L47.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[90775920, -1080180, -23149716; -1080180, 12856, 275468; -23149716, 275468, 5903651],[204, 4, 1],[-3362, -10037, -53426, -4160, -1246, -5912, -26, -127, -4170, -922, -1295, -22886; 59, 180, 969, 77, 24, 119, 1, 0, 51, 13, 21, 391; -13186, -39366, -209542, -16316, -4887, -23188, -102, -498, -16354, -3616, -5079, -89760],46,14]
%
% END OF LATTICE L47.14
%
%
% LATTICE L47.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-304725, -20808, 107049; -20808, -1139, 7310; 107049, 7310, -37606],[51, 17, 1],[-19866, -5071, 390, 1762, -44170, -36786, -111730, -389717, -131986, -199156, -153224, -29012; 49, 12, -1, -4, 111, 92, 279, 972, 329, 496, 381, 72; -56542, -14433, 1110, 5015, -125715, -104699, -318002, -1109199, -375654, -566831, -436101, -82573],46,15]
%
% END OF LATTICE L47.15
%
%
% LATTICE L47.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-4179144, -2090592, 13872; -2090592, -1045803, 6939; 13872, 6939, -46],[408, 3, 1],[-11, -30, -1469, -95, -81, -625, -117, -34, -707, -1, 17, 81; 24, 64, 3128, 202, 172, 1326, 248, 72, 1496, 2, -36, -170; 300, 605, 28764, 1818, 1516, 11526, 2124, 607, 12444, 0, -304, -1224],46,16]
%
% END OF LATTICE L47.16
%
%
% LATTICE L47.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-489192, 0, 4896; 0, 3, 0; 4896, 0, -49],[408, 3, 1],[1, 2, 95, 3, 5, 19, 7, 2, 41, 0, -1, -2; -16, -11, -408, -10, -12, -34, -8, -1, 0, 1, 0, -17; 96, 197, 9384, 297, 496, 1887, 696, 199, 4080, 0, -100, -204],46,17]
%
% END OF LATTICE L47.17
%
%
% LATTICE L47.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-4453422, -24276, 782952; -24276, -119, 4267; 782952, 4267, -137650],[102, 17, 1],[-167, -170, 127, 334, 1843, 454, 2183, 6218, 1889, 1178, 1181, 50; -68, -66, 52, 135, 738, 181, 868, 2466, 748, 465, 462, 19; -952, -969, 724, 1904, 10506, 2588, 12444, 35445, 10768, 6715, 6732, 285],46,18]
%
% END OF LATTICE L47.18
%
%
% LATTICE L47.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[22991208, -254388, -5865204; -254388, 2820, 64896; -5865204, 64896, 1496251],[204, 12, 1],[-411, -449, -2485, -101, -25, -3279, -385, -1143, -11047, -2287, -771, -10253; -2, -1, 0, 2, 0, -34, -4, -11, -102, -20, -6, -68; -1611, -1760, -9741, -396, -98, -12852, -1509, -4480, -43299, -8964, -3022, -40188],46,19]
%
% END OF LATTICE L47.19
%
%
% LATTICE L47.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[28236048, -1739916, -6913152; -1739916, 107232, 425988; -6913152, 425988, 1692577],[204, 12, 1],[-2135, -1054, -10501, 3, -12, -9431, -2285, -3366, -64639, -6633, -1093, -28139; -1439, -711, -7089, 1, -8, -6341, -1537, -2265, -43503, -4465, -736, -18955; -8358, -4126, -41106, 12, -47, -36924, -8946, -13178, -253062, -25968, -4279, -110160],46,20]
%
% END OF LATTICE L47.20
%
%
% LATTICE L47.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[51, -3468, -102; -3468, 250869, 7395; -102, 7395, 218],[51, 51, 1],[-359, -30, 7, 30, -269, -670, -2033, -2362, -2399, -3618, -927, -526; -192, -15, 4, 14, -148, -366, -1108, -1285, -1304, -1964, -502, -284; 6324, 493, -132, -459, 4879, 12063, 36516, 42347, 42972, 64719, 16541, 9357],46,21]
%
% END OF LATTICE L47.21
%
%
% LATTICE L47.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3216264, -44064, 14688; -44064, -584, 200; 14688, 200, -67],[408, 8, 1],[11, 61, 155, 11, 5, 5, -1, -1, 15, 4, 10, 80; 179, 987, 2499, 176, 78, 68, -17, -15, 255, 67, 165, 1309; 2942, 16296, 41378, 2932, 1326, 1292, -270, -264, 4046, 1076, 2682, 21420],46,22]
%
% END OF LATTICE L47.22
%
%
% LATTICE L47.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-11832, 816, 2040; 816, -56, -136; 2040, -136, -271],[408, 8, 1],[10, 109, 137, 19, 8, 5, -1, -1, 16, 8, 19, 148; 166, 1803, 2261, 312, 129, 68, -17, -15, 272, 135, 318, 2465; -9, -96, -119, -16, -6, 0, 1, 0, -17, -8, -18, -136],46,23]
%
% END OF LATTICE L47.23
%
%
% LATTICE L47.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[269484, 18768, -3672; 18768, 1292, -255; -3672, -255, 50],[204, 17, 1],[-5, -1, 1, 2, -1, -2, -15, -59, -21, -17, -29, -3; -28, -6, 4, 8, -24, -16, -108, -402, -140, -110, -180, -18; -510, -102, 94, 187, -204, -231, -1666, -6426, -2270, -1819, -3060, -313],46,24]
%
% END OF LATTICE L47.24
%
%
% LATTICE L47.25
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[75051294, -2720646, 36392172; -2720646, 98668, -1319234; 36392172, -1319234, 17646467],[102, 34, 1],[-305, -1088, -1619, -6413, -19066, -10135, -25611, -154408, -24297, -32461, -19808, -2823; 0, 3, 2, 7, 18, 9, 22, 129, 20, 26, 15, 2; 629, 2244, 3339, 13226, 39321, 20902, 52819, 318444, 50109, 66946, 40851, 5822],46,25]
%
% END OF LATTICE L47.25
%
%
% LATTICE L47.26
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1428, -408, 0; -408, 119, 0; 0, 0, -1],[204, 17, 1],[1, -1, -1, -1, 1, 1, 7, 13, 9, 7, 11, 1; 4, -3, -4, -5, -6, 1, 12, 27, 20, 17, 30, 3; 0, 0, -8, -17, -102, -27, -136, -204, -128, -85, -102, -7],46,26]
%
% END OF LATTICE L47.26
%
%
% LATTICE L47.27
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[35179698, 2281434, -9571986; 2281434, 148002, -620721; -9571986, -620721, 2604445],[102, 51, 1],[287, 170, 1521, 3013, 5973, 4763, 24073, 24190, 22839, 15257, 6207, 1327; -574, -339, -3038, -6019, -11934, -9517, -48102, -48337, -45638, -30488, -12404, -2652; 918, 544, 4866, 9639, 19108, 15237, 77010, 77384, 73062, 48807, 19856, 4245],46,27]
%
% END OF LATTICE L47.27
%
%
% LATTICE L47.28
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1496136, 8568, -6120; 8568, 17, -34; -6120, -34, 25],[408, 17, 1],[-9, -1, 1, 1, -11, -3, -39, -71, -49, -19, -61, -3; -80, -9, 8, 8, -108, -28, -360, -651, -448, -173, -552, -27; -2312, -255, 256, 255, -2856, -775, -10064, -18309, -12632, -4896, -15708, -772],46,28]
%
% END OF LATTICE L47.28
%
%
% LATTICE L47.29
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-65688, -4488, 408; -4488, -85, 17; 408, 17, -2],[408, 17, 1],[-1, 1, 1, 1, -1, -1, -7, -13, -9, -7, -11, -1; -16, 18, 16, 14, -36, -22, -144, -258, -176, -134, -204, -18; -340, 357, 332, 306, -612, -418, -2788, -5049, -3460, -2652, -4080, -364],46,29]
%
% END OF LATTICE L47.29
%
%
% LATTICE L47.30
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-408, 4488, -408; 4488, -48624, 4416; -408, 4416, -401],[408, 24, 1],[10, 10, 46, -1, -1, 13, 6, 22, 226, 25, 9, 123; 7, 9, 51, 1, -1, -17, -1, 3, 51, 8, 4, 68; 66, 88, 510, 12, -10, -204, -18, 8, 306, 60, 34, 612],46,30]
%
% END OF LATTICE L47.30
%
%
% LATTICE L47.31
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-4120392, -203592, 20400; -203592, -10032, 1008; 20400, 1008, -101],[408, 24, 1],[5, 10, 23, -1, -1, 13, 3, 22, 113, 25, 9, 123; -1, -1, 0, 1, 0, -17, -2, -11, -51, -10, -3, -34; 999, 2008, 4641, -192, -202, 2448, 585, 4328, 22287, 4944, 1786, 24480],46,31]
%
% END OF LATTICE L47.31
%
%
% LATTICE L47.32
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[132396, -7752, -816; -7752, 102, 51; -816, 51, 5],[204, 51, 1],[-19, -8, -13, -6, 1, 2, 11, 4, 5, 0, -5, -4; -24, -10, -16, -7, 2, 3, 16, 6, 8, 1, -6, -5; -2856, -1207, -1968, -918, 136, 294, 1632, 595, 744, 0, -748, -600],46,32]
%
% END OF LATTICE L47.32
%
%
% LATTICE L47.33
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[296004, 3468, 4284; 3468, -408, 51; 4284, 51, 62],[204, 51, 1],[167, 231, 253, 212, 129, 44, 93, 29, 7, -17, 1, 21; -16, -22, -24, -20, -12, -4, -8, -2, 0, 2, 0, -2; -11526, -15946, -17466, -14637, -8908, -3039, -6426, -2006, -486, 1173, -68, -1449],46,33]
%
% END OF LATTICE L47.33
%
%
% LATTICE L47.34
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-672573414, -403681218, -191281926; -403681218, -242291004, -114808140; -191281926, -114808140, -54401149],[102, 102, 1],[-34, -22, 26, 135, 123, 181, 434, 822, 374, 465, 77, 19; 5784, 3871, -4406, -23086, -21173, -31254, -75082, -142467, -64892, -80861, -13476, -3395; -12087, -8092, 9207, 48246, 44251, 65322, 156927, 297772, 135633, 169014, 28169, 7098],46,34]
%
% END OF LATTICE L47.34
%
%
% LATTICE L47.35
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-10200, -204, -2448; -204, 476, -408; -2448, -408, -319],[204, 68, 1],[13, 52, -15, -173, -545, -287, -359, -2128, -331, -865, -493, -59; -38, -153, 44, 508, 1602, 844, 1056, 6261, 974, 2546, 1452, 174; -51, -204, 59, 680, 2142, 1128, 1411, 8364, 1301, 3400, 1938, 232],46,35]
%
% END OF LATTICE L47.35
%
%
% LATTICE L47.36
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[12380352, 198900, 3006144; 198900, 3128, 48348; 3006144, 48348, 729899],[204, 68, 1],[26, 911, 74, -590, -1757, -2162, -5822, -18299, -5870, -8104, -2590, -736; -77, -2748, -223, 1781, 5304, 6527, 17577, 55248, 17723, 24469, 7821, 2223; -102, -3570, -290, 2312, 6885, 8472, 22814, 71706, 23002, 31756, 10149, 2884],46,36]
%
% END OF LATTICE L47.36
%
%
% LATTICE L47.37
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1346808, 655248, -3672; 655248, 318597, -1785; -3672, -1785, 10],[408, 51, 1],[-5, -2, -3, -1, 1, 1, 5, 2, 3, 1, -1, -1; 32, 12, 16, 2, -12, -10, -48, -20, -32, -14, 4, 6; 3876, 1411, 1764, 0, -1768, -1416, -6732, -2839, -4620, -2142, 340, 702],46,37]
%
% END OF LATTICE L47.37
%
%
% LATTICE L47.38
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-913512, 0, 6120; 0, 51, 0; 6120, 0, -41],[408, 51, 1],[11, 4, 5, 0, -5, -2, -19, -8, -13, -3, 1, 1; -8, -1, 0, 1, 0, -1, -16, -11, -24, -10, -12, -2; 1632, 595, 744, 0, -748, -300, -2856, -1207, -1968, -459, 136, 147],46,38]
%
% END OF LATTICE L47.38
%
%
% LATTICE L47.39
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[3876, -415140, 105876; -415140, 44125608, -11253660; 105876, -11253660, 2870099],[204, 204, 1],[-4, -11, -6, -20, -6, -4, -2, -1, 0, 2, 0, -2; 65, 815, 547, 2237, 737, 407, 39, -607, -443, -1925, -633, -303; 255, 3196, 2145, 8772, 2890, 1596, 153, -2380, -1737, -7548, -2482, -1188],46,39]
%
% END OF LATTICE L47.39
%
%
% LATTICE L47.40
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[408, -253164, 64464; -253164, 148640928, -37848936; 64464, -37848936, 9637601],[204, 204, 1],[-21, -31, -35, -61, -10, -15, -19, -9, -5, 1, 0, -5; -26, -1619, -2498, -5766, -1277, -2362, -3818, -2225, -1346, 0, 316, 440; -102, -6358, -9810, -22644, -5015, -9276, -14994, -8738, -5286, 0, 1241, 1728],46,40]
%
% END OF LATTICE L47.40
%
%
% LATTICE L47.41
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[816, 11832, 2856; 11832, 170680, 41208; 2856, 41208, 9949],[408, 136, 1],[-3, -35, -7, -13, -13, -3, -3, -1, 1, 4, 4, 0; 140, 792, 120, 149, 75, 7, -8, 0, 12, 49, 123, 59; -578, -3264, -494, -612, -306, -28, 34, 0, -50, -204, -510, -244],46,41]
%
% END OF LATTICE L47.41
%
%
% LATTICE L47.42
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[816, 6120, -816; 6120, 45832, -6120; -816, -6120, 817],[408, 136, 1],[3, 13, 0, -5, -10, -3, -2, -1, 1, 8, 13, 4; -16, -216, -18, -53, -39, -7, -2, 0, 0, -1, -15, -11; -119, -1632, -137, -408, -306, -56, -17, 0, 1, 0, -102, -80],46,42]
%
% END OF LATTICE L47.42
%
%
% LATTICE L47.43
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-4080, -4488, 408; -4488, -4488, 408; 408, 408, -37],[408, 408, 1],[-1, -1, 0, 1, 0, -1, -2, -11, -3, -10, -3, -2; 6, 14, 2, -1, -3, -3, -2, 2, 2, 13, 7, 7; 51, 136, 21, 0, -34, -48, -51, -136, -21, 0, 34, 48],46,43]
%
% END OF LATTICE L47.43
%
%
% LATTICE L47.44
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[64464, 325992, -1224; 325992, 1628328, -6120; -1224, -6120, 23],[408, 408, 1],[7, 9, 3, 1, -1, -1, -1, 3, 3, 8, 4, 4; 12, 14, 4, -1, -3, -3, -4, 2, 4, 13, 7, 7; 3570, 4216, 1230, -204, -850, -852, -1122, 680, 1218, 3876, 2074, 2076],46,44]
%
% END OF LATTICE L47.44
%

\medskip%
%------------------------------WEYL-GROUP-W48--------------------------------
%
\leavevmode\llap{}%
$W_{48\phantom{0}}$%
\qquad\llap{12} lattices, $\chi=18$%
\hfill%
$422422\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L48.1
%
\leavevmode%
${L_{48.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{2}{}17\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{2\rightarrow N_{48}}%
\EasyButWeakLineBreak%
{${2}\above{1pt}{1pt}{*}{4}{4}\above{1pt}{1pt}{b}{2}{102}\above{1pt}{1pt}{s}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-13414020\\36108\\52020
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
36108\\-94\\-145
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
52020\\-145\\-194
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
83095\\16031136\\10297512
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-247\\-47653\\-30609
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-286\\-55176\\-35443
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
6\\1157\\744
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
33\\6366\\4090
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
235\\45339\\29121
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-13414020, 36108, 52020; 36108, -94, -145; 52020, -145, -194],[204, 1, 1],[6, 33, 235, 7, -7, -14; 1157, 6366, 45339, 1351, -1350, -2703; 744, 4090, 29121, 867, -868, -1734],47,1]
%
% END OF LATTICE L48.1
%
%
% LATTICE L48.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-51, 0, 0; 0, 1, 0; 0, 0, 1],[51, 1, 1],[0, 0, -7, -1, -1, -10; -1, 1, 0, -2, -4, -51; 1, 0, -51, -7, -6, -51],47,2]
%
% END OF LATTICE L48.2
%
%
% LATTICE L48.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-55862034, -2075445, 19597719; -2075445, -77109, 728115; 19597719, 728115, -6875342],[51, 3, 1],[-215, 114, 3327, 1169, 840, 2079; -332, 161, 5644, 2048, 1555, 4080; -648, 342, 10081, 3549, 2559, 6358],47,3]
%
% END OF LATTICE L48.3
%
%
% LATTICE L48.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1873740, -857208, -12240; -857208, -392082, -5637; -12240, -5637, -62],[204, 3, 1],[-8, 391, 8, -334, -1075, -1946; 17, -830, -17, 709, 2282, 4131; 33, -1728, -34, 1476, 4746, 8585],47,4]
%
% END OF LATTICE L48.4
%
%
% LATTICE L48.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2047556568, -64542948, -522260808; -64542948, 2034520, 16462672; -522260808, 16462672, 133210655],[204, 4, 1],[-1073, -4693, -80413, -3749, -129, -1561; 10, 55, 969, 47, 2, 0; -4208, -18406, -315384, -14704, -506, -6120],47,5]
%
% END OF LATTICE L48.5
%
%
% LATTICE L48.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3315, 57477, -1224; 57477, -871522, 16014; -1224, 16014, -235],[51, 17, 1],[-1975, 966, 5876, 12050, 9109, 4199; -233, 114, 693, 1421, 1074, 495; -5593, 2737, 16632, 34102, 25772, 11877],47,6]
%
% END OF LATTICE L48.6
%
%
% LATTICE L48.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[8997727224, -133446396, -2272583460; -133446396, 1979160, 33704964; -2272583460, 33704964, 573993349],[204, 12, 1],[3477, 133, -295, 639, 3983, 23619; 2083, 78, -204, 374, 2379, 14127; 13644, 522, -1156, 2508, 15630, 92684],47,7]
%
% END OF LATTICE L48.7
%
%
% LATTICE L48.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[719151, 1016685, -357; 1016685, 1437333, -510; -357, -510, 2],[51, 51, 1],[-1103, -24, 2254, 16148, 15069, 2761; 781, 17, -1596, -11434, -10670, -1955; 2295, 51, -4691, -33609, -31365, -5747],47,8]
%
% END OF LATTICE L48.8
%
%
% LATTICE L48.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-5103876, 1475940, 45084; 1475940, -426802, -13039; 45084, -13039, -398],[204, 17, 1],[8, -55, -1, 47, 165, 56; 24, -158, -3, 135, 476, 162; 119, -1054, -15, 901, 3094, 1035],47,9]
%
% END OF LATTICE L48.9
%
%
% LATTICE L48.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-375564, 42432, 21216; 42432, -4794, -2397; 21216, -2397, -1198],[204, 51, 1],[0, -7, 0, 6, 19, 2; 25, -62, -1, 53, 218, 27; -51, 0, 2, 0, -102, -19],47,10]
%
% END OF LATTICE L48.10
%
%
% LATTICE L48.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[144556440, 7679988, 31132032; 7679988, 408136, 1653896; 31132032, 1653896, 6704735],[204, 68, 1],[10702, 477, 49, 2359, 12584, 13012; -31363, -1398, -144, -6914, -36879, -38133; -41956, -1870, -192, -9248, -49334, -51012],47,11]
%
% END OF LATTICE L48.11
%
%
% LATTICE L48.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[192984, 95268, -23868; 95268, 59160, -14892; -23868, -14892, 3749],[204, 204, 1],[47, 2, 0, 10, 55, 19; -4235, -183, 1, -889, -4941, -1709; -16524, -714, 4, -3468, -19278, -6668],47,12]
%
% END OF LATTICE L48.12
%

\medskip%
%------------------------------WEYL-GROUP-W49--------------------------------
%
\leavevmode\llap{}%
$W_{49\phantom{0}}$%
\qquad\llap{12} lattices, $\chi=30$%
\hfill%
$22242224\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L49.1
%
\leavevmode%
${L_{49.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{2}{}5\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{2}{}11\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{2\rightarrow N_{49}}%
\EasyButWeakLineBreak%
{${4}\above{1pt}{1pt}{*}{2}{20}\above{1pt}{1pt}{b}{2}{22}\above{1pt}{1pt}{s}{2}{2}\above{1pt}{1pt}{*}{4}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1472020\\-81400\\9240
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-81400\\-4494\\511
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
9240\\511\\-58
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
23099\\-23100\\3474240
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1290\\-1291\\194016
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-145\\145\\-21809
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\-2\\460
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
33\\-30\\4990
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
57\\-55\\8591
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
27\\-27\\4061
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-1472020, -81400, 9240; -81400, -4494, 511; 9240, 511, -58],[220, 1, 1],[3, 33, 57, 27, 17, 17, -2, -2; -2, -30, -55, -27, -18, -20, 0, 2; 460, 4990, 8591, 4061, 2548, 2530, -319, -301],48,1]
%
% END OF LATTICE L49.1
%
%
% LATTICE L49.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[330, 55, 0; 55, 9, 0; 0, 0, 1],[55, 1, 1],[0, -1, 6, 8, 6, 16, 27, 7; 0, 5, -33, -43, -32, -85, -143, -37; 1, 0, -11, -9, -5, -10, -11, -1],48,2]
%
% END OF LATTICE L49.2
%
%
% LATTICE L49.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1325170, 11495, -261800; 11495, -90, 2270; -261800, 2270, -51721],[55, 5, 1],[-119, 209, 6013, 3685, 1641, 552, 2358, 120; 60, -113, -3201, -1951, -864, -289, -1221, -59; 605, -1063, -30580, -18740, -8345, -2807, -11990, -610],48,3]
%
% END OF LATTICE L49.3
%
%
% LATTICE L49.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2407405, -32450, -439780; -32450, -429, -5929; -439780, -5929, -80338],[55, 11, 1],[-142, 1328, 685, 4595, 2036, 3407, 262, 140; 99, -865, -453, -3055, -1361, -2290, -178, -100; 770, -7205, -3716, -24926, -11044, -18480, -1421, -759],48,4]
%
% END OF LATTICE L49.4
%
%
% LATTICE L49.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[557859720, 64460, -142069620; 64460, 8, -16416; -142069620, -16416, 36180739],[220, 4, 1],[-355, -3359, -11743, -5735, -1939, -2376, -874, 0; -76, -745, -2629, -1291, -440, -545, -209, 1; -1394, -13190, -46112, -22520, -7614, -9330, -3432, 0],48,5]
%
% END OF LATTICE L49.5
%
%
% LATTICE L49.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-118324580, -185460, 941160; -185460, -290, 1475; 941160, 1475, -7486],[220, 5, 1],[11, 21, 175, 81, 49, 9, -10, -6; 340, 638, 5291, 2441, 1468, 266, -319, -181; 1450, 2766, 23045, 10665, 6450, 1184, -1320, -790],48,6]
%
% END OF LATTICE L49.6
%
%
% LATTICE L49.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-10454620, -238480, 47740; -238480, -5434, 1089; 47740, 1089, -218],[220, 11, 1],[11, 63, 8, 36, 17, 7, -1, -1; -2, -30, -5, -27, -18, -20, 0, 2; 2398, 13640, 1726, 7744, 3630, 1430, -219, -209],48,7]
%
% END OF LATTICE L49.7
%
%
% LATTICE L49.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[345510, -5080845, -968110; -5080845, 74731030, 14239335; -968110, 14239335, 2713179],[55, 55, 1],[9, -74, -159, -991, -405, -124, -39, 1; -3049, 25509, 54745, 341007, 139259, 42596, 13360, -482; 16005, -133903, -287370, -1790030, -731005, -223597, -70130, 2530],48,8]
%
% END OF LATTICE L49.8
%
%
% LATTICE L49.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[840637160, -18207860, -214100040; -18207860, 394520, 4637320; -214100040, 4637320, 54528671],[220, 20, 1],[6808, 13427, 237187, 116533, 39740, 9847, 18827, -163; 9, 17, 297, 145, 49, 12, 22, 0; 26730, 52718, 931260, 457540, 156030, 38662, 73920, -640],48,9]
%
% END OF LATTICE L49.9
%
%
% LATTICE L49.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[300208920, 45100, -76442300; 45100, 88, -11484; -76442300, -11484, 19464529],[220, 44, 1],[-5417, -39129, -11329, -57195, -17461, -18066, -110, 0; -45, -330, -96, -486, -149, -155, -1, 1; -21274, -153670, -44492, -224620, -68574, -70950, -432, 0],48,10]
%
% END OF LATTICE L49.10
%
%
% LATTICE L49.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2014540, 2248620, -412280; 2248620, -2509870, 460185; -412280, 460185, -84374],[220, 55, 1],[-673, -45, 44, 36, -475, -529, -331, -1471; -18, -4, 0, 2, -2, -6, -5, -27; 3190, 198, -215, -165, 2310, 2552, 1590, 7040],48,11]
%
% END OF LATTICE L49.11
%
%
% LATTICE L49.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[440, 67980, -17160; 67980, 193728920, -48915680; -17160, -48915680, 12350989],[220, 220, 1],[-1395, -289, -9, 1, -431, -624, -904, -4566; 31469, 6516, 202, 0, 9749, 14093, 20407, 103045; 124630, 25806, 800, 0, 38610, 55814, 80820, 408100],48,12]
%
% END OF LATTICE L49.12
%

\medskip%
%------------------------------WEYL-GROUP-W50--------------------------------
%
\leavevmode\llap{}%
$W_{50\phantom{0}}$%
\qquad\llap{12} lattices, $\chi=24$%
\hfill%
$22222222\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L50.1
%
\leavevmode%
${L_{50.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}11\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2\rightarrow N_{50}}%
\EasyButWeakLineBreak%
{${2}\above{1pt}{1pt}{b}{2}{4}\above{1pt}{1pt}{b}{2}{10}\above{1pt}{1pt}{l}{2}{44}\above{1pt}{1pt}{r}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-604340\\110220\\5280
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
110220\\-20102\\-963
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5280\\-963\\-46
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3079\\16940\\-1540
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-562\\-3092\\281
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-26\\-143\\12
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
21\\114\\23
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
11\\60\\6
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
9\\50\\-15
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-27\\-132\\-352
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-604340, 110220, 5280; 110220, -20102, -963; 5280, -963, -46],[220, 1, 1],[21, 11, 9, -27, -7, -7, 1, 203; 114, 60, 50, -132, -37, -38, 5, 1100; 23, 6, -15, -352, -30, -8, 10, 264],49,1]
%
% END OF LATTICE L50.1
%
%
% LATTICE L50.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-935, -165, 55; -165, -29, 10; 55, 10, -2],[55, 1, 1],[50, 6, 2, -2, -1, 1, 33, 310; -278, -33, -10, 11, 5, -6, -185, -1727; -81, -7, 5, 0, -3, -5, -65, -528],49,2]
%
% END OF LATTICE L50.2
%
%
% LATTICE L50.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-12815, 1705, -2475; 1705, -105, 330; -2475, 330, -478],[55, 5, 1],[-191, -63, -37, -532, -26, 32, 6, -832; -7, -2, -1, -11, 0, 1, 0, -33; 985, 325, 191, 2750, 135, -165, -31, 4290],49,3]
%
% END OF LATTICE L50.3
%
%
% LATTICE L50.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-40865, -1210, -7755; -1210, -33, -231; -7755, -231, -1471],[55, 11, 1],[-52, -18, -56, -16, -11, 9, 11, -20; 131, 43, 125, 32, 16, -22, -20, 52; 253, 88, 275, 79, 55, -44, -55, 97],49,4]
%
% END OF LATTICE L50.4
%
%
% LATTICE L50.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1218360, 40260, -302720; 40260, 1432, -9984; -302720, -9984, 75219],[220, 4, 1],[-1136, -352, -1788, -5567, -1517, -27, -107, -2771; 843, 261, 1325, 4125, 1124, 20, 80, 2057; -4460, -1382, -7020, -21857, -5956, -106, -420, -10879],49,5]
%
% END OF LATTICE L50.5
%
%
% LATTICE L50.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-18585380, -1579820, 27940; -1579820, -134290, 2375; 27940, 2375, -42],[220, 5, 1],[-2, -1, 4, 439, 37, 11, 1, 1; 23, 10, -47, -5104, -429, -126, -11, 0; -30, -100, 2, 3300, 345, 190, 43, 660],49,6]
%
% END OF LATTICE L50.6
%
%
% LATTICE L50.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[84260, 6160, -1100; 6160, 418, -77; -1100, -77, 14],[220, 11, 1],[3, 1, -1, -3, -3, -1, 1, 3; 53, 18, -25, -68, -67, -22, 15, 52; 528, 176, -220, -612, -605, -198, 165, 524],49,7]
%
% END OF LATTICE L50.7
%
%
% LATTICE L50.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[27610, -113740, -21725; -113740, 471955, 90145; -21725, 90145, 17218],[55, 55, 1],[14, 3, 2, 5, 7, 0, 1, 7; -1646, -409, -342, -929, -1364, -21, -88, -791; 8635, 2145, 1793, 4870, 7150, 110, 462, 4150],49,8]
%
% END OF LATTICE L50.8
%
%
% LATTICE L50.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[5281320, 86460, -1345960; 86460, 5240, -22100; -1345960, -22100, 343023],[220, 20, 1],[-835, -863, -8629, -213733, -70089, -9269, -1503, -9171; -56, -58, -580, -14366, -4711, -623, -101, -616; -3280, -3390, -33896, -839575, -275320, -36410, -5904, -36025],49,9]
%
% END OF LATTICE L50.9
%
%
% LATTICE L50.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[13049960, -281820, -3323100; -281820, 6072, 71764; -3323100, 71764, 846209],[220, 44, 1],[-381, 185, 897, 90, -11, -241, -1177, -202; -2, 6, 30, 5, 9, -5, -25, -3; -1496, 726, 3520, 353, -44, -946, -4620, -793],49,10]
%
% END OF LATTICE L50.10
%
%
% LATTICE L50.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2420, -440, 0; -440, -1430, 55; 0, 55, -2],[220, 55, 1],[1, -1, -3, -25, -22, -5, 0, 1; 1, -14, -25, -196, -169, -34, 1, 4; 0, -440, -748, -5820, -5005, -990, 33, 100],49,11]
%
% END OF LATTICE L50.11
%
%
% LATTICE L50.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[4840, -129580, 33000; -129580, 3463240, -881980; 33000, -881980, 224613],[220, 220, 1],[-34, -34, -74, -131, -435, -33, 7, -3; 559, 531, 1073, 1853, 6091, 419, -123, 47; 2200, 2090, 4224, 7295, 23980, 1650, -484, 185],49,12]
%
% END OF LATTICE L50.12
%

\medskip%
%------------------------------WEYL-GROUP-W51--------------------------------
%
\leavevmode\llap{}%
$W_{51\phantom{0}}$%
\qquad\llap{18} lattices, $\chi=20$%
\hfill%
$226226\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L51.1
%
\leavevmode%
${L_{51.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{-}{}9\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}19\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{23\rightarrow N_{51},3,2}%
\EasyButWeakLineBreak%
{${6}\above{1pt}{1pt}{b}{2}{38}\above{1pt}{1pt}{s}{2}{18}\above{1pt}{1pt}{}{6}{6}\above{1pt}{1pt}{b}{2}{342}\above{1pt}{1pt}{s}{2}{2}\above{1pt}{1pt}{}{6}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-9620460\\18468\\25992
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
18468\\-30\\-51
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
25992\\-51\\-70
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-65\\-324
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2\\-133\\-646
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\129\\648
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
16\\1046\\5175
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
101\\6612\\32661
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\66\\323
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-9620460, 18468, 25992; 18468, -30, -51; 25992, -51, -70],[684, 3, 1],[-1, -2, 2, 16, 101, 1; -65, -133, 129, 1046, 6612, 66; -324, -646, 648, 5175, 32661, 323],50,1]
%
% END OF LATTICE L51.1
%
%
% LATTICE L51.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[627, 0, 399; 0, -1, 0; 399, 0, 254],[57, 1, 1],[-2, -12, 2, 83, 183, 7; 0, 0, -2, -45, -95, -3; 3, 19, -3, -129, -285, -11],50,2]
%
% END OF LATTICE L51.2
%
%
% LATTICE L51.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-853548780, 11382900, -246924; 11382900, -151802, 3293; -246924, 3293, -70],[228, 1, 1],[62, 127, -41, -998, -2103, -63; 4647, 9519, -3073, -74802, -157624, -4722; -96, -190, 64, 1527, 3211, 95],50,3]
%
% END OF LATTICE L51.3
%
%
% LATTICE L51.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-2405115, 9234, 12996; 9234, -30, -51; 12996, -51, -70],[171, 3, 1],[-2, -4, 4, 32, 202, 2; -65, -133, 129, 1046, 6612, 66; -324, -646, 648, 5175, 32661, 323],50,4]
%
% END OF LATTICE L51.4
%
%
% LATTICE L51.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1235019, 313329, -406296; 313329, -79449, 103077; -406296, 103077, -133663],[57, 3, 1],[206, 23488, 6994, 18871, 97333, -635; -27, -3135, -935, -2526, -13034, 84; -647, -73815, -21981, -59311, -305919, 1995],50,5]
%
% END OF LATTICE L51.5
%
%
% LATTICE L51.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-8578500, -53808, 42864; -53808, -318, 267; 42864, 267, -214],[228, 3, 1],[-3, -6, 8, 45, 272, 6; -65, -133, 173, 977, 5909, 131; -682, -1368, 1818, 10231, 61845, 1365],50,6]
%
% END OF LATTICE L51.6
%
%
% LATTICE L51.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[379221000, 90203868, 94345488; 90203868, 21456968, 22441612; 94345488, 22441612, 23471989],[228, 4, 1],[-4091, -11219, -11103, -232060, -487322, -15136; -222, -608, -602, -12585, -26429, -821; 16656, 45676, 45204, 944796, 1984056, 61624],50,7]
%
% END OF LATTICE L51.7
%
%
% LATTICE L51.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-17896062, -154755, -5809326; -154755, -1330, -50236; -5809326, -50236, -1885793],[57, 19, 1],[1037, 2107, 11937, 96730, 8756, -1074; -96, -178, -1000, -8049, -727, 95; -3192, -6486, -36746, -297768, -26954, 3306],50,8]
%
% END OF LATTICE L51.8
%
%
% LATTICE L51.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[3068533896, -15685716, 753433980; -15685716, 80184, -3851400; 753433980, -3851400, 184994783],[228, 12, 1],[55, 2519, 2413, 14759, 91303, 2525; 0, -38, -24, -123, -741, -17; -224, -10260, -9828, -60112, -371868, -10284],50,9]
%
% END OF LATTICE L51.9
%
%
% LATTICE L51.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[127110, -8541165, -2771169; -8541165, 574518219, 186401628; -2771169, 186401628, 60477746],[57, 57, 1],[1, -71, -441, -1276, -354, 16; -1874, 107468, 668536, 1936190, 537304, -23764; 5776, -331236, -2060550, -5967691, -1656069, 73245],50,10]
%
% END OF LATTICE L51.10
%
%
% LATTICE L51.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-5700, 2052, -456; 2052, -646, 133; -456, 133, -26],[228, 19, 1],[-2, -1, -3, 2, 1, 3; -45, -11, -25, 18, 8, 22; -228, -42, -76, 57, 23, 57],50,11]
%
% END OF LATTICE L51.11
%
%
% LATTICE L51.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2916369432, -10491876, -733409424; -10491876, 37752, 2638500; -733409424, 2638500, 184438013],[684, 12, 1],[-341, -1529, -3911, -25180, -157046, -1532; 2, 0, 6, 61, 399, 5; -1356, -6080, -15552, -100128, -624492, -6092],50,12]
%
% END OF LATTICE L51.12
%
%
% LATTICE L51.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-40185, 4788, 2394; 4788, -570, -285; 2394, -285, -142],[171, 57, 1],[-2, 0, 4, 14, 4, 0; -17, -1, 33, 197, 63, 9; 0, 2, 0, -171, -63, -19],50,13]
%
% END OF LATTICE L51.13
%
%
% LATTICE L51.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-64524, -205200, 5700; -205200, -650370, 18069; 5700, 18069, -502],[228, 57, 1],[36, 11, 3, -3, 0, 8; 230, 72, 26, -17, -1, 45; 8683, 2715, 969, -646, -36, 1710],50,14]
%
% END OF LATTICE L51.14
%
%
% LATTICE L51.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2178312, 208164, -380304; 208164, 19912, -36328; -380304, -36328, 66407],[228, 76, 1],[6511, 645, 131, -112, 66, 580; -19815, -1963, -399, 339, -201, -1765; 26448, 2620, 532, -456, 268, 2356],50,15]
%
% END OF LATTICE L51.15
%
%
% LATTICE L51.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-160740, 9576, 4788; 9576, -570, -285; 4788, -285, -142],[684, 57, 1],[-1, 0, 2, 7, 2, 0; -17, -1, 33, 197, 63, 9; 0, 2, 0, -171, -63, -19],50,16]
%
% END OF LATTICE L51.16
%
%
% LATTICE L51.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[98952, -3687444, -905388; -3687444, 137416056, 33740124; -905388, 33740124, 8284301],[228, 228, 1],[-1389, -465, -287, -12, -2, -180; 4124, 1390, 888, 37, -3, 499; -16948, -5712, -3648, -152, 12, -2052],50,17]
%
% END OF LATTICE L51.17
%
%
% LATTICE L51.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[198360, 41724, 18468; 41724, 33288, -14592; 18468, -14592, 15647],[684, 228, 1],[459, -1, 1205, 12795, 4421, 1071; -1375, 3, -3609, -38324, -13242, -3208; -1824, 4, -4788, -50844, -17568, -4256],50,18]
%
% END OF LATTICE L51.18
%

\medskip%
%------------------------------WEYL-GROUP-W52--------------------------------
%
\leavevmode\llap{}%
$W_{52\phantom{0}}$%
\qquad\llap{44} lattices, $\chi=54$%
\hfill%
$222422222422\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L52.1
%
\leavevmode%
${L_{52.1}}$%
{} : {$1\above{1pt}{1pt}{2}{{\rm II}}4\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{2}{}19\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2\rightarrow N_{52}}%
\EasyButWeakLineBreak%
{${6}\above{1pt}{1pt}{l}{2}{4}\above{1pt}{1pt}{r}{2}{114}\above{1pt}{1pt}{b}{2}{2}\above{1pt}{1pt}{*}{4}{4}\above{1pt}{1pt}{*}{2}{76}\above{1pt}{1pt}{b}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-833340\\-411084\\2736
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-411084\\-202786\\1349
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2736\\1349\\-8
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-684191\\1393080\\904020
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-337109\\686387\\445422
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1662\\-3384\\-2197
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1967\\4005\\2598
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-609\\1240\\808
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-4619\\9405\\6156
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-138\\281\\186
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-165\\336\\226
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-877\\1786\\1216
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-833340, -411084, 2736; -411084, -202786, 1349; 2736, 1349, -8],[228, 1, 1],[-1967, -609, -4619, -138, -165, -877, 28, 55, -644, -139, -1497, -20175; 4005, 1240, 9405, 281, 336, 1786, -57, -112, 1311, 283, 3048, 41078; 2598, 808, 6156, 186, 226, 1216, -36, -76, 798, 180, 1970, 26600],51,1]
%
% END OF LATTICE L52.1
%
\hbox{}\par\smallskip%
%
% LATTICE L52.2
%
\leavevmode%
${L_{52.2}}$%
{} : {$1\above{1pt}{1pt}{2}{2}8\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{2}{}19\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{2\rightarrow N'_{29}}%
\EasyButWeakLineBreak%
{${12}\above{1pt}{1pt}{s}{2}{8}\above{1pt}{1pt}{l}{2}{57}\above{1pt}{1pt}{}{2}{1}\above{1pt}{1pt}{}{4}{2}\above{1pt}{1pt}{b}{2}{152}\above{1pt}{1pt}{*}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1477896\\-246696\\4560
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-246696\\-41179\\761
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4560\\761\\-14
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
6079\\-36480\\-9120
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1018\\-6109\\-1527
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-20\\120\\29
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
29\\-174\\-42
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\-4\\100
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-26\\171\\798
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3\\19\\55
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-7\\44\\111
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-97\\608\\1444
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-1477896, -246696, 4560; -246696, -41179, 761; 4560, 761, -14],[456, 1, 1],[29, 1, -26, -3, -7, -97, -1, 7, 64, 5, 19, 401; -174, -4, 171, 19, 44, 608, 6, -44, -399, -31, -116, -2432; -42, 100, 798, 55, 111, 1444, 0, -112, -855, -58, -129, -1900],51,2]
%
% END OF LATTICE L52.2
%
\hbox{}\par\smallskip%
%
% LATTICE L52.3
%
\leavevmode%
${L_{52.3}}$%
{} : {$1\above{1pt}{1pt}{-2}{2}8\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{2}{}19\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{m}%
\EasyButWeakLineBreak%
{${3}\above{1pt}{1pt}{r}{2}{8}\above{1pt}{1pt}{s}{2}{228}\above{1pt}{1pt}{*}{2}{4}\above{1pt}{1pt}{*}{4}{2}\above{1pt}{1pt}{l}{2}{152}\above{1pt}{1pt}{}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-508748712\\-3325152\\93024
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3325152\\-21733\\608
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
93024\\608\\-17
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
658615\\-100768248\\-282264
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4305\\-658666\\-1845
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-119\\18207\\50
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
50\\-7650\\-21
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
29\\-4436\\24
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
205\\-31350\\456
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5\\-764\\34
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\-305\\35
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
13\\-1976\\456
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-508748712, -3325152, 93024; -3325152, -21733, 608; 93024, 608, -17],[456, 1, 1],[50, 29, 205, 5, 2, 13, -1, -1, 61, 9, 40, 1051; -7650, -4436, -31350, -764, -305, -1976, 153, 152, -9348, -1378, -6121, -160816; -21, 24, 456, 34, 35, 456, 0, -36, -570, -40, -53, -912],51,3]
%
% END OF LATTICE L52.3
%
%
% LATTICE L52.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-912, -285, 0; -285, -89, 0; 0, 0, 1],[57, 1, 1],[727, 95, 1189, 17, 0, -6, 1, 9, 787, 87, 312, 3958; -2265, -296, -3705, -53, 0, 19, -3, -28, -2451, -271, -972, -12331; -123, -15, -171, -1, 1, 0, -3, -3, -171, -17, -55, -684],51,4]
%
% END OF LATTICE L52.4
%
%
% LATTICE L52.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[62130, -20748, 10146; -20748, 6929, -3388; 10146, -3388, 1657],[114, 1, 1],[59, 347, 13958, 1518, 10736, 135849, 12443, 3225, 19976, 268, -20, -113; 102, 592, 23769, 2584, 18269, 231154, 21171, 5486, 33972, 455, -35, -190; -153, -916, -36936, -4019, -28437, -359860, -32964, -8546, -52953, -712, 51, 304],51,5]
%
% END OF LATTICE L52.5
%
%
% LATTICE L52.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-63156, -21204, 684; -21204, -7118, 229; 684, 229, -7],[228, 1, 1],[29, 1, -52, -6, -7, -97, -1, 7, 128, 10, 19, 401; -87, -2, 171, 19, 22, 304, 3, -22, -399, -31, -58, -1216; -42, 24, 456, 34, 35, 456, 0, -36, -570, -40, -53, -912],51,6]
%
% END OF LATTICE L52.6
%
%
% LATTICE L52.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-71592, 3135, -23427; 3135, -111, 1026; -23427, 1026, -7666],[57, 3, 1],[18, 56, -404, -270, -1471, -19852, -1292, -602, -3054, -276, -167, -896; 0, 1, 0, -2, -15, -209, -14, -7, -38, -4, -3, -19; -55, -171, 1235, 825, 4494, 60648, 3947, 1839, 9329, 843, 510, 2736],51,7]
%
% END OF LATTICE L52.7
%
%
% LATTICE L52.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3428094, -22344, -1697004; -22344, -142, -11060; -1697004, -11060, -840065],[114, 2, 1],[1939, 5707, 458968, 49911, 352961, 2233073, 409066, 53008, 656617, 8804, -671, -1903; 990, 2910, 233985, 25444, 179929, 1138347, 208527, 27021, 334704, 4487, -343, -969; -3930, -11567, -930240, -101160, -715384, -4526009, -829098, -107437, -1330836, -17844, 1360, 3857],51,8]
%
% END OF LATTICE L52.8
%
%
% LATTICE L52.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3382266, -27132, 1141254; -27132, -213, 9156; 1141254, 9156, -385085],[114, 3, 1],[-499, -8813, -118128, -38538, -272534, -3448475, -105285, -81859, -169000, -6798, 518, 2939; 330, 5820, 77995, 25444, 179929, 2276694, 69509, 54042, 111568, 4487, -343, -1938; -1471, -25980, -348232, -113607, -803409, -10165836, -310372, -241314, -498199, -20040, 1527, 8664],51,9]
%
% END OF LATTICE L52.9
%
%
% LATTICE L52.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2498196, -19836, 13224; -19836, -156, 105; 13224, 105, -70],[228, 3, 1],[2, 7, 54, 15, 91, 1117, 33, 23, 41, 0, -1, 23; -4, -8, -38, -8, -34, -380, -10, -4, 0, 2, -2, -76; 371, 1308, 10127, 2817, 17112, 210102, 6209, 4332, 7733, 3, -192, 4218],51,10]
%
% END OF LATTICE L52.10
%
%
% LATTICE L52.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[30888870, 1133160, 14601804; 1133160, 41574, 535668; 14601804, 535668, 6902573],[114, 6, 1],[-1929, -17155, -460548, -150295, -1063173, -6726733, -410770, -159716, -659635, -26576, 1947, 5635; 34, 296, 7923, 2584, 18269, 115577, 7057, 2743, 11324, 455, -35, -95; 4078, 36267, 973636, 317736, 2247636, 14220873, 868402, 337653, 1394524, 56184, -4116, -11913],51,11]
%
% END OF LATTICE L52.11
%
%
% LATTICE L52.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-410172, 0, 5472; 0, 3, 0; 5472, 0, -73],[228, 3, 1],[4, 11, 73, 19, 54, 1307, 38, 25, 41, -1, 0, 61; -1, -6, -57, -17, -55, -1368, -41, -30, -57, -1, 1, 0; 299, 822, 5453, 1419, 4032, 97584, 2837, 1866, 3059, -75, 0, 4560],51,12]
%
% END OF LATTICE L52.12
%
%
% LATTICE L52.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[12027912, -73644, 2977680; -73644, 452, -18232; 2977680, -18232, 737167],[228, 4, 1],[3601, 503, 6937, 159, 107, 471, 109, 27, 3133, 371, 1483, 9599; -5268, -736, -10146, -232, -153, -665, -150, -38, -4560, -542, -2169, -14041; -14676, -2050, -28272, -648, -436, -1919, -444, -110, -12768, -1512, -6044, -39121],51,13]
%
% END OF LATTICE L52.13
%
%
% LATTICE L52.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[324413448, -2158932, 80740728; -2158932, 14368, -537320; 80740728, -537320, 20094929],[228, 4, 1],[25175, 1788, 49775, 1163, 580, 3611, 53, 14, 18701, 2441, 10232, 133341; -51000, -3623, -100890, -2360, -1181, -7372, -114, -28, -37848, -4942, -20725, -270104; -102516, -7281, -202692, -4736, -2362, -14706, -216, -57, -76152, -9940, -41666, -542982],51,14]
%
% END OF LATTICE L52.14
%
%
% LATTICE L52.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-277077, -6498, -88293; -6498, -152, -2071; -88293, -2071, -28135],[57, 19, 1],[19, 13, -23, -83, -423, -298, -1097, -167, -131, -71, -39, -10; -36, -38, 42, 180, 985, 700, 2598, 404, 324, 186, 113, 32; -57, -38, 69, 247, 1254, 883, 3249, 494, 387, 209, 114, 29],51,15]
%
% END OF LATTICE L52.15
%
%
% LATTICE L52.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-820344, -16416, 10944; -16416, -327, 219; 10944, 219, -146],[456, 3, 1],[2, 11, 73, 19, 54, 1307, 19, 25, 41, -1, 0, 61; -1, -12, -114, -34, -110, -2736, -41, -60, -114, -2, 2, 0; 148, 804, 5282, 1368, 3867, 93480, 1357, 1776, 2888, -78, 3, 4560],51,16]
%
% END OF LATTICE L52.16
%
%
% LATTICE L52.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-13400472, 912, 44232; 912, 3, -3; 44232, -3, -146],[456, 3, 1],[5, 17, 65, 18, 109, 2675, 79, 55, 49, 0, -1, 61; -2, -12, -57, -17, -110, -2736, -82, -60, -57, -1, 2, 0; 1514, 5148, 19684, 5451, 33009, 810084, 23924, 16656, 14839, 0, -303, 18468],51,17]
%
% END OF LATTICE L52.17
%
%
% LATTICE L52.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-5041194, -128022, -791616; -128022, -3211, -20102; -791616, -20102, -124307],[114, 19, 1],[-2476, -14553, -30793, -63621, -449898, -299615, -521404, -135127, -44047, -11219, 858, 255; -483, -2846, -6024, -12447, -88025, -58622, -102018, -26440, -8619, -2196, 167, 50; 15846, 93138, 197073, 407170, 2879317, 1917516, 3336951, 864804, 281898, 71801, -5491, -1632],51,18]
%
% END OF LATTICE L52.18
%
%
% LATTICE L52.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[68234928, -684, 16752984; -684, 24, -168; 16752984, -168, 4113179],[228, 12, 1],[2630, 1904, 55120, 14958, 44737, 547720, 32272, 5575, 39614, 0, 137, 20684; -31, -22, -627, -169, -502, -6137, -361, -62, -437, 1, -2, -247; -10712, -7755, -224504, -60924, -182214, -2230866, -131444, -22707, -161348, 0, -558, -84246],51,19]
%
% END OF LATTICE L52.19
%
%
% LATTICE L52.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[20951148, 0, 5140716; 0, 12, 0; 5140716, 0, 1261361],[228, 12, 1],[1059, 1615, 24093, 6619, 20016, 122810, 14509, 5057, 18163, 53, 0, 3958; -1, -3, -57, -17, -55, -342, -41, -15, -57, -1, 1, 0; -4316, -6582, -98192, -26976, -81576, -500517, -59132, -20610, -74024, -216, 0, -16131],51,20]
%
% END OF LATTICE L52.20
%
%
% LATTICE L52.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[92454, -199272, -64695; -199272, 441921, 143469; -64695, 143469, 46577],[57, 57, 1],[1, 0, 3, 23, 100, 69, 83, 36, 9, 13, 8, 3; -456, -37, -1618, -12314, -53120, -36607, -43980, -19007, -4730, -6730, -4012, -1481; 1406, 114, 4988, 37962, 163761, 112854, 135584, 58596, 14582, 20748, 12369, 4566],51,21]
%
% END OF LATTICE L52.21
%
%
% LATTICE L52.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-8721912, -108072, 35568; -108072, -1328, 440; 35568, 440, -145],[456, 8, 1],[71, 11, 167, 5, 6, 16, -1, -1, 23, 5, 54, 364; 1341, 209, 3192, 97, 119, 323, -18, -20, 399, 92, 1015, 6859; 21468, 3330, 50616, 1520, 1832, 4902, -300, -306, 6840, 1504, 16312, 110010],51,22]
%
% END OF LATTICE L52.22
%
%
% LATTICE L52.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-40584, -3192, 1368; -3192, -112, 72; 1368, 72, -37],[456, 8, 1],[71, 11, 167, 5, 6, 8, -1, -1, 23, 5, 54, 182; 1299, 202, 3078, 93, 113, 152, -18, -19, 399, 90, 985, 3325; 5112, 794, 12084, 364, 440, 589, -72, -74, 1596, 356, 3880, 13091],51,23]
%
% END OF LATTICE L52.23
%
%
% LATTICE L52.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[110580, 35568, -1596; 35568, 11438, -513; -1596, -513, 23],[228, 19, 1],[29, 7, 2, 0, -1, -1, -1, 1, 2, 4, 13, 17; -339, -86, -27, -5, 4, 4, 3, -10, -21, -43, -148, -196; -5586, -1444, -468, -114, 19, 20, 0, -152, -330, -684, -2413, -3212],51,24]
%
% END OF LATTICE L52.24
%
%
% LATTICE L52.25
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-24852, 6156, -228; 6156, -1520, 57; -228, 57, -2],[228, 19, 1],[79, 21, 7, 2, -1, -1, -2, 1, 4, 9, 67, 45; 216, 56, 18, 4, -6, -4, -6, 4, 12, 26, 186, 124; -3249, -912, -327, -133, -76, -6, 57, 0, -129, -323, -2660, -1818],51,25]
%
% END OF LATTICE L52.25
%
%
% LATTICE L52.26
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1045794390, 8113608, 515907798; 8113608, 62966, 4002578; 515907798, 4002578, 254505913],[114, 38, 1],[75304, 221741, 939067, 1940508, 13724641, 4570188, 15907033, 2061450, 1344124, 342683, -25495, -3806; -153, -458, -1944, -4019, -28437, -9470, -32964, -4273, -2787, -712, 51, 8; -152646, -449483, -1903548, -3933532, -27820712, -9264059, -32244558, -4178689, -2724624, -694640, 51680, 7715],51,26]
%
% END OF LATTICE L52.26
%
%
% LATTICE L52.27
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[837139278, -8890632, 290079384; -8890632, 94449, -3080736; 290079384, -3080736, 100516201],[114, 57, 1],[19327, 341465, 241016, 1494122, 10567486, 7037765, 4082617, 3174487, 344976, 263854, -19630, -5861; -38705, -683846, -482680, -2992263, -21163409, -14094470, -8176222, -6357520, -690881, -528420, 39311, 11738; -56962, -1006392, -710341, -4403592, -31145313, -20742246, -12032605, -9356094, -1016740, -777651, 57855, 17274],51,27]
%
% END OF LATTICE L52.27
%
%
% LATTICE L52.28
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[221160, -35568, 3192; -35568, 5719, -513; 3192, -513, 46],[456, 19, 1],[-29, -7, -1, 0, 1, 1, 1, -1, -1, -2, -13, -17; -678, -172, -27, -5, 8, 8, 6, -20, -21, -43, -296, -392; -5586, -1444, -234, -57, 19, 20, 0, -152, -165, -342, -2413, -3212],51,28]
%
% END OF LATTICE L52.28
%
%
% LATTICE L52.29
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-8331576, -925680, 9576; -925680, -102847, 1064; 9576, 1064, -11],[456, 19, 1],[-76, -37, -11, -1, 2, 1, -1, -7, -11, -21, -68, -89; 558, 268, 78, 4, -17, -8, 9, 56, 84, 158, 503, 656; -12369, -6384, -2064, -494, 95, 96, 0, -684, -1470, -3040, -10697, -14232],51,29]
%
% END OF LATTICE L52.29
%
%
% LATTICE L52.30
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-899688, 0, -446424; 0, 24, 0; -446424, 0, -221515],[456, 24, 1],[-129, -259, -4148, -1167, -7133, -43837, -2594, -908, -3243, 0, 131, -509; -2, -2, -19, -4, -17, -95, -5, -1, 0, 1, -1, -19; 260, 522, 8360, 2352, 14376, 88350, 5228, 1830, 6536, 0, -264, 1026],51,30]
%
% END OF LATTICE L52.30
%
%
% LATTICE L52.31
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-475152, -18696, 1824; -18696, -696, 72; 1824, 72, -7],[456, 24, 1],[1, 2, 32, 9, 55, 169, 20, 7, 25, 0, -1, 2; -1, -3, -57, -17, -110, -342, -41, -15, -57, -1, 2, 0; 248, 486, 7676, 2148, 13056, 40071, 4736, 1650, 5852, -12, -240, 513],51,31]
%
% END OF LATTICE L52.31
%
%
% LATTICE L52.32
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-10910623422, 26952853104, 13335577272; 26952853104, -66582471666, -32943291474; 13335577272, -32943291474, -16299491833],[114, 114, 1],[-161, -1423, -2008, -12447, -88025, -29311, -34006, -13220, -2873, -2196, 167, 25; -725518, -6396340, -9022739, -55925240, -395476951, -131686309, -152777755, -59390777, -12906300, -9861877, 754249, 112075; 1466230, 12926631, 18234430, 113021652, 799235874, 266130357, 308754940, 120025299, 26082880, 19930278, -1524294, -226497],51,32]
%
% END OF LATTICE L52.32
%
%
% LATTICE L52.33
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2296644, 549708, -10716; 549708, 131556, -2565; -10716, -2565, 50],[228, 57, 1],[3, 3, -1, -10, -91, -63, -38, -33, -4, -5, 1, 3; -4, -8, -2, -8, -34, -20, -10, -4, 0, 2, -2, -4; 437, 228, -319, -2565, -21318, -14574, -8683, -7296, -859, -969, 114, 438],51,33]
%
% END OF LATTICE L52.33
%
%
% LATTICE L52.34
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-66804, 0, 684; 0, 57, 0; 684, 0, -7],[228, 57, 1],[1, -1, -2, -14, -54, -73, -43, -35, -4, -4, 0, 1; -1, -6, -3, -17, -55, -72, -41, -30, -3, -1, 1, 0; 95, -114, -205, -1425, -5472, -7392, -4351, -3534, -403, -399, 0, 96],51,34]
%
% END OF LATTICE L52.34
%
%
% LATTICE L52.35
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1280220, 45600, -281352; 45600, 1292, -10260; -281352, -10260, 61661],[228, 76, 1],[14993, 2303, 1799, 951, 317, -13, -895, -289, 215, 1063, 5725, 2027; -43947, -6749, -5271, -2785, -928, 38, 2619, 845, -633, -3119, -16784, -5942; 61104, 9386, 7332, 3876, 1292, -53, -3648, -1178, 876, 4332, 23332, 8261],51,35]
%
% END OF LATTICE L52.35
%
%
% LATTICE L52.36
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[390336, -13452, -106020; -13452, 760, 3876; -106020, 3876, 28963],[228, 76, 1],[27118, 1947, 2884, 1326, 663, 202, -56, -14, 982, 2540, 10935, 7530; -82785, -5944, -8805, -4049, -2025, -617, 171, 43, -2997, -7753, -33381, -22987; 110352, 7923, 11736, 5396, 2698, 822, -228, -57, 3996, 10336, 44498, 30642],51,36]
%
% END OF LATTICE L52.36
%
%
% LATTICE L52.37
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-133608, -27816, 1368; -27816, -5757, 285; 1368, 285, -14],[456, 57, 1],[1, 5, 1, 3, 1, -1, -1, -5, -1, -3, -1, 1; -1, -12, -6, -34, -110, -144, -41, -60, -6, -2, 2, 0; 76, 228, -34, -456, -2337, -3288, -1007, -1824, -232, -342, -57, 96],51,37]
%
% END OF LATTICE L52.37
%
%
% LATTICE L52.38
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1485192, -129960, 4560; -129960, -11343, 399; 4560, 399, -14],[456, 57, 1],[1, -1, -1, -7, -54, -73, -43, -35, -2, -2, 0, 1; -2, -12, -3, -17, -110, -144, -82, -60, -3, -1, 2, 0; 266, -684, -416, -2793, -20919, -28140, -16492, -13224, -743, -684, 57, 324],51,38]
%
% END OF LATTICE L52.38
%
%
% LATTICE L52.39
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[228, 0, 0; 0, 3502308, 859560; 0, 859560, 210959],[228, 228, 1],[-1, -3, -3, -17, -55, -18, -41, -15, -3, -1, 1, 0; 429, 1315, 1557, 9289, 31896, 10565, 24379, 9317, 1987, 1343, 0, 67; -1748, -5358, -6344, -37848, -129960, -43047, -99332, -37962, -8096, -5472, 0, -273],51,39]
%
% END OF LATTICE L52.39
%
%
% LATTICE L52.40
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[456, 216372, 53124; 216372, 39634608, 9730584; 53124, 9730584, 2388929],[228, 228, 1],[35, 52, 95, 521, 1617, 1049, 1183, 209, 79, 1, -51, -5; -1978, -2953, -5384, -29502, -91445, -59306, -66860, -11798, -4450, 0, 2939, 302; 8056, 12027, 21928, 120156, 372438, 241542, 272308, 48051, 18124, 0, -11970, -1230],51,40]
%
% END OF LATTICE L52.40
%
%
% LATTICE L52.41
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[456, 0, 0; 0, -215384, 2584; 0, 2584, -31],[456, 152, 1],[1, 0, -2, -5, -41, -7, -50, -7, -5, -2, -1, 0; 0, -5, -15, -28, -173, -28, -189, -22, -12, 1, 11, 1; 0, -418, -1260, -2356, -14592, -2363, -15960, -1862, -1020, 76, 912, 83],51,41]
%
% END OF LATTICE L52.41
%
%
% LATTICE L52.42
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-11856, -2280, 912; -2280, 5624, -2128; 912, -2128, 805],[456, 152, 1],[1, -1, -2, -3, -11, -3, -8, 0, 1, 2, 5, 1; 87, -101, -219, -347, -1506, -440, -1305, -73, 45, 173, 462, 92; 228, -266, -576, -912, -3952, -1154, -3420, -190, 120, 456, 1216, 242],51,42]
%
% END OF LATTICE L52.42
%
%
% LATTICE L52.43
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-6302832, -1319208, 19608; -1319208, -275880, 4104; 19608, 4104, -61],[456, 456, 1],[-81, -34, -8, -9, 1, 1, 4, 1, -3, -24, -199, -34; -41, -15, -3, -1, 2, 0, -1, -3, -3, -17, -110, -18; -28880, -11970, -2780, -2964, 456, 321, 1216, 114, -1172, -8892, -71592, -12177],51,43]
%
% END OF LATTICE L52.43
%
%
% LATTICE L52.44
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[912, 13224, -5016; 13224, 175560, -66576; -5016, -66576, 25247],[456, 456, 1],[-5, -1, 0, 1, -1, -1, -2, -2, -1, -4, -17, -5; -2045, -821, -185, -173, 0, 16, 29, -43, -103, -691, -5184, -1744; -5396, -2166, -488, -456, 0, 42, 76, -114, -272, -1824, -13680, -4602],51,44]
%
% END OF LATTICE L52.44
%

\medskip%
%------------------------------WEYL-GROUP-W53--------------------------------
%
\leavevmode\llap{}%
$W_{53\phantom{0}}$%
\qquad\llap{12} lattices, $\chi=28$%
\hfill%
$22232223\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L53.1
%
\leavevmode%
${L_{53.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{2}{}13\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{2\rightarrow N_{53}}%
\EasyButWeakLineBreak%
{${2}\above{1pt}{1pt}{b}{2}{26}\above{1pt}{1pt}{l}{2}{20}\above{1pt}{1pt}{r}{2}{2}\above{1pt}{1pt}{-}{3}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-527020\\3120\\4680
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3120\\-18\\-29
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4680\\-29\\-38
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
12349\\1348620\\489060
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-75\\-8191\\-2970
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-105\\-11466\\-4159
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-109\\-40
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2\\-221\\-78
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7\\760\\280
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4\\436\\159
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-527020, 3120, 4680; 3120, -18, -29; 4680, -29, -38],[260, 1, 1],[-1, -2, 7, 4, 26, 67, 43, 1; -109, -221, 760, 436, 2839, 7319, 4700, 110; -40, -78, 280, 159, 1030, 2652, 1700, 39],52,1]
%
% END OF LATTICE L53.1
%
%
% LATTICE L53.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[1430, 585, -65; 585, 239, -26; -65, -26, 2],[65, 1, 1],[0, -10, 6, 11, 90, 244, 84, 7; 0, 26, -15, -28, -230, -624, -215, -18; 1, 13, -5, -11, -91, -247, -85, -7],52,2]
%
% END OF LATTICE L53.2
%
%
% LATTICE L53.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-995085, 9685, -395200; 9685, -90, 3845; -395200, 3845, -156954],[65, 5, 1],[-128, -282, 83, 492, 3238, 8368, 539, 130; 110, 208, -80, -449, -2900, -7462, -478, -109; 325, 715, -211, -1250, -8225, -21255, -1369, -330],52,3]
%
% END OF LATTICE L53.3
%
%
% LATTICE L53.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1921465, -32305, -740675; -32305, -494, -12454; -740675, -12454, -285511],[65, 13, 1],[-602, -88, 2182, 2453, 15852, 3138, 13068, 597; 39, 7, -120, -146, -969, -193, -810, -40; 1560, 228, -5655, -6357, -41080, -8132, -33865, -1547],52,4]
%
% END OF LATTICE L53.4
%
%
% LATTICE L53.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[13041080, -613340, 3204500; -613340, 28856, -150712; 3204500, -150712, 787421],[260, 4, 1],[63, 115, 444, 862, 5807, 15147, 2491, 312; 2, 0, 10, 21, 148, 390, 65, 9; -256, -468, -1805, -3504, -23604, -61568, -10125, -1268],52,5]
%
% END OF LATTICE L53.5
%
%
% LATTICE L53.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-151215740, 14271920, -1414660; 14271920, -1346990, 133515; -1414660, 133515, -13234],[260, 5, 1],[35, 68, -49, -139, -900, -2317, -297, -34; 691, 1339, -968, -2744, -17761, -45721, -5860, -670; 3230, 6240, -4528, -12825, -82980, -213590, -27372, -3125],52,6]
%
% END OF LATTICE L53.6
%
%
% LATTICE L53.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-18460, 2080, 1040; 2080, -234, -117; 1040, -117, -58],[260, 13, 1],[-1, 0, 7, 3, 16, 3, 23, 0; -9, -1, 60, 32, 199, 39, 320, 6; 0, 2, 0, -13, -130, -28, -260, -13],52,7]
%
% END OF LATTICE L53.7
%
%
% LATTICE L53.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[62010, -7087210, -2797665; -7087210, 810231565, 319837635; -2797665, 319837635, 126255403],[65, 65, 1],[8, -10, -44, -151, -758, -140, -106, 1; -10443, 12847, 56151, 192028, 960063, 177077, 133773, -2104; 26455, -32545, -142246, -486460, -2432105, -448585, -338884, 5330],52,8]
%
% END OF LATTICE L53.8
%
%
% LATTICE L53.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[19163300520, -329858620, 4713776860; -329858620, 5677880, -81138420; 4713776860, -81138420, 1159491929],[260, 20, 1],[1527, 12231, 4269, 37338, 234643, 601811, 19348, 9896; 112, 910, 316, 2761, 17338, 44460, 1429, 729; -6200, -49660, -17333, -151600, -952700, -2443480, -78557, -40180],52,9]
%
% END OF LATTICE L53.9
%
%
% LATTICE L53.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[43160, 7540, 10660; 7540, 2184, 1872; 10660, 1872, 2633],[260, 52, 1],[51, -1, 207, 446, 3199, 651, 1418, 204; 2, 0, 10, 21, 148, 30, 65, 9; -208, 4, -845, -1820, -13052, -2656, -5785, -832],52,10]
%
% END OF LATTICE L53.10
%
%
% LATTICE L53.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-21127340, 20969780, 200460; 20969780, -20813390, -198965; 200460, -198965, -1902],[260, 65, 1],[-11, -4, -11, -7, -4, 1, 5, 4; 199, 39, 64, 6, -9, -1, 12, 32; -21970, -4500, -7852, -1365, 520, 210, -728, -2925],52,11]
%
% END OF LATTICE L53.11
%
%
% LATTICE L53.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[10920, 905060, 222820; 905060, 105274520, 25912120; 222820, 25912120, 6377973],[260, 260, 1],[-19556, -3982, -1736, -1255, -314, 8, -251, -2719; -303109, -61717, -26905, -19444, -4861, 123, -3892, -42150; 1232140, 250880, 109369, 79040, 19760, -500, 15821, 171340],52,12]
%
% END OF LATTICE L53.12
%

\medskip%
%------------------------------WEYL-GROUP-W54--------------------------------
%
\leavevmode\llap{}%
$W_{54\phantom{0}}$%
\qquad\llap{32} lattices, $\chi=48$%
\hfill%
$\infty2222\infty2222\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L54.1
%
\leavevmode%
${L_{54.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}8\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{1}{}3\above{1pt}{1pt}{1}{}9\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}11\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{23\rightarrow N_{54},3,2}%
\EasyButWeakLineBreak%
{${66}\above{1pt}{1pt}{12,1}{\infty b}{264}\above{1pt}{1pt}{b}{2}{18}\above{1pt}{1pt}{s}{2}{22}\above{1pt}{1pt}{b}{2}{72}\above{1pt}{1pt}{b}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-114840\\24552\\9504
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
24552\\-5190\\-2181
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
9504\\-2181\\-410
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
375935\\1524864\\601920
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-88466\\-358835\\-141645
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-10680\\-43320\\-17101
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1874\\-7601\\-3003
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-8407\\-34100\\-13464
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1619\\-6567\\-2592
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1581\\-6413\\-2530
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-991\\-4020\\-1584
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-114840, 24552, 9504; 24552, -5190, -2181; 9504, -2181, -410],[792, 3, 1],[-1874, -8407, -1619, -1581, -991, -84, 575, 17, -377, -1145; -7601, -34100, -6567, -6413, -4020, -341, 2332, 69, -1529, -4644; -3003, -13464, -2592, -2530, -1584, -132, 924, 27, -605, -1836],53,1]
%
% END OF LATTICE L54.1
%
%
% LATTICE L54.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[66, 0, 0; 0, 0, -1; 0, -1, 0],[66, 1, 1],[-1, 1, 0, -2, -1, -10, -23, -3, -9, -1; 0, 0, -1, -11, -4, -33, -66, -8, -22, -2; -33, 0, 1, -11, -8, -99, -264, -37, -121, -16],53,2]
%
% END OF LATTICE L54.2
%
%
% LATTICE L54.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-2461272, -598752, -34320; -598752, -145658, -8349; -34320, -8349, -478],[264, 1, 1],[-128, 289, 8, -190, -213, -1115, -5261, -347, -1053, -239; 528, -1188, -33, 781, 876, 4587, 21648, 1428, 4334, 984; -33, 0, 2, 0, -8, -66, -396, -29, -99, -28],53,3]
%
% END OF LATTICE L54.3
%
%
% LATTICE L54.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-3804174, -354024, -132858; -354024, -32946, -12363; -132858, -12363, -4634],[198, 3, 1],[384, -65, -64, 108, 287, 1222, 3277, 1378, 1498, 589; -4411, 748, 735, -1243, -3300, -14047, -37664, -15837, -17215, -6768; 759, -132, -126, 220, 576, 2442, 6534, 2745, 2981, 1170],53,4]
%
% END OF LATTICE L54.4
%
%
% LATTICE L54.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1184700, 2178, -574398; 2178, -4, 1056; -574398, 1056, -278495],[66, 2, 1],[386, 467, 125, 387, 23, 65, -16, -2, 64, 18; 1023, 1551, 456, 1562, 111, 528, 0, -33, -11, 30; -792, -957, -256, -792, -47, -132, 33, 4, -132, -37],53,5]
%
% END OF LATTICE L54.5
%
%
% LATTICE L54.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-789690, 2178, -251262; 2178, -6, 693; -251262, 693, -79946],[66, 3, 1],[92, 227, 92, 288, 35, 18, -7, -2, 42, 25; 341, 1034, 456, 1562, 222, 176, 0, -33, -11, 60; -286, -704, -285, -891, -108, -55, 22, 6, -132, -78],53,6]
%
% END OF LATTICE L54.6
%
%
% LATTICE L54.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[164604, 10890, 80784; 10890, 3264, 5346; 80784, 5346, 39647],[66, 6, 1],[38435, 47844, 39070, 123888, 7766, 9382, -27, 53, 19563, 5275; 44, 55, 45, 143, 9, 11, 0, 0, 22, 6; -78320, -97493, -79614, -252450, -15825, -19118, 55, -108, -39864, -10749],53,7]
%
% END OF LATTICE L54.7
%
%
% LATTICE L54.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-842094, -80388, 21780; -80388, -7674, 2079; 21780, 2079, -544],[198, 3, 1],[373, -21, -22, 104, 61, 892, 2551, 367, 3691, 169; -3916, 220, 231, -1089, -640, -9361, -26774, -3852, -38742, -1774; -33, 0, 2, 0, -4, -66, -198, -29, -297, -14],53,8]
%
% END OF LATTICE L54.8
%
%
% LATTICE L54.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-66, -2178, 0; -2178, -5984, 363; 0, 363, 2],[66, 11, 1],[176, 541, 879, 275, 433, 95, 1, -66, -4, 109; -6, -18, -29, -9, -14, -3, 0, 2, 0, -4; 963, 2964, 4818, 1508, 2376, 522, 6, -363, -23, 594],53,9]
%
% END OF LATTICE L54.9
%
%
% LATTICE L54.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1687752, 397848, 16368; 397848, -93774, -3861; 16368, -3861, -158],[264, 3, 1],[15, -107, -3, 211, 213, 348, 1559, 300, 878, 183; 55, -396, -11, 781, 788, 1287, 5764, 1109, 3245, 676; 209, -1408, -42, 2772, 2808, 4598, 20636, 3975, 11649, 2436],53,10]
%
% END OF LATTICE L54.10
%
%
% LATTICE L54.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[5544, -35046, 3762; -35046, 688056, -37308; 3762, -37308, 2945],[198, 6, 1],[22359, 376, 205, 14655, 11888, 87179, 109162, 89417, 94883, 17986; -1309, -22, -12, -858, -696, -5104, -6391, -5235, -5555, -1053; -45144, -759, -414, -29590, -24003, -176022, -220407, -180540, -191576, -36315],53,11]
%
% END OF LATTICE L54.11
%
%
% LATTICE L54.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[21245400, -3236310, 10618146; -3236310, 493008, -1617462; 10618146, -1617462, 5306797],[198, 6, 1],[9566, 343, -1, 16355, 1519, 34115, 43338, 11914, 114688, 2452; -649, -22, 0, -1122, -104, -2332, -2959, -813, -7821, -167; -19338, -693, 2, -33066, -3071, -68970, -87615, -24086, -231858, -4957],53,12]
%
% END OF LATTICE L54.12
%
%
% LATTICE L54.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[5283696, 15246, 2516052; 15246, 44, 7260; 2516052, 7260, 1198123],[66, 22, 1],[-452, -545, -1605, -453, -299, -83, 10, 0, -82, -236; 195, 243, 728, 210, 145, 48, 0, 1, 33, 98; 948, 1143, 3366, 950, 627, 174, -21, 0, 172, 495],53,13]
%
% END OF LATTICE L54.13
%
%
% LATTICE L54.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3886608, 617496, -121704; 617496, -98064, 19336; -121704, 19336, -3811],[264, 8, 1],[590, -31, -33, 113, 61, 1643, 2264, 642, 2120, 142; -33, 0, 2, 0, -2, -66, -99, -29, -99, -7; -19008, 990, 1064, -3608, -1958, -52800, -72798, -20648, -68200, -4570],53,14]
%
% END OF LATTICE L54.14
%
%
% LATTICE L54.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1754082, -10758, -532686; -10758, 66, 3267; -532686, 3267, 161768],[66, 33, 1],[70, 169, 747, 211, 279, 13, -3, 0, 38, 219; -75, -176, -766, -212, -268, -10, 6, 1, -43, -242; 232, 560, 2475, 699, 924, 43, -10, 0, 126, 726],53,15]
%
% END OF LATTICE L54.15
%
%
% LATTICE L54.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3682008, -327096, 41976; -327096, -29058, 3729; 41976, 3729, -478],[792, 3, 1],[-16, 43, 1, -85, -31, -160, -747, -49, -443, -33; 176, -484, -11, 957, 348, 1793, 8360, 548, 4950, 368; -33, 0, 2, 0, -8, -66, -396, -29, -297, -28],53,16]
%
% END OF LATTICE L54.16
%
%
% LATTICE L54.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[25080, 11880, -528; 11880, 3146, 99; -528, 99, -38],[264, 11, 1],[-1, 35, 1, -23, -245, -106, -463, -322, -84, -183; 3, -108, -3, 71, 756, 327, 1428, 993, 259, 564; 21, -768, -22, 504, 5368, 2322, 10140, 7051, 1839, 4004],53,17]
%
% END OF LATTICE L54.17
%
%
% LATTICE L54.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[37620, 20130, 9306; 20130, -4884, -2244; 9306, -2244, -1031],[66, 66, 1],[-2, -3, -29, -9, -7, -1, 0, 2, 0, -2; -1707, -2633, -25700, -8050, -6349, -932, -6, 1949, 133, -1568; 3700, 5707, 55704, 17448, 13761, 2020, 13, -4224, -288, 3399],53,18]
%
% END OF LATTICE L54.18
%
%
% LATTICE L54.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-11757980784, -50527224, 135015936; -50527224, -217104, 580200; 135015936, 580200, -1550377],[264, 24, 1],[2691, -361, -393, 3947, 1371, 10773, 13825, 11409, 36445, 2301; -11, 0, 2, 0, -2, -22, -33, -29, -99, -7; 234344, -31438, -34224, 343728, 119394, 938168, 1203950, 993552, 3173808, 200382],53,19]
%
% END OF LATTICE L54.19
%
%
% LATTICE L54.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-208890, 743688, -61182; 743688, -2645742, 217635; -61182, 217635, -17902],[198, 33, 1],[-30, 29, 32, -48, -841, -262, -613, -2660, -244, -911; -61, 58, 66, -96, -1686, -526, -1232, -5349, -491, -1836; -639, 606, 693, -1003, -17622, -5499, -12882, -55935, -5135, -19206],53,20]
%
% END OF LATTICE L54.20
%
%
% LATTICE L54.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-196218, 105534, 9306; 105534, -55704, -4917; 9306, -4917, -434],[198, 33, 1],[2, -1, -1, 5, 11, 11, 27, 40, 34, 15; -68, 32, 35, -159, -356, -359, -886, -1316, -1122, -498; 813, -384, -418, 1908, 4268, 4302, 10614, 15763, 13437, 5962],53,21]
%
% END OF LATTICE L54.21
%
%
% LATTICE L54.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-28248, -3432, 2376; -3432, -198, 165; 2376, 165, -130],[264, 33, 1],[1, -1, -2, 2, 29, 5, 25, 56, 16, 43; 37, -36, -75, 71, 1044, 181, 908, 2037, 583, 1572; 65, -64, -132, 126, 1848, 320, 1604, 3597, 1029, 2772],53,22]
%
% END OF LATTICE L54.22
%
%
% LATTICE L54.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[988434216, -34860078, 488697462; -34860078, 1229448, -17235372; 488697462, -17235372, 241619731],[198, 66, 1],[2367, 79, 98, 1400, 12739, 8618, 10906, 98767, 9585, 20216; 329, 11, 3, 191, 1749, 1187, 1505, 13641, 1325, 2799; -4764, -159, -198, -2818, -25641, -17346, -21951, -198792, -19292, -40689],53,23]
%
% END OF LATTICE L54.23
%
%
% LATTICE L54.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[615558240, 17207190, 304654284; 17207190, 481008, 8516244; 304654284, 8516244, 150780587],[198, 66, 1],[1344, 46, -11, 2287, 2344, 4791, 6089, 18416, 16118, 3791; 43, 1, 4, 90, 87, 172, 214, 641, 555, 128; -2718, -93, 22, -4626, -4741, -9690, -12315, -37246, -32598, -7667],53,24]
%
% END OF LATTICE L54.24
%
%
% LATTICE L54.25
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-218422512, -17207784, -912384; -17207784, -1355664, -71880; -912384, -71880, -3811],[792, 24, 1],[238, -31, -35, 113, 119, 939, 1208, 998, 1064, 202; -2629, 341, 387, -1243, -1311, -10351, -13321, -11007, -11737, -2229; -7392, 990, 1080, -3608, -3762, -29568, -37950, -31320, -33352, -6318],53,25]
%
% END OF LATTICE L54.25
%
%
% LATTICE L54.26
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1471730832, -126917208, -12184128; -126917208, -10944912, -1050696; -12184128, -1050696, -100811],[792, 24, 1],[-12027, 629, 673, -6877, -1241, -33447, -46103, -13075, -129545, -2893; 144914, -7579, -8109, 82863, 14953, 403007, 555500, 157542, 1560900, 34858; -56760, 2970, 3176, -32472, -5858, -157872, -217602, -61712, -611424, -13654],53,26]
%
% END OF LATTICE L54.26
%
%
% LATTICE L54.27
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-9311021808, 9230066472, 77113872; 9230066472, -9149814960, -76443400; 77113872, -76443400, -638657],[264, 88, 1],[-386, 121, 139, -441, -1341, -2579, -3086, -9034, -2524, -1624; -3, 0, 2, 0, -2, -6, -9, -29, -9, -7; -46248, 14610, 16544, -53248, -161678, -310680, -371538, -1087328, -303680, -195250],53,27]
%
% END OF LATTICE L54.27
%
%
% LATTICE L54.28
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-84744, -415008, -34848; -415008, -1981650, -166221; -34848, -166221, -13942],[792, 33, 1],[144, 721, 1616, 154, 1243, 29, -29, -59, 19, 833; -737, -3692, -8277, -789, -6372, -149, 148, 303, -97, -4260; 8427, 42216, 94644, 9022, 72864, 1704, -1692, -3465, 1109, 48708],53,28]
%
% END OF LATTICE L54.28
%
%
% LATTICE L54.29
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1288584, 153648, -7128; 153648, -17886, 825; -7128, 825, -38],[792, 33, 1],[3, 13, 9, 7, 5, 0, -1, 0, 2, 7; 133, 580, 403, 315, 228, 1, -44, -1, 87, 308; 2322, 10140, 7051, 5517, 4004, 21, -768, -22, 1512, 5368],53,29]
%
% END OF LATTICE L54.29
%
%
% LATTICE L54.30
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2044944, -13626888, -3288120; -13626888, -90595824, -21860256; -3288120, -21860256, -5274755],[264, 264, 1],[-589, -683, -5903, -1617, -997, -63, 31, 35, -339, -959; 22805, 26440, 228494, 62584, 38578, 2434, -1201, -1343, 13133, 37139; -94144, -109150, -943272, -258360, -159258, -10048, 4958, 5544, -54216, -153318],53,30]
%
% END OF LATTICE L54.30
%
%
% LATTICE L54.31
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-151406640, -47522376, 4549248; -47522376, -14864784, 1423224; 4549248, 1423224, -136265],[792, 264, 1],[-589, -683, -5903, -539, -997, -63, 31, 35, -113, -959; -36457, -42274, -365358, -33360, -61704, -3898, 1919, 2163, -6995, -59361; -400440, -464334, -4013064, -366424, -677754, -42816, 21078, 23760, -76832, -652014],53,31]
%
% END OF LATTICE L54.31
%
%
% LATTICE L54.32
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1542234672, -2090830104, 712765152; -2090830104, -2834568528, 966306000; 712765152, 966306000, -329414257],[792, 264, 1],[-187, 61, 65, -667, -671, -1285, -1533, -4481, -3749, -801; -6121, 1982, 2142, -21672, -21832, -41842, -49945, -146031, -122217, -26131; -18360, 5946, 6424, -65016, -65494, -125520, -149826, -438064, -366624, -78386],53,32]
%
% END OF LATTICE L54.32
%

\medskip%
%------------------------------WEYL-GROUP-W55--------------------------------
%
\leavevmode\llap{}%
$W_{55\phantom{0}}$%
\qquad\llap{24} lattices, $\chi=20$%
\hfill%
$622622\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L55.1
%
\leavevmode%
${L_{55.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}8\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{-}{}9\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{2}{}11\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{23\rightarrow N_{55},3,2}%
\EasyButWeakLineBreak%
{${18}\above{1pt}{1pt}{}{6}{6}\above{1pt}{1pt}{b}{2}{72}\above{1pt}{1pt}{b}{2}{2}\above{1pt}{1pt}{}{6}{6}\above{1pt}{1pt}{b}{2}{8}\above{1pt}{1pt}{b}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-16860888\\101376\\-15048
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
101376\\-606\\87
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-15048\\87\\-10
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4\\783\\792
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-196\\-201
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-19\\-3720\\-3780
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-8\\-1566\\-1589
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3\\-587\\-594
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\196\\200
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-16860888, 101376, -15048; 101376, -606, 87; -15048, 87, -10],[792, 3, 1],[4, -1, -19, -8, -3, 1; 783, -196, -3720, -1566, -587, 196; 792, -201, -3780, -1589, -594, 200],54,1]
%
% END OF LATTICE L55.1
%
%
% LATTICE L55.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[2706, 858, 66; 858, 272, 21; 66, 21, 2],[66, 1, 1],[1, -2, 21, 74, 47, 9; -3, 6, -66, -232, -147, -28; -1, 3, -10, -39, -27, -6],54,2]
%
% END OF LATTICE L55.2
%
%
% LATTICE L55.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[52008, -5280, 264; -5280, -1006, 127; 264, 127, -14],[264, 1, 1],[4, -5, -33, -44, -19, 1; 79, -99, -652, -869, -375, 20; 792, -993, -6540, -8717, -3762, 200],54,3]
%
% END OF LATTICE L55.3
%
%
% LATTICE L55.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-922086, 3762, 7722; 3762, -12, -33; 7722, -33, -64],[198, 3, 1],[-1, 3, 11, 7, 1, -1; -42, 131, 474, 299, 40, -44; -99, 294, 1080, 688, 99, -98],54,4]
%
% END OF LATTICE L55.4
%
%
% LATTICE L55.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-305052, 6270, -150942; 6270, -128, 3102; -150942, 3102, -74687],[66, 2, 1],[30, -125, 757, 5275, 3308, 304; -33, 129, -744, -5197, -3267, -302; -62, 258, -1561, -10878, -6822, -627],54,5]
%
% END OF LATTICE L55.5
%
%
% LATTICE L55.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-358842, 8316, -118206; 8316, -192, 2739; -118206, 2739, -38938],[66, 3, 1],[19, -27, 997, 3471, 725, 399; -33, 43, -1488, -5197, -1089, -604; -60, 85, -3132, -10905, -2278, -1254],54,6]
%
% END OF LATTICE L55.6
%
%
% LATTICE L55.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[7591980, -217206, 3725634; -217206, 6240, -106590; 3725634, -106590, 1828291],[66, 6, 1],[53, 967, -33161, -225873, -46131, -12003; 0, 9, -300, -2045, -418, -109; -108, -1970, 67557, 460158, 93980, 24453],54,7]
%
% END OF LATTICE L55.7
%
%
% LATTICE L55.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1014882, -13794, 182094; -13794, -176, 2475; 182094, 2475, -32672],[66, 11, 1],[-77, 302, -3493, -12198, -7667, -1417; 2, -3, -10, -27, -12, 0; -429, 1683, -19470, -67991, -42735, -7898],54,8]
%
% END OF LATTICE L55.8
%
%
% LATTICE L55.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1577928, -12408, 18480; -12408, -42, 117; 18480, 117, -202],[264, 3, 1],[4, -5, -43, -44, -3, 11; 264, -331, -2844, -2909, -198, 728; 519, -649, -5580, -5709, -389, 1428],54,9]
%
% END OF LATTICE L55.9
%
%
% LATTICE L55.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[97777944, -1350558, 48384864; -1350558, 18660, -668316; 48384864, -668316, 23942977],[198, 6, 1],[196, 1541, 4859, 8273, 3462, 48; 3, 4, 9, 14, 5, 0; -396, -3114, -9819, -16718, -6996, -97],54,10]
%
% END OF LATTICE L55.10
%
%
% LATTICE L55.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[14370576, 18150, 6845652; 18150, 44, 8646; 6845652, 8646, 3261035],[66, 22, 1],[0, -3427, 38090, 259645, 159214, 13839; 1, 15, -184, -1251, -765, -66; 0, 7194, -79959, -545050, -334224, -29051],54,11]
%
% END OF LATTICE L55.11
%
%
% LATTICE L55.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-23228304, 936408, -11393976; 936408, -37744, 459328; -11393976, 459328, -5588987],[264, 8, 1],[-263, 1507, 1149, 4973, 1319, -207; -2, 3, 5, 27, 12, 0; 536, -3072, -2342, -10136, -2688, 422],54,12]
%
% END OF LATTICE L55.12
%
%
% LATTICE L55.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[4915482, -12936, -1484934; -12936, 66, 3927; -1484934, 3927, 448600],[66, 33, 1],[0, 519, -34611, -117965, -24112, -12575; 1, -1033, 68854, 234679, 47969, 25018; 0, 1727, -115170, -392535, -80234, -41844],54,13]
%
% END OF LATTICE L55.13
%
%
% LATTICE L55.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3989832, 210144, 112728; 210144, -11066, -5929; 112728, -5929, -3154],[264, 11, 1],[494, 209, -15, -44, 61, 375; 10967, 4641, -332, -977, 1353, 8324; -2959, -1254, 88, 264, -363, -2244],54,14]
%
% END OF LATTICE L55.14
%
%
% LATTICE L55.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-56240844, -37499154, -17325462; -37499154, -25002912, -11551914; -17325462, -11551914, -5337247],[66, 66, 1],[2, -1, -5, -27, -4, 0; 2345, -3119, 54850, 382825, 80153, 22184; -5082, 6754, -118701, -828498, -173470, -48015],54,15]
%
% END OF LATTICE L55.15
%
%
% LATTICE L55.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-72336, 40392, -915288; 40392, -17904, 409824; -915288, 409824, -9376313],[264, 24, 1],[6134, 443, -347, -439, 696, 1486; -270181, -19510, 15286, 19336, -30659, -65455; -12408, -896, 702, 888, -1408, -3006],54,16]
%
% END OF LATTICE L55.16
%
%
% LATTICE L55.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-56826, 72666, 23562; 72666, -92796, -30063; 23562, -30063, -9734],[198, 33, 1],[-221, -12, 41, 28, -115, -377; -433, -20, 82, 54, -229, -744; 803, 33, -154, -99, 429, 1386],54,17]
%
% END OF LATTICE L55.17
%
%
% LATTICE L55.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-528792, -509520, 41448; -509520, -490710, 39897; 41448, 39897, -3242],[264, 33, 1],[578, 40, -143, -53, 65, 563; -1161, -80, 288, 106, -131, -1132; -6897, -473, 1716, 627, -781, -6732],54,18]
%
% END OF LATTICE L55.18
%
%
% LATTICE L55.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[50275368, 5823378, 24972156; 5823378, 674520, 2892516; 24972156, 2892516, 12403859],[198, 66, 1],[-829, -332, -5, -98, -185, -502; -579, -247, -4, -3, -101, -336; 1804, 726, 11, 198, 396, 1089],54,19]
%
% END OF LATTICE L55.19
%
%
% LATTICE L55.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-114971472, -6002568, -90010008; -6002568, -313296, -4698840; -90010008, -4698840, -70465139],[792, 24, 1],[-931, 4416, 7564, 9242, 943, -735; -10239, 48575, 83199, 101653, 10369, -8085; 1872, -8880, -15210, -18584, -1896, 1478],54,20]
%
% END OF LATTICE L55.20
%
%
% LATTICE L55.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-19989552, -6269736, 138600; -6269736, -1966448, 43472; 138600, 43472, -961],[264, 88, 1],[-11, 65, 49, 211, 55, -9; 2, -3, -5, -27, -12, 0; -1496, 9240, 6842, 29216, 7392, -1298],54,21]
%
% END OF LATTICE L55.21
%
%
% LATTICE L55.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-27720, -26928, 17424; -26928, -6666, 6171; 17424, 6171, -5018],[792, 33, 1],[-445, -165, 57, 220, -58, -1063; -2652, -983, 340, 1311, -346, -6336; -4807, -1782, 616, 2376, -627, -11484],54,22]
%
% END OF LATTICE L55.22
%
%
% LATTICE L55.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-34320, -152856, 52008; -152856, -671088, 228360; 52008, 228360, -77707],[264, 264, 1],[156, 11, -9, -11, 18, 38; 3827, 237, -245, -267, 475, 957; 11352, 704, -726, -792, 1408, 2838],54,23]
%
% END OF LATTICE L55.23
%
%
% LATTICE L55.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-61517808, -35067384, 243144; -35067384, -19989552, 138600; 243144, 138600, -961],[792, 264, 1],[-9, -4, 0, 2, -1, -5; 103, 7, -9, -9, 53, 87; 12584, 0, -1298, -792, 7392, 11286],54,24]
%
% END OF LATTICE L55.24
%

\medskip%
%------------------------------WEYL-GROUP-W56--------------------------------
%
\leavevmode\llap{}%
$W_{56\phantom{0}}$%
\qquad\llap{12} lattices, $\chi=12$%
\hfill%
$222222$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L56.1
%
\leavevmode%
${L_{56.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{-2}{}23\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2\rightarrow N_{56}}%
\EasyButWeakLineBreak%
{${12}\above{1pt}{1pt}{*}{2}{92}\above{1pt}{1pt}{b}{2}{2}\above{1pt}{1pt}{b}{2}{138}\above{1pt}{1pt}{l}{2}{4}\above{1pt}{1pt}{r}{2}{46}\above{1pt}{1pt}{b}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-5244\\276\\0
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
276\\-2\\-5
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\-5\\2
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\18\\48
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5\\92\\230
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\-1
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-7\\-138\\-345
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-20\\-48
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-23\\-46
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-5244, 276, 0; 276, -2, -5; 0, -5, 2],[276, 1, 1],[1, 5, 0, -7, -1, -1; 18, 92, 0, -138, -20, -23; 48, 230, -1, -345, -48, -46],55,1]
%
% END OF LATTICE L56.1
%
%
% LATTICE L56.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[1794, -621, 0; -621, 215, 0; 0, 0, -1],[69, 1, 1],[1, 8, -1, -119, -9, -40; 3, 23, -3, -345, -26, -115; 0, 0, -1, -69, -5, -23],55,2]
%
% END OF LATTICE L56.2
%
%
% LATTICE L56.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-109434, 966, 36777; 966, 3, -327; 36777, -327, -12359],[69, 3, 1],[-49, 70, 74, -832, -288, -2029; -30, 46, 45, -529, -181, -1265; -145, 207, 219, -2461, -852, -6003],55,3]
%
% END OF LATTICE L56.3
%
%
% LATTICE L56.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-126132, -552, 1380; -552, 6, 3; 1380, 3, -14],[276, 3, 1],[1, 13, 0, -3, -1, 2; 38, 506, 1, -115, -40, 69; 106, 1380, 0, -322, -108, 207],55,4]
%
% END OF LATTICE L56.4
%
%
% LATTICE L56.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[3802728, -24012, 935640; -24012, 152, -5908; 935640, -5908, 230209],[276, 4, 1],[31, 102, 2, 340, 16, 249; 0, 23, 5, 69, 1, 0; -126, -414, -8, -1380, -65, -1012],55,5]
%
% END OF LATTICE L56.5
%
%
% LATTICE L56.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-563178, -6693, 195684; -6693, -23, 2323; 195684, 2323, -67993],[69, 23, 1],[-766, 17, 383, -587, -1540, -468; -99, 2, 50, -72, -192, -59; -2208, 49, 1104, -1692, -4439, -1349],55,6]
%
% END OF LATTICE L56.6
%
%
% LATTICE L56.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[22620408, -369012, 5569956; -369012, 6024, -90864; 5569956, -90864, 1371523],[276, 12, 1],[97, 1733, 133, 589, 48, 1087; -1, 0, 2, 0, -1, -23; -394, -7038, -540, -2392, -195, -4416],55,7]
%
% END OF LATTICE L56.7
%
%
% LATTICE L56.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[66102, 59133, 1311; 59133, 52923, 1173; 1311, 1173, 26],[69, 69, 1],[-1, 0, 1, -1, -7, -2; -3, 1, 2, -8, -49, -12; 184, -45, -138, 410, 2553, 639],55,8]
%
% END OF LATTICE L56.8
%
%
% LATTICE L56.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1380, 276, 276; 276, -46, -23; 276, -23, 58],[276, 23, 1],[1, 5, 11, 4, -1, -1; 6, 34, 75, 27, -8, -7; 0, -10, -23, -9, 0, 2],55,9]
%
% END OF LATTICE L56.9
%
%
% LATTICE L56.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[276, -276, -276; -276, 138, 69; -276, 69, -34],[276, 69, 1],[21, 11, 0, -1, -1, 4; 64, 34, 1, -3, -4, 12; -46, -24, 0, 2, 0, -9],55,10]
%
% END OF LATTICE L56.10
%
%
% LATTICE L56.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[9384, 22356, 14352; 22356, 52072, 33304; 14352, 33304, 21287],[276, 92, 1],[103, -25, -227, -175, -74, 1; -309, 76, 686, 528, 223, -3; 414, -102, -920, -708, -299, 4],55,11]
%
% END OF LATTICE L56.11
%
%
% LATTICE L56.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[85560, 170844, 42504; 170844, 341688, 85008; 42504, 85008, 21149],[276, 276, 1],[-1, 0, 2, 0, -1, -1; -194, -97, -1, -1, -51, -98; 782, 390, 0, 4, 207, 396],55,12]
%
% END OF LATTICE L56.12
%

\medskip%
%------------------------------WEYL-GROUP-W57--------------------------------
%
\leavevmode\llap{}%
$W_{57\phantom{0}}$%
\qquad\llap{16} lattices, $\chi=24$%
\hfill%
$22222222\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L57.1
%
\leavevmode%
${L_{57.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}8\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{2}{}7\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2\rightarrow N_{57}}%
\EasyButWeakLineBreak%
{${10}\above{1pt}{1pt}{s}{2}{14}\above{1pt}{1pt}{b}{2}{2}\above{1pt}{1pt}{l}{2}{56}\above{1pt}{1pt}{r}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3640\\1400\\0
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1400\\538\\1
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\1\\-2
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\0\\0
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\-1\\-1
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\1
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2\\5\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
8\\-21\\-14
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5\\-13\\-8
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
65\\-168\\-112
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[3640, 1400, 0; 1400, 538, 1; 0, 1, -2],[280, 1, 1],[-2, 8, 5, 65, 2, -8, -5, -65; 5, -21, -13, -168, -5, 21, 13, 168; 0, -14, -8, -112, -5, 7, 5, 56],56,1]
%
% END OF LATTICE L57.1
%
%
% LATTICE L57.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-1610, -770, 70; -770, -368, 35; 70, 35, 6],[70, 1, 1],[17, 17, -15, -305, -92, -122, -30, -115; -35, -35, 31, 630, 190, 252, 62, 238; 5, 7, -5, -112, -35, -49, -13, -56],56,2]
%
% END OF LATTICE L57.2
%
%
% LATTICE L57.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3080, -490, -1470; -490, 96, -244; -1470, -244, -701],[70, 2, 1],[-34, 184, 110, 351, 39, -177, -107, -337; 5, -21, -13, -42, -5, 21, 13, 42; 70, -378, -226, -721, -80, 364, 220, 693],56,3]
%
% END OF LATTICE L57.3
%
%
% LATTICE L57.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2590, -1120, -490; -1120, 240, 225; -490, 225, 92],[70, 5, 1],[3, -89, -53, -341, -4, 82, 50, 313; 1, -21, -13, -84, -1, 21, 13, 84; 14, -420, -250, -1610, -19, 385, 235, 1470],56,4]
%
% END OF LATTICE L57.4
%
%
% LATTICE L57.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[4970, -1540, -1400; -1540, 336, 441; -1400, 441, 394],[70, 7, 1],[21, -19, -79, -73, -31, 17, 73, 65; 5, -3, -13, -12, -5, 3, 13, 12; 70, -64, -266, -246, -105, 57, 245, 218],56,5]
%
% END OF LATTICE L57.5
%
%
% LATTICE L57.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1465660, -19530, 696430; -19530, 260, -9280; 696430, -9280, 330919],[70, 10, 1],[59, 333, 57, 16, -21, -67, 57, 516; 6, 28, -2, -49, -7, -35, -1, 35; -124, -700, -120, -35, 44, 140, -120, -1085],56,6]
%
% END OF LATTICE L57.6
%
%
% LATTICE L57.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[575540, -14490, 267470; -14490, 364, -6734; 267470, -6734, 124301],[70, 14, 1],[261, 41, 39, -9, -131, -15, 39, 61; 30, 4, -2, -7, -35, -5, -1, 5; -560, -88, -84, 19, 280, 32, -84, -131],56,7]
%
% END OF LATTICE L57.7
%
%
% LATTICE L57.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[31640, -560, -280; -560, 10, 5; -280, 5, 2],[280, 5, 1],[0, -4, -3, -57, -1, -3, 0, 1; 0, -182, -136, -2576, -45, -133, 1, 56; -1, -105, -75, -1400, -24, -70, 0, 0],56,8]
%
% END OF LATTICE L57.8
%
%
% LATTICE L57.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[5320, -280, 280; -280, 14, -21; 280, -21, -38],[280, 7, 1],[16, 4, 9, 13, -1, -1, 0, 11; 270, 68, 154, 224, -15, -17, -1, 184; -35, -9, -21, -32, 0, 2, 0, -24],56,9]
%
% END OF LATTICE L57.9
%
%
% LATTICE L57.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1680, -840, -280; -840, 176, 64; -280, 64, 23],[280, 8, 1],[-1, 1, 1, 2, 1, -1, -1, -2; 40, -14, -24, -49, -25, 35, 33, 70; -120, 56, 80, 161, 80, -112, -104, -217],56,10]
%
% END OF LATTICE L57.10
%
%
% LATTICE L57.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[267330, -15610, 50960; -15610, 910, -2975; 50960, -2975, 9714],[70, 35, 1],[-20, -16, -18, 1, 8, 4, -18, -49; 46, 36, 34, -16, -23, -13, 35, 108; 119, 95, 105, -10, -49, -25, 105, 290],56,11]
%
% END OF LATTICE L57.11
%
%
% LATTICE L57.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[77980, -237930, -116410; -237930, 709940, 347340; -116410, 347340, 169937],[70, 70, 1],[1, -3, -13, -6, -1, 3, 13, 6; 288, -1322, -5484, -2529, -425, 1185, 5073, 2255; -588, 2700, 11200, 5165, 868, -2420, -10360, -4605],56,12]
%
% END OF LATTICE L57.12
%
%
% LATTICE L57.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[113960, -4200, -840; -4200, 70, 35; -840, 35, 6],[280, 35, 1],[2, 2, 3, 1, -1, -1, 0, 7; 11, 11, 17, 8, -5, -5, 1, 40; 217, 215, 315, 80, -112, -110, 0, 760],56,13]
%
% END OF LATTICE L57.13
%
%
% LATTICE L57.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1081360, -92680, 5600; -92680, -7920, 480; 5600, 480, -29],[280, 40, 1],[-3, -13, -1, 2, 1, -1, -5, -16; -2, 0, 2, 0, -1, -21, -11, -21; -616, -2520, -160, 385, 176, -560, -1160, -3465],56,14]
%
% END OF LATTICE L57.14
%
%
% LATTICE L57.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[560, -13720, 280; -13720, 329616, -6720; 280, -6720, 137],[280, 56, 1],[14, 4, 10, 2, 1, -1, -1, 1; -5, 1, 5, 1, 0, -2, -8, -2; -280, 40, 224, 45, 0, -96, -392, -101],56,15]
%
% END OF LATTICE L57.15
%
%
% LATTICE L57.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-7280, -3640, 560; -3640, -1680, 280; 560, 280, -43],[280, 280, 1],[-3, -3, -1, 2, 5, 5, 7, 0; -2, 0, 2, 0, -1, -3, -11, -3; -56, -40, 0, 25, 56, 40, 0, -25],56,16]
%
% END OF LATTICE L57.16
%

\medskip%
%------------------------------WEYL-GROUP-W58--------------------------------
%
\leavevmode\llap{}%
$W_{58\phantom{0}}$%
\qquad\llap{12} lattices, $\chi=20$%
\hfill%
$2222232$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L58.1
%
\leavevmode%
${L_{58.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{-2}{}7\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{2}{}11\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2\rightarrow N_{58}}%
\EasyButWeakLineBreak%
{${28}\above{1pt}{1pt}{*}{2}{44}\above{1pt}{1pt}{b}{2}{14}\above{1pt}{1pt}{l}{2}{4}\above{1pt}{1pt}{r}{2}{154}\above{1pt}{1pt}{b}{2}{2}\above{1pt}{1pt}{+}{3}{2}\above{1pt}{1pt}{b}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-19740028\\77308\\-33264
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
77308\\-302\\127
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-33264\\127\\-42
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
11\\3122\\728
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-29\\-8228\\-1914
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-41\\-11634\\-2709
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-137\\-38876\\-9056
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-912\\-258797\\-60291
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-5\\-1419\\-331
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4\\1135\\264
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-19740028, 77308, -33264; 77308, -302, 127; -33264, 127, -42],[308, 1, 1],[11, -29, -41, -137, -912, -5, 4; 3122, -8228, -11634, -38876, -258797, -1419, 1135; 728, -1914, -2709, -9056, -60291, -331, 264],57,1]
%
% END OF LATTICE L58.1
%
%
% LATTICE L58.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[1386, 385, 0; 385, 107, 0; 0, 0, -1],[77, 1, 1],[-2, -3, 6, 23, 345, 5, 3; 7, 11, -21, -82, -1232, -18, -11; 0, 0, -7, -21, -308, -4, -3],57,2]
%
% END OF LATTICE L58.2
%
%
% LATTICE L58.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-38731, 7392, -11396; 7392, -1239, 2156; -11396, 2156, -3351],[77, 7, 1],[35, 64, -55, -857, -1713, -109, 86; -14, -22, 23, 353, 704, 44, -35; -128, -231, 202, 3143, 6281, 399, -315],57,3]
%
% END OF LATTICE L58.3
%
%
% LATTICE L58.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-479941, 7623, -133672; 7623, -55, 2123; -133672, 2123, -37230],[77, 11, 1],[536, 10, -901, -1961, -2486, -242, 193; -7, -1, -7, -2, 0, 2, -1; -1925, -36, 3234, 7040, 8925, 869, -693],57,4]
%
% END OF LATTICE L58.4
%
%
% LATTICE L58.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1021992664, -60679388, 251966176; -60679388, 3602760, -14960140; 251966176, -14960140, 62120753],[308, 4, 1],[107, -4718, -12928, -12208, -334119, -2593, -685; 0, -77, -203, -189, -5159, -39, -10; -434, 19118, 52388, 49471, 1353968, 10508, 2776],57,5]
%
% END OF LATTICE L58.5
%
%
% LATTICE L58.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1006852, -46816, 5852; -46816, -2114, 273; 5852, 273, -34],[308, 7, 1],[1, -29, -5, -109, -102, -3, 4; -2, 66, 11, 236, 220, 6, -9; 156, -4466, -773, -16884, -15807, -469, 616],57,6]
%
% END OF LATTICE L58.6
%
%
% LATTICE L58.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[12012, -1540, -308; -1540, -3322, 2079; -308, 2079, -1174],[308, 11, 1],[123, -29, -454, -1521, -921, -56, 44; 714, -168, -2632, -8820, -5341, -325, 255; 1232, -290, -4543, -15224, -9219, -561, 440],57,7]
%
% END OF LATTICE L58.7
%
%
% LATTICE L58.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[154, -197351, -55517; -197351, 275871211, 77605605; -55517, 77605605, 21831310],[77, 77, 1],[-6, -13, -28, -243, -39, 1, 5; -1999, -4281, -9274, -81467, -13126, 0, 1278; 7106, 15218, 32967, 289597, 46660, 0, -4543],57,8]
%
% END OF LATTICE L58.8
%
%
% LATTICE L58.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[660198616, 879956, 162849148; 879956, 1176, 217056; 162849148, 217056, 40169495],[308, 28, 1],[37, 3153, 1039, 6439, 24866, 1188, 297; 0, -77, -29, -189, -737, -39, -10; -150, -12782, -4212, -26103, -100804, -4816, -1204],57,9]
%
% END OF LATTICE L58.9
%
%
% LATTICE L58.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[106625288, -14705460, 26079592; -14705460, 2028136, -3596824; 26079592, -3596824, 6378835],[308, 44, 1],[113, -22, -1158, -1261, -3215, -339, -109; 0, -7, -203, -189, -469, -39, -10; -462, 86, 4620, 5049, 12880, 1364, 440],57,10]
%
% END OF LATTICE L58.10
%
%
% LATTICE L58.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-381612, 476168, 137676; 476168, -593978, -171787; 137676, -171787, -49670],[308, 77, 1],[61, -139, -276, -6151, -526, -187, 211; -2, 6, 11, 236, 20, 6, -9; 176, -406, -803, -17864, -1527, -539, 616],57,11]
%
% END OF LATTICE L58.11
%
%
% LATTICE L58.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[12936, -345268, -89320; -345268, 9352728, 2419340; -89320, 2419340, 625829],[308, 308, 1],[-2, -37, -145, -926, -327, -183, -46; 17, 263, 1019, 6479, 2286, 1268, 317; -66, -1022, -3960, -25179, -8884, -4928, -1232],57,12]
%
% END OF LATTICE L58.12
%

\medskip%
%------------------------------WEYL-GROUP-W59--------------------------------
%
\leavevmode\llap{}%
$W_{59\phantom{0}}$%
\qquad\llap{32} lattices, $\chi=28$%
\hfill%
$\infty222262$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L59.1
%
\leavevmode%
${L_{59.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}8\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{1}{}3\above{1pt}{1pt}{-}{}9\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{2}{}13\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{23\rightarrow N_{59},3,2}%
\EasyButWeakLineBreak%
{${78}\above{1pt}{1pt}{12,7}{\infty b}{312}\above{1pt}{1pt}{b}{2}{18}\above{1pt}{1pt}{l}{2}{24}\above{1pt}{1pt}{r}{2}{234}\above{1pt}{1pt}{b}{2}{6}\above{1pt}{1pt}{}{6}{18}\above{1pt}{1pt}{b}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-15718248\\-2834208\\-2395224
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2834208\\-485598\\-457431
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2395224\\-457431\\-339362
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-26015\\78325\\78039
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
222369\\-669500\\-667056
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
91435\\-275289\\-274284
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
195783\\-589456\\-587304
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
443503\\-1335282\\-1330407
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
13008\\-39164\\-39021
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-13102\\39447\\39303
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-15718248, -2834208, -2395224; -2834208, -485598, -457431; -2395224, -457431, -339362],[936, 3, 1],[-26015, 222369, 91435, 195783, 443503, 13008, -13102; 78325, -669500, -275289, -589456, -1335282, -39164, 39447; 78039, -667056, -274284, -587304, -1330407, -39021, 39303],58,1]
%
% END OF LATTICE L59.1
%
%
% LATTICE L59.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[78, 0, 0; 0, 0, -1; 0, -1, 0],[78, 1, 1],[-1, 1, 0, -1, -3, -1, -1; 0, 0, -1, -6, -13, -3, -2; -39, 0, 1, -6, -26, -12, -19],58,2]
%
% END OF LATTICE L59.2
%
%
% LATTICE L59.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-36514920, -18104112, -157872; -18104112, -8976026, -78273; -157872, -78273, -682],[312, 1, 1],[-1102, 2243, 58, -1535, -2591, -940, -995; 2223, -4524, -117, 3096, 5226, 1896, 2007; -39, 0, 2, 0, -13, -9, -17],58,3]
%
% END OF LATTICE L59.3
%
%
% LATTICE L59.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-1921842, 242658, -401544; 242658, -28110, 53187; -401544, 53187, -81452],[234, 3, 1],[5729, -24501, -20146, -21567, -97705, -2865, 2887; 16913, -72332, -59475, -63670, -288444, -8458, 8523; -17199, 73554, 60480, 64746, 293319, 8601, -8667],58,4]
%
% END OF LATTICE L59.4
%
%
% LATTICE L59.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2311764, 3042, -1126242; 3042, -4, 1482; -1126242, 1482, -548681],[78, 2, 1],[77, -19, -2, 19, 127, 47, 55; 741, 0, -39, -3, 234, 168, 321; -156, 39, 4, -39, -260, -96, -112],58,5]
%
% END OF LATTICE L59.5
%
%
% LATTICE L59.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1541046, 3042, 533442; 3042, -6, -1053; 533442, -1053, -184654],[78, 3, 1],[-22, 9, 2, -9, -94, -12, -44; 247, 0, -39, -2, 234, 56, 321; -65, 26, 6, -26, -273, -35, -129],58,6]
%
% END OF LATTICE L59.6
%
%
% LATTICE L59.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[9516, 3042, 4368; 3042, 4560, 1404; 4368, 1404, 2005],[78, 6, 1],[2729, -6, 11, 435, 8402, 1068, 4447; 13, 0, 0, 2, 39, 5, 21; -5954, 13, -24, -949, -18330, -2330, -9702],58,7]
%
% END OF LATTICE L59.7
%
%
% LATTICE L59.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1999530, 147888, -39546; 147888, -10938, 2925; -39546, 2925, -760],[234, 3, 1],[519, -25, -26, 21, 231, 137, 239; 7007, -338, -351, 284, 3120, 1850, 3227; -39, 0, 2, 0, -13, -9, -17],58,8]
%
% END OF LATTICE L59.8
%
%
% LATTICE L59.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1864824, 6240, 9360; 6240, -18, -33; 9360, -33, -46],[312, 3, 1],[-2, 17, 7, 15, 34, 1, -1; -169, 1404, 581, 1248, 2834, 84, -83; -286, 2444, 1005, 2152, 4875, 143, -144],58,9]
%
% END OF LATTICE L59.9
%
%
% LATTICE L59.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[78, -3042, 0; -3042, -9880, -507; 0, -507, -2],[78, 13, 1],[-113, -1, 78, 25, -33, -323, -629; -3, 0, 2, 0, -1, -9, -17; 735, 6, -507, -156, 216, 2106, 4095],58,10]
%
% END OF LATTICE L59.10
%
%
% LATTICE L59.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[526199238396, 7963029126, 261750015072; 7963029126, 120505368, 3961090860; 261750015072, 3961090860, 130203666959],[234, 6, 1],[2289, 20104, 26573, 13007, 111068, 2710, 1171; 13, 910, 1314, 686, 6201, 199, 129; -4602, -40443, -53460, -26169, -223470, -5454, -2358],58,11]
%
% END OF LATTICE L59.11
%
%
% LATTICE L59.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[40770288, 6800742, 20378826; 6800742, 1134444, 3399318; 20378826, 3399318, 10186255],[234, 6, 1],[-19301, -522, -1, -2611, -17226, -6784, -9913; -923, -26, 0, -124, -819, -323, -473; 38922, 1053, 2, 5265, 34736, 13680, 19990],58,12]
%
% END OF LATTICE L59.12
%
%
% LATTICE L59.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[51428208, 51714, 25209912; 51714, 52, 25350; 25209912, 25350, 12357803],[78, 26, 1],[-203, 25, 0, -631, -303, -1415, -1721; 57, 0, 1, 117, 58, 288, 401; 414, -51, 0, 1287, 618, 2886, 3510],58,13]
%
% END OF LATTICE L59.13
%
%
% LATTICE L59.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[624, 7176, 5616; 7176, -1136, -744; 5616, -744, -469],[312, 8, 1],[25, -188, -88, -65, -367, -23, 11; 975, -7371, -3449, -2547, -14378, -900, 431; -1248, 9438, 4416, 3261, 18408, 1152, -552],58,14]
%
% END OF LATTICE L59.14
%
%
% LATTICE L59.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-5257512, 818064, 59904; 818064, -127290, -9321; 59904, -9321, -682],[936, 3, 1],[38, -89, -2, 61, 101, 36, 37; 247, -572, -13, 392, 650, 232, 239; -39, 0, 2, 0, -13, -9, -17],58,15]
%
% END OF LATTICE L59.15
%
%
% LATTICE L59.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[42596658, -57642, 14611974; -57642, 78, -19773; 14611974, -19773, 5012360],[78, 39, 1],[-53, 13, 0, -329, -237, -369, -1347; 125, -26, 1, 736, 532, 834, 3095; 155, -38, 0, 962, 693, 1079, 3939],58,16]
%
% END OF LATTICE L59.16
%
%
% LATTICE L59.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-31561608, -3561480, 38376; -3561480, -401882, 4329; 38376, 4329, -46],[312, 13, 1],[-1, 41, 1, -365, -41, -166, -128; 9, -372, -9, 3312, 372, 1506, 1161; 12, -804, -13, 7176, 803, 3237, 2470],58,17]
%
% END OF LATTICE L59.17
%
%
% LATTICE L59.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-516204, 526890, 259428; 526890, 175812, 86580; 259428, 86580, 42637],[78, 78, 1],[-1, 0, 2, 0, -1, -3, -17; -23119, -97, 47855, 2490, -20338, -66188, -386297; 46952, 197, -97188, -5057, 41304, 134420, 784524],58,18]
%
% END OF LATTICE L59.18
%
%
% LATTICE L59.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-568464, 9672, -185952; 9672, -144, 3216; -185952, 3216, -60695],[312, 24, 1],[154, -337, -551, -147, -2657, -77, 80; 1053, -2314, -3780, -1008, -18213, -527, 549; -416, 910, 1488, 397, 7176, 208, -216],58,19]
%
% END OF LATTICE L59.19
%
%
% LATTICE L59.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-37674, -70902, -6552; -70902, -132834, -12285; -6552, -12285, -1136],[234, 39, 1],[-3, 11, 122, 133, 47, 19, -17; -7, 28, 303, 326, 114, 44, -45; 93, -366, -3978, -4290, -1503, -585, 585],58,20]
%
% END OF LATTICE L59.20
%
%
% LATTICE L59.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-328770, -165906, 13104; -165906, -82524, 6513; 13104, 6513, -514],[234, 39, 1],[2, -1, -1, 11, 3, 15, 18; -80, 38, 41, -416, -115, -581, -706; -963, 456, 494, -4992, -1381, -6981, -8489],58,21]
%
% END OF LATTICE L59.21
%
%
% LATTICE L59.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-26520, 2496, 1248; 2496, -234, -117; 1248, -117, -58],[312, 39, 1],[0, 1, 4, 7, 1, 0, -1; -1, 12, 59, 120, 20, 6, -11; 2, -4, -39, -104, -21, -13, 0],58,22]
%
% END OF LATTICE L59.22
%
%
% LATTICE L59.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[76810500, 1831518, 38096136; 1831518, 43680, 908388; 38096136, 908388, 18894755],[234, 78, 1],[-3, 544, 10463, 5561, 3926, 1744, 1279; 1, -38, -744, -400, -285, -131, -99; 6, -1095, -21060, -11193, -7902, -3510, -2574],58,23]
%
% END OF LATTICE L59.23
%
%
% LATTICE L59.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1190362680, -32894550, 590116176; -32894550, 909012, -16307304; 590116176, -16307304, 292547059],[234, 78, 1],[1938, 55, -13, 3342, 1705, 8771, 12880; -49, -1, -4, -101, -49, -241, -339; -3912, -111, 26, -6747, -3442, -17706, -26000],58,24]
%
% END OF LATTICE L59.24
%
%
% LATTICE L59.25
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1705392, -102024, -57096; -102024, -6000, -3432; -57096, -3432, -1909],[936, 24, 1],[-67, 157, 253, 67, 1204, 34, -37; 247, -572, -924, -245, -4407, -125, 135; 1560, -3666, -5904, -1563, -28080, -792, 864],58,25]
%
% END OF LATTICE L59.25
%
%
% LATTICE L59.26
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3944304, -88920, 2588040; -88920, -1680, 54312; 2588040, 54312, -1648037],[936, 24, 1],[-704, 5955, 2765, 2032, 11421, 695, -346; -23257, 196703, 91333, 67121, 377260, 22958, -11429; -1872, 15834, 7352, 5403, 30368, 1848, -920],58,26]
%
% END OF LATTICE L59.26
%
%
% LATTICE L59.27
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1040208, 93912, 3432; 93912, 8112, 104; 3432, 104, -1],[312, 104, 1],[-1, 14, 82, 59, 25, 17, -11; 24, -333, -1951, -1404, -595, -405, 262; -960, 13350, 78208, 56277, 23848, 16224, -10504],58,27]
%
% END OF LATTICE L59.27
%
%
% LATTICE L59.28
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-498888, 582192, -57096; 582192, -676650, 66417; -57096, 66417, -6518],[936, 39, 1],[11, -47, -314, -745, -140, -71, 26; -35, 148, 993, 2360, 444, 226, -81; -453, 1920, 12870, 30576, 5751, 2925, -1053],58,28]
%
% END OF LATTICE L59.28
%
%
% LATTICE L59.29
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2685384, -144144, 11232; -144144, -7410, 585; 11232, 585, -46],[936, 39, 1],[0, -1, 0, 9, 1, 4, 3; 1, -44, -1, 392, 44, 178, 137; 12, -804, -13, 7176, 803, 3237, 2470],58,29]
%
% END OF LATTICE L59.29
%
%
% LATTICE L59.30
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1872, 63336, 1560; 63336, -2115984, -52104; 1560, -52104, -1283],[312, 312, 1],[-1, 3, 59, 15, 20, 6, -11; -2, 3, 71, 20, 29, 13, -8; 80, -118, -2808, -793, -1152, -520, 312],58,30]
%
% END OF LATTICE L59.30
%
%
% LATTICE L59.31
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-761904, -506376, -3744; -506376, 19344, 0; -3744, 0, -1],[936, 312, 1],[-1, 3, 59, 15, 20, 6, -11; -26, 79, 1551, 394, 525, 157, -288; 3720, -11298, -221832, -56355, -75096, -22464, 41184],58,31]
%
% END OF LATTICE L59.31
%
%
% LATTICE L59.32
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-6741072, 9390888, -856440; 9390888, -13080912, 1193088; -856440, 1193088, -108809],[936, 312, 1],[23, -399, -2317, -1657, -698, -452, 315; -1, 14, 82, 59, 25, 17, -11; -192, 3294, 19136, 13689, 5768, 3744, -2600],58,32]
%
% END OF LATTICE L59.32
%

\medskip%
%------------------------------WEYL-GROUP-W60--------------------------------
%
\leavevmode\llap{}%
$W_{60\phantom{0}}$%
\qquad\llap{12} lattices, $\chi=48$%
\hfill%
$222222222222\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L60.1
%
\leavevmode%
${L_{60.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{2}{}5\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}17\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2\rightarrow N_{60}}%
\EasyButWeakLineBreak%
{${34}\above{1pt}{1pt}{l}{2}{4}\above{1pt}{1pt}{r}{2}{10}\above{1pt}{1pt}{b}{2}{2}\above{1pt}{1pt}{l}{2}{68}\above{1pt}{1pt}{r}{2}{10}\above{1pt}{1pt}{b}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
47940\\19040\\-340
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
19040\\7562\\-135
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-340\\-135\\2
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-89761\\227120\\68000
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-35376\\89511\\26800
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-330\\835\\249
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2197\\-5559\\-1666
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
215\\-544\\-164
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
83\\-210\\-65
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\-1
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-27\\68\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2\\5\\0
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[47940, 19040, -340; 19040, 7562, -135; -340, -135, 2],[340, 1, 1],[2197, 215, 83, 0, -27, -2, 47, 49, 247, 330, 17979, 2642; -5559, -544, -210, 0, 68, 5, -119, -124, -625, -835, -45492, -6685; -1666, -164, -65, -1, 0, 0, -34, -36, -185, -249, -13600, -2000],59,1]
%
% END OF LATTICE L60.1
%
%
% LATTICE L60.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[935, 0, 170; 0, -1, 0; 170, 0, 31],[85, 1, 1],[241, 13, 14, 2, 9, -1, -3, 1, 21, 33, 943, 281; -476, -25, -25, -3, -17, 0, 0, -3, -45, -67, -1887, -560; -1275, -69, -75, -11, -51, 5, 17, -5, -110, -174, -4981, -1485],59,2]
%
% END OF LATTICE L60.2
%
%
% LATTICE L60.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-420325, 2040, 168810; 2040, -5, -820; 168810, -820, -67797],[85, 5, 1],[-171, -175, -387, -2643, -72457, -4267, -17815, -883, -142, -2, 513, 35; -68, -63, -137, -931, -25483, -1500, -6256, -309, -49, 1, 187, 12; -425, -435, -962, -6570, -180115, -10607, -44285, -2195, -353, -5, 1275, 87],59,3]
%
% END OF LATTICE L60.3
%
%
% LATTICE L60.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[4621960, -32980, 1154980; -32980, 232, -8240; 1154980, -8240, 288617],[340, 4, 1],[-11829, -318, -672, -82, -21, 163, 235, -23, -1033, -1623, -23167, -13803; 18632, 503, 1075, 135, 34, -270, -408, 33, 1605, 2545, 36414, 21710; 47872, 1287, 2720, 332, 85, -660, -952, 93, 4180, 6568, 93755, 55860],59,4]
%
% END OF LATTICE L60.4
%
%
% LATTICE L60.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1118855, -10455, 460360; -10455, -85, 4301; 460360, 4301, -189418],[85, 17, 1],[-30, -475, -5169, -7027, -11315, -56614, -2778, -2333, -1851, 7, 83, 454; -4, -70, -775, -1059, -1708, -8550, -420, -354, -285, -1, 12, 70; -73, -1156, -12580, -17102, -27538, -137785, -6761, -5678, -4505, 17, 202, 1105],59,5]
%
% END OF LATTICE L60.5
%
%
% LATTICE L60.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-45900, 680, -340; 680, -10, 5; -340, 5, -2],[340, 5, 1],[-133, -13, -1, 0, 1, 0, -3, -3, -3, -20, -1089, -32; -9197, -896, -68, 2, 68, -1, -221, -212, -209, -1387, -75412, -2215; -2125, -200, -13, 5, 0, -3, -85, -60, -52, -330, -17680, -517],59,6]
%
% END OF LATTICE L60.6
%
%
% LATTICE L60.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1020, -340, 340; -340, -102, 153; 340, 153, 26],[340, 17, 1],[3, 7, -78, -157, -559, -1438, -75, -151, -102, -23, -17, -2; -7, -16, 185, 371, 1320, 3395, 177, 356, 240, 54, 40, 5; 2, 0, -85, -153, -532, -1360, -70, -136, -85, -17, -12, 0],59,7]
%
% END OF LATTICE L60.7
%
%
% LATTICE L60.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[59160, -340, 14620; -340, 1400, -80; 14620, -80, 3613],[340, 20, 1],[-145109, -3508, -1034, 84, -21, -85, -4117, -881, -3355, -22029, -298431, -35027; -1819, -44, -13, 1, 0, -1, -51, -11, -42, -276, -3740, -439; 587180, 14195, 4184, -340, 85, 344, 16660, 3565, 13576, 89140, 1207595, 141736],59,8]
%
% END OF LATTICE L60.8
%
%
% LATTICE L60.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[53210, 915705, -356065; 915705, 15792575, -6140825; -356065, -6140825, 2387814],[85, 85, 1],[1, 7, 14, 94, 151, 151, 37, 31, 5, 1, 1, 1; -490, -4859, -11126, -77776, -126513, -126980, -31374, -27005, -4806, -1884, -943, -476; -1260, -12495, -28611, -200005, -325335, -326536, -80680, -69445, -12359, -4845, -2425, -1224],59,9]
%
% END OF LATTICE L60.9
%
%
% LATTICE L60.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1449080, -202980, 363120; -202980, 28424, -50864; 363120, -50864, 90993],[340, 68, 1],[-1, 122, 3449, 5047, 4158, 41889, 2087, 921, 1766, 168, 14, -169; 0, -11, -315, -463, -382, -3850, -192, -85, -165, -17, -2, 10; 4, -493, -13940, -20400, -16807, -169320, -8436, -3723, -7140, -680, -57, 680],59,10]
%
% END OF LATTICE L60.10
%
%
% LATTICE L60.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1313420, -170000, 9860; -170000, -21930, 1275; 9860, 1275, -74],[340, 85, 1],[6, 53, 39, 232, 715, 353, 84, 127, 6, -7, 5, 7; 17, 144, 103, 605, 1856, 915, 217, 324, 14, -20, 16, 21; 1090, 9520, 6953, 41225, 126900, 62628, 14890, 22440, 1037, -1275, 940, 1292],59,11]
%
% END OF LATTICE L60.11
%
%
% LATTICE L60.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[26520, -1555500, -384200; -1555500, 92582680, 22867380; -384200, 22867380, 5648109],[340, 340, 1],[-36, -88, -279, -1715, -1337, -2650, -636, -248, -57, 35, -7, -38; 5537, 13414, 42337, 259799, 202420, 401135, 96233, 37471, 8548, -5374, 1120, 5945; -22420, -54315, -171428, -1051960, -819625, -1624248, -389660, -151725, -34612, 21760, -4535, -24072],59,12]
%
% END OF LATTICE L60.12
%

\medskip%
%------------------------------WEYL-GROUP-W61--------------------------------
%
\leavevmode\llap{}%
$W_{61\phantom{0}}$%
\qquad\llap{12} lattices, $\chi=30$%
\hfill%
$22422242\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L61.1
%
\leavevmode%
${L_{61.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{2}{}29\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{2\rightarrow N_{61}}%
\EasyButWeakLineBreak%
{${12}\above{1pt}{1pt}{r}{2}{58}\above{1pt}{1pt}{b}{2}{4}\above{1pt}{1pt}{*}{4}{2}\above{1pt}{1pt}{l}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-27083796\\37932\\54288
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
37932\\-50\\-79
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
54288\\-79\\-106
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
428735\\122111808\\128542848
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-660\\-187981\\-197880
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-803\\-228709\\-240755
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
125\\35604\\37476
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
644\\183425\\193082
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
135\\38450\\40476
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
8\\2278\\2399
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-27083796, 37932, 54288; 37932, -50, -79; 54288, -79, -106],[348, 1, 1],[125, 644, 135, 8, 7, -6, -3, 3; 35604, 183425, 38450, 2278, 1992, -1711, -854, 855; 37476, 193082, 40476, 2399, 2100, -1798, -900, 899],60,1]
%
% END OF LATTICE L61.1
%
%
% LATTICE L61.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-1131, 348, -87; 348, -106, 29; -87, 29, -2],[87, 1, 1],[1, -20, -1, 8, 107, 1064, 109, 10; 3, -58, -3, 23, 309, 3074, 315, 29; 0, 29, -1, -18, -210, -2059, -209, -17],60,2]
%
% END OF LATTICE L61.2
%
%
% LATTICE L61.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-121951554, 1669356, 40578453; 1669356, -22821, -555480; 40578453, -555480, -13502165],[87, 3, 1],[-30233, -935773, -98166, -11743, -1805, 6671, 2052, -4276; -42589, -1318224, -138287, -16543, -2543, 9396, 2891, -6023; -89108, -2758074, -289332, -34611, -5320, 19662, 6048, -12603],60,3]
%
% END OF LATTICE L61.3
%
%
% LATTICE L61.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3583356, 24012, 853644; 24012, -150, -5883; 853644, -5883, -200930],[348, 3, 1],[161, -412, -207, 206, 2867, 44318, 9291, 551; 7104, -18183, -9134, 9091, 126516, 1955673, 409994, 24314; 476, -1218, -612, 609, 8476, 131022, 27468, 1629],60,4]
%
% END OF LATTICE L61.4
%
%
% LATTICE L61.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[7169152872, -79295628, -1813167696; -79295628, 877064, 20054848; -1813167696, 20054848, 458572603],[348, 4, 1],[-28019, -565243, -58479, -6112, -1330, -2171, -219, -3671; 174, 3480, 358, 35, 6, 0, 2, 25; -110793, -2235088, -231238, -24168, -5259, -8584, -866, -14516],60,5]
%
% END OF LATTICE L61.5
%
%
% LATTICE L61.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1406400762, 2264436, 484358319; 2264436, -3103, -779868; 484358319, -779868, -166810903],[87, 29, 1],[-1323809, -470975, -1432808, -171404, -79045, 3357, 29954, -62405; -42969, -15287, -46506, -5563, -2565, 109, 972, -2026; -3843660, -1367469, -4160137, -497669, -229506, 9747, 86971, -181192],60,6]
%
% END OF LATTICE L61.6
%
%
% LATTICE L61.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[141166200, 205842348, -34142280; 205842348, 300150264, -49784772; -34142280, -49784772, 8257609],[348, 12, 1],[7, 505, -45, -347, -614, -35711, -3597, -260; 2, 0, 2, 25, 58, 3480, 358, 35; 41, 2088, -174, -1284, -2189, -126672, -12714, -864],60,7]
%
% END OF LATTICE L61.7
%
%
% LATTICE L61.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[95397675, 283712220, 3532896; 283712220, 843758799, 10506816; 3532896, 10506816, 130835],[87, 87, 1],[149, 157, 474, 53, 9, 1, 0, 26; -1513, -1572, -4703, -475, -59, 0, -13, -311; 117479, 122001, 364878, 36714, 4495, -27, 1044, 24273],60,8]
%
% END OF LATTICE L61.8
%
%
% LATTICE L61.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-108228, 12528, 6264; 12528, -1450, -725; 6264, -725, -362],[348, 29, 1],[53, 10, 63, 5, 7, 0, -3, 0; 792, 143, 878, 57, 60, -1, -26, 14; -696, -118, -696, -29, 0, 2, 0, -29],60,9]
%
% END OF LATTICE L61.9
%
%
% LATTICE L61.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-338427564, 1213476, -2887356; 1213476, -4350, 10353; -2887356, 10353, -24634],[348, 87, 1],[7, -2, -9, 29, 285, 148, 885, 44; 20, -1, -26, 14, 264, 143, 878, 57; -812, 234, 1044, -3393, -33292, -17286, -103356, -5133],60,10]
%
% END OF LATTICE L61.10
%
%
% LATTICE L61.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[61944, 24012, -2436; 24012, 19720, -8816; -2436, -8816, 6047],[348, 116, 1],[8542, 5887, 17555, 1707, 287, -1, 103, 1236; -25452, -17541, -52307, -5086, -855, 3, -307, -3683; -33669, -23204, -69194, -6728, -1131, 4, -406, -4872],60,11]
%
% END OF LATTICE L61.11
%
%
% LATTICE L61.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[59160, 3476172, -878700; 3476172, 389473944, -98450592; -878700, -98450592, 24886181],[348, 348, 1],[2, 0, 2, 25, 58, 120, 358, 35; -12440, 91, -13327, -159924, -368721, -762413, -2273639, -221237; -49213, 360, -52722, -632664, -1458671, -3016128, -8994582, -875220],60,12]
%
% END OF LATTICE L61.12
%

\medskip%
%------------------------------WEYL-GROUP-W62--------------------------------
%
\leavevmode\llap{}%
$W_{62\phantom{0}}$%
\qquad\llap{12} lattices, $\chi=42$%
\hfill%
$4222242222\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L62.1
%
\leavevmode%
${L_{62.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{2}{}7\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{2}{}13\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{2\rightarrow N_{62}}%
\EasyButWeakLineBreak%
{${2}\above{1pt}{1pt}{*}{4}{4}\above{1pt}{1pt}{b}{2}{14}\above{1pt}{1pt}{s}{2}{26}\above{1pt}{1pt}{l}{2}{28}\above{1pt}{1pt}{r}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-22161412\\108836\\217672
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
108836\\-534\\-1069
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
217672\\-1069\\-2138
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
586403\\1172808\\59096492
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2961\\-5923\\-298403
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-5760\\-11520\\-580481
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\2\\-1
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-5\\-2\\-508
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-62\\-105\\-6258
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-360\\-689\\-36296
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-767\\-1512\\-77308
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-22161412, 108836, 217672; 108836, -534, -1069; 217672, -1069, -2138],[364, 1, 1],[0, -5, -62, -360, -767, -162, -13, -1, 9, 11; 2, -2, -105, -689, -1512, -326, -34, -21, -13, 0; -1, -508, -6258, -36296, -77308, -16325, -1306, -91, 923, 1120],61,1]
%
% END OF LATTICE L62.1
%
%
% LATTICE L62.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[910, 0, 637; 0, -1, 0; 637, 0, 446],[91, 1, 1],[276, 9, -5, -9, 10, 12, 7, 117, 633, 662; -138, -5, 0, 0, -7, -6, -3, -56, -312, -329; -397, -13, 7, 13, -14, -17, -10, -168, -910, -952],61,2]
%
% END OF LATTICE L62.2
%
%
% LATTICE L62.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-970242, 11375, 139685; 11375, -133, -1638; 139685, -1638, -20110],[91, 7, 1],[-12, 13, 117, 5247, 818, 2460, 123, 19, 57, -2; -78, 77, 730, 32838, 5123, 15414, 775, 122, 390, -11; -77, 84, 753, 33761, 5263, 15827, 791, 122, 364, -13],61,3]
%
% END OF LATTICE L62.3
%
%
% LATTICE L62.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1727453, -14196, 264173; -14196, -78, 2171; 264173, 2171, -40399],[91, 13, 1],[-169, 167, 11078, 5476, 77741, 33415, 1680, 1851, 65, -167; 2, -1, -105, -53, -756, -326, -17, -21, -1, 0; -1105, 1092, 72436, 35806, 508326, 218491, 10985, 12103, 425, -1092],61,4]
%
% END OF LATTICE L62.4
%
%
% LATTICE L62.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[930684664, 364, -235332552; 364, 8, -92; -235332552, -92, 59506095],[364, 4, 1],[0, 1459, 94349, 606681, 331349, 284904, 14369, 16447, 10611, 1039; 1, -30, -1960, -12610, -6888, -5923, -299, -343, -221, -21; 0, 5770, 373128, 2399280, 1310407, 1126728, 56826, 65044, 41964, 4109],61,5]
%
% END OF LATTICE L62.5
%
%
% LATTICE L62.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-13166972, -314132, 48412; -314132, -7490, 1155; 48412, 1155, -178],[364, 7, 1],[-1, 7, 23, 1009, 313, 469, 45, 3, 5, -1; 2, -2, -15, -689, -216, -326, -34, -3, -13, 0; -259, 1890, 6155, 269815, 83684, 125377, 12012, 796, 1274, -272],61,6]
%
% END OF LATTICE L62.6
%
%
% LATTICE L62.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-8817172, 247520, -1318408; 247520, -6942, 37011; -1318408, 37011, -197138],[364, 13, 1],[2, 171, 2038, 904, 24993, 5272, 415, 13, -25, -381; 2, -2, -105, -53, -1512, -326, -34, -21, -1, 0; -13, -1144, -13650, -6056, -167440, -35321, -2782, -91, 167, 2548],61,7]
%
% END OF LATTICE L62.7
%
%
% LATTICE L62.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[182, -7098, -91; -7098, 332605, 4277; -91, 4277, 55],[91, 91, 1],[1, 6, 38, 128, 258, 773, 37, 5, 1, 0; 0, 6, 53, 183, 371, 1116, 56, 9, 3, 1; 0, -455, -4043, -13965, -28314, -85176, -4277, -689, -231, -78],61,8]
%
% END OF LATTICE L62.8
%
%
% LATTICE L62.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[735453992, 92820, -185914456; 92820, 56, -23464; -185914456, -23464, 46997073],[364, 28, 1],[0, -5213, -37987, -1682217, -130756, -784944, -38395, -5621, -18495, -68; 1, -71, -523, -23179, -1802, -10819, -530, -78, -260, -1; 0, -20622, -150272, -6654648, -517255, -3105144, -151886, -22236, -73164, -269],61,9]
%
% END OF LATTICE L62.9
%
%
% LATTICE L62.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1025160136, 7644, -258052340; 7644, 104, -1924; -258052340, -1924, 64956691],[364, 52, 1],[0, 5491, 355233, 175713, 1247599, 1072728, 54105, 61939, 3075, 3917; 1, -30, -1960, -970, -6888, -5923, -299, -343, -17, -21; 0, 21814, 1411228, 698052, 4956315, 4261608, 214942, 246064, 12216, 15561],61,10]
%
% END OF LATTICE L62.10
%
%
% LATTICE L62.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-923468, 1223404, 351624; 1223404, -1620710, -465829; 351624, -465829, -133886],[364, 91, 1],[-32, 621, 1757, 5849, 23511, 35150, 3281, 194, 4, -99; 2, -2, -15, -53, -216, -326, -34, -3, -1, 0; -91, 1638, 4667, 15547, 62504, 93457, 8736, 520, 14, -260],61,11]
%
% END OF LATTICE L62.11
%
%
% LATTICE L62.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[728, -13468, 3276; -13468, 11744824, -2874144; 3276, -2874144, 703349],[364, 364, 1],[1, -289, -2115, -7207, -7283, -43723, -2140, -314, -80, -4; 0, -2539, -18543, -63177, -63841, -383256, -18753, -2749, -699, -35; 0, -10374, -75764, -258132, -260845, -1565928, -76622, -11232, -2856, -143],61,12]
%
% END OF LATTICE L62.12
%

\medskip%
%------------------------------WEYL-GROUP-W63--------------------------------
%
\leavevmode\llap{}%
$W_{63\phantom{0}}$%
\qquad\llap{12} lattices, $\chi=32$%
\hfill%
$62226222\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L63.1
%
\leavevmode%
${L_{63.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}31\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{2\rightarrow N_{63}}%
\EasyButWeakLineBreak%
{${2}\above{1pt}{1pt}{}{6}{6}\above{1pt}{1pt}{l}{2}{4}\above{1pt}{1pt}{r}{2}{186}\above{1pt}{1pt}{b}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2765820\\13020\\6324
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
13020\\-58\\-31
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
6324\\-31\\-14
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
43151\\3980772\\10658544
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-200\\-18451\\-49400
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-100\\-9225\\-24701
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\184\\495
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-93\\-246
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-92\\-248
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
11\\1023\\2697
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-2765820, 13020, 6324; 13020, -58, -31; 6324, -31, -14],[372, 1, 1],[2, -1, -1, 11, 2, 49, 49, 361; 184, -93, -92, 1023, 185, 4521, 4520, 33294; 495, -246, -248, 2697, 493, 12102, 12104, 89187],62,1]
%
% END OF LATTICE L63.1
%
%
% LATTICE L63.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[5487, 1767, 93; 1767, 569, 30; 93, 30, 2],[93, 1, 1],[1, -2, 10, 391, 23, 290, 134, 1841; -3, 6, -31, -1209, -71, -894, -413, -5673; -1, 3, -4, -186, -12, -159, -74, -1023],62,2]
%
% END OF LATTICE L63.2
%
%
% LATTICE L63.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3503031, 25482, -1163523; 25482, -183, 8463; -1163523, 8463, -386461],[93, 3, 1],[-367, 30, 5060, 59289, 9663, 37154, 50716, 228887; 368, -31, -5052, -59179, -9643, -37069, -50598, -228346; 1113, -91, -15345, -179800, -29304, -112673, -153801, -694121],62,3]
%
% END OF LATTICE L63.3
%
%
% LATTICE L63.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1470516, 15996, 8556; 15996, -174, -93; 8556, -93, -46],[372, 3, 1],[3, -1, -1, 14, 5, 33, 97, 234; 277, -93, -92, 1302, 464, 3057, 8984, 21669; -3, 2, 0, -31, -9, -50, -144, -341],62,4]
%
% END OF LATTICE L63.4
%
%
% LATTICE L63.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[819385800, -3346884, 202607568; -3346884, 13672, -827576; 202607568, -827576, 50098289],[372, 4, 1],[1366, 181, 23, 11959, 1277, 31535, 7906, 233840; 23, 0, 1, 279, 27, 600, 149, 4371; -5524, -732, -93, -48360, -5164, -127524, -31971, -945624],62,5]
%
% END OF LATTICE L63.5
%
%
% LATTICE L63.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-30049230, -118203, -9701016; -118203, -434, -38161; -9701016, -38161, -3131851],[93, 31, 1],[-3804, 961, 52225, 59203, 99685, 1149611, 523061, 228440; 247, -60, -3410, -3867, -6513, -75132, -34186, -14931; 11780, -2976, -161727, -183336, -308698, -3560040, -1619781, -707418],62,6]
%
% END OF LATTICE L63.6
%
%
% LATTICE L63.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[665880, 343356, 165912; 343356, 179400, 85560; 165912, 85560, 41339],[372, 12, 1],[1519, -1, 69, 6224, 1798, 13269, 9882, 96603; 23, 0, 1, 93, 27, 200, 149, 1457; -6144, 4, -279, -25172, -7272, -53668, -39969, -390724],62,7]
%
% END OF LATTICE L63.7
%
%
% LATTICE L63.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[407526, -38335251, -12569043; -38335251, 3606953106, 1182617760; -12569043, 1182617760, 387746867],[93, 93, 1],[14, 1, -248, -95, -485, -1885, -2578, -376; -68607, -1240, 1129393, 430985, 2193899, 8502408, 11622359, 1694307; 209250, 3782, -3444627, -1314496, -6691350, -25932182, -35447973, -5167604],62,8]
%
% END OF LATTICE L63.8
%
%
% LATTICE L63.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1594020, -29016, -829188; -29016, -434, -14911; -829188, -14911, -430978],[372, 31, 1],[-962, 496, 481, -176, -977, -23764, -23749, -5641; -3849, 1986, 1924, -705, -3911, -95106, -95044, -22575; 1984, -1023, -992, 363, 2015, 49011, 48980, 11634],62,9]
%
% END OF LATTICE L63.9
%
%
% LATTICE L63.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-5499276, 85429056, -2758752; 85429056, -1326996354, 42852447; -2758752, 42852447, -1383826],[372, 93, 1],[-2465, -16188, -47557, -3699, -1458, 496, 481, -224; -5093, -33437, -98228, -7640, -3010, 1025, 992, -463; -152799, -1003160, -2946984, -229211, -90303, 30752, 29760, -13891],62,10]
%
% END OF LATTICE L63.10
%
%
% LATTICE L63.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[449610360, -291040524, -329473332; -291040524, 188395928, 213274048; -329473332, 213274048, 241437439],[372, 124, 1],[16095, -92, 749, 6445, 19183, 423428, 105085, 99389; -48271, 279, -2247, -19332, -57538, -1269987, -315180, -298095; 64604, -372, 3007, 25872, 77004, 1699668, 421817, 398952],62,11]
%
% END OF LATTICE L63.11
%
%
% LATTICE L63.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[671487528, -18845698188, -4657269252; -18845698188, 528915768504, 130709041452; -4657269252, 130709041452, 32301652805],[372, 372, 1],[-13347, -98950, -73724, -23257, -11393, -10, -496, -1483; -59863, -443293, -330246, -104170, -50968, -31, -2247, -6661; 240312, 1779524, 1325715, 418172, 204600, 124, 9021, 26740],62,12]
%
% END OF LATTICE L63.12
%

\medskip%
%------------------------------WEYL-GROUP-W64--------------------------------
%
\leavevmode\llap{}%
$W_{64\phantom{0}}$%
\qquad\llap{12} lattices, $\chi=40$%
\hfill%
$3222232222\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L64.1
%
\leavevmode%
${L_{64.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}19\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2\rightarrow N_{64}}%
\EasyButWeakLineBreak%
{${2}\above{1pt}{1pt}{+}{3}{2}\above{1pt}{1pt}{b}{2}{4}\above{1pt}{1pt}{b}{2}{10}\above{1pt}{1pt}{l}{2}{76}\above{1pt}{1pt}{r}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2676340\\-703760\\14820
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-703760\\-185058\\3897
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
14820\\3897\\-82
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-140449\\532000\\-106400
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-36927\\139874\\-27975
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
759\\-2875\\574
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-16\\61\\7
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-30\\114\\-5
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-77\\292\\-42
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-301\\1140\\-235
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2329\\8816\\-2052
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-2676340, -703760, 14820; -703760, -185058, 3897; 14820, 3897, -82],[380, 1, 1],[-16, -30, -77, -301, -2329, -50, -3, 11, 4, -179; 61, 114, 292, 1140, 8816, 189, 11, -42, -15, 684; 7, -5, -42, -235, -2052, -57, -20, -8, 10, 152],63,1]
%
% END OF LATTICE L64.1
%
%
% LATTICE L64.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-3135, 665, 95; 665, -141, -20; 95, -20, -2],[95, 1, 1],[-63, -20, -4, -2, 4, 1, -11, -27, -277, -1182; -295, -94, -19, -10, 19, 5, -51, -126, -1295, -5529; -107, -29, -3, 5, 0, -3, -26, -52, -500, -2090],63,2]
%
% END OF LATTICE L64.2
%
%
% LATTICE L64.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-187910, 7030, 38095; 7030, -185, -1425; 38095, -1425, -7723],[95, 5, 1],[230, -10543, -24393, -49231, -1045092, -55170, -16927, -3077, -215, 1232; -3, 160, 369, 744, 15789, 833, 255, 46, 3, -19; 1135, -52030, -120380, -242956, -5157550, -272265, -83535, -15185, -1061, 6080],63,3]
%
% END OF LATTICE L64.3
%
%
% LATTICE L64.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[24153560, -207100, -6047700; -207100, 1816, 51844; -6047700, 51844, 1514259],[380, 4, 1],[-1033, -3100, -5214, -47162, -96603, -9489, -2161, -47, -187, -3356; -1099, -3297, -5545, -50155, -102733, -10091, -2298, -50, -200, -3572; -4088, -12268, -20634, -186640, -382299, -37552, -8552, -186, -740, -13281],63,4]
%
% END OF LATTICE L64.4
%
%
% LATTICE L64.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-607810, -9025, 126730; -9025, -133, 1881; 126730, 1881, -26423],[95, 19, 1],[45, -1963, -4547, -45901, -10258, -10291, -3160, -576, -206, 12; 170, -7803, -18053, -182175, -40708, -40830, -12527, -2277, -795, 48; 228, -9975, -23104, -233225, -52121, -52288, -16055, -2926, -1045, 61],63,5]
%
% END OF LATTICE L64.5
%
%
% LATTICE L64.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-8964580, -74100, 29640; -74100, -610, 245; 29640, 245, -98],[380, 5, 1],[10, 6, 7, 3, 83, 0, -1, 3, 6, 297; -22, -9, -6, -1, 0, 2, -1, -14, -17, -760; 2965, 1790, 2100, 904, 25080, 5, -305, 870, 1769, 87780],63,6]
%
% END OF LATTICE L64.6
%
%
% LATTICE L64.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1087940, 81700, -5320; 81700, 6118, -399; -5320, -399, 26],[380, 19, 1],[-5, -2, -1, 1, 1, 1, 0, -3, -19, -9; -79, -29, -14, 5, 8, 9, -6, -56, -320, -148; -2242, -855, -418, 285, 328, 342, -95, -1482, -8835, -4128],63,7]
%
% END OF LATTICE L64.7
%
%
% LATTICE L64.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[414719080, -1900, -104785760; -1900, 40, 480; -104785760, 480, 26475887],[380, 20, 1],[-33160, -16201, -7911, -6253, -42942, 0, -379, -8669, -23591, -272078; -231, -112, -54, -42, -285, 1, -3, -61, -165, -1900; -131240, -64120, -31310, -24748, -169955, 0, -1500, -34310, -93368, -1076825],63,8]
%
% END OF LATTICE L64.8
%
%
% LATTICE L64.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[329270, -5415, 5795; -5415, 95, -95; 5795, -95, 102],[95, 95, 1],[7, -479, -1100, -2215, -2473, -2477, -756, -135, -8, 3; 16, -828, -1911, -3854, -4305, -4316, -1322, -239, -16, 5; -380, 26315, 60420, 121657, 135825, 136040, 41515, 7410, 437, -165],63,9]
%
% END OF LATTICE L64.9
%
%
% LATTICE L64.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[92354440, -549860, -23334280; -549860, 3192, 138928; -23334280, 138928, 5895641],[380, 76, 1],[8277, 845, -989, -4897, -212, 941, 3764, 5598, 46378, 4821; 144, 17, -15, -75, -3, 16, 63, 95, 795, 83; 32756, 3344, -3914, -19380, -839, 3724, 14896, 22154, 183540, 19079],63,10]
%
% END OF LATTICE L64.10
%
%
% LATTICE L64.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-26220, -36100, 760; -36100, -49590, 1045; 760, 1045, -22],[380, 95, 1],[-10, -1, 3, 2, 3, 0, -4, -13, -11, -23; -22, -9, -6, -1, 0, 2, -1, -14, -17, -40; -1425, -475, -190, 19, 100, 95, -190, -1140, -1216, -2760],63,11]
%
% END OF LATTICE L64.11
%
%
% LATTICE L64.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[760, -36100, 9120; -36100, 2688120, -679440; 9120, -679440, 171733],[380, 380, 1],[-391, -147, -49, -29, -10, 1, -48, -146, -322, -185; -5960, -2211, -721, -423, -148, 0, -769, -2259, -4941, -2832; -23560, -8740, -2850, -1672, -585, 0, -3040, -8930, -19532, -11195],63,12]
%
% END OF LATTICE L64.12
%

\medskip%
%------------------------------WEYL-GROUP-W65--------------------------------
%
\leavevmode\llap{}%
$W_{65\phantom{0}}$%
\qquad\llap{16} lattices, $\chi=32$%
\hfill%
$22262226\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L65.1
%
\leavevmode%
${L_{65.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}8\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}17\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2\rightarrow N_{65}}%
\EasyButWeakLineBreak%
{${6}\above{1pt}{1pt}{s}{2}{34}\above{1pt}{1pt}{b}{2}{24}\above{1pt}{1pt}{b}{2}{2}\above{1pt}{1pt}{}{6}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-15547656\\20808\\31824
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
20808\\-26\\-45
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
31824\\-45\\-62
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
395759\\136022712\\104361912
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-530\\-182162\\-139761
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-810\\-278397\\-213598
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
272\\93486\\71727
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
514\\176664\\135541
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
115\\39528\\30324
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\688\\527
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-15547656, 20808, 31824; 20808, -26, -45; 31824, -45, -62],[408, 1, 1],[272, 514, 115, 2, -2, -4, 5, 8; 93486, 176664, 39528, 688, -687, -1377, 1716, 2749; 71727, 135541, 30324, 527, -528, -1054, 1320, 2110],64,1]
%
% END OF LATTICE L65.1
%
%
% LATTICE L65.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-3162, -1530, 306; -1530, -740, 153; 306, 153, 46],[102, 1, 1],[25, 125, -47, -217, -7855, -14915, -1693, -73; -51, -255, 96, 443, 16035, 30447, 3456, 149; 3, 17, -6, -29, -1056, -2006, -228, -10],64,2]
%
% END OF LATTICE L65.2
%
%
% LATTICE L65.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2082840, 10914, -1033260; 10914, -52, 5412; -1033260, 5412, -512581],[102, 2, 1],[320, 638, -200, -1278, -43439, -82085, -4591, -319; -279, -561, 174, 1117, 37998, 71808, 4017, 280; -648, -1292, 405, 2588, 87966, 166226, 9297, 646],64,3]
%
% END OF LATTICE L65.3
%
%
% LATTICE L65.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2345694, 14076, -774792; 14076, -78, 4647; -774792, 4647, -255916],[102, 3, 1],[84, 502, -105, -1006, -11397, -64609, -2409, -251; -93, -561, 116, 1117, 12666, 71808, 2678, 280; -256, -1530, 320, 3066, 34735, 196911, 7342, 765],64,4]
%
% END OF LATTICE L65.4
%
%
% LATTICE L65.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[707401824, -9162558, 349513506; -9162558, 118680, -4527042; 349513506, -4527042, 172687837],[102, 6, 1],[503, 2671, 1129, 17405, 196084, 1111322, 20714, 4438; 2, 0, 2, 40, 475, 2703, 51, 13; -1018, -5406, -2285, -35226, -396854, -2249202, -41923, -8982],64,5]
%
% END OF LATTICE L65.5
%
%
% LATTICE L65.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-19120920, -76296, 60384; -76296, -282, 237; 60384, 237, -190],[408, 3, 1],[254, 1432, 105, 4, -2, -4, 7, 24; 18179, 102493, 7516, 287, -143, -289, 500, 1717; 103387, 582879, 42740, 1629, -814, -1632, 2848, 9768],64,6]
%
% END OF LATTICE L65.6
%
%
% LATTICE L65.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-6957114, -89556, 1224408; -89556, -1054, 15759; 1224408, 15759, -215488],[102, 17, 1],[-905, -107, 1129, 3623, 123242, 13700, 26057, 908; -120, -14, 150, 478, 16239, 1805, 3432, 119; -5151, -609, 6426, 20621, 701454, 77976, 148308, 5168],64,7]
%
% END OF LATTICE L65.7
%
%
% LATTICE L65.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-573648, 11016, -28152; 11016, -208, 552; -28152, 552, -1345],[408, 8, 1],[-2095, -3957, -221, -15, 16, 30, -10, -62; -60756, -114750, -6408, -434, 465, 867, -291, -1799; 18936, 35768, 1998, 136, -144, -272, 90, 560],64,8]
%
% END OF LATTICE L65.8
%
%
% LATTICE L65.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[867654024, -10328010, 420712158; -10328010, 122944, -5007894; 420712158, -5007894, 203996887],[102, 34, 1],[-2918, -160, -4822, -26888, -925585, -103007, -98345, -7501; 3, 1, 15, 67, 2184, 242, 228, 14; 6018, 330, 9945, 55454, 1908930, 212442, 202827, 15470],64,9]
%
% END OF LATTICE L65.9
%
%
% LATTICE L65.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[338364498, 7899186, -100834956; 7899186, 184416, -2354007; -100834956, -2354007, 30049516],[102, 51, 1],[457, 75, 1509, 12625, 144875, 48369, 30787, 3523; -913, -149, -3008, -25183, -289022, -96496, -61422, -7032; 1462, 240, 4828, 40392, 463505, 154749, 98498, 11271],64,10]
%
% END OF LATTICE L65.10
%
%
% LATTICE L65.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-24072, 3264, 1632; 3264, -442, -221; 1632, -221, -110],[408, 17, 1],[-2, 0, 5, 4, 110, 12, 43, 0; -15, -1, 36, 45, 1446, 160, 600, 8; 0, 2, 0, -34, -1377, -155, -612, -17],64,11]
%
% END OF LATTICE L65.11
%
%
% LATTICE L65.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-860880, -48552, -554880; -48552, -2256, -28968; -554880, -28968, -346427],[408, 24, 1],[298, 608, -260, -3576, -37873, -213533, -3915, -599; 3859, 7871, -3367, -46307, -490426, -2765084, -50696, -7756; -800, -1632, 698, 9600, 101672, 573240, 10510, 1608],64,12]
%
% END OF LATTICE L65.12
%
%
% LATTICE L65.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1044961032, -628251762, -297695466; -628251762, -377717424, -178980420; -297695466, -178980420, -84809407],[102, 102, 1],[-40, -14, 25, 478, 5413, 1805, 572, 119; 16709, 5917, -10425, -200553, -2273684, -758242, -240350, -50222; -35122, -12438, 21913, 421566, 4779346, 1593846, 505223, 105570],64,13]
%
% END OF LATTICE L65.13
%
%
% LATTICE L65.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-32790552, -1712784, 114240; -1712784, -89454, 5967; 114240, 5967, -398],[408, 51, 1],[-2, 0, 7, 20, 200, 66, 81, 2; -15, -1, 52, 165, 1707, 565, 700, 23; -799, -15, 2788, 8211, 82960, 27402, 33728, 918],64,14]
%
% END OF LATTICE L65.14
%
%
% LATTICE L65.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-14212272, 14437896, -94248; 14437896, -14667056, 95744; -94248, 95744, -625],[408, 136, 1],[-811, -91, -89, -9, 1, 1, -1, -21; 1446, 160, 150, 8, -15, -1, 9, 45; 343944, 38248, 36414, 2584, -2448, -304, 1530, 10064],64,15]
%
% END OF LATTICE L65.15
%
%
% LATTICE L65.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-715632, -1529592, -185232; -1529592, -3264816, -395352; -185232, -395352, -47875],[408, 408, 1],[-15, -1, 13, 165, 1707, 565, 175, 23; 287, 15, -249, -3091, -31760, -10506, -3248, -406; -2312, -120, 2006, 24888, 255680, 84576, 26146, 3264],64,16]
%
% END OF LATTICE L65.16
%

\medskip%
%------------------------------WEYL-GROUP-W66--------------------------------
%
\leavevmode\llap{}%
$W_{66\phantom{0}}$%
\qquad\llap{48} lattices, $\chi=36$%
\hfill%
$2222222222\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L66.1
%
\leavevmode%
${L_{66.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{1}{}3\above{1pt}{1pt}{-}{}9\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{2}{}5\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{2}{}7\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{23\rightarrow N_{66},3,2}%
\EasyButWeakLineBreak%
{${180}\above{1pt}{1pt}{r}{2}{42}\above{1pt}{1pt}{b}{2}{18}\above{1pt}{1pt}{s}{2}{70}\above{1pt}{1pt}{b}{2}{6}\above{1pt}{1pt}{l}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-21420\\-3780\\13860
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3780\\-642\\2001
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
13860\\2001\\-1070
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-9409\\67200\\3780
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1456\\10399\\585
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2464\\-17600\\-991
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-899\\6420\\360
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\7\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
134\\-957\\-54
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
348\\-2485\\-140
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
15\\-107\\-6
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-21420, -3780, 13860; -3780, -642, 2001; 13860, 2001, -1070],[1260, 3, 1],[-899, -1, 134, 348, 15, -1789, -783, -470, -1132, -127; 6420, 7, -957, -2485, -107, 12780, 5593, 3357, 8085, 907; 360, 0, -54, -140, -6, 720, 315, 189, 455, 51],65,1]
%
% END OF LATTICE L66.1
%
%
% LATTICE L66.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-3045, -630, -105; -630, -130, -21; -105, -21, -2],[105, 1, 1],[-1, 8, 2, 2, -4, -31, -64, -10, -58, -4; 5, -42, -10, 0, 24, 175, 357, 55, 315, 21; 0, 21, -3, -175, -63, -300, -546, -72, -350, -12],65,2]
%
% END OF LATTICE L66.2
%
%
% LATTICE L66.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-4620, -420, 840; -420, -38, 81; 840, 81, -34],[420, 1, 1],[-177, -194, -33, -213, -20, -47, -2, 5, 17, -8; 1800, 1974, 336, 2170, 204, 480, 21, -51, -175, 81; -100, -105, -17, -105, -9, -20, 0, 2, 0, -6],65,3]
%
% END OF LATTICE L66.3
%
%
% LATTICE L66.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-147105, -2205, -1890; -2205, -30, -36; -1890, -36, -5],[315, 3, 1],[-56, -43, -23, -51, -5, -16, 1, 5, 9, -1; 2745, 2114, 1134, 2520, 248, 795, -49, -249, -455, 47; 1125, 861, 459, 1015, 99, 315, -21, -99, -175, 21],65,4]
%
% END OF LATTICE L66.4
%
%
% LATTICE L66.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-103215, -1575, 35700; -1575, 111, 519; 35700, 519, -12343],[105, 3, 1],[782, -12, -178, -324, 130, 3622, 2581, 1279, 8031, 237; 435, -7, -99, -175, 73, 2025, 1442, 714, 4480, 132; 2280, -35, -519, -945, 379, 10560, 7525, 3729, 23415, 691],65,5]
%
% END OF LATTICE L66.5
%
%
% LATTICE L66.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-24045, -3045, -3990; -3045, 185, -615; -3990, -615, -641],[105, 5, 1],[-86, 20, 98, 36, -214, -398, -4255, -703, -883, -391; 87, -21, -99, -35, 219, 405, 4326, 714, 896, 396; 452, -105, -515, -189, 1125, 2092, 22365, 3695, 4641, 2055],65,6]
%
% END OF LATTICE L66.6
%
%
% LATTICE L66.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[26565, -4515, 4410; -4515, 259, -651; 4410, -651, 713],[105, 7, 1],[-298, 2, 68, 18, -148, -1378, -421, -487, -437, -271; 435, -3, -99, -25, 219, 2025, 618, 714, 640, 396; 2240, -15, -511, -135, 1113, 10360, 3165, 3661, 3285, 2037],65,7]
%
% END OF LATTICE L66.7
%
%
% LATTICE L66.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[7245, -945, 0; -945, 123, -3; 0, -3, -34],[315, 3, 1],[63, 134, 22, 412, 12, 13, -1, -3, -13, 7; 480, 1022, 168, 3150, 92, 100, -7, -23, -105, 53; -50, -105, -17, -315, -9, -10, 0, 2, 0, -6],65,8]
%
% END OF LATTICE L66.8
%
%
% LATTICE L66.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-275940, 82320, -1680; 82320, -24558, 501; -1680, 501, -10],[420, 3, 1],[41, 2, -5, -51, -2, 31, 19, 14, 114, 5; 140, 7, -17, -175, -7, 100, 63, 47, 385, 17; 120, 14, -12, -210, -16, -240, -49, -3, 105, 11],65,9]
%
% END OF LATTICE L66.9
%
%
% LATTICE L66.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[236996130, -4144140, -80435565; -4144140, 72465, 1406505; -80435565, 1406505, 27299518],[105, 15, 1],[-277, 368, -56, -2658, -1790, -5591, -17483, -7279, -7611, -655; -3, -14, 0, 28, 18, 51, 154, 60, 56, 2; -816, 1085, -165, -7833, -5275, -16476, -51520, -21450, -22428, -1930],65,10]
%
% END OF LATTICE L66.10
%
%
% LATTICE L66.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[7176120, -193620, 1795920; -193620, 5224, -48456; 1795920, -48456, 449453],[420, 4, 1],[1248, 4696, 654, 3428, 178, 58, -125, -1, 1143, 475; -540, -2037, -285, -1505, -81, -30, 42, 0, -490, -204; -5045, -18984, -2644, -13860, -720, -235, 504, 4, -4620, -1920],65,11]
%
% END OF LATTICE L66.11
%
%
% LATTICE L66.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[380100, 181440, 4200; 181440, 86610, 2005; 4200, 2005, 46],[420, 5, 1],[-23, -10, 13, 17, -4, -57, -340, -63, -87, -46; 48, 21, -27, -35, 9, 120, 714, 132, 182, 96; 8, 0, -10, -28, -30, -32, -105, -5, 7, 15],65,12]
%
% END OF LATTICE L66.12
%
%
% LATTICE L66.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[132197730, -3662190, -44965725; -3662190, 101451, 1245657; -44965725, 1245657, 15294638],[105, 21, 1],[-929, 86, -50, -2076, -1940, -29779, -2645, -7627, -5601, -619; -15, -2, 0, 20, 18, 255, 22, 60, 40, 2; -2730, 253, -147, -6105, -5705, -87570, -7778, -22428, -16470, -1820],65,13]
%
% END OF LATTICE L66.13
%
%
% LATTICE L66.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-4306260, -1545180, 36540; -1545180, -554442, 13111; 36540, 13111, -310],[420, 7, 1],[-1741, -191, -128, -52, 37, -91, -38, -101, -177, -266; 5820, 639, 429, 175, -123, 300, 126, 336, 590, 888; 40880, 4506, 3052, 1270, -840, 1960, 849, 2303, 4085, 6195],65,14]
%
% END OF LATTICE L66.14
%
%
% LATTICE L66.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[140036295, 4866015, -24370290; 4866015, 169085, -846825; -24370290, -846825, 4241122],[105, 35, 1],[-125, 178, -34, -284, -3980, -4071, -5423, -5211, -765, -1265; 372, -540, 102, 856, 11994, 12264, 16335, 15693, 2303, 3801; -644, 915, -175, -1461, -20475, -20944, -27900, -26810, -3936, -6510],65,15]
%
% END OF LATTICE L66.15
%
%
% LATTICE L66.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[28980, -12600, -1260; -12600, 5478, 543; -1260, 543, -34],[1260, 3, 1],[597, 648, 109, 2089, 64, 147, 3, -16, -136, 29; 1380, 1498, 252, 4830, 148, 340, 7, -37, -315, 67; -100, -105, -17, -315, -9, -20, 0, 2, 0, -6],65,16]
%
% END OF LATTICE L66.16
%
%
% LATTICE L66.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[296415, -31185, 11655; -31185, 3225, -1200; 11655, -1200, 446],[315, 15, 1],[2, -1, -11, -13, -17, -38, -104, -34, -8, 2; 93, -49, -525, -623, -817, -1833, -5026, -1650, -392, 92; 198, -105, -1125, -1337, -1755, -3942, -10815, -3555, -847, 195],65,17]
%
% END OF LATTICE L66.17
%
%
% LATTICE L66.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[684495, -99540, 5670; -99540, 14475, -825; 5670, -825, 46],[315, 15, 1],[3, -1, -7, -53, -17, -7, -34, 2, 32, 12; 20, -7, -47, -357, -115, -48, -238, 12, 210, 80; -11, 0, 20, 126, 30, -1, -105, -35, -189, -45],65,18]
%
% END OF LATTICE L66.18
%
%
% LATTICE L66.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[477960, 22260, 120540; 22260, 1800, 5688; 120540, 5688, 30407],[420, 12, 1],[-613, -215, -107, -4993, -637, -5123, -6477, -2761, -15083, -319; -240, -84, -42, -1960, -250, -2010, -2541, -1083, -5915, -125; 2475, 868, 432, 20160, 2572, 20685, 26152, 11148, 60900, 1288],65,19]
%
% END OF LATTICE L66.19
%
%
% LATTICE L66.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-69300, -38640, 420; -38640, -21390, 225; 420, 225, -2],[420, 15, 1],[-9, -3, 6, 16, 5, 9, 3, -6, -16, -5; 20, 7, -13, -35, -11, -20, -7, 13, 35, 11; 348, 140, -210, -588, -190, -372, -175, 195, 567, 185],65,20]
%
% END OF LATTICE L66.20
%
%
% LATTICE L66.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-439110, -77490, 945; -77490, -13629, 168; 945, 168, -2],[315, 21, 1],[136, 12, 34, 8, 2, -4, -1, -1, 3, 9; -495, -44, -126, -30, -8, 15, 4, 6, -10, -32; 22050, 1923, 5355, 1235, 273, -630, -138, 0, 550, 1512],65,21]
%
% END OF LATTICE L66.21
%
%
% LATTICE L66.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-315, -3780, 315; -3780, -44562, 3717; 315, 3717, -310],[315, 21, 1],[-199, -44, -30, -38, 8, -9, -8, -22, -118, -60; 25, 7, 7, 15, 1, -5, -2, -2, 0, 4; 70, 33, 49, 135, 21, -70, -33, -49, -135, -21],65,22]
%
% END OF LATTICE L66.22
%
%
% LATTICE L66.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[16582440, -351540, 4139940; -351540, 7400, -87760; 4139940, -87760, 1033569],[420, 20, 1],[-28, -2393, -109, 1623, 3463, 1758, 32668, 4434, 4432, 862; 10, 882, 40, -602, -1284, -652, -12117, -1645, -1645, -321; 113, 9660, 440, -6552, -13980, -7097, -131880, -17900, -17892, -3480],65,23]
%
% END OF LATTICE L66.23
%
%
% LATTICE L66.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[3780, -420, -420; -420, 42, 21; -420, 21, -94],[420, 21, 1],[387, 17, 48, 34, 3, -3, -1, 0, 14, 13; 4240, 186, 524, 370, 32, -40, -11, 1, 155, 143; -840, -37, -105, -75, -7, 0, 2, 0, -30, -28],65,24]
%
% END OF LATTICE L66.24
%
%
% LATTICE L66.25
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[23161110, 16137765, -5748960; 16137765, 11239095, -4003860; -5748960, -4003860, 1426351],[105, 105, 1],[87, -1, -99, -5, 73, 405, 206, 714, 128, 132; 14770, -166, -16840, -882, 12264, 68402, 34821, 120805, 21675, 22391; 41811, -470, -47670, -2496, 34720, 193641, 98575, 341985, 61359, 63385],65,25]
%
% END OF LATTICE L66.25
%
%
% LATTICE L66.26
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[207178440, -1782900, 51378600; -1782900, 15400, -442148; 51378600, -442148, 12741483],[420, 28, 1],[119152, 53815, 38453, 17971, -7631, 3942, 7732, 23094, 43576, 69178; -25585, -11556, -8258, -3860, 1638, -845, -1659, -4957, -9355, -14853; -481355, -217404, -155344, -72600, 30828, -15925, -31236, -93296, -176040, -279468],65,26]
%
% END OF LATTICE L66.26
%
%
% LATTICE L66.27
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1341060, 374640, 7140; 374640, -104650, -1995; 7140, -1995, -38],[420, 35, 1],[5, 8, 17, 5, 32, 35, 17, 8, 0, -7; 12, 18, 36, 10, 60, 60, 27, 9, -1, -15; 308, 555, 1295, 411, 2835, 3388, 1755, 1015, 51, -525],65,27]
%
% END OF LATTICE L66.27
%
%
% LATTICE L66.28
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[6749867880, -104286420, -1687956480; -104286420, 1611240, 26079168; -1687956480, 26079168, 422111533],[1260, 12, 1],[-1073, -1117, -253, 279, 213, 1157, 1215, 295, -181, -199; -255, -238, -60, -70, -4, -135, -217, -135, -385, -61; -4275, -4452, -1008, 1120, 852, 4635, 4872, 1188, -700, -792],65,28]
%
% END OF LATTICE L66.28
%
%
% LATTICE L66.29
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[859846680, 4590180, -214982460; 4590180, 24504, -1147656; -214982460, -1147656, 53750813],[1260, 12, 1],[2579, 9668, 1338, 20852, 346, 99, -295, 1, 7267, 993; -1405, -5257, -725, -11235, -181, -45, 182, 0, -3990, -544; 10285, 38556, 5336, 83160, 1380, 395, -1176, 4, 28980, 3960],65,29]
%
% END OF LATTICE L66.29
%
%
% LATTICE L66.30
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-772380, 386820, 1260; 386820, -193650, -585; 1260, -585, 26],[1260, 15, 1],[287, 164, -121, -129, -132, -263, -129, 136, 136, 137; 576, 329, -243, -259, -265, -528, -259, 273, 273, 275; -936, -525, 405, 427, 435, 864, 420, -450, -448, -450],65,30]
%
% END OF LATTICE L66.30
%
%
% LATTICE L66.31
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[12452580, -1786680, -23940; -1786680, 256350, 3435; -23940, 3435, 46],[1260, 15, 1],[5, 34, 7, 31, 6, 3, 1, -2, -10, -1; 36, 238, 48, 210, 40, 20, 7, -13, -63, -5; -92, -105, 55, 441, 135, 68, 0, -70, -504, -150],65,31]
%
% END OF LATTICE L66.31
%
%
% LATTICE L66.32
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[92165640, -705180, 22843380; -705180, 5400, -174780; 22843380, -174780, 5661763],[420, 60, 1],[176, 901, 401, 811, 307, 436, 2669, 1129, 1331, 203; -29, -154, -68, -126, -44, -61, -371, -157, -189, -31; -711, -3640, -1620, -3276, -1240, -1761, -10780, -4560, -5376, -820],65,32]
%
% END OF LATTICE L66.32
%
%
% LATTICE L66.33
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[364140, 112140, 0; 112140, 34314, 21; 0, 21, -2],[1260, 21, 1],[-1333, -58, -161, -37, -8, 37, 4, -1, -17, -46; 4320, 188, 522, 120, 26, -120, -13, 3, 55, 149; 44100, 1923, 5355, 1235, 273, -1260, -138, 0, 550, 1512],65,33]
%
% END OF LATTICE L66.33
%
%
% LATTICE L66.34
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-39653460, -999180, 110880; -999180, -25158, 2793; 110880, 2793, -310],[1260, 21, 1],[9, 4, 11, 59, 30, 199, 22, 15, 19, -4; 280, 122, 332, 1770, 896, 5920, 653, 443, 555, -121; 5740, 2529, 6923, 37035, 18795, 124460, 13746, 9352, 11790, -2520],65,34]
%
% END OF LATTICE L66.34
%
%
% LATTICE L66.35
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[630, -30870, 315; -30870, 1318485, -13440; 315, -13440, 137],[315, 105, 1],[-1, -1, 1, 1, 13, 37, 16, 44, 2, 2; -9, -4, 0, 2, 26, 69, 29, 75, 3, -1; -882, -390, 0, 194, 2520, 6678, 2805, 7245, 289, -105],65,35]
%
% END OF LATTICE L66.35
%
%
% LATTICE L66.36
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-375795, -281925, 3780; -281925, -211470, 2835; 3780, 2835, -38],[315, 105, 1],[-1, -4, -10, -10, -24, -15, -16, -10, -2, 4; 2, 10, 28, 30, 76, 50, 55, 37, 9, -11; 49, 345, 1085, 1233, 3255, 2219, 2490, 1750, 468, -420],65,36]
%
% END OF LATTICE L66.36
%
%
% LATTICE L66.37
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[792120, 290220, 197400; 290220, 106344, 72324; 197400, 72324, 49193],[420, 84, 1],[-3523, -660, -2066, -1684, -278, -443, -1, 83, -299, -383; -25, -5, -17, -15, -3, -5, 0, 2, 0, -2; 14175, 2656, 8316, 6780, 1120, 1785, 4, -336, 1200, 1540],65,37]
%
% END OF LATTICE L66.37
%
%
% LATTICE L66.38
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2286900, -26880, -8820; -26880, 210, 105; -8820, 105, 34],[420, 105, 1],[51, 11, 30, 4, 1, -3, -1, 0, 2, 9; 176, 38, 104, 14, 4, -8, -3, 1, 7, 31; 12684, 2735, 7455, 993, 245, -756, -250, 0, 498, 2240],65,38]
%
% END OF LATTICE L66.38
%
%
% LATTICE L66.39
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[37599240, 472500, -8953560; 472500, 6440, -112140; -8953560, -112140, 2132407],[420, 140, 1],[-636, -5392, -15666, -5900, -46894, -16250, -36823, -26549, -2543, 4679; 1929, 16353, 47511, 17893, 142215, 49281, 111672, 80514, 7712, -14190; -2569, -21780, -63280, -23832, -189420, -65639, -148740, -107240, -10272, 18900],65,39]
%
% END OF LATTICE L66.39
%
%
% LATTICE L66.40
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[6006709800, 78728580, -1503830160; 78728580, 1031880, -19710360; -1503830160, -19710360, 376496489],[1260, 60, 1],[-2684, -16539, -7043, -2767, -1249, -1036, -5161, -2257, -1573, -1851; 375, 2317, 987, 385, 169, 135, 658, 288, 210, 256; -10701, -65940, -28080, -11032, -4980, -4131, -20580, -9000, -6272, -7380],65,40]
%
% END OF LATTICE L66.40
%
%
% LATTICE L66.41
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[101619000, -1306620, -25498620; -1306620, 14520, 327840; -25498620, 327840, 6398209],[1260, 60, 1],[9017, 167168, 22582, 67120, 4078, -235, -13483, -627, 25091, 17877; -347, -6433, -869, -2583, -157, 9, 518, 24, -966, -688; 35953, 666540, 90040, 267624, 16260, -937, -53760, -2500, 100044, 71280],65,41]
%
% END OF LATTICE L66.41
%
%
% LATTICE L66.42
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1503363960, -8544060, -376908840; -8544060, 48552, 2142084; -376908840, 2142084, 94494931],[1260, 84, 1],[-59173, -9378, -22184, -4058, 632, 1027, -313, -6889, -5633, -10323; -3810, -605, -1437, -265, 37, 60, -20, -438, -360, -662; -235935, -37392, -88452, -16180, 2520, 4095, -1248, -27468, -22460, -41160],65,42]
%
% END OF LATTICE L66.42
%
%
% LATTICE L66.43
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[11241450360, -36732780, -2819340720; -36732780, 120120, 9212532; -2819340720, 9212532, 707086883],[1260, 84, 1],[-12421, -24372, -72802, -412124, -218090, -375641, -169659, -121229, -169969, 24059; -60, -119, -357, -2025, -1073, -1850, -836, -598, -840, 118; -49525, -97176, -290276, -1643220, -869568, -1497755, -676464, -483364, -677700, 95928],65,43]
%
% END OF LATTICE L66.43
%
%
% LATTICE L66.44
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[550620, -3241980, 102060; -3241980, 18357150, -579705; 102060, -579705, 18302],[1260, 105, 1],[9295, 2008, 5509, 249, 234, -319, -138, 101, 125, 1636; -18516, -4000, -10974, -496, -466, 636, 275, -201, -249, -3259; -638316, -137895, -378315, -17099, -16065, 21924, 9480, -6930, -8584, -112350],65,44]
%
% END OF LATTICE L66.44
%
%
% LATTICE L66.45
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-165060, -76860, 2520; -76860, -35070, 1155; 2520, 1155, -38],[1260, 105, 1],[15, 8, 5, 1, -2, 1, 2, 5, 5, 12; 80, 41, 23, 3, -13, 8, 14, 32, 30, 68; 3388, 1755, 1015, 153, -525, 308, 555, 1295, 1233, 2835],65,45]
%
% END OF LATTICE L66.45
%
%
% LATTICE L66.46
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[37800, -2994180, -741300; -2994180, 234585960, 58078860; -741300, 58078860, 14379181],[420, 420, 1],[-5, -5, -17, -3, -3, -1, 0, 2, 0, -2; -1721, -2872, -14246, -3176, -4506, -1357, 307, 6551, 1637, 1941; 6951, 11600, 57540, 12828, 18200, 5481, -1240, -26460, -6612, -7840],65,46]
%
% END OF LATTICE L66.46
%
%
% LATTICE L66.47
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1427800653720, 12698210700, 348468755040; 12698210700, 112932120, 3099122880; 348468755040, 3099122880, 85047217847],[1260, 420, 1],[-485, -2506, -16400, -1354, -6416, -1909, 511, 10415, 955, 4421; 939, 6805, 46011, 3837, 18349, 5457, -1475, -30021, -2771, -13019; 1953, 10020, 65520, 5408, 25620, 7623, -2040, -41580, -3812, -17640],65,47]
%
% END OF LATTICE L66.47
%
%
% LATTICE L66.48
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[365205960, 3080700, 89277300; 3080700, 26040, 753060; 89277300, 753060, 21824527],[1260, 420, 1],[5087, 11499, 8253, 2357, -1475, 223, 1776, 5022, 5608, 14750; -15369, -34742, -24936, -7122, 4456, -673, -5363, -15169, -16941, -44561; -20279, -45840, -32900, -9396, 5880, -889, -7080, -20020, -22356, -58800],65,48]
%
% END OF LATTICE L66.48
%

\medskip%
%------------------------------WEYL-GROUP-W67--------------------------------
%
\leavevmode\llap{}%
$W_{67\phantom{0}}$%
\qquad\llap{88} lattices, $\chi=27$%
\hfill%
$22422222$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L67.1
%
\leavevmode%
${L_{67.1}}$%
{} : {$1\above{1pt}{1pt}{2}{{\rm II}}4\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{2}{}5\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{2}{}7\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{2\rightarrow N_{67}}%
\EasyButWeakLineBreak%
{${20}\above{1pt}{1pt}{*}{2}{84}\above{1pt}{1pt}{*}{2}{4}\above{1pt}{1pt}{*}{4}{2}\above{1pt}{1pt}{s}{2}{30}\above{1pt}{1pt}{l}{2}{4}\above{1pt}{1pt}{r}{2}{70}\above{1pt}{1pt}{b}{2}{12}\above{1pt}{1pt}{*}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-5778780\\-1930740\\30240
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1930740\\-645076\\10103
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
30240\\10103\\-158
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-159\\490\\900
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
41\\-126\\-210
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
37\\-114\\-208
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-26\\80\\139
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-302\\930\\1665
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-187\\576\\1040
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1886\\5810\\10535
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-631\\1944\\3534
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-5778780, -1930740, 30240; -1930740, -645076, 10103; 30240, 10103, -158],[420, 1, 1],[-159, 41, 37, -26, -302, -187, -1886, -631; 490, -126, -114, 80, 930, 576, 5810, 1944; 900, -210, -208, 139, 1665, 1040, 10535, 3534],66,1]
%
% END OF LATTICE L67.1
%
\hbox{}\par\smallskip%
%
% LATTICE L67.2
%
\leavevmode%
${L_{67.2}}$%
{} : {$1\above{1pt}{1pt}{2}{2}8\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{2}{}5\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{2}{}7\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{2\rightarrow N'_{33}}%
\EasyButWeakLineBreak%
{${10}\above{1pt}{1pt}{s}{2}{42}\above{1pt}{1pt}{b}{2}{2}\above{1pt}{1pt}{}{4}{1}\above{1pt}{1pt}{r}{2}{60}\above{1pt}{1pt}{s}{2}{8}\above{1pt}{1pt}{s}{2}{140}\above{1pt}{1pt}{*}{2}{24}\above{1pt}{1pt}{b}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-24797640\\31920\\44520
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
31920\\-38\\-59
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
44520\\-59\\-79
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4\\875\\1600
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2\\-441\\-798
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-219\\-400
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\220\\399
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
19\\4170\\7590
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
11\\2412\\4396
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
107\\23450\\42770
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
35\\7668\\13992
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-24797640, 31920, 44520; 31920, -38, -59; 44520, -59, -79],[840, 1, 1],[4, -2, -1, 1, 19, 11, 107, 35; 875, -441, -219, 220, 4170, 2412, 23450, 7668; 1600, -798, -400, 399, 7590, 4396, 42770, 13992],66,2]
%
% END OF LATTICE L67.2
%
\hbox{}\par\smallskip%
%
% LATTICE L67.3
%
\leavevmode%
${L_{67.3}}$%
{} : {$1\above{1pt}{1pt}{-2}{2}8\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{2}{}5\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{2}{}7\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{m}%
\EasyButWeakLineBreak%
{${10}\above{1pt}{1pt}{b}{2}{42}\above{1pt}{1pt}{s}{2}{2}\above{1pt}{1pt}{*}{4}{4}\above{1pt}{1pt}{l}{2}{15}\above{1pt}{1pt}{r}{2}{8}\above{1pt}{1pt}{l}{2}{35}\above{1pt}{1pt}{}{2}{24}\above{1pt}{1pt}{r}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-32246760\\36960\\22680
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
36960\\-41\\-28
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
22680\\-28\\-13
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
8\\4925\\3345
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
13\\8001\\5439
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\615\\419
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-616\\-418
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-615\\-420
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\1848\\1252
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
32\\19705\\13370
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
29\\17856\\12120
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-32246760, 36960, 22680; 36960, -41, -28; 22680, -28, -13],[840, 1, 1],[8, 13, 1, -1, -1, 3, 32, 29; 4925, 8001, 615, -616, -615, 1848, 19705, 17856; 3345, 5439, 419, -418, -420, 1252, 13370, 12120],66,3]
%
% END OF LATTICE L67.3
%
%
% LATTICE L67.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[2730, 525, 0; 525, 101, 0; 0, 0, -1],[105, 1, 1],[-1, -4, 1, 7, 29, 5, 67, 8; 5, 21, -5, -36, -150, -26, -350, -42; 0, 0, -2, -8, -30, -5, -70, -9],66,4]
%
% END OF LATTICE L67.4
%
%
% LATTICE L67.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[100590, 52500, 95760; 52500, 27401, 49979; 95760, 49979, 91162],[210, 1, 1],[2408, 2456, -2, -28, 1069, 1151, 15257, 5915; -1650, -1680, 2, 19, -735, -790, -10465, -4056; -1625, -1659, 1, 19, -720, -776, -10290, -3990],66,5]
%
% END OF LATTICE L67.5
%
%
% LATTICE L67.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-9949380, 16380, 23940; 16380, -26, -41; 23940, -41, -55],[420, 1, 1],[8, 13, 1, -1, -2, 3, 64, 29; 2570, 4179, 322, -321, -645, 962, 20545, 9312; 1565, 2541, 195, -196, -390, 588, 12530, 5676],66,6]
%
% END OF LATTICE L67.6
%
%
% LATTICE L67.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-4974060, 20685, 1667610; 20685, -78, -6936; 1667610, -6936, -559085],[105, 3, 1],[-4771, -1145, 267, -268, -2482, -3054, -72718, -4466; -2050, -497, 112, -111, -1055, -1304, -31115, -1913; -14205, -3409, 795, -798, -7390, -9093, -216510, -13297],66,7]
%
% END OF LATTICE L67.7
%
%
% LATTICE L67.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-23489970, 44310, -11714430; 44310, -76, 22096; -11714430, 22096, -5841977],[210, 2, 1],[20592, 24238, 608, -607, 5741, 4085, 117143, 23462; -7525, -8841, -219, 220, -2115, -1497, -42875, -8583; -41320, -48636, -1220, 1218, -11520, -8197, -235060, -47079],66,8]
%
% END OF LATTICE L67.8
%
%
% LATTICE L67.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-7001400, 31605, -1391460; 31605, -130, 6280; -1391460, 6280, -276539],[105, 5, 1],[839, 3019, -235, 236, 1310, 2686, 12790, 11782; -410, -1491, 112, -111, -633, -1304, -6223, -5739; -4231, -15225, 1185, -1190, -6606, -13545, -64498, -59415],66,9]
%
% END OF LATTICE L67.9
%
%
% LATTICE L67.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-29108730, 60270, -9675120; 60270, -114, 20031; -9675120, 20031, -3215803],[210, 3, 1],[18212, 7146, 538, -537, 1692, 7225, 103598, 13833; -7525, -2947, -219, 220, -705, -2994, -42875, -5722; -54840, -21518, -1620, 1617, -5095, -21756, -311955, -41654],66,10]
%
% END OF LATTICE L67.10
%
%
% LATTICE L67.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-9074940, 42525, -1287930; 42525, -182, 6034; -1287930, 6034, -182785],[105, 7, 1],[3979, 409, -223, 224, 6214, 2548, 8666, 11176; -2050, -213, 112, -111, -3165, -1304, -4445, -5739; -28105, -2889, 1575, -1582, -43890, -17997, -61210, -78939],66,11]
%
% END OF LATTICE L67.11
%
%
% LATTICE L67.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-41043030, 92190, 16442790; 92190, -190, -36935; 16442790, -36935, -6587363],[210, 5, 1],[-6564, -38636, -970, 968, -1829, -13019, -37337, -74783; -1505, -8841, -219, 220, -423, -2994, -8575, -17166; -16376, -96390, -2420, 2415, -4563, -32480, -93149, -186570],66,12]
%
% END OF LATTICE L67.12
%
%
% LATTICE L67.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-372540, 79380, -2520; 79380, -16914, 537; -2520, 537, -17],[420, 3, 1],[12, 6, 1, -2, -1, 5, 101, 15; 55, 28, 5, -9, -5, 22, 455, 68; -45, -7, 9, 12, -10, -48, -630, -80],66,13]
%
% END OF LATTICE L67.13
%
%
% LATTICE L67.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[30444894060, -70747950, 15135332520; -70747950, 164406, -35171538; 15135332520, -35171538, 7524358273],[210, 6, 1],[-1538101, -523013, 1217, 17903, -227526, -367535, -9744324, -629650; -1650, -560, 2, 19, -245, -395, -10465, -676; 3093900, 1052044, -2448, -36012, 457670, 739299, 19600770, 1266545],66,14]
%
% END OF LATTICE L67.14
%
%
% LATTICE L67.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-15646260, 47040, 28140; 47040, -132, -87; 28140, -87, -50],[420, 3, 1],[13, 1, -3, -1, 3, 9, 107, 13; 1290, 98, -298, -98, 300, 896, 10640, 1292; 5070, 392, -1170, -393, 1165, 3504, 41685, 5066],66,15]
%
% END OF LATTICE L67.15
%
%
% LATTICE L67.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-53242770, 124110, 22842960; 124110, -266, -53249; 22842960, -53249, -9800407],[210, 7, 1],[-46748, -7862, -1382, 1379, -13024, -18543, -37986, -106517; -7525, -1263, -219, 220, -2115, -2994, -6125, -17166; -108920, -18318, -3220, 3213, -30345, -43204, -88505, -248178],66,16]
%
% END OF LATTICE L67.16
%
%
% LATTICE L67.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1579386165, -13240185, -535892910; -13240185, 111000, 4492455; -535892910, 4492455, 181830902],[105, 15, 1],[72921, 113553, -6143, -626, 26146, 190891, 976810, 310587; -157, -245, 13, 2, -56, -410, -2100, -668; 214917, 334670, -18105, -1845, 77059, 562605, 2878911, 915380],66,17]
%
% END OF LATTICE L67.17
%
%
% LATTICE L67.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1437880080, -4394460, 357472920; -4394460, 13432, -1092512; 357472920, -1092512, 88871729],[420, 4, 1],[2493, 863, 51, 1834, 11408, 1502, 58644, 9722; -3440, -1197, -70, -2523, -15705, -2069, -80815, -13401; -10070, -3486, -206, -7408, -46080, -6067, -236880, -39270],66,18]
%
% END OF LATTICE L67.18
%
%
% LATTICE L67.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[969298680, -15464820, 239968680; -15464820, 246740, -3828616; 239968680, -3828616, 59408899],[420, 4, 1],[7933, 14330, 1651, 207, 713, 1697, 64959, 7234; 55, 105, 13, 2, 0, 10, 420, 48; -32040, -57876, -6668, -836, -2880, -6854, -262360, -29217],66,19]
%
% END OF LATTICE L67.19
%
%
% LATTICE L67.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[578995620, -12595590, 275597280; -12595590, 274010, -5995400; 275597280, -5995400, 131182099],[210, 10, 1],[-54335, -277121, 219, 3161, -24116, -64922, -344242, -333655; -330, -1680, 2, 19, -147, -395, -2093, -2028; 114136, 582120, -460, -6640, 50658, 136375, 723114, 700875],66,20]
%
% END OF LATTICE L67.20
%
%
% LATTICE L67.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-18612300, 124320, 47040; 124320, -790, -325; 47040, -325, -116],[420, 5, 1],[9, -19, -11, 10, 20, 59, 116, 191; 558, -1176, -682, 619, 1239, 3656, 7189, 11838; 2086, -4410, -2550, 2320, 4638, 13680, 26894, 44280],66,21]
%
% END OF LATTICE L67.21
%
%
% LATTICE L67.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-818580, 267960, 5040; 267960, -87715, -1650; 5040, -1650, -31],[420, 5, 1],[5, 37, 2, -4, -1, 11, 43, 95; 14, 105, 6, -11, -3, 30, 119, 264; 67, 420, 5, -65, -3, 190, 651, 1380],66,22]
%
% END OF LATTICE L67.22
%
%
% LATTICE L67.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1590863295, -15722805, -540921780; -15722805, 155400, 5346033; -540921780, 5346033, 183923014],[105, 21, 1],[441303, 19635, -7433, -764, 158216, 231037, 844472, 375915; -785, -35, 13, 2, -280, -410, -1500, -668; 1297905, 57748, -21861, -2247, 465325, 679497, 2483655, 1105594],66,23]
%
% END OF LATTICE L67.23
%
%
% LATTICE L67.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1803480, 251160, 6720; 251160, -34977, -936; 6720, -936, -25],[840, 3, 1],[7, -1, -2, 1, 9, 17, 171, 19; 45, -7, -13, 7, 60, 112, 1120, 124; 195, -7, -51, 6, 170, 372, 3990, 460],66,24]
%
% END OF LATTICE L67.24
%
%
% LATTICE L67.25
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-26932920, 33600, 66360; 33600, -39, -84; 66360, -84, -163],[840, 3, 1],[14, 9, 3, -1, -1, 3, 46, 15; 1945, 1253, 419, -138, -140, 412, 6370, 2080; 4695, 3017, 1005, -336, -335, 1008, 15435, 5032],66,25]
%
% END OF LATTICE L67.25
%
%
% LATTICE L67.26
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-370860, 8400, 81480; 8400, -182, -1925; 81480, -1925, -17137],[420, 7, 1],[383, 88, 46, -49, -92, 147, 442, 1397; 8420, 1935, 1012, -1077, -2025, 3230, 9715, 30708; 875, 201, 105, -112, -210, 336, 1010, 3192],66,26]
%
% END OF LATTICE L67.26
%
%
% LATTICE L67.27
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[373231740, -11965590, 174065640; -11965590, 383614, -5580442; 174065640, -5580442, 81179717],[210, 14, 1],[-257109, -37465, 209, 2991, -114122, -61443, -232708, -315770; -1650, -240, 2, 19, -735, -395, -1495, -2028; 551180, 80316, -448, -6412, 244650, 131719, 498870, 676935],66,27]
%
% END OF LATTICE L67.27
%
%
% LATTICE L67.28
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1300740, 20160, 13020; 20160, -308, -203; 13020, -203, -130],[420, 7, 1],[13, 1, -3, -3, -1, 5, 11, 31; 250, 18, -58, -54, 0, 104, 220, 612; 910, 72, -210, -217, -105, 336, 755, 2142],66,28]
%
% END OF LATTICE L67.28
%
%
% LATTICE L67.29
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[402253530, 12858090, 143544660; 12858090, 411015, 4588425; 143544660, 4588425, 51224086],[210, 15, 1],[41320, 70248, -166, -2404, 6113, 98741, 261783, 169155; -330, -560, 2, 19, -49, -790, -2093, -1352; -115761, -196805, 465, 6735, -17126, -276630, -733404, -473900],66,29]
%
% END OF LATTICE L67.29
%
%
% LATTICE L67.30
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1487076675, 19624815, -277676595; 19624815, 259000, -3664465; -277676595, -3664465, 51849578],[105, 35, 1],[60523, 40393, -5097, -524, 65096, 158429, 115816, 773329; -181726, -121284, 15304, 1574, -195456, -475697, -347748, -2321991; 311283, 207750, -26215, -2695, 334803, 814835, 595667, 3977400],66,30]
%
% END OF LATTICE L67.30
%
%
% LATTICE L67.31
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-4036200, 28560, 518280; 28560, -190, -3795; 518280, -3795, -65203],[840, 5, 1],[52, -128, -65, 64, 245, 711, 1385, 2267; 2703, -6657, -3379, 3328, 12738, 36964, 72002, 117852; 256, -630, -320, 315, 1206, 3500, 6818, 11160],66,31]
%
% END OF LATTICE L67.31
%
%
% LATTICE L67.32
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-28581000, 44520, 89040; 44520, -65, -140; 89040, -140, -277],[840, 5, 1],[4, 41, 5, -1, -1, 3, 12, 61; 333, 3423, 419, -82, -84, 244, 994, 5064; 1117, 11445, 1395, -280, -279, 840, 3353, 17040],66,32]
%
% END OF LATTICE L67.32
%
%
% LATTICE L67.33
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1026087510, 24298680, 359019780; 24298680, 575421, 8501913; 359019780, 8501913, 125618138],[210, 21, 1],[389726, 18930, -316, -4534, 57661, 186269, 352737, 319095; -1650, -80, 2, 19, -245, -790, -1495, -1352; -1113735, -54097, 903, 12957, -164780, -532308, -1008030, -911890],66,33]
%
% END OF LATTICE L67.33
%
%
% LATTICE L67.34
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[5055637440, -37134300, 1251747420; -37134300, 272760, -9194244; 1251747420, -9194244, 309925627],[420, 12, 1],[6143, 669, 361, 5580, 10746, 4055, 154534, 8418; 25, 0, 1, 29, 55, 20, 735, 39; -24810, -2702, -1458, -22536, -43400, -16377, -624120, -33998],66,34]
%
% END OF LATTICE L67.34
%
%
% LATTICE L67.35
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[3023160, 31500, 750960; 31500, 492, 7836; 750960, 7836, 186541],[420, 12, 1],[-2244, -1283, -428, -107, -213, -587, -20077, -721; -625, -357, -119, -30, -60, -164, -5600, -201; 9060, 5180, 1728, 432, 860, 2370, 81060, 2911],66,35]
%
% END OF LATTICE L67.35
%
%
% LATTICE L67.36
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-8704920, 50400, -927360; 50400, -287, 5516; -927360, 5516, -94315],[840, 7, 1],[-922, -215, -117, 115, 119, -341, -524, -3331; -99355, -23169, -12609, 12392, 12825, -36744, -56465, -358944; 3255, 759, 413, -406, -420, 1204, 1850, 11760],66,36]
%
% END OF LATTICE L67.36
%
%
% LATTICE L67.37
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3916920, 1369200, -15960; 1369200, -478618, 5579; -15960, 5579, -65],[840, 7, 1],[23, -1, -6, 3, 83, 53, 77, 181; 65, -3, -17, 9, 240, 152, 220, 516; -70, -12, 14, 35, 210, 28, -30, -168],66,37]
%
% END OF LATTICE L67.37
%
%
% LATTICE L67.38
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-36108646770, 6699630, -17953995780; 6699630, -1140, 3331200; -17953995780, 3331200, -8927112847],[210, 30, 1],[593360, 1164174, 87680, -87501, 55113, 588439, 3375137, 1126686; -1505, -2947, -219, 220, -141, -1497, -8575, -2861; -1193352, -2341360, -176340, 175980, -110842, -1183455, -6787998, -2265965],66,38]
%
% END OF LATTICE L67.38
%
%
% LATTICE L67.39
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-4966500, 426720, 78120; 426720, -36600, -6705; 78120, -6705, -1228],[420, 15, 1],[9, 1, -11, -1, 3, 37, 83, 49; -160, -14, 196, 13, -55, -668, -1491, -878; 1446, 140, -1770, -135, 491, 6000, 13419, 7910],66,39]
%
% END OF LATTICE L67.39
%
%
% LATTICE L67.40
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-65100, 5040, 2520; 5040, -390, -195; 2520, -195, -97],[420, 15, 1],[1, 2, 0, -1, 0, 3, 10, 7; 17, 42, 7, -13, -1, 38, 147, 108; -9, -35, -15, 0, 2, 0, -42, -40],66,40]
%
% END OF LATTICE L67.40
%
%
% LATTICE L67.41
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-6112680, 46200, 1485960; 46200, -304, -11288; 1485960, -11288, -361157],[840, 8, 1],[768, -382, -192, 191, 1819, 527, 10257, 839; 3835, -1911, -959, 955, 9090, 2633, 51240, 4191; 3040, -1512, -760, 756, 7200, 2086, 40600, 3321],66,41]
%
% END OF LATTICE L67.41
%
%
% LATTICE L67.42
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-12337080, -5318040, 38640; -5318040, -2292400, 16656; 38640, 16656, -121],[840, 8, 1],[-42, 8, 10, -5, -71, -23, -473, -80; 105, -21, -25, 13, 180, 58, 1190, 201; 1040, -336, -248, 192, 2100, 638, 12740, 2118],66,42]
%
% END OF LATTICE L67.42
%
%
% LATTICE L67.43
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[9776090730, 96827220, -3869813010; 96827220, 959035, -38328535; -3869813010, -38328535, 1531844696],[210, 35, 1],[-351789, -256309, 1427, 20463, -156145, -840687, -318401, -4320505; -330, -240, 2, 19, -147, -790, -299, -4056; -888713, -647505, 3605, 51695, -394464, -2123800, -804366, -10914750],66,43]
%
% END OF LATTICE L67.43
%
%
% LATTICE L67.44
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[15246629160, -197517180, 3774718500; -197517180, 2558800, -48900760; 3774718500, -48900760, 934534421],[420, 20, 1],[1803, 1612, 359, 8839, 10283, 6404, 48161, 38959; 11, 21, 1, 38, 48, 32, 252, 210; -7282, -6510, -1450, -35700, -41532, -25865, -194516, -157350],66,44]
%
% END OF LATTICE L67.44
%
%
% LATTICE L67.45
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[9808260, -101640, 2421300; -101640, 1220, -25080; 2421300, -25080, 597731],[420, 20, 1],[913, 8422, 1015, 203, 101, 963, 7403, 4133; 248, 2289, 276, 55, 27, 261, 2009, 1122; -3688, -34020, -4100, -820, -408, -3890, -29904, -16695],66,45]
%
% END OF LATTICE L67.45
%
%
% LATTICE L67.46
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-118020, -43260, 5040; -43260, -15855, 1848; 5040, 1848, -215],[420, 21, 1],[-29, -3, -8, 2, 7, -1, -21, -27; 55, 6, 17, -3, -15, -2, 35, 48; -210, -19, -42, 21, 35, -42, -195, -224],66,46]
%
% END OF LATTICE L67.46
%
%
% LATTICE L67.47
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-93204327930, 12721170, -46341062670; 12721170, -1596, 6324948; -46341062670, 6324948, -23040712133],[210, 42, 1],[5559296, 311650, 164344, -163989, 516281, 1102577, 4517327, 2111180; -7525, -421, -219, 220, -705, -1497, -6125, -2861; -11181240, -626812, -330540, 329826, -1038380, -2217579, -9085560, -4246151],66,47]
%
% END OF LATTICE L67.47
%
%
% LATTICE L67.48
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-17375820, 127260, 83160; 127260, -924, -609; 83160, -609, -398],[420, 21, 1],[13, 1, -3, -10, -12, -9, -4, 1; -10, -2, 2, 20, 30, 32, 30, 16; 2730, 212, -630, -2121, -2555, -1932, -885, 182],66,48]
%
% END OF LATTICE L67.48
%
%
% LATTICE L67.49
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-6641599125, -4741706865, 1688938965; -4741706865, -3385296600, 1205801940; 1688938965, 1205801940, -429492151],[105, 105, 1],[-410, -71, 112, -111, -211, -1304, -889, -1913; -164381, -28189, 45957, -46108, -85482, -525996, -357866, -769276; -463113, -79420, 129465, -129885, -240821, -1481865, -1008207, -2167270],66,49]
%
% END OF LATTICE L67.49
%
%
% LATTICE L67.50
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[77367360, -1477980, 19146540; -1477980, 28280, -365764; 19146540, -365764, 4738303],[420, 28, 1],[2547, 49, 149, 2800, 15802, 1925, 10198, 11446; 25, 0, 1, 29, 165, 20, 105, 117; -10290, -198, -602, -11312, -63840, -7777, -41200, -46242],66,50]
%
% END OF LATTICE L67.50
%
%
% LATTICE L67.51
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[25881240, 22119300, 6552420; 22119300, 18904172, 5600000; 6552420, 5600000, 1658893],[420, 28, 1],[591, 212, 237, 55, -319, -5, 369, 379; 55, 15, 13, 2, 0, 10, 60, 48; -2520, -888, -980, -224, 1260, -14, -1660, -1659],66,51]
%
% END OF LATTICE L67.51
%
%
% LATTICE L67.52
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2035320, 651840, 23520; 651840, -208650, -7515; 23520, -7515, -269],[840, 15, 1],[25, 19, -26, -18, 5, 131, 347, 221; 101, 77, -105, -73, 20, 528, 1400, 892; -636, -490, 660, 465, -122, -3300, -8778, -5600],66,52]
%
% END OF LATTICE L67.52
%
%
% LATTICE L67.53
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-610474200, 357840, 715680; 357840, -195, -420; 715680, -420, -839],[840, 15, 1],[10, 37, 15, -1, -1, 3, 26, 47; 277, 1029, 419, -26, -28, 76, 714, 1296; 8391, 31045, 12585, -840, -839, 2520, 21819, 39440],66,53]
%
% END OF LATTICE L67.53
%
%
% LATTICE L67.54
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-392700, -73080, 12180; -73080, -13510, 2275; 12180, 2275, -377],[420, 35, 1],[-10, -1, 15, 17, -8, -61, -22, -287; 20, 3, -28, -33, 15, 118, 43, 564; -203, -15, 315, 350, -168, -1260, -452, -5880],66,54]
%
% END OF LATTICE L67.54
%
%
% LATTICE L67.55
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-13362465270, 6217890, -6375780180; 6217890, -2660, 2966810; -6375780180, 2966810, -3042146197],[210, 70, 1],[521064, 438158, 77020, -76853, 145169, 516712, 423401, 2968159; -1505, -1263, -219, 220, -423, -1497, -1225, -8583; -1092056, -918300, -161420, 161070, -304248, -1082935, -887372, -6220725],66,55]
%
% END OF LATTICE L67.55
%
%
% LATTICE L67.56
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-7279860, -33088860, -4738020; -33088860, -149985500, -21476945; -4738020, -21476945, -3075358],[420, 35, 1],[-621, -71, 759, 214, -476, -2263, -756, -9563; -19874, -2274, 24290, 6854, -15228, -72412, -24192, -306024; 139748, 15990, -170800, -48195, 107079, 509180, 170111, 2151870],66,56]
%
% END OF LATTICE L67.56
%
%
% LATTICE L67.57
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-12634440, 61320, -4872000; 61320, -273, 23856; -4872000, 23856, -1876909],[840, 21, 1],[-3991, -366, -852, 287, 284, -861, -1877, -4281; -79835, -7321, -17041, 5742, 5680, -17228, -37550, -85640; 9345, 857, 1995, -672, -665, 2016, 4395, 10024],66,57]
%
% END OF LATTICE L67.57
%
%
% LATTICE L67.58
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-286440, 15120, 7560; 15120, -798, -399; 7560, -399, -199],[840, 21, 1],[4, 0, -1, 0, 3, 7, 11, 9; 75, -1, -19, 10, 90, 172, 250, 196; 0, 2, 0, -21, -70, -84, -90, -56],66,58]
%
% END OF LATTICE L67.58
%
%
% LATTICE L67.59
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-74109840, -5052600, 450240; -5052600, -344472, 30696; 450240, 30696, -2735],[840, 24, 1],[17, 27, 3, -26, -43, -24, -317, -6; -260, -406, -44, 391, 645, 359, 4725, 89; -120, -112, 0, 108, 160, 78, 840, 11],66,59]
%
% END OF LATTICE L67.59
%
%
% LATTICE L67.60
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-18890760, 1239840, 147000; 1239840, -80904, -9600; 147000, -9600, -1139],[840, 24, 1],[21, 1, -5, -1, 6, 8, 184, 11; -1985, -91, 473, 90, -575, -761, -17465, -1043; 19440, 896, -4632, -888, 5620, 7446, 170940, 10210],66,60]
%
% END OF LATTICE L67.60
%
%
% LATTICE L67.61
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-7196467530, 5589360, 2585575440; 5589360, -3990, -2007915; 2585575440, -2007915, -928955633],[210, 105, 1],[352676, 98854, 52130, -52017, 32752, 699461, 286574, 1339309; -706857, -198129, -104479, 104254, -65645, -1401916, -574373, -2684340; 983136, 275570, 145320, -145005, 91301, 1949850, 798867, 3733520],66,61]
%
% END OF LATTICE L67.61
%
%
% LATTICE L67.62
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2103704400, 34113660, 520789500; 34113660, 553200, 8445120; 520789500, 8445120, 128925767],[420, 60, 1],[1412, 433, 438, 7513, 2829, 5193, 38705, 10381; 35, 14, 11, 177, 67, 124, 931, 251; -5706, -1750, -1770, -30360, -11432, -20985, -156408, -41950],66,62]
%
% END OF LATTICE L67.62
%
%
% LATTICE L67.63
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[110040, 16380, 27300; 16380, 5100, 4080; 27300, 4080, 6773],[420, 60, 1],[442, 1419, 534, 89, -1, 393, 3343, 639; 11, 35, 13, 2, 0, 10, 84, 16; -1788, -5740, -2160, -360, 4, -1590, -13524, -2585],66,63]
%
% END OF LATTICE L67.63
%
%
% LATTICE L67.64
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-956760, -111720, 25200; -111720, -12530, 2905; 25200, 2905, -661],[840, 35, 1],[14, 8, -15, -23, -17, 23, 17, 271; 57, 33, -61, -95, -72, 88, 68, 1092; 784, 450, -840, -1295, -966, 1260, 946, 15120],66,64]
%
% END OF LATTICE L67.64
%
%
% LATTICE L67.65
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3930360, 43680, -1447320; 43680, -455, 16240; -1447320, 16240, -532171],[840, 35, 1],[-467, -682, -580, 119, 116, -357, -201, -7139; -5607, -8187, -6961, 1430, 1392, -4292, -2414, -85728; 1099, 1605, 1365, -280, -273, 840, 473, 16800],66,65]
%
% END OF LATTICE L67.65
%
%
% LATTICE L67.66
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-645960, 32760, 219240; 32760, -1520, -11440; 219240, -11440, -73681],[840, 40, 1],[160, -382, -200, 191, 371, 541, 2113, 866; 799, -1911, -999, 955, 1854, 2703, 10556, 4326; 352, -840, -440, 420, 816, 1190, 4648, 1905],66,66]
%
% END OF LATTICE L67.66
%
%
% LATTICE L67.67
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-13563480, 5454120, -75600; 5454120, -2193200, 30400; -75600, 30400, -421],[840, 40, 1],[34, -76, -42, 39, 77, 113, 443, 364; 85, -189, -105, 97, 192, 282, 1106, 909; 32, 0, -40, 0, 36, 70, 308, 270],66,67]
%
% END OF LATTICE L67.67
%
%
% LATTICE L67.68
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[673039920, 1047060, 166626600; 1047060, 1848, 259224; 166626600, 259224, 41252269],[420, 84, 1],[15961, 51, 1071, 19174, 35492, 12774, 66904, 24834; 25, 0, 1, 29, 55, 20, 105, 39; -64470, -206, -4326, -77448, -143360, -51597, -270240, -100310],66,68]
%
% END OF LATTICE L67.68
%
%
% LATTICE L67.69
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[193620, 18480, 47460; 18480, 5460, 4452; 47460, 4452, 11635],[420, 84, 1],[3114, 259, 602, 83, 173, 737, 3811, 974; -265, -22, -51, -7, -15, -63, -325, -83; -12600, -1048, -2436, -336, -700, -2982, -15420, -3941],66,69]
%
% END OF LATTICE L67.69
%
%
% LATTICE L67.70
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2100, -76860, -1680; -76860, -2435475, -53130; -1680, -53130, -1159],[420, 105, 1],[-25, -13, -36, 4, 5, -9, -19, -119; 53, 28, 79, -7, -11, 14, 39, 248; -2394, -1265, -3570, 315, 497, -630, -1761, -11200],66,70]
%
% END OF LATTICE L67.70
%
%
% LATTICE L67.71
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1306236097110, 513346303890, 248021529000; 513346303890, 201743335920, 97471609830; 248021529000, 97471609830, 47093078339],[210, 210, 1],[-330, -80, 2, 19, -49, -395, -299, -676; -4743203, -1151961, 19171, 275925, -701754, -5667457, -4292996, -9708906; 9819054, 2384710, -39690, -571200, 1452724, 11732385, 8887068, 20098715],66,71]
%
% END OF LATTICE L67.71
%
%
% LATTICE L67.72
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-6037500, -187674060, -4471320; -187674060, -5832758400, -138965085; -4471320, -138965085, -3310834],[420, 105, 1],[-369, -43, 451, 431, 7, -737, -319, -1489; -4430, -518, 5414, 5192, 90, -8812, -3822, -17852; 186438, 21800, -227850, -218505, -3787, 370860, 160851, 751310],66,72]
%
% END OF LATTICE L67.72
%
%
% LATTICE L67.73
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-36047760, 6280680, -1195320; 6280680, -1094296, 208264; -1195320, 208264, -39635],[840, 56, 1],[-223, 11, 59, -32, -419, -132, -381, -223; -1120, 54, 296, -157, -2085, -659, -1905, -1116; 840, -48, -224, 140, 1680, 518, 1480, 861],66,73]
%
% END OF LATTICE L67.73
%
%
% LATTICE L67.74
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-9295440, -1200360, 158760; -1200360, -154952, 20496; 158760, 20496, -2711],[840, 56, 1],[21, 1, -5, -3, 8, 6, 22, 29; 430, 24, -102, -73, 105, 111, 425, 570; 4480, 240, -1064, -728, 1260, 1190, 4500, 6006],66,74]
%
% END OF LATTICE L67.74
%
%
% LATTICE L67.75
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[6897666909840, -373451250900, -1985748044700; -373451250900, 20219276840, 107511728380; -1985748044700, 107511728380, 571670877787],[420, 140, 1],[-9973, -1295, -3299, -53996, -60670, -36990, -39306, -221108; 28479, 3678, 9415, 154309, 173373, 105692, 112297, 631653; -39998, -5190, -13230, -216580, -243348, -148365, -157652, -886830],66,75]
%
% END OF LATTICE L67.75
%
%
% LATTICE L67.76
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[54001500, -2340240, -15075480; -2340240, 101500, 653380; -15075480, 653380, 4208633],[420, 140, 1],[-1537, -1988, -1627, -277, -187, -1679, -1811, -7036; 4576, 5919, 4844, 823, 555, 4997, 5391, 20946; -6216, -8040, -6580, -1120, -756, -6790, -7324, -28455],66,76]
%
% END OF LATTICE L67.76
%
%
% LATTICE L67.77
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-233413320, 72762480, 683760; 72762480, -22682415, -213150; 683760, -213150, -2003],[840, 105, 1],[4, -2, -5, 21, 17, 119, 29, 101; 15, -9, -19, 94, 74, 508, 122, 420; -231, 275, 315, -2835, -2072, -13440, -3084, -10220],66,77]
%
% END OF LATTICE L67.77
%
%
% LATTICE L67.78
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-85986600, 355320, -11979240; 355320, -1365, 49560; -11979240, 49560, -1668857],[840, 105, 1],[-1181, -624, -1770, 119, 118, -357, -439, -5553; -4727, -2497, -7081, 478, 472, -1436, -1758, -22232; 8337, 4405, 12495, -840, -833, 2520, 3099, 39200],66,78]
%
% END OF LATTICE L67.78
%
%
% LATTICE L67.79
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-220920, 28560, -9240; 28560, -3000, 960; -9240, 960, -307],[840, 120, 1],[-1, -1, 1, 1, 0, -1, -6, -1; -171, -189, 163, 182, 5, -154, -973, -165; -504, -560, 480, 540, 16, -450, -2856, -485],66,79]
%
% END OF LATTICE L67.79
%
%
% LATTICE L67.80
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-203280, -1228920, 31080; -1228920, -7285800, 184320; 31080, 184320, -4663],[840, 120, 1],[17, 1, -21, -1, 6, 36, 160, 47; 172, 14, -212, -15, 59, 359, 1603, 472; 6912, 560, -8520, -600, 2372, 14430, 64428, 18970],66,80]
%
% END OF LATTICE L67.80
%
%
% LATTICE L67.81
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-17200680, 331800, -4258800; 331800, -6384, 82152; -4258800, 82152, -1054457],[840, 168, 1],[-832, -2, 208, 21, -277, -343, -1099, -227; -5, -1, 1, 10, 15, 8, 15, 2; 3360, 8, -840, -84, 1120, 1386, 4440, 917],66,81]
%
% END OF LATTICE L67.81
%
%
% LATTICE L67.82
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-233520, -568680, -269640; -568680, -1380792, -654696; -269640, -654696, -310421],[840, 168, 1],[21, -1, -5, 11, 26, 20, 52, 19; -2000, 118, 480, -1279, -2865, -2139, -5455, -1966; 4200, -248, -1008, 2688, 6020, 4494, 11460, 4130],66,82]
%
% END OF LATTICE L67.82
%
%
% LATTICE L67.83
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[3542267400, 150256887060, 37209275880; 150256887060, 6373638566400, 1578353448000; 37209275880, 1578353448000, 390859880249],[420, 420, 1],[-5129, -82, -1721, -30807, -11405, -20524, -21499, -39901; 17147, 257, 5709, 103174, 38204, 68739, 71984, 133568; -68754, -1030, -22890, -413700, -153188, -275625, -288636, -535570],66,83]
%
% END OF LATTICE L67.83
%
%
% LATTICE L67.84
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[388500, 16841160, 4168500; 16841160, 730054500, 180702060; 4168500, 180702060, 44727119],[420, 420, 1],[329, 146, 367, 47, 3, 319, 369, 487; -964, -439, -1152, -209, -7, -891, -1057, -1406; 3864, 1760, 4620, 840, 28, 3570, 4236, 5635],66,84]
%
% END OF LATTICE L67.84
%
%
% LATTICE L67.85
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-371280, 183960, -26040; 183960, -91000, 12880; -26040, 12880, -1823],[840, 280, 1],[-1, -1, 1, 3, 2, 1, 0, -1; -10, -36, 2, 105, 99, 91, 35, 72; -56, -240, 0, 700, 672, 630, 248, 525],66,85]
%
% END OF LATTICE L67.85
%
%
% LATTICE L67.86
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-212520, -5822880, 48720; -5822880, -159223400, 1332240; 48720, 1332240, -11147],[840, 280, 1],[17, 1, -21, -3, 16, 34, 22, 137; 87, 9, -107, -28, 69, 161, 107, 675; 10472, 1080, -12880, -3360, 8316, 19390, 12884, 81270],66,86]
%
% END OF LATTICE L67.86
%
%
% LATTICE L67.87
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-31920, 318360, 15120; 318360, -3165960, -150360; 15120, -150360, -7141],[840, 840, 1],[-1, -1, 1, 10, 3, 8, 3, 2; -32, -2, 40, 21, -5, -49, -35, -38; 672, 40, -840, -420, 112, 1050, 744, 805],66,87]
%
% END OF LATTICE L67.87
%
%
% LATTICE L67.88
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-31920, -13088040, 32760; -13088040, -5363079960, 13424040; 32760, 13424040, -33601],[840, 840, 1],[17, 1, -21, -10, 3, 27, 19, 41; -32, 2, 40, -21, -19, -91, -53, -104; -12768, 800, 15960, -8400, -7588, -36330, -21156, -41510],66,88]
%
% END OF LATTICE L67.88
%

\medskip%
%------------------------------WEYL-GROUP-W68--------------------------------
%
\leavevmode\llap{}%
$W_{68\phantom{0}}$%
\qquad\llap{176} lattices, $\chi=72$%
\hfill%
$2222222222222222\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L68.1
%
\leavevmode%
${L_{68.1}}$%
{} : {$1\above{1pt}{1pt}{2}{{\rm II}}4\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{-}{}9\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{2}{}7\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{23\rightarrow N_{68},3,2}%
\EasyButWeakLineBreak%
{${36}\above{1pt}{1pt}{*}{2}{60}\above{1pt}{1pt}{b}{2}{2}\above{1pt}{1pt}{l}{2}{36}\above{1pt}{1pt}{r}{2}{42}\above{1pt}{1pt}{b}{2}{90}\above{1pt}{1pt}{s}{2}{6}\above{1pt}{1pt}{b}{2}{140}\above{1pt}{1pt}{*}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-15952860\\39060\\3780
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
39060\\-48\\-21
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3780\\-21\\2
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
145529\\42656460\\172986660
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-387\\-113435\\-460014
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-27\\-7914\\-32095
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
325\\95262\\386316
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
363\\106400\\431490
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
27\\7914\\32095
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
47\\13776\\55872
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
31\\9086\\36855
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
26\\7620\\30915
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\586\\2379
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
11\\3220\\13090
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-15952860, 39060, 3780; 39060, -48, -21; 3780, -21, 2],[1260, 3, 1],[325, 363, 27, 47, 31, 26, 2, 11, -1, -3, 0, 7, 32, 109, 43, 1249; 95262, 106400, 7914, 13776, 9086, 7620, 586, 3220, -294, -880, 0, 2052, 9380, 31950, 12604, 366100; 386316, 431490, 32095, 55872, 36855, 30915, 2379, 13090, -1188, -3570, -1, 8316, 38031, 129555, 51111, 1484630],67,1]
%
% END OF LATTICE L68.1
%
\hbox{}\par\smallskip%
%
% LATTICE L68.2
%
\leavevmode%
${L_{68.2}}$%
{} : {$1\above{1pt}{1pt}{-2}{2}8\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{1}{}3\above{1pt}{1pt}{1}{}9\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{2}{}7\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{3m,3,2}%
\EasyButWeakLineBreak%
{${18}\above{1pt}{1pt}{b}{2}{120}\above{1pt}{1pt}{*}{2}{4}\above{1pt}{1pt}{s}{2}{72}\above{1pt}{1pt}{s}{2}{84}\above{1pt}{1pt}{*}{2}{180}\above{1pt}{1pt}{l}{2}{3}\above{1pt}{1pt}{}{2}{280}\above{1pt}{1pt}{r}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
6749126720280\\-24187683240\\83739600
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-24187683240\\86684403\\-300108
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
83739600\\-300108\\1039
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
614748959\\171590920200\\16338543480
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2203188\\-614961686\\-58555419
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
8004\\2234105\\212726
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
12529\\3497139\\332955
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
27543\\7687900\\731940
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1983\\553502\\52696
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3181\\887892\\84528
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1805\\503818\\47964
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1141\\318480\\30330
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
8\\2233\\216
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\280\\280
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[6749126720280, -24187683240, 83739600; -24187683240, 86684403, -300108; 83739600, -300108, 1039],[2520, 3, 1],[12529, 27543, 1983, 3181, 1805, 1141, 8, 1, -1, 297, 105, 995, 3067, 9299, 1732, 97439; 3497139, 7687900, 553502, 887892, 503818, 318480, 2233, 280, -279, 82900, 29308, 277728, 856072, 2595570, 483442, 27197520; 332955, 731940, 52696, 84528, 47964, 30330, 216, 280, 9, 7980, 2798, 26460, 81522, 247140, 46029, 2589440],67,2]
%
% END OF LATTICE L68.2
%
\hbox{}\par\smallskip%
%
% LATTICE L68.3
%
\leavevmode%
${L_{68.3}}$%
{} : {$1\above{1pt}{1pt}{2}{2}8\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{1}{}3\above{1pt}{1pt}{1}{}9\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{2}{}7\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{32\rightarrow N'_{32},3,m}%
\EasyButWeakLineBreak%
{${18}\above{1pt}{1pt}{l}{2}{120}\above{1pt}{1pt}{}{2}{1}\above{1pt}{1pt}{r}{2}{72}\above{1pt}{1pt}{l}{2}{21}\above{1pt}{1pt}{}{2}{45}\above{1pt}{1pt}{r}{2}{12}\above{1pt}{1pt}{*}{2}{280}\above{1pt}{1pt}{b}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
9024120\\-22680\\0
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-22680\\57\\0
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\1
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2684639\\1071487200\\18476640
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-6715\\-2680076\\-46215
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-663\\-264615\\-4564
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-613\\-244659\\-4221
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1361\\-543200\\-9360
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-50\\-19956\\-343
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-169\\-67452\\-1152
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-53\\-21154\\-357
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-41\\-16365\\-270
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-5\\-1996\\-30
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-27\\-10780\\-140
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[9024120, -22680, 0; -22680, 57, 0; 0, 0, 1],[2520, 3, 1],[-613, -1361, -50, -169, -53, -41, -5, -27, 1, 1, -1, -35, -66, -214, -165, -4733; -244659, -543200, -19956, -67452, -21154, -16365, -1996, -10780, 399, 400, -399, -13968, -26341, -85410, -65854, -1889020; -4221, -9360, -343, -1152, -357, -270, -30, -140, 9, 0, -8, -252, -462, -1485, -1140, -32620],67,3]
%
% END OF LATTICE L68.3
%
%
% LATTICE L68.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-840, -105, 0; -105, -13, 0; 0, 0, 1],[105, 1, 1],[204, 682, 101, 29, 113, 31, 7, 24, 0, -2, 1, 5, 125, 139, 163, 2356; -1476, -4935, -731, -210, -819, -225, -51, -175, 0, 15, -7, -36, -903, -1005, -1179, -17045; -217, -720, -105, -29, -105, -25, -3, 0, 1, 0, -3, -7, -147, -155, -177, -2520],67,4]
%
% END OF LATTICE L68.4
%
%
% LATTICE L68.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[191730, 18270, -4200; 18270, 1741, -400; -4200, -400, 93],[210, 1, 1],[112, 319, 16, 1, -2, 16, 35, 1353, 128, 481, 44, 39, 142, 84, 65, 1447; -1127, -3210, -161, -10, 21, -160, -351, -13580, -1285, -4830, -442, -392, -1428, -845, -654, -14560; 211, 600, 30, 2, 0, 35, 72, 2730, 257, 960, 87, 76, 273, 160, 123, 2730],67,5]
%
% END OF LATTICE L68.5
%
%
% LATTICE L68.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-964740, -385140, 3360; -385140, -153754, 1341; 3360, 1341, -11],[420, 1, 1],[-366, -2599, -215, -155, -409, -161, -68, -613, -6, 119, 29, 31, -25, -149, -242, -8067; 921, 6540, 541, 390, 1029, 405, 171, 1540, 15, -300, -73, -78, 63, 375, 609, 20300; 475, 3360, 276, 196, 504, 190, 72, 420, -7, -240, -42, -40, 42, 200, 318, 10500],67,6]
%
% END OF LATTICE L68.6
%
%
% LATTICE L68.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-10946460, 1680, 32760; 1680, 8, -15; 32760, -15, -86],[420, 1, 1],[71, 257, 22, 17, 50, 23, 13, 209, 13, 23, -1, -3, -1, 12, 22, 771; 26970, 97620, 8356, 6456, 18984, 8730, 4932, 79240, 4926, 8700, -382, -1140, -378, 4560, 8358, 292880; 22336, 80850, 6921, 5348, 15729, 7235, 4089, 65730, 4088, 7230, -315, -944, -315, 3775, 6921, 242550],67,7]
%
% END OF LATTICE L68.7
%
%
% LATTICE L68.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-65786280, 13161120, 101640; 13161120, -2632997, -20334; 101640, -20334, -157],[840, 1, 1],[27, 11, -21, -29, 17, 139, 116, 7837, 357, 2549, 213, 157, 431, 181, 44, 1123; 135, 60, -104, -144, 84, 690, 576, 38920, 1773, 12660, 1058, 780, 2142, 900, 219, 5600; -7, -660, -126, -124, 126, 620, 495, 32760, 1483, 10500, 864, 616, 1596, 610, 120, 1680],67,8]
%
% END OF LATTICE L68.8
%
%
% LATTICE L68.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-588867720, 1475880, -159600; 1475880, -3699, 400; -159600, 400, -43],[840, 1, 1],[10, 43, 0, -3, -1, 6, 23, 821, 38, 277, 12, 19, 29, 14, 17, 299; 3993, 17160, -1, -1200, -399, 2400, 9198, 328300, 15195, 110760, 4798, 7596, 11592, 5595, 6792, 119420; 23, 0, -10, -28, 0, 55, 192, 6580, 301, 2160, 91, 136, 189, 80, 78, 980],67,9]
%
% END OF LATTICE L68.9
%
%
% LATTICE L68.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[1780065, 49455, -3780; 49455, 1374, -105; -3780, -105, 8],[315, 3, 1],[397, 439, 64, 53, 64, 46, 2, 3, -1, 1, 2, 13, 90, 284, 108, 1537; -14112, -15605, -2275, -1884, -2275, -1635, -71, -105, 36, -35, -71, -462, -3199, -10095, -3839, -54635; 2376, 2625, 382, 315, 378, 270, 12, 35, 0, 15, 14, 81, 546, 1710, 648, 9205],67,10]
%
% END OF LATTICE L68.10
%
%
% LATTICE L68.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-87570, -41580, 0; -41580, -19662, -9; 0, -9, 1],[630, 3, 1],[10, 19, 0, -37, -166, -562, -221, -6407, -1666, -1859, -138, -239, -156, -128, -9, -33; -21, -40, 0, 78, 350, 1185, 466, 13510, 3513, 3920, 291, 504, 329, 270, 19, 70; -180, -360, -1, 702, 3171, 10755, 4233, 122780, 31932, 35640, 2647, 4590, 3003, 2475, 177, 700],67,11]
%
% END OF LATTICE L68.11
%
%
% LATTICE L68.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[14888262060, 105590520, -888300; 105590520, 748869, -6300; -888300, -6300, 53],[1260, 3, 1],[469, 1039, 76, 127, 78, 58, 3, 13, -1, 1, 2, 29, 104, 332, 127, 3627; -65877, -145940, -10675, -17838, -10955, -8145, -421, -1820, 141, -140, -281, -4074, -14609, -46635, -17839, -509460; 29916, 66360, 4867, 8190, 5103, 3915, 237, 1540, 0, 120, 119, 1782, 6531, 21015, 8073, 231140],67,12]
%
% END OF LATTICE L68.12
%
%
% LATTICE L68.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-422205, 0, 144795; 0, 24, -15; 144795, -15, -49648],[105, 3, 1],[-133441, -141767, -56904, -12293, -8136, 962, 582, -70977, -9371, -16913, -14502, -11509, -47402, -119972, -40252, -1595163; -243300, -258480, -103751, -22413, -14833, 1755, 1061, -129430, -17088, -30840, -26443, -20985, -86429, -218745, -73391, -2908430; -389088, -413365, -165921, -35844, -23723, 2805, 1697, -206955, -27324, -49315, -42285, -33558, -138215, -349815, -117367, -4651185],67,13]
%
% END OF LATTICE L68.13
%
%
% LATTICE L68.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[12390, -3780, 6510; -3780, -1818, -1690; 6510, -1690, 3391],[210, 2, 1],[1329, 1196, -94, -149, -104, 1193, 2192, 38447, 7083, 12824, 2197, 850, 5011, 2312, 1313, 10623; -267, -240, 19, 30, 21, -240, -441, -7735, -1425, -2580, -442, -171, -1008, -465, -264, -2135; -2684, -2415, 190, 301, 210, -2410, -4428, -77665, -14308, -25905, -4438, -1717, -10122, -4670, -2652, -21455],67,14]
%
% END OF LATTICE L68.14
%
%
% LATTICE L68.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-222495, -1050, -41685; -1050, 40, -225; -41685, -225, -7792],[105, 5, 1],[73521, 46865, 31352, 6773, 13448, -106, -962, 7821, 5163, 5591, 7990, 6341, 78350, 13220, 66532, 175775; -243300, -155088, -103751, -22413, -44499, 351, 3183, -25886, -17088, -18504, -26443, -20985, -259287, -43749, -220173, -581686; -386330, -246261, -164745, -35590, -70665, 557, 5055, -41097, -27130, -29379, -41985, -33320, -411705, -69467, -349605, -923643],67,15]
%
% END OF LATTICE L68.15
%
%
% LATTICE L68.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-73290, 15330, -25620; 15330, -2727, 5310; -25620, 5310, -8951],[210, 3, 1],[874, 529, -59, -193, -23, 773, 474, 49909, 4598, 5551, 1427, 1105, 1087, 1507, 286, 13931; -267, -160, 19, 60, 7, -240, -147, -15470, -1425, -1720, -442, -342, -336, -465, -88, -4270; -2661, -1610, 180, 588, 70, -2355, -1444, -152040, -14007, -16910, -4347, -3366, -3311, -4590, -871, -42420],67,16]
%
% END OF LATTICE L68.16
%
%
% LATTICE L68.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-97545, -2100, -11655; -2100, 56, -315; -11655, -315, -1352],[105, 7, 1],[51051, 162709, 21770, 4703, 1334, -368, -668, 3879, 3585, 19411, 5548, 4403, 7772, 45898, 46198, 87181; -243300, -775440, -103751, -22413, -6357, 1755, 3183, -18490, -17088, -92520, -26443, -20985, -37041, -218745, -220173, -415490; -383572, -1222515, -163569, -35336, -10023, 2765, 5019, -29145, -26936, -145845, -41685, -33082, -58395, -344855, -347109, -655035],67,17]
%
% END OF LATTICE L68.17
%
%
% LATTICE L68.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-8190, 315, 1260; 315, -12, -45; 1260, -45, -89],[315, 3, 1],[28, 102, 53, 7, 43, 21, 13, 352, 8, 18, 1, -1, -1, 9, 17, 908; 835, 3040, 1578, 208, 1274, 620, 382, 10290, 233, 520, 24, -30, -28, 270, 508, 27090; -29, -105, -54, -7, -42, -20, -12, -315, -7, -15, 0, 1, 0, -10, -18, -945],67,18]
%
% END OF LATTICE L68.18
%
%
% LATTICE L68.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-623910, 53550, 247170; 53550, -4545, -21220; 247170, -21220, -97919],[210, 5, 1],[-1059, -391, 65, 227, 85, -182, -1678, -11791, -5433, -3937, -1688, -1309, -3872, -359, -1027, -3357; -267, -96, 19, 60, 21, -48, -441, -3094, -1425, -1032, -442, -342, -1008, -93, -264, -854; -2615, -966, 160, 560, 210, -449, -4140, -29092, -13405, -9714, -4165, -3230, -9555, -886, -2535, -8288],67,19]
%
% END OF LATTICE L68.19
%
%
% LATTICE L68.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-230580, 2100, 2100; 2100, -18, -21; 2100, -21, -16],[420, 3, 1],[-1, -1, 1, 7, 27, 88, 34, 2929, 253, 281, 62, 35, 22, 17, 1, 11; -68, -70, 67, 476, 1841, 6005, 2321, 199990, 17276, 19190, 4235, 2392, 1505, 1165, 69, 770; -42, -40, 42, 288, 1106, 3600, 1390, 119700, 10338, 11480, 2532, 1428, 896, 690, 40, 420],67,20]
%
% END OF LATTICE L68.20
%
%
% LATTICE L68.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[3375407070, -5937960, 1678000170; -5937960, 10446, -2951910; 1678000170, -2951910, 834176297],[210, 6, 1],[-21961, -10453, -3162, -88, 348, -2297, -1938, -116988, -22355, -14167, -7917, -3605, -8965, -16168, -4217, -141522; -1127, -535, -161, -5, 7, -160, -117, -6790, -1285, -805, -442, -196, -476, -845, -218, -7280; 44172, 21025, 6360, 177, -700, 4620, 3898, 235305, 44964, 28495, 15924, 7251, 18032, 32520, 8482, 284655],67,21]
%
% END OF LATTICE L68.21
%
%
% LATTICE L68.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-24780, -9660, 2100; -9660, -3753, 831; 2100, 831, -166],[420, 3, 1],[11, 19, -23, -151, -575, -1867, -720, -61961, -2675, -5939, -1309, -737, -461, -353, -20, -199; -23, -40, 48, 316, 1204, 3910, 1508, 129780, 5603, 12440, 2742, 1544, 966, 740, 42, 420; 24, 40, -51, -330, -1253, -4065, -1567, -134820, -5820, -12920, -2847, -1602, -1001, -765, -43, -420],67,22]
%
% END OF LATTICE L68.22
%
%
% LATTICE L68.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1319010, 91770, 562380; 91770, -6363, -39130; 562380, -39130, -239779],[210, 7, 1],[-1114, -2093, 61, 231, 13, -927, -1714, -8613, -5558, -20147, -1729, -1343, -569, -1853, -1066, -2507; -267, -480, 19, 60, 3, -240, -441, -2210, -1425, -5160, -442, -342, -144, -465, -264, -610; -2569, -4830, 140, 532, 30, -2135, -3948, -19840, -12803, -46410, -3983, -3094, -1311, -4270, -2457, -5780],67,23]
%
% END OF LATTICE L68.23
%
%
% LATTICE L68.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[172794615, -9884700, -58645755; -9884700, 565455, 3354825; -58645755, 3354825, 19904119],[105, 15, 1],[843371, 179073, 358827, 77128, 50221, -1409, -3499, 93909, 61453, 21999, 93585, 73676, 301655, 152213, 254839, 2017347; -960, -203, -403, -84, -49, 3, 3, -133, -84, -29, -119, -90, -357, -177, -293, -2303; 2485080, 527657, 1057320, 227265, 147980, -4152, -10310, 276717, 181080, 64823, 275760, 217095, 888860, 448512, 750910, 5944323],67,24]
%
% END OF LATTICE L68.24
%
%
% LATTICE L68.25
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[317418360, -1430940, 79167480; -1430940, 6452, -356892; 79167480, -356892, 19745203],[420, 4, 1],[5644, 10187, 3491, 1387, 9047, 4937, 3601, 19524, 2984, 4193, 823, 51, 1019, 2253, 3589, 30806; -9219, -16635, -5698, -2262, -14742, -8040, -5862, -31780, -4857, -6825, -1340, -84, -1680, -3690, -5868, -50330; -22796, -41145, -14100, -5602, -36540, -19940, -14544, -78855, -12052, -16935, -3324, -206, -4116, -9100, -14496, -124425],67,25]
%
% END OF LATTICE L68.25
%
%
% LATTICE L68.26
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[9251597040, -107772420, 2290588020; -107772420, 1255448, -26683200; 2290588020, -26683200, 567123001],[420, 4, 1],[19763, 72412, 12722, 2640, 36062, 20376, 15250, 167154, 12841, 36268, 3580, 77, 1976, 6794, 11920, 213226; 0, -15, -7, -3, -63, -45, -39, -455, -36, -105, -11, 0, 21, 15, 9, 35; -79822, -292470, -51384, -10663, -145656, -82300, -61596, -675150, -51866, -146490, -14460, -311, -7980, -27440, -48144, -861210],67,26]
%
% END OF LATTICE L68.26
%
%
% LATTICE L68.27
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-687732570, -7557480, 171990; -7557480, -83049, 1890; 171990, 1890, -43],[630, 3, 1],[9, 21, 1, -1, -1, 4, 8, 871, 27, 99, 26, 7, 22, 11, 7, 389; -817, -1910, -93, 90, 91, -360, -721, -78540, -2435, -8930, -2346, -632, -1988, -995, -634, -35280; 83, 30, -90, -44, 0, 175, 306, 31500, 961, 3450, 873, 218, 609, 260, 129, 5040],67,27]
%
% END OF LATTICE L68.27
%
%
% LATTICE L68.28
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[4620, 1260, -840; 1260, 45, -40; -840, -40, 33],[420, 5, 1],[0, -1, -1, -1, 1, 1, 8, 53, 12, 17, 7, 5, 13, 1, 2, 3; -13, -84, -73, -70, 63, 67, 537, 3556, 805, 1140, 469, 334, 861, 65, 123, 140; -20, -132, -115, -110, 105, 107, 855, 5656, 1280, 1812, 745, 530, 1365, 103, 195, 224],67,28]
%
% END OF LATTICE L68.28
%
%
% LATTICE L68.29
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-572460, 283920, 420; 283920, -140760, -155; 420, -155, 52],[420, 5, 1],[1359, 1043, 468, 311, 52, -155, -1291, -8465, -3819, -2683, -1083, -721, -1487, -50, 266, 2725; 2744, 2106, 945, 628, 105, -313, -2607, -17094, -7712, -5418, -2187, -1456, -3003, -101, 537, 5502; -2810, -2154, -965, -640, -105, 319, 2655, 17402, 7850, 5514, 2225, 1480, 3045, 101, -555, -5642],67,29]
%
% END OF LATTICE L68.29
%
%
% LATTICE L68.30
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[24030930, -646800, 11410980; -646800, 17410, -307130; 11410980, -307130, 5418453],[210, 10, 1],[-7191, -2050, -1030, -31, 200, -187, -2132, -8343, -7917, -2986, -2747, -1228, -9013, -1072, -4163, -9283; -1127, -321, -161, -5, 21, -32, -351, -1358, -1285, -483, -442, -196, -1428, -169, -654, -1456; 15080, 4299, 2160, 65, -420, 392, 4470, 17493, 16600, 6261, 5760, 2575, 18900, 2248, 8730, 19467],67,30]
%
% END OF LATTICE L68.30
%
%
% LATTICE L68.31
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[96660165, -8747550, -32877915; -8747550, 791637, 2975385; -32877915, 2975385, 11183069],[105, 21, 1],[809507, 859143, 344067, 73786, 6811, -7213, -3295, 65589, 59893, 106857, 90633, 71114, 41489, 731713, 244795, 1383411; -960, -1015, -403, -84, -7, 15, 3, -95, -84, -145, -119, -90, -51, -885, -293, -1645; 2380182, 2526125, 1011654, 216951, 20026, -21210, -9688, 192855, 176106, 314195, 266490, 209097, 121990, 2151450, 719768, 4067625],67,31]
%
% END OF LATTICE L68.31
%
%
% LATTICE L68.32
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[471240, -1680, -840; -1680, 6, 3; -840, 3, 1],[840, 3, 1],[0, -1, -1, -3, -9, -27, -5, -841, -36, -79, -17, -9, -5, -3, 0, 1; 1, -260, -262, -788, -2366, -7100, -1315, -221200, -9469, -20780, -4472, -2368, -1316, -790, 0, 280; 0, -40, -42, -132, -406, -1230, -229, -38640, -1656, -3640, -786, -420, -238, -150, -1, 0],67,32]
%
% END OF LATTICE L68.32
%
%
% LATTICE L68.33
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1073804760, 9111480, -487200; 9111480, -77313, 4134; -487200, 4134, -221],[840, 3, 1],[3, 1, -4, -39, -69, -219, -167, -14279, -615, -1361, -149, -165, -50, -36, -3, -1; 355, 120, -473, -4616, -8169, -25930, -19774, -1690780, -72823, -161160, -17644, -19540, -5922, -4265, -356, -140; 27, 40, -30, -372, -700, -2265, -1744, -149940, -6471, -14360, -1581, -1776, -553, -420, -46, -420],67,33]
%
% END OF LATTICE L68.33
%
%
% LATTICE L68.34
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[13020, -1680, 420; -1680, 168, -35; 420, -35, 6],[420, 7, 1],[-1, -11, -2, -3, -2, -9, -7, -21, -11, -29, -1, 1, 1, 4, 2, 1; -22, -240, -44, -68, -48, -230, -192, -620, -338, -960, -46, 8, 18, 80, 42, 20; -56, -630, -119, -196, -153, -805, -735, -2570, -1456, -4410, -259, -56, 27, 175, 105, 50],67,34]
%
% END OF LATTICE L68.34
%
%
% LATTICE L68.35
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[7501830, -427560, 3479490; -427560, 24374, -198310; 3479490, -198310, 1613853],[210, 14, 1],[-8233, -11731, -1178, -36, 28, -1113, -2494, -6936, -9203, -17329, -3181, -1417, -1481, -6152, -4771, -7594; -1127, -1605, -161, -5, 3, -160, -351, -970, -1285, -2415, -442, -196, -204, -845, -654, -1040; 17612, 25095, 2520, 77, -60, 2380, 5334, 14835, 19684, 37065, 6804, 3031, 3168, 13160, 10206, 16245],67,35]
%
% END OF LATTICE L68.35
%
%
% LATTICE L68.36
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[420, 0, 0; 0, 7, 0; 0, 0, -1],[420, 7, 1],[0, 1, 0, -1, -2, -16, -19, -79, -24, -161, -12, -7, -2, -4, -1, -1; 1, 0, -3, -14, -21, -155, -177, -720, -217, -1440, -105, -58, -15, -25, -3, 0; 0, 0, -7, -42, -69, -525, -609, -2500, -756, -5040, -371, -210, -57, -105, -21, -20],67,36]
%
% END OF LATTICE L68.36
%
%
% LATTICE L68.37
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[20864970, 738150, 7414890; 738150, 26115, 262320; 7414890, 262320, 2635067],[210, 15, 1],[5024, 955, 720, 43, -50, 128, 491, 11559, 5488, 1381, 1908, 1709, 2094, 748, 969, 12969; -1127, -214, -161, -10, 7, -32, -117, -2716, -1285, -322, -442, -392, -476, -169, -218, -2912; -14025, -2666, -2010, -120, 140, -357, -1370, -32256, -15315, -3854, -5325, -4770, -5845, -2088, -2705, -36204],67,37]
%
% END OF LATTICE L68.37
%
%
% LATTICE L68.38
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[156508590, 14369985, -22031310; 14369985, 1319395, -2022825; -22031310, -2022825, 3101291],[105, 35, 1],[551699, 351313, 234483, 50282, 13921, -985, -6733, 8945, 40837, 43711, 61785, 48474, 84835, 99741, 500513, 188567; -1656057, -1054548, -703852, -150930, -41784, 2958, 20208, -26854, -122595, -131220, -185474, -145512, -254658, -299400, -1502418, -566030; 2839060, 1807869, 1206660, 258755, 71640, -5068, -34650, 46029, 210140, 224931, 317940, 249445, 436560, 513268, 2575650, 970371],67,38]
%
% END OF LATTICE L68.38
%
%
% LATTICE L68.39
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[910445760, -871290, 453915630; -871290, 834, -434394; 453915630, -434394, 226306067],[630, 6, 1],[1247, 157, 1, 785, 8143, 28798, 11579, 170064, 88861, 49903, 7508, 6724, 9378, 8747, 936, 5146; -426, -50, 3, -249, -2653, -9435, -3803, -55930, -29238, -16430, -2475, -2223, -3115, -2925, -317, -1750; -2502, -315, -2, -1575, -16338, -57780, -23232, -341215, -178290, -100125, -15064, -13491, -18816, -17550, -1878, -10325],67,39]
%
% END OF LATTICE L68.39
%
%
% LATTICE L68.40
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3567060, -511560, 6300; -511560, -73362, 903; 6300, 903, -11],[1260, 3, 1],[-34, -243, -61, -15, -41, -17, -8, -283, -2, 3, 7, 3, -1, -13, -22, -2237; 249, 1780, 447, 110, 301, 125, 59, 2100, 15, -20, -51, -22, 7, 95, 161, 16380; 961, 6900, 1746, 436, 1218, 520, 258, 10080, 83, 60, -180, -88, 0, 350, 612, 63000],67,40]
%
% END OF LATTICE L68.40
%
%
% LATTICE L68.41
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-97711740, 45360, 91980; 45360, -12, -45; 91980, -45, -86],[1260, 3, 1],[27, 99, 26, 7, 22, 11, 7, 389, 9, 21, 1, -1, -1, 4, 8, 871; 6470, 23720, 6228, 1676, 5264, 2630, 1672, 92820, 2146, 5000, 234, -240, -238, 960, 1918, 208740; 25486, 93450, 24543, 6608, 20769, 10385, 6609, 367290, 8498, 19830, 945, -944, -945, 3775, 7551, 822150],67,41]
%
% END OF LATTICE L68.41
%
%
% LATTICE L68.42
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[166916610, 3393180, 83180790; 3393180, 76758, 1690920; 83180790, 1690920, 41452099],[630, 6, 1],[426829, 607133, 182344, 2040, -942, 69359, 143740, 8195858, 514703, 962087, 523805, 76421, 550169, 322946, 248565, 8280952; -3139, -4465, -1341, -15, 7, -510, -1057, -60270, -3785, -7075, -3852, -562, -4046, -2375, -1828, -60900; -856378, -1218135, -365850, -4093, 1890, -139160, -288396, -16443945, -1032686, -1930305, -1050948, -153329, -1103844, -647950, -498714, -16614675],67,42]
%
% END OF LATTICE L68.42
%
%
% LATTICE L68.43
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1067640, 10080, -9240; 10080, 90, -85; -9240, -85, 79],[840, 5, 1],[12, 17, 7, 5, 13, 1, 1, 3, 0, -1, -1, -1, 1, 1, 4, 53; 1077, 1524, 626, 444, 1134, 84, 75, 112, -33, -132, -104, -96, 84, 90, 360, 4760; 2560, 3624, 1490, 1060, 2730, 206, 195, 448, -40, -264, -230, -220, 210, 214, 855, 11312],67,43]
%
% END OF LATTICE L68.43
%
%
% LATTICE L68.44
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-401073960, -6366360, 168840; -6366360, -101055, 2680; 168840, 2680, -71],[840, 5, 1],[-83, -119, -25, -37, -50, -4, -17, -29, -1, 7, 4, 9, 1, -3, -53, -363; 5307, 7608, 1598, 2364, 3192, 255, 1080, 1820, 57, -456, -257, -576, -63, 192, 3390, 23212; 2935, 4176, 865, 1240, 1575, 112, 330, -308, -235, -576, -190, -340, 0, 113, 1920, 12908],67,44]
%
% END OF LATTICE L68.44
%
%
% LATTICE L68.45
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[26434170, 983010, 9227400; 983010, 36561, 343140; 9227400, 343140, 3221017],[210, 21, 1],[11822, 11231, 1692, 103, -14, 1582, 1187, 19833, 13162, 16529, 4554, 4061, 708, 8828, 2283, 21807; -1127, -1070, -161, -10, 1, -160, -117, -1940, -1285, -1610, -442, -392, -68, -845, -218, -2080; -33747, -32060, -4830, -294, 40, -4515, -3388, -56610, -37569, -47180, -12999, -11592, -2021, -25200, -6517, -62250],67,45]
%
% END OF LATTICE L68.45
%
%
% LATTICE L68.46
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-5864355, -977445, 28350; -977445, -162915, 4725; 28350, 4725, -137],[315, 15, 1],[1, 2, 0, -28, -260, -178, -352, -1024, -1333, -298, -222, -194, -258, -44, -18, -12; -6, -14, -1, 189, 1771, 1215, 2405, 7000, 9114, 2038, 1519, 1329, 1771, 303, 125, 84; 0, -69, -35, 720, 7245, 5049, 10065, 29407, 38340, 8589, 6425, 5670, 7665, 1341, 585, 413],67,46]
%
% END OF LATTICE L68.46
%
%
% LATTICE L68.47
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-484155, -6300, 2520; -6300, -15, 30; 2520, 30, -13],[315, 15, 1],[-2, -2, -7, -1, -1, 1, 9, 92, 14, 10, 25, 3, 15, 1, 1, -8; -25, -22, -69, -9, -7, 9, 79, 798, 121, 86, 213, 25, 119, 7, 1, -126; -460, -447, -1530, -215, -210, 214, 1920, 19593, 2980, 2127, 5310, 635, 3150, 206, 180, -1953],67,47]
%
% END OF LATTICE L68.47
%
%
% LATTICE L68.48
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[7406280, -390180, 1832040; -390180, 20592, -96516; 1832040, -96516, 453179],[420, 12, 1],[52, 47, 395, 574, 8809, 28753, 11125, 479737, 41456, 46073, 20359, 2885, 7333, 5837, 405, 4523; 1, 0, 4, 7, 112, 370, 144, 6230, 539, 600, 266, 38, 98, 80, 6, 70; -210, -190, -1596, -2319, -35588, -116160, -44944, -1938090, -167478, -186130, -82248, -11655, -29624, -23580, -1636, -18270],67,48]
%
% END OF LATTICE L68.48
%
%
% LATTICE L68.49
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[7979580, -259980, 2017260; -259980, 8472, -65724; 2017260, -65724, 509969],[420, 12, 1],[-3, 21, 154, 330, 2306, 7308, 2786, 59566, 10263, 5679, 4976, 1380, 1684, 1242, 64, 284; 1, -15, -115, -253, -1785, -5675, -2167, -46375, -7993, -4425, -3881, -1079, -1323, -985, -53, -245; 12, -85, -624, -1338, -9352, -29640, -11300, -241605, -41628, -23035, -20184, -5598, -6832, -5040, -260, -1155],67,49]
%
% END OF LATTICE L68.49
%
%
% LATTICE L68.50
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2702598360, 68685960, -371280; 68685960, -1745639, 9436; -371280, 9436, -51],[840, 7, 1],[557, 3721, 275, 157, 43, 79, 7, 1, -5, -41, 1, 27, 49, 381, 223, 1839; 21905, 146340, 10816, 6176, 1692, 3110, 276, 40, -197, -1620, 38, 1060, 1926, 14980, 8769, 72320; -2219, -13860, -882, -308, 6, 280, 105, 120, -49, -1260, -252, -448, -384, -2170, -1050, -7680],67,50]
%
% END OF LATTICE L68.50
%
%
% LATTICE L68.51
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[840, 0, 0; 0, -21, 7; 0, 7, -2],[840, 7, 1],[-24, -161, -6, -7, -1, -2, -1, -1, 0, 1, 0, -1, -1, -8, -19, -79; -434, -2880, -105, -116, -15, -25, -6, 0, 2, 0, -3, -28, -21, -155, -354, -1440; -2275, -15120, -553, -616, -81, -140, -42, -20, 7, 0, -14, -140, -108, -805, -1848, -7540],67,51]
%
% END OF LATTICE L68.51
%
%
% LATTICE L68.52
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-5127780, 23100, 23100; 23100, -90, -105; 23100, -105, -104],[420, 15, 1],[-1, -1, 1, 19, 83, 56, 110, 1913, 829, 185, 206, 119, 78, 13, 5, 19; -12, -14, 11, 252, 1113, 753, 1481, 25774, 11172, 2494, 2779, 1608, 1057, 177, 69, 266; -210, -208, 210, 3960, 17290, 11664, 22910, 398412, 172650, 38528, 42900, 24780, 16240, 2706, 1040, 3948],67,52]
%
% END OF LATTICE L68.52
%
%
% LATTICE L68.53
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-480309690, 3645600, -238822920; 3645600, -27270, 1812690; -238822920, 1812690, -118749191],[210, 30, 1],[100403, 6164, -6250, -10807, -2680, 17327, 53232, 560993, 516961, 62432, 160591, 62254, 122723, 34120, 32513, 159265; -267, -16, 19, 30, 7, -48, -147, -1547, -1425, -172, -442, -171, -336, -93, -88, -427; -201930, -12397, 12570, 21735, 5390, -34848, -107060, -1128267, -1039710, -125563, -322980, -125205, -246820, -68622, -65390, -320313],67,53]
%
% END OF LATTICE L68.53
%
%
% LATTICE L68.54
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-4498620, 21840, -2227680; 21840, -90, 10815; -2227680, 10815, -1103129],[420, 15, 1],[52, 103, -104, -1961, -8562, -5776, -11345, -197293, -42748, -19079, -21244, -12271, -8042, -1340, -515, -1955; 1, 0, -3, -14, -49, -31, -59, -1008, -217, -96, -105, -58, -35, -5, -1, 0; -105, -208, 210, 3960, 17290, 11664, 22910, 398412, 86325, 38528, 42900, 24780, 16240, 2706, 1040, 3948],67,54]
%
% END OF LATTICE L68.54
%
%
% LATTICE L68.55
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[5355, 945, 0; 945, 168, 0; 0, 0, -1],[315, 21, 1],[-1, 1, 1, 4, 3, 59, 21, 41, 73, 79, 11, 8, 1, 1, -1, -1; 6, -5, -6, -27, -22, -450, -164, -325, -582, -635, -90, -69, -10, -30, 4, 5; 0, 0, -7, -63, -69, -1575, -609, -1250, -2268, -2520, -371, -315, -57, -315, -21, -10],67,55]
%
% END OF LATTICE L68.55
%
%
% LATTICE L68.56
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[4095, -1260, 0; -1260, 168, 21; 0, 21, -2],[315, 21, 1],[-1, -3, 2, 3, 10, 76, 88, 541, 109, 363, 160, 15, 8, 14, 2, -1; -3, -10, 6, 10, 34, 260, 302, 1860, 375, 1250, 552, 52, 28, 50, 8, 0; -35, -105, 63, 98, 327, 2485, 2877, 17685, 3563, 11865, 5229, 490, 261, 455, 63, -45],67,56]
%
% END OF LATTICE L68.56
%
%
% LATTICE L68.57
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-14591640, 694680, -36120; 694680, -33072, 1720; -36120, 1720, -89],[840, 8, 1],[-158, -143, -49, -19, -113, -53, -31, -262, -34, -17, 1, 3, 1, -27, -49, -858; -3165, -2865, -982, -381, -2268, -1065, -624, -5285, -687, -345, 19, 60, 21, -540, -981, -17185; 2944, 2655, 904, 346, 2016, 920, 516, 4130, 512, 225, -40, -58, 0, 520, 924, 16030],67,57]
%
% END OF LATTICE L68.57
%
%
% LATTICE L68.58
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-330171240, 16515240, -196560; 16515240, -826096, 9832; -196560, 9832, -117],[840, 8, 1],[-158, -286, -49, -19, -113, -53, -31, -131, -34, -34, 1, 3, 1, -27, -49, -429; -3107, -5625, -964, -374, -2226, -1045, -612, -2590, -673, -675, 19, 59, 21, -530, -963, -8435; 4336, 7770, 1308, 490, 2772, 1220, 648, 2415, 560, 390, -84, -82, 84, 820, 1392, 11865],67,58]
%
% END OF LATTICE L68.58
%
%
% LATTICE L68.59
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[237532470, 3804150, -94047030; 3804150, 60935, -1506190; -94047030, -1506190, 37236357],[210, 35, 1],[-54013, -30787, -7730, -471, 190, -1449, -16291, -18141, -60191, -45349, -20821, -18563, -9707, -8068, -31294, -19927; -1127, -642, -161, -10, 3, -32, -351, -388, -1285, -966, -442, -392, -204, -169, -654, -416; -136465, -77784, -19530, -1190, 480, -3661, -41160, -45834, -152075, -114576, -52605, -46900, -24525, -20384, -79065, -50346],67,59]
%
% END OF LATTICE L68.59
%
%
% LATTICE L68.60
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-58360680, 26951400, 95760; 26951400, -12446358, -44223; 95760, -44223, -157],[2520, 3, 1],[63, 159, -67, -41, 13, 191, 164, 33659, 513, 3681, 931, 233, 659, 289, 76, 6661; 135, 340, -144, -88, 28, 410, 352, 72240, 1101, 7900, 1998, 500, 1414, 620, 163, 14280; 398, 1200, -306, -220, 42, 1010, 879, 181440, 2770, 19920, 5058, 1276, 3654, 1630, 441, 40320],67,60]
%
% END OF LATTICE L68.60
%
%
% LATTICE L68.61
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-43704508680, 367264800, -1370880; 367264800, -3086259, 11520; -1370880, 11520, -43],[2520, 3, 1],[8, 41, 2, -1, -1, 2, 9, 1021, 16, 119, 16, 9, 15, 8, 11, 659; 953, 4880, 237, -120, -119, 240, 1078, 122220, 1915, 14240, 1914, 1076, 1792, 955, 1312, 78540; 263, 240, -270, -268, 0, 535, 1872, 192780, 2941, 21120, 2673, 1336, 1869, 800, 798, 31500],67,61]
%
% END OF LATTICE L68.61
%
%
% LATTICE L68.62
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[26895540, -841680, 6657420; -841680, 26340, -208340; 6657420, -208340, 1647903],[420, 20, 1],[36, 13, 35, 47, 935, 197, 1129, 1614, 1392, 463, 679, 191, 731, 41, 61, 52; 43, 12, 11, -1, -21, -1, 9, 28, 29, 12, 25, 13, 105, 13, 51, 56; -140, -51, -140, -190, -3780, -796, -4560, -6517, -5620, -1869, -2740, -770, -2940, -164, -240, -203],67,62]
%
% END OF LATTICE L68.62
%
%
% LATTICE L68.63
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[5659212720, 89830860, 1410226020; 89830860, 1425920, 22385060; 1410226020, 22385060, 351415917],[420, 20, 1],[9846, 5753, 3111, 130, -1, 413, 4651, 18457, 8790, 6671, 6207, 1423, 21743, 2693, 10879, 25027; 3739, 2187, 1187, 52, 63, 167, 1815, 7133, 3389, 2565, 2377, 542, 8253, 1021, 4125, 9499; -39750, -23226, -12560, -525, 0, -1668, -18780, -74522, -35490, -26934, -25060, -5745, -87780, -10872, -43920, -101038],67,63]
%
% END OF LATTICE L68.63
%
%
% LATTICE L68.64
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[39060, 38220, 4200; 38220, 33054, 3507; 4200, 3507, 368],[420, 21, 1],[1129, 1307, 312, 209, 24, 179, 21, 51, -13, -67, -33, -23, 7, 286, 134, 1809; -5464, -6330, -1513, -1016, -117, -875, -103, -250, 64, 330, 163, 116, -33, -1375, -647, -8750; 39270, 45500, 10878, 7308, 842, 6300, 742, 1800, -462, -2380, -1176, -840, 236, 9870, 4648, 62880],67,64]
%
% END OF LATTICE L68.64
%
%
% LATTICE L68.65
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2184405090, 9150540, -1086086610; 9150540, -38178, 4549650; -1086086610, 4549650, -540002461],[210, 42, 1],[137071, 42826, -7622, -14273, -532, 114539, 70568, 531833, 686357, 414634, 213479, 82892, 23405, 228556, 43797, 154357; -267, -80, 19, 30, 1, -240, -147, -1105, -1425, -860, -442, -171, -48, -465, -88, -305; -275688, -86135, 15330, 28707, 1070, -230370, -141932, -1069665, -1380456, -833945, -429366, -166719, -47074, -459690, -88088, -310455],67,65]
%
% END OF LATTICE L68.65
%
%
% LATTICE L68.66
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2724540, 0, 19320; 0, 21, 0; 19320, 0, 137],[420, 21, 1],[684, 1519, 335, 189, 17, 93, 6, 17, 0, 1, 7, 39, 21, 477, 184, 2263; -217, -480, -105, -58, -5, -25, -1, 0, 1, 0, -3, -14, -7, -155, -59, -720; -96516, -214340, -47271, -26670, -2399, -13125, -847, -2400, 0, -140, -987, -5502, -2963, -67305, -25963, -319320],67,66]
%
% END OF LATTICE L68.66
%
%
% LATTICE L68.67
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-18079110, -151830, 34020; -151830, -1245, 285; 34020, 285, -64],[630, 15, 1],[613, 137, 51, 89, 59, 10, 4, 5, -1, -1, 0, 13, 60, 41, 81, 471; 8148, 1822, 679, 1188, 791, 135, 55, 70, -12, -14, -1, 168, 791, 543, 1075, 6258; 361845, 80874, 30110, 52560, 34860, 5913, 2370, 2968, -585, -594, -5, 7650, 35385, 24192, 47805, 278012],67,67]
%
% END OF LATTICE L68.67
%
%
% LATTICE L68.68
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[169660890, 11256210, -116550; 11256210, 746745, -7740; -116550, -7740, 79],[630, 15, 1],[-413, -287, -340, -71, -120, 1, 59, 1339, 209, 151, 187, 37, 1, -18, -144, -2767; 5805, 4034, 4779, 998, 1687, -14, -829, -18816, -2937, -2122, -2628, -520, -14, 253, 2024, 38892; -40565, -28188, -33390, -6970, -11760, 103, 5820, 131922, 20585, 14868, 18405, 3640, 105, -1768, -14145, -271782],67,68]
%
% END OF LATTICE L68.68
%
%
% LATTICE L68.69
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-61273590, -44163945, 15727635; -44163945, -31828755, 11334855; 15727635, 11334855, -4036568],[105, 105, 1],[-243300, -51696, -103751, -22413, -2119, 351, 1061, -3698, -17088, -6168, -26443, -20985, -12347, -43749, -73391, -83098; -18724777, -3978617, -7984890, -1724969, -163090, 27004, 81664, -284577, -1315019, -474671, -2035008, -1614997, -950232, -3366970, -5648274, -6395355; -53527950, -11373551, -22826160, -4931115, -466220, 77196, 233450, -813513, -3759210, -1356929, -5817420, -4616745, -2716400, -9625056, -16146550, -18282207],67,69]
%
% END OF LATTICE L68.69
%
%
% LATTICE L68.70
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[8166480, -231420, 2020620; -231420, 6552, -57260; 2020620, -57260, 499959],[420, 28, 1],[-59, 572, 534, 456, 2470, 17616, 19766, 39802, 23903, 78908, 11388, 1531, 1504, 2254, 104, -62; -4, 15, 19, 17, 93, 665, 747, 1505, 904, 2985, 431, 58, 57, 85, 3, -5; 238, -2310, -2156, -1841, -9972, -71120, -79800, -160690, -96502, -318570, -45976, -6181, -6072, -9100, -420, 250],67,70]
%
% END OF LATTICE L68.70
%
%
% LATTICE L68.71
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-42420, 0, -10500; 0, 28, 0; -10500, 0, -2599],[420, 28, 1],[0, -26, -7, 31, 139, 1139, 1367, 1429, 1740, 2926, 877, 259, 151, 311, 83, 21; 1, 0, -3, -7, -21, -155, -177, -180, -217, -360, -105, -29, -15, -25, -3, 0; 0, 105, 28, -126, -564, -4620, -5544, -5795, -7056, -11865, -3556, -1050, -612, -1260, -336, -85],67,71]
%
% END OF LATTICE L68.71
%
%
% LATTICE L68.72
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1595160, -4200, 8400; -4200, 30, 15; 8400, 15, -43],[840, 15, 1],[0, -1, -1, 9, 47, 33, 33, 1159, 252, 113, 127, 75, 51, 9, 2, 17; 1, -36, -38, 316, 1666, 1172, 1173, 41216, 8963, 4020, 4520, 2672, 1820, 322, 72, 616; 0, -208, -210, 1860, 9730, 6834, 6835, 240072, 52200, 23408, 26310, 15540, 10570, 1866, 415, 3528],67,72]
%
% END OF LATTICE L68.72
%
%
% LATTICE L68.73
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-8997240, 21840, -4455360; 21840, -45, 10815; -4455360, 10815, -2206258],[840, 15, 1],[52, 103, -52, -1961, -4281, -2888, -11345, -197293, -42748, -19079, -10622, -12271, -4021, -670, -515, -1955; 2, 0, -3, -28, -49, -31, -118, -2016, -434, -192, -105, -116, -35, -5, -2, 0; -105, -208, 105, 3960, 8645, 5832, 22910, 398412, 86325, 38528, 21450, 24780, 8120, 1353, 1040, 3948],67,73]
%
% END OF LATTICE L68.73
%
%
% LATTICE L68.74
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[804510, 7560, -5040; 7560, 21, -42; -5040, -42, 31],[630, 21, 1],[-467, -509, -36, -55, -4, -13, 1, 1, -1, -11, -3, -23, -9, -182, -66, -261; -9951, -10850, -768, -1176, -86, -285, 20, 20, -21, -230, -63, -486, -191, -3870, -1405, -5560; -89775, -97860, -6923, -10584, -771, -2520, 189, 190, -189, -2100, -574, -4410, -1728, -34965, -12684, -50170],67,74]
%
% END OF LATTICE L68.74
%
%
% LATTICE L68.75
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[8190, 2520, 0; 2520, 777, 0; 0, 0, -1],[630, 21, 1],[-109, -363, -80, -15, -4, -7, -1, 1, 1, 3, -1, -3, -5, -38, -44, -541; 375, 1250, 276, 52, 14, 25, 4, 0, -3, -10, 3, 10, 17, 130, 151, 1860; -749, -2520, -567, -112, -33, -70, -21, -90, -7, 0, 0, -14, -30, -245, -294, -3690],67,75]
%
% END OF LATTICE L68.75
%
%
% LATTICE L68.76
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[4620, -6720, 1260; -6720, 1610, -595; 1260, -595, 156],[420, 35, 1],[-11, -35, -29, -21, 17, 48, 340, 307, 959, 667, 266, 179, 62, 31, 55, 9; 32, 102, 85, 64, -45, -133, -951, -862, -2696, -1878, -751, -508, -177, -89, -159, -26; 210, 672, 560, 420, -300, -882, -6300, -5708, -17850, -12432, -4970, -3360, -1170, -588, -1050, -172],67,76]
%
% END OF LATTICE L68.76
%
%
% LATTICE L68.77
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-323668590, 4546500, -154439040; 4546500, -63630, 2169370; -154439040, 2169370, -73690861],[210, 70, 1],[62589, 11753, -3440, -6496, -730, 10427, 96388, 48434, 312543, 113291, 97223, 37757, 31991, 20834, 59917, 14088; -267, -48, 19, 30, 3, -48, -441, -221, -1425, -516, -442, -171, -144, -93, -264, -61; -131180, -24633, 7210, 13615, 1530, -21854, -202020, -101513, -655060, -237447, -203770, -79135, -67050, -43666, -125580, -29527],67,77]
%
% END OF LATTICE L68.77
%
%
% LATTICE L68.78
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[571620, 0, 6720; 0, 35, 0; 6720, 0, 79],[420, 35, 1],[0, 1, 7, 37, 59, 89, 514, 421, 636, 847, 311, 175, 47, 17, 16, 3; 1, 0, -3, -14, -21, -31, -177, -144, -217, -288, -105, -58, -15, -5, -3, 0; 0, -84, -595, -3150, -5025, -7581, -43785, -35864, -54180, -72156, -26495, -14910, -4005, -1449, -1365, -256],67,78]
%
% END OF LATTICE L68.78
%
%
% LATTICE L68.79
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[79258656960, -186733260, -19877780160; -186733260, 439944, 46832016; -19877780160, 46832016, 4985274281],[1260, 12, 1],[-434975, -485174, -71992, -31178, -82076, -69746, -5992, -28528, -2677, -1106, -950, -5293, -88122, -294964, -115578, -1673452; 1548, 1715, 251, 105, 259, 195, 11, 35, 0, 5, 7, 24, 343, 1095, 419, 5985; -1734390, -1934550, -287056, -124317, -327264, -278100, -23892, -113750, -10674, -4410, -3788, -21105, -351372, -1176120, -460848, -6672610],67,79]
%
% END OF LATTICE L68.79
%
%
% LATTICE L68.80
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-660140460, -7907760, 165577860; -7907760, -9516, 1983240; 165577860, 1983240, -41530597],[1260, 12, 1],[8484128, 4776686, 1444087, 1304923, 1830147, 1684823, 163017, 293257, 316, -63106, -30013, 109151, 1469359, 5385547, 2193773, 16204273; 79989, 45035, 13615, 12303, 17255, 15885, 1537, 2765, 3, -595, -283, 1029, 13853, 50775, 20683, 152775; 33829092, 19046265, 5758064, 5203170, 7297416, 6717960, 650004, 1169315, 1260, -251625, -119672, 435222, 5858832, 21474000, 8747316, 64611925],67,80]
%
% END OF LATTICE L68.80
%
%
% LATTICE L68.81
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[950047560, -2019780, -238174020; -2019780, 4308, 506352; -238174020, 506352, 59709499],[1260, 12, 1],[-10984, -19378, -19141, -2353, -14115, -7213, -5017, -80503, -4076, -5722, -3449, -157, -3455, -5337, -7533, -183047; -2105, -3715, -3672, -452, -2716, -1390, -968, -15540, -787, -1105, -666, -30, -658, -1020, -1442, -35070; -43796, -77265, -76320, -9382, -56280, -28760, -20004, -320985, -16252, -22815, -13752, -626, -13776, -21280, -30036, -729855],67,81]
%
% END OF LATTICE L68.81
%
%
% LATTICE L68.82
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[92138034240, -223862940, -23107945140; -223862940, 543912, 56144160; -23107945140, 56144160, 5795403961],[1260, 12, 1],[-66893, -248838, -134410, -9679, -137546, -79944, -61058, -2025428, -52087, -147762, -44060, -236, -1264, -19206, -38092, -2138872; 35, 125, 63, 4, 49, 25, 17, 525, 13, 35, 9, 0, 7, 15, 23, 1155; -266722, -992190, -535932, -38593, -548436, -318760, -243456, -8075970, -207686, -589170, -175680, -941, -5040, -76580, -151884, -8528310],67,82]
%
% END OF LATTICE L68.82
%
%
% LATTICE L68.83
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[5428920, 965160, -45360; 965160, 171591, -8064; -45360, -8064, 379],[840, 21, 1],[0, 33, 35, 111, 49, 1041, 194, 4679, 1404, 3087, 667, 357, 29, 129, 1, 1; 1, -100, -108, -344, -152, -3230, -602, -14520, -4357, -9580, -2070, -1108, -90, -400, -3, 0; 21, 1820, 1890, 5964, 2630, 55860, 10409, 251040, 75327, 165620, 35784, 19152, 1556, 6930, 56, 120],67,83]
%
% END OF LATTICE L68.83
%
%
% LATTICE L68.84
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[21325080, -5880, -76440; -5880, -63, 21; -76440, 21, 274],[840, 21, 1],[-7, 1, 14, 137, 35, 781, 597, 7303, 2203, 4879, 535, 595, 26, 134, 13, 17; 2, 0, -3, -28, -7, -155, -118, -1440, -434, -960, -105, -116, -5, -25, -2, 0; -1953, 280, 3906, 38220, 9764, 217875, 166544, 2037300, 614565, 1361080, 149247, 165984, 7253, 37380, 3626, 4740],67,84]
%
% END OF LATTICE L68.84
%
%
% LATTICE L68.85
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-36158220, -303660, 34020; -303660, -2490, 285; 34020, 285, -32],[1260, 15, 1],[613, 137, 51, 89, 59, 10, 4, 5, -1, -1, 0, 13, 60, 41, 81, 471; 8148, 1822, 679, 1188, 791, 135, 55, 70, -12, -14, -1, 168, 791, 543, 1075, 6258; 723690, 161748, 60220, 105120, 69720, 11826, 4740, 5936, -1170, -1188, -10, 15300, 70770, 48384, 95610, 556024],67,85]
%
% END OF LATTICE L68.85
%
%
% LATTICE L68.86
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[11344127130, -12667410, 5653996110; -12667410, 14160, -6313530; 5653996110, -6313530, 2817993103],[630, 30, 1],[4785526, 530978, 389749, 328597, 411021, 63499, 19707, 12982, 314, 782, 9071, 70223, 519559, 335321, 644993, 1848178; -6015, -667, -489, -411, -511, -78, -23, -14, 3, -1, -12, -90, -658, -423, -812, -2324; -9601650, -1065351, -781990, -659295, -824670, -127404, -39540, -26047, -630, -1569, -18200, -140895, -1042440, -672786, -1294110, -3708173],67,86]
%
% END OF LATTICE L68.86
%
%
% LATTICE L68.87
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-66058020, 1787940, 7951860; 1787940, -48390, -215265; 7951860, -215265, -956687],[1260, 15, 1],[48631, 21757, 8114, 14221, 9496, 1628, 671, 863, -67, -173, -20, 1967, 9390, 6466, 12819, 74681; 1361451, 609100, 227157, 398130, 265853, 45579, 18787, 24164, -1875, -4844, -561, 55062, 262871, 181017, 358873, 2090732; 97875, 43788, 16330, 28620, 19110, 3276, 1350, 1736, -135, -348, -40, 3960, 18900, 13014, 25800, 150304],67,87]
%
% END OF LATTICE L68.87
%
%
% LATTICE L68.88
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[3302460, -1421280, -7560; -1421280, 611670, 3255; -7560, 3255, 17],[1260, 15, 1],[-8, -23, -49, -15, 3, 11, 92, 1849, 140, 199, 247, 59, 151, 11, 18, -1; -18, -52, -111, -34, 7, 25, 209, 4200, 318, 452, 561, 134, 343, 25, 41, 0; -115, -276, -540, -160, 0, 106, 900, 18144, 1375, 1956, 2430, 580, 1470, 104, 150, -504],67,88]
%
% END OF LATTICE L68.88
%
%
% LATTICE L68.89
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-10827180, 5382720, -18900; 5382720, -2675940, 9465; -18900, 9465, 32],[1260, 15, 1],[1021, 1011, 1756, 499, 248, -249, -2239, -45751, -6961, -4971, -6211, -1489, -3713, -246, -236, 4171; 2046, 2026, 3519, 1000, 497, -499, -4487, -91686, -13950, -9962, -12447, -2984, -7441, -493, -473, 8358; -2180, -2154, -3735, -1060, -525, 529, 4755, 97146, 14780, 10554, 13185, 3160, 7875, 521, 495, -8946],67,89]
%
% END OF LATTICE L68.89
%
%
% LATTICE L68.90
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[178209726030, 1238300280, 88816116690; 1238300280, 8604390, 617143770; 88816116690, 617143770, 44264153027],[630, 30, 1],[-100609, -46548, -163952, -31821, -272446, -34487, -136066, -889589, -226667, -62544, -81505, 4548, 81535, 7214, -299, -255877; 873, 406, 1437, 280, 2401, 304, 1199, 7833, 1995, 550, 714, -41, -728, -65, -4, 2205; 201860, 93393, 328950, 63845, 546630, 69194, 273000, 1784853, 454780, 125487, 163530, -9125, -163590, -14474, 600, 513387],67,90]
%
% END OF LATTICE L68.90
%
%
% LATTICE L68.91
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-35449680, -578760, 52920; -578760, -9432, 864; 52920, 864, -79],[840, 24, 1],[-1, -1, 1, 5, 41, 136, 53, 1147, 397, 221, 98, 28, 36, 29, 2, 8; 2, 0, -3, -7, -49, -155, -59, -1260, -434, -240, -105, -29, -35, -25, -1, 0; -648, -670, 636, 3270, 26908, 89340, 34832, 754005, 261000, 145310, 64452, 18426, 23716, 19140, 1328, 5355],67,91]
%
% END OF LATTICE L68.91
%
%
% LATTICE L68.92
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-37143120, 56280, 110880; 56280, -72, -168; 110880, -168, -331],[840, 24, 1],[-1, -1, 1, 8, 69, 232, 91, 3953, 685, 191, 170, 49, 64, 53, 4, 37; 2, 0, -3, -7, -49, -155, -59, -2520, -434, -120, -105, -29, -35, -25, -1, 0; -336, -335, 336, 2682, 23128, 77760, 30500, 1324890, 229584, 64015, 56976, 16422, 21448, 17760, 1340, 12390],67,92]
%
% END OF LATTICE L68.92
%
%
% LATTICE L68.93
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-158448990, 3896760, 59638950; 3896760, -95445, -1466430; 59638950, -1466430, -22447429],[210, 105, 1],[42446, 5313, -2335, -8813, -165, 7073, 21794, 65707, 212002, 51231, 65947, 51221, 7233, 14131, 13546, 19109; -85159, -10658, 4689, 17686, 331, -14194, -43735, -131856, -425429, -102806, -132336, -102784, -14514, -28355, -27180, -38340; 118335, 14812, -6510, -24570, -460, 19719, 60760, 183186, 591045, 142828, 183855, 142800, 20165, 39396, 37765, 53274],67,93]
%
% END OF LATTICE L68.93
%
%
% LATTICE L68.94
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[485551080, -4714500, 120209040; -4714500, 45840, -1167180; 120209040, -1167180, 29760439],[420, 60, 1],[52, 51, 5511, 7936, 120653, 78497, 151585, 1305933, 564032, 125301, 276531, 39071, 98713, 15517, 5105, 10263; 1, 0, 4, 7, 112, 74, 144, 1246, 539, 120, 266, 38, 98, 16, 6, 14; -210, -206, -22260, -32055, -487340, -317064, -612280, -5274906, -2278230, -506114, -1116960, -157815, -398720, -62676, -20620, -41454],67,94]
%
% END OF LATTICE L68.94
%
%
% LATTICE L68.95
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[4484891880, 131460, 1117640580; 131460, 60, 32760; 1117640580, 32760, 278517409],[420, 60, 1],[0, 78, 16223, 46329, 351289, 228369, 440827, 1898473, 1639764, 182118, 803659, 226965, 286397, 44925, 14663, 14585; 1, 0, 4, 14, 112, 74, 144, 623, 539, 60, 266, 76, 98, 16, 6, 7; 0, -313, -65100, -185910, -1409660, -916404, -1768960, -7618233, -6580080, -730807, -3224940, -910770, -1149260, -180276, -58840, -58527],67,95]
%
% END OF LATTICE L68.95
%
%
% LATTICE L68.96
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1609020, 113400, -10080; 113400, 7728, -693; -10080, -693, 62],[1260, 21, 1],[-1, -11, -3, -23, -9, -182, -66, -261, -467, -509, -36, -55, -4, -13, 1, 1; -42, -460, -126, -972, -382, -7740, -2810, -11120, -19902, -21700, -1536, -2352, -172, -570, 40, 40; -630, -6930, -1897, -14616, -5739, -116235, -42189, -166930, -298746, -325710, -23051, -35280, -2577, -8505, 609, 610],67,96]
%
% END OF LATTICE L68.96
%
%
% LATTICE L68.97
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[591249330, -4267620, 294676200; -4267620, 30786, -2126964; 294676200, -2126964, 146865389],[630, 42, 1],[-751303, -415559, -60627, -50269, -8663, -43016, -1549, 466, 5275, 1099, -1542, -11900, -12060, -267829, -102066, -207696; 1479, 815, 118, 96, 16, 75, 2, 0, -3, 5, 5, 27, 25, 540, 203, 410; 1507464, 833805, 121646, 100863, 17382, 86310, 3108, -935, -10584, -2205, 3094, 23877, 24198, 537390, 204792, 416735],67,97]
%
% END OF LATTICE L68.97
%
%
% LATTICE L68.98
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[210420, 10080, 0; 10080, 483, 0; 0, 0, -1],[1260, 21, 1],[-1, 1, 1, 11, 5, 107, 40, 161, 145, 319, 23, 37, 3, 13, 0, -1; 21, -20, -21, -234, -107, -2295, -859, -3460, -3117, -6860, -495, -798, -65, -285, -1, 20; 0, 0, -7, -126, -69, -1575, -609, -2500, -2268, -5040, -371, -630, -57, -315, -21, -20],67,98]
%
% END OF LATTICE L68.98
%
%
% LATTICE L68.99
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[16380, 2520, 0; 2520, 168, 21; 0, 21, -2],[1260, 21, 1],[1, 3, -1, -3, -5, -38, -44, -541, -109, -363, -80, -15, -4, -7, -1, 1; -6, -20, 6, 20, 34, 260, 302, 3720, 750, 2500, 552, 104, 28, 50, 8, 0; -70, -210, 63, 196, 327, 2485, 2877, 35370, 7126, 23730, 5229, 980, 261, 455, 63, -90],67,99]
%
% END OF LATTICE L68.99
%
%
% LATTICE L68.100
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-151830, -5040, -75600; -5040, 546, -2520; -75600, -2520, -37643],[630, 42, 1],[-26811, -45377, -20663, -2097, -1289, -2896, -963, -2086, -321, 157, 314, -164, -972, -8409, -10342, -65744; 795, 1345, 612, 62, 38, 85, 28, 60, 9, -5, -9, 5, 29, 250, 307, 1950; 53788, 91035, 41454, 4207, 2586, 5810, 1932, 4185, 644, -315, -630, 329, 1950, 16870, 20748, 131895],67,100]
%
% END OF LATTICE L68.100
%
%
% LATTICE L68.101
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-777420, -272160, 1260; -272160, -95277, 441; 1260, 441, -2],[1260, 21, 1],[1, 7, -2, -7, -12, -92, -107, -1319, -133, -887, -196, -37, -10, -18, -3, -1; -3, -20, 6, 20, 34, 260, 302, 3720, 375, 2500, 552, 104, 28, 50, 8, 0; -35, 0, 63, -14, -93, -875, -1113, -14400, -1477, -10080, -2331, -490, -159, -385, -147, -720],67,101]
%
% END OF LATTICE L68.101
%
%
% LATTICE L68.102
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-207480, -13440, 840; -13440, 70, 35; 840, 35, -3],[840, 35, 1],[-156, -203, -71, -35, -7, -1, 2, 1, 0, -5, -7, -17, -19, -25, -67, -105; -1189, -1548, -542, -268, -54, -8, 15, 8, 1, -36, -52, -128, -144, -190, -510, -800; -57960, -75432, -26390, -13020, -2610, -378, 735, 368, 0, -1848, -2590, -6300, -7050, -9282, -24885, -39008],67,102]
%
% END OF LATTICE L68.102
%
%
% LATTICE L68.103
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[17724840, -11760, -52920; -11760, -105, 35; -52920, 35, 158],[840, 35, 1],[2155, 2863, 523, 581, 76, 26, 37, 3, -7, 1, 14, 135, 103, 153, 1753, 1429; -434, -576, -105, -116, -15, -5, -6, 0, 2, 0, -3, -28, -21, -31, -354, -288; 721805, 958944, 175175, 194600, 25455, 8708, 12390, 1004, -2345, 336, 4690, 45220, 34500, 51247, 587160, 478636],67,103]
%
% END OF LATTICE L68.103
%
%
% LATTICE L68.104
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[315, 0, 0; 0, 6195, -315; 0, -315, 16],[315, 105, 1],[1, 0, -1, -7, -7, -31, -59, -24, -217, -48, -35, -29, -5, -5, -1, 0; 0, 1, 7, 48, 49, 219, 419, 171, 1548, 343, 251, 210, 37, 39, 11, 1; 0, 21, 140, 945, 960, 4284, 8190, 3341, 30240, 6699, 4900, 4095, 720, 756, 210, 19],67,104]
%
% END OF LATTICE L68.104
%
%
% LATTICE L68.105
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-561645, -31185, 13545; -31185, -1365, 630; 13545, 630, -286],[315, 105, 1],[-1, -2, 2, 10, 38, 60, 354, 440, 445, 298, 664, 64, 36, 14, 16, 4; -58, -119, 102, 581, 2218, 3506, 20696, 25731, 26026, 17431, 38850, 3747, 2110, 822, 944, 237; -175, -357, 315, 1750, 6675, 10549, 62265, 77409, 78295, 52437, 116865, 11270, 6345, 2471, 2835, 711],67,105]
%
% END OF LATTICE L68.105
%
%
% LATTICE L68.106
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[840, 0, 0; 0, -120, 40; 0, 40, -13],[840, 40, 1],[-7, -1, -1, 0, 1, 0, -1, -5, -5, -1, -2, -1, -8, -1, -4, -9; -33, -6, -10, -3, 0, 3, 24, 77, 69, 12, 19, 6, 21, 0, -9, -35; -160, -27, -40, -10, 0, 8, 60, 182, 160, 27, 40, 10, 0, -8, -60, -182],67,106]
%
% END OF LATTICE L68.106
%
%
% LATTICE L68.107
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[31929240, 618240, -76440; 618240, 11960, -1480; -76440, -1480, 183],[840, 40, 1],[7, 1, -1, -1, 1, 2, 17, 29, 53, 19, 16, 6, 34, 3, 8, 6; -19, -9, -10, -4, 0, 5, 42, 70, 127, 45, 37, 13, 63, 4, 3, -7; 2760, 342, -500, -450, 420, 876, 7440, 12677, 23160, 8298, 6980, 2610, 14700, 1284, 3360, 2443],67,107]
%
% END OF LATTICE L68.107
%
%
% LATTICE L68.108
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[667639560, 20882820, 165117960; 20882820, 653184, 5164656; 165117960, 5164656, 40836317],[420, 84, 1],[-40052, -44137, -19165, -2594, -857, -3863, -35, 439, 344, 17, -689, -715, -1349, -29227, -10995, -66619; 6267, 6910, 3004, 408, 136, 630, 12, -40, -39, 10, 110, 111, 210, 4560, 1718, 10420; 161154, 177590, 77112, 10437, 3448, 15540, 140, -1770, -1386, -70, 2772, 2877, 5428, 117600, 44240, 268050],67,108]
%
% END OF LATTICE L68.108
%
%
% LATTICE L68.109
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-302535660, 0, -74933460; 0, 84, 0; -74933460, 0, -18559873],[420, 84, 1],[281124, 157437, 141311, 41559, 8023, 49101, 4279, 3236, 0, -1257, -749, 5295, 7595, 185169, 73811, 231034; -217, -120, -105, -29, -5, -25, -1, 0, 1, 0, -3, -7, -7, -155, -59, -180; -1135008, -635635, -570528, -167790, -32392, -198240, -17276, -13065, 0, 5075, 3024, -21378, -30664, -747600, -298004, -932775],67,109]
%
% END OF LATTICE L68.109
%
%
% LATTICE L68.110
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[69584760, 23158800, -27720; 23158800, 7707570, -9225; -27720, -9225, 11],[2520, 15, 1],[-1, 17, 17, 47, -37, -65, -82, -1065, -719, -337, -137, -287, -243, -55, -18, -55; 3, -52, -52, -144, 112, 198, 250, 3248, 2193, 1028, 418, 876, 742, 168, 55, 168; 0, -768, -770, -2340, 630, 2214, 2985, 39704, 27000, 12768, 5270, 11340, 9870, 2286, 765, 2296],67,110]
%
% END OF LATTICE L68.110
%
%
% LATTICE L68.111
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[148611960, 50195880, -108360; 50195880, 16954395, -36600; -108360, -36600, 79],[2520, 15, 1],[11, 25, 47, 13, -9, -11, -44, -1739, -131, -185, -227, -53, -131, -9, -6, 59; -33, -76, -144, -40, 28, 34, 136, 5376, 405, 572, 702, 164, 406, 28, 19, -168; -205, -924, -2250, -700, 630, 664, 2655, 105336, 7945, 11244, 13860, 3280, 8400, 626, 570, 3024],67,111]
%
% END OF LATTICE L68.111
%
%
% LATTICE L68.112
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1689022440, -20875680, 126884520; -20875680, -258015, 1567965; 126884520, 1567965, -9383494],[2520, 15, 1],[2042, 4979, 227, -58345, -138182, -94987, -376331, -2191499, -1426850, -638227, -118961, -416591, -138864, -23747, -19449, -24869; -167130, -407512, -18579, 4775316, 11309669, 7774323, 30801254, 179365816, 116782218, 52236440, 9736503, 34096380, 11365487, 1943601, 1591826, 2035432; -315, -768, -35, 9000, 21315, 14652, 58050, 338044, 220095, 98448, 18350, 64260, 21420, 3663, 3000, 3836],67,112]
%
% END OF LATTICE L68.112
%
%
% LATTICE L68.113
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-9273476520, -189254520, 811440; -189254520, -3862335, 16560; 811440, 16560, -71],[2520, 15, 1],[5, 3, -2, -3, -1, 1, 19, 403, 31, 45, 29, 15, 22, 2, 11, 101; -247, -152, 93, 144, 49, -48, -914, -19404, -1493, -2168, -1398, -724, -1064, -97, -536, -4956; -475, -1176, -1170, -700, 0, 233, 3960, 79884, 6055, 8616, 5355, 2560, 3255, 232, 690, -1764],67,113]
%
% END OF LATTICE L68.113
%
%
% LATTICE L68.114
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-352380, -22260, 1680; -22260, -1260, 105; 1680, 105, -8],[420, 105, 1],[-1, -1, -2, 1, 2, 11, 23, 59, 181, 41, 47, 29, 3, 4, 2, 1; 0, -2, -7, -12, -3, -9, -13, -26, -72, -14, -11, 0, 1, 3, 3, 2; -210, -238, -525, 0, 355, 2079, 4445, 11526, 35490, 8078, 9345, 5880, 625, 861, 455, 234],67,114]
%
% END OF LATTICE L68.114
%
%
% LATTICE L68.115
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[31903955790, 12526433220, 6052157580; 12526433220, 4918246830, 2376255420; 6052157580, 2376255420, 1148089963],[210, 210, 1],[-1127, -107, -161, -5, 1, -32, -117, -194, -1285, -161, -442, -196, -68, -169, -218, -208; -615843, -58511, -88166, -2676, 756, -16335, -61526, -102920, -683217, -85829, -236599, -105579, -36841, -91920, -118899, -113590; 1280580, 121667, 183330, 5565, -1570, 33978, 127960, 214041, 1420860, 178493, 492030, 219555, 76610, 191142, 247240, 236199],67,115]
%
% END OF LATTICE L68.115
%
%
% LATTICE L68.116
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-5460, 5460, -2520; 5460, -5355, 2520; -2520, 2520, -1163],[420, 105, 1],[1, 13, 46, 85, 24, 80, 127, 275, 395, 163, 152, 47, -2, -14, -17, -11; 1, 0, -3, -14, -7, -31, -59, -144, -217, -96, -105, -58, -5, -5, -1, 0; 0, -28, -105, -210, -65, -231, -385, -864, -1260, -532, -525, -210, -5, 21, 35, 24],67,116]
%
% END OF LATTICE L68.116
%
%
% LATTICE L68.117
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-351120, -17640, -4200; -17640, 1288, 392; -4200, 392, 117],[840, 56, 1],[133, 227, 35, 11, 7, 16, 5, 1, -1, -7, -2, 0, 4, 39, 50, 54; -18068, -30870, -4769, -1505, -963, -2215, -699, -140, 140, 990, 287, 11, -531, -5255, -6771, -7330; 65016, 111090, 17164, 5418, 3468, 7980, 2520, 505, -504, -3570, -1036, -42, 1908, 18900, 24360, 26375],67,117]
%
% END OF LATTICE L68.117
%
%
% LATTICE L68.118
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1157520, 318360, 69720; 318360, -87528, -19208; 69720, -19208, -4167],[840, 56, 1],[-2783, -2174, -554, -97, 4, 181, 140, 57, -37, -176, -151, -138, -239, -1356, -1315, -2407; -8386, -6555, -1673, -295, 9, 535, 417, 170, -110, -525, -451, -413, -717, -4075, -3957, -7250; -7952, -6195, -1568, -266, 24, 560, 420, 170, -112, -525, -448, -406, -696, -3920, -3780, -6890],67,118]
%
% END OF LATTICE L68.118
%
%
% LATTICE L68.119
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-12279960, -42840, -47880; -42840, 21, 0; -47880, 0, -23],[2520, 21, 1],[-1, 1, 1, 11, 5, 107, 20, 161, 145, 319, 23, 37, 3, 13, 0, -1; -2037, 2060, 2044, 22464, 10208, 218430, 40826, 328640, 295977, 651140, 46946, 75516, 6122, 26520, -1, -2040; 2079, -2100, -2086, -22932, -10422, -223020, -41685, -335560, -302211, -664860, -47936, -77112, -6252, -27090, 0, 2080],67,119]
%
% END OF LATTICE L68.119
%
%
% LATTICE L68.120
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1847160, 45360, -2520; 45360, -1113, 63; -2520, 63, -2],[2520, 21, 1],[-2, 1, 1, 25, 6, 131, 99, 401, 362, 799, 29, 95, 4, 19, 1, -1; -78, 40, 39, 972, 233, 5085, 3842, 15560, 14046, 31000, 1125, 3684, 155, 735, 38, -40; 63, 0, -35, -1008, -255, -5670, -4326, -17620, -15939, -35280, -1288, -4284, -186, -945, -84, -20],67,120]
%
% END OF LATTICE L68.120
%
%
% LATTICE L68.121
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-77759640, -4445280, -108360; -4445280, -254058, -6195; -108360, -6195, -151],[2520, 21, 1],[-2, -7, 11, 21, 33, 247, 142, 3479, 350, 2327, 511, 95, 25, 43, 3, 1; 7, 20, -42, -76, -118, -880, -505, -12360, -1243, -8260, -1812, -336, -88, -150, -10, 0; 1148, 4200, -6174, -11956, -18846, -141190, -81207, -1990080, -200228, -1331400, -292446, -54404, -14334, -24710, -1743, -720],67,121]
%
% END OF LATTICE L68.121
%
%
% LATTICE L68.122
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1378440, -35280, 0; -35280, 903, 0; 0, 0, -1],[2520, 21, 1],[1, 1, -1, -1, 0, 2, 7, 103, 11, 79, 10, 5, 1, 3, 3, 17; 39, 40, -39, -40, -1, 70, 254, 3780, 405, 2920, 372, 188, 38, 115, 116, 660; -7, 0, 0, -28, -30, -245, -588, -7380, -749, -5040, -567, -224, -33, -70, -42, -180],67,122]
%
% END OF LATTICE L68.122
%
%
% LATTICE L68.123
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[209450640, 7779660, -46161360; 7779660, 288960, -1714580; -46161360, -1714580, 10173619],[420, 140, 1],[-226, -31, 349, 375, 2123, 3063, 17269, 6971, 20950, 13847, 10013, 1352, 1331, 391, 1, -63; 685, 87, -1089, -1166, -6603, -9529, -53733, -21693, -65197, -43095, -31167, -4210, -4149, -1223, -27, 189; -910, -126, 1400, 1505, 8520, 12292, 69300, 27974, 84070, 55566, 40180, 5425, 5340, 1568, 0, -254],67,123]
%
% END OF LATTICE L68.123
%
%
% LATTICE L68.124
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-65796360, 420, 16299780; 420, 140, 0; 16299780, 0, -4037879],[420, 140, 1],[0, 463, 763, -2341, -10999, -18187, -109559, -22952, -139836, -47075, -70681, -20965, -12307, -5119, -6971, -354; 1, -1389, -2292, 7016, 32976, 54530, 328500, 68820, 419291, 141153, 211938, 62866, 36906, 15352, 20910, 1062; 0, 1869, 3080, -9450, -44400, -73416, -442260, -92651, -564480, -190029, -285320, -84630, -49680, -20664, -28140, -1429],67,124]
%
% END OF LATTICE L68.124
%
%
% LATTICE L68.125
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-17506440, -30240, 15120; -30240, 24, 24; 15120, 24, -13],[2520, 24, 1],[-1, -1, 0, 2, 18, 61, 24, 174, 181, 101, 15, 13, 17, 14, 1, 1; -33, -35, -1, 63, 581, 1980, 781, 5670, 5901, 3295, 490, 426, 560, 465, 34, 35; -1224, -1230, -4, 2430, 21924, 74340, 29256, 212135, 220680, 123150, 18292, 15858, 20748, 17100, 1224, 1225],67,125]
%
% END OF LATTICE L68.125
%
%
% LATTICE L68.126
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-138481560, -861840, 115920; -861840, -5304, 720; 115920, 720, -97],[2520, 24, 1],[-1, -1, 0, 5, 46, 157, 62, 901, 469, 131, 39, 34, 45, 38, 3, 9; -33, -35, -1, 168, 1561, 5340, 2111, 30695, 15981, 4465, 1330, 1161, 1540, 1305, 104, 315; -1440, -1455, -8, 7218, 66528, 227160, 89724, 1304030, 678816, 189615, 56456, 49230, 65184, 55080, 4356, 13090],67,126]
%
% END OF LATTICE L68.126
%
%
% LATTICE L68.127
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-552517560, 39465720, -221760; 39465720, -2818992, 15840; -221760, 15840, -89],[2520, 24, 1],[56, 51, 53, 7, 43, 21, 13, 352, 16, 9, 1, -1, -1, 9, 17, 908; 835, 760, 789, 104, 637, 310, 191, 5145, 233, 130, 12, -15, -14, 135, 254, 13545; 9064, 8175, 8352, 1066, 6216, 2840, 1596, 38430, 1592, 705, -360, -178, 0, 1600, 2844, 148050],67,127]
%
% END OF LATTICE L68.127
%
%
% LATTICE L68.128
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-493776360, 32888520, -395640; 32888520, -2190576, 26352; -395640, 26352, -317],[2520, 24, 1],[56, 102, 53, 7, 43, 21, 13, 176, 16, 18, 1, -1, -1, 9, 17, 454; 893, 1625, 843, 111, 679, 330, 203, 2730, 247, 275, 12, -16, -14, 145, 272, 7245; 4336, 7770, 3924, 490, 2772, 1220, 648, 7245, 560, 390, -252, -82, 84, 820, 1392, 35595],67,128]
%
% END OF LATTICE L68.128
%
%
% LATTICE L68.129
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[197190, 57330, -12600; 57330, 12705, -2835; -12600, -2835, 632],[630, 105, 1],[109, 27, 12, 29, 4, 7, 5, 1, -1, -3, -3, -11, -1, 2, 10, 11; 5538, 1418, 661, 1704, 247, 447, 329, 66, -66, -202, -205, -792, -95, 9, 431, 542; 26775, 6846, 3185, 8190, 1185, 2142, 1575, 316, -315, -966, -980, -3780, -450, 63, 2100, 2624],67,129]
%
% END OF LATTICE L68.129
%
%
% LATTICE L68.130
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-8190, 1260, 630; 1260, 105, 0; 630, 0, -17],[630, 105, 1],[205, 137, 152, 29, 8, 3, 3, 1, -1, -1, 1, 5, 9, 14, 82, 203; -1967, -1318, -1470, -284, -80, -31, -34, -12, 11, 14, 3, -42, -83, -132, -781, -1944; 6335, 4242, 4725, 910, 255, 98, 105, 36, -35, -42, 0, 140, 270, 427, 2520, 6264],67,130]
%
% END OF LATTICE L68.130
%
%
% LATTICE L68.131
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[45376508520, -25334820, -11380262040; -25334820, 14160, 6353880; -11380262040, 6353880, 2854128013],[1260, 60, 1],[-2408062, -534373, -392241, -165349, -413649, -63905, -19833, -13065, -158, -787, -9129, -35336, -522881, -337465, -649117, -1859995; -6015, -1334, -978, -411, -1022, -156, -46, -28, 3, -2, -24, -90, -1316, -846, -1624, -4648; -9601650, -2130702, -1563980, -659295, -1649340, -254808, -79080, -52094, -630, -3138, -36400, -140895, -2084880, -1345572, -2588220, -7416346],67,131]
%
% END OF LATTICE L68.131
%
%
% LATTICE L68.132
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[3730585320, 2501645580, -929650680; 2501645580, 1677546660, -623402580; -929650680, -623402580, 231666163],[1260, 60, 1],[1781632, 197632, 289985, 244169, 304645, 46829, 14231, 4541, -316, 292, 6901, 52717, 388089, 250057, 480579, 688193; -24375, -2704, -3968, -3342, -4172, -642, -196, -63, 3, -4, -94, -720, -5306, -3420, -6574, -9415; 7083900, 785799, 1153000, 970830, 1211280, 186192, 56580, 18053, -1260, 1161, 27440, 209610, 1543080, 994248, 1910820, 2736307],67,132]
%
% END OF LATTICE L68.132
%
%
% LATTICE L68.133
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[166881960, -2846340, -41936580; -2846340, 48180, 715260; -41936580, 715260, 10538447],[1260, 60, 1],[8151, 2273, 5959, -469, -10323, -1563, -6245, -18313, -4359, -1009, -271, 1101, 14747, 2195, 9405, 31585; -943, -263, -690, 54, 1190, 180, 718, 2100, 499, 115, 24, -128, -1708, -254, -1088, -3654; 32500, 9063, 23760, -1870, -41160, -6232, -24900, -73017, -17380, -4023, -1080, 4390, 58800, 8752, 37500, 125937],67,133]
%
% END OF LATTICE L68.133
%
%
% LATTICE L68.134
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[138000250080, 2150392860, -34538050260; 2150392860, 33508560, -538190160; -34538050260, -538190160, 8644019957],[1260, 60, 1],[-38713, -22647, -36925, -558, -1475, -1903, -19787, -230071, -36311, -27369, -75611, -5694, -86053, -10601, -42733, -295097; 5006, 2929, 4779, 73, 217, 251, 2585, 29967, 4726, 3559, 9819, 738, 11137, 1371, 5525, 38157; -154370, -90306, -147240, -2225, -5880, -7588, -78900, -917406, -144790, -109134, -301500, -22705, -343140, -42272, -170400, -1176714],67,134]
%
% END OF LATTICE L68.134
%
%
% LATTICE L68.135
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[22680, -15960, 0; -15960, 210, 105; 0, 105, -1],[840, 105, 1],[0, -3, -7, 3, 7, 39, 41, 211, 324, 147, 169, 105, 11, 15, 4, 5; 1, -4, -10, 4, 10, 56, 59, 304, 467, 212, 244, 152, 16, 22, 6, 8; 0, -448, -1050, 420, 1030, 5754, 6055, 31176, 47880, 21728, 24990, 15540, 1630, 2226, 595, 744],67,135]
%
% END OF LATTICE L68.135
%
%
% LATTICE L68.136
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1329720, -1353240, -5880; -1353240, 1376445, 5985; -5880, 5985, 26],[840, 105, 1],[9, -1, -17, -153, -38, -168, -639, -1559, -2349, -1039, -568, -627, -27, -27, -11, -1; 2, 0, -3, -28, -7, -31, -118, -288, -434, -192, -105, -116, -5, -5, -2, 0; 1575, -224, -3150, -28140, -6980, -30849, -117320, -286212, -431235, -190736, -104265, -115080, -4955, -4956, -2030, -228],67,136]
%
% END OF LATTICE L68.136
%
%
% LATTICE L68.137
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1680, 49560, -840; 49560, -1458360, 24720; -840, 24720, -419],[840, 120, 1],[-1, -1, 1, 17, 153, 104, 205, 893, 1549, 173, 386, 112, 148, 25, 10, 10; 2, 0, -3, -7, -49, -31, -59, -252, -434, -48, -105, -29, -35, -5, -1, 0; 120, 2, -180, -450, -3220, -2052, -3920, -16779, -28920, -3202, -7020, -1950, -2380, -348, -80, -21],67,137]
%
% END OF LATTICE L68.137
%
%
% LATTICE L68.138
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1680, -840, -1680; -840, -360, -840; -1680, -840, -1679],[840, 120, 1],[-1, -1, 1, 32, 293, 200, 395, 3445, 2989, 167, 746, 217, 288, 49, 20, 41; 2, 0, -3, -7, -49, -31, -59, -504, -434, -24, -105, -29, -35, -5, -1, 0; 0, 1, 0, -30, -280, -192, -380, -3318, -2880, -161, -720, -210, -280, -48, -20, -42],67,138]
%
% END OF LATTICE L68.138
%
%
% LATTICE L68.139
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[6293513520, -27839700, -1578405780; -27839700, 123144, 6982164; -1578405780, 6982164, 395862311],[1260, 84, 1],[-2623, -1106, 1524, 5894, 11952, 265466, 101172, 205884, 372379, 411946, 60102, 24919, 8590, 42664, 1538, -464; -33, 5, 33, 108, 211, 4635, 1757, 3565, 6441, 7115, 1035, 426, 145, 705, 23, -5; -10458, -4410, 6076, 23499, 47652, 1058400, 403368, 820850, 1484658, 1642410, 239624, 99351, 34248, 170100, 6132, -1850],67,139]
%
% END OF LATTICE L68.139
%
%
% LATTICE L68.140
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-280980, -40320, 70560; -40320, 14028, 10080; 70560, 10080, -17719],[1260, 84, 1],[316, 553, -309, -5467, -6567, -153581, -60063, -62022, -225568, -125693, -37233, -32075, -5947, -34129, -2507, -548; 3, 5, -3, -51, -61, -1425, -557, -575, -2091, -1165, -345, -297, -55, -315, -23, -5; 1260, 2205, -1232, -21798, -26184, -612360, -239484, -247295, -899388, -501165, -148456, -127890, -23712, -136080, -9996, -2185],67,140]
%
% END OF LATTICE L68.140
%
%
% LATTICE L68.141
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[60515280, -364140, -15174180; -364140, 2184, 91308; -15174180, 91308, 3804919],[1260, 84, 1],[165, -158, -316, 86, 1008, 8706, 10700, 67996, 13863, 46918, 21358, 1083, 1330, 2984, 990, 2144; 1, -5, -9, -1, -1, 5, 13, 105, 23, 85, 45, 3, 5, 15, 7, 15; 658, -630, -1260, 343, 4020, 34720, 42672, 271170, 55286, 187110, 85176, 4319, 5304, 11900, 3948, 8550],67,141]
%
% END OF LATTICE L68.141
%
%
% LATTICE L68.142
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[16421580, -124740, -4116420; -124740, 2184, 31248; -4116420, 31248, 1031869],[1260, 84, 1],[-1257, 79, 316, -2356, -10368, -85146, -102428, -321818, -130707, -220019, -198262, -19638, -11626, -24824, -7542, -8092; -84, 5, 21, -157, -691, -5675, -6827, -21450, -8712, -14665, -13215, -1309, -775, -1655, -503, -540; -5012, 315, 1260, -9394, -41340, -339500, -408408, -1283175, -521164, -877275, -790524, -78302, -46356, -98980, -30072, -32265],67,142]
%
% END OF LATTICE L68.142
%
%
% LATTICE L68.143
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[394380, -467460, 23940; -467460, 485310, -24885; 23940, -24885, 1276],[1260, 105, 1],[109, 27, 12, 29, 4, 7, 5, 1, -1, -3, -3, -11, -1, 2, 10, 11; -7368, -1906, -901, -2364, -347, -633, -469, -94, 96, 290, 295, 1152, 145, 27, -541, -714; -145530, -37632, -17780, -46620, -6840, -12474, -9240, -1852, 1890, 5712, 5810, 22680, 2850, 504, -10710, -14108],67,143]
%
% END OF LATTICE L68.143
%
%
% LATTICE L68.144
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2315011230, -162301230, 1153807830; -162301230, 11378640, -80891370; 1153807830, -80891370, 575060929],[630, 210, 1],[-656720, -72554, -52783, -43457, -7381, -7091, -941, 156, 5336, 178, -1499, -10825, -10713, -47191, -89529, -36344; 6687, 739, 538, 444, 76, 75, 14, 0, -27, 1, 17, 111, 109, 480, 911, 370; 1318590, 145677, 105980, 87255, 14820, 14238, 1890, -313, -10710, -357, 3010, 21735, 21510, 94752, 179760, 72973],67,144]
%
% END OF LATTICE L68.144
%
%
% LATTICE L68.145
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[5149620, 1716120, 20160; 1716120, 571935, 6720; 20160, 6720, 79],[1260, 105, 1],[-2125, -943, -346, -583, -52, -56, -17, -3, 1, -1, -8, -125, -66, -298, -573, -469; 8283, 3676, 1349, 2274, 203, 219, 67, 12, -3, 4, 31, 486, 257, 1161, 2233, 1828; -162540, -72156, -26495, -44730, -4005, -4347, -1365, -256, 0, -84, -595, -9450, -5025, -22743, -43785, -35864],67,145]
%
% END OF LATTICE L68.145
%
%
% LATTICE L68.146
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-492660, 1260, 0; 1260, 3360, -1365; 0, -1365, 554],[1260, 105, 1],[-1, -1, 1, 5, 9, 14, 82, 203, 205, 137, 152, 29, 8, 3, 3, 1; -398, -392, 384, 1932, 3476, 5406, 31660, 78372, 79142, 52888, 58674, 11192, 3086, 1156, 1150, 372; -980, -966, 945, 4760, 8565, 13321, 78015, 193122, 195020, 130326, 144585, 27580, 7605, 2849, 2835, 918],67,146]
%
% END OF LATTICE L68.146
%
%
% LATTICE L68.147
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[6570270, 750960, 3274110; 750960, 85890, 374220; 3274110, 374220, 1631561],[630, 210, 1],[61441, 20377, 44539, 4095, 2121, 718, 523, 148, 35, 115, 1568, 1028, 3002, 4405, 25092, 30590; 493, 163, 354, 32, 16, 5, 2, 0, -1, 1, 15, 9, 25, 36, 203, 246; -123410, -40929, -89460, -8225, -4260, -1442, -1050, -297, -70, -231, -3150, -2065, -6030, -8848, -50400, -61443],67,147]
%
% END OF LATTICE L68.147
%
%
% LATTICE L68.148
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-16380, 20160, -5040; 20160, -12705, 1155; -5040, 1155, 554],[1260, 105, 1],[-36, -69, 65, 331, 595, 925, 5416, 13405, 6768, 9045, 10033, 1913, 527, 197, 194, 59; -73, -140, 132, 672, 1208, 1878, 10996, 27216, 13741, 18364, 20370, 3884, 1070, 400, 394, 120; -175, -336, 315, 1610, 2895, 4501, 26355, 65232, 32935, 44016, 48825, 9310, 2565, 959, 945, 288],67,148]
%
% END OF LATTICE L68.148
%
%
% LATTICE L68.149
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-38640, -19320, 1680; -19320, -9576, 840; 1680, 840, -73],[840, 168, 1],[-1, -3, -2, 2, 4, 103, 42, 133, 325, 183, 83, 25, 5, 32, 3, 2; 2, 0, -3, -7, -7, -155, -59, -180, -434, -240, -105, -29, -5, -25, -1, 0; 0, -70, -84, -42, 4, 420, 224, 795, 2016, 1190, 588, 210, 52, 420, 56, 45],67,149]
%
% END OF LATTICE L68.149
%
%
% LATTICE L68.150
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2659440, -835800, 5880; -835800, -262584, 1848; 5880, 1848, -13],[840, 168, 1],[-1, -1, -2, -1, 0, 7, 4, 29, 37, 11, 11, 4, 1, 8, 1, 1; 2, 0, -3, -7, -7, -155, -59, -360, -434, -120, -105, -29, -5, -25, -1, 0; -168, -455, -1344, -1470, -1016, -19320, -6748, -39090, -46200, -12425, -10248, -2394, -272, 0, 308, 450],67,150]
%
% END OF LATTICE L68.150
%
%
% LATTICE L68.151
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[3360, -390180, -96600; -390180, 49759920, 12319440; -96600, 12319440, 3050017],[420, 420, 1],[1, -1, -17, -17, -33, -145, -275, -335, -1009, -223, -487, -67, -23, -23, -5, -1; 52, 357, 5199, 5173, 10091, 44441, 84397, 102897, 310016, 68547, 149835, 20666, 7135, 7237, 1733, 459; -210, -1442, -21000, -20895, -40760, -179508, -340900, -415626, -1252230, -276878, -605220, -83475, -28820, -29232, -7000, -1854],67,151]
%
% END OF LATTICE L68.151
%
%
% LATTICE L68.152
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[420, 1680, 420; 1680, 4650660, 1158780; 420, 1158780, 288727],[420, 420, 1],[1, 1, 25, 47, 45, 197, 373, 227, 1367, 151, 659, 181, 31, 31, 7, 1; 0, 75, 2093, 4029, 3877, 16995, 32197, 19600, 118044, 13041, 56929, 15645, 2681, 2679, 593, 74; 0, -301, -8400, -16170, -15560, -68208, -129220, -78663, -473760, -52339, -228480, -62790, -10760, -10752, -2380, -297],67,152]
%
% END OF LATTICE L68.152
%
%
% LATTICE L68.153
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-10653720, 13915440, -3564960; 13915440, -18175640, 4656400; -3564960, 4656400, -1192911],[840, 280, 1],[-95, 235, 419, -13, -977, -1900, -12187, -2635, -32461, -11087, -8558, -2700, -1736, -813, -1378, -78; -1, -3, -2, 8, 36, 59, 354, 74, 901, 303, 227, 67, 39, 16, 21, 1; 280, -714, -1260, 70, 3060, 5908, 37800, 8163, 100520, 34314, 26460, 8330, 5340, 2492, 4200, 237],67,153]
%
% END OF LATTICE L68.153
%
%
% LATTICE L68.154
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-9376080, -4688040, 23520; -4688040, -2343880, 11760; 23520, 11760, -59],[840, 280, 1],[-1, -1, -2, 3, 16, 27, 164, 69, 421, 71, 107, 32, 19, 8, 11, 1; 2, 0, -3, -7, -21, -31, -177, -72, -434, -72, -105, -29, -15, -5, -3, 0; 0, -399, -1400, -210, 2160, 4536, 29820, 13042, 80640, 13839, 21560, 6930, 4560, 2184, 3780, 398],67,154]
%
% END OF LATTICE L68.154
%
%
% LATTICE L68.155
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[172476360, -57609720, -153720; -57609720, 19242510, 51345; -153720, 51345, 137],[2520, 105, 1],[1, -11, -15, -101, -35, -133, -116, -179, -793, -341, -117, -163, -9, 1, 6, 3; 3, -28, -38, -252, -86, -324, -281, -432, -1911, -820, -280, -384, -20, 6, 16, 8; 0, -1848, -2590, -18900, -7050, -27846, -24885, -39008, -173880, -75432, -26390, -39060, -2610, -1134, 735, 368],67,155]
%
% END OF LATTICE L68.155
%
%
% LATTICE L68.156
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1419846120, -157646160, 473760; -157646160, 17503395, -52605; 473760, -52605, 158],[2520, 105, 1],[65, -1, -36, -1021, -257, -1141, -4349, -3541, -16013, -7087, -1293, -4295, -186, -188, -81, -3; 522, -8, -289, -8196, -2063, -9159, -34910, -28424, -128538, -56888, -10379, -34476, -1493, -1509, -650, -24; -21105, 336, 11725, 332640, 83745, 371826, 1417290, 1153996, 5218605, 2309664, 421400, 1399860, 60630, 61299, 26460, 1004],67,156]
%
% END OF LATTICE L68.156
%
%
% LATTICE L68.157
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-139257720, -4974480, 141120; -4974480, -177555, 5040; 141120, 5040, -143],[2520, 105, 1],[0, -3, -7, 1, 7, 13, 41, 211, 108, 147, 169, 35, 11, 5, 4, 5; 1, -28, -72, 0, 52, 102, 328, 1704, 875, 1196, 1386, 292, 94, 44, 37, 48; 35, -3948, -9450, 980, 8730, 16408, 51975, 268056, 137305, 187068, 215460, 44800, 14160, 6482, 5250, 6624],67,157]
%
% END OF LATTICE L68.157
%
%
% LATTICE L68.158
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1434704040, 628052040, -1428840; 628052040, 274934310, -625485; -1428840, -625485, 1423],[2520, 105, 1],[8, 3, -1, 13, 16, 27, 329, 833, 424, 573, 325, 131, 20, 9, 31, 31; -17, -8, 3, -16, -23, -40, -494, -1260, -643, -872, -498, -204, -32, -15, -56, -60; 560, -504, 315, 6020, 5955, 9527, 113190, 282528, 143080, 192024, 107415, 41860, 6015, 2443, 6510, 4752],67,158]
%
% END OF LATTICE L68.158
%
%
% LATTICE L68.159
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-93829680, 11221560, -113400; 11221560, -1341960, 13560; -113400, 13560, -137],[2520, 120, 1],[-1, -1, 0, 14, 130, 89, 176, 256, 1333, 149, 111, 97, 129, 22, 9, 3; -12, -14, -1, 189, 1771, 1215, 2405, 3500, 18228, 2038, 1519, 1329, 1771, 303, 125, 42; -360, -558, -100, 7110, 67620, 46548, 92280, 134407, 700200, 78318, 58420, 51210, 68460, 11772, 4920, 1673],67,159]
%
% END OF LATTICE L68.159
%
%
% LATTICE L68.160
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-398648880, -37464840, 471240; -37464840, -3519960, 44280; 471240, 44280, -557],[2520, 120, 1],[-1, -1, 0, 29, 270, 185, 366, 1065, 2773, 155, 231, 202, 269, 46, 19, 13; -12, -14, -1, 399, 3731, 2559, 5065, 14742, 38388, 2146, 3199, 2799, 3731, 639, 265, 182; -1800, -1959, -80, 56250, 525000, 359928, 712260, 2072854, 5397480, 301719, 449720, 393390, 524160, 89712, 37140, 25466],67,160]
%
% END OF LATTICE L68.160
%
%
% LATTICE L68.161
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-39536280, 5647320, -22680; 5647320, -806640, 3240; -22680, 3240, -13],[2520, 120, 1],[-28, -5, -25, -3, -15, -1, -1, 8, 4, 1, 7, 1, 1, -1, -9, -92; -173, -31, -156, -19, -98, -7, -10, 21, 17, 5, 39, 6, 7, -6, -55, -567; 5680, 987, 4680, 490, 1680, -8, -780, -8946, -2800, -507, -2520, -250, 0, 248, 1980, 19026],67,161]
%
% END OF LATTICE L68.161
%
%
% LATTICE L68.162
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2308524120, -364021560, 574560; -364021560, 57401040, -90600; 574560, -90600, 143],[2520, 120, 1],[-28, -10, -25, -3, -15, -1, -1, 4, 4, 2, 7, 1, 1, -1, -9, -46; -115, -41, -102, -12, -56, -3, 2, 42, 31, 13, 39, 5, 7, -4, -37, -189; 39640, 14202, 35820, 4450, 24780, 2116, 5280, 10521, 3560, 198, -3420, -850, 420, 1484, 12720, 65079],67,162]
%
% END OF LATTICE L68.162
%
%
% LATTICE L68.163
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[803880, -126000, -35280; -126000, 12264, 3528; -35280, 3528, 1013],[2520, 168, 1],[-1, -7, -3, -7, -3, -38, -9, -6, -35, -13, 0, 4, 2, 23, 4, 1; 135, 955, 412, 978, 434, 5745, 1444, 1040, 6381, 2665, 131, -435, -253, -3030, -539, -135; -504, -3570, -1540, -3654, -1620, -21420, -5376, -3865, -23688, -9870, -476, 1638, 948, 11340, 2016, 505],67,163]
%
% END OF LATTICE L68.163
%
%
% LATTICE L68.164
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3966480, -395640, 136080; -395640, -33096, 11424; 136080, 11424, -3943],[2520, 168, 1],[-1, -3, -3, -10, -7, -134, -47, -91, -323, -87, -24, -17, -2, -1, 2, 1; -510, -1595, -1607, -5403, -3809, -73185, -25729, -49890, -177186, -47765, -13201, -9405, -1127, -855, 1049, 530; -1512, -4725, -4760, -16002, -11280, -216720, -76188, -147730, -524664, -141435, -39088, -27846, -3336, -2520, 3108, 1570],67,164]
%
% END OF LATTICE L68.164
%
%
% LATTICE L68.165
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-115920, -3021480, -52920; -3021480, -78664152, -1377768; -52920, -1377768, -24131],[2520, 168, 1],[-1, -3, 1, 3, 11, 86, 101, 313, 253, 423, 188, 18, 10, 19, 4, 2; 2, 70, 75, 7, -25, -295, -401, -1335, -1106, -1910, -903, -99, -67, -165, -59, -45; -112, -3990, -4284, -406, 1404, 16660, 22680, 75555, 62608, 108150, 51156, 5614, 3804, 9380, 3360, 2565],67,165]
%
% END OF LATTICE L68.165
%
%
% LATTICE L68.166
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-7978320, -607320, -196560; -607320, -45192, -14616; -196560, -14616, -4727],[2520, 168, 1],[-1, -1, 1, 2, 7, 54, 63, 389, 157, 131, 116, 11, 6, 11, 2, 1; 430, 455, -339, -819, -2911, -22545, -26351, -162870, -65758, -54895, -48657, -4625, -2533, -4675, -869, -450; -1288, -1365, 1008, 2450, 8712, 67480, 78876, 487530, 196840, 164325, 145656, 13846, 7584, 14000, 2604, 1350],67,166]
%
% END OF LATTICE L68.166
%
%
% LATTICE L68.167
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[90201676320, 1449669060, 21531159720; 1449669060, 23298240, 346036320; 21531159720, 346036320, 5139492499],[1260, 420, 1],[-539780, -119281, -86797, -35759, -12179, -11809, -1789, 169, 3632, 137, -2561, -8920, -17607, -77549, -147141, -59741; 1594563, 352367, 256405, 105633, 35975, 34875, 5269, -505, -10779, -415, 7559, 26349, 52013, 229089, 434671, 176481; 2153970, 475986, 346360, 142695, 48600, 47124, 7140, -674, -14490, -546, 10220, 35595, 70260, 309456, 587160, 238394],67,167]
%
% END OF LATTICE L68.167
%
%
% LATTICE L68.168
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-443290680, 7679700, -116970840; 7679700, -131460, 2025240; -116970840, 2025240, -30864119],[1260, 420, 1],[1304704, 146296, 219329, 194489, 37843, 46829, 20855, 1043, -316, -1364, -1931, 22909, 34623, 170569, 341475, 71423; -3930171, -440689, -660688, -585864, -113996, -141066, -62824, -3142, 951, 4109, 5818, -69006, -104294, -513804, -1028626, -215148; -5202540, -583359, -874580, -775530, -150900, -186732, -83160, -4159, 1260, 5439, 7700, -91350, -138060, -680148, -1361640, -284801],67,168]
%
% END OF LATTICE L68.168
%
%
% LATTICE L68.169
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[9766517040, 942622380, 1740192300; 942622380, 90977880, 167955900; 1740192300, 167955900, 310066451],[1260, 420, 1],[931, 200, 2842, 1852, 13318, 20844, 122622, 152254, 153929, 103040, 229448, 11053, 12492, 4966, 6428, 2606; -2797, -599, -8511, -5555, -39959, -62545, -367957, -456885, -461915, -309209, -688557, -33171, -37493, -14907, -19303, -7827; -3710, -798, -11340, -7385, -53100, -83104, -488880, -607014, -613690, -410802, -914760, -44065, -49800, -19796, -25620, -10386],67,169]
%
% END OF LATTICE L68.169
%
%
% LATTICE L68.170
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[210673260, 49204260, 16046100; 49204260, 11492040, 3747660; 16046100, 3747660, 1222181],[1260, 420, 1],[-175, -58, -1582, -1352, -4378, -6648, -38538, -23729, -47837, -15946, -70436, -6650, -3624, -1354, -1472, -277; 521, 173, 4719, 4031, 13051, 19817, 114875, 70731, 142591, 47531, 209949, 19821, 10801, 4035, 4385, 825; 700, 231, 6300, 5390, 17460, 26516, 153720, 94653, 190820, 63609, 280980, 26530, 14460, 5404, 5880, 1107],67,170]
%
% END OF LATTICE L68.170
%
%
% LATTICE L68.171
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2995440, -6789720, 12600; -6789720, -15389640, 28560; 12600, 28560, -53],[840, 840, 1],[901, 101, 227, 67, 13, 16, 7, 1, -1, -1, -2, 8, 12, 59, 118, 74; -434, -48, -105, -29, -5, -5, -1, 0, 2, 0, -3, -7, -7, -31, -59, -36; -21000, -2002, -2940, 210, 380, 1092, 1120, 237, 840, -238, -2100, -1890, -940, -2772, -3920, -1917],67,171]
%
% END OF LATTICE L68.171
%
%
% LATTICE L68.172
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3297840, -13291320, 27720; -13291320, -53567640, 111720; 27720, 111720, -233],[840, 840, 1],[2341, 131, 587, 172, 33, 40, 17, 5, -1, -1, -2, 23, 32, 155, 308, 385; -434, -24, -105, -29, -5, -5, -1, 0, 2, 0, -3, -7, -7, -31, -59, -72; 69720, 4039, 19320, 6510, 1520, 2352, 1540, 594, 840, -119, -1680, -630, 440, 3528, 8260, 11166],67,172]
%
% END OF LATTICE L68.172
%
%
% LATTICE L68.173
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[5040, -7560, 2520; -7560, -10643640, 3561600; 2520, 3561600, -1191791],[2520, 840, 1],[2269, 255, 192, 172, 34, 43, 20, 1, -1, -3, -3, 17, 29, 146, 295, 62; 354168, 39872, 30123, 27195, 5441, 6999, 3373, 173, 0, -520, -609, 2319, 4397, 22515, 45817, 9665; 1058400, 119154, 90020, 81270, 16260, 20916, 10080, 517, 0, -1554, -1820, 6930, 13140, 67284, 136920, 28883],67,173]
%
% END OF LATTICE L68.173
%
%
% LATTICE L68.174
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[5040, -2520, 0; -2520, -2342760, 11760; 0, 11760, -59],[2520, 840, 1],[829, 47, 72, 67, 14, 19, 10, 1, -1, -1, -3, 2, 9, 50, 105, 45; 1224, 70, 109, 105, 23, 33, 19, 2, 0, -2, -7, -3, 11, 69, 151, 66; 241920, 13839, 21560, 20790, 4560, 6552, 3780, 398, 0, -399, -1400, -630, 2160, 13608, 29820, 13042],67,174]
%
% END OF LATTICE L68.174
%
%
% LATTICE L68.175
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-8986320, -8187480, -2716560; -8187480, -7458360, -2474640; -2716560, -2474640, -821071],[2520, 840, 1],[-1, -1, 1, 5, 19, 30, 177, 110, 445, 149, 332, 32, 18, 7, 8, 1; 94, 238, 417, -679, -2987, -4873, -29179, -18279, -74158, -24926, -55965, -5493, -3185, -1299, -1681, -237; -280, -714, -1260, 2030, 8940, 14588, 87360, 54729, 222040, 74634, 167580, 16450, 9540, 3892, 5040, 711],67,175]
%
% END OF LATTICE L68.175
%
%
% LATTICE L68.176
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-9893520, -3197880, -1038240; -3197880, -1032360, -335160; -1038240, -335160, -108811],[2520, 840, 1],[-1, -1, 1, 10, 39, 62, 367, 457, 925, 155, 692, 67, 38, 15, 18, 5; 94, 119, -3, -1099, -4367, -6973, -41359, -51558, -104398, -17503, -78225, -7593, -4325, -1719, -2101, -594; -280, -357, 0, 3290, 13080, 20888, 123900, 154458, 312760, 52437, 234360, 22750, 12960, 5152, 6300, 1782],67,176]
%
% END OF LATTICE L68.176
%

\medskip%
%------------------------------WEYL-GROUP-W69--------------------------------
%
\leavevmode\llap{}%
$W_{69\phantom{0}}$%
\qquad\llap{24} lattices, $\chi=6$%
\hfill%
$22222$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L69.1
%
\leavevmode%
${L_{69.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{2}{}7\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{2\rightarrow N_{69}}%
\EasyButWeakLineBreak%
{${12}\above{1pt}{1pt}{b}{2}{10}\above{1pt}{1pt}{l}{2}{84}\above{1pt}{1pt}{r}{2}{2}\above{1pt}{1pt}{b}{2}{140}\above{1pt}{1pt}{*}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3898860\\1115100\\10080
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1115100\\-318926\\-2883
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
10080\\-2883\\-26
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-19\\-66\\-48
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
13\\45\\50
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
121\\420\\336
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\7\\-1
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-101\\-350\\-350
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-3898860, 1115100, 10080; 1115100, -318926, -2883; 10080, -2883, -26],[420, 1, 1],[-19, 13, 121, 2, -101; -66, 45, 420, 7, -350; -48, 50, 336, -1, -350],68,1]
%
% END OF LATTICE L69.1
%
%
% LATTICE L69.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[3990, -1365, 0; -1365, 467, 0; 0, 0, -1],[105, 1, 1],[1, -12, 29, 11, 72; 3, -35, 84, 32, 210; 0, 5, -21, -6, -35],68,2]
%
% END OF LATTICE L69.2
%
%
% LATTICE L69.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-396795, 3885, 132825; 3885, -33, -1302; 132825, -1302, -44462],[105, 3, 1],[-26, -76, 104, 77, 71; -23, -70, 91, 69, 70; -77, -225, 308, 228, 210],68,3]
%
% END OF LATTICE L69.3
%
%
% LATTICE L69.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-583905, 5985, -116235; 5985, -55, 1190; -116235, 1190, -23138],[105, 5, 1],[62, 12, -248, -61, -11; -69, -14, 273, 69, 14; -315, -61, 1260, 310, 56],68,4]
%
% END OF LATTICE L69.4
%
%
% LATTICE L69.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-771855, 8085, -109725; 8085, -77, 1148; -109725, 1148, -15598],[105, 7, 1],[56, 54, -32, -55, -7; -69, -70, 39, 69, 10; -399, -385, 228, 392, 50],68,5]
%
% END OF LATTICE L69.5
%
%
% LATTICE L69.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3968580, -1698900, 18480; -1698900, -727278, 7911; 18480, 7911, -86],[420, 3, 1],[11, -2, -71, -14, 29; -26, 5, 168, 33, -70; -28, 30, 196, 27, -210],68,6]
%
% END OF LATTICE L69.6
%
%
% LATTICE L69.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[65606730, -1303365, -22261785; -1303365, 25905, 442260; -22261785, 442260, 7553906],[105, 15, 1],[-190, -170, -2482, -911, -1311; 1, 0, 7, 4, 7; -560, -501, -7315, -2685, -3864],68,7]
%
% END OF LATTICE L69.7
%
%
% LATTICE L69.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2697240, 66780, 687120; 66780, 2248, 17184; 687120, 17184, 175093],[420, 4, 1],[257, 411, 2033, 515, 3449; 300, 480, 2373, 601, 4025; -1038, -1660, -8211, -2080, -13930],68,8]
%
% END OF LATTICE L69.8
%
%
% LATTICE L69.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-513660, 172620, 5460; 172620, -58010, -1835; 5460, -1835, -58],[420, 5, 1],[-7, 1, 61, 2, -5; -18, 3, 168, 5, -14; -90, -1, 420, 30, -28],68,9]
%
% END OF LATTICE L69.9
%
%
% LATTICE L69.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[59913210, -1473675, -20372625; -1473675, 36267, 501102; -20372625, 501102, 6927418],[105, 21, 1],[-238, -964, -424, -1121, -1173; 1, 0, 1, 4, 5; -700, -2835, -1247, -3297, -3450],68,10]
%
% END OF LATTICE L69.10
%
%
% LATTICE L69.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[4620, -420, 420; -420, 14, -7; 420, -7, -2],[420, 7, 1],[-1, 1, 1, 0, -1; -54, 45, 48, 1, -50; -42, 35, 36, 0, -40],68,11]
%
% END OF LATTICE L69.11
%
%
% LATTICE L69.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[62682585, 1946070, -11050725; 1946070, 60445, -343070; -11050725, -343070, 1948214],[105, 35, 1],[-490, -132, -872, -769, -161; 1473, 396, 2619, 2311, 484; -2520, -679, -4485, -3955, -828],68,12]
%
% END OF LATTICE L69.12
%
%
% LATTICE L69.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[59125080, -595140, 14724360; -595140, 6072, -148224; 14724360, -148224, 3666919],[420, 12, 1],[51, 713, 1454, 1123, 5667; -30, -420, -854, -659, -3325; -206, -2880, -5873, -4536, -22890],68,13]
%
% END OF LATTICE L69.13
%
%
% LATTICE L69.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-45780, -11760, 1260; -11760, -2910, 315; 1260, 315, -34],[420, 15, 1],[-1, 0, 5, 1, -1; -10, 1, 56, 9, -14; -130, 9, 700, 120, -168],68,14]
%
% END OF LATTICE L69.14
%
%
% LATTICE L69.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2211720, -32340, 545160; -32340, 920, -7940; 545160, -7940, 134377],[420, 20, 1],[349, 299, 2365, 99, 149; 99, 85, 672, 28, 42; -1410, -1208, -9555, -400, -602],68,15]
%
% END OF LATTICE L69.15
%
%
% LATTICE L69.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[30660, -5460, 840; -5460, 966, -147; 840, -147, 22],[420, 21, 1],[-1, 1, 1, 1, -1; -10, 5, 8, 9, -10; -28, 0, 16, 21, -30],68,16]
%
% END OF LATTICE L69.16
%
%
% LATTICE L69.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-566627565, -404185110, 143966130; -404185110, -288312045, 102693465; 143966130, 102693465, -36578242],[105, 105, 1],[-23, -14, 13, 69, 2; -4356, -2546, 2484, 12881, 337; -12320, -7203, 7025, 36435, 954],68,17]
%
% END OF LATTICE L69.17
%
%
% LATTICE L69.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1341480, -128940, 331800; -128940, 12376, -31892; 331800, -31892, 82067],[420, 28, 1],[-73, -139, 23, 111, 47; -3, -5, 0, 2, 0; 294, 560, -93, -448, -190],68,18]
%
% END OF LATTICE L69.18
%
%
% LATTICE L69.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-19149060, 6404580, -93240; 6404580, -2142070, 31185; -93240, 31185, -454],[420, 35, 1],[-5, -4, -13, 2, 1; -18, -9, -24, 7, 2; -210, 203, 1020, 70, -68],68,19]
%
% END OF LATTICE L69.19
%
%
% LATTICE L69.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[33459720, -385140, 8282820; -385140, 4440, -95340; 8282820, -95340, 2050379],[420, 60, 1],[47, 95, 303, 89, 135; -3, -5, -21, -10, -14; -190, -384, -1225, -360, -546],68,20]
%
% END OF LATTICE L69.20
%
%
% LATTICE L69.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[645960, -65940, 159600; -65940, 6216, -16296; 159600, -16296, 39433],[420, 84, 1],[-59, -937, -30, 229, 171; -2, -30, -1, 7, 5; 238, 3780, 121, -924, -690],68,21]
%
% END OF LATTICE L69.21
%
%
% LATTICE L69.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-559020, -18235140, -521220; -18235140, -594213270, -16984695; -521220, -16984695, -485482],[420, 105, 1],[69, -200, -335, -69, 67; 276, -794, -1332, -277, 266; -9730, 27993, 46960, 9765, -9378],68,22]
%
% END OF LATTICE L69.22
%
%
% LATTICE L69.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[57021720, -412860, -14432880; -412860, 8120, 108360; -14432880, 108360, 3656039],[420, 140, 1],[5461, 6893, 7768, 1803, 53; -16590, -20940, -23598, -5477, -161; 22050, 27832, 31365, 7280, 214],68,23]
%
% END OF LATTICE L69.23
%
%
% LATTICE L69.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[276140760, 10013510220, 2480197860; 10013510220, 363113317560, 89937779400; 2480197860, 89937779400, 22276253093],[420, 420, 1],[-23, -1931, -1023, -2345, -69; 122, 7356, 3876, 8803, 259; -490, -29484, -15535, -35280, -1038],68,24]
%
% END OF LATTICE L69.24
%

\medskip%
%------------------------------WEYL-GROUP-W70--------------------------------
%
\leavevmode\llap{}%
$W_{70\phantom{0}}$%
\qquad\llap{24} lattices, $\chi=12$%
\hfill%
$222222$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L70.1
%
\leavevmode%
${L_{70.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{2}{}5\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{-2}{}7\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2\rightarrow N_{70}}%
\EasyButWeakLineBreak%
{${12}\above{1pt}{1pt}{*}{2}{28}\above{1pt}{1pt}{b}{2}{30}\above{1pt}{1pt}{b}{2}{14}\above{1pt}{1pt}{l}{2}{20}\above{1pt}{1pt}{r}{2}{2}\above{1pt}{1pt}{b}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-713580\\-355320\\420
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-355320\\-176926\\207
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
420\\207\\2
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
191\\-384\\-366
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
383\\-770\\-728
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
97\\-195\\-180
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-94\\189\\182
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-189\\380\\360
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\-1
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-713580, -355320, 420; -355320, -176926, 207; 420, 207, 2],[420, 1, 1],[191, 383, 97, -94, -189, 0; -384, -770, -195, 189, 380, 0; -366, -728, -180, 182, 360, -1],69,1]
%
% END OF LATTICE L70.1
%
%
% LATTICE L70.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[3045, 630, 315; 630, 130, 63; 315, 63, 19],[105, 1, 1],[4, 8, -17, -53, -53, -7; -21, -42, 90, 280, 280, 37; 3, 7, -15, -49, -50, -7],69,2]
%
% END OF LATTICE L70.2
%
%
% LATTICE L70.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-211785, 1365, 71190; 1365, -3, -459; 71190, -459, -23930],[105, 3, 1],[-38, -226, -37, 113, 111, -1; -3, -21, -5, 7, 10, 1; -113, -672, -110, 336, 330, -3],69,3]
%
% END OF LATTICE L70.3
%
%
% LATTICE L70.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-274575, 1995, -54390; 1995, -5, 395; -54390, 395, -10774],[105, 5, 1],[98, 194, 19, -97, -19, 1; -9, -21, -3, 7, 2, 1; -495, -980, -96, 490, 96, -5],69,4]
%
% END OF LATTICE L70.4
%
%
% LATTICE L70.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-341565, 2625, -48300; 2625, -7, 371; -48300, 371, -6830],[105, 7, 1],[92, 26, 89, -13, -89, 1; -9, -3, -15, 1, 10, 1; -651, -184, -630, 92, 630, -7],69,5]
%
% END OF LATTICE L70.5
%
%
% LATTICE L70.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[154140, 43680, -1260; 43680, 12378, -357; -1260, -357, 10],[420, 3, 1],[5, 43, 7, -2, -17, -2; -18, -154, -25, 7, 60, 7; -14, -84, -10, 0, 0, -3],69,6]
%
% END OF LATTICE L70.6
%
%
% LATTICE L70.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[46360965, -81165, -15730680; -81165, 150, 27540; -15730680, 27540, 5337557],[105, 15, 1],[-587, -3919, -265, -1817, -284, -341; 2, 7, 0, 0, 1, 3; -1730, -11550, -781, -5355, -837, -1005],69,7]
%
% END OF LATTICE L70.7
%
%
% LATTICE L70.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1454877480, -4713660, 362599860; -4713660, 15272, -1174788; 362599860, -1174788, 90370949],[420, 4, 1],[572, 1293, 1337, 617, 234, 106; -1149, -2618, -2730, -1260, -470, -207; -2310, -5222, -5400, -2492, -945, -428],69,8]
%
% END OF LATTICE L70.8
%
%
% LATTICE L70.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[312900, -134820, -2100; -134820, 58090, 905; -2100, 905, 14],[420, 5, 1],[5, -19, -4, 3, 7, 7; 12, -42, -9, 7, 16, 16; -30, -140, -18, 0, 16, 15],69,9]
%
% END OF LATTICE L70.9
%
%
% LATTICE L70.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[45613995, -95235, -15509760; -95235, 210, 32382; -15509760, 32382, 5273659],[105, 21, 1],[-695, -661, -1559, -305, -1678, -407; 2, 1, 0, 0, 5, 3; -2044, -1944, -4585, -897, -4935, -1197],69,10]
%
% END OF LATTICE L70.10
%
%
% LATTICE L70.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-5045460, -191100, -13860; -191100, -7238, -525; -13860, -525, -38],[420, 7, 1],[5, 1, -2, -1, -11, 0; -126, -26, 45, 25, 280, 1; -84, -6, 105, 19, 140, -14],69,11]
%
% END OF LATTICE L70.11
%
%
% LATTICE L70.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[39997545, 115185, -7709100; 115185, 350, -22190; -7709100, -22190, 1485853],[105, 35, 1],[-1429, -453, -641, -209, -230, -279; 4293, 1360, 1923, 627, 691, 840; -7350, -2330, -3297, -1075, -1183, -1435],69,12]
%
% END OF LATTICE L70.12
%
%
% LATTICE L70.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2672040, -60900, 667380; -60900, 1320, -15204; 667380, -15204, 166687],[420, 12, 1],[-253, -863, 99, 603, -26, -303; 99, 336, -40, -238, 10, 119; 1022, 3486, -400, -2436, 105, 1224],69,13]
%
% END OF LATTICE L70.13
%
%
% LATTICE L70.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2100, -840, 420; -840, -330, 195; 420, 195, 38],[420, 15, 1],[-15, 19, 4, -3, -23, -27; 34, -42, -9, 7, 52, 61; -10, 0, 2, 0, -12, -15],69,14]
%
% END OF LATTICE L70.14
%
%
% LATTICE L70.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-444360, -420, -110040; -420, 1400, 20; -110040, 20, -27239],[420, 20, 1],[-1166, -1369, 101, 1213, 25, -406; -417, -490, 36, 434, 9, -145; 4710, 5530, -408, -4900, -101, 1640],69,15]
%
% END OF LATTICE L70.15
%
%
% LATTICE L70.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-12700380, 2762340, -25200; 2762340, -600810, 5481; -25200, 5481, -50],[420, 21, 1],[-1, 1, 4, 1, 1, -2; -6, 4, 20, 6, 20, -9; -154, -66, 175, 153, 1680, 21],69,16]
%
% END OF LATTICE L70.16
%
%
% LATTICE L70.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-249420885, -178013535, 63406035; -178013535, -127049475, 45253320; 63406035, 45253320, -16118626],[105, 105, 1],[-3, -3, -1, 1, 2, 1; -5880, -5002, -1153, 2483, 3423, -151; -16520, -14055, -3241, 6975, 9618, -420],69,17]
%
% END OF LATTICE L70.17
%
%
% LATTICE L70.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[3755640, -279300, 931560; -279300, 24808, -69300; 931560, -69300, 231067],[420, 28, 1],[-1945, -789, -9049, -1157, -3233, -735; 42, 17, 195, 25, 70, 16; 7854, 3186, 36540, 4672, 13055, 2968],69,18]
%
% END OF LATTICE L70.18
%
%
% LATTICE L70.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-128100, -50820, 1680; -50820, -20090, 665; 1680, 665, -22],[420, 35, 1],[-1, -1, -1, 0, 1, 1; -18, -6, -3, 1, 4, 1; -630, -260, -168, 30, 196, 105],69,19]
%
% END OF LATTICE L70.19
%
%
% LATTICE L70.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[4340280, -398580, 1086540; -398580, 36600, -99780; 1086540, -99780, 272003],[420, 60, 1],[181, 677, -1, -209, 20, 223; -19, -70, 0, 14, -3, -25; -730, -2730, 4, 840, -81, -900],69,20]
%
% END OF LATTICE L70.20
%
%
% LATTICE L70.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[33849480, -168420, 8380680; -168420, 4200, -41664; 8380680, -41664, 2074945],[420, 84, 1],[-891, -1520, -8806, -4508, -13131, -2621; -37, -63, -365, -187, -545, -109; 3598, 6138, 35560, 18204, 53025, 10584],69,21]
%
% END OF LATTICE L70.21
%
%
% LATTICE L70.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-4620, 2940, 1260; 2940, 5250, 2205; 1260, 2205, 926],[420, 105, 1],[-1, -1, 0, 1, 3, 1; 118, 114, 3, -95, -284, -89; -280, -270, -7, 225, 672, 210],69,22]
%
% END OF LATTICE L70.22
%
%
% LATTICE L70.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[27522600, 191940, -6671280; 191940, 1400, -46480; -6671280, -46480, 1617103],[420, 140, 1],[-1819, -443, -395, -99, -123, -589; 5364, 1307, 1167, 293, 363, 1736; -7350, -1790, -1596, -400, -497, -2380],69,23]
%
% END OF LATTICE L70.23
%
%
% LATTICE L70.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[5865720, 13668060, 3383940; 13668060, 31848600, 7885080; 3383940, 7885080, 1952189],[420, 420, 1],[-4, 1, 3, 3, -1, -12; 331, 7, -133, -31, 172, 941; -1330, -30, 532, 120, -693, -3780],69,24]
%
% END OF LATTICE L70.24
%

\medskip%
%------------------------------WEYL-GROUP-W71--------------------------------
%
\leavevmode\llap{}%
$W_{71\phantom{0}}$%
\qquad\llap{48} lattices, $\chi=16$%
\hfill%
$222262$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L71.1
%
\leavevmode%
${L_{71.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{1}{}3\above{1pt}{1pt}{-}{}9\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}7\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{23\rightarrow N_{71},3,2}%
\EasyButWeakLineBreak%
{${28}\above{1pt}{1pt}{*}{2}{60}\above{1pt}{1pt}{b}{2}{126}\above{1pt}{1pt}{s}{2}{10}\above{1pt}{1pt}{b}{2}{18}\above{1pt}{1pt}{}{6}{6}\above{1pt}{1pt}{b}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-7158060\\-2882880\\10080
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2882880\\-1161066\\4059
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
10080\\4059\\-14
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-117\\294\\994
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-187\\470\\1620
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-142\\357\\1260
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\-5\\-10
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
37\\-93\\-324
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2\\5\\9
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-7158060, -2882880, 10080; -2882880, -1161066, 4059; 10080, 4059, -14],[1260, 3, 1],[-117, -187, -142, 2, 37, -2; 294, 470, 357, -5, -93, 5; 994, 1620, 1260, -10, -324, 9],70,1]
%
% END OF LATTICE L71.1
%
%
% LATTICE L71.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[2310, 315, 0; 315, 43, 0; 0, 0, -1],[105, 1, 1],[-1, -2, 3, 9, 7, 2; 7, 15, -21, -65, -51, -15; 0, 0, -7, -15, -11, -3],70,2]
%
% END OF LATTICE L71.2
%
%
% LATTICE L71.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-3371340, -674100, 7980; -674100, -134786, 1595; 7980, 1595, -18],[420, 1, 1],[-411, -601, -143, 1, 24, -25; 2072, 3030, 721, -5, -121, 126; 1386, 2040, 490, 0, -82, 81],70,3]
%
% END OF LATTICE L71.3
%
%
% LATTICE L71.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-3465, -630, 630; -630, 339, -99; 630, -99, -14],[315, 3, 1],[30, 48, 73, -1, -19, 1; 147, 235, 357, -5, -93, 5; 308, 495, 756, -10, -198, 9],70,4]
%
% END OF LATTICE L71.4
%
%
% LATTICE L71.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1095255, 328020, 367710; 328020, -97674, -110139; 367710, -110139, -123451],[105, 3, 1],[10236, 4977, 7078, -72, -1192, 421; 679, 330, 469, -5, -79, 28; 29883, 14530, 20664, -210, -3480, 1229],70,5]
%
% END OF LATTICE L71.5
%
%
% LATTICE L71.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1475565, 490770, -292740; 490770, -162790, 97355; -292740, 97355, -58077],[105, 5, 1],[-5836, -1703, -4038, 8, 680, -719; 679, 198, 469, -1, -79, 84; 30555, 8916, 21140, -42, -3560, 3765],70,6]
%
% END OF LATTICE L71.6
%
%
% LATTICE L71.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1870995, 653520, -265020; 653520, -227906, 92561; -265020, 92561, -37539],[105, 7, 1],[-598, -6109, -414, 28, 488, -515; 97, 990, 67, -5, -79, 84; 4461, 45570, 3088, -210, -3640, 3843],70,7]
%
% END OF LATTICE L71.7
%
%
% LATTICE L71.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-9909585, -51345, 40635; -51345, -246, 207; 40635, 207, -166],[315, 3, 1],[65, 29, 12, -4, -2, 4; 3612, 1610, 665, -225, -111, 223; 20412, 9105, 3766, -1260, -628, 1257],70,8]
%
% END OF LATTICE L71.8
%
%
% LATTICE L71.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3834180, 15540, 9240; 15540, -54, -39; 9240, -39, -22],[420, 3, 1],[23, 9, 4, -2, -1, 1; 1274, 500, 224, -110, -56, 55; 7392, 2890, 1281, -645, -321, 322],70,9]
%
% END OF LATTICE L71.9
%
%
% LATTICE L71.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[11223448635, -22618995, -3809101065; -22618995, 45585, 7676610; -3809101065, 7676610, 1292762269],[105, 15, 1],[-21946, -1838, -11365, -113, -341, -1839; 2779, 230, 1386, 8, 42, 239; -64680, -5417, -33495, -333, -1005, -5420],70,10]
%
% END OF LATTICE L71.10
%
%
% LATTICE L71.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[680928360, -4407900, 169485120; -4407900, 28536, -1097140; 169485120, -1097140, 42185357],[420, 4, 1],[6652, 8401, 3501, 203, 103, 1652; -5411, -6840, -2856, -170, -84, -1341; -26866, -33930, -14140, -820, -416, -6672],70,11]
%
% END OF LATTICE L71.11
%
%
% LATTICE L71.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-688380, 16800, 8400; 16800, -410, -205; 8400, -205, -102],[420, 5, 1],[17, 5, 6, 0, -1, 1; 728, 210, 245, -1, -41, 48; -70, -12, 0, 2, 0, -15],70,12]
%
% END OF LATTICE L71.12
%
%
% LATTICE L71.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[6659410065, -20615385, -2265034485; -20615385, 63819, 7011816; -2265034485, 7011816, 770395751],[105, 21, 1],[-3766, -11008, -1933, -607, -407, -2223; 397, 1150, 198, 40, 42, 239; -11076, -32375, -5685, -1785, -1197, -6538],70,13]
%
% END OF LATTICE L71.13
%
%
% LATTICE L71.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-464226420, 16415700, -693420; 16415700, -580482, 24521; -693420, 24521, -1034],[420, 7, 1],[-179, -1817, -61, 7, 72, -80; -4980, -50550, -1697, 195, 2003, -2226; 1942, 19740, 664, -70, -784, 861],70,14]
%
% END OF LATTICE L71.14
%
%
% LATTICE L71.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[5818166130, 24876600, -1115959005; 24876600, 106365, -4771480; -1115959005, -4771480, 214047601],[105, 35, 1],[-2582, -4528, -1325, -83, -279, -4573; 8143, 14274, 4173, 257, 879, 14436; -13280, -23289, -6815, -427, -1435, -23520],70,15]
%
% END OF LATTICE L71.15
%
%
% LATTICE L71.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-120870540, -181440, 142380; -181440, -246, 207; 142380, 207, -166],[1260, 3, 1],[65, 29, 6, -2, -1, 2; 20874, 9310, 1925, -645, -321, 643; 81774, 36480, 7546, -2520, -1258, 2517],70,16]
%
% END OF LATTICE L71.16
%
%
% LATTICE L71.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-58905, 4410, 2205; 4410, -330, -165; 2205, -165, -82],[315, 15, 1],[3, 1, 8, 0, -2, 0; 56, 16, 105, -1, -27, 7; -35, -6, 0, 2, 0, -15],70,17]
%
% END OF LATTICE L71.17
%
%
% LATTICE L71.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-38481030, 6230070, -61425; 6230070, -1008645, 9945; -61425, 9945, -98],[315, 15, 1],[-292, -28, -65, 1, 11, -13; -1701, -163, -378, 6, 64, -76; 10395, 1008, 2380, -18, -400, 435],70,18]
%
% END OF LATTICE L71.18
%
%
% LATTICE L71.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1175804280, -5869500, 291116280; -5869500, 29304, -1453224; 291116280, -1453224, 72077207],[420, 12, 1],[10555, 4172, 4742, 208, 514, 1029; 56, 25, 35, 5, 1, 4; -42630, -16850, -19152, -840, -2076, -4156],70,19]
%
% END OF LATTICE L71.19
%
%
% LATTICE L71.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2448180, -23100, 7980; -23100, -210, 75; 7980, 75, -26],[420, 15, 1],[9, 1, 4, 0, -1, 0; 140, 14, 49, -1, -13, 2; 3150, 346, 1365, -3, -345, 5],70,20]
%
% END OF LATTICE L71.20
%
%
% LATTICE L71.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1191330, 76230, 9135; 76230, -4557, -525; 9135, -525, -59],[315, 21, 1],[3, 33, 7, -1, -13, 1; 133, 1460, 309, -45, -573, 46; -718, -7875, -1665, 245, 3087, -252],70,21]
%
% END OF LATTICE L71.21
%
%
% LATTICE L71.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1100295, -45675, 371700; -45675, -1722, 15225; 371700, 15225, -125326],[315, 21, 1],[827, 2579, 152, -364, -178, 358; 3369, 10505, 619, -1485, -725, 1459; 2862, 8925, 526, -1260, -616, 1239],70,22]
%
% END OF LATTICE L71.22
%
%
% LATTICE L71.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[157080, 35700, 39060; 35700, 16440, 8920; 39060, 8920, 9713],[420, 20, 1],[7086, 1733, 3361, -1, 99, 1886; 147, 36, 70, 0, 2, 39; -28630, -7002, -13580, 4, -400, -7620],70,23]
%
% END OF LATTICE L71.23
%
%
% LATTICE L71.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-345660, 11760, -21420; 11760, -378, 777; -21420, 777, -1222],[420, 21, 1],[-67, -181, -11, 43, 20, -21; -1074, -2900, -176, 690, 320, -337; 492, 1330, 81, -315, -147, 154],70,24]
%
% END OF LATTICE L71.24
%
%
% LATTICE L71.25
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1505364105, -1024233000, 364818720; -1024233000, -696874185, 248217690; 364818720, 248217690, -88411973],[105, 105, 1],[97, 66, 67, -1, -79, 28; 119718, 81529, 82870, -1128, -97684, 34379; 336510, 229166, 232935, -3171, -274575, 96635],70,25]
%
% END OF LATTICE L71.25
%
%
% LATTICE L71.26
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[3527137320, 439422900, 875642880; 439422900, 54745208, 109090604; 875642880, 109090604, 217386051],[420, 28, 1],[34690, 291581, 15485, -3987, 3453, 67084; 703, 5910, 314, -80, 70, 1359; -140086, -1177470, -62532, 16100, -13944, -270900],70,26]
%
% END OF LATTICE L71.26
%
%
% LATTICE L71.27
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-70298340, 20821500, 607740; 20821500, -6167070, -180005; 607740, -180005, -5254],[420, 35, 1],[27, 47, 6, -2, -7, 22; 144, 258, 35, -9, -41, 108; -1810, -3402, -505, 77, 595, -1155],70,27]
%
% END OF LATTICE L71.27
%
%
% LATTICE L71.28
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[3781494360, -7082460, -947435580; -7082460, 13272, 1774476; -947435580, 1774476, 237375517],[1260, 12, 1],[-6759, -8329, -10681, -627, -1571, -1887; -3633, -4480, -5754, -340, -846, -1013; -26950, -33210, -42588, -2500, -6264, -7524],70,28]
%
% END OF LATTICE L71.28
%
%
% LATTICE L71.29
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[332439677640, -810639900, -83374601940; -810639900, 1976712, 203305392; -83374601940, 203305392, 20910031853],[1260, 12, 1],[-122515, -53623, -23897, -6907, -315, -9125; -231, -110, -56, -30, 0, -13; -488502, -213810, -95284, -27540, -1256, -36384],70,29]
%
% END OF LATTICE L71.29
%
%
% LATTICE L71.30
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1558620, 22680, 11340; 22680, -330, -165; 11340, -165, -82],[1260, 15, 1],[3, 1, 4, 0, -1, 0; 238, 74, 273, -1, -69, 7; -70, -12, 0, 2, 0, -15],70,30]
%
% END OF LATTICE L71.30
%
%
% LATTICE L71.31
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2462056380, 90861120, -491400; 90861120, -3353190, 18135; -491400, 18135, -98],[1260, 15, 1],[-635, -61, -71, 1, 12, -14; -17094, -1642, -1911, 27, 323, -377; 20790, 2016, 2380, -18, -400, 435],70,31]
%
% END OF LATTICE L71.31
%
%
% LATTICE L71.32
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[133288680, -716100, 33001080; -716100, 3960, -177300; 33001080, -177300, 8170771],[420, 60, 1],[15962, 1283, 7799, 205, 1129, 1540; -35, -3, -21, -1, -3, -3; -64470, -5182, -31500, -828, -4560, -6220],70,32]
%
% END OF LATTICE L71.32
%
%
% LATTICE L71.33
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[122220, -84420, 6300; -84420, -23898, 5187; 6300, 5187, -782],[1260, 21, 1],[-103, -1141, -122, 16, 227, -15; -418, -4630, -495, 65, 921, -61; -3602, -39900, -4266, 560, 7938, -525],70,33]
%
% END OF LATTICE L71.33
%
%
% LATTICE L71.34
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-26740980, -221760, -12195540; -221760, -1722, -100737; -12195540, -100737, -5560558],[1260, 21, 1],[-4951, -15451, -456, 1078, 533, -1069; -39486, -123230, -3637, 8595, 4251, -8525; 11574, 36120, 1066, -2520, -1246, 2499],70,34]
%
% END OF LATTICE L71.34
%
%
% LATTICE L71.35
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-125055, -88515, 6930; -88515, -61530, 4830; 6930, 4830, -379],[315, 105, 1],[5, 9, 7, -1, -13, 7; 43, 76, 57, -9, -105, 64; 640, 1134, 855, -133, -1575, 945],70,35]
%
% END OF LATTICE L71.35
%
%
% LATTICE L71.36
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-219870, -290430, 84735; -290430, -375585, 109620; 84735, 109620, -31994],[315, 105, 1],[49, 33, 11, -1, -13, 15; 2103, 1421, 476, -36, -562, 632; 7335, 4956, 1660, -126, -1960, 2205],70,36]
%
% END OF LATTICE L71.36
%
%
% LATTICE L71.37
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[91166040, 25769100, 22651020; 25769100, 7283976, 6402564; 22651020, 6402564, 5627849],[420, 84, 1],[1487, 4254, 738, 416, 438, 945; 8, 25, 5, 5, 1, 4; -5994, -17150, -2976, -1680, -1764, -3808],70,37]
%
% END OF LATTICE L71.37
%
%
% LATTICE L71.38
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-807660, 843360, 344400; 843360, -880530, -359625; 344400, -359625, -146858],[420, 105, 1],[443, 331, 180, -10, -327, 17; 20, 14, 7, -1, -13, 2; 990, 742, 405, -21, -735, 35],70,38]
%
% END OF LATTICE L71.38
%
%
% LATTICE L71.39
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[225898680, -5599860, -60125100; -5599860, 143080, 1493660; -60125100, 1493660, 16005279],[420, 140, 1],[27652, 47023, 12847, -201, 2911, 52294; -83935, -142734, -38996, 610, -8836, -158733; 111710, 189966, 51900, -812, 11760, 211260],70,39]
%
% END OF LATTICE L71.39
%
%
% LATTICE L71.40
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[849240, 64260, -212940; 64260, 37560, -16080; -212940, -16080, 53393],[1260, 60, 1],[-8761, -1997, -10429, 1, -1535, -2769; 35, 8, 42, 0, 6, 11; -34930, -7962, -41580, 4, -6120, -11040],70,40]
%
% END OF LATTICE L71.40
%
%
% LATTICE L71.41
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[7766083080, 266680260, -1947023820; 266680260, 9163560, -66859020; -1947023820, -66859020, 488135617],[1260, 60, 1],[1206011, 102623, 218531, 9805, 6325, 97403; -11823, -1006, -2142, -96, -62, -955; 4808790, 409194, 871360, 39096, 25220, 388380],70,41]
%
% END OF LATTICE L71.41
%
%
% LATTICE L71.42
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[118205768520, -1032447780, -29657373480; -1032447780, 9017736, 259037184; -29657373480, 259037184, 7440921139],[1260, 84, 1],[639, 4059, 163, -913, 443, 1855; 25, 230, 48, 30, 48, 43; 2546, 16170, 648, -3640, 1764, 7392],70,42]
%
% END OF LATTICE L71.42
%
%
% LATTICE L71.43
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[345027969720, 28945764540, -86357997180; 28945764540, 2428374984, -7244914824; -86357997180, -7244914824, 21614780051],[1260, 84, 1],[-60931, -190421, -12543, -31219, -855, -30001; -33, -110, -8, -30, 0, -13; -243450, -760830, -50116, -124740, -3416, -119868],70,43]
%
% END OF LATTICE L71.43
%
%
% LATTICE L71.44
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1171854180, -228808440, 2163420; -228808440, -44675610, 422415; 2163420, 422415, -3994],[1260, 105, 1],[13, 19, 4, -2, -7, 15; -42, -58, -9, 7, 15, -53; 2600, 4158, 1215, -343, -2205, 2520],70,44]
%
% END OF LATTICE L71.44
%
%
% LATTICE L71.45
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-30979620, -9452520, 996660; -9452520, -2883930, 303975; 996660, 303975, -31994],[1260, 105, 1],[-2005, -1355, -227, 17, 268, -301; 8118, 5486, 919, -69, -1085, 1219; 14670, 9912, 1660, -126, -1960, 2205],70,45]
%
% END OF LATTICE L71.45
%
%
% LATTICE L71.46
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[27720, 1204980, 304920; 1204980, 53019960, 13416900; 304920, 13416900, 3395197],[420, 420, 1],[-147, -81, -67, -9, -71, -103; 2668, 1465, 1201, 149, 1277, 1880; -10530, -5782, -4740, -588, -5040, -7420],70,46]
%
% END OF LATTICE L71.46
%
%
% LATTICE L71.47
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[5300363880, -27078660, 1349753580; -27078660, 167160, -6917400; 1349753580, -6917400, 343735199],[1260, 420, 1],[-92377, -144447, -103199, 941, -127351, -212357; 277821, 434420, 310368, -2830, 383004, 638657; 368330, 575946, 411480, -3752, 507780, 846720],70,47]
%
% END OF LATTICE L71.47
%
%
% LATTICE L71.48
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[93697125480, 8230981500, 17286447780; 8230981500, 723064440, 1518557040; 17286447780, 1518557040, 3189225679],[1260, 420, 1],[45413, 26799, 7999, 2023, 1651, 26241; -136848, -80755, -24103, -6093, -4975, -79078; -180990, -106806, -31880, -8064, -6580, -104580],70,48]
%
% END OF LATTICE L71.48
%

\medskip%
%------------------------------WEYL-GROUP-W72--------------------------------
%
\leavevmode\llap{}%
$W_{72\phantom{0}}$%
\qquad\llap{88} lattices, $\chi=24$%
\hfill%
$22222222$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L72.1
%
\leavevmode%
${L_{72.1}}$%
{} : {$1\above{1pt}{1pt}{2}{{\rm II}}4\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}7\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2\rightarrow N_{72}}%
\EasyButWeakLineBreak%
{${12}\above{1pt}{1pt}{b}{2}{14}\above{1pt}{1pt}{s}{2}{2}\above{1pt}{1pt}{b}{2}{210}\above{1pt}{1pt}{l}{2}{4}\above{1pt}{1pt}{r}{2}{10}\above{1pt}{1pt}{b}{2}{28}\above{1pt}{1pt}{*}{2}{4}\above{1pt}{1pt}{*}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-133966140\\1288140\\-32760
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1288140\\-12386\\315
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-32760\\315\\-8
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
11\\1146\\72
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
10\\1043\\112
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\209\\38
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
11\\1155\\420
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-104\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-105\\-40
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5\\518\\-84
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\312\\-2
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-133966140, 1288140, -32760; 1288140, -12386, 315; -32760, 315, -8],[420, 1, 1],[11, 10, 2, 11, -1, -1, 5, 3; 1146, 1043, 209, 1155, -104, -105, 518, 312; 72, 112, 38, 420, 0, -40, -84, -2],71,1]
%
% END OF LATTICE L72.1
%
\hbox{}\par\smallskip%
%
% LATTICE L72.2
%
\leavevmode%
${L_{72.2}}$%
{} : {$1\above{1pt}{1pt}{2}{2}8\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{-2}{}7\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2\rightarrow N'_{34}}%
\EasyButWeakLineBreak%
{${24}\above{1pt}{1pt}{*}{2}{28}\above{1pt}{1pt}{l}{2}{1}\above{1pt}{1pt}{}{2}{105}\above{1pt}{1pt}{r}{2}{8}\above{1pt}{1pt}{l}{2}{5}\above{1pt}{1pt}{}{2}{56}\above{1pt}{1pt}{r}{2}{2}\above{1pt}{1pt}{b}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-34131720\\52920\\26040
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
52920\\-79\\-42
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
26040\\-42\\-19
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
17\\5700\\10692
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
17\\5698\\10696
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\670\\1259
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
16\\5355\\10080
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-336\\-628
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-335\\-630
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5\\1680\\3136
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\671\\1257
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-34131720, 52920, 26040; 52920, -79, -42; 26040, -42, -19],[840, 1, 1],[17, 17, 2, 16, -1, -1, 5, 2; 5700, 5698, 670, 5355, -336, -335, 1680, 671; 10692, 10696, 1259, 10080, -628, -630, 3136, 1257],71,2]
%
% END OF LATTICE L72.2
%
\hbox{}\par\smallskip%
%
% LATTICE L72.3
%
\leavevmode%
${L_{72.3}}$%
{} : {$1\above{1pt}{1pt}{-2}{2}8\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{-2}{}7\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{m}%
\EasyButWeakLineBreak%
{${24}\above{1pt}{1pt}{}{2}{7}\above{1pt}{1pt}{r}{2}{4}\above{1pt}{1pt}{*}{2}{420}\above{1pt}{1pt}{s}{2}{8}\above{1pt}{1pt}{s}{2}{20}\above{1pt}{1pt}{*}{2}{56}\above{1pt}{1pt}{b}{2}{2}\above{1pt}{1pt}{l}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-434280\\-43680\\2520
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-43680\\-4393\\253
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2520\\253\\-14
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-23\\240\\192
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-6\\63\\56
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\-10\\-2
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
61\\-630\\-420
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5\\-52\\-40
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\10\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-27\\280\\196
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-5\\52\\39
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-434280, -43680, 2520; -43680, -4393, 253; 2520, 253, -14],[840, 1, 1],[-23, -6, 1, 61, 5, -1, -27, -5; 240, 63, -10, -630, -52, 10, 280, 52; 192, 56, -2, -420, -40, 0, 196, 39],71,3]
%
% END OF LATTICE L72.3
%
%
% LATTICE L72.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[3360, -1155, -105; -1155, 397, 35; -105, 35, -34],[105, 1, 1],[1, -72, 46, 3026, 165, 734, 689, 60; 3, -210, 134, 8820, 481, 2140, 2009, 175; 0, 7, -5, -315, -17, -75, -70, -6],71,4]
%
% END OF LATTICE L72.4
%
%
% LATTICE L72.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[28770, 14280, 630; 14280, 7088, 315; 630, 315, 59],[210, 1, 1],[-5741, -2451, 105, 988, -419, -4128, -14207, -3185; 11592, 4949, -212, -1995, 846, 8335, 28686, 6431; -606, -259, 11, 105, -44, -435, -1498, -336],71,5]
%
% END OF LATTICE L72.5
%
%
% LATTICE L72.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-217140, -43680, 1260; -43680, -8786, 253; 1260, 253, -7],[420, 1, 1],[-23, -12, 1, 61, 5, -1, -27, -5; 120, 63, -5, -315, -26, 5, 140, 26; 192, 112, -2, -420, -40, 0, 196, 39],71,6]
%
% END OF LATTICE L72.6
%
%
% LATTICE L72.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-132720, 4725, 44835; 4725, -123, -1596; 44835, -1596, -15146],[105, 3, 1],[258, 1312, 230, 272, -78, -76, 468, 233; -3, -14, -2, 0, 1, 0, -7, -3; 764, 3885, 681, 805, -231, -225, 1386, 690],71,7]
%
% END OF LATTICE L72.7
%
%
% LATTICE L72.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-120559740, 1221990, -60310950; 1221990, -12386, 611310; -60310950, 611310, -30171023],[210, 2, 1],[4660, 3804, -227, -1354, 402, 7124, 12011, 5289; -4137, -3353, 209, 1155, -366, -6385, -10731, -4712; -9399, -7672, 458, 2730, -811, -14370, -24227, -10668],71,8]
%
% END OF LATTICE L72.8
%
%
% LATTICE L72.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-145740, 6405, -28665; 6405, -205, 1260; -28665, 1260, -5638],[105, 5, 1],[-614, -1040, -182, -128, 62, 12, -372, -185; -9, -14, -2, 0, 1, 0, -7, -3; 3120, 5285, 925, 651, -315, -61, 1890, 940],71,9]
%
% END OF LATTICE L72.9
%
%
% LATTICE L72.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-187425210, 1866060, -62506710; 1866060, -18579, 622335; -62506710, 622335, -20846122],[210, 3, 1],[2185, 2684, -157, -323, 559, 4989, 16847, 3714; -2758, -3353, 209, 385, -732, -6385, -21462, -4712; -6634, -8148, 477, 980, -1698, -15150, -51156, -11277],71,10]
%
% END OF LATTICE L72.10
%
%
% LATTICE L72.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-165480, 8085, -23205; 8085, -287, 1134; -23205, 1134, -3254],[105, 7, 1],[-554, -134, -164, -82, 56, 54, -48, -167; -9, -2, -2, 0, 1, 0, -1, -3; 3948, 955, 1169, 585, -399, -385, 342, 1190],71,11]
%
% END OF LATTICE L72.11
%
%
% LATTICE L72.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-321297270, 3154200, 128486820; 3154200, -30965, -1261365; 128486820, -1261365, -51381896],[210, 5, 1],[-8923, -3672, 208, 271, -747, -1349, -22829, -5043; -8274, -3353, 209, 231, -732, -1277, -21462, -4712; -22110, -9100, 515, 672, -1850, -3342, -56560, -12495],71,12]
%
% END OF LATTICE L72.12
%
%
% LATTICE L72.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-4620, -1260, 2940; -1260, -318, 603; 2940, 603, -329],[420, 3, 1],[-77, -124, 9, 207, 53, -1, -251, -49; 404, 651, -47, -1085, -278, 5, 1316, 257; 52, 84, -6, -140, -36, 0, 168, 33],71,13]
%
% END OF LATTICE L72.13
%
%
% LATTICE L72.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[668268930, -5300190, 332214960; -5300190, 42528, -2634870; 332214960, -2634870, 165153241],[210, 6, 1],[481994, 1234615, -52907, -165857, 105553, 2079561, 3578450, 1604442; 1932, 4949, -212, -665, 423, 8335, 14343, 6431; -969527, -2483418, 106422, 333620, -212319, -4183020, -7198023, -3227322],71,14]
%
% END OF LATTICE L72.14
%
%
% LATTICE L72.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-529620, -14700, -3780; -14700, -408, -105; -3780, -105, -26],[420, 3, 1],[3, 3, -1, -8, -1, 4, 19, 5; -108, -112, 34, 280, 36, -140, -672, -178; 2, 21, 9, 35, 0, -15, -42, -6],71,15]
%
% END OF LATTICE L72.15
%
%
% LATTICE L72.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-455223090, 4442340, 195063330; 4442340, -43351, -1903545; 195063330, -1903545, -83584738],[210, 7, 1],[-10501, -620, 239, 233, -865, -7891, -3823, -5922; -8274, -479, 209, 165, -732, -6385, -3066, -4712; -24318, -1436, 553, 540, -2002, -18270, -8852, -13713],71,16]
%
% END OF LATTICE L72.16
%
%
% LATTICE L72.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[197382255, 52605, -66976035; 52605, 15, -17850; -66976035, -17850, 22726406],[105, 15, 1],[-1454, -7874, -1756, -1114, 0, -170, -3456, -1303; 25, 154, 40, 28, 1, 0, 35, 18; -4285, -23205, -5175, -3283, 0, -501, -10185, -3840],71,17]
%
% END OF LATTICE L72.17
%
%
% LATTICE L72.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[4375560, -75180, 1082760; -75180, 14176, -18480; 1082760, -18480, 267937],[420, 4, 1],[-27535, -49449, -10931, -102857, 26, -5413, -22017, -8276; -1068, -1918, -424, -3990, 1, -210, -854, -321; 111198, 199696, 44144, 415380, -105, 21860, 88914, 33422],71,18]
%
% END OF LATTICE L72.18
%
%
% LATTICE L72.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[36228360, -152460, 9000180; -152460, 644, -37876; 9000180, -37876, 2235907],[420, 4, 1],[329, 1213, 303, 3743, 51, 307, 331, 203; -276, -1022, -256, -3150, -42, -250, -273, -169; -1329, -4900, -1224, -15120, -206, -1240, -1337, -820],71,19]
%
% END OF LATTICE L72.19
%
%
% LATTICE L72.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-327180, 110460, 840; 110460, -37280, -285; 840, -285, -2],[420, 5, 1],[-13, 5, 13, 76, 29, 8, 41, -5; -36, 14, 36, 210, 80, 22, 112, -14; -330, 105, 325, 1953, 760, 217, 1190, -110],71,20]
%
% END OF LATTICE L72.20
%
%
% LATTICE L72.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[5921790, -637350, 2813790; -637350, 70880, -302820; 2813790, -302820, 1336997],[210, 10, 1],[281293, 240179, -10291, -19361, 20532, 80907, 696119, 312116; 5796, 4949, -212, -399, 423, 1667, 14343, 6431; -590685, -504350, 21610, 40656, -43115, -169896, -1461775, -655410],71,21]
%
% END OF LATTICE L72.21
%
%
% LATTICE L72.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-12180, 420, 1680; 420, 85, -160; 1680, -160, -127],[420, 5, 1],[73, 6, -13, -25, 9, 17, 269, 27; 432, 35, -77, -147, 54, 101, 1596, 160; 420, 35, -75, -147, 50, 97, 1540, 155],71,22]
%
% END OF LATTICE L72.22
%
%
% LATTICE L72.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[180471585, 59535, -61366725; 59535, 21, -20244; -61366725, -20244, 20866858],[105, 21, 1],[-1640, -1268, -1978, -896, 0, -964, -558, -1471; 25, 22, 40, 20, 1, 0, 5, 18; -4823, -3729, -5817, -2635, 0, -2835, -1641, -4326],71,23]
%
% END OF LATTICE L72.23
%
%
% LATTICE L72.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-150360, 0, 840; 0, 39, -12; 840, -12, -1],[840, 3, 1],[3, 9, 1, 2, -1, -1, 1, 1; 164, 490, 54, 105, -56, -55, 56, 55; 532, 1596, 177, 350, -180, -180, 168, 177],71,24]
%
% END OF LATTICE L72.24
%
%
% LATTICE L72.25
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2787960, 383040, 15960; 383040, -52626, -2193; 15960, -2193, -91],[840, 3, 1],[-1, 16, 19, 99, 9, -17, -75, -8; -8, 112, 134, 700, 64, -120, -532, -57; 16, 105, 102, 490, 36, -90, -336, -30],71,25]
%
% END OF LATTICE L72.25
%
%
% LATTICE L72.26
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1297380, 516600, -3780; 516600, 205702, -1505; -3780, -1505, 11],[420, 7, 1],[-5, 1, 6, 16, 5, -2, -3, -3; 12, -3, -17, -45, -14, 5, 8, 8; -84, -68, -266, -660, -196, 0, 64, 63],71,26]
%
% END OF LATTICE L72.26
%
%
% LATTICE L72.27
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-101220, 6300, -1680; 6300, -392, 105; -1680, 105, -26],[420, 7, 1],[-1, -1, -3, -4, 1, 8, 3, 3; -24, -16, -46, -60, 16, 120, 44, 42; -42, -1, 7, 15, 0, -35, -18, -28],71,27]
%
% END OF LATTICE L72.27
%
%
% LATTICE L72.28
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2326170, -465990, 1081080; -465990, 99232, -216510; 1081080, -216510, 502429],[210, 14, 1],[277370, 33833, -10147, -13637, 20245, 398889, 98058, 307762; 5796, 707, -212, -285, 423, 8335, 2049, 6431; -594321, -72494, 21742, 29220, -43379, -854700, -210109, -659442],71,28]
%
% END OF LATTICE L72.28
%
%
% LATTICE L72.29
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[4851210, 708750, 1725780; 708750, 106320, 252105; 1725780, 252105, 613933],[210, 15, 1],[-140293, -179681, 7699, 4828, -30721, -60528, -1041557, -233499; 3864, 4949, -212, -133, 846, 1667, 28686, 6431; 392780, 503055, -21555, -13517, 86010, 169461, 2916060, 653730],71,29]
%
% END OF LATTICE L72.29
%
%
% LATTICE L72.30
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[154856940, -71190, -30146235; -71190, 35, 13860; -30146235, 13860, 5868614],[105, 35, 1],[-3368, -868, -1354, -368, 0, -132, -382, -1007; 10179, 2626, 4102, 1116, 1, 396, 1151, 3039; -17325, -4465, -6965, -1893, 0, -679, -1965, -5180],71,30]
%
% END OF LATTICE L72.30
%
%
% LATTICE L72.31
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1455720, 11760, 26040; 11760, -95, -210; 26040, -210, -419],[840, 5, 1],[65, 73, 10, 20, -1, -1, 5, 6; 8172, 9184, 1259, 2520, -124, -126, 616, 753; -60, -70, -10, -21, 0, 1, 0, -5],71,31]
%
% END OF LATTICE L72.31
%
%
% LATTICE L72.32
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-15860040, -3967320, 38640; -3967320, -992405, 9665; 38640, 9665, -94],[840, 5, 1],[-281, -169, -99, -211, -1, 11, 27, -21; 1176, 707, 414, 882, 4, -46, -112, 88; 5400, 3220, 1870, 3948, 0, -208, -420, 415],71,32]
%
% END OF LATTICE L72.32
%
%
% LATTICE L72.33
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[7520730, 1031940, 2627310; 1031940, 148848, 360465; 2627310, 360465, 917831],[210, 21, 1],[-276865, -50657, 15193, 6806, -60625, -597246, -293639, -460803; 3864, 707, -212, -95, 846, 8335, 4098, 6431; 791014, 144729, -43407, -19445, 173208, 1706355, 838938, 1316532],71,33]
%
% END OF LATTICE L72.33
%
%
% LATTICE L72.34
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[762720, -102900, 189840; -102900, 14808, -25620; 189840, -25620, 47251],[420, 12, 1],[1118, 5534, 1064, 2878, -26, 966, 3256, 1119; -41, -203, -39, -105, 1, -35, -119, -41; -4514, -22344, -4296, -11620, 105, -3900, -13146, -4518],71,34]
%
% END OF LATTICE L72.34
%
%
% LATTICE L72.35
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[198217320, -6351660, 49486080; -6351660, 203532, -1585728; 49486080, -1585728, 12354481],[420, 12, 1],[-5, -253, -93, -177, 37, 341, 202, 50; -8, -42, -4, -70, -14, -110, -77, -29; 19, 1008, 372, 700, -150, -1380, -819, -204],71,35]
%
% END OF LATTICE L72.35
%
%
% LATTICE L72.36
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2252040, 26880, -5040; 26880, 259, -56; -5040, -56, 11],[840, 7, 1],[5, 1, 1, 1, -1, -2, -1, 0; 228, 46, 46, 45, -48, -95, -48, -1; 3444, 692, 693, 690, -700, -1400, -704, -7],71,36]
%
% END OF LATTICE L72.36
%
%
% LATTICE L72.37
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[12825960, -3853080, -16800; -3853080, 1157513, 5047; -16800, 5047, 22],[840, 7, 1],[7, -1, -11, -29, -9, 3, 5, 5; 24, -3, -34, -90, -28, 10, 16, 16; -168, -76, -602, -1500, -448, 0, 148, 147],71,37]
%
% END OF LATTICE L72.37
%
%
% LATTICE L72.38
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-171780, 11340, 2100; 11340, -330, -75; 2100, -75, -16],[420, 15, 1],[-1, 1, 3, 6, 7, 2, 11, -1; 70, -63, -205, -413, -484, -139, -770, 68; -460, 420, 1350, 2716, 3180, 912, 5040, -450],71,38]
%
% END OF LATTICE L72.38
%
%
% LATTICE L72.39
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-276792811680, 226771650, -137627568960; 226771650, -185790, 112755930; -137627568960, 112755930, -68431501609],[210, 30, 1],[138796, 342484, -19481, -8402, 34942, 126012, 1065929, 470811; -1379, -3353, 209, 77, -366, -1277, -10731, -4712; -279145, -688800, 39180, 16898, -70275, -253434, -2143785, -946890],71,39]
%
% END OF LATTICE L72.39
%
%
% LATTICE L72.40
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-7980, -2520, -1260; -2520, -465, -690; -1260, -690, 59],[420, 15, 1],[-87, -45, 46, 52, 13, -38, -733, -85; 176, 91, -93, -105, -26, 77, 1484, 172; 200, 105, -105, -119, -30, 87, 1680, 195],71,40]
%
% END OF LATTICE L72.40
%
%
% LATTICE L72.41
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[840, 0, 0; 0, 8, 0; 0, 0, -1],[840, 8, 1],[-1, -1, 0, 1, 0, -1, -1, -1; -3, 0, 1, 0, -1, -10, -7, -5; -30, -28, 0, 0, -2, -40, -35, -32],71,41]
%
% END OF LATTICE L72.41
%
%
% LATTICE L72.42
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-175560, 10920, 5880; 10920, 272, 112; 5880, 112, 43],[840, 8, 1],[1, -1, -1, 1, 1, 9, 12, 4; -222, 224, 223, -210, -222, -2000, -2667, -889; 441, -448, -444, 420, 442, 3980, 5306, 1768],71,42]
%
% END OF LATTICE L72.42
%
%
% LATTICE L72.43
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[68915910, 4027800, -27284040; 4027800, 248080, -1594635; -27284040, -1594635, 10801843],[210, 35, 1],[3758983, 229256, -68758, -18481, 274367, 540585, 1328907, 2085433; 11592, 707, -212, -57, 846, 1667, 4098, 6431; 9496410, 579175, -173705, -46689, 693140, 1365693, 3357250, 5268480],71,43]
%
% END OF LATTICE L72.43
%
%
% LATTICE L72.44
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[61333440, -385980, 15159480; -385980, 2440, -95400; 15159480, -95400, 3746893],[420, 20, 1],[52, 312, 926, 6988, 796, 1232, 5286, 359; 15, 91, 255, 1911, 217, 335, 1435, 97; -210, -1260, -3740, -28224, -3215, -4976, -21350, -1450],71,44]
%
% END OF LATTICE L72.44
%
%
% LATTICE L72.45
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2394420, -381360, 580020; -381360, 60740, -92380; 580020, -92380, 140503],[420, 20, 1],[85, -139, -5, 851, 299, 335, 925, 237; 9, -21, -1, 105, 37, 41, 112, 28; -345, 560, 20, -3444, -1210, -1356, -3745, -960],71,45]
%
% END OF LATTICE L72.45
%
%
% LATTICE L72.46
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[9660, -840, 0; -840, -147, 21; 0, 21, -2],[420, 21, 1],[1, 0, -1, -1, -1, 1, 1, 1; 16, 2, -8, -10, -12, 10, 12, 13; 140, 9, -105, -115, -126, 105, 120, 126],71,46]
%
% END OF LATTICE L72.46
%
%
% LATTICE L72.47
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-548940, 137340, -2100; 137340, -34356, 525; -2100, 525, -8],[420, 21, 1],[-3, 0, 2, 1, -1, -11, -5, -7; -18, -1, 9, 5, -4, -55, -26, -38; -406, -69, 63, 65, 0, -735, -402, -672],71,47]
%
% END OF LATTICE L72.47
%
%
% LATTICE L72.48
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-788204862060, 452787930, -391894606530; 452787930, -260106, 225125670; -391894606530, 225125670, -194849575307],[210, 42, 1],[212418, 75212, -29089, -9402, 52592, 958392, 232105, 718935; -1379, -479, 209, 55, -366, -6385, -1533, -4712; -427231, -151272, 58506, 18910, -105777, -1927590, -466827, -1445976],71,48]
%
% END OF LATTICE L72.48
%
%
% LATTICE L72.49
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-121405935, -86159430, 30688560; -86159430, -61144860, 21778785; 30688560, 21778785, -7757242],[105, 105, 1],[-3, -2, -2, 0, 1, 0, -1, -3; 34798, 25258, 30932, 1034, -10548, -2042, 9036, 31457; 97685, 70905, 86835, 2903, -29610, -5733, 25365, 88305],71,49]
%
% END OF LATTICE L72.49
%
%
% LATTICE L72.50
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[729120, 94500, 181440; 94500, 12712, 23520; 181440, 23520, 45151],[420, 28, 1],[-2674, -546, -548, -446, 26, -1318, -492, -1037; -93, -19, -19, -15, 1, -45, -17, -36; 10794, 2204, 2212, 1800, -105, 5320, 1986, 4186],71,50]
%
% END OF LATTICE L72.50
%
%
% LATTICE L72.51
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[37508520, -216300, 9299220; -216300, 1148, -53620; 9299220, -53620, 2305489],[420, 28, 1],[-1825, -1131, -1851, -1441, 565, 2877, 77, -617; 423, 262, 428, 330, -132, -670, -18, 143; 7371, 4568, 7476, 5820, -2282, -11620, -311, 2492],71,51]
%
% END OF LATTICE L72.51
%
%
% LATTICE L72.52
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[840, -4200, 840; -4200, -2730, 615; 840, 615, -137],[840, 15, 1],[19, 65, 9, 6, -1, -1, 1, 5; 260, 896, 125, 84, -12, -14, 0, 67; 1280, 4410, 615, 413, -60, -69, 0, 330],71,52]
%
% END OF LATTICE L72.52
%
%
% LATTICE L72.53
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-190680, 36960, 840; 36960, -6555, -195; 840, -195, -2],[840, 15, 1],[31, 60, 37, 27, 1, -5, -31, 5; 112, 217, 134, 98, 4, -18, -112, 18; 2080, 3990, 2430, 1736, 0, -348, -2100, 345],71,53]
%
% END OF LATTICE L72.53
%
%
% LATTICE L72.54
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[330540, 38220, -3360; 38220, 4340, -385; -3360, -385, 34],[420, 35, 1],[-11, -2, -4, -1, 1, 1, 1, -1; -108, -20, -42, -12, 4, 8, 8, -10; -2310, -425, -875, -237, 140, 189, 190, -210],71,54]
%
% END OF LATTICE L72.54
%
%
% LATTICE L72.55
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-113737994580, 222050850, -54269303970; 222050850, -433510, 105950040; -54269303970, 105950040, -25894226149],[210, 70, 1],[294029, 34716, -13393, -2608, 24231, 88394, 107056, 331653; -4137, -479, 209, 33, -366, -1277, -1533, -4712; -616245, -72760, 28070, 5466, -50785, -185262, -224375, -695100],71,55]
%
% END OF LATTICE L72.55
%
%
% LATTICE L72.56
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[141540, 68460, -2100; 68460, 33110, -1015; -2100, -1015, 31],[420, 35, 1],[-23, -5, -12, -4, -1, 2, 3, 0; 48, 11, 27, 9, 2, -5, -8, -1; 0, 20, 70, 24, 0, -28, -60, -35],71,56]
%
% END OF LATTICE L72.56
%
%
% LATTICE L72.57
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[19320, -8400, 3360; -8400, 1911, -756; 3360, -756, 299],[840, 21, 1],[1, 0, -1, -1, -1, 1, 1, 1; 160, -7, -220, -210, -204, 170, 180, 179; 392, -18, -546, -520, -504, 420, 444, 441],71,57]
%
% END OF LATTICE L72.57
%
%
% LATTICE L72.58
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-615720, -41160, -12600; -41160, -2751, -840; -12600, -840, -247],[840, 21, 1],[-13, -13, -21, -16, -25, 1, 7, 5; 204, 206, 334, 255, 400, -15, -112, -81; -28, -36, -63, -50, -84, 0, 24, 21],71,58]
%
% END OF LATTICE L72.58
%
%
% LATTICE L72.59
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[21560280, 0, -77280; 0, 24, 0; -77280, 0, 277],[840, 24, 1],[9, 25, 0, 1, 2, 37, 32, 29; -1, 0, 1, 0, -1, -10, -7, -5; 2510, 6972, 0, 280, 558, 10320, 8925, 8088],71,59]
%
% END OF LATTICE L72.59
%
%
% LATTICE L72.60
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-19320, 4200, 0; 4200, 1392, -48; 0, -48, 1],[840, 24, 1],[0, -3, -1, 1, 1, 7, 8, 2; 0, -14, -5, 0, 4, 30, 35, 9; -1, -672, -228, 140, 210, 1500, 1722, 432],71,60]
%
% END OF LATTICE L72.60
%
%
% LATTICE L72.61
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-60617695530, 198538620, 21887871180; 198538620, -650265, -71688435; 21887871180, -71688435, -7903284686],[210, 105, 1],[132829, 23524, -9077, -589, 32843, 59901, 145093, 224742; -268416, -47527, 18363, 1189, -66418, -121079, -293252, -454196; 370300, 65580, -25305, -1642, 91560, 166992, 404490, 626535],71,61]
%
% END OF LATTICE L72.61
%
%
% LATTICE L72.62
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[494576040, 10834740, 122456040; 10834740, 237360, 2682660; 122456040, 2682660, 30319871],[420, 60, 1],[47, 935, 1173, 2481, 776, 1111, 4523, 260; 2, 42, 28, 42, 10, 10, 28, -1; -190, -3780, -4740, -10024, -3135, -4488, -18270, -1050],71,62]
%
% END OF LATTICE L72.62
%
%
% LATTICE L72.63
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[139436220, -6403320, 34738200; -6403320, 294060, -1595280; 34738200, -1595280, 8654441],[420, 60, 1],[83, 519, 89, 195, 157, 221, 757, 283; -10, -91, -15, -7, 1, -5, -35, -22; -335, -2100, -360, -784, -630, -888, -3045, -1140],71,63]
%
% END OF LATTICE L72.63
%
%
% LATTICE L72.64
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[51240, 9240, 3360; 9240, 70, -35; 3360, -35, -37],[840, 35, 1],[41, 7, 7, 2, -1, -1, -1, 3; -2364, -406, -408, -117, 56, 59, 64, -169; 5880, 1010, 1015, 291, -140, -147, -160, 420],71,64]
%
% END OF LATTICE L72.64
%
%
% LATTICE L72.65
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[283080, -73080, -4200; -73080, 18865, 1085; -4200, 1085, 62],[840, 35, 1],[25, 3, 15, 5, 1, -3, -5, -1; 96, 11, 54, 18, 4, -10, -16, -2; 0, 10, 70, 24, 0, -28, -60, -35],71,65]
%
% END OF LATTICE L72.65
%
%
% LATTICE L72.66
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1953840, -170520, 5040; -170520, -14840, 440; 5040, 440, -13],[840, 40, 1],[-1, 1, 2, 11, 2, 1, 1, -1; 0, -7, -5, -21, -3, -1, 0, 2; -390, 140, 600, 3528, 670, 352, 385, -320],71,66]
%
% END OF LATTICE L72.66
%
%
% LATTICE L72.67
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-36669360, -442680, 59640; -442680, -5320, 720; 59640, 720, -97],[840, 40, 1],[-1, 1, 4, 25, 5, 3, 9, -1; 0, -7, -5, -21, -3, -1, 0, 2; -615, 560, 2420, 15204, 3050, 1836, 5530, -600],71,67]
%
% END OF LATTICE L72.67
%
%
% LATTICE L72.68
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[12762960, -205380, 3158400; -205380, 3696, -50820; 3158400, -50820, 781597],[420, 84, 1],[-3429, -1899, -1477, -317, 26, -7073, -2269, -4379; -161, -89, -69, -15, 1, -335, -107, -206; 13846, 7668, 5964, 1280, -105, 28560, 9162, 17682],71,68]
%
% END OF LATTICE L72.68
%
%
% LATTICE L72.69
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[9934260, -196140, 2459100; -196140, 3864, -48552; 2459100, -48552, 608719],[420, 84, 1],[220, 392, 686, 292, -52, -312, 23, 291; -3, -5, -9, -5, -1, -5, -1, -5; -889, -1584, -2772, -1180, 210, 1260, -93, -1176],71,69]
%
% END OF LATTICE L72.69
%
%
% LATTICE L72.70
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[171780, 639240, 17640; 639240, 2249310, 62055; 17640, 62055, 1712],[420, 105, 1],[-5, -2, 0, 1, 13, 5, 5, -1; 322, 133, 29, -57, -780, -305, -306, 64; -11620, -4800, -1050, 2056, 28140, 11004, 11040, -2310],71,70]
%
% END OF LATTICE L72.70
%
%
% LATTICE L72.71
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[9414938820, 3663236010, 1769890500; 3663236010, 1425330690, 688647750; 1769890500, 688647750, 332719787],[210, 210, 1],[1932, 707, -212, -19, 423, 1667, 2049, 6431; 8306058, 3039459, -911593, -81673, 1818775, 7167047, 8809286, 27648542; -17201765, -6294690, 1887900, 169144, -3766665, -14842884, -18243945, -57259860],71,71]
%
% END OF LATTICE L72.71
%
%
% LATTICE L72.72
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[370860, -1941240, -53760; -1941240, 10161165, 281400; -53760, 281400, 7793],[420, 105, 1],[7, 4, 9, 1, 1, -1, -1, 1; 44, 7, -7, -1, 6, 19, 48, 38; -1540, -225, 315, 43, -210, -693, -1740, -1365],71,72]
%
% END OF LATTICE L72.72
%
%
% LATTICE L72.73
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-40616520, 0, 64680; 0, 56, 0; 64680, 0, -103],[840, 56, 1],[-1, -1, 0, 13, 6, 29, 2, 5; -3, 0, 1, 0, -1, -10, -1, -5; -630, -628, 0, 8160, 3766, 18200, 1255, 3136],71,73]
%
% END OF LATTICE L72.73
%
%
% LATTICE L72.74
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-4454520, -256200, -106680; -256200, -14672, -6104; -106680, -6104, -2539],[840, 56, 1],[1, -1, -1, 13, 7, 39, 6, 10; -96, 104, 99, -1350, -722, -4000, -613, -1013; 189, -208, -196, 2700, 1442, 7980, 1222, 2016],71,74]
%
% END OF LATTICE L72.74
%
%
% LATTICE L72.75
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[82511520, 1189020, -19544280; 1189020, 17080, -281680; -19544280, -281680, 4629371],[420, 140, 1],[-260, 594, 2980, 1690, 771, 298, -250, -849; 783, -1771, -8891, -5043, -2301, -889, 747, 2536; -1050, 2400, 12040, 6828, 3115, 1204, -1010, -3430],71,75]
%
% END OF LATTICE L72.75
%
%
% LATTICE L72.76
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[3294060, 162120, -697200; 162120, 7420, -34720; -697200, -34720, 147269],[420, 140, 1],[1793, 787, 693, -95, -537, -97, 172, 1178; -5274, -2315, -2039, 279, 1579, 285, -506, -3465; 7245, 3180, 2800, -384, -2170, -392, 695, 4760],71,76]
%
% END OF LATTICE L72.76
%
%
% LATTICE L72.77
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1517880, -1074360, 54600; -1074360, 737205, -37485; 54600, -37485, 1906],[840, 105, 1],[15, 9, 10, 1, -1, -2, -5, 1; -1224, -742, -829, -83, 84, 169, 432, -68; -24500, -14850, -16590, -1661, 1680, 3381, 8640, -1365],71,77]
%
% END OF LATTICE L72.77
%
%
% LATTICE L72.78
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[741720, -1735440, -47880; -1735440, 4060770, 112035; -47880, 112035, 3091],[840, 105, 1],[7, 2, 9, 1, 1, -1, -1, 1; 88, 17, 56, 6, 12, 10, 36, 41; -3080, -585, -1890, -202, -420, -378, -1320, -1470],71,78]
%
% END OF LATTICE L72.78
%
%
% LATTICE L72.79
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-35449680, -1848840, 52920; -1848840, -96360, 2760; 52920, 2760, -79],[840, 120, 1],[-1, 1, 6, 13, 8, 5, 8, -1; 0, -7, -5, -7, -3, -1, 0, 2; -670, 420, 3840, 8456, 5250, 3312, 5355, -600],71,79]
%
% END OF LATTICE L72.79
%
%
% LATTICE L72.80
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-37143120, -5265960, 110880; -5265960, -746520, 15720; 110880, 15720, -331],[840, 120, 1],[-1, 1, 12, 27, 17, 11, 37, -1; 0, -7, -5, -7, -3, -1, 0, 2; -335, 0, 3780, 8708, 5550, 3636, 12390, -240],71,80]
%
% END OF LATTICE L72.80
%
%
% LATTICE L72.81
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3503640, 0, 10080; 0, 168, 0; 10080, 0, -29],[840, 168, 1],[-1, -1, 0, 3, 4, 17, 1, 1; -1, 0, 1, 0, -1, -10, -1, -5; -350, -348, 0, 1040, 1386, 5880, 345, 336],71,81]
%
% END OF LATTICE L72.81
%
%
% LATTICE L72.82
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-17086440, -257880, -106680; -257880, -3696, -1512; -106680, -1512, -617],[840, 168, 1],[0, -1, -1, 3, 5, 27, 4, 6; 3, 384, 379, -1150, -1912, -10300, -1523, -2273; -7, -768, -756, 2300, 3822, 20580, 3042, 4536],71,82]
%
% END OF LATTICE L72.82
%
%
% LATTICE L72.83
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[17082240, 615300420, 152357520; 615300420, 22163053080, 5487901020; 152357520, 5487901020, 1358885777],[420, 420, 1],[12, 150, 688, 130, 181, 94, -26, -145; 17, -1267, -5947, -1105, -1487, -585, 439, 1512; -70, 5100, 23940, 4448, 5985, 2352, -1770, -6090],71,83]
%
% END OF LATTICE L72.83
%
%
% LATTICE L72.84
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[25620, 981120, 242760; 981120, 37459380, 9268980; 242760, 9268980, 2293523],[420, 420, 1],[349, 459, 397, -21, -325, -65, 98, 686; 727, 953, 821, -43, -667, -123, 209, 1437; -2975, -3900, -3360, 176, 2730, 504, -855, -5880],71,84]
%
% END OF LATTICE L72.84
%
%
% LATTICE L72.85
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-182280, -151200, -21000; -151200, -97160, -13440; -21000, -13440, -1859],[840, 280, 1],[-7, -2, -1, 2, 5, 4, 1, -1; 621, 183, 118, -159, -424, -347, -88, 79; -4410, -1300, -840, 1128, 3010, 2464, 625, -560],71,85]
%
% END OF LATTICE L72.85
%
%
% LATTICE L72.86
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1157520, -578760, -190680; -578760, -289240, -95200; -190680, -95200, -31271],[840, 280, 1],[-176, -147, -326, -91, 25, 85, 57, -1; 525, 439, 975, 273, -73, -253, -170, 2; -525, -440, -980, -276, 70, 252, 170, 0],71,86]
%
% END OF LATTICE L72.86
%
%
% LATTICE L72.87
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-38640, -19320, 1680; -19320, -9240, 840; 1680, 840, -73],[840, 840, 1],[-3, -2, 3, 2, 11, 8, 2, -1; 0, -1, -5, -1, -3, -1, 0, 2; -70, -60, 0, 32, 210, 168, 45, 0],71,87]
%
% END OF LATTICE L72.87
%
%
% LATTICE L72.88
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2659440, -3799320, 5880; -3799320, -5427240, 8400; 5880, 8400, -13],[840, 840, 1],[-1, -2, -3, 0, 2, 2, 1, -1; 0, -1, -5, -1, -3, -1, 0, 2; -455, -1560, -4620, -652, -1050, 252, 450, 840],71,88]
%
% END OF LATTICE L72.88
%

\medskip%
%------------------------------WEYL-GROUP-W73--------------------------------
%
\leavevmode\llap{}%
$W_{73\phantom{0}}$%
\qquad\llap{32} lattices, $\chi=72$%
\hfill%
$\infty222222\infty222222\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L73.1
%
\leavevmode%
${L_{73.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}8\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{-}{}5\above{1pt}{1pt}{-}{}25\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}11\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{25\rightarrow N_{73},5,2*}%
\EasyButWeakLineBreak%
{${110}\above{1pt}{1pt}{20,19}{\infty a}{440}\above{1pt}{1pt}{b}{2}{50}\above{1pt}{1pt}{l}{2}{88}\above{1pt}{1pt}{r}{2}{10}\above{1pt}{1pt}{b}{2}{550}\above{1pt}{1pt}{s}{2}{2}\above{1pt}{1pt}{b}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
shares genus with 5-dual\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2584117800\\-1286540200\\1826000
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1286540200\\-640522510\\909115
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1826000\\909115\\-1282
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2951517359\\-5913532680\\10443879600
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1469189856\\-2943605329\\5198696160
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2235998\\4479949\\-7912031
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1411\\2827\\-5005
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
15175\\-30404\\53680
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
282\\-565\\1000
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-33161\\66440\\-117304
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-5621\\11262\\-19885
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-79828\\159940\\-282425
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-5060\\10138\\-17903
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-2584117800, -1286540200, 1826000; -1286540200, -640522510, 909115; 1826000, 909115, -1282],[2200, 5, 1],[-1411, 15175, 282, -33161, -5621, -79828, -5060, -100647, -831639, -371402, -1599767, -96437, -430462, -4218; 2827, -30404, -565, 66440, 11262, 159940, 10138, 201652, 1666236, 744125, 3205224, 193217, 862455, 8451; -5005, 53680, 1000, -117304, -19885, -282425, -17903, -356125, -2942720, -1314200, -5660776, -341245, -1523225, -14927],72,1]
%
% END OF LATTICE L73.1
%
%
% LATTICE L73.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[110, 0, 0; 0, 0, -1; 0, -1, 0],[110, 1, 1],[-1, 1, 0, -3, -1, -3, -1, -21, -89, -16, -173, -21, -19, -1; 0, 0, -1, -22, -5, -11, -3, -55, -220, -39, -418, -50, -44, -2; -55, 0, 1, -22, -10, -44, -18, -440, -1980, -361, -3938, -485, -451, -27],72,2]
%
% END OF LATTICE L73.2
%
%
% LATTICE L73.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-150449640, -74774480, -459360; -74774480, -37163418, -228305; -459360, -228305, -1402],[440, 1, 1],[-42314, -360707, -32466, -702651, -42704, -38733, -2063, -2214, 4483, 82, -9797, -1824, -5795, -1985; 85140, 725780, 65325, 1413808, 85925, 77935, 4151, 4455, -9020, -165, 19712, 3670, 11660, 3994; -385, -3520, -322, -7040, -435, -407, -25, -55, 0, 2, 0, -5, -33, -15],72,3]
%
% END OF LATTICE L73.3
%
%
% LATTICE L73.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-18072450, 1613150, -809600; 1613150, -143990, 72265; -809600, 72265, -36268],[550, 5, 1],[133, 615, 564, 1235, 153, 719, 9, 21, 1, -4, -3, 1, 51, 5; 4334, 19536, 17815, 38874, 4789, 22275, 267, 539, -44, -95, 110, 84, 2090, 176; 5665, 25190, 22900, 49874, 6125, 28325, 331, 605, -110, -100, 286, 145, 3025, 239],72,4]
%
% END OF LATTICE L73.4
%
%
% LATTICE L73.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-9147380, 6050, -4490530; 6050, -4, 2970; -4490530, 2970, -2204441],[110, 2, 1],[1519, 3283, 1186, 6431, 1569, 1433, 79, 109, -27, -2, 81, 59, 195, 69; 10340, 23650, 8655, 47311, 11695, 10945, 673, 1485, 0, -55, -11, 130, 880, 402; -3080, -6655, -2404, -13035, -3180, -2904, -160, -220, 55, 4, -165, -120, -396, -140],72,5]
%
% END OF LATTICE L73.5
%
%
% LATTICE L73.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3658490, 6050, 1496660; 6050, -10, -2475; 1496660, -2475, -612272],[110, 5, 1],[-343, -1505, -1364, -14825, -363, -1669, -95, -31, 9, 4, -135, -11, -201, -75; 2068, 9460, 8655, 94622, 2339, 10945, 673, 297, 0, -55, -22, 26, 880, 402; -847, -3718, -3370, -36630, -897, -4125, -235, -77, 22, 10, -330, -27, -495, -185],72,6]
%
% END OF LATTICE L73.6
%
%
% LATTICE L73.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[6820, 6050, 3080; 6050, 15120, 2750; 3080, 2750, 1391],[110, 10, 1],[24366, 54103, 98351, 535460, 26301, 121631, 7115, 2683, -5, 9, 5520, 748, 13614, 5180; 99, 220, 400, 2178, 107, 495, 29, 11, 0, 0, 22, 3, 55, 21; -54142, -120219, -218540, -1189815, -58442, -270270, -15810, -5962, 11, -20, -12265, -1662, -30250, -11510],72,7]
%
% END OF LATTICE L73.7
%
%
% LATTICE L73.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-990, -6050, -110; -6050, -16632, -605; -110, -605, -12],[110, 11, 1],[-919, -4211, -8479, -8429, -11464, -976, -662, -134, -1, 55, 5, -119, -77, -391; -35, -160, -322, -320, -435, -37, -25, -5, 0, 2, 0, -5, -3, -15; 10130, 46410, 93445, 92892, 126335, 10755, 7293, 1475, 10, -605, -52, 1320, 850, 4312],72,8]
%
% END OF LATTICE L73.8
%
%
% LATTICE L73.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-957000, -391160, -18480; -391160, -158650, -7865; -18480, -7865, -278],[440, 5, 1],[-80, 875, 16, -9561, -324, -4599, -1457, -5794, -47867, -21376, -460359, -5550, -24771, -1213; 165, -1804, -33, 19712, 668, 9482, 3004, 11946, 98692, 44073, 949168, 11443, 51073, 2501; 649, -7128, -130, 77880, 2639, 37455, 11865, 47179, 389752, 174050, 3748360, 45189, 201685, 9875],72,9]
%
% END OF LATTICE L73.9
%
%
% LATTICE L73.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[140627520, 78650, 69232020; 78650, 44, 38720; 69232020, 38720, 34083461],[110, 22, 1],[-4269, -9348, -37264, -18406, -49559, -4141, -2589, -389, 32, 0, -226, -1679, -517, -2069; 1220, 2710, 10839, 5365, 14495, 1219, 785, 135, 0, 1, 55, 410, 136, 570; 8670, 18985, 75680, 37381, 100650, 8410, 5258, 790, -65, 0, 459, 3410, 1050, 4202],72,10]
%
% END OF LATTICE L73.10
%
%
% LATTICE L73.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-11490050, 1020800, -133100; 1020800, -90690, 11825; -133100, 11825, -1512],[550, 5, 1],[9175, 41667, 7612, 415683, 10259, 9573, 2907, 1231, -43, -44, 557, 147, 833, 1823; 103224, 468776, 85639, 4676650, 115419, 107701, 32705, 13849, -484, -495, 6270, 1654, 9372, 20510; -385, -1760, -322, -17600, -435, -407, -125, -55, 0, 2, 0, -5, -33, -75],72,11]
%
% END OF LATTICE L73.11
%
%
% LATTICE L73.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-35111120, 3159640, 626560; 3159640, -284272, -56384; 626560, -56384, -11181],[440, 8, 1],[1591, -53, -55, 74, 236, 1198, 508, 12566, 28367, 10351, 28240, 13921, 12959, 779; 55, 0, -2, 0, 5, 33, 15, 385, 880, 322, 880, 435, 407, 25; 88880, -2970, -3072, 4147, 13200, 66968, 28392, 702240, 1585210, 578432, 1578093, 777920, 724152, 43528],72,12]
%
% END OF LATTICE L73.12
%
%
% LATTICE L73.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-7255160, -1648240, 29920; -1648240, -374374, 6787; 29920, 6787, -122],[440, 11, 1],[-2, 59, 1, -129, -237, -60, -206, -367, -3011, -2953, -5775, -3822, -309, -163; 10, -300, -5, 656, 1205, 305, 1047, 1865, 15300, 15005, 29344, 19420, 1570, 828; 65, -2220, -33, 4856, 8910, 2252, 7722, 13740, 112660, 110473, 216024, 142945, 11553, 6083],72,13]
%
% END OF LATTICE L73.13
%
%
% LATTICE L73.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[42549100, -601150, 21193700; -601150, 9880, -299410; 21193700, -299410, 10556579],[550, 10, 1],[-745120, -1660911, -3021981, -3292402, -809325, -3749171, -44199, -86007, -1343, -299, -32106, -21802, -406464, -31358; -24497, -54604, -99350, -108240, -26607, -123255, -1453, -2827, -44, -10, -1056, -717, -13365, -1031; 1495230, 3332945, 6064200, 6606853, 1624070, 7523450, 88694, 172590, 2695, 600, 64427, 43750, 815650, 62926],72,14]
%
% END OF LATTICE L73.14
%
%
% LATTICE L73.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[622538400, 62277050, 311244450; 62277050, 6230080, 31136050; 311244450, 31136050, 155609851],[550, 10, 1],[-558406, -1246233, -453623, -12357514, -607705, -563327, -166407, -65327, -1233, -1, -117146, -16028, -60406, -117108; -19437, -43384, -15792, -430210, -21157, -19613, -5795, -2277, -44, 0, -4070, -557, -2101, -4075; 1120790, 2501345, 910478, 24803075, 1219740, 1130668, 334000, 131120, 2475, 2, 235125, 32170, 121242, 235050],72,15]
%
% END OF LATTICE L73.15
%
%
% LATTICE L73.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[84823530, -96580, 34538020; -96580, 110, -39325; 34538020, -39325, 14063018],[110, 55, 1],[-876, -3837, -38240, -37777, -10172, -4250, -2658, -80, 13, 0, -463, -344, -530, -2122; 1996, 8758, 87319, 86284, 23243, 9719, 6101, 187, -26, 1, 1036, 770, 1196, 4814; 2157, 9448, 94160, 93020, 25047, 10465, 6545, 197, -32, 0, 1140, 847, 1305, 5225],72,16]
%
% END OF LATTICE L73.16
%
%
% LATTICE L73.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-39509800, 14410000, 235400; 14410000, -5255610, -85855; 235400, -85855, -1402],[2200, 5, 1],[2774, 23393, 2100, 226869, 2750, 2481, 643, 108, -337, -4, 3691, 132, 401, 667; 7612, 64196, 5763, 622600, 7547, 6809, 1765, 297, -924, -11, 10120, 362, 1100, 1830; -385, -3520, -322, -35200, -435, -407, -125, -55, 0, 2, 0, -5, -33, -75],72,17]
%
% END OF LATTICE L73.17
%
%
% LATTICE L73.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3693140, 6061770, 3000470; 6061770, -9492120, -4698430; 3000470, -4698430, -2325639],[110, 110, 1],[-7, -16, -322, -160, -87, -37, -25, -1, 0, 2, 0, -1, -3, -15; -290258, -664934, -13388377, -6654619, -3620207, -1540987, -1045037, -42283, -148, 86737, 3799, -37744, -121718, -617668; 586392, 1343329, 27047790, 13443955, 7313702, 3113170, 2111230, 85422, 299, -175230, -7675, 76252, 245900, 1247840],72,18]
%
% END OF LATTICE L73.18
%
%
% LATTICE L73.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-57111120, -7520040, 22487080; -7520040, -990160, 2960960; 22487080, 2960960, -8854121],[440, 40, 1],[-4887, 667, 709, -4656, -1594, -29976, -11326, -52192, -114825, -208269, -566134, -55485, -255419, -14619; 11, 0, -2, 0, 1, 33, 15, 77, 176, 322, 880, 87, 407, 25; -12408, 1694, 1800, -11825, -4048, -76120, -28760, -132528, -291566, -528840, -1437535, -140888, -648560, -37120],72,19]
%
% END OF LATTICE L73.19
%
%
% LATTICE L73.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-13814680, -70400, 55000; -70400, -330, 275; 55000, 275, -218],[440, 55, 1],[13, 113, 562, 1109, 149, 62, 38, 1, -1, -2, 11, 5, 8, 32; 786, 6836, 34003, 67104, 9017, 3753, 2303, 61, -60, -123, 656, 300, 482, 1932; 4269, 37112, 184580, 364240, 48939, 20365, 12485, 329, -328, -660, 3600, 1639, 2625, 10505],72,20]
%
% END OF LATTICE L73.20
%
%
% LATTICE L73.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1632950, -5744750, -290950; -5744750, -20201060, -1023165; -290950, -1023165, -51822],[550, 55, 1],[-51, 49, 54, -127, -491, -691, -515, -993, -4225, -41814, -8225, -10993, -4529, -529; -103, 98, 110, -254, -983, -1385, -1033, -1993, -8482, -83950, -16514, -22073, -9095, -1063; 2320, -2210, -2475, 5728, 22165, 31225, 23287, 44925, 191190, 1892275, 372232, 497530, 205000, 23958],72,21]
%
% END OF LATTICE L73.21
%
%
% LATTICE L73.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1573550, -469150, 44000; -469150, -139040, 13035; 44000, 13035, -1222],[550, 55, 1],[3, -1, -1, 13, 12, 4, 82, 34, 149, 297, 1467, 395, 33, 103; -169, 54, 57, -700, -654, -220, -4530, -1884, -8266, -16481, -81420, -21929, -1833, -5735; -1695, 540, 572, -7000, -6545, -2203, -45375, -18875, -82820, -165132, -815800, -219725, -18367, -57475],72,22]
%
% END OF LATTICE L73.22
%
%
% LATTICE L73.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2837332080, -972455880, -13234232000; -972455880, -333295600, -4535846304; -13234232000, -4535846304, -61728676015],[440, 88, 1],[-208257, 50741, 53249, -70842, -1170382, -357972, -1405010, -2825852, -6118959, -24326121, -5997376, -32204817, -2676137, -1629099; 1057275, -257600, -270334, 359648, 5941755, 1817341, 7132913, 14346205, 31064560, 123498174, 30447312, 163496525, 13586139, 8270567; -33040, 8050, 8448, -11239, -185680, -56792, -222904, -448320, -970770, -3859328, -951481, -5109280, -424568, -258456],72,23]
%
% END OF LATTICE L73.23
%
%
% LATTICE L73.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[80878430600, 686881250, 40298405400; 686881250, 5833520, 342244760; 40298405400, 342244760, 20079042901],[550, 110, 1],[9719, 187, 274, 3531, 26439, 45129, 38441, 83257, 185765, 3718766, 368373, 996297, 419751, 54535; -934, -18, 5, -333, -2509, -4305, -3675, -7969, -17788, -356125, -35279, -95424, -40210, -5228; -19490, -375, -550, -7081, -53020, -90500, -77088, -166960, -372525, -7457450, -738719, -1997930, -841750, -109362],72,24]
%
% END OF LATTICE L73.24
%
%
% LATTICE L73.25
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[6624534400, -131853150, 3300266200; -131853150, 2624380, -65687710; 3300266200, -65687710, 1644154341],[550, 110, 1],[6749, 132, -11, 11991, 18080, 6210, 132588, 57518, 128402, 514147, 1273349, 688857, 58057, 188747; -73, -1, -2, -145, -213, -71, -1495, -643, -1431, -5726, -14175, -7663, -645, -2085; -13550, -265, 22, -24075, -36300, -12468, -266200, -115480, -257795, -1032262, -2556525, -1383030, -116562, -378950],72,25]
%
% END OF LATTICE L73.25
%
%
% LATTICE L73.26
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-583796400, -245337400, -20550200; -245337400, -103101680, -8635960; -20550200, -8635960, -723109],[2200, 40, 1],[45955, -6417, -6627, 8960, 15240, 285218, 21504, 494706, 1087739, 1972667, 1072362, 525421, 2418087, 27647; -114697, 16016, 16540, -22363, -38037, -711865, -53671, -1234717, -2714844, -4923500, -2676465, -1311377, -6035205, -69003; 63800, -8910, -9200, 12441, 21160, 396000, 29856, 686840, 1510190, 2738800, 1488839, 729480, 3357200, 38384],72,26]
%
% END OF LATTICE L73.26
%
%
% LATTICE L73.27
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-285555600, -130686600, -20114600; -130686600, -59808080, -9203680; -20114600, -9203680, -1414581],[2200, 40, 1],[-963124, -2174245, -793377, -10822644, -1067017, -993291, -298559, -121971, 4055, 4217, -28306, -18078, -91804, -194666; 2414093, 5449796, 1988618, 27127210, 2674503, 2489707, 748345, 305723, -10164, -10570, 70950, 45313, 230109, 487935; -2011680, -4541350, -1657128, -22605275, -2228680, -2074688, -623600, -254760, 8470, 8808, -59125, -37760, -191752, -406600],72,27]
%
% END OF LATTICE L73.27
%
%
% LATTICE L73.28
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-58231800, -258944400, -12826000; -258944400, -1150030310, -56969165; -12826000, -56969165, -2822062],[2200, 55, 1],[-2806, 2799, 5628, -6145, -13986, -22397, -17925, -36420, -316607, -1574668, -621471, -417500, -173733, -21301; -6853, 6836, 13745, -15008, -34158, -54700, -43778, -88948, -773244, -3845785, -1517808, -1019653, -424305, -52023; 151095, -150720, -303050, 330896, 753115, 1206025, 965217, 1961125, 17048480, 84791850, 33464624, 22481305, 9355075, 1147003],72,28]
%
% END OF LATTICE L73.28
%
%
% LATTICE L73.29
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-73191800, -3115200, 94600; -3115200, -132110, 4015; 94600, 4015, -122],[2200, 55, 1],[6, 49, 48, 469, 62, 5, 13, 0, -1, 0, 11, 4, 1, 17; 517, 4236, 4153, 40600, 5372, 434, 1140, 2, -84, -1, 920, 337, 85, 1455; 21660, 177340, 173833, 1699200, 224785, 18153, 47575, 65, -3540, -33, 38800, 14190, 3572, 61050],72,29]
%
% END OF LATTICE L73.29
%
%
% LATTICE L73.30
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-15720468720, -10613273880, -7812000680; -10613273880, -7165281200, -5274073200; -7812000680, -5274073200, -3882031491],[440, 440, 1],[173259, 367793, 7276233, 1788514, 1911322, 786668, 457214, 8532, -4211, -4593, 29396, 88379, 122287, 451741; -7, -16, -322, -80, -87, -37, -25, -1, 0, 2, 0, -1, -3, -15; -348648, -740106, -14641880, -3599005, -3846128, -1583000, -920040, -17168, 8474, 9240, -59155, -177848, -246080, -909040],72,30]
%
% END OF LATTICE L73.30
%
%
% LATTICE L73.31
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-9655540400, 3722415400, -1587141600; 3722415400, -1435069680, 611876320; -1587141600, 611876320, -260887919],[2200, 440, 1],[-100449, -213235, -4218547, -207386, -1108134, -456092, -53018, -4948, 2441, 2667, -3408, -51233, -70893, -52379; -401803, -852956, -16874510, -829560, -4432623, -1824405, -212077, -19793, 9764, 10670, -13632, -204933, -283575, -209519; -331280, -703250, -13912800, -683961, -3654640, -1504200, -174856, -16320, 8050, 8800, -11239, -168960, -233800, -172744],72,31]
%
% END OF LATTICE L73.31
%
%
% LATTICE L73.32
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-78602343600, -10658016600, -1795694073800; -10658016600, -1445163280, -243485376640; -1795694073800, -243485376640, -41023135194311],[2200, 440, 1],[86374, -21159, -22017, 147706, 487581, 148993, 2922411, 1175097, 2544101, 10113785, 12467004, 13388600, 1112478, 3384944; 28503807, -6982576, -7265702, 48743720, 160904127, 49168409, 964409585, 387787577, 839565344, 3337596774, 4114170120, 4418301097, 367122975, 1117047335; -172960, 42370, 44088, -295775, -976360, -298352, -5852000, -2353080, -5094450, -20252408, -24964625, -26810080, -2227688, -6778200],72,32]
%
% END OF LATTICE L73.32
%

\medskip%
%------------------------------WEYL-GROUP-W74--------------------------------
%
\leavevmode\llap{}%
$W_{74\phantom{0}}$%
\qquad\llap{12} lattices, $\chi=38$%
\hfill%
$22642264\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L74.1
%
\leavevmode%
${L_{74.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{2}{}37\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2\rightarrow N_{74}}%
\EasyButWeakLineBreak%
{${4}\above{1pt}{1pt}{*}{2}{148}\above{1pt}{1pt}{b}{2}{6}\above{1pt}{1pt}{}{6}{2}\above{1pt}{1pt}{*}{4}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3066708\\21312\\20868
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
21312\\-146\\-145
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
20868\\-145\\-142
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
124319\\-124320\\18381600
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-917\\916\\-135585
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-847\\847\\-125236
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
37\\-40\\5474
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
327\\-370\\48396
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\-3\\150
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\2\\-149
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-3066708, 21312, 20868; 21312, -146, -145; 20868, -145, -142],[444, 1, 1],[37, 327, 1, -1, 5, 191, 20, 50; -40, -370, -3, 2, -2, -148, -18, -51; 5474, 48396, 150, -149, 736, 28194, 2955, 7394],73,1]
%
% END OF LATTICE L74.1
%
%
% LATTICE L74.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-3774, -1221, 0; -1221, -395, 0; 0, 0, 1],[111, 1, 1],[0, -12, 1, 81, 48, 604, 47, 31; 0, 37, -3, -248, -147, -1850, -144, -95; 1, 0, -3, -20, -10, -111, -6, -1],73,2]
%
% END OF LATTICE L74.2
%
%
% LATTICE L74.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-492951, 7437, -162060; 7437, -105, 2445; -162060, 2445, -53278],[111, 3, 1],[-144, -5803, -412, -3133, -1167, -10366, -25, 74; -1, -74, -6, -51, -20, -185, -1, 2; 438, 17649, 1253, 9528, 3549, 31524, 76, -225],73,3]
%
% END OF LATTICE L74.3
%
%
% LATTICE L74.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-19330428, -78588, 52392; -78588, -318, 213; 52392, 213, -142],[444, 3, 1],[31, 317, 2, 0, -1, 53, 3, 35; -40, -370, -1, 2, -2, -148, -6, -51; 11370, 116328, 736, 3, -372, 19314, 1097, 12828],73,4]
%
% END OF LATTICE L74.4
%
%
% LATTICE L74.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[679161048, 64380, -171362244; 64380, 8, -16244; -171362244, -16244, 43237195],[444, 4, 1],[-10952, -94645, -109, 0, -2125, -66638, -12968, -30513; 327, 2812, 0, 1, 66, 2035, 393, 916; -43406, -375106, -432, 0, -8422, -264106, -51396, -120932],73,5]
%
% END OF LATTICE L74.5
%
%
% LATTICE L74.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1753023, -44844, -569874; -44844, -1147, -14578; -569874, -14578, -185255],[111, 37, 1],[-62, -56, -413, -979, -352, -82, -1, 13; 72, 79, 624, 1585, 591, 142, 39, -38; 185, 166, 1221, 2886, 1036, 241, 0, -37],73,6]
%
% END OF LATTICE L74.6
%
%
% LATTICE L74.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1049776728, -1332, -264834456; -1332, 24, 336; -264834456, 336, 66811625],[444, 12, 1],[-50246, -500521, -5429, 0, -277, -122596, -11412, -117887; -283, -2812, -30, 1, -2, -703, -65, -666; -199170, -1984014, -21520, 0, -1098, -485958, -45236, -467292],73,7]
%
% END OF LATTICE L74.7
%
%
% LATTICE L74.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[100011, -283494, -93240; -283494, 1084470, 356643; -93240, 356643, 117287],[111, 111, 1],[22, 19, 46, 329, 119, 28, 1, 0; -20765, -17880, -43233, -308774, -111598, -26241, -888, -73; 63159, 54384, 131498, 939171, 339438, 79815, 2701, 222],73,8]
%
% END OF LATTICE L74.8
%
%
% LATTICE L74.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-45732, 61716, 11544; 61716, -83102, -15577; 11544, -15577, -2914],[444, 37, 1],[147, 169, 677, 1745, 1311, 317, 52, -44; -2, -4, -18, -51, -40, -10, -3, 2; 592, 690, 2775, 7178, 5402, 1308, 222, -185],73,9]
%
% END OF LATTICE L74.9
%
%
% LATTICE L74.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-48396, -24420, 23976; -24420, -12210, 12099; 23976, 12099, -11878],[444, 111, 1],[-1413, -415, -128, -56, 111, -19, -89, -1463; -40, -10, -1, 2, -2, -4, -6, -51; -2886, -846, -259, -111, 222, -42, -185, -2997],73,10]
%
% END OF LATTICE L74.10
%
%
% LATTICE L74.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[32856, -3108, 12432; -3108, 296, -1184; 12432, -1184, 4735],[444, 148, 1],[-5, -4, -28, -63, -22, -5, 1, 0; 243, 205, 1473, 3457, 1239, 289, 9, 1; 74, 62, 444, 1036, 370, 86, 0, 0],73,11]
%
% END OF LATTICE L74.11
%
%
% LATTICE L74.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[888, -50172, 12432; -50172, 5423016, -1343544; 12432, -1343544, 332861],[444, 444, 1],[343, 93, 39, 1, -1, 21, 75, 797; -20182, -5465, -2273, 0, 55, -1244, -4436, -46963; -81474, -22062, -9176, 0, 222, -5022, -17908, -189588],73,12]
%
% END OF LATTICE L74.12
%

\medskip%
%------------------------------WEYL-GROUP-W75--------------------------------
%
\leavevmode\llap{}%
$W_{75\phantom{0}}$%
\qquad\llap{16} lattices, $\chi=48$%
\hfill%
$222222222222\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L75.1
%
\leavevmode%
${L_{75.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}8\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}13\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{2\rightarrow N_{75}}%
\EasyButWeakLineBreak%
{${8}\above{1pt}{1pt}{b}{2}{26}\above{1pt}{1pt}{l}{2}{40}\above{1pt}{1pt}{r}{2}{2}\above{1pt}{1pt}{l}{2}{104}\above{1pt}{1pt}{r}{2}{10}\above{1pt}{1pt}{b}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-305240\\-121680\\2080
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-121680\\-48506\\829
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2080\\829\\-14
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
18199\\-46800\\-70200
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7245\\-18631\\-27945
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-112\\288\\431
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
17\\-44\\-84
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
278\\-715\\-1079
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
607\\-1560\\-2280
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
95\\-244\\-347
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1661\\-4264\\-5928
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
41\\-105\\-130
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-305240, -121680, 2080; -121680, -48506, 829; 2080, 829, -14],[520, 1, 1],[17, 278, 607, 95, 1661, 41, 11, -5, -47, -11, -205, -6; -44, -715, -1560, -244, -4264, -105, -28, 13, 120, 28, 520, 15; -84, -1079, -2280, -347, -5928, -130, -24, 26, 120, 23, 312, -5],74,1]
%
% END OF LATTICE L75.1
%
%
% LATTICE L75.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[7410, 3640, -130; 3640, 1788, -65; -130, -65, -16],[130, 1, 1],[-1, 96, -59, -93, -1945, -379, -445, -8793, -8861, -2583, -21247, -736; 2, -195, 120, 189, 3952, 770, 904, 17862, 18000, 5247, 43160, 1495; 0, 13, -10, -14, -286, -55, -64, -1261, -1270, -370, -3042, -105],74,2]
%
% END OF LATTICE L75.2
%
%
% LATTICE L75.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[9144980, -151970, 4577040; -151970, 2524, -76060; 4577040, -76060, 2290797],[130, 2, 1],[2599, 7541, -476, -586, 16140, 11493, 12189, 569191, 296236, 178042, 752836, 62447; -2294, -6656, 420, 517, -14248, -10145, -10759, -502411, -261480, -157153, -664508, -55120; -5269, -15288, 965, 1188, -32721, -23300, -24711, -1153932, -600565, -360948, -1526239, -126600],74,3]
%
% END OF LATTICE L75.3
%
%
% LATTICE L75.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[24667370, -394550, 4938180; -394550, 6310, -78985; 4938180, -78985, 988578],[130, 5, 1],[2429, 3524, -89, -274, 15081, 1074, 11391, 265966, 55369, 83194, 703559, 5836; -4588, -6656, 168, 517, -28496, -2029, -21518, -502411, -104592, -157153, -1329016, -11024; -12500, -18135, 458, 1410, -77610, -5527, -58620, -1368705, -284938, -428130, -3620630, -30033],74,4]
%
% END OF LATTICE L75.4
%
%
% LATTICE L75.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[466359140, -9304750, 230596600; -9304750, 185580, -4600840; 230596600, -4600840, 114021121],[130, 10, 1],[4468, -29314, -2116, 5489, 154512, 16305, 59967, 2542279, 259856, 767731, 3196108, 48130; 27, -117, -10, 24, 754, 81, 307, 13143, 1346, 3984, 16614, 253; -9035, 59280, 4279, -11100, -312455, -32972, -121265, -5140980, -525479, -1552500, -6463145, -97328],74,5]
%
% END OF LATTICE L75.5
%
%
% LATTICE L75.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[90015770, -72280, -27603680; -72280, 52, 22165; -27603680, 22165, 8464774],[130, 13, 1],[-21121, -2357, 3867, 2380, -10091, -46703, -99059, -177913, -2407467, -723460, -470629, -253747; -654, -73, 120, 74, -312, -1445, -3066, -5507, -74520, -22394, -14568, -7855; -68874, -7686, 12610, 7761, -32906, -152295, -323024, -580161, -7850570, -2359149, -1534686, -827450],74,6]
%
% END OF LATTICE L75.6
%
%
% LATTICE L75.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2096120, -949520, 41080; -949520, -430110, 18615; 41080, 18615, -802],[520, 5, 1],[-2497, -28609, -11871, -8890, -149921, -611, -455, -173, 63, 34, -3583, -127; 5072, 58110, 24112, 18057, 304512, 1241, 924, 351, -128, -69, 7280, 258; -10180, -116675, -48416, -36260, -611520, -2493, -1860, -715, 256, 140, -14560, -517],74,7]
%
% END OF LATTICE L75.7
%
%
% LATTICE L75.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[406374540, -2146690, 195103090; -2146690, 11284, -1030640; 195103090, -1030640, 93670277],[130, 26, 1],[-4575, 1665, 8894, -4344, -10246, -71277, -53695, -176475, -1174294, -694896, -222834, -220073; -13, -2, 5, 1, -9, -75, -72, -253, -1705, -1021, -331, -350; 9529, -3468, -18525, 9048, 21341, 148460, 111839, 367572, 2445885, 1447368, 464131, 458380],74,8]
%
% END OF LATTICE L75.8
%
%
% LATTICE L75.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1411280, -16120, 5200; -16120, -112, 56; 5200, 56, -19],[520, 8, 1],[-1, -1, 2, 5, 16, 8, 2, 40, 8, 7, 10, -3; -15, -13, 30, 74, 234, 115, 27, 481, 90, 70, 78, -55; -318, -312, 635, 1584, 5057, 2520, 622, 12168, 2405, 2064, 2847, -1000],74,9]
%
% END OF LATTICE L75.9
%
%
% LATTICE L75.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[520, 0, 0; 0, -26, 13; 0, 13, -6],[520, 13, 1],[-1, 0, 1, 0, -1, -2, -7, -6, -161, -24, -31, -8; 4, 1, 0, -5, -16, -20, -40, -28, -720, -103, -128, -25; 0, 2, 0, -13, -48, -65, -156, -119, -3120, -455, -576, -130],74,10]
%
% END OF LATTICE L75.10
%
%
% LATTICE L75.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[297478610, -2904330, -65031980; -2904330, 28210, 634855; -65031980, 634855, 14216654],[130, 65, 1],[-5631, 1026, 2191, -2676, -12619, -8778, -66121, -108654, -289199, -427836, -274389, -27098; 11236, -2054, -4380, 5353, 25220, 17541, 132098, 217055, 577716, 854651, 548116, 54126; -26260, 4785, 10218, -12480, -58850, -40937, -308360, -506715, -1348698, -1995240, -1279630, -126373],74,11]
%
% END OF LATTICE L75.11
%
%
% LATTICE L75.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[7951949460, 10593424010, 5154038760; 10593424010, 14112342140, 6866104700; 5154038760, 6866104700, 3340578997],[130, 130, 1],[-327, -73, 12, 74, -156, -289, -1533, -5507, -7452, -22394, -7284, -1571; -642524, -143404, 23526, 144785, -306994, -568317, -3013525, -10824743, -14647722, -44017373, -14317202, -3087732; 1321125, 294860, -48373, -297700, 631225, 1168544, 6196255, 22257280, 30117893, 90506260, 29438295, 6348836],74,12]
%
% END OF LATTICE L75.12
%
%
% LATTICE L75.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1040, -520, -2080; -520, -240, -1040; -2080, -1040, -4159],[520, 40, 1],[21, 5, -2, -1, 128, 32, 142, 6352, 328, 1957, 4110, 131; -3, -13, 0, 2, 0, -1, -9, -455, -24, -146, -312, -11; -10, 0, 1, 0, -65, -16, -70, -3120, -161, -960, -2015, -64],74,13]
%
% END OF LATTICE L75.13
%
%
% LATTICE L75.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[293070440, -91787280, -704600; -91787280, 28747030, 220675; -704600, 220675, 1694],[520, 65, 1],[47, 3, 1, 0, 27, 11, 225, 201, 1087, 816, 1061, 57; 188, 11, 0, -1, 112, 46, 928, 826, 4464, 3349, 4352, 233; -4940, -185, 416, 130, -3360, -1417, -27300, -23995, -129376, -96850, -125600, -6643],74,14]
%
% END OF LATTICE L75.14
%
%
% LATTICE L75.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[63440, -56680, 1040; -56680, 49712, -936; 1040, -936, 17],[520, 104, 1],[3, 3, -1, -18, -7, -69, -35, -99, -319, -366, -57, -91; 1, 1, 0, -5, -2, -20, -10, -28, -90, -103, -16, -25; -130, -128, 65, 832, 319, 3120, 1586, 4496, 14495, 16640, 2593, 4160],74,15]
%
% END OF LATTICE L75.15
%
%
% LATTICE L75.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-23979280, -34297640, 85800; -34297640, -49055760, 122720; 85800, 122720, -307],[520, 520, 1],[15, -1, -2, -1, 8, 26, 112, 382, 256, 1525, 246, 101; -3, -1, 0, 2, 0, -1, -9, -35, -24, -146, -24, -11; 2990, -680, -559, 520, 2235, 6864, 27690, 92720, 61919, 367640, 59125, 23816],74,16]
%
% END OF LATTICE L75.16
%

\medskip%
%------------------------------WEYL-GROUP-W76--------------------------------
%
\leavevmode\llap{}%
$W_{76\phantom{0}}$%
\qquad\llap{12} lattices, $\chi=48$%
\hfill%
$222222222222\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L76.1
%
\leavevmode%
${L_{76.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{-2}{}47\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2\rightarrow N_{76}}%
\EasyButWeakLineBreak%
{${12}\above{1pt}{1pt}{*}{2}{188}\above{1pt}{1pt}{b}{2}{2}\above{1pt}{1pt}{b}{2}{282}\above{1pt}{1pt}{l}{2}{4}\above{1pt}{1pt}{r}{2}{94}\above{1pt}{1pt}{b}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1188348\\1692\\3384
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1692\\-2\\-7
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3384\\-7\\2
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-9401\\-4808100\\-916500
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
18\\9206\\1755
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\1023\\194
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-29\\-14832\\-2826
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-195\\-99734\\-18988
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2\\-1023\\-194
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-35\\-17907\\-3384
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-512\\-96
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-517\\-94
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-1188348, 1692, 3384; 1692, -2, -7; 3384, -7, 2],[564, 1, 1],[-29, -195, -2, -35, -1, -1, 1, 7, 0, -59, -7, -93; -14832, -99734, -1023, -17907, -512, -517, 510, 3572, 0, -30174, -3580, -47564; -2826, -18988, -194, -3384, -96, -94, 96, 658, -1, -5781, -684, -9071],75,1]
%
% END OF LATTICE L76.1
%
%
% LATTICE L76.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[7050, -2397, 0; -2397, 815, 0; 0, 0, -1],[141, 1, 1],[1, 16, -1, -1579, -93, -2473, -386, -2601, -54, -1006, -17, -112; 3, 47, -3, -4653, -274, -7285, -1137, -7661, -159, -2961, -50, -329; 0, 0, -1, -705, -41, -1081, -168, -1128, -23, -423, -7, -47],75,2]
%
% END OF LATTICE L76.2
%
%
% LATTICE L76.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-397479, 1833, 133245; 1833, 3, -618; 133245, -618, -44666],[141, 3, 1],[-67, 95, 101, -10415, -1962, -54701, -2915, -60161, -1379, -9607, -594, -5365; -62, 94, 93, -9917, -1865, -51935, -2766, -57058, -1305, -9071, -559, -5029; -199, 282, 300, -30926, -5826, -162432, -8656, -178647, -4095, -28529, -1764, -15933],75,3]
%
% END OF LATTICE L76.3
%
%
% LATTICE L76.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1868532, 6768, 3384; 6768, -6, -21; 3384, -21, -2],[564, 3, 1],[-43, -853, -8, -43, -3, -1, 1, 7, -1, -98, -33, -422; -5776, -114586, -1075, -5781, -404, -141, 134, 940, -134, -13160, -4432, -56682; -12226, -242520, -2274, -12220, -852, -282, 284, 1974, -285, -27871, -9384, -119991],75,4]
%
% END OF LATTICE L76.4
%
%
% LATTICE L76.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[62943528, -2484420, 15619416; -2484420, 98072, -616508; 15619416, -616508, 3875953],[564, 4, 1],[24412, 158409, 2655, 39059, 173, 1073, 67, 5950, 842, 125300, 3324, 163286; 189, 1222, 20, 282, 1, 0, 0, 47, 7, 987, 26, 1269; -98346, -638166, -10696, -157356, -697, -4324, -270, -23970, -3392, -504780, -13391, -657812],75,5]
%
% END OF LATTICE L76.5
%
%
% LATTICE L76.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3087759, -34122, 1050873; -34122, -47, 11609; 1050873, 11609, -357649],[141, 47, 1],[-3070, 33, 1535, -10447, -30780, -18237, -136951, -20036, -21538, -9556, -9226, -1766; -105, 1, 53, -339, -1002, -595, -4473, -655, -707, -315, -306, -59; -9024, 97, 4512, -30708, -90475, -53606, -402555, -58894, -63309, -28089, -27119, -5191],75,6]
%
% END OF LATTICE L76.6
%
%
% LATTICE L76.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1580464488, -16106148, 392273844; -16106148, 164136, -3997572; 392273844, -3997572, 97363003],[564, 12, 1],[14512, 289013, 5549, 32291, 726, 9799, 69, 4690, 700, 65610, 5523, 283904; 63, 1222, 20, 94, 1, 0, 0, 47, 7, 329, 26, 1269; -58466, -1164378, -22356, -130096, -2925, -39480, -278, -18894, -2820, -264328, -22251, -1143792],75,7]
%
% END OF LATTICE L76.7
%
%
% LATTICE L76.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[143538, 249288, 2679; 249288, 433011, 4653; 2679, 4653, 50],[141, 141, 1],[-1, 0, 1, -5, -43, -25, -62, -27, -28, -4, -11, -2; -5, 1, 4, -58, -491, -282, -695, -301, -304, -42, -109, -18; 517, -93, -423, 5659, 47940, 27549, 67915, 29421, 29751, 4117, 10716, 1779],75,8]
%
% END OF LATTICE L76.8
%
%
% LATTICE L76.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2820, 564, 564; 564, -94, -47; 564, -47, 118],[564, 47, 1],[937, 127, 44, 11, -1, -1, 1, 7, 23, 56, 269, 68; 6420, 870, 301, 75, -8, -7, 6, 48, 158, 384, 1844, 466; -1974, -268, -94, -24, 0, 2, 0, -14, -47, -117, -564, -143],75,9]
%
% END OF LATTICE L76.9
%
%
% LATTICE L76.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-919884, 27072, 4512; 27072, -282, -141; 4512, -141, -22],[564, 141, 1],[279, 113, 38, 3, -3, -1, 1, 7, 22, 17, 243, 61; 824, 334, 113, 9, -8, -3, 2, 20, 64, 50, 716, 180; 51794, 20976, 7050, 556, -564, -186, 188, 1302, 4089, 3157, 45120, 11325],75,10]
%
% END OF LATTICE L76.10
%
%
% LATTICE L76.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[39480, 93060, 59784; 93060, 216952, 139120; 59784, 139120, 89183],[564, 188, 1],[-19832, -2753, -2243, -713, -152, 1, 211, -50, -560, -2090, -2651, -2804; 59685, 8285, 6749, 2145, 457, -3, -633, 151, 1687, 6291, 7979, 8439; -79806, -11078, -9024, -2868, -611, 4, 846, -202, -2256, -8412, -10669, -11284],75,11]
%
% END OF LATTICE L76.11
%
%
% LATTICE L76.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[120696, -7392348, -1834692; -7392348, 453346584, 112515180; -1834692, 112515180, 27924917],[564, 564, 1],[63, 26, 20, 2, 1, 0, 0, 1, 7, 7, 26, 27; 78552, 31765, 21137, 1785, 105, 137, 2123, 2810, 13438, 9740, 34470, 34438; -316498, -127986, -85164, -7192, -423, -552, -8554, -11322, -54144, -39244, -138885, -138756],75,12]
%
% END OF LATTICE L76.12
%

\medskip%
%------------------------------WEYL-GROUP-W77--------------------------------
%
\leavevmode\llap{}%
$W_{77\phantom{0}}$%
\qquad\llap{12} lattices, $\chi=64$%
\hfill%
$22222232222223\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L77.1
%
\leavevmode%
${L_{77.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}31\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2\rightarrow N_{77}}%
\EasyButWeakLineBreak%
{${2}\above{1pt}{1pt}{s}{2}{310}\above{1pt}{1pt}{b}{2}{4}\above{1pt}{1pt}{b}{2}{62}\above{1pt}{1pt}{s}{2}{10}\above{1pt}{1pt}{l}{2}{124}\above{1pt}{1pt}{r}{2}{2}\above{1pt}{1pt}{+}{3}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
156860\\-31620\\-620
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-31620\\6374\\125
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-620\\125\\2
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
463511\\2291520\\425320
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-94251\\-465961\\-86485
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2670\\13200\\2449
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-18\\-89\\-17
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-4546\\-22475\\-4185
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-481\\-2378\\-442
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-8208\\-40579\\-7533
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-7744\\-38285\\-7105
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-99349\\-491164\\-91140
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2670\\-13200\\-2449
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[156860, -31620, -620; -31620, 6374, 125; -620, 125, 2],[620, 1, 1],[-18, -4546, -481, -8208, -7744, -99349, -2670, -249, -3731, -53, -69, 1, 25, 0; -89, -22475, -2378, -40579, -38285, -491164, -13200, -1231, -18445, -262, -341, 5, 124, 0; -17, -4185, -442, -7533, -7105, -91140, -2449, -228, -3410, -48, -62, 0, 0, -1],76,1]
%
% END OF LATTICE L77.1
%
%
% LATTICE L77.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-8835, -1705, 155; -1705, -329, 30; 155, 30, -2],[155, 1, 1],[142, 2148, 16, 48, 2, -6, -1, 9, 2533, 135, 4633, 4377, 28092, 1511; -738, -11160, -83, -248, -10, 31, 5, -47, -13175, -702, -24087, -22755, -146041, -7855; -179, -2635, -17, -31, 5, 0, -3, -16, -3410, -178, -6014, -5660, -36270, -1947],76,2]
%
% END OF LATTICE L77.2
%
%
% LATTICE L77.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[109585, 14725, 21700; 14725, 1955, 2915; 21700, 2915, 4297],[155, 5, 1],[-1782, -5324, -186, -448, 6, 180, 1, -133, -6549, -1729, -58917, -11113, -356370, -19151; -363, -1085, -38, -93, 1, 31, 0, -27, -1333, -352, -11997, -2263, -72571, -3900; 9245, 27621, 965, 2325, -31, -930, -5, 690, 33976, 8970, 305660, 57654, 1848840, 99355],76,3]
%
% END OF LATTICE L77.3
%
%
% LATTICE L77.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[6173960, 53940, -1542560; 53940, 456, -13480; -1542560, -13480, 385407],[620, 4, 1],[313, 43207, 2149, 69847, 65093, 207723, 22186, 1921, 26047, 85, -593, -307, 39, 154; -251, -34255, -1701, -55211, -51435, -164114, -17525, -1514, -20460, -64, 496, 250, -31, -125; 1244, 171740, 8542, 277636, 258740, 825685, 88188, 7636, 103540, 338, -2356, -1220, 155, 612],76,4]
%
% END OF LATTICE L77.4
%
%
% LATTICE L77.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2429780, -49600, 19840; -49600, -1010, 405; 19840, 405, -162],[620, 5, 1],[16, 56, 7, 26, 2, 71, 0, -1, 37, 23, 439, 85, 5509, 150; -49, -155, -14, -31, -1, 0, 2, -1, -155, -86, -1519, -289, -18600, -502; 1830, 6448, 820, 3100, 242, 8680, 5, -125, 4123, 2590, 49755, 9647, 625580, 17045],76,5]
%
% END OF LATTICE L77.5
%
%
% LATTICE L77.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[310, 155, 0; 155, 62, 0; 0, 0, 1],[155, 31, 1],[101, 49, 11, 1, 1, 0, 0, 7, 59, 97, 107, 3131, 648, 1080; -228, -110, -24, -2, 0, 0, -1, -17, -135, -221, -243, -7105, -1470, -2449; -868, -420, -93, -8, 0, 1, 0, -62, -510, -837, -922, -26970, -5581, -9300],76,6]
%
% END OF LATTICE L77.6
%
%
% LATTICE L77.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[176448280, -3100, -44406260; -3100, 40, 780; -44406260, 780, 11175603],[620, 20, 1],[-33809, -109879, -5509, -32299, -2113, -18451, 0, -151, -100673, -28451, -1020461, -194855, -3139829, -339600; -592, -1922, -96, -558, -36, -310, 1, -3, -1767, -499, -17887, -3415, -55025, -5951; -134340, -436604, -21890, -128340, -8396, -73315, 0, -600, -400024, -113050, -4054800, -774256, -12476105, -1349400],76,7]
%
% END OF LATTICE L77.7
%
%
% LATTICE L77.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1860, -620, 0; -620, 186, 31; 0, 31, -46],[620, 31, 1],[-53, -21, 1, 1, 1, -7, -14, -14, -46, -135, -68, -1944, -797, -656; -163, -65, 2, 3, 5, -20, -41, -42, -140, -412, -208, -5950, -2440, -2009; -124, -50, 0, 2, 0, -16, -31, -31, -105, -310, -157, -4495, -1844, -1519],76,8]
%
% END OF LATTICE L77.8
%
%
% LATTICE L77.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-310, 775, 155; 775, 3255, 620; 155, 620, 118],[155, 155, 1],[49, 5, 7, 1, 1, 0, -2, 1, 5, 43, 49, 289, 300, 502; 1648, 156, 153, 8, -12, -1, 30, 152, 204, 1647, 1792, 10452, 10801, 17970; -8370, -792, -775, -40, 62, 5, -155, -775, -1037, -8370, -9105, -53103, -54875, -91295],76,9]
%
% END OF LATTICE L77.9
%
%
% LATTICE L77.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[184760, 56420, -45880; 56420, 17112, -14012; -45880, -14012, 11393],[620, 124, 1],[1275, 597, 109, 1, -157, -10, -1, 124, 802, 1290, 1398, 40728, 4207, 13991; -42, -20, -4, 0, 10, 1, 3, -3, -25, -41, -45, -1315, -136, -453; 5084, 2380, 434, 4, -620, -39, 0, 496, 3200, 5146, 5576, 162440, 16779, 55800],76,10]
%
% END OF LATTICE L77.10
%
%
% LATTICE L77.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-4142220, -869860, 15500; -869860, -182590, 3255; 15500, 3255, -58],[620, 155, 1],[-15, -1, 3, 1, 3, 3, -1, -5, -3, -43, -21, -119, -243, -199; -49, -5, -14, -1, -1, 0, 2, -1, -5, -86, -49, -289, -600, -502; -6820, -554, 0, 210, 744, 800, -155, -1395, -1089, -16430, -8425, -48391, -99380, -81995],76,11]
%
% END OF LATTICE L77.11
%
%
% LATTICE L77.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1240, 93620, -23560; 93620, 318552280, -80159800; -23560, -80159800, 20171237],[620, 620, 1],[-1318, -132, -172, -24, -34, -9, 1, -57, -143, -1203, -1351, -7941, -4116, -13751; -236363, -23667, -30813, -4303, -6147, -1652, 0, -10297, -25665, -215847, -242357, -1424481, -738328, -2466600; -939300, -94052, -122450, -17100, -24428, -6565, 0, -40920, -101992, -857770, -963120, -5660848, -2934095, -9802200],76,12]
%
% END OF LATTICE L77.12
%

\medskip%
%------------------------------WEYL-GROUP-W78--------------------------------
%
\leavevmode\llap{}%
$W_{78\phantom{0}}$%
\qquad\llap{24} lattices, $\chi=10$%
\hfill%
$26222$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L78.1
%
\leavevmode%
${L_{78.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{2}{}11\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{2\rightarrow N_{78}}%
\EasyButWeakLineBreak%
{${22}\above{1pt}{1pt}{b}{2}{6}\above{1pt}{1pt}{}{6}{2}\above{1pt}{1pt}{b}{2}{330}\above{1pt}{1pt}{l}{2}{4}\above{1pt}{1pt}{r}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-34021020\\23100\\36960
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
23100\\-14\\-27
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
36960\\-27\\-38
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2\\-1221\\-1078
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-609\\-540
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\610\\539
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
26\\15840\\14025
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\608\\540
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-34021020, 23100, 36960; 23100, -14, -27; 36960, -27, -38],[660, 1, 1],[-2, -1, 1, 26, 1; -1221, -609, 610, 15840, 608; -1078, -540, 539, 14025, 540],77,1]
%
% END OF LATTICE L78.1
%
%
% LATTICE L78.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[330, 165, 825; 165, 79, 330; 825, 330, 118],[165, 1, 1],[104, 26, -63, -1429, -24; -264, -66, 160, 3630, 61; 11, 3, -7, -165, -3],77,2]
%
% END OF LATTICE L78.2
%
%
% LATTICE L78.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-7347615, 18810, -2439360; 18810, -42, 6243; -2439360, 6243, -809851],[165, 3, 1],[6318, 106, -317, 14301, 2683; -5621, -93, 280, -12760, -2391; -19074, -320, 957, -43175, -8100],77,3]
%
% END OF LATTICE L78.3
%
%
% LATTICE L78.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-10172085, 28380, -4059825; 28380, -70, 11325; -4059825, 11325, -1620334],[165, 5, 1],[10916, 550, -548, 14822, 4635; -5621, -279, 280, -7656, -2391; -27390, -1380, 1375, -37191, -11630],77,4]
%
% END OF LATTICE L78.4
%
%
% LATTICE L78.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-18946455, 57090, -5158890; 57090, -154, 15543; -5158890, 15543, -1404703],[165, 11, 1],[1294, 718, -715, 8783, 6043; -511, -279, 280, -3480, -2391; -4758, -2640, 2629, -32295, -22220],77,5]
%
% END OF LATTICE L78.5
%
%
% LATTICE L78.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-41137140, 67320, 94380; 67320, -102, -159; 94380, -159, -214],[660, 3, 1],[20, 3, -3, -6, 5; 3476, 522, -521, -1045, 868; 6237, 935, -936, -1870, 1560],77,6]
%
% END OF LATTICE L78.6
%
%
% LATTICE L78.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[4951794705, -41653260, 1636929855; -41653260, 350385, -13769445; 1636929855, -13769445, 541124887],[165, 15, 1],[-438051, 1519, 7552, -249558, -213752; -440, 2, 7, -253, -216; 1325115, -4595, -22845, 754919, 646605],77,7]
%
% END OF LATTICE L78.7
%
%
% LATTICE L78.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[9317350680, -64311060, 2315115000; -64311060, 443896, -15979596; 2315115000, -15979596, 575244793],[660, 4, 1],[1465, 1309, 2124, 68878, 1101; 0, 6, 7, 165, 2; -5896, -5268, -8548, -277200, -4431],77,8]
%
% END OF LATTICE L78.8
%
%
% LATTICE L78.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-743820, 7260, 91080; 7260, -70, -915; 91080, -915, -10366],[660, 5, 1],[-46, -25, 23, 124, 25; -3333, -1809, 1666, 8976, 1808; -110, -60, 55, 297, 60],77,9]
%
% END OF LATTICE L78.9
%
%
% LATTICE L78.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[5630720865, -65881035, 1858114335; -65881035, 770847, -21740466; 1858114335, -21740466, 613169959],[165, 33, 1],[-67677, 2639, 12763, -192907, -363419; -40, 2, 7, -115, -216; 205083, -7997, -38676, 584570, 1101276],77,10]
%
% END OF LATTICE L78.10
%
%
% LATTICE L78.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-11220, 1320, 660; 1320, -154, -77; 660, -77, -38],[660, 11, 1],[0, -1, 0, 1, 1; -1, -9, 5, 15, 8; 2, 0, -11, -15, 0],77,11]
%
% END OF LATTICE L78.11
%
%
% LATTICE L78.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[18008782440, -184743900, 4474555140; -184743900, 1895208, -45902424; 4474555140, -45902424, 1111771091],[660, 12, 1],[22270, 6180, 489, 4209, 1177; 55, 17, 2, 0, 2; -89628, -24872, -1968, -16940, -4737],77,12]
%
% END OF LATTICE L78.12
%
%
% LATTICE L78.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[6230763330, 89469270, -2369629515; 89469270, 1284745, -34026135; -2369629515, -34026135, 901196854],[165, 55, 1],[105942, -12394, -19979, 181187, 568899; -317866, 37188, 59944, -543630, -1706913; 266565, -31185, -50270, 455892, 1431430],77,13]
%
% END OF LATTICE L78.13
%
%
% LATTICE L78.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-259525860, -22168740, 178200; -22168740, -1893630, 15225; 178200, 15225, -122],[660, 15, 1],[189, 2, -50, -1, 83; -2068, -22, 547, 11, -908; 17985, 175, -4770, -88, 7920],77,14]
%
% END OF LATTICE L78.14
%
%
% LATTICE L78.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[9486840, 12969660, 2393160; 12969660, 17731160, 3271740; 2393160, 3271740, 603701],[660, 20, 1],[-111, 461, 500, 2086, 107; 0, 6, 7, 33, 2; 440, -1860, -2020, -8448, -435],77,15]
%
% END OF LATTICE L78.15
%
%
% LATTICE L78.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-135365340, 32117580, -194040; 32117580, -7620294, 46035; -194040, 46035, -278],[660, 33, 1],[18, 5, -50, -1, 83; 91, 25, -253, -5, 420; 2505, 649, -6996, -130, 11616],77,16]
%
% END OF LATTICE L78.16
%
%
% LATTICE L78.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-272655428595, 43971031665, 16042815855; 43971031665, -7091190645, -2587218480; 16042815855, -2587218480, -943945777],[165, 165, 1],[-511, -93, 280, -232, -2391; -102384, -19018, 56699, -46287, -477886; 271935, 50545, -150645, 122923, 1269180],77,17]
%
% END OF LATTICE L78.17
%
%
% LATTICE L78.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[236280, 9900, 58740; 9900, 616, 2464; 58740, 2464, 14603],[660, 44, 1],[-1, 131, 131, 253, 30; 0, 6, 7, 15, 2; 4, -528, -528, -1020, -121],77,18]
%
% END OF LATTICE L78.18
%
%
% LATTICE L78.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-78479940, 248160, -295680; 248160, -770, 935; -295680, 935, -1114],[660, 55, 1],[-2, -5, 11, 4, 5; -1, -9, 5, 3, 8; 530, 1320, -2915, -1059, -1320],77,19]
%
% END OF LATTICE L78.19
%
%
% LATTICE L78.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[71475316440, 777715620, 17755793880; 777715620, 8462280, 193198980; 17755793880, 193198980, 4410868423],[660, 60, 1],[125458, 38276, 5397, 2941, 5356; -2893, -883, -124, -66, -123; -504900, -154040, -21720, -11836, -21555],77,20]
%
% END OF LATTICE L78.20
%
%
% LATTICE L78.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[71984493240, -536019660, 17883845760; -536019660, 3991416, -133168860; 17883845760, -133168860, 4443067177],[660, 132, 1],[-13359, -45189, -5773, -661, -5732; -383, -1295, -166, -20, -165; 53760, 181852, 23232, 2660, 23067],77,21]
%
% END OF LATTICE L78.21
%
%
% LATTICE L78.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1747020, 99000, 49500; 99000, -5610, -2805; 49500, -2805, -1402],[660, 165, 1],[1, 0, -3, 0, 5; 25, 27, -53, -1, 88; -15, -55, 0, 2, 0],77,22]
%
% END OF LATTICE L78.22
%
%
% LATTICE L78.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[3549832440, -2828100, -884268000; -2828100, 3080, 705100; -884268000, 705100, 220272799],[660, 220, 1],[333, -33131, -33131, -12653, -7367; -999, 99399, 99400, 37962, 22103; 1340, -133320, -133320, -50916, -29645],77,23]
%
% END OF LATTICE L78.23
%
%
% LATTICE L78.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[927960, 306900, 76560; 306900, 262680, 65340; 76560, 65340, 16253],[660, 660, 1],[5, 17, 2, 0, 2; 3203, 10925, 1311, -1, 1270; -12900, -44000, -5280, 4, -5115],77,24]
%
% END OF LATTICE L78.24
%

\medskip%
%------------------------------WEYL-GROUP-W79--------------------------------
%
\leavevmode\llap{}%
$W_{79\phantom{0}}$%
\qquad\llap{48} lattices, $\chi=60$%
\hfill%
$22222222222222\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L79.1
%
\leavevmode%
${L_{79.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{1}{}3\above{1pt}{1pt}{1}{}9\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{2}{}5\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{2}{}11\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{23\rightarrow N_{79},3,2}%
\EasyButWeakLineBreak%
{${18}\above{1pt}{1pt}{s}{2}{22}\above{1pt}{1pt}{b}{2}{12}\above{1pt}{1pt}{b}{2}{990}\above{1pt}{1pt}{l}{2}{4}\above{1pt}{1pt}{r}{2}{66}\above{1pt}{1pt}{b}{2}{10}\above{1pt}{1pt}{b}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
24993540\\79200\\-77220
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
79200\\246\\-243
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-77220\\-243\\238
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-121441\\-19005360\\-58655520
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-440\\-68861\\-212520
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
394\\61661\\190301
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5\\804\\2439
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
23\\3630\\11143
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
29\\4552\\14022
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
989\\154770\\477675
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
63\\9848\\30416
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
105\\16379\\50655
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
8\\1235\\3845
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[24993540, 79200, -77220; 79200, 246, -243; -77220, -243, 238],[1980, 3, 1],[5, 23, 29, 989, 63, 105, 8, 1, -1, -1, 1, 1, 5, 2; 804, 3630, 4552, 154770, 9848, 16379, 1235, 135, -187, -170, 165, 168, 836, 330; 2439, 11143, 14022, 477675, 30416, 50655, 3845, 459, -517, -498, 495, 496, 2475, 985],78,1]
%
% END OF LATTICE L79.1
%
%
% LATTICE L79.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[13035, 3465, 165; 3465, 921, 44; 165, 44, 2],[165, 1, 1],[0, -6, 4, 266, 32, 151, 31, 17, 193, 115, 2539, 240, 784, 54; 0, 22, -15, -990, -119, -561, -115, -63, -715, -426, -9405, -889, -2904, -200; 1, 11, -3, -275, -34, -165, -35, -19, -209, -123, -2695, -254, -825, -55],78,2]
%
% END OF LATTICE L79.2
%
%
% LATTICE L79.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-514140, 1320, 0; 1320, -2, -5; 0, -5, 18],[660, 1, 1],[-1, -3, -1, 1, 1, 4, 1, 0, -8, -13, -166, -33, -59, -6; -395, -1177, -390, 385, 388, 1551, 385, -7, -3245, -5238, -66715, -13252, -23661, -2395; -112, -330, -108, 110, 108, 429, 105, -5, -957, -1530, -19415, -3852, -6864, -690],78,3]
%
% END OF LATTICE L79.3
%
%
% LATTICE L79.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[990, 0, -495; 0, -15, -3; -495, -3, 247],[495, 3, 1],[-25, -21, -3, -1, 2, 17, 3, -11, -111, -81, -5939, -194, -677, -63; -6, 0, 1, 0, -1, -11, -5, -15, -77, -50, -3465, -111, -374, -30; -54, -44, -6, 0, 4, 33, 5, -27, -253, -183, -13365, -436, -1518, -140],78,4]
%
% END OF LATTICE L79.4
%
%
% LATTICE L79.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[36630, -5775, 13860; -5775, 285, -1983; 13860, -1983, 5179],[165, 3, 1],[288, 1070, 74, 54, -166, -533, -491, -153, 415, 241, 22221, 2326, 3008, 1166; -277, -1045, -73, -55, 164, 528, 490, 160, -242, -200, -19250, -2036, -2673, -1075; -879, -3267, -226, -165, 507, 1628, 1500, 468, -1254, -733, -67650, -7083, -9163, -3555],78,5]
%
% END OF LATTICE L79.5
%
%
% LATTICE L79.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[489390, -16005, 198000; -16005, 475, -6460; 198000, -6460, 80103],[165, 5, 1],[361, 1323, 272, 13, -203, -1951, -119, -177, 701, 1016, 6059, 3147, 12071, 303; -277, -1045, -219, -11, 164, 1584, 98, 160, -242, -600, -3850, -2036, -8019, -215; -915, -3355, -690, -33, 515, 4950, 302, 450, -1760, -2565, -15312, -7955, -30525, -767],78,6]
%
% END OF LATTICE L79.6
%
%
% LATTICE L79.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-12482415, 231165, -80190; 231165, -4281, 1485; -80190, 1485, -514],[495, 3, 1],[-43, -193, 0, 19, -1, -34, -98, -54, -3008, -679, -16024, -4655, -5301, -1357; -2373, -10659, -1, 1045, -54, -1870, -5400, -2978, -165924, -37456, -883960, -256794, -292435, -74865; -149, -693, -3, 55, 0, -99, -315, -181, -10197, -2307, -54505, -15840, -18051, -4635],78,7]
%
% END OF LATTICE L79.7
%
%
% LATTICE L79.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2061510, -46695, 564960; -46695, 1045, -12793; 564960, -12793, 154827],[165, 11, 1],[274, 88, 194, 4, -144, -125, -411, -105, 81, 989, 2531, 2848, 970, 1256; -277, -95, -219, -5, 164, 144, 490, 160, -22, -600, -1750, -2036, -729, -1075; -1023, -329, -726, -15, 539, 468, 1540, 396, -298, -3663, -9390, -10571, -3603, -4675],78,8]
%
% END OF LATTICE L79.8
%
%
% LATTICE L79.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[7169580, 3300, -22440; 3300, -6, -9; -22440, -9, 70],[660, 3, 1],[5, 69, 29, 989, 189, 105, 24, 1, -3, -1, 1, 3, 5, 6; 278, 3784, 1584, 53900, 10292, 5709, 1295, 49, -187, -58, 55, 172, 286, 340; 1635, 22539, 9470, 322905, 61704, 34276, 7830, 324, -990, -328, 330, 984, 1639, 1965],78,9]
%
% END OF LATTICE L79.9
%
%
% LATTICE L79.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1241874150, -16436145, 410509605; -16436145, 217530, -5433075; 410509605, -5433075, 135696629],[165, 15, 1],[48695, 74183, 200, -3011, 719, 12582, 7214, 60358, 1125400, 254257, 3601760, 1744129, 1986723, 101839; 304, 462, 1, -22, 3, 77, 45, 377, 7029, 1588, 22495, 10893, 12408, 636; -147300, -224400, -605, 9108, -2175, -38060, -21822, -182580, -3404280, -769115, -10895148, -5275905, -6009740, -308058],78,10]
%
% END OF LATTICE L79.10
%
%
% LATTICE L79.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[109278840, -2475660, 27147780; -2475660, 56088, -615020; 27147780, -615020, 6744233],[660, 4, 1],[1845, 2843, 79, 1421, 122, 2329, 1511, 2351, 43313, 29293, 690919, 33446, 228451, 19469; 30, 44, 0, 0, 1, 33, 25, 39, 715, 483, 11385, 551, 3762, 320; -7424, -11440, -318, -5720, -491, -9372, -6080, -9460, -174284, -117870, -2780140, -134581, -919248, -78340],78,11]
%
% END OF LATTICE L79.11
%
%
% LATTICE L79.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-20460, -9900, 660; -9900, -4790, 325; 660, 325, 78],[660, 5, 1],[-97, -395, -233, -267, -167, -16, 17, 20, -452, -845, -2274, -2297, -4219, -94; 200, 814, 480, 550, 344, 33, -35, -41, 935, 1746, 4697, 4744, 8712, 194; -15, -55, -30, -33, -20, 0, 2, 0, -110, -180, -462, -460, -825, -17],78,12]
%
% END OF LATTICE L79.12
%
%
% LATTICE L79.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[424301955, -14250225, 140006625; -14250225, 478566, -4702137; 140006625, -4702137, 46197890],[165, 33, 1],[99590, 13774, 363, -3074, 1187, 2312, 73726, 123472, 209288, 520115, 3349004, 3567805, 369458, 1041584; 304, 42, 1, -10, 3, 7, 225, 377, 639, 1588, 10225, 10893, 1128, 3180; -301785, -41739, -1100, 9315, -3597, -7006, -223410, -374154, -634200, -1576091, -10148400, -10811427, -1119559, -3156285],78,13]
%
% END OF LATTICE L79.13
%
%
% LATTICE L79.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-324072540, -1174140, 409860; -1174140, -4254, 1485; 409860, 1485, -514],[1980, 3, 1],[-47, -215, -1, 19, -1, -34, -103, -58, -3250, -1469, -17344, -10079, -5741, -1472; 12921, 59103, 274, -5225, 276, 9350, 28320, 15946, 893508, 403864, 4768280, 2770956, 1578335, 404685; -149, -693, -6, 55, 0, -99, -315, -181, -10197, -4614, -54505, -31680, -18051, -4635],78,14]
%
% END OF LATTICE L79.14
%
%
% LATTICE L79.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-30128340, 29700, 55440; 29700, -22, -55; 55440, -55, -102],[660, 11, 1],[-21, -3, -1, 1, 1, -1, -14, -25, -43, -643, -691, -1473, -229, -216; -535, -77, -30, 25, 28, -24, -350, -632, -1090, -16308, -17530, -37372, -5811, -5485; -11132, -1590, -528, 530, 528, -531, -7425, -13255, -22797, -340890, -366335, -780912, -121404, -114510],78,15]
%
% END OF LATTICE L79.15
%
%
% LATTICE L79.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[232650, -20295, 3960; -20295, 1770, -345; 3960, -345, 67],[495, 15, 1],[1, 17, 2, 5, 5, 1, -1, -1, -17, -2, -5, -5, -1, 1; 8, 198, 26, 66, 66, 11, -15, -19, -561, -103, -429, -594, -616, -18; -20, 0, 15, 44, 45, 0, -18, -40, -1980, -435, -2024, -2925, -3300, -162],78,16]
%
% END OF LATTICE L79.16
%
%
% LATTICE L79.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[42075, 3465, 1485; 3465, 285, 120; 1485, 120, 38],[495, 15, 1],[-14, -20, -6, -40, -4, 1, 1, 5, -13, -15, -257, -44, -166, -4; 186, 264, 79, 528, 53, -11, -13, -63, 187, 208, 3531, 603, 2266, 54; -45, -55, -15, -99, -10, 0, 2, 0, -110, -90, -1386, -230, -825, -17],78,17]
%
% END OF LATTICE L79.17
%
%
% LATTICE L79.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2893042680, -9409620, 718823160; -9409620, 30600, -2337972; 718823160, -2337972, 178603219],[660, 12, 1],[-18608, -346438, -78236, -5539958, -268244, -611003, -156473, -14887, -22007, 81, 13283, 284, -3072, -11002; 39, 715, 161, 11385, 551, 1254, 320, 30, 44, 0, 0, 1, 11, 25; 74892, 1394316, 314878, 22296780, 1079607, 2459116, 629760, 59916, 88572, -326, -53460, -1143, 12364, 44280],78,18]
%
% END OF LATTICE L79.18
%
%
% LATTICE L79.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[546052485, 20870025, -192122700; 20870025, 797610, -7342940; -192122700, -7342940, 67596253],[165, 55, 1],[-155965, -21571, -1705, 963, -1858, -10862, -23092, -193366, -327760, -2443612, -1048956, -5587438, -1735793, -326239; 468199, 64755, 5118, -2891, 5577, 32607, 69321, 580475, 983919, 7335600, 3148913, 16773207, 5210763, 979353; -392425, -54275, -4290, 2423, -4675, -27330, -58102, -486530, -824680, -6148395, -2639288, -14058605, -4367445, -820853],78,19]
%
% END OF LATTICE L79.19
%
%
% LATTICE L79.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-325380, 27060, -5940; 27060, -2250, 495; -5940, 495, -106],[660, 15, 1],[97, 149, 1, -7, 1, 23, 14, 119, 2227, 1007, 7135, 6911, 3937, 202; 1055, 1617, 10, -77, 12, 253, 153, 1297, 24255, 10966, 77693, 75252, 42867, 2199; -525, -825, -10, 33, 0, -110, -72, -630, -11880, -5380, -38148, -36960, -21065, -1083],78,20]
%
% END OF LATTICE L79.20
%
%
% LATTICE L79.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[238448760, -3831300, 59623080; -3831300, 61560, -958000; 59623080, -958000, 14908493],[660, 20, 1],[1502, 3720, 634, 1028, 118, -329, -1, 945, 23197, 16495, 79723, 19458, 134914, 2448; -515, -1287, -225, -385, -48, 66, 0, -322, -7920, -5634, -27236, -6648, -46101, -837; -6040, -14960, -2550, -4136, -475, 1320, 4, -3800, -93280, -66330, -320584, -78245, -542520, -9844],78,21]
%
% END OF LATTICE L79.21
%
%
% LATTICE L79.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2824965, 13365, -6930; 13365, -165, -33; -6930, -33, 17],[495, 33, 1],[-5, -1, -3, -1, 2, 2, 8, 14, 4, 24, 136, 46, 13, 7; -6, 0, 1, 0, -1, -1, -5, -15, -7, -50, -315, -111, -34, -30; -2079, -409, -1221, -405, 814, 813, 3245, 5643, 1597, 9537, 53865, 18194, 5127, 2695],78,22]
%
% END OF LATTICE L79.22
%
%
% LATTICE L79.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-10891485, -1815165, 16830; -1815165, -302511, 2805; 16830, 2805, -26],[495, 33, 1],[16, 10, 5, 2, -1, -1, 1, 11, 71, 184, 403, 1297, 136, 404; -88, -54, -26, -10, 6, 5, -15, -63, -399, -1031, -2255, -7254, -760, -2250; 847, 639, 429, 215, 0, -108, -990, 308, 2826, 7656, 17110, 55440, 5883, 18315],78,23]
%
% END OF LATTICE L79.23
%
%
% LATTICE L79.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1337820, 9900, 13200; 9900, -66, -99; 13200, -99, -130],[660, 33, 1],[-19, -3, -1, 1, 3, 0, -9, -20, -36, -181, -586, -1251, -65, -186; -291, -47, -18, 15, 52, 1, -125, -297, -541, -2726, -8835, -18868, -981, -2815; -1716, -270, -88, 90, 264, -1, -825, -1815, -3261, -16390, -53055, -113256, -5884, -16830],78,24]
%
% END OF LATTICE L79.24
%
%
% LATTICE L79.25
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[20169820440, -42053220, -5052724380; -42053220, 87672, 10534716; -5052724380, 10534716, 1265753641],[1980, 12, 1],[75394, 466076, 315532, 22335472, 360451, 2462573, 210029, 59729, 29375, -245, -40177, -123, 14682, 15176; 369, 2277, 1541, 109065, 1760, 12023, 1025, 291, 143, -1, -165, 0, 77, 75; 300960, 1860496, 1259550, 89159400, 1438859, 9830172, 838400, 238428, 117260, -978, -160380, -491, 58608, 60580],78,25]
%
% END OF LATTICE L79.25
%
%
% LATTICE L79.26
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[4201560, -5835060, -1045440; -5835060, 8557176, 1451340; -1045440, 1451340, 260129],[1980, 12, 1],[-180189, -905903, -12591, 11353, 620, -79460, -318886, -202892, -11735770, -2668976, -63219718, -9194564, -20989995, -5427329; -873, -4389, -61, 55, 3, -385, -1545, -983, -56859, -12931, -306295, -44547, -101695, -26295; -719296, -3616272, -50262, 45320, 2475, -317196, -1272960, -809924, -46847988, -10654278, -252366620, -36703755, -83789904, -21665340],78,26]
%
% END OF LATTICE L79.26
%
%
% LATTICE L79.27
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[29927951295, -4824026625, -1760021835; -4824026625, 777575205, 283694400; -1760021835, 283694400, 103504474],[165, 165, 1],[-277, -95, -73, -1, 164, 48, 98, 160, -22, -200, -350, -2036, -243, -215; -12735, -3769, -2600, -27, 5713, 1624, 3028, 2016, -6950, -22411, -32130, -177217, -19489, -13747; 30195, 8715, 5885, 57, -12870, -3635, -6633, -2805, 18675, 58025, 82113, 451110, 49285, 34023],78,27]
%
% END OF LATTICE L79.27
%
%
% LATTICE L79.28
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[3239526840, -10411500, 804936000; -10411500, 33528, -2586980; 804936000, -2586980, 200005123],[660, 44, 1],[86927, 12697, 4313, 651, 1506, 5698, 59256, 103370, 177600, 1327766, 2853804, 1520870, 945787, 892229; 30, 4, 0, 0, 1, 3, 25, 39, 65, 483, 1035, 551, 342, 320; -349844, -51100, -17358, -2620, -6061, -22932, -238480, -416020, -714764, -5343690, -11485340, -6120851, -3806388, -3590840],78,28]
%
% END OF LATTICE L79.28
%
%
% LATTICE L79.29
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[4773780, -437580, -19800; -437580, 40110, 1815; -19800, 1815, 82],[1980, 15, 1],[-3, -5, 3, 5, 11, 1, -2, -5, -259, -115, -269, -779, -441, -22; -29, -33, 34, 55, 120, 11, -21, -51, -2607, -1154, -2695, -7800, -4411, -219; -85, -495, -30, -11, 0, 0, -18, -80, -4950, -2280, -5434, -15840, -9075, -477],78,29]
%
% END OF LATTICE L79.29
%
%
% LATTICE L79.30
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-9900, -1980, -1980; -1980, -390, -345; -1980, -345, 38],[1980, 15, 1],[-52, -70, -41, -140, -29, -2, 3, 10, -84, -155, -1246, -419, -768, -17; 294, 396, 232, 792, 164, 11, -17, -57, 473, 874, 7029, 2364, 4334, 96; -45, -55, -30, -99, -20, 0, 2, 0, -110, -180, -1386, -460, -825, -17],78,30]
%
% END OF LATTICE L79.30
%
%
% LATTICE L79.31
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1492260, 735900, -7920; 735900, -362890, 3905; -7920, 3905, -42],[660, 55, 1],[-8, 0, 13, 2, 17, 1, -2, -15, -23, -335, -71, -753, -116, -21; -25, -1, 30, 5, 44, 3, -5, -41, -65, -954, -203, -2156, -333, -61; -825, -95, 330, 87, 880, 90, -88, -990, -1720, -25740, -5532, -58960, -9165, -1727],78,31]
%
% END OF LATTICE L79.31
%
%
% LATTICE L79.32
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[5286600, 614460, 1317360; 614460, 72120, 153120; 1317360, 153120, 328271],[660, 60, 1],[-27771, -46265, -609, 525, 41, -4211, -3323, -31455, -605221, -137585, -1954983, -473849, -1081599, -55903; -587, -979, -13, 11, 1, -88, -70, -664, -12782, -2906, -41294, -10009, -22847, -1181; 111720, 186120, 2450, -2112, -165, 16940, 13368, 126540, 2434740, 553490, 7864692, 1906245, 4351160, 224892],78,32]
%
% END OF LATTICE L79.32
%
%
% LATTICE L79.33
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1162260, -211860, 9900; -211860, -37290, 1749; 9900, 1749, -82],[1980, 33, 1],[-19, -1, -1, 1, 1, 0, -3, -20, -12, -181, -586, -417, -65, -62; -885, -47, -50, 45, 48, 1, -135, -921, -555, -8378, -27135, -19312, -3011, -2875; -21186, -1124, -1188, 1080, 1144, 21, -3245, -22077, -13297, -200706, -650025, -462616, -72126, -68860],78,33]
%
% END OF LATTICE L79.33
%
%
% LATTICE L79.34
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-174055860, -7252740, 67320; -7252740, -302214, 2805; 67320, 2805, -26],[1980, 33, 1],[-12, -8, -9, -2, 1, 1, 4, -7, -49, -257, -283, -1825, -96, -289; 296, 198, 224, 50, -24, -25, -105, 171, 1203, 6314, 6955, 44856, 2360, 7110; 847, 639, 858, 215, 0, -108, -990, 308, 2826, 15312, 17110, 110880, 5883, 18315],78,34]
%
% END OF LATTICE L79.34
%
%
% LATTICE L79.35
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-21646350, -6493905, 59400; -6493905, -1948155, 17820; 59400, 17820, -163],[495, 165, 1],[-14, -8, -3, 0, 5, 1, -1, -11, -67, -172, -75, -1205, -126, -74; 11, 9, 7, 1, 6, -1, -3, 3, 33, 91, 41, 666, 71, 45; -3905, -1935, -330, 109, 2475, 255, -693, -3685, -20835, -52800, -22879, -366795, -38205, -22077],78,35]
%
% END OF LATTICE L79.35
%
%
% LATTICE L79.36
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-495, 44055, -495; 44055, -3818265, 42900; -495, 42900, -482],[495, 165, 1],[59, 5, 11, 5, 4, -1, -1, 25, 23, 185, 247, 444, 141, 29; -27, -1, 2, 3, 5, 1, -1, -33, -19, -142, -183, -325, -101, -19; -2475, -95, 165, 261, 440, 90, -88, -2970, -1720, -12870, -16596, -29480, -9165, -1727],78,36]
%
% END OF LATTICE L79.36
%
%
% LATTICE L79.37
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[44311080, -1684980, 11007480; -1684980, 64680, -418572; 11007480, -418572, 2734409],[660, 132, 1],[27119, 3783, 235, 313, 828, 789, 20823, 33907, 57243, 142159, 915077, 487380, 100921, 284307; 30, 4, 0, 0, 1, 1, 25, 39, 65, 161, 1035, 551, 114, 320; -109164, -15228, -946, -1260, -3333, -3176, -83820, -136488, -230424, -572242, -3683520, -1961883, -406244, -1144440],78,37]
%
% END OF LATTICE L79.37
%
%
% LATTICE L79.38
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[660, 0, 0; 0, -235290, 1815; 0, 1815, -14],[660, 165, 1],[-12, -22, -111, -72, -769, -40, -23, -12, -2, -1, 0, 1, 0, -1; -7, -3, -6, -1, 0, 1, 3, 7, 3, 6, 1, 0, -1, -3; -990, -540, -1540, -624, -5280, -145, 231, 825, 375, 770, 129, 0, -130, -396],78,38]
%
% END OF LATTICE L79.38
%
%
% LATTICE L79.39
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-7052760, -104940, 1766160; -104940, 17880, 26400; 1766160, 26400, -442283],[1980, 60, 1],[12691, 91763, 4637, 4883, 124, -9755, -487, 7811, 584803, 138877, 671683, 491924, 1137365, 61993; -315, -2277, -115, -121, -3, 242, 12, -194, -14520, -3448, -16676, -12213, -28237, -1539; 50660, 366300, 18510, 19492, 495, -38940, -1944, 31180, 2334420, 554370, 2681228, 1963665, 4540140, 247464],78,39]
%
% END OF LATTICE L79.39
%
%
% LATTICE L79.40
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[49107960, -2528460, -12272040; -2528460, 130200, 631860; -12272040, 631860, 3066773],[1980, 60, 1],[5276, 4354, 744, 3670, 144, -331, 1, 3337, 27227, 19353, 280559, 22824, 158236, 2870; 255, 209, 35, 165, 6, -22, 0, 162, 1320, 938, 13596, 1106, 7667, 139; 21060, 17380, 2970, 14652, 575, -1320, 4, 13320, 108680, 77250, 1119888, 91105, 631620, 11456],78,40]
%
% END OF LATTICE L79.40
%
%
% LATTICE L79.41
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[64515000, 1024980, -15259860; 1024980, 17160, -241780; -15259860, -241780, 3609943],[660, 220, 1],[18917, 4185, 8119, 1507, 2638, 671, 503, 13395, 28127, 218065, 95429, 255858, 160889, 31809; -57416, -12702, -24642, -4574, -8007, -2037, -1527, -40657, -85371, -661869, -289645, -776577, -488328, -96546; 76120, 16840, 32670, 6064, 10615, 2700, 2024, 53900, 113180, 877470, 383996, 1029545, 647400, 127996],78,41]
%
% END OF LATTICE L79.41
%
%
% LATTICE L79.42
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[22995399240, -64391580, -5760505080; -64391580, 180312, 16130532; -5760505080, 16130532, 1443045995],[1980, 132, 1],[-39385, -1919, -711, -947, -361, -965, -9149, -47123, -26917, -201141, -1296673, -230327, -143215, -135031; -828, -42, -22, -30, -7, -17, -175, -951, -551, -4129, -26655, -4737, -2948, -2790; -157212, -7660, -2838, -3780, -1441, -3852, -36520, -188100, -107444, -802890, -5175900, -919391, -571668, -539000],78,42]
%
% END OF LATTICE L79.42
%
%
% LATTICE L79.43
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1933307640, -28814940, -484268400; -28814940, 435336, 7217760; -484268400, 7217760, 121302931],[1980, 132, 1],[-280318, -144616, -43830, -12876, 620, -1981, -333313, -273385, -1516493, -3832091, -8292669, -13289492, -2766534, -7972232; -1413, -729, -221, -65, 3, -10, -1680, -1378, -7644, -19316, -41800, -66987, -13945, -40185; -1119008, -577296, -174966, -51400, 2475, -7908, -1330560, -1091332, -6053724, -15297414, -33103700, -53050635, -11043792, -31824540],78,43]
%
% END OF LATTICE L79.43
%
%
% LATTICE L79.44
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1950300, 164340, -1980; 164340, 13530, -165; -1980, -165, 2],[1980, 165, 1],[-4, -2, -1, 0, 1, 0, -1, -4, -22, -111, -24, -769, -40, -23; -22, -12, -8, 0, 12, 1, -3, -19, -111, -566, -123, -3948, -206, -120; -5665, -2925, -1650, -1, 1980, 90, -1188, -5390, -30240, -153120, -33164, -1063260, -55365, -31977],78,44]
%
% END OF LATTICE L79.44
%
%
% LATTICE L79.45
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-141718500, 23530320, -261360; 23530320, -3906870, 43395; -261360, 43395, -482],[1980, 165, 1],[16, 2, 13, 4, 9, 0, -1, -4, 2, 43, 32, 119, 20, 5; 69, 11, 82, 27, 64, 1, -7, -57, -7, -26, 9, 64, 19, 11; -2475, -95, 330, 261, 880, 90, -88, -2970, -1720, -25740, -16596, -58960, -9165, -1727],78,45]
%
% END OF LATTICE L79.45
%
%
% LATTICE L79.46
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[9240, -1197900, -297660; -1197900, 155294040, 38588220; -297660, 38588220, 9588589],[660, 660, 1],[-908, -1662, -4192, -5438, -14520, -3021, -1737, -907, -153, -43, -7, 0, -4, -78; 813, 1493, 3767, 4887, 13049, 2715, 1561, 813, 133, 27, -9, -41, -5, 65; -3300, -6060, -15290, -19836, -52965, -11020, -6336, -3300, -540, -110, 36, 165, 20, -264],78,46]
%
% END OF LATTICE L79.46
%
%
% LATTICE L79.47
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1873971000, 3605580, 466731540; 3605580, 6600, 898260; 466731540, 898260, 116244047],[1980, 660, 1],[49876, 20246, -248, -494, -124, 3457, 22717, 62717, 317533, 788399, 338273, 2702356, 559508, 315062; -149751, -60789, 743, 1483, 372, -10379, -68205, -188303, -953373, -2367121, -1015645, -8113668, -1679891, -945957; -199100, -80820, 990, 1972, 495, -13800, -90684, -250360, -1267560, -3147210, -1350352, -10787535, -2233500, -1257696],78,47]
%
% END OF LATTICE L79.47
%
%
% LATTICE L79.48
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[639456840, 10448460, 152343180; 10448460, 244200, 2434080; 152343180, 2434080, 36335383],[1980, 660, 1],[-747461, -56959, -113169, -57959, -30104, -1999, -1499, -475657, -350747, -2740773, -3611395, -3231544, -2036531, -406207; 2239404, 170650, 339056, 173646, 90192, 5989, 4491, 1425075, 1050843, 8211395, 10819791, 9681752, 6101476, 1217002; 2983860, 227380, 451770, 231372, 120175, 7980, 5984, 1898820, 1400180, 10941150, 14416668, 12900305, 8129820, 1621576],78,48]
%
% END OF LATTICE L79.48
%

\medskip%
%------------------------------WEYL-GROUP-W80--------------------------------
%
\leavevmode\llap{}%
$W_{80\phantom{0}}$%
\qquad\llap{88} lattices, $\chi=72$%
\hfill%
$2222222222222222\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L80.1
%
\leavevmode%
${L_{80.1}}$%
{} : {$1\above{1pt}{1pt}{2}{{\rm II}}4\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{-2}{}11\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2\rightarrow N_{80}}%
\EasyButWeakLineBreak%
{${44}\above{1pt}{1pt}{*}{2}{20}\above{1pt}{1pt}{*}{2}{132}\above{1pt}{1pt}{*}{2}{4}\above{1pt}{1pt}{*}{2}{220}\above{1pt}{1pt}{b}{2}{6}\above{1pt}{1pt}{l}{2}{20}\above{1pt}{1pt}{r}{2}{2}\above{1pt}{1pt}{b}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
248820\\0\\-660
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\4\\-1
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-660\\-1\\2
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-551\\-52800\\-204600
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2\\-193\\-744
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\192\\743
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-21\\-2024\\-7810
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-9\\-870\\-3350
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-17\\-1650\\-6336
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-98\\-374
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-29\\-2860\\-10890
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2\\-198\\-753
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-100\\-380
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\-1
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[248820, 0, -660; 0, 4, -1; -660, -1, 2],[660, 1, 1],[-21, -9, -17, -1, -29, -2, -1, 0, -1, -1, -5, -1, -81, -8, -9, -2; -2024, -870, -1650, -98, -2860, -198, -100, 0, -88, -90, -462, -94, -7700, -762, -860, -192; -7810, -3350, -6336, -374, -10890, -753, -380, -1, -374, -370, -1848, -370, -30030, -2967, -3340, -743],79,1]
%
% END OF LATTICE L80.1
%
\hbox{}\par\smallskip%
%
% LATTICE L80.2
%
\leavevmode%
${L_{80.2}}$%
{} : {$1\above{1pt}{1pt}{2}{2}8\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}11\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{2\rightarrow N'_{36}}%
\EasyButWeakLineBreak%
{${88}\above{1pt}{1pt}{r}{2}{10}\above{1pt}{1pt}{b}{2}{66}\above{1pt}{1pt}{s}{2}{2}\above{1pt}{1pt}{b}{2}{440}\above{1pt}{1pt}{*}{2}{12}\above{1pt}{1pt}{s}{2}{40}\above{1pt}{1pt}{l}{2}{1}\above{1pt}{1pt}{}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3198360\\531960\\-2640
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
531960\\88477\\-439
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2640\\-439\\2
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-233531\\1408440\\885720
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-38600\\232799\\146400
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-193\\1164\\731
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1605\\-9680\\-6072
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
514\\-3100\\-1945
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1543\\-9306\\-5841
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
193\\-1164\\-731
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
21303\\-128480\\-80740
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1931\\-11646\\-7320
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1867\\-11260\\-7080
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
161\\-971\\-611
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[3198360, 531960, -2640; 531960, 88477, -439; -2640, -439, 2],[1320, 1, 1],[1605, 514, 1543, 193, 21303, 1931, 1867, 161, 2641, 451, 580, 0, -73, -1, 63, 32; -9680, -3100, -9306, -1164, -128480, -11646, -11260, -971, -15928, -2720, -3498, 0, 440, 6, -380, -193; -6072, -1945, -5841, -731, -80740, -7320, -7080, -611, -10032, -1715, -2211, -1, 220, 0, -240, -121],79,2]
%
% END OF LATTICE L80.2
%
\hbox{}\par\smallskip%
%
% LATTICE L80.3
%
\leavevmode%
${L_{80.3}}$%
{} : {$1\above{1pt}{1pt}{-2}{2}8\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}11\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{m}%
\EasyButWeakLineBreak%
{${88}\above{1pt}{1pt}{b}{2}{10}\above{1pt}{1pt}{s}{2}{66}\above{1pt}{1pt}{b}{2}{2}\above{1pt}{1pt}{l}{2}{440}\above{1pt}{1pt}{}{2}{3}\above{1pt}{1pt}{r}{2}{40}\above{1pt}{1pt}{s}{2}{4}\above{1pt}{1pt}{*}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
86152440\\195360\\0
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
195360\\443\\0
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\-1
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
862069\\-380325000\\-3651120
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1955\\-862501\\-8280
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-102\\45000\\431
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
107\\-47212\\-572
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
37\\-16325\\-185
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
119\\-52503\\-561
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
16\\-7059\\-71
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1869\\-824560\\-7920
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
86\\-37941\\-360
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
171\\-75440\\-700
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
31\\-13676\\-122
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[86152440, 195360, 0; 195360, 443, 0; 0, 0, -1],[1320, 1, 1],[107, 37, 119, 16, 1869, 86, 171, 31, 267, 48, 68, 1, 1, -1, -1, 3; -47212, -16325, -52503, -7059, -824560, -37941, -75440, -13676, -117788, -21175, -29997, -441, -440, 441, 440, -1324; -572, -185, -561, -71, -7920, -360, -700, -122, -1012, -175, -231, -1, 0, 0, -20, -22],79,3]
%
% END OF LATTICE L80.3
%
%
% LATTICE L80.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-1155, -495, 495; -495, -211, 198; 495, 198, -37],[165, 1, 1],[-52, -2, 455, 158, 16688, 3433, 2057, 997, 5618, 2532, 5111, 348, 11142, 1627, 473, 15; 132, 5, -1155, -401, -42350, -8712, -5220, -2530, -14256, -6425, -12969, -883, -28270, -4128, -1200, -38; 11, 0, -99, -34, -3575, -735, -440, -213, -1199, -540, -1089, -74, -2365, -345, -100, -3],79,4]
%
% END OF LATTICE L80.4
%
%
% LATTICE L80.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[37290, 1650, 990; 1650, 73, 44; 990, 44, 23],[330, 1, 1],[1, -3, -17, -3, -183, -17, -17, -3, -23, -7, -5, 1, 73, 7, 7, 1; -22, 65, 363, 63, 3740, 345, 340, 58, 418, 115, 33, -27, -1760, -165, -160, -22; 0, 5, 33, 7, 550, 54, 60, 13, 132, 55, 99, 5, 110, 6, 0, -1],79,5]
%
% END OF LATTICE L80.5
%
%
% LATTICE L80.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[292380, 97020, -660; 97020, 32194, -219; -660, -219, 1],[660, 1, 1],[2641, 451, 580, 0, -73, -1, 63, 64, 1605, 514, 1543, 193, 21303, 1931, 1867, 322; -7964, -1360, -1749, 0, 220, 3, -190, -193, -4840, -1550, -4653, -582, -64240, -5823, -5630, -971; -1012, -175, -231, -1, 0, 0, -20, -22, -572, -185, -561, -71, -7920, -720, -700, -122],79,6]
%
% END OF LATTICE L80.6
%
%
% LATTICE L80.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1248060, 8745, -414645; 8745, -51, 2904; -414645, 2904, -137758],[165, 3, 1],[-4198, -3071, -3451, -1457, -88116, -5454, -8264, -3080, -13622, -5029, -2489, -163, -984, 54, 164, -160; 1705, 1245, 1397, 589, 35585, 2202, 3335, 1242, 5489, 2025, 1001, 65, 385, -22, -65, 66; 12672, 9270, 10417, 4398, 265980, 16463, 24945, 9297, 41118, 15180, 7513, 492, 2970, -163, -495, 483],79,7]
%
% END OF LATTICE L80.7
%
%
% LATTICE L80.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[441870, -18480, 220440; -18480, 742, -9218; 220440, -9218, 109973],[330, 2, 1],[-257, -169, 1247, 529, 28958, 5984, 3607, 1759, 9937, 8969, 18113, 1231, 19442, 2816, 793, 1; 22, 15, -99, -43, -2365, -489, -295, -144, -814, -735, -1485, -101, -1595, -231, -65, 0; 517, 340, -2508, -1064, -58245, -12036, -7255, -3538, -19987, -18040, -36432, -2476, -39105, -5664, -1595, -2],79,8]
%
% END OF LATTICE L80.8
%
%
% LATTICE L80.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1787280, 13365, -713625; 13365, -85, 5335; -713625, 5335, -284936],[165, 5, 1],[-7278, -1065, -17954, -2527, -30568, -28381, -2867, -5343, -23632, -1745, -12956, -283, -342, 281, 57, -277; 1705, 249, 4191, 589, 7117, 6606, 667, 1242, 5489, 405, 3003, 65, 77, -66, -13, 66; 18260, 2672, 45045, 6340, 76692, 71205, 7193, 13405, 59290, 4378, 32505, 710, 858, -705, -143, 695],79,9]
%
% END OF LATTICE L80.9
%
%
% LATTICE L80.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[508530, -24090, -169950; -24090, 1113, 8052; -169950, 8052, 56797],[330, 3, 1],[355, 116, -292, -370, -40479, -1394, -5041, -1229, -13885, -6266, -4218, -860, -27171, -656, -1109, -1; 44, 15, -33, -43, -4730, -163, -590, -144, -1628, -735, -495, -101, -3190, -77, -130, 0; 1056, 345, -869, -1101, -120450, -4148, -15000, -3657, -41316, -18645, -12551, -2559, -80850, -1952, -3300, -3],79,10]
%
% END OF LATTICE L80.10
%
%
% LATTICE L80.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[663630, -35310, 132330; -35310, 1855, -7040; 132330, -7040, 26387],[330, 5, 1],[-217, -14, 554, 232, 5069, 2618, 631, 769, 8687, 784, 7916, 538, 3401, 1232, 139, 1; 44, 3, -99, -43, -946, -489, -118, -144, -1628, -147, -1485, -101, -638, -231, -26, 0; 1100, 71, -2805, -1175, -25674, -13260, -3196, -3895, -44000, -3971, -40095, -2725, -17226, -6240, -704, -5],79,11]
%
% END OF LATTICE L80.11
%
%
% LATTICE L80.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3436620, 27225, -936045; 27225, -187, 7414; -936045, 7414, -254954],[165, 11, 1],[-866, -6971, -2137, -3309, -18196, -37168, -18774, -6998, -2814, -11429, -1543, -371, -204, 368, 374, -362; 155, 1245, 381, 589, 3235, 6606, 3335, 1242, 499, 2025, 273, 65, 35, -66, -65, 66; 3184, 25630, 7857, 12166, 66900, 136653, 69025, 25729, 10346, 42020, 5673, 1364, 750, -1353, -1375, 1331],79,12]
%
% END OF LATTICE L80.12
%
%
% LATTICE L80.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[640860, -2640, -2640; -2640, 12, 9; -2640, 9, 14],[660, 3, 1],[-61, -29, -21, -5, -189, -5, -11, -1, -5, -1, -1, -1, -141, -5, -19, -5; -9284, -4410, -3190, -758, -28600, -756, -1660, -150, -748, -150, -154, -154, -21560, -764, -2900, -762; -5610, -2670, -1936, -462, -17490, -463, -1020, -93, -462, -90, -88, -90, -12870, -457, -1740, -459],79,13]
%
% END OF LATTICE L80.13
%
%
% LATTICE L80.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[84670410, -192720, 41552280; -192720, 438, -94578; 41552280, -94578, 20391917],[330, 6, 1],[-81, 751, 1501, 857, 29398, 1872, 2967, 1175, 5361, 4049, 2019, 103, -2998, -272, -567, -215; -11, 65, 121, 63, 1870, 115, 170, 58, 209, 115, 11, -27, -880, -55, -80, -22; 165, -1530, -3058, -1746, -59895, -3814, -6045, -2394, -10923, -8250, -4114, -210, 6105, 554, 1155, 438],79,14]
%
% END OF LATTICE L80.14
%
%
% LATTICE L80.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[119460, 47520, -1320; 47520, 18903, -525; -1320, -525, 14],[660, 3, 1],[761, 167, 108, 20, 1119, 25, 31, -4, -35, -2, 13, 13, 2511, 85, 299, 70; -1936, -425, -275, -51, -2860, -64, -80, 10, 88, 5, -33, -33, -6380, -216, -760, -178; -924, -210, -143, -30, -1980, -49, -90, -3, 0, 0, -11, -12, -2640, -91, -330, -81],79,15]
%
% END OF LATTICE L80.15
%
%
% LATTICE L80.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1416286410, -5400120, 468186345; -5400120, 20595, -1785135; 468186345, -1785135, 154769863],[165, 15, 1],[131781, 18106, 96963, 39208, 461255, 141761, 42444, 77573, 337743, 24578, 59545, 3476, 8269, 519, 240, 7795; 341, 46, 242, 96, 1111, 340, 101, 182, 781, 56, 132, 6, 11, 0, 1, 22; -398640, -54771, -293315, -118605, -1395306, -428830, -128394, -234660, -1021680, -74349, -180125, -10515, -25014, -1570, -726, -23580],79,16]
%
% END OF LATTICE L80.16
%
%
% LATTICE L80.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[42278280, -192060, 10569240; -192060, 868, -48012; 10569240, -48012, 2642227],[660, 4, 1],[-10958, -7877, -11152, -163, -41, 325, 77, -497, -4409, -6093, -19582, -2631, -76794, -28265, -14047, -5091; 14608, 10505, 14883, 219, 55, -438, -110, 656, 5852, 8095, 26037, 3501, 102245, 37638, 18710, 6784; 44099, 31700, 44880, 656, 165, -1308, -310, 2000, 17743, 24520, 78804, 10588, 309045, 113748, 56530, 20488],79,17]
%
% END OF LATTICE L80.17
%
%
% LATTICE L80.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-160754880, 246180, -39942540; 246180, -376, 61168; -39942540, 61168, -9924467],[660, 4, 1],[8642, 3471, 5887, 241, 3416, 152, -123, -162, 246, 569, 3001, 567, 41024, 7928, 2143, 1778; -143, -65, -132, -9, -275, -39, -5, 1, 11, 5, 0, -3, -385, -81, -25, -25; -34782, -13970, -23694, -970, -13750, -612, 495, 652, -990, -2290, -12078, -2282, -165110, -31908, -8625, -7156],79,18]
%
% END OF LATTICE L80.18
%
%
% LATTICE L80.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1848660, 614460, 5940; 614460, -204230, -1975; 5940, -1975, -19],[660, 5, 1],[837, 33, 272, 10, 47, 1, -5, -6, 65, 8, 179, 31, 855, 409, 87, 88; 2332, 92, 759, 28, 132, 3, -14, -17, 176, 22, 495, 86, 2376, 1137, 242, 245; 19140, 749, 6105, 215, 968, 0, -108, -110, 1980, 211, 4455, 745, 20152, 9600, 2028, 2030],79,19]
%
% END OF LATTICE L80.19
%
%
% LATTICE L80.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-15055260, 19800, -6615840; 19800, -20, 8965; -6615840, 8965, -2895694],[660, 5, 1],[-49581, -3751, -29027, -815, -1629, 82, 163, -82, -11425, -1795, -31979, -4731, -59377, -27812, -5709, -5464; -4363436, -330110, -2554530, -71722, -143352, 7218, 14344, -7220, -1005532, -157978, -2814438, -416366, -5225616, -2447658, -502432, -480868; 99770, 7548, 58410, 1640, 3278, -165, -328, 165, 22990, 3612, 64350, 9520, 119482, 55965, 11488, 10995],79,20]
%
% END OF LATTICE L80.20
%
%
% LATTICE L80.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1011724230, -860640, 503663820; -860640, 730, -428450; 503663820, -428450, 250737539],[330, 10, 1],[-575, 919, 27107, 5053, 33640, 31916, 3329, 6427, 28339, 4129, 28421, -5, -5876, -6676, -805, -1379; -11, 13, 363, 63, 374, 345, 34, 58, 209, 23, 33, -27, -176, -165, -16, -22; 1155, -1846, -54450, -10150, -67573, -64110, -6687, -12910, -56925, -8294, -57090, 10, 11803, 13410, 1617, 2770],79,21]
%
% END OF LATTICE L80.21
%
%
% LATTICE L80.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1160610, -68970, -422400; -68970, 4081, 25102; -422400, 25102, 153731],[330, 11, 1],[41, 141, -113, -511, -5059, -5746, -6921, -1686, -1731, -8591, -1577, -1179, -3391, -2704, -1529, -4; 4, 15, -9, -43, -430, -489, -590, -144, -148, -735, -135, -101, -290, -231, -130, 0; 112, 385, -309, -1397, -13830, -15708, -18920, -4609, -4732, -23485, -4311, -3223, -9270, -7392, -4180, -11],79,22]
%
% END OF LATTICE L80.22
%
%
% LATTICE L80.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[238920, 95040, -1320; 95040, 37806, -525; -1320, -525, 7],[1320, 3, 1],[761, 167, 108, 20, 1119, 25, 31, -2, -35, -2, 13, 13, 2511, 85, 299, 35; -1936, -425, -275, -51, -2860, -64, -80, 5, 88, 5, -33, -33, -6380, -216, -760, -89; -1848, -420, -286, -60, -3960, -98, -180, -3, 0, 0, -22, -24, -5280, -182, -660, -81],79,23]
%
% END OF LATTICE L80.23
%
%
% LATTICE L80.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-4584189720, 26192760, -233640; 26192760, -149658, 1335; -233640, 1335, -11],[1320, 3, 1],[-783, -224, -196, -61, -5453, -77, -387, -47, -207, -1, 31, 16, 503, 2, -63, -43; -136972, -39185, -34287, -10671, -953920, -13470, -67700, -8222, -36212, -175, 5423, 2799, 88000, 350, -11020, -7522; 7392, 2100, 1826, 564, 50160, 707, 3540, 426, 1848, 0, -286, -144, -3960, -7, 660, 414],79,24]
%
% END OF LATTICE L80.24
%
%
% LATTICE L80.25
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[878842470, -982410, -294620370; -982410, 1095, 329340; -294620370, 329340, 98767601],[330, 15, 1],[885, -707, -6951, -3887, -51751, -8183, -5121, -4943, -43587, -3175, -7283, 5, 9049, 1713, 1239, 1061; -22, 13, 121, 63, 748, 115, 68, 58, 418, 23, 11, -27, -352, -55, -32, -22; 2640, -2109, -20735, -11595, -154374, -24410, -15276, -14745, -130020, -9471, -21725, 15, 26994, 5110, 3696, 3165],79,25]
%
% END OF LATTICE L80.25
%
%
% LATTICE L80.26
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1625030385, -8579505, 536253465; -8579505, 45309, -2831202; 536253465, -2831202, 176961478],[165, 33, 1],[20682, 156053, 15173, 67387, 359888, 243256, 363942, 132890, 52542, 210067, 9235, 5837, 6232, 824, 2178, 13558; 31, 230, 22, 96, 505, 340, 505, 182, 71, 280, 12, 6, 5, 0, 5, 22; -62673, -472890, -45979, -204204, -1090575, -737143, -1102860, -402699, -159219, -636570, -27985, -17688, -18885, -2497, -6600, -41085],79,26]
%
% END OF LATTICE L80.26
%
%
% LATTICE L80.27
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-35931720, 5983560, 36960; 5983560, -996415, -6155; 36960, -6155, -38],[1320, 5, 1],[837, 33, 272, 10, 47, 1, -5, -3, 65, 8, 179, 31, 855, 409, 87, 44; 4664, 184, 1518, 56, 264, 6, -28, -17, 352, 44, 990, 172, 4752, 2274, 484, 245; 58520, 2289, 18645, 655, 2948, 0, -328, -165, 6160, 651, 13695, 2285, 61732, 29400, 6208, 3105],79,27]
%
% END OF LATTICE L80.27
%
%
% LATTICE L80.28
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-4672378920, 53705520, -497640; 53705520, -617305, 5720; -497640, 5720, -53],[1320, 5, 1],[487, 18, 134, 3, 9, -1, -1, 3, 151, 11, 185, 26, 629, 146, 59, 55; 42548, 1573, 11715, 263, 792, -87, -88, 260, 13156, 959, 16137, 2269, 54912, 12747, 5152, 4804; 19140, 749, 6105, 215, 968, 0, -108, -110, 1980, 211, 4455, 745, 20152, 4800, 2028, 2030],79,28]
%
% END OF LATTICE L80.28
%
%
% LATTICE L80.29
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-94380, -660, -1320; -660, 11, 0; -1320, 0, -13],[660, 11, 1],[9, 17, 2, 0, -1, -1, 1, 2, 5, 18, 5, 7, 71, 71, 69, 12; 544, 1025, 120, -1, -60, -57, 70, 125, 308, 1105, 306, 427, 4320, 4317, 4190, 727; -932, -1760, -207, 0, 100, 99, -110, -209, -520, -1870, -519, -726, -7360, -7359, -7150, -1243],79,29]
%
% END OF LATTICE L80.29
%
%
% LATTICE L80.30
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[21991530, -188760, 10747110; -188760, 1606, -92246; 10747110, -92246, 5252039],[330, 22, 1],[-22, 1667, 877, 1753, 5101, 10550, 5404, 2011, 764, 5753, 607, -269, -1391, -3130, -1694, -527; -1, 65, 33, 63, 170, 345, 170, 58, 19, 115, 3, -27, -80, -165, -80, -22; 45, -3410, -1794, -3586, -10435, -21582, -11055, -4114, -1563, -11770, -1242, 550, 2845, 6402, 3465, 1078],79,30]
%
% END OF LATTICE L80.30
%
%
% LATTICE L80.31
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[677820, -5940, -3300; -5940, 44, 33; -3300, 33, 14],[660, 11, 1],[9, 51, 11, 11, 41, 37, 29, 3, 1, -1, -1, -1, 9, 13, 21, 7; 496, 2810, 606, 606, 2260, 2040, 1600, 166, 56, -50, -54, -54, 500, 720, 1160, 386; 950, 5390, 1164, 1166, 4350, 3927, 3080, 319, 106, -110, -108, -110, 930, 1353, 2200, 737],79,31]
%
% END OF LATTICE L80.31
%
%
% LATTICE L80.32
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-36231360, 1149060, -9000420; 1149060, -36408, 285444; -9000420, 285444, -2235841],[660, 12, 1],[-27762, -12947, -9079, -2005, -67312, -3358, -1554, -152, 1230, 887, 235, -407, -65348, -4682, -4476, -4672; -143, -65, -44, -9, -275, -13, -5, 1, 11, 5, 0, -3, -385, -27, -25, -25; 111738, 52110, 36542, 8070, 270930, 13516, 6255, 612, -4950, -3570, -946, 1638, 263010, 18844, 18015, 18804],79,32]
%
% END OF LATTICE L80.32
%
%
% LATTICE L80.33
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[11298540, -120780, 2823480; -120780, 1272, -30180; 2823480, -30180, 705581],[660, 12, 1],[-7813, -7453, -5389, -1267, -22914, -2374, -2452, -316, -41, 313, 153, -161, -16356, -2386, -4688, -2540; 4301, 4105, 2970, 699, 12650, 1311, 1355, 175, 22, -175, -88, 87, 8965, 1309, 2575, 1397; 31449, 30000, 21692, 5100, 92235, 9556, 9870, 1272, 165, -1260, -616, 648, 65835, 9604, 18870, 10224],79,33]
%
% END OF LATTICE L80.33
%
%
% LATTICE L80.34
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1714231860, 11376090, -667726785; 11376090, 75515, -4431185; -667726785, -4431185, 260092651],[165, 55, 1],[-32377, -48859, -71258, -105491, -112677, -1142411, -113946, -208031, -82251, -65769, -43370, -9137, -1951, -3869, -682, -21225; 97162, 146623, 213840, 316569, 338132, 3428253, 341939, 624275, 246824, 197363, 130146, 27417, 5854, 11607, 2047, 63697; -81465, -122936, -179295, -265430, -283511, -2874465, -286704, -523435, -206955, -165484, -109125, -22990, -4909, -9735, -1716, -53405],79,34]
%
% END OF LATTICE L80.34
%
%
% LATTICE L80.35
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-8156940, -127380, 25080; -127380, -1965, 390; 25080, 390, -77],[660, 15, 1],[179, 7, 19, 2, 9, 0, -1, -1, 19, 2, 14, 7, 189, 30, 19, 19; 5720, 225, 616, 67, 308, 1, -34, -39, 484, 57, 418, 215, 5896, 939, 598, 603; 87120, 3414, 9295, 990, 4488, 5, -498, -525, 8580, 936, 6655, 3360, 91212, 14495, 9198, 9225],79,35]
%
% END OF LATTICE L80.35
%
%
% LATTICE L80.36
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-8548980, 423060, 79200; 423060, -20730, -3885; 79200, -3885, -728],[660, 15, 1],[949, 61, 115, -7, 9, 6, 13, 40, 833, 101, 479, 169, 1773, 264, 149, 122; -157278, -10112, -19074, 1156, -1474, -989, -2148, -6617, -137874, -16720, -79310, -27988, -293678, -43731, -24684, -20215; 942480, 60594, 114290, -6930, 8844, 5930, 12876, 39660, 826320, 100206, 475310, 167730, 1759956, 262070, 147924, 121140],79,36]
%
% END OF LATTICE L80.36
%
%
% LATTICE L80.37
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[3341101170, 6136680, 1639827420; 6136680, 11130, 3011910; 1639827420, 3011910, 804834643],[330, 30, 1],[46727, 6031, -79471, -99859, -1090950, -375632, -135805, -331013, -1869647, -337471, -1135809, -231581, -731970, -176768, -29915, -427; 22, 3, -33, -43, -473, -163, -59, -144, -814, -147, -495, -101, -319, -77, -13, 0; -95205, -12288, 161920, 203460, 2222781, 765340, 276699, 674430, 3809355, 687588, 2314180, 471840, 1491369, 360160, 60951, 870],79,37]
%
% END OF LATTICE L80.37
%
%
% LATTICE L80.38
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[361680, -3960, 1320; -3960, 8, 24; 1320, 24, -37],[1320, 8, 1],[1, -1, -13, -3, -113, -22, -12, -5, -12, -19, -31, -1, 3, 2, 2, 1; 132, -130, -1716, -398, -15070, -2937, -1605, -671, -1617, -2570, -4224, -142, 220, 237, 255, 131; 121, -120, -1584, -368, -13970, -2724, -1490, -624, -1507, -2400, -3960, -136, 110, 204, 230, 120],79,38]
%
% END OF LATTICE L80.38
%
%
% LATTICE L80.39
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-905520, 9240, 2640; 9240, 88, 8; 2640, 8, -1],[1320, 8, 1],[1, 1, -1, -1, -31, -13, -8, -4, -23, -21, -43, -3, -24, -7, -2, 0; -198, -200, 198, 200, 6215, 2607, 1605, 803, 4620, 4220, 8646, 604, 4840, 1413, 405, 1; 1034, 1040, -1056, -1048, -32505, -13632, -8390, -4196, -24134, -22040, -45144, -3152, -25245, -7368, -2110, -4],79,39]
%
% END OF LATTICE L80.39
%
%
% LATTICE L80.40
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1959870, 68970, -592680; 68970, 2409, -20856; -592680, -20856, 179231],[330, 33, 1],[-9, 347, 61, 367, 2147, 741, 2283, 427, 327, 1243, 45, -49, -557, -211, -693, -109; -2, 65, 11, 63, 340, 115, 340, 58, 38, 115, 1, -27, -160, -55, -160, -22; -30, 1155, 203, 1221, 7140, 2464, 7590, 1419, 1086, 4125, 149, -165, -1860, -704, -2310, -363],79,40]
%
% END OF LATTICE L80.40
%
%
% LATTICE L80.41
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[202140840, -984060, 50158680; -984060, 4820, -244180; 50158680, -244180, 12446239],[660, 20, 1],[43880, 6471, 48212, 1133, 1741, 1297, 81, 1779, 15729, 4367, 71006, 9705, 57868, 107083, 10757, 19897; 11858, 1749, 13035, 307, 473, 354, 22, 480, 4246, 1179, 19173, 2621, 15631, 28926, 2906, 5376; -176605, -26044, -194040, -4560, -7007, -5220, -326, -7160, -63305, -17576, -285780, -39060, -232903, -430980, -43294, -80080],79,41]
%
% END OF LATTICE L80.41
%
%
% LATTICE L80.42
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[26788539360, 11881831500, 6683550060; 11881831500, 5270086520, 2964432460; 6683550060, 2964432460, 1667498209],[660, 20, 1],[1255798, 91373, 663281, 12655, 25392, 328, 123, 27442, 481410, 66555, 1073927, 145273, 1711816, 1578952, 78841, 288414; 297, 22, 165, 4, 11, 3, 0, 5, 99, 14, 231, 32, 385, 357, 18, 67; -5033930, -366274, -2658810, -50730, -101794, -1320, -493, -110000, -1929730, -266786, -4304850, -582330, -6861866, -6329280, -316037, -1156120],79,42]
%
% END OF LATTICE L80.42
%
%
% LATTICE L80.43
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-267960, 0, -1320; 0, 22, 11; -1320, 11, -1],[1320, 11, 1],[5, 18, 5, 7, 71, 71, 69, 6, 9, 17, 2, 0, -1, -1, 1, 1; 528, 1895, 525, 733, 7420, 7416, 7200, 625, 936, 1765, 207, -1, -100, -96, 120, 107; -1040, -3740, -1038, -1452, -14720, -14718, -14300, -1243, -1864, -3520, -414, 0, 200, 198, -220, -209],79,43]
%
% END OF LATTICE L80.43
%
%
% LATTICE L80.44
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[649884840, -16663680, -137280; -16663680, 427273, 3520; -137280, 3520, 29],[1320, 11, 1],[39, 142, 40, 57, 589, 296, 581, 103, 79, 153, 19, 2, 1, -1, 9, 15; 1548, 5635, 1587, 2261, 23360, 11739, 23040, 4084, 3132, 6065, 753, 79, 40, -39, 360, 596; -3292, -11825, -3291, -4631, -47400, -23760, -46420, -8162, -6212, -11935, -1461, -121, -120, 0, -1100, -1342],79,44]
%
% END OF LATTICE L80.44
%
%
% LATTICE L80.45
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[84365490, 584430, 17181120; 584430, 4015, 119020; 17181120, 119020, 3498953],[330, 55, 1],[55, -419, -1103, -2207, -2573, -13309, -2729, -2543, -1937, -1463, -779, 325, 691, 3899, 847, 661; -2, 13, 33, 63, 68, 345, 68, 58, 38, 23, 3, -27, -32, -165, -32, -22; -270, 2057, 5415, 10835, 12632, 65340, 13398, 12485, 9510, 7183, 3825, -1595, -3392, -19140, -4158, -3245],79,45]
%
% END OF LATTICE L80.45
%
%
% LATTICE L80.46
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-16313880, -8660520, 50160; -8660520, -4597545, 26625; 50160, 26625, -154],[1320, 15, 1],[-465, -55, -404, -208, -5707, -909, -579, -292, -5541, -218, -597, -65, -299, -1, 33, 19; 968, 114, 836, 430, 11792, 1878, 1196, 603, 11440, 450, 1232, 134, 616, 2, -68, -39; 15840, 1791, 12925, 6585, 179652, 28580, 18168, 9135, 172920, 6789, 18535, 1995, 9108, 20, -1008, -555],79,46]
%
% END OF LATTICE L80.46
%
%
% LATTICE L80.47
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1851960, 85800, 17160; 85800, -3795, -765; 17160, -765, -154],[1320, 15, 1],[371, 22, 102, 35, 717, 53, 59, 47, 355, 11, 19, -2, 9, 2, 7, 19; -40744, -2418, -11220, -3854, -79024, -5843, -6508, -5190, -39248, -1218, -2112, 218, -968, -217, -764, -2082; 243540, 14451, 67045, 23025, 472032, 34900, 38868, 30990, 234300, 7269, 12595, -1305, 5808, 1300, 4572, 12450],79,47]
%
% END OF LATTICE L80.47
%
%
% LATTICE L80.48
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[4594260, -34320, -12540; -34320, 132, 99; -12540, 99, 34],[660, 33, 1],[5, -1, -1, -1, 69, 30, 131, 40, 49, 271, 19, 55, 201, 60, 139, 14; 72, -10, -14, -14, 980, 426, 1860, 568, 696, 3850, 270, 782, 2860, 854, 1980, 200; 1638, -330, -328, -330, 22590, 9823, 42900, 13101, 16050, 88770, 6224, 18018, 65850, 19657, 45540, 4587],79,48]
%
% END OF LATTICE L80.48
%
%
% LATTICE L80.49
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[28331490, -834900, 13950750; -834900, 24486, -411114; 13950750, -411114, 6869509],[330, 66, 1],[-353, -2437, 643, 8741, 43284, 32776, 59221, 28855, 14813, 147037, 8997, 20179, 29016, 15424, 13079, 65; 2, 15, -3, -43, -215, -163, -295, -144, -74, -735, -45, -101, -145, -77, -65, 0; 717, 4950, -1306, -17754, -87915, -66572, -120285, -58608, -30087, -298650, -18274, -40986, -58935, -31328, -26565, -132],79,49]
%
% END OF LATTICE L80.49
%
%
% LATTICE L80.50
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-660, 0, 0; 0, 33, 33; 0, 33, 34],[660, 33, 1],[1, 1, 0, 0, 7, 3, 13, 4, 5, 14, 1, 3, 23, 7, 17, 2; 16, 5, -1, -1, 180, 78, 340, 104, 128, 355, 25, 73, 540, 162, 380, 40; -12, 0, 1, 0, -180, -77, -330, -99, -120, -330, -23, -66, -480, -143, -330, -33],79,50]
%
% END OF LATTICE L80.50
%
%
% LATTICE L80.51
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-49489624635, 7979956545, 2911482585; 7979956545, -1286728410, -469462125; 2911482585, -469462125, -171282988],[165, 165, 1],[155, 249, 127, 589, 647, 2202, 667, 1242, 499, 405, 91, 65, 7, -22, -13, 66; 78614, 126592, 64691, 300560, 330594, 1125513, 341125, 635831, 255700, 207722, 46747, 33754, 3720, -11133, -6811, 32797; -212835, -342738, -175150, -813780, -895113, -3047440, -923637, -1721610, -692355, -562452, -126580, -91410, -10077, 30140, 18447, -88770],79,51]
%
% END OF LATTICE L80.51
%
%
% LATTICE L80.52
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[23883420, 905520, 5936040; 905520, 34364, 225060; 5936040, 225060, 1475357],[660, 44, 1],[-1412, -10936, -1363, -164, -128, -361, -629, -1225, -737, -10554, -2935, -4134, -10617, -42619, -20861, -7371; 1, 5, 0, -1, 0, 3, 5, 5, 2, 25, 6, 7, 15, 57, 25, 7; 5681, 44000, 5484, 660, 515, 1452, 2530, 4928, 2965, 42460, 11808, 16632, 42715, 171468, 83930, 29656],79,52]
%
% END OF LATTICE L80.52
%
%
% LATTICE L80.53
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[75907920, -2663100, 18857520; -2663100, 93368, -661584; 18857520, -661584, 4684703],[660, 44, 1],[-2362, -11179, -1883, -1077, -1484, -854, 642, 1268, 558, 2159, 79, -727, -7536, -17186, -5152, -4876; -13, -65, -12, -9, -25, -39, -5, 1, 1, 5, 0, -3, -35, -81, -25, -25; 9506, 44990, 7578, 4334, 5970, 3432, -2585, -5104, -2246, -8690, -318, 2926, 30330, 69168, 20735, 19624],79,53]
%
% END OF LATTICE L80.53
%
%
% LATTICE L80.54
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-868560, 43560, -5280; 43560, -2184, 264; -5280, 264, -31],[1320, 24, 1],[2, -1, -5, -3, -83, -5, -7, -2, -2, 1, 5, 3, 83, 5, 7, 2; 44, -20, -110, -68, -1980, -121, -175, -55, -77, -40, 66, 56, 1650, 101, 145, 43; 33, 0, -88, -72, -2970, -196, -330, -144, -363, -600, -352, -48, -330, -4, 30, 24],79,54]
%
% END OF LATTICE L80.54
%
%
% LATTICE L80.55
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[240240, 17160, -5280; 17160, 744, -240; -5280, -240, 77],[1320, 24, 1],[3, 1, -1, -1, -16, -2, -3, -1, -3, -1, 1, 1, 16, 2, 3, 1; 506, 170, -176, -178, -2970, -375, -575, -203, -704, -350, 44, 142, 2475, 315, 485, 167; 1782, 600, -616, -624, -10395, -1312, -2010, -708, -2442, -1200, 176, 504, 8745, 1112, 1710, 588],79,55]
%
% END OF LATTICE L80.55
%
%
% LATTICE L80.56
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[613140, 199320, -6600; 199320, 64790, -2145; -6600, -2145, 71],[660, 55, 1],[-11, -5, -4, -2, -1, -1, 1, 2, 1, 0, -1, -3, -9, -49, -11, -12; 12, 8, 9, 8, 4, 3, -6, -17, -24, -14, -15, -14, -16, -63, -6, 5; -680, -231, -105, 55, 28, 0, -88, -330, -640, -429, -555, -715, -1348, -6600, -1232, -990],79,56]
%
% END OF LATTICE L80.56
%
%
% LATTICE L80.57
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[759660, 249480, 5280; 249480, 81620, 1705; 5280, 1705, 34],[660, 55, 1],[-561, -441, -281, -41, -1, 35, -1, -81, -241, -361, -521, -761, -801, -4045, -801, -721; 2216, 1742, 1110, 162, 4, -138, 4, 320, 952, 1426, 2058, 3006, 3164, 15978, 3164, 2848; -24010, -18876, -12030, -1760, -46, 1485, -44, -3465, -10310, -15444, -22290, -32560, -34274, -173085, -34276, -30855],79,57]
%
% END OF LATTICE L80.57
%
%
% LATTICE L80.58
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[16822458510, -26259420, 8375008290; -26259420, 40810, -13073170; 8375008290, -13073170, 4169471651],[330, 110, 1],[-10751, -14797, 59189, 267737, 265078, 3010768, 362647, 883439, 453511, 900317, 826331, 617783, 177682, 1416832, 80113, 2081; 2, 3, -9, -43, -43, -489, -59, -144, -74, -147, -135, -101, -29, -231, -13, 0; 21595, 29722, -118890, -537790, -532449, -6047580, -728431, -1774520, -910945, -1808422, -1659810, -1240910, -356901, -2845920, -160919, -4180],79,58]
%
% END OF LATTICE L80.58
%
%
% LATTICE L80.59
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2135342220, -13375560, 530574000; -13375560, 83820, -3323460; 530574000, -3323460, 131833093],[660, 60, 1],[229131, 33352, 80791, 4696, 5305, 487, 243, 10361, 88758, 24446, 131135, 53102, 312584, 192173, 57555, 105235; -1067, -155, -374, -21, -22, -1, -1, -49, -418, -115, -616, -249, -1463, -899, -269, -491; -922185, -134232, -325160, -18900, -21351, -1960, -978, -41700, -357225, -98388, -527780, -213720, -1258059, -773440, -231642, -423540],79,59]
%
% END OF LATTICE L80.59
%
%
% LATTICE L80.60
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[19197859560, 292381980, 4770259560; 292381980, 4452960, 72650700; 4770259560, 72650700, 1185307987],[660, 60, 1],[789395, 50946, 97093, -5284, 10313, 10563, 5404, 65823, 685441, 83130, 394519, 139360, 1464523, 436357, 61634, 202329; 10736, 691, 1309, -75, 154, 152, 76, 914, 9460, 1145, 5423, 1911, 20042, 5968, 842, 2758; -3177570, -205074, -390830, 21270, -41514, -42520, -21753, -264960, -2759130, -334626, -1588070, -560970, -5895186, -1756480, -248097, -814440],79,60]
%
% END OF LATTICE L80.60
%
%
% LATTICE L80.61
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1320, 0, -1320; 0, 66, 297; -1320, 297, 17],[1320, 33, 1],[211, 584, 41, 119, 873, 261, 607, 31, 23, 1, -2, -2, 297, 129, 563, 86; 952, 2635, 185, 537, 3940, 1178, 2740, 140, 104, 5, -9, -9, 1340, 582, 2540, 388; -240, -660, -46, -132, -960, -286, -660, -33, -24, 0, 2, 0, -360, -154, -660, -99],79,61]
%
% END OF LATTICE L80.61
%
%
% LATTICE L80.62
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[25080, -1320, 1320; -1320, 66, -99; 1320, -99, -181],[1320, 33, 1],[115, 316, 22, 63, 457, 68, 313, 31, 11, -1, -1, 0, 173, 37, 317, 95; 1948, 5355, 373, 1069, 7760, 1155, 5320, 528, 188, -15, -17, -1, 2920, 625, 5360, 1608; -240, -660, -46, -132, -960, -143, -660, -66, -24, 0, 2, 0, -360, -77, -660, -198],79,62]
%
% END OF LATTICE L80.62
%
%
% LATTICE L80.63
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-135960, -151800, 7920; -151800, -148720, 7800; 7920, 7800, -409],[1320, 40, 1],[35, 22, 392, 58, 364, 341, 35, 67, 152, 46, 356, 10, 10, -1, -1, 1; 781, 493, 8811, 1307, 8217, 7701, 791, 1516, 3443, 1043, 8085, 229, 231, -21, -23, 20; 15565, 9824, 175560, 26040, 163702, 153420, 15758, 30200, 68585, 20776, 161040, 4560, 4598, -420, -458, 400],79,63]
%
% END OF LATTICE L80.63
%
%
% LATTICE L80.64
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-53714760, -1379400, 76560; -1379400, -35120, 1960; 76560, 1960, -109],[1320, 40, 1],[70, 22, 392, 58, 182, 341, 35, 67, 304, 46, 356, 10, 5, -1, -1, 1; 1507, 475, 8481, 1257, 3949, 7401, 760, 1456, 6611, 1001, 7755, 219, 110, -21, -22, 20; 76230, 23984, 427680, 63320, 198781, 372480, 38238, 73220, 332310, 50296, 389400, 10960, 5489, -1080, -1098, 1060],79,64]
%
% END OF LATTICE L80.64
%
%
% LATTICE L80.65
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[14816745570, 30182460, 4946548860; 30182460, 61215, 10076550; 4946548860, 10076550, 1651397989],[330, 165, 1],[-16573, -11405, 15207, 206363, 408627, 773534, 559033, 680926, 699103, 693935, 212303, 476167, 273903, 364016, 123497, 1604; 33150, 22813, -30417, -412769, -817340, -1547231, -1118184, -1361996, -1398354, -1388017, -424651, -952435, -547864, -728109, -247020, -3208; 49440, 34023, -45365, -615615, -1219002, -2307580, -1667688, -2031315, -2085540, -2070123, -633335, -1420485, -817098, -1085920, -368412, -4785],79,65]
%
% END OF LATTICE L80.65
%
%
% LATTICE L80.66
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1226280, -199320, 13200; -199320, 32395, -2145; 13200, -2145, 142],[1320, 55, 1],[-1, 0, 1, 3, 9, 49, 11, 6, 11, 5, 4, 2, 1, 1, -1, -1; -48, -28, -30, -28, -32, -126, -12, 5, 24, 16, 18, 16, 8, 6, -12, -17; -640, -429, -555, -715, -1348, -6600, -1232, -495, -680, -231, -105, 55, 28, 0, -88, -165],79,66]
%
% END OF LATTICE L80.66
%
%
% LATTICE L80.67
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-115213560, -12801360, 51480; -12801360, -1422355, 5720; 51480, 5720, -23],[1320, 55, 1],[-9, -5, -5, -4, -3, -4, 1, 5, 7, 4, 4, 3, 1, -1, -3, -7; 60, 31, 27, 13, -16, -69, -48, -76, -84, -43, -39, -25, -8, 9, 24, 52; -5260, -3509, -4515, -5775, -10808, -26400, -9812, -7810, -5300, -1771, -765, 495, 248, 0, -748, -2750],79,67]
%
% END OF LATTICE L80.67
%
%
% LATTICE L80.68
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2787829440, -24160620, 692681220; -24160620, 209352, -6003096; 692681220, -6003096, 172107829],[660, 132, 1],[4942, 13857, 81, -3001, -11308, -6680, -2911, 2394, 4274, 32223, 2991, 12217, 57388, 37400, 25951, 16038; 1, 5, 0, -3, -35, -27, -25, -25, -13, -65, -4, -9, -25, -13, -5, 1; -19890, -55770, -326, 12078, 45510, 26884, 11715, -9636, -17202, -129690, -12038, -49170, -230970, -150524, -104445, -64548],79,68]
%
% END OF LATTICE L80.68
%
%
% LATTICE L80.69
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[106260, 21780, 26400; 21780, 4488, 5412; 26400, 5412, 6559],[660, 132, 1],[11, -1, -1, 33, 332, 536, 1066, 590, 169, 1801, 121, 327, 568, 664, 734, 130; 1, 5, 0, -1, 0, 1, 5, 5, 2, 25, 2, 7, 15, 19, 25, 7; -45, 0, 4, -132, -1335, -2156, -4290, -2376, -681, -7260, -488, -1320, -2295, -2684, -2970, -528],79,69]
%
% END OF LATTICE L80.69
%
%
% LATTICE L80.70
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[7260, -1980, 0; -1980, -96690, 825; 0, 825, -7],[660, 165, 1],[-21, -14, -6, -23, -43, -70, -39, -31, -21, -7, -1, 2, 1, 0, -3, -11; -76, -51, -22, -85, -160, -261, -146, -117, -80, -27, -4, 7, 4, 1, -10, -39; -9000, -6039, -2605, -10065, -18948, -30910, -17292, -13860, -9480, -3201, -475, 825, 468, 110, -1188, -4620],79,70]
%
% END OF LATTICE L80.70
%
%
% LATTICE L80.71
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-28380, -97020, 33000; -97020, -331320, 112695; 33000, 112695, -38332],[660, 165, 1],[53, 69, 29, 109, 101, 164, 91, 72, 49, 33, 5, -7, 1, 6, 11, 30; -678, -962, -440, -1826, -1838, -3057, -1776, -1535, -1146, -862, -168, 2, 14, 17, -48, -289; -1950, -2772, -1270, -5280, -5322, -8855, -5148, -4455, -3330, -2508, -490, 0, 42, 55, -132, -825],79,71]
%
% END OF LATTICE L80.71
%
%
% LATTICE L80.72
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1786544640870, -4450804708020, -2217328207380; -4450804708020, 11088254999910, 5524012441530; -2217328207380, 5524012441530, 2751985182017],[330, 330, 1],[-1, 13, 11, 63, 34, 115, 34, 58, 19, 23, 1, -27, -16, -55, -16, -22; 59894, -912225, -800401, -4804111, -2799979, -9655026, -2969420, -5533233, -2106848, -3181683, -564235, 710203, 753025, 2831846, 922466, 1439325; -120225, 1831104, 1606640, 9643260, 5620377, 19380460, 5960493, 11106810, 4229055, 6386556, 1132580, -1425600, -1511547, -5684360, -1851663, -2889150],79,72]
%
% END OF LATTICE L80.72
%
%
% LATTICE L80.73
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-12514920, -2502720, 844800; -2502720, -500456, 168872; 844800, 168872, -56887],[1320, 88, 1],[-50, -1, 151, 205, -473, -1513, -1337, -956, -320, -7399, -1631, -1685, -3227, -5887, -2363, -524; 301, 5, -909, -1233, 2855, 9126, 8060, 5761, 1928, 44575, 9825, 10149, 19435, 35454, 14230, 3155; 151, 0, -456, -616, 1450, 4620, 4070, 2904, 971, 22440, 4944, 5104, 9770, 17820, 7150, 1584],79,73]
%
% END OF LATTICE L80.73
%
%
% LATTICE L80.74
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2077680, 658680, 319440; 658680, 207592, 100672; 319440, 100672, 48821],[1320, 88, 1],[1, 1, -1, -1, 4, 22, 17, 11, 7, 79, 17, 17, 16, 58, 23, 5; -460, -430, 492, 558, -1625, -9159, -7255, -4793, -3086, -35030, -7584, -7650, -7240, -26301, -10475, -2299; 942, 880, -1008, -1144, 3325, 18744, 14850, 9812, 6318, 71720, 15528, 15664, 14825, 53856, 21450, 4708],79,74]
%
% END OF LATTICE L80.74
%
%
% LATTICE L80.75
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[13320780, 374880, -3032040; 374880, 9020, -86460; -3032040, -86460, 689309],[660, 220, 1],[8050, 12723, 8168, 1257, -39, -3607, -235, 3771, 3181, 9739, 14294, 21205, 11270, 228227, 22697, 41153; -23952, -37856, -24303, -3740, 116, 10731, 699, -11221, -9465, -28978, -42531, -63094, -33533, -679071, -67533, -122447; 32405, 51216, 32880, 5060, -157, -14520, -946, 15180, 12805, 39204, 57540, 85360, 45367, 918720, 91366, 165660],79,75]
%
% END OF LATTICE L80.75
%
%
% LATTICE L80.76
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[469059360, -17903820, -129818040; -17903820, 683320, 4955060; -129818040, 4955060, 35928731],[660, 220, 1],[-11796, -10163, -7537, -2925, -586, 164, 380, 1586, -1160, -2793, -5419, -10031, -12370, -129724, -6858, -27498; 35157, 30287, 22458, 8711, 1745, -489, -1131, -4709, 3471, 8341, 16170, 29917, 36883, 386769, 20445, 81965; -47470, -40898, -30330, -11770, -2358, 660, 1529, 6380, -4670, -11242, -21810, -40370, -49782, -522060, -27599, -110660],79,76]
%
% END OF LATTICE L80.76
%
%
% LATTICE L80.77
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1320, 26400, -1320; 26400, -523560, 26160; -1320, 26160, -1307],[1320, 120, 1],[464, 221, 1029, 355, 1827, 541, 151, 242, 460, 115, 203, -19, 21, 19, 17, 94; 132, 61, 275, 91, 451, 132, 36, 55, 99, 23, 33, -7, 11, 8, 6, 29; 2145, 984, 4400, 1440, 7062, 2060, 558, 840, 1485, 336, 440, -120, 198, 140, 102, 480],79,77]
%
% END OF LATTICE L80.77
%
%
% LATTICE L80.78
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-15537720, -2851200, 71280; -2851200, -462360, 11520; 71280, 11520, -287],[1320, 120, 1],[433, 103, 479, 165, 424, 251, 70, 112, 425, 53, 93, -9, 5, 9, 8, 44; -94501, -22481, -104555, -36019, -92565, -54798, -15283, -24455, -92807, -11575, -20317, 1963, -1089, -1962, -1745, -9601; -3685770, -876816, -4077920, -1404840, -3610299, -2137280, -596082, -953820, -3619770, -451464, -792440, 76560, -42471, -76520, -68058, -374460],79,78]
%
% END OF LATTICE L80.78
%
%
% LATTICE L80.79
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[14520, 5280, 0; 5280, -46695, 825; 0, 825, -14],[1320, 165, 1],[59, 20, 3, -5, -3, -1, 7, 14, 55, 37, 16, 62, 117, 191, 107, 43; -160, -54, -8, 14, 8, 2, -20, -39, -152, -102, -44, -170, -320, -522, -292, -117; -9480, -3201, -475, 825, 468, 110, -1188, -2310, -9000, -6039, -2605, -10065, -18948, -30910, -17292, -6930],79,79]
%
% END OF LATTICE L80.79
%
%
% LATTICE L80.80
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-4267560, -943800, 17160; -943800, -48345, 825; 17160, 825, -14],[1320, 165, 1],[-5, -3, -1, -2, 1, 2, 5, 9, 11, 6, 2, 5, 5, 3, 1, -3; 1232, 742, 248, 498, -248, -497, -1244, -2242, -2744, -1498, -500, -1254, -1264, -763, -268, 730; 66420, 40029, 13385, 26895, -13392, -26840, -67188, -121110, -148260, -80949, -27025, -67815, -68448, -41360, -14652, 39270],79,80]
%
% END OF LATTICE L80.80
%
%
% LATTICE L80.81
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2640, -1320, 0; -1320, -778008, 4752; 0, 4752, -29],[1320, 264, 1],[1, -1, -1, -3, 17, 16, 38, 25, 8, 181, 13, 39, 73, 44, 52, 11; 2, 0, -2, -8, 20, 21, 55, 39, 13, 300, 22, 68, 130, 79, 95, 21; 327, 0, -328, -1320, 3210, 3388, 8910, 6336, 2115, 48840, 3584, 11088, 21210, 12892, 15510, 3432],79,81]
%
% END OF LATTICE L80.81
%
%
% LATTICE L80.82
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2640, -43560, -21120; -43560, 587928, 285120; -21120, 285120, 138271],[1320, 264, 1],[3, 1, -1, -1, 19, 33, 72, 44, 27, 299, 21, 61, 56, 67, 78, 16; -154, 0, 62, 128, -835, -1491, -3355, -2109, -1316, -14700, -1042, -3068, -2840, -3409, -3995, -831; 318, 0, -128, -264, 1725, 3080, 6930, 4356, 2718, 30360, 2152, 6336, 5865, 7040, 8250, 1716],79,82]
%
% END OF LATTICE L80.82
%
%
% LATTICE L80.83
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[50820, -5934060, -1474440; -5934060, 692882520, 172161000; -1474440, 172161000, 42776963],[660, 660, 1],[-53, -141, -61, -239, -116, -764, -218, -366, -67, -99, -19, -1, -4, -36, -22, -114; 48, -34, -85, -658, -446, -3177, -1035, -2135, -459, -788, -189, -164, 35, 437, 213, 491; -195, 132, 340, 2640, 1791, 12760, 4158, 8580, 1845, 3168, 760, 660, -141, -1760, -858, -1980],79,83]
%
% END OF LATTICE L80.83
%
%
% LATTICE L80.84
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1137840, -3233340, -803220; -3233340, 9224160, 2291520; -803220, 2291520, 569273],[660, 660, 1],[-795, -1076, -471, -1862, -1805, -5941, -846, -2821, -1017, -736, -133, 50, -7, -99, -60, -803; -35329, -47811, -20926, -82715, -80173, -263873, -37573, -125271, -45155, -32673, -5902, 2231, -311, -4407, -2669, -35697; 141090, 190938, 83570, 330330, 320178, 1053800, 150051, 500280, 180330, 130482, 23570, -8910, 1242, 17600, 10659, 142560],79,84]
%
% END OF LATTICE L80.84
%
%
% LATTICE L80.85
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1320, 0, 0; 0, -1531640, 11000; 0, 11000, -79],[1320, 440, 1],[-7, -11, -7, -1, 0, 1, 0, -2, -3, -9, -13, -19, -5, -101, -10, -18; 27, 49, 39, 19, 1, 0, -3, -11, -3, -1, 9, 29, 11, 240, 27, 59; 3730, 6776, 5400, 2640, 139, 0, -418, -1540, -430, -176, 1200, 3960, 1511, 33000, 3718, 8140],79,85]
%
% END OF LATTICE L80.85
%
%
% LATTICE L80.86
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[77973720, 19060800, -118800; 19060800, 4659160, -29040; -118800, -29040, 181],[1320, 440, 1],[9, 31, 23, 9, 1, 1, -1, -2, 1, 9, 17, 31, 19, 199, 21, 42; 26, 91, 69, 29, 3, 0, -4, -11, 1, 17, 39, 79, 51, 540, 58, 119; 10075, 34936, 26160, 10560, 1138, 660, -1298, -3080, 815, 8624, 17400, 33000, 20642, 217140, 23078, 46640],79,86]
%
% END OF LATTICE L80.86
%
%
% LATTICE L80.87
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-4594920, 14520000, 33000; 14520000, 39688440, 89760; 33000, 89760, 203],[1320, 1320, 1],[73, 189, 79, 295, 68, 441, 122, 192, 65, 87, 13, -19, 1, 19, 16, 84; -10151, -26281, -10985, -41019, -9455, -61318, -16963, -26695, -9037, -12095, -1807, 2643, -139, -2642, -2225, -11681; 4476570, 11589864, 4844360, 18089280, 4169631, 27041080, 7480638, 11772420, 3985290, 5333856, 796880, -1165560, 61299, 1165120, 981222, 5151300],79,87]
%
% END OF LATTICE L80.87
%
%
% LATTICE L80.88
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[33407880, 30228000, -27720; 30228000, 27346440, -25080; -27720, -25080, 23],[1320, 1320, 1],[14, 71, 29, 105, 47, 151, 41, 62, 10, 25, 3, -9, 1, 9, 7, 34; 12, 61, 25, 91, 41, 132, 36, 55, 9, 23, 3, -7, 1, 8, 6, 29; 29955, 152064, 62200, 225720, 101322, 325820, 88638, 134640, 21855, 55176, 6880, -18480, 2298, 19580, 14982, 72600],79,88]
%
% END OF LATTICE L80.88
%

\medskip%
%------------------------------WEYL-GROUP-W81--------------------------------
%
\leavevmode\llap{}%
$W_{81\phantom{0}}$%
\qquad\llap{48} lattices, $\chi=48$%
\hfill%
$222222222222\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L81.1
%
\leavevmode%
${L_{81.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{1}{}9\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{-2}{}11\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{23\rightarrow N_{81},3,2}%
\EasyButWeakLineBreak%
{${12}\above{1pt}{1pt}{*}{2}{1980}\above{1pt}{1pt}{b}{2}{2}\above{1pt}{1pt}{l}{2}{36}\above{1pt}{1pt}{r}{2}{30}\above{1pt}{1pt}{b}{2}{44}\above{1pt}{1pt}{*}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-7446780\\17820\\17820
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
17820\\-42\\-45
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
17820\\-45\\-34
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
29699\\9751500\\2643300
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-75\\-24626\\-6675
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-57\\-18715\\-5074
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
31\\10178\\2760
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
967\\317460\\86130
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
8\\2626\\713
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
23\\7548\\2052
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\655\\180
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-330\\-88
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-7446780, 17820, 17820; 17820, -42, -45; 17820, -45, -34],[1980, 3, 1],[31, 967, 8, 23, 2, -1, -1, 23, 1, 13, 13, 67; 10178, 317460, 2626, 7548, 655, -330, -328, 7590, 329, 4272, 4270, 22000; 2760, 86130, 713, 2052, 180, -88, -90, 1980, 88, 1152, 1155, 5962],80,1]
%
% END OF LATTICE L81.1
%
%
% LATTICE L81.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[9570, 3135, 0; 3135, 1027, 0; 0, 0, -1],[165, 1, 1],[-1, -18, 1, 21, 182, 595, 296, 3263, 176, 97, 113, 54; 3, 55, -3, -64, -555, -1815, -903, -9955, -537, -296, -345, -165; 0, 0, -1, -9, -75, -242, -120, -1320, -71, -39, -45, -22],80,2]
%
% END OF LATTICE L81.2
%
%
% LATTICE L81.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-149820, 2640, 660; 2640, -34, -15; 660, -15, -2],[660, 1, 1],[41, 417, 10, 9, 1, -3, -1, 23, 2, 7, 19, 91; 1200, 12210, 293, 264, 30, -88, -30, 660, 58, 204, 555, 2662; 4458, 45320, 1086, 976, 105, -330, -108, 2530, 219, 764, 2070, 9900],80,3]
%
% END OF LATTICE L81.3
%
%
% LATTICE L81.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-12271545, -24255, -69795; -24255, -42, -132; -69795, -132, -391],[495, 3, 1],[-46, -1417, -23, -32, -4, 2, 1, -68, -4, -22, -41, -101; -12431, -382965, -6217, -8652, -1085, 539, 271, -18315, -1079, -5940, -11075, -27291; 12405, 382140, 6203, 8631, 1080, -539, -270, 18315, 1078, 5931, 11055, 27236],80,4]
%
% END OF LATTICE L81.4
%
%
% LATTICE L81.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[165, 2310, 165; 2310, 333, 771; 165, 771, 91],[165, 3, 1],[-33, 109, 107, 260, 533, 4111, 633, 19691, 973, 460, 67, -151; -5, 0, 14, 36, 75, 583, 90, 2805, 139, 66, 10, -22; 101, -330, -327, -795, -1630, -12573, -1936, -60225, -2976, -1407, -205, 462],80,5]
%
% END OF LATTICE L81.5
%
%
% LATTICE L81.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[19635, 3960, 7920; 3960, 555, 1585; 7920, 1585, 3194],[165, 5, 1],[-112, 35, 128, 305, 373, 4782, 2207, 4574, 1129, 533, 46, -173; -15, 0, 14, 36, 45, 583, 270, 561, 139, 66, 6, -22; 285, -88, -325, -775, -948, -12155, -5610, -11627, -2870, -1355, -117, 440],80,6]
%
% END OF LATTICE L81.6
%
%
% LATTICE L81.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-907830, 8415, 17820; 8415, -78, -165; 17820, -165, -329],[495, 3, 1],[26, 333, 64, 15, 33, 104, 9, 52, -1, -1, 2, 127; 2846, 36465, 7011, 1644, 3620, 11418, 989, 5720, -108, -110, 215, 13893; -21, -275, -54, -13, -30, -99, -9, -55, 0, 1, 0, -99],80,7]
%
% END OF LATTICE L81.7
%
%
% LATTICE L81.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[62205, 8910, 16995; 8910, 1221, 2431; 16995, 2431, 4643],[165, 11, 1],[-61, 19, 85, 190, 1139, 263, 1331, 1251, 677, 318, 131, -9; -15, 0, 14, 36, 225, 53, 270, 255, 139, 66, 30, -2; 231, -70, -319, -715, -4290, -991, -5016, -4715, -2552, -1199, -495, 34],80,8]
%
% END OF LATTICE L81.8
%
%
% LATTICE L81.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1246740, -623700, 5940; -623700, -312006, 2967; 5940, 2967, -26],[660, 3, 1],[-159, -2429, 27, 53, -54, -3261, -641, -23971, -747, -1013, -346, -2019; 324, 4950, -55, -108, 110, 6644, 1306, 48840, 1522, 2064, 705, 4114; 646, 9900, -108, -216, 215, 13134, 2584, 96690, 3015, 4092, 1400, 8184],80,9]
%
% END OF LATTICE L81.9
%
%
% LATTICE L81.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[249987870, 526845, 82634145; 526845, 1110, 174150; 82634145, 174150, 27314933],[165, 15, 1],[319, 7058, 3828, 4904, 1475, 46635, 6656, 38977, 8727, 3466, -80, -600; -8, -176, -95, -119, -35, -1078, -152, -880, -193, -73, 3, 22; -965, -21351, -11580, -14835, -4462, -141075, -20135, -117909, -26400, -10485, 242, 1815],80,10]
%
% END OF LATTICE L81.10
%
%
% LATTICE L81.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[287257080, -486420, 71362500; -486420, 824, -120840; 71362500, -120840, 17728393],[660, 4, 1],[3946, 40203, 1935, 444, 328, 82, 79, 4072, 480, 361, 3697, 8773; 285, 2970, 148, 36, 45, 11, 0, 165, 23, 21, 240, 616; -15882, -161810, -7788, -1787, -1320, -330, -318, -16390, -1932, -1453, -14880, -35310],80,11]
%
% END OF LATTICE L81.11
%
%
% LATTICE L81.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[407220, -10560, 2640; -10560, 270, -65; 2640, -65, 14],[660, 5, 1],[-1, 5, 2, 5, 2, 31, 11, 17, 1, -1, -1, -9; -54, 264, 106, 264, 105, 1606, 564, 858, 47, -60, -54, -484; -60, 286, 115, 280, 108, 1540, 510, 704, 20, -100, -63, -550],80,12]
%
% END OF LATTICE L81.12
%
%
% LATTICE L81.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[55288035, 367950, 18242565; 367950, 2442, 121407; 18242565, 121407, 6019226],[165, 33, 1],[461, 4643, 5532, 7013, 10436, 5925, 9249, 24487, 11946, 4639, -726, -99; -8, -80, -95, -119, -175, -98, -152, -400, -193, -73, 15, 2; -1397, -14070, -16764, -21252, -31625, -17955, -28028, -74205, -36201, -14058, 2200, 300],80,13]
%
% END OF LATTICE L81.13
%
%
% LATTICE L81.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-396651420, 180180, -178144560; 180180, -78, 81345; -178144560, 81345, -79962134],[1980, 3, 1],[-12823, -164227, -15781, -7397, -8136, -51277, -4437, -25633, 247, 493, -494, -62639; -2821088, -36130270, -3471849, -1627352, -1789930, -11280984, -976142, -5639260, 54342, 108460, -108685, -13780734; 25698, 329120, 31626, 14824, 16305, 102762, 8892, 51370, -495, -988, 990, 125532],80,14]
%
% END OF LATTICE L81.14
%
%
% LATTICE L81.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-7667220, 19140, 20460; 19140, -22, -55; 20460, -55, -54],[660, 11, 1],[-1, 13, 10, 31, 79, 33, 161, 147, 38, 33, 1, -1; -48, 650, 499, 1544, 3930, 1640, 7998, 7300, 1886, 1636, 45, -50; -330, 4260, 3278, 10164, 25905, 10822, 52800, 48210, 12463, 10824, 330, -328],80,15]
%
% END OF LATTICE L81.15
%
%
% LATTICE L81.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[40590, 7920, 2475; 7920, -345, -150; 2475, -150, -61],[495, 15, 1],[7, 8, -1, -1, 0, 85, 18, 47, 46, 11, 5, 80; -538, -616, 75, 77, 1, -6468, -1372, -3586, -3513, -841, -383, -6138; 1605, 1837, -225, -230, -3, 19305, 4095, 10703, 10485, 2510, 1143, 18315],80,16]
%
% END OF LATTICE L81.16
%
%
% LATTICE L81.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[133155, 0, -2475; 0, 15, 0; -2475, 0, 46],[495, 15, 1],[0, 13, 3, 16, 6, 76, 35, 218, 18, 26, 1, 1; 1, 0, -1, -9, -4, -55, -26, -165, -14, -21, -1, 0; 0, 693, 160, 855, 321, 4070, 1875, 11682, 965, 1395, 54, 55],80,17]
%
% END OF LATTICE L81.17
%
%
% LATTICE L81.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2462152440, -11331540, 613661400; -11331540, 52152, -2824248; 613661400, -2824248, 152947603],[660, 12, 1],[1204, 21563, -3, 41, 1456, 27828, 5241, 191122, 11604, 3826, 4989, 14709; -827, -14850, -2, -27, -985, -18931, -3568, -130185, -7909, -2610, -3410, -10076; -4846, -86790, 12, -165, -5860, -112002, -21094, -769230, -46704, -15399, -20080, -59202],80,18]
%
% END OF LATTICE L81.18
%
%
% LATTICE L81.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[52813695, -464310, -21541245; -464310, 4070, 189365; -21541245, 189365, 8786061],[165, 55, 1],[-2164, -1453, -8656, -10973, -9797, -9270, -43411, -7662, -18689, -7257, 682, 155; 6468, 4343, 25873, 32800, 29286, 27712, 129777, 22906, 55874, 21698, -2037, -463; -5445, -3656, -21780, -27610, -24651, -23325, -109230, -19279, -47025, -18260, 1716, 390],80,19]
%
% END OF LATTICE L81.19
%
%
% LATTICE L81.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-40260, 3300, -1980; 3300, -270, 165; -1980, 165, -82],[660, 15, 1],[191, 1373, 205, 263, 16, 421, 29, 79, -7, 1, 6, 1031; 2094, 15048, 2246, 2880, 175, 4598, 316, 858, -77, 12, 66, 11308; -430, -3102, -465, -600, -37, -990, -70, -198, 15, 0, -13, -2310],80,20]
%
% END OF LATTICE L81.20
%
%
% LATTICE L81.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[44883960, -1314060, 11148060; -1314060, 38440, -326380; 11148060, -326380, 2768901],[660, 20, 1],[-589, -432, 328, 789, 2329, 34033, 16394, 35203, 9155, 2372, 832, 738; -12, -11, 5, 14, 42, 616, 297, 638, 166, 43, 15, 11; 2370, 1738, -1320, -3175, -9372, -136950, -65970, -141658, -36840, -9545, -3348, -2970],80,21]
%
% END OF LATTICE L81.21
%
%
% LATTICE L81.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[52470, 25245, 1980; 25245, 9042, 693; 1980, 693, 53],[495, 33, 1],[4, 2, -1, -1, -3, 2, 6, 8, 19, 5, 13, 4; -130, -65, 33, 34, 110, -54, -175, -240, -582, -156, -415, -129; 1551, 775, -396, -407, -1320, 639, 2079, 2855, 6930, 1859, 4950, 1539],80,22]
%
% END OF LATTICE L81.22
%
%
% LATTICE L81.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-495, -495, -990; -495, -462, -990; -990, -990, -1979],[495, 33, 1],[-1, 88, 44, 202, 341, 71, 346, 947, 163, 212, 4, -2; 1, 0, -1, -9, -20, -5, -26, -75, -14, -21, -5, 0; 0, -45, -22, -99, -165, -34, -165, -450, -77, -99, 0, 1],80,23]
%
% END OF LATTICE L81.23
%
%
% LATTICE L81.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-33660, -8580, 1980; -8580, -2178, 495; 1980, 495, -106],[660, 33, 1],[15, 13, -7, 1, 23, 67, 135, 437, 142, 179, 52, 23; -78, -70, 35, -4, -115, -338, -682, -2210, -719, -908, -265, -118; -88, -90, 33, 0, -110, -336, -682, -2220, -726, -924, -275, -126],80,24]
%
% END OF LATTICE L81.24
%
%
% LATTICE L81.25
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2260030437720, 501890655420, -565388600040; 501890655420, 111456122808, -125557271400; -565388600040, -125557271400, 141442461889],[1980, 12, 1],[-487862, -5964751, -1093301, -121162, -482176, -1441834, -119803, -719564, -496, -371, -125489, -2568755; 89, 1100, 204, 23, 95, 297, 26, 165, 3, 0, 20, 462; -1950054, -23841950, -4370076, -484301, -1927320, -5763186, -478866, -2876170, -1980, -1483, -501600, -10267686],80,25]
%
% END OF LATTICE L81.25
%
%
% LATTICE L81.26
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[720969480, -16768620, -180623520; -16768620, 390072, 4201020; -180623520, 4201020, 45251369],[1980, 12, 1],[-36667, -1126186, -18204, -12664, -3427, -237, -248, -92009, -3945, -9485, -33488, -80976; 124, 3795, 61, 42, 10, 0, 1, 330, 14, 33, 115, 275; -146370, -4495590, -72668, -50553, -13680, -946, -990, -367290, -15748, -37863, -133680, -323246],80,26]
%
% END OF LATTICE L81.26
%
%
% LATTICE L81.27
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[890244630, -144258180, -52632195; -144258180, 23376045, 8528685; -52632195, 8528685, 3111667],[165, 165, 1],[-5, 0, 14, 36, 15, 53, 90, 51, 139, 66, 2, -2; 2337, -382, -9365, -21209, -8512, -29543, -49872, -28139, -76198, -35833, -995, 1022; -6490, 1047, 25905, 58740, 23584, 81870, 138215, 77988, 211200, 99330, 2761, -2835],80,27]
%
% END OF LATTICE L81.27
%
%
% LATTICE L81.28
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2893042680, -29725740, 718823160; -29725740, 305448, -7385840; 718823160, -7385840, 178603219],[660, 44, 1],[410, 9007, 13141, 10826, 116432, 25862, 129305, 120708, 64688, 15117, 13283, 81; 3, 10, 12, 8, 75, 15, 72, 65, 33, 7, 0, 0; -1650, -36250, -52888, -43571, -468600, -104086, -520410, -485810, -260348, -60841, -53460, -326],80,28]
%
% END OF LATTICE L81.28
%
%
% LATTICE L81.29
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1213740, 1980, 1980; 1980, 510, 135; 1980, 135, 34],[1980, 15, 1],[-1, 5, 1, 11, 2, 47, 21, 127, 5, 13, 0, -3; 226, -1122, -225, -2472, -449, -10538, -4706, -28446, -1119, -2904, 1, 682; -840, 4158, 835, 9180, 1668, 39160, 17490, 105732, 4160, 10800, -3, -2530],80,29]
%
% END OF LATTICE L81.29
%
%
% LATTICE L81.30
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-19635660, -9733680, 7931880; -9733680, -4825110, 3931605; 7931880, 3931605, -3196606],[1980, 15, 1],[-85603, -223743, -109595, -52473, -11948, -382913, -33557, -38409, 2351, 4809, 32, -403543; 179360, 468798, 229629, 109944, 25034, 802296, 70310, 80476, -4926, -10076, -67, 845526; 8190, 21406, 10485, 5020, 1143, 36630, 3210, 3674, -225, -460, -3, 38610],80,30]
%
% END OF LATTICE L81.30
%
%
% LATTICE L81.31
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-652740, -18480, 1980; -18480, -330, 55; 1980, 55, -6],[660, 55, 1],[41, 7, 8, 5, -1, -1, -1, 1, 4, 11, 5, 9; 30, 4, 2, -4, -3, -2, 0, 2, 7, 16, 6, 8; 13530, 2294, 2585, 1540, -363, -350, -330, 346, 1375, 3740, 1683, 2990],80,31]
%
% END OF LATTICE L81.31
%
%
% LATTICE L81.32
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1983960, 333300, 495000; 333300, 56280, 83160; 495000, 83160, 123503],[660, 60, 1],[-10233, -74398, -22500, -7352, -1869, -26013, -1952, -6023, 567, 41, -568, -54408; -201, -1463, -443, -145, -37, -517, -39, -121, 11, 1, -11, -1067; 41150, 299178, 90480, 29565, 7516, 104610, 7850, 24222, -2280, -165, 2284, 218790],80,32]
%
% END OF LATTICE L81.32
%
%
% LATTICE L81.33
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-511970580, 502920, 502920; 502920, -462, -495; 502920, -495, -494],[1980, 33, 1],[181, 497, 43, 113, 2, -1, -1, 43, 11, 103, 88, 37; 5378, 14760, 1276, 3348, 55, -30, -28, 1290, 329, 3072, 2620, 1100; 178860, 491130, 42493, 111672, 1980, -988, -990, 42480, 10868, 101772, 86955, 36562],80,33]
%
% END OF LATTICE L81.33
%
%
% LATTICE L81.34
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-88884180, -5983560, -156420; -5983560, -402798, -10527; -156420, -10527, -274],[1980, 33, 1],[-803, -869, -850, -359, -317, -143, -97, -31, 40, -1, -133, -397; 12706, 13750, 13449, 5680, 5015, 2262, 1534, 490, -633, 16, 2105, 6282; -29766, -32200, -31482, -13288, -11715, -5274, -3564, -1130, 1485, -44, -4950, -14724],80,34]
%
% END OF LATTICE L81.34
%
%
% LATTICE L81.35
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[990, -186615, 3465; -186615, 35332770, -656040; 3465, -656040, 12181],[495, 165, 1],[-19, -3, -17, 0, 3, 7, 9, 1, -1, -4, -5, -13; 199, 44, 441, 97, 38, 51, 46, 5, 0, 1, 11, 96; 10725, 2371, 23760, 5225, 2046, 2745, 2475, 269, 0, 55, 594, 5175],80,35]
%
% END OF LATTICE L81.35
%
%
% LATTICE L81.36
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-15250455, 17759610, -77220; 17759610, -20681430, 89925; -77220, 89925, -391],[495, 165, 1],[-332, -182, -157, -205, -1, 2, 2, -16, -41, -191, -65, -68; -26, -15, -14, -21, -1, 0, 1, 0, -1, -9, -4, -5; 59565, 32481, 27775, 35640, -33, -395, -165, 3159, 7865, 35640, 11913, 12275],80,36]
%
% END OF LATTICE L81.36
%
%
% LATTICE L81.37
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[5270760, -609180, 1313400; -609180, 70488, -151800; 1313400, -151800, 327281],[660, 132, 1],[1021, 1571, -131, -41, 1037, 2059, 4329, 14479, 9761, 3251, 4313, 1151; -36, -55, 5, 1, -40, -76, -159, -530, -356, -118, -155, -41; -4114, -6330, 528, 165, -4180, -8298, -17446, -58350, -39336, -13101, -17380, -4638],80,37]
%
% END OF LATTICE L81.37
%
%
% LATTICE L81.38
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[660, 0, 0; 0, -13530, 165; 0, 165, -2],[660, 165, 1],[-3, -1, 0, 1, 0, -3, -7, -5, -9, -13, -1, -3; -2, 0, 2, 0, -1, -14, -28, -18, -29, -36, -2, -4; -220, -18, 165, 0, -88, -1260, -2530, -1632, -2640, -3300, -187, -390],80,38]
%
% END OF LATTICE L81.38
%
%
% LATTICE L81.39
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[18567519723720, -287839393380, -4642098949620; -287839393380, 4462174680, 71963243640; -4642098949620, 71963243640, 1160579494661],[1980, 60, 1],[-44902, -108891, -98909, -10842, -8448, -125050, -10323, -12604, -496, -203, -2597, -239435; 10813, 26103, 23589, 2565, 1961, 28281, 2257, 2651, -63, 49, 653, 57981; -180270, -437162, -397080, -43525, -33912, -501930, -41430, -50578, -1980, -815, -10428, -961290],80,39]
%
% END OF LATTICE L81.39
%
%
% LATTICE L81.40
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[20361064680, 166975380, -5100598800; 166975380, 1369320, -41828580; -5100598800, -41828580, 1277738101],[1980, 60, 1],[-263, -7291, -1493, -4295, -3415, -45937, -21607, -137051, -11629, -8827, -959, -2177; -4, -33, -3, 6, 10, 176, 89, 594, 54, 45, 7, 11; -1050, -29106, -5960, -17145, -13632, -183370, -86250, -547074, -46420, -35235, -3828, -8690],80,40]
%
% END OF LATTICE L81.40
%
%
% LATTICE L81.41
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[373759320, 685740, -92355780; 685740, 1320, -169400; -92355780, -169400, 22821111],[660, 220, 1],[-64693, -12388, -34492, -8623, -2591, -405, -82, -567, -4373, -4332, -10364, -12550; 193866, 37123, 103361, 25840, 7764, 1214, 249, 1700, 13108, 12983, 31059, 37609; -260370, -49858, -138820, -34705, -10428, -1630, -330, -2282, -17600, -17435, -41712, -50510],80,41]
%
% END OF LATTICE L81.41
%
%
% LATTICE L81.42
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[7406083080, 236140740, -1855713420; 236140740, 7530072, -59168868; -1855713420, -59168868, 464978891],[1980, 132, 1],[363381, 394357, 774245, 82547, 300737, 73691, 58709, 27733, -14483, 1871, 121353, 179563; 2939, 3190, 6264, 668, 2435, 597, 476, 225, -117, 15, 980, 1452; 1450614, 1574270, 3090780, 329527, 1200540, 294174, 234366, 110710, -57816, 7469, 484440, 716814],80,42]
%
% END OF LATTICE L81.42
%
%
% LATTICE L81.43
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[243984244680, -494899020, -61119786420; -494899020, 1003992, 123975720; -61119786420, 123975720, 15310940659],[1980, 132, 1],[-1210167, -3390886, -606194, -425249, -124497, -247, -248, -240359, -120055, -301000, -1085918, -241836; 124, 345, 61, 42, 10, 0, 1, 30, 14, 33, 115, 25; -4830870, -13536090, -2419868, -1697553, -496980, -986, -990, -959490, -479248, -1201563, -4334880, -965386],80,43]
%
% END OF LATTICE L81.43
%
%
% LATTICE L81.44
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-181666980, -8488260, 130680; -8488260, -396330, 6105; 130680, 6105, -94],[1980, 165, 1],[141, 77, 33, 85, 0, -1, -1, 7, 9, 83, 14, 29; 794, 432, 184, 468, -1, -6, -4, 42, 53, 480, 80, 164; 247500, 135054, 57805, 148500, -66, -1780, -1650, 12456, 15950, 146520, 24651, 50950],80,44]
%
% END OF LATTICE L81.44
%
%
% LATTICE L81.45
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[89086140, 29858400, -138600; 29858400, 10002630, -46365; -138600, -46365, 214],[1980, 165, 1],[-2537, -545, -2642, -1099, -186, -385, -213, -5, 167, -1, -89, -1265; 10120, 2174, 10539, 4384, 742, 1536, 850, 20, -666, 4, 355, 5046; 549450, 118036, 572220, 238040, 40293, 83430, 46200, 1094, -36135, 220, 19272, 273960],80,45]
%
% END OF LATTICE L81.45
%
%
% LATTICE L81.46
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1320, -108900, -27060; -108900, 8932440, 2219580; -27060, 2219580, 551533],[660, 660, 1],[-28, -9, 1, 0, -6, -56, -117, -78, -262, -87, -23, -31; 191, 64, 0, -41, -11, 141, 354, 263, 981, 368, 120, 186; -770, -258, 0, 165, 44, -570, -1430, -1062, -3960, -1485, -484, -750],80,46]
%
% END OF LATTICE L81.46
%
%
% LATTICE L81.47
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1381701027960, 8186850540, 339958101780; 8186850540, 48508680, 2014318680; 339958101780, 2014318680, 83644369231],[1980, 660, 1],[-211382, -52917, -597689, -75462, -74864, -116990, -120943, -13548, -496, 8997, 8399, -82405; 635981, 159207, 1798185, 227028, 225223, 351951, 363839, 40757, 1491, -27064, -25259, 247941; 843810, 211238, 2385900, 301235, 298848, 467010, 482790, 54082, 1980, -35915, -33528, 328950],80,47]
%
% END OF LATTICE L81.47
%
%
% LATTICE L81.48
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[151782392520, 169090020, 37895354640; 169090020, 188760, 42216240; 37895354640, 42216240, 9461294639],[1980, 660, 1],[1426587, 802934, 722566, 513239, 34125, 1731, 248, 53167, 133535, 342862, 251242, 283636; -4281407, -2409729, -2168533, -1540311, -102415, -5195, -743, -159561, -400757, -1028979, -754015, -851235; -5694810, -3205242, -2884420, -2048805, -136224, -6910, -990, -212238, -533060, -1368675, -1002936, -1132250],80,48]
%
% END OF LATTICE L81.48
%

\medskip%
%------------------------------WEYL-GROUP-W82--------------------------------
%
\leavevmode\llap{}%
$W_{82\phantom{0}}$%
\qquad\llap{24} lattices, $\chi=18$%
\hfill%
$2222222$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L82.1
%
\leavevmode%
${L_{82.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{2}{}5\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}11\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2\rightarrow N_{82}}%
\EasyButWeakLineBreak%
{${44}\above{1pt}{1pt}{*}{2}{60}\above{1pt}{1pt}{b}{2}{2}\above{1pt}{1pt}{l}{2}{132}\above{1pt}{1pt}{r}{2}{10}\above{1pt}{1pt}{l}{2}{4}\above{1pt}{1pt}{r}{2}{6}\above{1pt}{1pt}{b}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-13682460\\-6811200\\14520
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-6811200\\-3390650\\7227
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
14520\\7227\\-14
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2285\\4598\\3674
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2773\\5580\\4470
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-326\\656\\527
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-4723\\9504\\7656
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
82\\-165\\-130
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
163\\-328\\-264
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-82\\165\\129
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-13682460, -6811200, 14520; -6811200, -3390650, 7227; 14520, 7227, -14],[660, 1, 1],[-2285, -2773, -326, -4723, 82, 163, -82; 4598, 5580, 656, 9504, -165, -328, 165; 3674, 4470, 527, 7656, -130, -264, 129],81,1]
%
% END OF LATTICE L82.1
%
%
% LATTICE L82.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[4290, 1155, 0; 1155, 311, 0; 0, 0, -1],[165, 1, 1],[-3, -4, 3, 125, 27, 7, 4; 11, 15, -11, -462, -100, -26, -15; 0, 0, -3, -99, -20, -5, -3],81,2]
%
% END OF LATTICE L82.2
%
%
% LATTICE L82.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1431870, 36630, -474705; 36630, -789, 12144; -474705, 12144, -157378],[165, 3, 1],[228572, 40421, -1487, -3844, 7251, 28640, 35274; 649, 115, -4, -11, 20, 81, 100; -689403, -121915, 4485, 11594, -21870, -86382, -106391],81,3]
%
% END OF LATTICE L82.3
%
%
% LATTICE L82.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1851630, 53790, -738375; 53790, -1315, 21450; -738375, 21450, -294442],[165, 5, 1],[404297, 42898, -2630, -20398, 2565, 50658, 187177; 649, 69, -4, -33, 4, 81, 300; -1013815, -107571, 6595, 51150, -6432, -127030, -469365],81,4]
%
% END OF LATTICE L82.4
%
%
% LATTICE L82.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3221790, 105270, -876645; 105270, -2893, 28644; -876645, 28644, -238534],[165, 11, 1],[49154, 286853, -3517, -2480, 17151, 67748, 250324; 59, 345, -4, -3, 20, 81, 300; -180641, -1054185, 12925, 9114, -63030, -248974, -919941],81,5]
%
% END OF LATTICE L82.5
%
%
% LATTICE L82.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-708180, -350460, 660; -350460, -173382, 315; 660, 315, 2],[660, 3, 1],[-475, -211, -79, -367, 27, 53, 0; 968, 430, 161, 748, -55, -108, 0; 4290, 1910, 717, 3344, -240, -480, -1],81,6]
%
% END OF LATTICE L82.6
%
%
% LATTICE L82.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[24328329630, 597960, 8042312025; 597960, 15, 197670; 8042312025, 197670, 2658578854],[165, 15, 1],[-1529215, -54428, 8266, 26036, -8865, -189280, -234843; -9911, -351, 62, 165, -62, -1239, -1528; 4625940, 164647, -25005, -78760, 26817, 572580, 710410],81,7]
%
% END OF LATTICE L82.7
%
%
% LATTICE L82.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[24778489560, -53802540, 6183816540; -53802540, 116824, -13427172; 6183816540, -13427172, 1543257385],[660, 4, 1],[16099, 16094, 3266, 13669, 323, 41, 3271; -32351, -32355, -6571, -27522, -660, -82, -6567; -64790, -64770, -13144, -55011, -1300, -165, -13164],81,8]
%
% END OF LATTICE L82.8
%
%
% LATTICE L82.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-72720780, 26452140, 132660; 26452140, -9621950, -48255; 132660, -48255, -242],[660, 5, 1],[-1, -11, -1, 533, 15, 51, 26; 0, -30, -3, 1452, 41, 140, 72; -550, -48, 50, 2640, 47, 40, -105],81,9]
%
% END OF LATTICE L82.9
%
%
% LATTICE L82.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[29050263330, 969210, 9586487955; 969210, 33, 319836; 9586487955, 319836, 3163508374],[165, 33, 1],[-224594, -439661, 13351, 3824, -71601, -305788, -379400; -901, -1755, 62, 15, -310, -1239, -1528; 680595, 1332320, -40458, -11588, 216975, 926640, 1149709],81,10]
%
% END OF LATTICE L82.10
%
%
% LATTICE L82.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[28136460, 1772760, -27060; 1772760, 111694, -1705; -27060, -1705, 26],[660, 11, 1],[1, 29, 5, 7, -1, -5, -4; -16, -450, -77, -108, 15, 76, 60; -10, 660, 154, 204, -55, -220, -231],81,11]
%
% END OF LATTICE L82.11
%
%
% LATTICE L82.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[4178923320, -11862180, 1040339520; -11862180, 33672, -2953080; 1040339520, -2953080, 258991667],[660, 12, 1],[3526, 1389, 1139, 2151, 969, 41, 166; -2321, -925, -769, -1463, -670, -27, -105; -14190, -5590, -4584, -8657, -3900, -165, -668],81,12]
%
% END OF LATTICE L82.12
%
%
% LATTICE L82.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[29432433525, -1259445, -11698908375; -1259445, 55, 500610; -11698908375, 500610, 4650123718],[165, 55, 1],[351535, 412895, -20897, -17956, 22414, 478620, 1781513; -1055506, -1239738, 62753, 53913, -67304, -1437099, -5349123; 884515, 1038906, -52580, -45180, 56397, 1204280, 4482555],81,13]
%
% END OF LATTICE L82.13
%
%
% LATTICE L82.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-72698340, -6623100, 231000; -6623100, -603390, 21045; 231000, 21045, -734],[660, 15, 1],[19, -1, -2, 49, 5, 21, 5; -220, 10, 23, -484, -51, -220, -54; -330, -28, 30, 1540, 111, 300, 25],81,14]
%
% END OF LATTICE L82.14
%
%
% LATTICE L82.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[31647000, 15180, 7864560; 15180, 7480, 4320; 7864560, 4320, 1954453],[660, 20, 1],[29874, 407, 651, 89171, 9605, 9483, 28490; 8811, 120, 192, 26301, 2833, 2797, 8403; -120230, -1638, -2620, -358875, -38656, -38165, -114660],81,15]
%
% END OF LATTICE L82.15
%
%
% LATTICE L82.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[763620, 302280, 7920; 302280, 119658, 3135; 7920, 3135, 82],[660, 33, 1],[9, 9, -6, -3, 2, 19, 10; -22, -20, 16, 8, -5, -48, -25; -30, -110, -33, -16, 0, 0, -11],81,16]
%
% END OF LATTICE L82.16
%
%
% LATTICE L82.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-46415705325, 7478178345, 2728414590; 7478178345, -1204832310, -439583265; 2728414590, -439583265, -160382026],[165, 165, 1],[59, 23, -4, -1, 4, 81, 100; -4939477, -1921723, 353411, 83072, -344694, -6807968, -8384997; 13539375, 5267548, -968715, -227705, 944823, 18661005, 22983730],81,17]
%
% END OF LATTICE L82.17
%
%
% LATTICE L82.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[50591640, 1596540, 12561780; 1596540, 46376, 396440; 12561780, 396440, 3119059],[660, 44, 1],[-5310, -44033, -3105, 1429, 14049, -41, -17482; 123, 1020, 72, -33, -325, 1, 405; 21370, 177210, 12496, -5751, -56540, 165, 70356],81,18]
%
% END OF LATTICE L82.18
%
%
% LATTICE L82.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-214500, -19140, 660; -19140, -1210, 55; 660, 55, -2],[660, 55, 1],[-1, -1, 1, 5, 1, 1, -2; -4, -6, 1, 12, 3, 4, -6; -450, -528, 330, 1920, 407, 440, -825],81,19]
%
% END OF LATTICE L82.19
%
%
% LATTICE L82.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[20918040, 306900, 5195520; 306900, 38040, 76020; 5195520, 76020, 1290439],[660, 60, 1],[51082, 81, 1133, 55086, 17809, 17364, 17000; -1265, -2, -28, -1364, -441, -430, -421; -205590, -326, -4560, -221705, -71676, -69885, -68420],81,20]
%
% END OF LATTICE L82.20
%
%
% LATTICE L82.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-658680, -60060, -163020; -60060, 21912, -15180; -163020, -15180, -40343],[660, 132, 1],[1961, 5714, 1706, -43, -4101, 41, 2045; -91, -265, -79, 2, 190, -2, -95; -7890, -22990, -6864, 173, 16500, -165, -8228],81,21]
%
% END OF LATTICE L82.21
%
%
% LATTICE L82.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[16500, 21120, -660; 21120, 26070, -825; -660, -825, 26],[660, 165, 1],[-1, -1, 1, 5, 4, 11, 1; -2, -2, -1, 4, 4, 12, 1; -90, -88, 0, 260, 231, 660, 55],81,22]
%
% END OF LATTICE L82.22
%
%
% LATTICE L82.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[319296120, 833580, -78714240; 833580, 2200, -205480; -78714240, -205480, 19404983],[660, 220, 1],[-728, -2345, -3881, -2143, -809, -41, -164; 2177, 7011, 11603, 6408, 2420, 124, 495; -2930, -9438, -15620, -8625, -3256, -165, -660],81,23]
%
% END OF LATTICE L82.23
%
%
% LATTICE L82.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[6600, -308220, -76560; -308220, 14201880, 3527700; -76560, 3527700, 876269],[660, 660, 1],[3, -2, -30, -7, -11, 1, 11; -67, 71, 983, 247, 426, 41, -273; 270, -286, -3960, -995, -1716, -165, 1100],81,24]
%
% END OF LATTICE L82.24
%

\medskip%
%------------------------------WEYL-GROUP-W83--------------------------------
%
\leavevmode\llap{}%
$W_{83\phantom{0}}$%
\qquad\llap{16} lattices, $\chi=64$%
\hfill%
$23222222322222\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L83.1
%
\leavevmode%
${L_{83.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}8\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}17\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2\rightarrow N_{83}}%
\EasyButWeakLineBreak%
{${40}\above{1pt}{1pt}{b}{2}{2}\above{1pt}{1pt}{-}{3}{2}\above{1pt}{1pt}{l}{2}{136}\above{1pt}{1pt}{r}{2}{10}\above{1pt}{1pt}{l}{2}{8}\above{1pt}{1pt}{r}{2}{34}\above{1pt}{1pt}{b}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-156619640\\493680\\-116960
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
493680\\-1538\\349
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-116960\\349\\-66
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1845791\\749136960\\690421680
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-5510\\-2236301\\-2061025
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1044\\423720\\390509
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-713\\-289380\\-266700
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-181\\-73461\\-67703
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-50\\-20293\\-18702
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3175\\-1288600\\-1187552
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-309\\-125410\\-115575
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-97\\-39368\\-36280
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-87\\-35309\\-32538
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-156619640, 493680, -116960; 493680, -1538, 349; -116960, 349, -66],[680, 1, 1],[-713, -181, -50, -3175, -309, -97, -87, 17, 7, -8, -4713, -619, -367, -899; -289380, -73461, -20293, -1288600, -125410, -39368, -35309, 6900, 2841, -3247, -1912840, -251230, -148952, -364871; -266700, -67703, -18702, -1187552, -115575, -36280, -32538, 6360, 2618, -2993, -1762968, -231545, -137280, -336277],82,1]
%
% END OF LATTICE L83.1
%
%
% LATTICE L83.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-10710, 2210, 170; 2210, -456, -35; 170, -35, -2],[170, 1, 1],[-237, -83, 1, 7, -2, -7, -109, -87, -79, -55, -3679, -862, -209, -809; -1140, -399, 5, 34, -10, -34, -527, -420, -381, -265, -17714, -4150, -1006, -3893; -400, -146, -3, 0, 5, -4, -119, -110, -109, -82, -5780, -1365, -336, -1326],82,2]
%
% END OF LATTICE L83.2
%
%
% LATTICE L83.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-522580, 5270, -259760; 5270, -48, 2618; -259760, 2618, -129119],[170, 2, 1],[2068, 2114, 595, 9620, 3771, 302, 1143, -37, -83, 82, 13398, 7061, 1052, 10366; -1185, -1205, -334, -5304, -2065, -162, -578, 30, 50, -51, -7786, -4095, -608, -5967; -4185, -4278, -1204, -19465, -7630, -611, -2312, 75, 168, -166, -27115, -14290, -2129, -20978],82,3]
%
% END OF LATTICE L83.3
%
%
% LATTICE L83.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-630190, 8840, 127160; 8840, -120, -1785; 127160, -1785, -25658],[170, 5, 1],[-347, -889, -252, -8215, -323, -261, -506, 5, 34, -33, -11165, -589, -879, -4339; -474, -1205, -334, -10608, -413, -324, -578, 12, 50, -51, -15572, -819, -1216, -5967; -1686, -4320, -1225, -39950, -1571, -1270, -2465, 24, 165, -160, -54230, -2861, -4270, -21080],82,4]
%
% END OF LATTICE L83.4
%
%
% LATTICE L83.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[14808020, -466990, 7255770; -466990, 14740, -228820; 7255770, -228820, 3555249],[170, 10, 1],[-13705, -74497, -24584, -465628, -38511, -17818, -92484, -1016, 892, 49, -368562, -40001, -31252, -324611; -109, -592, -195, -3689, -305, -141, -731, -8, 7, 0, -2941, -319, -249, -2584; 27963, 152000, 50160, 950045, 78576, 36355, 188700, 2073, -1820, -100, 751995, 81616, 63765, 662320],82,5]
%
% END OF LATTICE L83.5
%
%
% LATTICE L83.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1448230, -17340, -427380; -17340, -136, -5117; -427380, -5117, -126122],[170, 17, 1],[14349, 7300, 2027, 3795, 12569, 1977, 209, -351, -301, 306, 5537, 24759, 7355, 2124; -20, -14, -7, -20, -75, -16, -3, -10, -1, 2, 0, -5, -4, -2; -48620, -24735, -6868, -12858, -42585, -6698, -708, 1190, 1020, -1037, -18762, -83895, -24922, -7197],82,6]
%
% END OF LATTICE L83.6
%
%
% LATTICE L83.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-30033560, 484840, -36040; 484840, -7690, 555; -36040, 555, -38],[680, 5, 1],[-97, -127, -38, -2563, -51, -85, -87, 1, 7, -2, -2877, -77, -235, -593; -9688, -12684, -3795, -255952, -5093, -8488, -8687, 100, 699, -200, -287368, -7691, -23472, -59228; -49508, -64815, -19390, -1307640, -26019, -43360, -44370, 512, 3570, -1025, -1468800, -39309, -119960, -302685],82,7]
%
% END OF LATTICE L83.7
%
%
% LATTICE L83.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1377680, -132600, -342040; -132600, -12048, -32912; -342040, -32912, -84919],[680, 8, 1],[-294, -338, 589, 36571, 38197, 2804, 54401, 10671, 10715, 2870, 22232, 17147, 655, 4402; -15, -17, 30, 1853, 1935, 142, 2754, 540, 542, 145, 1122, 865, 33, 221; 1190, 1368, -2384, -148019, -154600, -11349, -220184, -43190, -43368, -11616, -89981, -69400, -2651, -17816],82,8]
%
% END OF LATTICE L83.8
%
%
% LATTICE L83.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1311305540, 280330, 650801990; 280330, 68, 139128; 650801990, 139128, 322993549],[170, 34, 1],[430082, 467180, 153893, 171268, 1203639, 111294, 33945, 31597, -5501, 0, 136518, 1258649, 196492, 119948; -600, -653, -216, -241, -1695, -157, -48, -45, 8, 1, -189, -1745, -273, -167; -866575, -941324, -310080, -345089, -2425220, -224247, -68396, -63665, 11084, 0, -275071, -2536060, -395913, -241684],82,9]
%
% END OF LATTICE L83.9
%
%
% LATTICE L83.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-143480, 70040, -148240; 70040, -26146, 49453; -148240, 49453, -87906],[680, 17, 1],[1457, 595, -686, -23673, -52849, -31327, -4513, -60833, -15439, -4262, -15911, -26319, -8257, -435; 11620, 4745, -5471, -188792, -421470, -249832, -35991, -485140, -123125, -33989, -126888, -209890, -65848, -3469; 4080, 1666, -1921, -66288, -147985, -87720, -12637, -170340, -43231, -11934, -44552, -73695, -23120, -1218],82,10]
%
% END OF LATTICE L83.10
%
%
% LATTICE L83.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1269344610, -436050, 257061760; -436050, 170, -88315; 257061760, -88315, 52058954],[170, 85, 1],[109205, 296562, 97690, 217439, 152812, 141297, 21548, 8023, -3492, 0, 173321, 159796, 249463, 76142; -218650, -593777, -195596, -435360, -305963, -282908, -43144, -16064, 6992, 1, -347020, -319941, -499472, -152451; -539614, -1465400, -482715, -1074430, -755089, -698190, -106475, -39644, 17255, 0, -856430, -789599, -1232670, -376240],82,11]
%
% END OF LATTICE L83.11
%
%
% LATTICE L83.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-970074510160, -227319932920, -3788362280; -227319932920, -53268435920, -887736200; -3788362280, -887736200, -14794419],[680, 40, 1],[-209, -239, 2090, 89861, 18453, 6584, 123798, 4688, 22634, 5375, 37044, 5435, 881, 3107; 0, 2, -1, -136, -29, -11, -221, -9, -47, -14, -119, -19, -4, -34; 53518, 61080, -535120, -23002275, -4723464, -1685285, -31687320, -1199902, -5793000, -1375520, -9478605, -1390584, -225355, -793560],82,12]
%
% END OF LATTICE L83.12
%
%
% LATTICE L83.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-4207840340, 14593669550, 7235724280; 14593669550, -50613886820, -25094999480; 7235724280, -25094999480, -12442415283],[170, 170, 1],[-2, -14, -7, -10, -15, -8, -3, -1, -1, 2, 0, -1, -2, -2; 1425337, 7251641, 2013810, 1885416, 2497925, 982418, 207814, -34786, -298886, 303775, 2749754, 4918347, 3652752, 2109771; -2874751, -14625780, -4061640, -3802685, -5038052, -1981435, -419140, 70159, 602820, -612680, -5545955, -9919772, -7367205, -4255180],82,13]
%
% END OF LATTICE L83.13
%
%
% LATTICE L83.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-641240, 72080, 14960; 72080, -6630, -1615; 14960, -1615, -346],[680, 85, 1],[-449, -586, -174, -687, -232, -385, -23, 5, 31, -11, -793, -360, -1095, -162; 1104, 1442, 429, 1696, 573, 952, 57, -12, -77, 26, 1944, 883, 2688, 398; -24548, -32045, -9520, -37600, -12699, -21080, -1260, 272, 1700, -595, -43320, -19669, -59840, -8855],82,14]
%
% END OF LATTICE L83.14
%
%
% LATTICE L83.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-4489360, 3529880, 1783640; 3529880, -2775216, -1402432; 1783640, -1402432, -708647],[680, 136, 1],[-17879, -17999, -4857, -2229, -29308, -1129, -457, 461, 581, -949, -3577, -63588, -4677, -5349; 540, 542, 145, 66, 865, 33, 13, -15, -17, 30, 109, 1935, 142, 162; -46070, -46376, -12512, -5741, -75480, -2907, -1176, 1190, 1496, -2448, -9219, -163880, -12053, -13784],82,15]
%
% END OF LATTICE L83.15
%
%
% LATTICE L83.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-521708240, -183723080, 1529320; -183723080, -64699280, 538560; 1529320, 538560, -4483],[680, 680, 1],[-9, -47, -14, -7, -19, -4, -2, 0, 2, -1, -8, -29, -11, -13; 336, 1622, 385, 156, 389, 63, 13, -15, -17, 150, 379, 1323, 472, 522; 37298, 178840, 41480, 16355, 40256, 6205, 880, -1802, -1360, 17680, 42805, 149056, 52955, 58280],82,16]
%
% END OF LATTICE L83.16
%

\medskip%
%------------------------------WEYL-GROUP-W84--------------------------------
%
\leavevmode\llap{}%
$W_{84\phantom{0}}$%
\qquad\llap{24} lattices, $\chi=12$%
\hfill%
$222222$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L84.1
%
\leavevmode%
${L_{84.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}13\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2\rightarrow N_{84}}%
\EasyButWeakLineBreak%
{${4}\above{1pt}{1pt}{*}{2}{52}\above{1pt}{1pt}{b}{2}{10}\above{1pt}{1pt}{l}{2}{156}\above{1pt}{1pt}{r}{2}{2}\above{1pt}{1pt}{s}{2}{390}\above{1pt}{1pt}{b}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-11003460\\-3664440\\15600
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3664440\\-1220354\\5195
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
15600\\5195\\-22
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
39\\-118\\-210
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
43\\-130\\-208
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-38\\115\\210
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-361\\1092\\1872
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\3\\-1
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
451\\-1365\\-2535
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-11003460, -3664440, 15600; -3664440, -1220354, 5195; 15600, 5195, -22],[780, 1, 1],[39, 43, -38, -361, -1, 451; -118, -130, 115, 1092, 3, -1365; -210, -208, 210, 1872, -1, -2535],83,1]
%
% END OF LATTICE L84.1
%
%
% LATTICE L84.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[390, -195, 0; -195, 97, 0; 0, 0, 1],[195, 1, 1],[0, 6, -7, -145, -13, -181; 0, 13, -15, -312, -28, -390; 1, 0, -5, -39, -2, 0],83,2]
%
% END OF LATTICE L84.2
%
%
% LATTICE L84.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-4849845, 25155, 1617915; 25155, -123, -8394; 1617915, -8394, -539738],[195, 3, 1],[-5853, -19568, -1644, 854, 365, -36099; -5260, -17589, -1480, 767, 329, -32435; -17463, -58383, -4905, 2548, 1089, -107705],83,3]
%
% END OF LATTICE L84.3
%
%
% LATTICE L84.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-7741695, 40755, 1549665; 40755, -205, -8160; 1549665, -8160, -310198],[195, 5, 1],[-5021, -16786, -282, 2198, 313, -18581; -5260, -17589, -296, 2301, 329, -19461; -24945, -83395, -1401, 10920, 1555, -92313],83,4]
%
% END OF LATTICE L84.4
%
%
% LATTICE L84.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-693420, -780, 3120; -780, 6, 3; 3120, 3, -14],[780, 3, 1],[-1, -1, 1, 3, 0, -4; -18, -26, 15, 52, 1, -65; -228, -234, 225, 676, 0, -910],83,5]
%
% END OF LATTICE L84.5
%
%
% LATTICE L84.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-19293495, 103155, 8906040; 103155, -533, -47619; 8906040, -47619, -4111103],[195, 13, 1],[-25358, -6521, -7119, 854, 1580, -36094; -5260, -1353, -1480, 177, 329, -7485; -54873, -14111, -15405, 1848, 3419, -78105],83,6]
%
% END OF LATTICE L84.6
%
%
% LATTICE L84.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[150810270, -6193395, -52222365; -6193395, 254355, 2144640; -52222365, 2144640, 18083486],[195, 15, 1],[39501, 129880, 1914, -5828, -1807, 49585; -271, -897, -14, 39, 14, -338; 114105, 375180, 5529, -16835, -5220, 143234],83,7]
%
% END OF LATTICE L84.7
%
%
% LATTICE L84.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2415143640, -3986580, -605564700; -3986580, 6584, 999580; -605564700, 999580, 151837183],[780, 4, 1],[-877, -2045, -779, -7262, -1365, -36457; -1169, -2730, -1040, -9672, -1817, -48555; -3490, -8138, -3100, -28899, -5432, -145080],83,8]
%
% END OF LATTICE L84.8
%
%
% LATTICE L84.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[244140, -1560, -780; -1560, 10, 5; -780, 5, 2],[780, 5, 1],[-1, -3, 0, 1, 0, -2; -138, -416, 0, 156, 1, -273; -40, -130, -1, 0, 0, -78],83,9]
%
% END OF LATTICE L84.9
%
%
% LATTICE L84.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[266853990, 13284180, -85409415; 13284180, 661323, -4251741; -85409415, -4251741, 27336178],[195, 39, 1],[-88449, -22388, -21591, 1001, 4106, -42672; -271, -69, -70, 3, 14, -130; -276393, -69960, -67470, 3128, 12831, -133345],83,10]
%
% END OF LATTICE L84.10
%
%
% LATTICE L84.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[299125320, -347100, -75171720; -347100, 408, 87228; -75171720, 87228, 18891037],[780, 12, 1],[-481, -2019, -769, -722, -193, -3659; -2, -13, -5, 0, 2, 0; -1914, -8034, -3060, -2873, -768, -14560],83,11]
%
% END OF LATTICE L84.11
%
%
% LATTICE L84.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-22207380, 7417800, 56160; 7417800, -2477722, -18759; 56160, -18759, -142],[780, 13, 1],[-3, -5, 2, 43, 30, 32; -8, -14, 5, 120, 84, 90; -130, -128, 130, 1152, 767, 765],83,12]
%
% END OF LATTICE L84.12
%
%
% LATTICE L84.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3785340, -5460, 13260; -5460, 30, 15; 13260, 15, -46],[780, 15, 1],[-1, 17, 2, 27, 0, -2; -34, 546, 65, 884, 1, -65; -300, 5070, 597, 8060, 0, -598],83,13]
%
% END OF LATTICE L84.13
%
%
% LATTICE L84.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1581898695, -41755155, 334752990; -41755155, 1102205, -8836035; 334752990, -8836035, 70838666],[195, 65, 1],[184181, 46620, 8993, -6253, -8552, 53314; -552814, -139929, -26993, 18768, 25670, -160020; -939315, -237760, -45864, 31890, 43615, -271899],83,14]
%
% END OF LATTICE L84.14
%
%
% LATTICE L84.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-301080, -780, 75660; -780, 3080, 200; 75660, 200, -19013],[780, 20, 1],[299, 2254, 194, 49, -387, -353; -2, -13, -1, 0, 2, 0; 1190, 8970, 772, 195, -1540, -1404],83,15]
%
% END OF LATTICE L84.15
%
%
% LATTICE L84.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[501540, -7589400, 584220; -7589400, 111247266, -8562489; 584220, -8562489, 659038],[780, 39, 1],[129, 127, -129, -381, -761, -253; 2062, 2030, -2065, -6092, -12167, -4045; 26676, 26262, -26715, -78812, -157404, -52330],83,16]
%
% END OF LATTICE L84.16
%
%
% LATTICE L84.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-28987000770, 78222825135, -26326845870; 78222825135, -211088079345, 71044267710; -26326845870, 71044267710, -23910814813],[195, 195, 1],[-5260, -1353, -296, 59, 329, -499; 7149252, 1838461, 401373, -80260, -445372, 678414; 21247785, 5463960, 1192893, -238535, -1323660, 2016266],83,17]
%
% END OF LATTICE L84.17
%
%
% LATTICE L84.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[460906680, -3882060, -115924380; -3882060, 33176, 976404; -115924380, 976404, 29156579],[780, 52, 1],[-2620, -97, -6207, -5287, -12806, -17852; 271, 10, 640, 546, 1323, 1845; -10426, -386, -24700, -21039, -50960, -71040],83,18]
%
% END OF LATTICE L84.18
%
%
% LATTICE L84.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1814278440, -15410460, -455927160; -15410460, 130920, 3872640; -455927160, 3872640, 114574241],[780, 60, 1],[-867, -12839, -2319, -9621, -1357, -967; -2, -13, -1, 0, 2, 0; -3450, -51090, -9228, -38285, -5400, -3848],83,19]
%
% END OF LATTICE L84.19
%
%
% LATTICE L84.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-60567780, -34320, 117000; -34320, 130, 65; 117000, 65, -226],[780, 65, 1],[-1, 9, 12, 37, 0, -2; -6, 40, 54, 168, 1, -9; -520, 4670, 6227, 19200, 0, -1038],83,20]
%
% END OF LATTICE L84.20
%
%
% LATTICE L84.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[8674618616040, -136751229420, -2179995318540; -136751229420, 2155817976, 34366587528; -2179995318540, 34366587528, 547848821857],[780, 156, 1],[5953, -485, -31037, -2461, -6873, 2001; -1624, 129, 8255, 641, 1706, -600; 23790, -1938, -124020, -9833, -27456, 8000],83,21]
%
% END OF LATTICE L84.21
%
%
% LATTICE L84.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-780, 0, -780; 0, 390, 195; -780, 195, -682],[780, 195, 1],[-1, 29, 38, 39, 0, -2; -2, 14, 19, 20, 1, -1; 0, -30, -39, -40, 0, 2],83,22]
%
% END OF LATTICE L84.22
%
%
% LATTICE L84.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[27207674520, 78610740, 6777808440; 78610740, 227240, 19582940; 6777808440, 19582940, 1688445991],[780, 260, 1],[8265, 11572, 26840, 23291, 8559, 389; -24797, -34717, -80521, -69873, -25675, -1167; -32890, -46050, -106808, -92685, -34060, -1548],83,23]
%
% END OF LATTICE L84.23
%
%
% LATTICE L84.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[76440, 760500, -190320; 760500, 7601880, -1902420; -190320, -1902420, 476093],[780, 780, 1],[-2, -1, -1, 0, 2, 0; 293, 383, 859, 239, 195, 1; 1170, 1530, 3432, 955, 780, 4],83,24]
%
% END OF LATTICE L84.24
%

\medskip%
%------------------------------WEYL-GROUP-W85--------------------------------
%
\leavevmode\llap{}%
$W_{85\phantom{0}}$%
\qquad\llap{24} lattices, $\chi=42$%
\hfill%
$2224222242\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L85.1
%
\leavevmode%
${L_{85.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{2}{}5\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{2}{}13\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{2\rightarrow N_{85}}%
\EasyButWeakLineBreak%
{${20}\above{1pt}{1pt}{b}{2}{26}\above{1pt}{1pt}{s}{2}{30}\above{1pt}{1pt}{b}{2}{4}\above{1pt}{1pt}{*}{4}{2}\above{1pt}{1pt}{b}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-36481380\\30420\\42900
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
30420\\-22\\-37
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
42900\\-37\\-50
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
107639\\26479440\\72728760
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-75\\-18451\\-50675
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-132\\-32472\\-89189
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
11\\2710\\7430
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
31\\7631\\20943
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
47\\11565\\31755
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
43\\10578\\29054
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
14\\3443\\9460
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-36481380, 30420, 42900; 30420, -22, -37; 42900, -37, -50],[780, 1, 1],[11, 31, 47, 43, 14, 19, 8, -2, -1, 1; 2710, 7631, 11565, 10578, 3443, 4670, 1963, -495, -246, 247; 7430, 20943, 31755, 29054, 9460, 12840, 5408, -1350, -676, 675],84,1]
%
% END OF LATTICE L85.1
%
%
% LATTICE L85.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[2730, -585, -390; -585, 125, 78; -390, 78, -31],[195, 1, 1],[1, -40, 34, 75, 99, 154, 443, 431, 142, 56; 5, -195, 165, 365, 482, 750, 2158, 2100, 692, 273; 0, 13, -15, -28, -36, -55, -156, -150, -49, -19],84,2]
%
% END OF LATTICE L85.2
%
%
% LATTICE L85.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-16016910, -1635075, 5396235; -1635075, -166677, 550875; 5396235, 550875, -1818038],[195, 3, 1],[15896, 90743, 46203, 63762, 41789, 28744, 25321, -1563, -1266, 2851; -815, -4654, -2370, -3271, -2144, -1475, -1300, 80, 65, -146; 46935, 267930, 136420, 188265, 123387, 84870, 74763, -4615, -3738, 8418],84,3]
%
% END OF LATTICE L85.3
%
%
% LATTICE L85.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-13881270, -1964625, 2817555; -1964625, -277795, 398775; 2817555, 398775, -571894],[195, 5, 1],[1874, 53485, 16339, 37580, 24629, 3388, 14921, -553, -746, 1681; -163, -4654, -1422, -3271, -2144, -295, -1300, 48, 65, -146; 9119, 260260, 79506, 182865, 119845, 16486, 72605, -2691, -3630, 8180],84,4]
%
% END OF LATTICE L85.4
%
%
% LATTICE L85.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-88140, -14820, -1560; -14820, -2454, -285; -1560, -285, -14],[780, 3, 1],[-89, -311, -171, -493, -169, -251, -131, 1, 17, -1; 450, 1573, 865, 2494, 855, 1270, 663, -5, -86, 5; 750, 2613, 1435, 4134, 1416, 2100, 1092, -10, -144, 9],84,5]
%
% END OF LATTICE L85.5
%
%
% LATTICE L85.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-14917110, -3282825, 6911385; -3282825, -722267, 1521000; 6911385, 1521000, -3202178],[195, 13, 1],[18821, 8261, 164009, 75437, 49434, 33994, 2302, -5564, -1496, 3381; -815, -358, -7110, -3271, -2144, -1475, -100, 240, 65, -146; 40235, 17660, 350610, 161265, 105677, 72670, 4921, -11895, -3198, 7228],84,6]
%
% END OF LATTICE L85.6
%
%
% LATTICE L85.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[6889923690, 24716250, -2388778665; 24716250, 88665, -8569275; -2388778665, -8569275, 828204167],[195, 15, 1],[2431, 68165, 6957, 48345, 31991, 4517, 22159, -9, 291, 2749; 512, 14261, 1451, 10064, 6646, 935, 4550, -4, 65, 589; 7017, 196755, 20081, 139545, 92340, 13038, 63960, -26, 840, 7935],84,7]
%
% END OF LATTICE L85.7
%
%
% LATTICE L85.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[23660602680, -44527860, -5945665440; -44527860, 83800, 11189392; -5945665440, 11189392, 1494084407],[780, 4, 1],[-13753, -83289, -132047, -62511, -42323, -31107, -33347, -2533, -293, -2537; 45, 247, 375, 173, 114, 80, 78, 0, 2, 11; -54730, -331448, -525480, -248762, -168424, -123790, -132704, -10080, -1166, -10096],84,8]
%
% END OF LATTICE L85.8
%
%
% LATTICE L85.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3930420, 1300260, 10140; 1300260, -430150, -3355; 10140, -3355, -26],[780, 5, 1],[63, 163, -1, -21, 2, 23, 396, 130, 623, 213; 186, 481, -3, -62, 6, 68, 1170, 384, 1840, 629; 566, 1495, -3, -190, 5, 194, 3445, 1143, 5510, 1895],84,9]
%
% END OF LATTICE L85.9
%
%
% LATTICE L85.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2280616455, -22929075, -731209245; -22929075, 230529, 7351500; -731209245, 7351500, 234439666],[195, 39, 1],[-18793, -8083, -53549, -74361, -49162, -34652, -2606, 104, -462, -4283; 2560, 1097, 7255, 10064, 6646, 4675, 350, -20, 65, 589; -58695, -25245, -167245, -232245, -153543, -108225, -8139, 325, -1443, -13377],84,10]
%
% END OF LATTICE L85.10
%
%
% LATTICE L85.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[471277560, -2949180, -118229280; -2949180, 18456, 739860; -118229280, 739860, 29660149],[780, 12, 1],[731, 6153, 3673, 5597, 4061, 3339, 4429, 397, 101, 9; 155, 1391, 845, 1299, 950, 790, 1066, 100, 24, -5; 2910, 24492, 14620, 22278, 16164, 13290, 17628, 1580, 402, 36],84,11]
%
% END OF LATTICE L85.11
%
%
% LATTICE L85.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2420340, 26520, 307320; 26520, -286, -3445; 307320, -3445, -37706],[780, 13, 1],[691, 151, 2987, 2739, 894, 1219, 40, -122, -65, 61; 37450, 8183, 161865, 148422, 48443, 66050, 2167, -6615, -3522, 3307; 2210, 483, 9555, 8762, 2860, 3900, 128, -390, -208, 195],84,12]
%
% END OF LATTICE L85.12
%
%
% LATTICE L85.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-471900, 12480, 6240; 12480, -330, -165; 6240, -165, -82],[780, 15, 1],[1, 18, 2, 29, 10, 3, 8, 0, -1, 0; 46, 767, 83, 1186, 403, 118, 299, -1, -38, 7; -18, -195, -17, -210, -60, -12, 0, 2, 0, -15],84,13]
%
% END OF LATTICE L85.13
%
%
% LATTICE L85.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[15538444350, 77266020, 3002702625; 77266020, 384215, 14931150; 3002702625, 14931150, 580252622],[195, 65, 1],[7773, 16715, 66439, 153765, 101656, 14330, 5388, -130, 956, 8859; -22807, -49048, -194964, -451231, -298322, -42055, -15814, 378, -2803, -25988; -39637, -85235, -338793, -784095, -518375, -73073, -27475, 663, -4875, -45175],84,14]
%
% END OF LATTICE L85.14
%
%
% LATTICE L85.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[72079800, -1070940, -18184920; -1070940, 16120, 270200; -18184920, 270200, 4587851],[780, 20, 1],[-3589, -18425, -193, -485, -2136, -1844, -52204, -16106, -37546, -25029; 955, 4901, 51, 129, 569, 491, 13897, 4287, 9993, 6661; -14282, -73320, -768, -1930, -8500, -7338, -207740, -64092, -149410, -99600],84,15]
%
% END OF LATTICE L85.15
%
%
% LATTICE L85.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2044380, 16709160, -1287000; 16709160, -135158946, 10409919; -1287000, 10409919, -801770],[780, 39, 1],[-2113, -562, -4002, -11513, -3938, -5827, -232, 32, 397, -32; -55020, -14632, -104190, -299728, -102519, -151690, -6039, 835, 10334, -836; -710970, -189075, -1346345, -3873090, -1324752, -1960140, -78036, 10790, 133536, -10803],84,16]
%
% END OF LATTICE L85.16
%
%
% LATTICE L85.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-21706695075, 59912507070, -20164275690; 59912507070, -165364096170, 55655277795; -20164275690, 55655277795, -18731453914],[195, 195, 1],[-163, -358, -474, -3271, -2144, -295, -100, 16, 65, -146; -1133981, -2488693, -3293955, -22726221, -14892592, -2048236, -693524, 111738, 450702, -1018493; -3369132, -7394070, -9786556, -67521090, -44246865, -6085443, -2060505, 331981, 1339065, -3026010],84,17]
%
% END OF LATTICE L85.17
%
%
% LATTICE L85.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[10437960, 47072220, -2556060; 47072220, 212282824, -11527100; -2556060, -11527100, 625931],[780, 52, 1],[-6729, -2797, -54791, -25159, -16495, -11471, -843, 191, -321, -1705; 45, 19, 375, 173, 114, 80, 6, 0, 2, 11; -26650, -11072, -216840, -99554, -65260, -45370, -3332, 780, -1274, -6760],84,18]
%
% END OF LATTICE L85.18
%
%
% LATTICE L85.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[338520, 36660, -85020; 36660, 18600, -9180; -85020, -9180, 21353],[780, 60, 1],[-1211, -33133, -3349, -23157, -15247, -2137, -10391, 1, -279, -1493; 9, 247, 25, 173, 114, 16, 78, 0, 2, 11; -4818, -131820, -13324, -92130, -60660, -8502, -41340, 4, -1110, -5940],84,19]
%
% END OF LATTICE L85.19
%
%
% LATTICE L85.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-401700, -376740, 9360; -376740, -353210, 8775; 9360, 8775, -218],[780, 65, 1],[-5, -5, -19, -85, -27, -7, -1, 1, 1, -3; 24, 28, 114, 532, 177, 50, 9, -3, -14, 8; 754, 915, 3783, 17810, 5980, 1716, 320, -78, -520, 195],84,20]
%
% END OF LATTICE L85.20
%
%
% LATTICE L85.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[14058491823480, -220208555580, -3532863574500; -220208555580, 3449289480, 55337855196; -3532863574500, 55337855196, 887799715129],[780, 156, 1],[75094, 31350, 205192, 283120, 185959, 129771, 9623, -327, 3691, 18906; -17405, -7307, -47965, -66309, -43646, -30580, -2290, -20, -870, -4339; 299910, 125208, 819520, 1130766, 742716, 518310, 38436, -1300, 14742, 75504],84,21]
%
% END OF LATTICE L85.21
%
%
% LATTICE L85.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-818220, 705900, 24180; 705900, -591630, -20475; 24180, -20475, -706],[780, 195, 1],[-291, -50, 8, 85, -57, -151, -171, -229, -3179, -1048; 622, 107, -17, -182, 121, 322, 365, 489, 6790, 2239; -28002, -4815, 767, 8190, -5460, -14508, -16440, -22022, -305760, -100815],84,22]
%
% END OF LATTICE L85.22
%
%
% LATTICE L85.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[157845480, 1426620, 38585820; 1426620, 13000, 348660; 38585820, 348660, 9432487],[780, 260, 1],[-2752, -5506, -21140, -47882, -30919, -4177, -1423, 353, -621, -3726; 8433, 16871, 64773, 146707, 94731, 12797, 4359, -1083, 1903, 11419; 10946, 21900, 84084, 190450, 122980, 16614, 5660, -1404, 2470, 14820],84,23]
%
% END OF LATTICE L85.23
%
%
% LATTICE L85.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[7009080, 302487900, -76026600; 302487900, 13054356120, -3281051280; -76026600, -3281051280, 824651741],[780, 780, 1],[-179, -63, 3, -31, -154, -114, -230, -296, -2020, -1311; 9277, 3485, 13, 1275, 6473, 5237, 11029, 14501, 100323, 66097; 36894, 13860, 52, 5070, 25740, 20826, 43860, 57668, 398970, 262860],84,24]
%
% END OF LATTICE L85.24
%

\medskip%
%------------------------------WEYL-GROUP-W86--------------------------------
%
\leavevmode\llap{}%
$W_{86\phantom{0}}$%
\qquad\llap{48} lattices, $\chi=28$%
\hfill%
$22622222$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L86.1
%
\leavevmode%
${L_{86.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{1}{}3\above{1pt}{1pt}{-}{}9\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{2}{}13\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{23\rightarrow N_{86},3,2}%
\EasyButWeakLineBreak%
{${4}\above{1pt}{1pt}{*}{2}{2340}\above{1pt}{1pt}{b}{2}{6}\above{1pt}{1pt}{}{6}{18}\above{1pt}{1pt}{l}{2}{60}\above{1pt}{1pt}{r}{2}{234}\above{1pt}{1pt}{b}{2}{10}\above{1pt}{1pt}{s}{2}{78}\above{1pt}{1pt}{b}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-143865540\\159120\\10754640
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
159120\\-174\\-12363
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
10754640\\-12363\\-693998
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3027\\2125402\\9046
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
112363\\78895440\\335790
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
260\\182558\\777
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-259\\-181857\\-774
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-261\\-183260\\-780
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1292\\907179\\3861
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
691\\485185\\2065
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
6225\\4370873\\18603
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-143865540, 159120, 10754640; 159120, -174, -12363; 10754640, -12363, -693998],[2340, 3, 1],[3027, 112363, 260, -259, -261, 1292, 691, 6225; 2125402, 78895440, 182558, -181857, -183260, 907179, 485185, 4370873; 9046, 335790, 777, -774, -780, 3861, 2065, 18603],85,1]
%
% END OF LATTICE L86.1
%
%
% LATTICE L86.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-12090, 4095, 0; 4095, -1387, 0; 0, 0, 1],[195, 1, 1],[0, 22, -1, -138, -577, -465, -81, -79; 0, 65, -3, -409, -1710, -1378, -240, -234; 1, 0, -3, -27, -105, -78, -10, 0],85,2]
%
% END OF LATTICE L86.2
%
%
% LATTICE L86.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-8395140, 2811120, 25740; 2811120, -941306, -8619; 25740, -8619, -58],[780, 1, 1],[6579, 80051, 443, -222, -221, 1332, 1701, 13973; 19648, 239070, 1323, -663, -660, 3978, 5080, 41730; -54, -650, -3, 2, 0, -13, -15, -117],85,3]
%
% END OF LATTICE L86.3
%
%
% LATTICE L86.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-7842510, 41535, 1001520; 41535, -219, -5343; 1001520, -5343, -126353],[585, 3, 1],[607, 22973, 131, -64, -66, 317, 237, 2403; 71376, 2701335, 15403, -7527, -7760, 37284, 27870, 282568; 1793, 67860, 387, -189, -195, 936, 700, 7098],85,4]
%
% END OF LATTICE L86.4
%
%
% LATTICE L86.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-10155405, -2428335, 3399435; -2428335, -577338, 812916; 3399435, 812916, -1137931],[195, 3, 1],[457155, 5111309, -5897, 5942, 115082, 643091, 401133, 755045; -21016, -234975, 271, -273, -5290, -29562, -18440, -34710; 1350684, 15101580, -17423, 17556, 340015, 1900041, 1185165, 2230813],85,5]
%
% END OF LATTICE L86.5
%
%
% LATTICE L86.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-13403715, -3595995, 2693535; -3595995, -962230, 722670; 2693535, 722670, -541277],[195, 5, 1],[277053, 619527, -10723, 3602, 41848, 389747, 48621, 1372763; -21016, -46995, 813, -273, -3174, -29562, -3688, -104130; 1350630, 3020186, -52275, 17560, 204009, 1900015, 237027, 6692205],85,6]
%
% END OF LATTICE L86.6
%
%
% LATTICE L86.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-5256810, 33930, 18135; 33930, -219, -117; 18135, -117, -58],[585, 3, 1],[55, 226, 3, -1, -1, 6, 26, 76; 8559, 35165, 466, -156, -155, 936, 4050, 11830; -81, -325, -3, 2, 0, -13, -45, -117],85,7]
%
% END OF LATTICE L86.7
%
%
% LATTICE L86.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-31731180, 28860, 42900; 28860, -18, -39; 42900, -39, -58],[780, 3, 1],[35, 433, 1, -1, -1, 5, 8, 24; -54, -650, -1, 2, 0, -13, -15, -39; 25914, 320580, 740, -741, -740, 3705, 5925, 17771],85,8]
%
% END OF LATTICE L86.8
%
%
% LATTICE L86.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-27301755, -8266635, 12612210; -8266635, -2501798, 3818841; 12612210, 3818841, -5826286],[195, 13, 1],[630195, 541993, -24406, 8202, 476021, 68202, 553008, 240200; -21016, -18075, 813, -273, -15870, -2274, -18440, -8010; 1350414, 1161410, -52299, 17576, 1020045, 146147, 1185015, 514713],85,9]
%
% END OF LATTICE L86.9
%
%
% LATTICE L86.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[64855240905, 201668220, -22483132620; 201668220, 627090, -69911595; -22483132620, -69911595, 7794146554],[195, 15, 1],[433335, 980297, -2294, -26, 18519, 548818, 71808, 702048; 161009, 364221, -857, 0, 6886, 204009, 26687, 260871; 1251450, 2831049, -6625, -75, 53482, 1584960, 207378, 2027480],85,10]
%
% END OF LATTICE L86.10
%
%
% LATTICE L86.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[61707642360, 235749540, -15427084140; 235749540, 900664, -58938048; -15427084140, -58938048, 3856814423],[780, 4, 1],[-16126, -201079, -3079, 1, -833, -6416, -7358, -65704; 21809, 272025, 4179, 0, 1110, 8619, 9925, 88803; -64170, -800150, -12252, 4, -3315, -25532, -29280, -261456],85,11]
%
% END OF LATTICE L86.11
%
%
% LATTICE L86.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-4741620, 37440, 1605240; 37440, -290, -12675; 1605240, -12675, -543442],[780, 5, 1],[3771, 9479, 391, -66, -65, 396, 153, 7525; -54, -130, -3, 2, 0, -13, -3, -117; 11140, 28002, 1155, -195, -192, 1170, 452, 22230],85,12]
%
% END OF LATTICE L86.12
%
%
% LATTICE L86.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-95193540, 128700, 86580; 128700, -174, -117; 86580, -117, -58],[2340, 3, 1],[89, 361, 2, -1, -1, 6, 23, 63; 65928, 267410, 1481, -741, -740, 4446, 17040, 46670; -162, -650, -3, 2, 0, -13, -45, -117],85,13]
%
% END OF LATTICE L86.13
%
%
% LATTICE L86.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[27019792410, -209890395, -8660172300; -209890395, 1630434, 67272426; -8660172300, 67272426, 2775690617],[195, 39, 1],[-873060, -759617, 4635, 25, -186628, -85076, -723462, -108808; 161009, 140085, -857, 0, 34430, 15693, 133435, 20067; -2727855, -2373405, 14482, 78, -583115, -265818, -2260440, -339968],85,14]
%
% END OF LATTICE L86.14
%
%
% LATTICE L86.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-50004045, 93618135, -15381990; 93618135, -175236315, 28790955; -15381990, 28790955, -4730242],[585, 15, 1],[-64206, -497000, -17191, 1730, 1719, -8653, -4015, -242517; -185485, -1435785, -49663, 4998, 4966, -24999, -11599, -700609; -920180, -7122843, -246375, 24795, 24636, -124020, -57542, -3475680],85,15]
%
% END OF LATTICE L86.15
%
%
% LATTICE L86.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-43920045, 1812915, 339885; 1812915, -74715, -14010; 339885, -14010, -2627],[585, 15, 1],[139, 118, 11, -1, -1, 6, 10, 180; -27081, -22984, -2138, 197, 194, -1183, -1953, -35087; 162405, 137839, 12825, -1180, -1164, 7085, 11709, 210405],85,16]
%
% END OF LATTICE L86.16
%
%
% LATTICE L86.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[16829752680, 574860, -4229131920; 574860, 24, -144456; -4229131920, -144456, 1062734381],[780, 12, 1],[-54877, -684549, -3509, 0, -926, -21639, -24953, -74469; 71, 910, 6, 1, 0, 13, 25, 91; -218382, -2724150, -13964, 0, -3685, -86112, -99300, -296348],85,17]
%
% END OF LATTICE L86.17
%
%
% LATTICE L86.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3556020, -1580280, 25740; -1580280, -691886, 13169; 25740, 13169, 102],[780, 13, 1],[-23061, -21577, -1544, 782, 761, -361, -5976, -3770; 47272, 44230, 3165, -1603, -1560, 740, 12250, 7728; -283686, -265430, -18993, 9620, 9360, -4441, -73515, -46377],85,18]
%
% END OF LATTICE L86.18
%
%
% LATTICE L86.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-131642940, 113880, 225420; 113880, -90, -195; 225420, -195, -386],[780, 15, 1],[119, 305, 5, -1, -1, 5, 4, 76; -54, -130, -1, 2, 0, -13, -3, -39; 69510, 178152, 2920, -585, -584, 2925, 2337, 44395],85,19]
%
% END OF LATTICE L86.19
%
%
% LATTICE L86.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[184363459410, 707804565, 35747068110; 707804565, 2717390, 137239440; 35747068110, 137239440, 6931161319],[195, 65, 1],[1814910, 315817, -28907, -51, 232778, 176856, 300786, 678568; -5283721, -919434, 84150, 153, -677676, -514875, -875671, -1975503; -9255675, -1610603, 147420, 260, -1187121, -901930, -1533948, -3460560],85,20]
%
% END OF LATTICE L86.20
%
%
% LATTICE L86.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[130405080, -53820, -32128980; -53820, 40, 13260; -32128980, 13260, 7915883],[780, 20, 1],[12967, 32843, 2927, 0, 17, 3267, 1021, 51119; 240, 611, 57, 1, 0, 52, 18, 936; 52630, 133302, 11880, 0, 69, 13260, 4144, 207480],85,21]
%
% END OF LATTICE L86.21
%
%
% LATTICE L86.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3263985270, -582811515, 2964780; -582811515, -104065806, 529386; 2964780, 529386, -2693],[585, 39, 1],[366, 1063, 77, -41, -38, 16, 146, 112; -1839, -5340, -386, 207, 190, -81, -735, -563; 41431, 120555, 8892, -4446, -4485, 1692, 16250, 12630],85,22]
%
% END OF LATTICE L86.22
%
%
% LATTICE L86.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-18823098645, -2722961475, 17407845; -2722961475, -393905343, 2518230; 17407845, 2518230, -16099],[585, 39, 1],[796, 251, 42, -15, -13, 7, 383, 85; -2652, -835, -137, 51, 40, -24, -1290, -284; 445887, 140795, 23985, -8242, -7800, 3815, 212355, 47487],85,23]
%
% END OF LATTICE L86.23
%
%
% LATTICE L86.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[6402768840, 22791256020, 1608775740; 22791256020, 81127612824, 5726588088; 1608775740, 5726588088, 404225023],[2340, 12, 1],[46397, 1731566, 8616, -199, 2579, 57791, 21569, 189925; 99, 3705, 19, 0, 5, 117, 45, 403; -186058, -6943950, -34560, 792, -10335, -231660, -86480, -761592],85,24]
%
% END OF LATTICE L86.24
%
%
% LATTICE L86.25
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[24911640, 15862860, 6224400; 15862860, 10127544, 3963492; 6224400, 3963492, 1555223],[2340, 12, 1],[163676, 680517, 10455, -1, 2774, 21556, 74482, 222152; 297, 1235, 19, 0, 5, 39, 135, 403; -655830, -2726750, -41892, 4, -11115, -86372, -298440, -890136],85,25]
%
% END OF LATTICE L86.25
%
%
% LATTICE L86.26
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-4783740, 40560, 1476540; 40560, -234, -12519; 1476540, -12519, -455746],[780, 39, 1],[11291, 10741, 321, -325, -321, 125, 2588, 596; -54, -50, -1, 2, 0, -1, -15, -3; 36582, 34800, 1040, -1053, -1040, 405, 8385, 1931],85,26]
%
% END OF LATTICE L86.26
%
%
% LATTICE L86.27
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-468910260, 870173460, -142749360; 870173460, -1614174630, 264777375; -142749360, 264777375, -43431298],[2340, 15, 1],[-806803, -6203425, -101676, 20372, 20335, -101863, -27126, -1545884; -2397358, -18433038, -302123, 60534, 60424, -302679, -80603, -4593485; -11963620, -91987038, -1507695, 302085, 301536, -1510470, -402236, -22923030],85,27]
%
% END OF LATTICE L86.27
%
%
% LATTICE L86.28
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-394928820, 5431140, 1017900; 5431140, -74490, -13965; 1017900, -13965, -2618],[2340, 15, 1],[173, 145, 6, -1, -1, 6, 7, 115; -101262, -84864, -3508, 587, 584, -3523, -4101, -67327; 607410, 509054, 21045, -3520, -3504, 21125, 24597, 403845],85,28]
%
% END OF LATTICE L86.28
%
%
% LATTICE L86.29
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-38639589690, 107576880255, -36206307735; 107576880255, -299505750765, 100802303940; -36206307735, 100802303940, -33926241662],[195, 195, 1],[-21016, -3615, 271, -273, -1058, -2274, -3688, -2670; -189095547, -32525963, 2441038, -2461012, -9522245, -20464552, -33186930, -24024694; -561821910, -96637911, 7252570, -7311915, -28291549, -60802245, -98601711, -71379785],85,29]
%
% END OF LATTICE L86.29
%
%
% LATTICE L86.30
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[252237752520, 4152185700, -63538633860; 4152185700, 68350776, -1045934656; -63538633860, -1045934656, 16005367763],[780, 52, 1],[37550, 36069, 7291, 13, 1814, 1114, 16924, 11734; 5429, 5235, 1101, 6, 210, 147, 2365, 1683; 149422, 143530, 29016, 52, 7215, 4432, 67340, 46692],85,30]
%
% END OF LATTICE L86.30
%
%
% LATTICE L86.31
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[14371395480, 453180, -3611400780; 453180, 120, -113880; -3611400780, -113880, 907512121],[780, 60, 1],[-338813, -858177, -25501, 0, -146, -85263, -26669, -445197; 71, 182, 6, 1, 0, 13, 5, 91; -1348290, -3415074, -101480, 0, -581, -339300, -106128, -1771640],85,31]
%
% END OF LATTICE L86.31
%
%
% LATTICE L86.32
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1080645540, 1082683680, 538358340; 1082683680, -1084725590, -539373705; 538358340, -539373705, -268200526],[780, 65, 1],[303299, 58633, 31375, -5341, -5207, 2465, 12328, 46576; -54, -10, -3, 2, 0, -1, -3, -9; 608920, 117714, 62985, -10725, -10452, 4950, 24752, 93510],85,32]
%
% END OF LATTICE L86.32
%
%
% LATTICE L86.33
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-19499220, 210600, -542880; 210600, -2262, 5889; -542880, 5889, -15062],[2340, 39, 1],[-419, -1199, -37, 35, 39, -13, -94, -66; -17150, -49080, -1516, 1431, 1600, -531, -3845, -2701; 8398, 24030, 741, -702, -780, 261, 1885, 1323],85,33]
%
% END OF LATTICE L86.33
%
%
% LATTICE L86.34
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-12670624980, -1376256960, 11716380; -1376256960, -149486142, 1272609; 11716380, 1272609, -10834],[2340, 39, 1],[1319, 411, 29, -15, -13, 7, 344, 72; -4464, -1390, -97, 51, 40, -24, -1170, -244; 902070, 281200, 19968, -10231, -9360, 4751, 234585, 49203],85,34]
%
% END OF LATTICE L86.34
%
%
% LATTICE L86.35
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-550491435, -112698495, 2815605; -112698495, -23072010, 576420; 2815605, 576420, -14401],[585, 195, 1],[-9, -5, -1, 2, 0, -1, -1, -3; 1421, 846, 380, -39, -38, 15, 89, 413; 55120, 32886, 15015, -1170, -1521, 405, 3367, 15945],85,35]
%
% END OF LATTICE L86.35
%
%
% LATTICE L86.36
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-29367585, -289730610, -4904055; -289730610, -2858197290, -48378915; -4904055, -48378915, -818879],[585, 195, 1],[-92470, -6036, -7289, 678, 661, -313, -6679, -9219; -80031, -5224, -6308, 587, 572, -271, -5781, -7979; 5281965, 344779, 416325, -38740, -37752, 17885, 381537, 526605],85,36]
%
% END OF LATTICE L86.36
%
%
% LATTICE L86.37
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[144644760, -192660, -35370660; -192660, 312, 47112; -35370660, 47112, 8649353],[780, 156, 1],[17567, 16851, 1119, 0, 302, 537, 8011, 1835; 71, 70, 6, 1, 0, 1, 25, 7; 71838, 68910, 4576, 0, 1235, 2196, 32760, 7504],85,37]
%
% END OF LATTICE L86.37
%
%
% LATTICE L86.38
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[6214312597254840, -43724867502420, 1549941453637200; -43724867502420, 307654951080, -10905628520640; 1549941453637200, -10905628520640, 386578317731267],[2340, 60, 1],[816665, 6208103, 185167, 1168, 1020, 610861, 64053, 3216591; 182722, 1388673, 41327, 105, 233, 137436, 14362, 720044; -3269170, -24851502, -741240, -4680, -4083, -2445300, -256408, -12876240],85,38]
%
% END OF LATTICE L86.38
%
%
% LATTICE L86.39
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[3075306291720, 13161430620, 767510841240; 13161430620, 56327160, 3284726700; 767510841240, 3284726700, 191549340307],[2340, 60, 1],[1005877, 849244, 75694, -5, 435, 84419, 79189, 1321763; 3765, 3185, 289, 2, 1, 299, 291, 4927; -4030470, -3402854, -303300, 20, -1743, -338260, -317304, -5296200],85,39]
%
% END OF LATTICE L86.39
%
%
% LATTICE L86.40
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-9710220, 9598680, -1510860; 9598680, -9488310, 1493505; -1510860, 1493505, -235082],[780, 195, 1],[-10673, -2103, -446, 93, 89, -36, -361, -525; -54, -10, -1, 2, 0, -1, -3, -3; 68250, 13452, 2860, -585, -572, 225, 2301, 3355],85,40]
%
% END OF LATTICE L86.40
%
%
% LATTICE L86.41
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[236316386280, 8299980, 58767586020; 8299980, 520, 2063880; 58767586020, 2063880, 14614429631],[780, 260, 1],[-1995247, -388727, -450257, 0, -2648, -38709, -157147, -605093; 6110307, 1190450, 1378884, 1, 8109, 118543, 481251, 1853055; 8022430, 1562982, 1810380, 0, 10647, 155640, 631852, 2432940],85,41]
%
% END OF LATTICE L86.41
%
%
% LATTICE L86.42
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[5290744680, 600231060, 1320801300; 600231060, 68096184, 149843928; 1320801300, 149843928, 329729779],[2340, 156, 1],[100381, 290186, 20210, 701, 4332, 8393, 44067, 31167; 99, 285, 19, 0, 5, 9, 45, 31; -402142, -1162530, -80964, -2808, -17355, -33624, -176540, -124860],85,42]
%
% END OF LATTICE L86.42
%
%
% LATTICE L86.43
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[5558679963720, 1853244900, 1387280487060; 1853244900, 618072, 462514572; 1387280487060, 462514572, 346223772971],[2340, 156, 1],[-6418528, -2034391, -367139, 3491, -157241, -77966, -3145988, -682494; 71901, 22790, 4114, -39, 1760, 873, 35235, 7645; 25718238, 8151550, 1471080, -13988, 630045, 312400, 12605580, 2734668],85,43]
%
% END OF LATTICE L86.43
%
%
% LATTICE L86.44
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-551473455780, 91228880340, 712391940; 91228880340, -15091766430, -117849225; 712391940, -117849225, -920266],[2340, 195, 1],[12149, 7183, 1526, -314, -305, 121, 410, 1792; 48578, 28722, 6103, -1254, -1220, 483, 1639, 7165; 3183830, 1882332, 399750, -82485, -79872, 31815, 107497, 469665],85,44]
%
% END OF LATTICE L86.44
%
%
% LATTICE L86.45
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-29130660, 316702620, 4867200; 316702620, -3442804170, -52910325; 4867200, -52910325, -813146],[2340, 195, 1],[15533, 1001, 536, -91, -89, 42, 631, 795; -100002, -6444, -3448, 587, 572, -271, -4065, -5119; 6599970, 425294, 227565, -38740, -37752, 17885, 268281, 337845],85,45]
%
% END OF LATTICE L86.45
%
%
% LATTICE L86.46
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1560, 746460, -187200; 746460, 2849126280, -714530700; -187200, -714530700, 179196733],[780, 780, 1],[-6735, -1312, -506, 1, -3, -131, -531, -681; 539999, 105207, 40623, 0, 238, 10473, 42527, 54587; 2153190, 419502, 161980, 0, 949, 41760, 169572, 217660],85,46]
%
% END OF LATTICE L86.46
%
%
% LATTICE L86.47
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[63339649125480, 322303332780, -15566116473180; 322303332780, 1640042040, -79208064780; -15566116473180, -79208064780, 3825470862911],[2340, 780, 1],[45338015, 26499245, 10231589, -584, 59986, 2638219, 3570687, 13749409; -136168962, -79588281, -30729727, 1755, -180163, -7923672, -10724262, -41295208; 181664210, 106179426, 40996800, -2340, 240357, 10571040, 14307332, 55092300],85,47]
%
% END OF LATTICE L86.47
%
%
% LATTICE L86.48
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[26808239357640, -138808605780, -6794421290280; -138808605780, 718727880, 35180383680; -6794421290280, 35180383680, 1722013894831],[2340, 780, 1],[-327361, -21244, -24442, 65, -165, -2159, -25957, -33143; 1204428, 78177, 90115, -173, 586, 7900, 95322, 121888; -1316250, -85418, -98280, 260, -663, -8680, -104364, -133260],85,48]
%
% END OF LATTICE L86.48
%

\medskip%
%------------------------------WEYL-GROUP-W87--------------------------------
%
\leavevmode\llap{}%
$W_{87\phantom{0}}$%
\qquad\llap{12} lattices, $\chi=84$%
\hfill%
$222222222222222222\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L87.1
%
\leavevmode%
${L_{87.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{2}{}41\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2\rightarrow N_{87}}%
\EasyButWeakLineBreak%
{${4}\above{1pt}{1pt}{r}{2}{10}\above{1pt}{1pt}{b}{2}{82}\above{1pt}{1pt}{l}{2}{4}\above{1pt}{1pt}{r}{2}{410}\above{1pt}{1pt}{b}{2}{2}\above{1pt}{1pt}{b}{2}{10}\above{1pt}{1pt}{l}{2}{164}\above{1pt}{1pt}{r}{2}{2}\above{1pt}{1pt}{l}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
63140\\-25420\\-820
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-25420\\10234\\329
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-820\\329\\-38
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-560881\\-1394000\\39360
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
225378\\560149\\-15816
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-10431\\-25925\\731
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1125\\2796\\-80
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
338\\840\\-25
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
495\\1230\\-41
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
29\\72\\-4
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-412\\-1025\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-35\\-87\\2
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\5\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2573\\6396\\-164
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
140\\348\\-9
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[63140, -25420, -820; -25420, 10234, 329; -820, 329, -38],[820, 1, 1],[1125, 338, 495, 29, -412, -35, 2, 2573, 140, 243, 517, 6516, 3391, 70522, 2087, 5128, 81559, 2083; 2796, 840, 1230, 72, -1025, -87, 5, 6396, 348, 604, 1285, 16195, 8428, 175275, 5187, 12745, 202704, 5177; -80, -25, -41, -4, 0, 2, 0, -164, -9, -16, -35, -451, -236, -4920, -146, -360, -5740, -147],86,1]
%
% END OF LATTICE L87.1
%
%
% LATTICE L87.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-15785, -3075, 205; -3075, -599, 40; 205, 40, -2],[205, 1, 1],[162, 143, 423, 52, 1358, 16, 2, -8, -1, 6, 67, 1299, 368, 15862, 488, 1258, 10340, 547; -833, -735, -2173, -267, -6970, -82, -10, 41, 5, -31, -345, -6683, -1893, -81590, -2510, -6470, -53177, -2813; -162, -135, -369, -42, -1025, -9, 5, 0, -3, -10, -80, -1394, -388, -16605, -507, -1295, -10578, -556],86,2]
%
% END OF LATTICE L87.2
%
%
% LATTICE L87.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1151690, 13530, -227345; 13530, -155, 2670; -227345, 2670, -44878],[205, 5, 1],[-920, -123, -1159, -78, -168, 38, 8, -1198, -151, -152, -145, -9829, -2602, -21808, -3254, -1616, -64730, -3333; 993, 132, 1230, 81, 164, -42, -8, 1353, 168, 167, 158, 10660, 2819, 23616, 3522, 1748, 69987, 3602; 4720, 631, 5945, 400, 861, -195, -41, 6150, 775, 780, 744, 50430, 13350, 111889, 16695, 8291, 332100, 17100],86,3]
%
% END OF LATTICE L87.3
%
%
% LATTICE L87.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1678000440, 5014300, 419471000; 5014300, 14984, 1253488; 419471000, 1253488, 104860473],[820, 4, 1],[-1585, -2394, -5632, -270, -11019, -1, 199, -623, -238, -169, -1991, -30325, -4115, -348551, -10523, -26509, -107248, -11163; -2389, -3625, -8569, -412, -16810, 0, 330, -738, -329, -247, -2965, -45469, -6178, -523570, -15816, -39870, -161376, -16805; 6369, 9620, 22632, 1085, 44280, 4, -800, 2501, 956, 679, 8000, 121852, 16535, 1400560, 42284, 106520, 430951, 44856],86,4]
%
% END OF LATTICE L87.4
%
%
% LATTICE L87.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-491180, -246000, 3280; -246000, -123190, 1635; 3280, 1635, -18],[820, 5, 1],[-1303, -138, -2539, -747, -2239, -196, -39, -1199, 20, 39, -20, -3939, -2413, -10717, -1700, -909, -76537, -2074; 2672, 283, 5207, 1532, 4592, 402, 80, 2460, -41, -80, 41, 8077, 4948, 21976, 3486, 1864, 156948, 4253; 5240, 556, 10250, 3020, 9061, 795, 159, 4920, -80, -160, 79, 15785, 9680, 43009, 6825, 3651, 307500, 8335],86,5]
%
% END OF LATTICE L87.5
%
%
% LATTICE L87.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2536465, -66215, -496305; -66215, -1558, -12956; -496305, -12956, -97111],[205, 41, 1],[-8928, -5936, -270, -730, -181, 377, 361, -296, -1508, -1500, -7099, -2337, -25340, -25889, -31661, -78571, -15346, -32383; -40, -25, -1, -2, 0, 2, 0, -2, -9, -8, -35, -11, -118, -120, -146, -360, -70, -147; 45633, 30340, 1380, 3731, 925, -1927, -1845, 1513, 7708, 7667, 36285, 11945, 129519, 132325, 161827, 401595, 78437, 165517],86,6]
%
% END OF LATTICE L87.6
%
%
% LATTICE L87.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1215825480, -7539900, 303208940; -7539900, 46760, -1880340; 303208940, -1880340, 75615837],[820, 20, 1],[7153, 2799, 47731, 3342, 38878, 3184, 594, 5864, -5, 51, 803, 99951, 14668, 256486, 40040, 21018, 437182, 46831; -2914, -1142, -19516, -1369, -15949, -1311, -247, -2460, -2, -20, -325, -40631, -5966, -104345, -16293, -8555, -177981, -19069; -28755, -11252, -191880, -13435, -156292, -12800, -2388, -23575, 20, -205, -3228, -401800, -58965, -1031068, -160960, -84492, -1757465, -188260],86,7]
%
% END OF LATTICE L87.7
%
%
% LATTICE L87.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[555140, 521520, -7380; 521520, 489786, -6929; -7380, -6929, 98],[820, 41, 1],[-11, -7, 2, 65, 38, 53, 152, 65, 75, 51, 32, 3, 35, 12, 7, -2, -5, -10; 28, 25, -1, -68, -45, -69, -215, -96, -115, -84, -60, -6, -72, -25, -15, 5, 12, 24; 1148, 1230, 76, 0, -365, -943, -3895, -1948, -2542, -2132, -1845, -199, -2460, -865, -533, 205, 472, 943],86,8]
%
% END OF LATTICE L87.8
%
%
% LATTICE L87.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[410, 781460, 154365; 781460, 1692972205, 334419780; 154365, 334419780, 66059318],[205, 205, 1],[212, 30, 8, 30, 3, 1, 1, 8, 34, 32, 31, 53, 580, 119, 731, 365, 358, 759; -125857, -17032, -4246, -14821, -1410, 0, -1474, -6489, -25876, -22191, -19980, -32766, -355299, -72614, -444144, -220598, -215583, -455280; 637140, 86223, 21495, 75030, 7138, 0, 7462, 32850, 130995, 112340, 101147, 165875, 1798670, 367602, 2248440, 1116758, 1091370, 2304815],86,9]
%
% END OF LATTICE L87.9
%
%
% LATTICE L87.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[457856840, -2360780, 113931620; -2360780, 12136, -587448; 113931620, -587448, 28350377],[820, 164, 1],[-1397, -17539, -6553, -36475, -75359, -93283, -234941, -23176, -98871, -14021, -21006, -1156, -2070, -1731, 775, 3671, 49, -1346; 139, 1740, 650, 3618, 7475, 9253, 23305, 2299, 9808, 1391, 2085, 115, 207, 175, -73, -355, -4, 137; 5617, 70520, 26348, 146657, 303000, 375068, 944640, 93185, 397536, 56375, 84460, 4648, 8323, 6960, -3116, -14760, -197, 5412],86,10]
%
% END OF LATTICE L87.10
%
%
% LATTICE L87.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[164820, 8200, -4100; 8200, 410, -205; -4100, -205, 102],[820, 205, 1],[-17, -2, -1, -13, -1, -4, -1, -1, 0, 1, 0, -1, -27, -3, -20, -11, -23, -26; -428, -37, -13, -128, -8, -18, 0, 0, -1, -20, -19, -43, -992, -104, -654, -336, -672, -727; -1640, -164, -70, -820, -59, -205, -41, -40, 0, 0, -41, -135, -3280, -351, -2255, -1189, -2420, -2665],86,11]
%
% END OF LATTICE L87.11
%
%
% LATTICE L87.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1640, 151700, 37720; 151700, -332920, -82820; 37720, -82820, -20603],[820, 820, 1],[26, 10, 4, 11, 3, 9, 1, 0, -2, 0, 3, 9, 54, 23, 147, 77, 39, 171; -23193, -8849, -3501, -9532, -2578, -7544, -734, 46, 1835, -51, -2773, -8121, -48578, -20666, -131920, -68998, -34912, -152921; 93275, 35588, 14080, 38335, 10368, 30340, 2952, -185, -7380, 205, 11152, 32660, 195365, 83112, 530540, 277488, 140405, 615000],86,12]
%
% END OF LATTICE L87.12
%

\medskip%
%------------------------------WEYL-GROUP-W88--------------------------------
%
\leavevmode\llap{}%
$W_{88\phantom{0}}$%
\qquad\llap{32} lattices, $\chi=18$%
\hfill%
$2222222$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L88.1
%
\leavevmode%
${L_{88.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}8\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{2}{}5\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{2}{}7\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{2\rightarrow N_{88}}%
\EasyButWeakLineBreak%
{${168}\above{1pt}{1pt}{r}{2}{10}\above{1pt}{1pt}{b}{2}{6}\above{1pt}{1pt}{l}{2}{40}\above{1pt}{1pt}{r}{2}{42}\above{1pt}{1pt}{b}{2}{8}\above{1pt}{1pt}{b}{2}{2}\above{1pt}{1pt}{l}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-620760\\-248640\\2520
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-248640\\-99590\\1009
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2520\\1009\\-10
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-265\\672\\1008
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2\\5\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
13\\-33\\-54
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
79\\-200\\-280
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
25\\-63\\-63
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-11\\28\\52
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-13\\33\\53
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-620760, -248640, 2520; -248640, -99590, 1009; 2520, 1009, -10],[840, 1, 1],[-265, -2, 13, 79, 25, -11, -13; 672, 5, -33, -200, -63, 28, 33; 1008, 0, -54, -280, -63, 52, 53],87,1]
%
% END OF LATTICE L88.1
%
%
% LATTICE L88.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-16590, 6720, 210; 6720, -2722, -85; 210, -85, -2],[210, 1, 1],[17, -4, -34, -231, -298, -13, 2; 42, -10, -84, -570, -735, -32, 5; 0, 5, -9, -100, -147, -10, -3],87,2]
%
% END OF LATTICE L88.2
%
%
% LATTICE L88.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1060080, 114450, -527730; 114450, -12280, 56974; -527730, 56974, -262715],[210, 2, 1],[-3944, -104, 782, 1162, 1415, -169, -781; 168, 5, -33, -50, -63, 7, 33; 7959, 210, -1578, -2345, -2856, 341, 1576],87,3]
%
% END OF LATTICE L88.3
%
%
% LATTICE L88.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1141770, 145320, -378630; 145320, -18420, 48189; -378630, 48189, -125560],[210, 3, 1],[-1801, -69, 179, 1589, 320, -233, -536; 112, 5, -11, -100, -21, 14, 33; 5474, 210, -544, -4830, -973, 708, 1629],87,4]
%
% END OF LATTICE L88.4
%
%
% LATTICE L88.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1393350, 207060, 559020; 207060, -30700, -83075; 559020, -83075, -224282],[210, 5, 1],[7043, 17, -703, -413, -1231, 307, 701; 336, 1, -33, -20, -63, 14, 33; 17430, 42, -1740, -1022, -3045, 760, 1735],87,5]
%
% END OF LATTICE L88.5
%
%
% LATTICE L88.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[8323021140, -2913330, 4137607110; -2913330, 1020, -1448298; 4137607110, -1448298, 2056920475],[210, 6, 1],[7033, 2953, 521, 8941, 9201, 1302, 3299; 371, 170, 28, 435, 441, 62, 167; -14147, -5940, -1048, -17985, -18508, -2619, -6636],87,6]
%
% END OF LATTICE L88.6
%
%
% LATTICE L88.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1678530, 268800, 720930; 268800, -42980, -115451; 720930, -115451, -309640],[210, 7, 1],[1139, 91, -799, -2331, -196, 351, 796; 48, 5, -33, -100, -9, 14, 33; 2634, 210, -1848, -5390, -453, 812, 1841],87,7]
%
% END OF LATTICE L88.7
%
%
% LATTICE L88.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[75799500, -358890, 36018990; -358890, 1700, -170540; 36018990, -170540, 17115781],[210, 10, 1],[3448, 99, 257, 286, 4397, 207, 533; 1113, 34, 84, 87, 1323, 62, 167; -7245, -208, -540, -601, -9240, -435, -1120],87,8]
%
% END OF LATTICE L88.8
%
%
% LATTICE L88.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[19320, 7560, -840; 7560, 2958, -333; -840, -333, -34],[840, 3, 1],[-331, -2, 13, 79, -22, -63, -52; 840, 5, -33, -200, 56, 160, 132; -56, 0, 2, 0, -7, -12, -9],87,9]
%
% END OF LATTICE L88.9
%
%
% LATTICE L88.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[30237060, -268170, 14053830; -268170, 2380, -124642; 14053830, -124642, 6532055],[210, 14, 1],[449, 457, 235, 1289, 565, 186, 483; 159, 170, 84, 435, 189, 62, 167; -963, -980, -504, -2765, -1212, -399, -1036],87,10]
%
% END OF LATTICE L88.10
%
%
% LATTICE L88.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[61734750, 396690, 21964110; 396690, 2550, 141135; 21964110, 141135, 7814434],[210, 15, 1],[-1773, -76, -66, -443, -1136, -321, -412; 742, 34, 28, 174, 441, 124, 167; 4970, 213, 185, 1242, 3185, 900, 1155],87,11]
%
% END OF LATTICE L88.11
%
%
% LATTICE L88.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-7740600, -3911880, 25200; -3911880, -1976950, 12735; 25200, 12735, -82],[840, 5, 1],[-241, -10, -47, -53, -89, 21, 9; 504, 21, 99, 112, 189, -44, -19; 4200, 188, 930, 1104, 1995, -380, -185],87,12]
%
% END OF LATTICE L88.12
%
%
% LATTICE L88.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[97320090, 589260, 33999630; 589260, 3570, 205863; 33999630, 205863, 11878070],[210, 21, 1],[-459, -698, -120, -3967, -290, -573, -742; 106, 170, 28, 870, 63, 124, 167; 1312, 1995, 343, 11340, 829, 1638, 2121],87,13]
%
% END OF LATTICE L88.13
%
%
% LATTICE L88.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[271320, -57120, -1680; -57120, 11998, 357; -1680, 357, 10],[840, 7, 1],[19, 4, -7, -83, -7, -1, 5; 72, 15, -27, -320, -27, -4, 19; 624, 140, -210, -2520, -213, -28, 161],87,14]
%
% END OF LATTICE L88.14
%
%
% LATTICE L88.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1246557900, 15171870, -619814580; 15171870, -184200, 7543770; -619814580, 7543770, -308184733],[210, 30, 1],[-110176, -1608, 21982, 19390, 38599, -14387, -65767; 56, 1, -11, -10, -21, 7, 33; 221585, 3234, -44210, -38997, -77630, 28935, 132270],87,15]
%
% END OF LATTICE L88.15
%
%
% LATTICE L88.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1664880, -567000, 15120; -567000, -193072, 5120; 15120, 5120, -107],[840, 8, 1],[-425, 68, 214, 78, -167, -69, -211; 1281, -205, -645, -235, 504, 208, 636; 1239, -200, -624, -225, 504, 202, 616],87,16]
%
% END OF LATTICE L88.16
%
%
% LATTICE L88.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[892809750, 2304120, -353464860; 2304120, 5950, -912205; -353464860, -912205, 139937324],[210, 35, 1],[6199, 629, 1621, 3569, 3913, 2577, 3339; 318, 34, 84, 174, 189, 124, 167; 15660, 1589, 4095, 9016, 9885, 6510, 8435],87,17]
%
% END OF LATTICE L88.17
%
%
% LATTICE L88.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2966525520, 27681150, -1474951590; 27681150, -257880, 13763022; -1474951590, 13763022, -733343495],[210, 42, 1],[-23146, -11172, 32458, 142156, 7981, -21373, -97019; 8, 5, -11, -50, -3, 7, 33; 46553, 22470, -65282, -285915, -16052, 42987, 195132],87,18]
%
% END OF LATTICE L88.18
%
%
% LATTICE L88.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-44520, -21840, 4200; -21840, -10650, 1965; 4200, 1965, -254],[840, 15, 1],[-359, -6, 41, 335, 356, 77, -38; 840, 14, -96, -784, -833, -180, 89; 560, 9, -65, -528, -560, -120, 60],87,19]
%
% END OF LATTICE L88.19
%
%
% LATTICE L88.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-422914800, 13492710, -201789210; 13492710, -429800, 6437900; -201789210, 6437900, -96281533],[210, 70, 1],[-31927, -1022, 44788, 13069, 10993, -9836, -44621; 24, 1, -33, -10, -9, 7, 33; 66915, 2142, -93870, -27391, -23040, 20615, 93520],87,20]
%
% END OF LATTICE L88.20
%
%
% LATTICE L88.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[6828360, -1373400, -18480; -1373400, 276234, 3717; -18480, 3717, 50],[840, 21, 1],[5, 1, -2, -47, -1, 3, 5; 24, 5, -9, -200, -4, 16, 24; 64, 0, -70, -2520, -73, -84, 63],87,21]
%
% END OF LATTICE L88.21
%
%
% LATTICE L88.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-162960, 32760, -1680; 32760, -6576, 336; -1680, 336, -17],[840, 24, 1],[2, -1, -1, -1, 1, 1, 3; 14, -5, -7, -10, 0, 6, 20; 77, 0, -40, -105, -112, 18, 96],87,22]
%
% END OF LATTICE L88.22
%
%
% LATTICE L88.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-182555310, 10859310, 73277820; 10859310, -644700, -4358025; 73277820, -4358025, -29413112],[210, 105, 1],[-14427, -693, 10119, 17717, 2484, -13333, -30244; 28870, 1387, -20249, -35454, -4971, 26680, 60521; -40220, -1932, 28210, 49392, 6925, -37170, -84315],87,23]
%
% END OF LATTICE L88.23
%
%
% LATTICE L88.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-4066440, -1658160, 11760; -1658160, -676130, 4795; 11760, 4795, -34],[840, 35, 1],[-7, -1, 4, 19, 10, 9, 0; 24, 3, -15, -64, -33, -28, 1; 960, 77, -735, -2464, -1200, -840, 140],87,24]
%
% END OF LATTICE L88.24
%
%
% LATTICE L88.25
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-35449680, -1848840, 52920; -1848840, -96400, 2760; 52920, 2760, -79],[840, 40, 1],[8, 2, 8, 1, 11, -1, -1; 0, -1, -9, -2, -42, 0, 2; 5355, 1304, 5040, 599, 5880, -670, -600],87,25]
%
% END OF LATTICE L88.25
%
%
% LATTICE L88.26
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[119124727680, 46899107010, 22659274260; 46899107010, 18464061000, 8920899540; 22659274260, 8920899540, 4310127041],[210, 210, 1],[53, 34, 28, 87, 63, 62, 167; 8521, 5007, 4427, 15191, 11165, 11054, 27985; -17915, -10542, -9310, -31899, -23440, -23205, -58800],87,26]
%
% END OF LATTICE L88.26
%
%
% LATTICE L88.27
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1886640, 189000, -8400; 189000, -18928, 840; -8400, 840, -37],[840, 56, 1],[1, -1, -11, -16, -11, -1, 3; 12, -10, -132, -195, -135, -13, 35; 45, 0, -504, -805, -576, -70, 112],87,27]
%
% END OF LATTICE L88.27
%
%
% LATTICE L88.28
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[24360, -2520, 0; -2520, -5250, 105; 0, 105, -2],[840, 105, 1],[1, 0, -1, -7, -1, -1, 1; 8, 1, -11, -96, -15, -28, 5; 400, 63, -595, -5376, -850, -1680, 210],87,28]
%
% END OF LATTICE L88.28
%
%
% LATTICE L88.29
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1953840, -372120, 5040; -372120, -70800, 960; 5040, 960, -13],[840, 120, 1],[1, 1, 1, 0, -3, -1, -1; 0, -1, -3, -2, -14, 0, 2; 385, 312, 160, -153, -2240, -390, -240],87,29]
%
% END OF LATTICE L88.29
%
%
% LATTICE L88.30
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1680, -840, 0; -840, -777840, 6048; 0, 6048, -47],[840, 168, 1],[1, -1, -5, -16, -3, 1, 9; 2, 0, -10, -35, -7, 1, 17; 257, 0, -1288, -4515, -904, 126, 2184],87,30]
%
% END OF LATTICE L88.30
%
%
% LATTICE L88.31
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-38640, -19320, 1680; -19320, -9520, 840; 1680, 840, -73],[840, 280, 1],[2, 3, 5, -1, -7, -3, -1; 0, -1, -9, -2, -6, 0, 2; 45, 56, 0, -49, -240, -70, 0],87,31]
%
% END OF LATTICE L88.31
%
%
% LATTICE L88.32
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1680, -5880, 840; -5880, -475440, 68880; 840, 68880, -9979],[840, 840, 1],[1, 4, -2, -6, -9, -7, -1; 21, 73, -81, -155, -220, -152, 0; 145, 504, -560, -1071, -1520, -1050, 0],87,32]
%
% END OF LATTICE L88.32
%

\medskip%
%------------------------------WEYL-GROUP-W89--------------------------------
%
\leavevmode\llap{}%
$W_{89\phantom{0}}$%
\qquad\llap{48} lattices, $\chi=32$%
\hfill%
$22262226\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L89.1
%
\leavevmode%
${L_{89.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}8\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{-}{}9\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{-2}{}7\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{23\rightarrow N_{89},3,2}%
\EasyButWeakLineBreak%
{${18}\above{1pt}{1pt}{b}{2}{14}\above{1pt}{1pt}{b}{2}{72}\above{1pt}{1pt}{b}{2}{6}\above{1pt}{1pt}{}{6}{2}\above{1pt}{1pt}{b}{2}{126}\above{1pt}{1pt}{b}{2}{8}\above{1pt}{1pt}{b}{2}{6}\above{1pt}{1pt}{}{6}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-22538902680\\-1942920\\19106640
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1942920\\-138\\1629
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
19106640\\1629\\-16186
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-397\\-305694\\-499401
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-78\\-60060\\-98119
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
35\\26952\\44028
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
16\\12320\\20127
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-17\\-13091\\-21385
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-214\\-164787\\-269199
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-97\\-74692\\-122020
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-208\\-160163\\-261651
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-22538902680, -1942920, 19106640; -1942920, -138, 1629; 19106640, 1629, -16186],[2520, 3, 1],[-397, -78, 35, 16, -17, -214, -97, -208; -305694, -60060, 26952, 12320, -13091, -164787, -74692, -160163; -499401, -98119, 44028, 20127, -21385, -269199, -122020, -261651],88,1]
%
% END OF LATTICE L89.1
%
%
% LATTICE L89.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[23730, -10290, 210; -10290, 4462, -91; 210, -91, 2],[210, 1, 1],[0, 6, -13, -122, -112, -118, -19, -22; 0, 14, -30, -282, -259, -273, -44, -51; 1, 7, -4, -51, -50, -56, -10, -12],88,2]
%
% END OF LATTICE L89.2
%
%
% LATTICE L89.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-5985056280, 9843120, -310800; 9843120, -16186, 509; -310800, 509, -14],[840, 1, 1],[-1, -34, -65, -160, -111, -78, 1, 16; -628, -21350, -40816, -100470, -69701, -48979, 628, 10047; -633, -21427, -40956, -100809, -69934, -49140, 632, 10080],88,3]
%
% END OF LATTICE L89.3
%
%
% LATTICE L89.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-4831470, -2520, 9450; -2520, 24, -3; 9450, -3, -16],[630, 3, 1],[1, 13, 3, 13, 25, 5, -1, -1; 174, 2268, 524, 2272, 4371, 875, -174, -175; 557, 7245, 1672, 7245, 13932, 2786, -558, -558],88,4]
%
% END OF LATTICE L89.4
%
%
% LATTICE L89.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-6958140, 31290, -3471510; 31290, -136, 15610; -3471510, 15610, -1731983],[210, 2, 1],[-731, 26115, 20621, 250129, 195464, 168618, 7198, 242; 312, -11102, -8769, -106374, -83129, -71715, -3062, -105; 1468, -52444, -41411, -502308, -392530, -338618, -14455, -486],88,5]
%
% END OF LATTICE L89.5
%
%
% LATTICE L89.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-8908410, 43260, -2962470; 43260, -204, 14385; -2962470, 14385, -985162],[210, 3, 1],[-626, 22370, 35327, 71418, 167429, 144433, 12331, 69; 312, -11102, -17538, -35458, -83129, -71715, -6124, -35; 1887, -67431, -106488, -215279, -504690, -435372, -37170, -208],88,6]
%
% END OF LATTICE L89.6
%
%
% LATTICE L89.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-12950070, 67200, 5186580; 67200, -340, -26915; 5186580, -26915, -2077256],[210, 5, 1],[1093, -39069, -61697, -374183, -292405, -252243, -21535, -361; 312, -11102, -17538, -106374, -83129, -71715, -6124, -105; 2725, -97405, -153820, -932895, -729010, -628880, -53690, -900],88,7]
%
% END OF LATTICE L89.7
%
%
% LATTICE L89.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[5240814180, -14928690, 2605404690; -14928690, 42528, -7421610; 2605404690, -7421610, 1295244091],[210, 6, 1],[15818, -753492, -584110, -2351216, -5500773, -4731463, -199455, 521; 29, -1309, -1018, -4101, -9598, -8260, -349, 0; -31818, 1515654, 1174941, 4729486, 11064840, 9517368, 401205, -1048],88,8]
%
% END OF LATTICE L89.8
%
%
% LATTICE L89.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-17045490, 91140, 7311570; 91140, -476, -39095; 7311570, -39095, -3136258],[210, 7, 1],[1530, -7814, -86377, -523862, -409371, -50449, -30149, -505; 312, -1586, -17538, -106374, -83129, -10245, -6124, -105; 3563, -18197, -201152, -1219953, -953330, -117484, -70210, -1176],88,9]
%
% END OF LATTICE L89.9
%
%
% LATTICE L89.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[92688540, -2563050, 44112810; -2563050, 70880, -1219820; 44112810, -1219820, 20994397],[210, 10, 1],[2804, -133062, -103173, -1245974, -971695, -835829, -35240, 257; 29, -1309, -1018, -12303, -9598, -8260, -349, 0; -5890, 279510, 216725, 2617290, 2041140, 1755740, 74025, -540],88,10]
%
% END OF LATTICE L89.10
%
%
% LATTICE L89.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-5746440, 21840, 14280; 21840, -78, -57; 14280, -57, -34],[840, 3, 1],[-1, -2, 5, 8, 22, 23, 7, 1; -120, -238, 600, 958, 2633, 2751, 836, 119; -219, -441, 1092, 1751, 4818, 5040, 1536, 220],88,11]
%
% END OF LATTICE L89.11
%
%
% LATTICE L89.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[57649620, -2391690, 26880210; -2391690, 99232, -1115170; 26880210, -1115170, 12533399],[210, 14, 1],[2658, -17988, -97642, -1179208, -919637, -113009, -33355, 235; 29, -187, -1018, -12303, -9598, -1180, -349, 0; -5698, 38562, 209321, 2527938, 1971480, 242264, 71505, -504],88,12]
%
% END OF LATTICE L89.12
%
%
% LATTICE L89.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[65282910, 2634450, 23290050; 2634450, 106320, 939855; 23290050, 939855, 8308858],[210, 15, 1],[-2131, 101193, 156919, 315837, 738930, 635606, 53595, -66; 29, -1309, -2036, -4101, -9598, -8260, -698, 0; 5970, -283500, -439620, -884840, -2070165, -1780695, -150150, 185],88,13]
%
% END OF LATTICE L89.13
%
%
% LATTICE L89.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[12750180660, -38171070, 6354779130; -38171070, 114276, -19024728; 6354779130, -19024728, 3167266321],[630, 6, 1],[3124, 29390, 3598, 34426, 71681, 17221, 785, 311; -5, -21, 0, 11, 36, 14, 3, -2; -6268, -58968, -7219, -69072, -143820, -34552, -1575, -624],88,14]
%
% END OF LATTICE L89.14
%
%
% LATTICE L89.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1164743160, 9709560, 11670960; 9709560, -80930, -97015; 11670960, -97015, -110026],[840, 5, 1],[13879, 9750, -127, -2000, 128, 4257, 8131, 20009; 1748983, 1228661, -16004, -252033, 16130, 536452, 1024640, 2521464; -69950, -49140, 640, 10080, -645, -21455, -40980, -100845],88,15]
%
% END OF LATTICE L89.15
%
%
% LATTICE L89.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[160224330, 4883340, 56055090; 4883340, 148848, 1708455; 56055090, 1708455, 19611086],[210, 21, 1],[-4027, 27267, 296011, 595809, 1393968, 171296, 101115, -120; 29, -187, -2036, -4101, -9598, -1180, -698, 0; 11508, -77922, -845922, -1702666, -3983595, -489519, -288960, 343],88,16]
%
% END OF LATTICE L89.16
%
%
% LATTICE L89.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-82545960, 3058440, -3959760; 3058440, -113302, 146489; -3959760, 146489, -187022],[840, 7, 1],[-10113, -1014, 97, 1456, -100, -445, -5933, -14587; -303161, -30397, 2908, 43647, -2998, -13340, -177856, -437280; -23338, -2340, 224, 3360, -231, -1027, -13692, -33663],88,17]
%
% END OF LATTICE L89.17
%
%
% LATTICE L89.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-11354558880, 4875150, -5645732400; 4875150, -2040, 2424030; -5645732400, 2424030, -2807180329],[210, 30, 1],[-99121, 3542953, 2797487, 11310897, 26516680, 22874606, 976450, 10914; 312, -11102, -8769, -35458, -83129, -71715, -3062, -35; 199350, -7125510, -5626245, -22748230, -53329770, -46004910, -1963815, -21950],88,18]
%
% END OF LATTICE L89.18
%
%
% LATTICE L89.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-4362041040, 50595720, -397717320; 50595720, -586864, 4613176; -397717320, 4613176, -36262091],[840, 8, 1],[3068, 8254, 2082, 14686, 7929, 2743, -511, -547; 214761, 577787, 145743, 1028049, 555050, 192024, -35770, -38292; -6328, -17024, -4294, -30288, -16352, -5656, 1054, 1128],88,19]
%
% END OF LATTICE L89.19
%
%
% LATTICE L89.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1522451910, 19433400, -602660520; 19433400, 248080, -7692685; -602660520, -7692685, 238562348],[210, 35, 1],[18177, -123063, -1335983, -8067187, -6291395, -773111, -456365, 1621; 29, -187, -2036, -12303, -9598, -1180, -698, 0; 45920, -310890, -3375050, -20379870, -15893745, -1953085, -1152900, 4095],88,20]
%
% END OF LATTICE L89.20
%
%
% LATTICE L89.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-29784351660, 9333030, -14808739890; 9333030, -2856, 4640370; -14808739890, 4640370, -7362885707],[210, 42, 1],[-182261, 930827, 5144749, 20801365, 48765572, 6009646, 1795724, 20054; 312, -1586, -8769, -35458, -83129, -10245, -3062, -35; 366576, -1872144, -10347477, -41837152, -98080710, -12087018, -3611685, -40334],88,21]
%
% END OF LATTICE L89.21
%
%
% LATTICE L89.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2565990, -3150, 1047060; -3150, 120, 585; 1047060, 585, -423296],[630, 15, 1],[8989, 1797, -361, -361, 359, 4675, 1079, 4675; 126717, 25333, -5088, -5089, 5060, 65898, 15210, 65902; 22410, 4480, -900, -900, 895, 11655, 2690, 11655],88,22]
%
% END OF LATTICE L89.22
%
%
% LATTICE L89.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-696360, 17640, 224280; 17640, -390, -5865; 224280, -5865, -71642],[840, 15, 1],[-103, -212, 509, 822, 2266, 2375, 727, 105; -824, -1694, 4072, 6574, 18121, 18991, 5812, 839; -255, -525, 1260, 2035, 5610, 5880, 1800, 260],88,23]
%
% END OF LATTICE L89.23
%
%
% LATTICE L89.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1047690, -6930, -506520; -6930, 168, -1533; -506520, -1533, -229438],[630, 21, 1],[-8021, -229, 323, 323, -320, -596, -963, -4172; -159549, -4555, 6426, 6425, -6366, -11856, -19156, -82988; 18774, 536, -756, -756, 749, 1395, 2254, 9765],88,24]
%
% END OF LATTICE L89.24
%
%
% LATTICE L89.25
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-4274738580, 4564350, -2039654610; 4564350, -4760, 2177840; -2039654610, 2177840, -973203589],[210, 70, 1],[-85303, 435657, 2407906, 29207093, 22823830, 2812704, 840455, 28156; 312, -1586, -8769, -106374, -83129, -10245, -3062, -105; 178780, -913060, -5046545, -61212900, -47834710, -5894930, -1761445, -59010],88,25]
%
% END OF LATTICE L89.25
%
%
% LATTICE L89.26
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-5885880, -220920, 18480; -220920, -8274, 693; 18480, 693, -58],[840, 21, 1],[-1, 0, 5, 6, 15, 2, 3, 0; -19, -1, 92, 117, 299, 41, 68, 3; -546, -12, 2688, 3304, 8337, 1125, 1764, 35],88,26]
%
% END OF LATTICE L89.26
%
%
% LATTICE L89.27
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[261082080, -355430250, 128445660; -355430250, 483873360, -174862530; 128445660, -174862530, 63191957],[630, 30, 1],[25243, 6459, 469, -47, 618, 7720, 1134, 11660; 36, 14, 3, -2, -5, -21, 0, 11; -51210, -13090, -945, 90, -1270, -15750, -2305, -23670],88,27]
%
% END OF LATTICE L89.27
%
%
% LATTICE L89.28
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-5223120, 61320, 542640; 61320, -624, -6552; 542640, -6552, -56033],[840, 24, 1],[2530, 2648, 202, 116, -115, -233, 143, 919; 37943, 39711, 3029, 1739, -1725, -3493, 2145, 13783; 20064, 21000, 1602, 920, -912, -1848, 1134, 7288],88,28]
%
% END OF LATTICE L89.28
%
%
% LATTICE L89.29
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2292755430, 4094370, 825411720; 4094370, -7140, -1473885; 825411720, -1473885, -297155246],[210, 105, 1],[-57742, 294898, 3259843, 6590134, 15449545, 1903931, 1137815, 6353; 115796, -591382, -6537224, -13215726, -30982219, -3818107, -2281754, -12741; -160965, 822075, 9087330, 18371045, 43068060, 5307510, 3171840, 17710],88,29]
%
% END OF LATTICE L89.29
%
%
% LATTICE L89.30
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[11557435680, 3531095190, 5768825580; 3531095190, 1078840812, 1762525254; 5768825580, 1762525254, 2879475127],[630, 42, 1],[188351, 6641, 2672, 357, 6724, 9866, 9039, 89010; 36, 2, 3, -2, -5, -3, 0, 11; -377370, -13306, -5355, -714, -13468, -19764, -18109, -178332],88,30]
%
% END OF LATTICE L89.30
%
%
% LATTICE L89.31
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-11465160, 78960, 1648920; 78960, -490, -11515; 1648920, -11515, -236678],[840, 35, 1],[-2511, -252, 23, 362, -23, -110, -1471, -3620; -45202, -4536, 416, 6516, -417, -1981, -26484, -65169; -15295, -1535, 140, 2205, -140, -670, -8960, -22050],88,31]
%
% END OF LATTICE L89.31
%
%
% LATTICE L89.32
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-151576728240, -36019405800, -917158200; -36019405800, -8559345520, -217945680; -917158200, -217945680, -5549527],[840, 40, 1],[6941, 2403, -447, -479, 2684, 7222, 1822, 12854; -48567, -16807, 3129, 3351, -18787, -50547, -12751, -89949; 760240, 262920, -49010, -52440, 294240, 791560, 199650, 1408200],88,32]
%
% END OF LATTICE L89.32
%
%
% LATTICE L89.33
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-4663202040, -1968120, 1946316960; -1968120, -690, 815925; 1946316960, 815925, -812132474],[2520, 15, 1],[-198847, -39068, 17531, 8014, -8515, -107188, -48585, -104182; -19487010, -3828664, 1718040, 785372, -834471, -10504431, -4761332, -10209839; -496125, -97475, 43740, 19995, -21245, -267435, -121220, -259935],88,33]
%
% END OF LATTICE L89.33
%
%
% LATTICE L89.34
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[203693872620, 80003805210, 38653583220; 80003805210, 31422687240, 15181771080; 38653583220, 15181771080, 7335024257],[210, 210, 1],[29, -187, -1018, -4101, -9598, -1180, -349, 0; 243838, -1651828, -8965886, -36092704, -84443023, -10376627, -3062569, 7339; -504840, 3419880, 18562635, 74725000, 174827730, 21483390, 6340635, -15190],88,34]
%
% END OF LATTICE L89.34
%
%
% LATTICE L89.35
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-201658848720, -47393939880, 830067000; -47393939880, -11138541904, 195082664; 830067000, 195082664, -3416717],[840, 56, 1],[6447, 319, -415, -445, 2492, 958, 1692, 11938; -32215, -1593, 2075, 2223, -12459, -4789, -8457, -59661; -273112, -13456, 17654, 18816, -105952, -40696, -71806, -506184],88,35]
%
% END OF LATTICE L89.35
%
%
% LATTICE L89.36
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3386837160, -1980720, -1491147000; -1980720, -966, -867951; -1491147000, -867951, -656429938],[2520, 21, 1],[211526, 5937, -18649, -8525, 9058, 16289, 51683, 110825; 10576296, 296850, -932448, -426250, 452899, 814449, 2584148, 5541247; -494487, -13879, 43596, 19929, -21175, -38079, -120820, -259077],88,36]
%
% END OF LATTICE L89.36
%
%
% LATTICE L89.37
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-10589040, -1559880, 171360; -1559880, -229776, 25248; 171360, 25248, -2771],[2520, 24, 1],[46, 4, -56, -280, -237, -677, -13, -5; -249, -21, 303, 1513, 1280, 3654, 70, 26; 576, 56, -702, -3528, -2992, -8568, -166, -72],88,37]
%
% END OF LATTICE L89.37
%
%
% LATTICE L89.38
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2312730, -2227050, -1125180; -2227050, -2144310, -1083495; -1125180, -1083495, -547418],[630, 105, 1],[-13582, -380, 613, 560, -578, -1048, -1663, -7124; -60, -2, 0, 2, -1, -3, -6, -29; 28035, 785, -1260, -1155, 1190, 2160, 3430, 14700],88,38]
%
% END OF LATTICE L89.38
%
%
% LATTICE L89.39
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-6567960, -522480, 2635920; -522480, -41370, 209685; 2635920, 209685, -1057874],[840, 105, 1],[-757, -24, 3701, 4598, 11649, 1580, 2523, 70; -19, -1, 92, 117, 299, 41, 68, 3; -1890, -60, 9240, 11480, 29085, 3945, 6300, 175],88,39]
%
% END OF LATTICE L89.39
%
%
% LATTICE L89.40
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-17742480, 6001800, -73080; 6001800, -2030160, 24720; -73080, 24720, -301],[840, 120, 1],[0, 2, 0, -2, -7, -9, -1, -1; -19, -35, 23, 145, 397, 413, 31, 17; -1560, -3360, 1890, 12400, 34320, 36120, 2790, 1640],88,40]
%
% END OF LATTICE L89.40
%
%
% LATTICE L89.41
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[6308957340, 1433250, 3149396460; 1433250, 420, 715470; 3149396460, 715470, 1572161219],[630, 210, 1],[-689998, -24820, -11479, 0, -20477, -32887, -31956, -322041; 6375, 229, 105, 1, 192, 306, 296, 2978; 1382220, 49720, 22995, 0, 41020, 65880, 64015, 645120],88,41]
%
% END OF LATTICE L89.41
%
%
% LATTICE L89.42
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-15310238160, 15278293800, 36797040; 15278293800, -15246415632, -36720264; 36797040, -36720264, -88439],[840, 168, 1],[319, 11, -389, -1939, -4918, -668, -268, -32; -19, -1, 23, 117, 299, 41, 17, 3; 140616, 4992, -171402, -855344, -2170392, -294960, -118566, -14560],88,42]
%
% END OF LATTICE L89.42
%
%
% LATTICE L89.43
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-5290320, -21330120, 151200; -21330120, -85989680, 609560; 151200, 609560, -4321],[840, 280, 1],[198, 76, 134, 944, 509, 25, -33, -35; 197, 75, 131, 915, 489, 23, -33, -33; 34720, 13240, 23170, 162120, 86800, 4120, -5810, -5880],88,43]
%
% END OF LATTICE L89.43
%
%
% LATTICE L89.44
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-829450440, -827270640, 22954680; -827270640, -825095670, 22894305; 22954680, 22894305, -635258],[2520, 105, 1],[14710, 413, -1295, -593, 629, 1132, 3593, 7706; -29424, -826, 2592, 1186, -1259, -2265, -7188, -15415; -528885, -14845, 46620, 21315, -22645, -40725, -129220, -277095],88,44]
%
% END OF LATTICE L89.44
%
%
% LATTICE L89.45
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-275693040, 778680, -32760; 778680, 211920, -5400; -32760, -5400, 137],[2520, 120, 1],[-19, -1, 23, 113, 95, 269, 5, 1; 10509, 553, -12723, -62509, -52552, -148806, -2766, -554; 409680, 21560, -495990, -2436840, -2048680, -5801040, -107830, -21600],88,45]
%
% END OF LATTICE L89.45
%
%
% LATTICE L89.46
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-155771280, 26109720, -200309760; 26109720, -4372368, 33549264; -200309760, 33549264, -257417621],[2520, 168, 1],[94015, 2357, -3089, -3295, 6184, 9010, 6390, 51538; -2822388, -70758, 92736, 98918, -185651, -270489, -191833, -1547207; -441000, -11056, 14490, 15456, -29008, -42264, -29974, -241752],88,46]
%
% END OF LATTICE L89.46
%
%
% LATTICE L89.47
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-14211120, -8209320, -3493560; -8209320, -4739280, -2016840; -3493560, -2016840, -858283],[840, 840, 1],[299, 41, 17, 3, -19, -1, 23, 117; -72727, -9927, -4051, -601, 4680, 206, -5670, -28562; 169680, 23160, 9450, 1400, -10920, -480, 13230, 66640],88,47]
%
% END OF LATTICE L89.47
%
%
% LATTICE L89.48
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-248930640, 35025480, 48285720; 35025480, -4927440, -6794760; 48285720, -6794760, -9365329],[2520, 840, 1],[80113, 1981, -2741, -2811, 5435, 7831, 5505, 44133; 239340, 5918, -8190, -8398, 16239, 23397, 16447, 131851; 239400, 5920, -8190, -8400, 16240, 23400, 16450, 131880],88,48]
%
% END OF LATTICE L89.48
%

\medskip%
%------------------------------WEYL-GROUP-W90--------------------------------
%
\leavevmode\llap{}%
$W_{90\phantom{0}}$%
\qquad\llap{12} lattices, $\chi=37$%
\hfill%
$222462222$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L90.1
%
\leavevmode%
${L_{90.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{2}{}73\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2\rightarrow N_{90}}%
\EasyButWeakLineBreak%
{${4}\above{1pt}{1pt}{*}{2}{292}\above{1pt}{1pt}{b}{2}{6}\above{1pt}{1pt}{b}{2}{4}\above{1pt}{1pt}{*}{4}{2}\above{1pt}{1pt}{}{6}{6}\above{1pt}{1pt}{s}{2}{146}\above{1pt}{1pt}{b}{2}{2}\above{1pt}{1pt}{s}{2}{438}\above{1pt}{1pt}{b}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-263993988\\88065156\\275064
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
88065156\\-29377454\\-91759
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
275064\\-91759\\-286
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4225\\12598\\21556
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
79077\\235790\\403398
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2470\\7365\\12597
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1263\\3766\\6438
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
330\\984\\1679
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-329\\-981\\-1680
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-661\\-1971\\-3358
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
274\\817\\1400
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
49870\\148701\\254478
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-263993988, 88065156, 275064; 88065156, -29377454, -91759; 275064, -91759, -286],[876, 1, 1],[4225, 79077, 2470, 1263, 330, -329, -661, 274, 49870; 12598, 235790, 7365, 3766, 984, -981, -1971, 817, 148701; 21556, 403398, 12597, 6438, 1679, -1680, -3358, 1400, 254478],89,1]
%
% END OF LATTICE L90.1
%
%
% LATTICE L90.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-15330, -5037, 0; -5037, -1655, 0; 0, 0, 1],[219, 1, 1],[0, -24, 1, 30, 148, 265, 1203, 29, 433; 0, 73, -3, -91, -449, -804, -3650, -88, -1314; 1, 0, -3, -6, -23, -36, -146, -2, 0],89,2]
%
% END OF LATTICE L90.2
%
%
% LATTICE L90.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-4220787, 30441, -1397220; 30441, -213, 10077; -1397220, 10077, -462526],[219, 3, 1],[25820, 380814, 3919, -432, 146, 4929, 155429, 13631, 266877; -23, -365, -5, -1, 2, -1, -73, -9, -219; -78000, -1150407, -11839, 1305, -441, -14890, -469536, -41178, -806212],89,3]
%
% END OF LATTICE L90.3
%
%
% LATTICE L90.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-151983372, -312732, 208488; -312732, -642, 429; 208488, 429, -286],[876, 3, 1],[29, 421, 2, -1, 0, 3, 93, 8, 152; -46, -730, -5, -2, 2, -1, -73, -9, -219; 21066, 305724, 1450, -732, 3, 2185, 67671, 5817, 110449],89,4]
%
% END OF LATTICE L90.4
%
%
% LATTICE L90.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[4733639448, -58423068, -1208406960; -58423068, 721112, 14914300; -1208406960, 14914300, 308483023],[876, 4, 1],[-60579, -1149045, -73837, -20925, -17530, -877, -15327, -7667, -1421227; 80802, 1532635, 98487, 27911, 23383, 1170, 20440, 10226, 1895664; -241210, -4575202, -294000, -83318, -69800, -3492, -61028, -30528, -5658960],89,5]
%
% END OF LATTICE L90.5
%
%
% LATTICE L90.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[16460332584, -2628, -4133977152; -2628, 24, 660; -4133977152, 660, 1038239477],[876, 12, 1],[-140359, -2113043, -23849, -547, 0, -22755, -757479, -69359, -1421969; -397, -5986, -68, -2, 1, -63, -2117, -195, -4015; -558870, -8413542, -94960, -2178, 0, -90604, -3016068, -276168, -5661880],89,6]
%
% END OF LATTICE L90.6
%
%
% LATTICE L90.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-27544287, -367044, -9060906; -367044, -4891, -120742; -9060906, -120742, -2980655],[219, 73, 1],[13692, 2775, 6346, -195, 25, 7591, 1107, 7151, 5797; -12860, -2598, -5853, 216, -74, -7371, -1061, -6791, -5463; -41099, -8330, -19053, 584, -73, -22776, -3322, -21462, -17400],89,7]
%
% END OF LATTICE L90.7
%
%
% LATTICE L90.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[772851, -2254386, -746352; -2254386, 8825262, 2921679; -746352, 2921679, 967247],[219, 219, 1],[-4010, -814, -625, 52, 0, -729, -321, -2083, -565; 14481147, 2939588, 2257137, -187694, -145, 2632380, 1159154, 7522042, 2040344; -43745031, -8879985, -6818419, 566991, 438, -7951963, -3501603, -22722783, -6163525],89,8]
%
% END OF LATTICE L90.8
%
%
% LATTICE L90.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-9982020, 3433044, -158556; 3433044, -1180702, 54531; -158556, 54531, -2518],[876, 73, 1],[-717, -181, -400, -191, -36, 65, 1, -54, -118; -2098, -530, -1173, -562, -108, 189, 3, -157, -345; -292, -82, -219, -146, -73, 0, 2, 0, -42],89,9]
%
% END OF LATTICE L90.9
%
%
% LATTICE L90.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-190092, -95484, 94608; -95484, -47742, 47523; 94608, 47523, -47086],[876, 219, 1],[-1723, -303, -34, 219, -110, -363, -125, -650, -138; -46, -10, -5, -2, 2, -1, -1, -9, -3; -3504, -618, -73, 438, -219, -730, -252, -1314, -280],89,10]
%
% END OF LATTICE L90.10
%
%
% LATTICE L90.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2209272, -1779156, 1886904; -1779156, 1759592, -1764264; 1886904, -1764264, 1794815],[876, 292, 1],[-117485, -31211, -152419, -45931, -42302, -3739, -1, -10997, -36709; 350381, 93082, 454566, 136982, 126159, 11151, 3, 32797, 109479; 467930, 124310, 607068, 182938, 168484, 14892, 4, 43800, 146208],89,11]
%
% END OF LATTICE L90.11
%
%
% LATTICE L90.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1752, -193596, 48180; -193596, 41825496, -10408632; 48180, -10408632, 2590277],[876, 876, 1],[444, 91, 73, -1, 1, 76, 34, 224, 62; -51119, -10483, -8429, 109, 0, -8647, -3891, -25723, -7133; -205422, -42126, -33872, 438, 0, -34748, -15636, -103368, -28664],89,12]
%
% END OF LATTICE L90.12
%

\medskip%
%------------------------------WEYL-GROUP-W91--------------------------------
%
\leavevmode\llap{}%
$W_{91\phantom{0}}$%
\qquad\llap{24} lattices, $\chi=48$%
\hfill%
$222222222222\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L91.1
%
\leavevmode%
${L_{91.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{-2}{}7\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}11\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{2\rightarrow N_{91}}%
\EasyButWeakLineBreak%
{${12}\above{1pt}{1pt}{r}{2}{22}\above{1pt}{1pt}{b}{2}{84}\above{1pt}{1pt}{*}{2}{4}\above{1pt}{1pt}{b}{2}{66}\above{1pt}{1pt}{b}{2}{2}\above{1pt}{1pt}{l}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3898356\\4620\\7392
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4620\\-2\\-9
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7392\\-9\\-14
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-11705\\-403788\\-5933928
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
16\\551\\8112
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
22\\759\\11153
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\36\\504
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\33\\506
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-42\\-504
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-36\\-506
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-17\\-594\\-8613
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-6\\-208\\-3041
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-3898356, 4620, 7392; 4620, -2, -9; 7392, -9, -14],[924, 1, 1],[1, 1, -1, -1, -17, -6, -41, -45, -55, -3, -5, 0; 36, 33, -42, -36, -594, -208, -1416, -1551, -1890, -102, -165, 1; 504, 506, -504, -506, -8613, -3041, -20784, -22814, -27888, -1522, -2541, -1],90,1]
%
% END OF LATTICE L91.1
%
%
% LATTICE L91.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[16401, -5544, -231; -5544, 1874, 77; -231, 77, -38],[231, 1, 1],[1, -130, 227, 179, 6698, 2440, 8479, 18786, 11645, 669, 2630, 104; 3, -385, 672, 530, 19833, 7225, 25107, 55627, 34482, 1981, 7788, 308; 0, 11, -21, -16, -594, -216, -750, -1661, -1029, -59, -231, -9],90,2]
%
% END OF LATTICE L91.2
%
%
% LATTICE L91.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[426426, -104412, -142989; -104412, 25401, 35013; -142989, 35013, 47947],[231, 3, 1],[102, -390, -494, -393, -2421, -2015, -2002, -12150, -2166, -177, 331, 305; 3, -11, -14, -11, -66, -54, -53, -319, -56, -4, 11, 9; 302, -1155, -1463, -1164, -7172, -5970, -5932, -36003, -6419, -525, 979, 903],90,3]
%
% END OF LATTICE L91.3
%
%
% LATTICE L91.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[541002, -179256, 231231; -179256, 59269, -76615; 231231, -76615, 98831],[231, 7, 1],[-374, 490, 266, 499, 9413, 2645, 7954, 16186, 1250, 259, -1075, -371; 9, -11, -6, -11, -198, -54, -159, -319, -24, -4, 33, 9; 882, -1155, -627, -1176, -22176, -6230, -18732, -38115, -2943, -609, 2541, 875],90,4]
%
% END OF LATTICE L91.4
%
%
% LATTICE L91.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[692538, -254100, -63525; -254100, 93137, 23309; -63525, 23309, 5827],[231, 11, 1],[82, -10, -418, -113, -197, -615, -1862, -346, -2074, -65, 19, 81; 9, -1, -42, -11, -18, -54, -159, -29, -168, -4, 3, 9; 858, -105, -4389, -1188, -2076, -6490, -19668, -3657, -21945, -693, 195, 847],90,5]
%
% END OF LATTICE L91.5
%
%
% LATTICE L91.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1368444, 3696, 4620; 3696, -6, -15; 4620, -15, -14],[924, 3, 1],[1, 1, -1, -1, -2, -1, -1, -1, 1, 1, 2, 1; 124, 121, -126, -124, -242, -116, -104, -55, 154, 130, 253, 125; 196, 198, -196, -198, -407, -213, -236, -330, 140, 186, 385, 195],90,6]
%
% END OF LATTICE L91.6
%
%
% LATTICE L91.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[3080192808, -926772, -773408328; -926772, 280, 232704; -773408328, 232704, 194195779],[924, 4, 1],[-403, -1381, -2647, -1036, -34768, -12434, -21472, -94869, -58603, -3339, -13357, -691; 3, 0, 0, 3, 165, 65, 117, 528, 336, 21, 99, 7; -1605, -5500, -10542, -4126, -138468, -49520, -85515, -377828, -233394, -13298, -53196, -2752],90,7]
%
% END OF LATTICE L91.7
%
%
% LATTICE L91.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[3866158758, -1535919, -1296084867; -1535919, 609, 514899; -1296084867, 514899, 434497414],[231, 21, 1],[-589, -6892, 59, 3182, 42307, 46667, 54209, 360784, 10665, 12904, 16675, 1591; 35, 418, -5, -209, -2750, -3028, -3515, -23386, -691, -835, -1078, -104; -1757, -20559, 176, 9492, 126203, 139209, 161707, 1076229, 31814, 38493, 49742, 4746],90,8]
%
% END OF LATTICE L91.8
%
%
% LATTICE L91.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2471700, 17556, -5544; 17556, -14, -21; -5544, -21, 10],[924, 7, 1],[7, 1, -1, -1, 16, 9, 73, 87, 17, 9, 28, 3; 708, 99, -102, -102, 1617, 911, 7392, 8811, 1722, 912, 2838, 304; 5376, 770, -768, -770, 12243, 6895, 55944, 66682, 13032, 6902, 21483, 2303],90,9]
%
% END OF LATTICE L91.9
%
%
% LATTICE L91.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[234962574, -475167, -79746051; -475167, 957, 161271; -79746051, 161271, 27065726],[231, 33, 1],[-265, -284, 209, 1478, 1781, 21599, 25085, 15176, 34539, 5968, 701, 739; 35, 38, -35, -209, -250, -3028, -3515, -2126, -4837, -835, -98, -104; -781, -837, 616, 4356, 5249, 63657, 73931, 44727, 101794, 17589, 2066, 2178],90,10]
%
% END OF LATTICE L91.10
%
%
% LATTICE L91.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-14940156, -158004, 32340; -158004, -1430, 341; 32340, 341, -70],[924, 11, 1],[-89, -7, -55, 5, 5, 12, 49, 3, -1, -9, -7, -18; -216, -18, -168, 6, 9, 23, 96, 6, 0, -18, -15, -41; -42240, -3329, -26334, 2332, 2352, 5654, 23100, 1415, -462, -4246, -3309, -8525],90,11]
%
% END OF LATTICE L91.11
%
%
% LATTICE L91.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[402729096, -3380916, -101127180; -3380916, 28392, 848964; -101127180, 848964, 25393513],[924, 12, 1],[-286, -1591, -341, -574, -9424, -11034, -6609, -89423, -18965, -3563, -5745, -1377; 1, 0, 0, 3, 55, 65, 39, 528, 112, 21, 33, 7; -1139, -6336, -1358, -2286, -37532, -43944, -26321, -356136, -75530, -14190, -22880, -5484],90,12]
%
% END OF LATTICE L91.12
%
%
% LATTICE L91.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[23131185, 227766, -9327780; 227766, 2233, -91861; -9327780, -91861, 3761462],[231, 77, 1],[-481, -172, 55, 898, 3245, 13117, 45701, 9216, 8989, 3624, 1277, 449; 1548, 554, -180, -2903, -10485, -42379, -147648, -29774, -29040, -11707, -4125, -1451; -1155, -413, 132, 2156, 7791, 31493, 109725, 22127, 21582, 8701, 3066, 1078],90,13]
%
% END OF LATTICE L91.13
%
%
% LATTICE L91.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[3837372, 29568, -9240; 29568, -42, -63; -9240, -63, 22],[924, 21, 1],[7, 1, -1, -1, 31, 44, 113, 395, 25, 37, 35, 10; 96, 11, -14, -14, 429, 609, 1564, 5467, 346, 512, 484, 138; 3220, 462, -460, -462, 14245, 20223, 51940, 181566, 11492, 17010, 16093, 4599],90,14]
%
% END OF LATTICE L91.14
%
%
% LATTICE L91.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[11195444568, -45188220, -2811040848; -45188220, 182392, 11346216; -2811040848, 11346216, 705818389],[924, 28, 1],[-4561, -14771, -577, 805, 14849, 3171, 3296, 9205, 71, -1058, -17632, -3930; 3, 0, 0, 3, 165, 65, 117, 528, 48, 21, 99, 7; -18165, -58828, -2298, 3206, 59136, 12628, 13125, 36652, 282, -4214, -70224, -15652],90,15]
%
% END OF LATTICE L91.15
%
%
% LATTICE L91.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1961652, -43428, 17556; -43428, 66, 33; 17556, 33, -34],[924, 33, 1],[5, 1, -1, -5, -2, -21, -45, -13, -55, -7, 0, 3; 1340, 269, -266, -1348, -542, -5704, -12240, -3539, -14994, -1922, -3, 799; 3872, 777, -770, -3894, -1565, -16467, -35332, -10215, -43274, -5544, -8, 2310],90,16]
%
% END OF LATTICE L91.16
%
%
% LATTICE L91.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[74340724920, -15126804, -18666324600; -15126804, 3080, 3798212; -18666324600, 3798212, 4686955561],[924, 44, 1],[-139313, -58416, -421676, -28863, -14719, -16329, -11327, -1840, -116, -1265, -15409, -74055; -741, -311, -2247, -154, -78, -84, -54, -7, 21, -5, -81, -393; -554829, -232648, -1679370, -114950, -58620, -65032, -45111, -7328, -462, -5038, -61368, -294932],90,17]
%
% END OF LATTICE L91.17
%
%
% LATTICE L91.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[406335930, -75488259, 23852598; -75488259, 14024010, -4431273; 23852598, -4431273, 1400183],[231, 231, 1],[3, -1, -2, -11, -6, -54, -53, -29, -8, -4, 1, 9; -1468, 552, 1098, 6291, 3719, 35183, 35748, 20016, 5758, 3993, -291, -4331; -4697, 1764, 3509, 20097, 11872, 112266, 114037, 63840, 18359, 12705, -938, -13860],90,18]
%
% END OF LATTICE L91.18
%
%
% LATTICE L91.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[924, 0, 0; 0, -2926, 77; 0, 77, -2],[924, 77, 1],[1, 0, -1, -3, -4, -15, -101, -10, -19, -7, -1, 0; 0, -1, -6, -10, -9, -29, -180, -17, -30, -8, 0, 2; 0, -42, -264, -462, -441, -1463, -9240, -882, -1584, -462, -21, 77],90,19]
%
% END OF LATTICE L91.19
%
%
% LATTICE L91.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[11192583864, -31180380, -2810365404; -31180380, 86856, 7829136; -2810365404, 7829136, 705659551],[924, 84, 1],[-3278, -26449, -115, 2183, 4795, -2341, -3647, -64961, -2655, -6338, -20030, -10124; 1, 0, 0, 3, 55, 65, 39, 528, 16, 21, 33, 7; -13055, -105336, -458, 8694, 19096, -9324, -14525, -258720, -10574, -25242, -79772, -40320],90,20]
%
% END OF LATTICE L91.20
%
%
% LATTICE L91.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[13963452888, -694098636, -3506053320; -694098636, 34502424, 174279732; -3506053320, 174279732, 880327379],[924, 132, 1],[-1478, -681, -657, -1674, -3268, -43894, -26757, -33201, -78401, -15267, -2379, -6929; -7, -1, 7, -5, -17, -239, -148, -185, -441, -88, -14, -40; -5885, -2712, -2618, -6666, -13012, -174768, -106535, -132192, -312158, -60786, -9472, -27588],90,21]
%
% END OF LATTICE L91.21
%
%
% LATTICE L91.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[28838964, 71148, 93324; 71148, -8778, 231; 93324, 231, 302],[924, 231, 1],[2979, 852, 509, 441, 6, -77, 1, 42, 87, 453, 143, 1418; -60, -17, -10, -8, 0, 2, 0, -1, -2, -10, -3, -29; -920612, -263298, -157300, -136290, -1855, 23793, -308, -12978, -26884, -139986, -44191, -438207],90,22]
%
% END OF LATTICE L91.22
%
%
% LATTICE L91.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[8547000, 72996, 2091012; 72996, 616, 17864; 2091012, 17864, 511559],[924, 308, 1],[-58, -7, 83, 271, 739, 2787, 4703, 1865, 1775, 658, 190, 0; 174, 17, -267, -854, -2316, -8722, -14709, -5831, -5547, -2053, -591, 1; 231, 28, -330, -1078, -2940, -11088, -18711, -7420, -7062, -2618, -756, 0],90,23]
%
% END OF LATTICE L91.23
%
%
% LATTICE L91.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1848, -22269324, 5591124; -22269324, 264938799048, -66517765776; 5591124, -66517765776, 16700510381],[924, 924, 1],[-200, -236, -74, -79, -7, 1, 0, -4, -6, -41, -33, -361; -520676, -619195, -196333, -217952, -20914, 0, 6051, 1645, -9517, -90823, -82011, -926325; -2073841, -2466240, -781990, -868098, -83300, 0, 24101, 6552, -37906, -361746, -326648, -3689532],90,24]
%
% END OF LATTICE L91.24
%

\medskip%
%------------------------------WEYL-GROUP-W92--------------------------------
%
\leavevmode\llap{}%
$W_{92\phantom{0}}$%
\qquad\llap{24} lattices, $\chi=15$%
\hfill%
$222242$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L92.1
%
\leavevmode%
${L_{92.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{2}{}7\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{2}{}11\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2\rightarrow N_{92}}%
\EasyButWeakLineBreak%
{${44}\above{1pt}{1pt}{r}{2}{14}\above{1pt}{1pt}{l}{2}{12}\above{1pt}{1pt}{r}{2}{154}\above{1pt}{1pt}{b}{2}{4}\above{1pt}{1pt}{*}{4}{2}\above{1pt}{1pt}{l}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3694273044\\3152688\\6305376
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3152688\\-2690\\-5381
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
6305376\\-5381\\-10762
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
19\\0\\11132
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5\\-7\\2933
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-17\\-24\\-9948
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-101\\-77\\-59136
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-9\\-2\\-5272
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\2\\-1
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-3694273044, 3152688, 6305376; 3152688, -2690, -5381; 6305376, -5381, -10762],[924, 1, 1],[19, 5, -17, -101, -9, 0; 0, -7, -24, -77, -2, 2; 11132, 2933, -9948, -59136, -5272, -1],91,1]
%
% END OF LATTICE L92.1
%
%
% LATTICE L92.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-231, 0, -231; 0, 2, 21; -231, 21, -10],[231, 1, 1],[1, -6, 5, 82, 5, 4; 11, -63, 51, 847, 52, 42; 0, 7, -12, -154, -8, -5],91,2]
%
% END OF LATTICE L92.2
%
%
% LATTICE L92.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-6254094, 24255, 2089857; 24255, -93, -8106; 2089857, -8106, -698342],[231, 3, 1],[-78, 227, 178, 3823, 77, -76; -209, 630, 489, 10472, 209, -210; -231, 672, 527, 11319, 228, -225],91,3]
%
% END OF LATTICE L92.3
%
%
% LATTICE L92.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-11550462, 50127, -4945479; 50127, -217, 21462; -4945479, 21462, -2117470],[231, 7, 1],[98, -39, -650, -667, -95, 92; -209, 90, 1467, 1496, 209, -210; -231, 92, 1533, 1573, 224, -217],91,4]
%
% END OF LATTICE L92.4
%
%
% LATTICE L92.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-16920750, 75999, 1542849; 75999, -341, -6930; 1542849, -6930, -140678],[231, 11, 1],[-2, 59, 142, 93, 21, -20; -19, 630, 1467, 952, 209, -210; -21, 616, 1485, 973, 220, -209],91,5]
%
% END OF LATTICE L92.5
%
%
% LATTICE L92.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2493263388, 4486020, -828097116; 4486020, -8070, 1489959; -828097116, 1489959, -275039066],[924, 3, 1],[-5261, -1388, 1565, 27927, 2491, 1; 0, -7, -8, -77, -2, 2; 15840, 4179, -4712, -84084, -7500, -3],91,6]
%
% END OF LATTICE L92.6
%
%
% LATTICE L92.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[420882364056, 924, -105679222572; 924, 8, -232; -105679222572, -232, 26534963299],[924, 4, 1],[16072, 58297, 68378, 1023769, 26153, 0; -55, -203, -237, -3542, -90, 1; 64009, 232176, 272325, 4077304, 104158, 0],91,7]
%
% END OF LATTICE L92.7
%
%
% LATTICE L92.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[355787817, -13655565, -119273847; -13655565, 524391, 4577874; -119273847, 4577874, 39985210],[231, 21, 1],[-12390, -3539, -21110, -69163, -12911, -176; 11, 3, 17, 55, 10, 0; -36960, -10557, -62972, -206316, -38514, -525],91,8]
%
% END OF LATTICE L92.8
%
%
% LATTICE L92.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-252485772, 2180640, -71515752; 2180640, -18830, 617659; -71515752, 617659, -20256598],[924, 7, 1],[-2181, -83, 1927, 1645, 1031, 2; 0, -1, -24, -11, -2, 2; 7700, 293, -6804, -5808, -3640, -7],91,9]
%
% END OF LATTICE L92.9
%
%
% LATTICE L92.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[20903421, -4147605, -7094703; -4147605, 824043, 1407714; -7094703, 1407714, 2407970],[231, 33, 1],[-570, -12305, -10286, -21347, -6203, -56; 1, 21, 17, 35, 10, 0; -1680, -36267, -30316, -62916, -18282, -165],91,10]
%
% END OF LATTICE L92.10
%
%
% LATTICE L92.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-219314172, -3326400, 316932; -3326400, -50446, 4807; 316932, 4807, -458],[924, 11, 1],[-1, 3, 41, 16, 11, -1; 0, -7, -24, -7, -2, 2; -692, 2002, 28116, 10997, 7590, -671],91,11]
%
% END OF LATTICE L92.11
%
%
% LATTICE L92.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1561407593592, 6468, -391077605688; 6468, 24, -1620; -391077605688, -1620, 97951165537],[924, 12, 1],[53485, 194001, 75849, 3406873, 87031, 0; -55, -203, -79, -3542, -90, 1; 213543, 774564, 302833, 13602204, 347478, 0],91,12]
%
% END OF LATTICE L92.12
%
%
% LATTICE L92.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[30765966, 7690914, -3196347; 7690914, 1922767, -798798; -3196347, -798798, 332362],[231, 77, 1],[-350, -1077, -18862, -1863, -3785, -32; 1051, 3234, 56637, 5594, 11365, 96; -840, -2585, -45276, -4472, -9086, -77],91,13]
%
% END OF LATTICE L92.13
%
%
% LATTICE L92.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-43619268, 1569876, -8158920; 1569876, -56490, 293643; -8158920, 293643, -1526114],[924, 21, 1],[-1037, -41, 293, 765, 487, 4; 0, -1, -8, -11, -2, 2; 5544, 219, -1568, -4092, -2604, -21],91,14]
%
% END OF LATTICE L92.14
%
%
% LATTICE L92.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[132680284968, 13860, -33237391572; 13860, 56, -3472; -33237391572, -3472, 8326212133],[924, 28, 1],[23822, 12343, 101336, 216743, 38757, 0; -55, -29, -237, -506, -90, 1; 95095, 49272, 404523, 865216, 154714, 0],91,15]
%
% END OF LATTICE L92.15
%
%
% LATTICE L92.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-7934388, -1095864, 2679600; -1095864, -151338, 370095; 2679600, 370095, -904954],[924, 33, 1],[-77, 157, 967, 1157, 825, -56; 0, -7, -8, -7, -2, 2; -228, 462, 2860, 3423, 2442, -165],91,16]
%
% END OF LATTICE L92.16
%
%
% LATTICE L92.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[29355101160, 616308, -7370730444; 616308, 88, -154748; -7370730444, -154748, 1850706185],[924, 44, 1],[-173, -39905, -74101, -110027, -36099, 0; -1, -224, -411, -609, -199, 1; -689, -158928, -295119, -438200, -143770, 0],91,17]
%
% END OF LATTICE L92.17
%
%
% LATTICE L92.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-8803847283, 1758121596, -555573942; 1758121596, -351095514, 110947683; -555573942, 110947683, -35059942],[231, 231, 1],[-19, 90, 489, 136, 209, -210; -1356, 6499, 35200, 9781, 14989, -15140; -3990, 19140, 103642, 28797, 44121, -44583],91,18]
%
% END OF LATTICE L92.18
%
%
% LATTICE L92.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3281124, -1076460, -1391544; -1076460, -353122, -456533; -1391544, -456533, -590162],[924, 77, 1],[95, -9, -3127, -185, -979, 32; 0, -1, -24, -1, -2, 2; -224, 22, 7392, 437, 2310, -77],91,19]
%
% END OF LATTICE L92.19
%
%
% LATTICE L92.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[15404083464, 34188, -3860557008; 34188, 168, -8568; -3860557008, -8568, 967529191],[924, 84, 1],[14068, 7287, 19938, 127927, 22873, 0; -55, -29, -79, -506, -90, 1; 56133, 29076, 79555, 510444, 91266, 0],91,20]
%
% END OF LATTICE L92.20
%
%
% LATTICE L92.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[124083960, -54516, -30638916; -54516, 264, 13464; -30638916, 13464, 7565387],[924, 132, 1],[20, 4563, 2822, 12569, 4123, 0; -1, -224, -137, -609, -199, 1; 81, 18480, 11429, 50904, 16698, 0],91,21]
%
% END OF LATTICE L92.21
%
%
% LATTICE L92.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-7511666316, 7422455964, -24682812; 7422455964, -7334304978, 24389673; -24682812, 24389673, -81106],[924, 231, 1],[-61, 4, 655, 117, 625, -17; 0, -1, -8, -1, -2, 2; 18564, -1518, -201740, -35907, -190806, 5775],91,22]
%
% END OF LATTICE L92.22
%
%
% LATTICE L92.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2812491528, -187572, 704392920; -187572, 616, -47432; 704392920, -47432, 176416655],[924, 308, 1],[156, 4991, 64726, 13725, 31505, 0; -469, -15005, -194589, -41262, -94714, 1; -623, -19932, -258489, -54812, -125818, 0],91,23]
%
% END OF LATTICE L92.23
%
%
% LATTICE L92.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1848, -5398932, 1355508; -5398932, 906327241512, -227549981736; 1355508, -227549981736, 57130572509],[924, 924, 1],[82, 2620, 11326, 7205, 16539, 1; -4877, -155829, -673555, -428471, -983509, 0; -19425, -620664, -2682757, -1706592, -3917298, 0],91,24]
%
% END OF LATTICE L92.24
%

\medskip%
%------------------------------WEYL-GROUP-W93--------------------------------
%
\leavevmode\llap{}%
$W_{93\phantom{0}}$%
\qquad\llap{24} lattices, $\chi=54$%
\hfill%
$224222224222\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L93.1
%
\leavevmode%
${L_{93.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{2}{}5\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{2}{}17\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2\rightarrow N_{93}}%
\EasyButWeakLineBreak%
{${20}\above{1pt}{1pt}{*}{2}{68}\above{1pt}{1pt}{b}{2}{2}\above{1pt}{1pt}{*}{4}{4}\above{1pt}{1pt}{b}{2}{34}\above{1pt}{1pt}{s}{2}{6}\above{1pt}{1pt}{b}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3813780\\10200\\15300
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
10200\\-26\\-43
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
15300\\-43\\-58
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
220319\\42769620\\26355780
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-568\\-110264\\-67947
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-920\\-178595\\-110056
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
21\\4080\\2510
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
39\\7582\\4658
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\195\\119
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-194\\-120
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2\\-391\\-238
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\387\\240
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-3813780, 10200, 15300; 10200, -26, -43; 15300, -43, -58],[1020, 1, 1],[21, 39, 1, -1, -2, 2, 59, 505, 79, 273, 410, 22; 4080, 7582, 195, -194, -391, 387, 11450, 98022, 15335, 52996, 79594, 4272; 2510, 4658, 119, -120, -238, 240, 7060, 60418, 9451, 32658, 49045, 2631],92,1]
%
% END OF LATTICE L93.1
%
%
% LATTICE L93.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-4845, -1020, 1275; -1020, -214, 255; 1275, 255, -91],[255, 1, 1],[-1, -60, 11, 194, 1017, 263, 856, 5874, 1699, 2713, 7704, 250; 5, 306, -56, -989, -5185, -1341, -4365, -29954, -8664, -13835, -39287, -1275; 0, 17, -3, -55, -289, -75, -245, -1683, -487, -778, -2210, -72],92,2]
%
% END OF LATTICE L93.2
%
%
% LATTICE L93.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2753490, -1530, 914685; -1530, -3093, -240; 914685, -240, 303827],[255, 3, 1],[39344, 72551, 3628, -1674, -5861, 2697, 112726, 961525, 300512, 518712, 1556975, 27717; -10270, -18938, -947, 437, 1530, -704, -29425, -250988, -78443, -135400, -406419, -7235; -118455, -218433, -10923, 5040, 17646, -8120, -339390, -2894913, -904767, -1561713, -4687665, -83449],92,3]
%
% END OF LATTICE L93.3
%
%
% LATTICE L93.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[3178830, 43350, 630615; 43350, -5155, 8940; 630615, 8940, 125081],[255, 5, 1],[6910, 63711, 3186, -1470, -5147, 7105, 19798, 844361, 263894, 455506, 1367255, 73019; -2054, -18938, -947, 437, 1530, -2112, -5885, -250988, -78443, -135400, -406419, -21705; -34691, -319855, -15995, 7380, 25840, -35670, -99394, -4239035, -1324855, -2286825, -6864175, -366585],92,4]
%
% END OF LATTICE L93.4
%
%
% LATTICE L93.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-35759356860, -1822740, 105814800; -1822740, -78, 5391; 105814800, 5391, -313114],[1020, 3, 1],[-2447, -4541, -116, 117, 232, -78, -6883, -58903, -9214, -31839, -47815, -855; -146520, -271898, -6945, 7006, 13889, -4671, -412150, -3527058, -551725, -1906484, -2863106, -51196; -829470, -1539282, -39321, 39660, 78642, -26440, -2333160, -19966602, -3123309, -10792602, -16208055, -289823],92,5]
%
% END OF LATTICE L93.5
%
%
% LATTICE L93.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[792518792415, -1727890200, 262227517530; -1727890200, 3767235, -571721910; 262227517530, -571721910, 86765476867],[255, 15, 1],[-5027, -61174, -6899, -1350, 11053, 885, -7660, -370184, -119971, -214329, -658090, -13572; -134, -1292, -83, -7, 0, -46, -377, -16082, -5027, -8680, -26061, -465; 15192, 184875, 20850, 4080, -33405, -2675, 23148, 1118685, 362550, 647700, 1988745, 41015],92,6]
%
% END OF LATTICE L93.6
%
%
% LATTICE L93.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1162997880, -7667340, -291929100; -7667340, 50552, 1924612; -291929100, 1924612, 73278379],[1020, 4, 1],[-8692, -16513, -1011, -127, -495, -2009, -25293, -214585, -66959, -115422, -346152, -18382; 95, 187, 13, 2, 0, 18, 260, 2227, 697, 1205, 3621, 195; -34630, -65790, -4028, -506, -1972, -8004, -100770, -854930, -266772, -459854, -1379108, -73236],92,7]
%
% END OF LATTICE L93.7
%
%
% LATTICE L93.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-16120590, 207570, 7548255; 207570, -1003, -97410; 7548255, -97410, -3534343],[255, 17, 1],[-98939, -10732, -9123, 4210, 867, -20347, -283476, -142234, -755707, -1304421, -230316, -209102; -27500, -2983, -2536, 1170, 241, -5655, -78790, -39533, -210044, -362556, -64015, -58119; -210545, -22838, -19414, 8959, 1845, -43299, -603245, -302678, -1608166, -2775845, -490119, -444975],92,8]
%
% END OF LATTICE L93.8
%
%
% LATTICE L93.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-7730268900, 1092420, -37509480; 1092420, -130, 5305; -37509480, 5305, -182006],[1020, 5, 1],[-481, -4463, -114, 115, 228, -230, -1353, -57893, -9056, -31293, -46995, -2521; -17256, -160106, -4089, 4126, 8177, -8253, -48542, -2077026, -324901, -1122692, -1686026, -90444; 98626, 915110, 23375, -23580, -46750, 47160, 277424, 11870590, 1856875, 6416430, 9636025, 516915],92,9]
%
% END OF LATTICE L93.9
%
%
% LATTICE L93.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[44254639430040, -93064417500, -11107564851240; -93064417500, 195707976, 23358433512; -11107564851240, 23358433512, 2787911019353],[1020, 12, 1],[1481338, 2714367, 142427, 12269, 167227, 134335, 4562427, 38383235, 11945103, 20536532, 61479176, 1074418; 95, 187, 13, 2, 0, 6, 260, 2227, 697, 1205, 3621, 65; 5901930, 10814550, 567456, 48882, 666264, 535216, 18177570, 152926050, 47591544, 81821418, 244944636, 4280684],92,10]
%
% END OF LATTICE L93.10
%
%
% LATTICE L93.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[22596240795, 1440447570, 7748337690; 1440447570, 91824531, 493935000; 7748337690, 493935000, 2656934731],[255, 51, 1],[-65678, -7988, -10861, -1469, 468, -2630, -161447, -82862, -443389, -770756, -136743, -42795; 160, 17, 14, 0, 1, 15, 500, 247, 1306, 2244, 395, 117; 191505, 23292, 31671, 4284, -1365, 7667, 470730, 241602, 1292799, 2247315, 398706, 124780],92,11]
%
% END OF LATTICE L93.11
%
%
% LATTICE L93.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-7544940, 56100, 682380; 56100, -390, -5235; 682380, -5235, -60758],[1020, 15, 1],[1231, 52661, 8237, 28461, 42740, 764, 437, 4051, 103, -105, -206, 70; 54330, 2324206, 363543, 1256140, 1886354, 33720, 19288, 178806, 4547, -4634, -9095, 3089; 9144, 391170, 61185, 211410, 317475, 5675, 3246, 30090, 765, -780, -1530, 520],92,12]
%
% END OF LATTICE L93.12
%
%
% LATTICE L93.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-84660, 6120, 3060; 6120, -442, -221; 3060, -221, -110],[1020, 17, 1],[39, 19, 50, 171, 15, 13, 11, 1, 0, -1, 0, 2; 690, 344, 912, 3142, 277, 249, 230, 24, 8, -14, -1, 27; -340, -182, -493, -1734, -155, -153, -170, -22, -17, 0, 2, 0],92,13]
%
% END OF LATTICE L93.13
%
%
% LATTICE L93.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[9989403706920, 33613560420, -2506957062840; 33613560420, 113107000, -8435714000; -2506957062840, -8435714000, 629150037311],[1020, 20, 1],[-183318, -1680643, -88459, -7697, -102563, -248693, -564051, -23729903, -7385231, -12697576, -38013256, -1993414; 19, 187, 13, 2, 0, 18, 52, 2227, 697, 1205, 3621, 195; -730462, -6696810, -352480, -30670, -408680, -990960, -2247558, -94555870, -29427720, -50595670, -151470340, -7943100],92,14]
%
% END OF LATTICE L93.14
%
%
% LATTICE L93.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[119987762730, -4285210995, -26954687790; -4285210995, 153040885, 962652540; -26954687790, 962652540, 6055244113],[255, 85, 1],[25668, 15604, 21197, 2863, -910, 15472, 63141, 162014, 866893, 1506890, 267337, 250955; -76972, -46795, -63577, -8589, 2731, -46371, -189323, -485795, -2599373, -4518426, -801616, -752514; 126497, 76900, 104465, 14110, -4485, 76245, 311168, 798430, 4272185, 7426195, 1317480, 1236750],92,15]
%
% END OF LATTICE L93.15
%
%
% LATTICE L93.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2575827420, -1849260, 7601040; -1849260, -1326, 5457; 7601040, 5457, -22430],[1020, 51, 1],[457, 239, 643, 2247, 200, 64, 203, 25, 17, -3, -2, 2; 690, 344, 912, 3142, 277, 83, 230, 24, 8, -14, -1, 9; 155040, 81078, 218127, 762246, 67845, 21709, 68850, 8478, 5763, -1020, -678, 680],92,16]
%
% END OF LATTICE L93.16
%
%
% LATTICE L93.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[741109560, -561300900, -186851760; -561300900, 425117640, 141517620; -186851760, 141517620, 47109877],[1020, 60, 1],[-17749, -753741, -235279, -405706, -1217000, -21578, -6144, -58621, -3651, -475, -1543, -2315; 52, 2227, 697, 1205, 3621, 65, 19, 187, 13, 2, 0, 6; -70554, -2996250, -935280, -1612770, -4837860, -85780, -24426, -233070, -14520, -1890, -6120, -9200],92,17]
%
% END OF LATTICE L93.17
%
%
% LATTICE L93.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-46498224390, -29909990655, -9670186755; -29909990655, -19239600570, -6220347345; -9670186755, -6220347345, -2011097941],[255, 255, 1],[-5500, -2983, -2536, 1170, 241, -1885, -15758, -39533, -210044, -362556, -64015, -19373; -1371281, -743716, -632195, 291764, 60081, -470023, -3928970, -9856786, -52370315, -90396031, -15960834, -4830228; 4267833, 2314665, 1967580, -908055, -186990, 1462850, 12228117, 30677235, 162991920, 281339205, 49674840, 15033100],92,18]
%
% END OF LATTICE L93.18
%
%
% LATTICE L93.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[573240, 29580, -143820; 29580, 3400, -7412; -143820, -7412, 36083],[1020, 68, 1],[-12851, -6484, -34514, -59695, -10555, -9683, -4739, -552, -666, -111, 1, -871; 260, 131, 697, 1205, 213, 195, 95, 11, 13, 2, 0, 18; -51170, -25818, -137428, -237694, -42028, -38556, -18870, -2198, -2652, -442, 4, -3468],92,19]
%
% END OF LATTICE L93.19
%
%
% LATTICE L93.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-478517700, 1029180, -2331720; 1029180, -2210, 5015; -2331720, 5015, -11362],[1020, 85, 1],[45, 27, 17, -5, -2, 10, 107, 277, 743, 2589, 230, 218; 46, 24, 8, -14, -1, 27, 138, 344, 912, 3142, 277, 249; -9214, -5530, -3485, 1020, 410, -2040, -21896, -56690, -152065, -529890, -47075, -44625],92,20]
%
% END OF LATTICE L93.20
%
%
% LATTICE L93.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[20582565720, -8893380, -5166061320; -8893380, 10200, 2232168; -5166061320, 2232168, 1296640561],[1020, 204, 1],[4479569, 2259834, 12028414, 20803249, 3678223, 1124541, 1650381, 192146, 231486, 38581, -253, 101449; 260, 131, 697, 1205, 213, 65, 95, 11, 13, 2, 0, 6; 17847450, 9003606, 47923476, 82884078, 14654736, 4480384, 6575430, 765546, 922284, 153714, -1008, 404192],92,21]
%
% END OF LATTICE L93.21
%
%
% LATTICE L93.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-21017100, 21392460, -157080; 21392460, -21774450, 159885; -157080, 159885, -1174],[1020, 255, 1],[-47, -123, -331, -1157, -103, -33, -21, -13, -9, 1, 1, -1; 138, 344, 912, 3142, 277, 83, 46, 24, 8, -14, -1, 9; 25092, 63330, 168555, 582930, 51525, 15725, 9078, 5010, 2295, -2040, -270, 1360],92,22]
%
% END OF LATTICE L93.22
%
%
% LATTICE L93.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[5220986280, -6755460, 1315353240; -6755460, 17000, -1708160; 1315353240, -1708160, 331389223],[1020, 340, 1],[190117, 110782, 133878, 22313, -261, 174067, 515025, 1299502, 6917542, 11965101, 2115687, 1941359; -570332, -332335, -401621, -66937, 783, -522183, -1545023, -3898375, -20751929, -35894098, -6346848, -5823882; -757554, -441430, -533460, -88910, 1040, -693600, -2052206, -5178090, -27564140, -47677010, -8430320, -7735680],92,23]
%
% END OF LATTICE L93.23
%
%
% LATTICE L93.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[51000, -8632260, 2166480; -8632260, 1574788200, -395229600; 2166480, -395229600, 99192029],[1020, 1020, 1],[2970, 7517, 40053, 69343, 12269, 3769, 1117, 657, 817, 136, -8, 318; -192311, -486774, -2593754, -4490627, -794549, -244111, -72363, -42574, -52986, -8831, 527, -20563; -766326, -1939710, -10335660, -17894370, -3166140, -972740, -288354, -169650, -211140, -35190, 2100, -81940],92,24]
%
% END OF LATTICE L93.24
%

\medskip%
%------------------------------WEYL-GROUP-W94--------------------------------
%
\leavevmode\llap{}%
$W_{94\phantom{0}}$%
\qquad\llap{24} lattices, $\chi=16$%
\hfill%
$226222$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L94.1
%
\leavevmode%
${L_{94.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}17\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{2\rightarrow N_{94}}%
\EasyButWeakLineBreak%
{${4}\above{1pt}{1pt}{*}{2}{340}\above{1pt}{1pt}{b}{2}{6}\above{1pt}{1pt}{}{6}{2}\above{1pt}{1pt}{l}{2}{204}\above{1pt}{1pt}{r}{2}{10}\above{1pt}{1pt}{b}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-16365070740\\-63936660\\1970640
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-63936660\\-249794\\7699
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1970640\\7699\\-226
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
101\\-25858\\-204
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-583\\149260\\1190
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-200\\51204\\405
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-252\\64517\\509
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-4651\\1190748\\9384
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
49\\-12545\\-100
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-16365070740, -63936660, 1970640; -63936660, -249794, 7699; 1970640, 7699, -226],[1020, 1, 1],[101, -583, -200, -252, -4651, 49; -25858, 149260, 51204, 64517, 1190748, -12545; -204, 1190, 405, 509, 9384, -100],93,1]
%
% END OF LATTICE L94.1
%
%
% LATTICE L94.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-20910, -6885, 0; -6885, -2267, 0; 0, 0, 1],[255, 1, 1],[0, -28, 1, 34, 505, 33; 0, 85, -3, -103, -1530, -100; 1, 0, -3, -5, -51, 0],93,2]
%
% END OF LATTICE L94.2
%
%
% LATTICE L94.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2355945, 28305, -781065; 28305, -303, 9384; -781065, 9384, -258946],[255, 3, 1],[186, -1099, -247, -929, -2852, 184; 1, 0, -1, -5, -17, 0; -561, 3315, 745, 2802, 8602, -555],93,3]
%
% END OF LATTICE L94.3
%
%
% LATTICE L94.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2614515, 38505, -519435; 38505, -505, 7650; -519435, 7650, -103198],[255, 5, 1],[152, -179, -605, -759, -6992, 30; 1, 0, -3, -5, -51, 0; -765, 901, 3045, 3820, 35190, -151],93,4]
%
% END OF LATTICE L94.4
%
%
% LATTICE L94.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2253180, -1162800, -103020; -1162800, -600078, -53157; -103020, -53157, -4702],[1020, 3, 1],[-89, -2311, -23, 163, 1593, 143; 190, 4930, 49, -348, -3400, -305; -198, -5100, -50, 363, 3536, 315],93,5]
%
% END OF LATTICE L94.5
%
%
% LATTICE L94.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[7028887830, 311355, 2325692565; 311355, 15, 103020; 2325692565, 103020, 769516606],[255, 15, 1],[0, 6733, 2379, 9157, 33890, 404; 1, 51, 16, 46, 153, 0; 0, -20349, -7190, -27675, -102425, -1221],93,6]
%
% END OF LATTICE L94.6
%
%
% LATTICE L94.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[26083723560, -4349123940, -6529515720; -4349123940, 725160872, 1088712392; -6529515720, 1088712392, 1634527963],[1020, 4, 1],[-127, -572972, -120766, -153275, -848219, -32763; -2, -8925, -1881, -2387, -13209, -510; -506, -2282930, -481176, -610704, -3379617, -130540],93,7]
%
% END OF LATTICE L94.7
%
%
% LATTICE L94.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-6880155, -52020, 3231105; -52020, -391, 24429; 3231105, 24429, -1517413],[255, 17, 1],[-111, 42, 452, 555, 298, -119; -102, 35, 405, 509, 276, -100; -238, 90, 969, 1190, 639, -255],93,8]
%
% END OF LATTICE L94.8
%
%
% LATTICE L94.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-684420, 2040, 5100; 2040, 10, -15; 5100, -15, -38],[1020, 5, 1],[7, 21, 1, -1, 23, 1; -10, -34, -3, 2, 0, -1; 940, 2822, 135, -135, 3060, 134],93,9]
%
% END OF LATTICE L94.9
%
%
% LATTICE L94.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1112018280, -15627420, -276653580; -15627420, 219624, 3887868; -276653580, 3887868, 68827289],[1020, 12, 1],[-155, -15223, -901, -3010, -5505, -617; -89, -8840, -524, -1749, -3196, -355; -618, -60690, -3592, -12000, -21947, -2460],93,10]
%
% END OF LATTICE L94.10
%
%
% LATTICE L94.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[12703335, 2705040, 4359225; 2705040, 576402, 928251; 4359225, 928251, 1495894],[255, 51, 1],[35, 1713, 1988, 7118, 1515, 1224; 0, 5, 6, 23, 5, 5; -102, -4995, -5797, -20757, -4418, -3570],93,11]
%
% END OF LATTICE L94.11
%
%
% LATTICE L94.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-128843340, -794580, 158100; -794580, -4890, 975; 158100, 975, -194],[1020, 15, 1],[11, 21, -1, 1, 53, 3; -10, -34, -1, 2, 0, -1; 8910, 16932, -820, 825, 43180, 2439],93,12]
%
% END OF LATTICE L94.12
%
%
% LATTICE L94.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[8875020, 389640, 14280; 389640, 17102, 629; 14280, 629, 22],[1020, 17, 1],[9, 9, 1, -12, -17, -4; -190, -190, -21, 254, 360, 85; -408, -410, -51, 527, 744, 170],93,13]
%
% END OF LATTICE L94.13
%
%
% LATTICE L94.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[528496680, 133620, -132658140; 133620, 40, -33540; -132658140, -33540, 33298567],[1020, 20, 1],[-2111, -6085, -497, 0, -8257, -745; 8, 17, -3, 1, 51, 4; -8410, -24242, -1980, 0, -32895, -2968],93,14]
%
% END OF LATTICE L94.14
%
%
% LATTICE L94.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[39343695, -6143460, -11724900; -6143460, 960670, 1831665; -11724900, 1831665, 3494674],[255, 85, 1],[-69, -669, -11642, -13884, -8863, -476; 207, 2008, 34944, 41675, 26604, 1429; -340, -3297, -57375, -68425, -43680, -2346],93,15]
%
% END OF LATTICE L94.15
%
%
% LATTICE L94.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[20464260, 357000, -43860; 357000, 6222, -765; -43860, -765, 94],[1020, 51, 1],[-1, -1, 0, 2, 1, 1; -18, -20, -2, 17, 8, 5; -612, -630, -17, 1071, 532, 510],93,16]
%
% END OF LATTICE L94.16
%
%
% LATTICE L94.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[22110595080, -837420, -5549432400; -837420, 120, 210180; -5549432400, 210180, 1392825469],[1020, 60, 1],[-82411, -217937, -1019, 0, -121069, -32353; -141, -374, -2, 1, -204, -55; -328350, -868326, -4060, 0, -482375, -128904],93,17]
%
% END OF LATTICE L94.17
%
%
% LATTICE L94.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-20107970430, -12917868795, -4176485880; -12917868795, -8298765645, -2683080165; -4176485880, -2683080165, -867468667],[255, 255, 1],[-102, 7, 135, 509, 92, -20; -1655, 186, 2538, 8359, 1420, -513; 5610, -609, -8500, -28305, -4835, 1683],93,18]
%
% END OF LATTICE L94.18
%
%
% LATTICE L94.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[689758680, -19968540, -173060340; -19968540, 577864, 5010104; -173060340, 5010104, 43420811],[1020, 68, 1],[2193, -1413, -9011, -1536, 1228, 11861; 22, -15, -93, -17, 12, 120; 8738, -5630, -35904, -6120, 4893, 47260],93,19]
%
% END OF LATTICE L94.19
%
%
% LATTICE L94.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-251940, -141780, 59160; -141780, -79730, 33235; 59160, 33235, -13834],[1020, 85, 1],[173, 51, 169, -29, -59, -5; -520, -154, -513, 87, 180, 16; -510, -152, -510, 85, 180, 17],93,20]
%
% END OF LATTICE L94.20
%
%
% LATTICE L94.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[593576760, -2840700, -148980180; -2840700, 11832, 712980; -148980180, 712980, 37392121],[1020, 204, 1],[-5965, 3426, 7868, 5837, -825, -29697; -8, 5, 11, 9, -1, -40; -23766, 13650, 31348, 23256, -3287, -118320],93,21]
%
% END OF LATTICE L94.21
%
%
% LATTICE L94.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-12106380, -2080800, 16320; -2080800, -357510, 2805; 16320, 2805, -22],[1020, 255, 1],[-1, -1, -2, 0, 1, 1; -10, -2, -1, 2, 0, -1; -2040, -1002, -1615, 255, 740, 612],93,22]
%
% END OF LATTICE L94.22
%
%
% LATTICE L94.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[479210280, 48238860, 83764440; 48238860, 4855880, 8432000; 83764440, 8432000, 14641759],[1020, 340, 1],[58, 27, 271, 85, 13, -14; -281, -105, -921, -254, -51, 21; -170, -94, -1020, -340, -45, 68],93,23]
%
% END OF LATTICE L94.23
%
%
% LATTICE L94.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2040, -260100, 65280; -260100, 1560124680, -391568820; 65280, -391568820, 98278133],[1020, 1020, 1],[-130, -29, -43, 1, -5, -26; -47233, -10567, -15787, 0, -1846, -9421; -188190, -42102, -62900, 0, -7355, -37536],93,24]
%
% END OF LATTICE L94.24
%

\medskip%
%------------------------------WEYL-GROUP-W95--------------------------------
%
\leavevmode\llap{}%
$W_{95\phantom{0}}$%
\qquad\llap{24} lattices, $\chi=36$%
\hfill%
$2222222222\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L95.1
%
\leavevmode%
${L_{95.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{2}{}7\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}13\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2\rightarrow N_{95}}%
\EasyButWeakLineBreak%
{${42}\above{1pt}{1pt}{b}{2}{2}\above{1pt}{1pt}{s}{2}{182}\above{1pt}{1pt}{b}{2}{6}\above{1pt}{1pt}{l}{2}{52}\above{1pt}{1pt}{r}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5460\\-1092\\-1092
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1092\\218\\209
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1092\\209\\-2
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\0\\1092
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\-1\\-209
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\1
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4\\21\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-9\\-47\\2
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-331\\-1729\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-58\\-303\\-6
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-209\\-1092\\-52
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[5460, -1092, -1092; -1092, 218, 209; -1092, 209, -2],[1092, 1, 1],[4, -9, -331, -58, -209, -4, 9, 331, 58, 209; 21, -47, -1729, -303, -1092, -21, 47, 1729, 303, 1092; 0, 2, 0, -6, -52, -21, -3, -91, -15, -52],94,1]
%
% END OF LATTICE L95.1
%
%
% LATTICE L95.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[12831, 4914, 273; 4914, 1882, 105; 273, 105, 10],[273, 1, 1],[-3676, -70, -346, 16, -5, -104, -110, -16034, -3796, -9355; 9660, 184, 910, -42, 13, 273, 289, 42133, 9975, 24583; -861, -17, -91, 3, 0, -21, -25, -3731, -885, -2184],94,2]
%
% END OF LATTICE L95.2
%
%
% LATTICE L95.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1330329, -11193, 442806; -11193, 87, -3723; 442806, -3723, 147389],[273, 3, 1],[-30, -92, -2790, -148, -694, 37, 93, 2881, 155, 746; 35, 103, 3185, 171, 819, -35, -103, -3185, -171, -819; 91, 279, 8463, 449, 2106, -112, -282, -8736, -470, -2262],94,3]
%
% END OF LATTICE L95.3
%
%
% LATTICE L95.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2602509, -23205, 742833; -23205, 203, -6622; 742833, -6622, 212026],[273, 7, 1],[-11, -81, -341, -373, -564, 17, 83, 367, 415, 668; 15, 103, 455, 513, 819, -15, -103, -455, -513, -819; 39, 287, 1209, 1323, 2002, -60, -294, -1300, -1470, -2366],94,4]
%
% END OF LATTICE L95.4
%
%
% LATTICE L95.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-5033028, -2130492, -13104; -2130492, -901842, -5547; -13104, -5547, -34],[1092, 3, 1],[24, -11, -463, -28, -309, -3, 14, 736, 49, 621; -56, 26, 1092, 66, 728, 7, -33, -1729, -115, -1456; -119, -3, 273, 23, 312, 14, -12, -1638, -128, -1872],94,5]
%
% END OF LATTICE L95.5
%
%
% LATTICE L95.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[4478019, -41223, 1721538; -41223, 377, -15847; 1721538, -15847, 661831],[273, 13, 1],[-104, -114, -248, -490, -54, 209, 119, 283, 595, 74; 105, 103, 245, 513, 63, -105, -103, -245, -513, -63; 273, 299, 651, 1287, 142, -546, -312, -742, -1560, -194],94,6]
%
% END OF LATTICE L95.6
%
%
% LATTICE L95.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[214763640, 972972, 53680536; 972972, 4408, 243196; 53680536, 243196, 13417541],[1092, 4, 1],[251, -1, -20219, -5189, -6758, -6005, -273, -4715, -565, -366; 210, 0, -15470, -3972, -5174, -4599, -209, -3549, -417, -260; -1008, 4, 81172, 20832, 27131, 24108, 1096, 18928, 2268, 1469],94,7]
%
% END OF LATTICE L95.7
%
%
% LATTICE L95.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[450575034, -6694779, 149297967; -6694779, 99435, -2218314; 149297967, -2218314, 49469858],[273, 21, 1],[1063, 167, -43861, -26271, -204172, -4257, -3361, 2339, 3913, 38084; 2, 0, -104, -62, -481, -10, -8, 0, 6, 65; -3208, -504, 132366, 79282, 616161, 12847, 10143, -7059, -11809, -114933],94,8]
%
% END OF LATTICE L95.8
%
%
% LATTICE L95.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[116844, 38220, -1092; 38220, 12502, -357; -1092, -357, 10],[1092, 7, 1],[-1, 2, 74, 127, 641, 19, 4, 4, -1, -17; 3, -7, -247, -423, -2132, -63, -13, -13, 3, 52; -3, -35, -793, -1323, -6552, -186, -28, -26, 0, 0],94,9]
%
% END OF LATTICE L95.9
%
%
% LATTICE L95.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[357860958, -8133762, 118675557; -8133762, 184665, -2697357; 118675557, -2697357, 39355754],[273, 39, 1],[14878, 194, -52072, -57792, -34519, -65397, -7411, 1553, 7273, 5651; 14, 0, -56, -62, -37, -70, -8, 0, 6, 5; -44863, -585, 157017, 174265, 104088, 197197, 22347, -4683, -21931, -17040],94,10]
%
% END OF LATTICE L95.10
%
%
% LATTICE L95.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[240443112, -1243788, 60066552; -1243788, 6504, -310728; 60066552, -310728, 15005591],[1092, 12, 1],[-18678, -2472, -54674, -2748, -7490, -551, -275, -195303, -16481, -63932; 10479, 1387, 30667, 1541, 4199, 308, 154, 109564, 9246, 35867; 74984, 9924, 219492, 11032, 30069, 2212, 1104, 784056, 66164, 256659],94,11]
%
% END OF LATTICE L95.11
%
%
% LATTICE L95.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[3556644, 1975428, -21840; 1975428, 1097174, -12129; -21840, -12129, 134],[1092, 13, 1],[-10, 13, 65, 178, 61, 115, -8, -30, -73, -21; 21, -27, -133, -363, -124, -231, 17, 63, 153, 44; 273, -325, -1449, -3861, -1288, -2184, 234, 812, 1950, 560],94,12]
%
% END OF LATTICE L95.12
%
%
% LATTICE L95.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[568932, 12012, -1092; 12012, 210, -21; -1092, -21, 2],[1092, 21, 1],[0, -1, -25, -14, -209, -2, -1, -1, 0, 1; 0, -42, -1040, -582, -8684, -83, -41, -39, 1, 52; -1, -987, -24453, -13685, -204204, -1952, -966, -936, 14, 1092],94,13]
%
% END OF LATTICE L95.13
%
%
% LATTICE L95.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[536608527, 15212925, -139786920; 15212925, 430885, -3963323; -139786920, -3963323, 36414302],[273, 91, 1],[-9383, -285, 10949, 255185, 50807, 41252, 10908, -326, -32102, -8315; 28155, 855, -32855, -765741, -152458, -123786, -32732, 978, 96324, 24950; -32955, -1001, 38455, 896259, 178444, 144885, 38311, -1145, -112749, -29204],94,14]
%
% END OF LATTICE L95.14
%
%
% LATTICE L95.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[3304392, -53508, 825552; -53508, 616, -13356; 825552, -13356, 206251],[1092, 28, 1],[-263, -1053, -17393, -28201, -34200, -3691, -265, 259, 523, -68; 51, 203, 3341, 5415, 6565, 708, 50, -52, -102, 13; 1056, 4228, 69836, 113232, 137319, 14820, 1064, -1040, -2100, 273],94,15]
%
% END OF LATTICE L95.15
%
%
% LATTICE L95.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[22874124, 11709516, -29484; 11709516, 5994222, -15093; -29484, -15093, 38],[1092, 39, 1],[59, 2, -6, -7, -7, -3, 6, 62, 63, 71; -126, -4, 14, 16, 16, 7, -13, -133, -135, -152; -4277, -39, 903, 923, 924, 455, -507, -4725, -4745, -5292],94,16]
%
% END OF LATTICE L95.16
%
%
% LATTICE L95.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1647070152, -5572476, 410465328; -5572476, 18824, -1388712; 410465328, -1388712, 102291809],[1092, 52, 1],[10879, 531, -23327, -79261, -8019, -94375, -4507, -4505, -4235, 67; -1911, -93, 4123, 14007, 1417, 16674, 796, 798, 756, -11; -43680, -2132, 93660, 318240, 32197, 378924, 18096, 18088, 17004, -269],94,17]
%
% END OF LATTICE L95.17
%
%
% LATTICE L95.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[158045133246, 26977468791, 8314881120; 26977468791, 4604911311, 1419306252; 8314881120, 1419306252, 437452559],[273, 273, 1],[5, 103, 35, 171, 63, -5, -103, -35, -171, -63; -1035, -22733, -7335, -34687, -12052, 1624, 23322, 7924, 38810, 14408; 3263, 71799, 23133, 109291, 37905, -5174, -73710, -25044, -122668, -45549],94,18]
%
% END OF LATTICE L95.18
%
%
% LATTICE L95.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[320180952, -1165164, 79750944; -1165164, 4200, -290220; 79750944, -290220, 19864433],[1092, 84, 1],[-270, -1088, 3030, 2852, 13666, 793, 1611, 3769, 809, -68; 1, -5, -247, -143, -546, -22, -16, -26, -4, 0; 1084, 4368, -12168, -11452, -54873, -3184, -6468, -15132, -3248, 273],94,19]
%
% END OF LATTICE L95.19
%
%
% LATTICE L95.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1092, 0, -1092; 0, 182, 455; -1092, 455, 46],[1092, 91, 1],[37, 84, 84, 1721, 629, 209, -2, -2, 1, 27; 93, 211, 211, 4323, 1580, 525, -5, -5, 3, 68; -39, -91, -93, -1911, -700, -234, 0, 2, 0, -28],94,20]
%
% END OF LATTICE L95.20
%
%
% LATTICE L95.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1422860712, -4377828, 354463200; -4377828, 12792, -1090596; 354463200, -1090596, 88303907],[1092, 156, 1],[-68724, -14882, -15964, -4870, 609, 17589, 7577, -35171, -46265, -15219; 3647, 789, 847, 259, -32, -931, -401, 1869, 2457, 808; 275912, 59748, 64092, 19552, -2445, -70616, -30420, 141204, 185744, 61101],94,21]
%
% END OF LATTICE L95.21
%
%
% LATTICE L95.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-30474444, 15137304, -82992; 15137304, -7518966, 41223; -82992, 41223, -226],[1092, 273, 1],[6, 41, 41, 280, 307, 34, -1, -1, 0, 13; 18, 120, 118, 804, 880, 97, -5, -3, 1, 40; 1079, 6825, 6459, 43771, 47712, 5200, -546, -180, 182, 2520],94,22]
%
% END OF LATTICE L95.22
%
%
% LATTICE L95.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[3723720, -1241604, -1860768; -1241604, 414232, 620620; -1860768, 620620, 929975],[1092, 364, 1],[661, 1995, 2447, 51407, 4786, 6683, 453, 1, 1, 110; -1992, -6018, -7384, -155130, -14443, -20169, -1369, -3, 3, -331; 2652, 8008, 9824, 206388, 19215, 26832, 1820, 4, 0, 441],94,23]
%
% END OF LATTICE L95.23
%
%
% LATTICE L95.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[447720, -26534508, -6608784; -26534508, 1593326280, 396840444; -6608784, 396840444, 98838725],[1092, 1092, 1],[-139, -1097, -1279, -8907, -2478, -1142, -184, -2, -60, -84; -19248, -152054, -177348, -1235110, -343628, -158375, -25569, -275, -8251, -11618; 77272, 610428, 711972, 4958408, 1379511, 635804, 102648, 1104, 33124, 46641],94,24]
%
% END OF LATTICE L95.24
%

\medskip%
%------------------------------WEYL-GROUP-W96--------------------------------
%
\leavevmode\llap{}%
$W_{96\phantom{0}}$%
\qquad\llap{24} lattices, $\chi=56$%
\hfill%
$222262222262\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L96.1
%
\leavevmode%
${L_{96.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}7\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{2}{}13\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{2\rightarrow N_{96}}%
\EasyButWeakLineBreak%
{${28}\above{1pt}{1pt}{b}{2}{78}\above{1pt}{1pt}{b}{2}{14}\above{1pt}{1pt}{s}{2}{26}\above{1pt}{1pt}{b}{2}{2}\above{1pt}{1pt}{}{6}{6}\above{1pt}{1pt}{b}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-156692172\\269724\\-125580
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
269724\\-434\\177
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-125580\\177\\-50
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4129943\\3749189808\\2899620360
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-6851\\-6219383\\-4810065
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2976\\2701632\\2089439
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
13\\11802\\9128
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-29\\-26325\\-20358
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-54\\-49021\\-37912
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-290\\-263263\\-203606
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-149\\-135263\\-104612
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1214\\-1102077\\-852345
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-156692172, 269724, -125580; 269724, -434, 177; -125580, 177, -50],[1092, 1, 1],[13, -29, -54, -290, -149, -1214, -1315, -1180, -163, -113, -6, 5; 11802, -26325, -49021, -263263, -135263, -1102077, -1193766, -1071213, -147973, -102583, -5447, 4539; 9128, -20358, -37912, -203606, -104612, -852345, -923258, -828477, -114443, -79339, -4213, 3510],95,1]
%
% END OF LATTICE L96.1
%
%
% LATTICE L96.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[20202, 5733, 819; 5733, 1627, 234; 819, 234, 70],[273, 1, 1],[-9343, -16541, -2199, -1415, -53, 22, -2, -814, -916, -4370, -2172, -17377; 33131, 58656, 7798, 5018, 188, -78, 7, 2886, 3248, 15496, 7702, 61620; -1365, -2418, -322, -208, -8, 3, 0, -117, -133, -637, -317, -2538],95,2]
%
% END OF LATTICE L96.2
%
%
% LATTICE L96.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-4940705679, 54529566, -1646769033; 54529566, -601815, 18175050; -1646769033, 18175050, -548878726],[273, 3, 1],[6232441, 3581577, 1316281, 692961, -10021, 4014, 101978, 339730, 795192, 3228346, 1518216, 3917293; -6377070, -3664687, -1346821, -709033, 10255, -4108, -104349, -347620, -813652, -3303274, -1553450, -4008199; -18909996, -10866947, -3993759, -2102529, 30405, -12179, -309414, -1030783, -2412711, -9795201, -4606455, -11885551],95,3]
%
% END OF LATTICE L96.3
%
%
% LATTICE L96.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-11431685811, 126699846, -3266063346; 126699846, -1404235, 36198484; -3266063346, 36198484, -933123071],[273, 7, 1],[737587, 8901214, 155778, 574076, -8300, 9973, 12068, 844301, 94107, 2674429, 1257725, 9735542; -911010, -10994061, -192403, -709033, 10255, -12324, -14907, -1042860, -116236, -3303274, -1553450, -12024597; -2617000, -31582005, -552709, -2036853, 29449, -35385, -42818, -2995629, -333897, -9489025, -4462479, -34542249],95,4]
%
% END OF LATTICE L96.4
%
%
% LATTICE L96.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-13760292, -279552, 60060; -279552, -1878, 579; 60060, 579, -154],[1092, 3, 1],[13, -53, -194, -940, -469, -1253, -4045, -1195, -478, -308, -11, 5; 2338, -9529, -34881, -169013, -84327, -225292, -727300, -214864, -85946, -55380, -1978, 899; 13860, -56498, -206808, -1002066, -499968, -1335737, -4312098, -1273909, -509565, -328341, -11727, 5330],95,5]
%
% END OF LATTICE L96.5
%
%
% LATTICE L96.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-21168237909, 234955266, -8141497455; 234955266, -2607865, 90365938; -8141497455, 90365938, -3131294210],[273, 13, 1],[6633919, 879763, 1401093, 56741, -10661, 12808, 108530, 83444, 846390, 264328, 1616006, 12508883; -6377070, -845697, -1346821, -54541, 10255, -12324, -104349, -80220, -813652, -254098, -1553450, -12024597; -17432506, -2311827, -3681769, -149103, 28015, -33657, -285194, -219273, -2224131, -694597, -4246515, -32870643],95,6]
%
% END OF LATTICE L96.6
%
%
% LATTICE L96.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1281107923368, -6102459636, 319097083032; -6102459636, 29068600, -1519994556; 319097083032, -1519994556, 79480382989],[1092, 4, 1],[1217, -36643, -56507, -305317, -157685, -1290301, -700097, -1261277, -176453, -127323, -8715, -7619; 0, -312, -406, -2080, -1058, -8583, -4641, -8307, -1141, -793, -47, -36; -4886, 147108, 226856, 1225744, 633052, 5180124, 2810654, 5063604, 708400, 511160, 34988, 30588],95,7]
%
% END OF LATTICE L96.7
%
%
% LATTICE L96.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[3438235140522, -49906672998, 1139254175241; -49906672998, 724405395, -16536502962; 1139254175241, -16536502962, 377490201443],[273, 21, 1],[-66151448, -267396629, -14257039, -54734015, 199579, -617, -847702, -22933021, -8076011, -235595635, -111864829, -290329033; -169864, -686621, -36609, -140543, 513, -2, -2177, -58890, -20738, -604968, -287248, -745509; 199635657, 806964977, 43025715, 165179469, -602301, 1862, 2558244, 69208594, 24372252, 710994102, 337592136, 876171709],95,8]
%
% END OF LATTICE L96.8
%
%
% LATTICE L96.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[221676, -28392, 2184; -28392, -3038, 329; 2184, 329, -34],[1092, 7, 1],[1, -29, -6, -212, -107, -863, -133, -829, -16, -74, -3, 5; 50, -1443, -299, -10569, -5335, -43032, -6632, -41340, -798, -3692, -150, 249; 548, -15834, -3280, -115934, -58520, -472017, -72746, -453453, -8753, -40495, -1645, 2730],95,9]
%
% END OF LATTICE L96.9
%
%
% LATTICE L96.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2255997630705, -55091270598, 748140607305; -55091270598, 1345324305, -18269530110; 748140607305, -18269530110, 248100601118],[273, 39, 1],[-995761325, -44231333, -214606837, -9053717, 429385, -1496, -12761008, -3793540, -121567274, -38971156, -240553750, -624321853; -1189048, -52817, -256263, -10811, 513, -2, -15239, -4530, -145166, -46536, -287248, -745509; 3002603604, 133374491, 647122203, 27300441, -1294761, 4511, 38479350, 11438983, 366572115, 117513033, 725362131, 1882570651],95,10]
%
% END OF LATTICE L96.10
%
%
% LATTICE L96.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[4724327368488, -8789578980, 1176739240404; -8789578980, 16352952, -2189315364; 1176739240404, -2189315364, 293103151391],[1092, 12, 1],[5555, 30515, 83627, 367227, 177649, 466310, 747274, 435522, 167316, 98810, 1596, -273; 0, -208, -742, -3640, -1826, -4897, -7917, -4693, -1897, -1261, -59, -4; -22302, -122512, -335748, -1474356, -713232, -1872160, -3000186, -1748552, -671748, -396708, -6408, 1096],95,11]
%
% END OF LATTICE L96.11
%
%
% LATTICE L96.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-17147676, 313404, -1116024; 313404, -5642, 18993; -1116024, 18993, -49706],[1092, 13, 1],[1189, -203, -4926, -2036, -13601, -110825, -120049, -8287, -14884, -794, -549, 455; 83202, -14205, -344701, -142471, -951743, -7755087, -8400546, -579891, -1041523, -55561, -38417, 31839; 5096, -870, -21112, -8726, -58292, -474981, -514514, -35517, -63791, -3403, -2353, 1950],95,12]
%
% END OF LATTICE L96.12
%
%
% LATTICE L96.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-113016540, -1232868, 121212; -1232868, -13146, 1323; 121212, 1323, -130],[1092, 21, 1],[1, -53, -26, -862, -427, -1136, -523, -1078, -61, -269, -8, 5; -2, 117, 57, 1885, 933, 2481, 1142, 2353, 133, 585, 17, -11; 912, -48230, -23664, -784602, -388668, -1034033, -476058, -981253, -55527, -244881, -7287, 4550],95,13]
%
% END OF LATTICE L96.13
%
%
% LATTICE L96.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[3423424976790, 103665029013, -886153946496; 103665029013, 3139090045, -26833704352; -886153946496, -26833704352, 229381050545],[273, 91, 1],[209364103, 195297322, 45122226, 13325144, -631964, 6607, 2683070, 16749851, 25560165, 57357247, 354043919, 2756606642; -628262173, -586050417, -135403287, -39986243, 1896405, -19827, -8051387, -50263143, -76701233, -172118277, -1062419005, -8272056453; 735327632, 685922349, 158478073, 46800509, -2219581, 23205, 9423466, 58828749, 89772293, 201449857, 1243471411, 9681741069],95,14]
%
% END OF LATTICE L96.14
%
%
% LATTICE L96.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[56861560392, -133952364, 14162935332; -133952364, 315560, -33364520; 14162935332, -33364520, 3527668531],[1092, 28, 1],[135, 9791, 1043, 28373, 13095, 100094, 7542, 90010, 1516, 4894, -300, -293; 0, -312, -58, -2080, -1058, -8583, -663, -8307, -163, -793, -47, -36; -542, -39312, -4188, -113932, -52584, -401940, -30286, -361452, -6088, -19656, 1204, 1176],95,15]
%
% END OF LATTICE L96.15
%
%
% LATTICE L96.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[169260, -148512, 295932; -148512, -24414, 76011; 295932, 76011, -210826],[1092, 39, 1],[-473521, -10761, -55960, -2774, -1289, 585, 1525, -477, -22706, -8464, -54901, -146679; -6620404, -150452, -782390, -38784, -18022, 8179, 21322, -6669, -317457, -118337, -767583, -2050752; -3051594, -69349, -360633, -17877, -8307, 3770, 9828, -3074, -146328, -54546, -353808, -945269],95,16]
%
% END OF LATTICE L96.16
%
%
% LATTICE L96.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[137803848, -1606236996, 32559072; -1606236996, 18722246920, -379507440; 32559072, -379507440, 7692769],[1092, 52, 1],[43, -5335, -90563, -35733, -236369, -1917931, -1037149, -142823, -255139, -13653, -10561, -8123; 0, -24, -406, -160, -1058, -8583, -4641, -639, -1141, -61, -47, -36; -182, 21396, 363272, 143344, 948220, 7694076, 4160702, 572964, 1023568, 54776, 42380, 32604],95,17]
%
% END OF LATTICE L96.17
%
%
% LATTICE L96.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-747646811172534, -127612505363889, -39332164909947; -127612505363889, -21781610356506, -6713432105289; -39332164909947, -6713432105289, -2069184504481],[273, 273, 1],[-911010, -281899, -192403, -54541, 10255, -4108, -14907, -26740, -116236, -254098, -1553450, -4008199; 193972582, 60022191, 40966957, 11613273, -2182669, 874191, 3173636, 5693215, 24748449, 54102133, 330759699, 853426087; -612023607, -189382438, -129259260, -36642312, 6886698, -2758210, -10013445, -17963246, -78086424, -170703372, -1043615118, -2692735682],95,18]
%
% END OF LATTICE L96.18
%
%
% LATTICE L96.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[441319851336, 82123860, 109924039680; 82123860, 15288, 20455428; 109924039680, 20455428, 27379902497],[1092, 84, 1],[677, 105081, 50645, 1705413, 850405, 2272803, 524191, 2169347, 124311, 569015, 24375, 1625; 0, -208, -106, -3640, -1826, -4897, -1131, -4693, -271, -1261, -59, -4; -2718, -421876, -203328, -6846840, -3414180, -9124780, -2104506, -8709428, -499080, -2284464, -97860, -6524],95,19]
%
% END OF LATTICE L96.19
%
%
% LATTICE L96.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1547364, -616980, -68796; -616980, -245882, -27391; -68796, -27391, -3046],[1092, 91, 1],[-13, 41, 100, 264, 1717, 13778, 2119, 1012, 251, 87, 38, -89; 50, -159, -387, -1021, -6639, -53268, -8192, -3912, -970, -336, -146, 345; -156, 504, 1222, 3220, 20930, 167895, 25818, 12327, 3055, 1057, 455, -1092],95,20]
%
% END OF LATTICE L96.20
%
%
% LATTICE L96.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[26375244168, -21550660404, 6530134884; -21550660404, 17608593912, -5335636644; 6530134884, -5335636644, 1616768411],[1092, 156, 1],[-527054, -24186, -129432, -6874, -4992, -441, 1487, -841, -45757, -18153, -120143, -324910; -7917, -361, -1897, -97, -59, -4, 0, -16, -742, -280, -1826, -4897; 2102646, 96496, 516516, 27444, 19968, 1768, -6006, 3344, 182364, 72396, 479232, 1296152],95,21]
%
% END OF LATTICE L96.21
%
%
% LATTICE L96.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-14408940, 15989064, -5553912; 15989064, -17740086, 6162975; -5553912, 6162975, -2140750],[1092, 273, 1],[-363, 1440, 9203, 23489, 151300, 402582, 185355, 29392, 21629, 7343, 2860, -1766; -2, 9, 57, 145, 933, 2481, 1142, 181, 133, 45, 17, -11; 936, -3710, -23712, -60522, -389844, -1037309, -477594, -75733, -55731, -18921, -7371, 4550],95,22]
%
% END OF LATTICE L96.22
%
%
% LATTICE L96.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[74105304, -22009260, -34842444; -22009260, 6539624, 10350340; -34842444, 10350340, 16383631],[1092, 364, 1],[-149, -4459, -9927, -26629, -174631, -1410022, -108712, -104402, -26360, -9658, -6804, -5171; 445, 13311, 29633, 79489, 521281, 4208967, 324509, 311643, 78685, 28829, 20309, 15435; -598, -17892, -39832, -106848, -700700, -5657652, -436202, -418908, -105768, -38752, -27300, -20748],95,23]
%
% END OF LATTICE L96.23
%
%
% LATTICE L96.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[198744, 210778932, 52619112; 210778932, 223682277000, 55840318716; 52619112, 55840318716, 13940045837],[1092, 1092, 1],[-10, -168, -1070, -2788, -18106, -48441, -11177, -3561, -2659, -941, -539, -36; -1733, -26331, -166991, -434451, -2820115, -7542933, -1740223, -554321, -413661, -146201, -83145, -5543; 6942, 105476, 668928, 1740312, 11296740, 30215276, 6970938, 2220484, 1657032, 585648, 333060, 22204],95,24]
%
% END OF LATTICE L96.24
%

\medskip%
%------------------------------WEYL-GROUP-W97--------------------------------
%
\leavevmode\llap{}%
$W_{97\phantom{0}}$%
\qquad\llap{24} lattices, $\chi=60$%
\hfill%
$22222222222222\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L97.1
%
\leavevmode%
${L_{97.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{2}{}5\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}19\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{2\rightarrow N_{97}}%
\EasyButWeakLineBreak%
{${12}\above{1pt}{1pt}{b}{2}{38}\above{1pt}{1pt}{s}{2}{2}\above{1pt}{1pt}{l}{2}{228}\above{1pt}{1pt}{r}{2}{10}\above{1pt}{1pt}{l}{2}{4}\above{1pt}{1pt}{r}{2}{190}\above{1pt}{1pt}{b}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
22003140\\6840\\-30780
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
6840\\-2\\-5
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-30780\\-5\\38
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-13111\\-13686840\\-12402060
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-11\\-11485\\-10406
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
26\\27144\\24595
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
13\\13578\\12300
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
21\\21945\\19874
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\3137\\2840
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
85\\88920\\80484
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\2095\\1895
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\1048\\948
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\1045\\950
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[22003140, 6840, -30780; 6840, -2, -5; -30780, -5, 38],[1140, 1, 1],[13, 21, 3, 85, 2, 1, 1, -1, -2, 0, 29, 3, 9, 94; 13578, 21945, 3137, 88920, 2095, 1048, 1045, -1050, -2109, -5, 30096, 3125, 9392, 98135; 12300, 19874, 2840, 80484, 1895, 948, 950, -948, -1900, -2, 27360, 2835, 8512, 88920],96,1]
%
% END OF LATTICE L97.1
%
%
% LATTICE L97.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[21090, -7125, -855; -7125, 2407, 285; -855, 285, -122],[285, 1, 1],[1, -256, 62, 6625, 1233, 1837, 38404, 2663, 8692, 1270, 18683, 987, 383, 3776; 3, -760, 184, 19665, 3660, 5453, 114000, 7905, 25802, 3770, 55461, 2930, 1137, 11210; 0, 19, -5, -513, -95, -141, -2945, -204, -665, -97, -1425, -75, -29, -285],96,2]
%
% END OF LATTICE L97.2
%
%
% LATTICE L97.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[11480370, 78375, -3840660; 78375, 525, -26223; -3840660, -26223, 1284859],[285, 3, 1],[-1717, -44519, -14387, -127900, -45983, -45012, -825779, -16171, -125417, -12445, -42036, 1263, 292, -23901; 1685, 43681, 14115, 125476, 45110, 44156, 810065, 15863, 123025, 12207, 41230, -1240, -286, 23465; -5098, -132183, -42717, -379753, -136530, -133647, -2451855, -48014, -372381, -36951, -124811, 3750, 867, -70965],96,3]
%
% END OF LATTICE L97.3
%
%
% LATTICE L97.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[14202690, 112005, -5693160; 112005, 875, -44900; -5693160, -44900, 2282107],[285, 5, 1],[-6221, -53772, -17378, -463481, -11109, -54373, -199504, -58603, -151504, -15034, -152347, 305, 353, -5772; 5055, 43681, 14115, 376428, 9022, 44156, 162013, 47589, 123025, 12207, 123690, -248, -286, 4693; -15420, -133285, -43075, -1148835, -27536, -134775, -494513, -145260, -375535, -37265, -377625, 756, 875, -14307],96,4]
%
% END OF LATTICE L97.4
%
%
% LATTICE L97.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[40883820, 5700, -72960; 5700, -6, -9; -72960, -9, 130],[1140, 3, 1],[-1, -2, 2, 73, 18, 47, 474, 21, 97, 13, 117, 7, 3, 1; -98, -209, 189, 6992, 1730, 4528, 45695, 2026, 9367, 1257, 11324, 680, 292, 95; -568, -1140, 1134, 41420, 10215, 26676, 269040, 11920, 55062, 7380, 66424, 3975, 1704, 570],96,5]
%
% END OF LATTICE L97.5
%
%
% LATTICE L97.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[98926350, -8073195, -31324635; -8073195, 658830, 2556345; -31324635, 2556345, 9918821],[285, 15, 1],[4712, 109845, 33683, 290125, 20384, 97451, 354305, 34240, 260199, 24745, 79919, -908, -71, 15739; -132, -3097, -953, -8227, -579, -2773, -10089, -976, -7429, -709, -2299, 25, 3, -437; 14915, 347700, 106620, 918365, 64524, 308475, 1121532, 108385, 823650, 78330, 252985, -2874, -225, 49818],96,6]
%
% END OF LATTICE L97.6
%
%
% LATTICE L97.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[25657813560, -100095420, 6391851180; -100095420, 390488, -24935680; 6391851180, -24935680, 1592332153],[1140, 4, 1],[-39587, -110719, -12675, -73000, -1963, 496, 22341, 707, -12401, -6765, -111680, -30437, -16696, -637941; 132, 380, 46, 285, 15, 1, 0, 0, 38, 20, 342, 95, 54, 2090; 158910, 444448, 50880, 293037, 7880, -1991, -89680, -2838, 49780, 27156, 448305, 122180, 67021, 2560820],96,7]
%
% END OF LATTICE L97.7
%
%
% LATTICE L97.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[21861210, 150765, 5738760; 150765, 893, 39577; 5738760, 39577, 1506475],[285, 19, 1],[-21247, -9663, -59327, -83272, -189602, -185592, -179199, -200021, -27215, -51307, -27362, 5212, 1202, -5191; -63, -29, -179, -252, -575, -564, -545, -609, -83, -157, -84, 15, 4, -15; 80940, 36811, 226005, 317223, 722285, 707009, 682655, 761976, 103675, 195453, 104235, -19855, -4579, 19775],96,8]
%
% END OF LATTICE L97.8
%
%
% LATTICE L97.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[520980, -2280, -1140; -2280, 10, 5; -1140, 5, 2],[1140, 5, 1],[-5, -4, 0, 1, 0, -3, -8, -7, -15, -3, -115, -1, -7, -11; -1026, -817, 1, 228, 0, -620, -1653, -1446, -3097, -619, -23712, -206, -1440, -2261; -240, -190, 0, 0, -1, -160, -418, -360, -760, -150, -5700, -49, -340, -532],96,9]
%
% END OF LATTICE L97.9
%
%
% LATTICE L97.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[26019950520, -47580180, 6482001240; -47580180, 87000, -11853012; 6482001240, -11853012, 1614774019],[1140, 12, 1],[141, -53277, -26779, -146507, -119516, -66029, -2530373, -52569, -444789, -51863, -102526, -11554, 494, 40043; 0, 38, 20, 114, 95, 54, 2090, 44, 380, 46, 95, 15, 1, 0; -566, 213864, 107496, 588107, 479760, 265053, 10157400, 211022, 1785468, 208188, 411559, 46380, -1983, -160740],96,10]
%
% END OF LATTICE L97.10
%
%
% LATTICE L97.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[51251089155, 5439795, -17184299295; 5439795, 570, -1823943; -17184299295, -1823943, 5761831546],[285, 57, 1],[121335, 149804, 875764, 397883, 2660088, 2547863, 2439396, 896717, 359222, 651314, 111143, -114958, -2733, 105734; 38, 45, 257, 115, 760, 719, 685, 250, 99, 175, 29, -40, 1, 35; 361874, 446781, 2611911, 1186661, 7933545, 7598841, 7275345, 2674402, 1071357, 1942503, 331477, -342855, -8151, 315345],96,11]
%
% END OF LATTICE L97.11
%
%
% LATTICE L97.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[298619580, 11696400, 785460; 11696400, 458130, 30765; 785460, 30765, 2066],[1140, 15, 1],[75, 178, 0, 1, 1, 151, 394, 113, 715, 141, 1785, 46, 319, 499; -602, -1425, 1, 0, -8, -1216, -3173, -910, -5757, -1135, -14364, -370, -2564, -4009; -19550, -46455, -15, -380, -261, -39300, -102543, -29410, -186105, -36705, -464740, -11979, -83100, -130017],96,12]
%
% END OF LATTICE L97.12
%
%
% LATTICE L97.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1140, 0, -1140; 0, 38, 19; -1140, 19, -1130],[1140, 19, 1],[445, 39, 111, 175, 92, 73, 19, -1, -2, 0, 47, 93, 297, 166; 198, 17, 47, 72, 35, 24, 5, -6, -1, 1, 24, 45, 136, 75; -456, -40, -114, -180, -95, -76, -20, 0, 2, 0, -48, -95, -304, -170],96,13]
%
% END OF LATTICE L97.13
%
%
% LATTICE L97.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-645240, -1140, -160740; -1140, 4520, -280; -160740, -280, -40043],[1140, 20, 1],[-1039, 1041, 563, -71, -282, -2059, -19331, -7541, -28211, -4853, -40684, -1148, -1516, -7839; -6, 0, 2, 0, -1, -8, -76, -30, -114, -20, -171, -5, -7, -38; 4170, -4180, -2260, 285, 1132, 8265, 77596, 30270, 113240, 19480, 163305, 4608, 6085, 31464],96,14]
%
% END OF LATTICE L97.14
%
%
% LATTICE L97.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[51424525905, -7034655, 20656310370; -7034655, 950, -2825680; 20656310370, -2825680, 8297269633],[285, 95, 1],[-563923, -232079, -1356749, -1849222, -824211, -3947194, -755831, -4167629, -556513, -1009027, -516554, 35619, 4234, -32761; 1691883, 696282, 4070504, 5548011, 2472785, 11842301, 2267630, 12503637, 1669638, 3027256, 1549749, -106865, -12701, 98290; 1404480, 578005, 3379055, 4605585, 2052741, 9830695, 1882437, 10379700, 1386025, 2513035, 1286505, -88711, -10545, 81593],96,15]
%
% END OF LATTICE L97.15
%
%
% LATTICE L97.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-641820, -160740, 1140; -160740, -40242, 285; 1140, 285, -2],[1140, 57, 1],[1, 0, -2, -3, -13, -31, -16, -13, -3, -7, -3, -2, 1, 1; -6, -1, 3, 8, 40, 104, 55, 46, 11, 27, 12, 10, -4, -5; -304, -156, -798, -652, -1995, -3420, -1560, -1064, -186, -228, -32, 285, 0, -150],96,16]
%
% END OF LATTICE L97.16
%
%
% LATTICE L97.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-15955392120, 23307300, -3975058020; 23307300, -33720, 5806680; -3975058020, 5806680, -990328921],[1140, 60, 1],[63855, 410111, 21525, -9112, -10906, -9832, -3181, 11333, 304175, 91257, 366255, 48500, 103817, 717467; -667, -4275, -223, 95, 113, 97, -19, -125, -3249, -965, -3857, -509, -1087, -7505; -256310, -1646160, -86400, 36575, 43776, 39465, 12768, -45490, -1220940, -366300, -1470125, -194676, -416715, -2879868],96,17]
%
% END OF LATTICE L97.17
%
%
% LATTICE L97.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[918791194035, -1681338121995, 563122063935; -1681338121995, 3076757692125, -1030482875010; 563122063935, -1030482875010, 345134411594],[285, 285, 1],[-21, -29, -179, -84, -115, -564, -109, -203, -83, -157, -28, 3, 4, -3; 13127214, 17910487, 109963221, 51448487, 70285807, 343996355, 66429367, 123580174, 50443207, 95097861, 16905207, -1932113, -2227885, 1924327; 39194530, 53476170, 328322280, 153612130, 209855589, 1027085850, 198341238, 368979050, 150610620, 283938090, 50474660, -5768799, -6651900, 5745552],96,18]
%
% END OF LATTICE L97.18
%
%
% LATTICE L97.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[16240440, 108300, 4057260; 108300, 760, 27056; 4057260, 27056, 1013603],[1140, 76, 1],[-7433, -1347, -4025, -1672, -3987, -992, -1319, -655, -1, -19, -350, -2753, -2378, -5421; -30, -6, -20, -9, -25, -7, -10, -6, 0, 2, 0, -5, -8, -20; 29754, 5392, 16112, 6693, 15960, 3971, 5280, 2622, 4, 76, 1401, 11020, 9519, 21700],96,19]
%
% END OF LATTICE L97.19
%
%
% LATTICE L97.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-36804900, -43320, 80940; -43320, 190, 95; 80940, 95, -178],[1140, 95, 1],[401, 35, 99, 155, 16, 61, 3, -5, -2, 0, 43, 17, 269, 30; 198, 17, 47, 72, 7, 24, 1, -6, -1, 1, 24, 9, 136, 15; 182400, 15920, 45030, 70500, 7277, 27740, 1364, -2280, -910, 0, 19560, 7733, 122360, 13646],96,20]
%
% END OF LATTICE L97.20
%
%
% LATTICE L97.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[48794280, -338580, 12156960; -338580, 3192, -84360; 12156960, -84360, 3028873],[1140, 228, 1],[2963, 4233, 26809, 6420, 89174, 44516, 86633, 32593, 13545, 26525, 2469, -284, -71, 2257; -52, -74, -468, -112, -1555, -776, -1510, -568, -236, -462, -43, 5, 1, -40; -11894, -16992, -107616, -25771, -357960, -178695, -347760, -130834, -54372, -106476, -9911, 1140, 285, -9060],96,21]
%
% END OF LATTICE L97.21
%
%
% LATTICE L97.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[438900, -21660, -5700; -21660, 570, 285; -5700, 285, 74],[1140, 285, 1],[-5, -2, 0, 11, 13, 199, 22, 97, 25, 69, 35, 10, 31, 1; -2, -1, 1, 8, 9, 136, 15, 66, 17, 47, 24, 7, 24, 1; -380, -150, 0, 820, 969, 14820, 1638, 7220, 1860, 5130, 2600, 741, 2280, 72],96,22]
%
% END OF LATTICE L97.22
%
%
% LATTICE L97.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[26201506920, 9780060, -6519880020; 9780060, 3800, -2433520; -6519880020, -2433520, 1622381407],[1140, 380, 1],[-479803, -84729, -245179, -99296, -44757, -53272, -13793, -31949, -563, -10697, -28642, -40535, -159958, -71499; 1439379, 254181, 735517, 297879, 134266, 159809, 41377, 95841, 1689, 32093, 85926, 121604, 479866, 214493; -1926030, -340120, -984200, -398595, -179664, -213845, -55368, -128250, -2260, -42940, -114975, -162716, -642105, -287012],96,23]
%
% END OF LATTICE L97.23
%
%
% LATTICE L97.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[11400, -1537860, -383040; -1537860, 196214520, 48871800; -383040, 48871800, 12172661],[1140, 1140, 1],[-2, 0, 2, 0, -1, -8, -4, -10, -6, -20, -3, -5, -7, -2; -1751, 269, 5111, 1142, 2953, 4614, 1333, 1183, -553, -5963, -1284, -3237, -5324, -1617; 7030, -1080, -20520, -4585, -11856, -18525, -5352, -4750, 2220, 23940, 5155, 12996, 21375, 6492],96,24]
%
% END OF LATTICE L97.24
%

\medskip%
%------------------------------WEYL-GROUP-W98--------------------------------
%
\leavevmode\llap{}%
$W_{98\phantom{0}}$%
\qquad\llap{24} lattices, $\chi=18$%
\hfill%
$2222222$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L98.1
%
\leavevmode%
${L_{98.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{2}{}19\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2\rightarrow N_{98}}%
\EasyButWeakLineBreak%
{${12}\above{1pt}{1pt}{*}{2}{380}\above{1pt}{1pt}{b}{2}{2}\above{1pt}{1pt}{b}{2}{570}\above{1pt}{1pt}{l}{2}{4}\above{1pt}{1pt}{r}{2}{30}\above{1pt}{1pt}{b}{2}{76}\above{1pt}{1pt}{*}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-15644220\\9120\\5700
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
9120\\-2\\-7
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5700\\-7\\2
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-1098\\-990
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-9\\-9880\\-8930
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\-1
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
13\\14250\\12825
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\1096\\988
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\1095\\990
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-1102\\-988
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-15644220, 9120, 5700; 9120, -2, -7; 5700, -7, 2],[1140, 1, 1],[-1, -9, 0, 13, 1, 1, -1; -1098, -9880, 0, 14250, 1096, 1095, -1102; -990, -8930, -1, 12825, 988, 990, -988],97,1]
%
% END OF LATTICE L98.1
%
%
% LATTICE L98.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[27930, -9405, 0; -9405, 3167, 0; 0, 0, -1],[285, 1, 1],[1, 32, -1, -863, -35, -101, -64; 3, 95, -3, -2565, -104, -300, -190; 0, 0, -1, -285, -11, -30, -19],97,2]
%
% END OF LATTICE L98.2
%
%
% LATTICE L98.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-815333415, -7547085, 272094915; -7547085, -69774, 2518659; 272094915, 2518659, -90804122],[285, 3, 1],[-15523, 2376379, 291802, 5760788, 460891, 153566, -93331; 15529, -2377280, -291913, -5762985, -461067, -153625, 93366; -46084, 7054890, 866289, 17102375, 1368273, 455900, -277077],97,3]
%
% END OF LATTICE L98.3
%
%
% LATTICE L98.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1240849245, -12015315, 496643850; -12015315, -116290, 4809090; 496643850, 4809090, -198779269],[285, 5, 1],[-55793, 569417, 349601, 4141115, 552182, 110390, -111818; 46587, -475456, -291913, -3457791, -461067, -92175, 93366; -138270, 1411168, 866405, 10262793, 1368455, 273576, -277115],97,4]
%
% END OF LATTICE L98.4
%
%
% LATTICE L98.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[25306860, 12656280, -34200; 12656280, 6329562, -17103; -34200, -17103, 46],[1140, 3, 1],[3, 1223, 48, -47, -95, -94, -451; -6, -2470, -97, 95, 192, 190, 912; -2, -9120, -378, 380, 756, 755, 3762],97,5]
%
% END OF LATTICE L98.5
%
%
% LATTICE L98.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[58470445815, -4925200995, -18515625780; -4925200995, 414869505, 1559645685; -18515625780, 1559645685, 5863276622],[285, 15, 1],[14646, -480742, -291905, -1143711, -455741, -29838, 96047; -449, 14801, 8981, 35169, 14010, 916, -2964; 46370, -1522071, -924195, -3621077, -1442910, -94469, 304095],97,6]
%
% END OF LATTICE L98.6
%
%
% LATTICE L98.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[14668177080, -57292980, 3654125220; -57292980, 223784, -14272784; 3654125220, -14272784, 910312921],[1140, 4, 1],[1559, 25986, 1422, 77816, 1064, 3677, 4667; 3, 95, 7, 285, 3, 0, 0; -6258, -104310, -5708, -312360, -4271, -14760, -18734],97,7]
%
% END OF LATTICE L98.7
%
%
% LATTICE L98.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2903466570, -4564845, -762184905; -4564845, -6479, -1198311; -762184905, -1198311, -200080082],[285, 19, 1],[-196075, 526604, 1228601, 3829769, 1940535, 1939727, -20682; -9, 25, 58, 180, 91, 90, -1; 746928, -2006045, -4680232, -14589120, -7392273, -7389195, 78786],97,8]
%
% END OF LATTICE L98.8
%
%
% LATTICE L98.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[15979380, -6840, -14820; -6840, 10, 5; -14820, 5, 14],[1140, 5, 1],[-1, -1, 0, -7, -3, -1, -9; -186, -190, -1, -1311, -560, -186, -1672; -990, -988, 0, -6954, -2980, -993, -8930],97,9]
%
% END OF LATTICE L98.9
%
%
% LATTICE L98.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[18144588840, -32484300, 4525589100; -32484300, 58152, -8102172; 4525589100, -8102172, 1128763891],[1140, 12, 1],[-6353, -146399, 565, 17797, 71, -6776, -58588; 4279, 98610, -380, -11970, -47, 4565, 39463; 25502, 587670, -2268, -71440, -285, 27200, 235182],97,10]
%
% END OF LATTICE L98.10
%
%
% LATTICE L98.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[32371857218910, 42366960, -10854162474705; 42366960, 57, -14205483; -10854162474705, -14205483, 3639360022831],[285, 57, 1],[414454, -3595313, -8289991, -8542911, -12932058, -4227613, 143997; 54, -440, -1025, -1065, -1619, -540, 17; 1236083, -10722795, -24724377, -25478695, -38569050, -12608590, 429462],97,11]
%
% END OF LATTICE L98.11
%
%
% LATTICE L98.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[286140, -14820, 1140; -14820, 690, -45; 1140, -45, 2],[1140, 15, 1],[-1, -1, 1, 4, 3, 0, -9; -34, -38, 33, 133, 100, 0, -304; -190, -228, 180, 722, 540, -1, -1710],97,12]
%
% END OF LATTICE L98.12
%
%
% LATTICE L98.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-107224980, 76380, 185820; 76380, -38, -133; 185820, -133, -322],[1140, 19, 1],[-1, 9, 9, 22, 19, 1, -1; -18, 200, 198, 480, 412, 15, -22; -570, 5110, 5111, 12495, 10792, 570, -568],97,13]
%
% END OF LATTICE L98.13
%
%
% LATTICE L98.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-6389588280, 21385260, -1591769460; 21385260, -71560, 5327480; -1591769460, 5327480, -396540419],[1140, 20, 1],[4387, 4667, -1699, -42145, -3464, -2260, 4402; 3, 0, -2, 0, 1, 3, 19; -17610, -18734, 6820, 169176, 13905, 9072, -17670],97,14]
%
% END OF LATTICE L98.14
%
%
% LATTICE L98.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[32507940465285, -54810345, 13052565812760; -54810345, 95, -22007415; 13052565812760, -22007415, 5240857213901],[285, 95, 1],[-1926241, 1113986, 12843018, 7940908, 20034600, 3929701, -223083; 5778885, -3342046, -38530079, -23823363, -60105419, -11789427, 669266; 4797405, -2774441, -31986215, -19777251, -49897230, -9787128, 555600],97,15]
%
% END OF LATTICE L98.15
%
%
% LATTICE L98.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-22037340, 5509620, -23940; 5509620, -1377462, 5985; -23940, 5985, -26],[1140, 57, 1],[-9, -9, 2, 1, -1, -7, -5; -48, -50, 9, 5, -4, -35, -26; -2774, -3240, 228, 230, 0, -1615, -1386],97,16]
%
% END OF LATTICE L98.16
%
%
% LATTICE L98.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[403721880, -3931860, 100568520; -3931860, 38280, -979440; 100568520, -979440, 25051967],[1140, 60, 1],[-147, -2187, -583, 833, 497, 286, 2414; -3, -38, -10, 0, 4, 3, 19; 590, 8778, 2340, -3344, -1995, -1148, -9690],97,17]
%
% END OF LATTICE L98.17
%
%
% LATTICE L98.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-122003331109185, 223281946114740, -74782691649075; 223281946114740, -408634969252530, 136862041174335; -74782691649075, 136862041174335, -45838510464898],[285, 285, 1],[-3, 5, 58, 12, 91, 6, -1; 121159898, -195241459, -2277554434, -473302966, -3597322617, -239721657, 38339850; 361752400, -582940953, -6800193765, -1413161341, -10740683280, -715747423, 114472965],97,18]
%
% END OF LATTICE L98.18
%
%
% LATTICE L98.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[26019950520, -67511940, 6482001240; -67511940, 175256, -16818344; 6482001240, -16818344, 1614774019],[1140, 76, 1],[8321, 25806, 43432, 115346, 27003, 40043, 141; 3, 5, 7, 15, 3, 0, 0; -33402, -103590, -174344, -463020, -108395, -160740, -566],97,19]
%
% END OF LATTICE L98.19
%
%
% LATTICE L98.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[26451420, 2772480, -75240; 2772480, 290510, -7885; -75240, -7885, 214],[1140, 95, 1],[-1, 1, 5, 2, 7, -1, -1; -6, 12, 58, 24, 88, -9, -10; -570, 794, 3895, 1587, 5700, -684, -720],97,20]
%
% END OF LATTICE L98.20
%
%
% LATTICE L98.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1516480440, -6699780, 377766360; -6699780, 30552, -1668960; 377766360, -1668960, 94104361],[1140, 228, 1],[-35510, -52623, -13405, -1141, 71, -21963, -14689; -621, -920, -234, -20, 1, -385, -257; 142538, 211230, 53808, 4580, -285, 88160, 58962],97,21]
%
% END OF LATTICE L98.21
%
%
% LATTICE L98.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-337247340, -112361820, 592800; -112361820, -37435890, 197505; 592800, 197505, -1042],[1140, 285, 1],[-1, -1, 1, 4, 93, 9, 9; 2, -2, -3, 7, 172, 18, 20; -190, -948, 0, 3602, 85500, 8531, 8910],97,22]
%
% END OF LATTICE L98.22
%
%
% LATTICE L98.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[6849409560, 32228940, -1682225040; 32228940, 151240, -7915780; -1682225040, -7915780, 413156711],[1140, 380, 1],[-24565, -2386, 284, 8986, 16637, 14881, -421; 73584, 7147, -853, -26919, -49838, -44577, 1261; -98610, -9578, 1140, 36072, 66785, 59736, -1690],97,23]
%
% END OF LATTICE L98.23
%
%
% LATTICE L98.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[111720, -50799540, -12655140; -50799540, 24065785320, 5995246320; -12655140, 5995246320, 1493530253],[1140, 1140, 1],[-63, -2, -190, -300, -1706, -657, -359; 13395, 423, 40043, 63449, 360884, 139024, 75998; -53770, -1698, -160740, -254696, -1448655, -558068, -305070],97,24]
%
% END OF LATTICE L98.24
%

\medskip%
%------------------------------WEYL-GROUP-W99--------------------------------
%
\leavevmode\llap{}%
$W_{99\phantom{0}}$%
\qquad\llap{12} lattices, $\chi=98$%
\hfill%
$222242262222242262\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L99.1
%
\leavevmode%
${L_{99.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{2}{}97\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2\rightarrow N_{99}}%
\EasyButWeakLineBreak%
{${4}\above{1pt}{1pt}{*}{2}{388}\above{1pt}{1pt}{b}{2}{6}\above{1pt}{1pt}{s}{2}{194}\above{1pt}{1pt}{b}{2}{2}\above{1pt}{1pt}{*}{4}{4}\above{1pt}{1pt}{b}{2}{582}\above{1pt}{1pt}{s}{2}{2}\above{1pt}{1pt}{}{6}{6}\above{1pt}{1pt}{b}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-57207108\\148992\\147828
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
148992\\-386\\-385
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
147828\\-385\\-382
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
6104015\\-5307840\\2367031248
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-16583\\14419\\-6430599
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-15778\\13720\\-6118435
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
125\\-106\\48470
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3029\\-2522\\1174476
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
100\\-81\\38772
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
622\\-485\\241142
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
21\\-15\\8140
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
9\\-4\\3486
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
85\\0\\32883
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\2\\-389
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\-3\\390
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-57207108, 148992, 147828; 148992, -386, -385; 147828, -385, -382],[1164, 1, 1],[125, 3029, 100, 622, 21, 9, 85, -1, 1, 13, 1433, 107, 1609, 140, 359, 13301, 461, 344; -106, -2522, -81, -485, -15, -4, 0, 2, -3, -14, -1358, -99, -1455, -125, -316, -11640, -402, -297; 48470, 1174476, 38772, 241142, 8140, 3486, 32883, -389, 390, 5044, 555810, 41499, 624001, 54293, 139218, 5157975, 178769, 133395],98,1]
%
% END OF LATTICE L99.1
%
%
% LATTICE L99.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-27354, -9021, 0; -9021, -2975, 0; 0, 0, 1],[291, 1, 1],[0, -32, 1, 545, 77, 153, 13174, 496, 457, 114, 3718, 341, 3141, 189, 151, 8942, 264, 113; 0, 97, -3, -1649, -233, -463, -39867, -1501, -1383, -345, -11252, -1032, -9506, -572, -457, -27063, -799, -342; 1, 0, -3, -97, -11, -18, -1455, -53, -45, -10, -291, -24, -194, -10, -6, -291, -7, 0],98,2]
%
% END OF LATTICE L99.2
%
%
% LATTICE L99.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-10162011, 54417, -3369780; 54417, -285, 18045; -3369780, 18045, -1117438],[291, 3, 1],[24378, 1828816, 83749, 3496867, 291163, 355457, 8605848, 883838, 212337, 108630, 2471776, 49259, 803725, 19189, -769, -4664, 2882, 9343; 31, 2231, 101, 4171, 345, 418, 10088, 1034, 247, 125, 2813, 55, 873, 19, -2, 0, 6, 13; -73515, -5515032, -252556, -10545258, -878040, -1071927, -25952059, -2665329, -640330, -327588, -7453965, -148547, -2423739, -57867, 2319, 14065, -8691, -28175],98,3]
%
% END OF LATTICE L99.3
%
%
% LATTICE L99.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1164, -1164, -1164; -1164, -1158, -1161; -1164, -1161, -1162],[1164, 3, 1],[185, 4581, 52, 1010, 37, 21, 93, 1, -1, 13, 1821, 47, 2191, 194, 507, 6309, 659, 166; -106, -2522, -27, -485, -15, -4, 0, 2, -1, -14, -1358, -33, -1455, -125, -316, -3880, -402, -99; -90, -2328, -28, -582, -24, -18, -97, -3, 2, 0, -582, -17, -873, -81, -222, -2813, -297, -77],98,4]
%
% END OF LATTICE L99.4
%
%
% LATTICE L99.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[33256134168, 448140, -8342901324; 448140, 8, -112424; -8342901324, -112424, 2092967335],[1164, 4, 1],[-181053, -4425467, -295927, -1872663, -65601, -16328, -391294, 0, -289, -16617, -1965863, -297083, -4518667, -395629, -510792, -37956686, -1317800, -988061; 1983, 48500, 3246, 20564, 722, 181, 4365, 1, 0, 180, 21437, 3243, 49373, 4325, 5587, 415257, 14419, 10815; -721706, -17640614, -1179612, -7464732, -261496, -65086, -1559760, 0, -1152, -66238, -7836242, -1184220, -18012124, -1577040, -2036098, -151301376, -5252960, -3938568],98,5]
%
% END OF LATTICE L99.5
%
%
% LATTICE L99.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[6995640, 8148, -1750656; 8148, 24, -2040; -1750656, -2040, 438101],[1164, 12, 1],[7759, 189721, 4231, 80373, 2819, 704, 5630, 0, 1, 707, 84013, 4235, 193361, 16935, 21872, 541838, 56440, 14109; 1983, 48500, 1082, 20564, 722, 181, 1455, 1, 0, 180, 21437, 1081, 49373, 4325, 5587, 138419, 14419, 3605; 31014, 758346, 16912, 321264, 11268, 2814, 22504, 0, 4, 2826, 335814, 16928, 772896, 67692, 87426, 2165816, 225600, 56396],98,6]
%
% END OF LATTICE L99.6
%
%
% LATTICE L99.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-86570463, -874164, -28568634; -874164, -8827, -288478; -28568634, -288478, -9427775],[291, 97, 1],[11327, 8792, 117277, 16843, 136109, 166268, 124531, 413597, 298231, 50902, 11951, 69410, 3900, 9092, -324, -73, 1263, 12914; -12186, -9424, -125583, -18019, -145531, -177665, -133032, -441758, -318387, -54294, -12736, -73857, -4141, -9589, 385, 72, -1442, -14013; -33950, -26353, -351528, -50486, -407982, -498386, -373281, -1239757, -893952, -152581, -35824, -208065, -11691, -27257, 970, 219, -3783, -38703],98,7]
%
% END OF LATTICE L99.7
%
%
% LATTICE L99.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1816131, -5335194, -1769280; -5335194, 21001470, 6964503; -1769280, 6964503, 2309567],[291, 291, 1],[-2698, -2098, -9333, -4023, -32519, -39737, -9922, -98868, -23769, -12176, -2860, -5541, -935, -2187, 73, 6, -292, -1021; 17123192, 13315329, 59233672, 25532794, 206388758, 252199692, 62972213, 627488315, 150855540, 77277997, 18151734, 35167517, 5934269, 13880683, -463188, -38087, 1852945, 6479775; -51637077, -40154001, -178626373, -76997259, -622390509, -760538976, -189900400, -1892267658, -454923307, -233041239, -54738771, -106051943, -17895513, -41858895, 1396800, 114856, -5587782, -19540553],98,8]
%
% END OF LATTICE L99.8
%
%
% LATTICE L99.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1167492, -75660, 10476; -75660, -4850, 679; 10476, 679, -94],[1164, 97, 1],[1, 5, 41, 7, 62, 167, 65, 221, 170, 65, 17, 58, 4, 15, 9, 1, -1, -5; -14, -14, -99, -15, -125, -316, -120, -402, -297, -106, -26, -81, -5, -15, -4, 0, 2, -3; 0, 446, 3783, 661, 5917, 16102, 6291, 21437, 16587, 6402, 1688, 5820, 406, 1552, 970, 111, -97, -582],98,9]
%
% END OF LATTICE L99.9
%
%
% LATTICE L99.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-88055436, -26257512, 96612; -26257512, -7829646, 28809; 96612, 28809, -106],[1164, 291, 1],[125, 33, 38, 8, 31, 21, 1, 1, -3, 1, 9, 25, 13, 116, 315, 41, 419, 108; -106, -26, -27, -5, -15, -4, 0, 2, -1, -14, -14, -33, -15, -125, -316, -40, -402, -99; 84972, 22974, 27257, 5925, 24153, 18042, 911, 1455, -3007, -2910, 4380, 13774, 7752, 71586, 200790, 26443, 272085, 71392],98,10]
%
% END OF LATTICE L99.10
%
%
% LATTICE L99.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[172353480, -105924, 43321752; -105924, 776, -27160; 43321752, -27160, 10889503],[1164, 388, 1],[13093, 12811, 180479, 27311, 227497, 287608, 218486, 732040, 541145, 96713, 23791, 148939, 9291, 28717, 5208, 1126, 0, 7885; -39319, -38472, -541986, -82016, -683182, -863697, -656121, -2198341, -1625076, -290432, -71445, -447267, -27901, -86237, -15639, -3381, 1, -23679; -52186, -51062, -719352, -108856, -906756, -1146346, -870840, -2917760, -2156892, -385478, -94826, -593640, -37032, -114460, -20758, -4488, 0, -31428],98,11]
%
% END OF LATTICE L99.11
%
%
% LATTICE L99.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2328, -1688964, 423696; -1688964, 13925199720, -3493314156; 423696, -3493314156, 876342461],[1164, 1164, 1],[-7368, -1837, -3911, -751, -2455, -545, -43, 1, -91, -819, -892, -4276, -1978, -16648, -21287, -5415, -54581, -13554; -1788089, -445823, -949209, -182283, -595981, -132424, -10466, 0, -22095, -198709, -216443, -1037589, -479983, -4039881, -5165704, -1314066, -13245320, -3289235; -7127754, -1777158, -3783776, -726624, -2375724, -527874, -41720, 0, -88076, -792102, -862794, -4136080, -1913328, -16103940, -20591742, -5238184, -52799040, -13111684],98,12]
%
% END OF LATTICE L99.12
%

\medskip%
%------------------------------WEYL-GROUP-W100--------------------------------
%
\leavevmode\llap{}%
$W_{100}$%
\qquad\llap{32} lattices, $\chi=24$%
\hfill%
$22222222$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L100.1
%
\leavevmode%
${L_{100.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}8\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}11\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{2\rightarrow N_{100}}%
\EasyButWeakLineBreak%
{${8}\above{1pt}{1pt}{r}{2}{110}\above{1pt}{1pt}{b}{2}{2}\above{1pt}{1pt}{l}{2}{264}\above{1pt}{1pt}{r}{2}{10}\above{1pt}{1pt}{b}{2}{22}\above{1pt}{1pt}{b}{2}{40}\above{1pt}{1pt}{b}{2}{66}\above{1pt}{1pt}{l}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
703560\\-141240\\-1320
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-141240\\28354\\265
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1320\\265\\2
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-299\\-1488\\-176
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-641\\-3190\\-385
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\-1
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
53\\264\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\5\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-42\\-209\\-22
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-213\\-1060\\-120
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-683\\-3399\\-396
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[703560, -141240, -1320; -141240, 28354, 265; -1320, 265, 2],[1320, 1, 1],[-299, -641, 0, 53, 1, -42, -213, -683; -1488, -3190, 0, 264, 5, -209, -1060, -3399; -176, -385, -1, 0, 0, -22, -120, -396],99,1]
%
% END OF LATTICE L100.1
%
%
% LATTICE L100.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[37290, 18480, -2970; 18480, 9158, -1485; -2970, -1485, -514],[330, 1, 1],[-1, 1558, -80, -40441, -7668, -5226, -1963, -2788; 2, -3135, 161, 81378, 15430, 10516, 3950, 5610; 0, 55, -3, -1452, -275, -187, -70, -99],99,2]
%
% END OF LATTICE L100.2
%
%
% LATTICE L100.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[417120, 39270, 207900; 39270, 3512, 19570; 207900, 19570, 103621],[330, 2, 1],[-4466, -38319, 1, 1066, 164, -2438, -3168, -40768; -141, -1210, 0, 33, 5, -77, -100, -1287; 8987, 77110, -2, -2145, -330, 4906, 6375, 82038],99,3]
%
% END OF LATTICE L100.3
%
%
% LATTICE L100.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[426030, 48180, -142560; 48180, 5268, -16125; -142560, -16125, 47704],[330, 3, 1],[6017, 25811, -1, -481, -111, 1643, 4269, 9155; -282, -1210, 0, 22, 5, -77, -200, -429; 17886, 76725, -3, -1430, -330, 4884, 12690, 27214],99,4]
%
% END OF LATTICE L100.4
%
%
% LATTICE L100.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[487410, 66000, 97020; 66000, 8780, 13135; 97020, 13135, 19312],[330, 5, 1],[-3487, -2991, 1, 845, 13, -953, -495, -15919; -282, -242, 0, 66, 1, -77, -40, -1287; 17710, 15191, -5, -4290, -66, 4840, 2514, 80850],99,5]
%
% END OF LATTICE L100.5
%
%
% LATTICE L100.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[453447060, 390390, 222524610; 390390, 336, 191580; 222524610, 191580, 109201727],[330, 6, 1],[-623, -7614, -268, -27, 589, 907, 22, -1253; 289, 3025, 65, 11, -130, -132, 95, 726; 1269, 15510, 546, 55, -1200, -1848, -45, 2552],99,6]
%
% END OF LATTICE L100.6
%
%
% LATTICE L100.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[4907537580, 1658250, 2443099890; 1658250, 560, 825520; 2443099890, 825520, 1216238689],[330, 10, 1],[-4717, -10810, -1608, -575, 689, 4819, -116, -31543; 289, 605, 65, 33, -26, -132, 19, 2178; 9475, 21714, 3230, 1155, -1384, -9680, 233, 63360],99,7]
%
% END OF LATTICE L100.7
%
%
% LATTICE L100.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[734910, 119460, -267630; 119460, 19316, -43505; -267630, -43505, 97462],[330, 11, 1],[6303, 2456, -4, -143, -121, 157, 4479, 2617; -282, -110, 0, 6, 5, -7, -200, -117; 17182, 6695, -11, -390, -330, 428, 12210, 7134],99,8]
%
% END OF LATTICE L100.8
%
%
% LATTICE L100.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[147865237080, -844231080, 8193240; -844231080, 4820106, -46779; 8193240, -46779, 454],[1320, 3, 1],[787, 1726, 5, 1, -1, 96, 533, 589; 137880, 302390, 876, 176, -175, 16819, 93380, 103191; 3984, 8745, 27, 88, 15, 495, 2700, 2981],99,9]
%
% END OF LATTICE L100.9
%
%
% LATTICE L100.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[4261540470, 1892550, -1428631050; 1892550, 840, -634455; -1428631050, -634455, 478931666],[330, 15, 1],[7261, 8319, 1237, 295, -530, -3706, 179, 8094; 578, 605, 65, 22, -26, -132, 38, 726; 21660, 24816, 3690, 880, -1581, -11055, 534, 24145],99,10]
%
% END OF LATTICE L100.10
%
%
% LATTICE L100.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[6305640, 5280, -19800; 5280, -10, -15; -19800, -15, 62],[1320, 5, 1],[5, 5, 2, 101, 1, -2, -1, 1; 176, 176, 70, 3432, 33, -77, -36, 33; 1640, 1639, 655, 33000, 326, -660, -328, 330],99,11]
%
% END OF LATTICE L100.11
%
%
% LATTICE L100.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[80119380, 314490, 39148890; 314490, 1232, 153670; 39148890, 153670, 19129399],[330, 22, 1],[-2092, -2068, -570, -22, 1183, 131, -511, -1367; 289, 275, 65, 3, -130, -12, 95, 198; 4279, 4230, 1166, 45, -2420, -268, 1045, 2796],99,12]
%
% END OF LATTICE L100.12
%
%
% LATTICE L100.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2450635440, -11462550, 1202782680; -11462550, 52680, -5625870; 1202782680, -5625870, 590331043],[330, 30, 1],[751762, 1289665, -427, -60710, -5604, 410906, 106716, 2287976; -141, -242, 0, 11, 1, -77, -20, -429; -1531695, -2627658, 870, 123695, 11418, -837210, -217431, -4661690],99,13]
%
% END OF LATTICE L100.13
%
%
% LATTICE L100.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-984720, -6600, 6600; -6600, 16, 16; 6600, 16, -31],[1320, 8, 1],[-1, -9, 1, 2, -1, -5, -3, -25; -136, -1265, 131, 264, -130, -660, -400, -3366; -287, -2640, 280, 561, -280, -1408, -850, -7128],99,14]
%
% END OF LATTICE L100.14
%
%
% LATTICE L100.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[7540170, -118140, -2285250; -118140, 1848, 35805; -2285250, 35805, 692606],[330, 33, 1],[-851, -423, -119, -3, 248, 28, -197, -92; 578, 275, 65, 2, -130, -12, 190, 66; -2838, -1410, -396, -10, 825, 93, -660, -307],99,15]
%
% END OF LATTICE L100.15
%
%
% LATTICE L100.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[9240, -3960, -1320; -3960, 1694, 539; -1320, 539, -38],[1320, 11, 1],[221, 68, 35, 79, 2, -7, -41, 26; 536, 165, 85, 192, 5, -17, -100, 63; -88, -25, -11, -24, 0, 2, 0, -12],99,16]
%
% END OF LATTICE L100.16
%
%
% LATTICE L100.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[313401990, -983400, 63819690; -983400, 3080, -200255; 63819690, -200255, 12995938],[330, 55, 1],[5221, 517, 717, 55, -298, -166, 251, 1702; 578, 55, 65, 6, -26, -12, 38, 198; -25630, -2538, -3520, -270, 1463, 815, -1232, -8355],99,17]
%
% END OF LATTICE L100.17
%
%
% LATTICE L100.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2234760, -69960, 15840; -69960, -2190, 495; 15840, 495, -106],[1320, 15, 1],[1, -7, 2, 651, 37, 126, 19, 23; -32, 231, -67, -21560, -1225, -4169, -628, -759; 0, 33, -15, -3520, -198, -660, -96, -110],99,18]
%
% END OF LATTICE L100.18
%
%
% LATTICE L100.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[18155940, 1454970, 8940030; 1454970, 115896, 716430; 8940030, 716430, 4402093],[330, 66, 1],[-55220, -43037, 65, 416, 2112, -2750, -39234, -15284; -141, -110, 0, 1, 5, -7, -100, -39; 112167, 87420, -132, -845, -4290, 5586, 79695, 31046],99,19]
%
% END OF LATTICE L100.19
%
%
% LATTICE L100.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-393360, -3960, 3960; -3960, 48, 24; 3960, 24, -37],[1320, 24, 1],[-8, -129, 1, 1, -1, -13, -13, -51; -180, -2915, 21, 22, -20, -286, -290, -1144; -981, -15840, 120, 121, -120, -1584, -1590, -6248],99,20]
%
% END OF LATTICE L100.20
%
%
% LATTICE L100.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[10680665820, 45544950, 5317335870; 45544950, 193160, 22674410; 5317335870, 22674410, 2647218931],[330, 110, 1],[-1656886, -258249, 2081, 37570, 12716, -82538, -235476, -1375864; -141, -22, 0, 3, 1, -7, -20, -117; 3328105, 518732, -4180, -75465, -25542, 165790, 472989, 2763630],99,21]
%
% END OF LATTICE L100.21
%
%
% LATTICE L100.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[49564680, -9942240, -55440; -9942240, 1994322, 11121; -55440, 11121, 62],[1320, 33, 1],[39, 14, 9, 7, 1, -2, -23, 1; 184, 65, 41, 32, 5, -9, -100, 5; 1848, 855, 693, 520, 0, -174, -2640, -4],99,22]
%
% END OF LATTICE L100.22
%
%
% LATTICE L100.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2640, -1320, 0; -1320, -6160, 360; 0, 360, -19],[1320, 40, 1],[2, 17, 7, 41, 3, -9, -1, -1; 4, 33, 13, 66, 4, -22, -2, 0; 75, 616, 240, 1155, 64, -440, -38, 0],99,23]
%
% END OF LATTICE L100.23
%
%
% LATTICE L100.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[9123303090, -51557220, 3092826660; -51557220, 289740, -17476965; 3092826660, -17476965, 1048476634],[330, 165, 1],[-2554123, -199048, 1604, 19305, 9801, -63617, -362991, -353487; 5107964, 398074, -3208, -38608, -19601, 127227, 725942, 706935; 7619370, 593793, -4785, -57590, -29238, 189780, 1082862, 1054510],99,24]
%
% END OF LATTICE L100.24
%
%
% LATTICE L100.25
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2044680, 15840, 21120; 15840, -110, -165; 21120, -165, -218],[1320, 55, 1],[5, 0, -3, -49, -9, -2, -1, 1; 56, 1, -23, -432, -81, -19, -12, 9; 440, -1, -275, -4440, -814, -180, -88, 90],99,25]
%
% END OF LATTICE L100.25
%
%
% LATTICE L100.26
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[6634041756540, -16530135384510, -8235080591760; -16530135384510, 41188371411660, 20519466424710; -8235080591760, 20519466424710, 10222509119057],[330, 330, 1],[289, 55, 65, 1, -26, -12, 19, 66; 5622560, 1113904, 1546714, 19746, -643017, -358609, 269445, 1221399; -11285835, -2235876, -3104640, -39635, 1290696, 719820, -540837, -2451640],99,26]
%
% END OF LATTICE L100.26
%
%
% LATTICE L100.27
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2911920, 698280, -9240; 698280, -166672, 2200; -9240, 2200, -29],[1320, 88, 1],[2, 6, 4, 1, -1, -1, -3, 1; 20, 65, 47, 12, -10, -12, -40, 6; 869, 3000, 2288, 591, -440, -592, -2090, 120],99,27]
%
% END OF LATTICE L100.27
%
%
% LATTICE L100.28
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2721840, 175560, 7920; 175560, 7440, 240; 7920, 240, 7],[1320, 120, 1],[3, 5, -3, 1, 2, 20, 2, 26; -364, -605, 365, -121, -243, -2431, -243, -3157; 9075, 15048, -9120, 3025, 6072, 60720, 6066, 78760],99,28]
%
% END OF LATTICE L100.28
%
%
% LATTICE L100.29
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1320, 0, 0; 0, -235290, 1815; 0, 1815, -14],[1320, 165, 1],[1, 0, -1, -7, -4, -1, -1, 0; 0, 1, 9, 24, 11, 1, -4, -1; 0, 129, 1155, 3040, 1386, 120, -528, -130],99,29]
%
% END OF LATTICE L100.29
%
%
% LATTICE L100.30
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2640, -3960, 1320; -3960, -494736, 167112; 1320, 167112, -56447],[1320, 264, 1],[2, 11, 11, 1, -1, -3, -13, -1; -11, 365, 535, 51, 0, -154, -780, -108; -33, 1080, 1584, 151, 0, -456, -2310, -320],99,30]
%
% END OF LATTICE L100.30
%
%
% LATTICE L100.31
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1000560, -130680, -58080; -130680, -6160, -2640; -58080, -2640, -1129],[1320, 440, 1],[2, 2, 12, 11, 13, 1, -1, -1; -773, -769, -4589, -4170, -4909, -363, 389, 381; 1705, 1696, 10120, 9195, 10824, 800, -858, -840],99,31]
%
% END OF LATTICE L100.31
%
%
% LATTICE L100.32
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-60720, 4014120, -9240; 4014120, -189179760, 435600; -9240, 435600, -1003],[1320, 1320, 1],[23, 5, -13, 1, 12, 10, 12, 16; -411, -86, 252, -20, -235, -191, -223, -291; -178695, -37392, 109560, -8695, -102168, -83040, -96954, -126520],99,32]
%
% END OF LATTICE L100.32
%

\medskip%
%------------------------------WEYL-GROUP-W101--------------------------------
%
\leavevmode\llap{}%
$W_{101}$%
\qquad\llap{24} lattices, $\chi=22$%
\hfill%
$2262222$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L101.1
%
\leavevmode%
${L_{101.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{2}{}23\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2\rightarrow N_{101}}%
\EasyButWeakLineBreak%
{${60}\above{1pt}{1pt}{*}{2}{92}\above{1pt}{1pt}{b}{2}{6}\above{1pt}{1pt}{}{6}{2}\above{1pt}{1pt}{l}{2}{276}\above{1pt}{1pt}{r}{2}{10}\above{1pt}{1pt}{s}{2}{46}\above{1pt}{1pt}{b}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-579195660\\194669700\\-401580
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
194669700\\-65428814\\134783
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-401580\\134783\\-178
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-19003\\-56760\\-107070
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
10303\\30774\\58052
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4808\\14361\\27090
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-5037\\-15045\\-28381
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-612451\\-1829328\\-3450828
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-45867\\-137000\\-258435
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-61741\\-184414\\-347875
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-579195660, 194669700, -401580; 194669700, -65428814, 134783; -401580, 134783, -178],[1380, 1, 1],[-19003, 10303, 4808, -5037, -612451, -45867, -61741; -56760, 30774, 14361, -15045, -1829328, -137000, -184414; -107070, 58052, 27090, -28381, -3450828, -258435, -347875],100,1]
%
% END OF LATTICE L101.1
%
%
% LATTICE L101.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[13110, 1725, 0; 1725, 227, 0; 0, 0, -1],[345, 1, 1],[-2, -3, 2, 5, 163, 19, 15; 15, 23, -15, -38, -1242, -145, -115; 0, 0, -3, -6, -207, -25, -23],100,2]
%
% END OF LATTICE L101.2
%
%
% LATTICE L101.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1237759822695, 11185948110, -412695155490; 11185948110, -101090238, 3729630345; -412695155490, 3729630345, -137601243991],[345, 3, 1],[6336, -9344, -3187, 9230, 193025, 87429, 119147; -4870, 7245, 2454, -7131, -148879, -67405, -91793; -19135, 28221, 9625, -27876, -582958, -264045, -359835],100,3]
%
% END OF LATTICE L101.3
%
%
% LATTICE L101.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2113167226965, 18868871100, 422523583800; 18868871100, -168483730, -3772793245; 422523583800, -3772793245, -84482750153],[345, 5, 1],[-2684, 6572, 6745, -6502, -408223, -12329, -84035; -2922, 7245, 7362, -7131, -446637, -13481, -91793; -13293, 32545, 33405, -32200, -2021700, -61059, -416185],100,4]
%
% END OF LATTICE L101.4
%
%
% LATTICE L101.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-4637088420, 25149120, -1713960; 25149120, -135606, 9021; -1713960, 9021, -538],[1380, 3, 1],[-293, 135, 63, -129, -6539, -1546, -2258; -67190, 30958, 14447, -29582, -1499508, -354525, -517799; -193180, 89010, 41537, -85053, -4311304, -1019310, -1488744],100,5]
%
% END OF LATTICE L101.5
%
%
% LATTICE L101.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[270241525995, -6578213325, 88093642395; -6578213325, 160128885, -2144373510; 88093642395, -2144373510, 28716866521],[345, 15, 1],[158043, 1268786, 75, 1102309, 19860847, 1734406, 11832740; 2163, 17365, 1, 15086, 271814, 23737, 161943; -484661, -3890910, -230, -3380385, -60906070, -5318799, -36286755],100,6]
%
% END OF LATTICE L101.6
%
%
% LATTICE L101.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[6008791084440, -31829682060, 1487187136440; -31829682060, 168607736, -7877906396; 1487187136440, -7877906396, 368081623693],[1380, 4, 1],[-15712, 7373, -6539, -36163, -730745, -190866, -207456; -21135, 9890, -8784, -48593, -982008, -256505, -278829; 63030, -29578, 26232, 145072, 2931465, 765680, 832232],100,7]
%
% END OF LATTICE L101.7
%
%
% LATTICE L101.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-159736380, -51409140, -12578700; -51409140, -16544710, -4060785; -12578700, -4060785, -758962],[1380, 5, 1],[93341, -253093, -118082, 123735, 15043741, 225323, 1516473; -286248, 776158, 362121, -379457, -46134504, -690996, -4650554; -15438, 41860, 19530, -20465, -2488140, -37267, -250815],100,8]
%
% END OF LATTICE L101.8
%
%
% LATTICE L101.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-12897386218995, 2910574560, -1686614680380; 2910574560, -656834, 380621135; -1686614680380, 380621135, -220561672867],[345, 23, 1],[49672, -1071, -25030, 24245, 66023, 229171, 13569; -4530, 94, 2265, -2162, -5931, -20625, -1225; -379845, 8190, 191406, -185403, -504882, -1752485, -103763],100,9]
%
% END OF LATTICE L101.9
%
%
% LATTICE L101.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[415947509425320, -1265685451980, 103683626331420; -1265685451980, 3851350536, -315498601344; 103683626331420, -315498601344, 25845314915063],[1380, 12, 1],[-40829, 7327, -2409, -144268, -1069803, -872611, -1031109; -300, -23, -15, -967, -7268, -5960, -7130; 163790, -29394, 9664, 578748, 4291639, 3500580, 4136412],100,10]
%
% END OF LATTICE L101.10
%
%
% LATTICE L101.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-984708660, 25886040, 82068600; 25886040, -678030, -2112315; 82068600, -2112315, -6013706],[1380, 15, 1],[12519, -28845, -13459, 27561, 1397013, 66058, 482398; 575914, -1326962, -619157, 1267894, 64267060, 3038879, 22191849; -31444, 72450, 33805, -69225, -3508880, -165918, -1211640],100,11]
%
% END OF LATTICE L101.11
%
%
% LATTICE L101.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[24130231850865, -40827570135, 7993175520465; -40827570135, 69087147, -13524193890; 7993175520465, -13524193890, 2647751389039],[345, 69, 1],[-14799299, -1033142, -1379, -20643905, -16171889, -162409826, -9634968; -315, -22, 0, -439, -344, -3455, -205; 44676925, 3118905, 4163, 62320938, 48820574, 490291575, 29086563],100,12]
%
% END OF LATTICE L101.12
%
%
% LATTICE L101.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[4708729545163320, -50242196807580, 1177046902511760; -50242196807580, 536084800760, -12559103588460; 1177046902511760, -12559103588460, 294227858581433],[1380, 20, 1],[-5624, 2457, -7091, -44759, -939311, -49894, -282236; 1017, -1426, 1704, 9919, 203550, 10707, 59179; 22542, -9890, 28440, 179480, 3766365, 200056, 1131600],100,13]
%
% END OF LATTICE L101.13
%
%
% LATTICE L101.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-18947329620, -908287020, 3022200; -908287020, -43540978, 144877; 3022200, 144877, -482],[1380, 23, 1],[-419, 5, 106, -55, -397, -731, -47; 8550, -102, -2163, 1122, 8100, 14915, 959; -57270, 692, 14490, -7613, -54588, -100395, -6445],100,14]
%
% END OF LATTICE L101.14
%
%
% LATTICE L101.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[20720328456390, 48842270310, 4150818229515; 48842270310, 115145245, 9784363070; 4150818229515, 9784363070, 831516359081],[345, 115, 1],[-6424133, -747450, -2993, -14935301, -35099759, -23499814, -6970636; 19272210, 2242328, 8979, 44805464, 105298245, 70498751, 20911703; 31841637, 3704785, 14835, 74027800, 173974260, 116478371, 34550415],100,15]
%
% END OF LATTICE L101.15
%
%
% LATTICE L101.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[374888445391560, 115150992175140, 93617326960500; 115150992175140, 35369857785480, 28755562399440; 93617326960500, 28755562399440, 23378164931371],[1380, 60, 1],[-5405, 20167, -2133, -114040, -826249, -133527, -771469; -60, -23, -15, -967, -7268, -1192, -7130; 21718, -80730, 8560, 457860, 3317635, 536172, 3098100],100,16]
%
% END OF LATTICE L101.16
%
%
% LATTICE L101.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-794448060, -97343820, 1105380; -97343820, -11923062, 135447; 1105380, 135447, -1538],[1380, 69, 1],[-293, 3, 63, -96, -247, -1381, -91; 200, -2, -43, 65, 168, 940, 62; -192970, 1980, 41492, -63273, -162728, -909765, -59943],100,17]
%
% END OF LATTICE L101.17
%
%
% LATTICE L101.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-102545810471842365, 271973490454204530, 90166738340303880; 271973490454204530, -721332048276650805, -239141535246016260; 90166738340303880, -239141535246016260, -79282036638261493],[345, 345, 1],[-302, 94, 755, -2162, -1977, -4125, -1225; 7723852, -2497641, -19459788, 56544795, 51328489, 106899991, 31647677; -23298103, 7533840, 58698185, -170560755, -154826395, -322451352, -95461530],100,18]
%
% END OF LATTICE L101.18
%
%
% LATTICE L101.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[686395983720, 7029809700, 171086628840; 7029809700, 71997544, 1752204952; 171086628840, 1752204952, 42643947899],[1380, 92, 1],[536123, 1203, 108979, 726412, 676133, 4165259, 209019; -4485, -10, -912, -6079, -5658, -34855, -1749; -2150730, -4826, -437184, -2914100, -2712399, -16709500, -838508],100,19]
%
% END OF LATTICE L101.19
%
%
% LATTICE L101.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-369355620, -109940460, -13892460; -109940460, -32724170, -4135055; -13892460, -4135055, -522454],[1380, 115, 1],[-2207, 135, 2792, -1486, -10583, -3888, -1246; 8862, -542, -11211, 5966, 42492, 15611, 5003; -11454, 700, 14490, -7705, -54900, -20171, -6465],100,20]
%
% END OF LATTICE L101.20
%
%
% LATTICE L101.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[17613178240440, 3672192420, 4390453398600; 3672192420, 765624, 915370836; 4390453398600, 915370836, 1094412421321],[1380, 276, 1],[81928, 513, 4105, 258615, 84751, 1600262, 83468; -585, -2, -30, -1889, -617, -11635, -605; -328670, -2058, -16468, -1037484, -339995, -6419760, -334848],100,21]
%
% END OF LATTICE L101.21
%
%
% LATTICE L101.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-213716460, 326601840, 85230180; 326601840, -499102530, -130248885; 85230180, -130248885, -33989818],[1380, 345, 1],[-12395, 643, 13326, -20401, -52353, -58517, -19269; 40, -2, -43, 65, 168, 188, 62; -31234, 1620, 33580, -51405, -131920, -147453, -48555],100,22]
%
% END OF LATTICE L101.22
%
%
% LATTICE L101.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[43274511960, 20496473460, 4496140740; 20496473460, 9707920040, 2129546540; 4496140740, 2129546540, 467141599],[1380, 460, 1],[-38233, -217, -39919, -266012, -246812, -303683, -75943; 114354, 649, 119397, 795637, 738210, 908310, 227144; -153318, -870, -160080, -1066740, -989745, -1217804, -304540],100,23]
%
% END OF LATTICE L101.23
%
%
% LATTICE L101.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[3828120, -1756479180, -441286740; -1756479180, 805945256760, 202480597980; -441286740, 202480597980, 50869947077],[1380, 1380, 1],[-339, -8, -86, -5417, -1772, -6687, -1741; 11452, 309, 2889, 182007, 59585, 224926, 58604; -45586, -1230, -11500, -724500, -237185, -895344, -233280],100,24]
%
% END OF LATTICE L101.24
%

\medskip%
%------------------------------WEYL-GROUP-W102--------------------------------
%
\leavevmode\llap{}%
$W_{102}$%
\qquad\llap{24} lattices, $\chi=72$%
\hfill%
$2222222222222222\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L102.1
%
\leavevmode%
${L_{102.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{-2}{}7\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{2}{}17\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2\rightarrow N_{102}}%
\EasyButWeakLineBreak%
{${2}\above{1pt}{1pt}{l}{2}{68}\above{1pt}{1pt}{r}{2}{14}\above{1pt}{1pt}{b}{2}{12}\above{1pt}{1pt}{*}{2}{28}\above{1pt}{1pt}{b}{2}{34}\above{1pt}{1pt}{l}{2}{4}\above{1pt}{1pt}{r}{2}{714}\above{1pt}{1pt}{b}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-506940\\-252756\\1428
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-252756\\-126022\\713
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1428\\713\\178
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-7608385\\15268176\\-359856
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3794276\\7614188\\-179459
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-122692\\246213\\-5804
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
179\\-359\\2
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2679\\-5372\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
426\\-854\\-7
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-197\\396\\-30
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-5155\\10346\\-280
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-26252\\52683\\-1292
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-17403\\34924\\-836
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-264002\\529788\\-12495
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-506940, -252756, 1428; -252756, -126022, 713; 1428, 713, 178],[1428, 1, 1],[179, 2679, 426, -197, -5155, -26252, -17403, -264002, -1215, -12743, -1462, -691, -1061, -1424, -357, -178; -359, -5372, -854, 396, 10346, 52683, 34924, 529788, 2438, 25568, 2933, 1386, 2128, 2856, 716, 357; 2, 0, -7, -30, -280, -1292, -836, -12495, -51, -476, -42, -12, -14, -17, -4, 0],101,1]
%
% END OF LATTICE L102.1
%
%
% LATTICE L102.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[53193, -22848, -1785; -22848, 9814, 765; -1785, 765, 91],[357, 1, 1],[-1886, -7889, -957, 22, 3, -1298, -553, -19249, -179, -2141, -1108, -907, -6198, -53867, -17147, -507326; -4373, -18292, -2219, 51, 7, -3009, -1282, -44625, -415, -4964, -2569, -2103, -14371, -124899, -39758, -1176315; -236, -986, -119, 3, 0, -170, -72, -2499, -23, -272, -140, -114, -777, -6749, -2148, -63546],101,2]
%
% END OF LATTICE L102.2
%
%
% LATTICE L102.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[7181769, 714, -2414391; 714, -3, -240; -2414391, -240, 811678],[357, 3, 1],[-1297, -81012, -59197, -21973, -515561, -4609745, -1478878, -14657729, -171225, -756952, -113325, -2673, -2005, 943, 118, -6641; -25, -1615, -1183, -440, -10332, -92395, -29643, -293811, -3433, -15181, -2275, -54, -42, 17, 3, -119; -3858, -240975, -176085, -65360, -1533567, -13711962, -4399011, -43600291, -509319, -2251599, -337092, -7951, -5964, 2805, 351, -19754],101,3]
%
% END OF LATTICE L102.3
%
%
% LATTICE L102.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2936325, 714, -1266993; 714, -7, -308; -1266993, -308, 546694],[357, 7, 1],[-1625, -101514, -10597, -82603, -92293, -5776489, -1853188, -7871855, -214563, -948542, -20287, -10049, -359, 1181, 148, -3565; -25, -1615, -169, -1320, -1476, -92395, -29643, -125919, -3433, -15181, -325, -162, -6, 17, 3, -51; -3766, -235263, -24559, -191436, -213893, -13387262, -4294843, -18243363, -497259, -2198287, -47016, -23289, -832, 2737, 343, -8262],101,4]
%
% END OF LATTICE L102.4
%
%
% LATTICE L102.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-297996468, -2483292, -813960; -2483292, -20694, -6783; -813960, -6783, -2222],[1428, 3, 1],[2, 2199, 857, 671, 16067, 72115, 46321, 229709, 2700, 24049, 1845, 101, 145, 67, -1, -39; -239, -261868, -102053, -79902, -1913226, -8587295, -5515800, -27353221, -321509, -2863684, -219695, -12026, -17262, -7973, 120, 4641; -3, -6120, -2394, -1880, -45066, -202317, -129960, -644504, -7578, -67524, -5187, -286, -420, -204, 0, 119],101,5]
%
% END OF LATTICE L102.5
%
%
% LATTICE L102.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[130305899640, -183522276, 32576729808; -183522276, 258472, -45880928; 32576729808, -45880928, 8144246177],[1428, 4, 1],[-1, 19045, 29944, 35440, 283707, 2548241, 409261, 24357038, 95516, 212920, 65571, 5495, 2838, 3374, 89, -713; 0, -35785, -56259, -66585, -533036, -4787710, -768932, -45762759, -179459, -400044, -123200, -10326, -5341, -6409, -178, 714; 4, -76381, -120092, -142134, -1137822, -10219856, -1641363, -97685196, -383072, -853927, -262976, -22038, -11382, -13532, -357, 2856],101,6]
%
% END OF LATTICE L102.6
%
%
% LATTICE L102.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1069215, 714, -254898; 714, -17, -170; -254898, -170, 60767],[357, 17, 1],[-843, -3099, -38498, -42871, -335304, -176355, -961817, -1682284, -111360, -28959, -73705, -5216, -1305, 36, 77, -761; -25, -95, -1183, -1320, -10332, -5435, -29643, -51849, -3433, -893, -2275, -162, -42, 1, 3, -21; -3536, -12999, -161483, -179826, -1406461, -739736, -4034423, -7056483, -467109, -121471, -309162, -21879, -5474, 151, 323, -3192],101,7]
%
% END OF LATTICE L102.7
%
%
% LATTICE L102.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[31048647, 72114, -10054191; 72114, 147, -23352; -10054191, -23352, 3255754],[357, 21, 1],[4801, 255140, 26287, 67545, 225415, 14096169, 4521206, 6400675, 522677, 2306896, 49067, 7809, 647, -4971, 34, 4415; -21, -1241, -129, -334, -1118, -69955, -22441, -31773, -2597, -11475, -245, -40, -4, 17, 1, -17; 14826, 787899, 81177, 208586, 696105, 43530438, 13961955, 19765951, 1614081, 7123935, 151524, 24115, 1998, -15351, 105, 13634],101,8]
%
% END OF LATTICE L102.8
%
%
% LATTICE L102.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-21164388, -406980, -55692; -406980, -7826, -1071; -55692, -1071, -146],[1428, 7, 1],[2, 1247, 69, 1129, 1285, 40359, 25921, 55087, 1510, 13441, 147, 167, 11, 33, -1, -7; -103, -63784, -3529, -57738, -65714, -2063919, -1325572, -2817087, -77219, -687344, -7517, -8538, -562, -1683, 52, 357; -7, -7616, -424, -6972, -7950, -249781, -160440, -340986, -9352, -83300, -913, -1050, -72, -238, 0, 51],101,9]
%
% END OF LATTICE L102.9
%
%
% LATTICE L102.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[158505144, -22549548, 39578448; -22549548, 3216216, -5630604; 39578448, -5630604, 9882667],[1428, 12, 1],[11153, 1139552, 1752473, 678861, 16192109, 145243761, 23318549, 462493589, 5429821, 12074242, 3688501, 98421, 130813, 107973, -89, -10799; -123, -12563, -19320, -7484, -178507, -1601213, -257071, -5098674, -59860, -133110, -40663, -1085, -1442, -1190, 1, 119; -44736, -4570875, -7029372, -2722990, -64948422, -582589524, -93533397, -1855115276, -21779640, -48431181, -14795004, -394778, -524706, -433092, 357, 43316],101,10]
%
% END OF LATTICE L102.10
%
%
% LATTICE L102.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[10612182, -65688, -3641757; -65688, 357, 22542; -3641757, 22542, 1249733],[357, 51, 1],[-4568, -14261, -174827, -64168, -1498955, -787692, -4294945, -2503673, -496513, -128905, -326254, -7415, -4288, 279, -35, -1732; -21, -73, -903, -334, -7826, -4115, -22441, -13083, -2597, -675, -1715, -40, -28, 1, 1, -7; -13311, -41556, -509439, -186983, -4367895, -2295303, -12515298, -7295603, -1446819, -375624, -950691, -21607, -12495, 813, -102, -5047],101,11]
%
% END OF LATTICE L102.11
%
%
% LATTICE L102.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[704004, 371280, -1428; 371280, 195262, -731; -1428, -731, 2],[1428, 17, 1],[11, 151, 970, 2219, 17533, 4620, 50421, 44110, 2929, 1529, 1970, 301, 107, 0, -21, -10; -23, -316, -2030, -4644, -36694, -9669, -105524, -92316, -6130, -3200, -4123, -630, -224, 0, 44, 21; -544, -7644, -49147, -112506, -889168, -234310, -2557208, -2237151, -148563, -77560, -99960, -15300, -5474, -1, 1088, 546],101,12]
%
% END OF LATTICE L102.12
%
%
% LATTICE L102.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[7781172, -56301756, 8043924; -56301756, 405003018, -57862539; 8043924, -57862539, 8266786],[1428, 21, 1],[-704, -18485, -701, -2565, -7219, -217431, -138035, -97061, -7444, -60667, -463, 237, 235, -237, -1645, -1879; -36605, -961248, -36455, -133402, -375470, -11309029, -7179508, -5048371, -387189, -3155608, -24087, 12318, 12218, -12325, -85532, -97699; -255528, -6710172, -254481, -931238, -2621040, -78944838, -50117928, -35241119, -2702847, -22028328, -168144, 85988, 85290, -86037, -597072, -682006],101,13]
%
% END OF LATTICE L102.13
%
%
% LATTICE L102.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[27077736, -2437596, 6757296; -2437596, 227416, -608328; 6757296, -608328, 1686295],[1428, 28, 1],[5033, 568578, 125173, 1019917, 1159123, 72790093, 11686649, 99340439, 2721831, 6053806, 264379, 148739, 9533, 56131, -89, -4679; -55, -6205, -1366, -11130, -12649, -794325, -127531, -1084056, -29702, -66062, -2885, -1623, -104, -612, 1, 51; -20188, -2280635, -502084, -4091010, -4649382, -291969832, -46876557, -398466468, -10917592, -24282545, -1060456, -596610, -38238, -225148, 357, 18768],101,14]
%
% END OF LATTICE L102.14
%
%
% LATTICE L102.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[24151407, -151725, 10442607; -151725, 833, -65450; 10442607, -65450, 4514989],[357, 119, 1],[-13282, -41471, -72629, -559814, -622725, -2290670, -12490039, -3120377, -1443901, -374867, -135540, -64693, -1782, 811, -101, -2158; 39825, 124340, 217758, 1678440, 1867057, 6867895, 37447676, 9355524, 4329106, 1123926, 406375, 193959, 5342, -2432, 304, 6471; 31297, 97720, 171139, 1319115, 1467355, 5397609, 29430842, 7352685, 3402329, 883316, 319379, 152439, 4199, -1911, 238, 5085],101,15]
%
% END OF LATTICE L102.15
%
%
% LATTICE L102.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-50758260, -6344604, 54264; -6344604, -793050, 6783; 54264, 6783, -58],[1428, 51, 1],[636, 329, 411, 17, 1, -1, -1, 3, 8, 39, 233, 167, 3863, 1013, 11041, 3217; -4661, -2412, -3017, -126, -14, 7, 8, -21, -57, -284, -1701, -1222, -28294, -7421, -80888, -23569; 49521, 25512, 31416, 1156, -714, -117, 0, 350, 816, 3252, 18921, 13226, 302736, 79218, 862920, 251335],101,16]
%
% END OF LATTICE L102.16
%
%
% LATTICE L102.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[9352106232, -16766148, 2331948276; -16766148, 30056, -4180640; 2331948276, -4180640, 581471449],[1428, 68, 1],[4611, 6477, 157232, 171616, 1331607, 699261, 1906021, 6665710, 440148, 57060, 287527, 18995, 2670, -354, 89, 5675; -546, -761, -18459, -20133, -156170, -82004, -223520, -781683, -51611, -6690, -33698, -2220, -301, 43, -10, -672; -18496, -25981, -630700, -688398, -5341434, -2804924, -7645563, -26737956, -1765552, -228883, -1153348, -76194, -10710, 1420, -357, -22764],101,17]
%
% END OF LATTICE L102.17
%
%
% LATTICE L102.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[307432709258808, -2619486467556, 76640489122680; -2619486467556, 22319386152, -653016800352; 76640489122680, -653016800352, 19105854374197],[1428, 84, 1],[-29931, -613280, -122883, -306845, -1011709, -63112679, -10114669, -28626627, -2328649, -5114700, -214057, -30095, 889, 104899, 6469, -13273; -8194, -167144, -33475, -83567, -275508, -17186524, -2754363, -7795401, -634105, -1392725, -58282, -8190, 237, 27965, 1653, -3944; 119784, 2454375, 491784, 1228010, 4048914, 252580356, 40479453, 114565312, 9319380, 20469309, 856668, 120442, -3558, -419832, -25893, 53108],101,18]
%
% END OF LATTICE L102.18
%
%
% LATTICE L102.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[4704016926, -8399192550, 2810080875; -8399192550, 14997061275, -5017500768; 2810080875, -5017500768, 1678683143],[357, 357, 1],[-25, -95, -169, -440, -1476, -5435, -29643, -2469, -3433, -893, -325, -54, -6, 1, 3, -1; 639109, 2349063, 4168768, 10831919, 36307970, 133674541, 729043225, 60721262, 84409134, 21950435, 7980981, 1317830, 141277, -27302, -58285, 27483; 1910307, 7021392, 12460524, 32376806, 108525195, 399555681, 2179123716, 181496978, 252300468, 65610258, 23855301, 3939019, 422280, -81606, -174216, 82147],101,19]
%
% END OF LATTICE L102.19
%
%
% LATTICE L102.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-829668, 207060, -4284; 207060, -51646, 1071; -4284, 1071, -22],[1428, 119, 1],[-344, -177, -31, -23, 1, 1, 1, -1, -6, -23, -19, -277, -301, -551, -6001, -749; -1241, -640, -113, -90, 2, 3, 4, -3, -19, -80, -67, -990, -1082, -1983, -21604, -2697; 5593, 2800, 442, 0, -102, -49, 0, 48, 238, 532, 391, 4998, 5100, 9212, 99960, 12447],101,20]
%
% END OF LATTICE L102.20
%
%
% LATTICE L102.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1056642888, 9343404, 263394600; 9343404, 86088, 2329068; 263394600, 2329068, 65657675],[1428, 204, 1],[5671521, 738496, 3777471, 91991, 84193, 709, -89, 11343, 35803, 76836, 1929853, 723341, 17037779, 8967943, 24460049, 28525277; -56101, -7305, -37366, -910, -833, -7, 1, -112, -354, -760, -19089, -7155, -168532, -88708, -241951, -282163; -22750080, -2962317, -15152508, -369002, -337722, -2844, 357, -45500, -143616, -308211, -7741188, -2901526, -68343366, -35972964, -98116197, -114422980],101,21]
%
% END OF LATTICE L102.21
%
%
% LATTICE L102.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2477580, -278492844, -2340492; -278492844, -31297679490, -263030103; -2340492, -263030103, -2210542],[1428, 357, 1],[352, 2291, 2011, 10323, 34421, 63297, 690229, 28739, 39884, 20701, 3737, 1173, 67, -69, -469, 1; 1419, 9200, 8073, 41430, 138130, 254003, 2769788, 115325, 160043, 83064, 14993, 4702, 266, -277, -1868, 5; -169218, -1097124, -962727, -4940642, -16472388, -30290568, -330304968, -13752829, -19085577, -9905616, -1787958, -560728, -31722, 33033, 222768, -596],101,22]
%
% END OF LATTICE L102.22
%
%
% LATTICE L102.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[77520408, -1560804, -20497512; -1560804, 33320, 414120; -20497512, 414120, 5420903],[1428, 476, 1],[1139379, 148500, 108857, 56785, 2721, 363, -89, 727, 6171, 15150, 54793, 434165, 488229, 1799787, 4909589, 2454023; -3427766, -446755, -327491, -170835, -8186, -1092, 268, -2187, -18565, -45578, -164842, -1306164, -1468813, -5414571, -14770258, -7382808; 4570076, 595637, 436628, 227766, 10914, 1456, -357, 2916, 24752, 60767, 219776, 1741446, 1958298, 7218988, 19692477, 9843144],101,23]
%
% END OF LATTICE L102.23
%
%
% LATTICE L102.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1108153704, 133256971596, 33221700288; 133256971596, 16024329877416, 3994954096056; 33221700288, 3994954096056, 995964158981],[1428, 1428, 1],[-24392, -27794, -94289, -236349, -781290, -2868562, -7816539, -1301447, -1801355, -233027, -166532, -24472, -1173, -469, -8091, -2658; 92765, 105552, 358013, 897267, 2965867, 10889249, 29671987, 4940349, 6837879, 884540, 632079, 92825, 4409, 1763, 30773, 10111; -371280, -422457, -1432896, -3591182, -11870454, -43582644, -118757835, -19773032, -27367620, -3540243, -2529804, -371518, -17646, -7056, -123165, -40468],101,24]
%
% END OF LATTICE L102.24
%

\medskip%
%------------------------------WEYL-GROUP-W103--------------------------------
%
\leavevmode\llap{}%
$W_{103}$%
\qquad\llap{24} lattices, $\chi=48$%
\hfill%
$222222222222\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L103.1
%
\leavevmode%
${L_{103.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{2}{}7\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}17\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{2\rightarrow N_{103}}%
\EasyButWeakLineBreak%
{${12}\above{1pt}{1pt}{*}{2}{476}\above{1pt}{1pt}{b}{2}{2}\above{1pt}{1pt}{s}{2}{102}\above{1pt}{1pt}{l}{2}{4}\above{1pt}{1pt}{r}{2}{238}\above{1pt}{1pt}{b}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
51517956\\8568\\-52836
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
8568\\-2\\-5
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-52836\\-5\\50
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-52837\\-69056652\\-62663496
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-24\\-31369\\-28464
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
71\\92797\\84205
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-1314\\-1188
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-11\\-14518\\-13090
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\-3\\-1
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
44\\57477\\52173
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
23\\30056\\27276
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
237\\309757\\281078
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[51517956, 8568, -52836; 8568, -2, -5; -52836, -5, 50],[1428, 1, 1],[-1, -11, 0, 44, 23, 237, 25, 249, 1, 7, 1, 1; -1314, -14518, -3, 57477, 30056, 309757, 32682, 325584, 1310, 9180, 1312, 1309; -1188, -13090, -1, 52173, 27276, 281078, 29652, 295358, 1187, 8313, 1188, 1190],102,1]
%
% END OF LATTICE L103.1
%
%
% LATTICE L103.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[43554, -14637, 0; -14637, 4919, 0; 0, 0, -1],[357, 1, 1],[1, 40, -1, -1867, -487, -10032, -529, -5276, -43, -377, -41, -440; 3, 119, -3, -5559, -1450, -29869, -1575, -15708, -128, -1122, -122, -1309; 0, 0, -1, -561, -145, -2975, -156, -1547, -12, -102, -11, -119],102,2]
%
% END OF LATTICE L103.2
%
%
% LATTICE L103.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[22601670, 123879, -7555548; 123879, 669, -41415; -7555548, -41415, 2525755],[357, 3, 1],[-2343, -191984, -11030, -251116, -176368, -3453549, -56325, -1553389, -3637, 1777, 364, -37197; 2308, 189091, 10863, 247299, 173686, 3401020, 55468, 1529745, 3581, -1751, -358, 36652; -6971, -571200, -32817, -747133, -524739, -10275174, -167581, -4621722, -10821, 5287, 1083, -110670],102,3]
%
% END OF LATTICE L103.3
%
%
% LATTICE L103.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[34028526, 230979, -14601300; 230979, 1561, -99113; -14601300, -99113, 6265271],[357, 7, 1],[-9139, -35664, -14344, -979754, -229374, -641643, -219761, -288611, -4731, 6929, 474, -6907; 6924, 27013, 10863, 741897, 173686, 485860, 166404, 218535, 3581, -5253, -358, 5236; -21189, -82688, -33257, -2271591, -531811, -1487670, -509523, -669154, -10969, 16065, 1099, -16014],102,4]
%
% END OF LATTICE L103.4
%
%
% LATTICE L103.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[82502700, 7140, -117096; 7140, -6, -9; -117096, -9, 166],[1428, 3, 1],[-1, -11, 1, 77, 117, 1189, 41, 1201, 4, 8, 3, 1; -122, -1428, 118, 9248, 14060, 142919, 4930, 144466, 483, 969, 364, 119; -712, -7854, 711, 54791, 83256, 846090, 29176, 854658, 2847, 5695, 2136, 714],102,5]
%
% END OF LATTICE L103.5
%
%
% LATTICE L103.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[62567977080, -194452188, 15598031148; -194452188, 604328, -48476416; 15598031148, -48476416, 3888547897],[1428, 4, 1],[887, -66393, -6729, -654725, -79228, -3153163, -158099, -1492626, -6372, -13426, 622, 35125; 0, 119, 11, 1173, 143, 5712, 288, 2737, 13, 51, 1, 0; -3558, 266322, 26992, 2626296, 317807, 12648272, 634182, 5987366, 25560, 53856, -2495, -140896],102,6]
%
% END OF LATTICE L103.6
%
%
% LATTICE L103.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[65544486, 498729, -15438108; 498729, 3791, -117470; -15438108, -117470, 3636235],[357, 17, 1],[-5206, -8368, -8175, -32851, -130747, -150603, -125270, -67743, -2698, 232, 271, -1619; 6924, 11123, 10863, 43641, 173686, 200060, 166404, 89985, 3581, -309, -358, 2156; -21879, -35168, -34357, -138063, -549491, -632940, -526473, -284704, -11339, 975, 1139, -6804],102,7]
%
% END OF LATTICE L103.7
%
%
% LATTICE L103.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[341768595, -22225035, -110665359; -22225035, 1445262, 7196511; -110665359, 7196511, 35833666],[357, 21, 1],[14063, 150363, 57314, 1241706, 867101, 2418670, 274905, 1077751, 14928, -13592, -197, 37558; -160, -1717, -656, -14246, -9951, -27761, -3156, -12376, -173, 153, 3, -425; 43463, 464712, 177135, 3837631, 2679873, 7475172, 849625, 3330912, 46137, -42007, -609, 116076],102,8]
%
% END OF LATTICE L103.8
%
%
% LATTICE L103.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[16569084, 327012, -54264; 327012, 6454, -1071; -54264, -1071, 178],[1428, 7, 1],[133, 173, 1, 1, 3, 8, 11, 31, 5, 305, 141, 196; -6924, -9010, -53, -51, -152, -408, -564, -1598, -259, -15861, -7336, -10200; -1134, -1496, -14, 0, 0, -17, -42, -170, -35, -2499, -1176, -1649],102,9]
%
% END OF LATTICE L103.9
%
%
% LATTICE L103.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[64245522936, -93015636, 16016136696; -93015636, 134664, -23188404; 16016136696, -23188404, 3992755027],[1428, 12, 1],[177, -241186, -22296, -726550, -263918, -10507165, -175709, -4980891, -21587, -19461, 620, 63011; 0, 119, 11, 391, 143, 5712, 96, 2737, 13, 17, 1, 0; -710, 967470, 89436, 2914412, 1058655, 42147420, 704822, 19979862, 86592, 78064, -2487, -252756],102,10]
%
% END OF LATTICE L103.10
%
%
% LATTICE L103.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[144241566, 22501353, -49491981; 22501353, 3509922, -7720635; -49491981, -7720635, 16981625],[357, 51, 1],[-34559, -152466, -141325, -180349, -2141329, -2459656, -679025, -1096306, -37071, 1953, 577, -37888; -160, -707, -656, -838, -9951, -11431, -3156, -5096, -173, 9, 3, -175; -100793, -444675, -412182, -525998, -6245307, -7173726, -1980415, -3197439, -108120, 5696, 1683, -110502],102,11]
%
% END OF LATTICE L103.11
%
%
% LATTICE L103.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-173637660, 88536, 165648; 88536, -34, -85; 165648, -85, -158],[1428, 17, 1],[-1, -11, -8, -44, -361, -211, -359, -199, -7, -1, 1, 1; -54, -546, -395, -2163, -17740, -10367, -17634, -9772, -342, -48, 52, 49; -1020, -11242, -8177, -44979, -369036, -215698, -366996, -203434, -7157, -1023, 1020, 1022],102,12]
%
% END OF LATTICE L103.12
%
%
% LATTICE L103.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1986348, -124236, -17136; -124236, -7770, -1071; -17136, -1071, -146],[1428, 21, 1],[-3, -145, -42, -1310, -1897, -2693, -629, -2541, -37, -33, 1, 7; 50, 2448, 710, 22168, 32104, 45577, 10646, 43010, 627, 561, -16, -119; -14, -918, -273, -8687, -12600, -17901, -4186, -16932, -252, -238, 0, 51],102,13]
%
% END OF LATTICE L103.13
%
%
% LATTICE L103.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-6543096, 875364, -1633632; 875364, -92456, 218484; -1633632, 218484, -407873],[1428, 28, 1],[-122030, -153981, 705, 26699, -89, -13358, -12826, -37065, -11943, -599837, -67339, -368734; 1401, 1768, -8, -306, 1, 153, 147, 425, 137, 6885, 773, 4233; 489510, 617678, -2828, -107100, 357, 53584, 51450, 148682, 47908, 2406180, 270123, 1479136],102,14]
%
% END OF LATTICE L103.14
%
%
% LATTICE L103.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[721557690, 76873881, 208334490; 76873881, 8189818, 22195999; 208334490, 22195999, 60151793],[357, 119, 1],[-283073, -59464, -385811, -1476953, -5845373, -959188, -5560735, -427520, -101173, 16001, 1565, -14780; 848739, 178291, 1156777, 4428345, 17526168, 2875931, 16672737, 1281832, 303346, -47976, -4692, 44315; 667233, 140163, 909398, 3481338, 13778177, 2260910, 13107255, 1007711, 238476, -37716, -3689, 34838],102,15]
%
% END OF LATTICE L103.15
%
%
% LATTICE L103.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-61416852, 84252, 111384; 84252, -102, -153; 111384, -153, -202],[1428, 51, 1],[-1, -11, -7, -11, -267, -155, -87, -143, -4, 0, 3, 1; -10, -84, -50, -72, -1732, -1001, -558, -910, -21, 1, 28, 7; -544, -6006, -3825, -6017, -146064, -84798, -47600, -78246, -2193, -1, 1632, 546],102,16]
%
% END OF LATTICE L103.16
%
%
% LATTICE L103.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[40316309880, -93024204, 10050733812; -93024204, 214744, -23190652; 10050733812, -23190652, 2505617465],[1428, 68, 1],[12943, 67203, 92915, 528415, 1087064, 2545261, 2170229, 1206314, 89016, 17378, 4522, 1773; 0, 7, 11, 69, 143, 336, 288, 161, 13, 3, 1, 0; -51918, -269570, -372708, -2119620, -4360517, -10209752, -8705394, -4838862, -357068, -69708, -18139, -7112],102,17]
%
% END OF LATTICE L103.17
%
%
% LATTICE L103.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2413320, 672588, 599760; 672588, 213864, 167076; 599760, 167076, 149053],[1428, 84, 1],[1651, 48700, 26472, 795138, 286967, 1627117, 189601, 764121, 21341, 17683, -89, -1475; -19, -561, -305, -9163, -3307, -18751, -2185, -8806, -246, -204, 1, 17; -6622, -195330, -106176, -3189200, -1150989, -6526164, -760466, -3064794, -85596, -70924, 357, 5916],102,18]
%
% END OF LATTICE L103.18
%
%
% LATTICE L103.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[270917121930, -484037287251, 161942326077; -484037287251, 864810956478, -289336176360; 161942326077, -289336176360, 96801991607],[357, 357, 1],[2308, 1589, 10863, 14547, 173686, 28580, 55468, 12855, 3581, -103, -358, 308; 1594900, 1098568, 7512167, 10061973, 120139303, 19769139, 38368616, 8892311, 2478712, -71094, -248755, 212619; 4763213, 3280905, 22435308, 30050384, 358799637, 59041128, 114589027, 26557155, 7402752, -212324, -742917, 634992],102,19]
%
% END OF LATTICE L103.19
%
%
% LATTICE L103.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[4071228, -1186668, 2856; -1186668, 345814, -833; 2856, -833, 2],[1428, 119, 1],[5, 1, 3, 7, 51, 4, 43, 3, -1, -1, -3, 0; 12, 2, 5, 3, 8, 0, -12, -2, -5, -3, -8, 0; -2142, -584, -2142, -8400, -66640, -5473, -63546, -4890, -595, 189, 952, -1],102,20]
%
% END OF LATTICE L103.20
%
%
% LATTICE L103.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[5751832632, -12362196, 1433900496; -12362196, 27336, -3081828; 1433900496, -3081828, 357463571],[1428, 204, 1],[2297, 57430, 83760, 167874, 1040554, 2441419, 696059, 1164693, 90829, 6715, 6980, 2827; 0, 7, 11, 23, 143, 336, 96, 161, 13, 1, 1, 0; -9214, -230370, -335988, -673396, -4173993, -9793308, -2792114, -4671954, -364344, -26936, -27999, -11340],102,21]
%
% END OF LATTICE L103.21
%
%
% LATTICE L103.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1428, 0, 0; 0, -52122, 1071; 0, 1071, -22],[1428, 357, 1],[-47, -11, -2, 0, 1, 0, -1, -1, -4, -6, -145, -12; -2, -2, -7, -1, 0, 1, 10, 4, 8, 2, 24, 1; -476, -186, -357, -49, 0, 48, 476, 186, 357, 49, 0, -48],102,22]
%
% END OF LATTICE L103.22
%
%
% LATTICE L103.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[887059320, -2217684, -222809412; -2217684, 4760, 556444; -222809412, 556444, 55964287],[1428, 476, 1],[-178, 3749, 40703, 237077, 488525, 163526, 977050, 77657, 40703, 7141, -89, -714; 537, -11283, -122501, -713517, -1470286, -492155, -2940573, -233720, -122502, -21492, 268, 2149; -714, 15038, 163268, 950964, 1959573, 655936, 3919146, 311498, 163268, 28644, -357, -2864],102,23]
%
% END OF LATTICE L103.23
%
%
% LATTICE L103.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[31416, -1529388, -381276; -1529388, 74435928, 18556860; -381276, 18556860, 4626221],[1428, 1428, 1],[-568, -133, -49, -1, 0, -2, -16, -13, -97, -145, -876, -290; 4201, 983, 355, -7, -89, -15, 59, 82, 710, 1072, 6479, 2145; -16898, -3954, -1428, 28, 357, 60, -238, -330, -2856, -4312, -26061, -8628],102,24]
%
% END OF LATTICE L103.24
%

\medskip%
%------------------------------WEYL-GROUP-W104--------------------------------
%
\leavevmode\llap{}%
$W_{104}$%
\qquad\llap{24} lattices, $\chi=60$%
\hfill%
$22222222222222\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L104.1
%
\leavevmode%
${L_{104.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{2}{}7\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{2}{}11\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2\rightarrow N_{104}}%
\EasyButWeakLineBreak%
{${28}\above{1pt}{1pt}{*}{2}{44}\above{1pt}{1pt}{b}{2}{2}\above{1pt}{1pt}{b}{2}{154}\above{1pt}{1pt}{l}{2}{20}\above{1pt}{1pt}{r}{2}{14}\above{1pt}{1pt}{b}{2}{220}\above{1pt}{1pt}{*}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-103180\\-30800\\1540
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-30800\\-9194\\461
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1540\\461\\34
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-70841\\237160\\-9240
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-21183\\70916\\-2763
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-575\\1925\\-76
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-25\\84\\-14
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
125\\-418\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
26\\-87\\2
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-23\\77\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-251\\840\\-20
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-251\\840\\-21
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1249\\4180\\-110
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-103180, -30800, 1540; -30800, -9194, 461; 1540, 461, 34],[1540, 1, 1],[-25, 125, 26, -23, -251, -251, -1249, -297, -631, -95, -1748, -1129, -554, -1281; 84, -418, -87, 77, 840, 840, 4180, 994, 2112, 318, 5852, 3780, 1855, 4290; -14, 0, 2, 0, -20, -21, -110, -28, -66, -11, -231, -160, -84, -220],103,1]
%
% END OF LATTICE L104.1
%
%
% LATTICE L104.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[5005, -770, -385; -770, 118, 55; -385, 55, -9],[385, 1, 1],[1, -16, 7, 1009, 511, 696, 1289, 216, 357, 86, 1378, 419, 389, 416; 7, -110, 48, 6930, 3510, 4781, 8855, 1484, 2453, 591, 9471, 2880, 2674, 2860; 0, 11, -5, -693, -350, -476, -880, -147, -242, -58, -924, -280, -259, -275],103,2]
%
% END OF LATTICE L104.2
%
%
% LATTICE L104.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[10317230, 87780, -4118345; 87780, 745, -35040; -4118345, -35040, 1643926],[385, 5, 1],[43058, 42231, 3147, 7127, -66, -662, 1722, 6789, 36100, 18216, 541190, 42792, 249897, 76609; -40971, -40183, -2994, -6776, 63, 630, -1639, -6461, -34353, -17334, -514976, -40719, -237790, -72897; 106995, 104940, 7820, 17710, -164, -1645, 4279, 16870, 89705, 45265, 1344805, 106334, 620970, 190366],103,3]
%
% END OF LATTICE L104.3
%
%
% LATTICE L104.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[17191790, 133980, -2446675; 133980, 1043, -19068; -2446675, -19068, 348202],[385, 7, 1],[2277, 15633, 1165, 377, -122, -35, 3187, 359, 13363, 6743, 28619, 79202, 13215, 141793; -5853, -40183, -2994, -968, 315, 90, -8195, -923, -34353, -17334, -73568, -203595, -33970, -364485; 15679, 107646, 8022, 2596, -840, -241, 21945, 2472, 92015, 46431, 197065, 545370, 90996, 976360],103,4]
%
% END OF LATTICE L104.4
%
%
% LATTICE L104.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[31255070, 226380, -14196875; 226380, 1639, -102828; -14196875, -102828, 6448594],[385, 11, 1],[52655, 4695, 3849, 793, -402, -809, 957, 8301, 4013, 22275, 60163, 261642, 305589, 42583; -40971, -3653, -2994, -616, 315, 630, -745, -6461, -3123, -17334, -46816, -203595, -237790, -33135; 115269, 10278, 8426, 1736, -880, -1771, 2095, 18172, 8785, 48763, 131705, 572770, 668976, 93220],103,5]
%
% END OF LATTICE L104.5
%
%
% LATTICE L104.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[3112583320, -6894580, 778185100; -6894580, 15272, -1723732; 778185100, -1723732, 194556093],[1540, 4, 1],[3774, 2979, -1, -461, 283, 1550, 5294, 1777, 5744, 2380, 61522, 11612, 26205, 38321; -4375, -3454, 0, 462, -345, -1841, -6215, -2072, -6677, -2763, -71379, -13470, -30394, -44440; -15134, -11946, 4, 1848, -1135, -6216, -21230, -7126, -23034, -9544, -246708, -46565, -105084, -153670],103,6]
%
% END OF LATTICE L104.6
%
%
% LATTICE L104.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[18382980, 9073680, 58520; 9073680, 4478690, 28885; 58520, 28885, 186],[1540, 5, 1],[-27, 207, 41, -38, -79, -394, -391, -463, -977, -146, -2657, -341, -831, -379; 56, -418, -83, 77, 160, 798, 792, 938, 1980, 296, 5390, 692, 1687, 770; -210, -220, -10, 0, 8, 35, 22, 0, -110, -35, -1155, -188, -560, -352],103,7]
%
% END OF LATTICE L104.7
%
%
% LATTICE L104.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-5822740, 579040, -12320; 579040, -57582, 1225; -12320, 1225, -26],[1540, 7, 1],[1, -5, -4, -23, -137, -12, -273, -5, -39, -2, 1, 17, 2, 53; 10, -66, -45, -253, -1500, -131, -2970, -54, -418, -21, 11, 180, 21, 550; -4, -770, -231, -1045, -5880, -496, -10780, -178, -1232, -42, 44, 420, 41, 770],103,8]
%
% END OF LATTICE L104.8
%
%
% LATTICE L104.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[16123030, 2060520, -6602365; 2060520, 263095, -843780; -6602365, -843780, 2703662],[385, 35, 1],[12069, 88362, 8462, 5152, 292, -679, -377, 976, 55133, 30673, 138343, 77978, 65904, 143872; 87, 649, 66, 44, 3, -6, -11, 5, 363, 210, 968, 549, 466, 1023; 29500, 215985, 20685, 12595, 714, -1660, -924, 2385, 134750, 74970, 338140, 190596, 161085, 351659],103,9]
%
% END OF LATTICE L104.9
%
%
% LATTICE L104.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1566180, 15400, 3080; 15400, -22, -33; 3080, -33, -6],[1540, 11, 1],[45, 5, 4, 3, 11, 1, -1, -3, 1, 5, 18, 169, 104, 31; 434, 48, 38, 28, 100, 7, -10, -28, 10, 49, 175, 1640, 1008, 300; 20636, 2294, 1837, 1379, 5060, 462, -460, -1386, 456, 2288, 8246, 77440, 47663, 14210],103,10]
%
% END OF LATTICE L104.10
%
%
% LATTICE L104.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[240799790, -9988440, -95833045; -9988440, 413435, 3975180; -95833045, 3975180, 38139454],[385, 55, 1],[-563217, -53838, -57718, -22996, -2180, 33707, 425, -41828, -32597, -201587, -582049, -516430, -3058932, -86860; 609, 59, 66, 28, 3, -42, -1, 35, 33, 210, 616, 549, 3262, 93; -1415260, -135285, -145035, -57785, -5478, 84700, 1068, -105105, -81910, -506550, -1462580, -1297692, -7686525, -218263],103,11]
%
% END OF LATTICE L104.11
%
%
% LATTICE L104.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[689161935, 19988045, 83478395; 19988045, 578809, 2421804; 83478395, 2421804, 10111306],[385, 77, 1],[49097, 32853, 35223, 2005, 6654, -2939, -1299, 3645, 19889, 123003, 50737, 1575606, 266649, 265009; -245398, -164206, -176049, -10021, -33255, 14689, 6490, -18220, -99412, -614805, -253597, -7875285, -1332779, -1324580; -346566, -231903, -248633, -14153, -46970, 20746, 9170, -25729, -140392, -868252, -358142, -11121880, -1882221, -1870645],103,12]
%
% END OF LATTICE L104.12
%
%
% LATTICE L104.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1803367720, -11206580, 450778020; -11206580, 69560, -2801240; 450778020, -2801240, 112678529],[1540, 20, 1],[63554, 49949, -389, -30337, -98, 12428, 13018, 26235, 91148, 38870, 1018016, 38579, 436517, 128079; -24857, -19536, 152, 11858, 38, -4865, -5093, -10262, -35651, -15203, -398167, -15089, -170730, -50094; -254870, -200310, 1560, 121660, 393, -49840, -52206, -105210, -365530, -155880, -4082540, -154713, -1750560, -513634],103,13]
%
% END OF LATTICE L104.13
%
%
% LATTICE L104.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[92008840, -768460, 22932140; -768460, 7112, -191520; 22932140, -191520, 5715571],[1540, 28, 1],[-2129, -48193, -20129, -75485, -100357, -32517, -335431, -4839, -28455, -775, -1163, -4163, -2323, -47809; -120, -2717, -1135, -4257, -5660, -1834, -18920, -273, -1606, -44, -66, -235, -131, -2695; 8538, 193270, 80724, 302720, 402465, 130404, 1345190, 19406, 114114, 3108, 4664, 16695, 9316, 191730],103,14]
%
% END OF LATTICE L104.14
%
%
% LATTICE L104.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3278660, -1684760, 7700; -1684760, -865690, 3955; 7700, 3955, -18],[1540, 35, 1],[-1, 91, 31, 148, 169, 72, 317, 27, 195, 8, -5, -13, -7, -31; 2, -198, -67, -319, -364, -155, -682, -58, -418, -17, 11, 28, 15, 66; 10, -4620, -1470, -6820, -7728, -3275, -14322, -1200, -8470, -315, 275, 588, 300, 1232],103,15]
%
% END OF LATTICE L104.15
%
%
% LATTICE L104.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[6971854120, -4214980, 1738396660; -4214980, 2552, -1050984; 1738396660, -1050984, 433460439],[1540, 44, 1],[29145, 3238, 5332, 4950, 6377, 8755, 571, 192, 953, 7241, 24387, 56488, 137930, 20384; 112, 11, 13, 7, 5, 0, 0, 7, 6, 38, 112, 250, 595, 85; -116886, -12986, -21384, -19852, -25575, -35112, -2290, -770, -3822, -29040, -97804, -226545, -553168, -81750],103,16]
%
% END OF LATTICE L104.16
%
%
% LATTICE L104.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-34392820, 127820, 43120; 127820, -110, -165; 43120, -165, -54],[1540, 55, 1],[-3, 13, 49, 158, 289, 874, 51, 353, 37, 26, 17, 11, 1, -1; -28, 130, 489, 1575, 2880, 8708, 508, 3514, 368, 258, 168, 108, 7, -10; -2310, 9980, 37620, 121310, 221892, 671055, 39158, 271040, 28410, 19965, 13055, 8448, 770, -768],103,17]
%
% END OF LATTICE L104.17
%
%
% LATTICE L104.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-388879260, 260260, 344960; 260260, -154, -231; 344960, -231, -306],[1540, 77, 1],[-3, -11, -31, -12, -731, -61, -119, -21, -13, -5, 0, 11, 1, -1; -22, -74, -203, -77, -4660, -387, -750, -130, -78, -25, 1, 100, 7, -10; -3366, -12348, -34804, -13474, -820820, -68497, -133630, -23584, -14602, -5621, -1, 12320, 1122, -1120],103,18]
%
% END OF LATTICE L104.18
%
%
% LATTICE L104.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[315223438915, -760572982015, 305385595515; -760572982015, 1835114999410, -736836175075; 305385595515, -736836175075, 295854782438],[385, 385, 1],[-5853, -3653, -2994, -88, 63, 90, -149, -923, -3123, -17334, -6688, -40719, -33970, -6627; -10464101, -6531214, -5354223, -157569, 111915, 160784, -266269, -1649698, -5582585, -30987174, -11956230, -72794709, -60729779, -11847530; -26055150, -16262435, -13331780, -392340, 278663, 400345, -662998, -4107675, -13900390, -77156695, -29770485, -181255613, -151214470, -29499827],103,19]
%
% END OF LATTICE L104.19
%
%
% LATTICE L104.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1482068280, -6062980, 369635420; -6062980, 24920, -1512140; 369635420, -1512140, 92188967],[1540, 140, 1],[1713, 43199, 19409, 78389, 21404, 35387, 75147, 5897, 40511, 3421, 5321, 1426, 2663, 8563; -101, -2552, -1148, -4642, -1268, -2097, -4455, -350, -2409, -205, -319, -85, -158, -506; -6870, -173250, -77840, -314380, -85841, -141920, -301378, -23650, -162470, -13720, -21340, -5719, -10680, -34342],103,20]
%
% END OF LATTICE L104.20
%
%
% LATTICE L104.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[86970141720, -162366820, 21685765640; -162366820, 303160, -40485720; 21685765640, -40485720, 5407286019],[1540, 220, 1],[960, 18913, 141365, 461911, 212138, 2574302, 75456, 528569, 56734, 85576, 67618, 14803, 73343, 191; 7, 6, 38, 112, 50, 595, 17, 112, 11, 13, 7, 1, 0, 0; -3850, -75850, -566940, -1852480, -850773, -10324160, -302614, -2119810, -227530, -343200, -271180, -59367, -294140, -766],103,21]
%
% END OF LATTICE L104.21
%
%
% LATTICE L104.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[38959957960, -51634660, 9714600280; -51634660, 69608, -12875016; 9714600280, -12875016, 2422319313],[1540, 308, 1],[27741, 143297, 885419, 367713, 5723371, 1940729, 1934033, 361017, 245461, 280855, 21045, 107999, 3061, 9757; 1, 6, 38, 16, 250, 85, 85, 16, 11, 13, 1, 5, 0, 0; -111254, -574686, -3550932, -1474696, -22953315, -7783204, -7756350, -1447842, -984410, -1126356, -84400, -433125, -12276, -39130],103,22]
%
% END OF LATTICE L104.22
%
%
% LATTICE L104.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3469094860, 1650880, 2427040; 1650880, -770, -1155; 2427040, -1155, -1698],[1540, 385, 1],[23, 19, 17, 2, 11, 1, -1, -3, 1, 13, 8, 109, 49, 21; 126, 90, 59, 5, 20, -1, -2, 2, 38, 133, 59, 748, 321, 130; 32780, 27090, 24255, 2855, 15708, 1430, -1428, -4290, 1400, 18480, 11390, 155232, 69795, 29918],103,23]
%
% END OF LATTICE L104.23
%
%
% LATTICE L104.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[89320, -52620260, -13120800; -52620260, 53898592440, 13439550740; -13120800, 13439550740, 3351136197],[1540, 1540, 1],[16, 11, 13, 1, 1, 0, 0, 1, 6, 38, 16, 50, 85, 17; 2834585, 1953097, 2326255, 183037, 191557, 19529, 2489, 175953, 1057441, 6705359, 2827501, 8840057, 15033161, 3008049; -11367950, -7832790, -9329320, -734060, -768229, -78320, -9982, -705650, -4240810, -26891480, -11339540, -35452571, -60289680, -12063618],103,24]
%
% END OF LATTICE L104.24
%

\medskip%
%------------------------------WEYL-GROUP-W105--------------------------------
%
\leavevmode\llap{}%
$W_{105}$%
\qquad\llap{32} lattices, $\chi=72$%
\hfill%
$2222222222222222\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L105.1
%
\leavevmode%
${L_{105.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}8\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{2}{}5\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}13\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{2\rightarrow N_{105}}%
\EasyButWeakLineBreak%
{${24}\above{1pt}{1pt}{b}{2}{26}\above{1pt}{1pt}{b}{2}{6}\above{1pt}{1pt}{b}{2}{10}\above{1pt}{1pt}{s}{2}{78}\above{1pt}{1pt}{b}{2}{2}\above{1pt}{1pt}{l}{2}{312}\above{1pt}{1pt}{r}{2}{10}\above{1pt}{1pt}{b}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-23541960\\3623880\\34320
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3623880\\-557834\\-5283
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
34320\\-5283\\-50
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-15787201\\-101587200\\-103474800
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2430364\\15638863\\15929451
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
22632\\145632\\148337
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-13\\-84\\-48
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-107\\-689\\-650
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-172\\-1107\\-1104
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1317\\-8475\\-8590
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-10685\\-68757\\-69888
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2302\\-14813\\-15074
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-201073\\-1293864\\-1317576
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-12427\\-79965\\-81455
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-23541960, 3623880, 34320; 3623880, -557834, -5283; 34320, -5283, -50],[1560, 1, 1],[-13, -107, -172, -1317, -10685, -2302, -201073, -12427, -3299, -1089, -104, -63, -79, 2, 145, 7; -84, -689, -1107, -8475, -68757, -14813, -1293864, -79965, -21228, -7007, -669, -405, -507, 13, 936, 45; -48, -650, -1104, -8590, -69888, -15074, -1317576, -81455, -21660, -7189, -705, -455, -663, -1, 624, 50],104,1]
%
% END OF LATTICE L105.1
%
%
% LATTICE L105.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[15990, -2730, -390; -2730, 466, 65; -390, 65, -16],[390, 1, 1],[737, 566, 94, 138, 548, 76, 2429, 253, 1, -33, 29, 477, 4249, 949, 42343, 5282; 4350, 3341, 555, 815, 3237, 449, 14352, 1495, 6, -195, 171, 2815, 25077, 5601, 249912, 31175; -342, -260, -42, -60, -234, -32, -1014, -105, 0, 13, -15, -225, -1989, -443, -19734, -2460],104,2]
%
% END OF LATTICE L105.2
%
%
% LATTICE L105.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-62589946380, 323471850, -31295383470; 323471850, -1671736, 161738044; -31295383470, 161738044, -15647896877],[390, 2, 1],[-12202, 61521, 208355, 1849771, 15372793, 3343945, 73443035, 18201391, 1224808, 1690021, 195847, 171239, 391085, 24405, 121729, -12301; 12318, -62075, -210279, -1866905, -15515253, -3374939, -74123829, -18370120, -1236165, -1705704, -197670, -172840, -394758, -24636, -122889, 12415; 24531, -123682, -418878, -3718790, -30905550, -6722686, -147650295, -36592180, -2462361, -3397628, -393732, -344260, -786240, -49064, -244725, 24730],104,3]
%
% END OF LATTICE L105.3
%
%
% LATTICE L105.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-94044979470, 485620980, -31348737030; 485620980, -2507604, 161875779; -31348737030, 161875779, -10449715858],[390, 3, 1],[-5383, 40721, 45965, 1224211, 3391321, 2213075, 32403815, 12045956, 540397, 1118476, 43204, 113324, 86270, 16150, 53701, -8141; 8212, -62075, -70093, -1866905, -5171751, -3374939, -49415886, -18370120, -824110, -1705704, -65890, -172840, -131586, -24636, -81926, 12415; 16276, -123123, -138979, -3701505, -10253945, -6691419, -97975670, -36421965, -1633936, -3381807, -130631, -342645, -260845, -48831, -162370, 24615],104,4]
%
% END OF LATTICE L105.4
%
%
% LATTICE L105.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-156955167330, 809919240, -62782477680; 809919240, -4179340, 323969815; -62782477680, 323969815, -25113155372],[390, 5, 1],[-19217, 48482, 164138, 291430, 12109780, 2634156, 115707715, 2867583, 1929647, 1331273, 154267, 26975, 308015, 19219, 191705, -1938; 24636, -62075, -210279, -373381, -15515253, -3374939, -148247658, -3674024, -2472330, -1705704, -197670, -34568, -394758, -24636, -245778, 2483; 48360, -122005, -413055, -733387, -30474405, -6628885, -291179850, -7216307, -4855980, -3350165, -388215, -67883, -775125, -48365, -482430, 4877],104,5]
%
% END OF LATTICE L105.5
%
%
% LATTICE L105.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[30416530960140, -142097841210, 15161324312550; -142097841210, 663842856, -70829624112; 15161324312550, -70829624112, 7557264015793],[390, 6, 1],[-30942, -14964951, -9140713, -218173133, -593974651, -384942231, -2806551379, -2082929548, -46262631, -185640532, -6290478, -13294732, -7841798, -837544, -1925383, -281237; -64, -30979, -18923, -451665, -1229657, -796915, -5810181, -4312125, -95774, -384319, -13023, -27525, -16237, -1735, -3991, -585; 62075, 30022278, 18337850, 437693010, 1191615802, 772260642, 5630427101, 4178716650, 92810833, 372426990, 12619786, 26671530, 15732002, 1680258, 3862651, 564210],104,6]
%
% END OF LATTICE L105.6
%
%
% LATTICE L105.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[20890370747220, -152030275410, 10415339930190; -152030275410, 1106404760, -75797936630; 10415339930190, -75797936630, 5192789882671],[390, 10, 1],[-167125, -26952139, -49388575, -78588421, -3209348153, -693303471, -15164292664, -750295810, -249965312, -334350270, -33988904, -4789058, -42373528, -1508854, -10408514, -101501; -192, -30979, -56769, -90333, -3688971, -796915, -17430543, -862425, -287322, -384319, -39069, -5505, -48711, -1735, -11973, -117; 335205, 54058290, 99059370, 157625918, 6437035410, 1390568670, 30415238295, 1504879018, 501358995, 670611110, 68172030, 9605482, 84989190, 3026330, 20876505, 203582],104,7]
%
% END OF LATTICE L105.7
%
%
% LATTICE L105.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-229059480, 88110360, 195000; 88110360, -33892662, -75009; 195000, -75009, -166],[1560, 3, 1],[-17, -66, -7, 38, 198, 153, 4895, 943, 101, 157, 14, 67, 75, 22, 201, 2; -44, -169, -17, 125, 585, 443, 14040, 2695, 284, 429, 37, 175, 195, 57, 520, 5; -88, -1170, -544, -11910, -31928, -20562, -597376, -110655, -9740, -9477, -275, -375, -13, 87, 1144, 90],104,8]
%
% END OF LATTICE L105.8
%
%
% LATTICE L105.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-408596168370, 2107112280, 94291012530; 2107112280, -10866284, -486254561; 94291012530, -486254561, -21759369598],[390, 13, 1],[10855, -2111, -92821, -823929, -526709, -1489417, -5032595, -8106964, -1091053, -57900, -87212, -76236, -13390, -10858, -8329, 5479; 24636, -4775, -210279, -1866905, -1193481, -3374939, -11403666, -18370120, -2472330, -131208, -197670, -172840, -30366, -24636, -18906, 12415; 46488, -9041, -397527, -3528655, -2255745, -6378749, -21553170, -34719815, -4672668, -247969, -373503, -326495, -57345, -46501, -35670, 23465],104,9]
%
% END OF LATTICE L105.9
%
%
% LATTICE L105.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[20776739087130, -185691203490, 6901277359470; -185691203490, 1659607140, -61679866755; 6901277359470, -61679866755, 2292353433934],[390, 15, 1],[-90725, -21946749, -13405475, -63993451, -871109091, -564547311, -8232047491, -610955375, -135695503, -272256745, -9225563, -3899663, -11501391, -1228639, -5650341, -82651; -128, -30979, -18923, -90333, -1229657, -796915, -11620362, -862425, -191548, -384319, -13023, -5505, -16237, -1735, -7982, -117; 273130, 66071265, 40357535, 192653967, 2622496825, 1699584525, 24782795440, 1839297222, 408514880, 819636090, 27773800, 11740038, 34625240, 3698850, 17010500, 248823],104,10]
%
% END OF LATTICE L105.10
%
%
% LATTICE L105.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-148200, -45240, 6240; -45240, -13810, 1905; 6240, 1905, -262],[1560, 5, 1],[-61, -267, -388, -577, -23285, -5006, -436705, -5395, -7139, -2333, -212, -23, -115, 6, -95, -5; 192, 832, 1206, 1792, 72306, 15544, 1355952, 16751, 22164, 7241, 657, 71, 351, -19, 312, 16; -60, -325, -495, -747, -30225, -6505, -567840, -7017, -9300, -3055, -285, -33, -195, 5, 0, -3],104,11]
%
% END OF LATTICE L105.11
%
%
% LATTICE L105.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[654992319540, -43407195390, 324345182070; -43407195390, 2876652376, -21494778292; 324345182070, -21494778292, 160612260623],[390, 26, 1],[-129116, -1602227, -38168699, -303676653, -190790461, -535804911, -901492679, -2899251968, -193180543, -19876624, -26267854, -18506112, -2519198, -1166364, -619063, -392917; -192, -2383, -56769, -451665, -283767, -796915, -1340811, -4312125, -287322, -29563, -39069, -27525, -3747, -1735, -921, -585; 260715, 3235266, 77071410, 613193230, 385249962, 1081913742, 1820321721, 5854258670, 390076089, 40135490, 53040858, 37368110, 5086842, 2355158, 1250031, 793390],104,12]
%
% END OF LATTICE L105.12
%
%
% LATTICE L105.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-53343792246243720, -1156568806770, -26589713810548200; -1156568806770, -25076040, -576502574700; -26589713810548200, -576502574700, -13253892360392563],[390, 30, 1],[5716534, -86532119, -97652967, -520153961, -7204646325, -4701529487, -34419831755, -5118157837, -574016404, -2376100651, -91780323, -48145909, -183251985, -34302763, -57027025, 3459007; 4106, -62075, -70093, -373381, -5171751, -3374939, -24707943, -3674024, -412055, -1705704, -65890, -34568, -131586, -24636, -40963, 2483; -11468405, 173599140, 195909580, 1043523276, 14453828480, 9432121680, 69052431175, 10267953786, 1151581115, 4766889270, 184127990, 96589434, 367636750, 68817570, 114406565, -6939396],104,13]
%
% END OF LATTICE L105.13
%
%
% LATTICE L105.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-6835920, -57720, 18720; -57720, -400, 144; 18720, 144, -49],[1560, 8, 1],[-1, 5, 17, 151, 1255, 273, 2998, 1486, 100, 138, 16, 14, 32, 2, 5, -1; -117, 559, 1941, 17285, 143715, 31267, 343395, 170215, 11457, 15821, 1839, 1615, 3705, 233, 585, -115; -726, 3536, 12168, 108240, 899808, 195752, 2149797, 1065600, 71718, 99008, 11496, 10080, 23088, 1448, 3627, -720],104,14]
%
% END OF LATTICE L105.14
%
%
% LATTICE L105.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[137873579610, -24391009500, 44777479110; -24391009500, 4314978564, -7921517097; 44777479110, -7921517097, 14542471742],[390, 39, 1],[-32279, -600837, -4771103, -113879123, -23848887, -200927511, -225373921, -1087223113, -48295297, -7453759, -3283493, -6939817, -314901, -437389, -154767, -147347; -128, -2383, -18923, -451665, -94589, -796915, -893874, -4312125, -191548, -29563, -13023, -27525, -1249, -1735, -614, -585; 99320, 1848729, 14680315, 350397255, 73381181, 618238413, 693458126, 3345301440, 148600894, 22934640, 10103054, 21353280, 968926, 1345812, 476206, 453375],104,15]
%
% END OF LATTICE L105.15
%
%
% LATTICE L105.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-946920, 4680, 1560; 4680, 26, -13; 1560, -13, -2],[1560, 13, 1],[-1, -1, -22, -171, -107, -300, -2017, -1621, -431, -11, -14, -9, -1, 0, 1, 1; -60, -53, -1155, -8955, -5601, -15701, -105552, -84825, -22548, -575, -729, -465, -51, 1, 48, 45; -468, -463, -10179, -79105, -49497, -138775, -933024, -749840, -199368, -5088, -6474, -4160, -462, 0, 456, 455],104,16]
%
% END OF LATTICE L105.16
%
%
% LATTICE L105.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-903435000, -456727440, 884520; -456727440, -230896470, 447165; 884520, 447165, -866],[1560, 15, 1],[-12737, -12502, -381, -126, -220, 29, -145, -24, -103, -1408, -689, -3084, -41510, -26779, -778815, -28866; 27772, 27261, 831, 275, 481, -63, 312, 52, 224, 3068, 1502, 6724, 90506, 58388, 1698112, 62939; 1330720, 1306890, 39940, 13302, 23660, -2910, 13000, 2337, 10460, 146055, 71825, 321993, 4335175, 2797035, 81351920, 3015318],104,17]
%
% END OF LATTICE L105.17
%
%
% LATTICE L105.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[25875467670, 13641362280, 10746283860; 13641362280, 7191630940, 5665364315; 10746283860, 5665364315, 4463015636],[390, 65, 1],[62075, 385144, 9175000, 14599568, 45862238, 128796858, 433401863, 139384515, 92873527, 4777945, 6314267, 889699, 605563, 280367, 297613, 18888; -384, -2383, -56769, -90333, -283767, -796915, -2681622, -862425, -574644, -29563, -39069, -5505, -3747, -1735, -1842, -117; -148980, -924345, -22019985, -35038939, -110069295, -309112245, -1040163750, -334522604, -222896310, -11467060, -15154230, -2135276, -1453350, -672880, -714270, -45331],104,18]
%
% END OF LATTICE L105.18
%
%
% LATTICE L105.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2669820252302580, -417212363490, -1330761221741250; -417212363490, -65197704, -207957833148; -1330761221741250, -207957833148, -663312606068867],[390, 78, 1],[744094, -868351, -12726403, -338896577, -72214829, -612622603, -344998595, -3334531237, -74794708, -23815187, -11957135, -31356493, -1835785, -4465847, -570937, 2253607; 4106, -4775, -70093, -1866905, -397827, -3374939, -1900611, -18370120, -412055, -131208, -65890, -172840, -10122, -24636, -3151, 12415; -1492829, 1742118, 25532182, 679906890, 144880070, 1229066202, 692148985, 6689860320, 150055919, 47778912, 23988848, 62908560, 3683020, 8959548, 1145435, -4521270],104,19]
%
% END OF LATTICE L105.19
%
%
% LATTICE L105.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-227760, -88920, 7800; -88920, -18672, 1704; 7800, 1704, -155],[1560, 24, 1],[70, 294, 12, 34, 28, 6, 6, -1, -1, 5, 11, 311, 869, 569, 2087, 3106; 3559, 14963, 613, 1745, 1443, 311, 312, -50, -52, 234, 556, 15790, 44148, 28914, 106067, 157865; 42598, 179088, 7336, 20880, 17264, 3720, 3731, -600, -622, 2808, 6656, 189000, 528424, 346080, 1269541, 1889520],104,20]
%
% END OF LATTICE L105.20
%
%
% LATTICE L105.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-494369631319980, 231774913110, -246493390013130; 231774913110, -108662840, 115563296030; -246493390013130, 115563296030, -122901949211437],[390, 130, 1],[-1385969, 538941, 23699827, 42075031, 134485745, 380296349, 642492460, 413994313, 139290809, 14783819, 22268453, 3893249, 3419095, 2772651, 1063460, -279793; 12318, -4775, -210279, -373381, -1193481, -3374939, -5701833, -3674024, -1236165, -131208, -197670, -34568, -30366, -24636, -9453, 2483; 2779725, -1080910, -47532810, -84386458, -269727090, -762729370, -1288594725, -830314628, -279364215, -29650700, -44662020, -7808372, -6857400, -5560880, -2132895, 561158],104,21]
%
% END OF LATTICE L105.21
%
%
% LATTICE L105.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1215240, -237120, 7800; -237120, 46254, -1521; 7800, -1521, 50],[1560, 39, 1],[-1, -1, -6, -131, -27, -226, -505, -1216, -107, -8, -3, -4, 0, 1, 1, 1; -12, -13, -81, -1795, -371, -3109, -6952, -16745, -1476, -111, -43, -65, -1, 9, 8, 5; -208, -240, -1534, -34320, -7106, -59592, -133312, -321165, -28340, -2139, -845, -1365, -31, 117, 88, 0],104,22]
%
% END OF LATTICE L105.22
%
%
% LATTICE L105.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2542800, 32760, -1560; 32760, 80, -80; -1560, -80, 19],[1560, 40, 1],[1474, 1932, 178, 20, 110, -4, 5, 3, 11, 213, 317, 475, 19195, 4129, 45040, 4452; 149973, 196573, 18111, 2035, 11193, -407, 507, 305, 1119, 21671, 32253, 48329, 1953003, 420107, 4582617, 452971; 752190, 985920, 90840, 10208, 56160, -2040, 2535, 1528, 5610, 108680, 161760, 242392, 9795240, 2107040, 22984065, 2271872],104,23]
%
% END OF LATTICE L105.23
%
%
% LATTICE L105.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-497551068406470, -284777055810, 165094144476300; -284777055810, -162994260, 94492861905; 165094144476300, 94492861905, -54780460280498],[390, 195, 1],[755261, -440531, -6457419, -34392161, -36642915, -310854509, -350115865, -338399248, -75904271, -12084304, -6067416, -3182344, -931590, -2266366, -579515, 228703; -1502310, 876287, 12844745, 68410941, 72888003, 618334079, 696430508, 673124472, 150984432, 24037400, 12068942, 6330120, 1853058, 4508096, 1152728, -454923; 2273570, -1326135, -19438835, -103531077, -110306545, -935768535, -1053957400, -1018686747, -228495410, -36377505, -18264805, -9579843, -2804375, -6822465, -1744520, 688467],104,24]
%
% END OF LATTICE L105.24
%
%
% LATTICE L105.25
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2862600, -864240, 21840; -864240, -259610, 6565; 21840, 6565, -166],[1560, 65, 1],[-25, -11, -220, -333, -1037, -2902, -19489, -3131, -4151, -105, -128, -15, -7, 2, 1, -1; -528, -236, -4734, -7172, -22338, -62516, -419856, -67453, -89436, -2263, -2763, -325, -153, 41, 24, -20; -24180, -10785, -216255, -327587, -1020285, -2855385, -19176600, -3080857, -4084860, -103355, -126165, -14833, -6975, 1885, 1080, -923],104,25]
%
% END OF LATTICE L105.25
%
%
% LATTICE L105.26
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1444639183667940, 733755306706110, 361271782080690; 733755306706110, 372686035523880, 183495706238520; 361271782080690, 183495706238520, 90345950742809],[390, 390, 1],[-64, -2383, -18923, -90333, -94589, -796915, -446937, -862425, -95774, -29563, -13023, -5505, -1249, -1735, -307, -117; 3612766, 134492375, 1067970737, 5098172693, 5338368223, 44975894171, 25224006019, 48673106590, 5405243045, 1668459562, 734981200, 310683118, 70487588, 97904254, 17321099, 6595709; -7337395, -273149070, -2169009310, -10354201338, -10842029630, -91344387810, -51229029025, -98853290328, -10977849935, -3388580040, -1492719800, -630985992, -143157700, -198839940, -35178515, -13395642],104,26]
%
% END OF LATTICE L105.26
%
%
% LATTICE L105.27
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-321360, 276120, -4680; 276120, -216944, 3640; -4680, 3640, -61],[1560, 104, 1],[-5, -7, -131, -969, -601, -1679, -1408, -9044, -598, -60, -70, -36, -2, 4, 1, -1; -60, -86, -1620, -12010, -7452, -20822, -17463, -112175, -7419, -745, -873, -455, -27, 47, 12, -10; -3198, -4600, -86736, -643240, -399144, -1115296, -935391, -6008600, -397410, -39912, -46800, -24440, -1464, 2496, 639, -520],104,27]
%
% END OF LATTICE L105.27
%
%
% LATTICE L105.28
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3120, 10920, -4680; 10920, -37200, 15960; -4680, 15960, -6847],[1560, 120, 1],[824, 3232, 98, 32, 54, -8, 6, 7, 7, 369, 179, 799, 10749, 6933, 25201, 7472; -5871, -23075, -707, -237, -429, 49, -26, -39, -45, -2561, -1265, -5679, -76479, -49349, -179426, -53205; -14290, -56160, -1720, -576, -1040, 120, -65, -96, -110, -6240, -3080, -13824, -186160, -120120, -436735, -129504],104,28]
%
% END OF LATTICE L105.28
%
%
% LATTICE L105.29
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-5904600, -1059240, 35880; -1059240, -189930, 6435; 35880, 6435, -218],[1560, 195, 1],[-1051, -80, -33, -12, -2, 1, 1, 0, -5, -8, -55, -252, -262, -2201, -4929, -2376; -5012, -383, -161, -61, -11, 1, 8, 4, -16, -36, -258, -1196, -1246, -10476, -23472, -11317; -321620, -24525, -10205, -3783, -655, 195, 400, 117, -1300, -2385, -16705, -76947, -80075, -672945, -1507360, -726687],104,29]
%
% END OF LATTICE L105.29
%
%
% LATTICE L105.30
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[3120, -1560, 0; -1560, -3938064, 19344; 0, 19344, -95],[1560, 312, 1],[-3, -7, -33, -649, -131, -1087, -302, -5804, -126, -36, -10, 4, 2, 12, 1, -1; -6, -16, -82, -1680, -342, -2848, -793, -15255, -333, -97, -31, -15, 3, 23, 2, 0; -1222, -3264, -16744, -343200, -69872, -581880, -162023, -3116880, -68042, -19824, -6344, -3120, 608, 4680, 407, 0],104,30]
%
% END OF LATTICE L105.30
%
%
% LATTICE L105.31
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-71760, -422760, 170040; -422760, -2488720, 1001000; 170040, 1001000, -402617],[1560, 520, 1],[13, 15, 271, 397, 1229, 3431, 2876, 3694, 1220, 122, 140, 14, 4, -6, 1, 5; -159, -469, -10083, -15583, -48705, -136501, -114690, -147461, -48981, -4991, -6297, -797, -435, 1, 30, 41; -390, -1160, -24960, -38584, -120600, -338000, -283995, -365144, -121290, -12360, -15600, -1976, -1080, 0, 75, 104],104,31]
%
% END OF LATTICE L105.31
%
%
% LATTICE L105.32
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-4308720, -3714360, 751920; -3714360, -3198000, 647400; 751920, 647400, -131059],[1560, 1560, 1],[11, 39, 237, 1045, 1079, 9039, 2526, 9734, 1072, 322, 124, 38, 4, -14, 1, 13; 961, 3283, 19727, 86649, 89405, 748747, 209205, 806115, 88739, 26617, 10173, 3051, 295, -1247, 95, 1185; 4810, 16440, 98800, 433992, 447800, 3750240, 1047845, 4037592, 444470, 133320, 50960, 15288, 1480, -6240, 475, 5928],104,32]
%
% END OF LATTICE L105.32
%

\medskip%
%------------------------------WEYL-GROUP-W106--------------------------------
%
\leavevmode\llap{}%
$W_{106}$%
\qquad\llap{24} lattices, $\chi=27$%
\hfill%
$22242222$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L106.1
%
\leavevmode%
${L_{106.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{2}{}7\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{2}{}19\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2\rightarrow N_{106}}%
\EasyButWeakLineBreak%
{${6}\above{1pt}{1pt}{l}{2}{76}\above{1pt}{1pt}{r}{2}{42}\above{1pt}{1pt}{b}{2}{4}\above{1pt}{1pt}{*}{4}{2}\above{1pt}{1pt}{b}{2}{114}\above{1pt}{1pt}{b}{2}{4}\above{1pt}{1pt}{*}{2}{532}\above{1pt}{1pt}{b}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-165273780\\78204\\111720
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
78204\\-34\\-55
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
111720\\-55\\-74
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4\\2808\\3951
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
13\\9120\\12844
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2\\-1407\\-1974
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-702\\-988
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\703\\987
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
34\\23883\\33573
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
13\\9130\\12838
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
275\\193116\\271586
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-165273780, 78204, 111720; 78204, -34, -55; 111720, -55, -74],[1596, 1, 1],[4, 13, -2, -1, 1, 34, 13, 275; 2808, 9120, -1407, -702, 703, 23883, 9130, 193116; 3951, 12844, -1974, -988, 987, 33573, 12838, 271586],105,1]
%
% END OF LATTICE L106.1
%
%
% LATTICE L106.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[23541, -11172, 399; -11172, 5302, -189; 399, -189, 10],[399, 1, 1],[-20, 9, 130, 81, 112, 1114, 123, 1839; -42, 19, 273, 170, 235, 2337, 258, 3857; 3, 0, -21, -15, -22, -228, -26, -399],105,2]
%
% END OF LATTICE L106.2
%
%
% LATTICE L106.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-814530570, -165390687, -270711126; -165390687, -33578934, -54967950; -270711126, -54967950, -89971471],[399, 3, 1],[-77471, -403266, 29123, 25809, -54976, -636382, -368174, -7830873; -1825, -9500, 686, 608, -1295, -14991, -8673, -184471; 234214, 1219173, -88046, -78027, 166206, 1923940, 1113081, 23674665],105,3]
%
% END OF LATTICE L106.3
%
%
% LATTICE L106.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1145422866, -299579175, -163011450; -299579175, -78350846, -42634746; -163011450, -42634746, -23199059],[399, 7, 1],[-95537, -165766, 5131, 10609, -22600, -784802, -151346, -459863; -5475, -9500, 294, 608, -1295, -44973, -8673, -26353; 681366, 1182237, -36594, -75663, 161182, 5597172, 1079393, 3279723],105,4]
%
% END OF LATTICE L106.4
%
%
% LATTICE L106.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-273607068, -3560676, 81396; -3560676, -46338, 1059; 81396, 1059, -22],[1596, 3, 1],[-17, -215, 1, 17, -1, -90, -123, -2803; 1310, 16568, -77, -1310, 77, 6935, 9478, 215992; 161, 2052, -7, -162, 6, 836, 1152, 26334],105,5]
%
% END OF LATTICE L106.5
%
%
% LATTICE L106.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[196524784680, -351677004, -49254832704; -351677004, 629320, 88140496; -49254832704, 88140496, 12344695091],[1596, 4, 1],[-23134, -25424, -5179, -599, -7183, -196687, -36901, -782072; 39, 38, 0, 2, 17, 399, 71, 1463; -92304, -101441, -20664, -2390, -28660, -784776, -147234, -3120446],105,6]
%
% END OF LATTICE L106.6
%
%
% LATTICE L106.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2318205162, -702144639, 1098632934; -702144639, -212666582, 332757108; 1098632934, 332757108, -520658975],[399, 19, 1],[294319, 26876, -110675, -32681, 69636, 127258, 466272, 521959; -5475, -500, 2058, 608, -1295, -2367, -8673, -9709; 617538, 56391, -232218, -68571, 146110, 267012, 978329, 1095171],105,7]
%
% END OF LATTICE L106.7
%
%
% LATTICE L106.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[108577944891633, 32322515589, 36001097424852; 32322515589, 9622074, 10717149177; 36001097424852, 10717149177, 11936853447422],[399, 21, 1],[-109054, -640725, 252, -8307, -127432, -1056762, -573719, -1702275; 8609, 50464, -25, 665, 10114, 83676, 45390, 134615; 328895, 1932357, -760, 25053, 384321, 3187079, 1730274, 5133876],105,8]
%
% END OF LATTICE L106.8
%
%
% LATTICE L106.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-766828524, 10190460, -212268; 10190460, -135422, 2821; -212268, 2821, -58],[1596, 7, 1],[-53, -215, 1, 17, -3, -308, -135, -433; -3972, -16112, 75, 1274, -225, -23085, -10118, -32452; 777, 3192, -12, -252, 35, 4389, 1946, 6270],105,9]
%
% END OF LATTICE L106.9
%
%
% LATTICE L106.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2482900392, -106352652, -621820752; -106352652, 4556040, 26635092; -621820752, 26635092, 155729585],[1596, 12, 1],[-15184, -46043, -1193, -2597, -19185, -151467, -81325, -1682204; -263, -798, -21, -45, -332, -2622, -1408, -29127; -60584, -183711, -4760, -10362, -76548, -604352, -324486, -6711978],105,10]
%
% END OF LATTICE L106.10
%
%
% LATTICE L106.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[3007636809933, -8862878871, 1020083772666; -8862878871, 26117058, -3005974287; 1020083772666, -3005974287, 345976249466],[399, 57, 1],[77284, 23865, -1444, 5937, 90602, 39488, 407119, 444915; 8609, 2656, -175, 665, 10114, 4404, 45390, 49595; -227791, -70341, 4256, -17499, -267045, -116389, -1199964, -1311366],105,11]
%
% END OF LATTICE L106.11
%
%
% LATTICE L106.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-10343676, 86184, 3926160; 86184, -646, -33079; 3926160, -33079, -1488398],[1596, 19, 1],[2044, 351, -1010, -513, 505, 910, 6621, 7377; 24600, 4224, -12159, -6174, 6079, 10953, 79690, 88788; 4845, 832, -2394, -1216, 1197, 2157, 15694, 17486],105,12]
%
% END OF LATTICE L106.12
%
%
% LATTICE L106.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-228228, 12768, 6384; 12768, -714, -357; 6384, -357, -178],[1596, 21, 1],[1, 13, 0, -1, 0, 5, 7, 23; 21, 228, -1, -18, 10, 152, 184, 570; -7, 0, 2, 0, -21, -133, -126, -342],105,13]
%
% END OF LATTICE L106.13
%
%
% LATTICE L106.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2082553368, 145748316, -521665368; 145748316, 10204376, -36508948; -521665368, -36508948, 130673605],[1596, 28, 1],[118526, 118033, 803, 6607, 50849, 1197197, 213617, 630046; -897, -893, -6, -50, -385, -9063, -1617, -4769; 472920, 470953, 3204, 26362, 202888, 4776828, 852334, 2513890],105,14]
%
% END OF LATTICE L106.14
%
%
% LATTICE L106.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[38372822419533, 48357337665, -5502117698931; 48357337665, 60939802, -6933755367; -5502117698931, -6933755367, 788925527602],[399, 133, 1],[-540488, -55633, 1444, -13841, -211214, -276164, -949075, -148169; 1647291, 169555, -4407, 42188, 643756, 841704, 2892615, 451592; -3754989, -386505, 10032, -96159, -1467389, -1918623, -6593608, -1029390],105,15]
%
% END OF LATTICE L106.15
%
%
% LATTICE L106.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[20748, 4788, 1596; 4788, 570, 171; 1596, 171, 50],[1596, 57, 1],[-1, -1, -1, 1, 1, 0, -3, -5; 48, 48, 49, -42, -43, 1, 158, 252; -133, -132, -133, 114, 114, -4, -456, -714],105,16]
%
% END OF LATTICE L106.16
%
%
% LATTICE L106.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[7401657480, 2603128668, -1843668876; 2603128668, 915508312, -648409808; -1843668876, -648409808, 459236993],[1596, 76, 1],[13730, 832, 4373, 217, 3553, 5627, 20619, 23320; 39, 2, 0, 2, 17, 21, 71, 77; 55176, 3343, 17556, 874, 14288, 22620, 82878, 93730],105,17]
%
% END OF LATTICE L106.17
%
%
% LATTICE L106.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1382136, 59052, -346332; 59052, 6888, -14784; -346332, -14784, 86783],[1596, 84, 1],[-1067, -3101, 1, -179, -1432, -11070, -5886, -17291; 13, 38, 0, 2, 17, 133, 71, 209; -4256, -12369, 4, -714, -5712, -44156, -23478, -68970],105,18]
%
% END OF LATTICE L106.18
%
%
% LATTICE L106.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-18163856907105, -23525271202545, -7737986861619; -23525271202545, -30469210769634, -10022003597298; -7737986861619, -10022003597298, -3296460707947],[399, 399, 1],[-1825, -500, 98, 608, -1295, -789, -8673, -1387; 36102429, 9890184, -1939403, -12026385, 25625480, 15609994, 171584632, 27439581; -109755457, -30067275, 5896004, 36561567, -77904351, -47456143, -521636640, -83419422],105,19]
%
% END OF LATTICE L106.19
%
%
% LATTICE L106.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-45669540, -14295372, -197904; -14295372, -4473322, -61845; -197904, -61845, -850],[1596, 133, 1],[776, 167, -13, -251, 38, 233, 1955, 331; -3048, -656, 51, 986, -149, -915, -7678, -1300; 41097, 8848, -684, -13300, 1995, 12327, 103474, 17522],105,20]
%
% END OF LATTICE L106.20
%
%
% LATTICE L106.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[72678648, 3959676, -18216744; 3959676, 215688, -992484; -18216744, -992484, 4565987],[1596, 228, 1],[-838, -97, 533, 257, -857, -429, -4485, -4894; -3, 0, 7, 3, -4, -2, -20, -21; -3344, -387, 2128, 1026, -3420, -1712, -17898, -19530],105,21]
%
% END OF LATTICE L106.21
%
%
% LATTICE L106.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-914554284, 911022336, 1549716; 911022336, -907503954, -1543731; 1549716, -1543731, -2626],[1596, 399, 1],[-5, -1, 1, 1, -11, -4, -75, -11; 21, 12, -1, -18, 10, 8, 184, 30; -15295, -7644, 1178, 11172, -12369, -7063, -152418, -24126],105,22]
%
% END OF LATTICE L106.22
%
%
% LATTICE L106.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[136890436200, -3978488052, 37307339496; -3978488052, 115628072, -1084274520; 37307339496, -1084274520, 10167529775],[1596, 532, 1],[135194, 6612, -1657, 7533, 63997, 76607, 255655, 39312; -406839, -19897, 4989, -22669, -192592, -230538, -769354, -118303; -539448, -26383, 6612, -30058, -255360, -305676, -1020110, -156862],105,23]
%
% END OF LATTICE L106.23
%
%
% LATTICE L106.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[130872, 90967212, -22798860; 90967212, 67619944056, -16947414876; -22798860, -16947414876, 4247487557],[1596, 1596, 1],[-3331, -495, 28, -588, -4703, -1877, -18811, -2895; 332139, 49364, -2781, 58601, 468808, 187126, 1875432, 288635; 1325212, 196959, -11096, 233814, 1870512, 746620, 7482846, 1151634],105,24]
%
% END OF LATTICE L106.24
%

\medskip%
%------------------------------WEYL-GROUP-W107--------------------------------
%
\leavevmode\llap{}%
$W_{107}$%
\qquad\llap{24} lattices, $\chi=60$%
\hfill%
$22222222222222\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L107.1
%
\leavevmode%
${L_{107.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{2}{}11\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{-2}{}13\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2\rightarrow N_{107}}%
\EasyButWeakLineBreak%
{${44}\above{1pt}{1pt}{*}{2}{156}\above{1pt}{1pt}{b}{2}{2}\above{1pt}{1pt}{b}{2}{858}\above{1pt}{1pt}{l}{2}{4}\above{1pt}{1pt}{r}{2}{286}\above{1pt}{1pt}{b}{2}{12}\above{1pt}{1pt}{*}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-60078876\\27456\\20592
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
27456\\-10\\-13
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
20592\\-13\\-2
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
146431\\208995072\\148372224
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-60\\-85636\\-60795
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-60\\-85635\\-60796
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-1430\\-1012
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7\\9984\\7098
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\2854\\2027
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
511\\729300\\517803
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
31\\44244\\31412
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
571\\814957\\578578
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
89\\127026\\90180
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-60078876, 27456, 20592; 27456, -10, -13; 20592, -13, -2],[1716, 1, 1],[-1, 7, 2, 511, 31, 571, 89, 89, 97, 2, 61, 1, 1, -1; -1430, 9984, 2854, 729300, 44244, 814957, 127026, 127028, 138450, 2855, 87087, 1428, 1430, -1428; -1012, 7098, 2027, 517803, 31412, 578578, 90180, 90178, 98280, 2026, 61776, 1012, 1001, -1014],106,1]
%
% END OF LATTICE L107.1
%
%
% LATTICE L107.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[21450, 3861, 0; 3861, 695, 0; 0, 0, -1],[429, 1, 1],[-2, -7, 2, 1318, 43, 1679, 136, 145, 176, 11, 541, 9, 180, 7; 11, 39, -11, -7293, -238, -9295, -753, -803, -975, -61, -3003, -50, -1001, -39; 0, 0, -3, -1287, -41, -1573, -126, -132, -156, -9, -429, -7, -143, -6],106,2]
%
% END OF LATTICE L107.2
%
%
% LATTICE L107.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[39017550, 3861, -13036023; 3861, -15, -1290; -13036023, -1290, 4355422],[429, 3, 1],[2591, 2302, 1294, 49832, 3876, 123553, 2869, 6880, 1429, -433, -8791, -432, -430, 288; -11, -13, -10, -572, -49, -1716, -43, -121, -39, -2, 0, 1, 0, -1; 7755, 6890, 3873, 149149, 11601, 369798, 8587, 20592, 4277, -1296, -26312, -1293, -1287, 862],106,3]
%
% END OF LATTICE L107.3
%
%
% LATTICE L107.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[82356846, 10725, 14951079; 10725, -55, 1947; 14951079, 1947, 2714222],[429, 11, 1],[-356, -10436, -1955, -20525, -5853, -16959, -12994, -944, -6464, 655, 3625, 653, 59, -1306; -1, -39, -10, -156, -49, -156, -129, -11, -117, -2, 0, 1, 0, -3; 1961, 57486, 10769, 113061, 32241, 93418, 71577, 5200, 35607, -3608, -19968, -3597, -325, 7194],106,4]
%
% END OF LATTICE L107.4
%
%
% LATTICE L107.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1903443828, -13218348, 61776; -13218348, -91794, 429; 61776, 429, -2],[1716, 3, 1],[57, 17, 0, -7, -1, 2, 1, 9, 9, 3, 150, 25, 427, 21; -8272, -2470, -1, 1001, 144, -286, -144, -1298, -1300, -434, -21736, -3624, -61919, -3046; -14454, -4966, -225, -1573, 0, 429, -2, -462, -910, -453, -30745, -5424, -97383, -4970],106,5]
%
% END OF LATTICE L107.5
%
%
% LATTICE L107.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[93792270, 12441, 14407107; 12441, -65, 1911; 14407107, 1911, 2213026],[429, 13, 1],[-3844, -788, -1919, -17047, -5745, -14085, -12754, -10192, -488, 643, 3011, 641, 49, -1282; -11, -3, -10, -132, -49, -132, -129, -121, -9, -2, 0, 1, 0, -3; 25025, 5130, 12493, 110979, 37401, 91696, 83031, 66352, 3177, -4186, -19602, -4173, -319, 8346],106,6]
%
% END OF LATTICE L107.6
%
%
% LATTICE L107.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[65138285784, -214800300, 16246461660; -214800300, 708328, -53574404; 16246461660, -53574404, 4052110265],[1716, 4, 1],[2771, 33520, 14524, 3497174, 52662, 3859689, 299747, 298046, 321991, 12823, 413447, 2032, 50932, 1070; 0, 39, 21, 5577, 85, 6292, 492, 495, 546, 24, 858, 5, 143, 3; -11110, -134394, -58232, -14021436, -211141, -15474888, -1201794, -1194974, -1290978, -51412, -1657656, -8147, -204204, -4290],106,7]
%
% END OF LATTICE L107.7
%
%
% LATTICE L107.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[144058912998, 2383524, -48237038421; 2383524, 33, -798105; -48237038421, -798105, 16151807807],[429, 33, 1],[9319, 217961, 221659, 1380173, 1341048, 4382591, 1231143, 325943, 1234841, 113603, 72629, 0, -24185, -1849; 2, 39, 38, 234, 227, 741, 208, 55, 208, 19, 13, 1, 0, 1; 27831, 650936, 661980, 4121858, 4005012, 13088517, 3676783, 973422, 3687827, 339273, 216905, 0, -72228, -5522],106,8]
%
% END OF LATTICE L107.8
%
%
% LATTICE L107.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[146742021426, 2615184, -49148160633; 2615184, 39, -875901; -49148160633, -875901, 16461145009],[429, 39, 1],[112505, 18401, 243271, 1281703, 1471800, 4069909, 1351179, 3934945, 104249, 124679, 67447, 0, -22459, -2029; 22, 3, 38, 198, 227, 627, 208, 605, 16, 19, 11, 1, 0, 1; 335907, 54940, 726336, 3826790, 4394364, 12151557, 4034225, 11748594, 311257, 372255, 201377, 0, -67056, -6058],106,9]
%
% END OF LATTICE L107.9
%
%
% LATTICE L107.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-110484660, 125268, 125268; 125268, -110, -143; 125268, -143, -142],[1716, 11, 1],[39, 487, 12, 41, 11, 6, -1, -1, 7, 7, 206, 141, 241, 419; 992, 12402, 307, 1053, 284, 156, -24, -26, 156, 176, 5226, 3580, 6123, 10650; 33394, 416988, 10274, 35100, 9416, 5135, -858, -856, 6006, 5995, 176397, 120736, 206362, 358776],106,10]
%
% END OF LATTICE L107.10
%
%
% LATTICE L107.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[152686248, 475332, 38081472; 475332, 65640, 118404; 38081472, 118404, 9497899],[1716, 12, 1],[5864800, 1995731, 169895, 1155457, -107, -15408, 15620, 264257, 418746, 387292, 25403790, 1114481, 79693149, 2027399; -54439, -18525, -1577, -10725, 1, 143, -145, -2453, -3887, -3595, -235807, -10345, -739739, -18819; -23514018, -8001578, -681168, -4632628, 429, 61776, -62626, -1059498, -1678898, -1552788, -101852608, -4468341, -319517484, -8128546],106,11]
%
% END OF LATTICE L107.11
%
%
% LATTICE L107.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[89398452, 22308, -58344; 22308, -26, -13; -58344, -13, 38],[1716, 13, 1],[-295, -23, -4, -5, 1, 1, -1, -13, -5, -10, -149, -113, -155, -307; -23078, -1800, -314, -396, 76, 77, -78, -1012, -390, -781, -11649, -8836, -12122, -24012; -461032, -35946, -6253, -7821, 1560, 1562, -1560, -20306, -7812, -15626, -232848, -176592, -242231, -479778],106,12]
%
% END OF LATTICE L107.12
%
%
% LATTICE L107.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-842556, -70356, -25740; -70356, -5874, -2145; -25740, -2145, -766],[1716, 33, 1],[-27, -529, -255, -1550, -3001, -4889, -2741, -723, -2721, -120, -75, 1, 14, -9; 350, 6864, 3310, 20124, 38964, 63479, 35590, 9388, 35334, 1559, 975, -12, -182, 116; -72, -1430, -693, -4225, -8184, -13338, -7480, -1974, -7436, -330, -208, 0, 39, -22],106,13]
%
% END OF LATTICE L107.13
%
%
% LATTICE L107.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[135642557193, -4814667, -24547342248; -4814667, 143, 871299; -24547342248, 871299, 4442352185],[429, 143, 1],[10174, 54913, 241993, 347719, 1464068, 368048, 4032242, 355843, 311104, 124024, 18298, 0, -2031, -6055; -30520, -164730, -725941, -1043103, -4391977, -1104087, -12096102, -1067474, -933264, -372053, -54891, 1, 6093, 18168; 56225, 303468, 1337336, 1921614, 8090940, 2033959, 22283547, 1966510, 1719267, 685399, 101121, 0, -11224, -33462],106,14]
%
% END OF LATTICE L107.14
%
%
% LATTICE L107.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[7102524, 41184, -8580; 41184, -78, -39; -8580, -39, 10],[1716, 39, 1],[-13, -1, -4, -13, -27, -34, -21, -53, -1, 1, 2, 3, 1, -1; -440, -34, -137, -451, -940, -1188, -736, -1870, -36, 32, 66, 100, 33, -34; -12870, -992, -3978, -12980, -26988, -34023, -21034, -53196, -1010, 975, 1969, 2964, 990, -988],106,15]
%
% END OF LATTICE L107.15
%
%
% LATTICE L107.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[136724863704, -106733484, 34101165384; -106733484, 83336, -26620880; 34101165384, -26620880, 8505325579],[1716, 44, 1],[178294, 2135483, 88189, 262439, 14379, 28546, 214, 213, 185108, 90318, 2058152, 342635, 2292045, 1963363; 45, 546, 24, 78, 5, 13, 3, 0, 39, 21, 507, 85, 572, 492; -714850, -8561982, -353584, -1052220, -57651, -114452, -858, -854, -742170, -362120, -8251932, -1373757, -9189700, -7871886],106,16]
%
% END OF LATTICE L107.16
%
%
% LATTICE L107.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[92649794952, -139001148, 23108318376; -139001148, 208520, -34669076; 23108318376, -34669076, 5763578629],[1716, 52, 1],[-1378365, -113744, -56340, -119938, -4802, 4269, 15155, 2782, -11309, -68713, -1255645, -245304, -1379852, -1390738; 484, 39, 17, 33, 1, 0, 0, 11, 6, 28, 462, 89, 495, 495; 5526378, 456042, 225888, 480876, 19253, -17116, -60762, -11154, 45342, 275496, 5034348, 983515, 5532340, 5575986],106,17]
%
% END OF LATTICE L107.17
%
%
% LATTICE L107.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1115134676799, 939076975980, -317814048981; 939076975980, 790815300990, -267637498557; -317814048981, -267637498557, 90577193618],[429, 429, 1],[-1, -1, -10, -4, -49, -12, -43, -11, -3, -2, 0, 1, 0, -1; 405985, 305122, 2228785, 599779, 6669681, 1486394, 4934635, 1075232, 188617, -747568, -106040, -744813, -5177, 496494; 1199601, 901571, 6585579, 1772213, 19707402, 4391955, 14580709, 3177057, 557315, -2208921, -313327, -2200770, -15297, 1467037],106,18]
%
% END OF LATTICE L107.18
%
%
% LATTICE L107.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1980264, -1597596, 497640; -1597596, 1319208, -401544; 497640, -401544, 125057],[1716, 132, 1],[3091, 56010, 52492, 314682, 151985, 988647, 276791, 72848, 273059, 23447, 14387, -107, -1440, 1652; -28, -507, -475, -2847, -1375, -8944, -2504, -659, -2470, -212, -130, 1, 13, -15; -12390, -224510, -210408, -1261364, -609213, -3962868, -1109482, -292002, -1094522, -93984, -57668, 429, 5772, -6622],106,19]
%
% END OF LATTICE L107.19
%
%
% LATTICE L107.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-63308388, -1595880, 73788; -1595880, -39754, 1859; 73788, 1859, -86],[1716, 143, 1],[35, 37, 16, 5, 21, 1, -1, -3, -5, 0, 11, 107, 15, 353; 48, 54, 27, 9, 40, 2, 0, -6, -12, -6, 12, 128, 19, 462; 31018, 32868, 14300, 4482, 18876, 901, -858, -2704, -4554, -143, 9675, 94380, 13256, 312312],106,20]
%
% END OF LATTICE L107.20
%
%
% LATTICE L107.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[24551474376, -76051404, 6123503100; -76051404, 235560, -18968352; 6123503100, -18968352, 1527292807],[1716, 156, 1],[3638, -1063, -19571, -114461, -66699, -373178, -124890, -368717, -10000, -13618, -7232, 321, 8099, 3197; 11, 2, 28, 154, 89, 495, 165, 484, 13, 17, 11, 1, 0, 0; -14586, 4262, 78468, 458920, 267423, 1496220, 500734, 1478334, 40094, 54600, 28996, -1287, -32472, -12818],106,21]
%
% END OF LATTICE L107.21
%
%
% LATTICE L107.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-10266828, -153008856, -1062204; -153008856, -2272331490, -15774759; -1062204, -15774759, -109510],[1716, 429, 1],[57, 19, 21, 2, 23, 1, -1, -3, -1, 6, 7, 193, 26, 199; -17014, -5714, -6467, -625, -7304, -323, 282, 970, 366, -1555, -2049, -56872, -7699, -59110; 2450292, 822910, 931359, 90011, 1051908, 46518, -40612, -139698, -52712, 223938, 295088, 8190468, 1108779, 8512790],106,22]
%
% END OF LATTICE L107.22
%
%
% LATTICE L107.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[89812457592, 66352572, -22350894852; 66352572, 49192, -16512496; -22350894852, -16512496, 5562285263],[1716, 572, 1],[-451762, -412571, -212143, -46433, -30352, -4260, -214, -2769, -41960, -242388, -408098, -878710, -450271, -4999627; 1354931, 1237389, 636263, 139263, 91033, 12777, 645, 8305, 125847, 726973, 1223973, 2635439, 1350459, 14994951; -1811290, -1654158, -850564, -186168, -121693, -17080, -858, -11102, -168234, -971828, -1636224, -3523091, -1805312, -20045454],106,23]
%
% END OF LATTICE L107.23
%
%
% LATTICE L107.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[3957003336, 569832331068, 142125984000; 569832331068, 82059290319864, 20466998355804; 142125984000, 20466998355804, 5104821404909],[1716, 1716, 1],[-45820, -13943, -21463, -1559, -3025, -412, 48, -275, -1422, -24632, -13806, -89165, -45683, -169063; 447831, 136327, 210297, 15343, 30088, 4223, 71, 2745, 13865, 240279, 134849, 871064, 446353, 1652041; -1794234, -546194, -842556, -61472, -120549, -16920, -286, -10998, -55550, -962676, -540272, -3489915, -1788312, -6618898],106,24]
%
% END OF LATTICE L107.24
%

\medskip%
%------------------------------WEYL-GROUP-W108--------------------------------
%
\leavevmode\llap{}%
$W_{108}$%
\qquad\llap{24} lattices, $\chi=28$%
\hfill%
$22222262$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L108.1
%
\leavevmode%
${L_{108.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{-2}{}29\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2\rightarrow N_{108}}%
\EasyButWeakLineBreak%
{${20}\above{1pt}{1pt}{*}{2}{116}\above{1pt}{1pt}{b}{2}{2}\above{1pt}{1pt}{s}{2}{870}\above{1pt}{1pt}{b}{2}{4}\above{1pt}{1pt}{*}{2}{580}\above{1pt}{1pt}{b}{2}{6}\above{1pt}{1pt}{}{6}{2}\above{1pt}{1pt}{b}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-964563780\\5310480\\-210540
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5310480\\-29014\\1117
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-210540\\1117\\-38
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\230\\1220
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-335\\-77024\\-408030
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-52\\-11956\\-63337
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2486\\-571590\\-3028035
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-79\\-18164\\-96226
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1593\\-366270\\-1940390
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-14\\-3219\\-17055
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
13\\2989\\15834
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-964563780, 5310480, -210540; 5310480, -29014, 1117; -210540, 1117, -38],[1740, 1, 1],[1, -335, -52, -2486, -79, -1593, -14, 13; 230, -77024, -11956, -571590, -18164, -366270, -3219, 2989; 1220, -408030, -63337, -3028035, -96226, -1940390, -17055, 15834],107,1]
%
% END OF LATTICE L108.1
%
%
% LATTICE L108.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-18705, 7395, 3915; 7395, -2923, -1566; 3915, -1566, -271],[435, 1, 1],[2, 350, -37, -15749, -494, -19191, -1406, -455; 5, 870, -92, -39150, -1228, -47705, -3495, -1131; 0, 29, -3, -1305, -41, -1595, -117, -38],107,2]
%
% END OF LATTICE L108.2
%
%
% LATTICE L108.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-8256201690, 26534565, -2752419435; 26534565, -85278, 8845986; -2752419435, 8845986, -917590561],[435, 3, 1],[-90288, -769507, -166887, -2116703, -78617, -1273391, 2545, -2018; 198710, 1693629, 367312, 4658850, 173039, 2802850, -5599, 4437; 272745, 2324553, 504138, 6394210, 237489, 3846705, -7688, 6096],107,3]
%
% END OF LATTICE L108.3
%
%
% LATTICE L108.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-13965338310, 44552265, 5585780625; 44552265, -142130, -17819775; 5585780625, -17819775, -2234170379],[435, 5, 1],[21945, 935142, 202807, 1543361, 95536, 309482, -9281, 2454; 39742, 1693629, 367312, 2795310, 173039, 560570, -16797, 4437; 54549, 2324495, 504120, 3836352, 237475, 769283, -23070, 6100],107,4]
%
% END OF LATTICE L108.4
%
%
% LATTICE L108.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-5542180140, -885660, 6918240; -885660, -114, 1089; 6918240, 1089, -8626],[1740, 3, 1],[29, -251, -52, -978, -107, -2517, -14, 13; 15140, -131022, -27145, -510545, -55858, -1313990, -7309, 6786; 25170, -217848, -45132, -848830, -92868, -2184570, -12151, 11283],107,5]
%
% END OF LATTICE L108.5
%
%
% LATTICE L108.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[13384235730, 1623288195, 4610131740; 1623288195, 196878315, 559133340; 4610131740, 559133340, 1587936367],[435, 15, 1],[-398736, -17644766, -3887919, -10002581, -1894270, -6281555, 33116, -31; 3698, 163647, 36059, 92771, 17569, 58261, -307, 0; 1156317, 51169050, 11274795, 29007047, 5493300, 18216234, -96035, 90],107,6]
%
% END OF LATTICE L108.6
%
%
% LATTICE L108.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[93060519524520, -40517217180, -23318789159100; -40517217180, 17640616, 10152666776; -23318789159100, 10152666776, 5843143049543],[1740, 4, 1],[-1521, 136802, 47558, 2703632, 50388, 1291503, 54527, 1309; 0, -2987, -1005, -56115, -1033, -26245, -1089, -28; -6070, 545954, 189796, 10789740, 201090, 5154170, 217608, 5224],107,7]
%
% END OF LATTICE L108.7
%
%
% LATTICE L108.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-5596673460, 28495980, -1097940; 28495980, -145070, 5585; -1097940, 5585, -214],[1740, 5, 1],[1, -335, -54, -532, -87, -365, -20, 13; 230, -77024, -12416, -122322, -20004, -83926, -4599, 2989; 872, -291450, -46985, -462927, -75710, -317666, -17415, 11310],107,8]
%
% END OF LATTICE L108.8
%
%
% LATTICE L108.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-90821391045, 10886745, 6254108970; 10886745, -1247, -749679; 6254108970, -749679, -430668134],[435, 29, 1],[415603, 122146, 768235, 1008001, 361912, 202144, -35131, 9280; 0, -1, -9, -15, -7, -5, -3, 2; 6035335, 1773789, 11156213, 14638065, 5255641, 2935510, -510168, 134763],107,9]
%
% END OF LATTICE L108.9
%
%
% LATTICE L108.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[21921376299240, -91351306740, -5493000898320; -91351306740, 380681448, 22890570516; -5493000898320, 22890570516, 1376421738173],[1740, 12, 1],[-1962, 425323, 149667, 2942743, 169421, 4518101, 68989, 17792; 5, 116, 34, 580, 30, 725, 9, 1; -7830, 1697370, 597288, 11743840, 676122, 18030750, 275320, 71004],107,10]
%
% END OF LATTICE L108.10
%
%
% LATTICE L108.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-53169180, -2121060, 57420; -2121060, -82830, 2295; 57420, 2295, -62],[1740, 15, 1],[1, -251, -40, -126, -59, -225, -2, 13; -2, 522, 83, 261, 122, 464, 4, -27; 852, -213150, -33975, -107039, -50130, -191226, -1705, 11040],107,11]
%
% END OF LATTICE L108.11
%
%
% LATTICE L108.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[9607828828440, -29319586380, -2407504451520; -29319586380, 89472680, 7346824760; -2407504451520, 7346824760, 603266126779],[1740, 20, 1],[-217, 734586, 248274, 2779844, 256340, 1304379, 271387, 6981; 0, -2987, -1005, -11223, -1033, -5249, -1089, -28; -866, 2931610, 990820, 11093892, 1023010, 5205558, 1083060, 27860],107,12]
%
% END OF LATTICE L108.12
%
%
% LATTICE L108.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[16577898529035, -46511505, 5477933171700; -46511505, 174, -15369072; 5477933171700, -15369072, 1810105893763],[435, 87, 1],[-46661476, -14240709, -90998711, -40365079, -44337235, -25349623, 774747, 0; -870, -266, -1701, -755, -830, -475, 14, 1; 141211875, 43096734, 275389887, 122157055, 134178012, 76715700, -2344621, 0],107,13]
%
% END OF LATTICE L108.13
%
%
% LATTICE L108.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2039180820, 41422440, -31720200; 41422440, -841406, 644061; -31720200, 644061, -489374],[1740, 29, 1],[161, -1675, -7548, -12454, -11487, -7997, -2054, 1885; 8370, -87076, -392388, -647430, -597160, -415730, -106779, 97993; 580, -6030, -27173, -44835, -41354, -28790, -7395, 6786],107,14]
%
% END OF LATTICE L108.14
%
%
% LATTICE L108.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[6793508233545, 38438775, 2741174750250; 38438775, 290, 15509925; 2741174750250, 15509925, 1106061662666],[435, 145, 1],[-9417823, -14371221, -91832688, -24441008, -44743573, -5116389, 2345542, 0; 28253295, 43113397, 275496363, 73322571, 134229889, 15349072, -7036584, 1; 23339983, 35615880, 227586925, 60571611, 110887010, 12679834, -5812905, 0],107,15]
%
% END OF LATTICE L108.15
%
%
% LATTICE L108.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2726016716760, 230910180, -683078269320; 230910180, 19560, -57860880; -683078269320, -57860880, 171163998793],[1740, 60, 1],[-651, -100063, -31257, -114611, -31475, -162586, -11722, -3473; -2, -1015, -341, -1305, -369, -1943, -145, -38; -2598, -399330, -124740, -457388, -125610, -648846, -46780, -13860],107,16]
%
% END OF LATTICE L108.16
%
%
% LATTICE L108.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-261468060, -260448420, 8666940; -260448420, -259432086, 8633097; 8666940, 8633097, -287282],[1740, 87, 1],[-899, 269, 1615, 1047, 3321, 2693, 434, -404; 1800, -538, -3231, -2095, -6646, -5390, -869, 808; 26970, -8052, -48372, -31370, -99528, -80730, -13021, 12093],107,17]
%
% END OF LATTICE L108.17
%
%
% LATTICE L108.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-721793460268470, 1318068594638325, 437985459418500; 1318068594638325, -2406927903618810, -799806192137490; 437985459418500, -799806192137490, -265770297489883],[435, 435, 1],[0, -1, -9, -1, -7, -1, -1, 2; -252892619, -371626407, -2337337001, -204454599, -1101108391, -123003602, 35628578, -28234485; 761052249, 1118368395, 7033956090, 615283406, 3313663395, 370165677, -107220250, 84968550],107,18]
%
% END OF LATTICE L108.18
%
%
% LATTICE L108.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[7325577480, 63471140580, -1793503260; 63471140580, 549934228888, -15539484468; -1793503260, -15539484468, 439099027],[1740, 116, 1],[71, 39134, 381770, 734972, 392336, 343703, 413539, 10637; 0, -103, -1005, -1935, -1033, -905, -1089, -28; 290, 156198, 1523776, 2933520, 1565942, 1371830, 1650564, 42456],107,19]
%
% END OF LATTICE L108.19
%
%
% LATTICE L108.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-39830340, -17925480, -3279900; -17925480, -8066930, -1475955; -3279900, -1475955, -270026],[1740, 145, 1],[-25, 385, 1779, 599, 2817, 403, 605, -433; 98, -1516, -7004, -2358, -11088, -1586, -2379, 1705; -232, 3610, 16675, 5613, 26390, 3774, 5655, -4060],107,20]
%
% END OF LATTICE L108.20
%
%
% LATTICE L108.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1125887312760, -13267727940, -282042669120; -13267727940, 156350136, 3323658912; -282042669120, 3323658912, 70653666937],[1740, 348, 1],[218, 15327, 153613, 102897, 170405, 155639, 68069, 17010; 5, 806, 8086, 5420, 8980, 8205, 3591, 899; 870, 61146, 612828, 410500, 679818, 620910, 271556, 67860],107,21]
%
% END OF LATTICE L108.21
%
%
% LATTICE L108.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-13072620, 18677160, 445440; 18677160, -26683770, -636405; 445440, -636405, -15178],[1740, 435, 1],[9, -53, -252, -28, -389, -53, -19, 80; -2, 18, 83, 9, 122, 16, 4, -27; 348, -2310, -10875, -1199, -16530, -2226, -725, 3480],107,22]
%
% END OF LATTICE L108.22
%
%
% LATTICE L108.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1007212920, -919188060, 944967900; -919188060, 838873720, -862396200; 944967900, -862396200, 886579591],[1740, 580, 1],[247, 15344, 148446, 56876, 151278, 26435, 158177, 4067; -743, -46175, -446723, -171159, -455247, -79552, -476010, -12239; -986, -61270, -592760, -227112, -604070, -105558, -631620, -16240],107,23]
%
% END OF LATTICE L108.23
%
%
% LATTICE L108.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[567240, 66654180, -16705740; 66654180, 7845287640, -1966288740; -16705740, -1966288740, 492817037],[1740, 1740, 1],[-8, -117, -1133, -149, -1219, -221, -477, -126; 567, 7723, 74583, 9793, 80035, 14500, 31258, 8287; 2262, 30810, 297540, 39068, 319290, 57846, 124700, 33060],107,24]
%
% END OF LATTICE L108.24
%

\medskip%
%------------------------------WEYL-GROUP-W109--------------------------------
%
\leavevmode\llap{}%
$W_{109}$%
\qquad\llap{24} lattices, $\chi=90$%
\hfill%
$222422222222422222\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L109.1
%
\leavevmode%
${L_{109.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{2}{}5\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{2}{}29\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{2\rightarrow N_{109}}%
\EasyButWeakLineBreak%
{${10}\above{1pt}{1pt}{b}{2}{58}\above{1pt}{1pt}{l}{2}{60}\above{1pt}{1pt}{r}{2}{2}\above{1pt}{1pt}{*}{4}{4}\above{1pt}{1pt}{b}{2}{6}\above{1pt}{1pt}{s}{2}{290}\above{1pt}{1pt}{b}{2}{2}\above{1pt}{1pt}{l}{2}{348}\above{1pt}{1pt}{r}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-6396119940\\2136697380\\6986100
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2136697380\\-713788318\\-2333787
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
6986100\\-2333787\\-7630
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
593000351\\1775113200\\3069360
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-198098586\\-592996976\\-1025355
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-652050\\-1951875\\-3376
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1236\\3700\\-25
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5367\\16066\\-29
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4129\\12360\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-3\\2
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1987\\-5948\\-2
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-6871\\-20568\\-21
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-563347\\-1686350\\-2175
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-59522\\-178176\\-235
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1997591\\-5979684\\-8004
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-6396119940, 2136697380, 6986100; 2136697380, -713788318, -2333787; 6986100, -2333787, -7630],[1740, 1, 1],[1236, 5367, 4129, -1, -1987, -6871, -563347, -59522, -1997591, -33114, -89409, -73681, -8693, -3809, -1823, -24947, -1336, -19417; 3700, 16066, 12360, -3, -5948, -20568, -1686350, -178176, -5979684, -99125, -267641, -220560, -26022, -11402, -5457, -74675, -3999, -58116; -25, -29, 0, 2, -2, -21, -2175, -235, -8004, -140, -406, -360, -47, -28, -24, -870, -80, -2436],108,1]
%
% END OF LATTICE L109.1
%
%
% LATTICE L109.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-435, 0, 0; 0, 1, 0; 0, 0, 1],[435, 1, 1],[-8, -24, -11, -3, -1, -2, -84, -8, -125, -3, -5, -1, 0, 0, -1, -119, -13, -223; -25, -87, -45, -14, -6, -15, -725, -71, -1131, -30, -58, -15, -1, 1, 0, -290, -34, -609; -165, -493, -225, -61, -20, -39, -1595, -151, -2349, -55, -87, -15, 1, 0, -21, -2465, -269, -4611],108,2]
%
% END OF LATTICE L109.2
%
%
% LATTICE L109.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-32223930, 64815, -10727535; 64815, -129, 21576; -10727535, 21576, -3571258],[435, 3, 1],[-1703, -1699, 48, 142, -143, -665, -195969, -21077, -119290, -12388, -35450, -5172, -3985, -1138, -616, -64074, -5824, -29306; 4870, 4872, -135, -406, 405, 1892, 557960, 60014, 339677, 35280, 100978, 14735, 11356, 3245, 1758, 182990, 16636, 83723; 5145, 5133, -145, -429, 432, 2009, 592035, 63675, 360383, 37425, 107097, 15625, 12039, 3438, 1861, 193575, 17595, 88537],108,3]
%
% END OF LATTICE L109.3
%
%
% LATTICE L109.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-45952530, 99615, 18393975; 99615, -215, -39875; 18393975, -39875, -7362778],[435, 5, 1],[410, 2042, -35, -171, 173, 2408, 47290, 25430, 431771, 2989, 42763, 3743, 4806, 1372, 2227, 15437, 7015, 105889; 974, 4872, -81, -406, 405, 5676, 111592, 60014, 1019031, 7056, 100978, 8841, 11356, 3245, 5274, 36598, 16636, 251169; 1019, 5075, -87, -425, 430, 5985, 117537, 63205, 1073145, 7429, 106285, 9303, 11945, 3410, 5535, 38367, 17435, 263175],108,4]
%
% END OF LATTICE L109.4
%
%
% LATTICE L109.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-10399980, -577680, 40020; -577680, -32082, 2223; 40020, 2223, -154],[1740, 3, 1],[108, 307, 89, 34, 19, 5, 509, 46, 461, 13, 12, -1, -1, 3, 6, 1724, 185, 2091; -140, -406, -120, -47, -28, -8, -870, -80, -812, -25, -29, 0, 2, -2, -7, -2175, -235, -2668; 26025, 73863, 21380, 8151, 4530, 1183, 119625, 10791, 107996, 3015, 2697, -260, -231, 750, 1457, 416295, 44649, 504484],108,5]
%
% END OF LATTICE L109.5
%
%
% LATTICE L109.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[53895630, 8553840, 18563625; 8553840, 1357665, 2946255; 18563625, 2946255, 6393991],[435, 15, 1],[-3582, -22048, -140, -31, -2384, -7790, -434356, -232414, -1311178, -26921, -380037, -10952, -41564, -11481, -6075, -128563, -58751, -297162; 23, 145, 1, 0, 14, 47, 2639, 1413, 7975, 164, 2320, 67, 255, 71, 38, 812, 372, 1885; 10389, 63945, 406, 90, 6915, 22595, 1259847, 674115, 3803060, 78084, 1102290, 31766, 120555, 33300, 17620, 372882, 170400, 861880],108,6]
%
% END OF LATTICE L109.6
%
%
% LATTICE L109.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2483996970840, 4273410420, -620999245320; 4273410420, 7351880, -1068352608; -620999245320, -1068352608, 155249811983],[1740, 4, 1],[351174, 447108, 23984, 1, 41456, 421066, 39494152, 4230182, 35817959, 2456499, 6954939, 1507474, 765728, 213787, 344663, 12320177, 1129921, 8594323; -470245, -598705, -32115, 0, -55511, -563829, -52884835, -5664447, -47962230, -3289390, -9313060, -2018595, -1025355, -286274, -461526, -16497520, -1513038, -11508360; 1401460, 1784312, 95715, 4, 165442, 1680384, 157612680, 16881748, 142941783, 9803360, 27755668, 6016005, 3055856, 853178, 1375476, 49167180, 4509272, 34298097],108,7]
%
% END OF LATTICE L109.7
%
%
% LATTICE L109.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-5761140, -579420, 40020; -579420, -58270, 4025; 40020, 4025, -278],[1740, 5, 1],[3, 12, -1, -1, 5, 26, 484, 259, 8767, 30, 423, 73, 46, 25, 19, 125, 56, 1673; -5, -29, 0, 2, -2, -21, -435, -235, -8004, -28, -406, -72, -47, -28, -24, -174, -80, -2436; 359, 1305, -144, -115, 690, 3435, 63307, 33845, 1144920, 3909, 54955, 9456, 5935, 3190, 2385, 15457, 6895, 205320],108,8]
%
% END OF LATTICE L109.8
%
%
% LATTICE L109.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-219604965, -353220, 15127125; -353220, -406, 24331; 15127125, 24331, -1042007],[435, 29, 1],[10088, 348, -839, -841, 839, 11758, 39856, 124320, 72791, 73083, 7213, 91571, 23524, 6722, 10925, 13071, 34461, 17941; -25, -1, 0, 2, -1, -21, -75, -235, -138, -140, -14, -180, -47, -14, -24, -30, -80, -42; 146450, 5052, -12180, -12209, 12180, 170694, 578600, 1804786, 1056726, 1060965, 104713, 1329360, 341504, 97585, 158601, 189755, 500279, 260454],108,9]
%
% END OF LATTICE L109.9
%
%
% LATTICE L109.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[8693280120, 394980, -2178401700; 394980, 24, -98976; -2178401700, -98976, 545873813],[1740, 12, 1],[-197906, -557228, -40032, -60531, -16528, -8586, -892088, -81138, -204455, -24041, -27905, -322, 0, -3649, -11591, -3203843, -342579, -965811; -14795, -41673, -2995, -4531, -1239, -645, -67135, -6109, -15399, -1815, -2117, -25, 1, -271, -865, -239395, -25601, -72181; -789780, -2223720, -159755, -241560, -65958, -34264, -3560040, -323796, -815915, -95940, -111360, -1285, 0, -14562, -46256, -12785520, -1367124, -3854245],108,10]
%
% END OF LATTICE L109.10
%
%
% LATTICE L109.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1472549820, -16371660, 1129260; -16371660, -182010, 12555; 1129260, 12555, -866],[1740, 15, 1],[5, 12, -1, -1, 15, 22, 1180, 629, 7079, 72, 1003, 57, 106, 55, 13, 241, 106, 1041; -5, -29, 0, 2, -2, -7, -435, -235, -2668, -28, -406, -24, -47, -28, -8, -174, -80, -812; 6447, 15225, -1304, -1275, 19530, 28585, 1532331, 816765, 9191840, 93477, 1301955, 73976, 137535, 71310, 16835, 311721, 137055, 1345600],108,11]
%
% END OF LATTICE L109.11
%
%
% LATTICE L109.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2116957080, 193140, -530494680; 193140, 40, -48400; -530494680, -48400, 132938267],[1740, 20, 1],[-4663, -25435, -106, 0, -4027, -37303, -681629, -364129, -3078035, -41966, -589220, -25328, -63585, -17168, -26282, -178888, -80966, -609895; -387, -2117, -9, 1, -331, -3075, -56231, -30041, -253953, -3463, -48633, -2091, -5251, -1419, -2175, -14819, -6709, -50547; -18608, -101500, -423, 0, -16070, -148860, -2720084, -1453080, -12283095, -167468, -2351320, -101073, -253740, -68510, -104880, -713864, -323100, -2433825],108,12]
%
% END OF LATTICE L109.12
%
%
% LATTICE L109.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[112048693305, 4213410, 37024886235; 4213410, 174, 1392261; 37024886235, 1392261, 12234343483],[435, 87, 1],[-366967, -15965, -16003, 0, -44588, -149767, -1450079, -4503273, -876441, -2613472, -254984, -1067793, -812847, -226361, -121182, -446564, -1186656, -207355; 60, 2, 0, 1, 14, 40, 370, 1144, 222, 655, 63, 260, 194, 51, 25, 85, 221, 38; 1110555, 48315, 48430, 0, 134937, 453241, 4388385, 13628289, 2652380, 7909170, 771660, 3231470, 2459925, 685038, 366734, 1351440, 3591186, 627520],108,13]
%
% END OF LATTICE L109.13
%
%
% LATTICE L109.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-4383060, 984840, 1131000; 984840, -221270, -254127; 1131000, -254127, -291842],[1740, 29, 1],[144, -9, -449, -22, 239, 983, 2953, 9106, 10583, 5169, 492, 12041, 1471, 727, 466, 428, 1037, 1009; -25, -1, 0, 2, -2, -21, -75, -235, -276, -140, -14, -360, -47, -28, -24, -30, -80, -84; 580, -34, -1740, -87, 928, 3828, 11510, 35496, 41256, 20155, 1919, 46980, 5742, 2842, 1827, 1685, 4089, 3984],108,14]
%
% END OF LATTICE L109.14
%
%
% LATTICE L109.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[45886581825, -3480870, 18519751335; -3480870, 290, -1404905; 18519751335, -1404905, 7474542178],[435, 145, 1],[-74060, -16110, -9689, 0, -44993, -453382, -292650, -4544176, -2653205, -527442, -257300, -646495, -820230, -228417, -366848, -90124, -1197434, -627715; 222192, 48332, 29067, 1, 134993, 1360266, 878024, 13633672, 7960281, 1582457, 771963, 1939641, 2460884, 685302, 1100619, 270389, 3592523, 1883259; 183541, 39925, 24012, 0, 111505, 1123605, 725267, 11261715, 6575370, 1307146, 637660, 1602192, 2032755, 566080, 909150, 223352, 2967570, 1555650],108,15]
%
% END OF LATTICE L109.15
%
%
% LATTICE L109.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[359075263560, 2211540, -89975817600; 2211540, 120, -554160; -89975817600, -554160, 22545824161],[1740, 60, 1],[-137789, -708505, -326, 0, -131921, -399023, -21735887, -11604267, -32684135, -1334858, -18703660, -267428, -2008155, -537464, -270362, -5441144, -2452818, -6140195; -411, -2117, -1, 1, -391, -1185, -64583, -34481, -97121, -3967, -55593, -795, -5971, -1599, -805, -16211, -7309, -18299; -549888, -2827500, -1301, 0, -526470, -1592420, -86743524, -46310280, -130435765, -5327148, -74642520, -1067251, -8014140, -2144910, -1078960, -21714504, -9788700, -24504275],108,16]
%
% END OF LATTICE L109.16
%
%
% LATTICE L109.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-28489020, 33637680, -4924200; 33637680, -39716718, 5814123; -4924200, 5814123, -851126],[1740, 87, 1],[-3413, -94, 401, 258, -1055, -1898, -18406, -57165, -22251, -33173, -3232, -27009, -10236, -5597, -1428, -4876, -12681, -4357; -25, -1, 0, 2, -2, -7, -75, -235, -92, -140, -14, -120, -47, -28, -8, -30, -80, -28; 19575, 537, -2320, -1479, 6090, 10933, 105975, 329121, 128104, 190965, 18603, 155440, 58899, 32190, 8207, 28005, 72819, 25016],108,17]
%
% END OF LATTICE L109.17
%
%
% LATTICE L109.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1744976432625, 3186263880120, 1058774375235; 3186263880120, -5818002644505, -1933283728785; 1058774375235, -1933283728785, -642417373171],[435, 435, 1],[-5, -1, 0, 2, -1, -7, -15, -235, -46, -28, -14, -12, -47, -14, -8, -6, -80, -14; -6134806, -1058124, 170094, 2557193, -2551266, -11917714, -24238312, -378024094, -73779344, -44445141, -21932761, -18562802, -71529848, -20439619, -11073171, -7948927, -104784491, -18184196; 18462009, 3184305, -511879, -7695585, 7677750, 35865025, 72942483, 1137621135, 222030665, 133752669, 66004185, 55862671, 215261055, 61510740, 33323465, 23921403, 315337155, 54723295],108,18]
%
% END OF LATTICE L109.18
%
%
% LATTICE L109.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[998760, -1740, -231420; -1740, 232, 348; -231420, 348, 53635],[1740, 116, 1],[-1481, -65, -101, 0, -175, -1777, -5747, -17851, -5212, -10366, -1012, -6361, -3231, -902, -1454, -1792, -4766, -1250; -1550, -68, -105, 1, -182, -1854, -6000, -18638, -5442, -10825, -1057, -6645, -3376, -943, -1521, -1875, -4987, -1308; -6380, -280, -435, 0, -754, -7656, -24760, -76908, -22455, -44660, -4360, -27405, -13920, -3886, -6264, -7720, -20532, -5385],108,19]
%
% END OF LATTICE L109.19
%
%
% LATTICE L109.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-56826660, 66626340, 27410220; 66626340, -78115850, -32137075; 27410220, -32137075, -13221262],[1740, 145, 1],[29468, 14249, 70919, 44357, 23607, 17387, 3831, 49354, 50519, 2498, 281, -1175, -767, 5453, 26203, 16511, 255776, 298201; -28, -14, -72, -47, -28, -24, -6, -80, -84, -5, -1, 0, 2, -2, -21, -15, -235, -276; 61161, 29575, 147204, 92075, 49010, 36105, 7957, 102515, 104940, 5191, 585, -2436, -1595, 11310, 54375, 34267, 530845, 618900],108,20]
%
% END OF LATTICE L109.20
%
%
% LATTICE L109.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[45153664680, 4369140, -11303723820; 4369140, 696, -1093764; -11303723820, -1093764, 2829763057],[1740, 348, 1],[367639, 14735, 4973, 0, 55625, 176821, 1685693, 5227269, 508176, 3019954, 293228, 610953, 923889, 252338, 131142, 470048, 1239954, 107750; -11795, -473, -160, 1, -1781, -5665, -54015, -167501, -16284, -96775, -9397, -19580, -29611, -8089, -4205, -15075, -39769, -3456; 1468560, 58860, 19865, 0, 222198, 706324, 6733620, 20880696, 2029945, 12063420, 1171320, 2440495, 3690540, 1007982, 523856, 1877640, 4953084, 430415],108,21]
%
% END OF LATTICE L109.21
%
%
% LATTICE L109.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-48610380, 64628820, -15124080; 64628820, -85925550, 20107875; -15124080, 20107875, -4705534],[1740, 435, 1],[-24913, -11896, -19485, -35928, -18173, -4116, -2516, -31641, -10597, -1333, -34, 397, 138, -5687, -7814, -14186, -218889, -84843; -28, -14, -24, -47, -28, -8, -6, -80, -28, -5, -1, 0, 2, -2, -7, -15, -235, -92; 79953, 38175, 62524, 115275, 58290, 13195, 8061, 101355, 33940, 4263, 105, -1276, -435, 18270, 25085, 45531, 702525, 272300],108,22]
%
% END OF LATTICE L109.22
%
%
% LATTICE L109.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[16354388760, 2566500, 4076541600; 2566500, 1160, 639160; 4076541600, 639160, 1016130823],[1740, 580, 1],[674694, 326660, 407216, 1022325, 276048, 422642, 99208, 1302206, 338255, 75011, 14115, 1714, 0, 64727, 599683, 377877, 5854069, 1706395; -2047621, -991377, -1235856, -3102646, -837777, -1282677, -301087, -3952075, -1026573, -227652, -42838, -5202, 1, -196438, -1819968, -1146814, -17766440, -5178717; -2705468, -1309880, -1632903, -4099440, -1106930, -1694760, -397816, -5221740, -1356375, -300788, -56600, -6873, 0, -259550, -2404680, -1515256, -23474340, -6842505],108,23]
%
% END OF LATTICE L109.23
%
%
% LATTICE L109.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[3480, 1717380, -429780; 1717380, 54111442200, -13541713560; -429780, -13541713560, 3388895189],[1740, 1740, 1],[-15971, -7717, -3200, -24031, -6433, -3237, -2247, -29377, -2536, -1651, -293, -4, 1, -1577, -4773, -8967, -138833, -13484; 2933074, 1417180, 587641, 4412805, 1181146, 594238, 412448, 5392122, 465470, 302983, 53755, 733, 0, 289789, 876697, 1646861, 25497513, 2476400; 11720292, 5662920, 2348159, 17633160, 4719750, 2374520, 1648104, 21546420, 1859975, 1210692, 214800, 2929, 0, 1157970, 3503200, 6580704, 101885700, 9895465],108,24]
%
% END OF LATTICE L109.24
%

\medskip%
%------------------------------WEYL-GROUP-W110--------------------------------
%
\leavevmode\llap{}%
$W_{110}$%
\qquad\llap{24} lattices, $\chi=72$%
\hfill%
$2222222222222222\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L110.1
%
\leavevmode%
${L_{110.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{2}{}7\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}13\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{2\rightarrow N_{110}}%
\EasyButWeakLineBreak%
{${26}\above{1pt}{1pt}{l}{2}{140}\above{1pt}{1pt}{r}{2}{2}\above{1pt}{1pt}{b}{2}{260}\above{1pt}{1pt}{*}{2}{4}\above{1pt}{1pt}{b}{2}{2}\above{1pt}{1pt}{l}{2}{364}\above{1pt}{1pt}{r}{2}{10}\above{1pt}{1pt}{b}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1334060\\-267540\\-1820
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-267540\\53654\\365
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1820\\365\\2
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
6860671\\34190520\\3215940
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1377120\\-6862951\\-645525
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4864\\24240\\2279
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-7844\\-39091\\-3679
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-15507\\-77280\\-7280
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-365\\-1819\\-172
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2739\\-13650\\-1300
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-61\\-304\\-30
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\-1
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
73\\364\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\5\\0
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[1334060, -267540, -1820; -267540, 53654, 365; -1820, 365, 2],[1820, 1, 1],[-7844, -15507, -365, -2739, -61, 0, 73, 1, -60, -1517, -243, -13069, -2371, -4864, -442697, -24929; -39091, -77280, -1819, -13650, -304, 0, 364, 5, -299, -7560, -1211, -65130, -11816, -24240, -2206204, -124235; -3679, -7280, -172, -1300, -30, -1, 0, 0, -26, -700, -113, -6110, -1110, -2279, -207480, -11685],109,1]
%
% END OF LATTICE L110.1
%
%
% LATTICE L110.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-910, 455, 3185; 455, -223, -1365; 3185, -1365, 354],[455, 1, 1],[38253, 38617, 1968, 8429, 302, 193, 1921, -112, -280, 2277, 953, 29544, 5540, 23175, 1061323, 119873; 88790, 89635, 4568, 19565, 701, 448, 4459, -260, -650, 5285, 2212, 68575, 12859, 53792, 2463461, 278240; -1768, -1785, -91, -390, -14, -9, -91, 5, 13, -105, -44, -1365, -256, -1071, -49049, -5540],109,2]
%
% END OF LATTICE L110.2
%
%
% LATTICE L110.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-5175170, -447265, -1030575; -447265, -38490, -89065; -1030575, -89065, -205227],[455, 5, 1],[-22882, -54931, -87499, -469148, -425246, -1743971, -79352209, -1787263, -2810923, -555427, -130486, -97613, -10724, 91, 5669, -214; -1833, -4403, -7014, -37609, -34090, -139807, -6361355, -143278, -225342, -44527, -10461, -7826, -860, 7, 455, -17; 115700, 277753, 442430, 2372201, 2150215, 8818220, 401236745, 9037122, 14213160, 2808463, 659790, 493571, 54225, -460, -28665, 1082],109,3]
%
% END OF LATTICE L110.3
%
%
% LATTICE L110.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-5712070, -555555, 2451995; -555555, -53886, 238483; 2451995, 238483, -1052557],[455, 7, 1],[49554, 84959, 189459, 5079106, 920760, 3776111, 24545181, 19349227, 6086303, 859019, 282530, 1056751, 23218, -199, -1753, 2322; -1833, -3145, -7014, -188045, -34090, -139807, -908765, -716390, -225342, -31805, -10461, -39130, -860, 7, 65, -85; 115024, 197205, 439768, 11789505, 2137247, 8765022, 56973709, 44912980, 14127386, 1993935, 655802, 2452905, 53893, -462, -4069, 5390],109,4]
%
% END OF LATTICE L110.4
%
%
% LATTICE L110.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-7737730, -880425, -1782235; -880425, -100074, -202787; -1782235, -202787, -410503],[455, 13, 1],[-1986, -309697, -98655, -203438, -479436, -1966195, -6881799, -10074983, -243775, -3130957, -147106, -42323, -12086, 107, 491, -1218; -141, -22015, -7014, -14465, -34090, -139807, -489335, -716390, -17334, -222635, -10461, -3010, -860, 7, 35, -85; 8692, 1355445, 431782, 890385, 2098343, 8605428, 30119509, 44095090, 1066928, 13703235, 643838, 185235, 52897, -468, -2149, 5330],109,5]
%
% END OF LATTICE L110.5
%
%
% LATTICE L110.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[180394760, 507780, -45095960; 507780, 1416, -126940; -45095960, -126940, 11273307],[1820, 4, 1],[184731, 92471, 9141, 37229, 1140, 454, 114, -907, -443, 6761, 5035, 147059, 27212, 112954, 2579918, 582123; -147589, -73885, -7306, -29770, -913, -365, -91, 730, 364, -5390, -4019, -117455, -21737, -90235, -2061059, -465055; 737308, 369075, 36484, 148590, 4550, 1812, 455, -3620, -1768, 26985, 20096, 586950, 108610, 450828, 10297105, 2323400],109,6]
%
% END OF LATTICE L110.6
%
%
% LATTICE L110.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-482339746980, -5244841420, 13924820; -5244841420, -57031090, 151415; 13924820, 151415, -402],[1820, 5, 1],[503, 193, 20, 23, -1, -2, 61, 2, 17, 31, 20, 185, 161, 322, 29059, 326; -45968, -17640, -1829, -2106, 90, 183, -5460, -181, -1547, -2828, -1826, -16900, -14710, -29423, -2655380, -29790; 109265, 41104, 3875, 3458, -740, -350, 56420, 1103, 6175, 8624, 5005, 42718, 36260, 71390, 6408220, 71713],109,7]
%
% END OF LATTICE L110.7
%
%
% LATTICE L110.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[43513016820, 415393160, 2993900; 415393160, 3965514, 28581; 2993900, 28581, 206],[1820, 7, 1],[8561, 2421, 401, 3039, 71, 3, 1, -1, 58, 231, 262, 14199, 2581, 5301, 68951, 27184; -896129, -253420, -41975, -318110, -7432, -314, -104, 105, -6071, -24180, -27425, -1486290, -270168, -554886, -7217496, -2845505; -89908, -25420, -4207, -31850, -742, -35, -104, -35, -637, -2440, -2758, -149240, -27118, -55685, -724256, -285530],109,8]
%
% END OF LATTICE L110.8
%
%
% LATTICE L110.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[14558943490, -15589665, 2939512940; -15589665, 16695, -3147620; 2939512940, -3147620, 593500231],[455, 35, 1],[159307, 52731, 585433, 3130722, 2835879, 11625600, 75558033, 11911937, 18729043, 528449, 867517, 646948, 70021, -2000, -4633, 2253; 9880, 3264, 36229, 193713, 175463, 719289, 4674826, 736997, 1158755, 32694, 53666, 40014, 4327, -129, -286, 142; -788970, -261151, -2899365, -15504944, -14044730, -57575945, -374202205, -58994033, -92755845, -2617151, -4296390, -3204019, -346780, 9905, 22945, -11158],109,9]
%
% END OF LATTICE L110.9
%
%
% LATTICE L110.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[16380, -3640, -1820; -3640, 806, 377; -1820, 377, -58],[1820, 13, 1],[-4, -117, 5, 87, 245, 552, 3979, 2951, 76, 2133, 67, 57, 43, 24, 53, 1; -19, -560, 23, 410, 1156, 2606, 18788, 13935, 359, 10080, 317, 270, 204, 114, 252, 5; 2, 0, -13, -90, -234, -507, -3612, -2665, -67, -1820, -52, -40, -26, -13, -28, 0],109,10]
%
% END OF LATTICE L110.10
%
%
% LATTICE L110.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[25784031910, 28270515, 5130354320; 28270515, 31005, 5625100; 5130354320, 5625100, 1020807589],[455, 65, 1],[-36431, -1096509, -1738937, -715290, -8422911, -34529160, -120838323, -35379457, -4278959, -10986583, -2576453, -147788, -207869, 6040, 7403, -6741; 760, 22848, 36229, 14901, 175463, 719289, 2517214, 736997, 89135, 228858, 53666, 3078, 4327, -129, -154, 142; 183090, 5510687, 8739315, 3594808, 42330730, 173531995, 607292945, 177805303, 21504615, 55214887, 12948390, 742733, 1044680, -30355, -37205, 33878],109,11]
%
% END OF LATTICE L110.11
%
%
% LATTICE L110.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[31525031720, 85454460, -7898767240; 85454460, 370840, -21411380; -7898767240, -21411380, 1979078863],[1820, 20, 1],[-131994054, -12696199, -5337321, -3272107, -43543, -43315, -15787066, -1032265, -5075151, -2065100, -5206464, -24141734, -21044027, -84306965, -1903181804, -85426772; -1145833, -110215, -46333, -28405, -378, -376, -137046, -8961, -44057, -17927, -45197, -209573, -182682, -731864, -16521414, -741585; -526818240, -50673413, -21302460, -13059722, -173790, -172880, -63009765, -4120004, -20256080, -8242283, -20780180, -96355142, -83991490, -336488240, -7596030715, -340957644],109,12]
%
% END OF LATTICE L110.12
%
%
% LATTICE L110.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[26769248415, -34083140, 11568349520; -34083140, 43407, -14729078; 11568349520, -14729078, 4999270431],[455, 91, 1],[-95455, -2052161, -4556287, -9370858, -22069343, -90471794, -45230755, -463498523, -11211541, -20561831, -6750709, -1936138, -544649, 15826, 2771, -88313; 478035, 10277125, 22817664, 46928795, 110522178, 453078259, 226513377, 2321177600, 56146840, 102972625, 33807211, 9696080, 2727572, -79259, -13877, 442275; 222292, 4778995, 10610509, 21822500, 51394252, 210687295, 105331673, 1079377845, 26109013, 47883615, 15720796, 4508805, 1268358, -36855, -6453, 205660],109,13]
%
% END OF LATTICE L110.13
%
%
% LATTICE L110.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-727100920, 57331820, 182096460; 57331820, -3757768, -14359324; 182096460, -14359324, -45604563],[1820, 28, 1],[-23969353, -1617956, -873001, -1970603, 94648, 203432, 47779, -381321, -1005753, -303206, -1048161, -23004503, -3936972, -15572728, -49997991, -78386321; -130442, -8805, -4751, -10725, 515, 1107, 260, -2075, -5473, -1650, -5704, -125190, -21425, -84747, -272090, -426580; -95667208, -6457635, -3484348, -7865130, 377762, 811944, 190697, -1521940, -4014192, -1210165, -4183452, -91816270, -15713362, -62154344, -199553497, -312857860],109,14]
%
% END OF LATTICE L110.14
%
%
% LATTICE L110.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-103740, 507780, -67340; 507780, -2235590, 293615; -67340, 293615, -38526],[1820, 35, 1],[22454, 1333, 1304, 2417, 463, -47, -3439, -370, -1199, -25, 331, 6085, 6077, 13127, 173479, 13777; 57746, 3428, 3353, 6214, 1190, -121, -8840, -951, -3081, -64, 852, 15652, 15630, 33761, 446160, 35432; 400855, 23796, 23275, 43134, 8260, -840, -61360, -6601, -21385, -444, 5915, 108654, 108500, 234360, 3097120, 245959],109,15]
%
% END OF LATTICE L110.15
%
%
% LATTICE L110.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[133926520, 4038580, -33489820; 4038580, 121784, -1009892; -33489820, -1009892, 8374503],[1820, 52, 1],[1, 8093, 5797, 12809, 30698, 127156, 223256, 654669, 15957, 103613, 10161, 3149, 1218, 508, 156, -391; 0, -490, -351, -775, -1857, -7691, -13503, -39595, -965, -6265, -614, -190, -73, -29, -7, 30; 4, 32305, 23140, 51130, 122538, 507572, 891177, 2613260, 63696, 413595, 40560, 12570, 4862, 2028, 623, -1560],109,16]
%
% END OF LATTICE L110.16
%
%
% LATTICE L110.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-225641780, -31213000, 129220; -31213000, -4317690, 17875; 129220, 17875, -74],[1820, 65, 1],[-1, -11, -4, -1, -5, -2, 5, 2, 1, 11, 4, 1, 5, 2, -5, -2; -8, 0, 19, 6, 34, 15, -28, -13, -7, -84, -34, -12, -94, -135, -812, -110; -3695, -19292, -2405, -298, -520, 130, 1960, 351, 55, -1092, -1235, -1158, -14040, -29250, -205800, -30199],109,17]
%
% END OF LATTICE L110.17
%
%
% LATTICE L110.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[134255940, 53773720, 171080; 53773720, 21538062, 68523; 171080, 68523, 218],[1820, 91, 1],[3, 37, 27, 71, 143, 263, 253, 1273, 28, 87, 4, -9, -19, -15, -5, -2; -7, -80, -55, -130, -248, -436, -412, -2055, -43, -120, 5, 30, 48, 36, 12, 5; -154, -3900, -3913, -14910, -34398, -69615, -69312, -354445, -8491, -30680, -4732, -2380, -182, 455, 152, 0],109,18]
%
% END OF LATTICE L110.18
%
%
% LATTICE L110.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1444318886465, 2113715364670, 421266926080; 2113715364670, -3093356095830, -616510924575; 421266926080, -616510924575, -122871634673],[455, 455, 1],[-141, -629, -7014, -2893, -34090, -139807, -69905, -143278, -17334, -6361, -10461, -602, -860, 7, 5, -17; -6435292, -28672041, -319675117, -131841414, -1553532818, -6371128803, -3185618347, -6529262345, -789912473, -289867065, -476672648, -27428139, -39162712, 346683, 227287, -789328; 32288725, 143860392, 1603952350, 661507056, 7794765615, 31966788945, 15983665140, 32760215306, 3963342460, 1454392082, 2391678835, 137619181, 196496755, -1739465, -1140400, 3960411],109,19]
%
% END OF LATTICE L110.19
%
%
% LATTICE L110.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[202810669880, -2897077820, -50846304600; -2897077820, 41383720, 726321260; -50846304600, 726321260, 12747587161],[1820, 140, 1],[-473124, -6568, -20211, -13615, -893, -595, -6683, -2851, -13661, -921, -17234, -83742, -73997, -298965, -966887, -304198; 67223, 934, 2885, 1963, 142, 118, 1027, 425, 1937, 130, 2435, 11869, 10498, 42442, 137293, 43199; -1890980, -26251, -80780, -54418, -3570, -2380, -26715, -11396, -54600, -3681, -68880, -334698, -295750, -1194900, -3864445, -1215816],109,20]
%
% END OF LATTICE L110.20
%
%
% LATTICE L110.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[757618680, 2775500, -189827820; 2775500, 45240, -695500; -189827820, -695500, 47562979],[1820, 260, 1],[-530486, -678235, -313469, -17971, -28435, -28207, -60850, -39581, -10919, -79732, -227936, -90310, -1054375, -4303033, -7518820, -4399940; -4517, -5775, -2669, -153, -242, -240, -518, -337, -93, -679, -1941, -769, -8978, -36640, -64022, -37465; -2117280, -2706977, -1251120, -71726, -113490, -112580, -242865, -157976, -43580, -318227, -909740, -360446, -4208230, -17174300, -30009175, -17561076],109,21]
%
% END OF LATTICE L110.21
%
%
% LATTICE L110.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1222315640, -12734540, -306191340; -12734540, 114296, 3190096; -306191340, 3190096, 76701249],[1820, 364, 1],[1375, -103234, -523847, -1160209, -2781706, -11524178, -2890669, -59336799, -1446423, -1341814, -921201, -284839, -108390, -36206, 573, 89831; 24, -1805, -9159, -20285, -48635, -201487, -50540, -1037435, -25289, -23460, -16106, -4980, -1895, -633, 10, 1570; 5488, -412035, -2090816, -4630710, -11102546, -45996132, -11537447, -236829320, -5773068, -5355545, -3676764, -1136870, -432614, -144508, 2287, 358540],109,22]
%
% END OF LATTICE L110.22
%
%
% LATTICE L110.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[20185620, 3654560, -52780; 3654560, 661570, -9555; -52780, -9555, 138],[1820, 455, 1],[0, -1, -6, -5, -59, -121, -121, -124, -15, -11, -9, -1, -1, 1, 1, 1; -1, -20, -118, -100, -1186, -2441, -2444, -2506, -304, -224, -187, -22, -34, 1, 4, 5; -70, -1768, -10465, -8834, -104650, -215215, -215420, -220857, -26775, -19708, -16380, -1904, -2730, 455, 660, 728],109,23]
%
% END OF LATTICE L110.23
%
%
% LATTICE L110.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[112840, -14012180, 3510780; -14012180, 1594942440, -399615580; 3510780, -399615580, 100124373],[1820, 1820, 1],[16, 4, 1, -23, -341, -1571, -407, -1695, -221, -45, -206, -18, -69, -69, -3, 14; 9927, 2368, -2280, -15578, -227321, -1040159, -268952, -1119140, -145362, -29455, -133155, -11509, -43549, -43321, -1918, 8573; 39620, 9451, -9100, -62174, -907270, -4151420, -1073425, -4466644, -580160, -117559, -531440, -45934, -173810, -172900, -7655, 34216],109,24]
%
% END OF LATTICE L110.24
%

\medskip%
%------------------------------WEYL-GROUP-W111--------------------------------
%
\leavevmode\llap{}%
$W_{111}$%
\qquad\llap{24} lattices, $\chi=60$%
\hfill%
$22222222222222\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L111.1
%
\leavevmode%
${L_{111.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{2}{}31\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2\rightarrow N_{111}}%
\EasyButWeakLineBreak%
{${12}\above{1pt}{1pt}{*}{2}{124}\above{1pt}{1pt}{b}{2}{30}\above{1pt}{1pt}{b}{2}{62}\above{1pt}{1pt}{l}{2}{20}\above{1pt}{1pt}{r}{2}{2}\above{1pt}{1pt}{b}{2}{620}\above{1pt}{1pt}{*}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-526380\\-262260\\0
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-262260\\-130666\\-3
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\-3\\14
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1859\\-3720\\-1860
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
925\\-1851\\-925
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
8\\-16\\-9
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-275\\552\\114
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1081\\2170\\434
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-127\\255\\45
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
170\\-341\\-93
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
299\\-600\\-140
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
146\\-293\\-66
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
6951\\-13950\\-3100
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-526380, -262260, 0; -262260, -130666, -3; 0, -3, 14],[1860, 1, 1],[-275, -1081, -127, 170, 299, 146, 6951, 287, 1143, 142, -139, -279, -139, -6641; 552, 2170, 255, -341, -600, -293, -13950, -576, -2294, -285, 279, 560, 279, 13330; 114, 434, 45, -93, -140, -66, -3100, -126, -496, -60, 62, 120, 59, 2790],110,1]
%
% END OF LATTICE L111.1
%
%
% LATTICE L111.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[35805, 14415, 5115; 14415, 5803, 2046; 5115, 2046, 331],[465, 1, 1],[37, 370, -179, -4045, -2371, -2299, -58764, -2665, -13948, -6391, -9533, -2009, -767, -9126; -93, -930, 450, 10168, 5960, 5779, 147715, 6699, 35061, 16065, 23963, 5050, 1928, 22940; 3, 31, -15, -341, -200, -194, -4960, -225, -1178, -540, -806, -170, -65, -775],110,2]
%
% END OF LATTICE L111.2
%
%
% LATTICE L111.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-322710, 3255, 106950; 3255, -3, -1089; 106950, -1089, -35441],[465, 3, 1],[-73, -872, -72, 218, 216, 215, 5139, 71, 841, 67, -249, -226, -222, -5294; -75, -899, -75, 217, 220, 220, 5270, 73, 868, 70, -248, -230, -227, -5425; -218, -2604, -215, 651, 645, 642, 15345, 212, 2511, 200, -744, -675, -663, -15810],110,3]
%
% END OF LATTICE L111.3
%
%
% LATTICE L111.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-787710, 4185, -315270; 4185, -5, 1670; -315270, 1670, -126181],[465, 5, 1],[311, 1236, 61, -309, -61, -303, -1446, -299, -1174, -55, 371, 65, 317, 1508; -225, -899, -45, 217, 44, 220, 1054, 219, 868, 42, -248, -46, -227, -1085; -780, -3100, -153, 775, 153, 760, 3627, 750, 2945, 138, -930, -163, -795, -3782],110,4]
%
% END OF LATTICE L111.4
%
%
% LATTICE L111.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[24252540, 12129060, -33480; 12129060, 6065922, -16743; -33480, -16743, 46],[1860, 3, 1],[-183, -3189, -272, -1349, -623, -131, -3217, 3, 399, 47, -46, -277, -184, -10733; 370, 6448, 550, 2728, 1260, 265, 6510, -6, -806, -95, 93, 560, 372, 21700; 1478, 25854, 2215, 11067, 5160, 1104, 27900, -2, -2976, -370, 372, 2220, 1479, 86490],110,5]
%
% END OF LATTICE L111.5
%
%
% LATTICE L111.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2029670130, -8629005, -678544275; -8629005, 36690, 2884785; -678544275, 2884785, 226845893],[465, 15, 1],[-2168, -25650, -569, -17411, -1367, -6158, -32863, -2626, -48657, -1828, -56896, -3427, -10621, -41444; 4, 31, 0, 0, 1, 9, 62, 6, 124, 5, 155, 9, 26, 93; -6485, -76725, -1702, -52080, -4089, -18420, -98301, -7855, -145545, -5468, -170190, -10251, -31770, -123969],110,6]
%
% END OF LATTICE L111.6
%
%
% LATTICE L111.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[16694470920, -16265700, 4172746320; -16265700, 15848, -4065576; 4172746320, -4065576, 1042968773],[1860, 4, 1],[1654, 11121, 6631, 13735, 2012, 2365, 43231, 1178, 3511, 449, 897, 348, 939, 29929; -3237, -21731, -12945, -26815, -3930, -4624, -84630, -2313, -6944, -930, -1860, -695, -1851, -58745; -6630, -44578, -26580, -55056, -8065, -9480, -173290, -4722, -14074, -1800, -3596, -1395, -3764, -119970],110,7]
%
% END OF LATTICE L111.7
%
%
% LATTICE L111.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[112226820, 56119920, -91140; 56119920, 28063210, -45575; -91140, -45575, 74],[1860, 5, 1],[-23, 151, 16, -15, -31, -108, -1291, -337, -2011, -106, -915, -89, -102, -569; 48, -310, -33, 31, 64, 223, 2666, 696, 4154, 219, 1891, 184, 211, 1178; 1230, -4960, -618, 620, 1236, 4325, 51894, 13590, 81530, 4323, 37665, 3704, 4320, 24676],110,8]
%
% END OF LATTICE L111.8
%
%
% LATTICE L111.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-4518870, -16275, -292020; -16275, 217, -1054; -292020, -1054, -18871],[465, 31, 1],[481, 62, 481, -15, -471, -471, -364, -469, -60, -451, 17, 491, 485, 374; -63, -8, -60, 2, 60, 59, 45, 57, 7, 45, -3, -70, -66, -50; -7440, -959, -7440, 232, 7285, 7285, 5630, 7254, 928, 6975, -263, -7595, -7502, -5785],110,9]
%
% END OF LATTICE L111.9
%
%
% LATTICE L111.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[28366201560, -31127100, 7081432920; -31127100, 34152, -7770672; 7081432920, -7770672, 1767832471],[1860, 12, 1],[-6687, -153350, -33208, -217242, -32633, -38745, -702719, -6227, -46817, 923, 17075, 348, -6454, -298116; 4501, 103199, 22345, 146165, 21955, 26066, 472750, 4189, 31496, -620, -11470, -230, 4349, 200725; 26806, 614730, 133120, 870852, 130815, 155316, 2816970, 24962, 187674, -3700, -68448, -1395, 25872, 1195050],110,10]
%
% END OF LATTICE L111.10
%
%
% LATTICE L111.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-53940, -26040, 1860; -26040, -12570, 915; 1860, 915, 218],[1860, 15, 1],[-61, 151, 16, -15, -95, -348, -4267, -379, -6971, -126, -3395, -345, -422, -2553; 126, -310, -33, 31, 196, 718, 8804, 782, 14384, 260, 7006, 712, 871, 5270; -10, 0, 2, 0, -12, -45, -558, -50, -930, -17, -465, -48, -60, -372],110,11]
%
% END OF LATTICE L111.11
%
%
% LATTICE L111.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[68337028680, -35512980, 17050960380; -35512980, 18440, -8860940; 17050960380, -8860940, 4254432121],[1860, 20, 1],[-54340, -140359, 925, 47637, 347, -16185, -157001, -53876, -418757, -55033, -606753, -18383, -110067, -402115; 21867, 56482, -372, -19158, -139, 6519, 63209, 21687, 168547, 22149, 244187, 7398, 44294, 161820; 217830, 562650, -3708, -190960, -1391, 64880, 629362, 215970, 1678650, 220608, 2432260, 73691, 441220, 1611938],110,12]
%
% END OF LATTICE L111.12
%
%
% LATTICE L111.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[8877284310, -12254145, -2975084415; -12254145, 16926, 4106787; -2975084415, 4106787, 997053487],[465, 93, 1],[10358, 2977, 3844, 744, 18233, 24747, 25492, 14576, 9490, 58491, 11723, 106437, 62522, 36843; -2, 0, 5, 1, 5, -2, -5, -4, -3, -20, -4, -35, -19, -10; 30907, 8883, 11470, 2220, 54405, 73842, 76065, 43493, 28317, 174530, 34980, 317595, 186558, 109935],110,13]
%
% END OF LATTICE L111.13
%
%
% LATTICE L111.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-247380, -13020, 9300; -13020, -682, 465; 9300, 465, -166],[1860, 31, 1],[61, 33, 473, 46, 1059, 382, 521, 575, 73, 322, 7, 1, -11, 9; -1284, -694, -9945, -967, -22260, -8029, -10950, -12084, -1534, -6765, -147, -20, 231, -190; -186, -98, -1395, -135, -3100, -1116, -1520, -1674, -212, -930, -20, 0, 31, -30],110,14]
%
% END OF LATTICE L111.14
%
%
% LATTICE L111.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[6624262590, 13665885, -2622606975; 13665885, 28210, -5410430; -2622606975, -5410430, 1038314441],[465, 155, 1],[40939, 3922, 3038, 980, 4804, 32603, 6717, 57611, 12503, 46237, 15445, 28046, 82372, 9708; -122823, -11766, -9111, -2939, -14411, -97811, -20152, -172845, -37512, -138723, -46339, -84145, -247135, -29126; 102765, 9845, 7626, 2460, 12059, 81840, 16861, 144615, 31385, 116064, 38770, 70401, 206770, 24369],110,15]
%
% END OF LATTICE L111.15
%
%
% LATTICE L111.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1665455160, -28593780, 416392620; -28593780, 490920, -7148940; 416392620, -7148940, 104105363],[1860, 60, 1],[1335, 10443, -1, -929, 110, 2440, 17774, 1779, 37824, 1558, 49196, 1447, 8459, 30493; -151, -1178, 0, 62, -15, -301, -2139, -211, -4433, -181, -5673, -166, -966, -3472; -5350, -41850, 4, 3720, -441, -9780, -71238, -7130, -151590, -6244, -197160, -5799, -33900, -122202],110,16]
%
% END OF LATTICE L111.16
%
%
% LATTICE L111.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1860, 0, 0; 0, -4278, 93; 0, 93, -2],[1860, 93, 1],[-1, -1, -4, -1, -21, -7, -9, -3, -1, -1, 0, 1, 0, -1; -2, -4, -20, -6, -140, -51, -70, -26, -10, -15, -1, 0, 2, 0; -124, -222, -1085, -321, -7440, -2697, -3690, -1364, -522, -775, -51, 0, 93, -30],110,17]
%
% END OF LATTICE L111.17
%
%
% LATTICE L111.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-162854411565, 26590653930, -8570485215; 26590653930, -4341686865, 1399377510; -8570485215, 1399377510, -451036078],[465, 465, 1],[-21, -8, -4, 2, 12, 59, 9, 19, 7, 3, -3, -14, -66, -10; 92694, 35863, 18570, -8666, -54511, -272711, -42170, -90608, -34820, -17527, 9709, 56597, 280012, 43213; 287990, 111420, 57691, -26925, -169353, -847230, -131007, -281480, -108165, -54436, 30180, 175863, 870015, 134262],110,18]
%
% END OF LATTICE L111.18
%
%
% LATTICE L111.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[71427720, -14707020, 17841120; -14707020, 3028328, -3673500; 17841120, -3673500, 4456331],[1860, 124, 1],[12202, 4643, 118771, 10581, 58032, 80541, 53441, 56462, 6801, 52889, 863, -812, -433, 3779; -81, -31, -795, -71, -390, -542, -360, -381, -46, -360, -6, 5, 3, -25; -48918, -18614, -476160, -42420, -232655, -322896, -214250, -226362, -27266, -212040, -3460, 3255, 1736, -15150],110,19]
%
% END OF LATTICE L111.19
%
%
% LATTICE L111.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-90606180, -30481680, -252960; -30481680, -10254490, -85095; -252960, -85095, -706],[1860, 155, 1],[-235, -127, -364, -177, -815, -1470, -401, -2213, -281, -248, -27, -1, 42, -7; 876, 474, 1359, 661, 3044, 5491, 1498, 8268, 1050, 927, 101, 4, -157, 26; -21390, -11630, -33387, -16255, -74896, -135160, -36884, -203670, -25880, -22878, -2500, -124, 3875, -626],110,20]
%
% END OF LATTICE L111.20
%
%
% LATTICE L111.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[39792840, -172980, 9926820; -172980, 744, -43152; 9926820, -43152, 2476369],[1860, 372, 1],[201, 196, 1546, 380, 1971, 2597, 1653, 541, 175, 309, -9, -116, 0, 202; -16, -19, -165, -45, -250, -351, -235, -84, -31, -85, -5, 0, 1, -15; -806, -786, -6200, -1524, -7905, -10416, -6630, -2170, -702, -1240, 36, 465, 0, -810],110,21]
%
% END OF LATTICE L111.21
%
%
% LATTICE L111.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[200933940, -201279900, -269700; -201279900, 201604470, 270165; -269700, 270165, 362],[1860, 465, 1],[-1375, -527, -157, -52, -1, 95, -5, -121, -221, -217, -322, -1495, -2713, -743; -26, -10, -3, -1, 0, 2, 0, -2, -4, -4, -6, -28, -51, -14; -1005020, -385170, -114731, -37995, -744, 69285, -3726, -88660, -161670, -158689, -235425, -1092936, -1983225, -543114],110,22]
%
% END OF LATTICE L111.22
%
%
% LATTICE L111.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[31843203720, -469826700, -8294482140; -469826700, 6932840, 122380560; -8294482140, 122380560, 2160537911],[1860, 620, 1],[165884, 74843, 409165, 193787, 220413, 1577483, 214193, 1174180, 148501, 260867, 29557, 2931, -14075, 9151; -496221, -223884, -1223970, -579692, -659341, -4718867, -640735, -3512433, -444225, -780357, -88417, -8768, 42104, -27374; 664950, 300010, 1640148, 776800, 883531, 6323380, 858598, 4706730, 595270, 1045692, 118480, 11749, -56420, 36682],110,23]
%
% END OF LATTICE L111.23
%
%
% LATTICE L111.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[3720, -128163300, -31971540; -128163300, 4369329247560, 1089970252320; -31971540, 1089970252320, 271903325117],[1860, 1860, 1],[-3314, -1065, -365, 67, 149, 1, -253, -1258, -1221, -1921, -2353, -2435, -16003, -2033; -372665, -119299, -40151, 8307, 17191, 0, -28844, -143297, -138682, -217830, -266288, -275172, -1805867, -229137; 1493890, 478230, 160952, -33300, -68913, 0, 115626, 574430, 555930, 873208, 1067460, 1103073, 7239120, 918534],110,24]
%
% END OF LATTICE L111.24
%

\medskip%
%------------------------------WEYL-GROUP-W112--------------------------------
%
\leavevmode\llap{}%
$W_{112}$%
\qquad\llap{24} lattices, $\chi=66$%
\hfill%
$22222242222224\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L112.1
%
\leavevmode%
${L_{112.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{2}{}7\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{2}{}23\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2\rightarrow N_{112}}%
\EasyButWeakLineBreak%
{${2}\above{1pt}{1pt}{l}{2}{92}\above{1pt}{1pt}{r}{2}{14}\above{1pt}{1pt}{s}{2}{138}\above{1pt}{1pt}{l}{2}{28}\above{1pt}{1pt}{r}{2}{46}\above{1pt}{1pt}{b}{2}{4}\above{1pt}{1pt}{*}{4}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-648168612\\162288\\233772
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
162288\\-38\\-61
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
233772\\-61\\-82
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3894911\\6132322560\\6541288320
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1053\\-1657891\\-1768455
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1332\\-2097160\\-2237021
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\1575\\1679
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
703\\1106852\\1180636
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
234\\368424\\392987
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1210\\1905090\\2032119
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
751\\1182412\\1261260
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1037\\1632701\\1741583
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
271\\426674\\455130
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-648168612, 162288, 233772; 162288, -38, -61; 233772, -61, -82],[1932, 1, 1],[1, 703, 234, 1210, 751, 1037, 271, 8, 125, 18, 32, 5, -2, -1; 1575, 1106852, 368424, 1905090, 1182412, 1632701, 426674, 12595, 196788, 28336, 50370, 7868, -3151, -1574; 1679, 1180636, 392987, 2032119, 1261260, 1741583, 455130, 13436, 209944, 30233, 53751, 8400, -3358, -1680],111,1]
%
% END OF LATTICE L112.1
%
%
% LATTICE L112.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-483, 0, -3381; 0, 10, 483; -3381, 483, -338],[483, 1, 1],[456, 3137, 766, 950, 1, -160, 19, 128, 23727, 15586, 79642, 24527, 67320, 8741; 3146, 21643, 5285, 6555, 7, -1104, 131, 883, 163691, 107527, 549447, 169211, 464439, 60304; -67, -460, -112, -138, 0, 23, -3, -19, -3496, -2296, -11730, -3612, -9913, -1287],111,2]
%
% END OF LATTICE L112.2
%
%
% LATTICE L112.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-59355870, 804195, 19733931; 804195, -9906, -267498; 19733931, -267498, -6560885],[483, 3, 1],[-7069, -2539102, -1690873, -2915343, -2714694, -7498237, -979923, -58036, -455728, -132067, -79487, -19716, 11162, 3348; -2753, -988885, -658532, -1135418, -1057273, -2920287, -381644, -22603, -177491, -51436, -30958, -7679, 4347, 1304; -21150, -7596831, -5058984, -8722520, -8122191, -22434246, -2931867, -173640, -1363509, -395136, -237820, -58989, 33396, 10017],111,3]
%
% END OF LATTICE L112.3
%
%
% LATTICE L112.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-209565006, 2241603, 29878863; 2241603, -23114, -319662; 29878863, -319662, -4259993],[483, 7, 1],[-5321, -1911202, -181819, -6583201, -291910, -5643977, -737595, -43684, -343028, -14201, -179489, -2120, 8402, 2520; -2753, -988885, -94076, -3406254, -151039, -2920287, -381644, -22603, -177491, -7348, -92874, -1097, 4347, 1304; -37114, -13330639, -1268188, -45917844, -2036073, -39366754, -5144727, -304696, -2392621, -99052, -1251936, -14787, 58604, 17577],111,4]
%
% END OF LATTICE L112.4
%
%
% LATTICE L112.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-88147500, 104328, 20181672; 104328, -114, -24729; 20181672, -24729, -4545734],[1932, 3, 1],[392, 275875, 91829, 158283, 294723, 406964, 106353, 3140, 49069, 7067, 4189, 1965, -784, -393; 104293, 73397140, 24431302, 42111528, 78411676, 108273627, 28295438, 835403, 13054892, 1880186, 1114488, 522788, -208587, -104558; 1173, 825516, 274785, 473639, 881916, 1217781, 318246, 9396, 146832, 21147, 12535, 5880, -2346, -1176],111,5]
%
% END OF LATTICE L112.5
%
%
% LATTICE L112.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[820553008296, -1596085092, -205563982764; -1596085092, 3104600, 399849376; -205563982764, 399849376, 51497649247],[1932, 4, 1],[-15469, -2132631, -2828034, -14573212, -2256353, -12441163, -1622811, -92799, -357533, -203470, -367772, -17275, -9657, -1209; 19, 2323, 3073, 15801, 2443, 13455, 1753, 98, 368, 203, 345, 14, 0, 2; -61748, -8512875, -11288732, -58172244, -9006739, -49661692, -6477814, -370428, -1427173, -812196, -1468044, -68957, -38548, -4826],111,6]
%
% END OF LATTICE L112.6
%
%
% LATTICE L112.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1351290307017, -7647964002, -455339277792; -7647964002, 43285557, 2577106035; -455339277792, 2577106035, 153433985890],[483, 21, 1],[27455, 6674471, 630587, 7564595, 1002393, 19321151, 2517072, 140480, 1050539, 41153, 160415, 5217, -8626, 1953; -179, -46414, -4391, -52739, -6994, -134895, -17585, -994, -7544, -301, -1219, -44, 0, -10; 81480, 19808313, 1871439, 22450001, 2974875, 57340794, 7470099, 416913, 3117765, 122133, 476077, 15483, -25599, 5796],111,7]
%
% END OF LATTICE L112.7
%
%
% LATTICE L112.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1265535831, 1762467, 604827573; 1762467, -1909, -842352; 604827573, -842352, -289060477],[483, 23, 1],[-34653, -541195, -8289202, -1864168, -13308313, -1598209, -4803904, -284513, -97137, -647446, -50828, -96659, 2379, 16414; -3991, -62324, -954583, -214677, -1532580, -184049, -553215, -32764, -11186, -74557, -5853, -11130, 274, 1890; -72496, -1132210, -17341471, -3899943, -27841730, -3343542, -10050034, -595217, -203216, -1354493, -106335, -202216, 4977, 34339],111,8]
%
% END OF LATTICE L112.8
%
%
% LATTICE L112.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-14306460, 61824, 1027824; 61824, -266, -4501; 1027824, -4501, -70822],[1932, 7, 1],[384, 6013, 124, 1550, 35, -94, -49, 47, 33639, 1600, 57928, 5137, 49659, 12979; 66979, 1048800, 21628, 270342, 6104, -16399, -8546, 8199, 5867576, 279084, 10104222, 896032, 8661869, 2263886; 1316, 20608, 425, 5313, 120, -322, -168, 161, 115276, 5483, 198513, 17604, 170177, 44478],111,9]
%
% END OF LATTICE L112.9
%
%
% LATTICE L112.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[15253267512, 25014869460, -3789871092; 25014869460, 41023583544, -6215267028; -3789871092, -6215267028, 941642365],[1932, 12, 1],[-1835, -167860, -220448, -375358, -173358, -951473, -123519, -6419, -21982, -10664, -4326, 24, 2263, -291; 19, 2323, 3073, 5267, 2443, 13455, 1753, 98, 368, 203, 115, 14, 0, 2; -7260, -660261, -866964, -1475956, -681597, -3740628, -485562, -25188, -86043, -41580, -16652, 189, 9108, -1158],111,10]
%
% END OF LATTICE L112.10
%
%
% LATTICE L112.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[910247823429, 16491952890, -299073574884; 16491952890, 298802706, -5418642243; -299073574884, -5418642243, 98264451605],[483, 69, 1],[83587, 906781, 13800589, 1028797, 21955763, 2629245, 7880224, 442124, 144641, 919319, 22625, 124099, -690, 5441; 20, 277, 4235, 317, 6783, 814, 2445, 143, 49, 329, 9, 63, 1, 0; 254403, 2759856, 42003129, 3131221, 66824016, 8002305, 23984055, 1345638, 440226, 2798019, 68861, 377706, -2100, 16560],111,11]
%
% END OF LATTICE L112.11
%
%
% LATTICE L112.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2226094836, 70548912, -3294060; 70548912, -2235786, 104391; -3294060, 104391, -4874],[1932, 21, 1],[-20, -14359, -683, -8243, -2193, -21200, -5541, -164, -2569, -53, -221, -15, 40, 21; -1139, -818432, -38930, -469844, -125000, -1208397, -315838, -9349, -146464, -3022, -12604, -856, 2277, 1198; -10878, -7824600, -372195, -4492061, -1195104, -11553360, -3019716, -89397, -1400700, -28905, -120589, -8196, 21735, 11466],111,12]
%
% END OF LATTICE L112.12
%
%
% LATTICE L112.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3348156, 54096, 27048; 54096, -874, -437; 27048, -437, -218],[1932, 23, 1],[0, 13, 101, 23, 331, 20, 121, 4, 3, 11, 1, 5, 0, -1; 11, 996, 7700, 1746, 25060, 1511, 9122, 291, 212, 756, 66, 308, -1, -62; -23, -404, -3059, -681, -9660, -577, -3450, -92, -56, -161, -9, 0, 2, 0],111,13]
%
% END OF LATTICE L112.13
%
%
% LATTICE L112.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[32090520, 141760500, -7923132; 141760500, 626232824, -35000588; -7923132, -35000588, 1956217],[1932, 28, 1],[-28535, -107005, -8418, -99788, -573, 159, -593, -5573, -677479, -128014, -4607116, -101751, -3922579, -511027; 98, 368, 29, 345, 2, 0, 2, 19, 2323, 439, 15801, 349, 13455, 1753; -113820, -426811, -33576, -397992, -2285, 644, -2366, -22232, -2702385, -510632, -18377184, -405871, -15646624, -2038414],111,14]
%
% END OF LATTICE L112.14
%
%
% LATTICE L112.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[10870302615711, -87056553696, 1580386535679; -87056553696, 697206314, -12656777847; 1580386535679, -12656777847, 229765599953],[483, 161, 1],[-195275, -2118513, -4606051, -7210751, -7327913, -6142725, -18410636, -1032948, -337933, -306841, -158587, -41425, 1610, -12709; 585845, 6355816, 13818758, 21633204, 21984708, 18428989, 55234353, 3098987, 1013848, 920570, 475788, 124284, -4829, 38127; 1375423, 14921788, 32442811, 50789067, 51614300, 43266405, 129675679, 7275590, 2380238, 2161241, 1117011, 291778, -11340, 89516],111,15]
%
% END OF LATTICE L112.15
%
%
% LATTICE L112.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-41297209044, 4412104536, -63792708; 4412104536, -471379710, 6815475; -63792708, 6815475, -98542],[1932, 69, 1],[23, 443, 3362, 250, 10653, 637, 3813, 104, 65, 194, 4, 15, -2, -3; 333, 6652, 50526, 3760, 160300, 9589, 57422, 1579, 996, 3010, 64, 308, -29, -62; 8142, 173292, 1318107, 98213, 4190508, 250836, 1503096, 41883, 26808, 82593, 1837, 11592, -711, -2346],111,16]
%
% END OF LATTICE L112.16
%
%
% LATTICE L112.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1752265873848, -8023756356, -438980139276; -8023756356, 36741432, 2010122856; -438980139276, 2010122856, 109973928931],[1932, 84, 1],[-133393, -18239198, -3454684, -41533150, -2755692, -106353355, -13871577, -792109, -3047348, -247324, -1039942, -20814, -79375, -10953; 796, 109066, 20659, 248377, 16480, 636042, 82960, 4739, 18239, 1481, 6233, 125, 483, 65; -532476, -72806937, -13790352, -165791360, -11000127, -424539612, -55372338, -3161928, -12164355, -987264, -4151224, -83085, -316848, -43722],111,17]
%
% END OF LATTICE L112.17
%
%
% LATTICE L112.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2013144, 152628, -504252; 152628, 80776, -38180; -504252, -38180, 126305],[1932, 92, 1],[-6569, -34826, -1059546, -236860, -842256, -201681, -604337, -33767, -5510, -69862, -5156, -4800, 1, -703; 19, 101, 3073, 687, 2443, 585, 1753, 98, 16, 203, 15, 14, 0, 2; -26220, -139007, -4229148, -945420, -3361841, -805004, -2412194, -134780, -21993, -278852, -20580, -19159, 4, -2806],111,18]
%
% END OF LATTICE L112.18
%
%
% LATTICE L112.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-14031978670542, 46973983815108, -15726199275087; 46973983815108, -157251889097499, 52645620905073; -15726199275087, 52645620905073, -17624980001113],[483, 483, 1],[-3991, -62324, -136369, -71559, -218940, -184049, -553215, -32764, -11186, -10651, -1951, -1590, 274, 1890; 38568287, 602343107, 1317967988, 691598402, 2115997543, 1778786271, 5346684050, 316659409, 108112285, 102942796, 18856990, 15368633, -2647791, -18268610; 115206609, 1799247828, 3936877524, 2065860650, 6320656680, 5313379197, 15970979913, 945887397, 322940184, 307498500, 56327362, 45907356, -7909167, -54569823],111,19]
%
% END OF LATTICE L112.19
%
%
% LATTICE L112.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-207592571172, 40339588128, -83445012; 40339588128, -7838827570, 16215115; -83445012, 16215115, -33542],[1932, 161, 1],[23, 495, 538, 842, 1711, 717, 4297, 120, 77, 34, 16, 5, -2, -7; 149, 3420, 3722, 5832, 11860, 4973, 29822, 843, 548, 246, 120, 44, -13, -62; 14812, 421876, 460897, 724647, 1476876, 620354, 3726828, 108997, 73360, 34339, 18207, 8832, -1309, -12558],111,20]
%
% END OF LATTICE L112.20
%
%
% LATTICE L112.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[93421176072, -515888436, -23404145604; -515888436, 2908488, 129241968; -23404145604, 129241968, 5863274843],[1932, 276, 1],[-1317293, -6943545, -211224116, -15737874, -167876053, -40196177, -120440731, -6721845, -1095593, -13871748, -340402, -945845, 487, -146339; 8092, 42653, 1297513, 96675, 1031233, 246918, 739846, 41291, 6730, 85211, 2091, 5810, -3, 899; -5258352, -27717147, -843161508, -62822228, -670125309, -160454544, -480773646, -26832168, -4373373, -55373052, -1358812, -3775611, 1944, -584154],111,21]
%
% END OF LATTICE L112.21
%
%
% LATTICE L112.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-8796396, 16454844, 179676; 16454844, -30621234, -334719; 179676, -334719, -3658],[1932, 483, 1],[-133, -5177, -5680, -2988, -18313, -7707, -46391, -1406, -979, -476, -90, -155, 12, 221; 277, 10804, 11854, 6236, 38220, 16085, 96822, 2935, 2044, 994, 188, 324, -25, -462; -31878, -1242864, -1363647, -717367, -4396680, -1850352, -11137980, -337617, -235116, -114333, -21623, -37260, 2877, 53130],111,22]
%
% END OF LATTICE L112.22
%
%
% LATTICE L112.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[321240259032, 718713660, 79936787868; 718713660, 1809640, 178691968; 79936787868, 178691968, 19891425023],[1932, 644, 1],[4522481, 23788109, 103372308, 161736502, 82152303, 137690613, 412556279, 23014769, 3749141, 6776692, 3486998, 459447, -4363, 502471; -13545689, -71249902, -309619685, -484431525, -246061742, -412409523, -1235684369, -68933602, -11229389, -20297479, -10444221, -1376131, 13068, -1504996; -18052608, -94956155, -412636284, -645611484, -327931355, -549626336, -1646821022, -91869176, -14965629, -27050852, -13919220, -1833997, 17416, -2005738],111,23]
%
% END OF LATTICE L112.23
%
%
% LATTICE L112.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[106248408, 12016284588, -3010396032; 12016284588, 1358995442280, -340464180672; -3010396032, -340464180672, 85295251709],[1932, 1932, 1],[-836, -4319, -18761, -9781, -14901, -24970, -74802, -4157, -674, -1211, -205, -78, 5, -93; 45989, 243283, 1057328, 551494, 840437, 1408689, 4221047, 235753, 38459, 69640, 11990, 4789, 21, 5083; 183540, 970935, 4219764, 2200996, 3354159, 5622036, 16846074, 940884, 153489, 277932, 47852, 19113, 84, 20286],111,24]
%
% END OF LATTICE L112.24
%

\medskip%
%------------------------------WEYL-GROUP-W113--------------------------------
%
\leavevmode\llap{}%
$W_{113}$%
\qquad\llap{32} lattices, $\chi=80$%
\hfill%
$2226222222262222\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L113.1
%
\leavevmode%
${L_{113.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}8\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}19\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2\rightarrow N_{113}}%
\EasyButWeakLineBreak%
{${6}\above{1pt}{1pt}{b}{2}{10}\above{1pt}{1pt}{l}{2}{456}\above{1pt}{1pt}{r}{2}{2}\above{1pt}{1pt}{}{6}{6}\above{1pt}{1pt}{b}{2}{40}\above{1pt}{1pt}{b}{2}{114}\above{1pt}{1pt}{l}{2}{8}\above{1pt}{1pt}{r}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-4758603960\\3057480\\-704520
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3057480\\-1946\\429
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-704520\\429\\-74
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
9849599\\18693309600\\14597517600
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-6408\\-12161584\\-9496923
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1560\\2960685\\2311984
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-109\\-206868\\-161541
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-268\\-508630\\-397185
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-9401\\-17841912\\-13932624
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-183\\-347311\\-271213
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-512\\-971712\\-758805
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-499\\-947040\\-739540
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1199\\-2275554\\-1776975
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-277\\-525712\\-410528
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-4758603960, 3057480, -704520; 3057480, -1946, 429; -704520, 429, -74],[2280, 1, 1],[-109, -268, -9401, -183, -512, -499, -1199, -277, -107, -92, -1543, -9, 8, 19, -169, -107; -206868, -508630, -17841912, -347311, -971712, -947040, -2275554, -525712, -203073, -174605, -2928432, -17081, 15183, 36060, -320739, -203072; -161541, -397185, -13932624, -271213, -758805, -739540, -1776975, -410528, -158580, -136350, -2286840, -13339, 11856, 28160, -250458, -158576],112,1]
%
% END OF LATTICE L113.1
%
%
% LATTICE L113.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[78090, 10260, -570; 10260, 1348, -75; -570, -75, 4],[570, 1, 1],[2, 2, -1, -1, -8, -7, -56, -9, -11, -17, -227, -7, -13, -3, -1, 1; -15, -15, 0, 7, 57, 50, 399, 64, 78, 120, 1596, 49, 90, 20, 0, -8; 3, 5, -114, -10, -69, -60, -513, -86, -111, -185, -2622, -86, -183, -60, -171, -10],112,2]
%
% END OF LATTICE L113.2
%
%
% LATTICE L113.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-17278980, 34770, -8630940; 34770, -56, 17366; -8630940, 17366, -4311199],[570, 2, 1],[-8606, -7284, -30136, -663, 662, 332, -15196, -2314, -9259, -22491, -196154, -15217, -42347, -10257, -97949, -5626; 2217, 1875, 7752, 170, -171, -85, 3933, 598, 2391, 5805, 50616, 3926, 10923, 2645, 25251, 1450; 17238, 14590, 60363, 1328, -1326, -665, 30438, 4635, 18546, 45050, 392901, 30480, 84822, 20545, 196194, 11269],112,3]
%
% END OF LATTICE L113.3
%
%
% LATTICE L113.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-21261570, 46740, -7079400; 46740, -84, 15561; -7079400, 15561, -2357206],[570, 3, 1],[-2457, -6239, -17209, -568, 189, 569, -4337, -3963, -2643, -19261, -111991, -13032, -12089, -17569, -27963, -9637; 739, 1875, 5168, 170, -57, -170, 1311, 1196, 797, 5805, 33744, 3926, 3641, 5290, 8417, 2900; 7384, 18750, 51718, 1707, -568, -1710, 13034, 11910, 7943, 57885, 336566, 39165, 36331, 52800, 84037, 28962],112,4]
%
% END OF LATTICE L113.4
%
%
% LATTICE L113.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-29746590, 70680, 5956500; 70680, -140, -14155; 5956500, -14155, -1192738],[570, 5, 1],[6409, 1085, 44893, 494, -493, -99, 11309, 3445, 6893, 3349, 292091, 11330, 31531, 3055, 72937, 8379; 2217, 375, 15504, 170, -171, -34, 3933, 1196, 2391, 1161, 101232, 3926, 10923, 1058, 25251, 2900; 31980, 5414, 224010, 2465, -2460, -494, 56430, 17190, 34395, 16711, 1457490, 56535, 157335, 15244, 363945, 41810],112,5]
%
% END OF LATTICE L113.5
%
%
% LATTICE L113.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[105052857060, -66395310, 52415768730; -66395310, 41964, -33127716; 52415768730, -33127716, 26152671031],[570, 6, 1],[59225, 147349, 207280, 15160, 1421, 2133, 161577, 62782, 77233, 534941, 1521188, 348728, 316981, 225297, 702657, 119162; 56, 130, 171, 9, 0, 5, 190, 71, 85, 575, 1615, 367, 329, 230, 703, 117; -118700, -295320, -415435, -30384, -2848, -4275, -323836, -125829, -154792, -1072140, -3048797, -698928, -635300, -451545, -1408280, -238827],112,6]
%
% END OF LATTICE L113.6
%
%
% LATTICE L113.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[17008858140, -34490130, 8454628170; -34490130, 69940, -17144080; 8454628170, -17144080, 4202559449],[570, 10, 1],[97675, 16137, 339290, 8152, 2207, 255, 270299, 34912, 128603, 59289, 2526898, 192984, 525775, 24887, 1162795, 65656; 168, 26, 513, 9, 0, 1, 570, 71, 255, 115, 4845, 367, 987, 46, 2109, 117; -196500, -32464, -682575, -16400, -4440, -513, -543780, -70235, -258720, -119276, -5083545, -388240, -1057740, -50067, -2339280, -132085],112,7]
%
% END OF LATTICE L113.7
%
%
% LATTICE L113.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[148015320, -351120, -6840; -351120, -7134, 1359; -6840, 1359, -226],[2280, 3, 1],[-135, -948, -10835, -623, -568, -1619, -1261, -853, -105, -252, -1325, -17, 8, 19, -259, -427; -51013, -358225, -4094272, -235416, -214633, -611780, -476501, -322328, -39677, -95225, -500688, -6424, 3023, 7180, -97869, -161352; -302671, -2125425, -24292184, -1396773, -1273463, -3629820, -2827181, -1912440, -235412, -564990, -2970688, -38115, 17936, 42600, -580678, -957336],112,8]
%
% END OF LATTICE L113.8
%
%
% LATTICE L113.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[5022602310, -22954470, 1652104530; -22954470, 104910, -7550505; 1652104530, -7550505, 543433306],[570, 15, 1],[14350, 7112, 99685, 3592, 324, 225, 39718, 30779, 18896, 26134, 742547, 85064, 77250, 21939, 170840, 57877; 56, 26, 342, 9, 0, 2, 190, 142, 85, 115, 3230, 367, 329, 92, 703, 234; -43625, -21621, -303050, -10920, -985, -684, -120745, -93570, -57445, -79449, -2257390, -258600, -234845, -66696, -519365, -175950],112,9]
%
% END OF LATTICE L113.9
%
%
% LATTICE L113.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-91184610, 238260, -33587820; 238260, -532, 87761; -33587820, 87761, -12372062],[570, 19, 1],[-37115, -31419, -13685, -2862, 2855, 2869, -3445, -19943, -39907, -96951, -89011, -65602, -182573, -88449, -22229, -48521; 2217, 1875, 816, 170, -171, -170, 207, 1196, 2391, 5805, 5328, 3926, 10923, 5290, 1329, 2900; 100776, 85310, 37158, 7771, -7752, -7790, 9354, 54150, 108357, 263245, 241686, 178125, 495729, 240160, 60357, 131746],112,10]
%
% END OF LATTICE L113.10
%
%
% LATTICE L113.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-52966680, 759240, -52440; 759240, -9730, 625; -52440, 625, -38],[2280, 5, 1],[-88, -41, -7007, -134, -365, -69, -800, -179, -65, -10, -745, -2, 8, 1, -169, -93; -16533, -7703, -1316472, -25176, -68577, -12964, -150309, -33632, -12213, -1879, -139992, -376, 1503, 188, -31749, -17472; -150495, -70119, -11983680, -229175, -624255, -118012, -1368285, -306160, -111180, -17106, -1274520, -3425, 13680, 1712, -288990, -159040],112,11]
%
% END OF LATTICE L113.11
%
%
% LATTICE L113.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-705808404060, -26662890, -352157307660; -26662890, -840, -13303230; -352157307660, -13303230, -175705997017],[570, 30, 1],[2004314, 1017952, 7019814, 463477, -154178, -46442, 3536664, 1616040, 2155663, 3142025, 45673228, 10629795, 9860791, 1433101, 22809857, 3930596; 739, 375, 2584, 170, -57, -17, 1311, 598, 797, 1161, 16872, 3926, 3641, 529, 8417, 1450; -4017130, -2040222, -14069405, -928920, 309010, 93081, -7088330, -3238935, -4320470, -6297378, -91540195, -21304680, -19763410, -2872281, -45716470, -7877865],112,12]
%
% END OF LATTICE L113.12
%
%
% LATTICE L113.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-36136846320, -375878520, -201499560; -375878520, -3909712, -2095904; -201499560, -2095904, -1123559],[2280, 8, 1],[2372, 5946, 26306, 4121, 11632, 2862, 27814, 811, 2551, 2259, 4873, 255, -145, -127, 3365, 283; -225303, -564785, -2498709, -391440, -1104891, -271855, -2642007, -77036, -242319, -214585, -462897, -24224, 13773, 12065, -319599, -26880; -5112, -12800, -56601, -8864, -25008, -6150, -59736, -1741, -5472, -4840, -10431, -544, 312, 270, -7296, -611],112,13]
%
% END OF LATTICE L113.13
%
%
% LATTICE L113.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[373540531620, -315077190, 186392896170; -315077190, 265772, -157220288; 186392896170, -157220288, 93008144503],[570, 38, 1],[975575, 801697, 176590, 79032, 20251, 14079, 144733, 353928, 1300615, 2991953, 1340870, 1944248, 5290859, 1250471, 613997, 657712; 168, 130, 27, 9, 0, 5, 30, 71, 255, 575, 255, 367, 987, 230, 111, 117; -1955100, -1606640, -353895, -158384, -40584, -28215, -290052, -709289, -2606496, -5996020, -2687169, -3896368, -10603140, -2506005, -1230480, -1318087],112,14]
%
% END OF LATTICE L113.14
%
%
% LATTICE L113.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[365854140330, -381898290, 121646445690; -381898290, 398658, -126981123; 121646445690, -126981123, 40447424582],[570, 57, 1],[262650, 647512, 95085, 63832, 5452, 22743, 38966, 571721, 350160, 2416538, 721995, 1570328, 1424438, 2019957, 165304, 1062439; 56, 130, 18, 9, 0, 10, 10, 142, 85, 575, 170, 367, 329, 460, 37, 234; -789925, -1947405, -285970, -191976, -16397, -68400, -117191, -1719462, -1053113, -7267785, -2171414, -4722792, -4284025, -6075060, -497155, -3195306],112,15]
%
% END OF LATTICE L113.15
%
%
% LATTICE L113.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-20276040, 855000, -54720; 855000, -35670, 2235; -54720, 2235, -134],[2280, 15, 1],[-91, -42, -1059, -10, 8, 1, -259, -413, -128, -177, -10037, -574, -519, -293, -1128, -755; -3265, -1507, -38000, -359, 287, 36, -9291, -14816, -4592, -6350, -360088, -20593, -18620, -10512, -40470, -27088; -17300, -7986, -201400, -1905, 1520, 192, -49210, -78480, -24325, -33639, -1907600, -109095, -98645, -55692, -214415, -143520],112,16]
%
% END OF LATTICE L113.16
%
%
% LATTICE L113.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-289635240, 3276360, 9961320; 3276360, -36974, -110371; 9961320, -110371, -282046],[2280, 19, 1],[22393, 19258, 17003, 1886, -1672, -3981, 1859, 22373, 22796, 56057, 103501, 38282, 107113, 104401, 13204, 57963; 2239527, 1925995, 1700472, 188619, -167217, -398140, 185919, 2237528, 2279832, 5606270, 10351152, 3828589, 10712388, 10441160, 1320534, 5796888; -85500, -73530, -64920, -7201, 6384, 15200, -7098, -85424, -87039, -214035, -395184, -146167, -408975, -398620, -50415, -221312],112,17]
%
% END OF LATTICE L113.17
%
%
% LATTICE L113.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[400027048230, -515540490, -80252395890; -515540490, 664430, 103426405; -80252395890, 103426405, 16100028922],[570, 95, 1],[-641800, -105482, -232345, -51992, -13322, -3705, -95216, -465679, -855638, -393664, -1764239, -1279064, -3480700, -329059, -403930, -865377; 168, 26, 54, 9, 0, 2, 30, 142, 255, 115, 510, 367, 987, 92, 111, 234; -3199125, -525787, -1158150, -259160, -66405, -18468, -474615, -2321230, -4265025, -1962263, -8794050, -6375640, -17349945, -1640232, -2013435, -4313570],112,18]
%
% END OF LATTICE L113.18
%
%
% LATTICE L113.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-15234960, 1990440, -26044440; 1990440, -259824, 3400584; -26044440, 3400584, -44503757],[2280, 24, 1],[8020, 56826, 81545, 37625, 34464, 24692, 77418, 6584, 6557, 16059, 10776, 1247, -451, -397, 14903, 3134; -152681, -1081835, -1552433, -716297, -656121, -470085, -1473887, -125347, -124834, -305740, -205162, -23743, 8586, 7560, -283708, -59663; -16360, -115920, -166345, -76752, -70304, -50370, -157928, -13431, -13376, -32760, -21983, -2544, 920, 810, -30400, -6393],112,19]
%
% END OF LATTICE L113.19
%
%
% LATTICE L113.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-60655865248740, -475989330, -30264020426460; -475989330, -3192, -237493122; -30264020426460, -237493122, -15100121457623],[570, 114, 1],[33481526, 85029448, 6172634, 7745447, -2575502, -3882194, 3107744, 26985948, 36000205, 262379207, 40148520, 177539169, 164699541, 119685079, 20052833, 65656360; 739, 1875, 136, 170, -57, -85, 69, 598, 797, 5805, 888, 3926, 3641, 2645, 443, 1450; -67104466, -170418030, -12371339, -15523608, 5161882, 7780785, -6228614, -54085875, -72152462, -525866610, -80466613, -355828200, -330094714, -239875665, -40190362, -131590029],112,20]
%
% END OF LATTICE L113.20
%
%
% LATTICE L113.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1544277055440, 84716972760, 32479240680; 84716972760, -4647459760, -1781767680; 32479240680, -1781767680, -683103499],[2280, 40, 1],[92483, 17831, 206159, 13481, -1613, -1343, 38629, 5879, 58798, 32596, 751954, 120991, 354602, 18152, 919484, 27739; 1757151, 338785, 3916983, 256138, -30645, -25517, 733875, 111696, 1117125, 619307, 14286765, 2298774, 6737289, 344881, 17469873, 527032; -186000, -35864, -414675, -27120, 3240, 2702, -77520, -11815, -118200, -65536, -1511925, -243280, -713040, -36502, -1849080, -55785],112,21]
%
% END OF LATTICE L113.21
%
%
% LATTICE L113.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-8577400450620, -231079710, -4263568388940; -231079710, -5320, -114862790; -4263568388940, -114862790, -2119291912721],[570, 190, 1],[48578894, 8224708, 8955976, 3745999, -3736838, -375516, 4509076, 13051450, 52233283, 25379351, 58252142, 85864825, 238965251, 11576869, 29094983, 31753962; 2217, 375, 408, 170, -171, -17, 207, 598, 2391, 1161, 2664, 3926, 10923, 529, 1329, 1450; -97730490, -16546378, -18017535, -7536160, 7517730, 755459, -9071310, -26256765, -105082350, -51057902, -117191025, -172741920, -480747690, -23290219, -58532970, -63882275],112,22]
%
% END OF LATTICE L113.22
%
%
% LATTICE L113.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[3513480, 305520, -1525320; 305520, -135546, 381159; -1525320, 381159, -966214],[2280, 57, 1],[-33348, -234183, -140873, -153902, -140317, -399959, -16396, -210733, -25941, -62262, -17231, -4202, 1976, 4699, -3367, -105475; -666673, -4681645, -2816248, -3076716, -2805133, -7995740, -327779, -4212848, -518597, -1244705, -344472, -84004, 39503, 93940, -67311, -2108592; -210349, -1477155, -888584, -970767, -885077, -2522820, -103421, -1329240, -163628, -392730, -108688, -26505, 12464, 29640, -21238, -665304],112,23]
%
% END OF LATTICE L113.23
%
%
% LATTICE L113.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2527752362190, 153640080, 831546988050; 153640080, -7980, -50541615; 831546988050, -50541615, -273551476874],[570, 285, 1],[-7125183, -3619013, -2627189, -1648304, 548091, 330467, -661357, -11485725, -7661181, -11167351, -17087963, -37782000, -35049607, -10188043, -4267431, -27944579; 14251105, 7238401, 5254650, 3296778, -1096239, -660968, 1322783, 22972646, 15323159, 22335863, 34177702, 75567926, 70102855, 20377144, 8535305, 55892058; -21661900, -11002482, -7987150, -5011155, 1666300, 1004682, -2010650, -34918770, -23291435, -33950853, -51950630, -114864405, -106557415, -30973572, -12973795, -84956790],112,24]
%
% END OF LATTICE L113.24
%
%
% LATTICE L113.25
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-59492040, 3317400, 4959000; 3317400, -184870, -275595; 4959000, -275595, -405862],[2280, 95, 1],[18497, 8632, 77707, 28251, 77020, 14575, 8905, 37901, 13795, 2132, 8405, 453, -1672, -223, 1859, 19507; 407121, 189991, 1710336, 621806, 1695213, 320796, 195999, 834200, 303627, 46925, 184992, 9970, -36801, -4908, 40917, 429352; -50445, -23541, -211920, -77045, -210045, -39748, -24285, -103360, -37620, -5814, -22920, -1235, 4560, 608, -5070, -53200],112,25]
%
% END OF LATTICE L113.25
%
%
% LATTICE L113.26
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-8295191760, -500444040, 38565148920; -500444040, -30191280, 2326594440; 38565148920, 2326594440, -179291545273],[2280, 120, 1],[113636, 173442, 1287703, 607921, 575904, 85664, 1399818, 123394, 131221, 71415, 263058, 45031, -4571, -4045, 150943, 39844; -19432119, -29659153, -220201507, -103956535, -98481543, -14648839, -239373761, -21100809, -22439262, -12212228, -44983906, -7700481, 781654, 691712, -25811652, -6813445; -227720, -347568, -2580485, -1218240, -1154080, -171666, -2805160, -247275, -262960, -143112, -527155, -90240, 9160, 8106, -302480, -79845],112,26]
%
% END OF LATTICE L113.26
%
%
% LATTICE L113.27
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1486210185808440, 772929399888810, 382501432201410; 772929399888810, 401975348384220, 198926508020970; 382501432201410, 198926508020970, 98443239747113],[570, 570, 1],[56, 26, 9, 9, 0, 1, 10, 71, 85, 115, 85, 367, 329, 46, 37, 117; 40960521, 20196457, 7414604, 9955900, 850557, 354541, 6076331, 44577522, 54605013, 75369077, 56295752, 244885524, 222135689, 31500637, 25778847, 82843190; -82770080, -40811544, -14982895, -20118150, -1718740, -716433, -12278620, -90079095, -110341930, -152300466, -113758445, -494847210, -448875950, -63654237, -52092050, -167403585],112,27]
%
% END OF LATTICE L113.27
%
%
% LATTICE L113.28
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-107310480, -26058120, 337440; -26058120, -6325936, 81928; 337440, 81928, -1061],[2280, 152, 1],[337, 299, 34, 34, -19, -17, 23, 37, 311, 781, 182, 542, 1531, 377, 193, 107; 1659, 1475, 168, 169, -93, -85, 111, 180, 1518, 3820, 891, 2655, 7506, 1850, 948, 526; 235296, 209000, 23787, 23864, -13224, -11970, 15888, 25669, 216144, 543400, 126693, 377416, 1066584, 262770, 134592, 74651],112,28]
%
% END OF LATTICE L113.28
%
%
% LATTICE L113.29
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-4119960, 4404960, 487920; 4404960, -4655190, -510435; 487920, -510435, -55466],[2280, 285, 1],[-9445, -4352, -5765, -1018, 834, 93, -1423, -43057, -13334, -18427, -54979, -59726, -53985, -30465, -6170, -78431; -19083, -8793, -11648, -2057, 1685, 188, -2875, -86992, -26940, -37230, -111080, -120671, -109072, -61552, -12466, -158464; 92530, 42636, 56480, 9975, -8170, -912, 13940, 421800, 130625, 180519, 538600, 585105, 528865, 298452, 60445, 768360],112,29]
%
% END OF LATTICE L113.29
%
%
% LATTICE L113.30
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1578120240, -178521720, -58760160; -178521720, -20190768, -6645744; -58760160, -6645744, -2187431],[2280, 456, 1],[277, 679, 24, 53, -19, -17, 33, 132, 338, 2396, 181, 1587, 1454, 1042, 172, 278; -194366, -476540, -16847, -37241, 13326, 11970, -23132, -92554, -237031, -1680445, -126952, -1113151, -1019919, -730965, -120667, -195044; 583072, 1429560, 50539, 111720, -39976, -35910, 69392, 277647, 711056, 5041080, 380837, 3339288, 3059608, 2192790, 361984, 585105],112,30]
%
% END OF LATTICE L113.30
%
%
% LATTICE L113.31
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1011959760, 966093000, -2414520; 966093000, -922304080, 2305080; -2414520, 2305080, -5761],[2280, 760, 1],[-37, -17, -19, -55, -149, -7, -17, -9, -26, -4, -2, -1, 2, 0, -4, -5; 645, 367, 450, 1384, 4089, 211, 567, 327, 1101, 215, 132, 168, -15, -17, 15, 61; 273600, 153976, 188025, 576840, 1698600, 87362, 234000, 134615, 451440, 87704, 53655, 67640, -6840, -6802, 7680, 26505],112,31]
%
% END OF LATTICE L113.31
%
%
% LATTICE L113.32
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2540043120, -2651054040, 848889600; -2651054040, -2766912240, 885989760; 848889600, 885989760, -283701307],[2280, 2280, 1],[184921, 283159, 110802, 994785, 943617, 140555, 121061, 203006, 216338, 118100, 22951, 75239, -7346, -6802, 12692, 64500; 474, 724, 283, 2539, 2406, 358, 308, 516, 549, 299, 58, 189, -19, -17, 33, 166; 554800, 849528, 332425, 2984520, 2831000, 421686, 363200, 609045, 649040, 354312, 68855, 225720, -22040, -20406, 38080, 193515],112,32]
%
% END OF LATTICE L113.32
%

\medskip%
%------------------------------WEYL-GROUP-W114--------------------------------
%
\leavevmode\llap{}%
$W_{114}$%
\qquad\llap{24} lattices, $\chi=80$%
\hfill%
$2262222222622222\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L114.1
%
\leavevmode%
${L_{114.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{-2}{}41\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2\rightarrow N_{114}}%
\EasyButWeakLineBreak%
{${20}\above{1pt}{1pt}{*}{2}{164}\above{1pt}{1pt}{b}{2}{2}\above{1pt}{1pt}{}{6}{6}\above{1pt}{1pt}{s}{2}{82}\above{1pt}{1pt}{b}{2}{4}\above{1pt}{1pt}{*}{2}{820}\above{1pt}{1pt}{b}{2}{6}\above{1pt}{1pt}{b}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1509227220\\341940\\496920
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
341940\\-74\\-117
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
496920\\-117\\-158
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3630959\\7478567280\\5881348320
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-864\\-1779553\\-1399488
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1143\\-2354199\\-1851407
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
37\\76210\\59930
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
109\\224516\\176546
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\4120\\3239
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2\\-4119\\-3240
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-4\\-8241\\-6478
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\6178\\4860
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
387\\797040\\626890
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
19\\39132\\30777
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-1509227220, 341940, 496920; 341940, -74, -117; 496920, -117, -158],[2460, 1, 1],[37, 109, 2, -2, -4, 3, 387, 19, 53, 629, 61, 218, 742, 105, 3303, 62; 76210, 224516, 4120, -4119, -8241, 6178, 797040, 39132, 109160, 1295518, 125639, 449007, 1528275, 216266, 6803130, 127701; 59930, 176546, 3239, -3240, -6478, 4860, 626890, 30777, 85850, 1018850, 98807, 353112, 1201874, 170076, 5350090, 100425],113,1]
%
% END OF LATTICE L114.1
%
%
% LATTICE L114.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-41205, -16605, 7995; -16605, -6691, 3198; 7995, 3198, -547],[615, 1, 1],[-2, -686, 51, 2860, 15762, 1821, 85588, 5359, 4422, 36930, 6137, 18356, 56726, 3483, 95632, 2597; 5, 1722, -128, -7179, -39565, -4571, -214840, -13452, -11100, -92701, -15405, -46077, -142393, -8743, -240055, -6519; 0, 41, -3, -171, -943, -109, -5125, -321, -265, -2214, -368, -1101, -3403, -209, -5740, -156],113,2]
%
% END OF LATTICE L114.2
%
%
% LATTICE L114.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-230484165, 232470, -76716330; 232470, -222, 77373; -76716330, 77373, -25534921],[615, 3, 1],[-14758, -43474, -1595, 532, 3190, -1197, -154388, -5053, -21142, -250906, -48665, -57972, -591950, -41883, -1317512, -16487; 15350, 45223, 1660, -553, -3321, 1244, 160515, 5254, 21985, 260924, 50609, 60289, 615615, 43558, 1370220, 17147; 44385, 130749, 4797, -1600, -9594, 3600, 464325, 15197, 63585, 754605, 146361, 174352, 1780302, 125964, 3962445, 49585],113,3]
%
% END OF LATTICE L114.3
%
%
% LATTICE L114.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-297837735, 339480, -119036325; 339480, -370, 135675; -119036325, 135675, -47575054],[615, 5, 1],[-4697, -69181, -2538, 2540, 5076, -1905, -49139, -24124, -6729, -399285, -77444, -276764, -942008, -66651, -419327, -78710; 3070, 45223, 1660, -1659, -3321, 1244, 32103, 15762, 4397, 260924, 50609, 180867, 615615, 43558, 274044, 51441; 11761, 173225, 6355, -6360, -12710, 4770, 123041, 60405, 16849, 999785, 193915, 693000, 2358730, 166890, 1049969, 197085],113,4]
%
% END OF LATTICE L114.4
%
%
% LATTICE L114.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1784289660, -1168500, 924960; -1168500, -714, 597; 924960, 597, -478],[2460, 3, 1],[153, 1777, 171, 202, 2054, 289, 9043, 56, 97, 273, 4, -2, -4, 11, 1207, 19; 64190, 745544, 71744, 84751, 861779, 121254, 3794140, 23496, 40700, 114554, 1679, -839, -1681, 4614, 506350, 7971; 376230, 4369698, 420495, 496726, 5050872, 710664, 22237170, 137707, 238530, 671334, 9837, -4918, -9840, 27048, 2967990, 46721],113,5]
%
% END OF LATTICE L114.5
%
%
% LATTICE L114.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[999751451955, -2894727510, 332510935005; -2894727510, 8381535, -962767845; 332510935005, -962767845, 110591009077],[615, 15, 1],[126847, 2010680, 100312, 4199, 47659, 52623, 1227026, 197160, 166426, 10013513, 1952599, 2341985, 24000727, 1707015, 10797167, 682659; 43, 697, 37, 2, 0, 14, 369, 61, 53, 3239, 635, 766, 7872, 562, 3567, 227; -381387, -6045450, -301605, -12625, -143295, -158220, -3689262, -592795, -500388, -30107325, -5870820, -7041575, -72162255, -5132430, -32463513, -2052530],113,6]
%
% END OF LATTICE L114.6
%
%
% LATTICE L114.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[3206795774280, -6646307460, -803005746000; -6646307460, 13774936, 1664285304; -803005746000, 1664285304, 201078669643],[2460, 4, 1],[-218107, -691256, -34458, -4309, -16591, -18145, -2112782, -203626, -286378, -3445521, -671821, -2417219, -8256963, -587237, -18571103, -704447; 215, 697, 37, 6, 0, 14, 1845, 183, 265, 3239, 635, 2298, 7872, 562, 17835, 681; -871010, -2760530, -137608, -17208, -66256, -72462, -8437390, -813180, -1143650, -13759682, -2682916, -9653160, -32974168, -2345130, -74163670, -2813208],113,7]
%
% END OF LATTICE L114.7
%
%
% LATTICE L114.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-34890180, 118080, 5311140; 118080, -370, -18405; 5311140, -18405, -802234],[2460, 5, 1],[1535, 91075, 8832, 31562, 107424, 15201, 95633, 8975, 1071, 15771, 289, -290, -578, 435, 11213, 2752; 110728, 6569758, 637103, 2276751, 7749123, 1096538, 6898578, 647421, 77258, 1137668, 20848, -20919, -41697, 31378, 808848, 198516; 7622, 452230, 43855, 156720, 533410, 75480, 474862, 44565, 5318, 78310, 1435, -1440, -2870, 2160, 55678, 13665],113,8]
%
% END OF LATTICE L114.8
%
%
% LATTICE L114.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1610584755, -3324690, 432053490; -3324690, -6478, 891873; 432053490, 891873, -115902139],[615, 41, 1],[174918, 12569, 18916, -18905, -923, 14176, 44613, 179614, 250527, 72520, 576707, 2061041, 171101, 496358, 380832, 586187; 7210, 518, 779, -780, -38, 585, 1840, 7407, 10330, 2990, 23777, 84972, 7054, 20463, 15700, 24165; 652105, 46858, 70520, -70479, -3441, 52849, 166320, 669612, 933980, 270359, 2149999, 7683687, 637875, 1850453, 1419765, 2185341],113,9]
%
% END OF LATTICE L114.9
%
%
% LATTICE L114.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[18678019481160, -15569465460, -4677109932000; -15569465460, 12978264, 3898705728; -4677109932000, 3898705728, 1171181844953],[2460, 12, 1],[-578779, -6875630, -1334618, -1592817, -16282905, -1154197, -36388164, -457378, -417116, -1290709, -59635, -615, -49773, -40877, -4443531, -140159; -475, -5535, -1067, -1264, -12874, -908, -28495, -355, -315, -943, -39, 0, -82, -40, -3895, -119; -2311350, -27457782, -5329788, -6360904, -65025672, -4609278, -145315890, -1826536, -1665750, -5154438, -238152, -2456, -198768, -163242, -17745210, -559724],113,10]
%
% END OF LATTICE L114.10
%
%
% LATTICE L114.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-337858860, -1138980, 168126240; -1138980, -3570, 559005; 168126240, 559005, -83439158],[2460, 15, 1],[30081, 1746901, 168105, 198582, 2019254, 284113, 1778027, 55054, 19073, 268413, 3934, -1966, -3940, 10811, 237287, 18677; 2166430, 125811616, 12106904, 14301855, 145426467, 20461790, 128053332, 3964984, 1373636, 19331090, 283327, -141591, -283761, 778606, 17089374, 1345115; 75126, 4362810, 419835, 495950, 5043000, 709560, 4440546, 137495, 47634, 670350, 9825, -4910, -9840, 27000, 592614, 46645],113,11]
%
% END OF LATTICE L114.11
%
%
% LATTICE L114.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[4806116760, -2919387780, -1211577060; -2919387780, 1773328760, 735950340; -1211577060, 735950340, 305427239],[2460, 20, 1],[-7648, -462623, -90377, -325843, -1114163, -79347, -502485, -95527, -5957, -95182, -4858, -677, -1447, -2283, -55320, -26918; 53, 3239, 635, 2298, 7872, 562, 3567, 681, 43, 697, 37, 6, 0, 14, 369, 183; -30466, -1842950, -360040, -1298100, -4438660, -316110, -2001866, -380580, -23734, -379250, -19360, -2700, -5740, -9090, -220334, -107220],113,12]
%
% END OF LATTICE L114.12
%
%
% LATTICE L114.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[118268307465, -1339796565, 38438059035; -1339796565, 15177831, -435443616; 38438059035, -435443616, 12492648403],[615, 123, 1],[-374771, -29150, -60643, -2745, -507, -29342, -85806, -113837, -483904, -142585, -1141502, -1371135, -342963, -1001068, -772869, -401368; 265, 20, 38, 1, 1, 27, 70, 90, 370, 107, 851, 1015, 253, 735, 565, 291; 1153125, 89691, 186591, 8446, 1560, 90282, 264015, 350263, 1488915, 438717, 3512265, 4218818, 1055256, 3080166, 2378025, 1234961],113,13]
%
% END OF LATTICE L114.13
%
%
% LATTICE L114.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1148820, 59040, 29520; 59040, -3034, -1517; 29520, -1517, -758],[2460, 41, 1],[33, 9, 35, 122, 10, 57, 43, 32, 17, 1, 0, -2, 0, 3, 7, 13; 840, 238, 939, 3327, 275, 1586, 1210, 921, 530, 36, 20, -39, -1, 58, 160, 312; -410, -130, -533, -1968, -166, -984, -770, -615, -410, -34, -41, 0, 2, 0, -50, -123],113,14]
%
% END OF LATTICE L114.14
%
%
% LATTICE L114.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[202762696830, -2264764560, -84821516475; -2264764560, 25296385, 947416725; -84821516475, 947416725, 35483300314],[615, 205, 1],[-163182, -63461, -132016, -17923, -1105, -63892, -37365, -743554, -210711, -310432, -2485235, -8955509, -746681, -2179466, -336528, -2621483; 489599, 190403, 396086, 53772, 3316, 191703, 112109, 2230932, 632207, 931403, 7456556, 26869572, 2240296, 6539133, 1009697, 7865322; -403153, -156785, -326155, -44280, -2730, -157850, -92313, -1837005, -520577, -766945, -6139955, -22125240, -1844730, -5384530, -831417, -6476565],113,15]
%
% END OF LATTICE L114.15
%
%
% LATTICE L114.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1352234974440, 1580860749660, -337145076240; 1580860749660, 1848140860920, -394147044000; -337145076240, -394147044000, 84058469557],[2460, 60, 1],[108805, 6417998, 1242718, 1479223, 15101935, 1068591, 6726944, 421454, 76144, 1164911, 51925, 369, 63883, 41103, 855965, 133393; -95, -5535, -1067, -1264, -12874, -908, -5699, -355, -63, -943, -39, 0, -82, -40, -779, -119; 435954, 25715610, 4979340, 5927000, 60511080, 4281690, 26953974, 1688720, 305106, 4667850, 208080, 1480, 255840, 164670, 3429486, 534460],113,16]
%
% END OF LATTICE L114.16
%
%
% LATTICE L114.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-6872947260, -159639240, 4093440; -159639240, -3707958, 95079; 4093440, 95079, -2438],[2460, 123, 1],[133, 37, 145, 170, 42, 241, 183, 46, 77, 5, 2, -2, 0, 11, 27, 17; 2790, 784, 3084, 3631, 899, 5174, 3940, 996, 1700, 114, 59, -39, -1, 214, 550, 351; 332100, 92694, 363711, 427015, 105573, 606390, 460890, 116071, 195570, 12840, 5658, -4879, -39, 26814, 66780, 42230],113,17]
%
% END OF LATTICE L114.17
%
%
% LATTICE L114.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-6976729378995, 1231071561855, 419698342335; 1231071561855, -217227458085, -74057436540; 419698342335, -74057436540, -25247747017],[615, 615, 1],[1442, 518, 779, -260, -38, 585, 368, 2469, 2066, 2990, 23777, 28324, 7054, 20463, 3140, 8055; -2293463, -823984, -1239956, 413177, 60501, -929491, -584994, -3925292, -3284962, -4754441, -37809019, -45040577, -11217351, -32541059, -4993431, -12809983; 6751224, 2425545, 3650025, -1216265, -178095, 2736135, 1722039, 11554825, 9669891, 13995570, 111297780, 132585185, 33020325, 95790555, 14699076, 37708520],113,18]
%
% END OF LATTICE L114.18
%
%
% LATTICE L114.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[3389880, 218940, -848700; 218940, 41656, -54776; -848700, -54776, 212483],[2460, 164, 1],[-47338, -14121, -113529, -410947, -34339, -100529, -77823, -121867, -38507, -3048, -6654, -1109, 1, -2485, -8022, -32654; 265, 79, 635, 2298, 192, 562, 435, 681, 215, 17, 37, 6, 0, 14, 45, 183; -189010, -56382, -453296, -1640820, -137108, -401390, -310730, -486588, -153750, -12170, -26568, -4428, 4, -9922, -32030, -130380],113,19]
%
% END OF LATTICE L114.19
%
%
% LATTICE L114.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-169368537540, 50690760, -171922020; 50690760, -15170, 51455; -171922020, 51455, -174514],[2460, 205, 1],[115, 175, 708, 2578, 216, 1269, 197, 775, 99, 39, 41, -10, -2, 15, 17, 188; 168, 238, 939, 3327, 275, 1586, 242, 921, 106, 36, 20, -39, -1, 58, 32, 312; -113242, -172330, -697205, -2538720, -212710, -1249680, -194002, -763215, -97498, -38410, -40385, 9840, 1970, -14760, -16738, -185115],113,20]
%
% END OF LATTICE L114.20
%
%
% LATTICE L114.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[434430405960, -696910620, -108784489020; -696910620, 1122744, 174511416; -108784489020, 174511416, 27240416161],[2460, 492, 1],[-7999099, -2358894, -18888974, -22691105, -5675849, -16566953, -12789404, -6640670, -6193596, -479645, -980799, -17207, -1229, -464281, -1403291, -1874947; -6040, -1781, -14261, -17131, -4285, -12507, -9655, -5013, -4675, -362, -740, -13, -1, -351, -1060, -1416; -31944330, -9420222, -75432948, -90616724, -22666452, -66159978, -51074370, -26519456, -24734070, -1915458, -3916812, -68716, -4908, -1854102, -5604030, -7487584],113,21]
%
% END OF LATTICE L114.21
%
%
% LATTICE L114.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-502403340, 598916520, -100975620; 598916520, -713969490, 120373335; -100975620, 120373335, -20294602],[2460, 615, 1],[-26627, -37335, -146752, -172634, -42724, -245741, -37405, -47225, -16059, -5351, -2649, 1890, 38, -10375, -5281, -16804; 558, 784, 3084, 3631, 899, 5174, 788, 996, 340, 114, 59, -39, -1, 214, 110, 351; 135792, 190410, 748455, 880475, 217905, 1253370, 190782, 240875, 81918, 27300, 13530, -9635, -195, 52890, 26928, 85690],113,22]
%
% END OF LATTICE L114.22
%
%
% LATTICE L114.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[701508886440, -244954500, 175845247680; -244954500, 208280, -61494260; 175845247680, -61494260, 44078699959],[2460, 820, 1],[9099020, 13571991, 109117113, 394984615, 33005479, 96626255, 14960517, 117139639, 7403101, 2930130, 6397734, 1066289, -1237, 2386471, 1541604, 31379450; -27297007, -40715894, -327350704, -1184951547, -99016245, -289878203, -44881464, -351418236, -22209260, -8790373, -19193165, -3198861, 3711, -7159399, -4624803, -94138167; -36337234, -54200190, -435762760, -1577383980, -131808460, -385880110, -59745314, -467800980, -29564526, -11701570, -25549560, -4258260, 4940, -9530450, -6156446, -125314860],113,23]
%
% END OF LATTICE L114.23
%
%
% LATTICE L114.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[5613720, -2470432860, 618170940; -2470432860, 1087605364920, -272149079220; 618170940, -272149079220, 68099260733],[2460, 2460, 1],[-7518, -11087, -88785, -106663, -26681, -77881, -12025, -31221, -5825, -2256, -4616, -81, -5, -2177, -1318, -8808; 1751683, 2583384, 20688166, 24854443, 6217219, 18148081, 2802134, 7275442, 1357482, 525781, 1075989, 18877, 1111, 506909, 307031, 2052053; 7000422, 10324230, 82678140, 99328240, 24846480, 72526950, 11198442, 29075560, 5425038, 2101230, 4300080, 75440, 4440, 2025810, 1227018, 8200820],113,24]
%
% END OF LATTICE L114.24
%

\medskip%
%------------------------------WEYL-GROUP-W115--------------------------------
%
\leavevmode\llap{}%
$W_{115}$%
\qquad\llap{24} lattices, $\chi=84$%
\hfill%
$222222222222222222\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L115.1
%
\leavevmode%
${L_{115.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{2}{}43\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{2\rightarrow N_{115}}%
\EasyButWeakLineBreak%
{${12}\above{1pt}{1pt}{b}{2}{86}\above{1pt}{1pt}{s}{2}{2}\above{1pt}{1pt}{l}{2}{516}\above{1pt}{1pt}{r}{2}{10}\above{1pt}{1pt}{l}{2}{4}\above{1pt}{1pt}{r}{2}{1290}\above{1pt}{1pt}{b}{2}{2}\above{1pt}{1pt}{b}{2}{860}\above{1pt}{1pt}{*}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1684740\\-330240\\-2580
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-330240\\64706\\513
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2580\\513\\2
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1307201\\-6480960\\-23818560
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
261915\\1298546\\4772367
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
475\\2355\\8654
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2113\\-10476\\-38514
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-4059\\-20124\\-74003
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-261\\-1294\\-4761
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-12073\\-59856\\-220332
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-237\\-1175\\-4330
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-71\\-352\\-1300
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1301\\-6450\\-23865
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\-1
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
347\\1720\\6450
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[1684740, -330240, -2580; -330240, 64706, 513; -2580, 513, 2],[2580, 1, 1],[-2113, -4059, -261, -12073, -237, -71, -1301, 0, 347, 23, -26, -24, -4267, -238, -309, -19124, -475, -41197; -10476, -20124, -1294, -59856, -1175, -352, -6450, 0, 1720, 114, -129, -119, -21156, -1180, -1532, -94815, -2355, -204250; -38514, -74003, -4761, -220332, -4330, -1300, -23865, -1, 6450, 432, -430, -432, -77400, -4325, -5624, -348300, -8654, -750780],114,1]
%
% END OF LATTICE L115.1
%
%
% LATTICE L115.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[101910, -34185, -2580; -34185, 11467, 860; -2580, 860, -181],[645, 1, 1],[16510, 65191, 4433, 108349, 4794, 931, 47737, 431, 6408, 1, -648, 70, 20737, 2711, 2071, 274978, 7074, 316307; 49299, 194661, 13237, 323532, 14315, 2780, 142545, 1287, 19135, 3, -1935, 209, 61920, 8095, 6184, 821085, 21123, 944495; -1122, -4429, -301, -7353, -325, -63, -3225, -29, -430, 0, 43, -5, -1419, -185, -141, -18705, -481, -21500],114,2]
%
% END OF LATTICE L115.2
%
%
% LATTICE L115.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-12896130, 19350, 4305375; 19350, -21, -6465; 4305375, -6465, -1437347],[645, 3, 1],[-153, -10495, -2733, -61128, -18878, -11368, -453423, -33185, -1417281, -24014, -272918, -17040, -127814, -14077, -1814, -18932, 230, 216; -286, -19737, -5149, -115283, -35615, -21455, -855915, -62649, -2675890, -45342, -515355, -32183, -241445, -26605, -3433, -35905, 429, 430; -457, -31347, -8163, -182578, -56385, -33954, -1354285, -99117, -4233135, -71725, -815151, -50895, -381754, -42045, -5418, -56545, 687, 645],114,3]
%
% END OF LATTICE L115.3
%
%
% LATTICE L115.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-15798630, 25800, 3166305; 25800, -35, -5175; 3166305, -5175, -634577],[645, 5, 1],[-287, -6539, -1701, -114068, -2348, -7068, -169129, -20629, -176197, -44780, -169632, -10590, -238274, -1749, -1126, -7042, 144, 26; -858, -19737, -5149, -345849, -7123, -21455, -513549, -62649, -535178, -136026, -515355, -32183, -724335, -5321, -3433, -21543, 429, 86; -1425, -32465, -8445, -566310, -11657, -35090, -839661, -102415, -874749, -222315, -842155, -52575, -1182930, -8683, -5590, -34959, 715, 129],114,4]
%
% END OF LATTICE L115.4
%
%
% LATTICE L115.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-17133780, 3439140, 7740; 3439140, -690306, -1557; 7740, -1557, -2],[2580, 3, 1],[23, -26, -70, -4719, -813, -1091, -22858, -1717, -149987, -2575, -14938, -974, -15233, -927, -301, -2082, -23, 347; 114, -129, -347, -23392, -4030, -5408, -113305, -8511, -743470, -12764, -74046, -4828, -75508, -4595, -1492, -10320, -114, 1720; 260, -258, -780, -52804, -9105, -12228, -256280, -19254, -1682160, -28882, -167571, -10929, -170968, -10410, -3384, -23435, -261, 3870],114,5]
%
% END OF LATTICE L115.5
%
%
% LATTICE L115.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[759202410, -26615925, -256041135; -26615925, 933105, 8976225; -256041135, 8976225, 86349914],[645, 15, 1],[3856, 530701, 159099, 3822859, 241738, 746527, 6028733, 2220881, 19081350, 1622175, 18538208, 1171290, 8889747, 201725, 140399, 327570, -3566, -12441; -13, -1806, -542, -13029, -824, -2545, -20554, -7572, -65059, -5531, -63210, -3994, -30315, -688, -479, -1118, 12, 43; 11435, 1573800, 471810, 11336735, 716877, 2213835, 17878282, 6586050, 56585979, 4810580, 54975285, 3473475, 26362655, 598218, 416355, 971413, -10575, -36894],114,6]
%
% END OF LATTICE L115.6
%
%
% LATTICE L115.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[18084608040, -9600180, 4512205860; -9600180, 5096, -2395296; 4512205860, -2395296, 1125819353],[2580, 4, 1],[111572, 419286, 25724, 284422, 19939, 1126, 56672, -642, 6118, 1607, 23141, 5143, 158005, 31506, 9163, 2155463, 52087, 2206017; 89691, 337077, 20683, 228717, 16040, 907, 45795, -513, 4945, 1290, 18576, 4130, 126936, 25315, 7364, 1732470, 41868, 1773320; -446982, -1679752, -103056, -1139457, -79880, -4511, -227040, 2572, -24510, -6438, -92708, -20604, -633003, -126220, -36709, -8635260, -208672, -8837790],114,7]
%
% END OF LATTICE L115.7
%
%
% LATTICE L115.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-7118220, 5160, 7740; 5160, 10, -15; 7740, -15, -2],[2580, 5, 1],[-89, -171, -11, -509, -2, -3, -11, 0, 3, 1, -1, -1, -179, -2, -13, -161, -20, -347; -38514, -74003, -4761, -220332, -866, -1300, -4773, -1, 1290, 432, -430, -432, -77400, -865, -5624, -69660, -8654, -150156; -56400, -108360, -6970, -322500, -1267, -1900, -6966, 0, 1892, 630, -645, -635, -113520, -1268, -8240, -102039, -12675, -219902],114,8]
%
% END OF LATTICE L115.8
%
%
% LATTICE L115.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-67824330, -287025, -31549530; -287025, -43, -133515; -31549530, -133515, -14675749],[645, 43, 1],[17762, 9502, 106592, 166502, 737283, 444150, 1236188, 1296926, 1288252, 2815937, 248107, 666235, 348716, 550762, 71068, 51857, -8881, -207; -27, -13, -141, -216, -950, -568, -1575, -1649, -1635, -3570, -314, -840, -438, -685, -86, -60, 14, 0; -38184, -20427, -229147, -357939, -1584980, -954815, -2657505, -2788077, -2769430, -6053583, -533370, -1432244, -749655, -1184005, -152779, -111480, 19092, 445],114,9]
%
% END OF LATTICE L115.9
%
%
% LATTICE L115.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[11893970280, -37660260, 2966349840; -37660260, 119256, -9392448; 2966349840, -9392448, 739806067],[2580, 12, 1],[321, 41731, 13485, 171636, 110468, 34844, 2843463, 210677, 9096141, 155120, 1781168, 113694, 435997, 101497, 7549, 194702, 1288, 18354; 86, 11180, 3614, 46010, 29615, 9342, 762390, 56488, 2438960, 41593, 477601, 30487, 116917, 27220, 2025, 52245, 347, 4945; -1286, -167184, -54024, -687613, -442560, -139593, -11391560, -844020, -36441210, -621446, -7135764, -455484, -1746703, -406620, -30243, -780020, -5160, -73530],114,10]
%
% END OF LATTICE L115.10
%
%
% LATTICE L115.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-17804580, 48728460, -9739500; 48728460, -59628810, 11897445; -9739500, 11897445, -2373826],[2580, 15, 1],[69929, 405706, 26458, 413863, 5039, 8187, 11334, 629, -1889, -629, 644, 1892, 127937, 4411, 29613, 124116, 46621, 814589; 18181518, 105483429, 6879071, 107604232, 1310138, 2128616, 2946833, 163539, -491146, -163540, 167442, 491920, 33263596, 1146859, 7699372, 32270124, 12121446, 211792888; 90837550, 527010795, 34368855, 537606640, 6545643, 10634880, 14722813, 817065, -2453838, -817070, 836565, 2457705, 166189840, 5729877, 38467200, 161226307, 60560535, 1058148558],114,11]
%
% END OF LATTICE L115.11
%
%
% LATTICE L115.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[12457958280, -66411780, 3109630140; -66411780, 354040, -16577040; 3109630140, -16577040, 776194573],[2580, 20, 1],[217169, 832043, 53237, 614533, 9616, 3683, 60793, 1273, 6719, 1610, 23184, 6430, 240694, 10273, 16206, 794434, 98172, 848508; 162, 602, 36, 387, 5, 1, 0, -2, 0, 3, 43, 9, 258, 10, 14, 645, 77, 645; -870030, -3333360, -213280, -2461965, -38524, -14755, -243552, -5100, -26918, -6450, -92880, -25760, -964275, -41156, -64925, -3182688, -393300, -3399322],114,12]
%
% END OF LATTICE L115.12
%
%
% LATTICE L115.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2280083825535, -147495375, -761503627455; -147495375, 9546, 49260585; -761503627455, 49260585, 254327392762],[645, 129, 1],[-199017, -642462, -8290082, -4634327, -63013912, -38924425, -36553594, -115808808, -115701473, -84592723, -22482558, -61084978, -10782353, -52611188, -7325615, -1988106, 183708, 76373; -1, -2, -24, -13, -175, -107, -100, -316, -315, -230, -61, -165, -29, -140, -19, -5, 1, 0; -595894, -1923651, -24822051, -13876039, -188675400, -116546985, -109448275, -346753161, -346431780, -253286383, -67316970, -182899812, -32284375, -157527705, -21934257, -5952760, 550056, 228675],114,13]
%
% END OF LATTICE L115.13
%
%
% LATTICE L115.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2580, 0, 2580; 0, 86, 473; 2580, 473, 22],[2580, 43, 1],[-1, 2, 2, -61, -187, -305, -482, -539, -1131, -2551, -118, -350, -403, -393, -159, -98, -41, -29; 6, -11, -11, 336, 1030, 1680, 2655, 2969, 6230, 14052, 650, 1928, 2220, 2165, 876, 540, 226, 160; 0, 2, 0, -72, -215, -344, -540, -602, -1260, -2838, -131, -387, -444, -430, -172, -105, -43, -30],114,14]
%
% END OF LATTICE L115.14
%
%
% LATTICE L115.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2638234767345, 204825555, 528753621120; 204825555, 15910, 41051025; 528753621120, 41051025, 105972521974],[645, 215, 1],[497549, 535392, 6908492, 11585969, 10502456, 32437445, 18277036, 96508602, 19283831, 211484573, 18735710, 50904814, 26956235, 8768646, 6104759, 994066, -153092, -12729; -1492650, -1606178, -20725500, -34757946, -31507403, -97312442, -54831168, -289526122, -57851556, -634454409, -56207191, -152714607, -80868792, -26305966, -18314296, -2982201, 459277, 38187; -2481960, -2670735, -34462135, -57795135, -52390168, -161810075, -91172673, -481420905, -96194942, -1054963935, -93460710, -253932200, -134467755, -43741277, -30452815, -4958772, 763680, 63497],114,15]
%
% END OF LATTICE L115.15
%
%
% LATTICE L115.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[56103147753258120, -261952703713740, 14003974364861520; -261952703713740, 1223090356440, -65386330259880; 14003974364861520, -65386330259880, 3495548928452231],[2580, 60, 1],[781931, 9131717, 603699, 2395894, 120560, 53110, 332725, 35419, 101427, 312, 41860, 36318, 661965, 92779, 160229, 2725134, 1031276, 9072150; 173517, 2034803, 135643, 542531, 27753, 12611, 81313, 9445, 27047, -3, 43, 6323, 135751, 19569, 34711, 596969, 227165, 2007799; -3129350, -36545700, -2416020, -9588355, -482472, -212535, -1331452, -141720, -405834, -1250, -167700, -145380, -2649445, -371328, -641265, -10906348, -4127280, -36307566],114,16]
%
% END OF LATTICE L115.16
%
%
% LATTICE L115.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-202651260, -111569520, 237360; -111569520, -61424382, 130677; 237360, 130677, -278],[2580, 129, 1],[-1187, -165, -491, -189, -556, -227, -47, -60, -43, -1, 3, 5, -27, -254, -421, -223, -750, -1577; 2792, 388, 1154, 444, 1305, 532, 110, 140, 100, 2, -7, -11, 64, 600, 992, 525, 1765, 3710; 298850, 41493, 123195, 47324, 138675, 56244, 11575, 14577, 10290, 86, -729, -903, 7028, 65145, 106812, 56365, 189243, 397350],114,17]
%
% END OF LATTICE L115.17
%
%
% LATTICE L115.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-7526280084630, 20039924735685, -6699376485450; 20039924735685, -53359505354310, 17838161577990; -6699376485450, 17838161577990, -5963323804627],[645, 645, 1],[-9, -13, -141, -72, -190, -568, -105, -1649, -327, -1190, -314, -840, -146, -137, -86, -4, 14, 0; -14618982, -23461500, -263186518, -137036500, -364084291, -1096647428, -203484082, -3202228176, -636162128, -2317600721, -612598419, -1644993239, -287003446, -271975628, -175472410, -8535891, 21928581, 102209; -43729925, -70180650, -787272810, -409918835, -1089089466, -3280413885, -608684242, -9578861460, -1902958989, -6932665325, -1832472600, -4920686940, -858516665, -813563784, -524892615, -25533508, 65595210, 305739],114,18]
%
% END OF LATTICE L115.18
%
%
% LATTICE L115.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[29943480, -3661020, 7489740; -3661020, 447544, -915728; 7489740, -915728, 1873403],[2580, 172, 1],[-451, -1, 1331, 1780, 18032, 6236, 36977, 40099, 40993, 91124, 8244, 23398, 6463, 23183, 2007, 4238, 1116, 222; 6, 0, -22, -30, -305, -106, -630, -684, -700, -1557, -141, -401, -111, -400, -35, -75, -21, -5; 1806, 4, -5332, -7131, -72240, -24983, -148140, -160648, -164230, -365070, -33028, -93740, -25893, -92880, -8041, -16980, -4472, -890],114,19]
%
% END OF LATTICE L115.19
%
%
% LATTICE L115.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[669899580, -111427620, 647580; -111427620, 18534290, -107715; 647580, -107715, 626],[2580, 215, 1],[1, -1, -1, 31, 19, 155, 49, 274, 115, 1297, 60, 178, 205, 40, 81, 10, 21, 3; 6, -7, -11, 192, 120, 992, 315, 1765, 742, 8376, 388, 1154, 1332, 261, 532, 66, 140, 20; 0, -170, -860, 960, 989, 10320, 3504, 20210, 8692, 99330, 4685, 14405, 17100, 3526, 7740, 1011, 2365, 338],114,20]
%
% END OF LATTICE L115.20
%
%
% LATTICE L115.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[151815915240, -287228820, 37896090060; -287228820, 543864, -71697684; 37896090060, -71697684, 9459572401],[2580, 516, 1],[2486616, 680062, 1960708, 183476, 2043397, 190848, 148064, 164090, 63778, 9295, 641, 81401, 43425, 1360118, 489855, 986441, 3239425, 3339737; -42763, -11695, -33717, -3155, -35135, -3281, -2545, -2819, -1095, -159, -11, -1401, -747, -23395, -8425, -16965, -55711, -57435; -9961982, -2724492, -7855068, -735049, -8186340, -764583, -593180, -657384, -255510, -37238, -2568, -326112, -173971, -5448960, -1962477, -3951920, -12977916, -13379790],114,21]
%
% END OF LATTICE L115.21
%
%
% LATTICE L115.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[297259860, 84048660, -216720; 84048660, 23763090, -61275; -216720, -61275, 158],[2580, 645, 1],[351, 49, 147, 57, 34, 71, 3, 20, 3, 1, -1, -3, 7, 14, 121, 13, 220, 93; 900, 126, 380, 148, 89, 188, 8, 54, 8, 2, -3, -11, 16, 34, 304, 33, 561, 238; 830330, 116055, 348945, 135560, 81141, 170280, 7217, 48375, 7218, 2150, -2535, -8385, 15800, 32379, 283800, 30623, 519225, 219822],114,22]
%
% END OF LATTICE L115.22
%
%
% LATTICE L115.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[4401361320, 66060900, -1049120880; 66060900, 906440, -15810240; -1049120880, -15810240, 250023599],[2580, 860, 1],[167119, 1293, -279283, -347002, -693034, -1173858, -1378309, -7435239, -1513101, -16772114, -1510838, -4249352, -1162543, -816511, -335687, -131236, -112486, 3556; -501873, -3883, 838711, 1042077, 2081241, 3525197, 4139181, 22328665, 4543973, 50368107, 4537177, 12761171, 3491217, 2452053, 1008097, 394113, 337805, -10679; 669510, 5180, -1118860, -1390155, -2776424, -4702695, -5521764, -29786960, -6061766, -67192230, -6052700, -17023700, -4657365, -3271096, -1344825, -525756, -450640, 14246],114,23]
%
% END OF LATTICE L115.23
%
%
% LATTICE L115.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[500520, -426992580, -106582380; -426992580, 363283933080, 90679951440; -106582380, 90679951440, 22634784653],[2580, 2580, 1],[7279, 1959, 5461, 493, 1015, 391, 45, 3, -25, -129, -9, 389, 157, 935, 1559, 605, 9747, 1975; -4092494, -1101220, -3068646, -276910, -569551, -218798, -25042, 1288, 14448, 73523, 5137, -219603, -88451, -526532, -877285, -340319, -5481703, -1110531; 16395470, 4411740, 12293700, 1109365, 2281752, 876555, 100324, -5160, -57882, -294550, -20580, 879780, 354355, 2109408, 3514605, 1363396, 21960960, 4449042],114,24]
%
% END OF LATTICE L115.24
%

\medskip%
%------------------------------WEYL-GROUP-W116--------------------------------
%
\leavevmode\llap{}%
$W_{116}$%
\qquad\llap{24} lattices, $\chi=90$%
\hfill%
$224222222224222222\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L116.1
%
\leavevmode%
${L_{116.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{2}{}7\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{2}{}31\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2\rightarrow N_{116}}%
\EasyButWeakLineBreak%
{${6}\above{1pt}{1pt}{s}{2}{434}\above{1pt}{1pt}{b}{2}{2}\above{1pt}{1pt}{*}{4}{4}\above{1pt}{1pt}{*}{2}{868}\above{1pt}{1pt}{b}{2}{6}\above{1pt}{1pt}{l}{2}{124}\above{1pt}{1pt}{r}{2}{42}\above{1pt}{1pt}{s}{2}{62}\above{1pt}{1pt}{b}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2637852\\627564\\-5208
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
627564\\149302\\-1239
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-5208\\-1239\\10
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1702273\\7166208\\1374912
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-404690\\1703659\\326865
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1716\\-7224\\-1387
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
796\\-3351\\-645
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
6134\\-25823\\-4991
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
81\\-341\\-67
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
19\\-80\\-18
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
309\\-1302\\-434
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-5\\21\\-3
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-59\\248\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-5\\21\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
81\\-341\\-62
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[2637852, 627564, -5208; 627564, 149302, -1239; -5208, -1239, 10],[2604, 1, 1],[796, 6134, 81, 19, 309, -5, -59, -5, 81, 62, 2732, 205, 1125, 159279, 7727, 70987, 12875, 8785; -3351, -25823, -341, -80, -1302, 21, 248, 21, -341, -261, -11501, -863, -4736, -670530, -32529, -298840, -54201, -36983; -645, -4991, -67, -18, -434, -3, 0, 0, -62, -48, -2170, -164, -906, -128464, -6234, -57288, -10395, -7099],115,1]
%
% END OF LATTICE L116.1
%
%
% LATTICE L116.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[54033, -5208, -651; -5208, 502, 63; -651, 63, 10],[651, 1, 1],[1142, 8734, 112, 11, 185, -4, 3, 26, 162, 100, 4100, 302, 817, 115321, 11182, 51333, 18604, 12672; 12030, 92008, 1180, 116, 1953, -42, 31, 273, 1705, 1053, 43183, 3181, 8606, 1214766, 117789, 540733, 195972, 133486; -1161, -8897, -115, -12, -217, 3, 0, -21, -155, -99, -4123, -305, -828, -116963, -11343, -52080, -18879, -12865],115,2]
%
% END OF LATTICE L116.2
%
%
% LATTICE L116.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[569714187, -2454921, 189860895; -2454921, 10578, -818118; 189860895, -818118, 63272357],[651, 3, 1],[592, 77338, 5780, 15789, 2233088, 72206, 994812, 120249, 245995, 7415, 170879, 2227, 225, 865, -143, -1944, -144, 2222; -587, -76601, -5723, -15628, -2210145, -71463, -984560, -119007, -243443, -7337, -169043, -2201, -220, -651, 147, 1984, 147, -2201; -1784, -233058, -17418, -47580, -6729387, -217592, -2997855, -362369, -741303, -22345, -514941, -6711, -678, -2604, 431, 5859, 434, -6696],115,3]
%
% END OF LATTICE L116.3
%
%
% LATTICE L116.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1254313599, -5564097, -537605565; -5564097, 24682, 2384802; -537605565, 2384802, 230420641],[651, 7, 1],[-2384, -14850, -7772, -21239, -429168, -291422, -1338372, -69335, -330977, -29935, -32859, -3001, -307, -213, 551, 2520, 80, -2986; -1761, -10943, -5723, -15628, -315735, -214389, -984560, -51003, -243443, -22011, -24149, -2201, -220, -93, 441, 1984, 63, -2201; -5544, -34534, -18074, -49392, -998045, -677712, -3112431, -161241, -769699, -69615, -76415, -6979, -714, -496, 1281, 5859, 186, -6944],115,4]
%
% END OF LATTICE L116.4
%
%
% LATTICE L116.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[3247188, 1395744, -2604; 1395744, 599934, -1119; -2604, -1119, 2],[2604, 3, 1],[32, 4352, 329, 1817, 257613, 4167, 114877, 6948, 14234, 431, 10001, 134, 35, 741, 0, -53, -3, 119; -75, -10199, -771, -4258, -603694, -9765, -269204, -16282, -33356, -1010, -23436, -314, -82, -1736, 0, 124, 7, -279; -290, -39060, -2946, -16242, -2301936, -37232, -1026348, -62069, -127131, -3847, -89187, -1191, -306, -6510, -1, 372, 14, -1116],115,5]
%
% END OF LATTICE L116.5
%
%
% LATTICE L116.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[502941768, -762972, -125747160; -762972, 1144, 190764; -125747160, 190764, 31439719],[2604, 4, 1],[30515, 247327, 3893, 972, 33361, 1295, 163, -2587, -2577, 655, 74763, 6497, 19808, 2865449, 279235, 644017, 470137, 324667; 29097, 235879, 3715, 929, 31899, 1239, 155, -2478, -2480, 618, 71176, 6190, 18881, 2731596, 266196, 613955, 448203, 309535; 121872, 987784, 15548, 3882, 133238, 5172, 651, -10332, -10292, 2616, 298592, 25948, 79110, 11444146, 1115220, 2572101, 1877652, 1296668],115,6]
%
% END OF LATTICE L116.6
%
%
% LATTICE L116.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[540841035, 19768266, 183143226; 19768266, 721686, 6694065; 183143226, 6694065, 62017190],[651, 21, 1],[230, 150034, 98492, 314133, 6546587, 1491060, 20666499, 360052, 5245012, 166510, 588386, 68248, 19347, 99193, 9600, 9261, -2752, -76072; -2, -992, -650, -2071, -43152, -9828, -136214, -2373, -34565, -1097, -3875, -449, -127, -651, -63, -62, 18, 496; -679, -442959, -290787, -927444, -19328097, -4402195, -61015626, -1063015, -15485337, -491603, -1737147, -201495, -57120, -292857, -28343, -27342, 8125, 224595],115,7]
%
% END OF LATTICE L116.7
%
%
% LATTICE L116.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3221148, -1083264, 2604; -1083264, -364294, 875; 2604, 875, -2],[2604, 7, 1],[106, 686, 363, 2005, 40611, 13795, 126769, 3286, 15708, 1427, 1577, 148, 39, 123, 2, -41, -1, 133; -321, -2077, -1099, -6070, -122946, -41763, -383780, -9948, -47554, -4320, -4774, -448, -118, -372, -6, 124, 3, -403; -2499, -15965, -8421, -46396, -939238, -319011, -2931236, -75969, -363041, -32949, -36363, -3395, -868, -2666, -21, 868, 9, -3255],115,8]
%
% END OF LATTICE L116.8
%
%
% LATTICE L116.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[6372142287, 1414623, -615807591; 1414623, 310, -136710; -615807591, -136710, 59512009],[651, 31, 1],[-5779, -8109, -18781, -51286, -233967, -703555, -104226, -1171627, -25771, -72233, -17895, -7223, -722, -69, 1447, 210, 1447, -233; -48, -70, -164, -453, -2072, -6234, -924, -10395, -229, -645, -161, -67, -9, -7, -3, 0, 0, -2; -59799, -83909, -194339, -530689, -2421006, -7280133, -1078493, -12123573, -266669, -747441, -185171, -74741, -7471, -714, 14973, 2173, 14973, -2411],115,9]
%
% END OF LATTICE L116.9
%
%
% LATTICE L116.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1473306744, -1403556, -368692548; -1403556, 1320, 351240; -368692548, 351240, 92264693],[2604, 12, 1],[-3895, -428367, -30503, -80147, -11238931, -362765, -2494733, -601576, -1224558, -36340, -818918, -9732, -323, 13366, 650, 163, -1949, -22727; -2244, -246946, -17588, -46221, -6481790, -209218, -1438803, -346955, -706273, -20961, -472409, -5617, -189, 7595, 373, 93, -1120, -13082; -15556, -1710828, -121824, -320094, -44886450, -1448824, -9963555, -2402596, -4890684, -145136, -3270624, -38868, -1290, 53382, 2596, 651, -7784, -90768],115,10]
%
% END OF LATTICE L116.10
%
%
% LATTICE L116.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-643188, 5208, -2604; 5208, -42, 21; -2604, 21, -10],[2604, 21, 1],[-13, -43, -4, -1, -3, 0, 1, 0, -4, -1, -19, -10, -55, -1113, -126, -3473, -30, -430; -1655, -5487, -515, -136, -434, -3, 124, 1, -465, -123, -2387, -1263, -6976, -141298, -15999, -441068, -3811, -54653; -301, -1023, -105, -42, -186, -7, 0, 2, 0, -14, -372, -210, -1218, -24924, -2828, -78120, -677, -9765],115,11]
%
% END OF LATTICE L116.11
%
%
% LATTICE L116.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[91039845603, -6921432, 30149670558; -6921432, -186, -2292171; 30149670558, -2292171, 9984668018],[651, 93, 1],[3470, 394046, 1143560, 3643777, 17144061, 17291892, 7731047, 29226402, 1961810, 1930172, 1539596, 790082, 223507, 258717, 110886, 3521, -221772, -28168; 1, -7, -23, -78, -371, -375, -168, -637, -43, -43, -35, -19, -6, -7, -3, 0, 7, 1; -10478, -1189860, -3453090, -11002737, -51768150, -52214540, -23344644, -88251947, -5923875, -5828341, -4648959, -2385729, -674901, -781221, -334831, -10632, 669662, 85056],115,12]
%
% END OF LATTICE L116.12
%
%
% LATTICE L116.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2113088712, -2762844, -528953124; -2762844, 3640, 691600; -528953124, 691600, 132408737],[2604, 28, 1],[-55273, -334881, -174267, -475005, -9594049, -6514159, -14957105, -1549534, -7395232, -668450, -733472, -66974, -7477, -21128, 652, 163, -1301, -83239; -10605, -64263, -33443, -91160, -1841245, -1250169, -2870507, -297381, -1419273, -128289, -140771, -12855, -1436, -4061, 123, 31, -249, -15965; -220752, -1337464, -695996, -1897098, -38317178, -26016564, -59736411, -6188604, -29535436, -2669688, -2929376, -267484, -29862, -84382, 2604, 651, -5196, -332444],115,13]
%
% END OF LATTICE L116.13
%
%
% LATTICE L116.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[466116, -23436, -10416; -23436, 1178, 527; -10416, 527, 202],[2604, 31, 1],[2, -16, -49, -325, -1541, -2335, -697, -3961, -89, -266, -72, -39, -27, -43, -41, -7, 1, 1; 39, -301, -923, -6126, -29050, -44019, -13140, -74676, -1678, -5016, -1358, -736, -510, -812, -774, -132, 21, 19; 0, -42, -124, -806, -3808, -5766, -1720, -9765, -219, -651, -175, -93, -62, -98, -93, -16, 0, 2],115,14]
%
% END OF LATTICE L116.14
%
%
% LATTICE L116.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[8117979765, 3152142, 3513581757; 3152142, -434, 1366449; 3513581757, 1366449, 1520727370],[651, 217, 1],[6206, 33558, 681720, 2172195, 1460033, 30925076, 4608773, 7466990, 1169510, 3451948, 131116, 470998, 133241, 22033, 198310, 2099, -56660, -16792; -18615, -100675, -2045183, -6516663, -4380152, -92776353, -13826487, -22401243, -3508573, -10355973, -393353, -1413013, -399729, -66100, -594939, -6297, 169983, 50377; -14322, -77444, -1573250, -5012917, -3369414, -71367828, -10635968, -17232063, -2698955, -7966287, -302585, -1086953, -307489, -50847, -457653, -4844, 130758, 38752],115,15]
%
% END OF LATTICE L116.15
%
%
% LATTICE L116.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[3400824, -44268, -851508; -44268, 11256, 11088; -851508, 11088, 213203],[2604, 84, 1],[133811, 443815, 41727, 5626, 19513, 659, 163, 1, 38467, 9941, 192801, 102025, 281878, 5710031, 1293109, 8912461, 308039, 4417845; -215, -713, -67, -9, -31, -1, 0, 0, -62, -16, -310, -164, -453, -9176, -2078, -14322, -495, -7099; 534436, 1772580, 166656, 22470, 77934, 2632, 651, 4, 153636, 39704, 770040, 407484, 1125810, 22805646, 5164628, 35596029, 1230296, 17644704],115,16]
%
% END OF LATTICE L116.16
%
%
% LATTICE L116.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3152316468, -393878436, 908796; -393878436, -49214670, 113553; 908796, 113553, -262],[2604, 93, 1],[0, -20, -59, -383, -1809, -913, -817, -1546, -104, -103, -83, -44, -29, -45, -14, -7, 1, 1; -1, 175, 519, 3380, 15974, 8063, 7216, 13657, 919, 911, 735, 391, 260, 406, 127, 64, -7, -9; -434, 6468, 20274, 136338, 648060, 327484, 293400, 556171, 37539, 37541, 30639, 16833, 12090, 19866, 6479, 3456, 434, -432],115,17]
%
% END OF LATTICE L116.17
%
%
% LATTICE L116.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[3192504, 1486884, -796824; 1486884, 682744, -371132; -796824, -371132, 198881],[2604, 124, 1],[4285, 8021, 19779, 56651, 261063, 786655, 58384, 1316494, 29124, 83090, 21104, 9346, 1599, 1062, -280, -134, -5869, 1; -30, -56, -138, -395, -1820, -5484, -407, -9177, -203, -579, -147, -65, -11, -7, 3, 1, 42, 0; 17112, 32032, 78988, 226238, 1042566, 3141540, 233159, 5257476, 116308, 331824, 84280, 37324, 6386, 4242, -1116, -535, -23436, 4],115,18]
%
% END OF LATTICE L116.18
%
%
% LATTICE L116.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[22745381538999, -40241699464050, -13387023162009; -40241699464050, 71196623937579, 23684657119431; -13387023162009, 23684657119431, 7879067178197],[651, 651, 1],[-16, -10, -164, -453, -296, -2078, -924, -495, -229, -215, -23, -67, -9, -1, -1, 0, 0, -2; 3215479, 1933757, 31351403, 85613602, 55795839, 391491479, 173989022, 93135713, 43020773, 40194237, 4267631, 12058313, 1205830, 16653, -804035, -350158, -114893, 388943; -9665831, -5812935, -94243317, -257357226, -167724078, -1176835919, -523016571, -279968936, -129321822, -120825166, -12828636, -36247680, -3624768, -50061, 2416946, 1052583, 345371, -1169175],115,19]
%
% END OF LATTICE L116.19
%
%
% LATTICE L116.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-111542340, 27805512, -302064; 27805512, -6931414, 75299; -302064, 75299, -818],[2604, 217, 1],[4, 4, 79, 499, 335, 3547, 1057, 856, 134, 395, 15, 54, 33, 7, 44, 7, -1, -1; 9, 17, 343, 2196, 1478, 15657, 4668, 3783, 593, 1755, 67, 245, 156, 34, 219, 36, -3, -5; -651, 87, 2387, 17794, 12290, 130851, 39200, 31992, 5082, 15624, 626, 2604, 2170, 544, 3906, 728, 93, -91],115,20]
%
% END OF LATTICE L116.20
%
%
% LATTICE L116.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[54430729752, -156680076, -13628398560; -156680076, 465000, 39229632; -13628398560, 39229632, 3412286555],[2604, 372, 1],[-134809, -1076517, -2827729, -8562964, -39929129, -40201677, -8971786, -67666201, -4520979, -4388775, -3447067, -1695855, -484204, -783127, -510579, -75382, -187559, -2605; -724, -5782, -15188, -45993, -214466, -215930, -48189, -363447, -24283, -23573, -18515, -9109, -2601, -4207, -2743, -405, -1008, -14; -538408, -4299456, -11293548, -34199262, -159471270, -160559788, -35832039, -270249196, -18056148, -17528144, -13767096, -6773004, -1933842, -3127698, -2039180, -301065, -749084, -10404],115,21]
%
% END OF LATTICE L116.21
%
%
% LATTICE L116.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2604, 1372308, -2604; 1372308, -716017974, 1358637; -2604, 1358637, -2578],[2604, 651, 1],[190, 22, 83, 57, 13, 29, 15, 0, -2, -1, 5, 106, 699, 473, 1672, 1497, 405, 191; -42, -4, -6, 10, 4, 12, 8, 1, -1, -7, -3, -43, -206, -130, -453, -400, -106, -48; -22351, -2133, -3255, 5208, 2094, 6293, 4200, 527, -525, -3689, -1587, -22785, -109368, -69054, -240653, -212520, -56327, -25515],115,22]
%
% END OF LATTICE L116.22
%
%
% LATTICE L116.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1105403208, 17709804, 263488344; 17709804, 341992, 4177684; 263488344, 4177684, 62838911],[2604, 868, 1],[-183209, -61949, -1118379, -3334382, -2214025, -46781537, -3477888, -11231261, -1747759, -5062045, -187825, -630039, -162454, -33941, -425749, -18948, -8569, -659; 548796, 185566, 3350064, 9988021, 6632032, 140132406, 10417888, 33642837, 5235349, 15163173, 562623, 1887259, 486625, 101669, 1275315, 56758, 25668, 1974; 731724, 247420, 4466728, 13317290, 8842662, 186842208, 13890443, 44856876, 6980428, 20217456, 750160, 2516332, 648830, 135558, 1700412, 75677, 34224, 2632],115,23]
%
% END OF LATTICE L116.23
%
%
% LATTICE L116.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[67704, -35276388, 8832768; -35276388, 18381974520, -4602616872; 8832768, -4602616872, 1152437789],[2604, 2604, 1],[-51309, -5699, -18977, -4744, -957, -3865, -493, -25, -17, -1933, -1907, -34265, -101740, -67497, -475313, -105991, -114065, -53225; 80968, 8994, 29956, 7489, 1508, 6078, 772, 31, 21, 3039, 3007, 54051, 160525, 106501, 749985, 167242, 179984, 83986; 323764, 35964, 119784, 29946, 6030, 24304, 3087, 124, 84, 12152, 12024, 216132, 641886, 425862, 2998940, 668745, 719696, 335832],115,24]
%
% END OF LATTICE L116.24
%

\medskip%
%------------------------------WEYL-GROUP-W117--------------------------------
%
\leavevmode\llap{}%
$W_{117}$%
\qquad\llap{24} lattices, $\chi=104$%
\hfill%
$62222222226222222222\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L117.1
%
\leavevmode%
${L_{117.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}53\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{2\rightarrow N_{117}}%
\EasyButWeakLineBreak%
{${2}\above{1pt}{1pt}{}{6}{6}\above{1pt}{1pt}{b}{2}{1060}\above{1pt}{1pt}{*}{2}{4}\above{1pt}{1pt}{b}{2}{1590}\above{1pt}{1pt}{s}{2}{2}\above{1pt}{1pt}{l}{2}{636}\above{1pt}{1pt}{r}{2}{10}\above{1pt}{1pt}{b}{2}{106}\above{1pt}{1pt}{l}{2}{60}\above{1pt}{1pt}{r}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4060860\\810900\\-3180
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
810900\\161926\\-635
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3180\\-635\\2
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-23937769\\119905080\\8000880
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-4777812\\23932219\\1596920
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-16605\\83175\\5549
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
221\\-1107\\-73
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1217\\-6096\\-405
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
74701\\-374180\\-24910
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2103\\-10534\\-702
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
525817\\-2633835\\-175695
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
16605\\-83175\\-5549
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1408231\\-7053876\\-470640
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
48709\\-243985\\-16280
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
117014\\-586127\\-39114
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
39301\\-196860\\-13140
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[4060860, 810900, -3180; 810900, 161926, -635; -3180, -635, 2],[3180, 1, 1],[221, 1217, 74701, 2103, 525817, 16605, 1408231, 48709, 117014, 39301, 3100, 2104, 42641, 111, 2222, 0, -127, -1, 328, 551; -1107, -6096, -374180, -10534, -2633835, -83175, -7053876, -243985, -586127, -196860, -15528, -10539, -213590, -556, -11130, 0, 636, 5, -1643, -2760; -73, -405, -24910, -702, -175695, -5549, -470640, -16280, -39114, -13140, -1037, -705, -14310, -38, -795, -1, 0, 0, -106, -180],116,1]
%
% END OF LATTICE L117.1
%
%
% LATTICE L117.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-141510, -46905, 18285; -46905, -15547, 6095; 18285, 6095, 4834],[795, 1, 1],[-75449, -54019, -573316, -2372, -166319, -2021, -33211, 352, 3696, -1051, -3073, -24503, -813906, -23802, -12318679, -390589, -16613453, -1152008, -2778140, -470081; 227206, 162672, 1726475, 7143, 500850, 6086, 100011, -1060, -11130, 3165, 9254, 73788, 2450985, 71677, 37096290, 1176214, 50029509, 3469140, 8366050, 1415595; -1081, -774, -8215, -34, -2385, -29, -477, 5, 53, -15, -44, -351, -11660, -341, -176490, -5596, -238023, -16505, -39803, -6735],116,2]
%
% END OF LATTICE L117.2
%
%
% LATTICE L117.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-24828840570, 95290290, -8276691735; 95290290, -365709, 31765008; -8276691735, 31765008, -2759034433],[795, 3, 1],[-35474, -70507, -6606218, -187607, -31508804, -2987770, -42259765, -8774909, -21098027, -1183001, -562027, -128660, -3949633, -11560, -158749, 265, 36361, 11561, -13675, -12001; 35637, 70834, 6636925, 188480, 31655575, 3001689, 42456657, 8815795, 21196343, 1188515, 564648, 129261, 3968110, 11615, 159530, -264, -36517, -11615, 13727, 12055; 106827, 212326, 19894080, 564963, 94886165, 8997423, 127261798, 26424915, 63534969, 3562510, 1692498, 387449, 11893995, 34812, 478060, -798, -109498, -34815, 41181, 36140],116,3]
%
% END OF LATTICE L117.3
%
%
% LATTICE L117.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-41818706070, 159653490, 8363327655; 159653490, -609515, -31929120; 8363327655, -31929120, -1672582823],[795, 5, 1],[21434, 127801, 798290, 113351, 11422420, 1805186, 76598983, 1060345, 12747243, 428855, 339571, 233204, 477261, 6984, 57539, -161, -65923, -1397, 8267, 4351; 35637, 212502, 1327385, 188480, 18993345, 3001689, 127369971, 1763159, 21196343, 713109, 564648, 387783, 793622, 11615, 95718, -264, -109551, -2323, 13727, 7233; 106495, 634980, 3966308, 563185, 56752347, 8969075, 380582400, 5268329, 63334735, 2130768, 1687160, 1158675, 2371273, 34700, 285882, -800, -327540, -6941, 41075, 21618],116,4]
%
% END OF LATTICE L117.4
%
%
% LATTICE L117.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[10406395423380, 24489405780, 107862420; 24489405780, 57631002, 253833; 107862420, 253833, 1118],[3180, 3, 1],[6719, 1523, 92761, 247, 1729, 7, 1, -1, 680, 387, 472, 874, 161321, 4547, 379394, 35948, 1016327, 105469, 253402, 28377; -2854622, -647059, -39410270, -104940, -734580, -2974, -424, 425, -288903, -164420, -200533, -371326, -68538540, -1931830, -161188635, -15272801, -431794816, -44809365, -107659907, -12056200; -116583, -26422, -1609080, -4278, -29945, -123, -212, -15, -11925, -6740, -8202, -15173, -2799990, -78912, -6583660, -623802, -17636068, -1830165, -4397145, -492400],116,5]
%
% END OF LATTICE L117.5
%
%
% LATTICE L117.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[900496351335, -14350058460, 297306520470; -14350058460, 228678555, -4737793710; 297306520470, -4737793710, 98158273471],[795, 15, 1],[-546565, -1138209, -21642194, -3095506, -104751357, -49707953, -703556187, -29232824, -351730012, -3951067, -9422285, -2184741, -13581076, -227444, -918453, -136297, -909213, -9136, -502688, -36473; -3159, -6576, -125027, -17882, -605101, -287139, -4064093, -168863, -2031755, -22823, -54426, -12619, -78440, -1313, -5300, -786, -5247, -53, -2915, -211; 1655310, 3447145, 65544888, 9374955, 317246764, 150543990, 2130768805, 88533639, 1065238785, 11966081, 28536045, 6616640, 41131233, 688830, 2781599, 412785, 2753615, 27669, 1522425, 110461],116,6]
%
% END OF LATTICE L117.6
%
%
% LATTICE L117.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1024793160, -1605900, -256199880; -1605900, 2504, 401480; -256199880, 401480, 64050367],[3180, 4, 1],[3999, 27154, 873076, 25147, 12834659, 406291, 8630003, 1195703, 2879069, 242843, 77418, 54263, 565291, 1992, 110644, 794, 199, -1587, -2335, 1408; 3173, 21579, 694035, 19993, 10205415, 323065, 6862281, 950790, 2289388, 193110, 61567, 43161, 449705, 1587, 88245, 635, 159, -1270, -1908, 1110; 15976, 108480, 3487930, 100462, 51274320, 1623128, 34476765, 4776820, 11501848, 970155, 309284, 216780, 2258330, 7958, 442020, 3172, 795, -6340, -9328, 5625],116,7]
%
% END OF LATTICE L117.7
%
%
% LATTICE L117.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-571328340, -12720, 340260; -12720, 10, 5; 340260, 5, -202],[3180, 5, 1],[-1, 1, 83, 17, 1171, 191, 16601, 117, 1448, 103, 46, 44, 235, 13, 260, 34, 2479, 15, 142, 5; -425, 426, 35192, 7206, 496239, 80939, 7034796, 49579, 613581, 43644, 19490, 18639, 99534, 5504, 110028, 14386, 1048764, 6345, 60049, 2112; -1695, 1695, 140662, 28810, 1984479, 323685, 28133460, 198278, 2453900, 174552, 77955, 74565, 398242, 22030, 440589, 57615, 4200780, 25418, 240620, 8472],116,8]
%
% END OF LATTICE L117.8
%
%
% LATTICE L117.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-40712668680, 2745996780, 10188815400; 2745996780, -182773896, -687219312; 10188815400, -687219312, -2549868691],[3180, 12, 1],[-145522700, -31454427, -916686687, -1052752, 12262114, 2026700, 1285394, -3980961, -42434917, -3893197, -14272069, -21810496, -1906354232, -52212171, -8481384871, -801000545, -5647367232, -2339675651, -5603646921, -155901572; -456021, -98568, -2872600, -3299, 38425, 6351, 4028, -12475, -132977, -12200, -44724, -68347, -5973895, -163616, -26577910, -2510076, -17697018, -7331785, -17560013, -488545; -581359560, -125659652, -3662140470, -4205718, 48986840, 8096616, 5135117, -15903840, -169526436, -15553225, -57016560, -87132388, -7615837650, -208586322, -33882921200, -3199977216, -22561091357, -9346945920, -22386429804, -622822895],116,9]
%
% END OF LATTICE L117.9
%
%
% LATTICE L117.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-502896302970, 23333250, -66454276575; 23333250, -1007, 3083328; -66454276575, 3083328, -8781474131],[795, 53, 1],[-263769, -1572844, -926859, -1395044, -13262281, -22217149, -17787455, -65250541, -2960109, -26390557, -4179270, -2870195, -554154, -85969, -66836, 1954, 15299, 85969, -1917, -267677; -166, -999, -590, -889, -8460, -14174, -11349, -41635, -1889, -16845, -2669, -1836, -355, -56, -45, -1, 9, 55, -1, -165; 1996086, 11902581, 7014055, 10557070, 100363020, 168129462, 134607516, 493786955, 22400783, 199711950, 31626849, 21720354, 4193590, 650575, 505785, -14787, -115776, -650575, 14507, 2025660],116,10]
%
% END OF LATTICE L117.10
%
%
% LATTICE L117.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-233707740, -3498000, 219420; -3498000, -52230, 3285; 219420, 3285, -206],[3180, 15, 1],[29, 64, 2457, 353, 5993, 2845, 80559, 1674, 20149, 453, 541, 126, 1571, 27, 49, 5, 1, -2, -9, 3; -191, -420, -16112, -2314, -39273, -18643, -527880, -10969, -132023, -2968, -3544, -825, -10282, -176, -318, -32, 0, 13, 53, -20; 27840, 61465, 2359878, 339060, 5756542, 2732760, 77381060, 1607967, 19354275, 435136, 519675, 121040, 1509228, 25950, 47117, 4815, 1060, -1923, -8745, 2876],116,11]
%
% END OF LATTICE L117.11
%
%
% LATTICE L117.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[929734202280, -1467992940, -232726611420; -1467992940, 2317880, 367460960; -232726611420, 367460960, 58255010443],[3180, 20, 1],[-1587, -1592, -779366, -168735, -24675599, -4044839, -88223143, -2494077, -31005623, -556025, -1010808, -1010803, -2797763, -168730, -7518562, -1017136, -19090727, -475615, -4765667, -51412; -1, 3, -53, -13, -2067, -341, -7473, -212, -2650, -48, -89, -93, -265, -17, -795, -109, -2067, -52, -530, -6; -6340, -6360, -3113538, -674090, -98578092, -16158980, -352448145, -9963744, -123866300, -2221299, -4038140, -4038120, -11176958, -674070, -30036372, -4063420, -76266735, -1900064, -19038660, -205389],116,12]
%
% END OF LATTICE L117.12
%
%
% LATTICE L117.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[370736608462815, 4399122960, 123244921071840; 4399122960, 52311, 1462411722; 123244921071840, 1462411722, 40970625029407],[795, 159, 1],[21684123, 45139089, 80963384, 122745806, 391843327, 1970981823, 526354321, 5795553526, 263139394, 783308989, 373591281, 86619379, 50795084, 9012662, 3432077, 5395197, 679551, 1819066, 377542, 7241819; 40, 79, 140, 211, 670, 3368, 899, 9895, 449, 1335, 635, 146, 85, 14, 5, 7, 1, 5, 1, 15; -65228637, -135784198, -243548295, -369235206, -1178715235, -5928967377, -1583341643, -17433772035, -791557215, -2356294405, -1123810728, -260562257, -152798160, -27111249, -10324130, -16229448, -2044177, -5471985, -1135695, -21784325],116,13]
%
% END OF LATTICE L117.13
%
%
% LATTICE L117.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[3180, 0, -3180; 0, -106, -583; -3180, -583, -26],[3180, 53, 1],[-46, -430, -553, -867, -4276, -7194, -11557, -21251, -968, -17399, -1403, -1019, -413, -99, -71, -51, -35, -1, 2, 11; 253, 2364, 3040, 4766, 23505, 39545, 63528, 116815, 5321, 95640, 7712, 5601, 2270, 544, 390, 280, 192, 5, -11, -60; -53, -477, -610, -954, -4695, -7897, -12684, -23320, -1062, -19080, -1537, -1113, -450, -106, -75, -53, -36, 0, 2, 0],116,14]
%
% END OF LATTICE L117.14
%
%
% LATTICE L117.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1547825892360, 197939100, -387445243860; 197939100, 25320, -49547280; -387445243860, -49547280, 96983658001],[3180, 60, 1],[-187947, -370342, -6946486, -986917, -33188793, -15737535, -111310048, -9245851, -111167497, -623514, -2964318, -680413, -4191517, -63838, -225216, -23790, -69982, -793, -212533, -6939; -778, -1525, -28567, -4056, -136316, -64634, -457125, -37969, -456489, -2560, -12167, -2790, -17172, -259, -901, -91, -265, -3, -901, -29; -750840, -1479500, -27750906, -3942690, -132587768, -62870760, -444678745, -36936768, -444109260, -2490911, -11842320, -2718220, -16744926, -255030, -899728, -95040, -279575, -3168, -849060, -27721],116,15]
%
% END OF LATTICE L117.15
%
%
% LATTICE L117.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[314576275306110, -5231433105, 63156672641580; -5231433105, 87185, -1050301530; 63156672641580, -1050301530, 12679803317321],[795, 265, 1],[15573499, 97256443, 11629552, 88155822, 168852713, 1415555679, 1134080243, 832471270, 188986250, 337542683, 268312601, 186629657, 7296188, 6472878, 1478947, 3874821, 1464157, 261290, 271150, 3120637; -46720457, -291769092, -34888628, -264467255, -506557737, -4246663669, -3402238032, -2497411831, -566958301, -1012627248, -804937168, -559888533, -21888547, -19418620, -4436838, -11624456, -4392468, -783869, -813449, -9361902; -77573715, -484447560, -57928379, -439116130, -841078311, -7051075215, -5649007815, -4146652531, -941366195, -1681345977, -1336501530, -929627685, -36343304, -32242285, -7366836, -19301010, -7293165, -1301521, -1350635, -15544317],116,16]
%
% END OF LATTICE L117.16
%
%
% LATTICE L117.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[393261060, 157473600, 368880; 157473600, 63057174, 147711; 368880, 147711, 346],[3180, 159, 1],[-1966, -477, -581, -141, -34, -74, -17, -2, 3, 9, -62, -199, -771, -1211, -1994, -10066, -5391, -29742, -1355, -8121; 4638, 1125, 1370, 332, 80, 174, 40, 5, -7, -20, 147, 470, 1820, 2858, 4705, 23751, 12720, 70175, 3197, 19160; 115911, 28249, 34530, 8586, 2095, 4611, 1048, 0, -210, -1060, 3339, 11501, 44970, 70914, 117155, 591639, 316952, 1749000, 79710, 478060],116,17]
%
% END OF LATTICE L117.17
%
%
% LATTICE L117.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-21198097595234910, 56395015288759485, 18754065600479775; 56395015288759485, -150032225067883590, -49892959097572185; 18754065600479775, -49892959097572185, -16591817967011413],[795, 795, 1],[-166, -333, -118, -889, -564, -14174, -3783, -8327, -1889, -1123, -2669, -612, -71, -56, -3, -1, 3, 11, -1, -11; -1404168075, -2790998556, -986822069, -7426481044, -4706760757, -118272420087, -31563685991, -69471914299, -15758063831, -9365963185, -22248235410, -5093135939, -590004830, -457653451, -23719940, 10402662, 27148011, 91530743, -10205159, -94998209; 4222448520, 8392761470, 2967454863, 22332037335, 14153615464, 355654863360, 94914591415, 208907741712, 47385789810, 28164219133, 66902267820, 15315477310, 1774192893, 1376201445, 71327804, -31281660, -81636295, -275240448, 30687750, 285667403],116,18]
%
% END OF LATTICE L117.18
%
%
% LATTICE L117.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[45518520, -5561820, -11374860; -5561820, 679672, 1389872; -11374860, 1389872, 2842523],[3180, 212, 1],[5731, 39002, 23726, 36269, 349859, 587095, 235328, 1728279, 78533, 351214, 112070, 78799, 15541, 2998, 3544, 1910, 274, -531, 1, 2189; 77, 519, 315, 481, 4635, 7777, 3117, 22890, 1040, 4650, 1483, 1041, 205, 39, 45, 23, 3, -10, 0, 30; 22896, 155820, 94790, 144902, 1397760, 2345568, 940185, 6904840, 313756, 1403175, 447744, 314820, 62090, 11978, 14160, 7632, 1095, -2120, 4, 8745],116,19]
%
% END OF LATTICE L117.19
%
%
% LATTICE L117.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-445158660, 129426000, -143100; 129426000, -37629470, 41605; -143100, 41605, -46],[3180, 265, 1],[-5, -2, 1, 13, 17, 147, 241, 90, 21, 79, 35, 32, 3, 7, 1, 3, -1, -2, -1, -7; -21, -6, 4, 50, 63, 543, 888, 331, 77, 288, 126, 111, 10, 20, 0, -18, -48, -23, -7, -36; -3445, 795, 506, 4770, 4077, 33655, 53160, 19292, 4290, 14628, 5035, 795, -294, -3710, -3123, -25705, -40440, -14628, -3230, -10812],116,20]
%
% END OF LATTICE L117.20
%
%
% LATTICE L117.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[20209542360, -129937980, -5058391020; -129937980, 825528, 32523132; -5058391020, 32523132, 1266100897],[3180, 636, 1],[-7898512, -1817631, -1057421, -172174, -46338, -1592, 5793, 212531, 799, -71308, -471389, -972336, -1732546, -2617793, -8323563, -41847913, -5585727, -122971079, -5580733, -8298593; -79213, -18229, -10605, -1727, -465, -17, 58, 2130, 8, -715, -4727, -9751, -17375, -26253, -83475, -419683, -56018, -1233250, -55968, -83225; -31554504, -7261424, -4224390, -687834, -185120, -6360, 23143, 849060, 3192, -284875, -1883196, -3884476, -6921510, -10458066, -33252580, -167182140, -22314943, -491268660, -22294992, -33152825],116,21]
%
% END OF LATTICE L117.21
%
%
% LATTICE L117.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-32719020, 36471420, -76320; 36471420, -40651530, 85065; -76320, 85065, -178],[3180, 795, 1],[554, 135, 33, 41, 2, 22, 5, 0, -1, -1, 16, 55, 43, 339, 112, 2828, 1515, 1672, 381, 457; 1564, 383, 94, 120, 6, 68, 16, 1, -3, -4, 41, 152, 120, 950, 315, 7957, 4264, 4707, 1073, 1288; 509595, 125080, 30756, 39750, 2009, 23055, 5500, 477, -1005, -1484, 12720, 49025, 38886, 308460, 102454, 2588520, 1387340, 1531647, 349215, 419336],116,22]
%
% END OF LATTICE L117.22
%
%
% LATTICE L117.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[15107931960, 34544340, 3755824860; 34544340, 103880, 8569040; 3755824860, 8569040, 933710311],[3180, 1060, 1],[-207225, 796, -17136, -206827, -682249, -6006341, -2497262, -3769903, -895053, -870146, -1657800, -1865821, -107199, -414848, -436766, -3318784, -1232788, -1700837, -348297, -248869; 620768, -2385, 51333, 619576, 2043762, 17992744, 7480860, 11293215, 2681243, 2606631, 4966147, 5589300, 321128, 1242729, 1308387, 9941831, 3692970, 5095069, 1043367, 745518; 827860, -3180, 68458, 826270, 2725572, 23995220, 9976515, 15060692, 3575720, 3476217, 6622880, 7453920, 428258, 1657310, 1744872, 13258480, 4924965, 6794812, 1391440, 994227],116,23]
%
% END OF LATTICE L117.23
%
%
% LATTICE L117.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[756840, -254345940, 63666780; -254345940, 85587607560, -21423920760; 63666780, -21423920760, 5362743437],[3180, 3180, 1],[-31607, -7502, -898, -957, -89, -955, -66, -95, -9, -32, -1438, -3513, -1305, -10058, -6520, -164270, -21964, -96837, -22021, -6577; 5727950, 1359287, 162681, 173128, 16068, 171934, 11851, 16875, 1607, 5824, 261085, 637058, 236588, 1823217, 1181739, 29773241, 3980839, 17550961, 3991083, 1191983; 22883280, 5430380, 649914, 691650, 64192, 686880, 47345, 67416, 6420, 23267, 1043040, 2545060, 945174, 7283790, 4721072, 118944720, 15903535, 70116456, 15944460, 4761997],116,24]
%
% END OF LATTICE L117.24
%

\medskip%
%------------------------------WEYL-GROUP-W118--------------------------------
%
\leavevmode\llap{}%
$W_{118}$%
\qquad\llap{48} lattices, $\chi=36$%
\hfill%
$2222222222$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L118.1
%
\leavevmode%
${L_{118.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{2}{}7\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}11\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{2\rightarrow N_{118}}%
\EasyButWeakLineBreak%
{${60}\above{1pt}{1pt}{r}{2}{22}\above{1pt}{1pt}{b}{2}{4}\above{1pt}{1pt}{*}{2}{1540}\above{1pt}{1pt}{b}{2}{6}\above{1pt}{1pt}{b}{2}{110}\above{1pt}{1pt}{s}{2}{42}\above{1pt}{1pt}{b}{2}{10}\above{1pt}{1pt}{l}{2}{924}\above{1pt}{1pt}{r}{2}{2}\above{1pt}{1pt}{l}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
8560860\\-1714020\\-4620
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1714020\\343174\\925
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-4620\\925\\2
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-829\\-4140\\-240
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-663\\-3311\\-187
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-497\\-2482\\-138
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-22357\\-111650\\-6160
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-331\\-1653\\-90
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-826\\-4125\\-220
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-164\\-819\\-42
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\5\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
185\\924\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\-1
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[8560860, -1714020, -4620; -1714020, 343174, 925; -4620, 925, 2],[4620, 1, 1],[-829, -663, -497, -22357, -331, -826, -164, 1, 185, 0; -4140, -3311, -2482, -111650, -1653, -4125, -819, 5, 924, 0; -240, -187, -138, -6160, -90, -220, -42, 0, 0, -1],117,1]
%
% END OF LATTICE L118.1
%
%
% LATTICE L118.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[54285, -25410, -1155; -25410, 11894, 539; -1155, 539, -38],[1155, 1, 1],[7, -180, 101, 11521, 728, 5066, 3898, 2644, 28837, 144; 15, -385, 216, 24640, 1557, 10835, 8337, 5655, 61677, 308; 0, 11, -7, -770, -48, -330, -252, -170, -1848, -9],117,2]
%
% END OF LATTICE L118.2
%
%
% LATTICE L118.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-118750170, 21357105, -39548355; 21357105, -3840738, 7112733; -39548355, 7112733, -13171117],[1155, 3, 1],[237419, 1147375, 432816, 19545671, 194246, 1477666, 103296, 10044, -24551, -1151; -2235, -10802, -4075, -184030, -1829, -13915, -973, -95, 231, 11; -714095, -3451008, -1301799, -58788345, -584242, -4444440, -310688, -30210, 73843, 3462],117,3]
%
% END OF LATTICE L118.3
%
%
% LATTICE L118.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-147639030, 30742635, -29497545; 30742635, -6401230, 6142225; -29497545, 6142225, -5893463],[1155, 5, 1],[85841, 691381, 260798, 2355459, 351122, 178062, 186688, 1208, -44393, -689; -1341, -10802, -4075, -36806, -5487, -2783, -2919, -19, 693, 11; -431043, -3471710, -1309575, -11827739, -1763130, -894124, -937440, -6066, 222915, 3460],117,4]
%
% END OF LATTICE L118.4
%
%
% LATTICE L118.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-179678730, 40128165, -51308565; 40128165, -8961722, 11458888; -51308565, 11458888, -14651533],[1155, 7, 1],[617632, 994871, 375269, 2420918, 505220, 1280986, 38368, 8674, -9128, -985; -6705, -10802, -4075, -26290, -5487, -13915, -417, -95, 99, 11; -2168145, -3492412, -1317351, -8498435, -1773534, -4496800, -134688, -30450, 32043, 3458],117,5]
%
% END OF LATTICE L118.5
%
%
% LATTICE L118.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-246336090, 58899225, -44762025; 58899225, -14082706, 10702648; -44762025, 10702648, -8133761],[1155, 11, 1],[397072, 58141, 241229, 990286, 324740, 74846, 172576, 5554, -3736, -625; -6705, -982, -4075, -16730, -5487, -1265, -2919, -95, 63, 11; -2194005, -321256, -1332903, -5471795, -1794342, -413560, -953568, -30690, 20643, 3454],117,6]
%
% END OF LATTICE L118.6
%
%
% LATTICE L118.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-216627180, -86661960, 69300; -86661960, -34669218, 27723; 69300, 27723, -22],[4620, 3, 1],[-399, -553, -233, -6451, 2, 417, 81, -2, -1229, -81; 1000, 1386, 584, 16170, -5, -1045, -203, 5, 3080, 203; 3280, 4587, 1962, 55440, -2, -3300, -658, 0, 9856, 657],117,7]
%
% END OF LATTICE L118.7
%
%
% LATTICE L118.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[7509698480130, -188961465, 2499162654450; -188961465, 4755, -62884740; 2499162654450, -62884740, 831699700051],[1155, 15, 1],[-433205, -10543235, -3997208, -36200492, -1807207, -2774439, -993667, -26435, 202053, 23976; -34014, -827871, -313879, -2842686, -141918, -217888, -78050, -2080, 15862, 1891; 1301729, 31681155, 12011130, 108778131, 5430440, 8336856, 2985850, 79434, -607145, -72045],117,8]
%
% END OF LATTICE L118.8
%
%
% LATTICE L118.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[3074877960, 3358740, -768712560; 3358740, 3656, -839680; -768712560, -839680, 192176407],[4620, 4, 1],[12427, 33535, 10989, 456427, 11575, 19707, -1135, -2307, 289, 1154; -9945, -26829, -8789, -364980, -9252, -15730, 924, 1850, -231, -925; 49665, 134024, 43918, 1824130, 46260, 78760, -4536, -9220, 1155, 4612],117,9]
%
% END OF LATTICE L118.9
%
%
% LATTICE L118.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[25728780, 8482320, 23100; 8482320, 2796470, 7615; 23100, 7615, 22],[4620, 5, 1],[-103, -69, -35, -661, -104, -207, -1033, -172, -21353, -103; 312, 209, 106, 2002, 315, 627, 3129, 521, 64680, 312; 156, 110, 60, 1078, 165, 319, 1575, 261, 32340, 155],117,10]
%
% END OF LATTICE L118.10
%
%
% LATTICE L118.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[7339842079185, -221034660, 2443187522160; -221034660, 6657, -73575033; 2443187522160, -73575033, 813255272258],[1155, 21, 1],[-3285479, -15992441, -6063194, -39222313, -2741310, -21042726, -215336, -200584, 43781, 36405; -170070, -827871, -313879, -2030490, -141918, -1089440, -11150, -10400, 2266, 1891; 9870245, 48044535, 18215064, 117831780, 8235451, 63216615, 646913, 602595, -131527, -109368],117,11]
%
% END OF LATTICE L118.11
%
%
% LATTICE L118.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-132783420, 53102280, 87780; 53102280, -21236474, -35105; 87780, -35105, -58],[4620, 7, 1],[587, 305, 155, 763, 38, -67, -11, 2, 215, 33; 1440, 748, 380, 1870, 93, -165, -27, 5, 528, 81; 16800, 8855, 4578, 22880, 1218, -1540, -306, 0, 5808, 917],117,12]
%
% END OF LATTICE L118.12
%
%
% LATTICE L118.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[3330773660445, -186643380, 1108388893920; -186643380, 10461, -62109729; 1108388893920, -62109729, 368841015754],[1155, 33, 1],[-4015407, -1776883, -7410410, -30505733, -3350462, -2338098, -1842408, -245272, 34049, 44541; -170070, -75261, -313879, -1292130, -141918, -99040, -78050, -10400, 1442, 1891; 12066505, 5339625, 22268664, 91671300, 10068311, 7026105, 5536531, 737055, -102319, -133848],117,13]
%
% END OF LATTICE L118.13
%
%
% LATTICE L118.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[7525301124495, -288937110, 1502372743410; -288937110, 11095, -57684235; 1502372743410, -57684235, 299938012154],[1155, 35, 1],[-1546001, -12542225, -4755118, -6152095, -6449696, -3300592, -506638, -31462, 103007, 28551; -102042, -827871, -313879, -406098, -425754, -217888, -33450, -2080, 6798, 1891; 7743813, 62823145, 23818060, 30815422, 32306085, 16532439, 2537715, 157591, -515955, -143010],117,14]
%
% END OF LATTICE L118.14
%
%
% LATTICE L118.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1864224807060, 21996009420, -24652320; 21996009420, 259531162, -290873; -24652320, -290873, 326],[4620, 11, 1],[569, 40, 323, 1307, 209, 46, 94, -1, 1, 3; -48180, -3387, -27350, -110670, -17697, -3895, -7959, 85, -84, -254; 39600, 2779, 22462, 91000, 14586, 3240, 6930, 220, 672, 231],117,15]
%
% END OF LATTICE L118.15
%
%
% LATTICE L118.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[329055591480, -177079980, -82311569340; -177079980, 95304, 44295648; -82311569340, 44295648, 20589817109],[4620, 12, 1],[-25686, -191632, -60606, -2494073, -20779, -118903, -5773, -13857, -63214, -11545; -13710, -102289, -32351, -1331330, -11092, -63470, -3080, -7390, -33726, -6161; -102655, -765864, -242214, -9967650, -83044, -475200, -23072, -55380, -252637, -46140],117,16]
%
% END OF LATTICE L118.16
%
%
% LATTICE L118.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[3046121159235, -230429430, 607839759450; -230429430, 17435, -45981155; 607839759450, -45981155, 121291686658],[1155, 55, 1],[-1784497, -1316115, -5488798, -4519043, -7444936, -346360, -4093946, -36334, 75659, 32991; -102042, -75261, -313879, -258426, -425754, -19808, -234150, -2080, 4326, 1891; 8942769, 6595535, 27506380, 22646582, 37309305, 1735737, 20516265, 182083, -379155, -165330],117,17]
%
% END OF LATTICE L118.17
%
%
% LATTICE L118.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2499420, -1057980, -18480; -1057980, -447630, -8115; -18480, -8115, 286],[4620, 15, 1],[389, 410, -371, -2573, 3, 1164, 2708, 1547, 67691, 1161; -908, -957, 866, 6006, -7, -2717, -6321, -3611, -158004, -2710; -628, -660, 600, 4158, -5, -1881, -4375, -2499, -109340, -1875],117,18]
%
% END OF LATTICE L118.18
%
%
% LATTICE L118.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[3081252186705, -274215480, 879180946875; -274215480, 24409, -78242549; 879180946875, -78242549, 250858771211],[1155, 77, 1],[-15187766, -2240278, -9342978, -5494479, -12672697, -2947853, -995525, -309237, 18398, 56157; -510210, -75261, -313879, -184590, -425754, -99040, -33450, -10400, 618, 1891; 53228175, 7851445, 32744096, 19256360, 44413677, 10331265, 3488991, 1083775, -64479, -196812],117,19]
%
% END OF LATTICE L118.19
%
%
% LATTICE L118.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-25431168840, 59750460, 6359351460; 59750460, -140360, -14941280; 6359351460, -14941280, -1590227773],[4620, 20, 1],[1448, 15083, 583, -27243, -12761, -18573, -67363, -8135, -196808, -10; 381, 3960, 152, -7161, -3351, -4873, -17661, -2131, -51513, 1; 5787, 60280, 2330, -108878, -51000, -74228, -269220, -32512, -786555, -40],117,20]
%
% END OF LATTICE L118.20
%
%
% LATTICE L118.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[78540, -32340, -4620; -32340, 13314, 1869; -4620, 1869, -178],[4620, 21, 1],[709, 1152, 617, 3183, 64, -67, -11, 2, 233, 110; 1740, 2827, 1514, 7810, 157, -165, -27, 5, 572, 270; -140, -231, -126, -660, -14, 0, 2, 0, -44, -21],117,21]
%
% END OF LATTICE L118.21
%
%
% LATTICE L118.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-240795994770870, -179916589545, -80134943541345; -179916589545, -134425830, -59874773910; -80134943541345, -59874773910, -26668255767647],[1155, 105, 1],[-215363962, -5203569293, -1962805689, -2532472388, -880833792, -1340013430, -66893344, -9073770, 15914334, 5152087; -447, -10802, -4075, -5258, -1829, -2783, -139, -19, 33, 11; 647143147, 15636108180, 5897998155, 7609778979, 2646801010, 4026581328, 201006560, 27265602, -47820685, -15481410],117,22]
%
% END OF LATTICE L118.22
%
%
% LATTICE L118.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[59771647320, -37482060, -14958030780; -37482060, 23576, 9380000; -14958030780, 9380000, 3743291257],[4620, 28, 1],[-117308, -285918, -88196, -508999, -85313, -141803, -1153, -13837, -37760, -18447; 26850, 65439, 20185, 116490, 19524, 32450, 264, 3170, 8646, 4223; -468825, -1142680, -352478, -2034230, -340956, -566720, -4608, -55300, -150909, -73724],117,23]
%
% END OF LATTICE L118.23
%
%
% LATTICE L118.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[56128380, 11189640, -50820; 11189640, 2230734, -10131; -50820, -10131, 46],[4620, 33, 1],[3, 2, 23, 107, 7, 6, 6, -1, -5, -3; -20, -12, -136, -630, -41, -35, -35, 5, 28, 17; -1100, -435, -4554, -20580, -1298, -1080, -1078, 0, 644, 429],117,24]
%
% END OF LATTICE L118.24
%
%
% LATTICE L118.25
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[30927790740, 9488934840, 23682120; 9488934840, 2911293770, 7265895; 23682120, 7265895, 18134],[4620, 35, 1],[683, 485, 267, 681, 727, 1400, 986, 1143, 20227, 678; -2184, -1551, -854, -2178, -2325, -4477, -3153, -3655, -64680, -2168; -16884, -11935, -6510, -16676, -17850, -34496, -24330, -28224, -499620, -16765],117,25]
%
% END OF LATTICE L118.25
%
%
% LATTICE L118.26
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-203944220100390, -207561537645, -67870953324405; -207561537645, -211240590, -69074766750; -67870953324405, -69074766750, -22586893136251],[1155, 165, 1],[-171207698, -376034759, -1560181617, -1280962316, -700100496, -96815458, -372053984, -7184442, 8054334, 4042631; -447, -982, -4075, -3346, -1829, -253, -973, -19, 21, 11; 514458967, 1129940160, 4688161995, 3849140883, 2103719530, 290919048, 1117978400, 21588402, -24202325, -12147630],117,26]
%
% END OF LATTICE L118.26
%
%
% LATTICE L118.27
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-75515664840, -621708780, 18895929360; -621708780, -3863992, 155565916; 18895929360, 155565916, -4728239459],[4620, 44, 1],[-3159472, -105191, 1830427, 12409573, 6813101, 2731483, 13088695, 3123347, -396776, -1665708; -13545, -451, 7847, 53200, 29208, 11710, 56112, 13390, -1701, -7141; -12626955, -420400, 7315374, 49595350, 27228828, 10916480, 52309488, 12482580, -1585731, -6657068],117,27]
%
% END OF LATTICE L118.27
%
%
% LATTICE L118.28
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-44301180, -22203720, 50820; -22203720, -11128370, 25465; 50820, 25465, -58],[4620, 55, 1],[23, 11, -1, -67, -155, -22, -964, -131, -1285, -32; -48, -23, 2, 140, 324, 46, 2016, 274, 2688, 67; -924, -460, 0, 2758, 6435, 919, 40425, 5511, 54180, 1375],117,28]
%
% END OF LATTICE L118.28
%
%
% LATTICE L118.29
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-278251083895785, -286862399670, -92620560609885; -286862399670, -295736826, -95486982129; -92620560609885, -95486982129, -30830313857474],[1155, 231, 1],[-1182963807, -519644246, -2156022381, -1264405609, -967472122, -668948588, -73448992, -49640862, 1590047, 5586452; -2235, -982, -4075, -2390, -1829, -1265, -139, -95, 3, 11; 3553864930, 1561117467, 6477131661, 3798532740, 2906483888, 2009658210, 220655776, 149131290, -4776826, -16782843],117,29]
%
% END OF LATTICE L118.29
%
%
% LATTICE L118.30
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[470836110360, -2541512820, -117738353040; -2541512820, 13718760, 635536500; -117738353040, 635536500, 29441921449],[4620, 60, 1],[-1422, -19157, -1689, -7745, -65, -8323, -22139, -13881, -160010, -12596; -166, -2266, -200, -847, 3, -913, -2499, -1583, -18326, -1457; -5683, -76560, -6750, -30954, -260, -33264, -88480, -55476, -639485, -50340],117,30]
%
% END OF LATTICE L118.30
%
%
% LATTICE L118.31
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[47350380, 17842440, 83160; 17842440, 6723178, 31339; 83160, 31339, 146],[4620, 77, 1],[-367, -15, -67, -23, 5, 12, 10, -7, -17, -26; 780, 32, 144, 50, -9, -25, -21, 15, 36, 55; 41580, 1673, 7238, 2360, -924, -1470, -1188, 770, 1956, 3003],117,31]
%
% END OF LATTICE L118.31
%
%
% LATTICE L118.32
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[5639735640, 60184740, -1409987040; 60184740, 642264, -15046752; -1409987040, -15046752, 352510043],[4620, 84, 1],[4107, 32597, 10603, 62833, 3713, 19651, 1, -1051, 399, 1324; -290, -2321, -759, -4510, -268, -1430, 0, 90, -22, -89; 16415, 130284, 42378, 251130, 14840, 78540, 4, -4200, 1595, 5292],117,32]
%
% END OF LATTICE L118.32
%
%
% LATTICE L118.33
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-283153000860345, 373585639350, 56753326612290; 373585639350, -492894710, -74879046935; 56753326612290, -74879046935, -11375263801534],[1155, 385, 1],[556594207, 407494824, 1690710457, 198304415, 2276017978, 104915272, 172791776, 7785478, -3740651, -4380786; -1669783962, -1222485454, -5072135446, -594913723, -6828059421, -314746069, -518375745, -23356453, 11221962, 13142369; 2787944544, 2041115335, 8468659815, 993294046, 11400427500, 525513842, 865502880, 38996958, -18736680, -21943075],117,33]
%
% END OF LATTICE L118.33
%
%
% LATTICE L118.34
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-10288740, -258720, 4620; -258720, -4830, 105; 4620, 105, -2],[4620, 105, 1],[-1, -1, 1, 1, 0, -3, -1, -4, -25, -3; -24, -22, 24, 22, -1, -77, -25, -99, -616, -73; -3584, -3465, 3570, 3432, -70, -11088, -3650, -14532, -90640, -10815],117,34]
%
% END OF LATTICE L118.34
%
%
% LATTICE L118.35
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[20557087320, -21422940, -5143607700; -21422940, 21912, 5360256; -5143607700, 5360256, 1286986807],[4620, 132, 1],[30813, 21886, 74298, 266669, 21887, 4609, -20731, -44919, -3743, 9215; 745, 529, 1795, 6440, 528, 110, -504, -1090, -91, 223; 123145, 87468, 296934, 1065750, 87472, 18420, -82852, -179520, -14959, 36828],117,35]
%
% END OF LATTICE L118.35
%
%
% LATTICE L118.36
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-4615179870840, 15642613140, 1154654169900; 15642613140, -53017720, -3913565460; 1154654169900, -3913565460, -288878502979],[4620, 140, 1],[-95953, -1387967, -103777, 298583, 1135189, 1843661, 1038941, 958931, 3579751, 162330; -3351, -48477, -3625, 10428, 39648, 64394, 36288, 33494, 125037, 5671; -383481, -5547080, -414750, 1193302, 4536840, 7368284, 4152180, 3832416, 14306655, 648760],117,36]
%
% END OF LATTICE L118.36
%
%
% LATTICE L118.37
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[825727980, 412455120, -332640; 412455120, 206023290, -166155; -332640, -166155, 134],[4620, 165, 1],[7, 4, -1, -19, -14, -5, -61, -20, -53, 4; -16, -9, 2, 42, 31, 11, 133, 43, 112, -10; -2464, -1230, 0, 4914, 3685, 1227, 13475, 3663, 7280, -2475],117,37]
%
% END OF LATTICE L118.37
%
%
% LATTICE L118.38
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[132635219640, -288763860, -33185002620; -288763860, 628760, 72248000; -33185002620, 72248000, 8302805257],[4620, 220, 1],[-6614, -1151, -13239, -22444, -73654, -10356, -488990, -73632, -196442, -33359; -243, -42, -482, -819, -2691, -379, -17913, -2699, -7203, -1225; -26433, -4600, -52910, -89698, -294360, -41388, -1954260, -294272, -785085, -133320],117,38]
%
% END OF LATTICE L118.38
%
%
% LATTICE L118.39
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2489011140, 996090480, 1182720; 996090480, 398630694, 473319; 1182720, 473319, 562],[4620, 231, 1],[-139, -19, -101, -43, -6, 7, 3, -2, -5, -25; 340, 47, 254, 110, 17, -15, -7, 5, 12, 60; 6160, 399, -1386, -2160, -1694, -2100, -418, 0, 416, 2079],117,39]
%
% END OF LATTICE L118.39
%
%
% LATTICE L118.40
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[578856290648274870, 387628030253523675, 128372560854566490; 387628030253523675, 259573044753391215, 85964001266925705; 128372560854566490, 85964001266925705, 28469094396302717],[1155, 1155, 1],[-34014, -75261, -313879, -36918, -141918, -19808, -11150, -2080, 206, 1891; -1307990620, -2894034976, -12069439418, -1419574663, -5456943309, -761618199, -428678813, -79894811, 7922308, 72543009; 3949703219, 8739037650, 36445753575, 4286650488, 16478181335, 2299837491, 1294469605, 241256169, -23922775, -219056145],117,40]
%
% END OF LATTICE L118.40
%
%
% LATTICE L118.41
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[122381794920, -140868420, -30621068940; -140868420, 162008, 35246596; -30621068940, 35246596, 7661677651],[4620, 308, 1],[-169642, -43066, -157716, -85551, -168775, -25607, 4657, 54717, 2038, -11637; -3315, -841, -3079, -1670, -3294, -500, 90, 1060, 39, -229; -677985, -172116, -630322, -341910, -674520, -102340, 18612, 218680, 8145, -46508],117,41]
%
% END OF LATTICE L118.41
%
%
% LATTICE L118.42
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[155365980, -1501500, -198660; -1501500, 13090, 1925; -198660, 1925, 254],[4620, 385, 1],[-17, -4, 1, 3, 47, 6, 34, 29, 37, 1; -48, -11, 2, 8, 126, 16, 90, 76, 96, 1; -12936, -3045, 770, 2286, 35805, 4571, 25905, 22099, 28200, 770],117,42]
%
% END OF LATTICE L118.42
%
%
% LATTICE L118.43
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[189229018440, -114839340, -47348259420; -114839340, 69720, 28734720; -47348259420, 28734720, 11847324943],[4620, 420, 1],[-3750, -6936, -578, -15573, -16149, -109589, -26533, -92291, -135266, -53071; -4, 11, 1, -22, -24, -154, -36, -122, -176, -65; -14987, -27720, -2310, -62238, -64540, -437976, -106040, -368844, -540595, -212100],117,43]
%
% END OF LATTICE L118.43
%
%
% LATTICE L118.44
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[222524027880, -241852380, -55678516740; -241852380, 260040, 60514740; -55678516740, 60514740, 13931516771],[4620, 660, 1],[27411, -9233, -102141, -38663, 34625, 54245, 1199159, 637089, 610255, 410876; 332, -112, -1238, -469, 419, 657, 14525, 7717, 7392, 4977; 109549, -36900, -408210, -154518, 138380, 216792, 4792480, 2546148, 2438905, 1642080],117,44]
%
% END OF LATTICE L118.44
%
%
% LATTICE L118.45
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[33427372440, -135259740, -8363830860; -135259740, 467544, 33843348; -8363830860, 33843348, 2092706113],[4620, 924, 1],[-1017182, -765565, -2806879, -1529393, -1016893, -499181, 5791, 609211, 2606, -244378; -7030, -5291, -19399, -10570, -7028, -3450, 40, 4210, 18, -1689; -4065215, -3059616, -11217822, -6112290, -4064060, -1995000, 23144, 2434740, 10415, -976668],117,45]
%
% END OF LATTICE L118.45
%
%
% LATTICE L118.46
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[8791860, -4291980, 877800; -4291980, 2095170, -428505; 877800, -428505, 87638],[4620, 1155, 1],[-1, -1, 1, 1, 5, 2, 4, 11, 5, 2; -128, -45, 2, 18, 89, 17, -3, -119, -96, -232; -616, -210, 0, 78, 385, 63, -55, -693, -520, -1155],117,46]
%
% END OF LATTICE L118.46
%
%
% LATTICE L118.47
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[660077408760, 790200180, 164569814640; 790200180, 945560, 197012200; 164569814640, 197012200, 41030375191],[4620, 1540, 1],[-44564, 6901, 75333, 6326, 2312, -24150, -254156, -326610, -135992, -223109; 133689, -20702, -225990, -18977, -6927, 72449, 762453, 979809, 407967, 669311; 178101, -27580, -301070, -25282, -9240, 96516, 1015740, 1305304, 543495, 891660],117,47]
%
% END OF LATTICE L118.47
%
%
% LATTICE L118.48
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[31813320, -139491660, 34904100; -139491660, 608740440, -152321400; 34904100, -152321400, 38114453],[4620, 4620, 1],[15, -4, -44, -1, 31, 33, 99, 361, 49, 225; -12501, 3257, 36405, 815, -25811, -27443, -82331, -300255, -40759, -187226; -49973, 13020, 145530, 3258, -103180, -109704, -329120, -1200276, -162935, -748440],117,48]
%
% END OF LATTICE L118.48
%

\medskip%
%------------------------------WEYL-GROUP-W119--------------------------------
%
\leavevmode\llap{}%
$W_{119}$%
\qquad\llap{48} lattices, $\chi=90$%
\hfill%
$422222222422222222\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L119.1
%
\leavevmode%
${L_{119.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{2}{}5\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{2}{}7\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{2}{}11\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2\rightarrow N_{119}}%
\EasyButWeakLineBreak%
{${2}\above{1pt}{1pt}{*}{4}{4}\above{1pt}{1pt}{b}{2}{70}\above{1pt}{1pt}{b}{2}{132}\above{1pt}{1pt}{*}{2}{20}\above{1pt}{1pt}{b}{2}{42}\above{1pt}{1pt}{l}{2}{220}\above{1pt}{1pt}{r}{2}{6}\above{1pt}{1pt}{s}{2}{770}\above{1pt}{1pt}{b}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1671382020\\328020\\475860
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
328020\\-62\\-97
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
475860\\-97\\-130
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
352351\\918317400\\604503900
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-72\\-187651\\-123525
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-96\\-250200\\-164701
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\2607\\1715
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-2606\\-1716
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2\\-5215\\-3430
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
25\\65142\\42900
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
17\\44300\\29170
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
85\\221508\\145845
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
453\\1180520\\777260
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
28\\72969\\48042
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
368\\959035\\631400
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-1671382020, 328020, 475860; 328020, -62, -97; 475860, -97, -130],[4620, 1, 1],[1, -1, -2, 25, 17, 85, 453, 28, 368, 7, 17, 58, 151, 47, 139, 603, 28, 248; 2607, -2606, -5215, 65142, 44300, 221508, 1180520, 72969, 959035, 18243, 44306, 151165, 393558, 122500, 362292, 1571680, 72981, 646415; 1715, -1716, -3430, 42900, 29170, 145845, 777260, 48042, 631400, 12010, 29166, 99505, 259050, 80630, 238455, 1034440, 48033, 425425],118,1]
%
% END OF LATTICE L119.1
%
%
% LATTICE L119.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-1155, 0, 0; 0, 1, 0; 0, 0, 1],[1155, 1, 1],[0, 0, -1, -4, -2, -17, -43, -5, -61, -1, -1, -6, -7, -2, -11, -23, -2, -16; -1, 1, 0, -33, -20, -189, -495, -60, -770, -14, -16, -105, -132, -40, -231, -495, -45, -385; 1, 0, -35, -132, -65, -546, -1375, -159, -1925, -31, -30, -175, -198, -55, -294, -605, -51, -385],118,2]
%
% END OF LATTICE L119.2
%
%
% LATTICE L119.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2239968885, 10117800, -747025125; 10117800, -43782, 3374085; -747025125, 3374085, -249131362],[1155, 3, 1],[39526, -19125, -61202, 183175, 362101, 1191280, 9487319, 389302, 15277138, 288152, 346803, 2354948, 1018311, 948611, 1867048, 12139429, 375280, 9954068; -11189, 5414, 17325, -51854, -102505, -337232, -2685705, -110205, -4324705, -81571, -98174, -666645, -288266, -268535, -528528, -3436455, -106235, -2817815; -118671, 57420, 183750, -549956, -1087155, -3576643, -28484280, -1168822, -45867360, -865134, -1041225, -7070385, -3057329, -2848065, -5605537, -36446850, -1126723, -29885625],118,3]
%
% END OF LATTICE L119.3
%
%
% LATTICE L119.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-4316813655, 18006450, -863751735; 18006450, -72970, 3602775; -863751735, 3602775, -172828174],[1155, 5, 1],[34752, -16815, -10762, 483151, 63673, 3142178, 1668281, 1026842, 2686382, 253348, 304915, 414102, 2685949, 166807, 4924622, 2134639, 989858, 1750358; -11189, 5414, 3465, -155562, -20501, -1011696, -537141, -330615, -864941, -81571, -98174, -133329, -864798, -53707, -1585584, -687291, -318705, -563563; -173915, 84150, 53858, -2417910, -318649, -15724905, -8348846, -5138790, -13443892, -1267870, -1525935, -2072357, -13441725, -834779, -24645075, -10682716, -4953705, -8759597],118,4]
%
% END OF LATTICE L119.4
%
%
% LATTICE L119.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-6406973265, 25895100, -1830961440; 25895100, -102158, 7400085; -1830961440, 7400085, -523245473],[1155, 7, 1],[65443, -31665, -14476, 909841, 599526, 845309, 15708039, 1933688, 3613454, 477090, 574198, 557009, 5058022, 1570606, 1324823, 20099139, 1864043, 2354409; -11189, 5414, 2475, -155562, -102505, -144528, -2685705, -330615, -617815, -81571, -98174, -95235, -864798, -268535, -226512, -3436455, -318705, -402545; -229159, 110880, 50690, -3185952, -2099335, -2959983, -55004180, -6771114, -12653080, -1670606, -2010645, -1950455, -17711463, -5499725, -4639077, -70380310, -6527241, -8244335],118,5]
%
% END OF LATTICE L119.5
%
%
% LATTICE L119.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-10598186445, 41672400, -1927348500; 41672400, -160534, 7578285; -1927348500, 7578285, -350500741],[1155, 11, 1],[61723, -29865, -95572, 78011, 565446, 5580803, 1346829, 1823768, 2168758, 449970, 541558, 3677423, 433682, 1481326, 8746601, 1723329, 1758083, 1413093; -11189, 5414, 17325, -14142, -102505, -1011696, -244155, -330615, -393155, -81571, -98174, -666645, -78618, -268535, -1585584, -312405, -318705, -256165; -339647, 164340, 525910, -429276, -3111515, -30709833, -7411280, -10035762, -11934160, -2476078, -2980065, -20235985, -2386449, -8151385, -48130467, -9483070, -9674313, -7775915],118,6]
%
% END OF LATTICE L119.6
%
%
% LATTICE L119.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-332607660, 249480, 25008060; 249480, -186, -19149; 25008060, -19149, -1744702],[4620, 3, 1],[176, -177, -352, 1475, 3007, 5010, 80093, 1650, 65048, 1237, 3003, 10243, 8887, 8297, 8178, 106423, 1647, 43753; 182017, -183050, -364035, 1525414, 3109780, 5181246, 82830660, 1706399, 67271435, 1279283, 3105650, 10593135, 9190786, 8580620, 8457554, 110060940, 1703301, 45248665; 525, -528, -1050, 4400, 8970, 14945, 238920, 4922, 194040, 3690, 8958, 30555, 26510, 24750, 24395, 317460, 4913, 130515],118,7]
%
% END OF LATTICE L119.7
%
%
% LATTICE L119.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1819058361624735, -950262771150, 605368119169275; -950262771150, 496410315, -316239873675; 605368119169275, -316239873675, 201461683383937],[1155, 15, 1],[-364727, -15375, 20903, -705127, -276796, -4647456, -7461698, -1545519, -12321451, -1200643, -1549995, -2212421, -5034563, -975500, -9962664, -13201186, -2107011, -11785247; -479, -16, 0, -1144, -431, -7077, -11286, -2320, -18326, -1756, -2219, -3129, -7051, -1357, -13783, -18216, -2895, -16093; 1095960, 46200, -62811, 2118820, 831738, 13965035, 22421487, 4644095, 37024449, 3607785, 4657545, 6648054, 15128245, 2931258, 29936585, 39667947, 6331310, 35413224],118,8]
%
% END OF LATTICE L119.8
%
%
% LATTICE L119.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[4565645450520, -6018395460, -1142401906800; -6018395460, 7933400, 1505904592; -1142401906800, 1505904592, 285848327647],[4620, 4, 1],[-33493, -1733, -14993, -284591, -171456, -1653418, -2183122, -534601, -6977623, -131635, -163395, -1140903, -1531817, -489056, -2970166, -3266102, -621295, -5737233; 31, 2, 0, 198, 125, 1239, 1650, 408, 5390, 104, 133, 945, 1287, 415, 2541, 2805, 537, 5005; -133856, -6926, -59920, -1137378, -685230, -6607944, -8724925, -2136552, -27886320, -526084, -653014, -4559660, -6121962, -1954530, -11870376, -13053095, -2483028, -22929060],118,9]
%
% END OF LATTICE L119.9
%
%
% LATTICE L119.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-138373620, 39939900, -101640; 39939900, -11528170, 29335; -101640, 29335, -74],[4620, 5, 1],[421, 933, 597, 7291, 431, 6064, 5125, 1135, 1851, 4, -83, -2, 2059, 249, 5836, 6095, 1840, 4694; 1471, 3260, 2086, 25476, 1506, 21189, 17908, 3966, 6468, 14, -290, -7, 7194, 870, 20391, 21296, 6429, 16401; 4880, 10830, 6937, 84810, 5018, 70665, 59752, 13245, 21637, 55, -960, -28, 23760, 2878, 67515, 70532, 21300, 54362],118,10]
%
% END OF LATTICE L119.10
%
%
% LATTICE L119.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[3039962517263595, -1453511696175, 1011903297369195; -1453511696175, 694974441, -483826122780; 1011903297369195, -483826122780, 336829246219901],[1155, 21, 1],[-601934, -24990, 22843, -1183706, -2315018, -1108469, -62254327, -2577293, -14665397, -1997935, -2574879, -2622712, -8349147, -8084458, -2358023, -109337027, -3489068, -13933162; -479, -16, 0, -1144, -2155, -1011, -56430, -2320, -13090, -1756, -2219, -2235, -7051, -6785, -1969, -91080, -2895, -11495; 1808331, 75075, -68625, 3556091, 6954780, 3330064, 187024530, 7742707, 44057805, 6002199, 7735455, 7879155, 25082519, 24287340, 7083976, 328470450, 10481863, 41858025],118,11]
%
% END OF LATTICE L119.11
%
%
% LATTICE L119.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-565104540, -113263920, 244860; -113263920, -22701490, 49077; 244860, 49077, -106],[4620, 7, 1],[-230, -511, -234, -4009, -1187, -478, -14153, -628, -734, -3, 45, 1, -1117, -677, -454, -16603, -1003, -1829; 1155, 2566, 1175, 20130, 5960, 2400, 71060, 3153, 3685, 15, -226, -5, 5610, 3400, 2280, 83380, 5037, 9185; 3451, 7616, 3470, 59136, 17430, 6987, 206360, 9114, 10560, 14, -686, -5, 17094, 10290, 6873, 251020, 15141, 27555],118,12]
%
% END OF LATTICE L119.12
%
%
% LATTICE L119.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2943145648735215, -1792823830875, 979399436299515; -1792823830875, 1092102693, -596603382540; 979399436299515, -596603382540, 325917698376913],[1155, 33, 1],[-797774, -32670, 197173, -144750, -3104474, -10388395, -7573421, -3447013, -12473617, -2667223, -3432327, -24452152, -1010249, -10755514, -21951577, -13216561, -4637980, -11781362; -479, -16, 0, -104, -2155, -7077, -5130, -2320, -8330, -1756, -2219, -15645, -641, -6785, -13783, -8280, -2895, -7315; 2397351, 98175, -592515, 434981, 9329100, 31217648, 22758510, 10358447, 37483845, 8015139, 10314315, 73479945, 3035849, 32320860, 65965592, 39716430, 13937363, 35403585],118,13]
%
% END OF LATTICE L119.13
%
%
% LATTICE L119.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[3118735177014765, -1900632015975, 622634877097695; -1900632015975, 1158290735, -379448627250; 622634877097695, -379448627250, 124304940360323],[1155, 35, 1],[-472112, -19600, 3583, -2785276, -363150, -2608229, -9765629, -6064367, -2300509, -1567043, -2019555, -411414, -19645429, -1268174, -5548391, -17151217, -8209718, -2185632; -479, -16, 0, -3432, -431, -3033, -11286, -6960, -2618, -1756, -2219, -447, -21153, -1357, -5907, -18216, -8685, -2299; 2364775, 98175, -17947, 13951245, 1818992, 13064430, 48915328, 30375975, 11523083, 7849205, 10115805, 2060743, 98402535, 6352192, 27791490, 85909208, 41121885, 10947673],118,14]
%
% END OF LATTICE L119.14
%
%
% LATTICE L119.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-13495020, 97020, -2989140; 97020, -682, 21791; -2989140, 21791, -656246],[4620, 11, 1],[-139, 143, 278, -325, -2423, -12095, -5857, -3980, -4752, -993, -2407, -8202, -1939, -6633, -19601, -7727, -3944, -3172; -7473, 7690, 14945, -17478, -130300, -650412, -314960, -214023, -255535, -53397, -129430, -441035, -104262, -356660, -1053948, -415480, -212067, -170555; 385, -396, -770, 900, 6710, 33495, 16220, 11022, 13160, 2750, 6666, 22715, 5370, 18370, 54285, 21400, 10923, 8785],118,15]
%
% END OF LATTICE L119.15
%
%
% LATTICE L119.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[16790937240, 44351071380, -4187073660; 44351071380, 117147572328, -11059609128; -4187073660, -11059609128, 1044110021],[4620, 12, 1],[-22423, -1491, 1571, -45275, -86608, -287760, -1151611, -95103, -3778039, -73211, -94143, -671009, -305383, -295928, -604824, -2004311, -128043, -3585779; 31, 2, 0, 66, 125, 413, 1650, 136, 5390, 104, 133, 945, 429, 415, 847, 2805, 179, 5005; -89592, -5958, 6300, -180862, -345990, -1149596, -4600695, -379940, -15093540, -292488, -376122, -2680860, -1220098, -1182330, -2416484, -8007945, -511580, -14326620],118,16]
%
% END OF LATTICE L119.16
%
%
% LATTICE L119.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2694325115719545, -2214527682675, 537642814822575; -2214527682675, 1820171155, -441900975450; 537642814822575, -441900975450, 107284675722271],[1155, 55, 1],[-590952, -24200, 29209, -321676, -459934, -23085883, -1122015, -7660207, -1847985, -1975763, -2542515, -3622610, -2245039, -1593438, -48782137, -1958043, -10306798, -1745416; -479, -16, 0, -312, -431, -21231, -1026, -6960, -1666, -1756, -2219, -3129, -1923, -1357, -41349, -1656, -8685, -1463; 2961475, 121275, -146377, 1612035, 2304896, 115691730, 5622824, 38388075, 9260923, 9901265, 12741465, 18154213, 11250705, 7985296, 244464990, 9812464, 51651105, 8746913],118,17]
%
% END OF LATTICE L119.17
%
%
% LATTICE L119.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-233819479740, -31129384440, 149590980; -31129384440, -4144387650, 19915695; 149590980, 19915695, -95702],[4620, 15, 1],[14432, 32029, 20516, 83609, 14841, 69666, 176723, 13058, 63996, 163, -2839, -83, 23421, 8511, 66554, 208585, 20997, 160767; -105889, -235000, -150528, -613448, -108890, -511147, -1296636, -95808, -469546, -1196, 20830, 609, -171842, -62446, -488313, -1530408, -154057, -1179563; 522915, 1160490, 743337, 3029290, 537708, 2524060, 6402792, 473095, 2318547, 5895, -102870, -3003, 848650, 308388, 2411500, 7557792, 760795, 5825127],118,18]
%
% END OF LATTICE L119.18
%
%
% LATTICE L119.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2727261854690835, -2636231534475, 778178423715000; -2636231534475, 2548239617, -752204448765; 778178423715000, -752204448765, 222040160204642],[1155, 77, 1],[-1005971, -41195, 35514, -547591, -3914734, -5614159, -9550031, -13039966, -2247016, -3363336, -4328112, -4404821, -3821716, -13562494, -11863069, -16665811, -17545183, -2122291; -479, -16, 0, -312, -2155, -3033, -5130, -6960, -1190, -1756, -2219, -2235, -1923, -6785, -5907, -8280, -8685, -1045; 3525599, 144375, -124465, 1919127, 13719860, 19675788, 33469730, 45700809, 7875055, 11787391, 15168615, 15437455, 13393863, 47532100, 41576172, 58408210, 61490121, 7437935],118,19]
%
% END OF LATTICE L119.19
%
%
% LATTICE L119.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[98544258120, -197066100, -24668674800; -197066100, 394120, 49331740; -24668674800, 49331740, 6175332059],[4620, 20, 1],[74209, 91026, 126396, 845942, 53923, 1636261, 359782, 342100, 632022, 18556, 1739, 3475, 174473, 20289, 961159, 252467, 307255, 796559; -17074, -20945, -29085, -194667, -12409, -376551, -82797, -78729, -145453, -4271, -400, -798, -40128, -4667, -221109, -58080, -70686, -183260; 296580, 363790, 505148, 3380850, 215506, 6539400, 1437887, 1367220, 2525908, 74160, 6950, 13888, 697290, 81086, 3841320, 1008997, 1227960, 3183488],118,20]
%
% END OF LATTICE L119.20
%
%
% LATTICE L119.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-309350580, 123427920, -22808940; 123427920, -49246554, 9100581; -22808940, 9100581, -1681510],[4620, 21, 1],[-120, 3329, 43, -27579, -49931, -11133, -1220399, -24551, -134137, -16824, -37217, -16987, -96677, -85621, -11459, -1016209, -14985, -52247; -293, 8134, 105, -67386, -122000, -27202, -2981880, -59987, -327745, -41107, -90934, -41505, -236214, -209200, -27998, -2482920, -36613, -127655; 42, -1134, -15, 9394, 17010, 3793, 415800, 8365, 45705, 5733, 12684, 5790, 32956, 29190, 3907, 346500, 5110, 17820],118,21]
%
% END OF LATTICE L119.21
%
%
% LATTICE L119.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-8594044582510695, -116153244900, -2860027960202490; -116153244900, -1532370, -38654852775; -2860027960202490, -38654852775, -951793984148771],[1155, 105, 1],[-341940851, 165450195, 15127472, -1584645201, -626506828, -1472251579, -16414957289, -3367851532, -3776072434, -2492803834, -3000194880, -582076409, -8809418644, -1641288920, -2307408001, -21003672553, -3246552733, -2460365873; -11189, 5414, 495, -51854, -20501, -48176, -537141, -110205, -123563, -81571, -98174, -19047, -288266, -53707, -75504, -687291, -106235, -80509; 1027491675, -497158200, -45456258, 4761670760, 1882578663, 4423941265, 49324998492, 10119994150, 11346649512, 7490579670, 9015229545, 1749070527, 26471257505, 4931878413, 6933487195, 63113543262, 9755505655, 7393107447],118,22]
%
% END OF LATTICE L119.22
%
%
% LATTICE L119.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[134082647160, -212016420, -33543653220; -212016420, 335384, 53040456; -33543653220, 53040456, 8391665105],[4620, 28, 1],[-192723, -242925, -244657, -2319055, -744938, -649730, -5014061, -957863, -1271767, -54241, -4039, -2307, -397549, -242918, -338126, -3135751, -770885, -1444837; -22089, -27842, -28040, -265782, -85375, -74463, -574640, -109776, -145750, -6216, -463, -265, -45573, -27845, -38757, -359425, -88359, -165605; -770224, -970858, -977780, -9268182, -2977170, -2596668, -20038865, -3828132, -5082660, -216776, -16142, -9220, -1588818, -970830, -1351332, -12532135, -3080868, -5774340],118,23]
%
% END OF LATTICE L119.23
%
%
% LATTICE L119.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-30166507140, 8075760, -19348560; 8075760, -2046, 5181; -19348560, 5181, -12410],[4620, 33, 1],[-229, -555, -1891, -149, -1529, -1506, -1781, -303, -731, -32, 33, 64, -25, -559, -930, -1351, -306, -1096; -3897, -9442, -32165, -2534, -26000, -25606, -30280, -5151, -12425, -543, 562, 1085, -426, -9520, -15834, -23000, -5209, -18655; 355410, 861366, 2934855, 231250, 2373030, 2337335, 2764140, 470261, 1134525, 49665, -51216, -99330, 38800, 867570, 1443365, 2096760, 474914, 1701000],118,24]
%
% END OF LATTICE L119.24
%
%
% LATTICE L119.25
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-20813100, 212520, 106260; 212520, -2170, -1085; 106260, -1085, -542],[4620, 35, 1],[0, -1, 0, 25, 3, 10, 73, 22, 8, 5, 11, 1, 85, 5, 10, 59, 13, 3; 17, -98, -1, 2442, 300, 1014, 7436, 2253, 825, 523, 1178, 109, 9438, 564, 1146, 6820, 1527, 363; -35, 0, 2, 0, -14, -75, -616, -210, -88, -70, -210, -23, -2310, -154, -345, -2156, -525, -143],118,25]
%
% END OF LATTICE L119.25
%
%
% LATTICE L119.26
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-8781033812989515, -146908931400, -2922255585777990; -146908931400, -2408010, -48890079975; -2922255585777990, -48890079975, -972502542465823],[1155, 165, 1],[-398341483, 192739635, 123358528, -167819763, -729843332, -12005602229, -1738405019, -3923348156, -2799301018, -2903969642, -3495050760, -4746594103, -932950612, -1912005568, -18815968271, -2224368331, -3782044469, -1823934557; -11189, 5414, 3465, -4714, -20501, -337232, -48831, -110205, -78631, -81571, -98174, -133329, -26206, -53707, -528528, -62481, -106235, -51233; 1196969235, -579159900, -370677846, 504278620, 2193093243, 36075420535, 5223702312, 11789199070, 8411569824, 8726086710, 10502215845, 14262956169, 2803406695, 5745351513, 56539768285, 6683964822, 11364598135, 5480708499],118,26]
%
% END OF LATTICE L119.26
%
%
% LATTICE L119.27
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[131295992520, 9933069300, -32835624360; 9933069300, 751476616, -2484146896; -32835624360, -2484146896, 8211813677],[4620, 44, 1],[-18797, -985, -8473, -14513, -96156, -927194, -111292, -299777, -355693, -73811, -91623, -639783, -78095, -274276, -1665830, -166532, -348479, -292563; 31, 2, 0, 18, 125, 1239, 150, 408, 490, 104, 133, 945, 117, 415, 2541, 255, 537, 455; -75152, -3938, -33880, -58026, -384450, -3707088, -444965, -1198560, -1422120, -295108, -366322, -2557940, -312234, -1096590, -6660192, -665815, -1393260, -1169700],118,27]
%
% END OF LATTICE L119.27
%
%
% LATTICE L119.28
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-65146620, 33818400, 1136520; 33818400, -17484170, -586465; 1136520, -586465, -19654],[4620, 55, 1],[-29, 533, 15, -1199, -1597, -37456, -3557, -11815, -2741, -2706, -6003, -3844, -4271, -2779, -39124, -3007, -7330, -1088; -176, 3230, 91, -7266, -9678, -226989, -21556, -71601, -16611, -16399, -36380, -23296, -25884, -16842, -237111, -18224, -44424, -6594; 3575, -65560, -1848, 147480, 196438, 4607295, 437532, 1453320, 337162, 332860, 738430, 472857, 525390, 341858, 4812885, 369912, 901725, 133847],118,28]
%
% END OF LATTICE L119.28
%
%
% LATTICE L119.29
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-11981997831331605, -203050230075, -3988409824877940; -203050230075, -3371214, -67588689630; -3988409824877940, -67588689630, -1327609398291389],[1155, 231, 1],[-550659865, 266439690, 121806098, -231990922, -5044609303, -2370903063, -12015693982, -5423563590, -2764072652, -4014393674, -4831493229, -4686859637, -1289693591, -13215604853, -3715834989, -15374627252, -5228228001, -1800980887; -11189, 5414, 2475, -4714, -102505, -48176, -244155, -110205, -56165, -81571, -98174, -95235, -26206, -268535, -75504, -312405, -106235, -36595; 1654294719, -800439255, -365930400, 696948119, 15155036820, 7122677111, 36097599195, 16293492908, 8303838870, 12060058626, 14514792600, 14080283745, 3874502996, 39702376560, 11163127349, 46188520875, 15706664897, 5410514475],118,29]
%
% END OF LATTICE L119.29
%
%
% LATTICE L119.30
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[697705395756600, 2062453151220, -174596107394940; 2062453151220, 6096717960, -516115102560; -174596107394940, -516115102560, 43691507766553],[4620, 60, 1],[6156059, 7885026, 11215558, 25477994, 4932097, 50355227, 33359815, 10648250, 59580604, 1851766, 122799, -4603, 3884031, 1474163, 24384473, 19491830, 8036675, 63739901; 218913, 280393, 398825, 905993, 175384, 1790614, 1186262, 378647, 2118655, 65847, 4367, -161, 138127, 52424, 867146, 693154, 285793, 2266649; 24602880, 31512750, 44823324, 101823590, 19711278, 201246220, 133323531, 42556060, 238115724, 7400640, 490770, -18396, 15522650, 5891538, 97453300, 77899701, 32118820, 254738484],118,30]
%
% END OF LATTICE L119.30
%
%
% LATTICE L119.31
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-5761140, -16553460, 448140; -16553460, -38709286, 1033109; 448140, 1033109, -27542],[4620, 77, 1],[5376, 11981, 5499, 8585, 28017, 11305, 30463, 14899, 1589, 92, -1045, -31, 2351, 15727, 10567, 35153, 23377, 3879; -32091, -71518, -32825, -51246, -167240, -67482, -181840, -88935, -9485, -549, 6238, 185, -14034, -93880, -63078, -209840, -139545, -23155; -1116269, -2487716, -1141800, -1782564, -5817350, -2347323, -6325200, -3093552, -329930, -19096, 216986, 6435, -488166, -3265570, -2194137, -7299180, -4854003, -805435],118,31]
%
% END OF LATTICE L119.31
%
%
% LATTICE L119.32
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[12436753532280, 127286021940, -3109399639500; 127286021940, 1302729960, -31823667624; -3109399639500, -31823667624, 777402727571],[4620, 84, 1],[-92525, -6735, -3077, -219327, -404678, -188428, -5248076, -430585, -2424647, -324289, -410079, -413737, -1308991, -1262578, -367324, -8506786, -541981, -2160307; 5444, 395, 175, 12859, 23745, 11061, 308110, 25283, 142395, 19051, 24100, 24320, 76956, 74235, 21599, 500225, 31872, 127050; -369852, -26922, -12300, -876722, -1617630, -753208, -20978265, -1721188, -9692100, -1296288, -1639218, -1653840, -5232458, -5046930, -1468312, -34004355, -2166472, -8635440],118,32]
%
% END OF LATTICE L119.32
%
%
% LATTICE L119.33
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-12288206997561495, 265465489905, 2453416133973420; 265465489905, -5618690, -53001748800; 2453416133973420, -53001748800, -489839626490927],[1155, 385, 1],[431816833, -208936860, -19103598, 545768404, 791177041, 5577649201, 1884495040, 12759161518, 433506480, 3148010002, 3788763695, 735068965, 3034058431, 2072684427, 8741658139, 2411297162, 12299626327, 282458887; -1295461688, 626815994, 57311289, -1637319354, -2373551624, -16733092131, -5653533951, -38277815169, -1300530673, -9444111577, -11366389259, -2205225942, -9102253911, -6218106988, -26225200929, -7233953967, -36899197686, -847383980; 2162942705, -1046551275, -95688692, 2733718785, 3962954842, 27938085615, 9439314283, 63909818280, 2171406038, 15768179350, 18977673330, 3681913103, 15197403270, 10381942802, 43786402605, 12078032183, 61608036105, 1414818373],118,33]
%
% END OF LATTICE L119.33
%
%
% LATTICE L119.34
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1582305255300, 108008859420, 1029622440; 108008859420, -7372732710, -70282485; 1029622440, -70282485, -669986],[4620, 105, 1],[35, -3, -2, 25, 23, 35, 835, 92, 112, 85, 243, 26, 855, 169, 125, 2333, 188, 152; 787, -98, -45, 814, 608, 888, 20988, 2291, 2761, 2063, 5798, 615, 20086, 3952, 2912, 54252, 4359, 3509; -28770, 5670, 1647, -46970, -28434, -39365, -918456, -98945, -117513, -85785, -234780, -24558, -793100, -154854, -113375, -2105796, -168350, -134508],118,34]
%
% END OF LATTICE L119.34
%
%
% LATTICE L119.35
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[123034662449160, 38445417780, -30785228032020; 38445417780, 12013320, -9619654572; -30785228032020, -9619654572, 7702953347599],[4620, 132, 1],[-3213805, -3963073, -27563603, -1117819, -11750136, -23742492, -7113997, -4954561, -12450723, -788093, -38825, -449683, -216147, -4257456, -13608556, -4891697, -4383201, -15562563; 104, 133, 945, 39, 415, 847, 255, 179, 455, 31, 2, 0, 6, 125, 413, 150, 136, 490; -12844128, -15838614, -110159280, -4467418, -46959990, -94888024, -28431435, -19801144, -49759920, -3149652, -155166, -1797180, -863842, -17015130, -54387256, -19549905, -17517676, -62196540],118,35]
%
% END OF LATTICE L119.35
%
%
% LATTICE L119.36
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[11245080, 586740, -2813580; 586740, 317800, -146720; -2813580, -146720, 703973],[4620, 140, 1],[-26063, -1699, 1, -165889, -20952, -148376, -276655, -342077, -129133, -87227, -111591, -22659, -1080301, -69680, -304784, -471059, -450953, -120105; 31, 2, 0, 198, 25, 177, 330, 408, 154, 104, 133, 27, 1287, 83, 363, 561, 537, 143; -104160, -6790, 4, -662970, -83734, -592980, -1105643, -1367100, -516076, -348600, -445970, -90556, -4317390, -278474, -1218060, -1882573, -1802220, -479996],118,36]
%
% END OF LATTICE L119.36
%
%
% LATTICE L119.37
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[448140, -697620, 4620; -697620, 877470, -5775; 4620, -5775, 38],[4620, 165, 1],[3, 7, 4, 1, 1, -1, -1, -2, -2, -3, -7, -4, -1, -1, 1, 1, 2, 2; 73, 160, 84, 16, 2, -161, -60, -84, -70, -88, -190, -105, -26, -26, 21, 24, 49, 49; 10725, 23430, 12243, 2290, 132, -24640, -9072, -12595, -10437, -13035, -28050, -15477, -3830, -3828, 3080, 3528, 7205, 7203],118,37]
%
% END OF LATTICE L119.37
%
%
% LATTICE L119.38
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[104095406488920, 236524942500, -26045673455340; 236524942500, 537430520, -59180819060; -26045673455340, -59180819060, 6516878396689],[4620, 220, 1],[63914, 3771, -3391, 31747, 45819, 2315611, 56394, 771925, 186835, 200991, 261134, 374258, 233158, 166105, 5101729, 102549, 1082410, 184032; -2401, -150, 70, -1278, -1811, -90699, -2203, -30066, -7252, -7754, -10005, -14287, -8877, -6313, -193641, -3890, -41019, -6965; 255420, 15070, -13552, 126870, 183106, 9253860, 225367, 3084840, 746648, 803220, 1043570, 1495648, 931770, 663806, 20388060, 409817, 4325640, 735448],118,38]
%
% END OF LATTICE L119.38
%
%
% LATTICE L119.39
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-204522780, 13718706540, -138581520; 13718706540, -917494103526, 9268196091; -138581520, 9268196091, -93623990],[4620, 231, 1],[-246, 2657, 82, -1993, -40019, -8966, -89491, -19840, -9878, -13695, -30539, -14023, -7301, -71509, -9622, -77801, -12689, -4063; -21166, 228534, 7055, -171422, -3442130, -771189, -7697360, -1706493, -849635, -1177949, -2626764, -1206170, -627988, -6150790, -827631, -6692020, -1091442, -349480; -2094939, 22619520, 698280, -16966768, -340690350, -76329671, -761858580, -168902888, -84093990, -116589396, -259988190, -119382615, -62156122, -608784330, -81916109, -662353440, -108027227, -34590345],118,39]
%
% END OF LATTICE L119.39
%
%
% LATTICE L119.40
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[512364134824524440535, 343099219085878781295, 113625749281021060545; 343099219085878781295, 229752760071030031605, 76088280183229085310; 113625749281021060545, 76088280183229085310, 25198506339822517154],[1155, 1155, 1],[-479, -16, 0, -104, -431, -1011, -1026, -2320, -238, -1756, -2219, -447, -641, -1357, -1969, -1656, -2895, -209; -1312326125, -53741781, 9267164, -238110955, -1021360486, -2441246105, -2491628443, -5670275312, -586253750, -4387535950, -5646120294, -1149239579, -1661843070, -3538529174, -5158569995, -4348206047, -7629402863, -553718665; 3962643300, 162276345, -27982713, 718989635, 3084056283, 7371481865, 7523614182, 17121719615, 1770226617, 13248414795, 17048781750, 3470194332, 5018029730, 10684790193, 15576595595, 13129655532, 23037415940, 1671985002],118,40]
%
% END OF LATTICE L119.40
%
%
% LATTICE L119.41
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[794873373099960, -1494630267900, -198887142059760; -1494630267900, 2810409448, 373974965672; -198887142059760, 373974965672, 49764021057131],[4620, 308, 1],[82247, 110805, 115567, 102157, 367098, 324268, 228816, 485377, 59327, 29907, 1349, -3413, 9997, 81518, 124348, 107646, 299701, 52827; 9685, 12486, 12730, 11070, 39355, 34485, 24245, 51126, 6200, 2990, 189, -55, 1605, 11345, 16215, 13780, 37599, 6475; 328636, 442750, 461780, 408198, 1466850, 1295712, 914305, 1939476, 237060, 119504, 5390, -13640, 39942, 325710, 496848, 430115, 1197504, 211080],118,41]
%
% END OF LATTICE L119.41
%
%
% LATTICE L119.42
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-610030136100, 111762563220, -289978920; 111762563220, -20475825370, 53126535; -289978920, 53126535, -137842],[4620, 385, 1],[125, 331, 34, 295, 209, 455, 255, 668, 16, 35, -11, -2, 25, 47, 185, 129, 452, 16; 943, 2438, 247, 2118, 1488, 3216, 1796, 4677, 111, 227, -98, -13, 222, 384, 1464, 1012, 3513, 123; 100485, 243320, 23672, 195720, 133826, 282315, 155764, 397320, 9122, 13860, -14630, -803, 32970, 49126, 175065, 118664, 403095, 13747],118,42]
%
% END OF LATTICE L119.42
%
%
% LATTICE L119.43
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2820347570040, 6624345420, -705694632720; 6624345420, 15829800, -1657513620; -705694632720, -1657513620, 176575724191],[4620, 420, 1],[12685237, 845721, -1153, 26725817, 10131932, 23928078, 133865738, 55183431, 62509553, 42243383, 54082899, 10986877, 174679123, 33810964, 49310082, 228663154, 72983349, 58333411; -33044, -2203, 3, -69619, -26393, -62331, -348711, -143749, -162833, -110041, -140882, -28620, -455026, -88075, -128449, -595650, -190116, -151954; 50696940, 3379950, -4608, 106810550, 40492578, 95629300, 534998541, 220542280, 249821352, 168826980, 216143970, 43909392, 698110490, 135126558, 197069260, 913859331, 291680200, 233131272],118,43]
%
% END OF LATTICE L119.43
%
%
% LATTICE L119.44
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[652701837480, -634312140, -163316889120; -634312140, 616440, 158715480; -163316889120, 158715480, 40864610363],[4620, 660, 1],[-8257, -30138, -62654, -17142, -43151, -503621, -32215, -124130, -72112, -44918, -23037, -11791, -583, 611, 7321, 310, 55, -2333; 155, 617, 1295, 355, 894, 10430, 667, 2569, 1491, 925, 463, 217, 5, -30, -350, -19, -49, 21; -33000, -120450, -250404, -68510, -172458, -2012780, -128751, -496100, -288204, -179520, -92070, -47124, -2330, 2442, 29260, 1239, 220, -9324],118,44]
%
% END OF LATTICE L119.44
%
%
% LATTICE L119.45
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2769717628854394680, -5599342490912940, -693029195009733120; -5599342490912940, 11319795203640, 1401048171349596; -693029195009733120, 1401048171349596, 173407375586692969],[4620, 924, 1],[805000, 53027, -3303, 152177, 3183353, 1506103, 3831861, 3477069, 1791487, 2666609, 3418582, 3474912, 1005026, 10703083, 3122709, 6582966, 4623352, 1680122; -247883, -16532, -70, -47628, -992415, -468577, -1191440, -1080390, -556200, -826702, -1058053, -1074515, -310567, -3305925, -964203, -2032315, -1426975, -518385; 3219216, 212058, -13200, 608566, 12730410, 6022984, 15323805, 13904968, 7164240, 10663884, 13671042, 13896300, 4019134, 42801990, 12487816, 26325495, 18488932, 6718860],118,45]
%
% END OF LATTICE L119.45
%
%
% LATTICE L119.46
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-82462380, 278170200, 1136520; 278170200, -936952170, -3828825; 1136520, -3828825, -15646],[4620, 1155, 1],[-3323, -7805, -744, -2011, -4063, -2817, -4629, -3886, -262, -307, 545, 18, -409, -1745, -2023, -4083, -4584, -464; 6839, 16062, 1531, 4138, 8360, 5796, 9524, 7995, 539, 631, -1122, -37, 842, 3592, 4164, 8404, 9435, 955; -1914990, -4497570, -428703, -1158710, -2340954, -1622995, -2666916, -2238775, -150933, -176715, 314160, 10362, -235760, -1005774, -1165945, -2353176, -2641870, -267408],118,46]
%
% END OF LATTICE L119.46
%
%
% LATTICE L119.47
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[857782935240, 2406895260, 212825460540; 2406895260, 8023400, 596224860; 212825460540, 596224860, 52805071943],[4620, 1540, 1],[50557577, 64770381, 13162899, 57091541, 40527020, 177341834, 24922354, 262531793, 6359655, 15227963, 1015159, -5791, 8693999, 12101412, 85800326, 14548970, 197966987, 6797453; -151576762, -194188195, -39463711, -171166251, -121504131, -531688869, -74719754, -787097037, -19066893, -45654983, -3043550, 17362, -26065494, -36281265, -257238111, -43619293, -593525178, -20379456; -202055700, -258857830, -52606136, -228168990, -161968114, -708754860, -99603343, -1049220480, -25416656, -60859260, -4057130, 23144, -34745970, -48363854, -342904980, -58145633, -791184240, -27166336],118,47]
%
% END OF LATTICE L119.47
%
%
% LATTICE L119.48
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1471312920, 409114559700, -102367811700; 409114559700, 113758753203480, -28464483482820; -102367811700, -28464483482820, 7122325070621],[4620, 4620, 1],[-12016, -15459, -3149, -4561, -9725, -14199, -5989, -21045, -1531, -3689, -246, 8, -674, -2839, -6741, -3434, -15600, -1610; 957217, 1224845, 248751, 359447, 765196, 1115818, 470364, 1651239, 119963, 286703, 19075, 33, 55193, 229940, 542742, 275988, 1251241, 128821; 3825360, 4894890, 994092, 1436470, 3057978, 4459180, 1879731, 6598900, 479412, 1145760, 76230, 132, 220570, 918918, 2168980, 1102941, 5000380, 514812],118,48]
%
% END OF LATTICE L119.48
%

\medskip%
%------------------------------WEYL-GROUP-W120--------------------------------
%
\leavevmode\llap{}%
$W_{120}$%
\qquad\llap{48} lattices, $\chi=40$%
\hfill%
$2222262222$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L120.1
%
\leavevmode%
${L_{120.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}7\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{2}{}11\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2\rightarrow N_{120}}%
\EasyButWeakLineBreak%
{${14}\above{1pt}{1pt}{l}{2}{60}\above{1pt}{1pt}{r}{2}{154}\above{1pt}{1pt}{b}{2}{10}\above{1pt}{1pt}{l}{2}{28}\above{1pt}{1pt}{r}{2}{6}\above{1pt}{1pt}{}{6}{2}\above{1pt}{1pt}{s}{2}{2310}\above{1pt}{1pt}{b}{2}{4}\above{1pt}{1pt}{*}{2}{132}\above{1pt}{1pt}{b}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-929927460\\291060\\161700
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
291060\\-82\\-55
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
161700\\-55\\-26
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
12\\17815\\36939
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
43\\63840\\132360
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
39\\57904\\120043
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\2970\\6155
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-1484\\-3080
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-1485\\-3078
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\1484\\3079
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
263\\390390\\809655
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
9\\13360\\27706
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
67\\99462\\206250
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-929927460, 291060, 161700; 291060, -82, -55; 161700, -55, -26],[4620, 1, 1],[12, 43, 39, 2, -1, -1, 1, 263, 9, 67; 17815, 63840, 57904, 2970, -1484, -1485, 1484, 390390, 13360, 99462; 36939, 132360, 120043, 6155, -3080, -3078, 3079, 809655, 27706, 206250],119,1]
%
% END OF LATTICE L120.1
%
%
% LATTICE L120.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[123585, -57750, 1155; -57750, 26986, -539; 1155, -539, 38],[1155, 1, 1],[-144, 7, 1548, 886, 2183, 2212, 944, 66424, 591, 1867; -308, 15, 3311, 1895, 4669, 4731, 2019, 142065, 1264, 3993; 7, 0, -77, -45, -112, -114, -49, -3465, -31, -99],119,2]
%
% END OF LATTICE L120.2
%
%
% LATTICE L120.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-262884930, 292215, -87580185; 292215, -309, 97350; -87580185, 97350, -29177362],[1155, 3, 1],[-19597, -11142, -57623, -2303, 1154, 384, -2307, -164509, -8071, -19215; 5600, 3185, 16478, 660, -329, -110, 658, 46970, 2305, 5489; 58842, 33455, 173019, 6915, -3465, -1153, 6927, 493955, 24234, 57695],119,3]
%
% END OF LATTICE L120.3
%
%
% LATTICE L120.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-367112130, 444675, -73378305; 444675, -515, 88880; -73378305, 88880, -14666842],[1155, 5, 1],[-16979, -5792, -49923, -399, 1000, 998, -1999, -85523, -6993, -49945; 5600, 1911, 16478, 132, -329, -330, 658, 28182, 2305, 16467; 84980, 28989, 249865, 1997, -5005, -4995, 10005, 428043, 35000, 249975],119,4]
%
% END OF LATTICE L120.4
%
%
% LATTICE L120.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-473981970, 597135, -135381015; 597135, -721, 170555; -135381015, 170555, -38668178],[1155, 7, 1],[-4533, -54121, -13328, -3728, 267, 1865, -3736, -114166, -13069, -93340; 800, 9555, 2354, 660, -47, -330, 658, 20130, 2305, 16467; 15874, 189525, 46673, 13055, -935, -6531, 13083, 399795, 45766, 326865],119,5]
%
% END OF LATTICE L120.5
%
%
% LATTICE L120.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-689883810, 902055, -125392575; 902055, -1133, 163955; -125392575, 163955, -22791226],[1155, 11, 1],[-29691, -50641, -7936, -3488, 1749, 1745, -3496, -67982, -12229, -7940; 5600, 9555, 1498, 660, -329, -330, 658, 12810, 2305, 1497; 163394, 278685, 43673, 19195, -9625, -9603, 19239, 374115, 67298, 43695],119,6]
%
% END OF LATTICE L120.6
%
%
% LATTICE L120.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-541505580, 364980, 244860; 364980, -246, -165; 244860, -165, -82],[4620, 3, 1],[33, 41, 116, 7, -1, -1, 2, 216, 23, 59; 49000, 60880, 172249, 10395, -1484, -1485, 2969, 320705, 34150, 87604; -63, -80, -231, -15, 0, 2, -3, -385, -42, -110],119,7]
%
% END OF LATTICE L120.7
%
%
% LATTICE L120.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1708361050935, -914315325, 568528899015; -914315325, 489345, -304276830; 568528899015, -304276830, 189201872074],[1155, 15, 1],[704629, 80342, 2107143, 20291, 6150, 2664, 105139, 1292217, 305583, 709135; 315, 37, 1001, 11, 7, 0, 41, 539, 130, 308; -2117325, -241418, -6331710, -60972, -18480, -8005, -315930, -3882956, -918240, -2130865],119,8]
%
% END OF LATTICE L120.8
%
%
% LATTICE L120.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[9748078688040, -4076304540, -2439132391080; -4076304540, 1704568, 1019959600; -2439132391080, 1019959600, 610311735431],[4620, 4, 1],[-214855, -187426, -670018, -35816, -2601, -2309, -30030, -5699084, -90674, -638195; 245, 225, 847, 55, 7, 0, 27, 5775, 95, 693; -858676, -749055, -2677752, -143140, -10395, -9228, -120016, -22776600, -362382, -2550570],119,9]
%
% END OF LATTICE L120.9
%
%
% LATTICE L120.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-235615380, 314160, -30621360; 314160, -410, 42625; -30621360, 42625, -3616858],[4620, 5, 1],[-7338, -5257, -23831, -244, 615, 611, -613, -32195, -5507, -40985; -3712373, -2659572, -12056352, -123442, 311136, 309111, -310124, -16287810, -2786052, -20734758; 18375, 13164, 59675, 611, -1540, -1530, 1535, 80619, 13790, 102630],119,10]
%
% END OF LATTICE L120.10
%
%
% LATTICE L120.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2811619893390, -1387868790, 935895528645; -1387868790, 685083, -461975745; 935895528645, -461975745, 311528753441],[1155, 21, 1],[157057, 627278, 470460, 159202, 1428, 4045, 163480, 1437538, 476166, 1105583; 45, 185, 143, 55, 1, 0, 41, 385, 130, 308; -471831, -1884470, -1413357, -478275, -4290, -12152, -491127, -4318655, -1430499, -3321395],119,11]
%
% END OF LATTICE L120.11
%
%
% LATTICE L120.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-10400271420, 1413720, 2822820; 1413720, -182, -385; 2822820, -385, -766],[4620, 7, 1],[6, 133, 15, 2, -1, -1, 7, 179, 39, 265; 2637, 58440, 6589, 875, -440, -438, 3079, 78705, 17146, 116490; 20785, 460740, 51964, 6930, -3464, -3465, 24248, 620070, 135100, 917994],119,12]
%
% END OF LATTICE L120.12
%
%
% LATTICE L120.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2679381365430, -1698378990, 891625764645; -1698378990, 1076559, -565174665; 891625764645, -565174665, 296708977093],[1155, 33, 1],[1382671, 789534, 377148, 201346, 13068, 4949, 204904, 1148458, 598086, 126309; 315, 185, 91, 55, 7, 0, 41, 245, 130, 28; -4154997, -2372590, -1133349, -605055, -39270, -14872, -615747, -3451175, -1797279, -379565],119,13]
%
% END OF LATTICE L120.13
%
%
% LATTICE L120.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2884430377290, -1814782200, 575857434075; -1814782200, 1141805, -362309255; 575857434075, -362309255, 114966125371],[1155, 35, 1],[123177, 295178, 368974, 24972, 1120, 9517, 128214, 676460, 373448, 2601265; 45, 111, 143, 11, 1, 0, 41, 231, 130, 924; -616985, -1478526, -1848165, -125083, -5610, -47670, -642215, -3388341, -1870575, -13029555],119,14]
%
% END OF LATTICE L120.14
%
%
% LATTICE L120.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-88671660, 286440, 14553000; 286440, -902, -48455; 14553000, -48455, -2299006],[4620, 11, 1],[6648, 23803, 1961, 1102, -561, -553, 557, 13273, 4993, 3377; 1130815, 4048860, 333564, 187450, -95424, -94065, 94744, 2257710, 849300, 574422; 18249, 65340, 5383, 3025, -1540, -1518, 1529, 36435, 13706, 9270],119,15]
%
% END OF LATTICE L120.15
%
%
% LATTICE L120.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[96807480, 62476260, -24208800; 62476260, 40397304, -15623520; -24208800, -15623520, 6053933],[4620, 12, 1],[-272270, -83366, -941679, -61193, -7803, 1, -29975, -2138219, -105537, -256660; 245, 75, 847, 55, 7, 0, 27, 1925, 95, 231; -1088136, -333175, -3763452, -244560, -31185, 4, -119796, -8545460, -421782, -1025750],119,16]
%
% END OF LATTICE L120.16
%
%
% LATTICE L120.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2452817660370, -2097849600, 489450839955; -2097849600, 1794265, -418618255; 489450839955, -418618255, 97668134327],[1155, 55, 1],[1024159, 350890, 279358, 29828, 9680, 10997, 151774, 510404, 443008, 280675; 315, 111, 91, 11, 7, 0, 41, 147, 130, 84; -5132435, -1758438, -1399965, -149479, -48510, -55110, -760595, -2557821, -2220075, -1406565],119,17]
%
% END OF LATTICE L120.17
%
%
% LATTICE L120.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-105803493180, -1708258860, -114645300; -1708258860, -27580830, -1851015; -114645300, -1851015, -124226],[4620, 15, 1],[228, 57, 811, 10, -5, -7, 13, 293, 157, 405; -3206, -804, -11473, -143, 56, 99, -177, -4081, -2194, -5676; -162645, -40624, -577500, -7098, 3780, 4985, -9360, -209594, -112200, -289190],119,18]
%
% END OF LATTICE L120.18
%
%
% LATTICE L120.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2482772885670, -2497320210, 708417560235; -2497320210, 2511971, -712568395; 708417560235, -712568395, 202135057357],[1155, 77, 1],[249050, 2986472, 67933, 253871, 2354, 18719, 258353, 620587, 754099, 477772; 45, 555, 13, 55, 1, 0, 41, 105, 130, 84; -872839, -10466610, -238083, -889735, -8250, -65604, -905443, -2174955, -2642871, -1674435],119,19]
%
% END OF LATTICE L120.19
%
%
% LATTICE L120.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[3263651280120, 1098952557780, -816184792500; 1098952557780, 370044658760, -274829719340; -816184792500, -274829719340, 204114213907],[4620, 20, 1],[-358707, -63328, -1146042, -12896, -5683, -3001, -47750, -1855244, -148614, -1054027; 245, 45, 847, 11, 7, 0, 27, 1155, 95, 693; -1434020, -253167, -4581500, -51552, -22715, -12000, -190900, -7416948, -594130, -4213770],119,20]
%
% END OF LATTICE L120.20
%
%
% LATTICE L120.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-338844660, -8838060, 1325940; -8838060, -230286, 34545; 1325940, 34545, -5182],[4620, 21, 1],[9, 71, 26, 7, -1, -1, 8, 78, 53, 125; -3469, -27380, -10032, -2710, 384, 387, -3076, -30030, -20412, -48158; -20823, -164360, -60225, -16275, 2304, 2324, -18459, -180235, -122514, -289058],119,21]
%
% END OF LATTICE L120.21
%
%
% LATTICE L120.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-635382642965070, -2677642275, -211450162521675; -2677642275, -10815, -891097515; -211450162521675, -891097515, -70368889873658],[1155, 105, 1],[23685611, 18852695, 69640822, 3895874, -1395115, -3248303, 19521162, 39768972, 68287499, 162571870; 800, 637, 2354, 132, -47, -110, 658, 1342, 2305, 5489; -71172450, -56650111, -209262405, -11706639, 4192155, 9760765, -58658775, -119501041, -205195830, -488509175],119,22]
%
% END OF LATTICE L120.22
%
%
% LATTICE L120.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[17409273632520, -13411901580, -4356091005420; -13411901580, 10332392, 3355881760; -4356091005420, 3355881760, 1089966718201],[4620, 28, 1],[-333719, -2012992, -1012701, -348727, -866, -2312, -329103, -8936549, -994809, -6980975; 23, 135, 66, 20, 0, 3, 26, 660, 72, 495; -1333720, -8044995, -4047296, -1393700, -3461, -9240, -1315272, -35715240, -3975790, -27899718],119,23]
%
% END OF LATTICE L120.23
%
%
% LATTICE L120.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-209062294980, -16412055660, -99611820; -16412055660, -1288398606, -7819845; -99611820, -7819845, -47462],[4620, 33, 1],[426, 531, 137, 92, -11, -13, 25, 251, 295, 69; -2450, -3060, -791, -535, 56, 75, -141, -1435, -1690, -396; -490413, -610280, -157206, -104940, 13860, 14927, -29238, -290360, -340692, -79570],119,24]
%
% END OF LATTICE L120.24
%
%
% LATTICE L120.25
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1953007980, 1372140, -756506520; 1372140, -910, 532455; -756506520, 532455, -293019526],[4620, 35, 1],[-8300, -36799, -20753, -554, 1383, 1385, -9681, -49517, -53945, -366563; -365203, -1619172, -913143, -24377, 60852, 60942, -425965, -2178759, -2373594, -16128882; 20765, 92064, 51920, 1386, -3460, -3465, 24220, 123882, 134960, 917070],119,25]
%
% END OF LATTICE L120.25
%
%
% LATTICE L120.26
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-571305132896190, -3179235675, -190125633354195; -3179235675, -16995, -1058023395; -190125633354195, -1058023395, -63272241709234],[1155, 165, 1],[191623741, 21788911, 51218422, 4502266, -11287925, -3754039, 22562946, 29250084, 78925147, 17081410; 5600, 637, 1498, 132, -329, -110, 658, 854, 2305, 499; -575806770, -65473111, -153905325, -13528779, 33918885, 11280445, -67798995, -87893057, -237160770, -51327625],119,26]
%
% END OF LATTICE L120.26
%
%
% LATTICE L120.27
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[45341151240, 58529380140, -11313820980; 58529380140, 75553625048, -14604634220; -11313820980, -14604634220, 2823098701],[4620, 44, 1],[-70023, -66536, -23498, -18516, -2795, 527, -6282, -137024, -25490, -17381; 245, 225, 77, 55, 7, 0, 27, 525, 95, 63; -279356, -265485, -93772, -73920, -11165, 2112, -25036, -546420, -101662, -69330],119,27]
%
% END OF LATTICE L120.27
%
%
% LATTICE L120.28
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-37426620, 420420, -660660; 420420, -4510, 7425; -660660, 7425, -11662],[4620, 55, 1],[-639, -457, -188, -21, 55, 53, -54, -256, -481, -325; -623, -444, -182, -20, 56, 51, -54, -252, -472, -318; 35805, 25608, 10535, 1177, -3080, -2970, 3025, 14343, 26950, 18210],119,28]
%
% END OF LATTICE L120.28
%
%
% LATTICE L120.29
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-779493889872390, -4393986135, -259467672399705; -4393986135, -23793, -1462612305; -259467672399705, -1462612305, -86368185684614],[1155, 231, 1],[37842220, 150602041, 10114711, 31119059, -2229161, -5189483, 31190415, 28881811, 109104016, 23612885; 800, 3185, 214, 660, -47, -110, 658, 610, 2305, 499; -113685759, -452439295, -30386658, -93488010, 6696855, 15590267, -93702378, -86766860, -327770751, -70937930],119,29]
%
% END OF LATTICE L120.29
%
%
% LATTICE L120.30
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[13546101316440, -3465568260, -3389441018040; -3465568260, 887160, 867138000; -3389441018040, 867138000, 848089804321],[4620, 60, 1],[-8474184, -522743, -29733365, -395903, -267902, 1161, -900941, -13089185, -3245593, -7933736; -36295, -2239, -127358, -1696, -1148, 5, -3858, -56056, -13900, -33979; -33867540, -2089171, -118831020, -1582248, -1070685, 4640, -3600660, -52311644, -12971190, -31707610],119,30]
%
% END OF LATTICE L120.30
%
%
% LATTICE L120.31
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-109544820, 480480, -18082680; 480480, -2002, 79695; -18082680, 79695, -2983546],[4620, 77, 1],[-1244, -27587, -283, -418, 207, 209, -1449, -3371, -8081, -4993; -24883, -551820, -5661, -8365, 4140, 4182, -28981, -67425, -161634, -99870; 6875, 152460, 1564, 2310, -1144, -1155, 8008, 18630, 44660, 27594],119,31]
%
% END OF LATTICE L120.31
%
%
% LATTICE L120.32
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[4422028574040, -13371578220, -1106462640360; -13371578220, 40433736, 3345783840; -1106462640360, 3345783840, 276854740763],[4620, 84, 1],[-103555, -208547, -315262, -109296, -286, 7, -101246, -920464, -307784, -720853; -521, -1045, -1573, -535, -1, -2, -519, -4675, -1559, -3641; -413856, -833455, -1259940, -436800, -1143, 28, -404628, -3678620, -1230054, -2880878],119,32]
%
% END OF LATTICE L120.32
%
%
% LATTICE L120.33
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-799483527682455, 5744891460, 159614901694710; 5744891460, -39655, -1146952345; 159614901694710, -1146952345, -31866718900886],[1155, 385, 1],[-29675138, -70859527, -7931761, -4880593, 1748065, 12208477, -24458921, -13589135, -85557262, -55550305; 89026214, 212580492, 23795497, 14641911, -5244242, -36625761, 73377421, 40767771, 256674091, 166652412; -148640855, -354930807, -39729680, -24446576, 8755945, 61151475, -122513160, -68067102, -428550815, -278247900],119,33]
%
% END OF LATTICE L120.33
%
%
% LATTICE L120.34
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-66357060, 950911500, 27156360; 950911500, -13626731370, -389155515; 27156360, -389155515, -11113598],[4620, 105, 1],[1385, 2187, 4008, 217, -153, -155, 1226, 2396, 8145, 19221; -3449, -5448, -9988, -542, 380, 387, -3048, -5962, -20272, -47850; 124155, 196112, 359535, 19509, -13680, -13930, 109725, 214621, 729750, 1722490],119,34]
%
% END OF LATTICE L120.34
%
%
% LATTICE L120.35
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[55246513448280, -7881308820, -13823545021440; -7881308820, 1124904, 1972027200; -13823545021440, 1972027200, 3458867990623],[4620, 132, 1],[-17501580, -5440361, -5668237, -4254073, -607766, 5791, -1788263, -12061509, -6615067, -1478444; -166075, -51625, -53788, -40370, -5768, 55, -16968, -114450, -62770, -14029; -69945876, -21742655, -22653372, -17001600, -2428965, 23144, -7146876, -48204380, -26437422, -5908670],119,35]
%
% END OF LATTICE L120.35
%
%
% LATTICE L120.36
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[23520908916120, 4823474441940, -5882186217600; 4823474441940, 989158445240, -1206270343740; -5882186217600, -1206270343740, 1471036464701],[4620, 140, 1],[-829591, -1002034, -2523649, -174695, -2252, -1156, -812731, -4428749, -2467409, -17331451; 23, 27, 66, 4, 0, 3, 26, 132, 72, 495; -3317240, -4006779, -10091180, -698544, -9005, -4620, -3249820, -17708988, -9866290, -69302310],119,36]
%
% END OF LATTICE L120.36
%
%
% LATTICE L120.37
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-41908020, -14474460, 226380; -14474460, -3791370, 122925; 226380, 122925, 434],[4620, 165, 1],[-50748, -12617, -16234, -2159, 1513, 1542, -3056, -6028, -35327, -8243; 103306, 25684, 33047, 4395, -3080, -3139, 6221, 12271, 71914, 16780; -2789325, -693484, -892290, -118668, 83160, 84755, -167970, -331324, -1941720, -453070],119,37]
%
% END OF LATTICE L120.37
%
%
% LATTICE L120.38
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[191852125080, 147826140, -48001790760; 147826140, 113960, -36986400; -48001790760, -36986400, 12010145393],[4620, 220, 1],[-332909, -59093, -97764, -12374, -5876, -2477, -43320, -154706, -136758, -88489; 245, 45, 77, 11, 7, 0, 27, 105, 95, 63; -1330560, -236181, -390740, -49456, -23485, -9900, -173140, -618324, -546590, -353670],119,38]
%
% END OF LATTICE L120.38
%
%
% LATTICE L120.39
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-273379260, -3705845220, -48145020; -3705845220, -50234858058, -652633443; -48145020, -652633443, -8478782],[4620, 231, 1],[-1871, -14769, -492, -1463, 207, 209, -1658, -1472, -11007, -2361; -10349, -81700, -2722, -8100, 1144, 1157, -9166, -8140, -60872, -13058; 807213, 6372520, 212313, 631785, -89232, -90244, 714945, 634915, 4747974, 1018514],119,39]
%
% END OF LATTICE L120.39
%
%
% LATTICE L120.40
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[466432877615828970, 312341729450853795, 103439649717532590; 312341729450853795, 209156259427968930, 69267242162923035; 103439649717532590, 69267242162923035, 22939551749391383],[1155, 1155, 1],[45, 37, 13, 11, 1, 0, 41, 7, 130, 28; 324923176, 259753060, 88628535, 66241877, 3070926, 8141017, 337062523, 53976787, 983837949, 207775438; -981123660, -784338863, -267618810, -200021052, -9272835, -24582250, -1017779070, -162985918, -2970753555, -627389525],119,40]
%
% END OF LATTICE L120.40
%
%
% LATTICE L120.41
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[514900044120, 72068345580, -128789665620; 72068345580, 10087096712, -18026135820; -128789665620, -18026135820, 32213588171],[4620, 308, 1],[-188803, -1139132, -52111, -197607, -498, -1156, -185975, -459359, -562585, -358961; 23, 135, 6, 20, 0, 3, 26, 60, 72, 45; -754820, -4554165, -208336, -790020, -1991, -4620, -743512, -1836480, -2249170, -1435098],119,41]
%
% END OF LATTICE L120.41
%
%
% LATTICE L120.42
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-76772956260, 13392650040, 168537600; 13392650040, -2336279330, -29400525; 168537600, -29400525, -369986],[4620, 385, 1],[-923, -4043, -204, -47, 163, 127, -1122, -512, -6099, -3743; -3695, -16188, -817, -189, 652, 510, -4489, -2049, -24410, -14982; -126830, -555324, -28005, -6391, 22440, 17325, -154385, -70407, -838530, -514500],119,42]
%
% END OF LATTICE L120.42
%
%
% LATTICE L120.43
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[28611285327240, 75630947700, -7159303545240; 75630947700, 199922520, -18924871980; -7159303545240, -18924871980, 1791447908287],[4620, 420, 1],[66105, 26611, 201026, 13904, 176, 35, 64802, 117672, 196660, 460411; 56741, 22849, 172667, 11961, 155, 12, 55537, 100925, 168709, 395065; 264780, 106589, 805200, 55692, 705, 140, 259560, 471328, 787710, 1844150],119,43]
%
% END OF LATTICE L120.43
%
%
% LATTICE L120.44
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[304649921997960, 1738376395140, -76233597547800; 1738376395140, 9919426440, -434999902920; -76233597547800, -434999902920, 19076195250491],[4620, 660, 1],[551420, 33687, 172563, 24475, 15318, 55, 61433, 79183, 214605, 47364; 5159, 294, 1400, 146, 7, 9, 756, 854, 2228, 471; 2203740, 134629, 689640, 97812, 61215, 220, 245520, 316456, 857670, 189290],119,44]
%
% END OF LATTICE L120.44
%
%
% LATTICE L120.45
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[613584428420040, 1558856084940, -153527697486240; 1558856084940, 3960387816, -390048336216; -153527697486240, -390048336216, 38414850187969],[4620, 924, 1],[-533815, -1075177, -147780, -563926, -1494, 77, -521632, -431234, -1586274, -337771; -73487, -148045, -20353, -77745, -209, 26, -71737, -59335, -218293, -46489; -2134176, -4298525, -590820, -2254560, -5973, 308, -2085468, -1724060, -6341874, -1350398],119,45]
%
% END OF LATTICE L120.45
%
%
% LATTICE L120.46
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-30093169260, -5763091058340, 15047312280; -5763091058340, -1103679597250230, 2881684740165; 15047312280, 2881684740165, -7524019618],[4620, 1155, 1],[-122024, -192749, -32125, -19176, 13447, 13697, -107827, -19175, -717197, -153899; -243549, -384708, -64118, -38272, 26840, 27337, -215218, -38272, -1431472, -307170; -93522825, -147727888, -24621315, -14696451, 10306560, 10497410, -82643715, -14696449, -549685290, -117953290],119,46]
%
% END OF LATTICE L120.46
%
%
% LATTICE L120.47
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[12842199779640, 124465317900, 3119980636080; 124465317900, 1206315880, 30238532940; 3119980636080, 30238532940, 757991575591],[4620, 1540, 1],[6715861, 8114662, 1858577, 1417421, 18620, 1156, 6568057, 3256525, 19962539, 12750515; -20135315, -24329163, -5572336, -4249674, -55826, -3465, -19692172, -9763626, -59851150, -38228253; -26840000, -32430321, -7427820, -5664736, -74415, -4620, -26249300, -13014732, -79780470, -50957550],119,47]
%
% END OF LATTICE L120.47
%
%
% LATTICE L120.48
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[10971804255720, -4191184697935620, 1048708116737820; -4191184697935620, 1601015545191853560, -400602244537950840; 1048708116737820, -400602244537950840, 100237726492289117],[4620, 4620, 1],[-4868069, -1960771, -1347357, -1027813, -13569, -128, -4759901, -786755, -14468901, -3080639; 7334165, 2953990, 2029796, 1548206, 20401, 385, 7172112, 1185390, 21799640, 4641371; 29362080, 11826199, 8126220, 6198192, 81675, 1540, 28713300, 4745668, 87274110, 18581570],119,48]
%
% END OF LATTICE L120.48
%

\medskip%
%------------------------------WEYL-GROUP-W121--------------------------------
%
\leavevmode\llap{}%
$W_{121}$%
\qquad\llap{48} lattices, $\chi=84$%
\hfill%
$222222222222222222\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L121.1
%
\leavevmode%
${L_{121.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{2}{}7\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{2}{}13\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2\rightarrow N_{121}}%
\EasyButWeakLineBreak%
{${12}\above{1pt}{1pt}{b}{2}{14}\above{1pt}{1pt}{b}{2}{30}\above{1pt}{1pt}{l}{2}{4}\above{1pt}{1pt}{r}{2}{130}\above{1pt}{1pt}{b}{2}{28}\above{1pt}{1pt}{*}{2}{156}\above{1pt}{1pt}{b}{2}{2}\above{1pt}{1pt}{b}{2}{1820}\above{1pt}{1pt}{*}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-606294780\\55970460\\125580
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
55970460\\-5166946\\-11593
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
125580\\-11593\\-26
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-491401\\-5307120\\-7174440
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
45365\\489941\\662329
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
100\\1080\\1459
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-95\\-1026\\-1386
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-24\\-259\\-441
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-7\\-75\\-375
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7\\76\\-80
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
108\\1170\\-65
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
75\\812\\182
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
209\\2262\\858
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
11\\119\\69
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
589\\6370\\4550
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-606294780, 55970460, 125580; 55970460, -5166946, -11593; 125580, -11593, -26],[5460, 1, 1],[-95, -24, -7, 7, 108, 75, 209, 11, 589, 5, -11, -68, -67, -758, -495, -1379, -76, -5139; -1026, -259, -75, 76, 1170, 812, 2262, 119, 6370, 54, -119, -735, -724, -8190, -5348, -14898, -821, -55510; -1386, -441, -375, -80, -65, 182, 858, 69, 4550, 72, -70, -720, -796, -9425, -6314, -17940, -1018, -70980],120,1]
%
% END OF LATTICE L121.1
%
%
% LATTICE L121.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-58695, 8190, 9555; 8190, -1142, -1365; 9555, -1365, -281],[1365, 1, 1],[-8168, -4533, -3179, -309, -1484, 1, 224, -29, -13066, -706, -2369, -11611, -5607, -126696, -41413, -115586, -12789, -435564; -56886, -31570, -22140, -2152, -10335, 7, 1560, -202, -91000, -4917, -16499, -80865, -39050, -882375, -288421, -804999, -89069, -3033485; -1425, -791, -555, -54, -260, 0, 39, -5, -2275, -123, -413, -2025, -978, -22100, -7224, -20163, -2231, -75985],120,2]
%
% END OF LATTICE L121.2
%
%
% LATTICE L121.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-999652290, 625170, 333317985; 625170, -381, -208455; 333317985, -208455, -111139523],[1365, 3, 1],[-2382, -121444, -325266, -531470, -12562373, -4207453, -3986480, -1358668, -47484732, -310497, -608607, -196199, -94288, -995717, -172853, -80947, 2859, 31417; -1516, -77329, -207125, -338437, -7999680, -2679299, -2538588, -865201, -30238390, -197726, -387569, -124945, -60047, -634140, -110089, -51558, 1819, 20020; -7141, -364077, -975115, -1593294, -37660740, -12613524, -11951069, -4073151, -142354485, -930839, -1824543, -588185, -282666, -2985060, -518196, -242671, 8571, 94185],120,3]
%
% END OF LATTICE L121.3
%
%
% LATTICE L121.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1487880030, 982800, -595056735; 982800, -635, 393055; -595056735, 393055, -237984589],[1365, 5, 1],[12457, 211693, 340187, 926416, 4379543, 7334091, 20846723, 2368319, 16554297, 1623698, 1060872, 205198, 164354, 347127, 301299, 423292, -4984, -10952; -4548, -77329, -124275, -338437, -1599936, -2679299, -7615764, -865201, -6047678, -593178, -387569, -74967, -60047, -126828, -110089, -154674, 1819, 4004; -31155, -529445, -850809, -2316970, -10953254, -18342590, -52137735, -5923175, -41402361, -4060875, -2653245, -513201, -411050, -868166, -753550, -1058655, 12465, 27391],120,4]
%
% END OF LATTICE L121.4
%
%
% LATTICE L121.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1980224610, 1340430, 282982245; 1340430, -889, -191555; 282982245, -191555, -40439327],[1365, 7, 1],[-5846, -14192, -798218, -434750, -10276193, -491679, -9782980, -1111408, -5549016, -761971, -71121, -481477, -77128, -814497, -20199, -198641, 2339, 3671; -4548, -11047, -621375, -338437, -7999680, -382757, -7615764, -865201, -4319770, -593178, -55367, -374835, -60047, -634140, -15727, -154674, 1819, 2860; -40887, -99259, -5582745, -3040646, -71871800, -3438808, -68422263, -7773199, -38809875, -5329233, -497421, -3367455, -539434, -5696600, -141272, -1389297, 16359, 25675],120,5]
%
% END OF LATTICE L121.5
%
%
% LATTICE L121.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-115975860, 76440, 16380; 76440, 6, -15; 16380, -15, -2],[5460, 3, 1],[-11, -9, -2, -1, -1, 1, 1, 0, -53, -1, -5, -8, -23, -259, -169, -157, -26, -1767; -4322, -3535, -785, -392, -390, 392, 390, -1, -20930, -394, -1967, -3145, -9040, -101790, -66416, -61698, -10217, -694330; -57800, -47292, -10510, -5256, -5265, 5250, 5252, 0, -278460, -5254, -26271, -42035, -120852, -1360905, -888006, -824954, -136617, -9284730],120,6]
%
% END OF LATTICE L121.6
%
%
% LATTICE L121.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3462958590, 2413320, -266291025; 2413320, -1651, 185575; -266291025, 185575, -20476973],[1365, 13, 1],[5386, 91524, 735382, 400526, 728249, 3170813, 693296, 1023916, 2752716, 701987, 458655, 443573, 71056, 57721, 130261, 14077, -2155, -1821; -4548, -77329, -621375, -338437, -615360, -2679299, -585828, -865201, -2326030, -593178, -387569, -374835, -60047, -48780, -110089, -11898, 1819, 1540; -70083, -1190917, -9568845, -5211674, -9476030, -41258854, -9021219, -13323271, -35818545, -9134307, -5968053, -5771805, -924586, -751070, -1694966, -183171, 28041, 23695],120,7]
%
% END OF LATTICE L121.7
%
%
% LATTICE L121.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[9285708767790, -6761247675, -3098329076115; -6761247675, 4923105, 2256001215; -3098329076115, 2256001215, 1033808328902],[1365, 15, 1],[310932, 19767079, 10866601, 89209863, 422453861, 708092148, 671353038, 229028227, 1602372004, 52470753, 103390186, 6727294, 16353507, 34987409, 30851442, 14808867, -307592, -1327559; -63, -4032, -2218, -18211, -86242, -144557, -137059, -46758, -327145, -10713, -21112, -1374, -3341, -7150, -6307, -3029, 62, 273; 931865, 59242050, 32567266, 267362475, 1266096663, 2122156260, 2012048935, 686398920, 4802318157, 157255150, 309860985, 20161739, 49011555, 104857467, 92461950, 44382260, -921855, -3978702],120,8]
%
% END OF LATTICE L121.8
%
%
% LATTICE L121.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2006233320, -2549820, 500955000; -2549820, 4888, -636536; 500955000, -636536, 125088113],[5460, 4, 1],[217381, 163547, 203071, 22147, 639196, 154688, 334589, 23169, 549919, 3407, 8177, 164909, 51449, 2549964, 875656, 2535655, 295747, 10612141; 80397, 60487, 75105, 8191, 236405, 57211, 123747, 8569, 203385, 1260, 3024, 60990, 19028, 943085, 323855, 937794, 109380, 3924830; -870162, -654668, -812880, -88653, -2558660, -619206, -1339338, -92744, -2201290, -13638, -32732, -660120, -205947, -10207340, -3505194, -10150062, -1183856, -42479710],120,9]
%
% END OF LATTICE L121.9
%
%
% LATTICE L121.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-28430220, -2265900, 27300; -2265900, -180590, 2175; 27300, 2175, -26],[5460, 5, 1],[113, 34, 5, 3, -5, -31, -107, -7, -83, -5, 8, 13, 69, 161, 535, 1511, 85, 1175; -1488, -448, -66, -40, 65, 406, 1404, 92, 1092, 66, -105, -171, -908, -2119, -7042, -19890, -1119, -15470; -5850, -1785, -273, -200, 182, 1400, 5070, 345, 4186, 270, -385, -657, -3520, -8242, -27440, -77610, -4375, -60606],120,10]
%
% END OF LATTICE L121.10
%
%
% LATTICE L121.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[770158768470, -2303952105, -257707606065; -2303952105, 6892347, 770939715; -257707606065, 770939715, 86233141714],[1365, 21, 1],[111077, 1009090, 19416094, 31879635, 754832467, 36148764, 239912563, 81844876, 409014059, 18750850, 5278219, 12020451, 5844219, 62517703, 1575090, 5292488, -109859, -338974; -63, -576, -11090, -18211, -431210, -20651, -137059, -46758, -233675, -10713, -3016, -6870, -3341, -35750, -901, -3029, 62, 195; 331954, 3015669, 58025065, 95272401, 2255819475, 108030708, 716979536, 244593699, 1222339950, 56036981, 15773976, 35923160, 17465469, 186834375, 4707162, 15816619, -328314, -1013025],120,11]
%
% END OF LATTICE L121.11
%
%
% LATTICE L121.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[322140, -54600, -5460; -54600, 9254, 917; -5460, 917, -206],[5460, 7, 1],[629, 47, 568, 309, 2538, 191, 3085, 120, 747, 1, -12, -43, 111, 2012, 229, 5105, 335, 3803; 3720, 278, 3360, 1828, 15015, 1130, 18252, 710, 4420, 6, -71, -255, 656, 11895, 1354, 30186, 1981, 22490; -126, -9, -105, -56, -455, -34, -546, -21, -130, 0, 2, 0, -28, -455, -50, -1092, -70, -780],120,12]
%
% END OF LATTICE L121.12
%
%
% LATTICE L121.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[115178162190, -1150251375, 45775303665; -1150251375, 11487245, -457144870; 45775303665, -457144870, 18192497482],[1365, 35, 1],[-197803, -598991, -6915185, -18923614, -89613064, -21457752, -427233227, -48582771, -48557803, -33391277, -3133129, -4281175, -3469106, -7422056, -934968, -9424813, 65211, 40243; -189, -576, -6654, -18211, -86242, -20651, -411177, -46758, -46735, -32139, -3016, -4122, -3341, -7150, -901, -9087, 62, 39; 497700, 1507145, 17399571, 47614455, 225478981, 53990700, 1074978450, 122241035, 122178212, 84017115, 7883390, 10772034, 8728755, 18674929, 2352510, 23714145, -164080, -101257],120,13]
%
% END OF LATTICE L121.13
%
%
% LATTICE L121.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[5658675206730, -8510661705, -1889593913025; -8510661705, 12800073, 2841953985; -1889593913025, 2841953985, 630989591326],[1365, 39, 1],[432883, 27537550, 75696246, 124287825, 226372381, 986525292, 71949329, 319087024, 858639959, 73103810, 144048067, 46864909, 22785561, 18749929, 42988410, 1587364, -428021, -711874; -63, -4032, -11090, -18211, -33170, -144557, -10543, -46758, -125825, -10713, -21112, -6870, -3341, -2750, -6307, -233, 62, 105; 1296334, 82465383, 226683925, 372198801, 677906535, 2954300076, 215463212, 955554639, 2571327990, 218920481, 431373852, 140344100, 68234829, 56149515, 128735334, 4753603, -1281774, -2131815],120,14]
%
% END OF LATTICE L121.14
%
%
% LATTICE L121.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2970682947960, -487179420, 742126241220; -487179420, 79896, -121705560; 742126241220, -121705560, 185395536163],[5460, 12, 1],[175149, 268519, 51797, 5112, 19096, 2046, 17037, 19081, 1790249, 25215, 198997, 282143, 195252, 8663344, 2803050, 2587695, 849163, 28598291; 38, 70, 20, 4, 65, 7, 0, -2, 0, 1, 21, 45, 35, 1625, 539, 507, 171, 5915; -701110, -1074864, -207340, -20463, -76440, -8190, -68198, -76380, -7166250, -100934, -796572, -1129400, -781581, -34678800, -11220426, -10358374, -3399144, -114477090],120,15]
%
% END OF LATTICE L121.15
%
%
% LATTICE L121.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[21452340, 4045860, 21840; 4045860, 763022, 4121; 21840, 4121, 22],[5460, 13, 1],[-13, 18, 169, 185, 168, 1461, 319, 235, 1259, 319, 101, 86, 19, 2, -33, -13, -14, -69; 66, -91, -855, -936, -850, -7392, -1614, -1189, -6370, -1614, -511, -435, -96, -10, 168, 66, 71, 350; 546, -819, -7605, -8320, -7555, -65702, -14346, -10569, -56630, -14352, -4550, -3900, -884, -115, 1274, 540, 598, 2940],120,16]
%
% END OF LATTICE L121.16
%
%
% LATTICE L121.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[81173820, -327600, -70980; -327600, 1290, 285; -70980, 285, 62],[5460, 15, 1],[3, 9, 2, 25, 53, 167, 151, 24, 313, 9, 5, 0, -1, -1, 1, 5, 2, 51; -204, -616, -138, -1732, -3679, -11606, -10504, -1672, -21840, -630, -357, -1, 64, 65, -70, -338, -135, -3458; 4370, 13125, 2921, 36540, 77493, 244230, 220870, 35115, 458094, 13180, 7350, 4, -1440, -1443, 1470, 7280, 2910, 74256],120,17]
%
% END OF LATTICE L121.17
%
%
% LATTICE L121.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[4296337764810, -9573693675, 1716261326325; -9573693675, 21333455, -3824410720; 1716261326325, -3824410720, 685596222058],[1365, 65, 1],[-1747693, -37059437, -61122221, -167263864, -60929410, -1327644384, -290483549, -429420411, -231107815, -295144577, -193856773, -37841869, -30664316, -5046650, -57852876, -6408721, 576021, 191605; -189, -4032, -6654, -18211, -6634, -144557, -31629, -46758, -25165, -32139, -21112, -4122, -3341, -550, -6307, -699, 62, 21; 4375020, 92771315, 153007959, 418713555, 152525293, 3323507460, 727170810, 1074973055, 578534852, 738838815, 485283890, 94729986, 76762335, 12633337, 144823770, 16043025, -1441960, -479647],120,18]
%
% END OF LATTICE L121.18
%
%
% LATTICE L121.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[28430427480, -25197900, 7102782960; -25197900, 22360, -6295200; 7102782960, -6295200, 1774490581],[5460, 20, 1],[82222, 58442, 13592, 7136, 40777, 49611, 109412, 8154, 46876, 3395, 8149, 14947, 21403, 206561, 349935, 1003609, 115515, 818807; -5253, -3731, -867, -455, -2600, -3164, -6981, -521, -3003, -219, -525, -957, -1369, -13208, -22372, -64155, -7383, -52325; -329130, -233940, -54408, -28565, -163228, -198590, -437970, -32640, -187642, -13590, -32620, -59832, -85675, -826852, -1400770, -4017390, -462400, -3277638],120,19]
%
% END OF LATTICE L121.19
%
%
% LATTICE L121.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3812734380, 59574060, -87360; 59574060, -930846, 1365; -87360, 1365, -2],[5460, 21, 1],[3, 1, 6, 13, 128, 11, 67, 10, 87, 3, 0, -1, -1, 2, 1, 11, 3, 43; 190, 63, 375, 808, 7930, 680, 4134, 615, 5330, 182, -1, -65, -64, 130, 64, 702, 191, 2730; -1414, -705, -6335, -16884, -184275, -16878, -108290, -17577, -167310, -7028, -702, -700, 0, 1365, -6, -1456, -714, -15600],120,20]
%
% END OF LATTICE L121.20
%
%
% LATTICE L121.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[3788150645370, -10636725645, -542968844145; -10636725645, 29866837, 1524598985; -542968844145, 1524598985, 77825618174],[1365, 91, 1],[696749, 2110630, 121837358, 66682745, 121453021, 75612756, 115806487, 171196164, 65810917, 117664690, 11040641, 75431707, 12224881, 10059689, 3294870, 2554952, -229641, -54562; -189, -576, -33270, -18211, -33170, -20651, -31629, -46758, -17975, -32139, -3016, -20610, -3341, -2750, -901, -699, 62, 15; 4861038, 14725321, 850027815, 465228309, 847346395, 527530692, 807951984, 1194391471, 459145790, 820916187, 77027704, 526267560, 85289841, 70183855, 22987458, 17825241, -1602146, -380665],120,21]
%
% END OF LATTICE L121.21
%
%
% LATTICE L121.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-96347093929905, -1145091675, 32147894258025; -1145091675, -13335, 382079880; 32147894258025, 382079880, -10726707605494],[1365, 105, 1],[3879809, 28256339, 105950371, 865589146, 4091988974, 978935018, 6492651821, 2212818119, 2209622943, 505695841, 141602211, 63908179, 153562154, 324333326, 40216282, 131831629, -4656969, -1461793; -1516, -11047, -41425, -338437, -1599936, -382757, -2538588, -865201, -863954, -197726, -55367, -24989, -60047, -126828, -15727, -51558, 1819, 572; 11627770, 84684120, 317532782, 2594166750, 12263672421, 2933863815, 19458448100, 6631805880, 6622229952, 1515568145, 424381185, 191532523, 460225080, 972025509, 120528015, 395098795, -13956915, -4380987],120,22]
%
% END OF LATTICE L121.22
%
%
% LATTICE L121.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[9301688760, 67731300, 2325353940; 67731300, 493192, 16932328; 2325353940, 16932328, 581321423],[5460, 28, 1],[-26662, -2888, -24658, -2555, -69113, -2223, -30692, -1560, -2696, 661, -1, -18677, -6112, -306457, -15111, -307321, -35997, -185089; -2433, -263, -2235, -230, -6175, -197, -2691, -131, -195, 66, 0, -1710, -559, -28015, -1381, -28080, -3288, -16900; 106722, 11560, 98700, 10227, 276640, 8898, 122850, 6244, 10790, -2646, 4, 74760, 24465, 1226680, 60486, 1230138, 144088, 740870],120,23]
%
% END OF LATTICE L121.23
%
%
% LATTICE L121.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[81151980, 13486200, -70980; 13486200, 2241190, -11795; -70980, -11795, 62],[5460, 35, 1],[-71, -7, -20, -59, -101, -39, -643, -26, -33, -1, 3, 8, 11, -3, -9, -293, -26, -71; 444, 44, 126, 372, 637, 246, 4056, 164, 208, 6, -19, -51, -72, 13, 54, 1794, 161, 442; 3150, 355, 1071, 3220, 5551, 2150, 35490, 1435, 1794, 0, -180, -546, -1120, -1001, -50, 5460, 840, 2756],120,24]
%
% END OF LATTICE L121.24
%
%
% LATTICE L121.25
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[259912380, 2598960, -196560; 2598960, 21606, -1599; -196560, -1599, 118],[5460, 39, 1],[11, 37, 46, 121, 101, 839, 59, 124, 633, 49, 33, 4, -1, -1, 1, 1, 6, 67; -11504, -38696, -48110, -126552, -105635, -877506, -61708, -129692, -662060, -51250, -34517, -4185, 1044, 1045, -1050, -1046, -6275, -70070; -137566, -462735, -575315, -1513356, -1263225, -10493574, -737930, -1550913, -7917210, -612872, -412776, -50050, 12480, 12495, -12558, -12508, -75036, -837900],120,25]
%
% END OF LATTICE L121.25
%
%
% LATTICE L121.26
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3984888261494595, -10026368625, 1329624014473755; -10026368625, -24765, 3345464070; 1329624014473755, 3345464070, -443651089780426],[1365, 195, 1],[32378981, 1650643157, 884178511, 7223520934, 2626806704, 57185885984, 4167884393, 18466413431, 9929094141, 4220132059, 8271882603, 533325169, 1281501146, 208200656, 2349268576, 84626647, -38865591, -6568381; -1516, -77329, -41425, -338437, -123072, -2679299, -195276, -865201, -465206, -197726, -387569, -24989, -60047, -9756, -110089, -3966, 1819, 308; 97039930, 4946983860, 2649886382, 21648919890, 7872549747, 171386319195, 12491165480, 55343911740, 29757533148, 12647751935, 24790863825, 1598377573, 3840663840, 623978163, 7040766915, 253626385, -116480325, -19685463],120,26]
%
% END OF LATTICE L121.26
%
%
% LATTICE L121.27
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[46999603560, -47485620, 11742013920; -47485620, 47944, -11863436; 11742013920, -11863436, 2933533061],[5460, 52, 1],[-8905, -20551, -35659, -3095, -2788, 7320, 4747, 13627, 53913, 21181, 30099, 56119, 7187, 16428, 49968, 7529, 4105, -6173; 513, 1183, 2025, 169, 125, -581, -309, -839, -3255, -1260, -1764, -3270, -418, -955, -2905, -438, -240, 350; 35646, 82264, 142740, 12389, 11160, -29302, -19002, -54548, -215810, -84786, -120484, -224640, -28769, -65760, -200018, -30138, -16432, 24710],120,27]
%
% END OF LATTICE L121.27
%
%
% LATTICE L121.28
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[235975532520, 118181700, 58950544380; 118181700, 59160, 29523720; 58950544380, 29523720, 14726809367],[5460, 60, 1],[-21072, -187602, -55736, -195415, -1742759, -2826883, -2614814, -860502, -5810762, -178761, -278675, -10875, -4418, 10873, 29221, 16985, -5441, -250839; -17, -161, -49, -173, -1547, -2513, -2327, -767, -5187, -160, -252, -10, -4, 13, 35, 26, 0, -182; 84350, 750960, 223108, 782235, 6976164, 11315850, 10466950, 3444540, 23260146, 715570, 1115520, 43532, 17685, -43524, -116970, -67990, 21780, 1004094],120,28]
%
% END OF LATTICE L121.28
%
%
% LATTICE L121.29
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1268669220, 15288000, -447720; 15288000, 184210, -5395; -447720, -5395, 158],[5460, 65, 1],[-19, -6, -1, -1, 0, 3, 1, 1, 1, 1, -1, -2, -11, -2, -87, -19, -14, -15; -1404, -448, -78, -92, -3, 98, 48, 56, 56, 54, -77, -147, -808, -147, -6398, -1398, -1031, -1106; -101790, -32305, -5499, -5980, -103, 11830, 4470, 4745, 4746, 4680, -5460, -10686, -58760, -10687, -465010, -101580, -74880, -80276],120,29]
%
% END OF LATTICE L121.29
%
%
% LATTICE L121.30
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-236217933115710, -2888389140, 79042913639235; -2888389140, -34671, 966508725; 79042913639235, 966508725, -26449228956377],[1365, 273, 1],[9353934, 68121824, 1277147538, 2086796242, 3794278723, 2360053913, 1204056244, 5334744992, 2048861976, 1219150023, 341379495, 770359057, 370211672, 300734467, 96954001, 24447713, -11227845, -1355381; -1516, -11047, -207125, -338437, -615360, -382757, -195276, -865201, -332290, -197726, -55367, -124945, -60047, -48780, -15727, -3966, 1819, 220; 27954017, 203580507, 3816726095, 6236342658, 11339114850, 7052966934, 3598294441, 15942762927, 6122976975, 3643401853, 1020204783, 2302200355, 1106369082, 898738050, 289744806, 73061429, -33554157, -4050525],120,30]
%
% END OF LATTICE L121.30
%
%
% LATTICE L121.31
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[5024848920, -7059780, 1255286760; -7059780, 96936, -1763580; 1255286760, -1763580, 313590493],[5460, 84, 1],[-549059, -504725, -4320173, -2828165, -122560864, -5589488, -35748851, -11550017, -54721053, -2278765, -437883, -392867, 341, 21824, -66160, -1012861, -703887, -6548467; -1635, -1503, -12865, -8422, -364975, -16645, -106457, -34395, -162955, -6786, -1304, -1170, 1, 65, -197, -3016, -2096, -19500; 2197846, 2020380, 17293360, 11320953, 490602840, 22374342, 143100230, 46233936, 219044670, 9121742, 1752816, 1572620, -1365, -87360, 264834, 4054414, 2817612, 26213070],120,31]
%
% END OF LATTICE L121.31
%
%
% LATTICE L121.32
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[423384780, 70679700, 333060; 70679700, 11799242, 55601; 333060, 55601, 262],[5460, 91, 1],[-1, 2, 49, 37, 28, 31, 43, 27, 17, 19, -1, -34, -25, -18, -19, -25, -14, -7; 6, -11, -255, -184, -135, -146, -198, -119, -70, -60, 8, 210, 148, 105, 110, 144, 80, 40; 0, -208, -8190, -8008, -6965, -8450, -12684, -9100, -6780, -11466, -429, -1365, 364, 595, 806, 1218, 819, 410],120,32]
%
% END OF LATTICE L121.32
%
%
% LATTICE L121.33
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-12812889180, 1067741220, -1097460; 1067741220, -88978470, 91455; -1097460, 91455, -94],[5460, 105, 1],[19, 0, -1, -1, 16, 13, 115, 27, 71, 23, 7, 8, 85, 166, 71, 431, 64, 111; 234, -1, -13, -12, 208, 168, 1482, 347, 910, 294, 89, 101, 1068, 2080, 888, 5382, 797, 1378; 5810, -975, -973, 0, 15561, 11670, 99190, 22365, 56394, 17500, 4860, 4858, 46620, 85449, 34950, 203840, 28140, 44616],120,33]
%
% END OF LATTICE L121.33
%
%
% LATTICE L121.34
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-35010821253135, 1435574595, 13915514247180; 1435574595, -57785, -570586835; 13915514247180, -570586835, -5530905296671],[1365, 455, 1],[16566509, 40216263, 452384551, 1231956832, 447996551, 1393276681, 2132472667, 3149409323, 241912407, 2159204866, 201536112, 272872574, 218557418, 35508199, 57237569, 43298708, -6628448, -160032; -49704075, -120659836, -1357277928, -3696208933, -1344112725, -4180212800, -6398003829, -9449093170, -725803679, -6478207776, -604663703, -818692689, -655732301, -106534353, -171728434, -129908022, 19887163, 480140; 41685735, 101194795, 1138319637, 3099930470, 1127278264, 3505854040, 5365867395, 7924750015, 608715843, 5433132705, 507118365, 686619843, 549948490, 89348056, 144024920, 108951045, -16678935, -402683],120,34]
%
% END OF LATTICE L121.34
%
%
% LATTICE L121.35
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[25996359480, -67130700, 6494631780; -67130700, 172760, -16771160; 6494631780, -16771160, 1622544187],[5460, 140, 1],[-310624, -32626, -50300, -21413, -87023, -8841, -27962, 17662, 27858, 29221, 1359, -43501, -72388, -725919, -178761, -3630277, -424133, -434329; 5913, 621, 957, 407, 1651, 167, 507, -339, -533, -558, -26, 828, 1378, 13819, 3403, 69108, 8074, 8268; 1243410, 130600, 201348, 85715, 348348, 35390, 111930, -70700, -111514, -116970, -5440, 174132, 289765, 2905812, 715570, 14531790, 1697780, 1738594],120,35]
%
% END OF LATTICE L121.35
%
%
% LATTICE L121.36
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[39887939789880, -95282170620, 9964681801620; -95282170620, 227604936, -23803097292; 9964681801620, -23803097292, 2489346001087],[5460, 156, 1],[-71584, -647354, -978312, -690427, -2374707, -10030711, -714574, -3062606, -7969058, -639605, -1012087, -207003, -20762, 4077, 74065, 3385, -19213, -328147; 15, 231, 415, 307, 1075, 4585, 329, 1425, 3745, 306, 518, 120, 14, -5, -91, -8, -34, 0; 286546, 2591316, 3916120, 2763735, 9505800, 40152294, 2860394, 12259416, 31899630, 2560298, 4051320, 828620, 83109, -16320, -296478, -13550, 76908, 1313550],120,36]
%
% END OF LATTICE L121.36
%
%
% LATTICE L121.37
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[4405471980, 157695720, -2424240; 157695720, 5644470, -86775; -2424240, -86775, 1334],[5460, 195, 1],[309, 215, 6, -1, -1, 1, 5, 32, 75, 63, 219, 56, 745, 125, 5207, 367, 774, 793; 4526, 3143, 87, -20, -15, 14, 74, 473, 1106, 928, 3220, 822, 10928, 1833, 76342, 5380, 11344, 11620; 855920, 595140, 16562, -3120, -2793, 2730, 13900, 88920, 208236, 174850, 607425, 155233, 2064660, 346383, 14428050, 1016870, 2144415, 2196894],120,37]
%
% END OF LATTICE L121.37
%
%
% LATTICE L121.38
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[448411465320, -272699700, 112020674220; -272699700, 164840, -68124940; 112020674220, -68124940, 27984635593],[5460, 260, 1],[-542774, -637442, -219292, -137228, -62655, -960937, -147784, -91258, 10216, 138251, 322813, 84451, 2387, -27239, -926837, -256739, -493053, -324845; 417, 483, 165, 103, 47, 721, 111, 69, -7, -102, -238, -60, 2, 23, 749, 204, 386, 252; 2172690, 2551640, 877812, 549315, 250804, 3846570, 591570, 365300, -40894, -553410, -1292200, -338052, -9555, 109036, 3710070, 1027710, 1973660, 1300334],120,38]
%
% END OF LATTICE L121.38
%
%
% LATTICE L121.39
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-977340, -245700, -38220; -245700, -61698, -9555; -38220, -9555, -1454],[5460, 273, 1],[-1459, -144, -139, 1, 16, -13, -31, -171, -271, -311, -151, -1336, -3541, -2966, -3527, -1739, -3664, -2679; 7282, 719, 695, -4, -80, 64, 154, 851, 1350, 1550, 753, 6665, 17668, 14800, 17600, 8678, 18285, 13370; -9464, -936, -910, 0, 105, -78, -196, -1092, -1740, -2002, -975, -8645, -22932, -19215, -22854, -11270, -23751, -17370],120,39]
%
% END OF LATTICE L121.39
%
%
% LATTICE L121.40
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[53703572974138815, -8658632820479460, 2853214577430945; -8658632820479460, 1396032296696310, -460024091803185; 2853214577430945, -460024091803185, 151588301746418],[1365, 1365, 1],[-63, -576, -2218, -18211, -6634, -20651, -10543, -46758, -3595, -10713, -3016, -1374, -3341, -550, -901, -233, 62, 3; -39727172, -361032725, -1389389037, -11406388467, -4155019045, -12933908244, -6603076750, -29283888767, -2251451852, -6709028509, -1888552502, -860196190, -2091122895, -344151409, -563603118, -145678931, 39280816, 1866625; -120558620, -1095612960, -4216328662, -34614554520, -12609086007, -39250063515, -20038118170, -88866757980, -6832399494, -20359646125, -5731121955, -2610406253, -6345854970, -1044383823, -1710345975, -442086575, 119204085, 5664579],120,40]
%
% END OF LATTICE L121.40
%
%
% LATTICE L121.41
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[8498151480, -37821420, 2123055480; -37821420, 143416, -9448712; 2123055480, -9448712, 530393531],[5460, 364, 1],[-86887, -4105, 1310807, 436822, 1691189, 1085727, 1700083, 2591515, 1025523, 1921744, 207978, 1747288, 174797, 347541, 137511, 134774, 58834, -6158; 636, 30, -9600, -3199, -12385, -7951, -12450, -18978, -7510, -14073, -1523, -12795, -1280, -2545, -1007, -987, -431, 45; 347802, 16432, -5247060, -1748565, -6769700, -4346082, -6805302, -10373636, -4105090, -7692594, -832520, -6994260, -699699, -1391180, -550446, -539490, -235508, 24650],120,41]
%
% END OF LATTICE L121.41
%
%
% LATTICE L121.42
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[481838480760, -497225820, 120371007120; -497225820, 528360, -124215000; 120371007120, -124215000, 30070614809],[5460, 420, 1],[-3787077, -570347, -20467, 341, -1592334, -700654, -6644273, -3374327, -4900483, -1739013, -1271683, -1821563, -5526431, -46300446, -10351526, -65194897, -20572063, -19045907; -12025, -1811, -65, 1, -5057, -2225, -21099, -10715, -15561, -5522, -4038, -5784, -17548, -147017, -32869, -207012, -65322, -60476; 15159410, 2283060, 81928, -1365, 6374004, 2804670, 26596570, 13507200, 19616298, 6961150, 5090460, 7291592, 22121925, 185337516, 41436450, 260970710, 82348560, 76239462],120,42]
%
% END OF LATTICE L121.42
%
%
% LATTICE L121.43
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[38236380, -6295380, -2473380; -6295380, 1036490, 407225; -2473380, 407225, 159994],[5460, 455, 1],[1, -1, -2, 1, 1, 9, 17, 16, 3, 35, 3, 8, 23, 3, 15, 19, 10, 1; 6, 45, 417, 2152, 383, 2354, 3570, 2601, 394, 3432, 146, 156, 140, -1, -62, -132, -118, -12; 0, -130, -1092, -5460, -959, -5850, -8820, -6370, -956, -8190, -325, -273, 0, 49, 390, 630, 455, 46],120,43]
%
% END OF LATTICE L121.43
%
%
% LATTICE L121.44
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[9671991059640, -7430530380, 2416223797260; -7430530380, 5708040, -1856269740; 2416223797260, -1856269740, 603612782771],[5460, 780, 1],[-8246893, -12944339, -522619, -264372, 1361, 618573, 11569, -438233, -975143, -996920, -8624558, -2558652, -8979441, -6163903, -130031955, -9255382, -39618290, -20593754; 6130, 9618, 388, 196, -1, -455, -8, 330, 728, 743, 6419, 1903, 6677, 4583, 96677, 6881, 29453, 15309; 33011810, 51815400, 2092012, 1058265, -5448, -2476110, -46310, 1754220, 3903438, 3990610, 34523580, 10242128, 35944155, 24673728, 520509990, 37048730, 158589600, 82435542],120,44]
%
% END OF LATTICE L121.44
%
%
% LATTICE L121.45
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[52601640, 20393100, 13125840; 20393100, 7943208, 5088720; 13125840, 5088720, 3275329],[5460, 1092, 1],[219579, 42249, 37741, -341, -1574, 5398, 6971, 65205, 47437, 52155, 48329, 415149, 272075, 907354, 538070, 264763, 1112309, 405453; -696, -134, -120, 1, 5, -17, -22, -206, -150, -165, -153, -1315, -862, -2875, -1705, -839, -3525, -1285; -878878, -169104, -151060, 1365, 6300, -21606, -27902, -260988, -189870, -208754, -193440, -1661660, -1088997, -3631740, -2153658, -1059730, -4452084, -1622850],120,45]
%
% END OF LATTICE L121.45
%
%
% LATTICE L121.46
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[5460, 0, 0; 0, -37349130, 28665; 0, 28665, -22],[5460, 1365, 1],[-13, -1, 0, 1, 0, -1, -1, -4, -1, -5, -2, -3, -37, -6, -35, -17, -35, -5; -122, -13, -3, 0, 1, 6, 2, -1, -2, -16, -10, -20, -276, -47, -282, -140, -298, -44; -159250, -16965, -3913, 0, 1302, 7800, 2590, -1365, -2622, -20930, -13065, -26117, -360360, -61362, -368160, -182770, -389025, -57438],120,46]
%
% END OF LATTICE L121.46
%
%
% LATTICE L121.47
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[222298440, -36467340, -82860960; -36467340, 5747560, 13417040; -82860960, 13417040, 30754151],[5460, 1820, 1],[42955, 2013, -132547, -220798, -170967, -548805, -859363, -1310015, -103687, -971602, -105196, -177002, -88751, -35399, -70293, -69284, -31364, 504; -128949, -6043, 397899, 662824, 513234, 1647484, 2579763, 3932597, 311263, 2916699, 315793, 531351, 266426, 106266, 211016, 207987, 94153, -1513; 171990, 8060, -530712, -884065, -684544, -2197390, -3440850, -5245240, -415158, -3890250, -421200, -708708, -355355, -141736, -281450, -277410, -125580, 2018],120,47]
%
% END OF LATTICE L121.47
%
%
% LATTICE L121.48
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[120120, -156510900, -39099060; -156510900, 203926271640, 50944218780; -39099060, 50944218780, 12726724253],[5460, 5460, 1],[-3043, -559, -87, 0, -20, -186, -167, -1303, -169, -869, -745, -1217, -3912, -2588, -7638, -3745, -15649, -1135; 5681, 779, -91, -341, -21, 487, 507, 4091, 505, 2500, 1948, 2818, 8522, 5475, 15875, 7674, 31360, 2222; -22750, -3120, 364, 1365, 84, -1950, -2030, -16380, -2022, -10010, -7800, -11284, -34125, -21924, -63570, -30730, -125580, -8898],120,48]
%
% END OF LATTICE L121.48
%

\medskip%
%------------------------------WEYL-GROUP-W122--------------------------------
%
\leavevmode\llap{}%
$W_{122}$%
\qquad\llap{48} lattices, $\chi=108$%
\hfill%
$2222222222222222222222\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L122.1
%
\leavevmode%
${L_{122.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{2}{}5\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{2}{}7\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{-2}{}13\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{2\rightarrow N_{122}}%
\EasyButWeakLineBreak%
{${12}\above{1pt}{1pt}{b}{2}{910}\above{1pt}{1pt}{l}{2}{4}\above{1pt}{1pt}{r}{2}{210}\above{1pt}{1pt}{b}{2}{26}\above{1pt}{1pt}{s}{2}{14}\above{1pt}{1pt}{l}{2}{260}\above{1pt}{1pt}{r}{2}{2}\above{1pt}{1pt}{l}{2}{1092}\above{1pt}{1pt}{r}{2}{10}\above{1pt}{1pt}{b}{2}{28}\above{1pt}{1pt}{*}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-573936958140\\420774900\\139639500
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
420774900\\-308486\\-102375
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
139639500\\-102375\\-33974
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-262630369\\-358475530140\\746109000
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
192544\\262811619\\-547000
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
63800\\87083375\\-181251
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5\\6822\\-6
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-151\\-206115\\455
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-1364\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
244\\333060\\-735
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
423\\577382\\-1235
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
939\\1281700\\-2723
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
18151\\24775400\\-52520
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
943\\1287157\\-2726
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
59737\\81538548\\-172536
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
689\\940455\\-1985
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1039\\1418186\\-2982
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-573936958140, 420774900, 139639500; 420774900, -308486, -102375; 139639500, -102375, -33974],[5460, 1, 1],[5, -151, -1, 244, 423, 939, 18151, 943, 59737, 689, 1039, 523, 8159, 353, 1604, 721, 909, 13881, 641, 36359, 279, 193; 6822, -206115, -1364, 333060, 577382, 1281700, 24775400, 1287157, 81538548, 940455, 1418186, 713868, 11136580, 481824, 2189355, 984113, 1240715, 18946460, 874913, 49627032, 380810, 263424; -6, 455, 0, -735, -1235, -2723, -52520, -2726, -172536, -1985, -2982, -1494, -23205, -1000, -4515, -2015, -2527, -38480, -1774, -100464, -765, -518],121,1]
%
% END OF LATTICE L122.1
%
%
% LATTICE L122.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-148785, 70980, 1365; 70980, -33862, -651; 1365, -651, -10],[1365, 1, 1],[587, 12748, 179, 548, 6, -30, 31, 20, 1429, 88, 193, 211, 11458, 353, 5038, 3452, 5616, 48381, 4768, 143807, 2838, 1669; 1236, 26845, 377, 1155, 13, -63, 65, 42, 3003, 185, 406, 444, 24115, 743, 10605, 7267, 11823, 101855, 10038, 302757, 5975, 3514; -450, -10010, -146, -525, -39, 7, 0, -5, -546, -40, -112, -135, -7735, -244, -3570, -2496, -4102, -35490, -3505, -105924, -2105, -1253],121,2]
%
% END OF LATTICE L122.2
%
%
% LATTICE L122.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-304395, -307125, 101010; -307125, -101922, 102375; 101010, 102375, -33518],[1365, 3, 1],[151, -68856, -907, 21198, 122012, 275500, 2676253, 278674, 2947785, 205104, 155755, 26337, 2479264, 53883, 164218, 222332, 280748, 2144563, 198110, 1873031, 86264, 29661; -1, 455, 6, -140, -806, -1820, -17680, -1841, -19474, -1355, -1029, -174, -16380, -356, -1085, -1469, -1855, -14170, -1309, -12376, -570, -196; 452, -206115, -2715, 63455, 365235, 824691, 8011185, 834192, 8823997, 613965, 466242, 78838, 7421505, 161295, 491575, 665535, 840399, 6419595, 593028, 5606783, 258225, 88788],121,3]
%
% END OF LATTICE L122.3
%
%
% LATTICE L122.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1169805, -511875, -468195; -511875, -169870, -204750; -468195, -204750, -187387],[1365, 5, 1],[-539, 16459, 1080, -15235, -146035, -329699, -640524, -333478, -10582324, -49085, -186363, -94531, -593217, -64460, -117863, -265935, -335791, -512992, -236942, -6720416, -20633, -35467; -3, 91, 6, -84, -806, -1820, -3536, -1841, -58422, -271, -1029, -522, -3276, -356, -651, -1469, -1855, -2834, -1309, -37128, -114, -196; 1350, -41223, -2705, 38157, 365755, 825755, 1604239, 835220, 26504205, 122937, 466760, 236760, 1485757, 161445, 295197, 666055, 841015, 1284829, 593440, 16831815, 51677, 88830],121,4]
%
% END OF LATTICE L122.4
%
%
% LATTICE L122.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1893255, -716625, 270270; -716625, -237818, 102375; 270270, 102375, -38582],[1365, 7, 1],[193, -4228, -387, 3922, 52592, 16960, 1153173, 120074, 544325, 88364, 9585, 34031, 152532, 23203, 30302, 95712, 17264, 923083, 85270, 345499, 37124, 1823; -3, 65, 6, -60, -806, -260, -17680, -1841, -8346, -1355, -147, -522, -2340, -356, -465, -1469, -265, -14170, -1309, -5304, -570, -28; 1344, -29445, -2695, 27315, 366275, 118117, 8031205, 836248, 3790917, 615405, 66754, 237006, 1062295, 161595, 211035, 666575, 120233, 6428695, 593852, 2406183, 258545, 12696],121,5]
%
% END OF LATTICE L122.5
%
%
% LATTICE L122.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-193571376180, -424498620, 622440; -424498620, -930918, 1365; 622440, 1365, -2],[5460, 3, 1],[7, 362, 17, 29, 44, 60, 953, 45, 869, 22, 19, 1, 2, -1, -1, 8, 24, 503, 27, 587, 22, 37; -3194, -165165, -7756, -13230, -20072, -27370, -434720, -20527, -396396, -10035, -8666, -456, -910, 456, 455, -3653, -10955, -229580, -12323, -267904, -10040, -16884; -1408, -65520, -2820, -4235, -5655, -7077, -107640, -4959, -93548, -2130, -1428, -2, 1365, 0, -700, -3510, -7728, -148980, -7731, -163072, -5625, -8442],121,6]
%
% END OF LATTICE L122.6
%
%
% LATTICE L122.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3867045, -1330875, -297570; -1330875, -441662, -102375; -297570, -102375, -22898],[1365, 13, 1],[-101, 1208, 203, -14666, -2156, -63244, -47249, -63954, -156103, -47056, -35723, -18115, -43712, -12347, -112846, -3916, -64268, -37759, -45342, -98921, -19736, -6781; -3, 35, 6, -420, -62, -1820, -1360, -1841, -4494, -1355, -1029, -522, -1260, -356, -3255, -113, -1855, -1090, -1309, -2856, -570, -196; 1326, -15855, -2665, 192465, 28295, 830011, 620095, 839332, 2048697, 617565, 468832, 237744, 573685, 162045, 1481025, 51395, 843479, 495565, 595088, 1298283, 259025, 88998],121,7]
%
% END OF LATTICE L122.7
%
%
% LATTICE L122.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[27824721030015, 307125000, -9284181917010; 307125000, 3390, -102477375; -9284181917010, -102477375, 3097822032974],[1365, 15, 1],[-669, 1002, 5015, 14710, 280820, 579688, 1094183, 562636, 5884771, 79230, 286831, 45799, 820364, 85245, 48472, 305870, 368042, 548549, 249704, 2328889, 20056, 29079; -151, 91, 906, 2597, 48919, 100555, 189514, 97384, 1017926, 13679, 49371, 7851, 140049, 14494, 8183, 51181, 61145, 90766, 41216, 383474, 3261, 4529; -2005, 3003, 15030, 44086, 841620, 1737330, 3279276, 1686225, 17636710, 237453, 859635, 137260, 2458638, 255480, 145271, 916695, 1103025, 1644006, 748365, 6979700, 60108, 87150],121,8]
%
% END OF LATTICE L122.8
%
%
% LATTICE L122.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[9153875640, 1308407100, 2287750920; 1308407100, 187358536, 326999400; 2287750920, 326999400, 571758289],[5460, 4, 1],[-466717, 464669, 341, -8828746, -16281212, -36756738, -178677426, -37225501, -590969833, -27456501, -20943607, -10705844, -339365686, -3724528, -69379181, -32133219, -41451189, -160223591, -29809865, -425733218, -13509556, -5125702; -1371, 1365, 1, -25935, -47827, -107975, -524875, -109352, -1736007, -80655, -61523, -31449, -996905, -10941, -203805, -94393, -121765, -470665, -87568, -1250613, -39685, -15057; 1868238, -1860040, -1365, 35340900, 65172640, 147134848, 715234195, 149011276, 2365614069, 109906600, 83835906, 42854802, 1358458920, 14909045, 277720380, 128627200, 165926432, 641364685, 119326964, 1704182571, 54077880, 20517854],121,9]
%
% END OF LATTICE L122.9
%
%
% LATTICE L122.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-6259775340, 23013900, -371280; 23013900, -84610, 1365; -371280, 1365, -22],[5460, 5, 1],[5, 3, -1, -1, 8, 26, 111, 30, 1969, 5, 43, 25, 88, 21, 22, 57, 79, 253, 60, 3491, 6, 27; 1362, 819, -272, -273, 2171, 7063, 30160, 8152, 535080, 1359, 11690, 6798, 23933, 5712, 5985, 15509, 21497, 68848, 16328, 950040, 1633, 7350; 120, 182, 0, -63, -325, -595, -2132, -535, -32760, -68, -420, -150, -273, -20, 42, 260, 490, 1768, 445, 27300, 57, 350],121,10]
%
% END OF LATTICE L122.10
%
%
% LATTICE L122.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1333222207590, 79545375, -446123261220; 79545375, 4746, -26617500; -446123261220, -26617500, 149281914949],[1365, 21, 1],[-349, 261, 2354, 4882, 129716, 38182, 2520784, 259165, 387134, 182277, 18829, 21008, 268306, 38964, 15777, 138851, 23795, 1239154, 112697, 150000, 44972, 1830; -151, 65, 906, 1855, 48919, 14365, 947570, 97384, 145418, 68395, 7053, 7851, 100035, 14494, 5845, 51181, 8735, 453830, 41216, 54782, 16305, 647; -1043, 780, 7035, 14590, 387660, 114108, 7533435, 774522, 1156961, 544740, 56271, 62783, 801840, 116445, 47150, 414960, 71112, 3703245, 336798, 448279, 134400, 5469],121,11]
%
% END OF LATTICE L122.11
%
%
% LATTICE L122.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-47088115620, -240245460, 1337700; -240245460, -1225742, 6825; 1337700, 6825, -38],[5460, 7, 1],[29, 74, 25, 19, 70, 14, 1577, 75, 625, 38, 5, 7, 4, -1, -1, 8, 4, 607, 33, 311, 28, 7; -5682, -14495, -4896, -3720, -13702, -2740, -308620, -14677, -122304, -7435, -978, -1368, -780, 196, 195, -1573, -785, -119080, -6473, -60996, -5490, -1372; 336, 1560, 700, 705, 3185, 709, 83720, 4081, 34788, 2310, 356, 714, 715, 0, -180, -910, -184, -20020, -931, -7488, -385, -6],121,12]
%
% END OF LATTICE L122.12
%
%
% LATTICE L122.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[196396262790, 39414375, 78048384960; 39414375, 7910, 15663375; 78048384960, 15663375, 31016630909],[1365, 35, 1],[626, -31, -1405, -1748, -77400, -22782, -300811, -154633, -692957, -21751, -11234, -37601, -32014, -23245, -5647, -82825, -14193, -147819, -67217, -268393, -5364, -1091; -453, 13, 906, 1113, 48919, 14365, 189514, 97384, 436254, 13679, 7053, 23553, 20007, 14494, 3507, 51181, 8735, 90766, 41216, 164346, 3261, 647; -1575, 78, 3535, 4398, 194740, 57320, 756847, 389060, 1743495, 54726, 28265, 94605, 80548, 58485, 14208, 208390, 35710, 371917, 169120, 675285, 13496, 2745],121,13]
%
% END OF LATTICE L122.13
%
%
% LATTICE L122.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[3344124521010, 171682875, -1116702284880; 171682875, 8814, -57330000; -1116702284880, -57330000, 372899987791],[1365, 39, 1],[-1871, 561, 11786, 169866, 49388, 1321126, 958012, 1280155, 1029474, 899643, 649897, 103452, 710506, 191376, 541201, 52193, 812075, 464122, 548303, 392660, 217748, 61170; -151, 35, 906, 12985, 3763, 100555, 72890, 97384, 78302, 68395, 49371, 7851, 53865, 14494, 40915, 3937, 61145, 34910, 41216, 29498, 16305, 4529; -5603, 1680, 35295, 508690, 147900, 3956316, 2868915, 3833622, 3082919, 2694120, 1946217, 309803, 2127720, 573105, 1620710, 156300, 2431884, 1389885, 1641978, 1175881, 652080, 183183],121,14]
%
% END OF LATTICE L122.14
%
%
% LATTICE L122.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[5033366520, 4919460, 1257416160; 4919460, 634728, 1228500; 1257416160, 1228500, 314122843],[5460, 12, 1],[3427007, 326225149, 3583524, 22283388, 31014242, 40057448, 154937879, 28837325, 137331588, 13095599, 4990131, 156176, -155496, -341, 2798893, 15567137, 35189395, 171131774, 35659969, 188738065, 26319414, 20092150; -10028, -954590, -10486, -65205, -90753, -117215, -453375, -84383, -401856, -38320, -14602, -457, 455, 1, -8190, -45552, -102970, -500760, -104347, -552279, -77015, -58793; -13718078, -1305857280, -14344605, -89198900, -124147920, -160347264, -620205885, -115433868, -549729089, -52420800, -19975158, -625162, 622440, 1365, -11203780, -62314200, -140860776, -685028955, -142744452, -755505751, -105354840, -80427522],121,15]
%
% END OF LATTICE L122.15
%
%
% LATTICE L122.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-10068365580, -96811260, 141960; -96811260, -930878, 1365; 141960, 1365, -2],[5460, 13, 1],[-1, 1, 1, -2, -1, -33, -51, -35, -173, -27, -43, -23, -29, -17, -82, -3, -51, -61, -37, -163, -17, -13; 102, -105, -104, 210, 104, 3430, 5300, 3637, 17976, 2805, 4466, 2388, 3010, 1764, 8505, 311, 5285, 6320, 3833, 16884, 1760, 1344; -1404, -700, 0, 1365, -5, -1547, -3020, -2249, -11928, -2210, -4368, -2886, -4305, -2860, -16380, -710, -13468, -17000, -10621, -48132, -5655, -5642],121,16]
%
% END OF LATTICE L122.16
%
%
% LATTICE L122.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-753116828100, -8186052420, 8413860; -8186052420, -88978830, 91455; 8413860, 91455, -94],[5460, 15, 1],[5, 16, -1, -1, 8, 36, 163, 45, 1003, 8, 73, 15, 166, 41, 15, 122, 174, 565, 135, 2637, 14, 67; -456, -1456, 92, 91, -741, -3311, -14976, -4133, -92092, -734, -6692, -1374, -15197, -3752, -1372, -11154, -15904, -51636, -12337, -240968, -1279, -6118; 3890, 15561, 0, -973, -4875, 945, 19344, 6780, 178360, 1941, 23310, 5830, 72891, 19440, 7777, 68055, 101115, 334464, 80700, 1590680, 8751, 44730],121,17]
%
% END OF LATTICE L122.17
%
%
% LATTICE L122.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2535071876610, 192976875, 1012683884940; 192976875, 14690, 77088375; 1012683884940, 77088375, 404536321151],[1365, 65, 1],[7556, -151, -15865, -137192, -66480, -1778334, -257911, -1723183, -4157243, -242197, -874808, -417761, -191278, -257605, -437095, -70255, -1093101, -124947, -738047, -1585627, -58620, -82337; -453, 7, 906, 7791, 3763, 100555, 14578, 97384, 234906, 13679, 49371, 23553, 10773, 14494, 24549, 3937, 61145, 6982, 41216, 88494, 3261, 4529; -18915, 378, 39715, 343434, 166420, 4451720, 645631, 4313660, 10406865, 606294, 2189915, 1045785, 478828, 644865, 1094184, 175870, 2736370, 312781, 1847560, 3969315, 146744, 206115],121,18]
%
% END OF LATTICE L122.18
%
%
% LATTICE L122.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[410340840, -5487300, 102506040; -5487300, 490040, -1370460; 102506040, -1370460, 25606733],[5460, 20, 1],[-187595, -371099, 341, -92773, -1409337, -3480369, -3481393, -3670010, -58914239, -564827, -2259991, -1224475, -8195459, -471031, -1884125, -4709633, -6404121, -5085165, -4802410, -69584131, -470691, -1034839; -552, -1092, 1, -273, -4147, -10241, -10244, -10799, -173355, -1662, -6650, -3603, -24115, -1386, -5544, -13858, -18844, -14963, -14131, -204750, -1385, -3045; 750930, 1485484, -1365, 371364, 5641480, 13931680, 13935779, 14690800, 235829685, 2260964, 9046590, 4901490, 32805864, 1885505, 7542024, 18852340, 25635260, 20355569, 19223720, 278540535, 1884144, 4142390],121,19]
%
% END OF LATTICE L122.19
%
%
% LATTICE L122.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-652060276140, 10188441900, -9347520; 10188441900, -159194406, 146055; -9347520, 146055, -134],[5460, 21, 1],[7, 17, -1, -1, 8, 6, 971, 54, 173, 49, 13, 19, 152, 53, 14, 161, 33, 3761, 180, 503, 94, 13; 454, 1105, -64, -65, 507, 385, 62400, 3472, 11128, 3155, 838, 1226, 9815, 3424, 905, 10413, 2135, 243360, 11648, 32552, 6085, 842; 6538, 18525, 0, -1090, -5460, 1086, 278460, 17409, 60944, 20685, 6534, 10892, 94770, 34860, 9805, 118755, 25059, 2893800, 139461, 392236, 75180, 10896],121,20]
%
% END OF LATTICE L122.20
%
%
% LATTICE L122.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2232430726890, 214270875, -319985292900; 214270875, 20566, -30712500; -319985292900, -30712500, 45865068259],[1365, 91, 1],[-3013, 43, 6326, 39074, 26508, 101298, 514192, 687095, 236806, 482863, 49831, 166576, 54478, 102716, 124489, 28013, 62265, 249102, 294283, 90320, 116868, 4690; -453, 5, 906, 5565, 3763, 14365, 72890, 97384, 33558, 68395, 7053, 23553, 7695, 14494, 17535, 3937, 8735, 34910, 41216, 12642, 16305, 647; -21021, 300, 44135, 272610, 184940, 706732, 3587395, 4793698, 1652139, 3368820, 347659, 1162161, 380080, 716625, 868530, 195440, 434408, 1737925, 2053142, 630141, 815360, 32721],121,21]
%
% END OF LATTICE L122.21
%
%
% LATTICE L122.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-92599418730, 612714375, 30897416550; 612714375, -3567270, -204442875; 30897416550, -204442875, -10309463737],[1365, 105, 1],[-126138, 1658433, 758825, -512873, -103155355, -33265517, -452367895, -235513508, -355879889, -34663353, -18799904, -22249232, -59834395, -45509565, -3962201, -187724455, -33860593, -362095573, -167243152, -225879731, -14562461, -3575466; -1, 13, 6, -4, -806, -260, -3536, -1841, -2782, -271, -147, -174, -468, -356, -31, -1469, -265, -2834, -1309, -1768, -114, -28; -378035, 4970316, 2274195, -1537078, -309156120, -99696600, -1355744481, -705832890, -1066570375, -103885908, -56343225, -66680845, -179323404, -136391955, -11874698, -562609320, -101480040, -1085198751, -501226950, -676960505, -43643628, -10715655],121,22]
%
% END OF LATTICE L122.22
%
%
% LATTICE L122.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[6402166680, 35364420, 1599343200; 35364420, 476392, 8834280; 1599343200, 8834280, 399536407],[5460, 28, 1],[3894461, 18934267, 1544214, 4497962, 16042912, 3154574, 88189299, 16711195, 34696562, 8320819, 536673, 737158, 1136082, -341, 133657, 4027437, 1477045, 52303144, 11078519, 25514485, 8661784, 1007200; -11364, -55250, -4506, -13125, -46813, -9205, -257335, -48763, -101244, -24280, -1566, -2151, -3315, 1, -390, -11752, -4310, -152620, -32327, -74451, -25275, -2939; -15589266, -75792600, -6181385, -18005040, -64218700, -12627548, -353015845, -66893792, -138888009, -33307680, -2148266, -2950794, -4547660, 1365, -535020, -16121560, -5912512, -209365975, -44346568, -102132771, -34672540, -4031754],121,23]
%
% END OF LATTICE L122.23
%
%
% LATTICE L122.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-74199003060, -1854974940, 4095000; -1854974940, -46374370, 102375; 4095000, 102375, -226],[5460, 35, 1],[35, 6, -1, -1, 8, 8, 267, 75, 727, 14, 19, 85, 46, 81, 13, 252, 52, 1189, 285, 2393, 30, 21; -1368, -234, 40, 39, -325, -317, -10556, -2963, -28704, -552, -748, -3342, -1807, -3180, -510, -9880, -2038, -46592, -11167, -93756, -1175, -822; 14490, 2717, 0, -453, -2275, 1355, 56056, 16730, 170040, 3619, 5430, 26250, 14937, 27160, 4527, 90545, 19015, 438256, 105490, 889200, 11319, 8150],121,24]
%
% END OF LATTICE L122.24
%
%
% LATTICE L122.25
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-81184740, 2254980, 343980; 2254980, -62634, -9555; 343980, -9555, -1454],[5460, 39, 1],[-5, 16, 1, -139, -56, -1620, -2411, -1629, -2647, -1192, -1801, -303, -1094, -617, -939, -98, -1614, -1901, -1143, -1665, -502, -355; -176, 560, 36, -4865, -1961, -56735, -84440, -57053, -92708, -41750, -63084, -10614, -38325, -21616, -32900, -3434, -56560, -66620, -40057, -58352, -17595, -12446; -26, 105, 0, -910, -360, -10374, -15420, -10413, -16912, -7605, -11466, -1924, -6930, -3900, -5915, -615, -10101, -11880, -7137, -10388, -3120, -2184],121,25]
%
% END OF LATTICE L122.25
%
%
% LATTICE L122.26
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-4451589703470, 5529785625, 1485346685550; 5529785625, -6624930, -1845104625; 1485346685550, -1845104625, -495610539883],[1365, 195, 1],[-611112, 4384587, 3684695, -17742275, -39124855, -1147693451, -171486517, -1160580872, -944273909, -170786625, -648273062, -109579298, -158651161, -224065515, -136524299, -71065555, -1166305159, -137046631, -822846508, -598391831, -71632277, -123059808; -1, 7, 6, -28, -62, -1820, -272, -1841, -1498, -271, -1029, -174, -252, -356, -217, -113, -1855, -218, -1309, -952, -114, -196; -1831505, 13140624, 11043045, -53173666, -117257340, -3439641660, -513945747, -3478265310, -2829992515, -511848168, -1942876845, -328409575, -475478136, -671525205, -409163846, -212983740, -3495421020, -410729277, -2466074130, -1793382605, -214682208, -368810715],121,26]
%
% END OF LATTICE L122.26
%
%
% LATTICE L122.27
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[5144968920, -8064420, 1285305840; -8064420, 151528, -2014740; 1285305840, -2014740, 321092533],[5460, 52, 1],[711287, 638317, -341, -35464, 178674, 6537288, 2607482, 7250621, 9071801, 5856691, 4927177, 2819914, 7601152, 1177408, 24753871, 998393, 18181119, 5631987, 13936585, 15646606, 7091046, 3312292; -2106, -1890, 1, 105, -529, -19355, -7720, -21467, -26859, -17340, -14588, -8349, -22505, -3486, -73290, -2956, -53830, -16675, -41263, -46326, -20995, -9807; -2847234, -2555140, 1365, 141960, -715220, -26168324, -10437575, -29023748, -36313809, -23443940, -19723158, -11287926, -30426900, -4713085, -99088080, -3996500, -72777796, -22544465, -55787212, -62632311, -28384980, -13258882],121,27]
%
% END OF LATTICE L122.27
%
%
% LATTICE L122.28
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[481840184280, 496789020, 120371433000; 496789020, 640200, 124105800; 120371433000, 124105800, 30070721279],[5460, 60, 1],[1788806, 12203162, -341, 156853, 21820297, 58742127, 60217568, 64110591, 346171481, 10203628, 42289612, 7942899, 164913869, 9732046, 13467534, 104691868, 145623678, 116899463, 111060099, 539413674, 11206123, 25832323; -5189, -35399, 1, -455, -63297, -170401, -174681, -185974, -1004185, -29599, -122675, -23041, -478387, -28231, -39067, -303693, -422429, -339105, -322166, -1564745, -32507, -74935; -7160470, -48848436, 1365, -627872, -87345180, -235140780, -241046871, -256630380, -1385701135, -40844436, -169282470, -31794890, -660139116, -38956725, -53909632, -419074500, -582921780, -467940681, -444566100, -2159236625, -44857356, -103405050],121,28]
%
% END OF LATTICE L122.28
%
%
% LATTICE L122.29
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-4076321340, 203816340, -68113500; 203816340, -10190830, 3405675; -68113500, 3405675, -1138114],[5460, 65, 1],[785, 131, -1, -1186, -659, -18059, -5273, -17665, -85427, -2505, -18197, -8705, -1979, -5279, -4358, -661, -9661, -2119, -6095, -25453, -399, -283; 16482, 2751, -20, -24906, -13840, -379274, -110744, -371003, -1794156, -52611, -382186, -182832, -41566, -110880, -91539, -13885, -202951, -44516, -128047, -534744, -8384, -5964; 2340, 392, 0, -3549, -1975, -54145, -15812, -52975, -256200, -7514, -54600, -26130, -5943, -15860, -13104, -1990, -29120, -6392, -18395, -76860, -1209, -910],121,29]
%
% END OF LATTICE L122.29
%
%
% LATTICE L122.30
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-263909860305, 1593057375, 88309147290; 1593057375, -9274902, -533066625; 88309147290, -533066625, -29549883002],[1365, 273, 1],[-176429, 904188, 1063781, -3658842, -11295712, -47335664, -247548623, -335070278, -38945781, -246538212, -26737463, -31636515, -32717132, -64689669, -28154102, -20517232, -48103168, -197832593, -237562714, -24680107, -103404172, -5075481; -1, 5, 6, -20, -62, -260, -1360, -1841, -214, -1355, -147, -174, -180, -356, -155, -113, -265, -1090, -1309, -136, -570, -28; -527254, 2702145, 3179085, -10934365, -33756975, -141461541, -739793355, -1001349804, -116388569, -736773765, -79904292, -94544996, -97774395, -193323585, -84137885, -61315275, -143755209, -591218145, -709950696, -73755931, -309020985, -15167958],121,30]
%
% END OF LATTICE L122.30
%
%
% LATTICE L122.31
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[862835358840, -794184300, 215550229440; -794184300, 817656, -198400020; 215550229440, -198400020, 53847933949],[5460, 84, 1],[-2074081, -10192393, 341, -87301, -23807257, -9260727, -333275341, -71049378, -54864931, -56764751, -6748777, -8910841, -132611593, -10985263, -10897621, -118996729, -23694039, -666352561, -126679218, -87939055, -64069391, -4236145; -6177, -30355, 1, -260, -70902, -27580, -992550, -211597, -163397, -169055, -20099, -26538, -394940, -32716, -32455, -354393, -70565, -1984515, -377273, -261898, -190810, -12616; 8302406, 40799460, -1365, 349460, 95298840, 37070064, 1334078655, 284405856, 219620609, 227225460, 27014898, 35669494, 530835240, 43973265, 43622440, 476335860, 94845636, 2667364245, 507088344, 352014091, 256465440, 16957002],121,31]
%
% END OF LATTICE L122.31
%
%
% LATTICE L122.32
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-57925140, -3619980, 65520; -3619980, -226226, 4095; 65520, 4095, -74],[5460, 91, 1],[13, 1, -1, -7, -4, -14, -137, -90, -61, -59, -11, -31, -4, -11, -2, 1, 5, 53, 36, 25, 26, 5; -198, -15, 16, 105, 59, 205, 2000, 1312, 888, 855, 158, 438, 55, 144, 15, -19, -85, -880, -592, -408, -415, -78; 546, 55, 0, -390, -280, -1066, -10780, -7189, -4944, -5005, -1014, -3276, -510, -1820, -975, -175, -299, -1960, -1001, -516, 0, 104],121,32]
%
% END OF LATTICE L122.32
%
%
% LATTICE L122.33
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-322140, 27300, 16380; 27300, -2310, -1365; 16380, -1365, -682],[5460, 105, 1],[75, 124, 221, 12, 707, 147, 3373, 810, 2271, 86, 61, 35, 19, -1, -1, 8, 18, 631, 180, 589, 35, 49; 966, 1599, 2852, 155, 9139, 1901, 43628, 10478, 29380, 1113, 790, 454, 247, -12, -13, 91, 229, 8060, 2302, 7540, 449, 630; -140, -234, -420, -23, -1365, -285, -6552, -1575, -4420, -168, -120, -70, -39, 0, 2, 0, -30, -1092, -315, -1040, -63, -90],121,33]
%
% END OF LATTICE L122.33
%
%
% LATTICE L122.34
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-44015237175, -838245135, 16492895055; -838245135, -15458170, 314700750; 16492895055, 314700750, -6179313433],[1365, 455, 1],[-312463, 106757, 628000, -1295993, -6668395, -27944489, -29227940, -197807886, -68974628, -29108641, -15784393, -56029607, -3862895, -38189380, -9972421, -12112295, -28397581, -23357992, -140244534, -43709512, -12208877, -2996297; 937386, -320270, -1883994, 3887967, 20005123, 83833207, 87683548, 593421817, 206923242, 87325652, 47353032, 168088299, 11588649, 114567784, 29917170, 36336772, 85192478, 70073758, 420732293, 131128128, 36626517, 8988863; -786240, 268629, 1580215, -3261063, -16779455, -70315765, -73545269, -497737240, -173558505, -73245081, -39717730, -140985390, -9720071, -96094635, -25093263, -30477755, -71455865, -58774919, -352892540, -109984755, -30720781, -7539480],121,34]
%
% END OF LATTICE L122.34
%
%
% LATTICE L122.35
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[248753679720, 553813260, 62142454920; 553813260, 1289960, 138350940; 62142454920, 138350940, 15524130971],[5460, 140, 1],[2852176, 940952, -341, 13637, 10313657, 4057005, 29286462, 31253257, 72477541, 5012958, 2991274, 11896229, 11840999, 4916476, 2936044, 53596098, 10691400, 60187195, 57237173, 119251724, 5802539, 1924861; -8157, -2691, 1, -39, -29497, -11603, -83759, -89384, -207285, -14337, -8555, -34023, -33865, -14061, -8397, -153283, -30577, -172133, -163696, -341055, -16595, -5505; -11417070, -3766568, 1365, -54588, -41284880, -16239920, -117231751, -125104700, -290122755, -20066536, -11973870, -47619810, -47398728, -19680325, -11752788, -214541600, -42796960, -240925321, -229116580, -477356685, -23227176, -7705090],121,35]
%
% END OF LATTICE L122.35
%
%
% LATTICE L122.36
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[53256840, -20218380, 13289640; -20218380, 7989384, -5045040; 13289640, -5045040, 3316279],[5460, 156, 1],[-12750, 12066, 341, -289619, -122039, -3571453, -1334114, -3611749, -1469585, -2659572, -2024560, -344029, -2509519, -357120, -2207834, -234740, -3920906, -1163339, -2810273, -1027868, -1264997, -472893; -37, 35, 1, -840, -354, -10360, -3870, -10477, -4263, -7715, -5873, -998, -7280, -1036, -6405, -681, -11375, -3375, -8153, -2982, -3670, -1372; 51038, -48300, -1365, 1159340, 488520, 14296464, 5340435, 14457768, 5882723, 10646220, 8104278, 1377142, 10045560, 1429545, 8837920, 939660, 15695316, 4656825, 11249472, 4114537, 5063760, 1892982],121,36]
%
% END OF LATTICE L122.36
%
%
% LATTICE L122.37
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2390306100, -298787580, 229320; -298787580, -37348350, 28665; 229320, 28665, -22],[5460, 195, 1],[3, 1, -1, -3, -4, -102, -29, -96, -153, -13, -89, -13, -8, -19, -4, -1, -3, 1, 6, 13, 2, 19; -22, -7, 8, 21, 27, 679, 192, 634, 1008, 85, 574, 82, 49, 112, 21, 3, -49, -24, -94, -168, -19, -154; 2600, 1302, 0, -3913, -6525, -178815, -52212, -174915, -281960, -24804, -180180, -28730, -19593, -52260, -14378, -6540, -95550, -20952, -60255, -83860, -3939, -2730],121,37]
%
% END OF LATTICE L122.37
%
%
% LATTICE L122.38
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[6309565080, 6261533460, 1580822880; 6261533460, 6214128440, 1568789040; 1580822880, 1568789040, 396065489],[5460, 260, 1],[-409511, -43657, 341, -574816, -474314, -14389040, -1087898, -14800597, -18152969, -2220135, -8633833, -4522354, -2257880, -1644296, -6329795, -1169641, -20134015, -1213639, -14790593, -16370086, -1396566, -2873852; -1182, -126, 1, -1659, -1369, -41531, -3140, -42719, -52395, -6408, -24920, -13053, -6517, -4746, -18270, -3376, -58114, -3503, -42691, -47250, -4031, -8295; 1639170, 174748, -1365, 2300844, 1898560, 57595720, 4354583, 59243080, 72661785, 8886644, 34559070, 18101850, 9037728, 6581705, 25336584, 4681780, 80591420, 4857893, 59203040, 65525355, 5590104, 11503310],121,38]
%
% END OF LATTICE L122.38
%
%
% LATTICE L122.39
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1789149180, 447288660, -333060; 447288660, -111822438, 83265; -333060, 83265, -62],[5460, 273, 1],[9, 2, -1, -3, -4, -12, -109, -69, -15, -38, -5, -1, 2, 17, 7, 8, 24, 221, 141, 31, 82, 13; 44, 10, -4, -15, -21, -65, -600, -383, -84, -220, -32, -14, 5, 64, 30, 36, 110, 1020, 653, 144, 385, 62; 10738, 2685, 0, -4030, -6720, -22854, -220500, -143871, -32272, -91455, -16146, -13468, -4050, -5460, 2665, 5355, 18759, 182280, 119301, 26812, 76440, 13416],121,39]
%
% END OF LATTICE L122.39
%
%
% LATTICE L122.40
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[31640963084981250, -5101953401104560, 1681208563385715; -5101953401104560, 822665493371085, -271086809996730; 1681208563385715, -271086809996730, 89329209923546],[1365, 1365, 1],[-151, 1, 906, 371, 3763, 14365, 14578, 97384, 11186, 13679, 7053, 7851, 1539, 14494, 1169, 3937, 8735, 6982, 41216, 4214, 3261, 647; 102817, -1014, -668179, -276090, -2815132, -10764608, -10930783, -73039268, -8391741, -10269702, -5301533, -5910987, -1160620, -10948161, -885544, -2993038, -6659902, -5332093, -31507792, -3224599, -2508272, -506637; 314860, -3096, -2044770, -844831, -8613885, -32937645, -33445944, -223484625, -25676890, -31422846, -16221270, -18085795, -3551091, -33497100, -2709356, -9157050, -20375160, -16312674, -96392205, -9864980, -7673211, -1549665],121,40]
%
% END OF LATTICE L122.40
%
%
% LATTICE L122.41
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1065104040, 20655180, 266065800; 20655180, 427336, 5159700; 266065800, 5159700, 66463939],[5460, 364, 1],[61789, 5431, -341, 43453, 55679, 245805, 654237, 1784470, 313369, 1349901, 151423, 561557, 202351, 208123, 579893, 152103, 377541, 800237, 1955606, 309977, 935701, 56359; -171, -15, 1, -120, -154, -680, -1810, -4937, -867, -3735, -419, -1554, -560, -576, -1605, -421, -1045, -2215, -5413, -858, -2590, -156; -247338, -21740, 1365, -173940, -222880, -983944, -2618875, -7143136, -1254399, -5403580, -606138, -2247882, -810000, -833105, -2321280, -608860, -1511276, -3203305, -7828184, -1240821, -3745560, -225602],121,41]
%
% END OF LATTICE L122.41
%
%
% LATTICE L122.42
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[134392440, 22413300, 33589920; 22413300, 3738840, 5601960; 33589920, 5601960, 8395433],[5460, 420, 1],[7535, 23299, 9939, 2057, 117277, 24007, 136847, 131020, 91579, 13721, 4803, 2745, 3429, 341, -1, 16363, 6833, 50249, 54020, 42061, 8895, 5477; 34, 104, 44, 9, 507, 103, 585, 559, 390, 58, 20, 11, 13, 1, 0, 78, 32, 234, 251, 195, 41, 25; -30170, -93288, -39795, -8236, -469560, -96120, -547911, -524580, -366665, -54936, -19230, -10990, -13728, -1365, 4, -65520, -27360, -201201, -216300, -168415, -35616, -21930],121,42]
%
% END OF LATTICE L122.42
%
%
% LATTICE L122.43
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[5578083420, 17390100, 3063060; 17390100, -661570, 9555; 3063060, 9555, 1682],[5460, 455, 1],[-3667, -205, -5481, -1030, -1719, -4885, -8809, -27807, -18173, -3099, -2343, -4553, -69, 1, 208, 349, 775, 1137, 3147, 1733, 85, -397; 54, 3, 80, 15, 25, 71, 128, 404, 264, 45, 34, 66, 1, 0, -3, -5, -11, -16, -44, -24, -1, 6; 6677580, 373304, 9980880, 1875627, 3130295, 8895575, 16041172, 50636495, 33093000, 5643274, 4266600, 8291010, 125649, -1820, -378768, -635530, -1411280, -2070488, -5730725, -3155820, -154791, 722930],121,43]
%
% END OF LATTICE L122.43
%
%
% LATTICE L122.44
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[202676237400, 155986740, 50631824880; 155986740, 132600, 38968020; 50631824880, 38968020, 12648654443],[5460, 780, 1],[169753, 54539, -341, 237245, 587659, 17830203, 1348139, 18341508, 7498789, 2751499, 10701259, 1868647, 2799221, 2038741, 2616515, 1450741, 24976197, 1505621, 18349692, 6770011, 1732981, 3567541; -436, -140, 1, -609, -1509, -45787, -3462, -47101, -19257, -7066, -27482, -4799, -7189, -5236, -6720, -3726, -64148, -3867, -47129, -17388, -4451, -9163; -679510, -218316, 1365, -949676, -2352360, -71373120, -5396511, -73419840, -30017155, -11014068, -42836430, -7480070, -11205096, -8160945, -10473736, -5807220, -99978060, -6026901, -73452600, -27099905, -6937008, -14280630],121,44]
%
% END OF LATTICE L122.44
%
%
% LATTICE L122.45
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[606924984120, -453250980, 151619755560; -453250980, 342888, -113229480; 151619755560, -113229480, 37877086753],[5460, 1092, 1],[-245020, -80536, 341, -87361, -424519, -1945143, -5237212, -14353107, -843919, -11041586, -1261954, -1595017, -1759501, -1840378, -1752676, -1415518, -3574968, -7643047, -18767559, -996118, -9198821, -578083; -897, -295, 1, -320, -1554, -7120, -19170, -52537, -3089, -40415, -4619, -5838, -6440, -6736, -6415, -5181, -13085, -27975, -68693, -3646, -33670, -2116; 980798, 322380, -1365, 349700, 1699320, 7786272, 20964195, 57454488, 3378149, 44198700, 5051514, 6384742, 7043160, 7366905, 7015840, 5666220, 14310348, 30594585, 75125232, 3987391, 36822240, 2314026],121,45]
%
% END OF LATTICE L122.45
%
%
% LATTICE L122.46
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[5460, 0, 0; 0, -1984710, 9555; 0, 9555, -46],[5460, 1365, 1],[-1, 0, 1, 0, -1, -5, -11, -38, -9, -6, -7, -9, -1, -21, -1, -4, -10, -17, -52, -11, -5, -3; 22, 1, 0, -1, -5, -11, -16, -44, -8, -1, 6, 18, 3, 80, 5, 25, 71, 128, 404, 88, 45, 34; 4550, 207, 0, -208, -1050, -2340, -3444, -9555, -1760, -273, 1170, 3640, 612, 16380, 1027, 5145, 14625, 26376, 83265, 18140, 9282, 7020],121,46]
%
% END OF LATTICE L122.46
%
%
% LATTICE L122.47
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[12030995079940200, 31737183660, -3005526335087640; 31737183660, 83720, -7928433240; -3005526335087640, -7928433240, 750826385588567],[5460, 1820, 1],[-8091943, -596011, -3112312, -1760693, -2314327, -5720885, -2416510, -29464266, -4658386, -2780473, -800377, -622667, 15037, 207442, 17771, -590543, -2993725, -1650308, -22823394, -4056224, -3610241, -2104493; 24274791, 1787955, 9336521, 5281836, 6942646, 17161796, 7249160, 88388237, 13974429, 8340963, 2400983, 1867794, -45116, -622326, -53319, 1771549, 8980789, 4950713, 68467273, 12168156, 10830266, 6313212; -32391450, -2385788, -12458355, -7047924, -9264080, -22900280, -9673111, -117943280, -18647175, -11130028, -3203850, -2492490, 60192, 830375, 71136, -2363900, -11983660, -6606061, -91360360, -16236765, -14451528, -8424130],121,47]
%
% END OF LATTICE L122.47
%
%
% LATTICE L122.48
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[251160, -52170300, -13033020; -52170300, 10836538440, 2707149900; -13033020, 2707149900, 676291661],[5460, 5460, 1],[-69, -5, 0, -2, -80, -386, -211, -2909, -172, -457, -267, -346, -78, -415, -81, -335, -859, -370, -4561, -243, -456, -148; 227, -33, -341, -13, 839, 4285, 2365, 32722, 1939, 5181, 3019, 3863, 851, 4431, 831, 3251, 7985, 3361, 40898, 2151, 3817, 1071; -910, 132, 1365, 52, -3360, -17160, -9471, -131040, -7765, -20748, -12090, -15470, -3408, -17745, -3328, -13020, -31980, -13461, -163800, -8615, -15288, -4290],121,48]
%
% END OF LATTICE L122.48
%

\medskip%
%------------------------------WEYL-GROUP-W123--------------------------------
%
\leavevmode\llap{}%
$W_{123}$%
\qquad\llap{16} lattices, $\chi=3$%
\hfill%
$4222$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L123.1
%
\leavevmode%
${L_{123.1}}$%
{} : {$1\above{1pt}{1pt}{2}{2}8\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2\rightarrow N'_{3}}%
\EasyButWeakLineBreak%
{${2}\above{1pt}{1pt}{}{4}{1}\above{1pt}{1pt}{r}{2}{12}\above{1pt}{1pt}{*}{2}{8}\above{1pt}{1pt}{b}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1176\\-552\\120
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-552\\-259\\56
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
120\\56\\-11
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\-7\\-3
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-4\\9\\2
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-5\\12\\6
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
9\\-20\\-4
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-1176, -552, 120; -552, -259, 56; 120, 56, -11],[24, 1, 1],[3, -4, -5, 9; -7, 9, 12, -20; -3, 2, 6, -4],122,1]
%
% END OF LATTICE L123.1
%
\hbox{}\par\smallskip%
%
% LATTICE L123.2
%
\leavevmode%
${L_{123.2}}$%
{} : {$1\above{1pt}{1pt}{-2}{2}8\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{m}%
\EasyButWeakLineBreak%
{${2}\above{1pt}{1pt}{*}{4}{4}\above{1pt}{1pt}{l}{2}{3}\above{1pt}{1pt}{}{2}{8}\above{1pt}{1pt}{r}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2616\\120\\72
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
120\\-5\\-4
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
72\\-4\\-1
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\15\\11
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-16\\-10
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-15\\-12
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\16\\8
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-2616, 120, 72; 120, -5, -4; 72, -4, -1],[24, 1, 1],[1, -1, -1, 1; 15, -16, -15, 16; 11, -10, -12, 8],122,2]
%
% END OF LATTICE L123.2
%
%
% LATTICE L123.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-6, 0, 0; 0, 1, 0; 0, 0, 1],[6, 1, 1],[0, 0, -1, -1; -1, 1, 0, -2; 1, 0, -3, -2],122,3]
%
% END OF LATTICE L123.3
%
%
% LATTICE L123.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-588, 36, 72; 36, -2, -5; 72, -5, -7],[12, 1, 1],[1, -1, -2, 1; 10, -9, -21, 8; 3, -4, -6, 4],122,4]
%
% END OF LATTICE L123.4
%
%
% LATTICE L123.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-102, 30, -42; 30, -8, 12; -42, 12, -17],[6, 2, 1],[0, -1, 5, 3; -3, 2, 3, -1; -2, 4, -12, -9],122,5]
%
% END OF LATTICE L123.5
%
%
% LATTICE L123.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-138, -36, -60; -36, -3, -15; -60, -15, -26],[6, 3, 1],[6, -5, 0, 11; 2, -1, -1, 0; -15, 12, 1, -24],122,6]
%
% END OF LATTICE L123.6
%
%
% LATTICE L123.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[12, 0, 0; 0, -6, -3; 0, -3, -1],[12, 3, 1],[0, -1, 0, 1; 1, -1, -1, 0; -3, 0, 2, 0],122,7]
%
% END OF LATTICE L123.7
%
%
% LATTICE L123.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[12, 162, 66; 162, 2910, 1188; 66, 1188, 485],[6, 6, 1],[1, 1, -4, -6; 0, -5, 19, 31; 0, 12, -46, -75],122,8]
%
% END OF LATTICE L123.8
%
%
% LATTICE L123.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1140, 204, 444; 204, 40, 80; 444, 80, 173],[12, 4, 1],[3, 6, 4, 1; 1, 1, 3, 1; -8, -16, -12, -3],122,9]
%
% END OF LATTICE L123.9
%
%
% LATTICE L123.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-264, -96, -120; -96, -33, -42; -120, -42, -53],[24, 3, 1],[-1, 0, 1, 1; -1, -4, 2, 12; 3, 3, -4, -12],122,10]
%
% END OF LATTICE L123.10
%
%
% LATTICE L123.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-14376, 288, 576; 288, -3, -12; 576, -12, -23],[24, 3, 1],[3, -1, -1, 1; 11, -2, -4, 0; 69, -24, -23, 24],122,11]
%
% END OF LATTICE L123.11
%
%
% LATTICE L123.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[12, -36, -12; -36, 120, 36; -12, 36, 11],[12, 12, 1],[1, 2, 0, 0; 0, 1, -1, -1; 0, 0, 4, 3],122,12]
%
% END OF LATTICE L123.12
%
%
% LATTICE L123.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-48, 72, -24; 72, -88, 32; -24, 32, -11],[24, 8, 1],[-1, 2, 1, -1; 2, -1, -3, 0; 8, -8, -12, 2],122,13]
%
% END OF LATTICE L123.13
%
%
% LATTICE L123.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-24816, 552, 1080; 552, -8, -24; 1080, -24, -47],[24, 8, 1],[-1, 4, 1, -1; 2, -1, -3, 0; -24, 92, 24, -23],122,14]
%
% END OF LATTICE L123.14
%
%
% LATTICE L123.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-264, 1416, 168; 1416, -6864, -816; 168, -816, -97],[24, 24, 1],[2, -1, -1, 0; -11, 14, 5, -5; 96, -120, -44, 42],122,15]
%
% END OF LATTICE L123.15
%
%
% LATTICE L123.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-24, 504, -192; 504, -6864, 2616; -192, 2616, -997],[24, 24, 1],[2, -1, -1, 0; -9, 32, 3, -8; -24, 84, 8, -21],122,16]
%
% END OF LATTICE L123.16
%

\medskip%
%------------------------------WEYL-GROUP-W124--------------------------------
%
\leavevmode\llap{}%
$W_{124}$%
\qquad\llap{46} lattices, $\chi=12$%
\hfill%
$222222\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L124.1
%
\leavevmode%
${L_{124.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{4}8\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2\rightarrow N'_{4}}%
\EasyButWeakLineBreak%
{${4}\above{1pt}{1pt}{l}{2}{5}\above{1pt}{1pt}{}{2}{8}\above{1pt}{1pt}{}{2}{1}\above{1pt}{1pt}{r}{2}{20}\above{1pt}{1pt}{*}{2}{8}\above{1pt}{1pt}{*}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3320\\120\\120
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
120\\-4\\-5
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
120\\-5\\-3
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-18\\-10
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\20\\5
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\56\\24
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\18\\9
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\50\\30
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-20\\-8
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-3320, 120, 120; 120, -4, -5; 120, -5, -3],[40, 1, 1],[-1, 1, 3, 1, 3, -1; -18, 20, 56, 18, 50, -20; -10, 5, 24, 9, 30, -8],123,1]
%
% END OF LATTICE L124.1
%
\hbox{}\par\smallskip%
%
% LATTICE L124.2
%
\leavevmode%
${L_{124.2}}$%
{} : {$1\above{1pt}{1pt}{-2}{6}8\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{m}%
\EasyButWeakLineBreak%
{${1}\above{1pt}{1pt}{}{2}{5}\above{1pt}{1pt}{r}{2}{8}\above{1pt}{1pt}{l}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2120\\280\\80
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
280\\-19\\-10
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
80\\-10\\-3
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
79\\-80\\2320
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-9\\8\\-261
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3\\3\\-88
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\1\\-30
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\0\\25
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5\\-4\\144
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-2120, 280, 80; 280, -19, -10; 80, -10, -3],[40, 1, 1],[-1, 1, 5, 2, 4, -1; 1, 0, -4, -2, -5, 0; -30, 25, 144, 59, 120, -28],123,2]
%
% END OF LATTICE L124.2
%
\hbox{}\par\smallskip%
%
% LATTICE L124.3
%
\leavevmode%
${L_{124.3}}$%
{} : {$1\above{1pt}{1pt}{2}{6}8\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{1}{}$}\EasyButWeakLineBreak%
{${4}\above{1pt}{1pt}{*}{2}{20}\above{1pt}{1pt}{s}{2}{8}\above{1pt}{1pt}{s}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
920\\200\\0
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
200\\43\\1
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\1\\-2
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\0\\0
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\-1\\-1
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\1
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\-14\\-8
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
11\\-50\\-30
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\-4\\-4
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[920, 200, 0; 200, 43, 1; 0, 1, -2],[40, 1, 1],[3, 11, 1, -3, -11, -1; -14, -50, -4, 14, 50, 4; -8, -30, -4, 6, 20, 0],123,3]
%
% END OF LATTICE L124.3
%
\hbox{}\par\smallskip%
%
% LATTICE L124.4
%
\leavevmode%
${L_{124.4}}$%
{} : {$[1\above{1pt}{1pt}{1}{}2\above{1pt}{1pt}{1}{}]\above{1pt}{1pt}{}{2}16\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${1}\above{1pt}{1pt}{r}{2}{80}\above{1pt}{1pt}{*}{2}{8}\above{1pt}{1pt}{s}{2}{16}\above{1pt}{1pt}{*}{2}{20}\above{1pt}{1pt}{l}{2}{2}\above{1pt}{1pt}{}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5680\\2720\\-80
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2720\\1302\\-38
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-80\\-38\\1
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\-1
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-9\\20\\40
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\2\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5\\-12\\-48
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
17\\-40\\-150
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\-7\\-26
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[5680, 2720, -80; 2720, 1302, -38; -80, -38, 1],[80, 2, 1],[0, -9, -1, 5, 17, 3; 0, 20, 2, -12, -40, -7; -1, 40, 0, -48, -150, -26],123,4]
%
% END OF LATTICE L124.4
%
\hbox{}\par\smallskip%
%
% LATTICE L124.5
%
\leavevmode%
${L_{124.5}}$%
{} : {$[1\above{1pt}{1pt}{-}{}2\above{1pt}{1pt}{1}{}]\above{1pt}{1pt}{}{6}16\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{m}%
\EasyButWeakLineBreak%
{${4}\above{1pt}{1pt}{*}{2}{80}\above{1pt}{1pt}{s}{2}{8}\above{1pt}{1pt}{*}{2}{16}\above{1pt}{1pt}{l}{2}{5}\above{1pt}{1pt}{}{2}{2}\above{1pt}{1pt}{r}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4080\\-160\\80
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-160\\6\\-2
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
80\\-2\\-3
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\28\\6
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\20\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-30\\-8
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-28\\-8
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\30\\5
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\29\\6
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[4080, -160, 80; -160, 6, -2; 80, -2, -3],[80, 2, 1],[1, 1, -1, -1, 1, 1; 28, 20, -30, -28, 30, 29; 6, 0, -8, -8, 5, 6],123,5]
%
% END OF LATTICE L124.5
%
\hbox{}\par\smallskip%
%
% LATTICE L124.6
%
\leavevmode%
${L_{124.6}}$%
{} : {$[1\above{1pt}{1pt}{1}{}2\above{1pt}{1pt}{1}{}]\above{1pt}{1pt}{}{0}16\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{m}%
\EasyButWeakLineBreak%
{${1}\above{1pt}{1pt}{}{2}{80}\above{1pt}{1pt}{}{2}{2}\above{1pt}{1pt}{r}{2}{16}\above{1pt}{1pt}{s}{2}{20}\above{1pt}{1pt}{*}{2}{8}\above{1pt}{1pt}{l}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2480\\80\\80
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
80\\-2\\-4
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
80\\-4\\1
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\-1
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-7\\-160\\-80
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-23\\-10
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-24\\-8
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\20\\10
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\22\\8
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-2480, 80, 80; 80, -2, -4; 80, -4, 1],[80, 2, 1],[0, -7, -1, -1, 1, 1; 0, -160, -23, -24, 20, 22; -1, -80, -10, -8, 10, 8],123,6]
%
% END OF LATTICE L124.6
%
\hbox{}\par\smallskip%
%
% LATTICE L124.7
%
\leavevmode%
${L_{124.7}}$%
{} : {$[1\above{1pt}{1pt}{-}{}2\above{1pt}{1pt}{1}{}]\above{1pt}{1pt}{}{4}16\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{1}{}$}\EasyButWeakLineBreak%
{${4}\above{1pt}{1pt}{s}{2}{80}\above{1pt}{1pt}{l}{2}{2}\above{1pt}{1pt}{}{2}{16}\above{1pt}{1pt}{}{2}{5}\above{1pt}{1pt}{r}{2}{8}\above{1pt}{1pt}{*}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-64880\\1120\\1120
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1120\\-18\\-20
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1120\\-20\\-19
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-20\\-38
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7\\120\\280
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\37\\78
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5\\96\\192
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\40\\75
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-18\\-40
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-64880, 1120, 1120; 1120, -18, -20; 1120, -20, -19],[80, 2, 1],[-1, 7, 2, 5, 2, -1; -20, 120, 37, 96, 40, -18; -38, 280, 78, 192, 75, -40],123,7]
%
% END OF LATTICE L124.7
%
%
% LATTICE L124.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-30, -10, 0; -10, -3, 0; 0, 0, 1],[10, 1, 1],[0, -2, 1, 4, 22, 7; 0, 5, -2, -9, -50, -16; 1, 0, -2, -2, -5, 0],123,8]
%
% END OF LATTICE L124.8
%
%
% LATTICE L124.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[60, 20, -20; 20, 6, -9; -20, -9, -1],[20, 1, 1],[3, 11, 1, -3, -11, -1; -7, -25, -2, 7, 25, 2; 2, 0, -4, -4, -10, 0],123,9]
%
% END OF LATTICE L124.9
%
%
% LATTICE L124.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[20, 0, 0; 0, 2, 0; 0, 0, -1],[20, 2, 1],[-1, -3, -1, 0, 1, 0; 0, -5, -3, -1, 0, 1; -4, -15, -6, -1, 0, 0],123,10]
%
% END OF LATTICE L124.10
%
%
% LATTICE L124.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-1960, 360, -120; 360, -66, 22; -120, 22, -7],[40, 2, 1],[-1, 2, 1, 1, 1, -1; -4, 15, 6, 5, 0, -6; 4, 10, 1, -2, -20, -2],123,11]
%
% END OF LATTICE L124.11
%
%
% LATTICE L124.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-2840, 0, 160; 0, 2, 0; 160, 0, -9],[40, 2, 1],[0, 7, 1, 1, -1, -1; 1, 0, -1, -4, -5, 0; 0, 120, 17, 16, -20, -18],123,12]
%
% END OF LATTICE L124.12
%
%
% LATTICE L124.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-660, 70, -290; 70, -6, 30; -290, 30, -127],[10, 2, 1],[-6, -7, 2, 3, -8, -5; 9, 15, -2, -5, 5, 6; 16, 20, -5, -8, 20, 13],123,13]
%
% END OF LATTICE L124.13
%
%
% LATTICE L124.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-410, -150, -180; -150, -20, -65; -180, -65, -79],[10, 5, 1],[-28, -9, 13, 15, -4, -39; -2, -1, 0, 1, 0, -2; 65, 21, -30, -35, 9, 90],123,14]
%
% END OF LATTICE L124.14
%
%
% LATTICE L124.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[4760, -660, 1240; -660, 92, -172; 1240, -172, 323],[20, 4, 1],[-1, -37, -11, -9, -13, 1; 0, 70, 22, 18, 20, -4; 4, 180, 54, 44, 60, -6],123,15]
%
% END OF LATTICE L124.15
%
%
% LATTICE L124.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[460, 180, -40; 180, 70, -15; -40, -15, 3],[20, 5, 1],[-1, -1, -1, 1, 1, 1; 3, 3, 2, -5, -5, -6; 0, 2, 0, -10, -12, -20],123,16]
%
% END OF LATTICE L124.16
%
%
% LATTICE L124.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[10, 650, 290; 650, 49480, 22080; 290, 22080, 9853],[10, 10, 1],[3, 1, 0, 1, 3, 4; -67, -50, -29, 0, -17, -38; 150, 112, 65, 0, 38, 85],123,17]
%
% END OF LATTICE L124.17
%
%
% LATTICE L124.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2120, 120, 80; 120, 12, -4; 80, -4, -3],[40, 4, 1],[1, 3, -1, -1, 1, 3; -1, -5, 0, 1, 0, -2; 27, 80, -28, -28, 25, 80],123,18]
%
% END OF LATTICE L124.18
%
%
% LATTICE L124.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3320, 840, 320; 840, -212, -80; 320, -80, -29],[40, 4, 1],[-1, -7, -1, 3, 17, 5; -6, -35, -4, 15, 80, 22; 6, 20, 0, -8, -30, -4],123,19]
%
% END OF LATTICE L124.19
%
%
% LATTICE L124.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[680, 280, -80; 280, 95, -30; -80, -30, 9],[40, 5, 1],[1, 1, -1, -3, -1, -1; 2, 2, -4, -10, -4, -8; 15, 16, -20, -60, -23, -40],123,20]
%
% END OF LATTICE L124.20
%
%
% LATTICE L124.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[4440, 880, -200; 880, 165, -40; -200, -40, 9],[40, 5, 1],[2, 1, -1, -2, -1, 1; -2, -1, 0, 1, 0, -4; 35, 18, -20, -40, -23, 0],123,21]
%
% END OF LATTICE L124.21
%
%
% LATTICE L124.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[20, -20, 0; -20, 30, 0; 0, 0, -1],[20, 10, 1],[0, 1, 1, -1, -1, -2; -1, 0, 1, 0, -1, -3; -5, -4, 0, 0, -3, -10],123,22]
%
% END OF LATTICE L124.22
%
%
% LATTICE L124.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[120, 120, -40; 120, 35, -15; -40, -15, 6],[40, 5, 1],[1, 1, 1, -1, -1, -1; 6, 6, 4, -10, -10, -12; 20, 22, 20, -30, -32, -40],123,23]
%
% END OF LATTICE L124.23
%
%
% LATTICE L124.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2040, -560, 120; -560, -136, 32; 120, 32, -7],[40, 8, 1],[0, 7, 1, 1, -2, -1; 1, 10, 1, 0, -5, -1; 4, 160, 21, 16, -60, -22],123,24]
%
% END OF LATTICE L124.24
%
%
% LATTICE L124.25
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2840, 0, 160; 0, 8, 0; 160, 0, -9],[40, 8, 1],[0, 7, 2, 1, -2, -1; 1, 0, -1, -2, -5, 0; 0, 120, 34, 16, -40, -18],123,25]
%
% END OF LATTICE L124.25
%
%
% LATTICE L124.26
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-40, 160, -40; 160, -616, 152; -40, 152, -37],[40, 8, 1],[0, 17, 5, 3, -2, -2; 1, 10, 2, 0, -5, -1; 4, 20, 2, -4, -20, -2],123,26]
%
% END OF LATTICE L124.26
%
%
% LATTICE L124.27
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2040, 1040, -120; 1040, 510, -60; -120, -60, 7],[40, 10, 1],[1, 1, 1, 0, -1, -1; 0, 1, 1, -1, -4, -4; 20, 26, 25, -10, -52, -50],123,27]
%
% END OF LATTICE L124.27
%
%
% LATTICE L124.28
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-120, 0, 40; 0, 10, 0; 40, 0, -13],[40, 10, 1],[0, 3, 2, 1, -1, -3; 1, 0, -1, -4, -1, 0; 0, 8, 5, 0, -4, -10],123,28]
%
% END OF LATTICE L124.28
%
%
% LATTICE L124.29
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[220, -540, -120; -540, 1240, 280; -120, 280, 63],[20, 20, 1],[6, 0, -4, -4, 2, 6; -11, -1, 5, 3, -7, -13; 60, 4, -30, -20, 36, 70],123,29]
%
% END OF LATTICE L124.29
%
%
% LATTICE L124.30
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[5680, 80, -80; 80, -8, 0; -80, 0, 1],[80, 8, 1],[-1, -3, -1, 0, 1, 0; -6, -20, -7, 0, 10, 1; -72, -230, -80, -1, 80, 4],123,30]
%
% END OF LATTICE L124.30
%
%
% LATTICE L124.31
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1520, 0, -720; 0, 8, 0; -720, 0, -341],[80, 8, 1],[1, -19, 0, 23, 72, 25; -1, 0, 1, 0, -5, -3; -2, 40, 0, -48, -150, -52],123,31]
%
% END OF LATTICE L124.31
%
%
% LATTICE L124.32
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[80, 0, 0; 0, 8, 0; 0, 0, -1],[80, 8, 1],[0, 1, 0, -1, -3, -1; -1, 0, 1, 0, -5, -3; -2, 0, 0, -8, -30, -12],123,32]
%
% END OF LATTICE L124.32
%
%
% LATTICE L124.33
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1520, 240, 160; 240, 72, 32; 160, 32, 13],[80, 8, 1],[-1, 1, 2, 1, 1, -1; 24, -20, -43, -22, -20, 23; -48, 35, 80, 42, 40, -44],123,33]
%
% END OF LATTICE L124.33
%
%
% LATTICE L124.34
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[240, -80, 0; -80, 30, 0; 0, 0, -1],[80, 10, 1],[-1, -1, -1, 0, 1, 1; -4, -2, -1, 1, 4, 2; 0, -6, -10, -5, -8, 0],123,34]
%
% END OF LATTICE L124.34
%
%
% LATTICE L124.35
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[4440, 1320, -200; 1320, 380, -60; -200, -60, 9],[40, 20, 1],[-3, -1, -1, 1, 1, -1; 1, 0, -2, -1, -1, 0; -60, -23, -40, 15, 16, -20],123,35]
%
% END OF LATTICE L124.35
%
%
% LATTICE L124.36
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[8240, 2160, -400; 2160, 510, -100; -400, -100, 19],[80, 10, 1],[-1, 1, 3, 1, -3, -5; -4, 3, 9, 2, -12, -18; -40, 37, 110, 30, -128, -200],123,36]
%
% END OF LATTICE L124.36
%
%
% LATTICE L124.37
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-5040, 240, 400; 240, -10, -20; 400, -20, -31],[80, 10, 1],[1, 1, 5, 1, -1, -1; 16, 8, 34, 4, -8, -5; 0, 7, 40, 10, -8, -10],123,37]
%
% END OF LATTICE L124.37
%
%
% LATTICE L124.38
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2320, 0, -160; 0, 10, 0; -160, 0, 11],[80, 10, 1],[3, 3, 7, 1, 1, 0; 0, -2, -6, -1, 0, 1; 40, 42, 100, 15, 16, 0],123,38]
%
% END OF LATTICE L124.38
%
%
% LATTICE L124.39
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[40, 0, 0; 0, -620, -260; 0, -260, -109],[40, 20, 1],[0, -1, -3, -1, 0, 1; 17, 18, 26, -4, -5, 0; -40, -42, -60, 10, 12, 0],123,39]
%
% END OF LATTICE L124.39
%
%
% LATTICE L124.40
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[40, -80, 0; -80, -1960, 80; 0, 80, -3],[40, 40, 1],[0, 3, 2, 1, -2, -3; 1, 2, 1, 0, -1, -1; 20, 48, 25, 0, -28, -30],123,40]
%
% END OF LATTICE L124.40
%
%
% LATTICE L124.41
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2040, 2080, -120; 2080, 2040, -120; -120, -120, 7],[40, 40, 1],[0, 1, 1, -1, -2, -2; 1, 2, 2, 0, -1, -1; 20, 52, 50, -20, -52, -50],123,41]
%
% END OF LATTICE L124.41
%
%
% LATTICE L124.42
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-120, 0, 40; 0, 40, 0; 40, 0, -13],[40, 40, 1],[0, 3, 4, 1, -2, -3; 1, 0, -1, -2, -1, 0; 0, 8, 10, 0, -8, -10],123,42]
%
% END OF LATTICE L124.42
%
%
% LATTICE L124.43
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[240, -480, -80; -480, 680, 120; -80, 120, 21],[80, 40, 1],[-1, -1, -2, 0, 1, 1; 6, 6, 13, 1, -2, -3; -40, -38, -80, -5, 16, 20],123,43]
%
% END OF LATTICE L124.43
%
%
% LATTICE L124.44
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3280, 400, 320; 400, -40, -40; 320, -40, -31],[80, 40, 1],[1, 1, 5, 1, -1, -2; 6, 2, 7, 0, -2, -1; 0, 7, 40, 10, -8, -20],123,44]
%
% END OF LATTICE L124.44
%
%
% LATTICE L124.45
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[80, -80, 0; -80, 120, 0; 0, 0, -1],[80, 40, 1],[0, 1, 1, -1, -1, -2; -1, 0, 1, 0, -1, -3; -10, -8, 0, 0, -6, -20],123,45]
%
% END OF LATTICE L124.45
%
%
% LATTICE L124.46
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2320, -2320, 160; -2320, 2360, -160; 160, -160, 11],[80, 40, 1],[-3, -1, 1, -3, -4, -10; -1, 0, 1, 0, -1, -3; 30, 16, 0, 40, 42, 100],123,46]
%
% END OF LATTICE L124.46
%

\medskip%
%------------------------------WEYL-GROUP-W125--------------------------------
%
\leavevmode\llap{}%
$W_{125}$%
\qquad\llap{20} lattices, $\chi=18$%
\hfill%
$422422\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L125.1
%
\leavevmode%
${L_{125.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{2}8\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{2}{}7\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{2\rightarrow N'_{6}}%
\EasyButWeakLineBreak%
{${2}\above{1pt}{1pt}{*}{4}{4}\above{1pt}{1pt}{*}{2}{8}\above{1pt}{1pt}{b}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-28056\\392\\448
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
392\\-5\\-7
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
448\\-7\\-6
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
671\\27552\\17472
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-10\\-411\\-260
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-10\\-410\\-261
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\40\\27
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-42\\-26
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-40\\-28
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-28056, 392, 448; 392, -5, -7; 448, -7, -6],[56, 1, 1],[1, -1, -1, 1, 9, 9; 40, -42, -40, 42, 370, 368; 27, -26, -28, 25, 234, 236],124,1]
%
% END OF LATTICE L125.1
%
\hbox{}\par\smallskip%
%
% LATTICE L125.2
%
\leavevmode%
${L_{125.2}}$%
{} : {$1\above{1pt}{1pt}{2}{2}16\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{2}{}7\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{2,m}%
\EasyButWeakLineBreak%
{${1}\above{1pt}{1pt}{}{4}{2}\above{1pt}{1pt}{b}{2}{16}\above{1pt}{1pt}{*}{2}{4}\above{1pt}{1pt}{*}{4}{2}\above{1pt}{1pt}{l}{2}{16}\above{1pt}{1pt}{}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-115696\\-57232\\1792
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-57232\\-28311\\886
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1792\\886\\-27
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-17\\35\\20
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
16\\-33\\-21
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
35\\-72\\-40
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-31\\64\\42
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-146\\301\\185
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-295\\608\\368
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-115696, -57232, 1792; -57232, -28311, 886; 1792, 886, -27],[112, 1, 1],[-17, 16, 35, -31, -146, -295; 35, -33, -72, 64, 301, 608; 20, -21, -40, 42, 185, 368],124,2]
%
% END OF LATTICE L125.2
%
%
% LATTICE L125.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-14, 0, 0; 0, 1, 0; 0, 0, 1],[14, 1, 1],[0, 0, -1, -2, -4, -3; -1, 1, 0, -3, -9, -8; 1, 0, -4, -7, -12, -8],124,3]
%
% END OF LATTICE L125.3
%
%
% LATTICE L125.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-3836, 196, 140; 196, -10, -7; 140, -7, -3],[28, 1, 1],[1, 9, 9, 1, -1, -1; 21, 185, 184, 20, -21, -20; -3, -18, -16, -1, 2, 0],124,4]
%
% END OF LATTICE L125.4
%
%
% LATTICE L125.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-67256, 2632, 2632; 2632, -102, -103; 2632, -103, -103],[56, 1, 1],[-2, 0, 5, 3, 2, -1; -1, 1, 0, -3, -9, -16; -50, -1, 128, 80, 61, -8],124,5]
%
% END OF LATTICE L125.5
%
%
% LATTICE L125.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1582, -574, -728; -574, -204, -264; -728, -264, -335],[14, 2, 1],[-18, 7, 38, 120, 197, 64; -1, 1, 0, -3, -9, -4; 40, -16, -83, -260, -424, -137],124,6]
%
% END OF LATTICE L125.6
%
%
% LATTICE L125.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-406, 126, -252; 126, -35, 77; -252, 77, -156],[14, 7, 1],[-11, 4, 49, 79, 132, 87; 6, -1, -34, -60, -107, -74; 21, -7, -98, -161, -273, -182],124,7]
%
% END OF LATTICE L125.7
%
%
% LATTICE L125.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[4088, 2156, -1064; 2156, 1156, -560; -1064, -560, 277],[28, 4, 1],[-38, -205, -45, -13, 1, -6; 7, 40, 9, 3, 0, 1; -132, -708, -155, -44, 4, -21],124,8]
%
% END OF LATTICE L125.8
%
%
% LATTICE L125.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[28, 0, 0; 0, -21, -7; 0, -7, -2],[28, 7, 1],[-1, 0, 1, 0, -4, -5; -1, 2, 0, -3, -18, -16; 0, -7, 0, 7, 35, 28],124,9]
%
% END OF LATTICE L125.9
%
%
% LATTICE L125.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[168, -994, -462; -994, 7070, 3290; -462, 3290, 1531],[14, 14, 1],[3, 0, -13, -49, -92, -33; 72, -13, -272, -990, -1823, -646; -154, 28, 581, 2114, 3892, 1379],124,10]
%
% END OF LATTICE L125.10
%
%
% LATTICE L125.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-616, 168, -56; 168, -35, 21; -56, 21, -2],[56, 7, 1],[-5, 3, 7, -1, -27, -31; -12, 6, 16, -2, -62, -72; 21, -14, -28, 7, 126, 140],124,11]
%
% END OF LATTICE L125.11
%
%
% LATTICE L125.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1736, 1120, -336; 1120, -714, 217; -336, 217, -65],[56, 7, 1],[2, 2, -11, -13, -24, -33; -1, 1, 0, -3, -9, -16; -14, -7, 56, 56, 91, 112],124,12]
%
% END OF LATTICE L125.12
%
%
% LATTICE L125.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-8680, -7952, -3640; -7952, -7272, -3328; -3640, -3328, -1523],[56, 8, 1],[5, -2, -1, 5, 22, 11; -53, 15, 13, -31, -183, -97; 104, -28, -26, 56, 348, 186],124,13]
%
% END OF LATTICE L125.13
%
%
% LATTICE L125.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-73528, 0, 3976; 0, 8, 0; 3976, 0, -215],[56, 8, 1],[-13, 0, 2, 3, -20, -7; -1, 1, 0, -3, -9, -2; -240, 0, 37, 56, -368, -129],124,14]
%
% END OF LATTICE L125.14
%
%
% LATTICE L125.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-6160, -1120, -1232; -1120, -189, -210; -1232, -210, -233],[112, 7, 1],[3, 7, 11, 0, -1, 1; 106, 213, 304, -8, -33, 56; -112, -231, -336, 7, 35, -56],124,15]
%
% END OF LATTICE L125.15
%
%
% LATTICE L125.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[56, 196, -56; 196, 700, -196; -56, -196, 55],[28, 28, 1],[3, 1, 0, 2, 19, 5; -1, 0, 2, 7, 24, 4; 0, 0, 7, 28, 112, 21],124,16]
%
% END OF LATTICE L125.16
%
%
% LATTICE L125.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-224, 784, -112; 784, -2672, 384; -112, 384, -55],[112, 16, 1],[1, 21, 3, 4, -1, -1; -3, -18, -2, -1, 2, 0; -24, -176, -21, -16, 16, 2],124,17]
%
% END OF LATTICE L125.17
%
%
% LATTICE L125.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2651600, -1280888, 89264; -1280888, -618744, 43120; 89264, 43120, -3005],[56, 56, 1],[17, 100, 53, 29, -8, -7; -4, 29, 20, 18, -1, -6; 448, 3388, 1862, 1120, -252, -294],124,18]
%
% END OF LATTICE L125.18
%
%
% LATTICE L125.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[56, 0, 0; 0, -9352, -3472; 0, -3472, -1289],[56, 56, 1],[-3, -9, -2, -1, 1, 0; -21, 124, 44, 83, 0, -13; 56, -336, -119, -224, 0, 35],124,19]
%
% END OF LATTICE L125.19
%
%
% LATTICE L125.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-18704, 167440, 3472; 167440, -1490720, -30912; 3472, -30912, -641],[112, 112, 1],[-1, 2, 0, -3, -18, -2; 44, -23, -9, 31, 323, 42; -2128, 1120, 434, -1512, -15680, -2037],124,20]
%
% END OF LATTICE L125.20
%

\medskip%
%------------------------------WEYL-GROUP-W126--------------------------------
%
\leavevmode\llap{}%
$W_{126}$%
\qquad\llap{16} lattices, $\chi=30$%
\hfill%
$42224222\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L126.1
%
\leavevmode%
${L_{126.1}}$%
{} : {$1\above{1pt}{1pt}{2}{2}8\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{2}{}11\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2\rightarrow N'_{9}}%
\EasyButWeakLineBreak%
{${2}\above{1pt}{1pt}{}{4}{1}\above{1pt}{1pt}{r}{2}{44}\above{1pt}{1pt}{*}{2}{8}\above{1pt}{1pt}{b}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
616\\-176\\-88
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-176\\50\\23
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-88\\23\\-3
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
109\\440\\440
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-29\\-117\\-116
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\8\\7
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\11\\-6
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4\\15\\-3
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
35\\132\\-22
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\4\\0
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[616, -176, -88; -176, 50, 23; -88, 23, -3],[88, 1, 1],[3, 4, 35, 1, -4, -5, -57, -7; 11, 15, 132, 4, -15, -19, -220, -28; -6, -3, -22, 0, 2, -1, -66, -24],125,1]
%
% END OF LATTICE L126.1
%
\hbox{}\par\smallskip%
%
% LATTICE L126.2
%
\leavevmode%
${L_{126.2}}$%
{} : {$1\above{1pt}{1pt}{-2}{2}8\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{2}{}11\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{m}%
\EasyButWeakLineBreak%
{${2}\above{1pt}{1pt}{*}{4}{4}\above{1pt}{1pt}{l}{2}{11}\above{1pt}{1pt}{}{2}{8}\above{1pt}{1pt}{r}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-13816\\440\\352
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
440\\-14\\-11
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
352\\-11\\-5
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
461\\14784\\-616
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-15\\-481\\20
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-15\\-480\\19
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4\\129\\-6
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\98\\-6
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4\\132\\-11
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-32\\0
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-13816, 440, 352; 440, -14, -11; 352, -11, -5],[88, 1, 1],[4, 3, 4, -1, -1, 3, 29, 19; 129, 98, 132, -32, -33, 94, 924, 608; -6, -6, -11, 0, 2, -2, -33, -24],125,2]
%
% END OF LATTICE L126.2
%
%
% LATTICE L126.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-22, 0, 0; 0, 1, 0; 0, 0, 1],[22, 1, 1],[0, 0, -7, -3, -2, -2, -15, -3; -1, 1, 0, -2, -3, -5, -44, -10; 1, 0, -33, -14, -9, -8, -55, -10],125,3]
%
% END OF LATTICE L126.3
%
%
% LATTICE L126.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-396, -176, 44; -176, -78, 21; 44, 21, 5],[44, 1, 1],[8, 6, -5, -11, -5, 0, 71, 29; -17, -13, 11, 24, 11, 1, -143, -60; -1, 2, 0, -4, -3, -10, -88, -20],125,4]
%
% END OF LATTICE L126.4
%
%
% LATTICE L126.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-9966, 638, -4818; 638, -40, 308; -4818, 308, -2329],[22, 2, 1],[152, 441, 4693, 607, 272, -17, -29, 29; -203, -601, -6424, -833, -377, 21, 44, -37; -342, -994, -10582, -1369, -614, 38, 66, -65],125,5]
%
% END OF LATTICE L126.5
%
%
% LATTICE L126.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[123992, -6644, -30756; -6644, 356, 1648; -30756, 1648, 7629],[44, 4, 1],[-70, 1, 23, -3, -28, -197, -2179, -144; -103, 0, 22, -5, -41, -288, -3190, -211; -260, 4, 88, -11, -104, -732, -8096, -535],125,6]
%
% END OF LATTICE L126.6
%
%
% LATTICE L126.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-31130, -1452, -14388; -1452, -55, -671; -14388, -671, -6650],[22, 11, 1],[1224, 3621, 3518, 10035, 2270, -127, -24, 447; 38, 119, 117, 336, 78, -3, -1, 12; -2651, -7843, -7620, -21736, -4917, 275, 52, -968],125,7]
%
% END OF LATTICE L126.7
%
%
% LATTICE L126.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[44, 0, 0; 0, 11, 0; 0, 0, -1],[44, 11, 1],[0, -5, -6, -19, -3, -1, 0, 1; 1, -1, -3, -12, -3, -3, -1, 0; 0, -33, -41, -132, -22, -11, -3, 0],125,8]
%
% END OF LATTICE L126.8
%
%
% LATTICE L126.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[44, 6050, 2882; 6050, 1465926, 698324; 2882, 698324, 332661],[22, 22, 1],[-47, -144, -141, -202, -93, 4, 1, -8; 14400, 45317, 44611, 64103, 29848, -1069, -363, 2269; -30228, -95128, -93646, -134563, -62656, 2244, 762, -4763],125,9]
%
% END OF LATTICE L126.9
%
%
% LATTICE L126.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3432, -704, -176; -704, -136, -32; -176, -32, -7],[88, 8, 1],[-1, 0, 19, 2, 5, 4, 25, 1; 11, -1, -176, -18, -43, -31, -176, -6; -24, 4, 352, 35, 80, 52, 264, 7],125,10]
%
% END OF LATTICE L126.10
%
%
% LATTICE L126.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-36344, 0, -17600; 0, 8, 0; -17600, 0, -8523],[88, 8, 1],[31, 0, -575, -121, -151, -120, -745, -59; -1, 1, 0, -1, -3, -5, -44, -5; -64, 0, 1188, 250, 312, 248, 1540, 122],125,11]
%
% END OF LATTICE L126.11
%
%
% LATTICE L126.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1848, 1320, -176; 1320, 803, -110; -176, -110, 15],[88, 11, 1],[-1, -2, -3, -7, 0, 1, 1, 1; -9, -22, -38, -100, -7, 6, 6, 4; -77, -187, -320, -836, -55, 55, 56, 44],125,12]
%
% END OF LATTICE L126.12
%
%
% LATTICE L126.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[88, 0, 0; 0, -275, 44; 0, 44, -7],[88, 11, 1],[0, -5, -3, -19, -3, -1, 0, 1; -5, -28, -13, -72, -7, 4, 1, 0; -33, -198, -94, -528, -55, 22, 6, 0],125,13]
%
% END OF LATTICE L126.13
%
%
% LATTICE L126.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[44, 0, 0; 0, -308, 88; 0, 88, -25],[44, 44, 1],[1, -1, -3, -3, -3, -3, -1, 0; 0, -27, -31, -24, -14, -1, 3, 3; 0, -88, -100, -77, -44, 0, 12, 11],125,14]
%
% END OF LATTICE L126.14
%
%
% LATTICE L126.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-10296, -7744, -3696; -7744, -5720, -2728; -3696, -2728, -1301],[88, 88, 1],[1, -4, -5, -4, -5, 0, 1, 1; 41, 237, 244, 179, 175, -21, -28, -17; -88, -484, -496, -363, -352, 44, 56, 33],125,15]
%
% END OF LATTICE L126.15
%
%
% LATTICE L126.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[88, 0, 0; 0, -616, -264; 0, -264, -113],[88, 88, 1],[-3, -5, -4, -5, -1, 1, 0, -1; 1, 40, 45, 69, 39, 0, -5, -9; 0, -88, -100, -154, -88, 0, 12, 22],125,16]
%
% END OF LATTICE L126.16
%

\medskip%
%------------------------------WEYL-GROUP-W127--------------------------------
%
\leavevmode\llap{}%
$W_{127}$%
\qquad\llap{32} lattices, $\chi=9$%
\hfill%
$42222$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L127.1
%
\leavevmode%
${L_{127.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{2}8\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{2}{}5\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2\rightarrow N'_{11}}%
\EasyButWeakLineBreak%
{${2}\above{1pt}{1pt}{*}{4}{4}\above{1pt}{1pt}{s}{2}{24}\above{1pt}{1pt}{s}{2}{20}\above{1pt}{1pt}{*}{2}{8}\above{1pt}{1pt}{b}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-27480\\600\\1200
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
600\\-13\\-25
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1200\\-25\\-38
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2\\-110\\9
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\54\\-4
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5\\276\\-24
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-50\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-5\\-272\\20
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-27480, 600, 1200; 600, -13, -25; 1200, -25, -38],[120, 1, 1],[-2, 1, 5, -1, -5; -110, 54, 276, -50, -272; 9, -4, -24, 0, 20],126,1]
%
% END OF LATTICE L127.1
%
\hbox{}\par\smallskip%
%
% LATTICE L127.2
%
\leavevmode%
${L_{127.2}}$%
{} : {$1\above{1pt}{1pt}{2}{2}8\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{2}{}5\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{m}%
\EasyButWeakLineBreak%
{${2}\above{1pt}{1pt}{}{4}{1}\above{1pt}{1pt}{r}{2}{24}\above{1pt}{1pt}{l}{2}{5}\above{1pt}{1pt}{}{2}{8}\above{1pt}{1pt}{r}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-236280\\2280\\1560
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2280\\-22\\-15
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1560\\-15\\-7
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-105\\2
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\104\\-1
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7\\732\\-12
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\210\\-5
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-104\\0
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-236280, 2280, 1560; 2280, -22, -15; 1560, -15, -7],[120, 1, 1],[-1, 1, 7, 2, -1; -105, 104, 732, 210, -104; 2, -1, -12, -5, 0],126,2]
%
% END OF LATTICE L127.2
%
%
% LATTICE L127.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-30, 0, 0; 0, 1, 0; 0, 0, 1],[30, 1, 1],[0, 0, -1, -2, -1; -1, 1, 0, -5, -4; 1, 0, -6, -10, -4],126,3]
%
% END OF LATTICE L127.3
%
%
% LATTICE L127.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-154140, 5580, 1740; 5580, -202, -63; 1740, -63, -19],[60, 1, 1],[-2, 1, 5, -1, -5; -55, 27, 138, -25, -136; -1, 2, 0, -10, -8],126,4]
%
% END OF LATTICE L127.4
%
%
% LATTICE L127.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-26610, 1230, -12990; 1230, -56, 600; -12990, 600, -6341],[30, 2, 1],[12, -27, -32, -23, 7; -15, 28, 36, 30, -7; -26, 58, 69, 50, -15],126,5]
%
% END OF LATTICE L127.5
%
%
% LATTICE L127.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-30990, 1620, -10050; 1620, -84, 525; -10050, 525, -3259],[30, 3, 1],[7, -17, -13, -13, 9; -15, 28, 24, 30, -14; -24, 57, 44, 45, -30],126,6]
%
% END OF LATTICE L127.6
%
%
% LATTICE L127.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-41010, 2400, -7950; 2400, -140, 465; -7950, 465, -1541],[30, 5, 1],[3, -9, -19, -1, 5; -15, 28, 72, 6, -14; -20, 55, 120, 7, -30],126,7]
%
% END OF LATTICE L127.7
%
%
% LATTICE L127.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-6420, -3000, 180; -3000, -1401, 84; 180, 84, -5],[60, 3, 1],[-1, 1, 1, -1, -3; 2, -3, -2, 5, 8; -3, -15, 2, 45, 24],126,8]
%
% END OF LATTICE L127.8
%
%
% LATTICE L127.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[269580, -17910, 129150; -17910, 1218, -8580; 129150, -8580, 61873],[30, 6, 1],[23, 521, 178, 619, 36; 0, 11, 4, 15, 1; -48, -1086, -371, -1290, -75],126,9]
%
% END OF LATTICE L127.9
%
%
% LATTICE L127.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[26040, 12780, -6480; 12780, 6596, -3168; -6480, -3168, 1613],[60, 4, 1],[-92, 1, -85, -711, -135; 13, 0, 12, 100, 19; -344, 4, -318, -2660, -505],126,10]
%
% END OF LATTICE L127.10
%
%
% LATTICE L127.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1740, 420, 60; 420, -95, -15; 60, -15, -2],[60, 5, 1],[0, 1, -1, -1, -3; -1, 2, 0, -2, -8; 5, 15, -30, -17, -40],126,11]
%
% END OF LATTICE L127.11
%
%
% LATTICE L127.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[97620, -13650, 46350; -13650, 2030, -6480; 46350, -6480, 22007],[30, 10, 1],[19, 633, 664, 159, 50; 0, 11, 12, 3, 1; -40, -1330, -1395, -334, -105],126,12]
%
% END OF LATTICE L127.12
%
%
% LATTICE L127.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-67560, -3480, 2040; -3480, -165, 108; 2040, 108, -61],[120, 3, 1],[-5, 4, 11, 11, -3; 25, -21, -56, -55, 16; -123, 96, 268, 270, -72],126,13]
%
% END OF LATTICE L127.13
%
%
% LATTICE L127.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-5640, -1200, -240; -1200, -255, -51; -240, -51, -10],[120, 3, 1],[-1, 1, 1, -1, -3; 4, -6, -4, 10, 16; 3, 6, -4, -30, -12],126,14]
%
% END OF LATTICE L127.14
%
%
% LATTICE L127.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[155310, 21390, -34980; 21390, 3045, -4755; -34980, -4755, 7918],[30, 15, 1],[-14, -473, -331, -119, -75; 28, 957, 670, 241, 152; -45, -1515, -1060, -381, -240],126,15]
%
% END OF LATTICE L127.15
%
%
% LATTICE L127.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-51000, 3120, 240; 3120, -190, -15; 240, -15, -1],[120, 5, 1],[0, 1, -1, -1, -3; -1, 14, -12, -14, -44; 10, 30, -60, -34, -80],126,16]
%
% END OF LATTICE L127.16
%
%
% LATTICE L127.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-58200, -13080, -2040; -13080, -2935, -460; -2040, -460, -71],[120, 5, 1],[-7, 6, 47, 3, -5; 21, -19, -144, -9, 16; 65, -50, -420, -28, 40],126,17]
%
% END OF LATTICE L127.17
%
%
% LATTICE L127.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[39180, -1200, -10320; -1200, 60, 312; -10320, 312, 2719],[60, 12, 1],[-29, -29, -7, -113, -25; -18, -19, -5, -75, -16; -108, -108, -26, -420, -93],126,18]
%
% END OF LATTICE L127.18
%
%
% LATTICE L127.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2100, -2040, 360; -2040, -1950, 345; 360, 345, -61],[60, 15, 1],[1, 1, -1, -1, -1; 7, -1, -6, -1, 12; 45, 0, -40, -12, 60],126,19]
%
% END OF LATTICE L127.19
%
%
% LATTICE L127.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-6144180, -3650910, -1501350; -3650910, -2169390, -892110; -1501350, -892110, -366859],[30, 30, 1],[-15, 28, 12, 6, -7; 346, -775, -306, -131, 203; -780, 1770, 695, 294, -465],126,20]
%
% END OF LATTICE L127.20
%
%
% LATTICE L127.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-240, 360, -120; 360, -520, 176; -120, 176, -59],[120, 8, 1],[-1, 4, 4, 2, -1; 2, -1, -3, -5, 0; 8, -12, -18, -20, 2],126,21]
%
% END OF LATTICE L127.21
%
%
% LATTICE L127.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-240, -120, -240; -120, -56, -120; -240, -120, -239],[120, 8, 1],[-1, 8, 7, 2, -1; 2, -1, -3, -5, 0; 0, -8, -6, 0, 1],126,22]
%
% END OF LATTICE L127.22
%
%
% LATTICE L127.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[24900, 780, 6120; 780, 40, 180; 6120, 180, 1513],[60, 20, 1],[27, 0, 8, 28, 31; -77, 1, -21, -79, -88; -100, 0, -30, -104, -115],126,23]
%
% END OF LATTICE L127.23
%
%
% LATTICE L127.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[120, 0, 0; 0, -105, -15; 0, -15, -2],[120, 15, 1],[0, -1, -1, 0, 1; 2, -1, -4, -1, 0; -15, 0, 20, 6, 0],126,24]
%
% END OF LATTICE L127.24
%
%
% LATTICE L127.25
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-4200, -3480, 600; -3480, -2775, 480; 600, 480, -83],[120, 15, 1],[1, 1, -1, -1, -1; 17, 4, -16, -8, 12; 105, 30, -100, -54, 60],126,25]
%
% END OF LATTICE L127.25
%
%
% LATTICE L127.26
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-779280, -35160, 19680; -35160, -1560, 888; 19680, 888, -497],[120, 24, 1],[-11, 24, 10, 26, -5; 2, -1, -1, -5, 0; -432, 948, 394, 1020, -198],126,26]
%
% END OF LATTICE L127.26
%
%
% LATTICE L127.27
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2017680, 19080, 50760; 19080, -168, -480; 50760, -480, -1277],[120, 24, 1],[-3, 32, 9, 6, -4; 2, -1, -1, -5, 0; -120, 1272, 358, 240, -159],126,27]
%
% END OF LATTICE L127.27
%
%
% LATTICE L127.28
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1500, -8940, 2400; -8940, 53400, -14340; 2400, -14340, 3851],[60, 60, 1],[-11, -6, -2, -10, -11; -18, -1, -3, -21, -22; -60, 0, -10, -72, -75],126,28]
%
% END OF LATTICE L127.28
%
%
% LATTICE L127.29
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-343920, 30120, -14160; 30120, -2600, 1240; -14160, 1240, -583],[120, 40, 1],[-13, 32, 38, 6, -7; 2, -1, -3, -1, 0; 320, -780, -930, -148, 170],126,29]
%
% END OF LATTICE L127.29
%
%
% LATTICE L127.30
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1006320, 1023720, 41640; 1023720, -1041400, -42360; 41640, -42360, -1723],[120, 40, 1],[7, -49, -44, -3, 6; 2, -1, -3, -1, 0; 120, -1160, -990, -48, 145],126,30]
%
% END OF LATTICE L127.30
%
%
% LATTICE L127.31
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-7800, -36240, 9840; -36240, -138360, 37680; 9840, 37680, -10261],[120, 120, 1],[17, -61, -21, -7, 15; 257, -948, -324, -106, 233; 960, -3540, -1210, -396, 870],126,31]
%
% END OF LATTICE L127.31
%
%
% LATTICE L127.32
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-840, -30600, -1920; -30600, -1036560, -65040; -1920, -65040, -4081],[120, 120, 1],[2, -1, -1, -1, 0; 15, -128, -37, -6, 16; -240, 2040, 590, 96, -255],126,32]
%
% END OF LATTICE L127.32
%

\medskip%
%------------------------------WEYL-GROUP-W128--------------------------------
%
\leavevmode\llap{}%
$W_{128}$%
\qquad\llap{64} lattices, $\chi=12$%
\hfill%
$222222$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L128.1
%
\leavevmode%
${L_{128.1}}$%
{} : {$1\above{1pt}{1pt}{2}{2}8\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{1}{}9\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{3m,3,2}%
\EasyButWeakLineBreak%
{${8}\above{1pt}{1pt}{r}{2}{90}\above{1pt}{1pt}{b}{2}{2}\above{1pt}{1pt}{b}{2}{360}\above{1pt}{1pt}{*}{2}{12}\above{1pt}{1pt}{l}{2}{9}\above{1pt}{1pt}{}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1187640\\-8640\\6120
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-8640\\-51\\42
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
6120\\42\\-31
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\56\\272
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
8\\465\\2205
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\59\\277
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
11\\660\\3060
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-58\\-276
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-60\\-279
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-1187640, -8640, 6120; -8640, -51, 42; 6120, 42, -31],[360, 3, 1],[1, 8, 1, 11, -1, -1; 56, 465, 59, 660, -58, -60; 272, 2205, 277, 3060, -276, -279],127,1]
%
% END OF LATTICE L128.1
%
\hbox{}\par\smallskip%
%
% LATTICE L128.2
%
\leavevmode%
${L_{128.2}}$%
{} : {$1\above{1pt}{1pt}{-2}{2}8\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{1}{}3\above{1pt}{1pt}{1}{}9\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{32\rightarrow N'_{14},3,m}%
\EasyButWeakLineBreak%
{${72}\above{1pt}{1pt}{b}{2}{10}\above{1pt}{1pt}{s}{2}{18}\above{1pt}{1pt}{l}{2}{40}\above{1pt}{1pt}{}{2}{3}\above{1pt}{1pt}{r}{2}{4}\above{1pt}{1pt}{*}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1281240\\-428040\\4680
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-428040\\-142998\\1563
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4680\\1563\\-17
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
19\\-60\\-288
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
11\\-35\\-190
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\3\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-63\\200\\1040
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-11\\35\\189
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-5\\16\\94
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-1281240, -428040, 4680; -428040, -142998, 1563; 4680, 1563, -17],[360, 3, 1],[19, 11, -1, -63, -11, -5; -60, -35, 3, 200, 35, 16; -288, -190, 0, 1040, 189, 94],127,2]
%
% END OF LATTICE L128.2
%
%
% LATTICE L128.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[390, 180, -30; 180, 83, -15; -30, -15, -14],[30, 1, 1],[-1, 28, -12, -237, -74, -21; 2, -60, 26, 510, 159, 45; 0, 5, -3, -50, -15, -4],127,3]
%
% END OF LATTICE L128.3
%
%
% LATTICE L128.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[420, 120, -60; 120, 34, -19; -60, -19, -3],[60, 1, 1],[5, -3, -4, -31, -1, 4; -16, 10, 13, 100, 3, -13; 0, -5, -3, -20, 0, 2],127,4]
%
% END OF LATTICE L128.4
%
%
% LATTICE L128.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-2040, 120, 360; 120, -7, -20; 360, -20, -39],[120, 1, 1],[1, 6, 3, 17, -1, -1; 16, 115, 59, 340, -18, -20; 0, -5, -3, -20, 0, 1],127,5]
%
% END OF LATTICE L128.5
%
%
% LATTICE L128.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-4314840, 110640, -6240; 110640, -2837, 160; -6240, 160, -9],[120, 1, 1],[3, 6, 2, 7, -1, -1; 116, 235, 79, 280, -39, -40; -20, 15, 17, 120, 0, -18],127,6]
%
% END OF LATTICE L128.6
%
%
% LATTICE L128.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[16290, -1170, -540; -1170, 84, 39; -540, 39, 17],[90, 3, 1],[-1, 1, 1, 11, 0, -2; -12, 15, 13, 150, 1, -24; -4, 0, 2, 0, -3, -9],127,7]
%
% END OF LATTICE L128.7
%
%
% LATTICE L128.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[2426580, 115200, -2340; 115200, 5469, -111; -2340, -111, 2],[180, 3, 1],[13, 4, -1, -17, -5, 0; -276, -85, 21, 360, 106, 0; -108, -35, 0, 100, 33, -1],127,8]
%
% END OF LATTICE L128.8
%
%
% LATTICE L128.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-930, -30, -420; -30, 8, -16; -420, -16, -189],[30, 2, 1],[-5, 96, 94, 253, 71, -11; 4, -65, -67, -185, -54, 7; 11, -210, -206, -555, -156, 24],127,9]
%
% END OF LATTICE L128.9
%
%
% LATTICE L128.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-270, -60, -60; -60, 12, -21; -60, -21, -11],[30, 3, 1],[-5, 51, 49, 261, 12, -6; 8, -65, -67, -370, -18, 7; 18, -180, -174, -930, -43, 21],127,10]
%
% END OF LATTICE L128.10
%
%
% LATTICE L128.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[510, -120, 120; -120, 20, -25; 120, -25, 27],[30, 5, 1],[-1, 3, 13, 13, 8, -2; 8, -13, -67, -74, -54, 7; 10, -24, -110, -114, -75, 15],127,11]
%
% END OF LATTICE L128.11
%
%
% LATTICE L128.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[85260, -3270, 40830; -3270, 126, -1566; 40830, -1566, 19553],[30, 6, 1],[82, -719, -955, -2927, -327, 46; 3, -20, -30, -95, -11, 1; -171, 1500, 1992, 6105, 682, -96],127,12]
%
% END OF LATTICE L128.12
%
%
% LATTICE L128.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1260, -60, -60; -60, 3, 3; -60, 3, 2],[60, 3, 1],[-3, -2, 0, 1, 0, -1; -40, -25, 1, 20, 0, -14; -24, -15, 0, 0, -1, -9],127,13]
%
% END OF LATTICE L128.13
%
%
% LATTICE L128.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[84120, -5220, -20820; -5220, 324, 1292; -20820, 1292, 5153],[60, 4, 1],[13, 69, 18, 17, -13, 1; 14, 75, 19, 15, -18, 0; 49, 260, 68, 65, -48, 4],127,14]
%
% END OF LATTICE L128.14
%
%
% LATTICE L128.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[17190, -1980, 180; -1980, 228, -21; 180, -21, 1],[90, 3, 1],[5, 3, -1, -7, -2, 0; 42, 25, -9, -60, -17, 0; -18, -10, 0, 10, 3, -1],127,15]
%
% END OF LATTICE L128.15
%
%
% LATTICE L128.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1380, -540, -60; -540, 210, 25; -60, 25, 1],[60, 5, 1],[-7, 0, 3, 5, 1, -4; -16, 0, 7, 12, 3, -9; -20, -1, 5, 8, 0, -10],127,16]
%
% END OF LATTICE L128.16
%
%
% LATTICE L128.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[20820, -2130, 9870; -2130, 210, -1010; 9870, -1010, 4679],[30, 10, 1],[88, -135, -951, -593, -1013, 38; 3, -4, -30, -19, -33, 1; -185, 284, 2000, 1247, 2130, -80],127,17]
%
% END OF LATTICE L128.17
%
%
% LATTICE L128.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[9720, -240, -120; -240, 6, 3; -120, 3, 1],[120, 3, 1],[-3, -2, 0, 1, 0, -1; -100, -65, 1, 40, 0, -34; -48, -30, 0, 0, -1, -18],127,18]
%
% END OF LATTICE L128.18
%
%
% LATTICE L128.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1320, 0, 360; 0, 51, -54; 360, -54, -41],[120, 3, 1],[33, 4, -9, -47, 3, 10; 128, 15, -35, -180, 12, 39; 120, 15, -33, -180, 10, 36],127,19]
%
% END OF LATTICE L128.19
%
%
% LATTICE L128.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[27870, 3000, -6780; 3000, 315, -735; -6780, -735, 1646],[30, 15, 1],[-131, 100, 706, 881, 251, -28; 268, -204, -1442, -1800, -513, 57; -420, 321, 2265, 2826, 805, -90],127,20]
%
% END OF LATTICE L128.20
%
%
% LATTICE L128.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[61380, 8190, 30330; 8190, 1014, 4044; 30330, 4044, 14987],[90, 6, 1],[110, -137, -317, -71, 88, 89; 9, -10, -24, -5, 7, 7; -225, 280, 648, 145, -180, -182],127,21]
%
% END OF LATTICE L128.21
%
%
% LATTICE L128.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2520, -1170, -1260; -1170, 978, -546; -1260, -546, -629],[90, 6, 1],[20, 571, -1, -857, -208, -167; 1, 30, 0, -45, -11, -9; -41, -1170, 2, 1755, 426, 342],127,22]
%
% END OF LATTICE L128.22
%
%
% LATTICE L128.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[8820, 540, 540; 540, 33, 33; 540, 33, 34],[180, 3, 1],[1, 1, 0, 7, 1, 2; -12, -15, -1, -120, -14, -24; -4, 0, 1, 0, -3, -9],127,23]
%
% END OF LATTICE L128.23
%
%
% LATTICE L128.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[7080, -360, 0; -360, 10, 5; 0, 5, -3],[120, 5, 1],[-3, 0, 1, 1, -1, -1; -64, -1, 19, 20, -18, -20; -120, -4, 30, 32, -30, -35],127,24]
%
% END OF LATTICE L128.24
%
%
% LATTICE L128.25
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-20280, 2040, -600; 2040, -205, 60; -600, 60, -17],[120, 5, 1],[3, 1, 1, -1, -2, -1; 36, 11, 9, -16, -24, -10; 20, 3, -5, -24, -15, 0],127,25]
%
% END OF LATTICE L128.25
%
%
% LATTICE L128.26
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-660, 60, 180; 60, 216, -12; 180, -12, -49],[60, 12, 1],[7, -17, -13, 4, 14, 32; -1, 0, 1, 0, -1, -3; 27, -60, -48, 15, 52, 120],127,26]
%
% END OF LATTICE L128.26
%
%
% LATTICE L128.27
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[94380, 53850, 22110; 53850, 30690, 12600; 22110, 12600, 5173],[30, 30, 1],[4, -13, -67, -37, -18, 7; -87, 338, 1644, 881, 409, -197; 195, -768, -3720, -1989, -920, 450],127,27]
%
% END OF LATTICE L128.27
%
%
% LATTICE L128.28
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1980, -240, -120; -240, 30, 15; -120, 15, 7],[60, 15, 1],[1, 0, -1, -3, -1, 0; 8, 1, -2, -8, -3, 1; 0, -3, -15, -36, -10, 0],127,28]
%
% END OF LATTICE L128.28
%
%
% LATTICE L128.29
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-12720, 3720, -600; 3720, -984, 152; -600, 152, -23],[120, 8, 1],[1, -1, -3, -3, 2, 3; 12, -10, -36, -40, 21, 35; 53, -40, -160, -190, 84, 152],127,29]
%
% END OF LATTICE L128.29
%
%
% LATTICE L128.30
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[10680, 2400, 1680; 2400, 536, 368; 1680, 368, 237],[120, 8, 1],[7, 1, -15, -21, -11, 6; -41, -5, 89, 125, 66, -35; 14, 0, -32, -45, -24, 12],127,30]
%
% END OF LATTICE L128.30
%
%
% LATTICE L128.31
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[122760, -24480, -360; -24480, 4881, 72; -360, 72, 1],[360, 3, 1],[5, 1, -2, -13, -3, 0; 24, 5, -9, -60, -14, 0; 72, 5, -63, -340, -72, -1],127,31]
%
% END OF LATTICE L128.31
%
%
% LATTICE L128.32
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[360, 0, 0; 0, 3, 0; 0, 0, -1],[360, 3, 1],[-1, -2, 0, 1, 0, -1; -4, -15, -1, 0, 1, 0; -20, -45, -1, 0, 0, -18],127,32]
%
% END OF LATTICE L128.32
%
%
% LATTICE L128.33
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-60, 480, -360; 480, 740, -400; -360, -400, 189],[60, 20, 1],[-12, -15, -16, 2, 49, 11; 32, 40, 43, -5, -129, -29; 45, 56, 60, -7, -180, -40],127,33]
%
% END OF LATTICE L128.33
%
%
% LATTICE L128.34
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[90, -90, 0; -90, 60, 15; 0, 15, -7],[90, 15, 1],[1, 1, 1, -3, -6, -2; 0, 1, 3, -2, -5, -2; 0, 2, 0, -8, -15, -5],127,34]
%
% END OF LATTICE L128.34
%
%
% LATTICE L128.35
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[35010, 15390, -990; 15390, 6765, -435; -990, -435, 28],[90, 15, 1],[5, 5, 1, 1, 0, 4; -12, -12, -2, 0, 1, -9; -10, -9, 5, 36, 15, 0],127,35]
%
% END OF LATTICE L128.35
%
%
% LATTICE L128.36
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-46440, -600, 1200; -600, 30, 15; 1200, 15, -31],[120, 15, 1],[-3, -2, 0, 13, 4, 7; -4, -1, 1, 8, 2, 2; -120, -78, 0, 504, 155, 270],127,36]
%
% END OF LATTICE L128.36
%
%
% LATTICE L128.37
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[6840, -1320, 0; -1320, 30, 15; 0, 15, -1],[120, 15, 1],[-3, -1, 0, 5, 3, 1; -16, -5, 1, 28, 16, 5; -240, -78, 0, 384, 230, 75],127,37]
%
% END OF LATTICE L128.37
%
%
% LATTICE L128.38
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[180, 2700, 0; 2700, -552, 672; 0, 672, -11],[180, 12, 1],[-13, -221, -1, 232, 112, 62; 1, 15, 0, -15, -7, -3; 53, 900, 4, -945, -456, -252],127,38]
%
% END OF LATTICE L128.38
%
%
% LATTICE L128.39
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2672820, -334980, 658620; -334980, 41496, -82536; 658620, -82536, 162293],[180, 12, 1],[-187, 919, 1795, 842, -264, -570; 12, -60, -117, -55, 17, 37; 765, -3760, -7344, -3445, 1080, 2332],127,39]
%
% END OF LATTICE L128.39
%
%
% LATTICE L128.40
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[128340, 55620, -3600; 55620, 24105, -1560; -3600, -1560, 101],[180, 15, 1],[15, 7, 1, 1, 0, 13; -32, -15, -2, 0, 1, -27; 40, 18, 5, 36, 15, 45],127,40]
%
% END OF LATTICE L128.40
%
%
% LATTICE L128.41
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-360, -90, -180; -90, 210, -30; -180, -30, -89],[90, 30, 1],[-22, -1, 43, 9, 14, -5; -3, 0, 6, 1, 1, -1; 45, 2, -90, -19, -30, 10],127,41]
%
% END OF LATTICE L128.41
%
%
% LATTICE L128.42
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[30420, 180, -180; 180, -15, 0; -180, 0, 1],[180, 15, 1],[1, 0, -1, -1, -1, 0; 12, 0, -9, -8, -7, 1; 180, -1, -180, -172, -165, 5],127,42]
%
% END OF LATTICE L128.42
%
%
% LATTICE L128.43
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[58410, -6210, 28710; -6210, -60, -3030; 28710, -3030, 14111],[90, 30, 1],[-61, 334, 332, 145, -249, -703; 4, -21, -21, -9, 16, 45; 125, -684, -680, -297, 510, 1440],127,43]
%
% END OF LATTICE L128.43
%
%
% LATTICE L128.44
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[840, -240, 0; -240, 72, 0; 0, 0, -1],[120, 24, 1],[-1, -1, 1, 1, 0, -1; -3, -5, 3, 5, 1, -2; -6, 0, 0, -15, -8, -12],127,44]
%
% END OF LATTICE L128.44
%
%
% LATTICE L128.45
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1560, -480, -120; -480, 216, 48; -120, 48, 11],[120, 24, 1],[-1, -7, -1, -1, 0, -1; 6, 35, 3, 5, 1, 8; -39, -240, -24, -30, -4, -48],127,45]
%
% END OF LATTICE L128.45
%
%
% LATTICE L128.46
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[540, -420, 120; -420, -1560, 420; 120, 420, -113],[60, 60, 1],[0, -1, -3, -1, 0, 2; 4, 26, 65, 17, -11, -49; 15, 96, 240, 63, -40, -180],127,46]
%
% END OF LATTICE L128.46
%
%
% LATTICE L128.47
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[68520, 25200, -1200; 25200, 9160, -440; -1200, -440, 21],[120, 40, 1],[7, 7, -1, -1, 1, 10; 5, 5, -1, -1, 0, 7; 505, 504, -80, -78, 60, 720],127,47]
%
% END OF LATTICE L128.47
%
%
% LATTICE L128.48
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[120, 0, 0; 0, -40, 0; 0, 0, 1],[120, 40, 1],[-1, -1, -1, 0, 1, 0; 5, 3, 1, 0, 0, 3; -30, -16, 0, 1, 0, -20],127,48]
%
% END OF LATTICE L128.48
%
%
% LATTICE L128.49
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2520, 1440, -720; 1440, -795, 375; -720, 375, -158],[360, 15, 1],[-33, -10, 3, 17, -1, -20; -96, -30, 8, 48, -2, -57; -80, -27, 5, 36, 0, -45],127,49]
%
% END OF LATTICE L128.49
%
%
% LATTICE L128.50
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3960, -360, -720; -360, -30, -75; -720, -75, -97],[360, 15, 1],[1, -1, -1, 7, 7, 5; -12, 7, 9, -48, -49, -36; 0, 2, 0, -16, -15, -10],127,50]
%
% END OF LATTICE L128.50
%
%
% LATTICE L128.51
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-50040, 2880, -1080; 2880, -165, 60; -1080, 60, -17],[360, 15, 1],[3, 2, 0, -7, -2, -1; 60, 39, -1, -144, -40, -18; 20, 9, -5, -72, -15, 0],127,51]
%
% END OF LATTICE L128.51
%
%
% LATTICE L128.52
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[360, 0, -360; 0, -30, -105; -360, -105, -7],[360, 15, 1],[7, 2, -1, -15, -27, -4; -24, -7, 3, 52, 94, 14; 0, 2, 0, -16, -30, -5],127,52]
%
% END OF LATTICE L128.52
%
%
% LATTICE L128.53
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[218520, -74880, -2520; -74880, 25656, 864; -2520, 864, 29],[360, 24, 1],[-7, -7, 1, 2, 2, -1; -15, -15, 3, 5, 5, -2; -162, -160, 0, 25, 24, -28],127,53]
%
% END OF LATTICE L128.53
%
%
% LATTICE L128.54
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[34920, -15120, -1800; -15120, 6216, 744; -1800, 744, 89],[360, 24, 1],[-1, -3, -1, 1, 1, 0; 18, 55, 15, -25, -22, -1; -171, -520, -144, 230, 204, 8],127,54]
%
% END OF LATTICE L128.54
%
%
% LATTICE L128.55
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[720, -360, 0; -360, -4728, 336; 0, 336, -23],[360, 24, 1],[1, -1, -3, -13, 1, 8; 2, 0, -6, -30, 1, 15; 29, 0, -88, -450, 12, 216],127,55]
%
% END OF LATTICE L128.55
%
%
% LATTICE L128.56
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[720, -3240, -1440; -3240, 14136, 6288; -1440, 6288, 2797],[360, 24, 1],[1, 1, -1, -1, 1, 4; -6, 0, 14, 60, 11, -15; 14, 0, -32, -135, -24, 36],127,56]
%
% END OF LATTICE L128.56
%
%
% LATTICE L128.57
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[140760, 12780, -25380; 12780, -780, -3660; -25380, -3660, 3629],[180, 60, 1],[67, -158, -195, -68, 351, 1009; -192, 453, 559, 195, -1006, -2892; 275, -648, -800, -279, 1440, 4140],127,57]
%
% END OF LATTICE L128.57
%
%
% LATTICE L128.58
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1598040, 33660, -365760; 33660, 660, -7740; -365760, -7740, 83689],[180, 60, 1],[11, 43, 88, -53, -469, -171; -33, -129, -267, 158, 1402, 512; 45, 176, 360, -217, -1920, -700],127,58]
%
% END OF LATTICE L128.58
%
%
% LATTICE L128.59
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[240, -3000, -1440; -3000, 33480, 16080; -1440, 16080, 7723],[120, 120, 1],[-1, -1, 1, 1, 2, 1; 72, 46, 0, -10, -19, 29; -150, -96, 0, 21, 40, -60],127,59]
%
% END OF LATTICE L128.59
%
%
% LATTICE L128.60
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[159480, 152880, 75000; 152880, 146520, 71880; 75000, 71880, 35263],[120, 120, 1],[-1, -1, -1, -1, -1, -2; 82, 107, 1, -49, -48, 61; -165, -216, 0, 102, 100, -120],127,60]
%
% END OF LATTICE L128.60
%
%
% LATTICE L128.61
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[720, -37800, 360; -37800, 1866360, -17760; 360, -17760, 169],[360, 120, 1],[-1, -1, 1, 1, 7, 2; -6, -2, 0, 1, 7, 1; -630, -208, 0, 103, 720, 100],127,61]
%
% END OF LATTICE L128.61
%
%
% LATTICE L128.62
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[720, 4680, 2160; 4680, 19560, 9000; 2160, 9000, 4141],[360, 120, 1],[-1, -1, -1, 1, 4, 1; 21, 26, 0, -38, -139, -37; -45, -56, 0, 82, 300, 80],127,62]
%
% END OF LATTICE L128.62
%
%
% LATTICE L128.63
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[17640, 41760, -720; 41760, 97320, -1680; -720, -1680, 29],[360, 120, 1],[0, -1, -1, -1, 0, 1; 2, 3, -3, -3, 1, 12; 115, 144, -200, -198, 60, 720],127,63]
%
% END OF LATTICE L128.63
%
%
% LATTICE L128.64
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-204840, -204840, 2520; -204840, -204720, 2520; 2520, 2520, -31],[360, 120, 1],[-4, -4, 2, 1, -1, -11; -1, -3, -1, 0, 1, 0; -410, -576, 80, 81, 0, -900],127,64]
%
% END OF LATTICE L128.64
%

\medskip%
%------------------------------WEYL-GROUP-W129--------------------------------
%
\leavevmode\llap{}%
$W_{129}$%
\qquad\llap{92} lattices, $\chi=24$%
\hfill%
$22222222\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L129.1
%
\leavevmode%
${L_{129.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{4}8\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{-2}{}7\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{2\rightarrow N'_{17}}%
\EasyButWeakLineBreak%
{${8}\above{1pt}{1pt}{*}{2}{12}\above{1pt}{1pt}{*}{2}{4}\above{1pt}{1pt}{l}{2}{21}\above{1pt}{1pt}{}{2}{8}\above{1pt}{1pt}{}{2}{3}\above{1pt}{1pt}{}{2}{1}\above{1pt}{1pt}{r}{2}{84}\above{1pt}{1pt}{*}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-700728\\2016\\4032
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2016\\-5\\-12
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4032\\-12\\-23
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-68\\-140
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-72\\-138
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\66\\140
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
8\\546\\1113
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\208\\416
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\141\\276
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\72\\137
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5\\378\\672
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-700728, 2016, 4032; 2016, -5, -12; 4032, -12, -23],[168, 1, 1],[-1, -1, 1, 8, 3, 2, 1, 5; -68, -72, 66, 546, 208, 141, 72, 378; -140, -138, 140, 1113, 416, 276, 137, 672],128,1]
%
% END OF LATTICE L129.1
%
\hbox{}\par\smallskip%
%
% LATTICE L129.2
%
\leavevmode%
${L_{129.2}}$%
{} : {$1\above{1pt}{1pt}{-2}{6}8\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{-2}{}7\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{m}%
\EasyButWeakLineBreak%
{${8}\above{1pt}{1pt}{s}{2}{12}\above{1pt}{1pt}{l}{2}{1}\above{1pt}{1pt}{}{2}{21}\above{1pt}{1pt}{r}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1848\\-504\\0
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-504\\137\\1
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\1\\-2
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\0\\0
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\-1\\-1
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\1
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\4\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-5\\-18\\-12
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3\\-11\\-7
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-17\\-63\\-42
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[1848, -504, 0; -504, 137, 1; 0, 1, -2],[168, 1, 1],[1, -5, -3, -17, -1, 5, 3, 17; 4, -18, -11, -63, -4, 18, 11, 63; 0, -12, -7, -42, -4, 6, 4, 21],128,2]
%
% END OF LATTICE L129.2
%
\hbox{}\par\smallskip%
%
% LATTICE L129.3
%
\leavevmode%
${L_{129.3}}$%
{} : {$1\above{1pt}{1pt}{2}{6}8\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{-2}{}7\above{1pt}{1pt}{-}{}$}\EasyButWeakLineBreak%
{${8}\above{1pt}{1pt}{l}{2}{3}\above{1pt}{1pt}{r}{2}{4}\above{1pt}{1pt}{*}{2}{84}\above{1pt}{1pt}{s}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
241752\\336\\-2184
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
336\\-1\\-2
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2184\\-2\\19
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\3528\\1176
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\14\\5
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\-39\\-14
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\76\\120
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\84\\123
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\86\\124
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\84\\126
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[241752, 336, -2184; 336, -1, -2; -2184, -2, 19],[168, 1, 1],[1, 1, 1, 1, -1, -1, -1, -1; 76, 84, 86, 84, -88, -93, -104, -210; 120, 123, 124, 126, -124, -126, -130, -168],128,3]
%
% END OF LATTICE L129.3
%
\hbox{}\par\smallskip%
%
% LATTICE L129.4
%
\leavevmode%
${L_{129.4}}$%
{} : {$[1\above{1pt}{1pt}{-}{}2\above{1pt}{1pt}{1}{}]\above{1pt}{1pt}{}{6}16\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{-2}{}7\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${2}\above{1pt}{1pt}{r}{2}{48}\above{1pt}{1pt}{s}{2}{4}\above{1pt}{1pt}{*}{2}{336}\above{1pt}{1pt}{s}{2}{8}\above{1pt}{1pt}{*}{2}{12}\above{1pt}{1pt}{*}{2}{16}\above{1pt}{1pt}{l}{2}{21}\above{1pt}{1pt}{}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-380688\\2016\\2352
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2016\\-10\\-14
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2352\\-14\\-11
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\125\\54
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
11\\1368\\600
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5\\620\\274
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
55\\6804\\3024
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\122\\56
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-126\\-54
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-124\\-56
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\252\\105
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-380688, 2016, 2352; 2016, -10, -14; 2352, -14, -11],[336, 2, 1],[1, 11, 5, 55, 1, -1, -1, 2; 125, 1368, 620, 6804, 122, -126, -124, 252; 54, 600, 274, 3024, 56, -54, -56, 105],128,4]
%
% END OF LATTICE L129.4
%
\hbox{}\par\smallskip%
%
% LATTICE L129.5
%
\leavevmode%
${L_{129.5}}$%
{} : {$[1\above{1pt}{1pt}{1}{}2\above{1pt}{1pt}{1}{}]\above{1pt}{1pt}{}{2}16\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{-2}{}7\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{m}%
\EasyButWeakLineBreak%
{${2}\above{1pt}{1pt}{}{2}{48}\above{1pt}{1pt}{}{2}{1}\above{1pt}{1pt}{r}{2}{336}\above{1pt}{1pt}{*}{2}{8}\above{1pt}{1pt}{l}{2}{3}\above{1pt}{1pt}{r}{2}{16}\above{1pt}{1pt}{*}{2}{84}\above{1pt}{1pt}{l}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1594320\\4368\\9408
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4368\\-10\\-28
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
9408\\-28\\-53
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\251\\222
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
19\\2376\\2112
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4\\499\\445
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
83\\10332\\9240
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\122\\112
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-126\\-111
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-124\\-112
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
11\\1386\\1218
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-1594320, 4368, 9408; 4368, -10, -28; 9408, -28, -53],[336, 2, 1],[2, 19, 4, 83, 1, -1, -1, 11; 251, 2376, 499, 10332, 122, -126, -124, 1386; 222, 2112, 445, 9240, 112, -111, -112, 1218],128,5]
%
% END OF LATTICE L129.5
%
\hbox{}\par\smallskip%
%
% LATTICE L129.6
%
\leavevmode%
${L_{129.6}}$%
{} : {$[1\above{1pt}{1pt}{-}{}2\above{1pt}{1pt}{1}{}]\above{1pt}{1pt}{}{4}16\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{-2}{}7\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{m}%
\EasyButWeakLineBreak%
{${8}\above{1pt}{1pt}{*}{2}{48}\above{1pt}{1pt}{*}{2}{4}\above{1pt}{1pt}{s}{2}{336}\above{1pt}{1pt}{l}{2}{2}\above{1pt}{1pt}{}{2}{3}\above{1pt}{1pt}{}{2}{16}\above{1pt}{1pt}{}{2}{21}\above{1pt}{1pt}{r}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-423024\\2352\\2352
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2352\\-2\\-14
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2352\\-14\\-13
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\42\\496
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-12\\-168
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-14\\-166
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\0\\168
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\13\\166
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4\\54\\663
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
17\\232\\2816
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
26\\357\\4305
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-423024, 2352, 2352; 2352, -2, -14; 2352, -14, -13],[336, 2, 1],[3, -1, -1, 1, 1, 4, 17, 26; 42, -12, -14, 0, 13, 54, 232, 357; 496, -168, -166, 168, 166, 663, 2816, 4305],128,6]
%
% END OF LATTICE L129.6
%
\hbox{}\par\smallskip%
%
% LATTICE L129.7
%
\leavevmode%
${L_{129.7}}$%
{} : {$[1\above{1pt}{1pt}{1}{}2\above{1pt}{1pt}{1}{}]\above{1pt}{1pt}{}{0}16\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{-2}{}7\above{1pt}{1pt}{-}{}$}\EasyButWeakLineBreak%
{${8}\above{1pt}{1pt}{s}{2}{48}\above{1pt}{1pt}{l}{2}{1}\above{1pt}{1pt}{}{2}{336}\above{1pt}{1pt}{}{2}{2}\above{1pt}{1pt}{r}{2}{12}\above{1pt}{1pt}{s}{2}{16}\above{1pt}{1pt}{s}{2}{84}\above{1pt}{1pt}{*}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-72240\\0\\1344
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\2\\0
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1344\\0\\-25
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\-6\\52
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5\\-12\\264
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\-1\\53
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
19\\0\\1008
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\1\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\0\\-54
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-8\\-56
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\-42\\42
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-72240, 0, 1344; 0, 2, 0; 1344, 0, -25],[336, 2, 1],[1, 5, 1, 19, 0, -1, -1, 1; -6, -12, -1, 0, 1, 0, -8, -42; 52, 264, 53, 1008, 0, -54, -56, 42],128,7]
%
% END OF LATTICE L129.7
%
%
% LATTICE L129.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[1218, -420, 84; -420, 145, -28; 84, -28, 11],[42, 1, 1],[-5, 1, 25, 278, 43, 56, 32, 121; -14, 3, 70, 777, 120, 156, 89, 336; 2, 0, -11, -126, -20, -27, -16, -63],128,8]
%
% END OF LATTICE L129.8
%
%
% LATTICE L129.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[924, 420, 0; 420, 190, 1; 0, 1, -1],[84, 1, 1],[-1, 4, 5, 29, 1, -4, -5, -29; 2, -9, -11, -63, -2, 9, 11, 63; 0, -12, -14, -84, -4, 6, 8, 42],128,9]
%
% END OF LATTICE L129.9
%
%
% LATTICE L129.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-3139836, 156996, -5880; 156996, -7850, 294; -5880, 294, -11],[84, 2, 1],[2, 11, 5, 55, 1, -1, -1, 4; 41, 222, 100, 1092, 19, -21, -20, 84; 26, 48, -3, -252, -28, -27, 0, 105],128,10]
%
% END OF LATTICE L129.10
%
%
% LATTICE L129.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-190344, 2352, 1008; 2352, -22, -14; 1008, -14, -5],[168, 2, 1],[1, -1, -1, 4, 1, 11, 5, 55; 28, -27, -28, 105, 27, 300, 137, 1512; 122, -126, -124, 504, 125, 1368, 620, 6804],128,11]
%
% END OF LATTICE L129.11
%
%
% LATTICE L129.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[168, 0, 0; 0, 2, 0; 0, 0, -1],[168, 2, 1],[-1, -1, 0, 1, 0, -1, -3, -11; -4, 0, 1, 0, -1, -9, -20, -63; -14, -12, 0, 0, -1, -18, -48, -168],128,12]
%
% END OF LATTICE L129.12
%
%
% LATTICE L129.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-50484, 3234, -25578; 3234, -206, 1638; -25578, 1638, -12959],[42, 2, 1],[78, 1250, 1619, 11146, 447, 325, -44, -121; -72, -1137, -1469, -10101, -404, -291, 41, 105; -163, -2610, -3380, -23268, -933, -678, 92, 252],128,13]
%
% END OF LATTICE L129.13
%
%
% LATTICE L129.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-90426, 5292, 29778; 5292, -309, -1743; 29778, -1743, -9806],[42, 3, 1],[-121, -325, -1264, -2902, -699, -85, 34, 32; -144, -379, -1469, -3367, -808, -97, 41, 35; -342, -920, -3579, -8218, -1980, -241, 96, 91],128,14]
%
% END OF LATTICE L129.14
%
%
% LATTICE L129.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[37758, -7938, 15792; -7938, 1704, -3318; 15792, -3318, 6605],[42, 6, 1],[337, 1913, 7511, 17327, 2109, 533, -173, -205; 45, 257, 1010, 2331, 284, 72, -23, -28; -783, -4444, -17448, -40250, -4899, -1238, 402, 476],128,15]
%
% END OF LATTICE L129.15
%
%
% LATTICE L129.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[420, 168, -84; 168, 66, -39; -84, -39, -7],[84, 3, 1],[-15, -12, -29, -47, -1, 4, 5, -9; 34, 27, 65, 105, 2, -9, -11, 21; -12, -8, -18, -28, 0, 2, 0, -14],128,16]
%
% END OF LATTICE L129.16
%
%
% LATTICE L129.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-486654, 3822, -72198; 3822, -28, 567; -72198, 567, -10711],[42, 7, 1],[193, 1522, 1966, 1931, 1081, 389, -55, -20; -16, -150, -199, -198, -114, -45, 4, 3; -1302, -10269, -13265, -13029, -7294, -2625, 371, 135],128,17]
%
% END OF LATTICE L129.17
%
%
% LATTICE L129.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[152376, -2604, 37464; -2604, 44, -640; 37464, -640, 9211],[84, 4, 1],[9, 17, -3, -101, -11, -23, -3, 59; -20, -42, -4, 126, 18, 36, -2, -168; -38, -72, 12, 420, 46, 96, 12, -252],128,18]
%
% END OF LATTICE L129.18
%
%
% LATTICE L129.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-615720, 3192, 6888; 3192, -15, -36; 6888, -36, -77],[168, 3, 1],[-1, -1, 1, 5, 7, 2, 4, 11; -12, -16, 10, 70, 104, 31, 64, 182; -84, -82, 84, 413, 576, 164, 327, 896],128,19]
%
% END OF LATTICE L129.19
%
%
% LATTICE L129.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-69720, 17136, 1008; 17136, -4209, -249; 1008, -249, -14],[168, 3, 1],[1, -5, -3, 6, 19, 15, 18, 29; 4, -18, -11, 21, 68, 54, 65, 105; 0, -40, -21, 56, 156, 118, 138, 217],128,20]
%
% END OF LATTICE L129.20
%
%
% LATTICE L129.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-7224, 168, 168; 168, -3, -6; 168, -6, 1],[168, 3, 1],[-3, 0, 1, 1, -1, -1, -7, -15; -92, 0, 30, 28, -32, -31, -216, -462; -48, -1, 12, 14, -12, -14, -102, -224],128,21]
%
% END OF LATTICE L129.21
%
%
% LATTICE L129.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-924, 168, 252; 168, -30, -42; 252, -42, -41],[84, 6, 1],[6, 9, 11, 37, 1, -1, -1, 6; 41, 60, 72, 238, 5, -7, -6, 42; -6, -8, -9, -28, 0, 1, 0, -7],128,22]
%
% END OF LATTICE L129.22
%
%
% LATTICE L129.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[4949448, -10290, 2383836; -10290, 70, -4956; 2383836, -4956, 1148143],[42, 14, 1],[-5128, -87793, -114994, -113735, -32329, -24578, 2623, 1364; -10, -177, -233, -231, -66, -51, 5, 3; 10647, 182280, 238756, 236142, 67123, 51030, -5446, -2832],128,23]
%
% END OF LATTICE L129.23
%
%
% LATTICE L129.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[34692, 16800, -420; 16800, 8134, -203; -420, -203, 5],[84, 7, 1],[-1, 11, 16, 16, 9, 1, -4, -4; 2, -27, -39, -39, -22, -3, 9, 9; 0, -168, -238, -240, -140, -42, 28, 30],128,24]
%
% END OF LATTICE L129.24
%
%
% LATTICE L129.25
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-8102472, 402192, -13776; 402192, -19964, 684; -13776, 684, -23],[168, 4, 1],[-11, -31, -13, -128, -1, 13, 8, 1; -218, -615, -258, -2541, -20, 258, 159, 21; 104, 276, 113, 1092, 4, -114, -64, 21],128,25]
%
% END OF LATTICE L129.25
%
%
% LATTICE L129.26
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[291144, 504, -2352; 504, -4, -4; -2352, -4, 19],[168, 4, 1],[-1, -2, -1, -1, 1, 1, 1, 1; -2, -9, -10, -63, -4, 0, 1, 0; -124, -252, -130, -168, 120, 123, 124, 126],128,26]
%
% END OF LATTICE L129.26
%
%
% LATTICE L129.27
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[4143846, 11676, 1441398; 11676, 105, 4011; 1441398, 4011, 501412],[42, 21, 1],[-8301, -23686, -93074, -30685, -52333, -6631, 2123, 368; 16582, 47313, 185915, 61293, 104534, 13245, -4241, -735; 23730, 67711, 266070, 87719, 149604, 18956, -6069, -1052],128,27]
%
% END OF LATTICE L129.27
%
%
% LATTICE L129.28
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1848, -1848, 672; -1848, -1302, 486; 672, 486, -181],[168, 6, 1],[1, -1, -1, 6, 3, 9, 11, 37; 10, -15, -12, 91, 44, 128, 153, 504; 30, -44, -36, 266, 129, 376, 450, 1484],128,28]
%
% END OF LATTICE L129.28
%
%
% LATTICE L129.29
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-291144, 0, 2352; 0, 6, 0; 2352, 0, -19],[168, 6, 1],[-1, -1, 0, 5, 1, 1, 3, 1; -4, 0, 1, 0, -1, -3, -20, -21; -126, -124, 0, 616, 123, 122, 360, 112],128,29]
%
% END OF LATTICE L129.29
%
%
% LATTICE L129.30
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[169176, -15540, 42588; -15540, 1428, -3912; 42588, -3912, 10721],[84, 12, 1],[-59, -51, -87, -109, 7, -1, -69, -255; 32, 26, 40, 42, -6, 0, 38, 140; 246, 212, 360, 448, -30, 4, 288, 1064],128,30]
%
% END OF LATTICE L129.30
%
%
% LATTICE L129.31
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[69384, 16800, -840; 16800, 4067, -203; -840, -203, 10],[168, 7, 1],[-1, 11, 8, 8, 9, 1, -2, -2; 4, -54, -39, -39, -44, -6, 9, 9; 0, -168, -119, -120, -140, -42, 14, 15],128,31]
%
% END OF LATTICE L129.31
%
%
% LATTICE L129.32
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-10248, 1176, -168; 1176, -119, 14; -168, 14, -1],[168, 7, 1],[-1, -5, -5, -2, -1, 1, 1, 1; -12, -72, -74, -30, -16, 15, 16, 18; -28, -210, -224, -93, -56, 42, 49, 60],128,32]
%
% END OF LATTICE L129.32
%
%
% LATTICE L129.33
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-9996, 5040, -336; 5040, -2534, 168; -336, 168, -11],[84, 14, 1],[2, -1, -4, -11, -5, -4, -1, 1; 5, -12, -17, -42, -17, -12, -2, 3; 14, -168, -147, -324, -112, -63, 0, 15],128,33]
%
% END OF LATTICE L129.33
%
%
% LATTICE L129.34
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2856, 840, -168; 840, 245, -49; -168, -49, 10],[168, 7, 1],[1, -2, -9, -11, -9, -4, -3, -1; -4, 3, 22, 30, 28, 15, 14, 6; 0, -21, -56, -54, -28, 0, 14, 12],128,34]
%
% END OF LATTICE L129.34
%
%
% LATTICE L129.35
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[24864, 168, -168; 168, -8, 0; -168, 0, 1],[168, 8, 1],[-1, -1, 0, 1, 0, -2, -3, -22; -16, -15, 1, 21, 0, -33, -49, -357; -162, -156, 4, 168, -1, -336, -496, -3612],128,35]
%
% END OF LATTICE L129.35
%
%
% LATTICE L129.36
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[168, 0, 0; 0, 8, 0; 0, 0, -1],[168, 8, 1],[-1, -1, 0, 1, 0, -2, -3, -22; -2, 0, 1, 0, -1, -9, -10, -63; -14, -12, 0, 0, -2, -36, -48, -336],128,36]
%
% END OF LATTICE L129.36
%
%
% LATTICE L129.37
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-6888, 840, 504; 840, 112, 48; 504, 48, 19],[168, 8, 1],[1, -1, -1, 1, 1, 7, 7, 41; -45, 48, 47, -42, -46, -321, -320, -1869; 86, -96, -92, 84, 90, 624, 620, 3612],128,37]
%
% END OF LATTICE L129.37
%
%
% LATTICE L129.38
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-145916148, 354875010, 172466154; 354875010, -863072826, -419445852; 172466154, -419445852, -203847019],[42, 42, 1],[-8, -50, -199, -66, -57, -15, 4, 1; 32788, 172553, 668787, 218979, 183916, 44151, -18675, -2275; -67473, -355096, -1376298, -450638, -378483, -90860, 38430, 4682],128,38]
%
% END OF LATTICE L129.38
%
%
% LATTICE L129.39
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[31164, 14532, -588; 14532, 6762, -273; -588, -273, 11],[84, 21, 1],[-1, 1, 2, 0, -3, -3, -8, -2; 2, -5, -11, -1, 10, 11, 29, 7; 0, -70, -168, -26, 84, 112, 294, 68],128,39]
%
% END OF LATTICE L129.39
%
%
% LATTICE L129.40
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1330224, 7392, 7392; 7392, -30, -42; 7392, -42, -41],[336, 6, 1],[3, 9, 11, 37, 1, -1, -1, 3; 41, 120, 144, 476, 10, -14, -12, 42; 498, 1496, 1830, 6160, 168, -166, -168, 497],128,40]
%
% END OF LATTICE L129.40
%
%
% LATTICE L129.41
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-474600, 66864, -6048; 66864, -9420, 852; -6048, 852, -77],[168, 12, 1],[7, 4, 4, 11, -1, -1, 1, 5; 52, 31, 32, 91, -6, -8, 5, 35; 24, 28, 39, 140, 12, -10, -24, -7],128,41]
%
% END OF LATTICE L129.41
%
%
% LATTICE L129.42
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3696, 336, 1008; 336, -30, -84; 1008, -84, -167],[336, 6, 1],[6, 17, 10, 65, 1, -1, -1, 13; 83, 232, 135, 868, 10, -14, -12, 182; -6, -16, -9, -56, 0, 1, 0, -14],128,42]
%
% END OF LATTICE L129.42
%
%
% LATTICE L129.43
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-168, 168, 0; 168, -12, -12; 0, -12, 1],[168, 12, 1],[-1, -2, -7, -15, -3, 0, 1, 1; -2, -3, -10, -21, -4, 0, 1, 0; -12, -28, -102, -224, -48, -1, 12, 14],128,43]
%
% END OF LATTICE L129.43
%
%
% LATTICE L129.44
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1287888, -35952, 14448; -35952, -1002, 402; 14448, 402, -161],[336, 6, 1],[3, -1, -1, 5, 2, 2, 23, 11; -218, 68, 72, -336, -139, -141, -1632, -784; -276, 80, 90, -392, -168, -173, -2016, -973],128,44]
%
% END OF LATTICE L129.44
%
%
% LATTICE L129.45
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2286480, 0, 13776; 0, 6, 0; 13776, 0, -83],[336, 6, 1],[5, 7, 4, 25, 0, -1, -1, 5; -6, -4, -1, 0, 1, 0, -8, -14; 828, 1160, 663, 4144, 0, -166, -168, 826],128,45]
%
% END OF LATTICE L129.45
%
%
% LATTICE L129.46
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[34440, 5880, -672; 5880, 938, -112; -672, -112, 13],[168, 14, 1],[-5, -4, -1, 1, 1, -1, -4, -11; -20, -15, -4, 3, 3, -12, -19, -48; -434, -336, -84, 78, 77, -168, -378, -996],128,46]
%
% END OF LATTICE L129.46
%
%
% LATTICE L129.47
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[41496, 0, 840; 0, 14, 0; 840, 0, 17],[168, 14, 1],[7, 5, 0, 1, 1, 11, 27, 13; -4, 0, 1, 0, -1, -9, -20, -9; -350, -252, 0, -48, -49, -546, -1344, -648],128,47]
%
% END OF LATTICE L129.47
%
%
% LATTICE L129.48
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[453012, 21504, -93828; 21504, 980, -4480; -93828, -4480, 19417],[84, 28, 1],[-123, -319, -33, 157, 163, 439, 153, -37; 331, 855, 83, -429, -441, -1185, -413, 99; -518, -1344, -140, 660, 686, 1848, 644, -156],128,48]
%
% END OF LATTICE L129.48
%
%
% LATTICE L129.49
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1102416, -21168, 5040; -21168, -392, 96; 5040, 96, -23],[336, 8, 1],[1, 5, 1, 19, 0, -1, -1, 1; 13, 72, 15, 294, 1, -15, -18, 0; 272, 1392, 281, 5376, 4, -282, -296, 210],128,49]
%
% END OF LATTICE L129.49
%
%
% LATTICE L129.50
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[133695408, -6663552, 50400; -6663552, 332120, -2512; 50400, -2512, 19],[336, 8, 1],[3, 1, 1, 1, 0, 5, 4, 61; 61, 21, 22, 21, -1, 96, 79, 1218; 104, 123, 256, 126, -132, -576, -170, -840],128,50]
%
% END OF LATTICE L129.50
%
%
% LATTICE L129.51
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-48149808, 2427264, 48720; 2427264, -122360, -2456; 48720, -2456, -49],[336, 8, 1],[8, 13, -1, -73, -19, -59, -16, -85; 159, 258, -20, -1449, -377, -1170, -317, -1680; -16, -6, 8, 42, 4, -24, -22, -336],128,51]
%
% END OF LATTICE L129.51
%
%
% LATTICE L129.52
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-83119344, 4155984, -30240; 4155984, -207800, 1512; -30240, 1512, -11],[336, 8, 1],[2, 11, 5, 55, 1, -1, -1, 2; 41, 222, 100, 1092, 19, -21, -20, 42; 136, 264, -6, -1176, -140, -138, 0, 273],128,52]
%
% END OF LATTICE L129.52
%
%
% LATTICE L129.53
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[247128, 54936, -3024; 54936, 12201, -672; -3024, -672, 37],[168, 21, 1],[3, 3, 4, 1, 1, -1, -1, 0; -4, 2, 4, 1, 0, -4, -7, -2; 168, 280, 399, 100, 84, -154, -210, -37],128,53]
%
% END OF LATTICE L129.53
%
%
% LATTICE L129.54
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[12264, 11424, -672; 11424, 10731, -630; -672, -630, 37],[168, 21, 1],[-5, -1, -2, -1, -1, -1, -5, -1; -24, -3, -4, -2, -4, -8, -34, -6; -504, -70, -105, -52, -84, -154, -672, -121],128,54]
%
% END OF LATTICE L129.54
%
%
% LATTICE L129.55
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[84, 0, 0; 0, -5082, 294; 0, 294, -17],[84, 42, 1],[-2, 0, 1, 0, -1, -3, -5, -3; -7, -2, 0, 1, 5, 2, -3, -4; -126, -35, 0, 17, 84, 28, -63, -76],128,55]
%
% END OF LATTICE L129.55
%
%
% LATTICE L129.56
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-21000, 5376, -336; 5376, -1365, 84; -336, 84, -5],[168, 21, 1],[1, 1, 5, 1, -1, -1, -5, -1; 0, 5, 28, 6, -4, -6, -34, -8; -84, 14, 126, 32, 0, -35, -252, -74],128,56]
%
% END OF LATTICE L129.56
%
%
% LATTICE L129.57
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-19488, -6552, 504; -6552, -2136, 168; 504, 168, -13],[168, 24, 1],[-1, -1, 0, 5, 1, 2, 3, 2; -2, -1, 1, 7, 1, 1, -1, -7; -66, -52, 12, 280, 51, 88, 96, -28],128,57]
%
% END OF LATTICE L129.57
%
%
% LATTICE L129.58
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-291144, 0, 2352; 0, 24, 0; 2352, 0, -19],[168, 24, 1],[-1, -1, 0, 5, 2, 2, 3, 2; -2, 0, 1, 0, -1, -3, -10, -21; -126, -124, 0, 616, 246, 244, 360, 224],128,58]
%
% END OF LATTICE L129.58
%
%
% LATTICE L129.59
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-30072, -2856, -672; -2856, -240, -48; -672, -48, -7],[168, 24, 1],[1, -1, -1, 5, 3, 5, 13, 23; -17, 20, 19, -98, -58, -95, -244, -427; 30, -40, -36, 196, 114, 184, 468, 812],128,59]
%
% END OF LATTICE L129.59
%
%
% LATTICE L129.60
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-995568, -52080, 5376; -52080, -2674, 280; 5376, 280, -29],[336, 14, 1],[-5, -5, -1, 1, 2, 7, -1, -7; -34, -30, -4, 6, 11, 24, -16, -60; -1260, -1218, -224, 243, 476, 1512, -350, -1896],128,60]
%
% END OF LATTICE L129.60
%
%
% LATTICE L129.61
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-27384, -336, 168; -336, 140, 0; 168, 0, -1],[168, 28, 1],[1, -1, -2, -1, -1, 1, 1, 2; 0, -6, -7, -3, -2, 3, 2, 3; 140, -210, -364, -177, -168, 168, 161, 312],128,61]
%
% END OF LATTICE L129.61
%
%
% LATTICE L129.62
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-830256, -4032, 3024; -4032, 14, 14; 3024, 14, -11],[336, 14, 1],[-5, -2, -1, 1, 1, -1, -2, -11; -34, -12, -4, 6, 5, -24, -17, -84; -1428, -567, -280, 282, 280, -336, -581, -3168],128,62]
%
% END OF LATTICE L129.62
%
%
% LATTICE L129.63
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[22512, 1008, -336; 1008, -14, -14; -336, -14, 5],[336, 14, 1],[1, 1, -1, -1, -3, -7, -1, 1; 1, 0, -8, -3, -6, -12, -2, 0; 70, 63, -112, -81, -224, -504, -70, 72],128,63]
%
% END OF LATTICE L129.63
%
%
% LATTICE L129.64
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-84290640, 0, 759696; 0, 14, 0; 759696, 0, -6847],[336, 14, 1],[0, 67, 161, 71, 27, -53, -20, -61; 1, 0, -8, -6, -6, -12, -1, 0; 0, 7434, 17864, 7878, 2996, -5880, -2219, -6768],128,64]
%
% END OF LATTICE L129.64
%
%
% LATTICE L129.65
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1176, -504, -168; -504, 28, 28; -168, 28, 17],[168, 28, 1],[-1, 1, 2, 1, -1, -5, -5, -4; 22, -9, -23, -12, 12, 69, 74, 63; -56, 21, 56, 30, -28, -168, -182, -156],128,65]
%
% END OF LATTICE L129.65
%
%
% LATTICE L129.66
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[35448, 59136, 3864; 59136, 91434, 5964; 3864, 5964, 389],[168, 42, 1],[-5, -2, -1, 1, 3, 5, 2, -1; 154, 57, 28, -27, -80, -120, -23, 48; -2310, -854, -420, 404, 1197, 1792, 336, -724],128,66]
%
% END OF LATTICE L129.66
%
%
% LATTICE L129.67
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-54264, 0, 840; 0, 42, 0; 840, 0, -13],[168, 42, 1],[-7, -3, 0, 1, 1, -1, -15, -3; -4, 0, 1, 0, -1, -3, -20, -3; -462, -196, 0, 64, 63, -70, -1008, -200],128,67]
%
% END OF LATTICE L129.67
%
%
% LATTICE L129.68
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2940, -39732, -9492; -39732, 520968, 124488; -9492, 124488, 29747],[84, 84, 1],[-24, -8, 26, 16, 26, 10, -20, -14; 229, 73, -279, -167, -269, -113, 159, 127; -966, -308, 1176, 704, 1134, 476, -672, -536],128,68]
%
% END OF LATTICE L129.68
%
%
% LATTICE L129.69
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2117136, -155232, 12768; -155232, -11352, 936; 12768, 936, -77],[336, 24, 1],[0, -1, -1, 5, 5, 7, 4, 25; 1, -1, -4, 0, 3, 6, 4, 28; 12, -178, -216, 826, 864, 1232, 711, 4480],128,69]
%
% END OF LATTICE L129.69
%
%
% LATTICE L129.70
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[104496, -15120, 336; -15120, 2184, -48; 336, -48, 1],[336, 24, 1],[0, -1, -2, -9, -1, 0, 1, 1; -1, -10, -19, -84, -9, 0, 8, 7; -36, -128, -222, -952, -96, -1, 48, 14],128,70]
%
% END OF LATTICE L129.70
%
%
% LATTICE L129.71
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-4096176, 581280, -25200; 581280, -82488, 3576; -25200, 3576, -155],[336, 24, 1],[6, 9, 11, 37, 1, -1, -1, 6; 47, 68, 81, 266, 5, -8, -6, 49; 108, 104, 78, 112, -48, -22, 24, 154],128,71]
%
% END OF LATTICE L129.71
%
%
% LATTICE L129.72
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-9910320, 1651776, -20160; 1651776, -275304, 3360; -20160, 3360, -41],[336, 24, 1],[1, -1, -1, 3, 6, 9, 11, 37; 5, -7, -6, 21, 41, 60, 72, 238; -84, -82, 0, 245, 408, 488, 486, 1288],128,72]
%
% END OF LATTICE L129.72
%
%
% LATTICE L129.73
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3864, 840, -336; 840, 224, -112; -336, -112, 55],[168, 56, 1],[-2, -1, 1, 1, 0, -5, -7, -7; -83, -39, 38, 33, -3, -228, -305, -300; -182, -84, 84, 72, -7, -504, -672, -660],128,73]
%
% END OF LATTICE L129.73
%
%
% LATTICE L129.74
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[41496, -41496, -840; -41496, 41552, 840; -840, 840, 17],[168, 56, 1],[-9, -5, 1, -1, -3, -31, -37, -35; -2, 0, 1, 0, -1, -9, -10, -9; -350, -252, 0, -48, -98, -1092, -1344, -1296],128,74]
%
% END OF LATTICE L129.74
%
%
% LATTICE L129.75
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2184, -7224, 168; -7224, 24080, -560; 168, -560, 13],[168, 56, 1],[-5, -7, -1, 1, 1, -5, -11, -13; -5, -6, -1, 0, 0, -9, -14, -15; -154, -168, -28, -12, -14, -336, -476, -492],128,75]
%
% END OF LATTICE L129.75
%
%
% LATTICE L129.76
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-691152, -66864, 5712; -66864, -6258, 546; 5712, 546, -47],[336, 42, 1],[-5, -3, -1, 1, 6, 13, 11, 3; -34, -18, -4, 6, 35, 72, 56, 12; -1008, -574, -168, 191, 1134, 2408, 1974, 496],128,76]
%
% END OF LATTICE L129.76
%
%
% LATTICE L129.77
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[247128, 109872, -3024; 109872, 48804, -1344; -3024, -1344, 37],[168, 84, 1],[1, -1, -2, 0, 3, 3, 4, 2; 0, -2, -7, -1, -2, 1, 2, 1; 84, -154, -420, -37, 168, 280, 399, 200],128,77]
%
% END OF LATTICE L129.77
%
%
% LATTICE L129.78
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-162960, -29568, 1680; -29568, -4998, 294; 1680, 294, -17],[336, 42, 1],[-5, -1, -1, 1, 3, 5, 1, -1; -34, -6, -4, 6, 17, 24, 1, -12; -1092, -203, -168, 202, 588, 896, 105, -320],128,78]
%
% END OF LATTICE L129.78
%
%
% LATTICE L129.79
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-523824, -6384, -1344; -6384, 42, 42; -1344, 42, 25],[336, 42, 1],[2, 1, 5, 0, -3, -3, -1, 1; -287, -141, -672, 4, 446, 436, 144, -144; 588, 287, 1344, -11, -924, -896, -294, 296],128,79]
%
% END OF LATTICE L129.79
%
%
% LATTICE L129.80
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-22512, 0, 336; 0, 42, 0; 336, 0, -5],[336, 42, 1],[0, -1, -7, -1, -1, 1, 1, 1; 1, 0, -8, -2, -6, -4, -1, 0; 0, -70, -504, -74, -84, 56, 63, 64],128,80]
%
% END OF LATTICE L129.80
%
%
% LATTICE L129.81
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[168, -3192, 840; -3192, -2436, 672; 840, 672, -185],[168, 84, 1],[1, 1, 5, 1, -1, -2, -5, -1; 0, 24, 133, 28, -22, -59, -166, -39; 0, 91, 504, 106, -84, -224, -630, -148],128,81]
%
% END OF LATTICE L129.81
%
%
% LATTICE L129.82
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-112560, 56448, -336; 56448, -28168, 168; -336, 168, -1],[336, 56, 1],[1, 2, 3, 1, 0, -1, 0, 1; 3, 3, 2, 0, -1, 0, 1, 6; 140, -210, -728, -354, -168, 336, 161, 624],128,82]
%
% END OF LATTICE L129.82
%
%
% LATTICE L129.83
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[3713808, -1584576, 8400; -1584576, 676088, -3584; 8400, -3584, 19],[336, 56, 1],[1, 1, 3, 1, 2, 7, 3, 5; 1, 3, 10, 3, 5, 12, 4, 6; -252, 126, 560, 123, 56, -840, -574, -1080],128,83]
%
% END OF LATTICE L129.83
%
%
% LATTICE L129.84
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[955920, 584304, -4032; 584304, 357112, -2464; -4032, -2464, 17],[336, 56, 1],[2, 1, -1, -1, -1, 1, 2, 5; -11, -6, 2, 3, 3, -12, -13, -30; -1120, -630, 56, 198, 196, -1512, -1414, -3168],128,84]
%
% END OF LATTICE L129.84
%
%
% LATTICE L129.85
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-39984, 20160, -672; 20160, -10136, 336; -672, 336, -11],[336, 56, 1],[-5, -2, -1, 1, 2, -1, -4, -11; -17, -6, -2, 3, 5, -12, -17, -42; -224, -63, 0, 30, 28, -336, -294, -648],128,85]
%
% END OF LATTICE L129.85
%
%
% LATTICE L129.86
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[657888, 354312, -4368; 354312, 190680, -2352; -4368, -2352, 29],[168, 168, 1],[-7, -3, 0, 1, 1, -2, -15, -6; -2, -1, 1, 1, 1, 1, -1, -1; -1218, -532, 84, 232, 231, -224, -2352, -988],128,86]
%
% END OF LATTICE L129.86
%
%
% LATTICE L129.87
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-54264, 0, 840; 0, 168, 0; 840, 0, -13],[168, 168, 1],[-7, -3, 0, 1, 2, -2, -15, -6; -2, 0, 1, 0, -1, -3, -10, -3; -462, -196, 0, 64, 126, -140, -1008, -400],128,87]
%
% END OF LATTICE L129.87
%
%
% LATTICE L129.88
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-287112, -124824, -60480; -124824, -54096, -26208; -60480, -26208, -12697],[168, 168, 1],[-5, -3, -1, 1, 3, 1, -5, -3; 439, 224, 43, -74, -190, 25, 704, 323; -882, -448, -84, 148, 378, -56, -1428, -652],128,88]
%
% END OF LATTICE L129.88
%
%
% LATTICE L129.89
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[195216, 219744, -2688; 219744, 247128, -3024; -2688, -3024, 37],[336, 168, 1],[0, -1, -7, -1, -1, 1, 1, 1; 1, -1, -4, 0, 3, 6, 4, 4; 84, -154, -840, -74, 168, 560, 399, 400],128,89]
%
% END OF LATTICE L129.89
%
%
% LATTICE L129.90
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[110544, 672, -336; 672, -168, 0; -336, 0, 1],[336, 168, 1],[-2, 0, 1, 0, -1, -3, -5, -3; -1, 1, 4, 0, -3, -6, -8, -4; -588, 14, 336, -1, -336, -952, -1554, -920],128,90]
%
% END OF LATTICE L129.90
%
%
% LATTICE L129.91
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1834896, 1334592, -11088; 1334592, 970536, -8064; -11088, -8064, 67],[336, 168, 1],[5, 5, 4, 1, -2, -1, 1, 1; 5, 2, -3, -4, -7, -2, 0, 1; 1428, 1064, 294, -320, -1176, -406, 168, 286],128,91]
%
% END OF LATTICE L129.91
%
%
% LATTICE L129.92
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[336, 0, 0; 0, -239064, 2016; 0, 2016, -17],[336, 168, 1],[-1, -3, -5, -3, -2, 0, 1, 0; 5, 2, -3, -4, -7, -1, 0, 1; 588, 224, -378, -488, -840, -119, 0, 118],128,92]
%
% END OF LATTICE L129.92
%

\medskip%
%------------------------------WEYL-GROUP-W130--------------------------------
%
\leavevmode\llap{}%
$W_{130}$%
\qquad\llap{64} lattices, $\chi=18$%
\hfill%
$2222222$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L130.1
%
\leavevmode%
${L_{130.1}}$%
{} : {$1\above{1pt}{1pt}{2}{6}8\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{-}{}9\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{2}{}7\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{3,2}%
\EasyButWeakLineBreak%
{${6}\above{1pt}{1pt}{b}{2}{14}\above{1pt}{1pt}{l}{2}{24}\above{1pt}{1pt}{}{2}{63}\above{1pt}{1pt}{r}{2}{8}\above{1pt}{1pt}{s}{2}{36}\above{1pt}{1pt}{*}{2}{56}\above{1pt}{1pt}{b}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-94248\\-16128\\1008
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-16128\\-2757\\171
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1008\\171\\-10
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3\\20\\39
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2\\14\\35
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5\\-32\\-48
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
16\\-105\\-189
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\-20\\-40
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\6\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-17\\112\\196
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-94248, -16128, 1008; -16128, -2757, 171; 1008, 171, -10],[504, 3, 1],[-3, -2, 5, 16, 3, -1, -17; 20, 14, -32, -105, -20, 6, 112; 39, 35, -48, -189, -40, 0, 196],129,1]
%
% END OF LATTICE L130.1
%
\hbox{}\par\smallskip%
%
% LATTICE L130.2
%
\leavevmode%
${L_{130.2}}$%
{} : {$1\above{1pt}{1pt}{-2}{6}8\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{-}{}9\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{2}{}7\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{32\rightarrow N'_{18},3m,3,m}%
\EasyButWeakLineBreak%
{${6}\above{1pt}{1pt}{s}{2}{14}\above{1pt}{1pt}{b}{2}{24}\above{1pt}{1pt}{*}{2}{252}\above{1pt}{1pt}{s}{2}{8}\above{1pt}{1pt}{l}{2}{9}\above{1pt}{1pt}{}{2}{56}\above{1pt}{1pt}{r}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
915768\\504\\-7560
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
504\\-3\\-3
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-7560\\-3\\62
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\40\\123
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\126\\371
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\128\\372
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\42\\126
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-44\\-124
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-51\\-126
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\0\\112
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[915768, 504, -7560; 504, -3, -3; -7560, -3, 62],[504, 3, 1],[1, 3, 3, 1, -1, -1, 1; 40, 126, 128, 42, -44, -51, 0; 123, 371, 372, 126, -124, -126, 112],129,2]
%
% END OF LATTICE L130.2
%
%
% LATTICE L130.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-462, -210, 126; -210, -95, 63; 126, 63, 38],[42, 1, 1],[20, 40, -37, -123, -57, -66, -299; -42, -84, 78, 259, 120, 139, 630; 3, 7, -6, -21, -10, -12, -56],129,3]
%
% END OF LATTICE L130.3
%
%
% LATTICE L130.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[23772, -672, 0; -672, 19, 0; 0, 0, -1],[84, 1, 1],[-1, -1, 1, 3, 1, 0, -5; -36, -35, 36, 105, 34, -3, -196; -3, 0, 0, -7, -6, -13, -84],129,4]
%
% END OF LATTICE L130.4
%
%
% LATTICE L130.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-8904, -168, 336; -168, 5, -3; 336, -3, -2],[168, 1, 1],[-1, -1, 1, 3, 1, 0, -5; -72, -70, 72, 210, 68, -3, -392; -63, -63, 60, 182, 60, -2, -336],129,5]
%
% END OF LATTICE L130.5
%
%
% LATTICE L130.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[73752, 1512, 0; 1512, 31, 0; 0, 0, -1],[168, 1, 1],[2, 3, 1, -1, -1, 1, 15; -99, -147, -48, 49, 48, -52, -756; -9, -7, 0, 0, -4, -18, -140],129,6]
%
% END OF LATTICE L130.6
%
%
% LATTICE L130.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-626094, -28728, 10836; -28728, -1317, 498; 10836, 498, -187],[126, 3, 1],[9, 23, 11, 5, -3, -1, 19; -127, -329, -160, -84, 42, 15, -266; 183, 455, 210, 63, -62, -18, 392],129,7]
%
% END OF LATTICE L130.7
%
%
% LATTICE L130.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-47124, -16128, 504; -16128, -5514, 171; 504, 171, -5],[252, 3, 1],[-3, -2, 5, 32, 3, -1, -17; 10, 7, -16, -105, -10, 3, 56; 39, 35, -48, -378, -40, 0, 196],129,8]
%
% END OF LATTICE L130.8
%
%
% LATTICE L130.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[210, -168, 126; -168, 26, -84; 126, -84, 73],[42, 2, 1],[29, 67, 10, -20, -9, -11, 5; -9, -21, -3, 7, 3, 4, 0; -60, -140, -21, 42, 19, 24, -7],129,9]
%
% END OF LATTICE L130.9
%
%
% LATTICE L130.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1050, -252, -336; -252, 39, 84; -336, 84, 107],[42, 3, 1],[-8, -52, -5, 15, 13, 6, -25; -3, -21, -2, 7, 6, 4, 0; -23, -147, -14, 42, 36, 15, -84],129,10]
%
% END OF LATTICE L130.10
%
%
% LATTICE L130.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[4788, -168, -84; -168, 6, 3; -84, 3, 1],[84, 3, 1],[0, -4, -3, -9, -1, 0, 1; 0, -91, -68, -203, -22, 1, 28; -1, -63, -44, -126, -12, 0, 0],129,11]
%
% END OF LATTICE L130.11
%
%
% LATTICE L130.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[12810, -1008, 5334; -1008, 78, -420; 5334, -420, 2221],[42, 6, 1],[-15, -19, 3, 18, -4, -45, -176; -11, -21, 1, 7, -3, -32, -126; 34, 42, -7, -42, 9, 102, 399],129,12]
%
% END OF LATTICE L130.12
%
%
% LATTICE L130.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[14154, 0, 2184; 0, -7, 0; 2184, 0, 337],[42, 7, 1],[16, 6, 13, -2, -13, -11, -3; -9, -1, 0, 0, -2, -9, -10; -105, -39, -84, 13, 84, 70, 18],129,13]
%
% END OF LATTICE L130.13
%
%
% LATTICE L130.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[4620, 2688, 1176; 2688, 1132, 672; 1176, 672, 299],[84, 4, 1],[-103, 60, 25, -187, -113, -493, -786; -12, 7, 3, -21, -13, -57, -91; 432, -252, -105, 784, 474, 2068, 3297],129,14]
%
% END OF LATTICE L130.14
%
%
% LATTICE L130.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[63630, -2898, 1386; -2898, 132, -63; 1386, -63, 31],[126, 3, 1],[1, 1, 1, 3, 5, 3, 55; 19, 21, 22, 63, 102, 60, 1092; -6, 0, 0, -7, -18, -13, -252],129,15]
%
% END OF LATTICE L130.15
%
%
% LATTICE L130.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[51912, 25536, -336; 25536, 12561, -165; -336, -165, 2],[168, 3, 1],[0, 87, 65, 97, 21, -1, -27; 0, -182, -136, -203, -44, 2, 56; -1, -399, -296, -441, -96, 0, 84],129,16]
%
% END OF LATTICE L130.16
%
%
% LATTICE L130.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[168, 0, 0; 0, 3, 0; 0, 0, -1],[168, 3, 1],[0, -4, -3, -9, -1, 0, 1; -1, -21, -12, -28, 0, 1, 0; -1, -63, -44, -126, -12, 0, 0],129,17]
%
% END OF LATTICE L130.17
%
%
% LATTICE L130.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[508998, 0, 245238; 0, -14, 0; 245238, 0, 118157],[42, 14, 1],[1801, 159, -172, -53, 172, 1774, 993; 9, 1, 0, 0, 1, 9, 5; -3738, -330, 357, 110, -357, -3682, -2061],129,18]
%
% END OF LATTICE L130.18
%
%
% LATTICE L130.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[84, 0, 0; 0, -7, -7; 0, -7, -6],[84, 7, 1],[-1, 0, 1, 0, -1, -3, -3; -3, -1, 0, 2, 8, 8, 4; 0, 1, 0, -3, -14, -21, -16],129,19]
%
% END OF LATTICE L130.19
%
%
% LATTICE L130.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-57960, -12978, -28728; -12978, -2454, -6426; -28728, -6426, -14239],[126, 6, 1],[-127, -1427, 31, 710, 616, 521, 3692; -4, -42, 1, 21, 18, 15, 105; 258, 2898, -63, -1442, -1251, -1058, -7497],129,20]
%
% END OF LATTICE L130.20
%
%
% LATTICE L130.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[12536118, 449820, 6157872; 449820, 16158, 220956; 6157872, 220956, 3024811],[126, 6, 1],[1617, 8689, 3566, 16483, 30, -62, 1525; -53, -287, -118, -546, -1, 3, -49; -3288, -17668, -7251, -33516, -61, 126, -3101],129,21]
%
% END OF LATTICE L130.21
%
%
% LATTICE L130.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[30492, -1512, 0; -1512, 75, 0; 0, 0, -1],[252, 3, 1],[1, 1, -1, -1, 1, 2, 47; 20, 21, -20, -21, 18, 39, 924; -3, 0, 0, -7, -18, -13, -252],129,22]
%
% END OF LATTICE L130.22
%
%
% LATTICE L130.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[423990, -42, 148260; -42, -21, 0; 148260, 0, 51833],[42, 21, 1],[487, 129, -93, -43, 279, 1439, 1611; -971, -257, 186, 86, -556, -2869, -3212; -1393, -369, 266, 123, -798, -4116, -4608],129,23]
%
% END OF LATTICE L130.23
%
%
% LATTICE L130.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3192, 84, -756; 84, 324, 24; -756, 24, -179],[84, 12, 1],[-19, -340, -46, -401, 7, 37, -5; -1, -21, -3, -28, 0, 2, 0; 80, 1428, 193, 1680, -30, -156, 21],129,24]
%
% END OF LATTICE L130.24
%
%
% LATTICE L130.25
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1848, 168, 168; 168, -14, -7; 168, -7, 39],[168, 7, 1],[-1, -1, 1, 3, 13, 9, 13; -15, -13, 12, 38, 164, 112, 160; 0, 2, 0, -6, -28, -21, -32],129,25]
%
% END OF LATTICE L130.25
%
%
% LATTICE L130.26
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[168, 0, 0; 0, -14, -7; 0, -7, -3],[168, 7, 1],[-1, 0, 1, 0, -1, -3, -3; -3, -1, 0, 1, 8, 8, 4; 0, 2, 0, -3, -28, -42, -32],129,26]
%
% END OF LATTICE L130.26
%
%
% LATTICE L130.27
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-27384, 1008, 168; 1008, 72, -8; 168, -8, -1],[168, 8, 1],[1, -3, -1, 1, 1, 4, 6; 3, -7, -3, 0, 2, 9, 14; 144, -448, -150, 140, 146, 584, 875],129,27]
%
% END OF LATTICE L130.27
%
%
% LATTICE L130.28
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[140952, -21840, 672; -21840, 3384, -104; 672, -104, 3],[168, 8, 1],[-5, -5, 1, 11, 2, 2, -1; -33, -35, 6, 70, 13, 13, -7; -24, -112, -21, -56, 2, 4, -14],129,28]
%
% END OF LATTICE L130.28
%
%
% LATTICE L130.29
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[986328, 235368, 5544; 235368, 56166, 1323; 5544, 1323, 31],[504, 3, 1],[6, -5, -21, -15, -17, 3, 143; -25, 21, 88, 63, 72, -12, -588; -6, 0, 0, -7, -36, -26, -504],129,29]
%
% END OF LATTICE L130.29
%
%
% LATTICE L130.30
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-447048, 3024, 1008; 3024, -3, -9; 1008, -9, -2],[504, 3, 1],[1, 1, -1, -1, 1, 1, 47; 40, 42, -40, -42, 36, 39, 1848; 321, 315, -324, -322, 324, 322, 15120],129,30]
%
% END OF LATTICE L130.30
%
%
% LATTICE L130.31
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[252, -168, 84; -168, 126, -63; 84, -63, 31],[84, 21, 1],[0, -1, -5, -2, -1, 1, 1; -3, -8, -32, -11, -2, 1, -4; -7, -15, -56, -18, 0, 0, -12],129,31]
%
% END OF LATTICE L130.31
%
%
% LATTICE L130.32
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[4353930, -10580892, -5142186; -10580892, 25713366, 12496386; -5142186, 12496386, 6073093],[42, 42, 1],[-3, -1, 0, 0, -1, -9, -5; 1829, 1997, 711, -659, -2113, -3392, -368; -3766, -4110, -1463, 1356, 4347, 6972, 753],129,32]
%
% END OF LATTICE L130.32
%
%
% LATTICE L130.33
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[84, -84, -84; -84, 168, 140; -84, 140, 121],[84, 28, 1],[1, 1, 5, 4, 4, 10, 2; 0, -3, -15, -11, -9, -17, -3; 0, 4, 21, 16, 14, 28, 5],129,33]
%
% END OF LATTICE L130.33
%
%
% LATTICE L130.34
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[15246, -5166, 126; -5166, 1743, -42; 126, -42, 1],[126, 21, 1],[1, 1, 1, 0, -1, 0, 1; 1, 3, 4, 0, -6, -3, -6; -63, 9, 42, -1, -126, -112, -324],129,34]
%
% END OF LATTICE L130.34
%
%
% LATTICE L130.35
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[23310, -7812, -504; -7812, 2625, 168; -504, 168, 11],[126, 21, 1],[-5, -5, -31, -11, -1, 1, -1; -11, -11, -68, -24, -2, 3, -2; -63, -61, -378, -135, -14, 0, -16],129,35]
%
% END OF LATTICE L130.35
%
%
% LATTICE L130.36
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[9801288, -92484, -2479932; -92484, 876, 23400; -2479932, 23400, 627475],[252, 12, 1],[-61, -242, -106, -1217, -31, -311, -201; -29, -119, -52, -588, -14, -138, -91; -240, -952, -417, -4788, -122, -1224, -791],129,36]
%
% END OF LATTICE L130.36
%
%
% LATTICE L130.37
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[9324, 6048, -2268; 6048, 1452, -1512; -2268, -1512, 551],[252, 12, 1],[67, -320, -16, 327, 425, 525, 2351; -4, 21, 1, -21, -27, -33, -147; 264, -1260, -63, 1288, 1674, 2068, 9261],129,37]
%
% END OF LATTICE L130.37
%
%
% LATTICE L130.38
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[504, -168, 0; -168, 63, 0; 0, 0, -1],[168, 21, 1],[0, -1, -5, -1, -1, 1, 1; 1, -1, -8, -2, -4, 2, 4; -7, -15, -56, -9, 0, 0, -12],129,38]
%
% END OF LATTICE L130.38
%
%
% LATTICE L130.39
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[41496, 0, 840; 0, 21, 0; 840, 0, 17],[168, 21, 1],[1, 5, 23, 9, 5, 0, 1; -1, -3, -12, -4, 0, 1, 0; -49, -249, -1148, -450, -252, 0, -48],129,39]
%
% END OF LATTICE L130.39
%
%
% LATTICE L130.40
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-577080, -15960, 5208; -15960, -432, 144; 5208, 144, -47],[168, 24, 1],[2, 20, 1, 5, -1, -1, 4; 1, -7, -1, -14, -1, 1, 7; 224, 2184, 107, 504, -114, -108, 462],129,40]
%
% END OF LATTICE L130.40
%
%
% LATTICE L130.41
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-207816, -26376, 1512; -26376, -3312, 192; 1512, 192, -11],[168, 24, 1],[2, 20, 2, 5, -1, -1, 2; -1, -21, -3, -14, 0, 1, 0; 256, 2352, 218, 420, -138, -120, 273],129,41]
%
% END OF LATTICE L130.41
%
%
% LATTICE L130.42
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1015812, 334404, -5040; 334404, 110082, -1659; -5040, -1659, 25],[252, 21, 1],[-1, 0, 3, 2, 1, -1, -1; 4, -1, -28, -15, -6, 3, 4; 63, -67, -1260, -594, -196, 0, 64],129,42]
%
% END OF LATTICE L130.42
%
%
% LATTICE L130.43
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[309834, -10332, 152334; -10332, 210, -5082; 152334, -5082, 74897],[126, 42, 1],[-1075, -443, 31, 63, 31, -696, -1360; -37, -15, 1, 2, 0, -25, -48; 2184, 900, -63, -128, -63, 1414, 2763],129,43]
%
% END OF LATTICE L130.43
%
%
% LATTICE L130.44
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-365022, 18648, -179172; 18648, -798, 9156; -179172, 9156, -87947],[126, 42, 1],[-537, -63, 196, 407, 148, 62, -89; -19, -3, 4, 12, 5, 3, -3; 1092, 128, -399, -828, -301, -126, 181],129,44]
%
% END OF LATTICE L130.44
%
%
% LATTICE L130.45
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1260, 252, 252; 252, -42, -63; 252, -63, -31],[252, 21, 1],[-10, -4, 1, 1, -1, -14, -53; -31, -12, 4, 3, -6, -45, -168; -21, -9, 0, 2, 0, -28, -108],129,45]
%
% END OF LATTICE L130.45
%
%
% LATTICE L130.46
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-756, 2100, 504; 2100, -2520, -588; 504, -588, -137],[84, 84, 1],[3, 5, 4, 4, -2, -2, 1; 48, 85, 70, 73, -31, -41, 14; -196, -348, -287, -300, 126, 168, -57],129,46]
%
% END OF LATTICE L130.46
%
%
% LATTICE L130.47
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[336, -1176, 336; -1176, 280, -56; 336, -56, 9],[168, 56, 1],[1, -1, -1, 1, 3, 10, 2; 0, -14, -12, 13, 37, 115, 22; 0, -48, -42, 44, 126, 392, 75],129,47]
%
% END OF LATTICE L130.47
%
%
% LATTICE L130.48
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-7728, -3192, 336; -3192, -728, 56; 336, 56, -3],[168, 56, 1],[-5, -1, 1, 2, 3, 5, 1; 48, 10, -9, -19, -29, -49, -10; 336, 72, -63, -136, -210, -364, -78],129,48]
%
% END OF LATTICE L130.48
%
%
% LATTICE L130.49
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[126504, 30744, -2520; 30744, 7413, -609; -2520, -609, 50],[504, 21, 1],[1, 0, -3, -1, -1, 1, 1; 8, -2, -56, -15, -12, 6, 8; 147, -25, -840, -234, -196, 126, 148],129,49]
%
% END OF LATTICE L130.49
%
%
% LATTICE L130.50
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-85176, 4536, 0; 4536, -21, -21; 0, -21, 2],[504, 21, 1],[-2, 0, 3, 1, -1, -7, -5; -38, 0, 56, 18, -20, -135, -96; -399, -1, 588, 198, -196, -1386, -992],129,50]
%
% END OF LATTICE L130.50
%
%
% LATTICE L130.51
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[239400, 80136, -504; 80136, 26817, -168; -504, -168, 1],[504, 21, 1],[2, -1, -5, 0, 11, 9, 25; -7, 3, 16, 0, -36, -30, -84; -147, 9, 168, -1, -504, -476, -1404],129,51]
%
% END OF LATTICE L130.51
%
%
% LATTICE L130.52
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-4447800, 16128, 16632; 16128, -21, -63; 16632, -63, -62],[504, 21, 1],[10, 4, -1, -1, 1, 7, 53; 178, 72, -16, -18, 12, 123, 936; 2499, 999, -252, -250, 252, 1750, 13248],129,52]
%
% END OF LATTICE L130.52
%
%
% LATTICE L130.53
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1008, -504, 0; -504, -3336, 216; 0, 216, -13],[504, 24, 1],[-5, -1, 1, 4, -1, -5, -59; -10, 0, 2, 7, -3, -11, -126; -168, 0, 33, 112, -54, -188, -2142],129,53]
%
% END OF LATTICE L130.53
%
%
% LATTICE L130.54
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1008, -504, 0; -504, 264, 0; 0, 0, -1],[504, 24, 1],[-1, 1, 1, 3, 1, 0, -2; -2, 0, 2, 7, 3, 1, 0; 0, 0, -6, -28, -18, -16, -63],129,54]
%
% END OF LATTICE L130.54
%
%
% LATTICE L130.55
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-9845640, -425880, 38304; -425880, -18384, 1656; 38304, 1656, -149],[504, 24, 1],[6, 16, 2, 5, -1, -1, 6; 47, 119, 14, 21, -8, -6, 49; 2064, 5432, 669, 1512, -346, -324, 2086],129,55]
%
% END OF LATTICE L130.55
%
%
% LATTICE L130.56
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2520, -5544, 504; -5544, -3984, 408; 504, 408, -41],[504, 24, 1],[6, 16, 4, 5, -1, -1, 3; 41, 105, 25, 21, -7, -6, 21; 480, 1232, 294, 252, -82, -72, 245],129,56]
%
% END OF LATTICE L130.56
%
%
% LATTICE L130.57
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[12189492, 175392, 2960244; 175392, 2100, 42924; 2960244, 42924, 718645],[252, 84, 1],[-1067, -816, -2150, -2323, 345, 3137, 47; 3268, 2499, 6584, 7113, -1057, -9609, -144; 4200, 3212, 8463, 9144, -1358, -12348, -185],129,57]
%
% END OF LATTICE L130.57
%
%
% LATTICE L130.58
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[7812, 8064, -4032; 8064, 8148, -4032; -4032, -4032, 1985],[252, 84, 1],[44, 37, 16, -1, -31, 17, 32; -127, -108, -47, 3, 93, -45, -90; -168, -144, -63, 4, 126, -56, -117],129,58]
%
% END OF LATTICE L130.58
%
%
% LATTICE L130.59
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-164304, -164472, 2184; -164472, -164472, 2184; 2184, 2184, -29],[168, 168, 1],[-1, -3, -3, -2, 0, 1, 0; 4, -2, -6, -7, -5, -1, 1; 224, -384, -686, -684, -378, 0, 75],129,59]
%
% END OF LATTICE L130.59
%
%
% LATTICE L130.60
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3024, 2184, 840; 2184, 504, 168; 840, 168, 55],[168, 168, 1],[1, -1, -1, -2, -1, 1, 1; -42, 44, 44, 89, 47, -31, -38; 112, -120, -119, -240, -126, 84, 102],129,60]
%
% END OF LATTICE L130.60
%
%
% LATTICE L130.61
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-17136, -34776, 15120; -34776, -35448, 15456; 15120, 15456, -6739],[504, 168, 1],[-5, -1, 1, 1, 2, -2, -5; -874, -156, 173, 163, 273, -425, -960; -2016, -360, 399, 376, 630, -980, -2214],129,61]
%
% END OF LATTICE L130.61
%
%
% LATTICE L130.62
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[31248, 11592, -3024; 11592, 1848, -504; -3024, -504, 137],[504, 168, 1],[-1, 1, 1, 0, -2, -3, -2; -86, 72, 74, -1, -159, -241, -162; -336, 288, 294, -4, -630, -952, -639],129,62]
%
% END OF LATTICE L130.62
%
%
% LATTICE L130.63
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[504, 0, 0; 0, -540456, 5040; 0, 5040, -47],[504, 168, 1],[-1, -1, -3, -2, 0, 1, 0; 11, 1, -5, -9, -3, 0, 1; 1176, 104, -546, -972, -322, 0, 107],129,63]
%
% END OF LATTICE L130.63
%
%
% LATTICE L130.64
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2223144, 1318464, -9072; 1318464, 781032, -5376; -9072, -5376, 37],[504, 168, 1],[5, 1, 0, -2, -1, 1, 1; 17, 3, -1, -9, -4, 0, 3; 3696, 680, -147, -1800, -826, 252, 682],129,64]
%
% END OF LATTICE L130.64
%

\medskip%
%------------------------------WEYL-GROUP-W131--------------------------------
%
\leavevmode\llap{}%
$W_{131}$%
\qquad\llap{64} lattices, $\chi=36$%
\hfill%
$2222222222\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L131.1
%
\leavevmode%
${L_{131.1}}$%
{} : {$1\above{1pt}{1pt}{2}{6}8\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{1}{}3\above{1pt}{1pt}{-}{}9\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{-2}{}11\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{23\rightarrow N'_{20},3m,3,2,m}%
\EasyButWeakLineBreak%
{${24}\above{1pt}{1pt}{b}{2}{198}\above{1pt}{1pt}{s}{2}{6}\above{1pt}{1pt}{b}{2}{792}\above{1pt}{1pt}{*}{2}{4}\above{1pt}{1pt}{*}{2}{24}\above{1pt}{1pt}{b}{2}{22}\above{1pt}{1pt}{s}{2}{6}\above{1pt}{1pt}{b}{2}{88}\above{1pt}{1pt}{*}{2}{36}\above{1pt}{1pt}{*}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-84744\\0\\792
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\15\\-9
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
792\\-9\\-2
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-64\\-108
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\66\\99
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\64\\105
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
79\\5016\\8316
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\190\\316
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
9\\568\\948
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7\\440\\737
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\62\\105
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\176\\308
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-66\\-108
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-84744, 0, 792; 0, 15, -9; 792, -9, -2],[792, 3, 1],[-1, 1, 1, 79, 3, 9, 7, 1, 3, -1; -64, 66, 64, 5016, 190, 568, 440, 62, 176, -66; -108, 99, 105, 8316, 316, 948, 737, 105, 308, -108],130,1]
%
% END OF LATTICE L131.1
%
\hbox{}\par\smallskip%
%
% LATTICE L131.2
%
\leavevmode%
${L_{131.2}}$%
{} : {$1\above{1pt}{1pt}{-2}{2}16\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{1}{}9\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}11\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{3m,3,m}%
\EasyButWeakLineBreak%
{${48}\above{1pt}{1pt}{}{2}{99}\above{1pt}{1pt}{r}{2}{12}\above{1pt}{1pt}{*}{2}{1584}\above{1pt}{1pt}{b}{2}{2}\above{1pt}{1pt}{b}{2}{48}\above{1pt}{1pt}{*}{2}{44}\above{1pt}{1pt}{l}{2}{3}\above{1pt}{1pt}{}{2}{176}\above{1pt}{1pt}{r}{2}{18}\above{1pt}{1pt}{l}{2}$}%
\nopagebreak\par%
shares genus with 3-dual\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2051280\\-1018512\\1584
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1018512\\-505662\\783
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1584\\783\\-1
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
31\\-64\\-1008
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-16\\33\\495
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-31\\64\\1002
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2429\\5016\\79200
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-46\\95\\1504
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-275\\568\\9024
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-213\\440\\7018
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-15\\31\\501
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-85\\176\\2992
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
16\\-33\\-504
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-2051280, -1018512, 1584; -1018512, -505662, 783; 1584, 783, -1],[1584, 3, 1],[31, -16, -31, -2429, -46, -275, -213, -15, -85, 16; -64, 33, 64, 5016, 95, 568, 440, 31, 176, -33; -1008, 495, 1002, 79200, 1504, 9024, 7018, 501, 2992, -504],130,2]
%
% END OF LATTICE L131.2
%
%
% LATTICE L131.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-1254, 198, -66; 198, -31, 11; -66, 11, -2],[66, 1, 1],[1, -4, -2, 7, 2, 11, 26, 8, 37, 2; 6, -22, -12, 22, 9, 54, 132, 42, 198, 11; 0, 11, -3, -176, -25, -96, -187, -45, -176, -7],130,3]
%
% END OF LATTICE L131.3
%
%
% LATTICE L131.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-1716, 132, 396; 132, -10, -33; 396, -33, -49],[132, 1, 1],[1, -15, -13, -261, -27, -73, -51, -5, -3, 3; 12, -165, -144, -2904, -301, -816, -572, -57, -44, 33; 0, -11, -9, -176, -18, -48, -33, -3, 0, 2],130,4]
%
% END OF LATTICE L131.4
%
%
% LATTICE L131.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-503976, -125400, 2376; -125400, -31202, 591; 2376, 591, -11],[264, 1, 1],[29, -3, -14, -237, -11, -41, -8, 11, 193, 9; -120, 11, 57, 968, 45, 168, 33, -45, -792, -37; -192, -66, 36, 792, 41, 168, 44, -42, -880, -45],130,5]
%
% END OF LATTICE L131.5
%
%
% LATTICE L131.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-4080648, 5544, 20856; 5544, -5, -33; 20856, -33, -98],[264, 1, 1],[73, 51, 5, 3, -3, -1, 15, 13, 261, 27; 17640, 12320, 1206, 704, -726, -240, 3630, 3144, 63096, 6526; 9588, 6699, 657, 396, -394, -132, 1969, 1707, 34276, 3546],130,6]
%
% END OF LATTICE L131.6
%
%
% LATTICE L131.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-475728, -155760, 6864; -155760, -50998, 2247; 6864, 2247, -37],[528, 1, 1],[55, 1145, 436, 16073, 799, 4085, 1325, 163, -893, -109; -168, -3498, -1332, -49104, -2441, -12480, -4048, -498, 2728, 333; 0, -22, -9, -352, -18, -96, -33, -6, 0, 2],130,7]
%
% END OF LATTICE L131.7
%
%
% LATTICE L131.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-173250, -14256, 1386; -14256, -1173, 114; 1386, 114, -11],[198, 3, 1],[-3, -25, -3, -47, -1, -1, 1, 1, 1, -1; 34, 297, 37, 594, 13, 14, -11, -13, -22, 9; -30, -99, 3, 198, 8, 18, 11, -9, -110, -36],130,8]
%
% END OF LATTICE L131.8
%
%
% LATTICE L131.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-42372, 0, 396; 0, 30, -9; 396, -9, -1],[396, 3, 1],[-1, 1, 1, 79, 3, 9, 7, 1, 3, -1; -32, 33, 32, 2508, 95, 284, 220, 31, 88, -33; -108, 99, 105, 8316, 316, 948, 737, 105, 308, -108],130,9]
%
% END OF LATTICE L131.9
%
%
% LATTICE L131.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-493416, -47520, 2376; -47520, -4575, 228; 2376, 228, -11],[792, 3, 1],[3, -8, -3, -137, -2, -7, -1, 2, 31, 4; -32, 99, 35, 1584, 23, 80, 11, -23, -352, -45; -24, 297, 75, 3168, 44, 144, 11, -45, -616, -72],130,10]
%
% END OF LATTICE L131.10
%
%
% LATTICE L131.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2394546, 82500, -1200936; 82500, -2842, 41376; -1200936, 41376, -602305],[66, 2, 1],[103, -3301, -3409, -19861, -4364, -6421, -19865, -2909, -3305, 152; -111, 3465, 3591, 20955, 4607, 6783, 20999, 3081, 3509, -159; -213, 6820, 7044, 41041, 9018, 13269, 41052, 6012, 6831, -314],130,11]
%
% END OF LATTICE L131.11
%
%
% LATTICE L131.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3837570, 127908, -1282974; 127908, -4263, 42762; -1282974, 42762, -428923],[66, 3, 1],[43, -2102, -722, -25213, -2769, -2715, -12594, -614, -4179, 97; -74, 3465, 1197, 41910, 4607, 4522, 20999, 1027, 7018, -159; -136, 6633, 2279, 79596, 8742, 8572, 39765, 1939, 13200, -306],130,12]
%
% END OF LATTICE L131.12
%
%
% LATTICE L131.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-63228, 1056, 1980; 1056, -15, -33; 1980, -33, -62],[132, 3, 1],[17, 40, 2, 25, -1, -1, 4, 2, 151, 17; -16, -33, -1, 0, 2, 0, -11, -3, -176, -18; 548, 1287, 64, 792, -33, -32, 132, 65, 4884, 549],130,13]
%
% END OF LATTICE L131.13
%
%
% LATTICE L131.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[26290770, -767844, 12901548; -767844, 22506, -376800; 12901548, -376800, 6331117],[66, 6, 1],[-1541, 158245, 54335, 950977, 209070, 102643, 953877, 46767, 161145, -6866; -21, 2145, 737, 12903, 2837, 1393, 12947, 635, 2189, -93; 3139, -322344, -110680, -1937133, -425874, -209083, -1943040, -95264, -328251, 13986],130,14]
%
% END OF LATTICE L131.14
%
%
% LATTICE L131.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[220440, 22044, 55440; 22044, 2204, 5544; 55440, 5544, 13943],[132, 4, 1],[8, 52, 19, 37, 5, -5, -41, -16, -26, -1; 3, 33, 21, 99, 40, 27, 77, 9, 11, 0; -33, -220, -84, -187, -36, 9, 132, 60, 99, 4],130,15]
%
% END OF LATTICE L131.15
%
%
% LATTICE L131.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-22517682, 52602, 4040190; 52602, -121, -9438; 4040190, -9438, -724903],[66, 11, 1],[-521, 739, 8425, 8939, 10809, 31829, 4479, 7229, 1497, -373; 18, -17, -207, -226, -276, -822, -117, -195, -42, 8; -2904, 4119, 46959, 49824, 60247, 177408, 24965, 40293, 8344, -2079],130,16]
%
% END OF LATTICE L131.16
%
%
% LATTICE L131.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-370392, 3432, 3432; 3432, -30, -33; 3432, -33, -31],[264, 3, 1],[-1, 4, 2, 151, 17, 17, 40, 2, 25, -1; -44, 165, 85, 6468, 730, 732, 1727, 87, 1100, -42; -64, 264, 130, 9768, 1098, 1096, 2574, 128, 1584, -66],130,17]
%
% END OF LATTICE L131.17
%
%
% LATTICE L131.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1848, 528, 264; 528, -150, -69; 264, -69, 11],[264, 3, 1],[13, 74, 11, 401, 15, 15, 3, -4, -93, -1; 48, 275, 41, 1496, 56, 56, 11, -15, -352, -4; -16, -66, -8, -264, -9, -8, 0, 2, 0, -3],130,18]
%
% END OF LATTICE L131.18
%
%
% LATTICE L131.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[463122, -10692, 229482; -10692, 462, -5304; 229482, -5304, 113711],[198, 6, 1],[1593, 19499, 1737, 12395, 482, 337, 577, 193, 2945, 2414; -89, -1089, -97, -693, -27, -19, -33, -11, -165, -135; -3219, -39402, -3510, -25047, -974, -681, -1166, -390, -5951, -4878],130,19]
%
% END OF LATTICE L131.19
%
%
% LATTICE L131.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[132, 0, 0; 0, -3322, 341; 0, 341, -35],[132, 11, 1],[-13, -1, -2, -1, 0, 1, 0, -1, -3, -4; 84, 4, -3, -8, -9, 0, 3, 24, 36, 37; 792, 37, -33, -80, -88, 0, 29, 231, 344, 352],130,20]
%
% END OF LATTICE L131.20
%
%
% LATTICE L131.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[52207386, 122892, 24869988; 122892, 418, 58542; 24869988, 58542, 11847295],[66, 22, 1],[8033, -24855, -281831, -149523, -361637, -532709, -150037, -242845, -25369, 11853; 6, -17, -195, -104, -252, -372, -105, -171, -18, 8; -16863, 52176, 591624, 313881, 759154, 1118271, 314960, 509784, 53255, -24882],130,21]
%
% END OF LATTICE L131.21
%
%
% LATTICE L131.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-50160, 1056, 1584; 1056, -15, -33; 1584, -33, -50],[528, 3, 1],[-1, 4, 3, 203, 11, 21, 47, 1, 17, -1; 0, -11, -6, -352, -18, -32, -66, -1, 0, 2; -32, 132, 98, 6600, 357, 680, 1518, 32, 528, -33],130,22]
%
% END OF LATTICE L131.22
%
%
% LATTICE L131.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1408836, 3828, 340032; 3828, 24, 924; 340032, 924, 82069],[132, 12, 1],[355, 3313, 167, 661, 0, 7, 669, 195, 3321, 1448; 9, 88, 5, 22, 1, 0, 11, 4, 77, 35; -1471, -13728, -692, -2739, 0, -29, -2772, -808, -13761, -6000],130,23]
%
% END OF LATTICE L131.23
%
%
% LATTICE L131.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-38544, -16632, 4488; -16632, -6872, 1592; 4488, 1592, -133],[264, 8, 1],[-61, -1011, -463, -690, -202, -68, 65, 205, 217, 30; 186, 3080, 1410, 2101, 615, 207, -198, -624, -660, -91; 165, 2728, 1248, 1859, 544, 183, -176, -552, -583, -80],130,24]
%
% END OF LATTICE L131.24
%
%
% LATTICE L131.25
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[31152, 2904, 1056; 2904, 248, 88; 1056, 88, 31],[264, 8, 1],[-1, -1, 1, 5, 1, 1, 1, -1, -5, -1; 66, 110, -36, -220, -47, -48, -44, 54, 286, 59; -150, -264, 72, 462, 100, 102, 88, -120, -638, -132],130,25]
%
% END OF LATTICE L131.25
%
%
% LATTICE L131.26
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[17700474, -87252, -5371806; -87252, 627, 26598; -5371806, 26598, 1630327],[66, 33, 1],[-2433, 11292, 42680, 135861, 164297, 161345, 68164, 36776, 23051, -5385; 4870, -22601, -85425, -271930, -328846, -322938, -136433, -73609, -46138, 10778; -8096, 37575, 142021, 452088, 546711, 536888, 226821, 122375, 76704, -17919],130,26]
%
% END OF LATTICE L131.26
%
%
% LATTICE L131.27
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1219416, -45144, 9240; -45144, -1595, 341; 9240, 341, -70],[264, 11, 1],[-1, 3, 25, 39, 41, 97, 5, -1, -7, -9; 0, 6, 48, 72, 74, 168, 8, -6, -16, -18; -132, 425, 3531, 5492, 5764, 13596, 697, -165, -1004, -1276],130,27]
%
% END OF LATTICE L131.27
%
%
% LATTICE L131.28
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[264, 0, 0; 0, -77, 44; 0, 44, -25],[264, 11, 1],[1, 0, -1, -3, -2, -13, -1, -2, -1, 0; 0, 3, 21, 24, 10, 24, -1, -15, -16, -6; 0, 5, 33, 32, 11, 0, -5, -33, -32, -11],130,28]
%
% END OF LATTICE L131.28
%
%
% LATTICE L131.29
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[10428, 3564, 1056; 3564, 1023, 297; 1056, 297, 86],[132, 33, 1],[-3, -1, -1, -1, 1, 3, 1, 1, 1, -1; 100, 35, 39, 68, 8, -60, -25, -29, -28, 32; -308, -108, -121, -216, -33, 176, 75, 88, 84, -99],130,29]
%
% END OF LATTICE L131.29
%
%
% LATTICE L131.30
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1260973362, -836381172, -386427096; -836381172, -554756730, -256310208; -386427096, -256310208, -118421137],[66, 66, 1],[3, -17, -69, -113, -276, -137, -117, -65, -21, 8; 2623, -22595, -85725, -136331, -329615, -161719, -136501, -73371, -22765, 11423; -5687, 48960, 185768, 295443, 714318, 350471, 295824, 159016, 49341, -24750],130,30]
%
% END OF LATTICE L131.30
%
%
% LATTICE L131.31
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[38870568, -367092, -9819612; -367092, 3468, 92736; -9819612, 92736, 2480663],[396, 12, 1],[-25, -800, -197, -3326, -483, -360, -1145, -188, -303, -91; 1, 33, 5, 33, 2, -1, -11, -5, -11, -6; -99, -3168, -780, -13167, -1912, -1425, -4532, -744, -1199, -360],130,31]
%
% END OF LATTICE L131.31
%
%
% LATTICE L131.32
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3914064, 30096, 727056; 30096, -150, -7173; 727056, -7173, -104293],[1584, 3, 1],[-177, -3385, -357, -32389, -478, -1979, -424, 175, 2891, 356; -10264, -196284, -20701, -1878096, -27717, -114752, -24585, 10148, 167640, 20643; -528, -10098, -1065, -96624, -1426, -5904, -1265, 522, 8624, 1062],130,32]
%
% END OF LATTICE L131.32
%
%
% LATTICE L131.33
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[6602640, 1922976, 25344; 1922976, 560054, 7381; 25344, 7381, 97],[528, 11, 1],[581, 15, -5, -39, -25, 7, 19, 76, 235, 123; -2016, -52, 18, 136, 87, -24, -66, -264, -816, -427; 1584, 37, -66, -160, -88, 0, 58, 231, 688, 352],130,33]
%
% END OF LATTICE L131.33
%
%
% LATTICE L131.34
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1599972, 49632, -351780; 49632, 1540, -10912; -351780, -10912, 77345],[132, 44, 1],[127, 37, 68, 10, 11, 8, 8, 67, 35, 169; -585, -172, -321, -46, -43, -24, -31, -288, -157, -769; 495, 144, 264, 39, 44, 33, 32, 264, 137, 660],130,34]
%
% END OF LATTICE L131.34
%
%
% LATTICE L131.35
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[528, -264, 0; -264, -4776, 336; 0, 336, -23],[264, 24, 1],[1, -1, -3, -14, -4, 0, 23, 5, 25, 8; 2, 0, -6, -33, -11, -1, 22, 8, 44, 15; 29, 0, -88, -495, -168, -17, 264, 112, 627, 216],130,35]
%
% END OF LATTICE L131.35
%
%
% LATTICE L131.36
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[528, -2376, -1056; -2376, 10248, 4560; -1056, 4560, 2029],[264, 24, 1],[1, 1, -1, -5, 0, 1, 21, 3, 27, 4; -6, 0, 14, 264, 59, 28, 242, 8, -22, -15; 14, 0, -32, -594, -132, -62, -528, -16, 66, 36],130,36]
%
% END OF LATTICE L131.36
%
%
% LATTICE L131.37
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[990, -396, 0; -396, 165, 0; 0, 0, -1],[198, 33, 1],[5, 1, 3, 1, 1, -1, -1, -1, 1, 1; 2, 1, 5, 2, 3, -2, -3, -5, -6, -1; -132, -19, -33, -8, 0, 0, -9, -33, -108, -44],130,37]
%
% END OF LATTICE L131.37
%
%
% LATTICE L131.38
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[292512, 25872, -5280; 25872, 2288, -464; -5280, -464, 67],[528, 16, 1],[7, -1, -20, -61, -17, 1, 56, 35, 58, 37; -81, 11, 231, 704, 196, -12, -649, -405, -671, -428; -9, 0, 24, 66, 16, -6, -88, -48, -77, -48],130,38]
%
% END OF LATTICE L131.38
%
%
% LATTICE L131.39
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[20856, 22968, 1848; 22968, 23430, 1881; 1848, 1881, 151],[264, 33, 1],[3, 1, 1, 1, -1, -3, -1, -1, -1, 1; -52, -25, -31, -28, 38, 116, 41, 47, 92, 26; 616, 300, 374, 336, -462, -1408, -498, -572, -1128, -330],130,39]
%
% END OF LATTICE L131.39
%
%
% LATTICE L131.40
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[642840, 0, -7392; 0, 33, 0; -7392, 0, 85],[264, 33, 1],[75, 16, 9, 13, 0, 1, 3, 10, 63, 38; -16, -3, -1, 0, 1, 0, -1, -3, -16, -9; 6512, 1389, 781, 1128, 0, 88, 261, 869, 5472, 3300],130,40]
%
% END OF LATTICE L131.40
%
%
% LATTICE L131.41
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1277892, -143748, 7920; -143748, 16170, -891; 7920, -891, 49],[396, 33, 1],[-9, -4, -6, -19, -5, -7, 0, 2, 1, -1; -80, -36, -55, -180, -49, -76, -1, 16, 8, -9; 0, -9, -33, -216, -88, -264, -19, -33, -16, 0],130,41]
%
% END OF LATTICE L131.41
%
%
% LATTICE L131.42
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-17622, 792, -8712; 792, 330, 396; -8712, 396, -4307],[198, 66, 1],[-1095, -313, -523, -53, 98, 49, -107, -523, -887, -730; -25, -7, -11, -1, 3, 1, -3, -13, -21, -17; 2211, 632, 1056, 107, -198, -99, 216, 1056, 1791, 1474],130,42]
%
% END OF LATTICE L131.42
%
%
% LATTICE L131.43
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[297264, 167376, -13200; 167376, 94083, -7326; -13200, -7326, 515],[528, 33, 1],[-377, -137, -73, -143, 77, 469, 80, 169, 235, -31; 760, 276, 147, 288, -155, -944, -161, -340, -472, 63; 1144, 414, 220, 432, -231, -1408, -240, -506, -696, 99],130,43]
%
% END OF LATTICE L131.43
%
%
% LATTICE L131.44
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[218328, 637956, 154440; 637956, 1863708, 451176; 154440, 451176, 109223],[132, 132, 1],[1, 5, 12, 14, 59, 12, 8, 1, -1, -7; -3, -115, -313, -373, -1586, -321, -209, -11, 49, 290; 11, 468, 1276, 1521, 6468, 1309, 852, 44, -201, -1188],130,44]
%
% END OF LATTICE L131.44
%
%
% LATTICE L131.45
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[286704, -21384, 7920; -21384, -600, 288; 7920, 288, -133],[792, 24, 1],[1, -1, -3, -3, -1, 1, 47, 7, 31, 3; 179, -176, -538, -550, -201, 172, 8250, 1240, 5511, 535; 447, -440, -1344, -1375, -504, 429, 20592, 3096, 13761, 1336],130,45]
%
% END OF LATTICE L131.45
%
%
% LATTICE L131.46
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[7055928, 598752, 58608; 598752, 50808, 4968; 58608, 4968, 455],[792, 24, 1],[51, 45, -59, -313, -194, -73, -377, 37, 697, 50; -611, -539, 707, 3751, 2325, 875, 4521, -443, -8349, -599; 102, 88, -120, -638, -396, -150, -792, 72, 1386, 100],130,46]
%
% END OF LATTICE L131.46
%
%
% LATTICE L131.47
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-5808, 1320, -264; 1320, -88, 0; -264, 0, 5],[264, 88, 1],[-1, -1, -5, -1, -1, 1, 1, 5, 1, 1; -18, -16, -78, -16, -17, 12, 14, 72, 14, 13; -66, -56, -264, -50, -44, 66, 56, 264, 50, 44],130,47]
%
% END OF LATTICE L131.47
%
%
% LATTICE L131.48
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[25080, -25080, 792; -25080, 25168, -792; 792, -792, 25],[264, 88, 1],[-1, -4, -34, -8, -37, -26, -14, -20, -1, 1; 0, -1, -9, -2, -9, -6, -3, -3, 0, 1; 33, 96, 792, 189, 880, 627, 344, 528, 31, 0],130,48]
%
% END OF LATTICE L131.48
%
%
% LATTICE L131.49
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1056, 12144, -528; 12144, -139056, 6048; -528, 6048, -263],[528, 48, 1],[-1, 4, 5, 56, 53, 7, 139, 8, 31, -1; 0, -11, -3, -22, -18, -2, -33, -1, 0, 2; 2, -264, -80, -627, -528, -61, -1056, -40, -66, 48],130,49]
%
% END OF LATTICE L131.49
%
%
% LATTICE L131.50
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[5378472, 209088, -22968; 209088, 8085, -891; -22968, -891, 98],[792, 33, 1],[-9, -4, -6, -19, -5, -7, 0, 2, 1, -1; -160, -72, -110, -360, -98, -152, -2, 32, 16, -18; -3564, -1593, -2409, -7740, -2068, -3036, -19, 759, 380, -396],130,50]
%
% END OF LATTICE L131.50
%
%
% LATTICE L131.51
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[27720, 3168, 0; 3168, 363, 0; 0, 0, -1],[792, 33, 1],[1, 1, 2, 7, 1, 3, 0, -1, -1, -1; -8, -9, -19, -72, -11, -40, -1, 7, 8, 9; 0, -9, -33, -216, -44, -264, -19, -33, -16, 0],130,51]
%
% END OF LATTICE L131.51
%
%
% LATTICE L131.52
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[9977616, 31680, -22176; 31680, 33, -66; -22176, -66, 49],[1584, 33, 1],[-17, -4, -13, -47, -7, -27, -1, 1, 1, -1; -560, -132, -430, -1560, -233, -904, -34, 32, 32, -33; -8448, -1989, -6468, -23400, -3487, -13464, -500, 495, 496, -495],130,52]
%
% END OF LATTICE L131.52
%
%
% LATTICE L131.53
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-380556, -60192, -50688; -60192, 36564, -42768; -50688, -42768, 19453],[396, 132, 1],[75, 2045, 5832, 7496, 11053, 7190, 1740, 1433, -77, -4099; -224, -6108, -17419, -22389, -33013, -21475, -5197, -4280, 230, 12243; -297, -8100, -23100, -29691, -43780, -28479, -6892, -5676, 305, 16236],130,53]
%
% END OF LATTICE L131.53
%
%
% LATTICE L131.54
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[26508688272, 7184680272, 50200128; 7184680272, 1947272118, 13605801; 50200128, 13605801, 95065],[1584, 33, 1],[-257, -737, -740, -3791, -354, 1029, 155, 1673, 1521, 1448; 856, 2454, 2464, 12624, 1179, -3424, -516, -5570, -5064, -4821; 13200, 37962, 38115, 195120, 18194, -53328, -7999, -86262, -78416, -74646],130,54]
%
% END OF LATTICE L131.54
%
%
% LATTICE L131.55
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2640, 4488, -1848; 4488, 8184, -3432; -1848, -3432, 1439],[264, 264, 1],[-1, -1, 1, 5, 15, 9, 9, 7, 3, 1; -64, -70, 36, 266, 821, 502, 508, 402, 172, 55; -154, -168, 88, 642, 1980, 1210, 1224, 968, 414, 132],130,55]
%
% END OF LATTICE L131.55
%
%
% LATTICE L131.56
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-433488, -433752, 6072; -433752, -433752, 6072; 6072, 6072, -85],[264, 264, 1],[0, -1, -3, -2, -9, -2, -3, -1, 0, 1; -2, -2, 8, 11, 61, 17, 32, 22, 4, -1; -143, -216, 352, 639, 3696, 1067, 2064, 1496, 285, 0],130,56]
%
% END OF LATTICE L131.56
%
%
% LATTICE L131.57
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-54570384, -2654784, 68112; -2654784, -128976, 3312; 68112, 3312, -85],[1584, 48, 1],[6, 40, 7, 9, -1, -1, 1, 4, 47, 15; 64, 429, 76, 99, -9, -11, 0, 41, 495, 159; 7299, 48752, 8568, 11066, -1152, -1230, 792, 4800, 56925, 18208],130,57]
%
% END OF LATTICE L131.57
%
%
% LATTICE L131.58
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1584, -50688, 1584; -50688, -346128, 10992; 1584, 10992, -349],[1584, 48, 1],[25, 84, 15, 10, -1, -1, 1, 8, 193, 31; 271, 913, 164, 110, -9, -11, 0, 85, 2079, 335; 8646, 29128, 5232, 3509, -288, -351, 0, 2712, 66330, 10688],130,58]
%
% END OF LATTICE L131.58
%
%
% LATTICE L131.59
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[279312, -289344, -34320; -289344, 299728, 35552; -34320, 35552, 4217],[528, 176, 1],[-79, -47, -88, -11, -1, 5, -4, -65, -20, -203; 6, 4, 9, 1, -1, -3, -1, 0, 1, 13; -693, -416, -792, -98, 0, 66, -24, -528, -171, -1760],130,59]
%
% END OF LATTICE L131.59
%
%
% LATTICE L131.60
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-77616, -24552, 6336; -24552, -5016, 1320; 6336, 1320, -347],[792, 264, 1],[9, 3, 7, 1, 1, -1, -1, 1, 5, 5; 604, 210, 524, 78, 99, -82, -108, -2, 288, 315; 2442, 848, 2112, 314, 396, -330, -432, 0, 1170, 1276],130,60]
%
% END OF LATTICE L131.60
%
%
% LATTICE L131.61
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[792, 0, 0; 0, 25080, -792; 0, -792, 25],[792, 264, 1],[-2, -1, -1, 0, 1, 0, -1, -3, -2, -3; 20, 11, 17, 1, 0, 1, 9, 25, 18, 28; 627, 344, 528, 31, 0, 33, 288, 792, 567, 880],130,61]
%
% END OF LATTICE L131.61
%
%
% LATTICE L131.62
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1050720, -1501104, 3696; -1501104, -2144208, 5280; 3696, 5280, -13],[528, 528, 1],[-1, -1, 0, 1, 13, 2, 4, 3, 1, -1; 0, -1, -3, -2, -18, -2, -3, -1, 0, 2; -286, -696, -1232, -537, -3696, -253, -96, 440, 282, 528],130,62]
%
% END OF LATTICE L131.62
%
%
% LATTICE L131.63
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[3168, 90288, 11088; 90288, 2566608, 315216; 11088, 315216, 38713],[1584, 528, 1],[4, 3, 8, 1, -1, -3, -4, -3, 1, 7; 85, 51, 97, 12, 0, -8, 9, 65, 63, 216; -693, -416, -792, -98, 0, 66, -72, -528, -513, -1760],130,63]
%
% END OF LATTICE L131.63
%
%
% LATTICE L131.64
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[3168, 49104, -3168; 49104, 760848, -49104; -3168, -49104, 3169],[1584, 528, 1],[21, 7, 16, 1, -1, -2, -4, 1, 11, 23; -14, -3, -1, 0, 0, -2, -9, -17, -18, -24; -198, -40, 0, 1, 0, -33, -144, -264, -270, -352],130,64]
%
% END OF LATTICE L131.64
%

\medskip%
%------------------------------WEYL-GROUP-W132--------------------------------
%
\leavevmode\llap{}%
$W_{132}$%
\qquad\llap{32} lattices, $\chi=48$%
\hfill%
$222222222222\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L132.1
%
\leavevmode%
${L_{132.1}}$%
{} : {$1\above{1pt}{1pt}{2}{2}8\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}7\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{2\rightarrow N'_{23}}%
\EasyButWeakLineBreak%
{${10}\above{1pt}{1pt}{b}{2}{2}\above{1pt}{1pt}{l}{2}{40}\above{1pt}{1pt}{}{2}{1}\above{1pt}{1pt}{r}{2}{140}\above{1pt}{1pt}{*}{2}{8}\above{1pt}{1pt}{b}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-9764440\\82320\\840
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
82320\\-694\\-7
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
840\\-7\\1
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-949971\\-112791560\\8248520
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7995\\949259\\-69420
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-82\\-9736\\711
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4\\475\\-30
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
15\\1781\\-128
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
347\\41200\\-3000
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
82\\9736\\-711
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5763\\684250\\-50050
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1069\\126924\\-9288
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-9764440, 82320, 840; 82320, -694, -7; 840, -7, 1],[280, 1, 1],[4, 15, 347, 82, 5763, 1069, 201, 26, 63, 0, -23, -3; 475, 1781, 41200, 9736, 684250, 126924, 23865, 3087, 7480, 0, -2730, -356; -30, -128, -3000, -711, -50050, -9288, -1750, -228, -560, -1, 210, 32],131,1]
%
% END OF LATTICE L132.1
%
\hbox{}\par\smallskip%
%
% LATTICE L132.2
%
\leavevmode%
${L_{132.2}}$%
{} : {$1\above{1pt}{1pt}{-2}{2}8\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}7\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{m}%
\EasyButWeakLineBreak%
{${10}\above{1pt}{1pt}{s}{2}{2}\above{1pt}{1pt}{b}{2}{40}\above{1pt}{1pt}{*}{2}{4}\above{1pt}{1pt}{l}{2}{35}\above{1pt}{1pt}{}{2}{8}\above{1pt}{1pt}{r}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
466760\\-4480\\0
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-4480\\43\\0
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\-1
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-50051\\-5125120\\600600
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
480\\49151\\-5760
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-75\\-7680\\899
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-105\\-5
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\101\\-21
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
37\\3780\\-500
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
19\\1944\\-238
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
349\\35735\\-4200
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
131\\13416\\-1560
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[466760, -4480, 0; -4480, 43, 0; 0, 0, -1],[280, 1, 1],[-1, 1, 37, 19, 349, 131, 26, 4, 13, 1, 1, -1; -105, 101, 3780, 1944, 35735, 13416, 2665, 411, 1340, 104, 105, -104; -5, -21, -500, -238, -4200, -1560, -295, -39, -100, -2, 0, 0],131,2]
%
% END OF LATTICE L132.2
%
%
% LATTICE L132.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[2590, 1260, 0; 1260, 613, 0; 0, 0, -1],[70, 1, 1],[-907, -135, -213, -16, -102, -1, 17, -43, -677, -340, -12358, -2313; 1875, 279, 440, 33, 210, 2, -35, 89, 1400, 703, 25550, 4782; -405, -59, -90, -6, -35, 0, 5, -21, -310, -154, -5565, -1040],131,3]
%
% END OF LATTICE L132.3
%
%
% LATTICE L132.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-4620, -2240, 140; -2240, -1086, 69; 140, 69, 17],[140, 1, 1],[99, 26, 127, 18, -17, -35, -34, -13, 3, 34, 1837, 373; -200, -53, -260, -37, 35, 72, 70, 27, 0, -67, -3675, -748; -35, -3, 0, 2, 0, -4, -5, -5, -80, -34, -1120, -204],131,4]
%
% END OF LATTICE L132.4
%
%
% LATTICE L132.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[83370, -2520, 41720; -2520, 74, -1260; 41720, -1260, 20877],[70, 2, 1],[39, -149, -1082, -1071, -38606, -3605, -2799, -403, -298, -33, -34, 17; -35, 167, 1190, 1174, 42245, 3943, 3055, 437, 320, 34, 35, -17; -80, 308, 2235, 2212, 79730, 7445, 5780, 832, 615, 68, 70, -35],131,5]
%
% END OF LATTICE L132.5
%
%
% LATTICE L132.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[213570, -6300, -42700; -6300, 185, 1260; -42700, 1260, 8537],[70, 5, 1],[-4, 54, 163, 406, 2937, 2745, 214, 156, 47, 14, 3, -15; -7, 167, 476, 1174, 8449, 7886, 611, 437, 128, 34, 7, -34; -19, 245, 744, 1855, 13426, 12550, 979, 715, 216, 65, 14, -70],131,6]
%
% END OF LATTICE L132.6
%
%
% LATTICE L132.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[299670, -8820, -85610; -8820, 259, 2520; -85610, 2520, 24457],[70, 7, 1],[-31, 63, 991, 497, 2577, 3375, 1321, 195, 299, 19, 3, -21; -35, 167, 2380, 1174, 6035, 7886, 3055, 437, 640, 34, 5, -34; -105, 203, 3220, 1617, 8390, 10990, 4305, 637, 980, 63, 10, -70],131,7]
%
% END OF LATTICE L132.7
%
%
% LATTICE L132.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[12309080, -185780, -3074820; -185780, 2804, 46408; -3074820, 46408, 768093],[140, 4, 1],[-4207, -536, -319, 1, 71, -9, -123, -330, -1846, -3465, -121311, -5620; -6975, -889, -530, 0, 70, -17, -205, -547, -3060, -5744, -201110, -9317; -16420, -2092, -1245, 4, 280, -35, -480, -1288, -7205, -13524, -473480, -21935],131,8]
%
% END OF LATTICE L132.8
%
%
% LATTICE L132.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-7980, -3500, 0; -3500, -1510, -5; 0, -5, 1],[140, 5, 1],[61, 42, 23, 4, -3, -7, 0, 19, 99, 240, 1711, 1593; -138, -95, -52, -9, 7, 16, 0, -43, -224, -543, -3871, -3604; -679, -465, -252, -40, 42, 80, -1, -215, -1108, -2680, -19082, -17760],131,9]
%
% END OF LATTICE L132.9
%
%
% LATTICE L132.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[409990, -50400, 194740; -50400, 6130, -23940; 194740, -23940, 92499],[70, 10, 1],[-321, -5501, -6355, -30039, -211180, -97940, -14739, -9559, -1175, -81, 340, 50; -7, -121, -140, -662, -4655, -2159, -325, -211, -26, -2, 7, 1; 674, 11550, 13343, 63070, 443394, 205635, 30946, 20070, 2467, 170, -714, -105],131,10]
%
% END OF LATTICE L132.10
%
%
% LATTICE L132.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1260, -280, 0; -280, 63, 0; 0, 0, -1],[140, 7, 1],[54, 7, 17, 0, -1, -1, 1, 4, 93, 44, 221, 287; 205, 26, 60, -1, -5, -4, 5, 16, 360, 169, 845, 1096; -350, -49, -140, -7, -5, 0, 0, -21, -560, -273, -1395, -1820],131,11]
%
% END OF LATTICE L132.11
%
%
% LATTICE L132.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[141890, -35280, 65870; -35280, 8582, -16380; 65870, -16380, 30579],[70, 14, 1],[-1601, -5509, -31842, -30107, -151198, -98173, -73879, -9587, -5898, -85, 238, 49; -35, -121, -700, -662, -3325, -2159, -1625, -211, -130, -2, 5, 1; 3430, 11802, 68215, 64498, 323910, 210315, 158270, 20538, 12635, 182, -510, -105],131,12]
%
% END OF LATTICE L132.12
%
%
% LATTICE L132.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[840, 280, 280; 280, 90, 75; 280, 75, -7],[280, 5, 1],[3, 10, 17, 12, 103, 79, 0, -7, -11, -6, -19, -1; -11, -37, -64, -46, -406, -316, -1, 25, 40, 22, 70, 4; 2, 0, -24, -35, -546, -520, -22, -20, -16, -5, -14, 0],131,13]
%
% END OF LATTICE L132.13
%
%
% LATTICE L132.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2520, 280, 280; 280, -30, -35; 280, -35, -17],[280, 5, 1],[1, -1, -17, -47, -179, -339, -14, -12, -9, -5, -3, 1; 7, -11, -140, -380, -1435, -2712, -111, -93, -68, -36, -21, 8; 2, 0, -24, -70, -273, -520, -22, -20, -16, -10, -7, 0],131,14]
%
% END OF LATTICE L132.14
%
%
% LATTICE L132.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-8680, 0, 280; 0, 7, -7; 280, -7, -2],[280, 7, 1],[-1, -4, -93, -22, -221, -287, -54, -7, -17, 0, 1, 1; -30, -128, -3000, -711, -7150, -9288, -1750, -228, -560, -1, 30, 32; -35, -133, -3080, -728, -7310, -9492, -1785, -231, -560, 0, 30, 28],131,15]
%
% END OF LATTICE L132.15
%
%
% LATTICE L132.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-139720, 8680, -560; 8680, -539, 35; -560, 35, -2],[280, 7, 1],[-2, -4, -81, -37, -91, -235, -43, -5, -9, 1, 1, 1; -30, -64, -1320, -606, -1495, -3864, -710, -84, -160, 14, 15, 16; 35, -21, -980, -518, -1380, -3640, -735, -119, -420, -42, -20, 0],131,16]
%
% END OF LATTICE L132.16
%
%
% LATTICE L132.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[280, 0, 0; 0, -8, 8; 0, 8, -7],[280, 8, 1],[-39, -5, -3, 0, 1, 0, -1, -3, -17, -16, -561, -26; -225, -33, -25, -3, 0, 1, 5, -11, -85, -85, -3080, -144; -520, -72, -50, -4, 0, 1, 0, -32, -210, -204, -7280, -339],131,17]
%
% END OF LATTICE L132.17
%
%
% LATTICE L132.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-19320, 0, -9520; 0, 8, 0; -9520, 0, -4691],[280, 8, 1],[3021, 387, 116, 0, -69, 1, 79, 233, 659, 1240, 43469, 4029; -35, -3, 0, 1, 0, -1, -5, -5, -10, -17, -560, -51; -6120, -784, -235, 0, 140, -2, -160, -472, -1335, -2512, -88060, -8162],131,18]
%
% END OF LATTICE L132.18
%
%
% LATTICE L132.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1190, -1190, 210; -1190, 21455, -7560; 210, -7560, 2629],[70, 35, 1],[113, 1939, 4481, 10591, 10637, 69065, 5197, 3371, 829, 29, -17, -35; -233, -3999, -9242, -21844, -21939, -142448, -10719, -6953, -1710, -60, 35, 72; -679, -11655, -26936, -63665, -63942, -415170, -31241, -20265, -4984, -175, 102, 210],131,19]
%
% END OF LATTICE L132.19
%
%
% LATTICE L132.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2553320, -53900, -651840; -53900, 1140, 13760; -651840, 13760, 166409],[140, 20, 1],[-961, -674, -97, -103, -137, -9, -1, -288, -384, -3745, -26799, -6244; -345, -245, -36, -42, -56, -3, 1, -99, -136, -1334, -9576, -2233; -3736, -2620, -377, -400, -532, -35, -4, -1120, -1493, -14560, -104188, -24275],131,20]
%
% END OF LATTICE L132.20
%
%
% LATTICE L132.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[140, 1120, 0; 1120, 252, -280; 0, -280, -9],[140, 28, 1],[3086, 445, 332, 79, 41, -9, -36, 165, 1193, 2361, 12159, 3974; -315, -46, -35, -9, -5, 1, 5, -16, -120, -239, -1235, -404; 12040, 1736, 1295, 308, 160, -35, -140, 644, 4655, 9212, 47440, 15505],131,21]
%
% END OF LATTICE L132.21
%
%
% LATTICE L132.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[140, 0, 0; 0, -805, -175; 0, -175, -38],[140, 35, 1],[0, -4, -21, -51, -52, -339, -13, -9, -5, -1, 0, 1; 3, 21, 76, 168, 162, 1040, 37, 19, 4, -8, -2, 0; -14, -105, -392, -875, -849, -5460, -196, -105, -28, 35, 9, 0],131,22]
%
% END OF LATTICE L132.22
%
%
% LATTICE L132.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[3172610, -12328120, -6031970; -12328120, 47904570, 23439010; -6031970, 23439010, 11468367],[70, 70, 1],[-7, 167, 238, 1174, 1207, 3943, 611, 437, 64, 34, 1, -17; -221, -505, -86, 131, 436, 1683, 445, 729, 198, 317, 12, -227; 448, 1120, 301, 350, -256, -1365, -588, -1260, -371, -630, -24, 455],131,23]
%
% END OF LATTICE L132.23
%
%
% LATTICE L132.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[97720, -22960, 2240; -22960, 5390, -525; 2240, -525, 51],[280, 35, 1],[-2, 1, 3, 2, 1, 1, -1, -4, -9, -8, -13, -79; -45, -15, 8, 12, 6, 4, -7, -37, -112, -116, -214, -1356; -392, -210, -56, 35, 18, 0, -28, -210, -784, -875, -1698, -10920],131,24]
%
% END OF LATTICE L132.24
%
%
% LATTICE L132.25
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[280, 0, 0; 0, -1610, 175; 0, 175, -19],[280, 35, 1],[-13, -9, -5, -1, 0, 1, 0, -4, -21, -51, -26, -339; -37, -19, -4, 8, 1, 0, -3, -21, -76, -168, -81, -1040; -392, -210, -56, 70, 9, 0, -28, -210, -784, -1750, -849, -10920],131,25]
%
% END OF LATTICE L132.25
%
%
% LATTICE L132.26
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[185080, 0, -3360; 0, -40, 0; -3360, 0, 61],[280, 40, 1],[65, 47, 7, 4, 1, -1, -1, 17, 25, 124, 895, 209; 59, 39, 5, 1, 0, 0, 1, 21, 25, 119, 840, 195; 3536, 2560, 382, 220, 56, -55, -56, 920, 1358, 6740, 48664, 11365],131,26]
%
% END OF LATTICE L132.26
%
%
% LATTICE L132.27
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2520, 2520, -280; 2520, -2480, 280; -280, 280, -31],[280, 40, 1],[176, 114, 7, 1, -3, 0, 4, 66, 38, 359, 2523, 1170; -7, -3, 0, 1, 0, -1, -1, -5, -2, -17, -112, -51; -1752, -1120, -67, 0, 28, -10, -48, -680, -383, -3600, -25228, -11690],131,27]
%
% END OF LATTICE L132.27
%
%
% LATTICE L132.28
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[26040, 10640, -280; 10640, 3864, -112; -280, -112, 3],[280, 56, 1],[-13, 1, 2, 2, 1, -1, -7, -5, -7, -10, -41, -25; -35, -3, 0, 1, 0, -1, -5, -5, -10, -17, -80, -51; -2800, -56, 175, 224, 100, -126, -840, -672, -1085, -1680, -7380, -4606],131,28]
%
% END OF LATTICE L132.28
%
%
% LATTICE L132.29
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-4760, -1960, 280; -1960, -336, 56; 280, 56, -9],[280, 56, 1],[-22, -4, -4, -1, -1, 0, 2, 0, -6, -7, -39, -13; -215, -47, -55, -17, -20, -1, 35, 11, -35, -55, -340, -116; -2240, -448, -490, -140, -160, -7, 280, 56, -490, -644, -3760, -1267],131,29]
%
% END OF LATTICE L132.29
%
%
% LATTICE L132.30
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[5320, 24500, -6300; 24500, 113260, -29120; -6300, -29120, 7487],[140, 140, 1],[1, 42, 53, 511, 519, 845, 129, 88, 12, 9, 1, 0; 7, 171, 210, 2014, 2040, 3319, 505, 341, 46, 34, 8, 9; 28, 700, 861, 8260, 8368, 13615, 2072, 1400, 189, 140, 32, 35],131,30]
%
% END OF LATTICE L132.30
%
%
% LATTICE L132.31
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-12880, -74760, 19040; -74760, -433160, 110320; 19040, 110320, -28097],[280, 280, 1],[-3, -5, 1, 18, 23, 79, 15, 17, 2, 6, 1, -1; -28, -498, -287, -2711, -2721, -8832, -1328, -858, -52, -1, 9, 18; -112, -1960, -1127, -10640, -10676, -34650, -5208, -3360, -203, 0, 36, 70],131,31]
%
% END OF LATTICE L132.31
%
%
% LATTICE L132.32
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-12880, -147000, 1400; -147000, -1297240, 12320; 1400, 12320, -117],[280, 280, 1],[-3, -21, -19, -84, -81, -130, -37, -19, -1, 4, 1, 0; 28, 178, 154, 671, 641, 1026, 288, 138, 4, -39, -9, 1; 2912, 18480, 15974, 69580, 66456, 106365, 29848, 14280, 406, -4060, -936, 105],131,32]
%
% END OF LATTICE L132.32
%

\medskip%
%------------------------------WEYL-GROUP-W133--------------------------------
%
\leavevmode\llap{}%
$W_{133}$%
\qquad\llap{32} lattices, $\chi=54$%
\hfill%
$422222422222\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L133.1
%
\leavevmode%
${L_{133.1}}$%
{} : {$1\above{1pt}{1pt}{2}{2}8\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{2}{}5\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{2}{}7\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2\rightarrow N'_{24}}%
\EasyButWeakLineBreak%
{${2}\above{1pt}{1pt}{}{4}{1}\above{1pt}{1pt}{r}{2}{56}\above{1pt}{1pt}{l}{2}{5}\above{1pt}{1pt}{r}{2}{28}\above{1pt}{1pt}{*}{2}{8}\above{1pt}{1pt}{b}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
8680\\-2240\\0
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2240\\578\\-1
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\-1\\-15
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7349\\28560\\-2520
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1925\\-7481\\660
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-385\\-1496\\131
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-8\\-31\\2
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\4\\-1
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
223\\868\\-84
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
126\\490\\-45
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
443\\1722\\-154
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
351\\1364\\-120
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[8680, -2240, 0; -2240, 578, -1; 0, -1, -15],[280, 1, 1],[-8, 1, 223, 126, 443, 351, 113, 34, 267, 49, 47, -1; -31, 4, 868, 490, 1722, 1364, 439, 132, 1036, 190, 182, -4; 2, -1, -84, -45, -154, -120, -38, -11, -84, -15, -14, 0],132,1]
%
% END OF LATTICE L133.1
%
\hbox{}\par\smallskip%
%
% LATTICE L133.2
%
\leavevmode%
${L_{133.2}}$%
{} : {$1\above{1pt}{1pt}{-2}{2}8\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{2}{}5\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{2}{}7\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{m}%
\EasyButWeakLineBreak%
{${2}\above{1pt}{1pt}{*}{4}{4}\above{1pt}{1pt}{s}{2}{56}\above{1pt}{1pt}{s}{2}{20}\above{1pt}{1pt}{l}{2}{7}\above{1pt}{1pt}{}{2}{8}\above{1pt}{1pt}{r}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-668920\\-105840\\6440
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-105840\\-16745\\1019
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
6440\\1019\\-62
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
23309\\-31080\\1906240
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3681\\-4909\\301024
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-225\\300\\-18401
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\2\\-71
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\-2\\278
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
73\\-84\\6188
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
73\\-90\\6090
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
60\\-77\\4956
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
91\\-120\\7464
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-668920, -105840, 6440; -105840, -16745, 1019; 6440, 1019, -62],[280, 1, 1],[-1, 3, 73, 73, 60, 91, 28, 15, 53, 17, 3, -1; 2, -2, -84, -90, -77, -120, -38, -22, -84, -30, -7, 0; -71, 278, 6188, 6090, 4956, 7464, 2279, 1194, 4116, 1270, 196, -104],132,2]
%
% END OF LATTICE L133.2
%
%
% LATTICE L133.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-70, 0, 0; 0, 1, 0; 0, 0, 1],[70, 1, 1],[0, 0, -5, -6, -11, -9, -6, -2, -9, -4, -3, -1; -1, 1, 0, -5, -14, -14, -11, -5, -28, -15, -14, -6; 1, 0, -42, -50, -91, -74, -49, -16, -70, -30, -21, -6],132,3]
%
% END OF LATTICE L133.3
%
%
% LATTICE L133.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-334460, -105840, 3220; -105840, -33490, 1019; 3220, 1019, -31],[140, 1, 1],[-1, 3, 73, 73, 120, 91, 28, 15, 53, 17, 6, -1; 1, -1, -42, -45, -77, -60, -19, -11, -42, -15, -7, 0; -71, 278, 6188, 6090, 9912, 7464, 2279, 1194, 4116, 1270, 392, -104],132,4]
%
% END OF LATTICE L133.4
%
%
% LATTICE L133.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-365190, 7070, -180810; 7070, -136, 3500; -180810, 3500, -89521],[70, 2, 1],[32, -101, 3914, 9871, 18539, 7697, 10408, 3581, 8266, 7529, 5821, 1003; -35, 102, -3857, -9740, -18305, -7603, -10285, -3542, -8183, -7460, -5775, -997; -66, 208, -8057, -20320, -38164, -15845, -21426, -7372, -17017, -15500, -11984, -2065],132,5]
%
% END OF LATTICE L133.5
%
%
% LATTICE L133.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-575610, 14000, 116550; 14000, -340, -2835; 116550, -2835, -23599],[70, 5, 1],[-13, 44, -3477, -876, -8222, -6825, -4613, -1586, -7317, -666, -2572, -885; -35, 102, -7714, -1948, -18305, -15206, -10285, -3542, -16366, -1492, -5775, -1994; -60, 205, -16240, -4091, -38395, -31870, -21540, -7405, -34160, -3109, -12005, -4130],132,6]
%
% END OF LATTICE L133.6
%
%
% LATTICE L133.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-727790, 18620, 209300; 18620, -476, -5355; 209300, -5355, -60191],[70, 7, 1],[-17, 61, -699, -6159, -1651, -9591, -6481, -2227, -1467, -4671, -515, -1239; -35, 102, -1102, -9740, -2615, -15206, -10285, -3542, -2338, -7460, -825, -1994; -56, 203, -2332, -20545, -5507, -31990, -21616, -7427, -4892, -15575, -1717, -4130],132,7]
%
% END OF LATTICE L133.7
%
%
% LATTICE L133.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[32817960, 9380, -8451380; 9380, 4, -2416; -8451380, -2416, 2176425],[140, 4, 1],[0, -589, -5561, -10637, -17047, -3179, -3846, -1975, -3413, -2183, -901, -26; 1, -748, -7084, -13560, -21742, -4056, -4909, -2524, -4368, -2800, -1162, -34; 0, -2288, -21602, -41320, -66220, -12349, -14940, -7672, -13258, -8480, -3500, -101],132,8]
%
% END OF LATTICE L133.8
%
%
% LATTICE L133.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[664020, -87850, 315350; -87850, 11730, -41720; 315350, -41720, 149763],[70, 10, 1],[19, 1723, -88807, -44211, -412434, -170520, -229651, -78267, -179097, -32333, -123374, -20840; 0, 29, -1484, -739, -6895, -2851, -3840, -1309, -2996, -541, -2065, -349; -40, -3620, 186585, 92888, 866530, 358265, 482500, 164440, 376285, 67932, 259210, 43785],132,9]
%
% END OF LATTICE L133.9
%
%
% LATTICE L133.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-355180, -243880, 72520; -243880, -167450, 49795; 72520, 49795, -14807],[140, 5, 1],[-16, 113, 2173, 415, 3312, 2459, 739, 369, 1201, 67, 62, -49; 1, -1, -42, -9, -77, -60, -19, -11, -42, -3, -7, 0; -75, 550, 10500, 2002, 15960, 11840, 3555, 1770, 5740, 318, 280, -240],132,10]
%
% END OF LATTICE L133.10
%
%
% LATTICE L133.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[217980, -59290, 101150; -59290, 16422, -27510; 101150, -27510, 46937],[70, 14, 1],[13, 1593, -11708, -204017, -54380, -157387, -211969, -72245, -23618, -149243, -16272, -19243; 0, 29, -212, -3695, -985, -2851, -3840, -1309, -428, -2705, -295, -349; -28, -3416, 25107, 437500, 116614, 337505, 454552, 154924, 50647, 320040, 34894, 41265],132,11]
%
% END OF LATTICE L133.11
%
%
% LATTICE L133.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-417620, -312900, 120680; -312900, -234430, 90419; 120680, 90419, -34873],[140, 7, 1],[-23, 199, 527, 3493, 792, 4099, 1226, 603, 275, 517, 10, -89; 1, -1, -6, -45, -11, -60, -19, -11, -6, -15, -1, 0; -77, 686, 1808, 11970, 2712, 14028, 4193, 2058, 936, 1750, 32, -308],132,12]
%
% END OF LATTICE L133.12
%
%
% LATTICE L133.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3640, 2240, 840; 2240, -1230, -445; 840, -445, -159],[280, 5, 1],[91, 25, 181, 6, 23, -3, -4, 4, 225, 23, 383, 293; 641, 177, 1288, 43, 168, -20, -29, 27, 1568, 161, 2688, 2060; -1320, -365, -2660, -89, -350, 40, 60, -55, -3220, -331, -5530, -4240],132,13]
%
% END OF LATTICE L133.13
%
%
% LATTICE L133.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-710360, -243880, 145040; -243880, -83725, 49795; 145040, 49795, -29614],[280, 5, 1],[739, 369, 1201, 67, 31, -49, -16, 113, 2173, 415, 1656, 2459; -38, -22, -84, -6, -7, 0, 2, -2, -84, -18, -77, -120; 3555, 1770, 5740, 318, 140, -240, -75, 550, 10500, 2002, 7980, 11840],132,14]
%
% END OF LATTICE L133.14
%
%
% LATTICE L133.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-6440, -5880, 1120; -5880, -5285, 994; 1120, 994, -185],[280, 7, 1],[-214, -56, -55, -59, -5, 11, 7, -13, -83, -286, -133, -701; 533, 139, 136, 145, 12, -28, -17, 33, 208, 715, 332, 1748; 1561, 406, 396, 420, 34, -84, -49, 98, 612, 2100, 974, 5124],132,15]
%
% END OF LATTICE L133.15
%
%
% LATTICE L133.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1770440, -455560, 762720; -455560, -117215, 196259; 762720, 196259, -328586],[280, 7, 1],[3505, 1797, 863, 1787, 33, -193, -94, 477, 1411, 9583, 1104, 11563; -38, -22, -12, -30, -1, 0, 2, -2, -12, -90, -11, -120; 8113, 4158, 1996, 4130, 76, -448, -217, 1106, 3268, 22190, 2556, 26768],132,16]
%
% END OF LATTICE L133.16
%
%
% LATTICE L133.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-560, 840, -280; 840, -1240, 416; -280, 416, -139],[280, 8, 1],[-1, 6, 55, 104, 165, 61, 73, 18, 29, 16, 3, -1; 2, -1, -21, -45, -77, -30, -38, -11, -21, -15, -7, 0; 8, -16, -182, -360, -588, -222, -272, -72, -126, -80, -28, 2],132,17]
%
% END OF LATTICE L133.17
%
%
% LATTICE L133.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-43512560, 78120, 155960; 78120, -136, -280; 155960, -280, -559],[280, 8, 1],[-1, 12, 104, 194, 305, 56, 133, 32, 50, 26, 3, -1; 2, -1, -21, -45, -77, -15, -38, -11, -21, -15, -7, 0; -280, 3348, 29022, 54140, 85120, 15629, 37120, 8932, 13958, 7260, 840, -279],132,18]
%
% END OF LATTICE L133.18
%
%
% LATTICE L133.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2590, 6160, -1680; 6160, 41055, -13055; -1680, -13055, 4198],[70, 35, 1],[-6, -592, 8713, 15182, 20233, 117115, 78864, 26878, 17573, 11104, 6053, 14315; 12, 1213, -17850, -31103, -41451, -239932, -161568, -55065, -36002, -22749, -12401, -29328; 35, 3535, -52020, -90643, -120800, -699230, -470855, -160475, -104920, -66297, -36140, -85470],132,19]
%
% END OF LATTICE L133.19
%
%
% LATTICE L133.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[536200, 1540, -156100; 1540, 20, -460; -156100, -460, 45453],[140, 20, 1],[0, -289, -2731, -1045, -8375, -1562, -1890, -971, -1679, -215, -445, -13; 1, -748, -7084, -2712, -21742, -4056, -4909, -2524, -4368, -560, -1162, -34; 0, -1000, -9450, -3616, -28980, -5405, -6540, -3360, -5810, -744, -1540, -45],132,20]
%
% END OF LATTICE L133.20
%
%
% LATTICE L133.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[512680, -2100, -106120; -2100, 28, 448; -106120, 448, 21975],[140, 28, 1],[0, 223, 301, 4031, 923, 1205, 1458, 749, 185, 829, 49, 10; 1, -748, -1012, -13560, -3106, -4056, -4909, -2524, -624, -2800, -166, -34; 0, 1092, 1474, 19740, 4520, 5901, 7140, 3668, 906, 4060, 240, 49],132,21]
%
% END OF LATTICE L133.21
%
%
% LATTICE L133.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-8050420, 31318210, 15323910; 31318210, -121835910, -59613960; 15323910, -59613960, -29168939],[70, 70, 1],[-35, 102, -551, -1948, -2615, -7603, -10285, -3542, -1169, -1492, -825, -997; -146, 1225, -8012, -28059, -37487, -108663, -146566, -50129, -16440, -20845, -11417, -13597; 280, -2450, 16085, 56322, 75240, 218085, 294140, 100590, 32985, 41818, 22900, 27265],132,22]
%
% END OF LATTICE L133.22
%
%
% LATTICE L133.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1395940, 116760, 679140; 116760, -9730, -56805; 679140, -56805, -330409],[140, 35, 1],[6384, 2962, 1245, 388, -39, -613, -51, 1260, 2977, 3834, 4261, 21723; -19, -11, -6, -3, -1, 0, 1, -1, -6, -9, -11, -60; 13125, 6090, 2560, 798, -80, -1260, -105, 2590, 6120, 7882, 8760, 44660],132,23]
%
% END OF LATTICE L133.23
%
%
% LATTICE L133.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-38920, 4760, 280; 4760, -525, -35; 280, -35, -2],[280, 35, 1],[1, 1, 1, 0, -1, -9, -4, -2, -3, -1, -1, -1; 2, -1, -12, -9, -22, -120, -38, -11, -12, -3, -2, 0; 105, 140, 260, 98, 110, 140, -105, -140, -260, -98, -110, -140],132,24]
%
% END OF LATTICE L133.24
%
%
% LATTICE L133.25
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-23293480, 19598600, 11537960; 19598600, -16489795, -9707775; 11537960, -9707775, -5715098],[280, 35, 1],[-85, 3639, 8361, 10685, 5905, 59953, 17530, 7991, 3269, 945, -90, -1803; 2, -2, -12, -18, -11, -120, -38, -22, -12, -6, -1, 0; -175, 7350, 16900, 21602, 11940, 121240, 35455, 16170, 6620, 1918, -180, -3640],132,25]
%
% END OF LATTICE L133.25
%
%
% LATTICE L133.26
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-4243120, -162680, 76160; -162680, -6200, 2920; 76160, 2920, -1367],[280, 40, 1],[637, 162, 271, 32, 43, -7, -13, 46, 457, 176, 1413, 527; -38, -11, -21, -3, -7, 0, 2, -1, -21, -9, -77, -30; 35400, 9000, 15050, 1776, 2380, -390, -720, 2560, 25410, 9784, 78540, 29290],132,26]
%
% END OF LATTICE L133.26
%
%
% LATTICE L133.27
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-34436080, 155400, 13836480; 155400, -680, -62440; 13836480, -62440, -5559523],[280, 40, 1],[29685, 7144, 11166, 1162, 675, -223, -225, 2676, 23204, 8658, 68065, 12498; -38, -11, -21, -3, -7, 0, 2, -1, -21, -9, -77, -15; 73880, 17780, 27790, 2892, 1680, -555, -560, 6660, 57750, 21548, 169400, 31105],132,27]
%
% END OF LATTICE L133.27
%
%
% LATTICE L133.28
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-23140880, -449400, 193200; -449400, -8680, 3752; 193200, 3752, -1613],[280, 56, 1],[783, 198, 47, 192, 7, -9, -15, 58, 81, 1088, 249, 649; -38, -11, -3, -15, -1, 0, 2, -1, -3, -45, -11, -30; 93688, 23688, 5622, 22960, 836, -1078, -1792, 6944, 9694, 130200, 29796, 77658],132,28]
%
% END OF LATTICE L133.28
%
%
% LATTICE L133.29
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-24419920, 24265080, -7021280; 24265080, -24111192, 6976760; -7021280, 6976760, -2018777],[280, 56, 1],[-21211, -5107, -1141, -4161, -70, 159, 163, -1909, -2367, -30919, -6946, -8929; -38, -11, -3, -15, -1, 0, 2, -1, -3, -45, -11, -15; 73640, 17724, 3958, 14420, 240, -553, -560, 6636, 8222, 107380, 24120, 31003],132,29]
%
% END OF LATTICE L133.29
%
%
% LATTICE L133.30
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[140, -13860, 3360; -13860, 45099880, -10934420; 3360, -10934420, 2651039],[140, 140, 1],[431, 220, 54, 48, 14, 3, 1, 68, 90, 240, 274, 357; 42870, 22029, 5443, 4881, 1445, 297, 0, 6551, 8847, 23699, 27135, 35428; 176820, 90860, 22450, 20132, 5960, 1225, 0, 27020, 36490, 97748, 111920, 146125],132,30]
%
% END OF LATTICE L133.30
%
%
% LATTICE L133.31
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-43400, -490560, 126560; -490560, -5164040, 1332520; 126560, 1332520, -343841],[280, 280, 1],[-2593, -641, -148, -115, -16, 35, 37, -211, -278, -737, -836, -2165; -91873, -22698, -5237, -4064, -561, 1243, 1297, -7494, -9859, -26128, -29631, -76723; -357000, -88200, -20350, -15792, -2180, 4830, 5040, -29120, -38310, -101528, -115140, -298130],132,31]
%
% END OF LATTICE L133.31
%
%
% LATTICE L133.32
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-4760, -695800, -338240; -695800, -98622160, -47941880; -338240, -47941880, -23305349],[280, 280, 1],[-38, -11, -3, -3, -1, 0, 2, -1, -3, -9, -11, -15; -160885, -38724, -8648, -6302, -525, 1208, 1225, -14496, -17962, -46918, -52695, -67733; 330960, 79660, 17790, 12964, 1080, -2485, -2520, 29820, 36950, 96516, 108400, 139335],132,32]
%
% END OF LATTICE L133.32
%

\medskip%
%------------------------------WEYL-GROUP-W134--------------------------------
%
\leavevmode\llap{}%
$W_{134}$%
\qquad\llap{32} lattices, $\chi=21$%
\hfill%
$2222224$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L134.1
%
\leavevmode%
${L_{134.1}}$%
{} : {$1\above{1pt}{1pt}{2}{2}8\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{2}{}13\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{2\rightarrow N'_{27}}%
\EasyButWeakLineBreak%
{${2}\above{1pt}{1pt}{b}{2}{26}\above{1pt}{1pt}{l}{2}{8}\above{1pt}{1pt}{r}{2}{2}\above{1pt}{1pt}{b}{2}{104}\above{1pt}{1pt}{*}{2}{12}\above{1pt}{1pt}{l}{2}{1}\above{1pt}{1pt}{}{4}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1962168\\6864\\9672
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
6864\\-22\\-35
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
9672\\-35\\-47
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-83\\-144
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2\\-169\\-286
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\248\\432
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
6\\499\\862
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
113\\9412\\16224
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
11\\918\\1578
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\84\\143
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-1962168, 6864, 9672; 6864, -22, -35; 9672, -35, -47],[312, 1, 1],[-1, -2, 3, 6, 113, 11, 1; -83, -169, 248, 499, 9412, 918, 84; -144, -286, 432, 862, 16224, 1578, 143],133,1]
%
% END OF LATTICE L134.1
%
\hbox{}\par\smallskip%
%
% LATTICE L134.2
%
\leavevmode%
${L_{134.2}}$%
{} : {$1\above{1pt}{1pt}{-2}{2}8\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{2}{}13\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{m}%
\EasyButWeakLineBreak%
{${2}\above{1pt}{1pt}{s}{2}{26}\above{1pt}{1pt}{b}{2}{8}\above{1pt}{1pt}{b}{2}{2}\above{1pt}{1pt}{l}{2}{104}\above{1pt}{1pt}{}{2}{3}\above{1pt}{1pt}{r}{2}{4}\above{1pt}{1pt}{*}{4}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-8293272\\29016\\14664
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
29016\\-101\\-52
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
14664\\-52\\-25
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\621\\467
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
17\\3523\\2639
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7\\1452\\1084
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\623\\463
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
21\\4368\\3224
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-207\\-156
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-208\\-154
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-8293272, 29016, 14664; 29016, -101, -52; 14664, -52, -25],[312, 1, 1],[3, 17, 7, 3, 21, -1, -1; 621, 3523, 1452, 623, 4368, -207, -208; 467, 2639, 1084, 463, 3224, -156, -154],133,2]
%
% END OF LATTICE L134.2
%
%
% LATTICE L134.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[2262, 390, -78; 390, 67, -13; -78, -13, 2],[78, 1, 1],[0, -4, 1, 8, 87, 10, 3; 0, 26, -6, -50, -546, -63, -19; 1, 13, -2, -19, -208, -24, -7],133,3]
%
% END OF LATTICE L134.3
%
%
% LATTICE L134.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[3588, -1248, 0; -1248, 434, -1; 0, -1, -11],[156, 1, 1],[1, 36, 25, 16, 163, -1, -8; 3, 104, 72, 46, 468, -3, -23; -1, -13, -8, -5, -52, 0, 2],133,4]
%
% END OF LATTICE L134.4
%
%
% LATTICE L134.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1878474, 9594, -932568; 9594, -44, 4762; -932568, 4762, -462973],[78, 2, 1],[220, 5230, 1033, 3474, 11767, 1189, -219; -83, -2041, -406, -1373, -4667, -477, 84; -444, -10556, -2085, -7012, -23751, -2400, 442],133,5]
%
% END OF LATTICE L134.5
%
%
% LATTICE L134.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2321358, 13026, 779844; 13026, -66, -4377; 779844, -4377, -261983],[78, 3, 1],[-198, -4702, -1857, -3122, -21147, -356, 197; -83, -2041, -812, -1373, -9334, -159, 84; -588, -13962, -5514, -9270, -62790, -1057, 585],133,6]
%
% END OF LATTICE L134.6
%
%
% LATTICE L134.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[22823580, -762762, 10515648; -762762, 25494, -351432; 10515648, -351432, 4844939],[78, 6, 1],[83, -38977, -9458, -36521, -133921, -5636, 697; 2, -624, -152, -588, -2158, -91, 11; -180, 84552, 20517, 79224, 290511, 12226, -1512],133,7]
%
% END OF LATTICE L134.7
%
%
% LATTICE L134.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-93444, 3744, 1872; 3744, -150, -75; 1872, -75, -37],[156, 3, 1],[0, 4, 3, 2, 21, 0, -1; 4, 117, 80, 51, 520, -1, -25; -9, -39, -12, -3, 0, 2, 0],133,8]
%
% END OF LATTICE L134.8
%
%
% LATTICE L134.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[3381144, 58500, -846612; 58500, 1012, -14648; -846612, -14648, 211985],[156, 4, 1],[-32, -121, -6, 9, 76, 43, 1; 55, 221, 14, 1, -65, -54, 0; -124, -468, -23, 36, 299, 168, 4],133,9]
%
% END OF LATTICE L134.9
%
%
% LATTICE L134.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1376232, 9672, -183144; 9672, -66, 1341; -183144, 1341, -22901],[312, 3, 1],[39, 76, -117, -232, -4359, -141, -38; 3277, 6383, -9832, -19493, -366236, -11846, -3192; -120, -234, 360, 714, 13416, 434, 117],133,10]
%
% END OF LATTICE L134.10
%
%
% LATTICE L134.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-35328072, 52416, 104832; 52416, -75, -156; 104832, -156, -311],[312, 3, 1],[9, 43, 15, 5, 21, -1, -1; 467, 2223, 772, 255, 1040, -52, -50; 2799, 13377, 4668, 1557, 6552, -311, -312],133,11]
%
% END OF LATTICE L134.11
%
%
% LATTICE L134.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-6922734, -65598, -1068600; -65598, -611, -10127; -1068600, -10127, -164950],[78, 13, 1],[192, 362, 1871, 3162, 1653, 1097, -194; -144, -262, -1344, -2258, -1176, -771, 143; -1235, -2329, -12038, -20345, -10636, -7059, 1248],133,12]
%
% END OF LATTICE L134.12
%
%
% LATTICE L134.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[27768, 7956, -7020; 7956, 3612, -1992; -7020, -1992, 1775],[156, 12, 1],[-447, -2084, -195, -370, -912, 1, -37; 25, 117, 11, 21, 52, 0, 2; -1740, -8112, -759, -1440, -3549, 4, -144],133,13]
%
% END OF LATTICE L134.13
%
%
% LATTICE L134.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-5772, 936, -936; 936, -143, 169; -936, 169, -118],[156, 13, 1],[-19, -4, -1, 12, 17, 19, -6; -79, -17, -8, 47, 68, 78, -24; 39, 8, 0, -26, -36, -39, 13],133,14]
%
% END OF LATTICE L134.14
%
%
% LATTICE L134.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[377937690, -11148618, 185272698; -11148618, 328900, -5465278; 185272698, -5465278, 90824423],[78, 26, 1],[-1402, 47248, 149127, 575988, 162491, 266773, -10961; 1, -47, -148, -571, -161, -264, 11; 2860, -96384, -304213, -1174992, -331475, -544206, 22360],133,15]
%
% END OF LATTICE L134.15
%
%
% LATTICE L134.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-456456, 9672, -103584; 9672, -176, 2216; -103584, 2216, -23491],[312, 8, 1],[64, 126, -48, -382, -898, -349, -63; 193, 377, -145, -1151, -2704, -1050, -189; -264, -520, 198, 1576, 3705, 1440, 260],133,16]
%
% END OF LATTICE L134.16
%
%
% LATTICE L134.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-8941296, 60840, 25272; 60840, -376, -176; 25272, -176, -71],[312, 8, 1],[-5, -7, 2, 29, 133, 25, 4; -150, -208, 60, 868, 3978, 747, 119; -1408, -1976, 563, 8168, 37466, 7044, 1128],133,17]
%
% END OF LATTICE L134.17
%
%
% LATTICE L134.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[367116906, 13457418, 116375064; 13457418, 493350, 4265937; 116375064, 4265937, 36890599],[78, 39, 1],[-1094, 36864, 232705, 449400, 253559, 69381, -8552; 2189, -73775, -465706, -899371, -507440, -138850, 17115; 3198, -107760, -680238, -1313676, -741198, -202813, 24999],133,18]
%
% END OF LATTICE L134.18
%
%
% LATTICE L134.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-6275256, 90792, 402480; 90792, -1313, -5824; 402480, -5824, -25813],[312, 13, 1],[38, 16, 83, 34, 17, -13, -11; 609, 259, 1356, 563, 288, -207, -184; 455, 191, 988, 403, 200, -156, -130],133,19]
%
% END OF LATTICE L134.19
%
%
% LATTICE L134.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-34008, 3120, 1560; 3120, -286, -143; 1560, -143, -71],[312, 13, 1],[-1, 0, 3, 4, 5, 5, 0; -11, -1, 32, 55, 76, 90, 6; 0, 2, 0, -26, -48, -78, -13],133,20]
%
% END OF LATTICE L134.20
%
%
% LATTICE L134.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1716, 23400, -1872; 23400, -313638, 25077; -1872, 25077, -2005],[156, 39, 1],[-24, -10, -51, -20, -9, 6, 7; -61, -24, -116, -42, -16, 15, 13; -741, -291, -1404, -507, -192, 182, 156],133,21]
%
% END OF LATTICE L134.21
%
%
% LATTICE L134.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-7044362598, 17327630658, 8531912844; 17327630658, -42622278036, -20986687020; 8531912844, -20986687020, -10333587325],[78, 78, 1],[-144, -262, -672, -2258, -588, -257, 143; 122611, 230845, 596387, 2015333, 526702, 232919, -123802; -249132, -469044, -1211769, -4094844, -1070175, -473252, 251550],133,22]
%
% END OF LATTICE L134.22
%
%
% LATTICE L134.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-87672, 7176, 28392; 7176, -528, -2400; 28392, -2400, -9097],[312, 24, 1],[-72, -134, 54, 422, 987, 127, 67; -215, -403, 161, 1261, 2951, 380, 201; -168, -312, 126, 984, 2301, 296, 156],133,23]
%
% END OF LATTICE L134.23
%
%
% LATTICE L134.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3291600, 64584, 22776; 64584, -1128, -456; 22776, -456, -157],[312, 24, 1],[-13, -23, 5, 77, 359, 23, 12; -104, -182, 40, 614, 2860, 183, 95; -1584, -2808, 609, 9384, 43758, 2804, 1464],133,24]
%
% END OF LATTICE L134.24
%
%
% LATTICE L134.25
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[140244, -95316, 107484; -95316, 65000, -73216; 107484, -73216, 82501],[156, 52, 1],[369, 153, 214, 461, 93, 40, -26; -1099, -456, -638, -1374, -277, -117, 79; -1456, -604, -845, -1820, -367, -156, 104],133,25]
%
% END OF LATTICE L134.25
%
%
% LATTICE L134.26
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-6252168, 2371824, -62712; 2371824, -899769, 23790; -62712, 23790, -629],[312, 39, 1],[-3, -2, 9, 38, 63, 31, 13; -11, -9, 32, 159, 268, 134, 58; -117, -141, 312, 2223, 3852, 1976, 897],133,26]
%
% END OF LATTICE L134.26
%
%
% LATTICE L134.27
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-9707880, 495144, 4480320; 495144, -25194, -228423; 4480320, -228423, -2067587],[312, 39, 1],[2631, 959, 4305, 1405, 423, -294, -269; -10525, -3837, -17228, -5625, -1696, 1176, 1078; 6864, 2502, 11232, 3666, 1104, -767, -702],133,27]
%
% END OF LATTICE L134.27
%
%
% LATTICE L134.28
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[63804, -664092, 170976; -664092, 6916728, -1780740; 170976, -1780740, 458459],[156, 156, 1],[-301, -105, -125, -237, -46, -4, -38; 1176, 407, 480, 901, 174, 13, 157; 4680, 1620, 1911, 3588, 693, 52, 624],133,28]
%
% END OF LATTICE L134.28
%
%
% LATTICE L134.29
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-815880, 772512, -209352; 772512, -731432, 198224; -209352, 198224, -53719],[312, 104, 1],[81, -3, -61, -287, -42, -146, 19; 1, -1, -1, 7, 2, 15, 6; -312, 8, 234, 1144, 171, 624, -52],133,29]
%
% END OF LATTICE L134.29
%
%
% LATTICE L134.30
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-285168, -223080, -101712; -223080, -173368, -79040; -101712, -79040, -36035],[312, 104, 1],[-5, -1, 2, 35, 13, 34, 7; 528, 118, -210, -3838, -1440, -3813, -815; -1144, -256, 455, 8320, 3122, 8268, 1768],133,30]
%
% END OF LATTICE L134.30
%
%
% LATTICE L134.31
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-6864, 40872, 3120; 40872, -241176, -18408; 3120, -18408, -1405],[312, 312, 1],[1, -1, -1, 7, 2, 5, 6; 24, -2, -18, -70, -9, -7, 13; -312, 24, 234, 936, 123, 104, -156],133,31]
%
% END OF LATTICE L134.31
%
%
% LATTICE L134.32
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-6864, -1029912, 7176; -1029912, -154263720, 1074840; 7176, 1074840, -7489],[312, 312, 1],[-13, 1, 5, 41, 11, 5, -6; 24, 2, -9, -122, -42, -33, -13; 3432, 288, -1287, -17472, -6018, -4732, -1872],133,32]
%
% END OF LATTICE L134.32
%

\medskip%
%------------------------------WEYL-GROUP-W135--------------------------------
%
\leavevmode\llap{}%
$W_{135}$%
\qquad\llap{32} lattices, $\chi=72$%
\hfill%
$2222222222222222\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L135.1
%
\leavevmode%
${L_{135.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{6}8\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}23\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2\rightarrow N'_{30}}%
\EasyButWeakLineBreak%
{${6}\above{1pt}{1pt}{s}{2}{46}\above{1pt}{1pt}{b}{2}{24}\above{1pt}{1pt}{*}{2}{92}\above{1pt}{1pt}{s}{2}{8}\above{1pt}{1pt}{l}{2}{69}\above{1pt}{1pt}{}{2}{1}\above{1pt}{1pt}{}{2}{184}\above{1pt}{1pt}{r}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-113160\\552\\552
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
552\\5\\-5
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
552\\-5\\-2
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-3312\\-1656
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\-11\\-5
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\24\\11
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-48\\-159
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-46\\-161
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\48\\156
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5\\230\\782
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\44\\156
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
29\\1035\\4416
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\103\\455
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
67\\2208\\10120
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-113160, 552, 552; 552, 5, -5; 552, -5, -2],[552, 1, 1],[-1, -1, 1, 5, 1, 29, 3, 67, 1, 1, -1, -5, -1, -29, -3, -67; -48, -46, 48, 230, 44, 1035, 103, 2208, 24, -46, -96, -322, -52, -1449, -149, -3312; -159, -161, 156, 782, 156, 4416, 455, 10120, 147, 115, -180, -828, -160, -4623, -478, -10672],134,1]
%
% END OF LATTICE L135.1
%
\hbox{}\par\smallskip%
%
% LATTICE L135.2
%
\leavevmode%
${L_{135.2}}$%
{} : {$1\above{1pt}{1pt}{2}{6}8\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}23\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{m}%
\EasyButWeakLineBreak%
{${6}\above{1pt}{1pt}{b}{2}{46}\above{1pt}{1pt}{l}{2}{24}\above{1pt}{1pt}{}{2}{23}\above{1pt}{1pt}{r}{2}{8}\above{1pt}{1pt}{s}{2}{276}\above{1pt}{1pt}{*}{2}{4}\above{1pt}{1pt}{*}{2}{184}\above{1pt}{1pt}{b}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
25944\\-1104\\0
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1104\\47\\0
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\-1
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\1104\\7728
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\-48\\-329
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\7\\48
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\45\\-15
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5\\115\\-23
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\24\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-23\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-24\\-4
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-83\\-2208\\-1794
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-9\\-242\\-212
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-105\\-2852\\-2668
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[25944, -1104, 0; -1104, 47, 0; 0, 0, -1],[552, 1, 1],[2, 5, 1, -1, -1, -83, -9, -105, -2, -5, -1, 1, 1, 83, 9, 105; 45, 115, 24, -23, -24, -2208, -242, -2852, -57, -161, -48, 0, 20, 1794, 196, 2300; -15, -23, 0, 0, -4, -1794, -212, -2668, -69, -299, -168, -161, -24, -1104, -110, -1196],134,2]
%
% END OF LATTICE L135.2
%
%
% LATTICE L135.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-5934, -2898, 552; -2898, -1415, 276; 552, 276, 85],[138, 1, 1],[-3634, -14038, -3535, -5937, -267, -7036, -600, -5597, 34, 238, -65, -963, -333, -55064, -6300, -77203; 7377, 28497, 7176, 12052, 542, 14283, 1218, 11362, -69, -483, 132, 1955, 676, 111780, 12789, 156722; -351, -1357, -342, -575, -26, -690, -59, -552, 3, 23, -6, -92, -32, -5313, -608, -7452],134,3]
%
% END OF LATTICE L135.3
%
%
% LATTICE L135.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[19596, 828, 0; 828, 35, 0; 0, 0, -1],[276, 1, 1],[1, 1, -1, -5, -1, -58, -6, -67, -1, -1, 1, 5, 1, 58, 6, 67; -24, -23, 24, 115, 22, 1035, 103, 1104, 12, -23, -48, -161, -26, -1449, -149, -1656; -3, 0, 0, -23, -10, -2001, -231, -2852, -69, -276, -144, -253, -14, -483, -45, -460],134,4]
%
% END OF LATTICE L135.4
%
%
% LATTICE L135.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[23322, 1380, 11730; 1380, 58, 690; 11730, 690, 5899],[138, 2, 1],[1513, 3353, 164, -68, -33, 26779, 3290, 21353, 2435, 11781, 1810, 7635, 362, 41324, 4277, 24049; 549, 1219, 60, -23, -12, 9660, 1187, 7705, 879, 4255, 654, 2760, 131, 14973, 1550, 8717; -3072, -6808, -333, 138, 67, -54372, -6680, -43355, -4944, -23920, -3675, -15502, -735, -83904, -8684, -48829],134,5]
%
% END OF LATTICE L135.5
%
%
% LATTICE L135.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[42918, 2070, 14352; 2070, 87, 690; 14352, 690, 4799],[138, 3, 1],[328, 2180, 71, -45, -43, 5806, 2140, 27779, 528, 7664, 785, 4967, 471, 8960, 2782, 31285; 183, 1219, 40, -23, -24, 3220, 1187, 15410, 293, 4255, 436, 2760, 262, 4991, 1550, 17434; -1007, -6693, -218, 138, 132, -17825, -6570, -85284, -1621, -23529, -2410, -15249, -1446, -27508, -8541, -96048],134,6]
%
% END OF LATTICE L135.6
%
%
% LATTICE L135.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[51060, -552, -276; -552, 6, 3; -276, 3, 1],[276, 3, 1],[0, -12, -5, -55, -11, -412, -138, -1657, -12, -126, -19, -83, -1, -2, 0, 1; 0, -989, -412, -4531, -906, -33925, -11363, -136436, -988, -10373, -1564, -6831, -82, -161, 1, 92; -1, -345, -140, -1518, -300, -11132, -3726, -44712, -323, -3381, -508, -2208, -24, -46, 0, 0],134,7]
%
% END OF LATTICE L135.7
%
%
% LATTICE L135.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[34593978, 157320, 17145258; 157320, 714, 77970; 17145258, 77970, 8497429],[138, 6, 1],[-2833, -21887, -511, -1368, 284, -18625, -7300, -49618, -2139, -35291, -1975, -27221, -1527, -67142, -21289, -121916; 17, 161, 5, 23, -3, -230, -77, -460, -13, -115, -3, 0, 4, 299, 100, 598; 5716, 44160, 1031, 2760, -573, 37582, 14730, 100119, 4316, 71208, 3985, 54924, 3081, 135470, 42954, 245985],134,8]
%
% END OF LATTICE L135.8
%
%
% LATTICE L135.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[19596, -3312, 4968; -3312, 284, -828; 4968, -828, 1259],[276, 4, 1],[65, -136, -17, 657, 165, 66883, 7725, 23852, 2311, 9244, 1205, 8451, 231, 15089, 1383, 3472; -12, 23, 3, -115, -29, -11799, -1363, -4209, -408, -1633, -213, -1495, -41, -2691, -247, -621; -264, 552, 69, -2668, -670, -271584, -31368, -96853, -9384, -37536, -4893, -34316, -938, -61272, -5616, -14099],134,9]
%
% END OF LATTICE L135.9
%
%
% LATTICE L135.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-619896, 3312, 552; 3312, -3, -9; 552, -9, 2],[552, 3, 1],[16, 167, 25, 54, 1, -1, -1, -11, 0, 17, 7, 38, 15, 553, 185, 2219; 2120, 22126, 3312, 7153, 132, -138, -134, -1472, 0, 2254, 928, 5037, 1988, 73278, 24514, 294032; 5149, 53751, 8048, 17388, 324, -322, -324, -3588, -1, 5451, 2248, 12213, 4824, 177928, 59526, 714012],134,10]
%
% END OF LATTICE L135.10
%
%
% LATTICE L135.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[102120, -552, -552; -552, 3, 3; -552, 3, 2],[552, 3, 1],[-12, -126, -19, -83, -1, -1, 0, 1, 0, -12, -5, -55, -11, -206, -69, -1657; -1976, -20746, -3128, -13662, -164, -161, 1, 184, 0, -1978, -824, -9062, -1812, -33925, -11363, -272872; -323, -3381, -508, -2208, -24, -23, 0, 0, -1, -345, -140, -1518, -300, -5566, -1863, -44712],134,11]
%
% END OF LATTICE L135.11
%
%
% LATTICE L135.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[211278, 0, -37260; 0, -23, 0; -37260, 0, 6571],[138, 23, 1],[1667, 161, 365, -3, -73, 1273, 3598, 2031, 2665, 561, 3967, 364, 795, 1976, 4705, 2301; 51, 5, 12, 0, -2, 39, 110, 62, 81, 17, 120, 11, 24, 60, 143, 70; 9453, 913, 2070, -17, -414, 7218, 20401, 11516, 15111, 3181, 22494, 2064, 4508, 11205, 26680, 13048],134,12]
%
% END OF LATTICE L135.12
%
%
% LATTICE L135.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-36984, 276, -9108; 276, 1092, 72; -9108, 72, -2243],[276, 12, 1],[-67, -7004, -664, -27609, -2627, -188621, -62969, -188491, -5397, -55832, -2068, -35227, -105, 113, 133, -17; -1, -115, -11, -460, -44, -3174, -1060, -3174, -91, -943, -35, -598, -2, 0, 2, 0; 272, 28428, 2695, 112056, 10662, 765532, 255564, 765003, 21904, 226596, 8393, 142968, 426, -460, -540, 69],134,13]
%
% END OF LATTICE L135.13
%
%
% LATTICE L135.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-4200720, -45816, 11040; -45816, -488, 120; 11040, 120, -29],[552, 8, 1],[109, 385, 22, 130, 1, 13, 0, -3, -1, 29, 5, 77, 8, 1850, 207, 1245; 1506, 5336, 306, 1817, 15, 207, 1, -46, -18, 368, 66, 1035, 109, 25461, 2851, 17158; 47592, 168176, 9615, 56856, 442, 5796, 4, -1334, -456, 12512, 2169, 33488, 3486, 807300, 90340, 543398],134,14]
%
% END OF LATTICE L135.14
%
%
% LATTICE L135.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[552, 0, 0; 0, 8, 0; 0, 0, -1],[552, 8, 1],[-35, -119, -13, -36, 0, 1, 0, -1, -1, -19, -5, -33, -3, -622, -69, -206; -273, -943, -105, -299, -1, 0, 1, 0, -3, -115, -33, -230, -22, -4761, -530, -1587; -1128, -3864, -426, -1196, -2, 0, 0, -23, -24, -552, -150, -1012, -94, -19872, -2208, -6601],134,15]
%
% END OF LATTICE L135.15
%
%
% LATTICE L135.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[6108018, 0, 2985630; 0, -46, 0; 2985630, 0, 1459391],[138, 46, 1],[5801, 829, 1855, 131, -371, -4502, -11715, -3082, -6341, -919, -2125, -176, 326, 4097, 10680, 2812; -51, -5, -6, 0, 1, -39, -110, -31, -81, -17, -60, -11, -12, -60, -143, -35; -11868, -1696, -3795, -268, 759, 9210, 23966, 6305, 12972, 1880, 4347, 360, -667, -8382, -21850, -5753],134,16]
%
% END OF LATTICE L135.16
%
%
% LATTICE L135.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[276, 0, 0; 0, -23, -23; 0, -23, -22],[276, 23, 1],[-1, 0, 1, 0, -1, -13, -35, -19, -11, -2, -25, -2, -3, -5, -11, -5; -3, -1, 0, 4, 36, 270, 712, 380, 207, 35, 408, 30, 32, 36, 70, 28; 0, 1, 0, -5, -46, -357, -943, -504, -276, -47, -552, -41, -46, -57, -115, -48],134,17]
%
% END OF LATTICE L135.17
%
%
% LATTICE L135.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2155146, -138, -685308; -138, -69, 0; -685308, 0, 217891],[138, 69, 1],[-914, -392, -585, -62, 351, 711, 5551, 2921, 1002, 436, 673, 84, -307, -645, -5045, -2657; 1811, 779, 1166, 124, -700, -1435, -11212, -5904, -2031, -889, -1386, -179, 590, 1270, 9947, 5244; -2875, -1233, -1840, -195, 1104, 2236, 17457, 9186, 3151, 1371, 2116, 264, -966, -2029, -15870, -8358],134,18]
%
% END OF LATTICE L135.18
%
%
% LATTICE L135.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-6072, 552, 552; 552, -46, -23; 552, -23, 127],[552, 23, 1],[-1, -1, 1, 5, 45, 172, 454, 485, 265, 45, 527, 39, 43, 26, 52, 43; -15, -13, 12, 64, 576, 2199, 5804, 6200, 3387, 575, 6732, 498, 548, 330, 659, 544; 0, 2, 0, -10, -92, -357, -943, -1008, -552, -94, -1104, -82, -92, -57, -115, -96],134,19]
%
% END OF LATTICE L135.19
%
%
% LATTICE L135.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[552, 0, 0; 0, -46, -23; 0, -23, -11],[552, 23, 1],[-1, 0, 1, 0, -1, -13, -35, -19, -11, -2, -25, -1, -3, -5, -11, -5; -3, -1, 0, 2, 36, 270, 712, 380, 207, 35, 408, 15, 32, 36, 70, 28; 0, 2, 0, -5, -92, -714, -1886, -1008, -552, -94, -1104, -41, -92, -114, -230, -96],134,20]
%
% END OF LATTICE L135.20
%
%
% LATTICE L135.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[6060408, 0, -33120; 0, 24, 0; -33120, 0, 181],[552, 24, 1],[341, 3507, 129, 1088, 2, 1, 0, 20, 7, 495, 45, 913, 85, 6002, 2001, 5983; -91, -943, -35, -299, -1, 0, 1, 0, -1, -115, -11, -230, -22, -1587, -530, -1587; 62368, 641424, 23594, 198996, 366, 184, 0, 3657, 1280, 90528, 8230, 166980, 15546, 1097744, 365976, 1094271],134,21]
%
% END OF LATTICE L135.21
%
%
% LATTICE L135.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-10488, 6624, -552; 6624, -3576, 288; -552, 288, -23],[552, 24, 1],[-13, -147, -3, -58, -1, -5, 0, 7, 1, 9, 0, -11, -2, -202, -69, -421; -173, -1909, -38, -713, -10, -46, 1, 69, 9, 23, -3, -230, -31, -2783, -944, -5727; -1912, -20976, -415, -7728, -102, -460, 12, 690, 88, 0, -41, -2760, -354, -31004, -10500, -63618],134,22]
%
% END OF LATTICE L135.22
%
%
% LATTICE L135.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-276, 0, -276; 0, 138, 69; -276, 69, -241],[276, 69, 1],[758, 336, 1125, 203, -1, -2, 0, 23, 22, 54, 435, 187, 781, 1172, 8970, 4657; 357, 158, 528, 95, -2, -1, 1, 12, 11, 26, 208, 89, 370, 553, 4231, 2196; -805, -357, -1196, -216, 0, 2, 0, -24, -23, -57, -460, -198, -828, -1244, -9522, -4944],134,23]
%
% END OF LATTICE L135.23
%
%
% LATTICE L135.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[60137778, 34434588, 16531986; 34434588, 19717026, 9466110; 16531986, 9466110, 4544663],[138, 138, 1],[17, 5, 2, 0, -1, 13, 110, 31, 27, 17, 20, 11, 12, 20, 143, 35; -36955, -10713, -4056, 193, 2420, -28216, -239235, -67519, -59057, -37293, -43950, -24196, -26423, -43793, -312834, -76499; 76912, 22296, 8441, -402, -5037, 58724, 497904, 140523, 122912, 77616, 91471, 50358, 54993, 91144, 651084, 159213],134,24]
%
% END OF LATTICE L135.24
%
%
% LATTICE L135.25
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[276, -276, -276; -276, 2024, 1564; -276, 1564, 1225],[276, 92, 1],[1, 1, 17, 18, 58, 760, 1990, 264, 563, 93, 265, 76, 36, 86, 172, 18; 0, -3, -51, -53, -169, -2193, -5739, -761, -1620, -267, -759, -217, -101, -237, -471, -49; 0, 4, 69, 72, 230, 2988, 7820, 1037, 2208, 364, 1035, 296, 138, 324, 644, 67],134,25]
%
% END OF LATTICE L135.25
%
%
% LATTICE L135.26
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-36412680, 56856, 132480; 56856, -69, -207; 132480, -207, -482],[552, 69, 1],[11, 28, 227, 49, 411, 619, 4739, 2461, 401, 178, 597, 54, 1, -1, -1, 11; 22, 52, 416, 89, 740, 1106, 8462, 4392, 714, 316, 1056, 95, -4, -2, 2, 24; 3013, 7671, 62192, 13425, 112608, 169600, 1298442, 674292, 109871, 48771, 163576, 14796, 276, -274, -276, 3012],134,26]
%
% END OF LATTICE L135.26
%
%
% LATTICE L135.27
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-552, 0, -552; 0, 69, 69; -552, 69, -482],[552, 69, 1],[22, 54, 435, 187, 781, 586, 4485, 4657, 758, 336, 1125, 203, -1, -1, 0, 23; 22, 52, 416, 178, 740, 553, 4231, 4392, 714, 316, 1056, 190, -4, -1, 1, 24; -23, -57, -460, -198, -828, -622, -4761, -4944, -805, -357, -1196, -216, 0, 1, 0, -24],134,27]
%
% END OF LATTICE L135.27
%
%
% LATTICE L135.28
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[9660, 95220, 23736; 95220, 951096, 237084; 23736, 237084, 59099],[276, 276, 1],[-91, -41, -35, -26, -2, 0, 2, 0, -1, -5, -11, -20, -44, -138, -1060, -138; -12626, -5631, -4749, -3467, -103, -1, -69, -83, -298, -831, -1713, -2995, -6359, -19385, -148557, -19303; 50692, 22608, 19067, 13920, 414, 4, 276, 333, 1196, 3336, 6877, 12024, 25530, 77828, 596436, 77499],134,28]
%
% END OF LATTICE L135.28
%
%
% LATTICE L135.29
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-6780216, -2310672, 24840; -2310672, -786968, 8464; 24840, 8464, -91],[552, 184, 1],[-1, 43, 155, 99, 228, 2230, 5727, 1495, 2989, 455, 592, 150, 21, 11, 0, -1; -3, 43, 156, 100, 231, 2265, 5818, 1519, 3039, 463, 603, 153, 22, 12, 1, -1; -552, 15728, 56787, 36304, 83674, 818916, 2103212, 549054, 1097928, 167168, 217557, 55144, 7774, 4116, 92, -366],134,29]
%
% END OF LATTICE L135.29
%
%
% LATTICE L135.30
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-552, 0, -552; 0, 184, 0; -552, 0, -551],[552, 184, 1],[-1, 91, 655, 209, 481, 4702, 12075, 1576, 6301, 959, 2495, 316, 44, 23, 0, -1; -3, -5, -33, -10, -22, -207, -530, -69, -273, -41, -105, -13, -1, 0, 1, 0; 0, -96, -690, -220, -506, -4944, -12696, -1657, -6624, -1008, -2622, -332, -46, -24, 0, 1],134,30]
%
% END OF LATTICE L135.30
%
%
% LATTICE L135.31
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-7212432, -7212984, 20976; -7212984, -7212984, 20976; 20976, 20976, -61],[552, 552, 1],[-1, -5, -11, -10, -22, -69, -530, -69, -91, -41, -35, -13, -1, 0, 1, 0; 16, 38, 76, 65, 135, 403, 3083, 400, 520, 230, 192, 69, -1, -1, -1, 2; 5152, 11328, 22310, 18876, 38778, 114608, 876024, 113577, 147200, 64848, 53866, 19212, -690, -344, 0, 687],134,31]
%
% END OF LATTICE L135.31
%
%
% LATTICE L135.32
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1389936, 2704248, -9936; 2704248, 5256696, -19320; -9936, -19320, 71],[552, 552, 1],[19, 45, 45, 77, 160, 478, 3657, 949, 617, 273, 114, 82, -1, -1, 0, 5; 22, 52, 52, 89, 185, 553, 4231, 1098, 714, 316, 132, 95, -1, -1, 1, 6; 8648, 20448, 20447, 34992, 72726, 217348, 1662900, 431538, 280600, 124176, 51865, 37320, -414, -412, 276, 2334],134,32]
%
% END OF LATTICE L135.32
%

\medskip%
%------------------------------WEYL-GROUP-W136--------------------------------
%
\leavevmode\llap{}%
$W_{136}$%
\qquad\llap{64} lattices, $\chi=18$%
\hfill%
$2222222$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L136.1
%
\leavevmode%
${L_{136.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{6}8\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{2}{}7\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{2\rightarrow N'_{31}}%
\EasyButWeakLineBreak%
{${24}\above{1pt}{1pt}{}{2}{5}\above{1pt}{1pt}{r}{2}{168}\above{1pt}{1pt}{l}{2}{1}\above{1pt}{1pt}{}{2}{280}\above{1pt}{1pt}{r}{2}{6}\above{1pt}{1pt}{b}{2}{70}\above{1pt}{1pt}{l}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
472920\\157080\\-840
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
157080\\52174\\-279
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-840\\-279\\1
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
247\\-744\\-72
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
83\\-250\\-25
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
251\\-756\\-84
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\-1
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-93\\280\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\3\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
244\\-735\\-70
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[472920, 157080, -840; 157080, 52174, -279; -840, -279, 1],[840, 1, 1],[247, 83, 251, 0, -93, -1, 244; -744, -250, -756, 0, 280, 3, -735; -72, -25, -84, -1, 0, 0, -70],135,1]
%
% END OF LATTICE L136.1
%
\hbox{}\par\smallskip%
%
% LATTICE L136.2
%
\leavevmode%
${L_{136.2}}$%
{} : {$1\above{1pt}{1pt}{2}{6}8\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{2}{}7\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{m}%
\EasyButWeakLineBreak%
{${24}\above{1pt}{1pt}{*}{2}{20}\above{1pt}{1pt}{s}{2}{168}\above{1pt}{1pt}{s}{2}{4}\above{1pt}{1pt}{*}{2}{280}\above{1pt}{1pt}{b}{2}{6}\above{1pt}{1pt}{s}{2}{70}\above{1pt}{1pt}{b}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-867720\\288960\\3360
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
288960\\-96226\\-1119
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3360\\-1119\\-13
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-13\\-36\\-264
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-7\\-20\\-90
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\0\\252
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\8\\86
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
51\\140\\1120
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\3\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-13\\-35\\-350
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-867720, 288960, 3360; 288960, -96226, -1119; 3360, -1119, -13],[840, 1, 1],[-13, -7, 1, 3, 51, 1, -13; -36, -20, 0, 8, 140, 3, -35; -264, -90, 252, 86, 1120, 0, -350],135,2]
%
% END OF LATTICE L136.2
%
%
% LATTICE L136.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[9870, -1680, -210; -1680, 286, 35; -210, 35, 17],[210, 1, 1],[1, 12, -115, -50, -1091, -92, -174; 6, 70, -672, -292, -6370, -537, -1015; 0, 5, -42, -19, -420, -36, -70],135,3]
%
% END OF LATTICE L136.3
%
%
% LATTICE L136.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[60060, -20160, -420; -20160, 6767, 141; -420, 141, 2],[420, 1, 1],[-109, -74, -113, 0, 47, 1, -106; -324, -220, -336, 0, 140, 3, -315; -36, -25, -42, -1, 0, 0, -35],135,4]
%
% END OF LATTICE L136.4
%
%
% LATTICE L136.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[170310, 34230, 84840; 34230, 6488, 17046; 84840, 17046, 42263],[210, 2, 1],[-2738, -3719, -2839, 1, 1196, 104, -10642; -81, -110, -84, 0, 35, 3, -315; 5529, 7510, 5733, -2, -2415, -210, 21490],135,5]
%
% END OF LATTICE L136.5
%
%
% LATTICE L136.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[192990, 44100, 64050; 44100, 9732, 14631; 64050, 14631, 21257],[210, 3, 1],[-1207, -2459, -1251, 1, 1587, 23, -7037; -54, -110, -56, 0, 70, 1, -315; 3674, 7485, 3808, -3, -4830, -70, 21420],135,6]
%
% END OF LATTICE L136.6
%
%
% LATTICE L136.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[247170, 63840, -99120; 63840, 16220, -25605; -99120, -25605, 39749],[210, 5, 1],[4433, 602, 4591, -2, -391, -85, 1723; -162, -22, -168, 0, 14, 3, -63; 10950, 1487, 11340, -5, -966, -210, 4256],135,7]
%
% END OF LATTICE L136.7
%
%
% LATTICE L136.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[118020, -840, -420; -840, 6, 3; -420, 3, 1],[420, 3, 1],[-1, -2, -1, 0, 1, 0, -3; -128, -255, -126, 1, 140, 0, -385; -32, -60, -28, 0, 0, -1, -105],135,8]
%
% END OF LATTICE L136.8
%
%
% LATTICE L136.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[6404071380, 1604610, 3183632970; 1604610, 402, 797694; 3183632970, 797694, 1582668007],[210, 6, 1],[259, -701, -957, -695, -261, 521, 9187; 11, 205, 126, 69, 35, -46, -420; -521, 1410, 1925, 1398, 525, -1048, -18480],135,9]
%
% END OF LATTICE L136.9
%
%
% LATTICE L136.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[304710, 83580, -130830; 83580, 22708, -35889; -130830, -35889, 56173],[210, 7, 1],[4715, 3201, 697, -3, -299, -91, 1309; -162, -110, -24, 0, 10, 3, -45; 10878, 7385, 1608, -7, -690, -210, 3020],135,10]
%
% END OF LATTICE L136.10
%
%
% LATTICE L136.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[10266060, 74340, 2567040; 74340, 536, 18588; 2567040, 18588, 641891],[420, 4, 1],[-32, -322, -572, -102, -26, 101, 277; -36, -425, -777, -141, -35, 141, 420; 129, 1300, 2310, 412, 105, -408, -1120],135,11]
%
% END OF LATTICE L136.11
%
%
% LATTICE L136.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[50609580, 184170, 24039330; 184170, 670, 87480; 24039330, 87480, 11418577],[210, 10, 1],[64, -41, -550, -119, -10, 257, 253; 33, 41, 378, 69, 7, -138, -84; -135, 86, 1155, 250, 21, -540, -532],135,12]
%
% END OF LATTICE L136.12
%
%
% LATTICE L136.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[345660, 113400, -840; 113400, 37195, -275; -840, -275, 2],[420, 5, 1],[7, 0, -25, -6, -17, -1, 2; -24, 0, 84, 20, 56, 3, -7; -360, -1, 1050, 235, 588, 0, -119],135,13]
%
% END OF LATTICE L136.13
%
%
% LATTICE L136.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1294440, 645120, -1680; 645120, 321513, -837; -1680, -837, 2],[840, 3, 1],[127, 253, 125, -1, -139, 0, 382; -256, -510, -252, 2, 280, 0, -770; -452, -900, -448, 0, 420, -1, -1365],135,14]
%
% END OF LATTICE L136.14
%
%
% LATTICE L136.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-26040, 6720, 840; 6720, -1734, -213; 840, -213, 47],[840, 3, 1],[39, 68, 115, 9, -143, -10, 9; 152, 265, 448, 35, -560, -39, 35; -8, -15, -28, -3, 0, 2, 0],135,15]
%
% END OF LATTICE L136.15
%
%
% LATTICE L136.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[17657220, 128730, 8197770; 128730, 938, 59766; 8197770, 59766, 3806003],[210, 14, 1],[29, -229, -77, -111, -7, 235, 149; 33, 205, 54, 69, 5, -138, -60; -63, 490, 165, 238, 15, -504, -320],135,16]
%
% END OF LATTICE L136.16
%
%
% LATTICE L136.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[92820, 18060, -1260; 18060, 3514, -245; -1260, -245, 17],[420, 7, 1],[-7, -1, 1, 1, -1, -2, -2; 36, 5, -6, -7, 0, 9, 10; 0, 0, -12, -28, -80, -21, -5],135,17]
%
% END OF LATTICE L136.17
%
%
% LATTICE L136.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[42736470, -207270, 15194970; -207270, 1005, -73695; 15194970, -73695, 5402578],[210, 15, 1],[-39, 29, 275, 91, 15, -66, -202; 22, 41, 252, 69, 14, -46, -84; 110, -81, -770, -255, -42, 185, 567],135,18]
%
% END OF LATTICE L136.18
%
%
% LATTICE L136.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[691320, 226800, -840; 226800, 74390, -275; -840, -275, 1],[840, 5, 1],[7, 0, -25, -3, -17, -1, 2; -24, 0, 84, 10, 56, 3, -7; -720, -1, 2100, 235, 1176, 0, -238],135,19]
%
% END OF LATTICE L136.19
%
%
% LATTICE L136.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3491880, -1165920, 10080; -1165920, -389290, 3365; 10080, 3365, -29],[840, 5, 1],[19, -5, -211, -39, -97, -1, 11; -60, 16, 672, 124, 308, 3, -35; -360, 118, 4620, 830, 2016, 0, -238],135,20]
%
% END OF LATTICE L136.20
%
%
% LATTICE L136.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[59663730, -289800, 20834730; -289800, 1407, -101199; 20834730, -101199, 7275542],[210, 21, 1],[-39, 331, 77, 169, 21, -120, -236; 22, 205, 36, 69, 10, -46, -60; 112, -945, -220, -483, -60, 343, 675],135,21]
%
% END OF LATTICE L136.21
%
%
% LATTICE L136.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-86520, 420, -21420; 420, 1668, 108; -21420, 108, -5303],[420, 12, 1],[-183, -847, 45, 205, -26, -103, -3328; -2, -10, 0, 2, 0, -1, -35; 739, 3420, -182, -828, 105, 416, 13440],135,22]
%
% END OF LATTICE L136.22
%
%
% LATTICE L136.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[12221160, -315840, -840; -315840, 8162, 21; -840, 21, -1],[840, 7, 1],[13, -4, -13, -9, -33, -1, 4; 504, -155, -504, -349, -1280, -39, 155; -336, 105, 324, 217, 760, 0, -110],135,23]
%
% END OF LATTICE L136.23
%
%
% LATTICE L136.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[8300040, 826560, -16800; 826560, 82313, -1673; -16800, -1673, 34],[840, 7, 1],[-7, -1, 1, 1, -1, -2, -2; 72, 10, -12, -14, 0, 18, 20; 84, 0, -96, -196, -500, -105, -5],135,24]
%
% END OF LATTICE L136.24
%
%
% LATTICE L136.25
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1912260, 333900, 22680; 333900, 58305, 3960; 22680, 3960, 269],[420, 15, 1],[27, 10, 23, 0, 1, 1, 18; -84, -31, -70, 1, 0, -3, -56; -1040, -387, -910, -15, -84, -40, -693],135,25]
%
% END OF LATTICE L136.25
%
%
% LATTICE L136.26
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[219942030, 4668930, 109359810; 4668930, 97320, 2321490; 109359810, 2321490, 54376001],[210, 30, 1],[-69946, -56993, -72447, 179, 18492, 2680, -163118; -27, -22, -28, 0, 7, 1, -63; 140675, 114624, 145705, -360, -37191, -5390, 328062],135,26]
%
% END OF LATTICE L136.26
%
%
% LATTICE L136.27
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-855960, -3360, 5040; -3360, 8, 16; 5040, 16, -29],[840, 8, 1],[-1, -1, 2, 1, 2, -1, -13; -36, -40, 63, 34, 70, -33, -455; -195, -200, 378, 192, 385, -192, -2520],135,27]
%
% END OF LATTICE L136.27
%
%
% LATTICE L136.28
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[328440, -110880, -21840; -110880, 37432, 7376; -21840, 7376, 1439],[840, 8, 1],[-433, -584, -452, -6, 111, 1, -1717; -1227, -1655, -1281, -17, 315, 3, -4865; -282, -380, -294, -4, 70, 0, -1120],135,28]
%
% END OF LATTICE L136.28
%
%
% LATTICE L136.29
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[541247070, -1126860, -214289880; -1126860, 2345, 446145; -214289880, 446145, 84841388],[210, 35, 1],[499, -302, -1045, -762, -19, 1621, 211; 66, 41, 108, 69, 2, -138, -12; 1260, -763, -2640, -1925, -48, 4095, 533],135,29]
%
% END OF LATTICE L136.29
%
%
% LATTICE L136.30
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[67755660, -216300, 16790340; -216300, 680, -53600; 16790340, -53600, 4160767],[420, 20, 1],[-26, -206, -260, 822, 1208, 1337, 617; 6, 55, 63, -225, -329, -363, -168; 105, 832, 1050, -3320, -4879, -5400, -2492],135,30]
%
% END OF LATTICE L136.30
%
%
% LATTICE L136.31
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1719060, -4620, 8400; -4620, 42, 21; 8400, 21, -41],[420, 21, 1],[5, -2, -1, 0, 13, 3, 6; 28, -15, -6, 1, 80, 18, 35; 1036, -420, -208, 0, 2700, 623, 1245],135,31]
%
% END OF LATTICE L136.31
%
%
% LATTICE L136.32
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[536961390, 8597610, 266976360; 8597610, 136248, 4274718; 266976360, 4274718, 132740227],[210, 42, 1],[-96556, -393317, -14275, 355, 18354, 3724, -160838; -27, -110, -4, 0, 5, 1, -45; 194201, 791070, 28711, -714, -36915, -7490, 323490],135,32]
%
% END OF LATTICE L136.32
%
%
% LATTICE L136.33
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[333480, -21420, 83160; -21420, 644, -5320; 83160, -5320, 20737],[420, 28, 1],[-26, 589, 49, -395, -469, -790, -297; 3, -70, -6, 46, 55, 93, 35; 105, -2380, -198, 1596, 1895, 3192, 1200],135,33]
%
% END OF LATTICE L136.33
%
%
% LATTICE L136.34
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[262920, 129360, -42000; 129360, 63645, -20655; -42000, -20655, 6658],[840, 15, 1],[1407, 553, 1357, -1, -207, 12, 866; -3048, -1198, -2940, 2, 448, -26, -1876; -580, -228, -560, 0, 84, -5, -357],135,34]
%
% END OF LATTICE L136.34
%
%
% LATTICE L136.35
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-654360, -166320, -3360; -166320, -42270, -855; -3360, -855, -17],[840, 15, 1],[-11, -3, -15, 2, 31, 3, -2; 40, 11, 56, -7, -112, -11, 7; 160, 39, 140, -45, -504, -40, 42],135,35]
%
% END OF LATTICE L136.35
%
%
% LATTICE L136.36
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[76682130, 4193490, 36588090; 4193490, 227080, 2000880; 36588090, 2000880, 17457631],[210, 70, 1],[-132409, -35957, -19574, 167, 1679, 5110, -14704; -81, -22, -12, 0, 1, 3, -9; 277515, 75362, 41025, -350, -3519, -10710, 30818],135,36]
%
% END OF LATTICE L136.36
%
%
% LATTICE L136.37
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[171780, 420, -420; 420, -35, 0; -420, 0, 1],[420, 35, 1],[1, 0, -1, -2, -1, -1, 0; 12, 1, -6, -15, -8, -9, 0; 420, 7, -390, -805, -408, -420, -1],135,37]
%
% END OF LATTICE L136.37
%
%
% LATTICE L136.38
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3438120, -1723680, 16800; -1723680, -864129, 8421; 16800, 8421, -82],[840, 21, 1],[-23, 13, 5, -1, -67, -15, -29; 56, -30, -12, 2, 160, 36, 70; 1036, -420, -208, 0, 2700, 623, 1245],135,38]
%
% END OF LATTICE L136.38
%
%
% LATTICE L136.39
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-40616520, 0, 64680; 0, 21, 0; 64680, 0, -103],[840, 21, 1],[5, -1, -1, 0, 13, 3, 6; -8, -5, 0, 1, 0, -1, -5; 3136, -630, -628, 0, 8160, 1883, 3765],135,39]
%
% END OF LATTICE L136.39
%
%
% LATTICE L136.40
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1680, -840, 0; -840, -4488, 336; 0, 336, -23],[840, 24, 1],[1, 13, 4, -1, -16, -3, -1; 2, 25, 7, -3, -35, -6, 0; 29, 360, 98, -48, -525, -88, 0],135,40]
%
% END OF LATTICE L136.40
%
%
% LATTICE L136.41
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1680, -7560, -3360; -7560, 33576, 14928; -3360, 14928, 6637],[840, 24, 1],[1, 7, 3, 1, -3, -1, 1; -6, -25, 7, 27, 280, 14, 0; 14, 60, -14, -60, -630, -32, 0],135,41]
%
% END OF LATTICE L136.41
%
%
% LATTICE L136.42
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[57903510, 4456830, -17573850; 4456830, 340620, -1354395; -17573850, -1354395, 5332459],[210, 105, 1],[-59859, -24383, -8849, 113, 2277, 1155, -9971; 119664, 48744, 17690, -226, -4552, -2309, 19933; -166880, -67977, -24670, 315, 6348, 3220, -27798],135,42]
%
% END OF LATTICE L136.42
%
%
% LATTICE L136.43
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-42389340, 327600, -10504620; 327600, -2220, 81180; -10504620, 81180, -2603179],[420, 60, 1],[244, 1415, 3867, 1635, -463, -872, -1311; -12, -65, -175, -73, 21, 39, 56; -985, -5712, -15610, -6600, 1869, 3520, 5292],135,43]
%
% END OF LATTICE L136.43
%
%
% LATTICE L136.44
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[840, 0, -840; 0, -70, -245; -840, -245, -17],[840, 35, 1],[7, -6, -55, -33, -23, -1, 2; -24, 21, 192, 115, 80, 3, -7; 0, -7, -60, -35, -24, 0, 2],135,44]
%
% END OF LATTICE L136.44
%
%
% LATTICE L136.45
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-9240, -4200, 0; -4200, -1295, -35; 0, -35, 2],[840, 35, 1],[-11, -1, 5, 13, 7, 8, 0; 24, 2, -12, -30, -16, -18, 0; 420, 42, -180, -490, -268, -315, -1],135,45]
%
% END OF LATTICE L136.45
%
%
% LATTICE L136.46
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-28560, 10920, -840; 10920, -3320, 240; -840, 240, -17],[840, 40, 1],[-1, 0, 5, 2, 1, -1, -3; -15, -1, 63, 27, 14, -12, -42; -165, -16, 630, 280, 147, -120, -448],135,46]
%
% END OF LATTICE L136.46
%
%
% LATTICE L136.47
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-68880, -840, 0; -840, 920, 200; 0, 200, 43],[840, 40, 1],[-1, 0, 4, 2, 3, 1, -1; 84, 1, -315, -159, -238, -78, 84; -390, -4, 1470, 740, 1106, 360, -392],135,47]
%
% END OF LATTICE L136.47
%
%
% LATTICE L136.48
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[449904840, -2655660, 111384000; -2655660, 15708, -657468; 111384000, -657468, 27575599],[420, 84, 1],[1350, 4991, 51, 1123, 2269, 1733, 4382; -2, -10, 0, 2, 0, -1, -5; -5453, -20160, -206, -4536, -9165, -7000, -17700],135,48]
%
% END OF LATTICE L136.48
%
%
% LATTICE L136.49
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[93660, -4620, -2100; -4620, 210, 105; -2100, 105, 47],[420, 105, 1],[-3, -2, -1, 0, 1, 1, 0; 0, -3, -2, 1, 4, 4, 1; -140, -84, -40, 0, 36, 35, -3],135,49]
%
% END OF LATTICE L136.49
%
%
% LATTICE L136.50
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[72110791410, 28419879390, 13731070500; 28419879390, 11200675080, 5411608440; 13731070500, 5411608440, 2614619717],[210, 210, 1],[11, 41, 18, 69, 1, -46, -12; -11, -8363, -4237, -17525, -233, 12123, 4115; -35, 17094, 8675, 35910, 477, -24850, -8454],135,50]
%
% END OF LATTICE L136.50
%
%
% LATTICE L136.51
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-14280, 5040, -840; 5040, -1736, 280; -840, 280, -43],[840, 56, 1],[-1, 3, 2, 5, 2, -1, -3; -6, 10, 9, 24, 10, -3, -15; -21, 0, 18, 56, 25, 0, -40],135,51]
%
% END OF LATTICE L136.51
%
%
% LATTICE L136.52
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[333480, -107520, -51240; -107520, 34664, 16520; -51240, 16520, 7873],[840, 56, 1],[-1, 1, 1, 3, 3, 1, -1; 57, 70, 6, -4, -5, 3, 35; -126, -140, -6, 28, 30, 0, -80],135,52]
%
% END OF LATTICE L136.52
%
%
% LATTICE L136.53
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[19277160, 179340, -4639740; 179340, 1540, -43260; -4639740, -43260, 1116649],[420, 140, 1],[26, -617, -1285, -2877, -231, 208, 103; -78, 1850, 3852, 8622, 692, -627, -309; 105, -2492, -5190, -11620, -933, 840, 416],135,53]
%
% END OF LATTICE L136.53
%
%
% LATTICE L136.54
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[187320, 89040, -4200; 89040, 42315, -1995; -4200, -1995, 94],[840, 105, 1],[-3, 1, 1, -1, -3, -3, -1; 0, -6, -4, 2, 8, 8, 2; -140, -84, -40, 0, 36, 35, -3],135,54]
%
% END OF LATTICE L136.54
%
%
% LATTICE L136.55
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2309160, 0, 5040; 0, 105, 0; 5040, 0, -11],[840, 105, 1],[-3, -1, -1, 0, 1, 1, 0; -8, -1, 0, 1, 0, -1, -1; -1400, -462, -460, 0, 456, 455, -3],135,55]
%
% END OF LATTICE L136.55
%
%
% LATTICE L136.56
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-959280, -24360, -7560; -24360, 2040, 840; -7560, 840, 341],[840, 120, 1],[1, 3, 6, 1, -2, -3, -1; -196, -587, -1169, -187, 399, 590, 196; 505, 1512, 3010, 480, -1029, -1520, -504],135,56]
%
% END OF LATTICE L136.56
%
%
% LATTICE L136.57
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2709840, 506520, 247800; 506520, 94440, 46200; 247800, 46200, 22601],[840, 120, 1],[1, 1, 1, -1, -3, -1, 1; -294, -293, -245, 387, 1064, 338, -252; 590, 588, 490, -780, -2142, -680, 504],135,57]
%
% END OF LATTICE L136.57
%
%
% LATTICE L136.58
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-840, 69720, -840; 69720, -5497296, 66192; -840, 66192, -797],[840, 168, 1],[8, 3, -1, -1, 14, 14, 32; 5, -5, -1, 1, 15, 13, 25; 406, -420, -82, 84, 1230, 1064, 2040],135,58]
%
% END OF LATTICE L136.58
%
%
% LATTICE L136.59
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-36515640, -7162680, 87360; -7162680, -1404816, 17136; 87360, 17136, -209],[840, 168, 1],[4, 3, -1, -1, 7, 14, 32; -1, -5, 0, 1, 0, -1, -5; 1589, 840, -418, -336, 2925, 5768, 12960],135,59]
%
% END OF LATTICE L136.59
%
%
% LATTICE L136.60
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[7980, -118860, -29400; -118860, 1341480, 331800; -29400, 331800, 82067],[420, 420, 1],[-2, -2, 0, 2, 0, -1, -1; -736, -665, 47, 1039, 23, -381, -380; 2975, 2688, -190, -4200, -93, 1540, 1536],135,60]
%
% END OF LATTICE L136.60
%
%
% LATTICE L136.61
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1680, -88200, -43680; -88200, 3160360, 1565200; -43680, 1565200, 775181],[840, 280, 1],[-1, 3, 7, 17, 3, 1, -1; 312, -513, -1233, -2981, -514, 0, 206; -630, 1036, 2490, 6020, 1038, 0, -416],135,61]
%
% END OF LATTICE L136.61
%
%
% LATTICE L136.62
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1039080, -115080, -44520; -115080, -9520, -3640; -44520, -3640, -1391],[840, 280, 1],[2, -1, -1, 3, 1, 20, 2; -546, 269, 276, -785, -267, -5379, -541; 1365, -672, -690, 1960, 667, 13440, 1352],135,62]
%
% END OF LATTICE L136.62
%
%
% LATTICE L136.63
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2306640, -2307480, 9240; -2307480, -2307480, 9240; 9240, 9240, -37],[840, 840, 1],[-1, -1, 0, 1, 0, -1, -1; 2, -1, -1, -1, 1, 10, 4; 245, -504, -250, 0, 249, 2240, 744],135,63]
%
% END OF LATTICE L136.63
%
%
% LATTICE L136.64
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[26481840, 11980920, -35280; 11980920, 5418840, -15960; -35280, -15960, 47],[840, 840, 1],[5, -1, -1, 1, 3, 13, 5; 4, -1, -1, -1, 2, 10, 4; 5110, -1092, -1090, 420, 2934, 13160, 5112],135,64]
%
% END OF LATTICE L136.64
%

\medskip%
%------------------------------WEYL-GROUP-W137--------------------------------
%
\leavevmode\llap{}%
$W_{137}$%
\qquad\llap{64} lattices, $\chi=72$%
\hfill%
$2222222222222222\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L137.1
%
\leavevmode%
${L_{137.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{6}8\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{2}{}5\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}7\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2\rightarrow N'_{35}}%
\EasyButWeakLineBreak%
{${6}\above{1pt}{1pt}{s}{2}{14}\above{1pt}{1pt}{l}{2}{24}\above{1pt}{1pt}{}{2}{1}\above{1pt}{1pt}{r}{2}{40}\above{1pt}{1pt}{s}{2}{28}\above{1pt}{1pt}{*}{2}{60}\above{1pt}{1pt}{*}{2}{56}\above{1pt}{1pt}{b}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
8617560\\-9240\\-10920
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-9240\\13\\11
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-10920\\11\\14
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
41999\\6384000\\27783000
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-50\\-7601\\-33075
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-52\\-7904\\-34399
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-150\\-663
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-5\\-756\\-3311
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-19\\-2880\\-12576
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-4\\-607\\-2647
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-37\\-5620\\-24480
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-83\\-12614\\-54908
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-179\\-27210\\-118410
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-221\\-33600\\-146188
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[8617560, -9240, -10920; -9240, 13, 11; -10920, 11, 14],[840, 1, 1],[-1, -5, -19, -4, -37, -83, -179, -221, -23, -23, -29, -2, -3, -1, -1, -3; -150, -756, -2880, -607, -5620, -12614, -27210, -33600, -3498, -3500, -4416, -305, -460, -154, -150, -448; -663, -3311, -12576, -2647, -24480, -54908, -118410, -146188, -15213, -15211, -19176, -1322, -1980, -658, -660, -1988],136,1]
%
% END OF LATTICE L137.1
%
\hbox{}\par\smallskip%
%
% LATTICE L137.2
%
\leavevmode%
${L_{137.2}}$%
{} : {$1\above{1pt}{1pt}{2}{6}8\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{2}{}5\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}7\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{m}%
\EasyButWeakLineBreak%
{${6}\above{1pt}{1pt}{b}{2}{14}\above{1pt}{1pt}{b}{2}{24}\above{1pt}{1pt}{*}{2}{4}\above{1pt}{1pt}{s}{2}{40}\above{1pt}{1pt}{l}{2}{7}\above{1pt}{1pt}{}{2}{15}\above{1pt}{1pt}{}{2}{56}\above{1pt}{1pt}{r}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
152066040\\533400\\-47040
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
533400\\1871\\-165
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-47040\\-165\\14
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-655201\\186950400\\2074800
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2298\\655695\\7277
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
156\\-44512\\-495
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2\\570\\-3
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5\\-1428\\-35
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
37\\-10560\\-156
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
19\\-5422\\-70
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
101\\-28820\\-340
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
122\\-34811\\-392
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
271\\-77325\\-855
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
683\\-194880\\-2128
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[152066040, 533400, -47040; 533400, 1871, -165; -47040, -165, 14],[840, 1, 1],[-2, 5, 37, 19, 101, 122, 271, 683, 74, 79, 107, 17, 19, 4, -1, -11; 570, -1428, -10560, -5422, -28820, -34811, -77325, -194880, -21114, -22540, -30528, -4850, -5420, -1141, 285, 3136; -3, -35, -156, -70, -340, -392, -855, -2128, -225, -231, -300, -44, -40, -7, 0, 0],136,2]
%
% END OF LATTICE L137.2
%
%
% LATTICE L137.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[6090, 630, 630; 630, 65, 63; 630, 63, 38],[210, 1, 1],[4, 8, -13, -12, -87, -243, -569, -743, -172, -204, -155, -30, -53, -51, -61, -41; -42, -84, 138, 127, 920, 2569, 6015, 7854, 1818, 2156, 1638, 317, 560, 539, 645, 434; 3, 7, -12, -11, -80, -224, -525, -686, -159, -189, -144, -28, -50, -49, -60, -42],136,3]
%
% END OF LATTICE L137.3
%
%
% LATTICE L137.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[76033020, 533400, -23520; 533400, 3742, -165; -23520, -165, 7],[420, 1, 1],[74, 79, 107, 17, 19, 8, -2, -11, -2, 5, 37, 19, 101, 244, 542, 683; -10557, -11270, -15264, -2425, -2710, -1141, 285, 1568, 285, -714, -5280, -2711, -14410, -34811, -77325, -97440; -225, -231, -300, -44, -40, -14, 0, 0, -3, -35, -156, -70, -340, -784, -1710, -2128],136,4]
%
% END OF LATTICE L137.4
%
%
% LATTICE L137.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-206430, 14490, -102480; 14490, -548, 7186; -102480, 7186, -50875],[210, 2, 1],[850, -208, -1217, -1377, -3762, -18231, -40493, -25495, -11026, -11664, -3871, -1167, -478, 423, 2333, 1751; -27, 7, 39, 44, 120, 581, 1290, 812, 351, 371, 123, 37, 15, -14, -75, -56; -1716, 420, 2457, 2780, 7595, 36806, 81750, 51471, 22260, 23548, 7815, 2356, 965, -854, -4710, -3535],136,5]
%
% END OF LATTICE L137.5
%
%
% LATTICE L137.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-173670, 15540, -57330; 15540, -822, 5121; -57330, 5121, -18925],[210, 3, 1],[190, -138, -543, -922, -5039, -12211, -9041, -34155, -2462, -7814, -1729, -782, -641, 283, 521, 2347; -9, 7, 26, 44, 240, 581, 430, 1624, 117, 371, 82, 37, 30, -14, -25, -112; -578, 420, 1652, 2805, 15330, 37149, 27505, 103908, 7490, 23772, 5260, 2379, 1950, -861, -1585, -7140],136,6]
%
% END OF LATTICE L137.6
%
%
% LATTICE L137.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-152250, 17640, 61320; 17640, -1370, -7115; 61320, -7115, -24697],[210, 5, 1],[-716, 170, 2039, 1155, 1263, 15306, 6800, 42817, 9260, 9798, 6505, 981, 161, -354, -392, -2945; -27, 7, 78, 44, 48, 581, 258, 1624, 351, 371, 246, 37, 6, -14, -15, -112; -1770, 420, 5040, 2855, 3122, 37835, 16809, 105840, 22890, 24220, 16080, 2425, 398, -875, -969, -7280],136,7]
%
% END OF LATTICE L137.7
%
%
% LATTICE L137.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[166740, 66780, -420; 66780, 26745, -168; -420, -168, 1],[420, 3, 1],[0, 19, 31, 43, 213, 496, 362, 1355, 48, 149, 65, 29, 27, 8, -2, -11; 0, -49, -80, -111, -550, -1281, -935, -3500, -124, -385, -168, -75, -70, -21, 5, 28; -1, -252, -412, -573, -2850, -6657, -4865, -18228, -647, -2016, -884, -399, -390, -147, 5, 84],136,8]
%
% END OF LATTICE L137.8
%
%
% LATTICE L137.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[9492992040, -2559270, 4719221850; -2559270, 690, -1272282; 4719221850, -1272282, 2346052201],[210, 6, 1],[347, 2777, 954, 2601, 6674, 32238, 23917, 45319, 6585, 21485, 2512, 2598, 1991, 4155, 2078, 3205; 20, 182, 50, 119, 265, 1169, 835, 1540, 212, 630, 66, 55, 25, 49, 35, 84; -698, -5586, -1919, -5232, -13425, -64848, -48110, -91161, -13246, -43218, -5053, -5226, -4005, -8358, -4180, -6447],136,9]
%
% END OF LATTICE L137.9
%
%
% LATTICE L137.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-147630, 19740, 63630; 19740, -1918, -8519; 63630, -8519, -27425],[210, 7, 1],[-782, 26, 2219, 1258, 6881, 2383, 37057, 6667, 10094, 1526, 7093, 1070, 879, -55, -2137, -459; -27, 1, 78, 44, 240, 83, 1290, 232, 351, 53, 246, 37, 30, -2, -75, -16; -1806, 60, 5124, 2905, 15890, 5503, 85575, 15396, 23310, 3524, 16380, 2471, 2030, -127, -4935, -1060],136,10]
%
% END OF LATTICE L137.10
%
%
% LATTICE L137.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2349480, -707700, 586740; -707700, 199612, -176640; 586740, -176640, 146527],[420, 4, 1],[-156266, -154293, -47717, -25041, -6703, 3945, 11633, -494, -5818, -34805, -33325, -56001, -128367, -571239, -1227263, -377702; 4431, 4375, 1353, 710, 190, -112, -330, 14, 165, 987, 945, 1588, 3640, 16198, 34800, 10710; 631080, 623112, 192705, 101128, 27070, -15932, -46980, 1995, 23496, 140560, 134583, 226160, 518410, 2306948, 4956300, 1525349],136,11]
%
% END OF LATTICE L137.11
%
%
% LATTICE L137.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[78532440, -300510, 37307550; -300510, 1150, -142760; 37307550, -142760, 17723291],[210, 10, 1],[157, 433, 421, 371, 185, 4394, 1943, 6108, 2639, 2829, 977, 328, 48, 499, 154, 416; 60, 182, 150, 119, 53, 1169, 501, 1540, 636, 630, 198, 55, 5, 49, 21, 84; -330, -910, -885, -780, -389, -9240, -4086, -12845, -5550, -5950, -2055, -690, -101, -1050, -324, -875],136,12]
%
% END OF LATTICE L137.12
%
%
% LATTICE L137.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-8494500, 215460, -29400; 215460, -5465, 745; -29400, 745, -94],[420, 5, 1],[16, -10, -113, -60, -63, -747, -329, -2059, -220, -228, -295, -42, -5, 33, 23, 155; 639, -399, -4512, -2396, -2516, -29834, -13140, -82236, -8787, -9107, -11784, -1678, -200, 1316, 918, 6188; 60, -35, -420, -225, -238, -2835, -1251, -7840, -840, -875, -1140, -165, -22, 105, 81, 560],136,13]
%
% END OF LATTICE L137.13
%
%
% LATTICE L137.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-207480, 0, 840; 0, 15, -9; 840, -9, 2],[840, 3, 1],[0, 2, 3, 2, 19, 43, 31, 115, 4, 12, 5, 1, 1, -1, -1, -3; 0, 294, 440, 293, 2780, 6286, 4530, 16800, 584, 1750, 728, 145, 140, -154, -150, -448; -1, 483, 728, 486, 4620, 10458, 7540, 27972, 973, 2919, 1216, 243, 240, -252, -250, -756],136,14]
%
% END OF LATTICE L137.14
%
%
% LATTICE L137.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[333480, 68040, -840; 68040, 13881, -171; -840, -171, 2],[840, 3, 1],[0, 19, 31, 43, 213, 248, 181, 1355, 48, 149, 65, 29, 27, 4, -1, -11; 0, -98, -160, -222, -1100, -1281, -935, -7000, -248, -770, -336, -150, -140, -21, 5, 56; -1, -399, -652, -906, -4500, -5250, -3835, -28728, -1019, -3171, -1388, -624, -600, -105, 10, 168],136,15]
%
% END OF LATTICE L137.15
%
%
% LATTICE L137.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[47460, 2940, 1260; 2940, 182, 77; 1260, 77, 25],[420, 7, 1],[-8, -4, -89, -34, -143, -43, -631, -109, -76, -10, -79, -8, 3, 1, 1, -3; 138, 69, 1536, 587, 2470, 743, 10905, 1884, 1314, 173, 1368, 139, -50, -17, -15, 52; -21, -11, -252, -98, -420, -128, -1890, -328, -231, -31, -252, -28, 0, 2, 0, -8],136,16]
%
% END OF LATTICE L137.16
%
%
% LATTICE L137.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[28668360, -214830, 13315050; -214830, 1610, -99778; 13315050, -99778, 6184189],[210, 14, 1],[137, 55, 362, 313, 766, 514, 7919, 709, 2131, 323, 772, 254, 179, 53, 586, 47; 60, 26, 150, 119, 265, 167, 2505, 220, 636, 90, 198, 55, 25, 7, 105, 12; -294, -118, -777, -672, -1645, -1104, -17010, -1523, -4578, -694, -1659, -546, -385, -114, -1260, -101],136,17]
%
% END OF LATTICE L137.17
%
%
% LATTICE L137.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[65532810, 336210, 23305170; 336210, 1725, 119565; 23305170, 119565, 8287924],[210, 15, 1],[-41, -337, -221, -294, -295, -3516, -519, -9799, -707, -2281, -527, -267, -79, -411, -42, -673; 20, 182, 100, 119, 106, 1169, 167, 3080, 212, 630, 132, 55, 10, 49, 7, 168; 115, 945, 620, 825, 828, 9870, 1457, 27510, 1985, 6405, 1480, 750, 222, 1155, 118, 1890],136,18]
%
% END OF LATTICE L137.18
%
%
% LATTICE L137.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-136840200, -1748040, -189840; -1748040, -22330, -2425; -189840, -2425, -263],[840, 5, 1],[-7, -5, 41, 15, 39, 519, 239, 1543, 175, 201, 295, 27, 17, 69, 13, 25; 561, 399, -3288, -1202, -3124, -41566, -19140, -123564, -14013, -16093, -23616, -2161, -1360, -5516, -1038, -1988; -120, -70, 720, 255, 652, 8610, 3954, 25480, 2880, 3290, 4800, 435, 268, 1050, 186, 280],136,19]
%
% END OF LATTICE L137.19
%
%
% LATTICE L137.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-729960, 190680, 7560; 190680, -49805, -1970; 7560, -1970, -73],[840, 5, 1],[-37, 30, 281, 145, 149, 872, 382, 4763, 505, 516, 655, 89, 7, -53, -31, -395; -147, 119, 1116, 576, 592, 3465, 1518, 18928, 2007, 2051, 2604, 354, 28, -210, -123, -1568; 135, -105, -1020, -530, -548, -3220, -1413, -17640, -1875, -1925, -2460, -340, -32, 175, 108, 1400],136,20]
%
% END OF LATTICE L137.20
%
%
% LATTICE L137.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[95268390, 479640, 33273030; 479640, 2415, 167517; 33273030, 167517, 11620796],[210, 21, 1],[-71, -85, -377, -492, -2423, -816, -4197, -2257, -1133, -517, -827, -411, -587, -87, -318, -151; 20, 26, 100, 119, 530, 167, 835, 440, 212, 90, 132, 55, 50, 7, 35, 24; 203, 243, 1078, 1407, 6930, 2334, 12005, 6456, 3241, 1479, 2366, 1176, 1680, 249, 910, 432],136,21]
%
% END OF LATTICE L137.21
%
%
% LATTICE L137.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[8457540, -50400, 2100840; -50400, 276, -12516; 2100840, -12516, 521845],[420, 12, 1],[-103, -416, 24, 505, 1983, 11209, 8769, 8594, 1327, 4700, 588, 1331, 1077, 1643, 411, -26; 56, 217, -17, -297, -1135, -6363, -4965, -4858, -748, -2639, -329, -741, -595, -903, -225, 14; 416, 1680, -97, -2040, -8010, -45276, -35420, -34713, -5360, -18984, -2375, -5376, -4350, -6636, -1660, 105],136,22]
%
% END OF LATTICE L137.22
%
%
% LATTICE L137.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[11031720, -35280, -23520; -35280, 91, 77; -23520, 77, 50],[840, 7, 1],[8, 4, 89, 17, 143, 43, 631, 109, 76, 10, 79, 4, -3, -1, -1, 3; 276, 138, 3072, 587, 4940, 1486, 21810, 3768, 2628, 346, 2736, 139, -100, -34, -30, 104; 3339, 1669, 37128, 7091, 59640, 17932, 263130, 45452, 31689, 4169, 32928, 1666, -1260, -418, -420, 1252],136,23]
%
% END OF LATTICE L137.23
%
%
% LATTICE L137.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[316680, -28560, -840; -28560, 2569, 77; -840, 77, 2],[840, 7, 1],[-7, 0, 5, 1, -11, -4, -76, -31, -29, -6, -77, -19, -49, -5, -59, -17; -66, 0, 48, 10, -100, -37, -705, -288, -270, -56, -720, -178, -460, -47, -555, -160; -399, -1, 252, 42, -700, -240, -4515, -1832, -1701, -349, -4452, -1092, -2800, -285, -3360, -968],136,24]
%
% END OF LATTICE L137.24
%
%
% LATTICE L137.25
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-142311750, 1332030, -70760130; 1332030, -8220, 662310; -70760130, 662310, -35183293],[210, 30, 1],[22514, -16080, -32073, -108995, -59590, -1444277, -213881, -2020077, -291250, -924496, -102295, -92557, -7594, 33413, 12329, 138925; -9, 7, 13, 44, 24, 581, 86, 812, 117, 371, 41, 37, 3, -14, -5, -56; -45280, 32340, 64505, 219210, 119847, 2904720, 430156, 4062765, 585760, 1859340, 205735, 186150, 15273, -67200, -24796, -279405],136,25]
%
% END OF LATTICE L137.25
%
%
% LATTICE L137.26
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-8969100, -1283940, -53760; -1283940, -183795, -7695; -53760, -7695, -322],[420, 15, 1],[-109, -365, -173, -90, -25, -81, -3, 23, 5, 1, -35, -66, -79, -1011, -153, -2935; 893, 2989, 1416, 736, 204, 658, 24, -196, -41, -7, 288, 542, 648, 8288, 1254, 24052; -3145, -10500, -4960, -2565, -702, -2205, -73, 840, 145, 0, -1040, -1935, -2298, -29295, -4427, -84840],136,26]
%
% END OF LATTICE L137.26
%
%
% LATTICE L137.27
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[867720, -249480, 52080; -249480, 71728, -14976; 52080, -14976, 3115],[840, 8, 1],[32, 194, 70, 95, 159, 521, 941, 498, 136, 2, -28, -53, -89, -227, -311, -106; 111, 651, 234, 317, 530, 1736, 3135, 1659, 453, 7, -93, -176, -295, -749, -1020, -343; 0, -112, -45, -64, -110, -364, -660, -350, -96, 0, 21, 40, 70, 196, 300, 126],136,27]
%
% END OF LATTICE L137.27
%
%
% LATTICE L137.28
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2324280, 6720, 0; 6720, 56, 16; 0, 16, 7],[840, 8, 1],[-11, -13, -5, -2, -2, -5, -8, -2, -1, -1, -1, -1, -3, -16, -37, -12; 3819, 4515, 1737, 695, 695, 1736, 2775, 693, 345, 343, 345, 346, 1040, 5551, 12840, 4165; -8712, -10304, -3966, -1588, -1590, -3976, -6360, -1589, -792, -784, -786, -788, -2370, -12656, -29280, -9499],136,28]
%
% END OF LATTICE L137.28
%
%
% LATTICE L137.29
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[867548010, 1868580, -343473480; 1868580, 4025, -739795; -343473480, -739795, 135985594],[210, 35, 1],[956, 382, 5071, 2203, 2167, 3646, 11248, 10079, 15172, 2306, 11057, 1829, 521, 386, 848, 673; 60, 26, 300, 119, 106, 167, 501, 440, 636, 90, 396, 55, 10, 7, 21, 24; 2415, 965, 12810, 5565, 5474, 9210, 28413, 25460, 38325, 5825, 27930, 4620, 1316, 975, 2142, 1700],136,29]
%
% END OF LATTICE L137.29
%
%
% LATTICE L137.30
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[78540, 477540, 21840; 477540, 3137000, 133960; 21840, 133960, 6079],[420, 20, 1],[-743, -1387, -4454, -10738, -6680, -176992, -81494, -131617, -59821, -69271, -25828, -19544, -3414, -34982, -9352, -9699; -15, -28, -90, -217, -135, -3577, -1647, -2660, -1209, -1400, -522, -395, -69, -707, -189, -196; 3000, 5600, 17985, 43360, 26974, 714700, 329076, 531475, 241560, 279720, 104295, 78920, 13786, 141260, 37764, 39165],136,30]
%
% END OF LATTICE L137.30
%
%
% LATTICE L137.31
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1196580, 301980, -8820; 301980, -76209, 2226; -8820, 2226, -65],[420, 21, 1],[-37, -15, -41, -14, -1, 1, 1, -3, -3, -5, -39, -46, -199, -61, -301, -157; -127, -52, -144, -51, -10, 3, 5, -8, -9, -16, -128, -153, -670, -207, -1025, -536; 658, 249, 616, 147, -210, -33, 35, 132, 98, 129, 896, 987, 3990, 1167, 5635, 2892],136,31]
%
% END OF LATTICE L137.31
%
%
% LATTICE L137.32
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-268973670, 2075430, -133733040; 2075430, -11508, 1031898; -133733040, 1031898, -66491735],[210, 42, 1],[31922, -3192, -45311, -154111, -421456, -291907, -1513093, -408333, -412146, -186920, -144801, -131057, -53824, 6739, 87253, 28109; -9, 1, 13, 44, 120, 83, 430, 116, 117, 53, 41, 37, 15, -2, -25, -8; -64204, 6420, 91133, 309960, 847665, 587106, 3043250, 821271, 828940, 375948, 291235, 263592, 108255, -13554, -175490, -56535],136,32]
%
% END OF LATTICE L137.32
%
%
% LATTICE L137.33
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[66360, -44100, 16800; -44100, 26740, -11144; 16800, -11144, 4253],[420, 28, 1],[83, 210, 1628, 2899, 6953, 4537, 68977, 3056, 8989, 1302, 2908, 1637, 607, -1, -937, -32; -3, -7, -54, -96, -230, -150, -2280, -101, -297, -43, -96, -54, -20, 0, 30, 1; -336, -848, -6573, -11704, -28070, -18316, -278460, -12337, -36288, -5256, -11739, -6608, -2450, 4, 3780, 129],136,33]
%
% END OF LATTICE L137.33
%
%
% LATTICE L137.34
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-22877400, -3270960, -136080; -3270960, -467670, -19455; -136080, -19455, -809],[840, 15, 1],[-259, -869, -413, -108, -61, -207, -9, 23, 11, 1, -83, -78, -187, -2397, -363, -6967; 2093, 7021, 3336, 872, 492, 1666, 72, -196, -89, -7, 672, 631, 1512, 19376, 2934, 56308; -6770, -22680, -10760, -2805, -1572, -5250, -218, 840, 290, 0, -2200, -2055, -4908, -62790, -9502, -182280],136,34]
%
% END OF LATTICE L137.34
%
%
% LATTICE L137.35
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-26040, 26880, 3360; 26880, -20670, -2295; 3360, -2295, -239],[840, 15, 1],[344, 1139, 533, 271, 71, 101, 2, -143, -16, 9, 123, 221, 257, 1621, 244, 9327; 1355, 4487, 2100, 1068, 280, 399, 8, -560, -63, 35, 484, 870, 1012, 6384, 961, 36736; -8180, -27090, -12680, -6450, -1692, -2415, -49, 3360, 380, -210, -2920, -5250, -6108, -38535, -5801, -221760],136,35]
%
% END OF LATTICE L137.35
%
%
% LATTICE L137.36
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[40740, -1680, -840; -1680, 70, 35; -840, 35, 17],[420, 35, 1],[-2, 0, 1, 0, -1, -3, -11, -11, -10, -2, -25, -6, -3, -3, -7, -5; -3, 2, 24, 1, -10, -29, -105, -104, -93, -18, -216, -49, -22, -19, -39, -24; -105, -5, 0, 0, -28, -90, -336, -340, -315, -65, -840, -210, -112, -120, -294, -220],136,36]
%
% END OF LATTICE L137.36
%
%
% LATTICE L137.37
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-37666650, 999390, -17972010; 999390, -19180, 476840; -17972010, 476840, -8575043],[210, 70, 1],[43886, -1460, -62272, -70605, -38619, -133743, -415955, -187088, -566510, -85644, -199040, -60051, -4933, 3087, 23987, 12880; -27, 1, 39, 44, 24, 83, 258, 116, 351, 53, 123, 37, 3, -2, -15, -8; -91980, 3060, 130515, 147980, 80941, 280310, 871794, 392115, 1187340, 179500, 417165, 125860, 10339, -6470, -50274, -26995],136,37]
%
% END OF LATTICE L137.37
%
%
% LATTICE L137.38
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2157960, 110880, -16800; 110880, -5691, 861; -16800, 861, -130],[840, 21, 1],[37, 15, 41, 7, 1, -1, -1, 3, 3, 5, 39, 23, 199, 61, 301, 157; 1226, 496, 1352, 229, 20, -34, -30, 104, 102, 168, 1304, 767, 6620, 2026, 9990, 5208; 3325, 1341, 3640, 609, 0, -96, -70, 300, 287, 465, 3584, 2100, 18060, 5514, 27160, 14148],136,38]
%
% END OF LATTICE L137.38
%
%
% LATTICE L137.39
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[76440, -19320, 3360; -19320, -210, 21; 3360, 21, -1],[840, 21, 1],[-3, -2, -9, -7, -19, -2, -8, -7, -1, 0, 1, 1, -1, -1, -7, -9; 667, 445, 2004, 1560, 4240, 447, 1790, 1568, 225, 1, -220, -222, 220, 222, 1555, 2000; 3892, 2598, 11704, 9114, 24780, 2613, 10465, 9168, 1316, 6, -1288, -1302, 1260, 1293, 9065, 11664],136,39]
%
% END OF LATTICE L137.39
%
%
% LATTICE L137.40
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[151026960, 10804920, -105000; 10804920, 773016, -7512; -105000, -7512, 73],[840, 24, 1],[1, 1, 0, 0, 1, 9, 8, 17, 3, 13, 1, 3, 4, 12, 7, 11; -16, -14, 1, 7, 5, -35, -45, -112, -24, -126, -11, -37, -55, -175, -105, -168; -208, 0, 103, 720, 1950, 9324, 6860, 12894, 1840, 5712, 305, 504, 90, -756, -740, -1470],136,40]
%
% END OF LATTICE L137.40
%
%
% LATTICE L137.41
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2004240, -4200, -5880; -4200, -120, -48; -5880, -48, -11],[840, 24, 1],[-1, -1, 1, 4, 12, 61, 46, 44, 13, 43, 5, 5, 3, 2, -1, -2; 240, 238, -240, -959, -2875, -14609, -11015, -10535, -3112, -10290, -1196, -1195, -715, -469, 245, 483; -512, -504, 514, 2052, 6150, 31248, 23560, 22533, 6656, 22008, 2558, 2556, 1530, 1008, -520, -1029],136,41]
%
% END OF LATTICE L137.41
%
%
% LATTICE L137.42
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-16898070, 843150, 6666450; 843150, -28770, -323085; 6666450, -323085, -2623127],[210, 105, 1],[9918, -990, -28147, -47870, -52367, -90677, -94005, -253689, -128030, -58066, -89965, -40714, -6689, 2093, 5421, 17465; -19845, 1981, 56320, 95784, 104782, 181437, 188096, 507610, 256177, 116185, 180012, 81465, 13384, -4188, -10847, -34946; 27650, -2760, -78470, -133455, -145992, -252795, -262073, -707250, -356930, -161880, -250810, -113505, -18648, 5835, 15113, 48690],136,42]
%
% END OF LATTICE L137.42
%
%
% LATTICE L137.43
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[136349220, 6371820, 33710880; 6371820, 298200, 1575360; 33710880, 1575360, 8334653],[420, 60, 1],[-37711, -128053, -15528, -33882, -5488, -52116, -4370, -12977, -213, -4681, -3434, -23004, -13474, -346086, -52516, -252491; 1420, 4823, 585, 1277, 207, 1967, 165, 490, 8, 175, 129, 865, 507, 13027, 1977, 9506; 152260, 517020, 62695, 136800, 22158, 210420, 17644, 52395, 860, 18900, 13865, 92880, 54402, 1397340, 212036, 1019445],136,43]
%
% END OF LATTICE L137.43
%
%
% LATTICE L137.44
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[7490280, 3728760, -15960; 3728760, 1856225, -7945; -15960, -7945, 34],[840, 35, 1],[1, -2, -23, -1, 9, 13, 47, 93, 83, 16, 191, 43, 19, 8, 16, 19; -6, 4, 48, 2, -20, -29, -105, -208, -186, -36, -432, -98, -44, -19, -39, -48; -945, -5, 420, 0, -448, -675, -2478, -4960, -4515, -905, -11340, -2730, -1372, -690, -1617, -2320],136,44]
%
% END OF LATTICE L137.44
%
%
% LATTICE L137.45
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[840, 0, 0; 0, 35, 0; 0, 0, -1],[840, 35, 1],[-2, 0, 1, 0, -1, -3, -11, -11, -10, -2, -25, -3, -3, -3, -7, -5; -15, -1, 0, 1, 0, -4, -18, -20, -21, -5, -72, -10, -12, -14, -36, -28; -105, -5, 0, 0, -28, -90, -336, -340, -315, -65, -840, -105, -112, -120, -294, -220],136,45]
%
% END OF LATTICE L137.45
%
%
% LATTICE L137.46
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[14280, -1680, 0; -1680, 200, 0; 0, 0, -1],[840, 40, 1],[13, 13, 2, 1, 0, -2, -1, -3, -1, 1, 1, 2, 1, 23, 10, 31; 141, 147, 24, 14, 1, -7, -6, -21, -9, 7, 9, 19, 10, 238, 105, 329; -480, -560, -105, -80, -14, -140, -36, -70, 0, 0, -15, -40, -26, -700, -324, -1050],136,46]
%
% END OF LATTICE L137.46
%
%
% LATTICE L137.47
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-21000, 3360, 0; 3360, -520, -40; 0, -40, 91],[840, 40, 1],[-113, -181, -89, -47, -13, -194, -67, -86, -43, -1, 11, 8, 0, -79, -50, -96; -681, -1099, -543, -288, -80, -1197, -414, -532, -267, -7, 69, 51, 1, -462, -297, -574; -360, -560, -270, -140, -38, -560, -192, -245, -120, 0, 30, 20, -2, -280, -168, -315],136,47]
%
% END OF LATTICE L137.47
%
%
% LATTICE L137.48
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[10659180, 141960, 2641800; 141960, 2940, 35196; 2641800, 35196, 654751],[420, 84, 1],[-30196, -12635, -9021, -13919, -3693, -107, -1179, -616, -1928, -3427, -7041, -34267, -76617, -48079, -239751, -31508; -1429, -598, -427, -659, -175, -5, -55, -29, -91, -162, -333, -1621, -3625, -2275, -11345, -1491; 121912, 51012, 36421, 56196, 14910, 432, 4760, 2487, 7784, 13836, 28427, 138348, 309330, 194112, 967960, 127209],136,48]
%
% END OF LATTICE L137.48
%
%
% LATTICE L137.49
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[87164700, 64826160, 618660; 64826160, 48212535, 460110; 618660, 460110, 4391],[420, 105, 1],[95, 59, 255, 192, 103, 111, 91, 205, 33, 5, 1, 0, 25, 81, 101, 307; -96, -59, -252, -187, -98, -103, -83, -184, -28, -3, 4, 1, -26, -83, -103, -312; -3325, -2130, -9520, -7455, -4242, -4845, -4123, -9600, -1715, -390, -560, -105, -798, -2715, -3437, -10560],136,49]
%
% END OF LATTICE L137.49
%
%
% LATTICE L137.50
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[115771937610, 45585307950, 22024537920; 45585307950, 17949257340, 8672182260; 22024537920, 8672182260, 4189964171],[210, 210, 1],[20, 26, 50, 119, 53, 167, 167, 220, 212, 90, 66, 55, 5, 7, 7, 12; 2249, 2485, 6282, 17555, 9210, 32174, 33579, 45599, 46675, 21977, 18180, 19138, 3021, 4519, 3114, 3325; -4760, -5280, -13265, -36960, -19341, -67470, -70378, -95535, -97720, -45960, -37975, -39900, -6279, -9390, -6482, -6945],136,50]
%
% END OF LATTICE L137.50
%
%
% LATTICE L137.51
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[840, 0, 0; 0, -1400, -616; 0, -616, -271],[840, 56, 1],[-1, -1, -7, -6, -14, -9, -136, -6, -35, -5, -11, -3, -1, 0, 1, 0; -75, -29, -135, -91, -165, -88, -1215, -50, -249, -25, -27, 10, 30, 7, 0, -4; 168, 64, 294, 196, 350, 184, 2520, 103, 504, 48, 42, -28, -70, -16, 0, 9],136,51]
%
% END OF LATTICE L137.51
%
%
% LATTICE L137.52
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[35810040, 3604440, -85680; 3604440, 362768, -8624; -85680, -8624, 205],[840, 56, 1],[20, 10, 28, 43, 91, 55, 809, 70, 196, 26, 26, 11, -1, -1, 1, 2; 9, 3, 6, 7, 10, 4, 45, 3, 3, -1, -3, -4, -5, -1, 0, 1; 8736, 4304, 11949, 18256, 38430, 23140, 339780, 29362, 81984, 10816, 10731, 4424, -630, -460, 420, 878],136,52]
%
% END OF LATTICE L137.52
%
%
% LATTICE L137.53
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[20580, 24360, 13020; 24360, 4340, -2800; 13020, -2800, -5303],[420, 140, 1],[2702, 193, 26, -381, -45, 495, 2453, 709, 3118, 777, 2884, 3291, 1015, 2415, 6277, 1231; -8121, -580, -78, 1145, 135, -1489, -7377, -2132, -9375, -2336, -8670, -9893, -3051, -7259, -18867, -3700; 10920, 780, 105, -1540, -182, 2000, 9912, 2865, 12600, 3140, 11655, 13300, 4102, 9760, 25368, 4975],136,53]
%
% END OF LATTICE L137.53
%
%
% LATTICE L137.54
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1168440, 1643880, 45360; 1643880, 2294670, 63315; 45360, 63315, 1747],[840, 105, 1],[-1, 0, 3, 5, 5, 4, 4, 21, 5, 2, 5, 1, -1, -1, -1, -5; 219, 53, -172, -496, -576, -485, -494, -2624, -639, -263, -668, -134, 156, 170, 179, 944; -7910, -1920, 6160, 17850, 20748, 17475, 17801, 94560, 23030, 9480, 24080, 4830, -5628, -6135, -6461, -34080],136,54]
%
% END OF LATTICE L137.54
%
%
% LATTICE L137.55
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[21560280, 0, -77280; 0, 105, 0; -77280, 0, 277],[840, 105, 1],[95, 59, 255, 96, 103, 111, 91, 205, 33, 5, 1, 0, 25, 81, 101, 307; -7, -5, -24, -10, -12, -14, -12, -28, -5, -1, 0, 1, 0, -4, -6, -20; 26495, 16455, 71120, 26775, 28728, 30960, 25382, 57180, 9205, 1395, 280, 0, 6972, 22590, 28168, 85620],136,55]
%
% END OF LATTICE L137.55
%
%
% LATTICE L137.56
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1680, -7560, 1680; -7560, 30840, -6840; 1680, -6840, 1517],[840, 120, 1],[21, 69, 4, 8, 1, 5, 0, -3, -1, 1, 1, 7, 4, 100, 15, 143; 130, 392, 20, 29, -1, -91, -15, -140, -18, 0, 8, 55, 29, 679, 99, 924; 560, 1680, 85, 120, -6, -420, -68, -630, -80, 0, 35, 240, 126, 2940, 428, 3990],136,56]
%
% END OF LATTICE L137.56
%
%
% LATTICE L137.57
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1680, -5880, 1680; -5880, 19560, -5520; 1680, -5520, 1553],[840, 120, 1],[149, 491, 57, 57, 7, 30, -1, -16, -9, -1, 13, 48, 28, 705, 106, 506; 190, 616, 70, 67, 7, 7, -5, -35, -14, 0, 18, 65, 37, 917, 137, 651; 520, 1680, 190, 180, 18, 0, -16, -105, -40, 0, 50, 180, 102, 2520, 376, 1785],136,57]
%
% END OF LATTICE L137.57
%
%
% LATTICE L137.58
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2136164520, -3010560, 7628880; -3010560, -4200, 10752; 7628880, 10752, -27245],[840, 168, 1],[-203, -63, -25, 19, 67, 16, 1, -9, -57, -67, -105, -214, -392, -211, -976, -121; 421, 119, 33, -74, -180, -41, 0, 23, 143, 163, 249, 497, 885, 464, 2115, 259; -56672, -17592, -6986, 5292, 18690, 4464, 280, -2511, -15904, -18696, -29302, -59724, -109410, -58896, -272440, -33777],136,58]
%
% END OF LATTICE L137.58
%
%
% LATTICE L137.59
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1039080, -1362480, 7560; -1362480, 1786344, -9912; 7560, -9912, 55],[840, 168, 1],[-41, -17, -6, -9, -2, 0, -1, -1, -3, -5, -5, -24, -53, -33, -164, -43; 1, -1, -1, -4, -5, -1, 0, 1, 3, 3, 2, 7, 10, 4, 15, 3; 5768, 2136, 637, 504, -630, -180, 140, 318, 952, 1224, 1043, 4536, 9030, 5220, 25060, 6402],136,59]
%
% END OF LATTICE L137.59
%
%
% LATTICE L137.60
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2100, 2092440, 518280; 2092440, -149038260, -36928920; 518280, -36928920, -9150301],[420, 420, 1],[2058, 1615, 2059, 7225, 2283, 5521, 4825, 2858, 2130, 479, 35, -943, -189, 761, 1457, 1330; -74033, -58092, -74059, -259861, -82109, -198559, -173525, -102783, -76599, -17224, -1257, 33913, 6793, -27389, -52423, -47849; 298900, 234540, 299005, 1049160, 331506, 801660, 700588, 414975, 309260, 69540, 5075, -136920, -27426, 110580, 211652, 193185],136,60]
%
% END OF LATTICE L137.60
%
%
% LATTICE L137.61
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-590520, 1903440, -5040; 1903440, -6133400, 16240; -5040, 16240, -43],[840, 280, 1],[-7, -1, -1, 1, 1, 4, 13, 3, 19, 3, 7, 2, 0, -1, -4, -1; 9, 5, 27, 20, 8, 23, 66, 14, 75, 9, 15, 1, -1, -2, -3, 0; 4200, 2000, 10290, 7420, 2898, 8200, 23352, 4925, 26040, 3040, 4830, 140, -378, -640, -672, 115],136,61]
%
% END OF LATTICE L137.61
%
%
% LATTICE L137.62
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-9939720, -1472520, 15120; -1472520, -217840, 2240; 15120, 2240, -23],[840, 280, 1],[16, 6, 14, 19, 7, 19, 53, 22, 56, 6, 4, -1, -1, -1, 1, 2; -21, -5, -9, -10, -3, -7, -18, -7, -15, -1, 0, 1, 0, -2, -9, -5; 8400, 3440, 8295, 11480, 4298, 11780, 33012, 13750, 35280, 3840, 2625, -560, -658, -860, -252, 810],136,62]
%
% END OF LATTICE L137.62
%
%
% LATTICE L137.63
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[840, 0, 0; 0, -654360, -215880; 0, -215880, -71221],[840, 840, 1],[-5, -1, 0, 1, 0, -2, -3, -5, -7, -5, -3, -10, -3, -7, -6, -7; -1293, -475, -127, 0, 97, 297, 268, 307, 185, -79, -150, -831, -374, -1128, -1099, -1415; 3920, 1440, 385, 0, -294, -900, -812, -930, -560, 240, 455, 2520, 1134, 3420, 3332, 4290],136,63]
%
% END OF LATTICE L137.63
%
%
% LATTICE L137.64
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[26871600, 8785560, -43680; 8785560, 2871960, -14280; -43680, -14280, 71],[840, 840, 1],[25, 9, 5, 1, -1, -2, -1, 0, 3, 5, 9, 20, 8, 23, 22, 14; 46, 16, 8, -1, -3, -7, -5, -2, 2, 8, 16, 37, 15, 43, 41, 26; 24640, 8760, 4690, 420, -1218, -2640, -1624, -405, 2240, 4680, 8750, 19740, 7938, 22800, 21784, 13845],136,64]
%
% END OF LATTICE L137.64
%

\medskip%
%------------------------------WEYL-GROUP-W138--------------------------------
%
\leavevmode\llap{}%
$W_{138}$%
\qquad\llap{64} lattices, $\chi=72$%
\hfill%
$2222222222222222\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L138.1
%
\leavevmode%
${L_{138.1}}$%
{} : {$1\above{1pt}{1pt}{2}{2}8\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{-2}{}13\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{2\rightarrow N'_{37}}%
\EasyButWeakLineBreak%
{${2}\above{1pt}{1pt}{b}{2}{26}\above{1pt}{1pt}{b}{2}{8}\above{1pt}{1pt}{*}{2}{780}\above{1pt}{1pt}{l}{2}{1}\above{1pt}{1pt}{r}{2}{312}\above{1pt}{1pt}{l}{2}{5}\above{1pt}{1pt}{}{2}{104}\above{1pt}{1pt}{r}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1611480\\-106080\\0
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-106080\\-6982\\-1
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\-1\\1
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
477749\\-7254000\\-7059000
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
31703\\-481369\\-468428
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-245\\3720\\3619
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
11\\-167\\-160
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
6\\-91\\-78
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-5\\76\\80
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-77\\1170\\1170
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\-1
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
113\\-1716\\-1716
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
27\\-410\\-405
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
363\\-5512\\-5408
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-1611480, -106080, 0; -106080, -6982, -1; 0, -1, 1],[1560, 1, 1],[11, 6, -5, -77, 0, 113, 27, 363, 38, 631, 1083, 19187, 245, 3709, 218, 911; -167, -91, 76, 1170, 0, -1716, -410, -5512, -577, -9581, -16444, -291330, -3720, -56316, -3310, -13832; -160, -78, 80, 1170, -1, -1716, -405, -5408, -564, -9334, -16008, -283530, -3619, -54756, -3215, -13416],137,1]
%
% END OF LATTICE L138.1
%
\hbox{}\par\smallskip%
%
% LATTICE L138.2
%
\leavevmode%
${L_{138.2}}$%
{} : {$1\above{1pt}{1pt}{-2}{2}8\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{-2}{}13\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{m}%
\EasyButWeakLineBreak%
{${2}\above{1pt}{1pt}{s}{2}{26}\above{1pt}{1pt}{l}{2}{8}\above{1pt}{1pt}{}{2}{195}\above{1pt}{1pt}{r}{2}{4}\above{1pt}{1pt}{s}{2}{312}\above{1pt}{1pt}{s}{2}{20}\above{1pt}{1pt}{*}{2}{104}\above{1pt}{1pt}{b}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
69243720\\-118560\\0
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-118560\\203\\0
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\-1
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-887251\\-517647000\\8112000
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1519\\886227\\-13888
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-112\\-65344\\1023
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\583\\-15
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-585\\-13
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-584\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\585\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\584\\-2
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
31\\18096\\-156
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
11\\6420\\-70
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
63\\36764\\-468
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[69243720, -118560, 0; -118560, 203, 0; 0, 0, -1],[1560, 1, 1],[1, -1, -1, 1, 1, 31, 11, 63, 6, 92, 155, 1364, 69, 515, 59, 119; 583, -585, -584, 585, 584, 18096, 6420, 36764, 3501, 53677, 90432, 795795, 40256, 300456, 34420, 69420; -15, -13, 0, 0, -2, -156, -70, -468, -49, -819, -1408, -12480, -638, -4836, -570, -1196],137,2]
%
% END OF LATTICE L138.2
%
%
% LATTICE L138.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[76830, -17940, 390; -17940, 4189, -91; 390, -91, 2],[390, 1, 1],[0, 6, -7, -227, -10, -145, -36, -163, -26, -344, -279, -4843, -120, -869, -94, -175; 0, 26, -30, -975, -43, -624, -155, -702, -112, -1482, -1202, -20865, -517, -3744, -405, -754; 1, 13, -4, -195, -10, -156, -40, -182, -29, -377, -304, -5265, -130, -936, -100, -182],137,3]
%
% END OF LATTICE L138.3
%
%
% LATTICE L138.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-150540, -74880, 780; -74880, -37246, 389; 780, 389, 97],[780, 1, 1],[-289, -582, -195, -97, 98, 427, -276, -3595, -476, -9363, -16635, -298253, -7748, -60097, -7374, -16295; 581, 1170, 392, 195, -197, -858, 555, 7228, 957, 18824, 33444, 599625, 15577, 120822, 14825, 32760; -7, -13, -4, 0, 2, 0, -10, -104, -13, -247, -436, -7800, -202, -1560, -190, -416],137,4]
%
% END OF LATTICE L138.4
%
%
% LATTICE L138.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[14754090, -76440, 7377240; -76440, 394, -38220; 7377240, -38220, 3688717],[390, 2, 1],[-567, 207, 97, -194, -193, -3356, -2487, -7352, -2861, -44771, -18951, -668266, -16947, -63490, -14653, -14930; 581, -195, -97, 195, 194, 3393, 2520, 7462, 2907, 45539, 19281, 679965, 17246, 64623, 14920, 15210; 1140, -416, -195, 390, 388, 6747, 5000, 14781, 5752, 90012, 38101, 1343550, 34072, 127647, 29460, 30017],137,5]
%
% END OF LATTICE L138.5
%
%
% LATTICE L138.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[22194510, -114660, 7398300; -114660, 591, -38220; 7398300, -38220, 2466143],[390, 3, 1],[-372, 142, 129, -43, -128, -1479, -1642, -9699, -1886, -29496, -24967, -146727, -11162, -27875, -9648, -19655; 581, -195, -194, 65, 194, 2262, 2520, 14924, 2907, 45539, 38562, 226655, 17246, 43082, 14920, 30420; 1125, -429, -390, 130, 387, 4472, 4965, 29328, 5703, 89193, 75498, 443690, 33753, 84292, 29175, 59436],137,6]
%
% END OF LATTICE L138.6
%
%
% LATTICE L138.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[37044930, -191100, 14818050; -191100, 985, -76440; 14818050, -76440, 5927251],[390, 5, 1],[-435, 181, 155, -31, -153, -5269, -389, -11467, -2227, -34787, -29437, -103787, -13157, -98549, -2273, -23139; 581, -195, -194, 39, 194, 6786, 504, 14924, 2907, 45539, 38562, 135993, 17246, 129246, 2984, 30420; 1095, -455, -390, 78, 385, 13260, 979, 28860, 5605, 87555, 74090, 261222, 33115, 248040, 5721, 58240],137,7]
%
% END OF LATTICE L138.7
%
%
% LATTICE L138.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[224491020, -3507660, -87360; -3507660, 54807, 1365; -87360, 1365, 34],[780, 3, 1],[22, 350, 595, 3502, 267, 669, 233, 479, 5, 1, -1, 8, 3, 33, 37, 223; 1421, 22607, 38432, 226200, 17246, 43212, 15050, 30940, 323, 65, -64, 520, 194, 2132, 2390, 14404; -522, -8307, -14124, -83135, -6339, -15886, -5535, -11388, -120, -39, 0, -325, -81, -806, -885, -5304],137,8]
%
% END OF LATTICE L138.8
%
%
% LATTICE L138.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[5376236970, -24766560, 2679821820; -24766560, 114078, -12345060; 2679821820, -12345060, 1335775381],[390, 6, 1],[-93327, -90085, 486, 31428, -649, -64975, -191843, -666423, -284521, -4821939, -2078650, -24591548, -1888591, -2391037, -1697397, -1789589; -203, -195, 1, 65, -2, -143, -420, -1456, -621, -10517, -4533, -53625, -4118, -5213, -3700, -3900; 187230, 180726, -975, -63050, 1302, 130351, 384870, 1336959, 570798, 9673638, 4170129, 49334870, 3788838, 4796831, 3405270, 3590223],137,9]
%
% END OF LATTICE L138.9
%
%
% LATTICE L138.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[11625308760, -30113460, -2906251140; -30113460, 78004, 7528168; -2906251140, 7528168, 726543773],[780, 4, 1],[-1266, -1463, -49, 391, 1, -4565, -4667, -8317, -3600, -61795, -26714, -1898131, -48661, -185209, -43993, -23312; -2329, -2717, -97, 390, 0, -8346, -8540, -15236, -6599, -113347, -49007, -3482310, -89280, -339846, -80740, -42796; -5040, -5824, -195, 1560, 4, -18174, -18580, -33111, -14332, -246012, -106351, -7556640, -193724, -737334, -175140, -92807],137,10]
%
% END OF LATTICE L138.10
%
%
% LATTICE L138.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[432774420, 10819380, 163800; 10819380, 270485, 4095; 163800, 4095, 62],[780, 5, 1],[32, 506, 859, 3032, 385, 2891, 67, 687, 7, 1, -1, 10, 5, 151, 11, 327; -1257, -19877, -33744, -119106, -15124, -113568, -2632, -26988, -275, -39, 40, -390, -196, -5928, -432, -12844; -1520, -23985, -40700, -143637, -18235, -136890, -3171, -32500, -330, -65, 0, -663, -265, -7410, -529, -15600],137,11]
%
% END OF LATTICE L138.11
%
%
% LATTICE L138.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[3763437990, -26754000, 1876342650; -26754000, 190130, -13338780; 1876342650, -13338780, 935490833],[390, 10, 1],[-171515, -165213, 875, 33950, -1401, -360014, -70707, -1227042, -523649, -8871919, -3824277, -27145346, -3474419, -13195684, -624457, -3291524; -203, -195, 1, 39, -2, -429, -84, -1456, -621, -10517, -4533, -32175, -4118, -15639, -740, -3900; 344010, 331370, -1755, -68094, 2810, 722085, 141818, 2461095, 1050290, 17794530, 7670405, 54445794, 6968690, 26466765, 1252482, 6601855],137,12]
%
% END OF LATTICE L138.12
%
%
% LATTICE L138.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-678991560, -6456840, 174720; -6456840, -61401, 1662; 174720, 1662, -37],[1560, 3, 1],[-310, -5121, -8779, -51823, -1984, -10003, -1761, -7343, -87, -40, 45, 213, -1, -319, -224, -2979; 32543, 537589, 921596, 5440240, 208275, 1050088, 184865, 770848, 9133, 4199, -4724, -22360, 105, 33488, 23515, 312728; -2079, -34359, -58908, -347750, -13314, -67132, -11820, -49296, -585, -273, 300, 1430, -6, -2132, -1500, -19968],137,13]
%
% END OF LATTICE L138.13
%
%
% LATTICE L138.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1107926040, -17311320, -262080; -17311320, 270489, 4095; -262080, 4095, 62],[1560, 3, 1],[49, 809, 1387, 4094, 627, 1581, 557, 1163, 14, 10, -1, 1, 3, 57, 73, 475; 3176, 52442, 89912, 265395, 40646, 102492, 36110, 75400, 908, 650, -64, 65, 194, 3692, 4730, 30784; -2649, -44109, -75768, -223795, -34308, -86632, -30600, -64116, -795, -663, 0, -65, -132, -2912, -3840, -25428],137,14]
%
% END OF LATTICE L138.14
%
%
% LATTICE L138.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[96384210, -496860, -22242480; -496860, 2561, 114660; -22242480, 114660, 5132873],[390, 13, 1],[228, -10, -91, 7, 88, 227, 1078, 485, 1218, 1456, 15997, 21683, 7142, 4111, 6152, 961; 581, -15, -194, 15, 194, 522, 2520, 1148, 2907, 3503, 38562, 52305, 17246, 9942, 14920, 2340; 975, -43, -390, 30, 377, 972, 4615, 2076, 5213, 6231, 68458, 92790, 30563, 17592, 26325, 4112],137,15]
%
% END OF LATTICE L138.15
%
%
% LATTICE L138.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[3743083110, -32678100, 1243316490; -32678100, 285195, -10854480; 1243316490, -10854480, 412984657],[390, 15, 1],[-139665, -134533, 1425, 9215, -1141, -195441, -57577, -1998369, -426409, -7224429, -6228239, -7368177, -2829229, -7163521, -508497, -5360593; -203, -195, 2, 13, -2, -286, -84, -2912, -621, -10517, -9066, -10725, -4118, -10426, -740, -7800; 420465, 405015, -4290, -27742, 3435, 588380, 173337, 6016140, 1283715, 21749325, 18750270, 22182082, 8517465, 21565960, 1530843, 16138200],137,16]
%
% END OF LATTICE L138.16
%
%
% LATTICE L138.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-5637273720, -54671760, 10840440; -54671760, -530195, 105135; 10840440, 105135, -20846],[1560, 5, 1],[428, 7099, 12181, 43157, 2755, 41699, 490, 10233, 123, 64, -59, -179, 0, 1279, 61, 4093; -10276, -170430, -292432, -1036074, -66139, -1001052, -11763, -245648, -2952, -1534, 1416, 4290, -1, -30732, -1465, -98280; 170745, 2832115, 4859580, 17217408, 1099105, 16635840, 195487, 4082520, 49075, 25545, -23540, -71448, -5, 510120, 24333, 1632800],137,17]
%
% END OF LATTICE L138.17
%
%
% LATTICE L138.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[87732840, -2193360, -54600; -2193360, 54835, 1365; -54600, 1365, 34],[1560, 5, 1],[-43, -707, -1211, -2144, -547, -4135, -97, -1011, -12, -8, 1, -1, -3, -155, -13, -419; -1686, -27716, -47472, -84045, -21442, -162084, -3802, -39624, -470, -312, 40, -39, -118, -6084, -510, -16432; -1375, -22815, -39160, -69381, -17720, -134160, -3156, -33020, -405, -325, 0, -39, -80, -4680, -404, -13260],137,18]
%
% END OF LATTICE L138.18
%
%
% LATTICE L138.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-51479220, -1120860, 12930060; -1120860, -14232, 281580; 12930060, 281580, -3247649],[780, 12, 1],[4897, -28303, -22523, -618062, -56892, -89070, -84688, -59320, -9001, -25049, -49, 84542, 15852, 35718, 43648, 32644; -101, 598, 472, 12935, 1189, 1859, 1765, 1235, 187, 520, 1, -1755, -329, -741, -905, -676; 19488, -112632, -89631, -2459600, -226404, -354458, -337020, -236067, -35820, -99684, -195, 336440, 63084, 142142, 173700, 129909],137,19]
%
% END OF LATTICE L138.19
%
%
% LATTICE L138.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-187980, -88140, 0; -88140, -41158, -13; 0, -13, 1],[780, 13, 1],[100, 123, 2721, 3697, 1222, 707, 1068, 169, 23, 0, -15, -7, 8, 31, 162, 77; -213, -262, -5796, -7875, -2603, -1506, -2275, -360, -49, 0, 32, 15, -17, -66, -345, -164; -2743, -3379, -74776, -101610, -33592, -19440, -29380, -4652, -637, -1, 416, 210, -208, -840, -4420, -2108],137,20]
%
% END OF LATTICE L138.20
%
%
% LATTICE L138.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[127558470, -7949760, 63165960; -7949760, 494338, -3936660; 63165960, -3936660, 31279291],[390, 26, 1],[-135007, -9985, 676, 10088, -1249, -21895, -278963, -74421, -412721, -537743, -3013180, -8226008, -2737391, -799697, -2459677, -199443; -203, -15, 1, 15, -2, -33, -420, -112, -621, -809, -4533, -12375, -4118, -1203, -3700, -300; 272610, 20162, -1365, -20370, 2522, 44211, 563290, 150273, 833378, 1085826, 6084299, 16610190, 5527418, 1614771, 4966650, 402721],137,21]
%
% END OF LATTICE L138.21
%
%
% LATTICE L138.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[38220, -3120, 0; -3120, 255, 0; 0, 0, -1],[780, 15, 1],[2, 1, -1, -1, 0, 7, 2, 67, 7, 116, 199, 235, 90, 227, 16, 167; 24, 13, -12, -13, -1, 78, 23, 780, 82, 1365, 2344, 2769, 1061, 2678, 189, 1976; -15, 0, 0, -13, -15, -130, -27, -780, -75, -1170, -1980, -2327, -885, -2210, -153, -1560],137,22]
%
% END OF LATTICE L138.22
%
%
% LATTICE L138.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[12590310362370, 272890800, 6275758344570; 272890800, 5910, 136024980; 6275758344570, 136024980, 3128210637059],[390, 30, 1],[776505, -322897, -138315, 18442, 273071, 1567408, 694325, 10233852, 3975059, 62093229, 26271917, 61751890, 23484749, 29317758, 4057239, 20651314; 581, -195, -97, 13, 194, 1131, 504, 7462, 2907, 45539, 19281, 45331, 17246, 21541, 2984, 15210; -1557810, 647790, 277485, -36998, -547830, -3144505, -1392942, -20530965, -7974690, -124570290, -52706235, -123885502, -47114670, -58816745, -8139558, -41430285],137,23]
%
% END OF LATTICE L138.23
%
%
% LATTICE L138.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1560, 0, 0; 0, -8, 8; 0, 8, -7],[1560, 8, 1],[-3, -51, -11, -781, -20, -76, -18, -19, -1, -1, 0, 1, 0, -2, -2, -7; -23, -325, -67, -4680, -117, -429, -95, -91, -1, 13, 1, 0, -3, -39, -25, -65; -72, -1144, -243, -17160, -436, -1638, -380, -390, -16, 0, 1, 0, -4, -78, -60, -182],137,24]
%
% END OF LATTICE L138.24
%
%
% LATTICE L138.25
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-606840, 0, -302640; 0, 8, 0; -302640, 0, -150931],[1560, 8, 1],[1229, 20905, 9019, 320189, 8200, 31163, 7382, 3897, 411, 415, 1, -389, 0, 817, 818, 1433; -13, -247, -109, -3900, -101, -390, -95, -52, -7, -13, -1, 0, 1, 0, -5, -13; -2464, -41912, -18082, -641940, -16440, -62478, -14800, -7813, -824, -832, -2, 780, 0, -1638, -1640, -2873],137,25]
%
% END OF LATTICE L138.25
%
%
% LATTICE L138.26
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[26904930, -4471740, 8738340; -4471740, 741507, -1452360; 8738340, -1452360, 2838089],[390, 39, 1],[-50637, -3745, 507, 1261, -469, -5475, -104633, -55827, -154801, -201693, -2260325, -1028451, -1026721, -199963, -922557, -149611; -203, -15, 2, 5, -2, -22, -420, -224, -621, -809, -9066, -4125, -4118, -802, -3700, -600; 155805, 11523, -1560, -3880, 1443, 16846, 321945, 171774, 476307, 620589, 6954792, 3164440, 3159117, 615266, 2838615, 460338],137,26]
%
% END OF LATTICE L138.26
%
%
% LATTICE L138.27
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-237167580, 3356340, 59578740; 3356340, -40360, -843180; 59578740, -843180, -14966743],[780, 20, 1],[-39059, -428453, -163047, -2207572, -262794, -890912, -33166, -56660, 9423, 43185, 49, -104036, -33566, -264892, -26106, -135974; -777, -8528, -3246, -43953, -5233, -17745, -661, -1131, 187, 858, 1, -2067, -667, -5265, -519, -2704; -155440, -1705080, -648865, -8785296, -1045820, -3545490, -131988, -225485, 37500, 171860, 195, -414024, -133580, -1054170, -103892, -541125],137,27]
%
% END OF LATTICE L138.27
%
%
% LATTICE L138.28
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[17160, -4680, -1560; -4680, 1274, 403; -1560, 403, -71],[1560, 13, 1],[-6, -5, 1, 71, 30, 79, 137, 97, 101, 100, 2089, 2779, 445, 491, 338, 93; -23, -19, 4, 270, 114, 300, 520, 368, 383, 379, 7916, 10530, 1686, 1860, 1280, 352; 0, 2, 0, -30, -13, -36, -65, -48, -52, -54, -1144, -1530, -247, -276, -195, -56],137,28]
%
% END OF LATTICE L138.28
%
%
% LATTICE L138.29
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-76440, -4680, -3120; -4680, -286, -195; -3120, -195, -97],[1560, 13, 1],[1, -1, -1, 7, 13, 19, 71, 27, 30, 32, 683, 458, 297, 167, 239, 35; -17, 15, 16, -105, -196, -288, -1080, -412, -459, -491, -10488, -7035, -4564, -2568, -3680, -540; 0, 2, 0, -15, -26, -36, -130, -48, -52, -54, -1144, -765, -494, -276, -390, -56],137,29]
%
% END OF LATTICE L138.29
%
%
% LATTICE L138.30
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-410280, 1560, 1560; 1560, 15, -15; 1560, -15, -2],[1560, 15, 1],[-7, -116, -199, -235, -45, -227, -8, -167, -2, -1, 1, 1, 0, -7, -1, -67; -564, -9334, -16008, -18902, -3619, -18252, -643, -13416, -160, -78, 80, 78, -1, -572, -81, -5408; -1305, -21645, -37140, -43862, -8400, -42380, -1494, -31200, -375, -195, 180, 182, 0, -1300, -186, -12480],137,30]
%
% END OF LATTICE L138.30
%
%
% LATTICE L138.31
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-30081480, 751920, -7800; 751920, -18795, 195; -7800, 195, -2],[1560, 15, 1],[-5, -89, -155, -92, -71, -181, -13, -139, -2, -2, 1, 1, 1, -1, -1, -43; -204, -3614, -6288, -3731, -2878, -7332, -526, -5616, -80, -78, 40, 39, 38, -52, -42, -1768; -465, -6435, -10560, -6136, -4590, -11180, -738, -7020, -15, 195, 0, -104, -210, -1300, -222, -5460],137,31]
%
% END OF LATTICE L138.31
%
%
% LATTICE L138.32
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[4984590, 2484300, 2070510; 2484300, 1235845, 1031940; 2070510, 1031940, 860053],[390, 65, 1],[32420, 2398, -325, -485, 298, 10513, 13396, 35739, 99102, 129124, 1447067, 395051, 657312, 384053, 118126, 95783; -203, -15, 2, 3, -2, -66, -84, -224, -621, -809, -9066, -2475, -4118, -2406, -740, -600; -77805, -5755, 780, 1164, -715, -25230, -32149, -85770, -237835, -309885, -3472820, -948084, -1577485, -921690, -283491, -229870],137,32]
%
% END OF LATTICE L138.32
%
%
% LATTICE L138.33
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-16491540, -4123080, 31980; -4123080, -1030809, 7995; 31980, 7995, -62],[780, 39, 1],[1, 1, 1, -4, -11, -5, -53, -19, -20, -20, -419, -186, -179, -33, -137, -19; -7, -5, -4, 20, 54, 24, 250, 88, 91, 89, 1852, 820, 786, 144, 590, 80; -390, -129, 0, 515, 1287, 514, 4875, 1536, 1404, 1143, 22308, 9625, 8853, 1514, 5265, 492],137,33]
%
% END OF LATTICE L138.33
%
%
% LATTICE L138.34
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[629778240390, 98378280, 313910443860; 98378280, 15366, 49036260; 313910443860, 49036260, 156467404627],[390, 78, 1],[93309, -4169, -18759, 962, 36235, 15552, 442829, 99564, 499903, 597381, 3281425, 2965098, 2929825, 281054, 2523231, 197042; 581, -15, -97, 5, 194, 87, 2520, 574, 2907, 3503, 19281, 17435, 17246, 1657, 14920, 1170; -187200, 8364, 37635, -1930, -72696, -31201, -888420, -199749, -1002924, -1198488, -6583317, -5948690, -5877924, -563861, -5062200, -395313],137,34]
%
% END OF LATTICE L138.34
%
%
% LATTICE L138.35
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1283880, -40560, 4680; -40560, -1032, 144; 4680, 144, -17],[1560, 24, 1],[27, 419, 177, 2079, 158, 197, 136, 69, 5, -3, -1, 1, 2, 11, 24, 35; 131, 2041, 863, 10140, 771, 962, 665, 338, 25, -13, -5, 0, 9, 52, 115, 169; 8520, 132288, 55890, 656500, 49896, 62218, 42960, 21801, 1584, -936, -318, 260, 624, 3458, 7560, 11037],137,35]
%
% END OF LATTICE L138.35
%
%
% LATTICE L138.36
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[140878920, 0, -271440; 0, -24, 0; -271440, 0, 523],[1560, 24, 1],[63, 991, 210, 4939, 376, 470, 326, 333, 13, -3, -1, 1, 4, 24, 54, 161; 49, 819, 176, 4160, 319, 403, 285, 299, 15, 13, 0, 0, 1, 13, 35, 117; 32688, 514176, 108957, 2562560, 195084, 243854, 169140, 172770, 6744, -1560, -519, 520, 2076, 12454, 28020, 83538],137,36]
%
% END OF LATTICE L138.36
%
%
% LATTICE L138.37
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[624098280, -2796300, -156723840; -2796300, 12532, 702208; -156723840, 702208, 39356561],[780, 52, 1],[-6050, -7225, -39694, -215227, -70901, -20413, -61153, -2394, -1176, -1, -49, -1553, -1359, -1265, -11107, -1219; -899, -1069, -5867, -31800, -10470, -3012, -9010, -352, -169, 1, -7, -240, -210, -192, -1670, -182; -24076, -28752, -157963, -856500, -282152, -81234, -243360, -9527, -4680, -4, -195, -6180, -5408, -5034, -44200, -4851],137,37]
%
% END OF LATTICE L138.37
%
%
% LATTICE L138.38
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-99060, 12480, 24960; 12480, 2940, -3120; 24960, -3120, -6289],[780, 60, 1],[407, -588, -49, 601, 799, 3103, 1203, 8182, 3015, 45074, 18870, 88371, 33421, 41383, 5641, 14061; -8, 13, 1, -13, -17, -65, -25, -169, -62, -923, -386, -1807, -683, -845, -115, -286; 1620, -2340, -195, 2392, 3180, 12350, 4788, 32565, 12000, 179400, 75105, 351728, 133020, 164710, 22452, 55965],137,38]
%
% END OF LATTICE L138.38
%
%
% LATTICE L138.39
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-13042380, 3260400, -21060; 3260400, -815035, 5265; -21060, 5265, -34],[780, 65, 1],[-10, -8, -155, -40, -61, -31, -7, -3, 3, 1, 1, -2, -9, -11, -7, -11; -39, -35, -708, -186, -292, -156, -40, -24, 7, 3, 4, -6, -28, -36, -24, -40; 130, -495, -14300, -4209, -7735, -5130, -1911, -1900, -780, -155, 0, 309, 1235, 1230, 611, 600],137,39]
%
% END OF LATTICE L138.39
%
%
% LATTICE L138.40
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[116622482730, -54654600, 58148133030; -54654600, 25610, -27250860; 58148133030, -27250860, 28992740471],[390, 130, 1],[-58725, 2493, 11570, -356, -22427, -29011, -55173, -62113, -312163, -373381, -2051454, -1112308, -1832013, -527321, -315715, -123331; 581, -15, -97, 3, 194, 261, 504, 574, 2907, 3503, 19281, 10461, 17246, 4971, 2984, 1170; 117780, -5000, -23205, 714, 44980, 58185, 110656, 124575, 626080, 748860, 4114435, 2230866, 3674320, 1057605, 633204, 247355],137,40]
%
% END OF LATTICE L138.40
%
%
% LATTICE L138.41
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[11632920, -2015520, -23400; -2015520, 349167, 4056; -23400, 4056, 47],[1560, 39, 1],[-5, -2, 1, 9, 11, 9, 44, 29, 28, 25, 505, 221, 104, 37, 71, 17; -23, -9, 4, 40, 49, 40, 195, 128, 123, 109, 2196, 960, 451, 160, 305, 72; -507, -219, 156, 1030, 1248, 1028, 5070, 3384, 3315, 3027, 61620, 27050, 12792, 4588, 8970, 2232],137,41]
%
% END OF LATTICE L138.41
%
%
% LATTICE L138.42
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-31329480, 1957800, -31200; 1957800, -122343, 1950; -31200, 1950, -31],[1560, 39, 1],[1, 1, 1, -2, -11, -5, -53, -19, -20, -20, -419, -93, -179, -33, -137, -19; 13, 15, 16, -30, -166, -76, -810, -292, -309, -311, -6528, -1450, -2794, -516, -2150, -300; -195, -63, 0, 125, 624, 248, 2340, 732, 663, 531, 10296, 2215, 4056, 688, 2340, 204],137,42]
%
% END OF LATTICE L138.42
%
%
% LATTICE L138.43
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-8687640, -90480, 7800; -90480, -440, 80; 7800, 80, -7],[1560, 40, 1],[21, 317, 133, 935, 118, 439, 20, 50, 3, -5, -1, 1, 2, 29, 4, 28; 59, 897, 377, 2652, 335, 1248, 57, 143, 9, -13, -3, 0, 5, 78, 11, 78; 24040, 362960, 152290, 1070628, 135120, 502710, 22904, 57265, 3440, -5720, -1150, 1092, 2280, 33150, 4576, 32045],137,43]
%
% END OF LATTICE L138.43
%
%
% LATTICE L138.44
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-16353480, -74880, -26520; -74880, -40, -120; -26520, -120, -43],[1560, 40, 1],[57, 889, 188, 2651, 336, 1258, 58, 295, 11, -5, -1, 1, 4, 68, 10, 147; 167, 2613, 553, 7800, 989, 3705, 171, 871, 33, -13, -3, 0, 11, 195, 29, 429; -35640, -555880, -117555, -1657656, -210100, -786630, -36268, -184470, -6880, 3120, 625, -624, -2500, -42510, -6252, -91910],137,44]
%
% END OF LATTICE L138.44
%
%
% LATTICE L138.45
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[117372862230, 67152930, -38945913630; 67152930, 38415, -22282260; -38945913630, -22282260, 12922784359],[390, 195, 1],[48000, -2038, -18915, 97, 18332, 15809, 45098, 101541, 255158, 305196, 3353653, 303061, 1497458, 287349, 258060, 201617; -95419, 4061, 37636, -193, -36470, -31444, -89692, -201934, -507409, -606889, -6668744, -602635, -2977670, -571384, -513136, -400894; 144495, -6135, -56940, 292, 55185, 47590, 135759, 305670, 768105, 918735, 10095540, 912308, 4507815, 865010, 776841, 606930],137,45]
%
% END OF LATTICE L138.45
%
%
% LATTICE L138.46
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[10419240, 4815720, -34320; 4815720, 2225665, -15860; -34320, -15860, 113],[1560, 65, 1],[7, 2, -1, -5, -10, -23, -7, -21, -18, -13, -241, -61, -45, -43, -4, -1; -23, -7, 4, 18, 36, 84, 26, 80, 71, 55, 1052, 270, 204, 204, 22, 16; -1105, -375, 260, 1008, 2015, 4800, 1521, 4840, 4485, 3755, 74100, 19272, 14885, 15480, 1859, 1920],137,46]
%
% END OF LATTICE L138.46
%
%
% LATTICE L138.47
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-14272440, -1784640, 15600; -1784640, -223145, 1950; 15600, 1950, -17],[1560, 65, 1],[3, 1, 1, -1, -9, -11, -7, -11, -10, -8, -155, -20, -61, -31, -7, -3; -29, -9, -8, 9, 80, 96, 60, 92, 81, 61, 1152, 147, 440, 216, 44, 12; -585, -115, 0, 114, 910, 900, 442, 420, 65, -405, -11440, -1674, -6110, -4020, -1482, -1460],137,47]
%
% END OF LATTICE L138.47
%
%
% LATTICE L138.48
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[854830860, -6432660, -214770660; -6432660, 48984, 1616160; -214770660, 1616160, 53959723],[780, 156, 1],[-25481, -389, 49, -6418, -20228, -7294, -203456, -23098, -117095, -142187, -784217, -1419342, -1405532, -135282, -1222304, -48190; -653, -10, 1, -165, -519, -187, -5215, -592, -3001, -3644, -20098, -36375, -36021, -3467, -31325, -1235; -101400, -1548, 195, -25540, -80496, -29026, -809640, -91917, -465972, -565824, -3120741, -5648180, -5593224, -538346, -4864080, -191769],137,48]
%
% END OF LATTICE L138.48
%
%
% LATTICE L138.49
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[780, 0, 0; 0, -9165, -2145; 0, -2145, -502],[780, 195, 1],[-2, 0, 1, 0, -1, -1, -3, -7, -9, -11, -243, -22, -109, -21, -19, -15; 45, 7, 0, -4, -46, -12, -10, 12, 43, 81, 1936, 180, 926, 188, 186, 164; -195, -30, 0, 17, 195, 50, 39, -60, -195, -360, -8580, -797, -4095, -830, -819, -720],137,49]
%
% END OF LATTICE L138.49
%
%
% LATTICE L138.50
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[278513916330, 141419240040, 69629180010; 141419240040, 71807544510, 35355164130; 69629180010, 35355164130, 17407469357],[390, 390, 1],[-203, -15, 1, 1, -2, -11, -84, -112, -621, -809, -4533, -825, -4118, -401, -740, -300; 11321347, 837401, -56744, -56454, 104079, 611875, 4678013, 6240197, 34607333, 45091279, 252664484, 45985134, 229539321, 22352465, 41250667, 16724143; -22993230, -1700730, 115245, 114656, -211380, -1242695, -9500868, -12673605, -70286190, -91578690, -513152055, -93394076, -466185720, -45397015, -83778552, -33966105],137,50]
%
% END OF LATTICE L138.50
%
%
% LATTICE L138.51
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[30758520, 0, 63960; 0, -104, 0; 63960, 0, 133],[1560, 104, 1],[33, 37, 100, 539, 176, 50, 146, 11, 3, -1, -1, 1, 4, 4, 34, 7; 49, 63, 176, 960, 319, 93, 285, 23, 15, 1, 0, 0, 1, 3, 35, 9; -15912, -17848, -48243, -260040, -84916, -24126, -70460, -5310, -1456, 480, 481, -480, -1924, -1926, -16380, -3374],137,51]
%
% END OF LATTICE L138.51
%
%
% LATTICE L138.52
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-26520, 26520, -3120; 26520, -26416, 3120; -3120, 3120, -367],[1560, 104, 1],[446, 584, 3276, 8947, 2979, 871, 2683, 109, 150, 12, 2, -7, 1, 23, 297, 40; -13, -19, -109, -300, -101, -30, -95, -4, -7, -1, -1, 0, 1, 0, -5, -1; -3952, -5192, -29146, -79620, -26520, -7758, -23920, -973, -1352, -112, -26, 60, 0, -198, -2600, -353],137,52]
%
% END OF LATTICE L138.52
%
%
% LATTICE L138.53
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[3539640, 408720, -6240; 408720, 46680, -720; -6240, -720, 11],[1560, 120, 1],[-9, -193, -87, -209, -82, -107, -16, -45, -7, -15, -1, 1, 2, 3, 0, -7; -13, -247, -109, -260, -101, -130, -19, -52, -7, -13, -1, 0, 1, 0, -1, -13; -6000, -126360, -56790, -136292, -53400, -69550, -10368, -29055, -4440, -9360, -630, 572, 1200, 1690, -72, -4875],137,53]
%
% END OF LATTICE L138.53
%
%
% LATTICE L138.54
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-151320, -23400, 1560; -23400, 240, 0; 1560, 0, -1],[1560, 120, 1],[-4, -54, -11, -51, -19, -23, -3, -14, 0, 2, 0, -1, -1, -3, -1, -12; -393, -5291, -1077, -4992, -1859, -2249, -293, -1365, 1, 195, -1, -104, -101, -299, -99, -1183; -6360, -85800, -17475, -81016, -30180, -36530, -4764, -22230, 0, 3120, -15, -1664, -1620, -4810, -1596, -19110],137,54]
%
% END OF LATTICE L138.54
%
%
% LATTICE L138.55
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[644170020, -4133220, 164962980; -4133220, 27560, -1059240; 164962980, -1059240, 42245309],[780, 260, 1],[-134125, -164303, -908055, -986804, -1630406, -471508, -284818, -56362, -30967, -789, 49, -3748, -20514, -23768, -45366, -26184; 400326, 490399, 2710293, 2945337, 4866311, 1407321, 850103, 168225, 92428, 2355, -146, 11187, 61229, 70941, 135405, 78152; 533780, 653880, 3613805, 3927204, 6488560, 1876470, 1133496, 224305, 123240, 3140, -195, 14916, 81640, 94590, 180544, 104205],137,55]
%
% END OF LATTICE L138.55
%
%
% LATTICE L138.56
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[15183480, -3754920, -1227720; -3754920, 928590, 303615; -1227720, 303615, 99271],[1560, 195, 1],[-2, -1, 1, 1, 6, 5, 5, 17, 17, 16, 329, 29, 69, 25, 10, 13; 247, 45, 4, -28, -167, -104, -69, -88, 69, 271, 6948, 660, 1747, 736, 385, 720; -780, -150, 0, 98, 585, 380, 273, 480, 0, -630, -17160, -1658, -4485, -1940, -1053, -2040],137,56]
%
% END OF LATTICE L138.56
%
%
% LATTICE L138.57
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1560, 0, 0; 0, -125970, -41145; 0, -41145, -13439],[1560, 195, 1],[-2, 0, 1, 0, -1, -1, -3, -7, -9, -11, -243, -11, -109, -21, -19, -15; 255, 49, 0, -16, -382, -124, -178, -156, 1, 207, 5632, 272, 2942, 636, 690, 668; -780, -150, 0, 49, 1170, 380, 546, 480, 0, -630, -17160, -829, -8970, -1940, -2106, -2040],137,57]
%
% END OF LATTICE L138.57
%
%
% LATTICE L138.58
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-16495440, -563160, -124800; -563160, -18408, -4056; -124800, -4056, -893],[1560, 312, 1],[5, -1, -1, 2, 7, 2, 49, 5, 47, 53, 287, 258, 253, 24, 211, 8; -1252, 258, 254, -515, -1795, -511, -12495, -1273, -11952, -13462, -72876, -65505, -64225, -6091, -53525, -2028; 4992, -1032, -1014, 2060, 7176, 2042, 49920, 5085, 47736, 53760, 291018, 261580, 256464, 24322, 213720, 8097],137,58]
%
% END OF LATTICE L138.58
%
%
% LATTICE L138.59
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3527160, 10893480, 102960; 10893480, -30001296, -283608; 102960, -283608, -2681],[1560, 312, 1],[38, 4, 1, -1, -3, 1, 53, 16, 94, 128, 362, 661, 663, 65, 607, 50; -8451, -887, -219, 225, 664, -224, -11830, -3567, -20945, -28509, -80620, -147205, -147644, -14474, -135150, -11131; 895440, 93984, 23205, -23840, -70356, 23734, 1253460, 377946, 2219256, 3020712, 8542209, 15597320, 15643836, 1533614, 14320020, 1179402],137,59]
%
% END OF LATTICE L138.59
%
%
% LATTICE L138.60
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[391560, 1673100, -420420; 1673100, 7151820, -1797120; -420420, -1797120, 451583],[780, 780, 1],[30, 1, 0, 1, 17, 7, 41, 24, 124, 153, 847, 307, 1523, 147, 267, 53; 973, 45, 49, 46, 584, 222, 1284, 752, 3891, 4819, 26703, 9682, 48056, 4642, 8444, 1680; 3900, 180, 195, 184, 2340, 890, 5148, 3015, 15600, 19320, 107055, 38816, 192660, 18610, 33852, 6735],137,60]
%
% END OF LATTICE L138.60
%
%
% LATTICE L138.61
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-13044720, -1449240, 372840; -1449240, -159640, 41080; 372840, 41080, -10571],[1560, 520, 1],[3, -1, -1, 1, 6, 5, 8, 4, 37, 41, 221, 119, 194, 55, 32, 6; 776, -310, -292, 309, 1819, 1491, 2363, 1172, 10772, 11858, 63806, 34335, 55921, 15831, 9185, 1715; 3120, -1240, -1170, 1236, 7280, 5970, 9464, 4695, 43160, 47520, 255710, 137604, 224120, 63450, 36816, 6875],137,61]
%
% END OF LATTICE L138.61
%
%
% LATTICE L138.62
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1789320, -1014000, 15600; -1014000, -308360, 4680; 15600, 4680, -71],[1560, 520, 1],[-5, -1, 0, 1, 4, 2, 2, 1, 1, -3, -11, -13, -24, -8, -6, -3; 569, 115, 1, -114, -459, -231, -233, -119, -137, 317, 1187, 1410, 2619, 879, 665, 335; 36400, 7360, 65, -7296, -29380, -14790, -14924, -7630, -8840, 20200, 75725, 89976, 167180, 56130, 42484, 21410],137,62]
%
% END OF LATTICE L138.62
%
%
% LATTICE L138.63
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2617680, 45045000, -87360; 45045000, -689300040, 1336920; -87360, 1336920, -2593],[1560, 1560, 1],[-7, -3, -1, 1, 14, 3, 12, 5, 39, 35, 177, 31, 146, 13, 20, 3; 762, 304, 96, -101, -1403, -297, -1175, -483, -3710, -3252, -16310, -2847, -13337, -1177, -1773, -254; 393120, 156840, 49530, -52108, -723840, -153230, -606216, -249195, -1914120, -1677840, -8415030, -1468892, -6881160, -607270, -914784, -131055],137,63]
%
% END OF LATTICE L138.63
%
%
% LATTICE L138.64
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1007760, 192558600, -329160; 192558600, -36726788280, 62780640; -329160, 62780640, -107317],[1560, 1560, 1],[255, 49, 0, -16, -191, -31, -89, -39, 1, 207, 704, 272, 1471, 159, 345, 167; 764, 150, 1, -49, -589, -97, -285, -134, -72, 542, 1902, 741, 4049, 443, 977, 480; 446160, 87600, 585, -28616, -343980, -56650, -166452, -78270, -42120, 316440, 1110525, 432656, 2364180, 258670, 570492, 280290],137,64]
%
% END OF LATTICE L138.64
%

\medskip%
%------------------------------WEYL-GROUP-W139--------------------------------
%
\leavevmode\llap{}%
$W_{139}$%
\qquad\llap{64} lattices, $\chi=108$%
\hfill%
$2222222222222222222222\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L139.1
%
\leavevmode%
${L_{139.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{6}8\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{2}{}19\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{2\rightarrow N'_{38}}%
\EasyButWeakLineBreak%
{${1}\above{1pt}{1pt}{}{2}{285}\above{1pt}{1pt}{r}{2}{8}\above{1pt}{1pt}{s}{2}{60}\above{1pt}{1pt}{*}{2}{152}\above{1pt}{1pt}{b}{2}{6}\above{1pt}{1pt}{s}{2}{190}\above{1pt}{1pt}{b}{2}{24}\above{1pt}{1pt}{b}{2}{38}\above{1pt}{1pt}{b}{2}{6}\above{1pt}{1pt}{l}{2}{760}\above{1pt}{1pt}{}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3472440\\1155960\\-2280
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1155960\\384814\\-759
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2280\\-759\\1
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-17255041\\51838080\\3064320
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-5743166\\17253781\\1019928
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-7095\\21315\\1259
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\-1
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1423\\-4275\\-285
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
237\\-712\\-44
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
9227\\-27720\\-1650
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
57957\\-174116\\-10336
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
9935\\-29847\\-1770
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
83261\\-250135\\-14820
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
21997\\-66084\\-3912
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
35714\\-107293\\-6346
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
25543\\-76737\\-4536
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
719213\\-2160680\\-127680
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[3472440, 1155960, -2280; 1155960, 384814, -759; -2280, -759, 1],[2280, 1, 1],[0, 1423, 237, 9227, 57957, 9935, 83261, 21997, 35714, 25543, 719213, 7095, 133382, 1655, 4963, 13939, 1417, 6609, 707, 234, -1, -253; 0, -4275, -712, -27720, -174116, -29847, -250135, -66084, -107293, -76737, -2160680, -21315, -400710, -4972, -14910, -41876, -4257, -19855, -2124, -703, 3, 760; -1, -285, -44, -1650, -10336, -1770, -14820, -3912, -6346, -4536, -127680, -1259, -23655, -292, -870, -2432, -246, -1140, -120, -38, 0, 0],138,1]
%
% END OF LATTICE L139.1
%
\hbox{}\par\smallskip%
%
% LATTICE L139.2
%
\leavevmode%
${L_{139.2}}$%
{} : {$1\above{1pt}{1pt}{2}{6}8\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{2}{}19\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{m}%
\EasyButWeakLineBreak%
{${4}\above{1pt}{1pt}{*}{2}{1140}\above{1pt}{1pt}{s}{2}{8}\above{1pt}{1pt}{l}{2}{15}\above{1pt}{1pt}{}{2}{152}\above{1pt}{1pt}{r}{2}{6}\above{1pt}{1pt}{b}{2}{190}\above{1pt}{1pt}{l}{2}{24}\above{1pt}{1pt}{r}{2}{38}\above{1pt}{1pt}{s}{2}{6}\above{1pt}{1pt}{b}{2}{760}\above{1pt}{1pt}{*}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-40166760\\-13390440\\34200
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-13390440\\-4463986\\11401
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
34200\\11401\\-29
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
734159\\-2202480\\-419520
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
244846\\-734539\\-139912
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-665\\1995\\379
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
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0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-53\\160\\398
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1699\\5130\\13110
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-49\\148\\396
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-89\\270\\1155
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-347\\1064\\8664
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-10\\33\\1110
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
291\\-855\\6460
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
169\\-504\\1008
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
425\\-1273\\494
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
379\\-1137\\-216
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
11773\\-35340\\-14440
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-40166760, -13390440, 34200; -13390440, -4463986, 11401; 34200, 11401, -29],[2280, 1, 1],[-53, -1699, -49, -89, -347, -10, 291, 169, 425, 379, 11773, 263, 5689, 77, 194, 1411, 178, 1039, 167, 107, -1, -1133; 160, 5130, 148, 270, 1064, 33, -855, -504, -1273, -1137, -35340, -790, -17100, -232, -585, -4256, -537, -3135, -504, -323, 3, 3420; 398, 13110, 396, 1155, 8664, 1110, 6460, 1008, 494, -216, -14440, -518, -15390, -412, -1215, -9272, -1206, -7220, -1200, -798, 0, 8360],138,2]
%
% END OF LATTICE L139.2
%
%
% LATTICE L139.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-106590, -53010, 9120; -53010, -26363, 4560; 9120, 4560, 1489],[570, 1, 1],[-66440, -1201594, -4817, -6943, -8785, 142, 4402, -281, -11464, -16282, -299617, -7930, -211436, -5099, -67427, -368023, -119134, -946422, -118711, -365344, -251450, -3468463; 133349, 2411670, 9668, 13935, 17632, -285, -8835, 564, 23009, 32679, 601350, 15916, 424365, 10234, 135330, 738644, 239109, 1899525, 238260, 733267, 504675, 6961410; -1434, -25935, -104, -150, -190, 3, 95, -6, -247, -351, -6460, -171, -4560, -110, -1455, -7942, -2571, -20425, -2562, -7885, -5427, -74860],138,3]
%
% END OF LATTICE L139.3
%
%
% LATTICE L139.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-14322701220, -38194560, -1053360; -38194560, -101854, -2809; -1053360, -2809, -77],[1140, 1, 1],[148, 2972, 29, 119, 385, 44, 222, 25, -7, -26, -1019, -28, -692, -13, 1, 223, 52, 538, 167, 311, 242, 7099; -55535, -1115205, -10882, -44655, -144476, -16512, -83315, -9384, 2622, 9753, 382280, 10505, 259635, 4878, -375, -83676, -19512, -201875, -62664, -116698, -90807, -2663800; 1302, 26220, 260, 1110, 3724, 441, 2375, 324, 95, -123, -6080, -192, -5130, -112, 0, 1900, 447, 4655, 1452, 2717, 2121, 62320],138,4]
%
% END OF LATTICE L139.4
%
%
% LATTICE L139.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1248870, 252510, 623580; 252510, 48008, 126066; 623580, 126066, 311363],[570, 2, 1],[1, -187439, -7799, -606083, -1903198, -1304914, -10935368, -722228, -4690162, -3354332, -23611506, -931681, -17514481, -54313, -325597, -457058, -185774, -865912, -23116, -30350, 284, 8946; 0, -1995, -83, -6450, -20254, -13887, -116375, -7686, -49913, -35697, -251275, -9915, -186390, -578, -3465, -4864, -1977, -9215, -246, -323, 3, 95; -2, 376200, 15653, 1216440, 3819817, 2619030, 21947850, 1449549, 9413398, 6732318, 47389515, 1869932, 35152470, 109009, 653490, 917339, 372858, 1737930, 46395, 60914, -570, -17955],138,5]
%
% END OF LATTICE L139.5
%
%
% LATTICE L139.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1413030, 324900, 470250; 324900, 72012, 108111; 470250, 108111, 156497],[570, 3, 1],[1, -41548, -10373, -134356, -2531401, -289273, -7272453, -320207, -3119147, -743589, -31405227, -619606, -3882617, -72241, -72179, -607931, -41183, -575877, -10249, -20185, 63, 11907; 0, -665, -166, -2150, -40508, -4629, -116375, -5124, -49913, -11899, -502550, -9915, -62130, -1156, -1155, -9728, -659, -9215, -164, -323, 1, 190; -3, 125305, 31284, 405205, 7634466, 872420, 21933030, 965714, 9407052, 2242594, 94715190, 1868673, 11709605, 217872, 217685, 1833462, 124204, 1736790, 30910, 60876, -190, -35910],138,6]
%
% END OF LATTICE L139.6
%
%
% LATTICE L139.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1806330, 469680, -361950; 469680, 120020, -94125; -361950, -94125, 72527],[570, 5, 1],[-1, 15146, 6303, 48986, 1538247, 527345, 883847, 583739, 1895409, 1355569, 3816801, 376516, 1415611, 43899, 26317, 369429, 75079, 69991, 18685, 12267, -115, -1449; 0, -399, -166, -1290, -40508, -13887, -23275, -15372, -49913, -35697, -100510, -9915, -37278, -1156, -693, -9728, -1977, -1843, -492, -323, 3, 38; -5, 75069, 31240, 242793, 7624130, 2613720, 4380678, 2893230, 9394360, 6718710, 18917502, 1866155, 7016301, 217580, 130437, 1831030, 372120, 346902, 92610, 60800, -570, -7182],138,7]
%
% END OF LATTICE L139.7
%
%
% LATTICE L139.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-6793260, 2704080, 12540; 2704080, -1076367, -4992; 12540, -4992, -23],[1140, 3, 1],[153, 959, 17, -22, -641, -41, -1108, -103, -520, -126, -10709, -213, -1339, -25, 2, 337, 25, 728, 71, 368, 90, 7669; 379, 2375, 42, -55, -1596, -102, -2755, -256, -1292, -313, -26600, -529, -3325, -62, 5, 836, 62, 1805, 176, 912, 223, 19000; 1149, 7315, 150, -65, -3192, -221, -6270, -604, -3135, -772, -66120, -1329, -8455, -174, 5, 2280, 173, 5130, 508, 2679, 664, 57000],138,8]
%
% END OF LATTICE L139.8
%
%
% LATTICE L139.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[999844853460, 33493770, 498867737490; 33493770, 1122, 16711554; 498867737490, 16711554, 248907636667],[570, 6, 1],[-1895, -39342, -3082, -47919, -429644, -96323, -2378727, -51486, -985619, -232055, -4868229, -190300, -1177893, -9731, -16146, -57250, -6181, -55743, 234, 11831, 1421, -711; 189, 5225, 472, 9185, 84455, 19124, 476710, 10411, 201172, 47682, 1003865, 39441, 245765, 2170, 4025, 15941, 2012, 25270, 157, -380, -126, 95; 3798, 78850, 6177, 96040, 861099, 193052, 4767480, 103189, 1975392, 465088, 9756975, 381402, 2360750, 19503, 32360, 114741, 12388, 111720, -469, -23712, -2848, 1425],138,9]
%
% END OF LATTICE L139.9
%
%
% LATTICE L139.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[288445080, 82366140, 71638740; 82366140, 23576476, 20456452; 71638740, 20456452, 17792327],[1140, 4, 1],[-905673, -19228241, -123721, -1844597, -2153617, -1293179, -9560776, -556462, -3165619, -2056246, -13741947, -1003407, -17044279, -3551, -64483, -264551, -234085, -2530064, -207170, -1670717, -1380098, -10439733; 9692, 205770, 1324, 19740, 23047, 13839, 102315, 5955, 33877, 22005, 147060, 10738, 182400, 38, 690, 2831, 2505, 27075, 2217, 17879, 14769, 111720; 3635444, 77183700, 496626, 7404360, 8644791, 5190924, 38377720, 2233683, 12707048, 8253936, 55161275, 4027756, 68417100, 14254, 258840, 1061929, 939636, 10155880, 831597, 6706392, 5539824, 41905925],138,10]
%
% END OF LATTICE L139.10
%
%
% LATTICE L139.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[77138791980, 12010470, 38342516610; 12010470, 1870, 5969910; 38342516610, 5969910, 19058485909],[570, 10, 1],[-1019, -14110, -1956, -20257, -306522, -207193, -342723, -111776, -716651, -507917, -711655, -139456, -519695, -7409, -7838, -49348, -17567, -13147, -604, 4911, 2207, -85; 189, 3135, 472, 5511, 84455, 57372, 95342, 31233, 201172, 143046, 200773, 39441, 147459, 2170, 2415, 15941, 6036, 5054, 471, -380, -378, 19; 2050, 28386, 3935, 40752, 616645, 416820, 689472, 224865, 1441720, 1021800, 1431669, 280550, 1045494, 14905, 15768, 99275, 35340, 26448, 1215, -9880, -4440, 171],138,11]
%
% END OF LATTICE L139.11
%
%
% LATTICE L139.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[9607157340, -127809960, 1406760; -127809960, 1700335, -18715; 1406760, -18715, 206],[1140, 5, 1],[5, 235, 89, 658, 20587, 3524, 5899, 7783, 12621, 9019, 50767, 5005, 18803, 579, 344, 4797, 484, 447, 233, 71, -1, 1; 376, 17670, 6692, 49476, 1547968, 264975, 443555, 585216, 948993, 678153, 3817252, 376334, 1413828, 43536, 25866, 360696, 36393, 33611, 17520, 5339, -75, 76; 15, 513, 190, 1431, 44840, 7680, 12863, 16980, 27550, 19695, 110884, 10935, 41097, 1270, 759, 10640, 1080, 1007, 540, 190, 15, 76],138,12]
%
% END OF LATTICE L139.12
%
%
% LATTICE L139.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-13586520, -4126800, 25080; -4126800, -1253481, 7617; 25080, 7617, -46],[2280, 3, 1],[-113, -708, -25, 33, 955, 61, 1647, 153, 772, 187, 15891, 158, 993, 37, -3, -499, -37, -1077, -105, -544, -133, -11331; 379, 2375, 84, -110, -3192, -204, -5510, -512, -2584, -626, -53200, -529, -3325, -124, 10, 1672, 124, 3610, 352, 1824, 446, 38000; 1143, 7220, 276, -230, -7980, -527, -14535, -1372, -7011, -1711, -145920, -1458, -9215, -360, 20, 4788, 359, 10545, 1036, 5415, 1333, 114000],138,13]
%
% END OF LATTICE L139.13
%
%
% LATTICE L139.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-4475956920, -14667240, 487920; -14667240, -48063, 1599; 487920, 1599, -46],[2280, 3, 1],[281, 1831, 45, 11, -165, -21, -752, -83, -472, -122, -10681, -221, -1451, -37, -1, 469, 37, 1132, 115, 624, 158, 13721; -85698, -558410, -13724, -3355, 50312, 6404, 229330, 25312, 143944, 37206, 3257360, 67398, 442510, 11284, 305, -143032, -11284, -345230, -35072, -190304, -48186, -4184560; 1608, 10450, 252, 50, -1368, -143, -4845, -520, -2907, -745, -64980, -1338, -8740, -216, -5, 2736, 215, 6555, 664, 3591, 907, 78660],138,14]
%
% END OF LATTICE L139.14
%
%
% LATTICE L139.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[22520911470, 7948080, 7406876970; 7948080, 2805, 2614035; 7406876970, 2614035, 2436039346],[570, 15, 1],[-449, -2075, -1727, -2984, -270949, -30526, -151488, -32939, -316796, -74844, -629205, -61651, -76585, -6553, -1156, -43691, -2594, -5832, -181, 2156, 324, -75; 189, 1045, 944, 1837, 168910, 19124, 95342, 20822, 201172, 47682, 401546, 39441, 49153, 4340, 805, 31882, 2012, 5054, 314, -380, -126, 38; 1365, 6308, 5250, 9071, 823650, 92795, 460503, 100130, 963015, 227515, 1912692, 187410, 232807, 19920, 3514, 132810, 7885, 17727, 550, -6555, -985, 228],138,15]
%
% END OF LATTICE L139.15
%
%
% LATTICE L139.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[4814790, 1483140, 1773270; 1483140, 456076, 546231; 1773270, 546231, 653089],[570, 19, 1],[7, -7166, -11341, -440858, -145727, -949219, -418667, -1050745, -179569, -2440091, -1808013, -677752, -670579, -79025, -236887, -35005, -135173, -33163, -33647, -1163, 209, 693; 0, -105, -166, -6450, -2132, -13887, -6125, -15372, -2627, -35697, -26450, -9915, -9810, -1156, -3465, -512, -1977, -485, -492, -17, 3, 10; -19, 19545, 30932, 1202415, 397462, 2588940, 1141890, 2865846, 489764, 6655206, 4931250, 1848529, 1828965, 215536, 646095, 95474, 368676, 90450, 91770, 3172, -570, -1890],138,16]
%
% END OF LATTICE L139.16
%
%
% LATTICE L139.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1349266022040, 8823875880, 26411520; 8823875880, 57706030, 172725; 26411520, 172725, 517],[2280, 5, 1],[5650, 21229, 1309, 779, 10877, 1099, 1017, 533, 166, -1, 1, 5, 260, 199, 1483, 46427, 7949, 13309, 17563, 28486, 20359, 114607; -863341, -3243870, -200020, -119034, -1662044, -167931, -155401, -81444, -25365, 153, -152, -764, -39729, -30408, -226608, -7094220, -1214637, -2033665, -2683692, -4352767, -3110931, -17512376; -202165, -759639, -46860, -27906, -389880, -39420, -36518, -19200, -6080, -30, -304, -185, -9291, -7100, -53034, -1660600, -284340, -476102, -628320, -1019160, -728430, -4100656],138,17]
%
% END OF LATTICE L139.17
%
%
% LATTICE L139.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[699960, -234840, -2280; -234840, 78790, 765; -2280, 765, 7],[2280, 5, 1],[-679, -2383, -27, 1, 51, 1, -32, -97, -288, -286, -1869, -221, -1037, -93, -91, -4611, -721, -1108, -1343, -1992, -1334, -7251; -2014, -7068, -80, 3, 152, 3, -95, -288, -855, -849, -5548, -656, -3078, -276, -270, -13680, -2139, -3287, -3984, -5909, -3957, -21508; -1190, -4218, -60, -3, 0, 0, -38, -120, -380, -390, -2584, -310, -1482, -140, -147, -7600, -1200, -1862, -2280, -3420, -2310, -12616],138,18]
%
% END OF LATTICE L139.18
%
%
% LATTICE L139.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[130768260, -1167360, 32420460; -1167360, 10596, -289392; 32420460, -289392, 8037781],[1140, 12, 1],[28175, 201729, 4085, 21693, 77828, 15777, 354422, 6973, 120867, 26484, 534544, 39445, 226531, 423, 847, 7824, 2255, 73838, 2043, 50437, 14088, 321976; 15113, 108205, 2191, 11635, 41743, 8462, 190095, 3740, 64828, 14205, 286710, 21157, 121505, 227, 455, 4199, 1210, 39615, 1096, 27056, 7557, 172710; -113100, -809780, -16398, -87080, -312417, -63332, -1422720, -27991, -485184, -106312, -2145765, -158340, -909340, -1698, -3400, -31407, -9052, -296400, -8201, -202464, -56552, -1292475],138,19]
%
% END OF LATTICE L139.19
%
%
% LATTICE L139.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[42770588970, -177000390, 21340033920; -177000390, 720120, -88312890; 21340033920, -88312890, 10647434573],[570, 30, 1],[-943, 4656675, 2906827, 15060999, 709413128, 162134990, 815230260, 89736822, 1748260682, 416776904, 1760243712, 347285563, 435237177, 20245481, 8091309, 170374576, 23083474, 64557444, 2872410, 11314726, -35360, -668304; 0, -133, -83, -430, -20254, -4629, -23275, -2562, -49913, -11899, -50255, -9915, -12426, -578, -231, -4864, -659, -1843, -82, -323, 1, 19; 1890, -9333104, -5825985, -30185888, -1421835645, -324957770, -1633918794, -179854315, -3503937630, -835321810, -3527954523, -696044340, -872320666, -40576845, -16216942, -341471895, -46264870, -129388746, -5757005, -22677450, 70870, 1339443],138,20]
%
% END OF LATTICE L139.20
%
%
% LATTICE L139.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[607620, 9120, -1140; 9120, 105, -15; -1140, -15, 2],[1140, 15, 1],[-23, -27, -1, 0, 1, 0, -1, -1, -9, -3, -59, -7, -11, -3, -2, -153, -8, -37, -15, -67, -15, -245; -1456, -1710, -64, 0, 76, 1, -57, -60, -551, -185, -3648, -434, -684, -188, -126, -9652, -505, -2337, -948, -4237, -949, -15504; -23895, -28063, -1050, -1, 1140, 10, -969, -1000, -9120, -3055, -60192, -7155, -11267, -3090, -2069, -158460, -8290, -38361, -15560, -69540, -15575, -254448],138,21]
%
% END OF LATTICE L139.21
%
%
% LATTICE L139.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-101776920, -36480, 70680; -36480, 8, 24; 70680, 24, -49],[2280, 8, 1],[1, 46, 1, 37, 107, 71, 577, 37, 233, 163, 567, 44, 809, 2, 8, 7, 1, -7, -1, -5, -1, 3; 94, 4275, 92, 3330, 9595, 6357, 51585, 3303, 20767, 14511, 50445, 3911, 71820, 175, 675, 551, 51, -855, -99, -475, -93, 285; 1488, 68400, 1486, 54900, 158726, 105312, 855760, 54870, 345496, 241680, 840655, 65232, 1199280, 2962, 11820, 10298, 1440, -10640, -1494, -7448, -1488, 4465],138,22]
%
% END OF LATTICE L139.22
%
%
% LATTICE L139.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2396280, -802560, -139080; -802560, 268792, 46592; -139080, 46592, 7883],[2280, 8, 1],[-22, -31639, -1299, -100588, -157893, -216497, -1814133, -59903, -777967, -556363, -3916201, -154523, -2904716, -9004, -53957, -37864, -30775, -143437, -1915, -5061, 1, 1061; -65, -93480, -3838, -297195, -466507, -639657, -5359995, -176988, -2298563, -1643817, -11570715, -456550, -8582205, -26603, -159420, -111872, -90927, -423795, -5658, -14953, 3, 3135; -4, -5700, -234, -18120, -28443, -39000, -326800, -10791, -140144, -100224, -705470, -27836, -523260, -1622, -9720, -6821, -5544, -25840, -345, -912, 0, 190],138,23]
%
% END OF LATTICE L139.23
%
%
% LATTICE L139.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[170986038420, 34859490, 85319955810; 34859490, 7106, 17394462; 85319955810, 17394462, 42573621371],[570, 38, 1],[-9879, -41002, -22972, -1303801, -209726, -2703965, -1181289, -1469080, -497517, -6716737, -2479933, -1850256, -1819133, -101037, -556334, -38292, -272251, -58801, -19028, 1481, 20251, -247; 189, 825, 472, 27555, 4445, 57372, 25090, 31233, 10588, 143046, 52835, 39441, 38805, 2170, 12075, 839, 6036, 1330, 471, -20, -378, 5; 19798, 82170, 46037, 2612880, 420301, 5418876, 2367360, 2944107, 997048, 13460664, 4969905, 3708002, 3645630, 202483, 1114920, 76739, 545604, 117840, 38133, -2968, -40584, 495],138,24]
%
% END OF LATTICE L139.24
%
%
% LATTICE L139.25
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[18938820, -721620, 47880; -721620, 27493, -1824; 47880, -1824, 121],[1140, 19, 1],[-8, -8, -1, 1, 1, 4, 2, 11, 1, 14, 21, 8, 8, 1, -1, -1, -4, -2, -11, -1, -14, -21; -503, -495, -54, 45, 48, 192, 95, 516, 46, 633, 940, 353, 345, 34, -195, -88, -312, -145, -756, -66, -903, -1340; -4427, -4305, -418, 285, 328, 1311, 640, 3420, 297, 3990, 5840, 2147, 2025, 114, -2565, -936, -3135, -1400, -7068, -601, -8094, -11920],138,25]
%
% END OF LATTICE L139.25
%
%
% LATTICE L139.26
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[17244780, 4935060, 4309200; 4935060, -1766920, 1224740; 4309200, 1224740, 1076779],[1140, 20, 1],[-85534, -411176, -4402, 742282, 6287135, 4429229, 7604363, 2566921, 17036819, 12368317, 17547684, 6999604, 26684642, 465340, 640532, 2470687, 1102027, 1153459, 198707, 478825, 77009, -32040; -913, -4389, -47, 7923, 67108, 47277, 81168, 27399, 181849, 132018, 187302, 74713, 284829, 4967, 6837, 26372, 11763, 12312, 2121, 5111, 822, -342; 343340, 1650492, 17670, -2979576, -25237035, -17779260, -30524488, -10303815, -68387080, -49647360, -70437731, -28096940, -107114172, -1867910, -2571144, -9917525, -4423620, -4630072, -797625, -1922040, -309120, 128611],138,26]
%
% END OF LATTICE L139.26
%
%
% LATTICE L139.27
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[167318158530, 42233580, 55632937650; 42233580, 10659, 14042577; 55632937650, 14042577, 18497835374],[570, 57, 1],[-7979, -11039, -37109, -351032, -338797, -728010, -954144, -791065, -401852, -1808404, -4006161, -1494481, -489781, -163219, -149788, -61859, -73302, -47496, -10247, 1196, 5452, -399; 189, 275, 944, 9185, 8890, 19124, 25090, 20822, 10588, 47682, 105670, 39441, 12935, 4340, 4025, 1678, 2012, 1330, 314, -20, -126, 10; 23997, 33200, 111606, 1055735, 1018938, 2189503, 2869605, 2379142, 1208577, 5438807, 12048600, 4494678, 1473025, 490884, 450490, 186042, 220457, 142845, 30818, -3597, -16397, 1200],138,27]
%
% END OF LATTICE L139.27
%
%
% LATTICE L139.28
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[4854120, 2280, -2280; 2280, -15, 0; -2280, 0, 1],[2280, 15, 1],[-7, -11, -3, -1, -153, -8, -37, -15, -67, -15, -245, -23, -27, -1, 0, 1, 0, -1, -1, -9, -3, -59; -966, -1520, -416, -139, -21280, -1113, -5149, -2088, -9329, -2089, -34124, -3204, -3762, -140, 0, 152, 1, -133, -136, -1235, -413, -8132; -15780, -24814, -6780, -2264, -346560, -18125, -83847, -34000, -151905, -34015, -555636, -52170, -61256, -2280, -1, 2280, 5, -2223, -2240, -20235, -6755, -132924],138,28]
%
% END OF LATTICE L139.28
%
%
% LATTICE L139.29
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-118165560, -519840, 102600; -519840, -2265, 450; 102600, 450, -89],[2280, 15, 1],[4, 8, 7, 7, 587, 32, 154, 65, 303, 70, 1163, 56, 68, 9, 1, 21, 0, -2, -1, 1, 2, 53; 395, 798, 708, 714, 59964, 3271, 15751, 6652, 31027, 7171, 119168, 5740, 6973, 928, 104, 2204, 1, -209, -108, 57, 191, 5168; 6600, 13243, 11640, 11672, 979260, 53395, 257013, 108500, 505875, 116885, 1942104, 93525, 113582, 15060, 1678, 35340, 5, -3363, -1700, 1425, 3265, 87096],138,29]
%
% END OF LATTICE L139.29
%
%
% LATTICE L139.30
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[38760, -13680, -2280; -13680, 4826, 779; -2280, 779, -161],[2280, 19, 1],[3933, 3838, 791, 1943, 241, 371, 61, -29, -8, 1, 153, 72, 167, 277, 6067, 1895, 6037, 2609, 12845, 1076, 14417, 21207; 11298, 11025, 2272, 5580, 692, 1065, 175, -84, -23, 3, 440, 207, 480, 796, 17430, 5444, 17343, 7495, 36900, 3091, 41415, 60920; -1121, -1095, -228, -570, -72, -114, -20, 0, 2, 0, -40, -19, -45, -76, -1710, -536, -1710, -740, -3648, -306, -4104, -6040],138,30]
%
% END OF LATTICE L139.30
%
%
% LATTICE L139.31
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-973560, 25080, 27360; 25080, -646, -703; 27360, -703, -731],[2280, 19, 1],[1271, 1243, 131, 167, 43, 70, 13, 5, -1, -1, 19, 19, 47, 41, 478, 301, 962, 417, 2059, 173, 2323, 3421; 51692, 50550, 5324, 6780, 1744, 2835, 525, 192, -41, -39, 780, 778, 1920, 1672, 19455, 12248, 39141, 16965, 83760, 7037, 94485, 139140; -2242, -2190, -228, -285, -72, -114, -20, 0, 2, 0, -40, -38, -90, -76, -855, -536, -1710, -740, -3648, -306, -4104, -6040],138,31]
%
% END OF LATTICE L139.31
%
%
% LATTICE L139.32
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[182746972110, 56981760, -36662551050; 56981760, 17765, -11431635; -36662551050, -11431635, 7355211602],[570, 95, 1],[6499, 5395, 30227, 171562, 275971, 1779028, 155442, 1933117, 327334, 4419182, 652655, 1217351, 239375, 132953, 73208, 50389, 179132, 7738, 25043, -974, -13322, 65; 189, 165, 944, 5511, 8890, 57372, 5018, 62466, 10588, 143046, 21134, 39441, 7761, 4340, 2415, 1678, 6036, 266, 942, -20, -378, 2; 32395, 26892, 150670, 855171, 1375610, 8867775, 774819, 9635850, 1631635, 22027935, 3253236, 6068030, 1193193, 662720, 364914, 251170, 892905, 38571, 124830, -4855, -66405, 324],138,32]
%
% END OF LATTICE L139.32
%
%
% LATTICE L139.33
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[380760, 20520, 4560; 20520, 1104, 240; 4560, 240, 37],[2280, 24, 1],[-19, -159, -5, -33, -250, -52, -1194, -24, -424, -94, -954, -71, -411, -1, 3, 22, 4, 54, 0, -32, -14, -186; 387, 3230, 101, 665, 5035, 1047, 24035, 483, 8531, 1891, 19190, 1428, 8265, 20, -60, -437, -79, -1045, 1, 665, 287, 3800; -192, -1520, -42, -260, -1938, -400, -9120, -182, -3192, -704, -7125, -528, -3040, -6, 20, 114, 16, 0, -10, -456, -160, -1995],138,33]
%
% END OF LATTICE L139.33
%
%
% LATTICE L139.34
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-576035160, -29259240, 228000; -29259240, -1486128, 11544; 228000, 11544, -71],[2280, 24, 1],[-1691, -11293, -163, -421, -961, -274, -3588, -8, 754, 336, 8694, 431, 3313, 79, 1, -635, -398, -12372, -160, -7138, -1848, -40614; 33799, 225720, 3258, 8415, 19209, 5477, 71725, 160, -15067, -6715, -173755, -8614, -66215, -1579, -20, 12692, 7955, 247285, 3198, 142671, 36937, 811775; 65148, 435100, 6282, 16240, 37107, 10592, 139080, 317, -28728, -12872, -333450, -16548, -127300, -3042, -40, 24453, 15328, 476520, 6163, 274968, 71192, 1564650],138,34]
%
% END OF LATTICE L139.34
%
%
% LATTICE L139.35
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[35340, 4560, -1140; 4560, 399, -114; -1140, -114, 31],[1140, 57, 1],[-26, -8, -1, 1, 1, 1, 1, 1, 0, -1, -7, -4, -2, -3, -11, -9, -9, -11, -17, -4, -17, -73; -535, -165, -22, 15, 16, 16, 15, 12, -2, -29, -180, -95, -45, -62, -225, -184, -184, -225, -348, -82, -349, -1500; -2907, -895, -114, 95, 96, 95, 90, 76, -9, -152, -960, -513, -245, -342, -1235, -1008, -1007, -1230, -1900, -447, -1900, -8160],138,35]
%
% END OF LATTICE L139.35
%
%
% LATTICE L139.36
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[3202304701110, -2962775070, 1597778128680; -2962775070, 2736456, -1478265702; 1597778128680, -1478265702, 797205508771],[570, 114, 1],[-18941, 6478279, 15378869, 398547457, 197611660, 858119346, 1135458444, 474950758, 487005490, 2205907280, 2451737868, 1838117561, 606221261, 107161039, 214152083, 47468156, 122199918, 89940636, 15208874, 3154142, -188936, -939708; 0, -35, -83, -2150, -1066, -4629, -6125, -2562, -2627, -11899, -13225, -9915, -3270, -578, -1155, -256, -659, -485, -82, -17, 1, 5; 37962, -12983920, -30822693, -798778240, -396057963, -1719863090, -2275712670, -951907543, -976067922, -4421131546, -4913831025, -3683998692, -1215002990, -214774689, -429208670, -95136801, -244915966, -180261150, -30481985, -6321606, 378670, 1883385],138,36]
%
% END OF LATTICE L139.36
%
%
% LATTICE L139.37
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[365517060, -1277940, 91057500; -1277940, 4440, -318360; 91057500, -318360, 22684217],[1140, 60, 1],[3138, 1968, -710, -282, -71, 563, 5623, 913, 23855, 6731, 30770, 13452, 19046, 1816, 1388, 21085, 3861, 15391, 1299, 18173, 3223, 11258; -281, -323, -3, 1, 0, -3, -38, -7, -209, -64, -304, -139, -209, -25, -29, -532, -109, -494, -49, -855, -188, -760; -12600, -7904, 2850, 1132, 285, -2260, -22572, -3665, -95760, -27020, -123519, -54000, -76456, -7290, -5572, -84645, -15500, -61788, -5215, -72960, -12940, -45201],138,37]
%
% END OF LATTICE L139.37
%
%
% LATTICE L139.38
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[741174420, -6689520, 184636680; -6689520, 59812, -1666452; 184636680, -1666452, 45995521],[1140, 76, 1],[125911, 108701, -1865, -28117, -359, 6305, 8316, 17566, 8891, 151150, 62167, 106409, 123619, 17353, 260437, 15847, 179551, 69124, 75362, 22085, 267026, 92713; 991, 855, -15, -225, -3, 48, 65, 138, 70, 1191, 490, 839, 975, 137, 2055, 125, 1416, 545, 594, 174, 2103, 730; -505400, -436320, 7486, 112860, 1441, -25308, -33380, -70509, -35688, -606708, -249535, -427120, -496200, -69654, -1045380, -63609, -720708, -277460, -302499, -88648, -1071828, -372145],138,38]
%
% END OF LATTICE L139.38
%
%
% LATTICE L139.39
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-6808080, -15960, 20520; -15960, 40, 40; 20520, 40, -61],[2280, 40, 1],[-436, -1643, -26, -32, -229, -95, -91, -13, -21, -1, 1, 1, -10, -3, -55, -873, -601, -1011, -335, -2183, -1565, -1103; -16837, -63441, -1003, -1233, -8816, -3654, -3496, -498, -798, -36, 38, 37, -399, -117, -2127, -33744, -23226, -39064, -12942, -84322, -60444, -42598; -158160, -595992, -9430, -11604, -83030, -34440, -32984, -4710, -7600, -360, 361, 360, -3648, -1090, -19956, -316730, -218040, -366776, -121530, -791920, -567720, -400121],138,39]
%
% END OF LATTICE L139.39
%
%
% LATTICE L139.40
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[579120, -15960, 0; -15960, 440, 0; 0, 0, -1],[2280, 40, 1],[-105, -394, -6, -7, -24, -19, -17, -1, -1, 1, 1, 0, -5, -1, -14, -109, -149, -249, -41, -531, -379, -533; -3721, -13965, -213, -249, -855, -678, -608, -36, -38, 36, 38, 1, -171, -35, -495, -3857, -5274, -8816, -1452, -18810, -13428, -18886; -2380, -8892, -130, -144, -475, -360, -304, -15, 0, 0, -38, -20, -228, -30, -336, -2565, -3480, -5776, -945, -12160, -8640, -12122],138,40]
%
% END OF LATTICE L139.40
%
%
% LATTICE L139.41
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[452824562490, -1438322610, 225085502220; -1438322610, 4560760, -714947010; 225085502220, -714947010, 111883249069],[570, 190, 1],[-9161, 1878841, 7433679, 115587487, 95519514, 1244367010, 109769272, 688730612, 235403766, 3198807164, 237019230, 888490601, 175817447, 51798417, 62108801, 22944678, 177203294, 8694920, 22054540, 1524618, -273980, -90846; 0, -21, -83, -1290, -1066, -13887, -1225, -7686, -2627, -35697, -2645, -9915, -1962, -578, -693, -256, -1977, -97, -246, -17, 3, 1; 18430, -3779832, -14954995, -232537656, -192165125, -2503404090, -220832634, -1385580795, -473582750, -6435325650, -476832723, -1787455780, -353707638, -104207495, -124949814, -46159855, -356495670, -17492346, -44369085, -3067210, 551190, 182763],138,41]
%
% END OF LATTICE L139.41
%
%
% LATTICE L139.42
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[10712580, -3592140, 47880; -3592140, 1204505, -16055; 47880, -16055, 214],[1140, 95, 1],[-326, -64, -35, -19, -13, -23, -1, -7, 0, -1, -1, -4, -2, -9, -47, -75, -241, -21, -521, -44, -593, -175; -452, -90, -56, -36, -28, -57, -3, -36, -1, -3, 0, 2, 0, -4, -54, -92, -303, -27, -684, -59, -807, -240; 38855, 7533, 3610, 1539, 800, 855, -2, -1140, -75, 0, 224, 1045, 447, 1710, 6441, 9840, 31065, 2662, 64980, 5395, 71820, 21056],138,42]
%
% END OF LATTICE L139.42
%
%
% LATTICE L139.43
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[85844280, 2213880, -72960; 2213880, 57057, -1881; -72960, -1881, 62],[2280, 57, 1],[-2, -1, -3, -11, -9, -9, -11, -17, -4, -17, -73, -13, -4, -1, 1, 1, 1, 1, 1, 0, -1, -7; -95, -45, -124, -450, -368, -368, -450, -696, -164, -698, -3000, -535, -165, -44, 30, 32, 32, 30, 24, -4, -58, -360; -5244, -2545, -7296, -26600, -21756, -21755, -26595, -41116, -9681, -41173, -176880, -31521, -9710, -2508, 2090, 2148, 2147, 2085, 1900, -123, -2945, -19200],138,43]
%
% END OF LATTICE L139.43
%
%
% LATTICE L139.44
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[223984920, -14012880, -143640; -14012880, 875463, 9177; -143640, 9177, 62],[2280, 57, 1],[-3457, -1481, -1677, -2959, -4833, -4833, -5918, -9173, -2170, -9272, -39949, -14303, -4439, -691, -1, 97, 97, -2, -299, -198, -1384, -7411; -51890, -22230, -25172, -44415, -72544, -72544, -88830, -137688, -32572, -139174, -599640, -214690, -66630, -10372, -15, 1456, 1456, -30, -4488, -2972, -20774, -111240; -328548, -140750, -159372, -281200, -459288, -459287, -562395, -871720, -206217, -881125, -3796380, -1359222, -421840, -65664, -95, 9216, 9215, -195, -28424, -18819, -131537, -704340],138,44]
%
% END OF LATTICE L139.44
%
%
% LATTICE L139.45
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[137332385130, 970092120, -44534145600; 970092120, 6841140, -314588985; -44534145600, -314588985, 14441527711],[570, 285, 1],[4031, -275572, -6541843, -16953364, -84059813, -182512895, -48299997, -202033993, -103580911, -469173123, -208583475, -390948146, -25787369, -45584039, -9109577, -20191951, -25990633, -3825885, -6469535, -670853, 40185, 79947; -8062, 551137, 13083520, 33906298, 168117494, 365021161, 96598769, 404062862, 207159195, 938334347, 417161660, 781886377, 51574084, 91166922, 18218923, 40383390, 51980607, 7651673, 12938906, 1341689, -80369, -159892; 12255, -837791, -19888440, -51541433, -255557730, -554873720, -146841126, -614221550, -314905560, -1426375030, -634133214, -1188556305, -78398479, -138584100, -27694837, -61387350, -79016440, -11631414, -19668610, -2039520, 122170, 243054],138,45]
%
% END OF LATTICE L139.45
%
%
% LATTICE L139.46
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[23504520, 7790760, -50160; 7790760, 2582290, -16625; -50160, -16625, 107],[2280, 95, 1],[-689, -134, -133, -61, -35, -47, -1, 23, 2, -1, -7, -16, -7, -55, -221, -341, -1081, -93, -2279, -190, -2537, -745; 2330, 453, 448, 204, 116, 153, 3, -84, -7, 3, 24, 55, 24, 188, 750, 1156, 3663, 315, 7716, 643, 8583, 2520; 38855, 7533, 7220, 3078, 1600, 1710, -4, -2280, -150, 0, 448, 1045, 447, 3420, 12882, 19680, 62130, 5324, 129960, 10790, 143640, 42112],138,46]
%
% END OF LATTICE L139.46
%
%
% LATTICE L139.47
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2280, 0, -2280; 0, -190, -665; -2280, -665, -47],[2280, 95, 1],[-4871, -929, -363, -55, -39, -1, 2, 7, -18, -524, -207, -529, -151, -357, -485, -1401, -4319, -362, -8647, -702, -9196, -2673; 17020, 3246, 1268, 192, 136, 3, -7, -24, 63, 1833, 724, 1850, 528, 1248, 1695, 4896, 15093, 1265, 30216, 2453, 32133, 9340; -5130, -978, -380, -57, -40, 0, 2, 0, -20, -570, -224, -570, -162, -380, -513, -1480, -4560, -382, -9120, -740, -9690, -2816],138,47]
%
% END OF LATTICE L139.47
%
%
% LATTICE L139.48
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[30915660, -1124040, 7700700; -1124040, 40812, -279984; 7700700, -279984, 1918147],[1140, 228, 1],[10563, 3507, 653, 1041, 68, 19, -224, -175, -233, -1154, -1318, -2043, -667, -85, 1799, 500, 2253, 3064, 1311, 1369, 6266, 6998; -11, -5, -3, -5, 0, 2, 5, 3, 4, 21, 25, 41, 15, 5, 15, 2, 6, 5, 1, 0, -3, -5; -42408, -14080, -2622, -4180, -273, -76, 900, 703, 936, 4636, 5295, 8208, 2680, 342, -7220, -2007, -9044, -12300, -5263, -5496, -25156, -28095],138,48]
%
% END OF LATTICE L139.48
%
%
% LATTICE L139.49
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-78117360, -3586440, 1231200; -3586440, -164280, 56400; 1231200, 56400, -19363],[2280, 120, 1],[173, 208, 6, 1, 3, -1, -5, 0, 31, 15, 83, 22, 39, 7, 12, 244, 105, 499, 26, 957, 219, 905; 122519, 147345, 4267, 717, 2185, -706, -3648, -12, 21242, 10412, 57798, 15361, 27303, 4925, 8475, 172463, 74242, 352944, 18396, 677350, 155044, 640794; 367860, 442396, 12810, 2152, 6555, -2120, -10944, -35, 63840, 31280, 173622, 46140, 82004, 14790, 25448, 517845, 222920, 1059744, 55235, 2033760, 465520, 1923978],138,49]
%
% END OF LATTICE L139.49
%
%
% LATTICE L139.50
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-38760, 2280, -4560; 2280, 1680, 4320; -4560, 4320, 8513],[2280, 120, 1],[4207, 4951, 97, 1, -142, -20, 226, 72, 2832, 974, 2422, 1163, 1851, 261, 357, 13746, 2884, 13378, 1360, 24376, 5470, 11182; 37779, 44460, 871, 9, -1273, -179, 2033, 647, 25441, 8749, 21755, 10446, 16625, 2344, 3206, 123443, 25899, 120137, 12213, 218899, 49121, 100415; -16920, -19912, -390, -4, 570, 80, -912, -290, -11400, -3920, -9747, -4680, -7448, -1050, -1436, -55290, -11600, -53808, -5470, -98040, -22000, -44973],138,50]
%
% END OF LATTICE L139.50
%
%
% LATTICE L139.51
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[678849380022570, 353070296163690, 174724747760580; 353070296163690, 183632242588140, 90874530130530; 174724747760580, 90874530130530, 44971297578533],[570, 570, 1],[189, 55, 472, 1837, 4445, 19124, 5018, 10411, 10588, 47682, 10567, 39441, 2587, 2170, 805, 839, 2012, 266, 157, -20, -126, 1; -1298483, -360070, -3028866, -11475295, -27691944, -119015459, -31198273, -64667850, -65704129, -295689855, -65505383, -244371112, -16017903, -13349107, -4902678, -5064002, -12008325, -1557673, -844042, 192237, 886341, -6509; 2623140, 727388, 6118665, 23181254, 55940475, 240422960, 63023568, 130635355, 132728700, 597322000, 132327171, 493653060, 32357692, 26966415, 9903826, 10229685, 24257680, 3146592, 1704965, -388380, -1790560, 13149],138,51]
%
% END OF LATTICE L139.51
%
%
% LATTICE L139.52
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1140, 216600, -1140; 216600, -37652205, 198075; -1140, 198075, -1042],[1140, 285, 1],[2407, 153, 179, 18, 19, 0, -1, -1, 9, 87, 103, 263, 25, 177, 160, 693, 712, 179, 1425, 347, 1515, 1321; 2262, 144, 172, 18, 20, 1, -1, -4, 7, 73, 88, 228, 22, 160, 148, 644, 663, 167, 1332, 325, 1421, 1240; 427215, 27197, 32490, 3401, 3780, 190, -189, -760, 1320, 13775, 16608, 43035, 4153, 30210, 27949, 121620, 125210, 31539, 251560, 61380, 268375, 234192],138,52]
%
% END OF LATTICE L139.52
%
%
% LATTICE L139.53
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-185594280, -17150160, 129960; -17150160, -1584296, 12008; 129960, 12008, -91],[2280, 152, 1],[457, 446, 23, 113, 7, 43, 7, -1, -1, -1, 2, 8, 19, 8, 352, 55, 701, 303, 373, 125, 1675, 308; 2016, 1965, 100, 480, 29, 171, 25, -9, -5, -3, 10, 39, 90, 37, 1575, 245, 3117, 1345, 1653, 553, 7401, 1360; 918232, 895800, 46018, 224580, 13814, 83904, 13280, -2622, -2088, -1824, 4175, 16568, 39000, 16302, 710220, 110826, 1411776, 609920, 750462, 251368, 3367104, 619025],138,53]
%
% END OF LATTICE L139.53
%
%
% LATTICE L139.54
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-432757680, 72255480, 35613600; 72255480, -12064088, -5946392; 35613600, -5946392, -2930407],[2280, 152, 1],[250077, 243844, 12460, 60307, 1840, 22073, 3393, -427, -567, 1, 2551, 4818, 11051, 4533, 194588, 15153, 385759, 166537, 102385, 68539, 917621, 337309; 1250811, 1219635, 62321, 301635, 9203, 110400, 16970, -2136, -2836, 6, 12760, 24099, 55275, 22673, 973275, 75791, 1929456, 832970, 512100, 342812, 4589670, 1687120; 501068, 488580, 24966, 120840, 3687, 44232, 6800, -855, -1136, 0, 5110, 9652, 22140, 9082, 389880, 30361, 772920, 333680, 205143, 137328, 1838592, 675850],138,54]
%
% END OF LATTICE L139.54
%
%
% LATTICE L139.55
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[350633220, 1211820, -86446200; 1211820, 760, -301340; -86446200, -301340, 21310781],[1140, 380, 1],[-2098890, -413996, -118388, -135590, -24068, -177511, -8095, -16118, 289, 16189, 795, 0, -5782, -21538, -284188, -115858, -1501601, -131831, -823438, -280141, -3794191, -280647; 6325979, 1247769, 356817, 408663, 72540, 535011, 24398, 48579, -871, -48792, -2396, 1, 17427, 64915, 856533, 349192, 4525773, 397334, 2481813, 844335, 11435556, 845860; -8424600, -1661712, -475190, -544236, -96605, -712500, -32492, -64695, 1160, 64980, 3191, 0, -23208, -86450, -1140684, -465035, -6027180, -529148, -3305145, -1124440, -15229260, -1126471],138,55]
%
% END OF LATTICE L139.55
%
%
% LATTICE L139.56
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-298618440, -37544760, 394440; -37544760, -4719885, 49590; 394440, 49590, -521],[2280, 285, 1],[2407, 153, 179, 9, 19, 0, -1, -1, 9, 87, 103, 263, 25, 177, 80, 693, 712, 179, 1425, 347, 1515, 1321; 11890, 756, 888, 45, 96, 1, -5, -8, 43, 421, 500, 1280, 122, 868, 394, 3416, 3511, 883, 7032, 1713, 7481, 6524; 2953740, 187774, 220020, 11096, 23520, 95, -1233, -1520, 10905, 105925, 125556, 320910, 30536, 216600, 98059, 849720, 873145, 219543, 1748000, 425715, 1858865, 1620924],138,56]
%
% END OF LATTICE L139.56
%
%
% LATTICE L139.57
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2280, 216600, -2280; 216600, -20152635, 212040; -2280, 212040, -2231],[2280, 285, 1],[2486, 158, 369, 37, 39, 0, -2, -1, 19, 182, 215, 274, 26, 367, 331, 1433, 1472, 370, 2945, 717, 3130, 2729; 1131, 72, 172, 18, 20, 1, -1, -4, 7, 73, 88, 114, 11, 160, 148, 644, 663, 167, 1332, 325, 1421, 1240; 104880, 6677, 15960, 1672, 1860, 95, -93, -380, 645, 6745, 8136, 10545, 1018, 14820, 13718, 59700, 61465, 15483, 123500, 30135, 131765, 114984],138,57]
%
% END OF LATTICE L139.57
%
%
% LATTICE L139.58
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[384104760, -6582360, -506160; -6582360, -431376, 8664; -506160, 8664, 667],[2280, 456, 1],[-10051, -3187, -357, -1, 72, 794, 1088, 219, 370, 1284, 1156, 571, 27, -275, -3159, -704, -5850, -7408, -1483, -2898, -12660, -13796; 142, 45, 5, 0, -1, -11, -15, -3, -5, -17, -15, -7, 0, 4, 45, 10, 83, 105, 21, 41, 179, 195; -7629108, -2419060, -270978, -760, 54651, 602680, 825840, 166231, 280848, 974624, 877470, 433428, 20500, -208734, -2397800, -534363, -4440376, -5622960, -1125655, -2199696, -9609440, -10471710],138,58]
%
% END OF LATTICE L139.58
%
%
% LATTICE L139.59
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-825360, 6828600, -45600; 6828600, -47720856, 318744; -45600, 318744, -2129],[2280, 456, 1],[-90, -29, -4, -2, 1, 7, 11, 5, 5, 21, 11, 15, 4, -1, -23, -11, -47, -61, -25, -25, -111, -61; 8975, 2885, 387, 185, -96, -664, -1030, -462, -452, -1854, -955, -1265, -315, 127, 2385, 1124, 4776, 6170, 2518, 2508, 11106, 6095; 1345656, 432560, 58026, 27740, -14394, -99560, -154440, -69274, -67776, -278008, -143205, -189696, -47240, 19038, 357580, 168522, 716072, 925080, 377530, 376032, 1665160, 913845],138,59]
%
% END OF LATTICE L139.59
%
%
% LATTICE L139.60
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[111720, -20685300, -5152800; -20685300, 3830024940, 954076260; -5152800, 954076260, 237664643],[1140, 1140, 1],[-95861, -6077, -3423, -659, -180, -63, -2, -127, -551, -4504, -1276, -12559, -1151, -3805, -6569, -7048, -28849, -7226, -14329, -13905, -60548, -13180; -188512, -11946, -6692, -1272, -341, -95, -3, -261, -1109, -9017, -2550, -25058, -2292, -7546, -12966, -13897, -56857, -14235, -28215, -27367, -119125, -25926; 754680, 47824, 26790, 5092, 1365, 380, 12, 1045, 4440, 36100, 10209, 100320, 9176, 30210, 51908, 55635, 227620, 56988, 112955, 109560, 476900, 103791],138,60]
%
% END OF LATTICE L139.60
%
%
% LATTICE L139.61
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[4560, -2280, 0; -2280, -9183080, 37240; 0, 37240, -151],[2280, 760, 1],[19, 8, 15, 107, 81, 1019, 87, 529, 175, 2323, 85, 626, 121, 28, 22, 5, 13, -1, -13, -3, -1, 1; 37, 15, 27, 177, 132, 1650, 140, 846, 278, 3672, 134, 983, 189, 41, 27, 4, -18, -4, -30, -6, 0, 2; 9120, 3696, 6650, 43548, 32470, 405840, 34432, 208050, 68360, 902880, 32947, 241680, 46464, 10070, 6612, 970, -4560, -992, -7410, -1480, 0, 493],138,61]
%
% END OF LATTICE L139.61
%
%
% LATTICE L139.62
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[4560, -823080, -410400; -823080, 141322760, 70465680; -410400, 70465680, 35135261],[2280, 760, 1],[9, 4, 8, 67, 26, 661, 57, 175, 117, 1565, 115, 426, 83, 21, 20, 3, 35, 1, -1, -1, 1, 1; -3221, -1071, -1421, -909, 247, 12510, 1588, 6396, 5346, 81864, 6422, 25961, 5619, 2937, 5457, 1269, 23874, 1444, 2700, 718, 0, -358; 6460, 2148, 2850, 1824, -495, -25080, -3184, -12825, -10720, -164160, -12878, -52060, -11268, -5890, -10944, -2545, -47880, -2896, -5415, -1440, 0, 718],138,62]
%
% END OF LATTICE L139.62
%
%
% LATTICE L139.63
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-88049040, -14243160, 4799400; -14243160, -2300520, 775200; 4799400, 775200, -261217],[2280, 2280, 1],[1118, 71, 41, 8, 2, -1, -1, 0, 9, 85, 25, 127, 12, 42, 75, 81, 665, 167, 166, 323, 1409, 307; 624999, 39699, 22987, 4509, 1135, -506, -568, -32, 4918, 46852, 13810, 70281, 6653, 23365, 41843, 45217, 371322, 93272, 92736, 180490, 787484, 171598; 1875300, 119116, 68970, 13528, 3405, -1520, -1704, -95, 14760, 140600, 41442, 210900, 19964, 70110, 125552, 135675, 1114160, 279864, 278255, 541560, 2362840, 514878],138,63]
%
% END OF LATTICE L139.63
%
%
% LATTICE L139.64
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-108587280, -80791800, -40253400; -80791800, -60107640, -29947800; -40253400, -29947800, -14921077],[2280, 2280, 1],[1131, 72, 43, 9, 5, 1, -1, -1, 7, 73, 11, 114, 11, 40, 74, 161, 663, 167, 333, 325, 1421, 155; -1065931, -67809, -40101, -8229, -4446, -380, 946, 664, -7184, -72422, -10826, -111479, -10685, -38393, -70265, -152542, -627572, -157934, -314640, -306792, -1340470, -146162; 2136360, 135904, 80370, 16492, 8910, 760, -1896, -1330, 14400, 145160, 21699, 223440, 21416, 76950, 140828, 305730, 1257800, 316536, 630610, 614880, 2686600, 292941],138,64]
%
% END OF LATTICE L139.64
%

\medskip%
%------------------------------WEYL-GROUP-W140--------------------------------
%
\leavevmode\llap{}%
$W_{140}$%
\qquad\llap{4} lattices, $\chi=6$%
\hfill%
$\infty\slashtwo\infty|\rtimes D_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L140.1
%
\leavevmode%
${L_{140.1}}$%
{} : {$1\above{1pt}{1pt}{2}{0}4\above{1pt}{1pt}{1}{1}$}\EasyButWeakLineBreak%
{${4}\above{1pt}{1pt}{1,0}{\infty a}{4}\above{1pt}{1pt}{}{2}{1}\above{1pt}{1pt}{4,1}{\infty}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-44\\-16\\12
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-16\\-5\\4
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
12\\4\\-3
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\2\\6
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\0\\-4
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\-2\\-3
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-44, -16, 12; -16, -5, 4; 12, 4, -3],[4, 1, 1],[1, -1, 0; 2, 0, -2; 6, -4, -3],139,1]
%
% END OF LATTICE L140.1
%
\hbox{}\par\smallskip%
%
% LATTICE L140.2
%
\leavevmode%
${L_{140.2}}$%
{} : {$1\above{1pt}{1pt}{2}{{\rm II}}8\above{1pt}{1pt}{1}{1}$}\EasyButWeakLineBreak%
{${8}\above{1pt}{1pt}{1,0}{\infty a}{8}\above{1pt}{1pt}{r}{2}{2}\above{1pt}{1pt}{4,1}{\infty a}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
8\\0\\0
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\1
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\1\\-6
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\4\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\0\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\-4\\-1
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[8, 0, 0; 0, 0, 1; 0, 1, -6],[8, 1, 1],[-1, 1, 0; 4, 0, -4; 0, 0, -1],139,2]
%
% END OF LATTICE L140.2
%
%
% LATTICE L140.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[12, 16, 0; 16, 36, 4; 0, 4, 1],[4, 4, 1],[-1, 0, -2; 1, 0, 1; -2, -1, -4],139,3]
%
% END OF LATTICE L140.3
%
%
% LATTICE L140.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-720, 56, 104; 56, 0, -8; 104, -8, -15],[8, 8, 1],[2, -1, -1; -1, 0, 2; 14, -7, -8],139,4]
%
% END OF LATTICE L140.4
%

\medskip%
%------------------------------WEYL-GROUP-W141--------------------------------
%
\leavevmode\llap{}%
$W_{141}$%
\qquad\llap{17} lattices, $\chi=6$%
\hfill%
$\slashtwo2\slashinfty2\rtimes D_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L141.1
%
\leavevmode%
${L_{141.1}}$%
{} : {$1\above{1pt}{1pt}{2}{0}8\above{1pt}{1pt}{1}{1}$}\EasyButWeakLineBreak%
{${1}\above{1pt}{1pt}{r}{2}{4}\above{1pt}{1pt}{*}{2}{8}\above{1pt}{1pt}{1,0}{\infty b}{8}\above{1pt}{1pt}{}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-696\\72\\80
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
72\\-7\\-9
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
80\\-9\\-8
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\5\\4
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3\\-18\\-10
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3\\-16\\-12
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7\\40\\24
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-696, 72, 80; 72, -7, -9; 80, -9, -8],[8, 1, 1],[1, -3, -3, 7; 5, -18, -16, 40; 4, -10, -12, 24],140,1]
%
% END OF LATTICE L141.1
%
\hbox{}\par\smallskip%
%
% LATTICE L141.2
%
\leavevmode%
${L_{141.2}}$%
{} : {$[1\above{1pt}{1pt}{-}{}2\above{1pt}{1pt}{1}{}]\above{1pt}{1pt}{}{6}16\above{1pt}{1pt}{-}{3}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${16}\above{1pt}{1pt}{*}{2}{4}\above{1pt}{1pt}{l}{2}{2}\above{1pt}{1pt}{8,3}{\infty}{8}\above{1pt}{1pt}{s}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-848\\160\\32
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
160\\-30\\-6
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
32\\-6\\-1
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-4\\-8
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-6\\2
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\-1\\4
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\6\\-4
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-848, 160, 32; 160, -30, -6; 32, -6, -1],[16, 2, 1],[-1, -1, 0, 1; -4, -6, -1, 6; -8, 2, 4, -4],140,2]
%
% END OF LATTICE L141.2
%
\hbox{}\par\smallskip%
%
% LATTICE L141.3
%
\leavevmode%
${L_{141.3}}$%
{} : {$[1\above{1pt}{1pt}{1}{}2\above{1pt}{1pt}{1}{}]\above{1pt}{1pt}{}{2}16\above{1pt}{1pt}{1}{7}$}\spacer%
\instructions{m}%
\EasyButWeakLineBreak%
{${16}\above{1pt}{1pt}{l}{2}{1}\above{1pt}{1pt}{}{2}{2}\above{1pt}{1pt}{8,7}{\infty}{8}\above{1pt}{1pt}{*}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1296\\208\\96
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
208\\-30\\-16
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
96\\-16\\-7
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3\\-4\\-32
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\2\\9
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\3\\20
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3\\-6\\-28
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-1296, 208, 96; 208, -30, -16; 96, -16, -7],[16, 2, 1],[-3, 1, 2, -3; -4, 2, 3, -6; -32, 9, 20, -28],140,3]
%
% END OF LATTICE L141.3
%
\hbox{}\par\smallskip%
%
% LATTICE L141.4
%
\leavevmode%
${L_{141.4}}$%
{} : {$[1\above{1pt}{1pt}{-}{}2\above{1pt}{1pt}{1}{}]\above{1pt}{1pt}{}{4}16\above{1pt}{1pt}{-}{5}$}\spacer%
\instructions{m}%
\EasyButWeakLineBreak%
{${16}\above{1pt}{1pt}{s}{2}{4}\above{1pt}{1pt}{*}{2}{8}\above{1pt}{1pt}{8,3}{\infty z}{2}\above{1pt}{1pt}{r}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-304\\32\\32
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
32\\-2\\-4
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
32\\-4\\-3
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\0\\8
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-4\\-6
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-2\\-8
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\3\\6
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-304, 32, 32; 32, -2, -4; 32, -4, -3],[16, 2, 1],[1, -1, -1, 1; 0, -4, -2, 3; 8, -6, -8, 6],140,4]
%
% END OF LATTICE L141.4
%
\hbox{}\par\smallskip%
%
% LATTICE L141.5
%
\leavevmode%
${L_{141.5}}$%
{} : {$1\above{1pt}{1pt}{1}{1}8\above{1pt}{1pt}{1}{7}64\above{1pt}{1pt}{1}{1}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${64}\above{1pt}{1pt}{s}{2}{4}\above{1pt}{1pt}{*}{2}{32}\above{1pt}{1pt}{16,7}{\infty z}{8}\above{1pt}{1pt}{b}{2}$}%
\nopagebreak\par%
shares genus with {$ {L_{141.6}}$}%
; isometric to own %
2-dual\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-17344\\512\\512
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
512\\-8\\-16
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
512\\-16\\-15
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\0\\32
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-4\\-30
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-2\\-32
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\7\\60
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-17344, 512, 512; 512, -8, -16; 512, -16, -15],[64, 8, 1],[1, -1, -1, 2; 0, -4, -2, 7; 32, -30, -32, 60],140,5]
%
% END OF LATTICE L141.5
%
\hbox{}\par\smallskip%
%
% LATTICE L141.6
%
\leavevmode%
${L_{141.6}}$%
{} : {$1\above{1pt}{1pt}{1}{1}8\above{1pt}{1pt}{1}{7}64\above{1pt}{1pt}{1}{1}$}\EasyButWeakLineBreak%
{${64}\above{1pt}{1pt}{}{2}{1}\above{1pt}{1pt}{r}{2}{32}\above{1pt}{1pt}{16,15}{\infty z}{8}\above{1pt}{1pt}{l}{2}$}%
\nopagebreak\par%
shares genus with {$ {L_{141.5}}$}%
; isometric to own %
2-dual\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-266176\\2048\\4096
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2048\\-8\\-32
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4096\\-32\\-63
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\0\\64
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-4\\-63
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-2\\-64
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4\\15\\252
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-266176, 2048, 4096; 2048, -8, -32; 4096, -32, -63],[64, 8, 1],[1, -1, -1, 4; 0, -4, -2, 15; 64, -63, -64, 252],140,6]
%
% END OF LATTICE L141.6
%
%
% LATTICE L141.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[4, 0, 0; 0, -2, -2; 0, -2, -1],[4, 2, 1],[0, -1, 0, 1; -1, 0, 1, -1; 1, 0, -2, 0],140,7]
%
% END OF LATTICE L141.7
%
%
% LATTICE L141.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-424, 32, 80; 32, -2, -6; 80, -6, -15],[8, 2, 1],[-1, -1, 1, 0; 1, -4, -2, 2; -6, -4, 6, -1],140,8]
%
% END OF LATTICE L141.8
%
%
% LATTICE L141.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[8, 8, 0; 8, -6, -4; 0, -4, -1],[8, 2, 1],[1, -1, -1, 1; 0, 1, 0, -1; 0, -4, -2, 3],140,9]
%
% END OF LATTICE L141.9
%
%
% LATTICE L141.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[16, 0, 0; 0, -8, -8; 0, -8, -7],[16, 8, 1],[-1, 0, 1, 0; 0, -1, -1, 3; 0, 1, 0, -4],140,10]
%
% END OF LATTICE L141.10
%
%
% LATTICE L141.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[16, 0, 16; 0, -2, -8; 16, -8, -15],[16, 2, 1],[1, -1, -1, 2; 0, -4, -2, 7; 0, 1, 0, -2],140,11]
%
% END OF LATTICE L141.11
%
%
% LATTICE L141.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[8, 0, 0; 0, -12, -4; 0, -4, -1],[8, 4, 1],[0, -1, -1, 1; 1, 0, -2, 0; -4, -2, 4, 0],140,12]
%
% END OF LATTICE L141.12
%
%
% LATTICE L141.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-8, 16, 8; 16, -12, -12; 8, -12, -7],[8, 4, 1],[-2, 1, 5, -3; 1, 0, -2, 0; -4, 1, 8, -4],140,13]
%
% END OF LATTICE L141.13
%
%
% LATTICE L141.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-152, -256, 48; -256, -424, 80; 48, 80, -15],[8, 8, 1],[1, -2, -1, 1; -2, -1, 1, 0; -8, -12, 2, 3],140,14]
%
% END OF LATTICE L141.14
%
%
% LATTICE L141.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[16, -32, 0; -32, 72, 0; 0, 0, -1],[16, 8, 1],[-2, 1, 2, -3; -1, 0, 1, -1; -2, 0, 0, -4],140,15]
%
% END OF LATTICE L141.15
%
%
% LATTICE L141.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-816, -96, 64; -96, 8, 8; 64, 8, -5],[16, 8, 1],[1, -3, -2, 3; -1, 0, 1, -1; 10, -40, -24, 36],140,16]
%
% END OF LATTICE L141.16
%
%
% LATTICE L141.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3888, 224, 272; 224, -8, -16; 272, -16, -19],[16, 8, 1],[-3, 1, 3, -2; -4, 0, 3, -1; -40, 14, 40, -28],140,17]
%
% END OF LATTICE L141.17
%

\medskip%
%------------------------------WEYL-GROUP-W142--------------------------------
%
\leavevmode\llap{}%
$W_{142}$%
\qquad\llap{22} lattices, $\chi=9$%
\hfill%
$4\infty22$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L142.1
%
\leavevmode%
${L_{142.1}}$%
{} : {$1\above{1pt}{1pt}{2}{{\rm II}}4\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{2}{}9\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${2}\above{1pt}{1pt}{*}{4}{4}\above{1pt}{1pt}{3,2}{\infty b}{4}\above{1pt}{1pt}{r}{2}{18}\above{1pt}{1pt}{b}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1116\\288\\108
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
288\\-56\\-25
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
108\\-25\\-10
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2\\6\\-37
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\2\\-16
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\-8\\52
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\0\\9
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-1116, 288, 108; 288, -56, -25; 108, -25, -10],[36, 1, 1],[-2, -1, 3, 1; 6, 2, -8, 0; -37, -16, 52, 9],141,1]
%
% END OF LATTICE L142.1
%
\hbox{}\par\smallskip%
%
% LATTICE L142.2
%
\leavevmode%
${L_{142.2}}$%
{} : {$1\above{1pt}{1pt}{-2}{2}8\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{2}{}9\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${4}\above{1pt}{1pt}{*}{4}{2}\above{1pt}{1pt}{12,11}{\infty a}{8}\above{1pt}{1pt}{s}{2}{36}\above{1pt}{1pt}{*}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-47592\\-16128\\1728
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-16128\\-5465\\585
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1728\\585\\-62
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
13\\-42\\-34
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-10\\32\\23
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-21\\68\\56
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
17\\-54\\-36
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-47592, -16128, 1728; -16128, -5465, 585; 1728, 585, -62],[72, 1, 1],[13, -10, -21, 17; -42, 32, 68, -54; -34, 23, 56, -36],141,2]
%
% END OF LATTICE L142.2
%
\hbox{}\par\smallskip%
%
% LATTICE L142.3
%
\leavevmode%
${L_{142.3}}$%
{} : {$1\above{1pt}{1pt}{2}{2}8\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{2}{}9\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{m}%
\EasyButWeakLineBreak%
{${1}\above{1pt}{1pt}{}{4}{2}\above{1pt}{1pt}{12,11}{\infty b}{8}\above{1pt}{1pt}{l}{2}{9}\above{1pt}{1pt}{}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-38088\\576\\648
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
576\\-7\\-10
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
648\\-10\\-11
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\6\\53
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\1\\-1
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-8\\-52
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\9\\108
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-38088, 576, 648; 576, -7, -10; 648, -10, -11],[72, 1, 1],[1, 0, -1, 2; 6, 1, -8, 9; 53, -1, -52, 108],141,3]
%
% END OF LATTICE L142.3
%
%
% LATTICE L142.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-1764, 171, 234; 171, -14, -23; 234, -23, -31],[9, 1, 1],[-4, 4, 3, -8; -3, 4, 2, -9; -28, 27, 21, -54],141,4]
%
% END OF LATTICE L142.4
%
%
% LATTICE L142.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-234, 72, -36; 72, -22, 11; -36, 11, -5],[18, 1, 1],[1, 0, -1, 1; 3, 1, -4, 0; -1, 2, -2, -9],141,5]
%
% END OF LATTICE L142.5
%
%
% LATTICE L142.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-65700, 1008, 1440; 1008, -14, -23; 1440, -23, -31],[36, 1, 1],[-2, 2, 3, -4; -39, 40, 58, -81; -64, 63, 96, -126],141,6]
%
% END OF LATTICE L142.6
%
%
% LATTICE L142.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[720, 54, 342; 54, 14, 28; 342, 28, 163],[18, 2, 1],[-10, -1, -5, -49; -5, 0, -3, -27; 22, 2, 11, 108],141,7]
%
% END OF LATTICE L142.7
%
%
% LATTICE L142.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[72, 558, 81; 558, 4545, 657; 81, 657, 95],[9, 9, 1],[2, 7, 2, 0; 1, 7, 5, 1; -9, -54, -36, -7],141,8]
%
% END OF LATTICE L142.8
%
%
% LATTICE L142.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[662328, -52092, 144540; -52092, 4100, -11368; 144540, -11368, 31543],[36, 4, 1],[15, 73, 39, 55; 2, 7, 2, 0; -68, -332, -178, -252],141,9]
%
% END OF LATTICE L142.9
%
%
% LATTICE L142.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[110448, 2484, 23652; 2484, 56, 532; 23652, 532, 5065],[36, 4, 1],[4, 3, 1, 14; 13, 0, 3, 63; -20, -14, -5, -72],141,10]
%
% END OF LATTICE L142.10
%
%
% LATTICE L142.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[738, 18, 306; 18, 18, 9; 306, 9, 127],[18, 9, 1],[11, 0, 15, 7; 2, 1, 2, 1; -27, 0, -36, -17],141,11]
%
% END OF LATTICE L142.11
%
%
% LATTICE L142.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-36, -72, -36; -72, -126, -63; -36, -63, -31],[36, 9, 1],[-2, 0, 3, 0; 1, 4, -2, -1; 0, -9, 0, 2],141,12]
%
% END OF LATTICE L142.12
%
%
% LATTICE L142.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-90, -2070, -972; -2070, -43164, -20268; -972, -20268, -9517],[18, 18, 1],[-1, 2, -1, -1; 93, -17, -38, 16; -198, 36, 81, -34],141,13]
%
% END OF LATTICE L142.13
%
%
% LATTICE L142.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-12924, -1152, 720; -1152, -90, 63; 720, 63, -40],[36, 9, 1],[6, -1, -5, 1; 11, 0, -12, 1; 126, -18, -108, 20],141,14]
%
% END OF LATTICE L142.14
%
%
% LATTICE L142.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1368, 0, 648; 0, -8, 0; 648, 0, 307],[72, 8, 1],[-2, 15, 1, -17; 1, 3, 0, 0; 4, -32, -2, 36],141,15]
%
% END OF LATTICE L142.15
%
%
% LATTICE L142.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[72, 0, 0; 0, 8, 8; 0, 8, 7],[72, 8, 1],[0, -1, 0, 1; 1, 7, 1, 0; 0, -8, -2, 0],141,16]
%
% END OF LATTICE L142.16
%
%
% LATTICE L142.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-75240, 3456, 2160; 3456, -153, -99; 2160, -99, -62],[72, 9, 1],[-3, -4, 5, 1; 2, 8, -4, -2; -108, -153, 180, 38],141,17]
%
% END OF LATTICE L142.17
%
%
% LATTICE L142.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-11592, 1152, -4032; 1152, -99, 414; -4032, 414, -1391],[72, 9, 1],[39, -4, -31, 10; 77, -9, -60, 20; -90, 9, 72, -23],141,18]
%
% END OF LATTICE L142.18
%
%
% LATTICE L142.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[180, 180, 36; 180, 1656, 396; 36, 396, 95],[36, 36, 1],[2, 7, 2, 0; -9, -35, -13, -1; 36, 144, 54, 4],141,19]
%
% END OF LATTICE L142.19
%
%
% LATTICE L142.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1440, -12348, -2664; -12348, 107640, 23220; -2664, 23220, 5009],[36, 36, 1],[4, 1, 1, 2; -85, 4, -29, -55; 396, -18, 135, 256],141,20]
%
% END OF LATTICE L142.20
%
%
% LATTICE L142.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1872, 7560, -144; 7560, 30168, -576; -144, -576, 11],[72, 72, 1],[1, 3, 0, 0; -1, 2, -1, -1; -36, 144, -54, -52],141,21]
%
% END OF LATTICE L142.21
%
%
% LATTICE L142.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1872, 2376, 792; 2376, 2952, 1008; 792, 1008, 335],[72, 72, 1],[1, -33, 9, 8; -1, 2, -1, -1; 0, 72, -18, -16],141,22]
%
% END OF LATTICE L142.22
%

\medskip%
%------------------------------WEYL-GROUP-W143--------------------------------
%
\leavevmode\llap{}%
$W_{143}$%
\qquad\llap{22} lattices, $\chi=18$%
\hfill%
$2\infty\slashtwo\infty2|\rtimes D_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L143.1
%
\leavevmode%
${L_{143.1}}$%
{} : {$1\above{1pt}{1pt}{2}{{\rm II}}4\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{-2}{}9\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${2}\above{1pt}{1pt}{l}{2}{36}\above{1pt}{1pt}{1,0}{\infty}{36}\above{1pt}{1pt}{*}{2}{4}\above{1pt}{1pt}{3,1}{\infty a}{4}\above{1pt}{1pt}{r}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2556\\900\\144
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
900\\-316\\-51
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
144\\-51\\-8
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\5\\21
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
19\\36\\108
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\0\\-18
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3\\-6\\-16
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\0\\16
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-2556, 900, 144; 900, -316, -51; 144, -51, -8],[36, 1, 1],[3, 19, -1, -3, 1; 5, 36, 0, -6, 0; 21, 108, -18, -16, 16],142,1]
%
% END OF LATTICE L143.1
%
\hbox{}\par\smallskip%
%
% LATTICE L143.2
%
\leavevmode%
${L_{143.2}}$%
{} : {$1\above{1pt}{1pt}{-2}{2}8\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{-2}{}9\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${4}\above{1pt}{1pt}{s}{2}{72}\above{1pt}{1pt}{4,1}{\infty z}{18}\above{1pt}{1pt}{b}{2}{2}\above{1pt}{1pt}{12,7}{\infty b}{8}\above{1pt}{1pt}{s}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-52200\\-25488\\576
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-25488\\-12445\\281
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
576\\281\\-6
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\-2\\2
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-121\\252\\180
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-52\\108\\63
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\2\\-3
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
25\\-52\\-36
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-52200, -25488, 576; -25488, -12445, 281; 576, 281, -6],[72, 1, 1],[1, -121, -52, -1, 25; -2, 252, 108, 2, -52; 2, 180, 63, -3, -36],142,2]
%
% END OF LATTICE L143.2
%
\hbox{}\par\smallskip%
%
% LATTICE L143.3
%
\leavevmode%
${L_{143.3}}$%
{} : {$1\above{1pt}{1pt}{2}{2}8\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{-2}{}9\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{m}%
\EasyButWeakLineBreak%
{${1}\above{1pt}{1pt}{r}{2}{72}\above{1pt}{1pt}{4,3}{\infty z}{18}\above{1pt}{1pt}{s}{2}{2}\above{1pt}{1pt}{12,7}{\infty a}{8}\above{1pt}{1pt}{l}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-334728\\3456\\1656
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3456\\-35\\-18
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1656\\-18\\-7
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-71\\-54
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5\\360\\252
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
11\\783\\585
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\213\\161
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-72\\-52
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-334728, 3456, 1656; 3456, -35, -18; 1656, -18, -7],[72, 1, 1],[-1, 5, 11, 3, -1; -71, 360, 783, 213, -72; -54, 252, 585, 161, -52],142,3]
%
% END OF LATTICE L143.3
%
%
% LATTICE L143.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[9, 0, 0; 0, -1, -3; 0, -3, -8],[9, 1, 1],[1, 1, 0, -1, 1; 5, 0, -3, 0, 18; -3, -1, 1, 0, -9],142,4]
%
% END OF LATTICE L143.4
%
%
% LATTICE L143.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-90, 36, -36; 36, -14, 15; -36, 15, -13],[18, 1, 1],[3, 3, -2, -4, 13; 5, 6, -3, -9, 18; -3, -2, 2, 0, -18],142,5]
%
% END OF LATTICE L143.5
%
%
% LATTICE L143.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-9252, 360, 180; 360, -14, -7; 180, -7, -3],[36, 1, 1],[0, 5, 2, 0, -1; -1, 126, 54, 1, -26; 2, 0, -9, -3, 0],142,6]
%
% END OF LATTICE L143.6
%
%
% LATTICE L143.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[3168, 198, 1530; 198, 14, 96; 1530, 96, 739],[18, 2, 1],[-14, -8, -1, -25, -46; -7, -3, 0, -18, -27; 30, 17, 2, 54, 99],142,7]
%
% END OF LATTICE L143.7
%
%
% LATTICE L143.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[72, -27, 0; -27, 9, 0; 0, 0, 1],[9, 9, 1],[4, 3, 0, 0, 1; 9, 8, 1, 0, 2; 9, 9, 0, -1, 1],142,8]
%
% END OF LATTICE L143.8
%
%
% LATTICE L143.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2736, -180, 504; -180, 32, -24; 504, -24, 97],[36, 4, 1],[23, 25, 4, 3, 10; 49, 54, 9, 6, 21; -108, -117, -18, -14, -47],142,9]
%
% END OF LATTICE L143.9
%
%
% LATTICE L143.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1656, 756, 396; 756, 516, 188; 396, 188, 95],[36, 4, 1],[-1, 91, 143, 38, 11; 0, 18, 27, 7, 2; 4, -414, -648, -172, -50],142,10]
%
% END OF LATTICE L143.10
%
%
% LATTICE L143.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[4626, 270, 1998; 270, 18, 117; 1998, 117, 863],[18, 9, 1],[19, 15, 0, 6, 17; 6, 8, 1, 1, 4; -45, -36, 0, -14, -40],142,11]
%
% END OF LATTICE L143.11
%
%
% LATTICE L143.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-6228, -612, 468; -612, -54, 45; 468, 45, -35],[36, 9, 1],[-2, -1, 1, 5, 5; -7, -2, 3, 12, 6; -36, -16, 17, 81, 72],142,12]
%
% END OF LATTICE L143.12
%
%
% LATTICE L143.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-234, -3294, -1548; -3294, -35244, -16560; -1548, -16560, -7781],[18, 18, 1],[-3, -1, 2, 0, -1; 347, 165, -237, -47, 87; -738, -351, 504, 100, -185],142,13]
%
% END OF LATTICE L143.13
%
%
% LATTICE L143.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[15012, 1476, 1188; 1476, 144, 117; 1188, 117, 94],[36, 9, 1],[-7, -3, 1, 3, -9; 20, 8, -2, -2, 32; 63, 28, -10, -36, 72],142,14]
%
% END OF LATTICE L143.14
%
%
% LATTICE L143.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-113904, -4968, 360; -4968, -216, 16; 360, 16, -1],[72, 8, 1],[-1, -4, -1, 1, 0; 21, 81, 18, -20, 1; -32, -162, -72, 40, 10],142,15]
%
% END OF LATTICE L143.15
%
%
% LATTICE L143.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-140904, -1008, 2664; -1008, 24, 32; 2664, 32, -45],[72, 8, 1],[12, 28, -11, -7, 6; -227, -531, 207, 133, -113; 548, 1278, -504, -320, 274],142,16]
%
% END OF LATTICE L143.16
%
%
% LATTICE L143.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-12456, -6840, 936; -6840, -3753, 513; 936, 513, -70],[72, 9, 1],[5, -1, -7, -2, 1; -14, 12, 24, 6, -4; -36, 72, 81, 17, -16],142,17]
%
% END OF LATTICE L143.17
%
%
% LATTICE L143.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-78984, 1584, 792; 1584, -27, -18; 792, -18, -7],[72, 9, 1],[-1, 5, 5, 1, -1; -23, 120, 117, 23, -24; -54, 252, 261, 53, -52],142,18]
%
% END OF LATTICE L143.18
%
%
% LATTICE L143.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[216, -3924, -900; -3924, 32256, 7416; -900, 7416, 1705],[36, 36, 1],[-9, 0, 1, -4, -7; 214, -3, -27, 103, 175; -936, 13, 118, -450, -765],142,19]
%
% END OF LATTICE L143.19
%
%
% LATTICE L143.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1044, -4716, -1008; -4716, 22248, 4752; -1008, 4752, 1015],[36, 36, 1],[-2, 0, -1, -7, -8; 15, 3, 16, 83, 79; -72, -14, -76, -396, -378],142,20]
%
% END OF LATTICE L143.20
%
%
% LATTICE L143.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-432, -9576, -4608; -9576, -201240, -96840; -4608, -96840, -46601],[72, 72, 1],[-3, 0, 1, -1, -4; -277, -51, 50, 104, -199; 576, 106, -104, -216, 414],142,21]
%
% END OF LATTICE L143.21
%
%
% LATTICE L143.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-21096, -24192, -10872; -24192, -27720, -12456; -10872, -12456, -5597],[72, 72, 1],[14, 2, -3, -3, 12; -93, -17, 17, 35, -67; 180, 34, -32, -72, 126],142,22]
%
% END OF LATTICE L143.22
%

\medskip%
%------------------------------WEYL-GROUP-W144--------------------------------
%
\leavevmode\llap{}%
$W_{144}$%
\qquad\llap{16} lattices, $\chi=12$%
\hfill%
$2|2\infty|\infty\rtimes D_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L144.1
%
\leavevmode%
${L_{144.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{4}4\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{1}{}9\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{3}%
\EasyButWeakLineBreak%
{${12}\above{1pt}{1pt}{}{2}{9}\above{1pt}{1pt}{}{2}{3}\above{1pt}{1pt}{12,7}{\infty}{12}\above{1pt}{1pt}{3,1}{\infty b}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-612\\-180\\-792
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-180\\-33\\-177
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-792\\-177\\-868
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
17\\100\\-36
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-4\\-27\\9
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-14\\-85\\30
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3\\-16\\6
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-612, -180, -792; -180, -33, -177; -792, -177, -868],[36, 3, 1],[17, -4, -14, -3; 100, -27, -85, -16; -36, 9, 30, 6],143,1]
%
% END OF LATTICE L144.1
%
\hbox{}\par\smallskip%
%
% LATTICE L144.2
%
\leavevmode%
${L_{144.2}}$%
{} : {$1\above{1pt}{1pt}{2}{{\rm II}}8\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{1}{}3\above{1pt}{1pt}{-}{}9\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{3}%
\EasyButWeakLineBreak%
{${24}\above{1pt}{1pt}{r}{2}{18}\above{1pt}{1pt}{b}{2}{6}\above{1pt}{1pt}{12,7}{\infty b}{24}\above{1pt}{1pt}{3,2}{\infty a}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-19368\\-3672\\-1944
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3672\\-696\\-369
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1944\\-369\\-194
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
13\\-56\\-24
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\-6\\-9
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-7\\32\\9
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-5\\20\\12
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-19368, -3672, -1944; -3672, -696, -369; -1944, -369, -194],[72, 3, 1],[13, 2, -7, -5; -56, -6, 32, 20; -24, -9, 9, 12],143,2]
%
% END OF LATTICE L144.2
%
%
% LATTICE L144.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-420, -12, -204; -12, 0, -5; -204, -5, -97],[12, 1, 1],[1, 2, 5, -5; 12, 13, 24, -30; -3, -5, -12, 12],143,3]
%
% END OF LATTICE L144.3
%
%
% LATTICE L144.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-21288, -2232, 48; -2232, -234, 5; 48, 5, 0],[24, 1, 1],[5, 2, 1, -5; -48, -19, -9, 48; -24, -2, 12, 12],143,4]
%
% END OF LATTICE L144.4
%
%
% LATTICE L144.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-108, -96, 36; -96, -81, 30; 36, 30, -11],[12, 3, 1],[1, 1, 0, -1; -4, -1, 2, 2; -8, 0, 5, 2],143,5]
%
% END OF LATTICE L144.5
%
%
% LATTICE L144.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[372, -108, 168; -108, 48, -56; 168, -56, 79],[12, 4, 1],[-19, -9, -5, -2; 27, 12, 6, 3; 60, 28, 15, 6],143,6]
%
% END OF LATTICE L144.6
%
%
% LATTICE L144.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1656, 24, 192; 24, 0, -3; 192, -3, -22],[24, 3, 1],[0, -1, -1, 1; 4, -2, -8, 4; -1, -9, -8, 8],143,7]
%
% END OF LATTICE L144.7
%
%
% LATTICE L144.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1332, 144, -324; 144, -15, 36; -324, 36, -77],[36, 3, 1],[5, 1, -1, -3; 20, 5, -2, -14; -12, -2, 3, 6],143,8]
%
% END OF LATTICE L144.8
%
%
% LATTICE L144.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[108, 312, 96; 312, 900, 276; 96, 276, 85],[12, 12, 1],[-1, -5, -4, -1; 0, -2, -1, 1; 1, 12, 8, -2],143,9]
%
% END OF LATTICE L144.9
%
%
% LATTICE L144.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1392, -24, 72; -24, 32, 16; 72, 16, 3],[24, 8, 1],[2, 1, -7, -1; -15, -8, 54, 9; 33, 16, -120, -18],143,10]
%
% END OF LATTICE L144.10
%
%
% LATTICE L144.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-936, -576, 288; -576, -66, 45; 288, 45, -28],[72, 3, 1],[-3, 1, 4, -1; -56, 17, 71, -16; -120, 38, 156, -36],143,11]
%
% END OF LATTICE L144.11
%
%
% LATTICE L144.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[252, -2412, -1800; -2412, 32016, 23664; -1800, 23664, 17495],[36, 12, 1],[27, 175, 117, -4; -80, -519, -346, 13; 111, 720, 480, -18],143,12]
%
% END OF LATTICE L144.12
%
%
% LATTICE L144.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2448, -1188, -1440; -1188, 804, 864; -1440, 864, 967],[36, 12, 1],[12, 18, 37, 7; -37, -55, -113, -22; 51, 76, 156, 30],143,13]
%
% END OF LATTICE L144.13
%
%
% LATTICE L144.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-6816, -7848, -3528; -7848, -9024, -4056; -3528, -4056, -1823],[24, 24, 1],[-3, -3, 1, 2; 17, 35, -4, -17; -32, -72, 7, 34],143,14]
%
% END OF LATTICE L144.14
%
%
% LATTICE L144.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-80640, -25848, 1728; -25848, -8160, 552; 1728, 552, -37],[72, 24, 1],[-7, -11, 2, 6; -7, -9, 2, 5; -432, -648, 123, 354],143,15]
%
% END OF LATTICE L144.15
%
%
% LATTICE L144.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-12672, -2376, -936; -2376, -384, -144; -936, -144, -53],[72, 24, 1],[-3, 1, 1, -1; 73, -21, -23, 22; -144, 40, 45, -42],143,16]
%
% END OF LATTICE L144.16
%

\medskip%
%------------------------------WEYL-GROUP-W145--------------------------------
%
\leavevmode\llap{}%
$W_{145}$%
\qquad\llap{2} lattices, $\chi=6$%
\hfill%
$\slashinfty4|4\rtimes D_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L145.1
%
\leavevmode%
${L_{145.1}}$%
{} : {$1\above{1pt}{1pt}{2}{2}16\above{1pt}{1pt}{1}{7}$}\EasyButWeakLineBreak%
{${1}\above{1pt}{1pt}{8,7}{\infty}{4}\above{1pt}{1pt}{*}{4}{2}\above{1pt}{1pt}{}{4}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-656\\-48\\64
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-48\\-3\\5
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
64\\5\\-6
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\-1\\-1
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\6\\-6
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\-4\\7
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-656, -48, 64; -48, -3, 5; 64, 5, -6],[16, 1, 1],[0, -1, 1; -1, 6, -4; -1, -6, 7],144,1]
%
% END OF LATTICE L145.1
%
%
% LATTICE L145.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[32, 16, 0; 16, 16, 0; 0, 0, -1],[16, 16, 1],[-1, 1, -1; -1, -1, 2; -8, 0, 0],144,2]
%
% END OF LATTICE L145.2
%

\medskip%
%------------------------------WEYL-GROUP-W146--------------------------------
%
\leavevmode\llap{}%
$W_{146}$%
\qquad\llap{9} lattices, $\chi=12$%
\hfill%
$\slashtwo\slashinfty\slashtwo\slashinfty\rtimes D_{4}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L146.1
%
\leavevmode%
${L_{146.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{4}16\above{1pt}{1pt}{-}{5}$}\EasyButWeakLineBreak%
{${16}\above{1pt}{1pt}{l}{2}{1}\above{1pt}{1pt}{8,5}{\infty}{4}\above{1pt}{1pt}{s}{2}{16}\above{1pt}{1pt}{4,1}{\infty z}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3632\\64\\336
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
64\\-1\\-6
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
336\\-6\\-31
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3\\-8\\-32
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\4\\-1
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\4\\10
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-16\\-8
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-3632, 64, 336; 64, -1, -6; 336, -6, -31],[16, 1, 1],[-3, 0, 1, -1; -8, 4, 4, -16; -32, -1, 10, -8],145,1]
%
% END OF LATTICE L146.1
%
\hbox{}\par\smallskip%
%
% LATTICE L146.2
%
\leavevmode%
${L_{146.2}}$%
{} : {$1\above{1pt}{1pt}{2}{0}16\above{1pt}{1pt}{1}{1}$}\EasyButWeakLineBreak%
{${16}\above{1pt}{1pt}{}{2}{1}\above{1pt}{1pt}{8,1}{\infty}{4}\above{1pt}{1pt}{*}{2}{16}\above{1pt}{1pt}{1,0}{\infty b}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1392\\112\\208
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
112\\-8\\-17
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
208\\-17\\-31
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
11\\16\\64
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\4\\11
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3\\-4\\-18
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3\\-8\\-16
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-1392, 112, 208; 112, -8, -17; 208, -17, -31],[16, 1, 1],[11, 2, -3, -3; 16, 4, -4, -8; 64, 11, -18, -16],145,2]
%
% END OF LATTICE L146.2
%
\hbox{}\par\smallskip%
%
% LATTICE L146.3
%
\leavevmode%
${L_{146.3}}$%
{} : {$1\above{1pt}{1pt}{-2}{6}16\above{1pt}{1pt}{-}{3}$}\EasyButWeakLineBreak%
{${4}\above{1pt}{1pt}{l}{2}{1}\above{1pt}{1pt}{8,3}{\infty}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-80\\48\\16
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
48\\-15\\-8
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
16\\-8\\-3
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
15\\-16\\112
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-7\\6\\-49
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3\\3\\-22
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\0\\-6
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\1\\-8
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-80, 48, 16; 48, -15, -8; 16, -8, -3],[16, 1, 1],[-1, -1, 3, 2; 0, 1, -2, -2; -6, -8, 20, 15],145,3]
%
% END OF LATTICE L146.3
%
\hbox{}\par\smallskip%
%
% LATTICE L146.4
%
\leavevmode%
${L_{146.4}}$%
{} : {$1\above{1pt}{1pt}{1}{1}4\above{1pt}{1pt}{1}{7}16\above{1pt}{1pt}{1}{1}$}\EasyButWeakLineBreak%
{${16}\above{1pt}{1pt}{s}{2}{4}\above{1pt}{1pt}{4,1}{\infty z}{1}\above{1pt}{1pt}{}{2}{16}\above{1pt}{1pt}{4,3}{\infty}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2672\\112\\288
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
112\\-4\\-12
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
288\\-12\\-31
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-4\\-8
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\-2\\10
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\2\\-1
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3\\8\\-32
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-2672, 112, 288; 112, -4, -12; 288, -12, -31],[16, 4, 1],[-1, 1, 0, -3; -4, -2, 2, 8; -8, 10, -1, -32],145,4]
%
% END OF LATTICE L146.4
%
\hbox{}\par\smallskip%
%
% LATTICE L146.5
%
\leavevmode%
${L_{146.5}}$%
{} : {$1\above{1pt}{1pt}{1}{1}4\above{1pt}{1pt}{1}{1}16\above{1pt}{1pt}{1}{7}$}\EasyButWeakLineBreak%
{${4}\above{1pt}{1pt}{r}{2}{4}\above{1pt}{1pt}{4,3}{\infty z}{1}\above{1pt}{1pt}{}{2}{4}\above{1pt}{1pt}{8,7}{\infty}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-80\\48\\16
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
48\\-12\\-8
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
16\\-8\\-3
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\1\\-8
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\0\\-6
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\-1\\7
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\-1\\12
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-80, 48, 16; 48, -12, -8; 16, -8, -3],[16, 4, 1],[-1, -1, 1, 2; 1, 0, -1, -1; -8, -6, 7, 12],145,5]
%
% END OF LATTICE L146.5
%
%
% LATTICE L146.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[16, 0, 0; 0, -12, -4; 0, -4, -1],[16, 4, 1],[1, 1, -1, 0; -1, -4, 0, 1; 0, 8, 0, -4],145,6]
%
% END OF LATTICE L146.6
%
%
% LATTICE L146.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1616, -2080, 224; -2080, -2672, 288; 224, 288, -31],[16, 16, 1],[-2, -1, 1, 4; -1, 1, 0, -3; -24, 2, 7, 0],145,7]
%
% END OF LATTICE L146.7
%
%
% LATTICE L146.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-80, -80, 16; -80, -64, 16; 16, 16, -3],[16, 16, 1],[-1, -1, 1, 3; 1, 0, -1, -1; 0, -6, -2, 8],145,8]
%
% END OF LATTICE L146.8
%
%
% LATTICE L146.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-48, -192, 32; -192, -752, 128; 32, 128, -21],[16, 16, 1],[10, 9, -5, -4; -1, -2, 0, 1; 8, 0, -8, 0],145,9]
%
% END OF LATTICE L146.9
%

\medskip%
%------------------------------WEYL-GROUP-W147--------------------------------
%
\leavevmode\llap{}%
$W_{147}$%
\qquad\llap{4} lattices, $\chi=12$%
\hfill%
$2|2\infty|\infty\rtimes D_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L147.1
%
\leavevmode%
${L_{147.1}}$%
{} : {$1\above{1pt}{1pt}{2}{{\rm II}}16\above{1pt}{1pt}{1}{1}$}\EasyButWeakLineBreak%
{${16}\above{1pt}{1pt}{r}{2}{2}\above{1pt}{1pt}{b}{2}{16}\above{1pt}{1pt}{2,1}{\infty z}{16}\above{1pt}{1pt}{1,0}{\infty a}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
16\\0\\0
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\-4\\11
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\11\\-30
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\0\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\-8\\-3
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3\\-16\\-8
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\24\\8
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[16, 0, 0; 0, -4, 11; 0, 11, -30],[16, 1, 1],[1, 0, -3, -1; 0, -8, -16, 24; 0, -3, -8, 8],146,1]
%
% END OF LATTICE L147.1
%
\hbox{}\par\smallskip%
%
% LATTICE L147.2
%
\leavevmode%
${L_{147.2}}$%
{} : {$1\above{1pt}{1pt}{1}{7}8\above{1pt}{1pt}{-}{3}64\above{1pt}{1pt}{-}{3}$}\EasyButWeakLineBreak%
{${32}\above{1pt}{1pt}{*}{2}{64}\above{1pt}{1pt}{s}{2}{32}\above{1pt}{1pt}{16,1}{\infty z}{8}\above{1pt}{1pt}{8,3}{\infty b}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3392\\384\\64
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
384\\-40\\-8
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
64\\-8\\-1
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3\\-18\\-64
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-4\\-32
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\6\\16
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\-1\\4
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-3392, 384, 64; 384, -40, -8; 64, -8, -1],[64, 8, 1],[-3, -1, 1, 0; -18, -4, 6, -1; -64, -32, 16, 4],146,2]
%
% END OF LATTICE L147.2
%
%
% LATTICE L147.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-320, -16, 48; -16, 32, 0; 48, 0, -7],[16, 16, 1],[2, 0, -2, 1; 1, -1, -1, 1; 13, 0, -14, 6],146,3]
%
% END OF LATTICE L147.3
%
%
% LATTICE L147.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2624, 1152, -192; 1152, -488, 80; -192, 80, -13],[64, 8, 1],[-1, 0, 2, 1; -7, -1, 13, 10; -28, -6, 52, 48],146,4]
%
% END OF LATTICE L147.4
%

\medskip%
%------------------------------WEYL-GROUP-W148--------------------------------
%
\leavevmode\llap{}%
$W_{148}$%
\qquad\llap{16} lattices, $\chi=12$%
\hfill%
$2\infty2\infty\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L148.1
%
\leavevmode%
${L_{148.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}8\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{-2}{}9\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${18}\above{1pt}{1pt}{b}{2}{8}\above{1pt}{1pt}{6,1}{\infty z}{2}\above{1pt}{1pt}{b}{2}{72}\above{1pt}{1pt}{2,1}{\infty z}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
936\\288\\0
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
288\\82\\15
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\15\\-34
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
25\\-81\\-36
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
11\\-36\\-16
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-12\\39\\17
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-77\\252\\108
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[936, 288, 0; 288, 82, 15; 0, 15, -34],[72, 1, 1],[25, 11, -12, -77; -81, -36, 39, 252; -36, -16, 17, 108],147,1]
%
% END OF LATTICE L148.1
%
\hbox{}\par\smallskip%
%
% LATTICE L148.2
%
\leavevmode%
${L_{148.2}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}8\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{2}{}9\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${2}\above{1pt}{1pt}{b}{2}{8}\above{1pt}{1pt}{6,5}{\infty z}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-18648\\432\\216
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
432\\-10\\-5
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
216\\-5\\-2
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\0\\-216
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\-1\\5
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\1
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\1\\-3
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\44\\-4
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-18648, 432, 216; 432, -10, -5; 216, -5, -2],[72, 1, 1],[0, 1, 0, -1; 1, 44, -1, -44; -3, -4, 2, 0],147,2]
%
% END OF LATTICE L148.2
%
%
% LATTICE L148.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-1278, 450, 144; 450, -158, -51; 144, -51, -16],[18, 1, 1],[2, 19, -1, -3; 3, 36, 0, -6; 8, 54, -9, -8],147,3]
%
% END OF LATTICE L148.3
%
%
% LATTICE L148.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-990, 126, 72; 126, -16, -9; 72, -9, -4],[18, 1, 1],[2, 3, -1, -1; 17, 24, -9, -8; -3, -2, 2, 0],147,4]
%
% END OF LATTICE L148.4
%
%
% LATTICE L148.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[684, -90, 252; -90, 32, -24; 252, -24, 97],[18, 2, 1],[17, 50, 8, 3; 18, 54, 9, 3; -40, -117, -18, -7],147,5]
%
% END OF LATTICE L148.5
%
%
% LATTICE L148.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1584, 450, 756; 450, 136, 216; 756, 216, 361],[18, 2, 1],[21, 16, -1, 4; 7, 6, 0, 1; -48, -37, 2, -9],147,6]
%
% END OF LATTICE L148.6
%
%
% LATTICE L148.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[7218, -1404, 3096; -1404, 288, -603; 3096, -603, 1328],[18, 9, 1],[-45, -31, -3, -15; 7, 4, 0, 2; 108, 74, 7, 36],147,7]
%
% END OF LATTICE L148.7
%
%
% LATTICE L148.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[18, 0, 0; 0, 18, -9; 0, -9, 4],[18, 9, 1],[-1, -3, 0, 1; 3, 8, 1, 0; 9, 18, 0, 0],147,8]
%
% END OF LATTICE L148.8
%
%
% LATTICE L148.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-288, 10422, 4896; 10422, -363132, -170586; 4896, -170586, -80135],[18, 18, 1],[8, 3, -1, -4; 237, 118, -16, -165; -504, -251, 34, 351],147,9]
%
% END OF LATTICE L148.9
%
%
% LATTICE L148.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-72, 162, 72; 162, -288, -126; 72, -126, -55],[18, 18, 1],[-3, -1, 2, 0; -1, 12, 9, -4; 0, -27, -18, 9],147,10]
%
% END OF LATTICE L148.10
%
%
% LATTICE L148.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-720, 216, 72; 216, -48, -40; 72, -40, 13],[72, 8, 1],[32, 6, -7, -7; 81, 15, -18, -18; 72, 14, -16, -18],147,11]
%
% END OF LATTICE L148.11
%
%
% LATTICE L148.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-144, 216, -72; 216, -304, 104; -72, 104, -35],[72, 8, 1],[-1, -1, 3, 3; 2, 0, -3, -1; 8, 2, -16, -10],147,12]
%
% END OF LATTICE L148.12
%
%
% LATTICE L148.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[936, -72, 0; -72, -54, 45; 0, 45, -34],[72, 9, 1],[-2, -1, 1, 7; -27, -12, 13, 84; -36, -16, 17, 108],147,13]
%
% END OF LATTICE L148.13
%
%
% LATTICE L148.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-11160, -504, -2592; -504, -18, -117; -2592, -117, -602],[72, 9, 1],[2, 25, -2, -25; 2, 0, -3, -4; -9, -108, 9, 108],147,14]
%
% END OF LATTICE L148.14
%
%
% LATTICE L148.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-144, 360, 72; 360, -432, -72; 72, -72, -11],[72, 72, 1],[-1, -1, 5, 1; -2, -4, 17, 5; 8, 18, -72, -22],147,15]
%
% END OF LATTICE L148.15
%
%
% LATTICE L148.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2736, -7272, -1512; -7272, -12816, -2592; -1512, -2592, -523],[72, 72, 1],[-30, -28, 11, 9; 221, 209, -79, -67; -1008, -954, 360, 306],147,16]
%
% END OF LATTICE L148.16
%

\medskip%
%------------------------------WEYL-GROUP-W149--------------------------------
%
\leavevmode\llap{}%
$W_{149}$%
\qquad\llap{27} lattices, $\chi=18$%
\hfill%
$\slashtwo2\infty|\infty2\rtimes D_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L149.1
%
\leavevmode%
${L_{149.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{4}4\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{1}{}5\above{1pt}{1pt}{1}{}25\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{5}%
\EasyButWeakLineBreak%
{${100}\above{1pt}{1pt}{}{2}{1}\above{1pt}{1pt}{}{2}{20}\above{1pt}{1pt}{10,9}{\infty}{20}\above{1pt}{1pt}{5,4}{\infty z}{5}\above{1pt}{1pt}{}{2}$}%
\nopagebreak\par%
shares genus with 5-dual\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-11100\\-800\\-5200
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-800\\-55\\-375
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-5200\\-375\\-2436
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-47\\0\\100
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\-1\\-2
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
19\\-4\\-40
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-5\\4\\10
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-19\\3\\40
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-11100, -800, -5200; -800, -55, -375; -5200, -375, -2436],[100, 5, 1],[-47, 1, 19, -5, -19; 0, -1, -4, 4, 3; 100, -2, -40, 10, 40],148,1]
%
% END OF LATTICE L149.1
%
\hbox{}\par\smallskip%
%
% LATTICE L149.2
%
\leavevmode%
${L_{149.2}}$%
{} : {$1\above{1pt}{1pt}{2}{{\rm II}}4\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{1}{}5\above{1pt}{1pt}{1}{}25\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${100}\above{1pt}{1pt}{*}{2}{4}\above{1pt}{1pt}{*}{2}{20}\above{1pt}{1pt}{5,4}{\infty b}{20}\above{1pt}{1pt}{5,3}{\infty}{20}\above{1pt}{1pt}{*}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1900\\200\\0
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
200\\-20\\-5
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\-5\\24
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-10\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\28\\6
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
11\\102\\20
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\8\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-5\\-48\\-10
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-1900, 200, 0; 200, -20, -5; 0, -5, 24],[100, 5, 1],[-1, 3, 11, 1, -5; -10, 28, 102, 8, -48; 0, 6, 20, 0, -10],148,2]
%
% END OF LATTICE L149.2
%
\hbox{}\par\smallskip%
%
% LATTICE L149.3
%
\leavevmode%
${L_{149.3}}$%
{} : {$1\above{1pt}{1pt}{-2}{2}8\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{-}{}5\above{1pt}{1pt}{-}{}25\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${50}\above{1pt}{1pt}{b}{2}{2}\above{1pt}{1pt}{s}{2}{10}\above{1pt}{1pt}{20,19}{\infty b}{40}\above{1pt}{1pt}{20,13}{\infty z}{10}\above{1pt}{1pt}{s}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
143800\\-3600\\-1000
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3600\\90\\25
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1000\\25\\7
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-25\\-50
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\-1\\4
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\-3\\10
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-24\\-60
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-23\\-60
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[143800, -3600, -1000; -3600, 90, 25; -1000, 25, 7],[200, 5, 1],[-1, 0, 0, -1, -1; -25, -1, -3, -24, -23; -50, 4, 10, -60, -60],148,3]
%
% END OF LATTICE L149.3
%
\hbox{}\par\smallskip%
%
% LATTICE L149.4
%
\leavevmode%
${L_{149.4}}$%
{} : {$1\above{1pt}{1pt}{2}{2}8\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{-}{}5\above{1pt}{1pt}{-}{}25\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{m}%
\EasyButWeakLineBreak%
{${50}\above{1pt}{1pt}{s}{2}{2}\above{1pt}{1pt}{b}{2}{10}\above{1pt}{1pt}{20,19}{\infty a}{40}\above{1pt}{1pt}{20,3}{\infty z}{10}\above{1pt}{1pt}{b}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
442200\\-6400\\-2400
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-6400\\90\\35
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2400\\35\\13
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2\\-25\\-300
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\1\\-2
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\17\\140
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\16\\140
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-13\\-150
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[442200, -6400, -2400; -6400, 90, 35; -2400, 35, 13],[200, 5, 1],[-2, 0, 1, 1, -1; -25, 1, 17, 16, -13; -300, -2, 140, 140, -150],148,4]
%
% END OF LATTICE L149.4
%
\hbox{}\par\smallskip%
%
% LATTICE L149.5
%
\leavevmode%
${L_{149.5}}$%
{} : {$1\above{1pt}{1pt}{2}{{\rm II}}8\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{-}{}5\above{1pt}{1pt}{-}{}25\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{5}%
\EasyButWeakLineBreak%
{${200}\above{1pt}{1pt}{b}{2}{2}\above{1pt}{1pt}{l}{2}{40}\above{1pt}{1pt}{5,4}{\infty}{40}\above{1pt}{1pt}{5,2}{\infty z}{10}\above{1pt}{1pt}{b}{2}$}%
\nopagebreak\par%
shares genus with 5-dual\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2200\\600\\-2600
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
600\\-110\\425
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2600\\425\\-1568
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
53\\1060\\200
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-21\\-4
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-21\\-424\\-80
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5\\104\\20
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
21\\423\\80
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-2200, 600, -2600; 600, -110, 425; -2600, 425, -1568],[200, 5, 1],[53, -1, -21, 5, 21; 1060, -21, -424, 104, 423; 200, -4, -80, 20, 80],148,5]
%
% END OF LATTICE L149.5
%
%
% LATTICE L149.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-4780, 1060, 40; 1060, -235, -9; 40, -9, 0],[20, 1, 1],[1, -2, -9, 9, 8; 4, -9, -40, 40, 35; 8, -2, -20, 10, 20],148,6]
%
% END OF LATTICE L149.6
%
%
% LATTICE L149.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-6360, -1400, -40; -1400, -308, -9; -40, -9, 0],[40, 1, 1],[-1, 2, 9, -9, -8; 4, -9, -40, 40, 35; 12, -5, -40, 20, 35],148,7]
%
% END OF LATTICE L149.7
%
%
% LATTICE L149.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[25, 0, 0; 0, -20, -5; 0, -5, -1],[25, 5, 1],[-1, 0, 1, 1, 0; 0, -1, -4, -1, 1; 0, 3, 10, 0, -5],148,8]
%
% END OF LATTICE L149.8
%
%
% LATTICE L149.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-950, 200, 100; 200, -40, -25; 100, -25, -3],[50, 5, 1],[3, -1, -5, 1, 11; 11, -5, -19, 4, 41; 6, 0, -10, 0, 20],148,9]
%
% END OF LATTICE L149.9
%
%
% LATTICE L149.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[17900, -900, -500; -900, 45, 25; -500, 25, 14],[100, 5, 1],[-1, 0, 0, -1, -1; -5, -1, -3, -4, -3; -25, 2, 5, -30, -30],148,10]
%
% END OF LATTICE L149.10
%
%
% LATTICE L149.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2380, 820, 660; 820, 320, 236; 660, 236, 185],[20, 4, 1],[10, 11, 9, 22, 63; 12, 13, 10, 25, 75; -51, -56, -45, -110, -320],148,11]
%
% END OF LATTICE L149.11
%
%
% LATTICE L149.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-300, -20, -60; -20, 0, -5; -60, -5, -11],[20, 5, 1],[1, -1, -1, -1, 1; -2, 8, 4, 2, -4; -5, 0, 3, 4, -4],148,12]
%
% END OF LATTICE L149.12
%
%
% LATTICE L149.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-14200, 120, 560; 120, 0, -5; 560, -5, -22],[40, 5, 1],[-1, 1, 1, 1, -1; -4, 16, 8, 4, -8; -25, 20, 23, 24, -24],148,13]
%
% END OF LATTICE L149.13
%
%
% LATTICE L149.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-35680, 760, 1880; 760, -16, -40; 1880, -40, -99],[40, 8, 1],[0, -2, -2, -1, 2; -5, 3, 15, 25, -5; 2, -40, -45, -30, 40],148,14]
%
% END OF LATTICE L149.14
%
%
% LATTICE L149.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[300, -620, -140; -620, 1600, 360; -140, 360, 81],[20, 20, 1],[1, 1, 1, 0, 0; -13, -12, -15, -5, -2; 60, 55, 68, 22, 9],148,15]
%
% END OF LATTICE L149.15
%
%
% LATTICE L149.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[100, 50, 50; 50, 1430, 100; 50, 100, 29],[50, 10, 1],[17, -1, 19, 36, 105; 2, 0, 2, 4, 12; -36, 0, -40, -75, -220],148,16]
%
% END OF LATTICE L149.16
%
%
% LATTICE L149.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-111100, -2500, 2000; -2500, -55, 45; 2000, 45, -36],[100, 5, 1],[1, 1, 1, -1, -1; -5, 0, 3, 4, -4; 50, 56, 60, -50, -60],148,17]
%
% END OF LATTICE L149.17
%
%
% LATTICE L149.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-66200, -2800, -60000; -2800, -110, -2455; -60000, -2455, -53568],[200, 5, 1],[-49, -55, -59, 49, 59; -985, -1100, -1177, 984, 1176; 100, 112, 120, -100, -120],148,18]
%
% END OF LATTICE L149.18
%
%
% LATTICE L149.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-80, 40, 0; 40, 160, 40; 0, 40, 9],[40, 40, 1],[-1, 3, 1, 1, -1; -2, 10, 3, 3, -2; 10, -40, -13, -14, 8],148,19]
%
% END OF LATTICE L149.19
%
%
% LATTICE L149.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[10400, 9700, 2700; 9700, 9120, 2520; 2700, 2520, 701],[100, 20, 1],[-13, 10, 75, 28, 12; 0, 1, 6, 2, 1; 50, -42, -310, -115, -50],148,20]
%
% END OF LATTICE L149.20
%
%
% LATTICE L149.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[601100, -500, 143800; -500, 80, -120; 143800, -120, 34401],[100, 20, 1],[-311, -50, -311, -122, -61; 5, 1, 7, 3, 1; 1300, 209, 1300, 510, 255],148,21]
%
% END OF LATTICE L149.21
%
%
% LATTICE L149.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1239100, -7300, 305500; -7300, 80, -1800; 305500, -1800, 75321],[100, 20, 1],[-302, -71, -53, -106, -355; 5, 1, 1, 3, 7; 1225, 288, 215, 430, 1440],148,22]
%
% END OF LATTICE L149.22
%
%
% LATTICE L149.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[22100, 2100, 5300; 2100, -120, 500; 5300, 500, 1271],[100, 20, 1],[191, 21, -43, -74, 43; 10, 1, -2, -3, 3; -800, -88, 180, 310, -180],148,23]
%
% END OF LATTICE L149.23
%
%
% LATTICE L149.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-34600, -13600, 4600; -13600, -5320, 1800; 4600, 1800, -609],[200, 40, 1],[-1, -1, -3, 0, 1; -65, -19, -19, 17, 11; -200, -64, -80, 50, 40],148,24]
%
% END OF LATTICE L149.24
%
%
% LATTICE L149.25
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1028600, -275200, 10200; -275200, -73080, 2720; 10200, 2720, -101],[200, 40, 1],[-19, 7, 43, 10, -11; -55, 21, 127, 29, -33; -3400, 1272, 7760, 1790, -2000],148,25]
%
% END OF LATTICE L149.25
%
%
% LATTICE L149.26
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-64400, -5800, 26200; -5800, -480, 2360; 26200, 2360, -10659],[200, 40, 1],[-61, 23, 47, 53, -49; 0, -2, -2, -1, 2; -150, 56, 115, 130, -120],148,26]
%
% END OF LATTICE L149.26
%
%
% LATTICE L149.27
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-400, 3800, -200; 3800, -35680, 1880; -200, 1880, -99],[200, 40, 1],[-1, 3, 3, 5, -1; 0, -10, -2, -1, 2; 2, -200, -45, -30, 40],148,27]
%
% END OF LATTICE L149.27
%

\medskip%
%------------------------------WEYL-GROUP-W150--------------------------------
%
\leavevmode\llap{}%
$W_{150}$%
\qquad\llap{60} lattices, $\chi=12$%
\hfill%
$22|22\slashinfty\rtimes D_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L150.1
%
\leavevmode%
${L_{150.1}}$%
{} : {$1\above{1pt}{1pt}{2}{0}8\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{-}{}9\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{3}%
\EasyButWeakLineBreak%
{${24}\above{1pt}{1pt}{}{2}{9}\above{1pt}{1pt}{r}{2}{8}\above{1pt}{1pt}{s}{2}{36}\above{1pt}{1pt}{*}{2}{24}\above{1pt}{1pt}{3,1}{\infty a}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-28584\\144\\1080
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
144\\15\\-9
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1080\\-9\\-40
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
15\\88\\384
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
13\\75\\333
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5\\28\\128
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-7\\-42\\-180
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-7\\-40\\-180
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-28584, 144, 1080; 144, 15, -9; 1080, -9, -40],[72, 3, 1],[15, 13, 5, -7, -7; 88, 75, 28, -42, -40; 384, 333, 128, -180, -180],149,1]
%
% END OF LATTICE L150.1
%
\hbox{}\par\smallskip%
%
% LATTICE L150.2
%
\leavevmode%
${L_{150.2}}$%
{} : {$[1\above{1pt}{1pt}{1}{}2\above{1pt}{1pt}{-}{}]\above{1pt}{1pt}{}{4}16\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{-}{}9\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{3m,3,2}%
\EasyButWeakLineBreak%
{${6}\above{1pt}{1pt}{}{2}{9}\above{1pt}{1pt}{r}{2}{8}\above{1pt}{1pt}{*}{2}{144}\above{1pt}{1pt}{s}{2}{24}\above{1pt}{1pt}{24,1}{\infty z}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-75024\\4608\\288
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4608\\-282\\-18
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
288\\-18\\-1
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\-1\\12
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-15\\-27
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-14\\-40
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-12\\-72
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\14\\36
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-75024, 4608, 288; 4608, -282, -18; 288, -18, -1],[144, 6, 1],[0, -1, -1, -1, 1; -1, -15, -14, -12, 14; 12, -27, -40, -72, 36],149,2]
%
% END OF LATTICE L150.2
%
\hbox{}\par\smallskip%
%
% LATTICE L150.3
%
\leavevmode%
${L_{150.3}}$%
{} : {$[1\above{1pt}{1pt}{-}{}2\above{1pt}{1pt}{-}{}]\above{1pt}{1pt}{}{0}16\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{-}{}9\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{32,3,m}%
\EasyButWeakLineBreak%
{${6}\above{1pt}{1pt}{r}{2}{36}\above{1pt}{1pt}{*}{2}{8}\above{1pt}{1pt}{s}{2}{144}\above{1pt}{1pt}{*}{2}{24}\above{1pt}{1pt}{24,13}{\infty z}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-118224\\5904\\2304
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5904\\-282\\-120
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2304\\-120\\-43
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
6\\59\\156
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
23\\228\\594
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5\\50\\128
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-11\\-108\\-288
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-7\\-70\\-180
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-118224, 5904, 2304; 5904, -282, -120; 2304, -120, -43],[144, 6, 1],[6, 23, 5, -11, -7; 59, 228, 50, -108, -70; 156, 594, 128, -288, -180],149,3]
%
% END OF LATTICE L150.3
%
\hbox{}\par\smallskip%
%
% LATTICE L150.4
%
\leavevmode%
${L_{150.4}}$%
{} : {$[1\above{1pt}{1pt}{-}{}2\above{1pt}{1pt}{1}{}]\above{1pt}{1pt}{}{6}16\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{-}{}9\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{3m,3,m}%
\EasyButWeakLineBreak%
{${24}\above{1pt}{1pt}{*}{2}{36}\above{1pt}{1pt}{l}{2}{2}\above{1pt}{1pt}{}{2}{144}\above{1pt}{1pt}{}{2}{6}\above{1pt}{1pt}{24,1}{\infty}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-10224\\576\\1296
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
576\\-30\\-84
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1296\\-84\\-115
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-9\\-106\\-24
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-7\\-84\\-18
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\35\\8
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
55\\648\\144
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7\\83\\18
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-10224, 576, 1296; 576, -30, -84; 1296, -84, -115],[144, 6, 1],[-9, -7, 3, 55, 7; -106, -84, 35, 648, 83; -24, -18, 8, 144, 18],149,4]
%
% END OF LATTICE L150.4
%
\hbox{}\par\smallskip%
%
% LATTICE L150.5
%
\leavevmode%
${L_{150.5}}$%
{} : {$[1\above{1pt}{1pt}{1}{}2\above{1pt}{1pt}{1}{}]\above{1pt}{1pt}{}{2}16\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{-}{}9\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{3}%
\EasyButWeakLineBreak%
{${24}\above{1pt}{1pt}{l}{2}{9}\above{1pt}{1pt}{}{2}{2}\above{1pt}{1pt}{r}{2}{144}\above{1pt}{1pt}{l}{2}{6}\above{1pt}{1pt}{24,13}{\infty}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-60336\\1440\\-13392
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1440\\-30\\336
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-13392\\336\\-2911
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
15\\182\\-48
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
14\\168\\-45
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-5\\-61\\16
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-157\\-1896\\504
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-28\\-337\\90
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-60336, 1440, -13392; 1440, -30, 336; -13392, 336, -2911],[144, 6, 1],[15, 14, -5, -157, -28; 182, 168, -61, -1896, -337; -48, -45, 16, 504, 90],149,5]
%
% END OF LATTICE L150.5
%
%
% LATTICE L150.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[60, -24, 0; -24, 6, -2; 0, -2, -1],[12, 2, 1],[1, 1, -1, -2, -4; 3, 2, -3, -5, -9; -6, -4, 4, 7, 12],149,6]
%
% END OF LATTICE L150.6
%
%
% LATTICE L150.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-31080, 1176, 1248; 1176, -43, -49; 1248, -49, -48],[24, 1, 1],[-7, -7, 5, 9, 43; -96, -98, 68, 125, 600; -84, -82, 60, 106, 504],149,7]
%
% END OF LATTICE L150.7
%
%
% LATTICE L150.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-168, 24, 48; 24, -2, -6; 48, -6, -13],[24, 2, 1],[1, -1, -1, 0, 1; -6, 0, 4, 3, 0; 6, -4, -6, -2, 3],149,8]
%
% END OF LATTICE L150.8
%
%
% LATTICE L150.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-24, -96, 96; -96, -186, 172; 96, 172, -157],[24, 2, 1],[1, 4, 0, -15, -11; -6, -15, 1, 60, 42; -6, -14, 1, 56, 39],149,9]
%
% END OF LATTICE L150.9
%
%
% LATTICE L150.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-2064, -240, -288; -240, -26, -32; -288, -32, -39],[48, 2, 1],[-1, 0, 1, 1, -1; -21, -4, 10, 20, -6; 24, 3, -16, -24, 12],149,10]
%
% END OF LATTICE L150.10
%
%
% LATTICE L150.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-10704, 528, 720; 528, -26, -36; 720, -36, -43],[48, 2, 1],[-1, 3, 5, 1, -7; -21, 52, 90, 20, -126; 0, 6, 8, 0, -12],149,11]
%
% END OF LATTICE L150.11
%
%
% LATTICE L150.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-23664, -7584, 912; -7584, -2430, 292; 912, 292, -35],[48, 2, 1],[1, 3, 0, -11, -8; -6, -12, 1, 48, 33; -24, -22, 8, 112, 66],149,12]
%
% END OF LATTICE L150.12
%
%
% LATTICE L150.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-48, 0, 144; 0, 2, 24; 144, 24, -143],[48, 2, 1],[1, 3, 0, -23, -17; -6, -12, 1, 96, 69; 0, 1, 0, -8, -6],149,13]
%
% END OF LATTICE L150.13
%
%
% LATTICE L150.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[36, 0, 0; 0, -30, -6; 0, -6, -1],[36, 6, 1],[1, 1, 0, -1, 0; -1, -3, -1, 0, 1; 0, 9, 4, 0, -6],149,14]
%
% END OF LATTICE L150.14
%
%
% LATTICE L150.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-37512, 5472, 2592; 5472, -798, -378; 2592, -378, -179],[72, 6, 1],[1, -1, -1, -2, 0; 4, -24, -6, 3, 7; 6, 36, -2, -36, -15],149,15]
%
% END OF LATTICE L150.15
%
%
% LATTICE L150.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-5112, -2808, -648; -2808, -1482, -330; -648, -330, -71],[72, 6, 1],[-7, -10, 2, 55, 9; 28, 39, -8, -216, -35; -66, -90, 19, 504, 81],149,16]
%
% END OF LATTICE L150.16
%
%
% LATTICE L150.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[12, 0, 0; 0, -174, 66; 0, 66, -25],[12, 6, 1],[1, 1, 0, -1, 0; 1, 6, 7, 0, -3; 2, 15, 18, 0, -8],149,17]
%
% END OF LATTICE L150.17
%
%
% LATTICE L150.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2232, 240, 240; 240, -24, -27; 240, -27, -25],[24, 3, 1],[7, 6, 7, -3, -3; 24, 22, 28, -10, -12; 40, 33, 36, -18, -16],149,18]
%
% END OF LATTICE L150.18
%
%
% LATTICE L150.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[24, 0, 0; 0, -140, -12; 0, -12, -1],[24, 4, 1],[-1, -1, -1, 0, 1; -6, -2, 0, 1, 0; 60, 18, -4, -12, 0],149,19]
%
% END OF LATTICE L150.19
%
%
% LATTICE L150.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-120, 144, 72; 144, -140, -84; 72, -84, -43],[24, 4, 1],[37, 8, 5, -6, -7; -6, -1, 0, 1, 0; 72, 15, 8, -12, -12],149,20]
%
% END OF LATTICE L150.20
%
%
% LATTICE L150.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-8280, 240, 624; 240, -6, -18; 624, -18, -47],[24, 6, 1],[0, -2, -3, -1, 1; 2, 7, 4, -4, -2; -1, -30, -42, -12, 14],149,21]
%
% END OF LATTICE L150.21
%
%
% LATTICE L150.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-456, 120, 48; 120, -18, -12; 48, -12, -5],[24, 6, 1],[1, 7, 1, -1, -1; -1, -4, 0, 1, 0; 11, 72, 9, -12, -10],149,22]
%
% END OF LATTICE L150.22
%
%
% LATTICE L150.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-168, -144, 48; -144, -120, 40; 48, 40, -13],[24, 8, 1],[1, -1, -1, 0, 1; -3, 0, 2, 3, 0; -6, -4, 2, 8, 3],149,23]
%
% END OF LATTICE L150.23
%
%
% LATTICE L150.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1980, 288, -864; 288, -30, 126; -864, 126, -377],[36, 6, 1],[-21, -11, -16, 7, 8; -1, -1, -3, 0, 1; 48, 25, 36, -16, -18],149,24]
%
% END OF LATTICE L150.24
%
%
% LATTICE L150.25
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-136872, 3312, 3312; 3312, -75, -81; 3312, -81, -80],[72, 3, 1],[19, 4, 7, -3, -3; 112, 23, 36, -18, -16; 672, 142, 252, -106, -108],149,25]
%
% END OF LATTICE L150.25
%
%
% LATTICE L150.26
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-16560, -4224, 1488; -4224, -1074, 378; 1488, 378, -133],[48, 6, 1],[1, -1, -3, -1, 0; -18, 4, 50, 22, 5; -40, 0, 108, 51, 14],149,26]
%
% END OF LATTICE L150.26
%
%
% LATTICE L150.27
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-4464, -1344, 336; -1344, -402, 102; 336, 102, -25],[48, 6, 1],[-3, -3, 7, 9, 2; 6, 4, -14, -16, -3; -16, -24, 36, 54, 14],149,27]
%
% END OF LATTICE L150.27
%
%
% LATTICE L150.28
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3408, -960, 384; -960, -270, 108; 384, 108, -43],[48, 6, 1],[1, 7, 1, -1, -1; -5, -24, -1, 6, 2; -4, 0, 6, 6, -4],149,28]
%
% END OF LATTICE L150.28
%
%
% LATTICE L150.29
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-912, -768, 336; -768, -558, 240; 336, 240, -103],[48, 6, 1],[2, 11, 1, -1, -1; -25, -128, -9, 13, 10; -52, -264, -18, 27, 20],149,29]
%
% END OF LATTICE L150.29
%
%
% LATTICE L150.30
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-120, 24, -48; 24, 36, 12; -48, 12, -19],[24, 12, 1],[3, 5, -5, -13, -9; 0, 1, 0, -2, -2; -8, -12, 12, 30, 20],149,30]
%
% END OF LATTICE L150.30
%
%
% LATTICE L150.31
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-7464, 624, 432; 624, -36, -36; 432, -36, -25],[24, 12, 1],[-3, -2, 7, 5, 5; 0, 1, 0, -1, -2; -52, -36, 120, 87, 88],149,31]
%
% END OF LATTICE L150.31
%
%
% LATTICE L150.32
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-17040, 6576, -1344; 6576, -2536, 520; -1344, 520, -105],[48, 8, 1],[-31, -15, -6, 11, 10; -63, -31, -13, 22, 21; 84, 38, 12, -32, -24],149,32]
%
% END OF LATTICE L150.32
%
%
% LATTICE L150.33
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-62544, 26496, -1680; 26496, -11224, 712; -1680, 712, -45],[48, 8, 1],[-22, -11, -5, 7, 7; -45, -23, -11, 14, 15; 108, 46, 12, -40, -24],149,33]
%
% END OF LATTICE L150.33
%
%
% LATTICE L150.34
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-53904, 17088, -2928; 17088, -5416, 928; -2928, 928, -159],[48, 8, 1],[1, -1, -1, 0, 2; -3, -10, 1, 5, 27; -36, -40, 24, 29, 120],149,34]
%
% END OF LATTICE L150.34
%
%
% LATTICE L150.35
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-624, 432, -48; 432, -232, 40; -48, 40, -3],[48, 8, 1],[5, 5, -3, -7, -14; 3, 4, -1, -4, -9; -36, -32, 24, 50, 96],149,35]
%
% END OF LATTICE L150.35
%
%
% LATTICE L150.36
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-72, 72, -72; 72, -42, 30; -72, 30, -13],[72, 6, 1],[1, -1, -7, -1, 3; 4, -3, -24, -4, 10; 3, -2, -18, -4, 6],149,36]
%
% END OF LATTICE L150.36
%
%
% LATTICE L150.37
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1368, -1368, 504; -1368, -1122, 420; 504, 420, -157],[72, 6, 1],[3, 5, 1, -1, -1; 38, 60, 9, -13, -10; 111, 176, 27, -38, -30],149,37]
%
% END OF LATTICE L150.37
%
%
% LATTICE L150.38
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-5928, -7008, 528; -7008, -8280, 624; 528, 624, -47],[24, 24, 1],[1, 7, 2, -2, -1; 0, -4, -3, -1, 1; 11, 24, -18, -36, 2],149,38]
%
% END OF LATTICE L150.38
%
%
% LATTICE L150.39
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-7056, 288, 720; 288, 6, -36; 720, -36, -71],[144, 6, 1],[0, 2, 17, 1, -7; -1, 6, 54, 4, -22; 0, 17, 144, 8, -60],149,39]
%
% END OF LATTICE L150.39
%
%
% LATTICE L150.40
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-60624, -8208, 3456; -8208, -1110, 468; 3456, 468, -197],[144, 6, 1],[-1, 1, 7, 1, -3; 5, 2, -6, -4, 2; -6, 22, 108, 8, -48],149,40]
%
% END OF LATTICE L150.40
%
%
% LATTICE L150.41
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-236016, 2880, 2880; 2880, -30, -36; 2880, -36, -35],[144, 6, 1],[-1, -1, 1, 5, 3; -10, -12, 9, 56, 35; -72, -70, 72, 352, 210],149,41]
%
% END OF LATTICE L150.41
%
%
% LATTICE L150.42
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2736, 288, 720; 288, -30, -72; 720, -72, -143],[144, 6, 1],[-1, -1, 1, 9, 6; -10, -12, 9, 104, 71; 0, 1, 0, -8, -6],149,42]
%
% END OF LATTICE L150.42
%
%
% LATTICE L150.43
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[360, 144, 0; 144, 60, 0; 0, 0, -1],[72, 12, 1],[1, -1, -1, -1, 1; -4, 0, 2, 3, -2; -12, -18, -4, 0, 0],149,43]
%
% END OF LATTICE L150.43
%
%
% LATTICE L150.44
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-26856, -12528, 1080; -12528, -5844, 504; 1080, 504, -43],[72, 12, 1],[15, 13, 5, -7, -7; -32, -27, -10, 15, 14; 0, 9, 8, 0, -12],149,44]
%
% END OF LATTICE L150.44
%
%
% LATTICE L150.45
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-577944, 225792, -11304; 225792, -88212, 4416; -11304, 4416, -221],[72, 12, 1],[31, 13, 11, -5, -5; 92, 38, 30, -15, -14; 252, 94, 36, -44, -24],149,45]
%
% END OF LATTICE L150.45
%
%
% LATTICE L150.46
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-22392, -10800, 3168; -10800, -5052, 1476; 3168, 1476, -431],[72, 12, 1],[13, 3, 7, -2, -3; -238, -54, -120, 37, 52; -720, -163, -360, 112, 156],149,46]
%
% END OF LATTICE L150.46
%
%
% LATTICE L150.47
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[48, -48, 0; -48, -72, 48; 0, 48, -19],[48, 24, 1],[0, 4, 5, -1, -3; -1, 3, 5, 0, -3; -4, 6, 12, 0, -8],149,47]
%
% END OF LATTICE L150.47
%
%
% LATTICE L150.48
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2448, 672, 288; 672, 264, 72; 288, 72, 17],[48, 24, 1],[3, 6, 4, -3, -2; -39, -79, -53, 40, 27; 116, 234, 156, -120, -80],149,48]
%
% END OF LATTICE L150.48
%
%
% LATTICE L150.49
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-144, 672, -96; 672, -3048, 432; -96, 432, -61],[48, 24, 1],[-2, -3, 4, 3, 3; -1, -4, 1, 2, 3; -4, -24, 0, 9, 16],149,49]
%
% END OF LATTICE L150.49
%
%
% LATTICE L150.50
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-29808, 44736, -864; 44736, -67128, 1296; -864, 1296, -25],[48, 24, 1],[-3, -3, 7, 9, 4; -3, -2, 7, 8, 3; -52, 0, 120, 102, 16],149,50]
%
% END OF LATTICE L150.50
%
%
% LATTICE L150.51
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-576, 1512, 216; 1512, -3912, -552; 216, -552, -77],[72, 24, 1],[-3, 10, 4, 7, -2; -2, 9, 3, 3, -2; 6, -36, -10, 0, 9],149,51]
%
% END OF LATTICE L150.51
%
%
% LATTICE L150.52
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-14328, -1584, 432; -1584, -168, 48; 432, 48, -13],[72, 24, 1],[0, 1, 2, 0, -1; 1, 0, -3, -1, 1; 3, 32, 54, -4, -30],149,52]
%
% END OF LATTICE L150.52
%
%
% LATTICE L150.53
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[144, -288, 0; -288, 600, 0; 0, 0, -1],[144, 24, 1],[2, 1, -2, -7, -3; 1, 0, -1, -3, -1; 0, 0, -4, -18, -12],149,53]
%
% END OF LATTICE L150.53
%
%
% LATTICE L150.54
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-229680, -9504, 1728; -9504, 24, 72; 1728, 72, -13],[144, 24, 1],[-6, -7, 4, 16, 7; 1, 0, -1, -3, -1; -792, -936, 524, 2106, 924],149,54]
%
% END OF LATTICE L150.54
%
%
% LATTICE L150.55
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2469168, 19872, 17712; 19872, -120, -144; 17712, -144, -127],[144, 24, 1],[-6, -7, 4, 8, 7; -29, -36, 19, 39, 35; -804, -936, 536, 1071, 936],149,55]
%
% END OF LATTICE L150.55
%
%
% LATTICE L150.56
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[144, 0, 0; 0, -120, -72; 0, -72, -43],[144, 24, 1],[0, -1, 0, 1, 1; 7, 0, -5, -12, -1; -12, 0, 8, 18, 0],149,56]
%
% END OF LATTICE L150.56
%
%
% LATTICE L150.57
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-7920, -1872, -1728; -1872, -408, -408; -1728, -408, -377],[144, 24, 1],[5, 7, -7, -8, -18; 1, 0, -3, -1, -1; -24, -32, 36, 38, 84],149,57]
%
% END OF LATTICE L150.57
%
%
% LATTICE L150.58
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1208880, -102240, 9648; -102240, -8616, 816; 9648, 816, -77],[144, 24, 1],[-2, -3, 4, 4, 9; 1, 0, -3, -1, -1; -240, -376, 468, 490, 1116],149,58]
%
% END OF LATTICE L150.58
%
%
% LATTICE L150.59
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3518352, 21456, 27504; 21456, -120, -168; 27504, -168, -215],[144, 24, 1],[-2, -3, 4, 2, 9; -5, -10, 9, 6, 29; -252, -376, 504, 251, 1128],149,59]
%
% END OF LATTICE L150.59
%
%
% LATTICE L150.60
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-7920, 1152, -1152; 1152, -120, 192; -1152, 192, -155],[144, 24, 1],[8, 7, -16, -11, -21; 19, 16, -39, -26, -49; -36, -32, 72, 50, 96],149,60]
%
% END OF LATTICE L150.60
%

\medskip%
%------------------------------WEYL-GROUP-W151--------------------------------
%
\leavevmode\llap{}%
$W_{151}$%
\qquad\llap{30} lattices, $\chi=6$%
\hfill%
$\slashtwo22|22\rtimes D_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L151.1
%
\leavevmode%
${L_{151.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{4}8\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{1}{}$}\EasyButWeakLineBreak%
{${1}\above{1pt}{1pt}{r}{2}{4}\above{1pt}{1pt}{*}{2}{12}\above{1pt}{1pt}{s}{2}{8}\above{1pt}{1pt}{l}{2}{3}\above{1pt}{1pt}{}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-456\\48\\0
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
48\\-1\\-2
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\-2\\1
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\-1
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-10\\-20
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-12\\-18
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\8\\20
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\9\\18
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-456, 48, 0; 48, -1, -2; 0, -2, 1],[24, 1, 1],[0, -1, -1, 1, 1; 0, -10, -12, 8, 9; -1, -20, -18, 20, 18],150,1]
%
% END OF LATTICE L151.1
%
\hbox{}\par\smallskip%
%
% LATTICE L151.2
%
\leavevmode%
${L_{151.2}}$%
{} : {$[1\above{1pt}{1pt}{-}{}2\above{1pt}{1pt}{1}{}]\above{1pt}{1pt}{}{4}16\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${16}\above{1pt}{1pt}{*}{2}{4}\above{1pt}{1pt}{s}{2}{48}\above{1pt}{1pt}{l}{2}{2}\above{1pt}{1pt}{}{2}{3}\above{1pt}{1pt}{r}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3984\\144\\144
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
144\\-2\\-6
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
144\\-6\\-5
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-4\\-24
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-6\\-22
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\0\\24
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\5\\22
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\6\\21
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-3984, 144, 144; 144, -2, -6; 144, -6, -5],[48, 2, 1],[-1, -1, 1, 1, 1; -4, -6, 0, 5, 6; -24, -22, 24, 22, 21],150,2]
%
% END OF LATTICE L151.2
%
\hbox{}\par\smallskip%
%
% LATTICE L151.3
%
\leavevmode%
${L_{151.3}}$%
{} : {$[1\above{1pt}{1pt}{-}{}2\above{1pt}{1pt}{1}{}]\above{1pt}{1pt}{}{2}16\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{m}%
\EasyButWeakLineBreak%
{${16}\above{1pt}{1pt}{}{2}{1}\above{1pt}{1pt}{r}{2}{48}\above{1pt}{1pt}{*}{2}{8}\above{1pt}{1pt}{l}{2}{3}\above{1pt}{1pt}{}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-6000\\144\\288
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
144\\-2\\-8
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
288\\-8\\-13
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\8\\16
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\11\\15
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5\\60\\72
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-10\\-16
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-12\\-15
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-6000, 144, 288; 144, -2, -8; 288, -8, -13],[48, 2, 1],[1, 1, 5, -1, -1; 8, 11, 60, -10, -12; 16, 15, 72, -16, -15],150,3]
%
% END OF LATTICE L151.3
%
\hbox{}\par\smallskip%
%
% LATTICE L151.4
%
\leavevmode%
${L_{151.4}}$%
{} : {$[1\above{1pt}{1pt}{1}{}2\above{1pt}{1pt}{1}{}]\above{1pt}{1pt}{}{0}16\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{m}%
\EasyButWeakLineBreak%
{${16}\above{1pt}{1pt}{l}{2}{1}\above{1pt}{1pt}{}{2}{48}\above{1pt}{1pt}{}{2}{2}\above{1pt}{1pt}{r}{2}{12}\above{1pt}{1pt}{*}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
48\\0\\48
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\-2\\-12
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
48\\-12\\-23
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-4\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-6\\1
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\0\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\11\\-2
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5\\30\\-6
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[48, 0, 48; 0, -2, -12; 48, -12, -23],[48, 2, 1],[-1, -1, 1, 2, 5; -4, -6, 0, 11, 30; 0, 1, 0, -2, -6],150,4]
%
% END OF LATTICE L151.4
%
\hbox{}\par\smallskip%
%
% LATTICE L151.5
%
\leavevmode%
${L_{151.5}}$%
{} : {$[1\above{1pt}{1pt}{1}{}2\above{1pt}{1pt}{1}{}]\above{1pt}{1pt}{}{6}16\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{1}{}$}\EasyButWeakLineBreak%
{${16}\above{1pt}{1pt}{s}{2}{4}\above{1pt}{1pt}{*}{2}{48}\above{1pt}{1pt}{s}{2}{8}\above{1pt}{1pt}{*}{2}{12}\above{1pt}{1pt}{s}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-816\\48\\48
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
48\\-2\\-4
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
48\\-4\\-1
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\8\\8
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\10\\6
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\12\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-10\\-8
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-12\\-6
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-816, 48, 48; 48, -2, -4; 48, -4, -1],[48, 2, 1],[1, 1, 1, -1, -1; 8, 10, 12, -10, -12; 8, 6, 0, -8, -6],150,5]
%
% END OF LATTICE L151.5
%
%
% LATTICE L151.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[12, 0, 0; 0, 2, 0; 0, 0, -1],[12, 2, 1],[0, -1, -1, 0, 1; -1, -2, 0, 1, 0; -1, -4, -3, 0, 0],150,6]
%
% END OF LATTICE L151.6
%
%
% LATTICE L151.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[24, 24, 0; 24, -10, -6; 0, -6, -1],[24, 2, 1],[-1, -1, 2, 1, 1; 1, 0, -3, -1, 0; -6, -4, 12, 5, 0],150,7]
%
% END OF LATTICE L151.7
%
%
% LATTICE L151.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-408, 48, 24; 48, -2, -4; 24, -4, -1],[24, 2, 1],[1, 1, 1, -1, -1; 4, 3, 0, -4, -3; 8, 10, 12, -10, -12],150,8]
%
% END OF LATTICE L151.8
%
%
% LATTICE L151.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-24, 48, -24; 48, -3, -3; -24, -3, 4],[24, 3, 1],[1, -1, -1, 1, 1; 5, -6, -6, 4, 5; 9, -12, -10, 12, 10],150,9]
%
% END OF LATTICE L151.9
%
%
% LATTICE L151.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[12, 0, 0; 0, -6, 6; 0, 6, -5],[12, 6, 1],[1, 0, -1, -1, 0; 0, -2, -2, 1, 1; 0, -3, -4, 0, 1],150,10]
%
% END OF LATTICE L151.10
%
%
% LATTICE L151.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[552, -264, 24; -264, 124, -12; 24, -12, 1],[24, 4, 1],[1, 0, -2, -1, 1; 1, 0, -3, -2, 0; -12, -1, 12, 4, -18],150,11]
%
% END OF LATTICE L151.11
%
%
% LATTICE L151.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[120, 48, 0; 48, 20, 0; 0, 0, -1],[24, 4, 1],[0, -1, -1, 1, 1; -1, 2, 3, -2, -3; -4, -2, 0, 0, -3],150,12]
%
% END OF LATTICE L151.12
%
%
% LATTICE L151.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1032, 336, -72; 336, 102, -24; -72, -24, 5],[24, 6, 1],[-1, -2, -1, 1, 1; 0, 1, 0, -1, -1; -12, -24, -16, 9, 10],150,13]
%
% END OF LATTICE L151.13
%
%
% LATTICE L151.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[24, 0, 0; 0, -30, 6; 0, 6, -1],[24, 6, 1],[1, 0, -1, -1, 0; 0, -1, 0, 2, 1; 0, -6, -4, 6, 4],150,14]
%
% END OF LATTICE L151.14
%
%
% LATTICE L151.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[24, 0, 0; 0, 8, 0; 0, 0, -1],[24, 8, 1],[-1, 0, 1, 0, -2; 0, 1, 0, -1, -3; -4, 0, 0, -2, -12],150,15]
%
% END OF LATTICE L151.15
%
%
% LATTICE L151.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-48, -96, 96; -96, -42, 30; 96, 30, -17],[48, 6, 1],[-1, -3, -1, 2, 1; 4, 20, 8, -13, -7; 0, 18, 8, -12, -7],150,16]
%
% END OF LATTICE L151.16
%
%
% LATTICE L151.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-984, 144, 72; 144, -12, -12; 72, -12, -5],[24, 12, 1],[-1, 1, 2, 1, -1; -1, 2, 3, 0, -2; -12, 9, 20, 12, -10],150,17]
%
% END OF LATTICE L151.17
%
%
% LATTICE L151.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1392, -192, 96; -192, 6, 6; 96, 6, -5],[48, 6, 1],[-1, -1, -1, 1, 1; -4, -6, -8, 5, 6; -24, -27, -32, 24, 26],150,18]
%
% END OF LATTICE L151.18
%
%
% LATTICE L151.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-112848, 1152, 2304; 1152, -6, -24; 2304, -24, -47],[48, 6, 1],[1, 3, 7, -1, -1; 0, 11, 28, -2, -4; 48, 141, 328, -48, -47],150,19]
%
% END OF LATTICE L151.19
%
%
% LATTICE L151.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[24, -72, 24; -72, -516, 156; 24, 156, -47],[24, 12, 1],[2, -1, -1, 1, 1; -11, 2, 5, 0, -4; -36, 6, 16, 0, -13],150,20]
%
% END OF LATTICE L151.20
%
%
% LATTICE L151.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2928, 384, -144; 384, 42, -18; -144, -18, 7],[48, 6, 1],[1, -1, -1, 1, 1; 0, -4, -4, 2, 2; 24, -30, -32, 24, 26],150,21]
%
% END OF LATTICE L151.21
%
%
% LATTICE L151.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2064, 48, -48; 48, -8, 0; -48, 0, 1],[48, 8, 1],[-1, 0, 1, 0, -1; -4, 0, 6, 1, -3; -48, -1, 48, 4, -42],150,22]
%
% END OF LATTICE L151.22
%
%
% LATTICE L151.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[5232, 1056, -240; 1056, 200, -48; -240, -48, 11],[48, 8, 1],[-1, -1, 1, 2, 1; -1, -2, 0, 1, 0; -26, -32, 21, 48, 24],150,23]
%
% END OF LATTICE L151.23
%
%
% LATTICE L151.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[48, 0, 0; 0, 8, 0; 0, 0, -1],[48, 8, 1],[0, -1, -1, 0, 1; -1, -2, 0, 1, 0; -2, -8, -6, 0, 0],150,24]
%
% END OF LATTICE L151.24
%
%
% LATTICE L151.25
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1680, -672, 144; -672, -200, 48; 144, 48, -11],[48, 8, 1],[-1, 1, 5, 0, -2; -6, 4, 24, 1, -9; -40, 30, 168, 4, -66],150,25]
%
% END OF LATTICE L151.25
%
%
% LATTICE L151.26
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[24, 0, 0; 0, 456, 48; 0, 48, 5],[24, 24, 1],[1, 0, -1, -1, 0; 0, 1, 2, 2, 1; 0, -12, -20, -18, -8],150,26]
%
% END OF LATTICE L151.26
%
%
% LATTICE L151.27
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1776, -1440, 96; -1440, -984, 72; 96, 72, -5],[48, 24, 1],[-1, 1, 3, 0, -1; -2, 1, 4, 1, -1; -48, 33, 112, 12, -34],150,27]
%
% END OF LATTICE L151.27
%
%
% LATTICE L151.28
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1968, 96, -48; 96, -24, 0; -48, 0, 1],[48, 24, 1],[0, 1, 0, -1, -1; 1, 4, 0, -3, -2; 6, 48, -1, -48, -40],150,28]
%
% END OF LATTICE L151.28
%
%
% LATTICE L151.29
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2928, 2496, -144; 2496, 2040, -120; -144, -120, 7],[48, 24, 1],[1, -1, -1, 1, 1; 0, -2, -2, 1, 1; 24, -54, -56, 36, 38],150,29]
%
% END OF LATTICE L151.29
%
%
% LATTICE L151.30
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-528, 96, 48; 96, 168, 48; 48, 48, 13],[48, 24, 1],[-1, 1, 1, 1, -1; 9, -8, -8, -7, 10; -30, 24, 26, 24, -32],150,30]
%
% END OF LATTICE L151.30
%

\medskip%
%------------------------------WEYL-GROUP-W152--------------------------------
%
\leavevmode\llap{}%
$W_{152}$%
\qquad\llap{22} lattices, $\chi=90$%
\hfill%
$4\infty\infty2\infty24\infty\infty2\infty2\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L152.1
%
\leavevmode%
${L_{152.1}}$%
{} : {$1\above{1pt}{1pt}{2}{{\rm II}}4\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{2}{}25\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${2}\above{1pt}{1pt}{*}{4}{4}\above{1pt}{1pt}{5,4}{\infty b}{4}\above{1pt}{1pt}{5,3}{\infty}{4}\above{1pt}{1pt}{*}{2}{100}\above{1pt}{1pt}{1,0}{\infty b}{100}\above{1pt}{1pt}{r}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-47100\\-22000\\-700
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-22000\\-10276\\-327
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-700\\-327\\-10
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3001\\6000\\16500
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1402\\2803\\7711
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-36\\72\\197
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-15\\32\\3
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\2\\4
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
15\\-32\\-4
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
37\\-78\\-46
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
263\\-550\\-500
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
387\\-800\\-1100
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-47100, -22000, -700; -22000, -10276, -327; -700, -327, -10],[100, 1, 1],[-15, -1, 15, 37, 263, 387, 43, 53, -7, -25, -163, -187; 32, 2, -32, -78, -550, -800, -88, -106, 16, 54, 350, 400; 3, 4, -4, -46, -500, -1100, -157, -290, -40, -20, -50, 0],151,1]
%
% END OF LATTICE L152.1
%
\hbox{}\par\smallskip%
%
% LATTICE L152.2
%
\leavevmode%
${L_{152.2}}$%
{} : {$1\above{1pt}{1pt}{2}{2}8\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{2}{}25\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${1}\above{1pt}{1pt}{}{4}{2}\above{1pt}{1pt}{20,19}{\infty b}{8}\above{1pt}{1pt}{20,3}{\infty z}{2}\above{1pt}{1pt}{s}{2}{50}\above{1pt}{1pt}{4,3}{\infty b}{200}\above{1pt}{1pt}{l}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-448200\\2000\\2600
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2000\\-7\\-12
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2600\\-12\\-15
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
11699\\335400\\1747200
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-33\\-947\\-4928
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-72\\-2064\\-10753
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\31\\148
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\1\\-1
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-32\\-148
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4\\111\\599
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
54\\1525\\8075
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
267\\7600\\39900
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-448200, 2000, 2600; 2000, -7, -12; 2600, -12, -15],[200, 1, 1],[1, 0, -1, 4, 54, 267, 20, 39, 13, 5, 21, 33; 31, 1, -32, 111, 1525, 7600, 571, 1117, 376, 147, 625, 1000; 148, -1, -148, 599, 8075, 39900, 2988, 5825, 1940, 745, 3125, 4900],151,2]
%
% END OF LATTICE L152.2
%
\hbox{}\par\smallskip%
%
% LATTICE L152.3
%
\leavevmode%
${L_{152.3}}$%
{} : {$1\above{1pt}{1pt}{-2}{2}8\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{2}{}25\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{m}%
\EasyButWeakLineBreak%
{${4}\above{1pt}{1pt}{*}{4}{2}\above{1pt}{1pt}{20,19}{\infty a}{8}\above{1pt}{1pt}{20,13}{\infty z}{2}\above{1pt}{1pt}{b}{2}{50}\above{1pt}{1pt}{4,3}{\infty a}{200}\above{1pt}{1pt}{s}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-6269800\\2600\\60000
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2600\\-1\\-25
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
60000\\-25\\-574
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
122399\\18972000\\11954400
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-60\\-9301\\-5860
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1158\\-179490\\-113099
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-150\\-98
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\18\\-1
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\484\\292
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
13\\2028\\1269
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
138\\21450\\13475
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
599\\92900\\58500
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-6269800, 2600, 60000; 2600, -1, -25; 60000, -25, -574],[200, 1, 1],[-1, 0, 3, 13, 138, 599, 85, 78, 21, 5, 12, 1; -150, 18, 484, 2028, 21450, 92900, 13170, 12072, 3236, 762, 1800, 100; -98, -1, 292, 1269, 13475, 58500, 8302, 7619, 2052, 489, 1175, 100],151,3]
%
% END OF LATTICE L152.3
%
%
% LATTICE L152.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[350, 500, -275; 500, 715, -393; -275, -393, 216],[25, 1, 1],[1, -1, -3, -24, -253, -547, -155, -142, -19, -9, -22, -3; -4, -1, 1, -1, -25, -75, -24, -25, -5, -5, -25, -25; -6, -3, -2, -33, -375, -850, -246, -231, -34, -21, -75, -50],151,4]
%
% END OF LATTICE L152.4
%
%
% LATTICE L152.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-23550, 1550, -350; 1550, -102, 23; -350, 23, -5],[50, 1, 1],[1, 0, -1, -2, -12, -13, -1, 0, 1, 2, 12, 13; 16, 1, -16, -39, -275, -400, -44, -53, 8, 27, 175, 200; 3, 4, -4, -46, -500, -1100, -157, -290, -40, -20, -50, 0],151,5]
%
% END OF LATTICE L152.5
%
%
% LATTICE L152.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-4900, 100, 1300; 100, -2, -25; 1300, -25, -287],[100, 1, 1],[85, 78, 21, 5, 12, 1, -1, 0, 3, 13, 138, 599; 6585, 6036, 1618, 381, 900, 50, -75, 9, 242, 1014, 10725, 46450; -198, -181, -48, -11, -25, 0, 2, -1, -8, -31, -325, -1400],151,6]
%
% END OF LATTICE L152.6
%
%
% LATTICE L152.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[6900, -250, 3300; -250, 190, -108; 3300, -108, 1579],[50, 2, 1],[-99, -75, -37, -1353, -15423, -17501, -5067, -9519, -701, -861, -3027, -949; -13, -10, -5, -180, -2050, -2325, -673, -1264, -93, -114, -400, -125; 206, 156, 77, 2816, 32100, 36425, 10546, 19812, 1459, 1792, 6300, 1975],151,7]
%
% END OF LATTICE L152.7
%
%
% LATTICE L152.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1837600, -37300, 458500; -37300, 760, -9308; 458500, -9308, 114401],[100, 4, 1],[-102, -39, -19, -693, -7899, -8963, -5190, -4875, -359, -441, -1551, -487; 187, 70, 35, 1285, 14650, 16625, 9627, 9043, 666, 818, 2875, 900; 424, 162, 79, 2882, 32850, 37275, 21584, 20274, 1493, 1834, 6450, 2025],151,8]
%
% END OF LATTICE L152.8
%
%
% LATTICE L152.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[45400, 22700, 11200; 22700, 11348, 5600; 11200, 5600, 2763],[100, 4, 1],[995, 889, 107, 36, 37, -37, -1, 34, 35, 177, 1738, 3587; 280, 253, 32, 13, 25, 0, 0, 7, 8, 47, 475, 1000; -4596, -4112, -498, -172, -200, 150, 4, -152, -158, -812, -8000, -16550],151,9]
%
% END OF LATTICE L152.9
%
%
% LATTICE L152.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[25, -50, -75; -50, -250, -125; -75, -125, 9],[25, 25, 1],[-2, -36, 1, 254, 120, 277, 2018, 1908, 287, 178, 24, 11; 1, 20, 0, -135, -64, -148, -1079, -1021, -154, -96, -13, -6; 0, -25, 0, 175, 83, 192, 1400, 1325, 200, 125, 17, 8],151,10]
%
% END OF LATTICE L152.10
%
%
% LATTICE L152.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[3250, -400, 1450; -400, 200, -175; 1450, -175, 647],[50, 25, 1],[56, 45, 45, 785, 357, 809, 2926, 5493, 807, 493, 69, 43; 3, 3, 2, 33, 15, 34, 123, 231, 34, 21, 3, 2; -125, -100, -100, -1750, -796, -1804, -6525, -12250, -1800, -1100, -154, -96],151,11]
%
% END OF LATTICE L152.11
%
%
% LATTICE L152.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[256600, -14800, 308800; -14800, 856, -17840; 308800, -17840, 371979],[200, 8, 1],[57, 59, 5, 277, 3263, 3781, 1105, 2099, 161, 221, 887, 369; -1432, -1481, -122, -6881, -81125, -94050, -27492, -52235, -4010, -5515, -22175, -9250; -116, -120, -10, -560, -6600, -7650, -2236, -4248, -326, -448, -1800, -750],151,12]
%
% END OF LATTICE L152.12
%
%
% LATTICE L152.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1531600, -7800, -11000; -7800, 40, 56; -11000, 56, 79],[200, 8, 1],[-1, -1, 0, -3, -37, -44, -13, -25, -2, -3, -13, -6; 7, 6, -3, -44, -450, -475, -133, -240, -15, -10, 0, 25; -144, -144, 2, -384, -4800, -5750, -1704, -3288, -266, -408, -1800, -850],151,13]
%
% END OF LATTICE L152.13
%
%
% LATTICE L152.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-250, -21350, -10450; -21350, -1765100, -863950; -10450, -863950, -422871],[50, 50, 1],[3, 4, -2, -46, -20, -22, -157, -290, -20, -20, -2, 0; 416, -49, -208, -489, -37, 80, 956, 2597, 404, 1077, 233, 116; -850, 100, 425, 1000, 76, -163, -1950, -5300, -825, -2200, -476, -237],151,14]
%
% END OF LATTICE L152.14
%
%
% LATTICE L152.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-395100, -10100, 8800; -10100, -250, 225; 8800, 225, -196],[100, 25, 1],[-9, 1, 9, 11, 1, -3, -19, -53, -17, -23, -5, -5; 3, 4, -4, -46, -20, -44, -157, -290, -40, -20, -2, 0; -400, 50, 400, 450, 26, -176, -1000, -2650, -800, -1050, -226, -224],151,15]
%
% END OF LATTICE L152.15
%
%
% LATTICE L152.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-204500, -5700, 4500; -5700, -150, 125; 4500, 125, -99],[100, 25, 1],[408, 367, 91, 17, 1, -1, -2, 10, 25, 70, 28, 117; 973, 879, 222, 44, 3, -2, -7, 18, 54, 163, 66, 278; 19700, 17725, 4400, 825, 49, -48, -100, 475, 1200, 3375, 1351, 5648],151,16]
%
% END OF LATTICE L152.16
%
%
% LATTICE L152.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-89800, 6400, -36800; 6400, -375, 2700; -36800, 2700, -15007],[200, 25, 1],[203, -12, -191, 968, 510, 2493, 4648, 9021, 2963, 1111, 183, 279; 404, -25, -380, 1935, 1019, 4980, 9284, 18017, 5916, 2217, 365, 556; -425, 25, 400, -2025, -1067, -5216, -9725, -18875, -6200, -2325, -383, -584],151,17]
%
% END OF LATTICE L152.17
%
%
% LATTICE L152.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-409000, -210200, 9000; -210200, -108025, 4625; 9000, 4625, -198],[200, 25, 1],[5, -8, -29, -93, -38, -161, -565, -512, -131, -27, -2, 1; -14, 36, 108, 326, 132, 556, 1946, 1758, 444, 88, 6, -4; -100, 475, 1200, 3375, 1351, 5648, 19700, 17725, 4400, 825, 49, -48],151,18]
%
% END OF LATTICE L152.18
%
%
% LATTICE L152.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[400, 15900, 3800; 15900, 2681000, 640800; 3800, 640800, 153161],[100, 100, 1],[6, 3, 1, 33, 15, 17, 246, 231, 17, 21, 3, 1; -1219, -490, -245, -8545, -3886, -4403, -63699, -59791, -4392, -5366, -751, -234; 5100, 2050, 1025, 35750, 16258, 18421, 266500, 250150, 18375, 22450, 3142, 979],151,19]
%
% END OF LATTICE L152.19
%
%
% LATTICE L152.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[4500, -80300, -19200; -80300, 1527400, 365200; -19200, 365200, 87319],[100, 100, 1],[-362, -325, -40, -15, -1, 0, -2, -13, -12, -63, -25, -52; 72379, 65232, 8163, 3227, 240, 11, 239, 2199, 2211, 12334, 4947, 10363; -302800, -272900, -34150, -13500, -1004, -46, -1000, -9200, -9250, -51600, -20696, -43354],151,20]
%
% END OF LATTICE L152.20
%
%
% LATTICE L152.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1800400, 1237800, -12800; 1237800, 851000, -8800; -12800, -8800, 91],[200, 200, 1],[123, 231, 17, 21, 3, 1, 3, 3, 1, 33, 15, 17; -133, -240, -15, -10, 0, 1, 7, 6, -3, -44, -18, -19; 4500, 9400, 950, 2000, 424, 238, 1100, 1000, -150, 400, 376, 562],151,21]
%
% END OF LATTICE L152.21
%
%
% LATTICE L152.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1000, -42200, -20800; -42200, 1800400, 887400; -20800, 887400, 437391],[200, 200, 1],[-133, -240, -15, -10, 0, 1, 7, 6, -3, -44, -18, -19; -8777, -16469, -1208, -1479, -209, -68, -197, -197, -74, -2367, -1073, -1214; 17800, 33400, 2450, 3000, 424, 138, 400, 400, 150, 4800, 2176, 2462],151,22]
%
% END OF LATTICE L152.22
%

\medskip%
%------------------------------WEYL-GROUP-W153--------------------------------
%
\leavevmode\llap{}%
$W_{153}$%
\qquad\llap{22} lattices, $\chi=60$%
\hfill%
$\infty222\infty\infty222\infty\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L153.1
%
\leavevmode%
${L_{153.1}}$%
{} : {$1\above{1pt}{1pt}{2}{{\rm II}}4\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{-2}{}25\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${4}\above{1pt}{1pt}{5,2}{\infty b}{4}\above{1pt}{1pt}{r}{2}{50}\above{1pt}{1pt}{b}{2}{2}\above{1pt}{1pt}{l}{2}{4}\above{1pt}{1pt}{5,4}{\infty}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
255300\\86500\\-16400
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
86500\\29308\\-5557
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-16400\\-5557\\1054
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
179199\\-627200\\-518000
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
60608\\-212129\\-175195
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-11392\\39872\\32929
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-131\\458\\376
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1763\\6172\\5104
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-9311\\32600\\26975
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-478\\1674\\1387
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-411\\1440\\1196
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[255300, 86500, -16400; 86500, 29308, -5557; -16400, -5557, 1054],[100, 1, 1],[-131, -1763, -9311, -478, -411, 3, -29, -289, -34, -101; 458, 6172, 32600, 1674, 1440, -10, 100, 1000, 118, 352; 376, 5104, 26975, 1387, 1196, -6, 76, 775, 93, 284],152,1]
%
% END OF LATTICE L153.1
%
\hbox{}\par\smallskip%
%
% LATTICE L153.2
%
\leavevmode%
${L_{153.2}}$%
{} : {$1\above{1pt}{1pt}{-2}{2}8\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{-2}{}25\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${2}\above{1pt}{1pt}{20,7}{\infty b}{8}\above{1pt}{1pt}{s}{2}{100}\above{1pt}{1pt}{*}{2}{4}\above{1pt}{1pt}{s}{2}{8}\above{1pt}{1pt}{20,9}{\infty z}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-322600\\-97800\\8000
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-97800\\-29649\\2425
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
8000\\2425\\-198
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1302401\\4573200\\3374400
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-394416\\1384937\\1021896
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
31856\\-111858\\-82537
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-20\\70\\49
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
17\\-60\\-48
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
43\\-150\\-100
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-13\\46\\38
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-149\\524\\396
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-322600, -97800, 8000; -97800, -29649, 2425; 8000, 2425, -198],[200, 1, 1],[-20, 17, 43, -13, -149, -156, -4945, -26443, -1395, -1259; 70, -60, -150, 46, 524, 548, 17364, 92850, 4898, 4420; 49, -48, -100, 38, 396, 407, 12816, 68500, 3610, 3252],152,2]
%
% END OF LATTICE L153.2
%
\hbox{}\par\smallskip%
%
% LATTICE L153.3
%
\leavevmode%
${L_{153.3}}$%
{} : {$1\above{1pt}{1pt}{2}{2}8\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{-2}{}25\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{m}%
\EasyButWeakLineBreak%
{${2}\above{1pt}{1pt}{20,7}{\infty a}{8}\above{1pt}{1pt}{l}{2}{25}\above{1pt}{1pt}{}{2}{1}\above{1pt}{1pt}{r}{2}{8}\above{1pt}{1pt}{20,19}{\infty z}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1566600\\-311000\\6200
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-311000\\-61739\\1230
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
6200\\1230\\-23
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-8738101\\44494200\\23871600
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1736889\\8844197\\4745004
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
38836\\-197752\\-106097
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-54\\275\\149
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
55\\-280\\-148
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
54\\-275\\-150
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-22\\112\\59
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-447\\2276\\1216
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-1566600, -311000, 6200; -311000, -61739, 1230; 6200, 1230, -23],[200, 1, 1],[-54, 55, 54, -22, -447, -457, -14363, -38379, -2022, -3641; 275, -280, -275, 112, 2276, 2327, 73136, 195425, 10296, 18540; 149, -148, -150, 59, 1216, 1247, 39236, 104850, 5525, 9952],152,3]
%
% END OF LATTICE L153.3
%
%
% LATTICE L153.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[50, -25, 0; -25, 12, -5; 0, -5, -49],[25, 1, 1],[3, -5, -1, 9, 29, 52, 775, 8251, 431, 191; 5, -10, 0, 18, 56, 99, 1466, 15600, 814, 360; -1, 1, 0, -2, -7, -13, -197, -2100, -110, -49],152,4]
%
% END OF LATTICE L153.4
%
%
% LATTICE L153.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[127650, -49350, -8200; -49350, 19079, 3170; -8200, 3170, 527],[50, 1, 1],[-2, 21, 211, 25, 75, 98, 1323, 6989, 359, 309; -5, 50, 500, 59, 176, 229, 3086, 16300, 837, 720; -1, 26, 275, 34, 108, 147, 2018, 10675, 550, 476],152,5]
%
% END OF LATTICE L153.5
%
%
% LATTICE L153.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-161300, 63500, 4000; 63500, -24998, -1575; 4000, -1575, -99],[100, 1, 1],[118, 3737, 19982, 1054, 951, 15, -13, -32, 10, 113; 274, 8682, 46425, 2449, 2210, 35, -30, -75, 23, 262; 407, 12816, 68500, 3610, 3252, 49, -48, -100, 38, 396],152,6]
%
% END OF LATTICE L153.6
%
%
% LATTICE L153.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-39550, -7400, -22150; -7400, -1262, -4090; -22150, -4090, -12381],[50, 2, 1],[145, 11, -1717, -332, -530, -1311, -8173, -85733, -4332, -1802; 135, 10, -1600, -309, -493, -1219, -7598, -79700, -4027, -1675; -304, -23, 3600, 696, 1111, 2748, 17131, 179700, 9080, 3777],152,7]
%
% END OF LATTICE L153.7
%
%
% LATTICE L153.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[44200, 6500, 13400; 6500, 1252, 2100; 13400, 2100, 4119],[100, 4, 1],[1379, 22319, 239059, 12653, 5745, 216, 11, 191, 107, 635; 2523, 40832, 437350, 23148, 10510, 395, 20, 350, 196, 1162; -5772, -93418, -1000600, -52960, -24046, -904, -46, -800, -448, -2658],152,8]
%
% END OF LATTICE L153.8
%
%
% LATTICE L153.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-12073200, 246900, -2968400; 246900, -5048, 60704; -2968400, 60704, -729831],[100, 4, 1],[-555, -3463, -72658, -3672, -764, 61, 5, -1442, -280, -224; 1066, 6637, 139225, 7033, 1462, -119, -8, 2825, 543, 432; 2346, 14637, 307100, 15520, 3229, -258, -21, 6100, 1184, 947],152,9]
%
% END OF LATTICE L153.9
%
%
% LATTICE L153.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2450, -250, 1225; -250, 25, -125; 1225, -125, 613],[25, 25, 1],[-10, 0, 1, 1, -18, -47, -798, -343, -457, -210; 24, 1, 0, 8, 63, 142, 2323, 996, 1320, 601; 25, 0, -2, 0, 50, 125, 2100, 902, 1200, 550],152,10]
%
% END OF LATTICE L153.10
%
%
% LATTICE L153.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-5884350, 188000, -2812300; 188000, -5925, 89850; -2812300, 89850, -1344079],[50, 25, 1],[-1445, -215, 685, 3308, 10557, 13053, 162727, 34139, 43124, 35875; 23, 2, -11, -52, -164, -201, -2494, -523, -660, -548; 3025, 450, -1434, -6925, -22100, -27325, -340650, -71466, -90275, -75100],152,11]
%
% END OF LATTICE L153.11
%
%
% LATTICE L153.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[4200, 9600, -2200; 9600, 21928, -5024; -2200, -5024, 1151],[200, 8, 1],[-69, -520, -5541, -290, -129, -5, 2, -9, -6, -19; 221, 1657, 17650, 923, 410, 15, -5, 50, 21, 62; 832, 6234, 66400, 3472, 1542, 56, -18, 200, 80, 234],152,12]
%
% END OF LATTICE L153.12
%
%
% LATTICE L153.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[23454200, 9316000, -231400; 9316000, 3700312, -91912; -231400, -91912, 2283],[200, 8, 1],[-95, -717, -7641, -400, -178, -7, 3, -9, -8, -26; 299, 2248, 23950, 1253, 557, 21, -8, 50, 27, 83; 2408, 17826, 189700, 9900, 4382, 136, -18, 1100, 276, 706],152,13]
%
% END OF LATTICE L153.13
%
%
% LATTICE L153.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-4900, 1300, 100; 1300, -275, -25; 100, -25, -2],[100, 25, 1],[0, -5, -1, -1, 1, 2, 61, 13, 17, 15; -3, -4, 0, 2, 0, -5, -220, -48, -66, -64; 25, -250, -57, -75, 50, 150, 5150, 1107, 1475, 1350],152,14]
%
% END OF LATTICE L153.14
%
%
% LATTICE L153.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2304700, 523500, 24100; 523500, -118850, -5475; 24100, -5475, -252],[100, 25, 1],[-53, -17, 4, 23, 3, -93, -2027, -442, -607, -587; -56, -24, 3, 23, 4, -94, -2076, -453, -623, -604; -3850, -1100, 318, 1700, 200, -6850, -148700, -32418, -44500, -43000],152,15]
%
% END OF LATTICE L153.15
%
%
% LATTICE L153.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[26350, -6946500, -3402200; -6946500, 1832333950, 897425550; -3402200, 897425550, 439533753],[50, 50, 1],[-1, 13, 11, 34, 54, 147, 1009, 427, 550, 238; -2155, 11375, 9148, 27109, 40688, 106379, 718193, 303524, 389787, 167760; 4400, -23225, -18678, -55350, -83075, -217200, -1466375, -619722, -795850, -342525],152,16]
%
% END OF LATTICE L153.16
%
%
% LATTICE L153.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-39400, 4800, 200; 4800, -550, -25; 200, -25, -1],[200, 25, 1],[0, -5, -1, -1, 1, 2, 61, 13, 17, 15; -3, -24, -4, -2, 4, 3, 24, 4, 2, -4; 50, -500, -114, -150, 100, 300, 10300, 2214, 2950, 2700],152,17]
%
% END OF LATTICE L153.17
%
%
% LATTICE L153.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-52710600, -182800, -26549800; -182800, -575, -91900; -26549800, -91900, -13372351],[200, 25, 1],[-7389, -16727, -675, 1838, 1875, -9190, -447485, -49062, -68154, -134507; -44337, -100376, -4051, 11028, 11252, -55141, -2685008, -294383, -408940, -807076; 14975, 33900, 1368, -3725, -3800, 18625, 906900, 99432, 138125, 272600],152,18]
%
% END OF LATTICE L153.18
%
%
% LATTICE L153.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[200, 7100, 1700; 7100, 303700, 72700; 1700, 72700, 17403],[100, 100, 1],[8, 17, 5, 1, 1, 9, 221, 97, 135, 67; 311, 634, 178, 0, -12, 287, 7738, 3410, 4784, 2404; -1300, -2650, -744, 0, 50, -1200, -32350, -14256, -20000, -10050],152,19]
%
% END OF LATTICE L153.19
%
%
% LATTICE L153.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[25600, -1780500, -426300; -1780500, 124041800, 29699000; -426300, 29699000, 7110753],[100, 100, 1],[-223, -246, -144, -22, 1, -197, -2694, -2376, -3338, -841; -5522, -6079, -3559, -551, 6, -4947, -67204, -59255, -83201, -20944; 23050, 25375, 14856, 2300, -25, 20650, 280525, 247344, 347300, 87425],152,20]
%
% END OF LATTICE L153.20
%
%
% LATTICE L153.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-686200, -57400, -1200; -57400, -4400, 0; -1200, 0, 23],[200, 200, 1],[50, 5, -5, -23, -1, 92, 989, 431, 591, 285; -653, -66, 65, 300, 13, -1201, -12912, -5627, -7716, -3721; 2600, 250, -264, -1200, -50, 4800, 51550, 22464, 30800, 14850],152,21]
%
% END OF LATTICE L153.21
%
%
% LATTICE L153.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-454623600, 16186200, 8768800; 16186200, -576200, -312200; 8768800, -312200, -169133],[200, 200, 1],[-519, 32, 86, 275, -1, -1073, -11176, -4862, -6643, -3183; 50, 5, -5, -23, -1, 92, 989, 431, 591, 285; -27000, 1650, 4468, 14300, -50, -55800, -581250, -252868, -345500, -165550],152,22]
%
% END OF LATTICE L153.22
%

\medskip%
%------------------------------WEYL-GROUP-W154--------------------------------
%
\leavevmode\llap{}%
$W_{154}$%
\qquad\llap{3} lattices, $\chi=2$%
\hfill%
$\slashthree2\slashtwo2\rtimes D_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L154.1
%
\leavevmode%
${L_{154.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{1}{}3\above{1pt}{1pt}{-}{}9\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${6}\above{1pt}{1pt}{+}{3}{6}\above{1pt}{1pt}{b}{2}{4}\above{1pt}{1pt}{*}{2}{36}\above{1pt}{1pt}{b}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
252\\72\\-36
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
72\\6\\-27
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-36\\-27\\-14
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\-7\\6
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-7\\17\\-15
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\2\\-2
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
17\\-42\\36
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[252, 72, -36; 72, 6, -27; -36, -27, -14],[36, 3, 1],[3, -7, -1, 17; -7, 17, 2, -42; 6, -15, -2, 36],153,1]
%
% END OF LATTICE L154.1
%
%
% LATTICE L154.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[9, 0, 9; 0, -3, 3; 9, 3, 7],[9, 3, 1],[1, -3, -1, 1; -1, 2, 0, -1; 0, 3, 0, -1],153,2]
%
% END OF LATTICE L154.2
%
%
% LATTICE L154.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[45288, 8532, -5544; 8532, 1608, -1044; -5544, -1044, 679],[36, 12, 1],[5, 3, 1, 5; -11, -8, -4, -15; 24, 12, 2, 18],153,3]
%
% END OF LATTICE L154.3
%

\medskip%
%------------------------------WEYL-GROUP-W155--------------------------------
%
\leavevmode\llap{}%
$W_{155}$%
\qquad\llap{3} lattices, $\chi=2$%
\hfill%
$6\slashtwo6|\rtimes D_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L155.1
%
\leavevmode%
${L_{155.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{-}{}9\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${6}\above{1pt}{1pt}{}{6}{18}\above{1pt}{1pt}{b}{2}{2}\above{1pt}{1pt}{}{6}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-36\\36\\36
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
36\\-30\\-27
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
36\\-27\\-22
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\5\\-3
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2\\-3\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-3\\2
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-36, 36, 36; 36, -30, -27; 36, -27, -22],[36, 3, 1],[2, -2, -1; 5, -3, -3; -3, 0, 2],154,1]
%
% END OF LATTICE L155.1
%
%
% LATTICE L155.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-9, 18, 18; 18, -30, -27; 18, -27, -22],[9, 3, 1],[4, -4, -2; 5, -3, -3; -3, 0, 2],154,2]
%
% END OF LATTICE L155.2
%
%
% LATTICE L155.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1800, -540, -828; -540, 168, 252; -828, 252, 383],[36, 12, 1],[3, 1, 1; -8, 3, -3; 12, 0, 4],154,3]
%
% END OF LATTICE L155.3
%

\medskip%
%------------------------------WEYL-GROUP-W156--------------------------------
%
\leavevmode\llap{}%
$W_{156}$%
\qquad\llap{6} lattices, $\chi=18$%
\hfill%
$242242\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L156.1
%
\leavevmode%
${L_{156.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{2}{}27\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${54}\above{1pt}{1pt}{b}{2}{4}\above{1pt}{1pt}{*}{4}{2}\above{1pt}{1pt}{s}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1352484\\8316\\11556
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
8316\\-46\\-73
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
11556\\-73\\-98
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
38879\\1356480\\3572640
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-261\\-9107\\-23983
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-324\\-11304\\-29773
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-10\\-351\\-918
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-5\\-174\\-460
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5\\175\\459
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-1352484, 8316, 11556; 8316, -46, -73; 11556, -73, -98],[108, 1, 1],[-10, -5, 5, 253, 59, 4; -351, -174, 175, 8829, 2058, 139; -918, -460, 459, 23247, 5422, 368],155,1]
%
% END OF LATTICE L156.1
%
%
% LATTICE L156.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-22545, 6723, -13203; 6723, -1999, 3916; -13203, 3916, -7655],[27, 1, 1],[-3482, -407, -57, 107, 32, -68; -25407, -2969, -415, 783, 233, -497; -6993, -817, -114, 216, 64, -137],155,2]
%
% END OF LATTICE L156.2
%
%
% LATTICE L156.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[171471384, -2517156, -44527752; -2517156, 36952, 653656; -44527752, 653656, 11562983],[108, 4, 1],[-617, -41, -733, -28651, -3211, -351; 0, 2, 23, 783, 85, 6; -2376, -158, -2824, -110376, -12370, -1352],155,3]
%
% END OF LATTICE L156.3
%
%
% LATTICE L156.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-27891, -66690, 3105; -66690, -159462, 7425; 3105, 7425, -337],[27, 27, 1],[-993, -2854, -98, 60, 55, -835; 414, 1190, 41, -25, -23, 348; -29, -81, 0, 2, 0, -27],155,4]
%
% END OF LATTICE L156.4
%
%
% LATTICE L156.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-57132, 8424, 4212; 8424, -1242, -621; 4212, -621, -310],[108, 27, 1],[4, 29, 4, 0, -5, 0; 41, 274, 27, -1, -34, 13; -29, -162, 0, 2, 0, -27],155,5]
%
% END OF LATTICE L156.5
%
%
% LATTICE L156.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[30024, 19764, -4968; 19764, 15768, -3996; -4968, -3996, 1013],[108, 108, 1],[29, 85, 6, 0, 2, 23; -995, -2911, -199, 1, -71, -795; -3784, -11070, -756, 4, -270, -3024],155,6]
%
% END OF LATTICE L156.6
%

\medskip%
%------------------------------WEYL-GROUP-W157--------------------------------
%
\leavevmode\llap{}%
$W_{157}$%
\qquad\llap{8} lattices, $\chi=48$%
\hfill%
$\infty2|2\infty|\infty2|2\infty|\rtimes D_{4}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L157.1
%
\leavevmode%
${L_{157.1}}$%
{} : {$1\above{1pt}{1pt}{2}{0}4\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{-2}{}7\above{1pt}{1pt}{1}{}$}\EasyButWeakLineBreak%
{${28}\above{1pt}{1pt}{1,0}{\infty z}{7}\above{1pt}{1pt}{}{2}{1}\above{1pt}{1pt}{}{2}{28}\above{1pt}{1pt}{2,1}{\infty}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-868\\-56\\-728
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-56\\0\\-25
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-728\\-25\\-477
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
377\\5124\\-840
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
18\\243\\-40
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
279\\3782\\-621
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-25\\-350\\56
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-47\\-644\\105
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-13\\-177\\29
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-151\\-2044\\336
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-868, -56, -728; -56, 0, -25; -728, -25, -477],[28, 1, 1],[-25, -47, -13, -151, -101, -16, 4, 25; -350, -644, -177, -2044, -1358, -210, 55, 336; 56, 105, 29, 336, 224, 35, -9, -56],156,1]
%
% END OF LATTICE L157.1
%
\hbox{}\par\smallskip%
%
% LATTICE L157.2
%
\leavevmode%
${L_{157.2}}$%
{} : {$1\above{1pt}{1pt}{2}{{\rm II}}8\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{-2}{}7\above{1pt}{1pt}{1}{}$}\EasyButWeakLineBreak%
{${56}\above{1pt}{1pt}{1,0}{\infty a}{56}\above{1pt}{1pt}{r}{2}{2}\above{1pt}{1pt}{s}{2}{14}\above{1pt}{1pt}{4,3}{\infty b}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1736\\-672\\-56
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-672\\-254\\-25
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-56\\-25\\0
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
377\\-840\\-1512
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
153\\-341\\-612
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
9\\-20\\-37
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-101\\224\\420
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-151\\336\\616
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-13\\29\\52
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-47\\105\\182
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-1736, -672, -56; -672, -254, -25; -56, -25, 0],[56, 1, 1],[-101, -151, -13, -47, -25, 25, 4, -16; 224, 336, 29, 105, 56, -56, -9, 35; 420, 616, 52, 182, 84, -112, -16, 70],156,2]
%
% END OF LATTICE L157.2
%
%
% LATTICE L157.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[170352, 53116, -44772; 53116, 16564, -13960; -44772, -13960, 11767],[28, 4, 1],[195, 351, 80, 255, 407, 251, 6, 46; 0, 7, 3, 14, 28, 21, 1, 0; 742, 1344, 308, 987, 1582, 980, 24, 175],156,3]
%
% END OF LATTICE L157.3
%
%
% LATTICE L157.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[196, 56, 0; 56, -49, 14; 0, 14, -3],[28, 7, 1],[-5, -7, -4, -2, -1, 1, 1, -1; 18, 24, 13, 6, 2, -4, -3, 4; 78, 104, 56, 25, 6, -20, -14, 17],156,4]
%
% END OF LATTICE L157.4
%
%
% LATTICE L157.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-18424, 336, 336; 336, 0, -7; 336, -7, -6],[56, 7, 1],[5, 7, 4, 2, 1, -1, -1, 1; 36, 48, 26, 12, 4, -8, -6, 8; 232, 328, 189, 95, 48, -48, -49, 45],156,5]
%
% END OF LATTICE L157.5
%
%
% LATTICE L157.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-23408, -5544, -1792; -5544, -1312, -424; -1792, -424, -137],[56, 8, 1],[-3, -2, -1, 1, 3, 2, 1, -1; -63, -7, 12, 14, -35, -42, -40, -210; 238, 49, -24, -56, 70, 105, 112, 672],156,6]
%
% END OF LATTICE L157.6
%
%
% LATTICE L157.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[588, -3416, 952; -3416, 19796, -5516; 952, -5516, 1537],[28, 28, 1],[-5, -4, -11, -8, -5, -1, 1, -2; 13, 4, -2, -7, -7, -1, 8, 13; 50, 17, 0, -20, -22, -3, 28, 48],156,7]
%
% END OF LATTICE L157.7
%
%
% LATTICE L157.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-336, -1848, -784; -1848, -9632, -4088; -784, -4088, -1735],[56, 56, 1],[0, -1, -11, -13, -6, -2, -1, 1; -11, -18, -140, -126, -47, -11, 24, 10; 26, 43, 336, 304, 114, 27, -56, -24],156,8]
%
% END OF LATTICE L157.8
%

\medskip%
%------------------------------WEYL-GROUP-W158--------------------------------
%
\leavevmode\llap{}%
$W_{158}$%
\qquad\llap{2} lattices, $\chi=16$%
\hfill%
$3\infty3\infty\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L158.1
%
\leavevmode%
${L_{158.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}32\above{1pt}{1pt}{-}{5}$}\EasyButWeakLineBreak%
{${2}\above{1pt}{1pt}{+}{3}{2}\above{1pt}{1pt}{8,5}{\infty a}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
160\\32\\128
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
32\\6\\25
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
128\\25\\102
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\0\\0
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\0\\1
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\1\\0
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\-2\\-1
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-3\\2
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[160, 32, 128; 32, 6, 25; 128, 25, 102],[32, 1, 1],[1, -1, 2, 2; -2, -3, -1, 2; -1, 2, -2, -3],157,1]
%
% END OF LATTICE L158.1
%
%
% LATTICE L158.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[192, 800, 32; 800, 3264, 128; 32, 128, 5],[32, 32, 1],[-2, -3, -1, 2; -1, 2, -2, -3; 32, -32, 64, 64],157,2]
%
% END OF LATTICE L158.2
%

\medskip%
%------------------------------WEYL-GROUP-W159--------------------------------
%
\leavevmode\llap{}%
$W_{159}$%
\qquad\llap{2} lattices, $\chi=12$%
\hfill%
$\slashtwo4\slashinfty4\rtimes D_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L159.1
%
\leavevmode%
${L_{159.1}}$%
{} : {$1\above{1pt}{1pt}{2}{2}32\above{1pt}{1pt}{1}{7}$}\EasyButWeakLineBreak%
{${1}\above{1pt}{1pt}{r}{2}{4}\above{1pt}{1pt}{*}{4}{2}\above{1pt}{1pt}{8,7}{\infty a}{2}\above{1pt}{1pt}{}{4}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-47392\\1216\\608
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1216\\-31\\-16
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
608\\-16\\-7
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-31\\-16
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-32\\-14
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\93\\47
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\63\\29
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-47392, 1216, 608; 1216, -31, -16; 608, -16, -7],[32, 1, 1],[-1, -1, 3, 2; -31, -32, 93, 63; -16, -14, 47, 29],158,1]
%
% END OF LATTICE L159.1
%
%
% LATTICE L159.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[64, -96, 0; -96, 160, 0; 0, 0, -1],[32, 32, 1],[-3, -2, 3, 1; -3, -1, 2, -2; -16, 0, 0, -32],158,2]
%
% END OF LATTICE L159.2
%

\medskip%
%------------------------------WEYL-GROUP-W160--------------------------------
%
\leavevmode\llap{}%
$W_{160}$%
\qquad\llap{10} lattices, $\chi=24$%
\hfill%
$2\slashinfty2\infty|\infty\rtimes D_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L160.1
%
\leavevmode%
${L_{160.1}}$%
{} : {$1\above{1pt}{1pt}{2}{{\rm II}}32\above{1pt}{1pt}{1}{1}$}\EasyButWeakLineBreak%
{${32}\above{1pt}{1pt}{b}{2}{2}\above{1pt}{1pt}{8,1}{\infty b}{2}\above{1pt}{1pt}{l}{2}{32}\above{1pt}{1pt}{1,0}{\infty}{32}\above{1pt}{1pt}{1,0}{\infty z}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-26848\\992\\928
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
992\\-30\\-35
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
928\\-35\\-32
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-5\\-16\\-128
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-4\\-11\\-104
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5\\15\\128
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
67\\192\\1728
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
29\\80\\752
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-26848, 992, 928; 992, -30, -35; 928, -35, -32],[32, 1, 1],[-5, -4, 5, 67, 29; -16, -11, 15, 192, 80; -128, -104, 128, 1728, 752],159,1]
%
% END OF LATTICE L160.1
%
\hbox{}\par\smallskip%
%
% LATTICE L160.2
%
\leavevmode%
${L_{160.2}}$%
{} : {$1\above{1pt}{1pt}{-}{3}4\above{1pt}{1pt}{1}{1}64\above{1pt}{1pt}{-}{5}$}\EasyButWeakLineBreak%
{${16}\above{1pt}{1pt}{s}{2}{64}\above{1pt}{1pt}{8,1}{\infty z}{64}\above{1pt}{1pt}{*}{2}{16}\above{1pt}{1pt}{16,9}{\infty z}{4}\above{1pt}{1pt}{16,5}{\infty}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-14528\\-1344\\-1472
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1344\\-124\\-136
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1472\\-136\\-149
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\2\\8
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\24\\-32
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7\\-8\\-64
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5\\-30\\-24
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\-9\\8
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-14528, -1344, -1472; -1344, -124, -136; -1472, -136, -149],[64, 4, 1],[-1, 1, 7, 5, 0; 2, 24, -8, -30, -9; 8, -32, -64, -24, 8],159,2]
%
% END OF LATTICE L160.2
%
\hbox{}\par\smallskip%
%
% LATTICE L160.3
%
\leavevmode%
${L_{160.3}}$%
{} : {$1\above{1pt}{1pt}{-}{5}4\above{1pt}{1pt}{1}{1}64\above{1pt}{1pt}{-}{3}$}\EasyButWeakLineBreak%
{${16}\above{1pt}{1pt}{*}{2}{4}\above{1pt}{1pt}{8,3}{\infty z}{1}\above{1pt}{1pt}{r}{2}{16}\above{1pt}{1pt}{16,15}{\infty z}{4}\above{1pt}{1pt}{16,11}{\infty}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-21824\\576\\576
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
576\\-12\\-16
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
576\\-16\\-15
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-6\\-32
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-8\\-30
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\6\\31
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
11\\74\\336
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\15\\60
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-21824, 576, 576; 576, -12, -16; 576, -16, -15],[64, 4, 1],[-1, -1, 1, 11, 2; -6, -8, 6, 74, 15; -32, -30, 31, 336, 60],159,3]
%
% END OF LATTICE L160.3
%
\hbox{}\par\smallskip%
%
% LATTICE L160.4
%
\leavevmode%
${L_{160.4}}$%
{} : {$1\above{1pt}{1pt}{1}{1}4\above{1pt}{1pt}{1}{1}64\above{1pt}{1pt}{1}{7}$}\EasyButWeakLineBreak%
{${4}\above{1pt}{1pt}{r}{2}{4}\above{1pt}{1pt}{8,7}{\infty z}{1}\above{1pt}{1pt}{}{2}{4}\above{1pt}{1pt}{16,15}{\infty}{16}\above{1pt}{1pt}{16,3}{\infty z}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-13376\\960\\448
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
960\\-60\\-32
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
448\\-32\\-15
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\1\\-32
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\0\\-30
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\-2\\63
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
9\\-7\\280
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5\\-2\\152
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-13376, 960, 448; 960, -60, -32; 448, -32, -15],[64, 4, 1],[-1, -1, 2, 9, 5; 1, 0, -2, -7, -2; -32, -30, 63, 280, 152],159,4]
%
% END OF LATTICE L160.4
%
\hbox{}\par\smallskip%
%
% LATTICE L160.5
%
\leavevmode%
${L_{160.5}}$%
{} : {$1\above{1pt}{1pt}{1}{7}4\above{1pt}{1pt}{1}{1}64\above{1pt}{1pt}{1}{1}$}\EasyButWeakLineBreak%
{${4}\above{1pt}{1pt}{r}{2}{64}\above{1pt}{1pt}{2,1}{\infty a}{64}\above{1pt}{1pt}{}{2}{4}\above{1pt}{1pt}{16,1}{\infty}{16}\above{1pt}{1pt}{16,5}{\infty z}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
64\\0\\0
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\-1020\\-32
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\-32\\-1
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-7\\208
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-16\\480
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\0\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\1\\-32
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-2\\56
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[64, 0, 0; 0, -1020, -32; 0, -32, -1],[64, 4, 1],[-1, -1, 1, 0, -1; -7, -16, 0, 1, -2; 208, 480, 0, -32, 56],159,5]
%
% END OF LATTICE L160.5
%
%
% LATTICE L160.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-13376, 960, 448; 960, -48, -32; 448, -32, -15],[64, 16, 1],[-1, -1, 1, 11, 4; 1, 0, -1, -7, -1; -32, -30, 31, 336, 120],159,6]
%
% END OF LATTICE L160.6
%
%
% LATTICE L160.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-64, 480, -32; 480, -3328, 224; -32, 224, -15],[32, 32, 1],[3, 13, -1, -1, 1; -1, -2, 2, 0, -1; -23, -64, 32, 2, -18],159,7]
%
% END OF LATTICE L160.7
%
%
% LATTICE L160.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[64, -128, 0; -128, 272, 0; 0, 0, -1],[64, 16, 1],[-16, -17, 1, 2, -3; -7, -8, 0, 1, -1; -32, -32, 0, 0, -8],159,8]
%
% END OF LATTICE L160.8
%
%
% LATTICE L160.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-225728, 3840, 3712; 3840, -48, -64; 3712, -64, -61],[64, 16, 1],[-4, -5, 21, 22, 5; -11, -16, 56, 61, 15; -232, -288, 1216, 1272, 288],159,9]
%
% END OF LATTICE L160.9
%
%
% LATTICE L160.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-64, 576, -64; 576, -4720, 528; -64, 528, -59],[64, 16, 1],[-1, -1, 2, 11, 4; -1, 1, 1, -1, -3; -8, 10, 6, -24, -32],159,10]
%
% END OF LATTICE L160.10
%

\medskip%
%------------------------------WEYL-GROUP-W161--------------------------------
%
\leavevmode\llap{}%
$W_{161}$%
\qquad\llap{12} lattices, $\chi=24$%
\hfill%
$\slashinfty2|2\slashinfty2|2\rtimes D_{4}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L161.1
%
\leavevmode%
${L_{161.1}}$%
{} : {$1\above{1pt}{1pt}{2}{0}32\above{1pt}{1pt}{1}{1}$}\EasyButWeakLineBreak%
{${32}\above{1pt}{1pt}{1,0}{\infty b}{32}\above{1pt}{1pt}{}{2}{1}\above{1pt}{1pt}{r}{2}{32}\above{1pt}{1pt}{4,3}{\infty z}{32}\above{1pt}{1pt}{s}{2}{4}\above{1pt}{1pt}{*}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-63712\\256\\3968
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
256\\-1\\-16
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3968\\-16\\-247
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3\\-16\\-48
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\224\\32
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\44\\13
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7\\240\\96
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\0\\16
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-32\\-14
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-63712, 256, 3968; 256, -1, -16; 3968, -16, -247],[32, 1, 1],[-3, 3, 1, 7, 1, -1; -16, 224, 44, 240, 0, -32; -48, 32, 13, 96, 16, -14],160,1]
%
% END OF LATTICE L161.1
%
\hbox{}\par\smallskip%
%
% LATTICE L161.2
%
\leavevmode%
${L_{161.2}}$%
{} : {$[1\above{1pt}{1pt}{-}{}2\above{1pt}{1pt}{1}{}]\above{1pt}{1pt}{}{2}32\above{1pt}{1pt}{-}{3}$}\EasyButWeakLineBreak%
{${4}\above{1pt}{1pt}{8,3}{\infty z}{1}\above{1pt}{1pt}{r}{2}{8}\above{1pt}{1pt}{*}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3488\\160\\160
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
160\\-6\\-8
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
160\\-8\\-7
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
127\\896\\1792
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-6\\-43\\-84
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-6\\-42\\-85
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5\\36\\70
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\8\\13
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-6\\-16
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-3488, 160, 160; 160, -6, -8; 160, -8, -7],[32, 2, 1],[5, 1, -1, -1, 1, 5; 36, 8, -6, -8, 6, 34; 70, 13, -16, -14, 15, 72],160,2]
%
% END OF LATTICE L161.2
%
\hbox{}\par\smallskip%
%
% LATTICE L161.3
%
\leavevmode%
${L_{161.3}}$%
{} : {$[1\above{1pt}{1pt}{1}{}2\above{1pt}{1pt}{1}{}]\above{1pt}{1pt}{}{2}64\above{1pt}{1pt}{1}{7}$}\spacer%
\instructions{m}%
\EasyButWeakLineBreak%
{${2}\above{1pt}{1pt}{16,7}{\infty}{8}\above{1pt}{1pt}{l}{2}{1}\above{1pt}{1pt}{}{2}{2}\above{1pt}{1pt}{16,15}{\infty}{8}\above{1pt}{1pt}{*}{2}{4}\above{1pt}{1pt}{l}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-32320\\704\\704
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
704\\-14\\-16
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
704\\-16\\-15
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\13\\32
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7\\102\\216
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\30\\61
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\31\\60
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-14\\-32
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-16\\-30
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-32320, 704, 704; 704, -14, -16; 704, -16, -15],[64, 2, 1],[1, 7, 2, 2, -1, -1; 13, 102, 30, 31, -14, -16; 32, 216, 61, 60, -32, -30],160,3]
%
% END OF LATTICE L161.3
%
\hbox{}\par\smallskip%
%
% LATTICE L161.4
%
\leavevmode%
${L_{161.4}}$%
{} : {$1\above{1pt}{1pt}{-}{3}4\above{1pt}{1pt}{1}{7}32\above{1pt}{1pt}{-}{3}$}\EasyButWeakLineBreak%
{${32}\above{1pt}{1pt}{8,5}{\infty z}{32}\above{1pt}{1pt}{s}{2}{16}\above{1pt}{1pt}{*}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-4000\\992\\64
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
992\\-244\\-16
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
64\\-16\\-1
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-112\\1344
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\25\\-312
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\2\\-25
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3\\-12\\-16
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-12\\96
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\-2\\80
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-4000, 992, 64; 992, -244, -16; 64, -16, -1],[32, 4, 1],[-3, -1, 1, 3, 1, -1; -12, -12, -2, 4, 4, -2; -16, 96, 80, 112, 0, -32],160,4]
%
% END OF LATTICE L161.4
%
\hbox{}\par\smallskip%
%
% LATTICE L161.5
%
\leavevmode%
${L_{161.5}}$%
{} : {$1\above{1pt}{1pt}{1}{7}4\above{1pt}{1pt}{1}{1}32\above{1pt}{1pt}{1}{1}$}\EasyButWeakLineBreak%
{${32}\above{1pt}{1pt}{2,1}{\infty a}{32}\above{1pt}{1pt}{}{2}{4}\above{1pt}{1pt}{r}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
32\\0\\0
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\-252\\-16
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\-16\\-1
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-5\\-8\\96
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
15\\29\\-360
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\2\\-25
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3\\0\\-16
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-5\\-8\\96
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-3\\40
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[32, 0, 0; 0, -252, -16; 0, -16, -1],[32, 4, 1],[-3, -5, -1, -1, 1, 0; 0, -8, -3, -8, 0, 1; -16, 96, 40, 112, 0, -16],160,5]
%
% END OF LATTICE L161.5
%
%
% LATTICE L161.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-1312, 224, 96; 224, -30, -16; 96, -16, -7],[32, 2, 1],[7, 1, -1, -1, 2, 4; -4, 0, 1, 0, -2, -3; 102, 13, -16, -14, 31, 60],160,6]
%
% END OF LATTICE L161.6
%
%
% LATTICE L161.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1312, 224, 96; 224, -24, -16; 96, -16, -7],[32, 8, 1],[1, 5, 5, 1, -1, -1; 0, -2, -3, -1, 0, 1; 13, 70, 72, 15, -14, -16],160,7]
%
% END OF LATTICE L161.7
%
%
% LATTICE L161.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-32, 160, -32; 160, -712, 144; -32, 144, -29],[32, 8, 1],[2, 5, 5, 2, -1, -1; -3, -3, -1, 1, 1, -1; -18, -22, -12, 2, 6, -4],160,8]
%
% END OF LATTICE L161.8
%
%
% LATTICE L161.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[32, 0, 0; 0, -240, -16; 0, -16, -1],[32, 16, 1],[-3, -5, -2, -1, 1, 0; 0, -4, -3, -4, 0, 1; -16, 32, 32, 48, 0, -16],160,9]
%
% END OF LATTICE L161.9
%
%
% LATTICE L161.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-15328, -10624, 1088; -10624, -7344, 752; 1088, 752, -77],[32, 16, 1],[-1, 1, 0, -3, -5, -2; 36, -8, -9, 16, 60, 35; 336, -64, -88, 112, 512, 312],160,10]
%
% END OF LATTICE L161.10
%
%
% LATTICE L161.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-14624, -16576, 960; -16576, -18784, 1088; 960, 1088, -63],[32, 32, 1],[2, 5, 10, 1, -1, -2; -3, -4, -5, 0, 1, -1; -22, 6, 64, 15, 2, -48],160,11]
%
% END OF LATTICE L161.11
%
%
% LATTICE L161.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[64, -64, 0; -64, 96, 0; 0, 0, -1],[64, 32, 1],[-3, -3, -1, 1, 1, -1; -5, -3, 0, 1, -1, -4; -32, -16, 0, 0, -16, -32],160,12]
%
% END OF LATTICE L161.12
%

\medskip%
%------------------------------WEYL-GROUP-W162--------------------------------
%
\leavevmode\llap{}%
$W_{162}$%
\qquad\llap{16} lattices, $\chi=36$%
\hfill%
$\slashtwo\infty|\infty\slashtwo\infty|\infty\rtimes D_{4}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L162.1
%
\leavevmode%
${L_{162.1}}$%
{} : {$1\above{1pt}{1pt}{2}{0}4\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{-2}{}9\above{1pt}{1pt}{1}{}$}\EasyButWeakLineBreak%
{${9}\above{1pt}{1pt}{}{2}{4}\above{1pt}{1pt}{6,1}{\infty}{4}\above{1pt}{1pt}{3,1}{\infty z}{1}\above{1pt}{1pt}{}{2}{36}\above{1pt}{1pt}{2,1}{\infty}{36}\above{1pt}{1pt}{1,0}{\infty z}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-298476\\-100440\\-33696
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-100440\\-33799\\-11339
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-33696\\-11339\\-3804
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\9\\-18
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-13\\44\\-16
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
15\\-56\\34
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
55\\-191\\82
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
367\\-1260\\504
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
119\\-396\\126
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-298476, -100440, -33696; -100440, -33799, -11339; -33696, -11339, -3804],[36, 1, 1],[-1, -13, 15, 55, 367, 119; 9, 44, -56, -191, -1260, -396; -18, -16, 34, 82, 504, 126],161,1]
%
% END OF LATTICE L162.1
%
\hbox{}\par\smallskip%
%
% LATTICE L162.2
%
\leavevmode%
${L_{162.2}}$%
{} : {$1\above{1pt}{1pt}{2}{0}4\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{2}{}9\above{1pt}{1pt}{-}{}$}\EasyButWeakLineBreak%
{${4}\above{1pt}{1pt}{}{2}{1}\above{1pt}{1pt}{12,5}{\infty}{4}\above{1pt}{1pt}{3,2}{\infty a}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-348012\\-147888\\-3492
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-147888\\-62845\\-1484
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3492\\-1484\\-35
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
61559\\-139320\\-233280
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
26182\\-59255\\-99216
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
608\\-1376\\-2305
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-159\\360\\596
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-84\\190\\323
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-47\\106\\194
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-348012, -147888, -3492; -147888, -62845, -1484; -3492, -1484, -35],[36, 1, 1],[-159, -84, -47, 7, 8, -29; 360, 190, 106, -16, -18, 66; 596, 323, 194, -20, -35, 94],161,2]
%
% END OF LATTICE L162.2
%
\hbox{}\par\smallskip%
%
% LATTICE L162.3
%
\leavevmode%
${L_{162.3}}$%
{} : {$1\above{1pt}{1pt}{2}{{\rm II}}8\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{-2}{}9\above{1pt}{1pt}{-}{}$}\EasyButWeakLineBreak%
{${8}\above{1pt}{1pt}{r}{2}{18}\above{1pt}{1pt}{4,1}{\infty a}{72}\above{1pt}{1pt}{1,0}{\infty a}{72}\above{1pt}{1pt}{r}{2}{2}\above{1pt}{1pt}{12,1}{\infty a}{8}\above{1pt}{1pt}{3,2}{\infty a}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-741240\\333072\\-99000
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
333072\\-149664\\44485
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-99000\\44485\\-13222
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-41\\-96\\-16
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-121\\-288\\-63
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
233\\540\\72
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1531\\3600\\648
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
275\\648\\121
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
157\\372\\76
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-741240, 333072, -99000; 333072, -149664, 44485; -99000, 44485, -13222],[72, 1, 1],[-41, -121, 233, 1531, 275, 157; -96, -288, 540, 3600, 648, 372; -16, -63, 72, 648, 121, 76],161,3]
%
% END OF LATTICE L162.3
%
\hbox{}\par\smallskip%
%
% LATTICE L162.4
%
\leavevmode%
${L_{162.4}}$%
{} : {$1\above{1pt}{1pt}{2}{{\rm II}}8\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{2}{}9\above{1pt}{1pt}{1}{}$}\EasyButWeakLineBreak%
{${2}\above{1pt}{1pt}{l}{2}{8}\above{1pt}{1pt}{3,2}{\infty}{8}\above{1pt}{1pt}{3,1}{\infty z}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1289592\\-282096\\-9504
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-282096\\-61708\\-2079
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-9504\\-2079\\-70
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
83447\\-377712\\-109800
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
18259\\-82647\\-24025
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
608\\-2752\\-801
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
8\\-36\\-17
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7\\-32\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-47\\212\\84
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-1289592, -282096, -9504; -282096, -61708, -2079; -9504, -2079, -70],[72, 1, 1],[8, 7, -47, -84, -159, -29; -36, -32, 212, 380, 720, 132; -17, 0, 84, 117, 200, 16],161,4]
%
% END OF LATTICE L162.4
%
%
% LATTICE L162.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[109116, -13860, 28404; -13860, 1968, -3656; 28404, -3656, 7405],[36, 4, 1],[-349, 3, -308, -1605, -2591, -1658; 351, -3, 309, 1611, 2601, 1665; 1512, -13, 1334, 6952, 11223, 7182],161,5]
%
% END OF LATTICE L162.5
%
%
% LATTICE L162.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1599444, -49104, 377208; -49104, 1516, -11584; 377208, -11584, 88961],[36, 4, 1],[-754, -1479, -347, 2, -25, -405; 1382, 2710, 635, -4, 46, 743; 3377, 6624, 1554, -9, 112, 1814],161,6]
%
% END OF LATTICE L162.6
%
%
% LATTICE L162.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-345708, -3060, -153540; -3060, -27, -1359; -153540, -1359, -68192],[36, 9, 1],[7, 8, -55, -221, -36, -15; 12, -1, -112, -332, -49, -12; -16, -18, 126, 504, 82, 34],161,7]
%
% END OF LATTICE L162.7
%
%
% LATTICE L162.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[36, 0, 0; 0, -315, 297; 0, 297, -280],[36, 9, 1],[1, 0, -3, -9, -4, -1; 0, -17, 16, 200, 117, 84; 0, -18, 18, 216, 126, 90],161,8]
%
% END OF LATTICE L162.8
%
%
% LATTICE L162.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-204624, 2808, -66456; 2808, -32, 912; -66456, 912, -21583],[72, 8, 1],[39, 38, -193, -1801, -153, -76; 2, 0, -9, -54, -4, -1; -120, -117, 594, 5544, 471, 234],161,9]
%
% END OF LATTICE L162.9
%
%
% LATTICE L162.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-720720, 5112, 10152; 5112, -32, -72; 10152, -72, -143],[72, 8, 1],[-1, -1, 3, 37, 10, 6; 2, 0, -3, -18, -4, -1; -72, -71, 214, 2632, 711, 426],161,10]
%
% END OF LATTICE L162.10
%
%
% LATTICE L162.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1222776, -33840, 484200; -33840, -936, 13401; 484200, 13401, -191734],[72, 9, 1],[413, 88, 71, -7, -68, -17; -1528, -332, -276, 24, 268, 100; 936, 199, 160, -16, -153, -36],161,11]
%
% END OF LATTICE L162.11
%
%
% LATTICE L162.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[72, 0, 0; 0, -630, 297; 0, 297, -140],[72, 9, 1],[1, 0, -3, -9, -4, -1; 0, -17, 16, 200, 117, 84; 0, -36, 36, 432, 252, 180],161,12]
%
% END OF LATTICE L162.12
%
%
% LATTICE L162.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[11664, 41868, 10044; 41868, 224316, 53820; 10044, 53820, 12913],[36, 36, 1],[0, 1, 5, 8, 5, 1; 6, -743, -3538, -5536, -3431, -660; -25, 3096, 14742, 23067, 14296, 2750],161,13]
%
% END OF LATTICE L162.13
%
%
% LATTICE L162.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[10080, -10692, -2376; -10692, 11484, 2556; -2376, 2556, 569],[36, 36, 1],[0, 1, 17, 32, 63, 15; -2, 9, 156, 288, 563, 130; 9, -36, -630, -1161, -2268, -522],161,14]
%
% END OF LATTICE L162.14
%
%
% LATTICE L162.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-204624, 1648152, 366840; 1648152, -13274496, -2954592; 366840, -2954592, -657623],[72, 72, 1],[-1, -3, 3, 8, 101, 14; 78, 94, -163, -342, -4074, -459; -351, -424, 734, 1541, 18360, 2070],161,15]
%
% END OF LATTICE L162.15
%
%
% LATTICE L162.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-288, -25272, -5688; -25272, -1956816, -440424; -5688, -440424, -99127],[72, 72, 1],[-18, -4, -1, 2, 0, -3; -2933, -792, -474, 81, 79, -239; 13032, 3519, 2106, -360, -351, 1062],161,16]
%
% END OF LATTICE L162.16
%

\medskip%
%------------------------------WEYL-GROUP-W163--------------------------------
%
\leavevmode\llap{}%
$W_{163}$%
\qquad\llap{49} lattices, $\chi=36$%
\hfill%
$\slashtwo2\slashinfty2\slashtwo2\slashinfty2\rtimes D_{4}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L163.1
%
\leavevmode%
${L_{163.1}}$%
{} : {$1\above{1pt}{1pt}{2}{0}8\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{1}{}5\above{1pt}{1pt}{-}{}25\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{5}%
\EasyButWeakLineBreak%
{${25}\above{1pt}{1pt}{r}{2}{4}\above{1pt}{1pt}{*}{2}{40}\above{1pt}{1pt}{5,4}{\infty b}{40}\above{1pt}{1pt}{}{2}{1}\above{1pt}{1pt}{r}{2}{100}\above{1pt}{1pt}{*}{2}{40}\above{1pt}{1pt}{5,1}{\infty a}{40}\above{1pt}{1pt}{}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-733400\\1000\\8600
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1000\\35\\-25
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
8600\\-25\\-96
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
37\\1105\\3025
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
25\\746\\2044
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
125\\3728\\10220
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
91\\2712\\7440
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4\\119\\327
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-11\\-330\\-900
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-11\\-328\\-900
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
23\\688\\1880
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-733400, 1000, 8600; 1000, 35, -25; 8600, -25, -96],[200, 5, 1],[37, 25, 125, 91, 4, -11, -11, 23; 1105, 746, 3728, 2712, 119, -330, -328, 688; 3025, 2044, 10220, 7440, 327, -900, -900, 1880],162,1]
%
% END OF LATTICE L163.1
%
\hbox{}\par\smallskip%
%
% LATTICE L163.2
%
\leavevmode%
${L_{163.2}}$%
{} : {$[1\above{1pt}{1pt}{1}{}2\above{1pt}{1pt}{1}{}]\above{1pt}{1pt}{}{6}16\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{1}{}5\above{1pt}{1pt}{-}{}25\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{5m,5,2}%
\EasyButWeakLineBreak%
{${400}\above{1pt}{1pt}{*}{2}{4}\above{1pt}{1pt}{l}{2}{10}\above{1pt}{1pt}{40,19}{\infty}{40}\above{1pt}{1pt}{s}{2}{16}\above{1pt}{1pt}{*}{2}{100}\above{1pt}{1pt}{l}{2}{10}\above{1pt}{1pt}{40,11}{\infty}{40}\above{1pt}{1pt}{s}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-587600\\21600\\800
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
21600\\-790\\-30
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
800\\-30\\-1
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-20\\-200
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-22\\-146
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-4\\-89\\-560
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-9\\-202\\-1220
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3\\-68\\-392
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3\\-70\\-350
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\-1\\20
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\22\\140
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-587600, 21600, 800; 21600, -790, -30; 800, -30, -1],[400, 10, 1],[-1, -1, -4, -9, -3, -3, 0, 1; -20, -22, -89, -202, -68, -70, -1, 22; -200, -146, -560, -1220, -392, -350, 20, 140],162,2]
%
% END OF LATTICE L163.2
%
\hbox{}\par\smallskip%
%
% LATTICE L163.3
%
\leavevmode%
${L_{163.3}}$%
{} : {$[1\above{1pt}{1pt}{-}{}2\above{1pt}{1pt}{1}{}]\above{1pt}{1pt}{}{2}16\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{1}{}5\above{1pt}{1pt}{-}{}25\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{52,5,m}%
\EasyButWeakLineBreak%
{${400}\above{1pt}{1pt}{l}{2}{1}\above{1pt}{1pt}{}{2}{10}\above{1pt}{1pt}{40,39}{\infty}{40}\above{1pt}{1pt}{*}{2}{16}\above{1pt}{1pt}{l}{2}{25}\above{1pt}{1pt}{}{2}{10}\above{1pt}{1pt}{40,31}{\infty}{40}\above{1pt}{1pt}{*}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-931600\\27600\\10400
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
27600\\-790\\-320
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
10400\\-320\\-111
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-19\\-340\\-800
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4\\72\\167
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
44\\791\\1840
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
119\\2138\\4980
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
47\\844\\1968
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
34\\610\\1425
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
10\\179\\420
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-11\\-198\\-460
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-931600, 27600, 10400; 27600, -790, -320; 10400, -320, -111],[400, 10, 1],[-19, 4, 44, 119, 47, 34, 10, -11; -340, 72, 791, 2138, 844, 610, 179, -198; -800, 167, 1840, 4980, 1968, 1425, 420, -460],162,3]
%
% END OF LATTICE L163.3
%
\hbox{}\par\smallskip%
%
% LATTICE L163.4
%
\leavevmode%
${L_{163.4}}$%
{} : {$[1\above{1pt}{1pt}{-}{}2\above{1pt}{1pt}{-}{}]\above{1pt}{1pt}{}{0}16\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{1}{}5\above{1pt}{1pt}{-}{}25\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{5m,5,m}%
\EasyButWeakLineBreak%
{${400}\above{1pt}{1pt}{s}{2}{4}\above{1pt}{1pt}{*}{2}{40}\above{1pt}{1pt}{40,19}{\infty z}{10}\above{1pt}{1pt}{r}{2}{16}\above{1pt}{1pt}{s}{2}{100}\above{1pt}{1pt}{*}{2}{40}\above{1pt}{1pt}{40,11}{\infty z}{10}\above{1pt}{1pt}{r}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-676400\\8800\\201600
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
8800\\-90\\-2820
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
201600\\-2820\\-58499
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1853\\37040\\4600
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
315\\6296\\782
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1579\\31558\\3920
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
576\\11511\\1430
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
203\\4056\\504
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-141\\-2820\\-350
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-145\\-2898\\-360
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
141\\2819\\350
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-676400, 8800, 201600; 8800, -90, -2820; 201600, -2820, -58499],[400, 10, 1],[1853, 315, 1579, 576, 203, -141, -145, 141; 37040, 6296, 31558, 11511, 4056, -2820, -2898, 2819; 4600, 782, 3920, 1430, 504, -350, -360, 350],162,4]
%
% END OF LATTICE L163.4
%
\hbox{}\par\smallskip%
%
% LATTICE L163.5
%
\leavevmode%
${L_{163.5}}$%
{} : {$1\above{1pt}{1pt}{1}{1}8\above{1pt}{1pt}{-}{3}64\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{1}{}5\above{1pt}{1pt}{-}{}25\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{25,5,2}%
\EasyButWeakLineBreak%
{${1600}\above{1pt}{1pt}{}{2}{1}\above{1pt}{1pt}{r}{2}{160}\above{1pt}{1pt}{80,79}{\infty z}{40}\above{1pt}{1pt}{b}{2}{64}\above{1pt}{1pt}{s}{2}{100}\above{1pt}{1pt}{*}{2}{160}\above{1pt}{1pt}{80,71}{\infty z}{40}\above{1pt}{1pt}{l}{2}$}%
\nopagebreak\par%
shares genus with 2-dual${}\iso{}$5-dual; isometric to own %
2.5-dual\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-958400\\19200\\233600
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
19200\\-360\\-4880
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
233600\\-4880\\-55311
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1301\\26000\\3200
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
50\\999\\123
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
943\\18838\\2320
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
317\\6331\\780
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
91\\1816\\224
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-61\\-1220\\-150
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-65\\-1298\\-160
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
122\\2439\\300
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-958400, 19200, 233600; 19200, -360, -4880; 233600, -4880, -55311],[1600, 40, 1],[1301, 50, 943, 317, 91, -61, -65, 122; 26000, 999, 18838, 6331, 1816, -1220, -1298, 2439; 3200, 123, 2320, 780, 224, -150, -160, 300],162,5]
%
% END OF LATTICE L163.5
%
%
% LATTICE L163.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[260, -60, 0; -60, 10, -2; 0, -2, -1],[20, 2, 1],[-9, -3, -6, 1, 1, -1, -14, -21; -40, -13, -25, 5, 4, -5, -65, -95; 64, 21, 40, -10, -8, 7, 100, 150],162,6]
%
% END OF LATTICE L163.6
%
%
% LATTICE L163.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-206360, 4840, 5040; 4840, -111, -121; 5040, -121, -120],[40, 1, 1],[69, 25, 111, -11, -11, 4, 179, 301; 1514, 549, 2440, -240, -242, 87, 3920, 6600; 1370, 496, 2200, -220, -218, 80, 3560, 5980],162,7]
%
% END OF LATTICE L163.7
%
%
% LATTICE L163.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-33480, 280, 1200; 280, -2, -10; 1200, -10, -43],[40, 2, 1],[1, 1, -1, -2, -1, -1, 1, 2; 5, 24, 70, 30, 7, 0, -10, 0; 26, 20, -50, -65, -30, -28, 30, 55],162,8]
%
% END OF LATTICE L163.8
%
%
% LATTICE L163.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-120, -240, 280; -240, -286, 358; 280, 358, -443],[40, 2, 1],[49, 32, 133, 36, 3, -6, -3, 29; 200, 129, 530, 140, 8, -25, -10, 120; 192, 124, 510, 135, 8, -24, -10, 115],162,9]
%
% END OF LATTICE L163.9
%
%
% LATTICE L163.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-90960, -2800, -3120; -2800, -86, -96; -3120, -96, -107],[80, 2, 1],[1, 1, -1, -2, -1, -1, 1, 2; -4, 12, 10, -25, -24, -68, -150, -45; -26, -40, 20, 80, 50, 88, 100, -20],162,10]
%
% END OF LATTICE L163.10
%
%
% LATTICE L163.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-12560, 1040, 1200; 1040, -86, -100; 1200, -100, -111],[80, 2, 1],[4, 1, -11, -2, 2, 23, 71, 32; 40, 12, -110, -25, 18, 220, 690, 315; 7, 0, -20, 0, 5, 48, 140, 60],162,11]
%
% END OF LATTICE L163.11
%
%
% LATTICE L163.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-174640, 35760, 4160; 35760, -7322, -852; 4160, -852, -99],[80, 2, 1],[27, 41, 24, -3, -5, 3, 31, 113; 104, 160, 95, -10, -20, 8, 115, 430; 238, 344, 190, -40, -38, 56, 310, 1040],162,12]
%
% END OF LATTICE L163.12
%
%
% LATTICE L163.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[240, -160, 320; -160, 40, -24; 320, -24, -111],[80, 8, 1],[73, 12, 46, -11, -9, 4, 114, 171; 370, 61, 235, -55, -46, 20, 575, 865; 128, 21, 80, -20, -16, 7, 200, 300],162,13]
%
% END OF LATTICE L163.13
%
%
% LATTICE L163.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[100, 0, 0; 0, -90, -10; 0, -10, -1],[100, 10, 1],[2, 1, 2, 1, 0, -1, 0, 1; -5, -4, -11, -9, -1, 0, 1, -1; 25, 24, 70, 60, 7, 0, -10, 0],162,14]
%
% END OF LATTICE L163.14
%
%
% LATTICE L163.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-293800, 47200, 11600; 47200, -7570, -1860; 11600, -1860, -457],[200, 10, 1],[-3, -3, 0, 1, -1, -1, -4, -9; -128, -105, 11, 48, -80, -51, -191, -408; 444, 350, -45, -170, 300, 182, 675, 1430],162,15]
%
% END OF LATTICE L163.15
%
%
% LATTICE L163.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-110200, -46000, -6200; -46000, -18270, -2360; -6200, -2360, -293],[200, 10, 1],[88, 533, 43, -39, -46, 51, 154, 433; -469, -2840, -229, 208, 245, -272, -821, -2308; 1916, 11600, 935, -850, -1000, 1112, 3355, 9430],162,16]
%
% END OF LATTICE L163.16
%
%
% LATTICE L163.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-10471360, 2107200, 64640; 2107200, -424040, -13008; 64640, -13008, -399],[320, 8, 1],[81, 13, 213, 56, 3, -5, -3, 49; 320, 51, 830, 215, 8, -20, -10, 195; 2688, 443, 7440, 2060, 224, -158, -160, 1580],162,17]
%
% END OF LATTICE L163.17
%
%
% LATTICE L163.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[400, 0, 0; 0, -360, -200; 0, -200, -111],[400, 40, 1],[-1, 0, 1, 2, 1, 1, 1, 0; 0, -4, -69, -81, -28, -15, -1, 11; 0, 7, 120, 140, 48, 25, 0, -20],162,18]
%
% END OF LATTICE L163.18
%
%
% LATTICE L163.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-240, 80, 400; 80, -26, -120; 400, -120, -399],[80, 2, 1],[26, 81, 49, -3, -5, 3, 56, 213; 102, 320, 195, -10, -20, 8, 215, 830; -5, -16, -10, 0, 1, 0, -10, -40],162,19]
%
% END OF LATTICE L163.19
%
%
% LATTICE L163.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[40, 0, 0; 0, -396, -20; 0, -20, -1],[40, 4, 1],[-1, 0, 1, -1, -1, -2, -11, -9; 0, 1, 0, -10, -4, -5, -20, -10; -6, -20, 0, 180, 70, 84, 320, 140],162,20]
%
% END OF LATTICE L163.20
%
%
% LATTICE L163.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-360, 400, 200; 400, -396, -220; 200, -220, -111],[40, 4, 1],[4, -10, -11, 101, 23, 64, 281, 169; 0, 1, 0, -10, -2, -5, -20, -10; 7, -20, -20, 200, 45, 124, 540, 320],162,21]
%
% END OF LATTICE L163.21
%
%
% LATTICE L163.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[20, 0, 0; 0, -930, 200; 0, 200, -43],[20, 10, 1],[2, 5, 2, 1, 0, -1, 0, 1; 10, 44, 25, 21, 12, 0, -3, 1; 45, 200, 114, 96, 55, 0, -14, 4],162,22]
%
% END OF LATTICE L163.22
%
%
% LATTICE L163.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-48120, 1480, 1440; 1480, -40, -45; 1440, -45, -43],[40, 5, 1],[11, 37, 37, 27, 6, -3, -3, 7; 40, 138, 140, 104, 24, -10, -12, 24; 325, 1090, 1088, 792, 175, -90, -88, 208],162,23]
%
% END OF LATTICE L163.23
%
%
% LATTICE L163.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-33480, -4240, 1200; -4240, -536, 152; 1200, 152, -43],[40, 8, 1],[2, 1, -1, -2, -2, -1, 1, 2; 5, 12, 35, 15, 7, 0, -5, 0; 72, 68, 90, -5, -32, -28, 10, 55],162,24]
%
% END OF LATTICE L163.24
%
%
% LATTICE L163.25
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-35720, 640, 1680; 640, -10, -30; 1680, -30, -79],[40, 10, 1],[-1, -5, -4, -9, -15, -3, 0, 1; -4, 7, 8, 22, 44, 13, 2, -2; -20, -110, -89, -202, -340, -70, -1, 22],162,25]
%
% END OF LATTICE L163.25
%
%
% LATTICE L163.26
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2840, 360, 160; 360, -30, -20; 160, -20, -9],[40, 10, 1],[-1, 7, 4, 11, 11, 13, 1, -1; 1, 0, -1, -4, -5, -8, -1, 0; -20, 120, 71, 198, 200, 240, 19, -18],162,26]
%
% END OF LATTICE L163.26
%
%
% LATTICE L163.27
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-149360, 35840, -400; 35840, -8600, 96; -400, 96, -1],[80, 8, 1],[-8, -29, -76, -59, -6, 1, 6, -11; -33, -120, -315, -245, -25, 4, 25, -45; 22, 48, 80, 20, -6, -16, 0, 60],162,27]
%
% END OF LATTICE L163.27
%
%
% LATTICE L163.28
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2342960, 528560, -16560; 528560, -119240, 3736; -16560, 3736, -117],[80, 8, 1],[-28, -83, -191, -124, -8, 11, 11, -56; -113, -336, -775, -505, -33, 44, 45, -225; 354, 1016, 2280, 1420, 78, -152, -120, 740],162,28]
%
% END OF LATTICE L163.28
%
%
% LATTICE L163.29
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-38960, -24080, 4080; -24080, -14872, 2520; 4080, 2520, -427],[80, 8, 1],[1, 1, 4, 1, -1, -1, -4, -1; 84, 32, 75, -5, -16, 2, 95, 175; 504, 198, 480, -20, -104, 2, 520, 1020],162,29]
%
% END OF LATTICE L163.29
%
%
% LATTICE L163.30
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-71440, -19360, 4000; -19360, -5230, 1080; 4000, 1080, -223],[80, 10, 1],[-15, -3, 0, 1, -1, -5, -4, -9; 428, 96, 5, -26, 12, 124, 105, 246; 1800, 410, 24, -108, 40, 510, 436, 1028],162,30]
%
% END OF LATTICE L163.30
%
%
% LATTICE L163.31
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-35920, -7520, 1280; -7520, -1550, 260; 1280, 260, -43],[80, 10, 1],[59, 8, 2, -3, -3, 6, 12, 31; -580, -78, -19, 30, 28, -60, -119, -306; -1760, -235, -56, 92, 80, -185, -364, -932],162,31]
%
% END OF LATTICE L163.31
%
%
% LATTICE L163.32
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-12400, -4320, 960; -4320, -1490, 330; 960, 330, -73],[80, 10, 1],[7, -1, -1, 1, 13, 11, 11, 4; -64, 14, 10, -13, -152, -122, -118, -41; -200, 50, 32, -46, -520, -410, -392, -134],162,32]
%
% END OF LATTICE L163.32
%
%
% LATTICE L163.33
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-5680, -4480, 1040; -4480, -3250, 750; 1040, 750, -173],[80, 10, 1],[7, -1, -1, 2, 21, 8, 15, 5; -120, 21, 18, -41, -416, -155, -286, -93; -480, 85, 72, -166, -1680, -625, -1152, -374],162,33]
%
% END OF LATTICE L163.33
%
%
% LATTICE L163.34
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1080, 760, 200; 760, -500, -140; 200, -140, -37],[40, 20, 1],[29, 17, 5, -3, -3, 9, 21, 29; -5, -4, -2, 0, 1, 0, -2, -4; 180, 110, 36, -16, -20, 50, 124, 176],162,34]
%
% END OF LATTICE L163.34
%
%
% LATTICE L163.35
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3720, 560, 400; 560, -60, -60; 400, -60, -43],[40, 20, 1],[32, 9, 5, -3, -2, 6, 25, 33; -5, -2, -2, 0, 1, 0, -2, -4; 300, 85, 48, -28, -20, 55, 232, 308],162,35]
%
% END OF LATTICE L163.35
%
%
% LATTICE L163.36
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-29240, -32320, 1520; -32320, -35720, 1680; 1520, 1680, -79],[40, 40, 1],[-2, 7, 4, 11, 22, 13, 1, -1; -1, -10, -4, -9, -15, -6, 0, 1; -60, -80, -9, 18, 100, 120, 19, 2],162,36]
%
% END OF LATTICE L163.36
%
%
% LATTICE L163.37
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[80, -80, 0; -80, -1000, -200; 0, -200, -37],[80, 40, 1],[-23, -3, 2, 3, -1, -9, -14, -15; -28, -5, 1, 3, 0, -9, -15, -17; 160, 30, -4, -16, 0, 50, 84, 96],162,37]
%
% END OF LATTICE L163.37
%
%
% LATTICE L163.38
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-4080, 2720, -480; 2720, 200, -80; -480, -80, 23],[80, 40, 1],[39, 11, 3, -2, -3, 7, 15, 20; 516, 145, 39, -27, -40, 93, 199, 265; 2600, 730, 196, -136, -200, 470, 1004, 1336],162,38]
%
% END OF LATTICE L163.38
%
%
% LATTICE L163.39
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-240, 4960, -160; 4960, -99400, 3200; -160, 3200, -103],[80, 40, 1],[39, 11, 3, -2, -3, 7, 15, 20; 24, 8, 3, -1, -4, 2, 7, 11; 680, 230, 88, -28, -120, 50, 192, 308],162,39]
%
% END OF LATTICE L163.39
%
%
% LATTICE L163.40
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-14800, 22240, -800; 22240, -33400, 1200; -800, 1200, -43],[80, 40, 1],[59, 8, 4, -3, -3, 6, 24, 31; 54, 7, 3, -3, -2, 6, 23, 29; 400, 45, 8, -28, 0, 55, 192, 228],162,40]
%
% END OF LATTICE L163.40
%
%
% LATTICE L163.41
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-239600, 4800, -26800; 4800, -90, 560; -26800, 560, -2911],[400, 10, 1],[-299, -23, -217, -73, -21, 14, 15, -28; -6000, -462, -4362, -1469, -424, 280, 302, -561; 1600, 123, 1160, 390, 112, -75, -80, 150],162,41]
%
% END OF LATTICE L163.41
%
%
% LATTICE L163.42
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2600, 600, 0; 600, 140, 0; 0, 0, -1],[200, 20, 1],[-1, -1, -7, -7, -1, -1, 1, 1; 5, 4, 26, 24, 3, 0, -6, -4; 0, -6, -60, -80, -16, -50, -20, 0],162,42]
%
% END OF LATTICE L163.42
%
%
% LATTICE L163.43
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-727400, -177800, 9000; -177800, -43460, 2200; 9000, 2200, -111],[200, 20, 1],[-11, 4, 91, 125, 25, 37, 23, -11; 45, -16, -366, -504, -101, -150, -94, 44; 0, 7, 120, 140, 24, 25, 0, -20],162,43]
%
% END OF LATTICE L163.43
%
%
% LATTICE L163.44
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-110200, -34800, -70600; -34800, -10920, -22240; -70600, -22240, -45187],[200, 40, 1],[-202, -627, -53, 43, 118, -53, -170, -489; -407, -1260, -106, 87, 235, -108, -344, -987; 516, 1600, 135, -110, -300, 136, 435, 1250],162,44]
%
% END OF LATTICE L163.44
%
%
% LATTICE L163.45
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-191680, -119040, 7680; -119040, -73800, 4760; 7680, 4760, -307],[320, 40, 1],[21, 4, 15, 5, 7, -1, -1, 2; -240, -48, -186, -65, -104, 10, 14, -21; -3200, -645, -2512, -884, -1440, 130, 192, -276],162,45]
%
% END OF LATTICE L163.45
%
%
% LATTICE L163.46
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[400, -800, 0; -800, 1640, 0; 0, 0, -1],[400, 40, 1],[-2, 1, 2, -3, -12, -9, -24, -19; -1, 0, 1, -1, -5, -4, -11, -9; -6, 0, 0, -20, -50, -32, -80, -60],162,46]
%
% END OF LATTICE L163.46
%
%
% LATTICE L163.47
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3047600, -76000, 8000; -76000, 40, 200; 8000, 200, -21],[400, 40, 1],[7, -11, -10, 11, 47, 35, 92, 71; -1, 0, 1, -1, -5, -4, -11, -9; 2654, -4200, -3800, 4180, 17850, 13288, 34920, 26940],162,47]
%
% END OF LATTICE L163.47
%
%
% LATTICE L163.48
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-51047600, 156000, 130000; 156000, -360, -400; 130000, -400, -331],[400, 40, 1],[-11, 7, 71, 92, 35, 47, 11, -10; -100, 62, 631, 819, 312, 420, 99, -89; -4200, 2674, 27120, 35140, 13368, 17950, 4200, -3820],162,48]
%
% END OF LATTICE L163.48
%
%
% LATTICE L163.49
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-110705600, 211200, -21212800; 211200, -360, 40640; -21212800, 40640, -4063999],[1600, 40, 1],[-9403, -661, -5849, -1781, -357, 254, 255, -1016; -188080, -13222, -117002, -35629, -7144, 5080, 5102, -20321; 47200, 3318, 29360, 8940, 1792, -1275, -1280, 5100],162,49]
%
% END OF LATTICE L163.49
%

\medskip%
%------------------------------WEYL-GROUP-W164--------------------------------
%
\leavevmode\llap{}%
$W_{164}$%
\qquad\llap{44} lattices, $\chi=54$%
\hfill%
$42\infty2242\infty22\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L164.1
%
\leavevmode%
${L_{164.1}}$%
{} : {$1\above{1pt}{1pt}{2}{{\rm II}}4\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{2}{}9\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{2}{}5\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${4}\above{1pt}{1pt}{*}{4}{2}\above{1pt}{1pt}{l}{2}{20}\above{1pt}{1pt}{3,2}{\infty}{20}\above{1pt}{1pt}{*}{2}{36}\above{1pt}{1pt}{*}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-6278220\\29700\\59400
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
29700\\-140\\-281
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
59400\\-281\\-562
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-18181\\181800\\-2017980
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
91\\-911\\10101
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
172\\-1720\\19091
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
9\\-58\\982
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
10\\-102\\1111
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
13\\-200\\1480
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3\\-70\\-280
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-11\\-54\\-1134
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-6278220, 29700, 59400; 29700, -140, -281; 59400, -281, -562],[180, 1, 1],[9, 10, 13, -3, -11, -3, 0, 7, 13, 29; -58, -102, -200, -70, -54, -2, 2, 0, -30, -126; 982, 1111, 1480, -280, -1134, -316, -1, 740, 1390, 3132],163,1]
%
% END OF LATTICE L164.1
%
\hbox{}\par\smallskip%
%
% LATTICE L164.2
%
\leavevmode%
${L_{164.2}}$%
{} : {$1\above{1pt}{1pt}{-2}{2}8\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{2}{}9\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{2}{}5\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${2}\above{1pt}{1pt}{*}{4}{4}\above{1pt}{1pt}{s}{2}{40}\above{1pt}{1pt}{12,5}{\infty z}{10}\above{1pt}{1pt}{s}{2}{18}\above{1pt}{1pt}{b}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-6977160\\40320\\23040
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
40320\\-233\\-133
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
23040\\-133\\-70
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-230401\\-40406400\\921600
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1328\\232897\\-5312
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
624\\109434\\-2497
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-44\\-7716\\175
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-163\\-28586\\652
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-329\\-57700\\1320
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-63\\-11050\\255
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-55\\-9648\\225
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-6977160, 40320, 23040; 40320, -233, -133; 23040, -133, -70],[360, 1, 1],[-44, -163, -329, -63, -55, -4, 3, 9, -17, -89; -7716, -28586, -57700, -11050, -9648, -702, 526, 1580, -2980, -15606; 175, 652, 1320, 255, 225, 17, -12, -40, 65, 351],163,2]
%
% END OF LATTICE L164.2
%
\hbox{}\par\smallskip%
%
% LATTICE L164.3
%
\leavevmode%
${L_{164.3}}$%
{} : {$1\above{1pt}{1pt}{2}{2}8\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{2}{}9\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{2}{}5\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{m}%
\EasyButWeakLineBreak%
{${2}\above{1pt}{1pt}{}{4}{1}\above{1pt}{1pt}{r}{2}{40}\above{1pt}{1pt}{12,11}{\infty z}{10}\above{1pt}{1pt}{b}{2}{18}\above{1pt}{1pt}{s}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-133937640\\26822160\\347040
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
26822160\\-5371367\\-69498
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
347040\\-69498\\-899
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
39008339\\191483280\\255534840
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-7810964\\-38342289\\-51167864
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-101675\\-499100\\-666051
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
76\\373\\503
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-55\\-270\\-359
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-53\\-260\\-360
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
824\\4045\\5385
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3577\\17559\\23409
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-133937640, 26822160, 347040; 26822160, -5371367, -69498; 347040, -69498, -899],[360, 1, 1],[76, -55, -53, 824, 3577, 1667, 2960, 11673, 2081, 1652; 373, -270, -260, 4045, 17559, 8183, 14530, 57300, 10215, 8109; 503, -359, -360, 5385, 23409, 10915, 19389, 76480, 13645, 10845],163,3]
%
% END OF LATTICE L164.3
%
%
% LATTICE L164.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-15570, 450, 315; 450, -13, -9; 315, -9, -4],[45, 1, 1],[1, -1, -1, 6, 29, 14, 51, 51, 19, 16; 35, -36, -35, 215, 1035, 499, 1816, 1815, 675, 567; -1, 2, 0, -15, -63, -29, -102, -100, -35, -27],163,4]
%
% END OF LATTICE L164.4
%
%
% LATTICE L164.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-69210, 4410, 4410; 4410, -280, -281; 4410, -281, -281],[90, 1, 1],[-3, 0, 7, 13, 29, 9, 10, 13, -3, -11; -1, 1, 0, -15, -63, -29, -51, -100, -35, -27; -46, -1, 110, 220, 522, 172, 211, 310, -10, -144],163,5]
%
% END OF LATTICE L164.5
%
%
% LATTICE L164.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-8769780, 99900, 17820; 99900, -1138, -203; 17820, -203, -35],[180, 1, 1],[-44, -163, -329, -63, -55, -4, 3, 9, -17, -89; -3858, -14293, -28850, -5525, -4824, -351, 263, 790, -1490, -7803; -29, -102, -200, -35, -27, -1, 2, 0, -15, -63],163,6]
%
% END OF LATTICE L164.6
%
%
% LATTICE L164.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2375280, 90, 1157400; 90, 2, 44; 1157400, 44, 563965],[90, 2, 1],[-153, 0, -134, -1837, -7271, -3291, -5740, -5606, -3903, -3061; -24, 1, -20, -290, -1152, -522, -911, -890, -620, -486; 314, 0, 275, 3770, 14922, 6754, 11780, 11505, 8010, 6282],163,7]
%
% END OF LATTICE L164.7
%
%
% LATTICE L164.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-90, -45, -90; -45, -20, -45; -90, -45, -89],[45, 5, 1],[34, 131, 27, 11, 52, 5, -1, -1, 2, 65; -29, -102, -20, -7, -27, -1, 2, 0, -3, -63; -25, -100, -21, -9, -45, -5, 0, 1, -1, -45],163,8]
%
% END OF LATTICE L164.8
%
%
% LATTICE L164.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[103320, -1215, -19890; -1215, 18, 234; -19890, 234, 3829],[45, 9, 1],[-19, 0, -26, -199, -89, -365, -1280, -1254, -441, -39; 4, 1, 0, 15, 8, 35, 129, 130, 50, 5; -99, 0, -135, -1035, -463, -1899, -6660, -6525, -2295, -203],163,9]
%
% END OF LATTICE L164.9
%
%
% LATTICE L164.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-83070, -16920, 1890; -16920, -3440, 385; 1890, 385, -43],[90, 5, 1],[5, -1, -1, 3, 85, 43, 81, 33, 13, 59; -1, 1, 0, -3, -63, -29, -51, -20, -7, -27; 210, -35, -44, 104, 3150, 1620, 3085, 1264, 506, 2340],163,10]
%
% END OF LATTICE L164.10
%
%
% LATTICE L164.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[814680, 436500, 204120; 436500, 235780, 109388; 204120, 109388, 51143],[180, 4, 1],[14719, 51971, 51117, 18208, 14755, 872, -1, 853, 7777, 32018; 691, 2440, 2400, 855, 693, 41, 0, 40, 365, 1503; -60224, -212644, -209150, -74500, -60372, -3568, 4, -3490, -31820, -131004],163,11]
%
% END OF LATTICE L164.11
%
%
% LATTICE L164.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[130774320, 180, 31938480; 180, 8, 44; 31938480, 44, 7800205],[180, 4, 1],[-12245, -42720, -20863, -14529, -11399, -571, 0, -497, -6831, -27049; -261, -911, -445, -310, -243, -12, 1, -10, -145, -576; 50138, 174920, 85425, 59490, 46674, 2338, 0, 2035, 27970, 110754],163,12]
%
% END OF LATTICE L164.12
%
%
% LATTICE L164.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[126810, 90, 10800; 90, 9, 9; 10800, 9, 920],[90, 9, 1],[-13, 0, -23, -157, -69, -281, -490, -957, -333, -29; -24, 1, -40, -290, -128, -522, -911, -1780, -620, -54; 153, 0, 270, 1845, 811, 3303, 5760, 11250, 3915, 341],163,13]
%
% END OF LATTICE L164.13
%
%
% LATTICE L164.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-206100, -100980, 1980; -100980, -49475, 970; 1980, 970, -19],[180, 5, 1],[-34, -123, -49, -9, -37, -2, 3, 1, -3, -71; 77, 277, 110, 20, 81, 4, -7, -2, 7, 162; 380, 1295, 498, 81, 270, -5, -45, 2, 44, 855],163,14]
%
% END OF LATTICE L164.14
%
%
% LATTICE L164.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-166140, -16920, 3780; -16920, -1720, 385; 3780, 385, -86],[180, 5, 1],[43, 81, 33, 13, 59, 5, -1, -1, 3, 85; -58, -102, -40, -14, -54, -2, 2, 0, -6, -126; 1620, 3085, 1264, 506, 2340, 210, -35, -44, 104, 3150],163,15]
%
% END OF LATTICE L164.15
%
%
% LATTICE L164.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[4287780, 2970, 2093850; 2970, 10, 1450; 2093850, 1450, 1022489],[90, 10, 1],[713, 0, 21, 881, 19339, 9103, 16360, 3251, 2391, 10109; -62, 1, -2, -80, -1746, -820, -1471, -292, -214, -900; -1460, 0, -43, -1804, -39600, -18640, -33500, -6657, -4896, -20700],163,16]
%
% END OF LATTICE L164.16
%
%
% LATTICE L164.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-16020, 2340, 180; 2340, -315, -27; 180, -27, -2],[180, 9, 1],[0, 1, -1, -7, -3, -12, -41, -79, -13, -1; -1, 2, 0, -15, -7, -29, -102, -200, -35, -3; 9, 63, -90, -450, -187, -738, -2493, -4770, -765, -56],163,17]
%
% END OF LATTICE L164.17
%
%
% LATTICE L164.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-163980, 14400, 21420; 14400, -1260, -1881; 21420, -1881, -2798],[180, 9, 1],[-19, -1, 47, 103, 29, 91, 121, 193, 17, -5; -2, 2, 0, -30, -14, -58, -102, -200, -70, -6; -144, -9, 360, 810, 232, 738, 999, 1620, 180, -34],163,18]
%
% END OF LATTICE L164.18
%
%
% LATTICE L164.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-7757730, -198090, -3805200; -198090, -5040, -97164; -3805200, -97164, -1866467],[90, 18, 1],[-980, -53, 1214, 5342, 1508, 4742, 6323, 5056, 928, -254; -1, 1, 0, -15, -7, -29, -51, -50, -35, -3; 1998, 108, -2475, -10890, -3074, -9666, -12888, -10305, -1890, 518],163,19]
%
% END OF LATTICE L164.19
%
%
% LATTICE L164.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-412200, -110880, 3960; -110880, -29825, 1065; 3960, 1065, -38],[360, 5, 1],[-2, 3, 1, -3, -71, -34, -123, -49, -9, -37; 8, -14, -4, 14, 324, 154, 554, 220, 40, 162; 15, -80, -8, 79, 1665, 765, 2680, 1048, 181, 675],163,20]
%
% END OF LATTICE L164.20
%
%
% LATTICE L164.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-13661640, 49320, 24480; 49320, -175, -90; 24480, -90, -43],[360, 5, 1],[36, 66, 53, 10, 43, 3, -1, -1, 3, 74; 5155, 9453, 7592, 1433, 6165, 431, -143, -144, 429, 10593; 9695, 17770, 14268, 2691, 11565, 805, -270, -268, 809, 19935],163,21]
%
% END OF LATTICE L164.21
%
%
% LATTICE L164.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[90, 405, -90; 405, 24120, -5310; -90, -5310, 1169],[45, 45, 1],[35, 129, 26, 10, 5, 4, 1, 0, 3, 8; 1039, 3760, 750, 279, 133, 89, 0, 2, 97, 243; 4725, 17100, 3411, 1269, 605, 405, 0, 9, 441, 1105],163,22]
%
% END OF LATTICE L164.22
%
%
% LATTICE L164.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1109880, 0, 282240; 0, 8, 0; 282240, 0, -71773],[360, 8, 1],[419, 600, 511, 183, -55, -59, 0, 89, 417, 1135; -29, -51, -50, -35, -27, -1, 1, 0, -15, -63; 1648, 2360, 2010, 720, -216, -232, 0, 350, 1640, 4464],163,23]
%
% END OF LATTICE L164.23
%
%
% LATTICE L164.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-71480520, 153360, 261000; 153360, -328, -560; 261000, -560, -953],[360, 8, 1],[43, 71, 67, 41, 25, -1, -1, 3, 29, 101; 387, 650, 620, 395, 261, -3, -10, 20, 245, 891; 11552, 19068, 17990, 11000, 6696, -272, -268, 810, 7800, 27144],163,24]
%
% END OF LATTICE L164.24
%
%
% LATTICE L164.25
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-471240, 17280, 720; 17280, -630, -27; 720, -27, -1],[360, 9, 1],[-12, -41, -79, -13, -1, 0, 1, -1, -7, -3; -269, -922, -1780, -295, -23, -1, 22, -20, -155, -67; -1476, -4986, -9540, -1530, -112, 18, 126, -180, -900, -374],163,25]
%
% END OF LATTICE L164.25
%
%
% LATTICE L164.26
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-458297640, -1925640, -256129200; -1925640, -8091, -1076184; -256129200, -1076184, -143143147],[360, 9, 1],[4, 45, -89, -608, -259, -1033, -1760, -6771, -1107, -84; 245, 1261, -2760, -16905, -7125, -28283, -47991, -184160, -29825, -2221; -9, -90, 180, 1215, 517, 2061, 3510, 13500, 2205, 167],163,26]
%
% END OF LATTICE L164.26
%
%
% LATTICE L164.27
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2304900, -31320, 566100; -31320, 500, -7700; 566100, -7700, 139039],[180, 20, 1],[3678, 13403, 2685, 1015, 4484, 381, 127, 21, 338, 7693; -1531, -5577, -1117, -422, -1863, -158, -53, -9, -141, -3204; -15060, -54880, -10994, -4156, -18360, -1560, -520, -86, -1384, -31500],163,27]
%
% END OF LATTICE L164.27
%
%
% LATTICE L164.28
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[3867120, 5580, 943020; 5580, 40, 1360; 943020, 1360, 229961],[180, 20, 1],[4329, 15560, 1546, 1137, 4807, 339, 0, 10, 419, 9197; -410, -1471, -146, -107, -450, -31, 1, -1, -40, -873; -17750, -63800, -6339, -4662, -19710, -1390, 0, -41, -1718, -37710],163,28]
%
% END OF LATTICE L164.28
%
%
% LATTICE L164.29
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[637830, -2250, -62280; -2250, 45, 225; -62280, 225, 6082],[90, 45, 1],[-118, 0, -7, -146, -356, -1508, -2710, -1077, -396, -186; 174, 1, 10, 212, 518, 2196, 3949, 1570, 578, 272; -1215, 0, -72, -1503, -3665, -15525, -27900, -11088, -4077, -1915],163,29]
%
% END OF LATTICE L164.29
%
%
% LATTICE L164.30
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1895220, -10620, 462600; -10620, 72, -2592; 462600, -2592, 112915],[180, 36, 1],[167, 0, 22, 923, 461, 1969, 7120, 7098, 2637, 251; 8, 1, 5, 55, 26, 109, 389, 385, 140, 13; -684, 0, -90, -3780, -1888, -8064, -29160, -29070, -10800, -1028],163,30]
%
% END OF LATTICE L164.30
%
%
% LATTICE L164.31
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[852480, 900, 203220; 900, 72, 216; 203220, 216, 48445],[180, 36, 1],[-133, 0, -118, -1609, -707, -2879, -10040, -4902, -3411, -297; -12, 1, -10, -145, -64, -261, -911, -445, -310, -27; 558, 0, 495, 6750, 2966, 12078, 42120, 20565, 14310, 1246],163,31]
%
% END OF LATTICE L164.31
%
%
% LATTICE L164.32
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-26820, -26460, 2700; -26460, -26010, 2655; 2700, 2655, -271],[180, 45, 1],[-2, -1, 1, 1, 1, 2, 1, -1, -1, -1; 90, 371, 158, 35, 20, 21, -1, -10, 2, 17; 855, 3600, 1548, 351, 205, 225, 0, -108, 9, 155],163,32]
%
% END OF LATTICE L164.32
%
%
% LATTICE L164.33
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-444060, 527040, 195300; 527040, -625500, -231795; 195300, -231795, -85894],[180, 45, 1],[2939, 5677, 2343, 957, 503, 433, -57, -95, 167, 621; -58, -102, -40, -14, -6, -2, 2, 0, -6, -14; 6840, 13185, 5436, 2214, 1160, 990, -135, -216, 396, 1450],163,33]
%
% END OF LATTICE L164.33
%
%
% LATTICE L164.34
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-483660, -2724750, -1324800; -2724750, -15346710, -7461720; -1324800, -7461720, -3627961],[90, 90, 1],[-1, 1, 0, -3, -7, -29, -51, -10, -7, -3; -5776, 875, 617, -2590, -9052, -42266, -80945, -16631, -13424, -6962; 11880, -1800, -1269, 5328, 18620, 86940, 166500, 34209, 27612, 14320],163,34]
%
% END OF LATTICE L164.34
%
%
% LATTICE L164.35
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1583640, 0, 413640; 0, 40, 0; 413640, 0, -108041],[360, 40, 1],[-1233, -2560, -547, -489, -2539, -303, 0, 35, -23, -2069; -29, -51, -10, -7, -27, -1, 1, 0, -3, -63; -4720, -9800, -2094, -1872, -9720, -1160, 0, 134, -88, -7920],163,35]
%
% END OF LATTICE L164.35
%
%
% LATTICE L164.36
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-136943280, -16925400, 1099080; -16925400, -2091880, 135840; 1099080, 135840, -8821],[360, 40, 1],[-77, -169, -37, -35, -191, -25, -1, 3, 1, -115; 280, 571, 121, 106, 540, 62, -1, -7, 8, 486; -5280, -12260, -2746, -2728, -15480, -2160, -140, 266, 248, -6840],163,36]
%
% END OF LATTICE L164.36
%
%
% LATTICE L164.37
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-363240, -124560, 12600; -124560, -42705, 4320; 12600, 4320, -437],[360, 45, 1],[-2, -1, 1, 1, 1, 2, 1, -1, -1, -1; 175, 652, 264, 51, 25, 17, -12, -8, 13, 39; 1665, 6390, 2628, 531, 275, 225, -90, -108, 99, 355],163,37]
%
% END OF LATTICE L164.37
%
%
% LATTICE L164.38
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-101170440, -67313880, 3740400; -67313880, -44787375, 2488680; 3740400, 2488680, -138287],[360, 45, 1],[506, -169, -169, 506, 1387, 6073, 11134, 8941, 1687, 806; -743, 249, 248, -745, -2041, -8935, -16379, -13152, -2481, -1185; 315, -90, -108, 279, 785, 3465, 6390, 5148, 981, 475],163,38]
%
% END OF LATTICE L164.38
%
%
% LATTICE L164.39
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3169080, 3538800, -12960; 3538800, -3951576, 14472; -12960, 14472, -53],[360, 72, 1],[-7, 2, 7, 1, -5, -29, -62, -67, -61, -7; -1, 1, 0, -15, -7, -29, -51, -50, -35, -3; 1440, -216, -1710, -4320, -680, -792, 1296, 2790, 5400, 896],163,39]
%
% END OF LATTICE L164.39
%
%
% LATTICE L164.40
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-14447880, 208080, 129960; 208080, -2952, -1872; 129960, -1872, -1169],[360, 72, 1],[-17, -1, 27, 141, 45, 155, 231, 203, 89, 1; -11, -2, 20, 125, 43, 155, 242, 220, 115, 5; -1872, -108, 2970, 15480, 4936, 16992, 25308, 22230, 9720, 104],163,40]
%
% END OF LATTICE L164.40
%
%
% LATTICE L164.41
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[21780, -226260, -55260; -226260, 2354040, 574920; -55260, 574920, 140411],[180, 180, 1],[-399, -1450, -290, -109, -53, -39, -10, -2, -37, -93; 2863, 10367, 2069, 772, 371, 260, 43, 13, 269, 670; -11880, -43020, -8586, -3204, -1540, -1080, -180, -54, -1116, -2780],163,41]
%
% END OF LATTICE L164.41
%
%
% LATTICE L164.42
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[360, -16740, -4320; -16740, 6537600, 1682820; -4320, 1682820, 433169],[180, 180, 1],[-2536, -9111, -905, -665, -312, -197, 1, -6, -246, -599; 18689, 67160, 6672, 4905, 2303, 1459, 0, 44, 1811, 4413; -72630, -261000, -25929, -19062, -8950, -5670, 0, -171, -7038, -17150],163,42]
%
% END OF LATTICE L164.42
%
%
% LATTICE L164.43
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-4837680, -4838040, 48240; -4838040, -4838040, 48240; 48240, 48240, -481],[360, 360, 1],[-29, -51, -10, -7, -3, -1, 1, 0, -3, -7; 280, 571, 121, 106, 60, 62, -1, -7, 8, 54; 25200, 52200, 11142, 9936, 5720, 6120, 0, -702, 504, 4720],163,43]
%
% END OF LATTICE L164.43
%
%
% LATTICE L164.44
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-21754800, 2606684040, -18096480; 2606684040, -312282032040, 2167966440; -18096480, 2167966440, -15050749],[360, 360, 1],[34283, 71475, 15301, 13741, 7961, 8623, 35, -999, 561, 6341; 137412, 286471, 61325, 55070, 31904, 34554, 139, -4003, 2252, 25418; 19752120, 41178420, 8815086, 7915968, 4586000, 4966920, 19980, -575406, 323712, 3653680],163,44]
%
% END OF LATTICE L164.44
%

\medskip%
%------------------------------WEYL-GROUP-W165--------------------------------
%
\leavevmode\llap{}%
$W_{165}$%
\qquad\llap{12} lattices, $\chi=6$%
\hfill%
$22222$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L165.1
%
\leavevmode%
${L_{165.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{2}{}9\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${90}\above{1pt}{1pt}{l}{2}{4}\above{1pt}{1pt}{r}{2}{10}\above{1pt}{1pt}{l}{2}{36}\above{1pt}{1pt}{r}{2}{2}\above{1pt}{1pt}{b}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-400860\\-197640\\1080
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-197640\\-97442\\531
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1080\\531\\-2
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-44\\90\\135
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
43\\-88\\-144
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
22\\-45\\-70
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-299\\612\\1008
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-43\\88\\143
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-400860, -197640, 1080; -197640, -97442, 531; 1080, 531, -2],[180, 1, 1],[-44, 43, 22, -299, -43; 90, -88, -45, 612, 88; 135, -144, -70, 1008, 143],164,1]
%
% END OF LATTICE L165.1
%
%
% LATTICE L165.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-990, 450, 45; 450, -71, -18; 45, -18, -2],[45, 1, 1],[2, -2, -1, 16, 4; 0, 1, 0, -9, -2; 45, -54, -25, 432, 107],164,2]
%
% END OF LATTICE L165.2
%
%
% LATTICE L165.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-7515, 225, 315; 225, -5, -10; 315, -10, -13],[45, 5, 1],[-1, -1, 0, 5, 1; -9, -6, 1, 36, 5; -18, -20, -1, 90, 20],164,3]
%
% END OF LATTICE L165.3
%
%
% LATTICE L165.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[82035, -46575, -18135; -46575, 26442, 10296; -18135, 10296, 4009],[45, 9, 1],[21, 2, -27, 4, 23; 0, 0, 5, 2, 2; 95, 9, -135, 13, 99],164,4]
%
% END OF LATTICE L165.4
%
%
% LATTICE L165.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[210909240, -1307340, 52194420; -1307340, 8104, -323532; 52194420, -323532, 12916729],[180, 4, 1],[968, 11, 171, 596, 218; -1935, -22, -360, -1224, -443; -3960, -45, -700, -2439, -892],164,5]
%
% END OF LATTICE L165.5
%
%
% LATTICE L165.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[13140, -360, -180; -360, 10, 5; -180, 5, 2],[180, 5, 1],[-1, -1, 0, 1, 0; -27, -28, 0, 36, 1; -18, -20, -1, 0, 0],164,6]
%
% END OF LATTICE L165.6
%
%
% LATTICE L165.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[71460, 28080, 1260; 28080, 11034, 495; 1260, 495, 22],[180, 9, 1],[4, 11, 2, -3, -3; -10, -28, -5, 8, 8; -5, 0, 0, -8, -9],164,7]
%
% END OF LATTICE L165.7
%
%
% LATTICE L165.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1530, 2250, -405; 2250, 3735, -675; -405, -675, 122],[45, 45, 1],[0, 1, 1, 1, 0; -2, -17, -12, -15, -8; -11, -90, -63, -80, -45],164,8]
%
% END OF LATTICE L165.8
%
%
% LATTICE L165.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-15480, -180, -3780; -180, 680, -40; -3780, -40, -923],[180, 20, 1],[35, -33, -42, -11, 83; 0, -1, -1, 0, 2; -144, 135, 172, 45, -340],164,9]
%
% END OF LATTICE L165.9
%
%
% LATTICE L165.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[36360, -15660, 9540; -15660, 3096, -3960; 9540, -3960, 2497],[180, 36, 1],[328, 11, -661, -12, 282; -55, -2, 110, 2, -47; -1340, -45, 2700, 49, -1152],164,10]
%
% END OF LATTICE L165.10
%
%
% LATTICE L165.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[180, -180, -180; -180, 90, 45; -180, 45, -22],[180, 45, 1],[-1, -1, 4, 9, 0; -3, -4, 12, 28, 1; 2, 0, -9, -20, 0],164,11]
%
% END OF LATTICE L165.11
%
%
% LATTICE L165.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[36360, 72540, 18000; 72540, 145080, 36000; 18000, 36000, 8933],[180, 180, 1],[0, -1, -1, 0, 2; -1, -33, -62, -31, -1; 4, 135, 252, 125, 0],164,12]
%
% END OF LATTICE L165.12
%

\medskip%
%------------------------------WEYL-GROUP-W166--------------------------------
%
\leavevmode\llap{}%
$W_{166}$%
\qquad\llap{12} lattices, $\chi=24$%
\hfill%
$22|22|22|22|\rtimes D_{4}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L166.1
%
\leavevmode%
${L_{166.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{-2}{}9\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${4}\above{1pt}{1pt}{r}{2}{18}\above{1pt}{1pt}{b}{2}{10}\above{1pt}{1pt}{b}{2}{2}\above{1pt}{1pt}{l}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2340\\-1080\\0
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1080\\498\\1
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\1\\-2
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\0\\0
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\-1\\-1
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\1
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
11\\24\\8
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4\\9\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-7\\-15\\-10
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-6\\-13\\-8
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[2340, -1080, 0; -1080, 498, 1; 0, 1, -2],[180, 1, 1],[11, 4, -7, -6, -11, -4, 7, 6; 24, 9, -15, -13, -24, -9, 15, 13; 8, 0, -10, -8, -16, -9, 5, 5],165,1]
%
% END OF LATTICE L166.1
%
%
% LATTICE L166.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-3465, 90, 90; 90, -1, -3; 90, -3, -2],[45, 1, 1],[-1, -1, -1, 1, 1, 1, 1, -1; -12, -13, -15, 9, 12, 13, 15, -9; -29, -27, -25, 27, 25, 24, 20, -36],165,2]
%
% END OF LATTICE L166.2
%
%
% LATTICE L166.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[90, 0, 45; 0, -5, -5; 45, -5, 18],[45, 5, 1],[3, -1, -1, 1, 5, 7, 3, 17; 1, -4, -2, 0, 7, 10, 4, 18; -10, 0, 2, 0, -10, -15, -7, -45],165,3]
%
% END OF LATTICE L166.3
%
%
% LATTICE L166.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[585, 675, -90; 675, 927, -99; -90, -99, 14],[45, 9, 1],[-27, -19, -27, -5, -21, -17, -33, -7; 4, 3, 5, 1, 4, 3, 5, 1; -144, -99, -135, -25, -108, -90, -180, -38],165,4]
%
% END OF LATTICE L166.4
%
%
% LATTICE L166.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[377640, 6300, 95220; 6300, 104, 1588; 95220, 1588, 24009],[180, 4, 1],[9, 79, 39, -3, -13, -97, -49, -3; 20, 162, 80, -2, -22, -171, -85, -1; -37, -324, -160, 12, 53, 396, 200, 12],165,5]
%
% END OF LATTICE L166.5
%
%
% LATTICE L166.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1260, -540, 180; -540, -230, 85; 180, 85, 18],[180, 5, 1],[-25, 6, 5, -4, -47, -33, -14, -77; 56, -13, -11, 9, 104, 73, 31, 171; -20, 0, 2, 0, -20, -15, -7, -45],165,6]
%
% END OF LATTICE L166.6
%
%
% LATTICE L166.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[13860, 7920, -180; 7920, 4482, -99; -180, -99, 2],[180, 9, 1],[-5, 0, 13, 14, 37, 4, 7, -2; 12, 0, -30, -32, -84, -9, -15, 5; 144, -1, -315, -315, -792, -80, -90, 72],165,7]
%
% END OF LATTICE L166.7
%
%
% LATTICE L166.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[405, -2475, 540; -2475, 13815, -3015; 540, -3015, 658],[45, 45, 1],[9, 4, 0, 0, 3, 5, 3, 3; -136, -68, 2, 12, 20, -19, -31, -41; -630, -315, 9, 55, 90, -90, -144, -190],165,8]
%
% END OF LATTICE L166.8
%
%
% LATTICE L166.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1328760, -90180, 333000; -90180, 6120, -22600; 333000, -22600, 83453],[180, 20, 1],[168, 157, -1, -89, 28, 137, 99, 971; -54, -50, 0, 18, -12, -49, -33, -315; -685, -640, 4, 360, -115, -560, -404, -3960],165,9]
%
% END OF LATTICE L166.9
%
%
% LATTICE L166.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[4003560, -61380, 981540; -61380, 936, -15048; 981540, -15048, 240641],[180, 36, 1],[11, -42, 176, 642, 587, 341, 1319, 255; -2, 11, -35, -151, -140, -82, -320, -62; -45, 172, -720, -2628, -2403, -1396, -5400, -1044],165,10]
%
% END OF LATTICE L166.10
%
%
% LATTICE L166.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[13140, -1080, -540; -1080, 90, 45; -540, 45, 22],[180, 45, 1],[1, 0, -1, -2, -17, -6, -1, 0; 12, 1, -3, -5, -36, -10, 0, 2; 0, 0, -18, -40, -360, -135, -27, -5],165,11]
%
% END OF LATTICE L166.11
%
%
% LATTICE L166.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2520, -5940, -1440; -5940, -15480, -3780; -1440, -3780, -923],[180, 180, 1],[0, 2, 0, -2, -6, -11, -3, -1; -11, 219, 35, -151, -515, -1008, -298, -112; 45, -900, -144, 620, 2115, 4140, 1224, 460],165,12]
%
% END OF LATTICE L166.12
%

\medskip%
%------------------------------WEYL-GROUP-W167--------------------------------
%
\leavevmode\llap{}%
$W_{167}$%
\qquad\llap{4} lattices, $\chi=6$%
\hfill%
$4|42|2\rtimes D_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L167.1
%
\leavevmode%
${L_{167.1}}$%
{} : {$1\above{1pt}{1pt}{2}{2}16\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{-}{}$}\EasyButWeakLineBreak%
{${1}\above{1pt}{1pt}{}{4}{2}\above{1pt}{1pt}{*}{4}{4}\above{1pt}{1pt}{s}{2}{16}\above{1pt}{1pt}{l}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2352\\-672\\240
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-672\\-191\\67
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
240\\67\\-22
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\5\\4
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-4\\18\\11
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\-14\\-10
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
9\\-40\\-24
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-2352, -672, 240; -672, -191, 67; 240, 67, -22],[48, 1, 1],[-1, -4, 3, 9; 5, 18, -14, -40; 4, 11, -10, -24],166,1]
%
% END OF LATTICE L167.1
%
%
% LATTICE L167.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-7824, -720, -816; -720, -66, -75; -816, -75, -85],[48, 3, 1],[1, 0, -1, 1; -1, -7, 4, 16; -9, 6, 6, -24],166,2]
%
% END OF LATTICE L167.2
%
%
% LATTICE L167.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-480, -48, 192; -48, 16, 0; 192, 0, -59],[48, 16, 1],[7, -5, 0, 3; 23, -14, -1, 9; 24, -16, 0, 10],166,3]
%
% END OF LATTICE L167.3
%
%
% LATTICE L167.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[96, 48, 0; 48, 48, 0; 0, 0, -1],[48, 48, 1],[1, -1, -2, 0; -1, 2, -1, -1; 0, 0, -24, -6],166,4]
%
% END OF LATTICE L167.4
%

\medskip%
%------------------------------WEYL-GROUP-W168--------------------------------
%
\leavevmode\llap{}%
$W_{168}$%
\qquad\llap{6} lattices, $\chi=8$%
\hfill%
$6262\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L168.1
%
\leavevmode%
${L_{168.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}16\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{-}{}9\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{3}%
\EasyButWeakLineBreak%
{${6}\above{1pt}{1pt}{}{6}{18}\above{1pt}{1pt}{b}{2}{6}\above{1pt}{1pt}{}{6}{2}\above{1pt}{1pt}{b}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-48528\\1296\\720
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1296\\-30\\-21
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
720\\-21\\-10
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\31\\78
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2\\-30\\-81
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-16\\-39
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\15\\40
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-48528, 1296, 720; 1296, -30, -21; 720, -21, -10],[144, 3, 1],[2, -2, -1, 1; 31, -30, -16, 15; 78, -81, -39, 40],167,1]
%
% END OF LATTICE L168.1
%
%
% LATTICE L168.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-14736, 384, 192; 384, -10, -5; 192, -5, -2],[48, 1, 1],[-1, 0, 1, 0; -39, 1, 39, -1; 0, -3, -3, 2],167,2]
%
% END OF LATTICE L168.2
%
%
% LATTICE L168.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-21936, 960, 480; 960, -42, -21; 480, -21, -10],[48, 3, 1],[0, -1, 0, 1; 2, -23, -1, 24; -5, 0, 2, -3],167,3]
%
% END OF LATTICE L168.3
%
%
% LATTICE L168.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-29856, -1104, 864; -1104, -32, 32; 864, 32, -25],[48, 16, 1],[-7, 1, 7, -1; 0, -3, -3, 2; -240, 32, 240, -32],167,4]
%
% END OF LATTICE L168.4
%
%
% LATTICE L168.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-672, -10320, 624; -10320, -156576, 9456; 624, 9456, -571],[48, 48, 1],[2, -23, -1, 24; -5, 16, 2, -19; -80, 240, 32, -288],167,5]
%
% END OF LATTICE L168.5
%
%
% LATTICE L168.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-20448, 24912, -720; 24912, -29856, 864; -720, 864, -25],[144, 48, 1],[0, -1, -1, 2; -7, 7, 13, -15; -240, 272, 480, -576],167,6]
%
% END OF LATTICE L168.6
%

\medskip%
%------------------------------WEYL-GROUP-W169--------------------------------
%
\leavevmode\llap{}%
$W_{169}$%
\qquad\llap{36} lattices, $\chi=24$%
\hfill%
$2|2\slashinfty2|2\slashinfty\rtimes D_{4}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L169.1
%
\leavevmode%
${L_{169.1}}$%
{} : {$1\above{1pt}{1pt}{2}{6}16\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{1}{}9\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{3}%
\EasyButWeakLineBreak%
{${3}\above{1pt}{1pt}{r}{2}{144}\above{1pt}{1pt}{s}{2}{12}\above{1pt}{1pt}{24,1}{\infty z}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-305712\\-9360\\-9936
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-9360\\-285\\-303
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-9936\\-303\\-322
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-449\\-32256\\44352
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-13\\-937\\1287
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-14\\-1008\\1385
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\85\\-111
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\120\\-144
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-82\\108
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-305712, -9360, -9936; -9360, -285, -303; -9936, -303, -322],[144, 3, 1],[1, 1, -1, 0, 7, 3; 85, 120, -82, -13, 456, 226; -111, -144, 108, 12, -648, -306],168,1]
%
% END OF LATTICE L169.1
%
\hbox{}\par\smallskip%
%
% LATTICE L169.2
%
\leavevmode%
${L_{169.2}}$%
{} : {$1\above{1pt}{1pt}{-2}{4}16\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{1}{}9\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{3}%
\EasyButWeakLineBreak%
{${12}\above{1pt}{1pt}{*}{2}{36}\above{1pt}{1pt}{s}{2}{48}\above{1pt}{1pt}{12,1}{\infty z}{48}\above{1pt}{1pt}{l}{2}{9}\above{1pt}{1pt}{}{2}{3}\above{1pt}{1pt}{24,7}{\infty}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-30096\\4032\\-6336
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4032\\-492\\891
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-6336\\891\\-1297
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
57\\152\\-174
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
65\\174\\-198
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-165\\-440\\504
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-527\\-1408\\1608
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-239\\-639\\729
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-62\\-166\\189
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-30096, 4032, -6336; 4032, -492, 891; -6336, 891, -1297],[144, 3, 1],[57, 65, -165, -527, -239, -62; 152, 174, -440, -1408, -639, -166; -174, -198, 504, 1608, 729, 189],168,2]
%
% END OF LATTICE L169.2
%
\hbox{}\par\smallskip%
%
% LATTICE L169.3
%
\leavevmode%
${L_{169.3}}$%
{} : {$1\above{1pt}{1pt}{2}{0}16\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{1}{}9\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{3}%
\EasyButWeakLineBreak%
{${12}\above{1pt}{1pt}{l}{2}{9}\above{1pt}{1pt}{}{2}{48}\above{1pt}{1pt}{6,1}{\infty}{48}\above{1pt}{1pt}{*}{2}{36}\above{1pt}{1pt}{l}{2}{3}\above{1pt}{1pt}{24,19}{\infty}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-100944\\-20592\\-11808
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-20592\\-4128\\-2487
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-11808\\-2487\\-1297
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-95\\304\\282
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-106\\339\\315
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
275\\-880\\-816
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1293\\-4136\\-3840
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1315\\-4206\\-3906
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
207\\-662\\-615
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-100944, -20592, -11808; -20592, -4128, -2487; -11808, -2487, -1297],[144, 3, 1],[-95, -106, 275, 1293, 1315, 207; 304, 339, -880, -4136, -4206, -662; 282, 315, -816, -3840, -3906, -615],168,3]
%
% END OF LATTICE L169.3
%
\hbox{}\par\smallskip%
%
% LATTICE L169.4
%
\leavevmode%
${L_{169.4}}$%
{} : {$1\above{1pt}{1pt}{-}{3}4\above{1pt}{1pt}{1}{7}16\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{1}{}9\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{3}%
\EasyButWeakLineBreak%
{${12}\above{1pt}{1pt}{s}{2}{144}\above{1pt}{1pt}{l}{2}{12}\above{1pt}{1pt}{24,13}{\infty}{12}\above{1pt}{1pt}{}{2}{144}\above{1pt}{1pt}{}{2}{3}\above{1pt}{1pt}{12,1}{\infty}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-227952\\-35280\\9072
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-35280\\-5460\\1404
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
9072\\1404\\-361
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\-8\\-6
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-12\\-72
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2\\13\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3\\35\\60
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-7\\120\\288
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\7\\27
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-227952, -35280, 9072; -35280, -5460, 1404; 9072, 1404, -361],[144, 12, 1],[1, -1, -2, -3, -7, 0; -8, -12, 13, 35, 120, 7; -6, -72, 0, 60, 288, 27],168,4]
%
% END OF LATTICE L169.4
%
\hbox{}\par\smallskip%
%
% LATTICE L169.5
%
\leavevmode%
${L_{169.5}}$%
{} : {$1\above{1pt}{1pt}{-}{3}4\above{1pt}{1pt}{1}{1}16\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{1}{}9\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{3}%
\EasyButWeakLineBreak%
{${12}\above{1pt}{1pt}{l}{2}{36}\above{1pt}{1pt}{}{2}{48}\above{1pt}{1pt}{12,1}{\infty}{48}\above{1pt}{1pt}{l}{2}{36}\above{1pt}{1pt}{}{2}{3}\above{1pt}{1pt}{12,7}{\infty}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-30096\\15984\\-6336
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
15984\\-7980\\3228
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-6336\\3228\\-1297
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-19\\76\\282
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-22\\87\\324
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
55\\-220\\-816
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
177\\-704\\-2616
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
161\\-639\\-2376
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
21\\-83\\-309
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-30096, 15984, -6336; 15984, -7980, 3228; -6336, 3228, -1297],[144, 12, 1],[-19, -22, 55, 177, 161, 21; 76, 87, -220, -704, -639, -83; 282, 324, -816, -2616, -2376, -309],168,5]
%
% END OF LATTICE L169.5
%
%
% LATTICE L169.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-45744, 240, 1152; 240, -1, -6; 1152, -6, -29],[48, 1, 1],[1, -1, -1, -1, 1, 1; -12, 0, 9, 30, 24, 0; 42, -40, -42, -48, 32, 39],168,6]
%
% END OF LATTICE L169.6
%
%
% LATTICE L169.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-31632, 10896, 1056; 10896, -3753, -364; 1056, -364, -35],[48, 1, 1],[19, -9, -7, 26, 25, 137; 48, -24, -18, 69, 66, 360; 72, -22, -24, 66, 67, 384],168,7]
%
% END OF LATTICE L169.7
%
%
% LATTICE L169.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-1104, 432, 432; 432, -169, -168; 432, -168, -143],[48, 1, 1],[19, -9, -7, 53, 95, 245; 48, -24, -18, 141, 252, 648; 0, 1, 0, -6, -10, -24],168,8]
%
% END OF LATTICE L169.8
%
%
% LATTICE L169.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-45744, 480, 1152; 480, -4, -12; 1152, -12, -29],[48, 4, 1],[-2, -1, 1, 1, 1, -1; 9, 0, -6, 0, 12, 15; -84, -40, 42, 39, 32, -48],168,9]
%
% END OF LATTICE L169.9
%
%
% LATTICE L169.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-1104, 432, 432; 432, -140, -168; 432, -168, -169],[48, 4, 1],[19, -9, -7, 26, 50, 137; 0, 1, 0, -3, -5, -12; 48, -24, -18, 69, 132, 360],168,10]
%
% END OF LATTICE L169.10
%
%
% LATTICE L169.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-68112, 480, 2544; 480, -3, -18; 2544, -18, -95],[48, 3, 1],[-1, -1, 1, 0, -7, -3; -5, -16, 4, 4, 8, -6; -26, -24, 26, -1, -192, -80],168,11]
%
% END OF LATTICE L169.11
%
%
% LATTICE L169.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-10032, 336, 336; 336, -9, -12; 336, -12, -11],[48, 3, 1],[3, -1, -1, 1, 4, 9; 24, -6, -8, 6, 27, 64; 64, -24, -22, 23, 90, 200],168,12]
%
% END OF LATTICE L169.12
%
%
% LATTICE L169.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-5232, 528, 240; 528, -45, -24; 240, -24, -11],[48, 3, 1],[3, -1, -1, 2, 13, 13; 0, 1, 0, -2, -10, -8; 64, -24, -22, 47, 300, 296],168,13]
%
% END OF LATTICE L169.13
%
%
% LATTICE L169.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-6288, 2448, -480; 2448, -948, 184; -480, 184, -35],[48, 4, 1],[19, 10, 59, 13, -3, -4; 75, 39, 228, 48, -12, -15; 132, 67, 384, 72, -22, -24],168,14]
%
% END OF LATTICE L169.14
%
%
% LATTICE L169.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-9949104, 663984, -16992; 663984, -44313, 1134; -16992, 1134, -29],[144, 3, 1],[1, -7, -11, -4, -1, 5; 16, -104, -166, -61, -16, 76; 39, 32, -48, -42, -40, 42],168,15]
%
% END OF LATTICE L169.15
%
%
% LATTICE L169.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-311184, 3312, 3312; 3312, -33, -36; 3312, -36, -35],[144, 3, 1],[-1, -1, 3, 17, 3, 3; -22, -24, 64, 392, 70, 71; -72, -70, 216, 1200, 211, 210],168,16]
%
% END OF LATTICE L169.16
%
%
% LATTICE L169.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-15696, 720, 1584; 720, -33, -72; 1584, -72, -143],[144, 3, 1],[-1, -1, 3, 29, 11, 6; -22, -24, 64, 680, 260, 143; 0, 1, 0, -24, -10, -6],168,17]
%
% END OF LATTICE L169.17
%
%
% LATTICE L169.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-60624, 912, 2400; 912, -12, -36; 2400, -36, -95],[48, 12, 1],[-2, -1, 1, 0, -7, -3; 3, -4, -2, 2, 32, 9; -52, -24, 26, -1, -192, -80],168,18]
%
% END OF LATTICE L169.18
%
%
% LATTICE L169.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-5232, 528, 240; 528, -36, -24; 240, -24, -11],[48, 12, 1],[3, -1, -1, 1, 8, 9; 0, 1, 0, -1, -5, -4; 64, -24, -22, 23, 180, 200],168,19]
%
% END OF LATTICE L169.19
%
%
% LATTICE L169.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-240, -624, 192; -624, -1116, 336; 192, 336, -101],[48, 12, 1],[9, 4, 2, -1, -1, 3; -72, -30, -13, 9, 6, -28; -224, -93, -40, 28, 18, -88],168,20]
%
% END OF LATTICE L169.20
%
%
% LATTICE L169.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-45744, -8256, 1152; -8256, -1488, 208; 1152, 208, -29],[48, 16, 1],[-4, -1, 1, 1, 1, -2; 9, 0, -3, 0, 6, 15; -96, -40, 18, 39, 80, 24],168,21]
%
% END OF LATTICE L169.21
%
%
% LATTICE L169.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1104, 288, 144; 288, -48, -64; 144, -64, 7],[48, 16, 1],[19, -6, -7, 16, 40, 65; 48, -15, -18, 39, 99, 162; 48, -16, -18, 42, 104, 168],168,22]
%
% END OF LATTICE L169.22
%
%
% LATTICE L169.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-298320, 2208, 12960; 2208, -16, -96; 12960, -96, -563],[48, 16, 1],[11, 4, 8, -2, -1, 1; 72, 33, 87, 9, -6, -6; 240, 86, 168, -48, -22, 24],168,23]
%
% END OF LATTICE L169.23
%
%
% LATTICE L169.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-377712, 127296, -3312; 127296, -42900, 1116; -3312, 1116, -29],[144, 12, 1],[1, -3, -6, -5, -1, 3; 4, -8, -19, -17, -4, 10; 39, 32, -48, -84, -40, 42],168,24]
%
% END OF LATTICE L169.24
%
%
% LATTICE L169.25
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-15696, -7632, 2304; -7632, -3516, 1056; 2304, 1056, -317],[144, 12, 1],[3, 6, 17, 3, -1, -1; -74, -145, -404, -64, 25, 22; -225, -440, -1224, -192, 76, 66],168,25]
%
% END OF LATTICE L169.25
%
%
% LATTICE L169.26
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-720, 432, 288; 432, -132, -168; 288, -168, -115],[144, 12, 1],[-9, -7, 27, 73, 31, 14; 1, 0, -4, -8, -3, -1; -24, -18, 72, 192, 81, 36],168,26]
%
% END OF LATTICE L169.26
%
%
% LATTICE L169.27
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-171216, 5040, 2448; 5040, -132, -72; 2448, -72, -35],[144, 12, 1],[3, -1, -1, 6, 3, 17; -4, 0, 1, -1, -1, -8; 216, -70, -72, 420, 211, 1200],168,27]
%
% END OF LATTICE L169.27
%
%
% LATTICE L169.28
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-51312, -55776, 2208; -55776, -60624, 2400; 2208, 2400, -95],[48, 48, 1],[3, -2, -1, 1, 16, 9; -4, -1, 1, 0, -7, -6; -32, -72, 2, 23, 192, 56],168,28]
%
% END OF LATTICE L169.28
%
%
% LATTICE L169.29
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-5232, -5232, 240; -5232, -5184, 240; 240, 240, -11],[48, 48, 1],[3, -1, -1, 1, 11, 7; 0, 1, 0, -1, -5, -2; 64, 0, -22, -2, 120, 104],168,29]
%
% END OF LATTICE L169.29
%
%
% LATTICE L169.30
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-48, 672, -96; 672, -9072, 1296; -96, 1296, -185],[48, 48, 1],[13, 13, 8, -2, -2, 3; 0, 2, 3, 1, -1, -2; -8, 6, 16, 8, -6, -16],168,30]
%
% END OF LATTICE L169.30
%
%
% LATTICE L169.31
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1152, 5328, -1584; 5328, -24432, 7248; -1584, 7248, -2149],[144, 48, 1],[1, -26, -13, 17, 64, 8; 2, -27, -17, 11, 57, 8; 6, -72, -48, 24, 144, 21],168,31]
%
% END OF LATTICE L169.31
%
%
% LATTICE L169.32
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-140112, -80064, 2016; -80064, -45744, 1152; 2016, 1152, -29],[144, 48, 1],[0, 2, 5, 3, 0, -1; 1, 1, -2, -4, -1, 1; 39, 176, 264, 48, -40, -30],168,32]
%
% END OF LATTICE L169.32
%
%
% LATTICE L169.33
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[144, -144, 0; -144, -960, 432; 0, 432, -169],[144, 48, 1],[-7, -1, 19, 31, 35, -1; -7, 0, 19, 29, 30, -2; -18, 0, 48, 72, 72, -6],168,33]
%
% END OF LATTICE L169.33
%
%
% LATTICE L169.34
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-15696, -1008, 576; -1008, 192, -48; 576, -48, 7],[144, 48, 1],[3, 7, 11, 3, -1, -1; 61, 145, 230, 64, -21, -22; 186, 440, 696, 192, -64, -66],168,34]
%
% END OF LATTICE L169.34
%
%
% LATTICE L169.35
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-31392, 77616, -4896; 77616, -191760, 12096; -4896, 12096, -763],[144, 48, 1],[-1, 1, 2, 0, -2, -3; -11, -3, 19, 47, 39, 17; -168, -54, 288, 744, 630, 288],168,35]
%
% END OF LATTICE L169.35
%
%
% LATTICE L169.36
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-144, 6624, -288; 6624, -298320, 12960; -288, 12960, -563],[144, 48, 1],[3, -2, -2, 24, 11, 29; -2, -1, 1, 11, 4, 8; -48, -22, 24, 240, 86, 168],168,36]
%
% END OF LATTICE L169.36
%

\medskip%
%------------------------------WEYL-GROUP-W170--------------------------------
%
\leavevmode\llap{}%
$W_{170}$%
\qquad\llap{8} lattices, $\chi=12$%
\hfill%
$22|22\slashinfty\rtimes D_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L170.1
%
\leavevmode%
${L_{170.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{2}16\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{1}{}9\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{3}%
\EasyButWeakLineBreak%
{${12}\above{1pt}{1pt}{*}{2}{144}\above{1pt}{1pt}{b}{2}{2}\above{1pt}{1pt}{l}{2}{144}\above{1pt}{1pt}{}{2}{3}\above{1pt}{1pt}{24,1}{\infty}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1105776\\18288\\7200
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
18288\\-285\\-123
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7200\\-123\\-46
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-7\\-154\\-684
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-11\\-240\\-1080
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\66\\293
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
103\\2256\\10080
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
6\\131\\588
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-1105776, 18288, 7200; 18288, -285, -123; 7200, -123, -46],[144, 3, 1],[-7, -11, 3, 103, 6; -154, -240, 66, 2256, 131; -684, -1080, 293, 10080, 588],169,1]
%
% END OF LATTICE L170.1
%
%
% LATTICE L170.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-116592, 2352, 1872; 2352, -46, -39; 1872, -39, -29],[48, 1, 1],[-7, 1, 3, 11, -1; -180, 24, 77, 288, -24; -210, 32, 90, 320, -33],169,2]
%
% END OF LATTICE L170.2
%
%
% LATTICE L170.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-49104, -960, 2160; -960, -15, 42; 2160, 42, -95],[48, 3, 1],[2, 39, 4, -3, -3; 4, 64, 5, -8, -4; 47, 912, 93, -72, -70],169,3]
%
% END OF LATTICE L170.3
%
%
% LATTICE L170.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1124208, 9648, 5760; 9648, -78, -51; 5760, -51, -29],[144, 3, 1],[-1, 3, 4, 1, -3; -40, 128, 165, 40, -124; -129, 368, 504, 128, -378],169,4]
%
% END OF LATTICE L170.4
%
%
% LATTICE L170.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-353616, -120096, 15312; -120096, -40784, 5200; 15312, 5200, -663],[48, 16, 1],[1, -1, -1, 2, 11; -6, -7, 5, 19, 84; -24, -78, 16, 195, 912],169,5]
%
% END OF LATTICE L170.5
%
%
% LATTICE L170.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-163056, -49824, 6912; -49824, -15216, 2112; 6912, 2112, -293],[48, 48, 1],[-2, -3, 5, 9, 12; 1, -1, -3, 1, 3; -40, -78, 96, 219, 304],169,6]
%
% END OF LATTICE L170.6
%
%
% LATTICE L170.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-61200, -146304, 6336; -146304, -349008, 15120; 6336, 15120, -655],[144, 48, 1],[-6, -7, 5, 22, 28; -11, -15, 9, 45, 59; -312, -414, 256, 1251, 1632],169,7]
%
% END OF LATTICE L170.7
%
%
% LATTICE L170.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-4546512, -1474272, 63504; -1474272, -478032, 20592; 63504, 20592, -887],[144, 48, 1],[-2, -3, 5, 8, 36; 1, -1, -3, 2, 11; -120, -238, 288, 619, 2832],169,8]
%
% END OF LATTICE L170.8
%

\medskip%
%------------------------------WEYL-GROUP-W171--------------------------------
%
\leavevmode\llap{}%
$W_{171}$%
\qquad\llap{8} lattices, $\chi=48$%
\hfill%
$\infty2|2\infty|\infty2|2\infty|\rtimes D_{4}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L171.1
%
\leavevmode%
${L_{171.1}}$%
{} : {$1\above{1pt}{1pt}{2}{{\rm II}}16\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{1}{}3\above{1pt}{1pt}{1}{}9\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{3}%
\EasyButWeakLineBreak%
{${48}\above{1pt}{1pt}{3,2}{\infty a}{48}\above{1pt}{1pt}{r}{2}{18}\above{1pt}{1pt}{b}{2}{48}\above{1pt}{1pt}{6,1}{\infty z}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-8784\\1152\\2304
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1152\\-132\\-327
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2304\\-327\\-572
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
10943\\33120\\25056
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1862\\-5636\\-4263
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2318\\-7015\\-5308
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
179\\544\\408
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
629\\1904\\1440
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
263\\795\\603
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
575\\1736\\1320
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-8784, 1152, 2304; 1152, -132, -327; 2304, -327, -572],[144, 3, 1],[179, 629, 263, 575, 125, -21, -35, 33; 544, 1904, 795, 1736, 376, -64, -105, 104; 408, 1440, 603, 1320, 288, -48, -81, 72],170,1]
%
% END OF LATTICE L171.1
%
%
% LATTICE L171.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[48, 0, 0; 0, -60, 131; 0, 131, -286],[48, 1, 1],[-1, -11, -2, -17, -7, -5, 0, 1; 264, 1008, 144, 960, 216, -48, -24, 0; 120, 456, 65, 432, 96, -24, -11, 0],170,2]
%
% END OF LATTICE L171.2
%
%
% LATTICE L171.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2268144, 444768, 141744; 444768, -87216, -27795; 141744, -27795, -8858],[48, 3, 1],[-33, 1, 11, 19, -15, -97, -47, -115; -232, 0, 80, 176, -56, -576, -296, -752; 200, 16, -75, -248, -64, 256, 177, 520],170,3]
%
% END OF LATTICE L171.3
%
%
% LATTICE L171.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1400400, 437616, 20016; 437616, -136752, -6255; 20016, -6255, -286],[144, 3, 1],[93, 391, 58, 405, 107, 9, -8, -5; 280, 1184, 176, 1232, 328, 32, -24, -16; 384, 1464, 209, 1392, 312, -72, -35, 0],170,4]
%
% END OF LATTICE L171.4
%
%
% LATTICE L171.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1536, 1296, -624; 1296, -1088, 528; -624, 528, -253],[48, 16, 1],[17, 50, 131, 127, 44, 11, -9, -5; 6, 21, 57, 57, 21, 6, -3, -3; -30, -81, -208, -198, -66, -15, 16, 6],170,5]
%
% END OF LATTICE L171.5
%
%
% LATTICE L171.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-96, 1104, -48; 1104, -12096, 528; -48, 528, -23],[48, 48, 1],[6, 2, -1, -1, 1, 5, 43, 15; -1, 0, 2, 0, -1, -2, -14, -4; -38, -5, 48, 2, -26, -59, -432, -130],170,6]
%
% END OF LATTICE L171.6
%
%
% LATTICE L171.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[288, -144, 0; -144, -3264, -2064; 0, -2064, -1277],[144, 48, 1],[-5, -48, -437, -159, -68, -25, -1, 13; -11, -98, -888, -322, -137, -50, 0, 26; 18, 159, 1440, 522, 222, 81, 0, -42],170,7]
%
% END OF LATTICE L171.7
%
%
% LATTICE L171.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-288, 720, -288; 720, -1536, 624; -288, 624, -253],[144, 48, 1],[7, 19, 19, 7, 2, -1, -1, 2; -23, -70, -74, -29, -11, 2, 6, -5; -66, -198, -208, -81, -30, 6, 16, -15],170,8]
%
% END OF LATTICE L171.8
%

\medskip%
%------------------------------WEYL-GROUP-W172--------------------------------
%
\leavevmode\llap{}%
$W_{172}$%
\qquad\llap{16} lattices, $\chi=6$%
\hfill%
$2|22\slashtwo2\rtimes D_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L172.1
%
\leavevmode%
${L_{172.1}}$%
{} : {$1\above{1pt}{1pt}{2}{2}8\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{1}{}9\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{2,m}%
\EasyButWeakLineBreak%
{${8}\above{1pt}{1pt}{*}{2}{12}\above{1pt}{1pt}{*}{2}{72}\above{1pt}{1pt}{b}{2}{2}\above{1pt}{1pt}{s}{2}{18}\above{1pt}{1pt}{b}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-5976\\216\\216
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
216\\-6\\-9
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
216\\-9\\-7
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-12\\-16
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-10\\-18
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5\\60\\72
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\11\\16
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\9\\18
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-5976, 216, 216; 216, -6, -9; 216, -9, -7],[72, 3, 1],[-1, -1, 5, 1, 1; -12, -10, 60, 11, 9; -16, -18, 72, 16, 18],171,1]
%
% END OF LATTICE L172.1
%
\hbox{}\par\smallskip%
%
% LATTICE L172.2
%
\leavevmode%
${L_{172.2}}$%
{} : {$1\above{1pt}{1pt}{-2}{6}16\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{1}{}3\above{1pt}{1pt}{-}{}9\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{3,m}%
\EasyButWeakLineBreak%
{${16}\above{1pt}{1pt}{b}{2}{6}\above{1pt}{1pt}{l}{2}{144}\above{1pt}{1pt}{}{2}{1}\above{1pt}{1pt}{r}{2}{36}\above{1pt}{1pt}{*}{2}$}%
\nopagebreak\par%
shares genus with 3-dual\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
13968\\-288\\-144
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-288\\6\\3
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-144\\3\\1
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-40\\-16
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\1\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\48\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\-1
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-42\\-18
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[13968, -288, -144; -288, 6, 3; -144, 3, 1],[144, 3, 1],[-1, 0, 1, 0, -1; -40, 1, 48, 0, -42; -16, 0, 0, -1, -18],171,2]
%
% END OF LATTICE L172.2
%
%
% LATTICE L172.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[1680, 528, -48; 528, 166, -15; -48, -15, 1],[48, 1, 1],[7, -1, -5, 0, 3; -24, 3, 16, 0, -10; -16, 0, 0, -1, -6],171,3]
%
% END OF LATTICE L172.3
%
%
% LATTICE L172.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[18, -18, 0; -18, 12, 3; 0, 3, -1],[18, 3, 1],[1, -1, -1, 1, 1; 0, -1, 0, 3, 1; 0, -3, -4, 0, 2],171,4]
%
% END OF LATTICE L172.4
%
%
% LATTICE L172.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-828, 72, 108; 72, -3, -9; 108, -9, -14],[36, 3, 1],[5, -1, -1, 1, 1; 0, 2, 0, -3, -1; 36, -9, -8, 9, 8],171,5]
%
% END OF LATTICE L172.5
%
%
% LATTICE L172.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[72, 0, -72; 0, -6, -21; -72, -21, -1],[72, 3, 1],[-7, -2, 7, 2, -1; 24, 7, -24, -7, 3; -8, -3, 0, 2, 0],171,6]
%
% END OF LATTICE L172.6
%
%
% LATTICE L172.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-72, -18, -36; -18, 6, -6; -36, -6, -17],[18, 6, 1],[-4, 0, 2, 7, -1; -3, -1, 1, 6, 0; 9, 0, -5, -18, 2],171,7]
%
% END OF LATTICE L172.7
%
%
% LATTICE L172.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[48, -96, 48; -96, -21, 18; 48, 18, -13],[48, 3, 1],[1, 1, 5, -1, -1; 0, 7, 40, -6, -8; 0, 13, 72, -12, -15],171,8]
%
% END OF LATTICE L172.8
%
%
% LATTICE L172.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1332, -108, -324; -108, 24, 36; -324, 36, 85],[36, 12, 1],[-5, 0, -1, -7, -3; 18, 1, 3, 21, 10; -27, 0, -5, -36, -16],171,9]
%
% END OF LATTICE L172.9
%
%
% LATTICE L172.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-10224, 288, 144; 288, 33, -3; 144, -3, -2],[144, 3, 1],[-1, -1, 1, 1, 1; 0, 2, 0, -2, -3; -80, -75, 72, 74, 72],171,10]
%
% END OF LATTICE L172.10
%
%
% LATTICE L172.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[96, -48, 0; -48, -304, 48; 0, 48, -7],[48, 16, 1],[1, -1, -1, 0, 3; 2, 0, -2, -1, 5; 13, 0, -14, -8, 32],171,11]
%
% END OF LATTICE L172.11
%
%
% LATTICE L172.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[144, -72, 0; -72, -4872, 336; 0, 336, -23],[72, 24, 1],[-1, 3, 1, -1, -3; -3, 5, 2, 0, -6; -45, 72, 29, 0, -88],171,12]
%
% END OF LATTICE L172.12
%
%
% LATTICE L172.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[144, -648, -288; -648, 2472, 1104; -288, 1104, 493],[72, 24, 1],[-1, 1, 1, 1, -1; 24, -5, -6, 0, 14; -54, 12, 14, 0, -32],171,13]
%
% END OF LATTICE L172.13
%
%
% LATTICE L172.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1680, -960, 384; -960, -336, 144; 384, 144, -61],[48, 48, 1],[1, -1, -1, 1, 4; 14, -11, -15, 8, 51; 39, -32, -42, 24, 144],171,14]
%
% END OF LATTICE L172.14
%
%
% LATTICE L172.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-288, 3312, -144; 3312, -37488, 1632; -144, 1632, -71],[144, 48, 1],[4, -1, -1, 1, 4; 0, 2, 0, -3, -1; -9, 48, 2, -72, -32],171,15]
%
% END OF LATTICE L172.15
%
%
% LATTICE L172.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-288, -144, -288; -144, -48, -144; -288, -144, -287],[144, 48, 1],[17, -1, -1, 1, 8; 0, 2, 0, -3, -1; -18, 0, 1, 0, -8],171,16]
%
% END OF LATTICE L172.16
%

\medskip%
%------------------------------WEYL-GROUP-W173--------------------------------
%
\leavevmode\llap{}%
$W_{173}$%
\qquad\llap{8} lattices, $\chi=40$%
\hfill%
$3\infty\infty3\infty\infty\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L173.1
%
\leavevmode%
${L_{173.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}8\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{-2}{}25\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${2}\above{1pt}{1pt}{-}{3}{2}\above{1pt}{1pt}{20,17}{\infty b}{8}\above{1pt}{1pt}{10,7}{\infty z}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-45400\\600\\800
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
600\\-6\\-11
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
800\\-11\\-14
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
799\\7200\\39200
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-7\\-64\\-343
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-15\\-135\\-736
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\16\\99
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
8\\71\\393
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5\\48\\244
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-45400, 600, 800; 600, -6, -11; 800, -11, -14],[200, 1, 1],[2, 8, 5, 1, 0, -1; 16, 71, 48, 11, 1, -12; 99, 393, 244, 48, -1, -48],172,1]
%
% END OF LATTICE L173.1
%
%
% LATTICE L173.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-2350, 450, -100; 450, -86, 19; -100, 19, -4],[50, 1, 1],[1, 0, -1, -1, 0, 1; 6, 1, -6, -9, -9, 4; 3, 4, -4, -21, -52, -8],172,2]
%
% END OF LATTICE L173.2
%
%
% LATTICE L173.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[6700, -150, 3200; -150, 24, -68; 3200, -68, 1529],[50, 2, 1],[-26, -27, -13, -205, -589, -64; -9, -10, -5, -75, -214, -23; 54, 56, 27, 426, 1224, 133],172,3]
%
% END OF LATTICE L173.3
%
%
% LATTICE L173.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[12450, -900, 5900; -900, 200, -425; 5900, -425, 2796],[50, 25, 1],[83, 95, 95, 700, 1993, 427; 2, 3, 2, 13, 37, 8; -175, -200, -200, -1475, -4200, -900],172,4]
%
% END OF LATTICE L173.4
%
%
% LATTICE L173.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[101200, -600, 24800; -600, -16, -144; 24800, -144, 6077],[200, 8, 1],[-41, 2, 21, 41, -2, -21; 24, -7, -14, -27, -1, 13; 168, -8, -86, -168, 8, 86],172,5]
%
% END OF LATTICE L173.5
%
%
% LATTICE L173.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-200, -36550, -17900; -36550, -6384300, -3126650; -17900, -3126650, -1531247],[50, 50, 1],[3, 4, -2, -21, -52, -4; 906, -49, -453, -759, 441, 502; -1850, 100, 925, 1550, -900, -1025],172,6]
%
% END OF LATTICE L173.6
%
%
% LATTICE L173.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-21400, 23200, 10400; 23200, -25150, -11275; 10400, -11275, -5054],[200, 25, 1],[12, -11, -13, 54, 187, 101; 11, 1, -12, 16, 71, 48; 0, -25, 0, 75, 225, 100],172,7]
%
% END OF LATTICE L173.7
%
%
% LATTICE L173.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[591600, 591400, -5600; 591400, 590800, -5600; -5600, -5600, 53],[200, 200, 1],[24, -7, -14, -27, -1, 13; -7, 5, 5, 10, 3, -4; 1800, -200, -950, -1800, 200, 950],172,8]
%
% END OF LATTICE L173.8
%

\medskip%
%------------------------------WEYL-GROUP-W174--------------------------------
%
\leavevmode\llap{}%
$W_{174}$%
\qquad\llap{8} lattices, $\chi=30$%
\hfill%
$2\infty2\infty2\infty\rtimes C_{3}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L174.1
%
\leavevmode%
${L_{174.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}8\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{2}{}25\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${50}\above{1pt}{1pt}{b}{2}{8}\above{1pt}{1pt}{10,1}{\infty z}{2}\above{1pt}{1pt}{b}{2}{8}\above{1pt}{1pt}{10,9}{\infty z}{2}\above{1pt}{1pt}{b}{2}{200}\above{1pt}{1pt}{2,1}{\infty z}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
12200\\-5000\\200
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-5000\\2042\\-55
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
200\\-55\\-98
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-152\\-375\\-100
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-73\\-180\\-48
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
75\\185\\49
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
459\\1132\\300
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
176\\434\\115
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1379\\3400\\900
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[12200, -5000, 200; -5000, 2042, -55; 200, -55, -98],[200, 1, 1],[-152, -73, 75, 459, 176, 1379; -375, -180, 185, 1132, 434, 3400; -100, -48, 49, 300, 115, 900],173,1]
%
% END OF LATTICE L174.1
%
%
% LATTICE L174.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-29950, 12100, 1200; 12100, -4888, -485; 1200, -485, -48],[50, 1, 1],[3, 19, 20, 101, -1, -5; 5, 36, 39, 200, 0, -10; 24, 110, 105, 500, -25, -24],173,2]
%
% END OF LATTICE L174.2
%
%
% LATTICE L174.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[130100, -3350, 60750; -3350, 96, -1560; 60750, -1560, 28369],[50, 2, 1],[241, 318, 483, 1088, 24, 11; 220, 291, 443, 1000, 25, 10; -504, -665, -1010, -2275, -50, -23],173,3]
%
% END OF LATTICE L174.3
%
%
% LATTICE L174.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[636050, -66750, 304200; -66750, 7200, -31925; 304200, -31925, 145488],[50, 25, 1],[-2365, -6259, -4766, -861, -11, -215; 23, 60, 45, 8, 0, 2; 4950, 13100, 9975, 1802, 23, 450],173,4]
%
% END OF LATTICE L174.4
%
%
% LATTICE L174.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-41112400, -165000, 293200; -165000, -560, 1176; 293200, 1176, -2091],[200, 8, 1],[27, 23, -47, -111, -216, -526; 25, 23, -46, -110, -215, -525; 3800, 3238, -6616, -15626, -30408, -74050],173,5]
%
% END OF LATTICE L174.5
%
%
% LATTICE L174.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2400, 1068250, 523200; 1068250, -474214400, -232257400; 523200, -232257400, -113753399],[50, 50, 1],[24, 55, 105, 10, -1, -12; 3355, 10518, 22089, 2228, -48, -2755; -6850, -21475, -45100, -4549, 98, 5625],173,6]
%
% END OF LATTICE L174.6
%
%
% LATTICE L174.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-7000, -1800, 1200; -1800, -150, 125; 1200, 125, -98],[200, 25, 1],[-2, -1, 1, 31, 12, 19; -59, -28, 29, 884, 338, 528; -100, -48, 49, 1500, 575, 900],173,7]
%
% END OF LATTICE L174.7
%
%
% LATTICE L174.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-854800, -3979400, -946600; -3979400, -18436400, -4385400; -946600, -4385400, -1043139],[200, 200, 1],[-47, -555, -1080, -526, 27, 23; 1346, 15926, 31013, 15111, -767, -661; -5616, -66450, -129400, -63050, 3200, 2758],173,8]
%
% END OF LATTICE L174.8
%

\medskip%
%------------------------------WEYL-GROUP-W175--------------------------------
%
\leavevmode\llap{}%
$W_{175}$%
\qquad\llap{27} lattices, $\chi=12$%
\hfill%
$\slashtwo2|2\slashtwo2|2\rtimes D_{4}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L175.1
%
\leavevmode%
${L_{175.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{4}8\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{1}{}3\above{1pt}{1pt}{1}{}9\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${36}\above{1pt}{1pt}{l}{2}{1}\above{1pt}{1pt}{}{2}{3}\above{1pt}{1pt}{}{2}{9}\above{1pt}{1pt}{r}{2}{4}\above{1pt}{1pt}{*}{2}{12}\above{1pt}{1pt}{*}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1800\\288\\-72
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
288\\-15\\-6
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-72\\-6\\7
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-12\\-18
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\11\\20
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\22\\39
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\21\\36
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-12\\-22
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3\\-34\\-60
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-1800, 288, -72; 288, -15, -6; -72, -6, 7],[72, 3, 1],[-1, 1, 2, 2, -1, -3; -12, 11, 22, 21, -12, -34; -18, 20, 39, 36, -22, -60],174,1]
%
% END OF LATTICE L175.1
%
\hbox{}\par\smallskip%
%
% LATTICE L175.2
%
\leavevmode%
${L_{175.2}}$%
{} : {$1\above{1pt}{1pt}{-2}{2}8\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{1}{}3\above{1pt}{1pt}{1}{}9\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{m}%
\EasyButWeakLineBreak%
{${36}\above{1pt}{1pt}{*}{2}{4}\above{1pt}{1pt}{l}{2}{3}\above{1pt}{1pt}{r}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
8136\\-576\\288
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-576\\39\\-18
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
288\\-18\\7
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-96\\-288
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\4\\15
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\-1\\-4
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-24\\-18
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\22\\16
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\22\\15
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[8136, -576, 288; -576, 39, -18; 288, -18, 7],[72, 3, 1],[-1, 1, 1, 1, -1, -1; -24, 22, 22, 18, -24, -23; -18, 16, 15, 0, -22, -18],174,2]
%
% END OF LATTICE L175.2
%
\hbox{}\par\smallskip%
%
% LATTICE L175.3
%
\leavevmode%
${L_{175.3}}$%
{} : {$1\above{1pt}{1pt}{2}{2}8\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{1}{}3\above{1pt}{1pt}{1}{}9\above{1pt}{1pt}{1}{}$}\EasyButWeakLineBreak%
{${9}\above{1pt}{1pt}{}{2}{1}\above{1pt}{1pt}{r}{2}{12}\above{1pt}{1pt}{l}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1368\\144\\360
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
144\\-15\\-36
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
360\\-36\\-71
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
143\\1680\\-144
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-15\\-176\\15
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-33\\-385\\32
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\9\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-12\\1
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-10\\0
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-1368, 144, 360; 144, -15, -36; 360, -36, -71],[72, 3, 1],[1, -1, -1, 8, 4, 7; 9, -12, -10, 96, 47, 80; 0, 1, 0, -9, -4, -6],174,3]
%
% END OF LATTICE L175.3
%
\hbox{}\par\smallskip%
%
% LATTICE L175.4
%
\leavevmode%
${L_{175.4}}$%
{} : {$[1\above{1pt}{1pt}{-}{}2\above{1pt}{1pt}{1}{}]\above{1pt}{1pt}{}{4}16\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{1}{}3\above{1pt}{1pt}{1}{}9\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${4}\above{1pt}{1pt}{*}{2}{144}\above{1pt}{1pt}{l}{2}{3}\above{1pt}{1pt}{r}{2}{16}\above{1pt}{1pt}{*}{2}{36}\above{1pt}{1pt}{s}{2}{48}\above{1pt}{1pt}{s}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-5904\\864\\288
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
864\\-78\\-30
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
288\\-30\\-11
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\20\\-82
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-5\\108\\-432
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\1\\-3
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\-20\\80
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\-24\\90
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\16\\-72
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-5904, 864, 288; 864, -78, -30; 288, -30, -11],[144, 6, 1],[-1, -5, 0, 1, 1, -1; 20, 108, 1, -20, -24, 16; -82, -432, -3, 80, 90, -72],174,4]
%
% END OF LATTICE L175.4
%
\hbox{}\par\smallskip%
%
% LATTICE L175.5
%
\leavevmode%
${L_{175.5}}$%
{} : {$[1\above{1pt}{1pt}{1}{}2\above{1pt}{1pt}{1}{}]\above{1pt}{1pt}{}{0}16\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{1}{}3\above{1pt}{1pt}{1}{}9\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{m}%
\EasyButWeakLineBreak%
{${1}\above{1pt}{1pt}{r}{2}{144}\above{1pt}{1pt}{*}{2}{12}\above{1pt}{1pt}{*}{2}{16}\above{1pt}{1pt}{l}{2}{9}\above{1pt}{1pt}{}{2}{48}\above{1pt}{1pt}{}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-90576\\-6048\\2448
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-6048\\-402\\162
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2448\\162\\-65
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\-29\\-35
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5\\-132\\-144
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\32\\42
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\28\\32
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\-33\\-45
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5\\-152\\-192
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-90576, -6048, 2448; -6048, -402, 162; 2448, 162, -65],[144, 6, 1],[1, 5, -1, -1, 1, 5; -29, -132, 32, 28, -33, -152; -35, -144, 42, 32, -45, -192],174,5]
%
% END OF LATTICE L175.5
%
\hbox{}\par\smallskip%
%
% LATTICE L175.6
%
\leavevmode%
${L_{175.6}}$%
{} : {$[1\above{1pt}{1pt}{1}{}2\above{1pt}{1pt}{1}{}]\above{1pt}{1pt}{}{6}16\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{1}{}3\above{1pt}{1pt}{1}{}9\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{m}%
\EasyButWeakLineBreak%
{${4}\above{1pt}{1pt}{s}{2}{144}\above{1pt}{1pt}{s}{2}{12}\above{1pt}{1pt}{s}{2}{16}\above{1pt}{1pt}{s}{2}{36}\above{1pt}{1pt}{*}{2}{48}\above{1pt}{1pt}{*}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
8784\\432\\-288
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
432\\-6\\-6
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-288\\-6\\7
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-18\\-58
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-24\\-72
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\16\\54
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\16\\56
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-18\\-54
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3\\-52\\-168
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[8784, 432, -288; 432, -6, -6; -288, -6, 7],[144, 6, 1],[-1, -1, 1, 1, -1, -3; -18, -24, 16, 16, -18, -52; -58, -72, 54, 56, -54, -168],174,6]
%
% END OF LATTICE L175.6
%
\hbox{}\par\smallskip%
%
% LATTICE L175.7
%
\leavevmode%
${L_{175.7}}$%
{} : {$1\above{1pt}{1pt}{1}{1}8\above{1pt}{1pt}{-}{5}64\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{1}{}3\above{1pt}{1pt}{1}{}9\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{3,2}%
\EasyButWeakLineBreak%
{${64}\above{1pt}{1pt}{s}{2}{36}\above{1pt}{1pt}{*}{2}{192}\above{1pt}{1pt}{l}{2}{1}\above{1pt}{1pt}{}{2}{576}\above{1pt}{1pt}{r}{2}{12}\above{1pt}{1pt}{b}{2}$}%
\nopagebreak\par%
shares genus with 2-dual${}\iso{}$3-dual; isometric to own %
2.3-dual\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
318528\\576\\-576
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
576\\-24\\0
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-576\\0\\1
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-16\\-544
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-18\\-558
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-20\\-576
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\-1
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\24\\576
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\1\\6
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[318528, 576, -576; 576, -24, 0; -576, 0, 1],[576, 24, 1],[-1, -1, -1, 0, 1, 0; -16, -18, -20, 0, 24, 1; -544, -558, -576, -1, 576, 6],174,7]
%
% END OF LATTICE L175.7
%
%
% LATTICE L175.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-18, 0, -18; 0, 3, 6; -18, 6, -5],[18, 3, 1],[-1, 1, 2, 1, -1, -2; -2, 3, 4, 1, -6, -5; 1, 0, -3, -4, -9, 0],174,8]
%
% END OF LATTICE L175.8
%
%
% LATTICE L175.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-252, 0, 108; 0, 33, 30; 108, 30, -19],[36, 3, 1],[-4, -8, -11, -2, 6, 9; 9, 17, 23, 3, -13, -19; -9, -19, -27, -9, 13, 21],174,9]
%
% END OF LATTICE L175.9
%
%
% LATTICE L175.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[1764, -864, 108; -864, 426, -54; 108, -54, 7],[36, 6, 1],[1, 3, 3, 13, 1, -1; 3, 8, 8, 36, 3, -2; 9, 16, 15, 72, 7, 0],174,10]
%
% END OF LATTICE L175.10
%
%
% LATTICE L175.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[504, 144, 0; 144, 42, 0; 0, 0, -1],[72, 6, 1],[1, 1, 0, -5, -1, -1; -3, -4, -1, 12, 3, 4; 0, -4, -6, -36, -4, 0],174,11]
%
% END OF LATTICE L175.11
%
%
% LATTICE L175.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[4392, 1440, 144; 1440, 474, 48; 144, 48, 5],[72, 6, 1],[1, -1, -3, -23, -3, -1; -3, 4, 11, 84, 11, 4; 0, -8, -18, -144, -20, -12],174,12]
%
% END OF LATTICE L175.12
%
%
% LATTICE L175.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[31296, 10560, -192; 10560, 3560, -64; -192, -64, 1],[192, 8, 1],[-5, 0, 11, 3, 7, -1; 16, 0, -36, -10, -24, 3; 64, -1, -192, -58, -160, 6],174,13]
%
% END OF LATTICE L175.13
%
%
% LATTICE L175.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-3312, 144, 144; 144, 120, 24; 144, 24, 1],[144, 24, 1],[-1, 1, 5, 1, 5, -1; 8, -6, -34, -7, -36, 7; -32, 27, 144, 29, 144, -30],174,14]
%
% END OF LATTICE L175.14
%
%
% LATTICE L175.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1422, 324, 684; 324, 78, 156; 684, 156, 329],[18, 6, 1],[-1, 8, -11, -32, -107, -22; 0, 3, -2, -7, -24, -5; 2, -18, 24, 70, 234, 48],174,15]
%
% END OF LATTICE L175.15
%
%
% LATTICE L175.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[65736, 12276, -8352; 12276, 2292, -1560; -8352, -1560, 1061],[36, 12, 1],[17, -1, -17, -59, -13, 3; -42, 0, 34, 120, 26, -8; 72, -8, -84, -288, -64, 12],174,16]
%
% END OF LATTICE L175.16
%
%
% LATTICE L175.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2952, 720, -144; 720, 156, -36; -144, -36, 7],[72, 12, 1],[-1, 1, 1, 1, -1, -2; 0, -3, -1, -1, 0, 1; -22, 0, 15, 16, -18, -36],174,17]
%
% END OF LATTICE L175.17
%
%
% LATTICE L175.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1368, -1656, 504; -1656, -1716, 516; 504, 516, -155],[72, 12, 1],[2, 7, -1, -1, 1, 4; -25, -93, 10, 13, -9, -47; -77, -288, 30, 40, -27, -144],174,18]
%
% END OF LATTICE L175.18
%
%
% LATTICE L175.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[38160, 4608, -432; 4608, 570, -66; -432, -66, 19],[144, 6, 1],[-8, -113, -7, -7, -1, -11; 73, 1032, 64, 64, 9, 100; 71, 1008, 63, 64, 9, 96],174,19]
%
% END OF LATTICE L175.19
%
%
% LATTICE L175.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[72, 0, 0; 0, 24, 0; 0, 0, -1],[72, 24, 1],[1, 0, -1, -4, -1, 0; 0, -1, -2, -3, 0, 1; 0, -4, -12, -36, -8, 0],174,20]
%
% END OF LATTICE L175.20
%
%
% LATTICE L175.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[72, 0, 0; 0, -8760, 408; 0, 408, -19],[72, 24, 1],[1, 0, -1, -4, -1, 0; 0, 3, 4, -3, -4, -5; 0, 64, 84, -72, -88, -108],174,21]
%
% END OF LATTICE L175.21
%
%
% LATTICE L175.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[24696, 5472, -648; 5472, 1176, -144; -648, -144, 17],[72, 24, 1],[-1, 2, 3, -2, -3, -4; 0, -1, -2, -3, 0, 1; -36, 68, 96, -108, -116, -144],174,22]
%
% END OF LATTICE L175.22
%
%
% LATTICE L175.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1008, -576, -144; -576, 264, 72; -144, 72, 19],[144, 24, 1],[-1, -5, 0, 1, 1, -1; 5, 30, 1, -2, -3, 4; -26, -144, -3, 16, 18, -24],174,23]
%
% END OF LATTICE L175.23
%
%
% LATTICE L175.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-92304, -6624, 1008; -6624, -456, 72; 1008, 72, -11],[144, 24, 1],[1, 1, -1, -1, -5, 0; 2, 0, -4, -2, -6, 1; 104, 90, -120, -106, -504, 6],174,24]
%
% END OF LATTICE L175.24
%
%
% LATTICE L175.25
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2736, -1872, 144; -1872, 1272, -96; 144, -96, 7],[144, 24, 1],[-1, -1, 1, 1, -1, -3; -3, -6, 2, 2, -3, -8; -22, -72, 6, 8, -18, -48],174,25]
%
% END OF LATTICE L175.25
%
%
% LATTICE L175.26
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-27456, 13056, 1536; 13056, -5448, -648; 1536, -648, -77],[192, 24, 1],[1, -1, -1, 1, 13, 1; -32, 24, 28, -23, -312, -25; 288, -222, -256, 213, 2880, 230],174,26]
%
% END OF LATTICE L175.26
%
%
% LATTICE L175.27
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-40896, 9792, -2304; 9792, 552, -168; -2304, -168, 49],[576, 24, 1],[-1, 1, 7, 1, 1, -1; -80, 78, 548, 78, 72, -79; -320, 315, 2208, 314, 288, -318],174,27]
%
% END OF LATTICE L175.27
%

\medskip%
%------------------------------WEYL-GROUP-W176--------------------------------
%
\leavevmode\llap{}%
$W_{176}$%
\qquad\llap{34} lattices, $\chi=24$%
\hfill%
$222|222\slashinfty\rtimes D_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L176.1
%
\leavevmode%
${L_{176.1}}$%
{} : {$1\above{1pt}{1pt}{2}{0}8\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{-2}{}7\above{1pt}{1pt}{1}{}$}\EasyButWeakLineBreak%
{${56}\above{1pt}{1pt}{}{2}{1}\above{1pt}{1pt}{}{2}{7}\above{1pt}{1pt}{r}{2}{8}\above{1pt}{1pt}{s}{2}{28}\above{1pt}{1pt}{*}{2}{4}\above{1pt}{1pt}{*}{2}{56}\above{1pt}{1pt}{1,0}{\infty b}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-740040\\12600\\12992
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
12600\\-211\\-225
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
12992\\-225\\-224
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
211\\6328\\5880
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
49\\1469\\1366
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
181\\5425\\5047
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
41\\1228\\1144
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
23\\686\\644
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-15\\-450\\-418
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-15\\-448\\-420
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-740040, 12600, 12992; 12600, -211, -225; 12992, -225, -224],[56, 1, 1],[211, 49, 181, 41, 23, -15, -15; 6328, 1469, 5425, 1228, 686, -450, -448; 5880, 1366, 5047, 1144, 644, -418, -420],175,1]
%
% END OF LATTICE L176.1
%
\hbox{}\par\smallskip%
%
% LATTICE L176.2
%
\leavevmode%
${L_{176.2}}$%
{} : {$[1\above{1pt}{1pt}{-}{}2\above{1pt}{1pt}{1}{}]\above{1pt}{1pt}{}{4}16\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{-2}{}7\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2,m}%
\EasyButWeakLineBreak%
{${14}\above{1pt}{1pt}{r}{2}{4}\above{1pt}{1pt}{s}{2}{112}\above{1pt}{1pt}{l}{2}{2}\above{1pt}{1pt}{r}{2}{28}\above{1pt}{1pt}{*}{2}{16}\above{1pt}{1pt}{*}{2}{56}\above{1pt}{1pt}{8,5}{\infty z}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-345296\\7840\\8624
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7840\\-178\\-196
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
8624\\-196\\-211
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3\\-133\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5\\204\\14
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
73\\3024\\168
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5\\209\\10
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
23\\966\\42
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\44\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-15\\-630\\-28
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-345296, 7840, 8624; 7840, -178, -196; 8624, -196, -211],[112, 2, 1],[-3, 5, 73, 5, 23, 1, -15; -133, 204, 3024, 209, 966, 44, -630; 0, 14, 168, 10, 42, 0, -28],175,2]
%
% END OF LATTICE L176.2
%
\hbox{}\par\smallskip%
%
% LATTICE L176.3
%
\leavevmode%
${L_{176.3}}$%
{} : {$[1\above{1pt}{1pt}{1}{}2\above{1pt}{1pt}{1}{}]\above{1pt}{1pt}{}{6}16\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{-2}{}7\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{m}%
\EasyButWeakLineBreak%
{${56}\above{1pt}{1pt}{*}{2}{4}\above{1pt}{1pt}{*}{2}{112}\above{1pt}{1pt}{s}{2}{8}\above{1pt}{1pt}{l}{2}{7}\above{1pt}{1pt}{}{2}{16}\above{1pt}{1pt}{}{2}{14}\above{1pt}{1pt}{8,1}{\infty}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-655984\\-185808\\11312
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-185808\\-52630\\3204
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
11312\\3204\\-195
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\-14\\-56
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7\\-28\\-54
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-5\\28\\168
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-15\\62\\148
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-74\\301\\651
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-83\\336\\704
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-47\\189\\378
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-655984, -185808, 11312; -185808, -52630, 3204; 11312, 3204, -195],[112, 2, 1],[3, 7, -5, -15, -74, -83, -47; -14, -28, 28, 62, 301, 336, 189; -56, -54, 168, 148, 651, 704, 378],175,3]
%
% END OF LATTICE L176.3
%
\hbox{}\par\smallskip%
%
% LATTICE L176.4
%
\leavevmode%
${L_{176.4}}$%
{} : {$[1\above{1pt}{1pt}{-}{}2\above{1pt}{1pt}{1}{}]\above{1pt}{1pt}{}{2}16\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{-2}{}7\above{1pt}{1pt}{1}{}$}\EasyButWeakLineBreak%
{${56}\above{1pt}{1pt}{l}{2}{1}\above{1pt}{1pt}{r}{2}{112}\above{1pt}{1pt}{*}{2}{8}\above{1pt}{1pt}{*}{2}{28}\above{1pt}{1pt}{s}{2}{16}\above{1pt}{1pt}{l}{2}{14}\above{1pt}{1pt}{8,5}{\infty}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-560\\-112\\784
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-112\\-22\\168
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
784\\168\\-783
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\-14\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7\\-28\\1
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-5\\28\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-29\\118\\-4
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-295\\1190\\-42
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-167\\672\\-24
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-96\\385\\-14
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-560, -112, 784; -112, -22, 168; 784, 168, -783],[112, 2, 1],[3, 7, -5, -29, -295, -167, -96; -14, -28, 28, 118, 1190, 672, 385; 0, 1, 0, -4, -42, -24, -14],175,4]
%
% END OF LATTICE L176.4
%
\hbox{}\par\smallskip%
%
% LATTICE L176.5
%
\leavevmode%
${L_{176.5}}$%
{} : {$1\above{1pt}{1pt}{1}{7}8\above{1pt}{1pt}{1}{1}64\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{-2}{}7\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${56}\above{1pt}{1pt}{s}{2}{4}\above{1pt}{1pt}{b}{2}{448}\above{1pt}{1pt}{l}{2}{8}\above{1pt}{1pt}{r}{2}{28}\above{1pt}{1pt}{*}{2}{64}\above{1pt}{1pt}{s}{2}{224}\above{1pt}{1pt}{16,1}{\infty z}$}%
\nopagebreak\par%
shares genus with {$ {L_{176.6}}$}%
; isometric to own %
2-dual\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-189504\\-9856\\448
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-9856\\-504\\24
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
448\\24\\-1
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\-35\\476
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\-11\\170
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
11\\-112\\2016
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\1\\16
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\14\\-126
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\12\\-160
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\-14\\112
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-189504, -9856, 448; -9856, -504, 24; 448, 24, -1],[448, 8, 1],[3, 1, 11, 0, -1, -1, 1; -35, -11, -112, 1, 14, 12, -14; 476, 170, 2016, 16, -126, -160, 112],175,5]
%
% END OF LATTICE L176.5
%
\hbox{}\par\smallskip%
%
% LATTICE L176.6
%
\leavevmode%
${L_{176.6}}$%
{} : {$1\above{1pt}{1pt}{1}{7}8\above{1pt}{1pt}{1}{1}64\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{-2}{}7\above{1pt}{1pt}{1}{}$}\EasyButWeakLineBreak%
{${56}\above{1pt}{1pt}{b}{2}{4}\above{1pt}{1pt}{l}{2}{448}\above{1pt}{1pt}{}{2}{8}\above{1pt}{1pt}{}{2}{7}\above{1pt}{1pt}{r}{2}{64}\above{1pt}{1pt}{*}{2}{224}\above{1pt}{1pt}{16,9}{\infty z}$}%
\nopagebreak\par%
shares genus with {$ {L_{176.5}}$}%
; isometric to own %
2-dual\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3777088\\165312\\-54656
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
165312\\-7224\\2384
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-54656\\2384\\-785
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3\\-133\\-196
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
6\\249\\338
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
157\\6552\\8960
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
10\\419\\576
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
11\\462\\637
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\44\\64
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-29\\-1218\\-1680
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-3777088, 165312, -54656; 165312, -7224, 2384; -54656, 2384, -785],[448, 8, 1],[-3, 6, 157, 10, 11, 1, -29; -133, 249, 6552, 419, 462, 44, -1218; -196, 338, 8960, 576, 637, 64, -1680],175,6]
%
% END OF LATTICE L176.6
%
%
% LATTICE L176.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[700, -112, 0; -112, 14, -2; 0, -2, -1],[28, 2, 1],[-8, -4, -31, -2, -2, 1, 1; -49, -25, -196, -13, -14, 6, 7; 84, 43, 336, 22, 21, -12, -14],175,7]
%
% END OF LATTICE L176.7
%
%
% LATTICE L176.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-12712, 168, 1064; 168, -2, -14; 1064, -14, -89],[56, 2, 1],[3, 2, 11, 0, -2, -1, 1; 0, 7, 84, 5, 21, 0, -14; 35, 22, 112, -1, -28, -12, 14],175,8]
%
% END OF LATTICE L176.8
%
%
% LATTICE L176.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-280, -616, 560; -616, -1122, 992; 560, 992, -873],[56, 2, 1],[-61, -107, -190, -19, -5, 9, 3; 238, 420, 749, 76, 28, -35, -14; 231, 408, 728, 74, 28, -34, -14],175,9]
%
% END OF LATTICE L176.9
%
%
% LATTICE L176.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-2393104, 378448, -41328; 378448, -59848, 6536; -41328, 6536, -713],[112, 8, 1],[-183, -89, -675, -41, -15, 27, 22; -1099, -535, -4060, -247, -91, 162, 133; 532, 254, 1904, 112, 35, -80, -56],175,10]
%
% END OF LATTICE L176.10
%
%
% LATTICE L176.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-47376, -2912, -3136; -2912, -178, -192; -3136, -192, -207],[112, 2, 1],[-3, -1, -11, 0, 1, 1, -1; -133, -52, -672, -11, 21, 44, -14; 168, 63, 784, 10, -35, -56, 28],175,11]
%
% END OF LATTICE L176.11
%
%
% LATTICE L176.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[56, 0, 0; 0, -780, -28; 0, -28, -1],[56, 4, 1],[-1, -1, -5, -1, -1, 0, 1; -14, -6, -21, -2, 0, 1, 0; 364, 154, 532, 48, -7, -28, 0],175,12]
%
% END OF LATTICE L176.12
%
%
% LATTICE L176.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-728, 784, 392; 784, -780, -420; 392, -420, -211],[56, 4, 1],[197, 46, 341, 39, 23, -14, -15; -14, -3, -21, -2, 0, 1, 0; 392, 91, 672, 76, 42, -28, -28],175,13]
%
% END OF LATTICE L176.13
%
%
% LATTICE L176.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[28, 0, 0; 0, -2702, 406; 0, 406, -61],[28, 14, 1],[1, 3, 3, 1, 0, -1, 0; 1, 14, 22, 17, 5, 0, -3; 6, 91, 144, 112, 33, 0, -20],175,14]
%
% END OF LATTICE L176.14
%
%
% LATTICE L176.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-18424, 1064, 1064; 1064, -56, -63; 1064, -63, -61],[56, 7, 1],[7, 16, 10, 23, 5, -3, -3; 24, 58, 37, 88, 20, -10, -12; 96, 217, 135, 308, 66, -42, -40],175,15]
%
% END OF LATTICE L176.15
%
%
% LATTICE L176.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-12712, -3920, 1064; -3920, -1208, 328; 1064, 328, -89],[56, 8, 1],[3, 4, 11, 0, -4, -1, 1; 0, 7, 42, 5, 21, 0, -7; 35, 72, 280, 18, 28, -12, -14],175,16]
%
% END OF LATTICE L176.16
%
%
% LATTICE L176.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-95032, 1232, 3248; 1232, -14, -42; 3248, -42, -111],[56, 14, 1],[0, -4, -7, -3, -2, -1, 1; 2, 19, 24, 7, 3, -4, -2; -1, -126, -216, -91, -60, -28, 30],175,17]
%
% END OF LATTICE L176.17
%
%
% LATTICE L176.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-8680, 728, 336; 728, -42, -28; 336, -28, -13],[56, 14, 1],[1, 19, 6, 7, 3, -1, -1; -1, -12, -3, -2, 0, 1, 0; 27, 504, 158, 182, 76, -28, -26],175,18]
%
% END OF LATTICE L176.18
%
%
% LATTICE L176.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-8630608, 1395744, -43680; 1395744, -225720, 7064; -43680, 7064, -221],[112, 8, 1],[-106, -53, -409, -26, -23, 15, 15; -637, -319, -2464, -157, -140, 90, 91; 588, 278, 2072, 120, 70, -88, -56],175,19]
%
% END OF LATTICE L176.19
%
%
% LATTICE L176.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1483664, 207200, -34944; 207200, -28936, 4880; -34944, 4880, -823],[112, 8, 1],[1, -1, -2, 0, 11, 1, 6; -7, -22, 7, 25, 476, 33, 147; -84, -88, 126, 148, 2352, 153, 616],175,20]
%
% END OF LATTICE L176.20
%
%
% LATTICE L176.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-102256, 16016, -3808; 16016, -2504, 600; -3808, 600, -139],[112, 8, 1],[13, 13, -19, -22, -347, -45, -90; 63, 64, -91, -107, -1694, -220, -441; -84, -80, 126, 140, 2184, 282, 560],175,21]
%
% END OF LATTICE L176.21
%
%
% LATTICE L176.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-190064, -52864, 7728; -52864, -14658, 2142; 7728, 2142, -313],[112, 14, 1],[1, -1, -1, -3, -7, -2, 0; -34, 20, 33, 105, 264, 82, 5; -208, 112, 201, 644, 1632, 511, 34],175,22]
%
% END OF LATTICE L176.22
%
%
% LATTICE L176.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-118832, -21952, 2800; -21952, -3906, 490; 2800, 490, -61],[112, 14, 1],[-3, -3, 5, 10, 31, 23, 2; 54, 52, -90, -179, -552, -408, -35; 296, 280, -494, -980, -3016, -2226, -190],175,23]
%
% END OF LATTICE L176.23
%
%
% LATTICE L176.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-30352, -11648, 1792; -11648, -4382, 672; 1792, 672, -103],[112, 14, 1],[1, 19, 3, 7, 3, -1, -1; -21, -376, -58, -130, -52, 22, 18; -120, -2128, -327, -728, -288, 126, 100],175,24]
%
% END OF LATTICE L176.24
%
%
% LATTICE L176.25
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-17360, -13440, 2128; -13440, -9758, 1540; 2128, 1540, -243],[112, 14, 1],[2, 31, 9, 9, 3, -1, -1; -57, -864, -248, -242, -76, 29, 26; -344, -5208, -1494, -1456, -456, 175, 156],175,25]
%
% END OF LATTICE L176.25
%
%
% LATTICE L176.26
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3640, 2968, -1064; 2968, -2380, 868; -1064, 868, -311],[56, 28, 1],[7, 9, -5, -51, -46, -75, -17; 0, 1, 0, -2, -3, -6, -2; -24, -28, 17, 168, 148, 238, 52],175,26]
%
% END OF LATTICE L176.26
%
%
% LATTICE L176.27
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-104104, 3472, 2520; 3472, -84, -84; 2520, -84, -61],[56, 28, 1],[-3, -2, 5, 21, 17, 13, 5; 0, 1, 0, -2, -3, -3, -2; -124, -84, 206, 868, 704, 539, 208],175,27]
%
% END OF LATTICE L176.27
%
%
% LATTICE L176.28
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-82376, -88480, 3024; -88480, -95032, 3248; 3024, 3248, -111],[56, 56, 1],[1, 19, 12, 7, 3, -2, -1; 0, -8, -7, -6, -4, -1, 1; 27, 280, 120, 14, -36, -84, 2],175,28]
%
% END OF LATTICE L176.28
%
%
% LATTICE L176.29
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[112, -112, 0; -112, -3528, 1064; 0, 1064, -311],[112, 56, 1],[-7, -1, 5, 34, 41, 24, 0; -7, 0, 5, 33, 38, 21, -1; -24, 0, 17, 112, 128, 70, -4],175,29]
%
% END OF LATTICE L176.29
%
%
% LATTICE L176.30
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-5712, 6048, 1792; 6048, -952, -336; 1792, -336, -115],[112, 56, 1],[-2, -3, 3, 13, 21, 16, 3; 55, 80, -82, -353, -566, -429, -79; -192, -280, 286, 1232, 1976, 1498, 276],175,30]
%
% END OF LATTICE L176.30
%
%
% LATTICE L176.31
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-336, 3360, -224; 3360, -32872, 2184; -224, 2184, -145],[112, 56, 1],[-2, -3, 3, 13, 21, 8, 3; -1, -4, 1, 7, 14, 6, 3; -12, -56, 10, 84, 176, 77, 40],175,31]
%
% END OF LATTICE L176.31
%
%
% LATTICE L176.32
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-416304, 624512, -5040; 624512, -936824, 7560; -5040, 7560, -61],[112, 56, 1],[-3, -3, 5, 20, 31, 23, 4; -3, -2, 5, 19, 28, 20, 3; -124, 0, 206, 700, 904, 574, 40],175,32]
%
% END OF LATTICE L176.32
%
%
% LATTICE L176.33
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-6455232, -501312, 144256; -501312, -38920, 11200; 144256, 11200, -3223],[448, 56, 1],[1, -1, -1, -3, -7, -2, 0; 70, -116, -74, -203, -416, -99, 15; 288, -448, -302, -840, -1760, -434, 52],175,33]
%
% END OF LATTICE L176.33
%
%
% LATTICE L176.34
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-6078912, -672000, 186368; -672000, -73864, 20496; 186368, 20496, -5687],[448, 56, 1],[-5, -7, 2, 17, 55, 21, 4; -434, -620, 173, 1477, 4792, 1833, 351; -1728, -2464, 689, 5880, 19072, 7294, 1396],175,34]
%
% END OF LATTICE L176.34
%

\medskip%
%------------------------------WEYL-GROUP-W177--------------------------------
%
\leavevmode\llap{}%
$W_{177}$%
\qquad\llap{44} lattices, $\chi=24$%
\hfill%
$2|22|22|22|2\rtimes D_{4}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L177.1
%
\leavevmode%
${L_{177.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{4}16\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${48}\above{1pt}{1pt}{*}{2}{4}\above{1pt}{1pt}{*}{2}{12}\above{1pt}{1pt}{l}{2}{5}\above{1pt}{1pt}{}{2}{48}\above{1pt}{1pt}{}{2}{1}\above{1pt}{1pt}{}{2}{3}\above{1pt}{1pt}{r}{2}{20}\above{1pt}{1pt}{*}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-96720\\720\\240
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
720\\-4\\-5
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
240\\-5\\7
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-120\\-48
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-118\\-50
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-120\\-54
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\115\\45
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7\\816\\336
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\117\\49
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\234\\99
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\350\\150
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-96720, 720, 240; 720, -4, -5; 240, -5, 7],[240, 1, 1],[-1, -1, -1, 1, 7, 1, 2, 3; -120, -118, -120, 115, 816, 117, 234, 350; -48, -50, -54, 45, 336, 49, 99, 150],176,1]
%
% END OF LATTICE L177.1
%
\hbox{}\par\smallskip%
%
% LATTICE L177.2
%
\leavevmode%
${L_{177.2}}$%
{} : {$1\above{1pt}{1pt}{2}{0}16\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{m}%
\EasyButWeakLineBreak%
{${48}\above{1pt}{1pt}{l}{2}{1}\above{1pt}{1pt}{r}{2}{12}\above{1pt}{1pt}{*}{2}{20}\above{1pt}{1pt}{s}{2}{48}\above{1pt}{1pt}{s}{2}{4}\above{1pt}{1pt}{l}{2}{3}\above{1pt}{1pt}{}{2}{5}\above{1pt}{1pt}{r}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
205680\\1680\\-1200
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1680\\-19\\-10
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1200\\-10\\7
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\0\\-168
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\1\\-170
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\0\\-174
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7\\-10\\1180
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
19\\-24\\3216
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5\\-6\\848
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5\\-6\\849
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4\\-5\\680
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[205680, 1680, -1200; 1680, -19, -10; -1200, -10, 7],[240, 1, 1],[-1, -1, -1, 7, 19, 5, 5, 4; 0, 1, 0, -10, -24, -6, -6, -5; -168, -170, -174, 1180, 3216, 848, 849, 680],176,2]
%
% END OF LATTICE L177.2
%
\hbox{}\par\smallskip%
%
% LATTICE L177.3
%
\leavevmode%
${L_{177.3}}$%
{} : {$1\above{1pt}{1pt}{1}{7}4\above{1pt}{1pt}{1}{1}16\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{1}{}$}\EasyButWeakLineBreak%
{${48}\above{1pt}{1pt}{l}{2}{4}\above{1pt}{1pt}{r}{2}{12}\above{1pt}{1pt}{l}{2}{20}\above{1pt}{1pt}{}{2}{48}\above{1pt}{1pt}{}{2}{4}\above{1pt}{1pt}{}{2}{3}\above{1pt}{1pt}{}{2}{20}\above{1pt}{1pt}{r}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
205680\\4080\\-1200
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4080\\52\\-24
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1200\\-24\\7
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\0\\-168
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\1\\-168
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\0\\-174
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\-5\\320
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7\\-12\\1152
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\-3\\332
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\-3\\333
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\-5\\500
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[205680, 4080, -1200; 4080, 52, -24; -1200, -24, 7],[240, 4, 1],[-1, -1, -1, 2, 7, 2, 2, 3; 0, 1, 0, -5, -12, -3, -3, -5; -168, -168, -174, 320, 1152, 332, 333, 500],176,3]
%
% END OF LATTICE L177.3
%
\hbox{}\par\smallskip%
%
% LATTICE L177.4
%
\leavevmode%
${L_{177.4}}$%
{} : {$1\above{1pt}{1pt}{1}{1}4\above{1pt}{1pt}{1}{7}16\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{1}{}$}\EasyButWeakLineBreak%
{${12}\above{1pt}{1pt}{}{2}{1}\above{1pt}{1pt}{}{2}{48}\above{1pt}{1pt}{}{2}{5}\above{1pt}{1pt}{}{2}{12}\above{1pt}{1pt}{r}{2}{4}\above{1pt}{1pt}{s}{2}{48}\above{1pt}{1pt}{s}{2}{20}\above{1pt}{1pt}{l}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-30480\\1440\\0
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1440\\-4\\-8
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\-8\\1
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\21\\168
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\-1
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-5\\-108\\-864
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3\\-65\\-515
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-4\\-87\\-684
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-22\\-170
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-24\\-168
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\20\\170
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-30480, 1440, 0; 1440, -4, -8; 0, -8, 1],[240, 4, 1],[1, 0, -5, -3, -4, -1, -1, 1; 21, 0, -108, -65, -87, -22, -24, 20; 168, -1, -864, -515, -684, -170, -168, 170],176,4]
%
% END OF LATTICE L177.4
%
%
% LATTICE L177.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[4620, 180, -120; 180, 7, -5; -120, -5, -4],[60, 1, 1],[-4, -2, -7, -2, 1, 1, 1, -3; 99, 49, 168, 45, -27, -25, -24, 75; -6, -3, -12, -5, 0, 1, 0, -5],176,5]
%
% END OF LATTICE L177.5
%
%
% LATTICE L177.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-840, 360, 120; 360, -154, -49; 120, -49, 4],[120, 1, 1],[-16, -7, 5, 31, 31, 12, 25, -6; -39, -17, 12, 75, 75, 29, 60, -15; 0, 2, 0, -10, -12, -6, -24, -10],176,6]
%
% END OF LATTICE L177.6
%
%
% LATTICE L177.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1740, 300, -120; 300, -51, 21; -120, 21, -8],[60, 3, 1],[1, 0, -1, -2, 0, 1, 3, 7; 3, -1, -4, -5, 1, 5, 12, 25; -8, -3, 4, 15, 2, -3, -16, -45],176,7]
%
% END OF LATTICE L177.7
%
%
% LATTICE L177.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[6420, -3780, -1560; -3780, 2192, 920; -1560, 920, 379],[60, 4, 1],[25, -9, -32, -109, -49, 1, 20, 69; 3, -2, -6, -20, -9, 0, 3, 10; 96, -32, -117, -400, -180, 4, 75, 260],176,8]
%
% END OF LATTICE L177.8
%
%
% LATTICE L177.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[60, 0, 0; 0, -5, 5; 0, 5, -4],[60, 5, 1],[-2, 0, 1, 0, -1, -1, -7, -1; -15, -3, 0, 1, 3, -1, -24, -5; -30, -5, 0, 1, 0, -5, -60, -11],176,9]
%
% END OF LATTICE L177.9
%
%
% LATTICE L177.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-13080, -2760, -240; -2760, -582, -51; -240, -51, -4],[120, 3, 1],[3, 2, -1, -8, -2, -1, 3, 13; -13, -9, 4, 35, 9, 5, -12, -55; -16, -6, 8, 30, 4, -6, -32, -90],176,10]
%
% END OF LATTICE L177.10
%
%
% LATTICE L177.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[73560, -5880, 1440; -5880, 470, -115; 1440, -115, 28],[120, 5, 1],[-2, -1, 1, 1, 5, 2, 5, 0; -39, -15, 12, 13, 63, 23, 36, -5; -60, -10, 0, 2, 0, -10, -120, -22],176,11]
%
% END OF LATTICE L177.11
%
%
% LATTICE L177.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-741360, 3600, 2880; 3600, -12, -15; 2880, -15, -11],[240, 3, 1],[7, 2, 1, 3, -1, -1, 1, 6; 272, 77, 38, 110, -40, -38, 40, 235; 1456, 417, 209, 630, -208, -210, 206, 1245],176,12]
%
% END OF LATTICE L177.12
%
%
% LATTICE L177.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-83760, 2640, 960; 2640, -57, -30; 960, -30, -11],[240, 3, 1],[11, 7, 2, 4, -1, -1, 1, 17; -8, -6, -2, -5, 0, 1, 0, -10; 976, 624, 179, 360, -88, -90, 86, 1500],176,13]
%
% END OF LATTICE L177.13
%
%
% LATTICE L177.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[16140, 1020, -4200; 1020, 96, -264; -4200, -264, 1093],[60, 12, 1],[39, 19, 5, 63, 21, 41, 25, 237; -7, -4, -1, -10, -3, -6, -4, -40; 148, 72, 19, 240, 80, 156, 95, 900],176,14]
%
% END OF LATTICE L177.14
%
%
% LATTICE L177.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[4020, 300, 180; 300, -15, 15; 180, 15, 8],[60, 15, 1],[-1, 2, 13, 8, 8, 5, 1, -1; 1, -1, -8, -5, -5, -3, 0, 1; 20, -45, -280, -171, -170, -105, -20, 21],176,15]
%
% END OF LATTICE L177.15
%
%
% LATTICE L177.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[40080, 1920, 0; 1920, 92, 0; 0, 0, -1],[240, 4, 1],[-1, -1, 1, 9, 4, 3, 1, 1; 21, 20, -24, -200, -87, -64, -21, -20; 0, -8, -30, -120, -36, -16, -3, 0],176,16]
%
% END OF LATTICE L177.16
%
%
% LATTICE L177.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[480, -120, 0; -120, 32, 0; 0, 0, -1],[120, 8, 1],[1, 1, 1, 1, -1, -1, -1, -1; -9, 1, 3, 5, -3, -5, -9, -25; -72, -16, -6, 0, 0, -8, -30, -120],176,17]
%
% END OF LATTICE L177.17
%
%
% LATTICE L177.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[138480, 8880, -2880; 8880, 545, -180; -2880, -180, 59],[240, 5, 1],[-17, 0, 2, 1, -1, -3, -13, -2; -432, -3, 42, 22, -24, -70, -312, -49; -2160, -10, 225, 116, -120, -360, -1590, -248],176,18]
%
% END OF LATTICE L177.18
%
%
% LATTICE L177.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[878640, 29280, -7200; 29280, 965, -240; -7200, -240, 59],[240, 5, 1],[-5, 3, 5, 1, -1, -2, -13, -3; -24, -6, -6, -1, 0, 1, 0, -2; -720, 340, 585, 118, -120, -240, -1590, -376],176,19]
%
% END OF LATTICE L177.19
%
%
% LATTICE L177.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[3660, 540, 540; 540, 80, 80; 540, 80, 79],[60, 20, 1],[-13, -5, -4, -1, 1, 1, -2, -3; 24, 13, 12, 3, -6, -7, -3, 3; 60, 20, 15, 4, 0, 0, 15, 16],176,20]
%
% END OF LATTICE L177.20
%
%
% LATTICE L177.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2760, -1200, 120; -1200, 480, -45; 120, -45, 4],[120, 15, 1],[-2, -1, 1, 1, 1, 0, -3, -2; -13, -7, 4, 5, 5, -1, -20, -13; -85, -45, 20, 27, 25, -15, -140, -87],176,21]
%
% END OF LATTICE L177.21
%
%
% LATTICE L177.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-83760, -3120, 960; -3120, -84, 36; 960, 36, -11],[240, 12, 1],[1, 4, 7, 12, 1, -1, -1, 3; -1, -3, -4, -5, 0, 1, 0, -5; 83, 336, 592, 1020, 86, -84, -88, 240],176,22]
%
% END OF LATTICE L177.22
%
%
% LATTICE L177.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[28560, 1200, -480; 1200, -12, -12; -480, -12, 7],[240, 12, 1],[0, -1, -1, 1, 1, 1, 3, 2; -1, -12, -12, 10, 11, 11, 32, 20; -4, -90, -88, 90, 88, 87, 256, 165],176,23]
%
% END OF LATTICE L177.23
%
%
% LATTICE L177.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[240, 0, 0; 0, -12, 0; 0, 0, 1],[240, 12, 1],[0, -1, -1, -11, -1, -1, 0, 1; 0, 4, 5, 60, 6, 8, 1, 0; -1, 0, 8, 120, 14, 24, 4, 0],176,24]
%
% END OF LATTICE L177.24
%
%
% LATTICE L177.25
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[240, 360, 120; 360, 384, 120; 120, 120, 37],[120, 24, 1],[1, 5, 5, 19, 1, -1, -1, 1; -4, -20, -18, -60, -2, 8, 6, 0; 10, 48, 40, 120, 2, -24, -16, 0],176,25]
%
% END OF LATTICE L177.25
%
%
% LATTICE L177.26
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2640, 960, -240; 960, 195, -60; -240, -60, 17],[240, 15, 1],[-3, -3, -1, 1, 1, 1, -1, -1; -24, -22, -8, 6, 6, 5, -16, -9; -130, -120, -40, 36, 35, 30, -80, -48],176,26]
%
% END OF LATTICE L177.26
%
%
% LATTICE L177.27
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[30480, 6960, -720; 6960, 1560, -165; -720, -165, 17],[240, 15, 1],[-3, -2, -1, 1, 2, 5, 3, -1; 0, 1, 0, -1, -2, -6, -8, -2; -130, -75, -40, 33, 65, 150, 40, -66],176,27]
%
% END OF LATTICE L177.27
%
%
% LATTICE L177.28
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[240, -7500, 1980; -7500, 213420, -56340; 1980, -56340, 14873],[60, 60, 1],[-1, -4, -3, -6, -5, -2, 0, 0; -37, -111, -41, -35, 21, 95, 33, 19; -140, -420, -155, -132, 80, 360, 125, 72],176,28]
%
% END OF LATTICE L177.28
%
%
% LATTICE L177.29
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1890480, 331680, -4560; 331680, 58192, -800; -4560, -800, 11],[240, 16, 1],[-1, 0, -1, -6, -5, -2, -1, -4; 6, -1, 3, 25, 24, 11, 6, 25; 24, -72, -198, -680, -336, -32, 21, 160],176,29]
%
% END OF LATTICE L177.29
%
%
% LATTICE L177.30
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[4080, 720, 0; 720, 128, 0; 0, 0, -1],[240, 16, 1],[-1, -1, -1, -1, 1, 1, 1, 1; 6, 5, 3, -5, -12, -7, -6, -5; 0, -8, -30, -120, -72, -16, -6, 0],176,30]
%
% END OF LATTICE L177.30
%
%
% LATTICE L177.31
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[878640, 43920, -7200; 43920, 2180, -360; -7200, -360, 59],[240, 20, 1],[-17, 0, 2, 1, -1, -3, -13, -4; -12, -3, -3, -1, 0, 1, 0, -1; -2160, -20, 225, 116, -120, -360, -1590, -496],176,31]
%
% END OF LATTICE L177.31
%
%
% LATTICE L177.32
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[21840, 7200, -480; 7200, 2380, -160; -480, -160, 11],[240, 20, 1],[-28, -15, -4, -1, 1, -3, -19, -17; 105, 56, 15, 4, -3, 12, 72, 64; 300, 160, 45, 16, 0, 40, 210, 184],176,32]
%
% END OF LATTICE L177.32
%
%
% LATTICE L177.33
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[240, -120, 0; -120, 640, -80; 0, -80, 11],[120, 40, 1],[7, 13, 49, 15, 17, 3, -1, 1; 12, 22, 84, 26, 30, 6, 0, 2; 90, 160, 600, 184, 210, 40, 0, 16],176,33]
%
% END OF LATTICE L177.33
%
%
% LATTICE L177.34
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[677040, 47040, -5760; 47040, 3260, -400; -5760, -400, 49],[240, 20, 1],[-2, -1, 1, 1, 5, 1, 5, 0; -15, -4, 0, 2, 9, 1, -12, -2; -360, -150, 120, 134, 660, 125, 480, -17],176,34]
%
% END OF LATTICE L177.34
%
%
% LATTICE L177.35
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[56640, 240, -240; 240, -48, 0; -240, 0, 1],[240, 48, 1],[0, -1, -2, -11, -1, -1, 0, 1; 0, -3, -5, -25, -2, -1, 1, 5; -1, -240, -464, -2520, -226, -216, 8, 240],176,35]
%
% END OF LATTICE L177.35
%
%
% LATTICE L177.36
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[240, 0, 0; 0, 2832, -192; 0, -192, 13],[240, 48, 1],[0, -1, -2, -11, -1, -1, 0, 1; 1, 10, 17, 90, 8, 8, 1, 0; 14, 144, 248, 1320, 118, 120, 16, 0],176,36]
%
% END OF LATTICE L177.36
%
%
% LATTICE L177.37
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[30480, 5040, -720; 5040, 780, -120; -720, -120, 17],[240, 60, 1],[-1, -3, -3, -2, -1, 2, 1, 1; 0, 1, 0, -1, -4, -3, -1, -1; -40, -120, -130, -96, -80, 60, 35, 36],176,37]
%
% END OF LATTICE L177.37
%
%
% LATTICE L177.38
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[6960, -9600, -480; -9600, 22020, 1080; -480, 1080, 53],[240, 60, 1],[0, 3, 5, 13, 7, 11, 1, 1; 1, -40, -74, -196, -107, -172, -16, -16; -20, 840, 1550, 4104, 2240, 3600, 335, 336],176,38]
%
% END OF LATTICE L177.38
%
%
% LATTICE L177.39
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[30480, 76200, -720; 76200, 190560, -1800; -720, -1800, 17],[120, 120, 1],[-1, -5, -3, -5, -3, 1, 1, 1; 0, 2, 0, -2, -4, -6, -2, -2; -40, 0, -130, -432, -560, -600, -170, -168],176,39]
%
% END OF LATTICE L177.39
%
%
% LATTICE L177.40
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-535920, -121920, 2640; -121920, -27660, 600; 2640, 600, -13],[240, 60, 1],[1, 0, -3, -1, -2, -1, 1, 1; 3, 1, -4, -2, -5, -4, 0, 2; 340, 45, -800, -297, -640, -390, 200, 294],176,40]
%
% END OF LATTICE L177.40
%
%
% LATTICE L177.41
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[26160, 3600, -1680; 3600, 320, -160; -1680, -160, 79],[240, 80, 1],[-1, 1, 1, 1, 1, -1, -2, -1; -102, 31, 42, 45, 48, -49, -111, -63; -240, 80, 105, 112, 120, -120, -270, -152],176,41]
%
% END OF LATTICE L177.41
%
%
% LATTICE L177.42
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[240, 0, 0; 0, 2320, -160; 0, -160, 11],[240, 80, 1],[-7, -2, -1, 0, 1, 0, -2, -2; 42, 11, 6, 1, 0, 3, 15, 13; 600, 160, 90, 16, 0, 40, 210, 184],176,42]
%
% END OF LATTICE L177.42
%
%
% LATTICE L177.43
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-240, 1200, 480; 1200, 6720, 2640; 480, 2640, 1037],[240, 240, 1],[1, -1, -2, -5, -5, -3, 0, 1; -16, 47, 67, 161, 158, 95, 2, -19; 40, -120, -170, -408, -400, -240, -5, 48],176,43]
%
% END OF LATTICE L177.43
%
%
% LATTICE L177.44
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[14160, 92160, -960; 92160, 1032240, -10800; -960, -10800, 113],[240, 240, 1],[1, 8, 8, 18, 17, 10, 1, 0; -16, -125, -123, -275, -258, -149, -14, 1; -1520, -11880, -11690, -26136, -24520, -14160, -1330, 96],176,44]
%
% END OF LATTICE L177.44
%

\medskip%
%------------------------------WEYL-GROUP-W178--------------------------------
%
\leavevmode\llap{}%
$W_{178}$%
\qquad\llap{12} lattices, $\chi=18$%
\hfill%
$422422\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L178.1
%
\leavevmode%
${L_{178.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{2}{}9\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{2}{}7\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${2}\above{1pt}{1pt}{*}{4}{4}\above{1pt}{1pt}{b}{2}{18}\above{1pt}{1pt}{b}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-506772\\2268\\4032
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2268\\-10\\-19
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4032\\-19\\-26
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5039\\876960\\138600
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-22\\-3829\\-605
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-44\\-7656\\-1211
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\173\\28
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
21\\3654\\578
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
20\\3483\\549
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-506772, 2268, 4032; 2268, -10, -19; 4032, -19, -26],[252, 1, 1],[1, 21, 20, 1, -1, -2; 173, 3654, 3483, 175, -174, -351; 28, 578, 549, 27, -28, -54],177,1]
%
% END OF LATTICE L178.1
%
%
% LATTICE L178.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-1888173, 68292, -17388; 68292, -2470, 629; -17388, 629, -158],[63, 1, 1],[-16, 7, 28, -18, -177, -334; -437, 191, 765, -491, -4831, -9117; 21, -10, -36, 26, 245, 459],177,2]
%
% END OF LATTICE L178.2
%
%
% LATTICE L178.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-7245, 2835, -567; 2835, -1106, 224; -567, 224, -43],[63, 7, 1],[13, 125, 235, 11, -5, -19; 26, 245, 459, 21, -10, -36; -35, -364, -693, -35, 14, 63],177,3]
%
% END OF LATTICE L178.3
%
%
% LATTICE L178.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[12618081, -133749, -5309262; -133749, 1422, 56277; -5309262, 56277, 2233958],[63, 9, 1],[572, 125, 16, 1038, 7925, 1594; 17, 3, 1, 37, 267, 53; 1359, 297, 38, 2466, 18828, 3787],177,4]
%
% END OF LATTICE L178.4
%
%
% LATTICE L178.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[3499272, -413532, -891072; -413532, 48904, 105304; -891072, 105304, 226907],[252, 4, 1],[-367, -2995, -5507, -251, -95, -55; 6, 53, 99, 5, 2, 0; -1444, -11786, -21672, -988, -374, -216],177,5]
%
% END OF LATTICE L178.5
%
%
% LATTICE L178.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-108770508, -6986196, -506016; -6986196, -448714, -32501; -506016, -32501, -2354],[252, 7, 1],[-21, -431, -409, -20, 21, 40; 257, 5298, 5031, 247, -258, -495; 966, 19502, 18459, 889, -952, -1764],177,6]
%
% END OF LATTICE L178.6
%
%
% LATTICE L178.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2772, 504, 252; 504, -90, -45; 252, -45, -22],[252, 9, 1],[0, -1, 0, 1, 11, 1; 4, -6, -1, 5, 96, 10; -9, 0, 2, 0, -90, -11],177,7]
%
% END OF LATTICE L178.7
%
%
% LATTICE L178.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[9954, -61362, 27027; -61362, 379197, -167013; 27027, -167013, 73559],[63, 63, 1],[37, 267, 53, 17, 3, 1; -438, -3370, -679, -247, -55, -6; -1008, -7749, -1561, -567, -126, -14],177,8]
%
% END OF LATTICE L178.8
%
%
% LATTICE L178.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[905776200, -25407900, -229743864; -25407900, 712936, 6444536; -229743864, 6444536, 58272941],[252, 28, 1],[-21505, -142427, -249209, -7365, -1923, -10621; -764, -5057, -8847, -261, -68, -378; -84700, -560966, -981540, -29008, -7574, -41832],177,9]
%
% END OF LATTICE L178.9
%
%
% LATTICE L178.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[36792, 3276, -9324; 3276, 360, -828; -9324, -828, 2363],[252, 36, 1],[-46, -23, 1, -37, -392, -84; 5, 2, 0, 6, 53, 11; -180, -90, 4, -144, -1530, -328],177,10]
%
% END OF LATTICE L178.10
%
%
% LATTICE L178.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-49644, 55944, -1512; 55944, -62874, 1701; -1512, 1701, -46],[252, 63, 1],[-2, -71, -8, -5, 1, 1; 5, 96, 10, 4, -6, -1; 252, 5922, 637, 315, -252, -70],177,11]
%
% END OF LATTICE L178.11
%
%
% LATTICE L178.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2520, -148932, 37800; -148932, 9195480, -2333772; 37800, -2333772, 592301],[252, 252, 1],[38, 519, 115, 73, 36, -4; -575, -8338, -1860, -1214, -607, 71; -2268, -32886, -7336, -4788, -2394, 280],177,12]
%
% END OF LATTICE L178.12
%

\medskip%
%------------------------------WEYL-GROUP-W179--------------------------------
%
\leavevmode\llap{}%
$W_{179}$%
\qquad\llap{44} lattices, $\chi=72$%
\hfill%
$222\infty222222\infty222\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L179.1
%
\leavevmode%
${L_{179.1}}$%
{} : {$1\above{1pt}{1pt}{2}{{\rm II}}4\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{2}{}9\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}7\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${2}\above{1pt}{1pt}{s}{2}{126}\above{1pt}{1pt}{b}{2}{4}\above{1pt}{1pt}{*}{2}{28}\above{1pt}{1pt}{3,2}{\infty b}{28}\above{1pt}{1pt}{r}{2}{18}\above{1pt}{1pt}{s}{2}{14}\above{1pt}{1pt}{s}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-642852\\2772\\1512
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2772\\-8\\-9
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1512\\-9\\-2
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
109493\\13517532\\21639996
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-341\\-42099\\-67394
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-341\\-42098\\-67395
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\124\\197
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\126\\189
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-124\\-198
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-126\\-196
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
15\\1848\\2968
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
34\\4194\\6723
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
54\\6664\\10675
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-642852, 2772, 1512; 2772, -8, -9; 1512, -9, -2],[252, 1, 1],[1, 1, -1, -1, 15, 34, 54, 32, 2078, 309, 309, 139, 65, 23; 124, 126, -124, -126, 1848, 4194, 6664, 3950, 256536, 38148, 38150, 17164, 8028, 2842; 197, 189, -198, -196, 2968, 6723, 10675, 6325, 410697, 61070, 61068, 27468, 12843, 4543],178,1]
%
% END OF LATTICE L179.1
%
\hbox{}\par\smallskip%
%
% LATTICE L179.2
%
\leavevmode%
${L_{179.2}}$%
{} : {$1\above{1pt}{1pt}{-2}{6}8\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{2}{}9\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{-2}{}7\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${1}\above{1pt}{1pt}{r}{2}{252}\above{1pt}{1pt}{*}{2}{8}\above{1pt}{1pt}{b}{2}{14}\above{1pt}{1pt}{12,5}{\infty a}{56}\above{1pt}{1pt}{l}{2}{9}\above{1pt}{1pt}{r}{2}{28}\above{1pt}{1pt}{l}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-5026392\\-29232\\-504
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-29232\\-170\\-3
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-504\\-3\\1
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
266111\\-45671472\\-2794176
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1552\\-266363\\-16296
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-24\\4119\\251
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
24\\-4119\\-251
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3035\\-520884\\-31878
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
449\\-77060\\-4720
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
222\\-38101\\-2338
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
193\\-33124\\-2044
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
43\\-7380\\-459
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
27\\-4634\\-294
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-5026392, -29232, -504; -29232, -170, -3; -504, -3, 1],[504, 1, 1],[24, 3035, 449, 222, 193, 43, 27, 0, -11, -1, 2, 31, 29, 85; -4119, -520884, -77060, -38101, -33124, -7380, -4634, 0, 1890, 172, -343, -5320, -4977, -14588; -251, -31878, -4720, -2338, -2044, -459, -294, -1, 126, 16, -14, -308, -297, -882],178,2]
%
% END OF LATTICE L179.2
%
\hbox{}\par\smallskip%
%
% LATTICE L179.3
%
\leavevmode%
${L_{179.3}}$%
{} : {$1\above{1pt}{1pt}{2}{6}8\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{2}{}9\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{-2}{}7\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{m}%
\EasyButWeakLineBreak%
{${4}\above{1pt}{1pt}{l}{2}{63}\above{1pt}{1pt}{}{2}{8}\above{1pt}{1pt}{r}{2}{14}\above{1pt}{1pt}{12,5}{\infty b}{56}\above{1pt}{1pt}{s}{2}{36}\above{1pt}{1pt}{l}{2}{7}\above{1pt}{1pt}{r}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
289800\\4536\\0
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4536\\71\\0
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\-1
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
62495\\-4046616\\-484344
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
980\\-63456\\-7595
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-124\\8029\\960
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
23\\-1490\\-184
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
755\\-48888\\-5859
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
225\\-14568\\-1736
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
113\\-7315\\-861
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
103\\-6664\\-756
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
49\\-3168\\-342
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
9\\-581\\-56
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[289800, 4536, 0; 4536, 71, 0; 0, 0, -1],[504, 1, 1],[23, 755, 225, 113, 103, 49, 9, 1, 1, -1, -1, 9, 23, 19; -1490, -48888, -14568, -7315, -6664, -3168, -581, -64, -63, 64, 63, -588, -1494, -1232; -184, -5859, -1736, -861, -756, -342, -56, -2, 0, 0, -7, -112, -216, -161],178,3]
%
% END OF LATTICE L179.3
%
%
% LATTICE L179.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[126, 0, 63; 0, -1, -1; 63, -1, 31],[63, 1, 1],[-1, 1, 1, 3, 4, 7, 5, 1, -1, -1, -3, -4, -7, -5; -2, 0, 1, 0, -21, -90, -140, -82, -5292, -393, -392, -175, -162, -56; 2, 0, -2, -7, -14, -36, -42, -20, -1134, -82, -77, -28, -18, 0],178,4]
%
% END OF LATTICE L179.4
%
%
% LATTICE L179.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[250110, -4032, 0; -4032, 65, 0; 0, 0, -1],[126, 1, 1],[1, 1, -1, -1, 15, 34, 54, 32, 2078, 309, 309, 139, 65, 23; 62, 63, -62, -63, 924, 2097, 3332, 1975, 128268, 19074, 19075, 8582, 4014, 1421; -1, 0, 0, -7, -56, -108, -161, -92, -5859, -868, -861, -378, -171, -56],178,5]
%
% END OF LATTICE L179.5
%
%
% LATTICE L179.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-15372, -7560, 252; -7560, -3718, 125; 252, 125, 31],[252, 1, 1],[32, -31, -63, -93, -227, -172, -85, 10, 2677, 455, 289, 423, 298, 183; -65, 63, 128, 189, 462, 351, 175, -19, -5355, -912, -581, -854, -603, -371; 2, 0, -4, -7, -28, -36, -42, -20, -1134, -164, -77, -56, -18, 0],178,6]
%
% END OF LATTICE L179.6
%
%
% LATTICE L179.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[8442, 8064, 4284; 8064, 3970, 4032; 4284, 4032, 2173],[126, 2, 1],[-63, 1922, 31, -1929, -6445, -24040, -35253, -19932, -1261607, -93341, -184691, -40210, -35945, -11402; -2, 63, 1, -63, -210, -783, -1148, -649, -41076, -3039, -6013, -1309, -1170, -371; 128, -3906, -63, 3920, 13097, 48852, 71638, 40504, 2563722, 189679, 375312, 81711, 73044, 23170],178,7]
%
% END OF LATTICE L179.7
%
%
% LATTICE L179.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-63, 63, 0; 63, -7, -7; 0, -7, 1],[63, 7, 1],[-1, 1, 1, 0, -2, -59, -13, -53, -487, -253, -36, -16, -103, -5; -2, 0, 1, 0, -3, -90, -20, -82, -756, -393, -56, -25, -162, -8; -7, 9, 7, -1, -20, -567, -123, -497, -4545, -2359, -335, -148, -945, -45],178,8]
%
% END OF LATTICE L179.8
%
%
% LATTICE L179.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[10647, 441, -4788; 441, 18, -198; -4788, -198, 2153],[63, 9, 1],[0, 6, 4, 1, -22, -10, -136, -78, -552, -368, -365, -160, -16, -46; 1, 7, 0, -28, -161, -65, -847, -475, -3325, -2212, -2184, -945, -93, -259; 0, 14, 9, 0, -63, -28, -378, -216, -1526, -1017, -1008, -441, -44, -126],178,9]
%
% END OF LATTICE L179.9
%
%
% LATTICE L179.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-6930, 882, 504; 882, -112, -63; 504, -63, -31],[126, 7, 1],[4, 4, -1, -1, 3, 61, 15, 65, 617, 645, 93, 43, 146, 8; 35, 36, -8, -9, 24, 504, 125, 544, 5175, 5412, 781, 362, 1233, 68; -7, -9, 0, 2, -2, -63, -17, -77, -747, -784, -114, -54, -189, -11],178,10]
%
% END OF LATTICE L179.10
%
%
% LATTICE L179.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[127897560, -1047060, -31966452; -1047060, 8572, 261700; -31966452, 261700, 7989629],[252, 4, 1],[1, 127, -16, -284, -1473, -5321, -7695, -4315, -271909, -10050, -19848, -8593, -7621, -2371; 0, 126, -31, -497, -2548, -9198, -13300, -7458, -469980, -17371, -34307, -14854, -13176, -4102; 4, 504, -63, -1120, -5810, -20988, -30352, -17020, -1072512, -39641, -78288, -33894, -30060, -9352],178,11]
%
% END OF LATTICE L179.11
%
%
% LATTICE L179.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[153681696, -1562148, -39042864; -1562148, 15880, 396864; -39042864, 396864, 9918847],[252, 4, 1],[-318, -1984, -32, -345, -2036, -16552, -25278, -14664, -941882, -69884, -69571, -15443, -28394, -9680; 7, 63, 1, 0, 21, 189, 301, 179, 11655, 867, 868, 196, 369, 133; -1252, -7812, -126, -1358, -8015, -65160, -99512, -57728, -3707928, -275114, -273882, -60795, -111780, -38108],178,12]
%
% END OF LATTICE L179.12
%
%
% LATTICE L179.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[71946, 36288, 16002; 36288, 17865, 8064; 16002, 8064, 3559],[126, 9, 1],[-29, 93, 27, -851, -5701, -1182, -15604, -8824, -62064, -82655, -81777, -35613, -1769, -5053; -2, 7, 2, -63, -420, -87, -1148, -649, -4564, -6078, -6013, -2618, -130, -371; 135, -434, -126, 3969, 26586, 5512, 72765, 41148, 289415, 385434, 381339, 166068, 8249, 23562],178,13]
%
% END OF LATTICE L179.13
%
%
% LATTICE L179.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-22932, -10332, 0; -10332, -4606, -7; 0, -7, 1],[252, 7, 1],[5, -4, -9, 0, 19, 281, 62, 253, 2326, 2417, 172, 153, 493, 24; -11, 9, 20, 0, -42, -621, -137, -559, -5139, -5340, -380, -338, -1089, -53; -70, 72, 140, -1, -292, -4284, -942, -3836, -35226, -36596, -2603, -2312, -7434, -360],178,14]
%
% END OF LATTICE L179.14
%
%
% LATTICE L179.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1252188, 8820, 8820; 8820, -56, -63; 8820, -63, -62],[252, 7, 1],[4, 4, -1, -1, 3, 61, 15, 65, 617, 645, 93, 43, 146, 8; 70, 72, -16, -18, 48, 1008, 250, 1088, 10350, 10824, 1562, 724, 2466, 136; 497, 495, -126, -124, 376, 7623, 1873, 8113, 76995, 80486, 11604, 5364, 18207, 997],178,15]
%
% END OF LATTICE L179.15
%
%
% LATTICE L179.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[65520, 16758, 32508; 16758, 4354, 8316; 32508, 8316, 16129],[126, 14, 1],[158, 221, 31, -1, 124, 3953, 904, 3775, 35176, 18323, 5245, 1187, 7846, 407; 7, 9, 1, 0, 6, 189, 43, 179, 1665, 867, 248, 56, 369, 19; -322, -450, -63, 2, -253, -8064, -1844, -7700, -71748, -37373, -10698, -2421, -16002, -830],178,16]
%
% END OF LATTICE L179.16
%
%
% LATTICE L179.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[185724, 2016, -1260; 2016, -18, -9; -1260, -9, 8],[252, 9, 1],[1, 1, -1, -9, -33, -6, -74, -40, -274, -363, -355, -149, -7, -17; 21, 21, -22, -196, -728, -133, -1645, -891, -6111, -8098, -7924, -3332, -157, -385; 180, 182, -180, -1638, -6048, -1102, -13608, -7362, -50456, -66852, -65394, -27468, -1292, -3150],178,17]
%
% END OF LATTICE L179.17
%
%
% LATTICE L179.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[5796, 756, 0; 756, 99, 0; 0, 0, -1],[252, 9, 1],[0, -1, -1, 1, 19, 4, 53, 30, 211, 281, 139, 121, 6, 17; -1, 7, 8, -7, -154, -33, -441, -251, -1771, -2360, -1169, -1022, -51, -147; -9, -7, 0, 0, -126, -31, -441, -261, -1883, -2520, -1260, -1134, -59, -189],178,18]
%
% END OF LATTICE L179.18
%
%
% LATTICE L179.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[450048942, 725760, 222524190; 725760, 1170, 358848; 222524190, 358848, 110025845],[126, 18, 1],[-899, -90, 405, 187, -8567, -4128, -58069, -34108, -244959, -163771, -326919, -73116, -7541, -23614; 62, 7, -31, -63, 462, 233, 3332, 1975, 14252, 9537, 19075, 4291, 446, 1421; 1818, 182, -819, -378, 17325, 8348, 117432, 68976, 495376, 331191, 661122, 147861, 15250, 47754],178,19]
%
% END OF LATTICE L179.19
%
%
% LATTICE L179.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2520, 504, -504; 504, 98, -119; -504, -119, -17],[504, 7, 1],[-66, -1325, -1399, -103, -101, -184, -23, -9, -25, -1, 3, 1, -41, -27; 288, 5778, 6100, 449, 440, 801, 100, 39, 108, 4, -13, -4, 180, 118; -77, -1494, -1568, -114, -108, -189, -22, -7, -18, 0, 2, -4, -63, -34],178,20]
%
% END OF LATTICE L179.20
%
%
% LATTICE L179.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3528, 504, 504; 504, -70, -63; 504, -63, -31],[504, 7, 1],[89, 428, 897, 65, 61, 211, 6, 7, 4, -1, -1, 3, 77, 10; 760, 3663, 7680, 557, 524, 1818, 52, 62, 36, -8, -9, 24, 648, 85; -154, -747, -1568, -114, -108, -378, -11, -14, -9, 0, 2, -4, -126, -17],178,21]
%
% END OF LATTICE L179.21
%
%
% LATTICE L179.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[63, -126, 63; -126, 126, -63; 63, -63, 32],[63, 63, 1],[0, 0, 1, 1, 5, 14, 26, 102, 102, 475, 67, 29, 20, 8; 1, 1, 0, -4, -23, -65, -121, -475, -475, -2212, -312, -135, -93, -37; 0, 2, 0, -9, -54, -154, -288, -1134, -1136, -5292, -747, -324, -224, -90],178,22]
%
% END OF LATTICE L179.22
%
%
% LATTICE L179.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[504, 0, 0; 0, -8, 8; 0, 8, -7],[504, 8, 1],[-9, -568, -21, -83, -18, -16, -5, 0, 1, 0, -1, -3, -11, -16; -72, -4725, -176, -707, -161, -153, -56, -3, 0, 1, 7, -14, -72, -119; -164, -10584, -393, -1568, -350, -324, -112, -4, 0, 1, 0, -42, -180, -280],178,23]
%
% END OF LATTICE L179.23
%
%
% LATTICE L179.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-63000, 0, -31248; 0, 8, 0; -31248, 0, -15499],[504, 8, 1],[1227, 77426, 5725, 11313, 2453, 2180, 681, 0, -125, 1, 139, 410, 1501, 2182; -10, -567, -41, -77, -14, -9, 0, 1, 0, -1, -7, -7, -18, -21; -2472, -155988, -11534, -22792, -4942, -4392, -1372, 0, 252, -2, -280, -826, -3024, -4396],178,24]
%
% END OF LATTICE L179.24
%
%
% LATTICE L179.25
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-115416, 1512, 504; 1512, 9, -9; 504, -9, -2],[504, 9, 1],[-15, -211, -281, -139, -121, -3, -17, 0, 1, 1, -1, -19, -2, -53; -251, -3542, -4720, -2338, -2044, -51, -294, -1, 14, 16, -14, -308, -33, -882; -2781, -39116, -52092, -25767, -22428, -556, -3150, 0, 182, 180, -189, -3528, -371, -9828],178,25]
%
% END OF LATTICE L179.25
%
%
% LATTICE L179.26
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-121464, 15120, -504; 15120, -1881, 63; -504, 63, -2],[504, 9, 1],[-19, -64, -169, -82, -67, -3, -3, 1, 1, 1, -2, -17, -3, -18; -174, -595, -1576, -770, -644, -30, -35, 6, 7, 8, -14, -140, -26, -161; -954, -3556, -9576, -4851, -4536, -248, -441, -72, -35, 0, 63, -252, -94, -756],178,26]
%
% END OF LATTICE L179.26
%
%
% LATTICE L179.27
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[16006536, -201852, -4052160; -201852, 2548, 51100; -4052160, 51100, 1025831],[252, 28, 1],[-249, -311, -16, -1, -223, -6977, -1583, -6579, -61141, -15916, -4551, -2053, -13507, -693; -72, -90, -4, 1, -58, -1854, -424, -1770, -16488, -4294, -1229, -556, -3672, -190; -980, -1224, -63, -4, -878, -27468, -6232, -25900, -240696, -62657, -17916, -8082, -53172, -2728],178,27]
%
% END OF LATTICE L179.27
%
%
% LATTICE L179.28
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[64655136, -1060164, -16428888; -1060164, 17416, 269388; -16428888, 269388, 4174585],[252, 28, 1],[-1928, -1930, -32, -31, -1041, -63646, -14296, -59050, -546872, -284532, -40621, -9122, -119288, -6030; 7, 9, 1, 0, 3, 189, 43, 179, 1665, 867, 124, 28, 369, 19; -7588, -7596, -126, -122, -4097, -250488, -56264, -232400, -2152296, -1119818, -159870, -35901, -469476, -23732],178,28]
%
% END OF LATTICE L179.28
%
%
% LATTICE L179.29
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[3654, -8442, -4536; -8442, 19593, 10521; -4536, 10521, 5650],[126, 63, 1],[-25, -6, -27, 2, -11, -27, -62, -275, -294, -2773, -402, -189, -73, -38; 57, 13, 56, -4, 34, 75, 167, 729, 773, 7280, 1052, 490, 187, 95; -126, -29, -126, 9, -72, -161, -360, -1575, -1672, -15750, -2277, -1062, -406, -207],178,29]
%
% END OF LATTICE L179.29
%
%
% LATTICE L179.30
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[49590072, -849492, -12598740; -849492, 14544, 215820; -12598740, 215820, 3200807],[252, 36, 1],[311, -313, -407, -352, 1457, 1477, 21069, 12451, 89647, 59963, 59908, 13432, 2777, 8709; 2, 0, 0, 7, 28, 24, 322, 184, 1302, 868, 861, 189, 38, 112; 1224, -1232, -1602, -1386, 5733, 5812, 82908, 48996, 352772, 235962, 235746, 52857, 10928, 34272],178,30]
%
% END OF LATTICE L179.30
%
%
% LATTICE L179.31
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-4788, -3024, 1260; -3024, 828, 756; 1260, 756, -331],[252, 36, 1],[-183, -121, 16, 128, -737, -417, -6215, -3771, -27557, -9242, -18580, -8489, -901, -3011; -11, -7, 1, 7, -49, -27, -399, -241, -1757, -589, -1183, -539, -57, -189; -720, -476, 63, 504, -2898, -1640, -24444, -14832, -108388, -36351, -73080, -33390, -3544, -11844],178,31]
%
% END OF LATTICE L179.31
%
%
% LATTICE L179.32
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-95004, -13608, -3780; -13608, -1260, -315; -3780, -315, -76],[252, 63, 1],[7, 1, -1, -3, -3, 0, 4, 26, 32, 309, 47, 25, 11, 7; -311, -45, 42, 136, 152, 27, -127, -955, -1221, -11858, -1824, -996, -449, -295; 945, 137, -126, -414, -468, -91, 369, 2835, 3643, 35406, 5454, 2988, 1351, 891],178,32]
%
% END OF LATTICE L179.32
%
%
% LATTICE L179.33
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[252, 0, 0; 0, -1827, 504; 0, 504, -139],[252, 63, 1],[-1, 0, 1, 0, -3, -5, -10, -41, -42, -393, -28, -25, -9, -4; 17, 3, 0, -5, -26, -27, -41, -137, -123, -1120, -75, -54, -13, 1; 63, 11, 0, -18, -90, -91, -135, -441, -389, -3528, -234, -162, -35, 9],178,33]
%
% END OF LATTICE L179.33
%
%
% LATTICE L179.34
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-69804, -98910, -48258; -98910, -139230, -67914; -48258, -67914, -33127],[126, 126, 1],[35, 4, -4, -9, 12, 56, 125, 544, 575, 2706, 781, 181, 137, 68; -701, -77, 95, 182, -250, -1153, -2565, -11143, -11767, -55367, -15974, -3698, -2795, -1383; 1386, 152, -189, -360, 495, 2282, 5076, 22050, 23284, 109557, 31608, 7317, 5530, 2736],178,34]
%
% END OF LATTICE L179.34
%
%
% LATTICE L179.35
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[3717000, 0, 17136; 0, -56, 0; 17136, 0, 79],[504, 56, 1],[101, 944, 246, 141, 32, 212, 11, 4, 1, -1, -1, 3, 103, 24; 92, 837, 217, 123, 27, 171, 8, 1, 0, 0, 1, 4, 108, 23; -21980, -205416, -53529, -30680, -6962, -46116, -2392, -868, -216, 217, 216, -654, -22428, -5224],178,35]
%
% END OF LATTICE L179.35
%
%
% LATTICE L179.36
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-5544, 5544, -2016; 5544, -5488, 2016; -2016, 2016, -733],[504, 56, 1],[1319, 11893, 6156, 1738, 377, 2347, 105, 1, -13, 4, 22, 63, 1613, 335; -10, -81, -41, -11, -2, -9, 0, 1, 0, -1, -1, -1, -18, -3; -3696, -33300, -17234, -4864, -1054, -6552, -292, 0, 36, -14, -64, -178, -4536, -940],178,36]
%
% END OF LATTICE L179.36
%
%
% LATTICE L179.37
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[365400, -87696, 31248; -87696, 21042, -7497; 31248, -7497, 2671],[504, 63, 1],[18, 41, 391, 29, 29, 6, 7, 3, 1, 1, -1, -1, 1, 7; -80, -102, -844, -43, 8, 13, 36, 35, 12, 4, -17, -68, -28, -66; -441, -778, -7056, -468, -324, -35, 18, 63, 22, 0, -36, -180, -91, -270],178,37]
%
% END OF LATTICE L179.37
%
%
% LATTICE L179.38
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[504, 0, 0; 0, -3654, 1323; 0, 1323, -479],[504, 63, 1],[-41, -21, -393, -28, -25, -9, -2, -1, 0, 1, 0, -3, -5, -5; -304, -133, -2408, -159, -108, -22, 4, 46, 4, 0, -13, -64, -64, -47; -882, -389, -7056, -468, -324, -70, 9, 126, 11, 0, -36, -180, -182, -135],178,38]
%
% END OF LATTICE L179.38
%
%
% LATTICE L179.39
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[457128, 65520, -1512; 65520, 9000, -216; -1512, -216, 5],[504, 72, 1],[2, 1, -1, -9, -6, -1, -4, 1, 20, 15, 37, 13, 2, 11; 1, 0, -1, -7, -7, -2, -21, -10, -63, -41, -77, -14, -1, 0; 648, 308, -342, -3024, -2142, -400, -2268, -216, 2716, 2358, 7056, 3150, 544, 3276],178,39]
%
% END OF LATTICE L179.39
%
%
% LATTICE L179.40
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[504, 0, 0; 0, -2952, 144; 0, 144, -7],[504, 72, 1],[-3, -16, -5, -17, -2, 0, 1, 0, -5, -2, -11, -5, -1, -8; -4, -7, -1, 7, 7, 1, 0, -5, -56, -20, -91, -28, -4, -21; -108, -280, -63, 0, 126, 20, 0, -108, -1232, -441, -2016, -630, -92, -504],178,40]
%
% END OF LATTICE L179.40
%
%
% LATTICE L179.41
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[7068096, 20886012, -5306868; 20886012, 61717824, -15681708; -5306868, -15681708, 3984521],[252, 252, 1],[-17, -1, 3, -1, -13, -85, -169, -691, -707, -3307, -471, -105, -151, -67; -1595, -145, 31, -114, -1155, -7541, -14999, -61363, -62813, -293835, -41858, -9338, -13445, -5987; -6300, -572, 126, -450, -4563, -29792, -59256, -242424, -248152, -1160838, -165366, -36891, -53116, -23652],178,41]
%
% END OF LATTICE L179.41
%
%
% LATTICE L179.42
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[35028, -127008, 32256; -127008, 461412, -117180; 32256, -117180, 29759],[252, 252, 1],[11, 1, 0, 1, 17, 55, 109, 445, 455, 1064, 303, 135, 97, 43; -253, -17, 16, -18, -393, -1279, -2539, -10373, -10609, -24810, -7066, -3149, -2263, -1003; -1008, -68, 63, -72, -1566, -5096, -10116, -41328, -42268, -98847, -28152, -12546, -9016, -3996],178,42]
%
% END OF LATTICE L179.42
%
%
% LATTICE L179.43
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-194544, -21672, 9576; -21672, 8568, -3528; 9576, -3528, 1451],[504, 504, 1],[67, 74, 351, 103, 25, 20, 11, 8, 1, -1, -3, 0, 5, 14; 10111, 11217, 53246, 15650, 3815, 3067, 1701, 1265, 159, -158, -482, -23, 725, 2091; 24192, 26836, 127386, 37440, 9126, 7336, 4068, 3024, 380, -378, -1152, -54, 1736, 5004],178,43]
%
% END OF LATTICE L179.43
%
%
% LATTICE L179.44
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-20664, 217728, 1008; 217728, 1104264, 5040; 1008, 5040, 23],[504, 504, 1],[-5, -8, -20, -13, -4, -4, -3, -4, -1, -1, 1, 1, 1, 0; 108, 171, 427, 277, 85, 85, 64, 87, 24, 28, -17, -20, -20, 1; -23436, -37112, -92673, -60120, -18450, -18452, -13896, -18900, -5224, -6111, 3672, 4338, 4340, -216],178,44]
%
% END OF LATTICE L179.44
%

\medskip%
%------------------------------WEYL-GROUP-W180--------------------------------
%
\leavevmode\llap{}%
$W_{180}$%
\qquad\llap{2} lattices, $\chi=24$%
\hfill%
$\slashtwo\infty4|4\infty\rtimes D_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L180.1
%
\leavevmode%
${L_{180.1}}$%
{} : {$1\above{1pt}{1pt}{2}{2}64\above{1pt}{1pt}{1}{7}$}\EasyButWeakLineBreak%
{${1}\above{1pt}{1pt}{r}{2}{4}\above{1pt}{1pt}{16,15}{\infty z}{1}\above{1pt}{1pt}{}{4}{2}\above{1pt}{1pt}{*}{4}{4}\above{1pt}{1pt}{16,7}{\infty z}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-16960\\-896\\320
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-896\\-47\\17
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
320\\17\\-6
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\-1\\-3
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\-10\\24
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\-7\\32
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\2\\5
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\10\\-26
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-16960, -896, 320; -896, -47, 17; 320, 17, -6],[64, 1, 1],[0, 1, 1, 0, -1; -1, -10, -7, 2, 10; -3, 24, 32, 5, -26],179,1]
%
% END OF LATTICE L180.1
%
%
% LATTICE L180.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[640, -3520, 64; -3520, 21056, -384; 64, -384, 7],[64, 64, 1],[0, 1, -1, -3, -4; -3, -1, -3, -4, -9; -160, -64, -160, -192, -448],179,2]
%
% END OF LATTICE L180.2
%

\medskip%
%------------------------------WEYL-GROUP-W181--------------------------------
%
\leavevmode\llap{}%
$W_{181}$%
\qquad\llap{14} lattices, $\chi=12$%
\hfill%
$2|22\slashinfty2\rtimes D_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L181.1
%
\leavevmode%
${L_{181.1}}$%
{} : {$[1\above{1pt}{1pt}{1}{}2\above{1pt}{1pt}{-}{}]\above{1pt}{1pt}{}{4}32\above{1pt}{1pt}{-}{5}$}\EasyButWeakLineBreak%
{${32}\above{1pt}{1pt}{s}{2}{8}\above{1pt}{1pt}{*}{2}{32}\above{1pt}{1pt}{l}{2}{1}\above{1pt}{1pt}{8,5}{\infty}{4}\above{1pt}{1pt}{*}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-13664\\-416\\928
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-416\\-10\\28
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
928\\28\\-63
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3\\-8\\-48
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5\\6\\76
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
25\\40\\384
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\4\\31
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3\\-4\\-46
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-13664, -416, 928; -416, -10, 28; 928, 28, -63],[32, 2, 1],[-3, 5, 25, 2, -3; -8, 6, 40, 4, -4; -48, 76, 384, 31, -46],180,1]
%
% END OF LATTICE L181.1
%
\hbox{}\par\smallskip%
%
% LATTICE L181.2
%
\leavevmode%
${L_{181.2}}$%
{} : {$[1\above{1pt}{1pt}{1}{}2\above{1pt}{1pt}{1}{}]\above{1pt}{1pt}{}{0}64\above{1pt}{1pt}{1}{1}$}\spacer%
\instructions{m}%
\EasyButWeakLineBreak%
{${64}\above{1pt}{1pt}{*}{2}{4}\above{1pt}{1pt}{s}{2}{64}\above{1pt}{1pt}{l}{2}{2}\above{1pt}{1pt}{16,9}{\infty}{8}\above{1pt}{1pt}{s}{2}$}%
\nopagebreak\par%
shares genus with {$ {L_{181.3}}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-59840\\-2752\\-3008
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2752\\-126\\-138
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3008\\-138\\-151
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\48\\-64
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\24\\-42
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5\\64\\-160
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\-9\\8
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-22\\40
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-59840, -2752, -3008; -2752, -126, -138; -3008, -138, -151],[64, 2, 1],[1, 1, 5, 0, -1; 48, 24, 64, -9, -22; -64, -42, -160, 8, 40],180,2]
%
% END OF LATTICE L181.2
%
\hbox{}\par\smallskip%
%
% LATTICE L181.3
%
\leavevmode%
${L_{181.3}}$%
{} : {$[1\above{1pt}{1pt}{1}{}2\above{1pt}{1pt}{1}{}]\above{1pt}{1pt}{}{0}64\above{1pt}{1pt}{1}{1}$}\EasyButWeakLineBreak%
{${64}\above{1pt}{1pt}{l}{2}{1}\above{1pt}{1pt}{}{2}{64}\above{1pt}{1pt}{}{2}{2}\above{1pt}{1pt}{16,1}{\infty}{8}\above{1pt}{1pt}{*}{2}$}%
\nopagebreak\par%
shares genus with {$ {L_{181.2}}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-342464\\6656\\2880
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
6656\\-126\\-58
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2880\\-58\\-23
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-7\\-208\\-352
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\60\\99
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
45\\1344\\2240
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4\\119\\200
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-5\\-150\\-248
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-342464, 6656, 2880; 6656, -126, -58; 2880, -58, -23],[64, 2, 1],[-7, 2, 45, 4, -5; -208, 60, 1344, 119, -150; -352, 99, 2240, 200, -248],180,3]
%
% END OF LATTICE L181.3
%
\hbox{}\par\smallskip%
%
% LATTICE L181.4
%
\leavevmode%
${L_{181.4}}$%
{} : {$1\above{1pt}{1pt}{1}{1}4\above{1pt}{1pt}{1}{7}32\above{1pt}{1pt}{1}{1}$}\EasyButWeakLineBreak%
{${4}\above{1pt}{1pt}{*}{2}{16}\above{1pt}{1pt}{l}{2}{1}\above{1pt}{1pt}{}{2}{32}\above{1pt}{1pt}{4,3}{\infty}{32}\above{1pt}{1pt}{s}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-55776\\480\\3712
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
480\\-4\\-32
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3712\\-32\\-247
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-8\\-14
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\6\\-16
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\14\\13
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7\\64\\96
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\-8\\16
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-55776, 480, 3712; 480, -4, -32; 3712, -32, -247],[32, 4, 1],[-1, -1, 1, 7, 1; -8, 6, 14, 64, -8; -14, -16, 13, 96, 16],180,4]
%
% END OF LATTICE L181.4
%
\hbox{}\par\smallskip%
%
% LATTICE L181.5
%
\leavevmode%
${L_{181.5}}$%
{} : {$1\above{1pt}{1pt}{1}{1}4\above{1pt}{1pt}{1}{1}32\above{1pt}{1pt}{1}{7}$}\EasyButWeakLineBreak%
{${4}\above{1pt}{1pt}{l}{2}{4}\above{1pt}{1pt}{}{2}{1}\above{1pt}{1pt}{r}{2}{32}\above{1pt}{1pt}{8,7}{\infty z}{32}\above{1pt}{1pt}{*}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-46112\\2112\\2144
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2112\\-92\\-100
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2144\\-100\\-99
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-5\\-30\\-78
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\11\\32
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
9\\53\\141
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
41\\244\\640
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-5\\-28\\-80
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-46112, 2112, 2144; 2112, -92, -100; 2144, -100, -99],[32, 4, 1],[-5, 2, 9, 41, -5; -30, 11, 53, 244, -28; -78, 32, 141, 640, -80],180,5]
%
% END OF LATTICE L181.5
%
\hbox{}\par\smallskip%
%
% LATTICE L181.6
%
\leavevmode%
${L_{181.6}}$%
{} : {$1\above{1pt}{1pt}{1}{7}8\above{1pt}{1pt}{1}{1}64\above{1pt}{1pt}{1}{1}$}\EasyButWeakLineBreak%
{${64}\above{1pt}{1pt}{r}{2}{4}\above{1pt}{1pt}{b}{2}{64}\above{1pt}{1pt}{l}{2}{8}\above{1pt}{1pt}{16,9}{\infty}{8}\above{1pt}{1pt}{}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
64\\0\\0
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\-56\\-8
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\-8\\-1
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\0\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\-1\\6
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\-8\\32
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\-1\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\1\\-8
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[64, 0, 0; 0, -56, -8; 0, -8, -1],[64, 8, 1],[-1, 0, 3, 1, 0; 0, -1, -8, -1, 1; 0, 6, 32, 0, -8],180,6]
%
% END OF LATTICE L181.6
%
%
% LATTICE L181.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-22240, 224, 1184; 224, -2, -12; 1184, -12, -63],[32, 2, 1],[-1, -1, -5, 0, 1; -16, -5, 0, 4, 4; -16, -18, -96, -1, 18],180,7]
%
% END OF LATTICE L181.7
%
%
% LATTICE L181.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-18784, 416, 1088; 416, -8, -24; 1088, -24, -63],[32, 8, 1],[-1, -2, -5, 0, 1; -4, 3, 20, 2, -2; -16, -36, -96, -1, 18],180,8]
%
% END OF LATTICE L181.8
%
%
% LATTICE L181.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-96, 320, -64; 320, -1048, 208; -64, 208, -41],[32, 8, 1],[-3, 3, 17, 3, -2; -4, 1, 12, 3, -1; -16, 0, 32, 10, -2],180,9]
%
% END OF LATTICE L181.9
%
%
% LATTICE L181.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-13376, 960, 448; 960, -56, -32; 448, -32, -15],[64, 8, 1],[2, 3, -1, -1, 4; -1, -4, 0, 1, -1; 61, 96, -30, -32, 120],180,10]
%
% END OF LATTICE L181.10
%
%
% LATTICE L181.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-55776, 960, 3712; 960, -16, -64; 3712, -64, -247],[32, 16, 1],[1, -1, -1, 1, 7; 7, 3, -4, -4, 32; 13, -16, -14, 16, 96],180,11]
%
% END OF LATTICE L181.11
%
%
% LATTICE L181.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-224, 1216, -160; 1216, -5712, 752; -160, 752, -99],[32, 16, 1],[0, -1, -1, -1, 1; -5, 3, 17, 40, -4; -38, 24, 130, 304, -32],180,12]
%
% END OF LATTICE L181.12
%
%
% LATTICE L181.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-64, 1920, -128; 1920, -55776, 3712; -128, 3712, -247],[64, 32, 1],[-2, 3, 7, 16, -2; -1, -2, 2, 7, 1; -14, -32, 26, 96, 16],180,13]
%
% END OF LATTICE L181.13
%
%
% LATTICE L181.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-390208, -188032, 12352; -188032, -90592, 5952; 12352, 5952, -391],[64, 32, 1],[-3, 3, 5, 24, -2; -1, -2, 1, 7, 1; -110, 64, 173, 864, -48],180,14]
%
% END OF LATTICE L181.14
%

\medskip%
%------------------------------WEYL-GROUP-W182--------------------------------
%
\leavevmode\llap{}%
$W_{182}$%
\qquad\llap{6} lattices, $\chi=48$%
\hfill%
$\slashinfty\slashtwo\slashinfty\slashtwo\slashinfty\slashtwo\slashinfty\slashtwo\rtimes D_{8}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L182.1
%
\leavevmode%
${L_{182.1}}$%
{} : {$1\above{1pt}{1pt}{2}{0}64\above{1pt}{1pt}{1}{1}$}\EasyButWeakLineBreak%
{${64}\above{1pt}{1pt}{4,3}{\infty z}{64}\above{1pt}{1pt}{s}{2}{4}\above{1pt}{1pt}{16,1}{\infty z}{1}\above{1pt}{1pt}{}{2}{64}\above{1pt}{1pt}{2,1}{\infty}{64}\above{1pt}{1pt}{*}{2}{4}\above{1pt}{1pt}{16,9}{\infty z}{1}\above{1pt}{1pt}{r}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-181184\\448\\4800
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
448\\-1\\-12
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4800\\-12\\-127
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-15\\-608\\-512
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-64\\-32
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\40\\34
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\8\\-1
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-9\\-256\\-320
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-23\\-800\\-800
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-7\\-256\\-242
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3\\-116\\-103
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-181184, 448, 4800; 448, -1, -12; 4800, -12, -127],[64, 1, 1],[-15, -1, 1, 0, -9, -23, -7, -3; -608, -64, 40, 8, -256, -800, -256, -116; -512, -32, 34, -1, -320, -800, -242, -103],181,1]
%
% END OF LATTICE L182.1
%
\hbox{}\par\smallskip%
%
% LATTICE L182.2
%
\leavevmode%
${L_{182.2}}$%
{} : {$1\above{1pt}{1pt}{1}{1}4\above{1pt}{1pt}{1}{7}64\above{1pt}{1pt}{1}{1}$}\EasyButWeakLineBreak%
{${64}\above{1pt}{1pt}{2,1}{\infty b}{64}\above{1pt}{1pt}{}{2}{1}\above{1pt}{1pt}{8,1}{\infty}{4}\above{1pt}{1pt}{s}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-153536\\832\\4416
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
832\\-4\\-24
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4416\\-24\\-127
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1369\\-2736\\-47424
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
9\\17\\312
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
39\\78\\1351
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-23\\-32\\-800
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-9\\16\\-320
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\4\\-1
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\4\\34
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-153536, 832, 4416; 832, -4, -24; 4416, -24, -127],[64, 4, 1],[-23, -9, 0, 1, -1, -15, -3, -7; -32, 16, 4, 4, -16, -64, -10, -16; -800, -320, -1, 34, -32, -512, -103, -242],181,2]
%
% END OF LATTICE L182.2
%
\hbox{}\par\smallskip%
%
% LATTICE L182.3
%
\leavevmode%
${L_{182.3}}$%
{} : {$1\above{1pt}{1pt}{-}{5}4\above{1pt}{1pt}{1}{7}64\above{1pt}{1pt}{-}{5}$}\EasyButWeakLineBreak%
{${64}\above{1pt}{1pt}{8,3}{\infty z}{64}\above{1pt}{1pt}{l}{2}{1}\above{1pt}{1pt}{8,5}{\infty}{4}\above{1pt}{1pt}{*}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-120000\\-1728\\3904
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1728\\-20\\56
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3904\\56\\-127
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4799\\7200\\150400
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
60\\89\\1880
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-156\\-234\\-4889
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
99\\152\\3104
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
53\\88\\1664
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\4\\63
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3\\-4\\-94
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-120000, -1728, 3904; -1728, -20, 56; 3904, 56, -127],[64, 4, 1],[99, 53, 2, -3, -3, 43, 10, 27; 152, 88, 4, -4, -8, 56, 14, 40; 3104, 1664, 63, -94, -96, 1344, 313, 846],181,3]
%
% END OF LATTICE L182.3
%
%
% LATTICE L182.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-140480, 1600, 4224; 1600, -16, -48; 4224, -48, -127],[64, 16, 1],[-15, -1, 1, 0, -9, -23, -7, -3; 28, -4, -2, 2, 44, 76, 20, 7; -512, -32, 34, -1, -320, -800, -242, -103],181,4]
%
% END OF LATTICE L182.4
%
%
% LATTICE L182.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-192, 1152, -128; 1152, -6800, 752; -128, 752, -83],[64, 16, 1],[3, -2, -3, 27, 13, 18, 67, 37; 3, -1, -4, 12, 7, 11, 44, 28; 22, -6, -32, 64, 42, 70, 288, 192],181,5]
%
% END OF LATTICE L182.5
%
%
% LATTICE L182.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-123968, -131968, 3968; -131968, -140480, 4224; 3968, 4224, -127],[64, 64, 1],[14, -2, -1, 1, 22, 38, 10, 7; -15, -1, 1, 0, -9, -23, -7, -6; -64, -96, 2, 31, 384, 416, 78, 18],181,6]
%
% END OF LATTICE L182.6
%

\medskip%
%------------------------------WEYL-GROUP-W183--------------------------------
%
\leavevmode\llap{}%
$W_{183}$%
\qquad\llap{34} lattices, $\chi=18$%
\hfill%
$\slashinfty22\slashtwo22\rtimes D_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L183.1
%
\leavevmode%
${L_{183.1}}$%
{} : {$1\above{1pt}{1pt}{2}{0}8\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{2}{}9\above{1pt}{1pt}{1}{}$}\EasyButWeakLineBreak%
{${8}\above{1pt}{1pt}{6,1}{\infty}{8}\above{1pt}{1pt}{*}{2}{36}\above{1pt}{1pt}{l}{2}{1}\above{1pt}{1pt}{r}{2}{4}\above{1pt}{1pt}{l}{2}{9}\above{1pt}{1pt}{}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-444600\\4680\\4392
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4680\\-47\\-49
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4392\\-49\\-40
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
15\\808\\656
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-7\\-376\\-308
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-7\\-378\\-306
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\161\\132
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
17\\914\\746
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
46\\2475\\2016
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-444600, 4680, 4392; 4680, -47, -49; 4392, -49, -40],[72, 1, 1],[15, -7, -7, 3, 17, 46; 808, -376, -378, 161, 914, 2475; 656, -308, -306, 132, 746, 2016],182,1]
%
% END OF LATTICE L183.1
%
\hbox{}\par\smallskip%
%
% LATTICE L183.2
%
\leavevmode%
${L_{183.2}}$%
{} : {$[1\above{1pt}{1pt}{-}{}2\above{1pt}{1pt}{1}{}]\above{1pt}{1pt}{}{6}16\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{2}{}9\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${8}\above{1pt}{1pt}{24,1}{\infty z}{2}\above{1pt}{1pt}{r}{2}{36}\above{1pt}{1pt}{*}{2}{16}\above{1pt}{1pt}{*}{2}{4}\above{1pt}{1pt}{*}{2}{144}\above{1pt}{1pt}{s}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-463824\\-11520\\-12240
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-11520\\-286\\-304
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-12240\\-304\\-323
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\2\\36
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\-13\\12
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5\\-108\\-90
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\-28\\-88
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\0\\-38
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\36\\-72
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-463824, -11520, -12240; -11520, -286, -304; -12240, -304, -323],[144, 2, 1],[-1, 0, 5, 3, 1, 1; 2, -13, -108, -28, 0, 36; 36, 12, -90, -88, -38, -72],182,2]
%
% END OF LATTICE L183.2
%
\hbox{}\par\smallskip%
%
% LATTICE L183.3
%
\leavevmode%
${L_{183.3}}$%
{} : {$[1\above{1pt}{1pt}{1}{}2\above{1pt}{1pt}{1}{}]\above{1pt}{1pt}{}{2}16\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{2}{}9\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{m}%
\EasyButWeakLineBreak%
{${8}\above{1pt}{1pt}{24,13}{\infty z}{2}\above{1pt}{1pt}{}{2}{9}\above{1pt}{1pt}{r}{2}{16}\above{1pt}{1pt}{l}{2}{1}\above{1pt}{1pt}{r}{2}{144}\above{1pt}{1pt}{*}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-123408\\6048\\2448
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
6048\\-286\\-124
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2448\\-124\\-47
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-7\\-70\\-180
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
6\\59\\156
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
40\\396\\1035
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
31\\308\\800
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\30\\77
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-11\\-108\\-288
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-123408, 6048, 2448; 6048, -286, -124; 2448, -124, -47],[144, 2, 1],[-7, 6, 40, 31, 3, -11; -70, 59, 396, 308, 30, -108; -180, 156, 1035, 800, 77, -288],182,3]
%
% END OF LATTICE L183.3
%
\hbox{}\par\smallskip%
%
% LATTICE L183.4
%
\leavevmode%
${L_{183.4}}$%
{} : {$[1\above{1pt}{1pt}{-}{}2\above{1pt}{1pt}{1}{}]\above{1pt}{1pt}{}{4}16\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{2}{}9\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{m}%
\EasyButWeakLineBreak%
{${2}\above{1pt}{1pt}{24,13}{\infty}{8}\above{1pt}{1pt}{*}{2}{36}\above{1pt}{1pt}{s}{2}{16}\above{1pt}{1pt}{s}{2}{4}\above{1pt}{1pt}{s}{2}{144}\above{1pt}{1pt}{l}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-60336\\17712\\2880
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
17712\\-5198\\-848
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2880\\-848\\-133
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-28\\-87\\-52
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
25\\78\\44
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
29\\90\\54
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-41\\-128\\-72
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-61\\-190\\-110
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-671\\-2088\\-1224
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-60336, 17712, 2880; 17712, -5198, -848; 2880, -848, -133],[144, 2, 1],[-28, 25, 29, -41, -61, -671; -87, 78, 90, -128, -190, -2088; -52, 44, 54, -72, -110, -1224],182,4]
%
% END OF LATTICE L183.4
%
\hbox{}\par\smallskip%
%
% LATTICE L183.5
%
\leavevmode%
${L_{183.5}}$%
{} : {$1\above{1pt}{1pt}{1}{1}8\above{1pt}{1pt}{1}{7}64\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{2}{}9\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${8}\above{1pt}{1pt}{24,1}{\infty b}{32}\above{1pt}{1pt}{*}{2}{36}\above{1pt}{1pt}{s}{2}{64}\above{1pt}{1pt}{s}{2}{4}\above{1pt}{1pt}{s}{2}{576}\above{1pt}{1pt}{b}{2}$}%
\nopagebreak\par%
shares genus with {$ {L_{183.6}}$}%
; isometric to own %
2-dual\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-607680\\9216\\95040
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
9216\\-136\\-1488
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
95040\\-1488\\-14287
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
62\\2231\\180
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-33\\-1186\\-96
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-31\\-1116\\-90
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
55\\1976\\160
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
53\\1906\\154
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1289\\46368\\3744
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-607680, 9216, 95040; 9216, -136, -1488; 95040, -1488, -14287],[576, 8, 1],[62, -33, -31, 55, 53, 1289; 2231, -1186, -1116, 1976, 1906, 46368; 180, -96, -90, 160, 154, 3744],182,5]
%
% END OF LATTICE L183.5
%
\hbox{}\par\smallskip%
%
% LATTICE L183.6
%
\leavevmode%
${L_{183.6}}$%
{} : {$1\above{1pt}{1pt}{1}{1}8\above{1pt}{1pt}{1}{7}64\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{2}{}9\above{1pt}{1pt}{1}{}$}\EasyButWeakLineBreak%
{${8}\above{1pt}{1pt}{24,1}{\infty a}{32}\above{1pt}{1pt}{l}{2}{9}\above{1pt}{1pt}{}{2}{64}\above{1pt}{1pt}{}{2}{1}\above{1pt}{1pt}{}{2}{576}\above{1pt}{1pt}{r}{2}$}%
\nopagebreak\par%
shares genus with {$ {L_{183.5}}$}%
; isometric to own %
2-dual\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-42328512\\78336\\-13117824
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
78336\\-136\\24384
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-13117824\\24384\\-4063999
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1016\\-36577\\3060
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
255\\9182\\-768
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
254\\9144\\-765
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-425\\-15304\\1280
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-339\\-12205\\1021
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-18551\\-667872\\55872
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-42328512, 78336, -13117824; 78336, -136, 24384; -13117824, 24384, -4063999],[576, 8, 1],[-1016, 255, 254, -425, -339, -18551; -36577, 9182, 9144, -15304, -12205, -667872; 3060, -768, -765, 1280, 1021, 55872],182,6]
%
% END OF LATTICE L183.6
%
%
% LATTICE L183.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[36, 0, 0; 0, -34, -40; 0, -40, -47],[36, 2, 1],[-1, 0, 1, 0, -1, -4; -1, 7, 0, -6, -20, -36; 0, -6, 0, 5, 16, 27],182,7]
%
% END OF LATTICE L183.7
%
%
% LATTICE L183.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-231912, 720, 5760; 720, -2, -18; 5760, -18, -143],[72, 2, 1],[0, 1, -1, -1, -3, -5; 6, 18, -36, -19, -44, -45; -1, 38, -36, -38, -116, -198],182,8]
%
% END OF LATTICE L183.8
%
%
% LATTICE L183.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-30168, -9576, 720; -9576, -3038, 228; 720, 228, -17],[72, 2, 1],[-2, 3, 2, -5, -6, -59; 9, -12, -9, 20, 25, 252; 35, -34, -36, 56, 80, 864],182,9]
%
% END OF LATTICE L183.9
%
%
% LATTICE L183.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[144, 0, 0; 0, -136, 80; 0, 80, -47],[144, 8, 1],[0, 1, 2, 1, 0, -1; -7, 1, 18, 20, 3, 0; -12, 0, 27, 32, 5, 0],182,10]
%
% END OF LATTICE L183.10
%
%
% LATTICE L183.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-151920, -56016, 6912; -56016, -20654, 2548; 6912, 2548, -313],[144, 2, 1],[43, -19, -22, 31, 34, 857; -123, 54, 63, -88, -97, -2448; -52, 20, 27, -32, -39, -1008],182,11]
%
% END OF LATTICE L183.11
%
%
% LATTICE L183.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2232, 216, -72; 216, -20, 8; -72, 8, -1],[72, 4, 1],[1, -3, -17, -3, -1, 1; 8, -26, -144, -25, -8, 9; -8, -4, 18, 8, 6, 0],182,12]
%
% END OF LATTICE L183.12
%
%
% LATTICE L183.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-150840, 51840, 2664; 51840, -17812, -916; 2664, -916, -47],[72, 4, 1],[-7, 11, 38, 15, 3, -5; -14, 20, 72, 29, 6, -9; -124, 232, 747, 284, 53, -108],182,13]
%
% END OF LATTICE L183.13
%
%
% LATTICE L183.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-576, 1080, -288; 1080, -2008, 536; -288, 536, -143],[72, 8, 1],[0, -1, 1, 2, 3, 10; 3, 0, -9, -1, 5, 45; 11, 2, -36, -8, 12, 144],182,14]
%
% END OF LATTICE L183.14
%
%
% LATTICE L183.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-24012, 2808, -10620; 2808, -306, 1242; -10620, 1242, -4697],[36, 18, 1],[24, -207, -104, -271, -20, 23; 1, -1, -1, -4, -1, 0; -54, 468, 235, 612, 45, -52],182,15]
%
% END OF LATTICE L183.15
%
%
% LATTICE L183.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-765432, 18288, 18360; 18288, -423, -441; 18360, -441, -440],[72, 9, 1],[-7, 127, 30, 73, 3, -7; -40, 760, 179, 434, 17, -42; -252, 4536, 1072, 2610, 108, -250],182,16]
%
% END OF LATTICE L183.16
%
%
% LATTICE L183.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[144, 0, 0; 0, -56, 8; 0, 8, -1],[144, 8, 1],[1, 0, -1, 0, 1, 4; 1, -1, 0, 1, 4, 9; -4, -8, 0, 6, 16, 18],182,17]
%
% END OF LATTICE L183.17
%
%
% LATTICE L183.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-229680, 4320, 1728; 4320, 328, -32; 1728, -32, -13],[144, 8, 1],[7, -6, -7, 5, 23, 55; -1, 1, 0, -1, -4, -9; 932, -800, -936, 666, 3064, 7326],182,18]
%
% END OF LATTICE L183.18
%
%
% LATTICE L183.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2552112, 21024, 18288; 21024, -136, -152; 18288, -152, -131],[144, 8, 1],[-6, 7, 55, 23, 5, -7; -29, 35, 270, 112, 24, -36; -804, 936, 7362, 3080, 670, -936],182,19]
%
% END OF LATTICE L183.19
%
%
% LATTICE L183.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-407880, 2808, 7848; 2808, -18, -54; 7848, -54, -151],[72, 18, 1],[4, 1, -1, -1, 5, 3; 0, -6, 0, 5, 16, 3; 207, 54, -52, -54, 252, 154],182,20]
%
% END OF LATTICE L183.20
%
%
% LATTICE L183.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1656, -13752, 1584; -13752, -108774, 12546; 1584, 12546, -1447],[72, 18, 1],[27, -3, -3, 5, 31, 51; 116, -10, -13, 16, 129, 216; 1035, -90, -116, 144, 1152, 1928],182,21]
%
% END OF LATTICE L183.21
%
%
% LATTICE L183.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-861264, -168192, 19008; -168192, -32814, 3708; 19008, 3708, -419],[144, 18, 1],[4, 1, -1, -1, 5, 3; -175, -58, 44, 56, -180, -124; -1368, -468, 344, 450, -1368, -962],182,22]
%
% END OF LATTICE L183.22
%
%
% LATTICE L183.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-121104, -112032, 13248; -112032, -103374, 12222; 13248, 12222, -1445],[144, 18, 1],[-4, -7, 1, 3, 11, 0; 81, 114, -20, -49, -148, 7; 648, 900, -160, -387, -1152, 59],182,23]
%
% END OF LATTICE L183.23
%
%
% LATTICE L183.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1833264, 24336, 24336; 24336, -306, -324; 24336, -324, -323],[144, 18, 1],[-3, 27, 51, 31, 5, -3; -10, 107, 200, 120, 16, -12; -216, 1926, 3640, 2214, 360, -214],182,24]
%
% END OF LATTICE L183.24
%
%
% LATTICE L183.25
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3312, 1008, 2160; 1008, -306, -648; 2160, -648, -1295],[144, 18, 1],[-3, 54, 99, 29, 5, -3; -10, 215, 392, 114, 16, -12; 0, -18, -32, -9, 0, 1],182,25]
%
% END OF LATTICE L183.25
%
%
% LATTICE L183.26
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-504, 8352, -936; 8352, -120780, 13536; -936, 13536, -1517],[72, 36, 1],[-1, 1, 0, -1, -2, -1; 230, -8, -13, 6, 125, 106; 2052, -72, -116, 54, 1116, 946],182,26]
%
% END OF LATTICE L183.26
%
%
% LATTICE L183.27
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1224, -12168, -5328; -12168, -112500, -49212; -5328, -49212, -21527],[72, 36, 1],[127, -7, -7, 3, 73, 30; -990, 48, 55, -20, -559, -232; 2232, -108, -124, 45, 1260, 523],182,27]
%
% END OF LATTICE L183.27
%
%
% LATTICE L183.28
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-187992, -276912, 5328; -276912, -407880, 7848; 5328, 7848, -151],[72, 72, 1],[0, -3, 0, 5, 8, 3; 4, 1, -1, -2, 5, 6; 207, -54, -52, 72, 540, 416],182,28]
%
% END OF LATTICE L183.28
%
%
% LATTICE L183.29
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-909936, 1182528, -236016; 1182528, -1536696, 306720; -236016, 306720, -61217],[144, 72, 1],[76, -739, -366, -939, -62, 83; 1, -1, -1, -4, -1, 0; -288, 2844, 1406, 3600, 234, -320],182,29]
%
% END OF LATTICE L183.29
%
%
% LATTICE L183.30
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1260720, -804384, 23472; -804384, -513144, 14976; 23472, 14976, -437],[144, 72, 1],[-6, 63, 31, 79, 5, -7; 1, -1, -1, -4, -1, 0; -288, 3348, 1630, 4104, 234, -376],182,30]
%
% END OF LATTICE L183.30
%
%
% LATTICE L183.31
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-4494384, 74880, 82080; 74880, -1224, -1368; 82080, -1368, -1499],[144, 72, 1],[-6, 63, 31, 79, 5, -7; -5, 71, 34, 84, 4, -8; -324, 3384, 1666, 4248, 270, -376],182,31]
%
% END OF LATTICE L183.31
%
%
% LATTICE L183.32
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-909936, -875376, 218736; -875376, -842040, 210384; 218736, 210384, -52559],[144, 72, 1],[77, -692, -173, -897, -32, 77; -161, 1439, 360, 1868, 67, -160; -324, 2880, 721, 3744, 135, -320],182,32]
%
% END OF LATTICE L183.32
%
%
% LATTICE L183.33
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-109914048, 377280, 377280; 377280, -1224, -1296; 377280, -1296, -1295],[576, 72, 1],[-3, 54, 99, 29, 5, -3; -10, 215, 392, 114, 16, -12; -864, 15516, 28448, 8334, 1440, -862],182,33]
%
% END OF LATTICE L183.33
%
%
% LATTICE L183.34
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1729561536, 1497024, 2994048; 1497024, -1224, -2592; 2994048, -2592, -5183],[576, 72, 1],[-3, 108, 195, 28, 5, -3; -10, 431, 776, 111, 16, -12; -1728, 62172, 112256, 16119, 2880, -1727],182,34]
%
% END OF LATTICE L183.34
%

\medskip%
%------------------------------WEYL-GROUP-W184--------------------------------
%
\leavevmode\llap{}%
$W_{184}$%
\qquad\llap{34} lattices, $\chi=72$%
\hfill%
$\slashinfty2|2\slashinfty2|2\slashinfty2|2\slashinfty2|2\rtimes D_{8}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L184.1
%
\leavevmode%
${L_{184.1}}$%
{} : {$1\above{1pt}{1pt}{2}{0}8\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{-2}{}9\above{1pt}{1pt}{-}{}$}\EasyButWeakLineBreak%
{${72}\above{1pt}{1pt}{2,1}{\infty}{72}\above{1pt}{1pt}{*}{2}{4}\above{1pt}{1pt}{*}{2}{8}\above{1pt}{1pt}{3,2}{\infty b}{8}\above{1pt}{1pt}{}{2}{1}\above{1pt}{1pt}{}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-639288\\7128\\7200
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7128\\-79\\-81
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7200\\-81\\-80
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
41381\\2221560\\1472328
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-456\\-24481\\-16224
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-475\\-25500\\-16901
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
121\\6480\\4320
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
23\\1224\\828
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3\\-162\\-106
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3\\-160\\-108
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
19\\1024\\672
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
15\\807\\532
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-639288, 7128, 7200; 7128, -79, -81; 7200, -81, -80],[72, 1, 1],[121, 23, -3, -3, 19, 15, 221, 319, 79, 117, 95, 23; 6480, 1224, -162, -160, 1024, 807, 11880, 17136, 4242, 6280, 5096, 1233; 4320, 828, -106, -108, 672, 532, 7848, 11340, 2810, 4164, 3384, 820],183,1]
%
% END OF LATTICE L184.1
%
\hbox{}\par\smallskip%
%
% LATTICE L184.2
%
\leavevmode%
${L_{184.2}}$%
{} : {$[1\above{1pt}{1pt}{-}{}2\above{1pt}{1pt}{1}{}]\above{1pt}{1pt}{}{6}16\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{-2}{}9\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${72}\above{1pt}{1pt}{8,1}{\infty z}{18}\above{1pt}{1pt}{r}{2}{4}\above{1pt}{1pt}{l}{2}{2}\above{1pt}{1pt}{24,11}{\infty}{8}\above{1pt}{1pt}{s}{2}{16}\above{1pt}{1pt}{s}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-32976\\-8208\\-3456
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-8208\\-2042\\-856
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3456\\-856\\-345
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
20987\\-94248\\23760
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5141\\-23087\\5820
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1855\\-8330\\2099
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
757\\-3402\\864
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
202\\-909\\234
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
35\\-158\\42
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3\\13\\-2
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-29\\130\\-32
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\-4\\0
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-32976, -8208, -3456; -8208, -2042, -856; -3456, -856, -345],[144, 2, 1],[757, 202, 35, -3, -29, 1, 197, 275, 177, 162, 347, 423; -3402, -909, -158, 13, 130, -4, -882, -1233, -794, -727, -1558, -1900; 864, 234, 42, -2, -32, 0, 216, 306, 198, 182, 392, 480],183,2]
%
% END OF LATTICE L184.2
%
\hbox{}\par\smallskip%
%
% LATTICE L184.3
%
\leavevmode%
${L_{184.3}}$%
{} : {$[1\above{1pt}{1pt}{1}{}2\above{1pt}{1pt}{1}{}]\above{1pt}{1pt}{}{2}16\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{-2}{}9\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{m}%
\EasyButWeakLineBreak%
{${72}\above{1pt}{1pt}{8,5}{\infty z}{18}\above{1pt}{1pt}{}{2}{1}\above{1pt}{1pt}{}{2}{2}\above{1pt}{1pt}{24,23}{\infty}{8}\above{1pt}{1pt}{*}{2}{16}\above{1pt}{1pt}{*}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-65808\\1440\\2304
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1440\\-30\\-52
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2304\\-52\\-79
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3059\\52632\\53856
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-55\\-947\\-968
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-120\\-2064\\-2113
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
67\\1134\\1188
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
16\\261\\288
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\14\\19
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-21\\-16
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3\\-54\\-52
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\20\\16
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-65808, 1440, 2304; 1440, -30, -52; 2304, -52, -79],[144, 2, 1],[67, 16, 1, -1, -3, 1, 23, 29, 9, 16, 33, 39; 1134, 261, 14, -21, -54, 20, 414, 513, 158, 279, 570, 668; 1188, 288, 19, -16, -52, 16, 396, 504, 157, 280, 580, 688],183,3]
%
% END OF LATTICE L184.3
%
\hbox{}\par\smallskip%
%
% LATTICE L184.4
%
\leavevmode%
${L_{184.4}}$%
{} : {$[1\above{1pt}{1pt}{-}{}2\above{1pt}{1pt}{1}{}]\above{1pt}{1pt}{}{4}16\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{-2}{}9\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{m}%
\EasyButWeakLineBreak%
{${18}\above{1pt}{1pt}{8,5}{\infty}{72}\above{1pt}{1pt}{*}{2}{4}\above{1pt}{1pt}{*}{2}{8}\above{1pt}{1pt}{24,11}{\infty z}{2}\above{1pt}{1pt}{r}{2}{16}\above{1pt}{1pt}{l}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-396720\\3744\\3744
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3744\\-34\\-36
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3744\\-36\\-35
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
9935\\347760\\702144
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-90\\-3151\\-6360
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-96\\-3360\\-6785
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
19\\657\\1350
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7\\234\\504
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-36\\-70
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-34\\-72
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\107\\210
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
19\\672\\1336
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-396720, 3744, 3744; 3744, -34, -36; 3744, -36, -35],[144, 2, 1],[19, 7, -1, -1, 3, 19, 35, 101, 25, 37, 15, 29; 657, 234, -36, -34, 107, 672, 1233, 3546, 876, 1294, 523, 1008; 1350, 504, -70, -72, 210, 1336, 2466, 7128, 1766, 2616, 1062, 2056],183,4]
%
% END OF LATTICE L184.4
%
\hbox{}\par\smallskip%
%
% LATTICE L184.5
%
\leavevmode%
${L_{184.5}}$%
{} : {$1\above{1pt}{1pt}{1}{1}8\above{1pt}{1pt}{1}{7}64\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{-2}{}9\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${72}\above{1pt}{1pt}{8,1}{\infty b}{288}\above{1pt}{1pt}{*}{2}{4}\above{1pt}{1pt}{*}{2}{32}\above{1pt}{1pt}{48,23}{\infty z}{8}\above{1pt}{1pt}{b}{2}{64}\above{1pt}{1pt}{b}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
shares genus with {$ {L_{184.6}}$}%
; isometric to own %
2-dual\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-14837184\\46080\\46080
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
46080\\-136\\-144
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
46080\\-144\\-143
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
53999\\1911600\\15465600
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-150\\-5311\\-42960
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-170\\-6018\\-48689
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
62\\2205\\17748
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
173\\6138\\49536
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
21\\744\\6014
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
61\\2158\\17472
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
24\\847\\6876
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
45\\1584\\12896
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-14837184, 46080, 46080; 46080, -136, -144; 46080, -144, -143],[576, 8, 1],[62, 173, 21, 61, 24, 45, 28, 7, -1, -1, 6, 35; 2205, 6138, 744, 2158, 847, 1584, 981, 234, -36, -34, 215, 1248; 17748, 49536, 6014, 17472, 6876, 12896, 8028, 2016, -286, -288, 1716, 10016],183,5]
%
% END OF LATTICE L184.5
%
\hbox{}\par\smallskip%
%
% LATTICE L184.6
%
\leavevmode%
${L_{184.6}}$%
{} : {$1\above{1pt}{1pt}{1}{1}8\above{1pt}{1pt}{1}{7}64\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{-2}{}9\above{1pt}{1pt}{-}{}$}\EasyButWeakLineBreak%
{${72}\above{1pt}{1pt}{8,1}{\infty a}{288}\above{1pt}{1pt}{l}{2}{1}\above{1pt}{1pt}{r}{2}{32}\above{1pt}{1pt}{48,47}{\infty z}{8}\above{1pt}{1pt}{l}{2}{64}\above{1pt}{1pt}{r}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
shares genus with {$ {L_{184.5}}$}%
; isometric to own %
2-dual\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-202207680\\170496\\340992
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
170496\\-136\\-288
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
340992\\-288\\-575
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
371951\\13266288\\213913728
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-270\\-9631\\-155280
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-630\\-22470\\-362321
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
116\\4149\\66708
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
317\\11322\\182304
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
19\\678\\10927
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
109\\3886\\62688
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
42\\1495\\24156
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
77\\2736\\44288
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-202207680, 170496, 340992; 170496, -136, -288; 340992, -288, -575],[576, 8, 1],[116, 317, 19, 109, 42, 77, 46, 7, -1, -1, 12, 67; 4149, 11322, 678, 3886, 1495, 2736, 1629, 234, -36, -34, 431, 2400; 66708, 182304, 10927, 62688, 24156, 44288, 26460, 4032, -575, -576, 6900, 38528],183,6]
%
% END OF LATTICE L184.6
%
%
% LATTICE L184.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-1980, 288, -864; 288, -34, 126; -864, 126, -377],[36, 2, 1],[-223, -56, 7, 8, -21, -40, -317, -484, -247, -188, -159, -80; -27, -9, 0, 1, -1, -3, -27, -45, -24, -19, -17, -9; 504, 126, -16, -18, 48, 91, 720, 1098, 560, 426, 360, 181],183,7]
%
% END OF LATTICE L184.7
%
%
% LATTICE L184.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-6984, 720, -360; 720, -74, 38; -360, 38, -15],[72, 2, 1],[29, 23, 1, -3, -1, 2, 16, 67, 39, 33, 16, 18; 252, 198, 8, -26, -8, 19, 144, 594, 344, 290, 140, 157; -63, -54, -4, 6, 3, -2, -27, -126, -76, -66, -33, -38],183,8]
%
% END OF LATTICE L184.8
%
%
% LATTICE L184.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-19512, 1224, 576; 1224, -70, -36; 576, -36, -17],[72, 2, 1],[19, 7, -1, -1, 3, 19, 35, 101, 25, 37, 15, 29; -9, 0, 1, 0, -3, -16, -27, -72, -17, -24, -9, -16; 657, 234, -36, -34, 107, 672, 1233, 3546, 876, 1294, 523, 1008],183,9]
%
% END OF LATTICE L184.9
%
%
% LATTICE L184.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-7920, 5184, 864; 5184, -3336, -536; 864, -536, -79],[144, 8, 1],[12, -25, -26, -425, -664, -343, -264, -227, -58, -331, -92, 7; 27, -57, -59, -963, -1503, -776, -597, -513, -131, -747, -207, 16; -52, 112, 115, 1872, 2916, 1504, 1156, 992, 253, 1440, 396, -32],183,10]
%
% END OF LATTICE L184.10
%
%
% LATTICE L184.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-39024, 1152, 2448; 1152, -34, -72; 2448, -72, -143],[144, 2, 1],[28, 7, -1, -1, 6, 35, 62, 173, 21, 61, 24, 45; 981, 234, -36, -34, 215, 1248, 2205, 6138, 744, 2158, 847, 1584; -18, 0, 1, 0, -6, -32, -54, -144, -17, -48, -18, -32],183,11]
%
% END OF LATTICE L184.11
%
%
% LATTICE L184.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2166840, 262152, -21888; 262152, -31716, 2648; -21888, 2648, -221],[72, 4, 1],[521, 361, 49, 31, -5, -5, 37, 197, 75, 155, 191, 129; 4644, 3222, 438, 278, -44, -45, 324, 1746, 666, 1378, 1700, 1149; 4032, 2844, 394, 260, -32, -44, 216, 1404, 550, 1156, 1448, 988],183,12]
%
% END OF LATTICE L184.12
%
%
% LATTICE L184.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-23688, 1872, 1368; 1872, -140, -108; 1368, -108, -79],[72, 4, 1],[247, 167, 11, 13, -3, -2, 23, 103, 19, 77, 93, 62; -72, -54, -4, -6, 0, 1, 0, -18, -4, -18, -24, -17; 4356, 2952, 195, 232, -52, -36, 396, 1800, 333, 1352, 1636, 1092],183,13]
%
% END OF LATTICE L184.13
%
%
% LATTICE L184.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-16920, -1872, 504; -1872, -200, 56; 504, 56, -15],[72, 8, 1],[10, 7, 0, -1, 0, 3, 8, 29, 16, 13, 6, 13; -9, -9, -1, 1, 1, 2, 0, -9, -7, -7, -4, -10; 297, 198, -4, -30, 3, 104, 261, 918, 500, 402, 183, 392],183,14]
%
% END OF LATTICE L184.14
%
%
% LATTICE L184.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[36, 0, 0; 0, -5922, 684; 0, 684, -79],[36, 18, 1],[9, 12, 17, 4, 3, 4, 3, 0, -1, 0, 1, 4; 59, 103, 168, 45, 41, 66, 67, 23, 0, -3, 1, 18; 504, 882, 1440, 386, 352, 567, 576, 198, 0, -26, 8, 153],183,15]
%
% END OF LATTICE L184.15
%
%
% LATTICE L184.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-260280, 4608, 4536; 4608, -72, -81; 4536, -81, -79],[72, 9, 1],[113, 175, 135, 69, 59, 45, 85, 23, -3, -3, 7, 21; 416, 652, 506, 260, 224, 172, 328, 92, -10, -12, 24, 76; 6048, 9360, 7218, 3688, 3152, 2403, 4536, 1224, -162, -160, 376, 1125],183,16]
%
% END OF LATTICE L184.16
%
%
% LATTICE L184.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-7920, 144, -1728; 144, 24, 32; -1728, 32, -377],[144, 8, 1],[7, -20, -37, -290, -439, -223, -169, -142, -71, -196, -47, 7; 1, -1, -3, -27, -45, -24, -19, -17, -9, -27, -9, 0; -32, 92, 170, 1332, 2016, 1024, 776, 652, 326, 900, 216, -32],183,17]
%
% END OF LATTICE L184.17
%
%
% LATTICE L184.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1208880, -25056, 9648; -25056, -504, 200; 9648, 200, -77],[144, 8, 1],[-2, 9, 15, 113, 166, 83, 62, 51, 25, 67, 14, -3; 1, -1, -3, -27, -45, -24, -19, -17, -9, -27, -9, 0; -248, 1124, 1870, 14076, 20664, 10328, 7712, 6340, 3106, 8316, 1728, -376],183,18]
%
% END OF LATTICE L184.18
%
%
% LATTICE L184.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3863088, 23328, 29088; 23328, -136, -176; 29088, -176, -219],[144, 8, 1],[-2, 9, 15, 113, 166, 83, 62, 51, 25, 67, 14, -3; -17, 83, 136, 1017, 1485, 740, 551, 451, 220, 585, 117, -28; -252, 1128, 1882, 14184, 20844, 10424, 7788, 6408, 3142, 8424, 1764, -376],183,19]
%
% END OF LATTICE L184.19
%
%
% LATTICE L184.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-198504, 2016, 5328; 2016, -18, -54; 5328, -54, -143],[72, 18, 1],[-9, -12, -23, -7, -15, -55, -33, -9, -5, 0, 1, -1; 14, 26, 55, 18, 42, 164, 106, 34, 25, 2, -2, -4; -342, -459, -882, -269, -578, -2124, -1278, -351, -198, -1, 38, -36],183,20]
%
% END OF LATTICE L184.20
%
%
% LATTICE L184.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-19512, 1224, 576; 1224, -54, -36; 576, -36, -17],[72, 18, 1],[7, 13, 55, 9, 21, 41, 53, 17, 25, 1, -1, -1; 0, -3, -16, -3, -8, -17, -24, -9, -16, -1, 0, 1; 234, 441, 1872, 307, 718, 1404, 1818, 585, 864, 35, -34, -36],183,21]
%
% END OF LATTICE L184.21
%
%
% LATTICE L184.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-397008, -112032, 12672; -112032, -31518, 3564; 12672, 3564, -403],[144, 18, 1],[-15, -7, -23, -12, -9, -1, 1, 0, -5, -9, -33, -55; 662, 305, 992, 511, 370, 28, -42, 5, 248, 419, 1490, 2452; 5380, 2476, 8046, 4140, 2988, 216, -340, 44, 2034, 3420, 12132, 19944],183,22]
%
% END OF LATTICE L184.22
%
%
% LATTICE L184.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-277776, -48096, 4896; -48096, -7902, 792; 4896, 792, -79],[144, 18, 1],[57, 25, 39, 38, 23, -3, -3, 2, 15, 43, 139, 219; -1474, -647, -1010, -985, -598, 76, 78, -51, -386, -1109, -3590, -5660; -11252, -4940, -7713, -7524, -4572, 576, 596, -388, -2943, -8460, -27396, -43200],183,23]
%
% END OF LATTICE L184.23
%
%
% LATTICE L184.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-60336, -24480, 2880; -24480, -9666, 1134; 2880, 1134, -133],[144, 18, 1],[9, 21, 41, 53, 17, 25, 1, -1, -1, 7, 13, 55; -241, -566, -1110, -1442, -467, -696, -29, 26, 30, -178, -343, -1464; -1862, -4376, -8586, -11160, -3618, -5400, -226, 200, 234, -1368, -2646, -11304],183,24]
%
% END OF LATTICE L184.24
%
%
% LATTICE L184.25
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-39024, -29952, 3600; -29952, -21762, 2610; 3600, 2610, -313],[144, 18, 1],[12, 29, 29, 77, 26, 41, 2, -1, -1, 7, 16, 71; -421, -1022, -1025, -2730, -927, -1472, -73, 34, 37, -234, -555, -2480; -3374, -8192, -8217, -21888, -7434, -11808, -586, 272, 297, -1872, -4446, -19872],183,25]
%
% END OF LATTICE L184.25
%
%
% LATTICE L184.26
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-8568, 7416, 1872; 7416, -6372, -1620; 1872, -1620, -409],[72, 36, 1],[141, 121, 185, 175, 47, -7, -7, 13, 83, 227, 355, 275; -8, -6, -8, -6, 0, 1, 0, -2, -8, -18, -24, -17; 680, 580, 882, 828, 216, -36, -32, 68, 414, 1116, 1728, 1332],183,26]
%
% END OF LATTICE L184.26
%
%
% LATTICE L184.27
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-23688, 1872, 1368; 1872, -108, -108; 1368, -108, -79],[72, 36, 1],[61, 53, 41, 79, 23, -2, -3, 5, 17, 95, 151, 118; -8, -6, -4, -6, 0, 1, 0, -2, -4, -18, -24, -17; 1060, 920, 711, 1368, 396, -36, -52, 88, 297, 1656, 2628, 2052],183,27]
%
% END OF LATTICE L184.27
%
%
% LATTICE L184.28
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-177624, -187776, 5040; -187776, -198504, 5328; 5040, 5328, -143],[72, 72, 1],[7, 13, 55, 9, 21, 82, 53, 17, 25, 1, -1, -2; -9, -12, -46, -7, -15, -55, -33, -9, -10, 0, 1, -1; -90, 9, 216, 55, 178, 828, 630, 261, 504, 35, 2, -108],183,28]
%
% END OF LATTICE L184.28
%
%
% LATTICE L184.29
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[144, -144, 0; -144, -8424, -1872; 0, -1872, -409],[144, 72, 1],[-81, -76, -125, -130, -47, -1, 7, 2, -23, -92, -175, -295; -85, -79, -129, -133, -47, 0, 7, 1, -27, -101, -187, -312; 392, 364, 594, 612, 216, 0, -32, -4, 126, 468, 864, 1440],183,29]
%
% END OF LATTICE L184.29
%
%
% LATTICE L184.30
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-65808, -18576, -3888; -18576, -3960, -792; -3888, -792, -157],[144, 72, 1],[38, 33, 51, 49, 14, -3, -2, 3, 21, 59, 94, 147; -1105, -961, -1487, -1431, -411, 86, 59, -85, -605, -1707, -2727, -4270; 4640, 4036, 6246, 6012, 1728, -360, -248, 356, 2538, 7164, 11448, 17928],183,30]
%
% END OF LATTICE L184.30
%
%
% LATTICE L184.31
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-432, 15840, -288; 15840, -566856, 10296; -288, 10296, -187],[144, 72, 1],[38, 33, 51, 49, 14, -3, -2, 3, 21, 59, 94, 147; 23, 19, 28, 25, 5, -4, -1, 3, 16, 41, 61, 92; 1204, 992, 1458, 1296, 252, -216, -52, 160, 846, 2160, 3204, 4824],183,31]
%
% END OF LATTICE L184.31
%
%
% LATTICE L184.32
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-94608, 141984, -2736; 141984, -213048, 4104; -2736, 4104, -79],[144, 72, 1],[57, 50, 39, 76, 23, -3, -3, 4, 15, 86, 139, 219; 53, 47, 37, 73, 23, -2, -3, 3, 13, 77, 127, 202; 772, 704, 567, 1152, 396, 0, -52, 16, 153, 1008, 1764, 2880],183,32]
%
% END OF LATTICE L184.32
%
%
% LATTICE L184.33
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-607680, -156672, 18432; -156672, -40392, 4752; 18432, 4752, -559],[576, 72, 1],[2, -1, -1, 7, 16, 71, 12, 29, 29, 77, 26, 41; -11, 2, 6, -10, -49, -240, -43, -110, -114, -314, -113, -192; -28, -16, 18, 144, 108, 288, 28, 16, -18, -144, -108, -288],183,33]
%
% END OF LATTICE L184.33
%
%
% LATTICE L184.34
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-11952576, -1032192, 123840; -1032192, -88776, 10656; 123840, 10656, -1279],[576, 72, 1],[4, -1, -1, 7, 22, 103, 18, 45, 23, 125, 44, 73; 365, -94, -91, 662, 2039, 9520, 1661, 4146, 2117, 11494, 4039, 6688; 3428, -880, -855, 6192, 19116, 89280, 15580, 38896, 19863, 107856, 37908, 62784],183,34]
%
% END OF LATTICE L184.34
%

\medskip%
%------------------------------WEYL-GROUP-W185--------------------------------
%
\leavevmode\llap{}%
$W_{185}$%
\qquad\llap{12} lattices, $\chi=30$%
\hfill%
$22242224\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L185.1
%
\leavevmode%
${L_{185.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{2}{}25\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${2}\above{1pt}{1pt}{b}{2}{50}\above{1pt}{1pt}{s}{2}{6}\above{1pt}{1pt}{b}{2}{4}\above{1pt}{1pt}{*}{4}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-221700\\73800\\1800
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
73800\\-24566\\-601
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1800\\-601\\-10
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
61499\\183000\\70500
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-20541\\-61123\\-23547
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-328\\-976\\-377
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\3\\-1
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
294\\875\\325
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
124\\369\\141
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
287\\854\\330
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-221700, 73800, 1800; 73800, -24566, -601; 1800, -601, -10],[300, 1, 1],[1, 294, 124, 287, 204, 731, -1, -41; 3, 875, 369, 854, 607, 2175, -3, -122; -1, 325, 141, 330, 236, 850, 0, -48],184,1]
%
% END OF LATTICE L185.1
%
%
% LATTICE L185.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-479550, 5025, 6750; 5025, -46, -71; 6750, -71, -95],[75, 1, 1],[59, 283, 23, 4, -4, -8, 10, 29; 166, 800, 66, 12, -11, -25, 27, 81; 4066, 19500, 1584, 275, -276, -550, 690, 1999],184,2]
%
% END OF LATTICE L185.2
%
%
% LATTICE L185.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[72992850, -123675, 23313450; -123675, 210, -39501; 23313450, -39501, 7446167],[75, 3, 1],[4222, 20698, 612, 505, 23, 527, 237, 2042; 153, 775, 25, 23, 2, 0, 6, 70; -13218, -64800, -1916, -1581, -72, -1650, -742, -6393],184,3]
%
% END OF LATTICE L185.3
%
%
% LATTICE L185.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-753900, 10200, 5100; 10200, -138, -69; 5100, -69, -34],[300, 3, 1],[0, 7, 1, 7, 5, 18, 0, -1; 4, 550, 76, 524, 371, 1325, -1, -74; -9, -75, -5, -18, -6, 0, 2, 0],184,4]
%
% END OF LATTICE L185.4
%
%
% LATTICE L185.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[69484200, 973500, -17275500; 973500, 13640, -242036; -17275500, -242036, 4295119],[300, 4, 1],[-525, -4941, -1195, -1079, -1335, -4359, 79, -37; 703, 6625, 1605, 1453, 1802, 5900, -102, 50; -2072, -19500, -4716, -4258, -5268, -17200, 312, -146],184,5]
%
% END OF LATTICE L185.5
%
%
% LATTICE L185.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[992625, -1027575, 315975; -1027575, 1063775, -327100; 315975, -327100, 100582],[75, 25, 1],[3376, 654, 1400, 366, 9, 23, 631, 1665; 194, 38, 84, 23, 1, 1, 33, 94; -9975, -1931, -4125, -1075, -25, -69, -1875, -4925],184,6]
%
% END OF LATTICE L185.6
%
%
% LATTICE L185.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[72600, 21300, -18300; 21300, 15096, -5328; -18300, -5328, 4613],[300, 12, 1],[-1262, -12316, -1038, -3000, -3923, -13609, 1, -111; 23, 225, 19, 55, 72, 250, 0, 2; -4980, -48600, -4096, -11838, -15480, -53700, 4, -438],184,7]
%
% END OF LATTICE L185.7
%
%
% LATTICE L185.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-7125, -751575, -245550; -751575, -78280950, -25575675; -245550, -25575675, -8355994],[75, 75, 1],[4066, 780, 528, 275, -276, -22, 230, 1999; 62666, 12016, 8122, 4212, -4261, -335, 3559, 30831; -191925, -36801, -24875, -12900, 13050, 1026, -10900, -94425],184,8]
%
% END OF LATTICE L185.8
%
%
% LATTICE L185.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-5916900, -41400, -3001800; -41400, -250, -20925; -3001800, -20925, -1522738],[300, 25, 1],[-37, -266, -2776, -6391, -4528, -647, 37, 913; -151, -1065, -11109, -25570, -18114, -2588, 150, 3652; 75, 539, 5625, 12950, 9175, 1311, -75, -1850],184,9]
%
% END OF LATTICE L185.9
%
%
% LATTICE L185.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2316300, 28957800, -1160100; 28957800, -362015850, 14502975; -1160100, 14502975, -581014],[300, 75, 1],[-48, -103, -337, -2263, -1577, -222, 12, 313; -109, -217, -705, -4718, -3281, -461, 27, 650; -2625, -5211, -16925, -113250, -78750, -11064, 650, 15600],184,10]
%
% END OF LATTICE L185.10
%
%
% LATTICE L185.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[704160600, -463372500, 525916800; -463372500, 304922600, -346079700; 525916800, -346079700, 392792087],[300, 100, 1],[-31489, -12247, -77215, -74289, -97076, -13466, 76, -2850; 94474, 36744, 231666, 222890, 291261, 40403, -225, 8551; 125400, 48772, 307500, 295850, 386600, 53628, -300, 11350],184,11]
%
% END OF LATTICE L185.11
%
%
% LATTICE L185.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[29281800, -646434300, 163951200; -646434300, 14270904600, -3619442700; 163951200, -3619442700, 917977229],[300, 300, 1],[-7415, -2889, -6083, -17599, -23040, -3202, -8, -674; 33599, 13087, 27547, 79665, 104261, 14485, 25, 3051; 133800, 52116, 109700, 317250, 415200, 57684, 100, 12150],184,12]
%
% END OF LATTICE L185.12
%

\medskip%
%------------------------------WEYL-GROUP-W186--------------------------------
%
\leavevmode\llap{}%
$W_{186}$%
\qquad\llap{12} lattices, $\chi=10$%
\hfill%
$22226$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L186.1
%
\leavevmode%
${L_{186.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}25\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${6}\above{1pt}{1pt}{b}{2}{100}\above{1pt}{1pt}{*}{2}{4}\above{1pt}{1pt}{b}{2}{150}\above{1pt}{1pt}{s}{2}{2}\above{1pt}{1pt}{}{6}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2716400100\\11466900\\-790200
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
11466900\\-48386\\3309
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-790200\\3309\\-194
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
161\\40203\\29946
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
343\\85650\\63800
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-137\\-34210\\-25482
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2656\\-663225\\-494025
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-168\\-41951\\-31249
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-2716400100, 11466900, -790200; 11466900, -48386, 3309; -790200, 3309, -194],[300, 1, 1],[161, 343, -137, -2656, -168; 40203, 85650, -34210, -663225, -41951; 29946, 63800, -25482, -494025, -31249],185,1]
%
% END OF LATTICE L186.1
%
%
% LATTICE L186.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-7829850, 350250, 16875; 350250, -15667, -752; 16875, -752, -23],[75, 1, 1],[-119, -114, 51, 1876, 114; -2688, -2575, 1152, 42375, 2575; 576, 550, -247, -9075, -551],185,2]
%
% END OF LATTICE L186.2
%
%
% LATTICE L186.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[315119175, 36324300, 102446250; 36324300, 4187163, 11809146; 102446250, 11809146, 33305603],[75, 3, 1],[-17, 3072, 790, 10109, 2305; -2, 425, 110, 1425, 327; 53, -9600, -2469, -31600, -7206],185,3]
%
% END OF LATTICE L186.3
%
%
% LATTICE L186.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-10130700, 22200, 30900; 22200, -42, -69; 30900, -69, -94],[300, 3, 1],[2, 61, 3, -4, -2; 112, 3400, 166, -225, -111; 575, 17550, 864, -1150, -576],185,4]
%
% END OF LATTICE L186.4
%
%
% LATTICE L186.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[3882015911400, -71015676300, -983728425600; -71015676300, 1299125608, 17995840572; -983728425600, 17995840572, 249283268647],[300, 4, 1],[8971, -1153, 5215, 625777, 64571; -144, 0, -89, -10275, -1055; 35412, -4550, 20586, 2470200, 254888],185,5]
%
% END OF LATTICE L186.5
%
%
% LATTICE L186.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[3580350, 2394075, 698625; 2394075, 1600850, 467150; 698625, 467150, 136321],[75, 25, 1],[-2, -8, -55, -95, -191; 3, 0, 2, 9, 23; 0, 41, 275, 456, 900],185,6]
%
% END OF LATTICE L186.6
%
%
% LATTICE L186.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1637290200, -12857100, -414857100; -12857100, 100968, 3257736; -414857100, 3257736, 105116621],[300, 12, 1],[-1878, -24742, -1163, -1799, -301; 7, 75, 2, 0, 2; -7412, -97650, -4590, -7100, -1188],185,7]
%
% END OF LATTICE L186.7
%
%
% LATTICE L186.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1725, 232350, 75525; 232350, -21515025, -6994650; 75525, -6994650, -2273998],[75, 75, 1],[192, 22, -247, -121, -551; -3696, -425, 4752, 2331, 10625; 11375, 1308, -14625, -7174, -32700],185,8]
%
% END OF LATTICE L186.8
%
%
% LATTICE L186.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-207300, 529200, -11700; 529200, -1209650, 26375; -11700, 26375, -574],[300, 25, 1],[161, 7, -137, -76, -84; 597, 26, -508, -282, -312; 24150, 1052, -20550, -11409, -12625],185,9]
%
% END OF LATTICE L186.9
%
%
% LATTICE L186.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-137100, 12000, 6000; 12000, -1050, -525; 6000, -525, -262],[300, 75, 1],[0, 1, 3, 0, -2; 12, 20, 34, -1, -23; -25, -18, 0, 2, 0],185,10]
%
% END OF LATTICE L186.10
%
%
% LATTICE L186.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[87535411800, 722695500, 21634184100; 722695500, 5966600, 178612600; 21634184100, 178612600, 5346840919],[300, 100, 1],[-607, 37, -240, -1660, -4426; 1677, -111, 631, 4569, 12223; 2400, -146, 950, 6564, 17500],185,11]
%
% END OF LATTICE L186.11
%
%
% LATTICE L186.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[79800, 46500, -11700; 46500, 53400, -13500; -11700, -13500, 3413],[300, 300, 1],[7, 3, 2, 0, 2; -1270, -538, -343, 1, -381; -5000, -2118, -1350, 4, -1500],185,12]
%
% END OF LATTICE L186.12
%

\medskip%
%------------------------------WEYL-GROUP-W187--------------------------------
%
\leavevmode\llap{}%
$W_{187}$%
\qquad\llap{4} lattices, $\chi=8$%
\hfill%
$22232$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L187.1
%
\leavevmode%
${L_{187.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}16\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{-}{}$}\EasyButWeakLineBreak%
{${16}\above{1pt}{1pt}{r}{2}{10}\above{1pt}{1pt}{b}{2}{16}\above{1pt}{1pt}{b}{2}{2}\above{1pt}{1pt}{-}{3}{2}\above{1pt}{1pt}{l}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-57840\\-880\\1040
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-880\\-2\\13
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1040\\13\\-18
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-15\\-256\\-1056
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-15\\-70
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5\\88\\352
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\17\\70
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2\\-35\\-141
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-57840, -880, 1040; -880, -2, 13; 1040, 13, -18],[80, 1, 1],[-15, -1, 5, 1, -2; -256, -15, 88, 17, -35; -1056, -70, 352, 70, -141],186,1]
%
% END OF LATTICE L187.1
%
%
% LATTICE L187.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2480, -400, -720; -400, -10, -75; -720, -75, -178],[80, 5, 1],[81, 1, -27, -5, 11; 368, 5, -120, -23, 49; -480, -6, 160, 30, -65],186,2]
%
% END OF LATTICE L187.2
%
%
% LATTICE L187.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-160, -400, -80; -400, -928, -192; -80, -192, -39],[80, 16, 1],[2, 17, 1, -3, -2; 2, 10, 0, -2, 1; -13, -80, -2, 16, 0],186,3]
%
% END OF LATTICE L187.3
%
%
% LATTICE L187.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-18720, -46800, 1120; -46800, -116960, 2800; 1120, 2800, -67],[80, 80, 1],[7, 3, -3, -5, 12; -2, -2, 0, 2, -1; 35, -32, -50, 0, 160],186,4]
%
% END OF LATTICE L187.4
%

\medskip%
%------------------------------WEYL-GROUP-W188--------------------------------
%
\leavevmode\llap{}%
$W_{188}$%
\qquad\llap{4} lattices, $\chi=18$%
\hfill%
$42\slashinfty24|\rtimes D_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L188.1
%
\leavevmode%
${L_{188.1}}$%
{} : {$1\above{1pt}{1pt}{2}{2}16\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{2}{}5\above{1pt}{1pt}{1}{}$}\EasyButWeakLineBreak%
{${2}\above{1pt}{1pt}{*}{4}{4}\above{1pt}{1pt}{l}{2}{5}\above{1pt}{1pt}{8,3}{\infty}{20}\above{1pt}{1pt}{l}{2}{1}\above{1pt}{1pt}{}{4}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-16720\\480\\240
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
480\\-11\\-8
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
240\\-8\\-3
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\15\\39
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-16\\-38
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-15\\-40
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7\\110\\260
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4\\62\\151
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-16720, 480, 240; 480, -11, -8; 240, -8, -3],[80, 1, 1],[1, -1, -1, 7, 4; 15, -16, -15, 110, 62; 39, -38, -40, 260, 151],187,1]
%
% END OF LATTICE L188.1
%
%
% LATTICE L188.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-544400, 3280, 6560; 3280, -15, -40; 6560, -40, -79],[80, 5, 1],[5, 12, 3, -1, -1; 39, 87, 20, -8, -6; 395, 950, 238, -79, -80],187,2]
%
% END OF LATTICE L188.2
%
%
% LATTICE L188.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-26480, 31360, 3040; 31360, -37104, -3600; 3040, -3600, -349],[80, 16, 1],[19, -8, -23, 43, 58; -1, 1, 0, -10, -9; 176, -80, -200, 480, 600],187,3]
%
% END OF LATTICE L188.3
%
%
% LATTICE L188.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-105440, -105520, 2080; -105520, -105520, 2080; 2080, 2080, -41],[80, 80, 1],[-1, -9, -2, 0, 1; 12, 19, 1, -3, -1; 560, 520, -48, -152, 0],187,4]
%
% END OF LATTICE L188.4
%

\medskip%
%------------------------------WEYL-GROUP-W189--------------------------------
%
\leavevmode\llap{}%
$W_{189}$%
\qquad\llap{36} lattices, $\chi=36$%
\hfill%
$2\slashtwo2\slashinfty2\slashtwo2\slashinfty\rtimes D_{4}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L189.1
%
\leavevmode%
${L_{189.1}}$%
{} : {$1\above{1pt}{1pt}{2}{0}16\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{1}{}5\above{1pt}{1pt}{1}{}25\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{5}%
\EasyButWeakLineBreak%
{${20}\above{1pt}{1pt}{s}{2}{400}\above{1pt}{1pt}{s}{2}{4}\above{1pt}{1pt}{*}{2}{80}\above{1pt}{1pt}{5,4}{\infty b}{80}\above{1pt}{1pt}{}{2}{1}\above{1pt}{1pt}{r}{2}{400}\above{1pt}{1pt}{l}{2}{5}\above{1pt}{1pt}{40,21}{\infty}$}%
\nopagebreak\par%
shares genus with 5-dual\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2375600\\-43600\\-45200
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-43600\\-795\\-825
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-45200\\-825\\-856
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-298\\340
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\360\\-400
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\302\\-344
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7\\2064\\-2360
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
9\\2576\\-2960
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\279\\-322
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
11\\2920\\-3400
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\-21\\20
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-2375600, -43600, -45200; -43600, -795, -825; -45200, -825, -856],[400, 5, 1],[-1, 1, 1, 7, 9, 1, 11, 0; -298, 360, 302, 2064, 2576, 279, 2920, -21; 340, -400, -344, -2360, -2960, -322, -3400, 20],188,1]
%
% END OF LATTICE L189.1
%
\hbox{}\par\smallskip%
%
% LATTICE L189.2
%
\leavevmode%
${L_{189.2}}$%
{} : {$1\above{1pt}{1pt}{-2}{4}16\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{1}{}5\above{1pt}{1pt}{1}{}25\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{5}%
\EasyButWeakLineBreak%
{${20}\above{1pt}{1pt}{*}{2}{400}\above{1pt}{1pt}{*}{2}{4}\above{1pt}{1pt}{s}{2}{80}\above{1pt}{1pt}{20,9}{\infty z}{80}\above{1pt}{1pt}{l}{2}{1}\above{1pt}{1pt}{}{2}{400}\above{1pt}{1pt}{}{2}{5}\above{1pt}{1pt}{40,1}{\infty}$}%
\nopagebreak\par%
shares genus with 5-dual\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-13903600\\108800\\40400
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
108800\\-795\\-325
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
40400\\-325\\-116
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-11\\-418\\-2660
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-19\\-720\\-4600
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
9\\342\\2176
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
87\\3304\\21040
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
149\\5656\\36040
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
20\\759\\4838
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
291\\11040\\70400
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
10\\379\\2420
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-13903600, 108800, 40400; 108800, -795, -325; 40400, -325, -116],[400, 5, 1],[-11, -19, 9, 87, 149, 20, 291, 10; -418, -720, 342, 3304, 5656, 759, 11040, 379; -2660, -4600, 2176, 21040, 36040, 4838, 70400, 2420],188,2]
%
% END OF LATTICE L189.2
%
\hbox{}\par\smallskip%
%
% LATTICE L189.3
%
\leavevmode%
${L_{189.3}}$%
{} : {$1\above{1pt}{1pt}{-2}{6}16\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{1}{}5\above{1pt}{1pt}{1}{}25\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{5}%
\EasyButWeakLineBreak%
{${20}\above{1pt}{1pt}{*}{2}{100}\above{1pt}{1pt}{l}{2}{1}\above{1pt}{1pt}{}{2}{5}\above{1pt}{1pt}{40,39}{\infty}{20}\above{1pt}{1pt}{*}{2}{4}\above{1pt}{1pt}{l}{2}{25}\above{1pt}{1pt}{}{2}{5}\above{1pt}{1pt}{40,31}{\infty}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1072400\\288400\\-71200
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
288400\\-75055\\20390
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-71200\\20390\\-4111
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
957\\2376\\-4790
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1019\\2530\\-5100
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-377\\-936\\1887
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1916\\-4757\\9590
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-6769\\-16806\\33880
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3691\\-9164\\18474
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-6833\\-16965\\34200
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-990\\-2458\\4955
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-1072400, 288400, -71200; 288400, -75055, 20390; -71200, 20390, -4111],[400, 5, 1],[957, 1019, -377, -1916, -6769, -3691, -6833, -990; 2376, 2530, -936, -4757, -16806, -9164, -16965, -2458; -4790, -5100, 1887, 9590, 33880, 18474, 34200, 4955],188,3]
%
% END OF LATTICE L189.3
%
\hbox{}\par\smallskip%
%
% LATTICE L189.4
%
\leavevmode%
${L_{189.4}}$%
{} : {$1\above{1pt}{1pt}{2}{2}16\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{1}{}5\above{1pt}{1pt}{1}{}25\above{1pt}{1pt}{1}{}$}\EasyButWeakLineBreak%
{${20}\above{1pt}{1pt}{l}{2}{25}\above{1pt}{1pt}{}{2}{1}\above{1pt}{1pt}{r}{2}{20}\above{1pt}{1pt}{40,39}{\infty z}{5}\above{1pt}{1pt}{r}{2}{4}\above{1pt}{1pt}{*}{2}{100}\above{1pt}{1pt}{l}{2}{5}\above{1pt}{1pt}{40,11}{\infty}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-475600\\-47600\\-44800
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-47600\\-4670\\-4585
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-44800\\-4585\\-4111
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-99\\528\\490
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-106\\565\\525
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
39\\-208\\-193
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
503\\-2682\\-2490
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
510\\-2719\\-2525
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
595\\-3172\\-2946
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2373\\-12650\\-11750
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
209\\-1114\\-1035
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-475600, -47600, -44800; -47600, -4670, -4585; -44800, -4585, -4111],[400, 5, 1],[-99, -106, 39, 503, 510, 595, 2373, 209; 528, 565, -208, -2682, -2719, -3172, -12650, -1114; 490, 525, -193, -2490, -2525, -2946, -11750, -1035],188,4]
%
% END OF LATTICE L189.4
%
\hbox{}\par\smallskip%
%
% LATTICE L189.5
%
\leavevmode%
${L_{189.5}}$%
{} : {$1\above{1pt}{1pt}{-}{5}4\above{1pt}{1pt}{1}{7}16\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{1}{}5\above{1pt}{1pt}{1}{}25\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{5}%
\EasyButWeakLineBreak%
{${20}\above{1pt}{1pt}{s}{2}{400}\above{1pt}{1pt}{s}{2}{4}\above{1pt}{1pt}{s}{2}{80}\above{1pt}{1pt}{10,9}{\infty b}{80}\above{1pt}{1pt}{}{2}{1}\above{1pt}{1pt}{}{2}{400}\above{1pt}{1pt}{}{2}{5}\above{1pt}{1pt}{20,1}{\infty}$}%
\nopagebreak\par%
shares genus with 2-dual${}\iso{}$5-dual; isometric to own %
2.5-dual\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1775600\\164400\\40400
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
164400\\-15220\\-3740
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
40400\\-3740\\-919
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\28\\-70
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-60\\200
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-30\\78
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-7\\-184\\440
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-9\\-196\\400
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-18\\29
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-11\\-120\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\11\\-45
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-1775600, 164400, 40400; 164400, -15220, -3740; 40400, -3740, -919],[400, 20, 1],[1, -1, -1, -7, -9, -1, -11, 0; 28, -60, -30, -184, -196, -18, -120, 11; -70, 200, 78, 440, 400, 29, 0, -45],188,5]
%
% END OF LATTICE L189.5
%
\hbox{}\par\smallskip%
%
% LATTICE L189.6
%
\leavevmode%
${L_{189.6}}$%
{} : {$1\above{1pt}{1pt}{-}{5}4\above{1pt}{1pt}{1}{1}16\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{1}{}5\above{1pt}{1pt}{1}{}25\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{5}%
\EasyButWeakLineBreak%
{${20}\above{1pt}{1pt}{l}{2}{100}\above{1pt}{1pt}{}{2}{1}\above{1pt}{1pt}{}{2}{20}\above{1pt}{1pt}{40,39}{\infty}{20}\above{1pt}{1pt}{r}{2}{4}\above{1pt}{1pt}{l}{2}{100}\above{1pt}{1pt}{}{2}{5}\above{1pt}{1pt}{20,11}{\infty}$}%
\nopagebreak\par%
shares genus with 5-dual\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-456400\\-268000\\-44800
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-268000\\-152620\\-25140
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-44800\\-25140\\-4111
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-99\\528\\-2150
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-106\\565\\-2300
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
39\\-208\\847
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
397\\-2117\\8620
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
702\\-3743\\15240
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
383\\-2042\\8314
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1419\\-7565\\30800
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
103\\-549\\2235
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-456400, -268000, -44800; -268000, -152620, -25140; -44800, -25140, -4111],[400, 20, 1],[-99, -106, 39, 397, 702, 383, 1419, 103; 528, 565, -208, -2117, -3743, -2042, -7565, -549; -2150, -2300, 847, 8620, 15240, 8314, 30800, 2235],188,6]
%
% END OF LATTICE L189.6
%
%
% LATTICE L189.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-5680, 80, 720; 80, -1, -10; 720, -10, -91],[80, 1, 1],[3, 1, 5, 2, 1, -1, -1, -3; 160, 18, 40, 0, -20, 0, 16, 120; 0, 5, 32, 15, 10, -8, -10, -40],188,7]
%
% END OF LATTICE L189.7
%
%
% LATTICE L189.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-548080, 8000, 7120; 8000, -116, -105; 7120, -105, -91],[80, 1, 1],[77, 8, 15, -2, -11, 1, 9, 63; 3240, 338, 640, -80, -460, 40, 376, 2640; 2280, 235, 432, -65, -330, 32, 270, 1880],188,8]
%
% END OF LATTICE L189.8
%
%
% LATTICE L189.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-209680, -82960, 4560; -82960, -32823, 1804; 4560, 1804, -99],[80, 1, 1],[-261, -165, -71, -73, 11, 15, -4, -52; 700, 442, 190, 195, -30, -40, 11, 140; 730, 452, 191, 190, -40, -38, 16, 155],188,9]
%
% END OF LATTICE L189.9
%
%
% LATTICE L189.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-5680, 160, 720; 160, -4, -20; 720, -20, -91],[80, 4, 1],[2, 5, 1, 3, -3, -1, -1, 1; 0, 20, 9, 80, 60, 8, 0, -10; 15, 32, 5, 0, -40, -10, -8, 10],188,10]
%
% END OF LATTICE L189.10
%
%
% LATTICE L189.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-3280, -2960, 1760; -2960, -2620, 1536; 1760, 1536, -891],[80, 4, 1],[-83, -160, -185, -291, -114, -4, 17, 11; 220, 425, 492, 775, 305, 11, -45, -30; 215, 416, 482, 760, 300, 11, -44, -30],188,11]
%
% END OF LATTICE L189.11
%
%
% LATTICE L189.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[720, -160, 0; -160, 20, -4; 0, -4, -1],[80, 4, 1],[-13, -1, 1, 1, -6, -13, -8, -27; -60, -5, 4, 5, -25, -56, -35, -120; 200, 16, -16, -20, 80, 184, 116, 400],188,12]
%
% END OF LATTICE L189.12
%
%
% LATTICE L189.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-290800, 1280, 6800; 1280, -5, -30; 6800, -30, -159],[80, 5, 1],[-7, -5, -1, 1, 0, -11, -5, -9; -24, -24, -16, 4, 4, 24, -2, -16; -296, -210, -40, 42, -1, -480, -215, -384],188,13]
%
% END OF LATTICE L189.13
%
%
% LATTICE L189.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-238640, -2720, 6160; -2720, -25, 70; 6160, 70, -159],[80, 5, 1],[23, 13, -3, -3, 2, 67, 24, 37; 32, 16, -8, -4, 4, 112, 38, 56; 904, 510, -120, -118, 79, 2640, 945, 1456],188,14]
%
% END OF LATTICE L189.14
%
%
% LATTICE L189.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-40400, 880, 880; 880, -15, -20; 880, -20, -19],[80, 5, 1],[1, 7, 19, 7, 2, 2, -1, -1; 6, 47, 132, 50, 15, 16, -6, -8; 39, 270, 730, 268, 76, 75, -40, -38],188,15]
%
% END OF LATTICE L189.15
%
%
% LATTICE L189.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-5680, -5440, 720; -5440, -5200, 688; 720, 688, -91],[80, 16, 1],[2, 5, 2, 3, -3, -1, -1, 1; 0, 10, 9, 40, 30, 4, 0, -5; 15, 112, 82, 320, 200, 22, -8, -30],188,16]
%
% END OF LATTICE L189.16
%
%
% LATTICE L189.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[320, -80, 80; -80, -400, 48; 80, 48, 9],[80, 16, 1],[-31, -67, -41, -137, -63, -2, 7, 6; 25, 55, 34, 115, 55, 2, -5, -5; 150, 328, 202, 680, 320, 11, -32, -30],188,17]
%
% END OF LATTICE L189.17
%
%
% LATTICE L189.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[80, 0, 0; 0, -1008, -32; 0, -32, -1],[80, 16, 1],[-4, -1, 0, 1, -1, -2, -3, -6; -5, 0, 1, 0, -10, -9, -10, -15; 120, -8, -32, 0, 280, 248, 272, 400],188,18]
%
% END OF LATTICE L189.18
%
%
% LATTICE L189.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-270640, 2480, 6560; 2480, -20, -60; 6560, -60, -159],[80, 20, 1],[1, -1, -5, -7, -9, -5, -11, 0; -2, -4, 8, 16, 28, 19, 56, 2; 42, -40, -210, -296, -384, -215, -480, -1],188,19]
%
% END OF LATTICE L189.19
%
%
% LATTICE L189.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-27280, 1520, 720; 1520, -60, -40; 720, -40, -19],[80, 20, 1],[-1, -1, 2, 4, 7, 19, 14, 1; 0, 1, 0, -1, -3, -10, -9, -1; -38, -40, 75, 152, 268, 730, 540, 39],188,20]
%
% END OF LATTICE L189.20
%
%
% LATTICE L189.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-4080, -5360, -2080; -5360, -2700, -1000; -2080, -1000, -369],[80, 20, 1],[-3, -3, 13, 23, 37, 48, 67, 4; 83, 80, -359, -632, -1012, -1309, -1820, -107; -208, -200, 900, 1584, 2536, 3280, 4560, 268],188,21]
%
% END OF LATTICE L189.21
%
%
% LATTICE L189.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1092400, 73200, -10000; 73200, -4905, 670; -10000, 670, -91],[400, 5, 1],[-27, -21, -1, 5, 2, -3, -13, -29; -408, -320, -16, 76, 32, -40, -190, -432; -40, -50, -8, 10, 15, 32, 25, 0],188,22]
%
% END OF LATTICE L189.22
%
%
% LATTICE L189.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-12111600, 52800, 33200; 52800, -220, -145; 33200, -145, -91],[400, 5, 1],[15, 13, 1, -3, -2, -1, 4, 13; 144, 120, 8, -28, -16, 0, 50, 136; 5240, 4550, 352, -1050, -705, -368, 1375, 4520],188,23]
%
% END OF LATTICE L189.23
%
%
% LATTICE L189.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-244880, -257440, 6240; -257440, -270640, 6560; 6240, 6560, -159],[80, 80, 1],[-1, -2, 4, 8, 14, 19, 28, 1; 1, -1, -5, -7, -9, -10, -11, 0; 2, -120, -50, 24, 176, 330, 640, 39],188,24]
%
% END OF LATTICE L189.24
%
%
% LATTICE L189.25
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-27280, -27280, 720; -27280, -27200, 720; 720, 720, -19],[80, 80, 1],[-1, -1, 2, 7, 11, 14, 19, 1; 0, 1, 0, -1, -3, -5, -9, -1; -38, 0, 75, 224, 296, 330, 360, -2],188,25]
%
% END OF LATTICE L189.25
%
%
% LATTICE L189.26
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[80, 0, 0; 0, -4720, -1920; 0, -1920, -781],[80, 80, 1],[0, 1, 0, -1, -3, -10, -9, -2; 13, 0, -49, -36, -46, -99, -50, 3; -32, 0, 120, 88, 112, 240, 120, -8],188,26]
%
% END OF LATTICE L189.26
%
%
% LATTICE L189.27
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-111600, 21600, -3200; 21600, -4180, 620; -3200, 620, -91],[400, 20, 1],[15, 13, 1, -3, -2, -1, 4, 13; 72, 60, 4, -14, -8, 0, 25, 68; -40, -50, -8, 10, 15, 32, 25, 0],188,27]
%
% END OF LATTICE L189.27
%
%
% LATTICE L189.28
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-136400, -52400, 11200; -52400, -19420, 4160; 11200, 4160, -891],[400, 20, 1],[8, 2, -1, -1, 5, 10, 59, 19; 317, 75, -41, -38, 204, 405, 2380, 763; 1580, 375, -204, -190, 1015, 2016, 11850, 3800],188,28]
%
% END OF LATTICE L189.28
%
%
% LATTICE L189.29
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[400, 0, 0; 0, -380, -20; 0, -20, -1],[400, 20, 1],[1, 0, -1, 0, 1, 9, 1, 3; -8, -1, 0, 1, -1, -20, -3, -12; 120, 16, 0, -20, 0, 200, 36, 160],188,29]
%
% END OF LATTICE L189.29
%
%
% LATTICE L189.30
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[3600, 800, 0; 800, 180, 0; 0, 0, -1],[400, 20, 1],[-1, -1, -1, 1, 3, 4, 1, 0; 3, 4, 5, -4, -16, -25, -8, -3; -20, -8, 0, 0, -40, -100, -48, -40],188,30]
%
% END OF LATTICE L189.30
%
%
% LATTICE L189.31
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1072400, -270400, -316800; -270400, -68080, -79840; -316800, -79840, -93571],[400, 80, 1],[45, 118, -34, -368, -674, -187, -1412, -54; 91, 235, -69, -743, -1357, -376, -2835, -108; -230, -600, 174, 1880, 3440, 954, 7200, 275],188,31]
%
% END OF LATTICE L189.31
%
%
% LATTICE L189.32
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3560400, -142400, 18000; -142400, -5680, 720; 18000, 720, -91],[400, 80, 1],[6, 4, 0, -1, 0, 2, 9, 8; -3, -5, -1, 1, 2, 5, 10, 3; 1160, 750, -8, -190, 15, 432, 1850, 1600],188,32]
%
% END OF LATTICE L189.32
%
%
% LATTICE L189.33
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[400, -400, 0; -400, -2880, -1200; 0, -1200, -439],[400, 80, 1],[11, -1, -4, -57, -69, -14, -61, 5; 11, 0, -4, -58, -72, -15, -70, 4; -30, 0, 11, 160, 200, 42, 200, -10],188,33]
%
% END OF LATTICE L189.33
%
%
% LATTICE L189.34
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[400, -400, 0; -400, 480, 0; 0, 0, -1],[400, 80, 1],[-3, -1, -1, 1, 1, -1, -1, -3; -4, -1, 0, 1, -1, -10, -3, -6; -40, -8, 0, 0, -40, -200, -48, -80],188,34]
%
% END OF LATTICE L189.34
%
%
% LATTICE L189.35
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-8935600, -2072000, 55200; -2072000, -479920, 12800; 55200, 12800, -341],[400, 80, 1],[81, 16, -21, -20, 42, 289, 78, 143; -4, -1, 0, 1, -1, -10, -3, -6; 12960, 2552, -3400, -3200, 6760, 46400, 12512, 22920],188,35]
%
% END OF LATTICE L189.35
%
%
% LATTICE L189.36
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-95512400, -15821600, 405200; -15821600, -2620720, 67120; 405200, 67120, -1719],[400, 80, 1],[-10, -11, 8, 26, 53, 62, 62, 44; -39, -45, 31, 103, 212, 249, 250, 179; -3880, -4350, 3096, 10150, 20770, 24336, 24375, 17360],188,36]
%
% END OF LATTICE L189.36
%

\medskip%
%------------------------------WEYL-GROUP-W190--------------------------------
%
\leavevmode\llap{}%
$W_{190}$%
\qquad\llap{6} lattices, $\chi=6$%
\hfill%
$6223$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L190.1
%
\leavevmode%
${L_{190.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{-}{}27\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${6}\above{1pt}{1pt}{}{6}{2}\above{1pt}{1pt}{s}{2}{54}\above{1pt}{1pt}{b}{2}{6}\above{1pt}{1pt}{-}{3}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-124524\\2052\\-29592
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2052\\-30\\507
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-29592\\507\\-6934
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-26\\-410\\81
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-18\\-285\\56
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
52\\819\\-162
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
27\\427\\-84
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-124524, 2052, -29592; 2052, -30, 507; -29592, 507, -6934],[108, 3, 1],[-26, -18, 52, 27; -410, -285, 819, 427; 81, 56, -162, -84],189,1]
%
% END OF LATTICE L190.1
%
%
% LATTICE L190.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-10233, 567, 2187; 567, -30, -126; 2187, -126, -451],[27, 3, 1],[11, 8, -22, -12; 94, 67, -189, -101; 27, 20, -54, -30],189,2]
%
% END OF LATTICE L190.2
%
%
% LATTICE L190.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-513, 216, 108; 216, -90, -45; 108, -45, -22],[27, 9, 1],[0, 4, 0, -2; 4, 9, -1, -5; -9, 0, 2, 0],189,3]
%
% END OF LATTICE L190.3
%
%
% LATTICE L190.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2052, 432, 216; 432, -90, -45; 216, -45, -22],[108, 9, 1],[0, 2, 0, -1; 4, 9, -1, -5; -9, 0, 2, 0],189,4]
%
% END OF LATTICE L190.4
%
%
% LATTICE L190.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[22322520, 5509188, -5671080; 5509188, 1359672, -1399620; -5671080, -1399620, 1440749],[108, 12, 1],[-300, -283, -439, -95; 5, 2, 0, 2; -1176, -1112, -1728, -372],189,5]
%
% END OF LATTICE L190.5
%
%
% LATTICE L190.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1512, -324, 648; -324, 504, -468; 648, -468, 527],[108, 36, 1],[38, 29, -1, 19; -109, -81, 3, -55; -144, -108, 4, -72],189,6]
%
% END OF LATTICE L190.6
%

\medskip%
%------------------------------WEYL-GROUP-W191--------------------------------
%
\leavevmode\llap{}%
$W_{191}$%
\qquad\llap{22} lattices, $\chi=36$%
\hfill%
$2\infty222\infty22\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L191.1
%
\leavevmode%
${L_{191.1}}$%
{} : {$1\above{1pt}{1pt}{2}{{\rm II}}4\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{1}{}3\above{1pt}{1pt}{1}{}27\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${12}\above{1pt}{1pt}{*}{2}{4}\above{1pt}{1pt}{3,2}{\infty b}{4}\above{1pt}{1pt}{r}{2}{54}\above{1pt}{1pt}{b}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
9739332\\-38988\\-110160
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-38988\\156\\441
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-110160\\441\\1246
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-9217\\-230400\\-732672
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
38\\949\\3021
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
104\\2600\\8267
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\4\\-90
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-18\\-82
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\60\\244
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
25\\522\\2025
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[9739332, -38988, -110160; -38988, 156, 441; -110160, 441, 1246],[108, 3, 1],[-1, -1, 3, 25, 9, 5, 5, 11; 4, -18, 60, 522, 196, 118, 140, 378; -90, -82, 244, 2025, 726, 400, 392, 837],190,1]
%
% END OF LATTICE L191.1
%
\hbox{}\par\smallskip%
%
% LATTICE L191.2
%
\leavevmode%
${L_{191.2}}$%
{} : {$1\above{1pt}{1pt}{2}{2}8\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{-}{}27\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${24}\above{1pt}{1pt}{b}{2}{2}\above{1pt}{1pt}{12,5}{\infty a}{8}\above{1pt}{1pt}{s}{2}{108}\above{1pt}{1pt}{*}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-4970376\\-835272\\32616
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-835272\\-140367\\5481
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
32616\\5481\\-214
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-76321\\541872\\2243808
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-12820\\91021\\376908
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
500\\-3550\\-14701
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-11\\80\\372
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-14\\100\\427
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-85\\604\\2512
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-373\\2646\\10908
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-4970376, -835272, 32616; -835272, -140367, 5481; 32616, 5481, -214],[216, 3, 1],[-11, -14, -85, -373, -69, -6, 5, 13; 80, 100, 604, 2646, 488, 42, -36, -90; 372, 427, 2512, 10908, 1980, 161, -160, -324],190,2]
%
% END OF LATTICE L191.2
%
\hbox{}\par\smallskip%
%
% LATTICE L191.3
%
\leavevmode%
${L_{191.3}}$%
{} : {$1\above{1pt}{1pt}{-2}{2}8\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{-}{}27\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{m}%
\EasyButWeakLineBreak%
{${24}\above{1pt}{1pt}{r}{2}{2}\above{1pt}{1pt}{12,5}{\infty b}{8}\above{1pt}{1pt}{l}{2}{27}\above{1pt}{1pt}{}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-758376\\-250128\\4752
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-250128\\-82497\\1566
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4752\\1566\\-25
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-338005\\1030248\\283392
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-111523\\339925\\93504
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2290\\-6980\\-1921
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-147\\448\\120
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-167\\509\\139
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-979\\2984\\820
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2123\\6471\\1782
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-758376, -250128, 4752; -250128, -82497, 1566; 4752, 1566, -25],[216, 3, 1],[-147, -167, -979, -2123, -769, -62, 63, 62; 448, 509, 2984, 6471, 2344, 189, -192, -189; 120, 139, 820, 1782, 648, 53, -52, -54],190,3]
%
% END OF LATTICE L191.3
%
%
% LATTICE L191.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[54, -27, 0; -27, 12, -9; 0, -9, -53],[27, 3, 1],[8, 13, 33, 271, 22, 2, -3, -1; 16, 25, 62, 504, 40, 3, -6, 0; -3, -5, -13, -108, -9, -1, 1, 0],190,4]
%
% END OF LATTICE L191.4
%
%
% LATTICE L191.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[737694, -15174, -21438; -15174, 312, 441; -21438, 441, 623],[54, 3, 1],[-1, -1, 3, 25, 9, 5, 5, 11; 2, -9, 30, 261, 98, 59, 70, 189; -36, -28, 82, 675, 240, 130, 122, 243],190,5]
%
% END OF LATTICE L191.5
%
%
% LATTICE L191.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-210708, -72252, 4752; -72252, -24774, 1629; 4752, 1629, -107],[108, 3, 1],[-69, -6, 5, 13, -11, -14, -85, -373; 244, 21, -18, -45, 40, 50, 302, 1323; 648, 53, -52, -108, 120, 139, 820, 3564],190,6]
%
% END OF LATTICE L191.6
%
%
% LATTICE L191.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1431, -162, -729; -162, -18, -81; -729, -81, -364],[27, 9, 1],[-3, -1, 1, 0, -1, -5, -13, -4; 182, 126, -9, -9, 8, 159, 579, 199; -36, -27, 0, 2, 0, -27, -108, -38],190,7]
%
% END OF LATTICE L191.7
%
%
% LATTICE L191.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[700704, -21330, 336420; -21330, 498, -10242; 336420, -10242, 161521],[54, 6, 1],[-843, 391, 12, -5110, -1601, -2835, -2456, -16886; -13, 6, 0, -81, -25, -44, -38, -261; 1755, -814, -25, 10638, 3333, 5902, 5113, 35154],190,8]
%
% END OF LATTICE L191.8
%
%
% LATTICE L191.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-7076106, -2957364, 861732; -2957364, -1235880, 360027; 861732, 360027, -104807],[54, 9, 1],[14935, 11233, -37, -432, -67, 11069, 44641, 7866; -48538, -36507, 120, 1404, 218, -35973, -145080, -25564; -43938, -33048, 108, 1271, 198, -32562, -131328, -23141],190,9]
%
% END OF LATTICE L191.9
%
%
% LATTICE L191.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-540, 108, 432; 108, -18, -81; 432, -81, -337],[108, 9, 1],[-33, -13, -1, 1, 1, -11, -95, -17; 112, 39, -6, -3, 4, 48, 354, 61; -72, -27, 0, 2, 0, -27, -216, -38],190,10]
%
% END OF LATTICE L191.10
%
%
% LATTICE L191.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-14152212, -2957364, 1723464; -2957364, -617940, 360027; 1723464, 360027, -209614],[108, 9, 1],[14935, 11233, -37, -432, -67, 11069, 44641, 7866; -97076, -73014, 240, 2808, 436, -71946, -290160, -51128; -43938, -33048, 108, 1271, 198, -32562, -131328, -23141],190,11]
%
% END OF LATTICE L191.11
%
%
% LATTICE L191.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[6636086460, -1454655618, 3244884570; -1454655618, 318866094, -711291150; 3244884570, -711291150, 1586669483],[54, 18, 1],[-19937, -25169, 169, -39, -3045, -43777, -69115, -22943; 2543, 3228, -12, 5, 383, 5550, 8790, 2921; 41913, 52920, -351, 82, 6399, 92016, 145287, 48230],190,12]
%
% END OF LATTICE L191.12
%
%
% LATTICE L191.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[4833000, -138348, -1240056; -138348, 3972, 35496; -1240056, 35496, 318175],[108, 12, 1],[-672, -282, -13, -253, -121, -511, -1573, -14021; -323, -135, -6, -126, -59, -247, -758, -6750; -2583, -1084, -50, -972, -465, -1964, -6046, -53892],190,13]
%
% END OF LATTICE L191.13
%
%
% LATTICE L191.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[5940432, -121284, -1542888; -121284, 1992, 31500; -1542888, 31500, 400729],[108, 12, 1],[2370, -549, -20, 14276, 4486, 3977, 3448, 47428; -13, 3, 0, -81, -25, -22, -19, -261; 9126, -2114, -77, 54972, 17274, 15314, 13277, 182628],190,14]
%
% END OF LATTICE L191.14
%
%
% LATTICE L191.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-7675992, 8640, 71928; 8640, -9, -81; 71928, -81, -674],[216, 9, 1],[33, 13, 1, -1, -1, 11, 95, 17; 224, 78, -12, -6, 8, 96, 708, 122; 3492, 1377, 108, -106, -108, 1161, 10044, 1798],190,15]
%
% END OF LATTICE L191.15
%
%
% LATTICE L191.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-136843128, 45719640, 631584; 45719640, -15275043, -211014; 631584, -211014, -2915],[216, 9, 1],[655, 242, -7, -9, 5, 253, 1987, 174; 1304, 483, -12, -18, 8, 501, 3948, 346; 47520, 17469, -648, -647, 504, 18549, 144720, 12653],190,16]
%
% END OF LATTICE L191.16
%
%
% LATTICE L191.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[36396, 7344, 3456; 7344, 1548, 648; 3456, 648, 365],[108, 36, 1],[-157, -212, -13, -1, -20, -319, -1049, -353; 478, 645, 39, 3, 61, 972, 3195, 1075; 639, 864, 54, 4, 81, 1296, 4266, 1436],190,17]
%
% END OF LATTICE L191.17
%
%
% LATTICE L191.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[49093070112, 7913056428, 6437967588; 7913056428, 1275464376, 1037702484; 6437967588, 1037702484, 844262267],[108, 36, 1],[-15406, -9677, 91, -30, -2382, -17005, -26773, -17758; 48761, 30645, -279, 95, 7529, 53790, 84714, 56195; 57546, 36126, -351, 112, 8910, 63558, 100035, 66344],190,18]
%
% END OF LATTICE L191.18
%
%
% LATTICE L191.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[15180264, 1523880, -143208; 1523880, 152976, -14376; -143208, -14376, 1351],[216, 24, 1],[-4, 0, -1, -25, -6, -10, -9, -65; 19, 3, 0, 36, 13, 29, 32, 252; -222, 32, -106, -2268, -498, -752, -614, -4212],190,19]
%
% END OF LATTICE L191.19
%
%
% LATTICE L191.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[5400, -50760, 4536; -50760, 477264, -42648; 4536, -42648, 3811],[216, 24, 1],[-2, 0, -1, -25, -3, -10, -9, -65; 14, 5, -1, 36, 8, 39, 45, 360; 159, 56, -10, 432, 93, 448, 514, 4104],190,20]
%
% END OF LATTICE L191.20
%
%
% LATTICE L191.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-611233992, 673908552, 147148920; 673908552, -743009616, -162237240; 147148920, -162237240, -35424739],[216, 72, 1],[-7022, -10574, 13, 407, 36, -10384, -20971, -7393; -1853, -2799, 0, 108, 13, -2721, -5520, -1948; -20682, -31104, 54, 1196, 90, -30672, -61830, -21788],190,21]
%
% END OF LATTICE L191.21
%
%
% LATTICE L191.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3628368, -3627288, 671760; -3627288, -3605112, 668016; 671760, 668016, -123775],[216, 72, 1],[-925, -2797, -1, 108, 7, -2711, -5507, -1944; -9037, -27324, -9, 1055, 68, -26490, -53805, -18993; -53793, -162648, -54, 6280, 405, -157680, -320274, -113056],190,22]
%
% END OF LATTICE L191.22
%

\medskip%
%------------------------------WEYL-GROUP-W192--------------------------------
%
\leavevmode\llap{}%
$W_{192}$%
\qquad\llap{22} lattices, $\chi=36$%
\hfill%
$2\infty222\infty22\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L192.1
%
\leavevmode%
${L_{192.1}}$%
{} : {$1\above{1pt}{1pt}{2}{{\rm II}}4\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{1}{}3\above{1pt}{1pt}{-}{}27\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${108}\above{1pt}{1pt}{*}{2}{4}\above{1pt}{1pt}{3,1}{\infty a}{4}\above{1pt}{1pt}{r}{2}{6}\above{1pt}{1pt}{b}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1255068\\-800172\\84348
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-800172\\-510132\\53769
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
84348\\53769\\-5666
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-31051\\67500\\178200
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-19688\\42799\\112992
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2047\\-4450\\-11749
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2819\\-6192\\-16794
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
243\\-534\\-1450
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-11\\24\\64
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-121\\266\\723
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-1255068, -800172, 84348; -800172, -510132, 53769; 84348, 53769, -5666],[108, 3, 1],[2819, 243, -11, -121, -1991, -151, 57, 144; -6192, -534, 24, 266, 4392, 334, -124, -316; -16794, -1450, 64, 723, 12042, 922, -328, -855],191,1]
%
% END OF LATTICE L192.1
%
\hbox{}\par\smallskip%
%
% LATTICE L192.2
%
\leavevmode%
${L_{192.2}}$%
{} : {$1\above{1pt}{1pt}{2}{2}8\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{1}{}27\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${216}\above{1pt}{1pt}{b}{2}{2}\above{1pt}{1pt}{12,1}{\infty b}{8}\above{1pt}{1pt}{s}{2}{12}\above{1pt}{1pt}{*}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-603720\\-301536\\3672
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-301536\\-150603\\1833
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3672\\1833\\-22
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-25201\\52416\\160272
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-12575\\26155\\79977
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
150\\-312\\-955
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1453\\3024\\9396
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-99\\206\\637
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-125\\260\\796
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-51\\106\\318
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-603720, -301536, 3672; -301536, -150603, 1833; 3672, 1833, -22],[216, 3, 1],[-1453, -99, -125, -51, -347, -1, 25, 1; 3024, 206, 260, 106, 720, 2, -52, -2; 9396, 637, 796, 318, 2052, -1, -160, 0],191,2]
%
% END OF LATTICE L192.2
%
\hbox{}\par\smallskip%
%
% LATTICE L192.3
%
\leavevmode%
${L_{192.3}}$%
{} : {$1\above{1pt}{1pt}{-2}{2}8\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{1}{}27\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{m}%
\EasyButWeakLineBreak%
{${216}\above{1pt}{1pt}{r}{2}{2}\above{1pt}{1pt}{12,1}{\infty a}{8}\above{1pt}{1pt}{l}{2}{3}\above{1pt}{1pt}{}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1015848\\10368\\5184
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
10368\\-105\\-54
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5184\\-54\\-25
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3167\\226512\\166320
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-34\\-2432\\-1785
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-14\\-1001\\-736
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
59\\4248\\3024
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5\\359\\259
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
9\\644\\472
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\214\\159
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-1015848, 10368, 5184; 10368, -105, -54; 5184, -54, -25],[216, 3, 1],[59, 5, 9, 3, 85, 3, -1, -1; 4248, 359, 644, 214, 6048, 213, -72, -71; 3024, 259, 472, 159, 4536, 161, -52, -54],191,3]
%
% END OF LATTICE L192.3
%
%
% LATTICE L192.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-54, -27, -54; -27, -12, -27; -54, -27, -53],[27, 3, 1],[70, 10, 7, 7, 38, 2, -1, -1; 0, -1, -2, -4, -36, -3, 0, 2; -81, -11, -7, -6, -27, -1, 1, 0],191,4]
%
% END OF LATTICE L192.4
%
%
% LATTICE L192.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-627534, -46116, 42174; -46116, -3381, 3096; 42174, 3096, -2833],[54, 3, 1],[205, 16, -5, -14, -277, -24, 1, 12; 2196, 167, -62, -158, -3096, -267, 12, 133; 5454, 421, -142, -381, -7506, -649, 28, 324],191,5]
%
% END OF LATTICE L192.5
%
%
% LATTICE L192.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-33588, 0, 648; 0, 6, -3; 648, -3, -11],[108, 3, 1],[13, 0, -1, 0, 59, 4, 5, 2; 360, 1, -26, -1, 1512, 103, 130, 53; 648, -1, -52, 0, 3024, 205, 256, 102],191,6]
%
% END OF LATTICE L192.6
%
%
% LATTICE L192.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1431, -729, -54; -729, -360, -27; -54, -27, -2],[27, 9, 1],[-3, -11, -7, -2, -1, -1, 1, 0; 0, -3, -6, -4, -4, -9, 0, 2; 70, 297, 243, 99, 74, 135, -27, -27],191,7]
%
% END OF LATTICE L192.7
%
%
% LATTICE L192.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[38529054, -1899072, 18493974; -1899072, 93606, -911556; 18493974, -911556, 8877121],[54, 6, 1],[-21157, -5545, -1695, -1459, -9137, -1187, 12, -224; 1188, 311, 95, 82, 522, 69, 0, 13; 44199, 11584, 3541, 3048, 19089, 2480, -25, 468],191,8]
%
% END OF LATTICE L192.8
%
%
% LATTICE L192.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-24570, -7722, -3996; -7722, -1773, -1107; -3996, -1107, -616],[54, 9, 1],[177, 401, -5, -50, -29, 43, 227, 87; 442, 1002, -12, -125, -74, 102, 564, 217; -1942, -4401, 54, 549, 322, -459, -2484, -954],191,9]
%
% END OF LATTICE L192.9
%
%
% LATTICE L192.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-5724, 1512, 108; 1512, -333, -27; 108, -27, -2],[108, 9, 1],[-3, -4, -1, 1, 3, 4, 1, -1; 0, -3, -12, -4, -8, -9, 0, 2; -184, -216, 54, 99, 256, 324, 54, -81],191,10]
%
% END OF LATTICE L192.10
%
%
% LATTICE L192.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[108, 0, 0; 0, -360, 333; 0, 333, -308],[108, 9, 1],[3, 11, 7, 1, 1, 1, -1, 0; -22, -6, 96, 41, 86, 198, 0, -25; -22, 0, 108, 45, 94, 216, 0, -27],191,11]
%
% END OF LATTICE L192.11
%
%
% LATTICE L192.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[67359546, 4324482, 32624586; 4324482, 277632, 2094498; 32624586, 2094498, 15801229],[54, 18, 1],[586, 2336, 65, 35, 938, 6808, 2221, 727; -37, -129, 6, -2, -73, -531, -171, -53; -1205, -4806, -135, -72, -1927, -13986, -4563, -1494],191,12]
%
% END OF LATTICE L192.12
%
%
% LATTICE L192.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1544616, -92988, -401652; -92988, 5604, 24180; -401652, 24180, 104443],[108, 12, 1],[-1031, -160, -13, 3, -1327, -364, -249, -265; 18, 3, 0, -2, 0, 1, 2, 4; -3969, -616, -50, 12, -5103, -1400, -958, -1020],191,13]
%
% END OF LATTICE L192.13
%
%
% LATTICE L192.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[624286224, -15288804, -159533496; -15288804, 374424, 3906984; -159533496, 3906984, 40768057],[108, 12, 1],[8494, 551, -6, 208, 19694, 2581, 789, 1358; 9315, 607, -5, 229, 21501, 2817, 861, 1483; 32346, 2098, -23, 792, 75006, 9830, 3005, 5172],191,14]
%
% END OF LATTICE L192.14
%
%
% LATTICE L192.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-179928, 11016, 432; 11016, -666, -27; 432, -27, -1],[216, 9, 1],[-3, -4, -1, 1, 3, 4, 1, -1; -36, -51, -24, 8, 28, 39, 12, -10; -368, -432, 108, 198, 512, 648, 108, -162],191,15]
%
% END OF LATTICE L192.15
%
%
% LATTICE L192.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-58611384, -412776, -32615568; -412776, -2907, -229698; -32615568, -229698, -18149635],[216, 9, 1],[181, 251, 101, -23, -149, -203, -53, 27; 3376, 4893, 2724, -290, -2232, -3177, -1008, 433; -368, -513, -216, 45, 296, 405, 108, -54],191,16]
%
% END OF LATTICE L192.16
%
%
% LATTICE L192.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[977292, -8100, 260172; -8100, 72, -2160; 260172, -2160, 69265],[108, 36, 1],[164, 1207, 800, 262, 98, 365, -14, 0; -480, -3534, -2343, -767, -286, -1062, 45, 1; -631, -4644, -3078, -1008, -377, -1404, 54, 0],191,17]
%
% END OF LATTICE L192.17
%
%
% LATTICE L192.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[432648, 69228, 58320; 69228, 11088, 9324; 58320, 9324, 7867],[108, 36, 1],[233, 845, 275, 179, 143, 283, 7, 9; -666, -2415, -786, -512, -410, -813, -21, -26; -938, -3402, -1107, -720, -574, -1134, -27, -36],191,18]
%
% END OF LATTICE L192.18
%
%
% LATTICE L192.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-72889200, -7019784, 702000; -7019784, -676056, 67608; 702000, 67608, -6761],[216, 24, 1],[-125, -23, 0, 12, 143, 27, 1, -11; 288, 50, -1, -25, -216, -34, 5, 29; -10098, -1888, -10, 996, 12690, 2464, 154, -852],191,19]
%
% END OF LATTICE L192.19
%
%
% LATTICE L192.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-731625264, 4448520, 6860160; 4448520, -27048, -41712; 6860160, -41712, -64325],[216, 24, 1],[-49, -21, -1, 12, 112, 49, 8, -5; 144, 50, -1, -25, -108, -34, 5, 29; -5319, -2272, -106, 1296, 12015, 5248, 850, -552],191,20]
%
% END OF LATTICE L192.20
%
%
% LATTICE L192.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3592080, 526824, -601344; 526824, -77256, 88200; -601344, 88200, -100667],[216, 72, 1],[183, 809, -13, -99, -5, 259, 280, 188; 410, 1818, -27, -223, -18, 534, 615, 419; -734, -3240, 54, 396, 14, -1080, -1134, -756],191,21]
%
% END OF LATTICE L192.21
%
%
% LATTICE L192.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-6740495568, 74694744, 40224816; 74694744, -827640, -445752; 40224816, -445752, -240047],[216, 72, 1],[-278, -2563, -1, 324, 73, 103, -614, -529; -534, -4926, -3, 623, 142, 222, -1173, -1015; -45593, -420336, -162, 53136, 11969, 16848, -100710, -86760],191,22]
%
% END OF LATTICE L192.22
%

\medskip%
%------------------------------WEYL-GROUP-W193--------------------------------
%
\leavevmode\llap{}%
$W_{193}$%
\qquad\llap{6} lattices, $\chi=12$%
\hfill%
$222222\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L193.1
%
\leavevmode%
${L_{193.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{1}{}27\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${12}\above{1pt}{1pt}{*}{2}{108}\above{1pt}{1pt}{b}{2}{2}\above{1pt}{1pt}{b}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
756\\324\\-108
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
324\\138\\-51
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-108\\-51\\-10
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
179\\-396\\108
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
85\\-188\\51
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
15\\-33\\8
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\2\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-115\\252\\-54
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-10\\22\\-5
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[756, 324, -108; 324, 138, -51; -108, -51, -10],[108, 3, 1],[-1, -115, -10, -9, 25, 5; 2, 252, 22, 20, -54, -11; 0, -54, -5, -6, 0, 2],192,1]
%
% END OF LATTICE L193.1
%
%
% LATTICE L193.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-54, -54, -27; -54, -51, -27; -27, -27, -13],[27, 3, 1],[-1, 11, 3, 3, 7, -1; 1, 0, -1, -2, -9, 0; 0, -27, -5, -3, 0, 2],192,2]
%
% END OF LATTICE L193.2
%
%
% LATTICE L193.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[54, 162, -27; 162, 495, -81; -27, -81, 13],[27, 9, 1],[-3, -2, -2, 2, 1, -1; 1, 0, -3, -2, -1, 0; 0, -5, -27, -9, -4, 0],192,3]
%
% END OF LATTICE L193.3
%
%
% LATTICE L193.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[540, -108, 0; -108, -18, 9; 0, 9, -2],[108, 9, 1],[1, 1, 1, -1, -1, -1; 2, 4, 6, -4, -6, -9; 0, 14, 27, -18, -32, -54],192,4]
%
% END OF LATTICE L193.4
%
%
% LATTICE L193.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[462456, -31428, -115128; -31428, 2136, 7824; -115128, 7824, 28661],[108, 12, 1],[-11, 124, 36, 48, 209, 1; -8, 45, 17, 25, 108, 0; -42, 486, 140, 186, 810, 4],192,5]
%
% END OF LATTICE L193.5
%
%
% LATTICE L193.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[70200, 5076, 14364; 5076, 360, 1044; 14364, 1044, 2935],[108, 36, 1],[-51, -18, 28, 14, -19, -139; 145, 51, -81, -41, 53, 393; 198, 70, -108, -54, 74, 540],192,6]
%
% END OF LATTICE L193.6
%

\medskip%
%------------------------------WEYL-GROUP-W194--------------------------------
%
\leavevmode\llap{}%
$W_{194}$%
\qquad\llap{32} lattices, $\chi=18$%
\hfill%
$2\infty2222$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L194.1
%
\leavevmode%
${L_{194.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}8\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{2}{}9\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-}{}5\above{1pt}{1pt}{-}{}25\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{25,5,2*}%
\EasyButWeakLineBreak%
{${72}\above{1pt}{1pt}{r}{2}{10}\above{1pt}{1pt}{60,49}{\infty a}{40}\above{1pt}{1pt}{b}{2}{450}\above{1pt}{1pt}{l}{2}{8}\above{1pt}{1pt}{r}{2}{50}\above{1pt}{1pt}{l}{2}$}%
\nopagebreak\par%
shares genus with 5-dual\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-8854200\\1479600\\145800
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1479600\\-239810\\-20665
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
145800\\-20665\\-562
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-12367\\-92304\\185688
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1020\\-7613\\15315
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1007\\7516\\-15120
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2068\\15435\\-31050
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-731\\-5456\\10976
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2689\\-20070\\40375
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-8854200, 1479600, 145800; 1479600, -239810, -20665; 145800, -20665, -562],[1800, 5, 1],[-12367, -1020, 1007, 2068, -731, -2689; -92304, -7613, 7516, 15435, -5456, -20070; 185688, 15315, -15120, -31050, 10976, 40375],193,1]
%
% END OF LATTICE L194.1
%
%
% LATTICE L194.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-51767190, 1483380, 519390; 1483380, -42506, -14883; 519390, -14883, -5210],[90, 1, 1],[-967, -174, 59, 58, -51, -78; -34074, -6130, 2080, 2043, -1798, -2749; 936, 165, -60, -54, 52, 77],193,2]
%
% END OF LATTICE L194.2
%
%
% LATTICE L194.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-1041541560, -7672680, 319680; -7672680, -56522, 2355; 319680, 2355, -98],[360, 1, 1],[137, 2, -29, -1, 21, 10; -18432, -270, 3900, 135, -2824, -1345; 3960, 35, -880, -18, 640, 299],193,3]
%
% END OF LATTICE L194.3
%
%
% LATTICE L194.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-890550, 339750, -38250; 339750, -129610, 14595; -38250, 14595, -1642],[450, 5, 1],[-277, -36, 29, 44, -25, -142; -558, -73, 58, 90, -50, -285; 1494, 190, -160, -225, 138, 775],193,4]
%
% END OF LATTICE L194.4
%
%
% LATTICE L194.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[19042920, 4992570, 9451530; 4992570, 1309160, 2477958; 9451530, 2477958, 4691057],[90, 2, 1],[-79396, -33996, -667, -607, -4246, -10645; -4752, -2035, -40, -36, -254, -637; 162477, 69570, 1365, 1242, 8689, 21784],193,5]
%
% END OF LATTICE L194.5
%
%
% LATTICE L194.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-178110, 60030, 3960; 60030, -20230, -1335; 3960, -1335, -88],[90, 5, 1],[109, 2, -3, -1, 13, 13; 198, 3, -6, 0, 26, 25; 1890, 44, -44, -45, 190, 205],193,6]
%
% END OF LATTICE L194.6
%
%
% LATTICE L194.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[47304090, 16693560, 5204070; 16693560, 5891220, 1836513; 5204070, 1836513, 572516],[90, 9, 1],[-3313, -6381, -249, -13, -1597, -2000; -1056, -2035, -80, -4, -508, -637; 33502, 64530, 2520, 131, 16146, 20223],193,7]
%
% END OF LATTICE L194.7
%
%
% LATTICE L194.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2938860, -50130, 1431720; -50130, 880, -24420; 1431720, -24420, 697489],[90, 10, 1],[10175, 881, 21, 44, 525, 1343; 1458, 126, 3, 9, 76, 193; -20835, -1804, -43, -90, -1075, -2750],193,8]
%
% END OF LATTICE L194.8
%
%
% LATTICE L194.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-27658470420, -145470870, -13572666630; -145470870, -765108, -71386002; -13572666630, -71386002, -6660429035],[90, 18, 1],[28865, 93309, -15927, -3450, 13771, 41989; -1893, -6130, 1040, 227, -899, -2749; -58801, -190080, 32445, 7028, -28053, -85536],193,9]
%
% END OF LATTICE L194.9
%
%
% LATTICE L194.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[26280, 7560, 2160; 7560, 2090, 795; 2160, 795, -178],[360, 5, 1],[-3635, -60, 59, 121, -215, -158; 11088, 183, -180, -369, 656, 482; 5400, 89, -88, -180, 320, 235],193,10]
%
% END OF LATTICE L194.10
%
%
% LATTICE L194.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2110950, 30600, 708750; 30600, -440, -10275; 708750, -10275, -237962],[450, 5, 1],[4133, 148, -51, -49, 221, 67; 3690, 134, -44, -45, 190, 59; 12150, 435, -150, -144, 650, 197],193,11]
%
% END OF LATTICE L194.11
%
%
% LATTICE L194.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-216583920, 22333320, -1261800; 22333320, -2302928, 130112; -1261800, 130112, -7351],[360, 8, 1],[284, 181, -43, -47, 20, 102; 2835, 1805, -430, -468, 200, 1019; 1431, 880, -230, -216, 107, 528],193,12]
%
% END OF LATTICE L194.12
%
%
% LATTICE L194.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2872440, 198360, -51480; 198360, -13698, 3555; -51480, 3555, -922],[360, 9, 1],[-33, -22, 29, 1, -21, -14; -488, -330, 420, 15, -304, -205; -40, -45, 0, 2, 0, -9],193,13]
%
% END OF LATTICE L194.13
%
%
% LATTICE L194.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[245250, 30330, -15390; 30330, 3960, -1845; -15390, -1845, 982],[90, 45, 1],[-375, -146, -7, -1, -175, -223; 1074, 418, 20, 3, 502, 639; -3860, -1503, -72, -10, -1800, -2295],193,14]
%
% END OF LATTICE L194.14
%
%
% LATTICE L194.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[491832900, 2918250, 245115000; 2918250, 17320, 1454370; 245115000, 1454370, 122158081],[450, 10, 1],[11818, 5119, 122, 224, 608, 7793; 1656, 716, 17, 45, 86, 1095; -23733, -10280, -245, -450, -1221, -15650],193,15]
%
% END OF LATTICE L194.15
%
%
% LATTICE L194.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[34712100, -723150, 17114850; -723150, 15080, -356550; 17114850, -356550, 8438501],[450, 10, 1],[26746, 2264, 37, 71, 1492, 729; 495, 43, 1, 0, 25, 13; -54225, -4590, -75, -144, -3025, -1478],193,16]
%
% END OF LATTICE L194.16
%
%
% LATTICE L194.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3983400, -11513430, -5597910; -11513430, -33277680, -16179840; -5597910, -16179840, -7866751],[90, 90, 1],[11, 3, -3, 0, 13, 25; -2306, -1060, 443, 141, -1908, -4297; 4735, 2178, -909, -290, 3915, 8820],193,17]
%
% END OF LATTICE L194.17
%
%
% LATTICE L194.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1476919800, -18318600, 383400; -18318600, -227210, 4755; 383400, 4755, -98],[1800, 5, 1],[-937, -2, 41, 1, -149, -14; 75960, 162, -3324, -81, 12080, 1135; 19800, 35, -880, -18, 3200, 299],193,18]
%
% END OF LATTICE L194.18
%
%
% LATTICE L194.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-893664720, -61043400, -11062440; -61043400, -4169680, -755640; -11062440, -755640, -136939],[360, 40, 1],[-5, -1, 0, 2, 0, -1; 2169, 235, -83, -225, 193, 870; -11565, -1216, 458, 1080, -1065, -4720],193,19]
%
% END OF LATTICE L194.19
%
%
% LATTICE L194.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-158040, -135000, 5400; -135000, -113490, 4545; 5400, 4545, -182],[360, 45, 1],[7, 0, -3, 0, 11, 5; 120, 4, -44, -1, 160, 77; 3200, 99, -1188, -25, 4320, 2070],193,20]
%
% END OF LATTICE L194.20
%
%
% LATTICE L194.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[408613050, 5643000, 90458550; 5643000, 77940, 1249245; 90458550, 1249245, 20025668],[450, 45, 1],[1491, 2909, 139, 11, 687, 4418; 368, 716, 34, 5, 172, 1095; -6758, -13185, -630, -50, -3114, -20025],193,21]
%
% END OF LATTICE L194.21
%
%
% LATTICE L194.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[320319450, 4660200, 71527500; 4660200, 67860, 1040625; 71527500, 1040625, 15972128],[450, 45, 1],[-16537, -6291, -201, -23, -8341, -2032; 110, 43, 2, 0, 50, 13; 74050, 28170, 900, 103, 37350, 9099],193,22]
%
% END OF LATTICE L194.22
%
%
% LATTICE L194.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-61213680, -14397480, -3423240; -14397480, -3386160, -805104; -3423240, -805104, -191423],[360, 72, 1],[131, 1076, -43, -45, 20, 281; -2048, -16815, 675, 703, -314, -4396; 6271, 51480, -2070, -2152, 963, 13464],193,23]
%
% END OF LATTICE L194.23
%
%
% LATTICE L194.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-40007502900, -305538750, -19942064550; -305538750, -2332980, -152298270; -19942064550, -152298270, -9940283939],[450, 90, 1],[71683, 166346, -68122, -22331, 58737, 664397; -31, -73, 29, 10, -25, -285; -143809, -333720, 136665, 44800, -117837, -1332900],193,24]
%
% END OF LATTICE L194.24
%
%
% LATTICE L194.25
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-203143994100, 40279950, -101259942750; 40279950, -7920, 20078100; -101259942750, 20078100, -50474423579],[450, 90, 1],[-451521, -291063, 50133, 10708, -217243, -131741; 205, 134, -22, -5, 95, 59; 905825, 583920, -100575, -21482, 435825, 264294],193,25]
%
% END OF LATTICE L194.25
%
%
% LATTICE L194.26
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-7653243600, -40120200, 7500600; -40120200, -210320, 39320; 7500600, 39320, -7351],[1800, 40, 1],[-1, -1, 0, 2, 0, -1; 189, 86, -43, -45, 20, 415; -9, -560, -230, 1800, 107, 1200],193,26]
%
% END OF LATTICE L194.26
%
%
% LATTICE L194.27
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-78663600, 14596200, -366908400; 14596200, -2696720, 68441400; -366908400, 68441400, -1700175911],[1800, 40, 1],[5036843, 635849, -155108, -162754, 360686, 364509; 14990670, 1892416, -461633, -484389, 1073475, 1084853; -483525, -61040, 14890, 15624, -34625, -34992],193,27]
%
% END OF LATTICE L194.27
%
%
% LATTICE L194.28
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-111003406200, -7383319200, -49100400; -7383319200, -491096610, -3265875; -49100400, -3265875, -21718],[1800, 45, 1],[657, 103, -1217, -26, 885, 2122; -10488, -1644, 19428, 415, -14128, -33875; 91792, 14355, -170100, -3625, 123696, 296550],193,28]
%
% END OF LATTICE L194.28
%
%
% LATTICE L194.29
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-790200, 54000, 27000; 54000, -3690, -1845; 27000, -1845, -922],[1800, 45, 1],[7, 0, -3, 0, 11, 1; 200, 22, -44, -1, 160, 19; -200, -45, 0, 2, 0, -9],193,29]
%
% END OF LATTICE L194.29
%
%
% LATTICE L194.30
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-7094160, -23413320, -53277480; -23413320, -77259600, -175806720; -53277480, -175806720, -400053811],[360, 360, 1],[4791, 6231, -999, -1057, 2323, 13874; 43524, 56602, -9077, -9601, 21107, 126047; -19765, -25704, 4122, 4360, -9585, -57240],193,30]
%
% END OF LATTICE L194.30
%
%
% LATTICE L194.31
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-154184400, 211138200, 7653600; 211138200, -289064880, -10480680; 7653600, -10480680, -379919],[1800, 360, 1],[-1995, -12949, 2090, 2192, -972, -28939; 41, 266, -43, -45, 20, 595; -41321, -268200, 43290, 45400, -20133, -599400],193,31]
%
% END OF LATTICE L194.31
%
%
% LATTICE L194.32
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-645303600, -198801000, -160754400; -198801000, -61213680, -49524120; -160754400, -49524120, -40046231],[1800, 360, 1],[78126, 128361, -5121, -5369, 11908, 33508; 655, 1076, -43, -45, 100, 281; -314425, -516600, 20610, 21608, -47925, -134856],193,32]
%
% END OF LATTICE L194.32
%

\medskip%
%------------------------------WEYL-GROUP-W195--------------------------------
%
\leavevmode\llap{}%
$W_{195}$%
\qquad\llap{32} lattices, $\chi=72$%
\hfill%
$2\infty2|2\infty2|2\infty2|2\infty2|\rtimes D_{4}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L195.1
%
\leavevmode%
${L_{195.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}8\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{-2}{}9\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{-}{}5\above{1pt}{1pt}{-}{}25\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{25,5,2*}%
\EasyButWeakLineBreak%
{${8}\above{1pt}{1pt}{r}{2}{10}\above{1pt}{1pt}{60,29}{\infty b}{40}\above{1pt}{1pt}{b}{2}{50}\above{1pt}{1pt}{b}{2}{360}\above{1pt}{1pt}{10,1}{\infty z}{90}\above{1pt}{1pt}{l}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
shares genus with 5-dual\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-12431315950200\\-85733217000\\-591012000
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-85733217000\\-591263590\\-4075945
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-591012000\\-4075945\\-28098
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-726032161\\104802166080\\68540893200
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-5007114\\722772931\\472695405
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-34524\\4983512\\3259229
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1839\\265456\\173928
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1134\\163691\\107200
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1639\\236588\\154780
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-631\\91085\\59475
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2147\\309924\\201780
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-632\\91233\\59040
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-12431315950200, -85733217000, -591012000; -85733217000, -591263590, -4075945; -591012000, -4075945, -28098],[1800, 5, 1],[-1839, -1134, -1639, -631, -2147, -632, -177, 0, 127, 1, -2389, -2770; 265456, 163691, 236588, 91085, 309924, 91233, 25552, 1, -18332, -145, 344844, 399843; 173928, 107200, 154780, 59475, 201780, 59040, 16392, -145, -12040, 0, 226440, 262125],194,1]
%
% END OF LATTICE L195.1
%
%
% LATTICE L195.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-32514390, 932400, -61200; 932400, -26738, 1755; -61200, 1755, -112],[90, 1, 1],[-485, -319, 39, 40, -893, -2977, -1091, -1454, -1221, -237, -2653, -2342; -16914, -11125, 1360, 1395, -31140, -103815, -38046, -50705, -42580, -8265, -92520, -81675; -20, -15, 0, 2, 0, -45, -20, -30, -30, -7, -90, -90],194,2]
%
% END OF LATTICE L195.2
%
%
% LATTICE L195.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-522723960, -3601800, 231480; -3601800, -24818, 1595; 231480, 1595, -102],[360, 1, 1],[-583, -362, -531, -42, -743, -236, -73, -7, 39, 1, -733, -871; 84608, 52535, 77060, 6095, 107820, 34245, 10592, 1015, -5660, -145, 106380, 126405; -40, -30, -60, -7, -180, -90, -40, -15, 0, 2, 0, -45],194,3]
%
% END OF LATTICE L195.3
%
%
% LATTICE L195.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-2794950, 35550, 1121400; 35550, -440, -14265; 1121400, -14265, -449932],[450, 5, 1],[2863, 8392, 3335, -141, -145, 284, 601, 3299, 4459, 2306, 2743, 3613; 870, 2547, 1008, -45, -44, 89, 186, 1017, 1368, 705, 836, 1099; 7108, 20835, 8280, -350, -360, 705, 1492, 8190, 11070, 5725, 6810, 8970],194,4]
%
% END OF LATTICE L195.4
%
%
% LATTICE L195.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[14726520, 5828850, 7366770; 5828850, 2307296, 2915820; 7366770, 2915820, 3685141],[90, 2, 1],[-21975, -28661, -682, -1, -101716, -484663, -81777, -204781, -77132, -25937, -131726, -215663; -1284, -1675, -40, 0, -5940, -28305, -4776, -11960, -4505, -1515, -7695, -12600; 44945, 58620, 1395, 2, 208035, 991260, 167255, 418830, 157755, 53048, 269415, 441090],194,5]
%
% END OF LATTICE L195.5
%
%
% LATTICE L195.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-170190, 1980, 3870; 1980, -20, -45; 3870, -45, -88],[90, 5, 1],[99, 25, 19, 16, 31, 23, 21, 2, -1, -1, 23, 58; -20, -6, -6, -7, -18, -18, -20, -3, 0, 2, 0, -9; 4350, 1099, 836, 705, 1368, 1017, 930, 89, -44, -45, 1008, 2547],194,6]
%
% END OF LATTICE L195.6
%
%
% LATTICE L195.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[68502690, 26669250, 7614990; 26669250, 10382832, 2964645; 7614990, 2964645, 846508],[90, 9, 1],[-9125, -5946, -279, -1, -4703, -11202, -34019, -42591, -32079, -5392, -6083, -4977; -2568, -1675, -80, 0, -1320, -3145, -9552, -11960, -9010, -1515, -1710, -1400; 91080, 59355, 2790, 9, 46930, 111785, 339480, 425025, 320130, 53811, 60710, 49675],194,7]
%
% END OF LATTICE L195.7
%
%
% LATTICE L195.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[4237740, 3870, 2069550; 3870, 20, 1890; 2069550, 1890, 1010689],[90, 10, 1],[12563, 6292, 2370, 3985, 4048, 6628, 3377, 881, 21, 0, 3125, 14891; 67, 33, 12, 19, 18, 27, 13, 3, 0, 1, 18, 81; -25725, -12884, -4853, -8160, -8289, -13572, -6915, -1804, -43, 0, -6399, -30492],194,8]
%
% END OF LATTICE L195.8
%
%
% LATTICE L195.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-21802479120, -102436650, -10699426980; -102436650, -481284, -50270130; -10699426980, -50270130, -5250675259],[90, 18, 1],[117325, 154239, -9477, -19334, 24111, 160493, 264583, 705054, 295908, 114811, 71366, 125938; -8457, -11125, 680, 1395, -1730, -11535, -19023, -50705, -21290, -8265, -5140, -9075; -238995, -314190, 19305, 39384, -49115, -326930, -538965, -1436220, -602775, -233874, -145375, -256540],194,9]
%
% END OF LATTICE L195.9
%
%
% LATTICE L195.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-158040, 0, 1800; 0, 10, -5; 1800, -5, -18],[360, 5, 1],[7, 0, -1, 0, 19, 22, 73, 9, 13, 5, 17, 5; 320, 1, -44, -1, 828, 963, 3200, 395, 572, 221, 756, 225; 600, -1, -88, 0, 1656, 1917, 6360, 784, 1132, 435, 1476, 432],194,10]
%
% END OF LATTICE L195.10
%
%
% LATTICE L195.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-850950, 19350, 9900; 19350, -440, -225; 9900, -225, -112],[450, 5, 1],[61, 59, 67, 6, 31, 37, 139, 76, 23, -1, -1, 8; 2730, 2637, 2988, 267, 1376, 1639, 6150, 3357, 1008, -45, -44, 359; -100, -90, -90, -7, -30, -30, -100, -45, 0, 2, 0, -15],194,11]
%
% END OF LATTICE L195.11
%
%
% LATTICE L195.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-658073520, 69415560, 8140680; 69415560, -7322160, -858704; 8140680, -858704, -100703],[360, 8, 1],[-639, -12892, -7819, -1489, -4113, -10324, -1995, -22667, -4034, 172, 162, -1529; -5583, -112635, -68310, -13008, -35930, -90185, -17427, -198000, -35235, 1503, 1415, -13360; -4049, -81720, -49590, -9448, -26110, -65560, -12671, -144000, -25650, 1088, 1030, -9680],194,12]
%
% END OF LATTICE L195.12
%
%
% LATTICE L195.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-30704760, 1981080, -55080; 1981080, -127818, 3555; -55080, 3555, -98],[360, 9, 1],[-179, -2, 39, 1, -733, -856, -1709, -352, -511, -119, -683, -206; -2664, -30, 580, 15, -10900, -12730, -25416, -5235, -7600, -1770, -10160, -3065; 3960, 35, -880, -18, 16560, 19305, 38520, 7930, 11500, 2673, 15300, 4590],194,13]
%
% END OF LATTICE L195.13
%
%
% LATTICE L195.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[642330, -3060, -63000; -3060, 90, 315; -63000, 315, 6182],[90, 45, 1],[-4161, -1042, -785, -660, -149, -122, -1119, -146, -7, 0, -115, -274; 8456, 2117, 1594, 1339, 302, 247, 2264, 295, 14, 1, 234, 557; -42840, -10728, -8082, -6795, -1534, -1256, -11520, -1503, -72, 0, -1184, -2821],194,14]
%
% END OF LATTICE L195.14
%
%
% LATTICE L195.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[57873600, -814950, 28275300; -814950, 11480, -398160; 28275300, -398160, 13814461],[450, 10, 1],[4927, 29471, 6356, 171, 22, 1437, 1153, 11569, 7324, 7429, 4538, 12243; 123, 729, 153, 0, 1, 43, 33, 324, 198, 195, 116, 308; -10081, -60300, -13005, -350, -45, -2940, -2359, -23670, -14985, -15200, -9285, -25050],194,15]
%
% END OF LATTICE L195.15
%
%
% LATTICE L195.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[849600, 221850, 423900; 221850, 60080, 110700; 423900, 110700, 211501],[450, 10, 1],[17607, 34537, 21076, 4147, 12326, 32715, 65313, 77405, 16238, -1, 112, 4599; 165, 324, 198, 39, 116, 308, 615, 729, 153, 0, 1, 43; -35375, -69390, -42345, -8332, -24765, -65730, -131225, -155520, -32625, 2, -225, -9240],194,16]
%
% END OF LATTICE L195.16
%
%
% LATTICE L195.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1884060, -7697790, -3742740; -7697790, -31450320, -15291450; -3742740, -15291450, -7434851],[90, 90, 1],[-10, -6, -3, -7, -1, -2, -10, -3, 0, 2, 0, -1; -60538, -30551, -11591, -19471, -2089, -3085, -12622, -2371, 617, 1181, -1569, -7889; 124515, 62838, 23841, 40050, 4297, 6346, 25965, 4878, -1269, -2430, 3227, 16226],194,17]
%
% END OF LATTICE L195.17
%
%
% LATTICE L195.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-790200, 18000, 9000; 18000, -410, -205; 9000, -205, -102],[1800, 5, 1],[73, 22, 19, 0, -1, 0, 7, 5, 17, 1, 13, 9; 3280, 981, 828, -1, -44, 7, 400, 261, 828, 47, 596, 407; -200, -45, 0, 2, 0, -15, -200, -90, -180, -7, -60, -30],194,18]
%
% END OF LATTICE L195.18
%
%
% LATTICE L195.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-528034320, -64853640, -128781360; -64853640, -7965360, -15817040; -128781360, -15817040, -31408259],[360, 40, 1],[21364, 50644, 10435, -449, -419, 1292, 3826, 17369, 12236, 13044, 7976, 21379; -5, -9, 0, 2, 0, -3, -5, -18, -9, -7, -3, -6; -87595, -207648, -42786, 1840, 1718, -5296, -15685, -71208, -50166, -53480, -32702, -87656],194,19]
%
% END OF LATTICE L195.19
%
%
% LATTICE L195.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-158040, -7920, 5760; -7920, -270, 225; 5760, 225, -178],[360, 45, 1],[61, 11, 29, 22, 17, 11, 259, 25, 19, -2, -1, 1; 2720, 489, 1284, 971, 748, 483, 11360, 1095, 828, -91, -44, 45; 5400, 972, 2556, 1935, 1492, 964, 22680, 2187, 1656, -180, -88, 89],194,20]
%
% END OF LATTICE L195.20
%
%
% LATTICE L195.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2344707450, 11003850, 523030950; 11003850, 51660, 2454615; 523030950, 2454615, 116671858],[450, 45, 1],[-59515, -19781, -8537, -1054, -261, -8643, -13885, -7744, -9813, -44821, -54789, -73932; 246, 81, 34, 0, 2, 43, 66, 36, 44, 195, 232, 308; 266796, 88675, 38270, 4725, 1170, 38745, 62244, 34715, 43990, 200925, 245610, 331425],194,21]
%
% END OF LATTICE L195.21
%
%
% LATTICE L195.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1539450, 643950, 341550; 643950, 270360, 142875; 341550, 142875, 75778],[450, 45, 1],[14239, 1548, 1883, 1663, 9867, 13080, 52201, 3435, 1439, -2, 99, 1869; 330, 36, 44, 39, 232, 308, 1230, 81, 34, 0, 2, 43; -64800, -7045, -8570, -7569, -44910, -59535, -237600, -15635, -6550, 9, -450, -8505],194,22]
%
% END OF LATTICE L195.22
%
%
% LATTICE L195.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-37959120, 6524280, 16694640; 6524280, -1121328, -2869416; 16694640, -2869416, -7342399],[360, 72, 1],[-14397, -24191, -9162, -9216, -14846, -22013, -3021, -1936, 453, 507, -11281, -56368; -5, -10, -5, -7, -15, -30, -5, -5, 0, 2, 0, -15; -32733, -55000, -20830, -20952, -33750, -50040, -6867, -4400, 1030, 1152, -25650, -128160],194,23]
%
% END OF LATTICE L195.23
%
%
% LATTICE L195.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-448300128600, 60413850, -223461183600; 60413850, -7920, 30114090; -223461183600, 30114090, -111387210019],[450, 90, 1],[-3026312, -1971263, -391690, 298106, 153270, -600429, -635300, -774946, -523713, -4875121, -2899479, -7638198; 435, 283, 56, -45, -22, 89, 93, 113, 76, 705, 418, 1099; 6071283, 3954680, 785795, -598050, -307485, 1204560, 1274517, 1554670, 1050655, 9780300, 5816835, 15323490],194,24]
%
% END OF LATTICE L195.24
%
%
% LATTICE L195.25
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-15894021600, -11222550, -7922474100; -11222550, -7920, -5593950; -7922474100, -5593950, -3949006579],[450, 90, 1],[-105088, -22346, -12469, -19757, -50043, -117582, -218812, -26239, -3726, 3562, 1458, -28173; 1365, 293, 166, 267, 688, 1639, 3075, 373, 56, -45, -22, 359; 210825, 44830, 25015, 39636, 100395, 235890, 438975, 52640, 7475, -7146, -2925, 56520],194,25]
%
% END OF LATTICE L195.25
%
%
% LATTICE L195.26
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-49143600, -9048600, -17190000; -9048600, -1654320, -3165080; -17190000, -3165080, -6012911],[1800, 40, 1],[43999, 220105, 82082, 134144, 125726, 178235, 7843, 13184, -4319, -4539, 107563, 521632; 438, 2191, 817, 1335, 1251, 1773, 78, 131, -43, -45, 1071, 5193; -126017, -630400, -235090, -384200, -360090, -510480, -22463, -37760, 12370, 13000, -308070, -1494000],194,26]
%
% END OF LATTICE L195.26
%
%
% LATTICE L195.27
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-141483600, -16749000, -35281800; -16749000, -1978320, -4176680; -35281800, -4176680, -8798231],[1800, 40, 1],[131249, 298414, 53221, -2241, -2137, 19962, 41801, 168821, 102524, 19546, 54052, 135783; 2640, 6003, 1071, -45, -43, 401, 840, 3393, 2061, 393, 1087, 2731; -527575, -1199520, -213930, 9008, 8590, -80240, -168025, -678600, -412110, -78568, -217270, -545800],194,27]
%
% END OF LATTICE L195.27
%
%
% LATTICE L195.28
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[361800, -1731600, 88200; -1731600, -5420610, 340965; 88200, 340965, -20978],[1800, 45, 1],[-12159, -1002, 991, 2028, -18637, -24616, -51057, -10851, -16795, -21783, -28775, -10943; -29888, -2463, 2436, 4985, -45812, -60509, -125504, -26673, -41284, -53545, -70732, -26899; -536904, -44245, 43760, 89550, -822960, -1086975, -2254536, -479150, -741620, -961875, -1270620, -483210],194,28]
%
% END OF LATTICE L195.28
%
%
% LATTICE L195.29
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-790200, -162000, 9000; -162000, -31410, 1755; 9000, 1755, -98],[1800, 45, 1],[21, 0, -1, 0, 19, 22, 219, 9, 13, 3, 17, 5; 1000, 2, -44, -1, 828, 966, 9640, 397, 576, 134, 768, 231; 19800, 35, -880, -18, 16560, 19305, 192600, 7930, 11500, 2673, 15300, 4590],194,29]
%
% END OF LATTICE L195.29
%
%
% LATTICE L195.30
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-639738000, -581208840, -141750000; -581208840, -528034320, -128781360; -141750000, -128781360, -31408259],[360, 360, 1],[-5, -6, -3, -7, -1, -2, -5, -3, 0, 2, 0, -1; 9433, 14915, 11009, 36269, 7567, 20561, 62047, 49417, 10435, -529, -419, 883; -38655, -61128, -45126, -148680, -31022, -84296, -254385, -202608, -42786, 2160, 1718, -3616],194,30]
%
% END OF LATTICE L195.30
%
%
% LATTICE L195.31
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-4468323600, -411841800, -181130400; -411841800, -37959120, -16694640; -181130400, -16694640, -7342399],[1800, 360, 1],[-1, -1, 0, 2, 0, -3, -1, -2, -1, -7, -3, -6; 2556, 1471, -453, -1605, 11281, 54973, 13932, 23261, 8697, 42825, 13451, 19223; -5787, -3320, 1030, 3600, -25650, -124920, -31653, -52840, -19750, -97200, -30510, -43560],194,31]
%
% END OF LATTICE L195.31
%
%
% LATTICE L195.32
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-34743600, -67545000, 831879000; -67545000, -131235120, 1616271480; 831879000, 1616271480, -19905748759],[1800, 360, 1],[337922, 264919, 53221, -2257, -2137, 8797, 69578, 101831, 69029, 43007, 42887, 113453; -16902845, -13251248, -2662121, 112891, 106893, -440016, -3480245, -5093533, -3452806, -2151200, -2145202, -5674911; -1358325, -1064880, -213930, 9072, 8590, -35360, -279675, -409320, -277470, -172872, -172390, -456040],194,32]
%
% END OF LATTICE L195.32
%

\medskip%
%------------------------------WEYL-GROUP-W196--------------------------------
%
\leavevmode\llap{}%
$W_{196}$%
\qquad\llap{92} lattices, $\chi=36$%
\hfill%
$2222222222\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L196.1
%
\leavevmode%
${L_{196.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{4}8\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{2}{}9\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${45}\above{1pt}{1pt}{r}{2}{4}\above{1pt}{1pt}{*}{2}{72}\above{1pt}{1pt}{*}{2}{20}\above{1pt}{1pt}{*}{2}{8}\above{1pt}{1pt}{*}{2}{180}\above{1pt}{1pt}{l}{2}{1}\above{1pt}{1pt}{}{2}{72}\above{1pt}{1pt}{}{2}{5}\above{1pt}{1pt}{}{2}{8}\above{1pt}{1pt}{}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-34713720\\-239400\\-104400
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-239400\\-1651\\-720
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-104400\\-720\\-313
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
107\\-15435\\-180
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
25\\-3608\\-38
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
85\\-12276\\-108
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
17\\-2460\\-10
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\140\\12
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-79\\11340\\270
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-5\\719\\14
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-31\\4464\\72
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\145\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7\\-1008\\-16
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-34713720, -239400, -104400; -239400, -1651, -720; -104400, -720, -313],[360, 1, 1],[107, 25, 85, 17, -1, -79, -5, -31, -1, 7; -15435, -3608, -12276, -2460, 140, 11340, 719, 4464, 145, -1008; -180, -38, -108, -10, 12, 270, 14, 72, 0, -16],195,1]
%
% END OF LATTICE L196.1
%
\hbox{}\par\smallskip%
%
% LATTICE L196.2
%
\leavevmode%
${L_{196.2}}$%
{} : {$1\above{1pt}{1pt}{-2}{6}8\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{2}{}9\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{m}%
\EasyButWeakLineBreak%
{${45}\above{1pt}{1pt}{}{2}{1}\above{1pt}{1pt}{r}{2}{72}\above{1pt}{1pt}{l}{2}{5}\above{1pt}{1pt}{r}{2}{8}\above{1pt}{1pt}{l}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-388942920\\-2682360\\52200
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2682360\\-18499\\360
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
52200\\360\\-7
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
52919\\-7673400\\-52920
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
365\\-52926\\-365
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-7\\1015\\6
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
17\\-2475\\-540
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\-436\\-55
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
31\\-4500\\-288
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
6\\-870\\-5
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5\\-724\\48
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-388942920, -2682360, 52200; -2682360, -18499, 360; 52200, 360, -7],[360, 1, 1],[17, 3, 31, 6, 5, 28, 2, 5, -1, -1; -2475, -436, -4500, -870, -724, -4050, -289, -720, 145, 144; -540, -55, -288, -5, 48, 495, 50, 252, 0, -52],195,2]
%
% END OF LATTICE L196.2
%
\hbox{}\par\smallskip%
%
% LATTICE L196.3
%
\leavevmode%
${L_{196.3}}$%
{} : {$1\above{1pt}{1pt}{2}{6}8\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{2}{}9\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{1}{}$}\EasyButWeakLineBreak%
{${180}\above{1pt}{1pt}{*}{2}{4}\above{1pt}{1pt}{s}{2}{72}\above{1pt}{1pt}{s}{2}{20}\above{1pt}{1pt}{s}{2}{8}\above{1pt}{1pt}{s}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2359080\\1049040\\8280
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1049040\\-466489\\-3682
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
8280\\-3682\\-29
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
12959\\29160\\-3240
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-5764\\-12970\\1441
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-44\\-99\\10
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-403\\-900\\-810
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-35\\-78\\-92
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-49\\-108\\-288
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
31\\70\\-40
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
41\\92\\24
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-2359080, 1049040, 8280; 1049040, -466489, -3682; 8280, -3682, -29],[360, 1, 1],[-403, -35, -49, 31, 41, 763, 75, 193, 9, -25; -900, -78, -108, 70, 92, 1710, 168, 432, 20, -56; -810, -92, -288, -40, 24, 720, 82, 252, 30, -28],195,3]
%
% END OF LATTICE L196.3
%
\hbox{}\par\smallskip%
%
% LATTICE L196.4
%
\leavevmode%
${L_{196.4}}$%
{} : {$[1\above{1pt}{1pt}{1}{}2\above{1pt}{1pt}{1}{}]\above{1pt}{1pt}{}{2}16\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{2}{}9\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${180}\above{1pt}{1pt}{*}{2}{16}\above{1pt}{1pt}{s}{2}{72}\above{1pt}{1pt}{*}{2}{80}\above{1pt}{1pt}{*}{2}{8}\above{1pt}{1pt}{*}{2}{720}\above{1pt}{1pt}{l}{2}{1}\above{1pt}{1pt}{}{2}{18}\above{1pt}{1pt}{r}{2}{20}\above{1pt}{1pt}{l}{2}{2}\above{1pt}{1pt}{r}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
229680\\56880\\21600
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
56880\\14086\\5346
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
21600\\5346\\1993
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
259\\-1080\\90
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\4\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-635\\2646\\-216
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1291\\5380\\-440
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-657\\2738\\-224
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-30623\\127620\\-10440
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-836\\3484\\-285
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2693\\11223\\-918
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1027\\4280\\-350
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-6\\25\\-2
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[229680, 56880, 21600; 56880, 14086, 5346; 21600, 5346, 1993],[720, 2, 1],[259, -1, -635, -1291, -657, -30623, -836, -2693, -1027, -6; -1080, 4, 2646, 5380, 2738, 127620, 3484, 11223, 4280, 25; 90, 0, -216, -440, -224, -10440, -285, -918, -350, -2],195,4]
%
% END OF LATTICE L196.4
%
\hbox{}\par\smallskip%
%
% LATTICE L196.5
%
\leavevmode%
${L_{196.5}}$%
{} : {$[1\above{1pt}{1pt}{-}{}2\above{1pt}{1pt}{1}{}]\above{1pt}{1pt}{}{6}16\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{2}{}9\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{m}%
\EasyButWeakLineBreak%
{${45}\above{1pt}{1pt}{r}{2}{16}\above{1pt}{1pt}{*}{2}{72}\above{1pt}{1pt}{s}{2}{80}\above{1pt}{1pt}{s}{2}{8}\above{1pt}{1pt}{s}{2}{720}\above{1pt}{1pt}{*}{2}{4}\above{1pt}{1pt}{l}{2}{18}\above{1pt}{1pt}{}{2}{5}\above{1pt}{1pt}{}{2}{2}\above{1pt}{1pt}{}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-452880\\152640\\720
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
152640\\-51434\\-244
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
720\\-244\\-1
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
16\\45\\495
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-7\\-20\\-168
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-19\\-54\\-504
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7\\20\\160
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
19\\54\\496
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1331\\3780\\35280
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
81\\230\\2154
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
149\\423\\3978
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
37\\105\\995
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
6\\17\\166
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-452880, 152640, 720; 152640, -51434, -244; 720, -244, -1],[720, 2, 1],[16, -7, -19, 7, 19, 1331, 81, 149, 37, 6; 45, -20, -54, 20, 54, 3780, 230, 423, 105, 17; 495, -168, -504, 160, 496, 35280, 2154, 3978, 995, 166],195,5]
%
% END OF LATTICE L196.5
%
\hbox{}\par\smallskip%
%
% LATTICE L196.6
%
\leavevmode%
${L_{196.6}}$%
{} : {$[1\above{1pt}{1pt}{1}{}2\above{1pt}{1pt}{1}{}]\above{1pt}{1pt}{}{0}16\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{2}{}9\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{m}%
\EasyButWeakLineBreak%
{${180}\above{1pt}{1pt}{s}{2}{16}\above{1pt}{1pt}{l}{2}{18}\above{1pt}{1pt}{}{2}{80}\above{1pt}{1pt}{}{2}{2}\above{1pt}{1pt}{}{2}{720}\above{1pt}{1pt}{}{2}{1}\above{1pt}{1pt}{r}{2}{72}\above{1pt}{1pt}{*}{2}{20}\above{1pt}{1pt}{*}{2}{8}\above{1pt}{1pt}{*}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2159280\\8640\\8640
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
8640\\-34\\-36
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
8640\\-36\\-31
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
17\\3060\\1170
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7\\1256\\488
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
10\\1791\\702
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
17\\3040\\1200
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\357\\142
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
101\\18000\\7200
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\356\\143
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7\\1242\\504
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-180\\-70
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-178\\-72
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-2159280, 8640, 8640; 8640, -34, -36; 8640, -36, -31],[720, 2, 1],[17, 7, 10, 17, 2, 101, 2, 7, -1, -1; 3060, 1256, 1791, 3040, 357, 18000, 356, 1242, -180, -178; 1170, 488, 702, 1200, 142, 7200, 143, 504, -70, -72],195,6]
%
% END OF LATTICE L196.6
%
\hbox{}\par\smallskip%
%
% LATTICE L196.7
%
\leavevmode%
${L_{196.7}}$%
{} : {$[1\above{1pt}{1pt}{-}{}2\above{1pt}{1pt}{1}{}]\above{1pt}{1pt}{}{4}16\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{2}{}9\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{1}{}$}\EasyButWeakLineBreak%
{${45}\above{1pt}{1pt}{}{2}{16}\above{1pt}{1pt}{}{2}{18}\above{1pt}{1pt}{r}{2}{80}\above{1pt}{1pt}{l}{2}{2}\above{1pt}{1pt}{r}{2}{720}\above{1pt}{1pt}{s}{2}{4}\above{1pt}{1pt}{*}{2}{72}\above{1pt}{1pt}{l}{2}{5}\above{1pt}{1pt}{r}{2}{8}\above{1pt}{1pt}{l}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2720880\\7200\\7200
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7200\\-2\\-20
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7200\\-20\\-19
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
101\\1980\\36135
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
47\\920\\16816
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
41\\801\\14670
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
37\\720\\13240
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\19\\358
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\0\\360
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-20\\-358
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-18\\-360
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\40\\715
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7\\138\\2504
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-2720880, 7200, 7200; 7200, -2, -20; 7200, -20, -19],[720, 2, 1],[101, 47, 41, 37, 1, 1, -1, -1, 2, 7; 1980, 920, 801, 720, 19, 0, -20, -18, 40, 138; 36135, 16816, 14670, 13240, 358, 360, -358, -360, 715, 2504],195,7]
%
% END OF LATTICE L196.7
%
%
% LATTICE L196.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-7247970, 207090, -23940; 207090, -5917, 684; -23940, 684, -79],[90, 1, 1],[7, 4, 31, 16, 9, 128, 11, 23, -1, -3; 225, 140, 1098, 570, 322, 4590, 395, 828, -35, -108; -180, -1, 108, 85, 60, 945, 86, 198, 0, -26],195,8]
%
% END OF LATTICE L196.8
%
%
% LATTICE L196.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-244260, 97560, 3060; 97560, -38966, -1223; 3060, -1223, -37],[180, 1, 1],[1264, 116, 271, 2, -35, -274, -6, 125, 108, 79; 3105, 285, 666, 5, -86, -675, -15, 306, 265, 194; 1890, 172, 396, 0, -52, -360, -2, 216, 170, 120],195,9]
%
% END OF LATTICE L196.9
%
%
% LATTICE L196.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[160831620, -3655260, 83160; -3655260, 83074, -1890; 83160, -1890, 43],[180, 2, 1],[1, -1, 7, 21, 13, 673, 38, 128, 27, 2; 45, -44, 315, 940, 581, 30060, 1697, 5715, 1205, 89; 45, 0, 306, 700, 394, 19620, 1095, 3636, 745, 44],195,10]
%
% END OF LATTICE L196.10
%
%
% LATTICE L196.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[114840, 28800, -360; 28800, 7222, -90; -360, -90, 1],[360, 2, 1],[-11, -1, 13, 29, 15, 697, 38, 61, 23, 0; 45, 4, -54, -120, -62, -2880, -157, -252, -95, 0; 90, 4, -162, -340, -174, -8100, -442, -711, -270, -1],195,11]
%
% END OF LATTICE L196.11
%
%
% LATTICE L196.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[360, 0, 0; 0, 2, 0; 0, 0, -1],[360, 2, 1],[1, 0, -1, -1, -1, -23, -5, -4, -3, 0; 0, 1, 0, -5, -8, -225, -52, -45, -40, -1; 0, 0, -18, -20, -22, -540, -120, -99, -80, -1],195,12]
%
% END OF LATTICE L196.12
%
%
% LATTICE L196.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[791190, -93420, 384210; -93420, 11866, -45342; 384210, -45342, 186577],[90, 2, 1],[-82996, -12135, -27614, -19133, -3654, -88409, -6910, -6667, 88, -155; -4815, -704, -1602, -1110, -212, -5130, -401, -387, 5, -9; 169740, 24818, 56475, 39130, 7473, 180810, 14132, 13635, -180, 317],195,13]
%
% END OF LATTICE L196.13
%
%
% LATTICE L196.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[90, 0, 0; 0, 5, 0; 0, 0, -1],[90, 5, 1],[-8, -5, -19, -1, -1, -1, 0, 1, 0, -1; -45, -26, -90, -4, -2, 0, 1, 0, -1, -8; -126, -75, -270, -13, -10, -9, 0, 0, -2, -20],195,14]
%
% END OF LATTICE L196.14
%
%
% LATTICE L196.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[15429240, 334260, 3907620; 334260, 7244, 84656; 3907620, 84656, 989647],[180, 4, 1],[8657, 751, 901, 171, 21, 6283, 909, 2087, 1489, 311; 14940, 1294, 1548, 290, 36, 10890, 1576, 3618, 2580, 538; -35460, -3076, -3690, -700, -86, -25740, -3724, -8550, -6100, -1274],195,15]
%
% END OF LATTICE L196.15
%
%
% LATTICE L196.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[15030, 10530, 1800; 10530, 53397, 2538; 1800, 2538, 251],[90, 9, 1],[-1934, -2545, -1287, -4013, -1533, -2061, -1450, -311, 18, -65; -535, -704, -356, -1110, -424, -570, -401, -86, 5, -18; 19280, 25371, 12830, 40005, 15282, 20545, 14454, 3100, -180, 648],195,16]
%
% END OF LATTICE L196.16
%
%
% LATTICE L196.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3870, 0, -1890; 0, 10, 0; -1890, 0, -923],[90, 10, 1],[226, 145, 283, 31, 17, 35, 0, -22, -2, 12; -45, -26, -45, -4, -1, 0, 1, 0, -1, -4; -468, -300, -585, -64, -35, -72, 0, 45, 4, -25],195,17]
%
% END OF LATTICE L196.17
%
%
% LATTICE L196.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-121860, -540, 1260; -540, 10, 5; 1260, 5, -13],[180, 5, 1],[38, 20, 61, 2, -1, -2, 0, 11, 2, 9; 153, 79, 234, 7, -6, -9, 1, 54, 9, 38; 3708, 1950, 5940, 194, -100, -198, 0, 1080, 196, 880],195,18]
%
% END OF LATTICE L196.18
%
%
% LATTICE L196.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-5553720, 156960, -11880; 156960, -4436, 336; -11880, 336, -23],[360, 4, 1],[-73, -13, -23, 7, 11, 191, 9, 41, -1, -9; -2565, -457, -810, 245, 386, 6705, 316, 1440, -35, -316; 225, 36, 36, -40, -44, -720, -33, -144, 5, 32],195,19]
%
% END OF LATTICE L196.19
%
%
% LATTICE L196.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-10469880, -299160, -65520; -299160, -8548, -1872; -65520, -1872, -409],[360, 4, 1],[197, 19, 47, 1, -7, -107, -9, -11, 9, 11; -7110, -685, -1692, -35, 252, 3825, 320, 378, -330, -398; 990, 92, 216, 0, -32, -360, -22, 36, 70, 60],195,20]
%
% END OF LATTICE L196.20
%
%
% LATTICE L196.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-4985393310, -23042880, -2446560270; -23042880, -106506, -11308194; -2446560270, -11308194, -1200638903],[90, 18, 1],[-1438, -1997, -519, -3271, -597, -1347, -788, -38, 486, 40; 25, 140, 61, 570, 161, 510, 395, 46, -35, -54; 2930, 4068, 1057, 6660, 1215, 2740, 1602, 77, -990, -81],195,21]
%
% END OF LATTICE L196.21
%
%
% LATTICE L196.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[14940, -3060, 360; -3060, 558, -63; 360, -63, 7],[180, 9, 1],[-3, -3, -1, -1, 1, 3, 3, 1, 1, -1; -65, -65, -22, -25, 18, 55, 55, 18, 15, -22; -430, -432, -148, -180, 108, 340, 342, 112, 90, -144],195,22]
%
% END OF LATTICE L196.22
%
%
% LATTICE L196.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[7380, 900, 0; 900, 110, 0; 0, 0, -1],[180, 10, 1],[1, 1, -1, -1, -3, -29, -8, -26, -1, 0; -9, -8, 9, 8, 23, 216, 59, 189, 7, -1; -9, 0, 0, -4, -20, -252, -75, -270, -13, -10],195,23]
%
% END OF LATTICE L196.23
%
%
% LATTICE L196.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[360, 0, 0; 0, 5, 0; 0, 0, -1],[360, 5, 1],[-4, -5, -19, -1, -1, -1, 0, 1, 0, -1; -45, -52, -180, -8, -4, 0, 1, 0, -1, -16; -126, -150, -540, -26, -20, -18, 0, 0, -2, -40],195,24]
%
% END OF LATTICE L196.24
%
%
% LATTICE L196.25
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2408040, 0, 8640; 0, 5, 0; 8640, 0, -31],[360, 5, 1],[19, 10, 61, 1, -1, -1, 0, 11, 1, 9; -45, -26, -180, -4, -4, 0, 1, 0, -1, -16; 5274, 2775, 16920, 277, -280, -279, 0, 3060, 278, 2500],195,25]
%
% END OF LATTICE L196.25
%
%
% LATTICE L196.26
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-19080, 360, 360; 360, -5, -10; 360, -10, -1],[360, 5, 1],[37, 21, 71, 3, 1, -1, -1, 1, 1, 7; 1242, 704, 2376, 100, 32, -36, -34, 36, 34, 236; 648, 370, 1260, 54, 20, -18, -20, 0, 16, 120],195,26]
%
% END OF LATTICE L196.26
%
%
% LATTICE L196.27
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[113760, 360, -360; 360, -8, 0; -360, 0, 1],[360, 8, 1],[1, 0, -1, -2, -1, -46, -5, -4, -3, 0; 45, 1, -36, -75, -38, -1755, -191, -153, -115, 0; 360, 4, -342, -700, -354, -16380, -1784, -1431, -1080, -1],195,27]
%
% END OF LATTICE L196.27
%
%
% LATTICE L196.28
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[360, 0, 0; 0, 8, 0; 0, 0, -1],[360, 8, 1],[1, 0, -1, -2, -1, -46, -5, -8, -3, 0; 0, 1, 0, -5, -4, -225, -26, -45, -20, -1; 0, 0, -18, -40, -22, -1080, -120, -198, -80, -2],195,28]
%
% END OF LATTICE L196.28
%
%
% LATTICE L196.29
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-204840, 10080, -2520; 10080, -488, 120; -2520, 120, -29],[360, 8, 1],[11, 0, -2, -2, 0, 34, 5, 11, 7, 1; 450, 1, -81, -85, -3, 1215, 184, 414, 270, 40; 900, 4, -162, -180, -14, 1980, 316, 738, 500, 78],195,29]
%
% END OF LATTICE L196.29
%
%
% LATTICE L196.30
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1328220, 332100, -7560; 332100, -83034, 1890; -7560, 1890, -43],[180, 18, 1],[4, -1, -1, 1, 9, 77, 43, 18, 42, 8; 20, -4, -5, 0, 41, 360, 202, 85, 200, 39; 175, 0, -44, -180, 216, 2260, 1305, 566, 1395, 306],195,30]
%
% END OF LATTICE L196.30
%
%
% LATTICE L196.31
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-5026680, -335160, -162000; -335160, -22347, -10800; -162000, -10800, -5209],[360, 9, 1],[-283, -625, -257, -577, -91, -9, 25, 27, 1, -139; 4525, 9992, 4108, 9220, 1452, 140, -401, -432, -15, 2224; -580, -1278, -524, -1170, -180, -10, 54, 56, 0, -288],195,31]
%
% END OF LATTICE L196.31
%
%
% LATTICE L196.32
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-652680, 43560, -2160; 43560, -2907, 144; -2160, 144, -7],[360, 9, 1],[-7, -7, -5, -4, 1, 2, 2, 1, -1, -5; -115, -116, -84, -70, 12, 30, 31, 16, -15, -80; -220, -243, -200, -225, -72, -5, 18, 20, 0, -108],195,32]
%
% END OF LATTICE L196.32
%
%
% LATTICE L196.33
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[8280, -1440, 720; -1440, 171, -81; 720, -81, 38],[360, 9, 1],[-3, -3, -1, -1, 1, 3, 3, 1, 1, -1; -190, -194, -68, -90, 44, 150, 154, 52, 50, -60; -350, -360, -128, -180, 72, 260, 270, 92, 90, -108],195,33]
%
% END OF LATTICE L196.33
%
%
% LATTICE L196.34
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-43560, 4680, 1080; 4680, -370, -80; 1080, -80, -17],[360, 10, 1],[1, 1, -1, -1, -3, -29, -8, -13, -1, 0; 63, 60, -72, -64, -188, -1800, -495, -801, -61, 1; -234, -220, 270, 236, 690, 6588, 1810, 2925, 222, -5],195,34]
%
% END OF LATTICE L196.34
%
%
% LATTICE L196.35
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1410120, 0, 9720; 0, 10, 0; 9720, 0, 67],[360, 10, 1],[1, 0, 13, 3, 17, 85, 95, 79, 13, 1; 0, 1, 0, -1, -8, -45, -52, -45, -8, -1; -144, 0, -1890, -436, -2470, -12348, -13800, -11475, -1888, -145],195,35]
%
% END OF LATTICE L196.35
%
%
% LATTICE L196.36
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[12512520, -68220, 3055680; -68220, 380, -16660; 3055680, -16660, 746227],[180, 20, 1],[9635, 5343, 8813, 715, 105, 211, 127, 1033, 379, 989; -90, -52, -90, -8, -2, 0, 2, 0, -2, -8; -39456, -21880, -36090, -2928, -430, -864, -520, -4230, -1552, -4050],195,36]
%
% END OF LATTICE L196.36
%
%
% LATTICE L196.37
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[90, 90, 0; 90, 45, 0; 0, 0, 1],[90, 45, 1],[6, 30, 11, 4, 1, 0, 0, 1, 2, 11; -17, -86, -32, -12, -4, 0, 1, -2, -5, -30; 46, 225, 80, 27, 0, -1, 0, 10, 18, 90],195,37]
%
% END OF LATTICE L196.37
%
%
% LATTICE L196.38
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-150480, 5040, 2160; 5040, -136, -72; 2160, -72, -31],[720, 8, 1],[17, 7, 20, 17, 4, 101, 2, 7, -1, -1; 0, -2, -9, -10, -3, -90, -2, -9, 0, 1; 1170, 488, 1404, 1200, 284, 7200, 143, 504, -70, -72],195,38]
%
% END OF LATTICE L196.38
%
%
% LATTICE L196.39
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-29936880, 680400, -174240; 680400, -15464, 3960; -174240, 3960, -1013],[720, 8, 1],[-2431, -132, -422, -79, 0, 23, -1, -55, -107, -53; -109620, -5953, -19035, -3565, -1, 1035, -44, -2475, -4820, -2389; -10440, -570, -1836, -350, -4, 90, 0, -216, -440, -224],195,39]
%
% END OF LATTICE L196.39
%
%
% LATTICE L196.40
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1109520, 3600, 1440; 3600, 136, -16; 1440, -16, -1],[720, 8, 1],[133, 8, 29, 7, 1, 1, -1, -2, 1, 2; 6570, 395, 1431, 345, 49, 45, -50, -99, 50, 99; 85680, 5154, 18684, 4510, 644, 630, -648, -1296, 640, 1288],195,40]
%
% END OF LATTICE L196.40
%
%
% LATTICE L196.41
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-594474480, 13510800, -4546080; 13510800, -307064, 103320; -4546080, 103320, -34763],[720, 8, 1],[106, -1, -109, -143, -35, -379, 3, 118, 37, 36; 4770, -44, -4905, -6440, -1579, -17280, 122, 5265, 1660, 1619; 315, 0, -324, -440, -116, -1800, -30, 216, 95, 104],195,41]
%
% END OF LATTICE L196.41
%
%
% LATTICE L196.42
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2235240, 443880, -12600; 443880, -88146, 2502; -12600, 2502, -71],[360, 18, 1],[4, -1, -1, 1, 9, 77, 43, 9, 42, 4; 25, -4, -6, 0, 50, 440, 247, 52, 245, 24; 170, 36, -34, -180, 162, 1820, 1062, 233, 1170, 135],195,42]
%
% END OF LATTICE L196.42
%
%
% LATTICE L196.43
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2819160, 0, 15840; 0, 18, 0; 15840, 0, -89],[360, 18, 1],[9, 0, -1, -1, 7, 33, 75, 8, 77, 4; 0, 1, 0, -5, -8, -25, -52, -5, -40, -1; 1600, 0, -178, -180, 1242, 5860, 13320, 1421, 13680, 711],195,43]
%
% END OF LATTICE L196.43
%
%
% LATTICE L196.44
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[4816440, -155340, 1176480; -155340, 5004, -37944; 1176480, -37944, 287371],[180, 36, 1],[171, 361, 115, 837, 163, 269, 79, -27, -397, -75; 0, 14, 6, 50, 10, 10, -4, -4, -40, -8; -700, -1476, -470, -3420, -666, -1100, -324, 110, 1620, 306],195,44]
%
% END OF LATTICE L196.44
%
%
% LATTICE L196.45
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-720, -2160, 1440; -2160, 10, 20; 1440, 20, -31],[720, 10, 1],[-31, -7, -8, 0, 1, 1, -1, -11, -3, -5; -1764, -404, -477, -2, 53, 54, -52, -594, -164, -278; -2664, -610, -720, -3, 80, 81, -80, -900, -248, -420],195,45]
%
% END OF LATTICE L196.45
%
%
% LATTICE L196.46
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-475920, -5040, -5760; -5040, 10, 0; -5760, 0, -11],[720, 10, 1],[29, 4, 13, 1, 0, -1, -1, 1, 1, 3; 14652, 2020, 6561, 504, -1, -504, -500, 522, 508, 1518; -15264, -2105, -6840, -526, 0, 522, 520, -540, -528, -1580],195,46]
%
% END OF LATTICE L196.46
%
%
% LATTICE L196.47
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[461520, 115920, -720; 115920, 29110, -180; -720, -180, 1],[720, 10, 1],[17, -1, -13, 0, 11, 43, 107, 101, 21, 5; -72, 4, 54, 0, -46, -180, -448, -423, -88, -21; -648, 10, 360, -1, -360, -1413, -3520, -3330, -696, -170],195,47]
%
% END OF LATTICE L196.47
%
%
% LATTICE L196.48
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[4565520, 5760, -9360; 5760, -10, -10; -9360, -10, 19],[720, 10, 1],[-47, -6, -35, -1, 1, 1, -1, -5, -3, -3; -2664, -341, -1998, -58, 54, 54, -56, -279, -168, -169; -24624, -3145, -18360, -526, 520, 522, -520, -2610, -1568, -1570],195,48]
%
% END OF LATTICE L196.48
%
%
% LATTICE L196.49
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[360, 0, 0; 0, -20, 0; 0, 0, 1],[360, 20, 1],[-1, 0, 1, 0, -1, -4, -5, -19, -1, -1; 9, 1, 0, 0, 4, 18, 23, 90, 5, 6; 36, 5, 0, -1, 0, 27, 40, 180, 12, 20],195,49]
%
% END OF LATTICE L196.49
%
%
% LATTICE L196.50
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[360, 0, 0; 0, 20, 0; 0, 0, -1],[360, 20, 1],[-8, -5, -19, -1, -1, -1, 0, 1, 0, -1; -45, -26, -90, -4, -2, 0, 1, 0, -1, -8; -252, -150, -540, -26, -20, -18, 0, 0, -4, -40],195,50]
%
% END OF LATTICE L196.50
%
%
% LATTICE L196.51
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-90, 180, 90; 180, 3870, 1890; 90, 1890, 923],[90, 90, 1],[-5, -26, -5, -4, -1, 0, 1, 0, -1, -4; 438, 2239, 422, 325, 66, 1, -44, 17, 114, 373; -898, -4590, -865, -666, -135, -2, 90, -35, -234, -765],195,51]
%
% END OF LATTICE L196.51
%
%
% LATTICE L196.52
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-180, 0, -180; 0, 90, 45; -180, 45, -157],[180, 45, 1],[86, 420, 149, 50, -1, -2, 0, 19, 34, 169; 41, 199, 70, 23, -2, -1, 1, 10, 17, 82; -92, -450, -160, -54, 0, 2, 0, -20, -36, -180],195,52]
%
% END OF LATTICE L196.52
%
%
% LATTICE L196.53
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-4211280, -1056240, -522720; -1056240, -264906, -131076; -522720, -131076, -64813],[720, 18, 1],[381, -1, -85, -171, 593, 5593, 1589, 678, 3263, 339; -1910, 4, 426, 860, -2970, -28020, -7961, -3397, -16350, -1699; 790, 0, -176, -360, 1224, 11560, 3285, 1402, 6750, 702],195,53]
%
% END OF LATTICE L196.53
%
%
% LATTICE L196.54
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-942480, 50400, -6480; 50400, -2682, 342; -6480, 342, -43],[720, 18, 1],[2, -1, -1, 1, 9, 77, 43, 9, 21, 4; 60, -28, -30, 20, 262, 2260, 1264, 265, 620, 119; 175, -72, -88, 0, 720, 6320, 3546, 746, 1755, 342],195,54]
%
% END OF LATTICE L196.54
%
%
% LATTICE L196.55
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[6112080, 195120, -15840; 195120, 6174, -504; -15840, -504, 41],[720, 18, 1],[-7, -13, -1, -3, 1, 9, 2, 1, -1, -3; -140, -264, -21, -80, 17, 160, 36, 18, -20, -58; -4430, -8280, -646, -2160, 594, 5440, 1215, 608, -630, -1872],195,55]
%
% END OF LATTICE L196.55
%
%
% LATTICE L196.56
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-8475120, -660960, 77760; -660960, -51282, 6030; 77760, 6030, -709],[720, 18, 1],[29, 127, 13, 117, 5, 9, -1, -1, 2, 15; -4045, -17704, -1811, -16280, -693, -1240, 142, 138, -285, -2098; -31225, -136656, -13978, -125640, -5346, -9560, 1098, 1064, -2205, -16200],195,56]
%
% END OF LATTICE L196.56
%
%
% LATTICE L196.57
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-105480, -9720, -1440; -9720, 1548, -432; -1440, -432, 17],[360, 36, 1],[-117, -257, -105, -233, -35, -1, 11, 11, -1, -59; 575, 1263, 516, 1145, 172, 5, -54, -54, 5, 290; 4705, 10332, 4220, 9360, 1404, 40, -441, -440, 45, 2376],195,57]
%
% END OF LATTICE L196.57
%
%
% LATTICE L196.58
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[4680, -1080, 0; -1080, 252, 0; 0, 0, -1],[360, 36, 1],[3, 3, 1, 1, -1, -3, -3, -1, -1, 1; 10, 11, 4, 5, -4, -15, -16, -6, -10, 2; -50, -36, -8, 0, 0, -40, -54, -28, -90, -36],195,58]
%
% END OF LATTICE L196.58
%
%
% LATTICE L196.59
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[14760, 720, -8280; 720, -40, -160; -8280, -160, 3853],[360, 40, 1],[29, 8, -109, -50, -133, -1262, -693, -562, -87, -2; 234, 65, -873, -401, -1067, -10125, -5560, -4509, -698, -16; 72, 20, -270, -124, -330, -3132, -1720, -1395, -216, -5],195,59]
%
% END OF LATTICE L196.59
%
%
% LATTICE L196.60
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1410120, 0, 9720; 0, 40, 0; 9720, 0, 67],[360, 40, 1],[1, 0, 13, 6, 17, 170, 95, 158, 13, 2; 0, 1, 0, -1, -4, -45, -26, -45, -4, -1; -144, 0, -1890, -872, -2470, -24696, -13800, -22950, -1888, -290],195,60]
%
% END OF LATTICE L196.60
%
%
% LATTICE L196.61
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-617040, -228600, 3240; -228600, -84680, 1200; 3240, 1200, -17],[360, 40, 1],[-2, -1, 1, 1, 3, 29, 16, 26, 2, 0; 9, 3, -9, -5, -13, -117, -63, -99, -7, 1; 252, 20, -450, -164, -350, -2772, -1420, -2070, -116, 70],195,61]
%
% END OF LATTICE L196.61
%
%
% LATTICE L196.62
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[180, 0, 0; 0, -13342410, 303660; 0, 303660, -6911],[180, 90, 1],[-5, -13, -5, -2, -1, 0, 1, 0, -1, -4; -52, -210, -117, -76, -127, -16, 0, 33, 68, 43; -2284, -9225, -5140, -3339, -5580, -703, 0, 1450, 2988, 1890],195,62]
%
% END OF LATTICE L196.62
%
%
% LATTICE L196.63
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2819160, 0, 15840; 0, 45, 0; 15840, 0, -89],[360, 45, 1],[-1, 0, 9, 8, 79, 20, 195, 69, 23, -1; 0, 1, 0, -1, -16, -5, -52, -20, -8, -4; -178, 0, 1600, 1422, 14040, 3554, 34650, 12260, 4086, -180],195,63]
%
% END OF LATTICE L196.63
%
%
% LATTICE L196.64
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-46267560, 0, 128880; 0, 45, 0; 128880, 0, -359],[360, 45, 1],[-1, 0, 19, 17, 169, 43, 210, 149, 25, -1; 0, 1, 0, -1, -16, -5, -26, -20, -4, -4; -359, 0, 6820, 6102, 60660, 15434, 75375, 53480, 8973, -360],195,64]
%
% END OF LATTICE L196.64
%
%
% LATTICE L196.65
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2948040, 16200, 16200; 16200, -45, -90; 16200, -90, -89],[360, 45, 1],[-1, -1, 9, 17, 87, 45, 221, 79, 27, 1; -4, -2, 36, 66, 332, 170, 832, 296, 100, 0; -178, -180, 1600, 3024, 15480, 8008, 39330, 14060, 4806, 180],195,65]
%
% END OF LATTICE L196.65
%
%
% LATTICE L196.66
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2235960, -460080, 12600; -460080, -94536, 2592; 12600, 2592, -71],[360, 72, 1],[9, 0, -1, -2, 7, 66, 75, 8, 77, 4; 10, 1, -1, -5, 5, 55, 64, 7, 70, 4; 1960, 36, -214, -540, 1422, 13700, 15624, 1673, 16200, 855],195,66]
%
% END OF LATTICE L196.66
%
%
% LATTICE L196.67
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2819160, 0, 15840; 0, 72, 0; 15840, 0, -89],[360, 72, 1],[9, 0, -1, -2, 7, 66, 75, 16, 77, 8; 0, 1, 0, -5, -4, -25, -26, -5, -20, -1; 1600, 0, -178, -360, 1242, 11720, 13320, 2842, 13680, 1422],195,67]
%
% END OF LATTICE L196.67
%
%
% LATTICE L196.68
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-360, 12960, -360; 12960, -444456, 12312; -360, 12312, -341],[360, 72, 1],[19, 0, -2, -2, 16, 146, 165, 35, 167, 17; 10, 1, -1, -5, 5, 55, 64, 14, 70, 8; 340, 36, -34, -180, 162, 1820, 2124, 466, 2340, 270],195,68]
%
% END OF LATTICE L196.68
%
%
% LATTICE L196.69
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[7999920, -999360, 2880; -999360, 124840, -360; 2880, -360, 1],[720, 40, 1],[23, 57, 107, 11, 5, 7, -1, -8, 0, 6; 180, 446, 837, 86, 39, 54, -8, -63, 0, 47; -1413, -3520, -6660, -696, -340, -648, 10, 360, -1, -360],195,69]
%
% END OF LATTICE L196.69
%
%
% LATTICE L196.70
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[29520, 3600, 0; 3600, 440, 0; 0, 0, -1],[720, 40, 1],[-29, -8, -26, -1, 0, 1, 1, -1, -1, -3; 216, 59, 189, 7, -1, -9, -8, 9, 8, 23; -504, -150, -540, -26, -20, -18, 0, 0, -8, -40],195,70]
%
% END OF LATTICE L196.70
%
%
% LATTICE L196.71
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-9085680, 1080000, -10080; 1080000, -128360, 1200; -10080, 1200, -11],[720, 40, 1],[-7, -1, 34, 13, 30, 257, 34, 209, 7, -3; -54, -8, 261, 100, 231, 1980, 262, 1611, 54, -23; 522, 40, -2700, -1008, -2300, -19584, -2585, -15840, -526, 240],195,71]
%
% END OF LATTICE L196.71
%
%
% LATTICE L196.72
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[431280, 61200, -2880; 61200, 8360, -400; -2880, -400, 19],[720, 40, 1],[-47, -12, -35, -1, 1, 1, -1, -10, -3, -6; -486, -125, -369, -11, 9, 9, -10, -99, -30, -61; -17424, -4470, -13140, -386, 340, 342, -360, -3600, -1088, -2200],195,72]
%
% END OF LATTICE L196.72
%
%
% LATTICE L196.73
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2430360, 495720, -13680; 495720, 101070, -2790; -13680, -2790, 77],[360, 90, 1],[11, 32, 7, 7, 4, 1, 1, -1, -1, 5; 4, 15, 4, 5, 4, 1, 0, -2, -4, -2; 2092, 6210, 1385, 1422, 855, 214, 180, -250, -324, 810],195,73]
%
% END OF LATTICE L196.73
%
%
% LATTICE L196.74
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-807480, 0, 3240; 0, 90, 0; 3240, 0, -13],[360, 90, 1],[1, 15, 2, 5, 2, 1, 0, -1, -1, -1; -5, -52, -5, -8, -1, 0, 1, 0, -1, -8; 236, 3600, 485, 1224, 495, 248, 0, -250, -252, -270],195,74]
%
% END OF LATTICE L196.74
%
%
% LATTICE L196.75
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[4140, 40500, 10080; 40500, 404280, 100620; 10080, 100620, 25043],[180, 180, 1],[-10, -52, -10, -8, -2, 0, 2, 0, -2, -8; -1073, -5325, -967, -689, -67, -1, -45, -107, -385, -1007; 4316, 21420, 3890, 2772, 270, 4, 180, 430, 1548, 4050],195,75]
%
% END OF LATTICE L196.75
%
%
% LATTICE L196.76
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[16386480, 637200, -25920; 637200, 24696, -1008; -25920, -1008, 41],[720, 72, 1],[-7, -13, -2, -3, 2, 9, 2, 1, -1, -3; 0, -2, -1, -10, -3, -10, -2, -1, 0, 1; -4430, -8280, -1292, -2160, 1188, 5440, 1215, 608, -630, -1872],195,76]
%
% END OF LATTICE L196.76
%
%
% LATTICE L196.77
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-5312880, 1328400, 649440; 1328400, -332136, -162360; 649440, -162360, -79333],[720, 72, 1],[-2183, -1262, -548, -1353, -298, -171, -1, 43, 181, -207; -10940, -6323, -2745, -6775, -1491, -855, -4, 215, 900, -1039; 4520, 2610, 1132, 2790, 612, 350, 0, -88, -360, 432],195,77]
%
% END OF LATTICE L196.77
%
%
% LATTICE L196.78
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[720, -6480, -2880; -6480, -10728, -4680; -2880, -4680, -2041],[720, 72, 1],[77, 43, 18, 42, 8, 4, -1, -1, 1, 9; -2800, -1571, -661, -1555, -303, -155, 32, 39, 0, -319; 6320, 3546, 1492, 3510, 684, 350, -72, -88, 0, 720],195,78]
%
% END OF LATTICE L196.78
%
%
% LATTICE L196.79
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-49376880, 12344400, -46080; 12344400, -3086136, 11520; -46080, 11520, -43],[720, 72, 1],[2, -1, -1, 1, 9, 77, 43, 18, 21, 8; 10, -4, -5, 0, 41, 360, 202, 85, 100, 39; 535, 0, -268, -1080, 1332, 13880, 8010, 3472, 4275, 1872],195,79]
%
% END OF LATTICE L196.79
%
%
% LATTICE L196.80
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-4556880, -480240, 18000; -480240, -50130, 1890; 18000, 1890, -71],[720, 90, 1],[1, -1, -3, -3, 11, 25, 73, 16, 8, 9; 6, -4, -18, -20, 58, 140, 412, 91, 46, 53; 413, -360, -1240, -1296, 4320, 10048, 29430, 6470, 3249, 3690],195,80]
%
% END OF LATTICE L196.80
%
%
% LATTICE L196.81
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[163440, -3796560, 86400; -3796560, 87099210, -1982160; 86400, -1982160, 45109],[720, 90, 1],[1, 1, -1, -1, 5, 11, 16, 7, 7, 4; -204, -172, 238, 308, -774, -1996, -2962, -1321, -1356, -815; -8966, -7560, 10460, 13536, -34020, -87728, -130185, -58060, -59598, -35820],195,81]
%
% END OF LATTICE L196.81
%
%
% LATTICE L196.82
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2666160, 16560, 28800; 16560, -90, -180; 28800, -180, -311],[720, 90, 1],[9, 173, 15, 19, -1, -1, 1, 5, 4, 37; 76, 1472, 129, 168, -5, -8, 4, 38, 32, 306; 787, 15120, 1310, 1656, -90, -88, 90, 440, 351, 3240],195,82]
%
% END OF LATTICE L196.82
%
%
% LATTICE L196.83
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-480240, -2499120, 56880; -2499120, -12993930, 295740; 56880, 295740, -6731],[720, 90, 1],[1, -1, -1, -3, 1, 9, 14, 13, 7, 9; -24, -8, 25, 112, 51, -32, -98, -130, -96, -182; -1046, -360, 1090, 4896, 2250, -1328, -4185, -5600, -4158, -7920],195,83]
%
% END OF LATTICE L196.83
%
%
% LATTICE L196.84
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-360, 16200, -360; 16200, -633780, 14040; -360, 14040, -311],[360, 180, 1],[20, 195, 69, 23, -1, -1, 0, 9, 8, 79; 18, 173, 60, 19, -4, -1, 1, 10, 8, 74; 787, 7560, 2620, 828, -180, -44, 45, 440, 351, 3240],195,84]
%
% END OF LATTICE L196.84
%
%
% LATTICE L196.85
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2819160, 0, 15840; 0, 180, 0; 15840, 0, -89],[360, 180, 1],[-1, 0, 9, 16, 79, 40, 195, 69, 23, -1; 0, 1, 0, -1, -8, -5, -26, -10, -4, -2; -178, 0, 1600, 2844, 14040, 7108, 34650, 12260, 4086, -180],195,85]
%
% END OF LATTICE L196.85
%
%
% LATTICE L196.86
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[4907880, 3453840, -19440; 3453840, 2430360, -13680; -19440, -13680, 77],[360, 360, 1],[2, 15, 2, 5, 2, 1, 0, -1, -2, -1; 11, 64, 7, 14, 4, 2, 1, -1, -1, 5; 2452, 15120, 1745, 3744, 1215, 608, 180, -430, -684, 630],195,86]
%
% END OF LATTICE L196.86
%
%
% LATTICE L196.87
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-807480, 0, 3240; 0, 360, 0; 3240, 0, -13],[360, 360, 1],[2, 15, 4, 5, 4, 1, 0, -1, -2, -1; -5, -26, -5, -4, -1, 0, 1, 0, -1, -4; 472, 3600, 970, 1224, 990, 248, 0, -250, -504, -270],195,87]
%
% END OF LATTICE L196.87
%
%
% LATTICE L196.88
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1104120, 868320, -5040; 868320, 680760, -3960; -5040, -3960, 23],[360, 360, 1],[18, 105, 23, 23, 13, 3, 0, -2, -2, 8; 11, 64, 14, 14, 8, 2, 1, -1, -1, 5; 5836, 34020, 7450, 7452, 4230, 1004, 180, -610, -612, 2610],195,88]
%
% END OF LATTICE L196.88
%
%
% LATTICE L196.89
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2535120, 32400, 28080; 32400, -360, -360; 28080, -360, -311],[720, 360, 1],[-1, 1, 5, 4, 37, 9, 173, 30, 19, -2; -2, 0, 9, 8, 79, 20, 390, 69, 46, -1; -88, 90, 440, 351, 3240, 787, 15120, 2620, 1656, -180],195,89]
%
% END OF LATTICE L196.89
%
%
% LATTICE L196.90
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[720, 0, 0; 0, -659160, -162720; 0, -162720, -40169],[720, 360, 1],[0, 1, 0, -1, -4, -5, -13, -5, -2, -1; -39, 0, 79, 160, 89, -144, -555, -301, -191, -311; 158, 0, -320, -648, -360, 584, 2250, 1220, 774, 1260],195,90]
%
% END OF LATTICE L196.90
%
%
% LATTICE L196.91
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[13867920, 9117360, -38880; 9117360, 5993640, -25560; -38880, -25560, 109],[720, 360, 1],[11, 16, 14, 7, 8, 1, 1, -1, -1, 5; 20, 30, 27, 14, 17, 2, 0, -3, -4, 7; 8608, 12735, 11320, 5778, 6840, 826, 360, -1060, -1296, 3420],195,91]
%
% END OF LATTICE L196.91
%
%
% LATTICE L196.92
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-841680, -746640, -184320; -746640, -656280, -162000; -184320, -162000, -39989],[720, 360, 1],[1, -1, -2, -3, 2, 9, 28, 13, 7, 9; -129, 90, 259, 430, -91, -954, -3075, -1471, -821, -1121; 518, -360, -1040, -1728, 360, 3824, 12330, 5900, 3294, 4500],195,92]
%
% END OF LATTICE L196.92
%

\medskip%
%------------------------------WEYL-GROUP-W197--------------------------------
%
\leavevmode\llap{}%
$W_{197}$%
\qquad\llap{4} lattices, $\chi=24$%
\hfill%
$4|4\slashtwo4|4\slashtwo\rtimes D_{4}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L197.1
%
\leavevmode%
${L_{197.1}}$%
{} : {$1\above{1pt}{1pt}{2}{2}32\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{1}{}$}\EasyButWeakLineBreak%
{${1}\above{1pt}{1pt}{}{4}{2}\above{1pt}{1pt}{*}{4}{4}\above{1pt}{1pt}{l}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1347936\\11328\\5664
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
11328\\-95\\-48
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5664\\-48\\-23
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7039\\670560\\332640
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-60\\-5716\\-2835
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-28\\-2667\\-1324
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-95\\-48
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\287\\139
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
9\\858\\424
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-1347936, 11328, 5664; 11328, -95, -48; 5664, -48, -23],[96, 1, 1],[-1, 3, 9, 5, 5, -1; -95, 287, 858, 476, 475, -96; -48, 139, 424, 237, 239, -46],196,1]
%
% END OF LATTICE L197.1
%
%
% LATTICE L197.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1438752, 20256, -368160; 20256, -285, 5184; -368160, 5184, -94205],[96, 3, 1],[13, -74, -72, -127, -40, 15; 160, -949, -916, -1606, -497, 193; -42, 237, 231, 408, 129, -48],196,2]
%
% END OF LATTICE L197.2
%
%
% LATTICE L197.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2496, -96, -960; -96, 32, 0; -960, 0, -331],[96, 32, 1],[0, 11, -28, -67, -145, -39; -1, 34, -81, -197, -430, -117; 0, -32, 80, 192, 416, 112],196,3]
%
% END OF LATTICE L197.3
%
%
% LATTICE L197.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[192, 96, 0; 96, 96, 0; 0, 0, -1],[96, 96, 1],[0, -5, -4, -3, -1, 1; -5, -14, -5, -1, 2, -1; -48, -192, -96, -48, 0, 0],196,4]
%
% END OF LATTICE L197.4
%

\medskip%
%------------------------------WEYL-GROUP-W198--------------------------------
%
\leavevmode\llap{}%
$W_{198}$%
\qquad\llap{8} lattices, $\chi=32$%
\hfill%
$62\infty62\infty\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L198.1
%
\leavevmode%
${L_{198.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}32\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{1}{}3\above{1pt}{1pt}{-}{}9\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{3}%
\EasyButWeakLineBreak%
{${6}\above{1pt}{1pt}{}{6}{18}\above{1pt}{1pt}{b}{2}{6}\above{1pt}{1pt}{24,7}{\infty a}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3322656\\-643968\\-453600
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-643968\\-124806\\-87915
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-453600\\-87915\\-61922
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-250561\\760320\\756000
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-48546\\147311\\146475
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-34220\\103840\\103249
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-150\\457\\450
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
110\\-333\\-333
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
43\\-131\\-129
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-3322656, -643968, -453600; -643968, -124806, -87915; -453600, -87915, -61922],[288, 3, 1],[-150, 110, 43, -372, -632, -217; 457, -333, -131, 1127, 1917, 659; 450, -333, -129, 1125, 1908, 654],197,1]
%
% END OF LATTICE L198.1
%
%
% LATTICE L198.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-79392, -2688, 4512; -2688, -90, 137; 4512, 137, -10],[96, 1, 1],[-98, 1, 34, -1, -34, -67; 3243, -33, -1125, 33, 1125, 2217; 207, -2, -72, 0, 71, 141],197,2]
%
% END OF LATTICE L198.2
%
%
% LATTICE L198.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-198240, 4224, 2112; 4224, -90, -45; 2112, -45, -22],[96, 3, 1],[0, -1, 0, 3, 4, 1; 3, -47, -1, 141, 191, 49; -7, 0, 2, -2, -9, -5],197,3]
%
% END OF LATTICE L198.3
%
%
% LATTICE L198.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-511776, -2592, 2304; -2592, 6, 9; 2304, 9, -10],[288, 3, 1],[3, 0, -1, 0, 1, 2; 107, -1, -37, 1, 37, 73; 783, -2, -264, 0, 263, 525],197,4]
%
% END OF LATTICE L198.4
%
%
% LATTICE L198.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[192, 288, -288; 288, -320, 128; -288, 128, 15],[96, 32, 1],[107, -1, -37, 1, 37, 73; 207, -2, -72, 0, 71, 141; 288, 0, -96, 0, 96, 192],197,5]
%
% END OF LATTICE L198.5
%
%
% LATTICE L198.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2880, 87648, 2784; 87648, -2649792, -84192; 2784, -84192, -2675],[96, 96, 1],[3, -47, -1, 141, 191, 49; -7, 32, 2, -98, -137, -37; 224, -1056, -64, 3232, 4512, 1216],197,6]
%
% END OF LATTICE L198.6
%
%
% LATTICE L198.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-19850688, -207072, 202464; -207072, -2112, 2112; 202464, 2112, -2065],[288, 96, 1],[141, 191, 49, 3, -47, -1; -2, -9, -5, -7, 0, 2; 13824, 18720, 4800, 288, -4608, -96],197,7]
%
% END OF LATTICE L198.7
%
%
% LATTICE L198.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[590400, 266400, -72576; 266400, 118848, -31392; -72576, -31392, 7567],[288, 96, 1],[-2266, 21, 787, 1, -776, -1542; 6905, -64, -2398, -2, 2365, 4699; 6912, -64, -2400, 0, 2368, 4704],197,8]
%
% END OF LATTICE L198.8
%

\medskip%
%------------------------------WEYL-GROUP-W199--------------------------------
%
\leavevmode\llap{}%
$W_{199}$%
\qquad\llap{8} lattices, $\chi=12$%
\hfill%
$222|222|\rtimes D_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L199.1
%
\leavevmode%
${L_{199.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{2}32\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{1}{}9\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{3}%
\EasyButWeakLineBreak%
{${32}\above{1pt}{1pt}{l}{2}{3}\above{1pt}{1pt}{}{2}{288}\above{1pt}{1pt}{r}{2}{2}\above{1pt}{1pt}{b}{2}{288}\above{1pt}{1pt}{*}{2}{12}\above{1pt}{1pt}{s}{2}$}%
\nopagebreak\par%
shares genus with 3-dual\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
152352\\75456\\-576
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
75456\\37371\\-285
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-576\\-285\\2
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
39\\-80\\-160
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
20\\-41\\-81
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
281\\-576\\-1152
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\-1
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-47\\96\\144
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\2\\0
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[152352, 75456, -576; 75456, 37371, -285; -576, -285, 2],[288, 3, 1],[39, 20, 281, 0, -47, -1; -80, -41, -576, 0, 96, 2; -160, -81, -1152, -1, 144, 0],198,1]
%
% END OF LATTICE L199.1
%
%
% LATTICE L199.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[17184, 2784, -192; 2784, 451, -31; -192, -31, 2],[96, 1, 1],[7, 4, 19, 0, -5, -1; -48, -27, -128, 0, 32, 6; -64, -33, -160, -1, 16, 0],198,2]
%
% END OF LATTICE L199.2
%
%
% LATTICE L199.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[6240, -192, -96; -192, 6, 3; -96, 3, 1],[96, 3, 1],[-3, 0, 1, 0, -7, -1; -80, 0, 32, 1, -176, -26; -48, -1, 0, 0, -96, -14],198,3]
%
% END OF LATTICE L199.3
%
%
% LATTICE L199.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2460960, 74016, 288; 74016, 2226, 9; 288, 9, -1],[288, 3, 1],[-13, 5, 13, -1, -27, -5; 432, -166, -432, 33, 896, 166; 144, -54, -160, 0, 256, 51],198,4]
%
% END OF LATTICE L199.4
%
%
% LATTICE L199.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[96, 0, 0; 0, -1312, 96; 0, 96, -7],[96, 32, 1],[0, 1, 0, -1, -1, -2; -1, 0, 1, 5, 1, -3; -14, 0, 13, 64, 10, -48],198,5]
%
% END OF LATTICE L199.5
%
%
% LATTICE L199.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-11328, -5664, 384; -5664, -2784, 192; 384, 192, -13],[96, 96, 1],[2, 0, -1, -1, 2, 5; -1, -1, 0, 2, 0, -1; 42, -16, -30, 0, 57, 128],198,6]
%
% END OF LATTICE L199.6
%
%
% LATTICE L199.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[576, -288, 0; -288, -103584, 2208; 0, 2208, -47],[288, 96, 1],[8, 0, -1, -1, 3, 21; 15, -1, -2, 0, 6, 41; 702, -48, -94, 0, 281, 1920],198,7]
%
% END OF LATTICE L199.7
%
%
% LATTICE L199.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-288, 13536, -288; 13536, -583104, 12384; -288, 12384, -263],[288, 96, 1],[-1, -1, 8, 8, 5, 1; -1, 1, 9, 7, 3, -2; -46, 48, 414, 320, 135, -96],198,8]
%
% END OF LATTICE L199.8
%

\medskip%
%------------------------------WEYL-GROUP-W200--------------------------------
%
\leavevmode\llap{}%
$W_{200}$%
\qquad\llap{8} lattices, $\chi=24$%
\hfill%
$2\slashinfty222|22\rtimes D_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L200.1
%
\leavevmode%
${L_{200.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{6}32\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{-}{}9\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{3}%
\EasyButWeakLineBreak%
{${32}\above{1pt}{1pt}{b}{2}{6}\above{1pt}{1pt}{24,17}{\infty b}{6}\above{1pt}{1pt}{l}{2}{32}\above{1pt}{1pt}{}{2}{9}\above{1pt}{1pt}{r}{2}{32}\above{1pt}{1pt}{s}{2}{36}\above{1pt}{1pt}{*}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-202464\\-34272\\1440
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-34272\\-5799\\243
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1440\\243\\-10
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-19\\128\\368
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-5\\34\\105
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2\\14\\51
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5\\-32\\-64
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4\\-27\\-81
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7\\-48\\-160
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\6\\0
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-202464, -34272, 1440; -34272, -5799, 243; 1440, 243, -10],[288, 3, 1],[-19, -5, -2, 5, 4, 7, -1; 128, 34, 14, -32, -27, -48, 6; 368, 105, 51, -64, -81, -160, 0],199,1]
%
% END OF LATTICE L200.1
%
%
% LATTICE L200.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[24864, 8160, -576; 8160, 2678, -189; -576, -189, 13],[96, 1, 1],[211, 28, -1, -21, -1, 41, 27; -656, -87, 3, 64, 3, -128, -84; -192, -24, 0, 0, -1, -48, -26],199,2]
%
% END OF LATTICE L200.2
%
%
% LATTICE L200.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[16992, 8256, -192; 8256, 4011, -93; -192, -93, 2],[96, 3, 1],[249, 11, 0, -15, -1, 51, 16; -544, -24, 0, 32, 2, -112, -35; -1344, -59, -1, 48, 0, -288, -87],199,3]
%
% END OF LATTICE L200.3
%
%
% LATTICE L200.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[55584, -576, -864; -576, 6, 9; -864, 9, 13],[288, 3, 1],[1, 0, -1, -23, -1, -5, 0; 96, 1, -61, -1392, -60, -288, 1; 0, 0, -24, -576, -26, -144, -1],199,4]
%
% END OF LATTICE L200.4
%
%
% LATTICE L200.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-103776, -5376, 1248; -5376, -224, 64; 1248, 64, -15],[96, 32, 1],[-5, -13, 1, 1, 3, 0, -4; -7, -15, 3, 1, 2, -1, -7; -450, -1152, 96, 87, 256, -6, -368],199,5]
%
% END OF LATTICE L200.5
%
%
% LATTICE L200.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-29376, -29472, 384; -29472, -29472, 384; 384, 384, -5],[96, 96, 1],[0, -1, -3, -3, -2, 0, 1; 1, 4, 4, 2, -1, -1, -1; 75, 224, 64, -90, -240, -78, 0],199,6]
%
% END OF LATTICE L200.6
%
%
% LATTICE L200.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-866880, -64224, 5184; -64224, -4704, 384; 5184, 384, -31],[288, 96, 1],[-5, -5, 1, 2, 2, 1, -1; -6, -2, 2, 0, -1, -3, -3; -918, -864, 192, 333, 320, 126, -208],199,7]
%
% END OF LATTICE L200.7
%
%
% LATTICE L200.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[288, 0, 0; 0, -48480, 1056; 0, 1056, -23],[288, 96, 1],[0, -1, -3, -1, -2, 0, 1; 2, 19, 17, 3, -3, -1, 0; 91, 864, 768, 134, -144, -46, 0],199,8]
%
% END OF LATTICE L200.8
%

\medskip%
%------------------------------WEYL-GROUP-W201--------------------------------
%
\leavevmode\llap{}%
$W_{201}$%
\qquad\llap{8} lattices, $\chi=112$%
\hfill%
$3\infty2\infty2\infty\infty3\infty2\infty2\infty\infty\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L201.1
%
\leavevmode%
${L_{201.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}8\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{-2}{}49\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${2}\above{1pt}{1pt}{+}{3}{2}\above{1pt}{1pt}{28,25}{\infty b}{8}\above{1pt}{1pt}{b}{2}{98}\above{1pt}{1pt}{4,1}{\infty b}{392}\above{1pt}{1pt}{b}{2}{2}\above{1pt}{1pt}{28,1}{\infty b}{8}\above{1pt}{1pt}{14,11}{\infty z}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-446488\\1176\\2744
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1176\\-2\\-9
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2744\\-9\\-14
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
148175\\22950816\\14175504
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-423\\-65519\\-40467
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-864\\-133824\\-82657
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\156\\95
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\1\\-1
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-156\\-96
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\147\\98
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
47\\7252\\4508
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5\\773\\479
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
27\\4180\\2584
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-446488, 1176, 2744; 1176, -2, -9; 2744, -9, -14],[392, 1, 1],[1, 0, -1, 1, 47, 5, 27, 107, 441, 757, 1322, 1717, 40, 9; 156, 1, -156, 147, 7252, 773, 4180, 16572, 68305, 117252, 204771, 265972, 6197, 1396; 95, -1, -96, 98, 4508, 479, 2584, 10237, 42190, 72420, 126469, 164248, 3826, 860],200,1]
%
% END OF LATTICE L201.1
%
%
% LATTICE L201.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-23814, -1176, 98; -1176, -58, 5; 98, 5, 0],[98, 1, 1],[1, 0, -1, -5, 5, 2, 7, 59, 245, 211, 740, 485, 23, 3; -19, 1, 20, 98, -98, -39, -136, -1145, -4754, -4094, -14357, -9408, -446, -58; 11, 6, -6, -49, 0, 10, 46, 409, 1709, 1476, 5194, 3430, 165, 24],200,2]
%
% END OF LATTICE L201.2
%
%
% LATTICE L201.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[52920, 2842, 25774; 2842, 196, 1382; 25774, 1382, 12553],[98, 2, 1],[189, 283, 71, 480, 936, 383, 549, 8967, 37104, 15952, 111681, 36451, 3432, 214; -19, -28, -7, -49, -98, -40, -57, -929, -3843, -1652, -11564, -3773, -355, -22; -386, -578, -145, -980, -1911, -782, -1121, -18310, -75764, -32573, -228046, -74431, -7008, -437],200,3]
%
% END OF LATTICE L201.3
%
%
% LATTICE L201.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1120336, 59192, 551544; 59192, 2992, 29176; 551544, 29176, 271517],[392, 8, 1],[-899, -247, 244, 1786, -4911, -2535, -3842, -62857, -260090, -111817, -782797, -255426, -24030, -1471; 467, 128, -127, -931, 2548, 1316, 1995, 32641, 135063, 58066, 406504, 132643, 12479, 764; 1776, 488, -482, -3528, 9702, 5008, 7590, 124176, 513816, 220898, 1546440, 504602, 47472, 2906],200,4]
%
% END OF LATTICE L201.4
%
%
% LATTICE L201.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[235298, -13426, 115934; -13426, 882, -6615; 115934, -6615, 57122],[98, 49, 1],[652, 966, 483, 34, 135, 1352, 3863, 31508, 130354, 112077, 8006, 5225, 12048, 1497; 3, 5, 2, 0, 0, 1, 6, 57, 240, 208, 15, 10, 24, 4; -1323, -1960, -980, -69, -274, -2744, -7840, -63945, -264551, -227458, -16248, -10604, -24451, -3038],200,5]
%
% END OF LATTICE L201.5
%
%
% LATTICE L201.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[0, -66738, -33026; -66738, -107532068, -53213412; -33026, -53213412, -26333235],[98, 98, 1],[11, 6, -3, -1, 0, 10, 23, 409, 1709, 738, 106, 35, 165, 12; 6547, -97, -3322, -674, 337, 13191, 23060, 388601, 1613618, 694831, 99461, 32592, 151454, 9869; -13230, 196, 6713, 1362, -681, -26656, -46599, -785274, -3260754, -1404095, -200988, -65861, -306054, -19943],200,6]
%
% END OF LATTICE L201.6
%
%
% LATTICE L201.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-189336, -4312, 83888; -4312, -98, 1911; 83888, 1911, -37166],[392, 49, 1],[-733, -3063, -5291, -190, -251, -296, -87, -23, -24, -1, 1, -1, -19, -165; -1468, -5879, -9956, -349, -436, -459, -20, 52, 97, 44, -5, -36, -131, -452; -1715, -7154, -12348, -443, -584, -686, -196, -49, -49, 0, 2, -4, -49, -392],200,7]
%
% END OF LATTICE L201.7
%
%
% LATTICE L201.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-9882320, -2418248, 33712; -2418248, -497840, 8232; 33712, 8232, -115],[392, 392, 1],[32641, 135063, 58066, 8296, 2707, 12479, 764, 467, 128, -127, -19, 52, 1316, 1995; 1846, 7637, 3283, 469, 153, 705, 43, 26, 7, -7, -1, 3, 75, 113; 9702000, 40145112, 17259074, 2465832, 804602, 3709104, 227066, 138768, 38024, -37730, -5640, 15462, 391216, 592998],200,8]
%
% END OF LATTICE L201.8
%

\medskip%
%------------------------------WEYL-GROUP-W202--------------------------------
%
\leavevmode\llap{}%
$W_{202}$%
\qquad\llap{12} lattices, $\chi=15$%
\hfill%
$222224$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L202.1
%
\leavevmode%
${L_{202.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{2}{}9\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{2}{}11\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${2}\above{1pt}{1pt}{s}{2}{198}\above{1pt}{1pt}{b}{2}{4}\above{1pt}{1pt}{*}{2}{36}\above{1pt}{1pt}{b}{2}{22}\above{1pt}{1pt}{b}{2}{4}\above{1pt}{1pt}{*}{4}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-900900\\3960\\5544
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3960\\-14\\-25
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5544\\-25\\-34
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\27\\143
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
49\\1287\\7029
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5\\130\\718
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5\\126\\720
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2\\-55\\-286
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-26\\-144
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-900900, 3960, 5544; 3960, -14, -25; 5544, -25, -34],[396, 1, 1],[1, 49, 5, 5, -2, -1; 27, 1287, 130, 126, -55, -26; 143, 7029, 718, 720, -286, -144],201,1]
%
% END OF LATTICE L202.1
%
%
% LATTICE L202.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-55638, 2871, -1683; 2871, -146, 81; -1683, 81, -35],[99, 1, 1],[-7, -349, -18, -19, 12, 3; -173, -8613, -444, -468, 297, 74; -64, -3168, -163, -171, 110, 27],201,2]
%
% END OF LATTICE L202.2
%
%
% LATTICE L202.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[198, -2673, -198; -2673, 80469, 4473; -198, 4473, 271],[99, 9, 1],[257, 1349, 635, 89, -1, 45; -23, -121, -57, -8, 0, -4; 567, 2981, 1404, 197, 0, 99],201,3]
%
% END OF LATTICE L202.3
%
%
% LATTICE L202.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-8811, -3762, 693; -3762, -1606, 297; 693, 297, -49],[99, 11, 1],[-23, -71, -34, -19, 4, 3; 52, 162, 78, 45, -9, -7; -11, -27, -11, 0, 2, 0],201,4]
%
% END OF LATTICE L202.4
%
%
% LATTICE L202.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[287130888, -552420, -72528588; -552420, 1064, 139540; -72528588, 139540, 18320551],[396, 4, 1],[-293, -19405, -1121, -1705, -389, -49; 7, 297, 15, 18, 0, 2; -1160, -76824, -4438, -6750, -1540, -194],201,5]
%
% END OF LATTICE L202.5
%
%
% LATTICE L202.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-15153732, 45936, -109692; 45936, -126, 333; -109692, 333, -794],[396, 9, 1],[-8, -46, -43, -5, 16, 9; -39, -231, -218, -26, 77, 46; 1089, 6259, 5850, 680, -2178, -1224],201,6]
%
% END OF LATTICE L202.6
%
%
% LATTICE L202.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-101772, 3960, 1980; 3960, -154, -77; 1980, -77, -38],[396, 11, 1],[0, 2, 3, 5, 0, -1; 5, 63, 86, 126, -1, -26; -11, -27, -22, 0, 2, 0],201,7]
%
% END OF LATTICE L202.7
%
%
% LATTICE L202.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[48510, -183546, 81477; -183546, 694485, -308286; 81477, -308286, 136850],[99, 99, 1],[-23, -11, -57, -8, 0, -4; -94, -26, -103, -7, 4, -45; -198, -52, -198, -11, 9, -99],201,8]
%
% END OF LATTICE L202.8
%
%
% LATTICE L202.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2339956872, 7598052, -590729436; 7598052, 24696, -1918152; -590729436, -1918152, 149131495],[396, 36, 1],[-4217, -26437, -13219, -2109, -3499, -977; 7, 33, 15, 2, 0, 2; -16704, -104720, -52362, -8354, -13860, -3870],201,9]
%
% END OF LATTICE L202.9
%
%
% LATTICE L202.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[89496, 12276, -22572; 12276, 5896, -3080; -22572, -3080, 5693],[396, 44, 1],[-467, -1765, -973, -1151, 1, -139; 7, 27, 15, 18, 0, 2; -1848, -6984, -3850, -4554, 4, -550],201,10]
%
% END OF LATTICE L202.10
%
%
% LATTICE L202.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-130284, 45144, 4752; 45144, -12078, -1485; 4752, -1485, -166],[396, 99, 1],[-31, -17, -177, -21, 6, 41; 67, 37, 386, 46, -13, -90; -1485, -817, -8514, -1012, 288, 1980],201,11]
%
% END OF LATTICE L202.11
%
%
% LATTICE L202.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[954360, 19303812, -4879116; 19303812, 390461544, -98690724; -4879116, -98690724, 24944477],[396, 396, 1],[-35, -11, -47, -4, 2, -12; 1403, 593, 2955, 395, 9, 451; 5544, 2344, 11682, 1562, 36, 1782],201,12]
%
% END OF LATTICE L202.12
%

\medskip%
%------------------------------WEYL-GROUP-W203--------------------------------
%
\leavevmode\llap{}%
$W_{203}$%
\qquad\llap{4} lattices, $\chi=48$%
\hfill%
$\slashinfty22|22\slashinfty22|22\rtimes D_{4}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L203.1
%
\leavevmode%
${L_{203.1}}$%
{} : {$1\above{1pt}{1pt}{2}{6}16\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{-2}{}7\above{1pt}{1pt}{1}{}$}\EasyButWeakLineBreak%
{${28}\above{1pt}{1pt}{8,5}{\infty z}{7}\above{1pt}{1pt}{}{2}{16}\above{1pt}{1pt}{r}{2}{14}\above{1pt}{1pt}{b}{2}{16}\above{1pt}{1pt}{*}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
15120\\4256\\-224
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4256\\1198\\-63
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-224\\-63\\3
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1009\\3696\\2688
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-282\\1033\\752
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
9\\-33\\-25
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
27\\-98\\-42
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
25\\-91\\-49
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
57\\-208\\-128
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
44\\-161\\-112
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
37\\-136\\-112
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[15120, 4256, -224; 4256, 1198, -63; -224, -63, 3],[112, 1, 1],[27, 25, 57, 44, 37, 15, -4, -9, -2, 11; -98, -91, -208, -161, -136, -56, 14, 32, 7, -40; -42, -49, -128, -112, -112, -70, -7, 0, 0, -16],202,1]
%
% END OF LATTICE L203.1
%
%
% LATTICE L203.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3472, 224, -112; 224, -14, 7; -112, 7, -3],[112, 7, 1],[-1, 0, 1, 0, -3, -1, -1, -17, -2, -13; -22, -1, 16, 1, -40, -16, -18, -320, -39, -264; -22, -3, 0, 2, 0, -6, -11, -224, -30, -224],202,2]
%
% END OF LATTICE L203.2
%
%
% LATTICE L203.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[224, -112, 0; -112, -272, 48; 0, 48, -7],[112, 16, 1],[19, 37, 11, 71, 4, 16, -2, -1, -1, 1; 35, 63, 18, 112, 6, 21, -7, -2, 0, 2; 224, 392, 110, 672, 35, 112, -56, -14, 0, 13],202,3]
%
% END OF LATTICE L203.3
%
%
% LATTICE L203.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-224, 112, 0; 112, 784, 112; 0, 112, 15],[112, 112, 1],[10, 4, 1, -1, -1, 1, 7, 10, 23, 23; 27, 11, 3, -2, -2, 3, 19, 27, 62, 62; -200, -80, -21, 16, 14, -24, -144, -203, -464, -462],202,4]
%
% END OF LATTICE L203.4
%

\medskip%
%------------------------------WEYL-GROUP-W204--------------------------------
%
\leavevmode\llap{}%
$W_{204}$%
\qquad\llap{12} lattices, $\chi=36$%
\hfill%
$2222222222\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L204.1
%
\leavevmode%
${L_{204.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{2}{}9\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}13\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${234}\above{1pt}{1pt}{l}{2}{4}\above{1pt}{1pt}{r}{2}{18}\above{1pt}{1pt}{b}{2}{26}\above{1pt}{1pt}{b}{2}{2}\above{1pt}{1pt}{b}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-53820\\-26676\\468
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-26676\\-13222\\233
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
468\\233\\58
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
419795\\-845676\\-6084
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
208311\\-419642\\-3019
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
10557\\-21267\\-154
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-58\\117\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-117\\236\\-4
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-232\\468\\-9
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-219\\442\\-13
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
10\\-20\\-3
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-53820, -26676, 468; -26676, -13222, 233; 468, 233, 58],[468, 1, 1],[-58, -117, -232, -219, 10, 24277, 3153, 2095, 1116, 59; 117, 236, 468, 442, -20, -48906, -6352, -4221, -2249, -119; 0, -4, -9, -13, -3, -351, -40, -18, 0, 2],203,1]
%
% END OF LATTICE L204.1
%
%
% LATTICE L204.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[234, 0, 117; 0, -1, -2; 117, -2, 55],[117, 1, 1],[-352, -23, -31, -17, -1, 1, 1, 4, 4, 0; -7371, -465, -576, -260, -4, 0, 3, 9, -13, -17; -351, -20, -18, 0, 2, 0, -2, -9, -13, -3],203,2]
%
% END OF LATTICE L204.2
%
%
% LATTICE L204.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[92547, 2574, -20709; 2574, 63, -576; -20709, -576, 4634],[117, 9, 1],[-13331, -7504, -1010, -3856, 2, 32, 2, -13, -577, -343; 897, 505, 68, 260, 0, 0, 1, 1, 39, 23; -59462, -33471, -4505, -17199, 9, 143, 9, -58, -2574, -1530],203,3]
%
% END OF LATTICE L204.3
%
%
% LATTICE L204.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-6786, 6786, -117; 6786, -6773, 117; -117, 117, -2],[117, 13, 1],[1, 1, -2, -2, -18, -514, -419, -511, -17, -1; 0, 1, 0, -2, -20, -594, -485, -594, -20, -2; -63, 0, 117, -5, -169, -6255, -5148, -6435, -229, -65],203,4]
%
% END OF LATTICE L204.4
%
%
% LATTICE L204.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1511485560, -6569316, 377898768; -6569316, 28552, -1642448; 377898768, -1642448, 94481537],[468, 4, 1],[-233, 29, 634, 2812, 1662, 583244, 18242, 44213, 18781, -1; 234, -58, -1161, -5109, -3019, -1059903, -33151, -80352, -34138, 0; 936, -117, -2556, -11336, -6700, -2351232, -73539, -178236, -75712, 4],203,5]
%
% END OF LATTICE L204.5
%
%
% LATTICE L204.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[69732, 38376, -468; 38376, 20934, -243; -468, -243, 2],[468, 9, 1],[-6, -13, 0, 109, 82, 3477, 3929, 267, 1048, 7; 13, 28, 0, -234, -176, -7462, -8432, -573, -2249, -15; 182, 360, -1, -2925, -2187, -92495, -104508, -7100, -27846, -180],203,6]
%
% END OF LATTICE L204.6
%
%
% LATTICE L204.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-430092, -53820, 936; -53820, -6734, 117; 936, 117, -2],[468, 13, 1],[-217, -353, -214, -7, 0, 1, 1, -2, -1, -8; 1656, 2692, 1629, 53, -1, -9, -8, 18, 8, 62; -6255, -10296, -6435, -229, -65, -63, 0, 117, -5, -169],203,7]
%
% END OF LATTICE L204.7
%
%
% LATTICE L204.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[117, 1053, -234; 1053, 127179, -29133; -234, -29133, 6674],[117, 117, 1],[-5, 1, 1, -47, -497, -1681, -12365, -1687, -515, -65; 17, 0, -3, 155, 1639, 5545, 40788, 5565, 1699, 215; 74, 0, -13, 675, 7137, 24145, 177606, 24232, 7398, 936],203,8]
%
% END OF LATTICE L204.8
%
%
% LATTICE L204.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[220954968, -1162980, 54826668; -1162980, 6120, -288576; 54826668, -288576, 13604417],[468, 36, 1],[1147, 29, -114, 2552, 3114, 151616, 43058, 11865, 48369, 803; -260, -6, 27, -533, -679, -33319, -9465, -2610, -10660, -182; -4628, -117, 460, -10296, -12564, -611728, -173727, -47872, -195156, -3240],203,9]
%
% END OF LATTICE L204.9
%
%
% LATTICE L204.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[3645720, -62244, 904176; -62244, 1768, -15444; 904176, -15444, 224245],[468, 52, 1],[405982, 165898, 407365, 13813, 1727, 1151, -29, -232, 1266, 13352; -15723, -6425, -15777, -535, -67, -45, 1, 9, -49, -517; -1638036, -669357, -1643616, -55732, -6968, -4644, 117, 936, -5108, -53872],203,10]
%
% END OF LATTICE L204.10
%
%
% LATTICE L204.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[468, 0, 0; 0, -10062, 585; 0, 585, -34],[468, 117, 1],[0, 1, 0, -1, -10, -33, -485, -33, -10, -1; 1, 0, -3, -5, -25, -55, -792, -51, -13, 7; 17, 0, -52, -90, -468, -1070, -15444, -1001, -261, 117],203,11]
%
% END OF LATTICE L204.11
%
%
% LATTICE L204.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[15912, -273780, -67860; -273780, 4710888, 1167660; -67860, 1167660, 289421],[468, 468, 1],[-1, 0, -2, -20, -190, -620, -2277, -619, -187, -17; -7, -29, -13, -19, -127, -377, -1379, -371, -109, -1; 28, 117, 52, 72, 468, 1376, 5031, 1352, 396, 0],203,12]
%
% END OF LATTICE L204.12
%

\medskip%
%------------------------------WEYL-GROUP-W205--------------------------------
%
\leavevmode\llap{}%
$W_{205}$%
\qquad\llap{60} lattices, $\chi=12$%
\hfill%
$22|222|2\rtimes D_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L205.1
%
\leavevmode%
${L_{205.1}}$%
{} : {$1\above{1pt}{1pt}{2}{0}8\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{-}{}$}\EasyButWeakLineBreak%
{${60}\above{1pt}{1pt}{*}{2}{4}\above{1pt}{1pt}{s}{2}{40}\above{1pt}{1pt}{l}{2}{1}\above{1pt}{1pt}{}{2}{15}\above{1pt}{1pt}{r}{2}{8}\above{1pt}{1pt}{s}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
347640\\6240\\840
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
6240\\112\\15
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
840\\15\\1
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-17\\960\\-90
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-5\\282\\-26
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-11\\620\\-60
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\-1
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4\\-225\\15
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\-56\\4
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[347640, 6240, 840; 6240, 112, 15; 840, 15, 1],[120, 1, 1],[-17, -5, -11, 0, 4, 1; 960, 282, 620, 0, -225, -56; -90, -26, -60, -1, 15, 4],204,1]
%
% END OF LATTICE L205.1
%
\hbox{}\par\smallskip%
%
% LATTICE L205.2
%
\leavevmode%
${L_{205.2}}$%
{} : {$[1\above{1pt}{1pt}{1}{}2\above{1pt}{1pt}{1}{}]\above{1pt}{1pt}{}{0}16\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${15}\above{1pt}{1pt}{r}{2}{16}\above{1pt}{1pt}{*}{2}{40}\above{1pt}{1pt}{l}{2}{1}\above{1pt}{1pt}{}{2}{240}\above{1pt}{1pt}{}{2}{2}\above{1pt}{1pt}{}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-161040\\-960\\1680
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-960\\2\\8
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1680\\8\\-17
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\60\\225
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-28\\-112
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3\\-90\\-340
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\-1\\-1
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
13\\360\\1440
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\29\\112
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-161040, -960, 1680; -960, 2, 8; 1680, 8, -17],[240, 2, 1],[2, -1, -3, 0, 13, 1; 60, -28, -90, -1, 360, 29; 225, -112, -340, -1, 1440, 112],204,2]
%
% END OF LATTICE L205.2
%
\hbox{}\par\smallskip%
%
% LATTICE L205.3
%
\leavevmode%
${L_{205.3}}$%
{} : {$[1\above{1pt}{1pt}{-}{}2\above{1pt}{1pt}{1}{}]\above{1pt}{1pt}{}{4}16\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{m}%
\EasyButWeakLineBreak%
{${60}\above{1pt}{1pt}{*}{2}{16}\above{1pt}{1pt}{s}{2}{40}\above{1pt}{1pt}{*}{2}{4}\above{1pt}{1pt}{s}{2}{240}\above{1pt}{1pt}{l}{2}{2}\above{1pt}{1pt}{r}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
26160\\-6720\\2880
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-6720\\1726\\-740
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2880\\-740\\317
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-11\\-30\\30
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\4\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
37\\110\\-80
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
19\\56\\-42
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
163\\480\\-360
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\3\\-2
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[26160, -6720, 2880; -6720, 1726, -740; 2880, -740, 317],[240, 2, 1],[-11, 1, 37, 19, 163, 1; -30, 4, 110, 56, 480, 3; 30, 0, -80, -42, -360, -2],204,3]
%
% END OF LATTICE L205.3
%
\hbox{}\par\smallskip%
%
% LATTICE L205.4
%
\leavevmode%
${L_{205.4}}$%
{} : {$[1\above{1pt}{1pt}{-}{}2\above{1pt}{1pt}{1}{}]\above{1pt}{1pt}{}{2}16\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{m}%
\EasyButWeakLineBreak%
{${60}\above{1pt}{1pt}{s}{2}{16}\above{1pt}{1pt}{l}{2}{10}\above{1pt}{1pt}{}{2}{1}\above{1pt}{1pt}{r}{2}{240}\above{1pt}{1pt}{*}{2}{8}\above{1pt}{1pt}{*}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-24240\\960\\0
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
960\\-2\\-6
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\-6\\1
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-30\\-150
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\24\\152
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\25\\150
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\-1
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-7\\-180\\-1080
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-26\\-152
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-24240, 960, 0; 960, -2, -6; 0, -6, 1],[240, 2, 1],[-1, 1, 1, 0, -7, -1; -30, 24, 25, 0, -180, -26; -150, 152, 150, -1, -1080, -152],204,4]
%
% END OF LATTICE L205.4
%
\hbox{}\par\smallskip%
%
% LATTICE L205.5
%
\leavevmode%
${L_{205.5}}$%
{} : {$[1\above{1pt}{1pt}{1}{}2\above{1pt}{1pt}{1}{}]\above{1pt}{1pt}{}{6}16\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{-}{}$}\EasyButWeakLineBreak%
{${15}\above{1pt}{1pt}{}{2}{16}\above{1pt}{1pt}{}{2}{10}\above{1pt}{1pt}{r}{2}{4}\above{1pt}{1pt}{*}{2}{240}\above{1pt}{1pt}{s}{2}{8}\above{1pt}{1pt}{l}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
151440\\3120\\2880
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3120\\58\\56
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2880\\56\\53
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\75\\-135
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-56\\112
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2\\-125\\240
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-64\\122
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-60\\120
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\66\\-124
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[151440, 3120, 2880; 3120, 58, 56; 2880, 56, 53],[240, 2, 1],[1, -1, -2, -1, -1, 1; 75, -56, -125, -64, -60, 66; -135, 112, 240, 122, 120, -124],204,5]
%
% END OF LATTICE L205.5
%
%
% LATTICE L205.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[488940, -34920, 2520; -34920, 2494, -180; 2520, -180, 13],[60, 2, 1],[37, 3, 3, -1, 1, 2; 540, 44, 45, -14, 15, 29; 300, 27, 40, 0, 15, 14],204,6]
%
% END OF LATTICE L205.6
%
%
% LATTICE L205.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[13080, -3240, -120; -3240, 802, 30; -120, 30, 1],[120, 2, 1],[4, 1, -3, -2, -17, 0; 15, 4, -10, -7, -60, 0; 30, 4, -50, -28, -240, -1],204,7]
%
% END OF LATTICE L205.7
%
%
% LATTICE L205.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[97320, 120, -1680; 120, -2, -2; -1680, -2, 29],[120, 2, 1],[1, 1, 2, 1, -2, -1; 0, 1, 0, -4, -15, -2; 60, 58, 115, 56, -120, -58],204,8]
%
% END OF LATTICE L205.8
%
%
% LATTICE L205.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3480, 120, 120; 120, -3, -6; 120, -6, -1],[120, 3, 1],[2, 1, 1, -1, -1, 1; 35, 18, 20, -18, -20, 16; 20, 9, 0, -12, -10, 12],204,9]
%
% END OF LATTICE L205.9
%
%
% LATTICE L205.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[780, 180, 0; 180, 42, 0; 0, 0, -1],[60, 6, 1],[1, 1, -1, -1, -3, 0; -5, -4, 5, 4, 10, -1; -5, 0, 0, -3, -20, -6],204,10]
%
% END OF LATTICE L205.10
%
%
% LATTICE L205.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[12840, 6480, -120; 6480, 3268, -60; -120, -60, 1],[120, 4, 1],[13, 4, 9, 0, -7, -1; -30, -9, -20, 0, 15, 2; -210, -56, -120, -1, 60, 4],204,11]
%
% END OF LATTICE L205.11
%
%
% LATTICE L205.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[578040, -41280, -2520; -41280, 2948, 180; -2520, 180, 11],[120, 4, 1],[1, 2, 11, 3, 7, -1; 15, 29, 160, 44, 105, -14; -15, -16, -100, -34, -120, 0],204,12]
%
% END OF LATTICE L205.12
%
%
% LATTICE L205.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[87960, 21480, -840; 21480, 5245, -205; -840, -205, 8],[120, 5, 1],[1, 1, -1, -2, -2, -1; -6, -6, 4, 9, 9, 4; -48, -50, -4, 20, 21, 0],204,13]
%
% END OF LATTICE L205.13
%
%
% LATTICE L205.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-9780, 4920, -360; 4920, -2470, 180; -360, 180, -13],[60, 10, 1],[5, 0, -1, -1, 2, 4; 12, -1, -3, -2, 6, 11; 24, -15, -14, 0, 27, 40],204,14]
%
% END OF LATTICE L205.14
%
%
% LATTICE L205.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-4440, 600, 240; 600, -78, -30; 240, -30, -11],[120, 6, 1],[1, 1, -1, -1, -3, 0; 15, 12, -20, -15, -40, 1; -20, -12, 30, 18, 40, -3],204,15]
%
% END OF LATTICE L205.15
%
%
% LATTICE L205.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[8760, 2160, -240; 2160, 534, -60; -240, -60, 7],[120, 6, 1],[-1, 1, -2, -4, -17, -3; 5, -4, 10, 19, 80, 14; 10, 0, 15, 24, 100, 18],204,16]
%
% END OF LATTICE L205.16
%
%
% LATTICE L205.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[120, 0, 0; 0, 8, 0; 0, 0, -1],[120, 8, 1],[1, 0, -1, -1, -4, 0; 0, 1, 0, -2, -15, -1; 0, 0, -10, -12, -60, -2],204,17]
%
% END OF LATTICE L205.17
%
%
% LATTICE L205.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-61320, 21000, -1080; 21000, -7190, 370; -1080, 370, -19],[120, 10, 1],[-2, 1, 1, 0, -5, -2; -3, 4, 2, -1, -12, -4; 54, 20, -18, -20, 48, 35],204,18]
%
% END OF LATTICE L205.18
%
%
% LATTICE L205.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-120, 120, 0; 120, -10, -10; 0, -10, 1],[120, 10, 1],[1, 1, 0, -3, -2, -1; 0, 1, 0, -4, -3, -2; 12, 10, -1, -40, -24, -10],204,19]
%
% END OF LATTICE L205.19
%
%
% LATTICE L205.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-291120, -1920, 2400; -1920, 6, 12; 2400, 12, -19],[240, 6, 1],[-1, -1, -7, -1, 1, 1; -40, -31, -210, -28, 30, 29; -160, -147, -1020, -144, 145, 144],204,20]
%
% END OF LATTICE L205.20
%
%
% LATTICE L205.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-52080, -960, -1200; -960, 6, 0; -1200, 0, -7],[240, 6, 1],[3, 1, 1, -1, -1, 0; 480, 162, 170, -156, -160, -1; -520, -174, -180, 168, 170, 0],204,21]
%
% END OF LATTICE L205.21
%
%
% LATTICE L205.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-260880, 1440, 3120; 1440, -6, -18; 3120, -18, -37],[240, 6, 1],[3, 1, 3, 1, -1, -1; 100, 30, 85, 24, -30, -26; 200, 69, 210, 72, -70, -72],204,22]
%
% END OF LATTICE L205.22
%
%
% LATTICE L205.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-7320, 2280, 120; 2280, -708, -36; 120, -36, -1],[120, 12, 1],[-7, -2, -3, 2, 3, -1; -25, -7, -10, 7, 10, -4; 40, 9, 0, -12, -10, 12],204,23]
%
% END OF LATTICE L205.23
%
%
% LATTICE L205.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[97320, 6960, -1680; 6960, 492, -120; -1680, -120, 29],[120, 12, 1],[-1, -1, 1, 2, 2, 1; -5, -2, 0, 1, 0, -2; -80, -66, 60, 120, 115, 48],204,24]
%
% END OF LATTICE L205.24
%
%
% LATTICE L205.25
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[18480, -1200, 0; -1200, 78, 0; 0, 0, -1],[240, 6, 1],[-1, -1, -1, 1, 1, 1; -20, -16, -15, 16, 15, 14; -40, -6, 0, 0, -5, -12],204,25]
%
% END OF LATTICE L205.25
%
%
% LATTICE L205.26
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[43080, 960, -840; 960, -15, -15; -840, -15, 16],[120, 15, 1],[2, 7, 5, -1, -1, 1; 11, 39, 28, -6, -6, 4; 116, 405, 288, -60, -58, 60],204,26]
%
% END OF LATTICE L205.26
%
%
% LATTICE L205.27
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[60, 0, 0; 0, -27930, 2040; 0, 2040, -149],[60, 30, 1],[0, 1, 0, -1, -1, -1; -3, 0, 7, 12, 2, -11; -41, 0, 96, 165, 28, -150],204,27]
%
% END OF LATTICE L205.27
%
%
% LATTICE L205.28
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[50640, 240, -240; 240, -8, 0; -240, 0, 1],[240, 8, 1],[1, 0, -1, -1, -2, 0; 30, 0, -25, -24, -45, 1; 240, -1, -240, -232, -450, 4],204,28]
%
% END OF LATTICE L205.28
%
%
% LATTICE L205.29
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-42497040, 3035520, -26880; 3035520, -216824, 1920; -26880, 1920, -17],[240, 8, 1],[2, -1, -3, 0, 13, 2; 30, -14, -45, -1, 180, 29; 225, 0, -340, -114, -240, 112],204,29]
%
% END OF LATTICE L205.29
%
%
% LATTICE L205.30
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[26160, -1920, 0; -1920, 136, -8; 0, -8, -13],[240, 8, 1],[-11, -1, 7, 3, 13, -2; -150, -14, 95, 41, 180, -27; 90, 8, -60, -26, -120, 16],204,30]
%
% END OF LATTICE L205.30
%
%
% LATTICE L205.31
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2640, 720, -240; 720, -88, 48; -240, 48, -19],[240, 8, 1],[-17, -1, 2, 3, 4, -1; 60, 4, -5, -10, -15, 3; 360, 22, -40, -64, -90, 20],204,31]
%
% END OF LATTICE L205.31
%
%
% LATTICE L205.32
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-442320, -9360, 2400; -9360, -170, 50; 2400, 50, -13],[240, 10, 1],[1, -1, -1, 0, 5, 2; 6, -4, -6, -1, 24, 11; 207, -200, -208, -5, 1008, 410],204,32]
%
% END OF LATTICE L205.32
%
%
% LATTICE L205.33
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-180240, 37920, 4560; 37920, -7930, -970; 4560, -970, -113],[240, 10, 1],[-35, -17, 11, 15, -23, -21; -108, -52, 34, 46, -72, -65; -486, -240, 152, 210, -312, -290],204,33]
%
% END OF LATTICE L205.33
%
%
% LATTICE L205.34
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2695920, 6000, 13440; 6000, -10, -30; 13440, -30, -67],[240, 10, 1],[-1, 1, 1, 2, 5, -1; -6, 0, 5, 12, 36, -2; -198, 200, 198, 395, 984, -200],204,34]
%
% END OF LATTICE L205.34
%
%
% LATTICE L205.35
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2040, -360, -120; -360, -20, -20; -120, -20, -7],[120, 20, 1],[1, 1, -1, -2, -4, -1; 0, 1, 0, -1, -3, -2; -18, -20, 16, 35, 72, 20],204,35]
%
% END OF LATTICE L205.35
%
%
% LATTICE L205.36
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-8880, -2160, 480; -2160, -430, 100; 480, 100, -23],[240, 10, 1],[-1, -3, 0, 1, 1, -1; -15, -40, 1, 16, 12, -18; -87, -240, 4, 90, 72, -100],204,36]
%
% END OF LATTICE L205.36
%
%
% LATTICE L205.37
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-15720, -7920, -3840; -7920, -3980, -1920; -3840, -1920, -917],[120, 20, 1],[10, 18, -3, -25, -23, 1; -30, -55, 8, 74, 69, -2; 21, 40, -4, -50, -48, 0],204,37]
%
% END OF LATTICE L205.37
%
%
% LATTICE L205.38
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[56040, 0, -1440; 0, 24, 0; -1440, 0, 37],[120, 24, 1],[1, 0, 7, 9, 16, 2; 0, 1, 0, -2, -5, -1; 40, 0, 270, 348, 620, 78],204,38]
%
% END OF LATTICE L205.38
%
%
% LATTICE L205.39
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[75720, 13800, -1320; 13800, 2490, -240; -1320, -240, 23],[120, 30, 1],[1, -1, -1, 1, 1, 2; 0, -3, -2, 0, 1, 2; 56, -90, -78, 60, 68, 135],204,39]
%
% END OF LATTICE L205.39
%
%
% LATTICE L205.40
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[120, 0, 0; 0, -510, 60; 0, 60, -7],[120, 30, 1],[-1, -1, 0, 1, 0, -1; 0, -3, -1, 0, 1, 4; -4, -30, -9, 0, 8, 30],204,40]
%
% END OF LATTICE L205.40
%
%
% LATTICE L205.41
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-97320, 0, 1680; 0, 40, 0; 1680, 0, -29],[120, 40, 1],[5, 0, -1, -1, 4, 4; 0, 1, 0, -2, -3, -1; 288, 0, -58, -60, 228, 230],204,41]
%
% END OF LATTICE L205.41
%
%
% LATTICE L205.42
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-24720, 11760, -960; 11760, -5592, 456; -960, 456, -37],[240, 24, 1],[11, 2, 7, -1, -2, 0; 30, 5, 15, -4, -5, 1; 80, 9, 0, -24, -10, 12],204,42]
%
% END OF LATTICE L205.42
%
%
% LATTICE L205.43
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2163120, -524400, 7920; -524400, 127128, -1920; 7920, -1920, 29],[240, 24, 1],[3, 0, 1, 3, 2, 2; 10, -1, 5, 16, 10, 9; -160, -66, 60, 240, 115, 48],204,43]
%
% END OF LATTICE L205.43
%
%
% LATTICE L205.44
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[3120, 720, 0; 720, 168, 0; 0, 0, -1],[240, 24, 1],[-3, -1, -1, 1, 1, 0; 10, 4, 5, -4, -5, -1; -40, -6, 0, 0, -10, -12],204,44]
%
% END OF LATTICE L205.44
%
%
% LATTICE L205.45
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-293520, 63360, -1440; 63360, -13656, 312; -1440, 312, -7],[240, 24, 1],[9, 4, 8, -1, -3, -1; 30, 13, 25, -4, -10, -3; -520, -246, -540, 24, 170, 72],204,45]
%
% END OF LATTICE L205.45
%
%
% LATTICE L205.46
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-11760, -6240, 2400; -6240, -30, 60; 2400, 60, -41],[240, 30, 1],[3, -1, -3, -1, 1, 5; 136, -50, -142, -44, 47, 233; 368, -135, -384, -120, 127, 630],204,46]
%
% END OF LATTICE L205.46
%
%
% LATTICE L205.47
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[10320, -42960, 3120; -42960, 153570, -11160; 3120, -11160, 811],[240, 30, 1],[1, -1, -1, 1, 1, 2; -48, 76, 66, -52, -58, -115; -664, 1050, 912, -720, -802, -1590],204,47]
%
% END OF LATTICE L205.47
%
%
% LATTICE L205.48
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3038160, 10800, 25200; 10800, -30, -90; 25200, -90, -209],[240, 30, 1],[7, 7, 3, 1, -1, -1; 44, 42, 17, 0, -6, -2; 824, 825, 354, 120, -118, -120],204,48]
%
% END OF LATTICE L205.48
%
%
% LATTICE L205.49
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-111480, 3600, 1800; 3600, -60, -60; 1800, -60, -29],[120, 60, 1],[4, 7, 5, -1, -1, 1; 7, 13, 10, -1, -2, 0; 232, 405, 288, -60, -58, 60],204,49]
%
% END OF LATTICE L205.49
%
%
% LATTICE L205.50
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-120, 240, 0; 240, 3180, -60; 0, -60, 1],[120, 60, 1],[-1, -1, 1, 2, 0, -3; -1, -2, 0, 1, 0, -2; -52, -90, 12, 60, -1, -120],204,50]
%
% END OF LATTICE L205.50
%
%
% LATTICE L205.51
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[240, 0, 0; 0, -570, -240; 0, -240, -101],[240, 30, 1],[-1, -1, 0, 1, 0, -1; -4, 12, 5, 0, -3, -26; 8, -30, -12, 0, 7, 60],204,51]
%
% END OF LATTICE L205.51
%
%
% LATTICE L205.52
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-453840, 111840, -5520; 111840, -27560, 1360; -5520, 1360, -67],[240, 40, 1],[13, 4, 3, -1, -2, 0; 60, 18, 13, -6, -9, 1; 144, 35, 16, -40, -18, 20],204,52]
%
% END OF LATTICE L205.52
%
%
% LATTICE L205.53
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-39120, 19680, -720; 19680, -9880, 360; -720, 360, -13],[240, 40, 1],[5, 0, -1, -1, 1, 4; 12, -1, -3, -2, 3, 11; 48, -30, -28, 0, 27, 80],204,53]
%
% END OF LATTICE L205.53
%
%
% LATTICE L205.54
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-399120, -199680, -97680; -199680, -99880, -48840; -97680, -48840, -23863],[240, 40, 1],[79, -45, -43, 1, 85, 126; -240, 134, 129, -2, -255, -379; 168, -90, -88, 0, 174, 260],204,54]
%
% END OF LATTICE L205.54
%
%
% LATTICE L205.55
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[205680, -82320, 1200; -82320, 32920, -480; 1200, -480, 7],[240, 40, 1],[-1, 0, 0, -1, -1, -1; 0, -1, -1, -2, 0, 1; 168, -70, -68, 40, 174, 240],204,55]
%
% END OF LATTICE L205.55
%
%
% LATTICE L205.56
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2040, 0, 120; 0, 120, 0; 120, 0, -7],[120, 120, 1],[0, -3, -1, 0, 1, 2; -1, -2, 0, 1, 0, -1; -4, -60, -18, 0, 16, 30],204,56]
%
% END OF LATTICE L205.56
%
%
% LATTICE L205.57
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-240, 14400, -240; 14400, -759480, 12600; -240, 12600, -209],[240, 120, 1],[-2, -1, 11, 14, 15, 0; -1, -2, 5, 7, 8, 1; -58, -120, 288, 405, 464, 60],204,57]
%
% END OF LATTICE L205.57
%
%
% LATTICE L205.58
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[55920, 480, -240; 480, -120, 0; -240, 0, 1],[240, 120, 1],[-1, -1, 0, 1, 0, -1; -2, -1, 1, 4, 0, -3; -224, -210, 12, 240, -1, -240],204,58]
%
% END OF LATTICE L205.58
%
%
% LATTICE L205.59
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[240, 0, 0; 0, -31080, -7440; 0, -7440, -1781],[240, 120, 1],[0, 1, 0, -1, -1, -1; -11, 0, 23, 36, 2, -43; 46, 0, -96, -150, -8, 180],204,59]
%
% END OF LATTICE L205.59
%
%
% LATTICE L205.60
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[24240, -298800, 7680; -298800, 3361080, -86400; 7680, -86400, 2221],[240, 120, 1],[1, -1, -1, 1, 1, 4; -54, 67, 65, -40, -56, -231; -2104, 2610, 2532, -1560, -2182, -9000],204,60]
%
% END OF LATTICE L205.60
%

\medskip%
%------------------------------WEYL-GROUP-W206--------------------------------
%
\leavevmode\llap{}%
$W_{206}$%
\qquad\llap{120} lattices, $\chi=36$%
\hfill%
$2\slashinfty2222|222\rtimes D_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L206.1
%
\leavevmode%
${L_{206.1}}$%
{} : {$1\above{1pt}{1pt}{2}{0}8\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{1}{}9\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{2}{}5\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{3}%
\EasyButWeakLineBreak%
{${9}\above{1pt}{1pt}{}{2}{120}\above{1pt}{1pt}{6,1}{\infty}{120}\above{1pt}{1pt}{*}{2}{36}\above{1pt}{1pt}{l}{2}{5}\above{1pt}{1pt}{}{2}{3}\above{1pt}{1pt}{r}{2}{8}\above{1pt}{1pt}{s}{2}{12}\above{1pt}{1pt}{*}{2}{20}\above{1pt}{1pt}{l}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-330120\\-1800\\2520
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1800\\3\\12
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2520\\12\\-19
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-5\\-114\\-747
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-13\\-280\\-1920
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-7\\-140\\-1020
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-18\\-144
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\20\\145
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\19\\144
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\16\\140
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-32\\-162
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-7\\-170\\-1060
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-330120, -1800, 2520; -1800, 3, 12; 2520, 12, -19],[360, 3, 1],[-5, -13, -7, -1, 1, 1, 1, -1, -7; -114, -280, -140, -18, 20, 19, 16, -32, -170; -747, -1920, -1020, -144, 145, 144, 140, -162, -1060],205,1]
%
% END OF LATTICE L206.1
%
\hbox{}\par\smallskip%
%
% LATTICE L206.2
%
\leavevmode%
${L_{206.2}}$%
{} : {$[1\above{1pt}{1pt}{-}{}2\above{1pt}{1pt}{1}{}]\above{1pt}{1pt}{}{4}16\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{1}{}9\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{2}{}5\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{3,2}%
\EasyButWeakLineBreak%
{${36}\above{1pt}{1pt}{l}{2}{30}\above{1pt}{1pt}{24,19}{\infty}{120}\above{1pt}{1pt}{*}{2}{144}\above{1pt}{1pt}{l}{2}{5}\above{1pt}{1pt}{}{2}{48}\above{1pt}{1pt}{}{2}{2}\above{1pt}{1pt}{}{2}{3}\above{1pt}{1pt}{r}{2}{80}\above{1pt}{1pt}{*}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
223920\\14400\\-1440
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
14400\\174\\-36
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1440\\-36\\5
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-48\\-630
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2\\-95\\-1260
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-50\\-660
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7\\324\\4320
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\140\\1865
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7\\328\\4368
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\47\\626
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\47\\627
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\140\\1880
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[223920, 14400, -1440; 14400, 174, -36; -1440, -36, 5],[720, 6, 1],[-1, -2, -1, 7, 3, 7, 1, 1, 3; -48, -95, -50, 324, 140, 328, 47, 47, 140; -630, -1260, -660, 4320, 1865, 4368, 626, 627, 1880],205,2]
%
% END OF LATTICE L206.2
%
\hbox{}\par\smallskip%
%
% LATTICE L206.3
%
\leavevmode%
${L_{206.3}}$%
{} : {$[1\above{1pt}{1pt}{1}{}2\above{1pt}{1pt}{1}{}]\above{1pt}{1pt}{}{0}16\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{1}{}3\above{1pt}{1pt}{1}{}9\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{2}{}5\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{32,3m,3,m}%
\EasyButWeakLineBreak%
{${16}\above{1pt}{1pt}{s}{2}{120}\above{1pt}{1pt}{24,17}{\infty z}{30}\above{1pt}{1pt}{}{2}{1}\above{1pt}{1pt}{r}{2}{720}\above{1pt}{1pt}{*}{2}{12}\above{1pt}{1pt}{l}{2}{18}\above{1pt}{1pt}{r}{2}{48}\above{1pt}{1pt}{s}{2}{180}\above{1pt}{1pt}{*}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-712080\\0\\3600
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\30\\-6
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3600\\-6\\-17
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
11\\436\\2168
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
21\\830\\4140
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7\\275\\1380
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\39\\197
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
11\\420\\2160
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-40\\-198
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-39\\-198
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5\\200\\984
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
37\\1470\\7290
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-712080, 0, 3600; 0, 30, -6; 3600, -6, -17],[720, 6, 1],[11, 21, 7, 1, 11, -1, -1, 5, 37; 436, 830, 275, 39, 420, -40, -39, 200, 1470; 2168, 4140, 1380, 197, 2160, -198, -198, 984, 7290],205,3]
%
% END OF LATTICE L206.3
%
\hbox{}\par\smallskip%
%
% LATTICE L206.4
%
\leavevmode%
${L_{206.4}}$%
{} : {$[1\above{1pt}{1pt}{-}{}2\above{1pt}{1pt}{1}{}]\above{1pt}{1pt}{}{2}16\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{1}{}9\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{2}{}5\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{3m,3,m}%
\EasyButWeakLineBreak%
{${9}\above{1pt}{1pt}{r}{2}{120}\above{1pt}{1pt}{24,7}{\infty z}{30}\above{1pt}{1pt}{r}{2}{144}\above{1pt}{1pt}{s}{2}{20}\above{1pt}{1pt}{*}{2}{48}\above{1pt}{1pt}{s}{2}{8}\above{1pt}{1pt}{l}{2}{3}\above{1pt}{1pt}{}{2}{80}\above{1pt}{1pt}{}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
261856080\\-6681600\\141840
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-6681600\\170490\\-3618
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
141840\\-3618\\83
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-39\\9
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
277\\10810\\-2160
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
764\\29815\\-5970
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3749\\146304\\-29304
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1897\\74030\\-14830
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1415\\55220\\-11064
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
203\\7922\\-1588
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
41\\1600\\-321
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
41\\1600\\-320
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[261856080, -6681600, 141840; -6681600, 170490, -3618; 141840, -3618, 83],[720, 6, 1],[-1, 277, 764, 3749, 1897, 1415, 203, 41, 41; -39, 10810, 29815, 146304, 74030, 55220, 7922, 1600, 1600; 9, -2160, -5970, -29304, -14830, -11064, -1588, -321, -320],205,4]
%
% END OF LATTICE L206.4
%
\hbox{}\par\smallskip%
%
% LATTICE L206.5
%
\leavevmode%
${L_{206.5}}$%
{} : {$[1\above{1pt}{1pt}{1}{}2\above{1pt}{1pt}{1}{}]\above{1pt}{1pt}{}{6}16\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{1}{}9\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{2}{}5\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{3}%
\EasyButWeakLineBreak%
{${36}\above{1pt}{1pt}{*}{2}{120}\above{1pt}{1pt}{24,19}{\infty z}{30}\above{1pt}{1pt}{}{2}{144}\above{1pt}{1pt}{}{2}{5}\above{1pt}{1pt}{r}{2}{48}\above{1pt}{1pt}{*}{2}{8}\above{1pt}{1pt}{*}{2}{12}\above{1pt}{1pt}{s}{2}{80}\above{1pt}{1pt}{s}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-238320\\2880\\0
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2880\\-6\\-12
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\-12\\5
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-84\\-198
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3\\-250\\-600
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-85\\-210
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\72\\144
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\80\\185
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\244\\576
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\82\\196
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\82\\198
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\80\\200
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-238320, 2880, 0; 2880, -6, -12; 0, -12, 5],[720, 6, 1],[-1, -3, -1, 1, 1, 3, 1, 1, 1; -84, -250, -85, 72, 80, 244, 82, 82, 80; -198, -600, -210, 144, 185, 576, 196, 198, 200],205,5]
%
% END OF LATTICE L206.5
%
%
% LATTICE L206.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-22920, 9240, 600; 9240, -3725, -242; 600, -242, -15],[120, 1, 1],[13, 97, 23, -11, -29, -16, -13, 5, 53; 32, 240, 60, -26, -70, -39, -32, 12, 130; 3, 0, -60, -24, -35, -12, -4, 6, 20],205,6]
%
% END OF LATTICE L206.6
%
%
% LATTICE L206.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-5820, 540, -300; 540, -50, 28; -300, 28, -15],[60, 2, 1],[0, 4, 11, 7, 9, 5, 0, -1, -3; 2, 45, 105, 64, 80, 42, -1, -9, -20; 3, 0, -30, -24, -35, -24, -2, 3, 20],205,7]
%
% END OF LATTICE L206.7
%
%
% LATTICE L206.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-1250040, -59520, 3360; -59520, -2834, 160; 3360, 160, -9],[120, 2, 1],[3, 19, 13, 13, 14, 5, -1, -1, 7; -61, -390, -270, -272, -295, -108, 20, 21, -140; 34, 150, 45, 8, -30, -60, -18, 0, 120],205,8]
%
% END OF LATTICE L206.8
%
%
% LATTICE L206.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-26122440, -1243920, 31920; -1243920, -59234, 1520; 31920, 1520, -39],[120, 2, 1],[6, 17, 41, 19, 19, 5, -1, -1, 17; -121, -345, -840, -392, -395, -108, 20, 21, -340; 194, 465, 810, 268, 150, -120, -39, 0, 660],205,9]
%
% END OF LATTICE L206.9
%
%
% LATTICE L206.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-3688080, 17280, 8160; 17280, -78, -40; 8160, -40, -17],[240, 2, 1],[19, 41, 17, 3, 17, -1, -1, 5, 19; 2268, 4890, 2025, 357, 2020, -120, -119, 600, 2270; 3776, 8160, 3390, 599, 3400, -198, -200, 984, 3770],205,10]
%
% END OF LATTICE L206.10
%
%
% LATTICE L206.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-11874480, 303360, -14400; 303360, -7750, 368; -14400, 368, -15],[240, 2, 1],[33, 68, 179, 19, 127, -1, -19, -47, -1; 1288, 2655, 6990, 742, 4960, -39, -742, -1836, -40; -88, -150, -360, -37, -240, 3, 36, 72, -30],205,11]
%
% END OF LATTICE L206.11
%
%
% LATTICE L206.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-1204080, 5040, 4560; 5040, -18, -20; 4560, -20, -17],[240, 2, 1],[13, 13, 19, 3, 7, -1, -1, 5, 7; 768, 765, 1110, 174, 400, -60, -58, 300, 415; 2576, 2580, 3780, 598, 1400, -198, -200, 984, 1385],205,12]
%
% END OF LATTICE L206.12
%
%
% LATTICE L206.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[12720, 480, 240; 480, 18, 10; 240, 10, -3],[240, 2, 1],[-5, -11, -2, 1, 13, 2, 1, 1, -2; 124, 270, 45, -28, -340, -51, -25, -24, 50; 8, 0, -30, -26, -160, -15, -4, 0, 5],205,13]
%
% END OF LATTICE L206.13
%
%
% LATTICE L206.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[448020, -46800, 3060; -46800, 4890, -318; 3060, -318, 23],[180, 6, 1],[331, 128, 17, -1, 11, 11, 21, 133, 172; 3012, 1165, 155, -9, 100, 100, 191, 1210, 1565; -2412, -930, -120, 9, -80, -81, -154, -972, -1255],205,14]
%
% END OF LATTICE L206.14
%
%
% LATTICE L206.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[2948760, 65520, -16200; 65520, 1446, -360; -16200, -360, 89],[360, 6, 1],[-5, -1, 3, 1, -1, -2, -4, -11, -32; -12, -20, -5, -1, 0, 1, 0, -8, -45; -964, -270, 525, 178, -180, -360, -729, -2040, -6030],205,15]
%
% END OF LATTICE L206.15
%
%
% LATTICE L206.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[24720840, 1177200, -30240; 1177200, 56058, -1440; -30240, -1440, 37],[360, 6, 1],[121, 24, 7, -1, 1, 3, 7, 47, 62; -2448, -485, -140, 21, -20, -61, -142, -952, -1255; 3600, 735, 270, 0, 40, 78, 194, 1356, 1820],205,16]
%
% END OF LATTICE L206.16
%
%
% LATTICE L206.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-66840, 480, 1080; 480, 0, -9; 1080, -9, -17],[120, 3, 1],[-1, -3, 3, 4, 31, 5, 7, 1, 2; -18, -60, 40, 66, 530, 88, 128, 19, 40; -54, -160, 160, 213, 1650, 266, 372, 53, 105],205,17]
%
% END OF LATTICE L206.17
%
%
% LATTICE L206.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[60, 0, 0; 0, -6, 0; 0, 0, 1],[60, 6, 1],[0, -1, -4, -9, -13, -3, -1, 0, 1; 1, 5, 15, 32, 45, 10, 3, 0, 0; 3, 10, 20, 36, 45, 8, 0, -1, 0],205,18]
%
% END OF LATTICE L206.18
%
%
% LATTICE L206.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-8520, 1800, -360; 1800, -380, 76; -360, 76, -15],[120, 4, 1],[-4, -17, -13, -1, -2, 1, 1, -1, -4; -23, -90, -60, -4, -5, 6, 4, -9, -25; -24, -60, 0, 3, 20, 6, -4, -24, -35],205,19]
%
% END OF LATTICE L206.19
%
%
% LATTICE L206.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-8520, 960, 360; 960, -108, -40; 360, -40, -13],[120, 4, 1],[0, 13, 47, 17, 48, 8, 3, -1, -3; -1, 120, 450, 164, 465, 78, 30, -9, -30; 4, 0, -60, -26, -80, -15, -8, 0, 10],205,20]
%
% END OF LATTICE L206.20
%
%
% LATTICE L206.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[6360, 1080, -240; 1080, 175, -40; -240, -40, 9],[120, 5, 1],[1, 1, -1, -3, -1, -2, -1, 1, 1; 2, 0, -12, -26, -8, -15, -8, 0, 2; 35, 24, -84, -200, -63, -120, -60, 30, 36],205,21]
%
% END OF LATTICE L206.21
%
%
% LATTICE L206.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3180, -600, -120; -600, 130, -80; -120, -80, 9],[60, 10, 1],[7, -1, -26, -111, -34, -127, -17, -1, 7; -20, 3, 75, 320, 98, 366, 49, 3, -20; -85, 12, 318, 1360, 417, 1560, 210, 15, -84],205,22]
%
% END OF LATTICE L206.22
%
%
% LATTICE L206.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[13320, 840, -480; 840, -54, 6; -480, 6, 5],[120, 6, 1],[13, 9, 3, 2, -1, -1, -1, 1, 13; 304, 210, 70, 47, -20, -23, -23, 24, 305; 876, 610, 205, 138, -60, -68, -69, 64, 870],205,23]
%
% END OF LATTICE L206.23
%
%
% LATTICE L206.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[120, 0, 0; 0, 6, 0; 0, 0, -1],[120, 6, 1],[-9, -2, -1, 0, 1, 0, -1, -3, -13; -28, -5, 0, 1, 0, -1, -6, -12, -45; -120, -25, -10, 0, 0, -2, -18, -44, -180],205,24]
%
% END OF LATTICE L206.24
%
%
% LATTICE L206.25
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-101640, -16920, 960; -16920, -2816, 160; 960, 160, -9],[120, 8, 1],[5, 14, 8, 7, 13, 1, -1, -1, 7; -26, -75, -45, -41, -80, -9, 5, 6, -35; 68, 150, 45, 8, -60, -60, -18, 0, 120],205,25]
%
% END OF LATTICE L206.25
%
%
% LATTICE L206.26
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[124920, 31320, -360; 31320, 7851, -90; -360, -90, 1],[360, 3, 1],[0, 9, 31, 11, 46, 5, 5, -1, -7; 0, -40, -140, -50, -210, -23, -24, 4, 30; -1, -360, -1380, -512, -2205, -252, -324, 6, 180],205,26]
%
% END OF LATTICE L206.26
%
%
% LATTICE L206.27
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[180, 0, 0; 0, -6, 0; 0, 0, 1],[180, 6, 1],[0, -1, -4, -3, -13, -3, -1, 0, 1; 0, 5, 25, 20, 90, 22, 9, 1, 0; -1, 0, 30, 28, 135, 36, 18, 3, 0],205,27]
%
% END OF LATTICE L206.27
%
%
% LATTICE L206.28
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-600, 240, -120; 240, -90, 40; -120, 40, -13],[120, 10, 1],[5, 2, 5, 5, 3, -1, -3, -7, 0; 8, 6, 18, 19, 12, -3, -12, -36, -3; -40, -3, 6, 10, 8, 0, -10, -60, -14],205,28]
%
% END OF LATTICE L206.28
%
%
% LATTICE L206.29
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-12840, 4320, -600; 4320, -1450, 200; -600, 200, -27],[120, 10, 1],[11, 7, 4, 8, 5, -1, -2, -7, 1; 32, 24, 15, 31, 20, -3, -8, -36, 1; -20, 18, 21, 50, 36, 0, -15, -120, -18],205,29]
%
% END OF LATTICE L206.29
%
%
% LATTICE L206.30
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[53160, -13200, 240; -13200, 3276, -60; 240, -60, 1],[120, 12, 1],[20, 17, 3, -1, -4, 0, 5, 7, 59; 71, 60, 10, -4, -15, 0, 18, 25, 210; -504, -440, -100, 6, 60, -1, -120, -172, -1470],205,30]
%
% END OF LATTICE L206.30
%
%
% LATTICE L206.31
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-537840, -18960, 7200; -18960, -666, 252; 7200, 252, -95],[240, 6, 1],[25, 7, -1, -1, 7, 1, 4, 13, 22; -1444, -410, 55, 58, -380, -56, -227, -744, -1265; -1944, -560, 70, 78, -480, -73, -300, -992, -1695],205,31]
%
% END OF LATTICE L206.31
%
%
% LATTICE L206.32
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-74160, -480, 720; -480, 54, -6; 720, -6, -5],[240, 6, 1],[13, 9, 3, 1, -1, -1, -1, 1, 13; 268, 190, 65, 22, -20, -22, -23, 16, 260; 1488, 1040, 350, 117, -120, -118, -120, 104, 1470],205,32]
%
% END OF LATTICE L206.32
%
%
% LATTICE L206.33
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[240, 0, 0; 0, -6, 0; 0, 0, 1],[240, 6, 1],[-9, -2, -1, 0, 1, 0, -1, -3, -13; 64, 15, 10, 1, 0, 0, 6, 20, 90; 72, 20, 20, 3, 0, -1, 0, 16, 90],205,33]
%
% END OF LATTICE L206.33
%
%
% LATTICE L206.34
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-23760, -2400, 960; -2400, -198, 84; 960, 84, -35],[240, 6, 1],[19, 3, -1, -1, 1, 1, 5, 9, 16; 488, 75, -30, -26, 40, 28, 134, 236, 415; 1680, 260, -100, -90, 120, 94, 456, 808, 1425],205,34]
%
% END OF LATTICE L206.34
%
%
% LATTICE L206.35
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-216840, 0, 1920; 0, 12, 0; 1920, 0, -17],[120, 12, 1],[0, -3, -7, -3, -14, -1, 1, 1, 2; 1, 0, -10, -7, -45, -6, -6, -1, 0; 0, -340, -800, -345, -1620, -118, 108, 112, 225],205,35]
%
% END OF LATTICE L206.35
%
%
% LATTICE L206.36
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-110520, 1320, 1200; 1320, 0, -15; 1200, -15, -13],[120, 15, 1],[-1, -1, 1, 7, 11, 9, 13, 2, 1; -2, -4, 0, 14, 26, 24, 40, 7, 4; -90, -88, 88, 615, 966, 790, 1140, 175, 87],205,36]
%
% END OF LATTICE L206.36
%
%
% LATTICE L206.37
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-60, 900, -60; 900, -10110, 660; -60, 660, -43],[60, 30, 1],[0, -1, 0, 15, 7, 13, 11, 4, 5; 1, -1, -1, 2, 3, 8, 9, 4, 6; 15, -14, -16, 0, 33, 100, 120, 55, 84],205,37]
%
% END OF LATTICE L206.37
%
%
% LATTICE L206.38
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2399280, 262320, -6000; 262320, -28680, 656; -6000, 656, -15],[240, 8, 1],[0, 4, 11, 7, 9, 5, 0, -1, -3; 1, 45, 105, 64, 80, 42, -1, -9, -20; 43, 360, 180, -8, -110, -168, -44, 6, 320],205,38]
%
% END OF LATTICE L206.38
%
%
% LATTICE L206.39
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-196080, 19200, -3840; 19200, -1880, 376; -3840, 376, -75],[240, 8, 1],[3, 19, 26, 13, 7, 5, -1, -1, 7; 32, 195, 255, 124, 65, 42, -11, -9, 80; 6, 0, -60, -48, -35, -48, -4, 6, 40],205,39]
%
% END OF LATTICE L206.39
%
%
% LATTICE L206.40
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-664080, 7920, 3360; 7920, -72, -40; 3360, -40, -17],[240, 8, 1],[3, 19, 26, 13, 14, 5, -1, -1, 7; -3, -15, -15, -6, -5, 0, 1, 0, -10; 598, 3780, 5160, 2576, 2770, 984, -200, -198, 1400],205,40]
%
% END OF LATTICE L206.40
%
%
% LATTICE L206.41
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3120, 480, 240; 480, -72, -40; 240, -40, -13],[240, 8, 1],[-14, -37, -8, 1, 3, 1, -3, -7, -81; -73, -195, -45, 4, 15, 6, -15, -36, -420; -26, -60, 0, 8, 10, 0, -8, -15, -160],205,41]
%
% END OF LATTICE L206.41
%
%
% LATTICE L206.42
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[360, 0, 0; 0, 6, 0; 0, 0, -1],[360, 6, 1],[-3, -2, -1, 0, 1, 0, -1, -3, -13; -12, -10, -10, -1, 0, 1, 0, -8, -45; -64, -45, -30, -2, 0, 0, -18, -60, -270],205,42]
%
% END OF LATTICE L206.42
%
%
% LATTICE L206.43
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-60840, 2520, 1080; 2520, -30, -6; 1080, -6, 1],[360, 6, 1],[-4, -2, -1, 1, 1, 1, 0, -1, -7; -549, -275, -140, 132, 135, 136, 0, -137, -960; 1044, 525, 270, -252, -260, -264, -1, 258, 1820],205,43]
%
% END OF LATTICE L206.43
%
%
% LATTICE L206.44
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[6360, 2160, -240; 2160, 700, -80; -240, -80, 9],[120, 20, 1],[-3, -1, 1, 1, 1, 1, -1, -4, -1; -13, -6, 0, 1, 1, 0, -4, -15, -4; -200, -84, 24, 35, 36, 30, -60, -240, -63],205,44]
%
% END OF LATTICE L206.44
%
%
% LATTICE L206.45
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-37200, 3120, -240; 3120, 250, -60; -240, -60, 11],[240, 10, 1],[11, 7, 4, 4, 5, -1, -2, -7, 1; 252, 162, 93, 93, 116, -24, -47, -168, 22; 1600, 1032, 594, 595, 744, -150, -300, -1080, 138],205,45]
%
% END OF LATTICE L206.45
%
%
% LATTICE L206.46
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-378480, -45840, 2160; -45840, -5550, 260; 2160, 260, -11],[240, 10, 1],[-23, 1, 13, 8, 11, -1, -13, -59, -11; 200, -9, -114, -70, -96, 9, 114, 516, 96; 200, -18, -144, -85, -112, 15, 140, 600, 106],205,46]
%
% END OF LATTICE L206.46
%
%
% LATTICE L206.47
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[600, -240, 0; -240, 100, 0; 0, 0, -1],[120, 20, 1],[2, 1, -1, -3, -2, -2, -1, 1, 1; 3, 0, -6, -12, -7, -6, -2, 3, 2; -20, -24, -36, -50, -24, -15, 0, 0, -6],205,47]
%
% END OF LATTICE L206.47
%
%
% LATTICE L206.48
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1200, 240, 0; 240, 230, -50; 0, -50, 9],[240, 10, 1],[5, 2, 5, 5, 3, -1, -3, -7, 0; 56, 15, 30, 28, 16, -6, -14, -12, 4; 240, 72, 156, 150, 88, -30, -80, -120, 13],205,48]
%
% END OF LATTICE L206.48
%
%
% LATTICE L206.49
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[240, 0, 0; 0, 10, 0; 0, 0, -1],[240, 10, 1],[-1, -1, -1, -3, -3, -1, 0, 1, 0; -12, -6, -3, -6, -4, 0, 1, 0, -1; -40, -24, -18, -50, -48, -15, 0, 0, -3],205,49]
%
% END OF LATTICE L206.49
%
%
% LATTICE L206.50
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[97320, 30600, -1680; 30600, 9600, -528; -1680, -528, 29],[120, 24, 1],[9, 6, 2, 3, 1, -1, -1, 1, 19; -14, -5, 0, 1, 0, -1, -3, -6, -45; 252, 250, 115, 192, 60, -76, -114, -56, 240],205,50]
%
% END OF LATTICE L206.50
%
%
% LATTICE L206.51
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-6360, -9960, 1080; -9960, -10350, 1110; 1080, 1110, -119],[120, 30, 1],[2, 1, 5, 49, 13, 13, 1, -1, -1; -63, -30, -146, -1416, -373, -368, -25, 31, 28; -570, -271, -1318, -12780, -3366, -3320, -225, 280, 252],205,51]
%
% END OF LATTICE L206.51
%
%
% LATTICE L206.52
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-97320, 0, 1680; 0, 30, 0; 1680, 0, -29],[120, 30, 1],[0, -1, 0, 15, 7, 13, 11, 4, 5; 1, 0, -1, -28, -9, -12, -6, -1, 0; 0, -58, -1, 840, 396, 740, 630, 230, 288],205,52]
%
% END OF LATTICE L206.52
%
%
% LATTICE L206.53
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-116280, -5760, 1800; -5760, -276, 84; 1800, 84, -25],[360, 12, 1],[1, -1, -9, -11, -11, -4, -1, 0, 1; -48, 40, 410, 507, 510, 187, 48, 1, -45; -90, 60, 720, 900, 910, 336, 88, 3, -80],205,53]
%
% END OF LATTICE L206.53
%
%
% LATTICE L206.54
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[124920, 62640, -360; 62640, 31404, -180; -360, -180, 1],[360, 12, 1],[11, 31, 9, 0, -7, -1, 5, 10, 46; -25, -70, -20, 0, 15, 2, -12, -23, -105; -512, -1380, -360, -1, 180, 6, -324, -504, -2205],205,54]
%
% END OF LATTICE L206.54
%
%
% LATTICE L206.55
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[281520, -12960, 1440; -12960, 174, 6; 1440, 6, -5],[720, 6, 1],[-5, -1, 3, 1, -1, -1, -4, -11, -16; -316, -70, 185, 62, -60, -62, -249, -688, -1005; -1856, -420, 1080, 362, -360, -363, -1458, -4032, -5895],205,55]
%
% END OF LATTICE L206.55
%
%
% LATTICE L206.56
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[720, 0, 0; 0, -6, 0; 0, 0, 1],[720, 6, 1],[-3, -2, -1, 0, 1, 0, -1, -3, -13; 40, 25, 10, 0, 0, 1, 18, 44, 180; 56, 30, 0, -1, 0, 3, 36, 72, 270],205,56]
%
% END OF LATTICE L206.56
%
%
% LATTICE L206.57
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-978120, 108720, -4320; 108720, -12084, 480; -4320, 480, -19],[360, 12, 1],[-5, -13, -7, -1, 1, 2, 1, -1, -7; -57, -140, -70, -9, 10, 19, 8, -16, -85; -315, -600, -180, 0, 25, 24, -28, -186, -580],205,57]
%
% END OF LATTICE L206.57
%
%
% LATTICE L206.58
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[216720, -2160, 0; -2160, -150, 54; 0, 54, -17],[720, 6, 1],[9, 8, 9, 1, 1, -1, -1, 5, 16; 904, 805, 910, 102, 120, -100, -102, 500, 1605; 2864, 2550, 2880, 322, 360, -318, -324, 1584, 5085],205,58]
%
% END OF LATTICE L206.58
%
%
% LATTICE L206.59
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-15480, 0, 3960; 0, 12, 0; 3960, 0, -1013],[360, 12, 1],[-1, -61, -229, -85, -733, -42, -55, 0, 23; -1, -10, -20, -6, -45, -2, 0, 1, 0; -4, -240, -900, -334, -2880, -165, -216, 0, 90],205,59]
%
% END OF LATTICE L206.59
%
%
% LATTICE L206.60
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-510480, -3600, -4320; -3600, 30, 24; -4320, 24, 17],[720, 6, 1],[2, 2, 1, -1, -1, -1, 0, 1, 7; 1296, 1295, 650, -636, -640, -640, 1, 650, 4540; -1323, -1320, -660, 648, 650, 648, -2, -666, -4640],205,60]
%
% END OF LATTICE L206.60
%
%
% LATTICE L206.61
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[90120, 25440, -1560; 25440, 7160, -440; -1560, -440, 27],[120, 40, 1],[0, 1, 1, 5, 2, 1, -1, -4, -1; -13, -3, 0, 2, 1, 0, -2, -15, -8; -220, 6, 57, 320, 132, 60, -90, -480, -192],205,61]
%
% END OF LATTICE L206.61
%
%
% LATTICE L206.62
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[11160, -2160, 1080; -2160, 195, -90; 1080, -90, 41],[360, 15, 1],[-5, -3, -1, 0, 1, 1, -1, -2, -4; -434, -260, -88, -2, 78, 80, -96, -175, -348; -820, -492, -168, -5, 144, 150, -180, -330, -657],205,62]
%
% END OF LATTICE L206.62
%
%
% LATTICE L206.63
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-34920, 203040, -40680; 203040, -781185, 155820; -40680, 155820, -31079],[360, 15, 1],[-188, 31, 85, 29, -28, -140, -251, -415, -137; -3774, 616, 1700, 582, -560, -2801, -5024, -8312, -2746; -18675, 3048, 8412, 2880, -2771, -13860, -24860, -41130, -13588],205,63]
%
% END OF LATTICE L206.63
%
%
% LATTICE L206.64
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[31140, 13500, -900; 13500, 8790, -600; -900, -600, 41],[180, 30, 1],[17, 5, 2, 1, 1, 0, 4, 15, 14; -592, -175, -71, -36, -36, 1, -135, -518, -486; -8300, -2454, -996, -505, -504, 15, -1890, -7260, -6813],205,64]
%
% END OF LATTICE L206.64
%
%
% LATTICE L206.65
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[161100, 87480, -2340; 87480, 46950, -1230; -2340, -1230, 31],[180, 30, 1],[-167, -21, -10, -1, 9, 18, 8, -19, -12; 486, 61, 29, 3, -26, -52, -23, 56, 35; 6660, 834, 396, 45, -352, -705, -310, 780, 481],205,65]
%
% END OF LATTICE L206.65
%
%
% LATTICE L206.66
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[55440, 240, -240; 240, -24, 0; -240, 0, 1],[240, 24, 1],[0, -1, -4, -9, -13, -3, -1, 0, 1; 1, -5, -25, -58, -85, -20, -7, 0, 10; 6, -220, -920, -2088, -3030, -704, -240, -1, 240],205,66]
%
% END OF LATTICE L206.66
%
%
% LATTICE L206.67
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-41040, -7440, 1200; -7440, -1320, 216; 1200, 216, -35],[240, 24, 1],[0, -2, -3, -3, -1, 1, 2, 1, 7; 1, -5, -15, -28, -35, -6, 1, 2, 20; 6, -100, -200, -288, -270, -8, 72, 46, 360],205,67]
%
% END OF LATTICE L206.67
%
%
% LATTICE L206.68
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-23760, 12480, 1440; 12480, -4680, -552; 1440, -552, -65],[240, 24, 1],[-1, -1, 6, 19, 16, 9, 5, 1, 1; 32, 35, -185, -596, -505, -286, -161, -33, -40; -294, -320, 1700, 5472, 4635, 2624, 1476, 302, 360],205,68]
%
% END OF LATTICE L206.68
%
%
% LATTICE L206.69
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-45360, -29760, 480; -29760, -19416, 312; 480, 312, -5],[240, 24, 1],[2, 4, 1, -1, -3, -1, 0, 1, 21; -7, -15, -5, 2, 10, 4, 1, -3, -70; -249, -560, -220, 24, 330, 152, 60, -94, -2400],205,69]
%
% END OF LATTICE L206.69
%
%
% LATTICE L206.70
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-40440, 1800, 1320; 1800, -60, -60; 1320, -60, -43],[120, 60, 1],[1, -1, -1, 1, 3, 2, 9, 4, 3; 15, 0, -2, 0, 5, 4, 22, 13, 14; 0, -32, -28, 30, 84, 55, 240, 100, 66],205,70]
%
% END OF LATTICE L206.70
%
%
% LATTICE L206.71
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3601200, -644160, 43920; -644160, -112770, 7680; 43920, 7680, -523],[240, 30, 1],[73, 3, -1, -1, 11, 5, 16, 45, 14; -8172, -338, 111, 114, -1220, -556, -1783, -5024, -1565; -113880, -4712, 1546, 1590, -16992, -7745, -24840, -70000, -21807],205,71]
%
% END OF LATTICE L206.71
%
%
% LATTICE L206.72
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-67440, -14640, 2640; -14640, -3150, 570; 2640, 570, -103],[240, 30, 1],[49, 5, 1, 1, -1, -1, 1, 13, 13; 276, 30, 7, 9, -4, -8, 1, 64, 70; 2760, 292, 64, 75, -48, -70, 30, 680, 714],205,72]
%
% END OF LATTICE L206.72
%
%
% LATTICE L206.73
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-194640, -50400, 3360; -50400, -10110, 660; 3360, 660, -43],[240, 30, 1],[15, 0, -1, 0, 5, 2, 11, 13, 7; -896, -1, 58, 1, -288, -116, -642, -764, -414; -12600, -16, 812, 15, -4032, -1625, -9000, -10720, -5814],205,73]
%
% END OF LATTICE L206.73
%
%
% LATTICE L206.74
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-253200, -111360, 7680; -111360, -47070, 3240; 7680, 3240, -223],[240, 30, 1],[43, 1, -1, -1, 5, 5, 17, 25, 8; -2232, -53, 50, 54, -248, -252, -866, -1284, -413; -30960, -736, 692, 750, -3432, -3490, -12000, -17800, -5727],205,74]
%
% END OF LATTICE L206.74
%
%
% LATTICE L206.75
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-9960, 0, 360; 0, 60, 0; 360, 0, -13],[120, 60, 1],[0, -1, -1, 0, 2, 3, 7, 3, 1; 1, 0, -2, -7, -9, -6, -6, -1, 0; 0, -28, -32, -15, 36, 70, 180, 80, 27],205,75]
%
% END OF LATTICE L206.75
%
%
% LATTICE L206.76
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[291960, 11160, -5400; 11160, 384, -192; -5400, -192, 95],[360, 24, 1],[3, 6, 2, 1, 1, -1, -1, 1, 19; 154, 325, 115, 59, 60, -61, -69, 34, 915; 476, 990, 345, 176, 180, -180, -198, 120, 2880],205,76]
%
% END OF LATTICE L206.76
%
%
% LATTICE L206.77
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[20160, 6120, 1800; 6120, 456, 120; 1800, 120, 31],[360, 24, 1],[-8, -2, -1, 1, 2, 1, 0, -2, -7; 831, 205, 100, -99, -195, -95, 3, 215, 735; -2736, -675, -330, 324, 640, 312, -10, -708, -2420],205,77]
%
% END OF LATTICE L206.77
%
%
% LATTICE L206.78
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-188400, 78480, -1440; 78480, -32680, 600; -1440, 600, -11],[240, 40, 1],[1, -1, -2, -1, -1, 1, 2, 7, 1; -4, -3, -3, -1, 0, 3, 3, 6, 0; -360, -36, 96, 75, 128, 30, -100, -600, -134],205,78]
%
% END OF LATTICE L206.78
%
%
% LATTICE L206.79
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[102480, -42720, 960; -42720, 17800, -400; 960, -400, 9],[240, 40, 1],[7, 2, 1, 1, 1, 1, 1, 7, 1; 8, 3, 3, 4, 4, 3, 1, 6, 1; -400, -84, 24, 70, 72, 30, -60, -480, -63],205,79]
%
% END OF LATTICE L206.79
%
%
% LATTICE L206.80
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[256560, 42720, -1680; 42720, 7080, -280; -1680, -280, 11],[240, 40, 1],[2, 2, 1, -1, -1, -7, -2, -1, 1; -3, -3, -3, -6, -1, 0, 1, 0, -2; 230, 228, 72, -320, -182, -1080, -280, -150, 104],205,80]
%
% END OF LATTICE L206.80
%
%
% LATTICE L206.81
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[240, 0, 0; 0, 40, 0; 0, 0, -1],[240, 40, 1],[-3, -2, -1, -1, 0, 1, 0, -1, -3; -3, -3, -3, -6, -1, 0, 1, 0, -2; -50, -36, -24, -40, -6, 0, 0, -15, -48],205,81]
%
% END OF LATTICE L206.81
%
%
% LATTICE L206.82
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[159480, 16560, -1440; 16560, 1650, -150; -1440, -150, 13],[360, 30, 1],[7, 3, 1, 1, -1, -2, -2, 1, 4; -12, -4, -1, -1, 0, 1, 0, -8, -9; 620, 282, 99, 100, -108, -210, -225, 0, 324],205,82]
%
% END OF LATTICE L206.82
%
%
% LATTICE L206.83
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1410120, 0, 9720; 0, 30, 0; 9720, 0, 67],[360, 30, 1],[49, 7, 5, 2, 1, 0, 13, 45, 41; -12, -2, -2, -1, 0, 1, 0, -8, -9; -7120, -1017, -726, -290, -144, 0, -1890, -6540, -5958],205,83]
%
% END OF LATTICE L206.83
%
%
% LATTICE L206.84
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-16920, 5760, -360; 5760, -1950, 120; -360, 120, -7],[360, 30, 1],[-1, -1, 0, 13, 2, 11, 3, 3, 1; -3, -4, -1, 24, 5, 32, 10, 11, 4; 0, -18, -21, -360, -28, -60, 10, 30, 16],205,84]
%
% END OF LATTICE L206.84
%
%
% LATTICE L206.85
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2624760, 149400, -14760; 149400, 8490, -840; -14760, -840, 83],[360, 30, 1],[1, -1, 0, 8, 5, 7, 2, 9, 1; 0, -2, -2, -15, -4, -1, 1, 8, 1; 180, -198, -21, 1260, 844, 1230, 365, 1680, 188],205,85]
%
% END OF LATTICE L206.85
%
%
% LATTICE L206.86
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[13440, 360, -120; 360, -120, 0; -120, 0, 1],[120, 120, 1],[1, 0, -1, -14, -9, -6, -3, -1, 0; 3, 0, -2, -27, -17, -11, -5, -1, 1; 120, -1, -118, -1620, -1032, -680, -330, -100, 12],205,86]
%
% END OF LATTICE L206.86
%
%
% LATTICE L206.87
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[150480, -49680, -17280; -49680, 16392, 5712; -17280, 5712, 1979],[720, 24, 1],[-679, -293, -62, 7, 29, -1, -28, -235, -332; -1380, -595, -125, 15, 60, -2, -57, -478, -675; -1944, -840, -180, 18, 80, -3, -80, -672, -950],205,87]
%
% END OF LATTICE L206.87
%
%
% LATTICE L206.88
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[497520, 720, -720; 720, -24, 0; -720, 0, 1],[720, 24, 1],[-3, -4, -1, 0, 1, 0, -1, -3, -13; -70, -95, -25, 0, 30, 1, -21, -68, -300; -2104, -2820, -720, -1, 720, 6, -684, -2088, -9090],205,88]
%
% END OF LATTICE L206.88
%
%
% LATTICE L206.89
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2981520, 1151280, -8640; 1151280, -444552, 3336; -8640, 3336, -25],[720, 24, 1],[-85, -42, -13, 1, 11, 3, -1, -23, -38; -234, -115, -35, 3, 30, 8, -3, -64, -105; -1872, -840, -180, 54, 200, 30, -56, -600, -890],205,89]
%
% END OF LATTICE L206.89
%
%
% LATTICE L206.90
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[85680, 5040, -720; 5040, -24, -24; -720, -24, 5],[720, 24, 1],[1, -2, -3, -1, 1, 1, 1, 3, 1; 6, -25, -35, -12, 10, 11, 11, 32, 10; 144, -420, -600, -198, 200, 198, 196, 576, 185],205,90]
%
% END OF LATTICE L206.90
%
%
% LATTICE L206.91
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-560880, -35280, 5760; -35280, -2184, 360; 5760, 360, -59],[720, 24, 1],[-1, 1, 4, 1, 11, 0, -2, -3, -4; -20, -5, 35, 10, 120, 1, -21, -38, -60; -224, 60, 600, 158, 1800, 6, -324, -528, -765],205,91]
%
% END OF LATTICE L206.91
%
%
% LATTICE L206.92
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2461680, -37440, 6480; -37440, -456, 96; 6480, 96, -17],[720, 24, 1],[1, 9, 16, 9, 32, 5, -1, -1, 1; 9, 85, 155, 88, 315, 50, -9, -10, 0; 430, 3900, 6960, 3920, 13950, 2184, -432, -438, 360],205,92]
%
% END OF LATTICE L206.92
%
%
% LATTICE L206.93
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[5969520, 28800, -10080; 28800, 120, -48; -10080, -48, 17],[720, 24, 1],[1, -1, -4, -2, -7, -1, 0, 1, 1; 18, -25, -95, -48, -170, -25, -1, 20, 20; 648, -660, -2640, -1323, -4640, -666, -4, 648, 650],205,93]
%
% END OF LATTICE L206.93
%
%
% LATTICE L206.94
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3023280, 216000, -55440; 216000, -15432, 3960; -55440, 3960, -1013],[720, 24, 1],[-82, -219, -56, -1, 23, -1, -55, -41, -1421; -1233, -3295, -845, -16, 345, -14, -825, -616, -21360; -334, -900, -240, -8, 90, 0, -216, -165, -5760],205,94]
%
% END OF LATTICE L206.94
%
%
% LATTICE L206.95
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-12600, 360, 0; 360, 780, -180; 0, -180, 41],[360, 60, 1],[0, -1, -3, -5, -4, -4, -1, 1, 1; -1, -38, -112, -187, -150, -151, -42, 34, 33; -5, -168, -492, -820, -657, -660, -180, 150, 144],205,95]
%
% END OF LATTICE L206.95
%
%
% LATTICE L206.96
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1692720, -552240, -4320; -552240, 180150, 1410; -4320, 1410, 11],[720, 30, 1],[2, 2, 1, -7, -11, -21, -8, -3, 5; 5, 5, 2, -20, -30, -56, -21, -8, 12; 145, 144, 132, -200, -486, -1080, -450, -150, 432],205,96]
%
% END OF LATTICE L206.96
%
%
% LATTICE L206.97
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2211480, 336600, -8280; 336600, 51180, -1260; -8280, -1260, 31],[360, 60, 1],[1, -1, -1, 1, 1, 2, 3, 4, 1; -15, -4, -2, 0, 1, 2, 2, -1, -2; -360, -432, -348, 270, 308, 615, 880, 1020, 182],205,97]
%
% END OF LATTICE L206.97
%
%
% LATTICE L206.98
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-625680, 12960, -1440; 12960, 150, -90; -1440, -90, 31],[720, 30, 1],[43, 1, -1, -1, 3, 4, 4, 31, 3; 3324, 74, -79, -78, 236, 314, 313, 2416, 233; 11520, 252, -276, -270, 824, 1095, 1090, 8400, 809],205,98]
%
% END OF LATTICE L206.98
%
%
% LATTICE L206.99
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[318960, -23040, 5040; -23040, 1050, -210; 5040, -210, 41],[720, 30, 1],[1, 1, 3, 7, 2, 1, -2, -1, -1; 108, 107, 314, 716, 198, 64, -225, -109, -108; 430, 426, 1248, 2840, 783, 240, -900, -435, -432],205,99]
%
% END OF LATTICE L206.99
%
%
% LATTICE L206.100
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2820240, -291600, 19440; -291600, 33090, -2220; 19440, -2220, 149],[720, 30, 1],[1, 5, 7, 49, 41, 45, 13, 0, 1; 144, 722, 1013, 7096, 5940, 6524, 1890, 1, 144; 2015, 10104, 14178, 99320, 83142, 91320, 26460, 15, 2016],205,100]
%
% END OF LATTICE L206.100
%
%
% LATTICE L206.101
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[360, -360, 0; -360, 420, 0; 0, 0, -1],[360, 60, 1],[-5, -3, -1, 0, 1, 1, -1, -2, -8; -6, -4, -2, -1, 0, 1, 0, -2, -9; -50, -36, -24, -20, -18, 0, 0, -15, -72],205,101]
%
% END OF LATTICE L206.101
%
%
% LATTICE L206.102
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-9630000, -184320, 17280; -184320, -3450, 330; 17280, 330, -31],[720, 30, 1],[-11, -5, 0, 3, 1, -1, -11, -13, -41; -72, -34, -1, 16, 6, -4, -66, -82, -264; -6910, -3156, -12, 1840, 621, -600, -6840, -8130, -25704],205,102]
%
% END OF LATTICE L206.102
%
%
% LATTICE L206.103
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1875600, 249840, -8640; 249840, 33090, -1110; -8640, -1110, 31],[720, 30, 1],[-319, -20, -19, -1, 17, 17, 15, -37, -23; 2856, 179, 170, 9, -152, -152, -134, 332, 206; 13320, 834, 792, 45, -704, -705, -620, 1560, 962],205,103]
%
% END OF LATTICE L206.103
%
%
% LATTICE L206.104
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-35899560, 11966400, -307800; 11966400, -3988740, 102600; -307800, 102600, -2639],[360, 60, 1],[1, -25, -31, -22, 7, 55, 51, 70, 8; 3, -50, -64, -51, 11, 104, 100, 139, 16; 0, 972, 1128, 585, -388, -2370, -2060, -2760, -311],205,104]
%
% END OF LATTICE L206.104
%
%
% LATTICE L206.105
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1329840, -10080, -2880; -10080, 150, 90; -2880, 90, 49],[720, 30, 1],[13, 0, -1, -1, 1, 3, 3, 11, 1; -3936, 5, 314, 312, -312, -934, -930, -3388, -306; 7920, -12, -636, -630, 632, 1890, 1880, 6840, 617],205,105]
%
% END OF LATTICE L206.105
%
%
% LATTICE L206.106
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[523440, -524880, 38160; -524880, 516570, -37560; 38160, -37560, 2731],[720, 30, 1],[1, -1, 0, 4, 5, 7, 2, 9, 1; -156, 170, 17, -549, -732, -1064, -315, -1448, -162; -2160, 2352, 234, -7605, -10136, -14730, -4360, -20040, -2242],205,106]
%
% END OF LATTICE L206.106
%
%
% LATTICE L206.107
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-590640, -154800, 5040; -154800, -40440, 1320; 5040, 1320, -43],[240, 120, 1],[15, 0, -1, 0, 5, 2, 11, 13, 7; 2, -1, -1, 1, 6, 2, 9, 8, 3; 1800, -32, -148, 30, 768, 295, 1560, 1760, 906],205,107]
%
% END OF LATTICE L206.107
%
%
% LATTICE L206.108
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-240, 7200, -240; 7200, -202440, 6720; -240, 6720, -223],[240, 120, 1],[45, 1, -2, 0, 11, 9, 26, 33, 19; 2, -1, -1, 1, 6, 4, 9, 8, 3; 0, -32, -28, 30, 168, 110, 240, 200, 66],205,108]
%
% END OF LATTICE L206.108
%
%
% LATTICE L206.109
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1200, 14640, 960; 14640, -121320, -7920; 960, -7920, -517],[240, 120, 1],[43, 2, -1, -1, 5, 5, 17, 25, 8; 318, 13, -9, -6, 46, 43, 139, 196, 61; -4800, -196, 136, 90, -696, -650, -2100, -2960, -921],205,109]
%
% END OF LATTICE L206.109
%
%
% LATTICE L206.110
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[648240, 169200, -5520; 169200, 44040, -1440; -5520, -1440, 47],[240, 120, 1],[1, -1, 0, 4, 15, 7, 12, 9, 3; 0, -1, -1, 0, 4, 3, 7, 6, 2; 120, -148, -32, 465, 1872, 910, 1620, 1240, 414],205,110]
%
% END OF LATTICE L206.110
%
%
% LATTICE L206.111
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-360, 1080, 360; 1080, 1920, 600; 360, 600, 187],[360, 120, 1],[-9, -2, 0, 1, 1, -1, -5, -11, -17; 162, 37, 1, -13, -12, 19, 87, 194, 303; -500, -114, -3, 40, 36, -60, -270, -600, -936],205,111]
%
% END OF LATTICE L206.111
%
%
% LATTICE L206.112
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2624760, 298800, -14760; 298800, 33960, -1680; -14760, -1680, 83],[360, 120, 1],[1, -1, 0, 16, 5, 14, 4, 9, 2; 0, -1, -1, -15, -2, -1, 1, 4, 1; 180, -198, -21, 2520, 844, 2460, 730, 1680, 376],205,112]
%
% END OF LATTICE L206.112
%
%
% LATTICE L206.113
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[90000, 1440, -18720; 1440, -120, -240; -18720, -240, 3869],[720, 120, 1],[-379, -104, -29, -1, 29, 6, -109, -363, -323; -768, -211, -59, -2, 60, 13, -219, -734, -654; -1880, -516, -144, -5, 144, 30, -540, -1800, -1602],205,113]
%
% END OF LATTICE L206.113
%
%
% LATTICE L206.114
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[40150800, -16524720, 35280; -16524720, 6801000, -14520; 35280, -14520, 31],[720, 120, 1],[1, 0, 1, 17, 2, 9, 2, 1, 1; 3, -1, 1, 36, 5, 26, 7, 4, 4; 270, -468, -672, -2520, 62, 1920, 1000, 735, 736],205,114]
%
% END OF LATTICE L206.114
%
%
% LATTICE L206.115
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-475920, 132480, 16560; 132480, -36840, -4560; 16560, -4560, -511],[720, 120, 1],[369, 107, 32, -3, -71, -30, 58, 315, 151; 1466, 425, 127, -12, -282, -119, 231, 1252, 600; -1120, -324, -96, 10, 216, 90, -180, -960, -459],205,115]
%
% END OF LATTICE L206.115
%
%
% LATTICE L206.116
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[46800, 31680, -720; 31680, 20760, -480; -720, -480, 11],[720, 120, 1],[1, 1, 0, -3, -4, -7, -5, -1, 1; 1, 1, -1, -8, -9, -14, -9, -2, 0; 110, 108, -48, -560, -666, -1080, -720, -150, 72],205,116]
%
% END OF LATTICE L206.116
%
%
% LATTICE L206.117
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[3600, 1440, 0; 1440, 600, 0; 0, 0, -1],[720, 120, 1],[-2, -1, 0, 1, 1, 1, -1, -1, -7; 3, 1, -1, -4, -3, -2, 3, 2, 12; -50, -36, -24, -40, -18, 0, 0, -15, -144],205,117]
%
% END OF LATTICE L206.117
%
%
% LATTICE L206.118
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-30049200, 12703680, -29520; 12703680, -5370600, 12480; -29520, 12480, -29],[720, 120, 1],[1, 1, 0, -13, -2, -11, -3, -3, -1; 3, 1, -1, -24, -3, -14, -3, -2, 0; 270, -588, -432, 2880, 742, 5160, 1760, 2190, 1016],205,118]
%
% END OF LATTICE L206.118
%
%
% LATTICE L206.119
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-228240, 77040, -1440; 77040, 155400, -2760; -1440, -2760, 49],[720, 120, 1],[13, 0, -1, -1, 1, 3, 3, 11, 1; -798, 5, 67, 66, -66, -197, -195, -704, -63; -44640, 276, 3744, 3690, -3688, -11010, -10900, -39360, -3523],205,119]
%
% END OF LATTICE L206.119
%
%
% LATTICE L206.120
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1944720, -5936400, 152640; -5936400, 18061080, -464400; 152640, -464400, 11941],[720, 120, 1],[1, -1, 0, 4, 5, 7, 4, 9, 1; -120, 145, 29, -465, -620, -901, -533, -1222, -136; -4680, 5652, 1128, -18135, -24176, -35130, -20780, -47640, -5302],205,120]
%
% END OF LATTICE L206.120
%

\medskip%
%------------------------------WEYL-GROUP-W207--------------------------------
%
\leavevmode\llap{}%
$W_{207}$%
\qquad\llap{60} lattices, $\chi=18$%
\hfill%
$22|222\slashtwo2\rtimes D_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L207.1
%
\leavevmode%
${L_{207.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{4}8\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{2}{}5\above{1pt}{1pt}{1}{}$}\EasyButWeakLineBreak%
{${24}\above{1pt}{1pt}{}{2}{5}\above{1pt}{1pt}{r}{2}{8}\above{1pt}{1pt}{s}{2}{20}\above{1pt}{1pt}{*}{2}{24}\above{1pt}{1pt}{*}{2}{4}\above{1pt}{1pt}{l}{2}{1}\above{1pt}{1pt}{}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-39720\\480\\0
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
480\\-4\\-3
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\-3\\5
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5\\408\\240
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\80\\45
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-84\\-52
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3\\-250\\-150
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-84\\-48
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\82\\50
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\82\\49
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-39720, 480, 0; 480, -4, -3; 0, -3, 5],[120, 1, 1],[5, 1, -1, -3, -1, 1, 1; 408, 80, -84, -250, -84, 82, 82; 240, 45, -52, -150, -48, 50, 49],206,1]
%
% END OF LATTICE L207.1
%
\hbox{}\par\smallskip%
%
% LATTICE L207.2
%
\leavevmode%
${L_{207.2}}$%
{} : {$[1\above{1pt}{1pt}{-}{}2\above{1pt}{1pt}{1}{}]\above{1pt}{1pt}{}{6}16\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{2}{}5\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${24}\above{1pt}{1pt}{l}{2}{5}\above{1pt}{1pt}{}{2}{2}\above{1pt}{1pt}{}{2}{80}\above{1pt}{1pt}{}{2}{6}\above{1pt}{1pt}{r}{2}{16}\above{1pt}{1pt}{s}{2}{4}\above{1pt}{1pt}{*}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-364080\\2640\\2640
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2640\\-14\\-20
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2640\\-20\\-19
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-18\\-120
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\40\\235
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\39\\236
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
23\\440\\2720
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4\\75\\474
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\16\\120
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-20\\-118
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-364080, 2640, 2640; 2640, -14, -20; 2640, -20, -19],[240, 2, 1],[-1, 2, 2, 23, 4, 1, -1; -18, 40, 39, 440, 75, 16, -20; -120, 235, 236, 2720, 474, 120, -118],206,2]
%
% END OF LATTICE L207.2
%
\hbox{}\par\smallskip%
%
% LATTICE L207.3
%
\leavevmode%
${L_{207.3}}$%
{} : {$[1\above{1pt}{1pt}{1}{}2\above{1pt}{1pt}{1}{}]\above{1pt}{1pt}{}{2}16\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{2}{}5\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{m}%
\EasyButWeakLineBreak%
{${24}\above{1pt}{1pt}{*}{2}{20}\above{1pt}{1pt}{l}{2}{2}\above{1pt}{1pt}{r}{2}{80}\above{1pt}{1pt}{l}{2}{6}\above{1pt}{1pt}{}{2}{16}\above{1pt}{1pt}{}{2}{1}\above{1pt}{1pt}{r}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-4080\\240\\720
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
240\\-14\\-40
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
720\\-40\\-79
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-18\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
9\\180\\-10
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4\\79\\-4
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
43\\840\\-40
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7\\135\\-6
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\16\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-20\\1
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-4080, 240, 720; 240, -14, -40; 720, -40, -79],[240, 2, 1],[-1, 9, 4, 43, 7, 1, -1; -18, 180, 79, 840, 135, 16, -20; 0, -10, -4, -40, -6, 0, 1],206,3]
%
% END OF LATTICE L207.3
%
\hbox{}\par\smallskip%
%
% LATTICE L207.4
%
\leavevmode%
${L_{207.4}}$%
{} : {$[1\above{1pt}{1pt}{1}{}2\above{1pt}{1pt}{-}{}]\above{1pt}{1pt}{}{4}16\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{2}{}5\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{m}%
\EasyButWeakLineBreak%
{${6}\above{1pt}{1pt}{r}{2}{20}\above{1pt}{1pt}{*}{2}{8}\above{1pt}{1pt}{*}{2}{80}\above{1pt}{1pt}{s}{2}{24}\above{1pt}{1pt}{*}{2}{16}\above{1pt}{1pt}{l}{2}{1}\above{1pt}{1pt}{}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-169680\\1440\\1200
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1440\\-10\\-12
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1200\\-12\\-7
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\57\\72
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-60\\-70
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-58\\-72
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\180\\200
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5\\294\\348
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5\\292\\352
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\58\\71
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-169680, 1440, 1200; 1440, -10, -12; 1200, -12, -7],[240, 2, 1],[1, -1, -1, 3, 5, 5, 1; 57, -60, -58, 180, 294, 292, 58; 72, -70, -72, 200, 348, 352, 71],206,4]
%
% END OF LATTICE L207.4
%
\hbox{}\par\smallskip%
%
% LATTICE L207.5
%
\leavevmode%
${L_{207.5}}$%
{} : {$[1\above{1pt}{1pt}{-}{}2\above{1pt}{1pt}{-}{}]\above{1pt}{1pt}{}{0}16\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{2}{}5\above{1pt}{1pt}{1}{}$}\EasyButWeakLineBreak%
{${6}\above{1pt}{1pt}{}{2}{5}\above{1pt}{1pt}{r}{2}{8}\above{1pt}{1pt}{s}{2}{80}\above{1pt}{1pt}{*}{2}{24}\above{1pt}{1pt}{s}{2}{16}\above{1pt}{1pt}{*}{2}{4}\above{1pt}{1pt}{l}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
478320\\11280\\1200
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
11280\\266\\28
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1200\\28\\-5
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-5\\213\\-6
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\-85\\5
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7\\-298\\12
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
23\\-980\\40
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\42\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-11\\468\\-16
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-7\\298\\-10
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[478320, 11280, 1200; 11280, 266, 28; 1200, 28, -5],[240, 2, 1],[-5, 2, 7, 23, -1, -11, -7; 213, -85, -298, -980, 42, 468, 298; -6, 5, 12, 40, 0, -16, -10],206,5]
%
% END OF LATTICE L207.5
%
%
% LATTICE L207.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-17220, 1920, 720; 1920, -214, -80; 720, -80, -29],[60, 2, 1],[-1, -7, -1, 4, 8, 3, 3; -9, -70, -11, 35, 75, 29, 30; 0, 20, 6, 5, -6, -5, -8],206,6]
%
% END OF LATTICE L207.6
%
%
% LATTICE L207.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-2040, 360, 120; 360, -38, -20; 120, -20, -7],[120, 2, 1],[-1, 4, 2, 23, 4, 1, -1; 0, -5, -2, -20, -3, 0, 1; -18, 80, 39, 440, 75, 16, -20],206,7]
%
% END OF LATTICE L207.7
%
%
% LATTICE L207.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-9960, 1920, -240; 1920, -370, 46; -240, 46, -5],[120, 2, 1],[1, 11, 3, 3, -1, -2, -3; 6, 60, 16, 15, -6, -11, -16; 6, 20, 2, -10, -9, -6, -4],206,8]
%
% END OF LATTICE L207.8
%
%
% LATTICE L207.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2940, 0, 180; 0, 6, 0; 180, 0, 11],[60, 6, 1],[1, 1, 0, 7, 2, 5, 2; -1, 0, 1, 0, -1, -4, -2; -16, -15, 0, -120, -34, -84, -33],206,9]
%
% END OF LATTICE L207.9
%
%
% LATTICE L207.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2040, 360, -120; 360, 12, -9; -120, -9, 5],[120, 3, 1],[1, 2, 1, -1, -1, -1, 0; 32, 65, 32, -40, -36, -36, -1; 80, 165, 84, -90, -88, -90, -3],206,10]
%
% END OF LATTICE L207.10
%
%
% LATTICE L207.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-120, -120, 120; -120, 28, -16; 120, -16, 5],[120, 4, 1],[5, 1, -1, -3, -1, 1, 1; 54, 10, -12, -35, -12, 11, 11; 48, 5, -16, -40, -12, 12, 11],206,11]
%
% END OF LATTICE L207.11
%
%
% LATTICE L207.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-99480, 16560, -3480; 16560, -2756, 580; -3480, 580, -121],[120, 4, 1],[-23, -41, -17, -21, 1, 5, 1; -120, -210, -86, -105, 6, 25, 4; 84, 170, 76, 100, 0, -24, -10],206,12]
%
% END OF LATTICE L207.12
%
%
% LATTICE L207.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-14280, 240, 240; 240, 25, -5; 240, -5, -4],[120, 5, 1],[17, 1, -1, -1, -1, 3, 3; 24, 1, -4, -2, 0, 6, 5; 960, 56, -60, -58, -60, 170, 170],206,13]
%
% END OF LATTICE L207.13
%
%
% LATTICE L207.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-5460, 1800, 780; 1800, -590, -260; 780, -260, -109],[60, 10, 1],[1, 5, 3, -5, -44, -16, -17; 3, 10, 5, -11, -93, -33, -34; 0, 12, 10, -9, -90, -35, -40],206,14]
%
% END OF LATTICE L207.14
%
%
% LATTICE L207.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[54120, -6720, 240; -6720, 834, -30; 240, -30, 1],[120, 6, 1],[0, -2, -1, 1, 1, 3, 1; 0, -15, -8, 0, 6, 20, 7; -1, 30, 6, -180, -50, -108, -30],206,15]
%
% END OF LATTICE L207.15
%
%
% LATTICE L207.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[120, 0, 0; 0, -6, 0; 0, 0, 1],[120, 6, 1],[0, 1, 0, -2, -1, -1, -1; 0, 0, 1, 15, 6, 5, 4; -1, 0, 3, 30, 10, 6, 0],206,16]
%
% END OF LATTICE L207.16
%
%
% LATTICE L207.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-183840, -33720, 960; -33720, -6184, 176; 960, 176, -5],[120, 8, 1],[-1, -2, 0, 3, 1, 1, 0; 6, 15, 1, -15, -6, -7, -1; 18, 140, 34, 40, -21, -56, -36],206,17]
%
% END OF LATTICE L207.17
%
%
% LATTICE L207.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[110760, 5520, -1200; 5520, 250, -60; -1200, -60, 13],[120, 10, 1],[-1, 1, 2, 3, 1, -3, -2; 0, -1, -2, -4, -3, 0, 1; -90, 88, 175, 256, 75, -280, -180],206,18]
%
% END OF LATTICE L207.18
%
%
% LATTICE L207.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[32280, 1440, -480; 1440, 50, -20; -480, -20, 7],[120, 10, 1],[1, 1, 1, 0, -1, -1, -1; 6, 8, 8, -1, -12, -11, -12; 90, 92, 90, -4, -105, -100, -100],206,19]
%
% END OF LATTICE L207.19
%
%
% LATTICE L207.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-26160, 0, 240; 0, 30, 6; 240, 6, -1],[240, 6, 1],[0, 1, 1, -1, -1, -3, -1; 1, -20, -22, 20, 22, 68, 24; -2, 105, 108, -120, -112, -336, -114],206,20]
%
% END OF LATTICE L207.20
%
%
% LATTICE L207.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[18960, -480, -240; -480, 30, 12; -240, 12, 5],[240, 6, 1],[0, -1, -1, -7, -1, -1, 0; 1, 70, 66, 460, 66, 68, 1; -2, -210, -204, -1440, -208, -216, -3],206,21]
%
% END OF LATTICE L207.21
%
%
% LATTICE L207.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2640, 1920, -480; 1920, 66, -30; -480, -30, 11],[240, 6, 1],[1, -1, -1, -7, 0, 3, 1; 38, -40, -39, -280, -1, 112, 38; 148, -150, -150, -1080, -4, 432, 147],206,22]
%
% END OF LATTICE L207.22
%
%
% LATTICE L207.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[240, 0, 0; 0, 6, 0; 0, 0, -1],[240, 6, 1],[-1, -1, 0, 1, 0, -1, -1; -2, 0, 1, 0, -1, -8, -4; -16, -15, 0, 0, -2, -24, -18],206,23]
%
% END OF LATTICE L207.23
%
%
% LATTICE L207.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[47640, 11880, 720; 11880, 2964, 180; 720, 180, 11],[120, 12, 1],[-3, -1, 1, -7, -5, -7, -3; 14, 5, -4, 35, 24, 33, 14; -32, -15, 0, -120, -68, -84, -33],206,24]
%
% END OF LATTICE L207.24
%
%
% LATTICE L207.25
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[45960, -10320, 480; -10320, 2316, -108; 480, -108, 5],[120, 12, 1],[1, 1, -1, -4, -1, 0, 1; 2, 0, -4, -15, -4, -1, 2; -52, -90, 12, 60, 8, -24, -54],206,25]
%
% END OF LATTICE L207.25
%
%
% LATTICE L207.26
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-4020, 0, -1920; 0, 30, 0; -1920, 0, -917],[60, 30, 1],[-19, -10, 0, 23, 24, 29, -7; -1, 0, 1, 0, -1, -4, -2; 40, 21, 0, -48, -50, -60, 15],206,26]
%
% END OF LATTICE L207.26
%
%
% LATTICE L207.27
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[8040, 4920, -480; 4920, 2895, -285; -480, -285, 28],[120, 15, 1],[9, 2, 1, -1, -1, 3, 4; 40, 9, 4, -6, -8, 10, 17; 560, 126, 60, -78, -100, 150, 240],206,27]
%
% END OF LATTICE L207.27
%
%
% LATTICE L207.28
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-32880, 1680, 480; 1680, -40, -24; 480, -24, -7],[240, 8, 1],[2, -1, -1, 3, 5, 5, 1; -3, 0, 1, 0, -3, -4, -1; 144, -70, -72, 200, 348, 352, 71],206,28]
%
% END OF LATTICE L207.28
%
%
% LATTICE L207.29
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-68880, -7680, -1440; -7680, -856, -160; -1440, -160, -29],[240, 8, 1],[-8, -4, 1, 7, 1, -3, -3; 75, 35, -11, -70, -9, 30, 29; -12, 10, 12, 40, 0, -16, -10],206,29]
%
% END OF LATTICE L207.29
%
%
% LATTICE L207.30
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2842320, 315840, -10800; 315840, -35096, 1200; -10800, 1200, -41],[240, 8, 1],[8, 13, 5, 11, -1, -3, 0; 75, 125, 49, 110, -9, -30, -1; 84, 230, 116, 320, 0, -88, -30],206,30]
%
% END OF LATTICE L207.30
%
%
% LATTICE L207.31
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-40080, 18240, -1200; 18240, -8296, 544; -1200, 544, -35],[240, 8, 1],[4, 8, 9, 27, 1, -7, -3; 9, 20, 23, 70, 3, -18, -8; 0, 35, 48, 160, 12, -40, -22],206,31]
%
% END OF LATTICE L207.31
%
%
% LATTICE L207.32
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-17520, -2160, 960; -2160, -50, 50; 960, 50, -31],[240, 10, 1],[-1, 1, 4, 7, 4, -3, -3; -18, 20, 79, 136, 75, -64, -60; -60, 63, 250, 432, 240, -200, -190],206,32]
%
% END OF LATTICE L207.32
%
%
% LATTICE L207.33
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-175920, 9840, -1440; 9840, -550, 80; -1440, 80, -11],[240, 10, 1],[-1, 1, 2, 3, 1, -3, -1; -18, 20, 39, 56, 15, -64, -20; 0, 14, 20, 8, -30, -80, -15],206,33]
%
% END OF LATTICE L207.33
%
%
% LATTICE L207.34
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-200400, 3120, -1440; 3120, 110, -20; -1440, -20, 1],[240, 10, 1],[2, 1, 5, 3, 1, -3, -1; -177, -88, -438, -260, -78, 268, 88; -660, -329, -1640, -976, -300, 1000, 330],206,34]
%
% END OF LATTICE L207.34
%
%
% LATTICE L207.35
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[15600, 3840, -720; 3840, 770, -150; -720, -150, 29],[240, 10, 1],[5, 1, -1, -1, 1, 5, 2; 87, 16, -22, -20, 18, 92, 36; 570, 106, -140, -128, 120, 600, 235],206,35]
%
% END OF LATTICE L207.35
%
%
% LATTICE L207.36
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-14280, -1920, -720; -1920, -100, -20; -720, -20, 1],[120, 20, 1],[17, 1, -1, -1, -1, 3, 3; -528, -30, 38, 33, 30, -97, -95; 1080, 61, -80, -68, -60, 200, 195],206,36]
%
% END OF LATTICE L207.36
%
%
% LATTICE L207.37
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[120, 0, 0; 0, -220, 80; 0, 80, -29],[120, 20, 1],[-5, -1, -1, 0, 1, 0, -1; -18, 0, 8, 3, 0, -7, -10; -60, -2, 20, 8, 0, -20, -30],206,37]
%
% END OF LATTICE L207.37
%
%
% LATTICE L207.38
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[13920, 120, -120; 120, -24, 0; -120, 0, 1],[120, 24, 1],[0, 1, 0, -4, -1, -2, -1; 0, 5, 1, -5, -2, -5, -3; -1, 120, 6, -420, -110, -228, -120],206,38]
%
% END OF LATTICE L207.38
%
%
% LATTICE L207.39
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[32520, 24480, -600; 24480, 18390, -450; -600, -450, 11],[120, 30, 1],[-2, -2, -1, 1, 1, -1, -3; 5, 5, 2, -4, -4, 0, 7; 95, 96, 30, -108, -110, -60, 120],206,39]
%
% END OF LATTICE L207.39
%
%
% LATTICE L207.40
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-51240, -19800, 1320; -19800, -4710, 300; 1320, 300, -19],[120, 30, 1],[3, 5, 0, -1, -1, 2, 11; -116, -192, 1, 39, 38, -79, -428; -1625, -2688, 15, 546, 530, -1110, -6000],206,40]
%
% END OF LATTICE L207.40
%
%
% LATTICE L207.41
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[51360, 3480, -600; 3480, 200, -40; -600, -40, 7],[120, 40, 1],[1, 1, 1, 0, -1, -2, -1; 0, 1, 1, -1, -3, -5, -3; 90, 92, 90, -8, -105, -200, -100],206,41]
%
% END OF LATTICE L207.41
%
%
% LATTICE L207.42
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[256560, 29280, -1680; 29280, 3288, -192; -1680, -192, 11],[240, 24, 1],[0, -7, -2, -1, 1, 1, 3; -1, 0, 1, 0, -1, -1, -4; -20, -1080, -288, -150, 136, 135, 384],206,42]
%
% END OF LATTICE L207.42
%
%
% LATTICE L207.43
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[240, -240, 0; -240, 264, 0; 0, 0, -1],[240, 24, 1],[-1, -1, 1, 1, 0, -1, -3; -1, 0, 1, 0, -1, -2, -4; -4, 0, 0, -15, -16, -18, -24],206,43]
%
% END OF LATTICE L207.43
%
%
% LATTICE L207.44
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-38282160, -116400, -473760; -116400, -312, -1440; -473760, -1440, -5863],[240, 24, 1],[46, 191, -4, -67, -19, 6, 77; 45, 190, -3, -65, -19, 5, 74; -3728, -15480, 324, 5430, 1540, -486, -6240],206,44]
%
% END OF LATTICE L207.44
%
%
% LATTICE L207.45
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[184560, -41520, 960; -41520, 9336, -216; 960, -216, 5],[240, 24, 1],[1, 7, 1, 1, 0, 0, 1; 3, 20, 3, 5, 1, 1, 4; -64, -480, -60, 30, 44, 42, -24],206,45]
%
% END OF LATTICE L207.45
%
%
% LATTICE L207.46
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[65040, 30960, 14880; 30960, 14730, 7080; 14880, 7080, 3403],[240, 30, 1],[-2, -1, -1, 1, 1, -1, -3; -15, -8, 2, 44, 46, 60, -8; 40, 21, 0, -96, -100, -120, 30],206,46]
%
% END OF LATTICE L207.46
%
%
% LATTICE L207.47
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[42960, -39360, 2880; -39360, 40650, -2970; 2880, -2970, 217],[240, 30, 1],[-1, -1, -1, -1, -1, -3, -1; 75, 74, 78, 92, 94, 260, 79; 1040, 1026, 1080, 1272, 1300, 3600, 1095],206,47]
%
% END OF LATTICE L207.47
%
%
% LATTICE L207.48
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[8880, -2640, 960; -2640, 750, -270; 960, -270, 97],[240, 30, 1],[1, 0, -1, -3, -1, -1, 1; 18, -1, -25, -80, -29, -48, 14; 40, -3, -60, -192, -70, -120, 30],206,48]
%
% END OF LATTICE L207.48
%
%
% LATTICE L207.49
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-664080, 0, 3360; 0, 30, 0; 3360, 0, -17],[240, 30, 1],[-1, -1, 0, 5, 3, 11, 1; -2, 0, 1, 0, -1, -8, -2; -200, -198, 0, 984, 590, 2160, 195],206,49]
%
% END OF LATTICE L207.49
%
%
% LATTICE L207.50
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[120, 0, 0; 0, -4020, -1920; 0, -1920, -917],[120, 60, 1],[-1, 0, 1, 0, -1, -2, -1; -38, -10, 0, 23, 48, 29, -7; 80, 21, 0, -48, -100, -60, 15],206,50]
%
% END OF LATTICE L207.50
%
%
% LATTICE L207.51
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[39720, 30000, -720; 30000, 22380, -540; -720, -540, 13],[120, 60, 1],[-1, -1, 1, 4, 9, 8, 3; -2, -2, 0, 5, 12, 11, 4; -140, -138, 60, 432, 1000, 900, 330],206,51]
%
% END OF LATTICE L207.51
%
%
% LATTICE L207.52
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[57360, -28560, 240; -28560, 14200, -120; 240, -120, 1],[240, 40, 1],[1, 1, 1, 0, -2, -1, -1; -3, 0, 1, 0, -3, -2, -4; -540, -224, -120, -1, 120, 10, -200],206,52]
%
% END OF LATTICE L207.52
%
%
% LATTICE L207.53
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[31440, -29040, 960; -29040, 26680, -880; 960, -880, 29],[240, 40, 1],[1, -1, -1, 1, 10, 2, 5; 3, -4, -5, 2, 27, 6, 16; 60, -88, -120, 26, 480, 115, 320],206,53]
%
% END OF LATTICE L207.53
%
%
% LATTICE L207.54
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-21840, 7200, -2160; 7200, -2360, 720; -2160, 720, -209],[240, 40, 1],[46, 4, -7, -7, 1, 23, 19; 87, 7, -15, -14, 3, 46, 37; -180, -18, 20, 24, 0, -80, -70],206,54]
%
% END OF LATTICE L207.54
%
%
% LATTICE L207.55
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-7440, 2400, -480; 2400, -760, 160; -480, 160, -29],[240, 40, 1],[4, -1, -5, -3, 1, 7, 4; 3, -3, -11, -6, 3, 14, 7; -60, -2, 20, 16, 0, -40, -30],206,55]
%
% END OF LATTICE L207.55
%
%
% LATTICE L207.56
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-17880, -13680, 5760; -13680, -9960, 4200; 5760, 4200, -1771],[120, 120, 1],[2, 4, 1, -1, -1, 1, 6; 88, 187, 62, -34, -45, 24, 245; 215, 456, 150, -84, -110, 60, 600],206,56]
%
% END OF LATTICE L207.56
%
%
% LATTICE L207.57
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-240, 720, 240; 720, 3000, 960; 240, 960, 307],[240, 120, 1],[1, 0, -2, -3, -2, -1, 1; -13, 1, 39, 62, 45, 38, -10; 40, -3, -120, -192, -140, -120, 30],206,57]
%
% END OF LATTICE L207.57
%
%
% LATTICE L207.58
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1680, 1680, 480; 1680, -1560, -480; 480, -480, -137],[240, 120, 1],[10, 5, 1, -7, -7, -5, 3; -1, 0, 1, 0, -1, -4, -1; 40, 18, 0, -24, -20, 0, 15],206,58]
%
% END OF LATTICE L207.58
%
%
% LATTICE L207.59
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-11760, 46560, -1200; 46560, 421080, -10800; -1200, -10800, 277],[240, 120, 1],[4, 2, 1, -1, -1, 1, 3; -281, -137, -57, 82, 75, -74, -215; -10940, -5334, -2220, 3192, 2920, -2880, -8370],206,59]
%
% END OF LATTICE L207.59
%
%
% LATTICE L207.60
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-16080, -26880, 9600; -26880, -44760, 15960; 9600, 15960, -5687],[240, 120, 1],[-3, -10, -16, 23, 40, 93, 25; 9, 21, 31, -48, -81, -184, -47; 20, 42, 60, -96, -160, -360, -90],206,60]
%
% END OF LATTICE L207.60
%

\medskip%
%------------------------------WEYL-GROUP-W208--------------------------------
%
\leavevmode\llap{}%
$W_{208}$%
\qquad\llap{120} lattices, $\chi=48$%
\hfill%
$222|222|222|222|\rtimes D_{4}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L208.1
%
\leavevmode%
${L_{208.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{4}8\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{1}{}9\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{3}%
\EasyButWeakLineBreak%
{${8}\above{1pt}{1pt}{s}{2}{36}\above{1pt}{1pt}{*}{2}{12}\above{1pt}{1pt}{s}{2}{360}\above{1pt}{1pt}{l}{2}{3}\above{1pt}{1pt}{}{2}{9}\above{1pt}{1pt}{r}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-85179240\\2184120\\-28440
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2184120\\-56004\\729
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-28440\\729\\-7
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1634491\\-63825120\\-6172200
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
41899\\1636111\\158220
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-429\\-16752\\-1621
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
265\\10348\\1004
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
919\\35886\\3474
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
593\\23156\\2238
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3869\\151080\\14580
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
205\\8005\\771
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
185\\7224\\693
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-85179240, 2184120, -28440; 2184120, -56004, 729; -28440, 729, -7],[360, 3, 1],[265, 919, 593, 3869, 205, 185, 21, -61, -21, 421, 81, 244; 10348, 35886, 23156, 151080, 8005, 7224, 820, -2382, -820, 16440, 3163, 9528; 1004, 3474, 2238, 14580, 771, 693, 76, -234, -78, 1620, 309, 927],207,1]
%
% END OF LATTICE L208.1
%
\hbox{}\par\smallskip%
%
% LATTICE L208.2
%
\leavevmode%
${L_{208.2}}$%
{} : {$[1\above{1pt}{1pt}{-}{}2\above{1pt}{1pt}{-}{}]\above{1pt}{1pt}{}{0}16\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{1}{}9\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{3,2}%
\EasyButWeakLineBreak%
{${8}\above{1pt}{1pt}{*}{2}{144}\above{1pt}{1pt}{l}{2}{3}\above{1pt}{1pt}{}{2}{90}\above{1pt}{1pt}{r}{2}{48}\above{1pt}{1pt}{s}{2}{36}\above{1pt}{1pt}{*}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-182160\\26640\\5040
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
26640\\-3894\\-738
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5040\\-738\\-139
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4799\\24000\\46080
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-710\\-3551\\-6816
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-130\\-650\\-1249
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\6\\4
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
49\\252\\432
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
14\\71\\129
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
134\\675\\1260
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
83\\416\\792
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
65\\324\\630
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-182160, 26640, 5040; 26640, -3894, -738; 5040, -738, -139],[720, 6, 1],[1, 49, 14, 134, 83, 65, 19, 71, 6, 16, -3, -5; 6, 252, 71, 675, 416, 324, 94, 348, 29, 75, -16, -24; 4, 432, 129, 1260, 792, 630, 188, 720, 63, 180, -24, -54],207,2]
%
% END OF LATTICE L208.2
%
\hbox{}\par\smallskip%
%
% LATTICE L208.3
%
\leavevmode%
${L_{208.3}}$%
{} : {$[1\above{1pt}{1pt}{1}{}2\above{1pt}{1pt}{1}{}]\above{1pt}{1pt}{}{2}16\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{1}{}9\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{32,3,m}%
\EasyButWeakLineBreak%
{${2}\above{1pt}{1pt}{}{2}{144}\above{1pt}{1pt}{}{2}{3}\above{1pt}{1pt}{r}{2}{360}\above{1pt}{1pt}{*}{2}{48}\above{1pt}{1pt}{l}{2}{9}\above{1pt}{1pt}{}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-10658160\\30960\\-3222720
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
30960\\-78\\9480
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3222720\\9480\\-973279
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3654421\\-109651080\\11032560
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
8701\\261073\\-26268
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1124011\\-33726014\\3393347
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-53\\-1591\\160
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3959\\-118800\\11952
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1108\\-33247\\3345
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-21047\\-631530\\63540
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-6487\\-194644\\19584
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2531\\-75942\\7641
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-10658160, 30960, -3222720; 30960, -78, 9480; -3222720, 9480, -973279],[720, 6, 1],[-53, -3959, -1108, -21047, -6487, -2531, -738, -5533, -474, -2683, 159, 158; -1591, -118800, -33247, -631530, -194644, -75942, -22143, -166008, -14221, -80490, 4772, 4740; 160, 11952, 3345, 63540, 19584, 7641, 2228, 16704, 1431, 8100, -480, -477],207,3]
%
% END OF LATTICE L208.3
%
\hbox{}\par\smallskip%
%
% LATTICE L208.4
%
\leavevmode%
${L_{208.4}}$%
{} : {$[1\above{1pt}{1pt}{-}{}2\above{1pt}{1pt}{1}{}]\above{1pt}{1pt}{}{6}16\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{1}{}9\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{3m,3}%
\EasyButWeakLineBreak%
{${2}\above{1pt}{1pt}{r}{2}{144}\above{1pt}{1pt}{s}{2}{12}\above{1pt}{1pt}{*}{2}{360}\above{1pt}{1pt}{s}{2}{48}\above{1pt}{1pt}{*}{2}{36}\above{1pt}{1pt}{l}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-91440\\-4320\\2160
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-4320\\-42\\12
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2160\\12\\-1
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-301\\64200\\115200
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-5\\1069\\1920
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\-428\\-769
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\1\\2
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-5\\1080\\1944
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3\\644\\1158
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-29\\6210\\11160
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-9\\1924\\3456
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-7\\1494\\2682
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-91440, -4320, 2160; -4320, -42, 12; 2160, 12, -1],[720, 6, 1],[0, -5, -3, -29, -9, -7, -1, -7, -1, -1, 1, 1; 1, 1080, 644, 6210, 1924, 1494, 213, 1488, 212, 210, -212, -210; 2, 1944, 1158, 11160, 3456, 2682, 382, 2664, 378, 360, -384, -378],207,4]
%
% END OF LATTICE L208.4
%
\hbox{}\par\smallskip%
%
% LATTICE L208.5
%
\leavevmode%
${L_{208.5}}$%
{} : {$[1\above{1pt}{1pt}{1}{}2\above{1pt}{1pt}{-}{}]\above{1pt}{1pt}{}{4}16\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{1}{}9\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{3m,3,m}%
\EasyButWeakLineBreak%
{${8}\above{1pt}{1pt}{s}{2}{144}\above{1pt}{1pt}{*}{2}{12}\above{1pt}{1pt}{l}{2}{90}\above{1pt}{1pt}{}{2}{48}\above{1pt}{1pt}{}{2}{9}\above{1pt}{1pt}{r}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1625040\\101520\\30240
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
101520\\-6342\\-1890
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
30240\\-1890\\-559
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-21601\\-320400\\-86400
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1356\\20113\\5424
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
372\\5518\\1487
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-7\\-106\\-20
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5\\60\\72
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
19\\278\\90
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
127\\1875\\540
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
95\\1408\\384
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
44\\654\\171
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-1625040, 101520, 30240; 101520, -6342, -1890; 30240, -1890, -559],[720, 6, 1],[-7, 5, 19, 127, 95, 44, 31, 139, 29, 53, 1, -8; -106, 60, 278, 1875, 1408, 654, 462, 2076, 434, 795, 16, -120; -20, 72, 90, 540, 384, 171, 116, 504, 102, 180, 0, -27],207,5]
%
% END OF LATTICE L208.5
%
%
% LATTICE L208.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-387240, 1920, 5880; 1920, -7, -30; 5880, -30, -89],[120, 1, 1],[37, 12, 13, 27, -1, -3, 1, 7, 25, 163, 77, 41; 728, 237, 258, 540, -18, -60, 16, 135, 486, 3180, 1506, 804; 2196, 712, 771, 1600, -60, -178, 60, 416, 1485, 9680, 4572, 2434],207,6]
%
% END OF LATTICE L208.6
%
%
% LATTICE L208.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-60, 0, 180; 0, 2, -30; 180, -30, -89],[60, 2, 1],[-34, -45, -25, -27, 1, 3, 0, -23, -43, -143, -137, -37; -173, -228, -126, -135, 6, 15, -1, -120, -222, -735, -702, -189; -12, -16, -9, -10, 0, 1, 0, -8, -15, -50, -48, -13],207,7]
%
% END OF LATTICE L208.7
%
%
% LATTICE L208.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-5880, 120, 120; 120, -2, -4; 120, -4, 3],[120, 2, 1],[1, 5, 5, 11, 7, 1, 0, -1, -1, -1, 1, 1; 37, 184, 183, 400, 252, 35, -1, -40, -39, -40, 36, 37; 9, 40, 36, 70, 36, 2, -3, -16, -12, -10, 12, 10],207,8]
%
% END OF LATTICE L208.8
%
%
% LATTICE L208.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-520680, -21720, 4800; -21720, -906, 200; 4800, 200, -43],[120, 2, 1],[-29, -31, -113, -58, -34, -17, 1, 3, 1, -12, -22, -39; 722, 771, 2808, 1440, 843, 420, -26, -75, -24, 300, 549, 972; 118, 122, 432, 215, 120, 52, -10, -14, 0, 55, 96, 164],207,9]
%
% END OF LATTICE L208.9
%
%
% LATTICE L208.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-27551760, -1101360, 46080; -1101360, -44026, 1842; 46080, 1842, -77],[240, 2, 1],[-53, -71, -20, -22, 1, 5, 1, -33, -32, -108, -209, -57; 1334, 1788, 504, 555, -24, -126, -26, 828, 804, 2715, 5256, 1434; 192, 280, 87, 110, 24, -22, -24, 56, 81, 310, 648, 190],207,10]
%
% END OF LATTICE L208.10
%
%
% LATTICE L208.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-3866544240, 99157200, -1178400; 99157200, -2542878, 30220; -1178400, 30220, -359],[240, 2, 1],[-339, -885, -242, -513, 25, 27, -8, -503, -452, -2957, -2801, -374; -13183, -34416, -9411, -19950, 972, 1050, -311, -19560, -17577, -114990, -108924, -14544; 3028, 7888, 2151, 4540, -240, -239, 80, 4544, 4065, 26540, 25104, 3347],207,11]
%
% END OF LATTICE L208.11
%
%
% LATTICE L208.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-54960, -720, -960; -720, 6, 2; -960, 2, -3],[240, 2, 1],[0, 1, 1, 1, -1, -1, -1, -5, -5, -11, -7, -1; -1, 184, 186, 190, -180, -184, -185, -928, -930, -2050, -1308, -188; -2, -200, -198, -200, 192, 194, 194, 968, 966, 2120, 1344, 190],207,12]
%
% END OF LATTICE L208.12
%
%
% LATTICE L208.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[35760, 1440, 0; 1440, 58, 0; 0, 0, -1],[240, 2, 1],[3, 1, -1, -1, 1, 1, 5, 15, 17, 21, 31, 3; -78, -28, 24, 25, -24, -25, -126, -380, -432, -535, -792, -77; -28, -24, -6, 0, 0, -3, -20, -72, -90, -120, -192, -21],207,13]
%
% END OF LATTICE L208.13
%
%
% LATTICE L208.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-1249740, 89280, 26460; 89280, -6378, -1890; 26460, -1890, -559],[180, 6, 1],[-14, -38, -39, -97, -6, 5, 4, 8, -1, -53, -14, -65; -213, -582, -602, -1515, -97, 60, 59, 120, -14, -795, -211, -984; 58, 171, 192, 540, 45, 36, -10, -27, 0, 180, 51, 252],207,14]
%
% END OF LATTICE L208.14
%
%
% LATTICE L208.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-45720, 2160, 0; 2160, 42, -12; 0, -12, 1],[360, 6, 1],[-1, -7, -9, -29, -3, -5, 0, 1, 1, -1, -1, -7; -22, -153, -196, -630, -65, -108, 0, 21, 20, -30, -23, -156; -257, -1800, -2316, -7470, -774, -1296, -1, 252, 252, -270, -258, -1800],207,15]
%
% END OF LATTICE L208.15
%
%
% LATTICE L208.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-3750120, -234360, -74880; -234360, -14646, -4680; -74880, -4680, -1493],[360, 6, 1],[17, 119, 36, 103, 33, 1, -9, -71, -20, -43, -1, 23; -256, -1800, -547, -1575, -512, -27, 132, 1056, 299, 645, 16, -345; -50, -324, -90, -225, -48, 36, 38, 252, 66, 135, 0, -72],207,16]
%
% END OF LATTICE L208.16
%
%
% LATTICE L208.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-177720, 2280, 2280; 2280, -27, -30; 2280, -30, -29],[120, 3, 1],[25, 31, 21, 143, 8, 8, 5, -1, -1, 7, 2, 7; 476, 594, 404, 2760, 155, 156, 100, -18, -20, 120, 37, 132; 1464, 1812, 1226, 8340, 466, 465, 288, -60, -58, 420, 118, 411],207,17]
%
% END OF LATTICE L208.17
%
%
% LATTICE L208.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-5580, 1020, -360; 1020, -186, 66; -360, 66, -23],[60, 6, 1],[4, 6, 9, 33, 4, 9, 2, 0, -1, -3, 0, 3; 23, 31, 44, 155, 18, 38, 7, -1, -4, -5, 2, 22; 0, -9, -20, -90, -13, -36, -12, -3, 4, 30, 5, 12],207,18]
%
% END OF LATTICE L208.18
%
%
% LATTICE L208.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2691240, 299040, -15480; 299040, -33228, 1720; -15480, 1720, -89],[120, 4, 1],[37, 24, 13, 27, -1, -3, 1, 14, 25, 163, 77, 41; 364, 237, 129, 270, -9, -30, 8, 135, 243, 1590, 753, 402; 596, 404, 231, 520, 0, -58, -20, 172, 345, 2360, 1152, 634],207,19]
%
% END OF LATTICE L208.19
%
%
% LATTICE L208.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2040, 1080, 120; 1080, -356, -60; 120, -60, -7],[120, 4, 1],[1, -3, -1, 27, 26, 12, 37, 41, 77, 163, 50, 7; 0, 1, 0, -10, -9, -4, -12, -13, -24, -50, -15, -2; 16, -60, -18, 540, 516, 237, 728, 804, 1506, 3180, 972, 135],207,20]
%
% END OF LATTICE L208.20
%
%
% LATTICE L208.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3720, 240, -360; 240, -15, 20; -360, 20, -13],[120, 5, 1],[17, 17, 29, 11, 7, 1, -3, -3, -1, 3, 7, 6; 328, 324, 546, 204, 126, 15, -64, -60, -18, 60, 138, 117; 20, 10, 0, -8, -15, -10, -20, -10, 0, 8, 15, 10],207,21]
%
% END OF LATTICE L208.21
%
%
% LATTICE L208.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[60, 0, 0; 0, -30, 20; 0, 20, -13],[60, 10, 1],[-3, -4, -17, -4, -7, -5, -1, 0, 1, 0, -1, -3; 11, 9, 24, 3, 0, -6, -5, -3, 0, 3, 12, 18; 10, 5, 0, -4, -15, -20, -10, -5, 0, 4, 15, 20],207,22]
%
% END OF LATTICE L208.22
%
%
% LATTICE L208.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-9960, 840, 360; 840, -54, -30; 360, -30, -13],[120, 6, 1],[1, -1, -1, 7, 3, 19, 8, 19, 25, 83, 9, 17; 0, 1, 0, -10, -3, -16, -6, -13, -16, -50, -5, -8; 27, -30, -28, 210, 88, 552, 231, 546, 716, 2370, 256, 480],207,23]
%
% END OF LATTICE L208.23
%
%
% LATTICE L208.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[9960, -2160, -120; -2160, 462, 30; -120, 30, -1],[120, 6, 1],[-9, -5, -1, 7, 4, 17, 9, 5, 1, -7, -4, -17; -38, -21, -4, 30, 17, 72, 38, 21, 4, -30, -17, -72; -66, -36, -8, 45, 26, 108, 54, 24, -8, -75, -34, -132],207,24]
%
% END OF LATTICE L208.24
%
%
% LATTICE L208.25
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-480, -120, 0; -120, -8, -8; 0, -8, 3],[120, 8, 1],[-2, -5, -10, -11, -7, -2, 0, 1, 2, 1, -1, -2; 7, 17, 33, 35, 21, 5, -1, -5, -9, -5, 3, 7; 18, 40, 72, 70, 36, 4, -6, -16, -24, -10, 12, 20],207,25]
%
% END OF LATTICE L208.25
%
%
% LATTICE L208.26
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-5054760, 21240, 21240; 21240, -87, -90; 21240, -90, -89],[360, 3, 1],[5, 4, 13, 81, 37, 19, 49, 5, 5, 9, -1, -1; 288, 235, 766, 4780, 2186, 1124, 2904, 297, 298, 540, -58, -60; 900, 716, 2325, 14480, 6612, 3394, 8748, 892, 891, 1600, -180, -178],207,26]
%
% END OF LATTICE L208.26
%
%
% LATTICE L208.27
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-14940, 1080, 1260; 1080, -78, -90; 1260, -90, -89],[180, 6, 1],[2, 11, 19, 61, 57, 15, 40, 17, 9, 9, -1, -1; 27, 160, 278, 895, 838, 221, 591, 252, 134, 135, -14, -15; 0, -8, -15, -50, -48, -13, -36, -16, -9, -10, 0, 1],207,27]
%
% END OF LATTICE L208.27
%
%
% LATTICE L208.28
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[68520, 600, -1200; 600, -10, -10; -1200, -10, 21],[120, 10, 1],[6, 7, -1, -1, 1, 5, 7, 45, 53, 27, 103, 21; 8, 8, -3, -2, 0, 7, 10, 64, 75, 38, 144, 29; 345, 400, -60, -58, 60, 290, 405, 2600, 3060, 1558, 5940, 1210],207,28]
%
% END OF LATTICE L208.28
%
%
% LATTICE L208.29
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[120, 0, 0; 0, -90, 10; 0, 10, -1],[120, 10, 1],[-1, 0, 1, 0, -1, -3, -3, -4, -17, -2, -7, -5; 0, -1, 0, 1, 9, 16, 12, 13, 48, 5, 15, 8; -10, -10, 0, 7, 60, 100, 70, 70, 240, 23, 60, 20],207,29]
%
% END OF LATTICE L208.29
%
%
% LATTICE L208.30
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-248880, 16800, -2400; 16800, -1134, 162; -2400, 162, -23],[240, 6, 1],[-11, -13, -1, -2, 1, 1, -1, -11, -3, -28, -17, -13; -162, -188, -14, -25, 16, 14, -18, -172, -46, -425, -256, -194; 0, 24, 5, 30, 8, -6, -24, -72, -13, -90, -40, -18],207,30]
%
% END OF LATTICE L208.30
%
%
% LATTICE L208.31
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1037520, -38640, 16560; -38640, -1422, 612; 16560, 612, -263],[240, 6, 1],[14, 35, 3, 17, -1, -1, 1, 25, 7, 133, 41, 16; 697, 1736, 148, 830, -52, -49, 53, 1264, 352, 6670, 2052, 799; 2502, 6240, 533, 3000, -184, -177, 186, 4512, 1259, 23880, 7352, 2865],207,31]
%
% END OF LATTICE L208.31
%
%
% LATTICE L208.32
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-8520, -1920, 480; -1920, -396, 96; 480, 96, -23],[120, 12, 1],[7, 5, 1, 7, 0, -1, -1, 1, 1, 23, 4, 7; -134, -93, -18, -120, 1, 18, 14, -27, -22, -480, -81, -138; -420, -288, -55, -360, 4, 54, 36, -96, -73, -1560, -260, -438],207,32]
%
% END OF LATTICE L208.32
%
%
% LATTICE L208.33
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-130320, -9600, 3840; -9600, -702, 282; 3840, 282, -113],[240, 6, 1],[8, 19, 3, 7, -1, -1, 1, 17, 9, 83, 25, 19; 77, 176, 26, 50, -12, -8, 13, 184, 94, 850, 252, 188; 462, 1080, 166, 360, -64, -54, 66, 1032, 538, 4920, 1472, 1110],207,33]
%
% END OF LATTICE L208.33
%
%
% LATTICE L208.34
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-522480, -35280, 2400; -35280, -2382, 162; 2400, 162, -11],[240, 6, 1],[-1, -3, -1, -3, -1, 0, 1, 3, 1, 3, 1, 0; 30, 68, 20, 55, 16, -1, -18, -44, -12, -25, 0, 7; 216, 336, 74, 150, 16, -15, -48, 0, 38, 270, 208, 99],207,34]
%
% END OF LATTICE L208.34
%
%
% LATTICE L208.35
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-97320, 3480, 1680; 3480, -108, -60; 1680, -60, -29],[120, 12, 1],[5, -1, -1, 7, 4, 7, 25, 31, 21, 143, 16, 8; 0, 1, 0, -10, -3, -4, -12, -13, -8, -50, -5, -2; 288, -60, -58, 420, 236, 411, 1464, 1812, 1226, 8340, 932, 465],207,35]
%
% END OF LATTICE L208.35
%
%
% LATTICE L208.36
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-22680, 120, 360; 120, 60, 15; 360, 15, -1],[120, 15, 1],[29, 9, 3, 3, -1, -3, 1, 6, 7, 27, 21, 33; -556, -172, -57, -56, 20, 58, -20, -116, -135, -520, -404, -634; 1980, 615, 205, 204, -70, -210, 60, 405, 475, 1836, 1430, 2250],207,36]
%
% END OF LATTICE L208.36
%
%
% LATTICE L208.37
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[5220, -6420, -240; -6420, 7230, 300; -240, 300, 11],[60, 30, 1],[-12, 11, 7, 7, -1, -17, -42, -119, -43, -61, -71, -37; -1, 2, 1, 1, 0, -2, -5, -14, -5, -7, -8, -4; -240, 180, 125, 126, -20, -315, -780, -2220, -805, -1146, -1340, -705],207,37]
%
% END OF LATTICE L208.37
%
%
% LATTICE L208.38
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-4320240, 793920, -18240; 793920, -145896, 3352; -18240, 3352, -77],[240, 8, 1],[-22, -24, -89, -93, -14, -15, 0, 2, 1, -17, -8, -29; -101, -111, -414, -435, -66, -72, -1, 9, 6, -75, -36, -132; 812, 850, 3048, 3080, 441, 416, -44, -82, 24, 760, 327, 1120],207,38]
%
% END OF LATTICE L208.38
%
%
% LATTICE L208.39
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1195440, 199200, -10320; 199200, -33192, 1720; -10320, 1720, -89],[240, 8, 1],[-34, -37, -137, -143, -43, -23, 0, 3, 1, -27, -25, -45; -173, -189, -702, -735, -222, -120, -1, 15, 6, -135, -126, -228; 596, 634, 2304, 2360, 690, 344, -20, -58, 0, 520, 462, 808],207,39]
%
% END OF LATTICE L208.39
%
%
% LATTICE L208.40
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2030640, 408000, -17280; 408000, -81976, 3472; -17280, 3472, -147],[240, 8, 1],[0, -23, -43, -143, -137, -37, -34, -45, -25, -27, 1, 3; -1, -112, -207, -685, -654, -176, -161, -212, -117, -125, 6, 14; -24, 56, 162, 620, 648, 190, 192, 280, 174, 220, 24, -22],207,40]
%
% END OF LATTICE L208.40
%
%
% LATTICE L208.41
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-240, 0, 720; 0, 8, -120; 720, -120, -359],[240, 8, 1],[0, -47, -88, -293, -281, -38, -70, -93, -52, -57, 1, 3; -1, -240, -447, -1485, -1422, -192, -353, -468, -261, -285, 6, 15; 0, -16, -30, -100, -96, -13, -24, -32, -18, -20, 0, 1],207,41]
%
% END OF LATTICE L208.41
%
%
% LATTICE L208.42
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-29880, -9720, 3600; -9720, -2838, 1062; 3600, 1062, -397],[360, 6, 1],[20, 17, 9, 9, -1, -1, 1, 11, 19, 61, 57, 15; 609, 520, 277, 280, -28, -31, 27, 328, 571, 1840, 1724, 455; 1809, 1544, 822, 830, -84, -92, 81, 976, 1698, 5470, 5124, 1352],207,42]
%
% END OF LATTICE L208.42
%
%
% LATTICE L208.43
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-21260520, -1328760, 30240; -1328760, -83046, 1890; 30240, 1890, -43],[360, 6, 1],[35, 15, 8, 4, -1, -1, 1, 9, 16, 26, 49, 13; -534, -228, -121, -60, 16, 15, -18, -140, -247, -400, -752, -199; 1134, 524, 306, 175, 0, -44, -90, 172, 390, 695, 1392, 392],207,43]
%
% END OF LATTICE L208.43
%
%
% LATTICE L208.44
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[648240, 11760, -5520; 11760, 210, -100; -5520, -100, 47],[240, 10, 1],[9, 9, 31, 3, 4, 3, -1, -1, 1, 1, 4, 13; 22, 18, 48, 3, 0, -12, -10, -6, 0, 3, 12, 36; 1100, 1090, 3720, 356, 465, 320, -140, -130, 120, 124, 495, 1600],207,44]
%
% END OF LATTICE L208.44
%
%
% LATTICE L208.45
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-5634480, -663840, 19440; -663840, -78210, 2290; 19440, 2290, -67],[240, 10, 1],[-25, -26, -185, -37, -26, -23, 2, 3, 1, -9, -20, -69; 253, 264, 1884, 378, 267, 240, -19, -30, -12, 90, 201, 696; 1390, 1475, 10680, 2176, 1575, 1520, -70, -155, -120, 464, 1065, 3760],207,45]
%
% END OF LATTICE L208.45
%
%
% LATTICE L208.46
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[105360, 7920, -1440; 7920, 570, -100; -1440, -100, 17],[240, 10, 1],[6, 21, 103, 27, 53, 45, 7, 5, 1, -1, -1, 7; -185, -648, -3180, -834, -1638, -1392, -217, -156, -36, 30, 30, -216; -580, -2030, -9960, -2612, -5130, -4360, -680, -490, -120, 92, 90, -680],207,46]
%
% END OF LATTICE L208.46
%
%
% LATTICE L208.47
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-840, 240, -120; 240, -60, 40; -120, 40, -13],[120, 20, 1],[-17, -17, -29, -11, -7, -2, 3, 3, 1, -3, -7, -12; -40, -42, -75, -30, -21, -9, 4, 6, 3, -6, -15, -27; 20, 10, 0, -8, -15, -20, -20, -10, 0, 8, 15, 20],207,47]
%
% END OF LATTICE L208.47
%
%
% LATTICE L208.48
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[240, 0, 0; 0, -30, 20; 0, 20, -13],[240, 10, 1],[-3, -2, -17, -2, -7, -5, -1, 0, 1, 0, -1, -3; 22, 9, 48, 3, 0, -12, -10, -3, 0, 3, 24, 36; 20, 5, 0, -4, -30, -40, -20, -5, 0, 4, 30, 40],207,48]
%
% END OF LATTICE L208.48
%
%
% LATTICE L208.49
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3720, 2640, -480; 2640, 60, -40; -480, -40, 13],[120, 20, 1],[-3, 1, 14, 11, 29, 17, 17, 6, 14, 3, -1, -3; -54, 20, 267, 208, 546, 319, 318, 112, 261, 56, -18, -55; -280, 95, 1320, 1036, 2730, 1600, 1600, 565, 1320, 284, -90, -280],207,49]
%
% END OF LATTICE L208.49
%
%
% LATTICE L208.50
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-360, -960, -120; -960, -1848, -240; -120, -240, -31],[120, 24, 1],[4, 3, 0, -3, -1, 0, 2, 9, 8, 33, 9, 12; 7, 8, 1, -10, -6, -13, -7, -8, -1, 10, 6, 13; -66, -72, -8, 90, 52, 108, 54, 48, -8, -150, -68, -132],207,50]
%
% END OF LATTICE L208.50
%
%
% LATTICE L208.51
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[65640, 0, -1680; 0, -30, 0; -1680, 0, 43],[120, 30, 1],[21, 11, -1, -1, 1, 10, 27, 85, 33, 25, 63, 38; 14, 12, 1, 0, 0, 3, 10, 36, 15, 12, 32, 21; 810, 420, -40, -39, 40, 390, 1050, 3300, 1280, 969, 2440, 1470],207,51]
%
% END OF LATTICE L208.51
%
%
% LATTICE L208.52
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[74040, 18480, -720; 18480, 4590, -180; -720, -180, 7],[120, 30, 1],[4, 11, 2, 1, -1, -2, -1, 1, 2, 5, 9, 8; -6, -16, -3, -2, 0, 1, 0, -8, -5, -10, -16, -13; 255, 720, 130, 54, -100, -180, -105, -120, 70, 246, 500, 480],207,52]
%
% END OF LATTICE L208.52
%
%
% LATTICE L208.53
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-9213840, -616320, 26640; -616320, -41226, 1782; 26640, 1782, -77],[720, 6, 1],[1, -1, -1, 4, 4, 15, 35, 13, 49, 26, 8, 9; -18, 14, 16, -55, -56, -212, -498, -186, -704, -375, -116, -132; -72, -22, 24, 110, 87, 280, 576, 190, 648, 310, 81, 56],207,53]
%
% END OF LATTICE L208.53
%
%
% LATTICE L208.54
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-193422960, 131760, 263520; 131760, -78, -180; 263520, -180, -359],[720, 6, 1],[1, -1, -1, 19, 9, 33, 38, 14, 105, 111, 17, 19; 27, -30, -28, 570, 269, 984, 1131, 416, 3116, 3290, 503, 560; 720, -719, -720, 13660, 6471, 23728, 27324, 10067, 75504, 79820, 12225, 13664],207,54]
%
% END OF LATTICE L208.54
%
%
% LATTICE L208.55
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-25560, 0, 9000; 0, 12, 0; 9000, 0, -3169],[360, 12, 1],[-7, 13, 16, 383, 68, 121, 41, 89, 18, 127, 0, -19; -2, -15, -7, -120, -17, -24, -6, -9, -1, 0, 1, 0; -20, 36, 45, 1080, 192, 342, 116, 252, 51, 360, 0, -54],207,55]
%
% END OF LATTICE L208.55
%
%
% LATTICE L208.56
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2819160, 0, 15840; 0, 12, 0; 15840, 0, -89],[360, 12, 1],[-1, -1, 0, 9, 4, 7, 31, 11, 20, 41, 6, 3; -6, 0, 1, 0, -1, -3, -18, -8, -17, -40, -7, -5; -180, -178, 0, 1600, 711, 1244, 5508, 1954, 3552, 7280, 1065, 532],207,56]
%
% END OF LATTICE L208.56
%
%
% LATTICE L208.57
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-13408560, 34560, 34560; 34560, -78, -90; 34560, -90, -89],[720, 6, 1],[1, -1, -1, 9, 9, 17, 20, 15, 57, 61, 19, 11; 27, -30, -28, 270, 268, 504, 591, 442, 1676, 1790, 556, 320; 360, -358, -360, 3220, 3222, 6088, 7164, 5374, 20424, 21860, 6810, 3944],207,57]
%
% END OF LATTICE L208.57
%
%
% LATTICE L208.58
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-12240, -720, -1440; -720, -42, -90; -1440, -90, -89],[720, 6, 1],[1, -1, -1, 9, 17, 31, 71, 13, 97, 51, 31, 17; -18, 15, 16, -135, -256, -468, -1074, -197, -1472, -775, -472, -260; 0, 1, 0, -10, -18, -32, -72, -13, -96, -50, -30, -16],207,58]
%
% END OF LATTICE L208.58
%
%
% LATTICE L208.59
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-636840, 67320, -2160; 67320, -7116, 228; -2160, 228, -7],[360, 12, 1],[17, 58, 37, 239, 25, 11, 1, -4, -1, 31, 11, 16; 166, 567, 362, 2340, 245, 108, 10, -39, -10, 300, 107, 156; 152, 540, 354, 2340, 252, 117, 16, -36, -18, 180, 84, 135],207,59]
%
% END OF LATTICE L208.59
%
%
% LATTICE L208.60
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-291960, -51480, 15480; -51480, -8916, 2676; 15480, 2676, -803],[360, 12, 1],[5, 4, 26, 81, 37, 19, 49, 5, 10, 9, -1, -1; -288, -237, -1547, -4830, -2210, -1137, -2940, -301, -605, -550, 58, 61; -864, -713, -4656, -14540, -6654, -3424, -8856, -907, -1824, -1660, 174, 184],207,60]
%
% END OF LATTICE L208.60
%
%
% LATTICE L208.61
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[120, 0, 0; 0, -2840, 160; 0, 160, -9],[120, 40, 1],[-3, -3, -2, 0, 1, 0, -1, -5, -14, -4, -17, -8; 8, 4, -3, -1, 0, 7, 10, 32, 75, 19, 72, 29; 130, 60, -60, -18, 0, 120, 170, 540, 1260, 318, 1200, 480],207,61]
%
% END OF LATTICE L208.61
%
%
% LATTICE L208.62
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[38520, 15480, -720; 15480, 6180, -285; -720, -285, 13],[360, 15, 1],[3, 1, -2, -13, -13, -25, -9, -10, -4, -5, 1, 7; -12, 0, 13, 72, 68, 126, 44, 48, 19, 24, -4, -30; -100, 45, 165, 828, 750, 1350, 460, 495, 195, 252, -30, -270],207,62]
%
% END OF LATTICE L208.62
%
%
% LATTICE L208.63
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-4140, -2160, 900; -2160, -1110, 450; 900, 450, -173],[180, 30, 1],[14, 119, 43, 61, 71, 37, 4, -11, -7, -7, 1, 17; -43, -372, -136, -195, -230, -123, -15, 24, 20, 21, -2, -51; -40, -360, -135, -198, -240, -135, -20, 0, 15, 18, 0, -45],207,63]
%
% END OF LATTICE L208.63
%
%
% LATTICE L208.64
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-485640, -11880, 2520; -11880, -255, 60; 2520, 60, -13],[360, 15, 1],[1, 2, 7, 9, 21, 11, 29, 3, 3, 1, -1, -1; 0, 19, 70, 92, 218, 116, 312, 33, 34, 12, -10, -12; 180, 470, 1665, 2152, 5040, 2650, 7020, 730, 735, 248, -240, -250],207,64]
%
% END OF LATTICE L208.64
%
%
% LATTICE L208.65
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-61740, 30960, -900; 30960, -15510, 450; -900, 450, -13],[180, 30, 1],[-2, 3, 7, 5, 25, 7, 20, 9, 5, 1, -1, -1; -9, 4, 14, 11, 58, 17, 51, 24, 14, 3, -2, -3; -180, -80, -15, 26, 240, 95, 360, 200, 135, 34, 0, -35],207,65]
%
% END OF LATTICE L208.65
%
%
% LATTICE L208.66
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1692720, 410160, -6240; 410160, -99384, 1512; -6240, 1512, -23],[240, 24, 1],[2, 0, -1, -3, 0, 3, 4, 6, 9, 33, 2, 9; 7, -1, -4, -5, 1, 22, 23, 31, 44, 155, 9, 38; -84, -66, 8, 480, 65, 624, 420, 402, 440, 1200, 47, 48],207,66]
%
% END OF LATTICE L208.66
%
%
% LATTICE L208.67
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-526320, 119760, -2880; 119760, -27192, 672; -2880, 672, -11],[240, 24, 1],[-18, -19, -1, 127, 37, 187, 132, 133, 153, 443, 39, 41; -73, -77, -4, 515, 150, 758, 535, 539, 620, 1795, 158, 166; 252, 270, 16, -1800, -526, -2664, -1884, -1902, -2192, -6360, -562, -600],207,67]
%
% END OF LATTICE L208.67
%
%
% LATTICE L208.68
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-147120, 28560, -4080; 28560, -5544, 792; -4080, 792, -113],[240, 24, 1],[16, 19, 25, 83, 9, 17, 2, -1, -1, 7, 3, 19; 83, 96, 124, 405, 43, 78, 7, -6, -4, 45, 17, 102; 0, -18, -40, -180, -26, -72, -24, -6, 8, 60, 10, 24],207,68]
%
% END OF LATTICE L208.68
%
%
% LATTICE L208.69
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-583920, 114960, -7680; 114960, -22632, 1512; -7680, 1512, -101],[240, 24, 1],[4, 3, 9, 33, 4, 9, 2, 0, -1, -3, 0, 3; 35, 22, 60, 205, 23, 46, 7, -1, -4, 5, 5, 38; 216, 99, 208, 540, 38, 0, -48, -15, 16, 300, 74, 336],207,69]
%
% END OF LATTICE L208.69
%
%
% LATTICE L208.70
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[424080, 41280, -2160; 41280, 3990, -210; -2160, -210, 11],[240, 30, 1],[3, 7, 1, 1, 1, -1, -3, -7, -1, -1, -1, 1; -2, 4, 1, 1, 0, -4, -10, -28, -5, -7, -16, -8; 540, 1440, 215, 216, 200, -270, -780, -1920, -295, -336, -520, 30],207,70]
%
% END OF LATTICE L208.70
%
%
% LATTICE L208.71
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[240, 3120, 1440; 3120, 1530, 690; 1440, 690, 311],[240, 30, 1],[4, 11, 1, 1, -1, -1, -1, 1, 1, 5, 9, 4; -319, -888, -81, -78, 92, 90, 97, 0, -67, -366, -684, -312; 690, 1920, 175, 168, -200, -195, -210, 0, 145, 792, 1480, 675],207,71]
%
% END OF LATTICE L208.71
%
%
% LATTICE L208.72
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-360, 2400, 120; 2400, -6780, -360; 120, -360, -19],[120, 60, 1],[11, 9, 2, 3, 0, -3, -5, -3, 0, 3, 4, 9; -38, -29, -6, -8, 1, 10, 14, 5, -2, -16, -17, -34; 780, 600, 125, 168, -20, -210, -300, -120, 35, 312, 340, 690],207,72]
%
% END OF LATTICE L208.72
%
%
% LATTICE L208.73
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-720, 240, 0; 240, 1230, -120; 0, -120, 11],[240, 30, 1],[10, 27, 5, 3, -1, -3, -1, 9, 7, 15, 25, 21; 41, 104, 18, 10, -4, -8, 1, 64, 38, 74, 116, 92; 420, 1080, 190, 108, -40, -90, 0, 600, 370, 732, 1160, 930],207,73]
%
% END OF LATTICE L208.73
%
%
% LATTICE L208.74
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[467280, 4800, 5760; 4800, -390, 60; 5760, 60, 71],[240, 30, 1],[31, -9, -11, -6, 1, 15, 77, 225, 83, 60, 143, 39; -2, 4, 2, 1, 0, -2, -10, -28, -10, -7, -16, -4; -2520, 720, 890, 486, -80, -1215, -6240, -18240, -6730, -4866, -11600, -3165],207,74]
%
% END OF LATTICE L208.74
%
%
% LATTICE L208.75
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[120, 240, 0; 240, 540, 0; 0, 0, -1],[120, 60, 1],[1, -2, -1, 1, 3, 5, 17, 20, 13, 17, 9, 4; 0, 1, 0, -2, -3, -4, -12, -13, -8, -10, -5, -2; 0, 0, -10, -36, -40, -45, -120, -120, -70, -84, -40, -15],207,75]
%
% END OF LATTICE L208.75
%
%
% LATTICE L208.76
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1410120, 0, 9720; 0, 24, 0; 9720, 0, 67],[360, 24, 1],[8, 59, 40, 137, 31, 32, 2, 1, 0, 13, 9, 28; -3, -24, -17, -60, -14, -15, -1, 0, 1, 0, -2, -9; -1162, -8568, -5808, -19890, -4500, -4644, -290, -144, 0, -1890, -1308, -4068],207,76]
%
% END OF LATTICE L208.76
%
%
% LATTICE L208.77
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-332280, 0, -162360; 0, 24, 0; -162360, 0, -79333],[360, 24, 1],[-554, -256, -299, -171, 0, 43, 44, -84, -381, -679, -680, -383; -9, -3, -2, 0, 1, 0, -3, -5, -14, -20, -17, -8; 1134, 524, 612, 350, 0, -88, -90, 172, 780, 1390, 1392, 784],207,77]
%
% END OF LATTICE L208.77
%
%
% LATTICE L208.78
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[648240, 23520, -5520; 23520, 840, -200; -5520, -200, 47],[240, 40, 1],[9, 13, 4, 2, 1, -1, -1, 3, 4, 6, 31, 9; 11, 18, 6, 3, 0, -3, -5, -6, 0, 3, 24, 9; 1100, 1600, 495, 248, 120, -130, -140, 320, 465, 712, 3720, 1090],207,78]
%
% END OF LATTICE L208.78
%
%
% LATTICE L208.79
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[240, 0, 0; 0, -120, 40; 0, 40, -13],[240, 40, 1],[-3, -3, -1, 0, 1, 0, -1, -5, -7, -4, -17, -4; 11, 18, 12, 3, 0, -3, -5, -6, 0, 3, 24, 9; 20, 40, 30, 8, 0, -10, -20, -40, -30, -8, 0, 10],207,79]
%
% END OF LATTICE L208.79
%
%
% LATTICE L208.80
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[446640, 32640, -3840; 32640, 2360, -280; -3840, -280, 33],[240, 40, 1],[9, 9, 31, 6, 8, 3, -1, -1, 1, 2, 8, 13; 23, 22, 72, 13, 15, 2, -5, -4, 0, 5, 21, 34; 1240, 1230, 4200, 804, 1050, 360, -160, -150, 120, 276, 1110, 1800],207,80]
%
% END OF LATTICE L208.80
%
%
% LATTICE L208.81
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[240, 0, 0; 0, -67080, 2120; 0, 2120, -67],[240, 40, 1],[-3, -2, -17, -4, -7, -5, -1, 0, 1, 0, -1, -3; 47, 24, 168, 33, 45, 18, -5, -3, 0, 9, 39, 66; 1480, 755, 5280, 1036, 1410, 560, -160, -95, 0, 284, 1230, 2080],207,81]
%
% END OF LATTICE L208.81
%
%
% LATTICE L208.82
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[540360, 41040, -3960; 41040, 3090, -300; -3960, -300, 29],[360, 30, 1],[1, 13, 23, 19, 13, 35, 2, 5, 1, -1, -1, 1; 2, 39, 76, 66, 47, 132, 8, 21, 4, -6, -7, -12; 155, 2160, 3900, 3258, 2250, 6120, 355, 900, 180, -198, -210, 0],207,82]
%
% END OF LATTICE L208.82
%
%
% LATTICE L208.83
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-818280, 204480, -5040; 204480, -51090, 1260; -5040, 1260, -31],[360, 30, 1],[-11, -107, -42, -32, -81, -49, -9, -13, 2, 2, 1, -11; -34, -336, -133, -102, -260, -159, -30, -48, 5, 6, 4, -33; 410, 3780, 1440, 1071, 2640, 1530, 250, 180, -120, -81, 0, 450],207,83]
%
% END OF LATTICE L208.83
%
%
% LATTICE L208.84
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-213477480, 53369280, -1214640; 53369280, -13342290, 303660; -1214640, 303660, -6911],[360, 30, 1],[329, 85, 207, 10, -22, -81, -173, -33, 1, 16, 126, 185; 978, 251, 604, 28, -73, -248, -522, -99, 4, 48, 377, 552; -14850, -3910, -9840, -527, 660, 3340, 7470, 1450, 0, -703, -5580, -8260],207,84]
%
% END OF LATTICE L208.84
%
%
% LATTICE L208.85
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-317880, 52560, -3960; 52560, -1230, 120; -3960, 120, -11],[360, 30, 1],[10, 7, 25, 5, 7, 3, -1, -1, -1, 1, 5, 9; -1164, -811, -2884, -574, -797, -332, 126, 119, 116, -118, -587, -1052; -16245, -11320, -40260, -8014, -11130, -4640, 1755, 1660, 1620, -1646, -8190, -14680],207,85]
%
% END OF LATTICE L208.85
%
%
% LATTICE L208.86
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[56040, 0, -1440; 0, 120, 0; -1440, 0, 37],[120, 120, 1],[41, 51, 18, 6, 1, 0, 7, 45, 46, 42, 63, 96; -6, -8, -3, -1, 0, 1, 0, -4, -5, -5, -8, -13; 1590, 1980, 700, 234, 40, 0, 270, 1740, 1780, 1626, 2440, 3720],207,86]
%
% END OF LATTICE L208.86
%
%
% LATTICE L208.87
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1293503760, -85923360, -5415120; -85923360, -5707608, -359712; -5415120, -359712, -22669],[720, 24, 1],[-265, -1181, -123, -908, -15, 125, 53, -91, -89, -2272, -833, -761; 3313, 14766, 1538, 11355, 188, -1563, -663, 1134, 1112, 28395, 10412, 9513; 10732, 47808, 4977, 36720, 600, -5058, -2140, 3744, 3615, 92160, 33768, 30834],207,87]
%
% END OF LATTICE L208.87
%
%
% LATTICE L208.88
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-626286960, 44353440, -219600; 44353440, -3141096, 15552; -219600, 15552, -77],[720, 24, 1],[4, 2, 9, 11, 2, 3, 2, 0, -1, -1, 0, 1; 87, 39, 166, 195, 34, 48, 27, -1, -14, -5, 4, 28; 6156, 2170, 7848, 8000, 1161, 1136, -252, -202, 24, 1840, 807, 2800],207,88]
%
% END OF LATTICE L208.88
%
%
% LATTICE L208.89
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-4998960, 357120, -126000; 357120, -25512, 9000; -126000, 9000, -3169],[720, 24, 1],[44, 187, 37, 127, -1, -19, -6, 41, 39, 443, 153, 133; 657, 2796, 554, 1905, -14, -285, -91, 600, 578, 6585, 2278, 1983; 116, 504, 102, 360, 0, -54, -20, 72, 90, 1080, 384, 342],207,89]
%
% END OF LATTICE L208.89
%
%
% LATTICE L208.90
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-6398640, 509040, 30240; 509040, -40488, -2400; 30240, -2400, -139],[720, 24, 1],[-45, -191, -38, -134, -1, 17, 5, -49, -42, -466, -159, -137; -619, -2628, -523, -1845, -14, 234, 69, -672, -577, -6405, -2186, -1884; 896, 3816, 762, 2700, 24, -342, -104, 936, 822, 9180, 3144, 2718],207,90]
%
% END OF LATTICE L208.90
%
%
% LATTICE L208.91
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-104488560, 7463520, 2424240; 7463520, -533112, -173160; 2424240, -173160, -56239],[720, 24, 1],[-236, -973, -188, -643, -1, 38, 14, -359, -256, -2687, -887, -371; -3543, -14604, -2821, -9645, -14, 570, 209, -5400, -3847, -40365, -13322, -5571; 736, 3024, 582, 1980, 0, -117, -40, 1152, 810, 8460, 2784, 1161],207,91]
%
% END OF LATTICE L208.91
%
%
% LATTICE L208.92
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-552544560, 39467520, -221760; 39467520, -2819112, 15840; -221760, 15840, -89],[720, 24, 1],[40, 15, 57, 61, 19, 11, 2, -1, -1, 9, 9, 17; 591, 221, 838, 895, 278, 160, 27, -15, -14, 135, 134, 252; 5508, 1954, 7104, 7280, 2130, 1064, -180, -178, 0, 1600, 1422, 2488],207,92]
%
% END OF LATTICE L208.92
%
%
% LATTICE L208.93
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-41661360, 2769120, -120240; 2769120, -184056, 7992; -120240, 7992, -347],[720, 24, 1],[40, 15, 57, 61, 19, 11, 2, -1, -1, 9, 9, 17; 627, 234, 886, 945, 293, 168, 27, -16, -14, 145, 143, 268; 576, 190, 648, 620, 162, 56, -72, -22, 24, 220, 174, 280],207,93]
%
% END OF LATTICE L208.93
%
%
% LATTICE L208.94
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-59760, 4320, 5040; 4320, -312, -360; 5040, -360, -359],[720, 24, 1],[76, 14, 105, 111, 34, 19, 2, -1, -1, 19, 18, 33; 1131, 208, 1558, 1645, 503, 280, 27, -15, -14, 285, 269, 492; -72, -13, -96, -100, -30, -16, 0, 1, 0, -20, -18, -32],207,94]
%
% END OF LATTICE L208.94
%
%
% LATTICE L208.95
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[56880, 13680, -5040; 13680, 2670, -990; -5040, -990, 367],[720, 30, 1],[-1, -7, -1, -1, -1, 1, 1, 7, 1, 1, 1, -1; -158, -1164, -178, -201, -304, 30, 114, 900, 134, 135, 128, -162; -440, -3240, -495, -558, -840, 90, 320, 2520, 375, 378, 360, -450],207,95]
%
% END OF LATTICE L208.95
%
%
% LATTICE L208.96
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[720, 110880, -7200; 110880, 1504410, -98610; -7200, -98610, 6463],[720, 30, 1],[-22, 1, 46, 251, 469, 214, 73, 611, 56, 55, -61, -61; -157, 0, 326, 1782, 3332, 1521, 519, 4344, 398, 390, -436, -435; -2420, 0, 5025, 27468, 51360, 23445, 8000, 66960, 6135, 6012, -6720, -6705],207,96]
%
% END OF LATTICE L208.96
%
%
% LATTICE L208.97
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[85414320, 9746640, -63360; 9746640, 1112190, -7230; -63360, -7230, 47],[720, 30, 1],[7, 1, 1, 0, 0, 1, 5, 3, 15, 2, 4, 7; -66, -10, -8, 1, 4, 4, -18, -18, -104, -15, -32, -60; -720, -190, 120, 154, 615, 1960, 3960, 1270, 4200, 386, 465, 200],207,97]
%
% END OF LATTICE L208.97
%
%
% LATTICE L208.98
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-5638320, -339840, 19440; -339840, -20370, 1170; 19440, 1170, -67],[720, 30, 1],[-1, -1, -1, 3, 7, 25, 28, 10, 73, 15, 11, 11; -9, -6, -4, 18, 41, 144, 159, 56, 404, 82, 59, 56; -450, -395, -360, 1184, 2745, 9760, 10890, 3875, 28200, 5776, 4215, 4160],207,98]
%
% END OF LATTICE L208.98
%
%
% LATTICE L208.99
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1080720, -455760, 33120; -455760, 189870, -13800; 33120, -13800, 1003],[720, 30, 1],[2, 35, 13, 19, 23, 13, 1, 1, -1, -1, 1, 5; -339, -5856, -2156, -3126, -3748, -2082, -151, -24, 196, 186, -172, -858; -4730, -81720, -30090, -43632, -52320, -29070, -2110, -360, 2730, 2592, -2400, -11970],207,99]
%
% END OF LATTICE L208.99
%
%
% LATTICE L208.100
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-706680, 706680, -6120; 706680, -706620, 6120; -6120, 6120, -53],[360, 60, 1],[-7, -32, -12, -35, -21, -23, -3, 2, 2, 5, 1, -7; -2, -15, -7, -24, -17, -24, -6, -9, -1, 0, 1, 0; 580, 1980, 585, 1296, 480, -90, -340, -1260, -345, -576, 0, 810],207,100]
%
% END OF LATTICE L208.100
%
%
% LATTICE L208.101
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-807480, 0, 3240; 0, 60, 0; 3240, 0, -13],[360, 60, 1],[-5, -1, 0, 1, 2, 3, 11, 3, 4, 1, 0, -1; -6, 0, 1, 0, -1, -3, -18, -8, -17, -8, -7, -5; -1260, -250, 0, 248, 495, 740, 2700, 730, 960, 232, -15, -260],207,101]
%
% END OF LATTICE L208.101
%
%
% LATTICE L208.102
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-55440, -7200, 3600; -7200, -930, 450; 3600, 450, -173],[720, 30, 1],[29, 253, 93, 67, 159, 43, 11, -13, -13, -7, 1, 17; -262, -2292, -844, -609, -1448, -393, -102, 108, 116, 63, -8, -153; -80, -720, -270, -198, -480, -135, -40, 0, 30, 18, 0, -45],207,102]
%
% END OF LATTICE L208.102
%
%
% LATTICE L208.103
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-635760, -13680, 2880; -13680, -210, 60; 2880, 60, -13],[720, 30, 1],[-1, -1, -1, 1, 5, 9, 10, 7, 25, 5, 7, 3; -9, -6, -4, 6, 28, 48, 51, 34, 116, 22, 28, 8; -270, -250, -240, 248, 1230, 2200, 2430, 1690, 6000, 1192, 1650, 680],207,103]
%
% END OF LATTICE L208.103
%
%
% LATTICE L208.104
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-977040, -122400, 3600; -122400, -15330, 450; 3600, 450, -13],[720, 30, 1],[7, 1, 1, -1, -9, -15, -31, -5, -33, -3, -7, -1; -66, -9, -8, 9, 80, 132, 270, 43, 280, 25, 56, 4; -360, -35, 0, 34, 270, 400, 720, 95, 480, 26, -30, -160],207,104]
%
% END OF LATTICE L208.104
%
%
% LATTICE L208.105
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-56520, 19440, 360; 19440, -6420, -60; 360, -60, 13],[360, 60, 1],[-31, -71, -27, -11, 12, 23, 21, 41, 7, -19, -32, -38; -98, -225, -86, -36, 37, 72, 66, 129, 22, -60, -101, -120; 400, 900, 330, 108, -180, -315, -280, -540, -90, 252, 420, 495],207,105]
%
% END OF LATTICE L208.105
%
%
% LATTICE L208.106
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[360, -11880, -720; -11880, -19380, -1140; -720, -1140, -67],[360, 60, 1],[29, 3, 6, 1, -1, -1, 1, 2, 14, 9, 21, 11; -588, -62, -127, -22, 20, 23, 0, -36, -265, -174, -412, -219; 9720, 1025, 2100, 364, -330, -380, 0, 595, 4380, 2876, 6810, 3620],207,106]
%
% END OF LATTICE L208.106
%
%
% LATTICE L208.107
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-775920, -315360, 3840; -315360, -128040, 1560; 3840, 1560, -19],[240, 120, 1],[3, 7, 1, 2, 1, -1, -3, -7, -1, -2, -1, 1; 11, 18, 2, 3, 0, -3, -5, -6, 0, 3, 8, 9; 1500, 2880, 365, 648, 200, -450, -1020, -1920, -205, -168, 440, 930],207,107]
%
% END OF LATTICE L208.107
%
%
% LATTICE L208.108
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[424080, 212160, -2160; 212160, 105960, -1080; -2160, -1080, 11],[240, 120, 1],[3, 7, 2, 2, 1, -1, -3, -7, -2, -2, -1, 1; -1, 2, 1, 1, 0, -2, -5, -14, -5, -7, -8, -4; 480, 1560, 490, 492, 200, -390, -1080, -2760, -890, -1092, -1000, -210],207,108]
%
% END OF LATTICE L208.108
%
%
% LATTICE L208.109
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[275280, -284880, -3360; -284880, 294120, 3480; -3360, 3480, 41],[240, 120, 1],[40, 67, 15, 11, -1, -13, -22, -31, -3, 7, 25, 31; 11, 18, 4, 3, 0, -3, -5, -6, 0, 3, 8, 9; 2340, 3960, 890, 648, -80, -810, -1380, -2040, -250, 312, 1360, 1770],207,109]
%
% END OF LATTICE L208.109
%
%
% LATTICE L208.110
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[467280, -476880, -5760; -476880, 484920, 5880; -5760, 5880, 71],[240, 120, 1],[-32, 11, 12, 13, -1, -16, -82, -239, -88, -127, -151, -41; -1, 2, 1, 1, 0, -1, -5, -14, -5, -7, -8, -2; -2520, 720, 890, 972, -80, -1215, -6240, -18240, -6730, -9732, -11600, -3165],207,110]
%
% END OF LATTICE L208.110
%
%
% LATTICE L208.111
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[360, 0, 0; 0, 120, 0; 0, 0, -1],[360, 120, 1],[-2, -13, -8, -5, -5, -4, 0, 1, 0, -1, -3, -8; -3, -24, -17, -12, -14, -15, -1, 0, 1, 0, -2, -9; -50, -360, -240, -162, -180, -180, -10, 0, 0, -18, -60, -180],207,111]
%
% END OF LATTICE L208.111
%
%
% LATTICE L208.112
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-659160, 659160, 162720; 659160, -659040, -162720; 162720, -162720, -40169],[360, 120, 1],[413, 219, 279, 31, -29, -89, -203, -79, 1, 39, 309, 229; -9, -8, -17, -4, -14, -5, -3, 0, 1, 0, -2, -3; 1710, 920, 1200, 142, -60, -340, -810, -320, 0, 158, 1260, 940],207,112]
%
% END OF LATTICE L208.112
%
%
% LATTICE L208.113
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2327760, -24480, -4320; -24480, -120, 0; -4320, 0, 7],[720, 120, 1],[1, 7, 1, 2, 1, -1, -1, -7, -1, -2, -1, 1; -203, -1422, -203, -405, -200, 207, 205, 1434, 205, 411, 208, -201; 620, 4320, 615, 1224, 600, -630, -620, -4320, -615, -1224, -600, 630],207,113]
%
% END OF LATTICE L208.113
%
%
% LATTICE L208.114
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[34589520, -14927040, 40320; -14927040, 6441720, -17400; 40320, -17400, 47],[720, 120, 1],[-2, -5, -4, -5, -23, -6, -16, -7, -2, -1, -1, 0; -9, -12, -8, -9, -38, -9, -21, -8, -2, -1, -2, -1; -1620, -160, 465, 952, 5640, 1810, 5940, 3040, 975, 488, 120, -370],207,114]
%
% END OF LATTICE L208.114
%
%
% LATTICE L208.115
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[56880, 27360, 8640; 27360, 10680, 3360; 8640, 3360, 1057],[720, 120, 1],[-1, -1, 1, 2, 2, 7, 1, 1, -1, -2, -2, -7; 141, 144, -116, -243, -241, -810, -103, -30, 268, 357, 317, 1038; -440, -450, 360, 756, 750, 2520, 320, 90, -840, -1116, -990, -3240],207,115]
%
% END OF LATTICE L208.115
%
%
% LATTICE L208.116
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2824560, 1412640, -12240; 1412640, -706440, 6120; -12240, 6120, -53],[720, 120, 1],[6, 31, 7, 5, -1, -7, -4, -19, -3, 1, 9, 13; 15, 84, 20, 15, -2, -21, -13, -72, -16, -9, 10, 27; 340, 2520, 690, 576, 0, -810, -580, -3960, -1170, -1296, -960, 90],207,116]
%
% END OF LATTICE L208.116
%
%
% LATTICE L208.117
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-16560, -8640, -2880; -8640, -4440, -1440; -2880, -1440, -443],[720, 120, 1],[-26, -14, 1, 11, 8, -11, -16, -49, -169, -137, -92, -241; 77, 42, -2, -33, -25, 24, 45, 141, 490, 399, 269, 708; -80, -45, 0, 36, 30, 0, -40, -135, -480, -396, -270, -720],207,117]
%
% END OF LATTICE L208.117
%
%
% LATTICE L208.118
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3227760, 1614240, -6480; 1614240, -807240, 3240; -6480, 3240, -13],[720, 120, 1],[-2, 3, 7, 5, 25, 7, 20, 9, 5, 1, -1, -1; -9, 4, 14, 11, 58, 17, 51, 24, 14, 3, -2, -3; -1260, -520, -30, 232, 1920, 730, 2700, 1480, 990, 248, 0, -250],207,118]
%
% END OF LATTICE L208.118
%
%
% LATTICE L208.119
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-4731120, 1972800, -5760; 1972800, -822360, 2400; -5760, 2400, -7],[720, 120, 1],[20, 7, 25, 5, 7, 3, -2, -1, -1, 1, 5, 9; 87, 30, 106, 21, 29, 12, -9, -4, -2, 5, 23, 40; 13320, 4510, 15720, 3076, 4170, 1640, -1440, -550, 120, 884, 3750, 6280],207,119]
%
% END OF LATTICE L208.119
%
%
% LATTICE L208.120
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-12377520, 6189120, -28800; 6189120, -3094680, 14400; -28800, 14400, -67],[720, 120, 1],[56, 10, 73, 15, 22, 11, -2, -1, -1, 3, 14, 25; 159, 28, 202, 41, 59, 28, -9, -3, -2, 9, 41, 72; 10080, 1715, 12000, 2356, 3210, 1280, -1080, -215, 0, 644, 2790, 4720],207,120]
%
% END OF LATTICE L208.120
%

\medskip%
%------------------------------WEYL-GROUP-W209--------------------------------
%
\leavevmode\llap{}%
$W_{209}$%
\qquad\llap{11} lattices, $\chi=18$%
\hfill%
$\slashtwo2\infty|\infty2\rtimes D_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L209.1
%
\leavevmode%
${L_{209.1}}$%
{} : {$1\above{1pt}{1pt}{2}{{\rm II}}4\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{-}{}5\above{1pt}{1pt}{1}{}25\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${50}\above{1pt}{1pt}{b}{2}{2}\above{1pt}{1pt}{l}{2}{20}\above{1pt}{1pt}{5,4}{\infty}{20}\above{1pt}{1pt}{5,2}{\infty b}{20}\above{1pt}{1pt}{r}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
9300\\4800\\-1300
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4800\\2480\\-675
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1300\\-675\\188
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-54\\125\\75
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-9\\21\\13
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-39\\92\\60
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\-2\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-57\\132\\80
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[9300, 4800, -1300; 4800, 2480, -675; -1300, -675, 188],[100, 5, 1],[-54, -9, -39, 1, -57; 125, 21, 92, -2, 132; 75, 13, 60, 0, 80],208,1]
%
% END OF LATTICE L209.1
%
\hbox{}\par\smallskip%
%
% LATTICE L209.2
%
\leavevmode%
${L_{209.2}}$%
{} : {$1\above{1pt}{1pt}{-2}{2}8\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{1}{}5\above{1pt}{1pt}{-}{}25\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${100}\above{1pt}{1pt}{*}{2}{4}\above{1pt}{1pt}{s}{2}{40}\above{1pt}{1pt}{20,9}{\infty z}{10}\above{1pt}{1pt}{20,7}{\infty a}{40}\above{1pt}{1pt}{s}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-302600\\-148800\\-52000
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-148800\\-73165\\-25555
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-52000\\-25555\\-8894
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-407\\950\\-350
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
85\\-198\\72
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1453\\-3388\\1240
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
204\\-476\\175
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-211\\492\\-180
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-302600, -148800, -52000; -148800, -73165, -25555; -52000, -25555, -8894],[200, 5, 1],[-407, 85, 1453, 204, -211; 950, -198, -3388, -476, 492; -350, 72, 1240, 175, -180],208,2]
%
% END OF LATTICE L209.2
%
\hbox{}\par\smallskip%
%
% LATTICE L209.3
%
\leavevmode%
${L_{209.3}}$%
{} : {$1\above{1pt}{1pt}{2}{2}8\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{1}{}5\above{1pt}{1pt}{-}{}25\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{m}%
\EasyButWeakLineBreak%
{${25}\above{1pt}{1pt}{}{2}{1}\above{1pt}{1pt}{r}{2}{40}\above{1pt}{1pt}{20,19}{\infty z}{10}\above{1pt}{1pt}{20,7}{\infty b}{40}\above{1pt}{1pt}{l}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-74600\\-3800\\-10600
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3800\\-190\\-545
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-10600\\-545\\-1499
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-16\\105\\75
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\-14\\-9
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
91\\-612\\-420
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
15\\-99\\-70
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-13\\88\\60
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-74600, -3800, -10600; -3800, -190, -545; -10600, -545, -1499],[200, 5, 1],[-16, 2, 91, 15, -13; 105, -14, -612, -99, 88; 75, -9, -420, -70, 60],208,3]
%
% END OF LATTICE L209.3
%
%
% LATTICE L209.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[50, 0, -25; 0, -45, -5; -25, -5, 12],[25, 5, 1],[7, -1, -5, 3, 31; -2, 0, 1, -1, -9; 14, 0, -10, 5, 60],208,4]
%
% END OF LATTICE L209.4
%
%
% LATTICE L209.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[150, 0, 50; 0, 10, 25; 50, 25, 79],[50, 5, 1],[-1, -9, -11, 0, -3; -7, -60, -74, -1, -24; 3, 25, 30, 0, 10],208,5]
%
% END OF LATTICE L209.5
%
%
% LATTICE L209.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-37300, 1200, -5400; 1200, -30, 185; -5400, 185, -767],[100, 5, 1],[28, -6, -101, -14, 15; 195, -43, -714, -98, 106; -150, 32, 540, 75, -80],208,6]
%
% END OF LATTICE L209.6
%
%
% LATTICE L209.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-20800, -6250, -10150; -6250, -1870, -3050; -10150, -3050, -4953],[50, 10, 1],[-12, 23, 51, 25, -32; 1, 5, 1, -2, 1; 24, -50, -105, -50, 65],208,7]
%
% END OF LATTICE L209.7
%
%
% LATTICE L209.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[4902200, 734900, 1197500; 734900, 110180, 179520; 1197500, 179520, 292523],[100, 20, 1],[171, 243, 1095, 151, 51; 0, 2, 12, 3, 2; -700, -996, -4490, -620, -210],208,8]
%
% END OF LATTICE L209.8
%
%
% LATTICE L209.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1609200, 137100, -397900; 137100, -11680, 33900; -397900, 33900, -98387],[100, 20, 1],[3, -17, -24, 11, 20; 35, 21, 23, -16, -12; 0, 76, 105, -50, -85],208,9]
%
% END OF LATTICE L209.9
%
%
% LATTICE L209.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[200, 400, -600; 400, 680, -1040; -600, -1040, 1587],[200, 40, 1],[14, 1, -4, 17, 65; 41, 0, -13, 51, 192; 32, 0, -10, 40, 150],208,10]
%
% END OF LATTICE L209.10
%
%
% LATTICE L209.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[4603800, -5045200, 38800; -5045200, 5528920, -42520; 38800, -42520, 327],[200, 40, 1],[9, 8, 0, 7, 37; 8, 5, -1, 7, 34; -28, -300, -130, 80, 30],208,11]
%
% END OF LATTICE L209.11
%

\medskip%
%------------------------------WEYL-GROUP-W210--------------------------------
%
\leavevmode\llap{}%
$W_{210}$%
\qquad\llap{6} lattices, $\chi=12$%
\hfill%
$222222\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L210.1
%
\leavevmode%
${L_{210.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{1}{}5\above{1pt}{1pt}{-}{}25\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${4}\above{1pt}{1pt}{r}{2}{50}\above{1pt}{1pt}{b}{2}{10}\above{1pt}{1pt}{l}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5700\\2400\\200
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2400\\1010\\85
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
200\\85\\6
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
19\\-40\\-100
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
9\\-19\\-45
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\-1
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
11\\-24\\-28
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7\\-15\\-25
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-4\\9\\5
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[5700, 2400, 200; 2400, 1010, 85; 200, 85, 6],[100, 5, 1],[11, 7, -4, -7, -2, 5; -24, -15, 9, 16, 5, -11; -28, -25, 5, 8, 0, -10],209,1]
%
% END OF LATTICE L210.1
%
%
% LATTICE L210.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[50, -50, 25; -50, 35, -15; 25, -15, 6],[25, 5, 1],[-1, -1, 1, 1, 1, -1; -7, -10, 4, 3, 0, -6; -14, -25, 5, 4, 0, -10],209,2]
%
% END OF LATTICE L210.2
%
%
% LATTICE L210.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-25, -25, -25; -25, -15, -20; -25, -20, -22],[25, 5, 1],[2, -1, -1, 18, 3, 3; -5, -1, 1, 25, 3, 1; 0, 2, 0, -50, -7, -5],209,3]
%
% END OF LATTICE L210.3
%
%
% LATTICE L210.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[900, -100, -100; -100, 10, 5; -100, 5, -22],[100, 5, 1],[-3, -1, 0, 43, 3, 2; -40, -11, 1, 480, 33, 21; 0, 2, 0, -100, -7, -5],209,4]
%
% END OF LATTICE L210.4
%
%
% LATTICE L210.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[188200, -14900, 46500; -14900, 1160, -3680; 46500, -3680, 11489],[100, 20, 1],[32, 289, 53, -8, -169, -29; -11, -95, -17, 2, 50, 8; -133, -1200, -220, 33, 700, 120],209,5]
%
% END OF LATTICE L210.5
%
%
% LATTICE L210.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[44600, 16300, 11000; 16300, 5960, 4020; 11000, 4020, 2713],[100, 20, 1],[-103, -1, 19, -117, -43, -63; -5, 0, 2, 0, -1, -3; 425, 4, -80, 475, 176, 260],209,6]
%
% END OF LATTICE L210.6
%

\medskip%
%------------------------------WEYL-GROUP-W211--------------------------------
%
\leavevmode\llap{}%
$W_{211}$%
\qquad\llap{22} lattices, $\chi=12$%
\hfill%
$222|222|\rtimes D_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L211.1
%
\leavevmode%
${L_{211.1}}$%
{} : {$1\above{1pt}{1pt}{2}{{\rm II}}4\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{1}{}9\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${12}\above{1pt}{1pt}{*}{2}{20}\above{1pt}{1pt}{b}{2}{18}\above{1pt}{1pt}{s}{2}{30}\above{1pt}{1pt}{s}{2}{2}\above{1pt}{1pt}{b}{2}{180}\above{1pt}{1pt}{*}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3420\\-1260\\0
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1260\\462\\3
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\3\\-4
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\8\\6
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
11\\30\\20
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\3\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-13\\-35\\-30
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-7\\-19\\-16
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-77\\-210\\-180
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[3420, -1260, 0; -1260, 462, 3; 0, 3, -4],[180, 3, 1],[3, 11, 1, -13, -7, -77; 8, 30, 3, -35, -19, -210; 6, 20, 0, -30, -16, -180],210,1]
%
% END OF LATTICE L211.1
%
\hbox{}\par\smallskip%
%
% LATTICE L211.2
%
\leavevmode%
${L_{211.2}}$%
{} : {$1\above{1pt}{1pt}{2}{6}8\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{1}{}3\above{1pt}{1pt}{-}{}9\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${6}\above{1pt}{1pt}{b}{2}{40}\above{1pt}{1pt}{*}{2}{36}\above{1pt}{1pt}{l}{2}{15}\above{1pt}{1pt}{r}{2}{4}\above{1pt}{1pt}{*}{2}{360}\above{1pt}{1pt}{b}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1490040\\-2880\\5040
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2880\\6\\9
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5040\\9\\-17
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\19\\306
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\60\\920
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-18\\-306
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2\\-40\\-615
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-22\\-310
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-60\\-360
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-1490040, -2880, 5040; -2880, 6, 9; 5040, 9, -17],[360, 3, 1],[1, 3, -1, -2, -1, -1; 19, 60, -18, -40, -22, -60; 306, 920, -306, -615, -310, -360],210,2]
%
% END OF LATTICE L211.2
%
\hbox{}\par\smallskip%
%
% LATTICE L211.3
%
\leavevmode%
${L_{211.3}}$%
{} : {$1\above{1pt}{1pt}{-2}{6}8\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{1}{}3\above{1pt}{1pt}{-}{}9\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{m}%
\EasyButWeakLineBreak%
{${6}\above{1pt}{1pt}{l}{2}{40}\above{1pt}{1pt}{}{2}{9}\above{1pt}{1pt}{r}{2}{60}\above{1pt}{1pt}{l}{2}{1}\above{1pt}{1pt}{}{2}{360}\above{1pt}{1pt}{r}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
85251240\\-2185920\\56160
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2185920\\56049\\-1440
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
56160\\-1440\\37
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\79\\39
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\40\\40
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-39\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7\\280\\270
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4\\159\\116
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
133\\5280\\3600
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[85251240, -2185920, 56160; -2185920, 56049, -1440; 56160, -1440, 37],[360, 3, 1],[2, 1, -1, 7, 4, 133; 79, 40, -39, 280, 159, 5280; 39, 40, 0, 270, 116, 3600],210,3]
%
% END OF LATTICE L211.3
%
%
% LATTICE L211.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-495, 0, -45; 0, 3, 0; -45, 0, -4],[45, 3, 1],[0, -1, -1, 1, 1, 7; -1, 0, 3, 5, 1, 0; 0, 10, 9, -15, -13, -90],210,4]
%
% END OF LATTICE L211.4
%
%
% LATTICE L211.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[8190, 1710, -360; 1710, 357, -75; -360, -75, 16],[90, 3, 1],[-1, -19, -1, -1, -1, -3; 4, 90, 5, 5, 3, 10; -3, 0, 1, 0, -9, -20],210,5]
%
% END OF LATTICE L211.5
%
%
% LATTICE L211.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[21112020, 1019700, 35280; 1019700, 49251, 1704; 35280, 1704, 59],[180, 3, 1],[3, 1, -1, 22, 19, 293; -62, -20, 21, -455, -393, -6060; -3, -20, -9, -15, -11, -180],210,6]
%
% END OF LATTICE L211.6
%
%
% LATTICE L211.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[15030, -630, 7380; -630, -96, -300; 7380, -300, 3623],[90, 6, 1],[120, 373, -1, -161, -79, 61; -19, -60, 0, 25, 12, -10; -246, -765, 2, 330, 162, -125],210,7]
%
% END OF LATTICE L211.7
%
%
% LATTICE L211.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[90, -450, 45; -450, 1995, -195; 45, -195, 19],[45, 15, 1],[2, 1, -1, -1, 1, 1; 2, -3, -4, -2, 0, 1; 15, -36, -40, -18, 0, 8],210,8]
%
% END OF LATTICE L211.8
%
%
% LATTICE L211.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[30690, -9810, 1080; -9810, 3135, -345; 1080, -345, 38],[90, 15, 1],[2, 5, 1, 0, 1, 1; 8, 12, 1, -1, 3, 4; 15, -36, -20, -9, 0, 8],210,9]
%
% END OF LATTICE L211.9
%
%
% LATTICE L211.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1409220, 314640, -349560; 314640, -62052, 77916; -349560, 77916, -86707],[180, 12, 1],[-2171, -764, 3899, 6953, 441, -5512; 142, 50, -255, -455, -29, 360; 8880, 3125, -15948, -28440, -1804, 22545],210,10]
%
% END OF LATTICE L211.10
%
%
% LATTICE L211.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[105480, 9900, 27000; 9900, 912, 2532; 27000, 2532, 6911],[180, 12, 1],[-22, 17, 79, 73, -7, -199; -11, 10, 42, 40, -2, -90; 90, -70, -324, -300, 28, 810],210,11]
%
% END OF LATTICE L211.11
%
%
% LATTICE L211.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[82980, -28620, -1260; -28620, 9870, 435; -1260, 435, 19],[180, 15, 1],[3, -1, -3, -2, 1, 3; 8, 0, -7, -5, 3, 8; 15, -72, -40, -18, 0, 16],210,12]
%
% END OF LATTICE L211.12
%
%
% LATTICE L211.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[51390, -7110, 25020; -7110, 60, -3480; 25020, -3480, 12181],[90, 30, 1],[470, 824, 377, -47, -661, -24; 19, 33, 15, -2, -27, -1; -960, -1683, -770, 96, 1350, 49],210,13]
%
% END OF LATTICE L211.13
%
%
% LATTICE L211.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[30060, -11700, 360; -11700, 4470, -135; 360, -135, 4],[180, 15, 1],[3, 1, -1, -1, -1, 1; 16, 6, -5, -5, -3, 6; 270, 108, -80, -78, 0, 116],210,14]
%
% END OF LATTICE L211.14
%
%
% LATTICE L211.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[14760, -2520, 360; -2520, -690, 165; 360, 165, -37],[360, 15, 1],[4, 3, -1, -1, -1, 7; 79, 60, -18, -20, -22, 132; 390, 296, -90, -99, -110, 648],210,15]
%
% END OF LATTICE L211.15
%
%
% LATTICE L211.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-162360, -18000, 1080; -18000, -1995, 120; 1080, 120, -7],[360, 15, 1],[2, 1, -1, -1, 0, 5; -17, -8, 9, 8, -1, -48; 15, 16, 0, -18, -20, -72],210,16]
%
% END OF LATTICE L211.16
%
%
% LATTICE L211.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[222120, 9720, -3960; 9720, 48, -48; -3960, -48, 29],[360, 24, 1],[2, -1, -1, -1, 5, 3; 199, -105, -101, -100, 501, 300; 600, -315, -304, -300, 1512, 905],210,17]
%
% END OF LATTICE L211.17
%
%
% LATTICE L211.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-26280, -5400, -2880; -5400, -1104, -576; -2880, -576, -271],[360, 24, 1],[-24, -218, -21, 1, 17, -6; 143, 1305, 126, -5, -102, 35; -48, -450, -44, 0, 36, -10],210,18]
%
% END OF LATTICE L211.18
%
%
% LATTICE L211.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[172620, 28800, -20340; 28800, 3660, -4260; -20340, -4260, 1741],[180, 60, 1],[249, 446, 415, -41, -659, -10; -772, -1383, -1287, 127, 2043, 31; 1020, 1827, 1700, -168, -2700, -41],210,19]
%
% END OF LATTICE L211.19
%
%
% LATTICE L211.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[7777440, 156060, -1784700; 156060, 3120, -35820; -1784700, -35820, 409531],[180, 60, 1],[22, -163, -93, 91, 1277, 205; -67, 507, 289, -281, -3945, -633; 90, -666, -380, 372, 5220, 838],210,20]
%
% END OF LATTICE L211.20
%
%
% LATTICE L211.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-29880, -3240, -720; -3240, 240, 120; -720, 120, 49],[360, 120, 1],[6, 1, 5, -1, -1, 1; -161, -26, -123, 28, 27, -27; 480, 77, 360, -84, -80, 81],210,21]
%
% END OF LATTICE L211.21
%
%
% LATTICE L211.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-6120, 4320, -84240; 4320, -2280, 45000; -84240, 45000, -887651],[360, 120, 1],[59, -7, -89, 12, 109, 187; -2257, 263, 3384, -451, -4136, -7107; -120, 14, 180, -24, -220, -378],210,22]
%
% END OF LATTICE L211.22
%

\medskip%
%------------------------------WEYL-GROUP-W212--------------------------------
%
\leavevmode\llap{}%
$W_{212}$%
\qquad\llap{9} lattices, $\chi=12$%
\hfill%
$2\slashtwo2|2\slashtwo2|\rtimes D_{4}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L212.1
%
\leavevmode%
${L_{212.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{1}{}9\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-}{}5\above{1pt}{1pt}{-}{}25\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{25,5,2}%
\EasyButWeakLineBreak%
{${12}\above{1pt}{1pt}{r}{2}{50}\above{1pt}{1pt}{b}{2}{18}\above{1pt}{1pt}{l}{2}{300}\above{1pt}{1pt}{r}{2}{2}\above{1pt}{1pt}{b}{2}{450}\above{1pt}{1pt}{l}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
398700\\-126000\\-900
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-126000\\39810\\285
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-900\\285\\2
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3\\-8\\-204
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2\\-5\\-175
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\3\\27
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7\\20\\300
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\-1
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-11\\-30\\-675
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[398700, -126000, -900; -126000, 39810, 285; -900, 285, 2],[900, 15, 1],[-3, -2, 1, 7, 0, -11; -8, -5, 3, 20, 0, -30; -204, -175, 27, 300, -1, -675],211,1]
%
% END OF LATTICE L212.1
%
%
% LATTICE L212.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[315, 135, 0; 135, 57, -3; 0, -3, -10],[45, 3, 1],[1, 3, 1, -7, -6, -10; -2, -7, -3, 16, 14, 24; 0, 2, 0, -6, -5, -9],211,2]
%
% END OF LATTICE L212.2
%
%
% LATTICE L212.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[1260, 360, -180; 360, 102, -57; -180, -57, -10],[180, 3, 1],[5, -11, -8, -21, -1, 4; -16, 36, 26, 68, 3, -13; 0, -9, -5, -12, 0, 2],211,3]
%
% END OF LATTICE L212.3
%
%
% LATTICE L212.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-42075, 900, 1350; 900, -15, -30; 1350, -30, -43],[225, 15, 1],[-1, -8, 0, 3, 1, -1; -7, -45, 1, 25, 6, -10; -27, -225, -1, 75, 27, -25],211,4]
%
% END OF LATTICE L212.4
%
%
% LATTICE L212.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2250, -3465, -180; -3465, 4965, 300; -180, 300, 13],[45, 15, 1],[45, -8, -20, -7, 65, 39; 16, -3, -7, -2, 24, 14; 255, -45, -115, -45, 360, 220],211,5]
%
% END OF LATTICE L212.5
%
%
% LATTICE L212.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[781560, -48420, 196020; -48420, 3000, -12144; 196020, -12144, 49163],[180, 12, 1],[-36, -194, -52, -17, 35, -1; 14, 75, 19, 5, -18, 0; 147, 792, 212, 69, -144, 4],211,6]
%
% END OF LATTICE L212.6
%
%
% LATTICE L212.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2340, -3240, 720; -3240, -3630, 705; 720, 705, -122],[180, 15, 1],[-79, -29, -38, 19, 14, -7; 164, 60, 78, -40, -29, 15; 480, 175, 225, -120, -85, 45],211,7]
%
% END OF LATTICE L212.7
%
%
% LATTICE L212.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[24008760, 1365300, -4911480; 1365300, 77640, -279300; -4911480, -279300, 1004743],[180, 60, 1],[-10, -62, -260, -47, 5, 89; 14, 155, 687, 125, -16, -270; -45, -260, -1080, -195, 20, 360],211,8]
%
% END OF LATTICE L212.8
%
%
% LATTICE L212.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[46960200, -211500, 11682900; -211500, 840, -52620; 11682900, -52620, 2906507],[900, 60, 1],[277, 2439, 887, -56, -222, -448; 23, 205, 75, -5, -19, -45; -1113, -9800, -3564, 225, 892, 1800],211,9]
%
% END OF LATTICE L212.9
%

\medskip%
%------------------------------WEYL-GROUP-W213--------------------------------
%
\leavevmode\llap{}%
$W_{213}$%
\qquad\llap{6} lattices, $\chi=6$%
\hfill%
$2|22\slashtwo2\rtimes D_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L213.1
%
\leavevmode%
${L_{213.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{1}{}3\above{1pt}{1pt}{1}{}9\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{2}{}5\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${90}\above{1pt}{1pt}{l}{2}{12}\above{1pt}{1pt}{r}{2}{10}\above{1pt}{1pt}{b}{2}{36}\above{1pt}{1pt}{*}{2}{4}\above{1pt}{1pt}{b}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
47340\\900\\-720
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
900\\-6\\-9
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-720\\-9\\10
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\15\\90
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\52\\264
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\35\\175
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-18\\-90
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-18\\-88
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[47340, 900, -720; 900, -6, -9; -720, -9, 10],[180, 3, 1],[1, 3, 2, -1, -1; 15, 52, 35, -18, -18; 90, 264, 175, -90, -88],212,1]
%
% END OF LATTICE L213.1
%
%
% LATTICE L213.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[90, -45, 0; -45, 21, -3; 0, -3, -5],[45, 3, 1],[3, 2, -1, -1, -1; 5, 4, 0, -2, -3; -5, -3, 0, 1, 0],212,2]
%
% END OF LATTICE L213.2
%
%
% LATTICE L213.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[45, 270, 45; 270, -1875, -330; 45, -330, -58],[45, 15, 1],[-1, 2, 1, 1, -1; 3, -13, -5, 0, 6; -18, 75, 29, 0, -35],212,3]
%
% END OF LATTICE L213.3
%
%
% LATTICE L213.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[14954040, -211860, 3651480; -211860, 3000, -51732; 3651480, -51732, 891619],[180, 12, 1],[923, 74, -39, -145, 21; 0, 1, 5, 3, 0; -3780, -303, 160, 594, -86],212,4]
%
% END OF LATTICE L213.4
%
%
% LATTICE L213.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1569060, 7380, 9540; 7380, -30, -45; 9540, -45, -58],[180, 15, 1],[1, 3, 0, -5, -1; 3, 16, 1, -18, -6; 162, 480, -1, -810, -160],212,5]
%
% END OF LATTICE L213.5
%
%
% LATTICE L213.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[22293000, 203580, -5297040; 203580, 2040, -48240; -5297040, -48240, 1258727],[180, 60, 1],[-343, -590, -515, -1781, -193; 1029, 1771, 1546, 5346, 579; -1404, -2415, -2108, -7290, -790],212,6]
%
% END OF LATTICE L213.6
%

\medskip%
%------------------------------WEYL-GROUP-W214--------------------------------
%
\leavevmode\llap{}%
$W_{214}$%
\qquad\llap{26} lattices, $\chi=24$%
\hfill%
$22|22|22|22|\rtimes D_{4}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L214.1
%
\leavevmode%
${L_{214.1}}$%
{} : {$1\above{1pt}{1pt}{2}{{\rm II}}4\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{1}{}3\above{1pt}{1pt}{1}{}9\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${12}\above{1pt}{1pt}{*}{2}{4}\above{1pt}{1pt}{b}{2}{30}\above{1pt}{1pt}{b}{2}{36}\above{1pt}{1pt}{*}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
23580\\-540\\180
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-540\\12\\-3
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
180\\-3\\-2
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\360\\540
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\-11\\-15
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\8\\11
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-50\\-18
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-56\\-26
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-70\\-45
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\24\\-18
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[23580, -540, 180; -540, 12, -3; 180, -3, -2],[180, 3, 1],[-1, -1, -1, 1, 1, 1, 1, -1; -50, -56, -70, 24, 46, 48, 50, -48; -18, -26, -45, -18, 12, 14, 15, -18],213,1]
%
% END OF LATTICE L214.1
%
\hbox{}\par\smallskip%
%
% LATTICE L214.2
%
\leavevmode%
${L_{214.2}}$%
{} : {$1\above{1pt}{1pt}{-2}{6}8\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{-}{}9\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${6}\above{1pt}{1pt}{b}{2}{8}\above{1pt}{1pt}{*}{2}{60}\above{1pt}{1pt}{*}{2}{72}\above{1pt}{1pt}{b}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
230760\\4320\\-1800
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4320\\69\\-33
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1800\\-33\\14
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\720\\2160
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\19\\60
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\-6\\-19
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-10\\-153
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-16\\-172
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\-10\\90
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5\\24\\684
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[230760, 4320, -1800; 4320, 69, -33; -1800, -33, 14],[360, 3, 1],[-1, -1, 1, 5, 1, 1, -1, -5; -10, -16, -10, 24, 8, 8, -10, -48; -153, -172, 90, 684, 147, 148, -150, -756],213,2]
%
% END OF LATTICE L214.2
%
\hbox{}\par\smallskip%
%
% LATTICE L214.3
%
\leavevmode%
${L_{214.3}}$%
{} : {$1\above{1pt}{1pt}{2}{6}16\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{1}{}3\above{1pt}{1pt}{1}{}9\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2,m}%
\EasyButWeakLineBreak%
{${3}\above{1pt}{1pt}{}{2}{16}\above{1pt}{1pt}{r}{2}{30}\above{1pt}{1pt}{b}{2}{144}\above{1pt}{1pt}{*}{2}{12}\above{1pt}{1pt}{*}{2}{16}\above{1pt}{1pt}{b}{2}{30}\above{1pt}{1pt}{l}{2}{144}\above{1pt}{1pt}{}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-929520\\-4320\\-5760
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-4320\\3\\-6
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-5760\\-6\\-17
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\-1\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-448\\496
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-445\\495
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\456\\-504
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\448\\-498
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5\\2232\\-2488
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
6\\2675\\-2985
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
11\\4896\\-5472
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-929520, -4320, -5760; -4320, 3, -6; -5760, -6, -17],[720, 3, 1],[0, -1, -1, 1, 1, 5, 6, 11; -1, -448, -445, 456, 448, 2232, 2675, 4896; 0, 496, 495, -504, -498, -2488, -2985, -5472],213,3]
%
% END OF LATTICE L214.3
%
%
% LATTICE L214.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[13455, 2565, -315; 2565, 489, -60; -315, -60, 7],[45, 3, 1],[4, 2, -1, -4, -1, 4, 31, 22; -22, -11, 5, 21, 5, -23, -175, -123; -9, -4, 0, 0, -3, -20, -120, -72],213,4]
%
% END OF LATTICE L214.4
%
%
% LATTICE L214.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[990, -180, 0; -180, 33, 0; 0, 0, -1],[90, 3, 1],[1, 1, -1, -1, -1, -1, 1, 1; 5, 6, -5, -6, -7, -18, -5, 2; -3, 0, 0, -4, -9, -72, -60, -20],213,5]
%
% END OF LATTICE L214.5
%
%
% LATTICE L214.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[115380, 1620, -900; 1620, 3, -12; -900, -12, 7],[180, 3, 1],[-1, -1, 1, 5, 1, 1, -1, -5; -5, -8, -5, 12, 4, 4, -5, -24; -138, -148, 105, 648, 135, 136, -135, -684],213,6]
%
% END OF LATTICE L214.6
%
%
% LATTICE L214.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[53640, 2160, 0; 2160, 87, 0; 0, 0, -1],[360, 3, 1],[1, 5, 6, 11, 0, -1, -1, 1; -25, -128, -155, -288, -1, 24, 25, -24; -3, -40, -60, -144, -9, -8, 0, 0],213,7]
%
% END OF LATTICE L214.7
%
%
% LATTICE L214.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2070, 360, -990; 360, 66, 180; -990, 180, -473],[90, 6, 1],[-47, 22, 44, -24, -141, -586, -984, -164; -5, 3, 5, -3, -17, -69, -115, -19; 96, -45, -90, 49, 288, 1197, 2010, 335],213,8]
%
% END OF LATTICE L214.8
%
%
% LATTICE L214.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[180, 45, 0; 45, 15, 0; 0, 0, -1],[45, 15, 1],[-2, -1, 0, 1, 0, -3, -4, -13; 4, 1, -1, -3, 1, 9, 11, 33; -15, -10, -3, 0, 0, -20, -27, -90],213,9]
%
% END OF LATTICE L214.9
%
%
% LATTICE L214.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3690, -630, 90; -630, -105, 15; 90, 15, -2],[90, 15, 1],[0, 1, 0, -1, -2, -13, -2, -3; 2, -6, -1, 2, 8, 66, 11, 18; 15, 0, -9, -40, -45, -180, -21, -20],213,10]
%
% END OF LATTICE L214.10
%
%
% LATTICE L214.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[72720, -19980, 17640; -19980, 5304, -4848; 17640, -4848, 4279],[180, 12, 1],[-25, -262, -1616, -974, -119, -26, 176, 110; -1, -9, -55, -33, -4, -1, 5, 3; 102, 1070, 6600, 3978, 486, 106, -720, -450],213,11]
%
% END OF LATTICE L214.11
%
%
% LATTICE L214.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[32194620, -71280, 7864380; -71280, 156, -17412; 7864380, -17412, 1921081],[180, 12, 1],[-170, -287, -3019, -776, -85, 32, 469, 11; 7, 11, 115, 30, 4, 0, -5, 3; 696, 1175, 12360, 3177, 348, -131, -1920, -45],213,12]
%
% END OF LATTICE L214.12
%
%
% LATTICE L214.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-19260, 0, 180; 0, 330, -15; 180, -15, -1],[180, 15, 1],[1, -5, -1, 1, 3, 53, 9, 15; 5, -24, -5, 4, 14, 252, 43, 72; 105, -540, -108, 100, 315, 5580, 948, 1580],213,13]
%
% END OF LATTICE L214.13
%
%
% LATTICE L214.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-288180, -21240, 4680; -21240, -1560, 345; 4680, 345, -76],[180, 15, 1],[-5, -1, 1, 1, -3, -47, -9, -17; 2, -6, -1, 2, 8, 66, 11, 18; -300, -90, 57, 70, -150, -2610, -507, -970],213,14]
%
% END OF LATTICE L214.14
%
%
% LATTICE L214.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[28530, -1530, 13950; -1530, 240, -750; 13950, -750, 6821],[90, 30, 1],[-44, -22, 85, 276, 806, 2308, 677, 486; 1, 0, -2, -6, -17, -48, -14, -10; 90, 45, -174, -565, -1650, -4725, -1386, -995],213,15]
%
% END OF LATTICE L214.15
%
%
% LATTICE L214.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-38520, 0, 360; 0, 165, -15; 360, -15, -2],[360, 15, 1],[1, 15, 9, 53, 3, 1, -1, -5; 10, 144, 86, 504, 28, 8, -10, -48; 105, 1580, 948, 5580, 315, 100, -108, -540],213,16]
%
% END OF LATTICE L214.16
%
%
% LATTICE L214.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[360, 0, 0; 0, -105, 15; 0, 15, -2],[360, 15, 1],[0, -3, -1, -13, -1, -1, 0, 1; 2, 0, -1, -24, -4, -8, -1, 0; 15, -40, -21, -360, -45, -80, -9, 0],213,17]
%
% END OF LATTICE L214.17
%
%
% LATTICE L214.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-51480, 3600, 1080; 3600, -24, -24; 1080, -24, -11],[360, 24, 1],[-1, 1, 9, 7, 3, 1, 1, -1; 43, -45, -400, -309, -131, -43, -40, 45; -192, 194, 1740, 1350, 576, 190, 180, -198],213,18]
%
% END OF LATTICE L214.18
%
%
% LATTICE L214.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-559080, -111960, -3600; -111960, -22416, -720; -3600, -720, -23],[360, 24, 1],[2, -2, -31, -11, -8, -1, 1, 2; -13, 11, 175, 63, 47, 6, -5, -12; 96, -29, -600, -243, -216, -31, 0, 63],213,19]
%
% END OF LATTICE L214.19
%
%
% LATTICE L214.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-433157040, 28207440, 228960; 28207440, -1836885, -14910; 228960, -14910, -121],[720, 15, 1],[19, -17, -5, 1, 12, 533, 48, 171; 292, -264, -77, 16, 185, 8208, 739, 2632; -30, 360, 27, -80, -90, -2880, -237, -760],213,20]
%
% END OF LATTICE L214.20
%
%
% LATTICE L214.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[4002120, -16740, -988920; -16740, 240, 4260; -988920, 4260, 244451],[180, 60, 1],[-637, -637, -41, -349, -842, -8237, -2917, -2609; 1897, 1896, 122, 1040, 2509, 24540, 8690, 7772; -2610, -2610, -168, -1430, -3450, -33750, -11952, -10690],213,21]
%
% END OF LATTICE L214.21
%
%
% LATTICE L214.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[19376460, 291240, -4518900; 291240, 4380, -67920; -4518900, -67920, 1053881],[180, 60, 1],[-88, -55, -41, -72, -249, -956, -633, -265; 269, 168, 121, 213, 740, 2859, 1897, 796; -360, -225, -168, -295, -1020, -3915, -2592, -1085],213,22]
%
% END OF LATTICE L214.22
%
%
% LATTICE L214.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2376720, -475200, -154080; -475200, -94992, -30768; -154080, -30768, -9911],[720, 48, 1],[-40, 103, 1551, 272, 195, 26, -1, -79; 239, -613, -9235, -1620, -1162, -155, 5, 471; -120, 302, 4560, 801, 576, 77, 0, -234],213,23]
%
% END OF LATTICE L214.23
%
%
% LATTICE L214.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-210960, -644760, 6480; -644760, -1970040, 19800; 6480, 19800, -199],[360, 120, 1],[-1, -17, -7, -7, -5, -1, 1, 1; 10, 12, 1, -2, -8, -6, 1, 4; 960, 630, -132, -430, -960, -630, 132, 430],213,24]
%
% END OF LATTICE L214.24
%
%
% LATTICE L214.25
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[5040, 6840, -720; 6840, -840, -840; -720, -840, 101],[360, 120, 1],[179, 319, 203, 79, 15, -28, -9, 18; 20, 36, 23, 9, 2, -3, -1, 2; 1440, 2565, 1632, 635, 120, -225, -72, 145],213,25]
%
% END OF LATTICE L214.25
%
%
% LATTICE L214.26
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-277920, 85680, -2160; 85680, -25680, 960; -2160, 960, 101],[720, 240, 1],[-189, -337, -429, -167, -16, 59, 19, -19; -577, -1029, -1310, -510, -49, 180, 58, -58; 1440, 2565, 3264, 1270, 120, -450, -144, 145],213,26]
%
% END OF LATTICE L214.26
%

\medskip%
%------------------------------WEYL-GROUP-W215--------------------------------
%
\leavevmode\llap{}%
$W_{215}$%
\qquad\llap{34} lattices, $\chi=108$%
\hfill%
$22\slashtwo2222\slashinfty2222\slashtwo2222\slashinfty22\rtimes D_{4}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L215.1
%
\leavevmode%
${L_{215.1}}$%
{} : {$1\above{1pt}{1pt}{2}{0}8\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{2}{}17\above{1pt}{1pt}{1}{}$}\EasyButWeakLineBreak%
{${68}\above{1pt}{1pt}{*}{2}{8}\above{1pt}{1pt}{*}{2}{4}\above{1pt}{1pt}{l}{2}{1}\above{1pt}{1pt}{}{2}{8}\above{1pt}{1pt}{}{2}{17}\above{1pt}{1pt}{r}{2}{4}\above{1pt}{1pt}{*}{2}{136}\above{1pt}{1pt}{1,0}{\infty b}{136}\above{1pt}{1pt}{}{2}{1}\above{1pt}{1pt}{r}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-163064\\1632\\1632
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1632\\-16\\-17
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1632\\-17\\-15
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
9757\\652392\\317832
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-105\\-7021\\-3420
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-84\\-5616\\-2737
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
463\\30974\\15062
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
71\\4748\\2312
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
29\\1938\\946
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
13\\868\\425
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
53\\3536\\1736
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
155\\10336\\5083
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
31\\2066\\1018
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
95\\6324\\3128
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
41\\2720\\1360
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\132\\67
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-163064, 1632, 1632; 1632, -16, -17; 1632, -17, -15],[136, 1, 1],[463, 71, 29, 13, 53, 155, 31, 95, 41, 2, 13, -1, -1, 1, 17, 83, 25, 143, 197, 26; 30974, 4748, 1938, 868, 3536, 10336, 2066, 6324, 2720, 132, 850, -68, -66, 68, 1144, 5576, 1678, 9588, 13192, 1740; 15062, 2312, 946, 425, 1736, 5083, 1018, 3128, 1360, 67, 442, -32, -34, 31, 544, 2669, 806, 4624, 6392, 845],214,1]
%
% END OF LATTICE L215.1
%
\hbox{}\par\smallskip%
%
% LATTICE L215.2
%
\leavevmode%
${L_{215.2}}$%
{} : {$[1\above{1pt}{1pt}{1}{}2\above{1pt}{1pt}{1}{}]\above{1pt}{1pt}{}{2}16\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{2}{}17\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${17}\above{1pt}{1pt}{}{2}{2}\above{1pt}{1pt}{}{2}{1}\above{1pt}{1pt}{r}{2}{16}\above{1pt}{1pt}{*}{2}{8}\above{1pt}{1pt}{*}{2}{272}\above{1pt}{1pt}{l}{2}{1}\above{1pt}{1pt}{}{2}{34}\above{1pt}{1pt}{8,7}{\infty}{136}\above{1pt}{1pt}{*}{2}{16}\above{1pt}{1pt}{l}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-59024\\-1360\\1360
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1360\\2\\8
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1360\\8\\-15
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
475\\44744\\64736
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
21\\1973\\2856
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-18\\-1692\\-2449
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
32\\2992\\4335
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4\\369\\536
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\88\\129
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\60\\96
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-138\\-188
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-25\\-2924\\-4080
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-110\\-155
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-5\\-527\\-748
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-7\\-714\\-1020
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-100\\-144
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-59024, -1360, 1360; -1360, 2, 8; 1360, 8, -15],[272, 2, 1],[32, 4, 1, 1, -1, -25, -1, -5, -7, -1, 2, 1, 1, 7, 11, 161, 5, 22, 41, 17; 2992, 369, 88, 60, -138, -2924, -110, -527, -714, -100, 204, 101, 100, 692, 1078, 15708, 486, 2125, 3910, 1604; 4335, 536, 129, 96, -188, -4080, -155, -748, -1020, -144, 289, 144, 143, 992, 1548, 22576, 699, 3060, 5644, 2320],214,2]
%
% END OF LATTICE L215.2
%
\hbox{}\par\smallskip%
%
% LATTICE L215.3
%
\leavevmode%
${L_{215.3}}$%
{} : {$[1\above{1pt}{1pt}{-}{}2\above{1pt}{1pt}{1}{}]\above{1pt}{1pt}{}{6}16\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{2}{}17\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{m}%
\EasyButWeakLineBreak%
{${68}\above{1pt}{1pt}{l}{2}{2}\above{1pt}{1pt}{r}{2}{4}\above{1pt}{1pt}{*}{2}{16}\above{1pt}{1pt}{s}{2}{8}\above{1pt}{1pt}{s}{2}{272}\above{1pt}{1pt}{*}{2}{4}\above{1pt}{1pt}{l}{2}{34}\above{1pt}{1pt}{8,3}{\infty}{136}\above{1pt}{1pt}{s}{2}{16}\above{1pt}{1pt}{*}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
33456\\8160\\3536
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
8160\\1990\\862
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3536\\862\\373
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-29581\\148920\\-63920
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-7743\\38981\\-16732
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-4350\\21900\\-9401
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-5929\\29852\\-12818
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-434\\2185\\-938
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-325\\1636\\-702
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-519\\2612\\-1120
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-475\\2390\\-1024
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-5177\\26044\\-11152
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-237\\1192\\-510
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-301\\1513\\-646
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-129\\646\\-272
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\4\\0
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[33456, 8160, 3536; 8160, 1990, 862; 3536, 862, 373],[272, 2, 1],[-5929, -434, -325, -519, -475, -5177, -237, -301, -129, -1, 13, -1, -23, -177, -395, -6655, -459, -1178, -2829, -1391; 29852, 2185, 1636, 2612, 2390, 26044, 1192, 1513, 646, 4, -68, 5, 116, 892, 1990, 33524, 2312, 5933, 14246, 7004; -12818, -938, -702, -1120, -1024, -11152, -510, -646, -272, 0, 34, -2, -50, -384, -856, -14416, -994, -2550, -6120, -3008],214,3]
%
% END OF LATTICE L215.3
%
\hbox{}\par\smallskip%
%
% LATTICE L215.4
%
\leavevmode%
${L_{215.4}}$%
{} : {$[1\above{1pt}{1pt}{-}{}2\above{1pt}{1pt}{1}{}]\above{1pt}{1pt}{}{4}16\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{2}{}17\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{m}%
\EasyButWeakLineBreak%
{${68}\above{1pt}{1pt}{*}{2}{8}\above{1pt}{1pt}{*}{2}{4}\above{1pt}{1pt}{s}{2}{16}\above{1pt}{1pt}{l}{2}{2}\above{1pt}{1pt}{r}{2}{272}\above{1pt}{1pt}{s}{2}{4}\above{1pt}{1pt}{*}{2}{136}\above{1pt}{1pt}{8,3}{\infty z}{34}\above{1pt}{1pt}{r}{2}{16}\above{1pt}{1pt}{s}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-92208\\1632\\544
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1632\\-2\\-12
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
544\\-12\\-3
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5711\\66640\\761600
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-78\\-911\\-10400
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-36\\-420\\-4801
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
127\\1496\\16898
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
25\\294\\3328
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
15\\176\\1998
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
41\\480\\5464
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
29\\339\\3866
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
815\\9520\\108664
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
49\\572\\6534
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
207\\2414\\27608
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
92\\1071\\12274
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
75\\872\\10008
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-92208, 1632, 544; 1632, -2, -12; 544, -12, -3],[272, 2, 1],[127, 25, 15, 41, 29, 815, 49, 207, 92, 75, 281, 35, 9, 7, 1, 1, -1, -3, 10, 21; 1496, 294, 176, 480, 339, 9520, 572, 2414, 1071, 872, 3264, 406, 104, 80, 11, 0, -12, -34, 119, 248; 16898, 3328, 1998, 5464, 3866, 108664, 6534, 27608, 12274, 10008, 37502, 4672, 1202, 936, 134, 136, -134, -408, 1326, 2792],214,4]
%
% END OF LATTICE L215.4
%
\hbox{}\par\smallskip%
%
% LATTICE L215.5
%
\leavevmode%
${L_{215.5}}$%
{} : {$1\above{1pt}{1pt}{1}{1}8\above{1pt}{1pt}{1}{7}64\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{2}{}17\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${17}\above{1pt}{1pt}{r}{2}{32}\above{1pt}{1pt}{*}{2}{4}\above{1pt}{1pt}{s}{2}{64}\above{1pt}{1pt}{b}{2}{8}\above{1pt}{1pt}{l}{2}{1088}\above{1pt}{1pt}{}{2}{1}\above{1pt}{1pt}{r}{2}{544}\above{1pt}{1pt}{16,15}{\infty z}{136}\above{1pt}{1pt}{l}{2}{64}\above{1pt}{1pt}{}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
shares genus with {$ {L_{215.6}}$}%
; isometric to own %
2-dual\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1036864\\1088\\-1088
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1088\\-8\\0
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1088\\0\\1
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1089\\-133824\\-1166336
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-26\\-3199\\-27872
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4\\492\\4287
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-19\\-2329\\-20315
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-9\\-1102\\-9616
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-122\\-1066
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-120\\-1056
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\1\\4
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\136\\1088
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\-1
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3\\-374\\-3264
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-7\\-867\\-7548
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-11\\-1360\\-11840
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[1036864, 1088, -1088; 1088, -8, 0; -1088, 0, 1],[1088, 8, 1],[-19, -9, -1, -1, 0, 1, 0, -3, -7, -11, -15, -11, -3, -15, -10, -273, -4, -65, -27, -21; -2329, -1102, -122, -120, 1, 136, 0, -374, -867, -1360, -1853, -1358, -370, -1848, -1231, -33592, -492, -7990, -3315, -2576; -20315, -9616, -1066, -1056, 4, 1088, -1, -3264, -7548, -11840, -16133, -11824, -3222, -16096, -10724, -292672, -4287, -69632, -28900, -22464],214,5]
%
% END OF LATTICE L215.5
%
\hbox{}\par\smallskip%
%
% LATTICE L215.6
%
\leavevmode%
${L_{215.6}}$%
{} : {$1\above{1pt}{1pt}{1}{1}8\above{1pt}{1pt}{1}{7}64\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{2}{}17\above{1pt}{1pt}{1}{}$}\EasyButWeakLineBreak%
{${68}\above{1pt}{1pt}{*}{2}{32}\above{1pt}{1pt}{l}{2}{1}\above{1pt}{1pt}{}{2}{64}\above{1pt}{1pt}{r}{2}{8}\above{1pt}{1pt}{b}{2}{1088}\above{1pt}{1pt}{s}{2}{4}\above{1pt}{1pt}{*}{2}{544}\above{1pt}{1pt}{16,7}{\infty z}{136}\above{1pt}{1pt}{b}{2}{64}\above{1pt}{1pt}{s}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
shares genus with {$ {L_{215.5}}$}%
; isometric to own %
2-dual\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-294848\\16320\\8704
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
16320\\312\\128
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
8704\\128\\49
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
20671\\-5917360\\11783040
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
120\\-34351\\68400
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
24\\-6870\\13679
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
115\\-32912\\65518
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
25\\-7154\\14240
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\-286\\569
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\288\\-576
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\287\\-572
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\-272\\544
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\-286\\570
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
31\\-8874\\17680
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
44\\-12597\\25092
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
61\\-17464\\34784
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-294848, 16320, 8704; 16320, 312, 128; 8704, 128, 49],[1088, 8, 1],[115, 25, 1, -1, -1, 1, 1, 31, 44, 61, 157, 55, 7, 65, 41, 1087, 31, 241, 92, 67; -32912, -7154, -286, 288, 287, -272, -286, -8874, -12597, -17464, -44948, -15746, -2004, -18608, -11737, -311168, -8874, -68986, -26333, -19176; 65518, 14240, 569, -576, -572, 544, 570, 17680, 25092, 34784, 89522, 31360, 3991, 37056, 23372, 619616, 17670, 137360, 52428, 38176],214,6]
%
% END OF LATTICE L215.6
%
%
% LATTICE L215.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[967300, -60452, 3808; -60452, 3778, -238; 3808, -238, 15],[68, 2, 1],[883, 128, 47, 73, 65, 695, 31, 74, 11, -1, 1, 2, 5, 31, 65, 1073, 73, 368, 431, 209; 14739, 2137, 785, 1220, 1087, 11628, 519, 1241, 187, -16, 17, 33, 83, 516, 1083, 17884, 1217, 6137, 7191, 3488; 9503, 1384, 513, 808, 730, 7888, 357, 884, 170, 0, 17, 16, 47, 312, 670, 11152, 763, 3876, 4590, 2240],214,7]
%
% END OF LATTICE L215.7
%
%
% LATTICE L215.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[16728, 4216, -136; 4216, 1062, -34; -136, -34, 1],[136, 2, 1],[-4, 0, 2, 15, 33, 553, 38, 97, 231, 113, 480, 35, 26, 41, 37, 399, 18, 22, 7, -1; 17, 0, -9, -68, -150, -2516, -173, -442, -1054, -516, -2193, -160, -119, -188, -170, -1836, -83, -102, -34, 4; 34, -1, -34, -260, -578, -9724, -670, -1717, -4114, -2020, -8602, -629, -470, -748, -682, -7412, -338, -425, -170, 4],214,8]
%
% END OF LATTICE L215.8
%
%
% LATTICE L215.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[136, 0, 0; 0, 2, 0; 0, 0, -1],[136, 2, 1],[1, 0, -1, -2, -9, -76, -21, -27, -65, -16, -273, -10, -15, -6, -11, -60, -11, -7, -3, 0; 0, -1, -8, -11, -44, -357, -96, -119, -272, -65, -1088, -39, -56, -21, -36, -187, -32, -17, 0, 1; 0, -1, -16, -28, -122, -1020, -280, -357, -850, -208, -3536, -129, -192, -76, -138, -748, -136, -85, -34, 0],214,9]
%
% END OF LATTICE L215.9
%
%
% LATTICE L215.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-12784, -2448, 544; -2448, -184, 56; 544, 56, -15],[272, 8, 1],[104, 36, 9, 41, 51, 671, 19, 146, 109, 39, 66, 14, 1, -1, -1, 9, 1, 24, 61, 41; 1717, 595, 149, 680, 847, 11152, 316, 2431, 1819, 652, 1105, 235, 17, -16, -17, 136, 16, 391, 1003, 676; 10115, 3504, 877, 4000, 4980, 65552, 1857, 14280, 10676, 3824, 6477, 1376, 99, -96, -100, 816, 95, 2312, 5916, 3984],214,10]
%
% END OF LATTICE L215.10
%
%
% LATTICE L215.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-149192, 408, 1496; 408, 12, -4; 1496, -4, -15],[136, 4, 1],[155, 53, 13, 29, 71, 463, 26, 197, 143, 25, 83, 17, 1, -1, -1, 13, 2, 41, 95, 31; -102, -34, -8, -17, -40, -255, -14, -102, -68, -11, -34, -6, 0, 1, 0, -17, -2, -34, -68, -21; 15419, 5272, 1293, 2884, 7060, 46036, 2585, 19584, 14212, 2484, 8245, 1688, 99, -100, -100, 1292, 199, 4080, 9452, 3084],214,11]
%
% END OF LATTICE L215.11
%
%
% LATTICE L215.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[272, 0, 0; 0, 2, 0; 0, 0, -1],[272, 2, 1],[-30, -11, -3, -15, -10, -273, -8, -65, -27, -21, -38, -9, -1, -1, 0, 1, 0, -3, -7, -11; -187, -66, -17, -80, -51, -1360, -39, -306, -119, -88, -153, -34, -3, 0, 1, 0, -1, -34, -51, -72; -561, -204, -55, -272, -180, -4896, -143, -1156, -476, -368, -663, -156, -17, -16, 0, 0, -1, -68, -136, -208],214,12]
%
% END OF LATTICE L215.12
%
%
% LATTICE L215.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-4158200, 259896, 121856; 259896, -16244, -7616; 121856, -7616, -3569],[136, 4, 1],[-1577, -253, -111, -107, -229, -1373, -141, -449, -197, -15, 13, 23, 19, 15, -1, -191, -43, -333, -585, -169; -26996, -4334, -1904, -1839, -3944, -23681, -2436, -7786, -3468, -277, 68, 374, 320, 255, -16, -3247, -732, -5678, -9996, -2891; 3774, 612, 274, 272, 600, 3672, 386, 1292, 680, 80, 306, -12, -34, -32, 0, 408, 94, 748, 1360, 400],214,13]
%
% END OF LATTICE L215.13
%
%
% LATTICE L215.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[16320, 136, -136; 136, -8, 0; -136, 0, 1],[136, 8, 1],[1, 0, -1, -4, -9, -152, -21, -27, -65, -32, -273, -10, -15, -12, -11, -120, -11, -7, -3, 0; 17, 0, -13, -51, -114, -1921, -265, -340, -816, -401, -3417, -125, -187, -149, -136, -1479, -135, -85, -34, 1; 136, -1, -136, -532, -1190, -20060, -2768, -3553, -8534, -4196, -35768, -1309, -1960, -1564, -1430, -15572, -1424, -901, -374, 4],214,14]
%
% END OF LATTICE L215.14
%
%
% LATTICE L215.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-517616, 32368, -8704; 32368, -2024, 544; -8704, 544, -145],[272, 8, 1],[9, 0, -11, -89, -201, -3399, -235, -1210, -1459, -719, -3069, -450, -169, -271, -249, -2721, -125, -320, -71, -1; 153, -1, -189, -1524, -3439, -58140, -4019, -20689, -24939, -12288, -52445, -7689, -2887, -4628, -4251, -46444, -2133, -5457, -1207, -16; 34, -4, -50, -384, -856, -14416, -994, -5100, -6120, -3008, -12818, -1876, -702, -1120, -1024, -11152, -510, -1292, -272, 0],214,15]
%
% END OF LATTICE L215.15
%
%
% LATTICE L215.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-240720, -127568, 1632; -127568, -67592, 864; 1632, 864, -11],[272, 8, 1],[831, 123, 47, 77, 72, 795, 37, 97, 22, -1, -15, -3, 1, 19, 48, 837, 59, 311, 386, 193; -1870, -277, -106, -174, -163, -1802, -84, -221, -51, 2, 34, 7, -2, -42, -107, -1870, -132, -697, -867, -434; -23834, -3544, -1366, -2264, -2140, -23800, -1118, -2992, -748, 8, 442, 104, -10, -488, -1300, -22984, -1634, -8704, -10948, -5512],214,16]
%
% END OF LATTICE L215.16
%
%
% LATTICE L215.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[3536, 3264, -272; 3264, 136, -24; -272, -24, 3],[272, 8, 1],[1, 1, 1, 3, 4, 53, 3, 11, 6, 1, -1, -1, -1, -3, -4, -53, -3, -11, -6, -1; 17, 19, 19, 56, 73, 952, 53, 187, 85, 4, -85, -29, -23, -64, -83, -1088, -61, -221, -119, -20; 238, 244, 242, 712, 928, 12104, 674, 2380, 1088, 56, -1054, -364, -290, -808, -1048, -13736, -770, -2788, -1496, -248],214,17]
%
% END OF LATTICE L215.17
%
%
% LATTICE L215.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[80648, 8432, -1632; 8432, 867, -170; -1632, -170, 33],[136, 17, 1],[1, -1, -5, -7, -55, -13, -59, -17, -19, -38, -37, -89, -31, -11, -35, -5, -13, -1, 1, 2; 2, -4, -18, -28, -232, -56, -258, -76, -88, -180, -178, -436, -158, -60, -208, -32, -94, -12, 0, 4; 60, -68, -340, -493, -3944, -939, -4284, -1244, -1408, -2839, -2780, -6732, -2380, -867, -2856, -421, -1156, -116, 48, 119],214,18]
%
% END OF LATTICE L215.18
%
%
% LATTICE L215.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-35564, 0, 680; 0, 34, 0; 680, 0, -13],[68, 34, 1],[1, 0, -9, -17, -75, -37, -173, -26, -31, -129, -129, -160, -119, -47, -85, -27, -83, -6, -1, 1; 0, 1, 0, -3, -17, -9, -44, -7, -9, -39, -40, -51, -40, -17, -33, -11, -36, -3, -1, -1; 52, 0, -476, -901, -3978, -1963, -9180, -1380, -1646, -6851, -6852, -8500, -6324, -2499, -4522, -1437, -4420, -320, -54, 51],214,19]
%
% END OF LATTICE L215.19
%
%
% LATTICE L215.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-4488, 2312, 0; 2312, -34, -34; 0, -34, 1],[136, 34, 1],[17, 33, 47, 37, 57, 49, 207, 27, 13, 95, 87, 97, 57, 15, 8, 3, 1, -1, 0, 9; 32, 62, 88, 69, 106, 91, 384, 50, 24, 175, 160, 178, 104, 27, 14, 5, 0, -2, 0, 17; 1100, 2142, 3060, 2414, 3723, 3202, 13532, 1766, 851, 6222, 5700, 6358, 3740, 986, 527, 198, 68, -66, -1, 578],214,20]
%
% END OF LATTICE L215.20
%
%
% LATTICE L215.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-143480, 0, 2176; 0, 34, 0; 2176, 0, -33],[136, 34, 1],[8, 31, 22, 69, 53, 91, 96, 25, 12, 175, 40, 89, 26, 27, 7, 5, 0, -1, 0, 17; -11, -36, -21, -56, -39, -64, -65, -16, -7, -96, -21, -44, -11, -8, -1, 0, 1, 0, -1, -32; 516, 2006, 1428, 4488, 3451, 5928, 6256, 1630, 783, 11424, 2612, 5814, 1700, 1768, 459, 328, 0, -66, -1, 1088],214,21]
%
% END OF LATTICE L215.21
%
%
% LATTICE L215.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[223856, 25296, -2720; 25296, 2822, -306; -2720, -306, 33],[272, 34, 1],[-14, -29, -7, -9, -1, 1, 1, 0, -3, -47, -8, -26, -15, -79, -109, -89, -45, -11, -19, -129; -86, -177, -42, -52, -6, 4, 4, -1, -22, -324, -54, -173, -98, -508, -694, -564, -284, -69, -118, -796; -1959, -4046, -969, -1224, -136, 120, 119, -10, -456, -6936, -1169, -3774, -2159, -11288, -15504, -12632, -6375, -1554, -2672, -18088],214,22]
%
% END OF LATTICE L215.22
%
%
% LATTICE L215.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[161976, 23800, -2312; 23800, 3468, -340; -2312, -340, 33],[136, 68, 1],[-13, -55, -7, -5, -1, 1, 2, 1, -1, -13, -5, -35, -11, -31, -89, -37, -38, -19, -17, -59; -2, -6, 0, 1, 0, -1, -2, -2, -4, -21, -6, -34, -8, -17, -40, -15, -14, -6, -4, -11; -939, -3944, -493, -340, -68, 60, 119, 48, -116, -1156, -421, -2856, -867, -2380, -6732, -2780, -2839, -1408, -1244, -4284],214,23]
%
% END OF LATTICE L215.23
%
%
% LATTICE L215.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-47056, -43792, 2720; -43792, -22270, 1360; 2720, 1360, -83],[272, 34, 1],[49, 57, 37, 47, 33, 17, 9, 0, -1, 1, 3, 8, 15, 57, 97, 87, 95, 13, 27, 207; -2628, -3055, -1980, -2508, -1754, -900, -472, 1, 54, -60, -164, -435, -812, -3076, -5226, -4684, -5112, -699, -1450, -11108; -41474, -48212, -31246, -39576, -27676, -14200, -7446, 16, 852, -952, -2590, -6868, -12818, -48552, -82484, -73928, -80682, -11032, -22884, -175304],214,24]
%
% END OF LATTICE L215.24
%
%
% LATTICE L215.25
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[272, -272, 0; -272, 306, 0; 0, 0, -1],[272, 34, 1],[-8, -31, -3, -1, 1, 1, 0, -1, -2, -51, -8, -49, -13, -63, -41, -65, -32, -15, -6, -77; -9, -34, -3, 0, 1, 0, -1, -2, -3, -72, -11, -66, -17, -80, -51, -80, -39, -18, -7, -88; -55, -204, -17, 0, 0, -16, -17, -20, -24, -544, -81, -476, -119, -544, -340, -528, -255, -116, -44, -544],214,25]
%
% END OF LATTICE L215.25
%
%
% LATTICE L215.26
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[136, 0, 0; 0, -1292, -544; 0, -544, -229],[136, 68, 1],[-9, -17, -3, 0, 1, 0, -1, -1, -3, -18, -11, -33, -17, -20, -51, -20, -39, -9, -7, -22; 214, 438, 102, 29, 0, -5, -14, 2, 28, 207, 138, 442, 250, 323, 880, 357, 718, 174, 148, 497; -498, -1020, -238, -68, 0, 12, 34, -4, -64, -476, -318, -1020, -578, -748, -2040, -828, -1666, -404, -344, -1156],214,26]
%
% END OF LATTICE L215.26
%
%
% LATTICE L215.27
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-362032, -161568, 9792; -161568, -69122, 4182; 9792, 4182, -253],[272, 34, 1],[61, 133, 37, 35, 8, 5, -1, -1, 1, 49, 19, 67, 43, 125, 92, 155, 161, 41, 19, 271; -3594, -7830, -2174, -2048, -465, -288, 62, 58, -61, -2936, -1134, -3990, -2554, -7408, -5445, -9168, -9518, -2422, -1121, -15976; -57058, -124304, -34510, -32504, -7378, -4568, 986, 920, -970, -46648, -18014, -63376, -40562, -117640, -86462, -145576, -151130, -38456, -17798, -253640],214,27]
%
% END OF LATTICE L215.27
%
%
% LATTICE L215.28
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[13736, 4624, -136; 4624, -4488, 0; -136, 0, 1],[136, 136, 1],[16, 31, 44, 69, 53, 91, 192, 25, 12, 175, 80, 89, 52, 27, 7, 5, 0, -1, 0, 17; 17, 33, 47, 74, 57, 98, 207, 27, 13, 190, 87, 97, 57, 30, 8, 6, 1, -1, 0, 18; 2188, 4250, 6052, 9520, 7327, 12592, 26588, 3466, 1667, 24344, 11140, 12410, 7276, 3808, 1003, 736, 68, -134, -1, 2312],214,28]
%
% END OF LATTICE L215.28
%
%
% LATTICE L215.29
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[8976, -47056, 544; -47056, 247112, -2856; 544, -2856, 33],[272, 136, 1],[-89, -109, -79, -15, -52, -8, -47, -3, 0, 1, 1, -1, -9, -7, -58, -14, -129, -19, -22, -45; -104, -129, -96, -19, -69, -11, -68, -5, -1, 0, 0, -1, -8, -7, -61, -15, -140, -21, -25, -52; -7600, -9452, -7072, -1411, -5168, -829, -5168, -388, -88, -17, -16, -68, -544, -493, -4352, -1075, -10064, -1516, -1816, -3791],214,29]
%
% END OF LATTICE L215.29
%
%
% LATTICE L215.30
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-752624, 0, -373184; 0, 136, 0; -373184, 0, -185041],[272, 136, 1],[3246, 10217, 5648, 14297, 19220, 15495, 15494, 3723, 3122, 20771, 4442, 9003, 2040, 1079, 0, -119, -118, 121, 722, 9981; -11, -33, -17, -40, -51, -40, -39, -9, -7, -44, -9, -17, -3, 0, 1, 0, -1, -1, -3, -36; -6546, -20604, -11390, -28832, -38760, -31248, -31246, -7508, -6296, -41888, -8958, -18156, -4114, -2176, 0, 240, 238, -244, -1456, -20128],214,30]
%
% END OF LATTICE L215.30
%
%
% LATTICE L215.31
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-142256, 0, 1360; 0, 136, 0; 1360, 0, -13],[272, 136, 1],[-27, -85, -47, -119, -160, -129, -129, -31, -26, -173, -37, -75, -17, -9, 0, 1, 1, -1, -6, -83; -11, -33, -17, -40, -51, -40, -39, -9, -7, -44, -9, -17, -3, 0, 1, 0, -1, -1, -3, -36; -2874, -9044, -4998, -12648, -17000, -13704, -13702, -3292, -2760, -18360, -3926, -7956, -1802, -952, 0, 104, 102, -108, -640, -8840],214,31]
%
% END OF LATTICE L215.31
%
%
% LATTICE L215.32
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[13872, -35088, 544; -35088, 87992, -1360; 544, -1360, 21],[272, 136, 1],[-129, -160, -119, -47, -85, -27, -83, -6, -1, 1, 1, 0, -9, -17, -75, -37, -173, -26, -31, -129; -154, -191, -142, -56, -101, -32, -98, -7, -1, 2, 2, 1, -10, -20, -89, -44, -206, -31, -37, -154; -6632, -8228, -6120, -2414, -4352, -1378, -4216, -300, -40, 102, 104, 68, -408, -850, -3808, -1886, -8840, -1332, -1592, -6630],214,32]
%
% END OF LATTICE L215.32
%
%
% LATTICE L215.33
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[62016, -26112, -4352; -26112, 6392, 1088; -4352, 1088, 185],[1088, 136, 1],[1, 1, -1, -3, -31, -4, -77, -6, -15, -16, -65, -41, -63, -13, -49, -4, -51, -2, -1, 0; -72, -77, 88, 248, 2558, 330, 6352, 495, 1238, 1321, 5368, 3387, 5208, 1076, 4062, 332, 4240, 167, 86, 3; 448, 476, -544, -1530, -15776, -2035, -39168, -3052, -7632, -8143, -33088, -20876, -32096, -6630, -25024, -2045, -26112, -1028, -528, -17],214,33]
%
% END OF LATTICE L215.33
%
%
% LATTICE L215.34
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[35904, -112064, 1088; -112064, 350200, -3400; 1088, -3400, 33],[1088, 136, 1],[1, -1, -17, -7, -119, -29, -269, -20, -47, -97, -193, -119, -175, -17, -121, -19, -115, -4, -1, 1; 0, -1, -16, -7, -122, -30, -280, -21, -50, -104, -208, -129, -192, -19, -138, -22, -136, -5, -2, 0; -32, -68, -1088, -493, -8704, -2150, -20128, -1516, -3632, -7582, -15200, -9452, -14144, -1411, -10336, -1658, -10336, -388, -176, -34],214,34]
%
% END OF LATTICE L215.34
%

\medskip%
%------------------------------WEYL-GROUP-W216--------------------------------
%
\leavevmode\llap{}%
$W_{216}$%
\qquad\llap{4} lattices, $\chi=18$%
\hfill%
$24\slashinfty42|\rtimes D_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L216.1
%
\leavevmode%
${L_{216.1}}$%
{} : {$1\above{1pt}{1pt}{2}{2}16\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{2}{}9\above{1pt}{1pt}{-}{}$}\EasyButWeakLineBreak%
{${18}\above{1pt}{1pt}{b}{2}{2}\above{1pt}{1pt}{}{4}{1}\above{1pt}{1pt}{24,23}{\infty}{4}\above{1pt}{1pt}{*}{4}{2}\above{1pt}{1pt}{s}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-262800\\2016\\2880
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2016\\-14\\-23
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2880\\-23\\-31
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2\\-81\\-126
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-39\\-64
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\40\\63
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5\\196\\318
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\77\\128
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-262800, 2016, 2880; 2016, -14, -23; 2880, -23, -31],[144, 1, 1],[-2, -1, 1, 5, 2; -81, -39, 40, 196, 77; -126, -64, 63, 318, 128],215,1]
%
% END OF LATTICE L216.1
%
%
% LATTICE L216.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-5904, 864, 432; 864, -126, -63; 432, -63, -31],[144, 9, 1],[0, 2, 3, 0, -1; -1, 13, 28, 4, -7; 2, 0, -18, -9, 0],215,2]
%
% END OF LATTICE L216.2
%
%
% LATTICE L216.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-18288, 2160, 5616; 2160, -224, -688; 5616, -688, -1705],[144, 16, 1],[-58, 64, 77, 29, -32; -117, 125, 152, 58, -63; -144, 160, 192, 72, -80],215,3]
%
% END OF LATTICE L216.3
%
%
% LATTICE L216.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2016, 7920, 864; 7920, -30384, -3312; 864, -3312, -361],[144, 144, 1],[-1, 1, 4, 2, -3; -2, 16, 9, -15, -32; 16, -144, -72, 144, 288],215,4]
%
% END OF LATTICE L216.4
%

\medskip%
%------------------------------WEYL-GROUP-W217--------------------------------
%
\leavevmode\llap{}%
$W_{217}$%
\qquad\llap{12} lattices, $\chi=42$%
\hfill%
$2224222242\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L217.1
%
\leavevmode%
${L_{217.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{2}{}49\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${196}\above{1pt}{1pt}{b}{2}{6}\above{1pt}{1pt}{s}{2}{98}\above{1pt}{1pt}{b}{2}{2}\above{1pt}{1pt}{*}{4}{4}\above{1pt}{1pt}{*}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-11857562724\\60807432\\-344568
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
60807432\\-311830\\1767
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-344568\\1767\\-10
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-4842181\\-943687080\\97381620
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
24831\\4839285\\-499379
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-144\\-28064\\2895
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-87\\-16954\\1960
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-195\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
43\\8379\\-1078
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
8\\1559\\-180
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
151\\29428\\-3074
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-11857562724, 60807432, -344568; 60807432, -311830, 1767; -344568, 1767, -10],[588, 1, 1],[-87, -1, 43, 8, 151, 2733, 136, 398, 1, -7; -16954, -195, 8379, 1559, 29428, 532630, 26505, 77567, 195, -1364; 1960, 0, -1078, -180, -3074, -55174, -2715, -7791, -1, 178],216,1]
%
% END OF LATTICE L217.1
%
%
% LATTICE L217.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[14847, 4851, -147; 4851, 1585, -48; -147, -48, 1],[147, 1, 1],[5161, 526, 1604, 12, 0, -16, -1, 111, 23, 280; -15925, -1623, -4949, -37, 0, 49, 3, -343, -71, -864; -4557, -465, -1421, -11, -1, 0, 0, -98, -20, -247],216,2]
%
% END OF LATTICE L217.2
%
%
% LATTICE L217.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[345891, -7056, 115248; -7056, 138, -2349; 115248, -2349, 38399],[147, 3, 1],[-15240, -551, -5527, -97, -47, -48, 31, 431, -7, -785; 13622, 497, 5047, 95, 48, 49, -32, -490, -2, 696; 46599, 1685, 16905, 297, 144, 147, -95, -1323, 21, 2400],216,3]
%
% END OF LATTICE L217.3
%
%
% LATTICE L217.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-7164780, 588, 18228; 588, 6, -3; 18228, -3, -46],[588, 3, 1],[37, 2, 60, 7, 113, 2021, 33, 283, 0, -1; 3626, 195, 5831, 679, 10944, 195706, 3195, 27391, -1, -96; 14406, 779, 23373, 2727, 44022, 787332, 12856, 110250, 0, -390],216,4]
%
% END OF LATTICE L217.4
%
%
% LATTICE L217.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[443463720, 21213276, -111511260; 21213276, 1030472, -5334108; -111511260, -5334108, 28040087],[588, 4, 1],[428139, 28567, 432949, 77265, 1049666, 19480953, 2002973, 6203415, 58171, 33822; -8722, -582, -8820, -1574, -21383, -396851, -40803, -126371, -1185, -689; 1700986, 113496, 1720096, 306972, 4170298, 77397362, 7957764, 24646020, 231112, 134374],216,5]
%
% END OF LATTICE L217.5
%
%
% LATTICE L217.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2080046472, -10665732, -523585776; -10665732, 54696, 2684760; -523585776, 2684760, 131796125],[588, 12, 1],[-46401, -3811, -103459, -11575, -93686, -1676439, -54789, -470821, -145, -74; 49, 3, 49, 3, 7, 98, 2, 0, -2, 1; -184338, -15140, -411012, -45984, -372186, -6659982, -217660, -1870428, -576, -294],216,6]
%
% END OF LATTICE L217.6
%
%
% LATTICE L217.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[5847513, 7644, 1911735; 7644, -98, 2499; 1911735, 2499, 625006],[147, 49, 1],[-4741, -25424, -1756, -1618, -817, -17, 1634, 170, 32, -11871; 24, 117, 7, 1, -1, 0, 3, 1, 7, 65; 14501, 77763, 5371, 4949, 2499, 52, -4998, -520, -98, 36309],216,7]
%
% END OF LATTICE L217.7
%
%
% LATTICE L217.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[147, 727650, 240051; 727650, 2477661627, 817378065; 240051, 817378065, 269652197],[147, 147, 1],[-93, -155, -29, -11, -1, 0, 0, -2, -20, -247; 526981, 877245, 163781, 60037, 0, -1633, -1665, 11335, 115079, 1400928; -1597401, -2659132, -496458, -181986, 0, 4950, 5047, -34359, -348831, -4246536],216,8]
%
% END OF LATTICE L217.8
%
%
% LATTICE L217.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2940, -588, 0; -588, 98, -49; 0, -49, -122],[588, 49, 1],[129, 346, 24, 23, 45, 9, -1, -1, 0, 323; 638, 1713, 119, 115, 228, 46, -3, -5, -1, 1596; -274, -735, -51, -49, -98, -20, 0, 2, 0, -686],216,9]
%
% END OF LATTICE L217.9
%
%
% LATTICE L217.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1901004, -216384, 6468; -216384, -24402, 735; 6468, 735, -22],[588, 147, 1],[1, 2, 0, -5, -175, -67, -57, -11, -6, -1; 2, 3, -1, -17, -480, -182, -153, -29, -13, 0; 360, 686, -36, -2058, -67914, -25938, -22001, -4227, -2205, -294],216,10]
%
% END OF LATTICE L217.10
%
%
% LATTICE L217.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[43512, -72324, 65268; -72324, 119560, -107996; 65268, -107996, 97535],[588, 196, 1],[-1601, -8249, -539, -343, -170, -19, 149, -1, -197, -4150; 4804, 24756, 1618, 1032, 517, 59, -441, 3, 589, 12451; 6390, 32928, 2152, 1372, 686, 78, -588, 4, 784, 16562],216,11]
%
% END OF LATTICE L217.11
%
%
% LATTICE L217.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[12936, -2307900, 580944; -2307900, 424109112, -106756692; 580944, -106756692, 26872781],[588, 588, 1],[-2, -12, -14, -108, -1145, -427, -703, -129, -35, 1; -657, -3503, -4087, -31675, -338582, -126339, -208157, -38245, -10657, -74; -2610, -13916, -16236, -125832, -1345050, -501894, -826924, -151932, -42336, -294],216,12]
%
% END OF LATTICE L217.12
%

\medskip%
%------------------------------WEYL-GROUP-W218--------------------------------
%
\leavevmode\llap{}%
$W_{218}$%
\qquad\llap{32} lattices, $\chi=80$%
\hfill%
$62\infty22\infty62\infty22\infty\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L218.1
%
\leavevmode%
${L_{218.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}8\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{-}{}9\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{-2}{}25\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{23,3,2}%
\EasyButWeakLineBreak%
{${6}\above{1pt}{1pt}{}{6}{2}\above{1pt}{1pt}{b}{2}{24}\above{1pt}{1pt}{30,29}{\infty z}{6}\above{1pt}{1pt}{s}{2}{50}\above{1pt}{1pt}{b}{2}{24}\above{1pt}{1pt}{30,11}{\infty z}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-217800\\0\\-3600
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\6\\9
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3600\\9\\-46
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-28001\\-2528400\\1713600
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
100\\9029\\-6120
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-310\\-27993\\18971
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
100\\9029\\-6120
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
9\\812\\-551
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
19\\1712\\-1164
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\179\\-123
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\175\\-125
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-92\\60
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-217800, 0, -3600; 0, 6, 9; -3600, 9, -46],[1800, 3, 1],[100, 9, 19, 2, 2, -1, 0, 1, 21, 28, 248, 201; 9029, 812, 1712, 179, 175, -92, 1, 91, 1900, 2530, 22400, 18152; -6120, -551, -1164, -123, -125, 60, 0, -61, -1284, -1713, -15175, -12300],217,1]
%
% END OF LATTICE L218.1
%
%
% LATTICE L218.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-155743050, -3047400, -50850; -3047400, -59628, -995; -50850, -995, -16],[150, 1, 1],[-1, -43, -383, -976, -8522, -3433, -3389, -296, -295, -41, 47, 43; 51, 2196, 19560, 49845, 435225, 175326, 173079, 15117, 15066, 2094, -2400, -2196; 6, 95, 828, 2097, 18275, 7356, 7254, 631, 624, 81, -125, -96],217,2]
%
% END OF LATTICE L218.2
%
%
% LATTICE L218.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-977464200, -4863000, -239400; -4863000, -24194, -1191; -239400, -1191, -46],[600, 1, 1],[-8729, -785, -1655, -173, -169, 89, -1, -88, -1837, -2446, -21656, -17549; 1754829, 157812, 332712, 34779, 33975, -17892, 201, 17691, 369300, 491730, 4353600, 3527952; -6120, -551, -1164, -123, -125, 60, 0, -61, -1284, -1713, -15175, -12300],217,3]
%
% END OF LATTICE L218.3
%
%
% LATTICE L218.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-27450, 5400, -900; 5400, -678, 105; -900, 105, -16],[450, 3, 1],[80, 7, 7, 1, -1, -1, 0, 1, 9, 23, 201, 81; 3629, 317, 316, 44, -50, -46, 1, 46, 410, 1045, 9125, 3676; 19254, 1681, 1674, 231, -275, -246, 6, 245, 2178, 5547, 48425, 19506],217,4]
%
% END OF LATTICE L218.4
%
%
% LATTICE L218.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[47648100, -7719450, 23657550; -7719450, 1251116, -3832760; 23657550, -3832760, 11746107],[150, 2, 1],[-10147, -14810, -84004, -459739, -4108611, -835619, -1671383, -153343, -84149, -44720, -95214, -5146; 402, 587, 3330, 18225, 162875, 33126, 66258, 6079, 3336, 1773, 3775, 204; 20568, 30020, 170277, 931896, 8328200, 1693809, 3387912, 310828, 170571, 90648, 193000, 10431],217,5]
%
% END OF LATTICE L218.5
%
%
% LATTICE L218.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[48679650, -9556800, -16363950; -9556800, 1876674, 3212565; -16363950, 3212565, 5500838],[150, 3, 1],[2332, 10210, 38607, 105644, 2832364, 384035, 384068, 105710, 38673, 10276, 65636, 2365; 134, 587, 2220, 6075, 162875, 22084, 22086, 6079, 2224, 591, 3775, 136; 6859, 30030, 113552, 310723, 8330625, 1129534, 1129631, 310917, 113746, 30224, 193050, 6956],217,6]
%
% END OF LATTICE L218.6
%
%
% LATTICE L218.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-59927431200, 146424450, -28715278350; 146424450, -357768, 70161840; -28715278350, 70161840, -13759428599],[150, 6, 1],[70, 5281, 7770, 39501, 1033909, 69394, 136950, 35825, 5932, 1605, -6259, -884; 17, 2196, 3260, 16615, 435225, 29221, 57693, 15117, 2511, 698, -2400, -366; -146, -11010, -16199, -82352, -2155500, -144673, -285514, -74688, -12367, -3346, 13050, 1843],217,7]
%
% END OF LATTICE L218.7
%
%
% LATTICE L218.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2497050, 1035450, -130950; 1035450, -429366, 54303; -130950, 54303, -6866],[450, 3, 1],[-66, -356, -983, -2468, -64424, -8639, -8514, -2218, -733, -106, 74, 59; -133, -714, -1970, -4945, -129075, -17308, -17057, -4443, -1468, -212, 150, 118; 207, 1143, 3168, 7962, 207900, 27882, 27483, 7164, 2370, 345, -225, -192],217,8]
%
% END OF LATTICE L218.8
%
%
% LATTICE L218.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-36869400, 14721000, 105000; 14721000, -5877714, -41925; 105000, -41925, -298],[600, 3, 1],[12435, 3192, 2055, 122, -312, -153, 155, 585, 2981, 3655, 94737, 25333; 30885, 7928, 5104, 303, -775, -380, 385, 1453, 7404, 9078, 235300, 62920; 36301, 9321, 6004, 358, -900, -448, 449, 1704, 8696, 10667, 276525, 73948],217,9]
%
% END OF LATTICE L218.9
%
%
% LATTICE L218.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[778260600, -1961550, 387386550; -1961550, 4944, -976380; 387386550, -976380, 192825307],[450, 6, 1],[-36821, -3449, -1952, -1144, -2514, -115, -9, -234, -1731, -9905, -89561, -18300; -2264, -207, -113, -59, -125, -7, -16, -21, -115, -625, -5575, -1133; 73962, 6928, 3921, 2298, 5050, 231, 18, 470, 3477, 19896, 179900, 36759],217,10]
%
% END OF LATTICE L218.10
%
%
% LATTICE L218.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1630665900, 8284950, 813089700; 8284950, 42096, 4131078; 813089700, 4131078, 405426311],[450, 6, 1],[8925, 20572, 23666, 112747, 2898901, 193151, 377625, 95393, 14989, 3218, 224, 124; 2233, 5151, 5929, 28252, 726450, 48404, 94637, 23910, 3758, 809, 75, 31; -17922, -41310, -47523, -226404, -5821200, -387861, -758298, -191556, -30099, -6462, -450, -249],217,11]
%
% END OF LATTICE L218.11
%
%
% LATTICE L218.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1249120950, 6024750, 205450050; 6024750, 29100, 990925; 205450050, 990925, 33791542],[150, 25, 1],[-5033, -7348, -83365, -228125, -81549, -829283, -829357, -76091, -83513, -22192, -1890, -5107; 9, 10, 102, 273, 97, 984, 981, 89, 96, 24, 2, 6; 30600, 44675, 506850, 1386975, 495809, 5041950, 5042400, 462625, 507750, 134925, 11491, 31050],217,12]
%
% END OF LATTICE L218.12
%
%
% LATTICE L218.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1007295600, -41865000, -19526400; -41865000, 1739984, 811552; -19526400, 811552, 378519],[600, 8, 1],[6413, 563, 287, 110, 172, 10, 97, 88, 364, 1843, 16103, 3245; 162573, 14270, 7272, 2781, 4325, 249, 2457, 2233, 9231, 46728, 408250, 82266; -17736, -1552, -786, -288, -400, -18, -264, -248, -1014, -5112, -44600, -8982],217,13]
%
% END OF LATTICE L218.13
%
%
% LATTICE L218.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-55024200, 12364200, -5047200; 12364200, -2772822, 1128585; -5047200, 1128585, -457346],[1800, 3, 1],[-373916, -96011, -61845, -3688, 9268, 4615, -4624, -17551, -89571, -109874, -2848318, -761695; -2786827, -715578, -460936, -27487, 69075, 34396, -34463, -130809, -667580, -818900, -21228750, -5676976; -2750526, -706257, -454932, -27129, 68175, 33948, -34014, -129105, -658884, -808233, -20952225, -5603028],217,14]
%
% END OF LATTICE L218.14
%
%
% LATTICE L218.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-274492181400, 15095250, -135869106600; 15095250, -800, 7471900; -135869106600, 7471900, -67252968861],[150, 50, 1],[-7499, -322754, -1437395, -7325855, -2558647, -12884062, -25437871, -2221783, -1107142, -307756, 14110, 161377; 6, 95, 414, 2097, 731, 3678, 7254, 631, 312, 81, -5, -48; 15150, 652050, 2903925, 14800200, 5169156, 26029275, 51391350, 4488600, 2236725, 621750, -28506, -326025],217,15]
%
% END OF LATTICE L218.15
%
%
% LATTICE L218.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-231162057150, -16965900, -78074463450; -16965900, -1200, -5730225; -78074463450, -5730225, -26369473924],[150, 75, 1],[-1917, -247521, -734895, -1872740, -1962234, -6587217, -6502793, -1703892, -566047, -78673, 10821, 82507; 3836, 495137, 1470066, 3746179, 3925199, 13176886, 13008004, 3408415, 1132302, 157373, -21647, -165046; 5675, 732750, 2175550, 5543975, 5808909, 19500500, 19250575, 5044125, 1675700, 232900, -32034, -244250],217,16]
%
% END OF LATTICE L218.16
%
%
% LATTICE L218.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-142800, -541800, -67800; -541800, -2054064, -257064; -67800, -257064, -32171],[600, 24, 1],[-5693, -1678, -340, -249, -2011, -45, 23, -23, -227, -1452, -40514, -2790; -12190, -3591, -727, -531, -4275, -95, 50, -51, -487, -3111, -86775, -5975; 109408, 32232, 6526, 4768, 38400, 854, -448, 456, 4370, 27920, 778800, 53626],217,17]
%
% END OF LATTICE L218.17
%
%
% LATTICE L218.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-18899400, 169200, -9238800; 169200, -1150, 83075; -9238800, 83075, -4515942],[600, 25, 1],[661252, 59581, 126031, 13402, 554, -6421, -112, 6533, 138425, 184940, 65560, 1328701; 1322355, 119149, 252036, 26802, 1108, -12840, -225, 13064, 276816, 369837, 131105, 2657100; -1328475, -119700, -253200, -26925, -1113, 12900, 225, -13125, -278100, -371550, -131712, -2669400],217,18]
%
% END OF LATTICE L218.18
%
%
% LATTICE L218.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[4770263145900, -11828837173050, -5867355346500; -11828837173050, 29332006347300, 14549300302950; -5867355346500, 14549300302950, 7216763040313],[150, 150, 1],[3, 10, 17, 91, 97, 164, 327, 89, 16, 8, 2, 1; -1899314, -8318571, -15729263, -86084859, -92319531, -156468307, -312964466, -86140563, -15757115, -8374275, -2139603, -963583; 3829100, 16770600, 31710875, 173550800, 186120168, 315446875, 630949900, 173663100, 31767025, 16882900, 4313532, 1942625],217,19]
%
% END OF LATTICE L218.19
%
%
% LATTICE L218.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-15460650, 513000, 2470500; 513000, -16950, -81975; 2470500, -81975, -394768],[450, 75, 1],[31016, 2699, 2671, 349, -21, -409, 24, 405, 3537, 8963, 3125, 31449; 3629, 317, 316, 44, -2, -46, 1, 46, 410, 1045, 365, 3676; 193350, 16825, 16650, 2175, -131, -2550, 150, 2525, 22050, 55875, 19481, 196050],217,20]
%
% END OF LATTICE L218.20
%
%
% LATTICE L218.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-62437050, 63269550, 30807900; 63269550, -64113150, -31218675; 30807900, -31218675, -15201338],[450, 75, 1],[3110, 1534, 1121, 1194, 862, 2385, 1750, -76, -149, 264, 596, 2475; 2083, 966, 668, 667, 465, 1258, 887, -75, -74, 224, 426, 1712; 2025, 1125, 900, 1050, 792, 2250, 1725, 0, -150, 75, 333, 1500],217,21]
%
% END OF LATTICE L218.21
%
%
% LATTICE L218.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[13820400, 297000, 6894000; 297000, 6384, 148152; 6894000, 148152, 3438919],[1800, 24, 1],[131, 123, 503, 2536, 22126, 4456, 8799, 770, 390, 143, 199, 9; 32, 33, 131, 653, 5675, 1141, 2248, 195, 97, 31, 25, -1; -264, -248, -1014, -5112, -44600, -8982, -17736, -1552, -786, -288, -400, -18],217,22]
%
% END OF LATTICE L218.22
%
%
% LATTICE L218.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-428400, 1800, -68400; 1800, 48, 288; -68400, 288, -10921],[1800, 24, 1],[-5693, -1678, -340, -249, -2011, -45, 23, -23, -227, -1452, -40514, -2790; -302, -87, -17, -11, -75, -1, 2, -3, -13, -79, -2175, -149; 35664, 10512, 2130, 1560, 12600, 282, -144, 144, 1422, 9096, 253800, 17478],217,23]
%
% END OF LATTICE L218.23
%
%
% LATTICE L218.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-16378200, -220171200, -8802000; -220171200, -2957998350, -118255125; -8802000, -118255125, -4727614],[600, 75, 1],[-4697, -2787, -4613, -2751, -2085, -11869, -4553, 12, 913, -24, -690, -6631; -75181, -44603, -73820, -44020, -33362, -189912, -72849, 194, 14608, -389, -11047, -106148; 1889300, 1120875, 1855100, 1106225, 838389, 4772500, 1830700, -4875, -367100, 9775, 277611, 2667500],217,24]
%
% END OF LATTICE L218.24
%
%
% LATTICE L218.25
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1537543800, -13776750, 763741350; -13776750, 123600, -6843300; 763741350, -6843300, 379371859],[450, 150, 1],[-1801877, -165313, -90716, -48208, -4106, -5551, -10953, -15970, -90567, -495641, -177177, -900864; -2264, -207, -113, -59, -5, -7, -16, -21, -115, -625, -223, -1133; 3627450, 332800, 182625, 97050, 8266, 11175, 22050, 32150, 182325, 997800, 356684, 1813575],217,25]
%
% END OF LATTICE L218.25
%
%
% LATTICE L218.26
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[19781100, 3285450, 9923400; 3285450, 545700, 1648200; 9923400, 1648200, 4978199],[450, 150, 1],[12027, 5068, 1664, 3277, 2347, 3251, 4863, -1, 25, 1790, 2720, 5194; 37229, 15699, 5159, 10172, 7290, 10102, 15121, 6, 76, 5533, 8415, 16073; -36300, -15300, -5025, -9900, -7092, -9825, -14700, 0, -75, -5400, -8208, -15675],217,26]
%
% END OF LATTICE L218.26
%
%
% LATTICE L218.27
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[680674800, 230365800, -1528200; 230365800, 77964400, -517200; -1528200, -517200, 3431],[600, 200, 1],[2248, 195, 97, 31, 1, -1, 32, 33, 131, 653, 227, 1141; -87, -11, -9, -12, -2, -6, -3, 2, 0, -15, -7, -39; 988200, 85200, 41850, 12000, 144, -1350, 13800, 15000, 58350, 288600, 100056, 502350],217,27]
%
% END OF LATTICE L218.27
%
%
% LATTICE L218.28
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2334600, -3436200, 145800; -3436200, -4993950, 211575; 145800, 211575, -8962],[1800, 75, 1],[15264, 1376, 2913, 311, 13, -147, -4, 150, 3191, 4267, 1513, 30667; -97555, -8794, -18616, -1987, -83, 940, 25, -959, -20396, -27272, -9670, -196000; -2054775, -185225, -392100, -41850, -1748, 19800, 525, -20200, -429600, -574425, -203677, -4128300],217,28]
%
% END OF LATTICE L218.28
%
%
% LATTICE L218.29
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-4631934600, -3513600, -2340613800; -3513600, -2550, -1774575; -2340613800, -1774575, -1182753938],[1800, 75, 1],[-124728, 337, 25013, -674, -18926, -181831, -128772, -76387, -126413, -75376, -57124, -325169; -1995649, 5394, 400208, -10789, -302823, -2909348, -2060381, -1222203, -2022620, -1206020, -913986, -5202712; 249825, -675, -50100, 1350, 37908, 364200, 257925, 153000, 253200, 150975, 114417, 651300],217,29]
%
% END OF LATTICE L218.29
%
%
% LATTICE L218.30
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[16040400, 120600, 79800; 120600, 1200, 600; 79800, 600, 397],[600, 600, 1],[2, -3, 137, 921, 1041, 1801, 3698, 1113, 233, 189, 69, 49; -1, 2, 0, -5, -7, -13, -29, -11, -3, -4, -2, -2; -400, 600, -27550, -185200, -209328, -362150, -743600, -223800, -46850, -38000, -13872, -9850],217,30]
%
% END OF LATTICE L218.30
%
%
% LATTICE L218.31
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[63673200, 3187800, 16119000; 3187800, 159600, 807000; 16119000, 807000, 4080559],[1800, 600, 1],[-66327, -5714, -2802, -791, -7, 99, -923, -1011, -3923, -19384, -6718, -33724; -201229, -17337, -8503, -2404, -22, 298, -2801, -3066, -11900, -58805, -20381, -102313; 301800, 26000, 12750, 3600, 32, -450, 4200, 4600, 17850, 88200, 30568, 153450],217,31]
%
% END OF LATTICE L218.31
%
%
% LATTICE L218.32
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[3600, -5400, 0; -5400, 8400, 0; 0, 0, -1],[1800, 600, 1],[3, -5, -13, -74, -80, -136, -273, -76, -14, -7, -1, 1; 2, -3, -13, -79, -87, -149, -302, -87, -17, -11, -3, -1; 0, 0, -450, -3000, -3384, -5850, -12000, -3600, -750, -600, -216, -150],217,32]
%
% END OF LATTICE L218.32
%

\medskip%
%------------------------------WEYL-GROUP-W219--------------------------------
%
\leavevmode\llap{}%
$W_{219}$%
\qquad\llap{32} lattices, $\chi=60$%
\hfill%
$22222222222222\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L219.1
%
\leavevmode%
${L_{219.1}}$%
{} : {$1\above{1pt}{1pt}{2}{2}8\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{-2}{}25\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${2}\above{1pt}{1pt}{b}{2}{200}\above{1pt}{1pt}{*}{2}{12}\above{1pt}{1pt}{l}{2}{1}\above{1pt}{1pt}{r}{2}{300}\above{1pt}{1pt}{*}{2}{8}\above{1pt}{1pt}{b}{2}{50}\above{1pt}{1pt}{s}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-11650200\\23400\\49800
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
23400\\-47\\-100
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
49800\\-100\\-199
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
142349\\71131200\\-131400
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-286\\-142913\\264
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-611\\-305312\\563
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
6\\2997\\-5
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
557\\278300\\-500
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
79\\39474\\-72
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
40\\19988\\-37
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1931\\964950\\-1800
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
175\\87452\\-164
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
291\\145425\\-275
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-11650200, 23400, 49800; 23400, -47, -100; 49800, -100, -199],[600, 1, 1],[6, 557, 79, 40, 1931, 175, 291, 7, 93, -1, -1, 19, 7, 34; 2997, 278300, 39474, 19988, 964950, 87452, 145425, 3499, 46500, -498, -500, 9450, 3492, 16975; -5, -500, -72, -37, -1800, -164, -275, -7, -100, 0, 1, 0, -4, -25],218,1]
%
% END OF LATTICE L219.1
%
\hbox{}\par\smallskip%
%
% LATTICE L219.2
%
\leavevmode%
${L_{219.2}}$%
{} : {$1\above{1pt}{1pt}{-2}{2}8\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{-2}{}25\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{m}%
\EasyButWeakLineBreak%
{${2}\above{1pt}{1pt}{l}{2}{200}\above{1pt}{1pt}{}{2}{3}\above{1pt}{1pt}{r}{2}{4}\above{1pt}{1pt}{l}{2}{75}\above{1pt}{1pt}{}{2}{8}\above{1pt}{1pt}{r}{2}{50}\above{1pt}{1pt}{b}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-18996430200\\-94509600\\964800
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-94509600\\-470197\\4800
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
964800\\4800\\-49
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3894749\\-780681000\\211182000
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
19377\\-3884013\\1050664
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-198\\39688\\-10737
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5\\-1003\\195
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
407\\-81600\\20200
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
28\\-5613\\1464
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
55\\-11024\\3026
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
653\\-130875\\36900
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
117\\-23448\\6736
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
191\\-38275\\11325
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-18996430200, -94509600, 964800; -94509600, -470197, 4800; 964800, 4800, -49],[600, 1, 1],[5, 407, 28, 55, 653, 117, 191, 4, 43, -1, -1, 22, 9, 34; -1003, -81600, -5613, -11024, -130875, -23448, -38275, -801, -8600, 201, 200, -4425, -1808, -6825; 195, 20200, 1464, 3026, 36900, 6736, 11325, 293, 4200, 0, -98, -300, 96, 875],218,2]
%
% END OF LATTICE L219.2
%
%
% LATTICE L219.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-122550, -2400, -2400; -2400, -47, -47; -2400, -47, -46],[150, 1, 1],[0, -7, -1, 0, 19, 3, 18, 2, 57, 7, 6, 131, 11, 32; 6, 400, 51, -1, -975, -152, -900, -98, -2700, -327, -275, -5925, -492, -1400; -7, -50, 0, 1, 0, -2, -25, -5, -250, -36, -37, -900, -82, -275],218,3]
%
% END OF LATTICE L219.3
%
%
% LATTICE L219.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[14100, -4800, -300; -4800, 1634, 101; -300, 101, -23],[300, 1, 1],[54, 781, 1, -18, -127, 15, 153, 35, 3669, 533, 552, 13477, 1231, 2072; 159, 2300, 3, -53, -375, 44, 450, 103, 10800, 1569, 1625, 39675, 3624, 6100; -7, -100, 0, 2, 0, -4, -25, -5, -500, -72, -74, -1800, -164, -275],218,4]
%
% END OF LATTICE L219.4
%
%
% LATTICE L219.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[25350, -4650, 12600; -4650, 1636, -2326; 12600, -2326, 6263],[150, 2, 1],[-1224, -4553, -77, -1, -5923, -499, -7206, -1072, -24147, -6811, -6887, -166277, -7537, -50194; 47, 175, 3, 0, 225, 19, 275, 41, 925, 261, 264, 6375, 289, 1925; 2480, 9225, 156, 2, 12000, 1011, 14600, 2172, 48925, 13800, 13954, 336900, 15271, 101700],218,5]
%
% END OF LATTICE L219.5
%
%
% LATTICE L219.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[28650, -7050, -9600; -7050, 2454, 2349; -9600, 2349, 3217],[150, 3, 1],[856, 6369, 18, 1, 1384, 699, 5044, 750, 33781, 1588, 4817, 38766, 10543, 35106; 47, 350, 1, 0, 75, 38, 275, 41, 1850, 87, 264, 2125, 578, 1925; 2520, 18750, 53, 3, 4075, 2058, 14850, 2208, 99450, 4675, 14181, 114125, 31038, 103350],218,6]
%
% END OF LATTICE L219.6
%
%
% LATTICE L219.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[50700, -2100, 0; -2100, 87, 0; 0, 0, -1],[300, 3, 1],[1, 173, 9, 30, 253, 71, 124, 4, 77, 1, 0, -3, -1, 1; 24, 4100, 213, 709, 5975, 1676, 2925, 94, 1800, 23, -1, -75, -24, 25; -3, -900, -49, -171, -1475, -420, -750, -27, -600, -11, -9, -25, 0, 0],218,7]
%
% END OF LATTICE L219.7
%
%
% LATTICE L219.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-52991700, 122250, -25394400; 122250, -282, 58584; -25394400, 58584, -12169369],[150, 6, 1],[-161, -323, 24, 23, -456, -131, -1871, -259, -4927, -444, -1283, -10044, -1339, -8629; 6, 200, 17, -1, -325, -76, -900, -98, -1350, -109, -275, -1975, -246, -1400; 336, 675, -50, -48, 950, 273, 3900, 540, 10275, 926, 2676, 20950, 2793, 18000],218,8]
%
% END OF LATTICE L219.8
%
%
% LATTICE L219.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[60624600, 578700, -15161700; 578700, 5524, -144728; -15161700, -144728, 3791813],[300, 4, 1],[96, 208, -73, 1, 2581, 104, 1341, 170, 3117, 1669, 1595, 37319, 827, 5309; -101, -175, 102, 0, -3150, -127, -1625, -203, -3625, -1926, -1824, -42450, -937, -5975; 380, 825, -288, 4, 10200, 411, 5300, 672, 12325, 6600, 6308, 147600, 3271, 21000],218,9]
%
% END OF LATTICE L219.9
%
%
% LATTICE L219.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1878600, 4200, 2400; 4200, 3, -9; 2400, -9, -2],[600, 3, 1],[-4, -77, -1, 0, 3, 1, -1, -1, -173, -9, -15, -253, -71, -124; -612, -11800, -154, -1, 450, 152, -150, -152, -26400, -1374, -2291, -38650, -10848, -18950; -2073, -39900, -518, 0, 1550, 516, -525, -519, -89700, -4666, -7776, -131150, -36804, -64275],218,10]
%
% END OF LATTICE L219.10
%
%
% LATTICE L219.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[7229400, -301200, 12600; -301200, 12549, -525; 12600, -525, 22],[600, 3, 1],[28, 557, 4, 3, 1, -1, 16, 7, 1193, 31, 207, 874, 491, 859; 694, 13800, 99, 74, 25, -24, 400, 174, 29600, 769, 5134, 21675, 12176, 21300; 519, 10200, 71, 48, 25, 0, 375, 141, 22800, 589, 3912, 16475, 9240, 16125],218,11]
%
% END OF LATTICE L219.11
%
%
% LATTICE L219.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[12300, 8400, -3000; 8400, 2028, -2100; -3000, -2100, 731],[300, 12, 1],[79, 10428, 2329, 8303, 72307, 5178, 37306, 1395, 7997, 619, 541, 1393, -19, -456; -4, -550, -123, -439, -3825, -274, -1975, -74, -425, -33, -29, -75, 1, 25; 312, 41175, 9196, 32784, 285500, 20445, 147300, 5508, 31575, 2444, 2136, 5500, -75, -1800],218,12]
%
% END OF LATTICE L219.12
%
%
% LATTICE L219.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1632450, -150, 268500; -150, 25, -25; 268500, -25, 44162],[150, 25, 1],[-588, -175, -37, 0, -113, -477, -138, -514, -927, -3269, -3306, -3193, -7237, -964; 40, 12, 3, 1, 9, 36, 10, 36, 64, 225, 227, 219, 496, 66; 3575, 1064, 225, 0, 687, 2900, 839, 3125, 5636, 19875, 20100, 19413, 44000, 5861],218,13]
%
% END OF LATTICE L219.13
%
%
% LATTICE L219.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-42600, -5400, 1200; -5400, -304, 88; 1200, 88, -23],[600, 8, 1],[6, 9, -1, -1, 13, 1, 36, 6, 66, 37, 37, 887, 20, 264; 149, 225, -24, -25, 300, 24, 875, 147, 1625, 912, 913, 21900, 494, 6525; 880, 1325, -144, -148, 1800, 143, 5200, 872, 9625, 5400, 5404, 129600, 2923, 38600],218,14]
%
% END OF LATTICE L219.14
%
%
% LATTICE L219.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2832600, -31800, -7800; -31800, -304, -64; -7800, -64, -11],[600, 8, 1],[6, 18, -1, -1, 13, 2, 36, 6, 132, 37, 37, 887, 40, 264; -1191, -3575, 198, 199, -2550, -395, -7125, -1189, -26175, -7338, -7339, -175950, -7935, -52375; 2680, 8050, -444, -448, 5700, 886, 16000, 2672, 58850, 16500, 16504, 395700, 17846, 117800],218,15]
%
% END OF LATTICE L219.15
%
%
% LATTICE L219.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-300, 900, -900; 900, 1025, -500; -900, -500, 49],[300, 25, 1],[-84, -57, -31, 32, 37, 85, 3, -21, -153, -599, -662, -667, -1555, -108; 171, 116, 63, -65, -75, -172, -6, 43, 312, 1221, 1349, 1359, 3168, 220; 200, 136, 75, -75, -87, -200, -7, 50, 364, 1425, 1575, 1587, 3700, 257],218,16]
%
% END OF LATTICE L219.16
%
%
% LATTICE L219.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-216112350, 712650, -106972050; 712650, -2300, 352750; -106972050, 352750, -52949401],[150, 50, 1],[-594, -1135, -7499, 99, 5723, 11199, 5328, 14602, 8139, 49523, 41925, 36301, 37829, 8680; -7, -1, 0, 1, 0, -1, -1, -5, -5, -36, -37, -36, -41, -11; 1200, 2293, 15150, -200, -11562, -22625, -10764, -29500, -16443, -100050, -84700, -73338, -76425, -17536],218,17]
%
% END OF LATTICE L219.17
%
%
% LATTICE L219.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-185161350, -807750, -62001300; -807750, -3450, -270525; -62001300, -270525, -20761109],[150, 75, 1],[-456, -1741, -1917, 76, 1463, 17177, 4086, 11198, 12483, 12659, 32150, 9279, 58017, 6656; 905, 3480, 3834, -151, -2926, -34356, -8173, -22401, -24976, -25330, -64337, -18570, -116116, -13323; 1350, 5154, 5675, -225, -4331, -50850, -12096, -33150, -36954, -37475, -95175, -27469, -171750, -19704],218,18]
%
% END OF LATTICE L219.18
%
%
% LATTICE L219.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1507800, 46200, -12000; 46200, -1104, 264; -12000, 264, -61],[600, 24, 1],[8, 9, -1, -1, 21, 3, 86, 12, 116, 21, 61, 479, 32, 414; 1183, 1325, -149, -148, 3125, 446, 12775, 1781, 17200, 3113, 9040, 70975, 4741, 61325; 3552, 3975, -448, -444, 9400, 1341, 38400, 5352, 51675, 9352, 27156, 213200, 14241, 184200],218,19]
%
% END OF LATTICE L219.19
%
%
% LATTICE L219.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1597800, 0, 10800; 0, 24, 0; 10800, 0, -73],[600, 24, 1],[1, -7, -1, 0, 21, 5, 61, 7, 107, 9, 24, 179, 23, 139; -7, -25, 0, 1, 0, -1, -25, -5, -125, -12, -37, -300, -41, -275; 144, -1050, -148, 0, 3100, 738, 9000, 1032, 15750, 1324, 3528, 26300, 3378, 20400],218,20]
%
% END OF LATTICE L219.20
%
%
% LATTICE L219.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-173400, 19800, -1200; 19800, -2150, 125; -1200, 125, -7],[600, 25, 1],[-1, 1, 7, 5, 11, 27, 2, 2, 1, -1, -2, -5, -13, -1; -23, 12, 114, 88, 198, 492, 37, 39, 20, -18, -40, -102, -268, -21; -250, 16, 750, 675, 1578, 4000, 308, 350, 184, -150, -375, -978, -2600, -208],218,21]
%
% END OF LATTICE L219.21
%
%
% LATTICE L219.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-108600, 12000, -5400; 12000, -1325, 600; -5400, 600, -257],[600, 25, 1],[7, -3, -16, -51, -29, -145, -11, -12, -7, 1, 21, 14, 75, 6; 53, -32, -141, -432, -243, -1208, -91, -97, -56, 9, 168, 111, 592, 47; -25, -16, 0, 50, 36, 200, 17, 25, 16, 0, -50, -36, -200, -17],218,22]
%
% END OF LATTICE L219.22
%
%
% LATTICE L219.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[6231752850, -15455909250, -7666460400; -15455909250, 38333538300, 19014252000; -7666460400, 19014252000, 9431474243],[150, 150, 1],[40, 6, 1, 1, 3, 18, 10, 36, 32, 75, 227, 73, 248, 66; -668571, -99494, -14037, -74, -42859, -271304, -156951, -584497, -527040, -1239031, -3759130, -1210209, -4114434, -1096117; 1347900, 200589, 28300, 150, 86408, 546975, 316428, 1178400, 1062561, 2498000, 7578750, 2439892, 8295075, 2209872],218,23]
%
% END OF LATTICE L219.23
%
%
% LATTICE L219.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[300, 0, 0; 0, -12525, 525; 0, 525, -22],[300, 75, 1],[-6, -5, -2, -1, 0, 1, 0, -1, -9, -12, -41, -14, -99, -7; 23, 24, 14, 16, 2, 0, -1, -3, 16, 26, 104, 38, 280, 21; 525, 552, 325, 375, 47, 0, -24, -75, 348, 575, 2325, 853, 6300, 474],218,24]
%
% END OF LATTICE L219.24
%
%
% LATTICE L219.25
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[42257400, 3408300, 8047800; 3408300, 274900, 649100; 8047800, 649100, 1532681],[300, 100, 1],[328, 66, 305, 127, 139, 94, 43, 150, 173, 2563, 2741, 2729, 1579, 435; -997, -202, -948, -394, -420, -280, -127, -443, -518, -7692, -8246, -8220, -4760, -1313; -1300, -261, -1200, -500, -552, -375, -172, -600, -689, -10200, -10900, -10848, -6275, -1728],218,25]
%
% END OF LATTICE L219.25
%
%
% LATTICE L219.26
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[5719800, -1414800, 28200; -1414800, 349950, -6975; 28200, -6975, 139],[600, 75, 1],[44, 43, 23, 12, 3, 1, -1, -1, 43, 63, 117, 83, 601, 44; 199, 196, 106, 56, 14, 4, -5, -7, 188, 278, 520, 370, 2684, 197; 1050, 1104, 650, 375, 94, 0, -48, -150, 696, 1150, 2325, 1706, 12600, 948],218,26]
%
% END OF LATTICE L219.26
%
%
% LATTICE L219.27
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[600, 0, 0; 0, -25050, 525; 0, 525, -11],[600, 75, 1],[-6, -5, -1, -1, 0, 1, 0, -1, -9, -6, -41, -7, -99, -7; 23, 24, 7, 16, 1, 0, -1, -3, 16, 13, 104, 19, 280, 21; 1050, 1104, 325, 750, 47, 0, -48, -150, 696, 575, 4650, 853, 12600, 948],218,27]
%
% END OF LATTICE L219.27
%
%
% LATTICE L219.28
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[6600, -157500, 39900; -157500, 3758700, -952200; 39900, -952200, 241223],[300, 300, 1],[-166, -36, -63, -47, -5, 0, -1, -24, -59, -317, -1093, -375, -665, -189; 69, 19, 48, 74, 16, 19, 3, -1, 15, 88, 334, 120, 219, 65; 300, 81, 200, 300, 64, 75, 12, 0, 69, 400, 1500, 536, 975, 288],218,28]
%
% END OF LATTICE L219.28
%
%
% LATTICE L219.29
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[29400, -151800, 1200; -151800, 784400, -6200; 1200, -6200, 49],[600, 200, 1],[-30, -3, -13, -1, 1, 1, 0, -6, -6, -95, -107, -109, -64, -36; -31, -3, -12, -1, 0, 0, -1, -9, -7, -108, -119, -120, -70, -39; -3200, -307, -1200, -100, -24, -25, -128, -1000, -743, -11400, -12500, -12576, -7325, -4072],218,29]
%
% END OF LATTICE L219.29
%
%
% LATTICE L219.30
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-89400, 0, -44400; 0, 200, 0; -44400, 0, -22051],[600, 200, 1],[199, 7, -149, 0, 161, 323, 163, 497, 341, 2237, 2088, 1927, 2113, 533; -7, -1, 0, 1, 0, -1, -1, -5, -5, -36, -37, -36, -41, -11; -400, -14, 300, 0, -324, -650, -328, -1000, -686, -4500, -4200, -3876, -4250, -1072],218,30]
%
% END OF LATTICE L219.30
%
%
% LATTICE L219.31
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1530600, 1959000, 648000; 1959000, 2506800, 829200; 648000, 829200, 274283],[600, 600, 1],[0, -4, -23, -83, -29, -52, -30, -28, -3, -5, -1, 1, 3, 2; 397, 542, 2929, 10088, 3455, 6119, 3469, 2999, 307, 467, 100, -59, -176, -73; -1200, -1629, -8800, -30300, -10376, -18375, -10416, -9000, -921, -1400, -300, 176, 525, 216],218,31]
%
% END OF LATTICE L219.31
%
%
% LATTICE L219.32
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[600, 0, 0; 0, -229800, 92400; 0, 92400, -37153],[600, 600, 1],[-5, -5, -12, -37, -12, -41, -11, -7, -1, 0, 1, 0, -1, -1; -241, -557, -1487, -5064, -1725, -6089, -1717, -1447, -287, -201, 0, 37, 181, 29; -600, -1386, -3700, -12600, -4292, -15150, -4272, -3600, -714, -500, 0, 92, 450, 72],218,32]
%
% END OF LATTICE L219.32
%

\medskip%
%------------------------------WEYL-GROUP-W220--------------------------------
%
\leavevmode\llap{}%
$W_{220}$%
\qquad\llap{8} lattices, $\chi=48$%
\hfill%
$2\infty2222\infty222\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L220.1
%
\leavevmode%
${L_{220.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}32\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{-}{}5\above{1pt}{1pt}{-}{}25\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{5}%
\EasyButWeakLineBreak%
{${32}\above{1pt}{1pt}{r}{2}{10}\above{1pt}{1pt}{40,9}{\infty b}{10}\above{1pt}{1pt}{b}{2}{32}\above{1pt}{1pt}{b}{2}{50}\above{1pt}{1pt}{l}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
shares genus with 5-dual\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1055200\\7200\\1600
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7200\\-10\\-15
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1600\\-15\\-2
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\0\\-1600
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\-1\\15
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\1
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-9\\-416\\-4128
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2\\-93\\-910
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-47\\-450
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-48\\-448
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\45\\450
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-1055200, 7200, 1600; 7200, -10, -15; 1600, -15, -2],[800, 5, 1],[-9, -2, -1, -1, 1, 9, 2, 1, 1, -1; -416, -93, -47, -48, 45, 416, 93, 47, 48, -45; -4128, -910, -450, -448, 450, 4032, 895, 445, 432, -475],219,1]
%
% END OF LATTICE L220.1
%
%
% LATTICE L220.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[41760, -8480, -960; -8480, 1722, 195; -960, 195, 22],[160, 1, 1],[-301, -46, -9, -5, 1, 13, 1, -6, -43, -16; -1216, -185, -35, -16, 5, 64, 5, -25, -176, -65; -2400, -375, -85, -80, -1, 0, 0, -40, -320, -124],219,2]
%
% END OF LATTICE L220.2
%
%
% LATTICE L220.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-319840, -3360, 2400; -3360, -30, 25; 2400, 25, -18],[160, 5, 1],[-201, -6, -1, -1, 1, 9, 0, -1, -31, -11; -1216, -37, -7, -16, 5, 64, 1, -5, -176, -65; -28640, -856, -144, -160, 140, 1280, 1, -141, -4400, -1565],219,3]
%
% END OF LATTICE L220.3
%
%
% LATTICE L220.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[256800, -1600, -2400; -1600, 10, 15; -2400, 15, 22],[800, 5, 1],[-289, -9, -2, -9, 0, 1, 0, -1, -39, -3; -28960, -901, -199, -880, 1, 160, 1, -101, -3920, -301; -12000, -375, -85, -400, -1, 0, 0, -40, -1600, -124],219,4]
%
% END OF LATTICE L220.4
%
%
% LATTICE L220.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-287680, -9120, 2080; -9120, -192, 64; 2080, 64, -15],[160, 32, 1],[-31, -151, -29, -1, 3, 1, 1, -21, -9, -53; -102, -500, -100, -4, 8, 3, 5, -65, -29, -173; -4759, -23200, -4480, -158, 448, 151, 160, -3200, -1378, -8128],219,5]
%
% END OF LATTICE L220.5
%
%
% LATTICE L220.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-9280, -4640, 320; -4640, -2240, 160; 320, 160, -11],[160, 160, 1],[2, 4, 4, 4, 16, 7, 5, -1, -1, -1; 0, -1, -3, -5, -27, -15, -14, -2, 0, 2; 55, 96, 64, 30, 0, -55, -96, -64, -30, 0],219,6]
%
% END OF LATTICE L220.6
%
%
% LATTICE L220.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1600, -800, 0; -800, -492480, 6240; 0, 6240, -79],[800, 160, 1],[4, 36, 36, 8, 176, 17, 69, -1, -1, -1; 8, 71, 69, 15, 325, 31, 124, -4, -2, 0; 631, 5600, 5440, 1182, 25600, 2441, 9760, -320, -158, 0],219,7]
%
% END OF LATTICE L220.7
%
%
% LATTICE L220.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-5966400, -1895200, 13600; -1895200, -601920, 4320; 13600, 4320, -31],[800, 160, 1],[7, 10, 6, 4, 2, 2, -1, -3, -1, 1; -45, -47, -13, -5, -1, 0, 2, -2, -10, -14; -3275, -2240, 800, 1050, 736, 875, -160, -1600, -1850, -1536],219,8]
%
% END OF LATTICE L220.8
%

\medskip%
%------------------------------WEYL-GROUP-W221--------------------------------
%
\leavevmode\llap{}%
$W_{221}$%
\qquad\llap{8} lattices, $\chi=12$%
\hfill%
$\infty632$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L221.1
%
\leavevmode%
${L_{221.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}8\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{-}{}27\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${8}\above{1pt}{1pt}{6,5}{\infty z}{2}\above{1pt}{1pt}{}{6}{6}\above{1pt}{1pt}{-}{3}{6}\above{1pt}{1pt}{b}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-684504\\16416\\-3024
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
16416\\-390\\69
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3024\\69\\-10
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\52\\56
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3\\-155\\-163
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-52\\-57
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\155\\162
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-684504, 16416, -3024; 16416, -390, 69; -3024, 69, -10],[216, 3, 1],[1, -3, -1, 3; 52, -155, -52, 155; 56, -163, -57, 162],220,1]
%
% END OF LATTICE L221.1
%
%
% LATTICE L221.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-35046, 702, 1350; 702, -12, -27; 1350, -27, -52],[54, 3, 1],[-1, 2, 3, -1; 0, -3, -1, 2; -26, 53, 78, -27],220,2]
%
% END OF LATTICE L221.2
%
%
% LATTICE L221.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[554904, 1350, 266328; 1350, 12, 648; 266328, 648, 127825],[54, 6, 1],[12, 287, 239, 0; 0, 3, 4, 1; -25, -598, -498, 0],220,3]
%
% END OF LATTICE L221.3
%
%
% LATTICE L221.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-4212594, 17010, 162702; 17010, -36, -657; 162702, -657, -6284],[54, 9, 1],[73, -316, -73, 81; 0, -9, -1, 2; 1890, -8181, -1890, 2097],220,4]
%
% END OF LATTICE L221.4
%
%
% LATTICE L221.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[351705672, -104490, 168794496; -104490, 36, -50148; 168794496, -50148, 81009731],[54, 18, 1],[2786, 17027, 1961, 0; 0, 9, 4, 1; -5805, -35478, -4086, 0],220,5]
%
% END OF LATTICE L221.5
%
%
% LATTICE L221.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-308232, -19008, 75600; -19008, -1170, 4671; 75600, 4671, -18506],[216, 9, 1],[107, -121, -49, 27; -876, 996, 401, -223; 216, -243, -99, 54],220,6]
%
% END OF LATTICE L221.6
%
%
% LATTICE L221.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-83558736, 19310184, 1601208; 19310184, -4462512, -370032; 1601208, -370032, -30683],[216, 24, 1],[-17, 57, 102, -23; -153, 510, 917, -205; 958, -3176, -5736, 1272],220,7]
%
% END OF LATTICE L221.7
%
%
% LATTICE L221.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-9936, 48600, -1296; 48600, -237456, 6336; -1296, 6336, -169],[216, 72, 1],[-7, 41, 14, -9; 0, -9, -1, 2; 54, -648, -144, 144],220,8]
%
% END OF LATTICE L221.8
%

\medskip%
%------------------------------WEYL-GROUP-W222--------------------------------
%
\leavevmode\llap{}%
$W_{222}$%
\qquad\llap{8} lattices, $\chi=24$%
\hfill%
$2\infty22\infty2\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L222.1
%
\leavevmode%
${L_{222.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}8\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{1}{}27\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${54}\above{1pt}{1pt}{b}{2}{8}\above{1pt}{1pt}{6,1}{\infty z}{2}\above{1pt}{1pt}{s}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1367064\\-460944\\12096
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-460944\\-155418\\4077
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
12096\\4077\\-106
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-106201\\327600\\480600
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-35813\\110473\\162069
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
944\\-2912\\-4273
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
73\\-225\\-324
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
35\\-108\\-160
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-36\\111\\161
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-1367064, -460944, 12096; -460944, -155418, 4077; 12096, 4077, -106],[216, 3, 1],[73, 35, -36, -604, -271, -23; -225, -108, 111, 1863, 836, 71; -324, -160, 161, 2727, 1228, 106],221,1]
%
% END OF LATTICE L222.1
%
%
% LATTICE L222.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-37854, 12852, 1404; 12852, -4362, -477; 1404, -477, -52],[54, 3, 1],[-1, -3, 2, 64, 17, 5; 0, -6, 3, 117, 32, 10; -27, -26, 26, 648, 164, 43],221,2]
%
% END OF LATTICE L222.2
%
%
% LATTICE L222.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[296568, -9342, 141210; -9342, 312, -4446; 141210, -4446, 67237],[54, 6, 1],[26, 12, 287, 4069, 443, 168; 9, 3, 72, 1026, 112, 43; -54, -25, -598, -8478, -923, -350],221,3]
%
% END OF LATTICE L222.3
%
%
% LATTICE L222.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-62154, 17604, -4860; 17604, -4986, 1377; -4860, 1377, -364],[54, 9, 1],[-18, -17, 251, 111, 575, 28; -63, -60, 879, 389, 2016, 99; 2, 0, -27, -11, -54, 0],221,4]
%
% END OF LATTICE L222.4
%
%
% LATTICE L222.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1082592, 599346, 540270; 599346, 331848, 299106; 540270, 299106, 269623],[54, 18, 1],[-1, -91, -2509, -1315, -3857, -1439; 0, -6, -141, -73, -213, -78; 2, 189, 5184, 2716, 7965, 2970],221,5]
%
% END OF LATTICE L222.5
%
%
% LATTICE L222.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1593864, -172152, 22248; -172152, -18594, 2403; 22248, 2403, -310],[216, 9, 1],[-13, -179, -23, 1, 35, -13; 119, 1644, 213, -9, -324, 117; -11, -108, 0, 2, 0, -27],221,6]
%
% END OF LATTICE L222.6
%
%
% LATTICE L222.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-382801680, -156788568, -75967632; -156788568, -64217712, -31114944; -75967632, -31114944, -15075899],[216, 24, 1],[-2, 0, 1, 11, 1, 0; -1251, -1127, 2269, 58581, 7497, 4101; 2592, 2326, -4688, -120960, -15478, -8464],221,7]
%
% END OF LATTICE L222.7
%
%
% LATTICE L222.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-155088, -427464, -101520; -427464, -1175184, -279144; -101520, -279144, -66305],[216, 72, 1],[191, 517, 91, -27, -25, 401; 1027, 2775, 480, -146, -132, 2163; -4616, -12474, -2160, 656, 594, -9720],221,8]
%
% END OF LATTICE L222.8
%

\medskip%
%------------------------------WEYL-GROUP-W223--------------------------------
%
\leavevmode\llap{}%
$W_{223}$%
\qquad\llap{24} lattices, $\chi=36$%
\hfill%
$2222222222\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L223.1
%
\leavevmode%
${L_{223.1}}$%
{} : {$1\above{1pt}{1pt}{2}{6}8\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{1}{}3\above{1pt}{1pt}{-}{}27\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${216}\above{1pt}{1pt}{*}{2}{4}\above{1pt}{1pt}{*}{2}{24}\above{1pt}{1pt}{b}{2}{54}\above{1pt}{1pt}{s}{2}{6}\above{1pt}{1pt}{b}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-401544\\3240\\3240
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3240\\-21\\-27
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3240\\-27\\-26
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
16523\\290088\\1751544
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-126\\-2213\\-13356
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-135\\-2370\\-14311
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5\\72\\540
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-18\\-106
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-16\\-108
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
11\\198\\1161
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7\\124\\741
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-401544, 3240, 3240; 3240, -21, -27; 3240, -27, -26],[216, 3, 1],[5, -1, -1, 11, 7, 643, 55, 73, 70, 2; 72, -18, -16, 198, 124, 11304, 966, 1280, 1224, 34; 540, -106, -108, 1161, 741, 68148, 5830, 7740, 7425, 213],222,1]
%
% END OF LATTICE L223.1
%
\hbox{}\par\smallskip%
%
% LATTICE L223.2
%
\leavevmode%
${L_{223.2}}$%
{} : {$1\above{1pt}{1pt}{-2}{2}16\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{1}{}27\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${432}\above{1pt}{1pt}{r}{2}{2}\above{1pt}{1pt}{b}{2}{48}\above{1pt}{1pt}{*}{2}{108}\above{1pt}{1pt}{l}{2}{3}\above{1pt}{1pt}{}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
shares genus with {$ {L_{223.3}}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
432\\0\\432
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\-6\\-51
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
432\\-51\\-1
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
6479\\54864\\-7776
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-780\\-6605\\936
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-105\\-889\\125
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-17\\-144\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2\\-17\\2
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\8\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
49\\414\\-54
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
13\\110\\-15
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[432, 0, 432; 0, -6, -51; 432, -51, -1],[432, 3, 1],[-17, -2, 1, 49, 13, 2177, 92, 239, 221, 2; -144, -17, 8, 414, 110, 18432, 779, 2024, 1872, 17; 0, 2, 0, -54, -15, -2592, -110, -288, -270, -3],222,2]
%
% END OF LATTICE L223.2
%
\hbox{}\par\smallskip%
%
% LATTICE L223.3
%
\leavevmode%
${L_{223.3}}$%
{} : {$1\above{1pt}{1pt}{-2}{2}16\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{1}{}27\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{m}%
\EasyButWeakLineBreak%
{${432}\above{1pt}{1pt}{b}{2}{2}\above{1pt}{1pt}{l}{2}{48}\above{1pt}{1pt}{}{2}{27}\above{1pt}{1pt}{r}{2}{12}\above{1pt}{1pt}{*}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
shares genus with {$ {L_{223.2}}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-30672\\432\\1728
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
432\\-6\\-27
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1728\\-27\\-13
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-10369\\-654480\\-23328
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
160\\10099\\360
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
120\\7575\\269
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-72\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\63\\2
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\64\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-11\\-693\\-27
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-13\\-820\\-30
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-30672, 432, 1728; 432, -6, -27; 1728, -27, -13],[432, 3, 1],[-1, 1, 1, -11, -13, -1151, -49, -129, -61, -3; -72, 63, 64, -693, -820, -72648, -3093, -8144, -3852, -190; 0, 2, 0, -27, -30, -2592, -110, -288, -135, -6],222,3]
%
% END OF LATTICE L223.3
%
%
% LATTICE L223.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-1242, 162, 0; 162, -21, 0; 0, 0, 1],[54, 3, 1],[67, 5, 5, 5, -1, 5, 1, 3, 13, 3; 324, 23, 20, 9, -7, 36, 7, 20, 81, 17; -864, -70, -84, -135, 3, 0, -2, -12, -81, -27],222,4]
%
% END OF LATTICE L223.4
%
%
% LATTICE L223.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-2484, 324, 216; 324, -42, -27; 216, -27, -13],[108, 3, 1],[643, 55, 73, 70, 2, 5, -1, -1, 11, 7; 5652, 483, 640, 612, 17, 36, -9, -8, 99, 62; -1296, -110, -144, -135, -3, 0, 2, 0, -27, -15],222,5]
%
% END OF LATTICE L223.5
%
%
% LATTICE L223.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[216, 0, 216; 0, -3, -27; 216, -27, -26],[216, 3, 1],[1, -1, -1, 22, 13, 1151, 49, 129, 122, 3; 0, -9, -8, 198, 116, 10224, 435, 1144, 1080, 26; 0, 1, 0, -27, -15, -1296, -55, -144, -135, -3],222,6]
%
% END OF LATTICE L223.6
%
%
% LATTICE L223.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2214, 324, 1080; 324, 138, 162; 1080, 162, 527],[54, 6, 1],[7829, 1266, 757, 2423, -55, 91, 54, 123, 1537, 495; 675, 109, 65, 207, -5, 9, 5, 11, 135, 43; -16227, -2624, -1569, -5022, 114, -189, -112, -255, -3186, -1026],222,7]
%
% END OF LATTICE L223.7
%
%
% LATTICE L223.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[270, -108, 0; -108, 45, 0; 0, 0, -1],[54, 9, 1],[1, 1, -1, -1, -3, -9, -19, -7, -1, 1; 2, 3, -2, -3, -11, -42, -93, -38, -7, 1; -4, 0, 0, -5, -27, -140, -324, -144, -31, -9],222,8]
%
% END OF LATTICE L223.8
%
%
% LATTICE L223.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2484, 432, -216; 432, 9, -18; -216, -18, 13],[108, 9, 1],[1, -1, -5, -2, -6, -41, -89, -35, -3, 1; 8, -9, -44, -18, -55, -384, -837, -332, -29, 8; 28, -27, -144, -59, -180, -1252, -2727, -1080, -94, 27],222,9]
%
% END OF LATTICE L223.9
%
%
% LATTICE L223.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-918, 216, -432; 216, 90, 108; -432, 108, -203],[54, 18, 1],[-15, 26, 13, -31, -209, -577, -2690, -605, -265, -87; -1, 3, 1, -3, -19, -51, -237, -53, -23, -7; 31, -54, -27, 64, 432, 1193, 5562, 1251, 548, 180],222,10]
%
% END OF LATTICE L223.10
%
%
% LATTICE L223.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[55512, 9396, -14040; 9396, 1596, -2376; -14040, -2376, 3551],[108, 12, 1],[-2192, -739, -239, -881, -16, -22, 1, -7, -226, -107; 495, 168, 55, 207, 5, 9, 0, 1, 45, 23; -8343, -2812, -909, -3348, -60, -81, 4, -27, -864, -408],222,11]
%
% END OF LATTICE L223.11
%
%
% LATTICE L223.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[4968, 2376, -432; 2376, 693, -135; -432, -135, 26],[216, 9, 1],[-41, -89, -35, -3, 1, 1, -1, -5, -2, -6; -768, -1674, -664, -58, 16, 16, -18, -88, -36, -110; -4708, -10260, -4068, -355, 99, 100, -108, -540, -221, -675],222,12]
%
% END OF LATTICE L223.12
%
%
% LATTICE L223.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[7560, 864, 0; 864, 99, 0; 0, 0, -1],[216, 9, 1],[33, 37, 31, 3, 0, -1, -1, 1, 1, 4; -312, -351, -296, -29, -1, 8, 9, -8, -9, -37; -280, -324, -288, -31, -9, -8, 0, 0, -5, -27],222,13]
%
% END OF LATTICE L223.13
%
%
% LATTICE L223.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-358128, -3024, -3888; -3024, 9, 0; -3888, 0, -11],[432, 9, 1],[33, 37, 31, 3, 0, -1, -1, 1, 1, 2; 11104, 12447, 10424, 1008, -1, -336, -333, 344, 338, 674; -11728, -13149, -11016, -1066, 0, 352, 351, -360, -356, -711],222,14]
%
% END OF LATTICE L223.14
%
%
% LATTICE L223.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[655992, 56052, 127224; 56052, 4788, 10872; 127224, 10872, 24673],[108, 36, 1],[6, 113, 21, 11, -2, -48, -491, -63, -32, -19; -18, -342, -62, -29, 23, 182, 1818, 226, 111, 59; -23, -432, -81, -44, 0, 167, 1728, 225, 116, 72],222,15]
%
% END OF LATTICE L223.15
%
%
% LATTICE L223.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-57456, 3456, -432; 3456, -207, 27; -432, 27, -2],[432, 9, 1],[81, 92, 79, 4, 1, -1, -2, 1, 1, 9; 1200, 1362, 1168, 59, 14, -16, -30, 16, 15, 134; -1576, -1809, -1584, -83, -36, -8, 27, 0, -16, -162],222,16]
%
% END OF LATTICE L223.16
%
%
% LATTICE L223.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-548424, -104112, 5184; -104112, -19752, 984; 5184, 984, -49],[216, 24, 1],[173, 27, 15, 41, -3, 7, 3, 5, 49, 13; -153, -26, -17, -63, -1, 9, 2, 1, -9, -7; 15066, 2308, 1230, 3024, -336, 918, 356, 546, 4968, 1224],222,17]
%
% END OF LATTICE L223.17
%
%
% LATTICE L223.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-216, -1728, -216; -1728, -12984, -1632; -216, -1632, -205],[216, 24, 1],[226, 71, 20, 113, -7, 8, 7, 6, 121, 33; 63, 18, 4, 9, -5, 9, 6, 4, 63, 13; -783, -232, -57, -216, 48, -81, -56, -39, -648, -144],222,18]
%
% END OF LATTICE L223.18
%
%
% LATTICE L223.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-5616, 2376, 648; 2376, 360, 72; 648, 72, 13],[216, 72, 1],[1, 1, -1, -1, -1, 3, 17, 5, 3, 3; -30, -27, 32, 32, 34, -86, -495, -148, -90, -92; 118, 108, -126, -128, -144, 314, 1836, 558, 344, 360],222,19]
%
% END OF LATTICE L223.19
%
%
% LATTICE L223.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[216, 0, 0; 0, -22536, -720; 0, -720, -23],[216, 72, 1],[0, 1, 0, -1, -5, -6, -55, -6, -5, -1; 1, 0, -2, -5, -11, -5, -36, -2, 1, 7; -31, 0, 63, 160, 360, 175, 1296, 81, -16, -216],222,20]
%
% END OF LATTICE L223.20
%
%
% LATTICE L223.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-864, 2160, -864; 2160, -5136, 2064; -864, 2064, -829],[432, 48, 1],[131, 91, 31, 124, 5, 4, -1, -1, 11, 10; -621, -426, -142, -549, -17, -9, 6, 2, -81, -53; -1701, -1168, -390, -1512, -48, -27, 16, 6, -216, -144],222,21]
%
% END OF LATTICE L223.21
%
%
% LATTICE L223.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-864, 20304, -1296; 20304, -474576, 30288; -1296, 30288, -1933],[432, 48, 1],[397, 139, 24, 196, 9, 17, -1, -1, 11, 14; -54, -14, -1, 9, 5, 18, 2, -1, -27, -7; -1134, -320, -33, 0, 72, 270, 32, -15, -432, -120],222,22]
%
% END OF LATTICE L223.22
%
%
% LATTICE L223.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[864, -1296, -432; -1296, -93168, -30240; -432, -30240, -9815],[432, 144, 1],[1, -1, -3, -2, 1, 8, 163, 21, 11, 8; -25, 0, 76, 65, 47, -115, -2520, -356, -205, -187; 77, 0, -234, -200, -144, 355, 7776, 1098, 632, 576],222,23]
%
% END OF LATTICE L223.23
%
%
% LATTICE L223.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[864, -432, 0; -432, -22320, 720; 0, 720, -23],[432, 144, 1],[1, -1, -1, -2, -3, 1, 19, 2, 3, 4; 2, 0, -2, -5, -11, -10, -72, -2, 1, 7; 62, 0, -63, -160, -360, -350, -2592, -81, 16, 216],222,24]
%
% END OF LATTICE L223.24
%

\medskip%
%------------------------------WEYL-GROUP-W224--------------------------------
%
\leavevmode\llap{}%
$W_{224}$%
\qquad\llap{60} lattices, $\chi=18$%
\hfill%
$\slashtwo222|222\rtimes D_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L224.1
%
\leavevmode%
${L_{224.1}}$%
{} : {$1\above{1pt}{1pt}{2}{0}8\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{2}{}7\above{1pt}{1pt}{1}{}$}\EasyButWeakLineBreak%
{${1}\above{1pt}{1pt}{r}{2}{4}\above{1pt}{1pt}{*}{2}{28}\above{1pt}{1pt}{l}{2}{3}\above{1pt}{1pt}{r}{2}{56}\above{1pt}{1pt}{s}{2}{12}\above{1pt}{1pt}{l}{2}{7}\above{1pt}{1pt}{}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-13272\\168\\168
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
168\\-1\\-4
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
168\\-4\\1
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\-1
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-50\\-32
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-5\\-252\\-154
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-51\\-30
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-56\\-28
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\48\\30
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\49\\28
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-13272, 168, 168; 168, -1, -4; 168, -4, 1],[168, 1, 1],[0, -1, -5, -1, -1, 1, 1; 0, -50, -252, -51, -56, 48, 49; -1, -32, -154, -30, -28, 30, 28],223,1]
%
% END OF LATTICE L224.1
%
\hbox{}\par\smallskip%
%
% LATTICE L224.2
%
\leavevmode%
${L_{224.2}}$%
{} : {$[1\above{1pt}{1pt}{1}{}2\above{1pt}{1pt}{-}{}]\above{1pt}{1pt}{}{4}16\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{2}{}7\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${16}\above{1pt}{1pt}{}{2}{1}\above{1pt}{1pt}{r}{2}{112}\above{1pt}{1pt}{*}{2}{12}\above{1pt}{1pt}{*}{2}{56}\above{1pt}{1pt}{s}{2}{48}\above{1pt}{1pt}{l}{2}{7}\above{1pt}{1pt}{}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4368\\-336\\336
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-336\\10\\-6
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
336\\-6\\1
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\64\\48
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\-1
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3\\-196\\-168
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-66\\-54
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-70\\-56
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\60\\48
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\63\\49
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[4368, -336, 336; -336, 10, -6; 336, -6, 1],[336, 2, 1],[1, 0, -3, -1, -1, 1, 1; 64, 0, -196, -66, -70, 60, 63; 48, -1, -168, -54, -56, 48, 49],223,2]
%
% END OF LATTICE L224.2
%
\hbox{}\par\smallskip%
%
% LATTICE L224.3
%
\leavevmode%
${L_{224.3}}$%
{} : {$[1\above{1pt}{1pt}{-}{}2\above{1pt}{1pt}{-}{}]\above{1pt}{1pt}{}{0}16\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{2}{}7\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{m}%
\EasyButWeakLineBreak%
{${16}\above{1pt}{1pt}{s}{2}{4}\above{1pt}{1pt}{*}{2}{112}\above{1pt}{1pt}{l}{2}{3}\above{1pt}{1pt}{r}{2}{56}\above{1pt}{1pt}{*}{2}{48}\above{1pt}{1pt}{*}{2}{28}\above{1pt}{1pt}{s}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
306768\\-1680\\-1680
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1680\\10\\8
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1680\\8\\11
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-112\\-72
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-110\\-74
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-9\\-980\\-672
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-108\\-75
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3\\-322\\-224
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-108\\-72
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-112\\-70
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[306768, -1680, -1680; -1680, 10, 8; -1680, 8, 11],[336, 2, 1],[-1, -1, -9, -1, -3, -1, -1; -112, -110, -980, -108, -322, -108, -112; -72, -74, -672, -75, -224, -72, -70],223,3]
%
% END OF LATTICE L224.3
%
\hbox{}\par\smallskip%
%
% LATTICE L224.4
%
\leavevmode%
${L_{224.4}}$%
{} : {$[1\above{1pt}{1pt}{-}{}2\above{1pt}{1pt}{1}{}]\above{1pt}{1pt}{}{2}16\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{2}{}7\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{m}%
\EasyButWeakLineBreak%
{${16}\above{1pt}{1pt}{l}{2}{1}\above{1pt}{1pt}{}{2}{112}\above{1pt}{1pt}{}{2}{3}\above{1pt}{1pt}{}{2}{14}\above{1pt}{1pt}{r}{2}{48}\above{1pt}{1pt}{s}{2}{28}\above{1pt}{1pt}{*}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
38640\\336\\-672
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
336\\-2\\-4
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-672\\-4\\11
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-28\\-72
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\-1\\-1
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5\\112\\336
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\24\\69
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\49\\140
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\24\\72
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-28\\-70
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[38640, 336, -672; 336, -2, -4; -672, -4, 11],[336, 2, 1],[-1, 0, 5, 1, 2, 1, -1; -28, -1, 112, 24, 49, 24, -28; -72, -1, 336, 69, 140, 72, -70],223,4]
%
% END OF LATTICE L224.4
%
\hbox{}\par\smallskip%
%
% LATTICE L224.5
%
\leavevmode%
${L_{224.5}}$%
{} : {$[1\above{1pt}{1pt}{1}{}2\above{1pt}{1pt}{1}{}]\above{1pt}{1pt}{}{6}16\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{2}{}7\above{1pt}{1pt}{1}{}$}\EasyButWeakLineBreak%
{${16}\above{1pt}{1pt}{*}{2}{4}\above{1pt}{1pt}{s}{2}{112}\above{1pt}{1pt}{s}{2}{12}\above{1pt}{1pt}{l}{2}{14}\above{1pt}{1pt}{}{2}{48}\above{1pt}{1pt}{}{2}{7}\above{1pt}{1pt}{r}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-134736\\672\\1008
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
672\\-2\\-8
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1008\\-8\\-1
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\356\\160
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\118\\54
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\112\\56
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-120\\-54
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-119\\-56
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\120\\48
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\238\\105
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-134736, 672, 1008; 672, -2, -8; 1008, -8, -1],[336, 2, 1],[3, 1, 1, -1, -1, 1, 2; 356, 118, 112, -120, -119, 120, 238; 160, 54, 56, -54, -56, 48, 105],223,5]
%
% END OF LATTICE L224.5
%
%
% LATTICE L224.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[5124, 336, 0; 336, 22, 0; 0, 0, 1],[84, 2, 1],[0, -3, -10, -11, -9, -1, 1; 0, 44, 147, 162, 133, 15, -14; -1, 0, 7, 12, 14, 3, 0],223,6]
%
% END OF LATTICE L224.6
%
%
% LATTICE L224.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-20774712, 769440, -15120; 769440, -28498, 560; -15120, 560, -11],[168, 2, 1],[2, 5, 6, 1, -3, -1, 5; 55, 136, 161, 24, -84, -27, 140; 50, 48, -56, -156, -154, 0, 252],223,7]
%
% END OF LATTICE L224.7
%
%
% LATTICE L224.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[45528, -1680, 0; -1680, 62, 0; 0, 0, -1],[168, 2, 1],[1, 3, 4, 1, -1, -1, 1; 27, 80, 105, 24, -28, -27, 28; -2, -12, -28, -24, -7, 0, 0],223,8]
%
% END OF LATTICE L224.8
%
%
% LATTICE L224.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-254856, 0, 1848; 0, 15, -6; 1848, -6, -11],[168, 3, 1],[-1, -1, 11, 2, 33, 3, 2; -55, -56, 602, 110, 1820, 166, 112; -138, -138, 1512, 275, 4536, 412, 273],223,9]
%
% END OF LATTICE L224.9
%
%
% LATTICE L224.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[84, 0, 0; 0, -6, 0; 0, 0, 1],[84, 6, 1],[-1, 0, 1, 0, -2, -1, -3; 6, 1, 0, 0, 7, 4, 14; 12, 3, 0, -1, 0, 4, 21],223,10]
%
% END OF LATTICE L224.10
%
%
% LATTICE L224.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[233688, -12936, 504; -12936, 716, -28; 504, -28, 1],[168, 4, 1],[1, 0, -2, -1, 1, 2, 5; 17, 0, -35, -18, 14, 33, 84; -28, -1, 28, 6, -84, -72, -154],223,11]
%
% END OF LATTICE L224.11
%
%
% LATTICE L224.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[14952, -1008, 0; -1008, 68, 0; 0, 0, -1],[168, 4, 1],[0, -1, -5, -1, -1, 1, 1; -1, -16, -77, -15, -14, 15, 14; -8, -10, -28, -3, 0, 0, -7],223,12]
%
% END OF LATTICE L224.12
%
%
% LATTICE L224.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-6888, 0, -3360; 0, 6, 0; -3360, 0, -1639],[168, 6, 1],[0, 47, 144, 49, 103, 1, -41; 1, 0, -7, -4, -14, -1, 0; 0, -96, -294, -100, -210, -2, 84],223,13]
%
% END OF LATTICE L224.13
%
%
% LATTICE L224.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[168, 0, 0; 0, 6, 0; 0, 0, -1],[168, 6, 1],[0, -1, -3, -1, -1, 0, 1; 1, 0, -7, -4, -7, -1, 0; 0, -12, -42, -16, -21, -2, 0],223,14]
%
% END OF LATTICE L224.14
%
%
% LATTICE L224.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[209496, 1008, -1848; 1008, -7, -7; -1848, -7, 16],[168, 7, 1],[3, 5, 1, -1, -1, 1, 1; 57, 94, 18, -21, -20, 18, 19; 371, 616, 122, -126, -124, 126, 124],223,15]
%
% END OF LATTICE L224.15
%
%
% LATTICE L224.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-5460, -3276, 168; -3276, -1918, 98; 168, 98, -5],[84, 14, 1],[-1, -1, 0, 1, 0, -1, -1; 8, 12, 1, -6, -1, 3, 6; 119, 196, 19, -84, -20, 21, 80],223,16]
%
% END OF LATTICE L224.16
%
%
% LATTICE L224.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[5208, -1176, -168; -1176, 256, 40; -168, 40, 5],[168, 8, 1],[1, -1, -9, -5, -3, 1, 5; 3, -2, -21, -12, -7, 3, 14; 8, -20, -140, -72, -42, 12, 56],223,17]
%
% END OF LATTICE L224.17
%
%
% LATTICE L224.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[108528, 54432, -336; 54432, 27294, -168; -336, -168, 1],[336, 6, 1],[-1, 7, 25, 9, 19, 0, -13; 2, -16, -56, -20, -42, 0, 28; 6, -312, -966, -328, -672, -1, 336],223,18]
%
% END OF LATTICE L224.18
%
%
% LATTICE L224.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-207816, -8232, 1512; -8232, -300, 60; 1512, 60, -11],[168, 12, 1],[-1, -1, 2, 2, 19, 1, 4; 0, 1, 0, -1, -14, -1, -7; -138, -132, 273, 268, 2520, 131, 504],223,19]
%
% END OF LATTICE L224.19
%
%
% LATTICE L224.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-91056, 3696, 0; 3696, -6, -12; 0, -12, 1],[336, 6, 1],[-1, -3, -1, 1, 2, 0, -9; -25, -76, -28, 24, 49, 0, -224; -297, -888, -294, 296, 588, -1, -2688],223,20]
%
% END OF LATTICE L224.20
%
%
% LATTICE L224.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[30072, 1176, -168; 1176, -228, 84; -168, 84, -29],[168, 12, 1],[2, 2, -1, -1, -3, 1, 13; -90, -91, 42, 45, 140, -44, -581; -273, -276, 126, 136, 420, -134, -1764],223,21]
%
% END OF LATTICE L224.21
%
%
% LATTICE L224.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[28560, -672, 0; -672, -102, 36; 0, 36, -11],[336, 6, 1],[-1, -1, 2, 3, 6, 1, 1; -42, -44, 84, 128, 259, 44, 56; -138, -144, 273, 416, 840, 142, 168],223,22]
%
% END OF LATTICE L224.22
%
%
% LATTICE L224.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-500304, 62496, -2352; 62496, -7806, 294; -2352, 294, -11],[336, 6, 1],[1, 1, -4, -5, -17, -1, 5; 7, 8, -28, -36, -126, -8, 28; -27, 0, 105, 104, 252, -2, -336],223,23]
%
% END OF LATTICE L224.23
%
%
% LATTICE L224.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-77448, 25872, -1008; 25872, -8638, 336; -1008, 336, -13],[168, 14, 1],[6, 13, 2, 1, -1, -1, 3; 23, 48, 7, 0, -4, -3, 12; 126, 224, 24, -84, -26, 0, 76],223,24]
%
% END OF LATTICE L224.24
%
%
% LATTICE L224.25
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[168, 0, 168; 0, -14, -56; 168, -56, -55],[168, 14, 1],[13, 27, 4, 1, -1, -1, 7; 51, 104, 15, 0, -4, -3, 28; -14, -28, -4, 0, 1, 0, -8],223,25]
%
% END OF LATTICE L224.25
%
%
% LATTICE L224.26
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[109200, -36288, -336; -36288, 12056, 112; -336, 112, 1],[336, 8, 1],[-3, 0, 5, 1, -3, -7, -8; -8, 0, 14, 3, -7, -18, -21; -112, -1, 112, 6, -196, -312, -322],223,26]
%
% END OF LATTICE L224.26
%
%
% LATTICE L224.27
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-7728, 0, 336; 0, 40, 32; 336, 32, 11],[336, 8, 1],[-1, -3, -3, 1, 5, 1, 1; 19, 56, 56, -18, -91, -18, -14; -26, -72, -70, 24, 112, 21, 0],223,27]
%
% END OF LATTICE L224.27
%
%
% LATTICE L224.28
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[10416, 672, 0; 672, 40, 8; 0, 8, -19],[336, 8, 1],[1, -1, -9, -1, 4, 7, 6; -14, 16, 140, 15, -63, -108, -91; -8, 6, 56, 6, -28, -48, -42],223,28]
%
% END OF LATTICE L224.28
%
%
% LATTICE L224.29
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-35952, 1008, 336; 1008, -8, -16; 336, -16, -1],[336, 8, 1],[1, 3, 2, 1, -2, -1, 1; 17, 52, 35, 18, -35, -18, 14; 54, 160, 105, 48, -112, -54, 56],223,29]
%
% END OF LATTICE L224.29
%
%
% LATTICE L224.30
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[840, 840, -168; 840, 357, -84; -168, -84, 19],[168, 21, 1],[-1, -2, -1, -1, 1, 1, 1; -8, -15, -8, -10, 4, 6, 6; -42, -84, -45, -56, 24, 35, 36],223,30]
%
% END OF LATTICE L224.30
%
%
% LATTICE L224.31
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[84, -84, 0; -84, 7602, -378; 0, -378, 19],[84, 42, 1],[1, -1, 2, 11, 8, 7, 7; 1, 0, 2, 10, 7, 6, 6; 21, 0, 39, 196, 138, 119, 120],223,31]
%
% END OF LATTICE L224.31
%
%
% LATTICE L224.32
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-7896, 0, 2856; 0, 24, 0; 2856, 0, -1033],[168, 24, 1],[0, -13, -30, 3, 46, 16, 61; 1, 0, -7, -2, -7, -1, 0; 0, -36, -84, 8, 126, 44, 168],223,32]
%
% END OF LATTICE L224.32
%
%
% LATTICE L224.33
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-727440, -53424, 8064; -53424, -3878, 588; 8064, 588, -89],[336, 14, 1],[3, 13, 1, 1, -1, -1, 3; 66, 280, 21, 12, -22, -18, 68; 707, 3024, 229, 168, -236, -210, 720],223,33]
%
% END OF LATTICE L224.33
%
%
% LATTICE L224.34
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-89880, 3528, 672; 3528, -28, -28; 672, -28, -5],[168, 28, 1],[3, 5, 1, -2, -1, 1, 2; 5, 9, 2, -3, -2, 0, 3; 371, 616, 122, -252, -124, 126, 248],223,34]
%
% END OF LATTICE L224.34
%
%
% LATTICE L224.35
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1115184, -10416, -5712; -10416, 70, 56; -5712, 56, 29],[336, 14, 1],[5, -1, -1, -1, 3, 8, 9; 82, -16, -16, -12, 50, 132, 148; 826, -168, -166, -168, 496, 1323, 1488],223,35]
%
% END OF LATTICE L224.35
%
%
% LATTICE L224.36
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1947792, 2352, -11760; 2352, -14, -14; -11760, -14, 71],[336, 14, 1],[3, -1, -1, 1, 2, 10, 11; 4, -4, -2, 0, 3, 15, 16; 497, -168, -166, 168, 332, 1659, 1824],223,36]
%
% END OF LATTICE L224.36
%
%
% LATTICE L224.37
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3192, 8568, 1176; 8568, -19684, -2688; 1176, -2688, -367],[168, 28, 1],[-1, 6, 3, 23, 5, 1, -1; -10, 79, 38, 285, 60, 9, -13; 70, -560, -269, -2016, -424, -63, 92],223,37]
%
% END OF LATTICE L224.37
%
%
% LATTICE L224.38
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[336, -2352, 336; -2352, -10346, 1540; 336, 1540, -229],[336, 14, 1],[13, 27, 2, 1, -1, -1, 7; 116, 236, 17, 0, -9, -6, 64; 798, 1624, 117, 0, -62, -42, 440],223,38]
%
% END OF LATTICE L224.38
%
%
% LATTICE L224.39
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[168, -168, 0; -168, 210, 0; 0, 0, -1],[168, 42, 1],[1, -1, -1, -3, -1, 0, 1; 1, 0, -1, -4, -2, -1, 0; 0, 0, -6, -28, -18, -14, -12],223,39]
%
% END OF LATTICE L224.39
%
%
% LATTICE L224.40
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[41496, -41496, -840; -41496, 41538, 840; -840, 840, 17],[168, 42, 1],[1, -5, -4, -13, -3, -3, -1; 1, 0, -1, -4, -1, -1, 0; 0, -252, -150, -448, -99, -98, -48],223,40]
%
% END OF LATTICE L224.40
%
%
% LATTICE L224.41
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[108528, 336, -336; 336, -24, 0; -336, 0, 1],[336, 24, 1],[0, -1, -3, -1, -2, 0, 1; 1, -8, -28, -10, -21, 0, 14; 6, -312, -966, -328, -672, -1, 336],223,41]
%
% END OF LATTICE L224.41
%
%
% LATTICE L224.42
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[21840, 8736, -672; 8736, 3000, -240; -672, -240, 19],[336, 24, 1],[3, 1, 9, 0, -4, -1, 1; 22, 7, 56, -1, -35, -8, 7; 384, 123, 1008, -14, -588, -136, 126],223,42]
%
% END OF LATTICE L224.42
%
%
% LATTICE L224.43
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-37692816, 6006000, -39312; 6006000, -957000, 6264; -39312, 6264, -41],[336, 24, 1],[-1, -1, 1, 1, 12, 3, 4; -8, -6, 14, 7, 77, 18, 21; -264, 42, 1176, 110, 252, -128, -630],223,43]
%
% END OF LATTICE L224.43
%
%
% LATTICE L224.44
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-13776, 3696, 1008; 3696, 744, 168; 1008, 168, 37],[336, 24, 1],[-1, -1, 2, 3, 12, 1, 1; 47, 48, -91, -138, -553, -46, -42; -186, -192, 357, 544, 2184, 182, 168],223,44]
%
% END OF LATTICE L224.44
%
%
% LATTICE L224.45
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[168, 0, 0; 0, -8680, 336; 0, 336, -13],[168, 56, 1],[-1, -2, -1, -2, 0, 1, 0; 10, 9, 2, -3, -1, 0, 3; 252, 224, 48, -84, -26, 0, 76],223,45]
%
% END OF LATTICE L224.45
%
%
% LATTICE L224.46
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[4368, -2688, -672; -2688, 798, 210; -672, 210, 55],[336, 42, 1],[-1, 1, 1, 0, -1, -3, -1; 40, -30, -28, 2, 38, 108, 36; -168, 126, 120, -7, -156, -448, -150],223,46]
%
% END OF LATTICE L224.46
%
%
% LATTICE L224.47
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[37128, 7392, -840; 7392, 1428, -168; -840, -168, 19],[168, 84, 1],[-4, -1, 1, 1, 1, -1, -1; 1, 0, -1, -1, -2, -1, 0; -168, -42, 36, 35, 24, -56, -45],223,47]
%
% END OF LATTICE L224.47
%
%
% LATTICE L224.48
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-40656, 2352, 672; 2352, -42, -42; 672, -42, -11],[336, 42, 1],[-3, 2, 9, 3, 2, 1, -1; -4, 4, 16, 5, 3, 0, -2; -168, 105, 480, 161, 108, 56, -54],223,48]
%
% END OF LATTICE L224.48
%
%
% LATTICE L224.49
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-235536, 96096, 6720; 96096, -39018, -2730; 6720, -2730, -191],[336, 42, 1],[7, 1, -1, -1, 0, 3, 1; -124, -24, 16, 22, 5, -32, -15; 2016, 378, -264, -350, -72, 560, 249],223,49]
%
% END OF LATTICE L224.49
%
%
% LATTICE L224.50
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-10248, 0, 336; 0, 84, 0; 336, 0, -11],[168, 84, 1],[0, -2, -3, -3, -1, 1, 1; 1, 0, -1, -2, -2, -1, 0; 0, -63, -96, -98, -36, 28, 30],223,50]
%
% END OF LATTICE L224.50
%
%
% LATTICE L224.51
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[336, 0, 0; 0, 7518, -378; 0, -378, 19],[336, 42, 1],[1, 0, -1, -1, -1, -1, 0; 0, 1, 12, 12, 14, 20, 2; 0, 21, 240, 238, 276, 392, 39],223,51]
%
% END OF LATTICE L224.51
%
%
% LATTICE L224.52
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-5525520, 2776704, -22176; 2776704, -1395352, 11144; -22176, 11144, -89],[336, 56, 1],[-3, -13, -2, -1, 1, 1, -3; -3, -16, -3, -6, 1, 3, -2; 371, 1232, 122, -504, -124, 126, 496],223,52]
%
% END OF LATTICE L224.52
%
%
% LATTICE L224.53
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[762384, 9408, -4704; 9408, -56, -56; -4704, -56, 29],[336, 56, 1],[6, -1, -1, 1, 4, 10, 11; 11, -2, -2, 0, 7, 18, 20; 994, -168, -166, 168, 664, 1659, 1824],223,53]
%
% END OF LATTICE L224.53
%
%
% LATTICE L224.54
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1314096, -92400, 6384; -92400, -6440, 448; 6384, 448, -31],[336, 56, 1],[0, 5, 1, 13, 1, -1, -1; 1, 22, 4, 48, 3, -6, -4; 14, 1344, 263, 3360, 248, -294, -264],223,54]
%
% END OF LATTICE L224.54
%
%
% LATTICE L224.55
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-812112, 361200, -2016; 361200, -160552, 896; -2016, 896, -5],[336, 56, 1],[1, 1, 0, -1, 0, 1, 1; 8, 12, 1, -6, -1, 3, 6; 1022, 1736, 178, -672, -180, 126, 664],223,55]
%
% END OF LATTICE L224.55
%
%
% LATTICE L224.56
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[168, 0, 0; 0, -2856, -840; 0, -840, -247],[168, 168, 1],[1, 0, -1, -2, -1, -1, 0; 0, 25, 18, 17, 2, -8, -7; 0, -84, -60, -56, -6, 28, 24],223,56]
%
% END OF LATTICE L224.56
%
%
% LATTICE L224.57
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[7728, -9072, 1344; -9072, 10248, -1512; 1344, -1512, 223],[336, 168, 1],[-1, 1, 1, 0, -1, -3, -1; -26, 7, 8, -1, -15, -44, -16; -168, 42, 48, -7, -96, -280, -102],223,57]
%
% END OF LATTICE L224.57
%
%
% LATTICE L224.58
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-10416, 25200, 8064; 25200, -59304, -18984; 8064, -18984, -6077],[336, 168, 1],[7, 1, -1, -1, 0, 3, 1; -212, -13, 38, 22, -23, -142, -37; 672, 42, -120, -70, 72, 448, 117],223,58]
%
% END OF LATTICE L224.58
%
%
% LATTICE L224.59
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-44016, -14784, 1008; -14784, -4872, 336; 1008, 336, -23],[336, 168, 1],[1, -1, -1, -3, -1, 0, 1; 0, -8, -3, -6, -1, 1, 2; 42, -168, -90, -224, -60, 14, 72],223,59]
%
% END OF LATTICE L224.59
%
%
% LATTICE L224.60
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[336, 0, 0; 0, -10248, 336; 0, 336, -11],[336, 168, 1],[0, 1, 0, -1, -1, -1, -1; -2, 0, 1, 2, -1, -3, -6; -63, 0, 30, 56, -36, -98, -192],223,60]
%
% END OF LATTICE L224.60
%

\medskip%
%------------------------------WEYL-GROUP-W225--------------------------------
%
\leavevmode\llap{}%
$W_{225}$%
\qquad\llap{120} lattices, $\chi=72$%
\hfill%
$2222|2222|2222|2222|\rtimes D_{4}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L225.1
%
\leavevmode%
${L_{225.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{4}8\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{1}{}3\above{1pt}{1pt}{-}{}9\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{2}{}7\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{3}%
\EasyButWeakLineBreak%
{${24}\above{1pt}{1pt}{l}{2}{7}\above{1pt}{1pt}{}{2}{72}\above{1pt}{1pt}{}{2}{1}\above{1pt}{1pt}{r}{2}{504}\above{1pt}{1pt}{s}{2}{4}\above{1pt}{1pt}{*}{2}{72}\above{1pt}{1pt}{*}{2}{28}\above{1pt}{1pt}{s}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2306808\\5544\\7056
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5544\\-3\\-21
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7056\\-21\\-20
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
37925\\3705912\\9470664
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-84\\-8209\\-20976
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-119\\-11628\\-29717
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
27\\2636\\6744
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
16\\1561\\3997
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
17\\1656\\4248
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\97\\250
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\84\\252
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-98\\-250
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-96\\-252
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
11\\1078\\2744
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-2306808, 5544, 7056; 5544, -3, -21; 7056, -21, -20],[504, 3, 1],[27, 16, 17, 1, 1, -1, -1, 11, 15, 33, 109, 27, 881, 57, 127, 87; 2636, 1561, 1656, 97, 84, -98, -96, 1078, 1468, 3227, 10656, 2639, 86100, 5570, 12408, 8498; 6744, 3997, 4248, 250, 252, -250, -252, 2744, 3744, 8239, 27216, 6742, 219996, 14234, 31716, 21728],224,1]
%
% END OF LATTICE L225.1
%
\hbox{}\par\smallskip%
%
% LATTICE L225.2
%
\leavevmode%
${L_{225.2}}$%
{} : {$[1\above{1pt}{1pt}{1}{}2\above{1pt}{1pt}{1}{}]\above{1pt}{1pt}{}{2}16\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{1}{}3\above{1pt}{1pt}{-}{}9\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{2}{}7\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{3,2}%
\EasyButWeakLineBreak%
{${6}\above{1pt}{1pt}{r}{2}{112}\above{1pt}{1pt}{l}{2}{18}\above{1pt}{1pt}{}{2}{1}\above{1pt}{1pt}{r}{2}{504}\above{1pt}{1pt}{*}{2}{16}\above{1pt}{1pt}{s}{2}{72}\above{1pt}{1pt}{*}{2}{28}\above{1pt}{1pt}{l}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
996912\\-248976\\-1008
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-248976\\62178\\252
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1008\\252\\1
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-22933\\-85176\\-1598688
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5649\\20981\\393816
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
28\\104\\1951
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-11\\-41\\-738
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-45\\-168\\-2968
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-4\\-15\\-252
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\-1
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
11\\42\\504
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\4\\8
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-5\\-18\\-468
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-19\\-70\\-1442
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[996912, -248976, -1008; -248976, 62178, 252; -1008, 252, 1],[1008, 6, 1],[-11, -45, -4, 0, 11, 1, -5, -19, -10, -151, -59, -28, -893, -113, -121, -79; -41, -168, -15, 0, 42, 4, -18, -70, -37, -560, -219, -104, -3318, -420, -450, -294; -738, -2968, -252, -1, 504, 8, -468, -1442, -726, -10696, -4140, -1951, -61992, -7816, -8316, -5390],224,2]
%
% END OF LATTICE L225.2
%
\hbox{}\par\smallskip%
%
% LATTICE L225.3
%
\leavevmode%
${L_{225.3}}$%
{} : {$[1\above{1pt}{1pt}{1}{}2\above{1pt}{1pt}{1}{}]\above{1pt}{1pt}{}{0}16\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{1}{}3\above{1pt}{1pt}{-}{}9\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{2}{}7\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{32,3,m}%
\EasyButWeakLineBreak%
{${24}\above{1pt}{1pt}{s}{2}{112}\above{1pt}{1pt}{*}{2}{72}\above{1pt}{1pt}{l}{2}{1}\above{1pt}{1pt}{}{2}{126}\above{1pt}{1pt}{r}{2}{16}\above{1pt}{1pt}{l}{2}{18}\above{1pt}{1pt}{}{2}{7}\above{1pt}{1pt}{r}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-6762672\\23184\\11088
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
23184\\-66\\-42
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
11088\\-42\\-17
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
34271\\3821328\\12886272
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-132\\-14719\\-49632
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-52\\-5798\\-19553
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
17\\1894\\6396
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
43\\4788\\16184
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
13\\1446\\4896
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\111\\377
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4\\441\\1512
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-112\\-376
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-111\\-378
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\224\\749
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-6762672, 23184, 11088; 23184, -66, -42; 11088, -42, -17],[1008, 6, 1],[17, 43, 13, 1, 4, -1, -1, 2, 7, 69, 59, 15, 248, 65, 37, 26; 1894, 4788, 1446, 111, 441, -112, -111, 224, 782, 7700, 6582, 1673, 27657, 7248, 4125, 2898; 6396, 16184, 4896, 377, 1512, -376, -378, 749, 2628, 25928, 22176, 5639, 93240, 24440, 13914, 9779],224,3]
%
% END OF LATTICE L225.3
%
\hbox{}\par\smallskip%
%
% LATTICE L225.4
%
\leavevmode%
${L_{225.4}}$%
{} : {$[1\above{1pt}{1pt}{-}{}2\above{1pt}{1pt}{1}{}]\above{1pt}{1pt}{}{6}16\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{-}{}9\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{2}{}7\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{3m,3,m}%
\EasyButWeakLineBreak%
{${6}\above{1pt}{1pt}{}{2}{63}\above{1pt}{1pt}{r}{2}{8}\above{1pt}{1pt}{*}{2}{144}\above{1pt}{1pt}{s}{2}{56}\above{1pt}{1pt}{*}{2}{36}\above{1pt}{1pt}{l}{2}{2}\above{1pt}{1pt}{}{2}{1008}\above{1pt}{1pt}{}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1402128\\-15120\\6048
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-15120\\-138\\60
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
6048\\60\\-25
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-6581\\-655368\\-3174192
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-55\\-5479\\-26532
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
25\\2490\\12059
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2\\-197\\-960
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-25\\-2478\\-12033
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-9\\-894\\-4336
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-79\\-7860\\-38088
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-71\\-7070\\-34244
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-41\\-4086\\-19782
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-5\\-499\\-2414
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-121\\-12096\\-58464
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-1402128, -15120, 6048; -15120, -138, 60; 6048, 60, -25],[1008, 6, 1],[-2, -25, -9, -79, -71, -41, -5, -121, -3, -10, -1, -1, 1, 1, 0, -19; -197, -2478, -894, -7860, -7070, -4086, -499, -12096, -301, -1008, -102, -108, 98, 102, 1, -1848; -960, -12033, -4336, -38088, -34244, -19782, -2414, -58464, -1452, -4851, -488, -504, 476, 486, 2, -9072],224,4]
%
% END OF LATTICE L225.4
%
\hbox{}\par\smallskip%
%
% LATTICE L225.5
%
\leavevmode%
${L_{225.5}}$%
{} : {$[1\above{1pt}{1pt}{-}{}2\above{1pt}{1pt}{1}{}]\above{1pt}{1pt}{}{4}16\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{1}{}3\above{1pt}{1pt}{-}{}9\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{2}{}7\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{3m,3}%
\EasyButWeakLineBreak%
{${24}\above{1pt}{1pt}{*}{2}{112}\above{1pt}{1pt}{s}{2}{72}\above{1pt}{1pt}{*}{2}{4}\above{1pt}{1pt}{l}{2}{126}\above{1pt}{1pt}{}{2}{16}\above{1pt}{1pt}{}{2}{18}\above{1pt}{1pt}{r}{2}{28}\above{1pt}{1pt}{*}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-249517296\\-3972528\\294336
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3972528\\-63246\\4686
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
294336\\4686\\-347
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-163297\\10287648\\326592
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2598\\163673\\5196
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
188\\-11844\\-377
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
21\\-1346\\-360
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
71\\-4564\\-1400
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
31\\-1998\\-684
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7\\-452\\-166
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
25\\-1617\\-630
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\64\\16
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-7\\453\\180
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-17\\1106\\518
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-249517296, -3972528, 294336; -3972528, -63246, 4686; 294336, 4686, -347],[1008, 6, 1],[21, 71, 31, 7, 25, -1, -7, -17, -9, -15, 5, 9, 101, 33, 25, 45; -1346, -4564, -1998, -452, -1617, 64, 453, 1106, 590, 1036, -270, -556, -6321, -2080, -1587, -2870; -360, -1400, -684, -166, -630, 16, 180, 518, 336, 1288, 612, 134, 378, -80, -216, -574],224,5]
%
% END OF LATTICE L225.5
%
%
% LATTICE L225.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-312312, 2520, 2520; 2520, -20, -21; 2520, -21, -19],[168, 1, 1],[37, 23, 9, 2, 5, -1, -1, 11, 17, 40, 45, 34, 373, 73, 55, 115; 3048, 1897, 744, 166, 420, -82, -84, 896, 1392, 3283, 3696, 2794, 30660, 6002, 4524, 9464; 1524, 945, 368, 81, 196, -42, -40, 462, 708, 1659, 1864, 1407, 15428, 3018, 2272, 4746],224,6]
%
% END OF LATTICE L225.6
%
%
% LATTICE L225.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-3005436, 150276, -7560; 150276, -7514, 378; -7560, 378, -19],[84, 2, 1],[22, 57, 6, 3, 5, -1, -1, 4, 8, 83, 24, 37, 205, 81, 31, 66; 447, 1162, 123, 62, 105, -20, -21, 77, 159, 1666, 483, 746, 4137, 1636, 627, 1337; 132, 420, 58, 39, 98, 0, -20, -63, -24, 84, 50, 105, 658, 288, 128, 315],224,7]
%
% END OF LATTICE L225.7
%
%
% LATTICE L225.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-6216, 2184, 0; 2184, -766, -2; 0, -2, 3],[168, 2, 1],[-2, 41, 9, 34, 205, 87, 37, 87, 17, 99, 6, 6, 5, -7, -7, -17; -6, 112, 25, 95, 574, 244, 104, 245, 48, 280, 17, 17, 14, -20, -20, -49; -9, 0, 7, 36, 238, 108, 50, 126, 27, 168, 11, 12, 14, -12, -14, -42],224,8]
%
% END OF LATTICE L225.8
%
%
% LATTICE L225.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-13272, 672, 840; 672, -34, -42; 840, -42, -41],[168, 2, 1],[11, 125, 37, 58, 162, 129, 25, 108, 37, 99, 11, 6, 6, -1, -1, 4; 222, 2548, 756, 1187, 3318, 2644, 513, 2219, 762, 2044, 228, 125, 126, -20, -21, 77; -6, -84, -26, -42, -119, -96, -19, -84, -30, -84, -10, -6, -7, 0, 1, 0],224,9]
%
% END OF LATTICE L225.9
%
%
% LATTICE L225.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-56784, -14448, 1008; -14448, -3674, 254; 1008, 254, -15],[336, 2, 1],[-35, -163, -65, -143, -321, -25, -11, -25, 8, 37, 11, -1, -57, -11, -16, -227; 147, 686, 274, 604, 1358, 106, 47, 112, -33, -154, -46, 4, 238, 46, 67, 952; 132, 630, 256, 576, 1316, 105, 50, 168, -24, -126, -40, 0, 196, 39, 58, 840],224,10]
%
% END OF LATTICE L225.10
%
%
% LATTICE L225.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-26544, 1680, 672; 1680, -82, -42; 672, -42, -17],[336, 2, 1],[37, 54, 25, 129, 162, 29, 37, 125, 11, 2, -1, -1, 6, 3, 11, 99; -30, -42, -19, -96, -119, -21, -26, -84, -6, 0, 1, 0, -7, -3, -10, -84; 1524, 2219, 1026, 5288, 6636, 1187, 1512, 5096, 444, 77, -42, -40, 252, 125, 456, 4088],224,11]
%
% END OF LATTICE L225.11
%
%
% LATTICE L225.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-12432, -4368, 336; -4368, -1534, 118; 336, 118, -9],[336, 2, 1],[-4, -16, -17, -49, -131, -25, -9, -71, -5, -5, -1, 1, 5, 1, 0, -13; 15, 56, 58, 164, 434, 82, 29, 224, 15, 14, 2, -4, -14, -2, 1, 56; 42, 119, 108, 272, 672, 118, 36, 224, 6, -7, -12, -16, 0, 10, 12, 224],224,12]
%
% END OF LATTICE L225.12
%
%
% LATTICE L225.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-326969328, -5108880, 247296; -5108880, -79826, 3864; 247296, 3864, -187],[336, 2, 1],[89, 251, 57, 289, 359, 127, 79, 257, 19, 1, -3, -1, 19, 17, 29, 247; -5622, -15862, -3603, -18272, -22701, -8032, -4998, -16268, -1206, -70, 189, 64, -1197, -1072, -1830, -15596; 1524, 4158, 926, 4608, 5656, 1974, 1192, 3696, 204, -126, -62, 0, 392, 330, 536, 4368],224,13]
%
% END OF LATTICE L225.13
%
%
% LATTICE L225.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[45108, -2268, 0; -2268, 114, 0; 0, 0, 1],[252, 6, 1],[-14, -27, -4, 0, 1, -1, -7, -17, -16, -113, -86, -40, -631, -79, -83, -53; -283, -546, -81, 0, 21, -20, -141, -343, -323, -2282, -1737, -808, -12747, -1596, -1677, -1071; 18, 28, 0, -1, 0, 4, 18, 35, 30, 196, 144, 65, 1008, 124, 126, 77],224,14]
%
% END OF LATTICE L225.14
%
%
% LATTICE L225.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-235368, 2520, 504; 2520, -6, -12; 504, -12, 1],[504, 6, 1],[-2, -50, -9, -79, -71, -41, -5, -121, -3, -20, -1, -1, 1, 1, 0, -19; -115, -2877, -518, -4548, -4088, -2361, -288, -6972, -173, -1155, -58, -60, 56, 57, 0, -1092; -369, -9198, -1654, -14508, -13034, -7524, -917, -22176, -549, -3654, -182, -180, 182, 180, -1, -3528],224,15]
%
% END OF LATTICE L225.15
%
%
% LATTICE L225.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-4143384, 212688, -13608; 212688, -10914, 690; -13608, 690, -25],[504, 6, 1],[-51, -80, -28, -1, 109, 28, 115, 239, 63, 108, 46, 33, 17, -12, -79, -183; -1022, -1603, -561, -20, 2184, 561, 2304, 4788, 1262, 2163, 921, 660, 336, -241, -1584, -3668; -450, -700, -243, -8, 945, 242, 990, 2044, 534, 896, 369, 232, -63, -130, -738, -1652],224,16]
%
% END OF LATTICE L225.16
%
%
% LATTICE L225.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-166824, 3696, 840; 3696, -57, -21; 840, -21, -4],[168, 3, 1],[5, 5, -3, -1, 15, 4, 15, 34, 17, 149, 69, 89, 447, 40, 51, 43; 68, 70, -40, -14, 196, 53, 200, 455, 228, 2002, 928, 1198, 6020, 539, 688, 581; 688, 672, -420, -138, 2100, 558, 2088, 4725, 2360, 20664, 9564, 12330, 61908, 5538, 7056, 5943],224,17]
%
% END OF LATTICE L225.17
%
%
% LATTICE L225.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-70476, 11760, 3276; 11760, -1962, -546; 3276, -546, -151],[84, 6, 1],[6, 25, 5, -1, -23, -8, -10, -55, -4, -11, 1, 17, 65, 16, 16, 83; 39, 168, 35, -6, -161, -57, -73, -420, -33, -126, -17, 54, 287, 81, 91, 504; -10, -63, -18, 0, 84, 33, 48, 336, 34, 231, 90, 192, 420, 63, 24, 0],224,18]
%
% END OF LATTICE L225.18
%
%
% LATTICE L225.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-291144, 0, 2352; 0, 4, 0; 2352, 0, -19],[168, 4, 1],[7, 17, 7, 8, 37, 3, 3, 3, -1, -3, -1, 0, 5, 1, 3, 11; -30, -98, -48, -65, -336, -31, -42, -77, -18, -14, 0, 1, 0, -1, -6, -35; 852, 2058, 844, 960, 4424, 357, 352, 336, -132, -378, -124, 0, 616, 123, 368, 1344],224,19]
%
% END OF LATTICE L225.19
%
%
% LATTICE L225.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[327768, 22176, -1008; 22176, 1500, -68; -1008, -68, 3],[168, 4, 1],[-5, -13, -15, -23, -127, -25, -19, -40, -13, -8, -3, -1, 1, 1, 1, -2; 84, 217, 250, 383, 2114, 416, 316, 665, 216, 133, 50, 17, -14, -16, -16, 35; 216, 539, 616, 940, 5180, 1018, 772, 1624, 528, 329, 128, 52, 28, -26, -28, 112],224,20]
%
% END OF LATTICE L225.20
%
%
% LATTICE L225.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-9912, 840, 336; 840, -54, -18; 336, -18, -5],[168, 6, 1],[1, 17, 1, 1, 1, -1, -1, -2, 0, 11, 2, 7, 41, 17, 7, 16; 35, 588, 34, 33, 28, -36, -34, -63, 1, 420, 74, 255, 1484, 612, 250, 567; -61, -1008, -57, -54, -42, 60, 54, 84, -5, -840, -141, -474, -2730, -1116, -450, -1008],224,21]
%
% END OF LATTICE L225.21
%
%
% LATTICE L225.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2872296, 359016, 25200; 359016, -44874, -3150; 25200, -3150, -221],[168, 6, 1],[-37, -311, -37, -22, -25, 1, 4, 2, -7, -305, -95, -154, -437, -353, -70, -310; -264, -2212, -262, -155, -175, 8, 28, 7, -52, -2212, -686, -1109, -3143, -2536, -502, -2219; -458, -3948, -486, -300, -357, 0, 57, 126, -58, -3276, -1062, -1764, -5061, -4128, -831, -3738],224,22]
%
% END OF LATTICE L225.22
%
%
% LATTICE L225.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-840, -840, 168; -840, -231, 56; 168, 56, -13],[168, 7, 1],[-1, 1, 11, 10, 17, 25, 21, 7, 19, 2, 7, 2, 1, -1, -3, -1; -48, 1, 48, 58, 108, 170, 156, 56, 168, 19, 72, 22, 12, -10, -36, -16; -252, 8, 280, 329, 608, 952, 868, 310, 924, 104, 392, 119, 64, -56, -196, -86],224,23]
%
% END OF LATTICE L225.23
%
%
% LATTICE L225.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-54012, 27048, -840; 27048, -13538, 420; -840, 420, -13],[84, 14, 1],[-10, -7, -10, -11, -7, -15, -3, 0, 4, 3, 4, 3, 1, -1, -3, -2; -39, -32, -51, -64, -45, -110, -33, -7, -3, 4, 9, 8, 3, -2, -9, -7; -630, -600, -1036, -1407, -1040, -2688, -910, -237, -378, -72, 28, 63, 32, 0, -98, -99],224,24]
%
% END OF LATTICE L225.24
%
%
% LATTICE L225.25
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-91896, 15624, -1176; 15624, -2656, 200; -1176, 200, -15],[168, 8, 1],[-7, -59, -8, -47, -127, -49, -18, -73, -11, -25, -1, -1, 1, 1, 0, -11; -42, -343, -46, -268, -721, -277, -101, -406, -60, -133, -5, -4, 7, 5, -1, -70; -18, 0, 7, 72, 238, 108, 50, 252, 54, 168, 11, 24, 14, -12, -14, -84],224,25]
%
% END OF LATTICE L225.25
%
%
% LATTICE L225.26
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-5129208, 9576, 10080; 9576, -12, -21; 10080, -21, -19],[504, 3, 1],[5, 43, 17, 40, 149, 89, 23, 149, 17, 34, 5, 4, 5, -1, -1, 5; 688, 5943, 2352, 5538, 20636, 12330, 3188, 20664, 2360, 4725, 696, 558, 700, -138, -140, 672; 1884, 16191, 6400, 15057, 56084, 33498, 8656, 56070, 6396, 12789, 1880, 1503, 1876, -378, -376, 1890],224,26]
%
% END OF LATTICE L225.26
%
%
% LATTICE L225.27
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-268884, 44856, -2268; 44856, -7482, 378; -2268, 378, -19],[252, 6, 1],[2, 95, 10, 49, 93, 113, 15, 100, 12, 101, 4, 7, 5, -1, -1, -2; 11, 588, 63, 312, 595, 726, 97, 651, 79, 672, 27, 48, 35, -6, -7, -21; -24, 252, 50, 315, 658, 864, 128, 945, 132, 1260, 58, 117, 98, 0, -20, -189],224,27]
%
% END OF LATTICE L225.27
%
%
% LATTICE L225.28
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-16037616, 4904256, 148512; 4904256, -1499706, -45414; 148512, -45414, -1375],[336, 6, 1],[-74, -1409, -97, -65, -325, 1, 67, 209, 13, -299, -86, -179, -2237, -977, -433, -1063; -259, -4928, -339, -227, -1134, 4, 234, 728, 45, -1064, -303, -629, -7854, -3428, -1518, -3724; 562, 10584, 720, 477, 2352, -24, -492, -1470, -82, 2856, 720, 1443, 17808, 7704, 3372, 8190],224,28]
%
% END OF LATTICE L225.28
%
%
% LATTICE L225.29
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-92947344, -172368, 837984; -172368, -246, 1554; 837984, 1554, -7555],[336, 6, 1],[-471, -3791, -423, -116, -234, 37, 39, -71, -137, -4721, -1401, -1100, -6150, -4901, -951, -2057; -10, -84, -10, -3, -7, 0, 1, 0, -2, -84, -26, -21, -119, -96, -19, -42; -52244, -420504, -46920, -12867, -25956, 4104, 4326, -7875, -15196, -523656, -155400, -122013, -682164, -543624, -105486, -228165],224,29]
%
% END OF LATTICE L225.29
%
%
% LATTICE L225.30
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-104496, 1344, 336; 1344, 18, -6; 336, -6, -1],[336, 6, 1],[1, 17, 1, 1, 1, -1, -1, -1, 0, 11, 2, 7, 41, 17, 7, 8; 9, 168, 11, 12, 14, -12, -14, -21, -3, 0, 7, 36, 238, 108, 50, 63; 256, 4368, 258, 258, 252, -264, -264, -273, -4, 2688, 498, 1758, 10332, 4296, 1776, 2037],224,30]
%
% END OF LATTICE L225.30
%
%
% LATTICE L225.31
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-7896, 0, 2856; 0, 12, 0; 2856, 0, -1033],[168, 12, 1],[25, 123, 35, 12, 61, 0, -13, -45, -7, 3, 19, 24, 317, 72, 67, 171; -10, -35, -6, -1, 0, 1, 0, -14, -6, -77, -42, -31, -336, -65, -48, -98; 68, 336, 96, 33, 168, 0, -36, -126, -20, 0, 48, 63, 840, 192, 180, 462],224,31]
%
% END OF LATTICE L225.31
%
%
% LATTICE L225.32
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1011024, 126336, -18480; 126336, -15786, 2310; -18480, 2310, -337],[336, 6, 1],[-59, -503, -61, -37, -43, 1, 7, 11, -9, -449, -143, -235, -671, -545, -109, -487; -418, -3556, -430, -260, -301, 8, 49, 70, -66, -3220, -1022, -1676, -4781, -3880, -775, -3458; 368, 3192, 396, 246, 294, 0, -48, -126, 40, 2520, 828, 1386, 3990, 3264, 660, 2982],224,32]
%
% END OF LATTICE L225.32
%
%
% LATTICE L225.33
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[190680, 19488, -2352; 19488, 1980, -240; -2352, -240, 29],[168, 12, 1],[7, 65, 31, 41, 209, 38, 25, 22, 3, 5, -1, -1, 1, 2, 5, 13; 14, 119, 54, 68, 336, 59, 36, 28, 2, -7, -6, -4, 0, 5, 12, 28; 680, 6216, 2940, 3858, 19572, 3540, 2304, 1995, 256, 336, -132, -114, 84, 204, 504, 1281],224,33]
%
% END OF LATTICE L225.33
%
%
% LATTICE L225.34
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-83832, 25536, -504; 25536, -7770, 154; -504, 154, -3],[168, 14, 1],[-2, -3, -2, -3, -1, 1, 3, 2, 5, 7, 5, 11, 7, 15, 3, 0; -6, -8, -5, -7, -2, 4, 8, 5, 12, 16, 11, 23, 14, 28, 4, -1; 21, 88, 77, 140, 62, 28, -98, -82, -231, -368, -287, -700, -482, -1148, -322, -58],224,34]
%
% END OF LATTICE L225.34
%
%
% LATTICE L225.35
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-80808, 20160, -1176; 20160, -5026, 294; -1176, 294, -17],[168, 14, 1],[-19, -9, -9, -6, -1, 1, 2, 2, 7, 1, -3, -10, -5, -33, -8, -6; -72, -32, -30, -19, -3, 4, 6, 5, 12, -8, -30, -61, -27, -164, -36, -25; 42, 60, 98, 84, 17, 0, -35, -54, -294, -228, -350, -420, -143, -672, -91, -30],224,35]
%
% END OF LATTICE L225.35
%
%
% LATTICE L225.36
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-104794032, 5222784, -39648; 5222784, -260296, 1976; -39648, 1976, -15],[336, 8, 1],[5, 41, 11, 8, 86, 33, 12, 24, 7, 15, 1, 0, -2, -1, 0, 4; 99, 826, 223, 163, 1757, 676, 247, 497, 147, 322, 23, 1, -35, -20, -1, 77; -180, 392, 288, 317, 4032, 1784, 804, 2002, 852, 2744, 384, 131, 672, 8, -132, -434],224,36]
%
% END OF LATTICE L225.36
%
%
% LATTICE L225.37
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-12021744, 601104, 285600; 601104, -30056, -14280; 285600, -14280, -6781],[336, 8, 1],[32, 67, 19, -1, -93, -36, -52, -363, -110, -249, -97, -207, -453, -68, -26, -1; 663, 1400, 399, -20, -1953, -757, -1095, -7658, -2325, -5278, -2061, -4412, -9681, -1459, -567, -98; -48, -126, -40, 0, 196, 78, 116, 840, 264, 630, 256, 576, 1316, 210, 100, 168],224,37]
%
% END OF LATTICE L225.37
%
%
% LATTICE L225.38
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-116450544, 5822544, -47040; 5822544, -291128, 2352; -47040, 2352, -19],[336, 8, 1],[8, 83, 24, 37, 205, 81, 31, 66, 22, 57, 6, 3, 5, -1, -1, 4; 159, 1666, 483, 746, 4137, 1636, 627, 1337, 447, 1162, 123, 62, 105, -20, -21, 77; -132, 672, 352, 714, 4424, 1920, 844, 2058, 852, 2688, 368, 246, 616, 0, -124, -378],224,38]
%
% END OF LATTICE L225.38
%
%
% LATTICE L225.39
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-195888, -72576, 1344; -72576, -26872, 496; 1344, 496, -9],[336, 8, 1],[-5, 2, 4, 5, -2, -4, -9, -83, -31, -44, -40, -101, -250, -44, -27, -85; 15, -7, -13, -16, 7, 13, 29, 266, 99, 140, 127, 320, 791, 139, 85, 266; 72, -91, -120, -136, 84, 118, 252, 2240, 816, 1127, 1008, 2504, 6132, 1066, 636, 1904],224,39]
%
% END OF LATTICE L225.39
%
%
% LATTICE L225.40
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[831096, 1008, -7056; 1008, -6, -6; -7056, -6, 59],[504, 6, 1],[3, 4, -1, -1, 1, 1, 4, 29, 6, 38, 55, 49, 377, 23, 23, 55; 124, 161, -48, -44, 42, 43, 171, 1232, 254, 1603, 2316, 2060, 15834, 965, 963, 2296; 369, 490, -126, -124, 126, 124, 495, 3584, 741, 4690, 6786, 6044, 46494, 2836, 2835, 6776],224,40]
%
% END OF LATTICE L225.40
%
%
% LATTICE L225.41
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[33768, -1008, 1512; -1008, 30, -42; 1512, -42, -41],[504, 6, 1],[-27, -226, -17, -257, -106, -112, -23, -221, -5, 2, 1, 1, -6, -16, -9, -227; -950, -7959, -599, -9060, -3738, -3951, -812, -7812, -178, 63, 35, 36, -210, -561, -316, -7980; -30, -252, -19, -288, -119, -126, -26, -252, -6, 0, 1, 0, -7, -18, -10, -252],224,41]
%
% END OF LATTICE L225.41
%
%
% LATTICE L225.42
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-17304, 3024, -1344; 3024, -525, 231; -1344, 231, -100],[168, 21, 1],[-1, 1, 9, 4, 3, -1, -9, -7, -13, -8, -51, -32, -45, -55, -33, -7; -60, -3, 56, 33, 28, -6, -88, -78, -156, -105, -704, -465, -676, -858, -560, -138; -140, -24, 0, 21, 24, 0, -84, -90, -196, -144, -1008, -693, -1032, -1344, -924, -246],224,42]
%
% END OF LATTICE L225.42
%
%
% LATTICE L225.43
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[84, 0, 0; 0, -714, 294; 0, 294, -121],[84, 42, 1],[-5, -5, -3, -1, 0, 1, 0, -1, -3, -11, -21, -31, -24, -65, -24, -7; -27, -18, 1, 9, 5, 0, -17, -18, -39, -114, -199, -273, -203, -528, -181, -48; -70, -48, 0, 21, 12, 0, -42, -45, -98, -288, -504, -693, -516, -1344, -462, -123],224,43]
%
% END OF LATTICE L225.43
%
%
% LATTICE L225.44
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-9912, 8400, 1008; 8400, -6984, -840; 1008, -840, -101],[168, 24, 1],[2, 17, 1, 2, 1, -1, -1, -4, 0, 11, 2, 14, 41, 17, 7, 32; -1, -42, -5, -15, -14, 6, 11, 105, 13, 210, 23, 111, 266, 90, 25, 63; 26, 504, 51, 144, 126, -60, -102, -924, -110, -1680, -177, -816, -1890, -612, -150, -252],224,44]
%
% END OF LATTICE L225.44
%
%
% LATTICE L225.45
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1473360, -372624, -4704; -372624, 94234, 1190; -4704, 1190, 15],[336, 14, 1],[-22, -7, -7, 1, 3, 3, 2, -3, -11, -15, -59, -177, -69, -47, -35, -41; -69, -22, -22, 4, 10, 10, 7, -8, -33, -46, -182, -548, -214, -146, -109, -128; -1428, -450, -448, 0, 148, 147, 70, -312, -840, -1062, -4088, -12096, -4684, -3171, -2338, -2712],224,45]
%
% END OF LATTICE L225.45
%
%
% LATTICE L225.46
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1991472, 31584, -7056; 31584, 462, -112; -7056, -112, 25],[336, 14, 1],[-7, -1, -2, -1, 1, 3, 9, 9, 19, 3, 8, 33, 5, 5, 3, -1; -6, 0, 1, 0, -1, -3, -10, -12, -30, -6, -19, -96, -17, -21, -26, -12; -2016, -283, -560, -280, 278, 833, 2492, 2480, 5208, 815, 2156, 8792, 1318, 1295, 700, -352],224,46]
%
% END OF LATTICE L225.46
%
%
% LATTICE L225.47
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-54264, 0, 840; 0, 28, 0; 840, 0, -13],[168, 28, 1],[-19, -3, -3, 0, 1, 1, 1, -1, -11, -7, -27, -40, -31, -21, -31, -9; -18, -2, 0, 1, 0, -1, -6, -5, -30, -14, -48, -65, -48, -31, -42, -11; -1260, -198, -196, 0, 64, 63, 56, -72, -756, -474, -1820, -2688, -2080, -1407, -2072, -600],224,47]
%
% END OF LATTICE L225.47
%
%
% LATTICE L225.48
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-554736, -11760, 2688; -11760, -210, 56; 2688, 56, -13],[336, 14, 1],[-5, -1, -3, -1, 1, 3, 2, 3, 2, 0, -3, -15, -7, -11, -5, -7; -39, -7, -18, -4, 6, 16, 9, 8, -3, -7, -66, -220, -90, -128, -51, -64; -1218, -239, -700, -224, 232, 686, 448, 640, 378, -41, -980, -4256, -1912, -2926, -1288, -1760],224,48]
%
% END OF LATTICE L225.48
%
%
% LATTICE L225.49
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-50194704, -6274464, 315840; -6274464, -784322, 39480; 315840, 39480, -1987],[336, 14, 1],[-271, -49, -31, 1, 15, 73, 83, 47, 19, -35, -95, -673, -141, -409, -335, -215; 2430, 440, 279, -8, -135, -658, -750, -428, -186, 308, 843, 5992, 1257, 3650, 2994, 1924; 5208, 954, 616, 0, -298, -1470, -1708, -1032, -672, 558, 1652, 12096, 2566, 7518, 6244, 4056],224,49]
%
% END OF LATTICE L225.49
%
%
% LATTICE L225.50
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-287112, 0, -141624; 0, 28, 0; -141624, 0, -69859],[168, 28, 1],[1409, 111, 221, 0, -73, -145, -69, 77, 829, 262, 2017, 2984, 2311, 3129, 2307, 669; -18, -1, 0, 1, 0, -2, -6, -5, -30, -7, -48, -65, -48, -62, -42, -11; -2856, -225, -448, 0, 148, 294, 140, -156, -1680, -531, -4088, -6048, -4684, -6342, -4676, -1356],224,50]
%
% END OF LATTICE L225.50
%
%
% LATTICE L225.51
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1464624, -611856, -5040; -611856, 255606, 2106; -5040, 2106, 17],[1008, 6, 1],[46, 691, 97, 683, 537, 134, 24, 353, -3, -89, -11, 5, 65, 38, 19, 851; 109, 1638, 230, 1620, 1274, 318, 57, 840, -7, -210, -26, 12, 154, 90, 45, 2016; 132, 1890, 256, 1728, 1316, 315, 50, 504, -24, -378, -40, 0, 196, 117, 58, 2520],224,51]
%
% END OF LATTICE L225.51
%
%
% LATTICE L225.52
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1083600, -25200, 7056; -25200, -1182, 426; 7056, 426, -151],[1008, 6, 1],[27, 113, 17, 257, 106, 56, 23, 221, 5, -1, -1, -1, 6, 8, 9, 227; 7202, 30135, 4533, 68520, 28259, 14928, 6130, 58884, 1330, -273, -267, -264, 1603, 2136, 2402, 60564; 21576, 90279, 13580, 205272, 84658, 44721, 18364, 176400, 3984, -819, -800, -792, 4802, 6399, 7196, 181440],224,52]
%
% END OF LATTICE L225.52
%
%
% LATTICE L225.53
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1662192, 40320, -13104; 40320, 978, -318; -13104, -318, 103],[1008, 6, 1],[6, 29, 4, 1, 1, -1, -1, 2, 3, 55, 23, 23, 377, 49, 55, 19; -233, -1120, -153, -38, -42, 36, 30, -84, -121, -2184, -909, -906, -14826, -1924, -2154, -742; 42, 224, 36, 10, 0, -16, -36, -7, 6, 224, 108, 118, 2016, 272, 324, 119],224,53]
%
% END OF LATTICE L225.53
%
%
% LATTICE L225.54
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[504, 0, 0; 0, -12, 0; 0, 0, 1],[504, 12, 1],[-3, -3, -1, 0, 1, 0, -1, -3, -3, -11, -17, -4, -127, -8, -17, -11; 22, 21, 6, 0, 0, 1, 12, 28, 26, 91, 138, 32, 1008, 63, 132, 84; 36, 28, 0, -1, 0, 4, 36, 70, 60, 196, 288, 65, 2016, 124, 252, 154],224,54]
%
% END OF LATTICE L225.54
%
%
% LATTICE L225.55
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-65500344, -4366656, 35280; -4366656, -291108, 2352; 35280, 2352, -19],[504, 12, 1],[17, 149, 23, 89, 149, 40, 17, 86, 5, 5, -1, -1, 5, 4, 5, 68; -248, -2184, -338, -1311, -2198, -591, -252, -1281, -76, -84, 14, 15, -70, -57, -72, -987; 852, 6174, 844, 2880, 4424, 1071, 352, 1008, -132, -1134, -124, 0, 616, 369, 368, 4032],224,55]
%
% END OF LATTICE L225.55
%
%
% LATTICE L225.56
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-183610224, -3825360, 185472; -3825360, -79698, 3864; 185472, 3864, -187],[1008, 6, 1],[-79, -655, -49, -737, -303, -319, -65, -617, -13, 11, 3, 1, -19, -49, -27, -671; 3866, 32046, 2397, 36048, 14819, 15600, 3178, 30156, 634, -546, -147, -48, 931, 2400, 1322, 32844; 1524, 12474, 926, 13824, 5656, 5922, 1192, 11088, 204, -378, -62, 0, 392, 990, 536, 13104],224,56]
%
% END OF LATTICE L225.56
%
%
% LATTICE L225.57
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[809928, 4032, -3024; 4032, -12, -12; -3024, -12, 11],[504, 12, 1],[-3, -11, -3, -10, -15, -7, -1, -1, 1, 4, 1, 2, 1, -1, -1, -13; -94, -357, -100, -345, -532, -258, -42, -105, 22, 105, 28, 57, 28, -30, -30, -399; -936, -3465, -952, -3204, -4844, -2286, -340, -504, 288, 1197, 304, 612, 308, -306, -308, -4032],224,57]
%
% END OF LATTICE L225.57
%
%
% LATTICE L225.58
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[7176456, 3024, -28728; 3024, -12, -12; -28728, -12, 115],[504, 12, 1],[15, 11, -1, -1, 1, 2, 17, 16, 27, 87, 127, 57, 881, 54, 109, 33; 14, 7, -6, -2, 0, 3, 24, 21, 34, 105, 150, 66, 1008, 61, 120, 35; 3744, 2744, -252, -250, 252, 500, 4248, 3997, 6744, 21728, 31716, 14234, 219996, 13484, 27216, 8239],224,58]
%
% END OF LATTICE L225.58
%
%
% LATTICE L225.59
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[77784, 39144, -1008; 39144, 19530, -504; -1008, -504, 13],[168, 42, 1],[-1, -1, -1, 1, 1, 2, 1, 1, 0, -1, -5, -17, -7, -10, -4, -5; -9, -9, -10, 0, 4, 9, 4, 0, -3, -15, -62, -192, -76, -105, -40, -48; -427, -426, -462, 84, 234, 504, 231, 72, -119, -666, -2814, -8820, -3510, -4872, -1869, -2256],224,59]
%
% END OF LATTICE L225.59
%
%
% LATTICE L225.60
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[168, 0, 0; 0, -546, -126; 0, -126, -29],[168, 42, 1],[-3, -1, 0, 1, 0, -1, -3, -5, -5, -7, -12, -65, -12, -31, -21, -11; 18, 9, 5, 0, -2, -9, -8, 0, 6, 15, 31, 192, 38, 105, 80, 48; -70, -36, -21, 0, 9, 42, 42, 12, -14, -48, -105, -672, -135, -378, -294, -180],224,60]
%
% END OF LATTICE L225.60
%
%
% LATTICE L225.61
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-724080, 112560, -23184; 112560, -17496, 3600; -23184, 3600, -733],[336, 24, 1],[-21, -94, -20, 7, 110, 19, 49, 295, 25, 122, 32, 25, -26, -11, -37, -239; -149, -665, -141, 50, 777, 134, 345, 2072, 175, 847, 219, 158, -231, -82, -267, -1708; -68, -294, -60, 24, 336, 57, 144, 840, 68, 294, 60, -24, -336, -57, -144, -840],224,61]
%
% END OF LATTICE L225.61
%
%
% LATTICE L225.62
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-187201392, -31200288, 581616; -31200288, -5200056, 96936; 581616, 96936, -1807],[336, 24, 1],[-10, -11, 20, 56, 379, 175, 83, 215, 32, 319, 46, 32, 83, 1, -17, -61; 67, 0, -161, -423, -2821, -1290, -605, -1554, -229, -2268, -325, -225, -581, -6, 119, 420; 376, -3528, -2196, -4662, -29316, -12864, -5736, -14154, -1984, -18984, -2628, -1770, -4452, 0, 912, 2898],224,62]
%
% END OF LATTICE L225.62
%
%
% LATTICE L225.63
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-281904, 47040, -17136; 47040, -7848, 2856; -17136, 2856, -1033],[336, 24, 1],[-4, -38, -13, -1, 61, 25, 38, 281, 30, 220, 91, 209, 485, 79, 40, 83; -31, -273, -91, -6, 427, 174, 263, 1932, 205, 1491, 613, 1398, 3227, 522, 259, 504; -20, -126, -36, 0, 168, 66, 96, 672, 68, 462, 180, 384, 840, 126, 48, 0],224,63]
%
% END OF LATTICE L225.63
%
%
% LATTICE L225.64
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[361200, 19152, -1344; 19152, 456, -72; -1344, -72, 5],[336, 24, 1],[2, 95, 30, 49, 279, 113, 45, 50, 12, 101, 12, 7, 15, -1, -3, -1; -1, -42, -13, -21, -119, -48, -19, -21, -5, -42, -5, -3, -7, 0, 1, 0; 520, 24864, 7860, 12846, 73164, 29640, 11808, 13125, 3152, 26544, 3156, 1842, 3948, -264, -792, -273],224,64]
%
% END OF LATTICE L225.64
%
%
% LATTICE L225.65
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-377160, -101808, 3528; -101808, -27384, 952; 3528, 952, -33],[168, 56, 1],[17, 8, 4, 11, 2, 0, -3, -3, -5, 0, 2, 21, 10, 32, 15, 11; 0, 1, 1, 4, 1, 1, -1, -2, -6, -5, -4, -20, -7, -17, -5, -2; 1806, 880, 455, 1288, 242, 28, -350, -380, -714, -152, 91, 1624, 850, 2884, 1442, 1108],224,65]
%
% END OF LATTICE L225.65
%
%
% LATTICE L225.66
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[230328, 7056, -1008; 7056, -21, -21; -1008, -21, 4],[504, 21, 1],[-3, 0, 7, 3, 17, 9, 25, 3, 9, 1, 11, 1, 1, -1, -7, -1; -44, -1, 72, 35, 204, 110, 312, 38, 116, 13, 144, 13, 12, -14, -96, -14; -1008, -11, 2016, 910, 5220, 2786, 7812, 944, 2856, 319, 3528, 322, 324, -322, -2268, -328],224,66]
%
% END OF LATTICE L225.66
%
%
% LATTICE L225.67
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[163044, 54432, -2016; 54432, 18186, -672; -2016, -672, 25],[252, 42, 1],[20, 27, 160, 81, 191, 175, 199, 20, 46, 17, 38, 7, 7, 1, -1, 2; -41, -56, -333, -169, -399, -366, -417, -42, -97, -36, -81, -15, -15, -2, 3, -4; 504, 664, 3906, 1967, 4626, 4228, 4788, 479, 1092, 400, 882, 161, 162, 28, 0, 53],224,67]
%
% END OF LATTICE L225.67
%
%
% LATTICE L225.68
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-51912, 10080, -1008; 10080, -1596, 147; -1008, 147, -13],[504, 21, 1],[-13, -7, -3, -1, 1, 4, 3, 1, -1, -7, -11, -55, -15, -32, -17, -8; -272, -144, -60, -18, 20, 78, 56, 15, -40, -168, -252, -1230, -332, -702, -368, -171; -2100, -1098, -448, -126, 148, 567, 392, 81, -420, -1422, -2072, -9954, -2668, -5607, -2912, -1341],224,68]
%
% END OF LATTICE L225.68
%
%
% LATTICE L225.69
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[252, 0, 0; 0, -13566, 420; 0, 420, -13],[252, 42, 1],[-3, -1, 0, 1, 0, -1, -1, -5, -5, -7, -8, -65, -8, -31, -7, -11; -19, -9, -3, 0, 1, 6, 1, -6, -11, -21, -27, -240, -31, -126, -31, -54; -630, -297, -98, 0, 32, 189, 28, -216, -378, -711, -910, -8064, -1040, -4221, -1036, -1800],224,69]
%
% END OF LATTICE L225.69
%
%
% LATTICE L225.70
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-34272, 4536, 0; 4536, -24, -24; 0, -24, 1],[504, 24, 1],[-4, -100, -9, -79, -71, -82, -5, -121, -6, -40, -1, -1, 1, 2, 0, -19; -31, -777, -70, -615, -553, -639, -39, -945, -47, -315, -8, -9, 7, 15, 0, -147; -738, -18396, -1654, -14508, -13034, -15048, -917, -22176, -1098, -7308, -182, -180, 182, 360, -1, -3528],224,70]
%
% END OF LATTICE L225.70
%
%
% LATTICE L225.71
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[619416, 3024, -5040; 3024, -24, -24; -5040, -24, 41],[504, 24, 1],[6, 8, -1, -1, 1, 2, 4, 29, 12, 76, 55, 49, 377, 46, 23, 55; 7, 7, -3, -2, 0, 3, 6, 42, 17, 105, 75, 66, 504, 61, 30, 70; 738, 980, -126, -124, 126, 248, 495, 3584, 1482, 9380, 6786, 6044, 46494, 5672, 2835, 6776],224,71]
%
% END OF LATTICE L225.71
%
%
% LATTICE L225.72
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[38640, 7728, -3024; 7728, 1386, -546; -3024, -546, 215],[336, 42, 1],[-1, -1, -1, 1, 1, 1, 1, 1, 0, -1, -5, -17, -7, -5, -4, -5; -99, -96, -94, 60, 70, 69, 61, 24, -27, -156, -662, -2076, -826, -573, -439, -528; -266, -258, -252, 168, 192, 189, 168, 72, -70, -414, -1764, -5544, -2208, -1533, -1176, -1416],224,72]
%
% END OF LATTICE L225.72
%
%
% LATTICE L225.73
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[254352, 19488, 83328; 19488, 1386, 6384; 83328, 6384, 27299],[336, 42, 1],[147, 58, 110, 55, -53, -158, -467, -455, -311, -140, -356, -1367, -193, -170, -25, 127; -2, 0, 1, 0, -1, -3, -10, -12, -10, -6, -19, -96, -17, -21, -26, -12; -448, -177, -336, -168, 162, 483, 1428, 1392, 952, 429, 1092, 4200, 594, 525, 84, -384],224,73]
%
% END OF LATTICE L225.73
%
%
% LATTICE L225.74
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2856, 2856, 840; 2856, -2772, -840; 840, -840, -247],[168, 84, 1],[-65, -29, -25, 1, 7, 5, -7, -20, -53, -89, -329, -473, -361, -241, -347, -98; -6, -2, 0, 1, 0, -1, -6, -5, -10, -14, -48, -65, -48, -31, -42, -11; -196, -90, -84, 0, 24, 21, 0, -48, -140, -246, -924, -1344, -1032, -693, -1008, -288],224,74]
%
% END OF LATTICE L225.74
%
%
% LATTICE L225.75
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[5040, -672, 0; -672, 42, 42; 0, 42, -37],[336, 42, 1],[-8, -4, -9, -1, 3, 7, 3, -1, -3, -7, -57, -175, -69, -95, -36, -43; -71, -34, -70, -4, 22, 46, 13, -40, -39, -76, -590, -1756, -682, -926, -343, -400; -98, -45, -84, 0, 24, 42, 0, -96, -70, -123, -924, -2688, -1032, -1386, -504, -576],224,75]
%
% END OF LATTICE L225.75
%
%
% LATTICE L225.76
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[336, 0, 0; 0, -28938, -1512; 0, -1512, -79],[336, 42, 1],[-3, -1, 0, 1, 0, -1, -3, -5, -5, -7, -12, -65, -12, -31, -21, -11; -34, -18, -11, 0, 5, 24, 26, 12, -2, -18, -43, -288, -59, -168, -134, -84; 644, 342, 210, 0, -96, -462, -504, -240, 28, 330, 798, 5376, 1104, 3150, 2520, 1584],224,76]
%
% END OF LATTICE L225.76
%
%
% LATTICE L225.77
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-52248, 52248, 8232; 52248, -52164, -8232; 8232, -8232, -1297],[168, 84, 1],[-121, -28, -53, 1, 17, 31, 7, -26, -81, -73, -553, -809, -623, -839, -613, -176; -6, -1, 0, 1, 0, -2, -6, -5, -10, -7, -48, -65, -48, -62, -42, -11; -728, -171, -336, 0, 108, 210, 84, -132, -448, -417, -3192, -4704, -3636, -4914, -3612, -1044],224,77]
%
% END OF LATTICE L225.77
%
%
% LATTICE L225.78
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1271760, -521808, 4368; -521808, 214088, -1792; 4368, -1792, 15],[336, 56, 1],[-11, -6, -22, -63, -24, -16, -23, -13, -13, -2, -2, -1, 0, 0, -1, -3; -33, -19, -71, -206, -79, -53, -77, -44, -45, -7, -7, -2, 1, 1, -1, -8; -756, -530, -2100, -6328, -2472, -1687, -2520, -1480, -1596, -254, -252, 56, 120, 119, 168, -88],224,78]
%
% END OF LATTICE L225.78
%
%
% LATTICE L225.79
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1147440, -573888, -283248; -573888, -287000, -141624; -283248, -141624, -69859],[336, 56, 1],[-844, -159, 66, 144, 73, 1, -221, -223, -1418, -1349, -2328, -3160, -2335, -6033, -2041, -531; 2517, 472, -201, -433, -219, -2, 663, 668, 4245, 4036, 6963, 9449, 6981, 18034, 6099, 1586; -1680, -312, 140, 294, 148, 0, -448, -450, -2856, -2712, -4676, -6342, -4684, -12096, -4088, -1062],224,79]
%
% END OF LATTICE L225.79
%
%
% LATTICE L225.80
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-216048, 108192, -1680; 108192, -54152, 840; -1680, 840, -13],[336, 56, 1],[4, 0, -3, -15, -7, -11, -10, -7, -10, -2, -3, -1, 1, 3, 4, 3; -3, -7, -33, -110, -45, -64, -51, -32, -39, -7, -9, -2, 3, 8, 9, 4; -756, -474, -1820, -5376, -2080, -2814, -2072, -1200, -1260, -198, -196, 0, 64, 126, 56, -144],224,80]
%
% END OF LATTICE L225.80
%
%
% LATTICE L225.81
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-554736, -98784, -46704; -98784, -17304, -8176; -46704, -8176, -3863],[336, 56, 1],[4, 3, 4, 3, 1, -1, -3, -1, -10, -7, -10, -11, -7, -15, -3, 0; -339, -372, -565, -447, -155, 138, 467, 165, 1725, 1296, 1951, 2295, 1541, 3558, 919, 66; 672, 752, 1148, 910, 316, -280, -952, -337, -3528, -2656, -4004, -4718, -3172, -7336, -1904, -139],224,81]
%
% END OF LATTICE L225.81
%
%
% LATTICE L225.82
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-12600, -14616, 504; -14616, -15666, 546; 504, 546, -19],[504, 42, 1],[-5, -3, -2, 0, 1, 1, -1, -1, -4, -9, -25, -24, -55, -49, -53, -5; -28, -16, -9, 1, 6, 4, -12, -7, -26, -56, -153, -145, -330, -292, -312, -29; -945, -544, -315, 28, 198, 140, -378, -230, -861, -1864, -5103, -4844, -11034, -9772, -10458, -974],224,82]
%
% END OF LATTICE L225.82
%
%
% LATTICE L225.83
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1260504, 402192, 6048; 402192, 127218, 1848; 6048, 1848, 23],[504, 42, 1],[-267, -67, -35, 16, 16, -1, -67, -50, -333, -333, -1765, -816, -916, -1599, -833, -150; 1052, 264, 138, -63, -63, 4, 264, 197, 1312, 1312, 6954, 3215, 3609, 6300, 3282, 591; -14322, -3596, -1890, 854, 855, -56, -3591, -2680, -17850, -17852, -94626, -43750, -49113, -85736, -44667, -8044],224,83]
%
% END OF LATTICE L225.83
%
%
% LATTICE L225.84
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[6795432, 492912, -27216; 492912, 35742, -1974; -27216, -1974, 109],[504, 42, 1],[0, -1, -1, 1, 1, 8, 2, 13, 5, 11, 11, 79, 9, 32, 3, 7; -8, -9, -4, 0, 2, 15, 3, 12, 2, -3, -8, -96, -14, -63, -9, -36; -147, -414, -322, 252, 286, 2268, 553, 3456, 1281, 2682, 2590, 17892, 1982, 6804, 581, 1080],224,84]
%
% END OF LATTICE L225.84
%
%
% LATTICE L225.85
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[504, 0, 0; 0, -5082, 294; 0, 294, -17],[504, 42, 1],[-3, -1, 0, 1, 0, -1, -1, -5, -5, -7, -4, -65, -4, -31, -7, -11; -16, -9, -2, 0, 1, 15, 6, 12, 4, -3, -4, -96, -7, -63, -18, -36; -294, -162, -35, 0, 17, 252, 98, 180, 42, -90, -91, -2016, -143, -1260, -350, -684],224,85]
%
% END OF LATTICE L225.85
%
%
% LATTICE L225.86
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[996912, 498960, -1008; 498960, 249720, -504; -1008, -504, 1],[1008, 24, 1],[19, 39, 7, 0, -10, -1, 4, 16, 17, 129, 101, 24, 766, 97, 104, 68; -41, -84, -15, 0, 21, 2, -9, -35, -37, -280, -219, -52, -1659, -210, -225, -147; -1476, -2968, -504, -1, 504, 8, -468, -1442, -1452, -10696, -8280, -1951, -61992, -7816, -8316, -5390],224,86]
%
% END OF LATTICE L225.86
%
%
% LATTICE L225.87
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[26358192, -4153968, 21168; -4153968, 654648, -3336; 21168, -3336, 17],[1008, 24, 1],[-3, -26, -4, -31, -26, -7, -3, -31, -1, -2, 0, -1, -2, -1, -1, -25; -11, -105, -17, -138, -119, -33, -15, -168, -7, -21, -1, -6, -7, -3, -3, -84; 1572, 11718, 1636, 11448, 8960, 2223, 784, 5544, -132, -1638, -196, 72, 1120, 657, 656, 14616],224,87]
%
% END OF LATTICE L225.87
%
%
% LATTICE L225.88
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-426312432, 20158992, -1445472; 20158992, -953256, 68352; -1445472, 68352, -4901],[1008, 24, 1],[-142, -1037, -800, -376, -5965, -751, -797, -515, -140, -279, -46, 0, 43, -1, -49, -143; -2695, -19670, -15171, -7129, -113085, -14236, -15105, -9758, -2651, -5278, -867, 1, 819, -20, -933, -2716; 4296, 31528, 24372, 11474, 182196, 22960, 24408, 15806, 4320, 8680, 1476, 14, -1260, 16, 1440, 4298],224,88]
%
% END OF LATTICE L225.88
%
%
% LATTICE L225.89
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1450512, -69552, 4032; -69552, 3336, -192; 4032, -192, 13],[1008, 24, 1],[-40, -83, -16, -1, 1, -1, -13, -38, -38, -281, -218, -103, -1639, -207, -221, -144; -803, -1666, -321, -20, 21, -20, -261, -763, -763, -5642, -4377, -2068, -32907, -4156, -4437, -2891; 540, 1120, 216, 14, 0, 16, 180, 518, 516, 3808, 2952, 1394, 22176, 2800, 2988, 1946],224,89]
%
% END OF LATTICE L225.89
%
%
% LATTICE L225.90
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1075536, -179424, -85680; -179424, -29928, -14280; -85680, -14280, -6781],[1008, 24, 1],[120, 1159, 54, 110, 93, 1, -19, -187, -26, 157, 40, 266, 565, 751, 113, 845; -845, -8148, -379, -771, -651, -6, 133, 1302, 179, -1176, -287, -1893, -4011, -5322, -799, -5964; 264, 2520, 116, 234, 196, 0, -40, -378, -48, 504, 100, 630, 1316, 1728, 256, 1890],224,90]
%
% END OF LATTICE L225.90
%
%
% LATTICE L225.91
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-10474128, 1745856, -14112; 1745856, -291000, 2352; -14112, 2352, -19],[1008, 24, 1],[12, 100, 15, 113, 93, 49, 10, 95, 2, -2, -1, -1, 5, 7, 4, 101; 79, 651, 97, 726, 595, 312, 63, 588, 11, -21, -7, -6, 35, 48, 27, 672; 852, 6174, 844, 5760, 4424, 2142, 352, 2016, -132, -1134, -124, 0, 616, 738, 368, 8064],224,91]
%
% END OF LATTICE L225.91
%
%
% LATTICE L225.92
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1329552, -80640, -35280; -80640, -4584, -1992; -35280, -1992, -865],[1008, 24, 1],[12, 101, 4, 7, 5, -1, -1, -1, 2, 95, 10, 49, 93, 113, 15, 50; -2129, -17976, -715, -1257, -903, 174, 181, 210, -337, -16548, -1751, -8607, -16359, -19902, -2647, -8841; 4416, 37296, 1484, 2610, 1876, -360, -376, -441, 696, 34272, 3628, 17838, 33908, 41256, 5488, 18333],224,92]
%
% END OF LATTICE L225.92
%
%
% LATTICE L225.93
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[14235984, 696528, -38304; 696528, 34008, -1872; -38304, -1872, 103],[1008, 24, 1],[6, 55, 46, 23, 377, 49, 55, 19, 12, 29, 8, 1, 1, -1, -1, 2; 131, 1218, 1023, 513, 8421, 1096, 1233, 427, 271, 658, 183, 23, 21, -24, -27, 42; 4608, 42560, 35676, 17866, 293076, 38120, 42840, 14819, 9384, 22736, 6300, 790, 756, -808, -864, 1505],224,93]
%
% END OF LATTICE L225.93
%
%
% LATTICE L225.94
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-6888, -7728, 1176; -7728, -6552, 1008; 1176, 1008, -155],[168, 168, 1],[-2, -2, -1, 1, 1, 4, 1, 1, 0, -2, -5, -17, -7, -20, -4, -5; -47, -51, -31, 12, 22, 99, 28, 36, 11, -21, -77, -300, -130, -387, -82, -108; -322, -348, -210, 84, 150, 672, 189, 240, 70, -156, -546, -2100, -906, -2688, -567, -744],224,94]
%
% END OF LATTICE L225.94
%
%
% LATTICE L225.95
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-61488, 14112, -4032; 14112, 798, -252; -4032, -252, 79],[1008, 42, 1],[-5, -5, -53, -49, -55, -12, -25, -9, -4, -1, -1, 1, 1, 0, -2, -3; -1091, -1090, -11550, -10676, -11982, -2614, -5445, -1960, -871, -218, -222, 212, 210, -2, -441, -656; -3738, -3734, -39564, -36568, -41040, -8953, -18648, -6712, -2982, -746, -756, 728, 720, -7, -1512, -2248],224,95]
%
% END OF LATTICE L225.95
%
%
% LATTICE L225.96
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[3270960, 336672, -9072; 336672, 34062, -924; -9072, -924, 25],[1008, 42, 1],[-1, -1, -14, -31, -19, -9, -43, -9, -11, -1, -4, -1, 1, 1, 7, 1; -26, -18, -243, -528, -321, -151, -714, -148, -178, -16, -63, -16, 15, 15, 102, 12; -1344, -1033, -14112, -30856, -18810, -8869, -42084, -8752, -10584, -955, -3780, -952, 918, 917, 6300, 800],224,96]
%
% END OF LATTICE L225.96
%
%
% LATTICE L225.97
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2656080, 832608, -25200; 832608, 260862, -7896; -25200, -7896, 239],[1008, 42, 1],[0, -1, -1, 1, 1, 4, 2, 13, 5, 11, 11, 79, 9, 16, 3, 7; -19, -30, -18, 12, 14, 54, 25, 144, 49, 90, 78, 468, 46, 66, 5, -24; -630, -1098, -700, 504, 568, 2205, 1036, 6120, 2142, 4122, 3724, 23688, 2456, 3843, 476, -72],224,97]
%
% END OF LATTICE L225.97
%
%
% LATTICE L225.98
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[7198128, 1977696, 129024; 1977696, 535794, 34944; 129024, 34944, 2279],[1008, 42, 1],[-13, -4, -2, -1, 1, 8, 7, 17, 9, 2, 0, -31, -3, -16, -11, -25; 2234, 681, 337, 168, -167, -1332, -1158, -2772, -1430, -279, 65, 6264, 569, 2940, 1962, 4380; -33516, -10215, -5054, -2520, 2504, 19971, 17360, 41544, 21420, 4167, -994, -94248, -8552, -44163, -29456, -65736],224,98]
%
% END OF LATTICE L225.98
%
%
% LATTICE L225.99
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[124488, -70560, 2520; -70560, 60396, -2184; 2520, -2184, 79],[504, 84, 1],[31, 15, 157, 72, 161, 35, 145, 13, 23, 3, 5, 0, 1, 1, 17, 5; 1510, 732, 7668, 3519, 7872, 1712, 7098, 637, 1130, 148, 252, 1, 48, 48, 822, 243; 40740, 19750, 206892, 94948, 212400, 46193, 191520, 17188, 30492, 3994, 6804, 28, 1296, 1295, 22176, 6556],224,99]
%
% END OF LATTICE L225.99
%
%
% LATTICE L225.100
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2587536, -175392, 8064; -175392, 11886, -546; 8064, -546, 25],[1008, 42, 1],[-3, -2, -47, -47, -55, -25, -28, -11, -6, -1, -7, -1, 1, 1, 1, -1; -65, -42, -978, -972, -1134, -514, -573, -224, -121, -20, -138, -20, 18, 18, 15, -24; -462, -277, -6300, -6160, -7128, -3206, -3528, -1360, -714, -115, -756, -112, 72, 70, 0, -208],224,100]
%
% END OF LATTICE L225.100
%
%
% LATTICE L225.101
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-945430416, -116436096, 1657152; -116436096, -14334222, 203280; 1657152, 203280, -2789],[1008, 42, 1],[-14039, -7885, -43784, -84041, -48142, -42885, -92755, -17499, -17497, -2627, -3520, -55, 838, 837, -1853, -3525; 126602, 71106, 394839, 757872, 434139, 386732, 836454, 157804, 157786, 23690, 31743, 496, -7557, -7548, 16710, 31788; 885948, 497594, 2763054, 5303536, 3038076, 2706326, 5853456, 1104304, 1104180, 165782, 222138, 3472, -52884, -52822, 116928, 222448],224,101]
%
% END OF LATTICE L225.101
%
%
% LATTICE L225.102
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-487368, 162288, -2520; 162288, -54012, 840; -2520, 840, -13],[504, 84, 1],[13, 7, 3, 1, -1, -4, -3, -2, 1, 7, 11, 55, 15, 32, 17, 16; 20, 12, 6, 3, -2, -9, -8, -9, -8, 0, 6, 45, 14, 33, 20, 21; -1260, -594, -196, 0, 64, 189, 56, -216, -756, -1422, -1820, -8064, -2080, -4221, -2072, -1800],224,102]
%
% END OF LATTICE L225.102
%
%
% LATTICE L225.103
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1904112, 159264, -5040; 159264, -13314, 420; -5040, 420, -13],[1008, 42, 1],[-8, -4, -3, -1, 1, 7, 1, -1, -3, -7, -19, -175, -23, -95, -12, -43; -115, -57, -42, -12, 14, 96, 13, -24, -47, -105, -282, -2580, -338, -1392, -175, -624; -630, -297, -196, 0, 64, 378, 28, -432, -378, -711, -1820, -16128, -2080, -8442, -1036, -3600],224,103]
%
% END OF LATTICE L225.103
%
%
% LATTICE L225.104
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1008, 0, 0; 0, -784434, 39480; 0, 39480, -1987],[1008, 42, 1],[-3, -1, 0, 1, 0, -1, -1, -5, -5, -7, -4, -65, -4, -31, -7, -11; 262, 144, 31, 0, -15, -222, -86, -156, -34, 84, 83, 1824, 129, 1134, 314, 612; 5208, 2862, 616, 0, -298, -4410, -1708, -3096, -672, 1674, 1652, 36288, 2566, 22554, 6244, 12168],224,104]
%
% END OF LATTICE L225.104
%
%
% LATTICE L225.105
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[504, -1512, -504; -1512, 2436, 840; -504, 840, 289],[504, 84, 1],[25, 6, 125, 57, 127, 55, 113, 10, 17, 1, 1, -1, -1, 1, 13, 4; -158, -38, -792, -361, -804, -348, -714, -63, -106, -6, 0, 9, 12, -4, -78, -25; 504, 121, 2520, 1148, 2556, 1106, 2268, 200, 336, 19, 0, -28, -36, 14, 252, 80],224,105]
%
% END OF LATTICE L225.105
%
%
% LATTICE L225.106
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2583000, 860832, 424872; 860832, -286860, -141624; 424872, -141624, -69859],[504, 84, 1],[-1415, -334, -221, 1, 73, 433, 67, -236, -839, -793, -2033, -9017, -2327, -9449, -2321, -2018; -2836, -669, -442, 3, 146, 864, 132, -477, -1688, -1593, -4082, -18099, -4670, -18960, -4656, -4047; -2856, -675, -448, 0, 148, 882, 140, -468, -1680, -1593, -4088, -18144, -4684, -19026, -4676, -4068],224,106]
%
% END OF LATTICE L225.106
%
%
% LATTICE L225.107
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[122640, 26544, 8064; 26544, 5544, 1680; 8064, 1680, 509],[336, 168, 1],[0, -1, -5, -17, -7, -5, -8, -5, -2, -1, -1, 1, 1, 1, 2, 1; 43, 131, 561, 1768, 705, 490, 753, 454, 171, 83, 81, -56, -63, -62, -111, -26; -140, -414, -1764, -5544, -2208, -1533, -2352, -1416, -532, -258, -252, 168, 192, 189, 336, 72],224,107]
%
% END OF LATTICE L225.107
%
%
% LATTICE L225.108
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[336, 0, 0; 0, -52248, -8232; 0, -8232, -1297],[336, 168, 1],[-3, -11, -21, -31, -24, -65, -24, -7, -5, -5, -3, -1, 0, 1, 0, -1; 115, 330, 571, 777, 575, 1488, 505, 132, 71, 42, -13, -33, -17, 0, 53, 54; -728, -2088, -3612, -4914, -3636, -9408, -3192, -834, -448, -264, 84, 210, 108, 0, -336, -342],224,108]
%
% END OF LATTICE L225.108
%
%
% LATTICE L225.109
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[336, 0, 0; 0, -2856, -840; 0, -840, -247],[336, 168, 1],[-5, -7, -24, -65, -24, -31, -21, -11, -3, -1, 0, 1, 0, -1, -3, -5; 43, 75, 281, 816, 313, 420, 305, 174, 59, 27, 25, 0, -7, -12, 1, 30; -140, -246, -924, -2688, -1032, -1386, -1008, -576, -196, -90, -84, 0, 24, 42, 0, -96],224,109]
%
% END OF LATTICE L225.109
%
%
% LATTICE L225.110
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-121968, -80976, -12768; -80976, -49224, -7728; -12768, -7728, -1213],[336, 168, 1],[-16, -43, -72, -95, -69, -175, -57, -7, -6, -1, 6, 7, 3, -1, -9, -4; 563, 1534, 2587, 3437, 2507, 6388, 2101, 262, 239, 70, -181, -229, -101, 28, 305, 139; -3416, -9312, -15708, -20874, -15228, -38808, -12768, -1593, -1456, -432, 1092, 1386, 612, -168, -1848, -843],224,110]
%
% END OF LATTICE L225.110
%
%
% LATTICE L225.111
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-30744, 56448, 1008; 56448, 78456, 1344; 1008, 1344, 23],[504, 168, 1],[-8, -2, -1, 1, 1, 0, -2, -3, -10, -10, -53, -49, -55, -48, -25, -9; 251, 63, 33, -30, -30, 1, 63, 94, 313, 313, 1659, 1534, 1722, 1503, 783, 282; -14322, -3596, -1890, 1708, 1710, -56, -3591, -5360, -17850, -17852, -94626, -87500, -98226, -85736, -44667, -16088],224,111]
%
% END OF LATTICE L225.111
%
%
% LATTICE L225.112
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[4890312, 2131920, -19656; 2131920, 929208, -8568; -19656, -8568, 79],[504, 168, 1],[0, -2, -1, 1, 1, 16, 2, 13, 10, 22, 11, 79, 9, 64, 3, 7; -5, -9, -3, 0, 2, 33, 4, 24, 17, 33, 15, 96, 10, 63, 2, 0; -546, -1476, -574, 252, 466, 7560, 931, 5832, 4326, 9036, 4354, 29988, 3314, 22680, 959, 1728],224,112]
%
% END OF LATTICE L225.112
%
%
% LATTICE L225.113
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-61488, 28224, -4032; 28224, 3192, -504; -4032, -504, 79],[1008, 168, 1],[-10, -5, -53, -49, -55, -12, -50, -9, -8, -1, -1, 1, 1, 0, -4, -3; -1091, -545, -5775, -5338, -5991, -1307, -5445, -980, -871, -109, -111, 106, 105, -1, -441, -328; -7476, -3734, -39564, -36568, -41040, -8953, -37296, -6712, -5964, -746, -756, 728, 720, -7, -3024, -2248],224,113]
%
% END OF LATTICE L225.113
%
%
% LATTICE L225.114
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[60202800, 7925904, -119952; 7925904, 1043448, -15792; -119952, -15792, 239],[1008, 168, 1],[0, -1, -1, 1, 1, 4, 4, 13, 10, 11, 11, 79, 9, 16, 6, 7; -19, -9, -3, 0, 1, 3, 1, -6, -11, -21, -27, -240, -31, -63, -31, -54; -1260, -1098, -700, 504, 568, 2205, 2072, 6120, 4284, 4122, 3724, 23688, 2456, 3843, 952, -72],224,114]
%
% END OF LATTICE L225.114
%
%
% LATTICE L225.115
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[12082896, 4027968, -36288; 4027968, 1342824, -12096; -36288, -12096, 109],[1008, 168, 1],[102, 45, 451, 399, 437, 186, 370, 63, 48, 5, -1, 1, 13, 14, 80, 37; -209, -92, -921, -814, -891, -379, -753, -128, -97, -10, 3, -2, -27, -29, -165, -76; 10752, 4766, 47880, 42448, 46548, 19838, 39564, 6760, 5208, 554, 0, 112, 1332, 1442, 8316, 3880],224,115]
%
% END OF LATTICE L225.115
%
%
% LATTICE L225.116
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[27239184, 13880160, 66528; 13880160, 7075320, 33936; 66528, 33936, 163],[1008, 168, 1],[598, 308, 3311, 3103, 3511, 1545, 3272, 603, 572, 82, 199, 17, -1, 15, 238, 177; -1757, -905, -9729, -9118, -10317, -4540, -9615, -1772, -1681, -241, -585, -50, 3, -44, -699, -520; 121716, 62702, 674100, 631792, 714888, 314594, 666288, 122800, 116508, 16706, 40572, 3472, -216, 3038, 48384, 36016],224,116]
%
% END OF LATTICE L225.116
%
%
% LATTICE L225.117
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[4916016, 1416240, -11088; 1416240, 407400, -3192; -11088, -3192, 25],[1008, 168, 1],[-6, -2, -47, -47, -55, -25, -56, -11, -12, -1, -7, -1, 1, 1, 2, -1; -29, -9, -207, -204, -237, -107, -237, -46, -49, -4, -27, -4, 3, 3, 3, -6; -6384, -2041, -47376, -46984, -54756, -24794, -55188, -10768, -11592, -955, -6552, -952, 828, 826, 1260, -1216],224,117]
%
% END OF LATTICE L225.117
%
%
% LATTICE L225.118
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1008, 0, 0; 0, -287112, -141624; 0, -141624, -69859],[1008, 168, 1],[-3, -11, -7, -31, -8, -65, -8, -7, -5, -5, -1, -1, 0, 1, 0, -1; 1409, 4014, 2307, 9387, 2311, 17904, 2017, 1572, 829, 462, -69, -435, -73, 0, 221, 666; -2856, -8136, -4676, -19026, -4684, -36288, -4088, -3186, -1680, -936, 140, 882, 148, 0, -448, -1350],224,118]
%
% END OF LATTICE L225.118
%
%
% LATTICE L225.119
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1008, 0, 0; 0, -54264, 840; 0, 840, -13],[1008, 168, 1],[-3, -1, 0, 1, 0, -1, -1, -5, -5, -7, -8, -65, -8, -31, -7, -11; -19, -9, -3, 0, 1, 6, 1, -6, -11, -21, -27, -240, -31, -126, -31, -54; -1260, -594, -196, 0, 64, 378, 56, -432, -756, -1422, -1820, -16128, -2080, -8442, -2072, -3600],224,119]
%
% END OF LATTICE L225.119
%
%
% LATTICE L225.120
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3301200, -974736, -480816; -974736, -286104, -141120; -480816, -141120, -69607],[1008, 168, 1],[-16, -43, -24, -95, -23, -175, -19, -7, -6, -1, 2, 7, 1, -1, -3, -4; 5441, 14850, 8355, 33327, 8107, 62004, 6805, 2550, 2341, 714, -573, -2199, -325, 252, 977, 1341; -10920, -29808, -16772, -66906, -16276, -124488, -13664, -5121, -4704, -1440, 1148, 4410, 652, -504, -1960, -2691],224,120]
%
% END OF LATTICE L225.120
%

\medskip%
%------------------------------WEYL-GROUP-W226--------------------------------
%
\leavevmode\llap{}%
$W_{226}$%
\qquad\llap{12} lattices, $\chi=54$%
\hfill%
$422222422222\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L226.1
%
\leavevmode%
${L_{226.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{2}{}9\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{2}{}19\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${4}\above{1pt}{1pt}{*}{4}{2}\above{1pt}{1pt}{s}{2}{38}\above{1pt}{1pt}{s}{2}{18}\above{1pt}{1pt}{b}{2}{2}\above{1pt}{1pt}{s}{2}{342}\above{1pt}{1pt}{b}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-26853156\\-897408\\53352
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-897408\\-29978\\1783
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
53352\\1783\\-106
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
186731\\-186732\\90831780
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
6265\\-6266\\3047475
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-371\\371\\-180466
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\-2\\1476
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2\\2\\-973
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2\\0\\-1007
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
16\\-18\\7749
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
23\\-24\\11171
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1001\\-1026\\486495
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-26853156, -897408, 53352; -897408, -29978, 1783; 53352, 1783, -106],[684, 1, 1],[3, -2, -2, 16, 23, 1001, 67, 51, 135, 47, 12, 196; -2, 2, 0, -18, -24, -1026, -68, -51, -133, -45, -11, -171; 1476, -973, -1007, 7749, 11171, 486495, 32574, 24808, 65702, 22896, 5854, 95760],225,1]
%
% END OF LATTICE L226.1
%
%
% LATTICE L226.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-3672225, 11628, 16245; 11628, -34, -53; 16245, -53, -71],[171, 1, 1],[2, -2, -4, 14, 22, 976, 33, 51, 137, 49, 13, 221; 180, -179, -361, 1251, 1969, 87381, 2955, 4568, 12274, 4392, 1166, 19836; 323, -324, -646, 2268, 3562, 158004, 5342, 8255, 22173, 7929, 2103, 35739],225,2]
%
% END OF LATTICE L226.2
%
%
% LATTICE L226.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[175475583, -5412492, 18410715; -5412492, 166950, -567873; 18410715, -567873, 1931633],[171, 9, 1],[433, 35, 305, 233, 2893, 13997, 4222, 6482, 17384, 698, 1762, 3692; 17, 2, 0, 6, 84, 418, 128, 201, 551, 23, 61, 133; -4122, -333, -2907, -2219, -27549, -133285, -40203, -61722, -165528, -6646, -16776, -35150],225,3]
%
% END OF LATTICE L226.3
%
%
% LATTICE L226.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[56719497528, 660060, -14263484148; 660060, 8, -165988; -14263484148, -165988, 3586896727],[684, 4, 1],[-2133, 0, -4778, -18088, -22354, -944840, -31142, -46585, -121667, -41807, -10921, -193165; -280, 1, -665, -2457, -3019, -127395, -4195, -6266, -16340, -5598, -1456, -25650; -8482, 0, -19000, -71928, -88892, -3757212, -123838, -185248, -483816, -166248, -43428, -768132],225,4]
%
% END OF LATTICE L226.4
%
%
% LATTICE L226.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-171, -342, -171; -342, -646, -323; -171, -323, -161],[171, 19, 1],[25, 37, 5, 31, 7, 5, 0, -2, 0, 14, 18, 40; 21, 41, 7, 63, 23, 27, 9, 1, -1, -9, 7, 27; -76, -133, -21, -171, -57, -63, -19, 0, 2, 0, -38, -108],225,5]
%
% END OF LATTICE L226.5
%
%
% LATTICE L226.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-11091806244, -3253788, 29667816; -3253788, -954, 8703; 29667816, 8703, -79354],[684, 9, 1],[331, 255, 683, 27, 64, 120, 19, -10, -18, 8, 111, 545; 17886, 13792, 36974, 1464, 3478, 6536, 1044, -541, -1007, 429, 5987, 29431; 125712, 96849, 259407, 10255, 24309, 45581, 7218, -3798, -6840, 3038, 42156, 206986],225,6]
%
% END OF LATTICE L226.6
%
%
% LATTICE L226.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-318142764, -4191552, 465804; -4191552, -55214, 6137; 465804, 6137, -682],[684, 19, 1],[19, -1, -1, 7, 28, 74, 101, 85, 13, 101, 32, 34; -2, 2, 0, -18, -24, -54, -68, -51, -7, -45, -11, -9; 12958, -665, -683, 4617, 18905, 50049, 68362, 57589, 8815, 68571, 21755, 23139],225,7]
%
% END OF LATTICE L226.7
%
%
% LATTICE L226.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[103300037064, -785584260, -25977640104; -785584260, 5974920, 197556804; -25977640104, 197556804, 6532793255],[684, 36, 1],[1911443, 2854954, 7444456, 283334, 662984, 1297038, 127202, -851, 302395, 124395, 1375661, 6449813; 248, 371, 969, 37, 87, 171, 17, 0, 38, 16, 178, 836; 7600842, 11352708, 29602836, 1126676, 2636352, 5157664, 505818, -3384, 1202472, 494656, 5470308, 25647644],225,8]
%
% END OF LATTICE L226.8
%
%
% LATTICE L226.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1710, 1710, 171; 1710, 32661, 3591; 171, 3591, 395],[171, 171, 1],[128, 201, 29, 23, 61, 7, 17, 2, 0, 6, 84, 22; -1340, -2095, -301, -237, -623, -71, -170, -19, -1, -65, -887, -231; 12141, 18981, 2727, 2147, 5643, 643, 1539, 171, 9, 589, 8037, 2093],225,9]
%
% END OF LATTICE L226.9
%
%
% LATTICE L226.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[28228372200, 452124, -7098606036; 452124, 152, -113696; -7098606036, -113696, 1785090805],[684, 76, 1],[-55147, 0, -342, -233584, -343878, -799076, -512568, -794801, -113201, -788303, -223837, -222811; -153, 1, -1, -657, -965, -2241, -1437, -2227, -317, -2205, -625, -621; -219298, 0, -1360, -928872, -1367468, -3177612, -2038282, -3160612, -450156, -3134772, -890112, -886032],225,10]
%
% END OF LATTICE L226.10
%
%
% LATTICE L226.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-34523532, 38665836, -7723044; 38665836, -43305066, 8649693; -7723044, 8649693, -1727674],[684, 171, 1],[-14077, -11954, -1842, -1608, -4641, -553, -2833, 117, 151, -83, -3814, -1138; -68, -51, -7, -5, -11, -1, -2, 2, 0, -2, -24, -6; 62586, 53181, 8199, 7163, 20691, 2467, 12654, -513, -675, 361, 16929, 5057],225,11]
%
% END OF LATTICE L226.11
%
%
% LATTICE L226.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1368, 671004, -168264; 671004, 10926909576, -2740155984; -168264, -2740155984, 687152645],[684, 684, 1],[-13283, -20595, -2933, -2269, -5797, -641, -1427, 1, -9, -673, -8913, -2301; 962528, 1492463, 212559, 164457, 420243, 46477, 103517, 0, 650, 48752, 645802, 166732; 3838266, 5951484, 847620, 655804, 1675800, 185336, 412794, 0, 2592, 194408, 2575260, 664876],225,12]
%
% END OF LATTICE L226.12
%

\medskip%
%------------------------------WEYL-GROUP-W227--------------------------------
%
\leavevmode\llap{}%
$W_{227}$%
\qquad\llap{6} lattices, $\chi=8$%
\hfill%
$\slashthree22|22\rtimes D_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L227.1
%
\leavevmode%
${L_{227.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{1}{}3\above{1pt}{1pt}{-}{}9\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{-2}{}7\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${6}\above{1pt}{1pt}{+}{3}{6}\above{1pt}{1pt}{l}{2}{36}\above{1pt}{1pt}{r}{2}{42}\above{1pt}{1pt}{l}{2}{4}\above{1pt}{1pt}{r}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-203868\\-41580\\-24948
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-41580\\-8454\\-5115
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-24948\\-5115\\-3026
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-56\\172\\171
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
66\\-203\\-201
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
47\\-144\\-144
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-207\\637\\630
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-147\\452\\448
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-203868, -41580, -24948; -41580, -8454, -5115; -24948, -5115, -3026],[252, 3, 1],[-56, 66, 47, -207, -147; 172, -203, -144, 637, 452; 171, -201, -144, 630, 448],226,1]
%
% END OF LATTICE L227.1
%
%
% LATTICE L227.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-84798, -8001, -19215; -8001, -750, -1818; -19215, -1818, -4349],[63, 3, 1],[31, -54, -48, -95, 26; -98, 169, 151, 301, -81; -96, 168, 149, 294, -81],226,2]
%
% END OF LATTICE L227.2
%
%
% LATTICE L227.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-358470, -9261, 16254; -9261, -210, 420; 16254, 420, -737],[63, 21, 1],[-21, 40, 34, 9, -20; 2, -1, -2, -1, 0; -462, 882, 749, 198, -441],226,3]
%
% END OF LATTICE L227.3
%
%
% LATTICE L227.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[606260088, -12598740, -152605152; -12598740, 261816, 3171300; -152605152, 3171300, 38413105],[252, 12, 1],[-458, 3, -175, -1167, -212; -91, -1, -27, -196, -39; -1812, 12, -693, -4620, -839],226,4]
%
% END OF LATTICE L227.4
%
%
% LATTICE L227.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-350532, -10584, -84168; -10584, -210, -2541; -84168, -2541, -20210],[252, 21, 1],[126, -121, -289, -54, 121; 2, -1, -4, -1, 0; -525, 504, 1204, 225, -504],226,5]
%
% END OF LATTICE L227.5
%
%
% LATTICE L227.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[441125496, -258804, 111370140; -258804, 168, -65352; 111370140, -65352, 28117423],[252, 84, 1],[0, -2117, -965, -747, -778; 1, 6361, 2898, 2242, 2334; 0, 8400, 3829, 2964, 3087],226,6]
%
% END OF LATTICE L227.6
%

\medskip%
%------------------------------WEYL-GROUP-W228--------------------------------
%
\leavevmode\llap{}%
$W_{228}$%
\qquad\llap{6} lattices, $\chi=8$%
\hfill%
$6|62|2\rtimes D_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L228.1
%
\leavevmode%
${L_{228.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{-}{}9\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}7\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${2}\above{1pt}{1pt}{}{6}{6}\above{1pt}{1pt}{}{6}{18}\above{1pt}{1pt}{b}{2}{42}\above{1pt}{1pt}{b}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-115164\\-4536\\-33264
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-4536\\-174\\-1317
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-33264\\-1317\\-9598
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
10\\-41\\-29
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
26\\-110\\-75
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-28\\117\\81
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-51\\217\\147
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-115164, -4536, -33264; -4536, -174, -1317; -33264, -1317, -9598],[252, 3, 1],[10, 26, -28, -51; -41, -110, 117, 217; -29, -75, 81, 147],227,1]
%
% END OF LATTICE L228.1
%
%
% LATTICE L228.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-28791, 2268, -7623; 2268, -174, 603; -7623, 603, -2017],[63, 3, 1],[25, -23, -9, 45; 45, -40, -17, 77; -81, 75, 29, -147],227,2]
%
% END OF LATTICE L228.2
%
%
% LATTICE L228.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1953, 378, -63; 378, 294, 63; -63, 63, 5],[63, 21, 1],[-11, 10, 3, -3; -27, 23, 7, -7; 189, -168, -49, 51],227,3]
%
% END OF LATTICE L228.3
%
%
% LATTICE L228.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[64166760, -1874124, -16148412; -1874124, 54744, 471648; -16148412, 471648, 4063961],[252, 12, 1],[-557, -272, -263, -423; -11, -7, -9, -7; -2212, -1080, -1044, -1680],227,4]
%
% END OF LATTICE L228.4
%
%
% LATTICE L228.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-7812, 3024, -756; 3024, -462, 189; -756, 189, -58],[252, 21, 1],[8, -10, -2, 3; -27, 37, 7, -11; -189, 252, 49, -75],227,5]
%
% END OF LATTICE L228.5
%
%
% LATTICE L228.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[28362600, 1058148, 6383160; 1058148, 39480, 238140; 6383160, 238140, 1436567],[252, 84, 1],[509, 191, 71, -3; -1482, -559, -214, 8; -2016, -756, -280, 12],227,6]
%
% END OF LATTICE L228.6
%

\medskip%
%------------------------------WEYL-GROUP-W229--------------------------------
%
\leavevmode\llap{}%
$W_{229}$%
\qquad\llap{26} lattices, $\chi=36$%
\hfill%
$\slashtwo22|22\slashtwo22|22\rtimes D_{4}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L229.1
%
\leavevmode%
${L_{229.1}}$%
{} : {$1\above{1pt}{1pt}{2}{{\rm II}}4\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{1}{}3\above{1pt}{1pt}{-}{}9\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{2}{}7\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${36}\above{1pt}{1pt}{*}{2}{4}\above{1pt}{1pt}{*}{2}{252}\above{1pt}{1pt}{b}{2}{6}\above{1pt}{1pt}{b}{2}{28}\above{1pt}{1pt}{*}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1652364\\4788\\11088
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4788\\-12\\-33
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
11088\\-33\\-74
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4409\\252840\\546840
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-12\\-689\\-1488
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-30\\-1720\\-3721
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-54\\-126
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-58\\-124
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5\\252\\630
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\112\\249
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
31\\1764\\3850
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-1652364, 4788, 11088; 4788, -12, -33; 11088, -33, -74],[252, 3, 1],[-1, -1, 5, 2, 31, 19, 7, 121, 4, 11; -54, -58, 252, 112, 1764, 1086, 402, 6972, 232, 644; -126, -124, 630, 249, 3850, 2358, 868, 14994, 495, 1358],228,1]
%
% END OF LATTICE L229.1
%
\hbox{}\par\smallskip%
%
% LATTICE L229.2
%
\leavevmode%
${L_{229.2}}$%
{} : {$1\above{1pt}{1pt}{2}{2}8\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{1}{}9\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{2}{}7\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${2}\above{1pt}{1pt}{s}{2}{18}\above{1pt}{1pt}{b}{2}{56}\above{1pt}{1pt}{*}{2}{12}\above{1pt}{1pt}{*}{2}{504}\above{1pt}{1pt}{b}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-489384\\-8568\\-9072
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-8568\\-150\\-159
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-9072\\-159\\-163
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-4411\\244440\\7560
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-77\\4267\\132
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-84\\4656\\143
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\55\\2
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\57\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
25\\-1372\\-56
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
9\\-496\\-18
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
275\\-15204\\-504
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-489384, -8568, -9072; -8568, -150, -159; -9072, -159, -163],[504, 3, 1],[-1, -1, 25, 9, 275, 8, 22, 73, 5, 19; 55, 57, -1372, -496, -15204, -443, -1221, -4060, -280, -1092; 2, 0, -56, -18, -504, -14, -36, -112, -6, 0],228,2]
%
% END OF LATTICE L229.2
%
\hbox{}\par\smallskip%
%
% LATTICE L229.3
%
\leavevmode%
${L_{229.3}}$%
{} : {$1\above{1pt}{1pt}{-2}{6}16\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{1}{}3\above{1pt}{1pt}{-}{}9\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{2}{}7\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2,m}%
\EasyButWeakLineBreak%
{${36}\above{1pt}{1pt}{l}{2}{1}\above{1pt}{1pt}{}{2}{1008}\above{1pt}{1pt}{r}{2}{6}\above{1pt}{1pt}{l}{2}{112}\above{1pt}{1pt}{}{2}{9}\above{1pt}{1pt}{r}{2}{4}\above{1pt}{1pt}{*}{2}{1008}\above{1pt}{1pt}{b}{2}{6}\above{1pt}{1pt}{b}{2}{112}\above{1pt}{1pt}{*}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-216720\\4032\\9072
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4032\\-75\\-168
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
9072\\-168\\-335
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-54\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-56\\1
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
19\\1008\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4\\221\\-3
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
129\\7168\\-112
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
20\\1113\\-18
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
15\\836\\-14
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
527\\29400\\-504
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
9\\503\\-9
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
53\\2968\\-56
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-216720, 4032, 9072; 4032, -75, -168; 9072, -168, -335],[1008, 3, 1],[-1, -1, 19, 4, 129, 20, 15, 527, 9, 53; -54, -56, 1008, 221, 7168, 1113, 836, 29400, 503, 2968; 0, 1, 0, -3, -112, -18, -14, -504, -9, -56],228,3]
%
% END OF LATTICE L229.3
%
%
% LATTICE L229.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-315, 63, 63; 63, -12, -12; 63, -12, -11],[63, 3, 1],[0, -1, -3, -1, -5, 0, 1, 3, 1, 5; -1, -6, -7, 1, 63, 5, 18, 35, 7, 21; 1, 0, -14, -9, -126, -7, -18, -28, -3, 0],228,4]
%
% END OF LATTICE L229.4
%
%
% LATTICE L229.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-5922, -378, -504; -378, -24, -33; -504, -33, -37],[126, 3, 1],[-1, -1, 11, 4, 121, 7, 19, 31, 2, 5; 13, 15, -140, -52, -1596, -93, -255, -420, -28, -84; 2, 0, -28, -9, -252, -14, -36, -56, -3, 0],228,5]
%
% END OF LATTICE L229.5
%
%
% LATTICE L229.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-54180, 2016, 2016; 2016, -75, -75; 2016, -75, -74],[252, 3, 1],[-1, 0, 19, 2, 17, 4, 1, 23, 0, -3; -27, -1, 504, 56, 504, 123, 33, 840, 8, -56; 0, 1, 0, -3, -56, -18, -7, -252, -9, -28],228,6]
%
% END OF LATTICE L229.6
%
%
% LATTICE L229.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[12600, 4032, -504; 4032, 1290, -165; -504, -165, -37],[504, 3, 1],[10, -1, -253, -40, -2167, -59, -146, -433, -9, 109; -31, 3, 784, 124, 6720, 183, 453, 1344, 28, -336; 2, 0, -56, -9, -504, -14, -36, -112, -3, 0],228,7]
%
% END OF LATTICE L229.7
%
%
% LATTICE L229.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[64512, -10206, 32004; -10206, 1662, -5064; 32004, -5064, 15877],[126, 6, 1],[-1, -133, -521, -281, -3883, -431, -1163, -991, -151, -653; 0, 6, 21, 11, 147, 16, 42, 35, 5, 21; 2, 270, 1057, 570, 7875, 874, 2358, 2009, 306, 1323],228,8]
%
% END OF LATTICE L229.8
%
%
% LATTICE L229.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[63, -1134, 63; -1134, 19005, -1050; 63, -1050, 58],[63, 21, 1],[1, -1, -2, 0, 2, 11, 5, 14, 8, 2; 0, -2, -9, -8, -3, -6, 0, 3, 4, 1; 0, -35, -162, -147, -58, -126, -7, 36, 63, 16],228,9]
%
% END OF LATTICE L229.9
%
%
% LATTICE L229.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[315378, -102942, 3024; -102942, 33600, -987; 3024, -987, 29],[126, 21, 1],[1, 1, 1, 2, 11, 5, 17, 5, 4, 7; 1, 3, 4, 8, 36, 15, 45, 12, 8, 12; -70, 0, 32, 63, 72, -14, -252, -116, -147, -324],228,10]
%
% END OF LATTICE L229.10
%
%
% LATTICE L229.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[60904368, -1392300, -15475824; -1392300, 31848, 353784; -15475824, 353784, 3932413],[252, 12, 1],[-407, -31, -8612, -1866, -10924, -6133, -2149, -37168, -2494, -4336; 3, 0, 21, 5, 35, 21, 8, 147, 11, 21; -1602, -122, -33894, -7344, -42994, -24138, -8458, -146286, -9816, -17066],228,11]
%
% END OF LATTICE L229.11
%
%
% LATTICE L229.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[41076, 8820, -10332; 8820, 2616, -2208; -10332, -2208, 2599],[252, 12, 1],[-55, 1, -722, -330, -982, -1109, -389, -3352, -446, -376; 3, 0, 42, 19, 56, 63, 22, 189, 25, 21; -216, 4, -2835, -1296, -3857, -4356, -1528, -13167, -1752, -1477],228,12]
%
% END OF LATTICE L229.12
%
%
% LATTICE L229.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1029168, -19782, 506268; -19782, -462, -9744; 506268, -9744, 249043],[126, 42, 1],[-379, -3287, -95, 1137, 4771, 4803, 16559, 2307, 3287, 1865; -12, -102, -3, 35, 147, 148, 510, 71, 101, 57; 770, 6678, 193, -2310, -9693, -9758, -33642, -4687, -6678, -3789],228,13]
%
% END OF LATTICE L229.13
%
%
% LATTICE L229.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[39564, 25704, -1512; 25704, 16800, -987; -1512, -987, 58],[252, 21, 1],[-5, -17, -5, -4, -7, -1, -1, -1, -2, -11; -30, -114, -36, -32, -60, -10, -6, -4, -8, -60; -644, -2394, -746, -651, -1206, -196, -126, -94, -189, -1314],228,14]
%
% END OF LATTICE L229.14
%
%
% LATTICE L229.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[630756, -212436, 6048; -212436, 71547, -2037; 6048, -2037, 58],[252, 21, 1],[-5, -14, -7, -4, -5, 0, -1, -3, -6, -25; -15, -45, -24, -16, -24, -1, -3, -8, -16, -72; -7, -126, -116, -147, -324, -35, 0, 32, 63, 72],228,15]
%
% END OF LATTICE L229.15
%
%
% LATTICE L229.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1479240, 488376, -6552; 488376, 161238, -2163; -6552, -2163, 29],[504, 21, 1],[-5, -8, -1, 2, 13, 2, -1, -5, -5, -31; 15, 21, 0, -8, -48, -7, 3, 16, 16, 96; -14, -252, -232, -147, -648, -70, 0, 64, 63, 144],228,16]
%
% END OF LATTICE L229.16
%
%
% LATTICE L229.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[12214440, 1349712, -11592; 1349712, 149142, -1281; -11592, -1281, 11],[504, 21, 1],[2, 4, 1, -1, -5, -1, -1, 1, 3, 11; -11, -21, -4, 8, 36, 7, 9, -4, -16, -60; 826, 1764, 584, -126, -1080, -238, 0, 592, 1302, 4608],228,17]
%
% END OF LATTICE L229.17
%
%
% LATTICE L229.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-948528, 79128, -4032; 79128, -6600, 336; -4032, 336, -17],[504, 24, 1],[5, 13, 5, 1, -1, -1, -1, 2, 3, 22; 66, 168, 63, 11, -21, -14, -12, 28, 41, 294; 112, 216, 49, -24, -189, -40, 0, 77, 96, 567],228,18]
%
% END OF LATTICE L229.18
%
%
% LATTICE L229.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-694512, 114408, 50400; 114408, -18840, -8280; 50400, -8280, -3581],[504, 24, 1],[-191, -455, -319, -17, 187, 39, -1, -213, -135, -1783; -1332, -3174, -2226, -119, 1302, 272, -6, -1484, -941, -12432; 392, 936, 658, 36, -378, -80, 0, 434, 276, 3654],228,19]
%
% END OF LATTICE L229.19
%
%
% LATTICE L229.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-888048, -105840, 6048; -105840, -12369, 714; 6048, 714, -41],[1008, 21, 1],[11, 9, 47, 6, 5, -1, -1, -5, 1, 9; 81, 68, 360, 47, 40, -6, -8, -48, 5, 64; 3024, 2506, 13176, 1701, 1432, -252, -287, -1584, 231, 2432],228,20]
%
% END OF LATTICE L229.20
%
%
% LATTICE L229.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1224972, -36540, 338184; -36540, -1848, -7896; 338184, -7896, 91729],[252, 84, 1],[2523, 8699, 1212, 3454, 980, -199, -1727, -50, 1194, 2506; -7415, -25566, -3562, -10151, -2880, 585, 5076, 147, -3509, -7365; -9940, -34272, -4775, -13608, -3861, 784, 6804, 197, -4704, -9873],228,21]
%
% END OF LATTICE L229.21
%
%
% LATTICE L229.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-12288528, -187740, -2979396; -187740, -2856, -45528; -2979396, -45528, -722357],[252, 84, 1],[-517, -1829, -520, -770, -472, 25, 353, 28, -214, -1004; 1625, 5742, 1631, 2411, 1473, -81, -1110, -87, 677, 3159; 2030, 7182, 2042, 3024, 1854, -98, -1386, -110, 840, 3942],228,22]
%
% END OF LATTICE L229.22
%
%
% LATTICE L229.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-948528, 158256, -4032; 158256, -26400, 672; -4032, 672, -17],[1008, 48, 1],[-1, -1, -2, 2, 10, 13, 5, 22, 6, 2; -6, -7, -21, 11, 63, 84, 33, 147, 41, 14; 0, -40, -378, -48, 98, 216, 112, 567, 192, 77],228,23]
%
% END OF LATTICE L229.23
%
%
% LATTICE L229.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1008, -504, 0; -504, -778008, 6048; 0, 6048, -47],[504, 168, 1],[13, 9, 7, 9, 1, -1, -5, -4, -5, 0; 12, 14, 12, 17, 2, 0, -10, -9, -13, -1; 1512, 1792, 1539, 2184, 257, 0, -1288, -1161, -1680, -131],228,24]
%
% END OF LATTICE L229.24
%
%
% LATTICE L229.25
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1008, -7560, 2016; -7560, 53592, -14280; 2016, -14280, 3805],[504, 168, 1],[11, 5, 7, 4, 1, 1, -1, -1, 0, 1; -132, -14, 6, 23, 6, 0, -30, -72, -67, -28; -504, -56, 18, 84, 22, 0, -112, -270, -252, -106],228,25]
%
% END OF LATTICE L229.25
%
%
% LATTICE L229.26
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1008, 0, 0; 0, -3113040, 12096; 0, 12096, -47],[1008, 336, 1],[-7, -2, -1, -1, 0, 1, 0, -1, -3, -1; 6, 7, 6, 17, 1, 0, -5, -9, -13, -1; 1512, 1792, 1539, 4368, 257, 0, -1288, -2322, -3360, -262],228,26]
%
% END OF LATTICE L229.26
%

\medskip%
%------------------------------WEYL-GROUP-W230--------------------------------
%
\leavevmode\llap{}%
$W_{230}$%
\qquad\llap{52} lattices, $\chi=36$%
\hfill%
$\slashtwo22|22\slashtwo22|22\rtimes D_{4}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L230.1
%
\leavevmode%
${L_{230.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{2}8\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{1}{}3\above{1pt}{1pt}{1}{}9\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{2}{}7\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2m,2}%
\EasyButWeakLineBreak%
{${4}\above{1pt}{1pt}{*}{2}{36}\above{1pt}{1pt}{l}{2}{7}\above{1pt}{1pt}{}{2}{3}\above{1pt}{1pt}{}{2}{63}\above{1pt}{1pt}{r}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-6148296\\15120\\16128
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
15120\\-33\\-42
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
16128\\-42\\-41
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
44519\\6206088\\11138904
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-95\\-13244\\-23769
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-125\\-17425\\-31276
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
31\\4322\\7756
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
91\\12684\\22770
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
32\\4459\\8008
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\278\\501
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\273\\504
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-6148296, 15120, 16128; 15120, -33, -42; 16128, -42, -41],[504, 3, 1],[31, 91, 32, 2, 2, -1, -1, 3, 3, 103; 4322, 12684, 4459, 278, 273, -140, -138, 420, 419, 14364; 7756, 22770, 8008, 501, 504, -250, -252, 749, 750, 25767],229,1]
%
% END OF LATTICE L230.1
%
\hbox{}\par\smallskip%
%
% LATTICE L230.2
%
\leavevmode%
${L_{230.2}}$%
{} : {$1\above{1pt}{1pt}{2}{0}8\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{1}{}3\above{1pt}{1pt}{1}{}9\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{2}{}7\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{m}%
\EasyButWeakLineBreak%
{${4}\above{1pt}{1pt}{l}{2}{9}\above{1pt}{1pt}{}{2}{7}\above{1pt}{1pt}{r}{2}{12}\above{1pt}{1pt}{l}{2}{63}\above{1pt}{1pt}{}{2}{1}\above{1pt}{1pt}{r}{2}{36}\above{1pt}{1pt}{*}{2}{28}\above{1pt}{1pt}{l}{2}{3}\above{1pt}{1pt}{r}{2}{252}\above{1pt}{1pt}{*}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-54728856\\46872\\95760
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
46872\\-33\\-84
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
95760\\-84\\-167
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
59\\8242\\29680
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
86\\12012\\43263
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
60\\8379\\30184
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7\\976\\3522
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\273\\1008
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-140\\-503
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-138\\-504
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
13\\1820\\6538
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
6\\839\\3018
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
395\\55188\\198702
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-54728856, 46872, 95760; 46872, -33, -84; 95760, -84, -167],[504, 3, 1],[59, 86, 60, 7, 2, -1, -1, 13, 6, 395; 8242, 12012, 8379, 976, 273, -140, -138, 1820, 839, 55188; 29680, 43263, 30184, 3522, 1008, -503, -504, 6538, 3018, 198702],229,2]
%
% END OF LATTICE L230.2
%
\hbox{}\par\smallskip%
%
% LATTICE L230.3
%
\leavevmode%
${L_{230.3}}$%
{} : {$1\above{1pt}{1pt}{2}{2}8\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{1}{}3\above{1pt}{1pt}{1}{}9\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{2}{}7\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{m}%
\EasyButWeakLineBreak%
{${1}\above{1pt}{1pt}{}{2}{9}\above{1pt}{1pt}{r}{2}{28}\above{1pt}{1pt}{*}{2}{12}\above{1pt}{1pt}{*}{2}{252}\above{1pt}{1pt}{l}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2211048\\7056\\5040
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7056\\-15\\-18
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5040\\-18\\-11
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2519\\209160\\808920
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-11\\-914\\-3531
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-5\\-415\\-1606
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\82\\323
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\81\\324
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-84\\-322
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-82\\-324
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
17\\1428\\5418
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-2211048, 7056, 5040; 7056, -15, -18; 5040, -18, -11],[504, 3, 1],[1, 1, -1, -1, 17, 2, 8, 15, 3, 25; 82, 81, -84, -82, 1428, 167, 666, 1246, 248, 2058; 323, 324, -322, -324, 5418, 640, 2565, 4816, 966, 8064],229,3]
%
% END OF LATTICE L230.3
%
\hbox{}\par\smallskip%
%
% LATTICE L230.4
%
\leavevmode%
${L_{230.4}}$%
{} : {$[1\above{1pt}{1pt}{-}{}2\above{1pt}{1pt}{-}{}]\above{1pt}{1pt}{}{0}16\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{1}{}3\above{1pt}{1pt}{1}{}9\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{2}{}7\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${16}\above{1pt}{1pt}{s}{2}{36}\above{1pt}{1pt}{*}{2}{112}\above{1pt}{1pt}{l}{2}{3}\above{1pt}{1pt}{r}{2}{1008}\above{1pt}{1pt}{*}{2}{4}\above{1pt}{1pt}{s}{2}{144}\above{1pt}{1pt}{s}{2}{28}\above{1pt}{1pt}{*}{2}{48}\above{1pt}{1pt}{*}{2}{252}\above{1pt}{1pt}{s}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-60073776\\1097712\\-42336
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1097712\\-20058\\774
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-42336\\774\\-29
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7\\376\\-184
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-54\\18
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-37\\-1988\\952
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-7\\-376\\183
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-743\\-39900\\19656
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-53\\-2846\\1406
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-295\\-15840\\7848
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-97\\-5208\\2590
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-5\\-268\\144
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
25\\1344\\-630
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-60073776, 1097712, -42336; 1097712, -20058, 774; -42336, 774, -29],[1008, 6, 1],[7, -1, -37, -7, -743, -53, -295, -97, -5, 25; 376, -54, -1988, -376, -39900, -2846, -15840, -5208, -268, 1344; -184, 18, 952, 183, 19656, 1406, 7848, 2590, 144, -630],229,4]
%
% END OF LATTICE L230.4
%
\hbox{}\par\smallskip%
%
% LATTICE L230.5
%
\leavevmode%
${L_{230.5}}$%
{} : {$[1\above{1pt}{1pt}{-}{}2\above{1pt}{1pt}{1}{}]\above{1pt}{1pt}{}{2}16\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{1}{}3\above{1pt}{1pt}{1}{}9\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{2}{}7\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{m}%
\EasyButWeakLineBreak%
{${16}\above{1pt}{1pt}{l}{2}{9}\above{1pt}{1pt}{}{2}{112}\above{1pt}{1pt}{}{2}{3}\above{1pt}{1pt}{}{2}{1008}\above{1pt}{1pt}{}{2}{1}\above{1pt}{1pt}{r}{2}{144}\above{1pt}{1pt}{*}{2}{28}\above{1pt}{1pt}{s}{2}{48}\above{1pt}{1pt}{s}{2}{252}\above{1pt}{1pt}{*}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-209138832\\-3664080\\-1008
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3664080\\-64194\\-18
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1008\\-18\\1
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
213\\-12156\\-3992
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
170\\-9702\\-3195
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
523\\-29848\\-9856
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
14\\-799\\-267
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
209\\-11928\\-4032
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\-1
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-41\\2340\\792
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-13\\742\\266
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
15\\-856\\-264
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
641\\-36582\\-11970
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-209138832, -3664080, -1008; -3664080, -64194, -18; -1008, -18, 1],[1008, 6, 1],[213, 170, 523, 14, 209, 0, -41, -13, 15, 641; -12156, -9702, -29848, -799, -11928, 0, 2340, 742, -856, -36582; -3992, -3195, -9856, -267, -4032, -1, 792, 266, -264, -11970],229,5]
%
% END OF LATTICE L230.5
%
\hbox{}\par\smallskip%
%
% LATTICE L230.6
%
\leavevmode%
${L_{230.6}}$%
{} : {$[1\above{1pt}{1pt}{1}{}2\above{1pt}{1pt}{1}{}]\above{1pt}{1pt}{}{6}16\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{1}{}3\above{1pt}{1pt}{1}{}9\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{2}{}7\above{1pt}{1pt}{1}{}$}\EasyButWeakLineBreak%
{${16}\above{1pt}{1pt}{*}{2}{36}\above{1pt}{1pt}{s}{2}{112}\above{1pt}{1pt}{s}{2}{12}\above{1pt}{1pt}{s}{2}{1008}\above{1pt}{1pt}{s}{2}{4}\above{1pt}{1pt}{*}{2}{144}\above{1pt}{1pt}{l}{2}{7}\above{1pt}{1pt}{}{2}{48}\above{1pt}{1pt}{}{2}{63}\above{1pt}{1pt}{r}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1269072\\-35280\\14112
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-35280\\-978\\390
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
14112\\390\\-155
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\68\\80
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\72\\90
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5\\-336\\-392
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\-206\\-246
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
223\\-15456\\-18648
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
17\\-1180\\-1426
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
101\\-7020\\-8496
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
18\\-1253\\-1519
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5\\-352\\-432
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\-147\\-189
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-1269072, -35280, 14112; -35280, -978, 390; 14112, 390, -155],[1008, 6, 1],[-1, -1, 5, 3, 223, 17, 101, 18, 5, 2; 68, 72, -336, -206, -15456, -1180, -7020, -1253, -352, -147; 80, 90, -392, -246, -18648, -1426, -8496, -1519, -432, -189],229,6]
%
% END OF LATTICE L230.6
%
\hbox{}\par\smallskip%
%
% LATTICE L230.7
%
\leavevmode%
${L_{230.7}}$%
{} : {$[1\above{1pt}{1pt}{1}{}2\above{1pt}{1pt}{-}{}]\above{1pt}{1pt}{}{4}16\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{1}{}3\above{1pt}{1pt}{1}{}9\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{2}{}7\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{m}%
\EasyButWeakLineBreak%
{${16}\above{1pt}{1pt}{}{2}{9}\above{1pt}{1pt}{r}{2}{112}\above{1pt}{1pt}{*}{2}{12}\above{1pt}{1pt}{*}{2}{1008}\above{1pt}{1pt}{l}{2}{1}\above{1pt}{1pt}{}{2}{144}\above{1pt}{1pt}{}{2}{7}\above{1pt}{1pt}{r}{2}{48}\above{1pt}{1pt}{l}{2}{63}\above{1pt}{1pt}{}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
248976\\5040\\-2016
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5040\\102\\-42
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2016\\-42\\-41
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-97\\4744\\-112
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-70\\3423\\-81
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-193\\9436\\-224
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-5\\244\\-6
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5\\-252\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\-49\\1
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\-48\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-6\\294\\-7
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-21\\1028\\-24
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-164\\8022\\-189
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[248976, 5040, -2016; 5040, 102, -42; -2016, -42, -41],[1008, 6, 1],[-97, -70, -193, -5, 5, 1, 1, -6, -21, -164; 4744, 3423, 9436, 244, -252, -49, -48, 294, 1028, 8022; -112, -81, -224, -6, 0, 1, 0, -7, -24, -189],229,7]
%
% END OF LATTICE L230.7
%
%
% LATTICE L230.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[126, 0, 63; 0, -3, -12; 63, -12, -16],[63, 3, 1],[-1, -1, 5, 5, 167, 25, 73, 51, 3, 1; -8, -6, 42, 40, 1302, 194, 564, 392, 22, 0; 2, 0, -14, -12, -378, -56, -162, -112, -6, 0],229,8]
%
% END OF LATTICE L230.8
%
%
% LATTICE L230.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-7686, -504, -630; -504, -33, -42; -630, -42, -41],[126, 3, 1],[-1, -1, 4, 4, 64, 91, 31, 206, 6, 6; 15, 14, -63, -58, -917, -1302, -443, -2940, -85, -84; 0, 1, 0, -3, -56, -81, -28, -189, -6, -7],229,9]
%
% END OF LATTICE L230.9
%
%
% LATTICE L230.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[2772, -1008, -252; -1008, 366, 87; -252, 87, -16],[252, 3, 1],[-6, 1, 37, 30, 883, 129, 368, 250, 11, -22; -17, 3, 105, 85, 2499, 365, 1041, 707, 31, -63; 2, 0, -14, -12, -378, -56, -162, -112, -6, 0],229,10]
%
% END OF LATTICE L230.10
%
%
% LATTICE L230.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-47124, 1764, 2016; 1764, -66, -75; 2016, -75, -79],[252, 3, 1],[-1, -1, 6, 6, 206, 31, 91, 64, 4, 4; -29, -27, 175, 173, 5901, 887, 2601, 1827, 113, 105; 2, 0, -14, -12, -378, -56, -162, -112, -6, 0],229,11]
%
% END OF LATTICE L230.11
%
%
% LATTICE L230.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-6731172, -457884, 15120; -457884, -31146, 1026; 15120, 1026, -29],[252, 6, 1],[171, 965, 323, 23, -59, -21, -1, 103, 42, 2365; -2557, -14430, -4830, -344, 882, 314, 15, -1540, -628, -35364; -1313, -7416, -2485, -180, 441, 160, 9, -784, -321, -18144],229,12]
%
% END OF LATTICE L230.12
%
%
% LATTICE L230.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-21908376, 811440, 385560; 811440, -30054, -14280; 385560, -14280, -6781],[504, 6, 1],[19, -1, -93, -36, -1919, -137, -763, -251, -13, 67; 532, -27, -2604, -1009, -53844, -3845, -21420, -7049, -368, 1869; -40, 0, 196, 78, 4284, 308, 1728, 574, 36, -126],229,13]
%
% END OF LATTICE L230.13
%
%
% LATTICE L230.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-212229864, 7860384, -63504; 7860384, -291126, 2352; -63504, 2352, -19],[504, 6, 1],[-1, -1, 5, 3, 223, 17, 101, 36, 5, 4; -28, -27, 140, 83, 6132, 467, 2772, 987, 136, 105; -124, 0, 616, 246, 13608, 980, 5508, 1834, 120, -378],229,14]
%
% END OF LATTICE L230.14
%
%
% LATTICE L230.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[74214, -16884, 36918; -16884, 3894, -8400; 36918, -8400, 18365],[126, 6, 1],[-62, -1, -622, -225, -3218, -4519, -1526, -10067, -284, -345; 3, 0, 21, 8, 119, 168, 57, 378, 11, 14; 126, 2, 1260, 456, 6524, 9162, 3094, 20412, 576, 700],229,15]
%
% END OF LATTICE L230.15
%
%
% LATTICE L230.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[126, -1134, 63; -1134, 7665, -420; 63, -420, 23],[63, 21, 1],[-1, 1, 1, 5, 19, 19, 53, 5, 1, -1; -4, 0, 2, 10, 30, 28, 72, 6, -2, -6; -70, 0, 34, 168, 486, 448, 1134, 92, -42, -108],229,16]
%
% END OF LATTICE L230.16
%
%
% LATTICE L230.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-45486, 15120, -882; 15120, -5019, 294; -882, 294, -17],[126, 21, 1],[1, 2, 2, -1, -6, -64, -23, -23, -6, -1; 3, 4, 3, -4, -15, -156, -55, -54, -13, -2; 0, -35, -54, -21, 46, 567, 224, 243, 84, 17],229,17]
%
% END OF LATTICE L230.17
%
%
% LATTICE L230.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[296856, 69300, -74592; 69300, 16260, -17412; -74592, -17412, 18743],[252, 12, 1],[1, -119, -499, -379, -12713, -1909, -5605, -3953, -257, -643; 0, 6, 28, 22, 756, 114, 336, 238, 16, 42; 4, -468, -1960, -1488, -49896, -7492, -21996, -15512, -1008, -2520],229,18]
%
% END OF LATTICE L230.18
%
%
% LATTICE L230.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[5304600, 165060, -1327788; 165060, 5136, -41316; -1327788, -41316, 332357],[252, 12, 1],[1, -55, 99, 155, 7025, 1103, 3367, 2477, 213, 703; 0, 30, -28, -58, -2772, -438, -1344, -994, -88, -294; 4, -216, 392, 612, 27720, 4352, 13284, 9772, 840, 2772],229,19]
%
% END OF LATTICE L230.19
%
%
% LATTICE L230.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1196118, 41580, 589554; 41580, 1554, 20496; 589554, 20496, 290585],[126, 42, 1],[62, -193, -1028, -1799, -2828, -26675, -8678, -7843, -1158, -129; 3, -6, -33, -58, -91, -858, -279, -252, -37, -4; -126, 392, 2088, 3654, 5744, 54180, 17626, 15930, 2352, 262],229,20]
%
% END OF LATTICE L230.20
%
%
% LATTICE L230.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[223524, -76608, 2268; -76608, 26250, -777; 2268, -777, 23],[252, 21, 1],[-5, -17, -2, -2, -2, -1, -1, 0, 0, -4; -1, -15, -3, -7, -9, -5, -3, 1, 5, 3; 448, 1134, 92, -42, -108, -70, 0, 34, 168, 486],229,21]
%
% END OF LATTICE L230.21
%
%
% LATTICE L230.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[67788, -24192, -756; -24192, 8610, 273; -756, 273, 8],[252, 21, 1],[61, 170, 16, 3, -4, -4, 1, 3, 16, 61; 141, 393, 37, 7, -9, -9, 3, 7, 37, 141; 952, 2646, 248, 42, -72, -70, 0, 46, 252, 954],229,22]
%
% END OF LATTICE L230.22
%
%
% LATTICE L230.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-623448, -52920, 16128; -52920, -4020, 1212; 16128, 1212, -365],[504, 12, 1],[-1, -1, 6, 3, 206, 31, 91, 32, 4, 2; 141, 138, -847, -422, -28917, -4350, -12765, -4487, -559, -273; 424, 414, -2548, -1269, -86940, -13078, -38376, -13489, -1680, -819],229,23]
%
% END OF LATTICE L230.23
%
%
% LATTICE L230.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1131480, 11592, 3528; 11592, -60, -36; 3528, -36, -11],[504, 12, 1],[4, 8, 15, 3, 25, 1, 2, -1, -1, 17; -1, -3, -7, -2, -21, -1, -3, 0, 1, 0; 1280, 2565, 4816, 966, 8064, 323, 648, -322, -324, 5418],229,24]
%
% END OF LATTICE L230.24
%
%
% LATTICE L230.25
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-60984, -24696, 2016; -24696, -6279, 546; 2016, 546, -47],[504, 21, 1],[-1, -3, -1, 2, 7, 145, 51, 25, 6, 1; -18, -60, -21, 38, 137, 2844, 1002, 492, 119, 20; -252, -826, -288, 525, 1888, 39186, 13804, 6777, 1638, 275],229,25]
%
% END OF LATTICE L230.25
%
%
% LATTICE L230.26
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[655704, -1614816, -228816; -1614816, 3354456, 474789; -228816, 474789, 67201],[504, 21, 1],[41, 41, 44, -27, -110, -1186, -859, -865, -116, -39; 2784, 2785, 2988, -1838, -7476, -80601, -58376, -58782, -7882, -2650; -19530, -19537, -20961, 12894, 52445, 565425, 409514, 412362, 55293, 18590],229,26]
%
% END OF LATTICE L230.26
%
%
% LATTICE L230.27
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-323316, -68040, -2016; -68040, 6006, -1428; -2016, -1428, 37],[252, 42, 1],[-1, -101, -101, -169, -35, -331, -5, 91, 66, 33; 3, 300, 300, 502, 104, 984, 15, -270, -196, -98; 63, 6076, 6075, 10164, 2105, 19908, 301, -5472, -3969, -1984],229,27]
%
% END OF LATTICE L230.27
%
%
% LATTICE L230.28
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[53034408, 5885208, -49392; 5885208, 653079, -5481; -49392, -5481, 46],[504, 21, 1],[-1, 0, -1, -3, -7, -35, -12, -23, -5, -1; 9, -1, 6, 26, 66, 333, 115, 222, 50, 10; 0, -119, -360, -126, 344, 2079, 812, 1746, 588, 118],229,28]
%
% END OF LATTICE L230.28
%
%
% LATTICE L230.29
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-4707864, -784728, -186480; -784728, -130800, -31080; -186480, -31080, -7381],[504, 24, 1],[-19, 1, 113, 93, 2755, 403, 1151, 783, 35, -67; 133, -6, -791, -652, -19341, -2830, -8085, -5502, -247, 462; -80, 0, 476, 396, 11844, 1736, 4968, 3388, 156, -252],229,29]
%
% END OF LATTICE L230.29
%
%
% LATTICE L230.30
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-11493720, 1915704, -46368; 1915704, -319296, 7728; -46368, 7728, -187],[504, 24, 1],[-3, -1, 19, 17, 545, 81, 235, 163, 9, 1; -21, -6, 133, 118, 3759, 558, 1617, 1120, 61, 0; -124, 0, 784, 660, 20160, 2968, 8532, 5852, 288, -252],229,30]
%
% END OF LATTICE L230.30
%
%
% LATTICE L230.31
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-170698248, 27424656, -169848; 27424656, -4406088, 27288; -169848, 27288, -169],[504, 24, 1],[-2, -1, 12, 11, 356, 53, 154, 107, 6, 1; -15, -6, 91, 82, 2625, 390, 1131, 784, 43, 0; -412, 36, 2632, 2184, 66024, 9700, 27828, 19040, 912, -1008],229,31]
%
% END OF LATTICE L230.31
%
%
% LATTICE L230.32
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2581992, -860832, -424872; -860832, -286986, -141624; -424872, -141624, -69859],[504, 42, 1],[1, -221, -223, -377, -81, -803, -23, 179, 144, 73; -3, 884, 891, 1504, 321, 3156, 83, -732, -577, -292; 0, -448, -450, -756, -158, -1512, -28, 396, 294, 148],229,32]
%
% END OF LATTICE L230.32
%
%
% LATTICE L230.33
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-486360, 162288, -2520; 162288, -54138, 840; -2520, 840, -13],[504, 42, 1],[-1, -3, -2, -1, 2, 47, 9, 19, 3, 1; -3, -12, -9, -8, 5, 132, 27, 60, 11, 4; 0, -196, -198, -336, -74, -756, -28, 144, 126, 64],229,33]
%
% END OF LATTICE L230.33
%
%
% LATTICE L230.34
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[4002012, 70560, 963144; 70560, 924, 17220; 963144, 17220, 231617],[252, 84, 1],[6595, 20851, 2265, 1599, 667, -199, -1663, -133, 533, 5729; -19371, -61245, -6653, -4697, -1959, 585, 4887, 391, -1565, -16827; -25984, -82152, -8924, -6300, -2628, 784, 6552, 524, -2100, -22572],229,34]
%
% END OF LATTICE L230.34
%
%
% LATTICE L230.35
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[3860640, 194796, 836136; 194796, 9744, 42252; 836136, 42252, 181043],[252, 84, 1],[-1081, -4033, -501, -555, -247, 121, 1153, 181, 235, -713; 3157, 11787, 1465, 1625, 723, -355, -3381, -531, -691, 2079; 4256, 15876, 1972, 2184, 972, -476, -4536, -712, -924, 2808],229,35]
%
% END OF LATTICE L230.35
%
%
% LATTICE L230.36
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-555408, -111888, -4032; -111888, -22488, -816; -4032, -816, -29],[1008, 24, 1],[-1, 3, 13, -1, -37, -115, -21, -299, -3, -17; 3, -10, -42, 4, 126, 390, 71, 1008, 10, 56; 54, -136, -630, 24, 1582, 4968, 914, 13104, 135, 784],229,36]
%
% END OF LATTICE L230.36
%
%
% LATTICE L230.37
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-89712, -26208, 0; -26208, -7080, -24; 0, -24, 1],[1008, 24, 1],[39, 31, 95, 5, 37, 0, -7, -2, 3, 118; -132, -105, -322, -17, -126, 0, 24, 7, -10, -399; -3056, -2439, -7504, -402, -3024, -1, 576, 182, -216, -9198],229,37]
%
% END OF LATTICE L230.37
%
%
% LATTICE L230.38
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-60412464, 8615376, -96768; 8615376, -1228632, 13800; -96768, 13800, -155],[1008, 24, 1],[-1, -1, 5, 3, 223, 17, 101, 36, 5, 4; -8, -6, 42, 23, 1638, 124, 732, 259, 34, 21; -88, 90, 616, 174, 6552, 422, 2088, 574, -96, -630],229,38]
%
% END OF LATTICE L230.38
%
%
% LATTICE L230.39
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-9905616, 1651104, -20160; 1651104, -275208, 3360; -20160, 3360, -41],[1008, 24, 1],[77, 53, 89, 11, 3, -1, -1, 1, 3, 107; 525, 362, 609, 76, 21, -6, -7, 0, 20, 728; 5130, 3584, 6111, 816, 245, 0, -82, -504, 162, 7000],229,39]
%
% END OF LATTICE L230.39
%
%
% LATTICE L230.40
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[15810480, 302400, -24192; 302400, 5754, -462; -24192, -462, 37],[1008, 42, 1],[25, 5, 11, 1, 1, 1, -1, -1, -1, 1; 432, 90, 204, 20, 20, 18, -24, -24, -28, 16; 21672, 4382, 9720, 903, 904, 882, -952, -954, -1008, 850],229,40]
%
% END OF LATTICE L230.40
%
%
% LATTICE L230.41
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[111384, -228816, 8568; -228816, 418908, -15708; 8568, -15708, 589],[504, 84, 1],[64, 23, 23, 3, 1, -1, -2, -1, 1, 3; -2517, -910, -915, -122, -41, 42, 85, 45, -31, -117; -68040, -24598, -24732, -3297, -1108, 1134, 2296, 1215, -840, -3163],229,41]
%
% END OF LATTICE L230.41
%
%
% LATTICE L230.42
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[962640, 482832, -1008; 482832, 242130, -504; -1008, -504, 1],[1008, 42, 1],[-17, -1, 11, 13, 41, 193, 125, 28, 15, 0; 36, 2, -24, -28, -88, -414, -268, -60, -32, 0; 1008, 14, -936, -966, -2936, -13734, -8848, -1971, -1008, -1],229,42]
%
% END OF LATTICE L230.42
%
%
% LATTICE L230.43
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-15137136, -1664208, -3024; -1664208, -181230, -588; -3024, -588, 37],[1008, 42, 1],[-653, -5, 179, 65, 65, -1, -199, -199, -333, -69; 5868, 45, -1608, -584, -584, 9, 1788, 1788, 2992, 620; 39816, 301, -10944, -3969, -3968, 63, 12152, 12150, 20328, 4210],229,43]
%
% END OF LATTICE L230.43
%
%
% LATTICE L230.44
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2150568, 716688, -6048; 716688, -238812, 2016; -6048, 2016, -17],[504, 84, 1],[1, 1, 2, -1, -6, -32, -23, -23, -6, -1; 3, 2, 3, -4, -15, -78, -55, -54, -13, -2; 0, -119, -360, -126, 344, 2079, 1624, 1746, 588, 118],229,44]
%
% END OF LATTICE L230.44
%
%
% LATTICE L230.45
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1008, 0, 0; 0, -5082, -294; 0, -294, -17],[1008, 42, 1],[1, 0, -1, -1, -3, -7, -9, -2, -1, 0; 0, -2, -12, -2, 12, 36, 56, 15, 20, 1; 0, 35, 216, 42, -184, -567, -896, -243, -336, -17],229,45]
%
% END OF LATTICE L230.45
%
%
% LATTICE L230.46
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[504, 0, 0; 0, -25032, 3360; 0, 3360, -451],[504, 168, 1],[1, 0, -1, -2, -3, -28, -9, -8, -1, 0; 0, -15, -24, -11, 16, 207, 84, 93, 34, 7; 0, -112, -180, -84, 116, 1512, 616, 684, 252, 52],229,46]
%
% END OF LATTICE L230.46
%
%
% LATTICE L230.47
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[504, 0, 0; 0, -1848, 336; 0, 336, -61],[504, 168, 1],[1, 0, -1, -2, -3, -28, -9, -8, -1, 0; 0, -5, -6, 1, 14, 153, 56, 57, 16, 3; 0, -28, -36, 0, 68, 756, 280, 288, 84, 16],229,47]
%
% END OF LATTICE L230.47
%
%
% LATTICE L230.48
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[4001256, 1459080, -16128; 1459080, 531888, -5880; -16128, -5880, 65],[504, 168, 1],[1, -1, -1, 1, 5, 53, 19, 19, 5, 1; 0, -5, -6, 1, 14, 153, 56, 57, 16, 3; 252, -700, -792, 336, 2504, 26964, 9772, 9864, 2688, 520],229,48]
%
% END OF LATTICE L230.48
%
%
% LATTICE L230.49
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[3321360, 1208592, -11088; 1208592, 439320, -4032; -11088, -4032, 37],[1008, 168, 1],[-1, 1, 1, 1, 11, 5, 25, 1, -1, -1; -6, 3, 4, 4, 36, 15, 66, 2, -8, -6; -952, 630, 736, 735, 7200, 3122, 14616, 514, -1176, -954],229,49]
%
% END OF LATTICE L230.49
%
%
% LATTICE L230.50
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[992880, 2016, -1008; 2016, -168, 0; -1008, 0, 1],[1008, 168, 1],[-9, -14, -3, -1, -1, 0, 1, 0, -1, -2; -80, -123, -26, -8, -6, 1, 12, 0, -10, -18; -8848, -13734, -2936, -966, -936, 14, 1008, -1, -1008, -1971],229,50]
%
% END OF LATTICE L230.50
%
%
% LATTICE L230.51
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-809424, -272160, 2016; -272160, -89880, 672; 2016, 672, -5],[1008, 168, 1],[1, -1, -1, -1, 1, 25, 5, 11, 2, 1; 0, -4, -3, -2, 3, 72, 14, 30, 5, 2; 378, -952, -810, -672, 802, 19656, 3878, 8424, 1470, 664],229,51]
%
% END OF LATTICE L230.51
%
%
% LATTICE L230.52
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1008, 0, 0; 0, -239064, 2016; 0, 2016, -17],[1008, 168, 1],[-7, -9, -4, -1, 0, 1, 0, -1, -1, -3; 18, 28, 15, 10, 1, 0, -1, -6, -1, 6; 2079, 3248, 1746, 1176, 118, 0, -119, -720, -126, 688],229,52]
%
% END OF LATTICE L230.52
%

\medskip%
%------------------------------WEYL-GROUP-W231--------------------------------
%
\leavevmode\llap{}%
$W_{231}$%
\qquad\llap{8} lattices, $\chi=96$%
\hfill%
$2\infty2|2\infty22|22\infty2|2\infty22|2\rtimes D_{4}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L231.1
%
\leavevmode%
${L_{231.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{2}64\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{1}{}9\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{3}%
\EasyButWeakLineBreak%
{${576}\above{1pt}{1pt}{*}{2}{12}\above{1pt}{1pt}{48,25}{\infty z}{3}\above{1pt}{1pt}{r}{2}{576}\above{1pt}{1pt}{s}{2}{12}\above{1pt}{1pt}{48,1}{\infty z}{3}\above{1pt}{1pt}{}{2}{576}\above{1pt}{1pt}{r}{2}{2}\above{1pt}{1pt}{b}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
14400\\0\\-576
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\3\\-3
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-576\\-3\\26
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
383\\8832\\9792
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
10\\229\\255
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-24\\-552\\-613
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-349\\-8064\\-8928
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-27\\-622\\-690
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-10\\-229\\-255
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-181\\-4128\\-4608
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-17\\-386\\-432
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-9\\-203\\-228
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-205\\-4608\\-5184
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-22\\-25
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[14400, 0, -576; 0, 3, -3; -576, -3, 26],[576, 3, 1],[-349, -27, -10, -181, -17, -9, -205, -1, -35, -1, 0, -11, -3, -5, -179, -3; -8064, -622, -229, -4128, -386, -203, -4608, -22, -768, -22, -1, -288, -74, -119, -4224, -70; -8928, -690, -255, -4608, -432, -228, -5184, -25, -864, -24, 0, -288, -78, -129, -4608, -77],230,1]
%
% END OF LATTICE L231.1
%
%
% LATTICE L231.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[141888, -2304, -1920; -2304, 39, 31; -1920, 31, 26],[192, 1, 1],[-155, -14, -11, -19, -1, -1, -11, -1, -101, -14, -29, -109, -19, -55, -245, -7; -1216, -111, -90, -160, -9, -6, -64, -6, -704, -99, -210, -800, -141, -414, -1856, -54; -10048, -906, -708, -1216, -63, -66, -736, -67, -6656, -921, -1902, -7136, -1242, -3588, -15968, -455],230,2]
%
% END OF LATTICE L231.2
%
%
% LATTICE L231.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[7872, -960, -960; -960, 117, 117; -960, 117, 118],[192, 3, 1],[-533, -41, -15, -269, -25, -13, -293, -4, -43, -1, 0, -19, -5, -8, -283, -14; -3584, -274, -99, -1760, -162, -83, -1856, -24, -256, -6, -1, -160, -38, -57, -1984, -96; -864, -68, -26, -480, -46, -25, -576, -9, -96, -2, 1, 0, -4, -10, -384, -21],230,3]
%
% END OF LATTICE L231.3
%
%
% LATTICE L231.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1627200, 1152, -4032; 1152, 3, -3; -4032, -3, 10],[576, 3, 1],[-25, -2, -1, -1, 0, -1, -9, -2, -39, -5, -9, -31, -5, -13, -55, -4; -576, -47, -26, -32, -1, -22, -192, -42, -832, -107, -194, -672, -109, -286, -1216, -90; -10304, -825, -414, -416, 0, -408, -3680, -819, -16000, -2052, -3696, -12736, -2055, -5346, -22624, -1647],230,4]
%
% END OF LATTICE L231.4
%
%
% LATTICE L231.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-9600, -21312, 384; -21312, -46144, 832; 384, 832, -15],[192, 64, 1],[-7, -50, -34, -6, -25, -23, -5, -1, 0, 1, -1, -1, -10, -26, -9, -13; -25, -171, -105, -17, -63, -45, -8, 4, 1, 3, -15, -7, -57, -123, -40, -52; -1591, -10944, -6816, -1118, -4224, -3168, -590, 192, 55, 192, -864, -418, -3456, -7584, -2482, -3264],230,5]
%
% END OF LATTICE L231.5
%
%
% LATTICE L231.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[327552, 302784, -2496; 302784, 279360, -2304; -2496, -2304, 19],[192, 192, 1],[2, 6, 6, 4, 7, 9, 7, 5, 1, 1, -1, -1, -2, -2, -1, 1; -2, -1, 5, 5, 11, 17, 14, 12, 2, 1, -5, -5, -11, -17, -14, -12; 9, 640, 1376, 1122, 2240, 3232, 2610, 2112, 375, 256, -736, -738, -1600, -2336, -1842, -1344],230,6]
%
% END OF LATTICE L231.6
%
%
% LATTICE L231.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-866880, -128448, 5184; -128448, -18816, 768; 5184, 768, -31],[576, 192, 1],[-2, -1, 5, 5, 11, 17, 14, 4, 2, 1, -5, -5, -11, -17, -14, -4; -21, -50, -34, -18, -25, -23, -15, -1, 0, 1, -1, -3, -10, -26, -27, -13; -909, -1536, -96, 342, 1152, 2208, 1926, 640, 333, 192, -864, -918, -2112, -3552, -3078, -1024],230,7]
%
% END OF LATTICE L231.7
%
%
% LATTICE L231.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-14294592, -635328, 25920; -635328, -28032, 1152; 25920, 1152, -47],[576, 192, 1],[12, 49, 43, 9, 45, 55, 7, 28, 4, 7, -3, -1, -5, 1, 1, 20; -5, -23, -25, -6, -34, -50, -7, -39, -9, -26, -10, -1, -1, 1, 0, -3; 6482, 26400, 23040, 4802, 23904, 28992, 3673, 14400, 1966, 3168, -1920, -578, -2784, 576, 551, 10944],230,8]
%
% END OF LATTICE L231.8
%

\medskip%
%------------------------------WEYL-GROUP-W232--------------------------------
%
\leavevmode\llap{}%
$W_{232}$%
\qquad\llap{16} lattices, $\chi=12$%
\hfill%
$2|222|22\rtimes D_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L232.1
%
\leavevmode%
${L_{232.1}}$%
{} : {$[1\above{1pt}{1pt}{1}{}2\above{1pt}{1pt}{-}{}]\above{1pt}{1pt}{}{4}32\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{-}{}$}\EasyButWeakLineBreak%
{${96}\above{1pt}{1pt}{s}{2}{8}\above{1pt}{1pt}{*}{2}{96}\above{1pt}{1pt}{l}{2}{1}\above{1pt}{1pt}{}{2}{6}\above{1pt}{1pt}{r}{2}{4}\above{1pt}{1pt}{*}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
8160\\3936\\-96
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3936\\1898\\-46
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-96\\-46\\1
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
31\\-72\\-288
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\2\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-11\\24\\48
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\-1
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4\\-9\\-30
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7\\-16\\-58
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[8160, 3936, -96; 3936, 1898, -46; -96, -46, 1],[96, 2, 1],[31, -1, -11, 0, 4, 7; -72, 2, 24, 0, -9, -16; -288, 0, 48, -1, -30, -58],231,1]
%
% END OF LATTICE L232.1
%
\hbox{}\par\smallskip%
%
% LATTICE L232.2
%
\leavevmode%
${L_{232.2}}$%
{} : {$[1\above{1pt}{1pt}{1}{}2\above{1pt}{1pt}{1}{}]\above{1pt}{1pt}{}{0}32\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{-}{}$}\EasyButWeakLineBreak%
{${96}\above{1pt}{1pt}{}{2}{2}\above{1pt}{1pt}{r}{2}{96}\above{1pt}{1pt}{s}{2}{4}\above{1pt}{1pt}{*}{2}{24}\above{1pt}{1pt}{l}{2}{1}\above{1pt}{1pt}{}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-20640\\384\\384
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
384\\-2\\-8
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
384\\-8\\-7
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
19\\144\\864
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\7\\46
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\0\\48
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-8\\-46
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-6\\-48
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\8\\45
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-20640, 384, 384; 384, -2, -8; 384, -8, -7],[96, 2, 1],[19, 1, 1, -1, -1, 1; 144, 7, 0, -8, -6, 8; 864, 46, 48, -46, -48, 45],231,2]
%
% END OF LATTICE L232.2
%
\hbox{}\par\smallskip%
%
% LATTICE L232.3
%
\leavevmode%
${L_{232.3}}$%
{} : {$1\above{1pt}{1pt}{-}{3}4\above{1pt}{1pt}{1}{1}32\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{1}{}$}\EasyButWeakLineBreak%
{${12}\above{1pt}{1pt}{l}{2}{4}\above{1pt}{1pt}{}{2}{3}\above{1pt}{1pt}{r}{2}{32}\above{1pt}{1pt}{*}{2}{48}\above{1pt}{1pt}{s}{2}{32}\above{1pt}{1pt}{*}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-11040\\-288\\384
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-288\\4\\8
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
384\\8\\-13
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-12\\-42
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\5\\32
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\6\\33
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-4\\-32
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-5\\-30\\-168
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-5\\-36\\-176
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-11040, -288, 384; -288, 4, 8; 384, 8, -13],[96, 4, 1],[-1, 1, 1, -1, -5, -5; -12, 5, 6, -4, -30, -36; -42, 32, 33, -32, -168, -176],231,3]
%
% END OF LATTICE L232.3
%
\hbox{}\par\smallskip%
%
% LATTICE L232.4
%
\leavevmode%
${L_{232.4}}$%
{} : {$1\above{1pt}{1pt}{-}{3}4\above{1pt}{1pt}{1}{7}32\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{1}{}$}\EasyButWeakLineBreak%
{${12}\above{1pt}{1pt}{*}{2}{16}\above{1pt}{1pt}{l}{2}{3}\above{1pt}{1pt}{}{2}{32}\above{1pt}{1pt}{}{2}{12}\above{1pt}{1pt}{r}{2}{32}\above{1pt}{1pt}{s}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3360\\384\\0
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
384\\44\\0
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\-1
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\6\\-18
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\-10\\-8
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\-9\\-3
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\-8\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\9\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3\\24\\-16
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[3360, 384, 0; 384, 44, 0; 0, 0, -1],[96, 4, 1],[-1, 1, 1, 1, -1, -3; 6, -10, -9, -8, 9, 24; -18, -8, -3, 0, 0, -16],231,4]
%
% END OF LATTICE L232.4
%
%
% LATTICE L232.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-34656, -17664, 672; -17664, -8994, 342; 672, 342, -13],[96, 6, 1],[1, -1, -5, -1, 0, 1; -8, 2, 24, 6, 1, -4; -160, 0, 368, 105, 26, -54],231,5]
%
% END OF LATTICE L232.5
%
%
% LATTICE L232.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-32736, -4320, 1728; -4320, -570, 228; 1728, 228, -91],[96, 6, 1],[9, 2, 3, -1, -1, 1; -80, -15, -16, 10, 6, -11; -32, 0, 16, 6, -4, -9],231,6]
%
% END OF LATTICE L232.6
%
%
% LATTICE L232.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[8160, 96, -96; 96, -8, 0; -96, 0, 1],[96, 8, 1],[1, 0, -5, -1, -1, 0; 12, 1, -36, -8, -9, 0; 96, 4, -432, -90, -96, -1],231,7]
%
% END OF LATTICE L232.7
%
%
% LATTICE L232.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2208, 0, -1056; 0, 8, 0; -1056, 0, -505],[96, 8, 1],[139, 0, -23, 1, 29, 28; 0, 1, 0, -1, -3, -1; -288, 0, 48, -2, -60, -58],231,8]
%
% END OF LATTICE L232.8
%
%
% LATTICE L232.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-31584, -2400, 864; -2400, -132, 60; 864, 60, -23],[96, 12, 1],[1, 3, 1, -5, -3, -1; 6, 17, 4, -36, -18, -4; 53, 156, 46, -288, -160, -48],231,9]
%
% END OF LATTICE L232.9
%
%
% LATTICE L232.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[96, 0, 0; 0, -156, -60; 0, -60, -23],[96, 12, 1],[0, -1, -1, -3, 0, 1; -2, -10, 0, 16, 3, 0; 5, 24, -2, -48, -8, 0],231,10]
%
% END OF LATTICE L232.10
%
%
% LATTICE L232.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[7392, 4224, -288; 4224, 2320, -160; -288, -160, 11],[96, 16, 1],[-1, 0, 1, 3, 1, -1; -6, -1, 3, 10, 3, -6; -114, -16, 69, 224, 72, -112],231,11]
%
% END OF LATTICE L232.11
%
%
% LATTICE L232.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[480, 192, 0; 192, 80, 0; 0, 0, -1],[96, 16, 1],[-2, 0, 1, 1, -1, -3; 3, -1, -3, -2, 3, 6; -18, -8, -6, 0, 0, -16],231,12]
%
% END OF LATTICE L232.12
%
%
% LATTICE L232.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-34656, -8736, 672; -8736, -2136, 168; 672, 168, -13],[96, 24, 1],[7, 0, -3, -1, 1, 2; 12, 1, -4, -2, 1, 3; 512, 12, -208, -78, 64, 141],231,13]
%
% END OF LATTICE L232.13
%
%
% LATTICE L232.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-480, 0, -96; 0, 24, 0; -96, 0, -19],[96, 24, 1],[-3, 0, 7, 4, 1, -1; 0, 1, 0, -1, -1, -1; 16, 0, -32, -18, -4, 6],231,14]
%
% END OF LATTICE L232.14
%
%
% LATTICE L232.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[8544, 192, -96; 192, -48, 0; -96, 0, 1],[96, 48, 1],[-1, -1, 0, 1, 0, -3; -2, -3, 0, 4, 1, -4; -86, -96, -1, 96, 8, -240],231,15]
%
% END OF LATTICE L232.15
%
%
% LATTICE L232.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[96, 0, 0; 0, -1776, -384; 0, -384, -83],[96, 48, 1],[-1, -1, 0, 1, 0, -3; 5, -5, -3, 0, 7, 32; -22, 24, 14, 0, -32, -144],231,16]
%
% END OF LATTICE L232.16
%

\medskip%
%------------------------------WEYL-GROUP-W233--------------------------------
%
\leavevmode\llap{}%
$W_{233}$%
\qquad\llap{32} lattices, $\chi=24$%
\hfill%
$2\slashinfty222|22\rtimes D_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L233.1
%
\leavevmode%
${L_{233.1}}$%
{} : {$[1\above{1pt}{1pt}{1}{}2\above{1pt}{1pt}{1}{}]\above{1pt}{1pt}{}{2}32\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{1}{}9\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{3}%
\EasyButWeakLineBreak%
{${32}\above{1pt}{1pt}{l}{2}{3}\above{1pt}{1pt}{24,5}{\infty}{12}\above{1pt}{1pt}{*}{2}{32}\above{1pt}{1pt}{l}{2}{9}\above{1pt}{1pt}{}{2}{2}\above{1pt}{1pt}{r}{2}{36}\above{1pt}{1pt}{*}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3115872\\-67968\\25344
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-67968\\-1482\\552
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
25344\\552\\-205
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7\\-440\\-320
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\-190\\-141
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7\\-448\\-342
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
11\\-712\\-560
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\-69\\-63
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\63\\46
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\66\\54
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-3115872, -67968, 25344; -67968, -1482, 552; 25344, 552, -205],[288, 6, 1],[7, 3, 7, 11, 1, -1, -1; -440, -190, -448, -712, -69, 63, 66; -320, -141, -342, -560, -63, 46, 54],232,1]
%
% END OF LATTICE L233.1
%
\hbox{}\par\smallskip%
%
% LATTICE L233.2
%
\leavevmode%
${L_{233.2}}$%
{} : {$[1\above{1pt}{1pt}{-}{}2\above{1pt}{1pt}{1}{}]\above{1pt}{1pt}{}{2}32\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{1}{}9\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{3}%
\EasyButWeakLineBreak%
{${32}\above{1pt}{1pt}{}{2}{3}\above{1pt}{1pt}{24,17}{\infty}{12}\above{1pt}{1pt}{s}{2}{32}\above{1pt}{1pt}{s}{2}{36}\above{1pt}{1pt}{*}{2}{8}\above{1pt}{1pt}{l}{2}{9}\above{1pt}{1pt}{}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-4736736\\310176\\-9216
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
310176\\-20310\\606
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-9216\\606\\-13
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
67\\1008\\-512
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
23\\346\\-177
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
25\\376\\-198
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-17\\-256\\112
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-65\\-978\\486
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-23\\-346\\176
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-15\\9
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-4736736, 310176, -9216; 310176, -20310, 606; -9216, 606, -13],[288, 6, 1],[67, 23, 25, -17, -65, -23, -1; 1008, 346, 376, -256, -978, -346, -15; -512, -177, -198, 112, 486, 176, 9],232,2]
%
% END OF LATTICE L233.2
%
\hbox{}\par\smallskip%
%
% LATTICE L233.3
%
\leavevmode%
${L_{233.3}}$%
{} : {$1\above{1pt}{1pt}{1}{1}4\above{1pt}{1pt}{1}{7}32\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{1}{}3\above{1pt}{1pt}{-}{}9\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{3}%
\EasyButWeakLineBreak%
{${1}\above{1pt}{1pt}{}{2}{96}\above{1pt}{1pt}{12,11}{\infty}{96}\above{1pt}{1pt}{s}{2}{4}\above{1pt}{1pt}{*}{2}{288}\above{1pt}{1pt}{s}{2}{16}\above{1pt}{1pt}{*}{2}{288}\above{1pt}{1pt}{l}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-277920\\-7776\\2592
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-7776\\-84\\60
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2592\\60\\-23
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\14\\149
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
11\\152\\1632
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5\\64\\720
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-16\\-158
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-19\\-276\\-2880
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3\\-42\\-448
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-12\\-144
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-277920, -7776, 2592; -7776, -84, 60; 2592, 60, -23],[288, 12, 1],[1, 11, 5, -1, -19, -3, -1; 14, 152, 64, -16, -276, -42, -12; 149, 1632, 720, -158, -2880, -448, -144],232,3]
%
% END OF LATTICE L233.3
%
\hbox{}\par\smallskip%
%
% LATTICE L233.4
%
\leavevmode%
${L_{233.4}}$%
{} : {$1\above{1pt}{1pt}{-}{5}4\above{1pt}{1pt}{1}{1}32\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{1}{}3\above{1pt}{1pt}{-}{}9\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{3}%
\EasyButWeakLineBreak%
{${1}\above{1pt}{1pt}{r}{2}{96}\above{1pt}{1pt}{24,23}{\infty z}{96}\above{1pt}{1pt}{*}{2}{4}\above{1pt}{1pt}{s}{2}{288}\above{1pt}{1pt}{l}{2}{4}\above{1pt}{1pt}{}{2}{288}\above{1pt}{1pt}{}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
288\\0\\0
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\-156\\-60
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\-60\\-23
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\-2\\5
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-20\\48
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3\\-4\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\4\\-14
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-5\\48\\-144
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\3\\-8
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\0\\0
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[288, 0, 0; 0, -156, -60; 0, -60, -23],[288, 12, 1],[0, -1, -3, -1, -5, 0, 1; -2, -20, -4, 4, 48, 3, 0; 5, 48, 0, -14, -144, -8, 0],232,4]
%
% END OF LATTICE L233.4
%
%
% LATTICE L233.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[108192, -2016, -1632; -2016, 38, 30; -1632, 30, 25],[96, 2, 1],[5, 1, 1, 9, 3, 1, 1; 152, 30, 27, 248, 84, 29, 30; 144, 30, 33, 288, 94, 30, 29],232,5]
%
% END OF LATTICE L233.5
%
%
% LATTICE L233.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[102432, 25728, -3552; 25728, 6462, -892; -3552, -892, 123],[96, 2, 1],[-37, -5, 4, 15, 0, -7, -13; 176, 24, -18, -64, 1, 34, 62; 208, 30, -15, -32, 7, 44, 74],232,6]
%
% END OF LATTICE L233.6
%
%
% LATTICE L233.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-27552, -8448, 672; -8448, -2564, 200; 672, 200, -15],[96, 4, 1],[-4, -5, 29, 9, 11, -5, -23; 20, 24, -144, -44, -52, 26, 116; 87, 96, -624, -186, -208, 120, 512],232,7]
%
% END OF LATTICE L233.7
%
%
% LATTICE L233.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-71904, -2496, 1056; -2496, -44, 32; 1056, 32, -15],[96, 4, 1],[2, 1, -13, -3, -1, 2, 13; 20, 12, -132, -32, -16, 19, 128; 183, 96, -1200, -282, -112, 180, 1184],232,8]
%
% END OF LATTICE L233.8
%
%
% LATTICE L233.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-40224, 192, 480; 192, 18, -6; 480, -6, -5],[96, 6, 1],[17, 3, 1, 5, -1, -1, 1; 264, 46, 15, 72, -16, -15, 16; 1296, 230, 77, 384, -78, -78, 75],232,9]
%
% END OF LATTICE L233.9
%
%
% LATTICE L233.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[96, 0, 0; 0, -6, 0; 0, 0, 1],[96, 6, 1],[-11, -1, 0, 1, 0, -1, -3; 48, 4, 0, 0, 1, 6, 14; 48, 2, -1, 0, 3, 12, 18],232,10]
%
% END OF LATTICE L233.10
%
%
% LATTICE L233.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[82848, 47424, -1440; 47424, 27144, -824; -1440, -824, 25],[96, 8, 1],[-7, -1, 4, 13, 3, 0, -1; 20, 3, -9, -28, -6, 1, 3; 256, 42, -66, -176, -26, 32, 41],232,11]
%
% END OF LATTICE L233.11
%
%
% LATTICE L233.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[102432, 51456, -3552; 51456, 25848, -1784; -3552, -1784, 123],[96, 8, 1],[-37, -5, 4, 15, 0, -7, -13; 88, 12, -9, -32, 1, 17, 31; 208, 30, -15, -32, 14, 44, 74],232,12]
%
% END OF LATTICE L233.12
%
%
% LATTICE L233.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-10464, -1920, 384; -1920, -252, 60; 384, 60, -13],[96, 12, 1],[-7, -3, 3, 1, -1, -5, -19; -48, -24, 16, 6, -4, -30, -124; -438, -208, 160, 57, -48, -288, -1152],232,13]
%
% END OF LATTICE L233.13
%
%
% LATTICE L233.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[96, 0, 0; 0, 12, 0; 0, 0, -1],[96, 12, 1],[-3, -3, -1, 0, 1, 0, -5; -2, -4, -4, -1, 0, 1, 0; -30, -32, -16, -3, 0, 0, -48],232,14]
%
% END OF LATTICE L233.14
%
%
% LATTICE L233.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-138144, 62976, -1440; 62976, -28688, 656; -1440, 656, -15],[96, 16, 1],[0, -1, 1, 1, 3, 1, 1; 2, 0, -12, -2, 2, 5, 14; 87, 96, -624, -186, -208, 120, 512],232,15]
%
% END OF LATTICE L233.15
%
%
% LATTICE L233.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-51168, -3840, 768; -3840, -112, 48; 768, 48, -11],[96, 16, 1],[3, 1, -13, -4, -5, 2, 9; 15, 6, -66, -21, -28, 9, 44; 274, 96, -1200, -374, -480, 176, 816],232,16]
%
% END OF LATTICE L233.16
%
%
% LATTICE L233.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[404640, 9792, -3168; 9792, 246, -78; -3168, -78, 25],[288, 6, 1],[5, 0, 1, 17, 1, 2, 1; 168, -1, 38, 648, 38, 75, 36; 1152, -3, 246, 4176, 245, 486, 238],232,17]
%
% END OF LATTICE L233.17
%
%
% LATTICE L233.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[7200, 1152, -864; 1152, 138, -114; -864, -114, 91],[288, 6, 1],[-11, -1, 1, 25, 3, 5, 0; -144, -14, 16, 384, 46, 78, 1; -288, -27, 30, 720, 86, 144, 1],232,18]
%
% END OF LATTICE L233.18
%
%
% LATTICE L233.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[8928, 96, -96; 96, -24, 0; -96, 0, 1],[96, 24, 1],[-11, -1, 0, 1, 0, -1, -3; -20, -2, 0, 4, 1, -1, -5; -1008, -94, -1, 96, 6, -84, -270],232,19]
%
% END OF LATTICE L233.19
%
%
% LATTICE L233.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-29472, -1824, 384; -1824, -72, 24; 384, 24, -5],[96, 24, 1],[1, 1, 2, 13, 1, -1, -1; -4, -1, -1, -4, 0, 1, 0; 48, 70, 146, 960, 75, -72, -78],232,20]
%
% END OF LATTICE L233.20
%
%
% LATTICE L233.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-266400, 48672, 2880; 48672, -8868, -528; 2880, -528, -31],[288, 12, 1],[-11, -13, 5, 8, 15, 11, -3; -36, -40, 16, 24, 44, 30, -12; -414, -528, 192, 333, 640, 504, -80],232,21]
%
% END OF LATTICE L233.21
%
%
% LATTICE L233.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-15840, 4896, -864; 4896, -1164, 192; -864, 192, -31],[288, 12, 1],[-1, -5, 1, 4, 9, 5, 3; -24, -92, 20, 72, 160, 87, 48; -126, -432, 96, 333, 736, 396, 208],232,22]
%
% END OF LATTICE L233.22
%
%
% LATTICE L233.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[96, 0, 0; 0, -14352, 432; 0, 432, -13],[96, 48, 1],[0, -1, -3, -3, -5, 0, 1; 1, 2, -6, -10, -24, -5, 0; 33, 64, -208, -342, -816, -168, 0],232,23]
%
% END OF LATTICE L233.23
%
%
% LATTICE L233.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[96, 0, 0; 0, 48, 0; 0, 0, -1],[96, 48, 1],[-3, -3, -1, 0, 1, 0, -5; -1, -2, -2, -1, 0, 1, 0; -30, -32, -16, -6, 0, 0, -48],232,24]
%
% END OF LATTICE L233.24
%
%
% LATTICE L233.25
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1633248, 459360, -4608; 459360, -129192, 1296; -4608, 1296, -13],[288, 24, 1],[3, 1, 0, -1, -1, 0, 2; 8, 4, 1, 0, -3, -1, 3; -272, 42, 99, 352, 54, -100, -414],232,25]
%
% END OF LATTICE L233.25
%
%
% LATTICE L233.26
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[650016, 69696, -4032; 69696, 7464, -432; -4032, -432, 25],[288, 24, 1],[1, 0, -1, -11, -1, -1, 0; 24, 1, -7, -72, -6, -3, 1; 576, 18, -282, -3024, -266, -216, 17],232,26]
%
% END OF LATTICE L233.26
%
%
% LATTICE L233.27
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-88416, 42912, 4896; 42912, -15000, -1728; 4896, -1728, -199],[288, 24, 1],[7, 4, 3, 3, -1, -1, 1; -548, -317, -241, -244, 78, 81, -75; 4928, 2850, 2166, 2192, -702, -728, 675],232,27]
%
% END OF LATTICE L233.27
%
%
% LATTICE L233.28
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1348128, 153216, -9504; 153216, 17400, -1080; -9504, -1080, 67],[288, 24, 1],[13, 0, -1, 1, 1, 5, 2; -24, -2, -2, 0, 1, 3, -1; 1440, -33, -174, 144, 158, 756, 266],232,28]
%
% END OF LATTICE L233.28
%
%
% LATTICE L233.29
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[288, 0, 0; 0, -19632, 672; 0, 672, -23],[288, 48, 1],[0, -1, -3, -1, -5, 0, 1; 1, 10, 2, -2, -24, -3, 0; 29, 288, 48, -62, -720, -88, 0],232,29]
%
% END OF LATTICE L233.29
%
%
% LATTICE L233.30
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[288, 0, 0; 0, -1776, -384; 0, -384, -83],[288, 48, 1],[0, -1, -3, -1, -5, 0, 1; -3, -10, 22, 13, 96, 7, 0; 14, 48, -96, -58, -432, -32, 0],232,30]
%
% END OF LATTICE L233.30
%
%
% LATTICE L233.31
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1807776, 811296, -7488; 811296, -364080, 3360; -7488, 3360, -31],[288, 48, 1],[-1, -5, 1, 4, 9, 10, 3; -6, -16, 4, 12, 26, 27, 6; -414, -528, 192, 333, 640, 504, -80],232,31]
%
% END OF LATTICE L233.31
%
%
% LATTICE L233.32
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-38304, -11232, 864; -11232, -2928, 240; 864, 240, -19],[288, 48, 1],[5, 1, -5, -4, -1, 4, 5; 15, 4, -16, -15, -6, 9, 14; 414, 96, -432, -378, -128, 288, 400],232,32]
%
% END OF LATTICE L233.32
%

\medskip%
%------------------------------WEYL-GROUP-W234--------------------------------
%
\leavevmode\llap{}%
$W_{234}$%
\qquad\llap{6} lattices, $\chi=12$%
\hfill%
$\slashtwo|\slashtwo|\slashtwo|\slashtwo|\slashtwo|\slashtwo|\rtimes D_{12}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L234.1
%
\leavevmode%
${L_{234.1}}$%
{} : {$1\above{1pt}{1pt}{2}{2}16\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{1}{}3\above{1pt}{1pt}{-}{}9\above{1pt}{1pt}{1}{}$}\EasyButWeakLineBreak%
{${36}\above{1pt}{1pt}{s}{2}{16}\above{1pt}{1pt}{l}{2}{9}\above{1pt}{1pt}{}{2}{1}\above{1pt}{1pt}{r}{2}{144}\above{1pt}{1pt}{s}{2}{4}\above{1pt}{1pt}{*}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-22320\\432\\144
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
432\\-3\\-6
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
144\\-6\\1
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-36\\-54
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\32\\56
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\33\\54
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\-1
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-5\\-168\\-288
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-34\\-56
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-22320, 432, 144; 432, -3, -6; 144, -6, 1],[144, 3, 1],[-1, 1, 1, 0, -5, -1; -36, 32, 33, 0, -168, -34; -54, 56, 54, -1, -288, -56],233,1]
%
% END OF LATTICE L234.1
%
\hbox{}\par\smallskip%
%
% LATTICE L234.2
%
\leavevmode%
${L_{234.2}}$%
{} : {$1\above{1pt}{1pt}{-}{5}4\above{1pt}{1pt}{1}{1}16\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{1}{}3\above{1pt}{1pt}{-}{}9\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{3}%
\EasyButWeakLineBreak%
{${36}\above{1pt}{1pt}{r}{2}{16}\above{1pt}{1pt}{s}{2}{36}\above{1pt}{1pt}{l}{2}{4}\above{1pt}{1pt}{}{2}{144}\above{1pt}{1pt}{}{2}{1}\above{1pt}{1pt}{}{2}$}%
\nopagebreak\par%
shares genus with 2-dual${}\iso{}$3-dual; isometric to own %
2.3-dual\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3312\\720\\0
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
720\\-12\\-12
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\-12\\1
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\9\\108
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\4\\56
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-6\\-54
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-5\\-56
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-5\\-24\\-288
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\-1
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-3312, 720, 0; 720, -12, -12; 0, -12, 1],[144, 12, 1],[2, 1, -1, -1, -5, 0; 9, 4, -6, -5, -24, 0; 108, 56, -54, -56, -288, -1],233,2]
%
% END OF LATTICE L234.2
%
%
% LATTICE L234.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-2928, 1056, -144; 1056, -380, 52; -144, 52, -7],[48, 4, 1],[-1, -1, 1, 1, 0, -3; -2, -1, 4, 2, -1, -8; 5, 12, 8, -6, -8, 0],233,3]
%
% END OF LATTICE L234.3
%
%
% LATTICE L234.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1680, -1056, 288; -1056, -660, 180; 288, 180, -49],[48, 12, 1],[1, 1, -1, -1, 1, 2; 1, 12, 5, 0, -8, -3; 9, 48, 12, -6, -24, 0],233,4]
%
% END OF LATTICE L234.4
%
%
% LATTICE L234.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[119376, 864, -1728; 864, -12, -12; -1728, -12, 25],[144, 12, 1],[1, 2, 4, 3, -1, -1; 0, 3, 6, 4, -3, -2; 72, 140, 279, 208, -72, -70],233,5]
%
% END OF LATTICE L234.5
%
%
% LATTICE L234.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[144, 0, 0; 0, 2832, -192; 0, -192, 13],[144, 48, 1],[1, 0, -1, -1, -2, 0; 0, 1, 6, 6, 15, 1; 0, 16, 90, 88, 216, 14],233,6]
%
% END OF LATTICE L234.6
%

\medskip%
%------------------------------WEYL-GROUP-W235--------------------------------
%
\leavevmode\llap{}%
$W_{235}$%
\qquad\llap{34} lattices, $\chi=24$%
\hfill%
$2|22|22|22|2\rtimes D_{4}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L235.1
%
\leavevmode%
${L_{235.1}}$%
{} : {$[1\above{1pt}{1pt}{1}{}2\above{1pt}{1pt}{1}{}]\above{1pt}{1pt}{}{6}32\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{-}{}9\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{3}%
\EasyButWeakLineBreak%
{${288}\above{1pt}{1pt}{*}{2}{8}\above{1pt}{1pt}{s}{2}{288}\above{1pt}{1pt}{*}{2}{24}\above{1pt}{1pt}{s}{2}{32}\above{1pt}{1pt}{*}{2}{72}\above{1pt}{1pt}{s}{2}{32}\above{1pt}{1pt}{*}{2}{24}\above{1pt}{1pt}{s}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3168\\-1728\\-864
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1728\\-930\\-456
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-864\\-456\\-217
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
119\\-360\\288
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
11\\-34\\28
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
53\\-168\\144
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\2\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-13\\40\\-32
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-13\\42\\-36
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
9\\-24\\16
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
21\\-62\\48
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-3168, -1728, -864; -1728, -930, -456; -864, -456, -217],[288, 6, 1],[119, 11, 53, -1, -13, -13, 9, 21; -360, -34, -168, 2, 40, 42, -24, -62; 288, 28, 144, 0, -32, -36, 16, 48],234,1]
%
% END OF LATTICE L235.1
%
\hbox{}\par\smallskip%
%
% LATTICE L235.2
%
\leavevmode%
${L_{235.2}}$%
{} : {$[1\above{1pt}{1pt}{-}{}2\above{1pt}{1pt}{1}{}]\above{1pt}{1pt}{}{2}64\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{1}{}3\above{1pt}{1pt}{1}{}9\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{3m,3,m}%
\EasyButWeakLineBreak%
{${576}\above{1pt}{1pt}{}{2}{1}\above{1pt}{1pt}{r}{2}{576}\above{1pt}{1pt}{*}{2}{12}\above{1pt}{1pt}{s}{2}{64}\above{1pt}{1pt}{s}{2}{36}\above{1pt}{1pt}{*}{2}{64}\above{1pt}{1pt}{l}{2}{3}\above{1pt}{1pt}{}{2}$}%
\nopagebreak\par%
shares genus with 3-dual\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
318528\\159552\\-576
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
159552\\79914\\-288
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-576\\-288\\1
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
91\\-192\\-2880
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\-1
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-23\\48\\576
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\2\\6
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
15\\-32\\-544
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
17\\-36\\-558
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
53\\-112\\-1696
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
9\\-19\\-285
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[318528, 159552, -576; 159552, 79914, -288; -576, -288, 1],[576, 6, 1],[91, 0, -23, -1, 15, 17, 53, 9; -192, 0, 48, 2, -32, -36, -112, -19; -2880, -1, 576, 6, -544, -558, -1696, -285],234,2]
%
% END OF LATTICE L235.2
%
\hbox{}\par\smallskip%
%
% LATTICE L235.3
%
\leavevmode%
${L_{235.3}}$%
{} : {$1\above{1pt}{1pt}{1}{1}4\above{1pt}{1pt}{1}{1}32\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{1}{}3\above{1pt}{1pt}{1}{}9\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{3}%
\EasyButWeakLineBreak%
{${36}\above{1pt}{1pt}{l}{2}{4}\above{1pt}{1pt}{}{2}{9}\above{1pt}{1pt}{r}{2}{48}\above{1pt}{1pt}{*}{2}{4}\above{1pt}{1pt}{l}{2}{36}\above{1pt}{1pt}{}{2}{1}\above{1pt}{1pt}{r}{2}{48}\above{1pt}{1pt}{*}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1685088\\10944\\10944
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
10944\\-60\\-72
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
10944\\-72\\-71
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
29\\336\\4122
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4\\47\\568
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4\\48\\567
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-10\\-144
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-12\\-142
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\9\\144
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\34\\427
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
27\\310\\3840
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-1685088, 10944, 10944; 10944, -60, -72; 10944, -72, -71],[288, 12, 1],[29, 4, 4, -1, -1, 1, 3, 27; 336, 47, 48, -10, -12, 9, 34, 310; 4122, 568, 567, -144, -142, 144, 427, 3840],234,3]
%
% END OF LATTICE L235.3
%
\hbox{}\par\smallskip%
%
% LATTICE L235.4
%
\leavevmode%
${L_{235.4}}$%
{} : {$1\above{1pt}{1pt}{-}{5}4\above{1pt}{1pt}{1}{7}32\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{1}{}3\above{1pt}{1pt}{1}{}9\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{3}%
\EasyButWeakLineBreak%
{${36}\above{1pt}{1pt}{*}{2}{16}\above{1pt}{1pt}{l}{2}{9}\above{1pt}{1pt}{}{2}{12}\above{1pt}{1pt}{r}{2}{4}\above{1pt}{1pt}{*}{2}{144}\above{1pt}{1pt}{l}{2}{1}\above{1pt}{1pt}{}{2}{12}\above{1pt}{1pt}{r}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2571552\\27072\\13536
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
27072\\-276\\-144
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
13536\\-144\\-71
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
35\\828\\4986
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
9\\214\\1280
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4\\96\\567
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-23\\-144
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-24\\-142
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5\\114\\720
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4\\94\\571
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
17\\401\\2424
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-2571552, 27072, 13536; 27072, -276, -144; 13536, -144, -71],[288, 12, 1],[35, 9, 4, -1, -1, 5, 4, 17; 828, 214, 96, -23, -24, 114, 94, 401; 4986, 1280, 567, -144, -142, 720, 571, 2424],234,4]
%
% END OF LATTICE L235.4
%
\hbox{}\par\smallskip%
%
% LATTICE L235.5
%
\leavevmode%
${L_{235.5}}$%
{} : {$1\above{1pt}{1pt}{-}{3}8\above{1pt}{1pt}{1}{7}64\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{1}{}3\above{1pt}{1pt}{1}{}9\above{1pt}{1pt}{1}{}$}\EasyButWeakLineBreak%
{${576}\above{1pt}{1pt}{r}{2}{4}\above{1pt}{1pt}{b}{2}{576}\above{1pt}{1pt}{s}{2}{12}\above{1pt}{1pt}{s}{2}{64}\above{1pt}{1pt}{b}{2}{36}\above{1pt}{1pt}{l}{2}{64}\above{1pt}{1pt}{}{2}{3}\above{1pt}{1pt}{}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-400320\\-241920\\4608
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-241920\\-146184\\2784
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4608\\2784\\-53
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\24\\1152
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\3\\70
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-19\\48\\864
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\2\\18
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\-8\\-160
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4\\-9\\-126
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
9\\-16\\-64
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\-1\\33
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-400320, -241920, 4608; -241920, -146184, 2784; 4608, 2784, -53],[576, 24, 1],[-1, -1, -19, -1, 3, 4, 9, 1; 24, 3, 48, 2, -8, -9, -16, -1; 1152, 70, 864, 18, -160, -126, -64, 33],234,5]
%
% END OF LATTICE L235.5
%
%
% LATTICE L235.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-48864, 3264, 1440; 3264, -218, -96; 1440, -96, -41],[96, 2, 1],[29, 11, 111, 40, 75, 2, -7, -1; 464, 175, 1760, 633, 1184, 31, -112, -15; -64, -22, -208, -72, -128, -2, 16, 0],234,6]
%
% END OF LATTICE L235.6
%
%
% LATTICE L235.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-13152, -192, -384; -192, -2, -6; -384, -6, -11],[96, 2, 1],[1, 1, 3, 1, -1, -1, -3, -1; -8, -14, -56, -30, -8, 10, 40, 18; -32, -28, -80, -24, 32, 28, 80, 24],234,7]
%
% END OF LATTICE L235.7
%
%
% LATTICE L235.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[676416, -22464, 960; -22464, 746, -32; 960, -32, 1],[192, 2, 1],[13, 5, 47, 8, 27, 0, -7, -1; 384, 148, 1392, 237, 800, 0, -208, -30; -160, -58, -544, -93, -320, -1, 64, 6],234,8]
%
% END OF LATTICE L235.8
%
%
% LATTICE L235.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-27744, 288, 480; 288, 4, -8; 480, -8, -7],[96, 4, 1],[-1, 0, 2, 19, 7, 3, 1, -1; -20, -1, 38, 366, 136, 59, 20, -18; -46, 0, 91, 864, 318, 136, 45, -48],234,9]
%
% END OF LATTICE L235.9
%
%
% LATTICE L235.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-43296, 1056, 576; 1056, -20, -16; 576, -16, -7],[96, 4, 1],[-1, 1, 3, 13, 9, 7, 1, -1; -16, 14, 46, 201, 140, 110, 16, -15; -46, 48, 139, 600, 414, 320, 45, -48],234,10]
%
% END OF LATTICE L235.10
%
%
% LATTICE L235.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-20448, 0, -10080; 0, 6, 0; -10080, 0, -4969],[288, 6, 1],[427, 1, -71, 0, 79, 80, 245, 83; -48, -1, 0, 1, 0, -3, -16, -7; -864, -2, 144, 0, -160, -162, -496, -168],234,11]
%
% END OF LATTICE L235.11
%
%
% LATTICE L235.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-672, -864, 192; -864, -654, 90; 192, 90, -1],[96, 6, 1],[-145, -5, 29, 5, -7, -14, -181, -24; 320, 11, -64, -11, 16, 31, 400, 53; 912, 30, -192, -32, 48, 90, 1152, 152],234,12]
%
% END OF LATTICE L235.12
%
%
% LATTICE L235.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-31776, -3360, 1248; -3360, -354, 132; 1248, 132, -49],[96, 6, 1],[-19, -3, -1, 1, 3, -1, -15, -5; 40, 2, -8, -2, 8, 10, 56, 14; -384, -72, -48, 20, 96, 0, -240, -92],234,13]
%
% END OF LATTICE L235.13
%
%
% LATTICE L235.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[672, 192, 0; 192, 56, 0; 0, 0, -1],[96, 8, 1],[-3, -1, -1, 1, 3, 1, 1, -1; 4, 3, 4, -3, -12, -5, -12, -3; -48, -4, 0, 0, -16, -12, -64, -48],234,14]
%
% END OF LATTICE L235.14
%
%
% LATTICE L235.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-7392, -3744, 288; -3744, -1880, 144; 288, 144, -11],[96, 8, 1],[1, 1, 3, 1, -1, -1, -3, -1; -8, -5, -8, 3, 16, 7, 16, 3; -80, -40, -32, 60, 176, 64, 128, 12],234,15]
%
% END OF LATTICE L235.15
%
%
% LATTICE L235.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-28992, -14976, 384; -14976, -7734, 198; 384, 198, -5],[192, 6, 1],[13, 7, 79, 5, 59, 1, -7, -1; -32, -16, -176, -11, -128, -2, 16, 2; -288, -102, -960, -55, -576, -3, 96, 2],234,16]
%
% END OF LATTICE L235.16
%
%
% LATTICE L235.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-14880, -4032, 1152; -4032, -1092, 312; 1152, 312, -89],[96, 12, 1],[11, 4, 1, -1, -1, 1, 4, 11; -38, -11, -1, 6, 2, -7, -17, -42; 6, 12, 9, 8, -6, -12, -9, -8],234,17]
%
% END OF LATTICE L235.17
%
%
% LATTICE L235.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-89184, -117696, -30144; -117696, -149676, -38388; -30144, -38388, -9845],[96, 12, 1],[-237, -149, -12, 15, 13, -75, -100, -127; -4684, -2942, -236, 297, 256, -1486, -1978, -2511; 18990, 11928, 957, -1204, -1038, 6024, 8019, 10180],234,18]
%
% END OF LATTICE L235.18
%
%
% LATTICE L235.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-11616, 3840, -288; 3840, -1264, 96; -288, 96, -7],[96, 16, 1],[-7, -6, -1, 1, 1, 0, -2, -19; -16, -13, -2, 3, 2, -1, -5, -45; 62, 64, 13, 0, -14, -16, 11, 144],234,19]
%
% END OF LATTICE L235.19
%
%
% LATTICE L235.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[45984, -18432, 480; -18432, 7376, -192; 480, -192, 5],[96, 16, 1],[2, 2, 1, 1, 0, 0, 1, 5; 11, 11, 5, 3, -1, -1, 5, 27; 230, 232, 98, 24, -38, -40, 94, 552],234,20]
%
% END OF LATTICE L235.20
%
%
% LATTICE L235.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[96, 0, 0; 0, 456, -48; 0, -48, 5],[96, 24, 1],[-5, 0, 1, 0, -3, -2, -9, -2; -24, -1, 0, -1, -16, -9, -40, -9; -240, -12, 0, -8, -144, -84, -384, -88],234,21]
%
% END OF LATTICE L235.21
%
%
% LATTICE L235.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-147360, 53952, -2688; 53952, -19752, 984; -2688, 984, -49],[96, 24, 1],[1, -2, -5, 0, 7, 4, 13, 2; -16, -9, -16, 1, 24, 11, 24, 1; -384, -72, -48, 20, 96, 0, -240, -92],234,22]
%
% END OF LATTICE L235.22
%
%
% LATTICE L235.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-192960, -8640, 3456; -8640, -294, 126; 3456, 126, -53],[576, 6, 1],[43, 1, 1, -1, -1, 1, 13, 3; 3312, 78, 96, -76, -80, 75, 992, 230; 10656, 250, 288, -246, -256, 243, 3200, 741],234,23]
%
% END OF LATTICE L235.23
%
%
% LATTICE L235.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3936, -4608, 288; -4608, -1776, 96; 288, 96, -5],[96, 48, 1],[5, 5, 1, 0, -1, -1, 1, 4; -68, -67, -13, 1, 14, 13, -14, -55; -1026, -1008, -195, 16, 210, 192, -213, -832],234,24]
%
% END OF LATTICE L235.24
%
%
% LATTICE L235.25
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-34656, -6528, 768; -6528, -1200, 144; 768, 144, -17],[96, 48, 1],[2, 5, 5, 4, 2, -1, -1, 0; 3, 5, 3, 1, -1, -3, -1, 1; 114, 264, 246, 184, 78, -72, -54, 8],234,25]
%
% END OF LATTICE L235.25
%
%
% LATTICE L235.26
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[192, 0, 0; 0, -1312, 96; 0, 96, -7],[192, 32, 1],[-1, -1, 0, 1, 0, -1, -1, -7; 5, 10, 1, 0, -1, -2, 2, 24; 62, 128, 13, 0, -14, -32, 22, 288],234,26]
%
% END OF LATTICE L235.26
%
%
% LATTICE L235.27
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-6624, 0, -1440; 0, 24, 0; -1440, 0, -313],[288, 24, 1],[-61, -6, -31, 0, 7, 8, -3, -10; -24, -1, 0, 1, 0, -3, -8, -7; 288, 28, 144, 0, -32, -36, 16, 48],234,27]
%
% END OF LATTICE L235.27
%
%
% LATTICE L235.28
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-175968, -42336, 3456; -42336, -9912, 816; 3456, 816, -67],[288, 24, 1],[49, 4, 19, 0, -3, -2, 7, 10; 444, 37, 180, 1, -28, -21, 60, 89; 7920, 656, 3168, 12, -496, -360, 1088, 1596],234,28]
%
% END OF LATTICE L235.28
%
%
% LATTICE L235.29
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1182240, -203904, 8352; -203904, -35088, 1440; 8352, 1440, -59],[288, 48, 1],[-1, -1, 4, 20, 23, 7, 8, 0; -1, -3, 3, 17, 21, 7, 9, 1; -166, -216, 638, 3240, 3762, 1160, 1350, 24],234,29]
%
% END OF LATTICE L235.29
%
%
% LATTICE L235.30
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1431072, 0, 10080; 0, 48, 0; 10080, 0, -71],[288, 48, 1],[23, 7, 4, 0, -1, -1, 2, 20; -6, -1, 0, 1, 0, -3, -1, -7; 3258, 992, 567, 0, -142, -144, 283, 2832],234,30]
%
% END OF LATTICE L235.30
%
%
% LATTICE L235.31
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-17656128, -1954944, 20160; -1954944, -216456, 2232; 20160, 2232, -23],[576, 24, 1],[-11, -13, -7, 1, 1, 1, -2, -39; 111, 132, 72, -8, -10, -12, 20, 392; 1125, 1408, 846, 96, -94, -288, 187, 3840],234,31]
%
% END OF LATTICE L235.31
%
%
% LATTICE L235.32
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[168000, -149568, 2688; -149568, 127200, -2400; 2688, -2400, 43],[192, 96, 1],[-15, -31, 27, 111, 70, 141, 14, -1; -1, -2, 2, 8, 5, 10, 1, 0; 882, 1824, -1578, -6496, -4098, -8256, -819, 64],234,32]
%
% END OF LATTICE L235.32
%
%
% LATTICE L235.33
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-7630272, 3151872, -13248; 3151872, -1301856, 5472; -13248, 5472, -23],[576, 96, 1],[0, 1, 0, -1, -1, -1, -1, -1; -1, 0, 2, 38, 21, 12, 6, -2; -238, -576, 475, 9600, 5562, 3424, 1998, 96],234,33]
%
% END OF LATTICE L235.33
%
%
% LATTICE L235.34
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-19657152, 6524928, -68544; 6524928, -2165856, 22752; -68544, 22752, -239],[576, 96, 1],[5, 1, -1, -1, 8, 15, 13, 47; 19, 0, -4, -2, 33, 60, 51, 182; 374, -288, -94, 96, 846, 1408, 1125, 3840],234,34]
%
% END OF LATTICE L235.34
%

\medskip%
%------------------------------WEYL-GROUP-W236--------------------------------
%
\leavevmode\llap{}%
$W_{236}$%
\qquad\llap{8} lattices, $\chi=48$%
\hfill%
$2|222|222|222|22\rtimes D_{4}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L236.1
%
\leavevmode%
${L_{236.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{6}64\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{1}{}3\above{1pt}{1pt}{-}{}9\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{3}%
\EasyButWeakLineBreak%
{${64}\above{1pt}{1pt}{b}{2}{6}\above{1pt}{1pt}{l}{2}{64}\above{1pt}{1pt}{}{2}{9}\above{1pt}{1pt}{r}{2}{64}\above{1pt}{1pt}{s}{2}{36}\above{1pt}{1pt}{*}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
shares genus with 3-dual\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-18800064\\-286272\\6912
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-286272\\-4359\\105
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
6912\\105\\-2
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\0\\-6912
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\-1\\-105
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\1
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-27\\1792\\736
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-5\\332\\147
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-53\\3520\\1600
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-7\\465\\216
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-13\\864\\416
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\-66\\-18
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-18800064, -286272, 6912; -286272, -4359, 105; 6912, 105, -2],[576, 3, 1],[-27, -5, -53, -7, -13, 1, 27, 5, 53, 7, 13, -1; 1792, 332, 3520, 465, 864, -66, -1792, -332, -3520, -465, -864, 66; 736, 147, 1600, 216, 416, -18, -800, -153, -1664, -225, -448, 0],235,1]
%
% END OF LATTICE L236.1
%
%
% LATTICE L236.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-159168, -79872, 1344; -79872, -40079, 673; 1344, 673, -10],[192, 1, 1],[-347, -68, -725, -32, -173, 7, 411, 74, 789, 35, 205, -1; 704, 138, 1472, 65, 352, -14, -832, -150, -1600, -71, -416, 2; 736, 147, 1600, 72, 416, -6, -800, -153, -1664, -75, -448, 0],235,2]
%
% END OF LATTICE L236.2
%
%
% LATTICE L236.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[67776, 33408, -384; 33408, 16467, -189; -384, -189, 2],[192, 3, 1],[-31, 0, 431, 38, 631, 151, 1631, 50, 1169, 37, 169, -1; 64, 0, -896, -79, -1312, -314, -3392, -104, -2432, -77, -352, 2; 96, -1, -1920, -168, -2784, -666, -7200, -221, -5184, -165, -768, 0],235,3]
%
% END OF LATTICE L236.3
%
%
% LATTICE L236.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[55872, 27648, 0; 27648, 13677, 3; 0, 3, -2],[576, 3, 1],[5983, 183, 4273, 45, 617, -1, -95, 1, 1615, 47, 2327, 185; -12096, -370, -8640, -91, -1248, 2, 192, -2, -3264, -95, -4704, -374; -19296, -591, -13824, -146, -2016, 2, 288, -3, -5184, -151, -7488, -596],235,4]
%
% END OF LATTICE L236.4
%
%
% LATTICE L236.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-414912, -132288, 4416; -132288, -42112, 1408; 4416, 1408, -47],[192, 64, 1],[13, 52, 8, 1, -1, -1, 3, 44, 24, 47, 17, 49; -3, -15, -3, -2, 0, 1, 0, -3, -3, -7, -3, -10; 1127, 4416, 658, 32, -94, -64, 281, 4032, 2158, 4192, 1502, 4288],235,5]
%
% END OF LATTICE L236.5
%
%
% LATTICE L236.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-11136, -11328, 384; -11328, -11328, 384; 384, 384, -13],[192, 192, 1],[-3, -1, 0, 1, 0, -2, -3, -5, -3, -10, -3, -7; 16, 10, 2, -1, -1, -1, 4, 10, 8, 31, 11, 31; 366, 256, 57, 0, -30, -96, 18, 128, 135, 576, 222, 672],235,6]
%
% END OF LATTICE L236.6
%
%
% LATTICE L236.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[576, 0, 0; 0, -414912, 4416; 0, 4416, -47],[576, 192, 1],[0, -1, -1, -7, -1, -10, -1, -5, -1, -2, 0, 1; 3, 41, 21, 120, 14, 117, 10, 37, 5, -3, -1, 0; 281, 3840, 1966, 11232, 1310, 10944, 935, 3456, 466, -288, -94, 0],235,7]
%
% END OF LATTICE L236.7
%
%
% LATTICE L236.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-33984, -28224, 9792; -28224, -22656, 7872; 9792, 7872, -2735],[576, 192, 1],[22, 12, 2, -1, -1, 1, 10, 20, 14, 17, 17, 15; 555, 319, 57, -21, -30, 10, 207, 443, 324, 402, 411, 371; 1674, 960, 171, -64, -90, 32, 630, 1344, 981, 1216, 1242, 1120],235,8]
%
% END OF LATTICE L236.8
%

\medskip%
%------------------------------WEYL-GROUP-W237--------------------------------
%
\leavevmode\llap{}%
$W_{237}$%
\qquad\llap{32} lattices, $\chi=90$%
\hfill%
$242222222242222222\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L237.1
%
\leavevmode%
${L_{237.1}}$%
{} : {$1\above{1pt}{1pt}{2}{2}8\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{2}{}9\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{2}{}11\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${396}\above{1pt}{1pt}{l}{2}{1}\above{1pt}{1pt}{}{4}{2}\above{1pt}{1pt}{b}{2}{8}\above{1pt}{1pt}{*}{2}{44}\above{1pt}{1pt}{*}{2}{72}\above{1pt}{1pt}{b}{2}{2}\above{1pt}{1pt}{s}{2}{18}\above{1pt}{1pt}{b}{2}{8}\above{1pt}{1pt}{*}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-437976\\159984\\0
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
159984\\-58438\\-1
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\-1\\1
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-5044843\\-13814064\\-13317480
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1837617\\5031863\\4850980
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4917\\13464\\12979
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
217\\594\\594
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\-1
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-42\\-115\\-114
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-317\\-868\\-848
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1165\\-3190\\-3102
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2143\\-5868\\-5688
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-340\\-931\\-900
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-4000\\-10953\\-10566
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-20581\\-56356\\-54336
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-437976, 159984, 0; 159984, -58438, -1; 0, -1, 1],[792, 1, 1],[217, 0, -42, -317, -1165, -2143, -340, -4000, -20581, -265735, -4917, -3087, -5941, -8669, -5903, -107, -23, 19; 594, 0, -115, -868, -3190, -5868, -931, -10953, -56356, -727650, -13464, -8453, -16268, -23738, -16164, -293, -63, 52; 594, -1, -114, -848, -3102, -5688, -900, -10566, -54336, -701514, -12979, -8146, -15672, -22858, -15552, -280, -54, 56],236,1]
%
% END OF LATTICE L237.1
%
\hbox{}\par\smallskip%
%
% LATTICE L237.2
%
\leavevmode%
${L_{237.2}}$%
{} : {$1\above{1pt}{1pt}{-2}{2}8\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{2}{}9\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{2}{}11\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{m}%
\EasyButWeakLineBreak%
{${99}\above{1pt}{1pt}{r}{2}{4}\above{1pt}{1pt}{*}{4}{2}\above{1pt}{1pt}{l}{2}{8}\above{1pt}{1pt}{}{2}{11}\above{1pt}{1pt}{}{2}{72}\above{1pt}{1pt}{r}{2}{2}\above{1pt}{1pt}{b}{2}{18}\above{1pt}{1pt}{l}{2}{8}\above{1pt}{1pt}{}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
9379656\\-31680\\0
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-31680\\107\\0
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\-1
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1117315\\-329506056\\13814064
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3773\\1112691\\-46648
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-374\\-110296\\4623
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\297\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\296\\-2
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\591\\-13
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
11\\3248\\-96
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
18\\5313\\-176
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
61\\18000\\-648
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
9\\2655\\-103
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
100\\29493\\-1215
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
507\\149520\\-6256
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[9379656, -31680, 0; -31680, 107, 0; 0, 0, -1],[792, 1, 1],[1, 1, 2, 11, 18, 61, 9, 100, 507, 3266, 241, 75, 143, 103, 137, 2, -1, -1; 297, 296, 591, 3248, 5313, 18000, 2655, 29493, 149520, 963171, 71072, 22117, 42168, 30371, 40392, 589, -297, -296; 0, -2, -13, -96, -176, -648, -103, -1215, -6256, -40392, -2990, -939, -1808, -1320, -1800, -33, -9, 0],236,2]
%
% END OF LATTICE L237.2
%
%
% LATTICE L237.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[970398, -9900, 0; -9900, 101, 0; 0, 0, -1],[198, 1, 1],[1, 1, 5, 15, 51, 89, 27, 307, 783, 10097, 373, 233, 223, 323, 217, 7, -1, -1; 99, 98, 489, 1466, 4983, 8694, 2637, 29979, 76458, 985941, 36422, 22751, 21774, 31537, 21186, 683, -99, -98; 0, -1, -13, -48, -176, -324, -103, -1215, -3128, -40392, -1495, -939, -904, -1320, -900, -33, -9, 0],236,3]
%
% END OF LATTICE L237.3
%
%
% LATTICE L237.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-793980, 4356, -396; 4356, -14, -5; -396, -5, 5],[396, 1, 1],[-707, -26, -8, -15, -21, -13, 0, 2, 9, 113, 4, 1, 1, -1, -5, -1, -11, -55; -148203, -5451, -1678, -3148, -4411, -2736, -1, 414, 1868, 23463, 831, 208, 208, -209, -1044, -209, -2304, -11528; -205722, -7568, -2331, -4376, -6138, -3816, -3, 567, 2568, 32274, 1144, 287, 288, -286, -1440, -289, -3195, -16000],236,4]
%
% END OF LATTICE L237.4
%
%
% LATTICE L237.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[20394, 19800, 10296; 19800, 9802, 9900; 10296, 9900, 5197],[198, 2, 1],[4802, -99, -5403, -10559, -78674, -73123, -46849, -555601, -716131, -18498398, -684849, -430473, -207379, -606274, -207083, -15419, -4811, 49; 99, -2, -111, -217, -1617, -1503, -963, -11421, -14721, -380259, -14078, -8849, -4263, -12463, -4257, -317, -99, 1; -9702, 200, 10916, 21333, 158950, 147735, 94652, 1122516, 1446845, 37373490, 1383644, 869712, 418981, 1224894, 418383, 31152, 9720, -99],236,5]
%
% END OF LATTICE L237.5
%
%
% LATTICE L237.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[756552456, -5615676, -191075544; -5615676, 41684, 1418300; -191075544, 1418300, 48258205],[396, 4, 1],[-705223, -26589, -8797, -4475, -28119, -5438, -810, -2327, -1641, -75293, -2319, -401, -124, -789, -475, -504, -9499, -13470; 23760, 898, 299, 153, 968, 189, 29, 81, 53, 2376, 70, 9, 1, 0, 9, 15, 315, 453; -2792988, -105304, -34840, -17723, -111364, -21537, -3208, -9216, -6499, -298188, -9184, -1588, -491, -3124, -1881, -1996, -37620, -53347],236,6]
%
% END OF LATTICE L237.6
%
%
% LATTICE L237.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[175626, 89100, -39006; 89100, 44109, -19800; -39006, -19800, 8663],[198, 9, 1],[-245, 47, 2501, 9771, 36397, 7517, 21671, 28555, 662491, 950711, 316775, 199113, 191843, 280425, 21285, 7131, 247, -45; 11, -2, -111, -434, -1617, -334, -963, -1269, -29442, -42251, -14078, -8849, -8526, -12463, -946, -317, -11, 2; -1078, 207, 11007, 43002, 160182, 33082, 95373, 125669, 2915586, 4184026, 1394109, 876285, 844290, 1234134, 93674, 31383, 1087, -198],236,7]
%
% END OF LATTICE L237.7
%
%
% LATTICE L237.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-308682, -38610, 792; -38610, -4829, 99; 792, 99, -2],[198, 11, 1],[1, 0, -4, -15, -5, -101, -32, -376, -967, -1135, -462, -290, -279, -37, -277, -10, -2, 1; -9, -1, 30, 116, 39, 792, 252, 2970, 7644, 8973, 3653, 2294, 2208, 293, 2196, 80, 18, -8; -54, -55, -121, -264, -70, -1188, -319, -3267, -8096, -9450, -3817, -2343, -2200, -282, -1980, -33, 99, 0],236,8]
%
% END OF LATTICE L237.8
%
%
% LATTICE L237.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-52668, -24156, 0; -24156, -10998, -9; 0, -9, 1],[396, 9, 1],[-5, 6, 23, 149, 521, 103, 143, 183, 8429, 12083, 4020, 1258, 2413, 3505, 263, 40, 0, -11; 11, -13, -50, -324, -1133, -224, -311, -398, -18332, -26279, -8743, -2736, -5248, -7623, -572, -87, 0, 24; 110, -108, -441, -2880, -10098, -2000, -2781, -3563, -164160, -235334, -78300, -24507, -47016, -68310, -5128, -783, -1, 216],236,9]
%
% END OF LATTICE L237.9
%
%
% LATTICE L237.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[628763454, 1069200, 308559834; 1069200, 1818, 524700; 308559834, 524700, 151422877],[198, 18, 1],[-54, -539, -3119, -4917, -34114, -3357, -18581, -23733, -273161, -783102, -260513, -163005, -78145, -226938, -8509, -5151, 1, 243; 11, 98, 489, 733, 4983, 483, 2637, 3331, 38229, 109549, 36422, 22751, 10887, 31537, 1177, 683, -11, -49; 110, 1098, 6354, 10017, 69498, 6839, 37854, 48350, 556497, 1595374, 530730, 332082, 159201, 462330, 17335, 10494, -2, -495],236,10]
%
% END OF LATTICE L237.10
%
%
% LATTICE L237.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[9900, -1188, 0; -1188, 143, 0; 0, 0, -1],[396, 11, 1],[-1, 0, 2, 15, 5, 101, 16, 188, 967, 1135, 462, 145, 279, 37, 277, 5, 1, -1; -9, -1, 15, 116, 39, 792, 126, 1485, 7644, 8973, 3653, 1147, 2208, 293, 2196, 40, 9, -8; -9, -11, -22, -132, -41, -792, -121, -1386, -7084, -8307, -3377, -1056, -2024, -267, -1980, -33, 0, 0],236,11]
%
% END OF LATTICE L237.11
%
%
% LATTICE L237.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1044054, -21978, 516978; -21978, 1100, -10890; 516978, -10890, 255989],[198, 22, 1],[1951, 2439, 9560, 14193, 8779, 84521, 51502, 588560, 751597, 1762553, 716433, 447904, 214539, 56573, 209563, 13850, -392, -49; -45, -56, -219, -325, -201, -1935, -1179, -13473, -17205, -40347, -16400, -10253, -4911, -1295, -4797, -317, 9, 1; -3942, -4928, -19316, -28677, -17738, -170775, -104060, -1189188, -1518605, -3561246, -1447556, -904992, -433477, -114306, -423423, -27984, 792, 99],236,12]
%
% END OF LATTICE L237.12
%
%
% LATTICE L237.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3724776, -76032, -19008; -76032, -1544, -384; -19008, -384, -95],[792, 8, 1],[85, 0, -1, 2, 45, 26, 39, 517, 342, 17735, 660, 421, 103, 615, 109, 21, 23, 3; -8316, -1, 99, -193, -4356, -2520, -3783, -50175, -33195, -1721412, -64063, -40867, -9999, -59708, -10584, -2041, -2241, -293; 16632, 4, -200, 381, 8624, 4995, 7504, 99576, 65885, 3416688, 127156, 81120, 19849, 118536, 21015, 4056, 4464, 585],236,13]
%
% END OF LATTICE L237.13
%
%
% LATTICE L237.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-33990264, 0, -16937712; 0, 8, 0; -16937712, 0, -8440243],[792, 8, 1],[-25061, 0, 295, -1179, -13265, -15329, -11497, -152411, -201643, -5228275, -194568, -124111, -60729, -181303, -64267, -6191, -6781, -1769; 0, 1, -1, -5, -44, -45, -31, -387, -505, -13068, -485, -307, -149, -440, -153, -13, -9, -1; 50292, 0, -592, 2366, 26620, 30762, 23072, 305856, 404654, 10492020, 390456, 249064, 121870, 363836, 128970, 12424, 13608, 3550],236,14]
%
% END OF LATTICE L237.14
%
%
% LATTICE L237.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[5544, -1584, -792; -1584, 450, 207; -792, 207, -31],[792, 9, 1],[41, 16, 27, 89, 207, 27, 21, 11, 321, 421, 61, 22, 9, -53, -13, -14, -4, 1; 154, 60, 101, 332, 770, 100, 77, 39, 1100, 1430, 204, 67, 4, -242, -52, -53, -15, 4; -22, -9, -18, -72, -198, -32, -36, -38, -1656, -2354, -387, -234, -432, -594, -40, 0, 2, 0],236,15]
%
% END OF LATTICE L237.15
%
%
% LATTICE L237.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-124344, 3960, 3168; 3960, -126, -99; 3168, -99, -49],[792, 9, 1],[5, 9, 10, 43, 62, 21, 25, 28, 1243, 886, 585, 179, 335, 235, 33, 2, -1, -1; 165, 296, 327, 1400, 2013, 680, 807, 901, 39960, 28479, 18800, 5749, 10752, 7535, 1056, 61, -33, -32; -11, -18, -18, -72, -99, -32, -36, -38, -1656, -1177, -774, -234, -432, -297, -40, 0, 2, 0],236,16]
%
% END OF LATTICE L237.16
%
%
% LATTICE L237.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1035144, 4752, 1584; 4752, 11, -11; 1584, -11, -2],[792, 11, 1],[-1135, -231, -145, -279, -37, -277, -5, -1, 1, 1, 0, -2, -15, -5, -101, -16, -188, -967; -63774, -12979, -8146, -15672, -2078, -15552, -280, -54, 56, 54, -1, -114, -848, -282, -5688, -900, -10566, -54336; -556470, -113256, -71093, -136796, -18142, -135828, -2453, -495, 484, 486, 0, -979, -7348, -2450, -49500, -7843, -92169, -474100],236,17]
%
% END OF LATTICE L237.17
%
%
% LATTICE L237.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-303336, -38016, 792; -38016, -4763, 99; 792, 99, -2],[792, 11, 1],[-514, -419, -132, -255, -17, -257, -5, -2, 1, 1, 1, -1, -11, -2, -85, -14, -169, -875; 4005, 3266, 1030, 1992, 133, 2016, 40, 18, -8, -9, -10, 6, 80, 15, 648, 108, 1314, 6816; -9450, -7634, -2343, -4400, -282, -3960, -33, 99, 0, -54, -110, -121, -528, -70, -2376, -319, -3267, -16192],236,18]
%
% END OF LATTICE L237.18
%
%
% LATTICE L237.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[68047848, -570636, -17154720; -570636, 4788, 143856; -17154720, 143856, 4324669],[396, 36, 1],[-589, -491, -891, -1316, -17901, -871, -4782, -6081, -69918, -400823, -133313, -41683, -19971, -115903, -2170, -1300, -1, -25; -132, -110, -191, -277, -3740, -181, -989, -1253, -14393, -82500, -27434, -8573, -4105, -23804, -445, -263, 1, -5; -2332, -1944, -3528, -5211, -70884, -3449, -18936, -24080, -276867, -1587212, -527904, -165060, -79083, -458964, -8593, -5148, -4, -99],236,19]
%
% END OF LATTICE L237.19
%
%
% LATTICE L237.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-18612, 4752, 4752; 4752, 1100, -1188; 4752, -1188, -1213],[396, 44, 1],[209, 311, 522, 708, 841, 3923, 2321, 25886, 32846, 153907, 62477, 19456, 9281, 4867, 8920, 533, -200, -25; -9, -13, -21, -28, -33, -153, -90, -999, -1266, -5931, -2407, -749, -357, -187, -342, -20, 9, 1; 828, 1232, 2068, 2805, 3332, 15543, 9196, 102564, 130141, 609804, 247544, 77088, 36773, 19284, 35343, 2112, -792, -99],236,20]
%
% END OF LATTICE L237.20
%
%
% LATTICE L237.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[455994, 40194, 84942; 40194, 4950, 6831; 84942, 6831, 16129],[198, 99, 1],[98, 1103, 4322, 12831, 3968, 8489, 23276, 29554, 679327, 88504, 323771, 202416, 193907, 25566, 21045, 6258, -20, -45; -201, -2262, -8863, -26312, -8137, -17408, -47731, -60605, -1393064, -181491, -663942, -415085, -397636, -52427, -43156, -12833, 41, 92; -431, -4851, -19008, -56430, -17451, -37334, -102366, -129976, -2987622, -389233, -1423917, -890208, -852786, -112437, -92554, -27522, 88, 198],236,21]
%
% END OF LATTICE L237.21
%
%
% LATTICE L237.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[396, 0, 0; 0, -3465, -792; 0, -792, -181],[396, 99, 1],[-138, -505, -158, -303, -40, -33, -5, 0, 1, 0, -1, -3, -19, -6, -13, -18, -23, -1059; 1311, 4819, 1527, 2968, 399, 340, 66, 5, 0, -3, -23, -1, 84, 37, 96, 152, 213, 10028; -5953, -21879, -6930, -13464, -1809, -1540, -297, -22, 0, 13, 99, 0, -396, -171, -440, -693, -968, -45540],236,22]
%
% END OF LATTICE L237.22
%
%
% LATTICE L237.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-139583862, 435364182, 216170658; 435364182, -1357907364, -674239500; 216170658, -674239500, -334779025],[198, 198, 1],[-1, -1, 30, 58, 39, 44, 252, 330, 3822, 997, 3653, 2294, 1104, 293, 122, 80, 2, -4; 1098, 7963, 9251, 3607, -202, -2045, -19975, -33823, -413605, -108726, -402599, -260383, -129173, -35674, -15893, -15901, -2053, 1031; -2212, -16038, -18612, -7227, 432, 4147, 40392, 68332, 835461, 219616, 813186, 525888, 260865, 72036, 32087, 32076, 4136, -2079],236,23]
%
% END OF LATTICE L237.23
%
%
% LATTICE L237.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-84744, 28512, 792; 28512, 24984, 792; 792, 792, 25],[792, 72, 1],[8, -1, -1, 3, 64, 4, 53, 77, 457, 2632, 881, 561, 137, 816, 16, 27, 3, 3; 253, -32, -33, 94, 2013, 126, 1671, 2429, 14418, 83039, 27796, 17701, 4323, 25751, 505, 853, 95, 95; -8272, 1044, 1080, -3069, -65736, -4115, -54576, -79336, -470925, -2712248, -907884, -578160, -141201, -841104, -16495, -27864, -3104, -3105],236,24]
%
% END OF LATTICE L237.24
%
%
% LATTICE L237.25
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-295416, 0, 75240; 0, 72, 0; 75240, 0, -19163],[792, 72, 1],[213, 0, -55, 23, 505, 77, 569, 883, 10631, 30675, 10296, 6607, 3253, 9791, 391, 367, 53, 133; 0, 1, -1, -5, -44, -5, -31, -43, -505, -1452, -485, -307, -149, -440, -17, -13, -1, -1; 836, 0, -216, 90, 1980, 302, 2232, 3464, 41706, 120340, 40392, 25920, 12762, 38412, 1534, 1440, 208, 522],236,25]
%
% END OF LATTICE L237.25
%
%
% LATTICE L237.26
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1584, 65736, 1584; 65736, 56584, 1408; 1584, 1408, 35],[792, 88, 1],[4, -1, -1, 2, 4, 25, 37, 485, 320, 1508, 617, 393, 96, 52, 101, 19, 19, 2; 135, -35, -36, 67, 135, 846, 1254, 16452, 10857, 51165, 20935, 13336, 3258, 1765, 3429, 646, 648, 68; -5616, 1452, 1496, -2783, -5608, -35145, -52096, -683496, -451055, -2125656, -869748, -554048, -135355, -73328, -142461, -26840, -26928, -2827],236,26]
%
% END OF LATTICE L237.26
%
%
% LATTICE L237.27
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-100584, 0, -24552; 0, 88, 0; -24552, 0, -5993],[792, 88, 1],[-79, 0, 43, 27, 5, -47, -85, -1535, -2149, -5105, -2112, -1387, -699, -197, -817, -107, -193, -59; 0, 1, -1, -5, -4, -45, -31, -387, -505, -1188, -485, -307, -149, -40, -153, -13, -9, -1; 324, 0, -176, -110, -20, 198, 352, 6336, 8866, 21060, 8712, 5720, 2882, 812, 3366, 440, 792, 242],236,27]
%
% END OF LATTICE L237.27
%
%
% LATTICE L237.28
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[3235320, 1450944, -22968; 1450944, 650331, -10296; -22968, -10296, 163],[792, 99, 1],[-31, -59, -41, -87, -13, -13, -5, -1, 1, 1, 4, 6, 17, 3, 3, 0, -4, -231; -726, -1344, -869, -1724, -238, -212, -53, -7, 4, 6, 24, 29, 44, -2, -28, -67, -113, -5524; -50416, -93555, -60885, -121572, -16920, -15268, -4059, -583, 396, 520, 2079, 2673, 5148, 288, -1364, -4257, -7733, -382932],236,28]
%
% END OF LATTICE L237.28
%
%
% LATTICE L237.29
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[792, 0, 0; 0, -135531, 2178; 0, 2178, -35],[792, 99, 1],[-69, -505, -158, -303, -20, -33, -5, 0, 1, 0, -1, -3, -19, -3, -13, -18, -23, -1059; -301, -2216, -705, -1376, -93, -160, -33, -3, 0, 1, 16, 5, -24, -7, -40, -67, -97, -4600; -19070, -140382, -44649, -87120, -5886, -10120, -2079, -187, 0, 62, 990, 297, -1584, -450, -2552, -4257, -6149, -291456],236,29]
%
% END OF LATTICE L237.29
%
%
% LATTICE L237.30
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[71676, 313632, -79200; 313632, 1373724, -346896; -79200, -346896, 87599],[396, 396, 1],[1739, 6367, 1995, 958, 507, 105, 66, 1, 0, 1, 13, 35, 57, 73, 40, 224, 289, 3335; 25381, 92951, 29146, 14007, 7421, 1540, 985, 22, 25, 23, 197, 492, 812, 1047, 577, 3249, 4212, 48666; 102076, 373824, 117216, 56331, 29844, 6193, 3960, 88, 99, 92, 792, 1980, 3267, 4212, 2321, 13068, 16940, 195723],236,30]
%
% END OF LATTICE L237.30
%
%
% LATTICE L237.31
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-469656, -836352, -28112040; -836352, -1486584, -49968864; -28112040, -49968864, -1679613829],[792, 792, 1],[-116, -197, 1979, 1928, 2588, 1455, 16601, 21649, 125230, 65324, 239293, 150173, 36110, 19148, 3979, 5135, 87, -248; -7733, -13200, 131995, 128696, 172795, 97164, 1108771, 1446097, 8365292, 4363625, 15984804, 10031753, 2412241, 1279169, 265827, 343193, 5867, -16499; 232, 396, -3960, -3861, -5184, -2915, -33264, -43384, -250965, -130912, -479556, -300960, -72369, -38376, -7975, -10296, -176, 495],236,31]
%
% END OF LATTICE L237.31
%
%
% LATTICE L237.32
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[792, 0, 0; 0, -284328, 48312; 0, 48312, -8209],[792, 792, 1],[0, 1, -1, -5, -4, -5, -31, -43, -505, -132, -485, -307, -149, -40, -17, -13, -1, -1; 17, 0, -269, -437, -275, -295, -1613, -2031, -23285, -6065, -22176, -13843, -6619, -1741, -713, -403, 15, 101; 100, 0, -1584, -2574, -1620, -1738, -9504, -11968, -137214, -35740, -130680, -81576, -39006, -10260, -4202, -2376, 88, 594],236,32]
%
% END OF LATTICE L237.32
%

\medskip%
%------------------------------WEYL-GROUP-W238--------------------------------
%
\leavevmode\llap{}%
$W_{238}$%
\qquad\llap{23} lattices, $\chi=24$%
\hfill%
$2|2|2|2|2|2|2|2|\rtimes D_{8}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L238.1
%
\leavevmode%
${L_{238.1}}$%
{} : {$[1\above{1pt}{1pt}{-}{}2\above{1pt}{1pt}{1}{}]\above{1pt}{1pt}{}{2}16\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{1}{}9\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${3}\above{1pt}{1pt}{r}{2}{8}\above{1pt}{1pt}{*}{2}{48}\above{1pt}{1pt}{*}{2}{72}\above{1pt}{1pt}{l}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
30096\\3168\\-576
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3168\\318\\-60
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-576\\-60\\11
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\96\\576
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\13\\84
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\-2\\-13
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-4\\-75
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-6\\-88
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\-4\\24
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5\\6\\288
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[30096, 3168, -576; 3168, 318, -60; -576, -60, 11],[144, 6, 1],[-1, -1, 1, 5, 1, 1, -1, -5; -4, -6, -4, 6, 2, 2, -4, -18; -75, -88, 24, 288, 63, 64, -72, -360],237,1]
%
% END OF LATTICE L238.1
%
\hbox{}\par\smallskip%
%
% LATTICE L238.2
%
\leavevmode%
${L_{238.2}}$%
{} : {$[1\above{1pt}{1pt}{1}{}2\above{1pt}{1pt}{1}{}]\above{1pt}{1pt}{}{6}16\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{1}{}9\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{m}%
\EasyButWeakLineBreak%
{${12}\above{1pt}{1pt}{*}{2}{8}\above{1pt}{1pt}{s}{2}{48}\above{1pt}{1pt}{s}{2}{72}\above{1pt}{1pt}{*}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
100944\\24480\\-720
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
24480\\5934\\-174
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-720\\-174\\5
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-49\\240\\1440
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-10\\49\\300
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\-1
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7\\-34\\-174
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7\\-34\\-176
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
9\\-44\\-240
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\-6\\-72
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[100944, 24480, -720; 24480, 5934, -174; -720, -174, 5],[144, 6, 1],[7, 7, 9, 1, -3, -3, -1, 11; -34, -34, -44, -6, 14, 14, 4, -54; -174, -176, -240, -72, 54, 56, 0, -288],237,2]
%
% END OF LATTICE L238.2
%
\hbox{}\par\smallskip%
%
% LATTICE L238.3
%
\leavevmode%
${L_{238.3}}$%
{} : {$[1\above{1pt}{1pt}{1}{}2\above{1pt}{1pt}{-}{}]\above{1pt}{1pt}{}{4}32\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{1}{}3\above{1pt}{1pt}{-}{}9\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2,m}%
\EasyButWeakLineBreak%
{${96}\above{1pt}{1pt}{*}{2}{36}\above{1pt}{1pt}{l}{2}{6}\above{1pt}{1pt}{}{2}{1}\above{1pt}{1pt}{r}{2}{96}\above{1pt}{1pt}{l}{2}{9}\above{1pt}{1pt}{}{2}{6}\above{1pt}{1pt}{r}{2}{4}\above{1pt}{1pt}{*}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
13536\\864\\1440
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
864\\-282\\222
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1440\\222\\103
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-19\\56\\144
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-59\\174\\450
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-22\\65\\168
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3\\9\\23
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
63\\-184\\-480
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
46\\-135\\-351
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
33\\-97\\-252
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
17\\-50\\-130
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[13536, 864, 1440; 864, -282, 222; 1440, 222, 103],[288, 6, 1],[-19, -59, -22, -3, 63, 46, 33, 17; 56, 174, 65, 9, -184, -135, -97, -50; 144, 450, 168, 23, -480, -351, -252, -130],237,3]
%
% END OF LATTICE L238.3
%
\hbox{}\par\smallskip%
%
% LATTICE L238.4
%
\leavevmode%
${L_{238.4}}$%
{} : {$[1\above{1pt}{1pt}{1}{}2\above{1pt}{1pt}{1}{}]\above{1pt}{1pt}{}{0}32\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{1}{}3\above{1pt}{1pt}{-}{}9\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{m}%
\EasyButWeakLineBreak%
{${96}\above{1pt}{1pt}{s}{2}{36}\above{1pt}{1pt}{*}{2}{24}\above{1pt}{1pt}{l}{2}{1}\above{1pt}{1pt}{}{2}{96}\above{1pt}{1pt}{}{2}{9}\above{1pt}{1pt}{r}{2}{24}\above{1pt}{1pt}{*}{2}{4}\above{1pt}{1pt}{s}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
37728\\0\\-288
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\-30\\-6
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-288\\-6\\1
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\-32\\144
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\24\\-126
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\26\\-132
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\-1
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\-80\\384
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\-54\\261
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\-82\\396
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\-28\\134
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[37728, 0, -288; 0, -30, -6; -288, -6, 1],[288, 6, 1],[1, -1, -1, 0, 3, 2, 3, 1; -32, 24, 26, 0, -80, -54, -82, -28; 144, -126, -132, -1, 384, 261, 396, 134],237,4]
%
% END OF LATTICE L238.4
%
\hbox{}\par\smallskip%
%
% LATTICE L238.5
%
\leavevmode%
${L_{238.5}}$%
{} : {$1\above{1pt}{1pt}{-}{3}4\above{1pt}{1pt}{1}{1}32\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{1}{}9\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{m}%
\EasyButWeakLineBreak%
{${48}\above{1pt}{1pt}{*}{2}{32}\above{1pt}{1pt}{l}{2}{3}\above{1pt}{1pt}{r}{2}{288}\above{1pt}{1pt}{*}{2}{48}\above{1pt}{1pt}{s}{2}{32}\above{1pt}{1pt}{*}{2}{12}\above{1pt}{1pt}{*}{2}{288}\above{1pt}{1pt}{s}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-11808\\-1728\\576
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1728\\-60\\12
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
576\\12\\-1
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\-62\\-168
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\-60\\-160
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\1\\3
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-5\\324\\864
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3\\190\\504
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3\\188\\496
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\62\\162
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\60\\144
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-11808, -1728, 576; -1728, -60, 12; 576, 12, -1],[288, 12, 1],[1, 1, 0, -5, -3, -3, -1, -1; -62, -60, 1, 324, 190, 188, 62, 60; -168, -160, 3, 864, 504, 496, 162, 144],237,5]
%
% END OF LATTICE L238.5
%
\hbox{}\par\smallskip%
%
% LATTICE L238.6
%
\leavevmode%
${L_{238.6}}$%
{} : {$1\above{1pt}{1pt}{-}{3}4\above{1pt}{1pt}{1}{7}32\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{1}{}9\above{1pt}{1pt}{-}{}$}\EasyButWeakLineBreak%
{${12}\above{1pt}{1pt}{}{2}{32}\above{1pt}{1pt}{}{2}{3}\above{1pt}{1pt}{}{2}{288}\above{1pt}{1pt}{}{2}{12}\above{1pt}{1pt}{r}{2}{32}\above{1pt}{1pt}{s}{2}{12}\above{1pt}{1pt}{s}{2}{288}\above{1pt}{1pt}{l}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
90144\\0\\-1440
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\12\\0
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1440\\0\\23
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\1\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\0\\64
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\-1\\63
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
23\\-24\\1440
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5\\-5\\312
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
9\\-8\\560
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\-2\\186
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7\\0\\432
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[90144, 0, -1440; 0, 12, 0; -1440, 0, 23],[288, 12, 1],[0, 1, 1, 23, 5, 9, 3, 7; 1, 0, -1, -24, -5, -8, -2, 0; 0, 64, 63, 1440, 312, 560, 186, 432],237,6]
%
% END OF LATTICE L238.6
%
%
% LATTICE L238.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-11592, -5976, 216; -5976, -3075, 111; 216, 111, -4],[72, 3, 1],[0, -1, -1, 1, 1, 3, 3, 5; 1, 4, 2, -12, -5, -12, -10, -12; 27, 56, 0, -288, -87, -176, -120, -72],237,7]
%
% END OF LATTICE L238.7
%
%
% LATTICE L238.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-2844, 1440, -144; 1440, -726, 72; -144, 72, -7],[36, 6, 1],[2, 1, -1, -5, -2, -1, 1, 5; 5, 3, -2, -15, -7, -5, -2, 9; 9, 10, 0, -54, -33, -34, -48, -18],237,8]
%
% END OF LATTICE L238.8
%
%
% LATTICE L238.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-4824, 720, 288; 720, -102, -42; 288, -42, -17],[72, 6, 1],[-1, -1, -1, -1, 1, 1, 1, 1; 16, 8, 5, 0, -8, -4, -1, 12; -60, -38, -30, -18, 36, 26, 18, -18],237,9]
%
% END OF LATTICE L238.9
%
%
% LATTICE L238.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-72, 0, 0; 0, 6, 0; 0, 0, 1],[72, 6, 1],[-13, -3, -4, -2, 1, 0, -2, -7; -44, -10, -13, -6, 4, 0, -7, -24; -24, -7, -12, -9, 0, 1, 0, -9],237,10]
%
% END OF LATTICE L238.10
%
%
% LATTICE L238.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[908784, 103248, -3168; 103248, 11730, -360; -3168, -360, 11],[144, 6, 1],[-1, 1, 13, 13, 4, 2, -1, -4; 8, -9, -112, -111, -34, -17, 8, 33; -27, -8, 72, 108, 39, 20, -24, -72],237,11]
%
% END OF LATTICE L238.11
%
%
% LATTICE L238.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[5040, 576, 0; 576, 66, 0; 0, 0, -1],[144, 6, 1],[-1, 0, 3, 4, 3, 1, 1, -1; 8, -1, -32, -39, -28, -9, -8, 9; -6, -8, -48, -36, -18, -4, 0, 0],237,12]
%
% END OF LATTICE L238.12
%
%
% LATTICE L238.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[72, -72, 0; -72, 84, 0; 0, 0, -1],[72, 12, 1],[-1, -3, -3, -5, 0, 1, 1, -1; -1, -4, -5, -12, -1, 0, 1, 0; -3, -16, -24, -72, -9, -8, 0, 0],237,13]
%
% END OF LATTICE L238.13
%
%
% LATTICE L238.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2952, 0, 144; 0, 12, 0; 144, 0, -7],[72, 12, 1],[-3, -3, -2, -1, 1, 1, 0, -5; -2, -4, -5, -12, -2, 0, 1, 0; -66, -68, -48, -36, 18, 20, 0, -108],237,14]
%
% END OF LATTICE L238.14
%
%
% LATTICE L238.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2232, 0, 792; 0, 24, 0; 792, 0, -281],[72, 24, 1],[-8, -9, -21, -19, 0, 5, 13, 7; -5, -2, -2, 0, 1, 0, -2, -6; -24, -26, -60, -54, 0, 14, 36, 18],237,15]
%
% END OF LATTICE L238.15
%
%
% LATTICE L238.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[30096, 6336, -576; 6336, 1272, -120; -576, -120, 11],[144, 24, 1],[-1, 1, 1, 5, 1, -1, -1, -5; -2, 1, 1, 3, -2, -3, -2, -9; -72, 64, 63, 288, 24, -88, -75, -360],237,16]
%
% END OF LATTICE L238.16
%
%
% LATTICE L238.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-89136, -44640, -21600; -44640, -22344, -10800; -21600, -10800, -5209],[144, 24, 1],[1, 27, 25, -41, -121, -87, -85, -139; -2, -81, -76, 117, 358, 259, 254, 417; 0, 56, 54, -72, -240, -176, -174, -288],237,17]
%
% END OF LATTICE L238.17
%
%
% LATTICE L238.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-11376, 5760, -288; 5760, -2904, 144; -288, 144, -7],[144, 24, 1],[2, 1, -1, -5, -2, -1, 1, 5; 5, 3, -2, -15, -7, -5, -2, 9; 18, 20, 0, -108, -66, -68, -96, -36],237,18]
%
% END OF LATTICE L238.18
%
%
% LATTICE L238.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[66384, -27648, 576; -27648, 11496, -240; 576, -240, 5],[144, 24, 1],[-1, -1, -1, 1, 1, 1, 1, -1; -1, -1, -2, -3, -1, -1, -2, -3; 66, 68, 24, -252, -162, -164, -216, -36],237,19]
%
% END OF LATTICE L238.19
%
%
% LATTICE L238.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-34848, 8640, -3168; 8640, -2136, 792; -3168, 792, -281],[288, 24, 1],[-14, -10, 11, 8, 20, 19, 1, -5; -43, -33, 28, 23, 59, 57, 4, -15; 36, 18, -48, -26, -60, -54, 0, 14],237,20]
%
% END OF LATTICE L238.20
%
%
% LATTICE L238.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-31392, 2880, 0; 2880, 312, -24; 0, -24, 1],[288, 24, 1],[-1, 0, 3, 2, 3, 1, 1, -1; -11, 0, 32, 21, 31, 10, 8, -12; -264, -1, 768, 513, 768, 254, 240, -270],237,21]
%
% END OF LATTICE L238.21
%
%
% LATTICE L238.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[15840, -5760, 2016; -5760, 2064, -720; 2016, -720, 251],[288, 48, 1],[-1, -3, -3, -5, 0, 1, 1, -1; -26, -70, -67, -114, -1, 14, 11, -54; -66, -176, -168, -288, -3, 32, 24, -144],237,22]
%
% END OF LATTICE L238.22
%
%
% LATTICE L238.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[288, -288, 0; -288, 336, 0; 0, 0, -1],[288, 48, 1],[-1, -3, -3, -5, 0, 1, 1, -1; -1, -4, -5, -12, -1, 0, 1, 0; -6, -32, -48, -144, -18, -16, 0, 0],237,23]
%
% END OF LATTICE L238.23
%

\medskip%
%------------------------------WEYL-GROUP-W239--------------------------------
%
\leavevmode\llap{}%
$W_{239}$%
\qquad\llap{4} lattices, $\chi=36$%
\hfill%
$22\slashtwo2242|24\rtimes D_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L239.1
%
\leavevmode%
${L_{239.1}}$%
{} : {$1\above{1pt}{1pt}{2}{2}32\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{2}{}7\above{1pt}{1pt}{-}{}$}\EasyButWeakLineBreak%
{${2}\above{1pt}{1pt}{b}{2}{32}\above{1pt}{1pt}{*}{2}{4}\above{1pt}{1pt}{l}{2}{1}\above{1pt}{1pt}{}{2}{32}\above{1pt}{1pt}{r}{2}{2}\above{1pt}{1pt}{}{4}{1}\above{1pt}{1pt}{r}{2}{32}\above{1pt}{1pt}{s}{2}{4}\above{1pt}{1pt}{*}{4}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-231392\\56672\\3584
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
56672\\-13879\\-879
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3584\\-879\\-54
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
18\\70\\55
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
313\\1216\\976
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
155\\602\\486
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
94\\365\\296
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
577\\2240\\1824
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
84\\326\\267
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
41\\159\\132
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-37\\-144\\-112
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-17\\-66\\-54
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-231392, 56672, 3584; 56672, -13879, -879; 3584, -879, -54],[224, 1, 1],[18, 313, 155, 94, 577, 84, 41, -37, -17; 70, 1216, 602, 365, 2240, 326, 159, -144, -66; 55, 976, 486, 296, 1824, 267, 132, -112, -54],238,1]
%
% END OF LATTICE L239.1
%
%
% LATTICE L239.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-180768, -8288, -8736; -8288, -378, -399; -8736, -399, -421],[224, 7, 1],[6, 35, 5, 7, 11, 0, -1, 1, 4; 325, 1824, 251, 332, 464, -15, -52, 96, 229; -434, -2464, -343, -462, -672, 14, 70, -112, -301],238,2]
%
% END OF LATTICE L239.2
%
%
% LATTICE L239.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-294112, 0, -139104; 0, 32, 0; -139104, 0, -65791],[224, 32, 1],[15, 69, 295, 348, 61, 227, 0, -35, -159; -13, -5, -12, -9, -1, -1, 1, 0, -8; -32, -146, -624, -736, -129, -480, 0, 74, 336],238,3]
%
% END OF LATTICE L239.3
%
%
% LATTICE L239.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[224, 0, 0; 0, -37408, -6944; 0, -6944, -1289],[224, 224, 1],[-13, -5, -12, -9, -1, -1, 1, 0, -8; -1, 23, 103, 124, 22, 83, 0, -13, -63; 0, -126, -560, -672, -119, -448, 0, 70, 336],238,4]
%
% END OF LATTICE L239.4
%

\medskip%
%------------------------------WEYL-GROUP-W240--------------------------------
%
\leavevmode\llap{}%
$W_{240}$%
\qquad\llap{8} lattices, $\chi=18$%
\hfill%
$24|422|2\rtimes D_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L240.1
%
\leavevmode%
${L_{240.1}}$%
{} : {$1\above{1pt}{1pt}{2}{2}16\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{2}{}5\above{1pt}{1pt}{-}{}$}\EasyButWeakLineBreak%
{${16}\above{1pt}{1pt}{*}{2}{4}\above{1pt}{1pt}{*}{4}{2}\above{1pt}{1pt}{}{4}{1}\above{1pt}{1pt}{}{2}{16}\above{1pt}{1pt}{r}{2}{10}\above{1pt}{1pt}{b}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1422960\\4080\\4800
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4080\\-11\\-15
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4800\\-15\\-14
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-208\\-120
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-210\\-118
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\208\\119
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\627\\355
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
13\\2720\\1536
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\420\\235
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-1422960, 4080, 4800; 4080, -11, -15; 4800, -15, -14],[240, 1, 1],[-1, -1, 1, 3, 13, 2; -208, -210, 208, 627, 2720, 420; -120, -118, 119, 355, 1536, 235],239,1]
%
% END OF LATTICE L240.1
%
%
% LATTICE L240.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-313680, 3360, -47280; 3360, -33, 555; -47280, 555, -6338],[240, 3, 1],[39, 37, -38, -112, -483, -73; 1952, 1850, -1902, -5603, -24160, -3650; -120, -114, 117, 345, 1488, 225],239,2]
%
% END OF LATTICE L240.2
%
%
% LATTICE L240.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-110640, 2640, 13200; 2640, -55, -345; 13200, -345, -1462],[240, 5, 1],[301, 70, 24, -23, -25, 9; 5408, 1257, 430, -414, -448, 162; 1440, 335, 115, -110, -120, 43],239,3]
%
% END OF LATTICE L240.3
%
%
% LATTICE L240.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-13200, 1680, -1200; 1680, -165, 165; -1200, 165, -106],[240, 15, 1],[-147, -35, -13, 11, 15, -4; -304, -73, -28, 22, 32, -8; 1200, 285, 105, -90, -120, 33],239,4]
%
% END OF LATTICE L240.4
%
%
% LATTICE L240.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-184560, 0, 24720; 0, 16, 0; 24720, 0, -3311],[240, 16, 1],[13, 0, -15, 74, 63, 193; 0, 1, -1, -5, -3, -5; 97, 0, -112, 552, 470, 1440],239,5]
%
% END OF LATTICE L240.5
%
%
% LATTICE L240.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-43680, -240, 8880; -240, 48, 0; 8880, 0, -1757],[240, 48, 1],[16, 0, -19, 90, 77, 237; 80, -1, -94, 455, 388, 1190; 81, 0, -96, 456, 390, 1200],239,6]
%
% END OF LATTICE L240.6
%
%
% LATTICE L240.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-17760, -240, -6240; -240, 80, 0; -6240, 0, -2107],[240, 80, 1],[-105, -122, 27, 0, -22, -65; -312, -361, 82, -1, -66, -194; 310, 360, -80, 0, 65, 192],239,7]
%
% END OF LATTICE L240.7
%
%
% LATTICE L240.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[480, 240, 0; 240, 240, 0; 0, 0, -1],[240, 240, 1],[0, 1, -1, -5, -3, -1; -1, -1, 2, -1, -2, -2; -15, 0, 0, -120, -90, -48],239,8]
%
% END OF LATTICE L240.8
%

\medskip%
%------------------------------WEYL-GROUP-W241--------------------------------
%
\leavevmode\llap{}%
$W_{241}$%
\qquad\llap{12} lattices, $\chi=24$%
\hfill%
$22222222\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L241.1
%
\leavevmode%
${L_{241.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}16\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{-}{}5\above{1pt}{1pt}{-}{}25\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{5}%
\EasyButWeakLineBreak%
{${48}\above{1pt}{1pt}{r}{2}{10}\above{1pt}{1pt}{b}{2}{1200}\above{1pt}{1pt}{b}{2}{2}\above{1pt}{1pt}{l}{2}{1200}\above{1pt}{1pt}{r}{2}{10}\above{1pt}{1pt}{b}{2}{48}\above{1pt}{1pt}{b}{2}{50}\above{1pt}{1pt}{l}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-6478800\\1299600\\25200
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1299600\\-260690\\-5055
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
25200\\-5055\\-98
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-65\\-288\\-1872
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-9\\-39\\-305
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-31\\-120\\-1800
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\5\\-1
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
101\\480\\1200
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\9\\50
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-5\\-24\\-48
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-12\\-55\\-250
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-6478800, 1299600, 25200; 1299600, -260690, -5055; 25200, -5055, -98],[1200, 5, 1],[-65, -9, -31, 1, 101, 2, -5, -12; -288, -39, -120, 5, 480, 9, -24, -55; -1872, -305, -1800, -1, 1200, 50, -48, -250],240,1]
%
% END OF LATTICE L241.1
%
%
% LATTICE L241.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-79440, 480, 960; 480, -2, -7; 960, -7, -10],[240, 1, 1],[-37, -6, -7, 0, 5, 1, -1, -1; -2448, -395, -456, 1, 336, 65, -72, -67; -1872, -305, -360, -1, 240, 50, -48, -50],240,2]
%
% END OF LATTICE L241.2
%
%
% LATTICE L241.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-113520, 1920, 480; 1920, -6, -9; 480, -9, -2],[240, 3, 1],[5, 1, -1, -1, -5, -1, 1, 1; 32, 5, -8, -7, -32, -5, 8, 7; 1040, 210, -208, -210, -1072, -225, 200, 207],240,3]
%
% END OF LATTICE L241.3
%
%
% LATTICE L241.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-5520, 240, 720; 240, -10, -35; 720, -35, -62],[240, 5, 1],[-421, -12, -55, 2, 5, -1, -49, -15; -7104, -203, -936, 33, 96, -16, -816, -252; -960, -27, -120, 5, 0, -3, -120, -35],240,4]
%
% END OF LATTICE L241.4
%
%
% LATTICE L241.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1281840, 7440, 7680; 7440, -30, -45; 7680, -45, -46],[240, 15, 1],[-101, -9, -15, 1, 5, 0, -9, -10; -448, -41, -72, 3, 32, 2, -32, -42; -16480, -1467, -2440, 165, 800, -3, -1480, -1635],240,5]
%
% END OF LATTICE L241.5
%
%
% LATTICE L241.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-39840, -3600, 480; -3600, -160, 32; 480, 32, -5],[240, 16, 1],[1, 6, 2, 2, 1, -1, -1, -1; 6, 55, 21, 23, 12, -10, -12, -14; 117, 880, 318, 336, 171, -160, -174, -192],240,6]
%
% END OF LATTICE L241.6
%
%
% LATTICE L241.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[480, -240, 0; -240, -12000, 528; 0, 528, -23],[240, 48, 1],[4, 46, 4, 10, 2, -1, -1, -1; 6, 75, 7, 19, 4, 0, -2, -4; 133, 1680, 158, 432, 91, 0, -46, -96],240,7]
%
% END OF LATTICE L241.7
%
%
% LATTICE L241.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-363836400, 72814800, 344400; 72814800, -14572470, -68925; 344400, -68925, -326],[1200, 15, 1],[15, 16, 73, 6, 117, 2, -5, -12; 80, 81, 360, 29, 560, 9, -24, -55; -1072, -225, 1000, 207, 5200, 210, -208, -1050],240,8]
%
% END OF LATTICE L241.8
%
%
% LATTICE L241.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-20640, 240, 240; 240, 800, 320; 240, 320, 127],[240, 80, 1],[1, 3, 11, 23, 37, 16, 8, -4; -54, -167, -615, -1287, -2070, -895, -447, 225; 135, 416, 1530, 3200, 5145, 2224, 1110, -560],240,9]
%
% END OF LATTICE L241.9
%
%
% LATTICE L241.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-480, 4560, -960; 4560, -39840, 8400; -960, 8400, -1771],[240, 240, 1],[2, 11, 11, 63, 32, 40, 6, -12; -5, -39, -47, -295, -159, -207, -35, 49; -25, -192, -230, -1440, -775, -1008, -170, 240],240,10]
%
% END OF LATTICE L241.10
%
%
% LATTICE L241.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-125440800, -6128400, 157200; -6128400, -299360, 7680; 157200, 7680, -197],[1200, 80, 1],[11, -1, -1, 3, 7, 24, 28, 4; 0, 2, 0, -10, -6, -17, -15, -1; 8775, -720, -798, 2000, 5349, 18480, 21750, 3152],240,11]
%
% END OF LATTICE L241.11
%
%
% LATTICE L241.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2400, 142800, -1200; 142800, -8482080, 71280; -1200, 71280, -599],[1200, 240, 1],[12, -1, -1, 3, 6, 64, 26, 12; 0, 2, 0, -10, -2, -17, -5, -1; -25, 240, 2, -1200, -251, -2160, -650, -144],240,12]
%
% END OF LATTICE L241.12
%

\medskip%
%------------------------------WEYL-GROUP-W242--------------------------------
%
\leavevmode\llap{}%
$W_{242}$%
\qquad\llap{8} lattices, $\chi=12$%
\hfill%
$222|222|\rtimes D_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L242.1
%
\leavevmode%
${L_{242.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{2}16\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{1}{}$}\EasyButWeakLineBreak%
{${16}\above{1pt}{1pt}{l}{2}{3}\above{1pt}{1pt}{}{2}{80}\above{1pt}{1pt}{r}{2}{2}\above{1pt}{1pt}{b}{2}{80}\above{1pt}{1pt}{*}{2}{12}\above{1pt}{1pt}{s}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
106320\\17520\\-480
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
17520\\2887\\-79
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-480\\-79\\2
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
9\\-56\\-48
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
14\\-87\\-75
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
103\\-640\\-560
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\-1
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-13\\80\\40
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\6\\0
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[106320, 17520, -480; 17520, 2887, -79; -480, -79, 2],[240, 1, 1],[9, 14, 103, 0, -13, -1; -56, -87, -640, 0, 80, 6; -48, -75, -560, -1, 40, 0],241,1]
%
% END OF LATTICE L242.1
%
%
% LATTICE L242.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[240, 0, 0; 0, -3, -3; 0, -3, -2],[240, 3, 1],[-1, 0, 1, 0, -11, -1; -8, -1, 0, 2, 0, -2; 0, 1, 0, -3, -120, -8],241,2]
%
% END OF LATTICE L242.2
%
%
% LATTICE L242.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1680, 240, 0; 240, 10, 5; 0, 5, -1],[240, 5, 1],[1, 2, 3, 0, -1, -1; 0, -9, -16, -1, 8, 12; -40, -75, -112, 0, 32, 30],241,3]
%
% END OF LATTICE L242.3
%
%
% LATTICE L242.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-33360, -6720, 1200; -6720, -1335, 240; 1200, 240, -43],[240, 15, 1],[-1, 1, 1, -1, -11, -2; -16, 4, 8, -3, -64, -13; -120, 50, 72, -45, -672, -130],241,4]
%
% END OF LATTICE L242.4
%
%
% LATTICE L242.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1680, -3600, 480; -3600, -3424, 480; 480, 480, -67],[240, 16, 1],[-1, -1, 4, 4, 3, 1; -11, -9, 45, 43, 30, 6; -86, -72, 350, 336, 235, 48],241,5]
%
% END OF LATTICE L242.5
%
%
% LATTICE L242.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[8160, 6480, -240; 6480, 5136, -192; -240, -192, 7],[240, 48, 1],[1, 0, -2, -3, -1, 1; -1, -1, 0, 2, 0, -1; 6, -32, -75, -48, -30, 8],241,6]
%
% END OF LATTICE L242.6
%
%
% LATTICE L242.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[240, 0, 0; 0, -16720, 720; 0, 720, -31],[240, 80, 1],[0, -4, -1, -1, 0, 1; -3, -15, -1, 7, 1, 0; -70, -360, -26, 160, 23, 0],241,7]
%
% END OF LATTICE L242.7
%
%
% LATTICE L242.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-50160, 172800, 2160; 172800, -70320, -960; 2160, -960, -13],[240, 240, 1],[4, 7, 1, -7, -1, 2; -93, -162, -23, 163, 23, -47; 7530, 13120, 1863, -13200, -1866, 3800],241,8]
%
% END OF LATTICE L242.8
%

\medskip%
%------------------------------WEYL-GROUP-W243--------------------------------
%
\leavevmode\llap{}%
$W_{243}$%
\qquad\llap{8} lattices, $\chi=12$%
\hfill%
$22|222|2\rtimes D_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L243.1
%
\leavevmode%
${L_{243.1}}$%
{} : {$1\above{1pt}{1pt}{2}{6}16\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{1}{}$}\EasyButWeakLineBreak%
{${16}\above{1pt}{1pt}{}{2}{3}\above{1pt}{1pt}{r}{2}{80}\above{1pt}{1pt}{s}{2}{12}\above{1pt}{1pt}{*}{2}{16}\above{1pt}{1pt}{b}{2}{30}\above{1pt}{1pt}{l}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1595280\\-21360\\3360
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-21360\\286\\-45
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3360\\-45\\7
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3\\-224\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-75\\-3
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-80\\-40
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\72\\-18
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\72\\-16
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-75\\0
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[1595280, -21360, 3360; -21360, 286, -45; 3360, -45, 7],[240, 1, 1],[-3, -1, -1, 1, 1, -1; -224, -75, -80, 72, 72, -75; 0, -3, -40, -18, -16, 0],242,1]
%
% END OF LATTICE L243.1
%
%
% LATTICE L243.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[54960, 11040, -240; 11040, 2217, -48; -240, -48, 1],[240, 3, 1],[-3, 0, 7, 1, 1, -1; 16, 0, -40, -6, -8, 5; 48, -1, -240, -44, -120, 5],242,2]
%
% END OF LATTICE L243.2
%
%
% LATTICE L243.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[332880, 54720, -2160; 54720, 8995, -355; -2160, -355, 14],[240, 5, 1],[-5, -1, 1, 1, -1, -1; 32, 6, -8, -9, 0, 6; 40, 0, -48, -75, -160, -3],242,3]
%
% END OF LATTICE L243.3
%
%
% LATTICE L243.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1680, -720, 0; -720, -195, -15; 0, -15, 2],[240, 15, 1],[-7, -1, 3, 2, 13, 0; 16, 2, -8, -5, -32, 0; 120, 20, -48, -35, -240, -1],242,4]
%
% END OF LATTICE L243.4
%
%
% LATTICE L243.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[480, -240, 0; -240, -208, 48; 0, 48, -7],[240, 16, 1],[-1, -1, 3, 8, 1, -1; -2, -3, 5, 15, 2, 0; -14, -24, 30, 96, 13, 0],242,5]
%
% END OF LATTICE L243.5
%
%
% LATTICE L243.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[3360, -2640, 960; -2640, -48, 48; 960, 48, -29],[240, 48, 1],[-1, 0, 4, 3, 1, -1; -34, -3, 125, 97, 33, -30; -90, -8, 330, 256, 87, -80],242,6]
%
% END OF LATTICE L243.6
%
%
% LATTICE L243.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-302160, 9600, 2400; 9600, -80, -80; 2400, -80, -19],[240, 80, 1],[2, -2, -1, 1, 5, 11; 4, -3, -2, 0, 9, 21; 235, -240, -118, 120, 590, 1296],242,7]
%
% END OF LATTICE L243.7
%
%
% LATTICE L243.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-8600160, 47760, 43200; 47760, -240, -240; 43200, -240, -217],[240, 240, 1],[5, 1, -1, -2, 1, 3; 4, -1, -1, 1, 3, 4; 990, 200, -198, -400, 195, 592],242,8]
%
% END OF LATTICE L243.8
%

\medskip%
%------------------------------WEYL-GROUP-W244--------------------------------
%
\leavevmode\llap{}%
$W_{244}$%
\qquad\llap{16} lattices, $\chi=24$%
\hfill%
$2222|2222|\rtimes D_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L244.1
%
\leavevmode%
${L_{244.1}}$%
{} : {$1\above{1pt}{1pt}{2}{2}16\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{-}{}9\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{3}%
\EasyButWeakLineBreak%
{${80}\above{1pt}{1pt}{l}{2}{9}\above{1pt}{1pt}{r}{2}{20}\above{1pt}{1pt}{*}{2}{144}\above{1pt}{1pt}{b}{2}{2}\above{1pt}{1pt}{l}{2}{144}\above{1pt}{1pt}{}{2}{5}\above{1pt}{1pt}{r}{2}{36}\above{1pt}{1pt}{s}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1568880\\7920\\4320
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7920\\-39\\-24
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4320\\-24\\-7
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\480\\200
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-159\\-72
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-160\\-70
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5\\792\\360
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\159\\71
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
41\\6528\\2880
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7\\1115\\490
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7\\1116\\486
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-1568880, 7920, 4320; 7920, -39, -24; 4320, -24, -7],[720, 3, 1],[3, -1, -1, 5, 1, 41, 7, 7; 480, -159, -160, 792, 159, 6528, 1115, 1116; 200, -72, -70, 360, 71, 2880, 490, 486],243,1]
%
% END OF LATTICE L244.1
%
%
% LATTICE L244.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-32880, 480, 1680; 480, -7, -24; 1680, -24, -47],[240, 1, 1],[3, 5, 17, 35, 3, 7, -1, -1; 200, 354, 1210, 2496, 215, 504, -70, -72; 0, -4, -15, -32, -3, -8, 0, 1],243,2]
%
% END OF LATTICE L244.2
%
%
% LATTICE L244.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1271760, -7200, -18000; -7200, -21, -96; -18000, -96, -253],[240, 3, 1],[9, -4, -3, 29, 12, 137, 66, 19; 200, -96, -70, 696, 287, 3264, 1570, 450; -720, 321, 240, -2328, -963, -10992, -5295, -1524],243,3]
%
% END OF LATTICE L244.3
%
%
% LATTICE L244.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[112080, -10560, 1920; -10560, 610, -85; 1920, -85, 9],[240, 5, 1],[-1, -3, -3, -1, 4, 51, 5, 7; -40, -118, -118, -40, 157, 2000, 196, 274; -168, -475, -474, -160, 630, 8000, 783, 1090],243,4]
%
% END OF LATTICE L244.4
%
%
% LATTICE L244.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[769680, -5040, 3600; -5040, 33, -24; 3600, -24, -47],[720, 3, 1],[-7, -1, -1, 7, 8, 27, 37, 3; -1080, -152, -150, 1064, 1215, 4096, 5610, 454; 0, 1, 0, -8, -9, -32, -45, -4],243,5]
%
% END OF LATTICE L244.5
%
%
% LATTICE L244.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[105840, -13920, 11760; -13920, 1830, -1545; 11760, -1545, 1303],[240, 15, 1],[-9, 2, 3, -1, -6, -109, -12, -23; -88, 28, 38, -8, -71, -1232, -134, -250; -24, 15, 18, 0, -30, -480, -51, -90],243,6]
%
% END OF LATTICE L244.6
%
%
% LATTICE L244.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-167520, -33840, 2160; -33840, -6832, 432; 2160, 432, -23],[240, 16, 1],[-18, -5, 34, 15, 21, 4, -1, -12; 95, 27, -175, -78, -110, -21, 5, 63; 90, 32, -120, -62, -96, -19, 0, 56],243,7]
%
% END OF LATTICE L244.7
%
%
% LATTICE L244.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-91440, 446400, -89280; 446400, -232395, 45855; -89280, 45855, -9046],[720, 15, 1],[211, 127, 170, 469, 44, -39, -41, 0; 27000, 16254, 21759, 60032, 5634, -4992, -5250, -1; 134784, 81140, 108621, 299680, 28125, -24920, -26208, -5],243,8]
%
% END OF LATTICE L244.8
%
%
% LATTICE L244.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[3335760, 215280, -23760; 215280, 13845, -1530; -23760, -1530, 169],[720, 15, 1],[3, 4, 1, 1, -1, -11, 0, 5; 72, 102, 26, 24, -27, -384, -4, 102; 1072, 1485, 376, 360, -385, -5040, -37, 1620],243,9]
%
% END OF LATTICE L244.9
%
%
% LATTICE L244.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[240, 720, -240; 720, 1632, -480; -240, -480, 131],[240, 48, 1],[-13, -3, 29, 12, 16, 3, -1, -9; 15, 2, -45, -17, -21, -4, 0, 11; 30, 0, -120, -42, -48, -9, 0, 24],243,10]
%
% END OF LATTICE L244.10
%
%
% LATTICE L244.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-94560, 9360, 1680; 9360, -240, -80; 1680, -80, -19],[240, 80, 1],[3, 6, 1, -1, -3, 3, 8, 13; -71, -141, -23, 24, 70, -72, -191, -309; 562, 1120, 184, -190, -560, 565, 1504, 2440],243,11]
%
% END OF LATTICE L244.11
%
%
% LATTICE L244.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[64080, 52560, -3600; 52560, 20256, -1344; -3600, -1344, 89],[720, 48, 1],[-3, -5, -1, 2, 2, 1, -1, -5; 140, 243, 70, -75, -89, -45, 45, 228; 1990, 3456, 1000, -1062, -1264, -639, 640, 3240],243,12]
%
% END OF LATTICE L244.12
%
%
% LATTICE L244.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[720, 0, 0; 0, -19632, 672; 0, 672, -23],[720, 48, 1],[-2, 0, 1, 0, -1, -1, -14, -1; -15, -3, 0, 1, 15, 3, 15, -2; -450, -88, 0, 29, 432, 82, 360, -64],243,13]
%
% END OF LATTICE L244.13
%
%
% LATTICE L244.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[8160, 7920, -240; 7920, 6960, -240; -240, -240, 7],[240, 240, 1],[3, 7, 0, -2, -9, -1, 3, 10; -1, -3, -1, 0, 2, 0, -1, -3; 66, 120, -48, -75, -240, -30, 72, 240],243,14]
%
% END OF LATTICE L244.14
%
%
% LATTICE L244.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-108720, -164160, 1440; -164160, -245040, 2160; 1440, 2160, -19],[720, 240, 1],[7, 4, 1, -1, -5, 3, 22, 11; 6, 3, 0, -1, -3, 3, 21, 10; 1206, 640, 72, -190, -720, 565, 4032, 1960],243,15]
%
% END OF LATTICE L244.15
%
%
% LATTICE L244.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-750960, -207360, 79200; -207360, -52080, 19920; 79200, 19920, -7619],[720, 240, 1],[1, 10, 1, -1, -3, -2, 0, 7; 234, 2439, 250, -237, -753, -594, -67, 1488; 622, 6480, 664, -630, -2000, -1575, -176, 3960],243,16]
%
% END OF LATTICE L244.16
%

\medskip%
%------------------------------WEYL-GROUP-W245--------------------------------
%
\leavevmode\llap{}%
$W_{245}$%
\qquad\llap{16} lattices, $\chi=24$%
\hfill%
$222|2222|2\rtimes D_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L245.1
%
\leavevmode%
${L_{245.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{6}16\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{-}{}9\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{3}%
\EasyButWeakLineBreak%
{${80}\above{1pt}{1pt}{}{2}{9}\above{1pt}{1pt}{}{2}{5}\above{1pt}{1pt}{r}{2}{144}\above{1pt}{1pt}{s}{2}{20}\above{1pt}{1pt}{*}{2}{36}\above{1pt}{1pt}{*}{2}{80}\above{1pt}{1pt}{b}{2}{6}\above{1pt}{1pt}{l}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-488880\\1440\\4320
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1440\\-3\\-15
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4320\\-15\\-34
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
23\\2960\\1600
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4\\513\\279
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\255\\140
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\120\\72
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-130\\-70
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-126\\-72
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\400\\200
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\130\\69
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-488880, 1440, 4320; 1440, -3, -15; 4320, -15, -34],[720, 3, 1],[23, 4, 2, 1, -1, -1, 3, 1; 2960, 513, 255, 120, -130, -126, 400, 130; 1600, 279, 140, 72, -70, -72, 200, 69],244,1]
%
% END OF LATTICE L245.1
%
%
% LATTICE L245.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-392880, 2160, 4080; 2160, -11, -23; 4080, -23, -42],[240, 1, 1],[3, -1, -1, 3, 7, 4, 63, 2; 160, -46, -50, 136, 325, 187, 2960, 96; 200, -72, -70, 216, 500, 285, 4480, 141],244,2]
%
% END OF LATTICE L245.2
%
%
% LATTICE L245.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2160, -480, 240; -480, 27, -9; 240, -9, 2],[240, 3, 1],[13, 1, 2, 1, -1, -1, -7, 0; 560, 43, 85, 40, -50, -46, -320, 0; 960, 75, 150, 72, -90, -84, -600, -1],244,3]
%
% END OF LATTICE L245.3
%
%
% LATTICE L245.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3312240, 13680, 27840; 13680, -55, -115; 27840, -115, -234],[240, 5, 1],[35, 10, 3, 3, -1, -1, 7, 8; 32, 7, 1, -8, -2, 2, 16, 12; 4144, 1185, 356, 360, -118, -120, 824, 945],244,4]
%
% END OF LATTICE L245.4
%
%
% LATTICE L245.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1951920, 720, 5040; 720, 33, -21; 5040, -21, -2],[720, 3, 1],[133, 3, 17, 3, -1, -1, -7, 1; 27360, 617, 3495, 616, -210, -206, -1440, 206; 47520, 1072, 6075, 1072, -360, -358, -2520, 357],244,5]
%
% END OF LATTICE L245.5
%
%
% LATTICE L245.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-92880, -11040, 2400; -11040, -1305, 285; 2400, 285, -62],[240, 15, 1],[5, -1, -1, 1, 2, 7, 25, 2; 16, 2, -2, -8, 1, 7, 32, 4; 264, -30, -48, 0, 81, 300, 1104, 95],244,6]
%
% END OF LATTICE L245.6
%
%
% LATTICE L245.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[505680, 0, 6240; 0, 16, 0; 6240, 0, 77],[240, 16, 1],[4, 0, 1, 2, 36, 21, 43, 13; 0, 1, 0, -1, -15, -8, -15, -3; -325, 0, -80, -162, -2920, -1704, -3490, -1056],244,7]
%
% END OF LATTICE L245.7
%
%
% LATTICE L245.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-26705520, 27360, 72000; 27360, -15, -75; 72000, -75, -194],[720, 15, 1],[7, -1, -1, 1, 2, 22, 27, 7; 240, -30, -34, 24, 67, 741, 912, 238; 2504, -360, -358, 360, 716, 7875, 9664, 2505],244,8]
%
% END OF LATTICE L245.8
%
%
% LATTICE L245.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-9690480, -444240, 46800; -444240, -20355, 2145; 46800, 2145, -226],[720, 15, 1],[5, -1, -1, 3, 5, 5, 49, 3; 96, -14, -18, 40, 75, 77, 768, 50; 1944, -340, -378, 1000, 1746, 1765, 17424, 1095],244,9]
%
% END OF LATTICE L245.9
%
%
% LATTICE L245.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[240, 0, 0; 0, 48, 0; 0, 0, -1],[240, 48, 1],[-1, 0, 1, 0, -4, -3, -7, -1; 0, 1, 0, -1, -15, -8, -15, -1; -15, 0, 0, -6, -120, -72, -150, -16],244,10]
%
% END OF LATTICE L245.10
%
%
% LATTICE L245.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-11760, 11760, 5520; 11760, -11680, -5520; 5520, -5520, -2591],[240, 80, 1],[32, 49, 1, -15, -15, 1, 8, 110; -3, -8, -3, -1, 0, 1, 0, -3; 74, 120, 8, -30, -32, 0, 17, 240],244,11]
%
% END OF LATTICE L245.11
%
%
% LATTICE L245.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[18208080, -3034800, -37440; -3034800, 505824, 6240; -37440, 6240, 77],[720, 48, 1],[-48, -71, -41, -7, -1, 1, -4, -14; -245, -363, -210, -36, -5, 6, -20, -71; -3490, -5112, -2920, -486, -80, 0, -325, -1056],244,12]
%
% END OF LATTICE L245.12
%
%
% LATTICE L245.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[720, 0, 0; 0, 2832, -192; 0, -192, 13],[720, 48, 1],[-7, -1, -4, 0, 1, 0, -1, -1; 105, 16, 75, 1, 0, 1, 15, 13; 1530, 232, 1080, 14, 0, 16, 225, 192],244,13]
%
% END OF LATTICE L245.13
%
%
% LATTICE L245.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[240, 0, 0; 0, 387120, -4080; 0, -4080, 43],[240, 240, 1],[0, 1, 0, -1, -3, -8, -3, -1; 2, 0, 1, 6, 20, 57, 23, 11; 189, 0, 96, 570, 1896, 5400, 2178, 1040],244,14]
%
% END OF LATTICE L245.14
%
%
% LATTICE L245.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[720, 0, 0; 0, -11760, -5520; 0, -5520, -2591],[720, 240, 1],[-1, -8, -1, -1, 0, 1, 0, -1; -35, -171, -4, 42, 15, 0, -8, -113; 74, 360, 8, -90, -32, 0, 17, 240],244,15]
%
% END OF LATTICE L245.15
%
%
% LATTICE L245.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1161360, -979200, -12240; -979200, 1350480, 16800; -12240, 16800, 209],[720, 240, 1],[23, 19, 20, 2, 1, 0, 2, 11; -2187, -1808, -1905, -191, -96, 1, -189, -1043; 177138, 146440, 154296, 15470, 7776, -80, 15309, 84480],244,16]
%
% END OF LATTICE L245.16
%

\medskip%
%------------------------------WEYL-GROUP-W246--------------------------------
%
\leavevmode\llap{}%
$W_{246}$%
\qquad\llap{6} lattices, $\chi=36$%
\hfill%
$26322632\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L246.1
%
\leavevmode%
${L_{246.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{-}{}81\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${162}\above{1pt}{1pt}{b}{2}{2}\above{1pt}{1pt}{}{6}{6}\above{1pt}{1pt}{-}{3}{6}\above{1pt}{1pt}{s}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1920996\\17172\\602316
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
17172\\-138\\-5427
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
602316\\-5427\\-188734
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2411801\\19702224\\7130268
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-23467\\-191705\\-69378
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-750944\\-6134528\\-2220097
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-274\\-2241\\-810
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
115\\939\\340
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1377\\11248\\4071
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3923\\32047\\11598
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-1920996, 17172, 602316; 17172, -138, -5427; 602316, -5427, -188734],[324, 3, 1],[-274, 115, 1377, 3923, 20713, 642, 137, -138; -2241, 939, 11248, 32047, 169209, 5245, 1120, -1127; -810, 340, 4071, 11598, 61236, 1898, 405, -408],245,1]
%
% END OF LATTICE L246.1
%
%
% LATTICE L246.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-55971, 2835, -13527; 2835, -138, 690; -13527, 690, -3265],[81, 3, 1],[46, -20, -237, -674, -3556, -110, -23, 24; 135, -61, -716, -2033, -10719, -331, -68, 73; -162, 70, 831, 2364, 12474, 386, 81, -84],245,2]
%
% END OF LATTICE L246.2
%
%
% LATTICE L246.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-40905, 7128, 3564; 7128, -1242, -621; 3564, -621, -310],[81, 27, 1],[0, 10, 28, 74, 14, 32, 0, -4; -1, 57, 199, 553, 107, 261, 13, -23; 2, 0, -81, -270, -56, -162, -27, 0],245,3]
%
% END OF LATTICE L246.3
%
%
% LATTICE L246.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[100171080, 29039796, 25918704; 29039796, 8418696, 7513884; 25918704, 7513884, 6706319],[324, 12, 1],[-503, -187, -2122, -6147, -32761, -1045, -342, -13; 0, 6, 101, 308, 1674, 56, 23, 2; 1944, 716, 8088, 23412, 124740, 3976, 1296, 48],245,4]
%
% END OF LATTICE L246.4
%
%
% LATTICE L246.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-163620, 14256, 7128; 14256, -1242, -621; 7128, -621, -310],[324, 27, 1],[7, 16, 0, -2, 0, 5, 14, 37; 107, 261, 13, -23, -1, 57, 199, 553; -56, -162, -27, 0, 2, 0, -81, -270],245,5]
%
% END OF LATTICE L246.5
%
%
% LATTICE L246.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[117288, 48924, 7452; 48924, 28728, 9288; 7452, 9288, 5063],[324, 108, 1],[-3911, -10613, -1463, -133, 1, -1117, -6357, -19417; 11795, 32007, 4412, 401, -3, 3369, 19172, 58559; -15880, -43092, -5940, -540, 4, -4536, -25812, -78840],245,6]
%
% END OF LATTICE L246.6
%

\medskip%
%------------------------------WEYL-GROUP-W247--------------------------------
%
\leavevmode\llap{}%
$W_{247}$%
\qquad\llap{4} lattices, $\chi=24$%
\hfill%
$\infty|\infty|\infty|\infty|\rtimes D_{4}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L247.1
%
\leavevmode%
${L_{247.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}8\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{1}{}5\above{1pt}{1pt}{-}{}25\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${40}\above{1pt}{1pt}{10,3}{\infty z}{10}\above{1pt}{1pt}{20,13}{\infty b}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-124600\\2400\\1800
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2400\\-10\\-35
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1800\\-35\\-26
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-480\\0
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\1\\0
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\7\\-1
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7\\-4\\480
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\2\\205
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-124600, 2400, 1800; 2400, -10, -35; 1800, -35, -26],[200, 5, 1],[7, 3, -7, -3; -4, 2, -4, -3; 480, 205, -480, -205],246,1]
%
% END OF LATTICE L247.1
%
%
% LATTICE L247.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[1650, 100, -100; 100, -10, -5; -100, -5, 6],[50, 5, 1],[-1, -2, 1, 2; -2, -3, -2, 2; -20, -35, 20, 35],246,2]
%
% END OF LATTICE L247.2
%
%
% LATTICE L247.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[104200, -1550, 49750; -1550, 20, -740; 49750, -740, 23753],[50, 10, 1],[-31, 43, 117, 0; 2, 1, 2, 1; 65, -90, -245, 0],246,3]
%
% END OF LATTICE L247.3
%
%
% LATTICE L247.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-142800, 5800, 1000; 5800, -80, -40; 1000, -40, -7],[200, 40, 1],[2, -3, -2, 3; -1, 2, -1, -3; 290, -440, -290, 440],246,4]
%
% END OF LATTICE L247.4
%

\medskip%
%------------------------------WEYL-GROUP-W248--------------------------------
%
\leavevmode\llap{}%
$W_{248}$%
\qquad\llap{10} lattices, $\chi=48$%
\hfill%
$2\slashinfty22|22\slashinfty22|2\rtimes D_{4}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L248.1
%
\leavevmode%
${L_{248.1}}$%
{} : {$[1\above{1pt}{1pt}{1}{}2\above{1pt}{1pt}{1}{}]\above{1pt}{1pt}{}{0}128\above{1pt}{1pt}{1}{1}$}\EasyButWeakLineBreak%
{${128}\above{1pt}{1pt}{l}{2}{1}\above{1pt}{1pt}{16,9}{\infty}{4}\above{1pt}{1pt}{*}{2}{128}\above{1pt}{1pt}{s}{2}{8}\above{1pt}{1pt}{*}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
shares genus with {$ \main({L_{248.2}})$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3200\\-384\\-768
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-384\\46\\92
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-768\\92\\185
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
255\\1152\\512
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-28\\-127\\-56
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-64\\-288\\-129
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-117\\-480\\-256
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-8\\-34\\-17
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-15\\-68\\-30
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-101\\-480\\-192
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3\\-18\\-4
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[3200, -384, -768; -384, 46, 92; -768, 92, 185],[128, 2, 1],[-117, -8, -15, -101, -3, -11, 0, -1, -27, -5; -480, -34, -68, -480, -18, -96, -2, -4, -96, -18; -256, -17, -30, -192, -4, 0, 1, -2, -64, -12],247,1]
%
% END OF LATTICE L248.1
%
\hbox{}\par\smallskip%
%
% LATTICE L248.2
%
\leavevmode%
${L_{248.2}}$%
{} : {$[1\above{1pt}{1pt}{1}{}2\above{1pt}{1pt}{1}{}]\above{1pt}{1pt}{}{0}256\above{1pt}{1pt}{1}{1}$}\spacer%
\instructions{m*}%
\EasyButWeakLineBreak%
{${256}\above{1pt}{1pt}{s}{2}{8}\above{1pt}{1pt}{32,1}{\infty z}{2}\above{1pt}{1pt}{}{2}{256}\above{1pt}{1pt}{}{2}{1}\above{1pt}{1pt}{r}{2}{256}\above{1pt}{1pt}{*}{2}{8}\above{1pt}{1pt}{32,17}{\infty z}{2}\above{1pt}{1pt}{r}{2}{256}\above{1pt}{1pt}{s}{2}{4}\above{1pt}{1pt}{*}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4352\\0\\-256
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\2\\-2
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-256\\-2\\17
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-73\\-1088\\-1280
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-11\\-162\\-192
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-6\\-87\\-104
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-89\\-1280\\-1536
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-14\\-17
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-23\\-320\\-384
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-14\\-16
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\-1\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-7\\-128\\-128
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-16\\-18
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[4352, 0, -256; 0, 2, -2; -256, -2, 17],[256, 2, 1],[-73, -11, -6, -89, -1, -23, -1, 0, -7, -1; -1088, -162, -87, -1280, -14, -320, -14, -1, -128, -16; -1280, -192, -104, -1536, -17, -384, -16, 0, -128, -18],247,2]
%
% END OF LATTICE L248.2
%
\hbox{}\par\smallskip%
%
% LATTICE L248.3
%
\leavevmode%
${L_{248.3}}$%
{} : {$1\above{1pt}{1pt}{1}{1}8\above{1pt}{1pt}{1}{7}128\above{1pt}{1pt}{1}{1}$}\EasyButWeakLineBreak%
{${128}\above{1pt}{1pt}{}{2}{1}\above{1pt}{1pt}{8,1}{\infty}{4}\above{1pt}{1pt}{s}{2}{128}\above{1pt}{1pt}{b}{2}{8}\above{1pt}{1pt}{l}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4224\\-1024\\-896
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1024\\248\\216
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-896\\216\\185
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-289\\-1824\\768
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
66\\417\\-176
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
48\\304\\-129
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
111\\672\\-256
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7\\43\\-17
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
11\\70\\-30
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
63\\416\\-192
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\3\\-4
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[4224, -1024, -896; -1024, 248, 216; -896, 216, 185],[128, 8, 1],[111, 7, 11, 63, 0, -15, -1, 1, 33, 6; 672, 43, 70, 416, 3, -64, -5, 6, 192, 35; -256, -17, -30, -192, -4, 0, 1, -2, -64, -12],247,3]
%
% END OF LATTICE L248.3
%
\hbox{}\par\smallskip%
%
% LATTICE L248.4
%
\leavevmode%
${L_{248.4}}$%
{} : {$1\above{1pt}{1pt}{1}{7}8\above{1pt}{1pt}{1}{1}128\above{1pt}{1pt}{1}{1}$}\EasyButWeakLineBreak%
{${128}\above{1pt}{1pt}{r}{2}{4}\above{1pt}{1pt}{8,1}{\infty a}{4}\above{1pt}{1pt}{b}{2}{128}\above{1pt}{1pt}{l}{2}{8}\above{1pt}{1pt}{}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
254080\\5888\\-3456
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5888\\136\\-80
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3456\\-80\\47
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
671\\672\\51072
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
14\\13\\1064
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-9\\-9\\-685
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-33\\-64\\-2560
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-4\\-5\\-306
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3\\1\\-222
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-17\\32\\-1216
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\5\\8
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[254080, 5888, -3456; 5888, 136, -80; -3456, -80, 47],[128, 8, 1],[-33, -4, -3, -17, 0, 1, 0, -1, -15, -2; -64, -5, 1, 32, 5, 32, 1, -5, -64, -7; -2560, -306, -222, -1216, 8, 128, 2, -82, -1216, -160],247,4]
%
% END OF LATTICE L248.4
%
%
% LATTICE L248.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[4224, -512, -384; -512, 62, 46; -384, 46, 31],[128, 2, 1],[111, 7, 11, 63, 0, -15, -1, 1, 33, 3; 1088, 69, 110, 640, 1, -128, -9, 10, 320, 29; -256, -17, -30, -192, -2, 0, 1, -2, -64, -6],247,5]
%
% END OF LATTICE L248.5
%
%
% LATTICE L248.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-184448, -7168, 1664; -7168, -240, 64; 1664, 64, -15],[128, 16, 1],[0, 7, 17, 5, 3, 1, 1, -9, -3, -2; -4, -20, 4, 4, 5, 2, 4, -20, -8, -7; -23, 640, 1856, 562, 352, 119, 128, -1088, -370, -256],247,6]
%
% END OF LATTICE L248.6
%
%
% LATTICE L248.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-130944, -71680, 1408; -71680, -39184, 768; 1408, 768, -15],[128, 16, 1],[2, 3, -19, -7, -11, -2, -3, 19, 7, 11; -4, 8, 72, 24, 34, 6, 8, -56, -20, -30; -23, 640, 1856, 562, 704, 119, 128, -1088, -370, -512],247,7]
%
% END OF LATTICE L248.7
%
%
% LATTICE L248.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-184448, -14336, 1664; -14336, -960, 128; 1664, 128, -15],[128, 64, 1],[5, 17, 7, 0, -4, -3, -9, 1, 1, 6; 2, 2, -10, -2, -7, -4, -10, 2, 1, 5; 562, 1856, 640, -23, -512, -370, -1088, 128, 119, 704],247,8]
%
% END OF LATTICE L248.8
%
%
% LATTICE L248.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-28544, 53120, 13824; 53120, -98752, -25728; 13824, -25728, -6695],[128, 64, 1],[-71, -497, -791, -218, -242, -119, -263, 31, 28, 52; 1, 0, -8, -3, -5, -3, -8, 0, 1, 3; -150, -1024, -1600, -438, -480, -234, -512, 64, 54, 96],247,9]
%
% END OF LATTICE L248.9
%
%
% LATTICE L248.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1777920, -122624, 7424; -122624, -8320, 512; 7424, 512, -31],[256, 128, 1],[-1, -5, 1, 1, 13, 8, 33, 27, 5, 1; -1, -1, 1, 0, -2, -3, -15, -17, -4, -6; -258, -1216, 256, 239, 3072, 1858, 7616, 6144, 1122, 128],247,10]
%
% END OF LATTICE L248.10
%

\medskip%
%------------------------------WEYL-GROUP-W249--------------------------------
%
\leavevmode\llap{}%
$W_{249}$%
\qquad\llap{60} lattices, $\chi=30$%
\hfill%
$222|2222\slashtwo2\rtimes D_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L249.1
%
\leavevmode%
${L_{249.1}}$%
{} : {$1\above{1pt}{1pt}{2}{0}8\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{2}{}11\above{1pt}{1pt}{1}{}$}\EasyButWeakLineBreak%
{${132}\above{1pt}{1pt}{*}{2}{8}\above{1pt}{1pt}{*}{2}{44}\above{1pt}{1pt}{s}{2}{24}\above{1pt}{1pt}{l}{2}{11}\above{1pt}{1pt}{}{2}{8}\above{1pt}{1pt}{}{2}{33}\above{1pt}{1pt}{r}{2}{4}\above{1pt}{1pt}{l}{2}{1}\above{1pt}{1pt}{r}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-217272\\792\\528
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
792\\-1\\-4
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
528\\-4\\1
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-5\\-858\\-792
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-172\\-156
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-176\\-154
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\168\\156
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5\\847\\770
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5\\848\\768
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
14\\2376\\2145
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\170\\152
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\-1
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-217272, 792, 528; 792, -1, -4; 528, -4, 1],[264, 1, 1],[-5, -1, -1, 1, 5, 5, 14, 1, 0; -858, -172, -176, 168, 847, 848, 2376, 170, 0; -792, -156, -154, 156, 770, 768, 2145, 152, -1],248,1]
%
% END OF LATTICE L249.1
%
\hbox{}\par\smallskip%
%
% LATTICE L249.2
%
\leavevmode%
${L_{249.2}}$%
{} : {$[1\above{1pt}{1pt}{1}{}2\above{1pt}{1pt}{1}{}]\above{1pt}{1pt}{}{2}16\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{2}{}11\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${33}\above{1pt}{1pt}{}{2}{2}\above{1pt}{1pt}{r}{2}{176}\above{1pt}{1pt}{l}{2}{6}\above{1pt}{1pt}{}{2}{11}\above{1pt}{1pt}{r}{2}{8}\above{1pt}{1pt}{*}{2}{528}\above{1pt}{1pt}{l}{2}{1}\above{1pt}{1pt}{r}{2}{16}\above{1pt}{1pt}{l}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1833744\\4752\\8448
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4752\\-10\\-24
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
8448\\-24\\-37
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
61\\7953\\8745
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
10\\1303\\1434
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
73\\9504\\10472
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\129\\144
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-132\\-143
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-130\\-144
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
13\\1716\\1848
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\131\\143
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
11\\1436\\1576
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-1833744, 4752, 8448; 4752, -10, -24; 8448, -24, -37],[528, 2, 1],[61, 10, 73, 1, -1, -1, 13, 1, 11; 7953, 1303, 9504, 129, -132, -130, 1716, 131, 1436; 8745, 1434, 10472, 144, -143, -144, 1848, 143, 1576],248,2]
%
% END OF LATTICE L249.2
%
\hbox{}\par\smallskip%
%
% LATTICE L249.3
%
\leavevmode%
${L_{249.3}}$%
{} : {$[1\above{1pt}{1pt}{1}{}2\above{1pt}{1pt}{1}{}]\above{1pt}{1pt}{}{0}16\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{2}{}11\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{m}%
\EasyButWeakLineBreak%
{${33}\above{1pt}{1pt}{r}{2}{8}\above{1pt}{1pt}{*}{2}{176}\above{1pt}{1pt}{s}{2}{24}\above{1pt}{1pt}{*}{2}{44}\above{1pt}{1pt}{l}{2}{2}\above{1pt}{1pt}{}{2}{528}\above{1pt}{1pt}{}{2}{1}\above{1pt}{1pt}{}{2}{16}\above{1pt}{1pt}{}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
528\\0\\0
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\2\\0
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\-1
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-8\\-99\\-231
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3\\-34\\-84
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-13\\-132\\-352
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-6\\-24
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\0\\-22
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\1\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\0\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\-1\\-1
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-16\\-32
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[528, 0, 0; 0, 2, 0; 0, 0, -1],[528, 2, 1],[-8, -3, -13, -1, -1, 0, 1, 0, -1; -99, -34, -132, -6, 0, 1, 0, -1, -16; -231, -84, -352, -24, -22, 0, 0, -1, -32],248,3]
%
% END OF LATTICE L249.3
%
\hbox{}\par\smallskip%
%
% LATTICE L249.4
%
\leavevmode%
${L_{249.4}}$%
{} : {$[1\above{1pt}{1pt}{-}{}2\above{1pt}{1pt}{1}{}]\above{1pt}{1pt}{}{6}16\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{2}{}11\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{m}%
\EasyButWeakLineBreak%
{${132}\above{1pt}{1pt}{l}{2}{2}\above{1pt}{1pt}{}{2}{176}\above{1pt}{1pt}{}{2}{6}\above{1pt}{1pt}{r}{2}{44}\above{1pt}{1pt}{*}{2}{8}\above{1pt}{1pt}{s}{2}{528}\above{1pt}{1pt}{*}{2}{4}\above{1pt}{1pt}{*}{2}{16}\above{1pt}{1pt}{*}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-243408\\1584\\1584
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1584\\-10\\-12
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1584\\-12\\-1
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
83\\10758\\1914
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7\\907\\162
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
53\\6864\\1232
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\129\\24
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-132\\-22
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-130\\-24
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\132\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\130\\22
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7\\908\\160
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-243408, 1584, 1584; 1584, -10, -12; 1584, -12, -1],[528, 2, 1],[83, 7, 53, 1, -1, -1, 1, 1, 7; 10758, 907, 6864, 129, -132, -130, 132, 130, 908; 1914, 162, 1232, 24, -22, -24, 0, 22, 160],248,4]
%
% END OF LATTICE L249.4
%
\hbox{}\par\smallskip%
%
% LATTICE L249.5
%
\leavevmode%
${L_{249.5}}$%
{} : {$[1\above{1pt}{1pt}{-}{}2\above{1pt}{1pt}{1}{}]\above{1pt}{1pt}{}{4}16\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{2}{}11\above{1pt}{1pt}{1}{}$}\EasyButWeakLineBreak%
{${132}\above{1pt}{1pt}{*}{2}{8}\above{1pt}{1pt}{s}{2}{176}\above{1pt}{1pt}{*}{2}{24}\above{1pt}{1pt}{l}{2}{11}\above{1pt}{1pt}{}{2}{2}\above{1pt}{1pt}{r}{2}{528}\above{1pt}{1pt}{s}{2}{4}\above{1pt}{1pt}{s}{2}{16}\above{1pt}{1pt}{s}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
19536\\4752\\1056
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4752\\1154\\238
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1056\\238\\-131
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
157\\-660\\66
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
9\\-38\\4
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-639\\2684\\-264
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-347\\1458\\-144
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1191\\5005\\-495
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-558\\2345\\-232
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-12061\\50688\\-5016
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-197\\828\\-82
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-19\\80\\-8
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[19536, 4752, 1056; 4752, 1154, 238; 1056, 238, -131],[528, 2, 1],[157, 9, -639, -347, -1191, -558, -12061, -197, -19; -660, -38, 2684, 1458, 5005, 2345, 50688, 828, 80; 66, 4, -264, -144, -495, -232, -5016, -82, -8],248,5]
%
% END OF LATTICE L249.5
%
%
% LATTICE L249.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[132, 0, 0; 0, 2, 0; 0, 0, -1],[132, 2, 1],[1, 0, -1, -1, -13, -3, -16, -1, 0; 0, 1, 0, -3, -66, -17, -99, -8, -1; 0, 0, -11, -12, -176, -42, -231, -16, -1],248,6]
%
% END OF LATTICE L249.6
%
%
% LATTICE L249.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-121704, 1584, 792; 1584, -2, -12; 792, -12, -5],[264, 2, 1],[1, -1, -1, 1, 53, 7, 83, 7, 1; 0, -12, -11, 12, 616, 81, 957, 80, 11; 132, -130, -132, 129, 6864, 907, 10758, 908, 130],248,7]
%
% END OF LATTICE L249.7
%
%
% LATTICE L249.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[264, 0, 0; 0, -2, 0; 0, 0, 1],[264, 2, 1],[1, 0, -1, -1, -13, -3, -16, -1, 0; 0, 0, -11, -12, -176, -42, -231, -16, -1; 0, 1, 0, -6, -132, -34, -198, -16, -2],248,8]
%
% END OF LATTICE L249.8
%
%
% LATTICE L249.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[148632, -264, -792; -264, 3, 0; -792, 0, 5],[264, 3, 1],[-1, -1, -5, -1, -8, -7, -6, -1, 0; -88, -84, -418, -84, -682, -600, -517, -88, -1; -154, -156, -792, -160, -1287, -1128, -968, -162, 0],248,9]
%
% END OF LATTICE L249.9
%
%
% LATTICE L249.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[83292, 0, 1848; 0, 6, 0; 1848, 0, 41],[132, 6, 1],[1, 0, 8, 3, 137, 33, 61, 13, 1; 0, 1, 0, -1, -66, -17, -33, -8, -1; -44, 0, -363, -136, -6204, -1494, -2761, -588, -45],248,10]
%
% END OF LATTICE L249.10
%
%
% LATTICE L249.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[61512, 30888, -264; 30888, 15508, -132; -264, -132, 1],[264, 4, 1],[190, 71, 153, 23, 21, -1, -16, 0, 12; -396, -148, -319, -48, -44, 2, 33, 0, -25; -2079, -776, -1672, -252, -242, 4, 132, -1, -132],248,11]
%
% END OF LATTICE L249.11
%
%
% LATTICE L249.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-65208, 2376, 264; 2376, -4, -12; 264, -12, -1],[264, 4, 1],[1, -1, -2, 1, 10, 11, 67, 3, 1; 0, -6, -11, 6, 55, 60, 363, 16, 5; 198, -196, -396, 192, 1947, 2144, 13068, 586, 196],248,12]
%
% END OF LATTICE L249.12
%
%
% LATTICE L249.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1533576, -76560, 1320; -76560, 3822, -66; 1320, -66, 1],[264, 6, 1],[9, -1, -5, 0, 67, 10, 43, 13, 3; 176, -20, -99, 0, 1320, 197, 847, 256, 59; -220, 6, 66, -1, -1320, -195, -836, -252, -60],248,13]
%
% END OF LATTICE L249.13
%
%
% LATTICE L249.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-17160, -2112, 792; -2112, -174, 72; 792, 72, -29],[264, 6, 1],[-1, -1, 1, 1, 28, 7, 53, 3, 1; -33, -30, 44, 32, 869, 216, 1628, 91, 28; -110, -102, 132, 106, 2904, 723, 5456, 306, 96],248,14]
%
% END OF LATTICE L249.14
%
%
% LATTICE L249.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-270600, -6072, 2904; -6072, -128, 64; 2904, 64, -31],[264, 8, 1],[7, 0, -3, -1, -3, 0, 7, 1, 1; 132, 1, -55, -21, -110, -7, -33, 12, 17; 924, 2, -396, -138, -528, -17, 528, 116, 128],248,15]
%
% END OF LATTICE L249.15
%
%
% LATTICE L249.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1933800, 5808, 14520; 5808, -11, -44; 14520, -44, -109],[264, 11, 1],[19, 65, 5, 1, -1, -1, 5, 5, 21; 144, 488, 37, 0, -8, -4, 42, 40, 162; 2469, 8448, 650, 132, -130, -132, 648, 649, 2728],248,16]
%
% END OF LATTICE L249.16
%
%
% LATTICE L249.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-132, 0, -132; 0, 22, 0; -132, 0, -131],[132, 22, 1],[34, 57, 17, -1, -1, 0, 11, 10, 39; -9, -17, -6, -3, 0, 1, 0, -1, -8; -39, -66, -20, 0, 1, 0, -12, -11, -44],248,17]
%
% END OF LATTICE L249.17
%
%
% LATTICE L249.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[385176, -38280, 16368; -38280, 3804, -1632; 16368, -1632, 623],[264, 12, 1],[-62, -17, 273, 105, 2187, 1027, 926, 182, 4; -605, -166, 2662, 1024, 21329, 10016, 9031, 1775, 39; 44, 12, -198, -76, -1584, -744, -671, -132, -3],248,18]
%
% END OF LATTICE L249.18
%
%
% LATTICE L249.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-554928, -11088, 4224; -11088, -186, 78; 4224, 78, -31],[528, 6, 1],[5, -1, -2, 0, 47, 7, 15, 9, 1; 220, -46, -88, 1, 2200, 325, 693, 412, 45; 1232, -252, -495, 2, 11880, 1764, 3773, 2256, 249],248,19]
%
% END OF LATTICE L249.19
%
%
% LATTICE L249.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[89232, -77616, 14784; -77616, 63366, -11454; 14784, -11454, 1973],[528, 6, 1],[1693, -45, -503, 8, 10159, 1500, 6429, 1937, 461; 4444, -118, -1320, 21, 26664, 3937, 16874, 5084, 1210; 13112, -348, -3894, 62, 78672, 11616, 49786, 15000, 3570],248,20]
%
% END OF LATTICE L249.20
%
%
% LATTICE L249.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[5420976, 0, 30624; 0, 6, 0; 30624, 0, 173],[528, 6, 1],[1, 0, 19, 7, 313, 75, 69, 29, 1; 0, 1, 0, -2, -132, -34, -33, -16, -1; -176, 0, -3366, -1240, -55440, -13284, -12221, -5136, -177],248,21]
%
% END OF LATTICE L249.21
%
%
% LATTICE L249.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[55704, 1320, -528; 1320, -12, -12; -528, -12, 5],[264, 12, 1],[1, -1, -3, -1, -6, -1, 1, 1, 1; -11, -8, -11, -2, -11, -2, 0, 1, 0; 44, -144, -363, -112, -660, -108, 110, 108, 102],248,22]
%
% END OF LATTICE L249.22
%
%
% LATTICE L249.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-34320, 528, 528; 528, -6, -12; 528, -12, -1],[528, 6, 1],[53, 7, 14, 1, 1, -1, -1, 1, 3; 2200, 291, 583, 42, 44, -42, -44, 40, 124; 1144, 150, 297, 20, 0, -24, -22, 24, 66],248,23]
%
% END OF LATTICE L249.23
%
%
% LATTICE L249.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[244464, 528, -528; 528, -8, 0; -528, 0, 1],[528, 8, 1],[1, 0, -1, -1, -13, -3, -8, -1, 0; 66, 1, -55, -57, -748, -173, -462, -58, 0; 528, 4, -506, -516, -6776, -1568, -4191, -528, -1],248,24]
%
% END OF LATTICE L249.24
%
%
% LATTICE L249.25
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[528, 0, 0; 0, 8, 0; 0, 0, -1],[528, 8, 1],[-16, -3, -13, -1, -1, 0, 1, 0, -1; -99, -17, -66, -3, 0, 1, 0, -1, -8; -462, -84, -352, -24, -22, 0, 0, -2, -32],248,25]
%
% END OF LATTICE L249.25
%
%
% LATTICE L249.26
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-614064, -20064, 4752; -20064, -584, 144; 4752, 144, -35],[528, 8, 1],[13, 0, -2, -1, 7, 3, 23, 3, 1; 792, 1, -121, -63, 374, 169, 1320, 176, 60; 5016, 4, -770, -396, 2464, 1096, 8514, 1128, 382],248,26]
%
% END OF LATTICE L249.26
%
%
% LATTICE L249.27
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-753456, 0, 5280; 0, 8, 0; 5280, 0, -37],[528, 8, 1],[23, 3, 7, -1, -1, 0, 13, 1, 3; -99, -17, -66, -3, 0, 1, 0, -1, -8; 3234, 420, 968, -144, -143, 0, 1848, 142, 424],248,27]
%
% END OF LATTICE L249.27
%
%
% LATTICE L249.28
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-5016, -19800, 1848; -19800, -66242, 6204; 1848, 6204, -581],[264, 22, 1],[11, -1, -1, 1, 23, 37, 43, 47, 11; 144, -10, -13, 9, 284, 460, 537, 592, 141; 1572, -110, -142, 99, 3104, 5027, 5868, 6468, 1540],248,28]
%
% END OF LATTICE L249.28
%
%
% LATTICE L249.29
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-264, 2904, -264; 2904, -30602, 2772; -264, 2772, -251],[264, 22, 1],[11, 0, -1, -1, 17, 57, 34, 39, 10; 12, 1, -1, -6, 8, 32, 21, 28, 9; 120, 11, -10, -66, 68, 286, 192, 264, 88],248,29]
%
% END OF LATTICE L249.29
%
%
% LATTICE L249.30
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-20856, -14520, 792; -14520, -9600, 528; 792, 528, -29],[264, 24, 1],[-3, 0, 7, 1, 29, 3, 19, 1, -1; -22, 1, 55, 7, 176, 17, 99, 2, -9; -484, 18, 1188, 154, 3960, 387, 2288, 60, -192],248,30]
%
% END OF LATTICE L249.30
%
%
% LATTICE L249.31
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[23496, -7128, 792; -7128, 2112, -231; 792, -231, 25],[264, 33, 1],[1, -1, -1, -1, 2, 29, 3, 11, 3; 10, -4, -8, -8, 19, 272, 28, 102, 28; 62, 0, -42, -44, 111, 1584, 163, 594, 165],248,31]
%
% END OF LATTICE L249.31
%
%
% LATTICE L249.32
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-309804, 0, 3564; 0, 66, 0; 3564, 0, -41],[132, 66, 1],[3, 0, -1, -1, 11, 39, 8, 29, 8; 0, 1, 0, -1, -6, -17, -3, -8, -1; 260, 0, -87, -88, 948, 3366, 691, 2508, 693],248,32]
%
% END OF LATTICE L249.32
%
%
% LATTICE L249.33
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1864104, 615648, -14256; 615648, -203324, 4708; -14256, 4708, -109],[264, 44, 1],[5, -1, -1, 1, 10, 65, 19, 21, 5; 21, -2, -4, 0, 37, 244, 72, 81, 20; 252, 44, -42, -132, 288, 2024, 621, 748, 209],248,33]
%
% END OF LATTICE L249.33
%
%
% LATTICE L249.34
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-149717040, 140448, 280896; 140448, -110, -264; 280896, -264, -527],[528, 22, 1],[23, -1, -1, 1, 43, 70, 41, 91, 11; 276, -10, -12, 9, 504, 823, 483, 1076, 131; 12120, -528, -527, 528, 22664, 36894, 21609, 47960, 5797],248,34]
%
% END OF LATTICE L249.34
%
%
% LATTICE L249.35
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-8991312, 0, 34320; 0, 22, 0; 34320, 0, -131],[528, 22, 1],[11, 0, -1, -1, 17, 57, 17, 39, 5; 0, 1, 0, -6, -12, -34, -9, -16, -1; 2880, 0, -262, -264, 4448, 14916, 4449, 10208, 1309],248,35]
%
% END OF LATTICE L249.35
%
%
% LATTICE L249.36
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-9837168, 35904, 35904; 35904, -110, -132; 35904, -132, -131],[528, 22, 1],[11, -1, -1, 1, 23, 37, 43, 47, 11; 132, -10, -12, 9, 264, 427, 498, 548, 130; 2880, -264, -262, 264, 6032, 9702, 11274, 12320, 2882],248,36]
%
% END OF LATTICE L249.36
%
%
% LATTICE L249.37
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[264, -2904, -1320; -2904, -12628, -5676; -1320, -5676, -2551],[264, 44, 1],[38, 65, 5, 1, -1, -1, 5, 10, 21; -1011, -1714, -130, 0, 29, 20, -144, -279, -568; 2232, 3784, 287, 0, -64, -44, 318, 616, 1254],248,37]
%
% END OF LATTICE L249.37
%
%
% LATTICE L249.38
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[37488, 16896, 0; 16896, 7546, 22; 0, 22, -7],[528, 22, 1],[-173, -68, -9, 19, 9, -1, -19, -65, -55; 384, 151, 20, -42, -20, 2, 42, 144, 122; 1176, 462, 61, -132, -64, 0, 126, 440, 374],248,38]
%
% END OF LATTICE L249.38
%
%
% LATTICE L249.39
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[82896, 528, -29568; 528, -24, -96; -29568, -96, 10235],[528, 24, 1],[59, 4, -155, -55, -2213, -515, -461, -177, -1; 594, 41, -1551, -551, -22176, -5161, -4620, -1774, -10; 176, 12, -462, -164, -6600, -1536, -1375, -528, -3],248,39]
%
% END OF LATTICE L249.39
%
%
% LATTICE L249.40
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[5420976, 0, 30624; 0, 24, 0; 30624, 0, 173],[528, 24, 1],[1, 0, 19, 7, 313, 75, 138, 29, 2; 0, 1, 0, -1, -66, -17, -33, -8, -1; -176, 0, -3366, -1240, -55440, -13284, -24442, -5136, -354],248,40]
%
% END OF LATTICE L249.40
%
%
% LATTICE L249.41
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-8976, 6336, -528; 6336, -3864, 312; -528, 312, -25],[528, 24, 1],[5, 0, -4, -1, -19, -3, -3, 1, 1; 44, 1, -33, -9, -198, -35, -44, 4, 8; 440, 12, -330, -92, -2112, -384, -506, 24, 78],248,41]
%
% END OF LATTICE L249.41
%
%
% LATTICE L249.42
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-8093712, 0, 15840; 0, 24, 0; 15840, 0, -31],[528, 24, 1],[5, 0, -2, -1, -19, -3, -3, 1, 1; 0, 1, 0, -1, -66, -17, -33, -8, -1; 2552, 0, -1023, -512, -9768, -1548, -1562, 504, 510],248,42]
%
% END OF LATTICE L249.42
%
%
% LATTICE L249.43
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-109032, -117744, 1848; -117744, -126390, 1980; 1848, 1980, -31],[264, 66, 1],[1, -1, -3, -5, -33, -41, -13, -25, 1; -4, 2, 11, 19, 128, 160, 51, 100, -3; -196, 66, 522, 913, 6192, 7755, 2476, 4884, -132],248,43]
%
% END OF LATTICE L249.43
%
%
% LATTICE L249.44
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[264, -8712, 264; -8712, -597894, 18282; 264, 18282, -559],[264, 66, 1],[-1, -1, 11, 21, 38, 97, 63, 33, 1; -5, -2, 56, 104, 185, 470, 304, 157, 0; -164, -66, 1836, 3410, 6066, 15411, 9968, 5148, 0],248,44]
%
% END OF LATTICE L249.44
%
%
% LATTICE L249.45
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-888888, -455928, 6864; -455928, -233728, 3520; 6864, 3520, -53],[264, 88, 1],[5, 0, -1, -1, 7, 12, 29, 17, 9; 6, 1, -1, -3, 4, 8, 21, 14, 9; 1044, 66, -196, -330, 1168, 2079, 5136, 3124, 1760],248,45]
%
% END OF LATTICE L249.45
%
%
% LATTICE L249.46
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[401016, 284592, -3168; 284592, 201300, -2244; -3168, -2244, 25],[264, 132, 1],[2, 1, -1, -1, 7, 49, 5, 18, 5; 3, 0, -2, -2, 11, 78, 8, 29, 8; 524, 132, -306, -308, 1872, 13200, 1351, 4884, 1353],248,46]
%
% END OF LATTICE L249.46
%
%
% LATTICE L249.47
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-5419920, -1332144, 30624; -1332144, -327162, 7524; 30624, 7524, -173],[528, 66, 1],[7, -1, -1, 0, 37, 61, 12, 81, 10; 28, -2, -4, -1, 136, 227, 45, 308, 39; 2456, -264, -351, -44, 12456, 20658, 4079, 27720, 3465],248,47]
%
% END OF LATTICE L249.47
%
%
% LATTICE L249.48
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-218064, -113520, -54912; -113520, -58938, -28512; -54912, -28512, -13793],[528, 66, 1],[1, -1, -3, -5, -33, -41, -13, -25, 1; 60, 2, -148, -267, -1840, -2315, -742, -1484, 30; -128, 0, 318, 572, 3936, 4950, 1586, 3168, -66],248,48]
%
% END OF LATTICE L249.48
%
%
% LATTICE L249.49
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-7860336, 0, 17952; 0, 66, 0; 17952, 0, -41],[528, 66, 1],[3, 0, -1, -1, 11, 39, 4, 29, 4; 0, 1, 0, -2, -12, -34, -3, -16, -1; 1312, 0, -438, -440, 4800, 17028, 1747, 12672, 1749],248,49]
%
% END OF LATTICE L249.49
%
%
% LATTICE L249.50
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-139128, -113520, -55704; -113520, -91740, -45012; -55704, -45012, -22085],[264, 132, 1],[6, 29, 2, -1, -1, -1, 1, 6, 11; -545, -2496, -154, 174, 119, 66, -118, -655, -1082; 1096, 5016, 309, -352, -240, -132, 238, 1320, 2178],248,50]
%
% END OF LATTICE L249.50
%
%
% LATTICE L249.51
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-9269040, 34848, 34848; 34848, -66, -132; 34848, -132, -131],[528, 66, 1],[63, 97, 19, 21, 11, -1, -1, 1, 33; 240, 371, 73, 82, 44, -2, -4, 0, 124; 16504, 25410, 4977, 5500, 2880, -264, -262, 264, 8646],248,51]
%
% END OF LATTICE L249.51
%
%
% LATTICE L249.52
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-7458000, -1266144, 28512; -1266144, -214808, 4840; 28512, 4840, -109],[528, 88, 1],[11, 0, -1, -1, 17, 57, 17, 39, 5; 12, 1, -1, -3, 14, 49, 15, 36, 5; 3408, 44, -306, -396, 5064, 17072, 5109, 11792, 1529],248,52]
%
% END OF LATTICE L249.52
%
%
% LATTICE L249.53
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-8991312, 0, 34320; 0, 88, 0; 34320, 0, -131],[528, 88, 1],[11, 0, -1, -1, 17, 57, 34, 39, 10; 0, 1, 0, -3, -6, -17, -9, -8, -1; 2880, 0, -262, -264, 4448, 14916, 8898, 10208, 2618],248,53]
%
% END OF LATTICE L249.53
%
%
% LATTICE L249.54
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-528, 23232, -528; 23232, -981464, 22264; -528, 22264, -505],[528, 88, 1],[23, 0, -2, -1, 37, 123, 73, 83, 21; 12, 1, -1, -3, 14, 49, 30, 36, 10; 504, 44, -42, -132, 576, 2024, 1242, 1496, 418],248,54]
%
% END OF LATTICE L249.54
%
%
% LATTICE L249.55
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-528, 0, -528; 0, 88, 0; -528, 0, -527],[528, 88, 1],[23, 0, -1, -1, 37, 123, 73, 83, 21; 0, 1, 0, -3, -6, -17, -9, -8, -1; -24, 0, 1, 0, -40, -132, -78, -88, -22],248,55]
%
% END OF LATTICE L249.55
%
%
% LATTICE L249.56
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-505560, -270072, 3960; -270072, -143616, 2112; 3960, 2112, -31],[264, 264, 1],[-1, 0, 5, 9, 31, 39, 25, 25, -1; -1, 1, 6, 10, 33, 41, 26, 25, -2; -196, 66, 1044, 1826, 6192, 7755, 4952, 4884, -264],248,56]
%
% END OF LATTICE L249.56
%
%
% LATTICE L249.57
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[4917264, 1405536, -11088; 1405536, 401016, -3168; -11088, -3168, 25],[528, 264, 1],[3, 0, -1, -1, 11, 39, 4, 29, 4; 4, 1, -1, -1, 14, 49, 5, 36, 5; 1840, 132, -570, -572, 6648, 23496, 2407, 17424, 2409],248,57]
%
% END OF LATTICE L249.57
%
%
% LATTICE L249.58
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-7860336, 0, 17952; 0, 264, 0; 17952, 0, -41],[528, 264, 1],[3, 0, -1, -1, 11, 39, 8, 29, 8; 0, 1, 0, -1, -6, -17, -3, -8, -1; 1312, 0, -438, -440, 4800, 17028, 3494, 12672, 3498],248,58]
%
% END OF LATTICE L249.58
%
%
% LATTICE L249.59
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-13134000, -4994880, 37488; -4994880, -1898952, 14256; 37488, 14256, -107],[528, 264, 1],[7, 0, -2, -1, 31, 105, 21, 73, 19; 4, 1, -1, -1, 14, 49, 10, 36, 10; 2984, 132, -834, -484, 12720, 43296, 8686, 30360, 7986],248,59]
%
% END OF LATTICE L249.59
%
%
% LATTICE L249.60
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-21311664, 0, 60720; 0, 264, 0; 60720, 0, -173],[528, 264, 1],[7, 0, -1, -1, 31, 105, 21, 73, 19; 0, 1, 0, -1, -6, -17, -3, -8, -1; 2456, 0, -351, -352, 10872, 36828, 7366, 25608, 6666],248,60]
%
% END OF LATTICE L249.60
%

\medskip%
%------------------------------WEYL-GROUP-W250--------------------------------
%
\leavevmode\llap{}%
$W_{250}$%
\qquad\llap{8} lattices, $\chi=8$%
\hfill%
$2\slashthree22|2\rtimes D_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L250.1
%
\leavevmode%
${L_{250.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}8\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{1}{}3\above{1pt}{1pt}{-}{}9\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${90}\above{1pt}{1pt}{b}{2}{6}\above{1pt}{1pt}{+}{3}{6}\above{1pt}{1pt}{b}{2}{10}\above{1pt}{1pt}{l}{2}{24}\above{1pt}{1pt}{r}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-377640\\5040\\-56160
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5040\\-66\\765
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-56160\\765\\-8162
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
28\\1095\\-90
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
15\\589\\-48
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-14\\-548\\45
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-39\\-1530\\125
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-45\\-1768\\144
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-377640, 5040, -56160; 5040, -66, 765; -56160, 765, -8162],[360, 3, 1],[28, 15, -14, -39, -45; 1095, 589, -548, -1530, -1768; -90, -48, 45, 125, 144],249,1]
%
% END OF LATTICE L250.1
%
%
% LATTICE L250.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-94410, 2520, 15930; 2520, -66, -435; 15930, -435, -2612],[90, 3, 1],[-34, -18, 17, 47, 27; -705, -371, 352, 970, 556; -90, -48, 45, 125, 72],249,2]
%
% END OF LATTICE L250.2
%
%
% LATTICE L250.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[110880, -230130, 50490; -230130, 477732, -104790; 50490, -104790, 22991],[90, 6, 1],[41, 67, 378, 532, 149; 0, 2, 11, 15, 4; -90, -138, -780, -1100, -309],249,3]
%
% END OF LATTICE L250.3
%
%
% LATTICE L250.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-311130, 98280, -13320; 98280, -31020, 4215; -13320, 4215, -568],[90, 15, 1],[-4, -60, 7, 21, 87; -9, -131, 16, 46, 190; 27, 435, -45, -151, -630],249,4]
%
% END OF LATTICE L250.4
%
%
% LATTICE L250.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[37645380, 2964870, 18494910; 2964870, 233520, 1456620; 18494910, 1456620, 9086419],[90, 30, 1],[-185, 573, 3188, 810, 933; -9, 23, 131, 33, 37; 378, -1170, -6510, -1654, -1905],249,5]
%
% END OF LATTICE L250.5
%
%
% LATTICE L250.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-386860680, 42923880, -1119240; 42923880, -4762590, 124185; -1119240, 124185, -3238],[360, 15, 1],[-4, -63, 7, 22, 183; -33, -515, 58, 180, 1496; 117, 2025, -195, -701, -5880],249,6]
%
% END OF LATTICE L250.6
%
%
% LATTICE L250.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-29520, 3960, -1800; 3960, -528, 240; -1800, 240, -109],[360, 24, 1],[-2, 0, 1, 1, 0; -15, -11, 7, 25, 4; 0, -24, 0, 40, 9],249,7]
%
% END OF LATTICE L250.7
%
%
% LATTICE L250.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-5040, 1800, 0; 1800, 16080, 720; 0, 720, 31],[360, 120, 1],[-1, -11, 2, 4, 4; -3, -31, 5, 11, 11; 72, 720, -120, -256, -255],249,8]
%
% END OF LATTICE L250.8
%

\medskip%
%------------------------------WEYL-GROUP-W251--------------------------------
%
\leavevmode\llap{}%
$W_{251}$%
\qquad\llap{8} lattices, $\chi=8$%
\hfill%
$26|62|\rtimes D_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L251.1
%
\leavevmode%
${L_{251.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}8\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{-}{}9\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${24}\above{1pt}{1pt}{r}{2}{18}\above{1pt}{1pt}{}{6}{6}\above{1pt}{1pt}{}{6}{2}\above{1pt}{1pt}{l}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1572840\\10440\\213120
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
10440\\-66\\-1515
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
213120\\-1515\\-25822
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-81\\-7304\\-240
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-79\\-7125\\-234
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
80\\7214\\237
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
26\\2345\\77
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-1572840, 10440, 213120; 10440, -66, -1515; 213120, -1515, -25822],[360, 3, 1],[-81, -79, 80, 26; -7304, -7125, 7214, 2345; -240, -234, 237, 77],250,1]
%
% END OF LATTICE L251.1
%
%
% LATTICE L251.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-48690, 2070, 16560; 2070, -84, -705; 16560, -705, -5632],[90, 3, 1],[-21, 6, 41, -19; -14, 5, 28, -15; -60, 17, 117, -54],250,2]
%
% END OF LATTICE L251.2
%
%
% LATTICE L251.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[261720, -14130, 121140; -14130, 768, -6540; 121140, -6540, 56071],[90, 6, 1],[7, 41, 120, 25; 1, 5, 11, 0; -15, -88, -258, -54],250,3]
%
% END OF LATTICE L251.3
%
%
% LATTICE L251.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-94410, 100710, 44280; 100710, -107430, -47235; 44280, -47235, -20768],[90, 15, 1],[-29, 3, 51, -16; -14, 5, 28, -15; -30, -5, 45, 0],250,4]
%
% END OF LATTICE L251.4
%
%
% LATTICE L251.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[143820, 23490, 73080; 23490, 3840, 11940; 73080, 11940, 37139],[90, 30, 1],[5, 23, 48, -1; 16, 77, 173, 6; -15, -70, -150, 0],250,5]
%
% END OF LATTICE L251.5
%
%
% LATTICE L251.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-451080, 12240, -30240; 12240, -330, 825; -30240, 825, -2018],[360, 15, 1],[15, 11, -13, -3; 256, 183, -220, -49; -120, -90, 105, 25],250,6]
%
% END OF LATTICE L251.6
%
%
% LATTICE L251.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-268112880, -789267240, -87477840; -789267240, -2323408848, -257512944; -87477840, -257512944, -28541213],[360, 24, 1],[1797, 2095, -14375, -698; -5990, -6984, 47917, 2327; 48537, 56592, -388272, -18856],250,7]
%
% END OF LATTICE L251.7
%
%
% LATTICE L251.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-38347920, 2593800, 321120; 2593800, -175440, -21720; 321120, -21720, -2689],[360, 120, 1],[0, -1, -1, 2; 13, 10, -89, -15; -105, -200, 600, 360],250,8]
%
% END OF LATTICE L251.8
%

\medskip%
%------------------------------WEYL-GROUP-W252--------------------------------
%
\leavevmode\llap{}%
$W_{252}$%
\qquad\llap{16} lattices, $\chi=18$%
\hfill%
$22\slashtwo222|2\rtimes D_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L252.1
%
\leavevmode%
${L_{252.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{2}8\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{-}{}9\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{2}{}5\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${20}\above{1pt}{1pt}{*}{2}{72}\above{1pt}{1pt}{b}{2}{2}\above{1pt}{1pt}{b}{2}{18}\above{1pt}{1pt}{b}{2}{8}\above{1pt}{1pt}{*}{2}{180}\above{1pt}{1pt}{s}{2}{24}\above{1pt}{1pt}{s}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
49320\\-4320\\-360
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-4320\\375\\33
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-360\\33\\2
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\10\\20
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5\\48\\108
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\-1
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-7\\-66\\-171
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-17\\-160\\-412
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-67\\-630\\-1620
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3\\-28\\-72
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[49320, -4320, -360; -4320, 375, 33; -360, 33, 2],[360, 3, 1],[1, 5, 0, -7, -17, -67, -3; 10, 48, 0, -66, -160, -630, -28; 20, 108, -1, -171, -412, -1620, -72],251,1]
%
% END OF LATTICE L252.1
%
\hbox{}\par\smallskip%
%
% LATTICE L252.2
%
\leavevmode%
${L_{252.2}}$%
{} : {$1\above{1pt}{1pt}{2}{2}8\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{-}{}9\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{2}{}5\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{m}%
\EasyButWeakLineBreak%
{${5}\above{1pt}{1pt}{}{2}{72}\above{1pt}{1pt}{r}{2}{2}\above{1pt}{1pt}{s}{2}{18}\above{1pt}{1pt}{l}{2}{8}\above{1pt}{1pt}{}{2}{45}\above{1pt}{1pt}{r}{2}{24}\above{1pt}{1pt}{l}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
105480\\4320\\360
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4320\\177\\15
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
360\\15\\2
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\25\\-5
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\-24\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\-1
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-8\\198\\-45
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-21\\520\\-112
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-43\\1065\\-225
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-5\\124\\-24
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[105480, 4320, 360; 4320, 177, 15; 360, 15, 2],[360, 3, 1],[-1, 1, 0, -8, -21, -43, -5; 25, -24, 0, 198, 520, 1065, 124; -5, 0, -1, -45, -112, -225, -24],251,2]
%
% END OF LATTICE L252.2
%
%
% LATTICE L252.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-632970, 45810, -1620; 45810, -3315, 117; -1620, 117, -4],[90, 3, 1],[7, 5, 11, 3, 7, -1, -3; 105, 74, 162, 44, 102, -15, -44; 225, 136, 279, 71, 144, -35, -72],251,3]
%
% END OF LATTICE L252.3
%
%
% LATTICE L252.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[24660, -4860, -180; -4860, 957, 36; -180, 36, 1],[180, 3, 1],[1, 5, 0, -7, -17, -67, -3; 5, 24, 0, -33, -80, -315, -14; 5, 36, -1, -72, -172, -675, -30],251,4]
%
% END OF LATTICE L252.4
%
%
% LATTICE L252.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[3302190, -142110, 1611180; -142110, 6168, -69336; 1611180, -69336, 786115],[90, 6, 1],[-7261, -1173, -3230, -840, -2099, -1237, 22; -360, -58, -159, -41, -102, -60, 1; 14850, 2399, 6606, 1718, 4293, 2530, -45],251,5]
%
% END OF LATTICE L252.5
%
%
% LATTICE L252.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[7650, 90, -90; 90, -15, 0; -90, 0, 1],[90, 15, 1],[-4, -5, -4, 0, 1, 0, -1; -12, -14, -9, 1, 6, 0, -4; -333, -410, -315, 5, 90, -1, -90],251,6]
%
% END OF LATTICE L252.6
%
%
% LATTICE L252.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[57060, -6480, 13500; -6480, 516, -1548; 13500, -1548, 3193],[180, 12, 1],[127, -11, -43, -176, -35, -89, 63; 35, -3, -12, -51, -11, -45, 17; -520, 45, 176, 720, 143, 360, -258],251,7]
%
% END OF LATTICE L252.7
%
%
% LATTICE L252.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[352530, -7920, 172260; -7920, 150, -3870; 172260, -3870, 84173],[90, 30, 1],[809, 618, 1451, 171, -22, -43, -22; -12, -8, -15, -1, 0, 0, -1; -1656, -1265, -2970, -350, 45, 88, 45],251,8]
%
% END OF LATTICE L252.8
%
%
% LATTICE L252.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[15300, 1440, -180; 1440, 105, -15; -180, -15, 2],[180, 15, 1],[-4, -5, -2, 0, 1, 0, -1; -24, -28, -9, 1, 12, 0, -8; -513, -620, -225, 10, 180, -1, -150],251,9]
%
% END OF LATTICE L252.9
%
%
% LATTICE L252.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[121320, 360, -360; 360, -15, 0; -360, 0, 1],[360, 15, 1],[-2, -5, -2, 0, 1, 0, -1; -36, -88, -33, 1, 24, 0, -20; -693, -1720, -675, 5, 360, -1, -360],251,10]
%
% END OF LATTICE L252.10
%
%
% LATTICE L252.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-12600, -2160, -2520; -2160, -105, -765; -2520, -765, -86],[360, 15, 1],[157, 241, 131, -2, -373, -39, -25; -474, -728, -396, 6, 1128, 118, 76; -378, -580, -315, 5, 900, 94, 60],251,11]
%
% END OF LATTICE L252.11
%
%
% LATTICE L252.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-792360, -130680, 6840; -130680, -21552, 1128; 6840, 1128, -59],[360, 24, 1],[-7, -2, -8, -2, -2, 1, 1; 15, 9, 45, 13, 15, -5, -7; -540, -62, -72, 16, 54, 20, -18],251,12]
%
% END OF LATTICE L252.12
%
%
% LATTICE L252.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-241560, 1080, 1080; 1080, 336, 96; 1080, 96, 25],[360, 24, 1],[7, 1, 8, 2, 1, -1, -1; -645, -93, -747, -187, -93, 95, 94; 2160, 313, 2520, 632, 315, -320, -318],251,13]
%
% END OF LATTICE L252.13
%
%
% LATTICE L252.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1516500, 30780, -347940; 30780, 600, -7080; -347940, -7080, 79817],[180, 60, 1],[-782, -299, -703, -83, 11, 42, 22; 2307, 883, 2079, 246, -33, -125, -67; -3204, -1225, -2880, -340, 45, 172, 90],251,14]
%
% END OF LATTICE L252.14
%
%
% LATTICE L252.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-6840, -40320, -720; -40320, 169800, 3000; -720, 3000, 53],[360, 120, 1],[0, 1, 1, -1, -1, -4, -1; -1, 36, 37, -51, -42, -165, -40; 56, -2025, -2080, 2880, 2365, 9288, 2250],251,15]
%
% END OF LATTICE L252.15
%
%
% LATTICE L252.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[18000, 4680, 1080; 4680, 2040, 480; 1080, 480, 113],[360, 120, 1],[0, -1, -1, -7, -3, -4, 0; 1, 66, 68, 522, 234, 321, 7; -4, -270, -280, -2160, -970, -1332, -30],251,16]
%
% END OF LATTICE L252.16
%

\medskip%
%------------------------------WEYL-GROUP-W253--------------------------------
%
\leavevmode\llap{}%
$W_{253}$%
\qquad\llap{4} lattices, $\chi=36$%
\hfill%
$24\slashinfty422\slashtwo2\rtimes D_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L253.1
%
\leavevmode%
${L_{253.1}}$%
{} : {$1\above{1pt}{1pt}{2}{2}32\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{2}{}9\above{1pt}{1pt}{1}{}$}\EasyButWeakLineBreak%
{${36}\above{1pt}{1pt}{l}{2}{1}\above{1pt}{1pt}{}{4}{2}\above{1pt}{1pt}{24,23}{\infty b}{2}\above{1pt}{1pt}{*}{4}{4}\above{1pt}{1pt}{l}{2}{9}\above{1pt}{1pt}{}{2}{1}\above{1pt}{1pt}{r}{2}{4}\above{1pt}{1pt}{*}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-525600\\3744\\2016
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3744\\-23\\-16
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2016\\-16\\-7
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
43\\2736\\6102
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
12\\763\\1704
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
6\\381\\853
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\63\\143
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-64\\-142
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-63\\-144
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\64\\141
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7\\446\\992
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-525600, 3744, 2016; 3744, -23, -16; 2016, -16, -7],[288, 1, 1],[43, 12, 6, 1, -1, -1, 1, 7; 2736, 763, 381, 63, -64, -63, 64, 446; 6102, 1704, 853, 143, -142, -144, 141, 992],252,1]
%
% END OF LATTICE L253.1
%
%
% LATTICE L253.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-24977952, 42336, 84672; 42336, -63, -144; 84672, -144, -287],[288, 9, 1],[-1, -1, 9, 30, 52, 19, 23, 1; -16, -14, 143, 469, 808, 294, 352, 13; -287, -288, 2583, 8613, 14931, 5456, 6606, 288],252,2]
%
% END OF LATTICE L253.2
%
%
% LATTICE L253.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-366048, 469440, -23904; 469440, -601952, 30656; -23904, 30656, -1561],[288, 32, 1],[-754, -427, -219, -41, 18, 47, -30, -119; -45, -24, -11, -1, 1, 0, -3, -8; 10656, 6064, 3136, 608, -256, -720, 400, 1664],252,3]
%
% END OF LATTICE L253.3
%
%
% LATTICE L253.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-11404224, -11404512, 70272; -11404512, -11404512, 70272; 70272, 70272, -433],[288, 288, 1],[-5, -24, -11, -1, 1, 0, -3, -8; 45, 259, 160, 56, -1, -7, -5, 47; 6496, 38160, 24192, 8928, 0, -1136, -1296, 6336],252,4]
%
% END OF LATTICE L253.4
%

\medskip%
%------------------------------WEYL-GROUP-W254--------------------------------
%
\leavevmode\llap{}%
$W_{254}$%
\qquad\llap{22} lattices, $\chi=30$%
\hfill%
$22\slashtwo2222|22\rtimes D_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L254.1
%
\leavevmode%
${L_{254.1}}$%
{} : {$1\above{1pt}{1pt}{2}{{\rm II}}4\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{1}{}3\above{1pt}{1pt}{1}{}9\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{2}{}11\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${22}\above{1pt}{1pt}{b}{2}{12}\above{1pt}{1pt}{*}{2}{4}\above{1pt}{1pt}{*}{2}{36}\above{1pt}{1pt}{*}{2}{12}\above{1pt}{1pt}{b}{2}{198}\above{1pt}{1pt}{l}{2}{4}\above{1pt}{1pt}{r}{2}{66}\above{1pt}{1pt}{l}{2}{36}\above{1pt}{1pt}{r}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-489852\\1980\\1188
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1980\\12\\-9
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1188\\-9\\-2
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
15\\946\\4565
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7\\440\\2130
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\62\\304
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-66\\-306
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-64\\-306
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\66\\297
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\64\\304
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
9\\572\\2739
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
11\\696\\3348
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-489852, 1980, 1188; 1980, 12, -9; 1188, -9, -2],[396, 3, 1],[15, 7, 1, -1, -1, 1, 1, 9, 11; 946, 440, 62, -66, -64, 66, 64, 572, 696; 4565, 2130, 304, -306, -306, 297, 304, 2739, 3348],253,1]
%
% END OF LATTICE L254.1
%
\hbox{}\par\smallskip%
%
% LATTICE L254.2
%
\leavevmode%
${L_{254.2}}$%
{} : {$1\above{1pt}{1pt}{2}{2}8\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{-}{}9\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{2}{}11\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${396}\above{1pt}{1pt}{*}{2}{24}\above{1pt}{1pt}{b}{2}{18}\above{1pt}{1pt}{s}{2}{2}\above{1pt}{1pt}{b}{2}{24}\above{1pt}{1pt}{*}{2}{44}\above{1pt}{1pt}{s}{2}{72}\above{1pt}{1pt}{l}{2}{33}\above{1pt}{1pt}{r}{2}{8}\above{1pt}{1pt}{s}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-490248\\1584\\1584
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1584\\-3\\-9
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1584\\-9\\2
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-41\\-8250\\-4554
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-7\\-1408\\-780
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2\\-402\\-225
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\-1
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\200\\108
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\198\\110
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-204\\-108
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3\\-605\\-330
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3\\-604\\-332
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-490248, 1584, 1584; 1584, -3, -9; 1584, -9, 2],[792, 3, 1],[-41, -7, -2, 0, 1, 1, -1, -3, -3; -8250, -1408, -402, 0, 200, 198, -204, -605, -604; -4554, -780, -225, -1, 108, 110, -108, -330, -332],253,2]
%
% END OF LATTICE L254.2
%
\hbox{}\par\smallskip%
%
% LATTICE L254.3
%
\leavevmode%
${L_{254.3}}$%
{} : {$1\above{1pt}{1pt}{-2}{2}8\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{-}{}9\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{2}{}11\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{m}%
\EasyButWeakLineBreak%
{${99}\above{1pt}{1pt}{}{2}{24}\above{1pt}{1pt}{r}{2}{18}\above{1pt}{1pt}{b}{2}{2}\above{1pt}{1pt}{l}{2}{24}\above{1pt}{1pt}{}{2}{11}\above{1pt}{1pt}{r}{2}{72}\above{1pt}{1pt}{s}{2}{132}\above{1pt}{1pt}{s}{2}{8}\above{1pt}{1pt}{l}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
127512\\-3960\\0
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3960\\123\\0
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\-1
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\33\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-32\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-33\\-9
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\-1\\-11
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\88\\-96
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4\\121\\-88
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7\\216\\-108
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7\\220\\-66
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\32\\-4
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[127512, -3960, 0; -3960, 123, 0; 0, 0, -1],[792, 3, 1],[1, -1, -1, 0, 3, 4, 7, 7, 1; 33, -32, -33, -1, 88, 121, 216, 220, 32; 0, 0, -9, -11, -96, -88, -108, -66, -4],253,3]
%
% END OF LATTICE L254.3
%
%
% LATTICE L254.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[19503, 693, -297; 693, -15, -6; -297, -6, 4],[99, 3, 1],[19, 3, 4, 1, 1, -1, -2, -5, 0; 165, 28, 39, 10, 10, -11, -21, -55, -1; 1584, 258, 351, 89, 90, -88, -180, -462, -4],253,4]
%
% END OF LATTICE L254.4
%
%
% LATTICE L254.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[107910, -3366, 0; -3366, 105, 0; 0, 0, -1],[198, 3, 1],[15, 7, 1, -1, -1, 1, 1, 9, 11; 473, 220, 31, -33, -32, 33, 32, 286, 348; -88, -48, -11, -9, 0, 0, -2, -33, -54],253,5]
%
% END OF LATTICE L254.5
%
%
% LATTICE L254.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-245124, 1584, 792; 1584, -6, -9; 792, -9, 1],[396, 3, 1],[1, 1, 0, -2, -7, -41, -3, -6, -1; 99, 100, 0, -201, -704, -4125, -302, -605, -102; 110, 108, -1, -225, -780, -4554, -332, -660, -108],253,6]
%
% END OF LATTICE L254.6
%
%
% LATTICE L254.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-5742, 6732, -2772; 6732, 3270, 3366; -2772, 3366, -1337],[198, 6, 1],[-13220, -3699, -1775, -1577, 49, 1568, -50, -4247, -3898; -275, -77, -37, -33, 1, 33, -1, -88, -81; 26708, 7473, 3586, 3186, -99, -3168, 101, 8580, 7875],253,7]
%
% END OF LATTICE L254.7
%
%
% LATTICE L254.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[99, 0, 0; 0, 33, 0; 0, 0, -1],[99, 33, 1],[-1, -2, 0, 1, 0, -1, -1, -1, -5; -4, -11, -2, 0, 1, 0, -1, -2, -15; -25, -66, -11, 0, 0, -9, -11, -15, -99],253,8]
%
% END OF LATTICE L254.8
%
%
% LATTICE L254.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[314941968, -2029500, -79541352; -2029500, 13080, 512568; -79541352, 512568, 20088865],[396, 12, 1],[-12824, -3402, -739, -541, -50, -1600, -124, -5534, -2048; -11, -5, -2, -3, 1, 33, 1, 11, 0; -50776, -13470, -2926, -2142, -198, -6336, -491, -21912, -8109],253,9]
%
% END OF LATTICE L254.9
%
%
% LATTICE L254.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[31801176, -916740, -8033652; -916740, 26436, 231588; -8033652, 231588, 2029471],[396, 12, 1],[-289, -75, -201, -1600, -1072, -22801, -745, -2567, -241; 0, 1, 3, 21, 13, 264, 8, 22, 0; -1144, -297, -796, -6336, -4245, -90288, -2950, -10164, -954],253,10]
%
% END OF LATTICE L254.10
%
%
% LATTICE L254.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-18810, -9504, 198; -9504, -4785, 99; 198, 99, -2],[198, 33, 1],[1, 1, -2, -2, -7, -1, -5, 0, 1; -3, -2, 6, 4, 10, 1, 0, -1, -4; -54, 0, 99, -11, -264, -62, -594, -57, -110],253,11]
%
% END OF LATTICE L254.11
%
%
% LATTICE L254.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1041678, -20790, 515790; -20790, 528, -10296; 515790, -10296, 255395],[198, 66, 1],[481, -49, -98, 1252, 3805, 1445, 5732, 867, 626; -15, 1, 3, -37, -113, -43, -171, -26, -19; -972, 99, 198, -2530, -7689, -2920, -11583, -1752, -1265],253,12]
%
% END OF LATTICE L254.12
%
%
% LATTICE L254.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[237996, 31680, -2772; 31680, 4092, -363; -2772, -363, 32],[396, 33, 1],[-5, -33, -9, -11, -1, 1, 1, -1, -29; -51, -334, -90, -108, -10, 9, 8, -11, -300; -1015, -6666, -1804, -2178, -198, 189, 176, -213, -5940],253,13]
%
% END OF LATTICE L254.13
%
%
% LATTICE L254.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2772, -792, 0; -792, 231, 0; 0, 0, -1],[396, 33, 1],[-1, -7, -1, -1, 1, 1, 1, 0, -5; -5, -32, -4, -3, 4, 3, 2, -1, -30; -25, -132, -11, 0, 0, -9, -22, -15, -198],253,14]
%
% END OF LATTICE L254.14
%
%
% LATTICE L254.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[181368, 60984, 20592; 60984, 20496, 6912; 20592, 6912, 2323],[792, 24, 1],[27, -1, -28, -230, -74, -1525, -47, -129, 5; -110, 4, 113, 927, 298, 6138, 189, 517, -21; 88, -3, -88, -720, -231, -4752, -146, -396, 18],253,15]
%
% END OF LATTICE L254.15
%
%
% LATTICE L254.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-77616, 18216, 4752; 18216, -312, -120; 4752, -120, -41],[792, 24, 1],[37, 9, 3, -1, -1, 1, 1, 20, 13; -4059, -988, -330, 108, 110, -99, -109, -2189, -1425; 16148, 3930, 1312, -432, -438, 396, 434, 8712, 5670],253,16]
%
% END OF LATTICE L254.16
%
%
% LATTICE L254.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-289080, -36432, 792; -36432, -4587, 99; 792, 99, -2],[792, 33, 1],[1, 1, -2, -1, -3, 0, 5, 1, 3; -9, -8, 18, 8, 16, -1, -60, -10, -28; -54, 0, 99, -11, -528, -62, -1188, -114, -220],253,17]
%
% END OF LATTICE L254.17
%
%
% LATTICE L254.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[5544, -792, 0; -792, -429, 33; 0, 33, -2],[792, 33, 1],[1, 1, -1, -1, -7, -1, -5, 0, 1; 6, 8, -6, -8, -64, -10, -60, -1, 4; 90, 132, -99, -143, -1188, -190, -1188, -24, 44],253,18]
%
% END OF LATTICE L254.18
%
%
% LATTICE L254.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[94074552, 1462428, 22653180; 1462428, 22704, 352176; 22653180, 352176, 5454875],[396, 132, 1],[-1893, -5153, -895, 250, 717, 191, -214, -949, -3577; 5720, 15574, 2707, -747, -2162, -576, 646, 2866, 10806; 7492, 20394, 3542, -990, -2838, -756, 847, 3756, 14157],253,19]
%
% END OF LATTICE L254.19
%
%
% LATTICE L254.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-38808, -396, -9504; -396, 924, -792; -9504, -792, -1807],[396, 132, 1],[-325, -408, -111, 100, 25, -109, -161, -215, -1349; 964, 1210, 329, -297, -74, 324, 478, 638, 4002; 1288, 1617, 440, -396, -99, 432, 638, 852, 5346],253,20]
%
% END OF LATTICE L254.20
%
%
% LATTICE L254.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[588456, 296208, -3168; 296208, 147048, -1584; -3168, -1584, 17],[792, 264, 1],[2, 3, 23, 9, 5, 2, 1, -1, -1; 3, 5, 39, 15, 8, 3, 0, -2, -2; 648, 1023, 7920, 3080, 1683, 656, 198, -372, -374],253,21]
%
% END OF LATTICE L254.21
%
%
% LATTICE L254.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[13518648, 901296, -19800; 901296, 59928, -1320; -19800, -1320, 29],[792, 264, 1],[1, -1, -11, -7, -11, -3, -7, 0, 1; 0, -1, -9, -7, -13, -4, -12, -1, 0; 684, -726, -7920, -5104, -8118, -2236, -5346, -48, 682],253,22]
%
% END OF LATTICE L254.22
%

\medskip%
%------------------------------WEYL-GROUP-W255--------------------------------
%
\leavevmode\llap{}%
$W_{255}$%
\qquad\llap{24} lattices, $\chi=27$%
\hfill%
$42222222$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L255.1
%
\leavevmode%
${L_{255.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{2}{}9\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{2}{}5\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{2}{}7\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${2}\above{1pt}{1pt}{*}{4}{4}\above{1pt}{1pt}{*}{2}{36}\above{1pt}{1pt}{b}{2}{14}\above{1pt}{1pt}{s}{2}{90}\above{1pt}{1pt}{l}{2}{28}\above{1pt}{1pt}{r}{2}{10}\above{1pt}{1pt}{l}{2}{252}\above{1pt}{1pt}{r}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-102537540\\52920\\63000
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
52920\\-26\\-35
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
63000\\-35\\-34
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\1188\\629
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-1190\\-628
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-1188\\-630
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\3570\\1883
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
23\\27360\\14445
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
23\\27356\\14448
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
6\\7135\\3770
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
85\\101052\\53424
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-102537540, 52920, 63000; 52920, -26, -35; 63000, -35, -34],[1260, 1, 1],[1, -1, -1, 3, 23, 23, 6, 85; 1188, -1190, -1188, 3570, 27360, 27356, 7135, 101052; 629, -628, -630, 1883, 14445, 14448, 3770, 53424],254,1]
%
% END OF LATTICE L255.1
%
%
% LATTICE L255.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-2018835, -236565, 7245; -236565, -27710, 849; 7245, 849, -26],[315, 1, 1],[2, -1, -1, 6, 46, 23, 12, 85; -1, 1, 0, -7, -45, -21, -10, -63; 524, -246, -279, 1442, 11340, 5719, 3015, 21609],254,2]
%
% END OF LATTICE L255.2
%
%
% LATTICE L255.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1044855, -380520, -206640; -380520, -138550, -75255; -206640, -75255, -40867],[315, 5, 1],[-144, 56, 89, -302, -520, -1349, -147, -5459; -1, 1, 0, -7, -9, -21, -2, -63; 730, -285, -450, 1540, 2646, 6860, 747, 27720],254,3]
%
% END OF LATTICE L255.3
%
%
% LATTICE L255.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-523845, -318780, 76230; -318780, -193970, 46389; 76230, 46389, -11093],[315, 7, 1],[76, -22, -55, 14, 1036, 81, 327, 367; -1, 1, 0, -1, -45, -3, -10, -9; 518, -147, -378, 92, 6930, 544, 2205, 2484],254,4]
%
% END OF LATTICE L255.4
%
%
% LATTICE L255.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[685431810, 74655, -78416730; 74655, 9, -8541; -78416730, -8541, 8971255],[315, 9, 1],[-523, 0, -31, -1081, -771, -3452, -1848, -1724; -544, 1, -34, -1162, -820, -3654, -1945, -1806; -4572, 0, -271, -9450, -6740, -30177, -16155, -15071],254,5]
%
% END OF LATTICE L255.5
%
%
% LATTICE L255.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[41845298040, -253231020, -10494747900; -253231020, 1532456, 63510020; -10494747900, 63510020, 2632069519],[1260, 4, 1],[-10394, -157, -2686, -14824, -109382, -28758, -32769, -144208; 17, 0, 9, 35, 225, 56, 60, 252; -41444, -626, -10710, -59108, -436140, -114667, -130660, -575001],254,6]
%
% END OF LATTICE L255.6
%
%
% LATTICE L255.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-14816340, 45360, -1301580; 45360, -130, 4305; -1301580, 4305, -102778],[1260, 5, 1],[-124, 123, 125, -368, -566, -2833, -148, -10499; -22570, 22386, 22752, -66976, -103014, -515620, -26937, -1910916; 625, -620, -630, 1855, 2853, 14280, 746, 52920],254,7]
%
% END OF LATTICE L255.7
%
%
% LATTICE L255.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-8785980, 41580, 608580; 41580, -182, -3115; 608580, -3115, -38422],[1260, 7, 1],[90, -89, -91, 38, 2048, 293, 536, 1087; 9898, -9790, -10008, 4180, 225270, 32228, 58955, 119556; 623, -616, -630, 263, 14175, 2028, 3710, 7524],254,8]
%
% END OF LATTICE L255.8
%
%
% LATTICE L255.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-26062785, 21035070, -148050; 21035070, -16977205, 119490; -148050, 119490, -841],[315, 35, 1],[-35, 2, 34, 3, -23, -15, -17, -121; -1, 1, 0, -1, -9, -3, -2, -9; 6020, -210, -5985, -670, 2772, 2215, 2709, 20025],254,9]
%
% END OF LATTICE L255.9
%
%
% LATTICE L255.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-153028260, 219240, 219240; 219240, -306, -315; 219240, -315, -314],[1260, 9, 1],[9, -1, -1, 3, 7, 79, 26, 53; 629, -68, -70, 203, 485, 5488, 1810, 3696; 5652, -630, -628, 1890, 4400, 49644, 16335, 33292],254,10]
%
% END OF LATTICE L255.10
%
%
% LATTICE L255.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1651792590, -248220, 185620365; -248220, 45, -27900; 185620365, -27900, 20859113],[315, 45, 1],[2359, 0, 142, 4915, 699, 15629, 1671, 7787; -17057, 1, -1028, -35567, -5057, -113057, -12086, -56315; -21015, 0, -1265, -43785, -6227, -139230, -14886, -69370],254,11]
%
% END OF LATTICE L255.11
%
%
% LATTICE L255.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[6017130, 16380, 603225; 16380, 63, 1638; 603225, 1638, 60475],[315, 63, 1],[-197, 0, -12, -59, -293, -187, -699, -93; 441, 1, 26, 129, 645, 413, 1550, 207; 1953, 0, 119, 585, 2905, 1854, 6930, 922],254,12]
%
% END OF LATTICE L255.12
%
%
% LATTICE L255.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[26630777880, 8509842180, -6669478620; 8509842180, 2719312760, -2131226160; -6669478620, -2131226160, 1670320907],[1260, 20, 1],[-13344, -283, -2054, -15754, -25268, -34177, -8021, -180185; 17, 0, 9, 35, 45, 56, 12, 252; -53260, -1130, -8190, -62860, -100836, -136395, -32012, -719145],254,13]
%
% END OF LATTICE L255.13
%
%
% LATTICE L255.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1041014520, -871011540, -262211040; -871011540, 728770952, 219390640; -262211040, 219390640, 66045793],[1260, 28, 1],[-5508, -67, -1738, -1226, -61064, -2263, -17793, -11071; 17, 0, 9, 5, 225, 8, 60, 36; -21924, -266, -6930, -4884, -243180, -9011, -70840, -44073],254,14]
%
% END OF LATTICE L255.14
%
%
% LATTICE L255.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-384300, 21420, -18900; 21420, -910, 1085; -18900, 1085, -926],[1260, 35, 1],[-33, 31, 35, -13, -143, -103, -38, -389; -68, 62, 72, -26, -288, -208, -77, -792; 595, -560, -630, 235, 2583, 1860, 686, 7020],254,15]
%
% END OF LATTICE L255.15
%
%
% LATTICE L255.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[42832825560, -136847340, -10742418540; -136847340, 437256, 34321140; -10742418540, 34321140, 2694184999],[1260, 36, 1],[-51843, -158, -157, -53721, -52467, -130463, -155836, -77841; 34, 1, 0, 28, 30, 77, 95, 49; -206712, -630, -626, -214200, -209200, -520191, -621360, -310373],254,16]
%
% END OF LATTICE L255.16
%
%
% LATTICE L255.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-29906100, 216720, -5331060; 216720, -1530, 38745; -5331060, 38745, -950002],[1260, 45, 1],[-1107, 125, 123, -375, -173, -9749, -641, -6527; -15499, 1752, 1722, -5257, -2423, -136528, -8976, -91392; 5580, -630, -620, 1890, 872, 49140, 3231, 32900],254,17]
%
% END OF LATTICE L255.17
%
%
% LATTICE L255.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-21113820, 215460, 2739240; 215460, -2142, -28035; 2739240, -28035, -355262],[1260, 63, 1],[801, -91, -89, 39, 627, 1009, 2321, 675; 8009, -908, -890, 389, 6265, 10084, 23200, 6748; 5544, -630, -616, 270, 4340, 6984, 16065, 4672],254,18]
%
% END OF LATTICE L255.18
%
%
% LATTICE L255.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[315, 71820, -8190; 71820, 1024228170, -116894925; -8190, -116894925, 13341191],[315, 315, 1],[2273, 1, 142, 689, 681, 2169, 1618, 1075; -11828, 0, -739, -3590, -3548, -11299, -8427, -5597; -103635, 0, -6475, -31455, -31087, -99000, -73836, -49040],254,19]
%
% END OF LATTICE L255.19
%
%
% LATTICE L255.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1465110360, 14813820, -367229520; 14813820, 149800, -3713080; -367229520, -3713080, 92045981],[1260, 140, 1],[-6106, -193, -158, -752, -9854, -1994, -3425, -11336; 17, 0, 9, 5, 45, 8, 12, 36; -24360, -770, -630, -3000, -39312, -7955, -13664, -45225],254,20]
%
% END OF LATTICE L255.20
%
%
% LATTICE L255.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[27274335480, 6034466340, -6830652780; 6034466340, 1335130200, -1511286840; -6830652780, -1511286840, 1710685763],[1260, 180, 1],[-88003, -158, -283, -92149, -17927, -222564, -53090, -132396; 34, 1, 0, 28, 6, 77, 19, 49; -351360, -630, -1130, -367920, -71576, -888615, -211968, -528605],254,21]
%
% END OF LATTICE L255.21
%
%
% LATTICE L255.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1066486680, -729921780, -268626960; -729921780, 499571352, 183852900; -268626960, 183852900, 67661833],[1260, 252, 1],[-24795, -158, -67, -3579, -24699, -8804, -73882, -5292; 34, 1, 0, 4, 30, 11, 95, 7; -98532, -630, -266, -14220, -98140, -34983, -293580, -21029],254,22]
%
% END OF LATTICE L255.22
%
%
% LATTICE L255.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3559500, -5538960, 209160; -5538960, -8617770, 325395; 209160, 325395, -12286],[1260, 315, 1],[-325, 19, 37, -7, -43, -365, -175, -263; 649, -36, -74, 13, 85, 724, 348, 524; 11655, -630, -1330, 225, 1519, 12960, 6237, 9400],254,23]
%
% END OF LATTICE L255.23
%
%
% LATTICE L255.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[15888600, -317193660, 79524900; -317193660, 6332379480, -1587616380; 79524900, -1587616380, 398037701],[1260, 1260, 1],[-927, 1, -3, -141, -191, -338, -563, -200; -36059, 158, -123, -5603, -7535, -13296, -22078, -7816; -143640, 630, -490, -22320, -30016, -52965, -87948, -31135],254,24]
%
% END OF LATTICE L255.24
%

\medskip%
%------------------------------WEYL-GROUP-W256--------------------------------
%
\leavevmode\llap{}%
$W_{256}$%
\qquad\llap{24} lattices, $\chi=48$%
\hfill%
$222222222222\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L256.1
%
\leavevmode%
${L_{256.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{2}{}9\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{-2}{}7\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${2}\above{1pt}{1pt}{s}{2}{630}\above{1pt}{1pt}{b}{2}{4}\above{1pt}{1pt}{b}{2}{70}\above{1pt}{1pt}{b}{2}{36}\above{1pt}{1pt}{*}{2}{20}\above{1pt}{1pt}{b}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-658980\\1260\\2520
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1260\\-2\\-7
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2520\\-7\\2
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3961\\-1510740\\-291060
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
10\\3814\\735
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\763\\146
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2\\-763\\-146
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-52\\-19845\\-3780
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-382\\-72
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-385\\-70
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\378\\72
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\380\\70
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-658980, 1260, 2520; 1260, -2, -7; 2520, -7, 2],[1260, 1, 1],[-2, -52, -1, -1, 1, 1, 0, -38, -3, -29, -37, -21; -763, -19845, -382, -385, 378, 380, 0, -14490, -1144, -11060, -14112, -8010; -146, -3780, -72, -70, 72, 70, -1, -2835, -222, -2135, -2718, -1540],255,1]
%
% END OF LATTICE L256.1
%
%
% LATTICE L256.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[68670, 630, -945; 630, -17, -9; -945, -9, 13],[315, 1, 1],[4, 242, 6, 76, 38, 17, 1, -17, -1, -1, 7, 8; -5, -315, -8, -105, -54, -25, -2, 0, 1, 0, -9, -10; 287, 17325, 429, 5425, 2709, 1210, 70, -1260, -72, -70, 504, 575],255,2]
%
% END OF LATTICE L256.2
%
%
% LATTICE L256.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-334215, 5985, 2520; 5985, -85, -45; 2520, -45, -19],[315, 5, 1],[6, 88, 12, 34, 92, 9, 5, 11, -1, -1, 7, 2; -5, -63, -8, -21, -54, -5, -2, 0, 1, 0, -9, -2; 805, 11781, 1605, 4543, 12285, 1201, 665, 1449, -135, -133, 945, 269],255,3]
%
% END OF LATTICE L256.3
%
%
% LATTICE L256.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[23310, -1260, 315; -1260, 49, -7; 315, -7, -1],[315, 7, 1],[-1, -7, -1, -1, -1, 1, 1, 7, 1, 1, 1, -1; -36, -270, -41, -50, -99, 0, 29, 225, 34, 35, 36, -35; -70, -540, -84, -110, -252, -35, 49, 405, 63, 65, 63, -70],255,4]
%
% END OF LATTICE L256.4
%
%
% LATTICE L256.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[41913270, 19845, -4809105; 19845, 9, -2277; -4809105, -2277, 551794],[315, 9, 1],[32, 534, 159, 2638, 173, 826, 127, 261, 0, -253, -14, -31; 22, 210, 55, 840, 53, 245, 34, 70, 1, 0, 3, 35; 279, 4655, 1386, 22995, 1508, 7200, 1107, 2275, 0, -2205, -122, -270],255,5]
%
% END OF LATTICE L256.5
%
%
% LATTICE L256.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[75678120, -1357020, -18983160; -1357020, 24344, 340396; -18983160, 340396, 4761751],[1260, 4, 1],[-2835, -65729, -469, -597, -149, -474, -634, -90376, -3000, -51438, -31072, -16871; 28, 630, 4, 0, 0, 5, 7, 945, 31, 525, 315, 170; -11304, -262080, -1870, -2380, -594, -1890, -2528, -360360, -11962, -205100, -123894, -67270],255,6]
%
% END OF LATTICE L256.6
%
%
% LATTICE L256.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[29545740, 16380, -27720; 16380, -10, -15; -27720, -15, 26],[1260, 5, 1],[2, 4, -1, -1, 1, 1, 2, 32, 9, 13, 71, 7; 37, 63, -22, -21, 18, 20, 40, 630, 176, 252, 1368, 134; 2150, 4284, -1080, -1078, 1080, 1078, 2155, 34461, 9690, 13993, 76410, 7532],255,7]
%
% END OF LATTICE L256.7
%
%
% LATTICE L256.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[9146340, 1034460, -17640; 1034460, 116998, -1995; -17640, -1995, 34],[1260, 7, 1],[2, 34, 15, 17, 137, 71, 5, 11, -1, -2, -11, -1; -19, -315, -138, -155, -1242, -640, -44, -90, 12, 20, 108, 10; -77, -855, -322, -285, -1890, -770, 7, 405, 182, 135, 630, 70],255,8]
%
% END OF LATTICE L256.8
%
%
% LATTICE L256.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[315, 1575, 630; 1575, -770, -350; 630, -350, -157],[315, 35, 1],[29, 23, 9, 1, 1, -1, -1, 13, 19, 11, 251, 29; -469, -369, -142, -15, 0, 17, 14, -216, -313, -180, -4095, -472; 1155, 909, 350, 37, 0, -42, -35, 531, 770, 443, 10080, 1162],255,9]
%
% END OF LATTICE L256.9
%
%
% LATTICE L256.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[772380, -11340, 0; -11340, 126, 9; 0, 9, -2],[1260, 9, 1],[0, -2, -1, 1, 1, 9, 2, 12, 5, 29, 3, 11; -2, -140, -68, 70, 68, 610, 135, 805, 334, 1925, 198, 720; -27, -665, -306, 315, 302, 2700, 594, 3500, 1440, 8190, 832, 2970],255,10]
%
% END OF LATTICE L256.10
%
%
% LATTICE L256.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[44616915, -39375, 5140800; -39375, 45, -4545; 5140800, -4545, 592334],[315, 45, 1],[706, 1184, 1479, 4336, 1337, 1210, 773, 295, 0, 101, 142, 269; -4920, -8246, -10298, -30184, -9306, -8421, -5377, -2051, 1, -707, -991, -1876; -6165, -10339, -12915, -37863, -11675, -10566, -6750, -2576, 0, -882, -1240, -2349],255,11]
%
% END OF LATTICE L256.11
%
%
% LATTICE L256.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[4309515, 325080, 308070; 325080, 24507, 23247; 308070, 23247, 22018],[315, 63, 1],[-7, -113, -272, -721, -350, -1754, -315, -117, -50, 31, 28, 144; 33, 555, 1337, 3545, 1721, 8625, 1549, 575, 245, -155, -139, -715; 63, 995, 2394, 6345, 3080, 15435, 2772, 1030, 441, -270, -245, -1260],255,12]
%
% END OF LATTICE L256.12
%
%
% LATTICE L256.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[35253940680, -10827180, -8841568680; -10827180, 3320, 2715420; -8841568680, 2715420, 2217435419],[1260, 20, 1],[24869, 115531, 3935, -1889, -12121, -1102, 2518, 130952, 23452, 84050, 258604, 28489; 28, 126, 4, 0, 0, 1, 7, 189, 31, 105, 315, 34; 99160, 460656, 15690, -7532, -48330, -4394, 10040, 522144, 93510, 335132, 1031130, 113594],255,13]
%
% END OF LATTICE L256.13
%
%
% LATTICE L256.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[216626760, -1006740, -54313560; -1006740, 4312, 252420; -54313560, 252420, 13617721],[1260, 28, 1],[-941, 50471, 14891, 43263, 197663, 114272, 22886, 90604, 7054, 3762, -158, -4547; -61, 3285, 969, 2815, 12861, 7435, 1489, 5895, 459, 245, -9, -295; -3752, 201240, 59374, 172500, 788130, 455630, 91252, 361260, 28126, 15000, -630, -18130],255,14]
%
% END OF LATTICE L256.14
%
%
% LATTICE L256.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-21420, -10080, 0; -10080, -4130, -35; 0, -35, 2],[1260, 35, 1],[5, 29, 71, 18, 773, 85, 37, 25, 13, 0, -17, -1; -11, -63, -154, -39, -1674, -184, -80, -54, -28, 0, 36, 2; -175, -1053, -2590, -659, -28350, -3122, -1365, -927, -490, -1, 630, 42],255,15]
%
% END OF LATTICE L256.15
%
%
% LATTICE L256.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1066259880, -6860700, -267422400; -6860700, 44136, 1720692; -267422400, 1720692, 67070647],[1260, 36, 1],[5724, 10814, -158, -5372, 162, 4311, 3503, 35321, 9385, 143777, 9065, 41824; -55, -105, 1, 35, -3, -50, -36, -350, -92, -1400, -88, -405; 22824, 43120, -630, -21420, 646, 17190, 13968, 140840, 37422, 573300, 36146, 166770],255,16]
%
% END OF LATTICE L256.16
%
%
% LATTICE L256.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-28980, 1260, 0; 1260, 90, -45; 0, -45, 14],[1260, 45, 1],[0, -2, -7, -13, -9, -9, -4, -2, -1, 1, 1, 1; -1, -49, -170, -315, -218, -218, -97, -49, -26, 21, 22, 22; 0, -154, -540, -1008, -700, -702, -315, -161, -90, 63, 70, 72],255,17]
%
% END OF LATTICE L256.17
%
%
% LATTICE L256.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-792540, -39060, 1260; -39060, -1638, 63; 1260, 63, -2],[1260, 63, 1],[1, 1, 3, 2, 1, 1, -1, -1, -3, -2, -1, -1; -9, -5, -10, -5, -2, 0, 2, 0, -4, -10, -12, -70; 252, 430, 1512, 1080, 560, 630, -567, -655, -2142, -1755, -1190, -3780],255,18]
%
% END OF LATTICE L256.18
%
%
% LATTICE L256.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[446355, 861525, -99225; 861525, 1662885, -191520; -99225, -191520, 22058],[315, 315, 1],[73, 7, 29, 5, 5, 1, -3, 3, 41, 25, 65, 69; 869, 87, 384, 71, 74, 14, -71, 27, 414, 271, 724, 784; 7875, 787, 3465, 639, 665, 126, -630, 248, 3780, 2466, 6580, 7119],255,19]
%
% END OF LATTICE L256.19
%
%
% LATTICE L256.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[145043640, -830340, -36364860; -830340, 4760, 208180; -36364860, 208180, 9117277],[1260, 140, 1],[983, 3575, 4055, 1943, 40603, 4364, 3546, 2248, 474, -2, 158, 165; 33, 135, 157, 77, 1629, 177, 149, 99, 25, 1, 9, 5; 3920, 14256, 16170, 7748, 161910, 17402, 14140, 8964, 1890, -8, 630, 658],255,20]
%
% END OF LATTICE L256.20
%
%
% LATTICE L256.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[26281080, -1233540, -6592320; -1233540, 57960, 309420; -6592320, 309420, 1653611],[1260, 180, 1],[-271, -899, -1377, -4993, -1733, -1747, -1625, -997, -519, -695, -163, -149; -2, 0, 2, 14, 6, 7, 9, 7, 5, 7, 1, 0; -1080, -3584, -5490, -19908, -6910, -6966, -6480, -3976, -2070, -2772, -650, -594],255,21]
%
% END OF LATTICE L256.21
%
%
% LATTICE L256.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1121694840, 709380, -281320200; 709380, 504, -177912; -281320200, -177912, 70554889],[1260, 252, 1],[-30779, -13819, -10207, -7223, -1099, 158, 0, -8166, -20572, -58732, -29680, -154053; -134, -60, -44, -30, -4, 5, 1, -35, -89, -255, -129, -670; -122724, -55100, -40698, -28800, -4382, 630, 0, -32560, -82026, -234180, -118342, -614250],255,22]
%
% END OF LATTICE L256.22
%
%
% LATTICE L256.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-51660, 272160, 2520; 272160, 4943610, 45675; 2520, 45675, 422],[1260, 315, 1],[-1, -1, -23, -6, -29, -29, -13, -1, -5, 0, 1, 1; 131, 121, 2766, 719, 3470, 3466, 1549, 119, 594, 1, -110, -106; -14175, -13091, -299250, -77787, -375410, -374976, -167580, -12874, -64260, -108, 11900, 11466],255,23]
%
% END OF LATTICE L256.23
%
%
% LATTICE L256.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[28150920, 3044415780, -763520940; 3044415780, 329242079880, -82571908860; -763520940, -82571908860, 20708531957],[1260, 1260, 1],[-325, -85, -759, -313, -663, -586, -326, -8, 108, 34, 12, -65; -5053, -1827, -18163, -8493, -19463, -18607, -14533, -971, -1423, 99, -123, -979; -20160, -7288, -72450, -33876, -77630, -74214, -57960, -3872, -5670, 396, -490, -3906],255,24]
%
% END OF LATTICE L256.24
%

\medskip%
%------------------------------WEYL-GROUP-W257--------------------------------
%
\leavevmode\llap{}%
$W_{257}$%
\qquad\llap{16} lattices, $\chi=24$%
\hfill%
$222|2222|2\rtimes D_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L257.1
%
\leavevmode%
${L_{257.1}}$%
{} : {$[1\above{1pt}{1pt}{1}{}2\above{1pt}{1pt}{1}{}]\above{1pt}{1pt}{}{0}32\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{-}{}$}\EasyButWeakLineBreak%
{${160}\above{1pt}{1pt}{}{2}{1}\above{1pt}{1pt}{r}{2}{32}\above{1pt}{1pt}{*}{2}{40}\above{1pt}{1pt}{s}{2}{32}\above{1pt}{1pt}{*}{2}{4}\above{1pt}{1pt}{s}{2}{160}\above{1pt}{1pt}{l}{2}{2}\above{1pt}{1pt}{}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-70240\\800\\800
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
800\\-2\\-10
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
800\\-10\\-9
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
101\\960\\7840
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7\\67\\543
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
19\\184\\1472
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7\\70\\540
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-8\\-80
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-10\\-78
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\0\\80
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\9\\78
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-70240, 800, 800; 800, -2, -10; 800, -10, -9],[160, 2, 1],[101, 7, 19, 7, -1, -1, 1, 1; 960, 67, 184, 70, -8, -10, 0, 9; 7840, 543, 1472, 540, -80, -78, 80, 78],256,1]
%
% END OF LATTICE L257.1
%
\hbox{}\par\smallskip%
%
% LATTICE L257.2
%
\leavevmode%
${L_{257.2}}$%
{} : {$[1\above{1pt}{1pt}{1}{}2\above{1pt}{1pt}{-}{}]\above{1pt}{1pt}{}{4}32\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{-}{}$}\EasyButWeakLineBreak%
{${160}\above{1pt}{1pt}{*}{2}{4}\above{1pt}{1pt}{s}{2}{32}\above{1pt}{1pt}{l}{2}{10}\above{1pt}{1pt}{}{2}{32}\above{1pt}{1pt}{}{2}{1}\above{1pt}{1pt}{r}{2}{160}\above{1pt}{1pt}{*}{2}{8}\above{1pt}{1pt}{s}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
67360\\-1600\\-160
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1600\\38\\4
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-160\\4\\-7
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-101\\-4280\\-240
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-13\\-552\\-34
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-15\\-640\\-48
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-45\\-10
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5\\208\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\42\\1
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-40\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3\\-126\\-4
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[67360, -1600, -160; -1600, 38, 4; -160, 4, -7],[160, 2, 1],[-101, -13, -15, -1, 5, 1, -1, -3; -4280, -552, -640, -45, 208, 42, -40, -126; -240, -34, -48, -10, 0, 1, 0, -4],256,2]
%
% END OF LATTICE L257.2
%
\hbox{}\par\smallskip%
%
% LATTICE L257.3
%
\leavevmode%
${L_{257.3}}$%
{} : {$1\above{1pt}{1pt}{-}{5}4\above{1pt}{1pt}{1}{1}32\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{1}{}$}\EasyButWeakLineBreak%
{${20}\above{1pt}{1pt}{*}{2}{32}\above{1pt}{1pt}{l}{2}{1}\above{1pt}{1pt}{}{2}{20}\above{1pt}{1pt}{r}{2}{4}\above{1pt}{1pt}{*}{2}{32}\above{1pt}{1pt}{l}{2}{5}\above{1pt}{1pt}{}{2}{4}\above{1pt}{1pt}{r}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-219680\\1920\\2080
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1920\\-12\\-20
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2080\\-20\\-19
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
29\\840\\2270
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
29\\836\\2272
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\57\\157
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\25\\80
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-30\\-78
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-28\\-80
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\60\\155
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\59\\156
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-219680, 1920, 2080; 1920, -12, -20; 2080, -20, -19],[160, 4, 1],[29, 29, 2, 1, -1, -1, 2, 2; 840, 836, 57, 25, -30, -28, 60, 59; 2270, 2272, 157, 80, -78, -80, 155, 156],256,3]
%
% END OF LATTICE L257.3
%
\hbox{}\par\smallskip%
%
% LATTICE L257.4
%
\leavevmode%
${L_{257.4}}$%
{} : {$1\above{1pt}{1pt}{-}{5}4\above{1pt}{1pt}{1}{7}32\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{1}{}$}\EasyButWeakLineBreak%
{${5}\above{1pt}{1pt}{}{2}{32}\above{1pt}{1pt}{}{2}{1}\above{1pt}{1pt}{r}{2}{80}\above{1pt}{1pt}{*}{2}{4}\above{1pt}{1pt}{s}{2}{32}\above{1pt}{1pt}{s}{2}{20}\above{1pt}{1pt}{*}{2}{16}\above{1pt}{1pt}{l}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-593120\\39840\\-2560
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
39840\\-2676\\172
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2560\\172\\-11
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-9\\-130\\55
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-17\\-248\\64
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-15\\-3
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\10\\-80
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\14\\-14
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\16\\16
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3\\-40\\70
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3\\-42\\40
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-593120, 39840, -2560; 39840, -2676, 172; -2560, 172, -11],[160, 4, 1],[-9, -17, -1, 1, 1, 1, -3, -3; -130, -248, -15, 10, 14, 16, -40, -42; 55, 64, -3, -80, -14, 16, 70, 40],256,4]
%
% END OF LATTICE L257.4
%
%
% LATTICE L257.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[160, 0, 0; 0, -8, 8; 0, 8, -7],[160, 8, 1],[-19, -3, -5, -3, -1, 0, 1, 0; -120, -16, -20, -5, 4, 1, 0, -3; -240, -34, -48, -20, 0, 1, 0, -4],256,5]
%
% END OF LATTICE L257.5
%
%
% LATTICE L257.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[160, 0, 0; 0, 8, 0; 0, 0, -1],[160, 8, 1],[1, 0, -1, -3, -5, -3, -19, 0; 0, -1, -4, -5, -4, -1, 0, 1; 0, -2, -16, -40, -64, -38, -240, 0],256,6]
%
% END OF LATTICE L257.6
%
%
% LATTICE L257.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[34080, 1120, -320; 1120, -10, -10; -320, -10, 3],[160, 10, 1],[5, 1, -1, -1, -5, -1, 1, 1; 0, -1, -8, -2, -8, -2, 0, 1; 512, 95, -160, -116, -560, -110, 112, 110],256,7]
%
% END OF LATTICE L257.7
%
%
% LATTICE L257.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[11680, 1760, -480; 1760, -290, 40; -480, 40, -3],[160, 10, 1],[13, 2, -5, -1, -1, 7, 17, 7; 248, 38, -96, -19, -16, 136, 328, 134; 1216, 185, -480, -94, -80, 670, 1616, 660],256,8]
%
% END OF LATTICE L257.8
%
%
% LATTICE L257.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[23520, -4800, 160; -4800, 976, -32; 160, -32, 1],[160, 16, 1],[1, 1, 0, -2, -1, -5, -4, 0; 5, 6, 0, -15, -8, -42, -35, -1; 10, 32, -1, -160, -90, -496, -430, -24],256,9]
%
% END OF LATTICE L257.9
%
%
% LATTICE L257.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-595680, 137760, -2560; 137760, -31856, 592; -2560, 592, -11],[160, 16, 1],[2, 5, 1, 2, 0, -1, -1, 0; 15, 32, 5, 5, -1, -4, 0, 3; 335, 544, 34, -200, -54, 16, 230, 160],256,10]
%
% END OF LATTICE L257.10
%
%
% LATTICE L257.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-65440, 16480, -1440; 16480, -4140, 360; -1440, 360, -31],[160, 20, 1],[7, 29, 1, -1, -3, -1, 1, 4; 36, 140, 3, -7, -18, -4, 6, 23; 86, 240, -15, -36, -70, 0, 23, 80],256,11]
%
% END OF LATTICE L257.11
%
%
% LATTICE L257.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[172960, 18560, -2240; 18560, 1980, -240; -2240, -240, 29],[160, 20, 1],[1, 7, 0, -1, -1, 1, 1, 3; -1, -24, -4, -6, -4, 0, 2, 6; 67, 320, -35, -128, -110, 80, 94, 280],256,12]
%
% END OF LATTICE L257.12
%
%
% LATTICE L257.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[160, 0, 0; 0, -120, -40; 0, -40, -13],[160, 40, 1],[-1, 0, 1, 0, -3, -3, -5, -1; -4, -3, 0, 3, 32, 21, 28, 1; 16, 10, 0, -8, -80, -50, -64, 0],256,13]
%
% END OF LATTICE L257.13
%
%
% LATTICE L257.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[224160, 87200, -2880; 87200, 33880, -1120; -2880, -1120, 37],[160, 40, 1],[7, 1, -3, -1, 1, 5, 11, 4; -4, -2, -8, -1, 0, 2, 4, 1; 416, 15, -480, -108, 80, 450, 976, 340],256,14]
%
% END OF LATTICE L257.14
%
%
% LATTICE L257.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-185760, -24800, 2400; -24800, -3280, 320; 2400, 320, -31],[160, 80, 1],[1, 7, 0, -1, -1, 1, 1, 3; 1, 10, 1, -1, -3, -14, -2, 1; 87, 640, 10, -88, -110, -80, 54, 240],256,15]
%
% END OF LATTICE L257.15
%
%
% LATTICE L257.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[172960, 37120, -2240; 37120, 7920, -480; -2240, -480, 29],[160, 80, 1],[1, 1, -1, -1, 0, 7, 2, 3; 1, 0, -2, -3, -2, -12, -1, 3; 94, 80, -110, -128, -35, 320, 134, 280],256,16]
%
% END OF LATTICE L257.16
%

\medskip%
%------------------------------WEYL-GROUP-W258--------------------------------
%
\leavevmode\llap{}%
$W_{258}$%
\qquad\llap{8} lattices, $\chi=36$%
\hfill%
$24|42|24|42|\rtimes D_{4}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L258.1
%
\leavevmode%
${L_{258.1}}$%
{} : {$1\above{1pt}{1pt}{2}{2}16\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{2}{}7\above{1pt}{1pt}{1}{}$}\EasyButWeakLineBreak%
{${112}\above{1pt}{1pt}{l}{2}{1}\above{1pt}{1pt}{}{4}{2}\above{1pt}{1pt}{*}{4}{4}\above{1pt}{1pt}{s}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2258256\\557424\\22176
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
557424\\-137591\\-5477
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
22176\\-5477\\-214
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
742937\\2914128\\2403744
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-183749\\-720745\\-594512
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-6859\\-26904\\-22193
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5211\\20440\\16856
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
297\\1165\\960
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
78\\306\\251
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-77\\-302\\-250
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-2258256, 557424, 22176; 557424, -137591, -5477; 22176, -5477, -214],[336, 1, 1],[5211, 297, 78, -77, -157, 64, 283, 799; 20440, 1165, 306, -302, -616, 251, 1110, 3134; 16856, 960, 251, -250, -504, 208, 917, 2586],257,1]
%
% END OF LATTICE L258.1
%
%
% LATTICE L258.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-433776, 102816, 85008; 102816, -24357, -20256; 85008, -20256, -15781],[336, 3, 1],[35647, 5465, 1935, 437, -1081, -527, 534, 2032; 136640, 20948, 7417, 1675, -4144, -2020, 2047, 7789; 16632, 2550, 903, 204, -504, -246, 249, 948],257,2]
%
% END OF LATTICE L258.2
%
%
% LATTICE L258.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2679600, 895776, 21840; 895776, -299453, -7301; 21840, -7301, -178],[336, 7, 1],[53, 53, 16, 2, -3, -3, 9, 23; 152, 154, 48, 7, -8, -10, 24, 65; 264, 182, -7, -42, -40, 42, 119, 154],257,3]
%
% END OF LATTICE L258.3
%
%
% LATTICE L258.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-370660080, 0, -183022224; 0, 16, 0; -183022224, 0, -90371573],[336, 16, 1],[-2855, -1031, 6265, 14592, 28391, 15623, 8327, 0; 0, -2, -7, -9, -14, -6, -1, 1; 5782, 2088, -12688, -29552, -57498, -31640, -16864, 0],257,4]
%
% END OF LATTICE L258.4
%
%
% LATTICE L258.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-977424, -176064, 25536; -176064, -31710, 4599; 25536, 4599, -667],[336, 21, 1],[7, 5, 0, -1, -1, 1, 3, 4; 0, 52, 55, 33, 16, -36, -47, -25; 264, 546, 378, 189, 72, -210, -210, -21],257,5]
%
% END OF LATTICE L258.5
%
%
% LATTICE L258.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-101862096, 0, -16278528; 0, 48, 0; -16278528, 0, -2601463],[336, 48, 1],[8343, 4288, 1841, -303, -839, 0, 2447, 4591; -14, -9, -7, -2, 0, 1, -1, -6; -52206, -26832, -11520, 1896, 5250, 0, -15312, -28728],257,6]
%
% END OF LATTICE L258.6
%
%
% LATTICE L258.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-453757584, 0, -219855888; 0, 112, 0; -219855888, 0, -106525187],[336, 112, 1],[-1127, 0, 30335, 60263, 16091, 59856, 29521, -407; 0, 1, -1, -6, -2, -9, -7, -2; 2326, 0, -62608, -124376, -33210, -123536, -60928, 840],257,7]
%
% END OF LATTICE L258.7
%
%
% LATTICE L258.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[336, 0, 0; 0, -405841435440, -3553630416; 0, -3553630416, -31116313],[336, 336, 1],[0, -2, -7, -9, -2, -6, -1, 1; -1055, -381, 27635, 56032, 15063, 56413, 28397, 0; 120486, 43512, -3156048, -6399120, -1720266, -6442632, -3243072, 0],257,8]
%
% END OF LATTICE L258.8
%

\medskip%
%------------------------------WEYL-GROUP-W259--------------------------------
%
\leavevmode\llap{}%
$W_{259}$%
\qquad\llap{8} lattices, $\chi=16$%
\hfill%
$222226$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L259.1
%
\leavevmode%
${L_{259.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}16\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}7\above{1pt}{1pt}{-}{}$}\EasyButWeakLineBreak%
{${6}\above{1pt}{1pt}{b}{2}{16}\above{1pt}{1pt}{b}{2}{42}\above{1pt}{1pt}{l}{2}{16}\above{1pt}{1pt}{r}{2}{6}\above{1pt}{1pt}{b}{2}{2}\above{1pt}{1pt}{}{6}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2549904\\-6384\\-3696
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-6384\\-2\\33
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3696\\33\\-26
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\555\\420
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7\\1944\\1472
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-273\\-210
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-21\\-5824\\-4416
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-10\\-2775\\-2103
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3\\-833\\-631
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[2549904, -6384, -3696; -6384, -2, 33; -3696, 33, -26],[336, 1, 1],[2, 7, -1, -21, -10, -3; 555, 1944, -273, -5824, -2775, -833; 420, 1472, -210, -4416, -2103, -631],258,1]
%
% END OF LATTICE L259.1
%
%
% LATTICE L259.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-4693584, -31584, 19824; -31584, -150, 123; 19824, 123, -82],[336, 3, 1],[2, 7, -19, -117, -12, -5; 107, 376, -1015, -6256, -642, -268; 644, 2256, -6118, -37680, -3865, -1611],258,2]
%
% END OF LATTICE L259.2
%
%
% LATTICE L259.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[237552, -3696, 24864; -3696, -14, -1183; 24864, -1183, -6262],[336, 7, 1],[-70, -249, 5, 747, 356, 107; -2805, -9976, 201, 29936, 14265, 4287; 252, 896, -18, -2688, -1281, -385],258,3]
%
% END OF LATTICE L259.3
%
%
% LATTICE L259.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-31584, -21168, 177072; -21168, -13216, 102048; 177072, 102048, -708007],[336, 16, 1],[-1409, -857, 7891, 2084, 13525, 3475; 4110, 2500, -23016, -6079, -39453, -10137; 240, 146, -1344, -355, -2304, -592],258,4]
%
% END OF LATTICE L259.4
%
%
% LATTICE L259.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-373296, -23520, 82320; -23520, -1050, 4683; 82320, 4683, -17566],[336, 21, 1],[70, 247, -95, -4101, -421, -176; 555, 1960, -753, -32512, -3338, -1396; 476, 1680, -646, -27888, -2863, -1197],258,5]
%
% END OF LATTICE L259.5
%
%
% LATTICE L259.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-882336, 228144, 1924272; 228144, -58848, -496080; 1924272, -496080, -4181365],[336, 48, 1],[-173, -109, 1927, 777, 1313, 613; -3638, -2294, 40516, 16340, 27615, 12897; 352, 222, -3920, -1581, -2672, -1248],258,6]
%
% END OF LATTICE L259.6
%
%
% LATTICE L259.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-491232, 559440, -9744; 559440, -636832, 11088; -9744, 11088, -193],[336, 112, 1],[-7, -5, 5, 11, 74, 20; -12, -10, 6, 19, 135, 39; -336, -322, 96, 539, 4032, 1232],258,7]
%
% END OF LATTICE L259.7
%
%
% LATTICE L259.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2402400, -2250864, 762720; -2250864, -2108064, 714336; 762720, 714336, -242059],[336, 336, 1],[-7, -5, 11, 32, 55, 27; -410, -322, 628, 1880, 3281, 1679; -1232, -966, 1888, 5649, 9856, 5040],258,8]
%
% END OF LATTICE L259.8
%

\medskip%
%------------------------------WEYL-GROUP-W260--------------------------------
%
\leavevmode\llap{}%
$W_{260}$%
\qquad\llap{8} lattices, $\chi=18$%
\hfill%
$22|222\slashtwo2\rtimes D_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L260.1
%
\leavevmode%
${L_{260.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{6}16\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{2}{}7\above{1pt}{1pt}{1}{}$}\EasyButWeakLineBreak%
{${112}\above{1pt}{1pt}{b}{2}{6}\above{1pt}{1pt}{s}{2}{14}\above{1pt}{1pt}{b}{2}{6}\above{1pt}{1pt}{l}{2}{112}\above{1pt}{1pt}{}{2}{1}\above{1pt}{1pt}{r}{2}{4}\above{1pt}{1pt}{*}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
76272\\25200\\-336
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
25200\\8326\\-111
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-336\\-111\\1
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
831\\-2520\\-448
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
92\\-279\\-48
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
30\\-91\\-14
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\3\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-37\\112\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\-1
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
31\\-94\\-18
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[76272, 25200, -336; 25200, 8326, -111; -336, -111, 1],[336, 1, 1],[831, 92, 30, -1, -37, 0, 31; -2520, -279, -91, 3, 112, 0, -94; -448, -48, -14, 0, 0, -1, -18],259,1]
%
% END OF LATTICE L260.1
%
%
% LATTICE L260.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-72240, -4704, 3024; -4704, -237, 162; 3024, 162, -109],[336, 3, 1],[19, 2, 9, 3, 47, -1, -1; 1008, 109, 497, 167, 2632, -54, -56; 2016, 217, 987, 331, 5208, -108, -111],259,2]
%
% END OF LATTICE L260.2
%
%
% LATTICE L260.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1680, -672, -336; -672, 266, 119; -336, 119, -17],[336, 7, 1],[9, -14, -4, 1, 29, 12, 19; 24, -39, -11, 3, 80, 33, 52; -16, 0, 2, 0, -16, -7, -14],259,3]
%
% END OF LATTICE L260.3
%
%
% LATTICE L260.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-35616, -1008, 1008; -1008, 16, 16; 1008, 16, -25],[336, 16, 1],[1, -1, -9, -19, -19, -2, 1; 14, -12, -126, -276, -280, -31, 13; 49, -48, -448, -960, -966, -104, 48],259,4]
%
% END OF LATTICE L260.4
%
%
% LATTICE L260.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-376656, 62832, -4032; 62832, -10479, 672; -4032, 672, -43],[336, 21, 1],[7, 3, 1, 0, -5, -2, -1; 56, 23, 7, -3, -48, -16, -6; 216, 77, 15, -49, -288, -63, 0],259,5]
%
% END OF LATTICE L260.5
%
%
% LATTICE L260.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-52752, -13776, -4032; -13776, -2400, -672; -4032, -672, -187],[336, 48, 1],[6, 6, 16, 2, -2, -3, -1; -287, -285, -749, -87, 119, 145, 46; 903, 896, 2352, 272, -378, -456, -144],259,6]
%
% END OF LATTICE L260.6
%
%
% LATTICE L260.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[672, -336, 0; -336, -65744, 1904; 0, 1904, -55],[336, 112, 1],[-1, -19, -3, -1, 1, 7, 4; -4, -48, -6, 0, 2, 13, 5; -142, -1680, -208, 0, 69, 448, 168],259,7]
%
% END OF LATTICE L260.7
%
%
% LATTICE L260.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-75936, -76272, 1680; -76272, -76272, 1680; 1680, 1680, -37],[336, 336, 1],[0, -1, -1, -3, -1, 0, 1; 1, 6, 0, -14, -8, -11, -1; 45, 224, -48, -784, -414, -504, 0],259,8]
%
% END OF LATTICE L260.8
%

\medskip%
%------------------------------WEYL-GROUP-W261--------------------------------
%
\leavevmode\llap{}%
$W_{261}$%
\qquad\llap{16} lattices, $\chi=72$%
\hfill%
$2222|2222|2222|2222|\rtimes D_{4}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L261.1
%
\leavevmode%
${L_{261.1}}$%
{} : {$1\above{1pt}{1pt}{2}{6}16\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{1}{}3\above{1pt}{1pt}{1}{}9\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{2}{}7\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{3}%
\EasyButWeakLineBreak%
{${112}\above{1pt}{1pt}{s}{2}{12}\above{1pt}{1pt}{l}{2}{7}\above{1pt}{1pt}{}{2}{48}\above{1pt}{1pt}{r}{2}{126}\above{1pt}{1pt}{b}{2}{48}\above{1pt}{1pt}{*}{2}{28}\above{1pt}{1pt}{l}{2}{3}\above{1pt}{1pt}{r}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3865680\\8064\\3024
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
8064\\3\\-9
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3024\\-9\\-2
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-15553\\-2013984\\-14614992
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4\\517\\3759
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
16\\2072\\15035
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-9\\-1176\\-8456
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-5\\-650\\-4698
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-17\\-2205\\-15974
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-59\\-7648\\-55440
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-71\\-9198\\-66717
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-65\\-8416\\-61080
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-41\\-5306\\-38528
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-4\\-517\\-3759
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-3865680, 8064, 3024; 8064, 3, -9; 3024, -9, -2],[1008, 3, 1],[-9, -5, -17, -59, -71, -65, -41, -4, -23, -3, -3, -5, -1, 1, 1, 0; -1176, -650, -2205, -7648, -9198, -8416, -5306, -517, -2968, -386, -385, -640, -126, 128, 126, -1; -8456, -4698, -15974, -55440, -66717, -61080, -38528, -3759, -21616, -2820, -2821, -4704, -945, 936, 938, 0],260,1]
%
% END OF LATTICE L261.1
%
%
% LATTICE L261.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-21840, 1344, -1680; 1344, -2, -3; -1680, -3, 11],[336, 1, 1],[15, 5, 12, 37, 13, 31, 17, 1, 1, -1, -2, -5, -1, 1, 3, 1; 4648, 1542, 3682, 11328, 3969, 9432, 5152, 297, 224, -324, -637, -1584, -315, 312, 938, 312; 3528, 1170, 2793, 8592, 3010, 7152, 3906, 225, 168, -246, -483, -1200, -238, 240, 714, 237],260,2]
%
% END OF LATTICE L261.2
%
%
% LATTICE L261.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-234864, 1680, 672; 1680, -6, -9; 672, -9, 1],[336, 3, 1],[-69, -3, -9, -5, -1, 1, 3, 0, -27, -5, -51, -59, -71, -65, -123, -4; -6160, -268, -805, -448, -91, 88, 266, 0, -2408, -446, -4550, -5264, -6335, -5800, -10976, -357; -8904, -386, -1155, -640, -126, 128, 378, -1, -3528, -650, -6615, -7648, -9198, -8416, -15918, -517],260,3]
%
% END OF LATTICE L261.3
%
%
% LATTICE L261.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-7728, 336, 336; 336, -14, -7; 336, -7, 81],[336, 7, 1],[33, 10, 3, 1, -1, -5, 1, 17, 31, 46, 77, 895, 49, 901, 39, 95; 808, 246, 74, 24, -25, -144, 23, 408, 752, 1119, 1876, 21816, 1195, 21984, 952, 2322; -72, -21, -6, 0, 2, 0, -3, -42, -72, -105, -174, -2016, -110, -2016, -87, -210],260,4]
%
% END OF LATTICE L261.4
%
%
% LATTICE L261.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[4319280, 1442448, -7056; 1442448, 481710, -2355; -7056, -2355, 11],[1008, 3, 1],[-1273, -139, -982, -1001, -348, -819, -1327, -24, 1, 33, 187, 153, 30, -29, -263, -29; 3864, 422, 2982, 3040, 1057, 2488, 4032, 73, 0, -100, -567, -464, -91, 88, 798, 88; 10584, 1170, 8379, 8592, 3010, 7152, 11718, 225, 504, -246, -1449, -1200, -238, 240, 2142, 237],260,5]
%
% END OF LATTICE L261.5
%
%
% LATTICE L261.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-699216, 99792, -3024; 99792, -14240, 432; -3024, 432, -13],[336, 16, 1],[17, 5, 1, -2, -10, -1, 1, 5, 17, 29, 169, 70, 214, 35, 169, 29; 91, 24, -7, -15, -63, -6, 7, 30, 98, 165, 952, 393, 1197, 195, 938, 159; -966, -384, -504, -42, 224, 33, 0, -168, -714, -1296, -7896, -3318, -10304, -1713, -8400, -1512],260,6]
%
% END OF LATTICE L261.6
%
%
% LATTICE L261.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[850416, 5040, -4032; 5040, -42, -21; -4032, -21, 19],[336, 21, 1],[27, 25, 30, 229, 37, 223, 57, 11, 21, 3, 0, -5, -1, 1, 3, 3; 232, 214, 256, 1952, 315, 1896, 484, 93, 176, 24, -1, -48, -9, 8, 26, 26; 5976, 5530, 6633, 50624, 8178, 49280, 12594, 2429, 4632, 658, -3, -1120, -222, 224, 666, 665],260,7]
%
% END OF LATTICE L261.7
%
%
% LATTICE L261.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[336, 0, 0; 0, -19632, 672; 0, 672, -23],[336, 48, 1],[-4, -3, -62, -9, -87, -5, -76, -5, -11, -2, -13, -1, -3, 0, 1, 0; -21, -10, -147, -19, -161, -8, -105, -4, 0, 3, 42, 5, 35, 1, 0, -3; -630, -304, -4536, -590, -5040, -253, -3360, -136, -42, 80, 1176, 142, 1008, 29, 0, -88],260,8]
%
% END OF LATTICE L261.8
%
%
% LATTICE L261.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2551248, 54432, -7056; 54432, 525, -42; -7056, -42, 1],[1008, 21, 1],[7, 3, 0, -5, -1, 1, 1, 3, 9, 25, 10, 229, 37, 223, 19, 11; -1368, -586, 0, 976, 195, -200, -196, -587, -1760, -4888, -1955, -44768, -7233, -43592, -3714, -2150; -8032, -3444, -1, 5712, 1143, -1176, -1150, -3444, -10328, -28686, -11474, -262752, -42453, -255864, -21800, -12621],260,9]
%
% END OF LATTICE L261.9
%
%
% LATTICE L261.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-5040, 2016, 1008; 2016, -798, -357; 1008, -357, 53],[1008, 21, 1],[359, 65, 11, -23, -4, 3, 35, 39, 385, 369, 454, 3495, 190, 3469, 895, 178; 984, 178, 30, -64, -11, 8, 96, 107, 1056, 1012, 1245, 9584, 521, 9512, 2454, 488; -216, -42, -9, 0, 2, 0, -18, -21, -216, -210, -261, -2016, -110, -2016, -522, -105],260,10]
%
% END OF LATTICE L261.10
%
%
% LATTICE L261.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-100464, -35952, -672; -35952, 86688, 1792; -672, 1792, 37],[336, 112, 1],[1, 25, 29, 92, 44, 55, 41, 61, 7, 31, 11, 20, 4, 1, -1, -5; -30, -783, -918, -2919, -1399, -1752, -1308, -1953, -225, -1002, -357, -651, -131, -33, 33, 168; 1466, 38304, 44920, 142842, 68464, 85743, 64016, 95592, 11014, 49056, 17480, 31878, 6416, 1617, -1616, -8232],260,11]
%
% END OF LATTICE L261.11
%
%
% LATTICE L261.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1008, 0, 0; 0, -14352, 432; 0, 432, -13],[1008, 48, 1],[-11, -5, -76, -5, -29, -9, -62, -3, -4, 0, 1, 0, -1, -1, -13, -2; -84, -44, -735, -50, -301, -97, -693, -38, -63, -5, 0, 1, 7, -1, -42, -11; -2898, -1512, -25200, -1713, -10304, -3318, -23688, -1296, -2142, -168, 0, 33, 224, -42, -1512, -384],260,12]
%
% END OF LATTICE L261.12
%
%
% LATTICE L261.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3248784, 502992, -4032; 502992, -77856, 624; -4032, 624, -5],[1008, 48, 1],[3, 1, 1, 0, -2, 0, 1, 1, 3, 5, 29, 6, 110, 12, 29, 5; 42, 16, 21, 1, -21, -1, 7, 10, 35, 61, 364, 76, 1407, 155, 378, 67; 2786, 1176, 1792, 123, -1008, -126, 56, 432, 1918, 3528, 21728, 4581, 85680, 9534, 23464, 4272],260,13]
%
% END OF LATTICE L261.13
%
%
% LATTICE L261.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-137424, -58800, -16128; -58800, -22176, -6048; -16128, -6048, -1649],[336, 336, 1],[1, -3, -1, 1, 8, 12, 19, 17, 11, 31, 61, 27, 64, 44, 41, 11; -40, 176, 55, -58, -453, -669, -1051, -930, -593, -1653, -3220, -1419, -3345, -2285, -2114, -547; 138, -616, -192, 203, 1584, 2338, 3672, 3248, 2070, 5768, 11232, 4949, 11664, 7966, 7368, 1904],260,14]
%
% END OF LATTICE L261.14
%
%
% LATTICE L261.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-706608, -335664, -94752; -335664, -141792, -39984; -94752, -39984, -11275],[1008, 336, 1],[-1, -9, -29, -15, -14, -34, -37, -17, -5, -5, -1, 1, 2, 6, 7, 3; 414, 2818, 8559, 4366, 4023, 9665, 10425, 4684, 1347, 1291, 246, -257, -501, -1447, -1620, -575; -1458, -9912, -30096, -15351, -14144, -33978, -36648, -16464, -4734, -4536, -864, 903, 1760, 5082, 5688, 2016],260,15]
%
% END OF LATTICE L261.15
%
%
% LATTICE L261.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-58464, -23184, -58464; -23184, -7728, -21168; -58464, -21168, -55691],[1008, 336, 1],[-126, -1446, -1181, -1702, -4433, -3365, -1155, -1368, -113, -227, -14, 29, 131, 19, -40, -305; -383, -4399, -3595, -5182, -13500, -10250, -3519, -4171, -345, -697, -45, 86, 396, 58, -121, -925; 278, 3192, 2608, 3759, 9792, 7434, 2552, 3024, 250, 504, 32, -63, -288, -42, 88, 672],260,16]
%
% END OF LATTICE L261.16
%

\medskip%
%------------------------------WEYL-GROUP-W262--------------------------------
%
\leavevmode\llap{}%
$W_{262}$%
\qquad\llap{16} lattices, $\chi=72$%
\hfill%
$222|2222|2222|2222|2\rtimes D_{4}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L262.1
%
\leavevmode%
${L_{262.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{2}16\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{1}{}3\above{1pt}{1pt}{1}{}9\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{2}{}7\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{3}%
\EasyButWeakLineBreak%
{${112}\above{1pt}{1pt}{}{2}{3}\above{1pt}{1pt}{}{2}{7}\above{1pt}{1pt}{r}{2}{48}\above{1pt}{1pt}{s}{2}{28}\above{1pt}{1pt}{*}{2}{12}\above{1pt}{1pt}{*}{2}{112}\above{1pt}{1pt}{b}{2}{18}\above{1pt}{1pt}{l}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2339568\\5040\\-7056
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5040\\-6\\-9
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-7056\\-9\\19
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\28560\\34272
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\139\\168
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\-115\\-139
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
13\\2128\\5824
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\163\\447
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\322\\889
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\472\\1320
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\434\\1274
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\116\\390
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\-392\\-224
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-255\\-558
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[2339568, 5040, -7056; 5040, -6, -9; -7056, -9, 19],[1008, 3, 1],[13, 1, 2, 3, 3, 1, 1, -1, -13, -1, -2, -3, -3, -1, -1, 1; 2128, 163, 322, 472, 434, 116, -392, -255, -2688, -188, -357, -512, -504, -166, -168, 165; 5824, 447, 889, 1320, 1274, 390, -224, -558, -6496, -477, -931, -1368, -1358, -450, -448, 450],261,1]
%
% END OF LATTICE L262.1
%
%
% LATTICE L262.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-17808, -1344, 336; -1344, -101, 25; 336, 25, -6],[336, 1, 1],[-5, -1, -1, 1, 4, 4, 103, 6, 117, 11, 15, 7, 3, 1, 9, 0; 112, 18, 14, -24, -77, -75, -1904, -110, -2128, -198, -266, -120, -49, -15, -112, 2; 168, 18, 0, -48, -105, -96, -2352, -133, -2520, -228, -294, -120, -42, -9, 0, 7],261,2]
%
% END OF LATTICE L262.2
%
%
% LATTICE L262.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-56112, 336, 336; 336, 81, -3; 336, -3, -2],[336, 3, 1],[-685, -10, -37, -9, -17, -1, -1, 1, 13, 0, -5, -7, -67, -19, -671, -37; -2016, -29, -105, -24, -42, -2, 0, 2, 0, -1, -21, -24, -210, -58, -2016, -110; -116592, -1700, -6279, -1520, -2856, -166, -168, 165, 2016, -5, -882, -1208, -11466, -3244, -114408, -6303],261,3]
%
% END OF LATTICE L262.3
%
%
% LATTICE L262.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2108400, -1068144, 13776; -1068144, -541135, 6979; 13776, 6979, -90],[336, 7, 1],[33, 22, 9, 145, 45, 233, 357, 129, 319, 88, 13, 31, -1, -13, -5, 3; -64, -45, -19, -312, -98, -510, -784, -284, -704, -195, -29, -72, 2, 30, 16, -4; 80, -126, -97, -2016, -716, -3906, -6184, -2289, -5792, -1659, -260, -840, 2, 336, 472, 147],261,4]
%
% END OF LATTICE L262.4
%
%
% LATTICE L262.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[6557040, 38304, -18144; 38304, 219, -105; -18144, -105, 50],[1008, 3, 1],[-61, -1, -4, -1, 1, 1, 47, 1, 61, 1, 4, 1, -1, -1, -47, -1; -9072, -145, -567, -136, 126, 130, 6048, 128, 7728, 125, 483, 104, -294, -170, -7392, -152; -41328, -669, -2646, -648, 630, 636, 29736, 631, 38304, 624, 2457, 576, -1008, -726, -32760, -685],261,5]
%
% END OF LATTICE L262.5
%
%
% LATTICE L262.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[27552, 1008, -672; 1008, -16, -16; -672, -16, 15],[336, 16, 1],[-3, 1, 6, 2, 15, 10, 12, 9, 17, 4, 1, -1, -8, -5, -5, -3; -56, -3, 35, 15, 119, 81, 98, 74, 140, 33, 7, -9, -77, -51, -56, -38; -238, 24, 280, 102, 784, 528, 637, 480, 910, 216, 56, -54, -448, -288, -301, -192],261,6]
%
% END OF LATTICE L262.6
%
%
% LATTICE L262.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-183120, -23520, 3696; -23520, -2709, 420; 3696, 420, -65],[336, 21, 1],[179, 17, 8, 9, 1, -1, -1, 1, 13, 3, 4, 23, 23, 41, 193, 71; -12816, -1215, -570, -632, -66, 76, 72, -77, -960, -220, -291, -1664, -1656, -2946, -13848, -5089; -72816, -6902, -3237, -3584, -372, 434, 408, -441, -5472, -1253, -1656, -9464, -9414, -16744, -78696, -28917],261,7]
%
% END OF LATTICE L262.7
%
%
% LATTICE L262.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-40992, 44016, 672; 44016, -47088, -720; 672, -720, -11],[336, 48, 1],[106, 25, 94, 3, 25, 2, 5, -1, -1, 0, 11, 2, 80, 23, 205, 91; -126, -29, -105, -3, -21, -1, 0, 2, 0, -1, -21, -3, -105, -29, -252, -110; 14511, 3376, 12432, 374, 2856, 184, 294, -192, -63, 64, 2016, 314, 11592, 3256, 28602, 12576],261,8]
%
% END OF LATTICE L262.8
%
%
% LATTICE L262.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-48360816, 56448, 53424; 56448, -42, -63; 53424, -63, -59],[1008, 21, 1],[13, 10, 5, 93, 33, 181, 289, 323, 275, 80, 13, 51, 3, -1, -1, 1; 304, 235, 118, 2200, 782, 4292, 6856, 7665, 6528, 1900, 309, 1216, 72, -22, -24, 21; 11440, 8799, 4399, 81816, 29030, 159222, 254224, 284130, 241904, 70371, 11435, 44856, 2638, -882, -880, 882],261,9]
%
% END OF LATTICE L262.9
%
%
% LATTICE L262.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-29749104, 4363632, 49392; 4363632, -640059, -7245; 49392, -7245, -82],[1008, 21, 1],[-23, -6, -8, -45, -43, -75, -347, -42, -313, -29, -13, -11, 1, 5, 11, 0; -144, -35, -45, -248, -234, -406, -1872, -226, -1680, -155, -69, -56, 6, 26, 48, -2; -1152, -525, -846, -5208, -5238, -9324, -43704, -5341, -40176, -3780, -1737, -1680, 72, 714, 2376, 175],261,10]
%
% END OF LATTICE L262.10
%
%
% LATTICE L262.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[336, 2352, 336; 2352, 1120, 112; 336, 112, 9],[336, 112, 1],[2, 1, -1, -1, 5, 43, 22, 76, 14, 79, 17, 17, 11, 37, 10, 20; -11, 0, 7, 6, -32, -273, -139, -479, -88, -495, -106, -105, -67, -222, -59, -115; 75, 0, -48, -42, 216, 1848, 942, 3248, 597, 3360, 720, 714, 456, 1512, 402, 784],261,11]
%
% END OF LATTICE L262.11
%
%
% LATTICE L262.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-19360656, 3021984, -18144; 3021984, -471696, 2832; -18144, 2832, -17],[1008, 48, 1],[-88, -59, -68, -5, -9, 0, 1, 1, -3, -6, -23, -8, -82, -65, -183, -235; -658, -442, -511, -38, -70, -1, 7, 9, -21, -43, -168, -59, -609, -484, -1365, -1755; -15827, -10752, -12656, -1002, -2072, -168, 98, 432, -301, -768, -3472, -1302, -14056, -11352, -32354, -41904],261,12]
%
% END OF LATTICE L262.12
%
%
% LATTICE L262.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[60202800, 1927296, -119952; 1927296, 61680, -3840; -119952, -3840, 239],[1008, 48, 1],[16, 1, -8, -1, 1, 4, 59, 11, 47, 14, 71, 4, 62, 11, 67, 7; -63, -16, -63, -2, 0, 5, 63, 11, 42, 11, 42, 1, -21, -10, -105, -17; 6993, 240, -5040, -534, 504, 2088, 30618, 5696, 24255, 7200, 36288, 2022, 30744, 5352, 31878, 3232],261,13]
%
% END OF LATTICE L262.13
%
%
% LATTICE L262.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-690144, -996912, 6048; -996912, -1439760, 8736; 6048, 8736, -53],[336, 336, 1],[1, -1, -16, -20, -115, -232, -148, -921, -307, -254, -137, -31, -38, -23, -5, 3; 0, -1, -3, -3, -15, -29, -18, -110, -36, -29, -15, -3, -3, -1, 0, 2; 114, -280, -2328, -2786, -15648, -31360, -19923, -123648, -41106, -33880, -18168, -4046, -4848, -2800, -573, 672],261,14]
%
% END OF LATTICE L262.14
%
%
% LATTICE L262.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-41913648, -168336, 83664; -168336, -672, 336; 83664, 336, -167],[1008, 336, 1],[-12, -29, -5, -3, -1, -1, 0, 2, 0, -1, -1, -3, -5, -29, -6, -110; -327, -814, -147, -101, -42, -79, -6, 3, 1, -1, -16, -62, -121, -736, -157, -2937; -6722, -16296, -2824, -1722, -592, -672, -13, 1008, 2, -504, -536, -1638, -2768, -16128, -3347, -61488],261,15]
%
% END OF LATTICE L262.15
%
%
% LATTICE L262.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-126000, 27216, 4032; 27216, 7392, 1008; 4032, 1008, 137],[1008, 336, 1],[8, 9, 7, 3, 7, 9, 4, 6, 4, 1, -1, -1, -1, 1, 2, 6; -783, -881, -684, -292, -675, -860, -378, -559, -363, -74, 111, 101, 102, -95, -195, -587; 5526, 6216, 4824, 2058, 4752, 6048, 2655, 3920, 2538, 504, -792, -714, -720, 672, 1377, 4144],261,16]
%
% END OF LATTICE L262.16
%

\medskip%
%------------------------------WEYL-GROUP-W263--------------------------------
%
\leavevmode\llap{}%
$W_{263}$%
\qquad\llap{22} lattices, $\chi=36$%
\hfill%
$2\infty\infty\infty222$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L263.1
%
\leavevmode%
${L_{263.1}}$%
{} : {$1\above{1pt}{1pt}{2}{{\rm II}}4\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{-}{}7\above{1pt}{1pt}{1}{}49\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${98}\above{1pt}{1pt}{l}{2}{28}\above{1pt}{1pt}{7,1}{\infty}{28}\above{1pt}{1pt}{7,4}{\infty b}{28}\above{1pt}{1pt}{7,4}{\infty}{28}\above{1pt}{1pt}{*}{2}{196}\above{1pt}{1pt}{b}{2}{14}\above{1pt}{1pt}{s}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2940\\1568\\-588
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1568\\840\\-315
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-588\\-315\\118
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-5\\28\\49
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3\\16\\28
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\-2\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\16\\56
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\54\\154
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\112\\294
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\10\\21
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[2940, 1568, -588; 1568, 840, -315; -588, -315, 118],[196, 7, 1],[-5, -3, 1, 3, 3, 1, -1; 28, 16, -2, 16, 54, 112, 10; 49, 28, 0, 56, 154, 294, 21],262,1]
%
% END OF LATTICE L263.1
%
\hbox{}\par\smallskip%
%
% LATTICE L263.2
%
\leavevmode%
${L_{263.2}}$%
{} : {$1\above{1pt}{1pt}{2}{6}8\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{-}{}7\above{1pt}{1pt}{1}{}49\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${196}\above{1pt}{1pt}{s}{2}{56}\above{1pt}{1pt}{28,1}{\infty z}{14}\above{1pt}{1pt}{28,25}{\infty a}{56}\above{1pt}{1pt}{28,25}{\infty z}{14}\above{1pt}{1pt}{l}{2}{392}\above{1pt}{1pt}{}{2}{7}\above{1pt}{1pt}{r}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-526456\\-258328\\-68992
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-258328\\-126749\\-33845
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-68992\\-33845\\-9034
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-135\\406\\-490
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-71\\212\\-252
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
68\\-204\\245
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
903\\-2700\\3220
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
907\\-2710\\3227
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2869\\-8568\\10192
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
36\\-107\\126
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-526456, -258328, -68992; -258328, -126749, -33845; -68992, -33845, -9034],[392, 7, 1],[-135, -71, 68, 903, 907, 2869, 36; 406, 212, -204, -2700, -2710, -8568, -107; -490, -252, 245, 3220, 3227, 10192, 126],262,2]
%
% END OF LATTICE L263.2
%
\hbox{}\par\smallskip%
%
% LATTICE L263.3
%
\leavevmode%
${L_{263.3}}$%
{} : {$1\above{1pt}{1pt}{-2}{6}8\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{-}{}7\above{1pt}{1pt}{1}{}49\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{m}%
\EasyButWeakLineBreak%
{${49}\above{1pt}{1pt}{r}{2}{56}\above{1pt}{1pt}{28,15}{\infty z}{14}\above{1pt}{1pt}{28,25}{\infty b}{56}\above{1pt}{1pt}{28,11}{\infty z}{14}\above{1pt}{1pt}{b}{2}{392}\above{1pt}{1pt}{*}{2}{28}\above{1pt}{1pt}{l}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-756952\\-80752\\-25872
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-80752\\-8610\\-2765
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-25872\\-2765\\-879
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-36\\259\\245
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-21\\152\\140
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
29\\-209\\-196
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
281\\-2032\\-1876
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
259\\-1875\\-1722
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
769\\-5572\\-5096
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7\\-52\\-42
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-756952, -80752, -25872; -80752, -8610, -2765; -25872, -2765, -879],[392, 7, 1],[-36, -21, 29, 281, 259, 769, 7; 259, 152, -209, -2032, -1875, -5572, -52; 245, 140, -196, -1876, -1722, -5096, -42],262,3]
%
% END OF LATTICE L263.3
%
%
% LATTICE L263.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[98, 0, -49; 0, -91, -7; -49, -7, 24],[49, 7, 1],[-1, -7, 4, 65, 147, 250, 21; 0, 1, -1, -13, -29, -49, -4; 0, -14, 7, 126, 287, 490, 42],262,4]
%
% END OF LATTICE L263.4
%
%
% LATTICE L263.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[1470, 98, -294; 98, 14, -21; -294, -21, 59],[98, 7, 1],[9, 5, 0, 11, 30, 57, 4; 14, 8, -1, 8, 27, 56, 5; 49, 28, 0, 56, 154, 294, 21],262,5]
%
% END OF LATTICE L263.5
%
%
% LATTICE L263.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-16268, 1176, -1568; 1176, -70, 119; -1568, 119, -149],[196, 7, 1],[12, 7, -6, -83, -84, -267, -7; 35, 22, -18, -258, -263, -840, -23; -98, -56, 49, 672, 679, 2156, 56],262,6]
%
% END OF LATTICE L263.6
%
%
% LATTICE L263.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-98, -98, -49; -98, -91, -49; -49, -49, -24],[49, 7, 1],[-1, -1, 4, 23, 45, 10, 3; 0, 1, -1, -13, -29, -7, -4; 2, 0, -7, -28, -49, -10, 0],262,7]
%
% END OF LATTICE L263.7
%
%
% LATTICE L263.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-29694, -6174, 1078; -6174, -679, 154; 1078, 154, -31],[98, 7, 1],[2, 1, -12, -45, -76, -15, 1; 19, 10, -115, -438, -745, -148, 8; 164, 84, -987, -3724, -6307, -1248, 77],262,8]
%
% END OF LATTICE L263.8
%
%
% LATTICE L263.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-29988, 1274, -14504; 1274, -42, 616; -14504, 616, -7015],[98, 14, 1],[-47, 17, 27, -71, -419, -402, -54; 7, 1, -2, 1, 12, 14, 3; 98, -35, -56, 147, 868, 833, 112],262,9]
%
% END OF LATTICE L263.9
%
%
% LATTICE L263.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2156, 392, 196; 392, -70, -35; 196, -35, -17],[196, 7, 1],[0, -1, 0, 5, 6, 3, 1; -1, -6, 3, 50, 52, 24, 5; 2, 0, -7, -56, -49, -20, 0],262,10]
%
% END OF LATTICE L263.10
%
%
% LATTICE L263.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[119639674, -2031932, 58568524; -2031932, 34510, -994714; 58568524, -994714, 28671693],[98, 14, 1],[-46, 209, -1103, -6101, -26987, -3247, -1843; 1, -2, 25, 124, 543, 65, 36; 94, -427, 2254, 12467, 55146, 6635, 3766],262,11]
%
% END OF LATTICE L263.11
%
%
% LATTICE L263.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-232260, -93492, -3920; -93492, -37604, -1589; -3920, -1589, -62],[196, 7, 1],[-17, -9, 103, 393, 669, 133, -7; 38, 20, -230, -876, -1490, -296, 16; 101, 56, -616, -2380, -4074, -814, 35],262,12]
%
% END OF LATTICE L263.12
%
%
% LATTICE L263.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1464120, -724808, 7056; -724808, -358813, 3493; 7056, 3493, -34],[392, 7, 1],[1, 5, -3, -45, -46, -21, -2; -2, -12, 6, 100, 104, 48, 5; 2, -196, -7, 924, 1127, 568, 98],262,13]
%
% END OF LATTICE L263.13
%
%
% LATTICE L263.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-30890776, 38808, 77616; 38808, -35, -98; 77616, -98, -195],[392, 7, 1],[-1, -1, 7, 61, 55, 23, 1; -14, -12, 97, 828, 741, 308, 10; -391, -392, 2737, 23856, 21511, 8996, 392],262,14]
%
% END OF LATTICE L263.14
%
%
% LATTICE L263.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-65072, 3332, -15876; 3332, -168, 812; -15876, 812, -3873],[196, 28, 1],[2, 5, 3, -11, -59, -108, -12; 35, -3, -8, 18, 111, 217, 31; 0, -21, -14, 49, 266, 490, 56],262,15]
%
% END OF LATTICE L263.15
%
%
% LATTICE L263.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[134074192, -4302004, 33109496; -4302004, 138040, -1062376; 33109496, -1062376, 8176359],[196, 28, 1],[52, -67, 649, 3295, 14461, 3466, 1930; -11, 13, -138, -694, -3043, -729, -405; -212, 273, -2646, -13433, -58954, -14130, -7868],262,16]
%
% END OF LATTICE L263.16
%
%
% LATTICE L263.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[3817688, 137396, 941388; 137396, 4956, 33880; 941388, 33880, 232133],[196, 28, 1],[145, 31, 131, 1183, 2580, 2161, 345; 0, 2, 5, 30, 61, 49, 6; -588, -126, -532, -4802, -10472, -8771, -1400],262,17]
%
% END OF LATTICE L263.17
%
%
% LATTICE L263.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[23128, 2156, 5684; 2156, 252, 532; 5684, 532, 1397],[196, 28, 1],[-1, 17, 34, 173, 339, 38, 27; 0, 2, 5, 30, 61, 7, 6; 4, -70, -140, -714, -1400, -157, -112],262,18]
%
% END OF LATTICE L263.18
%
%
% LATTICE L263.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-25872, -5096, 11368; -5096, -952, 2240; 11368, 2240, -4995],[392, 56, 1],[528, 345, 175, 31, -25, -43, 13; -49, -29, -12, -1, 2, 0, -3; 1176, 770, 392, 70, -56, -98, 28],262,19]
%
% END OF LATTICE L263.19
%
%
% LATTICE L263.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2910992, 24696, -409248; 24696, -168, 3472; -409248, 3472, -57535],[392, 56, 1],[-2122, -1372, -685, -124, 63, 62, -63; -49, -29, -12, -1, 2, 0, -3; 15092, 9758, 4872, 882, -448, -441, 448],262,20]
%
% END OF LATTICE L263.20
%
%
% LATTICE L263.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-784, 10584, -392; 10584, -142072, 5264; -392, 5264, -195],[392, 56, 1],[12, 57, 31, 7, -1, -1, 1; -7, -29, -12, -1, 2, 0, -3; -216, -910, -392, -42, 56, 2, -84],262,21]
%
% END OF LATTICE L263.21
%
%
% LATTICE L263.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-119705040, 153272, 306152; 153272, -168, -392; 306152, -392, -783],[392, 56, 1],[22, 106, 59, 14, -1, -1, 1; -7, -29, -12, -1, 2, 0, -3; 8604, 41454, 23072, 5474, -392, -391, 392],262,22]
%
% END OF LATTICE L263.22
%

\medskip%
%------------------------------WEYL-GROUP-W264--------------------------------
%
\leavevmode\llap{}%
$W_{264}$%
\qquad\llap{3} lattices, $\chi=24$%
\hfill%
$\slashtwo2\slashtwo2\slashtwo2\slashtwo2\rtimes D_{4}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L264.1
%
\leavevmode%
${L_{264.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{1}{}7\above{1pt}{1pt}{-}{}49\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${196}\above{1pt}{1pt}{*}{2}{4}\above{1pt}{1pt}{b}{2}{98}\above{1pt}{1pt}{b}{2}{2}\above{1pt}{1pt}{b}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-140532\\2352\\980
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2352\\-14\\-21
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
980\\-21\\-6
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1177\\-21560\\-117992
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
15\\274\\1505
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
9\\165\\902
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-45\\-826\\-4508
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-7\\-128\\-702
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-20\\-364\\-2009
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-18\\-101
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-140532, 2352, 980; 2352, -14, -21; 980, -21, -6],[196, 7, 1],[-45, -7, -20, -1, 3, 1, -1, -2; -826, -128, -364, -18, 56, 18, -21, -37; -4508, -702, -2009, -101, 294, 100, -98, -200],263,1]
%
% END OF LATTICE L264.1
%
%
% LATTICE L264.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-637, 98, -49; 98, -14, 7; -49, 7, -3],[49, 7, 1],[0, 1, 0, -4, -1, -8, -1, -3; -1, 7, 1, -21, -7, -63, -9, -35; -3, 0, 2, 0, -4, -49, -9, -49],263,2]
%
% END OF LATTICE L264.2
%
%
% LATTICE L264.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[22993544, -620340, 5626180; -620340, 16744, -151788; 5626180, -151788, 1376643],[196, 28, 1],[4341, 628, 3406, 188, 216, 23, 1151, 463; 28, 5, 35, 3, 7, 0, 0, 2; -17738, -2566, -13916, -768, -882, -94, -4704, -1892],263,3]
%
% END OF LATTICE L264.3
%

\medskip%
%------------------------------WEYL-GROUP-W265--------------------------------
%
\leavevmode\llap{}%
$W_{265}$%
\qquad\llap{6} lattices, $\chi=28$%
\hfill%
$\slashtwo6|6\slashtwo6|6\rtimes D_{4}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L265.1
%
\leavevmode%
${L_{265.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{-}{}9\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{2}{}13\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${18}\above{1pt}{1pt}{b}{2}{2}\above{1pt}{1pt}{}{6}{6}\above{1pt}{1pt}{}{6}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2291796\\17784\\8892
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
17784\\-138\\-69
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
8892\\-69\\-34
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2573\\344916\\-30888
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-20\\-2681\\240
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-9\\-1206\\107
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-129\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\-1\\2
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\130\\-3
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-2291796, 17784, 8892; 17784, -138, -69; 8892, -69, -34],[468, 3, 1],[-1, 0, 1, 7, 2, 0; -129, -1, 130, 933, 269, 4; 0, 2, -3, -72, -26, -9],264,1]
%
% END OF LATTICE L265.1
%
%
% LATTICE L265.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-89271, 3510, 1755; 3510, -138, -69; 1755, -69, -34],[117, 3, 1],[0, -2, 0, 4, 14, 2; -1, -51, 4, 113, 387, 52; 2, 0, -9, -26, -72, -3],264,2]
%
% END OF LATTICE L265.2
%
%
% LATTICE L265.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-323739, -155025, 10998; -155025, -73281, 5187; 10998, 5187, -367],[117, 39, 1],[-1, -25, 4, 61, 205, 26; 15, 351, -61, -871, -2919, -367; 182, 4212, -741, -10478, -35100, -4407],264,3]
%
% END OF LATTICE L265.3
%
%
% LATTICE L265.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[152568, 36972, 37908; 36972, 29400, 9240; 37908, 9240, 9419],[468, 12, 1],[571, -1, 1600, 22073, 7549, 2174; 6, 0, 17, 234, 80, 23; -2304, 4, -6456, -89064, -30460, -8772],264,4]
%
% END OF LATTICE L265.4
%
%
% LATTICE L265.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-6084, -21996, 7020; -21996, -28470, 10179; 7020, 10179, -3574],[468, 39, 1],[163, 8, -172, -1393, -418, -33; 627, 31, -662, -5367, -1611, -128; 2106, 104, -2223, -18018, -5408, -429],264,5]
%
% END OF LATTICE L265.5
%
%
% LATTICE L265.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[909955800, 91390572, -156978432; 91390572, 9178728, -15765984; -156978432, -15765984, 27080687],[468, 156, 1],[-119, -103, -356, -3013, -941, -166; 381, 311, 1133, 9903, 3117, 581; -468, -416, -1404, -11700, -3640, -624],264,6]
%
% END OF LATTICE L265.6
%

\medskip%
%------------------------------WEYL-GROUP-W266--------------------------------
%
\leavevmode\llap{}%
$W_{266}$%
\qquad\llap{6} lattices, $\chi=14$%
\hfill%
$\slashtwo22\slashthree22\rtimes D_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L266.1
%
\leavevmode%
${L_{266.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{1}{}3\above{1pt}{1pt}{-}{}9\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{2}{}13\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${36}\above{1pt}{1pt}{*}{2}{4}\above{1pt}{1pt}{*}{2}{468}\above{1pt}{1pt}{b}{2}{6}\above{1pt}{1pt}{-}{3}{6}\above{1pt}{1pt}{b}{2}{52}\above{1pt}{1pt}{*}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2535156\\9828\\9828
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
9828\\-30\\-39
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
9828\\-39\\-38
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-24\\-234
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-26\\-232
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7\\156\\1638
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\50\\465
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\77\\696
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
11\\286\\2548
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-2535156, 9828, 9828; 9828, -30, -39; 9828, -39, -38],[468, 3, 1],[-1, -1, 7, 2, 3, 11; -24, -26, 156, 50, 77, 286; -234, -232, 1638, 465, 696, 2548],265,1]
%
% END OF LATTICE L266.1
%
%
% LATTICE L266.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-60957, 234, 819; 234, 6, -3; 819, -3, -11],[117, 3, 1],[1, 4, 7, 0, -1, 8; -1, -6, -13, -1, 2, 0; 74, 297, 520, 0, -75, 585],265,2]
%
% END OF LATTICE L266.2
%
%
% LATTICE L266.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-585, -2574, 117; -2574, -11154, 507; 117, 507, -23],[117, 39, 1],[2, 4, 0, -3, -1, 2; -1, -6, -1, -1, 2, 0; -13, -117, -23, -39, 39, 9],265,3]
%
% END OF LATTICE L266.3
%
%
% LATTICE L266.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[773501976, -2242188, 191693736; -2242188, 6504, -555672; 191693736, -555672, 47506651],[468, 12, 1],[58, 57, 13976, 2168, 2055, 4169; 3, 0, 39, 7, 10, 26; -234, -230, -56394, -8748, -8292, -16822],265,4]
%
% END OF LATTICE L266.4
%
%
% LATTICE L266.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[65052, -70200, 6084; -70200, 63258, -5499; 6084, -5499, 478],[468, 39, 1],[-3, -1, 1, 3, -1, -5; 182, 60, -58, -173, 70, 312; 2132, 702, -680, -2028, 819, 3654],265,5]
%
% END OF LATTICE L266.5
%
%
% LATTICE L266.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2903465448, 75694788, -663409188; 75694788, 1973400, -17295408; -663409188, -17295408, 151581535],[468, 156, 1],[-45, -988, -65, 543, 1396, 658; 131, 3033, 197, -1687, -4327, -2049; -182, -3978, -262, 2184, 5616, 2646],265,6]
%
% END OF LATTICE L266.6
%

\medskip%
%------------------------------WEYL-GROUP-W267--------------------------------
%
\leavevmode\llap{}%
$W_{267}$%
\qquad\llap{44} lattices, $\chi=72$%
\hfill%
$2\infty|\infty22|22\infty|\infty22|2\rtimes D_{4}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L267.1
%
\leavevmode%
${L_{267.1}}$%
{} : {$1\above{1pt}{1pt}{2}{{\rm II}}4\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{1}{}3\above{1pt}{1pt}{-}{}9\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-}{}5\above{1pt}{1pt}{-}{}25\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{23,3,2}%
\EasyButWeakLineBreak%
{${450}\above{1pt}{1pt}{l}{2}{60}\above{1pt}{1pt}{15,1}{\infty}{60}\above{1pt}{1pt}{15,8}{\infty b}{60}\above{1pt}{1pt}{r}{2}{18}\above{1pt}{1pt}{b}{2}{10}\above{1pt}{1pt}{b}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
13974300\\-264600\\-19800
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-264600\\5010\\375
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-19800\\375\\28
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2021\\-78780\\-363600
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
38\\1481\\6840
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\117\\539
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7\\195\\2250
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5\\176\\1140
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\124\\450
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
11\\476\\1380
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5\\219\\594
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\89\\220
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[13974300, -264600, -19800; -264600, 5010, 375; -19800, 375, 28],[900, 15, 1],[7, 5, 3, 11, 5, 2, 13, 3, -1, -3, -1, 0; 195, 176, 124, 476, 219, 89, 585, 136, -46, -164, -63, -11; 2250, 1140, 450, 1380, 594, 220, 1350, 300, -90, 60, 126, 140],266,1]
%
% END OF LATTICE L267.1
%
\hbox{}\par\smallskip%
%
% LATTICE L267.2
%
\leavevmode%
${L_{267.2}}$%
{} : {$1\above{1pt}{1pt}{2}{6}8\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{1}{}9\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{1}{}5\above{1pt}{1pt}{1}{}25\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{3m,3,2}%
\EasyButWeakLineBreak%
{${36}\above{1pt}{1pt}{s}{2}{120}\above{1pt}{1pt}{60,49}{\infty z}{30}\above{1pt}{1pt}{60,17}{\infty a}{120}\above{1pt}{1pt}{s}{2}{900}\above{1pt}{1pt}{*}{2}{20}\above{1pt}{1pt}{*}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-11417400\\-5657400\\-703800
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-5657400\\-2803245\\-348705
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-703800\\-348705\\-43354
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7762399\\-18108960\\19641600
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3846770\\-8974159\\9733680
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
478890\\-1117206\\1211759
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2513\\-5862\\6354
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
8517\\-19868\\21540
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2686\\-6266\\6795
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
25491\\-59468\\64500
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
63487\\-148110\\160650
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5959\\-13902\\15080
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-11417400, -5657400, -703800; -5657400, -2803245, -348705; -703800, -348705, -43354],[1800, 15, 1],[2513, 8517, 2686, 25491, 63487, 5959, 10007, 16523, 444, -451, -887, 301; -5862, -19868, -6266, -59468, -148110, -13902, -23346, -38548, -1036, 1052, 2070, -702; 6354, 21540, 6795, 64500, 160650, 15080, 25326, 41820, 1125, -1140, -2250, 760],266,2]
%
% END OF LATTICE L267.2
%
\hbox{}\par\smallskip%
%
% LATTICE L267.3
%
\leavevmode%
${L_{267.3}}$%
{} : {$1\above{1pt}{1pt}{-2}{6}8\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{1}{}9\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{1}{}5\above{1pt}{1pt}{1}{}25\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{32,3,m}%
\EasyButWeakLineBreak%
{${9}\above{1pt}{1pt}{r}{2}{120}\above{1pt}{1pt}{60,19}{\infty z}{30}\above{1pt}{1pt}{60,17}{\infty b}{120}\above{1pt}{1pt}{l}{2}{225}\above{1pt}{1pt}{}{2}{5}\above{1pt}{1pt}{}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-16061400\\-797400\\-266400
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-797400\\-39570\\-13245
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-266400\\-13245\\-4399
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1343899\\-20439360\\-19841400
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
67195\\-1021969\\-992070
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
21805\\-331632\\-321931
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
169\\-2571\\-2493
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1167\\-17752\\-17220
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
376\\-5719\\-5550
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3621\\-55072\\-53460
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4526\\-68835\\-66825
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
427\\-6494\\-6305
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-16061400, -797400, -266400; -797400, -39570, -13245; -266400, -13245, -4399],[1800, 15, 1],[169, 1167, 376, 3621, 4526, 427, 721, 2393, 69, -61, -76, 18; -2571, -17752, -5719, -55072, -68835, -6494, -10965, -36392, -1049, 928, 1155, -274; -2493, -17220, -5550, -53460, -66825, -6305, -10647, -35340, -1020, 900, 1125, -265],266,3]
%
% END OF LATTICE L267.3
%
%
% LATTICE L267.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-3675, 225, -675; 225, 15, 80; -675, 80, -72],[75, 5, 1],[13, 16, -28, -578, -235, -423, -1513, -916, -197, -322, -65, -27; 65, 81, -141, -2919, -1187, -2137, -7645, -4629, -996, -1629, -329, -137; -50, -60, 105, 2160, 878, 1580, 5650, 3420, 735, 1200, 242, 100],266,4]
%
% END OF LATTICE L267.4
%
%
% LATTICE L267.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-2929650, 218850, -21300; 218850, -16345, 1585; -21300, 1585, -144],[150, 5, 1],[-78, -11, 155, 1687, 324, 547, 1838, 2123, 373, 425, 28, -19; -1105, -156, 2196, 23904, 4591, 7751, 26045, 30084, 5286, 6024, 397, -269; -625, -90, 1245, 13590, 2611, 4410, 14825, 17130, 3015, 3450, 229, -150],266,5]
%
% END OF LATTICE L267.5
%
%
% LATTICE L267.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-176700, 4200, 600; 4200, -85, -15; 600, -15, -2],[300, 5, 1],[1, -1, -1, -7, -1, -1, -1, 1, 1, 7, 1, 1; -70, -108, -21, -108, -14, -12, -10, 12, 9, 12, -2, -12; 525, 150, -180, -1410, -207, -215, -225, 210, 225, 1770, 267, 305],266,6]
%
% END OF LATTICE L267.6
%
%
% LATTICE L267.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-2381700, -574800, -588000; -574800, -119110, -122145; -588000, -122145, -125252],[300, 5, 1],[3716, 4295, 757, 869, 58, -37, -156, -23, 311, 3403, 654, 1105; 1015445, 1173672, 206868, 237492, 15853, -10107, -42625, -6288, 84978, 929892, 178711, 301953; -1007700, -1164720, -205290, -235680, -15732, 10030, 42300, 6240, -84330, -922800, -177348, -299650],266,7]
%
% END OF LATTICE L267.7
%
%
% LATTICE L267.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-353400, 8400, 600; 8400, -170, -15; 600, -15, -1],[600, 5, 1],[-1, 1, 1, 7, 1, 1, 1, -1, -1, -7, -1, -1; -10, 12, 9, 12, -2, -12, -70, -108, -21, -108, -14, -12; -450, 420, 450, 3540, 534, 610, 1050, 300, -360, -2820, -414, -430],266,8]
%
% END OF LATTICE L267.8
%
%
% LATTICE L267.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-1746677400, 44802600, -15922200; 44802600, -1149195, 408410; -15922200, 408410, -144771],[600, 5, 1],[1737, 1753, -5210, -147821, -14610, -25513, -88727, -210529, -20887, -60955, -2788, -584; 67550, 68172, -202611, -5748588, -568166, -992171, -3450490, -8187228, -812271, -2370468, -108422, -22711; -475, -480, 1425, 40440, 3997, 6980, 24275, 57600, 5715, 16680, 763, 160],266,9]
%
% END OF LATTICE L267.9
%
%
% LATTICE L267.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[450, 0, -225; 0, -435, -15; -225, -15, 112],[225, 15, 1],[2741, 563, 129, 227, 145, 25, -1, -15, 8, 321, 403, 249; -240, -49, -11, -19, -12, -2, 0, 1, -1, -29, -36, -22; 5400, 1110, 255, 450, 288, 50, 0, -30, 15, 630, 792, 490],266,10]
%
% END OF LATTICE L267.10
%
%
% LATTICE L267.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[1303650, -57150, -8550; -57150, 2505, 375; -8550, 375, 56],[450, 15, 1],[13, 3, -1, -3, -1, 0, 7, 5, 3, 11, 5, 2; 195, 46, -16, -74, -33, -11, -15, 26, 34, 146, 69, 29; 675, 150, -45, 30, 63, 70, 1125, 570, 225, 690, 297, 110],266,11]
%
% END OF LATTICE L267.11
%
%
% LATTICE L267.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-362700, 12600, -17100; 12600, -390, 615; -17100, 615, -797],[900, 15, 1],[-2048, -823, -87, -277, -82, -10, 28, 15, -14, -531, -322, -192; -14415, -5794, -613, -1954, -579, -71, 195, 106, -98, -3734, -2265, -1351; 32850, 13200, 1395, 4440, 1314, 160, -450, -240, 225, 8520, 5166, 3080],266,12]
%
% END OF LATTICE L267.12
%
%
% LATTICE L267.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1709100, 255525, 557025; 255525, 38205, 83280; 557025, 83280, 181544],[75, 15, 1],[-217, 8, -52, -1370, -1697, -3109, -11323, -2316, -525, -938, -611, -353; -20, 1, -1, -69, -88, -166, -620, -129, -31, -59, -40, -26; 675, -25, 160, 4235, 5247, 9615, 35025, 7165, 1625, 2905, 1893, 1095],266,13]
%
% END OF LATTICE L267.13
%
%
% LATTICE L267.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[86136450, -13517550, 42303150; -13517550, 2121360, -6638710; 42303150, -6638710, 20775833],[150, 10, 1],[2023, -629, 9814, 98827, 40187, 72437, 259877, 157769, 68756, 58313, 12193, 6133; 60, -18, 291, 2922, 1188, 2141, 7680, 4662, 2031, 1722, 360, 181; -4100, 1275, -19890, -200295, -81448, -146810, -526700, -319755, -139350, -118185, -24712, -12430],266,14]
%
% END OF LATTICE L267.14
%
%
% LATTICE L267.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[39926550, -11271450, -13734150; -11271450, 3182040, 3877215; -13734150, 3877215, 4724347],[150, 15, 1],[-1402, 289, -2267, -45637, -27836, -50173, -179998, -72849, -15873, -26923, -8444, -4247; 60, -12, 97, 1948, 1188, 2141, 7680, 3108, 677, 1148, 360, 181; -4125, 850, -6670, -134270, -81897, -147615, -529575, -214330, -46700, -79210, -24843, -12495],266,15]
%
% END OF LATTICE L267.15
%
%
% LATTICE L267.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-61200, 5625, 24975; 5625, -435, -2295; 24975, -2295, -10192],[225, 15, 1],[5391, 3259, 697, 1131, 227, 275, -51, -55, 104, 2073, 841, 4531; -80, -49, -11, -19, -4, -6, 0, 1, -1, -29, -12, -66; 13225, 7995, 1710, 2775, 557, 675, -125, -135, 255, 5085, 2063, 11115],266,16]
%
% END OF LATTICE L267.16
%
%
% LATTICE L267.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-120900, 134100, -29100; 134100, -148155, 32070; -29100, 32070, -6931],[300, 15, 1],[-10088, -4047, -425, -1341, -394, -138, 148, 71, -72, -2635, -1594, -2844; -23565, -9454, -993, -3134, -921, -323, 345, 166, -168, -6154, -3723, -6643; -66675, -26750, -2810, -8870, -2607, -915, 975, 470, -475, -17410, -10533, -18795],266,17]
%
% END OF LATTICE L267.17
%
%
% LATTICE L267.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1026900, 429000, -22800; 429000, 179220, -9525; -22800, -9525, 506],[300, 15, 1],[1019, 481, 165, 463, 193, 204, 401, 87, -23, 105, 91, 222; -2380, -1124, -386, -1084, -452, -478, -940, -204, 54, -244, -212, -518; 1125, 520, 170, 460, 189, 195, 375, 80, -20, 140, 111, 255],266,18]
%
% END OF LATTICE L267.18
%
%
% LATTICE L267.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1176645600, -10742550, -563831100; -10742550, -98070, -5147670; -563831100, -5147670, -270179491],[150, 30, 1],[-8759, -213, 5825, 31851, 36725, 62046, 208639, 40189, 14163, 8125, 3251, -2082; -1105, -26, 732, 3984, 4591, 7751, 26045, 5014, 1762, 1004, 397, -269; 18300, 445, -12170, -66545, -76728, -129630, -435900, -83965, -29590, -16975, -6792, 4350],266,19]
%
% END OF LATTICE L267.19
%
%
% LATTICE L267.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[37880700, -128100, -9598800; -128100, 440, 32460; -9598800, 32460, 2432293],[300, 20, 1],[-38844, -23314, -4865, -7822, -1572, -674, -76, -38, -973, -15530, -6212, -11002; 455, 273, 57, 93, 19, 9, 5, 3, 12, 183, 73, 129; -153300, -92010, -19200, -30870, -6204, -2660, -300, -150, -3840, -61290, -24516, -43420],266,20]
%
% END OF LATTICE L267.20
%
%
% LATTICE L267.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[721485688200, 47764011900, -182741412900; 47764011900, 3162087440, -12097901820; -182741412900, -12097901820, 46285636063],[300, 20, 1],[-244869, -74033, -31808, -26642, -11061, -5465, -2191, -85, -5251, -47476, -38351, -68653; -18850, -5676, -2403, -1986, -818, -396, -190, -36, -453, -3726, -2990, -5316; -971700, -293775, -126210, -105705, -43884, -21680, -8700, -345, -20850, -188415, -152196, -272440],266,21]
%
% END OF LATTICE L267.21
%
%
% LATTICE L267.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[111150, 14850, -152550; 14850, -4695, 28065; -152550, 28065, -142034],[450, 15, 1],[716, 121, -1434, -15925, -3066, -15574, -17496, -20257, -3600, -4211, -290, 472; 12875, 2176, -25786, -286364, -55133, -280053, -314615, -364264, -64736, -75724, -5215, 8487; 1775, 300, -3555, -39480, -7601, -38610, -43375, -50220, -8925, -10440, -719, 1170],266,22]
%
% END OF LATTICE L267.22
%
%
% LATTICE L267.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3805800, -21000, -375600; -21000, 90, -2145; -375600, -2145, -37043],[600, 15, 1],[22477, 9023, 950, 3009, 887, 317, -317, -159, 158, 5855, 3545, 6331; -78630, -31564, -3323, -10524, -3102, -1108, 1110, 556, -553, -20484, -12402, -22148; -223350, -89660, -9440, -29900, -8814, -3150, 3150, 1580, -1570, -58180, -35226, -62910],266,23]
%
% END OF LATTICE L267.23
%
%
% LATTICE L267.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1225800, 643800, -147600; 643800, -336165, 77190; -147600, 77190, -17717],[600, 15, 1],[6186, 4957, 518, 1623, 237, 80, -96, -85, 91, 3249, 981, 1747; -32585, -26112, -2729, -8552, -1249, -422, 505, 448, -479, -17112, -5167, -9202; -193500, -155060, -16205, -50780, -7416, -2505, 3000, 2660, -2845, -101620, -30684, -54645],266,24]
%
% END OF LATTICE L267.24
%
%
% LATTICE L267.25
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-150300, -33300, 5400; -33300, -7365, 1200; 5400, 1200, -193],[900, 15, 1],[-178, -225, -28, -107, -12, -22, -2, 9, 1, -109, -24, -140; 535, 674, 83, 314, 35, 63, 5, -26, -2, 334, 73, 423; -1675, -2130, -270, -1050, -119, -225, -25, 90, 15, -990, -221, -1305],266,25]
%
% END OF LATTICE L267.25
%
%
% LATTICE L267.26
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[222300, 29700, 225900; 29700, -9390, -41595; 225900, -41595, -156112],[900, 15, 1],[25879, 29963, 5325, 6229, 429, -698, -1059, -179, 2121, 23555, 4535, 23036; 466135, 539696, 95914, 112196, 7727, -12573, -19075, -3224, 38204, 424276, 81685, 414927; -86750, -100440, -17850, -20880, -1438, 2340, 3550, 600, -7110, -78960, -15202, -77220],266,26]
%
% END OF LATTICE L267.26
%
%
% LATTICE L267.27
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[6399450, -224550, 3184650; -224550, 6540, -111750; 3184650, -111750, 1584823],[450, 30, 1],[-15679, 112, 2210, -15134, -21431, -14803, -178741, -38996, -21652, -23750, -17453, -4639; -90, 1, 13, -89, -126, -87, -1050, -229, -127, -139, -102, -27; 31500, -225, -4440, 30405, 43056, 29740, 359100, 78345, 43500, 47715, 35064, 9320],266,27]
%
% END OF LATTICE L267.27
%
%
% LATTICE L267.28
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[415831950, -1040570550, 203134050; -1040570550, 2603905440, -508319070; 203134050, -508319070, 99231053],[450, 30, 1],[-1173, 215, -5496, -53801, -21841, -117907, -140807, -85403, -37098, -31387, -6555, -9875; -10, 1, -47, -449, -182, -981, -1170, -709, -307, -259, -54, -81; 2350, -435, 11010, 107835, 43778, 236340, 282250, 171195, 74370, 62925, 13142, 19800],266,28]
%
% END OF LATTICE L267.28
%
%
% LATTICE L267.29
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[55220100, -9887400, -14271300; -9887400, 1770420, 2555340; -14271300, 2555340, 3688331],[300, 60, 1],[-91141, -18301, -3876, -6385, -3929, -1857, -679, -63, -715, -11979, -14435, -25689; 13635, 2739, 581, 959, 591, 281, 105, 9, 106, 1789, 2157, 3841; -362100, -72710, -15400, -25370, -15612, -7380, -2700, -250, -2840, -47590, -57348, -102060],266,29]
%
% END OF LATTICE L267.29
%
%
% LATTICE L267.30
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2774400, -361500, -692700; -361500, 45720, 90300; -692700, 90300, 172949],[300, 60, 1],[-60038, -6558, -3655, -4024, -5926, -4748, -5402, 14, 383, -2520, -7162, -14884; -7215, -788, -439, -483, -711, -569, -645, 2, 46, -303, -861, -1789; -236700, -25855, -14410, -15865, -23364, -18720, -21300, 55, 1510, -9935, -28236, -58680],266,30]
%
% END OF LATTICE L267.30
%
%
% LATTICE L267.31
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-15256200, -3000600, -590400; -3000600, -590160, -116120; -590400, -116120, -22847],[600, 40, 1],[63, 13, -140, -911, -357, -617, -2123, -1249, -478, -325, -55, -1; -340, -72, 759, 4968, 1948, 3369, 11600, 6828, 2619, 1788, 304, 9; 100, 30, -240, -1710, -676, -1180, -4100, -2430, -960, -690, -124, -20],266,31]
%
% END OF LATTICE L267.31
%
%
% LATTICE L267.32
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-181774200, -93610200, 1809000; -93610200, -48207440, 931600; 1809000, 931600, -18003],[600, 40, 1],[13, 1, -26, -143, -55, -93, -313, -181, -64, -37, -5, 3; 25, -6, -33, -36, -7, 2, 55, 54, 57, 84, 23, 22; 2600, -210, -4320, -16230, -5888, -9240, -28600, -15390, -3480, 630, 688, 1440],266,32]
%
% END OF LATTICE L267.32
%
%
% LATTICE L267.33
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-300600, 127800, 9000; 127800, -54330, -3825; 9000, -3825, -269],[1800, 15, 1],[-7, -5, 8, 237, 47, 247, 287, 341, 34, 99, 9, 5; -20, -16, 23, 704, 140, 738, 860, 1024, 103, 304, 28, 18; 50, 60, -60, -2100, -422, -2250, -2650, -3180, -330, -1020, -98, -90],266,33]
%
% END OF LATTICE L267.33
%
%
% LATTICE L267.34
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-46416600, 102600, -8627400; 102600, -195, 19260; -8627400, 19260, -1602431],[1800, 15, 1],[214, 215, -642, -18203, -1799, -9424, -10924, -25919, -2571, -7501, -343, -215; 6420, 6452, -19261, -546148, -53976, -282753, -327760, -777668, -77141, -225068, -10292, -6453; -1075, -1080, 3225, 91440, 9037, 47340, 54875, 130200, 12915, 37680, 1723, 1080],266,34]
%
% END OF LATTICE L267.34
%
%
% LATTICE L267.35
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[405379800, 9497700, 100984500; 9497700, 222540, 2365980; 100984500, 2365980, 25156333],[900, 60, 1],[163859, 32869, 6934, 11365, 6967, 1081, 1121, 127, 1315, 21631, 26029, 15417; 1320, 262, 53, 82, 48, 6, 0, 2, 13, 182, 216, 126; -657900, -131970, -27840, -45630, -27972, -4340, -4500, -510, -5280, -86850, -104508, -61900],266,35]
%
% END OF LATTICE L267.35
%
%
% LATTICE L267.36
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[10730700, 327600, 2663100; 327600, 10140, 81300; 2663100, 81300, 660917],[900, 60, 1],[22581, 13571, 2850, 4663, 953, 1343, 199, 97, 567, 9005, 3603, 19159; -1525, -917, -193, -317, -65, -93, -15, -7, -38, -607, -243, -1293; -90800, -54570, -11460, -18750, -3832, -5400, -800, -390, -2280, -36210, -14488, -77040],266,36]
%
% END OF LATTICE L267.36
%
%
% LATTICE L267.37
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[25597800, -1217700, 6369300; -1217700, 50640, -303000; 6369300, -303000, 1584823],[900, 60, 1],[-413941, -45146, -25050, -27443, -40301, -10687, -35839, 168, 2561, -17535, -49655, -34291; -2100, -229, -127, -139, -204, -54, -180, 1, 13, -89, -252, -174; 1663200, 181395, 100650, 110265, 161928, 42940, 144000, -675, -10290, 70455, 199512, 137780],266,37]
%
% END OF LATTICE L267.37
%
%
% LATTICE L267.38
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[214262407800, 34994934900, 53457055200; 34994934900, 5715633840, 8731005060; 53457055200, 8731005060, 13337182103],[900, 60, 1],[31993, 9251, 3321, 2284, 825, 745, 627, 535, 1572, 7502, 5699, 28613; -2340, -709, -307, -259, -108, -162, -20, 1, -47, -449, -364, -1962; -126700, -36615, -13110, -8985, -3236, -2880, -2500, -2145, -6270, -29775, -22604, -113400],266,38]
%
% END OF LATTICE L267.38
%
%
% LATTICE L267.39
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[6600, 36000, 22200; 36000, 195720, 120720; 22200, 120720, 74459],[600, 120, 1],[-54, 10, -31, -486, -606, -1117, -4086, -838, -383, -342, -222, -125; -175, 29, -93, -1471, -1835, -3384, -12385, -2541, -1163, -1041, -677, -384; 300, -50, 160, 2530, 3156, 5820, 21300, 4370, 2000, 1790, 1164, 660],266,39]
%
% END OF LATTICE L267.39
%
%
% LATTICE L267.40
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[55001400, -60295200, 463800; -60295200, 66098520, -508440; 463800, -508440, 3911],[600, 120, 1],[43, 0, 7, 142, 179, 334, 1237, 256, 121, 114, 77, 50; 30, -1, 7, 129, 162, 301, 1110, 229, 107, 99, 66, 41; -1200, -130, 80, -70, -168, -480, -2400, -590, -440, -650, -552, -600],266,40]
%
% END OF LATTICE L267.40
%
%
% LATTICE L267.41
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[68074200, -91800, -66600; -91800, 240, 120; -66600, 120, 73],[1800, 120, 1],[-13, -1, 0, -13, -17, -11, -127, -27, -14, -15, -11, -3; 5370, 412, 1, 5392, 7050, 4561, 52650, 11192, 5801, 6212, 4554, 1241; -20700, -1590, 0, -20730, -27108, -17540, -202500, -43050, -22320, -23910, -17532, -4780],266,41]
%
% END OF LATTICE L267.41
%
%
% LATTICE L267.42
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[975004200, 249726600, -2721600; 249726600, 63962160, -697080; -2721600, -697080, 7597],[1800, 120, 1],[-13, -1, 0, -13, -17, -11, -127, -27, -14, -15, -11, -3; 90, -1, 17, 329, 414, 257, 2850, 589, 277, 259, 174, 37; 3600, -450, 1560, 25530, 31896, 19640, 216000, 44370, 20400, 18390, 12024, 2320],266,42]
%
% END OF LATTICE L267.42
%
%
% LATTICE L267.43
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-52273800, -5086800, -46405800; -5086800, -494760, -4512600; -46405800, -4512600, -41154367],[1800, 120, 1],[1486, 12, -2747, -13216, -4994, -24793, -27186, -15432, -4963, -2204, -146, 1663; -49025, -397, 90629, 436043, 164771, 818022, 896985, 509173, 163759, 72733, 4821, -54858; 3700, 30, -6840, -32910, -12436, -61740, -67700, -38430, -12360, -5490, -364, 4140],266,43]
%
% END OF LATTICE L267.43
%
%
% LATTICE L267.44
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-186497269200, 32672892600, -72606600; 32672892600, -5724040440, 12720120; -72606600, 12720120, -28267],[1800, 120, 1],[43, 0, -79, -374, -141, -698, -763, -432, -137, -58, -3, 50; 245, -1, -448, -2101, -791, -3909, -4265, -2411, -758, -311, -13, 291; -200, -450, 1320, 15210, 6224, 33840, 40600, 24690, 10800, 9030, 1856, 2520],266,44]
%
% END OF LATTICE L267.44
%

\medskip%
%------------------------------WEYL-GROUP-W268--------------------------------
%
\leavevmode\llap{}%
$W_{268}$%
\qquad\llap{44} lattices, $\chi=36$%
\hfill%
$\infty222|222\infty|\rtimes D_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L268.1
%
\leavevmode%
${L_{268.1}}$%
{} : {$1\above{1pt}{1pt}{2}{{\rm II}}4\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{-}{}9\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{1}{}5\above{1pt}{1pt}{-}{}25\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{23,3,2}%
\EasyButWeakLineBreak%
{${60}\above{1pt}{1pt}{15,8}{\infty}{60}\above{1pt}{1pt}{*}{2}{900}\above{1pt}{1pt}{b}{2}{6}\above{1pt}{1pt}{s}{2}{90}\above{1pt}{1pt}{s}{2}{150}\above{1pt}{1pt}{b}{2}{36}\above{1pt}{1pt}{*}{2}{60}\above{1pt}{1pt}{15,4}{\infty b}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-188100\\6300\\0
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
6300\\-210\\-15
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\-15\\224
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\28\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-15\\-448\\-30
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-30\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
6\\179\\12
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
46\\1371\\90
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
156\\4645\\300
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
151\\4494\\288
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
111\\3302\\210
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-188100, 6300, 0; 6300, -210, -15; 0, -15, 224],[900, 15, 1],[1, -15, -1, 6, 46, 156, 151, 111; 28, -448, -30, 179, 1371, 4645, 4494, 3302; 0, -30, 0, 12, 90, 300, 288, 210],267,1]
%
% END OF LATTICE L268.1
%
\hbox{}\par\smallskip%
%
% LATTICE L268.2
%
\leavevmode%
${L_{268.2}}$%
{} : {$1\above{1pt}{1pt}{2}{6}8\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{1}{}3\above{1pt}{1pt}{1}{}9\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-}{}5\above{1pt}{1pt}{1}{}25\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{3m,3,2}%
\EasyButWeakLineBreak%
{${120}\above{1pt}{1pt}{60,53}{\infty z}{30}\above{1pt}{1pt}{l}{2}{1800}\above{1pt}{1pt}{}{2}{3}\above{1pt}{1pt}{r}{2}{180}\above{1pt}{1pt}{l}{2}{75}\above{1pt}{1pt}{}{2}{72}\above{1pt}{1pt}{r}{2}{30}\above{1pt}{1pt}{60,49}{\infty a}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
28529065800\\-37254600\\-18932400
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-37254600\\48630\\24705
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-18932400\\24705\\12547
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-29\\-47912\\50580
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
14\\23131\\-24420
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\1680\\-1800
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-7\\-11564\\12207
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-127\\-209814\\221490
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-248\\-409720\\432525
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-511\\-844224\\891216
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-199\\-328769\\347070
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[28529065800, -37254600, -18932400; -37254600, 48630, 24705; -18932400, 24705, 12547],[1800, 15, 1],[-29, 14, 1, -7, -127, -248, -511, -199; -47912, 23131, 1680, -11564, -209814, -409720, -844224, -328769; 50580, -24420, -1800, 12207, 221490, 432525, 891216, 347070],267,2]
%
% END OF LATTICE L268.2
%
\hbox{}\par\smallskip%
%
% LATTICE L268.3
%
\leavevmode%
${L_{268.3}}$%
{} : {$1\above{1pt}{1pt}{-2}{6}8\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{1}{}3\above{1pt}{1pt}{1}{}9\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-}{}5\above{1pt}{1pt}{1}{}25\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{32,3,m}%
\EasyButWeakLineBreak%
{${120}\above{1pt}{1pt}{60,23}{\infty z}{30}\above{1pt}{1pt}{b}{2}{1800}\above{1pt}{1pt}{*}{2}{12}\above{1pt}{1pt}{l}{2}{45}\above{1pt}{1pt}{r}{2}{300}\above{1pt}{1pt}{*}{2}{72}\above{1pt}{1pt}{b}{2}{30}\above{1pt}{1pt}{60,49}{\infty b}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
719389800\\-5914800\\-3114000
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-5914800\\48630\\25605
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3114000\\25605\\13477
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
31\\2728\\1980
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-16\\-1409\\-1020
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-29\\-2580\\-1800
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
13\\1142\\834
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
64\\5628\\4095
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
509\\44770\\32550
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
527\\46356\\33696
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
206\\18121\\13170
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[719389800, -5914800, -3114000; -5914800, 48630, 25605; -3114000, 25605, 13477],[1800, 15, 1],[31, -16, -29, 13, 64, 509, 527, 206; 2728, -1409, -2580, 1142, 5628, 44770, 46356, 18121; 1980, -1020, -1800, 834, 4095, 32550, 33696, 13170],267,3]
%
% END OF LATTICE L268.3
%
%
% LATTICE L268.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-1650, 75, -675; 75, 15, 80; -675, 80, -144],[75, 5, 1],[-40, 16, 13, -13, -59, -803, -145, -353; -201, 81, 65, -66, -298, -4050, -731, -1779; 75, -30, -25, 24, 110, 1500, 271, 660],267,4]
%
% END OF LATTICE L268.4
%
%
% LATTICE L268.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-1162050, -130500, 61500; -130500, -14655, 6905; 61500, 6905, -3248],[150, 5, 1],[-131, 47, 43, -19, -91, -1259, -457, -1117; 1308, -468, -430, 189, 907, 12555, 4558, 11142; 300, -105, -100, 42, 205, 2850, 1036, 2535],267,5]
%
% END OF LATTICE L268.5
%
%
% LATTICE L268.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-516900, -168600, 29100; -168600, -54990, 9485; 29100, 9485, -1624],[300, 5, 1],[-385, 133, 129, -53, -261, -3637, -1323, -3239; 1284, -444, -430, 177, 871, 12135, 4414, 10806; 600, -210, -200, 84, 410, 5700, 2072, 5070],267,6]
%
% END OF LATTICE L268.6
%
%
% LATTICE L268.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-6463227900, 29262300, -86100; 29262300, -132485, 390; -86100, 390, -1],[300, 5, 1],[-31, 14, 1, -14, -43, -508, -175, -205; -6822, 3081, 220, -3081, -9463, -111795, -38512, -45114; 8490, -3810, -300, 3807, 11715, 138525, 47736, 55935],267,7]
%
% END OF LATTICE L268.7
%
%
% LATTICE L268.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-12926455800, 58524600, 29176200; 58524600, -264970, -132095; 29176200, -132095, -65853],[600, 5, 1],[-31, 14, 1, -7, -43, -254, -175, -205; -15312, 6891, 520, -3444, -21178, -125160, -86248, -101049; 16980, -7620, -600, 3807, 23430, 138525, 95472, 111870],267,8]
%
% END OF LATTICE L268.8
%
%
% LATTICE L268.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-474595800, 11214000, 6026400; 11214000, -264970, -142395; 6026400, -142395, -76523],[600, 5, 1],[89, -16, -29, 13, 31, 857, 311, 380; 768, -129, -260, 102, 256, 7170, 2612, 3201; 5580, -1020, -1800, 834, 1965, 54150, 19632, 23970],267,9]
%
% END OF LATTICE L268.9
%
%
% LATTICE L268.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[225, 0, 0; 0, -210, -15; 0, -15, -1],[225, 15, 1],[1, 0, -1, 0, 2, 12, 7, 6; -1, 1, 0, -1, -9, -35, -18, -14; 0, -15, 0, 12, 90, 300, 144, 105],267,10]
%
% END OF LATTICE L268.10
%
%
% LATTICE L268.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[450, 0, 0; 0, -105, -15; 0, -15, -2],[450, 15, 1],[1, 0, -1, 0, 1, 6, 7, 6; -2, 2, 0, -1, -9, -35, -36, -28; 0, -15, 0, 6, 45, 150, 144, 105],267,11]
%
% END OF LATTICE L268.11
%
%
% LATTICE L268.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[353538900, 173783700, 5816700; 173783700, 85424190, 2859225; 5816700, 2859225, 95699],[900, 15, 1],[811, -420, -811, 336, 3331, 13266, 13741, 5373; -1682, 871, 1680, -697, -6909, -27515, -28500, -11144; 960, -495, -900, 402, 3960, 15750, 16308, 6375],267,12]
%
% END OF LATTICE L268.12
%
%
% LATTICE L268.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1020825, 210975, 335025; 210975, 43605, 69240; 335025, 69240, 109952],[75, 15, 1],[-72, 8, -121, -45, -385, -1603, -851, -681; -1, 1, -10, -3, -19, -65, -32, -24; 220, -25, 375, 139, 1185, 4925, 2613, 2090],267,13]
%
% END OF LATTICE L268.13
%
%
% LATTICE L268.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[21683850, -3381750, 10765200; -3381750, 527440, -1678910; 10765200, -1678910, 5344509],[150, 10, 1],[3391, -74, 702, 1129, 4167, 57923, 10596, 52204; -174, 3, -35, -57, -212, -2955, -541, -2667; -6885, 150, -1425, -2292, -8460, -117600, -21513, -105990],267,14]
%
% END OF LATTICE L268.14
%
%
% LATTICE L268.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[22035150, -4175250, -7408200; -4175250, 791160, 1403715; -7408200, 1403715, 2490631],[150, 15, 1],[-1471, 17, -921, -246, -2718, -12584, -13809, -11337; -116, 1, -70, -19, -212, -985, -1082, -889; -4310, 50, -2700, -721, -7965, -36875, -40464, -33220],267,15]
%
% END OF LATTICE L268.15
%
%
% LATTICE L268.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-243225, 7875, -47250; 7875, -210, 1530; -47250, 1530, -9179],[225, 15, 1],[-102, 35, 34, -28, -138, -1924, -350, -857; -1, 1, 0, -1, -3, -35, -6, -14; 525, -180, -175, 144, 710, 9900, 1801, 4410],267,16]
%
% END OF LATTICE L268.16
%
%
% LATTICE L268.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-310807200, 5228250, -148877100; 5228250, -87930, 2504340; -148877100, 2504340, -71312347],[150, 30, 1],[2722, -1933, -2698, 778, 11267, 52066, 28366, 46243; 218, -156, -215, 63, 907, 4185, 2279, 3714; -5675, 4030, 5625, -1622, -23490, -108550, -59139, -96410],267,17]
%
% END OF LATTICE L268.17
%
%
% LATTICE L268.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-62700, 54300, -9600; 54300, -46980, 8295; -9600, 8295, -1462],[300, 15, 1],[-27, 23, 29, -9, -95, -389, -407, -321; -56, 46, 60, -18, -192, -790, -828, -654; -140, 110, 150, -43, -465, -1925, -2022, -1600],267,18]
%
% END OF LATTICE L268.18
%
%
% LATTICE L268.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[29028300, 11506200, 2401800; 11506200, 4560705, 952005; 2401800, 952005, 198722],[300, 15, 1],[-69, 35, 49, -30, -289, -1144, -1183, -462; -592, 301, 440, -256, -2474, -9800, -10136, -3959; 3670, -1865, -2700, 1589, 15345, 60775, 62856, 24550],267,19]
%
% END OF LATTICE L268.19
%
%
% LATTICE L268.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[307746600, -12291900, -77225700; -12291900, 490960, 3084520; -77225700, 3084520, 19378959],[300, 20, 1],[-797, -38, -191, -403, -1709, -24869, -4609, -11465; -258, -9, -70, -138, -568, -8190, -1514, -3759; -3135, -150, -750, -1584, -6720, -97800, -18126, -45090],267,20]
%
% END OF LATTICE L268.20
%
%
% LATTICE L268.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[22439705100, 1192117800, -5683641900; 1192117800, 63332140, -301945620; -5683641900, -301945620, 1439581541],[300, 20, 1],[210953, -836, 19513, 66275, 251651, 3532249, 323990, 1599601; -753, 3, -70, -237, -899, -12615, -1157, -5712; 832710, -3300, 77025, 261612, 993360, 13943100, 1278909, 6314220],267,21]
%
% END OF LATTICE L268.21
%
%
% LATTICE L268.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2551950, 18000, -504000; 18000, -105, 3555; -504000, 3555, -99538],[450, 15, 1],[-237, 80, 79, -32, -159, -2222, -809, -1982; -2, 2, 0, -1, -3, -35, -12, -28; 1200, -405, -400, 162, 805, 11250, 4096, 10035],267,22]
%
% END OF LATTICE L268.22
%
%
% LATTICE L268.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[500088600, 3919800, -1353600; 3919800, 30585, -10590; -1353600, -10590, 3661],[600, 15, 1],[29, 199, 511, 248, 127, 7, -1, -14; 2592, 17789, 45680, 22170, 11354, 626, -80, -1251; 18220, 125035, 321072, 155825, 79800, 4399, -600, -8795],267,23]
%
% END OF LATTICE L268.23
%
%
% LATTICE L268.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[12600, -80400, 6600; -80400, 503610, -41325; 6600, -41325, 3391],[600, 15, 1],[-9, -64, -165, -161, -21, -5, -9, 4; -72, -519, -1340, -1310, -172, -42, -100, 31; -860, -6200, -16008, -15650, -2055, -502, -1200, 370],267,24]
%
% END OF LATTICE L268.24
%
%
% LATTICE L268.25
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[709650, 6750, 353250; 6750, 60, 3360; 353250, 3360, 175841],[450, 30, 1],[-127, 0, 112, -3, -269, -1569, -910, -1554; 7, 1, 0, 1, 18, 95, 54, 91; 255, 0, -225, 6, 540, 3150, 1827, 3120],267,25]
%
% END OF LATTICE L268.25
%
%
% LATTICE L268.26
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1636070850, 254250, 815429250; 254250, 60, 126720; 815429250, 126720, 406415689],[450, 30, 1],[8291, 0, 1408, 2503, 9699, 137037, 25186, 124522; 7, 1, 0, 1, 6, 95, 18, 91; -16635, 0, -2825, -5022, -19460, -274950, -50533, -249840],267,26]
%
% END OF LATTICE L268.26
%
%
% LATTICE L268.27
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-7452900, 42300, 2481300; 42300, -210, -14445; 2481300, -14445, -821744],[900, 15, 1],[963, -325, -321, 130, 646, 9028, 3287, 8053; 28888, -9748, -9630, 3899, 19377, 270805, 98598, 241562; 2400, -810, -800, 324, 1610, 22500, 8192, 20070],267,27]
%
% END OF LATTICE L268.27
%
%
% LATTICE L268.28
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-4330179900, -2188110600, 479245500; -2188110600, -1105688010, 242170575; 479245500, 242170575, -53040809],[900, 15, 1],[-3471, 922, 809, -842, -3175, -40832, -14487, -17389; 7802, -2071, -1820, 1891, 7133, 91745, 32552, 39074; 4260, -1125, -1000, 1026, 3880, 49950, 17728, 21285],267,28]
%
% END OF LATTICE L268.28
%
%
% LATTICE L268.29
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[421200, -201900, -113400; -201900, 98520, 54420; -113400, 54420, 30533],[300, 60, 1],[-407, -63, -38, -120, -2102, -11064, -6286, -5295; 58, 9, 5, 17, 299, 1575, 895, 754; -1615, -250, -150, -476, -8340, -43900, -24942, -21010],267,29]
%
% END OF LATTICE L268.29
%
%
% LATTICE L268.30
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[18062003700, 542288100, -4571503200; 542288100, 16281480, -137253420; -4571503200, -137253420, 1157050007],[300, 60, 1],[-2876, -101, 21381, 8058, 34740, 87166, 18339, 23337; -227, -8, 1675, 631, 2717, 6805, 1430, 1817; -11390, -400, 84675, 31912, 137580, 345200, 72627, 92420],267,30]
%
% END OF LATTICE L268.30
%
%
% LATTICE L268.31
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-33180600, 5841600, -828600; 5841600, -1028440, 145880; -828600, 145880, -20691],[600, 40, 1],[-208, 53, 73, -19, -188, -2993, -565, -2845; -1041, 267, 365, -96, -943, -15000, -2831, -14253; 990, -240, -350, 84, 880, 14100, 2666, 13440],267,31]
%
% END OF LATTICE L268.31
%
%
% LATTICE L268.32
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-125639400, 20883600, -8622600; 20883600, -3471240, 1433240; -8622600, 1433240, -591759],[600, 40, 1],[-1159, 197, 193, -79, -970, -15881, -1510, -15289; -5796, 987, 965, -396, -4853, -79440, -7553, -76473; 2850, -480, -475, 192, 2380, 39000, 3709, 37560],267,32]
%
% END OF LATTICE L268.32
%
%
% LATTICE L268.33
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-8660359800, -2188110600, 958491000; -2188110600, -552844005, 242170575; 958491000, 242170575, -106081618],[1800, 15, 1],[-3471, 922, 809, -421, -3175, -20416, -14487, -17389; 15604, -4142, -3640, 1891, 14266, 91745, 65104, 78148; 4260, -1125, -1000, 513, 3880, 24975, 17728, 21285],267,33]
%
% END OF LATTICE L268.33
%
%
% LATTICE L268.34
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-725923800, -46152000, 6456600; -46152000, -2934195, 410490; 6456600, 410490, -57427],[1800, 15, 1],[9, 4, -9, -5, -4, -53, -13, -10; 488, 191, -460, -242, -184, -2230, -500, -319; 4500, 1815, -4300, -2292, -1765, -21900, -5036, -3405],267,34]
%
% END OF LATTICE L268.34
%
%
% LATTICE L268.35
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2838600, 2823300, 712800; 2823300, 2808960, 708960; 712800, 708960, 178991],[900, 60, 1],[833, 112, -113, 221, 4213, 22411, 12761, 10765; 7, 1, 0, 2, 36, 190, 108, 91; -3345, -450, 450, -888, -16920, -90000, -51246, -43230],267,35]
%
% END OF LATTICE L268.35
%
%
% LATTICE L268.36
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1230683400, 1632278700, 309931200; 1632278700, 2164922160, 411067620; 309931200, 411067620, 78052039],[900, 60, 1],[-1033, 112, -617, -873, -2907, -38783, -7007, -17097; 7, 1, 0, 2, 12, 190, 36, 91; 4065, -450, 2450, 3456, 11480, 153000, 27634, 67410],267,36]
%
% END OF LATTICE L268.36
%
%
% LATTICE L268.37
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[18864660600, -924567300, 4724926200; -924567300, 45313260, -231571200; 4724926200, -231571200, 1183425881],[900, 60, 1],[13735, 478, -102004, -38437, -165671, -415559, -87413, -111209; -1696, -59, 12600, 4748, 20466, 51340, 10800, 13741; -55170, -1920, 409725, 154392, 665460, 1669200, 351117, 446700],267,37]
%
% END OF LATTICE L268.37
%
%
% LATTICE L268.38
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[345112943400, -9898605900, 86188522500; -9898605900, 283914060, -2472078300; 86188522500, -2472078300, 21524725609],[900, 60, 1],[-94111, 372, -8736, -29603, -112327, -1576353, -144581, -713797; 22936, -91, 2130, 7216, 27378, 384200, 35238, 173969; 379470, -1500, 35225, 119364, 452920, 6356100, 582973, 2878140],267,38]
%
% END OF LATTICE L268.38
%
%
% LATTICE L268.39
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-172200, 4800, -8400; 4800, 1080, 6720; -8400, 6720, 34247],[600, 120, 1],[-85, -1621, -1007, -1878, -427, -34, 89, 87; -2298, -43819, -27221, -50765, -11542, -919, 2405, 2351; 430, 8200, 5094, 9500, 2160, 172, -450, -440],267,39]
%
% END OF LATTICE L268.39
%
%
% LATTICE L268.40
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-10138800, 78033000, -1949400; 78033000, -600517080, 15001920; -1949400, 15001920, -374773],[600, 120, 1],[-188, -2921, -886, -3206, -661, -38, 94, 95; -951, -14788, -4486, -16235, -3349, -193, 475, 482; -37090, -576760, -174963, -633200, -130620, -7528, 18525, 18800],267,40]
%
% END OF LATTICE L268.40
%
%
% LATTICE L268.41
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-579600, -52200, 271800; -52200, -4440, 24480; 271800, 24480, -127459],[1800, 120, 1],[183, -169, -211, 62, 845, 3802, 2053, 3323; -1, 2, 0, -1, -9, -35, -18, -28; 390, -360, -450, 132, 1800, 8100, 4374, 7080],267,41]
%
% END OF LATTICE L268.41
%
%
% LATTICE L268.42
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-61448400, 243000, -4066200; 243000, -840, 16080; -4066200, 16080, -269071],[1800, 120, 1],[-268, 135, 134, -54, -941, -4566, -1262, -4161; -1, 2, 0, -1, -9, -35, -9, -28; 4050, -2040, -2025, 816, 14220, 69000, 19071, 62880],267,42]
%
% END OF LATTICE L268.42
%
%
% LATTICE L268.43
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-4280400, -671400, 1724400; -671400, -105240, 270480; 1724400, 270480, -694691],[1800, 120, 1],[399, -97, -141, 34, 355, 5686, 1075, 5419; -1, 2, 0, -1, -3, -35, -6, -28; 990, -240, -350, 84, 880, 14100, 2666, 13440],267,43]
%
% END OF LATTICE L268.43
%
%
% LATTICE L268.44
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-165243600, 387000, -32895000; 387000, -840, 77040; -32895000, 77040, -6548399],[1800, 120, 1],[-1284, 215, 214, -86, -1071, -17558, -1670, -16913; -1, 2, 0, -1, -3, -35, -3, -28; 6450, -1080, -1075, 432, 5380, 88200, 8389, 84960],267,44]
%
% END OF LATTICE L268.44
%

\medskip%
%------------------------------WEYL-GROUP-W269--------------------------------
%
\leavevmode\llap{}%
$W_{269}$%
\qquad\llap{6} lattices, $\chi=6$%
\hfill%
$2|22\slashtwo2\rtimes D_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L269.1
%
\leavevmode%
${L_{269.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{-}{}5\above{1pt}{1pt}{-}{}25\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${12}\above{1pt}{1pt}{r}{2}{10}\above{1pt}{1pt}{l}{2}{300}\above{1pt}{1pt}{r}{2}{2}\above{1pt}{1pt}{b}{2}{50}\above{1pt}{1pt}{l}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-107700\\-40200\\5700
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-40200\\-14990\\2135
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5700\\2135\\-298
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
23\\-48\\96
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
14\\-29\\60
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-431\\900\\-1800
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-24\\50\\-101
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-29\\60\\-125
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-107700, -40200, 5700; -40200, -14990, 2135; 5700, 2135, -298],[300, 5, 1],[23, 14, -431, -24, -29; -48, -29, 900, 50, 60; 96, 60, -1800, -101, -125],268,1]
%
% END OF LATTICE L269.1
%
%
% LATTICE L269.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-482550, 2475, 9750; 2475, -10, -50; 9750, -50, -197],[75, 5, 1],[-2, -1, 44, 4, 2; 0, 2, 0, -1, -5; -99, -50, 2175, 198, 100],268,2]
%
% END OF LATTICE L269.2
%
%
% LATTICE L269.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[5736975, 3525, 1830900; 3525, 30, 1125; 1830900, 1125, 584314],[75, 15, 1],[15, 0, 2593, 652, 742; 0, 1, 10, 2, 0; -47, 0, -8125, -2043, -2325],268,3]
%
% END OF LATTICE L269.3
%
%
% LATTICE L269.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[380100, 153600, 3600; 153600, 62070, 1455; 3600, 1455, 34],[300, 15, 1],[-5, -5, 9, 3, -2; 12, 12, -20, -7, 5; 16, 15, -100, -18, 0],268,4]
%
% END OF LATTICE L269.4
%
%
% LATTICE L269.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[64200, 39900, -20100; 39900, 26360, -12640; -20100, -12640, 6307],[300, 20, 1],[-16, 5, -1049, -180, -254; -6, 2, -390, -67, -95; -63, 20, -4125, -708, -1000],268,5]
%
% END OF LATTICE L269.5
%
%
% LATTICE L269.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2736600, -147900, -689100; -147900, 7320, 37260; -689100, 37260, 173521],[300, 60, 1],[20, -866, -728, 79, 2051; 2, -89, -75, 8, 210; 79, -3420, -2875, 312, 8100],268,6]
%
% END OF LATTICE L269.6
%

\medskip%
%------------------------------WEYL-GROUP-W270--------------------------------
%
\leavevmode\llap{}%
$W_{270}$%
\qquad\llap{24} lattices, $\chi=24$%
\hfill%
$22222222\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L270.1
%
\leavevmode%
${L_{270.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{-}{}9\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{-}{}5\above{1pt}{1pt}{1}{}25\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{23,3,2}%
\EasyButWeakLineBreak%
{${2}\above{1pt}{1pt}{b}{2}{900}\above{1pt}{1pt}{*}{2}{20}\above{1pt}{1pt}{b}{2}{150}\above{1pt}{1pt}{s}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
81900\\5400\\-900
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5400\\330\\-45
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-900\\-45\\2
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1919\\-41280\\-57600
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
92\\-1979\\-2760
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2\\43\\59
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\-43\\-59
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
71\\-1530\\-2250
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5\\-108\\-170
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
6\\-130\\-225
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[81900, 5400, -900; 5400, 330, -45; -900, -45, 2],[900, 15, 1],[2, 71, 5, 6, 0, -11, -1, 4; -43, -1530, -108, -130, 0, 240, 22, -85; -59, -2250, -170, -225, -1, 450, 50, -75],269,1]
%
% END OF LATTICE L270.1
%
%
% LATTICE L270.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[10275, 1950, 450; 1950, 370, 85; 450, 85, 18],[75, 5, 1],[2, 1, -3, -34, -6, -21, -1, 14; -11, -5, 17, 195, 35, 125, 7, -75; 2, 0, -5, -75, -17, -75, -10, 0],269,2]
%
% END OF LATTICE L270.2
%
%
% LATTICE L270.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-2100, 300, 0; 300, 70, -15; 0, -15, 2],[300, 5, 1],[-1, -13, -3, -4, 0, 3, 1, -1; -9, -110, -24, -30, 0, 20, 6, -15; -59, -750, -170, -225, -1, 150, 50, -75],269,3]
%
% END OF LATTICE L270.3
%
%
% LATTICE L270.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[225, 675, -225; 675, 195, -90; -225, -90, 38],[225, 15, 1],[1, 29, 3, 13, 1, 1, -1, -3; 7, 210, 22, 95, 7, 0, -8, -25; 23, 675, 70, 300, 22, 0, -25, -75],269,4]
%
% END OF LATTICE L270.4
%
%
% LATTICE L270.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[14550, 300, -375; 300, -5, -5; -375, -5, 9],[75, 5, 1],[1, 1, 2, 2, 4, 0, -1, -1; 10, 11, 22, 21, 35, -2, -13, -12; 50, 48, 95, 93, 175, -3, -50, -48],269,5]
%
% END OF LATTICE L270.5
%
%
% LATTICE L270.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[715650, -37275, 228375; -37275, 1935, -11895; 228375, -11895, 72878],[75, 15, 1],[359, 46, -19, -50, -884, -151, -86, 15; 0, 1, 3, 2, 30, 5, 3, 0; -1125, -144, 60, 157, 2775, 474, 270, -47],269,6]
%
% END OF LATTICE L270.6
%
%
% LATTICE L270.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[6675, -5325, 2325; -5325, 3510, -1830; 2325, -1830, 809],[75, 15, 1],[-1, -193, -29, 329, 367, 2023, 395, 281; 0, 20, 3, -35, -39, -215, -42, -30; 3, 600, 90, -1025, -1143, -6300, -1230, -875],269,7]
%
% END OF LATTICE L270.7
%
%
% LATTICE L270.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-117300, -48000, 900; -48000, -19630, 365; 900, 365, -6],[300, 5, 1],[-2, -13, -29, -16, -38, -3, 13, 8; 5, 34, 76, 42, 100, 8, -34, -21; 0, 116, 270, 153, 375, 34, -120, -78],269,8]
%
% END OF LATTICE L270.8
%
%
% LATTICE L270.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2744325, -455175, 9225; -455175, -75495, 1530; 9225, 1530, -31],[225, 15, 1],[1, -2, -2, -3, -11, -4, 0, 1; -5, 15, 14, 20, 70, 24, -1, -7; 50, 144, 95, 93, 175, -9, -50, -48],269,9]
%
% END OF LATTICE L270.9
%
%
% LATTICE L270.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[450, -2250, 225; -2250, 10995, -1095; 225, -1095, 109],[225, 15, 1],[1, 1, 7, 3, 29, 1, -1, -1; 0, 1, 6, 1, -15, -2, -9, -2; 0, 8, 45, 3, -225, -23, -90, -18],269,10]
%
% END OF LATTICE L270.10
%
%
% LATTICE L270.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1397025, -231750, 9675; -231750, 38445, -1605; 9675, -1605, 67],[225, 15, 1],[7, 11, 5, 1, -1, -1, 1, 9; 60, 100, 51, 25, -3, -5, 6, 70; 423, 800, 495, 450, 72, 25, 0, 375],269,11]
%
% END OF LATTICE L270.11
%
%
% LATTICE L270.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[231300, 17400, -1800; 17400, 1290, -135; -1800, -135, 14],[300, 15, 1],[-1, -9, -1, 1, 1, 9, 1, -1; -5, -50, -8, 0, 2, 20, 2, -5; -177, -1650, -210, 125, 147, 1350, 150, -175],269,12]
%
% END OF LATTICE L270.12
%
%
% LATTICE L270.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[900, -300, 0; -300, 90, 15; 0, 15, -22],[300, 15, 1],[-31, -7, 1, 1, 1, -5, -13, -3; -95, -22, 2, 3, 5, -14, -38, -9; -75, -18, 0, 2, 0, -12, -30, -7],269,13]
%
% END OF LATTICE L270.13
%
%
% LATTICE L270.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[42361800, -547500, -10689900; -547500, 7080, 138160; -10689900, 138160, 2697571],[300, 20, 1],[-1343, -335, -408, -368, -1242, -182, -109, -149; -430, -108, -133, -123, -425, -63, -38, -48; -5300, -1322, -1610, -1452, -4900, -718, -430, -588],269,14]
%
% END OF LATTICE L270.14
%
%
% LATTICE L270.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[3035400, -29100, -769800; -29100, 280, 7380; -769800, 7380, 195227],[300, 20, 1],[-135, -647, -104, -152, -2, -38, -33, -533; -9, -35, -3, 15, 3, 5, -3, -45; -532, -2550, -410, -600, -8, -150, -130, -2100],269,15]
%
% END OF LATTICE L270.15
%
%
% LATTICE L270.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[9900, 9900, 2700; 9900, 870, 225; 2700, 225, 58],[900, 15, 1],[-1, -3, -1, 1, 1, 3, 1, -1; 207, 630, 222, -185, -195, -590, -198, 205; -756, -2300, -810, 675, 711, 2150, 720, -750],269,16]
%
% END OF LATTICE L270.16
%
%
% LATTICE L270.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-229763700, -9582300, 195300; -9582300, -399630, 8145; 195300, 8145, -166],[900, 15, 1],[16, 13, 1, -1, -1, 5, 5, 4; -380, -312, -26, 23, 25, -114, -116, -94; 175, -18, -100, -48, 50, 288, 190, 93],269,17]
%
% END OF LATTICE L270.17
%
%
% LATTICE L270.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[29990700, 2007900, -53100; 2007900, 134430, -3555; -53100, -3555, 94],[900, 15, 1],[1, -1, -7, -1, -1, 1, 7, 1; -15, 18, 126, 19, 45, -14, -114, -17; 0, 116, 810, 153, 1125, 34, -360, -78],269,18]
%
% END OF LATTICE L270.18
%
%
% LATTICE L270.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[41400, 12900, -10200; 12900, 3960, -3180; -10200, -3180, 2513],[300, 60, 1],[377, 71, 53, 1, -77, -11, 7, 19; -25, -5, -4, 0, 10, 2, 1, -1; 1500, 282, 210, 4, -300, -42, 30, 76],269,19]
%
% END OF LATTICE L270.19
%
%
% LATTICE L270.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[20848200, -92100, -5283300; -92100, 360, 23340; -5283300, 23340, 1338881],[300, 60, 1],[73, 2243, 920, 1546, 368, -38, -479, -811; 3, 55, 21, 35, 9, 5, -9, -15; 288, 8850, 3630, 6100, 1452, -150, -1890, -3200],269,20]
%
% END OF LATTICE L270.20
%
%
% LATTICE L270.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[77131800, 1919700, 19191600; 1919700, 87720, 477540; 19191600, 477540, 4775171],[900, 60, 1],[190422, 94988, 19087, 893, 7143, 23551, 20426, 38620; -2135, -1065, -214, -10, -80, -264, -229, -433; -765100, -381654, -76690, -3588, -28700, -94626, -82070, -155172],269,21]
%
% END OF LATTICE L270.21
%
%
% LATTICE L270.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[207340200, -2663100, 51615000; -2663100, 32280, -662940; 51615000, -662940, 12848971],[900, 60, 1],[31583, 1001, -6115, -8673, -155003, -9229, -18569, 445; -570, -18, 111, 157, 2805, 167, 336, -8; -126900, -4022, 24570, 34848, 622800, 37082, 74610, -1788],269,22]
%
% END OF LATTICE L270.22
%
%
% LATTICE L270.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[38802600, -1293300, 9661500; -1293300, 43080, -322020; 9661500, -322020, 2405627],[900, 60, 1],[3791, 52303, 2566, 2016, -222, 1232, 1003, 15829; -49, -675, -33, -25, 3, -15, -13, -205; -15232, -210150, -10310, -8100, 892, -4950, -4030, -63600],269,23]
%
% END OF LATTICE L270.23
%
%
% LATTICE L270.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1326414600, 24369300, 330121800; 24369300, 447720, 6065100; 330121800, 6065100, 82161643],[900, 60, 1],[421, 211, -247, -449, 161, 759, 829, 1419; 6, 30, 33, 55, 15, 5, -12, -20; -1692, -850, 990, 1800, -648, -3050, -3330, -5700],269,24]
%
% END OF LATTICE L270.24
%

\medskip%
%------------------------------WEYL-GROUP-W271--------------------------------
%
\leavevmode\llap{}%
$W_{271}$%
\qquad\llap{9} lattices, $\chi=12$%
\hfill%
$\slashtwo2|2\slashtwo2|2\rtimes D_{4}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L271.1
%
\leavevmode%
${L_{271.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{1}{}3\above{1pt}{1pt}{1}{}9\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{1}{}5\above{1pt}{1pt}{-}{}25\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{23,3,2}%
\EasyButWeakLineBreak%
{${4}\above{1pt}{1pt}{*}{2}{900}\above{1pt}{1pt}{b}{2}{10}\above{1pt}{1pt}{b}{2}{36}\above{1pt}{1pt}{*}{2}{100}\above{1pt}{1pt}{b}{2}{90}\above{1pt}{1pt}{b}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-522900\\2249100\\-449100
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2249100\\-9335490\\1863315
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-449100\\1863315\\-371906
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
253\\5060\\25046
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3287\\65730\\325350
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\-1\\-5
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-251\\-5022\\-24858
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-249\\-4980\\-24650
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
254\\5082\\25155
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-522900, 2249100, -449100; 2249100, -9335490, 1863315; -449100, 1863315, -371906],[900, 15, 1],[253, 3287, 0, -251, -249, 254; 5060, 65730, -1, -5022, -4980, 5082; 25046, 325350, -5, -24858, -24650, 25155],270,1]
%
% END OF LATTICE L271.1
%
%
% LATTICE L271.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-1725, -450, 375; -450, -110, 75; 375, 75, -11],[75, 5, 1],[-14, -7, -12, -1, 4, 9; 75, 37, 63, 5, -21, -47; 25, 12, 20, 0, -7, -15],270,2]
%
% END OF LATTICE L271.2
%
%
% LATTICE L271.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-6900, 3900, -300; 3900, 790, -115; -300, -115, 14],[300, 5, 1],[-1, -3, -3, 11, 5, 4; -10, -28, -28, 100, 46, 37; -100, -294, -295, 1050, 484, 390],270,3]
%
% END OF LATTICE L271.3
%
%
% LATTICE L271.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[308025, 49950, -2475; 49950, 8085, -405; -2475, -405, 19],[225, 15, 1],[1, 10, 10, 62, 1, -17; -5, -51, -51, -315, -5, 87; 25, 216, 215, 1350, 23, -360],270,4]
%
% END OF LATTICE L271.4
%
%
% LATTICE L271.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[487425, -108900, 160125; -108900, 24330, -35775; 160125, -35775, 52603],[75, 15, 1],[-28, 6, 43, 168, 22, -15; -15, -4, -6, -20, -3, -1; 75, -21, -135, -525, -69, 45],270,5]
%
% END OF LATTICE L271.5
%
%
% LATTICE L271.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[219300, -22800, 19200; -22800, 2370, -1995; 19200, -1995, 1678],[300, 15, 1],[-1, 3, 2, -39, -11, -6; -10, 44, 32, -500, -146, -83; 0, 18, 15, -150, -48, -30],270,6]
%
% END OF LATTICE L271.6
%
%
% LATTICE L271.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[285054600, -1883100, -72254400; -1883100, 12440, 477320; -72254400, 477320, 18314731],[300, 20, 1],[-241, -36, -10, -164, -45, -71; -30, -1, 21, 115, 18, -4; -950, -142, -40, -650, -178, -280],270,7]
%
% END OF LATTICE L271.7
%
%
% LATTICE L271.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[28200, -74100, -7500; -74100, 130920, 19380; -7500, 19380, 1993],[300, 60, 1],[1477, 50, -1030, -5642, -883, 197; -30, -1, 21, 115, 18, -4; 5850, 198, -4080, -22350, -3498, 780],270,8]
%
% END OF LATTICE L271.8
%
%
% LATTICE L271.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2443762103400, -34299468900, 608110927200; -34299468900, 481410840, -8535152340; 608110927200, -8535152340, 151323608491],[900, 60, 1],[3822, 71149, 4681, 2801, 62, 224; 1013, 18975, 1261, 747, -15, 3; -15302, -284850, -18740, -11214, -250, -900],270,9]
%
% END OF LATTICE L271.9
%

\medskip%
%------------------------------WEYL-GROUP-W272--------------------------------
%
\leavevmode\llap{}%
$W_{272}$%
\qquad\llap{44} lattices, $\chi=36$%
\hfill%
$2222222222\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L272.1
%
\leavevmode%
${L_{272.1}}$%
{} : {$1\above{1pt}{1pt}{2}{{\rm II}}4\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{1}{}5\above{1pt}{1pt}{1}{}25\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${300}\above{1pt}{1pt}{*}{2}{4}\above{1pt}{1pt}{b}{2}{30}\above{1pt}{1pt}{s}{2}{50}\above{1pt}{1pt}{b}{2}{20}\above{1pt}{1pt}{*}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
270300\\13800\\-4500
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
13800\\680\\-225
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-4500\\-225\\74
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2069\\64860\\324300
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
129\\4041\\20210
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-39\\-1222\\-6111
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-89\\-2790\\-13950
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-13\\-404\\-2026
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-11\\-336\\-1695
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-11\\-330\\-1675
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3\\-88\\-450
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[270300, 13800, -4500; 13800, 680, -225; -4500, -225, 74],[300, 5, 1],[-89, -13, -11, -11, -3, -1, 1, 2, -4, -9; -2790, -404, -336, -330, -88, -30, 28, 54, -140, -288; -13950, -2026, -1695, -1675, -450, -150, 146, 285, -675, -1430],271,1]
%
% END OF LATTICE L272.1
%
\hbox{}\par\smallskip%
%
% LATTICE L272.2
%
\leavevmode%
${L_{272.2}}$%
{} : {$1\above{1pt}{1pt}{2}{6}8\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-}{}5\above{1pt}{1pt}{-}{}25\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${150}\above{1pt}{1pt}{l}{2}{8}\above{1pt}{1pt}{}{2}{15}\above{1pt}{1pt}{r}{2}{100}\above{1pt}{1pt}{*}{2}{40}\above{1pt}{1pt}{b}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-348600\\1200\\0
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1200\\35\\30
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\30\\23
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-2160\\3600
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\26\\-45
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\15\\-26
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-285\\375
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-288\\376
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-288\\375
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3\\-850\\1100
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-268\\340
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-348600, 1200, 0; 1200, 35, 30; 0, 30, 23],[600, 5, 1],[-1, -1, -1, -3, -1, 1, 1, 1, 3, 1; -285, -288, -288, -850, -268, 375, 312, 297, 880, 292; 375, 376, 375, 1100, 340, -525, -416, -390, -1150, -380],271,2]
%
% END OF LATTICE L272.2
%
\hbox{}\par\smallskip%
%
% LATTICE L272.3
%
\leavevmode%
${L_{272.3}}$%
{} : {$1\above{1pt}{1pt}{-2}{6}8\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-}{}5\above{1pt}{1pt}{-}{}25\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{m}%
\EasyButWeakLineBreak%
{${150}\above{1pt}{1pt}{b}{2}{8}\above{1pt}{1pt}{*}{2}{60}\above{1pt}{1pt}{l}{2}{25}\above{1pt}{1pt}{}{2}{40}\above{1pt}{1pt}{r}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-701400\\-43800\\1200
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-43800\\-2735\\75
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1200\\75\\-2
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2761\\38640\\-234600
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-173\\2421\\-14705
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4\\-56\\339
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\-30\\75
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\-16\\-4
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\-18\\-90
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2\\25\\-300
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-7\\96\\-680
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-701400, -43800, 1200; -43800, -2735, 75; 1200, 75, -2],[600, 5, 1],[2, 1, 1, -2, -7, -32, -9, -7, -3, -1; -30, -16, -18, 25, 96, 450, 128, 102, 45, 16; 75, -4, -90, -300, -680, -2625, -676, -420, -125, 0],271,3]
%
% END OF LATTICE L272.3
%
%
% LATTICE L272.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[75, 0, 0; 0, 5, 0; 0, 0, -1],[75, 5, 1],[1, 0, -1, -7, -4, -31, -4, -5, -3, 0; 0, -1, -6, -20, -9, -60, -7, -6, 0, 1; 0, -2, -15, -75, -40, -300, -38, -45, -25, 0],271,4]
%
% END OF LATTICE L272.4
%
%
% LATTICE L272.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[135150, 2550, -2250; 2550, 35, -40; -2250, -40, 37],[150, 5, 1],[-89, -13, -11, -11, -3, -1, 1, 2, -4, -9; -1395, -202, -168, -165, -44, -15, 14, 27, -70, -144; -6975, -1016, -855, -850, -230, -75, 76, 150, -325, -710],271,5]
%
% END OF LATTICE L272.5
%
%
% LATTICE L272.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[23700, 1500, 0; 1500, 95, 0; 0, 0, -1],[300, 5, 1],[-1, -1, -2, -3, -1, 1, 1, 2, 3, 1; -15, 8, 27, 45, 16, -15, -16, -33, -55, -24; -300, -76, -45, -25, 0, 0, -4, -15, -75, -80],271,6]
%
% END OF LATTICE L272.6
%
%
% LATTICE L272.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1725, -375, 75; -375, -80, 15; 75, 15, -2],[75, 5, 1],[1, 1, -2, -2, -5, -7, -21, -4, 0, 1; -6, -5, 12, 10, 23, 30, 85, 12, -2, -7; -9, 0, 15, -7, -40, -81, -300, -105, -23, -20],271,7]
%
% END OF LATTICE L272.7
%
%
% LATTICE L272.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[5550, -600, 0; -600, 65, 0; 0, 0, -1],[150, 5, 1],[-7, -21, -2, 0, 1, 1, 1, -1, -1, -5; -75, -230, -24, -1, 8, 9, 10, -9, -10, -52; -87, -300, -45, -8, -10, -3, 0, 0, -7, -50],271,8]
%
% END OF LATTICE L272.8
%
%
% LATTICE L272.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1650, 0, -525; 0, 15, 0; -525, 0, -167],[75, 15, 1],[-8, -2, 3, 93, 56, 148, 58, 25, 47, 0; 0, -1, -2, -20, -9, -20, -7, -2, 0, 1; 25, 6, -10, -300, -180, -475, -186, -80, -150, 0],271,9]
%
% END OF LATTICE L272.9
%
%
% LATTICE L272.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[27300, -3375, 8850; -3375, 435, -1095; 8850, -1095, 2869],[75, 15, 1],[15, -48, -8, 250, 910, 531, 5508, 554, 296, 182; -2, 5, 1, -31, -113, -66, -685, -69, -37, -23; -47, 150, 25, -783, -2850, -1663, -17250, -1735, -927, -570],271,10]
%
% END OF LATTICE L272.10
%
%
% LATTICE L272.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[25207050, -322800, 12430950; -322800, 4130, -159190; 12430950, -159190, 6130369],[150, 10, 1],[-51329, -3310, -4127, -2416, 37, 2219, 36, -784, -5769, -3311; 645, 42, 54, 35, 1, -15, 0, 9, 70, 41; 104100, 6713, 8370, 4900, -75, -4500, -73, 1590, 11700, 6715],271,11]
%
% END OF LATTICE L272.11
%
%
% LATTICE L272.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-7350, 1200, -3600; 1200, 370, 600; -3600, 600, -1763],[150, 10, 1],[-3121, -5441, -1673, -304, -190, -77, 111, 74, -229, -876; -135, -235, -72, -13, -8, -3, 5, 3, -10, -38; 6324, 11025, 3390, 616, 385, 156, -225, -150, 464, 1775],271,12]
%
% END OF LATTICE L272.12
%
%
% LATTICE L272.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2100, 0, 300; 0, -5, 15; 300, 15, -2],[300, 5, 1],[1, 1, -2, -1, -3, -1, -1, 2, 1, 3; -21, -20, 42, 20, 56, 15, -20, -48, -22, -64; -9, 0, 15, -7, -80, -81, -600, -105, -23, -40],271,13]
%
% END OF LATTICE L272.13
%
%
% LATTICE L272.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-168900, 900, 600; 900, 20, -5; 600, -5, -2],[300, 5, 1],[1, 1, -1, -1, -5, -7, -21, -2, 0, 1; 18, 20, -18, -20, -104, -150, -460, -48, -2, 16; 252, 250, -255, -257, -1290, -1812, -5450, -525, -3, 250],271,14]
%
% END OF LATTICE L272.14
%
%
% LATTICE L272.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[16354950, -318450, -5565150; -318450, 6195, 108360; -5565150, 108360, 1893671],[150, 15, 1],[11582, 4481, 931, 1634, -51, -502, -49, 177, 3906, 4483; 215, 84, 18, 35, 2, -5, 0, 3, 70, 82; 34025, 13164, 2735, 4800, -150, -1475, -144, 520, 11475, 13170],271,15]
%
% END OF LATTICE L272.15
%
%
% LATTICE L272.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1650, 1800, 600; 1800, 555, -600; 600, -600, -217],[150, 15, 1],[726, 7593, 389, 212, 265, 18, -153, -17, 160, 1223; -45, -470, -24, -13, -16, -1, 10, 1, -10, -76; 2137, 22350, 1145, 624, 780, 53, -450, -50, 471, 3600],271,16]
%
% END OF LATTICE L272.16
%
%
% LATTICE L272.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[7420200, 3000, -19200; 3000, -10, -5; -19200, -5, 49],[600, 5, 1],[-25, -159, -19, -1, 1, 1, -1, -5, -3, -33; -2505, -15940, -1908, -101, 96, 99, -100, -498, -300, -3304; -10062, -64000, -7650, -403, 400, 402, -400, -2010, -1207, -13280],271,17]
%
% END OF LATTICE L272.17
%
%
% LATTICE L272.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[328200, -8400, 0; -8400, 215, 0; 0, 0, -1],[600, 5, 1],[-1, -1, 1, 1, 3, 1, 1, -1, -1, -3; -45, -80, 36, 38, 116, 39, 40, -39, -40, -124; -87, -600, -45, -16, -20, -3, 0, 0, -14, -100],271,18]
%
% END OF LATTICE L272.18
%
%
% LATTICE L272.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1046100, 16500, -4800; 16500, 240, -75; -4800, -75, 22],[300, 15, 1],[-1, 1, 1, 3, -1, -9, -5, -2, -8, -3; -10, 8, 8, 10, -28, -130, -64, -22, -80, -28; -250, 246, 245, 675, -330, -2450, -1326, -515, -2025, -750],271,19]
%
% END OF LATTICE L272.19
%
%
% LATTICE L272.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[46636350, -116400, 22344450; -116400, 210, -55770; 22344450, -55770, 10705693],[150, 30, 1],[-51339, -11216, -6291, -18758, -2537, -551, 838, 1102, -7187, -7841; -465, -101, -56, -165, -22, -5, 7, 9, -70, -72; 107150, 23409, 13130, 39150, 5295, 1150, -1749, -2300, 15000, 16365],271,20]
%
% END OF LATTICE L272.20
%
%
% LATTICE L272.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[201900, 50400, -2100; 50400, 12585, -525; -2100, -525, 22],[300, 15, 1],[-1, -5, -5, -64, -65, -79, -59, -11, -16, 1; 5, 24, 24, 310, 316, 385, 288, 54, 80, -4; 25, 96, 95, 1275, 1320, 1625, 1224, 235, 375, 0],271,21]
%
% END OF LATTICE L272.21
%
%
% LATTICE L272.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2127450, 28800, 1019400; 28800, 390, 13800; 1019400, 13800, 488461],[150, 30, 1],[-499, -2694, -297, -184, -151, -47, -36, 24, -89, -395; -25, -115, -8, -1, 4, 3, 5, -3, -10, -26; 1042, 5625, 620, 384, 315, 98, 75, -50, 186, 825],271,22]
%
% END OF LATTICE L272.22
%
%
% LATTICE L272.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[300, 0, 0; 0, -735, 90; 0, 90, -11],[300, 15, 1],[0, 1, 0, -1, -7, -2, -41, -2, -1, -1; 1, 0, -3, -7, -32, -7, -120, -3, 1, 8; 8, 0, -25, -63, -300, -68, -1200, -35, 3, 60],271,23]
%
% END OF LATTICE L272.23
%
%
% LATTICE L272.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-14700, 1200, -300; 1200, 660, -225; -300, -225, 76],[300, 15, 1],[1, 1, -1, -1, -1, 1, 19, 2, 2, 5; 50, 50, -51, -57, -94, 26, 710, 89, 95, 246; 152, 150, -155, -171, -270, 88, 2250, 275, 291, 750],271,24]
%
% END OF LATTICE L272.24
%
%
% LATTICE L272.25
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[94213200, -1247700, -23876100; -1247700, 16520, 316200; -23876100, 316200, 6050831],[300, 20, 1],[25373, 3272, 4078, 2384, -38, -1103, -36, 776, 5706, 3274; 1335, 173, 219, 135, 1, -45, -1, 39, 295, 171; 100050, 12902, 16080, 9400, -150, -4350, -142, 3060, 22500, 12910],271,25]
%
% END OF LATTICE L272.25
%
%
% LATTICE L272.26
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[300, -6000, 0; -6000, 1580, 1500; 0, 1500, -19],[300, 20, 1],[-11404, -722, -1703, -887, 19, 304, -18, -517, -2813, -759; -585, -37, -87, -45, 1, 15, -1, -27, -145, -39; -45000, -2849, -6720, -3500, 75, 1200, -71, -2040, -11100, -2995],271,26]
%
% END OF LATTICE L272.26
%
%
% LATTICE L272.27
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[389100, -49500, -98100; -49500, 6280, 12480; -98100, 12480, 24733],[300, 20, 1],[-149, 133, 76, -1050, -1894, -6601, -11383, -6826, -1200, -356; -6, 5, 3, -41, -74, -258, -445, -267, -47, -14; -588, 525, 300, -4144, -7475, -26052, -44925, -26940, -4736, -1405],271,27]
%
% END OF LATTICE L272.27
%
%
% LATTICE L272.28
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[60855600, -299700, -15420000; -299700, 1480, 75940; -15420000, 75940, 3907223],[300, 20, 1],[-187, -114, -76, -822, -2876, -4967, -17066, -5078, -896, -560; 0, 5, 3, -3, -13, -24, -85, -27, -5, -3; -738, -450, -300, -3244, -11350, -19602, -67350, -20040, -3536, -2210],271,28]
%
% END OF LATTICE L272.28
%
%
% LATTICE L272.29
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-436200, -23400, 4200; -23400, -870, 165; 4200, 165, -31],[600, 15, 1],[-21, -17, -2, -9, -1, 1, 1, 0, -11, -15; -2655, -2152, -254, -1150, -132, 125, 128, 1, -1380, -1892; -17000, -13776, -1625, -7350, -840, 800, 816, 5, -8850, -12120],271,29]
%
% END OF LATTICE L272.29
%
%
% LATTICE L272.30
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-184200, 11400, -4800; 11400, -705, 300; -4800, 300, -109],[600, 15, 1],[369, 285, 59, 53, 1, -9, 3, 13, 127, 287; 5525, 4268, 884, 795, 16, -135, 44, 194, 1900, 4296; -1075, -828, -170, -150, 0, 25, -12, -40, -375, -840],271,30]
%
% END OF LATTICE L272.30
%
%
% LATTICE L272.31
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1979400, -76800, 6600; -76800, -2805, 255; 6600, 255, -22],[600, 15, 1],[-5, -79, -1, 1, 9, 1, -1, -3, -3, -25; -14, -240, -6, 1, 16, 2, 0, -6, -7, -64; -1673, -26700, -380, 309, 2880, 323, -300, -970, -984, -8280],271,31]
%
% END OF LATTICE L272.31
%
%
% LATTICE L272.32
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[600, 0, 0; 0, -30, -15; 0, -15, -7],[600, 15, 1],[-2, -41, -1, -1, -1, 0, 1, 0, -1, -7; 19, 360, 7, 4, -4, -1, 0, 2, 14, 76; -62, -1200, -25, -18, 0, 2, 0, -5, -42, -240],271,32]
%
% END OF LATTICE L272.32
%
%
% LATTICE L272.33
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[102537600, -730500, -25981800; -730500, 5160, 185100; -25981800, 185100, 6583477],[300, 60, 1],[-1381, -336, 522, 15736, 9434, 24871, 9732, 4176, 7754, -38; -5, -1, 3, 85, 51, 135, 53, 23, 45, 1; -5450, -1326, 2060, 62100, 37230, 98150, 38406, 16480, 30600, -150],271,33]
%
% END OF LATTICE L272.33
%
%
% LATTICE L272.34
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-5117100, 182700, 1293900; 182700, -6360, -46200; 1293900, -46200, -327173],[300, 60, 1],[-583, -92, 142, 6008, 1867, 10013, 1978, 1744, 3422, 19; -40, -6, 11, 425, 131, 700, 138, 121, 235, 1; -2300, -363, 560, 23700, 7365, 39500, 7803, 6880, 13500, 75],271,34]
%
% END OF LATTICE L272.34
%
%
% LATTICE L272.35
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1103700, -27000, -279600; -27000, 660, 6840; -279600, 6840, 70831],[300, 60, 1],[2, 19, 5, -13, -28, -34, -179, -37, -19, -4; -1, 0, -3, -35, -58, -65, -330, -63, -31, -8; 8, 75, 20, -48, -105, -128, -675, -140, -72, -15],271,35]
%
% END OF LATTICE L272.35
%
%
% LATTICE L272.36
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[52867200, -3572700, -13397700; -3572700, 241440, 905400; -13397700, 905400, 3395269],[300, 60, 1],[-37, -37, -5, -479, -1701, -985, -10183, -1017, -543, -343; 0, 15, 1, -23, -83, -48, -495, -49, -25, -13; -146, -150, -20, -1884, -6690, -3874, -40050, -4000, -2136, -1350],271,36]
%
% END OF LATTICE L272.36
%
%
% LATTICE L272.37
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1200, -600, 0; -600, -3880, 360; 0, 360, -31],[600, 40, 1],[-1, 1, 11, 26, 9, 91, 2, -2, -11, -3; 0, 2, 21, 45, 14, 120, 2, -9, -25, -6; 0, 23, 240, 500, 150, 1200, 17, -120, -300, -70],271,37]
%
% END OF LATTICE L272.37
%
%
% LATTICE L272.38
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1200, -600, 0; -600, -280, 80; 0, 80, -11],[600, 40, 1],[-1, 1, 5, 6, 0, -29, -3, -8, -11, -1; 0, 2, 9, 5, -2, -120, -10, -21, -25, -2; 0, 14, 60, 0, -25, -1200, -94, -180, -200, -15],271,38]
%
% END OF LATTICE L272.38
%
%
% LATTICE L272.39
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[6600, -2400, 600; -2400, 680, -160; 600, -160, 37],[600, 40, 1],[-19, -31, -8, -1, 0, 1, 1, -1, -2, -3; -357, -585, -153, -20, -1, 15, 15, -18, -37, -56; -1248, -2050, -540, -72, -5, 48, 50, -60, -128, -195],271,39]
%
% END OF LATTICE L272.39
%
%
% LATTICE L272.40
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[341400, -57000, 2400; -57000, 9520, -400; 2400, -400, 17],[600, 40, 1],[-44, -39, -25, -5, -4, -4, -1, 1, -3, -12; -225, -200, -129, -26, -21, -21, -5, 6, -15, -61; 888, 775, 480, 92, 70, 72, 25, 0, 68, 250],271,40]
%
% END OF LATTICE L272.40
%
%
% LATTICE L272.41
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1239600, -4411800, 113400; -4411800, -15700440, 403560; 113400, 403560, -10373],[600, 120, 1],[-1, 1, 4, 33, 13, 51, 4, 1, -8, -3; -10, -11, -33, -125, -6, 150, 25, 47, 195, 34; -400, -417, -1240, -4500, -90, 6400, 1017, 1840, 7500, 1290],271,41]
%
% END OF LATTICE L272.41
%
%
% LATTICE L272.42
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-159600, -535800, 13800; -535800, -1798440, 46320; 13800, 46320, -1193],[600, 120, 1],[-1, 1, 2, 13, 2, 11, 1, -1, -8, -1; -10, -2, 3, 135, 43, 470, 94, 43, 95, 3; -400, -66, 140, 5400, 1695, 18400, 3666, 1660, 3600, 105],271,42]
%
% END OF LATTICE L272.42
%
%
% LATTICE L272.43
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[6142800, 1175400, -13800; 1175400, 224760, -2640; -13800, -2640, 31],[600, 120, 1],[-3, -11, 0, 1, 1, 1, 1, -1, -2, -2; -14, -60, -3, 1, 2, 2, 0, -3, -7, -8; -2536, -10050, -260, 528, 615, 616, 450, -700, -1488, -1575],271,43]
%
% END OF LATTICE L272.43
%
%
% LATTICE L272.44
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[928200, 27000, -4200; 27000, -240, -120; -4200, -120, 19],[600, 120, 1],[46, 109, 17, 5, -2, -2, 1, 5, 17, 46; 19, 45, 7, 2, -1, -1, 0, 2, 7, 19; 10288, 24375, 3800, 1116, -450, -448, 225, 1120, 3804, 10290],271,44]
%
% END OF LATTICE L272.44
%

\medskip%
%------------------------------WEYL-GROUP-W273--------------------------------
%
\leavevmode\llap{}%
$W_{273}$%
\qquad\llap{8} lattices, $\chi=24$%
\hfill%
$2|22|22|22|2\rtimes D_{4}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L273.1
%
\leavevmode%
${L_{273.1}}$%
{} : {$[1\above{1pt}{1pt}{1}{}2\above{1pt}{1pt}{1}{}]\above{1pt}{1pt}{}{0}64\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{1}{}$}\EasyButWeakLineBreak%
{${192}\above{1pt}{1pt}{*}{2}{4}\above{1pt}{1pt}{s}{2}{192}\above{1pt}{1pt}{l}{2}{2}\above{1pt}{1pt}{}{2}{192}\above{1pt}{1pt}{}{2}{1}\above{1pt}{1pt}{r}{2}{192}\above{1pt}{1pt}{*}{2}{8}\above{1pt}{1pt}{s}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-27456\\960\\192
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
960\\-2\\-10
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
192\\-10\\-1
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-5\\-48\\-480
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-10\\-94
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\0\\96
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\9\\94
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
41\\384\\3840
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\19\\187
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
35\\336\\3264
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\10\\92
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-27456, 960, 192; 960, -2, -10; 192, -10, -1],[192, 2, 1],[-5, -1, 1, 1, 41, 2, 35, 1; -48, -10, 0, 9, 384, 19, 336, 10; -480, -94, 96, 94, 3840, 187, 3264, 92],272,1]
%
% END OF LATTICE L273.1
%
\hbox{}\par\smallskip%
%
% LATTICE L273.2
%
\leavevmode%
${L_{273.2}}$%
{} : {$1\above{1pt}{1pt}{-}{3}8\above{1pt}{1pt}{1}{1}64\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{1}{}$}\EasyButWeakLineBreak%
{${12}\above{1pt}{1pt}{*}{2}{64}\above{1pt}{1pt}{l}{2}{3}\above{1pt}{1pt}{}{2}{8}\above{1pt}{1pt}{r}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-6720\\192\\192
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
192\\8\\-8
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
192\\-8\\-5
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
95\\480\\2688
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2\\-11\\-56
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3\\-15\\-85
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-6\\-30
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-4\\-32
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\6\\27
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\11\\56
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-6720, 192, 192; 192, 8, -8; 192, -8, -5],[192, 8, 1],[-1, -1, 1, 2, 7, 9, 2, 0; -6, -4, 6, 11, 36, 44, 9, -1; -30, -32, 27, 56, 198, 256, 57, 0],272,2]
%
% END OF LATTICE L273.2
%
%
% LATTICE L273.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-10176, -2688, 960; -2688, -570, 210; 960, 210, -77],[192, 6, 1],[-3, -1, 7, 3, 31, 4, 21, 1; -80, -24, 192, 79, 800, 102, 528, 22; -256, -78, 608, 252, 2560, 327, 1696, 72],272,3]
%
% END OF LATTICE L273.3
%
%
% LATTICE L273.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[4800, -192, 0; -192, -56, 8; 0, 8, -1],[192, 8, 1],[-13, -1, -7, 0, 1, 0, -5, -1; -288, -23, -168, -1, 24, 1, -96, -21; -2496, -198, -1440, -8, 192, 6, -864, -184],272,4]
%
% END OF LATTICE L273.4
%
%
% LATTICE L273.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-229056, 2112, 2304; 2112, 24, -24; 2304, -24, -23],[192, 24, 1],[11, 41, 3, 0, -1, -1, 2, 10; 64, 236, 17, -1, -6, -4, 12, 59; 1030, 3840, 281, 0, -94, -96, 187, 936],272,5]
%
% END OF LATTICE L273.5
%
%
% LATTICE L273.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-767424, -32064, 5184; -32064, -1320, 216; 5184, 216, -35],[192, 24, 1],[7, 0, -3, -1, 5, 3, 15, 4; 40, 1, -16, -7, 16, 13, 72, 21; 1280, 6, -544, -192, 832, 522, 2656, 720],272,6]
%
% END OF LATTICE L273.6
%
%
% LATTICE L273.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-117312, 58752, -768; 58752, -29408, 384; -768, 384, -5],[192, 32, 1],[-1, -1, 1, 4, 7, 9, 4, 0; -3, -2, 3, 11, 18, 22, 9, -1; -78, 0, 75, 224, 294, 288, 66, -80],272,7]
%
% END OF LATTICE L273.7
%
%
% LATTICE L273.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[192, 0, 0; 0, -48480, 1056; 0, 1056, -23],[192, 96, 1],[0, 1, 0, -1, -1, -5, -1, -1; -1, 0, 2, 19, 10, 36, 5, -1; -46, 0, 91, 864, 454, 1632, 226, -48],272,8]
%
% END OF LATTICE L273.8
%

\medskip%
%------------------------------WEYL-GROUP-W274--------------------------------
%
\leavevmode\llap{}%
$W_{274}$%
\qquad\llap{16} lattices, $\chi=48$%
\hfill%
$2\slashinfty22|22\slashinfty22|2\rtimes D_{4}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L274.1
%
\leavevmode%
${L_{274.1}}$%
{} : {$[1\above{1pt}{1pt}{-}{}2\above{1pt}{1pt}{1}{}]\above{1pt}{1pt}{}{6}64\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{-}{}9\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{3}%
\EasyButWeakLineBreak%
{${576}\above{1pt}{1pt}{}{2}{6}\above{1pt}{1pt}{48,1}{\infty}{24}\above{1pt}{1pt}{*}{2}{576}\above{1pt}{1pt}{s}{2}{8}\above{1pt}{1pt}{*}{2}{576}\above{1pt}{1pt}{s}{2}{24}\above{1pt}{1pt}{48,1}{\infty z}{6}\above{1pt}{1pt}{r}{2}{576}\above{1pt}{1pt}{l}{2}{2}\above{1pt}{1pt}{}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
14400\\2880\\-576
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2880\\546\\-114
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-576\\-114\\23
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
29\\96\\1152
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4\\11\\150
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
11\\26\\396
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
65\\144\\2304
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\6\\104
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
25\\48\\864
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\2\\36
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-1\\-30
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-11\\0\\-288
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\1\\4
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[14400, 2880, -576; 2880, 546, -114; -576, -114, 23],[576, 6, 1],[29, 4, 11, 65, 3, 25, 1, -1, -11, 0; 96, 11, 26, 144, 6, 48, 2, -1, 0, 1; 1152, 150, 396, 2304, 104, 864, 36, -30, -288, 4],273,1]
%
% END OF LATTICE L274.1
%
\hbox{}\par\smallskip%
%
% LATTICE L274.2
%
\leavevmode%
${L_{274.2}}$%
{} : {$1\above{1pt}{1pt}{1}{7}8\above{1pt}{1pt}{-}{3}64\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{-}{}9\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{3}%
\EasyButWeakLineBreak%
{${576}\above{1pt}{1pt}{}{2}{24}\above{1pt}{1pt}{48,1}{\infty}{24}\above{1pt}{1pt}{r}{2}{576}\above{1pt}{1pt}{b}{2}{8}\above{1pt}{1pt}{l}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
14400\\-576\\-576
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-576\\24\\24
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-576\\24\\23
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
53\\-216\\1728
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3\\11\\-96
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2\\8\\-65
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-19\\48\\-576
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3\\11\\-96
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2\\13\\-72
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-7\\72\\-288
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\3\\-4
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[14400, -576, -576; -576, 24, 24; -576, 24, 23],[576, 24, 1],[-19, -3, -2, -7, 0, 1, 0, -1, -11, -1; 48, 11, 13, 72, 3, 24, 1, -1, 0, 1; -576, -96, -72, -288, -4, 0, 0, -24, -288, -28],273,2]
%
% END OF LATTICE L274.2
%
%
% LATTICE L274.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[181824, 4800, 18048; 4800, 118, 486; 18048, 486, 1781],[192, 2, 1],[295, 43, -20, -37, 11, 467, 169, 421, 799, 105; -2512, -366, 171, 320, -93, -3968, -1437, -3582, -6800, -894; -2304, -336, 156, 288, -86, -3648, -1320, -3288, -6240, -820],273,3]
%
% END OF LATTICE L274.3
%
%
% LATTICE L274.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[80448, 35904, 1344; 35904, 16024, 600; 1344, 600, 23],[192, 8, 1],[-197, -107, -94, -145, -12, -25, -4, -17, -77, -25; 448, 243, 213, 328, 27, 56, 9, 39, 176, 57; -192, -96, -72, -96, -4, 0, 0, -24, -96, -28],273,4]
%
% END OF LATTICE L274.4
%
%
% LATTICE L274.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[4800, -7488, 2688; -7488, 11526, -4140; 2688, -4140, 1487],[192, 6, 1],[-29, -4, -11, -65, -9, -25, -1, 1, 11, 0; 672, 83, 210, 1200, 158, 432, 18, -13, -96, 13; 1920, 238, 604, 3456, 456, 1248, 52, -38, -288, 36],273,5]
%
% END OF LATTICE L274.5
%
%
% LATTICE L274.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[88512, 28992, -2688; 28992, 9496, -880; -2688, -880, 81],[192, 8, 1],[3, 1, -16, -11, -17, -3, -1, 16, 11, 17; -7, 9, 63, 40, 58, 10, 3, -51, -34, -50; 21, 120, 144, 66, 64, 9, 0, -24, -6, 16],273,6]
%
% END OF LATTICE L274.6
%
%
% LATTICE L274.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-639936, -5760, -576; -5760, -30, -18; -576, -18, 7],[576, 6, 1],[23, 8, 19, 35, 13, 11, 1, -1, -1, 2; -2176, -757, -1798, -3312, -1230, -1040, -94, 95, 96, -189; -3712, -1290, -3060, -5632, -2088, -1760, -156, 162, 160, -324],273,7]
%
% END OF LATTICE L274.7
%
%
% LATTICE L274.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[4800, 4032, -1536; 4032, 3336, -1272; -1536, -1272, 485],[192, 24, 1],[1, 0, -1, -11, -3, -19, -3, -2, -7, 0; 72, 3, -11, -96, -19, -48, 1, 15, 120, 23; 192, 8, -32, -288, -60, -192, -8, 32, 288, 60],273,8]
%
% END OF LATTICE L274.8
%
%
% LATTICE L274.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1344, 16704, -2112; 16704, -153912, 19272; -2112, 19272, -2413],[192, 24, 1],[-19, -36, -43, -59, -57, -8, 0, 7, 5, -15; -381, -717, -851, -1164, -1118, -156, 1, 135, 90, -314; -3027, -5696, -6760, -9246, -8880, -1239, 8, 1072, 714, -2496],273,9]
%
% END OF LATTICE L274.9
%
%
% LATTICE L274.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-414912, -21504, 2496; -21504, -992, 128; 2496, 128, -15],[192, 32, 1],[1, 1, -7, -2, -2, 1, 11, 19, 5, 6; 2, 3, -15, -5, -7, -1, 9, 27, 8, 11; 183, 192, -1296, -378, -400, 150, 1872, 3360, 894, 1088],273,10]
%
% END OF LATTICE L274.10
%
%
% LATTICE L274.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1184832, -59328, 2880; -59328, -2856, 144; 2880, 144, -7],[576, 24, 1],[-7, -12, -13, -17, -5, -2, 0, 1, -1, -3; -6, -11, -13, -18, -6, -3, -1, 1, 0, -2; -3015, -5184, -5640, -7398, -2192, -891, -24, 432, -414, -1280],273,11]
%
% END OF LATTICE L274.11
%
%
% LATTICE L274.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-474048, -7488, -576; -7488, 24, 24; -576, 24, 7],[576, 24, 1],[7, 5, 6, 11, 4, 3, 0, -1, -1, 1; -656, -469, -563, -1032, -375, -280, 1, 95, 96, -93; 2816, 2016, 2424, 4448, 1620, 1216, 0, -408, -416, 396],273,12]
%
% END OF LATTICE L274.12
%
%
% LATTICE L274.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[96192, -1728, -2304; -1728, 24, 48; -2304, 48, 49],[576, 24, 1],[9, 21, 20, 4, 17, 1, -1, 0, 1, 23; 192, 445, 419, 83, 342, 18, -25, 1, 22, 498; 226, 528, 504, 101, 432, 26, -24, 0, 25, 576],273,13]
%
% END OF LATTICE L274.13
%
%
% LATTICE L274.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-181440, -68160, 1536; -68160, -25248, 576; 1536, 576, -13],[192, 96, 1],[5, 11, 15, 11, 12, 2, 1, -3, -2, 0; 1, 3, 5, 4, 5, 1, 1, -1, -1, -1; 630, 1424, 1984, 1470, 1632, 279, 160, -400, -282, -48],273,14]
%
% END OF LATTICE L274.14
%
%
% LATTICE L274.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-866880, -128448, 5184; -128448, -18912, 768; 5184, 768, -31],[576, 96, 1],[-2, -3, 1, 2, 4, 11, 15, 11, 5, 0; -3, -1, 1, 0, -1, -6, -11, -13, -9, -3; -414, -528, 192, 333, 640, 1674, 2208, 1488, 594, -80],273,15]
%
% END OF LATTICE L274.15
%
%
% LATTICE L274.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-14294592, -635328, 25920; -635328, -28128, 1152; 25920, 1152, -47],[576, 96, 1],[5, 27, 31, 7, 20, 1, 1, -3, 0, 8; -3, -13, -11, -2, -3, 0, 1, -1, -1, -9; 2678, 14544, 16800, 3806, 10944, 551, 576, -1680, -26, 4176],273,16]
%
% END OF LATTICE L274.16
%

\medskip%
%------------------------------WEYL-GROUP-W275--------------------------------
%
\leavevmode\llap{}%
$W_{275}$%
\qquad\llap{12} lattices, $\chi=12$%
\hfill%
$62223$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L275.1
%
\leavevmode%
${L_{275.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{-}{}27\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${6}\above{1pt}{1pt}{}{6}{2}\above{1pt}{1pt}{b}{2}{60}\above{1pt}{1pt}{*}{2}{108}\above{1pt}{1pt}{b}{2}{6}\above{1pt}{1pt}{-}{3}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-194940\\-76680\\62640
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-76680\\-29982\\24027
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
62640\\24027\\-18046
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
384\\-1285\\-378
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
909\\-3042\\-895
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1249\\-4180\\-1230
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-823\\2754\\810
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-326\\1091\\321
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-194940, -76680, 62640; -76680, -29982, 24027; 62640, 24027, -18046],[540, 3, 1],[384, 909, 1249, -823, -326; -1285, -3042, -4180, 2754, 1091; -378, -895, -1230, 810, 321],274,1]
%
% END OF LATTICE L275.1
%
%
% LATTICE L275.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-4590, -3105, -1755; -3105, -2073, -1161; -1755, -1161, -646],[135, 3, 1],[-9, -28, -23, 8, 11; 32, 102, 85, -27, -40; -33, -107, -90, 27, 42],274,2]
%
% END OF LATTICE L275.2
%
%
% LATTICE L275.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-32346405, -46845, 559305; -46845, -63, 810; 559305, 810, -9671],[135, 9, 1],[-54, -197, -14, 6, 7; -1, -15, -5, 0, 2; -3123, -11394, -810, 347, 405],274,3]
%
% END OF LATTICE L275.3
%
%
% LATTICE L275.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1402785, -16200, 16875; -16200, -105, 195; 16875, 195, -203],[135, 15, 1],[13, 38, 6, -13, -15; -1, -5, -1, 0, 2; 1080, 3155, 498, -1080, -1245],274,4]
%
% END OF LATTICE L275.4
%
%
% LATTICE L275.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-5436180, -220860, 18360; -220860, -8838, 747; 18360, 747, -62],[540, 9, 1],[-4, -41, -23, 1, 6; 8, 87, 50, -2, -13; -1089, -11097, -6210, 272, 1620],274,5]
%
% END OF LATTICE L275.5
%
%
% LATTICE L275.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-710505, 726030, 105030; 726030, -741870, -107325; 105030, -107325, -15526],[135, 45, 1],[-154, -574, -9, 17, 22; -1, -15, -1, 0, 2; -1035, -3780, -54, 115, 135],274,6]
%
% END OF LATTICE L275.6
%
%
% LATTICE L275.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[40520393640, -604547820, -10144920060; -604547820, 9019608, 151358088; -10144920060, 151358088, 2539940849],[540, 12, 1],[181, 116, -72, -151, 51; -152, -347, -295, -153, -5; 732, 484, -270, -594, 204],274,7]
%
% END OF LATTICE L275.7
%
%
% LATTICE L275.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-8063820, -97740, -5277420; -97740, -870, -59895; -5277420, -59895, -3401162],[540, 15, 1],[-1575, -3782, -1051, 3359, 1366; -40951, -98333, -27326, 87336, 35516; 3165, 7600, 2112, -6750, -2745],274,8]
%
% END OF LATTICE L275.8
%
%
% LATTICE L275.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[10689115320, 5750460, -2692370880; 5750460, 3096, -1448424; -2692370880, -1448424, 678153499],[540, 36, 1],[-4026, -17981, -3287, -67, -671; -83, -345, -55, 0, -14; -15984, -71388, -13050, -266, -2664],274,9]
%
% END OF LATTICE L275.9
%
%
% LATTICE L275.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1986660, -297540, 402300; -297540, -44190, 60255; 402300, 60255, -81466],[540, 45, 1],[-229, -2282, -253, 57, 330; 8, 87, 10, -2, -13; -1125, -11205, -1242, 280, 1620],274,10]
%
% END OF LATTICE L275.10
%
%
% LATTICE L275.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[204248166840, 98186543820, -51188520240; 98186543820, 47200410840, -24607436940; -51188520240, -24607436940, 12828828013],[540, 60, 1],[27211, 37019, 3407, -884, 4646; 13, 26, 4, 9, 1; 108600, 147760, 13602, -3510, 18540],274,11]
%
% END OF LATTICE L275.11
%
%
% LATTICE L275.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[69771240, -1038420, 18950220; -1038420, 15480, -282060; 18950220, -282060, 5146991],[540, 180, 1],[1122, 4909, 173, 13, 187; -3449, -15072, -530, -39, -575; -4320, -18900, -666, -50, -720],274,12]
%
% END OF LATTICE L275.12
%

\medskip%
%------------------------------WEYL-GROUP-W276--------------------------------
%
\leavevmode\llap{}%
$W_{276}$%
\qquad\llap{12} lattices, $\chi=36$%
\hfill%
$2222222222\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L276.1
%
\leavevmode%
${L_{276.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{1}{}3\above{1pt}{1pt}{1}{}27\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{2}{}5\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${270}\above{1pt}{1pt}{l}{2}{4}\above{1pt}{1pt}{r}{2}{30}\above{1pt}{1pt}{b}{2}{108}\above{1pt}{1pt}{*}{2}{12}\above{1pt}{1pt}{b}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
401220\\5400\\-4860
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5400\\66\\-63
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-4860\\-63\\58
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\13860\\17820
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\244\\315
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\-189\\-244
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-675\\-945
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-132\\-244
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2\\-130\\-315
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-7\\-396\\-1026
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-50\\-138
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[401220, 5400, -4860; 5400, 66, -63; -4860, -63, 58],[540, 3, 1],[-1, -1, -2, -7, -1, 1, 1, 2, 7, 1; -675, -132, -130, -396, -50, 45, 48, 95, 270, 22; -945, -244, -315, -1026, -138, 135, 136, 270, 864, 102],275,1]
%
% END OF LATTICE L276.1
%
%
% LATTICE L276.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[270, 0, -135; 0, -15, -3; -135, -3, 67],[135, 3, 1],[-1, 2, 8, -8, -7, -449, -32, -33, -37, -3; 0, -1, -5, -18, -5, -180, -11, -5, 0, 1; 0, 4, 15, -27, -18, -1080, -76, -75, -81, -6],275,2]
%
% END OF LATTICE L276.2
%
%
% LATTICE L276.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-34965, 5805, -270; 5805, -963, 45; -270, 45, -2],[135, 9, 1],[-51, -91, -23, -2, 0, 1, 1, -2, -3, -10; -315, -564, -145, -13, -1, 5, 6, -10, -18, -61; -425, -810, -270, -34, -27, -25, 0, 45, -11, -63],275,3]
%
% END OF LATTICE L276.3
%
%
% LATTICE L276.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[134190, 1620, -1215; 1620, -75, -15; -1215, -15, 11],[135, 15, 1],[-17, -8, -3, -23, -3, -1, 2, 2, 14, 1; -36, -11, -1, 0, 1, 0, -1, -1, -18, -5; -2052, -940, -339, -2565, -330, -108, 220, 219, 1485, 90],275,4]
%
% END OF LATTICE L276.4
%
%
% LATTICE L276.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-502740, -21060, 1080; -21060, -882, 45; 1080, 45, -2],[540, 9, 1],[-21, -73, -8, -1, 1, 1, 1, -2, -3, -9; 495, 1716, 185, 22, -26, -25, -24, 50, 72, 214; -425, -1620, -270, -68, -54, -25, 0, 45, -22, -126],275,5]
%
% END OF LATTICE L276.5
%
%
% LATTICE L276.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[135, 0, 0; 0, -90, 45; 0, 45, -22],[135, 45, 1],[-12, -109, -6, -3, -1, 0, 1, 0, -3, -11; -71, -630, -31, -13, 1, 1, 0, -4, -22, -71; -182, -1620, -81, -35, 0, 2, 0, -9, -55, -180],275,6]
%
% END OF LATTICE L276.6
%
%
% LATTICE L276.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[113679720, -939060, -28636740; -939060, 7752, 236556; -28636740, 236556, 7213801],[540, 12, 1],[130207, 4278, 6304, 4694, -65, -2857, -33, 771, 8041, 2895; 3195, 105, 155, 117, -1, -45, 0, 20, 198, 71; 516780, 16979, 25020, 18630, -258, -11340, -131, 3060, 31914, 11490],275,7]
%
% END OF LATTICE L276.7
%
%
% LATTICE L276.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-4149900, -110160, 11880; -110160, -2910, 315; 11880, 315, -34],[540, 15, 1],[-73, -49, -4, -35, -1, 1, 1, 0, -37, -15; -783, -528, -44, -396, -14, 9, 12, 1, -378, -158; -32832, -22060, -1809, -15930, -480, 432, 460, 9, -16470, -6720],275,8]
%
% END OF LATTICE L276.8
%
%
% LATTICE L276.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2249640, -147420, -565920; -147420, 10728, 37080; -565920, 37080, 142363],[540, 36, 1],[-81699, -74429, -41527, -4261, -1691, -811, 170, 272, -3990, -14811; -1495, -1362, -760, -78, -31, -15, 3, 5, -73, -271; -324380, -295515, -164880, -16918, -6714, -3220, 675, 1080, -15842, -58806],275,9]
%
% END OF LATTICE L276.9
%
%
% LATTICE L276.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[540, 0, 0; 0, -90, 45; 0, 45, -22],[540, 45, 1],[0, 1, 0, -3, -11, -6, -109, -3, -3, -1; 1, 0, -4, -44, -142, -71, -1260, -31, -26, 2; 2, 0, -9, -110, -360, -182, -3240, -81, -70, 0],275,10]
%
% END OF LATTICE L276.10
%
%
% LATTICE L276.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[521859240, -1469340, -131439780; -1469340, 4200, 370080; -131439780, 370080, 33105509],[540, 60, 1],[-210709, -35062, -11026, -47128, -1277, -2285, -437, -807, -59369, -22389; -1458, -243, -77, -333, -10, -18, -3, -5, -405, -154; -836568, -139205, -43776, -187110, -5070, -9072, -1735, -3204, -235710, -88890],275,11]
%
% END OF LATTICE L276.11
%
%
% LATTICE L276.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[329400, 36180, 55620; 36180, 3960, 6120; 55620, 6120, 9383],[540, 180, 1],[-1, -34, -18, -16, -17, 7, 61, 21, 19, 23; 3, 102, 53, 37, 13, -61, -363, -82, -66, -71; 4, 135, 72, 70, 90, -4, -135, -72, -70, -90],275,12]
%
% END OF LATTICE L276.12
%

\medskip%
%------------------------------WEYL-GROUP-W277--------------------------------
%
\leavevmode\llap{}%
$W_{277}$%
\qquad\llap{12} lattices, $\chi=24$%
\hfill%
$22222222\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L277.1
%
\leavevmode%
${L_{277.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{1}{}27\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${540}\above{1pt}{1pt}{b}{2}{2}\above{1pt}{1pt}{s}{2}{54}\above{1pt}{1pt}{b}{2}{12}\above{1pt}{1pt}{*}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-307260\\7560\\-3780
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7560\\-186\\93
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3780\\93\\-46
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2161\\-73440\\32400
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
53\\1801\\-795
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-24\\-816\\359
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
11\\450\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\39\\-4
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7\\261\\-54
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\106\\-36
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-307260, 7560, -3780; 7560, -186, 93; -3780, 93, -46],[540, 3, 1],[11, 1, 7, 3, 79, 2, 2, -1; 450, 39, 261, 106, 2610, 63, 45, -38; 0, -4, -54, -36, -1350, -41, -81, 6],276,1]
%
% END OF LATTICE L277.1
%
%
% LATTICE L277.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-12015, 270, -135; 270, -6, 3; -135, 3, -1],[135, 3, 1],[-46, -3, -7, 0, 1, 0, -2, -1; -2025, -133, -315, -1, 45, 1, -81, -43; -405, -29, -81, -3, 0, 2, 0, -6],276,2]
%
% END OF LATTICE L277.2
%
%
% LATTICE L277.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-270, 0, -135; 0, 9, -18; -135, -18, -31],[135, 9, 1],[16, 37, 5, 4, 4, -1, -1, 0; -70, -159, -21, -16, -15, 6, 4, -1; -35, -81, -11, -9, -10, 0, 2, 0],276,3]
%
% END OF LATTICE L277.3
%
%
% LATTICE L277.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-107865, -58320, -2025; -58320, -31530, -1095; -2025, -1095, -38],[135, 15, 1],[35, 14, 46, 3, 1, -2, -10, 1; -72, -27, -81, -4, 0, 3, 9, -4; 189, 25, -135, -45, -54, 20, 270, 60],276,4]
%
% END OF LATTICE L277.4
%
%
% LATTICE L277.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-57780, -2700, -3240; -2700, -126, -153; -3240, -153, -166],[540, 9, 1],[9, -1, -1, 1, 41, 46, 6, 9; -170, 21, 19, -22, -800, -894, -116, -172; -20, 0, 2, 0, -70, -81, -11, -18],276,5]
%
% END OF LATTICE L277.5
%
%
% LATTICE L277.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[270, -4860, 135; -4860, 79695, -2205; 135, -2205, 61],[135, 45, 1],[2, 26, 4, 4, 1, 1, -1, -1; -2, -9, 1, 4, 1, 0, -2, -5; -79, -405, 25, 135, 34, 0, -70, -180],276,6]
%
% END OF LATTICE L277.6
%
%
% LATTICE L277.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[212760, 13500, -53460; 13500, 3432, -3372; -53460, -3372, 13433],[540, 12, 1],[2923, 711, 6961, 2059, 73757, 4401, 8375, -355; -90, -22, -216, -64, -2295, -137, -261, 11; 11610, 2824, 27648, 8178, 292950, 17480, 33264, -1410],276,7]
%
% END OF LATTICE L277.7
%
%
% LATTICE L277.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3713580, -1317600, 11880; -1317600, -467490, 4215; 11880, 4215, -38],[540, 15, 1],[131, 21, 47, -1, -5, 0, 16, 15; -414, -67, -153, 2, 18, 1, -45, -46; -5022, -875, -2295, -90, 432, 110, 0, -420],276,8]
%
% END OF LATTICE L277.8
%
%
% LATTICE L277.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1327320, -282420, -332640; -282420, 60408, 70776; -332640, 70776, 83363],[540, 36, 1],[561, 299, 1, 267, 2834, 5812, 678, 412; 10, 6, 0, 4, 45, 93, 11, 7; 2230, 1188, 4, 1062, 11270, 23112, 2696, 1638],276,9]
%
% END OF LATTICE L277.9
%
%
% LATTICE L277.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[307260, -106920, 3240; -106920, 37170, -1125; 3240, -1125, 34],[540, 45, 1],[1, 10, 2, 5, 1, -1, -1, -3; 8, 66, 12, 28, 6, -3, -5, -14; 166, 1215, 205, 450, 104, 0, -70, -180],276,10]
%
% END OF LATTICE L277.10
%
%
% LATTICE L277.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[81441720, -369900, -20504340; -369900, 2040, 93120; -20504340, 93120, 5162317],[540, 60, 1],[-81295, -25107, -52229, 1141, -2081, -2685, -31147, -10405; -7749, -2393, -4977, 109, -198, -256, -2970, -992; -322758, -99680, -207360, 4530, -8262, -10660, -123660, -41310],276,11]
%
% END OF LATTICE L277.11
%
%
% LATTICE L277.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[34124760, 765180, 8019540; 765180, 16920, 180000; 8019540, 180000, 1884511],[540, 180, 1],[1350, 12508, 1138, -68, -353, -3535, -141, 1065; -4009, -37143, -3379, 203, 1049, 10503, 419, -3163; -5362, -49680, -4520, 270, 1402, 14040, 560, -4230],276,12]
%
% END OF LATTICE L277.12
%

\medskip%
%------------------------------WEYL-GROUP-W278--------------------------------
%
\leavevmode\llap{}%
$W_{278}$%
\qquad\llap{28} lattices, $\chi=96$%
\hfill%
$22\slashinfty2222|2222\slashinfty2222|22\rtimes D_{4}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L278.1
%
\leavevmode%
${L_{278.1}}$%
{} : {$[1\above{1pt}{1pt}{1}{}2\above{1pt}{1pt}{-}{}]\above{1pt}{1pt}{}{4}32\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{-2}{}7\above{1pt}{1pt}{1}{}$}\EasyButWeakLineBreak%
{${224}\above{1pt}{1pt}{s}{2}{8}\above{1pt}{1pt}{*}{2}{28}\above{1pt}{1pt}{8,3}{\infty z}{7}\above{1pt}{1pt}{r}{2}{8}\above{1pt}{1pt}{*}{2}{224}\above{1pt}{1pt}{l}{2}{1}\above{1pt}{1pt}{r}{2}{56}\above{1pt}{1pt}{*}{2}{4}\above{1pt}{1pt}{*}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-230048\\1344\\2464
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1344\\-6\\-16
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2464\\-16\\-25
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
14503\\783216\\919968
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-63\\-3403\\-3996
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-175\\-9450\\-11101
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
555\\30072\\35168
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
77\\4170\\4880
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
89\\4816\\5642
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
50\\2702\\3171
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
99\\5346\\6280
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
775\\41832\\49168
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
13\\701\\825
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
71\\3822\\4508
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
13\\698\\826
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-230048, 1344, 2464; 1344, -6, -16; 2464, -16, -25],[224, 2, 1],[555, 77, 89, 50, 99, 775, 13, 71, 13, 229, 21, 9, -1, -1, 9, 1, 27, 15; 30072, 4170, 4816, 2702, 5346, 41832, 701, 3822, 698, 12264, 1122, 476, -56, -54, 504, 55, 1470, 814; 35168, 4880, 5642, 3171, 6280, 49168, 825, 4508, 826, 14560, 1336, 574, -63, -64, 560, 63, 1708, 950],277,1]
%
% END OF LATTICE L278.1
%
\hbox{}\par\smallskip%
%
% LATTICE L278.2
%
\leavevmode%
${L_{278.2}}$%
{} : {$[1\above{1pt}{1pt}{1}{}2\above{1pt}{1pt}{1}{}]\above{1pt}{1pt}{}{0}64\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{-2}{}7\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{m}%
\EasyButWeakLineBreak%
{${448}\above{1pt}{1pt}{s}{2}{4}\above{1pt}{1pt}{*}{2}{56}\above{1pt}{1pt}{16,7}{\infty z}{14}\above{1pt}{1pt}{}{2}{1}\above{1pt}{1pt}{r}{2}{448}\above{1pt}{1pt}{*}{2}{8}\above{1pt}{1pt}{*}{2}{28}\above{1pt}{1pt}{l}{2}{2}\above{1pt}{1pt}{r}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
shares genus with {$ {L_{278.3}}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1430464\\-12544\\-448
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-12544\\110\\4
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-448\\4\\-7
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
59135\\6771072\\206976
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-520\\-59541\\-1820
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
116\\13282\\405
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-181\\-20832\\-1120
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-7\\-808\\-54
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-126\\-56
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4\\455\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\114\\1
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-112\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3\\-342\\-4
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-19\\-2170\\-42
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-10\\-1143\\-26
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[1430464, -12544, -448; -12544, 110, 4; -448, 4, -7],[448, 2, 1],[-181, -7, -1, 4, 1, -1, -3, -19, -10, -715, -49, -111, -60, -29, -895, -29, -37, -6; -20832, -808, -126, 455, 114, -112, -342, -2170, -1143, -81760, -5604, -12698, -6867, -3320, -102480, -3322, -4242, -689; -1120, -54, -56, 0, 1, 0, -4, -42, -26, -2016, -142, -336, -196, -99, -3136, -108, -154, -30],277,2]
%
% END OF LATTICE L278.2
%
\hbox{}\par\smallskip%
%
% LATTICE L278.3
%
\leavevmode%
${L_{278.3}}$%
{} : {$[1\above{1pt}{1pt}{1}{}2\above{1pt}{1pt}{1}{}]\above{1pt}{1pt}{}{0}64\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{-2}{}7\above{1pt}{1pt}{1}{}$}\EasyButWeakLineBreak%
{${448}\above{1pt}{1pt}{}{2}{1}\above{1pt}{1pt}{r}{2}{56}\above{1pt}{1pt}{16,15}{\infty z}{14}\above{1pt}{1pt}{r}{2}{4}\above{1pt}{1pt}{*}{2}{448}\above{1pt}{1pt}{s}{2}{8}\above{1pt}{1pt}{l}{2}{7}\above{1pt}{1pt}{}{2}{2}\above{1pt}{1pt}{}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
shares genus with {$ {L_{278.2}}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1179584\\11648\\11200
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
11648\\110\\108
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
11200\\108\\105
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-7841\\-799680\\1646400
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-94\\-9589\\19740
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-83\\-8466\\17429
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-181\\-19712\\39424
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-5\\-548\\1093
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-15\\-1666\\3304
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3\\-343\\672
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-116\\226
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-112\\224
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\118\\-228
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\133\\-245
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\23\\-26
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[1179584, 11648, 11200; 11648, 110, 108; 11200, 108, 105],[448, 2, 1],[-181, -5, -15, -3, -1, -1, 1, 1, 0, -43, -2, -13, -11, -13, -223, -9, -8, -4; -19712, -548, -1666, -343, -116, -112, 118, 133, 23, -3136, -166, -1190, -1085, -1312, -22736, -934, -847, -431; 39424, 1093, 3304, 672, 226, 224, -228, -245, -26, 7616, 377, 2576, 2268, 2714, 46816, 1908, 1715, 866],277,3]
%
% END OF LATTICE L278.3
%
\hbox{}\par\smallskip%
%
% LATTICE L278.4
%
\leavevmode%
${L_{278.4}}$%
{} : {$1\above{1pt}{1pt}{1}{7}4\above{1pt}{1pt}{1}{7}32\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{-2}{}7\above{1pt}{1pt}{1}{}$}\EasyButWeakLineBreak%
{${28}\above{1pt}{1pt}{*}{2}{16}\above{1pt}{1pt}{s}{2}{224}\above{1pt}{1pt}{8,1}{\infty z}{224}\above{1pt}{1pt}{*}{2}{16}\above{1pt}{1pt}{l}{2}{7}\above{1pt}{1pt}{}{2}{32}\above{1pt}{1pt}{}{2}{28}\above{1pt}{1pt}{r}{2}{32}\above{1pt}{1pt}{s}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-509152\\-2464\\3584
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2464\\-4\\16
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3584\\16\\-25
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-39984\\-45696
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\-351\\-400
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\308\\351
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
23\\392\\3430
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
11\\166\\1616
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
19\\196\\2688
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
9\\-140\\1008
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\-170\\-64
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-224\\-385
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3\\-192\\-608
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-5\\-217\\-896
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-7\\-256\\-1200
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-509152, -2464, 3584; -2464, -4, 16; 3584, 16, -25],[224, 4, 1],[23, 11, 19, 9, 1, -1, -3, -5, -7, -23, -11, -19, -9, -1, 1, 3, 5, 7; 392, 166, 196, -140, -170, -224, -192, -217, -256, -784, -362, -588, -252, -26, 28, 80, 119, 144; 3430, 1616, 2688, 1008, -64, -385, -608, -896, -1200, -3878, -1840, -3136, -1456, -160, 161, 480, 784, 1072],277,4]
%
% END OF LATTICE L278.4
%
\hbox{}\par\smallskip%
%
% LATTICE L278.5
%
\leavevmode%
${L_{278.5}}$%
{} : {$1\above{1pt}{1pt}{1}{7}4\above{1pt}{1pt}{1}{1}32\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{-2}{}7\above{1pt}{1pt}{1}{}$}\EasyButWeakLineBreak%
{${28}\above{1pt}{1pt}{l}{2}{4}\above{1pt}{1pt}{}{2}{224}\above{1pt}{1pt}{4,1}{\infty}{224}\above{1pt}{1pt}{l}{2}{4}\above{1pt}{1pt}{}{2}{7}\above{1pt}{1pt}{r}{2}{32}\above{1pt}{1pt}{s}{2}{112}\above{1pt}{1pt}{*}{2}{32}\above{1pt}{1pt}{*}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-161056\\-3584\\2240
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3584\\-28\\32
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2240\\32\\-25
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
8035\\433944\\1267392
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
301\\16253\\47472
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-154\\-8316\\-24289
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
149\\8092\\23590
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
41\\2225\\6488
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
187\\10136\\29568
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
205\\11088\\32368
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
50\\2701\\7888
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
97\\5236\\15295
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
51\\2748\\8032
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
67\\3598\\10528
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
23\\1228\\3600
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-161056, -3584, 2240; -3584, -28, 32; 2240, 32, -25],[224, 4, 1],[149, 41, 187, 205, 50, 97, 51, 67, 23, 47, 8, 9, -9, -1, 1, 5, 31, 33; 8092, 2225, 10136, 11088, 2701, 5236, 2748, 3598, 1228, 2492, 421, 448, -504, -55, 56, 276, 1694, 1796; 23590, 6488, 29568, 32368, 7888, 15295, 8032, 10528, 3600, 7322, 1240, 1344, -1456, -160, 161, 800, 4928, 5232],277,5]
%
% END OF LATTICE L278.5
%
\hbox{}\par\smallskip%
%
% LATTICE L278.6
%
\leavevmode%
${L_{278.6}}$%
{} : {$1\above{1pt}{1pt}{1}{7}8\above{1pt}{1pt}{1}{7}64\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{-2}{}7\above{1pt}{1pt}{1}{}$}\EasyButWeakLineBreak%
{${28}\above{1pt}{1pt}{s}{2}{64}\above{1pt}{1pt}{l}{2}{56}\above{1pt}{1pt}{16,9}{\infty}{56}\above{1pt}{1pt}{}{2}{64}\above{1pt}{1pt}{}{2}{7}\above{1pt}{1pt}{r}{2}{32}\above{1pt}{1pt}{s}{2}{448}\above{1pt}{1pt}{*}{2}{32}\above{1pt}{1pt}{*}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
6720\\-896\\0
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-896\\120\\0
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\-1
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
461\\4312\\9856
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-63\\-589\\-1344
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
6\\56\\127
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-19\\-196\\-602
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-23\\-232\\-672
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-15\\-147\\-392
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-20\\-189\\-448
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-43\\-400\\-896
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-22\\-203\\-441
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-13\\-118\\-240
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-41\\-364\\-672
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-9\\-78\\-128
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[6720, -896, 0; -896, 120, 0; 0, 0, -1],[448, 8, 1],[-19, -23, -15, -20, -43, -22, -13, -41, -9, -23, -19, -6, -1, 1, 1, 1, -1, -3; -196, -232, -147, -189, -400, -203, -118, -364, -78, -196, -160, -49, -7, 8, 7, 6, -28, -34; -602, -672, -392, -448, -896, -441, -240, -672, -128, -294, -224, -56, 0, 0, -7, -16, -224, -128],277,6]
%
% END OF LATTICE L278.6
%
%
% LATTICE L278.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[665056, 224, -6048; 224, -2, -2; -6048, -2, 55],[224, 2, 1],[43, 4, 13, 11, 13, 223, 9, 16, 4, 181, 10, 15, 3, 1, 1, -1, -2, 0; -1008, -71, -168, -98, -99, -1568, -54, -77, -15, -560, -27, -28, 0, 1, 0, -2, -21, -13; 4480, 422, 1386, 1183, 1402, 24080, 974, 1736, 435, 19712, 1090, 1638, 329, 110, 112, -110, -224, -3],277,7]
%
% END OF LATTICE L278.7
%
%
% LATTICE L278.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[44128, 224, -224; 224, -8, 0; -224, 0, 1],[224, 8, 1],[1, 0, -1, -6, -10, -99, -5, -24, -4, -225, -28, -27, -22, -18, -125, -3, -4, 0; 28, 1, -21, -133, -223, -2212, -112, -539, -90, -5068, -631, -609, -497, -407, -2828, -68, -91, 0; 224, 4, -210, -1302, -2180, -21616, -1094, -5264, -879, -49504, -6164, -5950, -4858, -3980, -27664, -666, -896, -1],277,8]
%
% END OF LATTICE L278.8
%
%
% LATTICE L278.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[665056, 24640, -6048; 24640, 904, -224; -6048, -224, 55],[224, 8, 1],[43, 8, 13, 11, 26, 223, 9, 32, 8, 181, 20, 15, 3, 2, 1, -1, -4, 0; -504, -71, -84, -49, -99, -784, -27, -77, -15, -280, -27, -14, 0, 1, 0, -1, -21, -13; 2464, 560, 1050, 987, 2408, 20944, 866, 3164, 810, 18592, 2072, 1582, 329, 224, 112, -114, -532, -58],277,9]
%
% END OF LATTICE L278.9
%
%
% LATTICE L278.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-11491424, 25312, 50624; 25312, -42, -112; 50624, -112, -223],[224, 14, 1],[381, 365, 59, 32, 435, 481, 55, 41, 49, 115, 69, 3, -1, -1, 15, 7, 21, 75; 2904, 2778, 448, 242, 3282, 3624, 413, 306, 362, 840, 498, 20, -8, -6, 120, 55, 162, 574; 84992, 81424, 13162, 7139, 97048, 107312, 12271, 9148, 10934, 25664, 15400, 670, -223, -224, 3344, 1561, 4684, 16730],277,10]
%
% END OF LATTICE L278.10
%
%
% LATTICE L278.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-224, 224, 0; 224, -14, -14; 0, -14, 1],[224, 14, 1],[-101, -50, -17, -10, -71, -161, -39, -8, -11, -59, -20, -3, 0, 1, 1, -1, -2, -9; -144, -71, -24, -14, -99, -224, -54, -11, -15, -80, -27, -4, 0, 1, 0, -2, -3, -13; -1664, -826, -282, -167, -1190, -2704, -658, -136, -189, -1024, -350, -54, -1, 14, 16, -14, -32, -147],277,11]
%
% END OF LATTICE L278.11
%
%
% LATTICE L278.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[448, 0, 0; 0, -8, 8; 0, 8, -7],[448, 8, 1],[-125, -9, -22, -27, -7, -225, -8, -12, -5, -99, -5, -6, -1, 0, 1, 0, -2, -3; -840, -58, -133, -147, -36, -1120, -37, -49, -17, -280, -12, -7, 7, 1, 0, -3, -21, -23; -2016, -142, -336, -392, -99, -3136, -108, -154, -60, -1120, -54, -56, 0, 1, 0, -4, -42, -52],277,12]
%
% END OF LATTICE L278.12
%
%
% LATTICE L278.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-650272, 0, 4032; 0, 16, 0; 4032, 0, -25],[224, 16, 1],[-103, -60, -149, -187, -98, -99, -57, -87, -37, -93, -38, -47, -9, 0, 1, 1, -11, -19; -126, -71, -168, -196, -99, -98, -54, -77, -30, -70, -27, -28, 0, 1, 0, -2, -21, -26; -16730, -9744, -24192, -30352, -15904, -16065, -9248, -14112, -6000, -15078, -6160, -7616, -1456, 0, 161, 160, -1792, -3088],277,13]
%
% END OF LATTICE L278.13
%
%
% LATTICE L278.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-537376, -28224, 3360; -28224, -1456, 176; 3360, 176, -21],[224, 16, 1],[-198, -98, -187, -149, -60, -103, -19, -11, 1, 2, 0, -9, -47, -38, -93, -37, -87, -57; -763, -379, -728, -588, -239, -413, -78, -49, 2, 7, 1, -28, -168, -139, -343, -138, -329, -218; -38234, -18936, -36176, -28896, -11656, -20034, -3712, -2184, 176, 378, 8, -1680, -8960, -7272, -17822, -7104, -16744, -10992],277,14]
%
% END OF LATTICE L278.14
%
%
% LATTICE L278.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-448, -2688, 448; -2688, 686, -84; 448, -84, 9],[448, 14, 1],[5, 5, 3, 3, 13, 65, 19, 5, 9, 59, 23, 5, 1, 1, -1, -3, -1, -1; 32, 54, 38, 41, 181, 912, 270, 72, 131, 864, 338, 74, 15, 15, -16, -46, -16, -19; -96, 182, 180, 218, 987, 5024, 1512, 410, 756, 5024, 1974, 436, 90, 91, -96, -280, -102, -140],277,15]
%
% END OF LATTICE L278.15
%
%
% LATTICE L278.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-21952, -5824, 896; -5824, -1330, 210; 896, 210, -33],[448, 14, 1],[-101, -25, -17, -10, -71, -161, -39, -4, -11, -59, -10, -3, 0, 1, 1, -1, -1, -9; -1856, -458, -310, -181, -1280, -2896, -698, -71, -193, -1024, -172, -50, 1, 20, 16, -22, -19, -167; -14656, -3619, -2452, -1434, -10150, -22976, -5544, -565, -1540, -8192, -1379, -404, 6, 154, 128, -168, -149, -1316],277,16]
%
% END OF LATTICE L278.16
%
%
% LATTICE L278.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1316896, -56448, 8512; -56448, -2380, 364; 8512, 364, -55],[224, 28, 1],[41, 155, 49, 51, 169, 23, 81, 7, 29, 7, 13, -1, -3, -1, 1, 15, 5, 67; 128, 478, 148, 148, 478, 64, 216, 17, 56, 8, -2, -12, -12, -2, 4, 56, 17, 216; 7166, 27048, 8528, 8832, 29176, 3963, 13888, 1188, 4816, 1122, 1960, -240, -544, -168, 181, 2688, 884, 11760],277,17]
%
% END OF LATTICE L278.17
%
%
% LATTICE L278.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-71904, 26432, -2016; 26432, -9604, 728; -2016, 728, -55],[224, 28, 1],[59, 113, 73, 79, 134, 37, 135, 25, 59, 17, 20, 3, -3, -1, 1, 17, 13, 93; 436, 833, 536, 576, 973, 268, 972, 178, 412, 116, 133, 16, -24, -7, 8, 132, 98, 692; 3582, 6832, 4384, 4688, 7896, 2171, 7840, 1424, 3248, 898, 1008, 96, -208, -56, 69, 1120, 816, 5712],277,18]
%
% END OF LATTICE L278.18
%
%
% LATTICE L278.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-489440, -128576, 4480; -128576, -33656, 1176; 4480, 1176, -41],[224, 56, 1],[133, 126, 20, 21, 140, 153, 17, 12, 13, 27, 14, 0, -1, 0, 7, 3, 8, 27; 104, 97, 15, 15, 97, 104, 11, 7, 6, 8, 1, -1, -1, 1, 8, 3, 7, 22; 17456, 16492, 2606, 2714, 18004, 19616, 2163, 1504, 1582, 3152, 1540, -30, -138, 28, 992, 413, 1072, 3570],277,19]
%
% END OF LATTICE L278.19
%
%
% LATTICE L278.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-224, 448, 0; 448, 2296, -56; 0, -56, 1],[224, 56, 1],[-161, -142, -10, -17, -100, -101, -18, -4, -1, 1, 2, 0, -3, -40, -59, -22, -16, -39; -112, -99, -7, -12, -71, -72, -13, -3, -1, 0, 1, 0, -2, -27, -40, -15, -11, -27; -5840, -5152, -363, -618, -3640, -3680, -658, -148, -42, 16, 56, -1, -110, -1456, -2144, -798, -580, -1414],277,20]
%
% END OF LATTICE L278.20
%
%
% LATTICE L278.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-23406656, 3901184, -24192; 3901184, -650208, 4032; -24192, 4032, -25],[448, 32, 1],[-40, -49, -65, -89, -97, -50, -30, -97, -22, -58, -49, -33, -9, -1, 1, 2, -1, -6; -343, -414, -539, -721, -778, -399, -237, -756, -169, -441, -370, -245, -63, -6, 7, 13, -28, -55; -16730, -19488, -24192, -30352, -31808, -16065, -9248, -28224, -6000, -15078, -12320, -7616, -1456, 0, 161, 160, -3584, -3088],277,21]
%
% END OF LATTICE L278.21
%
%
% LATTICE L278.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[11200, 1792, 0; 1792, 288, 0; 0, 0, -1],[448, 32, 1],[1, 1, -1, -13, -23, -29, -12, -59, -20, -71, -71, -69, -57, -47, -41, -8, -11, 0; -7, -6, 7, 77, 134, 168, 69, 336, 113, 399, 398, 385, 315, 258, 224, 43, 56, -1; -14, 0, 0, -112, -224, -294, -128, -672, -240, -882, -896, -896, -784, -672, -602, -128, -224, -16],277,22]
%
% END OF LATTICE L278.22
%
%
% LATTICE L278.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[448, 0, 0; 0, -1400, -616; 0, -616, -271],[448, 56, 1],[0, 1, 0, -1, -27, -5, -15, -11, -27, -7, -99, -7, -6, -71, -9, -13, -3, -1; -4, 0, 7, 17, 280, 42, 90, 36, 34, 0, -56, -11, -21, -336, -50, -106, -44, -50; 9, 0, -16, -40, -672, -102, -224, -96, -112, -9, 0, 16, 40, 672, 102, 224, 96, 112],277,23]
%
% END OF LATTICE L278.23
%
%
% LATTICE L278.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[53312, -3584, -896; -3584, -56, 56; -896, 56, 15],[448, 56, 1],[223, 50, 29, 26, 79, 163, 31, 4, 4, 1, -1, -1, 2, 19, 61, 25, 10, 52; -160, -36, -21, -19, -58, -120, -23, -3, -3, 0, 1, 1, -1, -12, -40, -17, -7, -37; 13824, 3101, 1800, 1616, 4914, 10144, 1932, 250, 252, 64, -63, -64, 120, 1162, 3744, 1540, 618, 3220],277,24]
%
% END OF LATTICE L278.24
%
%
% LATTICE L278.25
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-263648, 0, 3808; 0, 112, 0; 3808, 0, -55],[224, 112, 1],[1, 0, -3, -5, -14, -3, -1, 3, 27, 9, 70, 23, 25, 84, 23, 41, 7, 13; 0, 1, 0, -4, -27, -10, -30, -11, -54, -14, -99, -28, -24, -71, -18, -26, -3, -2; 69, 0, -208, -352, -1008, -222, -112, 192, 1792, 603, 4704, 1552, 1696, 5712, 1566, 2800, 480, 896],277,25]
%
% END OF LATTICE L278.25
%
%
% LATTICE L278.26
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-118496, -104384, 1792; -104384, -90832, 1568; 1792, 1568, -27],[224, 112, 1],[-3, -14, -5, -3, 0, 2, 13, 7, 41, 23, 84, 25, 23, 70, 18, 27, 3, -1; -7, -27, -8, -4, 1, 3, 18, 9, 50, 27, 97, 28, 24, 69, 17, 22, 1, -10; -614, -2520, -800, -432, 56, 306, 1904, 984, 5600, 3078, 11144, 3264, 2896, 8568, 2158, 3024, 248, -672],277,26]
%
% END OF LATTICE L278.26
%
%
% LATTICE L278.27
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[448, 0, 0; 0, -263648, 3808; 0, 3808, -55],[448, 224, 1],[0, 1, 0, -2, -27, -5, -15, -11, -27, -7, -99, -14, -12, -71, -9, -13, -3, -1; 1, 0, -3, -5, -28, -3, -1, 6, 27, 9, 140, 23, 25, 168, 23, 41, 14, 13; 69, 0, -208, -352, -2016, -222, -112, 384, 1792, 603, 9408, 1552, 1696, 11424, 1566, 2800, 960, 896],277,27]
%
% END OF LATTICE L278.27
%
%
% LATTICE L278.28
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[448, 0, 0; 0, -181216, -44352; 0, -44352, -10855],[448, 224, 1],[-9, -71, -12, -14, -99, -14, -27, -11, -15, -5, -27, -2, 0, 1, 0, -1, -3, -13; -2, 168, 75, 173, 1540, 243, 577, 306, 549, 222, 1372, 145, 47, 0, -23, -137, -86, -109; 10, -672, -304, -704, -6272, -990, -2352, -1248, -2240, -906, -5600, -592, -192, 0, 94, 560, 352, 448],277,28]
%
% END OF LATTICE L278.28
%

\medskip%
%------------------------------WEYL-GROUP-W279--------------------------------
%
\leavevmode\llap{}%
$W_{279}$%
\qquad\llap{8} lattices, $\chi=36$%
\hfill%
$222|2224\slashtwo4\rtimes D_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L279.1
%
\leavevmode%
${L_{279.1}}$%
{} : {$1\above{1pt}{1pt}{2}{2}32\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{2}{}5\above{1pt}{1pt}{1}{}$}\EasyButWeakLineBreak%
{${2}\above{1pt}{1pt}{b}{2}{32}\above{1pt}{1pt}{*}{2}{20}\above{1pt}{1pt}{s}{2}{32}\above{1pt}{1pt}{l}{2}{5}\above{1pt}{1pt}{}{2}{32}\above{1pt}{1pt}{r}{2}{2}\above{1pt}{1pt}{*}{4}{4}\above{1pt}{1pt}{l}{2}{1}\above{1pt}{1pt}{}{4}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-5553120\\-2770080\\18240
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2770080\\-1381807\\9098
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
18240\\9098\\-59
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
66\\-133\\-105
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
135\\-272\\-208
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-263\\530\\420
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1723\\3472\\2720
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2124\\4280\\3345
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-18993\\38272\\29888
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3919\\7897\\6165
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-931\\1876\\1462
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-67\\135\\104
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-5553120, -2770080, 18240; -2770080, -1381807, 9098; 18240, 9098, -59],[480, 1, 1],[66, 135, -263, -1723, -2124, -18993, -3919, -931, -67; -133, -272, 530, 3472, 4280, 38272, 7897, 1876, 135; -105, -208, 420, 2720, 3345, 29888, 6165, 1462, 104],278,1]
%
% END OF LATTICE L279.1
%
%
% LATTICE L279.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1376160, -682560, -122880; -682560, -338541, -60927; -122880, -60927, -10618],[480, 3, 1],[-649, -1241, 2597, 16597, 20351, 181663, 37456, 8863, 621; 1322, 2528, -5290, -33808, -41455, -370048, -76298, -18054, -1265; -75, -144, 300, 1920, 2355, 21024, 4335, 1026, 72],278,2]
%
% END OF LATTICE L279.2
%
%
% LATTICE L279.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-578400, -284640, 24960; -284640, -140075, 12275; 24960, 12275, -1006],[480, 5, 1],[189, 343, -151, -4731, -1155, -51473, -10606, -2501, -171; -388, -704, 310, 9712, 2371, 105664, 21772, 5134, 351; -45, -80, 36, 1120, 273, 12160, 2505, 590, 40],278,3]
%
% END OF LATTICE L279.3
%
%
% LATTICE L279.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-114720, -10560, -11040; -10560, -885, -930; -11040, -930, -977],[480, 15, 1],[34, 169, 4, 19, 1, 1, -1, 0, 7; 6157, 30720, 733, 3552, 196, 240, -193, -16, 1238; -6255, -31200, -744, -3600, -198, -240, 195, 15, -1260],278,4]
%
% END OF LATTICE L279.4
%
%
% LATTICE L279.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-960, 7200, -480; 7200, -53728, 3584; -480, 3584, -239],[480, 32, 1],[-1, -1, 2, 6, 137, 40, 269, 35, 8; 2, 0, -5, -3, -55, -15, -98, -11, -1; 32, 2, -80, -58, -1120, -311, -2048, -240, -32],278,5]
%
% END OF LATTICE L279.5
%
%
% LATTICE L279.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-50867520, -2865120, 318720; -2865120, -161184, 17952; 318720, 17952, -1997],[480, 96, 1],[-35, -5, 86, 76, 1531, 431, 2855, 345, 56; 2, 0, -5, -3, -55, -15, -98, -11, -1; -5568, -798, 13680, 12102, 243840, 68649, 454752, 54960, 8928],278,6]
%
% END OF LATTICE L279.6
%
%
% LATTICE L279.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-21501120, -2404320, 224640; -2404320, -268640, 25120; 224640, 25120, -2347],[480, 160, 1],[3393, 511, 361, 88, 18, -7, -37, 72, 415; -98, -15, -11, -3, -1, 0, 2, -1, -11; 323680, 48745, 34432, 8390, 1712, -670, -3520, 6880, 39600],278,7]
%
% END OF LATTICE L279.7
%
%
% LATTICE L279.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-805920, 13662240, 60960; 13662240, -231504960, -1032960; 60960, -1032960, -4609],[480, 480, 1],[-98, -15, -11, -3, -1, 0, 2, -1, -11; 6083, 911, 635, 148, 22, -17, -47, 152, 765; -1364640, -204375, -142464, -33210, -4944, 3810, 10560, -34080, -171600],278,8]
%
% END OF LATTICE L279.8
%

\medskip%
%------------------------------WEYL-GROUP-W280--------------------------------
%
\leavevmode\llap{}%
$W_{280}$%
\qquad\llap{8} lattices, $\chi=16$%
\hfill%
$222622$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L280.1
%
\leavevmode%
${L_{280.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}32\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{-}{}$}\EasyButWeakLineBreak%
{${96}\above{1pt}{1pt}{r}{2}{10}\above{1pt}{1pt}{b}{2}{96}\above{1pt}{1pt}{b}{2}{2}\above{1pt}{1pt}{}{6}{6}\above{1pt}{1pt}{b}{2}{2}\above{1pt}{1pt}{l}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-24512160\\61440\\30720
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
61440\\-154\\-77
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
30720\\-77\\-38
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
13\\5184\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\800\\-5
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5\\2016\\-48
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\4\\-9
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-399\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\-1\\2
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-24512160, 61440, 30720; 61440, -154, -77; 30720, -77, -38],[480, 1, 1],[13, 2, 5, 0, -1, 0; 5184, 800, 2016, 4, -399, -1; 0, -5, -48, -9, 0, 2],279,1]
%
% END OF LATTICE L280.1
%
%
% LATTICE L280.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[936480, -50880, 6720; -50880, -786, 249; 6720, 249, -58],[480, 3, 1],[-185, -16, 15, 6, -7, -32; -14400, -1245, 1168, 467, -545, -2491; -83264, -7200, 6752, 2700, -3151, -14403],279,2]
%
% END OF LATTICE L280.2
%
%
% LATTICE L280.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-26404853280, -685020480, -68952960; -685020480, -17771470, -1788845; -68952960, -1788845, -180062],[480, 5, 1],[65, 3, 73, 9, -5, -2; -1056, -64, -1920, -284, 81, 63; -14400, -513, -8880, -625, 1110, 140],279,3]
%
% END OF LATTICE L280.3
%
%
% LATTICE L280.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[258720, -27840, -36960; -27840, -3930, -17895; -36960, -17895, -63794],[480, 15, 1],[12039, 208, -977, -390, 456, 2083; 193024, 3335, -15664, -6253, 7311, 33397; -61120, -1056, 4960, 1980, -2315, -10575],279,4]
%
% END OF LATTICE L280.4
%
%
% LATTICE L280.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-34739520, -206880, 14100000; -206880, -1216, 83968; 14100000, 83968, -5722877],[480, 32, 1],[442, 2208, 358, 52, -1091, -13; 0, -5, -3, -9, 0, 2; 1089, 5440, 882, 128, -2688, -32],279,5]
%
% END OF LATTICE L280.5
%
%
% LATTICE L280.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-363387840, -85106400, -179927040; -85106400, -19932096, -42139392; -179927040, -42139392, -89088671],[480, 96, 1],[2543, 2379, -611, -761, 4912, 16306; -2, -10, 0, 2, -1, -9; -5135, -4800, 1234, 1536, -9920, -32928],279,6]
%
% END OF LATTICE L280.6
%
%
% LATTICE L280.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-622309440, -1957920, 1932480; -1957920, -6080, 6080; 1932480, 6080, -6001],[480, 160, 1],[32, 32, 26, 4, -79, -1; 0, -1, -3, -9, 0, 2; 10305, 10304, 8370, 1280, -25440, -320],279,7]
%
% END OF LATTICE L280.7
%
%
% LATTICE L280.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-99660480, -28276320, 3241440; -28276320, -8022720, 919680; 3241440, 919680, -105427],[480, 480, 1],[-2, -2, 0, 2, -1, -9; -240, -81, 47, 103, -400, -1454; -2155, -768, 410, 960, -3520, -12960],279,8]
%
% END OF LATTICE L280.8
%

\medskip%
%------------------------------WEYL-GROUP-W281--------------------------------
%
\leavevmode\llap{}%
$W_{281}$%
\qquad\llap{12} lattices, $\chi=48$%
\hfill%
$2|222|222|222|22\rtimes D_{4}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L281.1
%
\leavevmode%
${L_{281.1}}$%
{} : {$1\above{1pt}{1pt}{2}{6}32\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{-}{}9\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{3}%
\EasyButWeakLineBreak%
{${288}\above{1pt}{1pt}{r}{2}{6}\above{1pt}{1pt}{b}{2}{32}\above{1pt}{1pt}{*}{2}{60}\above{1pt}{1pt}{s}{2}{288}\above{1pt}{1pt}{l}{2}{15}\above{1pt}{1pt}{}{2}{32}\above{1pt}{1pt}{r}{2}{6}\above{1pt}{1pt}{b}{2}{288}\above{1pt}{1pt}{*}{2}{60}\above{1pt}{1pt}{s}{2}{32}\above{1pt}{1pt}{l}{2}{15}\above{1pt}{1pt}{}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1859040\\-8640\\-10080
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-8640\\6\\-3
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-10080\\-3\\-13
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
11\\10368\\-10944
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\-1\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-944\\992
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-940\\990
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\960\\-1008
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\1895\\-1995
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7\\6624\\-6976
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\1891\\-1992
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
35\\33072\\-34848
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
11\\10390\\-10950
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5\\4720\\-4976
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\2830\\-2985
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-1859040, -8640, -10080; -8640, 6, -3; -10080, -3, -13],[1440, 3, 1],[11, 0, -1, -1, 1, 2, 7, 2, 35, 11, 5, 3; 10368, -1, -944, -940, 960, 1895, 6624, 1891, 33072, 10390, 4720, 2830; -10944, 0, 992, 990, -1008, -1995, -6976, -1992, -34848, -10950, -4976, -2985],280,1]
%
% END OF LATTICE L281.1
%
%
% LATTICE L281.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[80160, 960, -1920; 960, -1, -3; -1920, -3, 14],[480, 1, 1],[3, 1, 5, 2, 1, -1, -3, -1, -5, -2, -1, 1; 992, 330, 1632, 645, 304, -390, -1056, -342, -1696, -675, -336, 330; 624, 207, 1024, 405, 192, -240, -656, -213, -1056, -420, -208, 210],280,2]
%
% END OF LATTICE L281.2
%
%
% LATTICE L281.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[455520, 47040, -960; 47040, 4857, -99; -960, -99, 2],[480, 3, 1],[-3, 0, 11, 3, 15, 11, 35, 2, 21, 2, 1, -1; 32, 0, -128, -35, -176, -130, -416, -24, -256, -25, -16, 10; 144, -1, -1056, -290, -1488, -1130, -3696, -221, -2496, -265, -288, 20],280,3]
%
% END OF LATTICE L281.3
%
%
% LATTICE L281.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[9120, 1440, 0; 1440, 215, 5; 0, 5, -2],[480, 5, 1],[-5, 1, 45, 7, 57, 25, 133, 23, 83, 5, 7, -1; 32, -6, -288, -45, -368, -162, -864, -150, -544, -33, -48, 6; 80, -15, -800, -126, -1040, -462, -2480, -435, -1600, -99, -160, 12],280,4]
%
% END OF LATTICE L281.4
%
%
% LATTICE L281.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-590880, -298560, 2880; -298560, -150855, 1455; 2880, 1455, -14],[480, 15, 1],[-15, 2, 215, 11, 267, 39, 623, 36, 393, 8, 37, -1; 32, -4, -448, -23, -560, -82, -1312, -76, -832, -17, -80, 2; 240, -5, -2400, -131, -3360, -512, -8400, -505, -5760, -124, -720, 2],280,5]
%
% END OF LATTICE L281.5
%
%
% LATTICE L281.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[480, 0, 0; 0, -1312, 96; 0, 96, -7],[480, 32, 1],[0, -1, -1, -11, -1, -16, -1, -5, -1, -4, 0, 1; 1, 15, 7, 60, 4, 45, 2, 3, -1, -15, -1, 0; 13, 192, 86, 720, 46, 480, 19, 0, -22, -240, -14, 0],280,6]
%
% END OF LATTICE L281.6
%
%
% LATTICE L281.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-5286240, 148320, 27360; 148320, -3930, -735; 27360, -735, -137],[1440, 15, 1],[-227, -12, -39, -2, -1, 1, 1, -2, -107, -5, -37, -15; 26160, 1381, 4480, 229, 96, -116, -112, 233, 12384, 578, 4272, 1730; -185760, -9810, -31840, -1629, -720, 822, 800, -1650, -87840, -4101, -30320, -12282],280,7]
%
% END OF LATTICE L281.7
%
%
% LATTICE L281.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-82508640, 583680, 515520; 583680, -3936, -3648; 515520, -3648, -3221],[480, 96, 1],[19, -5, -22, -176, -49, -251, -89, -65, -13, 1, 14, 76; 21, 1, -17, -145, -42, -220, -79, -59, -12, 0, 13, 75; 3018, -800, -3501, -28000, -7794, -39920, -14154, -10336, -2067, 160, 2226, 12080],280,8]
%
% END OF LATTICE L281.8
%
%
% LATTICE L281.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-153120, -16800, -2880; -16800, 2240, 480; -2880, 480, 101],[480, 160, 1],[1, 20, 12, 23, 9, 25, 7, 28, 4, 1, -1, -1; -75, -1497, -895, -1713, -669, -1854, -518, -2061, -291, -66, 76, 75; 385, 7680, 4590, 8784, 3430, 9504, 2655, 10560, 1490, 336, -390, -384],280,9]
%
% END OF LATTICE L281.9
%
%
% LATTICE L281.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-9493920, -1899360, 642240; -1899360, -379968, 128448; 642240, 128448, -43367],[1440, 96, 1],[-26, -390, -544, -1551, -103, -1151, -152, -70, 28, 401, 79, 1; 156, 2339, 3261, 9295, 617, 6890, 909, 415, -169, -2410, -474, -5; 77, 1152, 1602, 4560, 302, 3360, 441, 192, -86, -1200, -234, 0],280,10]
%
% END OF LATTICE L281.10
%
%
% LATTICE L281.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-19680, 27360, 1920; 27360, -12480, -960; 1920, -960, -73],[480, 480, 1],[17, 26, 14, 3, -1, -1, 1, 10, 22, 15, 19, 19; -244, -375, -203, -44, 14, 15, -13, -139, -311, -213, -271, -272; 3645, 5600, 3030, 656, -210, -224, 195, 2080, 4650, 3184, 4050, 4064],280,11]
%
% END OF LATTICE L281.11
%
%
% LATTICE L281.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1902240, -671040, -5760; -671040, -233760, -1440; -5760, -1440, 101],[1440, 480, 1],[931, 519, 26, -26, -79, 23, 101, 715, 539, 643, 232, 594; -2757, -1537, -77, 77, 234, -68, -299, -2117, -1596, -1904, -687, -1759; 13770, 7680, 385, -384, -1170, 336, 1490, 10560, 7965, 9504, 3430, 8784],280,12]
%
% END OF LATTICE L281.12
%

\medskip%
%------------------------------WEYL-GROUP-W282--------------------------------
%
\leavevmode\llap{}%
$W_{282}$%
\qquad\llap{12} lattices, $\chi=48$%
\hfill%
$2|222|222|222|22\rtimes D_{4}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L282.1
%
\leavevmode%
${L_{282.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{6}32\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{1}{}3\above{1pt}{1pt}{-}{}9\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{3}%
\EasyButWeakLineBreak%
{${160}\above{1pt}{1pt}{b}{2}{6}\above{1pt}{1pt}{l}{2}{1440}\above{1pt}{1pt}{}{2}{1}\above{1pt}{1pt}{r}{2}{1440}\above{1pt}{1pt}{s}{2}{4}\above{1pt}{1pt}{*}{2}{1440}\above{1pt}{1pt}{b}{2}{6}\above{1pt}{1pt}{l}{2}{160}\above{1pt}{1pt}{}{2}{9}\above{1pt}{1pt}{r}{2}{160}\above{1pt}{1pt}{s}{2}{36}\above{1pt}{1pt}{*}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
32142240\\-10710720\\-34560
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-10710720\\3569118\\11517
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-34560\\11517\\37
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
27\\80\\320
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
55\\163\\636
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5831\\17280\\67680
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
82\\243\\953
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
8099\\24000\\94320
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
463\\1372\\5398
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
41711\\123600\\486720
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1251\\3707\\14604
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
11987\\35520\\140000
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
407\\1206\\4761
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
783\\2320\\9200
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-83\\-246\\-954
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[32142240, -10710720, -34560; -10710720, 3569118, 11517; -34560, 11517, 37],[1440, 3, 1],[27, 55, 5831, 82, 8099, 463, 41711, 1251, 11987, 407, 783, -83; 80, 163, 17280, 243, 24000, 1372, 123600, 3707, 35520, 1206, 2320, -246; 320, 636, 67680, 953, 94320, 5398, 486720, 14604, 140000, 4761, 9200, -954],281,1]
%
% END OF LATTICE L282.1
%
%
% LATTICE L282.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[627360, -5280, 960; -5280, 37, -3; 960, -3, -2],[480, 1, 1],[9, 1, -1, -1, -29, -3, -201, -19, -191, -5, -19, 0; 1440, 162, -160, -162, -4720, -489, -32800, -3102, -31200, -818, -3120, -1; 2080, 237, -240, -238, -6960, -722, -48480, -4587, -46160, -1212, -4640, -3],281,2]
%
% END OF LATTICE L282.2
%
%
% LATTICE L282.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-37920, 480, 480; 480, -6, -3; 480, -3, 119],[480, 3, 1],[231, 2, 1, -3, 109, 18, 1561, 54, 1791, 59, 339, 10; 18560, 161, 80, -242, 8720, 1442, 125120, 4329, 143600, 4732, 27200, 803; -480, -4, 0, 6, -240, -39, -3360, -116, -3840, -126, -720, -21],281,3]
%
% END OF LATTICE L282.3
%
%
% LATTICE L282.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2058720, 7200, 3840; 7200, -10, -15; 3840, -15, -7],[480, 5, 1],[9, 1, -1, -1, 3, 3, 55, 29, 65, 11, 13, 2; 416, 45, -48, -46, 144, 142, 2592, 1365, 3056, 516, 608, 93; 4032, 450, -448, -450, 1328, 1335, 24512, 12930, 28992, 4910, 5808, 895],281,4]
%
% END OF LATTICE L282.4
%
%
% LATTICE L282.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[582240, 3360, -3360; 3360, -30, -15; -3360, -15, 19],[480, 15, 1],[39, 2, 1, -3, 13, 12, 217, 38, 255, 43, 51, 8; 640, 33, 16, -50, 208, 194, 3520, 617, 4144, 700, 832, 131; 7392, 380, 192, -570, 2448, 2265, 40992, 7180, 48192, 8130, 9648, 1515],281,5]
%
% END OF LATTICE L282.5
%
%
% LATTICE L282.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-11078880, -1926720, 11040; -1926720, -335072, 1920; 11040, 1920, -11],[480, 32, 1],[1, 1, -2, -4, -11, -17, -69, -103, -32, -13, -6, 0; -5, -3, 10, 19, 50, 76, 305, 453, 140, 56, 25, -1; 130, 480, -265, -704, -2330, -3824, -16130, -24480, -7735, -3296, -1670, -176],281,6]
%
% END OF LATTICE L282.6
%
%
% LATTICE L282.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-234720, -76320, 1440; -76320, -24810, 465; 1440, 465, -7],[1440, 15, 1],[-49, 1, 19, 13, 15, 17, -5, -11, -121, -6, -61, -9; 144, -5, -64, -42, -48, -54, 16, 35, 384, 19, 192, 28; -864, -180, -448, -135, -112, -90, 32, 60, 576, 25, 144, -10],281,7]
%
% END OF LATTICE L282.7
%
%
% LATTICE L282.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-565440, -50400, -15360; -50400, -4128, -1248; -15360, -1248, -377],[480, 96, 1],[-52, -55, -109, -26, -16, -5, -2, 1, 1, -1, -11, -22; 7075, 7478, 14810, 3527, 2165, 671, 265, -138, -130, 143, 1505, 2999; -21285, -22496, -44550, -10608, -6510, -2016, -795, 416, 390, -432, -4530, -9024],281,8]
%
% END OF LATTICE L282.8
%
%
% LATTICE L282.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-4435680, -37920, 18720; -37920, -320, 160; 18720, 160, -79],[480, 160, 1],[-4, -62, -8, -9, -1, -1, 0, 2, 0, -1, -1, -9; -58, -933, -125, -154, -20, -37, -4, 3, 1, -1, -11, -118; -1079, -16800, -2178, -2480, -282, -320, -9, 480, 2, -240, -262, -2400],281,9]
%
% END OF LATTICE L282.9
%
%
% LATTICE L282.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-11695680, -1893600, 40320; -1893600, -306528, 6528; 40320, 6528, -139],[1440, 96, 1],[-367, -183, -57, -70, -11, -1, 1, 1, -11, -7, -58, -30; -120, -62, -20, -27, -5, -3, 0, 2, 0, -1, -15, -9; -112230, -56064, -17495, -21600, -3430, -432, 290, 384, -3195, -2080, -17550, -9136],281,10]
%
% END OF LATTICE L282.10
%
%
% LATTICE L282.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-960, -36960, 12480; -36960, -1403040, 473760; 12480, 473760, -159973],[480, 480, 1],[-4, 1, 1, -1, -11, -118, -58, -311, -125, -154, -20, -37; -9, 54, 2, -81, -103, -969, -443, -2314, -906, -1049, -123, -161; -27, 160, 6, -240, -306, -2880, -1317, -6880, -2694, -3120, -366, -480],281,11]
%
% END OF LATTICE L282.11
%
%
% LATTICE L282.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2880, -344160, 1440; -344160, -41069280, 171840; 1440, 171840, -719],[1440, 480, 1],[-383, -951, -59, -358, -11, -1, 1, 1, -13, -39, -62, -158; -24, -62, -4, -27, -1, -3, 0, 2, 0, -1, -3, -9; -6534, -16800, -1079, -7200, -262, -720, 2, 480, -27, -320, -846, -2480],281,12]
%
% END OF LATTICE L282.12
%

\medskip%
%------------------------------WEYL-GROUP-W283--------------------------------
%
\leavevmode\llap{}%
$W_{283}$%
\qquad\llap{8} lattices, $\chi=36$%
\hfill%
$\infty\infty3\infty26$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L283.1
%
\leavevmode%
${L_{283.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}8\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{-}{}81\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${6}\above{1pt}{1pt}{36,35}{\infty b}{24}\above{1pt}{1pt}{18,5}{\infty z}{6}\above{1pt}{1pt}{-}{3}{6}\above{1pt}{1pt}{36,23}{\infty a}{24}\above{1pt}{1pt}{b}{2}{2}\above{1pt}{1pt}{}{6}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-669384\\6480\\-648
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
6480\\-30\\-3
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-648\\-3\\2
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4\\635\\2250
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\476\\1692
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\158\\567
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\-1\\3
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-160\\-564
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\-1
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-669384, 6480, -648; 6480, -30, -3; -648, -3, 2],[648, 3, 1],[4, 3, 1, 0, -1, 0; 635, 476, 158, -1, -160, 0; 2250, 1692, 567, 3, -564, -1],282,1]
%
% END OF LATTICE L283.1
%
%
% LATTICE L283.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[9558, 486, -1134; 486, 24, -57; -1134, -57, 134],[162, 3, 1],[-3, -1, 0, 1, 1, 0; -19, -8, 8, 23, 22, 2; -33, -12, 3, 18, 18, 1],282,2]
%
% END OF LATTICE L283.2
%
%
% LATTICE L283.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[134784, -5346, 66420; -5346, 192, -2634; 66420, -2634, 32731],[162, 6, 1],[177, -31, -186, -127, 28, 60; -11, 1, 7, 4, -2, -3; -360, 63, 378, 258, -57, -122],282,3]
%
% END OF LATTICE L283.3
%
%
% LATTICE L283.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[55543158, 109998, -695304; 109998, 216, -1377; -695304, -1377, 8704],[162, 27, 1],[70, 23, 1, -21, -21, 1; -19, -8, 8, 23, 22, 6; 5589, 1836, 81, -1674, -1674, 81],282,4]
%
% END OF LATTICE L283.4
%
%
% LATTICE L283.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[291527424, 857142, 143917884; 857142, 1728, 423144; 143917884, 423144, 71047715],[162, 54, 1],[59181, -8304, -49824, -30097, 11423, 56062; -11, 1, 7, 4, -2, -9; -119880, 16821, 100926, 60966, -23139, -113562],282,5]
%
% END OF LATTICE L283.5
%
%
% LATTICE L283.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[193224528, 18961128, -1044576; 18961128, 1860528, -102504; -1044576, -102504, 5647],[648, 24, 1],[-68, -25, 25, 119, 69, 21; -25, -10, 11, 50, 29, 9; -13032, -4806, 4824, 22920, 13290, 4048],282,6]
%
% END OF LATTICE L283.6
%
%
% LATTICE L283.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-182088, 7128, 648; 7128, -270, -27; 648, -27, -2],[648, 27, 1],[6, 3, 0, -1, -1, 1; 95, 44, -4, -19, -16, 18; 594, 324, 27, -81, -108, 81],282,7]
%
% END OF LATTICE L283.7
%
%
% LATTICE L283.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[406872720, 37247688, -677160; 37247688, 3408912, -61992; -677160, -61992, 1127],[648, 216, 1],[-406, -91, -157, -33, 33, 41; 131, 29, 50, 11, -10, -12; -236736, -53082, -91584, -19224, 19278, 23976],282,8]
%
% END OF LATTICE L283.8
%

\medskip%
%------------------------------WEYL-GROUP-W284--------------------------------
%
\leavevmode\llap{}%
$W_{284}$%
\qquad\llap{8} lattices, $\chi=72$%
\hfill%
$2\infty\infty\infty22\infty\infty\infty2\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L284.1
%
\leavevmode%
${L_{284.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}8\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{1}{}3\above{1pt}{1pt}{-}{}81\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${162}\above{1pt}{1pt}{s}{2}{6}\above{1pt}{1pt}{36,19}{\infty b}{24}\above{1pt}{1pt}{18,13}{\infty z}{6}\above{1pt}{1pt}{36,31}{\infty a}{24}\above{1pt}{1pt}{b}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-679752\\361584\\-213192
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
361584\\-180210\\101043
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-213192\\101043\\-54266
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-285698017\\-1274348376\\-1250420328
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
133304292\\594600236\\583435611
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-70578468\\-314813373\\-308902220
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3868\\17253\\16929
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1266\\-5647\\-5541
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-14663\\-65404\\-64176
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-33826\\-150880\\-148047
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1431831\\-6386644\\-6266724
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-679752, 361584, -213192; 361584, -180210, 101043; -213192, 101043, -54266],[648, 3, 1],[3868, -1266, -14663, -33826, -1431831, -3864652, -356214, -128329, -1922, 1911; 17253, -5647, -65404, -150880, -6386644, -17238177, -1588883, -572408, -8573, 8524; 16929, -5541, -64176, -148047, -6266724, -16914501, -1559049, -561660, -8412, 8364],283,1]
%
% END OF LATTICE L284.1
%
%
% LATTICE L284.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-113562, 42768, -7938; 42768, -16104, 2991; -7938, 2991, -554],[162, 3, 1],[26, -28, -115, -495, -10337, -55754, -5132, -917, -21, 17; 54, -56, -232, -1001, -20914, -112806, -10384, -1856, -43, 34; -81, 99, 396, 1692, 35280, 190269, 17511, 3126, 69, -60],283,2]
%
% END OF LATTICE L284.2
%
%
% LATTICE L284.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[19963260, 269730, 9903222; 269730, 3648, 133806; 9903222, 133806, 4912715],[162, 6, 1],[80, 638, 1693, 16209, 173054, 1869400, 172462, 15617, 1101, 46; 27, 143, 374, 3572, 38120, 411777, 37987, 3439, 241, 10; -162, -1290, -3423, -32772, -349887, -3779622, -348690, -31575, -2226, -93],283,3]
%
% END OF LATTICE L284.3
%
%
% LATTICE L284.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-105138, 12150, 6318; 12150, -1404, -729; 6318, -729, -364],[162, 27, 1],[2207, 5505, 1005, 42, -3, -3, 5, 97, 509, 11023; 19743, 49247, 8992, 377, -26, -27, 43, 866, 4552, 98606; -1298, -3240, -594, -27, 0, 2, 0, -54, -297, -6480],283,4]
%
% END OF LATTICE L284.4
%
%
% LATTICE L284.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[428328, 484542, 213516; 484542, 548964, 241542; 213516, 241542, 106435],[162, 54, 1],[155549, 387513, 35121, 2529, 120, -1, 1357, 3766, 36358, 388750; 1560, 3886, 352, 25, 1, 0, 14, 38, 365, 3899; -315578, -786186, -71253, -5130, -243, 2, -2754, -7641, -73764, -788697],283,5]
%
% END OF LATTICE L284.5
%
%
% LATTICE L284.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-113053968, -46886040, 13176432; -46886040, -19444560, 5464464; 13176432, 5464464, -1535641],[648, 24, 1],[3876701, 356623, 31746, 1253, -623, -689, 2267, 4143, 34636, 359513; -15505506, -1426372, -126973, -5011, 2492, 2754, -9068, -16571, -138533, -1437932; -21911472, -2015664, -179430, -7080, 3522, 3888, -12816, -23418, -195768, -2032002],283,6]
%
% END OF LATTICE L284.6
%
%
% LATTICE L284.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-265032, 18144, 9072; 18144, -1242, -621; 9072, -621, -310],[648, 27, 1],[0, 2, 11, 20, 803, 80, 198, 69, 0, -3; -1, 29, 212, 434, 17924, 1789, 4441, 1576, 13, -44; 2, 0, -108, -297, -12960, -1298, -3240, -1188, -27, 0],283,7]
%
% END OF LATTICE L284.7
%
%
% LATTICE L284.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1797552, -5688792, 339025176; -5688792, -16326576, 972723168; 339025176, 972723168, -57953952785],[648, 216, 1],[-8713, 29245, 166627, 1691806, 18219547, 7293317, 18182265, 1654524, 129345, -8037; 1045909, -3510583, -20001934, -203084647, -2187077095, -875490841, -2182601747, -198609299, -15526586, 964765; 17504, -58752, -334746, -3398760, -36602226, -14651936, -36527328, -3323862, -259848, 16146],283,8]
%
% END OF LATTICE L284.8
%

\medskip%
%------------------------------WEYL-GROUP-W285--------------------------------
%
\leavevmode\llap{}%
$W_{285}$%
\qquad\llap{4} lattices, $\chi=72$%
\hfill%
$\infty|\infty|\infty|\infty|\infty|\infty|\infty|\infty|\rtimes D_{8}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L285.1
%
\leavevmode%
${L_{285.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{4}4\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{-}{}5\above{1pt}{1pt}{1}{}25\above{1pt}{1pt}{-}{}$}\EasyButWeakLineBreak%
{${20}\above{1pt}{1pt}{5,2}{\infty a}{20}\above{1pt}{1pt}{10,3}{\infty}{20}\above{1pt}{1pt}{5,2}{\infty z}{5}\above{1pt}{1pt}{20,17}{\infty}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-8700\\-700\\2300
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-700\\-55\\185
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2300\\185\\-608
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-641\\160\\-2400
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-48\\11\\-180
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
168\\-42\\629
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
39\\4\\150
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
37\\-4\\140
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
51\\-16\\190
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
11\\-7\\40
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-8700, -700, 2300; -700, -55, 185; 2300, 185, -608],[100, 5, 1],[39, 37, 51, 11, 9, -5, -3, 5; 4, -4, -16, -7, -16, -4, 4, 3; 150, 140, 190, 40, 30, -20, -10, 20],284,1]
%
% END OF LATTICE L285.1
%
\hbox{}\par\smallskip%
%
% LATTICE L285.2
%
\leavevmode%
${L_{285.2}}$%
{} : {$1\above{1pt}{1pt}{2}{{\rm II}}8\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{1}{}5\above{1pt}{1pt}{-}{}25\above{1pt}{1pt}{1}{}$}\EasyButWeakLineBreak%
{${40}\above{1pt}{1pt}{5,1}{\infty b}{40}\above{1pt}{1pt}{5,2}{\infty}{40}\above{1pt}{1pt}{5,4}{\infty z}{10}\above{1pt}{1pt}{20,13}{\infty a}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1821400\\-14400\\10800
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-14400\\-110\\85
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
10800\\85\\-64
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3041\\-59280\\-592800
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-24\\-469\\-4680
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
18\\351\\3509
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
15\\304\\2940
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
17\\336\\3320
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
27\\524\\5260
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7\\133\\1360
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-1821400, -14400, 10800; -14400, -110, 85; 10800, 85, -64],[200, 5, 1],[15, 17, 27, 7, 9, -1, -3, 1; 304, 336, 524, 133, 164, -24, -56, 23; 2940, 3320, 5260, 1360, 1740, -200, -580, 200],284,2]
%
% END OF LATTICE L285.2
%
%
% LATTICE L285.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[300, -100, 100; -100, 80, -20; 100, -20, 37],[100, 20, 1],[32, 16, 50, 27, 22, 2, 4, 9; 23, 11, 33, 17, 13, 1, 3, 7; -70, -35, -110, -60, -50, -5, -10, -20],284,3]
%
% END OF LATTICE L285.3
%
%
% LATTICE L285.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-43200, -16200, 7000; -16200, -5920, 2560; 7000, 2560, -1107],[200, 40, 1],[9, 13, 7, 1, 0, -1, 2, 2; 638, 969, 548, 86, 13, -101, 103, 131; 1530, 2320, 1310, 205, 30, -240, 250, 315],284,4]
%
% END OF LATTICE L285.4
%

\medskip%
%------------------------------WEYL-GROUP-W286--------------------------------
%
\leavevmode\llap{}%
$W_{286}$%
\qquad\llap{1} lattice, $\chi=24$%
\hfill%
$\slashinfty|\slashinfty|\slashinfty|\slashinfty|\rtimes D_{8}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L286.1
%
\leavevmode%
${L_{286.1}}$%
{} : {$1\above{1pt}{1pt}{-}{5}8\above{1pt}{1pt}{1}{7}64\above{1pt}{1pt}{-}{5}$}\EasyButWeakLineBreak%
{${32}\above{1pt}{1pt}{16,3}{\infty z}{8}\above{1pt}{1pt}{8,5}{\infty b}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
6976\\768\\-192
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
768\\-8\\-16
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-192\\-16\\5
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-17\\-48\\-768
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
6\\17\\288
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\-1
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\2\\48
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-4\\-11\\-188
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[6976, 768, -192; 768, -8, -16; -192, -16, 5],[64, 8, 1],[1, -4, -5, 2; 2, -11, -14, 5; 48, -188, -240, 92],285,1]
%
% END OF LATTICE L286.1
%

\medskip%
%------------------------------WEYL-GROUP-W287--------------------------------
%
\leavevmode\llap{}%
$W_{287}$%
\qquad\llap{8} lattices, $\chi=60$%
\hfill%
$242|242|242|242|\rtimes D_{4}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L287.1
%
\leavevmode%
${L_{287.1}}$%
{} : {$1\above{1pt}{1pt}{2}{2}16\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{2}{}11\above{1pt}{1pt}{-}{}$}\EasyButWeakLineBreak%
{${66}\above{1pt}{1pt}{b}{2}{2}\above{1pt}{1pt}{*}{4}{4}\above{1pt}{1pt}{s}{2}{48}\above{1pt}{1pt}{l}{2}{1}\above{1pt}{1pt}{}{4}{2}\above{1pt}{1pt}{s}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2319504\\-584496\\14256
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-584496\\-147287\\3591
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
14256\\3591\\-86
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-599105\\2428800\\2100912
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-151108\\612599\\529899
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3848\\-15600\\-13495
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-749\\3036\\2607
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-38\\154\\131
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
37\\-150\\-130
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
77\\-312\\-264
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-128\\519\\452
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-331\\1342\\1165
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-2319504, -584496, 14256; -584496, -147287, 3591; 14256, 3591, -86],[528, 1, 1],[-749, -38, 37, 77, -128, -331, -2507, -554, -925, -1261, -316, -261; 3036, 154, -150, -312, 519, 1342, 10164, 2246, 3750, 5112, 1281, 1058; 2607, 131, -130, -264, 452, 1165, 8811, 1945, 3244, 4416, 1105, 911],286,1]
%
% END OF LATTICE L287.1
%
%
% LATTICE L287.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-170544, -68112, 2112; -68112, -27201, 843; 2112, 843, -26],[528, 3, 1],[-86, -57, -95, -43, -32, -26, -24, -3, 5, 3, -13, -34; 242, 160, 266, 120, 89, 72, 66, 8, -14, -8, 37, 96; 847, 549, 894, 392, 282, 219, 187, 15, -48, -16, 141, 345],286,2]
%
% END OF LATTICE L287.2
%
%
% LATTICE L287.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1019568, -31152, -32208; -31152, -946, -979; -32208, -979, -1013],[528, 11, 1],[7, 16, 25, 31, 7, 5, 1, 0, -1, 1, 5, 11; 1221, 2771, 4294, 5256, 1168, 813, 153, -23, -172, 240, 893, 1935; -1404, -3190, -4950, -6072, -1353, -946, -180, 22, 198, -264, -1023, -2222],286,3]
%
% END OF LATTICE L287.3
%
%
% LATTICE L287.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1030128, 33264, -44880; 33264, -992, 1488; -44880, 1488, -1937],[528, 16, 1],[-4594, -856, -587, -145, -199, -80, 62, 32, -31, -61, -419, -744; -36861, -6869, -4711, -1164, -1598, -643, 495, 257, -248, -489, -3361, -5969; 78144, 14560, 9984, 2466, 3384, 1360, -1056, -544, 528, 1038, 7128, 12656],286,4]
%
% END OF LATTICE L287.4
%
%
% LATTICE L287.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-705936, 188496, 15840; 188496, -50259, -4224; 15840, -4224, -355],[528, 33, 1],[0, -2, -4, -7, -19, -13, -2, -10, -5, -1, 1, 1; -7, -5, 54, 136, 438, 325, 53, 281, 153, 48, -24, -49; 83, -33, -825, -1936, -6072, -4455, -721, -3795, -2046, -616, 330, 627],286,5]
%
% END OF LATTICE L287.5
%
%
% LATTICE L287.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-309408, -230736, 15312; -230736, -171408, 11376; 15312, 11376, -755],[528, 48, 1],[-1, -3, -5, -1, -10, -13, -21, -9, -4, 0, 1, 1; -22, -152, -291, -63, -687, -944, -1606, -736, -375, -11, 21, 56; -352, -2352, -4488, -970, -10560, -14496, -24640, -11280, -5736, -166, 336, 864],286,6]
%
% END OF LATTICE L287.6
%
%
% LATTICE L287.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-218064, 852192, 25872; 852192, -3327632, -101024; 25872, -101024, -3067],[528, 176, 1],[-1, 1, 5, 4, 16, 23, 11, 19, 10, 1, -1, -3; -9, 43, 44, 3, -143, -331, -213, -487, -377, -114, -190, -113; 288, -1408, -1408, -66, 4840, 11088, 7104, 16192, 12496, 3762, 6248, 3696],286,7]
%
% END OF LATTICE L287.7
%
%
% LATTICE L287.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-32736, 573936, -17424; 573936, -10052592, 305184; -17424, 305184, -9265],[528, 528, 1],[-1, 1, 16, 5, 71, 111, 19, 107, 65, 4, 10, -3; -2, -32, 33, 21, 429, 760, 142, 872, 597, 49, 201, 80; -64, -1056, 1056, 682, 13992, 24816, 4640, 28512, 19536, 1606, 6600, 2640],286,8]
%
% END OF LATTICE L287.8
%

\medskip%
%------------------------------WEYL-GROUP-W288--------------------------------
%
\leavevmode\llap{}%
$W_{288}$%
\qquad\llap{12} lattices, $\chi=48$%
\hfill%
$3222632226\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L288.1
%
\leavevmode%
${L_{288.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{-}{}27\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}7\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${6}\above{1pt}{1pt}{-}{3}{6}\above{1pt}{1pt}{b}{2}{14}\above{1pt}{1pt}{b}{2}{54}\above{1pt}{1pt}{s}{2}{2}\above{1pt}{1pt}{}{6}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-52346196\\1488564\\-35532
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1488564\\-42330\\1011
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-35532\\1011\\-22
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1581929\\55269900\\-14999040
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-45036\\-1573481\\427008
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
891\\31130\\-8449
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-323\\-11285\\3066
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-583\\-20369\\5529
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-568\\-19845\\5383
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-619\\-21627\\5859
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-33\\-1153\\311
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-52346196, 1488564, -35532; 1488564, -42330, 1011; -35532, 1011, -22],[756, 3, 1],[-323, -583, -568, -619, -33, -1, 16, 1, -110, -48; -11285, -20369, -19845, -21627, -1153, -35, 559, 35, -3843, -1677; 3066, 5529, 5383, 5859, 311, 6, -153, -7, 1053, 457],287,1]
%
% END OF LATTICE L288.1
%
%
% LATTICE L288.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-11013030, -397278, 16065; -397278, -14331, 579; 16065, 579, -22],[189, 3, 1],[-1, 15, 1, -103, -45, -303, -547, -533, -581, -31; 28, -422, -28, 2898, 1266, 8524, 15388, 14994, 16344, 872; 6, -153, -7, 1053, 457, 3066, 5529, 5383, 5859, 311],287,2]
%
% END OF LATTICE L288.2
%
%
% LATTICE L288.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-542241, 13041, 144585; 13041, -306, -3537; 144585, -3537, -38086],[189, 9, 1],[2402, 4444, 13234, 552, 884, 86, -90, -172, 70, 982; 41296, 76405, 227535, 9491, 15201, 1480, -1547, -2961, 1203, 16881; 5283, 9774, 29106, 1214, 1944, 189, -198, -378, 154, 2160],287,3]
%
% END OF LATTICE L288.3
%
%
% LATTICE L288.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-51219, 6048, 3024; 6048, -714, -357; 3024, -357, -178],[189, 21, 1],[40, 72, 10, 76, 4, 0, -2, 0, 14, 6; 406, 745, 105, 819, 47, 10, -17, -1, 117, 57; -147, -294, -44, -378, -28, -21, 0, 2, 0, -14],287,4]
%
% END OF LATTICE L288.4
%
%
% LATTICE L288.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-10900764, 58968, -703836; 58968, -306, 3915; -703836, 3915, -44554],[756, 9, 1],[-1694, -3136, -9343, -390, -626, -62, 63, 124, -49, -691; -128282, -237479, -707511, -29533, -47403, -4694, 4771, 9387, -3711, -52329; 15489, 28674, 85428, 3566, 5724, 567, -576, -1134, 448, 6318],287,5]
%
% END OF LATTICE L288.5
%
%
% LATTICE L288.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1052625672, 43045884, 262174752; 43045884, 1760424, 10721328; 262174752, 10721328, 65299187],[756, 12, 1],[-108537, -203311, -203871, -234197, -14883, -8287, -1131, -571, -28657, -14323; -4132, -7741, -7763, -8919, -567, -316, -43, -21, -1089, -545; 436452, 817560, 819812, 941760, 59848, 33324, 4548, 2296, 115236, 57596],287,6]
%
% END OF LATTICE L288.6
%
%
% LATTICE L288.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-74466, -151956, -5859; -151956, -268065, -10395; -5859, -10395, -403],[189, 63, 1],[3, -17, -1, 13, 157, 357, 647, 271, 77, 113; 35, -220, -12, 168, 2022, 4589, 8312, 3480, 988, 1446; -945, 5922, 324, -4522, -54432, -123543, -223776, -93690, -26600, -38934],287,7]
%
% END OF LATTICE L288.7
%
%
% LATTICE L288.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-204876, 12096, 6048; 12096, -714, -357; 6048, -357, -178],[756, 21, 1],[0, -1, 0, 7, 3, 20, 36, 5, 38, 2; 10, -17, -1, 117, 57, 406, 745, 105, 819, 47; -21, 0, 2, 0, -14, -147, -294, -44, -378, -28],287,8]
%
% END OF LATTICE L288.8
%
%
% LATTICE L288.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[6144131448, 1685720484, 1530379116; 1685720484, 462498840, 419878944; 1530379116, 419878944, 381186545],[756, 36, 1],[110924, 205921, 615421, 25899, 43097, 7124, 663, 4331, 3613, 45439; 215, 404, 1218, 52, 90, 17, 2, 0, 6, 84; -445572, -827172, -2472120, -104036, -173124, -28620, -2664, -17388, -14512, -182520],287,9]
%
% END OF LATTICE L288.9
%
%
% LATTICE L288.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-15740676, -5626152, 254016; -5626152, -2010078, 90657; 254016, 90657, -4078],[756, 63, 1],[38, -246, -13, 188, 2260, 5126, 9283, 3886, 1103, 1613; -149, 967, 51, -739, -8883, -20147, -36485, -15273, -4335, -6339; -945, 6174, 324, -4718, -56700, -128583, -232848, -97470, -27664, -40446],287,10]
%
% END OF LATTICE L288.10
%
%
% LATTICE L288.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[337176, 40068, 83916; 40068, 12264, 9996; 83916, 9996, 20885],[756, 84, 1],[1336, 167, -1, 4133, 2157, 16616, 31249, 4489, 36259, 2331; 17, 2, 0, 54, 28, 215, 404, 58, 468, 30; -5376, -672, 4, -16632, -8680, -66864, -125748, -18064, -145908, -9380],287,11]
%
% END OF LATTICE L288.11
%
%
% LATTICE L288.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[70660811592, 2803336452, -15491678328; 2803336452, 111217176, -614603556; -15491678328, -614603556, 3396395999],[756, 252, 1],[24745, 2819, -913, 7385, 110317, 289231, 546639, 236395, 71109, 125165; -73648, -8389, 2721, -21975, -328293, -860752, -1626811, -703521, -211625, -372507; 99540, 11340, -3672, 29708, 443772, 1163484, 2198952, 950940, 286048, 503496],287,12]
%
% END OF LATTICE L288.12
%

\medskip%
%------------------------------WEYL-GROUP-W289--------------------------------
%
\leavevmode\llap{}%
$W_{289}$%
\qquad\llap{12} lattices, $\chi=36$%
\hfill%
$2222222222\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L289.1
%
\leavevmode%
${L_{289.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{1}{}3\above{1pt}{1pt}{1}{}27\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{2}{}7\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${378}\above{1pt}{1pt}{b}{2}{4}\above{1pt}{1pt}{*}{2}{84}\above{1pt}{1pt}{b}{2}{54}\above{1pt}{1pt}{l}{2}{12}\above{1pt}{1pt}{r}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-72721908\\-1136268\\12096
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1136268\\-17754\\189
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
12096\\189\\-2
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-32508\\-3315816
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\-509\\-51816
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\5\\509
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\-126\\189
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\-64\\-2
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5\\-322\\-210
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4\\-261\\-513
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\-68\\-408
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-72721908, -1136268, 12096; -1136268, -17754, 189; 12096, 189, -2],[756, 3, 1],[2, 1, 5, 4, 1, -2, -1, -5, -4, -1; -126, -64, -322, -261, -68, 63, 58, 308, 252, 64; 189, -2, -210, -513, -408, -6615, -610, -1218, -405, 0],288,1]
%
% END OF LATTICE L289.1
%
%
% LATTICE L289.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[378, 189, -189; 189, 93, -96; -189, -96, 94],[189, 3, 1],[-188, -10, -25, -25, -2, -1, 1, 4, -2, -4; -126, -5, -7, 0, 1, 0, -1, -7, -18, -5; -567, -28, -63, -54, -3, 0, 1, 0, -27, -15],288,2]
%
% END OF LATTICE L289.2
%
%
% LATTICE L289.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[3591, -567, 0; -567, 90, 0; 0, 0, -1],[189, 9, 1],[-1, -1, 1, 1, 4, 15, 19, 13, 1, 0; -7, -6, 7, 6, 23, 84, 105, 70, 5, -1; -7, 0, 0, -5, -27, -119, -162, -126, -13, -9],288,3]
%
% END OF LATTICE L289.3
%
%
% LATTICE L289.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[32130, 4725, -567; 4725, 651, -84; -567, -84, 10],[189, 21, 1],[1, -1, -1, -13, -2, -1, 1, 1, 13, 2; -18, -5, -1, 0, 1, 0, -1, -1, -18, -5; -135, -112, -69, -756, -105, -54, 49, 48, 567, 63],288,4]
%
% END OF LATTICE L289.4
%
%
% LATTICE L289.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-8316, 3024, 756; 3024, -1098, -261; 756, -261, 50],[756, 9, 1],[99, 157, 5, -6, -7, 62, 257, 317, 29, 99; 280, 444, 14, -17, -20, 175, 726, 896, 82, 280; -35, -54, 0, 2, 0, -28, -108, -126, -11, -36],288,5]
%
% END OF LATTICE L289.5
%
%
% LATTICE L289.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[12502728, 88452, 3108672; 88452, 13800, 21924; 3108672, 21924, 772939],[756, 12, 1],[-3008, 3100, 33725, 130955, 24284, 1529939, 69611, 135934, 87178, -47; 63, -65, -707, -2745, -509, -32067, -1459, -2849, -1827, 1; 12096, -12466, -135618, -526608, -97653, -6152328, -279926, -546630, -350568, 189],288,6]
%
% END OF LATTICE L289.6
%
%
% LATTICE L289.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[189, 0, 0; 0, -1827, 504; 0, 504, -139],[189, 63, 1],[-3, -28, -3, -2, -1, 0, 1, 0, -1, -5; -4, -9, 4, 9, 17, 3, 0, -5, -10, -19; -11, 0, 18, 35, 63, 11, 0, -18, -35, -63],288,7]
%
% END OF LATTICE L289.7
%
%
% LATTICE L289.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-114156, -14364, 4536; -14364, -1806, 567; 4536, 567, -170],[756, 21, 1],[386, 249, 71, 166, 1, -8, 3, 13, 212, 167; -3483, -2246, -640, -1494, -8, 72, -28, -118, -1917, -1508; -1350, -868, -246, -567, 0, 27, -14, -48, -756, -588],288,8]
%
% END OF LATTICE L289.8
%
%
% LATTICE L289.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[48479256, 1509732, 12114900; 1509732, 47016, 377280; 12114900, 377280, 3027497],[756, 36, 1],[738, 416, -157, -1, 159, 2083, 3211, 2978, 404, 244; 119, 75, -14, 0, 22, 294, 456, 427, 59, 37; -2968, -1674, 630, 4, -639, -8372, -12906, -11970, -1624, -981],288,9]
%
% END OF LATTICE L289.9
%
%
% LATTICE L289.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-4013604, 1351728, 18144; 1351728, -455238, -6111; 18144, -6111, -82],[756, 63, 1],[4, 49, 1, -2, -9, 0, 23, 7, 6, 25; 10, 120, 2, -5, -20, 1, 78, 20, 16, 64; 139, 1890, 72, -70, -504, -76, -756, 54, 133, 756],288,10]
%
% END OF LATTICE L289.10
%
%
% LATTICE L289.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[6941592, -948780, 1731240; -948780, 129864, -236628; 1731240, -236628, 431773],[756, 84, 1],[33757, 10731, 2980, 13148, -47, -322, 414, 735, 20287, 3762; -936, -298, -83, -369, 1, 9, -11, -20, -558, -104; -135864, -43190, -11994, -52920, 189, 1296, -1666, -2958, -81648, -15141],288,11]
%
% END OF LATTICE L289.11
%
%
% LATTICE L289.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[65262456, 1325268, -15231888; 1325268, 29736, -307188; -15231888, -307188, 3556631],[756, 252, 1],[-3692, -20396, -461, -369, -3462, -6647, -72655, -9878, -9970, -6877; 11157, 61635, 1393, 1115, 10462, 20087, 219561, 29851, 30129, 20782; -14848, -82026, -1854, -1484, -13923, -26732, -292194, -39726, -40096, -27657],288,12]
%
% END OF LATTICE L289.12
%

\medskip%
%------------------------------WEYL-GROUP-W290--------------------------------
%
\leavevmode\llap{}%
$W_{290}$%
\qquad\llap{12} lattices, $\chi=36$%
\hfill%
$2222222222\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L290.1
%
\leavevmode%
${L_{290.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{1}{}3\above{1pt}{1pt}{-}{}27\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{2}{}7\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${756}\above{1pt}{1pt}{*}{2}{4}\above{1pt}{1pt}{b}{2}{42}\above{1pt}{1pt}{l}{2}{108}\above{1pt}{1pt}{r}{2}{6}\above{1pt}{1pt}{b}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-285012\\1512\\756
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1512\\186\\-3
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
756\\-3\\-2
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-5167\\-10332\\-2138724
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-107\\-215\\-44298
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
13\\26\\5381
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\0\\378
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\-2\\380
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\-7\\1134
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7\\-36\\2484
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\-4\\-33
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-285012, 1512, 756; 1512, 186, -3; 756, -3, -2],[756, 3, 1],[1, 1, 3, 7, 0, -253, -13, -10, -25, -1; 0, -2, -7, -36, -4, -504, -22, -7, 0, 2; 378, 380, 1134, 2484, -33, -104706, -5348, -4032, -9936, -381],289,1]
%
% END OF LATTICE L290.1
%
%
% LATTICE L290.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[189, 0, 0; 0, -3, -3; 0, -3, -2],[189, 3, 1],[-505, -24, -27, -25, 0, 1, 0, -1, -11, -4; -252, -11, -7, 0, 2, 0, -1, -7, -18, -4; -4536, -217, -252, -243, -3, 0, 1, 0, -81, -33],289,2]
%
% END OF LATTICE L290.2
%
%
% LATTICE L290.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-68985, -11529, 378; -11529, -1926, 63; 378, 63, -2],[189, 9, 1],[-141, -181, -68, -7, 0, 1, 1, -2, -3, -10; 819, 1050, 392, 40, -1, -7, -6, 14, 18, 59; -1477, -1944, -819, -97, -36, -35, 0, 63, -11, -72],289,3]
%
% END OF LATTICE L290.3
%
%
% LATTICE L290.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[10962, -567, 378; -567, -21, -21; 378, -21, 13],[189, 21, 1],[1, -1, -1, 4, 5, 143, 49, 9, 68, 3; 0, -1, -1, -18, -4, -36, -11, -1, 0, 2; -27, 28, 27, -189, -168, -4509, -1540, -279, -2079, -84],289,4]
%
% END OF LATTICE L290.4
%
%
% LATTICE L290.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[9828, -756, 756; -756, 18, -9; 756, -9, -2],[756, 9, 1],[-141, -181, -34, -7, 0, 1, 1, -1, -3, -5; -10206, -13104, -2464, -508, -1, 70, 72, -70, -216, -361; -8624, -11070, -2079, -428, 0, 56, 54, -63, -184, -306],289,5]
%
% END OF LATTICE L290.5
%
%
% LATTICE L290.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[3411025128, 285012, 848196468; 285012, 24, 70872; 848196468, 70872, 210915259],[756, 12, 1],[-94, 93, 2047, 10561, 7630, 961474, 45687, 51363, 23774, 0; 63, 0, -56, -297, -215, -27027, -1284, -1442, -666, 1; 378, -374, -8232, -42471, -30684, -3866562, -183730, -206556, -95607, 0],289,6]
%
% END OF LATTICE L290.6
%
%
% LATTICE L290.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[189, 0, 0; 0, -3654, 1323; 0, 1323, -479],[189, 63, 1],[-24, -217, -12, -9, -1, 0, 1, 0, -3, -11; -272, -2412, -121, -79, 23, 4, 0, -13, -55, -157; -767, -6804, -342, -224, 63, 11, 0, -36, -154, -441],289,7]
%
% END OF LATTICE L290.7
%
%
% LATTICE L290.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-180684, -18900, 3024; -18900, -1974, 315; 3024, 315, -50],[756, 21, 1],[1, 1, 0, -59, -12, -469, -157, -13, -175, -1; -18, -14, 1, 936, 187, 7218, 2414, 199, 2664, 13; -54, -28, 6, 2268, 441, 16686, 5572, 456, 6048, 21],289,8]
%
% END OF LATTICE L290.8
%
%
% LATTICE L290.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[7183512, -449820, 1785672; -449820, 28152, -111816; 1785672, -111816, 443881],[756, 36, 1],[22341, 28366, 10086, 483, -197, 87, 470, 1128, 318, 1799; 28, 33, 7, 0, -2, 0, 3, 7, 1, 4; -89866, -114102, -40572, -1943, 792, -350, -1890, -4536, -1279, -7236],289,9]
%
% END OF LATTICE L290.9
%
%
% LATTICE L290.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1266300, -205632, 73332; -205632, 33390, -11907; 73332, -11907, 4246],[756, 63, 1],[1, 1, -1, -3, -2, 3, 35, 2, 5, 3; 14, 6, -19, -128, -169, -526, -4614, -109, -128, 41; 22, 0, -36, -308, -441, -1534, -13608, -342, -448, 63],289,10]
%
% END OF LATTICE L290.10
%
%
% LATTICE L290.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[6076728, -268380, 1512000; -268380, 12264, -66780; 1512000, -66780, 376213],[756, 84, 1],[443, 87, 173, 9913, 7517, 141253, 47145, 7699, 25511, 355; -9, -2, -4, -216, -163, -3051, -1018, -166, -549, -7; -1782, -350, -696, -39879, -30240, -568242, -189658, -30972, -102627, -1428],289,11]
%
% END OF LATTICE L290.11
%
%
% LATTICE L290.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[16963128, 2241540, -2543940; 2241540, 290808, -340200; -2543940, -340200, 378487],[756, 252, 1],[117, 4987, 233, -4912, -36759, -81037, -733267, -40693, -15318, -3701; -352, -15003, -701, 14777, 110584, 243788, 2205927, 122419, 46082, 11134; 470, 20034, 936, -19733, -147672, -325550, -2945754, -163476, -61537, -14868],289,12]
%
% END OF LATTICE L290.12
%

\medskip%
%------------------------------WEYL-GROUP-W291--------------------------------
%
\leavevmode\llap{}%
$W_{291}$%
\qquad\llap{28} lattices, $\chi=36$%
\hfill%
$222|2222\slashinfty2\rtimes D_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L291.1
%
\leavevmode%
${L_{291.1}}$%
{} : {$[1\above{1pt}{1pt}{1}{}2\above{1pt}{1pt}{-}{}]\above{1pt}{1pt}{}{4}32\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{2}{}9\above{1pt}{1pt}{-}{}$}\EasyButWeakLineBreak%
{${288}\above{1pt}{1pt}{*}{2}{8}\above{1pt}{1pt}{s}{2}{32}\above{1pt}{1pt}{s}{2}{72}\above{1pt}{1pt}{*}{2}{32}\above{1pt}{1pt}{*}{2}{8}\above{1pt}{1pt}{s}{2}{288}\above{1pt}{1pt}{*}{2}{4}\above{1pt}{1pt}{24,13}{\infty z}{1}\above{1pt}{1pt}{r}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
72864\\36000\\-288
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
36000\\17786\\-142
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-288\\-142\\1
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-35\\72\\144
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\2\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
27\\-56\\-160
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
113\\-234\\-648
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
143\\-296\\-816
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
115\\-238\\-656
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1009\\-2088\\-5760
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
29\\-60\\-166
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\-1
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[72864, 36000, -288; 36000, 17786, -142; -288, -142, 1],[288, 2, 1],[-35, -1, 27, 113, 143, 115, 1009, 29, 0; 72, 2, -56, -234, -296, -238, -2088, -60, 0; 144, 0, -160, -648, -816, -656, -5760, -166, -1],290,1]
%
% END OF LATTICE L291.1
%
\hbox{}\par\smallskip%
%
% LATTICE L291.2
%
\leavevmode%
${L_{291.2}}$%
{} : {$[1\above{1pt}{1pt}{1}{}2\above{1pt}{1pt}{1}{}]\above{1pt}{1pt}{}{0}64\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{2}{}9\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{m}%
\EasyButWeakLineBreak%
{${576}\above{1pt}{1pt}{l}{2}{1}\above{1pt}{1pt}{}{2}{64}\above{1pt}{1pt}{}{2}{9}\above{1pt}{1pt}{r}{2}{64}\above{1pt}{1pt}{l}{2}{1}\above{1pt}{1pt}{}{2}{576}\above{1pt}{1pt}{}{2}{2}\above{1pt}{1pt}{48,1}{\infty}{8}\above{1pt}{1pt}{*}{2}$}%
\nopagebreak\par%
shares genus with {$ {L_{291.4}}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
28224\\0\\-1152
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\2\\-2
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1152\\-2\\49
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-59\\-1296\\-1440
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2\\-44\\-49
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-13\\-288\\-320
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-4\\-90\\-99
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-9\\-208\\-224
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-24\\-25
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-23\\-576\\-576
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\-1\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-22\\-24
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[28224, 0, -1152; 0, 2, -2; -1152, -2, 49],[576, 2, 1],[-59, -2, -13, -4, -9, -1, -23, 0, -1; -1296, -44, -288, -90, -208, -24, -576, -1, -22; -1440, -49, -320, -99, -224, -25, -576, 0, -24],290,2]
%
% END OF LATTICE L291.2
%
\hbox{}\par\smallskip%
%
% LATTICE L291.3
%
\leavevmode%
${L_{291.3}}$%
{} : {$1\above{1pt}{1pt}{1}{1}4\above{1pt}{1pt}{1}{1}32\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{2}{}9\above{1pt}{1pt}{1}{}$}\EasyButWeakLineBreak%
{${36}\above{1pt}{1pt}{l}{2}{4}\above{1pt}{1pt}{}{2}{1}\above{1pt}{1pt}{}{2}{36}\above{1pt}{1pt}{r}{2}{4}\above{1pt}{1pt}{l}{2}{4}\above{1pt}{1pt}{}{2}{9}\above{1pt}{1pt}{r}{2}{32}\above{1pt}{1pt}{24,7}{\infty z}{32}\above{1pt}{1pt}{*}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
6624\\-576\\288
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-576\\68\\-40
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
288\\-40\\25
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-13\\-396\\-486
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3\\-91\\-112
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-30\\-37
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-4\\-117\\-144
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-28\\-34
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-27\\-32
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2\\-54\\-63
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-28\\-32
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3\\-92\\-112
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[6624, -576, 288; -576, 68, -40; 288, -40, 25],[288, 4, 1],[-13, -3, -1, -4, -1, -1, -2, -1, -3; -396, -91, -30, -117, -28, -27, -54, -28, -92; -486, -112, -37, -144, -34, -32, -63, -32, -112],290,3]
%
% END OF LATTICE L291.3
%
\hbox{}\par\smallskip%
%
% LATTICE L291.4
%
\leavevmode%
${L_{291.4}}$%
{} : {$[1\above{1pt}{1pt}{1}{}2\above{1pt}{1pt}{1}{}]\above{1pt}{1pt}{}{0}64\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{2}{}9\above{1pt}{1pt}{1}{}$}\EasyButWeakLineBreak%
{${576}\above{1pt}{1pt}{s}{2}{4}\above{1pt}{1pt}{*}{2}{64}\above{1pt}{1pt}{*}{2}{36}\above{1pt}{1pt}{s}{2}{64}\above{1pt}{1pt}{s}{2}{4}\above{1pt}{1pt}{*}{2}{576}\above{1pt}{1pt}{s}{2}{8}\above{1pt}{1pt}{48,1}{\infty z}{2}\above{1pt}{1pt}{r}{2}$}%
\nopagebreak\par%
shares genus with {$ {L_{291.2}}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1575360\\5184\\5184
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5184\\-2\\-18
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5184\\-18\\-17
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\0\\288
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-18\\-286
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-16\\-288
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7\\126\\1998
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
27\\480\\7712
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
13\\230\\3714
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
253\\4464\\72288
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
9\\158\\2572
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\17\\286
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-1575360, 5184, 5184; 5184, -2, -18; 5184, -18, -17],[576, 2, 1],[1, -1, -1, 7, 27, 13, 253, 9, 1; 0, -18, -16, 126, 480, 230, 4464, 158, 17; 288, -286, -288, 1998, 7712, 3714, 72288, 2572, 286],290,4]
%
% END OF LATTICE L291.4
%
\hbox{}\par\smallskip%
%
% LATTICE L291.5
%
\leavevmode%
${L_{291.5}}$%
{} : {$1\above{1pt}{1pt}{1}{1}4\above{1pt}{1pt}{1}{7}32\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{2}{}9\above{1pt}{1pt}{1}{}$}\EasyButWeakLineBreak%
{${36}\above{1pt}{1pt}{*}{2}{16}\above{1pt}{1pt}{l}{2}{1}\above{1pt}{1pt}{r}{2}{144}\above{1pt}{1pt}{*}{2}{4}\above{1pt}{1pt}{*}{2}{16}\above{1pt}{1pt}{l}{2}{9}\above{1pt}{1pt}{}{2}{32}\above{1pt}{1pt}{12,7}{\infty}{32}\above{1pt}{1pt}{s}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1435680\\44640\\6048
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
44640\\1388\\188
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
6048\\188\\25
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-35\\1152\\-198
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-15\\494\\-88
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2\\66\\-13
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-7\\234\\-72
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\-32\\-2
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5\\-162\\8
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5\\-162\\9
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\-32\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-9\\296\\-48
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[1435680, 44640, 6048; 44640, 1388, 188; 6048, 188, 25],[288, 4, 1],[-35, -15, -2, -7, 1, 5, 5, 1, -9; 1152, 494, 66, 234, -32, -162, -162, -32, 296; -198, -88, -13, -72, -2, 8, 9, 0, -48],290,5]
%
% END OF LATTICE L291.5
%
\hbox{}\par\smallskip%
%
% LATTICE L291.6
%
\leavevmode%
${L_{291.6}}$%
{} : {$1\above{1pt}{1pt}{1}{1}8\above{1pt}{1pt}{1}{1}64\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{2}{}9\above{1pt}{1pt}{1}{}$}\EasyButWeakLineBreak%
{${36}\above{1pt}{1pt}{*}{2}{64}\above{1pt}{1pt}{l}{2}{1}\above{1pt}{1pt}{r}{2}{576}\above{1pt}{1pt}{*}{2}{4}\above{1pt}{1pt}{*}{2}{64}\above{1pt}{1pt}{l}{2}{9}\above{1pt}{1pt}{}{2}{8}\above{1pt}{1pt}{48,31}{\infty}{8}\above{1pt}{1pt}{r}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-8193600\\23616\\24192
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
23616\\-56\\-72
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
24192\\-72\\-71
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
53\\2826\\15174
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
39\\2076\\11168
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\106\\573
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5\\252\\1440
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-54\\-286
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-52\\-288
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4\\216\\1143
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4\\215\\1144
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
9\\481\\2576
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-8193600, 23616, 24192; 23616, -56, -72; 24192, -72, -71],[576, 8, 1],[53, 39, 2, 5, -1, -1, 4, 4, 9; 2826, 2076, 106, 252, -54, -52, 216, 215, 481; 15174, 11168, 573, 1440, -286, -288, 1143, 1144, 2576],290,6]
%
% END OF LATTICE L291.6
%
%
% LATTICE L291.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[288, 0, 0; 0, 2, 0; 0, 0, -1],[288, 2, 1],[1, 0, -1, -2, -5, -2, -35, -1, 0; 0, 1, 0, -9, -32, -15, -288, -10, -1; 0, 0, -16, -36, -96, -40, -720, -22, -1],290,7]
%
% END OF LATTICE L291.7
%
%
% LATTICE L291.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[72864, 288, -288; 288, -8, 0; -288, 0, 1],[288, 8, 1],[-35, -4, -5, -4, -1, 0, 1, 0, -1; -1044, -119, -148, -117, -28, 1, 36, 0, -30; -9936, -1132, -1408, -1116, -272, 4, 288, -1, -286],290,8]
%
% END OF LATTICE L291.8
%
%
% LATTICE L291.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-20448, 0, -10080; 0, 8, 0; -10080, 0, -4969],[288, 8, 1],[2845, 324, 403, 320, 79, 0, -71, 1, 82; -144, -15, -16, -9, 0, 1, 0, -1, -5; -5760, -656, -816, -648, -160, 0, 144, -2, -166],290,9]
%
% END OF LATTICE L291.9
%
%
% LATTICE L291.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[42048, -576, -1728; -576, 8, 24; -1728, 24, 71],[576, 8, 1],[1, 0, -1, -2, -5, -2, -35, -1, 0; 72, 5, 16, 9, 8, 1, 0, -1, 1; 0, -2, -32, -54, -128, -50, -864, -24, 0],290,10]
%
% END OF LATTICE L291.10
%
%
% LATTICE L291.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[746208, 370368, -4320; 370368, 183824, -2144; -4320, -2144, 25],[288, 16, 1],[19, 8, 1, 2, -1, -4, -4, -1, 5; -54, -23, -3, -9, 2, 9, 9, 2, -14; -1350, -592, -85, -432, -2, 80, 81, 0, -336],290,11]
%
% END OF LATTICE L291.11
%
%
% LATTICE L291.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2016, -3168, 576; -3168, 848, -112; 576, -112, 13],[288, 16, 1],[-16, -6, -1, 4, 2, 6, 11, 1, -5; -243, -91, -15, 63, 31, 93, 171, 16, -76; -1386, -520, -86, 360, 178, 536, 990, 96, -432],290,12]
%
% END OF LATTICE L291.12
%
%
% LATTICE L291.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[3744, -576, 0; -576, 90, 0; 0, 0, -1],[288, 18, 1],[1, 1, -1, -1, -13, -11, -11, -3, 0; 8, 6, -8, -6, -72, -58, -56, -14, 1; -16, 0, 0, -8, -144, -144, -160, -54, -9],290,13]
%
% END OF LATTICE L291.13
%
%
% LATTICE L291.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[90144, 0, -1440; 0, 18, 0; -1440, 0, 23],[288, 18, 1],[1, 0, 7, 2, 51, 22, 45, 13, 1; 0, 1, 0, -1, -32, -15, -32, -10, -1; 64, 0, 432, 124, 3168, 1368, 2800, 810, 63],290,14]
%
% END OF LATTICE L291.14
%
%
% LATTICE L291.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[313920, 576, -576; 576, -18, 0; -576, 0, 1],[576, 18, 1],[-1, 0, 1, 0, -3, -1, -5, -1, -1; -16, 2, 32, 0, -80, -26, -128, -25, -22; -512, 9, 576, -1, -1728, -567, -2816, -558, -540],290,15]
%
% END OF LATTICE L291.15
%
%
% LATTICE L291.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1590048, -38016, 6048; -38016, -828, 144; 6048, 144, -23],[288, 36, 1],[-5, -9, -2, 0, 3, 5, 1, 1, -13; -12, -23, -6, -1, 4, 9, 2, 4, -28; -1394, -2520, -567, -8, 810, 1368, 275, 288, -3600],290,16]
%
% END OF LATTICE L291.16
%
%
% LATTICE L291.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1184832, 7488, -2880; 7488, -18, -18; -2880, -18, 7],[576, 18, 1],[1, -1, -9, -1, -13, -3, -3, 1, 1; 0, -2, -16, -2, -32, -10, -16, -2, 1; 416, -414, -3744, -418, -5472, -1278, -1312, 396, 414],290,17]
%
% END OF LATTICE L291.17
%
%
% LATTICE L291.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1299168, -684288, 5472; -684288, -360324, 2880; 5472, 2880, -23],[288, 36, 1],[11, 41, 5, 1, -5, -19, -2, -3, 27; -32, -118, -14, -2, 16, 58, 6, 8, -80; -1394, -5040, -567, -16, 810, 2736, 275, 288, -3600],290,18]
%
% END OF LATTICE L291.18
%
%
% LATTICE L291.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-111572928, 13627584, -78336; 13627584, -1664480, 9568; -78336, 9568, -55],[576, 32, 1],[-1, -1, 0, 5, 1, 7, 8, 2, 0; 0, -8, -1, 36, 10, 80, 99, 29, 7; 1422, 32, -174, -864, 314, 3936, 5814, 2192, 1216],290,19]
%
% END OF LATTICE L291.19
%
%
% LATTICE L291.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-91583424, 11448000, -80640; 11448000, -1431008, 10080; -80640, 10080, -71],[576, 32, 1],[4, -1, -1, 5, 2, 39, 53, 18, 8; 36, -8, -9, 36, 17, 336, 459, 157, 71; 567, 0, -142, -576, 141, 3392, 4950, 1840, 992],290,20]
%
% END OF LATTICE L291.20
%
%
% LATTICE L291.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[3744, -14976, 576; -14976, 28440, -1080; 576, -1080, 41],[288, 72, 1],[-11, -11, -13, -1, -1, 1, 1, 0, -3; -276, -275, -324, -25, -28, 21, 20, -1, -76; -7120, -7092, -8352, -644, -720, 540, 512, -27, -1962],290,21]
%
% END OF LATTICE L291.21
%
%
% LATTICE L291.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[288, -288, 0; -288, 360, 0; 0, 0, -1],[288, 72, 1],[1, 1, -1, -1, -13, -11, -11, -3, 0; 0, 1, 0, -1, -16, -15, -16, -5, -1; -16, 0, 0, -8, -144, -144, -160, -54, -18],290,22]
%
% END OF LATTICE L291.22
%
%
% LATTICE L291.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-55872, -40320, -12672; -40320, -12600, -3888; -12672, -3888, -1199],[576, 72, 1],[1, -1, -3, -3, 1, 39, 7, 13, 8; -101, 92, 304, 316, -89, -3764, -684, -1285, -803; 317, -288, -954, -992, 279, 11808, 2146, 4032, 2520],290,23]
%
% END OF LATTICE L291.23
%
%
% LATTICE L291.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1590048, -76032, 6048; -76032, -3312, 288; 6048, 288, -23],[288, 144, 1],[1, 10, 3, 0, -2, -18, -5, -13, 1; 1, 9, 2, -1, -3, -23, -6, -14, 2; 275, 2736, 810, -16, -567, -5040, -1394, -3600, 288],290,24]
%
% END OF LATTICE L291.24
%
%
% LATTICE L291.25
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-227808, 435168, 112320; 435168, -831024, -214560; 112320, -214560, -55379],[288, 144, 1],[-407, -1634, -480, -140, -7, 258, 66, 71, -875; -5, -19, -5, -1, 1, 5, 1, 0, -12; -806, -3240, -954, -280, -18, 504, 130, 144, -1728],290,25]
%
% END OF LATTICE L291.25
%
%
% LATTICE L291.26
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[304704, -14976, -8064; -14976, 72, 72; -8064, 72, 55],[576, 72, 1],[-9, -4, -7, 0, 5, 2, 3, 0, -3; 1800, 801, 1408, 1, -984, -395, -592, 1, 599; -3680, -1638, -2880, -2, 2016, 810, 1216, 0, -1224],290,26]
%
% END OF LATTICE L291.26
%
%
% LATTICE L291.27
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[576, 0, 0; 0, -380448, 128448; 0, 128448, -43367],[576, 288, 1],[-2, -15, -1, -1, 0, 1, 0, -1, -5; 125, 584, -3, -108, -79, 0, 26, 389, 535; 370, 1728, -9, -320, -234, 0, 77, 1152, 1584],290,27]
%
% END OF LATTICE L291.27
%
%
% LATTICE L291.28
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[9870912, 2221056, -34560; 2221056, 499680, -7776; -34560, -7776, 121],[576, 288, 1],[1, 1, -1, -1, 1, 17, 3, 11, 7; 1, 0, -2, -4, -3, -8, 0, 5, 7; 350, 288, -414, -544, 90, 4320, 854, 3456, 2448],290,28]
%
% END OF LATTICE L291.28
%

\medskip%
%------------------------------WEYL-GROUP-W292--------------------------------
%
\leavevmode\llap{}%
$W_{292}$%
\qquad\llap{6} lattices, $\chi=48$%
\hfill%
$22|222|222|222|2\rtimes D_{4}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L292.1
%
\leavevmode%
${L_{292.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{1}{}9\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}23\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${92}\above{1pt}{1pt}{b}{2}{18}\above{1pt}{1pt}{b}{2}{138}\above{1pt}{1pt}{b}{2}{2}\above{1pt}{1pt}{b}{2}{828}\above{1pt}{1pt}{*}{2}{12}\above{1pt}{1pt}{*}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
105156\\-35604\\0
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-35604\\12054\\3
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\3\\-10
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
6071\\17940\\5796
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2090\\-6176\\-1995
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
110\\325\\104
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1121\\-3312\\-1058
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-199\\-588\\-189
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-358\\-1058\\-345
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-23\\-68\\-23
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-373\\-1104\\-414
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
21\\62\\18
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[105156, -35604, 0; -35604, 12054, 3; 0, 3, -10],[828, 3, 1],[-1121, -199, -358, -23, -373, 21, 109, 1, -148, -43, -2663, -109; -3312, -588, -1058, -68, -1104, 62, 322, 3, -437, -127, -7866, -322; -1058, -189, -345, -23, -414, 18, 92, 0, -138, -40, -2484, -102],291,1]
%
% END OF LATTICE L292.1
%
%
% LATTICE L292.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[35635050, 1501578, 46989; 1501578, 63273, 1980; 46989, 1980, 62],[207, 3, 1],[1, -1, 103, 37, 1291, 59, 712, 280, 610, 56, 848, 3; -23, 24, -2438, -876, -30567, -1397, -16859, -6630, -14444, -1326, -20079, -71; -23, -9, -207, -67, -2277, -102, -1219, -477, -1035, -95, -1449, -6],291,2]
%
% END OF LATTICE L292.2
%
%
% LATTICE L292.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[80638920, 1108692, -20131992; 1108692, 15240, -276792; -20131992, -276792, 5026073],[828, 12, 1],[5418, 2414, 6100, 650, 10918, 107, -289, -407, -971, 19, 4469, 339; -2323, -1041, -2645, -283, -4761, -47, 138, 186, 460, -2, -1794, -143; 21574, 9612, 24288, 2588, 43470, 426, -1150, -1620, -3864, 76, 17802, 1350],291,3]
%
% END OF LATTICE L292.3
%
%
% LATTICE L292.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[414, -9522, 207; -9522, 175605, -3795; 207, -3795, 82],[207, 69, 1],[8, 89, 11, 31, 26, 11, 2, 1, -1, -1, 4, 9; 11, 126, 16, 46, 39, 17, 3, 0, -2, -4, 3, 11; 487, 5589, 711, 2047, 1737, 759, 134, 0, -90, -184, 126, 483],291,4]
%
% END OF LATTICE L292.4
%
%
% LATTICE L292.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[6551964, -2203308, -23184; -2203308, 740922, 7797; -23184, 7797, 82],[828, 69, 1],[27, 152, 19, 54, 91, 39, 7, 1, -2, -3, 11, 29; 70, 393, 49, 139, 234, 100, 18, 3, -5, -7, 30, 76; 974, 5589, 711, 2047, 3474, 1518, 268, 0, -90, -184, 252, 966],291,5]
%
% END OF LATTICE L292.5
%
%
% LATTICE L292.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[201126168, 4029876, 47510640; 4029876, 78936, 953304; 47510640, 953304, 11222095],[828, 276, 1],[-11181, -104839, -10259, -21957, -14059, -312, 1127, 14353, 205, -8205, -16103, -19796; 33322, 312444, 30574, 65436, 41898, 929, -3359, -42777, -611, 24453, 47991, 58997; 44506, 417312, 40836, 87400, 55962, 1242, -4486, -57132, -816, 32660, 64098, 78798],291,6]
%
% END OF LATTICE L292.6
%

\medskip%
%------------------------------WEYL-GROUP-W293--------------------------------
%
\leavevmode\llap{}%
$W_{293}$%
\qquad\llap{6} lattices, $\chi=48$%
\hfill%
$222|222|222|222|\rtimes D_{4}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L293.1
%
\leavevmode%
${L_{293.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{1}{}3\above{1pt}{1pt}{1}{}9\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{-2}{}23\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${12}\above{1pt}{1pt}{b}{2}{46}\above{1pt}{1pt}{l}{2}{36}\above{1pt}{1pt}{r}{2}{138}\above{1pt}{1pt}{l}{2}{4}\above{1pt}{1pt}{r}{2}{414}\above{1pt}{1pt}{b}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-378396\\15732\\4968
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
15732\\-654\\-207
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4968\\-207\\-62
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
94391\\2180952\\268272
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3952\\-91313\\-11232
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1083\\-25023\\-3079
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3\\-70\\-6
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7\\161\\23
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\24\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-43\\-989\\-138
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-21\\-484\\-64
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-347\\-8004\\-1035
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-378396, 15732, 4968; 15732, -654, -207; 4968, -207, -62],[828, 3, 1],[-3, 7, 1, -43, -21, -347, -35, -444, -457, -831, -131, -964; -70, 161, 24, -989, -484, -8004, -808, -10258, -10560, -19205, -3028, -22287; -6, 23, 0, -138, -64, -1035, -102, -1265, -1296, -2346, -368, -2691],292,1]
%
% END OF LATTICE L293.1
%
%
% LATTICE L293.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-392679, -16353, -4968; -16353, -681, -207; -4968, -207, -62],[207, 3, 1],[19, 490, 253, 923, 73, 1079, 2, -7, -1, 43, 11, 370; -440, -11362, -5868, -21413, -1694, -25047, -47, 161, 24, -989, -254, -8556; -51, -1265, -648, -2346, -184, -2691, -3, 23, 0, -138, -32, -1035],292,2]
%
% END OF LATTICE L293.2
%
%
% LATTICE L293.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[140760, 40572, -34776; 40572, 17688, -9936; -34776, -9936, 8593],[828, 12, 1],[499, -393, -52, 6311, 841, 58046, 3074, 82572, 21490, 158047, 6305, 188491; -29, 23, 3, -368, -49, -3381, -179, -4807, -1251, -9200, -367, -10971; 1986, -1564, -207, 25116, 3347, 231012, 12234, 328624, 85527, 629004, 25093, 750168],292,3]
%
% END OF LATTICE L293.3
%
%
% LATTICE L293.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[207, 0, 0; 0, -4278, 207; 0, 207, -10],[207, 69, 1],[-3, -4, -49, -8, -15, -10, -1, 0, 1, 0, -1, -2; 4, 10, 132, 23, 46, 33, 7, 1, 0, -1, -2, 0; 69, 187, 2484, 435, 874, 630, 138, 20, 0, -21, -46, -9],292,4]
%
% END OF LATTICE L293.4
%
%
% LATTICE L293.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[828, 0, 0; 0, -4278, 207; 0, 207, -10],[828, 69, 1],[-3, -2, -49, -4, -15, -5, -1, 0, 1, 0, -1, -1; 8, 10, 264, 23, 92, 33, 14, 1, 0, -1, -4, 0; 138, 187, 4968, 435, 1748, 630, 276, 20, 0, -21, -92, -9],292,5]
%
% END OF LATTICE L293.5
%
%
% LATTICE L293.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[11683080, 179676, 2799468; 179676, 2760, 43056; 2799468, 43056, 670799],[828, 276, 1],[174, 216, 1306, 421, 389, 509, 35, -7, -52, -3, 29, 118; -563, -707, -4284, -1384, -1282, -1683, -125, 19, 156, 8, -94, -381; -690, -856, -5175, -1668, -1541, -2016, -138, 28, 207, 12, -115, -468],292,6]
%
% END OF LATTICE L293.6
%

\medskip%
%------------------------------WEYL-GROUP-W294--------------------------------
%
\leavevmode\llap{}%
$W_{294}$%
\qquad\llap{8} lattices, $\chi=42$%
\hfill%
$42222|22224|\rtimes D_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L294.1
%
\leavevmode%
${L_{294.1}}$%
{} : {$1\above{1pt}{1pt}{2}{2}16\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{2}{}13\above{1pt}{1pt}{1}{}$}\EasyButWeakLineBreak%
{${2}\above{1pt}{1pt}{*}{4}{4}\above{1pt}{1pt}{l}{2}{13}\above{1pt}{1pt}{}{2}{16}\above{1pt}{1pt}{}{2}{1}\above{1pt}{1pt}{r}{2}{208}\above{1pt}{1pt}{s}{2}{4}\above{1pt}{1pt}{*}{2}{16}\above{1pt}{1pt}{*}{2}{52}\above{1pt}{1pt}{l}{2}{1}\above{1pt}{1pt}{}{4}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-70657392\\58656\\83616
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
58656\\-47\\-72
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
83616\\-72\\-95
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\1247\\815
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
67\\41756\\27318
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
148\\92235\\60346
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
99\\61696\\40368
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
18\\11217\\7340
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
241\\150176\\98280
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
13\\8100\\5302
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7\\4360\\2856
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3\\-1872\\-1222
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-623\\-408
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-70657392, 58656, 83616; 58656, -47, -72; 83616, -72, -95],[624, 1, 1],[2, 67, 148, 99, 18, 241, 13, 7, -3, -1; 1247, 41756, 92235, 61696, 11217, 150176, 8100, 4360, -1872, -623; 815, 27318, 60346, 40368, 7340, 98280, 5302, 2856, -1222, -408],293,1]
%
% END OF LATTICE L294.1
%
%
% LATTICE L294.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-4634448, 22464, 650832; 22464, -105, -3312; 650832, -3312, -85033],[624, 3, 1],[104, 1654, 14571, 4855, 1755, 11657, 309, 307, -105, -103; 12503, 198855, 1751828, 583704, 211000, 1401504, 37151, 36912, -12623, -12384; 309, 4914, 43290, 14424, 5214, 34632, 918, 912, -312, -306],293,2]
%
% END OF LATTICE L294.2
%
%
% LATTICE L294.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-251215536, 197808, 395616; 197808, -143, -312; 395616, -312, -623],[624, 13, 1],[13, 124, 81, 335, 113, 53, 15, 3, -1, -1; 311, 2950, 1926, 7960, 2682, 1256, 354, 64, -24, -22; 8099, 77259, 50468, 208728, 70408, 33024, 9347, 1872, -623, -624],293,3]
%
% END OF LATTICE L294.3
%
%
% LATTICE L294.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-584688, -186576, 221520; -186576, -59488, 70688; 221520, 70688, -83927],[624, 16, 1],[164, 2315, 10125, 418, 1193, 1949, 399, 42, -197, -67; -1, -26, -117, -5, -15, -26, -6, -1, 0, 1; 432, 6088, 26624, 1099, 3136, 5122, 1048, 110, -520, -176],293,4]
%
% END OF LATTICE L294.4
%
%
% LATTICE L294.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-83211024, 197184, -27079728; 197184, -429, 64272; -27079728, 64272, -8812405],[624, 39, 1],[-2678, 207, 206, -621, -3092, -10923, -23287, -69033, -16691, -25551; -21425, 1658, 1648, -4976, -24742, -87400, -186326, -552344, -133546, -204434; 8073, -624, -621, 1872, 9321, 32928, 70200, 208104, 50316, 77025],293,5]
%
% END OF LATTICE L294.5
%
%
% LATTICE L294.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-168621648, 174109728, -783120; 174109728, -179776272, 808608; -783120, 808608, -3637],[624, 48, 1],[-61, -883, -3868, -160, -458, -751, -155, -17, 71, 26; -1, -26, -117, -5, -15, -26, -6, -1, 0, 1; 12912, 184344, 806832, 33339, 95280, 155922, 32040, 3438, -15288, -5376],293,6]
%
% END OF LATTICE L294.6
%
%
% LATTICE L294.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3390816, -624, 217776; -624, 208, 0; 217776, 0, -13979],[624, 208, 1],[227, 0, -19, -5, 207, 99, 868, 328, 642, 1983; 682, -1, -57, -14, 627, 299, 2619, 989, 1935, 5975; 3536, 0, -296, -78, 3224, 1542, 13520, 5109, 10000, 30888],293,7]
%
% END OF LATTICE L294.7
%
%
% LATTICE L294.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-178527648, -178528272, 527904; -178528272, -178528272, 527904; 527904, 527904, -1561],[624, 624, 1],[-1, -26, -9, -5, -15, -2, -6, -1, 0, 1; 132, 1169, 379, 194, 515, 59, 125, -2, -11, -1; 44304, 386568, 125136, 63921, 169104, 19278, 40248, -1014, -3720, 0],293,8]
%
% END OF LATTICE L294.8
%

\medskip%
%------------------------------WEYL-GROUP-W295--------------------------------
%
\leavevmode\llap{}%
$W_{295}$%
\qquad\llap{32} lattices, $\chi=42$%
\hfill%
$2222\slashtwo22222|2\rtimes D_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L295.1
%
\leavevmode%
${L_{295.1}}$%
{} : {$1\above{1pt}{1pt}{2}{2}8\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{1}{}9\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{2}{}13\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{2,m}%
\EasyButWeakLineBreak%
{${104}\above{1pt}{1pt}{b}{2}{18}\above{1pt}{1pt}{l}{2}{8}\above{1pt}{1pt}{r}{2}{234}\above{1pt}{1pt}{b}{2}{2}\above{1pt}{1pt}{s}{2}{18}\above{1pt}{1pt}{b}{2}{26}\above{1pt}{1pt}{l}{2}{72}\above{1pt}{1pt}{r}{2}{2}\above{1pt}{1pt}{b}{2}{936}\above{1pt}{1pt}{*}{2}{12}\above{1pt}{1pt}{*}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-8501688\\12168\\-2959632
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
12168\\-15\\4485
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2959632\\4485\\-1004638
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1263\\-262704\\2548
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
58\\12066\\-117
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
115\\23920\\-232
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-406\\-84474\\819
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-173\\-35988\\349
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1325\\-275622\\2673
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3628\\-754676\\7319
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-6103\\-1269504\\12312
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1324\\-275408\\2671
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-45701\\-9506328\\92196
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-345\\-71762\\696
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-8501688, 12168, -2959632; 12168, -15, 4485; -2959632, 4485, -1004638],[936, 3, 1],[-1263, 58, 115, -406, -173, -1325, -3628, -6103, -1324, -45701, -345; -262704, 12066, 23920, -84474, -35988, -275622, -754676, -1269504, -275408, -9506328, -71762; 2548, -117, -232, 819, 349, 2673, 7319, 12312, 2671, 92196, 696],294,1]
%
% END OF LATTICE L295.1
%
\hbox{}\par\smallskip%
%
% LATTICE L295.2
%
\leavevmode%
${L_{295.2}}$%
{} : {$1\above{1pt}{1pt}{-2}{6}16\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{1}{}3\above{1pt}{1pt}{-}{}9\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{2}{}13\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{3,m}%
\EasyButWeakLineBreak%
{${1872}\above{1pt}{1pt}{}{2}{1}\above{1pt}{1pt}{r}{2}{144}\above{1pt}{1pt}{l}{2}{13}\above{1pt}{1pt}{}{2}{9}\above{1pt}{1pt}{r}{2}{4}\above{1pt}{1pt}{*}{2}{468}\above{1pt}{1pt}{s}{2}{16}\above{1pt}{1pt}{s}{2}{36}\above{1pt}{1pt}{*}{2}{208}\above{1pt}{1pt}{b}{2}{6}\above{1pt}{1pt}{l}{2}$}%
\nopagebreak\par%
shares genus with 3-dual\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-65008944\\10829520\\41184
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
10829520\\-1804035\\-6861
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
41184\\-6861\\-26
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4117\\24336\\99216
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
56\\331\\1355
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
467\\2760\\11376
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
121\\715\\2977
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
32\\189\\810
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-6\\-2
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-145\\-858\\-3276
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-23\\-136\\-544
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\6\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
211\\1248\\4888
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
23\\136\\543
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-65008944, 10829520, 41184; 10829520, -1804035, -6861; 41184, -6861, -26],[1872, 3, 1],[4117, 56, 467, 121, 32, -1, -145, -23, 1, 211, 23; 24336, 331, 2760, 715, 189, -6, -858, -136, 6, 1248, 136; 99216, 1355, 11376, 2977, 810, -2, -3276, -544, 0, 4888, 543],294,2]
%
% END OF LATTICE L295.2
%
%
% LATTICE L295.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-1880112, 18096, 8112; 18096, -155, -78; 8112, -78, -35],[624, 1, 1],[581, 53, 87, 167, 23, 6, 12, -1, -1, 9, 4; -520, -48, -80, -156, -22, -6, -13, 0, 1, 0, -3; 135720, 12382, 20328, 39026, 5376, 1403, 2808, -232, -234, 2080, 933],294,3]
%
% END OF LATTICE L295.3
%
%
% LATTICE L295.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-1267578, 4914, 9828; 4914, -15, -39; 9828, -39, -76],[234, 3, 1],[11, -1, -1, 7, 3, 23, 63, 53, 23, 397, 3; 286, -24, -26, 156, 74, 576, 1586, 1338, 582, 10062, 77; 1274, -117, -116, 819, 349, 2673, 7319, 6156, 2671, 46098, 348],294,4]
%
% END OF LATTICE L295.4
%
%
% LATTICE L295.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-4250844, 12168, -1479816; 12168, -30, 4485; -1479816, 4485, -502319],[468, 3, 1],[-45701, -1324, -6103, -3628, -1325, -173, -406, 115, 58, -1263, -345; -4753164, -137704, -634752, -377338, -137811, -17994, -42237, 11960, 6033, -131352, -35881; 92196, 2671, 12312, 7319, 2673, 349, 819, -232, -117, 2548, 696],294,5]
%
% END OF LATTICE L295.5
%
%
% LATTICE L295.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-5345496, 1779336, 8424; 1779336, -592278, -2805; 8424, -2805, -13],[936, 3, 1],[211, 1, -23, -145, -1, 64, 242, 467, 112, 4117, 23; 624, 3, -68, -429, -3, 189, 715, 1380, 331, 12168, 68; 2080, 0, -232, -1404, -2, 684, 2522, 4824, 1150, 42120, 231],294,6]
%
% END OF LATTICE L295.6
%
%
% LATTICE L295.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[193375494, -1121094, 95846868; -1121094, 6504, -555672; 95846868, -555672, 47506651],[234, 6, 1],[4169, 116, 57, 27952, 4450, 26132, 64706, 25735, 21342, 178673, 2055; 13, 3, 0, 39, 7, 45, 117, 48, 41, 351, 5; -8411, -234, -115, -56394, -8978, -52722, -130546, -51921, -43058, -360477, -4146],294,7]
%
% END OF LATTICE L295.7
%
%
% LATTICE L295.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[714480, 355680, -1248; 355680, 177063, -621; -1248, -621, 2],[624, 3, 1],[4733, 232, 835, 881, 139, 185, 553, 91, -1, -103, 0; -9568, -469, -1688, -1781, -281, -374, -1118, -184, 2, 208, 0; -17472, -855, -3072, -3237, -510, -678, -2028, -336, 0, 312, -1],294,8]
%
% END OF LATTICE L295.8
%
%
% LATTICE L295.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-15767856, 48672, 24336; 48672, -147, -78; 24336, -78, -35],[1872, 3, 1],[703, 21, 101, 63, 25, 2, 10, -1, -1, 9, 2; 145704, 4352, 20928, 13052, 5178, 414, 2067, -208, -207, 1872, 415; 163800, 4894, 23544, 14690, 5832, 467, 2340, -232, -234, 2080, 465],294,9]
%
% END OF LATTICE L295.9
%
%
% LATTICE L295.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[7125197976, 3157662924, 1776195252; 3157662924, 1399376580, 787153692; 1776195252, 787153692, 442776409],[468, 12, 1],[279169, 33329, 40163, 100915, 40714, 6921, 43382, 87, 232, 6602, 6457; 351, 41, 48, 117, 45, 7, 39, 0, 3, 13, 10; -1120509, -133772, -161199, -405028, -163404, -27776, -174096, -349, -936, -26507, -25920],294,10]
%
% END OF LATTICE L295.10
%
%
% LATTICE L295.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[13357968, 108576, -25584; 108576, 845, -208; -25584, -208, 49],[624, 13, 1],[33, 41, 71, 11, 21, 6, 1, -1, -2, -3, 1; -40, -48, -80, -12, -22, -6, -1, 0, 1, 0, -3; 17048, 21190, 36712, 5690, 10868, 3107, 518, -520, -1040, -1568, 507],294,11]
%
% END OF LATTICE L295.11
%
%
% LATTICE L295.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[32526, 8424, -3276; 8424, 1443, -585; -3276, -585, 236],[234, 39, 1],[7, 3, -1, -1, -13, -5, -5, -3, -1, 1, 3; 234, 76, -174, -56, -630, -228, -222, -130, -42, 42, 125; 666, 221, -468, -155, -1755, -637, -621, -364, -117, 118, 351],294,12]
%
% END OF LATTICE L295.12
%
%
% LATTICE L295.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1880112, 0, 8112; 0, 16, 0; 8112, 0, -35],[624, 16, 1],[11, 2, 0, -4, -1, 0, 9, 2, 7, 12, 5; -39, -11, -3, -13, 0, 1, 0, -1, -6, -13, -9; 2522, 456, -2, -936, -232, 0, 2080, 462, 1616, 2769, 1152],294,13]
%
% END OF LATTICE L295.13
%
%
% LATTICE L295.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[69697134, -8426106, 34545654; -8426106, 1018680, -4176432; 34545654, -4176432, 17122687],[234, 78, 1],[-2911, -4712, -5951, -1196, -6586, -1168, -506, 71, 1274, 57, -231; 90, 145, 183, 37, 207, 39, 21, 1, -15, 0, 8; 5895, 9542, 12051, 2422, 13338, 2366, 1026, -143, -2574, -115, 468],294,14]
%
% END OF LATTICE L295.14
%
%
% LATTICE L295.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1146132, 381888, -7488; 381888, 127257, -2496; -7488, -2496, 49],[468, 39, 1],[-161, -63, -307, -15, -80, -14, -7, -1, 1, -3, -11; 624, 244, 1188, 58, 309, 54, 27, 4, -3, 12, 43; 7164, 2795, 13572, 661, 3510, 611, 306, 52, 0, 152, 507],294,15]
%
% END OF LATTICE L295.15
%
%
% LATTICE L295.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-65520, -42120, 3744; -42120, -18696, 1704; 3744, 1704, -155],[936, 24, 1],[6, -1, -1, 7, 5, 41, 115, 49, 43, 187, 6; 156, -24, -26, 156, 126, 1044, 2938, 1254, 1102, 4797, 155; 1859, -288, -310, 1872, 1504, 12456, 35048, 14958, 13144, 57213, 1848],294,16]
%
% END OF LATTICE L295.16
%
%
% LATTICE L295.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-65520, 2808, 7488; 2808, -120, -312; 7488, -312, -623],[936, 24, 1],[25, -1, -1, 7, 9, 77, 219, 47, 83, 725, 12; 650, -24, -26, 156, 230, 1980, 5642, 1212, 2142, 18720, 311; -26, 0, 1, 0, -8, -72, -208, -45, -80, -702, -12],294,17]
%
% END OF LATTICE L295.17
%
%
% LATTICE L295.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[8112, -1248, 0; -1248, 195, 0; 0, 0, -1],[624, 39, 1],[1, 1, -1, -1, -5, -4, -2, -25, -7, -11, 0; 8, 6, -8, -6, -28, -21, -10, -120, -32, -48, 1; -24, 0, 0, -12, -78, -78, -45, -624, -195, -336, -13],294,18]
%
% END OF LATTICE L295.18
%
%
% LATTICE L295.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-8263632, -1559376, 39936; -1559376, -294240, 7536; 39936, 7536, -193],[624, 48, 1],[10, -1, -1, 7, 7, 17, 137, 19, 49, 70, 4; 13, 1, -1, -13, -2, 1, 26, 5, 16, 26, 3; 2574, -168, -246, 936, 1368, 3552, 29328, 4122, 10752, 15483, 944],294,19]
%
% END OF LATTICE L295.19
%
%
% LATTICE L295.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[910728, -308880, -6552; -308880, 104754, 2223; -6552, 2223, 47],[936, 39, 1],[3, 1, -11, -13, -17, -68, -10, -169, -28, -59, 3; 8, 3, -28, -33, -43, -171, -25, -420, -69, -144, 8; 40, 0, -208, -252, -338, -1404, -214, -3744, -650, -1440, 39],294,20]
%
% END OF LATTICE L295.20
%
%
% LATTICE L295.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[89227944, -9924408, -93600; -9924408, 1103817, 10413; -93600, 10413, 98],[936, 39, 1],[-3, 41, -1, -47, -94, -520, -95, -1907, -383, -961, -51; -24, 330, -8, -378, -756, -4182, -764, -15336, -3080, -7728, -410; -316, 4095, -104, -4725, -9451, -52299, -9557, -191880, -38545, -96732, -5148],294,21]
%
% END OF LATTICE L295.21
%
%
% LATTICE L295.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1821456, -308880, -13104; -308880, 52377, 2223; -13104, 2223, 94],[1872, 39, 1],[-59, -14, -169, -5, -34, -17, -13, -11, 1, 3, 3; -288, -69, -840, -25, -171, -86, -66, -56, 6, 16, 16; -1440, -325, -3744, -107, -702, -338, -252, -208, 0, 40, 39],294,22]
%
% END OF LATTICE L295.22
%
%
% LATTICE L295.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[31518864, 846144, -39312; 846144, 22542, -1053; -39312, -1053, 49],[1872, 39, 1],[19, 9, 53, 3, 19, 2, 1, -1, -4, -3, -1; 264, 128, 768, 44, 282, 30, 15, -16, -63, -48, -17; 20880, 9958, 58968, 3350, 21294, 2249, 1125, -1144, -4563, -3440, -1170],294,23]
%
% END OF LATTICE L295.23
%
%
% LATTICE L295.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-59721480, -1348308, 13808808; -1348308, -30108, 312000; 13808808, 312000, -3192695],[468, 156, 1],[7634, 10927, 11626, 1913, 7190, 219, -794, -480, 116, 367, 4175; -22626, -32385, -34455, -5669, -21303, -647, 2355, 1423, -345, -1088, -12376; 30807, 44096, 46917, 7720, 29016, 884, -3204, -1937, 468, 1481, 16848],294,24]
%
% END OF LATTICE L295.24
%
%
% LATTICE L295.25
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-526599216, -12821328, 555984; -12821328, -312096, 13536; 555984, 13536, -587],[1872, 48, 1],[12, -1, -1, 7, 5, 41, 115, 49, 43, 187, 12; 169, -12, -14, 78, 67, 558, 1573, 672, 591, 2574, 167; 15262, -1224, -1270, 8424, 6280, 51696, 145184, 61902, 54352, 236457, 15216],294,25]
%
% END OF LATTICE L295.25
%
%
% LATTICE L295.26
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-65520, -84240, 3744; -84240, -74784, 3408; 3744, 3408, -155],[1872, 48, 1],[6, -1, -1, 7, 5, 41, 115, 49, 43, 374, 12; 78, -12, -13, 78, 63, 522, 1469, 627, 551, 4797, 155; 1859, -288, -310, 1872, 1504, 12456, 35048, 14958, 13144, 114426, 3696],294,26]
%
% END OF LATTICE L295.26
%
%
% LATTICE L295.27
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2861040, 0, 8112; 0, 208, 0; 8112, 0, -23],[624, 208, 1],[-5, -22, -8, -4, -5, 0, 1, 2, 3, 0, -7; -3, -11, -3, -1, 0, 1, 0, -1, -6, -1, -9; -1774, -7800, -2834, -1416, -1768, 0, 352, 702, 1040, -3, -2496],294,27]
%
% END OF LATTICE L295.27
%
%
% LATTICE L295.28
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1872, -936, 0; -936, -3938376, 19344; 0, 19344, -95],[936, 312, 1],[22, 63, 67, 11, 41, 1, -5, -3, -1, 1, 12; 39, 110, 114, 18, 60, -2, -12, -6, 0, 2, 23; 7929, 22360, 23166, 3656, 12168, -416, -2448, -1222, 0, 407, 4680],294,28]
%
% END OF LATTICE L295.28
%
%
% LATTICE L295.29
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1872, -936, 0; -936, -177528, 2496; 0, 2496, -35],[936, 312, 1],[17, 23, 11, 3, 5, -3, -5, -1, -1, 1, 6; 24, 30, 12, 2, -12, -10, -12, -2, 0, 2, 11; 1674, 2080, 819, 128, -936, -728, -864, -143, 0, 142, 780],294,29]
%
% END OF LATTICE L295.29
%
%
% LATTICE L295.30
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-6535776, -6536400, 19968; -6536400, -6536400, 19968; 19968, 19968, -61],[624, 624, 1],[0, 1, 0, -1, -6, -11, -6, -10, -24, -5, -1; 1, -1, -5, -5, -13, -7, 1, 7, 29, 8, 8; 327, 0, -1638, -1968, -6240, -5928, -1656, -1014, 1560, 966, 2288],294,30]
%
% END OF LATTICE L295.30
%
%
% LATTICE L295.31
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1872, 0, 0; 0, -15755376, 38688; 0, 38688, -95],[1872, 624, 1],[0, 1, 0, -1, -2, -11, -2, -10, -8, -5, -1; 1, 0, -3, -6, -1, 30, 9, 57, 55, 39, 23; 407, 0, -1222, -2448, -416, 12168, 3656, 23166, 22360, 15858, 9360],294,31]
%
% END OF LATTICE L295.31
%
%
% LATTICE L295.32
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[251441424, 103603968, -269568; 103603968, 42688464, -111072; -269568, -111072, 289],[1872, 624, 1],[1, 1, -1, -1, 2, 25, 6, 35, 32, 11, 11; 3, 0, -4, -6, 3, 66, 17, 102, 95, 33, 35; 2086, 936, -2470, -3240, 3016, 48672, 12128, 71838, 66352, 22941, 23712],294,32]
%
% END OF LATTICE L295.32
%

\medskip%
%------------------------------WEYL-GROUP-W296--------------------------------
%
\leavevmode\llap{}%
$W_{296}$%
\qquad\llap{32} lattices, $\chi=72$%
\hfill%
$2222222222222222\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L296.1
%
\leavevmode%
${L_{296.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}8\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{2}{}9\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{2}{}7\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${504}\above{1pt}{1pt}{r}{2}{10}\above{1pt}{1pt}{s}{2}{126}\above{1pt}{1pt}{b}{2}{2}\above{1pt}{1pt}{l}{2}{56}\above{1pt}{1pt}{r}{2}{18}\above{1pt}{1pt}{b}{2}{14}\above{1pt}{1pt}{b}{2}{2}\above{1pt}{1pt}{l}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2552760\\-511560\\-2520
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-511560\\102514\\505
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2520\\505\\2
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2615759\\13048560\\997920
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-524536\\-2616617\\-200112
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2249\\11219\\857
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-174485\\-870408\\-66528
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-6921\\-34525\\-2640
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-21457\\-107037\\-8190
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1298\\-6475\\-496
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-8049\\-40152\\-3080
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-866\\-4320\\-333
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-87\\-434\\-35
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\-1
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[2552760, -511560, -2520; -511560, 102514, 505; -2520, 505, 2],[2520, 1, 1],[-174485, -6921, -21457, -1298, -8049, -866, -87, 0, 101, 1, -341, -86, -1639, -691, -1124, -2249; -870408, -34525, -107037, -6475, -40152, -4320, -434, 0, 504, 5, -1701, -429, -8176, -3447, -5607, -11219; -66528, -2640, -8190, -496, -3080, -333, -35, -1, 0, 0, -126, -32, -616, -261, -427, -857],295,1]
%
% END OF LATTICE L296.1
%
%
% LATTICE L296.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[161910, 32130, -630; 32130, 6376, -125; -630, -125, 2],[630, 1, 1],[-25, -1, 137, 35, 335, 283, 461, 923, 35809, 2841, 8809, 533, 1653, 356, 36, 0; 126, 5, -693, -177, -1694, -1431, -2331, -4667, -181062, -14365, -44541, -2695, -8358, -1800, -182, 0; 0, 0, -126, -32, -308, -261, -427, -857, -33264, -2640, -8190, -496, -1540, -333, -35, -1],295,2]
%
% END OF LATTICE L296.2
%
%
% LATTICE L296.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[4016880, -32130, 2008440; -32130, 232, -16060; 2008440, -16060, 1004219],[630, 2, 1],[-157, 623, 2449, -11, -1455, -3517, -7313, -16185, -319631, -51383, -162343, -10141, -16311, -7904, -1570, -312; 63, -250, -1008, -2, 553, 1359, 2849, 6323, 124929, 20090, 63504, 3970, 6391, 3105, 623, 125; 315, -1250, -4914, 22, 2919, 7056, 14672, 32472, 641277, 103090, 325710, 20346, 32725, 15858, 3150, 626],295,3]
%
% END OF LATTICE L296.3
%
%
% LATTICE L296.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[159390, -1260, -630; -1260, 10, 5; -630, 5, 2],[630, 5, 1],[-2017, -32, -496, -30, -93, -20, -2, 0, 1, 0, -8, -2, -19, -16, -26, -52; -220878, -3504, -54306, -3284, -10178, -2187, -217, 1, 126, 0, -882, -220, -2086, -1755, -2849, -5695; -73080, -1159, -17955, -1085, -3360, -720, -70, 0, 0, -1, -315, -75, -700, -585, -945, -1885],295,4]
%
% END OF LATTICE L296.4
%
%
% LATTICE L296.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[195930, -79380, -1260; -79380, 32158, 511; -1260, 511, 8],[630, 7, 1],[553, 318, 148, 68, 33, 65, 3, 9, 23, 2, -4, -4, -1, 7, 5, 95; 1314, 755, 351, 161, 78, 153, 7, 21, 54, 5, -9, -9, -2, 18, 12, 226; 2844, 1680, 810, 392, 200, 441, 25, 77, 180, 0, -54, -56, -32, -63, 17, 469],295,5]
%
% END OF LATTICE L296.5
%
%
% LATTICE L296.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[16995510, -133560, 7553070; -133560, 1044, -59355; 7553070, -59355, 3356702],[630, 9, 1],[-31, 538, 220, -44, -2847, -369, -6781, -14913, -65377, -47258, -16572, -9300, -29857, -799, -1395, -271; 14, -250, -112, -2, 1106, 151, 2849, 6323, 27762, 20090, 7056, 3970, 12782, 345, 623, 125; 70, -1215, -497, 99, 6426, 833, 15309, 33669, 147602, 106695, 37415, 20997, 67410, 1804, 3150, 612],295,6]
%
% END OF LATTICE L296.6
%
%
% LATTICE L296.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-395640, -1890, -197190; -1890, 1240, -940; -197190, -940, -98281],[630, 10, 1],[-722075, -22616, -343846, -20092, -29849, -10901, 593, 623, -157, -312, -17270, -2836, -10275, -14893, -20655, -37881; -3276, -103, -1575, -93, -140, -54, 0, 2, 0, -1, -63, -11, -42, -63, -91, -171; 1448685, 45374, 689850, 40310, 59885, 21870, -1190, -1250, 315, 626, 34650, 5690, 20615, 29880, 41440, 76000],295,7]
%
% END OF LATTICE L296.7
%
%
% LATTICE L296.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[13791960, -83790, 6868890; -83790, 448, -41734; 6868890, -41734, 3420953],[630, 14, 1],[-113480, -126677, -56509, -24219, -5434, -17081, -311, 307, 1700, 2477, 619, -621, -776, -10864, -2794, -40672; -13446, -15010, -6696, -2870, -644, -2025, -37, 35, 198, 290, 72, -74, -92, -1287, -331, -4819; 227691, 254170, 113382, 48594, 10903, 34272, 624, -616, -3411, -4970, -1242, 1246, 1557, 21798, 5606, 81606],295,8]
%
% END OF LATTICE L296.8
%
%
% LATTICE L296.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[11817140580, -36831690, 5898622590; -36831690, 114768, -18384840; 5898622590, -18384840, 2944345819],[630, 18, 1],[7425, 5346, -89680, -206086, -986777, -185299, -2717717, -5442559, -11731137, -16753506, -5772176, -3143546, -4875079, -233405, -213211, -593; 7, 5, -77, -177, -847, -159, -2331, -4667, -10059, -14365, -4949, -2695, -4179, -200, -182, 0; -14875, -10710, 179662, 412866, 1976877, 371222, 5444586, 10903446, 23501779, 33563430, 11563790, 6297678, 9766575, 467596, 427140, 1188],295,9]
%
% END OF LATTICE L296.9
%
%
% LATTICE L296.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2542680, -5040, -2520; -5040, 10, 5; -2520, 5, 2],[2520, 5, 1],[-2017, -16, -248, -15, -93, -10, -1, 0, 1, 0, -4, -1, -19, -8, -13, -26; -950040, -7536, -116802, -7064, -43792, -4707, -469, 1, 504, 0, -1890, -472, -8960, -3771, -6125, -12247; -146160, -1159, -17955, -1085, -6720, -720, -70, 0, 0, -1, -315, -75, -1400, -585, -945, -1885],295,10]
%
% END OF LATTICE L296.10
%
%
% LATTICE L296.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-60149880, -12040560, 45360; -12040560, -2410226, 9079; 45360, 9079, -34],[2520, 7, 1],[-12835, -3639, -1661, -740, -695, -628, -23, -58, -269, -1, 23, 12, -33, -191, -68, -1125; 65304, 18515, 8451, 3765, 3536, 3195, 117, 295, 1368, 5, -117, -61, 168, 972, 346, 5724; 314136, 89040, 40626, 18088, 16976, 15309, 557, 1393, 6408, 0, -558, -280, 832, 4725, 1669, 27545],295,11]
%
% END OF LATTICE L296.11
%
%
% LATTICE L296.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[101723097304080, -812237401080, 155922480; -812237401080, 6485543728, -1245008; 155922480, -1245008, 239],[2520, 8, 1],[1, -1, 283, 73, 177, 602, 988, 1986, 19277, 6121, 18995, 1151, 894, 775, 83, 3; 126, -125, 35469, 9149, 22183, 75447, 123823, 248899, 2415924, 767125, 2380581, 144251, 112042, 97128, 10402, 376; 3969, 1240, 138600, 34464, 82565, 279432, 456960, 917144, 8899695, 2825320, 8765064, 530848, 412083, 356544, 37688, 1488],295,12]
%
% END OF LATTICE L296.12
%
%
% LATTICE L296.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1651230, -4410, 13230; -4410, 70, 35; 13230, 35, -106],[630, 35, 1],[31, 6, 22, 16, 11, 38, 4, 26, 113, 10, 14, 0, -3, -20, -2, 0; 18, 3, 9, 5, 2, 0, -2, -40, -234, -27, -63, -29, -14, -27, -1, 1; 3870, 749, 2745, 1995, 1370, 4725, 495, 3185, 13770, 1211, 1665, -35, -390, -2520, -250, 0],295,13]
%
% END OF LATTICE L296.13
%
%
% LATTICE L296.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-93308040, -37336320, 65520; -37336320, -14939766, 26217; 65520, 26217, -46],[2520, 9, 1],[-107, -2, 8, 5, -127, -11, -242, -569, -5045, -1838, -652, -373, -2449, -35, -80, -29; 280, 5, -21, -13, 336, 29, 637, 1497, 13272, 4835, 1715, 981, 6440, 92, 210, 76; 7168, 0, -574, -288, 10584, 859, 18333, 42687, 377888, 137520, 48706, 27792, 181944, 2579, 5733, 2007],295,14]
%
% END OF LATTICE L296.14
%
%
% LATTICE L296.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-82530, 2520, -36540; 2520, 5580, 1125; -36540, 1125, -16178],[630, 45, 1],[-149545, -21097, -35689, -18817, -56093, -1154, 418, 538, -31, -271, -1705, -2551, -18695, -1517, -19115, -35261; -728, -103, -175, -93, -280, -6, 0, 2, 0, -1, -7, -11, -84, -7, -91, -171; 337610, 47628, 80570, 42480, 126630, 2605, -945, -1215, 70, 612, 3850, 5760, 42210, 3425, 43155, 79605],295,15]
%
% END OF LATTICE L296.15
%
%
% LATTICE L296.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-139230, -22050, -63000; -22050, 2016, -9639; -63000, -9639, -28486],[630, 63, 1],[-21517, -108092, -5358, -20670, -9277, -1621, -267, 251, 317, 2092, 58, -530, -1323, -1029, -2383, -34701; -2988, -15010, -744, -2870, -1288, -225, -37, 35, 44, 290, 8, -74, -184, -143, -331, -4819; 48596, 244125, 12101, 46683, 20952, 3661, 603, -567, -716, -4725, -131, 1197, 2988, 2324, 5382, 78372],295,16]
%
% END OF LATTICE L296.16
%
%
% LATTICE L296.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1176722820, -542430, 586463220; -542430, 280, -270340; 586463220, -270340, 292285577],[630, 70, 1],[16529, 5561, 24715, 23479, 11585, 115232, 23170, 303064, 828715, 182271, 397907, 164353, 35373, 96079, 309, 2163; 0, -1, -9, -11, -6, -63, -13, -171, -468, -103, -225, -93, -20, -54, 0, 2; -33165, -11158, -49590, -47110, -23245, -231210, -46490, -608090, -1662795, -365722, -798390, -329770, -70975, -192780, -620, -4340],295,17]
%
% END OF LATTICE L296.17
%
%
% LATTICE L296.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[11619552420, 1443330, 5799994830; 1443330, 180, 720450; 5799994830, 720450, 2895114959],[630, 90, 1],[-1808531, -516215, -888411, -483025, -747651, -35560, -30818, 0, -297, -593, -16003, -33783, -156763, -29041, -421389, -839813; -12271, -3504, -6034, -3284, -5089, -243, -217, 1, 7, 0, -98, -220, -1043, -195, -2849, -5695; 3623165, 1034172, 1779820, 967680, 1497825, 71240, 61740, 0, 595, 1188, 32060, 67680, 314055, 58180, 844200, 1682460],295,18]
%
% END OF LATTICE L296.18
%
%
% LATTICE L296.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[13632171840, 88830630, 6804609840; 88830630, 578844, 44340534; 6804609840, 44340534, 3396576541],[630, 126, 1],[-70547, -703788, -34542, -131072, -28909, -9553, -1213, -2453, -901, -10692, -1182, -11824, -6815, -8309, -16649, -229753; 73, 755, 39, 161, 39, 17, 7, 21, 3, 5, -1, -9, -1, 2, 12, 226; 141331, 1409940, 69200, 262584, 57915, 19138, 2430, 4914, 1805, 21420, 2368, 23688, 13653, 16646, 33354, 460278],295,19]
%
% END OF LATTICE L296.19
%
%
% LATTICE L296.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-237668760, -55440, 158760; -55440, 70, 35; 158760, 35, -106],[2520, 35, 1],[113, 5, 7, 0, -3, -10, -1, 0, 31, 3, 11, 8, 11, 19, 2, 13; 3600, 153, 189, -29, -136, -387, -37, 1, 1152, 111, 405, 293, 400, 684, 70, 428; 169920, 7511, 10485, -35, -4560, -15120, -1510, 0, 46800, 4529, 16605, 12075, 16600, 28665, 3015, 19565],295,20]
%
% END OF LATTICE L296.20
%
%
% LATTICE L296.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2121840, -1721160, 214200; -1721160, -42011440, 5254920; 214200, 5254920, -657301],[2520, 40, 1],[13414, 911, 15469, 1077, 963, 1211, 443, 87, -436, -87, -2491, -253, -242, -284, 278, 1252; 3378690, 229469, 3896613, 271311, 242606, 305118, 111636, 21926, -109872, -21925, -627795, -63767, -61005, -71631, 69965, 315333; 27015975, 1834832, 31157280, 2169400, 1939875, 2439720, 892640, 175320, -878535, -175312, -5019840, -509880, -487795, -572760, 559440, 2521400],295,21]
%
% END OF LATTICE L296.21
%
%
% LATTICE L296.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[107878680, 17438400, -385560; 17438400, 2818890, -62325; -385560, -62325, 1378],[2520, 45, 1],[14223, 1015, 1747, 950, 5883, 70, 61, 0, 1, 1, 31, 66, 1229, 57, 828, 1651; -57568, -4108, -7070, -3844, -23800, -283, -245, 1, 0, -4, -126, -268, -4984, -231, -3353, -6683; 1375640, 98181, 169015, 91935, 569520, 6785, 5985, 45, 280, 99, 2975, 6345, 118440, 5500, 80010, 159660],295,22]
%
% END OF LATTICE L296.22
%
%
% LATTICE L296.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[157847760, 4699800, -133560; 4699800, 139888, -3976; -133560, -3976, 113],[2520, 56, 1],[2, 1, -1, -1, 0, 4, 2, 36, 52, 119, 55, 25, 3, 23, 1, 3; 63, 30, -36, -38, -2, 81, 53, 997, 1449, 3330, 1548, 710, 86, 675, 31, 95; 4581, 2240, -2448, -2520, -71, 7560, 4224, 77560, 112347, 257600, 119376, 54488, 6567, 50904, 2272, 6888],295,23]
%
% END OF LATTICE L296.23
%
%
% LATTICE L296.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[47880, -2520, 2520; -2520, 126, -189; 2520, -189, -346],[2520, 63, 1],[15, -1, -1, 0, 35, 17, 48, 763, 961, 2441, 123, 488, 453, 44, 13, 30; 256, -15, -17, -1, 592, 288, 814, 12944, 16304, 41415, 2087, 8281, 7688, 747, 221, 511; -32, 0, 2, 0, -72, -35, -99, -1575, -1984, -5040, -254, -1008, -936, -91, -27, -63],295,24]
%
% END OF LATTICE L296.24
%
%
% LATTICE L296.25
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2988720, 209160, 93240; 209160, 14544, 6480; 93240, 6480, 2887],[2520, 72, 1],[2, 1, -1, -1, 1, 1, 25, 61, 68, 199, 71, 41, 34, 4, 10, 4; -350, -175, 189, 207, -98, -146, -3948, -9818, -10976, -32185, -11515, -6679, -5565, -663, -1715, -699; 721, 360, -392, -432, 189, 296, 8064, 20088, 22463, 65880, 23576, 13680, 11403, 1360, 3528, 1440],295,25]
%
% END OF LATTICE L296.25
%
%
% LATTICE L296.26
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[234623970, 514080, -103420800; 514080, 1260, -226485; -103420800, -226485, 45587356],[630, 315, 1],[-3077, -4658, -2300, -19664, -19405, -10723, -19405, -253819, -154235, -152654, -37028, -137648, -59251, -8941, -259, -1813; 6154, 9315, 4599, 39317, 38798, 21439, 38797, 507467, 308366, 305205, 74031, 275203, 118462, 17876, 518, 3628; -6950, -10521, -5195, -44415, -43830, -24220, -43830, -573300, -348370, -344799, -83635, -310905, -133830, -20195, -585, -4095],295,26]
%
% END OF LATTICE L296.26
%
%
% LATTICE L296.27
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-24573883320, -3178849590, -1545369210; -3178849590, -411212340, -199907190; -1545369210, -199907190, -97183087],[630, 630, 1],[1, 3, 1, 5, 1, 0, -2, -40, -13, -27, -7, -29, -7, -3, -1, 1; -7312, -25321, -10241, -66499, -22606, -17083, -15473, -90959, -20772, -30847, -3801, 10331, 8564, 10062, 8452, -314; 15025, 52038, 21050, 136710, 46485, 35140, 31860, 187740, 42935, 63882, 7930, -20790, -17505, -20650, -17370, 630],295,27]
%
% END OF LATTICE L296.27
%
%
% LATTICE L296.28
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-33228720, -738360, 37800; -738360, -16240, 840; 37800, 840, -43],[2520, 280, 1],[2, 2, 8, 6, 1, 13, 1, 1, -2, -2, -8, -6, -1, -13, -1, -1; 0, -1, -9, -11, -3, -63, -13, -171, -234, -103, -225, -93, -10, -54, 0, 2; 1755, 1736, 6840, 5040, 815, 10080, 600, -2800, -6795, -3976, -11880, -7280, -1095, -12600, -880, -840],295,28]
%
% END OF LATTICE L296.28
%
%
% LATTICE L296.29
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[9492840, -126000, -3003840; -126000, 630, 41265; -3003840, 41265, 948646],[2520, 315, 1],[-26173, -13411, -3417, -13790, -12993, -1310, -391, 0, 909, 779, 259, 1158, 361, -269, -1188, -20527; -104744, -53671, -13675, -55189, -52000, -5243, -1565, 1, 3640, 3119, 1037, 4637, 1448, -1076, -4754, -82148; -78320, -40131, -10225, -41265, -38880, -3920, -1170, 0, 2720, 2331, 775, 3465, 1080, -805, -3555, -61425],295,29]
%
% END OF LATTICE L296.29
%
%
% LATTICE L296.30
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-163653840, -9704520, 133560; -9704520, -575280, 7920; 133560, 7920, -109],[2520, 360, 1],[-911, -521, -899, -491, -382, -37, -37, -1, 1, 1, -11, -29, -73, -28, -418, -844; -182, -103, -175, -93, -70, -6, 0, 2, 0, -1, -7, -11, -21, -7, -91, -171; -1130185, -646272, -1114960, -608760, -473445, -45800, -45360, -1080, 1225, 1152, -14000, -36360, -91035, -34840, -519120, -1047240],295,30]
%
% END OF LATTICE L296.30
%
%
% LATTICE L296.31
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[5040, -1111320, 2520; -1111320, 233627184, -529704; 2520, -529704, 1201],[2520, 504, 1],[2, 1, -1, -1, 4, 16, 46, 736, 116, 2359, 119, 473, 55, 43, 13, 31; 3, 0, -2, -8, 4, 19, 59, 967, 153, 3120, 158, 632, 74, 59, 19, 47; 1319, 0, -880, -3528, 1755, 8344, 25920, 424872, 67225, 1370880, 69424, 277704, 32517, 25928, 8352, 20664],295,31]
%
% END OF LATTICE L296.31
%
%
% LATTICE L296.32
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-912003120, -941807160, 385560; -941807160, -972583920, 398160; 385560, 398160, -163],[2520, 2520, 1],[-119, -479, -119, -461, -52, -37, -7, -1, 1, 7, 1, -11, -7, -22, -52, -766; -26, -103, -25, -93, -10, -6, 0, 2, 0, -1, -1, -11, -3, -7, -13, -171; -345085, -1384992, -342640, -1317960, -147465, -102200, -16560, 2520, 2365, 14112, -80, -52920, -23895, -69160, -154800, -2230200],295,32]
%
% END OF LATTICE L296.32
%

\medskip%
%------------------------------WEYL-GROUP-W297--------------------------------
%
\leavevmode\llap{}%
$W_{297}$%
\qquad\llap{8} lattices, $\chi=36$%
\hfill%
$22222|22222|\rtimes D_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L297.1
%
\leavevmode%
${L_{297.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{2}32\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{2}{}7\above{1pt}{1pt}{1}{}$}\EasyButWeakLineBreak%
{${224}\above{1pt}{1pt}{s}{2}{12}\above{1pt}{1pt}{*}{2}{28}\above{1pt}{1pt}{l}{2}{3}\above{1pt}{1pt}{}{2}{224}\above{1pt}{1pt}{r}{2}{2}\above{1pt}{1pt}{b}{2}{224}\above{1pt}{1pt}{*}{2}{12}\above{1pt}{1pt}{l}{2}{7}\above{1pt}{1pt}{}{2}{3}\above{1pt}{1pt}{r}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-8766240\\7392\\16128
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7392\\-5\\-16
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
16128\\-16\\-25
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
37\\20608\\10640
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
11\\6132\\3162
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
19\\10598\\5460
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
13\\7254\\3735
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
177\\98784\\50848
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\559\\287
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
9\\5040\\2576
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-558\\-288
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-560\\-287
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\555\\288
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-8766240, 7392, 16128; 7392, -5, -16; 16128, -16, -25],[672, 1, 1],[37, 11, 19, 13, 177, 1, 9, -1, -1, 1; 20608, 6132, 10598, 7254, 98784, 559, 5040, -558, -560, 555; 10640, 3162, 5460, 3735, 50848, 287, 2576, -288, -287, 288],296,1]
%
% END OF LATTICE L297.1
%
%
% LATTICE L297.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-225120, 1344, 672; 1344, 165, -3; 672, -3, -2],[672, 3, 1],[29, 1, -1, -1, -55, -1, 1, 1, 3, 1; -112, -6, -14, -1, 0, 2, 0, -2, -7, -3; 9408, 308, -462, -362, -19488, -339, 336, 338, 1008, 331],296,2]
%
% END OF LATTICE L297.2
%
%
% LATTICE L297.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-206304, 2688, 8736; 2688, -35, -112; 8736, -112, -223],[672, 7, 1],[19, 1, -1, -1, 15, 7, 135, 67, 13, 47; 1504, 75, -80, -78, 1200, 559, 10752, 5334, 1034, 3732; -16, 0, 1, 0, -16, -7, -128, -63, -12, -42],296,3]
%
% END OF LATTICE L297.3
%
%
% LATTICE L297.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-253344, -24864, 4032; -24864, -2121, 336; 4032, 336, -53],[672, 21, 1],[-19, -11, -7, -10, -55, -1, 1, 1, 0, -2; 1488, 858, 544, 775, 4256, 75, -80, -76, 1, 158; 7968, 4592, 2910, 4144, 22752, 399, -432, -406, 6, 847],296,4]
%
% END OF LATTICE L297.4
%
%
% LATTICE L297.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3535392, -12768, 9408; -12768, 64, 32; 9408, 32, -25],[672, 32, 1],[-19, -19, -9, -1, 1, 2, -26, -37, -37, -31; -140, -138, -63, -6, 7, 13, -203, -285, -280, -231; -7350, -7344, -3472, -384, 385, 768, -10094, -14352, -14336, -12000],296,5]
%
% END OF LATTICE L297.5
%
%
% LATTICE L297.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1950816, 387072, 12096; 387072, -41952, -1344; 12096, -1344, -43],[672, 96, 1],[-19, -12, -51, -20, -47, -1, 1, 1, -2, -5; 3052, 1929, 8204, 3219, 7567, 163, -161, -162, 315, 802; -100758, -63680, -270816, -106256, -249774, -5376, 5313, 5344, -10416, -26480],296,6]
%
% END OF LATTICE L297.6
%
%
% LATTICE L297.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[672, 0, 0; 0, -263648, 3808; 0, 3808, -55],[672, 224, 1],[-1, -5, 0, 1, 0, -1, -3, -26, -3, -14; -2, -24, -3, 0, 1, 13, 7, 45, 2, -9; -142, -1680, -208, 0, 69, 896, 474, 3024, 128, -672],296,7]
%
% END OF LATTICE L297.7
%
%
% LATTICE L297.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-790944, 2558976, 11424; 2558976, 3060960, 13440; 11424, 13440, 59],[672, 672, 1],[11, 31, 10, 13, 1, -13, 7, 28, 15, 36; -760, -2142, -691, -898, -69, 899, -483, -1933, -1036, -2487; 170994, 481936, 155472, 202048, 15525, -202272, 108666, 434896, 233088, 559552],296,8]
%
% END OF LATTICE L297.8
%

\medskip%
%------------------------------WEYL-GROUP-W298--------------------------------
%
\leavevmode\llap{}%
$W_{298}$%
\qquad\llap{6} lattices, $\chi=40$%
\hfill%
$26|62|26|62|\rtimes D_{4}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L298.1
%
\leavevmode%
${L_{298.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{-}{}9\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}25\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${150}\above{1pt}{1pt}{s}{2}{18}\above{1pt}{1pt}{}{6}{6}\above{1pt}{1pt}{}{6}{2}\above{1pt}{1pt}{s}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-30392100\\1091700\\-9061200
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1091700\\-34842\\329757
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-9061200\\329757\\-2697358
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-362227951\\-1062468900\\1086939000
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
13177346\\38651131\\-39541320
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-107833621\\-316292182\\323576819
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
17021\\49925\\-51075
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
8527\\25011\\-25587
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-8511\\-24964\\25539
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-83754\\-245663\\251321
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-30392100, 1091700, -9061200; 1091700, -34842, 329757; -9061200, 329757, -2697358],[900, 3, 1],[17021, 8527, -8511, -83754, -762346, -276844, -21302, -5685; 49925, 25011, -24964, -245663, -2236075, -812025, -62482, -16675; -51075, -25587, 25539, 251321, 2287575, 830727, 63921, 17059],297,1]
%
% END OF LATTICE L298.1
%
%
% LATTICE L298.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-2231775, -149625, -588375; -149625, -9354, -40158; -588375, -40158, -154369],[225, 3, 1],[162933, 17899, 1817, -1825, -3633, 1217, 4555, 59173; -512375, -56287, -5714, 5739, 11425, -3827, -14324, -186081; -487725, -53579, -5439, 5463, 10875, -3643, -13635, -177129],297,2]
%
% END OF LATTICE L298.2
%
%
% LATTICE L298.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[54247780470600, 303049278900, 13536109377000; 303049278900, 1692951576, 75617991192; 13536109377000, 75617991192, 3377580713471],[900, 12, 1],[12501, 1823, 12110, 108513, 983649, 356791, 27736, 11025; 25, 93, 337, 2481, 22075, 7863, 547, 171; -50100, -7308, -48540, -434936, -3942600, -1430064, -111168, -44188],297,3]
%
% END OF LATTICE L298.3
%
%
% LATTICE L298.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-141975, 702225, -29700; 702225, -3472050, 146850; -29700, 146850, -6211],[225, 75, 1],[1, 23, -12, -159, -59, -545, -46, -15; -5, -81, 61, 673, 247, 2259, 181, 53; -123, -2025, 1500, 16675, 6123, 56025, 4500, 1325],297,4]
%
% END OF LATTICE L298.4
%
%
% LATTICE L298.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1188900, -4645800, -202500; -4645800, -18151050, -791175; -202500, -791175, -34486],[900, 75, 1],[-7, 27, 148, 2156, 242, 678, 87, -41; -19, 77, 410, 5931, 665, 1861, 236, -117; 477, -1925, -10275, -148725, -16677, -46675, -5925, 2925],297,5]
%
% END OF LATTICE L298.5
%
%
% LATTICE L298.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[11423788200, -149183100, -2955366000; -149183100, 1948200, 38594100; -2955366000, 38594100, 764561471],[900, 300, 1],[3, -6009, -19972, -291727, -32841, -92505, -12866, -3815; -8, 17286, 57439, 838908, 94438, 266004, 36991, 10962; 12, -24100, -80100, -1170000, -131712, -371000, -51600, -15300],297,6]
%
% END OF LATTICE L298.6
%

\medskip%
%------------------------------WEYL-GROUP-W299--------------------------------
%
\leavevmode\llap{}%
$W_{299}$%
\qquad\llap{6} lattices, $\chi=20$%
\hfill%
$222|222\slashthree\rtimes D_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L299.1
%
\leavevmode%
${L_{299.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{1}{}3\above{1pt}{1pt}{-}{}9\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{-2}{}25\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${6}\above{1pt}{1pt}{b}{2}{100}\above{1pt}{1pt}{*}{2}{36}\above{1pt}{1pt}{b}{2}{150}\above{1pt}{1pt}{b}{2}{4}\above{1pt}{1pt}{*}{2}{900}\above{1pt}{1pt}{b}{2}{6}\above{1pt}{1pt}{+}{3}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3536100\\4500\\3600
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4500\\6\\-9
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3600\\-9\\-2
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\-1\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\750\\2000
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\252\\666
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-250\\-675
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-252\\-670
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-41\\-10350\\-27450
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-253\\-669
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-3536100, 4500, 3600; 4500, 6, -9; 3600, -9, -2],[900, 3, 1],[0, 3, 1, -1, -1, -41, -1; -1, 750, 252, -250, -252, -10350, -253; 0, 2000, 666, -675, -670, -27450, -669],298,1]
%
% END OF LATTICE L299.1
%
%
% LATTICE L299.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[65025, 900, -1575; 900, -3, -6; -1575, -6, 22],[225, 3, 1],[-1, 1, 2, 16, 2, 53, 1; -101, 100, 201, 1600, 199, 5250, 97; -99, 100, 198, 1575, 196, 5175, 96],298,2]
%
% END OF LATTICE L299.2
%
%
% LATTICE L299.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[3072846600, -15531300, 764776800; -15531300, 78504, -3865464; 764776800, -3865464, 190339327],[900, 12, 1],[1111, 4119, 560, 4704, 1228, 51407, 2673; -2, 0, 3, 25, 3, 75, 1; -4464, -16550, -2250, -18900, -4934, -206550, -10740],298,3]
%
% END OF LATTICE L299.3
%
%
% LATTICE L299.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-57825, -33750, 900; -33750, -19650, 525; 900, 525, -14],[225, 75, 1],[-4, -1, -5, 0, 1, 1, 0; -1, -1, -9, -1, -1, 0, 2; -300, -104, -675, -39, 25, 63, 75],298,4]
%
% END OF LATTICE L299.4
%
%
% LATTICE L299.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[19619100, -3247200, 64800; -3247200, 537450, -10725; 64800, -10725, 214],[900, 75, 1],[12, 3, 1, -1, -1, 7, 11; 80, 20, 6, -7, -10, 42, 71; 375, 94, 0, -48, -200, -18, 225],298,5]
%
% END OF LATTICE L299.5
%
%
% LATTICE L299.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[77250600, 3948300, -16271100; 3948300, 184200, -844800; -16271100, -844800, 3417271],[900, 300, 1],[-11798, 568, 17137, 227, -13503, -27119, -40621; 35497, -1709, -51561, -683, 40627, 81594, 122218; -47400, 2282, 68850, 912, -54250, -108954, -163200],298,6]
%
% END OF LATTICE L299.6
%

\medskip%
%------------------------------WEYL-GROUP-W300--------------------------------
%
\leavevmode\llap{}%
$W_{300}$%
\qquad\llap{8} lattices, $\chi=24$%
\hfill%
$\infty22\infty\infty$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L300.1
%
\leavevmode%
${L_{300.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}8\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{-}{}7\above{1pt}{1pt}{1}{}49\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${56}\above{1pt}{1pt}{14,9}{\infty z}{14}\above{1pt}{1pt}{b}{2}{98}\above{1pt}{1pt}{b}{2}{56}\above{1pt}{1pt}{14,1}{\infty z}{14}\above{1pt}{1pt}{28,23}{\infty b}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-171304\\2744\\-8624
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2744\\-42\\147
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-8624\\147\\-394
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-45\\-1672\\364
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-7\\-263\\56
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
12\\441\\-98
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7\\260\\-56
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-6\\-221\\49
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-171304, 2744, -8624; 2744, -42, 147; -8624, 147, -394],[392, 7, 1],[-45, -7, 12, 7, -6; -1672, -263, 441, 260, -221; 364, 56, -98, -56, 49],299,1]
%
% END OF LATTICE L300.1
%
%
% LATTICE L300.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-4018, 588, 1764; 588, -84, -259; 1764, -259, -774],[98, 7, 1],[57, 35, -1, -7, 4; 50, 27, -7, -6, 6; 112, 70, 0, -14, 7],299,2]
%
% END OF LATTICE L300.2
%
%
% LATTICE L300.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2842, 490, 294; 490, -84, -49; 294, -49, -24],[98, 7, 1],[15, 5, -1, -1, 4; 92, 27, -7, -6, 27; -14, 0, 2, 0, -7],299,3]
%
% END OF LATTICE L300.3
%
%
% LATTICE L300.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[196, 98, 98; 98, 252, 84; 98, 84, 55],[98, 14, 1],[49, 57, -1, 3, 12; 22, 26, 0, 1, 5; -119, -140, 0, -7, -28],299,4]
%
% END OF LATTICE L300.4
%
%
% LATTICE L300.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[39592, 10094, 19600; 10094, 2604, 4998; 19600, 4998, 9703],[98, 14, 1],[289, 333, -1, 24, 75; 22, 26, 0, 1, 5; -595, -686, 2, -49, -154],299,5]
%
% END OF LATTICE L300.5
%
%
% LATTICE L300.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-14504, 784, 392; 784, -42, -21; 392, -21, -10],[392, 7, 1],[3, 1, 0, -1, 0; 64, 17, -1, -20, 3; -28, 0, 2, 0, -7],299,6]
%
% END OF LATTICE L300.6
%
%
% LATTICE L300.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-5761616, -1314376, 33712; -1314376, -298480, 7672; 33712, 7672, -197],[392, 56, 1],[14, -15, -27, 39, 37; 69, -75, -133, 195, 184; 5082, -5488, -9800, 14266, 13496],299,7]
%
% END OF LATTICE L300.7
%
%
% LATTICE L300.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3486448, -424536, -200312; -424536, -51632, -24360; -200312, -24360, -11493],[392, 56, 1],[-3, -3, 1, 9, 2; 388, 421, -129, -1243, -307; -770, -840, 256, 2478, 616],299,8]
%
% END OF LATTICE L300.8
%

\medskip%
%------------------------------WEYL-GROUP-W301--------------------------------
%
\leavevmode\llap{}%
$W_{301}$%
\qquad\llap{8} lattices, $\chi=24$%
\hfill%
$22222222$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L301.1
%
\leavevmode%
${L_{301.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}16\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{2}{}9\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{-}{}$}\EasyButWeakLineBreak%
{${144}\above{1pt}{1pt}{b}{2}{10}\above{1pt}{1pt}{l}{2}{16}\above{1pt}{1pt}{r}{2}{90}\above{1pt}{1pt}{b}{2}{16}\above{1pt}{1pt}{b}{2}{10}\above{1pt}{1pt}{l}{2}{144}\above{1pt}{1pt}{r}{2}{2}\above{1pt}{1pt}{b}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-633878640\\-7824240\\146880
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-7824240\\-96578\\1813
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
146880\\1813\\-34
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
109\\-8856\\-1368
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
61\\-4955\\-705
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
131\\-10640\\-1456
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
128\\-10395\\-1350
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7\\-568\\-48
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-4\\325\\50
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-55\\4464\\432
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\81\\-1
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-633878640, -7824240, 146880; -7824240, -96578, 1813; 146880, 1813, -34],[720, 1, 1],[109, 61, 131, 128, 7, -4, -55, -1; -8856, -4955, -10640, -10395, -568, 325, 4464, 81; -1368, -705, -1456, -1350, -48, 50, 432, -1],300,1]
%
% END OF LATTICE L301.1
%
%
% LATTICE L301.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1900080, 5040, 8640; 5040, -10, -25; 8640, -25, -38],[720, 5, 1],[-11, 0, 3, 1, -1, -3, -151, -2; -1080, 1, 304, 99, -104, -301, -15120, -199; -1800, -1, 480, 162, -160, -486, -24480, -325],300,2]
%
% END OF LATTICE L301.2
%
%
% LATTICE L301.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-894960, 3600, 1440; 3600, 18, -9; 1440, -9, -2],[720, 9, 1],[-3, -14, -29, -3, -1, 1, 1, 0; -152, -715, -1488, -155, -56, 45, 48, 1; -1504, -7020, -14544, -1505, -504, 495, 496, 0],300,3]
%
% END OF LATTICE L301.3
%
%
% LATTICE L301.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-10513440, -192240, 27360; -192240, -3424, 496; 27360, 496, -71],[720, 16, 1],[10, 24, 2, 7, -1, -1, 4, 4; 261, 615, 50, 135, -27, -25, 108, 107; 5670, 13520, 1117, 3600, -574, -560, 2295, 2288],300,4]
%
% END OF LATTICE L301.4
%
%
% LATTICE L301.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-4895280, 22320, 29520; 22320, -90, -135; 29520, -135, -178],[720, 45, 1],[-1, 1, 9, 0, -11, -12, -61, -5; -8, 5, 64, 1, -40, -55, -288, -27; -160, 162, 1440, -1, -1800, -1953, -9920, -810],300,5]
%
% END OF LATTICE L301.5
%
%
% LATTICE L301.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[15840, -9360, -3600; -9360, 1760, 720; -3600, 720, 293],[720, 80, 1],[7, 3, 1, -1, -1, -1, 1, 3; -369, -161, -54, 54, 56, 78, 18, -149; 990, 432, 145, -144, -150, -208, -45, 400],300,6]
%
% END OF LATTICE L301.6
%
%
% LATTICE L301.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1440, -2160, -720; -2160, -91872, -29808; -720, -29808, -9671],[720, 144, 1],[0, -36, -7, -17, -3, -1, 1, 8; 15, 1405, 237, 520, 76, 0, -25, -187; -46, -4320, -729, -1600, -234, 0, 77, 576],300,7]
%
% END OF LATTICE L301.7
%
%
% LATTICE L301.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1440, 48240, -19440; 48240, -1588320, 640080; -19440, 640080, -257947],[720, 720, 1],[-1, -1, 4, 4, 10, 44, 12, 3; 4, 58, -18, -45, -181, -1101, -328, -290; 10, 144, -45, -112, -450, -2736, -815, -720],300,8]
%
% END OF LATTICE L301.8
%

\medskip%
%------------------------------WEYL-GROUP-W302--------------------------------
%
\leavevmode\llap{}%
$W_{302}$%
\qquad\llap{22} lattices, $\chi=108$%
\hfill%
$\infty\infty2\infty22\infty\infty\infty2\infty22\infty\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L302.1
%
\leavevmode%
${L_{302.1}}$%
{} : {$1\above{1pt}{1pt}{2}{{\rm II}}4\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{1}{}9\above{1pt}{1pt}{1}{}81\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${36}\above{1pt}{1pt}{9,5}{\infty a}{36}\above{1pt}{1pt}{9,4}{\infty}{36}\above{1pt}{1pt}{*}{2}{4}\above{1pt}{1pt}{3,2}{\infty b}{4}\above{1pt}{1pt}{r}{2}{162}\above{1pt}{1pt}{l}{2}{36}\above{1pt}{1pt}{9,1}{\infty}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1895076\\-40176\\-5508
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-40176\\846\\117
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-5508\\117\\16
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\55440\\-362880
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\-1079\\7056
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\-165\\1079
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-10\\-270
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3\\-44\\-720
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-5\\-100\\-1026
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-26\\-166
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-52\\4
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-7\\-657\\1944
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3\\-512\\2340
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[1895076, -40176, -5508; -40176, 846, 117; -5508, 117, 16],[324, 9, 1],[-1, -3, -5, -1, -1, -7, -3, 1, 3, 5, 1, 1, 7, 3; -10, -44, -100, -26, -52, -657, -512, -100, -44, -10, 4, 8, 63, 28; -270, -720, -1026, -166, 4, 1944, 2340, 990, 1296, 1746, 310, 284, 1944, 828],301,1]
%
% END OF LATTICE L302.1
%
\hbox{}\par\smallskip%
%
% LATTICE L302.2
%
\leavevmode%
${L_{302.2}}$%
{} : {$1\above{1pt}{1pt}{-2}{2}8\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{-}{}9\above{1pt}{1pt}{-}{}81\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${18}\above{1pt}{1pt}{36,23}{\infty b}{72}\above{1pt}{1pt}{36,13}{\infty z}{18}\above{1pt}{1pt}{b}{2}{2}\above{1pt}{1pt}{12,11}{\infty a}{8}\above{1pt}{1pt}{s}{2}{324}\above{1pt}{1pt}{s}{2}{72}\above{1pt}{1pt}{36,1}{\infty z}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1470312\\-725112\\-90720
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-725112\\-357597\\-44703
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-90720\\-44703\\-5350
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
44039519\\-91012320\\13698720
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
21740144\\-44928305\\6762384
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2857326\\-5904966\\888785
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
42910\\-88678\\13347
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
54863\\-113380\\17064
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
20691\\-42760\\6435
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1772\\-3662\\551
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
451\\-932\\140
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1559\\3222\\-486
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-811\\1676\\-252
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-1470312, -725112, -90720; -725112, -357597, -44703; -90720, -44703, -5350],[648, 9, 1],[42910, 54863, 20691, 1772, 451, -1559, -811, 780, 15041, 22999, 6966, 34501, 473411, 385283; -88678, -113380, -42760, -3662, -932, 3222, 1676, -1612, -31084, -47530, -14396, -71300, -978354, -796228; 13347, 17064, 6435, 551, 140, -486, -252, 243, 4680, 7155, 2167, 10732, 147258, 119844],301,2]
%
% END OF LATTICE L302.2
%
\hbox{}\par\smallskip%
%
% LATTICE L302.3
%
\leavevmode%
${L_{302.3}}$%
{} : {$1\above{1pt}{1pt}{2}{2}8\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{-}{}9\above{1pt}{1pt}{-}{}81\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{m}%
\EasyButWeakLineBreak%
{${18}\above{1pt}{1pt}{36,23}{\infty a}{72}\above{1pt}{1pt}{36,31}{\infty z}{18}\above{1pt}{1pt}{s}{2}{2}\above{1pt}{1pt}{12,11}{\infty b}{8}\above{1pt}{1pt}{l}{2}{81}\above{1pt}{1pt}{r}{2}{72}\above{1pt}{1pt}{36,19}{\infty z}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2240136\\-133488\\-112752
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-133488\\-7758\\-6921
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-112752\\-6921\\-5467
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
14785091\\-136284120\\-132392232
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
949601\\-8753111\\-8503146
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
673630\\-6209300\\-6031981
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
10662\\-98279\\-95472
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
13609\\-125444\\-121860
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5120\\-47195\\-45846
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
436\\-4019\\-3904
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
105\\-968\\-940
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-208\\1917\\1863
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-197\\1816\\1764
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-2240136, -133488, -112752; -133488, -7758, -6921; -112752, -6921, -5467],[648, 9, 1],[10662, 13609, 5120, 436, 105, -208, -197, 203, 3775, 5745, 1737, 8587, 58879, 95809; -98279, -125444, -47195, -4019, -968, 1917, 1816, -1871, -34796, -52955, -16011, -79152, -542727, -883136; -95472, -121860, -45846, -3904, -940, 1863, 1764, -1818, -33804, -51444, -15554, -76892, -527229, -857916],301,3]
%
% END OF LATTICE L302.3
%
%
% LATTICE L302.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[162, 0, -81; 0, -153, -9; -81, -9, 40],[81, 9, 1],[5, 111, 364, 113, 287, 7939, 3243, 730, 477, 371, 34, 7, -1, -9; -1, -17, -55, -17, -43, -1188, -485, -109, -71, -55, -5, -1, 0, 1; 9, 216, 711, 221, 562, 15552, 6354, 1431, 936, 729, 67, 14, 0, -18],301,4]
%
% END OF LATTICE L302.4
%
%
% LATTICE L302.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[947538, -20088, -5508; -20088, 423, 117; -5508, 117, 32],[162, 9, 1],[-1, -3, -5, -1, -1, -7, -3, 1, 3, 5, 1, 1, 7, 3; -10, -44, -100, -26, -52, -657, -512, -100, -44, -10, 4, 8, 63, 28; -135, -360, -513, -83, 2, 972, 1170, 495, 648, 873, 155, 142, 972, 414],301,5]
%
% END OF LATTICE L302.5
%
%
% LATTICE L302.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-735156, 10044, -45360; 10044, -126, 657; -45360, 657, -2675],[324, 9, 1],[-26, -501, -766, -232, -1149, -15766, -12831, -1429, -1827, -689, -59, -15, 52, 27; -806, -15542, -23765, -7198, -35650, -489177, -398114, -44339, -56690, -21380, -1831, -466, 1611, 838; 243, 4680, 7155, 2167, 10732, 147258, 119844, 13347, 17064, 6435, 551, 140, -486, -252],301,6]
%
% END OF LATTICE L302.6
%
%
% LATTICE L302.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[81, 0, 0; 0, -72, -9; 0, -9, -1],[81, 9, 1],[2, 3, 5, 10, 17, 5, 17, 3, 1, 0, -1, 1, 1, 5; -17, -19, -26, -45, -63, -17, -55, -8, -1, 1, 0, -27, -13, -55; 99, 108, 144, 243, 324, 85, 270, 36, 0, -9, 0, 162, 77, 324],301,7]
%
% END OF LATTICE L302.7
%
%
% LATTICE L302.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-11502, 1296, 648; 1296, -144, -81; 648, -81, -5],[162, 9, 1],[39, 1, -9, -1, 163, 39, 329, 101, 111, 149, 253, 341, 45, 287; 307, 8, -71, -9, 1278, 306, 2582, 793, 872, 1171, 1989, 2682, 354, 2258; 72, 0, -18, 0, 324, 77, 648, 198, 216, 288, 486, 648, 85, 540],301,8]
%
% END OF LATTICE L302.8
%
%
% LATTICE L302.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[324, 162, 162; 162, 40266, 648; 162, 648, 89],[162, 18, 1],[1955, 280, 71, -1, 1877, 939, 4035, 2575, 1532, 4459, 8155, 6277, 1779, 5931; 56, 8, 2, 0, 54, 27, 116, 74, 44, 128, 234, 180, 51, 170; -3960, -567, -144, 0, -3807, -1904, -8181, -5220, -3105, -9036, -16524, -12717, -3604, -12015],301,9]
%
% END OF LATTICE L302.9
%
%
% LATTICE L302.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-83268, 3240, 1620; 3240, -126, -63; 1620, -63, -31],[324, 9, 1],[25, 33, 13, 11, 5, 0, -1, 0, 7, 12, 34, 175, 30, 221; 751, 982, 382, 315, 126, -1, -26, 4, 226, 373, 1044, 5310, 907, 6670; -261, -324, -117, -81, 0, 2, 0, -9, -108, -153, -405, -1944, -326, -2376],301,10]
%
% END OF LATTICE L302.10
%
%
% LATTICE L302.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[23743206, -214002, 11722806; -214002, 1872, -105660; 11722806, -105660, 5787937],[162, 18, 1],[1502, -5888, -47184, -15570, -20984, -590951, -243470, -112152, -38372, -63466, -6560, -1146, -6559, 40; 7, -26, -209, -69, -93, -2619, -1079, -497, -170, -281, -29, -5, -27, 1; -3042, 11925, 95562, 31534, 42499, 1196856, 493101, 227142, 77715, 128538, 13286, 2321, 13284, -81],301,11]
%
% END OF LATTICE L302.11
%
%
% LATTICE L302.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-23004, 1296, 0; 1296, -72, -9; 0, -9, 80],[324, 9, 1],[39, 1, -9, -1, 163, 39, 329, 101, 111, 149, 253, 341, 45, 287; 686, 16, -160, -18, 2880, 689, 5812, 1784, 1960, 2630, 4464, 6012, 793, 5056; 72, 0, -18, 0, 324, 77, 648, 198, 216, 288, 486, 648, 85, 540],301,12]
%
% END OF LATTICE L302.12
%
%
% LATTICE L302.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-8774568, -4363632, 23328; -4363632, -2170053, 11601; 23328, 11601, -62],[648, 9, 1],[-726, -949, -369, -304, -121, 1, 25, -4, -219, -361, -1010, -5135, -877, -6449; 1502, 1964, 764, 630, 252, -2, -52, 8, 452, 746, 2088, 10620, 1814, 13340; 7839, 10368, 4095, 3483, 1620, 2, -324, -9, 2160, 3735, 10611, 54756, 9394, 69228],301,13]
%
% END OF LATTICE L302.13
%
%
% LATTICE L302.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-146713032, 108216, 217728; 108216, -63, -162; 217728, -162, -323],[648, 9, 1],[286, 357, 130, 92, 5, -1, -1, 9, 115, 165, 439, 2119, 178, 2597; 15335, 19136, 6965, 4923, 252, -54, -52, 485, 6176, 8855, 23553, 113652, 9546, 139268; 185067, 231012, 84123, 59535, 3240, -647, -648, 5823, 74412, 106767, 284067, 1371168, 115181, 1680480],301,14]
%
% END OF LATTICE L302.14
%
%
% LATTICE L302.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[211248, 207684, 53460; 207684, 204480, 52560; 53460, 52560, 13529],[324, 36, 1],[1207, 176, 40, -41, 1060, 1081, 2337, 1508, 910, 2675, 4928, 3827, 2177, 3636; 28, 4, 1, 0, 27, 27, 58, 37, 22, 64, 117, 90, 51, 85; -4878, -711, -162, 162, -4293, -4376, -9459, -6102, -3681, -10818, -19926, -15471, -8800, -14697],301,15]
%
% END OF LATTICE L302.15
%
%
% LATTICE L302.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[94972824, -428004, 23445612; -428004, 1872, -105660; 23445612, -105660, 5787937],[324, 36, 1],[751, -2944, -23592, -7785, -10492, -590951, -121735, -56076, -19186, -31733, -3280, -573, -6559, 20; 7, -26, -209, -69, -93, -5238, -1079, -497, -170, -281, -29, -5, -54, 1; -3042, 11925, 95562, 31534, 42499, 2393712, 493101, 227142, 77715, 128538, 13286, 2321, 26568, -81],301,16]
%
% END OF LATTICE L302.16
%
%
% LATTICE L302.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[151508232, 39136932, 37549656; 39136932, 10109700, 9699660; 37549656, 9699660, 9306271],[324, 36, 1],[1167, 11687, 36350, 11091, 27715, 762919, 310919, 69548, 44885, 34365, 3052, 571, 803, 227; 7, 56, 169, 51, 126, 3456, 1406, 313, 200, 151, 13, 2, 0, 2; -4716, -47214, -146844, -44804, -111958, -3081888, -1255986, -280944, -181314, -138816, -12328, -2306, -3240, -918],301,17]
%
% END OF LATTICE L302.17
%
%
% LATTICE L302.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[61560, 9396, 15228; 9396, 4788, 2340; 15228, 2340, 3767],[324, 36, 1],[16322, 10421, 7859, 6074, 919, -1, 111, 373, 2935, 8836, 23977, 59183, 20035, 73347; 313, 200, 151, 117, 18, 0, 2, 7, 56, 169, 459, 1134, 384, 1406; -66168, -42246, -31860, -24624, -3726, 4, -450, -1512, -11898, -35820, -97200, -239922, -81220, -297342],301,18]
%
% END OF LATTICE L302.18
%
%
% LATTICE L302.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-377784, -42768, 648; -42768, -4824, 72; 648, 72, -1],[648, 72, 1],[-5, 0, 1, -1, -13, -6, -25, -15, -8, -21, -35, -23, -6, -19; 61, 1, -11, 9, 144, 67, 280, 169, 91, 241, 405, 270, 71, 226; 1008, 54, -144, 0, 1782, 856, 3618, 2232, 1242, 3384, 5832, 4050, 1088, 3510],301,19]
%
% END OF LATTICE L302.19
%
%
% LATTICE L302.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-21477960, -4262544, 83592; -4262544, -843336, 16560; 83592, 16560, -325],[648, 72, 1],[185, 18, -19, -35, 193, 101, 439, 285, 170, 489, 881, 653, 181, 595; 1289, 125, -133, -243, 1350, 706, 3068, 1991, 1187, 3413, 6147, 4554, 1262, 4148; 113256, 10998, -11664, -21384, 118422, 61948, 269226, 174744, 104202, 299664, 539784, 399978, 110852, 364374],301,20]
%
% END OF LATTICE L302.20
%
%
% LATTICE L302.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1811160, -362232, -894240; -362232, -72432, -178848; -894240, -178848, -441521],[648, 72, 1],[-928, -63, 142, 16, -141, -5755, -2745, -1742, -1005, -2812, -550, -393, -8663, -3129; 19, 4, 1, -1, -1, -18, -5, 1, 4, 19, 5, 5, 126, 49; 1872, 126, -288, -32, 286, 11664, 5562, 3528, 2034, 5688, 1112, 794, 17496, 6318],301,21]
%
% END OF LATTICE L302.21
%
%
% LATTICE L302.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-16612776, -400464, -165888; -400464, -9576, -3960; -165888, -3960, -1637],[648, 72, 1],[-11, -4, -3, 1, 3, 95, 41, 21, 8, 13, 1, -1, -41, -19; 2575, 949, 721, -237, -720, -22860, -9878, -5075, -1949, -3221, -263, 220, 9360, 4378; -5112, -1890, -1440, 472, 1438, 45684, 19746, 10152, 3906, 6480, 536, -430, -18468, -8658],301,22]
%
% END OF LATTICE L302.22
%

\medskip%
%------------------------------WEYL-GROUP-W303--------------------------------
%
\leavevmode\llap{}%
$W_{303}$%
\qquad\llap{16} lattices, $\chi=24$%
\hfill%
$22222222\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L303.1
%
\leavevmode%
${L_{303.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}8\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{1}{}5\above{1pt}{1pt}{-}{}25\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${24}\above{1pt}{1pt}{r}{2}{50}\above{1pt}{1pt}{s}{2}{6}\above{1pt}{1pt}{b}{2}{10}\above{1pt}{1pt}{l}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-877800\\-352200\\4800
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-352200\\-141310\\1925
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4800\\1925\\-26
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-13201\\34800\\138000
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-5313\\14006\\55545
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
77\\-203\\-806
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-55\\144\\504
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2\\5\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
8\\-21\\-78
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5\\-13\\-40
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-877800, -352200, 4800; -352200, -141310, 1925; 4800, 1925, -26],[600, 5, 1],[-55, -2, 8, 5, -209, -163, -41, -16; 144, 5, -21, -13, 552, 430, 108, 42; 504, 0, -78, -40, 2256, 1725, 423, 155],302,1]
%
% END OF LATTICE L303.1
%
%
% LATTICE L303.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[19950, -8250, -300; -8250, 3410, 125; -300, 125, 4],[150, 5, 1],[23, 43, 13, 7, 13, 2, -4, -4; 54, 100, 30, 16, 30, 5, -9, -9; 18, 75, 33, 25, 42, 0, -18, -20],302,2]
%
% END OF LATTICE L303.2
%
%
% LATTICE L303.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-8850, 300, -150; 300, -10, 5; -150, 5, -2],[150, 5, 1],[-121, -6, -26, 0, 1, 0, -4, -2; -3690, -182, -780, 2, 30, -1, -135, -63; -1200, -57, -225, 5, 0, -3, -75, -25],302,3]
%
% END OF LATTICE L303.3
%
%
% LATTICE L303.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[119100, -9750, 57900; -9750, 680, -4750; 57900, -4750, 28147],[150, 10, 1],[-1922, -5006, -944, -74, 176, 641, 71, -217; -336, -875, -165, -13, 30, 110, 12, -38; 3897, 10150, 1914, 150, -357, -1300, -144, 440],302,4]
%
% END OF LATTICE L303.4
%
%
% LATTICE L303.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[22800, -450, 11250; -450, 320, -220; 11250, -220, 5551],[150, 10, 1],[-36533, -3582, -15176, 74, -37, -75, -3109, -1293; -540, -53, -225, 1, 0, -1, -45, -19; 74025, 7258, 30750, -150, 75, 152, 6300, 2620],302,5]
%
% END OF LATTICE L303.5
%
%
% LATTICE L303.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[13650, -5250, -5100; -5250, 1020, 1875; -5100, 1875, 1898],[150, 15, 1],[875, 3419, 215, 51, -79, -434, -16, 148; -224, -875, -55, -13, 20, 110, 4, -38; 2572, 10050, 632, 150, -232, -1275, -47, 435],302,6]
%
% END OF LATTICE L303.6
%
%
% LATTICE L303.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[15450, -300, -5250; -300, 480, 105; -5250, 105, 1784],[150, 15, 1],[17003, 2501, 3533, -51, 17, 52, 722, 902; -360, -53, -75, 1, 0, -1, -15, -19; 50050, 7362, 10400, -150, 50, 153, 2125, 2655],302,7]
%
% END OF LATTICE L303.7
%
%
% LATTICE L303.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-143400, 1200, -600; 1200, -10, 5; -600, 5, -2],[600, 5, 1],[1, 0, -2, -1, -121, -3, -13, 0; 120, -1, -255, -123, -14640, -362, -1560, 2; 0, -3, -75, -25, -2400, -57, -225, 5],302,8]
%
% END OF LATTICE L303.8
%
%
% LATTICE L303.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[6955800, 377250, 3332700; 377250, 20460, 180750; 3332700, 180750, 1596781],[150, 30, 1],[-207, -1371, -59, 71, 5, -144, -42, -172; 9, 100, 10, 16, 5, 5, -3, -9; 431, 2850, 122, -150, -11, 300, 88, 360],302,9]
%
% END OF LATTICE L303.9
%
%
% LATTICE L303.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3765900, -15150, -1804650; -15150, -60, -7260; -1804650, -7260, -864803],[150, 30, 1],[-3148, -879, -1101, 115, -12, -69, -479, -431; -615, -182, -260, 2, 5, -1, -45, -63; 6575, 1836, 2300, -240, 25, 144, 1000, 900],302,10]
%
% END OF LATTICE L303.10
%
%
% LATTICE L303.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[11400, -600, 600; -600, 30, -45; 600, -45, -82],[600, 15, 1],[7, -1, -1, 0, 49, 106, 8, 7; 120, -15, -17, -1, 824, 1785, 135, 119; -16, 0, 2, 0, -104, -225, -17, -15],302,11]
%
% END OF LATTICE L303.11
%
%
% LATTICE L303.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-7495800, 339000, -28200; 339000, -15330, 1275; -28200, 1275, -106],[600, 15, 1],[109, 7, 7, -2, 11, 2, 8, 5; 3200, 203, 195, -63, 360, 64, 250, 152; 9400, 573, 475, -225, 1400, 237, 875, 495],302,12]
%
% END OF LATTICE L303.12
%
%
% LATTICE L303.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2600400, 465000, -13200; 465000, 83120, -2360; -13200, -2360, 67],[600, 40, 1],[2, 14, 4, 2, 1, 1, -1, -1; -6, -15, 3, 7, 3, 0, -6, -8; 177, 2200, 888, 640, 303, 200, -408, -480],302,13]
%
% END OF LATTICE L303.13
%
%
% LATTICE L303.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2050800, 353400, -14400; 353400, -60880, 2480; -14400, 2480, -101],[600, 40, 1],[1, -1, -31, -11, -136, -26, -104, 2; 15, -11, -375, -137, -1725, -331, -1335, 23; 225, -128, -4800, -1800, -23025, -4432, -18000, 280],302,14]
%
% END OF LATTICE L303.14
%
%
% LATTICE L303.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1200, -27000, -13200; -27000, 499440, 244200; -13200, 244200, 119401],[600, 120, 1],[5, 89, 7, 7, 1, 1, -1, -1; -229, -4395, -379, -469, -64, 0, 86, 176; 469, 9000, 776, 960, 131, 0, -176, -360],302,15]
%
% END OF LATTICE L303.15
%
%
% LATTICE L303.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-135600, -55800, 15000; -55800, -21840, 5880; 15000, 5880, -1583],[600, 120, 1],[1, 0, -6, -8, -36, -21, -29, 1; 85, 13, -415, -593, -2740, -1606, -2240, 62; 325, 48, -1600, -2280, -10525, -6168, -8600, 240],302,16]
%
% END OF LATTICE L303.16
%

\medskip%
%------------------------------WEYL-GROUP-W304--------------------------------
%
\leavevmode\llap{}%
$W_{304}$%
\qquad\llap{36} lattices, $\chi=36$%
\hfill%
$2|22\slashtwo22|22\slashtwo2\rtimes D_{4}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L304.1
%
\leavevmode%
${L_{304.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{2}8\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{-}{}9\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-}{}5\above{1pt}{1pt}{1}{}25\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{23,3m,3,2,m}%
\EasyButWeakLineBreak%
{${200}\above{1pt}{1pt}{*}{2}{180}\above{1pt}{1pt}{*}{2}{8}\above{1pt}{1pt}{b}{2}{450}\above{1pt}{1pt}{b}{2}{2}\above{1pt}{1pt}{b}{2}{1800}\above{1pt}{1pt}{*}{2}{20}\above{1pt}{1pt}{*}{2}{72}\above{1pt}{1pt}{b}{2}{50}\above{1pt}{1pt}{b}{2}{18}\above{1pt}{1pt}{b}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-12202200\\2309400\\12600
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2309400\\-437070\\-2385
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
12600\\-2385\\-13
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-13\\-60\\-1600
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-5\\-24\\-450
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\4\\232
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
17\\75\\2700
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\9\\286
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
119\\540\\16200
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7\\32\\910
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
13\\60\\1584
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\5\\50
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2\\-9\\-288
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-12202200, 2309400, 12600; 2309400, -437070, -2385; 12600, -2385, -13],[1800, 15, 1],[-13, -5, 1, 17, 2, 119, 7, 13, 1, -2; -60, -24, 4, 75, 9, 540, 32, 60, 5, -9; -1600, -450, 232, 2700, 286, 16200, 910, 1584, 50, -288],303,1]
%
% END OF LATTICE L304.1
%
\hbox{}\par\smallskip%
%
% LATTICE L304.2
%
\leavevmode%
${L_{304.2}}$%
{} : {$1\above{1pt}{1pt}{2}{2}16\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{1}{}3\above{1pt}{1pt}{1}{}9\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{1}{}5\above{1pt}{1pt}{-}{}25\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{5,3m,3,m}%
\EasyButWeakLineBreak%
{${400}\above{1pt}{1pt}{b}{2}{90}\above{1pt}{1pt}{l}{2}{16}\above{1pt}{1pt}{}{2}{225}\above{1pt}{1pt}{}{2}{1}\above{1pt}{1pt}{}{2}{3600}\above{1pt}{1pt}{r}{2}{10}\above{1pt}{1pt}{b}{2}{144}\above{1pt}{1pt}{*}{2}{100}\above{1pt}{1pt}{*}{2}{36}\above{1pt}{1pt}{*}{2}$}%
\nopagebreak\par%
shares genus with 3-dual${}\iso{}$5-dual; isometric to own %
3.5-dual\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-433292400\\-2851200\\298800
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2851200\\-18735\\1965
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
298800\\1965\\-206
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\320\\7400
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4\\444\\10035
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5\\560\\12592
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
14\\1575\\35325
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\113\\2528
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
91\\10320\\230400
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\228\\5075
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5\\576\\12744
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-110\\-2500
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-114\\-2538
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-433292400, -2851200, 298800; -2851200, -18735, 1965; 298800, 1965, -206],[3600, 15, 1],[3, 4, 5, 14, 1, 91, 2, 5, -1, -1; 320, 444, 560, 1575, 113, 10320, 228, 576, -110, -114; 7400, 10035, 12592, 35325, 2528, 230400, 5075, 12744, -2500, -2538],303,2]
%
% END OF LATTICE L304.2
%
%
% LATTICE L304.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[1050, -150, 0; -150, 20, -5; 0, -5, -17],[150, 5, 1],[5, 2, -1, -1, -1, 3, 6, 41, 5, 21; 34, 13, -10, -7, -5, 22, 43, 290, 35, 145; -12, -5, 0, 2, 0, -8, -15, -100, -12, -50],303,3]
%
% END OF LATTICE L304.3
%
%
% LATTICE L304.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-23100, -900, -900; -900, -35, -35; -900, -35, -34],[300, 5, 1],[-1, -1, -3, 0, 1, 1, 1, 3, 0, -1; 32, 38, 160, 5, -5, -16, -22, -80, -1, 25; -8, -15, -100, -6, -25, -12, -5, 0, 1, 0],303,4]
%
% END OF LATTICE L304.4
%
%
% LATTICE L304.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-18192240, -31680, 64800; -31680, -51, 111; 64800, 111, -230],[720, 3, 1],[21, 22, 7, -1, -1, 5, 4, 47, 3, 10; 3328, 3480, 1104, -162, -158, 816, 640, 7488, 477, 1587; 7520, 7875, 2504, -360, -358, 1800, 1435, 16848, 1075, 3582],303,5]
%
% END OF LATTICE L304.5
%
%
% LATTICE L304.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-46200, -1800, -2400; -1800, -70, -95; -2400, -95, -107],[600, 5, 1],[97, 7, 7, -1, -1, 3, 3, 13, 26, 6; -2240, -161, -160, 25, 23, -80, -71, -304, -605, -139; -200, -15, -16, 0, 2, 0, -5, -24, -50, -12],303,6]
%
% END OF LATTICE L304.6
%
%
% LATTICE L304.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[4200, -1800, -600; -1800, 770, 245; -600, 245, -17],[600, 5, 1],[601, 93, 51, 2, -7, -41, 19, 61, 138, 35; 1460, 226, 124, 5, -17, -100, 46, 148, 335, 85; -200, -30, -16, 0, 2, 0, -10, -24, -50, -12],303,7]
%
% END OF LATTICE L304.7
%
%
% LATTICE L304.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-99884400, 63600, 146400; 63600, -35, -95; 146400, -95, -214],[1200, 5, 1],[97, 7, 7, -1, -1, 3, 3, 13, 13, 3; 18800, 1358, 1360, -190, -194, 560, 578, 2512, 2515, 581; 58000, 4185, 4184, -600, -598, 1800, 1795, 7776, 7775, 1794],303,8]
%
% END OF LATTICE L304.8
%
%
% LATTICE L304.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-13050, 450, 450; 450, 330, -45; 450, -45, -13],[450, 15, 1],[119, 7, 13, 2, -4, -13, -5, 1, 34, 4; 270, 16, 30, 5, -9, -30, -12, 2, 75, 9; 3150, 185, 342, 50, -108, -350, -135, 26, 900, 106],303,9]
%
% END OF LATTICE L304.9
%
%
% LATTICE L304.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-6101100, 1154700, 12600; 1154700, -218535, -2385; 12600, -2385, -26],[900, 15, 1],[-13, -5, 1, 17, 2, 119, 7, 13, 1, -2; -60, -24, 4, 75, 9, 540, 32, 60, 5, -9; -800, -225, 116, 1350, 143, 8100, 455, 792, 25, -144],303,10]
%
% END OF LATTICE L304.10
%
%
% LATTICE L304.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-3799800, -1719000, 19800; -1719000, -777630, 8955; 19800, 8955, -103],[1800, 15, 1],[31, -2, -15, -119, -11, -593, -16, -55, -2, 8; -80, 6, 40, 315, 29, 1560, 42, 144, 5, -21; -1000, 135, 592, 4500, 406, 21600, 575, 1944, 50, -288],303,11]
%
% END OF LATTICE L304.11
%
%
% LATTICE L304.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[89400, 10350, 44400; 10350, 1190, 5140; 44400, 5140, 22051],[150, 10, 1],[-54, -94, -136, -1, 123, 24, 34, -14, -29, -273; -1, -3, -5, 0, 10, 3, 7, 15, 2, 0; 109, 190, 275, 2, -250, -49, -70, 25, 58, 550],303,12]
%
% END OF LATTICE L304.12
%
%
% LATTICE L304.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[92850, 12900, -31200; 12900, 1785, -4335; -31200, -4335, 10484],[150, 15, 1],[85, 71, 203, 1, -77, -25, -11, 97, 29, 227; -2, -3, -10, 0, 10, 6, 7, 30, 2, 0; 252, 210, 600, 3, -225, -72, -30, 300, 87, 675],303,13]
%
% END OF LATTICE L304.13
%
%
% LATTICE L304.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[339450, 7950, 162600; 7950, 120, 3810; 162600, 3810, 77887],[150, 30, 1],[-318, -259, 36, 118, 72, -200, -777, -2626, -636, -2662; 17, 13, -5, -7, -5, 11, 43, 145, 35, 145; 663, 540, -75, -246, -150, 417, 1620, 5475, 1326, 5550],303,14]
%
% END OF LATTICE L304.14
%
%
% LATTICE L304.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2439300, 486300, 24300; 486300, -96945, -4845; 24300, -4845, -242],[300, 15, 1],[7, -12, -31, -66, -16, -267, -40, -21, 1, 3; 20, -46, -116, -245, -59, -980, -146, -76, 5, 11; 300, -285, -792, -1725, -426, -7200, -1095, -588, 0, 81],303,15]
%
% END OF LATTICE L304.15
%
%
% LATTICE L304.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[30900, -2100, -7800; -2100, 1640, 520; -7800, 520, 1969],[300, 20, 1],[108, 688, 1094, 257, 1113, 150, 344, 196, 1, 177; 3, 19, 30, 7, 30, 4, 9, 5, 0, 5; 427, 2720, 4325, 1016, 4400, 593, 1360, 775, 4, 700],303,16]
%
% END OF LATTICE L304.16
%
%
% LATTICE L304.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-214890600, -14323200, 359400; -14323200, -954690, 23955; 359400, 23955, -601],[600, 15, 1],[-79, -16, 7, 7, 1, -53, -50, -667, -40, -166; 1272, 257, -120, -113, -15, 856, 807, 10760, 645, 2675; 3456, 675, -600, -318, 0, 2424, 2265, 30000, 1788, 7350],303,17]
%
% END OF LATTICE L304.17
%
%
% LATTICE L304.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-6600, 10800, 1800; 10800, -10515, -1530; 1800, -1530, -211],[600, 15, 1],[83, 27, -47, -9, 4, 69, 125, 807, 47, 186; 324, 106, -180, -35, 15, 268, 486, 3140, 183, 725; -1644, -540, 900, 177, -75, -1356, -2460, -15900, -927, -3675],303,18]
%
% END OF LATTICE L304.18
%
%
% LATTICE L304.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[225360, 18720, -720; 18720, 825, -45; -720, -45, 2],[720, 15, 1],[9, 2, 3, -1, -1, -7, 0, 11, 1, 4; 112, 24, 32, -18, -14, -96, 0, 144, 13, 51; 5840, 1287, 1880, -720, -670, -4680, -1, 7200, 655, 2610],303,19]
%
% END OF LATTICE L304.19
%
%
% LATTICE L304.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[57888900, -355950, 28805400; -355950, 2190, -177120; 28805400, -177120, 14333509],[450, 30, 1],[3247, 423, 533, 647, 215, 311, 403, 101, 2239, 207; 30, 7, 12, 20, 6, 0, -9, -2, -30, 0; -6525, -850, -1071, -1300, -432, -625, -810, -203, -4500, -416],303,20]
%
% END OF LATTICE L304.20
%
%
% LATTICE L304.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-26101200, 128713200, -25741200; 128713200, -633299145, 126650925; -25741200, 126650925, -25328402],[1200, 15, 1],[-92733, -6950, -7347, 199, 993, 1393, -2184, -10921, -11517, -2780; -2967280, -222386, -235088, 6370, 31774, 44560, -69886, -349456, -368525, -88955; -14743200, -1104945, -1168056, 31650, 157872, 221400, -347235, -1736304, -1831050, -441981],303,21]
%
% END OF LATTICE L304.21
%
%
% LATTICE L304.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[35424300, -1122900, -8994600; -1122900, 35880, 285120; -8994600, 285120, 2283823],[300, 60, 1],[-3593, -5764, -2317, -16349, -3577, -14657, -8836, -1333, -1901, -73; 195, 313, 126, 890, 195, 800, 483, 73, 105, 4; -14175, -22740, -9141, -64500, -14112, -57825, -34860, -5259, -7500, -288],303,22]
%
% END OF LATTICE L304.22
%
%
% LATTICE L304.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[23363400, 4693200, -45600; 4693200, 942760, -9160; -45600, -9160, 89],[600, 40, 1],[0, 0, 1, 1, 9, 1, 4, 4, 1, 1; 1, 7, 5, -1, -35, -5, -23, -25, -7, -5; 103, 720, 1025, 408, 1000, -3, -320, -525, -208, 0],303,23]
%
% END OF LATTICE L304.23
%
%
% LATTICE L304.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[125400, -27600, -12600; -27600, 6040, 2760; -12600, 2760, 1261],[600, 40, 1],[1, 4, 13, 3, 11, 1, 0, -3, -1, -1; -33, -119, -375, -85, -315, -31, -9, 55, 21, -5; 82, 300, 950, 216, 800, 78, 20, -150, -56, 0],303,24]
%
% END OF LATTICE L304.24
%
%
% LATTICE L304.25
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1161360, 195840, -12240; 195840, 36624, -2304; -12240, -2304, 145],[720, 48, 1],[2, 11, 13, 6, 19, 5, 43, 1, 1, 0; -189, -1045, -1239, -573, -1818, -479, -4125, -96, -96, 1; -2835, -15680, -18594, -8600, -27288, -7190, -61920, -1441, -1440, 16],303,25]
%
% END OF LATTICE L304.25
%
%
% LATTICE L304.26
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-32223600, -194400, 21600; -194400, 165, 105; 21600, 105, -14],[3600, 15, 1],[89, 20, 7, -1, -1, -7, 2, 31, 11, 8; 3040, 684, 240, -30, -34, -240, 68, 1056, 375, 273; 160000, 35955, 12584, -1800, -1798, -12600, 3595, 55728, 19775, 14382],303,26]
%
% END OF LATTICE L304.26
%
%
% LATTICE L304.27
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[374318100, -1788300, 93137400; -1788300, 8760, -444960; 93137400, -444960, 23174341],[900, 60, 1],[2943, 10438, 1277, 26207, 1999, 26711, 5998, 3277, 3111, 1111; 150, 531, 65, 1335, 102, 1365, 307, 168, 160, 57; -11825, -41940, -5131, -105300, -8032, -107325, -24100, -13167, -12500, -4464],303,27]
%
% END OF LATTICE L304.27
%
%
% LATTICE L304.28
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1200, -15000, -4800; -15000, 169080, 54120; -4800, 54120, 17323],[600, 120, 1],[-1, 1, 1, 19, 5, 11, 7, 1, 1, -1; 120, 77, 3, -190, -84, -215, -153, -22, 0, 46; -375, -240, -9, 600, 264, 675, 480, 69, 0, -144],303,28]
%
% END OF LATTICE L304.28
%
%
% LATTICE L304.29
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1200, 25800, 600; 25800, -453720, -10800; 600, -10800, -257],[600, 120, 1],[-13, 2, 7, 71, 19, 83, 26, 7, -1, -5; 60, -7, -30, -310, -84, -370, -117, -32, 0, 22; -2550, 300, 1278, 13200, 3576, 15750, 4980, 1362, 0, -936],303,29]
%
% END OF LATTICE L304.29
%
%
% LATTICE L304.30
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-999600, -187200, -90000; -187200, -22960, -10960; -90000, -10960, -5231],[1200, 80, 1],[1, 15, 23, 5, 16, 1, -3, -4, -2, -1; -401, -6003, -9185, -1992, -6335, -387, 1247, 1620, 803, 390; 823, 12320, 18850, 4088, 13000, 794, -2560, -3325, -1648, -800],303,30]
%
% END OF LATTICE L304.30
%
%
% LATTICE L304.31
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[720, 0, 0; 0, 505680, 6240; 0, 6240, 77],[720, 240, 1],[0, -1, -1, -5, -2, -5, -1, -1, 0, 1; 4, 39, 25, 102, 35, 81, 15, 15, 1, 0; -325, -3168, -2030, -8280, -2840, -6570, -1216, -1215, -80, 0],303,31]
%
% END OF LATTICE L304.31
%
%
% LATTICE L304.32
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[5144400, -905400, -442800; -905400, 159240, 77880; -442800, 77880, 38089],[1800, 120, 1],[0, -2, -1, -1, 1, 1, 2, 8, 1, 7; 23, 693, 300, 276, -190, -210, -419, -1605, -186, -840; -47, -1440, -625, -576, 400, 441, 880, 3375, 392, 1800],303,32]
%
% END OF LATTICE L304.32
%
%
% LATTICE L304.33
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[392400, 178200, 86400; 178200, 83640, 40560; 86400, 40560, 19669],[1800, 120, 1],[-1, -5, -3, -1, -1, -1, -1, -11, -1, -17; 426, 2193, 1340, 456, 390, 360, 361, 4170, 394, 7020; -874, -4500, -2750, -936, -800, -738, -740, -8550, -808, -14400],303,33]
%
% END OF LATTICE L304.33
%
%
% LATTICE L304.34
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1200, -2400, 7200; -2400, -68880, 194880; 7200, 194880, -551237],[1200, 240, 1],[-427, -305, -22, -1, 46, 121, 157, 7, -184, -83; 3835, 2727, 196, 0, -409, -1065, -1363, -51, 1705, 750; 1350, 960, 69, 0, -144, -375, -480, -18, 600, 264],303,34]
%
% END OF LATTICE L304.34
%
%
% LATTICE L304.35
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[635864400, 119646000, 568800; 119646000, 22524960, 107520; 568800, 107520, 529],[3600, 240, 1],[-321, -3124, -400, -8153, -559, -6464, -1196, -239, -79, -1; 1930, 18783, 2405, 49020, 3361, 38865, 7191, 1437, 475, 6; -47125, -458640, -58726, -1197000, -82072, -949050, -175600, -35091, -11600, -144],303,35]
%
% END OF LATTICE L304.35
%
%
% LATTICE L304.36
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-39600, 21600, 0; 21600, 45840, -240; 0, -240, 1],[3600, 240, 1],[-3, -5, 0, 8, 1, 7, 3, 1, -1, -2; -5, -9, 0, 15, 2, 15, 7, 3, 0, -3; -1150, -2160, -1, 3600, 496, 3825, 1840, 846, 200, -648],303,36]
%
% END OF LATTICE L304.36
%

\medskip%
%------------------------------WEYL-GROUP-W305--------------------------------
%
\leavevmode\llap{}%
$W_{305}$%
\qquad\llap{46} lattices, $\chi=36$%
\hfill%
$2\slashtwo22|22\slashtwo22|2\rtimes D_{4}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L305.1
%
\leavevmode%
${L_{305.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{4}8\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{1}{}5\above{1pt}{1pt}{1}{}25\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${24}\above{1pt}{1pt}{}{2}{25}\above{1pt}{1pt}{r}{2}{4}\above{1pt}{1pt}{*}{2}{600}\above{1pt}{1pt}{*}{2}{20}\above{1pt}{1pt}{*}{2}{24}\above{1pt}{1pt}{*}{2}{100}\above{1pt}{1pt}{l}{2}{1}\above{1pt}{1pt}{}{2}{600}\above{1pt}{1pt}{}{2}{5}\above{1pt}{1pt}{}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-258600\\2400\\2400
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2400\\-20\\-25
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2400\\-25\\-19
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
11\\648\\528
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
11\\650\\525
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\178\\142
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
13\\780\\600
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-58\\-50
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-60\\-48
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\170\\150
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\58\\49
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
37\\2160\\1800
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\176\\145
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-258600, 2400, 2400; 2400, -20, -25; 2400, -25, -19],[600, 5, 1],[11, 11, 3, 13, -1, -1, 3, 1, 37, 3; 648, 650, 178, 780, -58, -60, 170, 58, 2160, 176; 528, 525, 142, 600, -50, -48, 150, 49, 1800, 145],304,1]
%
% END OF LATTICE L305.1
%
\hbox{}\par\smallskip%
%
% LATTICE L305.2
%
\leavevmode%
${L_{305.2}}$%
{} : {$1\above{1pt}{1pt}{2}{2}8\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{1}{}5\above{1pt}{1pt}{1}{}25\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{m}%
\EasyButWeakLineBreak%
{${24}\above{1pt}{1pt}{l}{2}{25}\above{1pt}{1pt}{}{2}{1}\above{1pt}{1pt}{r}{2}{600}\above{1pt}{1pt}{l}{2}{5}\above{1pt}{1pt}{r}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2292600\\17400\\6600
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
17400\\-95\\-50
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
6600\\-50\\-19
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4159\\-3120\\1450800
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-36\\26\\-12555
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-12\\9\\-4186
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
17\\-12\\5928
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
16\\-10\\5575
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\-1\\696
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
13\\0\\4500
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\1\\-350
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-2292600, 17400, 6600; 17400, -95, -50; 6600, -50, -19],[600, 5, 1],[17, 16, 2, 13, -1, -1, 4, 2, 67, 5; -12, -10, -1, 0, 1, 0, -5, -2, -60, -4; 5928, 5575, 696, 4500, -350, -348, 1400, 699, 23400, 1745],304,2]
%
% END OF LATTICE L305.2
%
\hbox{}\par\smallskip%
%
% LATTICE L305.3
%
\leavevmode%
${L_{305.3}}$%
{} : {$1\above{1pt}{1pt}{-2}{2}8\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{1}{}5\above{1pt}{1pt}{1}{}25\above{1pt}{1pt}{1}{}$}\EasyButWeakLineBreak%
{${24}\above{1pt}{1pt}{s}{2}{100}\above{1pt}{1pt}{*}{2}{4}\above{1pt}{1pt}{s}{2}{600}\above{1pt}{1pt}{s}{2}{20}\above{1pt}{1pt}{s}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2789400\\9000\\9000
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
9000\\-5\\-30
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
9000\\-30\\-29
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
14839\\171720\\4420200
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-21\\-244\\-6255
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-49\\-567\\-14596
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
23\\264\\6852
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
71\\820\\21150
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
15\\174\\4468
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
139\\1620\\41400
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
9\\106\\2680
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-2789400, 9000, 9000; 9000, -5, -30; 9000, -30, -29],[600, 5, 1],[23, 71, 15, 139, 9, 5, -1, -1, 1, 5; 264, 820, 174, 1620, 106, 60, -10, -12, 0, 56; 6852, 21150, 4468, 41400, 2680, 1488, -300, -298, 300, 1490],304,3]
%
% END OF LATTICE L305.3
%
\hbox{}\par\smallskip%
%
% LATTICE L305.4
%
\leavevmode%
${L_{305.4}}$%
{} : {$[1\above{1pt}{1pt}{-}{}2\above{1pt}{1pt}{-}{}]\above{1pt}{1pt}{}{0}16\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{1}{}5\above{1pt}{1pt}{1}{}25\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${600}\above{1pt}{1pt}{s}{2}{16}\above{1pt}{1pt}{*}{2}{100}\above{1pt}{1pt}{l}{2}{6}\above{1pt}{1pt}{}{2}{5}\above{1pt}{1pt}{}{2}{150}\above{1pt}{1pt}{r}{2}{4}\above{1pt}{1pt}{*}{2}{400}\above{1pt}{1pt}{s}{2}{24}\above{1pt}{1pt}{*}{2}{80}\above{1pt}{1pt}{*}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1232400\\-49200\\10800
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-49200\\-1930\\420
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
10800\\420\\-91
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\-90\\-300
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\76\\232
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\80\\250
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\-75\\-228
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\-152\\-465
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
32\\-2445\\-7500
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7\\-536\\-1646
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
67\\-5140\\-15800
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
11\\-846\\-2604
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5\\-388\\-1200
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-1232400, -49200, 10800; -49200, -1930, 420; 10800, 420, -91],[1200, 10, 1],[1, -1, -1, 1, 2, 32, 7, 67, 11, 5; -90, 76, 80, -75, -152, -2445, -536, -5140, -846, -388; -300, 232, 250, -228, -465, -7500, -1646, -15800, -2604, -1200],304,4]
%
% END OF LATTICE L305.4
%
\hbox{}\par\smallskip%
%
% LATTICE L305.5
%
\leavevmode%
${L_{305.5}}$%
{} : {$[1\above{1pt}{1pt}{-}{}2\above{1pt}{1pt}{1}{}]\above{1pt}{1pt}{}{6}16\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{1}{}5\above{1pt}{1pt}{1}{}25\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{m}%
\EasyButWeakLineBreak%
{${150}\above{1pt}{1pt}{r}{2}{16}\above{1pt}{1pt}{s}{2}{100}\above{1pt}{1pt}{*}{2}{24}\above{1pt}{1pt}{l}{2}{5}\above{1pt}{1pt}{r}{2}{600}\above{1pt}{1pt}{*}{2}{4}\above{1pt}{1pt}{s}{2}{400}\above{1pt}{1pt}{l}{2}{6}\above{1pt}{1pt}{}{2}{80}\above{1pt}{1pt}{}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-53223600\\17756400\\69600
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
17756400\\-5923870\\-23220
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
69600\\-23220\\-91
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-26\\-75\\-750
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-11\\-32\\-248
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7\\20\\250
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
31\\90\\744
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
22\\64\\495
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
587\\1710\\12600
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
59\\172\\1234
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
521\\1520\\10600
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
38\\111\\738
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
19\\56\\240
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-53223600, 17756400, 69600; 17756400, -5923870, -23220; 69600, -23220, -91],[1200, 10, 1],[-26, -11, 7, 31, 22, 587, 59, 521, 38, 19; -75, -32, 20, 90, 64, 1710, 172, 1520, 111, 56; -750, -248, 250, 744, 495, 12600, 1234, 10600, 738, 240],304,5]
%
% END OF LATTICE L305.5
%
\hbox{}\par\smallskip%
%
% LATTICE L305.6
%
\leavevmode%
${L_{305.6}}$%
{} : {$[1\above{1pt}{1pt}{1}{}2\above{1pt}{1pt}{-}{}]\above{1pt}{1pt}{}{4}16\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{1}{}5\above{1pt}{1pt}{1}{}25\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{m}%
\EasyButWeakLineBreak%
{${600}\above{1pt}{1pt}{*}{2}{16}\above{1pt}{1pt}{l}{2}{25}\above{1pt}{1pt}{}{2}{6}\above{1pt}{1pt}{r}{2}{20}\above{1pt}{1pt}{l}{2}{150}\above{1pt}{1pt}{}{2}{1}\above{1pt}{1pt}{r}{2}{400}\above{1pt}{1pt}{*}{2}{24}\above{1pt}{1pt}{s}{2}{80}\above{1pt}{1pt}{s}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
66404400\\1581600\\-8400
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1581600\\37670\\-200
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-8400\\-200\\1
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
73\\-3090\\-4500
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
19\\-804\\-1136
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
26\\-1100\\-1525
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
10\\-423\\-576
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7\\-296\\-390
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
11\\-465\\-600
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\-1
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-9\\380\\400
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\42\\12
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5\\-212\\-360
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[66404400, 1581600, -8400; 1581600, 37670, -200; -8400, -200, 1],[1200, 10, 1],[73, 19, 26, 10, 7, 11, 0, -9, -1, 5; -3090, -804, -1100, -423, -296, -465, 0, 380, 42, -212; -4500, -1136, -1525, -576, -390, -600, -1, 400, 12, -360],304,6]
%
% END OF LATTICE L305.6
%
\hbox{}\par\smallskip%
%
% LATTICE L305.7
%
\leavevmode%
${L_{305.7}}$%
{} : {$[1\above{1pt}{1pt}{1}{}2\above{1pt}{1pt}{1}{}]\above{1pt}{1pt}{}{2}16\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{1}{}5\above{1pt}{1pt}{1}{}25\above{1pt}{1pt}{1}{}$}\EasyButWeakLineBreak%
{${150}\above{1pt}{1pt}{}{2}{16}\above{1pt}{1pt}{}{2}{25}\above{1pt}{1pt}{r}{2}{24}\above{1pt}{1pt}{*}{2}{20}\above{1pt}{1pt}{*}{2}{600}\above{1pt}{1pt}{l}{2}{1}\above{1pt}{1pt}{}{2}{400}\above{1pt}{1pt}{}{2}{6}\above{1pt}{1pt}{r}{2}{80}\above{1pt}{1pt}{l}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
560400\\-14400\\1200
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-14400\\370\\-30
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1200\\-30\\-29
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-121\\-4725\\-150
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-51\\-1992\\-64
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-59\\-2305\\-75
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-37\\-1446\\-48
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-7\\-274\\-10
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7\\270\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\39\\1
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\40\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-5\\-195\\-6
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-33\\-1288\\-40
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[560400, -14400, 1200; -14400, 370, -30; 1200, -30, -29],[1200, 10, 1],[-121, -51, -59, -37, -7, 7, 1, 1, -5, -33; -4725, -1992, -2305, -1446, -274, 270, 39, 40, -195, -1288; -150, -64, -75, -48, -10, 0, 1, 0, -6, -40],304,7]
%
% END OF LATTICE L305.7
%
%
% LATTICE L305.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[150, 0, 150; 0, -5, -30; 150, -30, -29],[150, 5, 1],[139, 15, 71, 23, 5, 1, -1, -1, 5, 9; 810, 87, 410, 132, 28, 0, -6, -5, 30, 53; -150, -16, -75, -24, -5, 0, 1, 0, -6, -10],304,8]
%
% END OF LATTICE L305.8
%
%
% LATTICE L305.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-8700, -300, -900; -300, -10, -35; -900, -35, -47],[300, 5, 1],[5, -1, -1, 1, 5, 23, 71, 15, 139, 9; -114, 25, 23, -30, -117, -534, -1645, -347, -3210, -207; -12, 0, 2, 0, -10, -48, -150, -32, -300, -20],304,9]
%
% END OF LATTICE L305.9
%
%
% LATTICE L305.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-731100, 135000, -2100; 135000, -24830, 410; -2100, 410, -1],[300, 10, 1],[74, 517, 59, 589, 44, 29, -1, -15, -74, 15; 375, 2620, 299, 2985, 223, 147, -5, -76, -375, 76; -1662, -11600, -1323, -13200, -985, -648, 25, 336, 1650, -340],304,10]
%
% END OF LATTICE L305.10
%
%
% LATTICE L305.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-6196200, -247800, 9000; -247800, -9910, 360; 9000, 360, -13],[600, 10, 1],[1, -1, -1, 1, 5, 11, 67, 7, 32, 4; -24, 25, 24, -30, -124, -270, -1640, -171, -780, -97; 27, 0, -28, -150, 20, 126, 900, 104, 525, 80],304,11]
%
% END OF LATTICE L305.11
%
%
% LATTICE L305.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-62446200, -2497800, -1221000; -2497800, -99910, -48840; -1221000, -48840, -23863],[600, 10, 1],[-85, -1, 43, 113, -35, -101, -1433, -165, -1661, -126; 2040, 25, -1032, -2715, 836, 2421, 34360, 3957, 39840, 3023; 174, 0, -88, -225, 80, 213, 3000, 344, 3450, 260],304,12]
%
% END OF LATTICE L305.12
%
%
% LATTICE L305.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[101550, 13500, 50550; 13500, 1790, 6720; 50550, 6720, 25163],[150, 10, 1],[-43, -30, -229, -56, -55, -112, -1, 74, 25, 24; 45, 9, 40, 6, 2, 0, 0, 5, 3, 7; 75, 58, 450, 111, 110, 225, 2, -150, -51, -50],304,13]
%
% END OF LATTICE L305.13
%
%
% LATTICE L305.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[120450, 18000, -40350; 18000, 2685, -6030; -40350, -6030, 13517],[150, 15, 1],[113, 53, 321, 45, 55, 67, 1, -51, -9, -1; 30, 9, 40, 4, 2, 0, 0, 5, 2, 7; 350, 162, 975, 136, 165, 200, 3, -150, -26, 0],304,14]
%
% END OF LATTICE L305.14
%
%
% LATTICE L305.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[308850, 4500, 148050; 4500, -30, 2160; 148050, 2160, 70969],[150, 30, 1],[-2243, -1448, -6837, -368, -475, -12, 95, 72, -83, -878; 135, 87, 410, 22, 28, 0, -6, -5, 5, 53; 4675, 3018, 14250, 767, 990, 25, -198, -150, 173, 1830],304,15]
%
% END OF LATTICE L305.15
%
%
% LATTICE L305.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[681900, -133500, 3600; -133500, 26130, -705; 3600, -705, 19],[300, 15, 1],[-1, 1, 1, 3, -1, -3, -31, -7, -23, -5; -2, 5, 3, 10, -1, -6, -65, -15, -50, -11; 116, 0, -78, -200, 150, 344, 3450, 768, 2500, 540],304,16]
%
% END OF LATTICE L305.16
%
%
% LATTICE L305.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[406200, -104100, -102000; -104100, 26740, 26140; -102000, 26140, 25613],[300, 20, 1],[217, 329, 1, 113, 217, 541, 3461, 757, 3677, 541; 6, 10, 0, 0, 4, 12, 80, 18, 90, 14; 858, 1300, 4, 450, 860, 2142, 13700, 2996, 14550, 2140],304,17]
%
% END OF LATTICE L305.17
%
%
% LATTICE L305.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[275700, 9000, 3600; 9000, -510, 120; 3600, 120, 47],[300, 30, 1],[-3, -107, -15, -58, -16, -4, 1, 9, 23, 11; 1, 30, 4, 15, 4, 1, 0, -2, -5, -2; 226, 8100, 1137, 4400, 1215, 304, -75, -684, -1750, -840],304,18]
%
% END OF LATTICE L305.18
%
%
% LATTICE L305.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-439800, 29400, -1800; 29400, -1965, 120; -1800, 120, -7],[600, 15, 1],[5, 47, 5, 31, 3, 1, -1, -1, -1, 3; 76, 720, 77, 480, 47, 16, -15, -16, -20, 44; 4, 150, 24, 200, 30, 16, 0, -18, -100, -30],304,19]
%
% END OF LATTICE L305.19
%
%
% LATTICE L305.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-12589800, 839400, -21600; 839400, -55965, 1440; -21600, 1440, -37],[600, 15, 1],[13, 61, 13, 81, 8, 3, -1, -1, -1, 4; 204, 960, 205, 1280, 127, 48, -15, -16, -20, 62; 344, 1725, 384, 2500, 270, 116, 0, -39, -200, 75],304,20]
%
% END OF LATTICE L305.20
%
%
% LATTICE L305.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-40200, 4200, -600; 4200, -435, 60; -600, 60, -7],[600, 15, 1],[3, 31, 7, 23, 5, 1, -1, -1, -3, 1; 32, 340, 78, 260, 58, 12, -10, -12, -40, 8; 4, 150, 48, 200, 60, 16, 0, -18, -100, -30],304,21]
%
% END OF LATTICE L305.21
%
%
% LATTICE L305.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2292600, -48600, 6600; -48600, -980, 140; 6600, 140, -19],[600, 20, 1],[13, 3, 11, 11, 3, 37, 1, 3, -1, -1; 0, -1, -5, -6, -2, -30, -1, -5, 0, 1; 4500, 1032, 3775, 3768, 1025, 12600, 339, 1000, -348, -340],304,22]
%
% END OF LATTICE L305.22
%
%
% LATTICE L305.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2429400, 486000, -8400; 486000, -97220, 1680; -8400, 1680, -29],[600, 20, 1],[139, 15, 71, 23, 5, 1, -1, -1, 5, 9; 810, 87, 410, 132, 28, 0, -6, -5, 30, 53; 6600, 688, 3150, 972, 170, -300, -58, 0, 288, 460],304,23]
%
% END OF LATTICE L305.23
%
%
% LATTICE L305.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[335400, -83400, -600; -83400, 20730, 150; -600, 150, 1],[600, 30, 1],[-3, 1, 4, 0, -3, -11, -8, -83, -5, -9; -10, 4, 15, 0, -11, -40, -29, -300, -18, -32; -250, 12, 150, -1, -150, -575, -426, -4500, -278, -540],304,24]
%
% END OF LATTICE L305.24
%
%
% LATTICE L305.25
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-774600, 154800, 37200; 154800, -30930, -7440; 37200, -7440, -1781],[600, 30, 1],[-31, -23, 1, 11, 42, 147, 37, 253, 3, -33; -125, -92, 5, 44, 167, 580, 145, 980, 11, -136; -125, -96, 0, 46, 180, 650, 168, 1200, 17, -120],304,25]
%
% END OF LATTICE L305.25
%
%
% LATTICE L305.26
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[23039400, 145500, -5833200; 145500, 780, -36840; -5833200, -36840, 1476871],[300, 60, 1],[349, 3723, 155, -1203, -2173, -815, -10713, -1553, -1127, 775; -18, -190, -8, 60, 108, 40, 520, 74, 50, -42; 1378, 14700, 612, -4750, -8580, -3218, -42300, -6132, -4450, 3060],304,26]
%
% END OF LATTICE L305.26
%
%
% LATTICE L305.27
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-241800, -48600, 1800; -48600, -9760, 360; 1800, 360, -13],[600, 40, 1],[-1, 1, 1, 2, -3, -8, -51, -11, -26, -7; 6, -5, -6, -15, 16, 45, 290, 63, 150, 41; 27, 0, -28, -150, 20, 126, 900, 208, 525, 160],304,27]
%
% END OF LATTICE L305.27
%
%
% LATTICE L305.28
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2491800, -498600, -244200; -498600, -99760, -48840; -244200, -48840, -23863],[600, 40, 1],[85, 1, -43, -223, 37, 205, 1449, 333, 1673, 253; -510, -5, 258, 1335, -224, -1233, -8710, -2001, -10050, -1519; 174, 0, -88, -450, 80, 426, 3000, 688, 3450, 520],304,28]
%
% END OF LATTICE L305.28
%
%
% LATTICE L305.29
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[39853200, 7223400, -38400; 7223400, 1309240, -6960; -38400, -6960, 37],[600, 40, 1],[1, 1, 0, 2, 2, 4, 24, 5, 23, 3; -3, -5, -1, -15, -9, -15, -85, -17, -75, -9; 474, 100, -188, -750, 380, 1326, 8900, 1988, 9750, 1420],304,29]
%
% END OF LATTICE L305.29
%
%
% LATTICE L305.30
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[862800, 8400, 0; 8400, -1410, 330; 0, 330, -73],[1200, 30, 1],[24, 15, 137, 7, 7, -3, -3, -1, 1, 5; -2465, -1540, -14060, -718, -716, 310, 308, 100, -103, -514; -11150, -6966, -63600, -3248, -3240, 1400, 1392, 450, -466, -2325],304,30]
%
% END OF LATTICE L305.30
%
%
% LATTICE L305.31
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[19138800, 613200, -30000; 613200, 19590, -960; -30000, -960, 47],[1200, 30, 1],[17, 5, 43, 1, 1, -1, -1, 1, 1, 2; 370, 108, 920, 21, 16, -25, -24, 20, 22, 44; 18400, 5394, 46200, 1066, 960, -1150, -1128, 1050, 1088, 2175],304,31]
%
% END OF LATTICE L305.31
%
%
% LATTICE L305.32
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[310800, -16800, -6000; -16800, 510, 210; -6000, 210, 83],[1200, 30, 1],[14, 4, 67, 3, 1, -3, -1, 2, 1, 7; -1045, -298, -4980, -222, -68, 230, 76, -150, -75, -524; 3650, 1041, 17400, 776, 240, -800, -264, 525, 262, 1830],304,32]
%
% END OF LATTICE L305.32
%
%
% LATTICE L305.33
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[5080200, 1254600, 15600; 1254600, 309660, 3840; 15600, 3840, 47],[600, 60, 1],[131, 17, 122, 7, -12, -51, -10, -1, 9, 18; -640, -83, -595, -34, 59, 250, 49, 5, -44, -88; 8800, 1137, 8100, 452, -840, -3500, -684, -75, 608, 1215],304,33]
%
% END OF LATTICE L305.33
%
%
% LATTICE L305.34
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-46200, 9000, -600; 9000, -1740, 120; -600, 120, -7],[600, 60, 1],[3, 1, 1, -1, -5, -23, -7, -31, -3, -1; 10, 4, 5, -4, -21, -100, -31, -140, -14, -6; -100, -18, 0, 16, 60, 200, 48, 150, 4, -30],304,34]
%
% END OF LATTICE L305.34
%
%
% LATTICE L305.35
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1200, 0, 0; 0, -510, 60; 0, 60, -7],[1200, 30, 1],[-1, 0, 1, 0, -1, -2, -3, -4, -1, -1; -10, -1, 0, 1, 16, 15, 16, 15, 2, -2; -100, -9, 0, 8, 120, 100, 96, 75, 4, -30],304,35]
%
% END OF LATTICE L305.35
%
%
% LATTICE L305.36
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-457316400, 50842800, -204000; 50842800, -5652520, 22680; -204000, 22680, -91],[1200, 40, 1],[-11, -67, -7, -64, -2, -2, 1, 1, -1, -5; -93, -560, -58, -525, -16, -15, 10, 8, -15, -44; 1476, 10600, 1234, 12600, 495, 744, 250, -248, -1500, 240],304,36]
%
% END OF LATTICE L305.36
%
%
% LATTICE L305.37
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1395600, -464400, -1200; -464400, 154520, 400; -1200, 400, 1],[1200, 40, 1],[1, 7, 0, -16, -5, -14, -18, -13, -49, -3; 3, 20, 0, -45, -14, -39, -50, -36, -135, -8; 12, 400, -1, -1200, -390, -1152, -1525, -1136, -4500, -360],304,37]
%
% END OF LATTICE L305.37
%
%
% LATTICE L305.38
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[200400, 75600, 0; 75600, 26920, 40; 0, 40, -1],[1200, 40, 1],[-17, -121, -14, -142, -11, -8, -2, 3, 17, -3; 45, 320, 37, 375, 29, 21, 5, -8, -45, 8; 1776, 12600, 1454, 14700, 1130, 804, 150, -328, -1800, 320],304,38]
%
% END OF LATTICE L305.38
%
%
% LATTICE L305.39
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1232400, -40800, -7200; -40800, -280, 0; -7200, 0, 11],[1200, 40, 1],[11, 67, 7, 64, 4, 2, -1, -1, 1, 5; -1593, -9710, -1015, -9285, -581, -291, 145, 146, -135, -722; 7152, 43600, 4558, 41700, 2610, 1308, -650, -656, 600, 3240],304,39]
%
% END OF LATTICE L305.39
%
%
% LATTICE L305.40
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[348600, 1200, -600; 1200, -120, 0; -600, 0, 1],[600, 120, 1],[-1, 0, 1, 0, -1, -2, -3, -16, -1, -2; -5, 1, 10, 0, -8, -15, -22, -115, -7, -13; -550, 12, 600, -1, -600, -1175, -1752, -9300, -578, -1140],304,40]
%
% END OF LATTICE L305.40
%
%
% LATTICE L305.41
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[600, 0, 0; 0, -31080, -7440; 0, -7440, -1781],[600, 120, 1],[-1, 0, 1, 0, -1, -4, -3, -16, -1, -2; 60, 23, 0, -11, -86, -155, -80, -285, -8, 29; -250, -96, 0, 46, 360, 650, 336, 1200, 34, -120],304,41]
%
% END OF LATTICE L305.41
%
%
% LATTICE L305.42
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1050600, 117000, 35400; 117000, 12720, 3840; 35400, 3840, 1159],[600, 120, 1],[-1, -1, 1, 1, 9, 21, 13, 59, 3, 3; 115, 107, -100, -104, -934, -2170, -1340, -6065, -307, -299; -350, -324, 300, 314, 2820, 6550, 4044, 18300, 926, 900],304,42]
%
% END OF LATTICE L305.42
%
%
% LATTICE L305.43
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[51502800, 2010000, -49200; 2010000, 78360, -1920; -49200, -1920, 47],[1200, 120, 1],[-2, -1, 1, 1, 2, 17, 5, 43, 2, 1; -5, -2, 0, 1, 2, 15, 4, 30, 1, -2; -2300, -1128, 1050, 1088, 2175, 18400, 5394, 46200, 2132, 960],304,43]
%
% END OF LATTICE L305.43
%
%
% LATTICE L305.44
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-121200, -13200, 4800; -13200, 5640, -1920; 4800, -1920, 653],[1200, 120, 1],[-2, -1, 1, 1, 4, 17, 5, 43, 2, 1; -345, -174, 155, 167, 673, 2865, 843, 7250, 337, 166; -1000, -504, 450, 484, 1950, 8300, 2442, 21000, 976, 480],304,44]
%
% END OF LATTICE L305.44
%
%
% LATTICE L305.45
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-5665200, 1401600, -25200; 1401600, -346440, 6720; -25200, 6720, 617],[1200, 120, 1],[527, 343, 169, -170, -846, -3872, -1175, -10373, -499, -315; 2105, 1370, 675, -679, -3379, -15465, -4693, -41430, -1993, -1258; -1400, -912, -450, 452, 2250, 10300, 3126, 27600, 1328, 840],304,45]
%
% END OF LATTICE L305.45
%
%
% LATTICE L305.46
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1200, 0, 0; 0, -56040, 1440; 0, 1440, -37],[1200, 120, 1],[-4, -3, -4, -1, -1, -1, 0, 1, 0, -1; 65, 40, 45, 9, 4, -5, -1, 0, 3, 28; 2500, 1536, 1725, 344, 150, -200, -39, 0, 116, 1080],304,46]
%
% END OF LATTICE L305.46
%

\medskip%
%------------------------------WEYL-GROUP-W306--------------------------------
%
\leavevmode\llap{}%
$W_{306}$%
\qquad\llap{32} lattices, $\chi=96$%
\hfill%
$2\infty|\infty22\slashinfty22\infty|\infty22\slashinfty2\rtimes D_{4}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L306.1
%
\leavevmode%
${L_{306.1}}$%
{} : {$1\above{1pt}{1pt}{1}{7}4\above{1pt}{1pt}{1}{7}64\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{1}{}9\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{3}%
\EasyButWeakLineBreak%
{${576}\above{1pt}{1pt}{*}{2}{48}\above{1pt}{1pt}{48,25}{\infty z}{12}\above{1pt}{1pt}{48,13}{\infty}{48}\above{1pt}{1pt}{s}{2}{576}\above{1pt}{1pt}{*}{2}{12}\above{1pt}{1pt}{24,13}{\infty z}{3}\above{1pt}{1pt}{r}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1222848\\-37440\\-38592
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-37440\\-1140\\-1176
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-38592\\-1176\\-1213
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-6913\\-1168128\\1354752
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-198\\-33463\\38808
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-206\\-34814\\40375
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
71\\11304\\-13248
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
13\\2018\\-2376
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\-25\\24
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-190\\216
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\264\\-288
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\196\\-222
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\364\\-417
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-1222848, -37440, -38592; -37440, -1140, -1176; -38592, -1176, -1213],[576, 12, 1],[71, 13, 0, -1, 1, 1, 2, 73, 23, 6, 37, 143, 11, 4; 11304, 2018, -25, -190, 264, 196, 364, 13032, 4066, 1039, 6274, 24072, 1832, 650; -13248, -2376, 24, 216, -288, -222, -417, -14976, -4680, -1200, -7272, -27936, -2130, -759],305,1]
%
% END OF LATTICE L306.1
%
\hbox{}\par\smallskip%
%
% LATTICE L306.2
%
\leavevmode%
${L_{306.2}}$%
{} : {$1\above{1pt}{1pt}{1}{1}4\above{1pt}{1pt}{1}{7}64\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{1}{}9\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{3}%
\EasyButWeakLineBreak%
{${36}\above{1pt}{1pt}{*}{2}{48}\above{1pt}{1pt}{48,7}{\infty z}{12}\above{1pt}{1pt}{48,43}{\infty}{48}\above{1pt}{1pt}{l}{2}{9}\above{1pt}{1pt}{}{2}{192}\above{1pt}{1pt}{12,7}{\infty}{192}\above{1pt}{1pt}{s}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-403776\\7488\\77184
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7488\\-132\\-1488
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
77184\\-1488\\-14287
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
373751\\8957520\\1085760
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-6981\\-167311\\-20280
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-71063\\-1703130\\-206441
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-31\\-744\\-90
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-33\\-790\\-96
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
62\\1487\\180
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1603\\38426\\4656
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1007\\24138\\2925
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3371\\80800\\9792
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4197\\100592\\12192
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-403776, 7488, 77184; 7488, -132, -1488; 77184, -1488, -14287],[576, 12, 1],[-31, -33, 62, 1603, 1007, 3371, 4197, 3253, 3255, 475, 1619, 604, 925, 99; -744, -790, 1487, 38426, 24138, 80800, 100592, 77964, 78010, 11383, 38794, 14472, 22160, 2368; -90, -96, 180, 4656, 2925, 9792, 12192, 9450, 9456, 1380, 4704, 1755, 2688, 288],305,2]
%
% END OF LATTICE L306.2
%
\hbox{}\par\smallskip%
%
% LATTICE L306.3
%
\leavevmode%
${L_{306.3}}$%
{} : {$1\above{1pt}{1pt}{-}{3}4\above{1pt}{1pt}{1}{7}64\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{1}{}9\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{3}%
\EasyButWeakLineBreak%
{${576}\above{1pt}{1pt}{l}{2}{12}\above{1pt}{1pt}{48,25}{\infty}{48}\above{1pt}{1pt}{48,37}{\infty z}{12}\above{1pt}{1pt}{}{2}{576}\above{1pt}{1pt}{}{2}{3}\above{1pt}{1pt}{24,1}{\infty}{12}\above{1pt}{1pt}{s}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
112997952\\55301760\\2316096
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
55301760\\27064956\\1133508
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2316096\\1133508\\47471
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-24431401\\51191280\\-30340800
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-11953935\\25047161\\-14845320
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-495830\\1038916\\-615761
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
56425\\-118224\\69984
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5429\\-11375\\6732
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
505\\-1058\\624
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-264\\553\\-324
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-505\\1056\\-576
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
198\\-415\\249
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2221\\-4654\\2766
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[112997952, 55301760, 2316096; 55301760, 27064956, 1133508; 2316096, 1133508, 47471],[576, 12, 1],[56425, 5429, 505, -264, -505, 198, 2221, 43295, 7036, 7805, 12729, 100225, 3957, 6089; -118224, -11375, -1058, 553, 1056, -415, -4654, -90720, -14743, -16354, -26671, -210000, -8291, -12758; 69984, 6732, 624, -324, -576, 249, 2766, 53856, 8748, 9696, 15804, 124416, 4911, 7554],305,3]
%
% END OF LATTICE L306.3
%
\hbox{}\par\smallskip%
%
% LATTICE L306.4
%
\leavevmode%
${L_{306.4}}$%
{} : {$1\above{1pt}{1pt}{-}{5}4\above{1pt}{1pt}{1}{7}64\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{1}{}9\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{3}%
\EasyButWeakLineBreak%
{${36}\above{1pt}{1pt}{l}{2}{12}\above{1pt}{1pt}{48,7}{\infty}{48}\above{1pt}{1pt}{48,19}{\infty z}{12}\above{1pt}{1pt}{}{2}{9}\above{1pt}{1pt}{r}{2}{192}\above{1pt}{1pt}{24,7}{\infty z}{192}\above{1pt}{1pt}{*}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1155502656\\8633088\\549064512
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
8633088\\-64500\\-4102212
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
549064512\\-4102212\\-260900947
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-204281569\\11446812000\\-609890688
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1526502\\-85536751\\4557432
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
97074020\\-5439492500\\289818319
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-223\\12510\\-666
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-201\\11257\\-600
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1069\\-59930\\3192
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7733\\-433367\\23088
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
9806\\-549525\\29277
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
33119\\-1855928\\98880
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
41769\\-2340568\\124704
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-1155502656, 8633088, 549064512; 8633088, -64500, -4102212; 549064512, -4102212, -260900947],[576, 12, 1],[-223, -201, 1069, 7733, 9806, 33119, 41769, 32587, 16383, 9719, 8449, 6376, 10033, 1383; 12510, 11257, -59930, -433367, -549525, -1855928, -2340568, -1826010, -918007, -544570, -473383, -357225, -562072, -77432; -666, -600, 3192, 23088, 29277, 98880, 124704, 97290, 48912, 29016, 25224, 19035, 29952, 4128],305,4]
%
% END OF LATTICE L306.4
%
%
% LATTICE L306.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-284352, 5760, 576; 5760, -116, -12; 576, -12, -1],[192, 4, 1],[9, 7, 1, 1, -1, -1, -1, -9, -7, -1, -1, 1, 1, 1; 280, 234, 39, 42, -40, -42, -45, -424, -342, -57, -150, -104, 6, 27; 1344, 936, 96, 72, -96, -78, -57, -384, -216, 24, 648, 1056, 318, 177],305,5]
%
% END OF LATTICE L306.5
%
%
% LATTICE L306.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-1488192, 500928, 14592; 500928, -168612, -4912; 14592, -4912, -143],[192, 4, 1],[233, 1133, 53, -7, -9, 19, 509, 118, 973, 298, 2113, 711, 2789, 2299; 618, 3006, 141, -18, -24, 48, 1344, 312, 2574, 789, 5598, 1884, 7392, 6096; 2543, 12336, 564, -96, -94, 288, 5760, 1321, 10848, 3300, 23280, 7822, 30624, 25152],305,6]
%
% END OF LATTICE L306.6
%
%
% LATTICE L306.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-1290563520, 8020416, -38592; 8020416, -49844, 240; -38592, 240, -1],[192, 4, 1],[-929, -268, -25, 11, 1, -11, -113, -727, -353, -389, -632, -1657, -196, -301; -148720, -42903, -4002, 1761, 160, -1761, -18090, -116384, -56511, -62274, -101175, -265264, -31377, -48186; 158688, 45792, 4296, -1872, -192, 1869, 19254, 123936, 60192, 66360, 107856, 282816, 33459, 51402],305,7]
%
% END OF LATTICE L306.7
%
%
% LATTICE L306.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-2837249088, 190083456, -13365696; 190083456, -12734772, 895444; -13365696, 895444, -62963],[192, 4, 1],[1353, 3278, 593, -28, -49, 173, 3115, 711, 2914, 3535, 6220, 4177, 16339, 13397; 20391, 49401, 8934, -423, -738, 2616, 46968, 10719, 43929, 53286, 93753, 62958, 246264, 201912; 2783, 6720, 1176, -72, -94, 480, 6720, 1513, 6168, 7416, 12960, 8686, 33888, 27648],305,8]
%
% END OF LATTICE L306.8
%
%
% LATTICE L306.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-272448, 34368, 11136; 34368, -4332, -1404; 11136, -1404, -455],[192, 12, 1],[-71, -13, 0, 1, -1, -1, -2, -73, -23, -6, -37, -143, -11, -4; 2072, 398, 9, -18, -8, 16, 42, 1624, 526, 145, 942, 3704, 292, 112; -8160, -1552, -28, 80, 0, -74, -179, -6816, -2192, -596, -3824, -14976, -1174, -445],305,9]
%
% END OF LATTICE L306.9
%
%
% LATTICE L306.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-134592, -17472, 4992; -17472, -2268, 648; 4992, 648, -185],[192, 12, 1],[32, 51, 2, -1, -1, 3, 29, 19, 51, 15, 103, 103, 133, 107; -237, -374, -13, 10, 6, -32, -240, -153, -406, -117, -790, -786, -1008, -800; 27, 56, 8, 8, -6, -32, -64, -27, -56, -8, -8, 6, 32, 64],305,10]
%
% END OF LATTICE L306.10
%
%
% LATTICE L306.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[9240768, -4018368, 954048; -4018368, 1747380, -414864; 954048, -414864, 98497],[192, 12, 1],[-6231, -599, -55, 28, 39, -23, -249, -4833, -784, -867, -1411, -11103, -438, -673; -40928, -3935, -362, 185, 272, -150, -1632, -31696, -5143, -5690, -9263, -72896, -2876, -4420; -112032, -10772, -992, 508, 768, -409, -4462, -86688, -14068, -15568, -25348, -199488, -7871, -12098],305,11]
%
% END OF LATTICE L306.11
%
%
% LATTICE L306.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-41066688, -2474880, -810624; -2474880, -149148, -48852; -810624, -48852, -16001],[192, 12, 1],[47, 37, 5, -1, -1, 7, 49, 31, 41, 47, 79, 157, 201, 159; -2935, -2299, -290, 69, 50, -504, -3224, -2015, -2651, -3010, -5019, -9950, -12696, -9976; 6579, 5144, 632, -160, -102, 1184, 7360, 4581, 6016, 6808, 11320, 22422, 28576, 22400],305,12]
%
% END OF LATTICE L306.12
%
%
% LATTICE L306.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-118464, -34752, -6720; -34752, -10192, -1968; -6720, -1968, -377],[192, 16, 1],[-21, -14, 53, 664, 1109, 347, 430, 1773, 1328, 385, 650, 643, 91, 8; 84, 57, -213, -2679, -4476, -1401, -1737, -7164, -5367, -1557, -2631, -2604, -369, -33; -64, -48, 168, 2160, 3616, 1134, 1410, 5824, 4368, 1272, 2160, 2144, 306, 30],305,13]
%
% END OF LATTICE L306.13
%
%
% LATTICE L306.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-9585600, -3170880, 75648; -3170880, -1048912, 25024; 75648, 25024, -597],[192, 16, 1],[-9, -7, -2, -1, 1, 1, 1, 9, 7, 2, 1, -1, -1, -1; 904, 543, 45, -9, -16, 6, 36, 512, 519, 309, 1071, 1432, 348, 141; 36736, 21864, 1632, -504, -544, 378, 1635, 22592, 22632, 13200, 45000, 59872, 14454, 5781],305,14]
%
% END OF LATTICE L306.14
%
%
% LATTICE L306.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1055040, 360000, -12288; 360000, -122832, 4192; -12288, 4192, -143],[192, 16, 1],[46, 376, 227, 796, 267, 1043, 853, 86, 416, 37, -4, -3, 13, 203; 180, 1473, 891, 3129, 1050, 4104, 3360, 339, 1641, 147, -15, -12, 48, 792; 1321, 10848, 6600, 23280, 7822, 30624, 25152, 2543, 12336, 1128, -96, -94, 288, 5760],305,15]
%
% END OF LATTICE L306.15
%
%
% LATTICE L306.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-4667712, 1162560, -51264; 1162560, -289552, 12768; -51264, 12768, -563],[192, 16, 1],[-2, -4, 25, 296, 123, 613, 755, 194, 580, 167, 280, 69, 155, 13; -9, -15, 111, 1281, 531, 2640, 3240, 831, 2481, 711, 1185, 291, 648, 48; -22, 24, 240, 2088, 838, 4032, 4704, 1174, 3432, 912, 1368, 314, 576, -96],305,16]
%
% END OF LATTICE L306.16
%
%
% LATTICE L306.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1932480, 586944, 19584; 586944, -178260, -5952; 19584, -5952, -197],[576, 12, 1],[-21, -69, -28, -39, 29, 37, 47, 485, 417, 86, 387, 435, 79, 11; -72, -214, -85, -118, 88, 112, 142, 1464, 1258, 259, 1162, 1304, 236, 32; 64, -408, -216, -312, 224, 294, 381, 3968, 3432, 720, 3336, 3808, 714, 123],305,17]
%
% END OF LATTICE L306.17
%
%
% LATTICE L306.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-13748544, 44352, 44352; 44352, -132, -144; 44352, -144, -143],[576, 12, 1],[27, 131, 6, -1, -1, 3, 61, 14, 115, 35, 247, 83, 325, 267; 638, 3098, 143, -22, -24, 64, 1424, 328, 2698, 823, 5818, 1956, 7664, 6304; 7727, 37488, 1716, -288, -286, 864, 17472, 4009, 32928, 10020, 70704, 23758, 93024, 76416],305,18]
%
% END OF LATTICE L306.18
%
%
% LATTICE L306.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-475162560, -242201088, 77936256; -242201088, -123455364, 39725868; 77936256, 39725868, -12783113],[576, 12, 1],[-111039, -32531, -3945, 1054, 911, -942, -11705, -77657, -38230, -43229, -71815, -189607, -22645, -35469; 237808, 69671, 8450, -2257, -1952, 2017, 25066, 166304, 81871, 92578, 153799, 406064, 48497, 75962; 62048, 18180, 2208, -588, -512, 525, 6534, 43360, 21348, 24144, 40116, 105920, 12651, 19818],305,19]
%
% END OF LATTICE L306.19
%
%
% LATTICE L306.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1185768000, 9052416, 8640576; 9052416, -69108, -65964; 8640576, -65964, -62963],[576, 12, 1],[32, 77, 13, -1, -1, 7, 81, 18, 73, 87, 151, 101, 393, 319; -4329, -10439, -1802, 121, 142, -824, -10648, -2385, -9703, -11626, -20263, -13570, -52888, -43064; 8927, 21504, 3672, -264, -286, 1824, 22272, 4969, 20184, 24120, 41952, 28078, 109344, 88896],305,20]
%
% END OF LATTICE L306.20
%
%
% LATTICE L306.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-87360, 8448, -2304; 8448, 2448, -864; -2304, -864, 301],[192, 48, 1],[-5, -4, 5, 94, 485, 52, 67, 845, 214, 65, 116, 355, 18, 3; -288, -229, 285, 5363, 27672, 2967, 3823, 48216, 12211, 3709, 6619, 20256, 1027, 171; -864, -688, 856, 16112, 83136, 8914, 11486, 144864, 36688, 11144, 19888, 60864, 3086, 514],305,21]
%
% END OF LATTICE L306.21
%
%
% LATTICE L306.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1344, 17664, -576; 17664, -182448, 5904; -576, 5904, -191],[192, 48, 1],[845, 214, 65, 116, 355, 9, 3, -5, -4, 5, 94, 485, 26, 67; 2392, 605, 183, 325, 992, 25, 8, -16, -11, 15, 269, 1384, 74, 190; 71328, 18040, 5456, 9688, 29568, 745, 238, -480, -328, 448, 8024, 41280, 2207, 5666],305,22]
%
% END OF LATTICE L306.22
%
%
% LATTICE L306.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-40128, -64704, 4224; -64704, -97200, 6336; 4224, 6336, -413],[192, 48, 1],[32, 51, 4, -1, -1, 3, 29, 19, 51, 30, 103, 103, 133, 107; -990, -1575, -121, 33, 30, -100, -916, -597, -1599, -937, -3207, -3204, -4132, -3316; -14865, -23648, -1816, 496, 450, -1504, -13760, -8967, -24016, -14072, -48160, -48114, -62048, -49792],305,23]
%
% END OF LATTICE L306.23
%
%
% LATTICE L306.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-192, 1344, -192; 1344, -9072, 1296; -192, 1296, -185],[192, 48, 1],[103, 103, 30, 51, 38, 29, 3, -1, -1, 4, 51, 64, 107, 133; 19, 17, 3, 1, -1, -4, -4, -1, 1, 3, 17, 19, 28, 28; 6, -8, -16, -56, -54, -64, -32, -6, 8, 16, 56, 54, 64, 32],305,24]
%
% END OF LATTICE L306.24
%
%
% LATTICE L306.25
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[576, -1152, 0; -1152, 2352, 0; 0, 0, -1],[576, 48, 1],[-215, -70, -39, -128, -505, -40, -31, -289, -56, -3, 2, 1, -2, -11; -96, -31, -17, -55, -216, -17, -13, -120, -23, -1, 1, 0, -1, -5; -864, -288, -168, -576, -2304, -186, -150, -1440, -288, -24, 0, 0, -6, -42],305,25]
%
% END OF LATTICE L306.25
%
%
% LATTICE L306.26
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-150971328, 324864, 266112; 324864, -528, -576; 266112, -576, -469],[576, 48, 1],[1357, 262, 13, -12, -13, 9, 26, 1019, 332, 185, 606, 2389, 189, 73; 14856, 2869, 143, -131, -144, 98, 284, 11136, 3629, 2023, 6629, 26136, 2068, 799; 751680, 145128, 7200, -6648, -7200, 4986, 14403, 564480, 183912, 102480, 335688, 1323360, 104694, 40437],305,26]
%
% END OF LATTICE L306.26
%
%
% LATTICE L306.27
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-31680, -7488, -3456; -7488, -1680, -816; -3456, -816, -377],[576, 48, 1],[7, 5, -18, -229, -383, -120, -149, -615, -461, -134, -227, -225, -32, -3; 0, 1, -1, -23, -40, -13, -17, -72, -55, -17, -31, -32, -5, -1; -64, -48, 168, 2160, 3616, 1134, 1410, 5824, 4368, 1272, 2160, 2144, 306, 30],305,27]
%
% END OF LATTICE L306.27
%
%
% LATTICE L306.28
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-101458368, 237312, 266688; 237312, -528, -624; 266688, -624, -701],[576, 48, 1],[525, 394, 115, 196, 195, 14, 3, -5, -4, 15, 194, 325, 51, 127; 1576, 1181, 343, 581, 576, 41, 8, -16, -11, 47, 589, 984, 154, 382; 198304, 148824, 43440, 74040, 73664, 5289, 1134, -1888, -1512, 5664, 73272, 122752, 19263, 47970],305,28]
%
% END OF LATTICE L306.28
%
%
% LATTICE L306.29
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-120384, 8640, 41472; 8640, -528, -2976; 41472, -2976, -14287],[576, 48, 1],[1007, 1603, 124, -33, -31, 99, 925, 604, 1619, 950, 3255, 3253, 4197, 3371; -15, -23, -1, 1, 0, -4, -20, -12, -31, -17, -55, -54, -68, -52; 2925, 4656, 360, -96, -90, 288, 2688, 1755, 4704, 2760, 9456, 9450, 12192, 9792],305,29]
%
% END OF LATTICE L306.29
%
%
% LATTICE L306.30
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1806912, -5760, -42624; -5760, 624, -96; -42624, -96, -1003],[576, 48, 1],[503, 628, 321, 968, 928, 1129, 799, 433, 308, -9, -32, 8, 119, 449; 1341, 1675, 857, 2587, 2481, 3020, 2140, 1161, 827, -23, -85, 21, 316, 1196; -21510, -26856, -13728, -41400, -39690, -48288, -34176, -18522, -13176, 384, 1368, -342, -5088, -19200],305,30]
%
% END OF LATTICE L306.30
%
%
% LATTICE L306.31
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-11695680, 82368, 40896; 82368, -528, -288; 40896, -288, -143],[576, 48, 1],[27, 131, 12, -1, -1, 3, 61, 14, 115, 70, 247, 83, 325, 267; -5, -23, -1, 1, 0, -4, -20, -4, -31, -17, -55, -18, -68, -52; 7727, 37488, 3432, -288, -286, 864, 17472, 4009, 32928, 20040, 70704, 23758, 93024, 76416],305,31]
%
% END OF LATTICE L306.31
%
%
% LATTICE L306.32
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-576, 13248, -576; 13248, -298320, 12960; -576, 12960, -563],[576, 48, 1],[83, 247, 70, 115, 28, 61, 3, -1, -1, 12, 131, 54, 267, 325; 55, 161, 43, 65, 15, 28, -4, -1, 1, 11, 97, 39, 188, 220; 1174, 3432, 912, 1368, 314, 576, -96, -22, 24, 240, 2088, 838, 4032, 4704],305,32]
%
% END OF LATTICE L306.32
%

\medskip%
%------------------------------WEYL-GROUP-W307--------------------------------
%
\leavevmode\llap{}%
$W_{307}$%
\qquad\llap{16} lattices, $\chi=48$%
\hfill%
$\slashtwo2|2\slashtwo2|2\slashtwo2|2\slashtwo2|2\rtimes D_{8}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L307.1
%
\leavevmode%
${L_{307.1}}$%
{} : {$1\above{1pt}{1pt}{1}{1}4\above{1pt}{1pt}{1}{1}64\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{1}{}3\above{1pt}{1pt}{-}{}9\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{3}%
\EasyButWeakLineBreak%
{${64}\above{1pt}{1pt}{*}{2}{36}\above{1pt}{1pt}{l}{2}{4}\above{1pt}{1pt}{}{2}{9}\above{1pt}{1pt}{r}{2}{64}\above{1pt}{1pt}{*}{2}{144}\above{1pt}{1pt}{s}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
shares genus with 3-dual\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-61632\\-1152\\-576
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1152\\-12\\-24
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-576\\-24\\13
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\192\\0
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\1\\0
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\4\\-1
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-9\\360\\256
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-7\\282\\198
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\41\\28
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\45\\27
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\-24\\-32
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5\\-186\\-144
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-61632, -1152, -576; -1152, -12, -24; -576, -24, 13],[576, 12, 1],[-9, -7, -1, -1, 1, 5, 9, 7, 1, 1, -1, -5; 360, 282, 41, 45, -24, -186, -344, -270, -39, -39, 40, 198; 256, 198, 28, 27, -32, -144, -256, -198, -28, -27, 32, 144],306,1]
%
% END OF LATTICE L307.1
%
\hbox{}\par\smallskip%
%
% LATTICE L307.2
%
\leavevmode%
${L_{307.2}}$%
{} : {$1\above{1pt}{1pt}{-}{5}4\above{1pt}{1pt}{1}{1}64\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{1}{}3\above{1pt}{1pt}{-}{}9\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{3}%
\EasyButWeakLineBreak%
{${64}\above{1pt}{1pt}{s}{2}{36}\above{1pt}{1pt}{*}{2}{16}\above{1pt}{1pt}{l}{2}{9}\above{1pt}{1pt}{}{2}{64}\above{1pt}{1pt}{}{2}{36}\above{1pt}{1pt}{r}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
shares genus with 3-dual\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
54398016\\-3626496\\57600
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3626496\\241764\\-3840
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
57600\\-3840\\61
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
83879\\1330896\\4563072
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-5595\\-88775\\-304368
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
90\\1428\\4895
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
25\\400\\1568
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
35\\558\\2070
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
21\\334\\1192
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
41\\651\\2259
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
119\\1888\\6464
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
46\\729\\2448
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[54398016, -3626496, 57600; -3626496, 241764, -3840; 57600, -3840, 61],[576, 12, 1],[25, 35, 21, 41, 119, 46, 95, 55, 9, 4, 1, -1; 400, 558, 334, 651, 1888, 729, 1504, 870, 142, 63, 16, -15; 1568, 2070, 1192, 2259, 6464, 2448, 4960, 2826, 440, 189, 64, 0],306,2]
%
% END OF LATTICE L307.2
%
%
% LATTICE L307.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[27456, -192, -192; -192, -140, 60; -192, 60, -23],[192, 4, 1],[-1, 1, 3, 9, 41, 11, 33, 3, 1, -1, -9, -3; -40, 42, 125, 372, 1688, 450, 1336, 120, 37, -48, -392, -126; -96, 101, 300, 890, 4032, 1072, 3168, 283, 84, -122, -960, -304],306,3]
%
% END OF LATTICE L307.3
%
%
% LATTICE L307.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-99264, 6144, 3072; 6144, -380, -192; 3072, -192, -83],[192, 4, 1],[1, 3, 9, -5, -65, -18, -201, -28, -59, -45, -135, -7; 16, 45, 134, -78, -992, -273, -3040, -423, -890, -678, -2032, -105; 0, 7, 24, -2, -96, -32, -384, -55, -120, -94, -288, -16],306,4]
%
% END OF LATTICE L307.4
%
%
% LATTICE L307.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3648, -2496, 9792; -2496, -420, 2292; 9792, 2292, -11197],[192, 12, 1],[-393, -59, 21, 94, 1089, 379, 1449, 323, 111, 38, -33, -115; -3944, -596, 205, 934, 10840, 3778, 14456, 3224, 1109, 380, -328, -1150; -1152, -174, 60, 273, 3168, 1104, 4224, 942, 324, 111, -96, -336],306,5]
%
% END OF LATTICE L307.5
%
%
% LATTICE L307.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[192, 0, 0; 0, -708, 96; 0, 96, -13],[192, 12, 1],[-7, -3, -5, -3, -25, -3, -17, -3, -1, 0, 1, 0; -96, -32, -42, -20, -144, -13, -48, -4, 6, 2, 0, -5; -672, -222, -288, -135, -960, -84, -288, -18, 48, 15, 0, -36],306,6]
%
% END OF LATTICE L307.6
%
%
% LATTICE L307.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-313536, 78336, -2688; 78336, -19568, 672; -2688, 672, -23],[192, 16, 1],[-33, -3, -2, 1, 9, 3, 1, -1, -6, -9, -41, -11; -124, -12, -11, 0, 20, 9, 4, -3, -19, -30, -140, -39; 192, -5, -96, -122, -480, -88, 0, 29, 144, 170, 672, 136],306,7]
%
% END OF LATTICE L307.7
%
%
% LATTICE L307.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-27840, 6912, 1536; 6912, -1712, -384; 1536, -384, -83],[192, 16, 1],[-71, -24, -32, -31, -113, -21, -41, -4, 4, 3, 1, -7; -220, -75, -101, -99, -364, -69, -140, -15, 11, 9, 4, -21; -288, -94, -120, -110, -384, -64, -96, -2, 24, 14, 0, -32],306,8]
%
% END OF LATTICE L307.8
%
%
% LATTICE L307.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1070784, -17280, 5184; -17280, -12, 60; 5184, 60, -23],[576, 12, 1],[-41, -3, -2, 1, 49, 7, 89, 7, 8, 1, -1, -3; -1080, -80, -57, 24, 1224, 178, 2280, 180, 207, 26, -24, -78; -12096, -890, -612, 283, 14112, 2032, 25920, 2042, 2340, 293, -288, -880],306,9]
%
% END OF LATTICE L307.9
%
%
% LATTICE L307.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[576, 0, 0; 0, -156, -60; 0, -60, -23],[576, 12, 1],[-7, -1, -5, -1, -25, -1, -17, -1, -1, 0, 1, 0; 96, 8, 18, 0, -48, -5, -144, -12, -30, -2, 0, 3; -288, -26, -72, -5, 0, 8, 288, 26, 72, 5, 0, -8],306,10]
%
% END OF LATTICE L307.10
%
%
% LATTICE L307.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[192, 0, 0; 0, -12048, 4320; 0, 4320, -1549],[192, 48, 1],[-7, -3, -5, -3, -25, -6, -17, -3, -1, 0, 1, 0; -240, -62, -51, -5, 72, 61, 312, 80, 69, 14, 0, -43; -672, -174, -144, -15, 192, 168, 864, 222, 192, 39, 0, -120],306,11]
%
% END OF LATTICE L307.11
%
%
% LATTICE L307.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[192, 0, 0; 0, 48, 0; 0, 0, -1],[192, 48, 1],[-25, -6, -5, -3, -7, 0, 1, 0, -1, -3, -17, -6; -24, -5, -3, -1, 0, 1, 0, -1, -3, -5, -24, -7; -384, -90, -72, -42, -96, 0, 0, -6, -24, -54, -288, -96],306,12]
%
% END OF LATTICE L307.12
%
%
% LATTICE L307.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1831104, -470016, 576; -470016, -114672, -240; 576, -240, 25],[576, 48, 1],[-553, -553, -173, -1, 34, 34, -71, -279, -451, -831, -346, -242; 2196, 2196, 687, 4, -135, -135, 282, 1108, 1791, 3300, 1374, 961; 33822, 33824, 10584, 64, -2079, -2080, 4338, 17056, 27576, 50816, 21159, 14800],306,13]
%
% END OF LATTICE L307.13
%
%
% LATTICE L307.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2177856, -725760, 11520; -725760, 241872, -3840; 11520, -3840, 61],[576, 48, 1],[87, 50, 8, 7, 1, -1, 25, 34, 20, 77, 111, 85; 340, 195, 31, 27, 4, -3, 100, 135, 79, 303, 436, 333; 4960, 2826, 440, 378, 64, 0, 1568, 2070, 1192, 4518, 6464, 4896],306,14]
%
% END OF LATTICE L307.14
%
%
% LATTICE L307.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[576, 0, 0; 0, -19632, 672; 0, 672, -23],[576, 48, 1],[1, 0, -1, -1, -17, -2, -25, -1, -5, -1, -7, 0; 0, 1, 15, 6, 72, 5, 24, 0, -9, -4, -48, -3; 0, 29, 432, 170, 2016, 136, 576, -5, -288, -122, -1440, -88],306,15]
%
% END OF LATTICE L307.15
%
%
% LATTICE L307.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[576, 0, 0; 0, -1776, -384; 0, -384, -83],[576, 48, 1],[-25, -2, -5, -1, -7, 0, 1, 0, -1, -1, -17, -2; 264, 25, 81, 21, 192, 7, 0, -3, -15, 1, 72, 15; -1152, -110, -360, -94, -864, -32, 0, 14, 72, -2, -288, -64],306,16]
%
% END OF LATTICE L307.16
%

\medskip%
%------------------------------WEYL-GROUP-W308--------------------------------
%
\leavevmode\llap{}%
$W_{308}$%
\qquad\llap{16} lattices, $\chi=48$%
\hfill%
$6222362223\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L308.1
%
\leavevmode%
${L_{308.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}8\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{-}{}27\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${6}\above{1pt}{1pt}{}{6}{2}\above{1pt}{1pt}{s}{2}{54}\above{1pt}{1pt}{l}{2}{8}\above{1pt}{1pt}{r}{2}{6}\above{1pt}{1pt}{-}{3}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-233462520\\127440\\247320
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
127440\\-66\\-135
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
247320\\-135\\-262
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
955151\\-868320\\901967400
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-550\\499\\-519375
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1012\\920\\-955651
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
19\\-19\\17943
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4\\-5\\3778
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4\\-9\\3780
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\0\\-944
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\2\\-945
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-233462520, 127440, 247320; 127440, -66, -135; 247320, -135, -262],[1080, 3, 1],[19, 4, 4, -1, -1, 3, 18, 194, 177, 89; -19, -5, -9, 0, 2, -1, -15, -171, -160, -82; 17943, 3778, 3780, -944, -945, 2832, 16997, 183195, 167144, 84045],307,1]
%
% END OF LATTICE L308.1
%
%
% LATTICE L308.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-4811670, 18090, 35910; 18090, -66, -135; 35910, -135, -268],[270, 3, 1],[6, 31, 329, 149, 149, 31, 6, 4, -1, -1; -1, -15, -171, -80, -82, -19, -5, -9, 0, 2; 804, 4159, 44145, 19994, 19995, 4161, 806, 540, -134, -135],307,2]
%
% END OF LATTICE L308.2
%
%
% LATTICE L308.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[422625060, 35910, 209723580; 35910, 12, 17820; 209723580, 17820, 104073289],[270, 6, 1],[8051, 40783, 433039, 98130, 196392, 41047, 8315, 8843, 66, 0; 22, 105, 1107, 250, 499, 103, 20, 18, 0, 1; -16224, -82184, -872640, -197747, -395760, -82716, -16756, -17820, -133, 0],307,3]
%
% END OF LATTICE L308.3
%
%
% LATTICE L308.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-422394210, 44416620, -2453220; 44416620, -4670604, 257967; -2453220, 257967, -14248],[270, 9, 1],[-513, -341, -15, 35, 34, -69, -1405, -567, -7019, -2362; -4463, -2964, -130, 306, 295, -602, -12231, -4935, -61086, -20555; 7524, 5049, 229, -486, -513, 981, 20466, 8276, 102546, 34533],307,4]
%
% END OF LATTICE L308.4
%
%
% LATTICE L308.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-8574390, 54000, -1693440; 54000, -330, 10665; -1693440, 10665, -334454],[270, 15, 1],[-474, -2454, -26050, -11799, -11800, -2456, -476, -320, 79, 80; -1, -15, -171, -80, -82, -19, -5, -9, 0, 2; 2400, 12425, 131895, 59740, 59745, 12435, 2410, 1620, -400, -405],307,5]
%
% END OF LATTICE L308.5
%
%
% LATTICE L308.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[877760820, 30258630, 436016250; 30258630, 1044288, 15030594; 436016250, 15030594, 216585391],[270, 18, 1],[588775, 373490, 17488, 11726, -813, 107236, 1714543, 678523, 4164340, 2784857; 13700, 8691, 407, 273, -19, 2495, 39894, 15788, 96897, 64799; -1186236, -752490, -35234, -23625, 1638, -216054, -3454380, -1367056, -8390115, -5610798],307,6]
%
% END OF LATTICE L308.6
%
%
% LATTICE L308.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1514161080, 152550, 753060510; 152550, 60, 75870; 753060510, 75870, 374530913],[270, 30, 1],[34093, 172713, 1833905, 415579, 831720, 173837, 35217, 37465, 281, 0; 22, 105, 1107, 250, 499, 103, 20, 18, 0, 1; -68550, -347270, -3687390, -835595, -1672320, -349530, -70810, -75330, -565, 0],307,7]
%
% END OF LATTICE L308.7
%
%
% LATTICE L308.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-127054440, 38844360, 1138320; 38844360, -11875878, -348021; 1138320, -348021, -10198],[1080, 9, 1],[114, 3326, 1376, 34451, 5846, 1317, 967, 55, -107, -122; 332, 9681, 4005, 100272, 17015, 3833, 2814, 160, -312, -355; 1395, 40878, 16916, 423576, 71883, 16200, 11907, 679, -1296, -1503],307,8]
%
% END OF LATTICE L308.8
%
%
% LATTICE L308.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-131070749130, 11943450, 978302070; 11943450, -990, -89145; 978302070, -89145, -7301972],[270, 45, 1],[-30023, -20074, -900, 1981, 2025, -3962, -81881, -33085, -409801, -137965; -19, -15, -1, 0, 2, -1, -45, -19, -240, -82; -4022415, -2689470, -120580, 265410, 271305, -530820, -10970235, -4432655, -54904230, -18484245],307,9]
%
% END OF LATTICE L308.9
%
%
% LATTICE L308.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-8377560, 54000, -1654560; 54000, -330, 10665; -1654560, 10665, -326774],[1080, 15, 1],[-1508, -318, -320, 79, 80, -237, -1427, -15385, -14039, -7060; -19, -5, -9, 0, 2, -1, -15, -171, -160, -82; 7635, 1610, 1620, -400, -405, 1200, 7225, 77895, 71080, 35745],307,10]
%
% END OF LATTICE L308.10
%
%
% LATTICE L308.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[37512325724940, -72158850, 18615122899560; -72158850, 180, -35808120; 18615122899560, -35808120, 9237571754591],[270, 90, 1],[22825837, 14332091, 648705, 397868, 0, 4246873, 66886039, 26424005, 162038392, 108290840; 103, 60, 2, 0, 1, 22, 315, 123, 750, 499; -45997560, -28881360, -1307240, -801765, 0, -8558100, -134785620, -53248420, -326532195, -218222640],307,11]
%
% END OF LATTICE L308.11
%
%
% LATTICE L308.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-229438398960, -11133720, -114485510160; -11133720, -528, -5555520; -114485510160, -5555520, -57126148439],[1080, 24, 1],[123456, 561921, 5873471, 660147, 2625401, 531547, 93082, 21556, -5144, -5389; -1, -15, -171, -20, -82, -19, -5, -9, 0, 2; -247416, -1126136, -11770920, -1322989, -5261520, -1065264, -186544, -43200, 10309, 10800],307,12]
%
% END OF LATTICE L308.12
%
%
% LATTICE L308.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-6738120, -97200, -1650240; -97200, -990, -23805; -1650240, -23805, -404162],[1080, 45, 1],[-529, -14977, -6185, -154729, -26240, -5896, -4298, -240, 529, 540; -1, -45, -19, -480, -82, -19, -15, -1, 0, 2; 2160, 61155, 25255, 631800, 107145, 24075, 17550, 980, -2160, -2205],307,13]
%
% END OF LATTICE L308.13
%
%
% LATTICE L308.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-150999120, 151494840, -31142880; 151494840, -151992144, 31245120; -31142880, 31245120, -6423077],[1080, 72, 1],[-2273, -34036, -13326, -40661, -54135, -11186, -6341, -133, 284, 299; -1, -45, -19, -60, -82, -19, -15, -1, 0, 2; 11016, 164808, 64520, 196857, 262080, 54144, 30672, 640, -1377, -1440],307,14]
%
% END OF LATTICE L308.14
%
%
% LATTICE L308.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-16517427120, 16524106920, -4983269040; 16524106920, -16530789360, 4985284320; -4983269040, 4985284320, -1503440587],[1080, 120, 1],[192802, 33761, 7811, -1866, -1953, 44783, 203824, 2130454, 239451, 952293; -19, -5, -9, 0, 2, -1, -15, -171, -20, -82; -639120, -111920, -25920, 6185, 6480, -148440, -675640, -7062120, -793745, -3156720],307,15]
%
% END OF LATTICE L308.15
%
%
% LATTICE L308.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1811572560, 1815411960, -7304040; 1815411960, -1819259280, 7319520; -7304040, 7319520, -29449],[1080, 360, 1],[-345, -5192, -2034, -6208, -8267, -1710, -973, -21, 43, 47; -1, -45, -19, -60, -82, -19, -15, -1, 0, 2; 85320, 1276560, 499760, 1524825, 2030040, 419400, 237600, 4960, -10665, -11160],307,16]
%
% END OF LATTICE L308.16
%

\medskip%
%------------------------------WEYL-GROUP-W309--------------------------------
%
\leavevmode\llap{}%
$W_{309}$%
\qquad\llap{120} lattices, $\chi=48$%
\hfill%
$222|222222|222\rtimes D_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L309.1
%
\leavevmode%
${L_{309.1}}$%
{} : {$1\above{1pt}{1pt}{2}{0}8\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{-2}{}7\above{1pt}{1pt}{1}{}$}\EasyButWeakLineBreak%
{${105}\above{1pt}{1pt}{}{2}{8}\above{1pt}{1pt}{}{2}{5}\above{1pt}{1pt}{r}{2}{56}\above{1pt}{1pt}{s}{2}{20}\above{1pt}{1pt}{*}{2}{8}\above{1pt}{1pt}{*}{2}{420}\above{1pt}{1pt}{l}{2}{1}\above{1pt}{1pt}{}{2}{7}\above{1pt}{1pt}{r}{2}{24}\above{1pt}{1pt}{s}{2}{28}\above{1pt}{1pt}{*}{2}{4}\above{1pt}{1pt}{l}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-4037880\\8400\\9240
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
8400\\-16\\-21
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
9240\\-21\\-19
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
163\\40950\\33915
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
17\\4272\\3536
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7\\1760\\1455
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5\\1260\\1036
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-250\\-210
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-252\\-208
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
11\\2730\\2310
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\250\\209
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5\\1253\\1043
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
11\\2760\\2292
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
31\\7784\\6454
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
17\\4270\\3538
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-4037880, 8400, 9240; 8400, -16, -21; 9240, -21, -19],[840, 1, 1],[163, 17, 7, 5, -1, -1, 11, 1, 5, 11, 31, 17; 40950, 4272, 1760, 1260, -250, -252, 2730, 250, 1253, 2760, 7784, 4270; 33915, 3536, 1455, 1036, -210, -208, 2310, 209, 1043, 2292, 6454, 3538],308,1]
%
% END OF LATTICE L309.1
%
\hbox{}\par\smallskip%
%
% LATTICE L309.2
%
\leavevmode%
${L_{309.2}}$%
{} : {$[1\above{1pt}{1pt}{1}{}2\above{1pt}{1pt}{1}{}]\above{1pt}{1pt}{}{2}16\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{-2}{}7\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${105}\above{1pt}{1pt}{}{2}{2}\above{1pt}{1pt}{r}{2}{20}\above{1pt}{1pt}{*}{2}{56}\above{1pt}{1pt}{*}{2}{80}\above{1pt}{1pt}{s}{2}{8}\above{1pt}{1pt}{*}{2}{1680}\above{1pt}{1pt}{l}{2}{1}\above{1pt}{1pt}{}{2}{112}\above{1pt}{1pt}{}{2}{6}\above{1pt}{1pt}{r}{2}{28}\above{1pt}{1pt}{*}{2}{16}\above{1pt}{1pt}{l}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2471280\\1233120\\-1680
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1233120\\615302\\-838
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1680\\-838\\1
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5014\\-10080\\-22995
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
289\\-581\\-1326
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
577\\-1160\\-2650
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
383\\-770\\-1764
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
189\\-380\\-880
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\2\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-209\\420\\840
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\-1
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
195\\-392\\-896
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
97\\-195\\-444
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
773\\-1554\\-3542
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
965\\-1940\\-4424
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[2471280, 1233120, -1680; 1233120, 615302, -838; -1680, -838, 1],[1680, 2, 1],[5014, 289, 577, 383, 189, -1, -209, 0, 195, 97, 773, 965; -10080, -581, -1160, -770, -380, 2, 420, 0, -392, -195, -1554, -1940; -22995, -1326, -2650, -1764, -880, 0, 840, -1, -896, -444, -3542, -4424],308,2]
%
% END OF LATTICE L309.2
%
\hbox{}\par\smallskip%
%
% LATTICE L309.3
%
\leavevmode%
${L_{309.3}}$%
{} : {$[1\above{1pt}{1pt}{-}{}2\above{1pt}{1pt}{1}{}]\above{1pt}{1pt}{}{6}16\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{-2}{}7\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{m}%
\EasyButWeakLineBreak%
{${420}\above{1pt}{1pt}{l}{2}{2}\above{1pt}{1pt}{}{2}{5}\above{1pt}{1pt}{r}{2}{56}\above{1pt}{1pt}{s}{2}{80}\above{1pt}{1pt}{*}{2}{8}\above{1pt}{1pt}{s}{2}{1680}\above{1pt}{1pt}{*}{2}{4}\above{1pt}{1pt}{s}{2}{112}\above{1pt}{1pt}{l}{2}{6}\above{1pt}{1pt}{}{2}{7}\above{1pt}{1pt}{r}{2}{16}\above{1pt}{1pt}{*}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-186730320\\73920\\146160
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
73920\\-26\\-60
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
146160\\-60\\-113
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
23\\14490\\22050
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\1259\\1918
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
6\\3775\\5755
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
27\\16982\\25900
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
59\\37100\\56600
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
25\\15718\\23984
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
781\\490980\\749280
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
17\\10686\\16310
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
45\\28280\\43176
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\627\\960
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-630\\-959
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-628\\-960
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-186730320, 73920, 146160; 73920, -26, -60; 146160, -60, -113],[1680, 2, 1],[23, 2, 6, 27, 59, 25, 781, 17, 45, 1, -1, -1; 14490, 1259, 3775, 16982, 37100, 15718, 490980, 10686, 28280, 627, -630, -628; 22050, 1918, 5755, 25900, 56600, 23984, 749280, 16310, 43176, 960, -959, -960],308,3]
%
% END OF LATTICE L309.3
%
\hbox{}\par\smallskip%
%
% LATTICE L309.4
%
\leavevmode%
${L_{309.4}}$%
{} : {$[1\above{1pt}{1pt}{-}{}2\above{1pt}{1pt}{1}{}]\above{1pt}{1pt}{}{4}16\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{-2}{}7\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{m}%
\EasyButWeakLineBreak%
{${420}\above{1pt}{1pt}{*}{2}{8}\above{1pt}{1pt}{l}{2}{5}\above{1pt}{1pt}{}{2}{14}\above{1pt}{1pt}{}{2}{80}\above{1pt}{1pt}{}{2}{2}\above{1pt}{1pt}{r}{2}{1680}\above{1pt}{1pt}{s}{2}{4}\above{1pt}{1pt}{*}{2}{112}\above{1pt}{1pt}{s}{2}{24}\above{1pt}{1pt}{*}{2}{28}\above{1pt}{1pt}{s}{2}{16}\above{1pt}{1pt}{s}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-21871920\\25200\\25200
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
25200\\-2\\-30
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
25200\\-30\\-29
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
473\\14070\\396270
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
29\\862\\24296
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
16\\475\\13405
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
13\\385\\10892
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
19\\560\\15920
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\29\\838
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\0\\840
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-30\\-838
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-28\\-840
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5\\150\\4188
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
31\\924\\25970
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
43\\1280\\36024
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-21871920, 25200, 25200; 25200, -2, -30; 25200, -30, -29],[1680, 2, 1],[473, 29, 16, 13, 19, 1, 1, -1, -1, 5, 31, 43; 14070, 862, 475, 385, 560, 29, 0, -30, -28, 150, 924, 1280; 396270, 24296, 13405, 10892, 15920, 838, 840, -838, -840, 4188, 25970, 36024],308,4]
%
% END OF LATTICE L309.4
%
\hbox{}\par\smallskip%
%
% LATTICE L309.5
%
\leavevmode%
${L_{309.5}}$%
{} : {$[1\above{1pt}{1pt}{1}{}2\above{1pt}{1pt}{1}{}]\above{1pt}{1pt}{}{0}16\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{-2}{}7\above{1pt}{1pt}{1}{}$}\EasyButWeakLineBreak%
{${105}\above{1pt}{1pt}{r}{2}{8}\above{1pt}{1pt}{*}{2}{20}\above{1pt}{1pt}{l}{2}{14}\above{1pt}{1pt}{r}{2}{80}\above{1pt}{1pt}{l}{2}{2}\above{1pt}{1pt}{}{2}{1680}\above{1pt}{1pt}{}{2}{1}\above{1pt}{1pt}{r}{2}{112}\above{1pt}{1pt}{*}{2}{24}\above{1pt}{1pt}{l}{2}{7}\above{1pt}{1pt}{}{2}{16}\above{1pt}{1pt}{}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1680\\0\\0
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\2\\0
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\-1
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-26\\-315\\-1155
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3\\-34\\-132
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3\\-30\\-130
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-7\\-42
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\0\\-40
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\1\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\0\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\-1\\-1
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-28\\-56
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-18\\-48
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2\\-28\\-91
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-5\\-64\\-224
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[1680, 0, 0; 0, 2, 0; 0, 0, -1],[1680, 2, 1],[-26, -3, -3, -1, -1, 0, 1, 0, -1, -1, -2, -5; -315, -34, -30, -7, 0, 1, 0, -1, -28, -18, -28, -64; -1155, -132, -130, -42, -40, 0, 0, -1, -56, -48, -91, -224],308,5]
%
% END OF LATTICE L309.5
%
%
% LATTICE L309.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[420, 0, 0; 0, 2, 0; 0, 0, -1],[420, 2, 1],[-52, -3, -3, -2, -1, 0, 1, 0, -1, -1, -4, -5; -315, -17, -15, -7, 0, 1, 0, -1, -14, -9, -28, -32; -1155, -66, -65, -42, -20, 0, 0, -1, -28, -24, -91, -112],308,6]
%
% END OF LATTICE L309.6
%
%
% LATTICE L309.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-10305960, 24360, 11760; 24360, -46, -30; 11760, -30, -13],[840, 2, 1],[8, 1, 7, 17, 39, 17, 541, 12, 33, 1, -1, -1; 945, 119, 835, 2030, 4660, 2032, 64680, 1435, 3948, 120, -119, -120; 5040, 629, 4400, 10682, 24500, 10678, 339780, 7536, 20720, 627, -630, -628],308,7]
%
% END OF LATTICE L309.7
%
%
% LATTICE L309.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[840, 0, 0; 0, 2, 0; 0, 0, -1],[840, 2, 1],[1, 0, -1, -1, -3, -3, -52, -5, -4, -1, -1, 0; 0, -1, -20, -14, -35, -32, -525, -48, -35, -6, 0, 1; 0, -1, -40, -35, -100, -98, -1680, -160, -126, -30, -28, 0],308,8]
%
% END OF LATTICE L309.8
%
%
% LATTICE L309.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3619560, 20160, 2520; 20160, -48, -21; 2520, -21, -1],[840, 3, 1],[11, -1, -3, 1, 6, 17, 58, 19, 37, 5, 8, 2; 910, -84, -250, 84, 500, 1416, 4830, 1582, 3080, 416, 665, 166; 8470, -768, -2310, 756, 4605, 13056, 44555, 14598, 28434, 3844, 6153, 1539],308,9]
%
% END OF LATTICE L309.9
%
%
% LATTICE L309.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2724540, 0, 19320; 0, 6, 0; 19320, 0, 137],[420, 6, 1],[1, 0, 17, 36, 56, 57, 333, 97, 79, 7, 25, 1; 0, 1, 0, -7, -15, -17, -105, -32, -28, -3, -14, -1; -140, 0, -2400, -5082, -7905, -8046, -47005, -13692, -11151, -988, -3528, -141],308,10]
%
% END OF LATTICE L309.10
%
%
% LATTICE L309.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-4037880, -1680, 9240; -1680, 28, -4; 9240, -4, -19],[840, 4, 1],[163, 17, 7, 5, -1, -1, 11, 1, 10, 11, 31, 17; 20475, 2136, 880, 630, -125, -126, 1365, 125, 1253, 1380, 3892, 2135; 74865, 7808, 3215, 2296, -460, -460, 5040, 459, 4592, 5052, 14238, 7808],308,11]
%
% END OF LATTICE L309.11
%
%
% LATTICE L309.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-267932280, 2576280, 1223040; 2576280, -24772, -11760; 1223040, -11760, -5581],[840, 4, 1],[221, 23, 39, 47, 19, -1, -199, -17, -46, -25, -9, 3; 22890, 2398, 4080, 4928, 1995, -104, -20895, -1786, -4837, -2634, -959, 299; 210, -12, -50, -84, -40, 0, 420, 38, 112, 72, 49, 28],308,12]
%
% END OF LATTICE L309.12
%
%
% LATTICE L309.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-22023960, 47880, 47880; 47880, -95, -105; 47880, -105, -104],[840, 5, 1],[83, 41, 3, 5, -1, -1, 19, 5, 19, 35, 87, 45; 3423, 1688, 123, 196, -42, -40, 798, 209, 791, 1452, 3598, 1858; 34734, 17160, 1256, 2100, -418, -420, 7938, 2090, 7945, 14640, 36400, 18830],308,13]
%
% END OF LATTICE L309.13
%
%
% LATTICE L309.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-915180, 45780, -4200; 45780, -2290, 210; -4200, 210, -19],[420, 10, 1],[25, 5, 3, 9, 1, 2, 2, -1, -3, -2, 1, 2; 420, 89, 56, 175, 20, 41, 42, -20, -63, -45, -14, 30; -1008, -140, -52, -70, -1, 10, 21, 0, -35, -60, -420, -125],308,14]
%
% END OF LATTICE L309.14
%
%
% LATTICE L309.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-842520, 5880, 840; 5880, 138, -24; 840, -24, 1],[840, 6, 1],[3, 1, 6, 13, 27, 11, 111, 7, 17, 0, -2, -1; 175, 59, 355, 770, 1600, 652, 6580, 415, 1008, 0, -119, -60; 1750, 585, 3510, 7602, 15780, 6426, 64820, 4086, 9912, -1, -1176, -588],308,15]
%
% END OF LATTICE L309.15
%
%
% LATTICE L309.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[21560280, 0, -77280; 0, 6, 0; -77280, 0, 277],[840, 6, 1],[1, 1, 37, 32, 91, 89, 508, 145, 114, 9, 25, 0; 0, -1, -20, -14, -35, -32, -175, -48, -35, -2, 0, 1; 280, 279, 10320, 8925, 25380, 24822, 141680, 40440, 31794, 2510, 6972, 0],308,16]
%
% END OF LATTICE L309.16
%
%
% LATTICE L309.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[59640, -22680, -840; -22680, 8617, 322; -840, 322, 11],[840, 7, 1],[14, 1, -8, -5, -21, -5, 13, 6, 3, 31, 7, 17; 30, 0, -20, -12, -50, -12, 30, 14, 7, 72, 16, 38; 165, 56, -35, -32, -140, -28, 120, 49, 24, 252, 62, 168],308,17]
%
% END OF LATTICE L309.17
%
%
% LATTICE L309.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[748860, 0, -6300; 0, 14, 0; -6300, 0, 53],[420, 14, 1],[113, 45, 44, 4, 13, 0, 1, 1, 3, 17, 9, 77; -45, -17, -15, -1, 0, 1, 0, -1, -2, -9, -4, -32; 13395, 5334, 5215, 474, 1540, 0, 120, 119, 356, 2016, 1067, 9128],308,18]
%
% END OF LATTICE L309.18
%
%
% LATTICE L309.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[618240, 840, -840; 840, -8, 0; -840, 0, 1],[840, 8, 1],[1, 0, -1, -2, -6, -3, -104, -5, -8, -1, -1, 0; 105, 0, -95, -189, -565, -282, -9765, -469, -749, -93, -91, 1; 840, -1, -840, -1666, -4980, -2486, -86100, -4136, -6608, -822, -812, 4],308,19]
%
% END OF LATTICE L309.19
%
%
% LATTICE L309.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2509080, 36960, -4200; 36960, 430, -60; -4200, -60, 7],[840, 10, 1],[2, 1, 1, 9, 3, 5, 25, 2, 1, -1, -3, -1; 21, 11, 11, 98, 32, 52, 252, 19, 0, -12, -35, -12; 1386, 695, 694, 6230, 2068, 3430, 17052, 1350, 560, -705, -2100, -700],308,20]
%
% END OF LATTICE L309.20
%
%
% LATTICE L309.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[18289320, 0, -54600; 0, 10, 0; -54600, 0, 163],[840, 10, 1],[1, 1, 7, 30, 17, 83, 284, 135, 106, 25, 23, 0; 0, -1, -4, -14, -7, -32, -105, -48, -35, -6, 0, 1; 336, 335, 2344, 10045, 5692, 27790, 95088, 45200, 35490, 8370, 7700, 0],308,21]
%
% END OF LATTICE L309.21
%
%
% LATTICE L309.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[828240, 411600, -97440; 411600, 204546, -48396; -97440, -48396, 11009],[1680, 6, 1],[-2263, -1, 7729, 15559, 23437, 11743, 67938, 39241, 31461, 1321, 8119, 24; 4620, 2, -15780, -31766, -47850, -23975, -138705, -80116, -64232, -2697, -16576, -49; 280, 0, -960, -1932, -2910, -1458, -8435, -4872, -3906, -164, -1008, -3],308,22]
%
% END OF LATTICE L309.22
%
%
% LATTICE L309.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-150360, 0, 840; 0, 156, -24; 840, -24, -1],[840, 12, 1],[4, -1, -2, 1, 4, 11, 37, 12, 23, 3, 9, 1; 105, -28, -55, 28, 110, 302, 1015, 329, 630, 82, 245, 27; 700, -180, -360, 168, 705, 1944, 6545, 2124, 4074, 532, 1596, 177],308,23]
%
% END OF LATTICE L309.23
%
%
% LATTICE L309.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-48019440, -30240, 30240; -30240, 6, 18; 30240, 18, -19],[1680, 6, 1],[111, 11, 27, 13, 3, 1, 3, -1, -1, 0, 17, 7; 7420, 738, 1820, 882, 205, 69, 210, -68, -70, -1, 1120, 466; 183400, 18180, 44640, 21504, 4965, 1656, 4970, -1656, -1659, -2, 28056, 11562],308,24]
%
% END OF LATTICE L309.24
%
%
% LATTICE L309.25
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-14503440, 42000, 10080; 42000, -6, -30; 10080, -30, -7],[1680, 6, 1],[1, 1, 17, 11, 13, 23, 123, 33, 23, 1, -3, -1; 0, 9, 160, 105, 125, 222, 1190, 320, 224, 10, -28, -10; 1400, 1398, 23760, 15372, 18165, 32136, 171850, 46104, 32130, 1396, -4200, -1398],308,25]
%
% END OF LATTICE L309.25
%
%
% LATTICE L309.26
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[175302960, 0, 312480; 0, 6, 0; 312480, 0, 557],[1680, 6, 1],[1, 0, 37, 39, 121, 123, 359, 209, 85, 15, 53, 1; 0, 1, 0, -7, -30, -34, -105, -64, -28, -6, -28, -1; -560, 0, -20760, -21882, -67890, -69012, -201425, -117264, -47691, -8416, -29736, -561],308,26]
%
% END OF LATTICE L309.26
%
%
% LATTICE L309.27
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-474323640, 13950720, -3527160; 13950720, -410316, 103740; -3527160, 103740, -26227],[840, 12, 1],[177, -1, -91, -269, -311, -265, -1363, -175, -108, 1, 92, 45; 6195, -34, -3185, -9422, -10900, -9292, -47810, -6141, -3794, 32, 3213, 1574; 700, 0, -360, -1092, -1290, -1116, -5810, -756, -483, -8, 336, 174],308,27]
%
% END OF LATTICE L309.27
%
%
% LATTICE L309.28
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-69720, -56280, 8400; -56280, -41398, 6202; 8400, 6202, -929],[840, 14, 1],[14, 7, 37, 11, 159, 65, 283, 42, 15, 1, -1, -1; 435, 216, 1135, 336, 4840, 1974, 8580, 1271, 452, 27, -31, -28; 3030, 1505, 7910, 2342, 33740, 13762, 59820, 8862, 3152, 189, -216, -196],308,28]
%
% END OF LATTICE L309.28
%
%
% LATTICE L309.29
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-40616520, 0, 64680; 0, 14, 0; 64680, 0, -103],[840, 14, 1],[13, 3, 29, 2, 27, 21, 44, 25, 2, -1, -1, 0; 0, -1, -20, -2, -35, -32, -75, -48, -5, -6, 0, 1; 8160, 1883, 18200, 1255, 16940, 13174, 27600, 15680, 1254, -630, -628, 0],308,29]
%
% END OF LATTICE L309.29
%
%
% LATTICE L309.30
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1022280, -53760, 5880; -53760, -2505, 285; 5880, 285, -32],[840, 15, 1],[20, 29, 2, 1, -1, -1, 5, 4, 15, 9, 65, 33; 819, 1184, 81, 28, -42, -40, 210, 167, 623, 372, 2674, 1354; 10948, 15840, 1086, 420, -558, -540, 2786, 2220, 8295, 4960, 35700, 18090],308,30]
%
% END OF LATTICE L309.30
%
%
% LATTICE L309.31
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-6899340, 1149960, -12600; 1149960, -191670, 2100; -12600, 2100, -23],[420, 30, 1],[-61, -25, -9, -11, 0, 2, 1, -1, -8, -4, -79, -23; -462, -191, -70, -91, -1, 13, 7, -6, -56, -29, -588, -173; -8848, -3780, -1476, -2310, -93, 90, 91, 0, -735, -460, -10500, -3225],308,31]
%
% END OF LATTICE L309.31
%
%
% LATTICE L309.32
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2471280, 1680, -1680; 1680, -8, 0; -1680, 0, 1],[1680, 8, 1],[-26, -3, -3, -2, -1, 0, 1, 0, -1, -1, -4, -5; -5040, -581, -580, -385, -190, 1, 210, 0, -196, -195, -777, -970; -43155, -4976, -4970, -3304, -1640, 4, 1680, -1, -1680, -1668, -6650, -8304],308,32]
%
% END OF LATTICE L309.32
%
%
% LATTICE L309.33
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-703920, 0, -351120; 0, 8, 0; -351120, 0, -175141],[1680, 8, 1],[-419, 0, 439, 880, 1322, 1323, 22943, 2207, 1767, 443, 447, 1; 0, 1, 0, -7, -15, -17, -315, -32, -28, -9, -14, -1; 840, 0, -880, -1764, -2650, -2652, -45990, -4424, -3542, -888, -896, -2],308,33]
%
% END OF LATTICE L309.33
%
%
% LATTICE L309.34
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1680, 0, 0; 0, 8, 0; 0, 0, -1],[1680, 8, 1],[1, 0, -1, -2, -3, -3, -52, -5, -2, -1, -1, 0; 0, 1, 0, -7, -15, -17, -315, -32, -14, -9, -14, -1; 0, 0, -40, -84, -130, -132, -2310, -224, -91, -48, -56, -2],308,34]
%
% END OF LATTICE L309.34
%
%
% LATTICE L309.35
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-703920, 31920, 16800; 31920, 392, 160; 16800, 160, 61],[1680, 8, 1],[263, 14, 6, 5, -1, -1, 1, 1, 13, 8, 24, 27; -115290, -6137, -2630, -2191, 440, 439, -420, -438, -5698, -3507, -10521, -11836; 229950, 12240, 5245, 4368, -880, -876, 840, 874, 11368, 6996, 20986, 23608],308,35]
%
% END OF LATTICE L309.35
%
%
% LATTICE L309.36
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-24617040, -26880, 21840; -26880, 10, 20; 21840, 20, -19],[1680, 10, 1],[25, 5, 3, 9, 1, 1, 1, -1, -3, -1, 1, 1; 2940, 598, 364, 1106, 124, 125, 126, -124, -378, -129, 56, 114; 31584, 6340, 3816, 11480, 1278, 1280, 1281, -1280, -3850, -1290, 1120, 1255],308,36]
%
% END OF LATTICE L309.36
%
%
% LATTICE L309.37
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1896720, -45360, 11760; -45360, -770, 220; 11760, 220, -61],[1680, 10, 1],[73, 13, 7, 19, 1, 2, 5, -1, -2, -1, 13, 7; 8988, 1606, 868, 2366, 125, 251, 630, -124, -252, -129, 1568, 858; 46368, 8280, 4472, 12180, 643, 1290, 3234, -640, -1295, -660, 8120, 4430],308,37]
%
% END OF LATTICE L309.37
%
%
% LATTICE L309.38
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-22023960, -383040, -143640; -383040, -6580, -2460; -143640, -2460, -919],[840, 20, 1],[19, -1, -1, 5, 3, 41, 83, 45, 87, 35, 38, 5; -5565, 290, 293, -1442, -874, -11956, -24213, -13131, -25396, -10224, -11109, -1463; 11928, -620, -628, 3080, 1871, 25600, 51849, 28120, 54390, 21900, 23800, 3135],308,38]
%
% END OF LATTICE L309.38
%
%
% LATTICE L309.39
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2793840, 45360, 1680; 45360, -10, -30; 1680, -30, -1],[1680, 10, 1],[1, 1, 3, 9, 2, 17, 53, 23, 15, 1, -5, -1; 0, 5, 16, 49, 11, 94, 294, 128, 84, 6, -28, -6; 1512, 1510, 4528, 13580, 3017, 25640, 79926, 34680, 22610, 1500, -7560, -1510],308,39]
%
% END OF LATTICE L309.39
%
%
% LATTICE L309.40
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-110911920, 0, 105840; 0, 10, 0; 105840, 0, -101],[1680, 10, 1],[17, 0, -1, -1, 1, 9, 20, 23, 12, 11, 27, 2; 0, 1, 0, -7, -6, -34, -63, -64, -28, -18, -28, -1; 17808, 0, -1048, -1050, 1046, 9420, 20937, 24080, 12565, 11520, 28280, 2095],308,40]
%
% END OF LATTICE L309.40
%
%
% LATTICE L309.41
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1799430360, 89971560, 44553600; 89971560, -4498580, -2227680; 44553600, -2227680, -1103129],[840, 20, 1],[-1955, -1, 103, 215, -305, -2449, -10523, -2965, -3019, -2665, -3182, -925; -41055, -20, 2163, 4508, -6408, -51446, -221046, -62281, -63413, -55974, -66829, -19426; 3948, 0, -208, -420, 622, 4980, 21378, 6020, 6125, 5400, 6440, 1870],308,41]
%
% END OF LATTICE L309.41
%
%
% LATTICE L309.42
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[3370920, 132720, -11760; 132720, 5187, -462; -11760, -462, 41],[840, 21, 1],[-17, -43, -23, -5, -11, -1, 1, 1, 0, -3, -7, -33; -210, -528, -280, -60, -130, -12, 10, 10, -1, -40, -88, -410; -7255, -18312, -9765, -2112, -4620, -420, 400, 399, -12, -1316, -3006, -14112],308,42]
%
% END OF LATTICE L309.42
%
%
% LATTICE L309.43
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[420, -420, 0; -420, 462, 0; 0, 0, -1],[420, 42, 1],[-12, -14, -13, -1, -1, 1, 1, 0, -1, -2, -3, -25; -15, -17, -15, -1, 0, 1, 0, -1, -2, -3, -4, -32; -115, -126, -105, -6, 0, 0, -20, -21, -24, -28, -33, -252],308,43]
%
% END OF LATTICE L309.43
%
%
% LATTICE L309.44
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[208320, 840, 74760; 840, -24, 120; 74760, 120, 25627],[840, 24, 1],[-93, 1, 279, 544, 1614, 803, 9252, 1331, 2120, 87, 251, -4; -1855, 20, 5575, 10871, 32255, 16048, 184905, 26601, 42371, 1739, 5019, -79; 280, -3, -840, -1638, -4860, -2418, -27860, -4008, -6384, -262, -756, 12],308,44]
%
% END OF LATTICE L309.44
%
%
% LATTICE L309.45
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[364560, 179760, 45360; 179760, 88634, 22358; 45360, 22358, 5623],[1680, 14, 1],[133, -1, -1271, -367, -3883, -1949, -4838, -6527, -749, -665, -199, -8; -300, 2, 2860, 826, 8740, 4387, 10890, 14692, 1686, 1497, 448, 18; 120, 0, -1120, -324, -3430, -1722, -4275, -5768, -662, -588, -176, -7],308,45]
%
% END OF LATTICE L309.45
%
%
% LATTICE L309.46
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2252040, 53760, -5040; 53760, 1036, -112; -5040, -112, 11],[840, 28, 1],[2, -1, -4, -1, -2, -1, 1, 2, 1, 5, 1, 1; 45, -24, -95, -24, -50, -30, 15, 41, 22, 114, 23, 23; 1380, -700, -2800, -704, -1435, -784, 585, 1316, 678, 3444, 692, 693],308,46]
%
% END OF LATTICE L309.46
%
%
% LATTICE L309.47
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-139440, 5040, 11760; 5040, -182, -420; 11760, -420, -839],[1680, 14, 1],[523, 121, 299, 21, 36, 14, 29, -1, -1, 1, 27, 77; 15540, 3598, 8900, 626, 1075, 419, 870, -28, -30, 27, 800, 2286; -480, -112, -280, -20, -35, -14, -30, 0, 1, 0, -24, -70],308,47]
%
% END OF LATTICE L309.47
%
%
% LATTICE L309.48
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[121133040, 0, 168000; 0, 14, 0; 168000, 0, 233],[1680, 14, 1],[1, 0, 33, 5, 109, 111, 139, 189, 11, 41, 7, 1; 0, 1, 0, -1, -30, -34, -45, -64, -4, -18, -4, -1; -720, 0, -23800, -3606, -78610, -80052, -100245, -136304, -7933, -29568, -5048, -721],308,48]
%
% END OF LATTICE L309.48
%
%
% LATTICE L309.49
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-5437470360, 388390800, -1869840; 388390800, -27742204, 133560; -1869840, 133560, -643],[840, 28, 1],[-13, -1, 31, 17, 171, 167, 407, 135, 15, 47, 2, -5; -195, -14, 465, 254, 2550, 2488, 6060, 2009, 223, 696, 29, -76; -2700, 0, 6440, 3324, 32410, 31164, 75210, 24724, 2701, 7896, 208, -1246],308,49]
%
% END OF LATTICE L309.49
%
%
% LATTICE L309.50
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-115807440, -2019360, 310800; -2019360, -35042, 5390; 310800, 5390, -829],[1680, 14, 1],[13, 4, 49, 4, 31, 53, 119, 73, 7, 5, -1, -1; -6600, -2035, -24960, -2039, -15810, -27038, -60720, -37256, -3574, -2562, 508, 512; -38040, -11732, -143920, -11758, -91175, -155932, -350190, -214872, -20614, -14784, 2928, 2954],308,50]
%
% END OF LATTICE L309.50
%
%
% LATTICE L309.51
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2430120, 139440, -8400; 139440, 7890, -480; -8400, -480, 29],[840, 30, 1],[1, 1, 0, -11, -9, -25, -61, -23, -79, -2, -8, -1; 7, 7, -1, -98, -76, -208, -504, -189, -644, -16, -63, -8; 406, 405, -18, -4830, -3876, -10710, -26068, -9810, -33600, -845, -3360, -420],308,51]
%
% END OF LATTICE L309.51
%
%
% LATTICE L309.52
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2082360, 0, 9240; 0, 30, 0; 9240, 0, 41],[840, 30, 1],[1, 1, 5, 20, 11, 53, 60, 85, 66, 5, 13, 0; 0, -1, -4, -14, -7, -32, -35, -48, -35, -2, 0, 1; -224, -225, -1128, -4515, -2484, -11970, -13552, -19200, -14910, -1130, -2940, 0],308,52]
%
% END OF LATTICE L309.52
%
%
% LATTICE L309.53
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[76440, -2520, 0; -2520, -1295, -105; 0, -105, -8],[840, 35, 1],[1, -1, -1, -1, 0, 5, 2, 9, 3, 11, 1, 2; 30, -32, -30, -28, 3, 184, 69, 302, 98, 348, 31, 61; -396, 420, 392, 360, -49, -2520, -933, -4060, -1310, -4620, -410, -805],308,53]
%
% END OF LATTICE L309.53
%
%
% LATTICE L309.54
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-5460, 0, -2520; 0, 70, 0; -2520, 0, -1163],[420, 70, 1],[-11, 0, 13, 14, 23, 99, 44, 133, 12, 1, -9, -16; 0, 1, 0, -1, -3, -17, -9, -32, -4, -9, -2, -1; 24, 0, -28, -30, -49, -210, -93, -280, -25, 0, 20, 35],308,54]
%
% END OF LATTICE L309.54
%
%
% LATTICE L309.55
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[127680, 840, 52920; 840, -40, 240; 52920, 240, 21677],[840, 40, 1],[-67, 2, 67, 642, 378, 937, 6464, 1547, 2456, 299, 279, -8; -399, 12, 401, 3843, 2263, 5610, 38703, 9263, 14707, 1791, 1673, -47; 168, -5, -168, -1610, -948, -2350, -16212, -3880, -6160, -750, -700, 20],308,55]
%
% END OF LATTICE L309.55
%
%
% LATTICE L309.56
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-11592840, -237720, -99120; -237720, -4578, -1890; -99120, -1890, -779],[840, 42, 1],[4, 6, 31, 9, 127, 51, 73, 32, 11, 0, -1, -1; -1475, -2210, -11405, -3308, -46640, -18718, -26780, -11733, -4028, 3, 369, 364; 3070, 4599, 23730, 6882, 97020, 38934, 55700, 24402, 8376, -7, -768, -756],308,56]
%
% END OF LATTICE L309.56
%
%
% LATTICE L309.57
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3503640, 0, 10080; 0, 42, 0; 10080, 0, -29],[840, 42, 1],[3, 2, 17, 1, 11, 7, 4, 5, 0, -1, -1, 0; 0, -1, -20, -2, -35, -32, -25, -48, -5, -2, 0, 1; 1040, 693, 5880, 345, 3780, 2394, 1360, 1680, -6, -350, -348, 0],308,57]
%
% END OF LATTICE L309.57
%
%
% LATTICE L309.58
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[828240, 1680, -304080; 1680, -24, -168; -304080, -168, 104291],[1680, 24, 1],[187, 4, -521, -1066, -1613, -1619, -4687, -2709, -2174, -183, -561, -1; 9170, 197, -25530, -52241, -79050, -79345, -229705, -132766, -106547, -8969, -27496, -49; 560, 12, -1560, -3192, -4830, -4848, -14035, -8112, -6510, -548, -1680, -3],308,58]
%
% END OF LATTICE L309.58
%
%
% LATTICE L309.59
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-230160, 0, 38640; 0, 24, 0; 38640, 0, -6487],[1680, 24, 1],[-2829, -489, -488, -324, -161, 0, 47, -1, -169, -55, -655, -817; -105, -17, -15, -7, 0, 1, 0, -1, -14, -3, -28, -32; -16870, -2916, -2910, -1932, -960, 0, 280, -6, -1008, -328, -3906, -4872],308,59]
%
% END OF LATTICE L309.59
%
%
% LATTICE L309.60
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[175302960, 0, 312480; 0, 24, 0; 312480, 0, 557],[1680, 24, 1],[718, 123, 121, 78, 37, 0, 1, 2, 53, 15, 85, 209; -105, -17, -15, -7, 0, 1, 0, -1, -14, -3, -14, -32; -402850, -69012, -67890, -43764, -20760, 0, -560, -1122, -29736, -8416, -47691, -117264],308,60]
%
% END OF LATTICE L309.60
%
%
% LATTICE L309.61
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2743440, 28560, 1680; 28560, 1176, -24; 1680, -24, -1],[1680, 24, 1],[1, -1, -3, 1, 3, 8, 53, 17, 16, 2, 11, 1; 0, -7, -20, 7, 20, 53, 350, 112, 105, 13, 70, 6; 1400, -1524, -4560, 1512, 4545, 12120, 80290, 25752, 24234, 3028, 16632, 1506],308,61]
%
% END OF LATTICE L309.61
%
%
% LATTICE L309.62
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3837120, -523320, 18480; -523320, -71288, 2520; 18480, 2520, -89],[840, 56, 1],[13, 3, 29, 4, 54, 21, 88, 25, 4, -1, -1, 0; 15, 3, 25, 3, 35, 12, 45, 11, 1, -3, -1, 1; 3120, 707, 6720, 914, 12180, 4690, 19500, 5488, 856, -294, -236, 28],308,62]
%
% END OF LATTICE L309.62
%
%
% LATTICE L309.63
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3156720, -16800, 10080; -16800, 510, -150; 10080, -150, 37],[1680, 30, 1],[-45, -17, -5, -1, 1, 2, 1, -1, -9, -2, -67, -9; -11172, -4230, -1252, -294, 242, 489, 245, -244, -2212, -493, -16576, -2231; -32816, -12420, -3672, -840, 714, 1440, 721, -720, -6510, -1450, -48720, -6555],308,63]
%
% END OF LATTICE L309.63
%
%
% LATTICE L309.64
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-7840560, -18480, 13440; -18480, 30, 30; 13440, 30, -23],[1680, 30, 1],[-61, -25, -9, -11, 0, 1, 1, -1, -4, -2, -79, -23; -924, -382, -140, -182, -1, 13, 14, -12, -56, -29, -1176, -346; -37016, -15180, -5472, -6720, -3, 600, 602, -600, -2415, -1210, -47880, -13950],308,64]
%
% END OF LATTICE L309.64
%
%
% LATTICE L309.65
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[840, 21000, 840; 21000, 7620, 240; 840, 240, 7],[840, 60, 1],[5, -1, -1, 1, 2, 29, 20, 33, 65, 9, 30, 4; -63, 12, 13, 0, -23, -342, -238, -395, -784, -110, -371, -50; 1568, -300, -324, 0, 573, 8520, 5929, 9840, 19530, 2740, 9240, 1245],308,65]
%
% END OF LATTICE L309.65
%
%
% LATTICE L309.66
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1953840, 11760, -5040; 11760, -30, -30; -5040, -30, 13],[1680, 30, 1],[1, 1, 1, -1, -1, -13, -17, -27, -25, -3, -15, -1; 0, 1, 0, -7, -3, -34, -42, -64, -56, -6, -28, -2; 392, 390, 384, -420, -399, -5160, -6734, -10680, -9870, -1180, -5880, -390],308,66]
%
% END OF LATTICE L309.66
%
%
% LATTICE L309.67
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-59393040, 0, 36960; 0, 30, 0; 36960, 0, -23],[1680, 30, 1],[3, 0, -1, -3, -1, -3, -1, -1, 1, 1, 11, 1; 0, 1, 0, -7, -6, -34, -21, -64, -28, -6, -28, -1; 4816, 0, -1608, -4830, -1614, -4860, -1631, -1680, 1575, 1600, 17640, 1605],308,67]
%
% END OF LATTICE L309.67
%
%
% LATTICE L309.68
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-139355160, 23226000, 11546640; 23226000, -3871020, -1924440; 11546640, -1924440, -956687],[840, 60, 1],[-863, -1, 173, 1051, -167, -2041, -3243, -2907, -3170, -1031, -3960, -1207; -6041, -6, 1211, 7350, -1172, -14304, -22722, -20365, -22204, -7220, -27727, -8450; 1736, 0, -348, -2100, 342, 4140, 6566, 5880, 6405, 2080, 7980, 2430],308,68]
%
% END OF LATTICE L309.68
%
%
% LATTICE L309.69
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[518280, 49560, 13440; 49560, -490, -210; 13440, -210, -79],[840, 70, 1],[2, 5, 5, 7, 19, 37, 31, 22, 7, -1, -1, -1; -405, -1011, -1009, -1410, -3820, -7428, -6216, -4405, -1396, 210, 203, 200; 1416, 3535, 3528, 4930, 13356, 25970, 21732, 15400, 4880, -735, -710, -700],308,69]
%
% END OF LATTICE L309.69
%
%
% LATTICE L309.70
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2309160, 0, 5040; 0, 70, 0; 5040, 0, -11],[840, 70, 1],[1, 1, 1, 0, -1, -7, -4, -15, -2, -5, -1, 0; 0, -1, -4, -2, -7, -32, -15, -48, -5, -6, 0, 1; 456, 455, 448, -5, -476, -3290, -1872, -7000, -930, -2310, -460, 0],308,70]
%
% END OF LATTICE L309.70
%
%
% LATTICE L309.71
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3731280, -374640, 18480; -374640, -37160, 1840; 18480, 1840, -91],[1680, 40, 1],[20, 9, 1, -2, -1, 0, 17, 2, 27, 11, 24, 23; 420, 187, 20, -49, -22, 1, 378, 44, 588, 237, 511, 486; 12537, 5600, 606, -1400, -648, 20, 11088, 1295, 17360, 7020, 15190, 14480],308,71]
%
% END OF LATTICE L309.71
%
%
% LATTICE L309.72
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[234126480, -11692800, 16800; -11692800, 583960, -840; 16800, -840, 1],[1680, 40, 1],[-19, -9, 0, 44, 35, 96, 697, 87, 295, 43, 25, -1; -378, -179, 0, 875, 696, 1909, 13860, 1730, 5866, 855, 497, -20; 1722, 840, -1, -4200, -3344, -9180, -66696, -8330, -28280, -4140, -2450, 40],308,72]
%
% END OF LATTICE L309.72
%
%
% LATTICE L309.73
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-8327760, -4542720, 18480; -4542720, -2477960, 10080; 18480, 10080, -41],[1680, 40, 1],[-8, -4, -1, -1, 3, 11, 89, 12, 45, 8, 5, -1; 21, 11, 3, 7, -6, -25, -210, -29, -112, -21, -14, 2; 1554, 900, 286, 1260, -128, -1200, -11592, -1730, -7280, -1560, -1190, 40],308,73]
%
% END OF LATTICE L309.73
%
%
% LATTICE L309.74
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-10220748720, 511037520, -789600; 511037520, -25551880, 39480; -789600, 39480, -61],[1680, 40, 1],[5, 4, 2, 19, 7, 13, 73, 7, 13, -2, -2, -1; 105, 83, 41, 385, 140, 257, 1428, 135, 238, -45, -42, -20; 3234, 1940, 646, 3220, -8, -1960, -20832, -3250, -14280, -3240, -1295, 0],308,74]
%
% END OF LATTICE L309.74
%
%
% LATTICE L309.75
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[152880, -8400, 0; -8400, 462, 0; 0, 0, -1],[1680, 42, 1],[-6, -7, -13, -1, -1, 1, 1, 0, -1, -1, -3, -25; -105, -123, -230, -18, -20, 18, 20, 1, -16, -17, -52, -436; -115, -126, -210, -12, 0, 0, -40, -21, -48, -28, -66, -504],308,75]
%
% END OF LATTICE L309.75
%
%
% LATTICE L309.76
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[3370920, 265440, -11760; 265440, 20748, -924; -11760, -924, 41],[840, 84, 1],[-17, -43, -23, -5, -11, -1, 1, 1, 0, -3, -7, -33; -105, -264, -140, -30, -65, -6, 5, 5, -1, -20, -44, -205; -7255, -18312, -9765, -2112, -4620, -420, 400, 399, -24, -1316, -3006, -14112],308,76]
%
% END OF LATTICE L309.76
%
%
% LATTICE L309.77
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-356228880, -4242000, 314160; -4242000, -50358, 3738; 314160, 3738, -277],[1680, 42, 1],[9, 13, 33, 19, 267, 107, 153, 67, 23, 0, -1, -1; 270, 389, 985, 566, 7940, 3178, 4540, 1986, 680, -1, -30, -28; 13850, 19992, 50715, 29184, 409920, 164220, 234760, 102774, 35256, -14, -1539, -1512],308,77]
%
% END OF LATTICE L309.77
%
%
% LATTICE L309.78
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[9376080, 0, -23520; 0, 42, 0; -23520, 0, 59],[1680, 42, 1],[29, 69, 67, 3, 19, 0, 1, 1, 5, 9, 7, 119; -15, -34, -30, -1, 0, 1, 0, -1, -4, -6, -4, -64; 11545, 27468, 26670, 1194, 7560, 0, 400, 399, 1992, 3584, 2787, 47376],308,78]
%
% END OF LATTICE L309.78
%
%
% LATTICE L309.79
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-37083480, 9271080, 4611600; 9271080, -2317812, -1152900; 4611600, -1152900, -573421],[840, 84, 1],[9331, 11423, 11609, 1141, 2089, -1, -189, -187, 192, 1145, 1048, 9333; 46640, 57098, 58030, 5704, 10445, -4, -945, -936, 959, 5722, 5238, 46649; -18730, -22932, -23310, -2292, -4200, 0, 380, 378, -384, -2296, -2103, -18732],308,79]
%
% END OF LATTICE L309.79
%
%
% LATTICE L309.80
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-724080, 665280, -33600; 665280, -507738, 25662; -33600, 25662, -1297],[1680, 42, 1],[29, 39, 23, 3, 37, 3, 3, -1, -1, 1, 5, 53; -8650, -11650, -6885, -901, -11160, -911, -920, 298, 308, -286, -1484, -15784; -171890, -231504, -136815, -17904, -221760, -18102, -18280, 5922, 6120, -5684, -29490, -313656],308,80]
%
% END OF LATTICE L309.80
%
%
% LATTICE L309.81
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[115080, -213360, 10920; -213360, 325605, -16695; 10920, -16695, 856],[840, 105, 1],[1, -1, -3, -5, -3, -19, -1, -5, 1, 5, 2, 5; -62, 64, 194, 332, 209, 1408, 81, 502, -18, -284, -121, -309; -1222, 1260, 3822, 6540, 4116, 27720, 1594, 9870, -360, -5600, -2385, -6090],308,81]
%
% END OF LATTICE L309.81
%
%
% LATTICE L309.82
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1393980, 0, 7560; 0, 210, 0; 7560, 0, -41],[420, 210, 1],[1, 0, -5, -6, -11, -51, -8, -77, -8, -3, 1, 4; 0, 1, 0, -1, -3, -17, -3, -32, -4, -3, -2, -1; 184, 0, -924, -1110, -2037, -9450, -1483, -14280, -1485, -560, 180, 735],308,82]
%
% END OF LATTICE L309.82
%
%
% LATTICE L309.83
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[364560, 1680, -162960; 1680, -56, -504; -162960, -504, 71887],[1680, 56, 1],[-2453, -1971, -1953, -182, -601, 12, 103, -3, -103, -685, -382, -3317; -22095, -17753, -17590, -1639, -5410, 109, 930, -27, -928, -6171, -3441, -29878; -5715, -4592, -4550, -424, -1400, 28, 240, -7, -240, -1596, -890, -7728],308,83]
%
% END OF LATTICE L309.83
%
%
% LATTICE L309.84
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-89040, 0, 31920; 0, 56, 0; 31920, 0, -11443],[1680, 56, 1],[43, 0, -401, -116, -1228, -1233, -3061, -2065, -237, -421, -63, -5; 0, 1, 0, -1, -15, -17, -45, -32, -4, -9, -2, -1; 120, 0, -1120, -324, -3430, -3444, -8550, -5768, -662, -1176, -176, -14],308,84]
%
% END OF LATTICE L309.84
%
%
% LATTICE L309.85
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[121133040, 0, 168000; 0, 56, 0; 168000, 0, 233],[1680, 56, 1],[1, 0, 33, 10, 109, 111, 278, 189, 11, 41, 7, 2; 0, 1, 0, -1, -15, -17, -45, -32, -2, -9, -2, -1; -720, 0, -23800, -7212, -78610, -80052, -200490, -136304, -7933, -29568, -5048, -1442],308,85]
%
% END OF LATTICE L309.85
%
%
% LATTICE L309.86
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[12571440, 539280, -11760; 539280, 22904, -504; -11760, -504, 11],[1680, 56, 1],[-7, -4, -3, -1, -7, -1, 1, 1, 1, 2, 0, -3; -30, -15, -10, -3, -20, -3, 0, 2, 2, 3, -1, -16; -8910, -4984, -3675, -1208, -8400, -1204, 1080, 1162, 1160, 2268, -50, -3976],308,86]
%
% END OF LATTICE L309.86
%
%
% LATTICE L309.87
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-116760, 7560, -3360; 7560, 960, -480; -3360, -480, 239],[840, 120, 1],[1, 0, -1, -9, -5, -12, -27, -19, -29, -1, -1, 1; 189, -7, -219, -1918, -1056, -2525, -5670, -3983, -6062, -207, -203, 202; 392, -15, -456, -3990, -2196, -5250, -11788, -8280, -12600, -430, -420, 420],308,87]
%
% END OF LATTICE L309.87
%
%
% LATTICE L309.88
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-677040, -349440, 5040; -349440, -180110, 2590; 5040, 2590, -37],[1680, 70, 1],[-13, -1, 7, 5, 3, -2, -4, -45, -9, -20, -17, -10; 36, 2, -20, -14, -8, 7, 12, 132, 26, 57, 48, 28; 744, 0, -448, -300, -154, 210, 291, 3080, 590, 1260, 1040, 595],308,88]
%
% END OF LATTICE L309.88
%
%
% LATTICE L309.89
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[51240, -136920, 2520; -136920, 241780, -4480; 2520, -4480, 83],[840, 140, 1],[1, -1, -1, -1, 0, 5, 2, 9, 3, 11, 2, 2; -27, 28, 29, 32, 5, -86, -42, -203, -72, -282, -53, -54; -1488, 1540, 1596, 1760, 273, -4760, -2319, -11200, -3970, -15540, -2920, -2975],308,89]
%
% END OF LATTICE L309.89
%
%
% LATTICE L309.90
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-166291440, -4525920, 164640; -4525920, -122990, 4480; 164640, 4480, -163],[1680, 70, 1],[79, 93, 47, 17, 6, 12, 5, -1, -1, -1, 19, 57; 444, 526, 268, 98, 35, 71, 30, -4, -6, -9, 104, 318; 91968, 108360, 54824, 19860, 7021, 14070, 5874, -1120, -1175, -1260, 22040, 66290],308,90]
%
% END OF LATTICE L309.90
%
%
% LATTICE L309.91
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-104692560, 0, 105840; 0, 70, 0; 105840, 0, -107],[1680, 70, 1],[5, 0, -3, -1, -1, 3, 2, 21, 2, 17, 7, 4; 0, 1, 0, -1, -6, -34, -9, -64, -4, -18, -4, -1; 4944, 0, -2968, -990, -994, 2940, 1971, 20720, 1975, 16800, 6920, 3955],308,91]
%
% END OF LATTICE L309.91
%
%
% LATTICE L309.92
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[38640, -3360, -1680; -3360, 70, 70; -1680, 70, 47],[1680, 70, 1],[1, 2, 5, 2, 3, 25, 11, 33, 3, 1, -1, -1; -24, -47, -112, -43, -62, -502, -216, -632, -54, 6, 28, 24; 72, 140, 336, 130, 189, 1540, 666, 1960, 170, 0, -80, -70],308,92]
%
% END OF LATTICE L309.92
%
%
% LATTICE L309.93
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-19320, -10080, -5040; -10080, -5180, -2520; -5040, -2520, -1163],[840, 140, 1],[11, 1, -13, -29, -49, -215, -97, -149, -14, -11, 8, 31; -33, -2, 39, 86, 144, 628, 282, 431, 40, 24, -25, -94; 24, 0, -28, -60, -98, -420, -186, -280, -25, 0, 20, 70],308,93]
%
% END OF LATTICE L309.93
%
%
% LATTICE L309.94
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[7815360, 782040, -10080; 782040, 77784, -1008; -10080, -1008, 13],[840, 168, 1],[3, 2, 17, 2, 22, 7, 8, 5, 0, -1, -1, 0; 5, 3, 25, 3, 35, 12, 15, 11, 1, -1, -1, 1; 2720, 1785, 15120, 1782, 19740, 6342, 7340, 4704, 72, -854, -852, 84],308,94]
%
% END OF LATTICE L309.94
%
%
% LATTICE L309.95
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[782040, 3605280, 39480; 3605280, 15957690, 174720; 39480, 174720, 1913],[840, 210, 1],[1, 7, 6, 7, 15, 23, 5, 7, -1, -2, -2, -1; -59, -412, -349, -400, -832, -1226, -252, -305, 108, 125, 121, 60; 5368, 37485, 31752, 36390, 75684, 111510, 22916, 27720, -9840, -11375, -11010, -5460],308,95]
%
% END OF LATTICE L309.95
%
%
% LATTICE L309.96
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1047480, 0, 351120; 0, 210, 0; 351120, 0, -117697],[840, 210, 1],[59, 176, 169, -5, -197, -1337, -252, -2815, -372, -305, -181, 0; 0, -1, -4, -2, -7, -32, -5, -48, -5, -2, 0, 1; 176, 525, 504, -15, -588, -3990, -752, -8400, -1110, -910, -540, 0],308,96]
%
% END OF LATTICE L309.96
%
%
% LATTICE L309.97
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-28560, 3360, 0; 3360, 18120, -360; 0, -360, 7],[1680, 120, 1],[-1, -3, -1, -6, -1, 0, 3, 1, 11, 1, 2, -1; -7, -23, -8, -49, -8, 1, 28, 9, 98, 9, 21, -4; -371, -1200, -414, -2520, -408, 60, 1456, 465, 5040, 460, 1050, -240],308,97]
%
% END OF LATTICE L309.97
%
%
% LATTICE L309.98
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[7622160, 2830800, 16800; 2830800, 1051320, 6240; 16800, 6240, 37],[1680, 120, 1],[211, 90, 35, 54, 2, -3, -3, -1, 17, 11, 251, 77; -518, -221, -86, -133, -5, 7, 7, 2, -42, -27, -616, -189; -8456, -3600, -1392, -2100, -66, 180, 182, 120, -630, -440, -10080, -3090],308,98]
%
% END OF LATTICE L309.98
%
%
% LATTICE L309.99
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[7951440, -1317120, -453600; -1317120, 218040, 75360; -453600, 75360, 25507],[1680, 120, 1],[199, 278, -1, -1391, -1097, -3001, -7253, -2713, -9183, -444, -766, 39; 994, 1389, -5, -6951, -5482, -14997, -36246, -13558, -45892, -2219, -3829, 194; 602, 840, -3, -4200, -3312, -9060, -21896, -8190, -27720, -1340, -2310, 120],308,99]
%
% END OF LATTICE L309.99
%
%
% LATTICE L309.100
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-27597360, 4599840, -25200; 4599840, -766680, 4200; -25200, 4200, -23],[1680, 120, 1],[-61, -25, -9, -11, 0, 2, 1, -1, -4, -4, -79, -23; -462, -191, -70, -91, -1, 13, 7, -6, -28, -29, -588, -173; -17696, -7560, -2952, -4620, -186, 180, 182, 0, -735, -920, -21000, -6450],308,100]
%
% END OF LATTICE L309.100
%
%
% LATTICE L309.101
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[107520, 346920, -2520; 346920, 1117480, -8120; -2520, -8120, 59],[840, 280, 1],[1, 1, 1, 0, -2, -7, -8, -15, -4, -5, -1, 0; 3, 3, 5, 3, 7, 12, 9, 11, 1, -3, -1, 1; 456, 455, 728, 410, 868, 1330, 876, 840, -40, -630, -180, 140],308,101]
%
% END OF LATTICE L309.101
%
%
% LATTICE L309.102
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[152880, -487200, -8400; -487200, 982632, 16968; -8400, 16968, 293],[1680, 168, 1],[1, 1, -1, -1, -13, -14, -6, -25, -3, -2, -1, 0; -110, -117, 130, 123, 1600, 1725, 740, 3086, 371, 249, 128, 4; 6400, 6804, -7560, -7152, -93030, -100296, -43025, -179424, -21570, -14476, -7440, -231],308,102]
%
% END OF LATTICE L309.102
%
%
% LATTICE L309.103
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1680, -1680, 0; -1680, 1848, 0; 0, 0, -1],[1680, 168, 1],[1, 1, -1, -1, -13, -14, -12, -25, -3, -2, -1, 0; 0, 1, 0, -1, -15, -17, -15, -32, -4, -3, -2, -1; -40, 0, 0, -12, -210, -252, -230, -504, -66, -56, -48, -42],308,103]
%
% END OF LATTICE L309.103
%
%
% LATTICE L309.104
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[9376080, -9376080, 23520; -9376080, 9376248, -23520; 23520, -23520, 59],[1680, 168, 1],[-1, 1, -19, -7, -82, -86, -73, -151, -9, -12, -7, -3; 0, 1, 0, -1, -15, -17, -15, -32, -2, -3, -2, -1; 400, 0, 7560, 2388, 26670, 27468, 23090, 47376, 2787, 3584, 1992, 798],308,104]
%
% END OF LATTICE L309.104
%
%
% LATTICE L309.105
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[68880, -213360, 1680; -213360, 661416, -5208; 1680, -5208, 41],[1680, 168, 1],[1, -1, -21, -5, -24, -46, -37, -73, -8, -4, -1, 1; 0, -1, -20, -5, -25, -49, -40, -80, -9, -5, -2, 0; -40, -84, -1680, -432, -2205, -4368, -3590, -7224, -822, -476, -216, -42],308,105]
%
% END OF LATTICE L309.105
%
%
% LATTICE L309.106
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[248571120, 124031040, -204960; 124031040, 61888470, -102270; -204960, -102270, 169],[1680, 210, 1],[-1, -1, 1, 1, 1, 1, 0, -3, -1, -1, -3, -2; 4, 2, -12, -14, -24, -53, -8, -148, -14, -1, 8, 8; 1208, 0, -6048, -7260, -13314, -30870, -4843, -93240, -9690, -1820, 1200, 2415],308,106]
%
% END OF LATTICE L309.106
%
%
% LATTICE L309.107
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1517880, 7728840, 90720; 7728840, 38681580, 454020; 90720, 454020, 5329],[840, 420, 1],[1, -1, -3, -5, -3, -19, -1, -5, 1, 5, 4, 5; -81, 84, 253, 432, 271, 1818, 104, 637, -28, -374, -317, -404; 6884, -7140, -21504, -36720, -23037, -154560, -8843, -54180, 2370, 31780, 26940, 34335],308,107]
%
% END OF LATTICE L309.107
%
%
% LATTICE L309.108
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-8314320, -1800960, 18480; -1800960, -387870, 3990; 18480, 3990, -41],[1680, 210, 1],[5, 23, 15, 7, 3, 7, 1, -1, -1, -2, -1, 7; 20, 106, 76, 38, 17, 41, 6, -4, -6, -13, -16, 18; 4168, 20580, 14112, 6840, 3003, 7140, 1034, -840, -1035, -2170, -2040, 4830],308,108]
%
% END OF LATTICE L309.108
%
%
% LATTICE L309.109
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-677040, -26880, -3360; -26880, 3570, 630; -3360, 630, 109],[1680, 210, 1],[1, 4, 7, 2, 2, 11, 1, 3, -1, -3, -3, -1; -104, -415, -720, -203, -198, -1046, -88, -152, 122, 322, 316, 104; 632, 2520, 4368, 1230, 1197, 6300, 526, 840, -750, -1960, -1920, -630],308,109]
%
% END OF LATTICE L309.109
%
%
% LATTICE L309.110
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[840, 0, 0; 0, -5078220, 36960; 0, 36960, -269],[840, 420, 1],[0, 1, 0, -1, -3, -17, -3, -16, -2, -3, -1, -1; -3, 0, 11, 24, 40, 174, 26, 119, 11, 2, -7, -26; -412, 0, 1512, 3300, 5502, 23940, 3578, 16380, 1515, 280, -960, -3570],308,110]
%
% END OF LATTICE L309.110
%
%
% LATTICE L309.111
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1680, 0, 0; 0, -388290, -3990; 0, -3990, -41],[1680, 210, 1],[-5, -8, -7, -1, -1, -1, 0, 1, 0, -1, -5, -6; 0, 7, 16, 5, 10, 26, 1, 0, -2, -10, -12, -5; 32, -630, -1512, -480, -966, -2520, -97, 0, 195, 980, 1200, 525],308,111]
%
% END OF LATTICE L309.111
%
%
% LATTICE L309.112
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-677040, -727440, 5040; -727440, -764120, 5320; 5040, 5320, -37],[1680, 280, 1],[2, 3, -1, -2, -3, 0, 5, 4, 7, 17, 4, 21; 6, 7, -4, -7, -10, 1, 18, 14, 24, 57, 13, 66; 1131, 1400, -714, -1280, -1848, 140, 3264, 2555, 4400, 10500, 2410, 12320],308,112]
%
% END OF LATTICE L309.112
%
%
% LATTICE L309.113
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-6372240, 0, -1585920; 0, 280, 0; -1585920, 0, -394703],[1680, 280, 1],[569, 1359, 338, 224, 223, 0, -221, -331, -219, -209, 117, 1603; -9, -17, -3, -1, 0, 1, 0, -1, -2, -9, -4, -32; -2286, -5460, -1358, -900, -896, 0, 888, 1330, 880, 840, -470, -6440],308,113]
%
% END OF LATTICE L309.113
%
%
% LATTICE L309.114
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-104692560, 0, 105840; 0, 280, 0; 105840, 0, -107],[1680, 280, 1],[4, 3, -1, -2, -3, 0, 5, 8, 7, 17, 2, 21; -9, -17, -3, -1, 0, 1, 0, -1, -2, -9, -2, -32; 3942, 2940, -994, -1980, -2968, 0, 4944, 7910, 6920, 16800, 1975, 20720],308,114]
%
% END OF LATTICE L309.114
%
%
% LATTICE L309.115
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-6372240, -3373440, 100800; -3373440, -1785560, 53200; 100800, 53200, -1513],[1680, 280, 1],[-367, -409, 13, 120, 223, 104, -221, -435, -427, -1145, -299, -1725; 738, 823, -26, -241, -448, -209, 444, 874, 858, 2301, 601, 3468; 1494, 1680, -49, -480, -896, -420, 888, 1750, 1720, 4620, 1210, 7000],308,115]
%
% END OF LATTICE L309.115
%
%
% LATTICE L309.116
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[3352440, -89969880, 322560; -89969880, 2409973440, -8640240; 322560, -8640240, 30977],[840, 840, 1],[1, 3, 5, 3, 7, 12, 3, 11, 1, -1, -1, 1; -151, -452, -725, -410, -874, -1351, -300, -885, 28, 205, 177, -140; -42128, -126105, -202272, -114390, -243852, -376950, -83708, -246960, 7800, 57190, 49380, -39060],308,116]
%
% END OF LATTICE L309.116
%
%
% LATTICE L309.117
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[248571120, 85574160, -204960; 85574160, 29459640, -70560; -204960, -70560, 169],[1680, 840, 1],[1, 0, -5, -6, -11, -51, -4, -77, -8, -3, 1, 2; 2, 1, -6, -7, -12, -53, -4, -74, -7, -1, 4, 4; 2048, 420, -8568, -10200, -18354, -84000, -6523, -124320, -12630, -4060, 2880, 4095],308,117]
%
% END OF LATTICE L309.117
%
%
% LATTICE L309.118
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-59907120, 0, -29904000; 0, 840, 0; -29904000, 0, -14927261],[1680, 840, 1],[4835, 30819, 6646, 3624, 3019, 0, -603, -2411, -599, 1817, 4837, 46543; -3, -17, -3, -1, 0, 1, 0, -1, -2, -3, -4, -32; -9686, -61740, -13314, -7260, -6048, 0, 1208, 4830, 1200, -3640, -9690, -93240],308,118]
%
% END OF LATTICE L309.118
%
%
% LATTICE L309.119
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-5575920, 0, 15120; 0, 840, 0; 15120, 0, -41],[1680, 840, 1],[-8, -51, -11, -6, -5, 0, 1, 4, 1, -3, -4, -77; -3, -17, -3, -1, 0, 1, 0, -1, -2, -3, -2, -32; -2966, -18900, -4074, -2220, -1848, 0, 368, 1470, 360, -1120, -1485, -28560],308,119]
%
% END OF LATTICE L309.119
%
%
% LATTICE L309.120
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-59907120, -39091920, -19496400; -39091920, -25508280, -12721800; -19496400, -12721800, -6344771],[1680, 840, 1],[1, -1, -5, -5, -4, -34, -5, -45, -4, 0, 3, 5; -604, 211, 3024, 3419, 3012, 27283, 4210, 39868, 4001, 1187, -1022, -2626; 1208, -420, -6048, -6840, -6027, -54600, -8426, -79800, -8010, -2380, 2040, 5250],308,120]
%
% END OF LATTICE L309.120
%

\medskip%
%------------------------------WEYL-GROUP-W310--------------------------------
%
\leavevmode\llap{}%
$W_{310}$%
\qquad\llap{120} lattices, $\chi=72$%
\hfill%
$2222|2222|2222|2222|\rtimes D_{4}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L310.1
%
\leavevmode%
${L_{310.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{4}8\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{2}{}7\above{1pt}{1pt}{-}{}$}\EasyButWeakLineBreak%
{${280}\above{1pt}{1pt}{l}{2}{1}\above{1pt}{1pt}{}{2}{168}\above{1pt}{1pt}{}{2}{5}\above{1pt}{1pt}{r}{2}{24}\above{1pt}{1pt}{s}{2}{20}\above{1pt}{1pt}{*}{2}{168}\above{1pt}{1pt}{*}{2}{4}\above{1pt}{1pt}{s}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
19418280\\-57960\\0
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-57960\\173\\0
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\-1
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-47251\\-15813000\\252000
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
141\\47187\\-752
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-12\\-4016\\63
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
159\\53200\\-980
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
8\\2677\\-46
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
125\\41832\\-672
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
16\\5355\\-80
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
19\\6360\\-84
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
23\\7700\\-90
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
71\\23772\\-252
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7\\2344\\-22
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[19418280, -57960, 0; -57960, 173, 0; 0, 0, -1],[840, 1, 1],[159, 8, 125, 16, 19, 23, 71, 7, 51, 1, 1, -1, -1, 7, 55, 11; 53200, 2677, 41832, 5355, 6360, 7700, 23772, 2344, 17080, 335, 336, -335, -336, 2340, 18396, 3680; -980, -46, -672, -80, -84, -90, -252, -22, -140, -2, 0, 0, -12, -70, -420, -74],309,1]
%
% END OF LATTICE L310.1
%
\hbox{}\par\smallskip%
%
% LATTICE L310.2
%
\leavevmode%
${L_{310.2}}$%
{} : {$[1\above{1pt}{1pt}{-}{}2\above{1pt}{1pt}{1}{}]\above{1pt}{1pt}{}{2}16\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{2}{}7\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${280}\above{1pt}{1pt}{*}{2}{16}\above{1pt}{1pt}{s}{2}{168}\above{1pt}{1pt}{*}{2}{80}\above{1pt}{1pt}{s}{2}{24}\above{1pt}{1pt}{*}{2}{20}\above{1pt}{1pt}{l}{2}{42}\above{1pt}{1pt}{}{2}{1}\above{1pt}{1pt}{r}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-64681680\\45360\\38640
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
45360\\-22\\-28
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
38640\\-28\\-23
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
30239\\4203360\\45662400
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-22\\-3059\\-33220
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-18\\-2502\\-27181
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
43\\5950\\64960
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
11\\1524\\16616
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
53\\7350\\80052
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
33\\4580\\49840
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
13\\1806\\19632
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
21\\2920\\31710
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
40\\5565\\60396
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5\\696\\7549
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-64681680, 45360, 38640; 45360, -22, -28; 38640, -28, -23],[1680, 2, 1],[43, 11, 53, 33, 13, 21, 40, 5, 97, 13, 31, 7, -1, -1, 2, 1; 5950, 1524, 7350, 4580, 1806, 2920, 5565, 696, 13510, 1812, 4326, 980, -138, -140, 273, 138; 64960, 16616, 80052, 49840, 19632, 31710, 60396, 7549, 146440, 19624, 46788, 10560, -1512, -1510, 3024, 1511],309,2]
%
% END OF LATTICE L310.2
%
\hbox{}\par\smallskip%
%
% LATTICE L310.3
%
\leavevmode%
${L_{310.3}}$%
{} : {$[1\above{1pt}{1pt}{1}{}2\above{1pt}{1pt}{-}{}]\above{1pt}{1pt}{}{4}16\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{2}{}7\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{m}%
\EasyButWeakLineBreak%
{${70}\above{1pt}{1pt}{r}{2}{16}\above{1pt}{1pt}{l}{2}{42}\above{1pt}{1pt}{}{2}{80}\above{1pt}{1pt}{}{2}{6}\above{1pt}{1pt}{r}{2}{20}\above{1pt}{1pt}{*}{2}{168}\above{1pt}{1pt}{l}{2}{1}\above{1pt}{1pt}{}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-108076080\\114240\\50400
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
114240\\-106\\-56
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
50400\\-56\\-23
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
61739\\17246040\\93268560
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-75\\-20951\\-113300
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-27\\-7542\\-40789
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
39\\10885\\58940
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
19\\5304\\28712
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
44\\12285\\66486
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
53\\14800\\80080
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
10\\2793\\15108
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
31\\8660\\46830
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
115\\32130\\173712
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7\\1956\\10573
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-108076080, 114240, 50400; 114240, -106, -56; 50400, -56, -23],[1680, 2, 1],[39, 19, 44, 53, 10, 31, 115, 7, 66, 17, 19, 7, -1, -1, 11, 2; 10885, 5304, 12285, 14800, 2793, 8660, 32130, 1956, 18445, 4752, 5313, 1960, -279, -280, 3066, 558; 58940, 28712, 66486, 80080, 15108, 46830, 173712, 10573, 99680, 25672, 28686, 10560, -1512, -1510, 16632, 3023],309,3]
%
% END OF LATTICE L310.3
%
\hbox{}\par\smallskip%
%
% LATTICE L310.4
%
\leavevmode%
${L_{310.4}}$%
{} : {$[1\above{1pt}{1pt}{-}{}2\above{1pt}{1pt}{-}{}]\above{1pt}{1pt}{}{0}16\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{2}{}7\above{1pt}{1pt}{-}{}$}\EasyButWeakLineBreak%
{${70}\above{1pt}{1pt}{}{2}{16}\above{1pt}{1pt}{}{2}{42}\above{1pt}{1pt}{r}{2}{80}\above{1pt}{1pt}{l}{2}{6}\above{1pt}{1pt}{}{2}{5}\above{1pt}{1pt}{r}{2}{168}\above{1pt}{1pt}{*}{2}{4}\above{1pt}{1pt}{l}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-22900080\\8400\\23520
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
8400\\22\\-20
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
23520\\-20\\-19
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
69299\\26306280\\58045680
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5\\1897\\4188
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-85\\-32266\\-71197
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-385\\-840
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\1136\\2512
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
17\\6447\\14238
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
33\\12520\\27640
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
10\\3795\\8376
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
23\\8730\\19265
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
211\\80094\\176736
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
31\\11768\\25966
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-22900080, 8400, 23520; 8400, 22, -20; 23520, -20, -19],[1680, 2, 1],[-1, 3, 17, 33, 10, 23, 211, 31, 176, 57, 88, 67, 5, 2, -1, -1; -385, 1136, 6447, 12520, 3795, 8730, 80094, 11768, 66815, 21640, 33411, 25440, 1899, 760, -378, -380; -840, 2512, 14238, 27640, 8376, 19265, 176736, 25966, 147420, 47744, 73710, 56120, 4188, 1675, -840, -838],309,4]
%
% END OF LATTICE L310.4
%
\hbox{}\par\smallskip%
%
% LATTICE L310.5
%
\leavevmode%
${L_{310.5}}$%
{} : {$[1\above{1pt}{1pt}{1}{}2\above{1pt}{1pt}{1}{}]\above{1pt}{1pt}{}{6}16\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{2}{}7\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{m}%
\EasyButWeakLineBreak%
{${280}\above{1pt}{1pt}{s}{2}{16}\above{1pt}{1pt}{*}{2}{168}\above{1pt}{1pt}{s}{2}{80}\above{1pt}{1pt}{*}{2}{24}\above{1pt}{1pt}{l}{2}{5}\above{1pt}{1pt}{}{2}{42}\above{1pt}{1pt}{r}{2}{4}\above{1pt}{1pt}{*}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1745520\\-588000\\6720
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-588000\\198074\\-2260
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
6720\\-2260\\13
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
309119\\920640\\255360
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-103868\\-309347\\-85804
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
276\\822\\227
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2797\\8330\\2240
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
689\\2052\\560
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3173\\9450\\2604
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1887\\5620\\1560
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
691\\2058\\576
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
507\\1510\\425
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1798\\5355\\1512
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
415\\1236\\350
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[1745520, -588000, 6720; -588000, 198074, -2260; 6720, -2260, 13],[1680, 2, 1],[2797, 689, 3173, 1887, 691, 507, 1798, 415, 3643, 415, 691, -47, -139, -47, 134, 137; 8330, 2052, 9450, 5620, 2058, 1510, 5355, 1236, 10850, 1236, 2058, -140, -414, -140, 399, 408; 2240, 560, 2604, 1560, 576, 425, 1512, 350, 3080, 352, 588, -40, -120, -45, 84, 106],309,5]
%
% END OF LATTICE L310.5
%
%
% LATTICE L310.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-158789820, -1871520, 57540; -1871520, -22058, 678; 57540, 678, -17],[420, 2, 1],[-358, -22, -67, 11, 34, 153, 326, 87, 428, 28, 109, -1, -28, -133, -284, -75; 30415, 1869, 5691, -935, -2889, -13000, -27699, -7392, -36365, -2379, -9261, 85, 2379, 11300, 24129, 6372; 1260, 73, 168, -65, -144, -620, -1302, -344, -1680, -109, -420, 5, 108, 500, 1050, 272],309,6]
%
% END OF LATTICE L310.6
%
%
% LATTICE L310.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[1603560, 7560, -4200; 7560, -38, -20; -4200, -20, 11],[840, 2, 1],[176, 57, 88, 67, 5, 4, -1, -1, -1, 3, 17, 33, 10, 46, 211, 31; -210, -68, -105, -80, -6, -5, 0, 1, 0, -4, -21, -40, -12, -55, -252, -37; 66815, 21640, 33411, 25440, 1899, 1520, -378, -380, -385, 1136, 6447, 12520, 3795, 17460, 80094, 11768],309,7]
%
% END OF LATTICE L310.7
%
%
% LATTICE L310.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-1501400040, -17663520, 128520; -17663520, -207806, 1512; 128520, 1512, -11],[840, 2, 1],[97, 13, 31, 7, -1, -1, 2, 2, 43, 11, 53, 33, 13, 21, 40, 10; -8260, -1108, -2646, -600, 84, 85, -168, -169, -3640, -932, -4494, -2800, -1104, -1785, -3402, -851; -2170, -428, -1554, -700, -138, 0, 273, 136, 2030, 404, 1470, 660, 126, -20, -315, -148],309,8]
%
% END OF LATTICE L310.8
%
%
% LATTICE L310.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-880663560, 16012080, -129360; 16012080, -291129, 2352; -129360, 2352, -19],[840, 3, 1],[229, 15, 23, 7, -1, -1, 5, 3, 121, 15, 47, 43, 11, 26, 65, 12; 12600, 824, 1260, 380, -56, -55, 280, 167, 6720, 832, 2604, 2380, 608, 1435, 3584, 661; 420, -138, -644, -630, -124, 0, 616, 246, 7980, 858, 2324, 1830, 364, 600, 1064, 114],309,9]
%
% END OF LATTICE L310.9
%
%
% LATTICE L310.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2529660, -181860, 13020; -181860, -13074, 936; 13020, 936, -67],[420, 6, 1],[62, 9, 8, 7, 0, -1, -1, 0, 8, 3, 6, 13, 2, 11, 15, 6; -875, -130, -119, -110, -1, 15, 21, 5, -35, -26, -63, -150, -25, -145, -203, -83; -210, -72, -112, -180, -14, 15, 98, 69, 1050, 216, 280, 420, 38, 105, 70, 3],309,10]
%
% END OF LATTICE L310.10
%
%
% LATTICE L310.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1072680, 12600, 0; 12600, 148, 0; 0, 0, 1],[840, 4, 1],[-19, -4, -55, -22, -23, -24, -211, -15, -331, -26, -155, -28, -7, -1, 1, 0; 1610, 339, 4662, 1865, 1950, 2035, 17892, 1272, 28070, 2205, 13146, 2375, 594, 85, -84, 0; 0, 4, 84, 40, 48, 55, 504, 37, 840, 68, 420, 80, 24, 5, 0, -1],309,11]
%
% END OF LATTICE L310.11
%
%
% LATTICE L310.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-36120, -13440, 840; -13440, -4972, 304; 840, 304, -17],[840, 4, 1],[-81, -6, -23, 2, 11, 33, 163, 25, 291, 24, 149, 28, 7, -3, -37, -7; 280, 21, 84, -5, -36, -110, -546, -84, -980, -81, -504, -95, -24, 10, 126, 24; 980, 76, 336, 0, -108, -350, -1764, -274, -3220, -268, -1680, -320, -84, 30, 420, 82],309,12]
%
% END OF LATTICE L310.12
%
%
% LATTICE L310.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-189420, 8820, 5460; 8820, -410, -260; 5460, -260, -109],[420, 10, 1],[-43, -29, -286, -18, -71, -45, -421, -103, -97, -31, -134, -2, 11, 5, 1, -17; -861, -581, -5733, -361, -1425, -904, -8463, -2072, -1953, -625, -2709, -41, 219, 100, 21, -340; -98, -65, -630, -39, -150, -92, -840, -200, -182, -55, -210, -1, 30, 12, 0, -40],309,13]
%
% END OF LATTICE L310.13
%
%
% LATTICE L310.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-140280, 1680, 0; 1680, -20, -5; 0, -5, 209],[840, 5, 1],[-13, -2, 13, 2, 35, 19, 463, 71, 167, 35, 449, 9, 31, 3, -1, -5; -1092, -170, 1008, 164, 2892, 1574, 38388, 5890, 13860, 2906, 37296, 748, 2580, 250, -84, -418; -28, -5, 0, 3, 60, 34, 840, 130, 308, 65, 840, 17, 60, 6, 0, -10],309,14]
%
% END OF LATTICE L310.14
%
%
% LATTICE L310.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-9939720, 39480, 15120; 39480, -114, -60; 15120, -60, -23],[840, 6, 1],[241, 43, 99, 66, 5, 53, 10, 7, 4, -1, -1, 4, 2, 87, 39, 77; -210, -37, -84, -55, -4, -40, -7, -4, 0, 1, 0, -5, -2, -80, -35, -68; 158865, 28344, 65254, 43500, 3295, 34920, 6587, 4608, 2625, -660, -658, 2640, 1319, 57360, 25711, 50760],309,15]
%
% END OF LATTICE L310.15
%
%
% LATTICE L310.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-832845720, 15142680, -184800; 15142680, -275322, 3360; -184800, 3360, -41],[840, 6, 1],[167, 18, 25, 41, 9, 73, 41, 27, 113, 6, 3, -1, -1, 7, 15, 21; 9240, 997, 1386, 2275, 500, 4060, 2282, 1504, 6300, 335, 168, -55, -56, 380, 826, 1160; 4410, 564, 889, 1620, 406, 3660, 2198, 1548, 6930, 408, 245, 0, -82, -420, 70, 396],309,16]
%
% END OF LATTICE L310.16
%
%
% LATTICE L310.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[25955160, -1038240, -21000; -1038240, 41531, 840; -21000, 840, 17],[840, 7, 1],[-23, -23, -35, -83, -73, -66, -77, -36, -107, -55, -43, -47, -5, 1, -1, -3; -560, -560, -852, -2020, -1776, -1605, -1872, -875, -2600, -1336, -1044, -1140, -120, 25, -24, -73; -740, -742, -1140, -2730, -2436, -2240, -2640, -1246, -3740, -1946, -1548, -1750, -252, 0, -48, -98],309,17]
%
% END OF LATTICE L310.17
%
%
% LATTICE L310.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-347340, 73920, 840; 73920, -15134, -84; 840, -84, 13],[420, 14, 1],[-1, -51, -67, -417, -233, -499, -316, -316, -499, -549, -233, -583, -67, -1, 16, 16; -5, -258, -339, -2110, -1179, -2525, -1599, -1599, -2525, -2778, -1179, -2950, -339, -5, 81, 81; 30, 1624, 2136, 13300, 7434, 15925, 10086, 10087, 15930, 17528, 7440, 18620, 2142, 35, -510, -511],309,18]
%
% END OF LATTICE L310.18
%
%
% LATTICE L310.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3678360, 787080, -12600; 787080, -168416, 2696; -12600, 2696, -43],[840, 8, 1],[39, -1, -13, -21, -7, 1, 40, 21, 171, 37, 76, 81, 25, 59, 86, 15; 175, -6, -63, -100, -33, 5, 189, 99, 805, 174, 357, 380, 117, 275, 399, 69; -490, -88, -147, -120, -18, 20, 126, 52, 350, 64, 105, 80, 6, -60, -210, -76],309,19]
%
% END OF LATTICE L310.19
%
%
% LATTICE L310.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[4630920, 89040, -21840; 89040, 1690, -420; -21840, -420, 103],[840, 10, 1],[-3, -5, -4, 1, 4, 5, 127, 20, 24, 41, 67, 11, 5, 1, -1, -2; 0, -4, -21, -8, -12, -11, -252, -37, -42, -68, -105, -16, -6, -1, 0, 1; -637, -1080, -945, 176, 795, 1012, 25830, 4080, 4907, 8400, 13755, 2264, 1035, 208, -210, -420],309,20]
%
% END OF LATTICE L310.20
%
%
% LATTICE L310.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1420440, 24360, -11760; 24360, 410, -200; -11760, -200, 97],[840, 10, 1],[-1, 0, 4, 1, 7, 7, 83, 25, 29, 12, 38, 3, 5, 1, 1, -1; -56, -9, 126, 37, 276, 284, 3402, 1032, 1204, 501, 1596, 127, 216, 44, 42, -48; -238, -20, 735, 196, 1410, 1428, 17010, 5140, 5978, 2480, 7875, 624, 1050, 212, 210, -220],309,21]
%
% END OF LATTICE L310.21
%
%
% LATTICE L310.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-52454640, -325920, 129360; -325920, -2022, 804; 129360, 804, -319],[1680, 6, 1],[113, 27, 41, 73, 9, 41, 25, 9, 167, 21, 15, 7, -1, -1, 3, 3; -3010, -724, -1106, -1980, -246, -1130, -693, -251, -4690, -596, -434, -220, 26, 30, -77, -79; 38220, 9120, 13832, 24600, 3028, 13770, 8386, 3015, 55860, 7008, 4984, 2280, -340, -330, 1022, 1017],309,22]
%
% END OF LATTICE L310.22
%
%
% LATTICE L310.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-356215440, -1374240, 514080; -1374240, -5298, 1980; 514080, 1980, -739],[1680, 6, 1],[109, 51, 38, 133, 8, 71, 85, 15, 136, 33, 11, 7, -1, -1, 13, 6; -48755, -22816, -17003, -59520, -3581, -31790, -38066, -6719, -60935, -14792, -4935, -3160, 447, 450, -5810, -2683; -54810, -25656, -19124, -66960, -4030, -35790, -42868, -7569, -68670, -16680, -5572, -3600, 502, 510, -6524, -3015],309,23]
%
% END OF LATTICE L310.23
%
%
% LATTICE L310.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-46457040, -252000, 102480; -252000, -1362, 552; 102480, 552, -223],[1680, 6, 1],[4, 7, 10, 53, 5, 33, 99, 43, 241, 77, 39, 87, 2, 2, -1, -1; -1505, -2656, -3801, -20160, -1903, -12565, -37702, -16378, -91805, -29336, -14861, -33160, -763, -765, 378, 382; -1890, -3360, -4816, -25560, -2414, -15945, -47852, -20790, -116550, -37248, -18872, -42120, -970, -975, 476, 486],309,24]
%
% END OF LATTICE L310.24
%
%
% LATTICE L310.25
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[160440, 21000, 10080; 21000, 2028, 612; 10080, 612, -61],[840, 12, 1],[1381, 150, 411, 328, 67, 116, 219, 27, 229, -12, -89, -98, -21, -1, 103, 42; -20650, -2243, -6146, -4905, -1002, -1735, -3276, -404, -3430, 179, 1330, 1465, 314, 15, -1540, -628; 21000, 2280, 6244, 4980, 1016, 1755, 3304, 405, 3360, -192, -1372, -1500, -320, -15, 1568, 639],309,25]
%
% END OF LATTICE L310.25
%
%
% LATTICE L310.26
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-25276440, -1201200, 41160; -1201200, -57084, 1956; 41160, 1956, -67],[840, 12, 1],[-93, -11, -33, -29, -7, -31, -37, -13, -117, -7, -9, -1, 1, 1, -5, -5; 2030, 239, 714, 625, 150, 660, 784, 274, 2450, 145, 182, 15, -22, -20, 112, 110; 2100, 216, 560, 420, 76, 210, 140, 6, -420, -72, -224, -180, -28, 30, 196, 138],309,26]
%
% END OF LATTICE L310.26
%
%
% LATTICE L310.27
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-22154160, 168000, -67200; 168000, -1266, 498; -67200, 498, -187],[1680, 6, 1],[271, 63, 93, 161, 19, 41, 48, 33, 289, 33, 19, -1, -3, -1, 8, 15; 49210, 11444, 16898, 29260, 3454, 7455, 8729, 6002, 52570, 6004, 3458, -180, -546, -185, 1449, 2722; 33600, 7824, 11564, 20040, 2368, 5115, 5992, 4122, 36120, 4128, 2380, -120, -376, -135, 980, 1854],309,27]
%
% END OF LATTICE L310.27
%
%
% LATTICE L310.28
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-102754680, -4110120, 54600; -4110120, -164402, 2184; 54600, 2184, -29],[840, 14, 1],[9, 13, 7, 23, 5, 1, -1, -4, -9, -13, -7, -23, -5, -1, 1, 4; -220, -320, -174, -580, -132, -45, 18, 85, 200, 296, 162, 540, 120, 25, -24, -97; 370, 364, 66, -420, -546, -1540, -537, -1148, -1910, -2212, -990, -2660, -378, 0, 75, 224],309,28]
%
% END OF LATTICE L310.28
%
%
% LATTICE L310.29
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-6364680, -254520, 8400; -254520, -10178, 336; 8400, 336, -11],[840, 14, 1],[2, 5, 1, 3, -1, -9, -7, -8, -7, -17, -4, -23, -2, -1, 1, 2; -50, -128, -27, -100, 18, 195, 156, 181, 160, 392, 93, 540, 48, 25, -24, -49; -5, -112, -69, -840, -231, -980, -618, -616, -485, -1064, -225, -1120, -63, 0, 30, 28],309,29]
%
% END OF LATTICE L310.29
%
%
% LATTICE L310.30
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-41189820, 6917400, -102900; 6917400, -1161690, 17280; -102900, 17280, -257],[420, 30, 1],[59, 14, 6, -3, -7, -7, 1, 23, 53, 34, 106, 19, 23, 39, 111, 73; 497, 124, 77, -20, -53, -54, 7, 178, 413, 266, 833, 150, 183, 314, 903, 602; 9828, 2745, 2800, -141, -760, -828, 70, 2760, 6552, 4275, 13580, 2481, 3100, 5508, 16310, 11280],309,30]
%
% END OF LATTICE L310.30
%
%
% LATTICE L310.31
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[5049240, 5880, -18480; 5880, -60, -15; -18480, -15, 67],[840, 15, 1],[193, 40, 169, 10, 11, 3, -1, -5, -11, -1, 13, 3, 15, 23, 183, 83; 5236, 1086, 4592, 272, 300, 82, -28, -138, -308, -30, 336, 80, 404, 622, 4956, 2250; 54348, 11265, 47600, 2817, 3100, 846, -280, -1410, -3108, -285, 3640, 843, 4220, 6474, 51520, 23370],309,31]
%
% END OF LATTICE L310.31
%
%
% LATTICE L310.32
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-64681680, 90720, 38640; 90720, -88, -56; 38640, -56, -23],[1680, 8, 1],[43, 11, 53, 33, 13, 21, 80, 5, 97, 13, 31, 7, -1, -1, 4, 1; 2975, 762, 3675, 2290, 903, 1460, 5565, 348, 6755, 906, 2163, 490, -69, -70, 273, 69; 64960, 16616, 80052, 49840, 19632, 31710, 120792, 7549, 146440, 19624, 46788, 10560, -1512, -1510, 6048, 1511],309,32]
%
% END OF LATTICE L310.32
%
%
% LATTICE L310.33
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-5945520, -2316720, -10080; -2316720, -902728, -3928; -10080, -3928, -17],[1680, 8, 1],[319, 25, 142, 22, -1, -39, -107, -33, -179, -13, -58, -2, 13, 79, 191, 57; -805, -63, -357, -55, 3, 100, 273, 84, 455, 33, 147, 5, -33, -200, -483, -144; -3220, -274, -1764, -350, -108, 0, 336, 152, 980, 82, 420, 30, -84, -640, -1680, -536],309,33]
%
% END OF LATTICE L310.33
%
%
% LATTICE L310.34
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1782480, 275520, 13440; 275520, -42568, -2080; 13440, -2080, -101],[1680, 8, 1],[-17, 2, 44, 19, 19, 67, 131, 33, 157, 10, 40, 1, -7, -27, -47, -9; -105, 7, 189, 85, 87, 310, 609, 154, 735, 47, 189, 5, -33, -130, -231, -46; -140, 118, 1932, 770, 732, 2520, 4872, 1216, 5740, 362, 1428, 30, -252, -920, -1512, -256],309,34]
%
% END OF LATTICE L310.34
%
%
% LATTICE L310.35
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2014320, 0, 3360; 0, 344, -80; 3360, -80, 13],[1680, 8, 1],[26, 7, 34, 21, 8, 6, 43, 5, 44, 5, 8, -1, -2, -1, -1, 1; 3605, 972, 4725, 2920, 1113, 835, 5985, 696, 6125, 696, 1113, -140, -279, -140, -147, 138; 15400, 4160, 20244, 12520, 4776, 3585, 25704, 2990, 26320, 2992, 4788, -600, -1200, -605, -672, 586],309,35]
%
% END OF LATTICE L310.35
%
%
% LATTICE L310.36
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-43658160, -68880, 36960; -68880, 130, 50; 36960, 50, -31],[1680, 10, 1],[66, 57, 379, 8, 16, 9, 17, -1, -3, -3, -1, 1, 11, 27, 172, 109; 2891, 2496, 16590, 350, 699, 392, 735, -48, -133, -132, -42, 44, 483, 1184, 7539, 4776; 83314, 71950, 478380, 10097, 20190, 11352, 21420, -1280, -3794, -3790, -1260, 1263, 13890, 34088, 217140, 137600],309,36]
%
% END OF LATTICE L310.36
%
%
% LATTICE L310.37
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-616560, 15120, -3360; 15120, -370, 80; -3360, 80, -11],[1680, 10, 1],[24, 10, 127, 5, 4, 1, -4, -5, -3, -1, -1, 1, 5, 11, 67, 41; 1043, 434, 5502, 216, 171, 40, -189, -224, -133, -44, -42, 44, 219, 480, 2919, 1784; 196, 75, 840, 26, 0, -32, -210, -120, -56, -15, 0, 14, 60, 112, 630, 360],309,37]
%
% END OF LATTICE L310.37
%
%
% LATTICE L310.38
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[441840, -10080, 0; -10080, 130, 10; 0, 10, -1],[1680, 10, 1],[-1, 0, 4, 1, 7, 7, 83, 25, 29, 6, 38, 3, 5, 1, 1, -1; -42, 1, 189, 46, 318, 316, 3738, 1124, 1302, 269, 1701, 134, 222, 44, 42, -44; -448, -5, 1680, 426, 3000, 3008, 35700, 10760, 12488, 2585, 16380, 1294, 2160, 432, 420, -440],309,38]
%
% END OF LATTICE L310.38
%
%
% LATTICE L310.39
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[18480, 0, -3360; 0, -10, 80; -3360, 80, -29],[1680, 10, 1],[-13, -7, -25, -1, -1, 5, 85, 31, 41, 19, 67, 3, 13, 3, -1, -7; -574, -310, -1113, -45, -54, 212, 3654, 1340, 1778, 826, 2919, 131, 570, 132, -42, -308; -84, -50, -210, -11, -60, -16, 0, 40, 84, 50, 210, 11, 60, 16, 0, -40],309,39]
%
% END OF LATTICE L310.39
%
%
% LATTICE L310.40
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[840, 0, 0; 0, -220, 80; 0, 80, -29],[840, 20, 1],[-1, -1, -13, -1, -5, -2, -43, -6, -13, -5, -29, -1, -1, 0, 1, 0; -28, -16, -126, -6, -12, 1, 84, 19, 56, 28, 210, 10, 24, 3, 0, -7; -84, -50, -420, -22, -60, -8, 0, 20, 84, 50, 420, 22, 60, 8, 0, -20],309,40]
%
% END OF LATTICE L310.40
%
%
% LATTICE L310.41
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1412040, -78120, 20160; -78120, 3140, -760; 20160, -760, 181],[840, 20, 1],[-13, -3, -29, 0, 11, 8, 211, 34, 83, 18, 239, 5, 19, 2, -1, -4; -1666, -386, -3780, -3, 1374, 1009, 26670, 4303, 10514, 2282, 30324, 635, 2418, 255, -126, -511; -5544, -1285, -12600, -11, 4560, 3352, 88620, 14300, 34944, 7585, 100800, 2111, 8040, 848, -420, -1700],309,41]
%
% END OF LATTICE L310.41
%
%
% LATTICE L310.42
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-12182520, 812280, -12600; 812280, -54159, 840; -12600, 840, -13],[840, 21, 1],[-23, -15, -5, -23, -3, -1, 1, 3, 13, 9, 3, 13, 1, -4, -3, -6; -400, -256, -84, -380, -48, -15, 16, 47, 200, 136, 44, 180, 8, -85, -56, -107; -3660, -2058, -596, -2310, -196, 0, 64, 126, 300, 42, -76, -1050, -476, -1680, -736, -1134],309,42]
%
% END OF LATTICE L310.42
%
%
% LATTICE L310.43
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[9449580, -2436840, 26460; -2436840, 627186, -6762; 26460, -6762, 71],[420, 42, 1],[379, 471, 75, 653, 37, 1, -18, -90, -179, -231, -35, -253, 3, 199, 58, 210; 1875, 2330, 371, 3230, 183, 5, -89, -445, -885, -1142, -173, -1250, 15, 985, 287, 1039; 37320, 46368, 7382, 64260, 3640, 105, -1768, -8841, -17580, -22680, -3434, -24780, 308, 19635, 5716, 20685],309,43]
%
% END OF LATTICE L310.43
%
%
% LATTICE L310.44
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-93859080, -6714120, 113400; -6714120, -480288, 8112; 113400, 8112, -137],[840, 24, 1],[111, 25, 36, 61, 7, 59, 17, 23, 99, 11, 6, -1, -1, 1, 4, 13; -1505, -337, -483, -815, -93, -780, -224, -302, -1295, -143, -77, 15, 13, -20, -56, -178; 2730, 732, 1190, 2220, 286, 2640, 805, 1152, 5250, 636, 406, 60, -58, -360, -7, 216],309,44]
%
% END OF LATTICE L310.44
%
%
% LATTICE L310.45
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-582960, -43680, 8400; -43680, -3262, 630; 8400, 630, -121],[1680, 14, 1],[9, 2, 1, -1, -5, -23, -7, -13, -9, -2, -1, 1, 5, 23, 7, 13; -10, -4, -3, 0, 18, 140, 54, 124, 110, 34, 33, 100, 42, 60, 6, -4; 580, 119, 54, -70, -252, -840, -192, -224, -20, 49, 114, 630, 588, 1960, 528, 896],309,45]
%
% END OF LATTICE L310.45
%
%
% LATTICE L310.46
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2088240, 40320, -8400; 40320, 602, -140; -8400, -140, 31],[1680, 14, 1],[2, 1, 1, -1, -2, -23, -4, -17, -7, -4, -7, -9, -1, 3, 1, 5; 155, 78, 78, -80, -159, -1840, -321, -1368, -565, -324, -570, -740, -87, 200, 75, 384; 1240, 623, 624, -630, -1260, -14560, -2538, -10808, -4460, -2555, -4488, -5810, -672, 1680, 606, 3080],309,46]
%
% END OF LATTICE L310.46
%
%
% LATTICE L310.47
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1460760, 243600, 6720; 243600, 40628, 1120; 6720, 1120, 31],[840, 28, 1],[37, 7, 7, 1, -1, 23, 25, 35, 73, 26, 59, 54, 67, 87, 41, 31; -190, -36, -36, -5, 6, -115, -126, -177, -370, -132, -300, -275, -342, -445, -210, -159; -1160, -217, -216, -35, 0, -840, -876, -1204, -2480, -875, -1968, -1785, -2184, -2800, -1308, -980],309,47]
%
% END OF LATTICE L310.47
%
%
% LATTICE L310.48
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2655240, 101640, -5880; 101640, 3836, -224; -5880, -224, 13],[840, 28, 1],[1, 1, 1, 1, -1, -6, -5, -6, -11, -7, -7, -11, -5, -4, -1, 0; 10, 12, 12, 10, -18, -95, -78, -93, -170, -108, -108, -170, -78, -65, -18, -3; 620, 658, 660, 630, -756, -4340, -3600, -4312, -7900, -5026, -5028, -7910, -3612, -2940, -768, -56],309,48]
%
% END OF LATTICE L310.48
%
%
% LATTICE L310.49
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[324240, -112560, 3360; -112560, 39074, -1162; 3360, -1162, 19],[1680, 14, 1],[-559, -317, -139, -182, -97, -7, 31, 87, 59, 17, -11, -68, -203, -993, -331, -687; -1630, -924, -405, -530, -282, -20, 90, 252, 170, 48, -33, -200, -594, -2900, -966, -2004; -580, -322, -138, -175, -84, 0, 24, 56, 20, -14, -30, -105, -252, -1120, -360, -728],309,49]
%
% END OF LATTICE L310.49
%
%
% LATTICE L310.50
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-6036240, -1680, -1680; -1680, 4886, -826; -1680, -826, 139],[1680, 14, 1],[-26, -29, -25, -16, -4, -1, 1, 5, 1, -1, -5, -9, -11, -99, -16, -65; 13525, 15084, 13002, 8320, 2079, 520, -519, -2592, -515, 528, 2610, 4690, 5727, 51520, 8325, 33816; 80050, 89278, 76956, 49245, 12306, 3080, -3072, -15344, -3050, 3122, 15444, 27755, 33894, 304920, 49272, 200144],309,50]
%
% END OF LATTICE L310.50
%
%
% LATTICE L310.51
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[7031640, 354480, -14280; 354480, 17790, -720; -14280, -720, 29],[840, 30, 1],[37, 61, 32, 15, 2, 1, -1, -2, -2, -1, 3, 5, 3, 9, 71, 32; -42, -68, -35, -16, -2, -1, 0, 1, 0, -4, -7, -8, -4, -11, -84, -37; 17157, 28320, 14875, 6984, 935, 468, -490, -960, -987, -600, 1295, 2256, 1375, 4152, 32830, 14820],309,51]
%
% END OF LATTICE L310.51
%
%
% LATTICE L310.52
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[246120, 23520, -1680; 23520, 2010, -150; -1680, -150, 11],[840, 30, 1],[3, 2, 3, 1, 1, 1, 1, -1, -3, -2, -3, -1, -1, -1, -1, 1; 28, 25, 42, 15, 16, 16, 14, -20, -56, -37, -56, -19, -20, -24, -42, -4; 798, 630, 1015, 354, 370, 372, 350, -420, -1218, -810, -1225, -414, -430, -492, -770, 60],309,52]
%
% END OF LATTICE L310.52
%
%
% LATTICE L310.53
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-215880, 8400, 1680; 8400, -35, -70; 1680, -70, -13],[840, 35, 1],[7, 33, 47, 21, 85, 14, 77, 34, 19, 45, 31, 5, -7, -1, 1, 5; 12, 58, 84, 38, 156, 26, 144, 64, 36, 86, 60, 10, -12, -2, 0, 8; 832, 3920, 5580, 2492, 10080, 1659, 9120, 4025, 2248, 5320, 3660, 588, -840, -119, 120, 595],309,53]
%
% END OF LATTICE L310.53
%
%
% LATTICE L310.54
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-25620, 14280, 1260; 14280, -3010, -210; 1260, -210, -13],[420, 70, 1],[4, 37, 26, 23, 46, 15, 41, 36, 10, 47, 16, 5, -4, -1, 1, 6; 63, 584, 411, 364, 729, 238, 651, 572, 159, 748, 255, 80, -63, -16, 15, 94; -634, -5880, -4140, -3668, -7350, -2401, -6570, -5775, -1606, -7560, -2580, -812, 630, 161, -150, -945],309,54]
%
% END OF LATTICE L310.54
%
%
% LATTICE L310.55
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[4189920, 83160, -20160; 83160, 1640, -400; -20160, -400, 97],[840, 40, 1],[-1, 0, 4, 2, 7, 7, 83, 25, 29, 24, 38, 6, 5, 1, 1, -1; -7, -9, -21, -5, -9, -5, -42, -9, -7, -3, 0, 1, 3, 1, 0, -3; -238, -40, 735, 392, 1410, 1428, 17010, 5140, 5978, 4960, 7875, 1248, 1050, 212, 210, -220],309,55]
%
% END OF LATTICE L310.55
%
%
% LATTICE L310.56
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-13508040, 2701440, -25200; 2701440, -540246, 5040; -25200, 5040, -47],[840, 42, 1],[-11, -12, -3, -41, -11, -103, -9, -45, -29, -12, -1, 1, 3, 23, 1, -3; -60, -59, -14, -185, -48, -440, -38, -188, -120, -49, -4, 5, 12, 80, 2, -28; -570, 84, 103, 2100, 742, 7980, 746, 3948, 2670, 1176, 107, 0, -322, -3780, -326, -1428],309,56]
%
% END OF LATTICE L310.56
%
%
% LATTICE L310.57
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-5973240, 1194480, -10080; 1194480, -238854, 2016; -10080, 2016, -17],[840, 42, 1],[2, 0, -1, -11, -2, -43, -2, -21, -7, -6, -1, 1, 1, 23, 1, 9; 0, -11, -8, -65, -10, -200, -9, -92, -30, -25, -4, 5, 4, 80, 3, 20; -1215, -1344, -370, -1260, -7, 1680, 115, 1512, 585, 588, 118, 0, -119, -4200, -241, -3024],309,57]
%
% END OF LATTICE L310.57
%
%
% LATTICE L310.58
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-10471440, 804720, 92400; 804720, -55176, -6360; 92400, -6360, -733],[1680, 24, 1],[167, 9, 50, 41, 9, 73, 41, 27, 113, 3, 6, -1, -1, 7, 15, 21; -65345, -3523, -19579, -16060, -3527, -28620, -16079, -10592, -44345, -1178, -2359, 390, 393, -2720, -5859, -8212; 588000, 31701, 176176, 144510, 31736, 257520, 144676, 95304, 399000, 10599, 21224, -3510, -3536, 24480, 52724, 73896],309,58]
%
% END OF LATTICE L310.58
%
%
% LATTICE L310.59
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-566837040, -38184720, 194880; -38184720, -2572296, 13128; 194880, 13128, -67],[1680, 24, 1],[62, 6, 15, 11, 2, 13, 6, 3, 8, 0, -1, -1, 0, 7, 8, 9; -875, -83, -203, -145, -25, -150, -63, -26, -35, 5, 21, 15, -1, -110, -119, -130; 8820, 1182, 3836, 3570, 916, 8400, 5096, 3624, 16380, 978, 1204, 30, -196, -1200, -56, 696],309,59]
%
% END OF LATTICE L310.59
%
%
% LATTICE L310.60
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-52454640, -3756480, 129360; -3756480, -269016, 9264; 129360, 9264, -319],[1680, 24, 1],[167, 18, 50, 41, 9, 73, 41, 27, 113, 6, 6, -1, -1, 7, 15, 21; -2345, -251, -693, -565, -123, -990, -553, -362, -1505, -79, -77, 15, 13, -110, -217, -298; -420, 6, 140, 210, 76, 840, 560, 432, 2100, 138, 196, 30, -28, -360, -224, -144],309,60]
%
% END OF LATTICE L310.60
%
%
% LATTICE L310.61
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[72240, -16800, 5040; -16800, -312, 240; 5040, 240, -121],[1680, 24, 1],[166, 9, 9, -1, -2, -1, 12, 21, 184, 21, 61, 26, 12, 101, 58, 39; 6755, 364, 357, -45, -83, -40, 497, 868, 7595, 866, 2513, 1070, 493, 4140, 2373, 1592; 20160, 1086, 1064, -135, -248, -120, 1484, 2592, 22680, 2586, 7504, 3195, 1472, 12360, 7084, 4752],309,61]
%
% END OF LATTICE L310.61
%
%
% LATTICE L310.62
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-4101720, -820680, 10920; -820680, -164192, 2184; 10920, 2184, -29],[840, 56, 1],[-7, -9, -4, -9, 1, 19, 4, 19, 17, 21, 10, 29, 5, 1, -1, -7; 40, 50, 21, 40, -12, -135, -27, -125, -110, -134, -63, -180, -30, -5, 6, 41; 370, 364, 66, -420, -546, -3080, -537, -2296, -1910, -2212, -990, -2660, -378, 0, 75, 448],309,62]
%
% END OF LATTICE L310.62
%
%
% LATTICE L310.63
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[656880, 55440, -5040; 55440, 3930, -390; -5040, -390, 37],[1680, 30, 1],[-2, 3, 10, 13, 7, 10, 155, 69, 79, 129, 67, 31, 4, 1, -1, -3; -21, 56, 147, 184, 97, 137, 2114, 938, 1071, 1744, 903, 416, 53, 13, -14, -38; -504, 960, 2870, 3672, 1960, 2787, 43120, 19170, 21924, 35760, 18550, 8568, 1100, 273, -280, -810],309,63]
%
% END OF LATTICE L310.63
%
%
% LATTICE L310.64
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1832880, -35280, -11760; -35280, 570, 210; -11760, 210, 73],[1680, 30, 1],[-2, -1, 3, 5, 3, 9, 71, 16, 37, 61, 32, 15, 2, 1, -1, -1; 91, 64, -105, -192, -119, -362, -2870, -649, -1505, -2488, -1309, -616, -83, -42, 42, 43; -588, -360, 770, 1344, 820, 2478, 19600, 4425, 10248, 16920, 8890, 4176, 560, 282, -280, -285],309,64]
%
% END OF LATTICE L310.64
%
%
% LATTICE L310.65
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[492240, -278880, 20160; -278880, 138930, -10050; 20160, -10050, 727],[1680, 30, 1],[3, 1, -1, -1, -1, -1, -3, -1, -3, -1, 1, 1, 1, 1, 3, 1; -742, -68, 686, 444, 390, 376, 1113, 368, 1106, 380, -322, -340, -338, -324, -931, -290; -10332, -960, 9520, 6168, 5420, 5226, 15470, 5115, 15372, 5280, -4480, -4728, -4700, -4506, -12950, -4035],309,65]
%
% END OF LATTICE L310.65
%
%
% LATTICE L310.66
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-13949040, -446880, 53760; -446880, -13290, 1620; 53760, 1620, -197],[1680, 30, 1],[67, 55, 57, 13, 3, 0, -4, -5, -11, -7, -1, 3, 5, 4, 32, 29; 10290, 8468, 8806, 2020, 478, 8, -567, -736, -1638, -1052, -154, 452, 758, 610, 4893, 4444; 102984, 84720, 88060, 20184, 4760, 69, -5740, -7410, -16464, -10560, -1540, 4536, 7600, 6111, 49000, 44490],309,66]
%
% END OF LATTICE L310.66
%
%
% LATTICE L310.67
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[14974680, -67200, -53760; -67200, -660, 240; -53760, 240, 193],[840, 60, 1],[-123, -38, -43, 2, 15, 19, 127, 47, 81, 20, 1, -8, -21, -25, -169, -65; 56, 19, 28, 1, -4, -6, -42, -16, -28, -7, 0, 3, 8, 10, 70, 28; -34356, -10620, -12040, 552, 4180, 5298, 35420, 13110, 22596, 5580, 280, -2232, -5860, -6978, -47180, -18150],309,67]
%
% END OF LATTICE L310.67
%
%
% LATTICE L310.68
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[33026280, 2274720, -47040; 2274720, 156540, -3240; -47040, -3240, 67],[840, 60, 1],[109, 46, 99, 12, 7, 1, -1, -2, -11, -4, -1, 2, 7, 6, 99, 23; -84, -37, -84, -11, -8, -2, -14, -1, 0, 1, 0, -1, -4, -4, -70, -17; 72408, 30480, 65380, 7884, 4520, 603, -1400, -1455, -7728, -2760, -700, 1356, 4720, 4017, 66080, 15315],309,68]
%
% END OF LATTICE L310.68
%
%
% LATTICE L310.69
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[704760, 57120, -840; 57120, 1610, -70; -840, -70, 1],[840, 70, 1],[0, 7, 5, 13, 19, 17, 55, 56, 9, 101, 22, 23, 8, 1, -1, -2; 0, -4, -3, -8, -12, -11, -36, -37, -6, -68, -15, -16, -6, -1, 0, 1; -1, 5600, 4005, 10416, 15225, 13622, 44070, 44870, 7211, 80920, 17625, 18424, 6405, 798, -810, -1610],309,69]
%
% END OF LATTICE L310.69
%
%
% LATTICE L310.70
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-822360, 152880, 10920; 152880, -25270, -1820; 10920, -1820, -131],[840, 70, 1],[1, 5, 1, -1, -7, -4, -7, -15, -5, -29, -13, -7, -5, 0, 1, 3; -78, -404, -96, 56, 486, 287, 507, 1093, 366, 2132, 960, 520, 378, 1, -75, -229; 1166, 6020, 1410, -868, -7350, -4326, -7635, -16450, -5506, -32060, -14430, -7812, -5670, -14, 1125, 3430],309,70]
%
% END OF LATTICE L310.70
%
%
% LATTICE L310.71
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-757680, 35280, -15120; 35280, -1640, 720; -15120, 720, -209],[1680, 40, 1],[55, 36, 344, 21, 79, 47, 419, 97, 85, 24, 76, -1, -19, -7, 1, 23; 1099, 719, 6867, 419, 1575, 936, 8337, 1928, 1687, 475, 1491, -21, -381, -140, 21, 460; -196, -130, -1260, -78, -300, -184, -1680, -400, -364, -110, -420, -2, 60, 24, 0, -80],309,71]
%
% END OF LATTICE L310.71
%
%
% LATTICE L310.72
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-52080, 1680, -3360; 1680, -40, 160; -3360, 160, -29],[1680, 40, 1],[13, 7, 50, 2, 1, -5, -85, -31, -41, -19, -134, -6, -13, -3, 1, 7; 259, 139, 987, 39, 15, -104, -1743, -632, -833, -385, -2709, -121, -261, -60, 21, 140; -84, -50, -420, -22, -60, -16, 0, 40, 84, 50, 420, 22, 60, 16, 0, -40],309,72]
%
% END OF LATTICE L310.72
%
%
% LATTICE L310.73
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[3052560, -613200, 23520; -613200, 123080, -4720; 23520, -4720, 181],[1680, 40, 1],[29, 25, 83, 7, 7, 1, 8, 0, -1, -1, 1, 1, 5, 3, 76, 6; 637, 544, 1785, 148, 141, 18, 105, -4, -35, -28, 21, 24, 117, 68, 1701, 133; 12824, 10920, 35700, 2944, 2760, 338, 1680, -105, -784, -600, 420, 496, 2400, 1382, 34440, 2685],309,73]
%
% END OF LATTICE L310.73
%
%
% LATTICE L310.74
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-381005520, 18925200, 586320; 18925200, -940040, -29160; 586320, -29160, -719],[1680, 40, 1],[-260, -817, -5144, -727, -1534, -233, -8219, -921, -1490, -683, -106, 227, 784, 108, 2969, 171; -5201, -16346, -102921, -14546, -30693, -4662, -164451, -18428, -29813, -13666, -2121, 4542, 15687, 2161, 59409, 3422; -1064, -3280, -20580, -2904, -6120, -929, -32760, -3670, -5936, -2720, -420, 904, 3120, 429, 11760, 670],309,74]
%
% END OF LATTICE L310.74
%
%
% LATTICE L310.75
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-18212880, -109200, -33600; -109200, -42, 84; -33600, 84, 71],[1680, 42, 1],[11, 6, 3, 41, 11, 103, 9, 45, 29, 6, 1, -1, -3, -23, -1, 3; -5350, -2929, -1467, -20070, -5390, -50500, -4414, -22076, -14230, -2945, -491, 490, 1474, 11340, 498, -1420; 11460, 6279, 3146, 43050, 11564, 108360, 9472, 47376, 30540, 6321, 1054, -1050, -3164, -24360, -1072, 3024],309,75]
%
% END OF LATTICE L310.75
%
%
% LATTICE L310.76
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[3106320, 16238880, -1162560; 16238880, 70159614, -5024544; -1162560, -5024544, 359837],[1680, 42, 1],[188, 35, -43, -619, -124, -2757, -130, -1379, -463, -200, -67, 69, 69, 1657, 75, 719; 21785, 4048, -4994, -71820, -14383, -319760, -15077, -159928, -53695, -23194, -7770, 8000, 8001, 192120, 8695, 83344; 304800, 56637, -69872, -1004850, -201236, -4473840, -210946, -2237592, -751260, -324513, -108712, 111930, 111944, 2688000, 121654, 1166088],309,76]
%
% END OF LATTICE L310.76
%
%
% LATTICE L310.77
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[585480, 390600, -13440; 390600, 155316, -3780; -13440, -3780, 53],[840, 84, 1],[-1853, -573, -371, -844, -237, -512, -35, 30, 163, 66, 33, -1, -101, -1178, -303, -1044; 9210, 2848, 1844, 4195, 1178, 2545, 174, -149, -810, -328, -164, 5, 502, 5855, 1506, 5189; 186960, 57813, 37432, 85155, 23912, 51660, 3532, -3024, -16440, -6657, -3328, 105, 10192, 118860, 30572, 105336],309,77]
%
% END OF LATTICE L310.77
%
%
% LATTICE L310.78
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[27915720, 2686320, -44520; 2686320, 258468, -4284; -44520, -4284, 71],[840, 84, 1],[-1, 1, 1, 9, 3, 16, 3, 8, 11, 5, 1, 1, -1, -6, -1, -2; -40, -22, -6, -20, 0, 15, 4, 13, 20, 10, 2, 0, -4, -35, -8, -25; -3060, -714, 260, 4410, 1876, 10920, 2120, 5796, 8100, 3738, 748, 630, -868, -5880, -1112, -2772],309,78]
%
% END OF LATTICE L310.78
%
%
% LATTICE L310.79
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[18480, 0, -3360; 0, -42, 168; -3360, 168, -61],[1680, 42, 1],[-17, -15, -3, -16, -5, -1, 3, 33, 37, 27, 5, 26, 9, 41, 1, -9; -390, -338, -67, -355, -110, -20, 66, 724, 810, 590, 109, 565, 194, 860, 18, -220; -180, -126, -22, -105, -28, 0, 16, 168, 180, 126, 22, 105, 28, 0, -16, -168],309,79]
%
% END OF LATTICE L310.79
%
%
% LATTICE L310.80
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3324720, -1433040, 72240; -1433040, -616434, 31080; 72240, 31080, -1567],[1680, 42, 1],[-16, -21, -7, -16, -2, -1, 1, 21, 11, 15, 5, 11, 1, -19, -2, -33; -305, -428, -150, -360, -49, -40, 25, 544, 295, 416, 146, 350, 47, 0, -27, -568; -6780, -9450, -3296, -7875, -1064, -840, 542, 11760, 6360, 8946, 3128, 7455, 980, -840, -626, -12768],309,80]
%
% END OF LATTICE L310.80
%
%
% LATTICE L310.81
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-271320, -88200, 4200; -88200, -20265, 945; 4200, 945, -44],[840, 105, 1],[-11, -17, -11, -5, -7, -3, -1, 1, 1, 2, 1, 0, -3, -7, -9, -31; 700, 1079, 696, 315, 436, 182, 56, -82, -68, -131, -64, 1, 196, 450, 576, 1978; 13968, 21525, 13880, 6279, 8680, 3612, 1100, -1680, -1368, -2625, -1280, 21, 3920, 8988, 11500, 39480],309,81]
%
% END OF LATTICE L310.81
%
%
% LATTICE L310.82
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-50820, -61740, 2940; -61740, -66570, 3150; 2940, 3150, -149],[420, 210, 1],[-4, -11, -3, -2, 0, 3, 2, 13, 2, 5, 1, 0, -2, -7, -4, -25; 59, 155, 39, 21, -13, -70, -41, -250, -37, -89, -17, 1, 35, 114, 63, 382; 1164, 3045, 760, 399, -280, -1428, -830, -5040, -744, -1785, -340, 21, 700, 2268, 1250, 7560],309,82]
%
% END OF LATTICE L310.82
%
%
% LATTICE L310.83
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[9093840, 152880, -16800; 152880, 2408, -280; -16800, -280, 31],[1680, 56, 1],[4, 5, 2, 3, -2, -9, -7, -4, -14, -17, -8, -23, -4, -1, 1, 1; 35, 42, 15, 10, -27, -100, -75, -42, -145, -174, -81, -230, -39, -10, 9, 9; 2480, 3080, 1212, 1680, -1344, -5810, -4488, -2555, -8920, -10808, -5076, -14560, -2520, -630, 624, 623],309,83]
%
% END OF LATTICE L310.83
%
%
% LATTICE L310.84
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[13881840, -2602320, -13440; -2602320, 487816, 2520; -13440, 2520, 13],[1680, 56, 1],[-41, -45, -19, -47, -5, 1, 2, 2, 1, -3, -5, -33, -19, -41, -26, -26; -175, -192, -81, -200, -21, 5, 9, 9, 5, -12, -21, -140, -81, -175, -111, -111; -8460, -9296, -3936, -9800, -1092, 70, 324, 322, 60, -784, -1104, -7000, -3948, -8470, -5364, -5362],309,84]
%
% END OF LATTICE L310.84
%
%
% LATTICE L310.85
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3062640, 1102080, 8400; 1102080, -396536, -3024; 8400, -3024, -23],[1680, 56, 1],[-47, -53, -23, -59, -7, 2, 4, 5, 7, 5, -1, -21, -17, -42, -28, -29; -105, -118, -51, -130, -15, 5, 9, 11, 15, 10, -3, -50, -39, -95, -63, -65; -3380, -3864, -1704, -4480, -588, 70, 276, 378, 580, 504, 24, -1120, -1092, -2870, -1956, -2058],309,85]
%
% END OF LATTICE L310.85
%
%
% LATTICE L310.86
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[37509360, 1165920, -72240; 1165920, 36008, -2240; -72240, -2240, 139],[1680, 56, 1],[2, 5, 2, -1, -8, -16, -25, -29, -52, -65, -32, -99, -22, -9, -5, -1; 35, 96, 39, -20, -159, -320, -501, -582, -1045, -1308, -645, -2000, -447, -185, -105, -24; 1600, 4144, 1668, -840, -6720, -13475, -21072, -24458, -43880, -54880, -27036, -83720, -18648, -7665, -4296, -910],309,86]
%
% END OF LATTICE L310.86
%
%
% LATTICE L310.87
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[6414240, 733320, -8400; 733320, 83640, -960; -8400, -960, 11],[840, 120, 1],[3, 4, 3, 2, 1, 1, 1, -1, -3, -4, -3, -2, -1, -1, -1, 1; -7, -3, 0, 1, 1, 1, 0, -3, -7, -9, -7, -5, -3, -5, -14, -9; 1638, 2760, 2275, 1608, 850, 852, 770, -1020, -2898, -3840, -2905, -1968, -1030, -1212, -2030, -60],309,87]
%
% END OF LATTICE L310.87
%
%
% LATTICE L310.88
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1947120, -164640, 5040; -164640, -13090, 420; 5040, 420, -13],[1680, 70, 1],[5, 45, 31, 27, 53, 17, 23, 20, 11, 51, 17, 5, -5, -1, 1, 4; 18, 164, 114, 100, 198, 64, 87, 76, 42, 196, 66, 20, -18, -4, 3, 14; 2512, 22680, 15660, 13664, 26880, 8638, 11700, 10185, 5608, 26040, 8700, 2576, -2520, -518, 480, 1995],309,88]
%
% END OF LATTICE L310.88
%
%
% LATTICE L310.89
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-5404560, -455280, 8400; -455280, -37310, 700; 8400, 700, -13],[1680, 70, 1],[2, 37, 13, 23, 23, 15, 41, 18, 5, 47, 8, 5, -2, -1, 1, 3; 15, 280, 99, 176, 177, 116, 318, 140, 39, 368, 63, 40, -15, -8, 6, 22; 2096, 38920, 13710, 24304, 24360, 15918, 43560, 19145, 5324, 50120, 8550, 5376, -2100, -1078, 960, 3115],309,89]
%
% END OF LATTICE L310.89
%
%
% LATTICE L310.90
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-626640, -55440, -13440; -55440, 1330, 420; -13440, 420, 127],[1680, 70, 1],[15, 169, 37, 39, 14, 1, -1, -3, 0, 11, 8, 21, 31, 14, 91, 93; -2783, -31360, -6867, -7240, -2601, -186, 186, 560, 1, -2024, -1479, -3888, -5745, -2596, -16878, -17252; 10784, 121520, 26610, 28056, 10080, 721, -720, -2170, -4, 7840, 5730, 15064, 22260, 10059, 65400, 66850],309,90]
%
% END OF LATTICE L310.90
%
%
% LATTICE L310.91
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[840, 0, 0; 0, -6020, -280; 0, -280, -13],[840, 140, 1],[-1, -4, -5, -2, -7, -1, -5, -2, -1, -2, -1, 0, 1, 0, -1, -1; 0, 5, 12, 7, 36, 7, 42, 20, 12, 31, 24, 5, 0, -1, -6, -2; -8, -140, -300, -168, -840, -161, -960, -455, -272, -700, -540, -112, 0, 21, 120, 35],309,91]
%
% END OF LATTICE L310.91
%
%
% LATTICE L310.92
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-44945880, 16276680, -68040; 16276680, -5894420, 24640; -68040, 24640, -103],[840, 140, 1],[3, 16, 25, 12, 53, 19, 55, 51, 15, 38, 29, 6, 1, -1, -1, 3; 6, 29, 42, 19, 78, 26, 72, 64, 18, 43, 30, 5, -6, -2, 0, 8; -548, -3640, -6480, -3388, -16380, -6342, -19140, -18410, -5612, -14840, -12000, -2772, -2100, 182, 660, -70],309,92]
%
% END OF LATTICE L310.92
%
%
% LATTICE L310.93
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[14846160, 5792640, -18480; 5792640, 2260090, -7210; -18480, -7210, 23],[1680, 70, 1],[-1, -5, -1, 1, 7, 2, 7, 15, 5, 29, 13, 7, 5, 0, -1, -3; 6, 28, 6, -4, -30, -8, -27, -56, -18, -100, -42, -20, -6, 2, 9, 20; 1076, 4760, 1080, -448, -3780, -903, -2850, -5530, -1636, -8120, -2760, -672, 2100, 623, 2010, 3850],309,93]
%
% END OF LATTICE L310.93
%
%
% LATTICE L310.94
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[840, 0, 0; 0, -540456, 5040; 0, 5040, -47],[840, 168, 1],[-8, -11, -1, -21, -2, -14, -1, -4, -2, -1, 0, 1, 0, -6, -1, -8; -5, 2, 1, 40, 7, 75, 7, 37, 25, 22, 1, 0, -3, -35, -3, -13; -570, 168, 103, 4200, 742, 7980, 746, 3948, 2670, 2352, 107, 0, -322, -3780, -326, -1428],309,94]
%
% END OF LATTICE L310.94
%
%
% LATTICE L310.95
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2307480, -734160, 9240; -734160, -233310, 2940; 9240, 2940, -37],[840, 210, 1],[1, -2, -1, 1, 5, 51, 17, 241, 22, 140, 47, 45, 18, 41, 6, 35; 0, 1, 0, -1, -2, -16, -5, -68, -6, -37, -12, -11, -4, -8, -1, -4; 249, -420, -250, 168, 1085, 11424, 3835, 54600, 5001, 31920, 10750, 10332, 4165, 9576, 1415, 8400],309,95]
%
% END OF LATTICE L310.95
%
%
% LATTICE L310.96
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2702280, 2116800, 25200; 2116800, -1354710, -16170; 25200, -16170, -193],[840, 210, 1],[5, 11, 1, 0, -3, -7, -3, -13, -1, 1, 1, 4, 7, 15, 7, 37; -538, -1181, -107, 1, 322, 744, 316, 1348, 98, -139, -113, -441, -762, -1624, -756, -3988; 45726, 100380, 9095, -84, -27370, -63252, -26870, -114660, -8346, 11760, 9595, 37464, 64750, 138012, 64250, 338940],309,96]
%
% END OF LATTICE L310.96
%
%
% LATTICE L310.97
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1036175280, 172082400, -599760; 172082400, -28578360, 99600; -599760, 99600, -347],[1680, 120, 1],[423, 473, 671, 223, 123, 97, 526, 164, 249, 103, 1, -31, -27, -1, 146, 124; 2863, 3202, 4543, 1510, 833, 657, 3563, 1111, 1687, 698, 7, -210, -183, -7, 987, 839; 90636, 101520, 144200, 47976, 26500, 20922, 113540, 35430, 53844, 22320, 280, -6696, -5860, -282, 30940, 26490],309,97]
%
% END OF LATTICE L310.97
%
%
% LATTICE L310.98
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[527669520, -88082400, 319200; -88082400, 14703240, -53280; 319200, -53280, 193],[1680, 120, 1],[-151, -95, -57, 3, 17, 22, 148, 55, 95, 47, 1, -19, -25, -30, -204, -79; -1029, -646, -385, 22, 117, 151, 1015, 377, 651, 322, 7, -130, -171, -205, -1393, -539; -34356, -21240, -12040, 1104, 4180, 5298, 35420, 13110, 22596, 11160, 280, -4464, -5860, -6978, -47180, -18150],309,98]
%
% END OF LATTICE L310.98
%
%
% LATTICE L310.99
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1483440, 319200, -5040; 319200, -68520, 1080; -5040, 1080, -17],[1680, 120, 1],[-3, -1, 1, 1, 1, 1, 6, 1, 3, 1, -1, -1, -1, -1, -6, -1; -35, -14, 7, 10, 11, 12, 77, 14, 49, 26, 7, -6, -9, -10, -63, -11; -1344, -600, 140, 336, 400, 462, 3080, 585, 2184, 1320, 700, -96, -280, -342, -2240, -405],309,99]
%
% END OF LATTICE L310.99
%
%
% LATTICE L310.100
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[656880, -126000, -8400; -126000, 23640, 1320; -8400, 1320, -53],[1680, 120, 1],[171, 89, 13, -29, -41, -25, -342, -133, -255, -161, -97, 5, 29, 19, 258, 97; 1015, 528, 77, -172, -243, -148, -2023, -786, -1505, -948, -567, 32, 173, 113, 1533, 576; -1848, -960, -140, 312, 440, 267, 3640, 1410, 2688, 1680, 980, -72, -320, -207, -2800, -1050],309,100]
%
% END OF LATTICE L310.100
%
%
% LATTICE L310.101
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-822360, -611520, 10920; -611520, -285320, 5040; 10920, 5040, -89],[840, 280, 1],[1, 5, 1, -1, -7, -8, -7, -30, -5, -29, -13, -7, -5, 0, 1, 6; -76, -384, -81, 70, 516, 595, 522, 2241, 374, 2172, 975, 526, 378, 1, -75, -453; -4182, -21140, -4470, 3836, 28350, 32704, 28695, 123200, 20562, 119420, 53610, 28924, 20790, 56, -4125, -24920],309,101]
%
% END OF LATTICE L310.101
%
%
% LATTICE L310.102
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[485520, 278880, 90720; 278880, 159096, 51744; 90720, 51744, 16829],[1680, 168, 1],[14, 21, 4, 43, 4, 11, 1, 0, -4, -9, -2, -23, -2, -1, 1, 3; -805, -1184, -219, -2260, -189, -360, 1, 89, 515, 836, 161, 1680, 131, 70, -59, -176; 2400, 3528, 652, 6720, 560, 1050, -8, -273, -1560, -2520, -484, -5040, -392, -210, 176, 525],309,102]
%
% END OF LATTICE L310.102
%
%
% LATTICE L310.103
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1108647120, -256914000, 280560; -256914000, 59536344, -65016; 280560, -65016, 71],[1680, 168, 1],[1, 0, 0, 1, 1, 23, 3, 21, 19, 12, 4, 19, 3, 17, 1, 3; 15, 5, 1, 5, 3, 80, 11, 80, 75, 49, 17, 85, 15, 100, 7, 28; 9780, 4578, 916, 630, -1204, -17640, -1784, -9744, -6420, -2562, -244, 2730, 1876, 24360, 2456, 13776],309,103]
%
% END OF LATTICE L310.103
%
%
% LATTICE L310.104
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[74136720, -18315360, 28560; -18315360, 4524744, -7056; 28560, -7056, 11],[1680, 168, 1],[-14, -6, -1, 1, 2, 23, 2, 9, 4, 0, -1, -11, -4, -43, -4, -21; -45, -19, -3, 5, 7, 80, 7, 32, 15, 1, -3, -35, -13, -140, -13, -68; 7500, 3402, 676, 630, -700, -8400, -704, -2856, -780, 630, 668, 6090, 2044, 21840, 2048, 10920],309,104]
%
% END OF LATTICE L310.104
%
%
% LATTICE L310.105
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[556080, -210000, 26880; -210000, 1848, 0; 26880, 0, -31],[1680, 168, 1],[22, 21, 2, -1, -4, -16, -7, -21, -32, -33, -4, -19, 2, 11, 5, 15; 2485, 2378, 227, -110, -455, -1830, -803, -2416, -3695, -3830, -469, -2310, 213, 1225, 561, 1690; 18960, 18144, 1732, -840, -3472, -13965, -6128, -18438, -28200, -29232, -3580, -17640, 1624, 9345, 4280, 12894],309,105]
%
% END OF LATTICE L310.105
%
%
% LATTICE L310.106
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-169680, -191520, 5040; -191520, -215670, 5670; 5040, 5670, -149],[1680, 210, 1],[9, 8, 1, -1, -3, 5, 7, 67, 15, 28, 11, 25, 27, 43, 17, 77; -22, -21, -3, 2, 10, 4, -6, -84, -22, -45, -19, -46, -54, -92, -38, -180; -528, -525, -80, 42, 280, 336, 20, -840, -312, -735, -340, -882, -1120, -2016, -860, -4200],309,106]
%
% END OF LATTICE L310.106
%
%
% LATTICE L310.107
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-7128240, -194880, 70560; -194880, -2730, 1050; 70560, 1050, -401],[1680, 210, 1],[3, 5, 1, -1, -1, 5, 3, 55, 6, 22, 17, 19, 10, 31, 6, 53; 1559, 2593, 514, -526, -521, 2616, 1567, 28712, 3131, 11477, 8866, 9906, 5211, 16144, 3123, 27568; 4608, 7665, 1520, -1554, -1540, 7728, 4630, 84840, 9252, 33915, 26200, 29274, 15400, 47712, 9230, 81480],309,107]
%
% END OF LATTICE L310.107
%
%
% LATTICE L310.108
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-27792240, -646800, -300720; -646800, -14070, -6510; -300720, -6510, -3011],[1680, 210, 1],[1, -3, -1, 1, 7, 67, 22, 309, 28, 177, 59, 28, 22, 49, 7, 39; -665, 1984, 666, -658, -4629, -44352, -14567, -204632, -18545, -117244, -39086, -18552, -14581, -32488, -4643, -25888; 1338, -3990, -1340, 1323, 9310, 89208, 29300, 411600, 37302, 235830, 78620, 37317, 29330, 65352, 9340, 52080],309,108]
%
% END OF LATTICE L310.108
%
%
% LATTICE L310.109
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-271320, -176400, 8400; -176400, -106260, 5040; 8400, 5040, -239],[840, 420, 1],[1, 2, 1, 0, -3, -7, -9, -31, -11, -17, -11, -5, -7, -3, -1, 1; -38, -68, -32, 1, 98, 219, 278, 949, 334, 512, 328, 147, 198, 77, 18, -61; -768, -1365, -640, 21, 1960, 4368, 5540, 18900, 6648, 10185, 6520, 2919, 3920, 1512, 340, -1260],309,109]
%
% END OF LATTICE L310.109
%
%
% LATTICE L310.110
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-31841880, -4077360, 68880; -4077360, -522060, 8820; 68880, 8820, -149],[840, 420, 1],[-1, 1, 1, 1, -1, -6, -9, -34, -13, -43, -15, -15, -13, -8, -5, -8; 4, 10, 2, 0, -4, -7, -8, -25, -8, -22, -6, -4, 0, 3, 4, 13; -228, 1050, 580, 462, -700, -3192, -4640, -17220, -6492, -21210, -7300, -7182, -6020, -3528, -2080, -2940],309,110]
%
% END OF LATTICE L310.110
%
%
% LATTICE L310.111
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1735440, 3307920, 38640; 3307920, -6239730, -72870; 38640, -72870, -851],[1680, 210, 1],[3, 1, -1, -2, -5, -1, 3, 37, 9, 35, 7, 8, 17, 25, 9, 35; 110, 116, -13, -42, -122, -28, 74, 932, 230, 904, 183, 212, 462, 708, 266, 1108; -9276, -9870, 1070, 3507, 10220, 2352, -6200, -78120, -19284, -75810, -15350, -17787, -38780, -59472, -22360, -93240],309,111]
%
% END OF LATTICE L310.111
%
%
% LATTICE L310.112
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-5404560, -910560, 8400; -910560, -149240, 1400; 8400, 1400, -13],[1680, 280, 1],[4, 3, 1, -1, -4, 5, 16, 47, 10, 18, 41, 15, 46, 23, 26, 37; 15, 11, 3, -4, -15, 20, 63, 184, 39, 70, 159, 58, 177, 88, 99, 140; 4192, 3115, 960, -1078, -4200, 5376, 17100, 50120, 10648, 19145, 43560, 15918, 48720, 24304, 27420, 38920],309,112]
%
% END OF LATTICE L310.112
%
%
% LATTICE L310.113
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1342320, -2142000, 11760; -2142000, -3416840, 18760; 11760, 18760, -103],[1680, 280, 1],[0, -3, -4, -5, -14, -6, -19, -19, -6, -33, -14, -7, -4, 0, 1, 1; -3, -38, -33, -34, -81, -31, -93, -89, -27, -142, -57, -26, -9, 1, 3, -1; -548, -7280, -6480, -6776, -16380, -6342, -19140, -18410, -5612, -29680, -12000, -5544, -2100, 182, 660, -70],309,113]
%
% END OF LATTICE L310.113
%
%
% LATTICE L310.114
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-195473040, -42818160, 235200; -42818160, -9379160, 51520; 235200, 51520, -283],[1680, 280, 1],[1, 5, 1, -1, -7, -4, -14, -15, -5, -29, -13, -7, -5, 0, 2, 3; 1, -12, -21, -28, -81, -35, -111, -111, -35, -192, -81, -40, -21, 1, 9, 9; 1012, 1960, -3000, -5936, -20580, -9702, -31860, -32690, -10532, -59080, -25560, -13104, -7980, 182, 3300, 4130],309,114]
%
% END OF LATTICE L310.114
%
%
% LATTICE L310.115
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[14846160, 4500720, -18480; 4500720, 1362760, -5600; -18480, -5600, 23],[1680, 280, 1],[2, 7, 7, 1, 2, -3, -8, -21, -4, -13, -13, -2, -8, -1, 2, 9; 3, 10, 9, 1, -3, -10, -21, -50, -9, -28, -27, -4, -15, -2, 3, 14; 2336, 8050, 7800, 1043, 840, -4872, -11580, -29120, -5416, -17290, -17040, -2583, -10080, -1288, 2340, 10640],309,115]
%
% END OF LATTICE L310.115
%
%
% LATTICE L310.116
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2702280, -8467200, 25200; -8467200, -7676760, 22680; 25200, 22680, -67],[840, 840, 1],[5, 22, 1, 0, -3, -7, -3, -13, -1, 2, 1, 8, 7, 15, 7, 37; -536, -2357, -107, 1, 322, 750, 321, 1388, 106, -223, -108, -861, -752, -1610, -751, -3968; -179562, -789600, -35845, 336, 107870, 251244, 107530, 464940, 35502, -74760, -36185, -288456, -251930, -539364, -251590, -1329300],309,116]
%
% END OF LATTICE L310.116
%
%
% LATTICE L310.117
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-10421040, -433440, -137760; -433440, -10920, -3360; -137760, -3360, -1031],[1680, 840, 1],[12, 22, 17, 19, 20, 31, 12, 53, 6, 5, 1, -1, -2, 5, 6, 55; -6169, -11307, -8735, -9760, -10269, -15908, -6155, -27168, -3073, -2556, -507, 518, 1027, -2576, -3087, -28284; 18504, 33915, 26200, 29274, 30800, 47712, 18460, 81480, 9216, 7665, 1520, -1554, -3080, 7728, 9260, 84840],309,117]
%
% END OF LATTICE L310.117
%
%
% LATTICE L310.118
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-136857840, -66013920, 142800; -66013920, -31841880, 68880; 142800, 68880, -149],[1680, 840, 1],[2, 5, 1, 0, -2, -7, -4, -25, -4, -11, -3, -2, 0, 3, 2, 13; -1, 1, 1, 1, -1, -12, -9, -68, -13, -43, -15, -15, -13, -16, -5, -16; 1452, 5250, 1420, 462, -2380, -12264, -8000, -55440, -9852, -30450, -9820, -8862, -6020, -4536, -400, 5040],309,118]
%
% END OF LATTICE L310.118
%
%
% LATTICE L310.119
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-57931440, -74526480, 161280; -74526480, -95875080, 207480; 161280, 207480, -449],[1680, 840, 1],[5, 11, 2, 0, -3, -7, -3, -13, -1, 1, 2, 4, 7, 15, 7, 37; -1, 1, 1, 1, -1, -12, -9, -68, -13, -43, -15, -15, -13, -16, -5, -16; 1332, 4410, 1180, 462, -1540, -8064, -5240, -36120, -6372, -19530, -6220, -5502, -3500, -2016, 200, 5880],309,119]
%
% END OF LATTICE L310.119
%
%
% LATTICE L310.120
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2004240, 1001280, -337680; 1001280, 493080, -166320; -337680, -166320, 56101],[1680, 840, 1],[6, 23, 9, 5, 10, 13, 4, 11, 0, -5, -3, -2, -4, -1, 2, 25; 935, 3566, 1385, 762, 1491, 1844, 525, 1112, -97, -1052, -547, -343, -653, -168, 313, 3916; 2808, 10710, 4160, 2289, 4480, 5544, 1580, 3360, -288, -3150, -1640, -1029, -1960, -504, 940, 11760],309,120]
%
% END OF LATTICE L310.120
%

\medskip%
%------------------------------WEYL-GROUP-W311--------------------------------
%
\leavevmode\llap{}%
$W_{311}$%
\qquad\llap{6} lattices, $\chi=36$%
\hfill%
$\slashtwo22|22\slashtwo22|22\rtimes D_{4}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L311.1
%
\leavevmode%
${L_{311.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{1}{}5\above{1pt}{1pt}{-}{}25\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{2}{}7\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${100}\above{1pt}{1pt}{*}{2}{4}\above{1pt}{1pt}{b}{2}{350}\above{1pt}{1pt}{s}{2}{10}\above{1pt}{1pt}{s}{2}{14}\above{1pt}{1pt}{b}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1332100\\-67200\\11200
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-67200\\-3390\\565
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
11200\\565\\-94
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3919\\-82320\\-29400
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
198\\-4159\\-1485
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-32\\672\\239
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
93\\-1970\\-800
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
17\\-362\\-158
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
47\\-1015\\-525
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\19\\-5
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\21\\7
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-1332100, -67200, 11200; -67200, -3390, 565; 11200, 565, -94],[700, 5, 1],[93, 17, 47, -1, -1, 7, 3, 23, 3, 15; -1970, -362, -1015, 19, 21, -130, -58, -455, -61, -315; -800, -158, -525, -5, 7, 50, 8, 0, -10, -112],310,1]
%
% END OF LATTICE L311.1
%
%
% LATTICE L311.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-159775, -10500, 1750; -10500, -690, 115; 1750, 115, -19],[175, 5, 1],[-2, -1, -16, -2, -8, -23, -4, -19, 1, 1; 35, 16, 245, 29, 105, 290, 49, 210, -16, -14; 25, 4, 0, -10, -112, -400, -79, -525, -5, 7],310,2]
%
% END OF LATTICE L311.2
%
%
% LATTICE L311.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[175, 2625, 175; 2625, -29855, -2030; 175, -2030, -138],[175, 35, 1],[-1, 1, 1, 13, 101, 101, 499, 19, 7, -1; 8, 0, -7, -99, -795, -798, -3950, -151, -59, 5; -119, 0, 104, 1470, 11800, 11844, 58625, 2241, 875, -75],310,3]
%
% END OF LATTICE L311.3
%
%
% LATTICE L311.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1051400, -48300, -263900; -48300, 6360, 12080; -263900, 12080, 66239],[700, 20, 1],[-56117, -10815, -68301, -171, -169, -3483, -1105, -15139, -2213, -16519; -2330, -449, -2835, -7, -7, -145, -46, -630, -92, -686; -223150, -43006, -271600, -680, -672, -13850, -4394, -60200, -8800, -65688],310,4]
%
% END OF LATTICE L311.4
%
%
% LATTICE L311.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-140700, 9800, 0; 9800, -70, -35; 0, -35, 2],[700, 35, 1],[-91, -457, -9, -5, -1, 1, 7, 0, -4, -44; -1324, -6650, -131, -73, -15, 14, 100, 0, -58, -640; -23002, -115500, -2274, -1260, -250, 252, 1750, -1, -1015, -11125],310,5]
%
% END OF LATTICE L311.5
%
%
% LATTICE L311.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[417344200, -4846100, -104941900; -4846100, 56280, 1218560; -104941900, 1218560, 26387817],[700, 140, 1],[-21392, -108509, -4363, -2957, -1559, -433, -616, -2, -1408, -20266; 85, 420, 16, 6, 0, 0, 5, 1, 11, 85; -85078, -431550, -17352, -11760, -6200, -1722, -2450, -8, -5600, -80600],310,6]
%
% END OF LATTICE L311.6
%

\medskip%
%------------------------------WEYL-GROUP-W312--------------------------------
%
\leavevmode\llap{}%
$W_{312}$%
\qquad\llap{6} lattices, $\chi=36$%
\hfill%
$\slashtwo22|22\slashtwo22|22\rtimes D_{4}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L312.1
%
\leavevmode%
${L_{312.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{-}{}5\above{1pt}{1pt}{-}{}25\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{2}{}7\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${50}\above{1pt}{1pt}{b}{2}{2}\above{1pt}{1pt}{l}{2}{700}\above{1pt}{1pt}{r}{2}{10}\above{1pt}{1pt}{l}{2}{28}\above{1pt}{1pt}{r}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
169820700\\-3086300\\55300
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3086300\\56090\\-1005
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
55300\\-1005\\18
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
174299\\9795660\\11329500
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3165\\-177874\\-205725
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
55\\3091\\3574
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
28\\1575\\1900
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\169\\218
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
149\\8400\\11200
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\113\\165
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\56\\56
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[169820700, -3086300, 55300; -3086300, 56090, -1005; 55300, -1005, 18],[700, 5, 1],[28, 3, 149, 2, 1, -3, 2, 551, 28, 139; 1575, 169, 8400, 113, 56, -170, 112, 30940, 1573, 7812; 1900, 218, 11200, 165, 56, -275, 107, 34300, 1785, 9044],311,1]
%
% END OF LATTICE L312.1
%
%
% LATTICE L312.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-243425, 16625, 875; 16625, -1135, -60; 875, -60, -3],[175, 5, 1],[-1, -3, 1, 2, 37, 1, 3, -1, -2, -37; -13, -35, 28, 33, 560, 14, 40, -14, -27, -490; -34, -200, -336, -105, -700, 9, 75, -14, -45, -1050],311,2]
%
% END OF LATTICE L312.2
%
%
% LATTICE L312.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-350, -175, 0; -175, -70, 0; 0, 0, 1],[175, 35, 1],[1, 7, 2, 5, 6, 0, -2, 0, 1, 4; -6, -60, -22, -63, -90, -5, 5, 0, -3, -20; -28, -350, -141, -420, -625, -42, 0, 1, 0, -75],311,3]
%
% END OF LATTICE L312.3
%
%
% LATTICE L312.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[149431800, -2494100, -37580200; -2494100, 37640, 627220; -37580200, 627220, 9450943],[700, 20, 1],[-219747, -16917, -143219, 3525, 5331, 352, -26962, -1392546, -266799, -312484; 3170, 244, 2065, -51, -77, -5, 389, 20090, 3849, 4508; -874000, -67284, -569625, 14020, 21203, 1400, -107236, -5538575, -1061140, -1242843],311,4]
%
% END OF LATTICE L312.4
%
%
% LATTICE L312.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-10719100, -30800, -60900; -30800, -70, -175; -60900, -175, -346],[700, 35, 1],[182, 15, 83, 1, -1, -2, 21, 637, 215, 145; -60, -6, -40, -3, 0, 5, -5, -180, -63, -44; -32025, -2639, -14600, -175, 176, 350, -3696, -112100, -37835, -25516],311,5]
%
% END OF LATTICE L312.5
%
%
% LATTICE L312.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1037107400, -125300, -260725500; -125300, 280, 31500; -260725500, 31500, 65545561],[700, 140, 1],[332774, 29156, 44139, 7919, 45, -7919, 35815, 280716, 381907, 64926; 85, 7, 10, 1, 0, 0, 10, 75, 101, 17; 1323700, 115976, 175575, 31500, 179, -31500, 142464, 1116625, 1519140, 258261],311,6]
%
% END OF LATTICE L312.6
%

\medskip%
%------------------------------WEYL-GROUP-W313--------------------------------
%
\leavevmode\llap{}%
$W_{313}$%
\qquad\llap{12} lattices, $\chi=12$%
\hfill%
$22|222|2\rtimes D_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L313.1
%
\leavevmode%
${L_{313.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{1}{}9\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{2}{}7\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${140}\above{1pt}{1pt}{b}{2}{18}\above{1pt}{1pt}{l}{2}{84}\above{1pt}{1pt}{r}{2}{2}\above{1pt}{1pt}{b}{2}{1260}\above{1pt}{1pt}{*}{2}{12}\above{1pt}{1pt}{*}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-7006860\\12600\\3780
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
12600\\-6\\-15
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3780\\-15\\2
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-350\\-700
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\345\\702
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\1036\\2100
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\-1
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-17\\-5880\\-11970
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-346\\-702
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-7006860, 12600, 3780; 12600, -6, -15; 3780, -15, 2],[1260, 3, 1],[-1, 1, 3, 0, -17, -1; -350, 345, 1036, 0, -5880, -346; -700, 702, 2100, -1, -11970, -702],312,1]
%
% END OF LATTICE L313.1
%
%
% LATTICE L313.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-193410, 2205, 315; 2205, 3, -12; 315, -12, 2],[315, 3, 1],[16, 0, -2, -1, 3, 1; 945, 0, -119, -60, 175, 59; 3150, -1, -399, -198, 595, 198],312,2]
%
% END OF LATTICE L313.2
%
%
% LATTICE L313.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[107415, 2520, -1575; 2520, 15, -30; -1575, -30, 22],[315, 15, 1],[1, -1, -8, -2, -4, 1; 14, -15, -119, -30, -63, 14; 91, -90, -735, -185, -378, 90],312,3]
%
% END OF LATTICE L313.3
%
%
% LATTICE L313.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2998170, -191205, 14175; -191205, -12138, 903; 14175, 903, -67],[315, 21, 1],[13, 0, -1, -1, 4, 6; 60, -1, -5, -3, 20, 29; 3555, -14, -279, -252, 1115, 1659],312,4]
%
% END OF LATTICE L313.4
%
%
% LATTICE L313.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[12116167560, -57147300, -3038713020; -57147300, 269544, 14332440; -3038713020, 14332440, 762103757],[1260, 12, 1],[-6127, -1571, -1817, -950, -27334, -787; 0, 0, 7, 5, 105, 1; -24430, -6264, -7245, -3788, -108990, -3138],312,5]
%
% END OF LATTICE L313.5
%
%
% LATTICE L313.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-32645340, 34020, 71820; 34020, -30, -75; 71820, -75, -158],[1260, 15, 1],[11, 2, 15, 1, -1, -1; 168, 28, 196, 9, -14, -10; 4914, 895, 6720, 450, -448, -450],312,6]
%
% END OF LATTICE L313.6
%
%
% LATTICE L313.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-184341780, 94500, 204120; 94500, -42, -105; 204120, -105, -226],[1260, 21, 1],[-1, 1, 3, 3, 13, -1; -50, 45, 148, 150, 660, -46; -880, 882, 2640, 2639, 11430, -882],312,7]
%
% END OF LATTICE L313.7
%
%
% LATTICE L313.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[630, 4095, -630; 4095, 26565, -4095; -630, -4095, 631],[315, 105, 1],[1, -1, -2, -2, 2, 7; 0, 0, -2, -5, -3, -1; 1, 0, -15, -35, -18, 0],312,8]
%
% END OF LATTICE L313.8
%
%
% LATTICE L313.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[3671622360, -5038740, -920845800; -5038740, 7080, 1263720; -920845800, 1263720, 230948857],[1260, 60, 1],[-57166, -14722, -23727, -5011, -783, -1723; 21, 5, 7, 0, 0, 1; -227934, -58700, -94605, -19980, -3122, -6870],312,9]
%
% END OF LATTICE L313.9
%
%
% LATTICE L313.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[17656861320, -66244500, -4428292680; -66244500, 248808, 16613940; -4428292680, 16613940, 1110603731],[1260, 84, 1],[-1101, -13841, -10146, -44360, -122542, -4877; 0, 0, 1, 5, 15, 1; -4390, -55188, -40455, -176876, -488610, -19446],312,10]
%
% END OF LATTICE L313.10
%
%
% LATTICE L313.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-456436260, 330120, 725760; 330120, -210, -525; 725760, -525, -1154],[1260, 105, 1],[-1, 1, 15, 17, 17, -1; -2, -3, 28, 34, 36, 2; -628, 630, 9420, 10675, 10674, -630],312,11]
%
% END OF LATTICE L313.11
%
%
% LATTICE L313.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[39128415480, 41016780, 9782496360; 41016780, 44520, 10253460; 9782496360, 10253460, 2445723079],[1260, 420, 1],[157, 49297, 39956, 175524, 95926, 16485; -471, -147891, -119867, -526567, -287775, -49454; -626, -196560, -159315, -699860, -382482, -65730],312,12]
%
% END OF LATTICE L313.12
%

\medskip%
%------------------------------WEYL-GROUP-W314--------------------------------
%
\leavevmode\llap{}%
$W_{314}$%
\qquad\llap{12} lattices, $\chi=24$%
\hfill%
$22|2222|22\rtimes D_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L314.1
%
\leavevmode%
${L_{314.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{1}{}9\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{2}{}5\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{-2}{}7\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${180}\above{1pt}{1pt}{r}{2}{14}\above{1pt}{1pt}{b}{2}{30}\above{1pt}{1pt}{b}{2}{126}\above{1pt}{1pt}{l}{2}{20}\above{1pt}{1pt}{r}{2}{18}\above{1pt}{1pt}{b}{2}{12}\above{1pt}{1pt}{b}{2}{2}\above{1pt}{1pt}{l}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
764820\\220500\\-1260
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
220500\\63570\\-363
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1260\\-363\\2
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-17\\60\\180
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2\\7\\14
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7\\-25\\-120
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
230\\-819\\-3654
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
191\\-680\\-3020
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
59\\-210\\-927
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
9\\-32\\-138
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\-1
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[764820, 220500, -1260; 220500, 63570, -363; -1260, -363, 2],[1260, 3, 1],[-17, -2, 7, 230, 191, 59, 9, 0; 60, 7, -25, -819, -680, -210, -32, 0; 180, 14, -120, -3654, -3020, -927, -138, -1],313,1]
%
% END OF LATTICE L314.1
%
%
% LATTICE L314.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-1583505, -526365, 6300; -526365, -174966, 2094; 6300, 2094, -25],[315, 3, 1],[192, 461, 13, -9, -34, -1, 9, 119; -595, -1428, -40, 28, 105, 3, -28, -369; -1465, -3465, -75, 77, 225, -1, -78, -927],313,2]
%
% END OF LATTICE L314.2
%
%
% LATTICE L314.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1102185, 185220, -5355; 185220, -31125, 900; -5355, 900, -26],[315, 15, 1],[-2, 1, 1, 11, 0, -4, -2, -2; -9, 7, 5, 21, -3, -30, -11, -10; 99, 35, -33, -1575, -107, -225, 30, 65],313,3]
%
% END OF LATTICE L314.3
%
%
% LATTICE L314.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-334215, -16695, 2520; -16695, -798, 126; 2520, 126, -19],[315, 21, 1],[8, 1, 9, 11, 26, 11, -1, -1; -15, -1, -5, -3, -5, 0, 1, 0; 945, 125, 1155, 1431, 3395, 1449, -126, -133],313,4]
%
% END OF LATTICE L314.4
%
%
% LATTICE L314.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[122877720, -265860, -30791880; -265860, 552, 66624; -30791880, 66624, 7716125],[1260, 12, 1],[79, -941, -1881, -19087, -3362, -3124, 158, 314; 30, -364, -730, -7476, -1320, -1233, 59, 121; 315, -3752, -7500, -76104, -13405, -12456, 630, 1252],313,5]
%
% END OF LATTICE L314.5
%
%
% LATTICE L314.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3887100, 502740, 10080; 502740, -65010, -1305; 10080, -1305, -26],[1260, 15, 1],[11, 1, -2, -73, -9, -7, 5, 4; 72, 7, -13, -483, -60, -48, 32, 26; 648, 35, -123, -4095, -484, -315, 330, 245],313,6]
%
% END OF LATTICE L314.6
%
%
% LATTICE L314.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-285766740, -18385920, 225540; -18385920, -1182930, 14511; 225540, 14511, -178],[1260, 21, 1],[117, 23, 14, 1, 1, -2, -1, 29; -1820, -357, -215, -15, 0, 31, 14, -453; -140, 36, 210, 44, 1260, -7, -126, -189],313,7]
%
% END OF LATTICE L314.7
%
%
% LATTICE L314.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[68670, 7560, -945; 7560, 735, -105; -945, -105, 13],[315, 105, 1],[-4, -5, 1, 1, 2, -1, -3, -17; -1, -3, -1, -1, -3, 0, 1, 0; -308, -405, 63, 65, 126, -70, -210, -1260],313,8]
%
% END OF LATTICE L314.8
%
%
% LATTICE L314.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[863974440, -4713660, -216727560; -4713660, 25800, 1182420; -216727560, 1182420, 54366001],[1260, 60, 1],[-1799, -3757, -313, -85007, -3672, -24062, -2656, -1876; 63, 133, 11, 2919, 126, 825, 91, 65; -7173, -14980, -1248, -338940, -14641, -95940, -10590, -7480],313,9]
%
% END OF LATTICE L314.9
%
%
% LATTICE L314.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[62942040, 298620, -15786540; 298620, 120792, -75264; -15786540, -75264, 3959435],[1260, 84, 1],[-244367, -185539, -99541, -13545, -99146, -2205, -6773, -260197; -2995, -2274, -1220, -166, -1215, -27, -83, -3189; -974365, -739800, -396900, -54008, -395325, -8792, -27006, -1037484],313,10]
%
% END OF LATTICE L314.10
%
%
% LATTICE L314.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-144900, 20160, -12600; 20160, -2730, 1785; -12600, 1785, -1082],[1260, 105, 1],[151, 131, 6, -3, -37, -5, 31, 230; 440, 381, 17, -9, -108, -14, 92, 672; -1036, -900, -42, 20, 252, 35, -210, -1575],313,11]
%
% END OF LATTICE L314.11
%
%
% LATTICE L314.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[43684200, -5363820, 14973840; -5363820, 659400, -1839180; 14973840, -1839180, 5133103],[1260, 420, 1],[-3703, -13081, -821, -411, -742, -456, -1526, -22102; 11094, 39189, 2459, 1231, 2223, 1367, 4573, 66219; 14777, 52200, 3276, 1640, 2961, 1820, 6090, 88200],313,12]
%
% END OF LATTICE L314.12
%

\medskip%
%------------------------------WEYL-GROUP-W315--------------------------------
%
\leavevmode\llap{}%
$W_{315}$%
\qquad\llap{12} lattices, $\chi=24$%
\hfill%
$22|22|22|22|\rtimes D_{4}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L315.1
%
\leavevmode%
${L_{315.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{1}{}3\above{1pt}{1pt}{1}{}9\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{2}{}7\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${84}\above{1pt}{1pt}{r}{2}{10}\above{1pt}{1pt}{b}{2}{12}\above{1pt}{1pt}{b}{2}{90}\above{1pt}{1pt}{l}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-817740\\311220\\-76860
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
311220\\-117618\\28407
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-76860\\28407\\-6362
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
12599\\43680\\42840
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-4605\\-15965\\-15657
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
990\\3432\\3365
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2819\\-9772\\-9576
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-789\\-2735\\-2680
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-371\\-1286\\-1260
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
662\\2295\\2250
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-817740, 311220, -76860; 311220, -117618, 28407; -76860, 28407, -6362],[1260, 3, 1],[-2819, -789, -371, 662, 3239, 864, 401, -437; -9772, -2735, -1286, 2295, 11228, 2995, 1390, -1515; -9576, -2680, -1260, 2250, 11004, 2935, 1362, -1485],314,1]
%
% END OF LATTICE L315.1
%
%
% LATTICE L315.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[631890, 8190, -3465; 8190, 93, -45; -3465, -45, 19],[315, 3, 1],[-4, -3, -1, -1, 4, 3, 1, 1; -7, 0, 1, 0, -7, -5, -2, -15; -756, -550, -180, -180, 714, 535, 177, 135],314,2]
%
% END OF LATTICE L315.2
%
%
% LATTICE L315.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-763245, -7245, 3150; -7245, -30, 30; 3150, 30, -13],[315, 15, 1],[24, 1, -1, -1, 4, 1, 3, 7; -7, 0, 1, 0, -7, -1, -2, -3; 5775, 241, -240, -243, 945, 239, 720, 1683],314,3]
%
% END OF LATTICE L315.3
%
%
% LATTICE L315.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[630, 3150, -315; 3150, 15771, -1575; -315, -1575, 157],[315, 21, 1],[2, 8, 0, -74, -12, -33, -5, -1; -1, -5, -2, -15, -1, 0, 1, 0; -6, -35, -21, -315, -36, -70, 0, 0],314,4]
%
% END OF LATTICE L315.4
%
%
% LATTICE L315.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2242011240, 122692500, -550483920; 122692500, 6714264, -30124848; -550483920, -30124848, 135161029],[1260, 12, 1],[-1931, -1709, -585, -9023, -3879, -2441, -245, -3427; 707, 630, 218, 3360, 1442, 905, 89, 1245; -7707, -6820, -2334, -36000, -15477, -9740, -978, -13680],314,5]
%
% END OF LATTICE L315.5
%
%
% LATTICE L315.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-12525660, -3006360, -1675800; -3006360, -720390, -401985; -1675800, -401985, -224158],[1260, 15, 1],[-1887, -290, 267, 577, 18323, 2051, 907, 10; -4312, -663, 610, 1319, 41888, 4689, 2074, 23; 21840, 3357, -3090, -6679, -212100, -23742, -10500, -116],314,6]
%
% END OF LATTICE L315.6
%
%
% LATTICE L315.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[9667980, -79958340, 11428200; -79958340, 660900198, -94460289; 11428200, -94460289, 13500898],[1260, 21, 1],[343, 663, 321, -314, -315, -628, -307, 419; 15752, 30465, 14758, -14445, -14488, -28885, -14126, 19185; 109920, 212590, 102984, -100800, -101100, -201565, -98574, 133875],314,7]
%
% END OF LATTICE L315.7
%
%
% LATTICE L315.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[123165, 20475, -1890; 20475, 3255, -315; -1890, -315, 29],[315, 105, 1],[-8, -5, -5, -1, 2, 2, 2, -8; -1, 0, 1, 0, -1, -1, -2, -3; -540, -329, -315, -63, 120, 119, 105, -567],314,8]
%
% END OF LATTICE L315.8
%
%
% LATTICE L315.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[564246494280, 3943380420, -141394431780; 3943380420, 27559320, -988171020; -141394431780, -988171020, 35432006297],[1260, 60, 1],[-12179, -983, -1721, -10169, -85989, -41089, -12303, -3855; -490, -45, -79, -421, -3535, -1680, -496, -154; -48615, -3924, -6870, -40592, -343245, -164016, -49110, -15388],314,9]
%
% END OF LATTICE L315.9
%
%
% LATTICE L315.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[55093759204680, -532987699860, -13817717010720; -532987699860, 5156226264, 133675271268; -13817717010720, 133675271268, 3465534139339],[1260, 84, 1],[32717, 118259, -8037, -119767, -1179, 39431, 39575, 592837; -9031, -32660, 2204, 32850, 314, -10925, -10921, -163605; 130797, 472780, -32130, -478800, -4713, 157640, 158214, 2370060],314,10]
%
% END OF LATTICE L315.10
%
%
% LATTICE L315.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3461220, -120960, -35280; -120960, -3990, -1155; -35280, -1155, -334],[1260, 105, 1],[1, 0, -3, -7, -9, -2, -1, 1; -256, -2, 760, 1800, 2324, 519, 274, -249; 780, 7, -2310, -5481, -7080, -1582, -840, 756],314,11]
%
% END OF LATTICE L315.11
%
%
% LATTICE L315.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1093506120, -179737740, 409482360; -179737740, 29543640, -67306260; 409482360, -67306260, 153338039],[1260, 420, 1],[899, 1292, 6372, 33934, 11634, 11241, 6161, 3665; -2698, -3877, -19123, -101847, -34918, -33739, -18493, -11001; -3585, -5152, -25410, -135324, -46395, -44828, -24570, -14616],314,12]
%
% END OF LATTICE L315.12
%

\medskip%
%------------------------------WEYL-GROUP-W316--------------------------------
%
\leavevmode\llap{}%
$W_{316}$%
\qquad\llap{44} lattices, $\chi=96$%
\hfill%
$22222|22222|22222|22222|\rtimes D_{4}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L316.1
%
\leavevmode%
${L_{316.1}}$%
{} : {$1\above{1pt}{1pt}{2}{{\rm II}}4\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{1}{}3\above{1pt}{1pt}{1}{}9\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}7\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${210}\above{1pt}{1pt}{l}{2}{4}\above{1pt}{1pt}{r}{2}{90}\above{1pt}{1pt}{b}{2}{28}\above{1pt}{1pt}{*}{2}{36}\above{1pt}{1pt}{*}{2}{12}\above{1pt}{1pt}{*}{2}{4}\above{1pt}{1pt}{*}{2}{252}\above{1pt}{1pt}{b}{2}{10}\above{1pt}{1pt}{l}{2}{36}\above{1pt}{1pt}{r}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-15499260\\-187740\\12600
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-187740\\-2274\\153
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
12600\\153\\-8
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
306641\\-25032000\\4130280
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3724\\-304001\\50160
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-196\\16000\\-2641
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
653\\-53305\\8820
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
81\\-6612\\1096
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
611\\-49875\\8280
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
419\\-34202\\5684
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
139\\-11346\\1890
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
21\\-1714\\288
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5\\-408\\70
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
17\\-1386\\252
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3\\245\\-40
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-5\\408\\-72
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-15499260, -187740, 12600; -187740, -2274, 153; 12600, 153, -8],[1260, 3, 1],[653, 81, 611, 419, 139, 21, 5, 17, -3, -5, 33, 17, 271, 267, 155, 77, 93, 2041, 297, 299; -53305, -6612, -49875, -34202, -11346, -1714, -408, -1386, 245, 408, -2695, -1388, -22125, -21798, -12654, -6286, -7592, -166614, -24245, -24408; 8820, 1096, 8280, 5684, 1890, 288, 70, 252, -40, -72, 420, 224, 3600, 3556, 2070, 1032, 1250, 27468, 4000, 4032],315,1]
%
% END OF LATTICE L316.1
%
\hbox{}\par\smallskip%
%
% LATTICE L316.2
%
\leavevmode%
${L_{316.2}}$%
{} : {$1\above{1pt}{1pt}{-2}{2}8\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{-}{}9\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{-2}{}7\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${420}\above{1pt}{1pt}{s}{2}{8}\above{1pt}{1pt}{s}{2}{180}\above{1pt}{1pt}{*}{2}{56}\above{1pt}{1pt}{b}{2}{18}\above{1pt}{1pt}{l}{2}{24}\above{1pt}{1pt}{r}{2}{2}\above{1pt}{1pt}{b}{2}{504}\above{1pt}{1pt}{*}{2}{20}\above{1pt}{1pt}{s}{2}{72}\above{1pt}{1pt}{s}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-199080\\20160\\0
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
20160\\-2037\\-3
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\-3\\2
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
44981\\442680\\642600
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-4662\\-45881\\-66600
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
63\\620\\899
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-761\\-7490\\-10920
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-89\\-876\\-1280
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-637\\-6270\\-9180
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-421\\-4144\\-6076
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-64\\-630\\-927
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-13\\-128\\-192
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\-1
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
17\\168\\252
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\10\\20
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-11\\-108\\-144
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-199080, 20160, 0; 20160, -2037, -3; 0, -3, 2],[2520, 3, 1],[-761, -89, -637, -421, -64, -13, 0, 17, 1, -11, -121, -37, -497, -461, -125, -113, -63, -2663, -379, -367; -7490, -876, -6270, -4144, -630, -128, 0, 168, 10, -108, -1190, -364, -4890, -4536, -1230, -1112, -620, -26208, -3730, -3612; -10920, -1280, -9180, -6076, -927, -192, -1, 252, 20, -144, -1680, -520, -7020, -6524, -1773, -1608, -899, -38052, -5420, -5256],315,2]
%
% END OF LATTICE L316.2
%
\hbox{}\par\smallskip%
%
% LATTICE L316.3
%
\leavevmode%
${L_{316.3}}$%
{} : {$1\above{1pt}{1pt}{2}{2}8\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{-}{}9\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{-2}{}7\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{m}%
\EasyButWeakLineBreak%
{${105}\above{1pt}{1pt}{r}{2}{8}\above{1pt}{1pt}{l}{2}{45}\above{1pt}{1pt}{}{2}{56}\above{1pt}{1pt}{r}{2}{18}\above{1pt}{1pt}{b}{2}{24}\above{1pt}{1pt}{b}{2}{2}\above{1pt}{1pt}{l}{2}{504}\above{1pt}{1pt}{}{2}{5}\above{1pt}{1pt}{r}{2}{72}\above{1pt}{1pt}{l}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
68415480\\-204120\\-5040
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-204120\\609\\15
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-5040\\15\\2
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
656501\\219995160\\4019400
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1960\\-656801\\-12000
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
49\\16420\\299
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-289\\-96845\\-1785
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-67\\-22452\\-416
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-238\\-79755\\-1485
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-313\\-104888\\-1960
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-47\\-15750\\-297
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-9\\-3016\\-60
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\-1
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\336\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-335\\-5
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-13\\-4356\\-72
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[68415480, -204120, -5040; -204120, 609, 15; -5040, 15, 2],[2520, 3, 1],[-289, -67, -238, -313, -47, -9, 0, 1, -1, -13, -54, -31, -203, -373, -100, -89, -49, -2059, -146, -281; -96845, -22452, -79755, -104888, -15750, -3016, 0, 336, -335, -4356, -18095, -10388, -68025, -124992, -33510, -29824, -16420, -689976, -48925, -94164; -1785, -416, -1485, -1960, -297, -60, -1, 0, -5, -72, -315, -184, -1215, -2240, -603, -540, -299, -12600, -895, -1728],315,3]
%
% END OF LATTICE L316.3
%
%
% LATTICE L316.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-1394190, 7560, 3465; 7560, -33, -21; 3465, -21, -8],[315, 3, 1],[241, 55, 109, 374, 17, 14, 28, 48, 97, 3, 11, -1, -1, 4, 1, 4, 26, 78, 227, 15; 16730, 3819, 7570, 25977, 1181, 973, 1947, 3339, 6750, 209, 770, -69, -70, 273, 69, 277, 1803, 5411, 15750, 1041; 60270, 13752, 27250, 93492, 4249, 3498, 6993, 11984, 24210, 748, 2730, -252, -250, 1008, 251, 1002, 6507, 19516, 56790, 3752],315,4]
%
% END OF LATTICE L316.4
%
%
% LATTICE L316.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-7375396770, 70924770, -355950; 70924770, -682041, 3423; -355950, 3423, -16],[630, 3, 1],[-8124, -1011, -7648, -5255, -1751, -269, -67, -265, 34, 67, -374, -203, -3278, -3243, -1891, -945, -1147, -25229, -3676, -3709; -844655, -105114, -795165, -546364, -182052, -27968, -6966, -27552, 3535, 6966, -38885, -21106, -340815, -337176, -196608, -98252, -119254, -2623068, -382195, -385626; 30135, 3752, 28395, 19516, 6507, 1002, 251, 1008, -125, -252, 1365, 748, 12105, 11984, 6993, 3498, 4249, 93492, 13625, 13752],315,5]
%
% END OF LATTICE L316.5
%
%
% LATTICE L316.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[1488060, -297360, -1260; -297360, 59421, 252; -1260, 252, 1],[1260, 3, 1],[-761, -89, -637, -421, -64, -13, 0, 17, 1, -11, -121, -37, -497, -461, -125, -113, -63, -2663, -379, -367; -3745, -438, -3135, -2072, -315, -64, 0, 84, 5, -54, -595, -182, -2445, -2268, -615, -556, -310, -13104, -1865, -1806; -14805, -1730, -12375, -8176, -1242, -252, -1, 252, 5, -234, -2415, -730, -9765, -9044, -2448, -2208, -1229, -51912, -7385, -7146],315,6]
%
% END OF LATTICE L316.6
%
%
% LATTICE L316.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2765433510, 478503270, 1379861280; 478503270, 82800516, 238757568; 1379861280, 238757568, 688505851],[630, 6, 1],[-17546639, -1080729, -16229633, -5550304, -3663466, -274620, -145712, -519262, -32661, -15857, -1414989, -273673, -8149603, -3930510, -4462946, -1079782, -2563092, -27923180, -8093751, -4047349; -112840, -6950, -104370, -35693, -23559, -1766, -937, -3339, -210, -102, -9100, -1760, -52410, -25277, -28701, -6944, -16483, -179571, -52050, -26028; 35205030, 2168341, 32562630, 11135957, 7350264, 550989, 292352, 1041831, 65530, 31815, 2838990, 549089, 16351110, 7886053, 8954316, 2166441, 5142508, 56024199, 16239050, 8120475],315,7]
%
% END OF LATTICE L316.7
%
%
% LATTICE L316.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-904995, -71190, 7245; -71190, -5565, 570; 7245, 570, -58],[315, 15, 1],[72, 18, 44, 64, 13, -2, -1, 32, 4, 22, 40, 22, 100, 216, 107, 42, 41, 808, 44, 98; -14, -3, -6, -7, 0, 1, 0, -21, -2, -9, -14, -7, -30, -63, -30, -11, -10, -189, -10, -21; 8841, 2215, 5427, 7910, 1620, -240, -125, 3780, 479, 2655, 4851, 2675, 12177, 26320, 13050, 5130, 5015, 98910, 5389, 12015],315,8]
%
% END OF LATTICE L316.8
%
%
% LATTICE L316.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2520, 5355, -315; 5355, 3927, -252; -315, -252, 16],[315, 21, 1],[-17, -6, -73, -3, -4, 1, 1, 1, -1, -4, -7, -6, -143, -9, -32, -13, -13, -37, -71, -32; -190, -69, -870, -37, -57, 7, 9, 9, -10, -39, -70, -61, -1470, -93, -333, -137, -139, -399, -770, -351; -3375, -1225, -15435, -656, -1008, 126, 161, 162, -175, -693, -1245, -1085, -26145, -1654, -5922, -2436, -2471, -7092, -13685, -6237],315,9]
%
% END OF LATTICE L316.9
%
%
% LATTICE L316.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-37170, -13230, 1260; -13230, -2760, 285; 1260, 285, -29],[630, 15, 1],[13, 15, 35, 153, 77, 31, 31, 619, 17, 77, 29, 15, 19, 57, 13, -1, -1, 11, 1, 13; 266, 308, 720, 3150, 1587, 640, 641, 12810, 352, 1596, 602, 312, 396, 1190, 273, -20, -21, 210, 20, 264; 3171, 3670, 8577, 37520, 18900, 7620, 7630, 152460, 4189, 18990, 7161, 3710, 4707, 14140, 3240, -240, -250, 2520, 239, 3150],315,10]
%
% END OF LATTICE L316.10
%
%
% LATTICE L316.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1503810, -250740, -6930; -250740, 41811, 1155; -6930, 1155, 32],[630, 21, 1],[-107, -343, -341, -335, -107, -89, -181, -45, -323, -21, -7, 1, -1, -7, -7, -25, -161, -69, -703, -93; -545, -1746, -1735, -1704, -544, -452, -918, -228, -1635, -106, -35, 6, -5, -36, -36, -128, -822, -352, -3585, -474; -3525, -11340, -11305, -11124, -3563, -2982, -6111, -1528, -11025, -728, -255, 0, -35, -216, -217, -798, -5229, -2252, -22995, -3052],315,11]
%
% END OF LATTICE L316.11
%
%
% LATTICE L316.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[53296740, -236880, -13382460; -236880, 948, 59472; -13382460, 59472, 3360247],[1260, 12, 1],[-36341, -1721, -19367, -2572, -614, 237, 315, 79, -1259, -2045, -20751, -2357, -54037, -11701, -11620, -2276, -4393, -42898, -23209, -10189; 9485, 447, 4995, 658, 147, -64, -84, -21, 335, 543, 5495, 623, 14265, 3087, 3063, 599, 1154, 11256, 6085, 2667; -144900, -6862, -77220, -10255, -2448, 945, 1256, 315, -5020, -8154, -82740, -9398, -215460, -46655, -46332, -9075, -17516, -171045, -92540, -40626],315,12]
%
% END OF LATTICE L316.12
%
%
% LATTICE L316.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[52423560, 4159260, -13164480; 4159260, 331104, -1044468; -13164480, -1044468, 3305833],[1260, 12, 1],[-601353, -18358, -547091, -186087, -60659, -8663, -2046, -13051, -627, -553, -56143, -5124, -298261, -142661, -80233, -38301, -44918, -973193, -281157, -69893; -9730, -297, -8850, -3010, -981, -140, -33, -210, -10, -9, -910, -83, -4830, -2310, -1299, -620, -727, -15750, -4550, -1131; -2397780, -73199, -2181420, -741986, -241866, -34542, -8158, -52038, -2500, -2205, -223860, -20431, -1189260, -568834, -319914, -152718, -179102, -3880422, -1121060, -278685],315,13]
%
% END OF LATTICE L316.13
%
%
% LATTICE L316.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-26269740, -192780, 39060; -192780, -1380, 285; 39060, 285, -58],[1260, 15, 1],[29, 15, 19, 57, 13, -1, -1, 11, 1, 13, 13, 15, 35, 153, 77, 31, 31, 619, 17, 77; 1204, 624, 792, 2380, 546, -40, -42, 420, 40, 528, 532, 616, 1440, 6300, 3174, 1280, 1282, 25620, 704, 3192; 25431, 13160, 16677, 50050, 11430, -870, -880, 9450, 869, 11340, 11361, 13120, 30627, 133910, 67410, 27150, 27160, 542430, 14899, 67500],315,14]
%
% END OF LATTICE L316.14
%
%
% LATTICE L316.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1496809440, -6027210, 746009460; -6027210, 24270, -3003960; 746009460, -3003960, 371810933],[630, 30, 1],[3223, 1916, 9167, 20284, 20765, 4313, 8945, 91202, 5079, 11818, 9293, 2554, 6925, 11006, 6055, 157, -5, 2668, 285, 1592; -161, -86, -387, -833, -822, -161, -316, -3129, -171, -384, -287, -74, -189, -287, -138, 1, -4, -231, -21, -96; -6468, -3845, -18396, -40705, -41670, -8655, -17950, -183015, -10192, -23715, -18648, -5125, -13896, -22085, -12150, -315, 10, -5355, -572, -3195],315,15]
%
% END OF LATTICE L316.15
%
%
% LATTICE L316.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-74340, -50400, 2520; -50400, -33195, 1545; 2520, 1545, -58],[1260, 15, 1],[-573, -297, -377, -1133, -130, 19, 10, -199, -19, -251, -253, -293, -685, -2997, -755, -609, -305, -12191, -335, -1519; 1204, 624, 792, 2380, 273, -40, -21, 420, 40, 528, 532, 616, 1440, 6300, 1587, 1280, 641, 25620, 704, 3192; 7161, 3710, 4707, 14140, 1620, -240, -125, 2520, 239, 3150, 3171, 3670, 8577, 37520, 9450, 7620, 3815, 152460, 4189, 18990],315,16]
%
% END OF LATTICE L316.16
%
%
% LATTICE L316.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-91980, 17640, 2520; 17640, -1806, -273; 2520, -273, -41],[1260, 21, 1],[-23, -19, -137, -13, -14, -3, 0, 1, 1, -1, -3, -7, -97, -13, -25, -23, -13, -79, -79, -77; 1685, 1394, 10065, 956, 1032, 224, 1, -72, -75, 66, 215, 506, 7035, 944, 1818, 1676, 949, 5772, 5775, 5634; -12660, -10472, -75600, -7180, -7749, -1680, -7, 540, 560, -504, -1620, -3808, -52920, -7100, -13671, -12600, -7133, -43380, -43400, -42336],315,17]
%
% END OF LATTICE L316.17
%
%
% LATTICE L316.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-810180, -34020, -12600; -34020, -1428, -525; -12600, -525, -164],[1260, 21, 1],[-503, -429, -3187, -309, -701, -97, -19, -7, 11, 1, -43, -117, -1727, -237, -937, -449, -527, -1631, -1649, -1639; 12565, 10716, 79605, 7718, 17508, 2422, 474, 174, -275, -24, 1075, 2924, 43155, 5922, 23412, 11218, 13166, 40746, 41195, 40944; -1545, -1316, -9765, -946, -2142, -294, -56, -18, 35, 0, -135, -364, -5355, -734, -2898, -1386, -1624, -5022, -5075, -5040],315,18]
%
% END OF LATTICE L316.18
%
%
% LATTICE L316.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-70288470, 688590, -35026110; 688590, -6468, 343140; -35026110, 343140, -17454191],[630, 42, 1],[-85899, -141139, -285697, -141758, -92118, -39678, -167420, -21316, -312421, -10735, -8089, 157, 3733, 776, -1870, -7316, -114544, -25678, -533471, -36259; -1390, -2283, -4620, -2292, -1489, -641, -2703, -344, -5040, -173, -130, 3, 60, 12, -31, -119, -1857, -416, -8640, -587; 172350, 283185, 573230, 284427, 184828, 79611, 335916, 42769, 626850, 21539, 16230, -315, -7490, -1557, 3752, 14679, 229824, 51521, 1070370, 72751],315,19]
%
% END OF LATTICE L316.19
%
%
% LATTICE L316.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[125055, 121275, 3465; 121275, 162960, 4620; 3465, 4620, 131],[315, 105, 1],[17, 32, 85, 19, 35, 1, 0, 7, 5, 26, 7, 28, 131, 41, 145, 59, 60, 173, 67, 154; 605, 1138, 3021, 675, 1242, 35, 1, 255, 181, 936, 251, 1002, 4683, 1465, 5178, 2105, 2139, 6165, 2387, 5484; -21789, -40985, -108801, -24310, -44730, -1260, -35, -9180, -6517, -33705, -9039, -36085, -168651, -52760, -186480, -75810, -77035, -222030, -85967, -197505],315,20]
%
% END OF LATTICE L316.20
%
%
% LATTICE L316.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[5929560, 2520, -2520; 2520, -15, 0; -2520, 0, 1],[2520, 15, 1],[-6, -29, -3, -211, -5, -9, -10, -37, -4, -3, -1, -1, 0, 1, 0, -1, -5, -33, -5, -7; -910, -4404, -456, -32088, -761, -1372, -1527, -5656, -612, -460, -154, -156, 0, 168, 1, -148, -753, -4984, -756, -1060; -14889, -72000, -7451, -524160, -12425, -22380, -24885, -92120, -9963, -7480, -2499, -2520, -1, 2520, 5, -2460, -12375, -81760, -12393, -17360],315,21]
%
% END OF LATTICE L316.21
%
%
% LATTICE L316.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-148680, 100800, -2520; 100800, -66390, 1545; -2520, 1545, -29],[2520, 15, 1],[573, 1519, 335, 12191, 305, 609, 755, 2997, 685, 293, 253, 251, 19, 199, -10, -19, 130, 1133, 377, 297; 1204, 3192, 704, 25620, 641, 1280, 1587, 6300, 1440, 616, 532, 528, 40, 420, -21, -40, 273, 2380, 792, 624; 14322, 37980, 8378, 304920, 7630, 15240, 18900, 75040, 17154, 7340, 6342, 6300, 478, 5040, -250, -480, 3240, 28280, 9414, 7420],315,22]
%
% END OF LATTICE L316.22
%
%
% LATTICE L316.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-183960, 17640, 2520; 17640, -1407, -210; 2520, -210, -31],[2520, 21, 1],[-3, -1, 1, 1, 0, -3, -14, -13, -137, -19, -23, -77, -79, -79, -13, -23, -25, -13, -97, -7; 100, 24, -40, -36, 1, 112, 507, 468, 4920, 680, 820, 2736, 2800, 2796, 459, 808, 873, 452, 3360, 240; -930, -252, 350, 324, -7, -1008, -4599, -4252, -44730, -6188, -7470, -24948, -25550, -25524, -4193, -7392, -8001, -4148, -30870, -2212],315,23]
%
% END OF LATTICE L316.23
%
%
% LATTICE L316.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[245757960, 10022040, 136080; 10022040, 408723, 5565; 136080, 5565, 86],[2520, 21, 1],[-242, -247, -1, -47, -47, -619, -2486, -2249, -11728, -3209, -1917, -12707, -6476, -12907, -2112, -3699, -3991, -2069, -7703, -1109; 6055, 6180, 25, 1176, 1176, 15488, 62202, 56272, 293445, 80292, 47965, 317940, 162035, 322944, 52844, 92552, 99858, 51768, 192735, 27748; -8895, -9072, -35, -1728, -1729, -22764, -91413, -82696, -431235, -117992, -70485, -467208, -238105, -474552, -77651, -135996, -146727, -76064, -283185, -40768],315,24]
%
% END OF LATTICE L316.24
%
%
% LATTICE L316.25
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2726640, 1171800, 20160; 1171800, -503592, -8664; 20160, -8664, -149],[2520, 24, 1],[632, 40, 614, 213, 145, 6, 7, 19, -2, -4, 12, 6, 214, 109, 131, 17, 85, 947, 278, 142; 1505, 95, 1455, 504, 342, 14, 16, 42, -5, -9, 35, 15, 525, 266, 318, 41, 204, 2268, 665, 339; -2100, -118, -1620, -518, -288, -3, 16, 126, 20, -18, -420, -62, -1620, -742, -792, -87, -376, -3906, -1100, -522],315,25]
%
% END OF LATTICE L316.25
%
%
% LATTICE L316.26
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-5576760, 22680, 12600; 22680, 336, 72; 12600, 72, 7],[2520, 24, 1],[241, 15, 227, 39, 52, 4, 2, 2, -1, -1, 11, 3, 97, 24, 56, 14, 34, 187, 109, 55; -63595, -3958, -59895, -10290, -13719, -1055, -527, -525, 265, 264, -2905, -792, -25605, -6335, -14781, -3695, -8973, -49350, -28765, -14514; 220920, 13750, 208080, 35749, 47664, 3666, 1832, 1827, -920, -918, 10080, 2750, 88920, 22001, 51336, 12834, 31168, 171423, 99920, 50418],315,26]
%
% END OF LATTICE L316.26
%
%
% LATTICE L316.27
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1951110, -772380, 5040; -772380, 305760, -1995; 5040, -1995, 13],[630, 105, 1],[2, 13, 26, 15, 47, 15, 11, 25, 4, 11, 0, -3, -8, -5, -17, -5, -1, 5, 2, 19; 5, 32, 63, 36, 111, 34, 23, 48, 7, 12, -1, -12, -27, -16, -51, -14, -3, 12, 5, 48; -9, -140, -441, -310, -1260, -630, -770, -2430, -497, -2520, -159, -700, -1071, -530, -1260, -210, -70, -90, -7, 0],315,27]
%
% END OF LATTICE L316.27
%
%
% LATTICE L316.28
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[18975393360, -42914340, -4758977160; -42914340, 97080, 10762800; -4758977160, 10762800, 1193538557],[1260, 60, 1],[-148270, -19398, -100526, -154404, -38485, -158, -785, -101912, -9422, -22064, -76010, -20652, -187834, -406296, -201815, -79942, -79315, -1580188, -86698, -98086; -287, -37, -189, -287, -69, 1, -2, -231, -21, -48, -161, -43, -387, -833, -411, -161, -158, -3129, -171, -192; -591192, -77345, -400824, -615650, -153450, -630, -3130, -406350, -37568, -87975, -303072, -82345, -748944, -1620010, -804690, -318750, -316250, -6300630, -345688, -391095],315,28]
%
% END OF LATTICE L316.28
%
%
% LATTICE L316.29
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2648065140, -16033500, -663609240; -16033500, 97080, 4018020; -663609240, 4018020, 166301507],[1260, 60, 1],[-8914, -2456, -6674, -5312, -2935, -79, 5, -1186, -258, -1468, -3014, -1804, -8662, -9598, -9845, -2051, -4265, -43544, -4854, -11312; -1589, -431, -1155, -910, -489, -10, -2, -315, -63, -327, -623, -359, -1689, -1855, -1881, -385, -788, -7980, -885, -2043; -35532, -9790, -26604, -21175, -11700, -315, 20, -4725, -1028, -5850, -12012, -7190, -34524, -38255, -39240, -8175, -17000, -173565, -19348, -45090],315,29]
%
% END OF LATTICE L316.29
%
%
% LATTICE L316.30
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2144169720, 19201140, -537756660; 19201140, 171948, -4815636; -537756660, -4815636, 134869093],[1260, 84, 1],[-15021, -6023, -84709, -1975, -8155, -353, 14, -70, -913, -1675, -3311, -3143, -80279, -2608, -19343, -4230, -9180, -13679, -54083, -25823; 350, 146, 2130, 51, 225, 14, 5, 3, 10, 18, 50, 54, 1470, 49, 375, 86, 195, 297, 1190, 582; -59880, -24010, -337680, -7873, -32508, -1407, 56, -279, -3640, -6678, -13200, -12530, -320040, -10397, -77112, -16863, -36596, -54531, -215600, -102942],315,30]
%
% END OF LATTICE L316.30
%
%
% LATTICE L316.31
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[418320, -835380, -103320; -835380, 1726032, 206220; -103320, 206220, 25519],[1260, 84, 1],[-124261, -26844, -807269, -39465, -91280, -13681, -3451, -2785, 667, 395, -8651, -6384, -388939, -26991, -108088, -52775, -63005, -196583, -399403, -100079; -935, -202, -6075, -297, -687, -103, -26, -21, 5, 3, -65, -48, -2925, -203, -813, -397, -474, -1479, -3005, -753; -495540, -107051, -3219300, -157382, -364014, -54558, -13762, -11106, 2660, 1575, -34500, -25459, -1551060, -107638, -431046, -210462, -251258, -783954, -1592780, -399105],315,31]
%
% END OF LATTICE L316.31
%
%
% LATTICE L316.32
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[3902220, -772380, 10080; -772380, 152880, -1995; 10080, -1995, 26],[1260, 105, 1],[0, 11, 4, 25, 11, 15, 47, 15, 26, 13, 2, 19, 2, 5, -1, -5, -17, -5, -8, -3; -2, 24, 14, 96, 46, 68, 222, 72, 126, 64, 10, 96, 10, 24, -6, -28, -102, -32, -54, -24; -159, -2520, -497, -2430, -770, -630, -1260, -310, -441, -140, -9, 0, -7, -90, -70, -210, -1260, -530, -1071, -700],315,32]
%
% END OF LATTICE L316.32
%
%
% LATTICE L316.33
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3113460, -303030, -1552950; -303030, 12390, -150990; -1552950, -150990, -774589],[630, 210, 1],[2524, 14357, 76994, 25402, 191543, 42443, 91829, 136166, 53646, 127015, 14516, 28243, 76366, 17198, 64057, 157, -6629, -8366, -2526, 785; 19, 108, 579, 191, 1440, 319, 690, 1023, 403, 954, 109, 212, 573, 129, 480, 1, -50, -63, -19, 6; -5064, -28805, -154476, -50965, -384300, -85155, -184240, -273195, -107632, -254835, -29124, -56665, -153216, -34505, -128520, -315, 13300, 16785, 5068, -1575],315,33]
%
% END OF LATTICE L316.33
%
%
% LATTICE L316.34
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[8173620, 2028600, 57960; 2028600, 548835, 15645; 57960, 15645, 446],[1260, 105, 1],[18, 329, 72, 373, 65, 129, 160, 91, 146, 63, 8, 61, 6, 17, 0, 1, 35, 39, 88, 67; 2530, 46248, 10122, 52440, 9139, 18140, 22503, 12800, 20538, 8864, 1126, 8592, 846, 2400, 1, 140, 4917, 5480, 12366, 9416; -91089, -1665090, -364427, -1888020, -329035, -653100, -810180, -460840, -739431, -319130, -40539, -309330, -30457, -86400, -35, -5040, -177030, -197300, -445221, -339010],315,34]
%
% END OF LATTICE L316.34
%
%
% LATTICE L316.35
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[864360, 2520, -249480; 2520, -105, -630; -249480, -630, 71923],[2520, 105, 1],[-97, -721, -2, 103, 10, -601, -3155, -2999, -3191, -4487, -552, -18749, -1945, -19573, -3255, -5889, -6580, -3491, -2650, -2003; -292, -2172, -6, 312, 31, -1804, -9483, -9016, -9594, -13492, -1660, -56388, -5850, -58872, -9791, -17716, -19797, -10504, -7974, -6028; -339, -2520, -7, 360, 35, -2100, -11025, -10480, -11151, -15680, -1929, -65520, -6797, -68400, -11375, -20580, -22995, -12200, -9261, -7000],315,35]
%
% END OF LATTICE L316.35
%
%
% LATTICE L316.36
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-194040, -25200, 7560; -25200, -3255, 945; 7560, 945, -218],[2520, 105, 1],[41, 275, 21, 37, -8, 1, 214, 239, 539, 409, 109, 1975, 429, 2213, 383, 749, 911, 511, 811, 341; -370, -2484, -190, -336, 72, -8, -1926, -2152, -4854, -3684, -982, -17796, -3866, -19944, -3452, -6752, -8214, -4608, -7314, -3076; -186, -1260, -98, -180, 35, 0, -945, -1060, -2394, -1820, -486, -8820, -1918, -9900, -1715, -3360, -4095, -2300, -3654, -1540],315,36]
%
% END OF LATTICE L316.36
%
%
% LATTICE L316.37
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-106349040, -3938760, -1260000; -3938760, -145560, -46560; -1260000, -46560, -14893],[2520, 120, 1],[36, 49, 22, 202, 41, 21, 107, 54, 50, 11, 20, 11, 2, 8, -1, -1, 13, 16, 22, 9; -23597, -32157, -14449, -132720, -26954, -13820, -70488, -35595, -32973, -7261, -13223, -7293, -1331, -5355, 654, 670, -8412, -10430, -14367, -5889; 70728, 96390, 43312, 397845, 80800, 41430, 211320, 106715, 98856, 21770, 39648, 21870, 3992, 16065, -1960, -2010, 25200, 31255, 43056, 17650],315,37]
%
% END OF LATTICE L316.37
%
%
% LATTICE L316.38
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-111429360, 83893320, -2159640; 83893320, -63126120, 1625040; -2159640, 1625040, -41833],[2520, 120, 1],[50, 70, 32, 593, 61, 16, 167, 171, 80, 18, 34, 20, 4, 37, -1, -1, 13, 39, 28, 12; -16331, -22911, -10487, -194460, -20022, -5260, -54984, -56350, -26379, -5943, -11249, -6639, -1333, -12390, 322, 335, -4116, -12600, -9081, -3907; -636972, -893610, -409028, -7584570, -780920, -205155, -2144520, -2197790, -1028844, -231790, -438732, -258930, -51988, -483210, 12560, 13065, -160560, -491470, -354204, -152390],315,38]
%
% END OF LATTICE L316.38
%
%
% LATTICE L316.39
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-45236520, -153720, -30240; -153720, 2352, 840; -30240, 840, 289],[2520, 168, 1],[-7, -5, -1, 1, 4, 4, 26, 2, 67, 3, 3, -1, -11, -4, -8, -6, -38, -3, -103, -5; 5155, 3678, 735, -735, -2939, -2935, -19023, -1460, -48825, -2176, -2135, 852, 8325, 3000, 5959, 4445, 28083, 2215, 76005, 3686; -15720, -11214, -2240, 2241, 8960, 8946, 57960, 4447, 148680, 6622, 6480, -2646, -25480, -9171, -18200, -13566, -85680, -6757, -231840, -11242],315,39]
%
% END OF LATTICE L316.39
%
%
% LATTICE L316.40
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-275438520, -14384160, 151200; -14384160, -751128, 7896; 151200, 7896, -83],[2520, 168, 1],[-3, -1, 1, 1, 1, 0, -11, -3, -67, -5, -13, -23, -49, -25, -17, -4, -37, -5, -77, -3; -10, -6, 0, 3, 5, 2, 15, 1, 0, -2, -10, -24, -60, -33, -25, -7, -75, -11, -180, -8; -6420, -2394, 1820, 2106, 2296, 189, -18648, -5378, -122220, -9310, -24660, -44226, -95060, -48726, -33376, -7959, -74592, -10162, -157500, -6230],315,40]
%
% END OF LATTICE L316.40
%
%
% LATTICE L316.41
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-766080, 699300, -716940; 699300, 49560, 138180; -716940, 138180, -283501],[1260, 420, 1],[14680, 64225, 54252, 137704, 46433, 42922, 96851, 25688, 77860, 7259, 2552, 395, -2556, -8464, -3353, 158, 32389, 17392, 77228, 14281; -43931, -192198, -162353, -412089, -138954, -128447, -289833, -76873, -233001, -21723, -7637, -1182, 7649, 25329, 10034, -473, -96927, -52047, -231111, -42737; -58536, -256095, -216328, -549090, -185150, -171150, -386190, -102430, -310464, -28945, -10176, -1575, 10192, 33750, 13370, -630, -129150, -69350, -307944, -56945],315,41]
%
% END OF LATTICE L316.41
%
%
% LATTICE L316.42
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1053023477940, 10020670380, -271630287180; 10020670380, -95357640, 2584859340; -271630287180, 2584859340, -70067775751],[1260, 420, 1],[9412, 106316, 52560, 72161, 54695, 31148, 174725, 26587, 178960, 42532, 12452, 57664, 13032, 9829, -35, -3818, -10745, 743, 17816, 12128; -28427, -320865, -158569, -217668, -164947, -93904, -526614, -80121, -539253, -128137, -37505, -173625, -39227, -29577, 117, 11489, 32124, -2294, -54135, -36693; -37536, -423990, -209608, -287775, -218120, -124215, -696780, -106025, -713664, -169610, -49656, -229950, -51968, -39195, 140, 15225, 42840, -2965, -71064, -48370],315,42]
%
% END OF LATTICE L316.42
%
%
% LATTICE L316.43
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-115920, 14759640, -52920; 14759640, -1868379240, 6699000; -52920, 6699000, -24019],[2520, 840, 1],[3, 14, 3, 2, -1, -3, -17, -1, -5, 0, 1, 16, 9, 13, 21, 13, 77, 6, 41, 10; -35, -219, -57, -45, 2, 70, 804, 80, 627, 193, 79, 549, 189, 210, 218, 40, -144, -25, -231, -83; -9768, -61110, -15904, -12555, 560, 19530, 224280, 22315, 174888, 53830, 22032, 153090, 52696, 58545, 60760, 11130, -40320, -6985, -64512, -23170],315,43]
%
% END OF LATTICE L316.43
%
%
% LATTICE L316.44
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-7978320, 419018040, -1501920; 419018040, -21992822040, 78830640; -1501920, 78830640, -282559],[2520, 840, 1],[1, 5, 1, 1, -1, -1, -17, -3, -11, -3, -1, -5, -1, -1, 1, 1, 17, 3, 11, 3; -191, -1479, -365, -450, 282, 455, 10884, 2240, 8943, 2853, 1243, 9369, 3521, 8340, 4978, 860, 4896, 390, 525, -223; -53292, -412650, -101836, -125550, 78680, 126945, 3036600, 624950, 2495052, 795970, 346788, 2613870, 982324, 2326770, 1388800, 239925, 1365840, 108790, 146412, -62230],315,44]
%
% END OF LATTICE L316.44
%

\medskip%
%------------------------------WEYL-GROUP-W317--------------------------------
%
\leavevmode\llap{}%
$W_{317}$%
\qquad\llap{32} lattices, $\chi=36$%
\hfill%
$2222|22222|2\rtimes D_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L317.1
%
\leavevmode%
${L_{317.1}}$%
{} : {$[1\above{1pt}{1pt}{1}{}2\above{1pt}{1pt}{1}{}]\above{1pt}{1pt}{}{2}32\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{2}{}5\above{1pt}{1pt}{-}{}$}\EasyButWeakLineBreak%
{${32}\above{1pt}{1pt}{}{2}{3}\above{1pt}{1pt}{r}{2}{160}\above{1pt}{1pt}{*}{2}{4}\above{1pt}{1pt}{*}{2}{40}\above{1pt}{1pt}{l}{2}{1}\above{1pt}{1pt}{r}{2}{160}\above{1pt}{1pt}{*}{2}{12}\above{1pt}{1pt}{s}{2}{32}\above{1pt}{1pt}{l}{2}{2}\above{1pt}{1pt}{}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
222240\\-36960\\-480
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-36960\\6146\\80
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-480\\80\\1
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-55\\-304\\-2016
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-32\\-177\\-1167
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-253\\-1400\\-9200
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-13\\-72\\-470
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-9\\-50\\-320
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\-1
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7\\40\\160
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\6\\6
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3\\-16\\-144
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2\\-11\\-76
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[222240, -36960, -480; -36960, 6146, 80; -480, 80, 1],[480, 2, 1],[-55, -32, -253, -13, -9, 0, 7, 1, -3, -2; -304, -177, -1400, -72, -50, 0, 40, 6, -16, -11; -2016, -1167, -9200, -470, -320, -1, 160, 6, -144, -76],316,1]
%
% END OF LATTICE L317.1
%
\hbox{}\par\smallskip%
%
% LATTICE L317.2
%
\leavevmode%
${L_{317.2}}$%
{} : {$[1\above{1pt}{1pt}{-}{}2\above{1pt}{1pt}{1}{}]\above{1pt}{1pt}{}{2}32\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{2}{}5\above{1pt}{1pt}{-}{}$}\EasyButWeakLineBreak%
{${32}\above{1pt}{1pt}{*}{2}{12}\above{1pt}{1pt}{s}{2}{160}\above{1pt}{1pt}{s}{2}{4}\above{1pt}{1pt}{l}{2}{10}\above{1pt}{1pt}{}{2}{1}\above{1pt}{1pt}{}{2}{160}\above{1pt}{1pt}{}{2}{3}\above{1pt}{1pt}{r}{2}{32}\above{1pt}{1pt}{*}{2}{8}\above{1pt}{1pt}{s}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1011360\\12480\\0
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
12480\\154\\0
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\1
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-85\\6872\\64
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-97\\7842\\66
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-379\\30640\\240
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-19\\1536\\10
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-6\\485\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\-1
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\-80\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\81\\3
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-9\\728\\16
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-7\\566\\8
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[1011360, 12480, 0; 12480, 154, 0; 0, 0, 1],[480, 2, 1],[-85, -97, -379, -19, -6, 0, 1, -1, -9, -7; 6872, 7842, 30640, 1536, 485, 0, -80, 81, 728, 566; 64, 66, 240, 10, 0, -1, 0, 3, 16, 8],316,2]
%
% END OF LATTICE L317.2
%
\hbox{}\par\smallskip%
%
% LATTICE L317.3
%
\leavevmode%
${L_{317.3}}$%
{} : {$1\above{1pt}{1pt}{1}{1}4\above{1pt}{1pt}{1}{1}32\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{2}{}5\above{1pt}{1pt}{1}{}$}\EasyButWeakLineBreak%
{${1}\above{1pt}{1pt}{r}{2}{96}\above{1pt}{1pt}{*}{2}{20}\above{1pt}{1pt}{s}{2}{32}\above{1pt}{1pt}{l}{2}{20}\above{1pt}{1pt}{}{2}{32}\above{1pt}{1pt}{}{2}{5}\above{1pt}{1pt}{r}{2}{96}\above{1pt}{1pt}{*}{2}{4}\above{1pt}{1pt}{l}{2}{4}\above{1pt}{1pt}{}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
206880\\-61920\\-480
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-61920\\18532\\144
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-480\\144\\1
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\-1
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
11\\36\\96
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\10\\10
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-5\\-16\\-80
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-17\\-55\\-220
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-79\\-256\\-992
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-91\\-295\\-1135
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-359\\-1164\\-4464
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-37\\-120\\-458
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-4\\-13\\-48
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[206880, -61920, -480; -61920, 18532, 144; -480, 144, 1],[480, 4, 1],[0, 11, 3, -5, -17, -79, -91, -359, -37, -4; 0, 36, 10, -16, -55, -256, -295, -1164, -120, -13; -1, 96, 10, -80, -220, -992, -1135, -4464, -458, -48],316,3]
%
% END OF LATTICE L317.3
%
\hbox{}\par\smallskip%
%
% LATTICE L317.4
%
\leavevmode%
${L_{317.4}}$%
{} : {$1\above{1pt}{1pt}{-}{5}4\above{1pt}{1pt}{1}{7}32\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{2}{}5\above{1pt}{1pt}{1}{}$}\EasyButWeakLineBreak%
{${4}\above{1pt}{1pt}{s}{2}{96}\above{1pt}{1pt}{s}{2}{20}\above{1pt}{1pt}{*}{2}{32}\above{1pt}{1pt}{*}{2}{80}\above{1pt}{1pt}{s}{2}{32}\above{1pt}{1pt}{l}{2}{5}\above{1pt}{1pt}{}{2}{96}\above{1pt}{1pt}{}{2}{1}\above{1pt}{1pt}{r}{2}{16}\above{1pt}{1pt}{*}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5520480\\221760\\-5280
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
221760\\8908\\-212
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-5280\\-212\\5
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\-26\\-46
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\-24\\48
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3\\80\\230
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-5\\132\\320
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-11\\290\\680
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-15\\396\\944
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-14\\370\\895
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-49\\1296\\3168
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2\\53\\133
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\-26\\-48
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[5520480, 221760, -5280; 221760, 8908, -212; -5280, -212, 5],[480, 4, 1],[1, 1, -3, -5, -11, -15, -14, -49, -2, 1; -26, -24, 80, 132, 290, 396, 370, 1296, 53, -26; -46, 48, 230, 320, 680, 944, 895, 3168, 133, -48],316,4]
%
% END OF LATTICE L317.4
%
%
% LATTICE L317.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-5280, 960, 0; 960, 150, -18; 0, -18, 1],[480, 6, 1],[15, 5, 53, 1, -1, -1, -7, 0, 3, 1; 64, 20, 200, 3, -10, -6, -40, 0, 16, 5; 1392, 458, 4800, 87, -120, -102, -720, -1, 288, 96],316,5]
%
% END OF LATTICE L317.5
%
%
% LATTICE L317.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[480, 0, 0; 0, -6, 0; 0, 0, 1],[480, 6, 1],[-13, -5, -59, -3, -1, 0, 1, 0, -1, -1; 152, 60, 720, 38, 15, 1, 0, 0, 8, 10; 240, 98, 1200, 66, 30, 3, 0, -1, 0, 12],316,6]
%
% END OF LATTICE L317.6
%
%
% LATTICE L317.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[222240, -73920, -480; -73920, 24584, 160; -480, 160, 1],[480, 8, 1],[-3, 1, 7, 0, -9, -13, -253, -64, -55, -4; -8, 3, 20, 0, -25, -36, -700, -177, -152, -11; -144, 6, 160, -1, -320, -470, -9200, -2334, -2016, -152],316,7]
%
% END OF LATTICE L317.7
%
%
% LATTICE L317.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-284640, 56160, -2880; 56160, -11080, 568; -2880, 568, -29],[480, 8, 1],[-31, -17, -129, -6, -2, 1, 11, 1, -3, -3; -184, -102, -780, -37, -15, 5, 60, 6, -16, -17; -544, -321, -2560, -134, -100, -2, 80, 18, -16, -36],316,8]
%
% END OF LATTICE L317.8
%
%
% LATTICE L317.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-98400, 8160, 1920; 8160, -370, -80; 1920, -80, -17],[480, 10, 1],[-29, -17, -27, -7, -1, 0, 1, 1, -1, -1; -3936, -2304, -3656, -946, -134, 1, 136, 132, -144, -137; 15200, 8895, 14112, 3650, 516, -5, -528, -510, 560, 530],316,9]
%
% END OF LATTICE L317.9
%
%
% LATTICE L317.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[5367840, -344640, 13440; -344640, 22130, -860; 13440, -860, 37],[480, 10, 1],[1407, 1703, 1381, 375, 33, 17, 17, -1, 43, 79; 21192, 25650, 20800, 5648, 497, 256, 256, -15, 648, 1190; -18560, -22470, -18224, -4950, -436, -225, -224, 15, -560, -1040],316,10]
%
% END OF LATTICE L317.10
%
%
% LATTICE L317.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-135840, -6720, 1920; -6720, -276, 84; 1920, 84, -25],[480, 12, 1],[-9, -29, -22, -19, -4, -1, 1, 1, 0, -1; -382, -1236, -940, -816, -175, -48, 40, 44, 1, -41; -1986, -6416, -4875, -4224, -900, -240, 210, 224, 3, -216],316,11]
%
% END OF LATTICE L317.11
%
%
% LATTICE L317.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-8160, -1440, 480; -1440, -60, 12; 480, 12, -1],[480, 12, 1],[-3, -9, -13, -5, -1, 1, 1, 1, 0, -1; 158, 472, 680, 260, 50, -52, -50, -48, 1, 54; 414, 1232, 1770, 672, 120, -144, -135, -128, 3, 144],316,12]
%
% END OF LATTICE L317.12
%
%
% LATTICE L317.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[206880, 83040, -480; 83040, 33328, -192; -480, -192, 1],[480, 16, 1],[23, 223, 113, 49, 21, 3, -2, -7, 0, 5; -60, -582, -295, -128, -55, -8, 5, 18, 0, -13; -458, -4464, -2270, -992, -440, -80, 10, 96, -1, -96],316,13]
%
% END OF LATTICE L317.13
%
%
% LATTICE L317.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1151520, -207360, 2400; -207360, 37328, -432; 2400, -432, 5],[480, 16, 1],[0, 1, 1, 1, 2, 3, 3, 11, 1, 0; -1, 6, 10, 12, 25, 36, 35, 126, 11, -1; -86, 48, 390, 560, 1200, 1664, 1575, 5568, 466, -88],316,14]
%
% END OF LATTICE L317.14
%
%
% LATTICE L317.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-751200, -37440, 3840; -37440, -1660, 180; 3840, 180, -19],[480, 20, 1],[-1, 7, 1, 11, 2, 25, 9, 77, 3, -1; -24, 156, 23, 256, 47, 592, 214, 1836, 72, -23; -430, 2880, 419, 4640, 848, 10640, 3838, 32880, 1285, -420],316,15]
%
% END OF LATTICE L317.15
%
%
% LATTICE L317.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[6163680, 209280, -25920; 209280, 7100, -880; -25920, -880, 109],[480, 20, 1],[-1, 1, 1, 7, 3, 21, 4, 71, 3, -1; -4, 0, 2, 12, 2, -12, -5, -120, -8, -10; -270, 240, 254, 1760, 728, 4880, 907, 15840, 645, -320],316,16]
%
% END OF LATTICE L317.16
%
%
% LATTICE L317.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[221280, 480, -480; 480, -24, 0; -480, 0, 1],[480, 24, 1],[-1, 0, 1, 0, -2, -3, -59, -5, -13, -1; -16, 0, 20, 1, -25, -41, -820, -70, -184, -15; -480, -1, 480, 6, -900, -1374, -27120, -2302, -6000, -468],316,17]
%
% END OF LATTICE L317.17
%
%
% LATTICE L317.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-402720, -15360, 1440; -15360, -264, 48; 1440, 48, -5],[480, 24, 1],[7, 1, 1, -1, -2, 1, 61, 6, 19, 3; 52, 7, 0, -8, -15, 8, 480, 47, 148, 23; 2496, 350, 240, -366, -720, 363, 22080, 2170, 6864, 1080],316,18]
%
% END OF LATTICE L317.18
%
%
% LATTICE L317.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-18274080, -228480, 50400; -228480, -2850, 630; 50400, 630, -139],[480, 30, 1],[19, 2, 5, -1, -1, 1, 17, 9, 31, 3; 176, 20, 56, -6, -10, 3, 104, 60, 224, 25; 7680, 815, 2064, -390, -408, 375, 6624, 3530, 12240, 1200],316,19]
%
% END OF LATTICE L317.19
%
%
% LATTICE L317.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3891360, -367200, 24480; -367200, -31710, 2100; 24480, 2100, -139],[480, 30, 1],[31, 4, 13, 0, -1, -3, 1, 3, 19, 7; -4936, -636, -2064, 1, 159, 470, -192, -492, -3064, -1118; -69120, -8905, -28896, 15, 2226, 6570, -2736, -6910, -42960, -15660],316,20]
%
% END OF LATTICE L317.20
%
%
% LATTICE L317.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-23520, 7200, -1440; 7200, 680, -160; -1440, -160, 37],[480, 40, 1],[-29, -34, -27, -7, -1, 0, 1, 1, -1, -2; -2436, -2859, -2272, -590, -85, -1, 80, 81, -84, -167; -11680, -13710, -10896, -2830, -408, -5, 384, 390, -400, -800],316,21]
%
% END OF LATTICE L317.21
%
%
% LATTICE L317.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-12000, -14880, 480; -14880, -15880, 520; 480, 520, -17],[480, 40, 1],[-1, 1, 1, 0, -1, -7, -27, -17, -29, -2; -12, 6, 8, 1, -7, -53, -208, -132, -228, -17; -400, 210, 272, 30, -244, -1830, -7168, -4545, -7840, -580],316,22]
%
% END OF LATTICE L317.22
%
%
% LATTICE L317.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[22560, -5280, 1920; -5280, 1200, -432; 1920, -432, 155],[480, 48, 1],[-9, -29, -44, -19, -8, -1, 1, 1, 0, -2; -188, -604, -915, -394, -165, -22, 15, 16, -1, -43; -414, -1328, -2010, -864, -360, -48, 30, 32, -3, -96],316,23]
%
% END OF LATTICE L317.23
%
%
% LATTICE L317.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[6240, 1440, 0; 1440, 336, 0; 0, 0, -1],[480, 48, 1],[-3, -9, -13, -5, -1, 1, 1, 1, 0, -1; 11, 34, 50, 20, 5, -4, -5, -6, -1, 3; -42, -112, -150, -48, 0, 0, -15, -32, -18, -24],316,24]
%
% END OF LATTICE L317.24
%
%
% LATTICE L317.25
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[284640, 13920, -1440; 13920, 300, -60; -1440, -60, 7],[480, 60, 1],[-2, -7, -1, 3, 1, 9, 1, 3, -1, -2; -16, -60, -10, 16, 7, 64, 7, 20, -8, -15; -555, -2000, -306, 720, 264, 2400, 267, 800, -270, -540],316,25]
%
% END OF LATTICE L317.25
%
%
% LATTICE L317.26
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1184160, -289920, -139200; -289920, 70980, 34080; -139200, 34080, 16363],[480, 60, 1],[1, -1, -1, -5, -1, 1, 1, 9, 2, 3; 278, 880, 264, 556, 42, 4, -6, -40, 1, 70; -570, -1840, -558, -1200, -96, 0, 21, 160, 15, -120],316,26]
%
% END OF LATTICE L317.26
%
%
% LATTICE L317.27
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[228000, 480, -480; 480, -80, 0; -480, 0, 1],[480, 80, 1],[0, 1, 0, -1, -1, -11, -5, -49, -5, -1; 1, 6, 0, -4, -3, -28, -12, -114, -11, -1; 10, 480, -1, -480, -464, -5040, -2282, -22320, -2270, -440],316,27]
%
% END OF LATTICE L317.27
%
%
% LATTICE L317.28
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[6163680, 418560, -25920; 418560, 28400, -1760; -25920, -1760, 109],[480, 80, 1],[3, 71, 8, 21, 3, 7, 1, 1, -1, -1; -4, -60, -5, -6, 1, 6, 1, 0, -2, -5; 645, 15840, 1814, 4880, 728, 1760, 254, 240, -270, -320],316,28]
%
% END OF LATTICE L317.28
%
%
% LATTICE L317.29
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3507360, -667200, 22080; -667200, -126840, 4200; 22080, 4200, -139],[480, 120, 1],[31, 4, 13, 0, -2, -3, 1, 3, 19, 7; 12, 2, 8, 1, -1, -5, -16, -6, -12, 1; 5280, 695, 2304, 30, -348, -630, -336, 290, 2640, 1140],316,29]
%
% END OF LATTICE L317.29
%
%
% LATTICE L317.30
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-103200, 103680, -1920; 103680, 3000, 0; -1920, 0, -1],[480, 120, 1],[19, 4, 5, -1, -1, 1, 17, 9, 31, 6; -648, -137, -172, 34, 35, -31, -556, -297, -1032, -203; -36000, -7610, -9552, 1890, 1944, -1725, -30912, -16510, -57360, -11280],316,30]
%
% END OF LATTICE L317.30
%
%
% LATTICE L317.31
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[69600, -71040, -23040; -71040, 72240, 23520; -23040, 23520, 7627],[480, 240, 1],[-676, -2235, -689, -1537, -146, -163, -1, 55, 11, -120; -11, -38, -12, -28, -3, -4, 0, 2, 1, -1; -2010, -6640, -2046, -4560, -432, -480, -3, 160, 30, -360],316,31]
%
% END OF LATTICE L317.31
%
%
% LATTICE L317.32
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[480, 0, 0; 0, -1680, -480; 0, -480, -137],[480, 240, 1],[-1, -1, 0, 1, 0, -5, -3, -11, -2, -2; -8, -22, -5, 0, 7, 72, 31, 98, 14, 1; 30, 80, 18, 0, -24, -240, -102, -320, -45, 0],316,32]
%
% END OF LATTICE L317.32
%

\medskip%
%------------------------------WEYL-GROUP-W318--------------------------------
%
\leavevmode\llap{}%
$W_{318}$%
\qquad\llap{48} lattices, $\chi=48$%
\hfill%
$22|222|222|222|2\rtimes D_{4}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L318.1
%
\leavevmode%
${L_{318.1}}$%
{} : {$[1\above{1pt}{1pt}{-}{}2\above{1pt}{1pt}{1}{}]\above{1pt}{1pt}{}{6}32\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{1}{}9\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{3}%
\EasyButWeakLineBreak%
{${32}\above{1pt}{1pt}{l}{2}{45}\above{1pt}{1pt}{}{2}{2}\above{1pt}{1pt}{r}{2}{180}\above{1pt}{1pt}{*}{2}{32}\above{1pt}{1pt}{s}{2}{120}\above{1pt}{1pt}{*}{2}{288}\above{1pt}{1pt}{l}{2}{5}\above{1pt}{1pt}{}{2}{18}\above{1pt}{1pt}{r}{2}{20}\above{1pt}{1pt}{*}{2}{288}\above{1pt}{1pt}{s}{2}{120}\above{1pt}{1pt}{*}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1703520\\18720\\1440
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
18720\\102\\-24
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1440\\-24\\-1
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-24\\-880
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\45\\1755
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\23\\878
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
61\\1410\\53550
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
37\\856\\32480
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
73\\1690\\64080
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
115\\2664\\100944
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
11\\255\\9655
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4\\93\\3510
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\70\\2630
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\24\\864
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3\\-70\\-2640
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-1703520, 18720, 1440; 18720, 102, -24; 1440, -24, -1],[1440, 6, 1],[-1, 2, 1, 61, 37, 73, 115, 11, 4, 3, 1, -3; -24, 45, 23, 1410, 856, 1690, 2664, 255, 93, 70, 24, -70; -880, 1755, 878, 53550, 32480, 64080, 100944, 9655, 3510, 2630, 864, -2640],317,1]
%
% END OF LATTICE L318.1
%
\hbox{}\par\smallskip%
%
% LATTICE L318.2
%
\leavevmode%
${L_{318.2}}$%
{} : {$[1\above{1pt}{1pt}{1}{}2\above{1pt}{1pt}{1}{}]\above{1pt}{1pt}{}{6}32\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{1}{}9\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{3}%
\EasyButWeakLineBreak%
{${32}\above{1pt}{1pt}{s}{2}{180}\above{1pt}{1pt}{*}{2}{8}\above{1pt}{1pt}{l}{2}{45}\above{1pt}{1pt}{}{2}{32}\above{1pt}{1pt}{}{2}{30}\above{1pt}{1pt}{r}{2}{288}\above{1pt}{1pt}{s}{2}{20}\above{1pt}{1pt}{*}{2}{72}\above{1pt}{1pt}{l}{2}{5}\above{1pt}{1pt}{}{2}{288}\above{1pt}{1pt}{}{2}{30}\above{1pt}{1pt}{r}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-5418720\\21600\\2880
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
21600\\-6\\-18
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2880\\-18\\-1
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-96\\-1168
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\90\\1170
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\94\\1168
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
17\\1605\\19845
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
21\\1984\\24512
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
21\\1985\\24510
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
67\\6336\\78192
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
13\\1230\\15170
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5\\474\\5832
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\95\\1165
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\96\\1152
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-95\\-1170
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-5418720, 21600, 2880; 21600, -6, -18; 2880, -18, -1],[1440, 6, 1],[-1, 1, 1, 17, 21, 21, 67, 13, 5, 1, 1, -1; -96, 90, 94, 1605, 1984, 1985, 6336, 1230, 474, 95, 96, -95; -1168, 1170, 1168, 19845, 24512, 24510, 78192, 15170, 5832, 1165, 1152, -1170],317,2]
%
% END OF LATTICE L318.2
%
\hbox{}\par\smallskip%
%
% LATTICE L318.3
%
\leavevmode%
${L_{318.3}}$%
{} : {$1\above{1pt}{1pt}{1}{1}4\above{1pt}{1pt}{1}{7}32\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{1}{}3\above{1pt}{1pt}{-}{}9\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{3}%
\EasyButWeakLineBreak%
{${4}\above{1pt}{1pt}{*}{2}{1440}\above{1pt}{1pt}{s}{2}{16}\above{1pt}{1pt}{*}{2}{1440}\above{1pt}{1pt}{l}{2}{1}\above{1pt}{1pt}{}{2}{60}\above{1pt}{1pt}{r}{2}{36}\above{1pt}{1pt}{*}{2}{160}\above{1pt}{1pt}{s}{2}{144}\above{1pt}{1pt}{*}{2}{160}\above{1pt}{1pt}{l}{2}{9}\above{1pt}{1pt}{}{2}{60}\above{1pt}{1pt}{r}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-5916960\\-56160\\12960
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-56160\\204\\60
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
12960\\60\\-23
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-7\\-436\\-5090
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-109\\-6780\\-79200
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3\\-186\\-2176
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-60\\-720
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\62\\725
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
13\\805\\9420
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
13\\804\\9414
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
23\\1420\\16640
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5\\306\\3600
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-13\\-820\\-9520
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-7\\-438\\-5103
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-23\\-1435\\-16740
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-5916960, -56160, 12960; -56160, 204, 60; 12960, 60, -23],[1440, 12, 1],[-7, -109, -3, -1, 1, 13, 13, 23, 5, -13, -7, -23; -436, -6780, -186, -60, 62, 805, 804, 1420, 306, -820, -438, -1435; -5090, -79200, -2176, -720, 725, 9420, 9414, 16640, 3600, -9520, -5103, -16740],317,3]
%
% END OF LATTICE L318.3
%
\hbox{}\par\smallskip%
%
% LATTICE L318.4
%
\leavevmode%
${L_{318.4}}$%
{} : {$1\above{1pt}{1pt}{-}{5}4\above{1pt}{1pt}{1}{1}32\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{1}{}3\above{1pt}{1pt}{-}{}9\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{3}%
\EasyButWeakLineBreak%
{${4}\above{1pt}{1pt}{s}{2}{1440}\above{1pt}{1pt}{l}{2}{4}\above{1pt}{1pt}{}{2}{1440}\above{1pt}{1pt}{}{2}{1}\above{1pt}{1pt}{r}{2}{240}\above{1pt}{1pt}{*}{2}{36}\above{1pt}{1pt}{s}{2}{160}\above{1pt}{1pt}{l}{2}{36}\above{1pt}{1pt}{}{2}{160}\above{1pt}{1pt}{}{2}{9}\above{1pt}{1pt}{r}{2}{240}\above{1pt}{1pt}{*}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1440\\0\\0
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\-156\\-60
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\-60\\-23
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\16\\-50
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-11\\240\\-720
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\3\\-8
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\0\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\-2\\5
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-50\\120
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-24\\54
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3\\-40\\80
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-3\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-7\\40\\-160
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2\\18\\-63
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-9\\110\\-360
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[1440, 0, 0; 0, -156, -60; 0, -60, -23],[1440, 12, 1],[-1, -11, 0, 1, 0, -1, -1, -3, -1, -7, -2, -9; 16, 240, 3, 0, -2, -50, -24, -40, -3, 40, 18, 110; -50, -720, -8, 0, 5, 120, 54, 80, 0, -160, -63, -360],317,4]
%
% END OF LATTICE L318.4
%
%
% LATTICE L318.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-1972320, -4800, 6240; -4800, 2, 12; 6240, 12, -19],[480, 2, 1],[-5, -3, 0, 4, 17, 37, 21, 13, 1, 1, -1, -7; -456, -280, -3, 340, 1464, 3210, 1832, 1140, 89, 90, -88, -630; -1936, -1170, -4, 1515, 6464, 14100, 8016, 4970, 384, 385, -384, -2700],317,5]
%
% END OF LATTICE L318.5
%
%
% LATTICE L318.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[14880, -960, 0; -960, 62, 0; 0, 0, -1],[480, 2, 1],[-3, -3, -1, -1, -1, 1, 3, 3, 1, 1, 1, -1; -48, -50, -18, -25, -48, -15, 16, 30, 14, 15, 16, -15; -16, -30, -20, -75, -256, -240, -240, -130, -12, -5, 0, 0],317,6]
%
% END OF LATTICE L318.6
%
%
% LATTICE L318.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[411360, -2880, -480; -2880, -116, 60; -480, 60, -23],[480, 4, 1],[5, 29, 3, 1, -1, -14, -5, -29, -3, -1, 1, 14; 508, 2940, 302, 60, -106, -1455, -516, -2980, -306, -100, 102, 1425; 1218, 7040, 720, 80, -261, -3540, -1250, -7200, -736, -240, 245, 3420],317,7]
%
% END OF LATTICE L318.7
%
%
% LATTICE L318.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-81395040, 2088960, -24000; 2088960, -53612, 616; -24000, 616, -7],[480, 4, 1],[-3, -89, -14, -381, -79, -577, -35, -291, -5, 1, 3, 7; -116, -3440, -541, -14720, -3052, -22290, -1352, -11240, -193, 40, 116, 270; 77, 2400, 388, 10800, 2254, 16560, 1011, 8480, 156, 80, -78, -240],317,8]
%
% END OF LATTICE L318.8
%
%
% LATTICE L318.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-11040, -1440, 480; -1440, -78, 42; 480, 42, -17],[480, 6, 1],[49, 13, 1, -1, -5, -3, -1, 2, 2, 31, 53, 33; 424, 110, 7, -20, -56, -30, -8, 20, 19, 280, 472, 290; 2352, 615, 42, -90, -288, -160, -48, 105, 102, 1530, 2592, 1600],317,9]
%
% END OF LATTICE L318.9
%
%
% LATTICE L318.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-20640, -480, 0; -480, -6, -6; 0, -6, 7],[480, 6, 1],[1, -1, -1, -2, -5, -1, -1, 1, 1, 2, 5, 1; -16, 60, 46, 90, 224, 45, 48, -40, -42, -80, -192, -35; -48, 30, 36, 75, 192, 40, 48, -30, -36, -75, -192, -40],317,10]
%
% END OF LATTICE L318.10
%
%
% LATTICE L318.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1132320, 12960, -5760; 12960, 136, -64; -5760, -64, 29],[480, 8, 1],[13, 3, 0, -1, -1, 1, 3, 2, 2, 11, 17, 29; 552, 125, -3, -50, -48, 45, 136, 90, 89, 480, 736, 1245; 3776, 865, -8, -310, -304, 300, 896, 595, 592, 3230, 4976, 8460],317,11]
%
% END OF LATTICE L318.11
%
%
% LATTICE L318.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[37920, -2400, 0; -2400, 152, 0; 0, 0, -1],[480, 8, 1],[-17, -11, -2, -4, -3, -1, 1, 1, 0, -6, -13, -29; -288, -185, -33, -65, -48, -15, 16, 15, -1, -105, -224, -495; -256, -150, -20, -30, -16, 0, 0, -10, -12, -130, -240, -480],317,12]
%
% END OF LATTICE L318.12
%
%
% LATTICE L318.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-58080, -23040, 4320; -23040, -8930, 1480; 4320, 1480, -61],[480, 10, 1],[177, -27, -121, -247, -4493, -1771, -4641, -531, -158, -32, 29, 97; -536, 82, 367, 749, 13624, 5370, 14072, 1610, 479, 97, -88, -294; -480, 74, 330, 673, 12240, 4824, 12640, 1446, 430, 87, -80, -264],317,13]
%
% END OF LATTICE L318.13
%
%
% LATTICE L318.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-109920, 6720, 3840; 6720, -410, -240; 3840, -240, -101],[480, 10, 1],[-35, -3, 7, 13, 255, 53, 291, 35, 25, 3, 1, -5; -528, -46, 102, 193, 3792, 789, 4336, 522, 374, 45, 16, -75; -80, -6, 20, 33, 640, 132, 720, 86, 60, 7, 0, -12],317,14]
%
% END OF LATTICE L318.14
%
%
% LATTICE L318.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-225120, -11520, 1920; -11520, -156, 60; 1920, 60, -13],[480, 12, 1],[1, -11, -7, -119, -13, -33, -25, -109, -5, -1, 1, 3; 20, -260, -158, -2660, -290, -735, -556, -2420, -110, -20, 22, 65; 234, -2880, -1776, -30000, -3273, -8300, -6282, -27360, -1248, -240, 249, 740],317,15]
%
% END OF LATTICE L318.15
%
%
% LATTICE L318.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[480, 0, 0; 0, 12, 0; 0, 0, -1],[480, 12, 1],[-1, -9, -1, -21, -2, -9, -3, -11, 0, 1, 0, -1; -6, -40, -3, -40, -3, -10, -2, 0, 1, 0, -1, -10; -30, -240, -24, -480, -45, -200, -66, -240, 0, 0, -3, -40],317,16]
%
% END OF LATTICE L318.16
%
%
% LATTICE L318.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-248160, 16320, -1440; 16320, -1072, 96; -1440, 96, -7],[480, 16, 1],[-21, -103, -8, -27, -1, 1, 1, 3, -2, -73, -9, -151; -298, -1460, -113, -380, -14, 15, 14, 40, -29, -1040, -128, -2145; 206, 1040, 88, 320, 13, 0, -14, -80, 8, 640, 83, 1440],317,17]
%
% END OF LATTICE L318.17
%
%
% LATTICE L318.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[189889440, -13446720, 100320; -13446720, 952208, -7104; 100320, -7104, 53],[480, 16, 1],[0, 3, 2, 47, 11, 89, 12, 57, 4, 13, 1, 1; -1, 40, 31, 760, 179, 1455, 197, 940, 67, 220, 17, 15; -134, -320, 368, 12880, 3166, 26520, 3686, 18080, 1408, 4880, 386, 120],317,18]
%
% END OF LATTICE L318.18
%
%
% LATTICE L318.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-800160, -22560, 2400; -22560, -340, 60; 2400, 60, -7],[480, 20, 1],[9, 13, 11, 17, 7, 8, 7, 3, -3, -1, 1, 4; 102, 148, 126, 196, 81, 93, 82, 36, -34, -12, 11, 45; 3950, 5712, 4840, 7488, 3085, 3528, 3090, 1328, -1320, -448, 435, 1752],317,19]
%
% END OF LATTICE L318.19
%
%
% LATTICE L318.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-157920, -21600, 4800; -21600, -2860, 640; 4800, 640, -143],[480, 20, 1],[1, 7, 6, 35, 37, 55, 17, 29, 3, 1, -1, -1; 25, 184, 161, 952, 1010, 1506, 467, 800, 85, 32, -26, -30; 145, 1056, 920, 5424, 5750, 8568, 2655, 4544, 480, 176, -150, -168],317,20]
%
% END OF LATTICE L318.20
%
%
% LATTICE L318.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3467040, 866880, -7680; 866880, -216744, 1920; -7680, 1920, -17],[480, 24, 1],[49, 13, 2, -1, -5, -3, -1, 2, 4, 31, 53, 33; 212, 55, 7, -10, -28, -15, -4, 10, 19, 140, 236, 145; 1728, 315, -120, -690, -912, -340, 0, 225, 336, 1770, 2640, 1420],317,21]
%
% END OF LATTICE L318.21
%
%
% LATTICE L318.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-22560, -5760, -1440; -5760, -1464, -360; -1440, -360, -83],[480, 24, 1],[1, 7, -4, -152, -317, -231, -401, -257, -46, -98, -83, -19; -4, -35, 19, 745, 1556, 1135, 1972, 1265, 227, 485, 412, 95; 0, 30, -12, -570, -1200, -880, -1536, -990, -180, -390, -336, -80],317,22]
%
% END OF LATTICE L318.22
%
%
% LATTICE L318.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-147360, 18720, -1440; 18720, -2370, 180; -1440, 180, -13],[480, 30, 1],[145, 8, 4, 1, -5, -1, -1, 1, 5, 17, 149, 19; 1384, 76, 37, 8, -56, -10, -8, 10, 49, 164, 1432, 182; 2880, 153, 60, -6, -240, -28, 0, 27, 120, 366, 3120, 388],317,23]
%
% END OF LATTICE L318.23
%
%
% LATTICE L318.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[35040, 19680, -1440; 19680, -5070, 270; -1440, 270, -13],[480, 30, 1],[385, 43, 23, 2, -5, -1, -1, 5, 25, 22, 389, 25; 7344, 820, 438, 38, -96, -19, -16, 96, 478, 420, 7424, 477; 109680, 12246, 6540, 567, -1440, -284, -240, 1434, 7140, 6273, 110880, 7124],317,24]
%
% END OF LATTICE L318.24
%
%
% LATTICE L318.25
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[224160, -74400, 480; -74400, 24680, -160; 480, -160, 1],[480, 40, 1],[51, 3, 4, 1, 1, -1, -3, 0, 2, 5, 47, 19; 120, 7, 9, 2, 0, -3, -8, 0, 5, 12, 112, 45; -4960, -299, -440, -142, -400, 12, 160, -1, -160, -458, -4400, -1812],317,25]
%
% END OF LATTICE L318.25
%
%
% LATTICE L318.26
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-495840, 123840, 29760; 123840, -30920, -7440; 29760, -7440, -1781],[480, 40, 1],[1, 11, 42, 48, 371, 125, 271, 23, -8, -14, -99, -23; 4, 33, 125, 141, 1084, 363, 780, 65, -27, -43, -300, -69; 0, 46, 180, 214, 1680, 576, 1280, 114, -20, -54, -400, -96],317,26]
%
% END OF LATTICE L318.26
%
%
% LATTICE L318.27
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[480, 0, 0; 0, -14352, 432; 0, 432, -13],[480, 48, 1],[-3, -11, 0, 1, 0, -1, -1, -9, -2, -21, -2, -9; -28, -120, -5, 0, 1, 5, 0, -20, -9, -140, -15, -75; -954, -4080, -168, 0, 33, 160, -6, -720, -312, -4800, -513, -2560],317,27]
%
% END OF LATTICE L318.27
%
%
% LATTICE L318.28
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[480, 0, 0; 0, 48, 0; 0, 0, -1],[480, 48, 1],[-1, -9, -2, -21, -4, -9, -3, -11, 0, 1, 0, -1; -3, -20, -3, -20, -3, -5, -1, 0, 1, 0, -1, -5; -30, -240, -48, -480, -90, -200, -66, -240, 0, 0, -6, -40],317,28]
%
% END OF LATTICE L318.28
%
%
% LATTICE L318.29
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[11040, -3360, -480; -3360, 660, 120; -480, 120, 19],[480, 60, 1],[-13, -13, -5, -1, 1, 1, 5, 5, 1, -7, -5, -3; 54, 52, 18, 4, -3, -3, -14, -12, 2, 36, 23, 13; -690, -672, -240, -48, 45, 44, 210, 192, 0, -432, -285, -164],317,29]
%
% END OF LATTICE L318.29
%
%
% LATTICE L318.30
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[820320, 0, -8640; 0, 60, 0; -8640, 0, 91],[480, 60, 1],[51, 37, 0, 1, 3, 7, 25, 39, 19, 75, 35, 31; -2, 0, 1, 0, -1, -2, -6, -8, -3, -8, -3, -2; 4830, 3504, 0, 96, 285, 664, 2370, 3696, 1800, 7104, 3315, 2936],317,30]
%
% END OF LATTICE L318.30
%
%
% LATTICE L318.31
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[283680, 146880, -2880; 146880, 76008, -1488; -2880, -1488, 29],[1440, 24, 1],[3, 11, 1, -8, -15, -38, -73, -17, -11, -4, -19, -2; -8, -30, -3, 15, 32, 85, 168, 40, 27, 10, 48, 5; -112, -450, -56, -45, 128, 540, 1296, 350, 288, 115, 576, 60],317,31]
%
% END OF LATTICE L318.31
%
%
% LATTICE L318.32
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-67315680, -4448160, -120960; -4448160, -293928, -7992; -120960, -7992, -217],[1440, 24, 1],[-1, 23, -2, -388, -275, -609, -1069, -231, -128, -94, -247, -61; 16, -375, 33, 6345, 4496, 9955, 17472, 3775, 2091, 1535, 4032, 995; -32, 990, -100, -17370, -12272, -27120, -47520, -10250, -5652, -4130, -10800, -2640],317,32]
%
% END OF LATTICE L318.32
%
%
% LATTICE L318.33
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-169440, -28800, -960; -28800, 11920, -720; -960, -720, 13],[480, 80, 1],[243, 243, 100, 71, 14, -1, -15, -15, 14, 157, 100, 343; -712, -712, -293, -208, -41, 3, 44, 44, -41, -460, -293, -1005; -21490, -21488, -8840, -6272, -1235, 96, 1330, 1328, -1240, -13888, -8845, -30336],317,33]
%
% END OF LATTICE L318.33
%
%
% LATTICE L318.34
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3245280, 1292160, -8640; 1292160, -514480, 3440; -8640, 3440, -23],[480, 80, 1],[1, 1, 0, -3, -4, -7, -5, -5, -2, -1, 0, 1; 5, 8, 7, 8, 5, 3, -1, -4, -5, -4, -1, 3; 370, 816, 1040, 2304, 2230, 3048, 1710, 1264, 0, -224, -150, 72],317,34]
%
% END OF LATTICE L318.34
%
%
% LATTICE L318.35
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1536480, -25920, 11520; -25920, 330, -90; 11520, -90, 19],[1440, 30, 1],[69, 23, 2, 1, -1, -1, 1, 1, 7, 4, 211, 27; 20424, 6810, 593, 297, -296, -298, 264, 294, 2067, 1183, 62424, 7990; 55120, 18378, 1600, 801, -800, -804, 720, 794, 5580, 3193, 168480, 21564],317,35]
%
% END OF LATTICE L318.35
%
%
% LATTICE L318.36
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1440, -7200, 1440; -7200, -9930, 1890; 1440, 1890, -359],[1440, 30, 1],[149, 25, 9, 5, -1, -1, 1, 1, 29, 17, 451, 29; -2784, -468, -170, -96, 16, 19, 0, -18, -534, -316, -8400, -541; -14080, -2367, -860, -486, 80, 96, 0, -91, -2700, -1598, -42480, -2736],317,36]
%
% END OF LATTICE L318.36
%
%
% LATTICE L318.37
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[480, 0, 0; 0, -9960, 360; 0, 360, -13],[480, 120, 1],[1, 0, -1, -3, -29, -4, -33, -2, -3, -1, -3, 0; 0, 1, 9, 14, 120, 15, 112, 6, 5, 0, -8, -1; 0, 27, 240, 366, 3120, 388, 2880, 153, 120, -6, -240, -28],317,37]
%
% END OF LATTICE L318.37
%
%
% LATTICE L318.38
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[480, 0, 0; 0, -99960, -48840; 0, -48840, -23863],[480, 120, 1],[-29, -3, -1, 0, 1, 0, -3, -1, -3, -4, -33, -4; -5040, -589, -381, -85, 0, 43, 352, 3, -205, -501, -4688, -629; 10320, 1206, 780, 174, 0, -88, -720, -6, 420, 1026, 9600, 1288],317,38]
%
% END OF LATTICE L318.38
%
%
% LATTICE L318.39
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1440, 0, 0; 0, -19632, 672; 0, 672, -23],[1440, 48, 1],[-1, -11, 0, 1, 0, -1, -1, -3, -2, -7, -2, -9; -8, -120, -3, 0, 1, 25, 12, 20, 3, -20, -9, -55; -242, -3600, -88, 0, 29, 720, 342, 560, 72, -640, -279, -1680],317,39]
%
% END OF LATTICE L318.39
%
%
% LATTICE L318.40
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1440, 0, 0; 0, -1776, -384; 0, -384, -83],[1440, 48, 1],[-4, -7, -2, -3, -1, -1, 0, 1, 0, -11, -1, -9; 117, 180, 33, 20, -3, -25, -3, 0, 7, 480, 37, 295; -522, -800, -144, -80, 18, 120, 14, 0, -32, -2160, -166, -1320],317,40]
%
% END OF LATTICE L318.40
%
%
% LATTICE L318.41
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1694880, -59040, -20160; -59040, 1740, 720; -20160, 720, 293],[1440, 60, 1],[1, 3, 13, 7, 17, 3, 1, -1, -3, -13, -3, -1; -288, -948, -4182, -2260, -5496, -971, -324, 324, 974, 4260, 992, 341; 765, 2528, 11160, 6032, 14670, 2592, 865, -864, -2600, -11376, -2650, -912],317,41]
%
% END OF LATTICE L318.41
%
%
% LATTICE L318.42
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[57065760, 172800, -99360; 172800, -780, -300; -99360, -300, 173],[1440, 60, 1],[53, 25, -5, -19, -59, -25, -5, 1, 8, 133, 45, 63; 18, 8, -3, -8, -24, -10, -2, 0, 3, 48, 16, 22; 30465, 14368, -2880, -10928, -33930, -14376, -2875, 576, 4600, 76464, 25870, 36216],317,42]
%
% END OF LATTICE L318.42
%
%
% LATTICE L318.43
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[267360, -60000, 2880; -60000, -219120, -720; 2880, -720, 31],[480, 240, 1],[-967, -829, -173, -1, 34, 34, -1, -139, -311, -967, -518, -518; -28, -24, -5, 0, 1, 1, 0, -4, -9, -28, -15, -15; 89190, 76464, 15960, 96, -3135, -3136, 90, 12816, 28680, 89184, 47775, 47776],317,43]
%
% END OF LATTICE L318.43
%
%
% LATTICE L318.44
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[820320, 0, -8640; 0, 240, 0; -8640, 0, 91],[480, 240, 1],[70, 75, 38, 39, 25, 7, 6, 1, 0, 37, 51, 31; -3, -4, -3, -4, -3, -1, -1, 0, 1, 0, -1, -1; 6630, 7104, 3600, 3696, 2370, 664, 570, 96, 0, 3504, 4830, 2936],317,44]
%
% END OF LATTICE L318.44
%
%
% LATTICE L318.45
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2057760, 1440, -1440; 1440, -120, 0; -1440, 0, 1],[1440, 120, 1],[-1, -1, -1, -2, -11, -4, -29, -1, -1, 0, 1, 0; -4, -6, -7, -15, -84, -31, -228, -8, -9, 0, 12, 1; -1360, -1386, -1400, -2817, -15520, -5652, -41040, -1418, -1440, -1, 1440, 12],317,45]
%
% END OF LATTICE L318.45
%
%
% LATTICE L318.46
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1440, -122400, -2880; -122400, -493320, -11520; -2880, -11520, -269],[1440, 120, 1],[211, 8, 14, 1, 1, -1, -1, 2, 4, 23, 69, 27; -6960, -263, -453, -31, 0, 35, 32, -69, -135, -765, -2288, -893; 295920, 11182, 19260, 1318, 0, -1488, -1360, 2934, 5740, 32526, 97280, 37968],317,46]
%
% END OF LATTICE L318.46
%
%
% LATTICE L318.47
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[57065760, -1935360, -99360; -1935360, -98160, 3360; -99360, 3360, 173],[1440, 240, 1],[-29, 1, 88, 709, 237, 327, 269, 121, -82, -115, -347, -145; 1, 0, -3, -24, -8, -11, -9, -4, 3, 4, 12, 5; -16675, 576, 50600, 407664, 136270, 188016, 154665, 69568, -47160, -66128, -199530, -83376],317,47]
%
% END OF LATTICE L318.47
%
%
% LATTICE L318.48
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-42467040, 1105920, 73440; 1105920, -8880, -1920; 73440, -1920, -127],[1440, 240, 1],[502, 153, 134, 13, -23, -25, -14, 1, 32, 421, 161, 255; 117, 36, 33, 4, -3, -5, -3, 0, 7, 96, 37, 59; 288630, 87968, 77040, 7472, -13230, -14376, -8050, 576, 18400, 242064, 92570, 146616],317,48]
%
% END OF LATTICE L318.48
%

\medskip%
%------------------------------WEYL-GROUP-W319--------------------------------
%
\leavevmode\llap{}%
$W_{319}$%
\qquad\llap{40} lattices, $\chi=48$%
\hfill%
$22|222|222|222|2\rtimes D_{4}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L319.1
%
\leavevmode%
${L_{319.1}}$%
{} : {$[1\above{1pt}{1pt}{1}{}2\above{1pt}{1pt}{-}{}]\above{1pt}{1pt}{}{4}32\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{1}{}$}\EasyButWeakLineBreak%
{${480}\above{1pt}{1pt}{l}{2}{1}\above{1pt}{1pt}{r}{2}{120}\above{1pt}{1pt}{*}{2}{4}\above{1pt}{1pt}{*}{2}{480}\above{1pt}{1pt}{s}{2}{8}\above{1pt}{1pt}{*}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-988559520\\-12201600\\88800
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-12201600\\-150602\\1096
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
88800\\1096\\-7
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-4330241\\350940480\\14901120
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-53448\\4331645\\183924
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
408\\-33066\\-1405
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3179\\257640\\11040
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-113\\9158\\391
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1427\\115650\\4920
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-295\\23908\\1014
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-5249\\425400\\18000
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-205\\16614\\700
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-988559520, -12201600, 88800; -12201600, -150602, 1096; 88800, 1096, -7],[480, 2, 1],[-3179, -113, -1427, -295, -5249, -205, -2261, -23, 67, 23, -191, -67; 257640, 9158, 115650, 23908, 425400, 16614, 183240, 1864, -5430, -1864, 15480, 5430; 11040, 391, 4920, 1014, 18000, 700, 7680, 77, -240, -78, 720, 236],318,1]
%
% END OF LATTICE L319.1
%
\hbox{}\par\smallskip%
%
% LATTICE L319.2
%
\leavevmode%
${L_{319.2}}$%
{} : {$1\above{1pt}{1pt}{1}{7}4\above{1pt}{1pt}{1}{1}32\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{-}{}$}\EasyButWeakLineBreak%
{${15}\above{1pt}{1pt}{r}{2}{32}\above{1pt}{1pt}{s}{2}{240}\above{1pt}{1pt}{*}{2}{32}\above{1pt}{1pt}{*}{2}{60}\above{1pt}{1pt}{l}{2}{4}\above{1pt}{1pt}{}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-348960\\-1440\\-2400
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1440\\4\\-4
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2400\\-4\\-13
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-641\\-86400\\145920
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2\\-271\\456
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-4\\-540\\911
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-135\\225
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-132\\224
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\150\\-240
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\412\\-688
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
13\\1770\\-2970
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\271\\-456
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-348960, -1440, -2400; -1440, 4, -4; -2400, -4, -13],[480, 4, 1],[-1, -1, 1, 3, 13, 2, 11, 9, 19, 5, 7, 0; -135, -132, 150, 412, 1770, 271, 1485, 1212, 2550, 668, 930, -1; 225, 224, -240, -688, -2970, -456, -2505, -2048, -4320, -1136, -1590, 0],318,2]
%
% END OF LATTICE L319.2
%
\hbox{}\par\smallskip%
%
% LATTICE L319.3
%
\leavevmode%
${L_{319.3}}$%
{} : {$[1\above{1pt}{1pt}{1}{}2\above{1pt}{1pt}{1}{}]\above{1pt}{1pt}{}{0}64\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{m}%
\EasyButWeakLineBreak%
{${960}\above{1pt}{1pt}{s}{2}{8}\above{1pt}{1pt}{*}{2}{60}\above{1pt}{1pt}{l}{2}{2}\above{1pt}{1pt}{}{2}{960}\above{1pt}{1pt}{}{2}{1}\above{1pt}{1pt}{r}{2}{960}\above{1pt}{1pt}{*}{2}{8}\above{1pt}{1pt}{l}{2}{15}\above{1pt}{1pt}{}{2}{2}\above{1pt}{1pt}{r}{2}{960}\above{1pt}{1pt}{s}{2}{4}\above{1pt}{1pt}{*}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-7901760\\11520\\20160
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
11520\\-14\\-32
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
20160\\-32\\-49
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
263\\62640\\67200
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
15\\3574\\3832
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
37\\8820\\9450
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
6\\1431\\1532
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
173\\41280\\44160
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\239\\255
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
17\\4080\\4320
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-238\\-256
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-240\\-255
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\237\\256
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
107\\25440\\27360
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5\\1190\\1278
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-7901760, 11520, 20160; 11520, -14, -32; 20160, -32, -49],[960, 2, 1],[263, 15, 37, 6, 173, 1, 17, -1, -1, 1, 107, 5; 62640, 3574, 8820, 1431, 41280, 239, 4080, -238, -240, 237, 25440, 1190; 67200, 3832, 9450, 1532, 44160, 255, 4320, -256, -255, 256, 27360, 1278],318,3]
%
% END OF LATTICE L319.3
%
\hbox{}\par\smallskip%
%
% LATTICE L319.4
%
\leavevmode%
${L_{319.4}}$%
{} : {$1\above{1pt}{1pt}{1}{7}4\above{1pt}{1pt}{1}{7}32\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{-}{}$}\EasyButWeakLineBreak%
{${15}\above{1pt}{1pt}{}{2}{32}\above{1pt}{1pt}{}{2}{60}\above{1pt}{1pt}{r}{2}{32}\above{1pt}{1pt}{s}{2}{60}\above{1pt}{1pt}{*}{2}{16}\above{1pt}{1pt}{l}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
759840\\-47520\\-2880
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-47520\\2972\\180
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2880\\180\\11
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
8059\\122760\\104160
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-507\\-7723\\-6552
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-26\\-396\\-337
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-15\\-15
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\16\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-7\\-105\\-120
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-19\\-288\\-272
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-77\\-1170\\-1050
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-23\\-350\\-304
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[759840, -47520, -2880; -47520, 2972, 180; -2880, 180, 11],[480, 4, 1],[-1, 1, -7, -19, -77, -23, -64, -53, -58, -33, -53, -3; -15, 16, -105, -288, -1170, -350, -975, -808, -885, -504, -810, -46; -15, 0, -120, -272, -1050, -304, -825, -672, -720, -400, -630, -32],318,4]
%
% END OF LATTICE L319.4
%
%
% LATTICE L319.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-517920, 3840, 1920; 3840, -2, -16; 1920, -16, -7],[480, 2, 1],[109, 4, 26, 11, 199, 4, 91, 1, -1, -1, 1, 1; 1680, 62, 405, 172, 3120, 63, 1440, 16, -15, -16, 0, 15; 25920, 951, 6180, 2614, 47280, 950, 21600, 237, -240, -238, 240, 238],318,5]
%
% END OF LATTICE L319.5
%
%
% LATTICE L319.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1638240, -48480, 18240; -48480, -1434, 540; 18240, 540, -203],[480, 6, 1],[79, 8, 16, 19, 109, 6, 41, 1, -1, -1, 11, 3; -1280, -131, -265, -318, -1840, -103, -720, -19, 15, 18, -160, -47; 3680, 369, 730, 858, 4880, 264, 1760, 39, -50, -42, 560, 144],318,6]
%
% END OF LATTICE L319.6
%
%
% LATTICE L319.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-468960, -15360, 6240; -15360, -498, 204; 6240, 204, -83],[480, 6, 1],[47, 5, 21, 13, 77, 9, 33, 1, -1, -1, 3, 3; 360, 37, 150, 90, 520, 58, 200, 5, -10, -6, 40, 26; 4400, 465, 1940, 1194, 7040, 816, 2960, 87, -100, -90, 320, 288],318,7]
%
% END OF LATTICE L319.7
%
%
% LATTICE L319.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[29280, -480, 0; -480, -56, 8; 0, 8, -1],[480, 8, 1],[-41, -2, -8, -1, -11, 0, 1, 0, -2, -1, -29, -2; -2340, -115, -465, -59, -660, -1, 60, 1, -105, -55, -1620, -113; -19680, -966, -3900, -494, -5520, -8, 480, 6, -900, -466, -13680, -952],318,8]
%
% END OF LATTICE L319.8
%
%
% LATTICE L319.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-517920, 7680, 1920; 7680, -8, -32; 1920, -32, -7],[480, 8, 1],[1, -1, -2, 1, 91, 8, 199, 11, 52, 4, 109, 2; 0, -8, -15, 8, 720, 63, 1560, 86, 405, 31, 840, 15; 240, -238, -480, 237, 21600, 1900, 47280, 2614, 12360, 951, 25920, 476],318,9]
%
% END OF LATTICE L319.9
%
%
% LATTICE L319.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-5193120, -199200, 42720; -199200, -7610, 1630; 42720, 1630, -349],[480, 10, 1],[13, -1, -1, 1, 31, 8, 91, 27, 14, 12, 73, 5; -1440, 114, 111, -115, -3504, -901, -10224, -3030, -1569, -1343, -8160, -557; -5136, 410, 396, -415, -12576, -3230, -36624, -10850, -5616, -4805, -29184, -1990],318,10]
%
% END OF LATTICE L319.10
%
%
% LATTICE L319.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2169120, -81600, 18240; -81600, -3010, 670; 18240, 670, -149],[480, 10, 1],[5, -1, -1, 1, 23, 11, 59, 17, 17, 7, 41, 5; -744, 154, 150, -155, -3528, -1682, -9000, -2590, -2586, -1063, -6216, -754; -2736, 570, 552, -575, -13056, -6220, -33264, -9570, -9552, -3925, -22944, -2780],318,11]
%
% END OF LATTICE L319.11
%
%
% LATTICE L319.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[216480, 52800, -1920; 52800, 12876, -468; -1920, -468, 17],[480, 12, 1],[3, 3, 1, -1, -1, -1, -3, -3, -1, 1, 1, 1; -30, -28, -10, 4, 5, 5, 10, 4, -10, -28, -15, -11; -490, -432, -160, 0, 25, 24, -70, -240, -400, -672, -305, -192],318,12]
%
% END OF LATTICE L319.12
%
%
% LATTICE L319.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-70921920, 58560, 115200; 58560, -42, -96; 115200, -96, -187],[960, 6, 1],[173, 31, 27, 14, 143, 3, 27, -1, -1, 1, 57, 9; 13680, 2454, 2140, 1111, 11360, 239, 2160, -78, -80, 77, 4480, 710; 99520, 17832, 15530, 8052, 82240, 1725, 15520, -576, -575, 576, 32800, 5178],318,13]
%
% END OF LATTICE L319.13
%
%
% LATTICE L319.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1161120, 72480, -2880; 72480, -4524, 180; -2880, 180, -7],[480, 12, 1],[13, 13, 3, 1, -1, -3, -3, -1, 2, 11, 6, 9; 190, 192, 45, 16, -15, -46, -50, -24, 25, 152, 85, 130; -490, -432, -80, 0, 25, 48, -70, -240, -200, -672, -305, -384],318,14]
%
% END OF LATTICE L319.14
%
%
% LATTICE L319.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[54240, 3840, 0; 3840, 272, 0; 0, 0, -1],[480, 16, 1],[-11, -9, -19, -5, -7, 0, 1, 1, -1, -3, -13, -4; 150, 122, 255, 66, 90, -1, -15, -14, 15, 42, 180, 55; -105, -96, -240, -80, -150, -16, -15, 0, 0, -16, -90, -32],318,15]
%
% END OF LATTICE L319.15
%
%
% LATTICE L319.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-510240, 36480, -13440; 36480, -2608, 960; -13440, 960, -349],[480, 16, 1],[11, -1, -43, -37, -124, -32, -151, -55, -97, -19, -16, 4; 165, -14, -645, -558, -1875, -485, -2295, -838, -1485, -294, -255, 59; 30, 0, -120, -112, -390, -104, -510, -192, -360, -80, -90, 8],318,16]
%
% END OF LATTICE L319.16
%
%
% LATTICE L319.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[582240, 24480, 10080; 24480, 980, 400; 10080, 400, 163],[480, 20, 1],[1, 7, 5, 11, 5, 2, 1, 1, -1, -3, -1, 0; -138, -1020, -750, -1676, -768, -311, -156, -156, 162, 500, 180, 17; 279, 2080, 1536, 3440, 1578, 640, 321, 320, -336, -1040, -378, -40],318,17]
%
% END OF LATTICE L319.17
%
%
% LATTICE L319.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-139410240, 105600, 210240; 105600, -70, -160; 210240, -160, -317],[960, 10, 1],[155, 47, 25, 22, 137, 5, 29, -1, -1, 1, 47, 13; 7344, 2230, 1188, 1047, 6528, 239, 1392, -46, -48, 45, 2208, 614; 99072, 30040, 15978, 14060, 87552, 3195, 18528, -640, -639, 640, 30048, 8310],318,18]
%
% END OF LATTICE L319.18
%
%
% LATTICE L319.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-244320, -30720, -15360; -30720, -3860, -1920; -15360, -1920, -917],[480, 20, 1],[-71, -245, -38, -49, 5, 37, 10, 1, -23, -195, -127, -159; 636, 2192, 339, 432, -48, -334, -90, -8, 207, 1752, 1140, 1426; -141, -480, -72, -80, 18, 80, 21, 0, -48, -400, -258, -320],318,19]
%
% END OF LATTICE L319.19
%
%
% LATTICE L319.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1025760, -22080, 3360; -22080, -456, 72; 3360, 72, -11],[480, 24, 1],[3, 0, -1, -1, -7, -1, -3, 0, 1, 1, 7, 1; 20, 1, -5, -7, -60, -11, -60, -7, -5, 1, 20, 5; 1040, 6, -340, -354, -2560, -384, -1360, -54, 260, 306, 2240, 336],318,20]
%
% END OF LATTICE L319.20
%
%
% LATTICE L319.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-468960, 78720, 9120; 78720, -12792, -1488; 9120, -1488, -173],[480, 24, 1],[3, -1, -1, 1, 33, 9, 77, 13, 21, 5, 47, 3; -140, 42, 45, -41, -1380, -379, -3260, -552, -895, -214, -2020, -131; 1360, -414, -440, 405, 13600, 3732, 32080, 5430, 8800, 2103, 19840, 1284],318,21]
%
% END OF LATTICE L319.21
%
%
% LATTICE L319.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-19680, -70560, 4800; -70560, -228930, 15600; 4800, 15600, -1063],[480, 30, 1],[67, 32, 12, 67, 73, 18, 21, 1, -1, -1, 15, 15; 1120, 533, 199, 1106, 1200, 293, 336, 13, -17, -14, 256, 253; 16736, 7965, 2974, 16530, 17936, 4380, 5024, 195, -254, -210, 3824, 3780],318,22]
%
% END OF LATTICE L319.22
%
%
% LATTICE L319.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2122080, -459360, 31680; -459360, -97530, 6720; 31680, 6720, -463],[480, 30, 1],[35, 17, 13, 37, 41, 21, 13, 1, -1, -1, 7, 15; -3592, -1747, -1338, -3814, -4232, -2174, -1352, -107, 102, 106, -712, -1534; -49744, -24195, -18532, -52830, -58624, -30120, -18736, -1485, 1412, 1470, -9856, -21240],318,23]
%
% END OF LATTICE L319.23
%
%
% LATTICE L319.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-792480, 145440, -4800; 145440, -26680, 880; -4800, 880, -29],[480, 40, 1],[11, 4, 5, 5, 17, 3, 5, 0, -1, -1, -1, 1; 72, 29, 39, 41, 144, 27, 48, 1, -9, -11, -24, 3; 336, 210, 348, 410, 1536, 320, 624, 30, -108, -170, -576, -80],318,24]
%
% END OF LATTICE L319.24
%
%
% LATTICE L319.25
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-585120, -213600, 13920; -213600, -77960, 5080; 13920, 5080, -331],[480, 40, 1],[5, -1, -1, 1, 23, 11, 59, 17, 17, 7, 41, 5; -48, 6, 9, -5, -144, -73, -408, -120, -123, -52, -312, -41; -528, 50, 96, -35, -1248, -660, -3792, -1130, -1176, -505, -3072, -420],318,25]
%
% END OF LATTICE L319.25
%
%
% LATTICE L319.26
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-293280, 73440, 35520; 73440, -18384, -8880; 35520, -8880, -4267],[480, 48, 1],[241, 211, 77, -1, -12, -22, 39, 125, 203, 337, 152, 190; 1200, 1052, 385, -4, -60, -111, 190, 616, 1005, 1672, 755, 945; -490, -432, -160, 0, 25, 48, -70, -240, -400, -672, -305, -384],318,26]
%
% END OF LATTICE L319.26
%
%
% LATTICE L319.27
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3288480, 822240, -4800; 822240, -205584, 1200; -4800, 1200, -7],[480, 48, 1],[1, -1, -3, -5, -4, -2, -1, 1, 3, 5, 4, 2; 5, -4, -15, -28, -25, -15, -15, -8, 5, 16, 15, 9; 170, 0, -520, -1392, -1570, -1224, -1930, -2112, -1240, -720, -190, 168],318,27]
%
% END OF LATTICE L319.27
%
%
% LATTICE L319.28
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[356640, 281760, -6240; 281760, 222060, -4920; -6240, -4920, 109],[480, 60, 1],[1, -3, -1, 1, 1, 7, 7, 51, 9, 47, 3, 5; 2, -28, -6, 4, 5, 35, 34, 244, 42, 212, 13, 19; 146, -1440, -328, 240, 283, 1980, 1934, 13920, 2408, 12240, 757, 1140],318,28]
%
% END OF LATTICE L319.28
%
%
% LATTICE L319.29
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-896756160, 463680, 927360; 463680, -210, -480; 927360, -480, -959],[960, 30, 1],[137, 127, 23, 62, 131, 15, 31, -1, -1, 1, 37, 33; 2160, 2006, 364, 983, 2080, 239, 496, -14, -16, 13, 576, 518; 131392, 121800, 22058, 59460, 125632, 14385, 29728, -960, -959, 960, 35488, 31650],318,29]
%
% END OF LATTICE L319.29
%
%
% LATTICE L319.30
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[480, 0, 0; 0, -20940, 480; 0, 480, -11],[480, 60, 1],[-1, -3, 0, 1, 0, -1, -1, -9, -1, -13, -1, -5; -2, -16, -1, 0, 1, 14, 6, 40, 3, 24, 1, -2; -94, -720, -44, 0, 43, 600, 254, 1680, 124, 960, 37, -120],318,30]
%
% END OF LATTICE L319.30
%
%
% LATTICE L319.31
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-24375360, 0, 34560; 0, 32, 0; 34560, 0, -49],[960, 32, 1],[1, 0, -17, -8, -28, -15, -37, -14, -53, -6, -7, 1; 0, 1, 0, -3, -15, -10, -30, -13, -60, -9, -15, -2; 705, 0, -12000, -5648, -19770, -10592, -26130, -9888, -37440, -4240, -4950, 704],318,31]
%
% END OF LATTICE L319.31
%
%
% LATTICE L319.32
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-62880, -31680, -7680; -31680, -15920, -3840; -7680, -3840, -917],[480, 80, 1],[-37, -129, -41, -29, 1, 18, 5, 1, -23, -99, -65, -82; 108, 374, 117, 78, -6, -55, -15, -2, 69, 294, 192, 241; -141, -480, -144, -80, 18, 80, 21, 0, -96, -400, -258, -320],318,32]
%
% END OF LATTICE L319.32
%
%
% LATTICE L319.33
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-5280, -2880, -960; -2880, -1520, -480; -960, -480, -137],[480, 80, 1],[-13, -17, -1, 11, 8, 10, 5, 1, -7, -27, -16, -18; 33, 38, -3, -42, -27, -31, -15, -2, 21, 78, 45, 49; -18, 0, 24, 80, 42, 40, 18, 0, -24, -80, -42, -40],318,33]
%
% END OF LATTICE L319.33
%
%
% LATTICE L319.34
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-5818080, -741600, 24480; -741600, -94440, 3120; 24480, 3120, -103],[480, 120, 1],[25, 24, 9, 25, 27, 13, 7, 0, -1, -1, 5, 11; 16, 17, 7, 21, 24, 13, 8, 1, -1, -3, 0, 5; 6416, 6210, 2348, 6570, 7136, 3480, 1904, 30, -268, -330, 1184, 2760],318,34]
%
% END OF LATTICE L319.34
%
%
% LATTICE L319.35
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-19680, 73440, 4800; 73440, -248280, -16200; 4800, -16200, -1057],[480, 120, 1],[41, 37, 13, 17, 35, 15, 7, -1, -1, 1, 13, 21; 656, 596, 211, 278, 576, 251, 120, -14, -17, 13, 200, 331; -9872, -8970, -3176, -4185, -8672, -3780, -1808, 210, 256, -195, -3008, -4980],318,35]
%
% END OF LATTICE L319.35
%
%
% LATTICE L319.36
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-47881920, 0, 56640; 0, 96, 0; 56640, 0, -67],[960, 96, 1],[-7, -6, -3, 2, 3, 5, 1, 0, -7, -8, -8, -11; -10, -13, -20, -9, -5, -2, 0, 1, 0, -3, -5, -10; -5930, -5088, -2560, 1680, 2530, 4224, 845, 0, -5920, -6768, -6770, -9312],318,36]
%
% END OF LATTICE L319.36
%
%
% LATTICE L319.37
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[480, 0, 0; 0, -472560, -234000; 0, -234000, -115871],[480, 240, 1],[-1, -3, 0, 1, 0, -1, -1, -9, -2, -13, -1, -5; 106, 832, 103, 0, -51, -713, -304, -2020, -301, -1188, -48, 119; -214, -1680, -208, 0, 103, 1440, 614, 4080, 608, 2400, 97, -240],318,37]
%
% END OF LATTICE L319.37
%
%
% LATTICE L319.38
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[480, 0, 0; 0, -83760, 960; 0, 960, -11],[480, 240, 1],[-1, -9, -2, -13, -2, -5, -1, -3, 0, 1, 0, -1; 3, 20, 3, 12, 1, -1, -1, -8, -1, 0, 1, 7; 254, 1680, 248, 960, 74, -120, -94, -720, -88, 0, 86, 600],318,38]
%
% END OF LATTICE L319.38
%
%
% LATTICE L319.39
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-4787520, 0, 19200; 0, 160, 0; 19200, 0, -77],[960, 160, 1],[-4, -8, -5, 0, 1, 9, 5, 10, 7, 2, -1, -7; -3, -3, 0, 1, 0, -2, -3, -9, -12, -13, -6, -10; -1002, -2000, -1248, 0, 249, 2240, 1242, 2480, 1728, 480, -258, -1760],318,39]
%
% END OF LATTICE L319.39
%
%
% LATTICE L319.40
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-47117760, 0, 74880; 0, 480, 0; 74880, 0, -119],[960, 480, 1],[7, 50, 17, 42, 5, 13, 0, -8, -3, 0, 1, 29; -1, -9, -4, -13, -2, -10, -1, -3, 0, 1, 0, -2; 4402, 31440, 10688, 26400, 3142, 8160, -2, -5040, -1888, 0, 629, 18240],318,40]
%
% END OF LATTICE L319.40
%

\medskip%
%------------------------------WEYL-GROUP-W320--------------------------------
%
\leavevmode\llap{}%
$W_{320}$%
\qquad\llap{8} lattices, $\chi=48$%
\hfill%
$2|2|2|2|2|2|2|2|2|2|2|2|\rtimes D_{12}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L320.1
%
\leavevmode%
${L_{320.1}}$%
{} : {$1\above{1pt}{1pt}{1}{1}4\above{1pt}{1pt}{1}{1}16\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{1}{}3\above{1pt}{1pt}{-}{}9\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{3}%
\EasyButWeakLineBreak%
{${1}\above{1pt}{1pt}{}{2}{720}\above{1pt}{1pt}{}{2}{4}\above{1pt}{1pt}{}{2}{45}\above{1pt}{1pt}{}{2}{16}\above{1pt}{1pt}{}{2}{180}\above{1pt}{1pt}{r}{2}{4}\above{1pt}{1pt}{s}{2}{720}\above{1pt}{1pt}{l}{2}{4}\above{1pt}{1pt}{r}{2}{180}\above{1pt}{1pt}{s}{2}{16}\above{1pt}{1pt}{l}{2}{180}\above{1pt}{1pt}{}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
769680\\9360\\-1440
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
9360\\-444\\168
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1440\\168\\-59
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\-459\\-1381
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
133\\-20340\\-61200
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
8\\-1223\\-3680
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
32\\-4890\\-14715
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
11\\-1680\\-5056
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
29\\-4425\\-13320
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\-152\\-458
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-7\\1080\\3240
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\153\\460
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\150\\450
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\-460\\-1384
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
34\\-5205\\-15660
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[769680, 9360, -1440; 9360, -444, 168; -1440, 168, -59],[720, 12, 1],[3, 133, 8, 32, 11, 29, 1, -7, -1, -1, 3, 34; -459, -20340, -1223, -4890, -1680, -4425, -152, 1080, 153, 150, -460, -5205; -1381, -61200, -3680, -14715, -5056, -13320, -458, 3240, 460, 450, -1384, -15660],319,1]
%
% END OF LATTICE L320.1
%
%
% LATTICE L320.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-32880, 1680, 480; 1680, -44, -24; 480, -24, -7],[240, 4, 1],[3, 3, -1, -1, 3, 14, 4, 63, 12, 17, 19, 19; -2, 0, 1, 0, -4, -15, -4, -60, -11, -15, -16, -15; 210, 200, -72, -70, 216, 1000, 285, 4480, 852, 1205, 1344, 1340],319,2]
%
% END OF LATTICE L320.2
%
%
% LATTICE L320.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-65822160, 130320, -812160; 130320, -132, 1608; -812160, 1608, -10021],[240, 12, 1],[-207, 67, 69, -191, -201, -1283, -1287, -1154, -816, -4291, -273, -958; -4, 0, 1, 0, -2, -15, -16, -15, -11, -60, -4, -15; 16776, -5430, -5592, 15480, 16290, 103980, 104304, 93525, 66132, 347760, 22125, 77640],319,3]
%
% END OF LATTICE L320.3
%
%
% LATTICE L320.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-821040, 14160, 6960; 14160, -220, -120; 6960, -120, -59],[240, 20, 1],[3, 6, 10, 35, 36, 11, 67, 15, 15, 7, -1, -1; -4, -3, -4, -12, -11, -3, -16, -3, -2, 0, 1, 0; 360, 712, 1185, 4144, 4260, 1301, 7920, 1772, 1770, 824, -120, -118],319,4]
%
% END OF LATTICE L320.4
%
%
% LATTICE L320.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-186480, 2160, 1440; 2160, -12, -24; 1440, -24, -7],[720, 12, 1],[25, 9, 5, 3, -1, -1, 1, 4, 4, 23, 14, 7; 984, 355, 198, 120, -39, -40, 36, 155, 156, 900, 549, 275; 1728, 620, 342, 200, -72, -70, 72, 280, 279, 1600, 972, 485],319,5]
%
% END OF LATTICE L320.5
%
%
% LATTICE L320.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-255120, 13680, -82800; 13680, -660, 4440; -82800, 4440, -26873],[240, 60, 1],[39, -257, -555, -557, -2493, -410, -1344, -1309, -375, -226, -117, 37; 1, 0, -2, -3, -16, -3, -11, -12, -4, -3, -4, 0; -120, 792, 1710, 1716, 7680, 1263, 4140, 4032, 1155, 696, 360, -114],319,6]
%
% END OF LATTICE L320.6
%
%
% LATTICE L320.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-7904880, 43200, 21600; 43200, -60, -120; 21600, -120, -59],[720, 60, 1],[169, 13, 41, 7, -1, -1, 1, 4, 22, 27, 86, 9; 660, 51, 162, 28, -3, -4, 0, 15, 84, 104, 333, 35; 60480, 4652, 14670, 2504, -360, -358, 360, 1432, 7875, 9664, 30780, 3221],319,7]
%
% END OF LATTICE L320.7
%
%
% LATTICE L320.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1992240, 700560, 33840; 700560, -218220, -10560; 33840, -10560, -511],[720, 60, 1],[3, 10, 5, 49, 16, 14, 27, 17, 5, 5, -1, -1; -604, -2001, -999, -9780, -3191, -2790, -5376, -3381, -992, -984, 201, 198; 12680, 42012, 20975, 205344, 67000, 58581, 112880, 70992, 20830, 20664, -4220, -4158],319,8]
%
% END OF LATTICE L320.8
%

\medskip%
%------------------------------WEYL-GROUP-W321--------------------------------
%
\leavevmode\llap{}%
$W_{321}$%
\qquad\llap{12} lattices, $\chi=48$%
\hfill%
$22|222|222|222|2\rtimes D_{4}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L321.1
%
\leavevmode%
${L_{321.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{1}{}9\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{1}{}7\above{1pt}{1pt}{1}{}49\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{23,3,2}%
\EasyButWeakLineBreak%
{${1764}\above{1pt}{1pt}{r}{2}{2}\above{1pt}{1pt}{b}{2}{252}\above{1pt}{1pt}{b}{2}{98}\above{1pt}{1pt}{l}{2}{36}\above{1pt}{1pt}{r}{2}{14}\above{1pt}{1pt}{l}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-82908\\24696\\-1764
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
24696\\-6846\\483
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1764\\483\\-34
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
503\\11844\\142884
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-142\\-3338\\-40257
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
10\\235\\2834
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-65\\-1596\\-19404
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-25\\-305
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-30\\-378
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\21\\245
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\24\\288
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\1\\14
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-82908, 24696, -1764; 24696, -6846, 483; -1764, 483, -34],[1764, 21, 1],[-65, -1, -1, 1, 1, 0, -103, -3, -23, -29, -25, -2; -1596, -25, -30, 21, 24, 1, -2352, -69, -534, -679, -588, -48; -19404, -305, -378, 245, 288, 14, -28224, -829, -6426, -8183, -7092, -581],320,1]
%
% END OF LATTICE L321.1
%
%
% LATTICE L321.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[26166, -3381, 882; -3381, 399, -98; 882, -98, 23],[147, 7, 1],[1, 15, 4, 5, 37, 3, 1, -1, -2, -3, -23, -2; 10, 231, 71, 93, 700, 60, 20, -21, -41, -63, -490, -45; -5, 343, 140, 197, 1519, 140, 47, -49, -98, -155, -1225, -119],320,2]
%
% END OF LATTICE L321.2
%
%
% LATTICE L321.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[476868, -67032, -2940; -67032, 9422, 413; -2940, 413, 18],[588, 7, 1],[-137, -7, -5, -1, 1, 1, -143, -13, -35, -139, -41, -11; -1036, -53, -38, -7, 8, 8, -1064, -97, -262, -1043, -308, -83; 1372, 72, 56, 0, -20, -21, 980, 96, 280, 1176, 356, 105],320,3]
%
% END OF LATTICE L321.3
%
%
% LATTICE L321.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-18081, 1323, 0; 1323, 210, -84; 0, -84, 23],[441, 21, 1],[-76, -3, -5, -1, 2, 2, 34, 1, -1, -13, -8, -3; -1071, -42, -69, -14, 27, 27, 399, 10, -27, -210, -123, -43; -3969, -155, -252, -49, 99, 98, 1323, 29, -126, -833, -477, -161],320,4]
%
% END OF LATTICE L321.4
%
%
% LATTICE L321.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[6099030, -391755, 1988763; -391755, 25158, -127743; 1988763, -127743, 648493],[147, 21, 1],[4149, 29599, 4098, 3389, 20229, 302, -3, -577, 48, 757, 8793, 1771; 157, 1120, 155, 128, 763, 11, -1, -28, 1, 28, 329, 67; -12693, -90552, -12537, -10368, -61887, -924, 9, 1764, -147, -2316, -26901, -5418],320,5]
%
% END OF LATTICE L321.5
%
%
% LATTICE L321.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[882, 1764, 441; 1764, 3297, 798; 441, 798, 190],[441, 21, 1],[-24, -11, -3, -1, 2, 17, 94, 41, 13, 211, 8, -2; 63, 24, 5, 0, -3, -24, -91, -36, -9, -84, -1, 18; -196, -72, -14, 0, 8, 63, 196, 72, 14, 0, -8, -63],320,6]
%
% END OF LATTICE L321.6
%
%
% LATTICE L321.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[5292, 5880, 5292; 5880, -5502, -1617; 5292, -1617, 622],[588, 21, 1],[-85, 45, 349, 483, 9413, 750, 2749, 9279, 2315, 849, 9235, -84; -172, 91, 706, 977, 19040, 1517, 5560, 18767, 4682, 1717, 18676, -170; 276, -147, -1134, -1569, -30576, -2436, -8928, -30135, -7518, -2757, -29988, 273],320,7]
%
% END OF LATTICE L321.7
%
%
% LATTICE L321.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[8106168, 158172, -2037420; 158172, 2856, -39760; -2037420, -39760, 512089],[588, 28, 1],[4971, 727, -215, -1875, -36, 578, 15308, 5067, 6009, 42433, 2933, 2319; -399, -58, 18, 154, 3, -47, -1239, -410, -486, -3430, -237, -187; 19747, 2888, -854, -7448, -143, 2296, 60809, 20128, 23870, 168560, 11651, 9212],320,8]
%
% END OF LATTICE L321.8
%
%
% LATTICE L321.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[3205188, -149940, 24696; -149940, 7014, -1155; 24696, -1155, 190],[1764, 21, 1],[-1, -1, -1, 1, 1, 4, 57, 13, 9, 83, 7, 2; -84, -33, -26, 21, 24, 96, 1288, 291, 198, 1785, 148, 33; -392, -72, -28, 0, 16, 63, 392, 72, 28, 0, -16, -63],320,9]
%
% END OF LATTICE L321.9
%
%
% LATTICE L321.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2220056328, 88532220, -556706052; 88532220, 3530520, -22200528; -556706052, -22200528, 139600795],[588, 84, 1],[-43, -1625, -391, -283, -568, 227, 586, 9227, 1477, 1369, 4369, 316; 3, 77, 33, 79, 378, 118, 114, 1561, 201, 155, 441, -1; -171, -6468, -1554, -1116, -2205, 924, 2355, 37044, 5922, 5484, 17493, 1260],320,10]
%
% END OF LATTICE L321.10
%
%
% LATTICE L321.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[863672040, -3469788, 215421444; -3469788, 13944, -865452; 215421444, -865452, 53731505],[1764, 84, 1],[-13532, -939, -1163, -929, -119, -7, -16393, -1911, -7387, -19021, -4156, -1418; -609, -41, -45, -35, -6, -4, -882, -101, -381, -959, -207, -67; 54243, 3764, 4662, 3724, 477, 28, 65709, 7660, 29610, 76244, 16659, 5684],320,11]
%
% END OF LATTICE L321.11
%
%
% LATTICE L321.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[11349576, -784980, 2829456; -784980, 43176, -195720; 2829456, -195720, 705385],[1764, 84, 1],[18689, 9061, -227, -14521, -114, 4526, 47902, 48017, 19253, 414067, 9627, 24013; 161, 78, -2, -126, -1, 39, 413, 414, 166, 3570, 83, 207; -74921, -36324, 910, 58212, 457, -18144, -192031, -192492, -77182, -1659924, -38593, -96264],320,12]
%
% END OF LATTICE L321.12
%

\medskip%
%------------------------------WEYL-GROUP-W322--------------------------------
%
\leavevmode\llap{}%
$W_{322}$%
\qquad\llap{12} lattices, $\chi=24$%
\hfill%
$22222222\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L322.1
%
\leavevmode%
${L_{322.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{1}{}7\above{1pt}{1pt}{-}{}49\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${2}\above{1pt}{1pt}{s}{2}{294}\above{1pt}{1pt}{l}{2}{4}\above{1pt}{1pt}{r}{2}{42}\above{1pt}{1pt}{b}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
105252\\-5292\\-2352
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-5292\\266\\119
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2352\\119\\46
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
503\\9324\\1764
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-26\\-482\\-91
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-6\\-111\\-22
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\19\\2
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\21\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3\\-56\\-8
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-8\\-150\\-21
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[105252, -5292, -2352; -5292, 266, 119; -2352, 119, 46],[588, 7, 1],[1, 1, -3, -8, -3, -43, -5, 2; 19, 21, -56, -150, -56, -798, -92, 39; 2, 0, -8, -21, -9, -147, -20, 0],321,1]
%
% END OF LATTICE L322.1
%
%
% LATTICE L322.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[294, 0, 147; 0, -7, -7; 147, -7, 67],[147, 7, 1],[-1, 1, 2, 10, 4, 62, 4, -1; -2, 0, 3, 15, 5, 63, 3, -6; 2, 0, -4, -21, -9, -147, -10, 0],321,2]
%
% END OF LATTICE L322.2
%
%
% LATTICE L322.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[17934, 1323, -588; 1323, 91, -42; -588, -42, 19],[147, 7, 1],[1, 1, 5, 1, -1, -1, -5, -1; 7, 9, 42, 6, -28, -18, -84, -15; 49, 51, 245, 42, -98, -72, -343, -63],321,3]
%
% END OF LATTICE L322.3
%
%
% LATTICE L322.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[90258, 5145, 29841; 5145, 273, 1701; 29841, 1701, 9866],[147, 21, 1],[-1, -81, -5, 30, 98, 760, 199, 67; 0, 0, 1, 2, 4, 28, 7, 2; 3, 245, 15, -91, -297, -2303, -603, -203],321,4]
%
% END OF LATTICE L322.4
%
%
% LATTICE L322.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[744114, -23373, 242697; -23373, 714, -7623; 242697, -7623, 79157],[147, 21, 1],[479, 15, -335, -114, -766, -56, -239, 73; -14, 0, 21, 5, 35, 3, 21, -2; -1470, -46, 1029, 350, 2352, 172, 735, -224],321,5]
%
% END OF LATTICE L322.5
%
%
% LATTICE L322.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-21756, 588, -588; 588, -14, 21; -588, 21, -2],[588, 7, 1],[-5, -1, -1, 2, 5, 1, 1, -2; -140, -30, -56, 51, 133, 27, 28, -54; -49, -51, -588, -84, -98, -12, 0, 21],321,6]
%
% END OF LATTICE L322.6
%
%
% LATTICE L322.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-140532, -20580, 2940; -20580, -2730, 399; 2940, 399, -58],[588, 21, 1],[1, -1, -1, 0, 3, 29, 17, 4; 25, -21, -24, -1, 71, 693, 408, 97; 222, -196, -216, -7, 639, 6223, 3660, 868],321,7]
%
% END OF LATTICE L322.7
%
%
% LATTICE L322.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[588, 0, 0; 0, -42, 21; 0, 21, -10],[588, 21, 1],[-5, -1, -29, -1, -2, 0, 1, 0; -49, -7, -168, -3, 7, 1, 0, -3; -147, -23, -588, -14, 0, 2, 0, -7],321,8]
%
% END OF LATTICE L322.8
%
%
% LATTICE L322.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[128184, 67620, -31752; 67620, 32872, -16772; -31752, -16772, 7865],[588, 28, 1],[1, -1333, -31, 296, 422, 10216, 454, 973; 0, 42, 1, -9, -13, -315, -14, -30; 4, -5292, -123, 1176, 1676, 40572, 1803, 3864],321,9]
%
% END OF LATTICE L322.9
%
%
% LATTICE L322.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1694616, 155820, -425712; 155820, 14392, -39144; -425712, -39144, 106945],[588, 28, 1],[14010, 8644, 21200, 9091, 6857, 299, -333, -148; -287, -177, -434, -186, -140, -6, 7, 3; 55664, 34344, 84231, 36120, 27244, 1188, -1323, -588],321,10]
%
% END OF LATTICE L322.10
%
%
% LATTICE L322.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[268912392, -4350612, -67694088; -4350612, 70392, 1095192; -67694088, 1095192, 17040827],[588, 84, 1],[-553, -839, -34, 7, -949, -9675, -1468, -1509; -12, -14, -1, -3, -29, -273, -40, -38; -2196, -3332, -135, 28, -3768, -38416, -5829, -5992],321,11]
%
% END OF LATTICE L322.11
%
%
% LATTICE L322.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[175224, -12348, -44100; -12348, 840, 3108; -44100, 3108, 11099],[588, 84, 1],[-299, -65, -485, -71, -149, 1, 37, 7; -49, -9, -63, -8, -14, 0, 0, -1; -1176, -256, -1911, -280, -588, 4, 147, 28],321,12]
%
% END OF LATTICE L322.12
%

\medskip%
%------------------------------WEYL-GROUP-W323--------------------------------
%
\leavevmode\llap{}%
$W_{323}$%
\qquad\llap{30} lattices, $\chi=24$%
\hfill%
$22|22|22|22|\rtimes D_{4}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L323.1
%
\leavevmode%
${L_{323.1}}$%
{} : {$1\above{1pt}{1pt}{2}{0}8\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{1}{}3\above{1pt}{1pt}{-}{}9\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{-}{}$}\EasyButWeakLineBreak%
{${360}\above{1pt}{1pt}{s}{2}{4}\above{1pt}{1pt}{*}{2}{60}\above{1pt}{1pt}{*}{2}{36}\above{1pt}{1pt}{s}{2}{40}\above{1pt}{1pt}{l}{2}{9}\above{1pt}{1pt}{}{2}{15}\above{1pt}{1pt}{}{2}{1}\above{1pt}{1pt}{r}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2711160\\720\\-15480
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
720\\-3\\-3
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-15480\\-3\\88
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\60\\180
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-62\\-178
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-70\\-180
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7\\414\\1242
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
17\\1020\\3020
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
8\\483\\1422
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7\\425\\1245
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\61\\178
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[2711160, 720, -15480; 720, -3, -3; -15480, -3, 88],[360, 3, 1],[1, -1, -1, 7, 17, 8, 7, 1; 60, -62, -70, 414, 1020, 483, 425, 61; 180, -178, -180, 1242, 3020, 1422, 1245, 178],322,1]
%
% END OF LATTICE L323.1
%
\hbox{}\par\smallskip%
%
% LATTICE L323.2
%
\leavevmode%
${L_{323.2}}$%
{} : {$[1\above{1pt}{1pt}{-}{}2\above{1pt}{1pt}{1}{}]\above{1pt}{1pt}{}{2}16\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{1}{}3\above{1pt}{1pt}{-}{}9\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${10}\above{1pt}{1pt}{}{2}{9}\above{1pt}{1pt}{r}{2}{240}\above{1pt}{1pt}{l}{2}{1}\above{1pt}{1pt}{}{2}{90}\above{1pt}{1pt}{r}{2}{16}\above{1pt}{1pt}{s}{2}{60}\above{1pt}{1pt}{s}{2}{144}\above{1pt}{1pt}{l}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
23253840\\415440\\5040
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
415440\\7422\\90
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5040\\90\\1
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-7\\395\\-250
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-5\\282\\-171
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-11\\620\\-360
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\-1
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4\\-225\\90
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\-56\\8
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3\\170\\-150
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-17\\960\\-648
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[23253840, 415440, 5040; 415440, 7422, 90; 5040, 90, 1],[720, 6, 1],[-7, -5, -11, 0, 4, 1, -3, -17; 395, 282, 620, 0, -225, -56, 170, 960; -250, -171, -360, -1, 90, 8, -150, -648],322,2]
%
% END OF LATTICE L323.2
%
\hbox{}\par\smallskip%
%
% LATTICE L323.3
%
\leavevmode%
${L_{323.3}}$%
{} : {$[1\above{1pt}{1pt}{1}{}2\above{1pt}{1pt}{1}{}]\above{1pt}{1pt}{}{0}16\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{1}{}3\above{1pt}{1pt}{-}{}9\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{m}%
\EasyButWeakLineBreak%
{${40}\above{1pt}{1pt}{l}{2}{9}\above{1pt}{1pt}{}{2}{240}\above{1pt}{1pt}{}{2}{1}\above{1pt}{1pt}{r}{2}{360}\above{1pt}{1pt}{*}{2}{16}\above{1pt}{1pt}{l}{2}{15}\above{1pt}{1pt}{r}{2}{144}\above{1pt}{1pt}{*}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3378960\\-51840\\22320
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-51840\\-786\\336
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
22320\\336\\-143
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
9\\-1550\\-2240
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5\\-864\\-1251
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
21\\-3640\\-5280
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\-174\\-253
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7\\-1230\\-1800
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\172\\248
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\175\\255
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5\\-852\\-1224
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-3378960, -51840, 22320; -51840, -786, 336; 22320, 336, -143],[720, 6, 1],[9, 5, 21, 1, 7, -1, -1, 5; -1550, -864, -3640, -174, -1230, 172, 175, -852; -2240, -1251, -5280, -253, -1800, 248, 255, -1224],322,3]
%
% END OF LATTICE L323.3
%
\hbox{}\par\smallskip%
%
% LATTICE L323.4
%
\leavevmode%
${L_{323.4}}$%
{} : {$[1\above{1pt}{1pt}{1}{}2\above{1pt}{1pt}{1}{}]\above{1pt}{1pt}{}{6}16\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{1}{}3\above{1pt}{1pt}{-}{}9\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{m}%
\EasyButWeakLineBreak%
{${10}\above{1pt}{1pt}{r}{2}{36}\above{1pt}{1pt}{*}{2}{240}\above{1pt}{1pt}{*}{2}{4}\above{1pt}{1pt}{l}{2}{90}\above{1pt}{1pt}{}{2}{16}\above{1pt}{1pt}{}{2}{15}\above{1pt}{1pt}{}{2}{144}\above{1pt}{1pt}{}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3054960\\2160\\7920
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2160\\42\\-18
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7920\\-18\\-17
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
8\\815\\2860
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7\\714\\2502
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-100\\-360
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-102\\-358
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-105\\-360
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\304\\1072
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
6\\610\\2145
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
29\\2952\\10368
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-3054960, 2160, 7920; 2160, 42, -18; 7920, -18, -17],[720, 6, 1],[8, 7, -1, -1, -1, 3, 6, 29; 815, 714, -100, -102, -105, 304, 610, 2952; 2860, 2502, -360, -358, -360, 1072, 2145, 10368],322,4]
%
% END OF LATTICE L323.4
%
\hbox{}\par\smallskip%
%
% LATTICE L323.5
%
\leavevmode%
${L_{323.5}}$%
{} : {$[1\above{1pt}{1pt}{-}{}2\above{1pt}{1pt}{1}{}]\above{1pt}{1pt}{}{4}16\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{1}{}3\above{1pt}{1pt}{-}{}9\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{-}{}$}\EasyButWeakLineBreak%
{${40}\above{1pt}{1pt}{*}{2}{36}\above{1pt}{1pt}{s}{2}{240}\above{1pt}{1pt}{s}{2}{4}\above{1pt}{1pt}{*}{2}{360}\above{1pt}{1pt}{s}{2}{16}\above{1pt}{1pt}{*}{2}{60}\above{1pt}{1pt}{*}{2}{144}\above{1pt}{1pt}{s}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1711440\\-25200\\10080
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-25200\\-354\\138
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
10080\\138\\-53
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7\\-1370\\-2240
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7\\-1374\\-2250
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
13\\-2560\\-4200
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\-198\\-326
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\-210\\-360
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\196\\320
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\200\\330
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5\\-972\\-1584
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-1711440, -25200, 10080; -25200, -354, 138; 10080, 138, -53],[720, 6, 1],[7, 7, 13, 1, 1, -1, -1, 5; -1370, -1374, -2560, -198, -210, 196, 200, -972; -2240, -2250, -4200, -326, -360, 320, 330, -1584],322,5]
%
% END OF LATTICE L323.5
%
%
% LATTICE L323.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[14940, -1080, 0; -1080, 78, 0; 0, 0, 1],[180, 6, 1],[1, -1, -6, -19, -13, -8, -7, 0; 15, -14, -85, -270, -185, -114, -100, 0; 0, 4, 15, 36, 20, 9, 0, -1],322,6]
%
% END OF LATTICE L323.6
%
%
% LATTICE L323.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[222120, -1080, -360; -1080, -438, 150; -360, 150, -49],[360, 6, 1],[8, 29, 12, 3, -1, -1, -1, 7; 825, 2988, 1235, 308, -105, -103, -100, 723; 2465, 8928, 3690, 920, -315, -308, -300, 2160],322,7]
%
% END OF LATTICE L323.7
%
%
% LATTICE L323.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-855720, 5040, 2520; 5040, -6, -18; 2520, -18, -7],[360, 6, 1],[7, 5, -1, -1, 1, 1, 13, 7; 250, 180, -35, -36, 30, 35, 460, 249; 1870, 1332, -270, -268, 270, 268, 3480, 1872],322,8]
%
% END OF LATTICE L323.8
%
%
% LATTICE L323.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2495160, 2160, -14040; 2160, -12, -12; -14040, -12, 79],[360, 12, 1],[17, 7, -1, -1, 1, 2, 7, 16; 20, 6, -5, -2, 0, 3, 10, 21; 3020, 1242, -180, -178, 180, 356, 1245, 2844],322,9]
%
% END OF LATTICE L323.9
%
%
% LATTICE L323.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[360, 0, 0; 0, -12, 0; 0, 0, 1],[360, 12, 1],[-3, -1, -1, 0, 1, 0, -1, -2; 20, 6, 5, 0, 0, 1, 10, 15; 40, 9, 0, -1, 0, 4, 30, 36],322,10]
%
% END OF LATTICE L323.10
%
%
% LATTICE L323.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[397080, 3960, -1800; 3960, -15, -15; -1800, -15, 8],[360, 15, 1],[1, -1, -1, -1, 1, 4, 1, 1; 12, -14, -14, -18, 12, 51, 13, 13; 252, -250, -252, -270, 244, 990, 249, 250],322,11]
%
% END OF LATTICE L323.11
%
%
% LATTICE L323.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-255780, 87120, 4140; 87120, -29670, -1410; 4140, -1410, -67],[180, 30, 1],[-1, -1, 0, 5, 1, 4, 1, 0; 3, -2, -1, 6, 3, 18, 8, 4; -126, -20, 21, 180, -2, -135, -108, -85],322,12]
%
% END OF LATTICE L323.12
%
%
% LATTICE L323.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-37080, -7560, -3600; -7560, -1536, -720; -3600, -720, -313],[360, 24, 1],[29, 43, 21, -3, -43, -7, 1, 31; -175, -261, -130, 17, 255, 42, -5, -186; 70, 108, 60, -4, -90, -16, 0, 72],322,13]
%
% END OF LATTICE L323.13
%
%
% LATTICE L323.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-29880, -33480, 3600; -33480, -33870, 3630; 3600, 3630, -389],[360, 30, 1],[1, 7, 4, 41, 2, 7, -1, -1; -27, -204, -119, -1236, -61, -219, 28, 31; -243, -1840, -1074, -11160, -551, -1980, 252, 280],322,14]
%
% END OF LATTICE L323.14
%
%
% LATTICE L323.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-92520, -34200, 6480; -34200, -11010, 2070; 6480, 2070, -389],[360, 30, 1],[5, -1, -1, 5, 3, 19, 9, 5; -276, 52, 55, -252, -160, -1023, -488, -273; -1386, 260, 276, -1260, -802, -5130, -2448, -1370],322,15]
%
% END OF LATTICE L323.15
%
%
% LATTICE L323.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[509040, 254880, -720; 254880, 127608, -360; -720, -360, 1],[720, 24, 1],[11, 13, 2, -1, -7, 0, 9, 4; -25, -30, -5, 2, 15, 0, -20, -9; -1040, -1368, -330, 8, 360, -1, -720, -351],322,16]
%
% END OF LATTICE L323.16
%
%
% LATTICE L323.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[642875760, -45528480, 225360; -45528480, 3224328, -15960; 225360, -15960, 79],[720, 24, 1],[1, 1, 2, 11, 7, 4, 3, 0; 15, 18, 35, 186, 115, 63, 40, -1; 180, 784, 1365, 6192, 3260, 1314, -480, -202],322,17]
%
% END OF LATTICE L323.17
%
%
% LATTICE L323.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[707760, -47520, 2880; -47520, 3192, -192; 2880, -192, 13],[720, 24, 1],[-33, -43, -11, -1, 1, -1, -27, -23; -465, -606, -155, -14, 15, -14, -380, -324; 440, 576, 150, 16, 0, 14, 360, 306],322,18]
%
% END OF LATTICE L323.18
%
%
% LATTICE L323.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-242640, -136080, 3600; -136080, -76296, 2016; 3600, 2016, -53],[720, 24, 1],[-34, -1, 9, 25, 12, 2, -17, -4; 75, 2, -20, -54, -25, -3, 40, 9; 540, 8, -150, -360, -140, 18, 360, 70],322,19]
%
% END OF LATTICE L323.19
%
%
% LATTICE L323.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-215783280, -23958000, 120240; -23958000, -2660010, 13350; 120240, 13350, -67],[720, 30, 1],[-2, -2, -7, -7, -1, -1, 1, 1; 21, 20, 68, 66, 9, 0, -10, -8; 594, 395, 984, 585, -2, -1800, -198, 200],322,20]
%
% END OF LATTICE L323.20
%
%
% LATTICE L323.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-25241040, -1371600, 141840; -1371600, -73770, 7620; 141840, 7620, -787],[720, 30, 1],[11, 5, 17, 17, 5, 5, -1, -1; -2034, -926, -3152, -3156, -930, -948, 185, 188; -17712, -8065, -27456, -27495, -8104, -8280, 1611, 1640],322,21]
%
% END OF LATTICE L323.21
%
%
% LATTICE L323.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2367720, 15120, 9360; 15120, -60, -60; 9360, -60, -37],[360, 60, 1],[1, -1, -1, -1, 1, 8, 1, 2; 0, -2, -1, 6, 4, 21, 2, 3; 252, -250, -252, -270, 244, 1980, 249, 500],322,22]
%
% END OF LATTICE L323.22
%
%
% LATTICE L323.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-863280, -95040, 17280; -95040, -10410, 1890; 17280, 1890, -343],[720, 30, 1],[1, -1, -1, 7, 2, 41, 2, 7; -45, 40, 44, -276, -81, -1680, -83, -296; -198, 170, 192, -1170, -346, -7200, -357, -1280],322,23]
%
% END OF LATTICE L323.23
%
%
% LATTICE L323.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-291960, 100800, 5040; 100800, -25980, -1320; 5040, -1320, -67],[360, 60, 1],[5, 2, 3, 5, 1, -2, -1, 0; -288, -116, -175, -294, -60, 111, 58, 1; 6048, 2435, 3672, 6165, 1256, -2340, -1218, -20],322,24]
%
% END OF LATTICE L323.24
%
%
% LATTICE L323.25
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2561040, -280800, 29520; -280800, -30570, 3210; 29520, 3210, -337],[720, 30, 1],[5, 5, 9, 19, 3, 5, -1, -1; -318, -322, -584, -1242, -198, -348, 64, 68; -2592, -2630, -4776, -10170, -1624, -2880, 522, 560],322,25]
%
% END OF LATTICE L323.25
%
%
% LATTICE L323.26
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-8280, -86400, -3600; -86400, -886440, -36960; -3600, -36960, -1541],[360, 120, 1],[8, 2, -5, -46, -6, -31, 0, 7; 15, -1, -16, -123, -15, -72, 1, 16; -378, 20, 396, 3060, 374, 1800, -24, -400],322,26]
%
% END OF LATTICE L323.26
%
%
% LATTICE L323.27
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-61287120, 24216480, -64080; 24216480, -9568680, 25320; -64080, 25320, -67],[720, 120, 1],[-1, 0, 1, 2, 1, 5, 0, -1; 3, 2, 8, 9, 3, 6, -1, -2; 2088, 755, 2064, 1485, 176, -2520, -378, 200],322,27]
%
% END OF LATTICE L323.27
%
%
% LATTICE L323.28
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-27124560, 11712960, -31680; 11712960, -5057880, 13680; -31680, 13680, -37],[720, 120, 1],[-1, -5, 0, 1, 1, 0, -1, -4; -1, 6, 1, 6, 3, -1, -4, -9; 484, 6480, 369, 1360, 252, -370, -624, 90],322,28]
%
% END OF LATTICE L323.28
%
%
% LATTICE L323.29
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[3383280, -1336320, -8640; -1336320, 482520, 4560; -8640, 4560, -7],[720, 120, 1],[293, 235, 353, 589, 59, -235, -59, -1; 591, 474, 712, 1188, 119, -474, -119, -2; 23328, 18710, 28104, 46890, 4696, -18720, -4698, -80],322,29]
%
% END OF LATTICE L323.29
%
%
% LATTICE L323.30
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-120600720, 40128480, -201600; 40128480, -13352280, 67080; -201600, 67080, -337],[720, 120, 1],[3, 5, -1, -1, 5, 5, 9, 19; 9, 6, -4, -2, 21, 19, 32, 63; -4, -1800, -198, 200, 1188, 790, 984, 1170],322,30]
%
% END OF LATTICE L323.30
%

\medskip%
%------------------------------WEYL-GROUP-W324--------------------------------
%
\leavevmode\llap{}%
$W_{324}$%
\qquad\llap{38} lattices, $\chi=72$%
\hfill%
$22|22|22|22|22|22|22|22|\rtimes D_{8}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L324.1
%
\leavevmode%
${L_{324.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{4}8\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{-}{}9\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{2}{}5\above{1pt}{1pt}{1}{}$}\EasyButWeakLineBreak%
{${24}\above{1pt}{1pt}{}{2}{5}\above{1pt}{1pt}{r}{2}{72}\above{1pt}{1pt}{s}{2}{20}\above{1pt}{1pt}{*}{2}{24}\above{1pt}{1pt}{*}{2}{180}\above{1pt}{1pt}{s}{2}{8}\above{1pt}{1pt}{l}{2}{45}\above{1pt}{1pt}{}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
362520\\1800\\-2160
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1800\\-3\\-6
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2160\\-6\\11
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-379\\-36720\\-93960
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-14\\-1361\\-3480
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7\\680\\1739
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5\\488\\1248
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\195\\500
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\96\\252
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-100\\-250
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-100\\-252
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7\\660\\1710
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\288\\740
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
16\\1545\\3960
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[362520, 1800, -2160; 1800, -3, -6; -2160, -6, 11],[360, 3, 1],[5, 2, 1, -1, -1, 7, 3, 16, 9, 12, 41, 29, 15, 77, 11, 26; 488, 195, 96, -100, -100, 660, 288, 1545, 872, 1165, 3984, 2820, 1460, 7500, 1072, 2535; 1248, 500, 252, -250, -252, 1710, 740, 3960, 2232, 2980, 10188, 7210, 3732, 19170, 2740, 6480],323,1]
%
% END OF LATTICE L324.1
%
\hbox{}\par\smallskip%
%
% LATTICE L324.2
%
\leavevmode%
${L_{324.2}}$%
{} : {$[1\above{1pt}{1pt}{-}{}2\above{1pt}{1pt}{-}{}]\above{1pt}{1pt}{}{0}16\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{-}{}9\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{2}{}5\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${24}\above{1pt}{1pt}{*}{2}{720}\above{1pt}{1pt}{s}{2}{8}\above{1pt}{1pt}{l}{2}{45}\above{1pt}{1pt}{}{2}{6}\above{1pt}{1pt}{}{2}{5}\above{1pt}{1pt}{r}{2}{72}\above{1pt}{1pt}{s}{2}{80}\above{1pt}{1pt}{*}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
18641520\\442800\\-14400
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
442800\\10518\\-342
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-14400\\-342\\11
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-4429\\191880\\177120
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-105\\4549\\4200
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\-130\\-121
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5\\-214\\-108
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
91\\-3900\\-2160
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
9\\-386\\-224
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
29\\-1245\\-765
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5\\-215\\-144
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
8\\-345\\-265
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
19\\-822\\-720
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
17\\-740\\-800
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[18641520, 442800, -14400; 442800, 10518, -342; -14400, -342, 11],[720, 6, 1],[5, 91, 9, 29, 5, 8, 19, 17, 1, -19, -3, -11, -2, -2, -1, 7; -214, -3900, -386, -1245, -215, -345, -822, -740, -46, 780, 126, 465, 85, 85, 42, -300; -108, -2160, -224, -765, -144, -265, -720, -800, -132, -720, -16, 45, 24, 25, 0, -160],323,2]
%
% END OF LATTICE L324.2
%
\hbox{}\par\smallskip%
%
% LATTICE L324.3
%
\leavevmode%
${L_{324.3}}$%
{} : {$[1\above{1pt}{1pt}{1}{}2\above{1pt}{1pt}{-}{}]\above{1pt}{1pt}{}{4}16\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{-}{}9\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{2}{}5\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{m}%
\EasyButWeakLineBreak%
{${24}\above{1pt}{1pt}{s}{2}{720}\above{1pt}{1pt}{*}{2}{8}\above{1pt}{1pt}{*}{2}{180}\above{1pt}{1pt}{l}{2}{6}\above{1pt}{1pt}{r}{2}{20}\above{1pt}{1pt}{*}{2}{72}\above{1pt}{1pt}{*}{2}{80}\above{1pt}{1pt}{s}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
195120\\2880\\-2160
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2880\\42\\-30
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2160\\-30\\17
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
251\\-21000\\-5040
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\-251\\-60
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\-1
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\86\\24
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\-60\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\-82\\-20
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
13\\-1080\\-270
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\-167\\-42
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
11\\-920\\-230
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
19\\-1590\\-396
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
27\\-2260\\-560
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[195120, 2880, -2160; 2880, 42, -30; -2160, -30, 17],[720, 6, 1],[-1, 1, 1, 13, 2, 11, 19, 27, 7, 71, 5, 23, 1, 1, -1, -3; 86, -60, -82, -1080, -167, -920, -1590, -2260, -586, -5940, -418, -1920, -83, -80, 90, 260; 24, 0, -20, -270, -42, -230, -396, -560, -144, -1440, -100, -450, -18, -10, 36, 80],323,3]
%
% END OF LATTICE L324.3
%
\hbox{}\par\smallskip%
%
% LATTICE L324.4
%
\leavevmode%
${L_{324.4}}$%
{} : {$[1\above{1pt}{1pt}{1}{}2\above{1pt}{1pt}{1}{}]\above{1pt}{1pt}{}{2}16\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{-}{}9\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{2}{}5\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{m}%
\EasyButWeakLineBreak%
{${6}\above{1pt}{1pt}{r}{2}{720}\above{1pt}{1pt}{l}{2}{2}\above{1pt}{1pt}{r}{2}{180}\above{1pt}{1pt}{*}{2}{24}\above{1pt}{1pt}{*}{2}{20}\above{1pt}{1pt}{l}{2}{18}\above{1pt}{1pt}{r}{2}{80}\above{1pt}{1pt}{l}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-49981680\\1281600\\-18720
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1281600\\-32862\\480
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-18720\\480\\-7
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-65089\\-2549280\\-650880
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1668\\65329\\16680
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-24\\-940\\-241
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\79\\66
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
119\\4680\\2520
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7\\275\\128
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
107\\4200\\1710
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
23\\902\\312
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
49\\1920\\550
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
37\\1449\\360
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
93\\3640\\760
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-49981680, 1281600, -18720; 1281600, -32862, 480; -18720, 480, -7],[720, 6, 1],[2, 119, 7, 107, 23, 49, 37, 93, 10, 169, 5, 37, 1, -1, -1, 3; 79, 4680, 275, 4200, 902, 1920, 1449, 3640, 391, 6600, 195, 1440, 38, -40, -39, 120; 66, 2520, 128, 1710, 312, 550, 360, 760, 54, 360, -8, -270, -72, -70, 0, 200],323,4]
%
% END OF LATTICE L324.4
%
\hbox{}\par\smallskip%
%
% LATTICE L324.5
%
\leavevmode%
${L_{324.5}}$%
{} : {$1\above{1pt}{1pt}{-}{5}8\above{1pt}{1pt}{1}{1}64\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{-}{}9\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{2}{}5\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{3,2}%
\EasyButWeakLineBreak%
{${96}\above{1pt}{1pt}{*}{2}{20}\above{1pt}{1pt}{l}{2}{72}\above{1pt}{1pt}{}{2}{320}\above{1pt}{1pt}{r}{2}{24}\above{1pt}{1pt}{b}{2}{2880}\above{1pt}{1pt}{l}{2}{8}\above{1pt}{1pt}{}{2}{45}\above{1pt}{1pt}{r}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
shares genus with 2-dual${}\iso{}$3-dual; isometric to own %
2.3-dual\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-29338879680\\752279040\\-1123200
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
752279040\\-19289208\\28800
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1123200\\28800\\-43
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1882369\\-74510400\\-734123520
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
48264\\1910449\\18822960
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-72\\-2850\\-28081
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\38\\-672
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-40\\-670
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-39\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
11\\440\\7360
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5\\199\\2676
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
263\\10440\\122400
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
15\\595\\6688
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
56\\2220\\24075
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-29338879680, 752279040, -1123200; 752279040, -19289208, 28800; -1123200, 28800, -43],[2880, 24, 1],[1, -1, -1, 11, 5, 263, 15, 56, 47, 49, 73, 181, 19, 313, 9, 16; 38, -40, -39, 440, 199, 10440, 595, 2220, 1862, 1940, 2889, 7160, 751, 12360, 355, 630; -672, -670, 0, 7360, 2676, 122400, 6688, 24075, 19392, 19390, 28080, 67520, 6684, 102240, 2672, 4005],323,5]
%
% END OF LATTICE L324.5
%
%
% LATTICE L324.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-372420, 41400, -1620; 41400, -4602, 180; -1620, 180, -7],[180, 6, 1],[2, 1, -1, -3, -1, 1, 1, 13, 4, 11, 19, 27, 7, 71, 5, 23; 19, 10, -9, -30, -11, -30, 5, 90, 31, 90, 159, 230, 61, 630, 45, 210; 24, 25, 0, -80, -54, -1080, -112, -765, -144, -265, -360, -400, -66, -360, -8, 45],323,6]
%
% END OF LATTICE L324.6
%
%
% LATTICE L324.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-900360, 4320, 2160; 4320, -6, -12; 2160, -12, -5],[360, 6, 1],[0, 2, 5, 9, 3, 37, 3, 16, 1, 2, 1, -1, -1, -13, -1, -4; 2, 85, 204, 360, 118, 1440, 116, 615, 38, 75, 36, -40, -38, -480, -36, -135; -9, 640, 1638, 2980, 1002, 12420, 1010, 5400, 339, 680, 342, -340, -342, -4500, -350, -1440],323,7]
%
% END OF LATTICE L324.7
%
%
% LATTICE L324.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-11102040, -533520, 11160; -533520, -25638, 534; 11160, 534, -5],[360, 6, 1],[37, 473, 217, 324, 179, 962, 71, 1379, 35, 103, -1, -36, -35, -98, 1, 349; -776, -9920, -4551, -6795, -3754, -20175, -1489, -28920, -734, -2160, 21, 755, 734, 2055, -21, -7320; -297, -3760, -1719, -2560, -1410, -7560, -557, -10800, -273, -800, 9, 280, 270, 720, -13, -2880],323,8]
%
% END OF LATTICE L324.8
%
%
% LATTICE L324.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-19289280, 0, 28800; 0, 8, 0; 28800, 0, -43],[960, 8, 1],[29, 12, 10, 61, 4, 11, 0, -1, -1, 2, 4, 51, 10, 101, 14, 29; -54, -20, -15, -80, -3, 0, 1, 0, -6, -10, -15, -160, -27, -240, -31, -60; 19392, 8025, 6688, 40800, 2676, 7360, 0, -670, -672, 1335, 2672, 34080, 6684, 67520, 9360, 19390],323,9]
%
% END OF LATTICE L324.9
%
%
% LATTICE L324.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-1489680, 165600, 79920; 165600, -18408, -8880; 79920, -8880, -4267],[720, 24, 1],[53, 77, -1, -12, -22, -11, 13, 431, 73, 427, 379, 138, 148, 389, 113, 1081; 529, 770, -9, -120, -221, -120, 125, 4230, 721, 4230, 3759, 1370, 1471, 3870, 1125, 10770; -108, -160, 0, 25, 48, 45, -16, -720, -132, -800, -720, -265, -288, -765, -224, -2160],323,10]
%
% END OF LATTICE L324.10
%
%
% LATTICE L324.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-588780720, 15096960, -159120; 15096960, -387102, 4080; -159120, 4080, -43],[720, 6, 1],[5, 263, 15, 112, 47, 49, 73, 181, 19, 313, 9, 32, 1, -1, -1, 11; 199, 10440, 595, 4440, 1862, 1940, 2889, 7160, 751, 12360, 355, 1260, 38, -40, -39, 440; 378, 17280, 944, 6795, 2736, 2735, 3960, 9520, 942, 14400, 376, 1125, -96, -95, 0, 1040],323,11]
%
% END OF LATTICE L324.11
%
%
% LATTICE L324.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-164520, 27360, -1080; 27360, -4548, 180; -1080, 180, -7],[360, 12, 1],[3, 19, 3, 7, 1, -1, -7, -7, -5, -31, -5, -13, -3, -1, 1, 3; 14, 75, 10, 15, -4, -15, -66, -55, -34, -195, -30, -75, -16, -5, 6, 15; -108, -1080, -224, -765, -288, -265, -720, -400, -132, -360, -16, 45, 48, 25, 0, -80],323,12]
%
% END OF LATTICE L324.12
%
%
% LATTICE L324.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[567720, 3240, -2520; 3240, -12, -12; -2520, -12, 11],[360, 12, 1],[5, 52, 11, 77, 15, 29, 41, 24, 9, 32, 3, 7, -1, -1, 1, 4; 94, 975, 206, 1440, 280, 540, 762, 445, 166, 585, 54, 120, -20, -20, 18, 75; 1248, 12960, 2740, 19170, 3732, 7210, 10188, 5960, 2232, 7920, 740, 1710, -252, -250, 252, 1000],323,13]
%
% END OF LATTICE L324.13
%
%
% LATTICE L324.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-188100, 62640, -1440; 62640, -20850, 480; -1440, 480, -11],[180, 30, 1],[-31, -61, -21, -19, -8, -1, 1, 1, 1, -11, -9, -17, -22, -11, -91, -25; -71, -138, -47, -42, -17, -2, 3, 2, 1, -30, -23, -42, -53, -26, -213, -58; 930, 1908, 680, 639, 300, 43, 0, -44, -90, 108, 160, 369, 540, 293, 2520, 716],323,14]
%
% END OF LATTICE L324.14
%
%
% LATTICE L324.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2331000, 2880, -13320; 2880, -15, -15; -13320, -15, 76],[360, 15, 1],[111, 109, 75, 34, 29, 2, 1, -1, -1, 23, 35, 32, 81, 20, 329, 45; 1496, 1470, 1012, 459, 392, 27, 12, -14, -16, 306, 468, 429, 1088, 269, 4428, 606; 19740, 19386, 13340, 6048, 5160, 356, 180, -178, -180, 4086, 6220, 5688, 14400, 3556, 58500, 8002],323,15]
%
% END OF LATTICE L324.15
%
%
% LATTICE L324.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1440, 360, 0; 360, -1752, 96; 0, 96, -5],[360, 24, 1],[0, -4, -5, -9, -3, -37, -3, -32, -1, -4, -1, 1, 1, 13, 1, 8; 1, 25, 27, 45, 14, 165, 13, 135, 4, 15, 3, -5, -4, -45, -3, -15; 15, 440, 486, 820, 258, 3060, 242, 2520, 75, 280, 54, -100, -78, -900, -62, -360],323,16]
%
% END OF LATTICE L324.16
%
%
% LATTICE L324.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1092600, 8280, -4320; 8280, -30, -30; -4320, -30, 17],[360, 30, 1],[7, 32, 35, 101, 51, 41, 149, 18, 18, 28, 15, 19, -1, -1, 1, 2; 53, 243, 266, 768, 388, 312, 1134, 137, 137, 213, 114, 144, -8, -8, 6, 15; 1875, 8568, 9370, 27036, 13650, 10972, 39870, 4816, 4815, 7488, 4010, 5076, -270, -268, 270, 536],323,17]
%
% END OF LATTICE L324.17
%
%
% LATTICE L324.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2300760, 569880, -12960; 569880, -141150, 3210; -12960, 3210, -73],[360, 30, 1],[-1, -5, -1, -2, -1, 0, 1, 1, 1, 5, 1, 2, 1, 0, -1, -1; 10, 108, 31, 93, 98, 41, 153, 76, 40, 132, 19, 27, 2, -1, -3, 4; 615, 5616, 1535, 4428, 4470, 1796, 6525, 3152, 1575, 4896, 655, 828, -90, -44, 45, 352],323,18]
%
% END OF LATTICE L324.18
%
%
% LATTICE L324.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-16652880, 1850400, -10800; 1850400, -205608, 1200; -10800, 1200, -7],[720, 24, 1],[-1, -3, -1, 1, 2, 23, 5, 71, 7, 27, 19, 11, 4, 13, 1, 1; -11, -30, -9, 10, 19, 210, 45, 630, 61, 230, 159, 90, 31, 90, 5, -30; -348, -520, 0, 170, 168, 450, -16, -1800, -372, -2360, -2160, -1610, -888, -4770, -704, -6840],323,19]
%
% END OF LATTICE L324.19
%
%
% LATTICE L324.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[9202320, -985680, 10080; -985680, 105576, -1080; 10080, -1080, 11],[720, 24, 1],[10, 16, 19, 17, 1, -19, -3, -22, -4, -4, -1, 7, 5, 91, 9, 58; 85, 135, 159, 140, 7, -180, -27, -195, -35, -35, -9, 60, 43, 780, 77, 495; -828, -1430, -1836, -1880, -240, -360, 92, 990, 228, 230, 36, -520, -360, -6840, -692, -4590],323,20]
%
% END OF LATTICE L324.20
%
%
% LATTICE L324.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-64080, 10080, 4320; 10080, -1560, -672; 4320, -672, -289],[720, 24, 1],[4, 11, 19, 27, 7, 71, 5, 23, 2, 1, -1, -3, -1, 1, 1, 13; 13, -5, -39, -90, -35, -450, -37, -195, -23, -15, 9, 50, 25, 330, 27, 135; 36, 190, 396, 640, 192, 2160, 164, 810, 84, 50, -36, -160, -72, -720, -44, -90],323,21]
%
% END OF LATTICE L324.21
%
%
% LATTICE L324.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[5511600, 317520, -20880; 317520, 18210, -1200; -20880, -1200, 79],[720, 30, 1],[51, 101, 35, 16, 7, 1, 1, -1, -1, 19, 15, 14, 18, 9, 149, 41; 962, 1908, 662, 303, 133, 19, 18, -20, -22, 348, 278, 261, 337, 169, 2802, 772; 28080, 55656, 19300, 8829, 3870, 553, 540, -568, -600, 10296, 8180, 7659, 9870, 4943, 81900, 22552],323,22]
%
% END OF LATTICE L324.22
%
%
% LATTICE L324.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2980080, 393120, -27360; 393120, 47550, -3300; -27360, -3300, 229],[720, 30, 1],[31, 61, 21, 19, 4, 1, -1, -1, -1, 11, 9, 17, 11, 11, 91, 25; -7714, -15180, -5226, -4728, -995, -248, 258, 252, 254, -2724, -2234, -4224, -2735, -2736, -22638, -6220; -107460, -211464, -72800, -65862, -13860, -3454, 3600, 3512, 3540, -37944, -31120, -58842, -38100, -38114, -315360, -86648],323,23]
%
% END OF LATTICE L324.23
%
%
% LATTICE L324.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-66498480, -7388640, 62640; -7388640, -820950, 6960; 62640, 6960, -59],[720, 30, 1],[14, 139, 39, 115, 119, 49, 181, 89, 46, 149, 21, 29, 1, -1, -1, 7; -113, -1128, -317, -936, -970, -400, -1479, -728, -377, -1224, -173, -240, -10, 8, 9, -56; 1530, 14472, 4000, 11646, 11880, 4822, 17640, 8584, 4350, 13752, 1880, 2466, -120, -118, 0, 824],323,24]
%
% END OF LATTICE L324.24
%
%
% LATTICE L324.25
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-13680, -1440, -2160; -1440, -150, -240; -2160, -240, -239],[720, 30, 1],[29, 283, 79, 116, 239, 49, 361, 177, 91, 293, 41, 28, 1, -1, -1, 15; -233, -2280, -637, -936, -1930, -396, -2919, -1432, -737, -2376, -333, -228, -10, 8, 9, -120; -30, -288, -80, -117, -240, -49, -360, -176, -90, -288, -40, -27, 0, 1, 0, -16],323,25]
%
% END OF LATTICE L324.25
%
%
% LATTICE L324.26
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[360, 0, 0; 0, -20940, 480; 0, 480, -11],[360, 60, 1],[-9, -8, -5, -2, -1, 0, 1, 0, -1, -4, -5, -4, -9, -2, -31, -4; 44, 45, 32, 15, 14, 1, 0, -1, -4, 3, 8, 9, 26, 7, 120, 17; 1860, 1908, 1360, 639, 600, 43, 0, -44, -180, 108, 320, 369, 1080, 293, 5040, 716],323,26]
%
% END OF LATTICE L324.26
%
%
% LATTICE L324.27
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[939960, 10800, -5400; 10800, -60, -60; -5400, -60, 31],[360, 60, 1],[29, 68, 75, 109, 111, 45, 329, 40, 81, 64, 35, 23, -1, -1, 1, 4; 52, 123, 136, 198, 202, 82, 600, 73, 148, 117, 64, 42, -2, -2, 0, 7; 5160, 12096, 13340, 19386, 19740, 8002, 58500, 7112, 14400, 11376, 6220, 4086, -180, -178, 180, 712],323,27]
%
% END OF LATTICE L324.27
%
%
% LATTICE L324.28
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[960, 0, 0; 0, 24, 0; 0, 0, -1],[960, 24, 1],[-3, -3, -2, -9, 0, 1, 0, -1, -1, -3, -4, -39, -2, -49, -6, -11; -18, -20, -15, -80, -1, 0, 1, 0, -2, -10, -15, -160, -9, -240, -31, -60; -128, -135, -96, -480, -4, 0, 0, -30, -32, -105, -144, -1440, -76, -1920, -240, -450],323,28]
%
% END OF LATTICE L324.28
%
%
% LATTICE L324.29
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-54605760, 0, 114240; 0, 40, 0; 114240, 0, -239],[960, 40, 1],[82, 87, 36, 4, -1, -1, 0, 15, 28, 89, 74, 18, 221, 45, 110, 161; -27, -32, -15, -2, -6, 0, 1, 0, -3, -16, -15, -4, -54, -12, -31, -48; 39180, 41568, 17200, 1911, -480, -478, 0, 7168, 13380, 42528, 35360, 8601, 105600, 21502, 52560, 76928],323,29]
%
% END OF LATTICE L324.29
%
%
% LATTICE L324.30
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-5370120, 32400, 19800; 32400, -120, -120; 19800, -120, -73],[360, 120, 1],[7, 64, 35, 101, 51, 41, 149, 36, 18, 56, 15, 19, -1, -1, 1, 4; 13, 123, 68, 198, 101, 82, 300, 73, 37, 117, 32, 42, -1, -2, 0, 7; 1875, 17136, 9370, 27036, 13650, 10972, 39870, 9632, 4815, 14976, 4010, 5076, -270, -268, 270, 1072],323,30]
%
% END OF LATTICE L324.30
%
%
% LATTICE L324.31
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-94029808320, 2411020800, -4193280; 2411020800, -61821048, 107520; -4193280, 107520, -187],[2880, 24, 1],[1, -1, -1, 27, 11, 551, 31, 229, 95, 49, 145, 357, 37, 601, 17, 59; 38, -40, -39, 1080, 439, 21960, 1235, 9120, 3782, 1950, 5769, 14200, 1471, 23880, 675, 2340; -576, -575, 0, 15520, 5748, 270720, 14944, 108630, 44256, 22415, 65520, 159200, 16092, 253440, 6896, 22410],323,31]
%
% END OF LATTICE L324.31
%
%
% LATTICE L324.32
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-4251600, 1416960, 702000; 1416960, -472200, -234000; 702000, -234000, -115871],[720, 120, 1],[2219, 4547, 1619, 760, 712, 51, 1, -103, -209, 277, 391, 446, 1298, 351, 6029, 1711; 4429, 9078, 3233, 1518, 1423, 102, 3, -206, -419, 546, 777, 888, 2587, 700, 12027, 3414; 4500, 9216, 3280, 1539, 1440, 103, 0, -208, -420, 576, 800, 909, 2640, 713, 12240, 3472],323,32]
%
% END OF LATTICE L324.32
%
%
% LATTICE L324.33
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-752400, 250560, -2880; 250560, -83400, 960; -2880, 960, -11],[720, 120, 1],[-31, -61, -21, -19, -8, -1, 1, 1, 1, -11, -9, -17, -22, -11, -91, -25; -71, -138, -47, -42, -17, -2, 3, 2, 1, -30, -23, -42, -53, -26, -213, -58; 1860, 3816, 1360, 1278, 600, 86, 0, -88, -180, 216, 320, 738, 1080, 586, 5040, 1432],323,33]
%
% END OF LATTICE L324.33
%
%
% LATTICE L324.34
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[16069680, -6652800, 22320; -6652800, 2754120, -9240; 22320, -9240, 31],[720, 120, 1],[0, 0, 1, 1, 3, 13, 7, 10, 10, 4, 29, 7, 7, 11, 3, 2; -1, -1, 3, 10, 35, 162, 89, 129, 131, 53, 387, 94, 95, 150, 41, 27; -300, -298, 180, 2264, 8280, 38952, 21500, 31266, 31860, 12922, 94500, 22984, 23280, 36792, 10060, 6606],323,34]
%
% END OF LATTICE L324.34
%
%
% LATTICE L324.35
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-19051920, 9568800, -53280; 9568800, -4805880, 26760; -53280, 26760, -149],[720, 120, 1],[0, 1, 1, -7, -27, -131, -73, -107, -110, -45, -331, -81, -83, -133, -37, -25; -1, 1, 3, -6, -25, -126, -71, -105, -109, -45, -333, -82, -85, -138, -39, -27; -180, -178, 180, 1424, 5160, 24192, 13340, 19386, 19740, 8002, 58500, 14224, 14400, 22752, 6220, 4086],323,35]
%
% END OF LATTICE L324.35
%
%
% LATTICE L324.36
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-49024320, 0, 61440; 0, 120, 0; 61440, 0, -77],[960, 120, 1],[8, 13, 0, -1, -1, 3, 28, 69, 22, 131, 90, 37, 61, 15, 62, 75; -1, 0, 1, 0, -2, -2, -15, -32, -9, -48, -31, -12, -18, -4, -15, -16; 6380, 10368, 0, -798, -800, 2391, 22320, 55008, 17540, 104448, 71760, 29502, 48640, 11961, 49440, 59808],323,36]
%
% END OF LATTICE L324.36
%
%
% LATTICE L324.37
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-4423043520, -491448960, 1028160; -491448960, -54605400, 114240; 1028160, 114240, -239],[2880, 120, 1],[91, 177, 361, 49, 239, 58, 79, 283, 29, 15, -1, -1, 1, 14, 41, 293; -737, -1432, -2919, -396, -1930, -468, -637, -2280, -233, -120, 9, 8, -10, -114, -333, -2376; 39180, 76928, 157680, 21502, 105600, 25803, 35360, 127584, 13380, 7168, 0, -478, -480, 5733, 17200, 124704],323,37]
%
% END OF LATTICE L324.37
%
%
% LATTICE L324.38
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3816515520, -424056960, 673920; -424056960, -47117400, 74880; 673920, 74880, -119],[2880, 120, 1],[-1, -3, -1, 1, 31, 37, 41, 239, 61, 99, 181, 11, 89, 35, 19, 49; 7, 24, 9, -8, -250, -300, -333, -1944, -497, -808, -1479, -90, -730, -288, -157, -408; -1260, -1888, 0, 629, 18240, 20754, 22640, 130176, 32700, 52192, 94320, 5659, 44640, 16974, 8800, 20736],323,38]
%
% END OF LATTICE L324.38
%

\medskip%
%------------------------------WEYL-GROUP-W325--------------------------------
%
\leavevmode\llap{}%
$W_{325}$%
\qquad\llap{12} lattices, $\chi=36$%
\hfill%
$2222222222\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L325.1
%
\leavevmode%
${L_{325.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{2}{}9\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{1}{}5\above{1pt}{1pt}{-}{}25\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${50}\above{1pt}{1pt}{l}{2}{36}\above{1pt}{1pt}{r}{2}{10}\above{1pt}{1pt}{l}{2}{4}\above{1pt}{1pt}{r}{2}{90}\above{1pt}{1pt}{b}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
6811107300\\-193193100\\-997200
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-193193100\\5479810\\28285
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-997200\\28285\\146
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5702399\\201427200\\-74880000
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-161766\\-5714099\\2124200
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-891\\-31473\\11699
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-35\\-50
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\36\\-144
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\106\\-45
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
331\\11692\\-4348
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1742\\61533\\-22860
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[6811107300, -193193100, -997200; -193193100, 5479810, 28285; -997200, 28285, 146],[900, 5, 1],[-1, 1, 3, 331, 1742, 3961, 7127, 96, 65, 40; -35, 36, 106, 11692, 61533, 139915, 251748, 3391, 2296, 1413; -50, -144, -45, -4348, -22860, -51950, -93456, -1255, -852, -540],324,1]
%
% END OF LATTICE L325.1
%
%
% LATTICE L325.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-37575, 450, 225; 450, 10, -5; 225, -5, -1],[225, 5, 1],[-121, -109, -3, -1, -1, 1, 1, 0, -5, -53; -2535, -2286, -64, -22, -27, 15, 18, 1, -104, -1107; -15925, -14346, -395, -132, -135, 125, 126, 0, -658, -6975],324,2]
%
% END OF LATTICE L325.2
%
%
% LATTICE L325.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-5850, -2250, 675; -2250, -865, 260; 675, 260, -77],[225, 5, 1],[-3, -17, 4, -139, -313, -149, -3403, -23, -51, -29; 7, 45, -9, 265, 603, 289, 6615, 46, 105, 63; -3, 0, 5, -350, -765, -357, -8100, -50, -100, -45],324,3]
%
% END OF LATTICE L325.3
%
%
% LATTICE L325.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-323100, 1800, -900; 1800, -10, 5; -900, 5, -2],[900, 5, 1],[0, 1, 0, -33, -35, -16, -721, -2, -7, -1; -1, 180, 2, -5940, -6309, -2887, -130140, -363, -1280, -189; -3, 0, 5, -700, -765, -357, -16200, -50, -200, -45],324,4]
%
% END OF LATTICE L325.4
%
%
% LATTICE L325.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[3371175, 93600, -1276425; 93600, 2610, -35415; -1276425, -35415, 483346],[225, 45, 1],[-72512, -7309, -2018, -823, -222, -1088, -51, 178, -2857, -3458; 362525, 36541, 10087, 4113, 1109, 5435, 255, -888, 14285, 17289; -164925, -16624, -4590, -1872, -505, -2475, -116, 405, -6498, -7865],324,5]
%
% END OF LATTICE L325.5
%
%
% LATTICE L325.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[518850, 23175, -179325; 23175, 1035, -8010; -179325, -8010, 61978],[225, 45, 1],[5, 12, -1, -414, -97, -397, -992, -48, -76, -1; -42, -75, 22, 575, 124, 474, 1155, 32, -35, -16; 9, 25, 0, -1125, -265, -1089, -2725, -135, -225, -5],324,6]
%
% END OF LATTICE L325.6
%
%
% LATTICE L325.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-386620200, -12222900, -96294600; -12222900, -307240, -3043880; -96294600, -3043880, -23983871],[900, 20, 1],[-127157, 15391, 67832, 86019, 1520687, 2992557, 1274039, 3803, -14384, -231257; -2900, 351, 1547, 1962, 34686, 68260, 29061, 87, -328, -5274; 510900, -61839, -272540, -345613, -6109920, -12023700, -5118921, -15280, 57793, 929160],324,7]
%
% END OF LATTICE L325.7
%
%
% LATTICE L325.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[408600, -900, 101700; -900, 3640, -220; 101700, -220, 25313],[900, 20, 1],[-225, -56, 224, -37702, -160973, -73927, -834154, -9493, -8643, -5869; -1, 0, 1, -175, -747, -343, -3870, -44, -40, -27; 904, 225, -900, 151475, 646740, 297016, 3351375, 38140, 34725, 23580],324,8]
%
% END OF LATTICE L325.8
%
%
% LATTICE L325.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[14127300, 5667300, 38700; 5667300, 2273490, 15525; 38700, 15525, 106],[900, 45, 1],[-2, -5, -10, -27, -11, -158, -27, 6, 11, 3; 5, 12, 24, 76, 33, 515, 92, -11, -24, -7; 0, 68, 135, -1296, -830, -18000, -3668, -585, -504, -70],324,9]
%
% END OF LATTICE L325.9
%
%
% LATTICE L325.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-6867900, -1046700, 38700; -1046700, -159390, 5895; 38700, 5895, -218],[900, 45, 1],[4, 9, -4, 127, 17, 76, 391, 14, 73, 3; 43, 100, -42, 1100, 151, 685, 3540, 133, 720, 31; 1872, 4300, -1845, 52200, 7090, 31968, 164900, 6075, 32400, 1370],324,10]
%
% END OF LATTICE L325.10
%
%
% LATTICE L325.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[103699800, -2157300, 25830000; -2157300, 39240, -537300; 25830000, -537300, 6433849],[900, 180, 1],[-20609, -170, 8378, 55194, 125899, 2529529, 125616, 54345, 7529, -453; 730, 6, -297, -1957, -4464, -89690, -4454, -1927, -267, 16; 82800, 683, -33660, -221751, -505820, -10162800, -504683, -218340, -30249, 1820],324,11]
%
% END OF LATTICE L325.11
%
%
% LATTICE L325.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[4455725400, -20843100, 1108938600; -20843100, 97560, -5187420; 1108938600, -5187420, 275992057],[900, 180, 1],[8099, 4324, -7660, 209922, 102855, 434837, 549346, 63027, 66913, 7879; -114, -60, 109, -3005, -1472, -6222, -7860, -901, -955, -112; -32544, -17375, 30780, -843525, -413300, -1747296, -2207425, -253260, -268875, -31660],324,12]
%
% END OF LATTICE L325.12
%

\medskip%
%------------------------------WEYL-GROUP-W326--------------------------------
%
\leavevmode\llap{}%
$W_{326}$%
\qquad\llap{4} lattices, $\chi=48$%
\hfill%
$6222362223\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L326.1
%
\leavevmode%
${L_{326.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}16\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{-}{}27\above{1pt}{1pt}{-}{}$}\EasyButWeakLineBreak%
{${6}\above{1pt}{1pt}{}{6}{2}\above{1pt}{1pt}{b}{2}{54}\above{1pt}{1pt}{s}{2}{2}\above{1pt}{1pt}{b}{2}{6}\above{1pt}{1pt}{-}{3}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-13665456\\-44928\\35856
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-44928\\-138\\117
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
35856\\117\\-94
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
664289\\25895232\\285523920
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2365\\92191\\1016520
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1760\\-68608\\-756481
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\79\\861
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-39\\-430
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2\\-81\\-864
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4\\155\\1718
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
21\\817\\9024
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-13665456, -44928, 35856; -44928, -138, 117; 35856, 117, -94],[432, 3, 1],[2, -1, -2, 4, 21, 53, 276, 497, 51, 34; 79, -39, -81, 155, 817, 2065, 10759, 19377, 1989, 1327; 861, -430, -864, 1718, 9024, 22779, 118630, 213624, 21922, 14616],325,1]
%
% END OF LATTICE L326.1
%
%
% LATTICE L326.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-132624, 3456, 1728; 3456, -90, -45; 1728, -45, -22],[432, 9, 1],[7, 106, 7, 19, 4, 0, -1, 0, 2, 3; 292, 4479, 297, 813, 175, 4, -39, -1, 75, 121; -63, -1080, -74, -216, -54, -9, 0, 2, 0, -18],325,2]
%
% END OF LATTICE L326.2
%
%
% LATTICE L326.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[864, -14256, 1296; -14256, -21216, 1728; 1296, 1728, -139],[432, 48, 1],[369, 1927, 3473, 357, 239, 15, -7, -17, 27, 145; -2576, -13449, -24237, -2491, -1667, -104, 49, 117, -189, -1013; -28560, -149104, -268704, -27616, -18480, -1152, 544, 1296, -2096, -11232],325,3]
%
% END OF LATTICE L326.3
%
%
% LATTICE L326.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-268704, -128304, -2160; -128304, 3744, 0; -2160, 0, -1],[432, 144, 1],[4, -7, -1, 11, 25, 68, 1087, 73, 205, 47; 137, -240, -34, 384, 866, 2351, 37560, 2522, 7080, 1622; -8640, 15120, 2144, -24192, -54576, -148176, -2367360, -158960, -446256, -102240],325,4]
%
% END OF LATTICE L326.4
%

\medskip%
%------------------------------WEYL-GROUP-W327--------------------------------
%
\leavevmode\llap{}%
$W_{327}$%
\qquad\llap{32} lattices, $\chi=36$%
\hfill%
$222|22222|22\rtimes D_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L327.1
%
\leavevmode%
${L_{327.1}}$%
{} : {$[1\above{1pt}{1pt}{-}{}2\above{1pt}{1pt}{1}{}]\above{1pt}{1pt}{}{6}32\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{2}{}7\above{1pt}{1pt}{1}{}$}\EasyButWeakLineBreak%
{${7}\above{1pt}{1pt}{}{2}{6}\above{1pt}{1pt}{r}{2}{224}\above{1pt}{1pt}{l}{2}{2}\above{1pt}{1pt}{}{2}{224}\above{1pt}{1pt}{}{2}{6}\above{1pt}{1pt}{r}{2}{28}\above{1pt}{1pt}{*}{2}{96}\above{1pt}{1pt}{*}{2}{56}\above{1pt}{1pt}{s}{2}{96}\above{1pt}{1pt}{l}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-261408\\0\\-672
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\22\\18
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-672\\18\\13
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-315\\385
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-315\\384
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-5\\-1568\\1904
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\1\\-2
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
9\\2912\\-3584
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\645\\-792
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5\\1610\\-1974
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5\\1608\\-1968
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\322\\-392
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-312\\384
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-261408, 0, -672; 0, 22, 18; -672, 18, 13],[672, 2, 1],[-1, -1, -5, 0, 9, 2, 5, 5, 1, -1; -315, -315, -1568, 1, 2912, 645, 1610, 1608, 322, -312; 385, 384, 1904, -2, -3584, -792, -1974, -1968, -392, 384],326,1]
%
% END OF LATTICE L327.1
%
\hbox{}\par\smallskip%
%
% LATTICE L327.2
%
\leavevmode%
${L_{327.2}}$%
{} : {$[1\above{1pt}{1pt}{1}{}2\above{1pt}{1pt}{1}{}]\above{1pt}{1pt}{}{6}32\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{2}{}7\above{1pt}{1pt}{1}{}$}\EasyButWeakLineBreak%
{${7}\above{1pt}{1pt}{r}{2}{24}\above{1pt}{1pt}{*}{2}{224}\above{1pt}{1pt}{s}{2}{8}\above{1pt}{1pt}{*}{2}{224}\above{1pt}{1pt}{s}{2}{24}\above{1pt}{1pt}{*}{2}{28}\above{1pt}{1pt}{s}{2}{96}\above{1pt}{1pt}{l}{2}{14}\above{1pt}{1pt}{}{2}{96}\above{1pt}{1pt}{}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1375584\\-449568\\-8736
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-449568\\146926\\2856
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-8736\\2856\\55
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
57\\168\\329
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
59\\174\\336
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
19\\56\\112
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-21\\-62\\-116
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-359\\-1064\\-1792
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-103\\-306\\-480
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-75\\-224\\-294
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\0\\144
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
31\\91\\196
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
163\\480\\960
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[1375584, -449568, -8736; -449568, 146926, 2856; -8736, 2856, 55],[672, 2, 1],[57, 59, 19, -21, -359, -103, -75, 1, 31, 163; 168, 174, 56, -62, -1064, -306, -224, 0, 91, 480; 329, 336, 112, -116, -1792, -480, -294, 144, 196, 960],326,2]
%
% END OF LATTICE L327.2
%
\hbox{}\par\smallskip%
%
% LATTICE L327.3
%
\leavevmode%
${L_{327.3}}$%
{} : {$1\above{1pt}{1pt}{1}{7}4\above{1pt}{1pt}{1}{1}32\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{2}{}7\above{1pt}{1pt}{1}{}$}\EasyButWeakLineBreak%
{${224}\above{1pt}{1pt}{s}{2}{48}\above{1pt}{1pt}{*}{2}{28}\above{1pt}{1pt}{l}{2}{4}\above{1pt}{1pt}{}{2}{7}\above{1pt}{1pt}{r}{2}{48}\above{1pt}{1pt}{*}{2}{224}\above{1pt}{1pt}{l}{2}{3}\above{1pt}{1pt}{r}{2}{112}\above{1pt}{1pt}{*}{2}{12}\above{1pt}{1pt}{*}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1907808\\-6720\\7392
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-6720\\4\\16
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7392\\16\\-25
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
19\\2548\\7168
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
11\\1494\\4176
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
9\\1232\\3430
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\139\\384
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\140\\385
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-138\\-384
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-9\\-1260\\-3472
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-141\\-387
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3\\-434\\-1176
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\126\\366
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-1907808, -6720, 7392; -6720, 4, 16; 7392, 16, -25],[672, 4, 1],[19, 11, 9, 1, 1, -1, -9, -1, -3, 1; 2548, 1494, 1232, 139, 140, -138, -1260, -141, -434, 126; 7168, 4176, 3430, 384, 385, -384, -3472, -387, -1176, 366],326,3]
%
% END OF LATTICE L327.3
%
\hbox{}\par\smallskip%
%
% LATTICE L327.4
%
\leavevmode%
${L_{327.4}}$%
{} : {$1\above{1pt}{1pt}{-}{3}4\above{1pt}{1pt}{1}{7}32\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{2}{}7\above{1pt}{1pt}{1}{}$}\EasyButWeakLineBreak%
{${224}\above{1pt}{1pt}{}{2}{12}\above{1pt}{1pt}{r}{2}{28}\above{1pt}{1pt}{*}{2}{16}\above{1pt}{1pt}{l}{2}{7}\above{1pt}{1pt}{}{2}{12}\above{1pt}{1pt}{r}{2}{224}\above{1pt}{1pt}{s}{2}{12}\above{1pt}{1pt}{l}{2}{28}\above{1pt}{1pt}{}{2}{3}\above{1pt}{1pt}{}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
16570848\\2688\\-30240
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2688\\-4\\-4
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-30240\\-4\\55
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
29\\3136\\16128
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
8\\873\\4452
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
13\\1428\\7238
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\334\\1672
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\336\\1673
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\225\\1116
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\112\\560
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-114\\-558
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-119\\-560
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\105\\555
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[16570848, 2688, -30240; 2688, -4, -4; -30240, -4, 55],[672, 4, 1],[29, 8, 13, 3, 3, 2, 1, -1, -1, 1; 3136, 873, 1428, 334, 336, 225, 112, -114, -119, 105; 16128, 4452, 7238, 1672, 1673, 1116, 560, -558, -560, 555],326,4]
%
% END OF LATTICE L327.4
%
%
% LATTICE L327.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1047648, -12096, 5376; -12096, -138, 60; 5376, 60, -25],[672, 6, 1],[-19, -3, -51, -1, -9, 0, 1, 1, -1, -5; 2534, 401, 6832, 135, 1232, 1, -133, -136, 126, 664; 1974, 314, 5376, 108, 1008, 2, -105, -112, 84, 512],326,5]
%
% END OF LATTICE L327.5
%
%
% LATTICE L327.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[583968, -10080, 0; -10080, 174, 0; 0, 0, -1],[672, 6, 1],[-1, -1, -13, -1, 1, 1, 3, 3, 2, 1; -42, -54, -728, -58, 56, 58, 175, 176, 119, 64; -210, -52, -336, 0, 0, -4, -21, -32, -42, -80],326,6]
%
% END OF LATTICE L327.6
%
%
% LATTICE L327.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[542308704, -20046432, 172704; -20046432, 741016, -6384; 172704, -6384, 55],[672, 8, 1],[3, 2, 1, 0, 43, 20, 27, 31, 11, 13; 84, 57, 28, -1, 1148, 537, 728, 840, 301, 360; 329, 336, 112, -116, -1792, -480, -294, 144, 392, 960],326,7]
%
% END OF LATTICE L327.7
%
%
% LATTICE L327.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[811104, 276864, -2016; 276864, 94504, -688; -2016, -688, 5],[672, 8, 1],[9, 5, 5, -1, -9, -1, 2, 7, 6, 13; -35, -21, -28, 3, 28, 3, -7, -24, -21, -48; -1218, -900, -1904, 8, 224, 12, -154, -480, -476, -1392],326,8]
%
% END OF LATTICE L327.8
%
%
% LATTICE L327.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-944160, -49056, 13440; -49056, -2532, 696; 13440, 696, -191],[672, 12, 1],[205, 27, 47, 1, -1, -1, 9, 1, 31, 9; 3892, 510, 882, 17, -21, -18, 196, 20, 602, 172; 28560, 3752, 6510, 132, -147, -136, 1344, 143, 4368, 1258],326,9]
%
% END OF LATTICE L327.9
%
%
% LATTICE L327.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[17499552, 4032, -52416; 4032, -12, -12; -52416, -12, 157],[672, 12, 1],[141, 12, 55, 11, 10, 2, 1, -1, -1, 2; 112, 11, 56, 14, 14, 3, 0, -2, -7, 1; 47040, 4004, 18354, 3672, 3339, 668, 336, -334, -336, 667],326,10]
%
% END OF LATTICE L327.10
%
%
% LATTICE L327.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[4427808, 189504, -26880; 189504, 8078, -1148; -26880, -1148, 163],[672, 14, 1],[1, 10, 11, 3, 9, 7, 1, -5, -1, 1; 25, 249, 272, 73, 208, 153, 18, -168, -26, 24; 341, 3402, 3728, 1008, 2944, 2226, 290, -2016, -348, 336],326,11]
%
% END OF LATTICE L327.11
%
%
% LATTICE L327.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-47712, 17472, 0; 17472, -6202, -14; 0, -14, 1],[672, 14, 1],[0, 11, 3, -5, -55, -163, -29, -209, -4, -35; 0, 30, 8, -14, -152, -450, -80, -576, -11, -96; -1, 420, 128, -168, -2000, -5964, -1066, -7728, -150, -1344],326,12]
%
% END OF LATTICE L327.12
%
%
% LATTICE L327.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[39648, 18144, -672; 18144, 8272, -304; -672, -304, 11],[672, 16, 1],[19, 11, 9, 2, 2, -1, -9, -1, -3, 1; -84, -45, -35, -7, -7, 3, 28, 3, 7, -6; -1232, -600, -434, -72, -70, 24, 224, 21, 0, -114],326,13]
%
% END OF LATTICE L327.13
%
%
% LATTICE L327.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2656416, 98784, -12096; 98784, 3632, -448; -12096, -448, 55],[672, 16, 1],[1, 4, 3, 3, 13, 16, 29, 2, -2, -1; 14, 57, 42, 41, 168, 201, 350, 21, -35, -15; 336, 1344, 1001, 992, 4214, 5136, 9184, 606, -728, -342],326,14]
%
% END OF LATTICE L327.14
%
%
% LATTICE L327.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1995168, 187488, 18816; 187488, 17256, 1728; 18816, 1728, 173],[672, 24, 1],[-1, -1, -13, -1, 1, 1, 3, 3, 4, 1; 210, 137, 1624, 113, -112, -111, -329, -324, -413, -76; -1974, -1256, -14784, -1020, 1008, 1000, 2961, 2912, 3696, 656],326,15]
%
% END OF LATTICE L327.15
%
%
% LATTICE L327.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[600096, 81312, 1344; 81312, 10968, 168; 1344, 168, -1],[672, 24, 1],[-158, -44, -325, -6, 25, 6, 17, -1, -33, -51; 1239, 345, 2548, 47, -196, -47, -133, 8, 259, 400; -4410, -1228, -9072, -168, 672, 164, 462, -32, -924, -1424],326,16]
%
% END OF LATTICE L327.16
%
%
% LATTICE L327.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-97440, -19488, 2688; -19488, -2324, 364; 2688, 364, -55],[672, 28, 1],[-3, -1, 1, 7, 15, 155, 49, 37, 3, -1; -60, -18, 20, 139, 296, 3054, 964, 726, 58, -21; -544, -168, 181, 1260, 2686, 27720, 8752, 6594, 528, -189],326,17]
%
% END OF LATTICE L327.17
%
%
% LATTICE L327.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-53864160, -5984832, 54432; -5984832, -664972, 6048; 54432, 6048, -55],[672, 28, 1],[7, -1, -1, 1, 7, 89, 67, 65, 6, 10; -56, 9, 8, -10, -58, -735, -552, -534, -49, -81; 768, 0, -110, -112, 547, 7224, 5584, 5586, 548, 987],326,18]
%
% END OF LATTICE L327.18
%
%
% LATTICE L327.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[96096, 43680, -2016; 43680, 18942, -882; -2016, -882, 41],[672, 42, 1],[-1, 0, 3, 2, 9, 3, 1, 1, -1, -5; -14, -5, 16, 17, 80, 27, 9, 8, -10, -56; -354, -112, 480, 462, 2160, 728, 243, 224, -264, -1456],326,19]
%
% END OF LATTICE L327.19
%
%
% LATTICE L327.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[45024, -6720, -2016; -6720, 966, 294; -2016, 294, 89],[672, 42, 1],[-7, -13, -13, -1, 1, 1, 0, -3, -1, -17; 106, 198, 200, 18, -8, -10, 1, 48, 15, 256; -510, -952, -960, -84, 48, 56, -3, -224, -72, -1232],326,20]
%
% END OF LATTICE L327.20
%
%
% LATTICE L327.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[442848, 672, -672; 672, -48, 0; -672, 0, 1],[672, 48, 1],[1, 0, -1, -1, -8, -4, -27, -1, -2, 0; 14, 1, -7, -9, -77, -39, -266, -10, -21, 0; 672, 8, -630, -648, -5250, -2632, -17808, -662, -1344, -1],326,21]
%
% END OF LATTICE L327.21
%
%
% LATTICE L327.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[17499552, 1266048, -52416; 1266048, 91536, -3792; -52416, -3792, 157],[672, 48, 1],[141, 24, 55, 11, 10, 4, 1, -1, -2, 4; 56, 11, 28, 7, 7, 3, 0, -1, -7, 1; 48384, 8272, 19026, 3840, 3507, 1408, 336, -358, -840, 1358],326,22]
%
% END OF LATTICE L327.22
%
%
% LATTICE L327.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[436128, -109536, 672; -109536, 27496, -168; 672, -168, 1],[672, 56, 1],[0, 2, 1, 0, -5, -16, -3, -23, -1, -5; 0, 9, 4, -1, -28, -87, -16, -120, -5, -24; -1, 168, 16, -140, -1216, -3528, -618, -4368, -160, -672],326,23]
%
% END OF LATTICE L327.23
%
%
% LATTICE L327.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-5869920, 1693440, -8736; 1693440, -488488, 2520; -8736, 2520, -13],[672, 56, 1],[0, -1, -1, -1, -3, -7, -1, -5, 0, 1; -1, -3, 4, 9, 44, 117, 19, 120, 3, 0; -194, 84, 1440, 2408, 10512, 27300, 4342, 26544, 580, -672],326,24]
%
% END OF LATTICE L327.24
%
%
% LATTICE L327.25
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-35085792, -6358464, 229824; -6358464, -1134588, 40992; 229824, 40992, -1481],[672, 84, 1],[139, 123, 29, 1, -1, -1, 15, 7, 25, 45; -29388, -26010, -6134, -215, 211, 214, -3164, -1478, -5282, -9512; -791856, -700840, -165282, -5796, 5685, 5768, -85248, -39823, -142320, -256298],326,25]
%
% END OF LATTICE L327.25
%
%
% LATTICE L327.26
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3075744, 20160, 12768; 20160, -84, -84; 12768, -84, -53],[672, 84, 1],[-3, 0, 1, 5, 1, 2, 1, -1, -1, -1; 16, 11, 8, 14, 2, 3, 0, -2, -1, 1; -768, -28, 222, 1176, 237, 476, 240, -238, -240, -245],326,26]
%
% END OF LATTICE L327.26
%
%
% LATTICE L327.27
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[13095264, -5419008, 19488; -5419008, 2242352, -8064; 19488, -8064, 29],[672, 112, 1],[1, 1, 0, 0, 1, 13, 5, 5, 1, 1; 10, 3, -1, -1, 13, 171, 66, 66, 13, 12; 2112, 168, -278, -280, 2942, 38808, 14992, 14994, 2944, 2667],326,27]
%
% END OF LATTICE L327.27
%
%
% LATTICE L327.28
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[434784, 218400, -672; 218400, 109648, -336; -672, -336, 1],[672, 112, 1],[19, 56, 5, 3, 0, -4, -1, 1, 2, 16; -46, -135, -12, -7, 0, 9, 2, -3, -5, -39; -2560, -7392, -646, -336, -1, 336, 16, -294, -312, -2226],326,28]
%
% END OF LATTICE L327.28
%
%
% LATTICE L327.29
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-672, 2016, -672; 2016, 3864, -1344; -672, -1344, 467],[672, 168, 1],[-7, -13, -13, -1, 1, 1, 0, -3, -2, -17; -174, -325, -328, -29, 16, 19, -1, -76, -49, -420; -510, -952, -960, -84, 48, 56, -3, -224, -144, -1232],326,29]
%
% END OF LATTICE L327.29
%
%
% LATTICE L327.30
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[10587360, 37632, 47040; 37632, -1848, 168; 47040, 168, 209],[672, 168, 1],[-10, -29, -35, -3, 71, 77, 43, 107, 12, 1; 1, 3, 4, 1, -4, -5, -3, -8, -1, 0; 2250, 6524, 7872, 672, -15984, -17332, -9678, -24080, -2700, -224],326,30]
%
% END OF LATTICE L327.30
%
%
% LATTICE L327.31
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-15241632, -2577792, 45696; -2577792, -435792, 7728; 45696, 7728, -137],[672, 336, 1],[51, 44, 10, -1, -1, 0, 7, 3, 10, 17; 40, 33, 7, -3, -1, 1, 8, 3, 9, 14; 19248, 16520, 3726, -504, -390, 56, 2784, 1169, 3840, 6454],326,31]
%
% END OF LATTICE L327.31
%
%
% LATTICE L327.32
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3075744, -2104704, 12768; -2104704, -1439760, 8736; 12768, 8736, -53],[672, 336, 1],[-3, 0, 1, 5, 1, 4, 1, -1, -2, -2; 8, 11, 4, 7, 1, 3, 0, -1, -1, 1; 576, 1792, 894, 2352, 405, 1456, 240, -406, -648, -322],326,32]
%
% END OF LATTICE L327.32
%

\medskip%
%------------------------------WEYL-GROUP-W328--------------------------------
%
\leavevmode\llap{}%
$W_{328}$%
\qquad\llap{32} lattices, $\chi=96$%
\hfill%
$2|22222|22222|22222|2222\rtimes D_{4}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L328.1
%
\leavevmode%
${L_{328.1}}$%
{} : {$[1\above{1pt}{1pt}{1}{}2\above{1pt}{1pt}{1}{}]\above{1pt}{1pt}{}{0}32\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}7\above{1pt}{1pt}{-}{}$}\EasyButWeakLineBreak%
{${672}\above{1pt}{1pt}{}{2}{2}\above{1pt}{1pt}{r}{2}{672}\above{1pt}{1pt}{s}{2}{4}\above{1pt}{1pt}{*}{2}{24}\above{1pt}{1pt}{s}{2}{32}\above{1pt}{1pt}{*}{2}{168}\above{1pt}{1pt}{s}{2}{32}\above{1pt}{1pt}{*}{2}{24}\above{1pt}{1pt}{l}{2}{1}\above{1pt}{1pt}{}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
81312\\-2016\\2016
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2016\\14\\-8
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2016\\-8\\1
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2113\\-598752\\-517440
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4\\1133\\980
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4\\1134\\979
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-173\\-49056\\-42336
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3\\-851\\-734
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-103\\-29232\\-25200
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3\\-852\\-734
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-5\\-1422\\-1224
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3\\-856\\-736
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-294\\-252
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\280\\240
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\282\\240
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\-1
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[81312, -2016, 2016; -2016, 14, -8; 2016, -8, 1],[672, 2, 1],[-173, -3, -103, -3, -5, -3, -1, 1, 1, 0, -19, -1, -89, -5, -19, -29, -71, -33, -25, -4; -49056, -851, -29232, -852, -1422, -856, -294, 280, 282, 0, -5376, -283, -25200, -1416, -5382, -8216, -20118, -9352, -7086, -1134; -42336, -734, -25200, -734, -1224, -736, -252, 240, 240, -1, -4704, -246, -21840, -1226, -4656, -7104, -17388, -8080, -6120, -979],327,1]
%
% END OF LATTICE L328.1
%
\hbox{}\par\smallskip%
%
% LATTICE L328.2
%
\leavevmode%
${L_{328.2}}$%
{} : {$[1\above{1pt}{1pt}{1}{}2\above{1pt}{1pt}{-}{}]\above{1pt}{1pt}{}{4}32\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}7\above{1pt}{1pt}{-}{}$}\EasyButWeakLineBreak%
{${672}\above{1pt}{1pt}{*}{2}{8}\above{1pt}{1pt}{s}{2}{672}\above{1pt}{1pt}{*}{2}{4}\above{1pt}{1pt}{l}{2}{6}\above{1pt}{1pt}{}{2}{32}\above{1pt}{1pt}{}{2}{42}\above{1pt}{1pt}{r}{2}{32}\above{1pt}{1pt}{l}{2}{6}\above{1pt}{1pt}{}{2}{1}\above{1pt}{1pt}{r}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
250656\\2016\\-1344
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2016\\-22\\-8
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1344\\-8\\7
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-937\\-13104\\-192192
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-21\\-295\\-4312
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
6\\84\\1231
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
65\\840\\13104
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\10\\192
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-5\\-168\\-1344
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-18\\-218
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2\\-33\\-426
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-5\\-80\\-1056
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-4\\-63\\-840
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-16\\-208
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\15\\210
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\15\\209
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[250656, 2016, -1344; 2016, -22, -8; -1344, -8, 7],[672, 2, 1],[65, 1, -5, -1, -2, -5, -4, -1, 1, 1, 79, 5, 149, 7, 11, 29, 31, 25, 8, 2; 840, 10, -168, -18, -33, -80, -63, -16, 15, 15, 1176, 74, 2184, 102, 159, 416, 441, 352, 111, 27; 13104, 192, -1344, -218, -426, -1056, -840, -208, 210, 209, 16464, 1040, 30912, 1450, 2274, 5984, 6384, 5136, 1638, 407],327,2]
%
% END OF LATTICE L328.2
%
\hbox{}\par\smallskip%
%
% LATTICE L328.3
%
\leavevmode%
${L_{328.3}}$%
{} : {$1\above{1pt}{1pt}{-}{5}4\above{1pt}{1pt}{1}{1}32\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{-2}{}7\above{1pt}{1pt}{-}{}$}\EasyButWeakLineBreak%
{${84}\above{1pt}{1pt}{l}{2}{4}\above{1pt}{1pt}{}{2}{21}\above{1pt}{1pt}{r}{2}{32}\above{1pt}{1pt}{*}{2}{48}\above{1pt}{1pt}{l}{2}{1}\above{1pt}{1pt}{}{2}{84}\above{1pt}{1pt}{r}{2}{4}\above{1pt}{1pt}{*}{2}{48}\above{1pt}{1pt}{s}{2}{32}\above{1pt}{1pt}{*}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2250528\\750624\\4032
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
750624\\-250348\\-1336
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4032\\-1336\\1
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1231201\\-3712800\\3964800
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
409374\\1234505\\-1318296
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1026\\3094\\-3305
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-7507\\-22638\\24150
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-834\\-2515\\2684
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-5773\\-17409\\18585
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-4169\\-12572\\13424
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-6349\\-19146\\20448
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1026\\-3094\\3305
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-8656\\-26103\\27888
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1731\\-5220\\5578
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-4423\\-13338\\14256
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2243\\-6764\\7232
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-2250528, 750624, 4032; 750624, -250348, -1336; 4032, -1336, 1],[672, 4, 1],[-7507, -834, -5773, -4169, -6349, -1026, -8656, -1731, -4423, -2243, -4805, -192, -383, 65, 193, 0, -578, -321, -1733, -1861; -22638, -2515, -17409, -12572, -19146, -3094, -26103, -5220, -13338, -6764, -14490, -579, -1155, 196, 582, 0, -1743, -968, -5226, -5612; 24150, 2684, 18585, 13424, 20448, 3305, 27888, 5578, 14256, 7232, 15498, 620, 1239, -208, -624, -1, 1848, 1030, 5568, 5984],327,3]
%
% END OF LATTICE L328.3
%
\hbox{}\par\smallskip%
%
% LATTICE L328.4
%
\leavevmode%
${L_{328.4}}$%
{} : {$1\above{1pt}{1pt}{-}{5}4\above{1pt}{1pt}{1}{7}32\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{-2}{}7\above{1pt}{1pt}{-}{}$}\EasyButWeakLineBreak%
{${21}\above{1pt}{1pt}{r}{2}{16}\above{1pt}{1pt}{*}{2}{84}\above{1pt}{1pt}{s}{2}{32}\above{1pt}{1pt}{l}{2}{12}\above{1pt}{1pt}{}{2}{1}\above{1pt}{1pt}{r}{2}{336}\above{1pt}{1pt}{*}{2}{4}\above{1pt}{1pt}{l}{2}{12}\above{1pt}{1pt}{}{2}{32}\above{1pt}{1pt}{}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-867552\\-672\\2688
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-672\\76\\-8
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2688\\-8\\-7
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
13259\\578760\\4411680
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
85\\3709\\28280
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-51\\-2226\\-16969
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
16\\693\\5313
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
11\\478\\3656
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
109\\4746\\36246
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
47\\2048\\15632
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
43\\1875\\14304
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
16\\698\\5323
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
307\\13398\\102144
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
35\\1528\\11646
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
52\\2271\\17304
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
65\\2840\\21632
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-867552, -672, 2688; -672, 76, -8; 2688, -8, -7],[672, 4, 1],[16, 11, 109, 47, 43, 16, 307, 35, 52, 65, 86, 23, 95, 21, 8, 1, -1, -1, -1, 3; 693, 478, 4746, 2048, 1875, 698, 13398, 1528, 2271, 2840, 3759, 1006, 4158, 920, 351, 44, -42, -44, -45, 128; 5313, 3656, 36246, 15632, 14304, 5323, 102144, 11646, 17304, 21632, 28623, 7656, 31626, 6992, 2664, 333, -336, -334, -336, 992],327,4]
%
% END OF LATTICE L328.4
%
%
% LATTICE L328.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[4103904, 509376, -6720; 509376, 63222, -834; -6720, -834, 11],[672, 6, 1],[-9, 0, 5, 1, 1, 3, 1, -1, -1, -1, -23, -2, -37, -5, -5, -19, -13, -15, -3, -1; 0, -5, -112, -16, -14, -40, -14, 8, 10, 10, 224, 19, 336, 44, 42, 152, 98, 104, 18, 4; -5600, -384, -5488, -606, -452, -1200, -448, 0, 148, 147, 2912, 216, 2800, 270, 116, -144, -560, -1344, -484, -315],327,5]
%
% END OF LATTICE L328.5
%
%
% LATTICE L328.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-495264, -16800, 4704; -16800, -366, 120; 4704, 120, -37],[672, 6, 1],[155, 13, 57, 3, 0, -5, -2, -1, 1, 3, 85, 17, 183, 27, 15, 125, 47, 121, 14, 12; 10248, 858, 3752, 196, -1, -336, -133, -64, 67, 200, 5656, 1130, 12152, 1792, 995, 8288, 3115, 8016, 927, 794; 52864, 4428, 19376, 1014, -4, -1728, -686, -336, 344, 1029, 29120, 5820, 62608, 9234, 5128, 42720, 16058, 41328, 4780, 4095],327,6]
%
% END OF LATTICE L328.6
%
%
% LATTICE L328.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-200928, 672, 672; 672, 56, -16; 672, -16, 1],[672, 8, 1],[-173, -6, -103, -3, -5, -3, -1, 1, 1, 0, -19, -2, -89, -5, -19, -29, -71, -33, -25, -4; -9996, -347, -5964, -174, -291, -176, -63, 56, 57, 0, -1092, -115, -5124, -288, -1095, -1672, -4095, -1904, -1443, -231; -42336, -1468, -25200, -734, -1224, -736, -252, 240, 240, -1, -4704, -492, -21840, -1226, -4656, -7104, -17388, -8080, -6120, -979],327,7]
%
% END OF LATTICE L328.7
%
%
% LATTICE L328.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[81312, -4032, 0; -4032, 200, 0; 0, 0, -1],[672, 8, 1],[89, 2, 19, 0, -1, -1, 1, 3, 5, 3, 103, 6, 173, 8, 25, 33, 71, 29, 19, 5; 1680, 37, 336, -1, -21, -20, 21, 60, 99, 59, 2016, 117, 3360, 155, 483, 636, 1365, 556, 363, 95; -1680, -48, -672, -14, -12, 0, 0, -16, -36, -26, -1008, -64, -2016, -98, -324, -448, -1008, -432, -300, -86],327,8]
%
% END OF LATTICE L328.8
%
%
% LATTICE L328.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3208800, -57792, 7392; -57792, -996, 132; 7392, 132, -17],[672, 12, 1],[30, 13, 39, 29, 9, 5, 3, 0, -1, -1, 2, 3, 25, 35, 23, 27, 45, 16, 33, 65; 392, 169, 504, 372, 114, 62, 35, -1, -14, -12, 28, 41, 336, 468, 306, 358, 595, 211, 434, 852; 16051, 6948, 20818, 15456, 4784, 2646, 1568, -9, -544, -528, 1085, 1620, 13454, 18816, 12352, 14490, 24136, 8577, 17680, 34800],327,9]
%
% END OF LATTICE L328.9
%
%
% LATTICE L328.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-979104, -30240, 8064; -30240, -876, 240; 8064, 240, -65],[672, 12, 1],[53, 17, 9, 7, 0, -1, -1, 1, 3, 25, 39, 29, 37, 85, 23, 47, 139, 22, 20, 67; 2408, 770, 406, 312, -1, -46, -42, 47, 139, 1152, 1792, 1330, 1694, 3888, 1051, 2146, 6342, 1003, 911, 3048; 15442, 4944, 2611, 2016, -4, -294, -280, 297, 884, 7344, 11438, 8496, 10829, 24864, 6724, 13734, 40600, 6423, 5836, 19536],327,10]
%
% END OF LATTICE L328.10
%
%
% LATTICE L328.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[117600, 19488, -2688; 19488, 2786, -392; -2688, -392, 55],[672, 14, 1],[35, 8, 73, 25, 83, 115, 37, 111, 77, 11, 61, 6, 23, 3, 1, -3, -1, 1, 7, 3; 1392, 317, 2880, 984, 3258, 4504, 1446, 4328, 2994, 426, 2352, 229, 864, 108, 18, -136, -42, 40, 282, 120; 11616, 2646, 24048, 8218, 27216, 37632, 12084, 36176, 25032, 3563, 19680, 1918, 7248, 910, 168, -1120, -348, 336, 2352, 1001],327,11]
%
% END OF LATTICE L328.11
%
%
% LATTICE L328.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-309792, -22848, 3360; -22848, -490, 42; 3360, 42, -1],[672, 14, 1],[49, 23, 107, 37, 62, 173, 28, 169, 59, 17, 95, 19, 37, 5, 1, -5, -1, -1, 4, 4; -4536, -2130, -9912, -3428, -5745, -16032, -2595, -15664, -5469, -1576, -8808, -1762, -3432, -464, -93, 464, 93, 96, -369, -370; -26352, -12376, -57600, -19922, -33390, -93184, -15084, -91056, -31794, -9163, -51216, -10248, -19968, -2702, -546, 2688, 540, 560, -2142, -2149],327,12]
%
% END OF LATTICE L328.12
%
%
% LATTICE L328.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-37178923488, 1858946208, -16759680; 1858946208, -92947312, 837984; -16759680, 837984, -7555],[672, 16, 1],[-611, -58, -71, -1, 37, 14, 74, -5, -77, -115, -541, -134, -505, -383, -613, -206, -1802, -187, -499, -269; -12852, -1219, -1491, -20, 777, 293, 1533, -109, -1635, -2432, -11424, -2827, -10647, -8072, -12915, -4339, -37947, -3937, -10503, -5660; -70098, -6544, -7875, 0, 4104, 1442, 5880, -998, -10536, -14640, -66990, -16304, -60669, -45696, -72648, -24290, -211512, -21850, -58008, -31056],327,13]
%
% END OF LATTICE L328.13
%
%
% LATTICE L328.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-57105888, 2855328, 698880; 2855328, -142768, -34944; 698880, -34944, -8551],[672, 16, 1],[-400, -44, -113, -1, 47, 25, 268, 15, 77, 29, -8, -24, -295, -135, -251, -93, -880, -49, -281, -165; -8421, -925, -2373, -20, 987, 524, 5607, 313, 1599, 592, -231, -517, -6279, -2864, -5313, -1966, -18585, -1034, -5925, -3476; 1722, 184, 462, 0, -192, -98, -1008, -53, -240, -48, 294, 152, 1554, 672, 1200, 434, 4032, 221, 1248, 720],327,14]
%
% END OF LATTICE L328.14
%
%
% LATTICE L328.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[4103904, 1099392, -6720; 1099392, 294504, -1800; -6720, -1800, 11],[672, 24, 1],[-9, 0, 5, 1, 1, 3, 1, -1, -1, -1, -23, -4, -37, -5, -5, -19, -13, -15, -3, -1; 0, -5, -56, -8, -7, -20, -7, 4, 5, 5, 112, 19, 168, 22, 21, 76, 49, 52, 9, 2; -5600, -828, -6160, -702, -536, -1440, -532, 48, 208, 207, 4256, 660, 4816, 534, 368, 768, 28, -720, -376, -291],327,15]
%
% END OF LATTICE L328.15
%
%
% LATTICE L328.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[11047008, 1380960, 24192; 1380960, 172632, 3024; 24192, 3024, 53],[672, 24, 1],[201, 44, 523, 81, 95, 413, 323, 433, 105, 96, 663, 64, 341, 27, 13, 19, 1, -1, 3, 12; -1428, -313, -3724, -577, -677, -2944, -2303, -3088, -749, -685, -4732, -457, -2436, -193, -93, -136, -7, 8, -21, -85; -10304, -2232, -26320, -4062, -4748, -20592, -16072, -21504, -5204, -4746, -32704, -3144, -16688, -1314, -628, -912, -56, 0, -172, -630],327,16]
%
% END OF LATTICE L328.16
%
%
% LATTICE L328.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-303072, 75936, -3360; 75936, -19012, 840; -3360, 840, -37],[672, 28, 1],[7, 3, 1, -1, -11, -3, -5, -9, -29, -19, -7, -3, -1, 1, 11, 3, 5, 9, 29, 19; 36, 17, 6, -4, -66, -19, -33, -62, -210, -148, -60, -31, -18, -52, -18, 5, 15, 34, 126, 92; 174, 112, 45, 0, -504, -161, -300, -602, -2184, -1680, -750, -448, -333, -1344, -1512, -175, -132, -70, 168, 336],327,17]
%
% END OF LATTICE L328.17
%
%
% LATTICE L328.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[23520, 2688, 0; 2688, 308, 0; 0, 0, -1],[672, 28, 1],[7, 5, 1, 1, -1, -1, -1, 0, 2, 7, 5, 9, 5, 27, 22, 15, 19, 7, 19, 21; -66, -46, -9, -8, 9, 8, 6, -2, -27, -80, -54, -94, -51, -272, -219, -148, -186, -68, -183, -200; -102, -56, -9, 0, 0, -14, -48, -35, -168, -336, -186, -280, -135, -672, -504, -322, -384, -133, -336, -336],327,18]
%
% END OF LATTICE L328.18
%
%
% LATTICE L328.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[4374048, -539616, 25536; -539616, 66570, -3150; 25536, -3150, 149],[672, 42, 1],[87, 27, 37, 17, 5, -3, -1, 1, 7, 10, 41, 29, 91, 95, 107, 451, 49, 447, 105, 46; 800, 247, 336, 152, 42, -40, -10, 8, 66, 94, 384, 271, 848, 884, 994, 4184, 454, 4136, 970, 424; 1984, 588, 752, 294, 28, -336, -40, 0, 196, 273, 1088, 756, 2320, 2394, 2660, 11088, 1192, 10752, 2492, 1071],327,19]
%
% END OF LATTICE L328.19
%
%
% LATTICE L328.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[49056, 39648, -2016; 39648, -12642, 504; -2016, 504, -19],[672, 42, 1],[165, 103, 71, 33, 5, -5, -1, -1, 6, 18, 75, 107, 169, 177, 100, 845, 46, 841, 99, 87; 3144, 1962, 1352, 628, 95, -96, -19, -16, 115, 344, 1432, 2042, 3224, 3376, 1907, 16112, 877, 16032, 1887, 1658; 65824, 41076, 28304, 13146, 1988, -2016, -398, -336, 2408, 7203, 29984, 42756, 67504, 70686, 39928, 337344, 18362, 335664, 39508, 34713],327,20]
%
% END OF LATTICE L328.20
%
%
% LATTICE L328.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-950880, 158592, -4032; 158592, -26448, 672; -4032, 672, -17],[672, 48, 1],[25, 6, 2, -1, -1, 0, 6, 5, 9, 29, 39, 26, 30, 65, 33, 32, 90, 27, 23, 35; 168, 41, 14, -6, -7, -1, 35, 31, 57, 186, 252, 169, 196, 426, 217, 211, 595, 179, 153, 234; 686, 192, 77, 0, -40, -42, -56, 30, 104, 432, 658, 480, 595, 1344, 712, 714, 2072, 642, 568, 912],327,21]
%
% END OF LATTICE L328.21
%
%
% LATTICE L328.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-26352480, 4392192, 2175264; 4392192, -732048, -362544; 2175264, -362544, -179525],[672, 48, 1],[-1830, -510, -409, -1, 103, 105, 118, -47, -295, -1195, -1802, -1306, -3223, -3631, -1919, -1921, -5566, -861, -1521, -2437; -12817, -3571, -2863, -6, 721, 734, 819, -331, -2071, -8382, -12635, -9155, -22589, -25446, -13447, -13460, -38997, -6032, -10655, -17070; 3710, 1032, 826, 0, -208, -210, -224, 99, 608, 2448, 3682, 2664, 6566, 7392, 3904, 3906, 11312, 1749, 3088, 4944],327,22]
%
% END OF LATTICE L328.22
%
%
% LATTICE L328.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2657760, 172704, -12096; 172704, 11144, -784; -12096, -784, 55],[672, 56, 1],[73, 16, 35, 3, 7, 1, -1, -3, 1, 3, 23, 12, 61, 11, 77, 111, 37, 115, 83, 25; 564, 125, 276, 24, 57, 8, -9, -32, -3, 18, 156, 85, 444, 81, 573, 832, 279, 872, 633, 192; 24048, 5292, 11616, 1001, 2352, 336, -348, -1120, 168, 910, 7248, 3836, 19680, 3563, 25032, 36176, 12084, 37632, 27216, 8218],327,23]
%
% END OF LATTICE L328.23
%
%
% LATTICE L328.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[5826912, -1520064, 15456; -1520064, 396536, -4032; 15456, -4032, 41],[672, 56, 1],[-31, -4, -5, 0, -1, -7, -5, -27, -31, -15, -65, -24, -91, -28, -83, -105, -31, -85, -53, -13; -120, -17, -24, -1, -3, -20, -15, -84, -99, -49, -216, -81, -312, -97, -291, -372, -111, -308, -195, -49; -144, -168, -480, -98, 84, 672, 408, 1904, 1932, 826, 3216, 1064, 3552, 994, 2604, 2912, 744, 1680, 756, 70],327,24]
%
% END OF LATTICE L328.24
%
%
% LATTICE L328.25
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1156512, -331296, 7392; -331296, -93660, 2100; 7392, 2100, -47],[672, 84, 1],[7, 19, 7, 29, 5, -1, -1, -3, -5, -1, 1, 9, 9, 83, 51, 57, 13, 31, 61, 113; 38, 101, 36, 140, 18, -14, -7, -19, -30, -4, 6, 53, 52, 476, 290, 322, 73, 173, 338, 620; 2791, 7476, 2698, 10752, 1568, -798, -472, -1323, -2128, -336, 425, 3780, 3734, 34272, 20944, 23310, 5296, 12579, 24640, 45360],327,25]
%
% END OF LATTICE L328.25
%
%
% LATTICE L328.26
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[672, 0, 0; 0, 18060, -672; 0, -672, 25],[672, 84, 1],[-2, -13, -3, -17, -3, -2, -1, -1, 0, 1, 0, -1, -1, -11, -4, -5, -5, -13, -7, -29; 34, 214, 48, 264, 45, 29, 14, 14, 1, 0, 2, 38, 24, 240, 81, 97, 94, 238, 125, 504; 907, 5712, 1282, 7056, 1204, 777, 376, 378, 28, 0, 53, 1008, 638, 6384, 2156, 2583, 2504, 6342, 3332, 13440],327,26]
%
% END OF LATTICE L328.26
%
%
% LATTICE L328.27
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-303072, 151872, -3360; 151872, -76048, 1680; -3360, 1680, -37],[672, 112, 1],[1, 6, 7, 19, 29, 9, 10, 6, 11, 1, -1, -6, -7, -19, -29, -9, -10, -6, -11, -1; 3, 17, 18, 46, 63, 17, 15, 5, -9, -26, -9, -31, -30, -74, -105, -31, -33, -19, -33, -2; 45, 224, 174, 336, 168, -70, -264, -350, -1512, -1344, -333, -896, -750, -1680, -2184, -602, -600, -322, -504, 0],327,27]
%
% END OF LATTICE L328.27
%
%
% LATTICE L328.28
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-61152, -30912, -7392; -30912, -15568, -3696; -7392, -3696, -865],[672, 112, 1],[7, 12, -16, -91, -263, -63, -208, -195, -677, -505, -223, -264, -200, -413, -493, -63, -116, -57, -79, 1; -21, -37, 45, 262, 765, 184, 609, 572, 1989, 1486, 657, 779, 591, 1222, 1461, 187, 345, 170, 237, -2; 30, 56, -54, -336, -1008, -245, -816, -770, -2688, -2016, -894, -1064, -810, -1680, -2016, -259, -480, -238, -336, 0],327,28]
%
% END OF LATTICE L328.28
%
%
% LATTICE L328.29
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[16596384, 6279840, -49728; 6279840, 2376024, -18816; -49728, -18816, 149],[672, 168, 1],[87, 54, 37, 17, 5, -3, -1, 1, 7, 10, 41, 58, 91, 95, 107, 451, 49, 447, 105, 46; 52, 31, 20, 8, 1, -8, -1, 0, 5, 7, 28, 39, 60, 62, 69, 288, 31, 280, 65, 28; 35584, 21924, 14864, 6678, 1792, -2016, -460, 336, 2968, 4221, 17216, 24276, 37936, 39522, 44408, 186816, 20260, 184464, 43232, 18879],327,29]
%
% END OF LATTICE L328.29
%
%
% LATTICE L328.30
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[656544, 369600, -2688; 369600, 207816, -1512; -2688, -1512, 11],[672, 168, 1],[-13, -9, -7, -4, -2, -3, 0, 1, 0, -1, -3, -5, -9, -10, -12, -53, -6, -57, -14, -13; -12, -7, -4, -1, 1, 8, 1, 8, 1, -1, -4, -7, -12, -13, -15, -64, -7, -64, -15, -13; -4864, -3192, -2288, -1134, -364, 336, 136, 1344, 140, -378, -1280, -2184, -3856, -4242, -5012, -21840, -2440, -22848, -5516, -4998],327,30]
%
% END OF LATTICE L328.30
%
%
% LATTICE L328.31
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[672, 0, 0; 0, -3113040, 12096; 0, 12096, -47],[672, 336, 1],[-3, -13, -2, -29, -14, -13, -5, -10, -8, -11, -1, -1, 0, 1, 0, -1, -1, -4, -6, -17; 4, 25, 5, 84, 47, 49, 21, 47, 43, 72, 8, 17, 1, 0, -5, -7, -3, -5, -1, 12; 1018, 6384, 1279, 21504, 12040, 12558, 5384, 12054, 11032, 18480, 2054, 4368, 257, 0, -1288, -1806, -776, -1302, -280, 3024],327,31]
%
% END OF LATTICE L328.31
%
%
% LATTICE L328.32
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[672, 0, 0; 0, -12432, 1680; 0, 1680, -227],[672, 336, 1],[-1, -1, 0, 1, 0, -1, -1, -2, -6, -17, -3, -13, -4, -29, -14, -13, -5, -5, -8, -11; 7, 23, 3, 0, -15, -28, -17, -25, -59, -132, -19, -65, -15, -84, -27, -14, -1, 4, 17, 48; 50, 168, 22, 0, -112, -210, -128, -189, -448, -1008, -146, -504, -118, -672, -224, -126, -16, 21, 112, 336],327,32]
%
% END OF LATTICE L328.32
%

\medskip%
%------------------------------WEYL-GROUP-W329--------------------------------
%
\leavevmode\llap{}%
$W_{329}$%
\qquad\llap{8} lattices, $\chi=144$%
\hfill%
$\infty\infty\infty2|2\infty\infty\infty|\infty\infty\infty2|2\infty\infty\infty|\rtimes D_{4}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L329.1
%
\leavevmode%
${L_{329.1}}$%
{} : {$1\above{1pt}{1pt}{2}{0}4\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{-}{}7\above{1pt}{1pt}{1}{}49\above{1pt}{1pt}{1}{}$}\EasyButWeakLineBreak%
{${28}\above{1pt}{1pt}{7,4}{\infty z}{7}\above{1pt}{1pt}{28,11}{\infty}{28}\above{1pt}{1pt}{7,1}{\infty b}{28}\above{1pt}{1pt}{}{2}{49}\above{1pt}{1pt}{}{2}{7}\above{1pt}{1pt}{28,15}{\infty}{28}\above{1pt}{1pt}{7,4}{\infty a}{28}\above{1pt}{1pt}{14,9}{\infty}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-143668\\-1960\\-84476
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1960\\-21\\-1113
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-84476\\-1113\\-49400
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-883\\-10584\\1764
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-7\\-85\\14
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-484\\-5808\\967
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
173\\2400\\-350
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
90\\1243\\-182
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
381\\5228\\-770
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
499\\6812\\-1008
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
267\\3619\\-539
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
125\\1669\\-252
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
49\\596\\-98
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-69\\-988\\140
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-143668, -1960, -84476; -1960, -21, -1113; -84476, -1113, -49400],[196, 7, 1],[173, 90, 381, 499, 267, 125, 49, -69, -159, -83, -339, -429, -218, -90, -7, 83; 2400, 1243, 5228, 6812, 3619, 1669, 596, -988, -2232, -1159, -4724, -5972, -3031, -1249, -92, 1156; -350, -182, -770, -1008, -539, -252, -98, 140, 322, 168, 686, 868, 441, 182, 14, -168],328,1]
%
% END OF LATTICE L329.1
%
\hbox{}\par\smallskip%
%
% LATTICE L329.2
%
\leavevmode%
${L_{329.2}}$%
{} : {$1\above{1pt}{1pt}{2}{{\rm II}}8\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{-}{}7\above{1pt}{1pt}{1}{}49\above{1pt}{1pt}{1}{}$}\EasyButWeakLineBreak%
{${56}\above{1pt}{1pt}{7,2}{\infty z}{14}\above{1pt}{1pt}{28,11}{\infty b}{56}\above{1pt}{1pt}{7,2}{\infty a}{56}\above{1pt}{1pt}{r}{2}{98}\above{1pt}{1pt}{s}{2}{14}\above{1pt}{1pt}{28,15}{\infty a}{56}\above{1pt}{1pt}{7,1}{\infty b}{56}\above{1pt}{1pt}{7,2}{\infty}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-56840\\18424\\7448
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
18424\\-5964\\-2401
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7448\\-2401\\-954
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2057\\8232\\-4704
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-686\\-2745\\1568
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-301\\-1204\\687
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
127\\516\\-308
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
85\\344\\-203
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
475\\1916\\-1120
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
741\\2984\\-1736
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
484\\1946\\-1127
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
312\\1252\\-721
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
319\\1276\\-728
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
53\\208\\-112
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-56840, 18424, 7448; 18424, -5964, -2401; 7448, -2401, -954],[392, 7, 1],[127, 85, 475, 741, 484, 312, 319, 53, -29, -36, -181, -251, -141, -67, -25, 45; 516, 344, 1916, 2984, 1946, 1252, 1276, 208, -124, -148, -740, -1024, -574, -272, -100, 184; -308, -203, -1120, -1736, -1127, -721, -728, -112, 84, 91, 448, 616, 343, 161, 56, -112],328,2]
%
% END OF LATTICE L329.2
%
%
% LATTICE L329.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-621908, -3724, 3528; -3724, -21, 21; 3528, 21, -20],[196, 7, 1],[7, 3, 3, 1, 0, -1, -1, 0, 3, 7, 27, 24, 5, 51, 31, 5; 204, 76, 64, 17, -1, -20, -8, 11, 132, 260, 944, 823, 169, 1700, 1016, 157; 1470, 616, 602, 196, -1, -196, -182, 14, 686, 1540, 5866, 5194, 1079, 10976, 6650, 1064],328,3]
%
% END OF LATTICE L329.3
%
%
% LATTICE L329.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-25480, -1176, 1176; -1176, -42, 49; 1176, 49, -52],[392, 7, 1],[11, 3, 7, 5, 0, -2, -5, -3, -1, 2, 23, 45, 5, 27, 35, 13; 176, 45, 92, 48, -3, -45, -92, -48, -8, 39, 412, 792, 87, 465, 596, 216; 420, 112, 252, 168, -2, -84, -196, -112, -28, 84, 924, 1792, 198, 1064, 1372, 504],328,4]
%
% END OF LATTICE L329.4
%
%
% LATTICE L329.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[51144436, 16879324, 12698448; 16879324, 5570768, 4190900; 12698448, 4190900, 3152847],[196, 28, 1],[-3210, -6517, -24548, -21712, -63145, -45959, -27928, -4526, -6590, -3283, -4852, -2788, -5455, -3041, -1472, -374; 5, 9, 33, 29, 84, 61, 37, 6, 9, 5, 9, 6, 14, 9, 5, 1; 12922, 26236, 98826, 87409, 254212, 185024, 112434, 18221, 26530, 13216, 19530, 11221, 21952, 12236, 5922, 1505],328,5]
%
% END OF LATTICE L329.5
%
%
% LATTICE L329.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[5428612, -76636, 1328880; -76636, 1232, -18760; 1328880, -18760, 325299],[196, 28, 1],[-8742, -1465, -2368, -1501, -47, -293, -1148, -2015, -7522, -6667, -46424, -79819, -16217, -40367, -47644, -14249; 37, 6, 9, 5, 0, 1, 5, 9, 33, 29, 201, 345, 70, 174, 205, 61; 35714, 5985, 9674, 6132, 192, 1197, 4690, 8232, 30730, 27237, 189658, 326088, 66252, 164913, 194642, 58212],328,6]
%
% END OF LATTICE L329.6
%
%
% LATTICE L329.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-136416, -38024, -12544; -38024, -10528, -3472; -12544, -3472, -1145],[392, 56, 1],[-17, -13, -84, -281, -391, -68, -78, -43, -11, -1, 0, 1, -1, -2, -6, -13; 982, 734, 4685, 15599, 21623, 3746, 4275, 2321, 572, 43, -23, -59, 133, 139, 387, 787; -2786, -2079, -13258, -44128, -61152, -10591, -12082, -6552, -1610, -119, 70, 168, -392, -399, -1106, -2240],328,7]
%
% END OF LATTICE L329.7
%
%
% LATTICE L329.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-374752, -93688, -183456; -93688, -23408, -45864; -183456, -45864, -89809],[392, 56, 1],[-1159, -916, -6019, -20262, -4048, -4953, -5719, -3214, -859, -93, -35, 82, 12, -92, -335, -822; 4, 5, 39, 139, 29, 37, 45, 29, 10, 2, 3, 1, -1, -2, -3, -1; 2366, 1869, 12278, 41328, 8256, 10101, 11662, 6552, 1750, 189, 70, -168, -24, 189, 686, 1680],328,8]
%
% END OF LATTICE L329.8
%

\medskip%
%------------------------------WEYL-GROUP-W330--------------------------------
%
\leavevmode\llap{}%
$W_{330}$%
\qquad\llap{8} lattices, $\chi=36$%
\hfill%
$2\infty2\infty\infty\infty$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L330.1
%
\leavevmode%
${L_{330.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}8\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{1}{}9\above{1pt}{1pt}{-}{}81\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${72}\above{1pt}{1pt}{b}{2}{162}\above{1pt}{1pt}{12,1}{\infty b}{648}\above{1pt}{1pt}{b}{2}{18}\above{1pt}{1pt}{36,1}{\infty b}{72}\above{1pt}{1pt}{18,13}{\infty z}{18}\above{1pt}{1pt}{36,13}{\infty a}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1577880\\14256\\-166536
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
14256\\-90\\1521
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-166536\\1521\\-17570
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
63\\244\\-576
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
124\\477\\-1134
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-815\\-3168\\7452
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-375\\-1454\\3429
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-811\\-3140\\7416
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-62\\-239\\567
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-1577880, 14256, -166536; 14256, -90, 1521; -166536, 1521, -17570],[648, 9, 1],[63, 124, -815, -375, -811, -62; 244, 477, -3168, -1454, -3140, -239; -576, -1134, 7452, 3429, 7416, 567],329,1]
%
% END OF LATTICE L330.1
%
%
% LATTICE L330.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-11502, 1296, 5184; 1296, -144, -585; 5184, -585, -2336],[162, 9, 1],[-9, -1, 163, 114, 101, 5; -8, -9, 144, 107, 100, 8; -18, 0, 324, 225, 198, 9],329,2]
%
% END OF LATTICE L330.2
%
%
% LATTICE L330.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1023678, 6480, 12798; 6480, -36, -81; 12798, -81, -160],[162, 9, 1],[39, 2, -1, -1, 9, 11; -38, -3, 0, 2, -2, -7; 3132, 161, -80, -81, 720, 882],329,3]
%
% END OF LATTICE L330.3
%
%
% LATTICE L330.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[324, 162, 162; 162, 576, 144; 162, 144, 89],[162, 18, 1],[4, -1, 176, 259, 122, 24; 1, 0, 54, 79, 37, 7; -9, 0, -405, -594, -279, -54],329,4]
%
% END OF LATTICE L330.4
%
%
% LATTICE L330.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[43961292, 12798, 21702330; 12798, 36, 6318; 21702330, 6318, 10713769],[162, 18, 1],[20780, 3041, 39, 0, 2768, 8655; 22, 3, 0, 1, 4, 10; -42093, -6160, -79, 0, -5607, -17532],329,5]
%
% END OF LATTICE L330.5
%
%
% LATTICE L330.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-960984, -648, 6480; -648, 18, -9; 6480, -9, -34],[648, 9, 1],[13, 0, -1, 0, 7, 3; 1532, 1, -116, -1, 812, 350; 2052, -1, -160, 0, 1116, 477],329,6]
%
% END OF LATTICE L330.6
%
%
% LATTICE L330.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-690768, -34344, 308448; -34344, -1584, 15336; 308448, 15336, -137731],[648, 72, 1],[1697, 2027, -217, -193, 201, 772; -19, -27, 0, 2, -1, -7; 3798, 4536, -486, -432, 450, 1728],329,7]
%
% END OF LATTICE L330.7
%
%
% LATTICE L330.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1296, 22680, -648; 22680, -395568, 11304; -648, 11304, -323],[648, 72, 1],[33, 3, -1, -1, 9, 20; -19, -3, 0, 2, -1, -7; -738, -112, 2, 72, -54, -288],329,8]
%
% END OF LATTICE L330.8
%

\medskip%
%------------------------------WEYL-GROUP-W331--------------------------------
%
\leavevmode\llap{}%
$W_{331}$%
\qquad\llap{12} lattices, $\chi=20$%
\hfill%
$\slashthree222|222\rtimes D_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L331.1
%
\leavevmode%
${L_{331.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{1}{}3\above{1pt}{1pt}{-}{}9\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{2}{}11\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${6}\above{1pt}{1pt}{+}{3}{6}\above{1pt}{1pt}{b}{2}{22}\above{1pt}{1pt}{l}{2}{36}\above{1pt}{1pt}{r}{2}{330}\above{1pt}{1pt}{l}{2}{4}\above{1pt}{1pt}{r}{2}{198}\above{1pt}{1pt}{b}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-100585980\\132660\\-7815060
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
132660\\-174\\10491
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-7815060\\10491\\-572006
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
99\\57391\\-300
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-98\\-56810\\297
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-657\\-380864\\1991
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1283\\-743760\\3888
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2668\\-1546655\\8085
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-165\\-95652\\500
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
196\\113619\\-594
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-100585980, 132660, -7815060; 132660, -174, 10491; -7815060, 10491, -572006],[1980, 3, 1],[99, -98, -657, -1283, -2668, -165, 196; 57391, -56810, -380864, -743760, -1546655, -95652, 113619; -300, 297, 1991, 3888, 8085, 500, -594],330,1]
%
% END OF LATTICE L331.1
%
%
% LATTICE L331.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-7994745, 37620, 1115730; 37620, -174, -5379; 1115730, -5379, -150221],[495, 3, 1],[-102, 101, 677, 661, 2749, 85, -202; -12779, 12655, 84821, 82815, 344410, 10649, -25311; -300, 297, 1991, 1944, 8085, 250, -594],330,2]
%
% END OF LATTICE L331.2
%
%
% LATTICE L331.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3775365, 57915, 1064745; 57915, -870, -16560; 1064745, -16560, -297499],[495, 15, 1],[-240, 233, 1579, 1546, 1289, 200, -466; -6269, 6088, 41250, 40386, 33671, 5224, -12177; -510, 495, 3355, 3285, 2739, 425, -990],330,3]
%
% END OF LATTICE L331.3
%
%
% LATTICE L331.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3626416530, 602423415, -11400345; 602423415, -100075074, 1893837; -11400345, 1893837, -35839],[495, 33, 1],[-342, 49, 127, 1631, 703, 283, -10; -1739, 250, 646, 8295, 3575, 1439, -51; 16896, -2376, -6262, -80487, -34710, -13981, 486],330,4]
%
% END OF LATTICE L331.4
%
%
% LATTICE L331.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[85891184280, 42923570580, -21491494200; 42923570580, 21450780168, -10740236916; -21491494200, -10740236916, 5377552153],[1980, 12, 1],[-1151, -18988, -67318, -27329, -200787, -3164, -5747; 2, 29, 99, 39, 275, 4, 0; -4596, -75828, -268840, -109143, -801900, -12637, -22968],330,5]
%
% END OF LATTICE L331.5
%
%
% LATTICE L331.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-79390549260, -2992851180, 100053360; -2992851180, -112823970, 3771795; 100053360, 3771795, -126094],[1980, 15, 1],[-105, 104, 697, 1361, 566, 175, -208; 1651, -1634, -10956, -21396, -8899, -2752, 3267; -33930, 33645, 225335, 439920, 182919, 56540, -67320],330,6]
%
% END OF LATTICE L331.6
%
%
% LATTICE L331.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3376695443220, -160777782000, 735981840; -160777782000, -7655264034, 35042997; 735981840, 35042997, -160414],[1980, 33, 1],[345, -49, -128, -3289, -709, -571, 10; -6929, 985, 2571, 66060, 14240, 11468, -201; 69201, -9636, -25622, -658944, -142125, -114532, 1971],330,7]
%
% END OF LATTICE L331.7
%
%
% LATTICE L331.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-191070, 934560, -20295; 934560, -4358145, 94545; -20295, 94545, -2051],[495, 165, 1],[-29, 5, 11, 140, 12, 24, -1; -289, 44, 108, 1383, 119, 239, -9; -13035, 1980, 4870, 62370, 5367, 10780, -405],330,8]
%
% END OF LATTICE L331.8
%
%
% LATTICE L331.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[39837196757160, 59461995780, -9979671121200; 59461995780, 88754520, -14895906600; -9979671121200, -14895906600, 2500021181069],[1980, 60, 1],[-32571, -747164, -2848998, -1219079, -1912331, -168162, -686471; -328, -7531, -28721, -12291, -19283, -1696, -6930; -130020, -2982600, -11372900, -4866435, -7633824, -671285, -2740320],330,9]
%
% END OF LATTICE L331.9
%
%
% LATTICE L331.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[66070269448920, 450035544420, -16551615201660; 450035544420, 3065406168, -112740801888; -16551615201660, -112740801888, 4146433306067],[1980, 132, 1],[720061, 10120997, 3130011, 13531375, 8648166, 1376813, -10903; 4151, 58346, 18044, 78006, 49855, 7937, -63; 2874432, 40402296, 12494780, 54016281, 34522860, 5496139, -43524],330,10]
%
% END OF LATTICE L331.10
%
%
% LATTICE L331.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-432715140, -141177960, -2910600; -141177960, -46060410, -949575; -2910600, -949575, -19574],[1980, 165, 1],[-333, 49, 124, 3181, 137, 551, -10; 1303, -191, -485, -12444, -536, -2156, 39; -13695, 1980, 5090, 130680, 5631, 22660, -405],330,11]
%
% END OF LATTICE L331.11
%
%
% LATTICE L331.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[351456609240, -13802677020, 98435955420; -13802677020, 542069880, -3865853640; 98435955420, -3865853640, 27569939359],[1980, 660, 1],[18847, 267495, 82537, 355985, 45338, 35779, -1037; -56686, -804547, -248247, -1070697, -136363, -107612, 3120; -75240, -1067880, -329500, -1421145, -180996, -142835, 4140],330,12]
%
% END OF LATTICE L331.12
%

\medskip%
%------------------------------WEYL-GROUP-W332--------------------------------
%
\leavevmode\llap{}%
$W_{332}$%
\qquad\llap{12} lattices, $\chi=40$%
\hfill%
$6|62|26|62|2\rtimes D_{4}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L332.1
%
\leavevmode%
${L_{332.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{-}{}9\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{2}{}11\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${18}\above{1pt}{1pt}{}{6}{6}\above{1pt}{1pt}{}{6}{2}\above{1pt}{1pt}{b}{2}{330}\above{1pt}{1pt}{b}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-72232380\\-24025320\\7611120
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-24025320\\-7991094\\2531511
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7611120\\2531511\\-801646
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-45972829\\142920360\\14844060
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-15290131\\47533969\\4936995
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4834932\\-15030840\\-1561141
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-23051\\71661\\7443
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-11102\\34514\\3585
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1994\\6199\\644
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5113\\-15895\\-1650
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-72232380, -24025320, 7611120; -24025320, -7991094, 2531511; 7611120, 2531511, -801646],[1980, 3, 1],[-23051, -11102, -1994, 5113, 2564, -2556, -4835, -80232; 71661, 34514, 6199, -15895, -7971, 7946, 15031, 249425; 7443, 3585, 644, -1650, -828, 825, 1561, 25905],331,1]
%
% END OF LATTICE L332.1
%
%
% LATTICE L332.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-18058095, 6045435, -1848825; 6045435, -2023869, 618960; -1848825, 618960, -189217],[495, 3, 1],[1297, -1291, -2444, -40564, -11656, -5615, -1009, 2581; 3621, -3604, -6823, -113245, -32541, -15676, -2817, 7205; -828, 825, 1561, 25905, 7443, 3585, 644, -1650],331,2]
%
% END OF LATTICE L332.2
%
%
% LATTICE L332.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2828430, -1027125, -165825; -1027125, -350610, -56490; -165825, -56490, -9101],[495, 15, 1],[-53, 2, 49, 199, 323, 178, 41, -1; 4752, -175, -4389, -17831, -28947, -15955, -3676, 88; -28530, 1050, 26350, 107052, 173790, 95790, 22070, -528],331,3]
%
% END OF LATTICE L332.3
%
%
% LATTICE L332.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-14090670, -6529545, -535095; -6529545, -2986962, -244728; -535095, -244728, -20051],[495, 33, 1],[-53, 5, 52, 94, 332, 181, 41, -1; 6978, -649, -6837, -12365, -43683, -23821, -5398, 130; -83754, 7788, 82060, 148410, 524304, 285912, 64790, -1560],331,4]
%
% END OF LATTICE L332.4
%
%
% LATTICE L332.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[7768393233480, -33858334620, -1942391367180; -33858334620, 147570648, 8465860944; -1942391367180, 8465860944, 485671117553],[1980, 12, 1],[-43423, -21200, -4551, -6293, -605, -8152, -10125, -155143; -33147, -16247, -3514, -5060, -438, -6143, -7681, -118085; -173088, -84504, -18140, -25080, -2412, -32496, -40360, -618420],331,5]
%
% END OF LATTICE L332.5
%
%
% LATTICE L332.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-40568023980, 1239749280, 42482880; 1239749280, -37886370, -1298385; 42482880, -1298385, -44306],[1980, 15, 1],[-4814, 177, 4446, 18063, 29324, 16163, 3724, -89; -154101, 5666, 142321, 578215, 938691, 517394, 119209, -2849; -99990, 3675, 92345, 375177, 609075, 335715, 77350, -1848],331,6]
%
% END OF LATTICE L332.6
%
%
% LATTICE L332.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-73725020820, -4846826160, -84807360; -4846826160, -318639354, -5575251; -84807360, -5575251, -97502],[1980, 33, 1],[-7040, 654, 6897, 12474, 44069, 24032, 5446, -131; 112587, -10459, -110300, -199490, -704772, -384331, -87095, 2095; -314424, 29205, 308033, 557115, 1968219, 1073325, 243232, -5850],331,7]
%
% END OF LATTICE L332.7
%
%
% LATTICE L332.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-16830, -2210175, 41085; -2210175, -290234010, 5395170; 41085, 5395170, -100291],[495, 165, 1],[-53, 27, 74, 24, 398, 203, 41, -1; -18, 55, 71, 19, 273, 115, 14, -2; -990, 2970, 3850, 1032, 14850, 6270, 770, -108],331,8]
%
% END OF LATTICE L332.8
%
%
% LATTICE L332.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[66919987605240, -3870712749420, -16771856086260; -3870712749420, 223885534440, 970099360560; -16771856086260, 970099360560, 4203455001181],[1980, 60, 1],[117553, 937704, 1051805, 3056247, 4075127, 1857416, 345755, 18385; -960, -7649, -8581, -24937, -33255, -15161, -2824, -154; 469260, 3743220, 4198700, 12200232, 16267500, 7414620, 1380220, 73392],331,9]
%
% END OF LATTICE L332.9
%
%
% LATTICE L332.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[383169808046520, 10046659231620, -96005008837980; 10046659231620, 263422011864, -2517238018416; -96005008837980, -2517238018416, 24054509328307],[1980, 132, 1],[-237185, -1952469, -2182170, -2873316, -8399086, -3805045, -696587, -5441; -1878, -15473, -17291, -22765, -66537, -30137, -5514, -40; -946836, -7794204, -8711164, -11470200, -33528924, -15189636, -2780756, -21720],331,10]
%
% END OF LATTICE L332.10
%
%
% LATTICE L332.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-210746414340, -70228952640, 320544180; -70228952640, -23403035370, 106817865; 320544180, 106817865, -487546],[1980, 165, 1],[-44, -28, 11, 8, 179, 118, 34, 1; 123, 139, 30, -8, -318, -269, -95, -5; -1980, 12045, 13805, 3507, 48015, 18645, 1540, -438],331,11]
%
% END OF LATTICE L332.11
%
%
% LATTICE L332.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[35282178360, 57330900, 8795270880; 57330900, 2020920, 12838980; 8795270880, 12838980, 2193612071],[1980, 660, 1],[-891323, -7427857, -8283192, -2177530, -31764232, -14342513, -2601993, 493; 2681199, 22343822, 24916765, 6550253, 95550351, 43143878, 7827085, -1483; 3558060, 29651160, 33065560, 8692452, 126799200, 57253680, 10386860, -1968],331,12]
%
% END OF LATTICE L332.12
%

\medskip%
%------------------------------WEYL-GROUP-W333--------------------------------
%
\leavevmode\llap{}%
$W_{333}$%
\qquad\llap{12} lattices, $\chi=72$%
\hfill%
$2222|2222|2222|2222|\rtimes D_{4}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L333.1
%
\leavevmode%
${L_{333.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{-}{}9\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{2}{}5\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}11\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${132}\above{1pt}{1pt}{r}{2}{2}\above{1pt}{1pt}{b}{2}{60}\above{1pt}{1pt}{*}{2}{44}\above{1pt}{1pt}{b}{2}{6}\above{1pt}{1pt}{b}{2}{396}\above{1pt}{1pt}{*}{2}{60}\above{1pt}{1pt}{b}{2}{18}\above{1pt}{1pt}{l}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-137952540\\146520\\14172840
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
146520\\-138\\-18891
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
14172840\\-18891\\-620074
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-19556701\\-12750837000\\-58538700
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
27683\\18049129\\82863
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
503652\\328377720\\1507571
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-21785\\-14203684\\-65208
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1480\\-964951\\-4430
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-13751\\-8965570\\-41160
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-12561\\-8189698\\-37598
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-885\\-577015\\-2649
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-8401\\-5477406\\-25146
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-441\\-287530\\-1320
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
884\\576363\\2646
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-137952540, 146520, 14172840; 146520, -138, -18891; 14172840, -18891, -620074],[1980, 3, 1],[-21785, -1480, -13751, -12561, -885, -8401, -441, 884, 7497, 587, 4821, 3631, -8, -18389, -8489, -3563; -14203684, -964951, -8965570, -8189698, -577015, -5477406, -287530, 576363, 4888004, 382721, 3143270, 2367398, -5215, -11989494, -5534770, -2323053; -65208, -4430, -41160, -37598, -2649, -25146, -1320, 2646, 22440, 1757, 14430, 10868, -24, -55044, -25410, -10665],332,1]
%
% END OF LATTICE L333.1
%
%
% LATTICE L333.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-111195810, 1710720, 545985; 1710720, -26319, -8400; 545985, -8400, -2674],[495, 3, 1],[124, 49, 1, -202, -52, -478, -559, -133, -1108, -418, -616, -1643, -71, -137, -56, 10; 7997, 3162, 65, -13035, -3356, -30855, -36085, -8586, -71533, -26988, -39775, -106095, -4586, -8855, -3625, 644; 198, 72, 0, -297, -75, -671, -780, -184, -1518, -567, -825, -2178, -90, -154, -45, 19],332,2]
%
% END OF LATTICE L333.2
%
%
% LATTICE L333.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[212850, -11385, -12375; -11385, 390, -915; -12375, -915, -10637],[495, 15, 1],[-1025, -121, -52, 18, 157, 4696, 370, 1325, 3617, 445, 376, 1602, 167, 164, -46, -353; -22561, -2664, -1145, 396, 3457, 103422, 8149, 29184, 79673, 9803, 8284, 35299, 3682, 3663, -1010, -7767; 3135, 370, 159, -55, -480, -14355, -1131, -4050, -11055, -1360, -1149, -4895, -510, -495, 141, 1080],332,3]
%
% END OF LATTICE L333.3
%
%
% LATTICE L333.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1050885, -210870, 74250; -210870, -42306, 14883; 74250, 14883, -5210],[495, 33, 1],[-89, -196, -1309, -135, -372, -451, -1539, -772, -135, -112, -231, -5, 64, 31, -1, -152; 526, 1159, 7745, 799, 2203, 2673, 9125, 4581, 802, 667, 1385, 31, -377, -183, 5, 897; 234, 517, 3465, 358, 990, 1206, 4125, 2079, 366, 308, 660, 17, -165, -81, 0, 396],332,4]
%
% END OF LATTICE L333.4
%
%
% LATTICE L333.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[45374238360, 178086595500, -11275428780; 178086595500, 698961275016, -44254246392; -11275428780, -44254246392, 2801926793],[1980, 12, 1],[-576591, -121943, -452241, -350619, -20321, -44917, 5459, 331, -73121, -40485, -359899, -461521, -142107, -2391503, -817599, -487615; 1210, 256, 950, 737, 43, 99, -10, 0, 154, 85, 755, 968, 298, 5016, 1715, 1023; -2301189, -486676, -1804890, -1399310, -81096, -179190, 21810, 1332, -291819, -161576, -1436370, -1841950, -567156, -9544590, -3263070, -1946088],332,5]
%
% END OF LATTICE L333.5
%
%
% LATTICE L333.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-295020, 13860, 0; 13860, 1650, -225; 0, -225, 22],[1980, 15, 1],[-39, -4, 3, 107, 9, 131, 29, 16, 247, 43, 23, 283, 4, -1, -3, -3; -836, -87, 62, 2244, 190, 2772, 614, 339, 5236, 912, 488, 6006, 85, -22, -64, -64; -8580, -900, 624, 22770, 1935, 28270, 6264, 3460, 53460, 9315, 4986, 61380, 870, -220, -654, -655],332,6]
%
% END OF LATTICE L333.6
%
%
% LATTICE L333.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[5490540, 1916640, 1063260; 1916640, 668910, 370359; 1063260, 370359, 201634],[1980, 33, 1],[3625, 3962, 52037, 5315, 7176, 16823, 56427, 13642, 4503, 1626, 3843, -235, -1588, -1583, -547, 3122; -11596, -12674, -166460, -17002, -22955, -53814, -180500, -43638, -14404, -5201, -12290, 752, 5080, 5064, 1750, -9987; 2184, 2387, 31350, 3202, 4323, 10134, 33990, 8217, 2712, 979, 2310, -142, -957, -954, -330, 1881],332,7]
%
% END OF LATTICE L333.7
%
%
% LATTICE L333.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-224730, 5129190, 77715; 5129190, -116928075, -1771605; 77715, -1771605, -26842],[495, 165, 1],[81, 179, 240, 124, 343, 418, 286, 721, 127, 107, 46, 6, -57, -28, 0, 137; 239, 532, 719, 373, 1040, 1281, 881, 2244, 401, 348, 161, 27, -160, -81, -1, 396; -15540, -34595, -46761, -24260, -67650, -83340, -57321, -146025, -26100, -22660, -10494, -1765, 10395, 5265, 66, -25740],332,8]
%
% END OF LATTICE L333.8
%
%
% LATTICE L333.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[21587405400, -65159820, -5407958160; -65159820, 196680, 16323480; -5407958160, 16323480, 1354771957],[1980, 60, 1],[-5249, -6673, -3335, -60260, -5636, -29400, -5875, -5611, -19219, -11678, -2782, -31495, -481, -1185, -242, -506; 176, 234, 116, 2079, 191, 957, 188, 174, 572, 327, 71, 726, -4, -22, -1, 13; -20955, -26640, -13314, -240570, -22500, -117370, -23454, -22400, -76725, -46620, -11106, -125730, -1920, -4730, -966, -2020],332,9]
%
% END OF LATTICE L333.9
%
%
% LATTICE L333.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[396621518040, -24896739780, -99119851380; -24896739780, 1562819016, 6221954772; -99119851380, 6221954772, 24771083995],[1980, 132, 1],[1418, 12960, 130898, 15809, 55961, 87235, 329938, 198112, 21322, 49575, 181777, 12616, 6574, -1960, -17263, -10507; 28, 281, 2905, 353, 1259, 1971, 7465, 4491, 484, 1127, 4135, 287, 149, -51, -425, -267; 5667, 51788, 523050, 63170, 223608, 348570, 1318350, 791604, 85197, 198088, 726330, 50410, 26268, -7830, -68970, -41976],332,10]
%
% END OF LATTICE L333.10
%
%
% LATTICE L333.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-120191940, -35647920, -7405200; -35647920, -10572870, -2196315; -7405200, -2196315, -456238],[1980, 165, 1],[-1681, -814, -937, -247, 170, 221, 25, -518, -719, -836, -2363, -1253, -1820, -4721, -3325, -4432; 6640, 3213, 3694, 972, -676, -876, -98, 2055, 2848, 3310, 9352, 4958, 7199, 18666, 13144, 17514; -4680, -2255, -2574, -670, 495, 630, 66, -1485, -2040, -2365, -6666, -3530, -5115, -13230, -9306, -12375],332,11]
%
% END OF LATTICE L333.11
%
%
% LATTICE L333.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[4273501320, 1104687540, 238655340; 1104687540, 285572760, 61680960; 238655340, 61680960, 13335887],[1980, 660, 1],[249648, 561965, 402939, 138016, 65446, 18232, 7123, 102631, 51740, 266852, 425878, 238719, 763371, 1111973, 821694, 2383820; -750382, -1689132, -1211138, -414843, -196715, -54801, -21410, -308484, -155518, -802093, -1280087, -717532, -2294510, -3342324, -2469815, -7165191; -996975, -2244220, -1609146, -551170, -261360, -72810, -28446, -409860, -206625, -1065680, -1700754, -953330, -3048540, -4440690, -3281454, -9519840],332,12]
%
% END OF LATTICE L333.12
%

\medskip%
%------------------------------WEYL-GROUP-W334--------------------------------
%
\leavevmode\llap{}%
$W_{334}$%
\qquad\llap{4} lattices, $\chi=24$%
\hfill%
$\slashinfty2|2\slashinfty2|2\rtimes D_{4}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L334.1
%
\leavevmode%
${L_{334.1}}$%
{} : {$1\above{1pt}{1pt}{1}{7}8\above{1pt}{1pt}{-}{5}64\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{-}{}9\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{3}%
\EasyButWeakLineBreak%
{${24}\above{1pt}{1pt}{24,7}{\infty b}{96}\above{1pt}{1pt}{*}{2}{576}\above{1pt}{1pt}{s}{2}{96}\above{1pt}{1pt}{48,1}{\infty z}{24}\above{1pt}{1pt}{b}{2}{36}\above{1pt}{1pt}{s}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-300096\\11520\\576
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
11520\\-408\\-24
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
576\\-24\\-1
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3\\-43\\-732
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-5\\-70\\-1248
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-12\\-288
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\14\\240
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\-1\\12
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-15\\-234
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-300096, 11520, 576; 11520, -408, -24; 576, -24, -1],[576, 24, 1],[-3, -5, -1, 1, 0, -1; -43, -70, -12, 14, -1, -15; -732, -1248, -288, 240, 12, -234],333,1]
%
% END OF LATTICE L334.1
%
%
% LATTICE L334.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-114240, -1920, 384; -1920, -24, 8; 384, 8, -1],[192, 8, 1],[-2, -5, -1, 1, 1, 0; 63, 150, 28, -30, -27, 1; -300, -768, -160, 144, 156, 2],333,2]
%
% END OF LATTICE L334.2
%
%
% LATTICE L334.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-522432, -36672, 12672; -36672, -2568, 888; 12672, 888, -307],[192, 24, 1],[1, 0, -1, -3, -5, -1; 30, 7, -25, -91, -166, -52; 128, 20, -114, -388, -688, -192],333,3]
%
% END OF LATTICE L334.3
%
%
% LATTICE L334.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-28224, -13824, -2880; -13824, -6744, -1392; -2880, -1392, -281],[576, 24, 1],[-5, -37, -15, 1, 14, 3; 13, 106, 44, -2, -41, -9; -12, -144, -64, 0, 60, 14],333,4]
%
% END OF LATTICE L334.4
%

\medskip%
%------------------------------WEYL-GROUP-W335--------------------------------
%
\leavevmode\llap{}%
$W_{335}$%
\qquad\llap{8} lattices, $\chi=24$%
\hfill%
$22|22\infty|\infty\rtimes D_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L335.1
%
\leavevmode%
${L_{335.1}}$%
{} : {$1\above{1pt}{1pt}{1}{1}8\above{1pt}{1pt}{1}{1}64\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{-}{}9\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{3}%
\EasyButWeakLineBreak%
{${96}\above{1pt}{1pt}{l}{2}{9}\above{1pt}{1pt}{}{2}{8}\above{1pt}{1pt}{r}{2}{36}\above{1pt}{1pt}{*}{2}{96}\above{1pt}{1pt}{48,7}{\infty z}{24}\above{1pt}{1pt}{24,13}{\infty b}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-241344\\5760\\59328
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5760\\-120\\-1488
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
59328\\-1488\\-14287
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
661\\7910\\1920
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
158\\1890\\459
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
11\\131\\32
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-31\\-372\\-90
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-33\\-394\\-96
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
62\\743\\180
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-241344, 5760, 59328; 5760, -120, -1488; 59328, -1488, -14287],[576, 24, 1],[661, 158, 11, -31, -33, 62; 7910, 1890, 131, -372, -394, 743; 1920, 459, 32, -90, -96, 180],334,1]
%
% END OF LATTICE L335.1
%
%
% LATTICE L335.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-1373376, -453120, 14016; -453120, -149496, 4624; 14016, 4624, -143],[192, 8, 1],[-137, -10, 0, 3, 1, -17; 570, 42, 1, -12, -6, 69; 4992, 377, 32, -94, -96, 564],334,2]
%
% END OF LATTICE L335.2
%
%
% LATTICE L335.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2237376, 397632, 66816; 397632, -70648, -11872; 66816, -11872, -1995],[192, 8, 1],[61, 87, 5, -1, -5, 13; -1377, -1952, -109, 32, 111, -306; 10236, 14528, 816, -224, -828, 2256],334,3]
%
% END OF LATTICE L335.3
%
%
% LATTICE L335.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-80448, 32640, 3840; 32640, -13032, -1536; 3840, -1536, -181],[192, 24, 1],[21, 5, 1, -1, -1, 2; -410, -99, -23, 18, 22, -37; 3920, 945, 216, -174, -208, 356],334,4]
%
% END OF LATTICE L335.4
%
%
% LATTICE L335.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[3794112, -712128, 198336; -712128, 133656, -37224; 198336, -37224, 10367],[192, 24, 1],[-5, -1, 15, 247, 57, 11; -79, -32, 227, 3776, 873, 170; -188, -96, 528, 8832, 2044, 400],334,5]
%
% END OF LATTICE L335.5
%
%
% LATTICE L335.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-12701376, 42624, 42624; 42624, -120, -144; 42624, -144, -143],[576, 24, 1],[53, 4, 1, -1, -1, 6; 614, 46, 9, -12, -10, 71; 15168, 1145, 288, -286, -288, 1716],334,6]
%
% END OF LATTICE L335.6
%
%
% LATTICE L335.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[100777536, -4906944, -348480; -4906944, 238920, 16968; -348480, 16968, 1205],[576, 24, 1],[57, 247, 5, -1, -5, 11; 575, 2496, 51, 0, -49, 110; 8388, 36288, 728, -288, -756, 1632],334,7]
%
% END OF LATTICE L335.7
%
%
% LATTICE L335.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-18293184, -9470592, -2436480; -9470592, -4903032, -1261392; -2436480, -1261392, -324515],[576, 24, 1],[778, 1059, 142, -53, -56, 219; -2395, -3264, -441, 160, 173, -670; 3468, 4736, 648, -224, -252, 960],334,8]
%
% END OF LATTICE L335.8
%

\medskip%
%------------------------------WEYL-GROUP-W336--------------------------------
%
\leavevmode\llap{}%
$W_{336}$%
\qquad\llap{4} lattices, $\chi=12$%
\hfill%
$2|222|22\rtimes D_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L336.1
%
\leavevmode%
${L_{336.1}}$%
{} : {$1\above{1pt}{1pt}{-}{3}8\above{1pt}{1pt}{1}{7}64\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{1}{}$}\EasyButWeakLineBreak%
{${64}\above{1pt}{1pt}{b}{2}{4}\above{1pt}{1pt}{l}{2}{64}\above{1pt}{1pt}{}{2}{3}\above{1pt}{1pt}{r}{2}{32}\above{1pt}{1pt}{*}{2}{12}\above{1pt}{1pt}{s}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1478208\\170112\\-4032
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
170112\\19576\\-464
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-4032\\-464\\11
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\-8\\32
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\-1\\-42
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\-32\\-256
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\-9\\-15
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\-6\\112
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\-6\\114
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[1478208, 170112, -4032; 170112, 19576, -464; -4032, -464, 11],[192, 8, 1],[1, 0, 3, 1, 1, 1; -8, -1, -32, -9, -6, -6; 32, -42, -256, -15, 112, 114],335,1]
%
% END OF LATTICE L336.1
%
%
% LATTICE L336.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[192, 0, 0; 0, -8, 8; 0, 8, -7],[192, 8, 1],[-1, -1, 0, 1, 0, -7; -4, 4, 1, 0, -3, -48; -10, 0, 1, 0, -4, -96],335,2]
%
% END OF LATTICE L336.2
%
%
% LATTICE L336.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[192, 0, 0; 0, -24, 0; 0, 0, 1],[192, 24, 1],[-5, 0, 1, 0, -1, -1; 24, 1, 0, 0, 2, 4; -96, -6, 0, 1, 0, -14],335,3]
%
% END OF LATTICE L336.3
%
%
% LATTICE L336.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-7104, 768, 192; 768, -24, -24; 192, -24, -5],[192, 24, 1],[1, -3, -1, 1, 2, 9; 2, -4, -2, 0, 3, 16; 27, -96, -30, 32, 60, 256],335,4]
%
% END OF LATTICE L336.4
%

\medskip%
%------------------------------WEYL-GROUP-W337--------------------------------
%
\leavevmode\llap{}%
$W_{337}$%
\qquad\llap{16} lattices, $\chi=36$%
\hfill%
$2222|22222|2\rtimes D_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L337.1
%
\leavevmode%
${L_{337.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{2}16\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{2}{}7\above{1pt}{1pt}{-}{}$}\EasyButWeakLineBreak%
{${560}\above{1pt}{1pt}{}{2}{3}\above{1pt}{1pt}{r}{2}{140}\above{1pt}{1pt}{*}{2}{48}\above{1pt}{1pt}{b}{2}{10}\above{1pt}{1pt}{l}{2}{48}\above{1pt}{1pt}{}{2}{35}\above{1pt}{1pt}{r}{2}{12}\above{1pt}{1pt}{*}{2}{560}\above{1pt}{1pt}{b}{2}{2}\above{1pt}{1pt}{l}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-132714960\\25200\\65520
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
25200\\-1\\-16
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
65520\\-16\\-29
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
183\\255920\\272160
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
8\\11187\\11898
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
81\\113260\\120470
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
35\\48936\\52056
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\2795\\2975
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\1392\\1488
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2\\-2800\\-2975
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-1398\\-1488
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
13\\18200\\19320
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\1399\\1487
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-132714960, 25200, 65520; 25200, -1, -16; 65520, -16, -29],[1680, 1, 1],[183, 8, 81, 35, 2, 1, -2, -1, 13, 1; 255920, 11187, 113260, 48936, 2795, 1392, -2800, -1398, 18200, 1399; 272160, 11898, 120470, 52056, 2975, 1488, -2975, -1488, 19320, 1487],336,1]
%
% END OF LATTICE L337.1
%
%
% LATTICE L337.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[485520, -6720, 1680; -6720, 93, -24; 1680, -24, -47],[1680, 3, 1],[667, 21, 172, 53, 13, 7, -1, -1, -23, 2; 47880, 1508, 12355, 3808, 935, 504, -70, -72, -1680, 143; -840, -26, -210, -64, -15, -8, 0, 1, 0, -3],336,2]
%
% END OF LATTICE L337.2
%
%
% LATTICE L337.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-71435280, 38640, 72240; 38640, -5, -40; 72240, -40, -73],[1680, 5, 1],[123, 26, 51, 107, 1, 1, -1, -1, 17, 4; 6832, 1443, 2828, 5928, 55, 48, -56, -54, 952, 223; 117936, 24930, 48902, 102600, 959, 960, -959, -960, 16296, 3835],336,3]
%
% END OF LATTICE L337.3
%
%
% LATTICE L337.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-19788720, 20160, 47040; 20160, -7, -56; 47040, -56, -107],[1680, 7, 1],[19, -1, -1, 1, 7, 155, 53, 38, 129, 6; 3800, -198, -200, 192, 1395, 30936, 10580, 7587, 25760, 1199; 6360, -336, -335, 336, 2345, 51912, 17750, 12726, 43200, 2009],336,4]
%
% END OF LATTICE L337.4
%
%
% LATTICE L337.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-10421040, 473760, 82320; 473760, -16635, -2925; 82320, -2925, -514],[1680, 15, 1],[5, -1, -1, 7, 3, 69, 46, 29, 191, 4; -2576, 521, 518, -3648, -1562, -35904, -23933, -15086, -99344, -2078; 15456, -3125, -3108, 21880, 9369, 215360, 143556, 90490, 595896, 12465],336,5]
%
% END OF LATTICE L337.5
%
%
% LATTICE L337.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-62160, -8400, 3360; -8400, 32, 32; 3360, 32, -29],[1680, 16, 1],[24, 7, 27, 1, -2, -2, -13, -1, 2, 2; 1645, 477, 1820, 66, -145, -141, -910, -69, 140, 139; 4550, 1320, 5040, 183, -400, -390, -2520, -192, 385, 384],336,6]
%
% END OF LATTICE L337.6
%
%
% LATTICE L337.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[287453040, -19177200, 174720; -19177200, 1279383, -11655; 174720, -11655, 106],[1680, 21, 1],[451, 32, 87, 43, -37, 1, 21, 43, 361, 48; 7200, 511, 1390, 688, -590, 16, 335, 686, 5760, 766; 48240, 3437, 9420, 4760, -3885, 112, 2220, 4550, 38280, 5103],336,7]
%
% END OF LATTICE L337.7
%
%
% LATTICE L337.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1680, 0, 1680; 0, -35, -280; 1680, -280, -559],[1680, 35, 1],[141, 206, 57, 827, 7, 1, -1, -1, 23, 34; 1120, 1635, 452, 6552, 55, 0, -8, -6, 184, 271; -144, -210, -58, -840, -7, 0, 1, 0, -24, -35],336,8]
%
% END OF LATTICE L337.8
%
%
% LATTICE L337.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1680, 0, 0; 0, -19632, 672; 0, 672, -23],[1680, 48, 1],[-9, -2, -29, -1, -1, 0, 1, 0, -3, -1; 35, 11, 210, 9, 25, 1, 0, -3, -35, -3; 945, 304, 5880, 254, 720, 29, 0, -88, -1050, -96],336,9]
%
% END OF LATTICE L337.9
%
%
% LATTICE L337.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-10612560, -381360, 13440; -381360, -13280, 480; 13440, 480, -17],[1680, 80, 1],[1, -1, -3, -2, 0, 4, 17, 19, 12, 4; 7, -6, -21, -15, -1, 24, 105, 120, 77, 27; 987, -960, -2968, -2010, -32, 3825, 16352, 18360, 11634, 3920],336,10]
%
% END OF LATTICE L337.10
%
%
% LATTICE L337.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[88440240, 3902640, -85680; 3902640, 172095, -3780; -85680, -3780, 83],[1680, 105, 1],[-1, -3, -1, -13, -1, 1, 1, 2, 5, 2; -24, -44, -13, -160, -11, 8, 10, 20, 48, 17; -2136, -5110, -1626, -20720, -1533, 1400, 1488, 2975, 7344, 2835],336,11]
%
% END OF LATTICE L337.11
%
%
% LATTICE L337.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-556080, 62160, -5040; 62160, -6944, 560; -5040, 560, -43],[1680, 112, 1],[2, -1, -3, -2, 6, 13, 37, 55, 24, 10; 20, -9, -30, -21, 55, 126, 360, 537, 235, 99; 25, 0, -40, -42, 0, 105, 320, 504, 230, 112],336,12]
%
% END OF LATTICE L337.12
%
%
% LATTICE L337.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-10298485680, 31852800, 30649920; 31852800, -98160, -94800; 30649920, -94800, -91219],[1680, 240, 1],[207, 88, 1, -29, -145, -259, -1205, -314, -198, 91; 203, 85, 0, -28, -139, -245, -1134, -293, -182, 93; 69342, 29480, 336, -9715, -48576, -86770, -403704, -105200, -66339, 30480],336,13]
%
% END OF LATTICE L337.13
%
%
% LATTICE L337.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-21840, 2236080, -20160; 2236080, -227557344, 2051616; -20160, 2051616, -18497],[1680, 336, 1],[2, -1, -3, 0, 16, 7, 57, 27, 34, 12; -25, 1, 40, 13, -15, -39, -350, -181, -245, -115; -2775, 112, 4440, 1442, -1680, -4333, -38880, -20104, -27210, -12768],336,14]
%
% END OF LATTICE L337.14
%
%
% LATTICE L337.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1680, 0, 0; 0, -7374640, 15120; 0, 15120, -31],[1680, 560, 1],[0, 1, 0, -1, -1, -4, -2, -13, -1, -1; 1, 0, -1, -3, 3, 30, 17, 126, 11, 23; 487, 0, -488, -1470, 1456, 14595, 8272, 61320, 5354, 11200],336,15]
%
% END OF LATTICE L337.15
%
%
% LATTICE L337.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-22123920, -15568560, 5204640; -15568560, -10950240, 3660720; 5204640, 3660720, -1223797],[1680, 1680, 1],[14, 55, 23, 14, 6, 0, -1, -1, 1, 26; 6473, 25289, 10510, 6357, 2575, -117, -488, -373, 487, 12319; 19422, 75880, 31536, 19075, 7728, -350, -1464, -1120, 1461, 36960],336,16]
%
% END OF LATTICE L337.16
%

\medskip%
%------------------------------WEYL-GROUP-W338--------------------------------
%
\leavevmode\llap{}%
$W_{338}$%
\qquad\llap{12} lattices, $\chi=24$%
\hfill%
$2222|2222|\rtimes D_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L338.1
%
\leavevmode%
${L_{338.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{1}{}3\above{1pt}{1pt}{1}{}9\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}13\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${156}\above{1pt}{1pt}{r}{2}{10}\above{1pt}{1pt}{b}{2}{468}\above{1pt}{1pt}{*}{2}{4}\above{1pt}{1pt}{b}{2}{390}\above{1pt}{1pt}{b}{2}{36}\above{1pt}{1pt}{*}{2}{52}\above{1pt}{1pt}{b}{2}{90}\above{1pt}{1pt}{l}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
73848060\\-24605100\\-65520
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-24605100\\8198058\\21831
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-65520\\21831\\58
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
861\\2548\\13572
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
49\\145\\775
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-79\\-234\\-1170
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-25\\-74\\-388
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
22\\65\\390
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
221\\654\\3492
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
615\\1820\\9698
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
517\\1530\\8145
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[73848060, -24605100, -65520; -24605100, 8198058, 21831; -65520, 21831, 58],[2340, 3, 1],[861, 49, -79, -25, 22, 221, 615, 517; 2548, 145, -234, -74, 65, 654, 1820, 1530; 13572, 775, -1170, -388, 390, 3492, 9698, 8145],337,1]
%
% END OF LATTICE L338.1
%
%
% LATTICE L338.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[1622790, -12285, 1170; -12285, 93, -9; 1170, -9, -17],[585, 3, 1],[28, 3, -5, -1, -1, 7, 20, 34; 3692, 395, -663, -132, -130, 924, 2639, 4485; -39, -5, 0, 1, 0, -9, -26, -45],337,2]
%
% END OF LATTICE L338.2
%
%
% LATTICE L338.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[585, 3510, 585; 3510, -5835, -1020; 585, -1020, -178],[585, 15, 1],[36, 8, 22, 7, -1, -1, 1, 1; -559, -126, -351, -114, 13, 16, 0, -15; 3315, 747, 2080, 675, -78, -95, 0, 89],337,3]
%
% END OF LATTICE L338.3
%
%
% LATTICE L338.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-670995, -237510, 19305; -237510, -76947, 6240; 19305, 6240, -506],[585, 39, 1],[4, 9, 1, -1, -1, 7, 2, 52; -467, -1045, -114, 118, 115, -828, -235, -6090; -5607, -12545, -1368, 1417, 1380, -9945, -2822, -73125],337,4]
%
% END OF LATTICE L338.4
%
%
% LATTICE L338.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[28704419640, -37760580, 7159585680; -37760580, 49656, -9418416; 7159585680, -9418416, 1785776119],[2340, 12, 1],[-9159, -9309, -31711, 291, 56453, 13679, 17176, 4088; -4082, -4155, -14157, 130, 25220, 6114, 7683, 1845; 36699, 37300, 127062, -1166, -226200, -54810, -68822, -16380],337,5]
%
% END OF LATTICE L338.5
%
%
% LATTICE L338.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-124020, -37440, 0; -37440, -11190, -15; 0, -15, 2],[2340, 15, 1],[63, 10, 71, 31, 4, -3, -47, 0; -208, -33, -234, -102, -13, 10, 156, 0; -1560, -243, -1690, -720, -78, 80, 1170, -1],337,6]
%
% END OF LATTICE L338.6
%
%
% LATTICE L338.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-203104980, 67775760, 320580; 67775760, -22616646, -106977; 320580, -106977, -506],[2340, 39, 1],[5, 61, 7, 41, 2, -5, -7, -3; 16, 180, 20, 114, 5, -14, -18, -5; -216, 585, 206, 1872, 210, -208, -630, -845],337,7]
%
% END OF LATTICE L338.7
%
%
% LATTICE L338.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1170, -115245, -1755; -115245, -11062155, -168480; -1755, -168480, -2566],[585, 195, 1],[12, 26, 4, 7, -1, -1, 7, 7; 17, 30, 3, -9, -2, 1, 15, 12; -1125, -1989, -200, 585, 132, -65, -990, -793],337,8]
%
% END OF LATTICE L338.8
%
%
% LATTICE L338.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[734146920, -2159820, 183266460; -2159820, 6360, -539160; 183266460, -539160, 45749147],[2340, 60, 1],[1606, 1159, 5483, 3167, 2297, 287, 1460, 2; -130, -99, -481, -282, -208, -26, -117, 1; -6435, -4644, -21970, -12690, -9204, -1150, -5850, -8],337,9]
%
% END OF LATTICE L338.9
%
%
% LATTICE L338.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2792223720, -7696260, 696788820; -7696260, 27768, -1920516; 696788820, -1920516, 173881003],[2340, 156, 1],[22197, 552458, 22342, 91979, 2321, 2031, 24083, 112581; 766, 19065, 771, 3174, 80, 70, 831, 3885; -88941, -2213640, -89522, -368550, -9300, -8138, -96498, -451100],337,10]
%
% END OF LATTICE L338.10
%
%
% LATTICE L338.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-139934340, 46797660, 177840; 46797660, -15650310, -59475; 177840, -59475, -226],[2340, 195, 1],[35, 32, 7, -13, -2, 1, 29, 12; 88, 81, 18, -30, -5, 2, 72, 30; 4380, 3861, 770, -2340, -258, 260, 3870, 1547],337,11]
%
% END OF LATTICE L338.11
%
%
% LATTICE L338.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[15185912040, 97870500, -3716509680; 97870500, 634920, -23949120; -3716509680, -23949120, 909558791],[2340, 780, 1],[-35298, -160949, -30505, -115339, -581, -12491, -52582, -40672; 106138, 483960, 91726, 346815, 1747, 37559, 158109, 122297; -141435, -644904, -122230, -462150, -2328, -50050, -210690, -162968],337,12]
%
% END OF LATTICE L338.12
%

\medskip%
%------------------------------WEYL-GROUP-W339--------------------------------
%
\leavevmode\llap{}%
$W_{339}$%
\qquad\llap{32} lattices, $\chi=36$%
\hfill%
$2222|22222|2\rtimes D_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L339.1
%
\leavevmode%
${L_{339.1}}$%
{} : {$1\above{1pt}{1pt}{2}{6}8\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{1}{}3\above{1pt}{1pt}{-}{}9\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{2}{}7\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${70}\above{1pt}{1pt}{s}{2}{6}\above{1pt}{1pt}{b}{2}{2520}\above{1pt}{1pt}{*}{2}{4}\above{1pt}{1pt}{s}{2}{168}\above{1pt}{1pt}{s}{2}{36}\above{1pt}{1pt}{*}{2}{280}\above{1pt}{1pt}{b}{2}{6}\above{1pt}{1pt}{s}{2}{630}\above{1pt}{1pt}{b}{2}{24}\above{1pt}{1pt}{b}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3903480\\-652680\\148680
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-652680\\109131\\-24864
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
148680\\-24864\\5539
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
15297\\90825\\-2905
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5387\\31985\\-1023
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
298583\\1772820\\-56700
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3581\\21262\\-680
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2655\\15764\\-504
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\6\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-731\\-4340\\140
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
16\\95\\-3
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
8294\\49245\\-1575
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2717\\16132\\-516
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[3903480, -652680, 148680; -652680, 109131, -24864; 148680, -24864, 5539],[2520, 3, 1],[15297, 5387, 298583, 3581, 2655, 1, -731, 16, 8294, 2717; 90825, 31985, 1772820, 21262, 15764, 6, -4340, 95, 49245, 16132; -2905, -1023, -56700, -680, -504, 0, 140, -3, -1575, -516],338,1]
%
% END OF LATTICE L339.1
%
\hbox{}\par\smallskip%
%
% LATTICE L339.2
%
\leavevmode%
${L_{339.2}}$%
{} : {$1\above{1pt}{1pt}{-2}{6}8\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{1}{}3\above{1pt}{1pt}{-}{}9\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{2}{}7\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{m}%
\EasyButWeakLineBreak%
{${70}\above{1pt}{1pt}{b}{2}{6}\above{1pt}{1pt}{l}{2}{2520}\above{1pt}{1pt}{}{2}{1}\above{1pt}{1pt}{r}{2}{168}\above{1pt}{1pt}{l}{2}{9}\above{1pt}{1pt}{}{2}{280}\above{1pt}{1pt}{r}{2}{6}\above{1pt}{1pt}{b}{2}{630}\above{1pt}{1pt}{l}{2}{24}\above{1pt}{1pt}{r}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4236120\\-5040\\-2520
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-5040\\6\\3
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2520\\3\\1
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-805\\-70
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\1\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\840\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\-1
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-812\\-84
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2\\-1620\\-153
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-37\\-29960\\-2800
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2\\-1619\\-150
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-17\\-13755\\-1260
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-808\\-72
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[4236120, -5040, -2520; -5040, 6, 3; -2520, 3, 1],[2520, 3, 1],[-1, 0, 1, 0, -1, -2, -37, -2, -17, -1; -805, 1, 840, 0, -812, -1620, -29960, -1619, -13755, -808; -70, 0, 0, -1, -84, -153, -2800, -150, -1260, -72],338,2]
%
% END OF LATTICE L339.2
%
%
% LATTICE L339.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[265230, -1260, -630; -1260, 6, 3; -630, 3, 1],[630, 3, 1],[-2, 0, 1, 0, -1, -4, -37, -4, -34, -1; -385, 1, 210, 0, -196, -780, -7210, -779, -6615, -194; -70, 0, 0, -1, -42, -153, -1400, -150, -1260, -36],338,3]
%
% END OF LATTICE L339.3
%
%
% LATTICE L339.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[222178936140, 1576399860, 10571400; 1576399860, 11184843, 75006; 10571400, 75006, 503],[1260, 3, 1],[586, 6, 1, -1, 151, 219, 18427, 335, 963, 177; -82530, -845, -140, 141, -21266, -30843, -2595180, -47180, -135625, -24928; -9135, -96, -140, -9, -2394, -3433, -288540, -5241, -15050, -2760],338,4]
%
% END OF LATTICE L339.4
%
%
% LATTICE L339.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-395640, -630, -197190; -630, 1254, -312; -197190, -312, -98281],[630, 6, 1],[593, 625, -157, -313, -2041, -9133, -38291, -7569, -55579, -477; 0, 2, 0, -1, -7, -33, -140, -28, -210, -2; -1190, -1254, 315, 628, 4095, 18324, 76825, 15186, 111510, 957],338,5]
%
% END OF LATTICE L339.5
%
%
% LATTICE L339.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-22533210, -8820, 42210; -8820, 30, 15; 42210, 15, -79],[630, 15, 1],[-2, 0, 29, 4, 23, 32, 47, 20, 22, -1; -49, 1, 714, 98, 560, 774, 1134, 481, 525, -26; -1078, 0, 15624, 2155, 12390, 17235, 25312, 10770, 11844, -540],338,6]
%
% END OF LATTICE L339.6
%
%
% LATTICE L339.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1692810, -3150, 13860; -3150, 42, 21; 13860, 21, -113],[630, 21, 1],[-2, 0, 31, 6, 5, 50, 53, 32, 26, -1; -25, 1, 390, 75, 62, 615, 650, 391, 315, -14; -250, 0, 3870, 749, 624, 6237, 6610, 3990, 3240, -126],338,7]
%
% END OF LATTICE L339.7
%
%
% LATTICE L339.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3911315940, 238691880, 980368200; 238691880, -14351604, -59828436; 980368200, -59828436, -245728501],[1260, 12, 1],[1603699, 220926, 185606, -426049, -1003015, -1375489, -25346108, -1629283, -3782588, -67557; 15120, 2083, 1750, -4017, -9457, -12969, -238980, -15362, -35665, -637; 6394500, 880908, 740075, -1698804, -3999366, -5484548, -101063655, -6496512, -15082480, -269373],338,8]
%
% END OF LATTICE L339.8
%
%
% LATTICE L339.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3063060, -15120, -17640; -15120, 15, 0; -17640, 0, -17],[1260, 15, 1],[3, 5, 53, 3, 1, -1, -1, 0, 2, 3; 3031, 5054, 53592, 3035, 1022, -1005, -1008, -1, 2016, 3028; -3122, -5205, -55188, -3125, -1050, 1035, 1036, 0, -2079, -3120],338,9]
%
% END OF LATTICE L339.9
%
%
% LATTICE L339.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[15712298280, -34166790, 7831116090; -34166790, 74310, -17028960; 7831116090, -17028960, 3903081403],[630, 30, 1],[1877, 4381, 67415, 17205, 54897, 198625, 159681, 151391, 211445, 7663; 0, 2, 0, -1, -7, -33, -28, -28, -42, -2; -3766, -8790, -135261, -34520, -110145, -398520, -320383, -303750, -424242, -15375],338,10]
%
% END OF LATTICE L339.10
%
%
% LATTICE L339.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1008784980, 48014820, -131040; 48014820, 2285346, -6237; -131040, -6237, 17],[1260, 21, 1],[-17, -11, -17, -1, 5, 19, 181, 18, 4, -7; 360, 233, 360, 21, -106, -403, -3840, -382, -85, 148; 1035, 693, 1040, 0, -348, -1400, -13680, -1407, -355, 336],338,11]
%
% END OF LATTICE L339.11
%
%
% LATTICE L339.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1176722820, -7980210, 586463220; -7980210, 54138, -3977232; 586463220, -3977232, 292285577],[630, 42, 1],[309, 1549, 16529, 5868, 2624, 65120, 37187, 49065, 48443, 2313; 0, 2, 0, -1, -1, -33, -20, -28, -30, -2; -620, -3108, -33165, -11774, -5265, -130662, -74615, -98448, -97200, -4641],338,12]
%
% END OF LATTICE L339.12
%
%
% LATTICE L339.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-6126120, -30240, -32760; -30240, 30, 15; -32760, 15, -1],[2520, 15, 1],[3, 5, 53, 3, 1, -1, -1, 0, 2, 3; 6153, 10259, 108780, 6160, 2072, -2040, -2044, -1, 4095, 6148; -6244, -10410, -110376, -6250, -2100, 2070, 2072, 0, -4158, -6240],338,13]
%
% END OF LATTICE L339.13
%
%
% LATTICE L339.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-86957640, -20160, 83160; -20160, 30, 15; 83160, 15, -79],[2520, 15, 1],[-1, 0, 29, 2, 23, 16, 47, 10, 11, -1; -133, 1, 3864, 266, 3052, 2118, 6216, 1321, 1449, -136; -1078, 0, 31248, 2155, 24780, 17235, 50624, 10770, 11844, -1080],338,14]
%
% END OF LATTICE L339.14
%
%
% LATTICE L339.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[9285602760, 221036760, -561960; 221036760, 5261613, -13377; -561960, -13377, 34],[2520, 21, 1],[4, 18, 181, 19, 5, -1, -17, -11, -17, -7; -170, -764, -7680, -806, -212, 42, 720, 466, 720, 296; -775, -3087, -30060, -3080, -768, 0, 2300, 1533, 2295, 756],338,15]
%
% END OF LATTICE L339.15
%
%
% LATTICE L339.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-251942040, -35280, 168840; -35280, 42, 21; 168840, 21, -113],[2520, 21, 1],[-1, 0, 31, 3, 5, 25, 53, 16, 13, -1; -85, 1, 2640, 255, 424, 2115, 4480, 1351, 1095, -88; -1510, 0, 46800, 4529, 7548, 37737, 80000, 24150, 19620, -1512],338,16]
%
% END OF LATTICE L339.16
%
%
% LATTICE L339.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2915640, -12600, -456120; -12600, 48, 2112; -456120, 2112, 68279],[2520, 24, 1],[-12004, -1414, -6546, -1417, -179, -1, 158, 0, -702, -176; -1044435, -123029, -569555, -123291, -15575, -87, 13755, 1, -61075, -15313; -47880, -5640, -26110, -5652, -714, -4, 630, 0, -2800, -702],338,17]
%
% END OF LATTICE L339.17
%
%
% LATTICE L339.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-397688760, 19716480, 635040; 19716480, -977496, -31488; 635040, -31488, -997],[2520, 24, 1],[4129, 701, 1978, 1042, 333, 86, 446, -83, -453, -4; 82635, 14029, 39585, 20853, 6664, 1721, 8925, -1661, -9065, -80; 20160, 3432, 9695, 5112, 1638, 424, 2205, -408, -2240, -21],338,18]
%
% END OF LATTICE L339.18
%
%
% LATTICE L339.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-630, 0, -630; 0, 210, 105; -630, 105, -577],[630, 105, 1],[-2, 0, 35, 34, 29, 302, 65, 200, 34, -1; -1, 1, 18, 17, 14, 141, 30, 91, 15, -2; 2, 0, -36, -35, -30, -315, -68, -210, -36, 0],338,19]
%
% END OF LATTICE L339.19
%
%
% LATTICE L339.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[5810304780, 267744960, -1457169840; 267744960, 12337980, -67147920; -1457169840, -67147920, 365444503],[1260, 60, 1],[13742, 21457, 54934, 11897, 895, 361, 1824, 3792, 16495, 4059; 7, 14, 42, 11, 7, 3, 0, -1, 0, 1; 54796, 85560, 219051, 47440, 3570, 1440, 7273, 15120, 65772, 16185],338,20]
%
% END OF LATTICE L339.20
%
%
% LATTICE L339.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[3719668680, -74270700, -932702400; -74270700, 1475796, 18623304; -932702400, 18623304, 233873993],[1260, 84, 1],[91279, 1896, -18239, -118753, -5527, 99807, 363457, 210983, 100122, 41928; 825, 17, -165, -1074, -50, 902, 3285, 1907, 905, 379; 363960, 7560, -72725, -473508, -22038, 397964, 1449225, 841260, 399220, 167181],338,21]
%
% END OF LATTICE L339.21
%
%
% LATTICE L339.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[165060, 39060, 11340; 39060, 7665, 2205; 11340, 2205, 634],[1260, 105, 1],[1, 3, 1, 1, -1, -3, -5, -2, 0, 3; -93, -287, -96, -96, 100, 328, 576, 253, 5, -256; 306, 945, 316, 315, -330, -1085, -1908, -840, -17, 840],338,22]
%
% END OF LATTICE L339.22
%
%
% LATTICE L339.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[3570840, 198450, 1783530; 198450, 11130, 99120; 1783530, 99120, 890821],[630, 210, 1],[-1, -105, -463, -874, -412, -10382, -1189, -7865, -1555, -367; 0, 2, 0, -1, -1, -33, -4, -28, -6, -2; 2, 210, 927, 1750, 825, 20790, 2381, 15750, 3114, 735],338,23]
%
% END OF LATTICE L339.23
%
%
% LATTICE L339.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[41607720, -23786280, -657720; -23786280, 13598130, 376005; -657720, 376005, 10397],[2520, 105, 1],[0, -2, -5, -3, -1, 1, 1, 3, 1, 3; 25, 223, 276, 78, -20, 54, 44, 133, 57, 284; -904, -8190, -10296, -3010, 660, -1890, -1528, -4620, -1998, -10080],338,24]
%
% END OF LATTICE L339.24
%
%
% LATTICE L339.25
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[27720, -2520, -2520; -2520, 210, 105; -2520, 105, -577],[2520, 105, 1],[-1, 0, 35, 17, 29, 151, 65, 100, 17, -1; -13, 1, 456, 221, 376, 1953, 840, 1291, 219, -16; 2, 0, -72, -35, -60, -315, -136, -210, -36, 0],338,25]
%
% END OF LATTICE L339.25
%
%
% LATTICE L339.26
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-4412520, -27720, -2237760; -27720, 240, -13440; -2237760, -13440, -1133933],[2520, 120, 1],[446, 0, -2446, -667, -1777, -4211, -2878, -2210, -1756, 224; 1337, 1, -7329, -1999, -5327, -12627, -8631, -6629, -5271, 671; -896, 0, 4914, 1340, 3570, 8460, 5782, 4440, 3528, -450],338,26]
%
% END OF LATTICE L339.26
%
%
% LATTICE L339.27
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3361680, -320040, 7560; -320040, -30360, 720; 7560, 720, -17],[2520, 120, 1],[-1, -1, 1, 1, 4, 13, 5, 9, 11, 0; 0, 2, 0, -1, -7, -33, -14, -28, -42, -1; -448, -360, 441, 400, 1470, 4320, 1603, 2760, 3024, -45],338,27]
%
% END OF LATTICE L339.27
%
%
% LATTICE L339.28
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-26734680, -78120, -13804560; -78120, 336, -36960; -13804560, -36960, -7107823],[2520, 168, 1],[878, 0, -5702, -2193, -877, -16217, -8326, -9638, -7004, 440; 10535, 1, -68415, -26313, -10523, -194589, -99905, -115649, -84045, 5279; -1760, 0, 11430, 4396, 1758, 32508, 16690, 19320, 14040, -882],338,28]
%
% END OF LATTICE L339.28
%
%
% LATTICE L339.29
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-33228720, -738360, 37800; -738360, -16296, 840; 37800, 840, -43],[2520, 168, 1],[-1, -1, 2, 2, 1, 22, 6, 15, 13, 0; 0, 2, 0, -1, -1, -33, -10, -28, -30, -1; -880, -840, 1755, 1736, 858, 18648, 5065, 12600, 10800, -21],338,29]
%
% END OF LATTICE L339.29
%
%
% LATTICE L339.30
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[366280740, -54072900, 132549480; -54072900, 7982520, -19567800; 132549480, -19567800, 47966881],[1260, 420, 1],[-911, -631, 78, 3790, 188, -4490, -3218, -9261, -879, -1868; 2742, 1903, -234, -11391, -565, 13513, 9684, 27868, 2645, 5621; 3636, 2520, -311, -15120, -750, 17920, 12843, 36960, 3508, 7455],338,30]
%
% END OF LATTICE L339.30
%
%
% LATTICE L339.31
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-744188760, -793800, -371700000; -793800, 1680, -396480; -371700000, -396480, -185653019],[2520, 840, 1],[-30172, -179150, -29230, -272501, -13201, -31117, -16030, 0, 1886, 944; 15, 91, 15, 141, 7, 17, 9, 1, -1, -1; 60408, 358680, 58522, 545580, 26430, 62300, 32094, 0, -3776, -1890],338,31]
%
% END OF LATTICE L339.31
%
%
% LATTICE L339.32
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1108542960, -307664280, 587160; -307664280, -85388520, 162960; 587160, 162960, -311],[2520, 840, 1],[17, 99, 8, 148, 7, 16, 4, -1, -1, 0; -6, -28, -2, -33, -1, -1, 0, 2, 0, -1; 28944, 172200, 14053, 262080, 12690, 29680, 7551, -840, -1888, -525],338,32]
%
% END OF LATTICE L339.32
%

\medskip%
%------------------------------WEYL-GROUP-W340--------------------------------
%
\leavevmode\llap{}%
$W_{340}$%
\qquad\llap{16} lattices, $\chi=72$%
\hfill%
$2|2222|2222|2222|222\rtimes D_{4}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L340.1
%
\leavevmode%
${L_{340.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}8\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{1}{}3\above{1pt}{1pt}{-}{}9\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{2}{}5\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{2}{}7\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${360}\above{1pt}{1pt}{r}{2}{42}\above{1pt}{1pt}{l}{2}{40}\above{1pt}{1pt}{r}{2}{6}\above{1pt}{1pt}{b}{2}{90}\above{1pt}{1pt}{l}{2}{168}\above{1pt}{1pt}{r}{2}{10}\above{1pt}{1pt}{b}{2}{6}\above{1pt}{1pt}{l}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-11473560\\-5040\\4919040
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-5040\\6\\393
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4919040\\393\\-1728470
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
352031\\226695840\\1053360
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
386\\248569\\1155
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-200720\\-129256400\\-600601
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
6617\\4261320\\19800
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
779\\501676\\2331
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
909\\585400\\2720
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\1\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-391\\-251805\\-1170
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1179\\-759304\\-3528
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-132\\-85015\\-395
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3\\-1943\\-9
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-11473560, -5040, 4919040; -5040, 6, 393; 4919040, 393, -1728470],[2520, 3, 1],[6617, 779, 909, 0, -391, -1179, -132, -3, 2647, 765, 2179, 386, 1549, 4267, 518, 389; 4261320, 501676, 585400, 1, -251805, -759304, -85015, -1943, 1704360, 492604, 1403160, 248569, 997515, 2747864, 333585, 250513; 19800, 2331, 2720, 0, -1170, -3528, -395, -9, 7920, 2289, 6520, 1155, 4635, 12768, 1550, 1164],339,1]
%
% END OF LATTICE L340.1
%
%
% LATTICE L340.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-8364510, -1890, 16380; -1890, 6, 3; 16380, 3, -32],[630, 3, 1],[-7, -9, -31, -3, -3, -9, -4, 0, 3, 5, 19, 2, 2, 5, 1, -1; -450, -560, -1890, -179, -175, -518, -225, 1, 170, 280, 1050, 109, 105, 238, 15, -71; -3650, -4683, -16110, -1557, -1555, -4662, -2070, 0, 1550, 2583, 9810, 1032, 1030, 2562, 495, -525],339,2]
%
% END OF LATTICE L340.2
%
%
% LATTICE L340.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[5601137220, -5841990, 2791643400; -5841990, 6096, -2911686; 2791643400, -2911686, 1391373317],[630, 6, 1],[95532, 182934, 250636, 35649, 23141, 25800, 11573, 939, 6412, 20954, 55196, 15323, 27831, 76144, 141343, 50033; -70, -133, -180, -25, -15, -14, 0, 2, 0, -7, -30, -10, -20, -56, -105, -37; -191675, -367038, -502875, -71526, -46430, -51765, -23220, -1884, -12865, -42042, -110745, -30744, -55840, -152775, -283590, -100386],339,3]
%
% END OF LATTICE L340.3
%
%
% LATTICE L340.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-4249350, -5040, 15750; -5040, 30, 15; 15750, 15, -58],[630, 15, 1],[3, 26, 23, 14, 4, 89, 14, 20, 13, 54, 25, 6, 0, -9, -2, 0; 86, 742, 654, 397, 113, 2506, 393, 559, 362, 1498, 690, 163, -1, -266, -57, 1; 836, 7245, 6408, 3900, 1114, 24780, 3897, 5565, 3616, 15015, 6948, 1665, -1, -2520, -558, 0],339,4]
%
% END OF LATTICE L340.4
%
%
% LATTICE L340.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[257670, -81270, -32130; -81270, 25620, 10143; -32130, 10143, 4000],[630, 21, 1],[49, -1, -863, -187, -479, -439, -3122, -1198, -4781, -675, -13333, -996, -704, -237, -427, 15; 100, -2, -1740, -377, -965, -884, -6285, -2411, -9620, -1358, -26820, -2003, -1415, -476, -855, 31; 140, -3, -2520, -546, -1400, -1284, -9135, -3507, -14000, -1977, -39060, -2919, -2065, -696, -1260, 42],339,5]
%
% END OF LATTICE L340.5
%
%
% LATTICE L340.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[3164648760, -15527610, 1577264850; -15527610, 76200, -7738980; 1577264850, -7738980, 786110749],[630, 30, 1],[3585, 56414, 26021, 33029, 10593, 132871, 46417, 76943, 28191, 261346, 69307, 46411, 5295, 26009, 1247, 2497; 0, -7, -6, -10, -4, -56, -21, -37, -14, -133, -36, -25, -3, -14, 0, 2; -7193, -113190, -52209, -66270, -21254, -266595, -93132, -154380, -56563, -524370, -139059, -93120, -10624, -52185, -2502, -5010],339,6]
%
% END OF LATTICE L340.6
%
%
% LATTICE L340.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[4578840, -712530, 2265480; -712530, 110460, -352548; 2265480, -352548, 1120895],[630, 42, 1],[-122, -472, -1726, 857, 5889, 3538, 56767, 24317, 51558, 15168, 156034, 24861, 19829, 3810, 20387, 1401; -5, -19, -75, 32, 230, 139, 2235, 959, 2035, 599, 6165, 983, 785, 151, 810, 56; 245, 948, 3465, -1722, -11830, -7107, -114030, -48846, -103565, -30468, -313425, -49938, -39830, -7653, -40950, -2814],339,7]
%
% END OF LATTICE L340.7
%
%
% LATTICE L340.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-15092280, -12600, 30240; -12600, 30, 15; 30240, 15, -58],[2520, 15, 1],[3, 13, 23, 7, 2, 89, 7, 10, 13, 27, 25, 3, 0, -9, -1, 0; 424, 1834, 3240, 985, 281, 12488, 981, 1399, 1816, 3766, 3480, 415, -1, -1288, -141, 1; 1672, 7245, 12816, 3900, 1114, 49560, 3897, 5565, 7232, 15015, 13896, 1665, -1, -5040, -558, 0],339,8]
%
% END OF LATTICE L340.8
%
%
% LATTICE L340.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1030680, 352800, 126000; 352800, 120750, 43113; 126000, 43113, 15382],[2520, 21, 1],[-1643, -1, 89, 13, -416, -457, -677, -956, -25573, -647, -9161, -1147, -2986, -839, -457, -178; 6600, 4, -360, -53, 1665, 1832, 2715, 3835, 102600, 2596, 36760, 4603, 11985, 3368, 1835, 715; -5040, -3, 280, 42, -1260, -1392, -2065, -2919, -78120, -1977, -28000, -3507, -9135, -2568, -1400, -546],339,9]
%
% END OF LATTICE L340.9
%
%
% LATTICE L340.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-912003120, -7209720, 385560; -7209720, -56976, 3048; 385560, 3048, -163],[2520, 24, 1],[11, 38, 23, 5, 1, -1, -7, -1, 1, 10, 13, 7, 11, 13, 43, 13; -35, -133, -90, -25, -15, -7, 0, 2, 0, -7, -15, -10, -20, -28, -105, -37; 25355, 87360, 52695, 11352, 2080, -2499, -16560, -2328, 2365, 23520, 30465, 16368, 25640, 30219, 99720, 30048],339,10]
%
% END OF LATTICE L340.10
%
%
% LATTICE L340.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[7585830, -43470, -18270; -43470, 210, 105; -18270, 105, 44],[630, 105, 1],[1, 1, 1, -2, -2, -11, -17, -35, -29, -21, -85, -33, -5, -9, -4, 0; 4, 4, 12, 1, -3, -20, -33, -71, -60, -44, -180, -71, -11, -20, -9, 1; 406, 405, 378, -840, -826, -4530, -6993, -14385, -11914, -8625, -34902, -13545, -2051, -3690, -1638, 0],339,11]
%
% END OF LATTICE L340.11
%
%
% LATTICE L340.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[881139420, -2303910, 439164180; -2303910, 5460, -1148280; 439164180, -1148280, 218881567],[630, 210, 1],[1406, -6250, -39218, -65311, -24687, -46718, -117811, -196561, -71406, -93750, -170782, -109689, -10313, -3282, 12811, 21561; 0, -1, -6, -10, -4, -8, -21, -37, -14, -19, -36, -25, -3, -2, 0, 2; -2821, 12540, 78687, 131040, 49532, 93735, 236376, 394380, 143269, 188100, 342657, 220080, 20692, 6585, -25704, -43260],339,12]
%
% END OF LATTICE L340.12
%
%
% LATTICE L340.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-108360, -88200, 624960; -88200, 210, 28035; 624960, 28035, -395734],[2520, 105, 1],[-8915, -816, -1383, -35, 778, 2363, 528, 2383, 8747, 796, 1327, 0, -799, -2403, -535, -2418; -178320, -16322, -27664, -701, 15561, 47264, 10561, 47665, 174960, 15922, 26544, 1, -15981, -48064, -10701, -48365; -26712, -2445, -4144, -105, 2331, 7080, 1582, 7140, 26208, 2385, 3976, 0, -2394, -7200, -1603, -7245],339,13]
%
% END OF LATTICE L340.13
%
%
% LATTICE L340.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-164450160, -60805080, -5916960; -60805080, -22482480, -2187720; -5916960, -2187720, -212831],[2520, 120, 1],[256, 9535, 2221, 5611, 1681, 9718, 6328, 9466, 1597, 27525, 3338, 3654, 172, -453, -769, -201; -767, -28567, -6654, -16810, -5036, -29113, -18957, -28357, -4784, -82453, -9999, -10945, -515, 1358, 2304, 602; 767, 28560, 6651, 16800, 5032, 29085, 18936, 28320, 4777, 82320, 9981, 10920, 512, -1365, -2304, -600],339,14]
%
% END OF LATTICE L340.14
%
%
% LATTICE L340.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-163653840, -3293640, 133560; -3293640, -66192, 2688; 133560, 2688, -109],[2520, 168, 1],[-187, -37, -64, -62, -152, -5, -19, -5, -2, 1, 1, -1, -37, -4, -44, -58; -90, -19, -35, -37, -105, -4, -20, -10, -15, -1, 0, 2, 0, -1, -15, -25; -231525, -45840, -79345, -76944, -189000, -6231, -23800, -6384, -2835, 1200, 1225, -1176, -45360, -4929, -54320, -71736],339,15]
%
% END OF LATTICE L340.15
%
%
% LATTICE L340.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1002960, 1010520, -224280; 1010520, -1016400, 225960; -224280, 225960, -50153],[2520, 840, 1],[-149, -156, -35, -1, 329, 167, 355, 2207, 1367, 1316, 441, 2031, 889, 123, 51, -177; 6, 5, 1, -1, -9, -4, -8, -46, -27, -25, -8, -34, -12, -1, 1, 11; 693, 720, 161, 0, -1512, -765, -1624, -10080, -6237, -6000, -2009, -9240, -4032, -555, -224, 840],339,16]
%
% END OF LATTICE L340.16
%

\medskip%
%------------------------------WEYL-GROUP-W341--------------------------------
%
\leavevmode\llap{}%
$W_{341}$%
\qquad\llap{4} lattices, $\chi=48$%
\hfill%
$2\infty|\infty2|2\infty|\infty2|\rtimes D_{4}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L341.1
%
\leavevmode%
${L_{341.1}}$%
{} : {$1\above{1pt}{1pt}{1}{7}8\above{1pt}{1pt}{1}{1}256\above{1pt}{1pt}{1}{1}$}\EasyButWeakLineBreak%
{${256}\above{1pt}{1pt}{*}{2}{32}\above{1pt}{1pt}{32,17}{\infty z}{8}\above{1pt}{1pt}{32,9}{\infty}{32}\above{1pt}{1pt}{s}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
shares genus with {$ {L_{342.1}}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-239360\\-11008\\-11520
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-11008\\-504\\-528
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-11520\\-528\\-553
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1153\\-56448\\78336
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-50\\-2451\\3400
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-53\\-2597\\3603
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\112\\-128
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\202\\-256
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\115\\-152
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
13\\650\\-896
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-239360, -11008, -11520; -11008, -504, -528; -11520, -528, -553],[256, 8, 1],[1, 3, 2, 13, 31, 9, 0, -1; 112, 202, 115, 650, 1456, 386, -17, -62; -128, -256, -152, -896, -2048, -560, 16, 80],340,1]
%
% END OF LATTICE L341.1
%
\hbox{}\par\smallskip%
%
% LATTICE L341.2
%
\leavevmode%
${L_{341.2}}$%
{} : {$1\above{1pt}{1pt}{1}{1}8\above{1pt}{1pt}{1}{1}256\above{1pt}{1pt}{1}{7}$}\EasyButWeakLineBreak%
{${1}\above{1pt}{1pt}{}{2}{8}\above{1pt}{1pt}{32,31}{\infty}{32}\above{1pt}{1pt}{32,7}{\infty z}{8}\above{1pt}{1pt}{r}{2}{4}\above{1pt}{1pt}{*}{2}{32}\above{1pt}{1pt}{32,15}{\infty z}{8}\above{1pt}{1pt}{32,7}{\infty}{32}\above{1pt}{1pt}{l}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1272064\\8960\\8960
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
8960\\-56\\-64
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
8960\\-64\\-63
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
10\\154\\1263
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
29\\445\\3664
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
11\\166\\1392
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\13\\128
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-16\\-126
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-14\\-128
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4\\63\\504
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
55\\850\\6944
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-1272064, 8960, 8960; 8960, -56, -64; 8960, -64, -63],[256, 8, 1],[10, 29, 11, 1, -1, -1, 4, 55; 154, 445, 166, 13, -16, -14, 63, 850; 1263, 3664, 1392, 128, -126, -128, 504, 6944],340,2]
%
% END OF LATTICE L341.2
%
%
% LATTICE L341.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[256, -512, 0; -512, 1056, 0; 0, 0, -1],[256, 32, 1],[-113, -44, -11, -6, 1, 2, -3, -36; -48, -19, -5, -3, 0, 1, -1, -15; -384, -144, -32, -16, 0, 0, -16, -128],340,3]
%
% END OF LATTICE L341.3
%
%
% LATTICE L341.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-256, 3840, -256; 3840, -55776, 3712; -256, 3712, -247],[256, 32, 1],[-1, -1, 8, 55, 20, 58, 11, 2; -1, 1, 7, 33, 11, 29, 3, -3; -14, 16, 96, 432, 142, 368, 32, -48],340,4]
%
% END OF LATTICE L341.4
%

\medskip%
%------------------------------WEYL-GROUP-W342--------------------------------
%
\leavevmode\llap{}%
$W_{342}$%
\qquad\llap{2} lattices, $\chi=24$%
\hfill%
$2|22\infty|\infty2\rtimes D_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L342.1
%
\leavevmode%
${L_{342.1}}$%
{} : {$1\above{1pt}{1pt}{1}{7}8\above{1pt}{1pt}{1}{1}256\above{1pt}{1pt}{1}{1}$}\EasyButWeakLineBreak%
{${256}\above{1pt}{1pt}{r}{2}{4}\above{1pt}{1pt}{b}{2}{256}\above{1pt}{1pt}{l}{2}{8}\above{1pt}{1pt}{32,17}{\infty}{32}\above{1pt}{1pt}{32,25}{\infty z}{8}\above{1pt}{1pt}{}{2}$}%
\nopagebreak\par%
shares genus with {$ {L_{341.1}}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
13951232\\6751744\\425216
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
6751744\\3267528\\205784
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
425216\\205784\\12959
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-209\\448\\-256
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
84\\-181\\118
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
8929\\-19232\\12416
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1411\\-3039\\1960
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
209\\-450\\288
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-112\\241\\-152
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[13951232, 6751744, 425216; 6751744, 3267528, 205784; 425216, 205784, 12959],[256, 8, 1],[-209, 84, 8929, 1411, 209, -112; 448, -181, -19232, -3039, -450, 241; -256, 118, 12416, 1960, 288, -152],341,1]
%
% END OF LATTICE L342.1
%
%
% LATTICE L342.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-999680, 16128, 7936; 16128, -224, -128; 7936, -128, -63],[256, 32, 1],[10, 3, -1, -1, 8, 55; -3, -4, 0, 1, -1, -15; 1263, 384, -126, -128, 1008, 6944],341,2]
%
% END OF LATTICE L342.2
%

\medskip%
%------------------------------WEYL-GROUP-W343--------------------------------
%
\leavevmode\llap{}%
$W_{343}$%
\qquad\llap{2} lattices, $\chi=24$%
\hfill%
$222\slashinfty222|\rtimes D_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L343.1
%
\leavevmode%
${L_{343.1}}$%
{} : {$1\above{1pt}{1pt}{1}{1}8\above{1pt}{1pt}{1}{7}256\above{1pt}{1pt}{1}{1}$}\EasyButWeakLineBreak%
{${256}\above{1pt}{1pt}{l}{2}{1}\above{1pt}{1pt}{}{2}{256}\above{1pt}{1pt}{r}{2}{8}\above{1pt}{1pt}{16,1}{\infty a}{8}\above{1pt}{1pt}{b}{2}{256}\above{1pt}{1pt}{s}{2}{4}\above{1pt}{1pt}{*}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
385280\\8448\\-2560
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
8448\\184\\-56
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2560\\-56\\17
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3\\-16\\-512
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\1\\3
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\32\\256
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\1\\4
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-9\\-180
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-15\\-128\\-2688
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-8\\-178
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[385280, 8448, -2560; 8448, 184, -56; -2560, -56, 17],[256, 8, 1],[-3, 0, 1, 0, -1, -15, -1; -16, 1, 32, 1, -9, -128, -8; -512, 3, 256, 4, -180, -2688, -178],342,1]
%
% END OF LATTICE L343.1
%
%
% LATTICE L343.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[256, 0, 0; 0, -1312, 96; 0, 96, -7],[256, 32, 1],[0, 1, 0, -1, -3, -1, -3; -1, 0, 1, 10, 6, 0, -8; -14, 0, 13, 128, 64, -6, -128],342,2]
%
% END OF LATTICE L343.2
%

\medskip%
%------------------------------WEYL-GROUP-W344--------------------------------
%
\leavevmode\llap{}%
$W_{344}$%
\qquad\llap{32} lattices, $\chi=96$%
\hfill%
$2222\infty\infty\infty2222\infty\infty\infty\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L344.1
%
\leavevmode%
${L_{344.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}8\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{1}{}3\above{1pt}{1pt}{-}{}9\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-}{}7\above{1pt}{1pt}{-}{}49\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{23,3,2}%
\EasyButWeakLineBreak%
{${42}\above{1pt}{1pt}{l}{2}{3528}\above{1pt}{1pt}{r}{2}{6}\above{1pt}{1pt}{s}{2}{882}\above{1pt}{1pt}{b}{2}{168}\above{1pt}{1pt}{42,1}{\infty z}{42}\above{1pt}{1pt}{84,37}{\infty b}{168}\above{1pt}{1pt}{42,37}{\infty z}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-49106232\\190512\\-1090152
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
190512\\-714\\4389
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1090152\\4389\\-23186
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1834561\\-248900400\\39143160
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7176\\973589\\-153111
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-40352\\-5474680\\860971
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-6174\\-837638\\131733
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-96233\\-13056120\\2053296
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-900\\-122105\\19203
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-6676\\-905751\\142443
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3807\\-516508\\81228
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-250\\-33919\\5334
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-689\\-93484\\14700
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-49106232, 190512, -1090152; 190512, -714, 4389; -1090152, 4389, -23186],[3528, 21, 1],[-6174, -96233, -900, -6676, -3807, -250, -689, -690, -8599, -36, 124, 63, -62, -3055; -837638, -13056120, -122105, -905751, -516508, -33919, -93484, -93622, -1166760, -4885, 16821, 8548, -8411, -414476; 131733, 2053296, 19203, 142443, 81228, 5334, 14700, 14721, 183456, 768, -2646, -1344, 1323, 65184],343,1]
%
% END OF LATTICE L344.1
%
%
% LATTICE L344.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-21963270, 1455006, -464814; 1455006, -96390, 30793; -464814, 30793, -9836],[294, 7, 1],[-8821, -22943, -1291, -3209, -2761, -374, -547, -1145, -2425, -68, 38, 43, -79, -2171; -119148, -309904, -17439, -43351, -37302, -5055, -7398, -15492, -32816, -921, 511, 582, -1065, -29322; 43827, 113974, 6411, 15925, 13692, 1848, 2688, 5607, 11858, 330, -196, -210, 399, 10794],343,2]
%
% END OF LATTICE L344.2
%
%
% LATTICE L344.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[26016648, 411600, -45864; 411600, 6510, -707; -45864, -707, -114],[1176, 7, 1],[1403, 6113, 98, -8, -179, 7, 3187, 6715, 35215, 1009, 2591, 4607, 362, 1241; -89634, -390544, -6261, 511, 11436, -447, -203604, -428994, -2249744, -64461, -165529, -294324, -23127, -79284; -8547, -37240, -597, 49, 1092, -42, -19404, -40887, -214424, -6144, -15778, -28056, -2205, -7560],343,3]
%
% END OF LATTICE L344.3
%
%
% LATTICE L344.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-369558, 17640, 176400; 17640, -840, -8421; 176400, -8421, -84200],[882, 21, 1],[474, 3095, 33, -1, -21, 11, 617, 2562, 20089, 381, 2899, 849, 127, 211; 475, 3066, 31, -21, -20, 20, 736, 3023, 23646, 446, 3360, 974, 139, 218; 945, 6174, 66, 0, -42, 21, 1218, 5061, 39690, 753, 5733, 1680, 252, 420],343,4]
%
% END OF LATTICE L344.4
%
%
% LATTICE L344.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-6175470, -406896, 37926; -406896, -26810, 2499; 37926, 2499, -220],[294, 7, 1],[-13907, -5139, -13991, -693, -4067, -478, -545, -943, -261, -184, 18, 17, -197, -3505; 210951, 77952, 212226, 10512, 61692, 7251, 8268, 14307, 3960, 2793, -273, -258, 2988, 53166; -1323, -488, -1323, -65, -378, -42, -42, -63, -16, 0, 2, 0, -21, -336],343,5]
%
% END OF LATTICE L344.5
%
%
% LATTICE L344.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[118548444, 10971198, 58986984; 10971198, 1015756, 5459020; 58986984, 5459020, 29350569],[294, 14, 1],[-2871994, -3731558, -419089, -1038349, -445643, -119795, -91703, -403322, -437026, -27545, -3797, -991, -29083, -354931; -52485, -68194, -7659, -18977, -8145, -2190, -1677, -7377, -7994, -504, -70, -18, -531, -6486; 5781720, 7512141, 843684, 2090340, 897141, 241164, 184611, 811944, 879795, 55452, 7644, 1995, 58548, 714525],343,6]
%
% END OF LATTICE L344.6
%
%
% LATTICE L344.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[26106024, -9958074, 13058010; -9958074, 3798956, -4980948; 13058010, -4980948, 6531505],[294, 14, 1],[1485409, 275378, 1511248, 76018, 227102, 59291, 43514, 186965, 28690, 85109, -1, 949, 16726, 184537; -28545, -5292, -29043, -1461, -4365, -1140, -837, -3597, -552, -1638, 0, -18, -321, -3546; -2991450, -554581, -3043488, -153092, -457359, -119406, -87633, -376530, -57779, -171402, 2, -1911, -33684, -371637],343,7]
%
% END OF LATTICE L344.7
%
%
% LATTICE L344.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[103401270, 12549684, -34686120; 12549684, 1523634, -4209807; -34686120, -4209807, 11635514],[294, 21, 1],[661764, 5158941, 96566, 717762, 205367, 27602, 42257, 92924, 604131, 6346, 2622, 457, 6702, 163567; -17495, -136388, -2553, -18977, -5430, -730, -1118, -2459, -15988, -168, -70, -12, -177, -4324; 1966426, 15329748, 286945, 2132823, 610246, 82019, 125566, 276122, 1795164, 18857, 7791, 1358, 19915, 486038],343,8]
%
% END OF LATTICE L344.8
%
%
% LATTICE L344.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[40642854, -15218028, -13542522; -15218028, 5698434, 5070765; -13542522, 5070765, 4512476],[294, 21, 1],[-333519, -370981, -339312, -51202, -101973, -13309, -19531, -41955, -38627, -19095, 1, -429, -3758, -82871; -9515, -10584, -9681, -1461, -2910, -380, -558, -1199, -1104, -546, 0, -12, -107, -2364; -990241, -1101468, -1007440, -152022, -302764, -39515, -57988, -124565, -114684, -56693, 3, -1274, -11158, -246050],343,9]
%
% END OF LATTICE L344.9
%
%
% LATTICE L344.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-72823800, -1273608, 114072; -1273608, -22274, 1995; 114072, 1995, -178],[1176, 7, 1],[-161, -97, -65, 1, 17, -10, -601, -1225, -911, -1258, -64, -773, -53, -155; 9201, 5544, 3717, -57, -972, 570, 34308, 69933, 52008, 71820, 3654, 44136, 3027, 8856; -63, -32, 0, 2, 0, -21, -672, -1323, -976, -1323, -65, -756, -42, -84],343,10]
%
% END OF LATTICE L344.10
%
%
% LATTICE L344.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-38250250248, -148733718, -18727179954; -148733718, -578340, -72819474; -18727179954, -72819474, -9168757505],[294, 42, 1],[1110031, 4330285, 162407, 1210571, 173518, 46904, 34184, 142803, 453263, 8434, -14684, -2677, 10043, 136657; -39716, -154952, -5813, -43351, -6217, -1685, -1233, -5164, -16408, -307, 511, 97, -355, -4887; -2266922, -8843373, -331670, -2472246, -354361, -95788, -69811, -291634, -925659, -17224, 29988, 5467, -20510, -279083],343,11]
%
% END OF LATTICE L344.11
%
%
% LATTICE L344.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-9131883432, 38327310, -4470780678; 38327310, -160860, 18764256; -4470780678, 18764256, -2188801469],[294, 42, 1],[646809, 358540, 650841, 96737, 94647, 22286, 12751, 44277, 18416, 8832, -2498, -408, 9127, 81488; 70317, 38976, 70742, 10512, 10282, 2417, 1378, 4769, 1980, 931, -273, -43, 996, 8861; -1320550, -732009, -1328782, -197502, -193235, -45500, -26033, -90398, -37599, -18032, 5100, 833, -18634, -166369],343,12]
%
% END OF LATTICE L344.12
%
%
% LATTICE L344.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2620422, 48510, 1126314; 48510, -840, -20853; 1126314, -20853, -484114],[882, 21, 1],[5832, 12321, 341, -211, -217, 425, 11357, 46088, 119839, 6739, 16731, 14377, 1935, 2803; 538, 1134, 31, -21, -20, 41, 1072, 4346, 11298, 635, 1575, 1352, 181, 260; 13545, 28616, 792, -490, -504, 987, 26376, 107037, 278320, 15651, 38857, 33390, 4494, 6510],343,13]
%
% END OF LATTICE L344.13
%
%
% LATTICE L344.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-4137462, 59976, 1389150; 59976, -840, -20139; 1389150, -20139, -466406],[882, 21, 1],[3246, 2855, 1089, -97, -99, 389, 8303, 33318, 37033, 33813, 5083, 10071, 1273, 1669; 664, 582, 217, -21, -20, 83, 1744, 6992, 7770, 7091, 1065, 2108, 265, 344; 9639, 8478, 3234, -288, -294, 1155, 24654, 98931, 109962, 100401, 15093, 29904, 3780, 4956],343,14]
%
% END OF LATTICE L344.14
%
%
% LATTICE L344.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-334278, 16758, 8820; 16758, -840, -441; 8820, -441, -220],[882, 21, 1],[54, 15, 11, -1, -1, 11, 197, 782, 289, 787, 39, 229, 27, 31; 1105, 306, 217, -21, -20, 230, 4096, 16253, 6006, 16352, 810, 4754, 559, 638; -63, -16, 0, 2, 0, -21, -336, -1323, -488, -1323, -65, -378, -42, -42],343,15]
%
% END OF LATTICE L344.15
%
%
% LATTICE L344.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-36456, 170520, 17640; 170520, -106470, -6237; 17640, -6237, -118],[1176, 21, 1],[-19020, -296377, -2770, -20522, -11687, -762, -2073, -2056, -25511, -104, 404, 191, -196, -9423; -64922, -1011640, -9455, -70049, -39892, -2601, -7076, -7018, -87080, -355, 1379, 652, -669, -32164; 588287, 9166920, 85676, 634746, 361480, 23569, 64120, 63595, 789096, 3217, -12495, -5908, 6062, 291452],343,16]
%
% END OF LATTICE L344.16
%
%
% LATTICE L344.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-92904, -28224, 2352; -28224, -8274, 693; 2352, 693, -58],[1176, 21, 1],[36, 81, 38, 6, 25, 2, 7, 8, 15, 4, 0, -1, 0, 17; 892, 2000, 931, 145, 596, 45, 148, 164, 304, 77, -1, -20, 3, 428; 12047, 27024, 12593, 1965, 8092, 616, 2044, 2275, 4224, 1078, -12, -280, 35, 5768],343,17]
%
% END OF LATTICE L344.17
%
%
% LATTICE L344.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1764, 882, 882; 882, 8400, 840; 882, 840, 461],[882, 42, 1],[2015, 6493, 131, -1, 10, 180, 1988, 16003, 62303, 2326, 17200, 2447, 639, 469; 215, 693, 14, 0, 1, 19, 211, 1699, 6615, 247, 1827, 260, 68, 50; -4242, -13671, -276, 0, -21, -378, -4179, -33642, -130977, -4890, -36162, -5145, -1344, -987],343,18]
%
% END OF LATTICE L344.18
%
%
% LATTICE L344.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[61570656, -856422, 30282588; -856422, 11928, -421218; 30282588, -421218, 14894029],[882, 42, 1],[19276, 20946, 1337, 241, 31, 1281, 16291, 132084, 171694, 19303, 47919, 20609, 5599, 4349; 215, 231, 14, 0, 1, 19, 211, 1699, 2205, 247, 609, 260, 68, 50; -39186, -42581, -2718, -490, -63, -2604, -33117, -268506, -349027, -39240, -97412, -41895, -11382, -8841],343,19]
%
% END OF LATTICE L344.19
%
%
% LATTICE L344.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[272222244, -2835630, 135165618; -2835630, 29568, -1407966; 135165618, -1407966, 67113341],[882, 42, 1],[58790, 27238, 27737, 143, 73, 4317, 52565, 425254, 236786, 434305, 65863, 65933, 17685, 13441; 215, 99, 98, 0, 1, 19, 211, 1699, 945, 1729, 261, 260, 68, 50; -118398, -54855, -55860, -288, -147, -8694, -105861, -856422, -476865, -874650, -132642, -132783, -35616, -27069],343,20]
%
% END OF LATTICE L344.20
%
%
% LATTICE L344.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[3146976, 794682, 1571724; 794682, 202440, 396900; 1571724, 396900, 784981],[882, 42, 1],[41605, 6383, 18917, -1, 220, 3750, 41218, 331713, 61493, 337432, 16970, 50687, 13219, 9689; 215, 33, 98, 0, 1, 19, 211, 1699, 315, 1729, 87, 260, 68, 50; -83412, -12797, -37926, 2, -441, -7518, -82635, -665028, -123283, -676494, -34022, -101619, -26502, -19425],343,21]
%
% END OF LATTICE L344.21
%
%
% LATTICE L344.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-385184688, -64335432, -27692448; -64335432, -10745616, -4625320; -27692448, -4625320, -1990895],[1176, 56, 1],[1269601, 808056, 172927, 390045, 150779, 18758, 2123, -355, -354, 152, 13806, 22300, 38935, 170956; -8888661, -5657316, -1210686, -2730756, -1055622, -131325, -14862, 2487, 2478, -1065, -96663, -156129, -272592, -1196889; 2990904, 1903601, 407376, 918848, 355194, 44184, 4998, -840, -833, 360, 32536, 52542, 91728, 402738],343,22]
%
% END OF LATTICE L344.22
%
%
% LATTICE L344.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-38845239216, 6475586376, -16554552; 6475586376, -1079494416, 2759680; -16554552, 2759680, -7055],[1176, 56, 1],[69239, 6297, 66071, 3045, 8251, 1042, 127, -5, -3, 16, 102, 1190, 2105, 9314; 483219, 43947, 461118, 21252, 57588, 7275, 888, -33, -21, 105, 711, 8301, 14688, 65001; 26549544, 2414663, 25338096, 1167968, 3165498, 400680, 49350, -1176, -1175, 3528, 38776, 454734, 806064, 3570882],343,23]
%
% END OF LATTICE L344.23
%
%
% LATTICE L344.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-439633051704, 8973418608, 41013000; 8973418608, -183157842, -837123; 41013000, -837123, -3826],[3528, 21, 1],[7219, 37861, 1085, 2787, 4957, 390, 1339, 1515, 6603, 106, -8, -193, 7, 3425; 347278, 1821344, 52195, 134071, 238460, 18761, 64412, 72878, 317632, 5099, -385, -9284, 337, 164764; 1400553, 7345688, 210528, 540862, 962136, 75747, 260232, 294525, 1283800, 20619, -1519, -37548, 1302, 664356],343,24]
%
% END OF LATTICE L344.24
%
%
% LATTICE L344.25
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-13337964501624, -234009678672, -593825904; -234009678672, -4105613694, -10418457; -593825904, -10418457, -26438],[3528, 21, 1],[-12831, -28781, -13410, -2092, -8613, -655, -2171, -2415, -4483, -1143, 13, 297, -38, -6145; 719428, 1613736, 751891, 117297, 482924, 36725, 121724, 135404, 251352, 64085, -729, -16652, 2131, 344548; 4692135, 10525176, 4904361, 765189, 3150756, 239736, 795060, 884667, 1642392, 418950, -4716, -108864, 13755, 2246832],343,25]
%
% END OF LATTICE L344.25
%
%
% LATTICE L344.26
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-278712, 14112, 7056; 14112, -714, -357; 7056, -357, -178],[3528, 21, 1],[8, 5, 4, 0, -1, 0, 17, 36, 27, 38, 2, 25, 2, 7; 185, 112, 77, -1, -20, 10, 652, 1333, 992, 1372, 70, 848, 59, 176; -63, -32, 0, 2, 0, -21, -672, -1323, -976, -1323, -65, -756, -42, -84],343,26]
%
% END OF LATTICE L344.26
%
%
% LATTICE L344.27
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-31189872, -239444184, -4278288; -239444184, -1837988208, -32840472; -4278288, -32840472, -586781],[1176, 168, 1],[-174469, -332968, -23724, -160150, -20580, -2483, -236, 119, 118, -51, -6275, -3195, -5442, -23539; -1233062, -2353253, -167669, -1131851, -145447, -17547, -1667, 842, 833, -361, -44359, -22583, -38463, -166363; 70283080, 134132649, 9556936, 64514184, 8290310, 1000160, 95018, -47992, -47481, 20576, 2528400, 1287202, 2192344, 9482494],343,27]
%
% END OF LATTICE L344.27
%
%
% LATTICE L344.28
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-359115120, 77643048, 1378272; 77643048, -16693488, -296352; 1378272, -296352, -5261],[1176, 168, 1],[7811, 2131, 7452, 1030, 930, 117, 14, -1, -1, 3, 35, 135, 238, 1051; -3055974, -833731, -2915507, -402973, -363847, -45771, -5475, 394, 391, -1183, -13697, -52823, -93119, -411195; 174189064, 47522271, 166182520, 22969272, 20739110, 2608928, 312074, -22456, -22287, 67424, 780720, 3010882, 5307736, 23437918],343,28]
%
% END OF LATTICE L344.28
%
%
% LATTICE L344.29
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-352778832, 814968, -16726248; 814968, -1680, 38640; -16726248, 38640, -793039],[3528, 168, 1],[-339669, -648248, -46188, -311798, -40068, -4835, -460, 231, 230, -99, -12211, -6219, -10594, -45827; -1454, -2772, -197, -1323, -169, -19, -1, 2, 0, -1, -63, -29, -47, -197; 7164024, 13672323, 974160, 6576192, 845082, 101976, 9702, -4872, -4851, 2088, 257544, 131166, 223440, 966546],343,29]
%
% END OF LATTICE L344.29
%
%
% LATTICE L344.30
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-577131408, 1012536, -82160064; 1012536, -1680, 144144; -82160064, 144144, -11696255],[3528, 168, 1],[287, 286, -123, -11161, -18027, -31474, -138195, -1026301, -653204, -139788, -315298, -121884, -15163, -1716; 2, 0, -1, -21, -29, -47, -197, -1454, -924, -197, -441, -169, -19, -1; -2016, -2009, 864, 78400, 126630, 221088, 970746, 7209216, 4588409, 981936, 2214800, 856170, 106512, 12054],343,30]
%
% END OF LATTICE L344.30
%
%
% LATTICE L344.31
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-4320424080, 2762424, -1438302096; 2762424, -1680, 919632; -1438302096, 919632, -478821727],[3528, 168, 1],[783, 782, -2349, -27373, -105579, -186130, -821939, -6108621, -1666556, -5827860, -805514, -727308, -91499, -10948; 2, 0, -7, -9, -29, -47, -197, -1454, -396, -1379, -189, -169, -19, -1; -2352, -2349, 7056, 82224, 317142, 559104, 2468970, 18349296, 5006061, 17505936, 2419632, 2184714, 274848, 32886],343,31]
%
% END OF LATTICE L344.31
%
%
% LATTICE L344.32
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-87762281040, 12443256, 24882984; 12443256, -1680, -3528; 24882984, -3528, -7055],[3528, 168, 1],[22595, 2055, 21564, 994, 2694, 341, 42, -1, -1, 3, 33, 387, 686, 3039; -1454, -132, -1379, -63, -169, -19, -1, 2, 0, -7, -3, -29, -47, -197; 79692984, 7248023, 76056624, 3505856, 9501786, 1202712, 148134, -3528, -3527, 10584, 116392, 1364958, 2419536, 10718610],343,32]
%
% END OF LATTICE L344.32
%

\medskip%
%------------------------------WEYL-GROUP-W345--------------------------------
%
\leavevmode\llap{}%
$W_{345}$%
\qquad\llap{16} lattices, $\chi=48$%
\hfill%
$222|222|222|222|\rtimes D_{4}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L345.1
%
\leavevmode%
${L_{345.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}8\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{1}{}9\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{1}{}7\above{1pt}{1pt}{1}{}49\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{23,3,2*}%
\EasyButWeakLineBreak%
{${14}\above{1pt}{1pt}{l}{2}{72}\above{1pt}{1pt}{r}{2}{98}\above{1pt}{1pt}{b}{2}{126}\above{1pt}{1pt}{b}{2}{2}\above{1pt}{1pt}{l}{2}{3528}\above{1pt}{1pt}{r}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
shares genus with 3-dual; isometric to own %
7-dual\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5761224\\1481760\\-3528
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1481760\\380982\\-903
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3528\\-903\\2
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
16463\\-68208\\-1728720
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4151\\-17198\\-435855
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-7\\29\\734
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-6\\25\\707
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-23\\96\\2808
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-5\\21\\686
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
8\\-33\\-756
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7\\-29\\-734
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1297\\-5376\\-137592
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[5761224, 1481760, -3528; 1481760, 380982, -903; -3528, -903, 2],[3528, 21, 1],[-6, -23, -5, 8, 7, 1297, 48, 191, 54, 13, 0, -121; 25, 96, 21, -33, -29, -5376, -199, -792, -224, -54, 0, 504; 707, 2808, 686, -756, -734, -137592, -5117, -20448, -5831, -1449, -1, 14112],344,1]
%
% END OF LATTICE L345.1
%
%
% LATTICE L345.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[1273314, -180222, 5292; -180222, 25508, -749; 5292, -749, 22],[294, 7, 1],[2, 1, 1, 1, 3, 97, 22, 15, 27, 3, 1, 15; 16, 8, 7, 5, 17, 560, 128, 88, 161, 19, 7, 112; 63, 32, 0, -70, -144, -4312, -945, -620, -1029, -77, -3, 196],344,2]
%
% END OF LATTICE L345.2
%
%
% LATTICE L345.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[6278664, 2687160, -11760; 2687160, 1150058, -5033; -11760, -5033, 22],[1176, 7, 1],[-17, -167, -3, 2, 73, 97, 77, 727, 13, 8, -3, -17; 40, 392, 7, -5, -175, -232, -184, -1736, -31, -19, 7, 40; 63, 392, -3, -77, -1029, -1240, -945, -8624, -144, -70, 0, 64],344,3]
%
% END OF LATTICE L345.3
%
%
% LATTICE L345.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[46919754, -2335536, 9702; -2335536, 116256, -483; 9702, -483, 2],[882, 21, 1],[-1, -11, 0, 4, 20, 37, 19, 263, 3, 5, 1, -1; -19, -210, 0, 78, 392, 726, 373, 5166, 59, 99, 21, -18; 266, 2646, -1, -567, -2303, -4050, -2030, -27342, -293, -315, 245, 522],344,4]
%
% END OF LATTICE L345.4
%
%
% LATTICE L345.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[5603640, -24990, 2782416; -24990, -364, -12418; 2782416, -12418, 1381573],[294, 14, 1],[1766, -221, -5889, -883, 2945, 58087, 28270, 10233, 40931, 5889, 2061, 11997; 71, -9, -238, -36, 118, 2331, 1135, 411, 1645, 237, 83, 483; -3556, 445, 11858, 1778, -5930, -116963, -56924, -20605, -82418, -11858, -4150, -24157],344,5]
%
% END OF LATTICE L345.5
%
%
% LATTICE L345.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[3665886, -26166, -1234800; -26166, -546, 8799; -1234800, 8799, 415924],[294, 21, 1],[-1202, 301, 4009, 601, -2005, -79091, -19246, -13933, -27865, -4009, -1403, -16333; 71, -18, -238, -36, 118, 4662, 1135, 822, 1645, 237, 83, 966; -3570, 894, 11907, 1785, -5955, -234906, -57162, -41382, -82761, -11907, -4167, -48510],344,6]
%
% END OF LATTICE L345.6
%
%
% LATTICE L345.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2005914372, 17521518, 982067604; 17521518, 153048, 8578290; 982067604, 8578290, 480806555],[294, 42, 1],[2673, 680, -144, -3434, -7200, -108316, -47583, -15650, -52251, -4051, -285, 3526; 16, 4, 7, 5, 17, 280, 128, 44, 161, 19, 7, 56; -5460, -1389, 294, 7014, 14706, 221235, 97188, 31965, 106722, 8274, 582, -7203],344,7]
%
% END OF LATTICE L345.7
%
%
% LATTICE L345.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[6891066, -323694, 34398; -323694, 15204, -1617; 34398, -1617, 170],[882, 21, 1],[-47, -93, -14, -6, -22, 3, 29, 65, 11, 5, 1, -7; -927, -1834, -276, -118, -420, 62, 585, 1302, 219, 99, 21, -138; 693, 1372, 207, 91, 441, -20, -315, -784, -144, -70, 0, 104],344,8]
%
% END OF LATTICE L345.8
%
%
% LATTICE L345.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1017240, -288120, -42336; -288120, 81606, 11991; -42336, 11991, 1762],[1176, 21, 1],[196, 263, 229, 22, 5, 95, 2, 1, 2, 11, 28, 1753; 788, 1056, 917, 87, 19, 336, 4, 0, 7, 45, 113, 7056; -651, -864, -735, -63, -9, 0, 21, 24, 0, -42, -96, -5880],344,9]
%
% END OF LATTICE L345.9
%
%
% LATTICE L345.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[547723764, 2900898, 273248010; 2900898, 13776, 1447194; 273248010, 1447194, 136317757],[882, 42, 1],[-18047, -4180, 4842, -3080, -260138, -284128, -312079, -2306702, -59863, -161983, -125009, -45998; -86, -21, 23, -15, -1239, -1353, -1486, -10983, -285, -771, -595, -219; 36176, 8379, -9706, 6174, 521458, 569547, 625576, 4623885, 119998, 324702, 250586, 92205],344,10]
%
% END OF LATTICE L345.10
%
%
% LATTICE L345.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[165106872, 9614682, 82389384; 9614682, 559104, 4797786; 82389384, 4797786, 41112829],[882, 42, 1],[-11063, 5158, 7570, 10232, 243326, 21130, 179273, 125672, 20465, -887, -47081, -2440; -51, 21, 33, 45, 1071, 93, 789, 553, 90, -4, -210, -11; 22176, -10339, -15174, -20510, -487746, -42355, -359352, -251909, -41022, 1778, 94374, 4891],344,11]
%
% END OF LATTICE L345.11
%
%
% LATTICE L345.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3544464, -217560, 12936; -217560, -12880, 784; 12936, 784, -47],[1176, 56, 1],[-39, -6, -34, 0, 2, 12, 9, 1, -1, -5, -7, -47; -368, -57, -329, -3, 17, 105, 80, 9, -7, -45, -65, -441; -16912, -2609, -14896, -56, 832, 5047, 3808, 425, -392, -2128, -3016, -20335],344,12]
%
% END OF LATTICE L345.12
%
%
% LATTICE L345.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[45726408, 10897992, 88200; 10897992, 2597322, 21021; 88200, 21021, 170],[3528, 21, 1],[-95, -29, -5, 8, 11, 43, -13, -19, -121, -14, -29, -379; 393, 120, 21, -33, -45, -168, 57, 80, 504, 58, 120, 1568; 693, 208, 0, -70, -144, -1568, -315, -40, 441, 91, 207, 2744],344,13]
%
% END OF LATTICE L345.13
%
%
% LATTICE L345.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2352, -1176, 0; -1176, -38640, -25368; 0, -25368, -16405],[1176, 168, 1],[1585, 251, 1534, 56, -46, -331, -271, -32, -1, 163, 265, 1864; 3153, 499, 3045, 109, -93, -665, -543, -64, 0, 326, 528, 3710; -4872, -771, -4704, -168, 144, 1029, 840, 99, 0, -504, -816, -5733],344,14]
%
% END OF LATTICE L345.14
%
%
% LATTICE L345.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-114808176, -1372392, -419832; -1372392, -14448, -4368; -419832, -4368, -1319],[3528, 168, 1],[-45, -22, -48, -10, 0, 8, 3, 1, -1, -11, -7, -155; 47366, 23160, 50547, 10551, 5, -8358, -3146, -1050, 1043, 11559, 7365, 163128; -142520, -69687, -152096, -31752, -16, 25137, 9464, 3159, -3136, -34776, -22160, -490833],344,15]
%
% END OF LATTICE L345.15
%
%
% LATTICE L345.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[7056, -3528, 0; -3528, -5842704, 35448; 0, 35448, -215],[3528, 168, 1],[80, 39, 23, 9, 1, -3, -80, -39, -23, -9, -1, 3; 159, 77, 45, 17, -21, -7, -177, -84, -48, -18, 0, 6; 26208, 12691, 7416, 2800, -3528, -1157, -29232, -13867, -7920, -2968, 0, 989],344,16]
%
% END OF LATTICE L345.16
%

\medskip%
%------------------------------WEYL-GROUP-W346--------------------------------
%
\leavevmode\llap{}%
$W_{346}$%
\qquad\llap{12} lattices, $\chi=60$%
\hfill%
$22|222\slashtwo222|222\slashtwo2\rtimes D_{4}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L346.1
%
\leavevmode%
${L_{346.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{1}{}9\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{2}{}7\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{2}{}11\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${396}\above{1pt}{1pt}{r}{2}{14}\above{1pt}{1pt}{l}{2}{12}\above{1pt}{1pt}{r}{2}{126}\above{1pt}{1pt}{l}{2}{44}\above{1pt}{1pt}{r}{2}{18}\above{1pt}{1pt}{b}{2}{2}\above{1pt}{1pt}{l}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-84537684\\-42139944\\63756
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-42139944\\-21005718\\31779
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
63756\\31779\\-46
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-6674977\\13408164\\11467764
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3326824\\6682660\\5715561
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4472\\-8983\\-7684
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-6637\\13332\\11484
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
115\\-231\\-196
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
229\\-460\\-396
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1150\\2310\\1953
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-6199\\12452\\10604
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2869\\5763\\4914
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1262\\2535\\2164
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-84537684, -42139944, 63756; -42139944, -21005718, 31779; 63756, 31779, -46],[2772, 3, 1],[-6637, 115, 229, -1150, -6199, -2869, -1262, -38771, -2523, -1605, -6074, -8937, -2291, -458; 13332, -231, -460, 2310, 12452, 5763, 2535, 77880, 5068, 3224, 12201, 17952, 4602, 920; 11484, -196, -396, 1953, 10604, 4914, 2164, 66528, 4333, 2760, 10458, 15400, 3951, 791],345,1]
%
% END OF LATTICE L346.1
%
%
% LATTICE L346.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-1764378, 38808, 9009; 38808, -789, -198; 9009, -198, -46],[693, 3, 1],[268, 36, 12, 95, 72, 38, 8, 62, -1, -2, 10, 38, 37, 17; -99, -14, -5, -42, -33, -18, -4, -33, 0, 1, 0, -11, -12, -6; 52866, 7105, 2370, 18774, 14234, 7515, 1583, 12276, -196, -396, 1953, 7480, 7290, 3352],345,2]
%
% END OF LATTICE L346.2
%
%
% LATTICE L346.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-422138178, -35353395, 202356; -35353395, -2960790, 16947; 202356, 16947, -97],[693, 21, 1],[857, 12, 15, 7, 15, -2, -2, 1, 1, 11, 32, 271, 197, 67; -9768, -137, -172, -81, -176, 21, 23, 0, -11, -124, -363, -3080, -2241, -763; 81081, 1096, 1239, 450, 539, -504, -154, 2079, 164, 1281, 3330, 27181, 19404, 6454],345,3]
%
% END OF LATTICE L346.3
%
%
% LATTICE L346.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[5099094, 204435, -13167; 204435, 8151, -528; -13167, -528, 34],[693, 33, 1],[2, -1, -2, -25, -2, -13, -3, -2, 1, 2, 25, 2, 13, 3; -3, 0, 1, 0, -1, -12, -6, -9, -14, -5, -42, -3, -18, -4; 729, -385, -759, -9702, -793, -5247, -1265, -927, 154, 693, 9009, 727, 4752, 1100],345,4]
%
% END OF LATTICE L346.4
%
%
% LATTICE L346.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[330405418728, -501867828, 82565442036; -501867828, 762312, -125412408; 82565442036, -125412408, 20632386251],[2772, 12, 1],[59141, 685, 173, 104240, 87837, 145643, 57979, 419128, 100766, 14320, 200113, 71586, 71752, 14486; -39501, -462, -115, -69531, -58597, -97164, -38682, -279642, -67235, -9556, -133560, -47784, -47901, -9673; -236907, -2744, -693, -417564, -351857, -583416, -232252, -1678941, -403648, -57363, -801612, -286759, -287424, -58028],345,5]
%
% END OF LATTICE L346.5
%
%
% LATTICE L346.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[3661812, 30492, -2772; 30492, 210, -21; -2772, -21, 2],[2772, 21, 1],[1, 0, -1, -2, -37, -14, -5, -133, -1, -3, -1, -7, -1, 0; 132, 0, -116, -231, -4268, -1614, -576, -15312, -115, -344, -114, -792, -111, 1; 2772, -1, -2604, -5184, -95788, -36225, -12929, -343728, -2582, -7728, -2565, -17864, -2520, 14],345,6]
%
% END OF LATTICE L346.6
%
%
% LATTICE L346.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[3254230980, -161097552, 332640; -161097552, 7974978, -16467; 332640, -16467, 34],[2772, 33, 1],[-3, -25, -5, -1, 7, 5, 22, 7, 46, 9, 8, 5, 0, -7; -64, -525, -104, -21, 144, 103, 453, 144, 945, 184, 161, 96, -3, -153; -1652, -9702, -1452, -385, 1260, 968, 4158, 1256, 7623, 1056, -308, -2448, -1463, -5643],345,7]
%
% END OF LATTICE L346.7
%
%
% LATTICE L346.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-4505886, -643797, 14553; -643797, -91938, 2079; 14553, 2079, -47],[693, 231, 1],[-9, -11, -3, 0, 1, 1, -1, -1, -4, -7, -5, -31, -26, -74; -27, -30, -5, 1, 3, 0, -24, -7, -21, -29, -18, -105, -85, -231; -3997, -4752, -1155, 44, 441, 308, -1386, -623, -2178, -3465, -2354, -14301, -11858, -33264],345,8]
%
% END OF LATTICE L346.8
%
%
% LATTICE L346.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[5290434072, -7614684, 1320697224; -7614684, 10920, -1900920; 1320697224, -1900920, 329697173],[2772, 84, 1],[-173, -690, -1211, -719, 6247, 15664, 8206, 67988, 2745, 3266, 6884, 16358, 15161, 2069; 0, 1, -2, -30, -154, -243, -91, -627, -20, -17, -27, -55, -42, -4; 693, 2764, 4851, 2880, -25025, -62748, -32872, -272349, -10996, -13083, -27576, -65527, -60732, -8288],345,9]
%
% END OF LATTICE L346.9
%
%
% LATTICE L346.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[15998525928, -67085172, 3993761772; -67085172, 262680, -16746708; 3993761772, -16746708, 996975169],[2772, 132, 1],[123053, 1706473, 173, -187609, -43441, -25615, 247835, 39633, 1709933, 162513, 1326411, 531499, 839045, 2192455; 739, 10248, 1, -1127, -261, -154, 1488, 238, 10269, 976, 7966, 3192, 5039, 13167; -492923, -6835752, -693, 751520, 174015, 102608, -992772, -158761, -6849612, -650991, -5313308, -2129067, -3361028, -8782488],345,10]
%
% END OF LATTICE L346.10
%
%
% LATTICE L346.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1361052, 60984, 673596; 60984, 2310, 29799; 673596, 29799, 333022],[2772, 231, 1],[19117, 1569, 4617, 1484, 903, 1259, -70, -229, 5, 1679, 3238, 5393, 22351, 7940; 38172, 3133, 9220, 2964, 1804, 2517, -139, -456, 10, 3352, 6465, 10768, 44628, 15854; -42084, -3454, -10164, -3267, -1988, -2772, 154, 504, -11, -3696, -7128, -11872, -49203, -17479],345,11]
%
% END OF LATTICE L346.11
%
%
% LATTICE L346.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[6306527304, -995383620, -2321979660; -995383620, 157104024, 366486120; -2321979660, 366486120, 854921407],[2772, 924, 1],[-100235, -37361, -35269, -62242, -12267, -112213, -12545, 488, 4112, 2020, -37505, -20982, -386522, -153700; 300648, 112063, 105790, 186699, 36796, 336597, 37631, -1464, -12335, -6062, 112485, 62932, 1159323, 461009; -401121, -149512, -141141, -249084, -49091, -449064, -50204, 1953, 16456, 8085, -150084, -83965, -1546776, -615076],345,12]
%
% END OF LATTICE L346.12
%

\medskip%
%------------------------------WEYL-GROUP-W347--------------------------------
%
\leavevmode\llap{}%
$W_{347}$%
\qquad\llap{4} lattices, $\chi=24$%
\hfill%
$22|22|22|22|\rtimes D_{4}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L347.1
%
\leavevmode%
${L_{347.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{2}16\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{1}{}9\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{1}{}$}\EasyButWeakLineBreak%
{${18}\above{1pt}{1pt}{l}{2}{80}\above{1pt}{1pt}{}{2}{3}\above{1pt}{1pt}{}{2}{720}\above{1pt}{1pt}{r}{2}{2}\above{1pt}{1pt}{b}{2}{720}\above{1pt}{1pt}{*}{2}{12}\above{1pt}{1pt}{*}{2}{80}\above{1pt}{1pt}{b}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-137520\\2160\\-720
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2160\\-6\\-9
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-720\\-9\\11
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\117\\162
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
11\\1280\\1760
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\116\\159
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
23\\2640\\3600
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\-1\\-2
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-13\\-1560\\-2160
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-118\\-162
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-120\\-160
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-137520, 2160, -720; 2160, -6, -9; -720, -9, 11],[720, 3, 1],[1, 11, 1, 23, 0, -13, -1, -1; 117, 1280, 116, 2640, -1, -1560, -118, -120; 162, 1760, 159, 3600, -2, -2160, -162, -160],346,1]
%
% END OF LATTICE L347.1
%
%
% LATTICE L347.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-9206640, 20880, 19440; 20880, -30, -45; 19440, -45, -41],[720, 15, 1],[1, 11, 7, 55, 4, 19, -1, -1; 21, 256, 164, 1296, 95, 456, -22, -24; 450, 4928, 3135, 24624, 1790, 8496, -450, -448],346,2]
%
% END OF LATTICE L347.2
%
%
% LATTICE L347.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-7883280, -1452960, 12240; -1452960, -267792, 2256; 12240, 2256, -19],[720, 48, 1],[1, 1, 0, -17, -5, -19, -7, -3; -3, -5, -1, 75, 23, 90, 34, 15; 288, 50, -120, -2070, -496, -1575, -480, -155],346,3]
%
% END OF LATTICE L347.3
%
%
% LATTICE L347.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-15163920, -85680, 42480; -85680, -480, 240; 42480, 240, -119],[720, 240, 1],[2, 0, -1, -2, -2, -1, -1, 0; 3, 1, -1, -27, -39, -30, -56, -5; 720, 2, -360, -774, -800, -423, -480, -11],346,4]
%
% END OF LATTICE L347.4
%

\medskip%
%------------------------------WEYL-GROUP-W348--------------------------------
%
\leavevmode\llap{}%
$W_{348}$%
\qquad\llap{12} lattices, $\chi=32$%
\hfill%
$222|2222\slashthree2\rtimes D_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L348.1
%
\leavevmode%
${L_{348.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{1}{}3\above{1pt}{1pt}{-}{}9\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}17\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${340}\above{1pt}{1pt}{*}{2}{36}\above{1pt}{1pt}{b}{2}{10}\above{1pt}{1pt}{l}{2}{204}\above{1pt}{1pt}{r}{2}{90}\above{1pt}{1pt}{b}{2}{4}\above{1pt}{1pt}{*}{2}{3060}\above{1pt}{1pt}{b}{2}{6}\above{1pt}{1pt}{+}{3}{6}\above{1pt}{1pt}{b}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-23993460\\-1407600\\18360
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1407600\\-82578\\1077
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
18360\\1077\\-14
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-29\\510\\1190
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\18\\72
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\-35\\-70
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
27\\-476\\-1224
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
11\\-195\\-585
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\-54\\-226
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
83\\-1530\\-9180
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\17\\-6
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2\\35\\69
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-23993460, -1407600, 18360; -1407600, -82578, 1077; 18360, 1077, -14],[3060, 3, 1],[-29, -1, 2, 27, 11, 3, 83, -1, -2; 510, 18, -35, -476, -195, -54, -1530, 17, 35; 1190, 72, -70, -1224, -585, -226, -9180, -6, 69],347,1]
%
% END OF LATTICE L348.1
%
%
% LATTICE L348.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-14512815, 39015, 18360; 39015, -93, -51; 18360, -51, -23],[765, 3, 1],[443, 8, 22, 12, -1, -1, 6, 2, 7; 37230, 672, 1845, 1003, -85, -84, 510, 169, 589; 270810, 4891, 13455, 7344, -610, -612, 3655, 1221, 4278],347,2]
%
% END OF LATTICE L348.2
%
%
% LATTICE L348.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-503370, 15300, 8415; 15300, -465, -255; 8415, -255, -127],[765, 15, 1],[211, 18, 8, 12, -1, -1, 8, 8, 19; 7089, 604, 267, 391, -34, -33, 272, 271, 640; -306, -25, -9, 0, 2, 0, -17, -15, -30],347,3]
%
% END OF LATTICE L348.3
%
%
% LATTICE L348.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1799420760, -2848860, 449321220; -2848860, 4632, -711372; 449321220, -711372, 112196971],[3060, 12, 1],[27037, 2665, 1523, 17330, 46469, 14855, 793411, 11427, 3047; -2125, -210, -120, -1360, -3645, -1165, -62220, -896, -239; -108290, -10674, -6100, -69411, -186120, -59498, -3177810, -45768, -12204],347,4]
%
% END OF LATTICE L348.4
%
%
% LATTICE L348.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1513170, -182835, 6885; -182835, -21318, 816; 6885, 816, -31],[765, 51, 1],[1, -1, -7, -4, -71, -17, -47, -7, 3; 10, -9, -70, -41, -735, -178, -495, -76, 29; 485, -459, -3400, -1971, -35190, -8483, -23535, -3570, 1428],347,5]
%
% END OF LATTICE L348.5
%
%
% LATTICE L348.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[33660, -6120, -3060; -6120, 1110, 525; -3060, 525, -82],[3060, 15, 1],[65, 1, -4, -47, 11, 77, 977, 51, 28; 374, 6, -23, -272, 63, 442, 5610, 293, 161; -34, 0, 2, 0, -9, -50, -612, -30, -15],347,6]
%
% END OF LATTICE L348.6
%
%
% LATTICE L348.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[22175820, 1413720, -52020; 1413720, 90066, -3315; -52020, -3315, 122],[3060, 51, 1],[-7, -3, -8, -1, -1, 1, 1, 1, 0; -270, -104, -240, -28, -25, 18, 20, 20, -13; -10350, -4114, -9945, -1188, -1105, 918, 970, 969, -357],347,7]
%
% END OF LATTICE L348.7
%
%
% LATTICE L348.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[378772920, 9489060, 94679460; 9489060, 237720, 2371920; 94679460, 2371920, 23666423],[3060, 60, 1],[-501, 337, -1, -5412, -3209, -5231, -56005, -4045, -839; -17, 18, 0, -238, -141, -229, -2448, -176, -35; 2006, -1350, 4, 21675, 12852, 20950, 224298, 16200, 3360],347,8]
%
% END OF LATTICE L348.8
%
%
% LATTICE L348.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[765, 0, 0; 0, -1591455, 9690; 0, 9690, -59],[765, 255, 1],[-5, -8, -5, -1, 0, 1, 0, -1, -6; 0, -5, -12, -5, -3, 0, 1, 14, 11; -18, -850, -1989, -825, -493, 0, 164, 2295, 1785],347,9]
%
% END OF LATTICE L348.9
%
%
% LATTICE L348.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[19602978120, -28760940, 4894313940; -28760940, 42024, -7180800; 4894313940, -7180800, 1221972947],[3060, 204, 1],[-181987, -56374, -158146, -2459, 9083, 16273, 1136, -10594, -47673; 945, 293, 825, 13, -45, -81, -5, 55, 247; 728910, 225794, 633420, 9849, -36380, -65178, -4550, 42432, 190944],347,10]
%
% END OF LATTICE L348.10
%
%
% LATTICE L348.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[203927580, 62632080, -379440; 62632080, 19235670, -116535; -379440, -116535, 706],[3060, 255, 1],[1, 1, -1, -1, 2, 17, 13, 12, 7; 8, 6, -9, -16, 0, 92, 78, 83, 56; 1858, 1530, -2023, -3180, 1071, 24310, 19854, 20145, 13005],347,11]
%
% END OF LATTICE L348.11
%
%
% LATTICE L348.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[282810457080, 416909700, -70297734960; 416909700, 614040, -103630980; -70297734960, -103630980, 17473793239],[3060, 1020, 1],[-1896, -101993, -2275, 35829, 365494, 586534, 366631, 439805, 67486; 5679, 305484, 6814, -107312, -1094697, -1756737, -1098102, -1317266, -202127; -7594, -408510, -9112, 143505, 1463904, 2349230, 1468458, 1761540, 270300],347,12]
%
% END OF LATTICE L348.12
%

\medskip%
%------------------------------WEYL-GROUP-W349--------------------------------
%
\leavevmode\llap{}%
$W_{349}$%
\qquad\llap{30} lattices, $\chi=120$%
\hfill%
$22|222|222|222|222|222|222|222|2\rtimes D_{8}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L349.1
%
\leavevmode%
${L_{349.1}}$%
{} : {$1\above{1pt}{1pt}{2}{0}8\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{-}{}9\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{2}{}11\above{1pt}{1pt}{1}{}$}\EasyButWeakLineBreak%
{${99}\above{1pt}{1pt}{}{2}{8}\above{1pt}{1pt}{}{2}{33}\above{1pt}{1pt}{}{2}{72}\above{1pt}{1pt}{}{2}{11}\above{1pt}{1pt}{r}{2}{24}\above{1pt}{1pt}{s}{2}{44}\above{1pt}{1pt}{*}{2}{72}\above{1pt}{1pt}{*}{2}{132}\above{1pt}{1pt}{*}{2}{8}\above{1pt}{1pt}{*}{2}{396}\above{1pt}{1pt}{s}{2}{24}\above{1pt}{1pt}{l}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1016136\\-3960\\-1584
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3960\\15\\9
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1584\\9\\-16
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
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0\\0\\0
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\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1099\\-241560\\0
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\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5\\1099\\0
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\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3\\-660\\-1
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-23\\-5643\\-990
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-5\\-1232\\-224
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-9\\-2233\\-429
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-11\\-2760\\-576
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-4\\-1023\\-242
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-284\\-108
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\594\\-110
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7\\1560\\36
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
15\\3454\\264
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5\\1168\\116
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
53\\12474\\1386
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7\\1660\\204
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[1016136, -3960, -1584; -3960, 15, 9; -1584, 9, -16],[792, 3, 1],[-23, -5, -9, -11, -4, -1, 3, 7, 15, 5, 53, 7, 32, 7, 13, 17, 7, 3, 3, -1, -7, -3, -35, -5; -5643, -1232, -2233, -2760, -1023, -284, 594, 1560, 3454, 1168, 12474, 1660, 7623, 1672, 3113, 4080, 1683, 724, 726, -240, -1694, -728, -8514, -1220; -990, -224, -429, -576, -242, -108, -110, 36, 264, 116, 1386, 204, 990, 224, 429, 576, 242, 108, 110, -36, -264, -116, -1386, -204],348,1]
%
% END OF LATTICE L349.1
%
\hbox{}\par\smallskip%
%
% LATTICE L349.2
%
\leavevmode%
${L_{349.2}}$%
{} : {$[1\above{1pt}{1pt}{1}{}2\above{1pt}{1pt}{1}{}]\above{1pt}{1pt}{}{2}16\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{-}{}9\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{2}{}11\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${1584}\above{1pt}{1pt}{l}{2}{2}\above{1pt}{1pt}{}{2}{33}\above{1pt}{1pt}{}{2}{18}\above{1pt}{1pt}{r}{2}{176}\above{1pt}{1pt}{l}{2}{6}\above{1pt}{1pt}{}{2}{11}\above{1pt}{1pt}{r}{2}{72}\above{1pt}{1pt}{*}{2}{528}\above{1pt}{1pt}{*}{2}{8}\above{1pt}{1pt}{l}{2}{99}\above{1pt}{1pt}{}{2}{6}\above{1pt}{1pt}{r}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-73806480\\-34848\\52272
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-34848\\6\\24
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
52272\\24\\-37
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-20701\\-1062600\\-30056400
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-21\\-1079\\-30492
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
15\\770\\21779
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-131\\-6072\\-189288
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-4\\-187\\-5782
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-17\\-803\\-24585
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-13\\-621\\-18810
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-51\\-2464\\-73832
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-4\\-197\\-5796
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-10\\-506\\-14509
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-17\\-882\\-24696
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-35\\-1892\\-50952
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3\\-174\\-4384
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-8\\-528\\-11781
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\-17\\-24
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-73806480, -34848, 52272; -34848, 6, 24; 52272, 24, -37],[1584, 6, 1],[-131, -4, -17, -13, -51, -4, -10, -17, -35, -3, -8, 0, 23, 1, 5, 4, 15, 1, 1, -1, -13, -3, -19, -3; -6072, -187, -803, -621, -2464, -197, -506, -882, -1892, -174, -528, -17, 528, 33, 187, 159, 616, 43, 44, -42, -572, -134, -858, -137; -189288, -5782, -24585, -18810, -73832, -5796, -14509, -24696, -50952, -4384, -11781, -24, 32472, 1426, 7161, 5742, 21560, 1440, 1441, -1440, -18744, -4328, -27423, -4332],348,2]
%
% END OF LATTICE L349.2
%
\hbox{}\par\smallskip%
%
% LATTICE L349.3
%
\leavevmode%
${L_{349.3}}$%
{} : {$[1\above{1pt}{1pt}{-}{}2\above{1pt}{1pt}{1}{}]\above{1pt}{1pt}{}{6}16\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{-}{}9\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{2}{}11\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{m}%
\EasyButWeakLineBreak%
{${1584}\above{1pt}{1pt}{}{2}{2}\above{1pt}{1pt}{r}{2}{132}\above{1pt}{1pt}{l}{2}{18}\above{1pt}{1pt}{}{2}{176}\above{1pt}{1pt}{}{2}{6}\above{1pt}{1pt}{r}{2}{44}\above{1pt}{1pt}{*}{2}{72}\above{1pt}{1pt}{s}{2}{528}\above{1pt}{1pt}{s}{2}{8}\above{1pt}{1pt}{*}{2}{396}\above{1pt}{1pt}{l}{2}{6}\above{1pt}{1pt}{}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2659536\\-4752\\-7920
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-4752\\6\\-6
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-7920\\-6\\-19
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-5125\\-1465464\\2608848
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-7\\-2003\\3564
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-14\\-4004\\7127
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
115\\33000\\-58608
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4\\1147\\-2038
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
39\\11176\\-19866
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
17\\4869\\-8658
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
75\\21472\\-38192
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7\\2003\\-3564
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
43\\12298\\-21890
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
43\\12294\\-21888
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
111\\31724\\-56496
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
13\\3714\\-6616
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
107\\30558\\-54450
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5\\1427\\-2544
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-2659536, -4752, -7920; -4752, 6, -6; -7920, -6, -19],[1584, 6, 1],[115, 4, 39, 17, 75, 7, 43, 43, 111, 13, 107, 5, 137, 3, 17, 4, 9, 0, -1, -1, 1, 1, 19, 2; 33000, 1147, 11176, 4869, 21472, 2003, 12298, 12294, 31724, 3714, 30558, 1427, 39072, 855, 4840, 1137, 2552, -1, -286, -282, 308, 290, 5478, 575; -58608, -2038, -19866, -8658, -38192, -3564, -21890, -21888, -56496, -6616, -54450, -2544, -69696, -1526, -8646, -2034, -4576, 0, 506, 504, -528, -512, -9702, -1020],348,3]
%
% END OF LATTICE L349.3
%
\hbox{}\par\smallskip%
%
% LATTICE L349.4
%
\leavevmode%
${L_{349.4}}$%
{} : {$[1\above{1pt}{1pt}{-}{}2\above{1pt}{1pt}{1}{}]\above{1pt}{1pt}{}{4}16\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{-}{}9\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{2}{}11\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{m}%
\EasyButWeakLineBreak%
{${1584}\above{1pt}{1pt}{s}{2}{8}\above{1pt}{1pt}{*}{2}{132}\above{1pt}{1pt}{*}{2}{72}\above{1pt}{1pt}{s}{2}{176}\above{1pt}{1pt}{*}{2}{24}\above{1pt}{1pt}{l}{2}{11}\above{1pt}{1pt}{}{2}{18}\above{1pt}{1pt}{r}{2}{528}\above{1pt}{1pt}{l}{2}{2}\above{1pt}{1pt}{}{2}{99}\above{1pt}{1pt}{r}{2}{24}\above{1pt}{1pt}{*}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1699632\\-9504\\4752
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-9504\\-30\\24
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4752\\24\\-13
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
815\\44880\\376992
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\109\\924
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2\\-110\\-925
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
91\\4884\\41976
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5\\270\\2308
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
19\\1034\\8778
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
13\\714\\6012
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
23\\1276\\10648
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\170\\1392
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\176\\1397
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\123\\936
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5\\352\\2376
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\5\\4
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2\\-66\\-891
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-46\\-456
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-1699632, -9504, 4752; -9504, -30, 24; 4752, 24, -13],[1584, 6, 1],[91, 5, 19, 13, 23, 3, 3, 2, 5, 0, -2, -1, -19, -1, -3, -1, 1, 1, 3, 4, 27, 2, 20, 5; 4884, 270, 1034, 714, 1276, 170, 176, 123, 352, 5, -66, -46, -924, -50, -154, -54, 44, 50, 154, 207, 1408, 105, 1056, 266; 41976, 2308, 8778, 6012, 10648, 1392, 1397, 936, 2376, 4, -891, -456, -8712, -460, -1386, -468, 440, 456, 1375, 1836, 12408, 920, 9207, 2304],348,4]
%
% END OF LATTICE L349.4
%
\hbox{}\par\smallskip%
%
% LATTICE L349.5
%
\leavevmode%
${L_{349.5}}$%
{} : {$[1\above{1pt}{1pt}{1}{}2\above{1pt}{1pt}{1}{}]\above{1pt}{1pt}{}{0}16\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{-}{}9\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{2}{}11\above{1pt}{1pt}{1}{}$}\EasyButWeakLineBreak%
{${1584}\above{1pt}{1pt}{*}{2}{8}\above{1pt}{1pt}{l}{2}{33}\above{1pt}{1pt}{r}{2}{72}\above{1pt}{1pt}{*}{2}{176}\above{1pt}{1pt}{s}{2}{24}\above{1pt}{1pt}{*}{2}{44}\above{1pt}{1pt}{l}{2}{18}\above{1pt}{1pt}{}{2}{528}\above{1pt}{1pt}{}{2}{2}\above{1pt}{1pt}{r}{2}{396}\above{1pt}{1pt}{*}{2}{24}\above{1pt}{1pt}{s}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3923568\\-39600\\11088
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-39600\\-354\\108
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
11088\\108\\-31
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
12959\\541728\\6500736
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
170\\7105\\85272
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-40\\-1672\\-20065
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
367\\15444\\184536
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
21\\882\\10552
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
42\\1760\\21087
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
61\\2550\\30600
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
115\\4796\\57640
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
17\\706\\8508
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
41\\1694\\20482
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
17\\699\\8478
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
69\\2816\\34320
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\121\\1486
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
35\\1386\\17226
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\34\\468
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-3923568, -39600, 11088; -39600, -354, 108; 11088, 108, -31],[1584, 6, 1],[367, 21, 42, 61, 115, 17, 41, 17, 69, 3, 35, 1, -7, -1, -2, -1, 5, 3, 19, 13, 91, 7, 145, 19; 15444, 882, 1760, 2550, 4796, 706, 1694, 699, 2816, 121, 1386, 34, -396, -46, -88, -42, 220, 130, 814, 555, 3872, 297, 6138, 802; 184536, 10552, 21087, 30600, 57640, 8508, 20482, 8478, 34320, 1486, 17226, 468, -3960, -520, -1023, -504, 2552, 1524, 9614, 6570, 45936, 3530, 73062, 9564],348,5]
%
% END OF LATTICE L349.5
%
%
% LATTICE L349.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[66924, 3168, 0; 3168, 150, 0; 0, 0, -1],[396, 6, 1],[-115, -8, -39, -34, -75, -14, -43, -43, -111, -13, -107, -10, -137, -6, -17, -8, -9, 0, 1, 1, -1, -1, -19, -4; 2376, 165, 803, 699, 1540, 287, 880, 879, 2266, 265, 2178, 203, 2772, 121, 341, 159, 176, -1, -22, -21, 22, 21, 396, 83; -792, -58, -297, -270, -616, -120, -385, -396, -1056, -128, -1089, -108, -1584, -74, -231, -126, -176, -12, -11, 0, 0, -4, -99, -24],348,6]
%
% END OF LATTICE L349.6
%
%
% LATTICE L349.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-1329768, 14256, 5544; 14256, -150, -60; 5544, -60, -23],[792, 6, 1],[-107, -13, -111, -43, -43, -7, -75, -17, -39, -4, -115, -2, -19, -1, -1, 1, 1, 0, -9, -4, -17, -3, -137, -5; -3333, -406, -3476, -1350, -1353, -221, -2376, -540, -1243, -128, -3696, -65, -627, -34, -44, 30, 33, 1, -264, -120, -517, -92, -4224, -155; -17226, -2090, -17820, -6894, -6886, -1119, -11968, -2709, -6204, -635, -18216, -315, -2970, -154, -132, 162, 154, -3, -1496, -657, -2772, -487, -22176, -807],348,7]
%
% END OF LATTICE L349.7
%
%
% LATTICE L349.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[300168, 3960, -1584; 3960, -6, -12; -1584, -12, 7],[792, 6, 1],[91, 5, 19, 13, 23, 3, 6, 2, 5, 0, -4, -1, -19, -1, -3, -1, 1, 1, 6, 4, 27, 2, 40, 5; 4092, 224, 847, 576, 1012, 130, 253, 81, 176, -3, -231, -50, -924, -48, -143, -48, 44, 46, 275, 183, 1232, 91, 1815, 226; 27324, 1498, 5676, 3870, 6820, 882, 1738, 567, 1320, -11, -1386, -318, -5940, -310, -924, -306, 308, 306, 1826, 1215, 8184, 605, 12078, 1506],348,8]
%
% END OF LATTICE L349.8
%
%
% LATTICE L349.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[27720, -2376, 0; -2376, 204, 0; 0, 0, -1],[792, 12, 1],[-38, -5, -23, -19, -20, -7, -10, -19, -23, -5, -19, -3, -16, -1, -1, 1, 2, 1, 1, 1, -1, -1, -8, -3; -495, -66, -308, -258, -275, -98, -143, -276, -341, -76, -297, -50, -297, -22, -44, -6, 11, 10, 11, 12, -11, -12, -99, -38; -792, -116, -594, -540, -616, -240, -385, -792, -1056, -256, -1089, -216, -1584, -148, -462, -252, -176, -24, -11, 0, 0, -8, -99, -48],348,9]
%
% END OF LATTICE L349.9
%
%
% LATTICE L349.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[137016, 1584, -1584; 1584, -12, -12; -1584, -12, 17],[792, 12, 1],[-85, -11, -25, -41, -43, -15, -43, -41, -50, -11, -85, -7, -41, -3, -3, -1, 1, 1, 1, -1, -6, -3, -41, -7; -2079, -270, -616, -1014, -1067, -374, -1078, -1032, -1265, -280, -2178, -182, -1089, -82, -88, -42, 11, 22, 22, -24, -143, -72, -990, -170; -9504, -1232, -2805, -4608, -4840, -1692, -4862, -4644, -5676, -1252, -9702, -804, -4752, -352, -363, -144, 88, 108, 110, -108, -660, -332, -4554, -780],348,10]
%
% END OF LATTICE L349.10
%
%
% LATTICE L349.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-8788032, -754776, 14256; -754776, -64824, 1224; 14256, 1224, -23],[792, 24, 1],[460, 29, 257, 103, 212, 36, 201, 47, 224, 12, 361, 14, 152, 5, 15, -1, -8, -2, 3, 4, 48, 5, 251, 20; -5643, -356, -3157, -1266, -2607, -443, -2475, -579, -2761, -148, -4455, -173, -1881, -62, -187, 12, 99, 25, -33, -48, -583, -61, -3069, -245; -15444, -986, -8844, -3582, -7436, -1278, -7216, -1701, -8184, -443, -13464, -534, -5940, -202, -660, 18, 308, 90, 88, -81, -1320, -151, -7920, -654],348,11]
%
% END OF LATTICE L349.11
%
%
% LATTICE L349.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-827244, 275616, 135432; 275616, -91806, -45144; 135432, -45144, -22151],[396, 66, 1],[968, 1187, 837, 3233, 268, 820, 333, 1406, 114, 172, 109, -70, -86, -109, -53, 1, 26, 258, 255, 1828, 278, 906, 1655, 1148; 1920, 2353, 1658, 6399, 530, 1619, 656, 2763, 223, 333, 204, -145, -174, -219, -106, 3, 52, 515, 508, 3639, 553, 1801, 3288, 2279; 2007, 2464, 1740, 6732, 559, 1716, 700, 2970, 243, 374, 252, -132, -171, -220, -108, 0, 53, 528, 524, 3762, 573, 1870, 3420, 2376],348,12]
%
% END OF LATTICE L349.12
%
%
% LATTICE L349.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1253736, -65736, 3168; -65736, -3201, 165; 3168, 165, -8],[792, 33, 1],[55, 69, 25, 199, 17, 55, 6, 109, 5, 19, 5, 3, -1, -3, -1, -1, 1, 11, 3, 89, 7, 47, 22, 63; 78, 96, 34, 264, 22, 68, 7, 120, 5, 16, 3, -4, -6, -8, -2, 0, 2, 20, 5, 144, 11, 72, 33, 92; 23220, 29084, 10518, 83556, 7124, 22968, 2495, 45144, 2058, 7744, 2007, 1056, -540, -1364, -438, -396, 436, 4752, 1285, 38016, 2982, 19976, 9333, 26664],348,13]
%
% END OF LATTICE L349.13
%
%
% LATTICE L349.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2422282896, 115346880, -299376; 115346880, -5492712, 14256; -299376, 14256, -37],[1584, 24, 1],[-131, -8, -34, -26, -51, -8, -10, -17, -35, -3, -8, 0, 23, 2, 10, 8, 15, 2, 1, -1, -13, -3, -19, -6; -3036, -187, -803, -621, -1232, -197, -253, -441, -946, -87, -264, -17, 264, 33, 187, 159, 308, 43, 22, -21, -286, -67, -429, -137; -110088, -7340, -34386, -28980, -62216, -11208, -16621, -32472, -81576, -9280, -37125, -6576, -84744, -3484, -8910, -3492, -2728, 384, 385, 0, -5016, -1544, -11583, -4248],348,14]
%
% END OF LATTICE L349.14
%
%
% LATTICE L349.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[267696, 12672, 0; 12672, 600, 0; 0, 0, -1],[1584, 24, 1],[-115, -8, -39, -34, -75, -14, -43, -43, -111, -13, -107, -10, -137, -6, -17, -8, -9, 0, 1, 1, -1, -1, -19, -4; 2376, 165, 803, 699, 1540, 287, 880, 879, 2266, 265, 2178, 203, 2772, 121, 341, 159, 176, -1, -22, -21, 22, 21, 396, 83; -1584, -116, -594, -540, -1232, -240, -770, -792, -2112, -256, -2178, -216, -3168, -148, -462, -252, -352, -24, -22, 0, 0, -8, -198, -48],348,15]
%
% END OF LATTICE L349.15
%
%
% LATTICE L349.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-189536688, 8916336, -60192; 8916336, -419448, 2832; -60192, 2832, -19],[1584, 24, 1],[875, 109, 955, 379, 387, 130, 719, 334, 395, 84, 1255, 48, 259, 17, 53, -1, -9, -4, 37, 44, 109, 42, 1013, 78; 18183, 2265, 19844, 7875, 8041, 2701, 14938, 6939, 8206, 1745, 26070, 997, 5379, 353, 1100, -21, -187, -83, 770, 915, 2266, 873, 21054, 1621; -61974, -7732, -67848, -26964, -27566, -9276, -51392, -23904, -28314, -6032, -90288, -3468, -18810, -1244, -3960, 36, 638, 300, -2464, -3024, -7590, -2944, -71280, -5508],348,16]
%
% END OF LATTICE L349.16
%
%
% LATTICE L349.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[239150736, -7421040, 64944; -7421040, 230280, -2016; 64944, -2016, 17],[1584, 24, 1],[1004, 129, 1165, 475, 496, 172, 981, 466, 283, 124, 1909, 78, 454, 33, 131, 11, -10, -10, -9, 20, 41, 38, 1007, 84; 32043, 4117, 37180, 15159, 15829, 5489, 31306, 14871, 9031, 3957, 60918, 2489, 14487, 1053, 4180, 351, -319, -319, -286, 639, 1309, 1213, 32142, 2681; -35838, -4612, -41712, -17028, -17798, -6180, -35288, -16776, -10197, -4472, -68904, -2820, -16434, -1196, -4752, -396, 374, 372, 440, -648, -1419, -1336, -35640, -2988],348,17]
%
% END OF LATTICE L349.17
%
%
% LATTICE L349.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[17410536, 846648, -38016; 846648, 41118, -1848; -38016, -1848, 83],[792, 66, 1],[25, 11, 11, 58, 25, 28, 17, 197, 49, 67, 53, 30, 83, 22, 13, 41, 11, 5, 1, 1, -1, -1, 1, 3; 156, 70, 71, 378, 164, 185, 113, 1314, 328, 450, 357, 203, 564, 150, 89, 282, 76, 35, 7, 6, -8, -10, 3, 17; 14904, 6589, 6612, 34947, 15088, 16929, 10294, 119394, 29724, 40678, 32202, 18249, 50544, 13409, 7932, 25047, 6728, 3069, 614, 594, -636, -682, 522, 1749],348,18]
%
% END OF LATTICE L349.18
%
%
% LATTICE L349.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[32472, 303336, -9504; 303336, -7367250, 231000; -9504, 231000, -7243],[792, 66, 1],[28, 24, 47, 122, 26, 115, 69, 397, 49, 133, 209, 117, 80, 42, 49, 76, 10, 17, 3, -1, -1, -1, 7, 15; -5421, -4657, -9136, -23745, -5065, -22426, -13468, -77532, -9575, -26004, -40884, -22906, -15675, -8235, -9616, -14931, -1967, -3358, -596, 180, 199, 220, -1308, -2878; -172926, -148555, -291432, -757449, -161570, -715374, -429620, -2473218, -305436, -829510, -1304172, -730686, -500022, -262691, -306744, -476289, -62746, -107118, -19012, 5742, 6348, 7018, -41724, -91806],348,19]
%
% END OF LATTICE L349.19
%
%
% LATTICE L349.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-381744, -74448, 26928; -74448, -6666, 2508; 26928, 2508, -941],[1584, 66, 1],[1, -3, -3, -1, 1, 11, 25, 94, 15, 51, 193, 70, 62, 157, 115, 463, 20, 66, 59, 137, 13, 26, 59, 7; 135, -446, -436, -138, 145, 1591, 3608, 13557, 2162, 7347, 27792, 10075, 8919, 22578, 16532, 66534, 2873, 9475, 8464, 19641, 1862, 3719, 8424, 991; 387, -1276, -1248, -396, 415, 4554, 10328, 38808, 6189, 21032, 79560, 28842, 25533, 64636, 47328, 190476, 8225, 27126, 24232, 56232, 5331, 10648, 24120, 2838],348,20]
%
% END OF LATTICE L349.20
%
%
% LATTICE L349.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[6023952, -10257984, 321552; -10257984, 17330214, -543246; 321552, -543246, 17029],[1584, 66, 1],[1, -1, -1, 1, 1, 5, 11, 41, 13, 22, 83, 30, 53, 67, 49, 197, 17, 28, 25, 58, 11, 11, 25, 3; -492, 638, 596, -558, -576, -2879, -6312, -23499, -7442, -12581, -47424, -17123, -30216, -38170, -27892, -112038, -9660, -15887, -14160, -32799, -6206, -6185, -13992, -1643; -15714, 20372, 19032, -17820, -18394, -91938, -201568, -750420, -237654, -401764, -1514448, -546810, -964926, -1218932, -890712, -3577860, -308486, -507342, -452192, -1047420, -198186, -197516, -446832, -52470],348,21]
%
% END OF LATTICE L349.21
%
%
% LATTICE L349.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[792, 0, 0; 0, -92004, -45144; 0, -45144, -22151],[792, 132, 1],[-1, -1, 0, 1, 0, -1, -1, -17, -3, -11, -11, -17, -8, -21, -8, -67, -3, -21, -5, -49, -5, -11, -7, -5; 84, 216, 53, 0, -26, -518, -257, -3690, -562, -1834, -1677, -2330, -984, -2416, -853, -6600, -274, -1682, -343, -2910, -238, -366, -123, 130; -171, -440, -108, 0, 53, 1056, 524, 7524, 1146, 3740, 3420, 4752, 2007, 4928, 1740, 13464, 559, 3432, 700, 5940, 486, 748, 252, -264],348,22]
%
% END OF LATTICE L349.22
%
%
% LATTICE L349.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1253736, -340560, -167112; -340560, -91212, -44748; -167112, -44748, -21953],[792, 132, 1],[-1, -3, -1, -1, 1, 11, 6, 89, 7, 47, 44, 63, 55, 69, 25, 199, 17, 55, 12, 109, 5, 19, 10, 3; 366, 810, 251, 198, -250, -2696, -1445, -21312, -1667, -11140, -10389, -14804, -12858, -16078, -5803, -46002, -3914, -12572, -2719, -24492, -1109, -4128, -2103, -464; -738, -1628, -504, -396, 502, 5412, 2900, 42768, 3345, 22352, 20844, 29700, 25794, 32252, 11640, 92268, 7850, 25212, 5452, 49104, 2223, 8272, 4212, 924],348,23]
%
% END OF LATTICE L349.23
%
%
% LATTICE L349.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-26907408, -700128, 33264; -700128, -17754, 858; 33264, 858, -41],[1584, 66, 1],[40, 42, 49, 76, 5, 17, 3, -1, -1, -1, 7, 15, 14, 24, 47, 122, 13, 115, 69, 397, 49, 133, 209, 117; 789, 829, 968, 1503, 99, 338, 60, -18, -20, -22, 132, 290, 273, 469, 920, 2391, 255, 2258, 1356, 7806, 964, 2618, 4116, 2306; 48933, 51392, 59976, 93060, 6125, 20856, 3688, -1188, -1230, -1276, 8424, 18216, 17055, 29260, 57336, 148896, 15871, 140448, 84296, 485100, 59886, 162580, 255528, 143088],348,24]
%
% END OF LATTICE L349.24
%
%
% LATTICE L349.25
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[64944, -72864, 1584; -72864, -327030, 7524; 1584, 7524, -173],[1584, 66, 1],[185, 97, 113, 175, 23, 39, 7, -1, -1, -1, 19, 37, 67, 57, 111, 287, 61, 269, 161, 925, 57, 309, 485, 271; 3678, 1929, 2248, 3483, 458, 778, 140, -18, -20, -22, 372, 730, 1326, 1129, 2200, 5691, 1210, 5338, 3196, 18366, 1132, 6138, 9636, 5386; 161622, 84766, 98784, 153054, 20126, 34188, 6152, -792, -879, -968, 16344, 32076, 58266, 49610, 96672, 250074, 53170, 234564, 140440, 807048, 49743, 269720, 423432, 236676],348,25]
%
% END OF LATTICE L349.25
%
%
% LATTICE L349.26
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[29050560, 2186712, -49104; 2186712, 164472, -3696; -49104, -3696, 83],[792, 264, 1],[25, 11, 22, 58, 25, 56, 34, 197, 49, 67, 106, 60, 83, 22, 26, 41, 11, 10, 2, 1, -1, -1, 2, 6; 3, 2, 5, 15, 7, 17, 11, 66, 17, 24, 39, 23, 33, 9, 11, 18, 5, 5, 1, 0, -1, -2, -3, -1; 14904, 6589, 13224, 34947, 15088, 33858, 20588, 119394, 29724, 40678, 64404, 36498, 50544, 13409, 15864, 25047, 6728, 6138, 1228, 594, -636, -682, 1044, 3498],348,26]
%
% END OF LATTICE L349.26
%
%
% LATTICE L349.27
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-18021168, 6006528, 1989504; 6006528, -2001912, -663168; 1989504, -663168, -219599],[1584, 264, 1],[-4, -205, -151, 1, 50, 1048, 1145, 8506, 1342, 4520, 8489, 6102, 2677, 6739, 4903, 19601, 841, 5486, 2419, 11096, 1034, 2014, 2203, 432; -9, -411, -302, 3, 100, 2095, 2288, 16995, 2681, 9029, 16956, 12187, 5346, 13457, 9790, 39135, 1679, 10951, 4828, 22143, 2063, 4017, 4392, 859; -9, -616, -456, 0, 151, 3168, 3464, 25740, 4062, 13684, 25704, 18480, 8109, 20416, 14856, 59400, 2549, 16632, 7336, 33660, 3138, 6116, 6696, 1320],348,27]
%
% END OF LATTICE L349.27
%
%
% LATTICE L349.28
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-16481520, 5493312, 1362240; 5493312, -1830840, -454080; 1362240, -454080, -112571],[1584, 264, 1],[-185, -241, -119, 1, 59, 588, 585, 4204, 641, 2094, 3833, 2666, 2255, 2771, 1959, 7589, 631, 1942, 795, 3386, 279, 436, 307, -136; -372, -483, -238, 3, 118, 1175, 1168, 8391, 1279, 4177, 7644, 5315, 4494, 5521, 3902, 15111, 1256, 3863, 1580, 6723, 553, 861, 600, -277; -738, -968, -480, 0, 238, 2376, 2368, 17028, 2598, 8492, 15552, 10824, 9162, 11264, 7968, 30888, 2570, 7920, 3248, 13860, 1146, 1804, 1296, -528],348,28]
%
% END OF LATTICE L349.28
%
%
% LATTICE L349.29
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[350064, 153648, 49104; 153648, 62040, 19800; 49104, 19800, 6319],[1584, 264, 1],[17, 197, 49, 67, 53, 60, 83, 44, 13, 82, 11, 10, 1, 1, -1, -1, 1, 6, 25, 22, 11, 116, 25, 56; -2385, -27657, -6884, -9419, -7455, -8447, -11694, -6203, -1834, -11577, -1554, -1415, -141, -129, 148, 157, -123, -815, -3462, -3059, -1534, -16209, -3498, -7847; 7342, 85140, 21192, 28996, 22950, 26004, 36000, 19096, 5646, 35640, 4784, 4356, 434, 396, -456, -484, 378, 2508, 10656, 9416, 4722, 49896, 10768, 24156],348,29]
%
% END OF LATTICE L349.29
%
%
% LATTICE L349.30
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-16472016, 7007616, -625680; 7007616, -2980824, 266376; -625680, 266376, -23669],[1584, 264, 1],[-1951, -22934, -5787, -8018, -6413, -7385, -10367, -5559, -832, -10639, -1443, -1347, -125, 98, 251, 406, 185, -227, -2089, -2053, -552, -12197, -2709, -6265; -3885, -45669, -11524, -15967, -12771, -14707, -20646, -11071, -1657, -21189, -2874, -2683, -249, 195, 500, 809, 369, -451, -4158, -4087, -1099, -24285, -5394, -12475; 7850, 92268, 23280, 32252, 25794, 29700, 41688, 22352, 3345, 42768, 5800, 5412, 502, -396, -1008, -1628, -738, 924, 8424, 8272, 2223, 49104, 10904, 25212],348,30]
%
% END OF LATTICE L349.30
%

\medskip%
%------------------------------WEYL-GROUP-W350--------------------------------
%
\leavevmode\llap{}%
$W_{350}$%
\qquad\llap{12} lattices, $\chi=84$%
\hfill%
$2\slashtwo2|2\slashtwo2|2\slashtwo2|2\slashtwo2|2\slashtwo2|2\slashtwo2|\rtimes D_{12}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L350.1
%
\leavevmode%
${L_{350.1}}$%
{} : {$1\above{1pt}{1pt}{2}{2}16\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{1}{}3\above{1pt}{1pt}{-}{}9\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{2}{}13\above{1pt}{1pt}{1}{}$}\EasyButWeakLineBreak%
{${1872}\above{1pt}{1pt}{l}{2}{1}\above{1pt}{1pt}{}{2}{144}\above{1pt}{1pt}{}{2}{13}\above{1pt}{1pt}{r}{2}{36}\above{1pt}{1pt}{*}{2}{4}\above{1pt}{1pt}{l}{2}{117}\above{1pt}{1pt}{}{2}{16}\above{1pt}{1pt}{}{2}{9}\above{1pt}{1pt}{r}{2}{208}\above{1pt}{1pt}{s}{2}{36}\above{1pt}{1pt}{*}{2}{16}\above{1pt}{1pt}{*}{2}{468}\above{1pt}{1pt}{l}{2}{1}\above{1pt}{1pt}{}{2}{9}\above{1pt}{1pt}{r}{2}{52}\above{1pt}{1pt}{*}{2}{144}\above{1pt}{1pt}{*}{2}{4}\above{1pt}{1pt}{s}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-57528432\\48672\\44928
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
48672\\-30\\-39
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
44928\\-39\\-35
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
443\\45552\\517608
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
8\\823\\9347
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
97\\9984\\113328
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
38\\3913\\44395
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
41\\4224\\47898
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
11\\1134\\12850
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
62\\6396\\72423
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
11\\1136\\12848
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4\\414\\4671
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
9\\936\\10504
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-102\\-1170
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-104\\-1168
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7\\702\\8190
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\102\\1169
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7\\717\\8181
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
37\\3796\\43238
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
61\\6264\\71280
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
13\\1336\\15190
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-57528432, 48672, 44928; 48672, -30, -39; 44928, -39, -35],[1872, 3, 1],[443, 8, 97, 38, 41, 11, 62, 11, 4, 9, -1, -1, 7, 1, 7, 37, 61, 13; 45552, 823, 9984, 3913, 4224, 1134, 6396, 1136, 414, 936, -102, -104, 702, 102, 717, 3796, 6264, 1336; 517608, 9347, 113328, 44395, 47898, 12850, 72423, 12848, 4671, 10504, -1170, -1168, 8190, 1169, 8181, 43238, 71280, 15190],349,1]
%
% END OF LATTICE L350.1
%
\hbox{}\par\smallskip%
%
% LATTICE L350.2
%
\leavevmode%
${L_{350.2}}$%
{} : {$1\above{1pt}{1pt}{1}{1}4\above{1pt}{1pt}{1}{1}16\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{1}{}3\above{1pt}{1pt}{-}{}9\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{2}{}13\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{3}%
\EasyButWeakLineBreak%
{${52}\above{1pt}{1pt}{s}{2}{144}\above{1pt}{1pt}{s}{2}{4}\above{1pt}{1pt}{s}{2}{1872}\above{1pt}{1pt}{l}{2}{4}\above{1pt}{1pt}{}{2}{144}\above{1pt}{1pt}{}{2}{52}\above{1pt}{1pt}{r}{2}{36}\above{1pt}{1pt}{l}{2}{4}\above{1pt}{1pt}{}{2}{117}\above{1pt}{1pt}{}{2}{16}\above{1pt}{1pt}{}{2}{9}\above{1pt}{1pt}{}{2}{208}\above{1pt}{1pt}{}{2}{36}\above{1pt}{1pt}{r}{2}{16}\above{1pt}{1pt}{l}{2}{468}\above{1pt}{1pt}{}{2}{1}\above{1pt}{1pt}{}{2}{36}\above{1pt}{1pt}{r}{2}$}%
\nopagebreak\par%
shares genus with 2-dual${}\iso{}$3-dual; isometric to own %
2.3-dual\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-57528432\\-172224\\44928
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-172224\\-444\\132
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
44928\\132\\-35
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
37\\1898\\54626
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
61\\3132\\90072
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
13\\668\\19198
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
443\\22776\\654264
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
16\\823\\23632
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
97\\4992\\143280
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
76\\3913\\112268
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
41\\2112\\60570
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
11\\567\\16252
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
62\\3198\\91611
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
11\\568\\16256
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4\\207\\5913
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
9\\468\\13312
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-51\\-1476
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-52\\-1480
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7\\351\\10296
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\51\\1475
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
14\\717\\20664
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-57528432, -172224, 44928; -172224, -444, 132; 44928, 132, -35],[1872, 12, 1],[37, 61, 13, 443, 16, 97, 76, 41, 11, 62, 11, 4, 9, -1, -1, 7, 1, 14; 1898, 3132, 668, 22776, 823, 4992, 3913, 2112, 567, 3198, 568, 207, 468, -51, -52, 351, 51, 717; 54626, 90072, 19198, 654264, 23632, 143280, 112268, 60570, 16252, 91611, 16256, 5913, 13312, -1476, -1480, 10296, 1475, 20664],349,2]
%
% END OF LATTICE L350.2
%
%
% LATTICE L350.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-1880112, 1872, 8112; 1872, 20, -8; 8112, -8, -35],[624, 4, 1],[11, -1, -1, 9, 2, 19, 38, 21, 27, 154, 67, 34, 321, 29, 47, 89, 12, 3; -13, 0, 1, 0, -1, -12, -26, -15, -20, -117, -52, -27, -260, -24, -40, -78, -11, -3; 2548, -232, -232, 2080, 463, 4400, 8801, 4864, 6254, 35672, 15520, 7876, 74360, 6718, 10888, 20618, 2780, 695],349,3]
%
% END OF LATTICE L350.3
%
%
% LATTICE L350.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-59280, 624, 20592; 624, 60, -216; 20592, -216, -7153],[624, 12, 1],[217, -25, -25, 271, 74, 296, 2195, 1159, 715, 7913, 838, 1651, 3794, 665, 517, 935, 467, 49; 0, 1, 0, -13, -3, -11, -78, -40, -24, -260, -27, -52, -117, -20, -15, -26, -12, -1; 624, -72, -72, 780, 213, 852, 6318, 3336, 2058, 22776, 2412, 4752, 10920, 1914, 1488, 2691, 1344, 141],349,4]
%
% END OF LATTICE L350.4
%
%
% LATTICE L350.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1872, 5616, -1872; 5616, -444, 72; -1872, 72, 1],[1872, 12, 1],[25, 43, 19, 332, 49, 76, 243, 67, 37, 215, 10, 8, 11, -1, -1, 1, 1, 35; 611, 1053, 466, 8151, 1204, 1869, 5980, 1650, 912, 5304, 247, 198, 273, -24, -25, 0, 24, 852; 1859, 3204, 1418, 24804, 3664, 5688, 18200, 5022, 2776, 16146, 752, 603, 832, -72, -76, 0, 73, 2592],349,5]
%
% END OF LATTICE L350.5
%
%
% LATTICE L350.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[13357968, 162864, -25584; 162864, 1924, -312; -25584, -312, 49],[624, 52, 1],[0, -5, -2, -3, -3, -1, 1, 3, 10, 5, 31, 17, 13, 16, 27, 4, 7, 3; -2, -12, -1, 0, 1, 0, -1, -3, -11, -6, -40, -24, -20, -27, -52, -9, -20, -15; -15, -2704, -1053, -1568, -1560, -520, 516, 1547, 5148, 2570, 15912, 8710, 6648, 8164, 13728, 2024, 3510, 1456],349,6]
%
% END OF LATTICE L350.6
%
%
% LATTICE L350.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[37831248, 1439568, -43056; 1439568, 54717, -1638; -43056, -1638, 49],[1872, 39, 1],[-1, 1, 13, 1, 4, 1, 1, -1, -7, -3, -8, -13, -4, -7, -19, -1, -23, -1; -48, -8, 24, 4, 21, 6, 6, -8, -54, -24, -66, -112, -36, -66, -192, -11, -288, -17; -2520, 598, 12168, 1010, 4212, 1079, 1080, -1144, -7956, -3440, -9243, -15184, -4725, -8372, -23166, -1250, -29952, -1456],349,7]
%
% END OF LATTICE L350.7
%
%
% LATTICE L350.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[3433248, 1872, -1872; 1872, -48, 0; -1872, 0, 1],[1872, 48, 1],[-2, -4, -1, -38, -3, -10, -17, -5, -3, -19, -2, -1, -4, -1, 0, 1, 0, -1; -65, -129, -32, -1209, -95, -315, -533, -156, -93, -585, -61, -30, -117, -27, 1, 39, 0, -33; -3718, -7416, -1850, -70200, -5536, -18432, -31304, -9198, -5512, -34866, -3664, -1827, -7280, -1800, 8, 1872, -1, -1872],349,8]
%
% END OF LATTICE L350.8
%
%
% LATTICE L350.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1655472, 99216, 546624; 99216, 5772, 32760; 546624, 32760, 180491],[624, 156, 1],[-356, -2469, -1492, -1227, -1621, -2985, -485, -978, -296, -99, 103, 309, 317, 219, 619, 15, -205, -591; -9, -52, -27, -20, -24, -40, -6, -11, -3, -1, 0, 1, 0, -1, -12, -2, -15, -20; 1080, 7488, 4524, 3720, 4914, 9048, 1470, 2964, 897, 300, -312, -936, -960, -663, -1872, -45, 624, 1794],349,9]
%
% END OF LATTICE L350.9
%
%
% LATTICE L350.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[37831248, 2879136, -43056; 2879136, 218868, -3276; -43056, -3276, 49],[1872, 156, 1],[1, 1, 8, 1, 13, 1, -1, -2, -23, -2, -19, -7, -4, -13, -8, -3, -7, -1; 3, 3, 21, 2, 12, -4, -24, -17, -144, -11, -96, -33, -18, -56, -33, -12, -27, -4; 1080, 1079, 8424, 1010, 12168, 598, -2520, -2912, -29952, -2500, -23166, -8372, -4725, -15184, -9243, -3440, -7956, -1144],349,10]
%
% END OF LATTICE L350.10
%
%
% LATTICE L350.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[45850896, -37374480, 735696; -37374480, 30320628, -596856; 735696, -596856, 11749],[1872, 156, 1],[-11, -3, -37, -1, -11, -1, 2, 9, 22, 7, 31, 21, 11, 8, 8, 1, -1, -3; 3456, 948, 11820, 325, 3699, 422, -483, -2548, -6477, -2092, -9354, -6384, -3360, -2455, -2466, -309, 312, 937; 176256, 48347, 602784, 16573, 188604, 21502, -24660, -130000, -330408, -106712, -477126, -325624, -171378, -125216, -125775, -15760, 15912, 47788],349,11]
%
% END OF LATTICE L350.11
%
%
% LATTICE L350.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-87984, -9360, 3744; -9360, 38688, -14976; 3744, -14976, 5797],[1872, 624, 1],[1, 0, -7, -1, -25, -6, -17, -17, -55, -7, -26, -15, -7, -9, -4, -1, -1, 1; 279, -5, -2175, -306, -7614, -1823, -5160, -5157, -16680, -2123, -7887, -4553, -2127, -2740, -1224, -310, -363, 282; 720, -13, -5616, -790, -19656, -4706, -13320, -13312, -43056, -5480, -20358, -11752, -5490, -7072, -3159, -800, -936, 728],349,12]
%
% END OF LATTICE L350.12
%

\medskip%
%------------------------------WEYL-GROUP-W351--------------------------------
%
\leavevmode\llap{}%
$W_{351}$%
\qquad\llap{4} lattices, $\chi=48$%
\hfill%
$222|222|222|222|\rtimes D_{4}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L351.1
%
\leavevmode%
${L_{351.1}}$%
{} : {$1\above{1pt}{1pt}{-}{5}8\above{1pt}{1pt}{1}{7}64\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{1}{}$}\EasyButWeakLineBreak%
{${8}\above{1pt}{1pt}{b}{2}{64}\above{1pt}{1pt}{s}{2}{20}\above{1pt}{1pt}{*}{2}{32}\above{1pt}{1pt}{l}{2}{5}\above{1pt}{1pt}{}{2}{64}\above{1pt}{1pt}{r}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
11375680\\-733440\\12160
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-733440\\47288\\-784
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
12160\\-784\\13
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3759\\56400\\-120320
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-242\\-3631\\7744
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4\\60\\-129
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\-1\\-60
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\16\\32
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\50\\210
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\50\\208
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4\\65\\175
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
9\\144\\256
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[11375680, -733440, 12160; -733440, 47288, -784; 12160, -784, 13],[320, 8, 1],[0, 1, 3, 3, 4, 9, 2, 15, 17, 9, 6, 7; -1, 16, 50, 50, 65, 144, 31, 224, 250, 130, 85, 96; -60, 32, 210, 208, 175, 256, -4, -544, -850, -592, -495, -768],350,1]
%
% END OF LATTICE L351.1
%
%
% LATTICE L351.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2505920, 14080, 14080; 14080, -72, -80; 14080, -80, -79],[320, 8, 1],[-1, -1, 7, 3, 97, 4, 17, 17, 313, 21, 223, 4; -18, -20, 120, 57, 1880, 78, 334, 336, 6200, 417, 4440, 80; -160, -158, 1120, 476, 15360, 633, 2688, 2686, 49440, 3316, 35200, 631],350,2]
%
% END OF LATTICE L351.2
%
%
% LATTICE L351.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[320, 0, 0; 0, -40, 0; 0, 0, 1],[320, 40, 1],[-2, -7, -1, -1, 0, 1, 0, -9, -3, -11, -2, -17; 11, 32, 4, 2, 0, 0, 3, 80, 24, 82, 14, 112; -60, -160, -18, 0, 1, 0, -20, -480, -142, -480, -81, -640],350,3]
%
% END OF LATTICE L351.3
%
%
% LATTICE L351.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-333760, -7360, 1920; -7360, -40, 40; 1920, 40, -11],[320, 40, 1],[-3, -1, 3, 4, 21, 4, 15, 13, 45, 14, 27, 2; -10, -4, 8, 13, 72, 14, 54, 48, 168, 53, 104, 8; -560, -190, 544, 740, 3904, 745, 2800, 2430, 8416, 2620, 5056, 375],350,4]
%
% END OF LATTICE L351.4
%

\medskip%
%------------------------------WEYL-GROUP-W352--------------------------------
%
\leavevmode\llap{}%
$W_{352}$%
\qquad\llap{12} lattices, $\chi=72$%
\hfill%
$2|2222|2222|2222|222\rtimes D_{4}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L352.1
%
\leavevmode%
${L_{352.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{1}{}3\above{1pt}{1pt}{1}{}9\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{2}{}19\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${684}\above{1pt}{1pt}{*}{2}{12}\above{1pt}{1pt}{*}{2}{76}\above{1pt}{1pt}{b}{2}{30}\above{1pt}{1pt}{l}{2}{4}\above{1pt}{1pt}{r}{2}{570}\above{1pt}{1pt}{l}{2}{36}\above{1pt}{1pt}{r}{2}{30}\above{1pt}{1pt}{b}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
181639620\\-30595320\\160740
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-30595320\\5153466\\-27075
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
160740\\-27075\\142
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1231199\\7284600\\-4924800
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-207384\\-1227023\\829536
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1044\\6177\\-4177
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2155\\12768\\-5130
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
59\\350\\-54
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
333\\1976\\-190
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
123\\730\\-45
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
31\\184\\-8
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-16\\-95\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-95\\-564\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-112\\-665\\-15
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[181639620, -30595320, 160740; -30595320, 5153466, -27075; 160740, -27075, 142],[3420, 3, 1],[2155, 59, 333, 123, 31, -16, -95, -112, -787, -35, 123, 177, 161, 2296, 671, 412; 12768, 350, 1976, 730, 184, -95, -564, -665, -4674, -208, 722, 1045, 952, 13585, 3972, 2440; -5130, -54, -190, -45, -8, 0, 0, -15, -342, -42, -1634, -1155, -760, -9120, -2304, -1185],351,1]
%
% END OF LATTICE L352.1
%
%
% LATTICE L352.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-15829470, -4615290, -636975; -4615290, -1343301, -188079; -636975, -188079, -23258],[855, 3, 1],[54451, 10146, 494305, 710956, 236943, 5736473, 730867, 761051, 1673276, 20165, 81604, 46819, 5545, 22617, -3403, -3276; -164217, -30599, -1490759, -2144150, -714589, -17300450, -2204199, -2295230, -5046381, -60815, -246107, -141200, -16723, -68210, 10263, 9880; -163305, -30429, -1482475, -2132235, -710618, -17204310, -2191950, -2282475, -5018337, -60477, -244739, -140415, -16630, -67830, 10206, 9825],351,2]
%
% END OF LATTICE L352.2
%
%
% LATTICE L352.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[12353895, 106020, -17955; 106020, 735, -150; -17955, -150, 26],[855, 15, 1],[36, 9, 728, 66, 316, 495, 102, 61, 211, 4, 13, -1, -4, -1, 2, 4; 665, 166, 13395, 1214, 5811, 9101, 1875, 1121, 3876, 73, 228, -19, -75, -19, 37, 74; 28690, 7170, 579690, 52551, 251595, 394098, 81205, 48561, 167960, 3180, 10260, -801, -3195, -798, 1595, 3189],351,3]
%
% END OF LATTICE L352.3
%
%
% LATTICE L352.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[6129782280, 30974940, -1532498580; 30974940, 156216, -7744020; -1532498580, -7744020, 383137897],[3420, 12, 1],[-4051004, -38221, -112944, -36072, 215, 80749, -214, -40367, -355153, -39080, -1355775, -1896453, -309419, -14767939, -927398, -1892158; 905673, 8545, 25251, 8065, -48, -18050, 48, 9025, 79401, 8737, 303107, 423985, 69176, 3301630, 207336, 423025; -16185150, -152706, -451250, -144120, 859, 322620, -855, -161280, -1418958, -156138, -5416786, -7576980, -1236235, -59002980, -3705273, -7559820],351,4]
%
% END OF LATTICE L352.4
%
%
% LATTICE L352.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[884070, -90630, 11115; -90630, 9291, -1140; 11115, -1140, 142],[855, 57, 1],[-5, -16, -43, -1179, -394, -503, -1220, -1274, -148, -35, -8, -96, -14, -7, -4, -1; -51, -163, -437, -11980, -4003, -5110, -12393, -12940, -1503, -355, -81, -970, -141, -70, -39, -10; -18, -57, -146, -3990, -1330, -1695, -4104, -4275, -495, -114, -25, -285, -38, -15, 0, 0],351,5]
%
% END OF LATTICE L352.5
%
%
% LATTICE L352.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[162337140, 27394200, -64980; 27394200, 4622730, -10965; -64980, -10965, 26],[3420, 15, 1],[-1309, -19, -83, -5, -5, 3, 17, 3, 55, -3, -335, -50, -171, -421, -545, -58; 8436, 122, 532, 32, 32, -19, -108, -19, -342, 20, 2166, 323, 1104, 2717, 3516, 374; 285570, 3960, 16910, 999, 1000, -513, -3060, -516, -6840, 930, 76000, 11226, 38120, 93423, 120420, 12741],351,6]
%
% END OF LATTICE L352.6
%
%
% LATTICE L352.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-159710580, -2612880, -63629100; -2612880, -42522, -1040079; -63629100, -1040079, -25346402],[3420, 57, 1],[-4527, -3189, -1073, 1044, 7517, 2163, 3999, 6644, 389, -949, -11341, -52769, -106829, -22853, -37103, -58369; -54332, -38270, -12876, 12530, 90204, 25955, 47984, 79715, 4666, -11396, -136122, -633355, -1282188, -274285, -445312, -700540; 13594, 9576, 3222, -3135, -22572, -6495, -12008, -19950, -1168, 2850, 34056, 158460, 320796, 68625, 111416, 175275],351,7]
%
% END OF LATTICE L352.7
%
%
% LATTICE L352.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[84806362440, -49401900, -21225870900; -49401900, 28680, 12364620; -21225870900, 12364620, 5312544749],[3420, 60, 1],[5224606, 45721, 114942, 3418, -3205, -35895, -214, 12819, 523445, 55122, 1801075, 500797, 406577, 3867929, 1210330, 491396; 235581, 2062, 5187, 155, -144, -1615, -9, 578, 23598, 2485, 81206, 22580, 18332, 174401, 54573, 22157; 20873970, 182670, 459230, 13656, -12805, -143412, -855, 51216, 2091330, 220230, 7195870, 2000844, 1624405, 15453612, 4835655, 1963284],351,8]
%
% END OF LATTICE L352.8
%
%
% LATTICE L352.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[118845, 85500, -68400; 85500, 48165, -44745; -68400, -44745, 37874],[855, 285, 1],[166, 955, 2682, 14743, 24667, 6303, 76483, 15984, 9287, 2196, 469, 1012, 541, -1, -859, -229; 165, 952, 2675, 14705, 24604, 6287, 76290, 15944, 9264, 2191, 468, 1010, 540, -1, -858, -229; 495, 2850, 8005, 44004, 73625, 18813, 228285, 47709, 27720, 6555, 1400, 3021, 1615, -3, -2565, -684],351,9]
%
% END OF LATTICE L352.9
%
%
% LATTICE L352.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2931041348280, 334847107620, -733127831460; 334847107620, 38253498456, -83753760084; -733127831460, -83753760084, 183373877539],[3420, 228, 1],[-389802, -99253, -21002, -856, -99524, -182947, -132323, -1488081, -106149, -396698, -1466851, -12397919, -5851888, -4776563, -1851481, -10910694; -183, -46, -9, 5, -45, -85, -62, -700, -50, -187, -690, -5830, -2751, -2245, -870, -5125; -1558510, -396834, -83970, -3420, -397917, -731460, -529055, -5949660, -424406, -1586082, -5864778, -49569480, -23397075, -19097700, -7402609, -43623240],351,10]
%
% END OF LATTICE L352.10
%
%
% LATTICE L352.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-26098020, -2636820, -272902320; -2636820, -263910, -27305565; -272902320, -27305565, -2825154814],[3420, 285, 1],[811, 5517, 15837, 43585, 145981, 18662, 453163, 47390, 55121, 13127, 2807, 3025, 3171, -18, -5707, -780; -259524, -1765406, -5067668, -13946714, -46712260, -5971625, -145006872, -15164237, -17638050, -4200452, -898190, -967931, -1014604, 5767, 1826280, 249592; 2430, 16530, 47450, 130587, 437380, 55914, 1357740, 141987, 165150, 39330, 8410, 9063, 9500, -54, -17100, -2337],351,11]
%
% END OF LATTICE L352.11
%
%
% LATTICE L352.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2248227267363720, 747065591610300, 1751487178680; 747065591610300, 248243140838040, 582003351840; 1751487178680, 582003351840, 1364500559],[3420, 1140, 1],[271516, 1479903, 6133392, 34414016, 29247719, 15107407, 92639294, 39310153, 23296313, 6376040, 1722551, 4865699, 2176053, 604479, 1632022, -30438; -814557, -4439758, -18400379, -103243187, -87744125, -45322721, -277920948, -117931760, -69889710, -19128331, -5167710, -14597258, -6528231, -1813457, -4896120, 91315; -1086030, -5919450, -24532930, -137652492, -116987845, -60428064, -370547595, -157236552, -93182850, -25503510, -6890030, -19462308, -8703995, -2417856, -6527925, 121752],351,12]
%
% END OF LATTICE L352.12
%

\medskip%
%------------------------------WEYL-GROUP-W353--------------------------------
%
\leavevmode\llap{}%
$W_{353}$%
\qquad\llap{24} lattices, $\chi=36$%
\hfill%
$2222222222\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L353.1
%
\leavevmode%
${L_{353.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{1}{}5\above{1pt}{1pt}{-}{}25\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{2}{}7\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${84}\above{1pt}{1pt}{r}{2}{50}\above{1pt}{1pt}{b}{2}{140}\above{1pt}{1pt}{*}{2}{300}\above{1pt}{1pt}{b}{2}{10}\above{1pt}{1pt}{l}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2674574700\\-18958800\\-277200
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-18958800\\-134390\\-1965
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-277200\\-1965\\-26
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-9154741\\1291076220\\28366800
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-64894\\9151881\\201080
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-923\\130169\\2859
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
6073\\-856464\\-18816
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2164\\-305185\\-6700
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1947\\-274582\\-6020
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1799\\-253710\\-5550
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\141\\5
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-2674574700, -18958800, -277200; -18958800, -134390, -1965; -277200, -1965, -26],[2100, 5, 1],[6073, 2164, 1947, 1799, -1, -109, -34, 41, 331, 72; -856464, -305185, -274582, -253710, 141, 15372, 4795, -5782, -46680, -10154; -18816, -6700, -6020, -5550, 5, 336, 100, -140, -1050, -225],352,1]
%
% END OF LATTICE L353.1
%
%
% LATTICE L353.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[255675, 5775, -2100; 5775, 10, -20; -2100, -20, 11],[525, 5, 1],[-44, -29, -11, -7, 1, 2, -1, -3, -8, -2; -3381, -2235, -854, -555, 74, 147, -75, -224, -600, -151; -14721, -9725, -3710, -2400, 325, 651, -325, -980, -2625, -660],352,2]
%
% END OF LATTICE L353.2
%
%
% LATTICE L353.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[525, 0, -525; 0, -10, 75; -525, 75, -37],[525, 5, 1],[-5879, -170, -393, -76, -5, -1, 2, 1, -8, -23; -43890, -1269, -2933, -567, -37, 0, 15, 7, -60, -172; -6300, -182, -420, -81, -5, 0, 2, 0, -9, -25],352,3]
%
% END OF LATTICE L353.3
%
%
% LATTICE L353.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1058031975, -6949425, 350643300; -6949425, 45645, -2303115; 350643300, -2303115, 116207002],[525, 15, 1],[-14733, -32033, -14856, -4788, -169, 747, 2063, 870, -207, -830; 434, 935, 427, 135, 3, 0, -5, 7, 20, 28; 44464, 96675, 44835, 14450, 510, -2254, -6225, -2625, 625, 2505],352,4]
%
% END OF LATTICE L353.4
%
%
% LATTICE L353.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[736575, 78750, 246225; 78750, 8430, 26325; 246225, 26325, 82309],[525, 15, 1],[-33693, -2897, -6588, -414, -35, -117, -1, -174, -69, -448; -2240, -192, -434, -27, -1, 0, 0, -14, -5, -31; 101500, 8727, 19845, 1247, 105, 350, 3, 525, 208, 1350],352,5]
%
% END OF LATTICE L353.5
%
%
% LATTICE L353.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[3882900, -39900, 21000; -39900, 410, -215; 21000, -215, -2],[2100, 5, 1],[43, 3, -1, -25, -34, -16843, -243, -1119, -215, -6; 4200, 293, -98, -2442, -3321, -1645140, -23735, -109298, -21000, -586; 0, 2, 0, -18, -25, -12600, -182, -840, -162, -5],352,6]
%
% END OF LATTICE L353.6
%
%
% LATTICE L353.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-352275, 99750, -3675; 99750, -27755, 1015; -3675, 1015, -37],[525, 35, 1],[2, -1, -1, -8, 2, 40, 211, 15, 113, 5; 24, -10, -12, -105, 19, 444, 2350, 168, 1275, 59; 459, -175, -230, -2100, 315, 8151, 43225, 3100, 23625, 1120],352,7]
%
% END OF LATTICE L353.7
%
%
% LATTICE L353.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1050, -22575, -1575; -22575, -483595, -33740; -1575, -33740, -2354],[525, 35, 1],[14, 8, 8, 31, 45, 1066, 208, 64, 77, -9; 15, 4, 1, -3, -12, -435, -88, -29, -39, -2; -225, -63, -20, 21, 140, 5475, 1113, 370, 504, 35],352,8]
%
% END OF LATTICE L353.8
%
%
% LATTICE L353.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-8696100, 27300, 4200; 27300, 30, -15; 4200, -15, -2],[2100, 15, 1],[1, 1, -1, -3, -2, -57, -61, -55, -17, 0; 28, 25, -42, -100, -64, -1792, -1915, -1722, -530, 1; 1876, 1875, -1890, -5650, -3765, -107296, -114825, -103530, -32000, 0],352,9]
%
% END OF LATTICE L353.9
%
%
% LATTICE L353.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[78210300, 905100, -88200; 905100, 8430, -915; -88200, -915, 94],[2100, 15, 1],[33, 3, -1, -7, -28, -4513, -195, -895, -57, -4; 3220, 293, -98, -684, -2736, -441000, -19055, -87458, -5570, -391; 62300, 5667, -1890, -13226, -52905, -8527400, -368457, -1691130, -107704, -7560],352,10]
%
% END OF LATTICE L353.10
%
%
% LATTICE L353.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1937497800, -367002300, 483972300; -367002300, 69532360, -91674420; 483972300, -91674420, 120892621],[2100, 20, 1],[-3327827, -4734693, -2124909, -1962419, 519, -51766, -93297, -128153, -451576, -161452; 18900, 26890, 12068, 11145, -3, 294, 530, 728, 2565, 917; 13336701, 18974900, 8515850, 7864650, -2080, 207459, 373900, 513590, 1809750, 647040],352,11]
%
% END OF LATTICE L353.11
%
%
% LATTICE L353.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[54780600, 15302700, 13700400; 15302700, 4273960, 3827140; 13700400, 3827140, 3426413],[2100, 20, 1],[38383, -1, -3441, 1801, 8843, 1440332, 84499, 200603, 40448, 5240; 315, 0, -28, 15, 73, 11865, 696, 1652, 333, 43; -153825, 4, 13790, -7218, -35440, -5772375, -338644, -803950, -162102, -21000],352,12]
%
% END OF LATTICE L353.12
%
%
% LATTICE L353.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[840896175, -8904000, 278675775; -8904000, 94290, -2950815; 278675775, -2950815, 92354074],[525, 105, 1],[-299, 696, -179, -7019, -11242, -27545, -418356, -27665, -62591, -2680; -7, 5, -4, -145, -232, -571, -8675, -574, -1300, -57; 902, -2100, 540, 21175, 33915, 83098, 1262100, 83460, 188825, 8085],352,13]
%
% END OF LATTICE L353.13
%
%
% LATTICE L353.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[10054275, 131775, 3333225; 131775, 1785, 43680; 3333225, 43680, 1105042],[525, 105, 1],[-616, -916, -914, -1219, -5489, -45184, -26564, -8246, -3361, 909; 205, 304, 303, 404, 1819, 14975, 8804, 2733, 1114, -301; 1850, 2751, 2745, 3661, 16485, 135700, 79779, 24765, 10094, -2730],352,14]
%
% END OF LATTICE L353.14
%
%
% LATTICE L353.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1850100, 571200, 2100; 571200, -175630, -665; 2100, -665, -2],[2100, 35, 1],[13, 2, -5, -43, 5, 215, 568, 81, 613, 14; 36, 5, -14, -120, 14, 600, 1585, 226, 1710, 39; 1632, 350, -600, -5250, 595, 26088, 68950, 9840, 74550, 1715],352,15]
%
% END OF LATTICE L353.15
%
%
% LATTICE L353.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-873921300, -58325400, 1434300; -58325400, -3892630, 95725; 1434300, 95725, -2354],[2100, 35, 1],[13, 6, 15, 65, 51, 2567, 252, 157, 193, -8; -180, -88, -224, -978, -771, -38940, -3824, -2384, -2934, 119; 600, 77, 30, -168, -280, -19500, -1967, -1290, -1722, -35],352,16]
%
% END OF LATTICE L353.16
%
%
% LATTICE L353.17
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[35066274600, -15747900, 8749834800; -15747900, 7080, -3929460; 8749834800, -3929460, 2183283223],[2100, 60, 1],[3268, 34509, 48365, 46274, 41830, 241963, 1016481, 442097, 128891, -6797; 0, -5, -7, -5, -3, -7, -25, -7, 0, 2; -13097, -138300, -193830, -185450, -167640, -969703, -4073700, -1771770, -516550, 27240],352,17]
%
% END OF LATTICE L353.17
%
%
% LATTICE L353.18
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[5572587085800, -8249889900, 1390487527800; -8249889900, 12213480, -2058535620; 1390487527800, -2058535620, 346958340031],[2100, 60, 1],[-31134, 1045, 26357, 3398, 5270, -276971, -53863, -149599, -12201, -14073; 140, -1, -63, -1, 53, 3745, 667, 1617, 112, 58; 124775, -4188, -105630, -13618, -21120, 1110025, 215868, 599550, 48898, 56400],352,18]
%
% END OF LATTICE L353.18
%
%
% LATTICE L353.19
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1119300, -216300, 46200; -216300, 41790, -8925; 46200, -8925, 1906],[2100, 105, 1],[1, 1, -1, -3, 1, 15, 119, 17, 43, 3; 12, 5, -18, -90, -17, 72, 625, 102, 300, 38; 32, 0, -60, -350, -105, -32, 0, 60, 350, 105],352,19]
%
% END OF LATTICE L353.19
%
%
% LATTICE L353.20
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-34311900, 214588500, -6522600; 214588500, -1342015710, 40791765; -6522600, 40791765, -1239902],[2100, 105, 1],[-20289, -6127, -4003, -1771, -86, 569, 211, 59, -201, -900; 53900, 16279, 10638, 4708, 232, -1520, -565, -162, 530, 2387; 1880000, 567798, 371040, 164206, 8085, -53000, -19698, -5640, 18494, 83265],352,20]
%
% END OF LATTICE L353.20
%
%
% LATTICE L353.21
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[18744486600, -29780100, 4676891100; -29780100, 47320, -7430360; 4676891100, -7430360, 1166919683],[2100, 140, 1],[3775, 27073, 781, 1834, 1048, 16556, 176237, 12773, 99821, 5729; 126, 900, 26, 75, 43, 582, 6180, 446, 3465, 193; -15129, -108500, -3130, -7350, -4200, -66351, -706300, -51190, -400050, -22960],352,21]
%
% END OF LATTICE L353.21
%
%
% LATTICE L353.22
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[268300200, -6281100, 66958500; -6281100, 383320, -1568000; 66958500, -1568000, 16710539],[2100, 140, 1],[113089, 111918, 111658, 446893, 670991, 8288621, 3248766, 1008570, 1233449, -110877; -870, -861, -859, -3438, -5162, -63765, -24993, -7759, -9489, 853; -453225, -448532, -447490, -1791006, -2689120, -33218175, -13020028, -4042030, -4943274, 444360],352,22]
%
% END OF LATTICE L353.22
%
%
% LATTICE L353.23
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[42205800, -3038700, 10529400; -3038700, 210840, -758100; 10529400, -758100, 2626849],[2100, 420, 1],[-154, -11007, -307, 8823, 15829, 19023, 577077, 38045, 85522, 3040; -1, -70, -2, 55, 99, 119, 3610, 238, 535, 19; 617, 44100, 1230, -35350, -63420, -76217, -2312100, -152430, -342650, -12180],352,23]
%
% END OF LATTICE L353.23
%
%
% LATTICE L353.24
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[6067524149400, -33364348500, 1514110878000; -33364348500, 183465240, -8325854460; 1514110878000, -8325854460, 377836444393],[2100, 420, 1],[1504074, 1769241, 549671, 224390, -58946, 20971, 60813, 60347, 80619, 363955; 203225, 239056, 74272, 30321, -7959, 2835, 8216, 8152, 10891, 49171; -6022825, -7084644, -2201070, -898534, 236040, -83975, -243516, -241650, -322826, -1457400],352,24]
%
% END OF LATTICE L353.24
%

\medskip%
%------------------------------WEYL-GROUP-W354--------------------------------
%
\leavevmode\llap{}%
$W_{354}$%
\qquad\llap{12} lattices, $\chi=24$%
\hfill%
$222|2222|2\rtimes D_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L354.1
%
\leavevmode%
${L_{354.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{-}{}5\above{1pt}{1pt}{1}{}25\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}7\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${700}\above{1pt}{1pt}{*}{2}{12}\above{1pt}{1pt}{b}{2}{50}\above{1pt}{1pt}{l}{2}{20}\above{1pt}{1pt}{r}{2}{2}\above{1pt}{1pt}{b}{2}{300}\above{1pt}{1pt}{*}{2}{28}\above{1pt}{1pt}{b}{2}{30}\above{1pt}{1pt}{b}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-48300\\21000\\2100
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
21000\\-9130\\-905
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2100\\-905\\58
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2241\\5180\\-350
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
257\\594\\-42
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
132\\305\\-25
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-19\\-44\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-16\\-37\\2
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
13\\30\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
109\\252\\-14
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
109\\252\\-15
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-48300, 21000, 2100; 21000, -9130, -905; 2100, -905, 58],[2100, 5, 1],[2241, 257, 132, -19, -16, 13, 109, 109; 5180, 594, 305, -44, -37, 30, 252, 252; -350, -42, -25, 0, 2, 0, -14, -15],353,1]
%
% END OF LATTICE L354.1
%
%
% LATTICE L354.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-1050, 0, 525; 0, 5, -35; 525, -35, -17],[525, 5, 1],[-83, -10, -12, 0, 1, 1, -3, -7; -1190, -144, -175, -1, 14, 15, -42, -99; -175, -21, -25, 0, 2, 0, -7, -15],353,2]
%
% END OF LATTICE L354.2
%
%
% LATTICE L354.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[45150, 18375, 15225; 18375, 7365, 6195; 15225, 6195, 5134],[525, 15, 1],[516, 9, -76, -35, -1, 116, 160, 43; 35, 1, 0, -1, 0, 5, 7, 2; -1575, -28, 225, 105, 3, -350, -483, -130],353,3]
%
% END OF LATTICE L354.3
%
%
% LATTICE L354.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-6817650, -423150, 15225; -423150, -26215, 945; 15225, 945, -34],[525, 35, 1],[1, 8, -1, -1, 9, 10, 13, 10; -1, -15, 0, 1, 0, -3, -5, -6; 419, 3150, -448, -420, 4025, 4389, 5675, 4305],353,4]
%
% END OF LATTICE L354.4
%
%
% LATTICE L354.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-54896100, 15705900, 37800; 15705900, -4493490, -10815; 37800, -10815, -26],[2100, 15, 1],[33, 3, -5, -13, 16, 17, 493, 10; 112, 10, -17, -44, 55, 58, 1680, 34; 1386, 200, -198, -600, 375, 586, 17850, 395],353,5]
%
% END OF LATTICE L354.5
%
%
% LATTICE L354.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2408914200, 12862500, 602193900; 12862500, 68680, 3215440; 602193900, 3215440, 150539813],[2100, 20, 1],[25416, 3559, 6039, 413, -1, -337, 248, 1078; 8435, 1179, 1995, 136, 0, -90, 91, 363; -101850, -14262, -24200, -1655, 4, 1350, -994, -4320],353,6]
%
% END OF LATTICE L354.6
%
%
% LATTICE L354.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1633614675, 218925, 541405200; 218925, 105, 72555; 541405200, 72555, 179430067],[525, 105, 1],[5012, 25809, 1037, 0, 25751, 9275, 36812, 10312; -28, -145, -6, 1, -135, -50, -200, -57; -15123, -77875, -3129, 0, -77700, -27986, -111075, -31115],353,7]
%
% END OF LATTICE L354.7
%
%
% LATTICE L354.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[46433100, -1537200, 153300; -1537200, 50890, -5075; 153300, -5075, 506],[2100, 35, 1],[21, 17, 9, -1, -1, 1, 1, 7; 640, 510, 255, -44, -33, 30, 32, 222; 50, -42, -175, -140, -28, 0, 18, 105],353,8]
%
% END OF LATTICE L354.8
%
%
% LATTICE L354.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[6211266600, -16487100, 1549535400; -16487100, 44040, -4113060; 1549535400, -4113060, 386565271],[2100, 60, 1],[14892, 8621, 1045, 5618, 84139, 17507, 390116, 7316; 1141, 660, 80, 431, 6455, 1343, 29925, 561; -59682, -34550, -4188, -22515, -337200, -70162, -1563450, -29320],353,9]
%
% END OF LATTICE L354.9
%
%
% LATTICE L354.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1337700, -571200, 12600; -571200, 242970, -5355; 12600, -5355, 118],[2100, 105, 1],[1, 1, -1, -3, 2, 3, 13, 2; 12, 10, -13, -44, 5, 30, 140, 24; 438, 350, -483, -1680, 0, 1036, 4950, 875],353,10]
%
% END OF LATTICE L354.10
%
%
% LATTICE L354.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[34343400, -4080300, 8565900; -4080300, 382760, -1017800; 8565900, -1017800, 2136499],[2100, 140, 1],[132438, 132439, 231439, 16323, -531, -40087, -266, 32908; 495, 495, 865, 61, -2, -150, -1, 123; -530750, -530754, -927500, -65415, 2128, 160650, 1066, -131880],353,11]
%
% END OF LATTICE L354.11
%
%
% LATTICE L354.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[6136960200, -33450900, 1531292700; -33450900, 182280, -8346660; 1531292700, -8346660, 382087753],[2100, 420, 1],[-274, -4629, -545, 3118, 46639, 8947, 26838, 2166; -5, -75, -9, 46, 690, 132, 395, 31; 1098, 18550, 2184, -12495, -186900, -35854, -107550, -8680],353,12]
%
% END OF LATTICE L354.12
%

\medskip%
%------------------------------WEYL-GROUP-W355--------------------------------
%
\leavevmode\llap{}%
$W_{355}$%
\qquad\llap{8} lattices, $\chi=120$%
\hfill%
$\infty\infty\infty\infty\infty22\infty\infty\infty\infty\infty22\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L355.1
%
\leavevmode%
${L_{355.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}8\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{1}{}11\above{1pt}{1pt}{-}{}121\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${88}\above{1pt}{1pt}{22,1}{\infty z}{22}\above{1pt}{1pt}{44,3}{\infty b}{88}\above{1pt}{1pt}{22,5}{\infty z}{22}\above{1pt}{1pt}{44,27}{\infty b}{88}\above{1pt}{1pt}{22,3}{\infty z}{22}\above{1pt}{1pt}{s}{2}{242}\above{1pt}{1pt}{b}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-6018056\\31944\\-303952
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
31944\\-154\\1727
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-303952\\1727\\-14522
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3926209\\-321231768\\43981080
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
17160\\1403984\\-192225
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-225160\\-18421985\\2522224
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-22935\\-1876480\\256916
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2234\\-182781\\25025
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3543\\-289884\\39688
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-382\\-31256\\4279
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-711\\-58180\\7964
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-110\\-9003\\1232
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
108\\8833\\-1210
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-6018056, 31944, -303952; 31944, -154, 1727; -303952, 1727, -14522],[968, 11, 1],[-22935, -2234, -3543, -382, -711, -110, 108, 55, -54, -1033, -762, -8441, -5610, -12692; -1876480, -182781, -289884, -31256, -58180, -9003, 8833, 4500, -4417, -84512, -62343, -690612, -458992, -1038422; 256916, 25025, 39688, 4279, 7964, 1232, -1210, -616, 605, 11572, 8536, 94556, 62843, 142175],354,1]
%
% END OF LATTICE L355.1
%
%
% LATTICE L355.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-26378, 2420, 12100; 2420, -220, -1111; 12100, -1111, -5550],[242, 11, 1],[4191, 830, 679, 161, 177, 77, -1, -11, 6, 157, 257, 1495, 2013, 4599; 4190, 826, 670, 155, 164, 67, -11, -10, 10, 166, 263, 1508, 2023, 4609; 8272, 1639, 1342, 319, 352, 154, 0, -22, 11, 308, 506, 2948, 3971, 9075],354,2]
%
% END OF LATTICE L355.2
%
%
% LATTICE L355.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-21538, 2178, 1210; 2178, -220, -121; 1210, -121, -60],[242, 11, 1],[981, 190, 149, 31, 27, 7, -1, -1, 6, 47, 67, 365, 483, 99; 10240, 1981, 1550, 320, 274, 67, -11, -10, 65, 496, 703, 3818, 5048, 1034; -1210, -231, -176, -33, -22, 0, 2, 0, -11, -66, -88, -462, -605, -123],354,3]
%
% END OF LATTICE L355.3
%
%
% LATTICE L355.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[484, 242, 242; 242, 1100, 220; 242, 220, 131],[242, 22, 1],[5935, 2336, 945, 435, 232, 197, -1, 5, 40, 243, 753, 2144, 5743, 13069; 1374, 541, 219, 101, 54, 46, 0, 1, 9, 56, 174, 496, 1329, 3025; -13189, -5192, -2101, -968, -517, -440, 0, -11, -88, -539, -1672, -4763, -12760, -29040],354,4]
%
% END OF LATTICE L355.4
%
%
% LATTICE L355.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[239096, 60742, 119064; 60742, 15620, 30250; 119064, 30250, 59291],[242, 22, 1],[61655, 24261, 9810, 4510, 2402, 2037, -1, 60, 425, 2533, 7833, 22284, 59678, 12344; 1374, 541, 219, 101, 54, 46, 0, 1, 9, 56, 174, 496, 1329, 275; -124509, -48994, -19811, -9108, -4851, -4114, 2, -121, -858, -5115, -15818, -45001, -120516, -24928],354,5]
%
% END OF LATTICE L355.5
%
%
% LATTICE L355.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-876040, 11616, 5808; 11616, -154, -77; 5808, -77, -38],[968, 11, 1],[201, 20, 33, 4, 9, 2, 0, -1, 0, 7, 6, 71, 48, 10; 16136, 1601, 2628, 314, 692, 149, -1, -76, 5, 584, 489, 5732, 3866, 804; -2420, -231, -352, -33, -44, 0, 2, 0, -11, -132, -88, -924, -605, -123],354,6]
%
% END OF LATTICE L355.6
%
%
% LATTICE L355.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-849904, -150040, 50336; -150040, -26224, 8800; 50336, 8800, -2953],[968, 88, 1],[-5, -6, -9, -19, -44, -111, -241, -105, -38, -13, -3, 0, 1, -1; -1071, -1235, -1786, -3699, -8463, -21266, -46024, -19994, -7191, -2427, -514, 37, 201, -319; -3278, -3784, -5478, -11352, -25982, -65296, -141328, -61402, -22088, -7458, -1584, 110, 616, -968],354,7]
%
% END OF LATTICE L355.7
%
%
% LATTICE L355.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-6266832, -1044472, -3107280; -1044472, -174064, -517880; -3107280, -517880, -1540681],[968, 88, 1],[-730, -1047, -1779, -3974, -9511, -24243, -4825, -23295, -8563, -3026, -831, -99, 218, 20; -5, -1, 6, 21, 61, 164, 34, 170, 67, 27, 12, 5, 1, -1; 1474, 2112, 3586, 8008, 19162, 48840, 9720, 46926, 17248, 6094, 1672, 198, -440, -40],354,8]
%
% END OF LATTICE L355.8
%

\medskip%
%------------------------------WEYL-GROUP-W356--------------------------------
%
\leavevmode\llap{}%
$W_{356}$%
\qquad\llap{4} lattices, $\chi=32$%
\hfill%
$222\slashthree2222|2\rtimes D_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L356.1
%
\leavevmode%
${L_{356.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}16\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{1}{}3\above{1pt}{1pt}{-}{}9\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{-2}{}7\above{1pt}{1pt}{-}{}$}\EasyButWeakLineBreak%
{${144}\above{1pt}{1pt}{r}{2}{42}\above{1pt}{1pt}{b}{2}{16}\above{1pt}{1pt}{b}{2}{6}\above{1pt}{1pt}{-}{3}{6}\above{1pt}{1pt}{b}{2}{144}\above{1pt}{1pt}{b}{2}{42}\above{1pt}{1pt}{l}{2}{16}\above{1pt}{1pt}{r}{2}{6}\above{1pt}{1pt}{l}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-7917647472\\2568704544\\24677856
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2568704544\\-833359026\\-8006175
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
24677856\\-8006175\\-76910
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-282263\\-878352\\865872
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-75612\\-235291\\231945
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-14425\\-44888\\44248
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3309\\-10297\\10149
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2969\\9239\\-9108
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
6949\\21624\\-21312
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-31666\\-98539\\97146
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-60605\\-188592\\185920
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-17823\\-55462\\54675
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-7917647472, 2568704544, 24677856; 2568704544, -833359026, -8006175; 24677856, -8006175, -76910],[1008, 3, 1],[-282263, -75612, -14425, -3309, 2969, 6949, -31666, -60605, -17823; -878352, -235291, -44888, -10297, 9239, 21624, -98539, -188592, -55462; 865872, 231945, 44248, 10149, -9108, -21312, 97146, 185920, 54675],355,1]
%
% END OF LATTICE L356.1
%
%
% LATTICE L356.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-11804688, 2401056, -1055376; 2401056, -488082, 215229; -1055376, 215229, -93242],[1008, 21, 1],[-111713, -4271, -5687, -1292, 1179, 2707, -1800, -24059, -7064; -448656, -17153, -22840, -5189, 4735, 10872, -7229, -96624, -28370; 228816, 8748, 11648, 2646, -2415, -5544, 3687, 49280, 14469],355,2]
%
% END OF LATTICE L356.2
%
%
% LATTICE L356.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-5130720, -1055376, 2332512; -1055376, -217056, 479856; 2332512, 479856, -1060271],[1008, 48, 1],[2515, 11629, 341, 1039, -249, -265, 2613, 409, 2242; -5802, -26831, -787, -2399, 574, 612, -6020, -943, -5171; 2907, 13440, 394, 1200, -288, -306, 3024, 473, 2592],355,3]
%
% END OF LATTICE L356.3
%
%
% LATTICE L356.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1530738720, -351706320, 2079504; -351706320, -80808672, 477792; 2079504, 477792, -2825],[1008, 336, 1],[199, 130, 26, 76, -21, -19, 33, 34, 181; -12, -7, -1, -1, 2, 0, -4, -3, -13; 144459, 94512, 18970, 55776, -15120, -13986, 23616, 24521, 131040],355,4]
%
% END OF LATTICE L356.4
%

\medskip%
%------------------------------WEYL-GROUP-W357--------------------------------
%
\leavevmode\llap{}%
$W_{357}$%
\qquad\llap{4} lattices, $\chi=48$%
\hfill%
$22|222|222|222|2\rtimes D_{4}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L357.1
%
\leavevmode%
${L_{357.1}}$%
{} : {$1\above{1pt}{1pt}{1}{1}8\above{1pt}{1pt}{1}{7}128\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{-}{}$}\EasyButWeakLineBreak%
{${384}\above{1pt}{1pt}{}{2}{1}\above{1pt}{1pt}{r}{2}{96}\above{1pt}{1pt}{*}{2}{4}\above{1pt}{1pt}{s}{2}{384}\above{1pt}{1pt}{b}{2}{8}\above{1pt}{1pt}{l}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
384\\0\\0
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\-8\\8
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\8\\-7
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-97\\-672\\-1536
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-18\\-127\\-288
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
14\\98\\223
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-97\\-672\\-1536
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-4\\-29\\-65
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-11\\-90\\-192
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-5\\-46\\-94
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-49\\-480\\-960
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\-3\\-4
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[384, 0, 0; 0, -8, 8; 0, 8, -7],[384, 8, 1],[-97, -4, -11, -5, -49, 0, 1, 0, -1, -3, -47, -2; -672, -29, -90, -46, -480, -3, 0, 1, 6, -10, -192, -11; -1536, -65, -192, -94, -960, -4, 0, 1, 0, -34, -576, -28],356,1]
%
% END OF LATTICE L357.1
%
%
% LATTICE L357.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-908160, -113664, 3456; -113664, -14224, 432; 3456, 432, -13],[384, 16, 1],[23, 81, 25, 159, 31, 23, 37, 79, 5, 1, -1, -3; -222, -776, -237, -1496, -291, -214, -342, -728, -45, -8, 9, 26; -1314, -4416, -1272, -7680, -1473, -1024, -1566, -3264, -168, 0, 33, 64],356,2]
%
% END OF LATTICE L357.2
%
%
% LATTICE L357.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1785984, 3072, 13824; 3072, -24, 24; 13824, 24, 107],[384, 24, 1],[415, 53, 53, 79, 271, 4, 1, -1, -1, 25, 145, 22; -224, -29, -30, -46, -160, -3, 0, 1, 2, -10, -64, -11; -53632, -6849, -6848, -10206, -35008, -516, -128, 129, 128, -3234, -18752, -2844],356,3]
%
% END OF LATTICE L357.3
%
%
% LATTICE L357.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[384, 0, 0; 0, -19632, 672; 0, 672, -23],[384, 48, 1],[-5, -47, -4, -65, -4, -7, -3, -17, 0, 1, 0, -1; 2, 0, -3, -96, -7, -22, -14, -96, -3, 0, 1, 10; 38, -192, -104, -3072, -221, -672, -422, -2880, -88, 0, 29, 288],356,4]
%
% END OF LATTICE L357.4
%

\medskip%
%------------------------------WEYL-GROUP-W358--------------------------------
%
\leavevmode\llap{}%
$W_{358}$%
\qquad\llap{12} lattices, $\chi=88$%
\hfill%
$262|2622|2262|2622|2\rtimes D_{4}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L358.1
%
\leavevmode%
${L_{358.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{-}{}9\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{2}{}23\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${828}\above{1pt}{1pt}{b}{2}{6}\above{1pt}{1pt}{}{6}{18}\above{1pt}{1pt}{l}{2}{276}\above{1pt}{1pt}{r}{2}{2}\above{1pt}{1pt}{}{6}{6}\above{1pt}{1pt}{b}{2}{92}\above{1pt}{1pt}{*}{2}{60}\above{1pt}{1pt}{*}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-4899644460\\14092560\\-1184040
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
14092560\\-36786\\2769
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1184040\\2769\\-178
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
119343089\\82102473480\\483342300720
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-267280\\-183876161\\-1082490240
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
15934\\10961848\\64533071
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-7955\\-5472666\\-32217894
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-788\\-542107\\-3191415
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-875\\-601959\\-3543768
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-9147\\-6292708\\-37045548
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-492\\-338473\\-1992611
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2591\\-1782487\\-10493610
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-11867\\-8163942\\-48061628
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2487\\-1710940\\-10072410
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-4899644460, 14092560, -1184040; 14092560, -36786, 2769; -1184040, 2769, -178],[4140, 3, 1],[-7955, -788, -875, -9147, -492, -2591, -11867, -2487, -27511, -1782, -667, -2675, -22, 21, 45, -83; -5472666, -542107, -601959, -6292708, -338473, -1782487, -8163942, -1710940, -18926286, -1225933, -458865, -1840276, -15135, 14447, 30958, -57100; -32217894, -3191415, -3543768, -37045548, -1992611, -10493610, -48061628, -10072410, -111420234, -7217145, -2701368, -10833828, -89101, 85050, 182252, -336150],357,1]
%
% END OF LATTICE L358.1
%
%
% LATTICE L358.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-5730464835, -423315, 12792600; -423315, -21, 945; 12792600, 945, -28558],[1035, 3, 1],[-5955, -2602, -495, -4609, -884, -799, -4042, -44, 21, 22, -21, -1325, -664, -1781, -13760, -1246; -460, -202, -39, -368, -72, -67, -345, -5, 0, 2, -1, -92, -48, -133, -1035, -95; -2667563, -1165575, -221737, -2064618, -395991, -357915, -1810629, -19710, 9407, 9855, -9407, -593538, -297441, -797805, -6163839, -558150],357,2]
%
% END OF LATTICE L358.2
%
%
% LATTICE L358.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-164595015, -160425, -31949415; -160425, -105, -31140; -31949415, -31140, -6201677],[1035, 15, 1],[196238, 85745, 16312, 151883, 29131, 26330, 133199, 290, -692, -725, 692, 43663, 21881, 58690, 453439, 8212; -460, -202, -39, -368, -72, -67, -345, -1, 0, 2, -1, -92, -48, -133, -1035, -19; -1010965, -441735, -84035, -782460, -150075, -135645, -686205, -1494, 3565, 3735, -3565, -224940, -112725, -302355, -2335995, -42306],357,3]
%
% END OF LATTICE L358.3
%
%
% LATTICE L358.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[6322357455786360, -3115958708340, -1582118013201660; -3115958708340, 1535692776, 779743068204; -1582118013201660, 779743068204, 395912035218173],[4140, 12, 1],[9130159, 1859691, 2163365, 5851204, 1287413, 6956313, 16068087, 3442874, 39004241, 5116309, 2022235, 2171196, 107787, 19687, -23287, 45126; -28635, -5771, -6606, -17687, -3867, -20756, -47840, -10195, -114885, -15029, -5874, -6233, -293, -44, 0, -205; 36485406, 7431588, 8645112, 23382237, 5144684, 27798408, 64210342, 13758210, 155866446, 20445492, 8081136, 8676405, 430732, 78672, -93058, 180330],357,4]
%
% END OF LATTICE L358.4
%
%
% LATTICE L358.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1106096220, 14788080, 373618440; 14788080, -183930, -4234935; 373618440, -4234935, -84266258],[4140, 15, 1],[17504381, 3821845, 725722, 13492221, 1290661, 1162330, 11733913, 24485, -66379, -30975, 32452, 3945781, 983861, 2628540, 40580093, 733689; 2415628866, 527419913, 100150643, 1861945220, 178113009, 160403153, 1619296278, 3378964, -9160394, -4274593, 4478421, 544523252, 135774183, 362742167, 5600109138, 101250100; -43790620, -9561090, -1815535, -33753420, -3228840, -2907795, -29354670, -61254, 166060, 77490, -81185, -9871140, -2461320, -6575805, -101519010, -1835466],357,5]
%
% END OF LATTICE L358.5
%
%
% LATTICE L358.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-890534268405, -21473145, 901393920; -21473145, -483, 21735; 901393920, 21735, -912386],[1035, 69, 1],[21, 22, -483, -841, -8980, -22571, -7468, -15106, -3051, -30322, -5577, -2189, -9200, -7729, -1622, -44; 0, 2, -1, -4, -48, -133, -45, -95, -20, -202, -39, -16, -72, -67, -15, -5; 20747, 21735, -477181, -830868, -8871813, -22299075, -7378029, -14924010, -3014243, -29956695, -5509811, -2162628, -9089163, -7635885, -1602459, -43470],357,6]
%
% END OF LATTICE L358.6
%
%
% LATTICE L358.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[7104032656487640, 2185308359136540, -1776668420133900; 2185308359136540, 672234047256360, -546530194563060; -1776668420133900, -546530194563060, 444332230401337],[4140, 60, 1],[3359987, 1422161, 244585, 1030558, 332725, 219071, 856271, -8362, -55163, 14719, 42791, 621854, 529403, 1217809, 9058201, 152050; -47840, -20756, -3867, -17687, -6606, -5771, -28635, -41, 0, -44, -293, -6233, -5874, -15029, -114885, -2039; 13376110, 5661000, 973220, 4098945, 1322280, 868860, 3388590, -33486, -220570, 58800, 170740, 2478825, 2109600, 4850940, 36078030, 605466],357,7]
%
% END OF LATTICE L358.7
%
%
% LATTICE L358.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2240265780, -43581780, 1039140; -43581780, -846078, 20217; 1039140, 20217, -482],[4140, 69, 1],[-869, -1287, -469, -79, -11, 21, 1, -83, -277, -623, -677, -303, -371, -1931, -383, -1827; 1764, 2612, 951, 160, 22, -43, -2, 170, 564, 1268, 1377, 616, 754, 3923, 778, 3710; -1799514, -2665125, -971244, -163608, -22793, 43470, 2072, -171810, -573534, -1289955, -1401804, -627408, -768223, -3998550, -793088, -3783270],357,8]
%
% END OF LATTICE L358.8
%
%
% LATTICE L358.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-116715901545, 116733284370, -46832298930; 116733284370, -116750669610, 46839273795; -46832298930, 46839273795, -18791477374],[1035, 345, 1],[520493, 2480208, 2952254, 702445, 1789648, 9730278, 979061, 969499, 2396473, 7243012, 2881678, 269877, 154996, -7058, -6739, 2823; -15, -67, -72, -16, -39, -202, -20, -19, -45, -133, -48, -4, -1, 2, 0, -1; -1297215, -6181365, -7357815, -1750680, -4460275, -24250395, -2440075, -2416242, -5972625, -18051435, -7181865, -672600, -386285, 17595, 16795, -7038],357,9]
%
% END OF LATTICE L358.9
%
%
% LATTICE L358.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[58751658160920, 3874903380, -14702133235680; 3874903380, 255576, -969663624; -14702133235680, -969663624, 3679091423899],[4140, 276, 1],[-4280584, -12874326, -5023573, -231376, -248180, -37227, -517, -185617, -1076996, -4984274, -5691587, -661554, -3323540, -17821373, -1785343, -8743683; -4995, -15029, -5874, -271, -293, -44, 0, -205, -1245, -5771, -6606, -769, -3867, -20756, -2080, -10195; -17105778, -51447504, -20074860, -924609, -991760, -148764, -2066, -741750, -4303818, -19917816, -22744332, -2643657, -13281304, -71216556, -7134466, -34940910],357,10]
%
% END OF LATTICE L358.10
%
%
% LATTICE L358.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-602200260, -50512140, 120681000; -50512140, -4230390, 10122645; 120681000, 10122645, -24184486],[4140, 345, 1],[-159223, -802745, -154218, -125943, -281369, -258890, -115099, -6889, 417, 8715, -4588, -32863, -195049, -535140, -361319, -151917; 778, 3923, 754, 616, 1377, 1268, 564, 34, -2, -43, 22, 160, 951, 2612, 1764, 742; -794200, -4004070, -769235, -628200, -1403460, -1291335, -574110, -34362, 2080, 43470, -22885, -163920, -972900, -2669265, -1802250, -757758],357,11]
%
% END OF LATTICE L358.11
%
%
% LATTICE L358.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[458440192440, -765374220, 115745950260; -765374220, 1277880, -193240020; 115745950260, -193240020, 29223277631],[4140, 1380, 1],[414873, 4141093, 772172, 153681, 1321891, 1157218, 249994, 8563, 103, 8667, 57780, 53807, 1167965, 2992542, 994934, 406413; -1246699, -12444035, -2320383, -461812, -3972279, -3477425, -751227, -25730, -309, -26045, -173633, -161692, -3509769, -8992655, -2989797, -1221278; -1651450, -16484100, -3073720, -611745, -5261940, -4606440, -995130, -34086, -410, -34500, -230000, -214185, -4649220, -11912160, -3960450, -1617774],357,12]
%
% END OF LATTICE L358.12
%

\medskip%
%------------------------------WEYL-GROUP-W359--------------------------------
%
\leavevmode\llap{}%
$W_{359}$%
\qquad\llap{3} lattices, $\chi=24$%
\hfill%
$2|2|2|2|2|2|2|2|\rtimes D_{8}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L359.1
%
\leavevmode%
${L_{359.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{1}{}3\above{1pt}{1pt}{1}{}9\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{-}{}5\above{1pt}{1pt}{-}{}25\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${300}\above{1pt}{1pt}{r}{2}{10}\above{1pt}{1pt}{l}{2}{12}\above{1pt}{1pt}{r}{2}{90}\above{1pt}{1pt}{l}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
146700\\-47700\\-1800
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-47700\\15510\\585
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1800\\585\\22
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
89\\180\\2700
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-29\\-59\\-870
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-2\\-31
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\20\\-300
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\4\\-25
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\4\\-24
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-3\\0
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[146700, -47700, -1800; -47700, 15510, 585; -1800, 585, 22],[900, 15, 1],[3, 1, 1, -1, -13, -2, -3, -2; 20, 4, 4, -3, -40, -6, -8, -3; -300, -25, -24, 0, 0, -5, -36, -90],358,1]
%
% END OF LATTICE L359.1
%
%
% LATTICE L359.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[36675, 12825, -900; 12825, 4485, -315; -900, -315, 22],[225, 15, 1],[-1, -2, -7, -1, 1, 2, 7, 1; 2, 4, 10, -3, -4, -6, -20, -3; -12, -25, -150, -90, -18, -5, 0, 0],358,2]
%
% END OF LATTICE L359.2
%
%
% LATTICE L359.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1456200, 54900, 363600; 54900, 840, 13680; 363600, 13680, 90787],[900, 60, 1],[-1549, -214, 53, 851, -56, -428, -374, -2777; -140, -19, 5, 78, -5, -39, -34, -252; 6225, 860, -213, -3420, 225, 1720, 1503, 11160],358,3]
%
% END OF LATTICE L359.3
%

\medskip%
%------------------------------WEYL-GROUP-W360--------------------------------
%
\leavevmode\llap{}%
$W_{360}$%
\qquad\llap{12} lattices, $\chi=54$%
\hfill%
$2\slashtwo222222|22222\rtimes D_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L360.1
%
\leavevmode%
${L_{360.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{1}{}3\above{1pt}{1pt}{-}{}9\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{2}{}7\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{2}{}19\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${42}\above{1pt}{1pt}{b}{2}{36}\above{1pt}{1pt}{*}{2}{4}\above{1pt}{1pt}{b}{2}{42}\above{1pt}{1pt}{l}{2}{76}\above{1pt}{1pt}{r}{2}{6}\above{1pt}{1pt}{b}{2}{532}\above{1pt}{1pt}{*}{2}{36}\above{1pt}{1pt}{b}{2}{114}\above{1pt}{1pt}{b}{2}{4}\above{1pt}{1pt}{*}{2}{4788}\above{1pt}{1pt}{b}{2}{6}\above{1pt}{1pt}{l}{2}{684}\above{1pt}{1pt}{r}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-66566189844\\146268612\\-2322180
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
146268612\\-321402\\5103
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2322180\\5103\\-50
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2896\\-1317701\\16086
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1795\\-816738\\9972
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-415\\-188828\\2306
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-971\\-441812\\5397
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1531\\-696616\\8512
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-455\\6
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
957\\435442\\-5320
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
139\\63246\\-774
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-134\\-60971\\741
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-687\\-312590\\3814
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-70279\\-31977456\\390222
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-826\\-375836\\4587
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-25493\\-11599500\\141588
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-66566189844, 146268612, -2322180; 146268612, -321402, 5103; -2322180, 5103, -50],[4788, 3, 1],[-2896, -1795, -415, -971, -1531, -1, 957, 139, -134, -687, -70279, -826, -25493; -1317701, -816738, -188828, -441812, -696616, -455, 435442, 63246, -60971, -312590, -31977456, -375836, -11599500; 16086, 9972, 2306, 5397, 8512, 6, -5320, -774, 741, 3814, 390222, 4587, 141588],359,1]
%
% END OF LATTICE L360.1
%
%
% LATTICE L360.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-590775759, 4475583, 1420839; 4475583, -33906, -10764; 1420839, -10764, -3413],[1197, 3, 1],[43, 1, -15, -279, -550, -143, -2671, -292, -252, -36, -1895, -5, 98; 5656, 132, -1973, -36701, -72352, -18812, -351386, -38415, -33155, -4737, -249375, -659, 12882; 63, 0, -22, -399, -779, -201, -3724, -405, -342, -47, -2394, -3, 171],359,2]
%
% END OF LATTICE L360.2
%
%
% LATTICE L360.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-25703181, -1428021, 7182; -1428021, -79338, 399; 7182, 399, -2],[1197, 21, 1],[-2, -3, -13, -6, -185, -12, -73, -5, -2, 1, 1, 0, -11; 35, 53, 231, 107, 3306, 215, 1311, 90, 38, -18, -19, -1, 190; -219, -224, -693, -240, -5985, -273, -1026, -28, 399, 0, -209, -210, -1729],359,3]
%
% END OF LATTICE L360.3
%
%
% LATTICE L360.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[363544384392, 43367975532, 90841938768; 43367975532, 5173459800, 10836726264; 90841938768, 10836726264, 22699450723],[4788, 12, 1],[-8718421, -2543537, -546032, -2380334, -926734, -9583, -907299, -201535, -1289345, -1274433, -123145550, -2725906, -19983581; -25564, -7458, -1601, -6979, -2717, -28, -2660, -591, -3781, -3737, -361095, -7993, -58596; 34902840, 10182654, 2185954, 9529296, 3710035, 38364, 3632230, 806814, 5161692, 5101994, 492994026, 10912740, 80001153],359,4]
%
% END OF LATTICE L360.4
%
%
% LATTICE L360.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[23037462, 549423, -8434062; 549423, 12939, -200925; -8434062, -200925, 3087433],[1197, 57, 1],[-400, -1600, -1073, -11733, -948, -3676, -2746, -4571, -9, 635, 3095, 1181, 394; -1603, -6411, -4300, -47026, -3800, -14737, -11011, -18333, -37, 2541, 12390, 4730, 1578; -1197, -4788, -3211, -35112, -2837, -11001, -8218, -13680, -27, 1900, 9261, 3534, 1179],359,5]
%
% END OF LATTICE L360.5
%
%
% LATTICE L360.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1833804, 0, 4788; 0, 42, -21; 4788, -21, -2],[4788, 21, 1],[-1, -3, -13, -3, -185, -6, -73, -5, -1, 1, 1, 0, -11; -193, -578, -2502, -577, -35568, -1153, -14022, -960, -190, 192, 190, -1, -2128; -387, -1162, -5040, -1164, -71820, -2331, -28386, -1946, -399, 378, 380, 0, -4256],359,6]
%
% END OF LATTICE L360.6
%
%
% LATTICE L360.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[280217700, -46611180, 172368; -46611180, 7753254, -28671; 172368, -28671, 106],[4788, 57, 1],[103, 27, 71, 68, 19, 2, -31, -13, -2, 1, 13, 17, 13; 665, 174, 456, 434, 120, 11, -210, -86, -13, 6, 84, 110, 84; 12369, 3154, 7866, 6783, 1548, -285, -6426, -2128, -264, 0, 1582, 2109, 1580],359,7]
%
% END OF LATTICE L360.7
%
%
% LATTICE L360.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[4298905800, -38107692, 1073819124; -38107692, 337848, -9518880; 1073819124, -9518880, 268228141],[4788, 84, 1],[4745, 7725, 36289, 17859, 287338, 39321, 254491, 18482, 19136, 2990, 1775, -21, 12724; 1, 3, 18, 10, 171, 25, 171, 13, 19, 3, 0, -2, 0; -18996, -30926, -145278, -71496, -1150317, -157416, -1018818, -73990, -76608, -11970, -7106, 84, -50939],359,8]
%
% END OF LATTICE L360.8
%
%
% LATTICE L360.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1197, -159201, 1197; -159201, -1694285670, 12839421; 1197, 12839421, -97298],[1197, 399, 1],[468, 383, -137, -326, -183, -666, -37, 1, 112, 1059, 683, 1716, 1039; 463, 390, -129, -314, -177, -647, -36, 0, 109, 1036, 669, 1684, 1023; 61104, 51471, -17024, -41439, -23359, -85386, -4751, 0, 14385, 136724, 88290, 222243, 135009],359,9]
%
% END OF LATTICE L360.9
%
%
% LATTICE L360.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[61121510856, -149486148, 15267208320; -149486148, 364344, -37339332; 15267208320, -37339332, 3813512569],[4788, 228, 1],[498733, 102505, 425008, 1321184, 148963, 353675, 755905, 133677, -1199, -68941, -22182, 1196, 10490; 5803, 1193, 4947, 15379, 1734, 4117, 8799, 1556, -14, -804, -259, 13, 122; -1996596, -410362, -1701450, -5289144, -596349, -1415880, -3026142, -535154, 4800, 275994, 88802, -4788, -41995],359,10]
%
% END OF LATTICE L360.10
%
%
% LATTICE L360.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[529605468, 3769204572, -28560420; 3769204572, 26825436330, -203264565; -28560420, -203264565, 1540198],[4788, 399, 1],[8, 15, 41, 6, 13, 3, -1, -5, -1, 1, 1, 9, 7; -170, 12, 1518, 571, 2280, 1738, 1320, 1982, 91, 18, -54, -485, -228; -22287, 1862, 201096, 75468, 301140, 229425, 174186, 261478, 11991, 2394, -7108, -63840, -29960],359,11]
%
% END OF LATTICE L360.11
%
%
% LATTICE L360.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[16288693655976, 40892100732, -4038129352656; 40892100732, 102657912, -10137558984; -4038129352656, -10137558984, 1001092476343],[4788, 1596, 1],[-362988, -486328, -1944847, -848851, -665248, -1566400, -478834, -594209, 2811, 160825, 2343, -108811, -59795; 1055933, 1414729, 5657565, 2469311, 1935210, 4556669, 1392933, 1728562, -8176, -467826, -6815, 316535, 173944; -1453500, -1947386, -7787682, -3399024, -2663829, -6272280, -1917378, -2379370, 11256, 643986, 9382, -435708, -239435],359,12]
%
% END OF LATTICE L360.12
%

\medskip%
%------------------------------WEYL-GROUP-W361--------------------------------
%
\leavevmode\llap{}%
$W_{361}$%
\qquad\llap{12} lattices, $\chi=112$%
\hfill%
$22226|62222|22226|62222|\rtimes D_{4}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L361.1
%
\leavevmode%
${L_{361.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{-}{}9\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{-2}{}29\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${870}\above{1pt}{1pt}{s}{2}{2}\above{1pt}{1pt}{b}{2}{1044}\above{1pt}{1pt}{*}{2}{20}\above{1pt}{1pt}{b}{2}{18}\above{1pt}{1pt}{}{6}{6}\above{1pt}{1pt}{}{6}{2}\above{1pt}{1pt}{b}{2}{180}\above{1pt}{1pt}{*}{2}{116}\above{1pt}{1pt}{b}{2}{18}\above{1pt}{1pt}{s}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-37618707780\\31246920\\-1237140
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
31246920\\-25878\\1005
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1237140\\1005\\-34
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
84550949\\117519887100\\397247063400
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-66804\\-92852873\\-313866288
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1767\\2456006\\8301923
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-7664\\-10652425\\-36007995
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-386\\-536513\\-1813553
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-19585\\-27221778\\-92016594
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1711\\-2378170\\-8038820
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1381\\-1919493\\-6488370
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-56\\-77836\\-263103
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-124\\-172351\\-582580
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1097\\-1524750\\-5153940
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1147\\-1594246\\-5388838
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-149\\-207099\\-700029
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-37618707780, 31246920, -1237140; 31246920, -25878, 1005; -1237140, 1005, -34],[5220, 3, 1],[-7664, -386, -19585, -1711, -1381, -56, -124, -1097, -1147, -149, -601, -13, -251, 1, 13, -1, -332, -4033, -5465, -1048; -10652425, -536513, -27221778, -2378170, -1919493, -77836, -172351, -1524750, -1594246, -207099, -835345, -18069, -348870, 1390, 18069, -1390, -461457, -5605590, -7595970, -1456647; -36007995, -1813553, -92016594, -8038820, -6488370, -263103, -582580, -5153940, -5388838, -700029, -2823585, -61075, -1179198, 4700, 61074, -4701, -1559852, -18948420, -25676426, -4923855],360,1]
%
% END OF LATTICE L361.1
%
%
% LATTICE L361.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-2650495455, -347130, 8680860; -347130, -39, 1131; 8680860, 1131, -28426],[1305, 3, 1],[-40289, -2003, -50320, -4363, -6974, -251, -490, -2081, -2096, -505, -1761, -27, -140, 13, 14, -39, -1830, -10969, -14724, -5585; -11685985, -580979, -14595555, -1265510, -2022846, -72805, -142132, -603630, -607985, -146487, -510835, -7833, -40629, 3770, 4062, -11311, -530796, -3181590, -4270743, -1619949; -12768555, -634799, -15947622, -1382740, -2210229, -79548, -155293, -659520, -664274, -160047, -558105, -8557, -44370, 4120, 4437, -12360, -579971, -3476340, -4666390, -1770021],360,2]
%
% END OF LATTICE L361.2
%
%
% LATTICE L361.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-103065587910, -4738455, 123018435; -4738455, -195, 5655; 123018435, 5655, -146834],[1305, 15, 1],[-1257, -1909, -8128, -1633, -1946, -1031, -29438, -3691, -213184, -8503, -34297, -23837, -62980, -9401, -7862, -195, 14, 13, -140, -79; -36482, -55398, -235857, -47385, -56466, -29914, -854088, -107087, -6185091, -246696, -995048, -691572, -1827203, -272745, -228094, -5656, 408, 377, -4089, -2294; -1054527, -1601505, -6818770, -1369962, -1632545, -864930, -24696225, -3096466, -178845030, -7133365, -28772553, -19997415, -52835390, -7886718, -6595615, -163590, 11745, 10906, -117450, -66275],360,3]
%
% END OF LATTICE L361.3
%
%
% LATTICE L361.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1247666653639080, -849289568220, 311677443131580; -849289568220, 578113368, -212159554260; 311677443131580, -212159554260, 77859601580039],[5220, 12, 1],[-308683769, -15332405, -384930523, -33358453, -53287199, -1902698, -3716725, -15801311, -15944777, -3860191, -13724601, -232137, -1959521, 5863, -76945, -320808, -14071323, -84256459, -113018571, -42833435; -325235, -16157, -405681, -35160, -56172, -2009, -3934, -16740, -16907, -4101, -14645, -251, -2175, 0, -84, -335, -14818, -88740, -119045, -45123; 1235681880, 61376648, 1540902762, 133536130, 213312240, 7616628, 14878300, 63253710, 63828014, 15452604, 54940500, 929260, 7844094, -23470, 308016, 1284216, 56328452, 337284270, 452420938, 171465120],360,4]
%
% END OF LATTICE L361.4
%
%
% LATTICE L361.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1376602740, -13384080, 516780; -13384080, -129390, 5025; 516780, 5025, -194],[5220, 15, 1],[-2542, -1750, -9177, -1361, -564, -7, 13, 1, -251, -15, -155, -203, -1611, -313, -180, -86, -2245, -559, -32113, -636; 5191, 3573, 18734, 2778, 1151, 14, -27, -2, 522, 31, 319, 417, 3306, 642, 369, 176, 4587, 1142, 65598, 1299; -6637143, -4569255, -23961250, -3553596, -1472620, -18285, 33930, 2612, -655110, -39155, -404637, -529965, -4205870, -817164, -469940, -224535, -5861610, -1459532, -83846250, -1660585],360,5]
%
% END OF LATTICE L361.5
%
%
% LATTICE L361.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2445570, 57420, -708615; 57420, -1131, 16356; -708615, 16356, -204959],[1305, 87, 1],[879, 7309, 1046, 30116, 7091, 3632, 100907, 63128, 25106, 28981, 20101, 80807, 7346, 158704, 26477, 564, -203, -188, 70, 391; -4400, -36582, -5235, -150720, -35487, -18175, -504921, -315880, -125625, -145014, -100580, -404334, -36757, -794100, -132481, -2821, 1017, 940, -351, -1958; -3390, -28188, -4034, -116145, -27347, -14007, -389151, -243455, -96822, -111766, -77520, -311634, -28330, -612045, -102109, -2175, 783, 725, -270, -1508],360,6]
%
% END OF LATTICE L361.6
%
%
% LATTICE L361.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[88031872099080, 802674180, 21991077798660; 802674180, 7320, 200514540; 21991077798660, 200514540, 5493550133779],[5220, 60, 1],[23784411, 16492973, 43499289, 6483521, 5411289, 119788, 29947, 651, 866507, 96351, 1098923, 1525993, 6267379, 1238893, 1453079, 738258, 20563157, 2573487, 148433497, 5909971; -65047, -45123, -119045, -17748, -14818, -335, -84, 0, -2175, -251, -2929, -4101, -16907, -3348, -3934, -2009, -56172, -7032, -405681, -16157; -95210712, -66022560, -174130790, -25954002, -21661780, -479520, -119880, -2606, -3468690, -385700, -4399068, -6108660, -25088770, -4959378, -5816780, -2955300, -82315800, -10301854, -594189990, -23658040],360,7]
%
% END OF LATTICE L361.7
%
%
% LATTICE L361.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-63793620, 6921720, -5324400; 6921720, -750462, 575853; -5324400, 575853, -438218],[5220, 87, 1],[-3029, -21821, -5799, -160937, -18204, -8240, -203701, -252431, -99653, -56970, -39016, -154768, -27837, -595873, -49068, -169, 1885, 161, -1255, -1893; -36305, -261543, -69506, -1928970, -218191, -98764, -2441553, -3025630, -1194438, -682841, -467645, -1855047, -333654, -7142130, -588129, -2026, 22593, 1930, -15042, -22689; -10905, -78561, -20878, -579420, -65540, -29667, -733410, -908860, -358794, -205117, -140475, -557235, -100226, -2145420, -176668, -609, 6786, 580, -4518, -6815],360,8]
%
% END OF LATTICE L361.8
%
%
% LATTICE L361.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-4412965815, 147626820, 9817515; 147626820, -4938555, -328425; 9817515, -328425, -21841],[1305, 435, 1],[-15, -299, -27, -116, -96, -1, 2, 0, -1, -3, -1, -37, -5, -28, -32, -15, -386, -48, -95, -109; -2036, -41130, -3754, -16275, -13639, -377, -27, 27, 18, -80, -62, -2928, -442, -2607, -3145, -1721, -50325, -6321, -12606, -14606; 23877, 484155, 44320, 192618, 161965, 5220, 1305, -406, -720, -145, 483, 27405, 4400, 26622, 32915, 19140, 583335, 73486, 146880, 170665],360,9]
%
% END OF LATTICE L361.9
%
%
% LATTICE L361.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[6577126920, 13139162820, 1655622180; 13139162820, 26248186056, 3307445592; 1655622180, 3307445592, 416760211],[5220, 348, 1],[-134741, -1093991, -155509, -4465039, -1049269, -535778, -14979343, -9376037, -3730399, -4308509, -2990629, -12032563, -1094639, -23663291, -3951323, -89296, -22433, -73, -20045, -67009; -505, -4101, -583, -16740, -3934, -2009, -56172, -35160, -13989, -16157, -11215, -45123, -4105, -88740, -14818, -335, -84, 0, -75, -251; 539280, 4378536, 622402, 17870670, 4199548, 2144376, 59952744, 37526290, 14930406, 17244212, 11969580, 48158676, 4381142, 94709070, 15814628, 357396, 89784, 290, 80226, 268192],360,10]
%
% END OF LATTICE L361.10
%
%
% LATTICE L361.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-116265060, 137176380, 40063500; 137176380, -161840010, -47269275; 40063500, -47269275, -13805386],[5220, 435, 1],[-79493, -1587227, -287041, -1234621, -511685, -6429, 11660, 917, -7763, -13504, -4824, -183430, -50227, -283085, -162851, -77888, -2035268, -506819, -1004041, -576715; 179, 3573, 646, 2778, 1151, 14, -27, -2, 18, 31, 11, 417, 114, 642, 369, 176, 4587, 1142, 2262, 1299; -231303, -4618395, -835210, -3592404, -1488860, -18705, 33930, 2668, -22590, -39295, -14037, -533745, -146150, -823716, -473860, -226635, -5922090, -1474708, -2921490, -1678085],360,11]
%
% END OF LATTICE L361.11
%
%
% LATTICE L361.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[431581341960, 302619060, -107888604300; 302619060, 212280, -75649980; -107888604300, -75649980, 26970468431],[5220, 1740, 1],[-497247, -10000853, -909641, -3932213, -3282329, -73228, -18307, -247, -17563, -57391, -22759, -919273, -130371, -747841, -877719, -446778, -12461837, -1559771, -3102473, -3582651; 1477438, 29714880, 2702756, 11683521, 9752561, 217573, 54393, 735, 52188, 170530, 67624, 2731422, 387368, 2222037, 2607935, 1327489, 37027095, 4634451, 9218184, 10644904; -1984968, -39922560, -3631210, -15697062, -13102780, -292320, -73080, -986, -70110, -229100, -90852, -3669660, -520430, -2985318, -3503780, -1783500, -49746600, -6226474, -12384810, -14301640],360,12]
%
% END OF LATTICE L361.12
%

\medskip%
%------------------------------WEYL-GROUP-W362--------------------------------
%
\leavevmode\llap{}%
$W_{362}$%
\qquad\llap{4} lattices, $\chi=48$%
\hfill%
$\infty\infty|\infty\infty2\slashinfty2\rtimes D_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L362.1
%
\leavevmode%
${L_{362.1}}$%
{} : {$1\above{1pt}{1pt}{1}{7}16\above{1pt}{1pt}{-}{5}256\above{1pt}{1pt}{-}{5}$}\EasyButWeakLineBreak%
{${64}\above{1pt}{1pt}{32,17}{\infty z}{16}\above{1pt}{1pt}{16,13}{\infty b}{64}\above{1pt}{1pt}{32,9}{\infty z}{16}\above{1pt}{1pt}{16,5}{\infty a}{64}\above{1pt}{1pt}{s}{2}{256}\above{1pt}{1pt}{16,1}{\infty z}{256}\above{1pt}{1pt}{*}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-58112\\-3328\\256
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3328\\-176\\16
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
256\\16\\-1
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-27\\278\\-2720
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-7\\73\\-696
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-5\\54\\-480
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\1\\8
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\-10\\96
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\8\\-128
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-15\\152\\-1536
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-58112, -3328, 256; -3328, -176, 16; 256, 16, -1],[256, 16, 1],[-27, -7, -5, 0, 1, -1, -15; 278, 73, 54, 1, -10, 8, 152; -2720, -696, -480, 8, 96, -128, -1536],361,1]
%
% END OF LATTICE L362.1
%
\hbox{}\par\smallskip%
%
% LATTICE L362.2
%
\leavevmode%
${L_{362.2}}$%
{} : {$1\above{1pt}{1pt}{1}{1}16\above{1pt}{1pt}{-}{5}256\above{1pt}{1pt}{-}{3}$}\EasyButWeakLineBreak%
{${64}\above{1pt}{1pt}{32,31}{\infty z}{16}\above{1pt}{1pt}{16,11}{\infty a}{64}\above{1pt}{1pt}{32,23}{\infty z}{16}\above{1pt}{1pt}{16,3}{\infty b}{64}\above{1pt}{1pt}{*}{2}{4}\above{1pt}{1pt}{8,3}{\infty z}{1}\above{1pt}{1pt}{r}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1131776\\8448\\8448
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
8448\\-48\\-64
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
8448\\-64\\-63
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
47\\314\\5952
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
16\\111\\2024
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
19\\138\\2400
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4\\31\\504
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-6\\-128
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-8\\-126
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\6\\127
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-1131776, 8448, 8448; 8448, -48, -64; 8448, -64, -63],[256, 16, 1],[47, 16, 19, 4, -1, -1, 1; 314, 111, 138, 31, -6, -8, 6; 5952, 2024, 2400, 504, -128, -126, 127],361,2]
%
% END OF LATTICE L362.2
%
%
% LATTICE L362.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[4866304, -380672, -37632; -380672, 29776, 2944; -37632, 2944, 291],[256, 16, 1],[-3, 7, 22, 105, 95, 97, -1; -17, 42, 135, 650, 591, 608, 0; -216, 480, 1480, 7008, 6312, 6400, -128],361,3]
%
% END OF LATTICE L362.3
%
%
% LATTICE L362.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-4063488, -351488, -159744; -351488, -30384, -13808; -159744, -13808, -6275],[256, 16, 1],[-1, 9, 13, 49, 39, 4, -1; 117, -1122, -1579, -5874, -4635, -467, 127; -232, 2240, 3144, 11680, 9208, 926, -254],361,4]
%
% END OF LATTICE L362.4
%

\medskip%
%------------------------------WEYL-GROUP-W363--------------------------------
%
\leavevmode\llap{}%
$W_{363}$%
\qquad\llap{12} lattices, $\chi=72$%
\hfill%
$2|2222|2222|2222|222\rtimes D_{4}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L363.1
%
\leavevmode%
${L_{363.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{1}{}5\above{1pt}{1pt}{-}{}25\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{-2}{}11\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${4}\above{1pt}{1pt}{r}{2}{10}\above{1pt}{1pt}{l}{2}{100}\above{1pt}{1pt}{r}{2}{6}\above{1pt}{1pt}{b}{2}{1100}\above{1pt}{1pt}{*}{2}{60}\above{1pt}{1pt}{*}{2}{44}\above{1pt}{1pt}{b}{2}{150}\above{1pt}{1pt}{l}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-12035100\\19800\\13200
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
19800\\-10\\-25
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
13200\\-25\\-14
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
102299\\11130240\\76418100
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-185\\-20129\\-138195
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-110\\-11968\\-82171
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
39\\4244\\29132
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\327\\2240
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
13\\1420\\9700
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\219\\1491
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
17\\1870\\12650
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-108\\-750
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-110\\-748
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\105\\750
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-12035100, 19800, 13200; 19800, -10, -25; 13200, -25, -14],[3300, 5, 1],[39, 3, 13, 2, 17, -1, -1, 1, 1, 2, 187, 73, 1633, 181, 331, 374; 4244, 327, 1420, 219, 1870, -108, -110, 105, 108, 217, 20340, 7941, 177650, 19692, 36014, 40695; 29132, 2240, 9700, 1491, 12650, -750, -748, 750, 748, 1495, 139700, 54534, 1219900, 135210, 247258, 279375],362,1]
%
% END OF LATTICE L363.1
%
%
% LATTICE L363.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[67650, -825, 4125; -825, 10, -55; 4125, -55, -109],[825, 5, 1],[77, 19, 71, 34, 259, 14, 10, -1, -1, 0, 309, 251, 2876, 328, 617, 1426; 5909, 1459, 5455, 2613, 19910, 1077, 770, -75, -77, -1, 23705, 19257, 220660, 25167, 47344, 109425; -81, -20, -75, -36, -275, -15, -11, 0, 1, 0, -325, -264, -3025, -345, -649, -1500],362,2]
%
% END OF LATTICE L363.2
%
%
% LATTICE L363.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[3625050, 1268025, -1209450; 1268025, 443445, -423060; -1209450, -423060, 403517],[825, 15, 1],[1459, 34, -1183, -307, -9672, -318, -1281, -644, 1, 331, 8483, 2132, 69897, 2508, 13326, 9769; 4, 3, 20, 4, 110, 3, 11, 5, 0, -2, 0, 1, 55, 3, 22, 20; 4377, 105, -3525, -916, -28875, -950, -3828, -1925, 3, 990, 25425, 6391, 209550, 7520, 39963, 29300],362,3]
%
% END OF LATTICE L363.3
%
%
% LATTICE L363.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1650, 7425, -1650; 7425, 33385, -7425; -1650, -7425, 1651],[825, 55, 1],[18, 9, 46, 25, 19, 14, 1, -1, -2, -5, 34, 35, 41, 58, 11, 301; -146, -26, -70, -27, -15, -3, 0, 0, -2, -11, -670, -528, -540, -663, -111, -2775; -649, -110, -275, -99, -50, 0, 1, 0, -11, -55, -3025, -2376, -2425, -2970, -496, -12375],362,4]
%
% END OF LATTICE L363.4
%
%
% LATTICE L363.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-150813300, -303392100, -60700200; -303392100, -606533370, -121351635; -60700200, -121351635, -24279322],[3300, 15, 1],[273, -137, -108453, -14615, -1002007, -37971, -213619, -82087, -26497, -3141, -22667, -1775, -79733, -1365, -2729, 137; 72620, -36446, -28849820, -3887767, -266545950, -10100742, -56825208, -21836120, -7048516, -835541, -6029660, -472168, -21209760, -363102, -725934, 36445; -363648, 182505, 144466800, 19468172, 1334741100, 50579930, 284554842, 109345375, 35295768, 4184010, 30193800, 2364403, 106208850, 1818250, 3635148, -182500],362,5]
%
% END OF LATTICE L363.5
%
%
% LATTICE L363.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[44350805400, -39306300, 11074189500; -39306300, 34840, -9814600; 11074189500, -9814600, 2765173529],[3300, 20, 1],[49433, 15591, 18671, 13133, 73473, 412, 2049, 13933, 1435, 9843, 235669, 368377, 4123137, 457400, 837273, 1893617; 73, 26, 35, 27, 165, 3, 0, 0, 1, 11, 335, 528, 5940, 663, 1221, 2775; -197973, -62440, -74775, -52596, -294250, -1650, -8206, -55800, -5747, -39420, -943825, -1475304, -16512650, -1831830, -3353174, -7583700],362,6]
%
% END OF LATTICE L363.6
%
%
% LATTICE L363.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-594825, 22275, 198825; 22275, -330, -7425; 198825, -7425, -66458],[825, 165, 1],[-11629, -2306, -6863, -948, -1697, -183, 1, 366, -11, -604, -51337, -13602, -41953, -17277, -8731, -73116; 1423, 283, 845, 117, 210, 23, 0, -45, 1, 73, 6275, 1663, 5130, 2113, 1068, 8945; -34947, -6930, -20625, -2849, -5100, -550, 3, 1100, -33, -1815, -154275, -40876, -126075, -51920, -26238, -219725],362,7]
%
% END OF LATTICE L363.7
%
%
% LATTICE L363.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[441021900, 273900, -270600; 273900, -110, -165; -270600, -165, 166],[3300, 55, 1],[629, 53, 263, 47, 47, -1, -1, 1, 11, 27, 2937, 1153, 2353, 2881, 481, 5999; 11236, 947, 4700, 840, 840, -18, -18, 15, 196, 482, 52460, 20595, 42030, 51462, 8592, 107160; 1036552, 87340, 433400, 77451, 77450, -1650, -1648, 1650, 18128, 44495, 4840000, 1900074, 3877600, 4747710, 792658, 9885975],362,8]
%
% END OF LATTICE L363.8
%
%
% LATTICE L363.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[31730410086889800, 114864506991300, 7923016033152000; 114864506991300, 415811044680, 28681423531560; 7923016033152000, 28681423531560, 1978360282444643],[3300, 60, 1],[617, 70544, 4071067, 2169915, 73885591, 2777985, 15509518, 11848302, 947377, 403453, 668903, 200070, 4323914, 65997, 132383, 1623; -137, -14997, -855055, -455662, -15513410, -583197, -3255527, -2486735, -198801, -84472, -139635, -41683, -898975, -13617, -26950, 10; -2469, -282300, -16291575, -8683556, -295675050, -11116930, -62065938, -47414500, -3791211, -1614540, -2676825, -800644, -17303550, -264110, -529782, -6500],362,9]
%
% END OF LATTICE L363.9
%
%
% LATTICE L363.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-4168160700, 831689100, 3187800; 831689100, -165950070, -636075; 3187800, -636075, -2438],[3300, 165, 1],[-5591, -566, -3469, -245, -901, -113, -7, 74, -1, -133, -24491, -3250, -20069, -8275, -4187, -17549; -23812, -2411, -14780, -1044, -3840, -482, -30, 315, -4, -566, -104300, -13841, -85470, -35242, -17832, -74740; -1097976, -111045, -679800, -47971, -176250, -22000, -1326, 14575, -264, -26235, -4811400, -638429, -3942150, -1625360, -822354, -3446575],362,10]
%
% END OF LATTICE L363.10
%
%
% LATTICE L363.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1844020061400, -1345452900, 460444861800; -1345452900, 981640, -335954520; 460444861800, -335954520, 114971347219],[3300, 220, 1],[663601, 164415, 121471, 33718, -16842, -66991, 411, 338663, 31853, 183312, 3355799, 5182187, 5232747, 6326077, 1042770, 25740862; 73, 26, 35, 27, 15, 3, 0, 0, 1, 11, 335, 528, 540, 663, 111, 2775; -2657633, -658460, -486475, -135036, 67450, 268290, -1646, -1356300, -127567, -734140, -13439525, -20753964, -20956450, -25335090, -4176154, -103088700],362,11]
%
% END OF LATTICE L363.11
%
%
% LATTICE L363.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[955578142200, -4216835700, 238598962800; -4216835700, 18610680, -1052904600; 238598962800, -1052904600, 59575938937],[3300, 660, 1],[7609109, 3165137, 5094979, 1494258, 2875562, 446469, 71057, -89541, 10885, 644860, 33004991, 17555727, 54274393, 22413513, 11358934, 95339466; 36959, 15373, 24745, 7257, 13965, 2168, 345, -435, 53, 3133, 160315, 85273, 263625, 108868, 55173, 463085; -30473487, -12675960, -20404725, -5984308, -11516250, -1788050, -284574, 358600, -43593, -2582580, -132180675, -70308392, -217361850, -89763190, -45491046, -381822100],362,12]
%
% END OF LATTICE L363.12
%

\medskip%
%------------------------------WEYL-GROUP-W364--------------------------------
%
\leavevmode\llap{}%
$W_{364}$%
\qquad\llap{4} lattices, $\chi=32$%
\hfill%
$2622|2262|\rtimes D_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L364.1
%
\leavevmode%
${L_{364.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}32\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{-}{}9\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{-}{}$}\EasyButWeakLineBreak%
{${96}\above{1pt}{1pt}{b}{2}{18}\above{1pt}{1pt}{}{6}{6}\above{1pt}{1pt}{b}{2}{2}\above{1pt}{1pt}{l}{2}{96}\above{1pt}{1pt}{r}{2}{18}\above{1pt}{1pt}{b}{2}{6}\above{1pt}{1pt}{}{6}{2}\above{1pt}{1pt}{b}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3627360\\-1248480\\-642240
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1248480\\429018\\202803
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-642240\\202803\\-369406
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-52331\\-155056\\5856
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-20911\\-61959\\2340
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
24423\\72365\\-2733
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
37202\\110229\\-4163
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
645133\\1911520\\-72192
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
167369\\495912\\-18729
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
80186\\237590\\-8973
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
30205\\89497\\-3380
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[3627360, -1248480, -642240; -1248480, 429018, 202803; -642240, 202803, -369406],[1440, 3, 1],[-52331, -20911, 24423, 37202, 645133, 167369, 80186, 30205; -155056, -61959, 72365, 110229, 1911520, 495912, 237590, 89497; 5856, 2340, -2733, -4163, -72192, -18729, -8973, -3380],363,1]
%
% END OF LATTICE L364.1
%
%
% LATTICE L364.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-663840, 191520, 120960; 191520, -55230, -35085; 120960, -35085, -20582],[1440, 15, 1],[1163, 437, -545, -812, -13965, -3601, -1710, -631; 3728, 1401, -1747, -2603, -44768, -11544, -5482, -2023; 480, 180, -225, -335, -5760, -1485, -705, -260],363,2]
%
% END OF LATTICE L364.2
%
%
% LATTICE L364.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-4565551680, 760926240, -154524960; 760926240, -126821184, 25754208; -154524960, 25754208, -5230013],[1440, 96, 1],[-622, -23962, -9995, -4001, -813, -1, 2007, 14; -3085, -118857, -49579, -19847, -4033, -6, 9956, 71; 3186, 122688, 51168, 20480, 4161, 0, -10272, -64],363,3]
%
% END OF LATTICE L364.3
%
%
% LATTICE L364.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2880, -1440, 0; -1440, -155576640, 966240; 0, 966240, -6001],[1440, 480, 1],[25, 953, 396, 158, 32, -1, -79, 1; 49, 1887, 787, 315, 64, 0, -158, -1; 7890, 303840, 126720, 50720, 10305, 0, -25440, -160],363,4]
%
% END OF LATTICE L364.4
%

\medskip%
%------------------------------WEYL-GROUP-W365--------------------------------
%
\leavevmode\llap{}%
$W_{365}$%
\qquad\llap{12} lattices, $\chi=144$%
\hfill%
$2\slashtwo222|222\slashtwo222|222\slashtwo222|222\slashtwo222|22\rtimes D_{8}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L365.1
%
\leavevmode%
${L_{365.1}}$%
{} : {$1\above{1pt}{1pt}{2}{2}32\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{-}{}9\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-}{}5\above{1pt}{1pt}{1}{}25\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{5,3}%
\EasyButWeakLineBreak%
{${800}\above{1pt}{1pt}{r}{2}{18}\above{1pt}{1pt}{b}{2}{50}\above{1pt}{1pt}{l}{2}{288}\above{1pt}{1pt}{}{2}{5}\above{1pt}{1pt}{r}{2}{7200}\above{1pt}{1pt}{s}{2}{20}\above{1pt}{1pt}{*}{2}{288}\above{1pt}{1pt}{b}{2}{50}\above{1pt}{1pt}{s}{2}{18}\above{1pt}{1pt}{b}{2}{800}\above{1pt}{1pt}{*}{2}{180}\above{1pt}{1pt}{s}{2}{32}\above{1pt}{1pt}{l}{2}{45}\above{1pt}{1pt}{}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
shares genus with 3-dual${}\iso{}$5-dual; isometric to own %
3.5-dual\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1635199200\\-331164000\\410400
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-331164000\\-67068030\\83115
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
410400\\83115\\-103
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2864431\\15128640\\794253600
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-580199\\3064351\\160878480
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
721\\-3808\\-199921
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3121\\16480\\862400
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-313\\1653\\86688
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-514\\2715\\142750
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1799\\9504\\500832
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-95\\502\\26545
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2497\\13200\\702000
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-135\\714\\38230
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1007\\5328\\286848
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-239\\1265\\68450
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-115\\609\\33192
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-921\\4880\\268000
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-121\\642\\35910
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-15\\80\\4784
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\6\\855
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-1635199200, -331164000, 410400; -331164000, -67068030, 83115; 410400, 83115, -103],[7200, 15, 1],[-3121, -313, -514, -1799, -95, -2497, -135, -1007, -239, -115, -921, -121, -15, -1, 31, 4, -1, -55, -8, -593, -71, -847, -276, -194, -2169, -497, -191, -308; 16480, 1653, 2715, 9504, 502, 13200, 714, 5328, 1265, 609, 4880, 642, 80, 6, -160, -21, 5, 288, 42, 3120, 374, 4464, 1455, 1023, 11440, 2622, 1008, 1626; 862400, 86688, 142750, 500832, 26545, 702000, 38230, 286848, 68450, 33192, 268000, 35910, 4784, 855, -5600, -1008, 50, 13248, 2015, 154800, 18890, 227232, 74350, 52488, 588800, 135450, 52336, 84825],364,1]
%
% END OF LATTICE L365.1
%
%
% LATTICE L365.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-3034080, 37440, -18720; 37440, -462, 231; -18720, 231, -115],[1440, 3, 1],[509, 29, 88, 175, 86, 53, 137, 119, 53, 15, 229, 19, 31, 2, 13, 0, -1, -1, 1, 5, 37, 55, 34, 14, 293, 39, 143, 27; 39264, 2239, 6801, 13536, 6660, 4112, 10650, 9264, 4131, 1171, 17904, 1490, 2448, 160, 1056, 1, -81, -96, 60, 368, 2790, 4176, 2589, 1069, 22416, 2990, 10992, 2080; -4320, -242, -720, -1408, -675, -400, -990, -832, -360, -98, -1440, -110, -144, -5, 0, 2, 0, -32, -45, -80, -450, -608, -360, -142, -2880, -370, -1296, -235],364,2]
%
% END OF LATTICE L365.2
%
%
% LATTICE L365.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[103200, 40800, -2400; 40800, 16130, -955; -2400, -955, -107],[2400, 5, 1],[-68017, -2284, -11313, -13261, -2116, -18763, -3087, -7765, -5588, -910, -22217, -1011, -431, -40, 127, 21, -2, -317, -147, -3867, -1439, -5813, -5727, -1353, -45673, -3515, -4095, -2223; 171680, 5765, 28555, 33472, 5341, 47360, 7792, 19600, 14105, 2297, 56080, 2552, 1088, 101, -320, -53, 5, 800, 371, 9760, 3632, 14672, 14455, 3415, 115280, 8872, 10336, 5611; -7200, -242, -1200, -1408, -225, -2000, -330, -832, -600, -98, -2400, -110, -48, -5, 0, 2, 0, -32, -15, -400, -150, -608, -600, -142, -4800, -370, -432, -235],364,3]
%
% END OF LATTICE L365.3
%
%
% LATTICE L365.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1936800, 1440, -1440; 1440, -15, 0; -1440, 0, 1],[1440, 15, 1],[-271, -15, -44, -85, -8, -23, -11, -45, -19, -5, -71, -1, -5, 0, 1, 0, -1, -5, -1, -7, -7, -45, -26, -10, -199, -5, -85, -3; -23136, -1281, -3759, -7264, -684, -1968, -942, -3856, -1629, -429, -6096, -86, -432, 0, 96, 1, -81, -416, -84, -592, -594, -3824, -2211, -851, -16944, -426, -7248, -256; -385920, -21365, -62685, -121120, -11403, -32800, -15696, -64240, -27135, -7145, -101520, -1432, -7200, -1, 1440, 5, -1395, -7040, -1413, -9920, -9936, -63920, -36945, -14215, -282960, -7112, -120960, -4271],364,4]
%
% END OF LATTICE L365.4
%
%
% LATTICE L365.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-609885600, -110505600, 765600; -110505600, -20022585, 138720; 765600, 138720, -961],[2400, 15, 1],[61, 16, -1, -247, -115, -3041, -1135, -4591, -4526, -1070, -36139, -2783, -3245, -1763, -53971, -1813, -8984, -10535, -1682, -14929, -2459, -6191, -4459, -727, -17771, -811, -349, -34; -320, -85, 5, 1312, 611, 16160, 6032, 24400, 24055, 5687, 192080, 14792, 17248, 9371, 286880, 9637, 47755, 56000, 8941, 79360, 13072, 32912, 23705, 3865, 94480, 4312, 1856, 181; 2400, 477, -75, -7392, -3420, -90000, -33510, -135408, -133425, -31527, -1064400, -81930, -95472, -51840, -1586400, -53277, -263925, -309408, -49380, -438000, -72090, -181392, -130575, -21273, -519600, -23670, -10128, -960],364,5]
%
% END OF LATTICE L365.5
%
%
% LATTICE L365.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[7200, 0, -7200; 0, -30, -465; -7200, -465, -7],[7200, 15, 1],[-6521, -89, -1639, -759, -905, -1833, -620, -1295, -3314, -223, -19921, -217, -1199, -343, -13369, -132, -1676, -567, -421, -377, -43, -31, -1, 2, 31, -4, -127, -99; 101040, 1379, 25395, 11760, 14022, 28400, 9606, 20064, 51345, 3455, 308640, 3362, 18576, 5314, 207120, 2045, 25965, 8784, 6522, 5840, 666, 480, 15, -31, -480, 62, 1968, 1534; -7200, -98, -1800, -832, -990, -2000, -675, -1408, -3600, -242, -21600, -235, -1296, -370, -14400, -142, -1800, -608, -450, -400, -45, -32, 0, 2, 0, -5, -144, -110],364,6]
%
% END OF LATTICE L365.6
%
%
% LATTICE L365.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-14362560, -1268640, 442080; -1268640, -111840, 38976; 442080, 38976, -13583],[1440, 96, 1],[80, 145, 437, 27, 421, 16, 326, 35, 247, 69, 65, 42, 8, 7, 1, -1, -5, 0, 11, 2, 106, 19, 185, 75, 97, 102, 46, 137; 18876, 34234, 103248, 6383, 99615, 3791, 77355, 8314, 58728, 16426, 15492, 10035, 1923, 1705, 249, -234, -1248, -8, 2385, 459, 24645, 4436, 43272, 17574, 22758, 23965, 10827, 32295; 56763, 102944, 310464, 19193, 299520, 11398, 232560, 24994, 176544, 49376, 46566, 30160, 5778, 5120, 747, -704, -3744, -23, 7200, 1382, 74160, 13346, 130176, 52864, 68454, 72080, 32562, 97120],364,7]
%
% END OF LATTICE L365.7
%
%
% LATTICE L365.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-66206400, 13725600, -88800; 13725600, -2844640, 18400; -88800, 18400, -119],[2400, 160, 1],[1, -1, -3, -2, 1, 2, 42, 119, 79, 491, 43, 138, 106, 193, 38, 1041, 211, 197, 207, 24, 166, 271, 129, 549, 35, 70, 24, 15; 12, -10, -36, -25, 9, 23, 489, 1390, 924, 5750, 504, 1619, 1245, 2269, 447, 12250, 2484, 2320, 2439, 283, 1959, 3200, 1524, 6490, 414, 829, 285, 179; 1109, -800, -3328, -2375, 640, 2062, 44240, 126050, 83872, 522400, 45818, 147280, 113350, 206720, 40741, 1116800, 226528, 211625, 222560, 25838, 178960, 292450, 139328, 593600, 37882, 75920, 26150, 16480],364,8]
%
% END OF LATTICE L365.8
%
%
% LATTICE L365.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-7462080, 166649760, -1048320; 166649760, -3719555040, 23398080; -1048320, 23398080, -147187],[1440, 480, 1],[-46, -79, -223, -13, -37, -6, -20, -9, -53, -11, -7, 0, 2, 1, 1, -1, -17, -2, -11, -4, -28, -21, -187, -69, -83, -16, -32, -17; 14760, 25678, 73680, 4361, 12729, 2165, 7725, 3718, 23640, 5662, 4500, 357, -159, -193, -225, 162, 3840, 484, 2775, 1065, 7779, 5972, 53880, 20178, 24570, 4811, 9849, 5361; 2346705, 4082560, 11714400, 693355, 2023776, 344210, 1228176, 591110, 3758400, 900160, 715410, 56752, -25290, -30688, -35775, 25760, 610560, 76955, 441216, 169330, 1236816, 949510, 8566560, 3208160, 3906450, 764912, 1565910, 852352],364,9]
%
% END OF LATTICE L365.9
%
%
% LATTICE L365.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[4800, -2400, 0; -2400, -8533920, -5671680; 0, -5671680, -3768893],[2400, 480, 1],[-75379, -35999, -153851, -9847, -19850, -6926, -4465, -308, -1, 925, 773, 161, -460, -10598, -30731, -20593, -129109, -11375, -36742, -28444, -52127, -10303, -282959, -57517, -53828, -56753, -6614, -45994; -150810, -72022, -307800, -19700, -39711, -13855, -8931, -616, 0, 1850, 1545, 319, -921, -21211, -61500, -41210, -258360, -22762, -73521, -56915, -104301, -20615, -566160, -115082, -107700, -113551, -13233, -92021; 226950, 108384, 463200, 29646, 59760, 20850, 13440, 927, 0, -2784, -2325, -480, 1386, 31920, 92550, 62016, 388800, 34254, 110640, 85650, 156960, 31023, 852000, 173184, 162075, 170880, 19914, 138480],364,10]
%
% END OF LATTICE L365.10
%
%
% LATTICE L365.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-654098400, -21038400, -6883200; -21038400, -670560, -219360; -6883200, -219360, -71759],[7200, 480, 1],[-2, -5, -1, 1, 5, 22, 20, 29, 149, 103, 71, 128, 6, 151, 47, 149, 241, 26, 43, 68, 28, 25, 91, 41, 19, 16, 0, -7; 4340, 10803, 2125, -2160, -10782, -47355, -42997, -62307, -320025, -221145, -152395, -274641, -12867, -323646, -100700, -319155, -516045, -55656, -92002, -145365, -59787, -53325, -193895, -87207, -40325, -33711, 19, 15294; -13075, -32544, -6400, 6507, 32480, 142650, 129520, 187686, 964000, 666144, 459050, 827280, 38758, 974880, 303325, 961344, 1554400, 167643, 277120, 437850, 180080, 160614, 584000, 262656, 121450, 101520, -58, -46080],364,11]
%
% END OF LATTICE L365.11
%
%
% LATTICE L365.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[14400, -7200, 0; -7200, -11775840, 37440; 0, 37440, -119],[7200, 480, 1],[761, 121, 1549, 33, 199, 23, 44, 1, -1, -3, -7, 0, 5, 37, 319, 71, 1331, 39, 377, 97, 532, 35, 2881, 195, 547, 192, 67, 155; 1470, 234, 3000, 64, 387, 45, 87, 2, 0, -6, -15, -1, 9, 69, 600, 134, 2520, 74, 717, 185, 1017, 67, 5520, 374, 1050, 369, 129, 299; 462150, 73568, 943200, 20122, 121680, 14150, 27360, 629, 0, -1888, -4725, -320, 2826, 21680, 188550, 42112, 792000, 23258, 225360, 58150, 319680, 21061, 1735200, 117568, 330075, 116000, 40554, 94000],364,12]
%
% END OF LATTICE L365.12
%

\medskip%
%------------------------------WEYL-GROUP-W366--------------------------------
%
\leavevmode\llap{}%
$W_{366}$%
\qquad\llap{8} lattices, $\chi=84$%
\hfill%
$\infty\infty\infty222\infty\infty\infty222\rtimes C_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L366.1
%
\leavevmode%
${L_{366.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}8\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{-}{}13\above{1pt}{1pt}{-}{}169\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{2*}%
\EasyButWeakLineBreak%
{${26}\above{1pt}{1pt}{52,25}{\infty a}{104}\above{1pt}{1pt}{26,9}{\infty z}{26}\above{1pt}{1pt}{52,17}{\infty a}{104}\above{1pt}{1pt}{b}{2}{338}\above{1pt}{1pt}{l}{2}{8}\above{1pt}{1pt}{r}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
shares genus with 13-dual\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3081208\\28392\\-163592
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
28392\\-234\\1573
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-163592\\1573\\-8530
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-192193\\-6090240\\2563392
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1463\\46359\\-19513
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-10934\\-346480\\145833
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-272\\-8626\\3627
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-581\\-18420\\7748
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-193\\-6117\\2574
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1579\\-50036\\21060
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1077\\-34125\\14365
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-529\\-16760\\7056
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-3081208, 28392, -163592; 28392, -234, 1573; -163592, 1573, -8530],[1352, 13, 1],[-272, -581, -193, -1579, -1077, -529, -960, -959, -38, 39, 76, -87; -8626, -18420, -6117, -50036, -34125, -16760, -30414, -30380, -1203, 1236, 2405, -2760; 3627, 7748, 2574, 21060, 14365, 7056, 12805, 12792, 507, -520, -1014, 1160],365,1]
%
% END OF LATTICE L366.1
%
%
% LATTICE L366.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-52390, 4056, 24336; 4056, -312, -1885; 24336, -1885, -11304],[338, 13, 1],[482, 225, 7, -13, -1, 47, 254, 235, 131, 473, 599, 137; 519, 248, 12, -12, -13, 42, 233, 222, 129, 482, 624, 146; 949, 442, 13, -26, 0, 94, 507, 468, 260, 936, 1183, 270],365,2]
%
% END OF LATTICE L366.2
%
%
% LATTICE L366.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[338, 0, 0; 0, -78, -13; 0, -13, -2],[338, 13, 1],[32, 19, 4, 5, 0, -1, 0, 1, 2, 15, 2, 105; -258, -158, -37, -54, -1, 0, 2, -2, -11, -106, -15, -832; 1053, 650, 156, 234, 5, 0, -13, 0, 39, 416, 60, 3380],365,3]
%
% END OF LATTICE L366.3
%
%
% LATTICE L366.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[343408, 4394, 170690; 4394, 52, 2184; 170690, 2184, 84841],[338, 26, 1],[-6624, -1973, -841, -537, -3, 84, 0, -97, -401, -1533, -411, -10848; 495, 149, 66, 45, 1, 0, 1, 6, 27, 110, 30, 806; 13312, 3965, 1690, 1079, 6, -169, 0, 195, 806, 3081, 826, 21801],365,4]
%
% END OF LATTICE L366.4
%
%
% LATTICE L366.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[676, 338, 338; 338, 1872, 312; 338, 312, 181],[338, 26, 1],[1731, 424, 60, 6, -1, 69, 749, 351, 405, 769, 2016, 241; 323, 79, 11, 1, 0, 13, 141, 66, 76, 144, 377, 45; -3770, -923, -130, -13, 0, -151, -1638, -767, -884, -1677, -4394, -525],365,5]
%
% END OF LATTICE L366.5
%
%
% LATTICE L366.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-31096, 2704, 1352; 2704, -234, -117; 1352, -117, -58],[1352, 13, 1],[10, 9, 0, -1, 0, 29, 6, 11, 3, 21, 1, 75; 201, 196, 6, -12, -1, 312, 71, 144, 45, 352, 18, 1456; -195, -208, -13, 0, 2, 0, -13, -52, -26, -260, -15, -1352],365,6]
%
% END OF LATTICE L366.6
%
%
% LATTICE L366.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-51789712, 193336, -3955952; 193336, -624, 14768; -3955952, 14768, -302175],[1352, 104, 1],[143, -284, -1565, -6548, -1796, -24205, -29759, -8971, -3988, -2707, -55, 142; 2, -1, -11, -53, -15, -208, -258, -79, -37, -27, -1, 0; -1872, 3718, 20488, 85722, 23512, 316875, 389584, 117442, 52208, 35438, 720, -1859],365,7]
%
% END OF LATTICE L366.7
%
%
% LATTICE L366.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-4933515600, 1826552, 3651752; 1826552, -624, -1352; 3651752, -1352, -2703],[1352, 104, 1],[-1, 26, 107, 406, 1412, 110, 1745, 519, 220, 139, 5, -1; 2, -1, -11, -53, -195, -16, -258, -79, -37, -27, -13, 0; -1352, 35126, 144560, 548522, 1907672, 148615, 2357576, 701194, 297232, 187798, 6760, -1351],365,8]
%
% END OF LATTICE L366.8
%

\medskip%
%------------------------------WEYL-GROUP-W367--------------------------------
%
\leavevmode\llap{}%
$W_{367}$%
\qquad\llap{12} lattices, $\chi=48$%
\hfill%
$222|222|222|222|\rtimes D_{4}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L367.1
%
\leavevmode%
${L_{367.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}4\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-}{}7\above{1pt}{1pt}{-}{}49\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${84}\above{1pt}{1pt}{r}{2}{10}\above{1pt}{1pt}{b}{2}{588}\above{1pt}{1pt}{*}{2}{140}\above{1pt}{1pt}{*}{2}{12}\above{1pt}{1pt}{b}{2}{490}\above{1pt}{1pt}{l}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-38634540\\-1073100\\8820
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1073100\\-29806\\245
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
8820\\245\\-2
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-14280\\-1899240
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\-398\\-52801
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\3\\398
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\36\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\35\\-130
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-11\\378\\-2352
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-3\\100\\-1050
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\30\\-792
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2\\35\\-4900
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-38634540, -1073100, 8820; -1073100, -29806, 245; 8820, 245, -2],[2940, 7, 1],[-1, -1, -11, -3, -1, -2, 1, 1, 11, 3, 1, 2; 36, 35, 378, 100, 30, 35, -48, -40, -420, -110, -36, -70; 0, -130, -2352, -1050, -792, -4900, -1596, -535, -3234, -280, -6, 245],366,1]
%
% END OF LATTICE L367.1
%
%
% LATTICE L367.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[3670590, 22785, -21315; 22785, 119, -126; -21315, -126, 122],[735, 7, 1],[-8, -69, -7, -13, -41, -7, -4, -1, 1, 3, -1, -3; -573, -4900, -495, -915, -2877, -490, -279, -70, 69, 205, -105, -220; -1995, -17150, -1737, -3220, -10143, -1730, -987, -245, 246, 735, -294, -755],366,2]
%
% END OF LATTICE L367.2
%
%
% LATTICE L367.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2812659045, -22885695, -941426955; -22885695, 186207, 7660086; -941426955, 7660086, 315105634],[735, 21, 1],[11256, 208379, 5627, 22423, 16549, 5297, -164, -14269, -81, 5307, 22273, 22433; 43, 805, 22, 90, 70, 25, 1, -35, 0, 20, 84, 85; 33628, 622545, 16811, 66990, 49441, 15825, -490, -42630, -242, 15855, 66542, 67020],366,3]
%
% END OF LATTICE L367.3
%
%
% LATTICE L367.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1659960015, -22697535, -666289260; -22697535, 310345, 9110535; -666289260, 9110535, 267441007],[735, 35, 1],[39956, 49310, 19972, 5305, 58712, 1252, -590, -3383, -289, 1256, 79069, 5309; 129, 161, 66, 18, 210, 5, 3, -7, 0, 4, 252, 17; 99540, 122843, 49755, 13216, 146265, 3119, -1470, -8428, -720, 3129, 196980, 13226],366,4]
%
% END OF LATTICE L367.4
%
%
% LATTICE L367.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-148831620, -4139520, 5880; -4139520, -115122, 147; 5880, 147, 22],[2940, 21, 1],[-523, -524, -1051, -267, -1, 247, -1, -131, -783, -1043, -261, -4832; 18824, 18860, 37828, 9610, 36, -8890, 36, 4715, 28182, 37540, 9394, 173915; 14000, 14025, 28126, 7140, 26, -6615, 28, 3510, 20972, 27930, 6988, 129360],366,5]
%
% END OF LATTICE L367.5
%
%
% LATTICE L367.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[5196948330, 3325140, -1697690505; 3325140, 1785, -1086225; -1697690505, -1086225, 554585666],[735, 105, 1],[-31945, -164758, -27811, -30932, -162389, -16618, -15801, -2353, 3938, 7059, -4722, -7255; -191, -980, -165, -183, -959, -98, -93, -14, 23, 41, -35, -44; -97790, -504357, -85135, -94689, -497105, -50871, -48370, -7203, 12055, 21609, -14455, -22209],366,6]
%
% END OF LATTICE L367.6
%
%
% LATTICE L367.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[247036440, 661500, -61845840; 661500, 4984, -165620; -61845840, -165620, 15483173],[2940, 28, 1],[184, -17649, -174653, -83466, -68023, -877313, -75193, -107366, -350410, -41549, -6986, 2208; 3, -280, -2772, -1325, -1080, -13930, -1194, -1705, -5565, -660, -111, 35; 735, -70500, -697662, -333410, -271722, -3504480, -300363, -428880, -1399734, -165970, -27906, 8820],366,7]
%
% END OF LATTICE L367.7
%
%
% LATTICE L367.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-6470940, 179340, -79380; 179340, -4970, 2205; -79380, 2205, -902],[2940, 35, 1],[839, 57, 1753, 33, 11, -20, 1, 13, 1187, 107, 409, 510; 29352, 1994, 61320, 1154, 384, -700, 36, 455, 41538, 3744, 14310, 17843; -2100, -143, -4410, -84, -30, 49, 0, -32, -2940, -266, -1020, -1274],366,8]
%
% END OF LATTICE L367.8
%
%
% LATTICE L367.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[84707168280, -2829864660, -21201859980; -2829864660, 94539144, 708303624; -21201859980, 708303624, 5306739391],[2940, 84, 1],[-66820, -278358, -294228, -95417, -4792, 6624, -1649, -63987, -185055, -246928, -63677, -2403039; -352, -1465, -1547, -500, -25, 35, -9, -340, -980, -1305, -336, -12670; -266917, -1111920, -1175314, -381150, -19142, 26460, -6587, -255600, -739214, -986370, -254362, -9599100],366,9]
%
% END OF LATTICE L367.9
%
%
% LATTICE L367.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-2359770420, -338017680, -2460780; -338017680, -48418230, -352485; -2460780, -352485, -2566],[2940, 105, 1],[-1, -45, -1371, -371, -473, -1770, -971, -198, -2031, -115, -13, 69; 8, 347, 10570, 2860, 3646, 13643, 7484, 1526, 15652, 886, 100, -532; -140, -4512, -137200, -37086, -47240, -176694, -96880, -19743, -202370, -11424, -1270, 6909],366,10]
%
% END OF LATTICE L367.10
%
%
% LATTICE L367.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[330497160, 85486380, -82666920; 85486380, 22114120, -21382620; -82666920, -21382620, 20677393],[2940, 140, 1],[101957, 29064, 472856, 11071, 8764, -2306, -920, 4615, 234403, 22608, 92273, 238059; -312, -89, -1449, -34, -27, 7, 3, -14, -714, -69, -282, -728; 407295, 116104, 1888950, 44226, 35010, -9212, -3675, 18436, 936390, 90314, 368610, 950992],366,11]
%
% END OF LATTICE L367.11
%
%
% LATTICE L367.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[290647712040, 3331411020, -72764902980; 3331411020, 38187240, -834033060; -72764902980, -834033060, 18217005971],[2940, 420, 1],[8683, 144117, 2185049, 596798, 778611, 5906661, 824990, 689556, 3650662, 236875, 55062, -70950; 47, 782, 11858, 3239, 4226, 32060, 4478, 3743, 19817, 1286, 299, -385; 34685, 575688, 8728370, 2383962, 3110230, 23594676, 3295495, 2754492, 14582890, 946218, 219950, -283416],366,12]
%
% END OF LATTICE L367.12
%

\medskip%
%------------------------------WEYL-GROUP-W368--------------------------------
%
\leavevmode\llap{}%
$W_{368}$%
\qquad\llap{16} lattices, $\chi=36$%
\hfill%
$2222|22222|2\rtimes D_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L368.1
%
\leavevmode%
${L_{368.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}8\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-}{}5\above{1pt}{1pt}{-}{}25\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{2}{}7\above{1pt}{1pt}{-}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${168}\above{1pt}{1pt}{r}{2}{50}\above{1pt}{1pt}{b}{2}{8}\above{1pt}{1pt}{b}{2}{1050}\above{1pt}{1pt}{l}{2}{40}\above{1pt}{1pt}{r}{2}{42}\above{1pt}{1pt}{b}{2}{200}\above{1pt}{1pt}{b}{2}{2}\above{1pt}{1pt}{l}{2}{4200}\above{1pt}{1pt}{r}{2}{10}\above{1pt}{1pt}{l}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-509338200\\97032600\\483000
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
97032600\\-18485410\\-92015
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
483000\\-92015\\-458
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
257\\1344\\1008
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\5\\50
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-13\\-68\\-48
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-61\\-315\\-1050
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
41\\216\\-160
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
104\\546\\-21
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
267\\1400\\300
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
50\\262\\91
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
5933\\31080\\12600
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
30\\157\\95
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-509338200, 97032600, 483000; 97032600, -18485410, -92015; 483000, -92015, -458],[4200, 5, 1],[257, 1, -13, -61, 41, 104, 267, 50, 5933, 30; 1344, 5, -68, -315, 216, 546, 1400, 262, 31080, 157; 1008, 50, -48, -1050, -160, -21, 300, 91, 12600, 95],367,1]
%
% END OF LATTICE L368.1
%
%
% LATTICE L368.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-533671950, 166950, 1003800; 166950, -40, -315; 1003800, -315, -1888],[1050, 5, 1],[1621, 28, 79, 68, 17, 11, -3, -1, 61, 15; 67830, 1171, 3300, 2835, 706, 420, -126, -40, 2562, 629; 850500, 14691, 41450, 35679, 8920, 5775, -1574, -525, 32004, 7870],367,2]
%
% END OF LATTICE L368.2
%
%
% LATTICE L368.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[679955883600, -520263450, 339327886800; -520263450, 398080, -259634340; 339327886800, -259634340, 169339537369],[1050, 10, 1],[6491003, 243781, 407432, 899429, 164173, 1654256, 261, 524, 161045, 80391; 525, 19, 30, 63, 11, 105, 0, 5, 21, 8; -13006875, -488496, -816425, -1802304, -328975, -3314850, -523, -1050, -322707, -161090],367,3]
%
% END OF LATTICE L368.3
%
%
% LATTICE L368.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[451571004150, -519268050, -150956208900; -519268050, 597120, 173586735; -150956208900, 173586735, 50463330896],[1050, 15, 1],[-2893223, -162990, -544811, -200450, -219529, -368673, -349, -351, -71783, -53749; 350, 19, 60, 21, 22, 35, 0, 5, 14, 8; -8654800, -487569, -1629750, -599627, -656700, -1102850, -1044, -1050, -214732, -160785],367,4]
%
% END OF LATTICE L368.4
%
%
% LATTICE L368.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-10649718718800, -57767850, -5294255721300; -57767850, -240, -28717920; -5294255721300, -28717920, -2631913985957],[1050, 30, 1],[24381723, 2526927, 3564806, 2045657, 767143, 331111, -135368, -90303, 917475, 1353680; 11305, 1171, 1650, 945, 353, 140, -63, -40, 427, 629; -49045325, -5083068, -7170825, -4114964, -1543155, -666050, 272301, 181650, -1845557, -2723010],367,5]
%
% END OF LATTICE L368.5
%
%
% LATTICE L368.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[101122350, -7175700, -114450; -7175700, 509180, 8155; -114450, 8155, 34],[1050, 35, 1],[6313, 716, 1709, 140, -13, -517, -145, -71, 289, 505; 88470, 10034, 23950, 1962, -182, -7245, -2032, -995, 4050, 7077; 31050, 3521, 8400, 687, -70, -2550, -714, -350, 1422, 2485],367,6]
%
% END OF LATTICE L368.6
%
%
% LATTICE L368.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-15443400, -12427800, -2045400; -12427800, -9995730, -1644945; -2045400, -1644945, -270694],[4200, 15, 1],[12053, 260, 841, -26, -477, -1026, -139, 148, 977, 275; -88480, -1909, -6180, 189, 3496, 7525, 1020, -1085, -7168, -2018; 446600, 9636, 31200, -952, -17640, -37975, -5148, 5475, 36176, 10185],367,7]
%
% END OF LATTICE L368.7
%
%
% LATTICE L368.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[6305319300, -2015167350, 3142546050; -2015167350, 644042840, -1004351390; 3142546050, -1004351390, 1566232447],[1050, 70, 1],[609968, 173708, 322694, 110096, 149496, 229061, 255, -95717, -6574, 24977; 2475, 705, 1310, 447, 607, 930, 1, -390, -27, 101; -1222275, -348082, -646625, -220614, -299565, -459000, -511, 191800, 13173, -50050],367,8]
%
% END OF LATTICE L368.8
%
%
% LATTICE L368.9
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1819491450, -1325801400, -610933050; -1325801400, 966064260, 445166085; -610933050, 445166085, 205133798],[1050, 105, 1],[-271763, -116099, -431387, -24531, -199863, -51038, -337, 64058, 2941, -16673; 1650, 705, 2620, 149, 1214, 310, 2, -390, -18, 101; -812950, -347298, -1290450, -73382, -597870, -152675, -1008, 191625, 8798, -49875],367,9]
%
% END OF LATTICE L368.9
%
%
% LATTICE L368.10
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[41861400, -14536200, 37800; -14536200, 5047630, -13125; 37800, -13125, 34],[4200, 35, 1],[41, 12, -15, -46, -49, -1, 89, 27, 533, 28; 120, 35, -44, -135, -144, -3, 260, 79, 1560, 82; 744, 175, -308, -975, -1120, -48, 1400, 476, 9600, 525],367,10]
%
% END OF LATTICE L368.10
%
%
% LATTICE L368.11
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-495600, -323400, 16800; -323400, -151120, 7960; 16800, 7960, -419],[4200, 40, 1],[10, -1, -1, 11, 3, 47, 27, 19, 274, 10; 420, -40, -42, 420, 124, 1953, 1125, 793, 11445, 419; 8379, -800, -838, 8400, 2475, 38976, 22450, 15824, 228375, 8360],367,11]
%
% END OF LATTICE L368.11
%
%
% LATTICE L368.12
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2027119749900, 2488580850, 1007734703850; 2488580850, 3055080, 1237139190; 1007734703850, 1237139190, 500971505701],[1050, 210, 1],[346044, 235381, 280551, 15257, -2662, -57092, -23916, -23488, 15858, 166295; 14745, 10034, 11975, 654, -91, -2415, -1016, -995, 675, 7077; -696125, -473508, -564375, -30692, 5355, 114850, 48111, 47250, -31901, -334530],367,12]
%
% END OF LATTICE L368.12
%
%
% LATTICE L368.13
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1054200, 29400, 12600; 29400, 6510, 2625; 12600, 2625, 1058],[4200, 105, 1],[13, 2, 7, 0, -3, -1, -1, 1, 1, 2; -8200, -1253, -4260, 7, 2048, 660, 648, -640, -640, -1279; 20200, 3087, 10500, -17, -5040, -1625, -1596, 1575, 1576, 3150],367,13]
%
% END OF LATTICE L368.13
%
%
% LATTICE L368.14
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-54541200, 1827000, 121800; 1827000, -57360, -3840; 121800, -3840, -257],[4200, 120, 1],[5, 23, 1, 9, 0, -1, -1, 1, 11, 4; -2254, -10355, -449, -4025, 1, 448, 440, -460, -5005, -1809; 36043, 165600, 7182, 64400, -15, -7168, -7050, 7344, 79975, 28920],367,14]
%
% END OF LATTICE L368.14
%
%
% LATTICE L368.15
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-74785200, 16300200, -63000; 16300200, -3550960, 13720; -63000, 13720, -53],[4200, 280, 1],[1, -1, -1, -7, 0, 2, 12, 10, 22, 7; 12, -10, -12, -90, -2, 21, 135, 115, 255, 83; 1917, -1400, -1918, -15000, -525, 3048, 20650, 17864, 39825, 13160],367,15]
%
% END OF LATTICE L368.15
%
%
% LATTICE L368.16
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-495600, -71400, 4200; -71400, 52080, -2520; 4200, -2520, 121],[4200, 840, 1],[1, 11, -1, -1, 2, 2, 28, 22, 16, 15; 39, 420, -40, -40, 79, 79, 1105, 867, 630, 589; 779, 8400, -798, -800, 1575, 1576, 22050, 17304, 12575, 11760],367,16]
%
% END OF LATTICE L368.16
%

\medskip%
%------------------------------WEYL-GROUP-W369--------------------------------
%
\leavevmode\llap{}%
$W_{369}$%
\qquad\llap{8} lattices, $\chi=24$%
\hfill%
$22|2222|22\rtimes D_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L369.1
%
\leavevmode%
${L_{369.1}}$%
{} : {$1\above{1pt}{1pt}{1}{1}8\above{1pt}{1pt}{1}{7}64\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{-}{}$}\EasyButWeakLineBreak%
{${960}\above{1pt}{1pt}{b}{2}{8}\above{1pt}{1pt}{s}{2}{60}\above{1pt}{1pt}{b}{2}{8}\above{1pt}{1pt}{l}{2}{960}\above{1pt}{1pt}{}{2}{1}\above{1pt}{1pt}{r}{2}{160}\above{1pt}{1pt}{*}{2}{4}\above{1pt}{1pt}{s}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
807360\\960\\-960
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
960\\-8\\0
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-960\\0\\1
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-29\\-3120\\-27360
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-107\\-940
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-105\\-930
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\1\\4
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\120\\960
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\-1
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-110\\-960
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-108\\-946
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[807360, 960, -960; 960, -8, 0; -960, 0, 1],[960, 8, 1],[-29, -1, -1, 0, 1, 0, -1, -1; -3120, -107, -105, 1, 120, 0, -110, -108; -27360, -940, -930, 4, 960, -1, -960, -946],368,1]
%
% END OF LATTICE L369.1
%
%
% LATTICE L369.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-55496640, -3468480, 30720; -3468480, -216776, 1920; 30720, 1920, -17],[960, 8, 1],[-11, -1, 11, 3, 2, -1, -3, -9; 150, 10, -180, -46, -30, 16, 45, 128; -2970, -688, -480, 224, 225, 0, -340, -1824],368,2]
%
% END OF LATTICE L369.2
%
%
% LATTICE L369.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1202880, -83520, 6720; -83520, -5592, 456; 6720, 456, -37],[960, 24, 1],[11, 0, -1, -1, 1, 1, 7, 1; 280, 1, -25, -27, 0, 22, 170, 25; 5440, 12, -490, -516, 160, 450, 3360, 489],368,3]
%
% END OF LATTICE L369.3
%
%
% LATTICE L369.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3059520, 191040, -7680; 191040, -11928, 480; -7680, 480, -19],[960, 24, 1],[23, 17, 7, -3, -1, 1, 7, 41; 340, 250, 100, -46, -15, 16, 105, 608; -730, -576, -320, 48, 25, 0, -180, -1248],368,4]
%
% END OF LATTICE L369.4
%
%
% LATTICE L369.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-6653760, -429120, 21120; -429120, -27560, 1360; 21120, 1360, -67],[960, 40, 1],[13, 0, -1, -1, 7, 3, 3, 2; 120, 1, -9, -11, 48, 24, 26, 18; 6528, 20, -498, -540, 3168, 1430, 1472, 995],368,5]
%
% END OF LATTICE L369.5
%
%
% LATTICE L369.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-611520, -76800, 2880; -76800, -9640, 360; 2880, 360, -13],[960, 40, 1],[-1, -7, -7, -3, 1, 9, 1, 1; 9, 62, 60, 22, -12, -88, -9, -8; 27, 160, 96, -80, -126, -480, -28, 0],368,6]
%
% END OF LATTICE L369.6
%
%
% LATTICE L369.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-47693760, -6019200, 99840; -6019200, -759480, 12600; 99840, 12600, -209],[960, 120, 1],[15, 0, -1, -1, 13, 13, 11, 7; 16, 1, -1, -3, 8, 10, 10, 7; 8128, 60, -538, -660, 6688, 6810, 5856, 3765],368,7]
%
% END OF LATTICE L369.7
%
%
% LATTICE L369.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[960, 0, 0; 0, -3988920, 102600; 0, 102600, -2639],[960, 120, 1],[-1, -5, -1, -1, 0, 1, 0, -7; 38, 74, -28, -142, -8, 0, 25, 432; 1478, 2880, -1088, -5520, -311, 0, 972, 16800],368,8]
%
% END OF LATTICE L369.8
%

\medskip%
%------------------------------WEYL-GROUP-W370--------------------------------
%
\leavevmode\llap{}%
$W_{370}$%
\qquad\llap{4} lattices, $\chi=24$%
\hfill%
$2|22|22|22|2\rtimes D_{4}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L370.1
%
\leavevmode%
${L_{370.1}}$%
{} : {$1\above{1pt}{1pt}{1}{7}8\above{1pt}{1pt}{1}{1}64\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{-}{}$}\EasyButWeakLineBreak%
{${960}\above{1pt}{1pt}{l}{2}{8}\above{1pt}{1pt}{}{2}{15}\above{1pt}{1pt}{r}{2}{64}\above{1pt}{1pt}{*}{2}{60}\above{1pt}{1pt}{l}{2}{8}\above{1pt}{1pt}{}{2}{960}\above{1pt}{1pt}{r}{2}{4}\above{1pt}{1pt}{b}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
960\\0\\0
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\8\\0
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\-1
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-11\\-120\\-480
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-9\\-40
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2\\-15\\-75
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-4\\-32
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\0\\-30
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\1\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\0\\0
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\-1\\-2
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[960, 0, 0; 0, 8, 0; 0, 0, -1],[960, 8, 1],[-11, -1, -2, -1, -1, 0, 1, 0; -120, -9, -15, -4, 0, 1, 0, -1; -480, -40, -75, -32, -30, 0, 0, -2],369,1]
%
% END OF LATTICE L370.1
%
%
% LATTICE L370.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-19289280, 0, 28800; 0, 24, 0; 28800, 0, -43],[960, 24, 1],[11, 0, -1, -1, 3, 7, 39, 2; 0, 1, 0, -4, -5, -9, -40, -1; 7360, 0, -670, -672, 2005, 4680, 26080, 1338],369,2]
%
% END OF LATTICE L370.2
%
%
% LATTICE L370.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-49024320, 0, 61440; 0, 40, 0; 61440, 0, -77],[960, 40, 1],[49, 15, 4, -1, -1, 0, 13, 4; -24, -9, -3, -4, 0, 1, 0, -1; 39072, 11960, 3189, -800, -798, 0, 10368, 3190],369,3]
%
% END OF LATTICE L370.3
%
%
% LATTICE L370.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-54605760, 0, 114240; 0, 120, 0; 114240, 0, -239],[960, 120, 1],[15, 0, -1, -1, 5, 55, 59, 14; 0, 1, 0, -4, -1, -9, -8, -1; 7168, 0, -478, -480, 2389, 26280, 28192, 6690],369,4]
%
% END OF LATTICE L370.4
%

\medskip%
%------------------------------WEYL-GROUP-W371--------------------------------
%
\leavevmode\llap{}%
$W_{371}$%
\qquad\llap{4} lattices, $\chi=144$%
\hfill%
$\infty|\infty222\infty|\infty222\infty|\infty222\infty|\infty222\rtimes D_{4}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L371.1
%
\leavevmode%
${L_{371.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{{\rm II}}8\above{1pt}{1pt}{-}{5}{\cdot}1\above{1pt}{1pt}{1}{}17\above{1pt}{1pt}{1}{}289\above{1pt}{1pt}{1}{}$}\spacer%
\instructions{2}%
\EasyButWeakLineBreak%
{${136}\above{1pt}{1pt}{34,1}{\infty z}{34}\above{1pt}{1pt}{68,13}{\infty a}{136}\above{1pt}{1pt}{b}{2}{2}\above{1pt}{1pt}{b}{2}{2312}\above{1pt}{1pt}{b}{2}{34}\above{1pt}{1pt}{68,1}{\infty b}{136}\above{1pt}{1pt}{34,21}{\infty z}{34}\above{1pt}{1pt}{b}{2}{8}\above{1pt}{1pt}{b}{2}{578}\above{1pt}{1pt}{b}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-37498328\\136408\\-1583720
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
136408\\-442\\6001
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1583720\\6001\\-65826
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-15181273\\-1151705528\\260259528
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
47637\\3613912\\-816663
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-674739\\-51188111\\11567360
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
119\\9028\\-2040
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-118\\-8951\\2023
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-4379\\-332196\\75072
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-383\\-29055\\6566
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-14565\\-1104932\\249696
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2961\\-224629\\50762
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-7937\\-602124\\136068
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-5687\\-431434\\97495
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-2781\\-210976\\47676
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-36497\\-2768790\\625685
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-37498328, 136408, -1583720; 136408, -442, 6001; -1583720, 6001, -65826],[2312, 17, 1],[119, -118, -4379, -383, -14565, -2961, -7937, -5687, -2781, -36497, -37091, -5570, -32593, -1750, -33783, -3438, -3439, -712, -63, 236; 9028, -8951, -332196, -29055, -1104932, -224629, -602124, -431434, -210976, -2768790, -2813856, -422561, -2472632, -132762, -2562920, -260822, -260900, -54017, -4780, 17901; -2040, 2023, 75072, 6566, 249696, 50762, 136068, 97495, 47676, 625685, 635868, 95489, 558756, 30001, 579156, 58939, 58956, 12206, 1080, -4046],370,1]
%
% END OF LATTICE L371.1
%
%
% LATTICE L371.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%IMPLICIT%[[-156638, 9248, 73984; 9248, -544, -4369; 73984, -4369, -34944],[578, 17, 1],[397, 9, -17, -1, 13, 205, 445, 848, 4079, 416, 3841, 1295, 4255, 8314, 313, 1262, 859, 619, 1463, 73; 460, 16, -16, -17, 12, 205, 458, 885, 4284, 439, 4064, 1376, 4540, 8891, 336, 1361, 934, 681, 1632, 83; 782, 17, -34, 0, 26, 408, 884, 1683, 8092, 825, 7616, 2567, 8432, 16473, 620, 2499, 1700, 1224, 2890, 144],370,2]
%
% END OF LATTICE L371.2
%
%
% LATTICE L371.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1156, 578, 578; 578, 4352, 544; 578, 544, 305],[578, 34, 1],[1014, 112, 8, -1, 22, 765, 869, 3397, 8270, 1703, 7904, 5376, 8910, 34987, 664, 5409, 1875, 2777, 3392, 355; 137, 15, 1, 0, 3, 104, 118, 461, 1122, 231, 1072, 729, 1208, 4743, 90, 733, 254, 376, 459, 48; -2159, -238, -17, 0, -47, -1632, -1853, -7242, -17629, -3630, -16847, -11458, -18989, -74562, -1415, -11526, -3995, -5916, -7225, -756],370,3]
%
% END OF LATTICE L371.3
%
%
% LATTICE L371.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-8901200, -233512, 4193968; -233512, -5712, 110024; 4193968, 110024, -1976067],[2312, 136, 1],[30872, 23903, 44682, 10962, 66182, 35374, 14595, 26851, 2389, 92601, 19113, 6857, 5303, 573, -817, -769, 785, 7754, 1456, 103494; -67, -53, -101, -25, -153, -83, -35, -66, -6, -238, -50, -19, -16, -2, 0, 2, -1, -15, -3, -221; 65518, 50728, 94826, 23264, 140454, 75072, 30974, 56984, 5070, 196520, 40562, 14552, 11254, 1216, -1734, -1632, 1666, 16456, 3090, 219640],370,4]
%
% END OF LATTICE L371.4
%

\medskip%
%------------------------------WEYL-GROUP-W372--------------------------------
%
\leavevmode\llap{}%
$W_{372}$%
\qquad\llap{8} lattices, $\chi=72$%
\hfill%
$22|2222|2222|2222|22\rtimes D_{4}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L372.1
%
\leavevmode%
${L_{372.1}}$%
{} : {$1\above{1pt}{1pt}{1}{1}8\above{1pt}{1pt}{-}{5}64\above{1pt}{1pt}{1}{7}{\cdot}1\above{1pt}{1pt}{2}{}3\above{1pt}{1pt}{1}{}{\cdot}1\above{1pt}{1pt}{2}{}7\above{1pt}{1pt}{1}{}$}\EasyButWeakLineBreak%
{${448}\above{1pt}{1pt}{r}{2}{12}\above{1pt}{1pt}{b}{2}{56}\above{1pt}{1pt}{s}{2}{12}\above{1pt}{1pt}{b}{2}{448}\above{1pt}{1pt}{s}{2}{4}\above{1pt}{1pt}{*}{2}{64}\above{1pt}{1pt}{l}{2}{1}\above{1pt}{1pt}{}{2}$}\relax$\,(\times2)$%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1735104\\-577920\\-1344
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-577920\\192488\\448
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1344\\448\\1
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\hfil\penalty500%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-37633\\-110208\\-1171968
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
12404\\36325\\386296
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
42\\123\\1307
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1587\\-4648\\-49280
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-169\\-495\\-5238
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-184\\-539\\-5684
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-128\\-375\\-3942
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1013\\-2968\\-31136
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-43\\-126\\-1318
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-15\\-44\\-448
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\-1
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[1735104, -577920, -1344; -577920, 192488, 448; -1344, 448, 1],[1344, 8, 1],[-1587, -169, -184, -128, -1013, -43, -15, 0, 19, 1, -12, -40, -555, -41, -97, -42; -4648, -495, -539, -375, -2968, -126, -44, 0, 56, 3, -35, -117, -1624, -120, -284, -123; -49280, -5238, -5684, -3942, -31136, -1318, -448, -1, 448, 6, -420, -1290, -17696, -1298, -3040, -1307],371,1]
%
% END OF LATTICE L372.1
%
%
% LATTICE L372.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-3530688, -6720, 9408; -6720, 40, 16; 9408, 16, -25],[1344, 8, 1],[-33, -41, -9, -1, 1, 3, 0, -23, -37, -79, -61, -119, -36, -63, -5, -37; -476, -588, -126, -12, 14, 40, -1, -352, -560, -1188, -910, -1764, -532, -928, -73, -536; -12754, -15840, -3472, -384, 385, 1152, -2, -8928, -14350, -30624, -23632, -46080, -13937, -24384, -1934, -14304],371,2]
%
% END OF LATTICE L372.2
%
%
% LATTICE L372.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-24835776, -542976, 36288; -542976, -11784, 792; 36288, 792, -53],[1344, 24, 1],[295, 8, 13, 1, 1, -1, -1, 5, 265, 12, 57, 19, 559, 31, 41, 10; 4032, 109, 175, 13, 0, -14, -12, 70, 3696, 167, 791, 263, 7728, 428, 564, 137; 262080, 7102, 11508, 878, 672, -894, -864, 4467, 236544, 10706, 50820, 16930, 497952, 27606, 36480, 8889],371,3]
%
% END OF LATTICE L372.3
%
%
% LATTICE L372.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[117216960, -15421056, 65856; -15421056, 2028792, -8664; 65856, -8664, 37],[1344, 24, 1],[3, 3, 11, 11, 12, 25, 3, 35, 39, 21, 31, 13, 9, 11, 0, 1; 28, 28, 98, 92, 98, 200, 23, 256, 280, 148, 210, 84, 56, 64, -1, 8; 1218, 1216, 3360, 1952, 1575, 2304, 42, -2400, -3906, -2752, -6048, -3488, -2919, -4608, -234, 96],371,4]
%
% END OF LATTICE L372.4
%
%
% LATTICE L372.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-803737536, -93062592, 267456; -93062592, -10775464, 30968; 267456, 30968, -89],[1344, 56, 1],[33, 25, 4, 20, 23, 7, 3, 0, -1, -1, 0, 4, 9, 5, 13, 6; -224, -165, -25, -117, -128, -36, -4, 3, 16, 9, -1, -39, -80, -42, -100, -42; 21184, 17682, 3316, 19362, 24544, 8498, 7616, 1043, 2560, 126, -348, -1554, -800, 406, 4256, 3409],371,5]
%
% END OF LATTICE L372.5
%
%
% LATTICE L372.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-9425472, 786240, -22848; 786240, -65576, 1904; -22848, 1904, -55],[1344, 56, 1],[6, 169, 17, 209, 17, 97, 6, 27, 1, -1, -3, -41, -3, -13, 1, 57; 80, 2268, 230, 2844, 232, 1328, 83, 376, 14, -12, -42, -588, -44, -200, 11, 752; 267, 8064, 880, 11424, 954, 5600, 378, 1792, 69, 0, -208, -3360, -282, -1568, -42, 2240],371,6]
%
% END OF LATTICE L372.6
%
%
% LATTICE L372.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[138432, -155904, 1344; -155904, 175560, -1512; 1344, -1512, 13],[1344, 168, 1],[7, 2, 1, 1, 1, -1, -7, -4, -23, -6, -3, -5, -17, -5, -1, 1; 0, 1, 1, 1, 0, -2, -12, -8, -48, -13, -7, -13, -48, -16, -12, -1; -768, -98, 12, 14, -96, -126, -672, -525, -3264, -910, -516, -1022, -3936, -1386, -1344, -231],371,7]
%
% END OF LATTICE L372.7
%
%
% LATTICE L372.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[1344, 0, 0; 0, -164472, 2184; 0, 2184, -29],[1344, 168, 1],[-3, -9, -1, -1, 0, 1, 0, -13, -3, -15, -5, -23, -3, -37, -3, -23; -10, -20, 2, 12, 1, 0, -5, -168, -34, -156, -46, -188, -23, -264, -17, -96; -774, -1568, 144, 896, 75, 0, -378, -12768, -2586, -11872, -3504, -14336, -1755, -20160, -1302, -7392],371,8]
%
% END OF LATTICE L372.8
%

\medskip%
%------------------------------WEYL-GROUP-W373--------------------------------
%
\leavevmode\llap{}%
$W_{373}$%
\qquad\llap{8} lattices, $\chi=72$%
\hfill%
$2222|2222|2222|2222|\rtimes D_{4}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L373.1
%
\leavevmode%
${L_{373.1}}$%
{} : {$1\above{1pt}{1pt}{-2}{2}16\above{1pt}{1pt}{-}{3}{\cdot}1\above{1pt}{1pt}{-}{}3\above{1pt}{1pt}{1}{}9\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{-2}{}5\above{1pt}{1pt}{-}{}{\cdot}1\above{1pt}{1pt}{2}{}7\above{1pt}{1pt}{-}{}$}\EasyButWeakLineBreak%
{${18}\above{1pt}{1pt}{b}{2}{560}\above{1pt}{1pt}{*}{2}{12}\above{1pt}{1pt}{l}{2}{315}\above{1pt}{1pt}{}{2}{48}\above{1pt}{1pt}{}{2}{35}\above{1pt}{1pt}{r}{2}{12}\above{1pt}{1pt}{*}{2}{5040}\above{1pt}{1pt}{b}{2}{2}\above{1pt}{1pt}{l}{2}{5040}\above{1pt}{1pt}{}{2}{3}\above{1pt}{1pt}{r}{2}{140}\above{1pt}{1pt}{*}{2}{48}\above{1pt}{1pt}{*}{2}{1260}\above{1pt}{1pt}{l}{2}{3}\above{1pt}{1pt}{}{2}{560}\above{1pt}{1pt}{r}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-362633040\\120960\\201600
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
120960\\-33\\-72
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
201600\\-72\\-109
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
19\\15927\\24615
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
311\\260680\\402920
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
15\\12572\\19434
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
53\\44415\\68670
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
3\\2512\\3888
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-840\\-1295
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-838\\-1296
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
37\\31080\\47880
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\839\\1295
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
607\\509040\\786240
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
9\\7547\\11658
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
93\\77980\\120470
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
41\\34376\\53112
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
391\\327810\\506520
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
17\\14252\\22023
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
501\\420000\\649040
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-362633040, 120960, 201600; 120960, -33, -72; 201600, -72, -109],[5040, 3, 1],[19, 311, 15, 53, 3, -1, -1, 37, 1, 607, 9, 93, 41, 391, 17, 501; 15927, 260680, 12572, 44415, 2512, -840, -838, 31080, 839, 509040, 7547, 77980, 34376, 327810, 14252, 420000; 24615, 402920, 19434, 68670, 3888, -1295, -1296, 47880, 1295, 786240, 11658, 120470, 53112, 506520, 22023, 649040],372,1]
%
% END OF LATTICE L373.1
%
%
% LATTICE L373.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-13827154320, 1582560, 3139920; 1582560, -165, -360; 3139920, -360, -713],[5040, 15, 1],[55, 305, 53, 251, 137, 65, 33, 467, 5, 65, -1, -1, 3, 25, 39, 171; 9207, 51072, 8876, 42042, 22952, 10892, 5531, 78288, 839, 10920, -166, -168, 496, 4179, 6524, 28616; 237555, 1317344, 228915, 1084104, 591720, 280742, 142530, 2017008, 21595, 280728, -4320, -4319, 12960, 107982, 168450, 738584],372,2]
%
% END OF LATTICE L373.2
%
%
% LATTICE L373.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-4319446320, 1043280, 2081520; 1043280, -231, -504; 2081520, -504, -1003],[5040, 21, 1],[73, 291, 71, 241, 185, 63, 45, 457, 7, 67, -1, -1, 3, 23, 51, 161; 8727, 34800, 8492, 28830, 22136, 7540, 5387, 54720, 839, 8040, -118, -120, 352, 2745, 6092, 19240; 147105, 586400, 143073, 485640, 372792, 126950, 90678, 920880, 14105, 135000, -2016, -2015, 6048, 46350, 102774, 324440],372,3]
%
% END OF LATTICE L373.3
%
%
% LATTICE L373.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1232485082640, -34235293680, -61180560; -34235293680, -950969184, -1699440; -61180560, -1699440, -3037],[5040, 48, 1],[3362, 6948, 1355, 9817, 41, 1, -47, 1216, 186, 6728, 1585, 8161, 898, 34297, 2987, 5514; -120465, -248955, -48551, -351750, -1469, -35, 1684, -43575, -6665, -241080, -56794, -292425, -32177, -1228920, -107029, -197575; -318096, -658070, -128472, -932400, -3927, -560, 4488, -112770, -17392, -632835, -149232, -769160, -84714, -3238200, -282192, -521185],372,4]
%
% END OF LATTICE L373.4
%
%
% LATTICE L373.5
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-549360, 25200, 55440; 25200, -1155, -2520; 55440, -2520, -5039],[5040, 105, 1],[325, 141, 219, 19, 3, -1, -1, 71, 35, 437, 213, 59, 857, 221, 323, 263; 7767, 3368, 5228, 453, 64, -24, -22, 1704, 839, 10464, 5099, 1412, 20504, 5286, 7724, 6288; -315, -136, -210, -18, 0, 1, 0, -72, -35, -432, -210, -58, -840, -216, -315, -256],372,5]
%
% END OF LATTICE L373.5
%
%
% LATTICE L373.6
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[231179760, 38530800, 171360; 38530800, 6421920, 28560; 171360, 28560, 127],[5040, 240, 1],[-446, -186, -183, -269, -6, -1, 7, -26, -22, -169, -201, -209, -116, -893, -391, -145; 3207, 1337, 1315, 1932, 43, 7, -50, 189, 159, 1218, 1448, 1505, 835, 6426, 2813, 1043; -119520, -49742, -48840, -71568, -1575, -224, 1800, -7434, -6080, -45927, -54480, -56504, -31290, -240408, -105120, -38941],372,6]
%
% END OF LATTICE L373.6
%
%
% LATTICE L373.7
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-33228720, 34705440, 700560; 34705440, -36247344, -731472; 700560, -731472, -14659],[5040, 336, 1],[-18725, -4696, -18383, -31258, -6007, -8169, -11632, -7337, -1741, -1759, 422, 441, 10, -5428, -6329, -5087; -18681, -4685, -18340, -31185, -5993, -8150, -11605, -7320, -1737, -1755, 421, 440, 10, -5415, -6314, -5075; 37296, 9355, 36624, 62280, 11970, 16280, 23184, 14625, 3472, 3510, -840, -880, -21, 10800, 12600, 10130],372,7]
%
% END OF LATTICE L373.7
%
%
% LATTICE L373.8
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-1108542960, 1723871520, 307077120; 1723871520, -2680754160, -477528240; 307077120, -477528240, -85062911],[5040, 1680, 1],[-29713, -22837, -177448, -24465, -88411, -90722, -264083, -13388, -262409, -14071, -86213, -14492, 262, 945, 422, -7559; -29681, -22812, -177253, -24438, -88313, -90621, -263788, -13373, -262113, -14055, -86114, -14475, 262, 944, 421, -7551; 59360, 45621, 354480, 48872, 176610, 181224, 527520, 26743, 524160, 28106, 172200, 28944, -525, -1888, -840, 15102],372,8]
%
% END OF LATTICE L373.8
%

\medskip%
%------------------------------WEYL-GROUP-W374--------------------------------
%
\leavevmode\llap{}%
$W_{374}$%
\qquad\llap{4} lattices, $\chi=72$%
\hfill%
$222222|2222222\slashinfty2\rtimes D_{2}$%
\nopagebreak\smallskip\hrule\nopagebreak\medskip%
%
% LATTICE L374.1
%
\leavevmode%
${L_{374.1}}$%
{} : {$1\above{1pt}{1pt}{1}{1}8\above{1pt}{1pt}{1}{7}256\above{1pt}{1pt}{1}{1}{\cdot}1\above{1pt}{1pt}{2}{}9\above{1pt}{1pt}{1}{}$}\EasyButWeakLineBreak%
{${2304}\above{1pt}{1pt}{}{2}{1}\above{1pt}{1pt}{r}{2}{256}\above{1pt}{1pt}{*}{2}{36}\above{1pt}{1pt}{s}{2}{256}\above{1pt}{1pt}{s}{2}{4}\above{1pt}{1pt}{*}{2}{2304}\above{1pt}{1pt}{l}{2}{1}\above{1pt}{1pt}{}{2}{256}\above{1pt}{1pt}{}{2}{9}\above{1pt}{1pt}{r}{2}{256}\above{1pt}{1pt}{*}{2}{4}\above{1pt}{1pt}{s}{2}{2304}\above{1pt}{1pt}{b}{2}{8}\above{1pt}{1pt}{48,1}{\infty b}{8}\above{1pt}{1pt}{l}{2}$}%
\nopagebreak\par%
\nopagebreak\par\leavevmode%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-96876288\\82944\\82944
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
82944\\-8\\-72
\end{tabular}\endgroup%
\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
82944\\-72\\-71
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
\EasyButWeakLineBreak%
{$\left[\!\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\right.$}%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2737\\48672\\3147264
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
47\\836\\54045
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
607\\10800\\697984
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
179\\3186\\205830
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
363\\6464\\417408
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
33\\588\\37946
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
541\\9648\\622080
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
7\\125\\8049
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
59\\1056\\67840
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
4\\72\\4599
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-16\\-1152
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
-1\\-18\\-1150
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
1\\0\\1152
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
2\\35\\2300
\end{tabular}\endgroup%
\HardButStrongLineBreak\kern3pt%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
21\\373\\24148
\end{tabular}\endgroup%
{$\left.\llap{\phantom{%
\begingroup \smaller\smaller\smaller\begin{tabular}{@{}c@{}}%
0\\0\\0
\end{tabular}\endgroup%
}}\!\right]$}%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%EXPLICIT%[[-96876288, 82944, 82944; 82944, -8, -72; 82944, -72, -71],[2304, 8, 1],[2737, 47, 607, 179, 363, 33, 541, 7, 59, 4, -1, -1, 1, 2, 21; 48672, 836, 10800, 3186, 6464, 588, 9648, 125, 1056, 72, -16, -18, 0, 35, 373; 3147264, 54045, 697984, 205830, 417408, 37946, 622080, 8049, 67840, 4599, -1152, -1150, 1152, 2300, 24148],373,1]
%
% END OF LATTICE L374.1
%
%
% LATTICE L374.2
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-37156608, -4349952, 16128; -4349952, -509216, 1888; 16128, 1888, -7],[2304, 32, 1],[1, 1, 0, -1, 0, 1, 1, 5, 1, 35, 2, 21, 5, 3, 1; 0, -8, -1, 0, 1, 40, 27, 112, 20, 648, 35, 352, 81, 42, 6; 2286, 128, -270, -2304, 269, 13056, 9558, 41600, 7674, 254592, 14002, 142848, 33255, 18176, 3904],373,2]
%
% END OF LATTICE L374.2
%
%
% LATTICE L374.3
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[-16128, 9216, 0; 9216, -72, -72; 0, -72, 1],[2304, 72, 1],[1, -1, -9, 0, 19, 3, 29, 17, 195, 11, 343, 27, 177, 13, 2; 0, -2, -16, 0, 32, 5, 48, 28, 320, 18, 560, 44, 288, 21, 3; 128, -126, -1152, -1, 2304, 369, 3584, 2106, 24192, 1366, 42624, 3357, 22016, 1620, 252],373,3]
%
% END OF LATTICE L374.3
%
%
% LATTICE L374.4
%
% PARI-readable data for this lattice:
% [IP matrix, Elementary Divisors, Simple Roots, Weyl Group #, Lattice # with this Weyl group]
%DUALITY%[[2304, 0, 0; 0, -380448, 128448; 0, 128448, -43367],[2304, 288, 1],[0, 1, 0, -1, -1, -15, -1, -35, -3, -21, -10, -99, -5, -11, -1; 26, 0, -79, -216, -6, 1168, 125, 5448, 532, 4064, 2061, 21400, 1122, 2918, 778; 77, 0, -234, -640, -18, 3456, 370, 16128, 1575, 12032, 6102, 63360, 3322, 8640, 2304],373,4]
%
% END OF LATTICE L374.4
%
\endgroup

\end{document}

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