function AddArrays(X)
return [&+[i[j]:i in X]:j in [1..#X[1]]];
end function;

q:=2887;
F:=GF(q);
u:=F!2;
u481:=u^3;
u13:=u^111;
u37:=u^39;

EigsCoeffs481:=[
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[0,0,0,0,1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,0,0,0,
0,0,0,1,0,0,1,0,0,0,0,0,0,0,0,1,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,0,0,0,0,0,0,
1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,0,0,0,0,1,0,0,1,0,0,0,0,0,0,0,0,1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,0,0,0,0,1,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,
0,0,0,0,0,0,0,1,0,1,0,0,0,0,0,0,0,0,1,0,0,1,0,0,0,0,0,0,0,0,1,0,0,1,0,0,0,0],
[0,0,0,1,0,0,0,0,0,1,1,0,0,0,0,1,1,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,1,1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,1,
0,0,0,0,1,1,0,0,0,0,1,1,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,1,0,0,0,0,1,1,0,0,0,0,1,1,
0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]];


EigsOfMats:=[[u^1441,722,722,722,722,722,722,722,1444,722,1444,722,1444,722,1444,1444,722,1444,1444,722,1444,1444,1444,722,1444,1444,1444,
1444,1444,1444,1444,1444,1444,1444,1444,1444,1444,1444,1444,1444,1444,1444,1444,1444,1444,1444,1,1444,1444,1444,1444,1444,1,
1444,1444,1444,1444,1444,1,1,1444,1444,1444,1444,1,1,1444,1444,1444,1444,1,1,1,1444,1444,1444,1444,1,1,1,1,1444,1444,1444,
1,1,1,1,1,1444,1444,1,1,1,1,1,1444,1444,1,1,1,1,1,1,1444,1,1,1,1,1,1,1444,1,1,1,1,1,1,1,1444,1,1,1,1,1,1,1,1,
2,1,1,1,1,1,1,1,2,1,1,1,1,1,1,2,1,1,1,1,1,1,2,2,1,1,1,1,1,2,2,1,1,1,1,1,2,2,2,1,1,1,1,2,2,2,2,1,1,1,2,
2,2,2,1,1,2,2,2,2,1,1,2,2,2,2,2,1,2,2,2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,2,2,2,4,2,
2,4,2,2,4,2,4,2,4,2,4,4,4,4,4,4,4,4],
[361,361,361,361,361,361,722,361,361,722,722,722,722,722,722,722,722,722,722,722,722,722,722,722,1444,722,722,722,1444,722,
722,722,1444,1444,722,722,1444,1444,1444,722,722,1444,1444,1444,1444,722,1444,1444,1444,1444,1444,722,1444,1444,1444,1444,1444,
1444,1444,1444,1444,1444,1444,1444,1444,1444,1444,1444,1444,1444,1444,1444,1444,1,1444,1444,1444,1,1444,1444,1444,1,1444,1444,
1,1,1444,1444,1444,1,1444,1,1,1,1444,1444,1,1444,1,1,1,1,1444,1444,1,1,1,1,1,1,1444,1,1,1,1,1,1,1,1444,1,1,1,1,1,
1,1,1,1,1,2,1,1,1,1,1,1,1,2,1,1,1,1,1,1,2,2,1,1,1,1,2,1,2,2,1,1,1,2,1,2,2,2,1,1,2,2,1,2,2,2,1,2,2,2,1,
2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,2,2,2,2,2,4,2,2,2,2,4,4,2,2,2,4,4,2,2,4,4,4,2,4,4,4,2,4,4,
4,4,4,4,4,4,4,4,4,4,4,4,4,8,8,4,8,8,8,8,8,8],
[1624,1624,1624,1624,1624,1624,1624,361,361,361,361,361,361,361,722,361,361,722,361,361,722,722,361,361,722,722,722,361,722,
722,722,722,722,722,722,722,722,722,722,722,722,1444,722,722,722,722,1444,1444,722,722,722,722,1444,1444,1444,722,722,722,
1444,1444,1444,1444,722,722,1444,1444,1444,1444,1444,722,1444,1444,1444,1444,1444,1444,722,1444,1,1444,1444,1444,1444,1444,1,
1444,1,1444,1444,1444,1444,1,1,1444,1,1444,1444,1444,1,1,1,1444,1,1444,1444,1,1,1,1,1444,1,1444,1,1,1,1,1,1444,1,1,1,
1,1,1,1,1,1,1,1,1,2,1,1,1,1,1,2,1,2,1,1,1,1,2,2,1,2,1,1,1,2,2,2,1,2,1,1,2,2,2,2,1,2,1,2,2,2,2,2,1,2,4,
2,2,2,2,2,2,4,2,2,2,2,2,4,4,2,2,2,2,4,4,4,2,2,2,4,4,4,4,2,2,4,4,4,4,2,4,4,4,4,4,4,4,4,4,4,4,4,4,8,4,4,
4,8,8,4,4,8,8,4,8,8,4,8,8,8,8,8,8,8,16,16,16,16,16,16,16],
[406,406,406,406,406,812,812,812,812,812,812,1624,1624,1624,1624,1624,1624,1624,1624,1624,361,1624,1624,1624,361,361,1624,
1624,361,361,361,1624,361,361,361,361,722,361,361,361,361,722,722,361,361,361,722,722,722,722,361,361,722,722,722,722,722,
361,722,722,722,722,722,722,722,722,1444,722,722,722,1444,722,722,1444,1444,722,722,1444,1444,1444,722,1444,1444,722,1444,
1444,1444,1444,722,1444,1444,1,1444,1444,1444,1444,1444,1444,1,1,1444,1444,1444,1444,1444,1,1,1,1444,1444,1444,1,1,1,1,1,
1444,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,1,2,2,2,1,1,1,2,2,2,2,2,1,1,2,2,2,2,2,2,1,2,2,4,2,2,2,2,4,2,
2,4,2,2,2,4,4,2,2,4,4,2,4,4,4,2,4,4,4,4,4,4,4,4,8,4,4,4,4,4,8,8,4,4,4,4,8,8,8,4,4,8,8,8,8,4,8,8,8,8,16,
8,8,8,16,16,8,8,16,16,16,8,16,16,16,16,16,16,16,16,16,32,32,32,32,32,32,64,64,64,64,64],
[812,812,812,812,1624,1624,1624,1624,1624,1624,1624,1624,1624,361,1624,361,361,361,361,361,361,361,361,361,361,361,361,361,
361,722,361,361,722,361,722,361,722,722,361,722,722,722,722,722,722,722,722,722,722,722,722,722,722,722,722,1444,722,722,
722,722,1444,722,1444,722,1444,722,1444,1444,722,1444,1444,1444,722,1444,1444,1444,1444,1444,1444,1444,1444,1444,1444,1444,
1444,1444,1444,1444,1444,1444,1444,1444,1444,1444,1444,1444,1444,1,1,1444,1444,1444,1444,1,1,1,1,1444,1444,1,1,1,1,1,1,
1444,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,2,2,1,1,1,1,2,2,2,2,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,
2,2,2,2,2,2,2,2,2,2,4,2,2,2,4,2,2,4,2,4,2,4,2,4,4,4,4,2,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,8,4,4,8,4,8,4,
8,8,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,8,16,16,16,16,16,16,16,16,16,32,32,32,32],
[1624,1624,1624,361,361,361,361,361,361,361,361,361,361,361,361,361,722,361,722,722,361,722,722,722,361,722,722,722,722,
722,722,722,722,722,722,722,722,722,722,1444,722,722,722,1444,722,1444,722,722,1444,722,1444,1444,722,1444,722,1444,1444,
1444,1444,722,1444,1444,1444,1444,1444,1444,1444,1444,1444,1444,1444,1444,1444,1444,1444,1444,1,1444,1444,1444,1444,1444,1444,
1,1444,1444,1444,1444,1,1444,1,1444,1444,1444,1444,1,1,1,1444,1444,1444,1,1,1,1,1,1444,1444,1,1,1,1,1,1,1444,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,2,2,1,1,1,1,1,2,2,2,1,1,1,2,2,2,2,1,2,1,2,2,2,2,1,2,2,2,2,2,
2,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,2,2,2,2,4,2,4,2,2,4,2,4,4,2,4,2,4,4,4,2,4,4,4,4,4,4,4,4,4,4,4,4,
4,4,8,4,4,4,8,4,4,8,4,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16],
[361,361,722,722,722,722,722,722,722,722,722,722,722,722,722,722,722,722,722,1444,722,722,1444,1444,722,722,1444,1444,722,
722,1444,1444,722,1444,1444,1444,722,1444,1444,1444,1444,722,1444,1444,1444,1444,722,1444,1444,1444,1444,1,1444,1444,1444,1444,
1444,1,1444,1444,1444,1444,1444,1,1444,1444,1444,1444,1,1,1444,1444,1,1444,1444,1,1,1444,1444,1444,1,1444,1,1,1444,1444,
1444,1,1,1,1,1444,1444,1,1,1,1,1,1444,1444,1,1,1,1,1,1444,1444,1,1,1,1,1,1,1444,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,2,1,1,1,1,1,1,2,2,1,1,1,1,1,2,2,1,1,1,1,1,2,2,1,1,1,1,2,2,2,1,1,2,1,2,2,2,1,1,2,2,1,2,2,1,1,
2,2,2,2,1,2,2,2,2,2,1,2,2,2,2,2,1,2,2,2,2,4,2,2,2,2,4,2,2,2,2,4,2,2,2,4,2,2,4,4,2,2,4,4,2,2,4,4,2,4,4,
4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,8,8],
[722,1444,1444,1444,1444,1444,1444,1444,1444,1444,1444,1444,1444,1444,1444,1444,1444,1444,1444,1444,1444,1444,1444,1,1444,1444,
1444,1,1444,1444,1444,1,1444,1444,1444,1,1444,1444,1,1444,1,1444,1444,1444,1,1,1444,1444,1444,1,1,1,1444,1444,1,1444,1,1,
1444,1,1444,1,1,1,1444,1,1444,1,1,1,1444,1,1,1444,1,1,1,1444,1444,1,1,1,1,1,1444,1,1,1,1,1,1,1444,1,1,1,1,1,1,
1444,1,1,1,1,1,1,1444,1,1,1,1,1,1,1444,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,2,1,1,1,
1,1,1,2,1,1,1,1,1,1,2,1,1,1,1,1,1,2,1,1,1,1,1,2,2,1,1,1,2,1,1,2,1,1,1,2,1,2,1,1,1,2,1,2,1,1,2,1,2,2,1,
1,1,2,2,2,1,1,2,2,2,1,2,1,2,2,1,2,2,2,1,2,2,2,1,2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4]
];

RepsFor37s:=[[13,15,15,20,22,30,5,9],[35,14,10,11,36,16,4,4],[33,13,17,4,18,28,2,24],[17,15,29,12,29,35,28,3],[29,20,35,22,20,4,8,11],
[35,23,30,21,20,20,3,22],[23,18,13,13,14,19,2,1],[32,10,1,20,25,6,29,32],[32,11,4,3,11,19,23,4],[6,29,18,4,27,32,5,5],
[11,9,15,1,15,20,15,4],[0,35,23,20,2,16,18,17],[16,7,5,9,3,36,28,22],[26,19,26,9,15,26,4,20],[26,22,20,31,16,15,8,34],
[22,15,18,2,11,2,22,9],[20,10,31,24,34,15,19,16],[2,11,26,11,28,17,3,25],[12,33,16,9,9,9,1,35],[22,22,26,17,12,21,26,23],
[15,21,13,17,33,36,7,33],[19,13,6,7,16,33,2,4],[22,2,33,8,33,27,9,35],[19,27,13,26,5,13,23,7],[35,9,30,33,5,29,31,23],
[16,7,1,23,20,13,0,27],[5,26,18,26,16,31,13,35],[10,28,14,22,32,32,2,25],[27,1,28,19,12,33,35,3],[13,20,8,19,7,12,14,5],
[24,35,6,23,30,22,2,8],[31,6,35,22,31,16,3,12],[35,34,21,14,20,9,26,8],[36,16,23,11,12,33,30,2],[35,6,12,23,14,34,21,28],
[35,33,25,35,36,9,16,35],[6,16,28,33,6,26,32,4],[18,36,34,8,19,5,26,21],[7,3,14,12,24,20,6,5],[28,25,35,4,13,26,14,0],
[34,12,8,22,15,19,24,15],[16,3,34,35,23,8,6,29],[19,16,28,36,21,32,27,18],[31,13,24,18,4,27,9,36],[18,35,28,31,11,31,13,29],
[11,28,19,7,15,29,21,36],[36,24,30,5,25,7,30,32],[24,5,13,7,33,16,32,20],[30,32,36,9,7,34,3,32],[33,8,29,0,8,17,2,0],
[20,30,26,12,13,1,31,35],[3,5,0,5,7,2,35,21],[24,27,20,23,32,32,14,9],[11,32,23,15,23,31,16,8],[1,17,8,9,31,30,8,12],
[6,13,26,23,18,33,13,12],[31,19,14,17,19,2,19,13],[12,31,36,18,17,34,23,27],[9,0,26,7,25,23,29,7],[31,9,22,27,21,34,13,31],
[11,8,6,2,7,0,14,18],[1,31,14,35,29,12,36,36],[33,2,10,29,33,1,22,6],[25,25,2,35,22,1,32,21],[16,18,24,13,33,11,23,8],
[6,29,31,36,35,22,19,13],[27,7,0,5,27,5,28,0],[23,28,25,26,23,4,10,15],[9,24,11,7,2,18,3,19],[22,20,3,28,16,15,8,19]];

ASOnes:=[[51,71,100,129],[51,71,80,100,101,129],[51,71,80,100,101,129],[48,51,56,71,80,100,101,105,109,129],
[48,51,56,71,80,100,101,105,109,117,129],[48,51,56,71,80,100,101,105,129],[48,51,77,80,88,100,101,105,110,123,129],
[48,51,56,71,80,100,101,105,109,117,129],[48,51,77,88,105,109,129],[48,51,71,77,80,100,101,105,110,123,129],
[48,51,56,57,61,71,77,80,100,101,105,109,110,117,119,123,129],[48,51,56,71,77,80,100,101,105,109,110,117,123,129],
[48,51,56,71,77,80,100,101,105,109,110,117,123,129],[48,51,56,71,77,80,100,101,105,109,110,117,123,129],
[48,51,71,77,80,100,101,105,110,123,129],[48,51,56,71,80,100,101,105,109,117,129],[48,51,56,61,71,80,100,101,105,117,129],
[48,51,56,57,61,71,77,80,100,101,105,109,110,117,119,123,129],[48,51,56,71,80,100,101,105,109,117,129],
[51,57,101,109,129],[48,51,56,71,80,100,101,105,109,117,129],[48,51,56,61,71,77,80,100,101,105,110,117,119,123,129],
[48,51,56,57,61,71,77,80,100,101,105,109,110,117,119,123,129],[48,51,71,77,80,92,100,101,104,110,129],
[48,51,71,77,80,92,100,101,106,123,129],[48,51,56,57,61,71,100,101,105,109,129],
[48,51,54,57,61,64,69,71,73,77,98,100,110,115,119,123],[48,51,54,57,61,64,69,71,73,77,98,100,110,115,119,123],
[48,51,54,64,69,73,104,106,115],[48,51,56,71,77,80,100,101,105,109,110,117,123,129],[48,51,56,61,71,77,100,105,110,123,129],
[48,51,56,71,77,80,100,101,105,109,110,117,123,129],[51,56,80,117,119,129],[48,51,56,71,77,80,100,101,105,109,110,117,123,129],
[51,56,57,61,71,100,109,117,119],[51,92,106],[48,51,56,57,61,71,77,80,100,101,105,109,110,123,129],
[48,51,71,77,80,100,101,105,110,123,129],[48,51,56,71,80,100,101,105,109,117,129],
[48,51,56,57,61,71,77,80,100,101,105,109,110,117,119,123,129],[48,51,54,57,61,64,69,71,73,77,98,100,110,115,119,123],
[48,51,71,80,92,100,101,110,123],[48,51,64,92,104,115],[48,51,100,101,105,117,129],[48,51,80,88],[56,57,61,109],[48,56,92],
[48,51,56,61,63,66,71,83,88,100,105,109,117],[48,110],[48,92],[48,51,56,92,106],[56,61,119],[48,51,77,88],[48,88],[48,51,56,57,66,109],
[51,92],[51,117],[48,51,56,106],[48,51,104],[48,51,57,59,109],[51,104,106],[51,92,104],[51,92,106],[51,100,117,119],[56,66,83],
[48,106,123],[56],[56,61,92],[56,83],[48,104]];

EigsOfMats481:=[[i^3:i in j]:j in EigsOfMats];

load "Subgroups/E8/Suz512/E8RepsOrder13Case10";
AllSolna:=[];
AllSoln2:=[];
AllSoln3:=[];

for jj in [10*jjj-9..Minimum(10*jjj,#ASOnes)] do
  Soln:=[];
  Soln2:=[];
  Soln3:=[];

  BaseAdd:=[13*i:i in RepsFor37s[jj]];
  Mat481:=Matrix(Rationals(),[EigsCoeffs481[i]:i in [1..46] cat ASOnes[jj]]);
  time for iii in [1..#classof13s] do
    Elt:=AddArrays([BaseAdd,[37*i:i in classof13s[iii]]]);
    EigsOfElt481:=SequenceToMultiset([&*[EigsOfMats481[j,i]^Elt[j]:j in [1..8]]:i in [1..124]]);
    EigsEltCoeff481:=[Multiplicity(EigsOfElt481,u481^j)+Multiplicity(EigsOfElt481,u481^(481-j)):j in [0..240]];
    MatElt:=Matrix(Rationals(),[EigsEltCoeff481]);
    try ss:=Solution(Mat481,MatElt); if(&and[ss[1,i] in Integers() and ss[1,i] ge 0:i in [1..NumberOfRows(Mat481)]]) then Append(~Soln,ss); Append(~Soln2,Elt); Append(~Soln3,iii); end if; catch e; end try;
    if(IsDivisibleBy(iii,10000)) then Soln,Soln2,Soln3,iii,#classof13s; end if;
    delete Elt; delete EigsOfElt481; delete EigsEltCoeff481; delete MatElt;
  end for;

  Solna:=[[i[1,j]:j in [1..46]]:i in Soln];
  for i in [1..#Soln] do for j in [1..#ASOnes[jj]] do
    if(Soln[i,1,46+j] eq 2) then Solna[i] cat:=[ASOnes[jj,j],ASOnes[jj,j]]; elif(Soln[i,1,46+j] eq 1) then Solna[i] cat:=[ASOnes[jj,j]]; end if;
  end for; end for;

  AllSolna cat:=Solna;
  AllSoln2 cat:=Soln2;
  AllSoln3 cat:=Soln3;

end for;
Soln2:=AllSoln2;

Solnb:=[{*i^^Integers()!j[i]:i in [1..46]*} join {*j[i]:i in [47..#j]*}:j in AllSolna];
Solnb,Soln2;

Solnc:=[];
Soln2c:=[];
for i in [1..#Solnb] do if({*48,49,51,52,56,57,62*} meet Solnb[i] ne {**}) then Append(~Solnc,Solnb[i]); Append(~Soln2c,Soln2[i]); end if; end for;
Solnc,Soln2c;
