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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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],
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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]
];

ASOnes:=[[49,50,51,52,55,58,68,70,71,81,82,85,90,94,99,100,102,105,108,114,116,124,125],
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[47,48,50,51,55,56,58,61,63,66,67,68,70,82,84,88,94,99,102,108,114,116,125],[47,55,57,62,78,82,105,109,129],
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[47,48,49,50,51,52,54,55,56,57,58,60,61,62,64,65,69,70,73,77,78,79,80,81,82,85,86,89,91,92,93,94,98,101,102,103,104,106,107,109,110,113,114,115,116,118,120,123,124,125,126,129],
[47,48,50,51,54,55,56,57,58,61,64,65,67,69,70,73,77,78,79,82,84,85,86,87,89,91,92,94,98,102,103,104,106,107,108,109,110,114,115,116,117,119,120,123,125,126],
[47,48,50,51,54,55,56,58,61,64,65,67,69,70,73,77,78,79,82,84,85,86,87,89,91,92,94,98,102,103,104,106,107,108,110,114,115,116,117,119,120,123,125,126],
[47,50,54,55,64,69,73,89,103,104,106,107,115],
[47,48,49,50,51,54,55,56,57,58,60,61,62,64,65,67,68,69,70,71,73,77,78,79,80,82,84,85,86,87,89,91,92,93,94,98,99,100,101,102,103,104,105,106,108,109,110,113,114,115,116,117,118,119,120,123,125,126,129],
[47,48,49,50,51,52,54,55,58,60,64,65,69,70,71,73,78,79,81,82,85,86,89,92,93,94,98,100,102,104,105,108,113,114,115,116,118,120,124,125,126],
[47,48,49,50,51,54,55,56,57,58,60,61,62,64,65,67,68,69,70,71,73,77,78,79,80,82,84,85,86,87,89,91,92,93,94,98,99,100,101,102,103,104,105,106,108,109,110,113,114,115,116,117,118,119,120,123,125,126,129],
[47,48,49,50,51,52,55,56,61,67,69,78,82,84,86,89,91,92,103,104,106,107,117,120,124],
[47,49,51,52,55,56,61,62,68,70,71,81,82,85,100,102,105,113,117,119,120,124],
[47,48,49,50,51,52,54,55,56,57,58,60,61,62,64,65,67,68,69,70,71,73,77,78,79,80,81,82,84,85,86,87,92,93,94,98,99,100,101,102,104,105,106,108,109,110,113,114,115,116,117,118,119,120,123,124,125,126,129],
[47,48,49,50,51,52,54,55,56,57,58,61,62,65,67,69,70,78,82,84,85,86,87,89,91,92,102,103,104,106,107,109,117,119,120,124,125],
[47,50,55,57,61,65,69,89,91,92,103,104,106,107,119],
[47,48,50,51,54,55,56,57,58,60,61,63,64,66,67,68,70,71,73,77,79,80,82,83,84,85,86,87,89,91,92,94,98,100,101,102,103,104,105,106,108,109,110,114,115,116,117,118,119,120,123,125,126,129],
[47,48,50,51,54,55,56,57,58,60,61,62,63,66,67,68,70,73,77,79,80,82,83,84,85,86,87,88,90,92,94,99,101,102,104,106,108,109,110,114,115,116,117,118,119,120,123,125,126,129],
[47,48,49,50,51,54,55,56,57,60,61,62,63,64,66,67,68,69,70,71,77,78,79,80,82,84,85,86,89,90,93,94,98,99,100,101,102,103,104,105,106,109,113,115,116,117,118,119,120,123,125,126,129],
[47,48,49,50,51,52,54,55,56,57,58,60,61,62,63,64,65,66,67,68,69,70,71,73,77,78,79,81,82,83,84,85,86,87,89,91,92,93,94,98,100,102,103,104,105,106,108,109,110,113,114,115,116,117,118,119,120,123,124,125,126],
[47,48,50,51,54,55,56,57,58,61,64,65,67,69,70,73,77,78,79,82,84,85,86,87,89,91,92,98,102,103,104,106,107,108,109,110,115,116,117,119,120,123,125,126],
[47,48,50,51,54,55,57,58,60,61,63,66,67,70,71,73,82,83,84,85,87,89,91,92,94,98,100,102,105,106,108,110,114,115,116,118,119,123,125],
[47,50,54,55,64,65,69,73,89,92,98,104,115],[47,48,50,51,52,55,56,57,60,61,62,67,68,71,77,80,81,82,85,90,93,94,99,100,101,102,105,113,116,117,118,119,120,123,129],
[47,48,50,51,55,56,57,60,61,63,66,67,68,83,85,87,88,94,116,123],[47,56,57,61,62,97,109],[47,48,55,56,57,61,71,74,90,94],
[47,48,53,55,56,61,63,68,70,74,84,90,92,94,102,116,117],[47,48,50,63,84,114,116],[47,55,109],[47,48,50,70,95],[47,48,55,79,85,86,95,103,106,107,120,122],
[47,55,83],[47,56,61,62,111,117,119,128],[47,83,87],[47,50,55,63,88],[47,50,55,56,57,66,67,72,109],[47,57,109,119],[55,91],[47,50,55,83,112,117],
[47,55,103,106],[47,50,76,83,87,104,108,112],[47,53,65,76,89,104,107,126],[47,57,89,103,104],[47,107],[47,107],[50,55,107],[47,91,92],[47,55,117,119],
[47,50,55,66,83,88],[47,48,50,66,67,85,106,122],[47,50,66,67],[47,56],[47,83],[47,89]];


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

EigsOfMats481:=[[i^3:i in j]:j in EigsOfMats];
Mat481:=Matrix(Rationals(),[EigsCoeffs481[i]:i in [1..46] cat ASOnes[jj]]);

load "Subgroups/E8/Suz512/E8RepsOrder13Case16";

Soln:=[];
Soln2:=[];
Soln3:=[];
BaseAdd:=[13*i:i in RepsFor37s[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;

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

Solnc:=[];
Soln2c:=[];
for i in [1..#Solnb] do if({*47,50,55*} meet Solnb[i] ne {**}) then Append(~Solnc,Solnb[i]); Append(~Soln2c,Soln2[i]); end if; end for;
Solnc,Soln2c;
