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

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

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); Append(~Soln,ss); Append(~Soln2,Elt); Append(~Soln3,iii); 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;

Soln,Soln2,Soln3;
