# Character: X4
# Comment: complex conjugate of X.3
# Ind: 0
# Ring: C
# Sparsity: 23%
# Checker result: pass
# Conjugacy class representative result: pass

local b, B, w, W, i, result, delta, idmat;

result := rec();

w := E(3); W := E(3)^2;
b := E(7)+E(7)^2+E(7)^4; B := -1-b;  # b7, b7**
i := E(4);
result.comment := "M24 as 45 x 45 matrices\n";

result.generators := [
[[1/2,0,0,0,0,0,0,0,0,-1/8*B,-1/8*B,0,0,-1/8*B,1/8*B,1/8*B,0,-1/8*B,
  1/8*B,1/8*B,0,1/8*B,0,1/8*B,-1/8*B,-1/8*B,0,1/4,0,0,0,1/4,0,0,0,
  1/4,-1/4,0,0,0,1/8*B,1/8*B,1/8*B,0,1/8*B],
[0,0,0,0,0,1/4*b,0,-1/4*b,0,1/8,-1/8,-1/8*b,1/8*b,-1/8,-1/8,1/8,-1/8*b,
  1/8,1/8,-1/8,1/8*b,1/8,1/8*b,-1/8,-1/8,1/8,1/8*b,0,0,1/4,0,0,1/4,
  0,1/4,0,0,1/4,0,1/8*b,-1/8,1/8,-1/8,1/8*b,1/8],
[0,0,0,0,0,-1/4*b,0,-1/4*b,0,1/8,-1/8,1/8*b,-1/8*b,-1/8,-1/8,-1/8,
  -1/8*b,-1/8,-1/8,1/8,1/8*b,1/8,-1/8*b,-1/8,-1/8,1/8,-1/8*b,0,-1/4,
  0,1/4,0,0,1/4,0,0,0,0,1/4,1/8*b,1/8,-1/8,1/8,1/8*b,-1/8],
[0,0,0,1/4,0,0,-1/4,0,0,1/8*b,1/8,1/8,-1/8,-1/8*b,1/8,-1/8,1/8,1/8*b,
  1/8*b,1/8,-1/8,-1/8*b,1/8,-1/8,-1/8,-1/8*b,1/8,0,0,-1/4*b,0,0,1/4*b,
  1/4,0,0,0,0,-1/4,1/8,1/8*b,1/8,-1/8,1/8,-1/8*b],
[0,0,0,0,0,-1/4,0,1/4,0,1/8*b,-1/8,-1/8,1/8,-1/8*b,-1/8,1/8,-1/8,1/8*b,
  1/8*b,-1/8,1/8,1/8*b,1/8,-1/8,-1/8,1/8*b,1/8,0,0,-1/4*b,0,0,-1/4*b,
  0,-1/4,0,0,-1/4,0,1/8,-1/8*b,1/8,-1/8,1/8,1/8*b],
[0,1/4*B,-1/4*B,0,-1/4,0,0,0,1/4,0,1/8*B,-1/8*B,-1/8*B,0,-1/8*B,1/8*B,
  1/8*B,0,0,1/8*B,1/8*B,0,1/8*B,1/8*B,-1/8*B,0,-1/8*B,0,0,0,0,0,0,
  0,0,1/4,1/4,0,0,1/8*B,0,-1/8*B,-1/8*B,-1/8*B,0],
[0,0,0,-1/4,0,0,1/4,0,0,1/8,1/8*b,1/8,-1/8,-1/8,1/8*b,-1/8*b,1/8,1/8,
  1/8,1/8*b,-1/8,-1/8,1/8,-1/8*b,-1/8*b,-1/8,1/8,0,0,1/4,0,0,-1/4,
  -1/4*b,0,0,0,0,1/4*b,1/8,1/8,1/8*b,-1/8*b,1/8,-1/8],
[0,-1/4*B,-1/4*B,0,1/4,0,0,0,1/4,-1/8*B,0,1/8*B,1/8*B,-1/8*B,0,0,1/8*B,
  -1/8*B,1/8*B,0,1/8*B,-1/8*B,-1/8*B,0,0,1/8*B,1/8*B,1/4,0,0,0,-1/4,
  0,0,0,0,0,0,0,1/8*B,-1/8*B,0,0,-1/8*B,-1/8*B],
[0,0,0,0,0,1/4,0,1/4,0,1/8,-1/8*b,1/8,-1/8,-1/8,-1/8*b,-1/8*b,-1/8,
  -1/8,-1/8,1/8*b,1/8,1/8,-1/8,-1/8*b,-1/8*b,1/8,-1/8,0,1/4,0,-1/4,
  0,0,-1/4*b,0,0,0,0,-1/4*b,1/8,1/8,-1/8*b,1/8*b,1/8,-1/8],
[-1/8*b,1/8,1/8,1/8*B,1/8*B,0,1/8,-1/8*b,1/8,-1/4,0,0,1/8,1/8*b,1/8,
  -1/8,-1/8*b,-1/8,-1/8*B,-1/4,-1/8*B,-1/8,-1/8,-1/8*b,1/8*B,1/8*B,
  0,0,-1/8*B,1/8*B,-1/8,1/8*b,-1/8,1/8*b,-1/8,-1/8,1/8*B,-1/8*B,0,
  0,0,-1/4,-1/8,-1/8,-1/8*b],
[-1/8*b,-1/8,-1/8,1/8,-1/8,1/8*b,1/8*B,0,-1/8*B,0,1/4,0,-1/8,1/8*b,
  -1/8,-1/8*B,0,1/8*B,-1/8,-1/8*b,-1/8,-1/8*B,-1/8*B,-1/4,1/8,-1/8,
  1/8*b,1/8*b,-1/8,-1/8,-1/8*B,0,1/8*B,-1/8*b,-1/8,-1/8,1/8*B,-1/8*B,
  0,0,1/4,0,1/8,1/8,-1/8*b],
[0,-1/8*B,1/8*B,1/8,-1/8,-1/8*b,1/8,1/8*b,1/8,0,0,1/4,-1/8*B,0,1/8*B,
  1/8,-1/8*b,1/8,1/8,1/8*b,1/8,1/8,1/8,1/8*b,-1/8,1/8,1/8*b,-1/8*b,
  -1/8,-1/8,-1/8,-1/8*b,-1/8,0,1/8*B,-1/8*B,-1/4*b-1/8*B,1/4*b+1/8*B,
  0,-1/4,0,0,1/8*B,-1/8*B,0],
[0,1/8*B,-1/8*B,-1/8,1/8,-1/8*b,-1/8,1/8*b,-1/8,1/8,-1/8,-1/8*b,1/8,
  -1/8,1/8*b,0,1/4,0,0,1/8*B,-1/8*B,0,-1/8*B,1/8*B,0,0,-1/4,-1/8*b,
  1/8,-1/8,1/8,-1/8*b,-1/8,0,1/4*b+1/8*B,1/4*b+1/8*B,1/8*B,1/8*B,0,
  1/8*b,-1/8,1/8,1/8*b,1/8,1/8],
[-1/8*b,-1/8,-1/8,-1/8*B,-1/8*B,0,-1/8,-1/8*b,-1/8,1/8*B,1/8*B,0,-1/8,
  1/8,-1/8*b,-1/4,0,0,-1/8*b,-1/8,-1/8,-1/8*b,1/8,1/8,0,-1/4,0,1/8*b,
  1/8,-1/8,1/8*B,0,1/8*B,0,-1/8*B,-1/8*B,1/8,-1/8,1/8*b,1/8*b,1/8,
  -1/8,-1/4,-1/8*B,-1/8*B],
[1/8*b,-1/8,-1/8,1/8,-1/8,-1/8*b,1/8*B,0,-1/8*B,1/8,-1/8,1/8*b,1/8*B,
  -1/8*B,1/4,0,0,1/4,1/8*b,-1/8,-1/8,1/8*b,1/8,1/8,-1/4,0,0,0,-1/8*B,
  -1/8*B,-1/8,-1/8*b,1/8,0,1/8*B,1/8*B,-1/8,1/8,1/8*b,0,1/8*B,1/8*B,
  1/8*b,1/8,1/8],
[1/8*b,1/8,-1/8,-1/8,1/8,1/8*b,-1/8*B,0,-1/8*B,-1/8,-1/8*b,1/8,0,-1/4,
  0,-1/4,0,0,-1/8,1/8*b,-1/8,1/8,1/8*b,-1/8,-1/8*B,-1/4,-1/8*B,1/8*B,
  -1/8*B,0,1/8,1/8,1/8*b,-1/8*B,1/8*B,0,1/8*b,-1/8,1/8,0,1/8*B,1/8*B,
  1/8,1/8,1/8*b],
[0,-1/8*B,-1/8*B,1/8,-1/8,1/8*b,1/8,1/8*b,-1/8,-1/8*B,0,-1/8*B,1/4,
  0,0,0,1/4,0,1/8*B,0,-1/8*B,1/8,-1/8*b,-1/8,-1/8,-1/8*b,-1/8,1/4*b+1/8*B,
  -1/4*b-1/8*B,0,1/8*B,-1/8*B,0,-1/8,-1/8,-1/8*b,1/8*b,1/8,-1/8,1/8*b,
  1/8,-1/8,1/8,1/8,1/8*b],
[-1/8*b,1/8,-1/8,1/8*B,1/8*B,0,1/8,-1/8*b,-1/8,-1/8,1/8*b,1/8,0,0,
  1/4,0,0,1/4,-1/8,-1/8*b,-1/8,-1/8*B,0,-1/8*B,1/8,1/8*b,1/8,-1/8*B,
  1/8*B,0,-1/8,-1/8,1/8*b,-1/8,-1/8,1/8*b,0,1/8*B,1/8*B,1/8*b,-1/8,
  1/8,-1/8*B,-1/8*B,-1/4],
[1/8*b,1/8,-1/8,1/8*B,1/8*B,0,1/8,1/8*b,-1/8,-1/8*b,-1/8,1/8,0,-1/8*B,
  1/8*B,-1/8,1/8*b,-1/8,1/4,1/8*B,1/8*B,0,0,-1/4,-1/8*b,1/8,1/8,1/8,
  -1/8,-1/8*b,1/8*B,1/8*B,0,-1/8*B,-1/8*B,0,1/8*b,1/8,1/8,0,1/4,0,
  1/8*b,1/8,1/8],
[1/8*b,-1/8,1/8,1/8,-1/8,1/8*b,1/8*B,0,1/8*B,-1/4,-1/8*B,1/8*B,1/8*b,
  -1/8,-1/8,1/8*B,0,-1/8*B,1/8*b,1/8,1/8,1/4,0,0,-1/8*b,-1/8,-1/8,
  1/8,-1/8,1/8*b,1/8*B,1/8*B,0,1/8,-1/8,-1/8*b,0,1/8*B,-1/8*B,0,0,
  -1/4,1/8*b,-1/8,-1/8],
[0,1/8*B,1/8*B,-1/8,1/8,1/8*b,-1/8,1/8*b,1/8,-1/8*b,-1/8,1/8,-1/8*b,
  -1/8,-1/8,-1/8,-1/8*b,-1/8,1/8*b,1/8,1/8,0,1/4,0,0,-1/8*B,1/8*B,
  -1/8*B,-1/8*B,0,1/4*b+1/8*B,1/4*b+1/8*B,0,-1/8,1/8,-1/8*b,1/8*b,
  -1/8,-1/8,-1/4,0,0,0,-1/8*B,1/8*B],
[1/8*b,1/8,1/8,-1/8*B,1/8*B,0,-1/8,-1/8*b,1/8,-1/8,-1/8*b,1/8,0,-1/8*B,
  1/8*B,1/8,1/8,-1/8*b,0,1/4,0,-1/4,0,0,1/8,-1/8*b,1/8,-1/8*b,1/8,
  -1/8,1/8*B,0,1/8*B,0,-1/8*B,1/8*B,-1/8,-1/8,1/8*b,-1/8*B,1/8*B,1/4,
  1/8,1/8*b,-1/8],
[0,1/8*B,-1/8*B,1/8,1/8,1/8*b,1/8,-1/8*b,-1/8,-1/8,-1/8*b,1/8,-1/8*b,
  1/8,1/8,1/8*B,-1/8*B,0,0,0,1/4,0,1/4,0,-1/8*B,0,1/8*B,-1/8*b,-1/8,
  1/8,-1/8,-1/8*b,1/8,0,-1/4*b-1/8*B,1/4*b+1/8*B,1/8*B,-1/8*B,0,-1/8,
  1/8,1/8*b,1/8,-1/8*b,-1/8],
[1/8*b,-1/8,-1/8,-1/8,-1/8,1/8*b,-1/8*B,0,-1/8*B,-1/8*B,-1/4,1/8*B,
  1/8*b,1/8,1/8,-1/8,-1/8,-1/8*b,-1/4,0,0,0,0,1/4,-1/8,-1/8*b,-1/8,
  0,1/8*B,1/8*B,1/8,-1/8*b,-1/8,0,-1/8*B,1/8*B,-1/8,-1/8,-1/8*b,-1/8,
  1/8,1/8*b,1/8*B,0,1/8*B],
[-1/8*b,-1/8,-1/8,-1/8,-1/8,-1/8*b,-1/8*B,0,-1/8*B,1/8*b,1/8,-1/8,
  0,0,-1/4,-1/8*b,-1/8,1/8,-1/8*B,-1/8*B,0,1/8,-1/8*b,-1/8,1/4,1/8*B,
  1/8*B,1/8*b,1/8,1/8,1/8*B,0,-1/8*B,1/8*b,1/8,-1/8,1/8*B,1/8*B,0,
  -1/8,-1/8*b,1/8,0,0,1/4],
[-1/8*b,1/8,1/8,-1/8*B,1/8*B,0,-1/8,1/8*b,1/8,1/8*b,-1/8,1/8,0,-1/4,
  0,-1/4,-1/8*B,1/8*B,1/8,-1/8,-1/8*b,-1/8*B,0,-1/8*B,1/8*b,1/8,1/8,
  0,1/8*B,-1/8*B,1/8,1/8*b,1/8,-1/8*b,1/8,-1/8,1/8*B,1/8*B,0,1/8,-1/8*b,
  -1/8,-1/4,0,0],
[0,1/8*B,-1/8*B,1/8,1/8,-1/8*b,1/8,1/8*b,-1/8,0,1/8*B,1/8*B,-1/4,0,
  0,-1/8*b,-1/8,1/8,1/8,-1/8,1/8*b,1/8,1/8*b,-1/8,1/8*b,1/8,1/8,1/8*b,
  -1/8,-1/8,-1/8,1/8*b,-1/8,0,1/8*B,1/8*B,1/4*b+1/8*B,1/4*b+1/8*B,
  0,-1/8*B,0,-1/8*B,0,-1/4,0],
[1/4,0,0,0,0,0,0,1/4,0,0,1/8*B,-1/8*B,-1/8*B,1/8*B,0,1/8*b,1/8*b+1/4*B,
  -1/8*b,1/8,1/8,-1/8*b,-1/8*B,-1/8*B,0,1/8*B,0,1/8*B,1/8,1/8*b,-1/8,
  -1/8*b,1/8,-1/8,-1/8,-1/8*b,1/8,-1/8,-1/8*b,-1/8,-1/8*b-1/4*B,1/8*b,
  1/8*b,1/8,-1/8*b,1/8],
[0,0,-1/4,0,0,0,0,0,1/4,-1/8*b,-1/8,-1/8,1/8,1/8,-1/8*b,-1/8*b,-1/8*b-1/4*B,
  1/8*b,-1/8,-1/8,-1/8*b,1/8,-1/8,1/8*b,1/8,1/8*b,-1/8,1/8*B,0,1/8*B,
  0,-1/8*B,-1/8*B,1/8*B,0,1/8*B,1/8*B,0,-1/8*B,-1/8*b-1/4*B,1/8*b,
  1/8*b,1/8,1/8*b,1/8],
[0,1/4,0,-1/4*B,-1/4*B,0,1/4,0,0,1/8*b,-1/8,-1/8,-1/8,-1/8,-1/8*b,
  0,0,0,-1/8*B,1/8*B,0,-1/8,1/8,1/8*b,1/8,-1/8*b,-1/8,-1/8,1/8*b,1/8,
  1/8*b,1/8,-1/8,-1/8,1/8*b,1/8,1/8,-1/8*b,1/8,0,0,0,-1/8*B,0,1/8*B
  ],
[0,0,1/4,0,0,0,0,0,-1/4,-1/8,-1/8*b,-1/8,1/8,1/8*b,-1/8,1/8,1/8*b,
  -1/8,1/8*b,1/8*b,1/8*b+1/4*B,1/8*b,-1/8,1/8,1/8*b,1/8,-1/8,-1/8*B,
  0,1/8*B,0,1/8*B,-1/8*B,1/8*B,0,-1/8*B,-1/8*B,0,-1/8*B,1/8*b,-1/8,
  -1/8,-1/8*b,-1/8*b-1/4*B,-1/8*b],
[1/4,0,0,0,0,0,0,-1/4,0,1/8*B,0,-1/8*B,-1/8*B,0,-1/8*B,1/8,-1/8*b,
  -1/8,1/8*b,1/8*b,1/8*b+1/4*B,0,-1/8*B,-1/8*B,0,1/8*B,1/8*B,1/8,-1/8*b,
  1/8,1/8*b,1/8,1/8,1/8,1/8*b,1/8,-1/8,1/8*b,1/8,1/8*b,1/8,1/8,1/8*b,
  1/8*b+1/4*B,1/8*b],
[0,1/4,0,1/4*B,-1/4*B,0,-1/4,0,0,-1/8,1/8*b,-1/8,-1/8,1/8*b,1/8,1/8*B,
  0,1/8*B,0,0,0,1/8*b,1/8,-1/8,-1/8*b,1/8,-1/8,-1/8,-1/8*b,-1/8,-1/8*b,
  1/8,1/8,1/8,-1/8*b,1/8,1/8,1/8*b,-1/8,0,1/8*B,-1/8*B,0,0,0],
[0,0,1/4,1/4,0,0,-1/4*B,0,-1/4*B,1/8*B,-1/8*B,0,0,0,0,-1/8*b,-1/8,
  -1/8,-1/8*b,1/8,-1/8,0,0,0,1/8*B,-1/8*B,0,-1/8,1/8*b,-1/8,1/8*b,
  1/8,1/8,1/8,1/8*b,-1/8,-1/8,-1/8*b,-1/8,-1/8,-1/8,1/8*b,-1/8,1/8,
  1/8*b],
[0,1/4,0,0,-1/4,0,0,0,0,-1/8,-1/8,1/8*b,1/8*b+1/4*B,-1/8*b,1/8*b,1/8*b,
  -1/8,-1/8,-1/8*b,-1/8,1/8,-1/8*b,-1/8*b-1/4*B,-1/8*b,1/8,1/8,1/8*b,
  -1/8*B,0,1/8*B,0,1/8*B,-1/8*B,1/8*B,0,1/8*B,1/8*B,0,-1/8*B,-1/8,
  -1/8,-1/8*b,1/8,-1/8,1/8*b],
[1/4,0,0,0,0,1/4,0,0,0,-1/8,-1/8,-1/8*b,1/8*b+1/4*B,-1/8*b,1/8*b,0,
  -1/8*B,1/8*B,0,-1/8*B,-1/8*B,1/8*b,1/8*b+1/4*B,1/8*b,-1/8,-1/8,1/8*b,
  1/8,1/8*b,1/8,-1/8*b,1/8,1/8,-1/8,1/8*b,1/8,-1/8,1/8*b,-1/8,1/8*B,
  -1/8*B,0,-1/8*B,-1/8*B,0],
[-1/4,0,0,0,0,1/4,0,0,0,1/8*b,1/8*b,-1/8*b-1/4*B,1/8*b,1/8,-1/8,1/8*B,
  1/8*B,0,1/8*B,0,1/8*B,-1/8,1/8*b,-1/8,1/8*b,1/8*b,1/8*b+1/4*B,-1/8,
  1/8*b,1/8,-1/8*b,-1/8,1/8,-1/8,1/8*b,-1/8,1/8,1/8*b,-1/8,-1/8*B,
  0,1/8*B,0,1/8*B,1/8*B],
[0,1/4,0,0,-1/4,0,0,0,0,-1/8*b,-1/8*b,1/8*b+1/4*B,1/8*b,-1/8,1/8,-1/8,
  1/8,1/8*b,1/8,1/8*b,-1/8,-1/8,-1/8*b,-1/8,1/8*b,1/8*b,1/8*b+1/4*B,
  -1/8*B,0,-1/8*B,0,1/8*B,1/8*B,-1/8*B,0,1/8*B,1/8*B,0,1/8*B,1/8,1/8*b,
  1/8,-1/8*b,1/8,-1/8],
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  0,0,0,-1/8*b,1/8,-1/8,1/8,1/8,1/8*b],
[0,-1/8*B,-1/8*B,1/8*B,0,-1/8*B,0,0,0,1/8*b,1/8,1/8,1/8*b,1/8,-1/8,
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  -1/8*b],
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  0,0,0,-1/8,1/8*b,-1/8,1/8,1/8*b,1/8],
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  0,0,0,0,1/8*B,0,-1/8*B,-1/8*B,0,1/8*B],
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  1/8*b,-1/8],
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  1/8,0,0,-1/4,0,-1/4,0,1/8,-1/8*b,1/8,-1/8,-1/8,-1/8*b],
[-1/4,1/4,-1/4*b,0,1/8*B,-1/8*B,1/8*B,0,1/8*B,1/8*B,1/8*B,0,0,-1/8*B,
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  0,-1/4,0,0,0,-1/4,-1/8*B,0,1/8*B,1/8*B,-1/8*B,0],
[0,0,0,-1/8*b,1/8,1/8,1/8,1/8*b,-1/8,1/8,-1/8,1/8*b,1/8*b,1/8,-1/8,
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  1/8,1/4,0,0,-1/4,0,0,1/8,1/8*b,1/8,-1/8,-1/8,1/8*b],
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  1/4,0,0,1/4,0,0,1/8*b,1/8,-1/8,1/8,-1/8*b,1/8],
[-1/4,1/4*b,-1/4,-1/8*B,1/8*B,0,0,-1/8*B,1/8*B,0,-1/8*B,1/8*B,-1/8*B,
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  0,0,-1/4,0,0,0,1/4,0,-1/8*B,-1/8*B,-1/8*B,0,1/8*B],
[0,0,0,1/8,1/8,1/8*b,1/8*b,-1/8,-1/8,1/8*b,-1/8,-1/8,-1/8,1/8*b,-1/8,
  0,1/4*b,0,-1/4*b,0,0,1/4,0,0,0,0,1/4,1/8,1/8*b,-1/8,1/8,1/8,-1/8*b,
  0,0,-1/4,0,-1/4,0,-1/8*b,1/8,-1/8,1/8,1/8*b,1/8]]];

return result;