# Character: X2 # Comment: Weil rep. # Ind: 1 # Ring: C # Sparsity: 64% # Checker result: pass # Conjugacy class representative result: pass local a, A, b, B, c, C, w, W, i, result, delta, idmat; result := rec(); w := E(3); W := E(3)^2; a := E(5)+E(5)^4; A := -1-a; # b5, b5* b := E(7)+E(7)^2+E(7)^4; B := -1-b; # b7, b7** c := E(11)+E(11)^3+E(11)^4+E(11)^5+E(11)^9; C := -1-c; # b11, b11** i := E(4); result.comment := "S65 as 63 x 63 matrices\n"; result.generators := [ [[1/5,0,0,1/5*E(5)^4,0,0,0,0,1/5*E(5),0,0,0,0,0,0,1/5*E(5)^4,0,0,0, 0,1/5*E(5)^4,0,0,0,0,1/5*E(5)^2,0,0,0,0,1/5*E(5)^2,0,0,0,0,1/5*E(5)^3, 0,0,0,0,0,1/5*E(5),0,0,0,0,1/5*E(5)^2,0,0,0,0,1/5*E(5),0,0,0,0,1/5*E(5)^3, 0,0,0,0,1/5*E(5)^3,0], [0,1/5,0,0,1/5,0,1/5*E(5)^3,0,0,1/5*E(5)^3,0,1/5*E(5)^4,0,0,1/5*E(5)^3, 0,0,1/5,0,1/5*E(5)^4,0,0,1/5*E(5)^4,0,1/5*E(5)^3,0,0,1/5*E(5),0, 1/5,0,0,1/5*E(5)^4,0,1/5,0,0,1/5*E(5),1/5*E(5)^3,0,0,0,1/5*E(5)^4, 1/5*E(5)^3,0,0,0,1/5*E(5),1/5*E(5),0,0,0,1/5*E(5),1/5*E(5),0,0,0, 1/5,1/5*E(5)^2,0,0,0,1/5*E(5)^4], [0,0,1/5,0,0,1/5*E(5),0,1/5*E(5)^2,0,0,1/5,0,1/5*E(5)^2,1/5*E(5)^2, 0,0,1/5*E(5),0,1/5*E(5)^4,0,0,1/5*E(5)^4,0,1/5*E(5)^4,0,0,1/5,0, 1/5*E(5)^3,0,0,1/5*E(5),0,1/5*E(5)^2,0,0,1/5*E(5)^4,0,0,1/5,1/5*E(5)^2, 0,0,0,1/5*E(5)^4,1/5,0,0,0,1/5*E(5),1/5*E(5),0,0,0,1/5*E(5)^4,1/5*E(5)^2, 0,0,0,1/5*E(5),1/5,0,0], [2/5*E(5),0,0,2/5,0,0,0,0,2/5*E(5)^2,0,0,0,0,0,0,1/5*a,0,0,0,0,1/5*a, 0,0,0,0,1/5*E(5)^2+1/5*E(5)^4,0,0,0,0,1/5*E(5)^2+1/5*E(5)^4,0,0, 0,0,-1/5*E(5)-1/5*E(5)^2-1/5*E(5)^4,0,0,0,0,0,-1/5*E(5)-1/5*E(5)^2-1/5*E(5)^3, 0,0,0,0,-1/5*E(5)^2-1/5*E(5)^3-1/5*E(5)^4,0,0,0,0,-1/5*E(5)-1/5*E(5)^2-1/5*E(5)^3, 0,0,0,0,1/5*E(5)+1/5*E(5)^2,0,0,0,0,1/5*E(5)+1/5*E(5)^2,0], [0,1/5,0,0,1/5,0,1/5*E(5)^3,0,0,1/5*E(5)^3,0,1/5*E(5)^4,0,0,1/5*E(5)^4, 0,0,1/5*E(5)^4,0,1/5,0,0,1/5*E(5)^3,0,1/5*E(5)^4,0,0,1/5,0,1/5*E(5), 0,0,1/5*E(5)^3,0,1/5*E(5),0,0,1/5,1/5*E(5),0,0,0,1/5*E(5),1/5*E(5), 0,0,0,1/5*E(5)^3,1/5*E(5)^4,0,0,0,1/5*E(5)^3,1/5*E(5)^4,0,0,0,1/5*E(5)^2, 1/5,0,0,0,1/5*E(5)], [0,0,1/5*E(5)^4,0,0,1/5,0,1/5*E(5),0,0,1/5*E(5)^4,0,1/5*E(5),1/5*E(5)^2, 0,0,1/5*E(5)^4,0,1/5*E(5)^4,0,0,1/5*E(5)^2,0,1/5*E(5)^4,0,0,1/5*E(5)^3, 0,1/5*E(5)^3,0,0,1/5*E(5)^4,0,1/5*E(5)^2,0,0,1/5*E(5)^2,0,0,1/5*E(5)^2, 1/5*E(5)^3,0,0,0,1/5*E(5),1/5*E(5),0,0,0,1/5*E(5)^3,1/5*E(5)^2,0, 0,0,1/5*E(5),1/5*E(5)^3,0,0,0,1/5*E(5)^3,1/5*E(5),0,0], [0,1/5*E(5)^2,0,0,1/5*E(5)^2,0,1/5,0,0,1/5,0,1/5*E(5),0,0,1/5*E(5)^4, 0,0,1/5*E(5)^3,0,1/5,0,0,1/5*E(5)^2,0,1/5*E(5)^4,0,0,1/5*E(5)^4, 0,1/5*E(5),0,0,1/5*E(5)^2,0,1/5*E(5),0,0,1/5*E(5)^4,1/5*E(5)^2,0, 0,0,1/5*E(5)^4,1/5*E(5)^2,0,0,0,1/5*E(5),1/5,0,0,0,1/5*E(5),1/5, 0,0,0,1/5,1/5*E(5),0,0,0,1/5*E(5)^4], [0,0,1/5*E(5)^3,0,0,1/5*E(5)^4,0,1/5,0,0,1/5*E(5)^3,0,1/5,1/5*E(5)^4, 0,0,1/5,0,1/5*E(5),0,0,1/5*E(5)^3,0,1/5*E(5),0,0,1/5*E(5)^4,0,1/5, 0,0,1/5,0,1/5*E(5)^4,0,0,1/5*E(5)^3,0,0,1/5,1/5*E(5)^3,0,0,0,1/5*E(5)^4, 1/5*E(5),0,0,0,1/5*E(5),1/5*E(5)^2,0,0,0,1/5*E(5)^4,1/5*E(5)^3,0, 0,0,1/5*E(5),1/5*E(5),0,0], [2/5*E(5)^4,0,0,2/5*E(5)^3,0,0,0,0,2/5,0,0,0,0,0,0,-1/5*E(5)^2-1/5*E(5)^3-1/5*E(5)^4, 0,0,0,0,-1/5*E(5)^2-1/5*E(5)^3-1/5*E(5)^4,0,0,0,0,1/5*E(5)^3+1/5*E(5)^4, 0,0,0,0,1/5*E(5)^3+1/5*E(5)^4,0,0,0,0,-1/5*E(5)-1/5*E(5)^2-1/5*E(5)^3, 0,0,0,0,0,1/5*a,0,0,0,0,-1/5*E(5)-1/5*E(5)^3-1/5*E(5)^4,0,0,0,0, 1/5*a,0,0,0,0,1/5*E(5)+1/5*E(5)^3,0,0,0,0,1/5*E(5)+1/5*E(5)^3,0], [0,1/5*E(5)^2,0,0,1/5*E(5)^2,0,1/5,0,0,1/5,0,1/5*E(5),0,0,1/5*E(5)^2, 0,0,1/5,0,1/5*E(5)^3,0,0,1/5*E(5)^4,0,1/5*E(5)^2,0,0,1/5*E(5),0, 1/5*E(5)^4,0,0,1/5*E(5)^4,0,1/5*E(5)^4,0,0,1/5*E(5),1/5*E(5),0,0, 0,1/5,1/5*E(5),0,0,0,1/5*E(5)^2,1/5*E(5)^4,0,0,0,1/5*E(5)^2,1/5*E(5)^4, 0,0,0,1/5*E(5),1/5,0,0,0,1/5], [0,0,1/5,0,0,1/5*E(5),0,1/5*E(5)^2,0,0,1/5,0,1/5*E(5)^2,1/5*E(5)^4, 0,0,1/5*E(5)^4,0,1/5*E(5),0,0,1/5*E(5)^2,0,1/5*E(5),0,0,1/5*E(5)^3, 0,1/5,0,0,1/5*E(5)^4,0,1/5*E(5)^4,0,0,1/5*E(5)^2,0,0,1/5*E(5),1/5*E(5), 0,0,0,1/5,1/5*E(5)^4,0,0,0,1/5*E(5)^2,1/5,0,0,0,1/5,1/5*E(5),0,0, 0,1/5*E(5)^2,1/5*E(5)^4,0,0], [0,1/5*E(5),0,0,1/5*E(5),0,1/5*E(5)^4,0,0,1/5*E(5)^4,0,1/5,0,0,1/5*E(5)^2, 0,0,1/5*E(5)^3,0,1/5*E(5)^3,0,0,1/5*E(5)^2,0,1/5*E(5)^2,0,0,1/5*E(5)^4, 0,1/5*E(5)^4,0,0,1/5*E(5)^2,0,1/5*E(5)^4,0,0,1/5*E(5)^4,1/5*E(5)^3, 0,0,0,1/5*E(5),1/5*E(5)^3,0,0,0,1/5*E(5)^3,1/5*E(5),0,0,0,1/5*E(5)^3, 1/5*E(5),0,0,0,1/5*E(5)^2,1/5*E(5)^2,0,0,0,1/5*E(5)], [0,0,1/5*E(5)^3,0,0,1/5*E(5)^4,0,1/5,0,0,1/5*E(5)^3,0,1/5,1/5*E(5)^3, 0,0,1/5*E(5),0,1/5,0,0,1/5*E(5)^4,0,1/5,0,0,1/5,0,1/5*E(5)^4,0,0, 1/5*E(5),0,1/5*E(5)^3,0,0,1/5*E(5)^4,0,0,1/5*E(5)^2,1/5*E(5),0,0, 0,1/5*E(5),1/5*E(5)^4,0,0,0,1/5*E(5)^3,1/5,0,0,0,1/5*E(5),1/5*E(5), 0,0,0,1/5*E(5)^3,1/5*E(5)^4,0,0], [0,0,1/5*E(5)^3,0,0,1/5*E(5)^3,0,1/5*E(5),0,0,1/5*E(5),0,1/5*E(5)^2, 1/5,0,0,1/5*E(5)^4,0,1/5*E(5),0,0,1/5*E(5)^3,0,1/5,0,0,1/5,0,1/5*E(5)^2, 0,0,1/5*E(5)^3,0,1/5*E(5)^2,0,0,1/5,0,0,1/5*E(5)^3,1/5,0,0,0,1/5*E(5)^3, 1/5*E(5)^2,0,0,0,1/5*E(5),1/5*E(5)^2,0,0,0,1/5*E(5),1/5*E(5),0,0, 0,1/5*E(5)^2,1/5,0,0], [0,1/5*E(5)^2,0,0,1/5*E(5),0,1/5*E(5),0,0,1/5*E(5)^3,0,1/5*E(5)^3, 0,0,1/5,0,0,1/5*E(5)^2,0,1/5,0,0,1/5*E(5)^2,0,1/5*E(5)^3,0,0,1/5, 0,1/5*E(5)^3,0,0,1/5,0,1/5*E(5)^4,0,0,1/5*E(5),1/5,0,0,0,1/5*E(5), 1/5*E(5),0,0,0,1/5*E(5)^2,1/5,0,0,0,1/5*E(5),1/5*E(5)^2,0,0,0,1/5*E(5)^3, 1/5*E(5)^2,0,0,0,1/5*E(5)^3], [2/5*E(5),0,0,1/5*a,0,0,0,0,-1/5*E(5)-1/5*E(5)^2-1/5*E(5)^3,0,0,0, 0,0,0,2/5,0,0,0,0,1/5*a,0,0,0,0,-1/5*E(5)^2-1/5*E(5)^3-1/5*E(5)^4, 0,0,0,0,1/5*E(5)^2+1/5*E(5)^4,0,0,0,0,1/5*E(5)+1/5*E(5)^2,0,0,0, 0,0,2/5*E(5)^2,0,0,0,0,1/5*E(5)^2+1/5*E(5)^4,0,0,0,0,-1/5*E(5)-1/5*E(5)^2-1/5*E(5)^3, 0,0,0,0,-1/5*E(5)-1/5*E(5)^2-1/5*E(5)^4,0,0,0,0,1/5*E(5)+1/5*E(5)^2, 0], [0,0,1/5*E(5)^4,0,0,1/5*E(5),0,1/5,0,0,1/5*E(5),0,1/5*E(5)^4,1/5*E(5), 0,0,1/5,0,1/5*E(5)^4,0,0,1/5*E(5)^2,0,1/5,0,0,1/5*E(5)^2,0,1/5*E(5), 0,0,1/5*E(5),0,1/5*E(5)^4,0,0,1/5,0,0,1/5*E(5)^4,1/5*E(5),0,0,0, 1/5*E(5)^2,1/5,0,0,0,1/5*E(5)^3,1/5*E(5)^2,0,0,0,1/5*E(5)^4,1/5, 0,0,0,1/5*E(5)^2,1/5*E(5)^2,0,0], [0,1/5,0,0,1/5*E(5),0,1/5*E(5)^2,0,0,1/5,0,1/5*E(5)^2,0,0,1/5*E(5)^3, 0,0,1/5,0,1/5,0,0,1/5*E(5)^3,0,1/5,0,0,1/5*E(5)^4,0,1/5*E(5)^4,0, 0,1/5,0,1/5*E(5)^3,0,0,1/5*E(5)^3,1/5*E(5)^3,0,0,0,1/5*E(5)^4,1/5*E(5)^2, 0,0,0,1/5*E(5)^2,1/5*E(5)^4,0,0,0,1/5*E(5)^3,1/5*E(5)^2,0,0,0,1/5*E(5)^4, 1/5*E(5)^4,0,0,0,1/5*E(5)^2], [0,0,1/5*E(5),0,0,1/5*E(5),0,1/5*E(5)^4,0,0,1/5*E(5)^4,0,1/5,1/5*E(5)^4, 0,0,1/5*E(5),0,1/5,0,0,1/5,0,1/5*E(5)^4,0,0,1/5*E(5)^2,0,1/5*E(5), 0,0,1/5,0,1/5*E(5),0,0,1/5*E(5)^2,0,0,1/5*E(5)^4,1/5,0,0,0,1/5*E(5)^4, 1/5*E(5)^2,0,0,0,1/5*E(5)^2,1/5*E(5)^2,0,0,0,1/5*E(5)^2,1/5*E(5), 0,0,0,1/5*E(5)^3,1/5,0,0], [0,1/5*E(5),0,0,1/5,0,1/5,0,0,1/5*E(5)^2,0,1/5*E(5)^2,0,0,1/5,0,0, 1/5,0,1/5,0,0,1/5,0,1/5*E(5)^3,0,0,1/5*E(5)^3,0,1/5*E(5)^3,0,0,1/5*E(5)^3, 0,1/5*E(5)^4,0,0,1/5*E(5)^4,1/5*E(5)^2,0,0,0,1/5*E(5)^2,1/5*E(5)^3, 0,0,0,1/5*E(5)^3,1/5*E(5)^2,0,0,0,1/5*E(5)^2,1/5*E(5)^4,0,0,0,1/5*E(5)^4, 1/5*E(5)^4,0,0,0,1/5*E(5)^4], [2/5*E(5),0,0,1/5*a,0,0,0,0,-1/5*E(5)-1/5*E(5)^2-1/5*E(5)^3,0,0,0, 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0,0,0,0,-1/5*E(5)-1/5*E(5)^3,0,0,0,0,-1/5*E(5)^2-1/5*E(5)^4,0,0, 0,0,-2/5*E(5)^4,0,0,0,0]]]; return result;