# Character: X4 # Comment: Galois conjugate of X.2 # Ind: 0 # Ring: C # Sparsity: 82% # 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 := "U34 as 13 x 13 matrices\n"; result.generators := [ [[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], [0,0,1,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,1,0,0,0,0,0,0,0], [0,0,-E(5)^4,-E(5)^4,-1,-E(5)^4,0,0,0,0,0,0,0], [0,0,0,1,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,1,0,0,0,0], [E(5)^3,E(5)^3,-E(5)-E(5)^3,-E(5)-E(5)^3,0,-E(5)-E(5)^3,E(5)+E(5)^2+E(5)^4, -1,E(5)+E(5)^2+E(5)^4,0,0,0,0], [0,0,0,0,0,0,1,0,0,0,0,0,0], [-1,-1,-E(5),0,0,0,0,0,0,-1,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,1,0], [0,0,0,0,0,0,0,0,0,0,1,0,0], [E(5)^2+E(5)^4,E(5)^2+E(5)^4,E(5),2*E(5)+E(5)^3+E(5)^4,0,2*E(5)+E(5)^3+E(5)^4, -E(5)^2-E(5)^4,0,-E(5)^2-E(5)^4,0,-E(5)^2,-E(5)^2,-1]] , [[0,0,1,0,0,0,0,0,0,0,0,0,0], [0,0,0,1,0,0,0,0,0,0,0,0,0], [0,0,0,0,1,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,1,0,0,0,0,0,0], [1,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,1,0,0,0,0,0], [0,1,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,1,0,0,0], [0,0,0,0,0,0,0,0,0,0,1,0,0], [0,0,0,0,0,1,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,1], [E(5)+E(5)^3,2*E(5)+2*E(5)^3+E(5)^4,-E(5)-E(5)^3-E(5)^4,-2*a-A,E(5)^4, -a,E(5)^2-E(5)^3+E(5)^4,E(5)+E(5)^2+E(5)^4,-E(5)-E(5)^2-2*E(5)^3-E(5)^4, -E(5)^2,E(5)^3+E(5)^4,1,E(5)+E(5)^2+E(5)^3], [0,0,0,0,0,0,0,0,1,0,0,0,0]]]; return result;