# Character: X4 # Comment: Galois conjugate of X.5 # Ind: 1 # Ring: C # Sparsity: 73% # 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 := "L28 as 7 x 7 matrices\n"; result.generators := [ [[0,1,0,0,0,0,0], [1,0,0,0,0,0,0], [0,0,-1,0,0,0,0], [0,0,0,0,0,1,0], [0,0,0,0,-1,0,0], [0,0,0,1,0,0,0], [-E(9)^2-E(9)^7,E(9)^2+E(9)^7,-E(9)^2+E(9)^3-E(9)^4-E(9)^5+E(9)^6-E(9)^7, 1,-E(9)^2+E(9)^3-E(9)^4-E(9)^5+E(9)^6-E(9)^7,-1,1]] , [[0,0,1,0,0,0,0], [0,0,0,1,0,0,0], [0,0,0,0,1,0,0], [0,0,0,0,0,0,1], [1,0,0,0,0,0,0], [1/3*E(9)^3-1/3*E(9)^4-1/3*E(9)^5+1/3*E(9)^6,-2/3*E(9)^2-1/3*E(9)^3-1/3*E(9)^6-2/3*E(9)^7, -2/3*E(9)^3+2/3*E(9)^4+2/3*E(9)^5-2/3*E(9)^6,1/3*E(9)^2+2/3*E(9)^3+2/3*E(9)^6+1/3*E(9)^7, 1/3*E(9)^3-1/3*E(9)^4-1/3*E(9)^5+1/3*E(9)^6,1,1/3*E(9)^2-1/3*E(9)^3-1/3*E(9)^6+1/3*E(9)^7 ], [0,1,0,0,0,0,0]]]; return result;