# Character: X4 # Comment: complex conjugate of X.3 # Ind: 0 # Ring: Q(w) # Sparsity: 81% # 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 := "U38 as 57 x 57 matrices\n"; result.generators := [ [[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, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1], [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, 0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], 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2/3*w-32/3*W,19/3*w+2/3*W,14/3*w+13/3*W,-6*w+6*W,8*w+5*W,7*w+4*W, 2/3*w-5/3*W,1/3*w+5/3*W,-4*w,10/3*w+11/3*W,-5*w+2*W,-11*W,2/3*w-11/3*W, 4*w+9*W,5/3*w-2/3*W,3*w+7*W,-14/3*w-10/3*W,-5*w+2*W,-6*w+2*W], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [-37*w-5*W,-28*w-16*W,59/3*w-32/3*W,43/3*w-19/3*W,-46/3*w-2/3*W,37/3*w-7/3*W, -80/3*w-97/3*W,-19/3*w+13/3*W,-8*w-30*W,115/3*w+83/3*W,5*w-5*W,62/3*w+34/3*W, -15*w-8*W,62/3*w+46/3*W,-119/3*w-40/3*W,-17*w+W,28/3*w+47/3*W,-49/3*w-5/3*W, 97/3*w+11/3*W,-10/3*w+19/3*W,-53/3*w-31/3*W,4*w+W,27*w+13*W,-50/3*w-46/3*W, -1/3*w-32/3*W,3*w-3*W,97/3*w+59/3*W,2*w+37*W,-46/3*w-44/3*W,35/3*w-2/3*W, 6*w+24*W,14*w-7*W,20*w+12*W,25/3*w+20/3*W,2*w+25*W,11/3*w+61/3*W, 9*w+28*W,-100/3*w-74/3*W,64/3*w-67/3*W,50/3*w+28/3*W,40/3*w+53/3*W, -34*w-3*W,18*w+22*W,-20,16/3*w+2/3*W,2/3*w+16/3*W,-12*w-6*W,20/3*w+52/3*W, -19*w-6*W,21*w-18*W,28/3*w-34/3*W,-w+24*W,34/3*w+14/3*W,20*W,-34/3*w-53/3*W, -20*w-5*W,-31*w-9*W]]]; return result;