# Character: X3 # Comment: complex conjugate of X.4 # Ind: 0 # Ring: C # Sparsity: 9% # 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 := "A9 as 21 x 21 matrices\n"; result.generators := [ [[2/5*E(15)+2/5*E(15)^2+2/5*E(15)^4+3/5*E(15)^7+2/5*E(15)^8+3/5*E(15)^11+3/5*E(15)^13+3/5*E(15)^14, 1/3*E(15)^7+1/3*E(15)^11+1/3*E(15)^13+1/3*E(15)^14,-2/3*E(15)-2/3*E(15)^2-2/3*E(15)^4-E(15)^7-2/3*E(15)^8-E(15)^11-E(15)^13-E(15)^14, 17/30*E(15)+17/30*E(15)^2+17/30*E(15)^4+3/5*E(15)^7+17/30*E(15)^8+3/5*E(15)^11+3/5*E(15)^13+3/5*E(15)^14, 3/5*E(15)+3/5*E(15)^2+3/5*E(15)^4+17/30*E(15)^7+3/5*E(15)^8+17/30*E(15)^11+17/30*E(15)^13+17/30*E(15)^14, -8/5*E(15)-8/5*E(15)^2-8/5*E(15)^4-7/5*E(15)^7-8/5*E(15)^8-7/5*E(15)^11-7/5*E(15)^13-7/5*E(15)^14, E(15)+E(15)^2+E(15)^4+4/3*E(15)^7+E(15)^8+4/3*E(15)^11+4/3*E(15)^13+4/3*E(15)^14, 1/3*E(15)+1/3*E(15)^2+1/3*E(15)^4+1/3*E(15)^8,-2/15*E(15)-2/15*E(15)^2-2/15*E(15)^4-1/5*E(15)^7-2/15*E(15)^8-1/5*E(15)^11-1/5*E(15)^13-1/5*E(15)^14, -18/5*E(15)-18/5*E(15)^2-18/5*E(15)^4-41/15*E(15)^7-18/5*E(15)^8-41/15*E(15)^11-41/15*E(15)^13-41/15*E(15)^14, 43/30*E(15)+43/30*E(15)^2+43/30*E(15)^4+17/30*E(15)^7+43/30*E(15)^8+17/30*E(15)^11+17/30*E(15)^13+17/30*E(15)^14, 11/15*E(15)+11/15*E(15)^2+11/15*E(15)^4+23/30*E(15)^7+11/15*E(15)^8+23/30*E(15)^11+23/30*E(15)^13+23/30*E(15)^14, -97/30*E(15)-97/30*E(15)^2-97/30*E(15)^4-34/15*E(15)^7-97/30*E(15)^8-34/15*E(15)^11-34/15*E(15)^13-34/15*E(15)^14, -7/15*E(15)-7/15*E(15)^2-7/15*E(15)^4-8/15*E(15)^7-7/15*E(15)^8-8/15*E(15)^11-8/15*E(15)^13-8/15*E(15)^14, 61/15*E(15)+61/15*E(15)^2+61/15*E(15)^4+44/15*E(15)^7+61/15*E(15)^8+44/15*E(15)^11+44/15*E(15)^13+44/15*E(15)^14, -107/30*E(15)-107/30*E(15)^2-107/30*E(15)^4-73/30*E(15)^7-107/30*E(15)^8-73/30*E(15)^11-73/30*E(15)^13-73/30*E(15)^14, -2,10/3*E(15)+10/3*E(15)^2+10/3*E(15)^4+8/3*E(15)^7+10/3*E(15)^8+8/3*E(15)^11+8/3*E(15)^13+8/3*E(15)^14, 3/2,-31/6*E(15)-31/6*E(15)^2-31/6*E(15)^4-23/6*E(15)^7-31/6*E(15)^8-23/6*E(15)^11-23/6*E(15)^13-23/6*E(15)^14, 13/3*E(15)+13/3*E(15)^2+13/3*E(15)^4+11/3*E(15)^7+13/3*E(15)^8+11/3*E(15)^11+11/3*E(15)^13+11/3*E(15)^14 ], [-2/5*E(15)-2/5*E(15)^2-2/5*E(15)^4-3/5*E(15)^7-2/5*E(15)^8-3/5*E(15)^11-3/5*E(15)^13-3/5*E(15)^14, 4/15*E(15)+4/15*E(15)^2+4/15*E(15)^4+1/15*E(15)^7+4/15*E(15)^8+1/15*E(15)^11+1/15*E(15)^13+1/15*E(15)^14, 1/3*E(15)^7+1/3*E(15)^11+1/3*E(15)^13+1/3*E(15)^14,-3/10*E(15)-3/10*E(15)^2-3/10*E(15)^4-8/15*E(15)^7-3/10*E(15)^8-8/15*E(15)^11-8/15*E(15)^13-8/15*E(15)^14, -4/15*E(15)-4/15*E(15)^2-4/15*E(15)^4-17/30*E(15)^7-4/15*E(15)^8-17/30*E(15)^11-17/30*E(15)^13-17/30*E(15)^14, 8/5*E(15)+8/5*E(15)^2+8/5*E(15)^4+7/5*E(15)^7+8/5*E(15)^8+7/5*E(15)^11+7/5*E(15)^13+7/5*E(15)^14, -11/15*E(15)-11/15*E(15)^2-11/15*E(15)^4-14/15*E(15)^7-11/15*E(15)^8-14/15*E(15)^11-14/15*E(15)^13-14/15*E(15)^14, -E(15)-E(15)^2-E(15)^4-2/3*E(15)^7-E(15)^8-2/3*E(15)^11-2/3*E(15)^13-2/3*E(15)^14, 2/5*E(15)+2/5*E(15)^2+2/5*E(15)^4+4/15*E(15)^7+2/5*E(15)^8+4/15*E(15)^11+4/15*E(15)^13+4/15*E(15)^14, 29/15*E(15)+29/15*E(15)^2+29/15*E(15)^4+41/15*E(15)^7+29/15*E(15)^8+41/15*E(15)^11+41/15*E(15)^13+41/15*E(15)^14, -23/30*E(15)-23/30*E(15)^2-23/30*E(15)^4-37/30*E(15)^7-23/30*E(15)^8-37/30*E(15)^11-37/30*E(15)^13-37/30*E(15)^14, 1/5*E(15)+1/5*E(15)^2+1/5*E(15)^4+3/10*E(15)^7+1/5*E(15)^8+3/10*E(15)^11+3/10*E(15)^13+3/10*E(15)^14, 67/30*E(15)+67/30*E(15)^2+67/30*E(15)^4+34/15*E(15)^7+67/30*E(15)^8+34/15*E(15)^11+34/15*E(15)^13+34/15*E(15)^14, -3/5*E(15)-3/5*E(15)^2-3/5*E(15)^4-2/5*E(15)^7-3/5*E(15)^8-2/5*E(15)^11-2/5*E(15)^13-2/5*E(15)^14, -31/15*E(15)-31/15*E(15)^2-31/15*E(15)^4-44/15*E(15)^7-31/15*E(15)^8-44/15*E(15)^11-44/15*E(15)^13-44/15*E(15)^14, 37/30*E(15)+37/30*E(15)^2+37/30*E(15)^4+53/30*E(15)^7+37/30*E(15)^8+53/30*E(15)^11+53/30*E(15)^13+53/30*E(15)^14, -1,-5/3*E(15)-5/3*E(15)^2-5/3*E(15)^4-4/3*E(15)^7-5/3*E(15)^8-4/3*E(15)^11-4/3*E(15)^13-4/3*E(15)^14, 1/2,17/6*E(15)+17/6*E(15)^2+17/6*E(15)^4+19/6*E(15)^7+17/6*E(15)^8+19/6*E(15)^11+19/6*E(15)^13+19/6*E(15)^14, -2/3*E(15)-2/3*E(15)^2-2/3*E(15)^4-4/3*E(15)^7-2/3*E(15)^8-4/3*E(15)^11-4/3*E(15)^13-4/3*E(15)^14 ], [-14/15*E(15)-14/15*E(15)^2-14/15*E(15)^4-16/15*E(15)^7-14/15*E(15)^8-16/15*E(15)^11-16/15*E(15)^13-16/15*E(15)^14, 2/3*E(15)+2/3*E(15)^2+2/3*E(15)^4+1/3*E(15)^7+2/3*E(15)^8+1/3*E(15)^11+1/3*E(15)^13+1/3*E(15)^14, 2/5*E(15)+2/5*E(15)^2+2/5*E(15)^4+3/5*E(15)^7+2/5*E(15)^8+3/5*E(15)^11+3/5*E(15)^13+3/5*E(15)^14, -1/10*E(15)-1/10*E(15)^2-1/10*E(15)^4-2/5*E(15)^7-1/10*E(15)^8-2/5*E(15)^11-2/5*E(15)^13-2/5*E(15)^14, -1,31/15*E(15)+31/15*E(15)^2+31/15*E(15)^4+29/15*E(15)^7+31/15*E(15)^8+29/15*E(15)^11+29/15*E(15)^13+29/15*E(15)^14, -4/3*E(15)-4/3*E(15)^2-4/3*E(15)^4-5/3*E(15)^7-4/3*E(15)^8-5/3*E(15)^11-5/3*E(15)^13-5/3*E(15)^14, -8/5*E(15)-8/5*E(15)^2-8/5*E(15)^4-7/5*E(15)^7-8/5*E(15)^8-7/5*E(15)^11-7/5*E(15)^13-7/5*E(15)^14, 1/5*E(15)+1/5*E(15)^2+1/5*E(15)^4-1/5*E(15)^7+1/5*E(15)^8-1/5*E(15)^11-1/5*E(15)^13-1/5*E(15)^14, 52/15*E(15)+52/15*E(15)^2+52/15*E(15)^4+53/15*E(15)^7+52/15*E(15)^8+53/15*E(15)^11+53/15*E(15)^13+53/15*E(15)^14, -37/30*E(15)-37/30*E(15)^2-37/30*E(15)^4-19/15*E(15)^7-37/30*E(15)^8-19/15*E(15)^11-19/15*E(15)^13-19/15*E(15)^14, -3/5*E(15)-3/5*E(15)^2-3/5*E(15)^4-2/5*E(15)^7-3/5*E(15)^8-2/5*E(15)^11-2/5*E(15)^13-2/5*E(15)^14, 9/2*E(15)+9/2*E(15)^2+9/2*E(15)^4+4*E(15)^7+9/2*E(15)^8+4*E(15)^11+4*E(15)^13+4*E(15)^14, 1/5*E(15)+1/5*E(15)^2+1/5*E(15)^4+4/5*E(15)^7+1/5*E(15)^8+4/5*E(15)^11+4/5*E(15)^13+4/5*E(15)^14, -68/15*E(15)-68/15*E(15)^2-68/15*E(15)^4-67/15*E(15)^7-68/15*E(15)^8-67/15*E(15)^11-67/15*E(15)^13-67/15*E(15)^14, 113/30*E(15)+113/30*E(15)^2+113/30*E(15)^4+56/15*E(15)^7+113/30*E(15)^8+56/15*E(15)^11+56/15*E(15)^13+56/15*E(15)^14, 2/3*E(15)+2/3*E(15)^2+2/3*E(15)^4+1/3*E(15)^7+2/3*E(15)^8+1/3*E(15)^11+1/3*E(15)^13+1/3*E(15)^14, -13/3*E(15)-13/3*E(15)^2-13/3*E(15)^4-11/3*E(15)^7-13/3*E(15)^8-11/3*E(15)^11-11/3*E(15)^13-11/3*E(15)^14, -11/6*E(15)-11/6*E(15)^2-11/6*E(15)^4-5/3*E(15)^7-11/6*E(15)^8-5/3*E(15)^11-5/3*E(15)^13-5/3*E(15)^14, 37/6*E(15)+37/6*E(15)^2+37/6*E(15)^4+16/3*E(15)^7+37/6*E(15)^8+16/3*E(15)^11+16/3*E(15)^13+16/3*E(15)^14, -4], [-2/5*E(15)-2/5*E(15)^2-2/5*E(15)^4-3/5*E(15)^7-2/5*E(15)^8-3/5*E(15)^11-3/5*E(15)^13-3/5*E(15)^14, -2/15*E(15)-2/15*E(15)^2-2/15*E(15)^4-1/5*E(15)^7-2/15*E(15)^8-1/5*E(15)^11-1/5*E(15)^13-1/5*E(15)^14, 2/15*E(15)+2/15*E(15)^2+2/15*E(15)^4+8/15*E(15)^7+2/15*E(15)^8+8/15*E(15)^11+8/15*E(15)^13+8/15*E(15)^14, -1/30*E(15)-1/30*E(15)^2-1/30*E(15)^4-2/15*E(15)^7-1/30*E(15)^8-2/15*E(15)^11-2/15*E(15)^13-2/15*E(15)^14, -7/15*E(15)-7/15*E(15)^2-7/15*E(15)^4-7/10*E(15)^7-7/15*E(15)^8-7/10*E(15)^11-7/10*E(15)^13-7/10*E(15)^14, 3/5*E(15)+3/5*E(15)^2+3/5*E(15)^4+2/5*E(15)^7+3/5*E(15)^8+2/5*E(15)^11+2/5*E(15)^13+2/5*E(15)^14, -2/15*E(15)-2/15*E(15)^2-2/15*E(15)^4-1/5*E(15)^7-2/15*E(15)^8-1/5*E(15)^11-1/5*E(15)^13-1/5*E(15)^14, 2/15*E(15)+2/15*E(15)^2+2/15*E(15)^4-7/15*E(15)^7+2/15*E(15)^8-7/15*E(15)^11-7/15*E(15)^13-7/15*E(15)^14, -1/3,26/15*E(15)+26/15*E(15)^2+26/15*E(15)^4+8/5*E(15)^7+26/15*E(15)^8+8/5*E(15)^11+8/5*E(15)^13+8/5*E(15)^14, -43/30*E(15)-43/30*E(15)^2-43/30*E(15)^4-17/30*E(15)^7-43/30*E(15)^8-17/30*E(15)^11-17/30*E(15)^13-17/30*E(15)^14, -6/5*E(15)-6/5*E(15)^2-6/5*E(15)^4-13/10*E(15)^7-6/5*E(15)^8-13/10*E(15)^11-13/10*E(15)^13-13/10*E(15)^14, 41/30*E(15)+41/30*E(15)^2+41/30*E(15)^4+32/15*E(15)^7+41/30*E(15)^8+32/15*E(15)^11+32/15*E(15)^13+32/15*E(15)^14, 1,-29/15*E(15)-29/15*E(15)^2-29/15*E(15)^4-31/15*E(15)^7-29/15*E(15)^8-31/15*E(15)^11-31/15*E(15)^13-31/15*E(15)^14, 77/30*E(15)+77/30*E(15)^2+77/30*E(15)^4+73/30*E(15)^7+77/30*E(15)^8+73/30*E(15)^11+73/30*E(15)^13+73/30*E(15)^14, 2,-4/3*E(15)-4/3*E(15)^2-4/3*E(15)^4-5/3*E(15)^7-4/3*E(15)^8-5/3*E(15)^11-5/3*E(15)^13-5/3*E(15)^14, -5/2,19/6*E(15)+19/6*E(15)^2+19/6*E(15)^4+17/6*E(15)^7+19/6*E(15)^8+17/6*E(15)^11+17/6*E(15)^13+17/6*E(15)^14, -10/3*E(15)-10/3*E(15)^2-10/3*E(15)^4-8/3*E(15)^7-10/3*E(15)^8-8/3*E(15)^11-8/3*E(15)^13-8/3*E(15)^14 ], [-4/15*E(15)-4/15*E(15)^2-4/15*E(15)^4-11/15*E(15)^7-4/15*E(15)^8-11/15*E(15)^11-11/15*E(15)^13-11/15*E(15)^14, 8/15*E(15)+8/15*E(15)^2+8/15*E(15)^4+7/15*E(15)^7+8/15*E(15)^8+7/15*E(15)^11+7/15*E(15)^13+7/15*E(15)^14, -1/5*E(15)-1/5*E(15)^2-1/5*E(15)^4+1/5*E(15)^7-1/5*E(15)^8+1/5*E(15)^11+1/5*E(15)^13+1/5*E(15)^14, 3/5*E(15)+3/5*E(15)^2+3/5*E(15)^4+2/5*E(15)^7+3/5*E(15)^8+2/5*E(15)^11+2/5*E(15)^13+2/5*E(15)^14, -3/5*E(15)-3/5*E(15)^2-3/5*E(15)^4-9/10*E(15)^7-3/5*E(15)^8-9/10*E(15)^11-9/10*E(15)^13-9/10*E(15)^14, 11/15*E(15)+11/15*E(15)^2+11/15*E(15)^4+19/15*E(15)^7+11/15*E(15)^8+19/15*E(15)^11+19/15*E(15)^13+19/15*E(15)^14, -7/15*E(15)-7/15*E(15)^2-7/15*E(15)^4-8/15*E(15)^7-7/15*E(15)^8-8/15*E(15)^11-8/15*E(15)^13-8/15*E(15)^14, -1/5*E(15)-1/5*E(15)^2-1/5*E(15)^4-4/5*E(15)^7-1/5*E(15)^8-4/5*E(15)^11-4/5*E(15)^13-4/5*E(15)^14, -3/5*E(15)-3/5*E(15)^2-3/5*E(15)^4-2/5*E(15)^7-3/5*E(15)^8-2/5*E(15)^11-2/5*E(15)^13-2/5*E(15)^14, 23/15*E(15)+23/15*E(15)^2+23/15*E(15)^4+37/15*E(15)^7+23/15*E(15)^8+37/15*E(15)^11+37/15*E(15)^13+37/15*E(15)^14, -31/15*E(15)-31/15*E(15)^2-31/15*E(15)^4-43/30*E(15)^7-31/15*E(15)^8-43/30*E(15)^11-43/30*E(15)^13-43/30*E(15)^14, -2/5*E(15)-2/5*E(15)^2-2/5*E(15)^4-11/10*E(15)^7-2/5*E(15)^8-11/10*E(15)^11-11/10*E(15)^13-11/10*E(15)^14, 7/5*E(15)+7/5*E(15)^2+7/5*E(15)^4+13/5*E(15)^7+7/5*E(15)^8+13/5*E(15)^11+13/5*E(15)^13+13/5*E(15)^14, 2/5*E(15)+2/5*E(15)^2+2/5*E(15)^4+3/5*E(15)^7+2/5*E(15)^8+3/5*E(15)^11+3/5*E(15)^13+3/5*E(15)^14, -22/15*E(15)-22/15*E(15)^2-22/15*E(15)^4-38/15*E(15)^7-22/15*E(15)^8-38/15*E(15)^11-38/15*E(15)^13-38/15*E(15)^14, 29/15*E(15)+29/15*E(15)^2+29/15*E(15)^4+77/30*E(15)^7+29/15*E(15)^8+77/30*E(15)^11+77/30*E(15)^13+77/30*E(15)^14, 1/3*E(15)+1/3*E(15)^2+1/3*E(15)^4+2/3*E(15)^7+1/3*E(15)^8+2/3*E(15)^11+2/3*E(15)^13+2/3*E(15)^14, -2/3*E(15)-2/3*E(15)^2-2/3*E(15)^4-4/3*E(15)^7-2/3*E(15)^8-4/3*E(15)^11-4/3*E(15)^13-4/3*E(15)^14, -5/3*E(15)-5/3*E(15)^2-5/3*E(15)^4-11/6*E(15)^7-5/3*E(15)^8-11/6*E(15)^11-11/6*E(15)^13-11/6*E(15)^14, 7/3*E(15)+7/3*E(15)^2+7/3*E(15)^4+19/6*E(15)^7+7/3*E(15)^8+19/6*E(15)^11+19/6*E(15)^13+19/6*E(15)^14, -2], [1/5*E(15)+1/5*E(15)^2+1/5*E(15)^4+4/5*E(15)^7+1/5*E(15)^8+4/5*E(15)^11+4/5*E(15)^13+4/5*E(15)^14, -1/3*E(15)^7-1/3*E(15)^11-1/3*E(15)^13-1/3*E(15)^14,1/15*E(15)+1/15*E(15)^2+1/15*E(15)^4-2/5*E(15)^7+1/15*E(15)^8-2/5*E(15)^11-2/5*E(15)^13-2/5*E(15)^14, -19/30*E(15)-19/30*E(15)^2-19/30*E(15)^4-8/15*E(15)^7-19/30*E(15)^8-8/15*E(15)^11-8/15*E(15)^13-8/15*E(15)^14, 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-7/3*E(15)-7/3*E(15)^2-7/3*E(15)^4-5/3*E(15)^7-7/3*E(15)^8-5/3*E(15)^11-5/3*E(15)^13-5/3*E(15)^14, 1/3*E(15)+1/3*E(15)^2+1/3*E(15)^4+2/3*E(15)^7+1/3*E(15)^8+2/3*E(15)^11+2/3*E(15)^13+2/3*E(15)^14, 7/3*E(15)+7/3*E(15)^2+7/3*E(15)^4+5/3*E(15)^7+7/3*E(15)^8+5/3*E(15)^11+5/3*E(15)^13+5/3*E(15)^14, -2/3*E(15)-2/3*E(15)^2-2/3*E(15)^4-1/3*E(15)^7-2/3*E(15)^8-1/3*E(15)^11-1/3*E(15)^13-1/3*E(15)^14, -5/3*E(15)-5/3*E(15)^2-5/3*E(15)^4-E(15)^7-5/3*E(15)^8-E(15)^11-E(15)^13-E(15)^14, 1/3*E(15)+1/3*E(15)^2+1/3*E(15)^4+1/3*E(15)^8,-5/3,-7/3*E(15)-7/3*E(15)^2-7/3*E(15)^4-5/3*E(15)^7-7/3*E(15)^8-5/3*E(15)^11-5/3*E(15)^13-5/3*E(15)^14, -1/3*E(15)^7-1/3*E(15)^11-1/3*E(15)^13-1/3*E(15)^14,5/3*E(15)+5/3*E(15)^2+5/3*E(15)^4+E(15)^7+5/3*E(15)^8+E(15)^11+E(15)^13+E(15)^14, -7/3,E(15)+E(15)^2+E(15)^4+2/3*E(15)^7+E(15)^8+2/3*E(15)^11+2/3*E(15)^13+2/3*E(15)^14 ]]]; return result;