# Character: X17
# Comment: restrict 63-dim Weil rep of S6(5) and split. Possibly X.18?
# Ind: 0
# Ring: Q(w)
# Sparsity: 59%

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 := "3U35 as 21 x 21 matrices\n";

result.generators := [
[[0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0],
[0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0],
[-9/19*w-15/19*W,-73/57*w-71/57*W,-5/57*w-40/57*W,1,10/57*w-34/57*W,
  10/57*w+23/57*W,46/57*w+83/57*W,46/57*w+26/57*W,23/57*w-44/57*W,
  2/19*w+16/19*W,-23/57*w-13/57*W,-22/57*w-5/57*W,25/57*w+29/57*W,
  4/57*w+32/57*W,-13/57*w-47/57*W,-7/19*w+1/19*W,-14/57*w+59/57*W,
  -46/57*w-26/57*W,-5/57*w+17/57*W,-32/57*w-28/57*W,10/19*w+4/19*W
  ],
[-39/38*w-27/38*W,18/19*w+41/38*W,8/19*w+33/38*W,2*w+W,3/19*w-47/38*W,
  -13/38*w-9/38*W,1/38*w-15/19*W,-9/19*w-34/19*W,-9/38*w+2/19*W,-21/19*w+3/19*W,
  -29/38*w-21/19*W,59/38*w+35/38*W,17/19*w+25/38*W,5/19*w+2/19*W,17/19*w+3/19*W,
  71/38*w-1/19*W,3/38*w+5/38*W,9/19*w+15/19*W,-41/38*w+7/19*W,-2/19*w+22/19*W,
  9/19*w-4/19*W],
[0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[47/38*w+17/19*W,-1/38*w-27/38*W,4/19*w-6/19*W,0,-8/19*w+5/38*W,11/19*w+12/19*W,
  -14/19*w+23/38*W,5/19*w+21/19*W,31/19*w+20/19*W,-1/19*w-8/19*W,7/19*w-1/19*W,
  1/38*w+4/19*W,17/38*w+3/38*W,-7/19*w+1/19*W,17/38*w+3/38*W,-6/19*w-1/38*W,
  -27/38*w+6/19*W,-5/19*w-2/19*W,-15/19*w-31/38*W,-1/19*w-8/19*W,-5/19*w+17/19*W
  ],
[-4/19*w+6/19*W,14/57*w-2/57*W,40/57*w+35/57*W,0,-23/57*w-13/57*W,
  -23/57*w-13/57*W,-26/57*w-37/57*W,-26/57*w+20/57*W,-13/57*w+10/57*W,
  3/19*w+5/19*W,13/57*w-10/57*W,5/57*w-17/57*W,28/57*w-4/57*W,-32/57*w-28/57*W,
  -10/57*w-23/57*W,-1/19*w-8/19*W,-2/57*w-16/57*W,26/57*w-20/57*W,
  -17/57*w-22/57*W,28/57*w-4/57*W,-4/19*w+6/19*W],
[7/19*w-1/19*W,23/57*w+13/57*W,-7/114*w+29/57*W,-1,64/57*w+55/114*W,
  7/57*w+55/114*W,-59/57*w-73/57*W,-2/57*w-16/57*W,-59/114*w+41/114*W,
  -10/19*w-4/19*W,59/114*w-41/114*W,-4/57*w+25/57*W,-11/57*w+26/57*W,
  -20/57*w-46/57*W,73/114*w+64/57*W,16/19*w+14/19*W,-44/57*w-67/57*W,
  2/57*w+16/57*W,25/57*w-28/57*W,46/57*w+26/57*W,-12/19*w-1/19*W],
[29/38*w-17/19*W,-149/114*w-223/114*W,-50/57*w-58/57*W,2,-14/57*w+61/114*W,
  43/57*w+2/57*W,4/57*w+235/114*W,61/57*w+89/57*W,59/57*w+16/57*W,
  1/19*w-11/19*W,55/57*w+41/57*W,-155/114*w-50/57*W,-13/114*w+67/114*W,
  -17/57*w+35/57*W,25/114*w-85/114*W,-32/19*w+1/38*W,5/114*w+77/57*W,
  -61/57*w-32/57*W,7/57*w-59/114*W,-35/57*w-109/57*W,5/19*w+21/19*W
  ],
[9/38*w+17/19*W,73/114*w+185/114*W,5/114*w+97/114*W,w+2*W,47/114*w-23/114*W,
  -67/114*w+17/57*W,-23/57*w-197/114*W,-23/57*w-13/57*W,-40/57*w+101/114*W,
  -1/19*w-8/19*W,40/57*w+13/114*W,-35/114*w+31/57*W,-25/114*w-29/114*W,
  -59/57*w-73/57*W,-22/57*w+52/57*W,13/19*w+37/38*W,-43/114*w-58/57*W,
  23/57*w+13/57*W,-26/57*w-131/114*W,16/57*w+14/57*W,-24/19*w-21/19*W
  ],
[4/19*w+7/38*W,-47/114*w-17/57*W,-61/114*w-16/57*W,-w,65/114*w+32/57*W,
  4/57*w+7/114*W,-43/114*w-59/114*W,7/57*w+56/57*W,7/114*w+113/114*W,
  16/19*w-5/19*W,107/114*w+1/114*W,-100/57*w-61/114*W,-37/114*w+23/57*W,
  13/57*w-10/57*W,-28/57*w+4/57*W,-17/38*w+35/38*W,-17/57*w-101/114*W,
  -7/57*w+1/57*W,53/114*w-89/114*W,10/57*w-34/57*W,-15/19*w-6/19*W
  ]]
,
[[0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0],
[0,0,0,W,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[w,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1],
[3/19*w+5/19*W,56/57*w-8/57*W,46/57*w+26/57*W,w-W,-35/57*w-52/57*W,
  22/57*w+5/57*W,-47/57*w-34/57*W,-104/57*w-34/57*W,-52/57*w-17/57*W,
  12/19*w+20/19*W,-5/57*w+17/57*W,20/57*w-68/57*W,-2/57*w-16/57*W,
  -14/57*w+2/57*W,17/57*w-35/57*W,-4/19*w-32/19*W,-8/57*w-7/57*W,-10/57*w-23/57*W,
  46/57*w+26/57*W,112/57*w+41/57*W,3/19*w+5/19*W],
[25/38*w+5/19*W,-97/114*w-35/114*W,-10/19*w-4/19*W,-1/3*w+1/3*W,41/57*w+29/114*W,
  22/57*w+5/57*W,-28/57*w-49/114*W,29/57*w+61/57*W,5/57*w+40/57*W,
  17/57*w-35/57*W,71/57*w-2/57*W,-131/114*w-11/57*W,-61/114*w+25/114*W,
  -71/57*w-55/57*W,-23/114*w+101/114*W,-4/19*w+31/38*W,-73/114*w-7/57*W,
  3/19*w+5/19*W,-10/19*w-65/38*W,-2/57*w-73/57*W,-16/19*w+5/19*W],
[6/19*w+10/19*W,-2/57*w-16/57*W,35/57*w-5/57*W,0,-13/57*w+10/57*W,
  -13/57*w+10/57*W,-37/57*w-11/57*W,20/57*w+46/57*W,10/57*w+23/57*W,
  5/19*w+2/19*W,-10/57*w-23/57*W,-17/57*w-22/57*W,-4/57*w-32/57*W,
  -28/57*w+4/57*W,-23/57*w-13/57*W,-8/19*w-7/19*W,-16/57*w-14/57*W,
  -20/57*w-46/57*W,-22/57*w-5/57*W,-4/57*w-32/57*W,6/19*w+10/19*W],
[-4/19*w+31/38*W,47/114*w+17/57*W,-5/38*w-1/19*W,-1/3*w+1/3*W,49/114*w+25/57*W,
  -23/57*w+31/114*W,43/114*w-55/114*W,-7/57*w+1/57*W,-83/114*w-37/114*W,
  47/57*w+34/57*W,7/114*w-1/114*W,5/57*w+23/114*W,-1/114*w-4/57*W,
  25/57*w-28/57*W,-67/57*w-23/57*W,17/38*w+3/38*W,-2/57*w-89/114*W,
  -4/19*w+6/19*W,33/38*w+17/38*W,28/57*w+53/57*W,-4/19*w-13/19*W],
[-1/38*w+49/38*W,37/19*w+41/38*W,27/19*w+33/38*W,2*w,-16/19*w-47/38*W,
  -13/38*w+29/38*W,-75/38*w-53/19*W,-47/19*w-34/19*W,-47/38*w+2/19*W,
  -2/19*w+22/19*W,-29/38*w-2/19*W,59/38*w-3/38*W,-2/19*w-13/38*W,-14/19*w-17/19*W,
  -2/19*w+3/19*W,33/38*w-39/19*W,-35/38*w-33/38*W,9/19*w-4/19*W,35/38*w+26/19*W,
  36/19*w+41/19*W,-10/19*w-23/19*W],
[-11/38*w-6/19*W,-3/38*w-5/38*W,-7/19*w+1/19*W,0,14/19*w+15/38*W,-5/19*w-2/19*W,
  15/19*w+31/38*W,15/19*w-13/19*W,17/19*w-16/19*W,-22/19*w-5/19*W,
  -17/19*w-3/19*W,41/38*w+12/19*W,13/38*w+9/38*W,17/19*w+3/19*W,13/38*w-29/38*W,
  20/19*w+35/38*W,-5/38*w-1/19*W,4/19*w-6/19*W,-7/19*w+21/38*W,-3/19*w+14/19*W,
  23/19*w+13/19*W],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-W,0,0,0,0],
[-1/38*w+11/38*W,73/57*w+85/114*W,43/57*w+61/114*W,1/3*w-1/3*W,-10/57*w+11/114*W,
  -13/38*w-9/38*W,-35/114*w-26/57*W,-46/57*w-26/57*W,-9/38*w+2/19*W,
  13/57*w+47/57*W,-11/114*w+13/57*W,21/38*w-3/38*W,-2/19*w-13/38*W,
  5/19*w+2/19*W,-2/19*w-16/19*W,-5/38*w-20/19*W,3/38*w+5/38*W,8/57*w+7/57*W,
  29/114*w+59/57*W,17/19*w+22/19*W,9/19*w-4/19*W],
[1/19*w+35/38*W,145/114*w+10/57*W,25/38*w-9/38*W,1/3*w-4/3*W,-56/57*w-41/114*W,
  -17/114*w-11/57*W,-139/114*w-29/114*W,-41/57*w+14/57*W,46/57*w+109/114*W,
  31/57*w+20/57*W,-8/57*w+43/114*W,13/57*w-77/114*W,43/114*w+1/57*W,
  8/57*w+7/57*W,31/57*w-17/114*W,-9/38*w-53/38*W,-28/57*w-49/114*W,
  1/19*w-11/19*W,-13/38*w-9/38*W,50/57*w+1/57*W,1/19*w+8/19*W]]];

result.symmetricforms := [ ]
result.antisymmetricforms := [ ] 
result.hermitianforms := [ ] 
result.centralizeralgebra := [ ];

return result;