Good basis in BCCK

B6:=[[],[2],[2,2],[1],[1,2],[1,2,2],[2,1],[2,2,1],[2,1,2],[2,1,2,2],[2,2,1,2],[2,2,1,2,2],
[ 1, 2, 1, 2, 1, 2 ], [ 2, 1, 2, 1, 2, 1, 2 ], [ 2, 2, 1, 2, 1, 2, 1, 2 ], 
  [ 1, 1, 2, 1, 2, 1, 2 ], [ 1, 2, 1, 2, 1, 2, 1, 2 ], 
  [ 1, 2, 2, 1, 2, 1, 2, 1, 2 ], [ 2, 1, 1, 2, 1, 2, 1, 2 ], 
  [ 2, 2, 1, 1, 2, 1, 2, 1, 2 ], [ 2, 1, 2, 1, 2, 1, 2, 1, 2 ], 
  [ 2, 1, 2, 2, 1, 2, 1, 2, 1, 2 ], [ 2, 2, 1, 2, 1, 2, 1, 2, 1, 2 ], 
  [ 2, 2, 1, 2, 2, 1, 2, 1, 2, 1, 2 ],
[ 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2 ], 
  [ 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2 ], 
  [ 2, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2 ], 
  [ 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2 ], 
  [ 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2 ], 
  [ 1, 2, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2 ], 
  [ 2, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2 ], 
  [ 2, 2, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2 ], 
  [ 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2 ], 
  [ 2, 1, 2, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2 ], 
  [ 2, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2 ], 
  [ 2, 2, 1, 2, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2 ],
[ 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2 ], 
  [ 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2 ], 
  [ 2, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2 ], 
  [ 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2 ], 
  [ 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2 ], 
  [ 1, 2, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2 ], 
  [ 2, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2 ], 
  [ 2, 2, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2 ], 
  [ 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2 ], 
  [ 2, 1, 2, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2 ], 
  [ 2, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2 ], 
  [ 2, 2, 1, 2, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2 ] ];

Good right basis with respect to the first generator

Br1:=[[],[2],[2,2],[2,1,2,1,2,1],[2,1,2,1,2,1,2],[2,1,2,1,2,1,2,2],
[2,1,2,1,2,1,2,1,2,1,2,1],[2,1,2,1,2,1,2,1,2,1,2,1,2],[2,1,2,1,2,1,2,1,2,1,2,1,2,2],[2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1],[2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2],[2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,2],
[2,1,2,1],[2,2,1,2,1],[2,1,2,1,-2],
[2,1,2,1,2,1,2,1,2,1],[2,2,1,2,1,2,1,2,1,2,1,],[2,1,2,1,2,1,2,1,2,1,-2],
[2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1],[2,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1],[2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,-2],
[2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1],[2,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1],[2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,-2],
[1],[2,1],[2,2,1],[2,1,2,1,2,1,1],[2,1,2,1,2,1,2,1],[2,1,2,1,2,1,2,2,1],
[2,1,2,1,2,1,2,1,2,1,2,1,1],[2,1,2,1,2,1,2,1,2,1,2,1,2,1],[2,1,2,1,2,1,2,1,2,1,2,1,2,2,1],[2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,1],[2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1],[2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,2,1],
[2,1,2,1,1],[2,2,1,2,1,1],[2,1,2,1,-2,1],
[2,1,2,1,2,1,2,1,2,1,1],[2,2,1,2,1,2,1,2,1,2,1,1],[2,1,2,1,2,1,2,1,2,1,-2,1],
[2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,1],[2,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,1],[2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,-2,1],
[2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,1],[2,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,1],[2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,-2,1]];

Good left basis with respect to the first generator

Bl1:=[[],[2],[2,1,2,1,2,1],[2,1,2,1,2,1,2],
[2,1,2,1,2,1,2,1,2,1,2,1],[2,1,2,1,2,1,2,1,2,1,2,1,2],[2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1],[2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2],
[2,1],[2,1,2],[2,1,2,1,2,1,2,1],[2,1,2,1,2,1,2,1,2],
[2,1,2,1,2,1,2,1,2,1,2,1,2,1],[2,1,2,1,2,1,2,1,2,1,2,1,2,1,2],[2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1],[2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2],
[2,1,2,1],[2,2,1,2,1],
[2,1,2,1,2,1,2,1,2,1],[2,2,1,2,1,2,1,2,1,2,1,],
[2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1],[2,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1],
[2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1],[2,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1],
[1],[1,2],[1,2,1,2,1,2,1],[1,2,1,2,1,2,1,2],
[1,2,1,2,1,2,1,2,1,2,1,2,1],[1,2,1,2,1,2,1,2,1,2,1,2,1,2],[1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1],[1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2],
[1,2,1],[1,2,1,2],[1,2,1,2,1,2,1,2,1],[1,2,1,2,1,2,1,2,1,2],
[1,2,1,2,1,2,1,2,1,2,1,2,1,2,1],[1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2],[1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1],[1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2],
[1,2,1,2,1],[1,2,2,1,2,1],
[1,2,1,2,1,2,1,2,1,2,1],[1,2,2,1,2,1,2,1,2,1,2,1,],
[1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1],[1,2,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1],
[1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1],[1,2,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1]];

Good left basis with respect to the second generator

Bl2:=[[],[2,1],[2,1,2,1],[2,1,2,1,2,1],[2,1,2,1,2,1,2,1],[2,1,2,1,2,1,2,1,2,1],
[2,1,2,1,2,1,2,1,2,1,2,1],[2,1,2,1,2,1,2,1,2,1,2,1,2,1],[2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1],[2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1],[2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1],[2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1],
[2,1,2,1,-2],[2,1,2,1,2,1,2,1,2,1,-2],[2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,-2],
[2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,-2],
[2],[2,2,1],[2,2,1,2,1],[2,2,1,2,1,2,1],[2,2,1,2,1,2,1,2,1],[2,2,1,2,1,2,1,2,1,2,1],
[2,2,1,2,1,2,1,2,1,2,1,2,1],[2,2,1,2,1,2,1,2,1,2,1,2,1,2,1],[2,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1],[2,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1],[2,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1],[2,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1],
[2,2,1,2,1,-2],[2,2,1,2,1,2,1,2,1,2,1,-2],[2,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,-2],
[2,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,-2],
[2,2],[2,2,2,1],[2,2,2,1,2,1],[2,2,2,1,2,1,2,1],[2,2,2,1,2,1,2,1,2,1],[2,2,2,1,2,1,2,1,2,1,2,1],
[2,2,2,1,2,1,2,1,2,1,2,1,2,1],[2,2,2,1,2,1,2,1,2,1,2,1,2,1,2,1],[2,2,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1],[2,2,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1],[2,2,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1],[2,2,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1],
[2,2,2,1,2,1,-2],[2,2,2,1,2,1,2,1,2,1,2,1,-2],[2,2,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,-2],
[2,2,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,-2]];

Good right basis with respect to the second generator

Br2:=[[],[2,1],[2,1,2,1],[2,1,2,1,2,1],[2,1,2,1,2,1,2,1],[2,1,2,1,2,1,2,1,2,1],
[2,1,2,1,2,1,2,1,2,1,2,1],[2,1,2,1,2,1,2,1,2,1,2,1,2,1],[2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1],[2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1],[2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1],[2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1],
[1,2,1],[1,2,1,2,1,2,1,2,1],[1,2,1,2,1,2,1,2,1,2,1,2,1,2,1],
[1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1],
[ 2 ], [ 2, 1, 2 ], [ 2, 1, 2, 1, 2 ], [ 2, 1, 2, 1, 2, 1, 2 ], 
  [ 2, 1, 2, 1, 2, 1, 2, 1, 2 ], [ 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2 ], 
  [ 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2 ], 
  [ 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2 ], 
  [ 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2 ], 
  [ 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2 ], 
  [ 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2 ], 
  [ 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2 ], 
  [ 1, 2, 1, 2 ], [ 1, 2, 1, 2, 1, 2, 1, 2, 1, 2 ], 
  [ 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2 ], 
  [ 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2 ],
 [ 2, 2 ], [ 2, 1, 2, 2 ], [ 2, 1, 2, 1, 2, 2 ], [ 2, 1, 2, 1, 2, 1, 2, 2 ], 
  [ 2, 1, 2, 1, 2, 1, 2, 1, 2, 2 ], [ 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 2 ], 
  [ 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 2 ], 
  [ 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 2 ], 
  [ 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 2 ], 
  [ 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 2 ], 
  [ 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 2 ], 
  [ 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 2 ], 
   [ 1, 2, 1, 2, 2 ], [ 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 2 ], 
  [ 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 2 ], 
  [ 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 2 ] ];