G4 
Hecke(G4,[[1,x,x^2]])

gap> DefBlock(H,1,1,[[1,0]]);                                      
[ [ 2 ], [ [ [ 1, 0 ] ], [ [ 1, 4 ] ], [ [ 1, 8 ] ] ] ]
gap> DefBlock(H,1,1,[[2,1]]);
[ [ 2 ], [ [ [ 2, 5 ] ], [ [ 2, 3 ] ], [ [ 2, 1 ] ] ] ]
gap> DefBlock(H,2,1,[[1,0],[2,1]]);
[ [ 2 ], [ [ [ 1, 0 ] ], [ [ 1, 8 ] ], [ [ 2, 5 ] ], [ [ 2, 1 ] ], [ [ 3, 2 ] ] ] ]
gap> DefBlock(H,6,1,[[1,0],[1,4],[1,8]]);
[ [ 2 ], [ [ [ 1, 0 ] ], [ [ 1, 4 ] ], [ [ 1, 8 ] ], [ [ 2, 5 ] ], [ [ 2, 1 ] ], [ [ 3, 2 ] ] ] ]
gap> DefBlock(H,12,1,[[1,0],[1,8]]);      
[ [ 1 ], [ [ [ 1, 0 ] ], [ [ 1, 8 ] ], [ [ 2, 3 ] ] ] ]

##############################################################################

G5
Hecke(G5,[[1,x,x^2]])

gap> DefBlock(H,1,1,[[1,0]]);          
[ [ 4 ], [ [ [ 1, 0 ] ], [ [ 1, 4, 1 ] ], [ [ 1, 8, 1 ] ], [ [ 1, 4, 2 ] ], 
      [ [ 1, 8, 2 ] ], [ [ 1, 12, 1 ] ], [ [ 1, 8, 3 ] ], [ [ 1, 12, 2 ] ], 
      [ [ 1, 16 ] ] ] ]
gap> DefBlock(H,1,1,[[2,1]]);
[ [ 4 ], [ [ [ 2, 9 ] ], [ [ 2, 7, 1 ] ], [ [ 2, 5, 1 ] ], [ [ 2, 7, 2 ] ], 
      [ [ 2, 5, 2 ] ], [ [ 2, 3, 1 ] ], [ [ 2, 5, 3 ] ], [ [ 2, 3, 2 ] ], 
      [ [ 2, 1 ] ] ] ]
gap> DefBlock(H,2,1,[[2,1]]);
[ [ 2 ], [ [ [ 2, 9 ] ], [ [ 2, 5, 1 ] ], [ [ 2, 5, 3 ] ], [ [ 2, 1 ] ] ] ]
gap> DefBlock(H,2,1,[[1,0],[1,4,1],[1,4,2]]);
[ [ 4 ], [ [ [ 1, 0 ] ], [ [ 1, 4, 1 ] ], [ [ 1, 8, 1 ] ], [ [ 1, 4, 2 ] ], 
      [ [ 1, 12, 1 ] ], [ [ 1, 8, 3 ] ], [ [ 1, 12, 2 ] ], [ [ 1, 16 ] ], 
      [ [ 2, 7, 1 ] ], [ [ 2, 7, 2 ] ], [ [ 2, 3, 1 ] ], [ [ 2, 3, 2 ] ], 
      [ [ 3, 6 ] ] ] ]
gap> DefBlock(H,4,1,[[1,0],[1,8,2],[1,16]]); 
[ [ 2 ], 
  [ [ [ 1, 0 ] ], [ [ 1, 8, 2 ] ], [ [ 1, 16 ] ], [ [ 2, 9 ] ], [ [ 2, 1 ] ], 
      [ [ 3, 6 ] ] ] ]
gap> DefBlock(H,4,1,[[1,4,1],[1,12,1]]);       
[ [ 1 ], [ [ [ 1, 4, 1 ] ], [ [ 1, 12, 1 ] ], [ [ 2, 5, 3 ] ] ] ]
ggap> DefBlock(H,4,1,[[1,4,2],[1,12,2]]);
[ [ 1 ], [ [ [ 1, 4, 2 ] ], [ [ 1, 12, 2 ] ], [ [ 2, 5, 1 ] ] ] ]
gap> DefBlock(H,6,1,[[1,12,1],[1,0],[1,12,2]]);
[ [ 2 ], [ [ [ 1, 0 ] ], [ [ 1, 12, 1 ] ], [ [ 1, 12, 2 ] ], [ [ 2, 3, 1 ] ], 
      [ [ 2, 3, 2 ] ], [ [ 3, 2 ] ] ] ]
gap> DefBlock(H,6,1,[[1,4,1],[1,16],[1,4,2]]);  
[ [ 2 ], [ [ [ 1, 4, 1 ] ], [ [ 1, 4, 2 ] ], [ [ 1, 16 ] ], [ [ 2, 7, 1 ] ], 
      [ [ 2, 7, 2 ] ], [ [ 3, 4 ] ] ] ]
gap> DefBlock(H,8,1,[[1,0],[1,16]]);            
[ [ 1 ], [ [ [ 1, 0 ] ], [ [ 1, 16 ] ], [ [ 2, 5, 2 ] ] ] ]
gap> DefBlock(H,12,1,[[1,0],[2,9]]); 
[ [ 1 ], [ [ [ 1, 0 ] ], [ [ 2, 9 ] ], [ [ 3, 4 ] ] ] ]
gap> DefBlock(H,12,1,[[1,16],[2,1]]);
[ [ 1 ], [ [ [ 1, 16 ] ], [ [ 2, 1 ] ], [ [ 3, 2 ] ] ] ]

####################################################################

G5
Hecke(G5,[[1,x,x^2],[1,x^2,x^4]])

gap> DefBlock(H,1,1,[[1,0]]);
[ [ [ 4 ] ], 
  [ [ [ 1, 0 ] ], [ [ 1, 4, 1 ] ], [ [ 1, 8, 1 ] ], [ [ 1, 4, 2 ] ], 
      [ [ 1, 8, 2 ] ], [ [ 1, 12, 1 ] ], [ [ 1, 8, 3 ] ], [ [ 1, 12, 2 ] ], 
      [ [ 1, 16 ] ] ] ]
gap> DefBlock(H,1,1,[[2,1]]);   
[ [ [ 4 ] ], 
  [ [ [ 2, 9 ] ], [ [ 2, 7, 1 ] ], [ [ 2, 5, 1 ] ], [ [ 2, 7, 2 ] ], 
      [ [ 2, 5, 2 ] ], [ [ 2, 3, 1 ] ], [ [ 2, 5, 3 ] ], [ [ 2, 3, 2 ] ], 
      [ [ 2, 1 ] ] ] ]
gap> DefBlock(H,2,1,[[1,0],[1,4,2]]);
[ [ [ 6 ] ], 
  [ [ [ 1, 0 ] ], [ [ 1, 4, 1 ] ], [ [ 1, 8, 1 ] ], [ [ 1, 4, 2 ] ], 
      [ [ 1, 8, 2 ] ], [ [ 1, 12, 1 ] ], [ [ 1, 8, 3 ] ], [ [ 1, 12, 2 ] ], 
      [ [ 1, 16 ] ], [ [ 2, 9 ] ], [ [ 2, 7, 1 ] ], [ [ 2, 5, 1 ] ], 
      [ [ 2, 5, 3 ] ], [ [ 2, 3, 2 ] ], [ [ 2, 1 ] ], [ [ 3, 6 ] ] ] ]
gap> DefBlock(H,2,1,[[2,3,1]]);              
[ [ [ 2 ] ], [ [ [ 2, 7, 2 ] ], [ [ 2, 5, 2 ] ], [ [ 2, 3, 1 ] ] ] ]
gap> DefBlock(H,4,1,[[1,0],[1,8,3]]);
[ [ [ 2 ] ], [ [ [ 1, 0 ] ], [ [ 1, 8, 1 ] ], [ [ 1, 8, 3 ] ], [ [ 1, 16 ] ], 
      [ [ 2, 5, 2 ] ] ] ]
gap> DefBlock(H,4,1,[[1,4,2],[2,3,1]]);
[ [ [ 2 ] ], 
  [ [ [ 1, 4, 2 ] ], [ [ 1, 12, 1 ] ], [ [ 2, 7, 2 ] ], [ [ 2, 3, 1 ] ], 
      [ [ 3, 6 ] ] ] ]
gap> DefBlock(H,4,1,[[2,1]]);          
[ [ [ 1 ] ], [ [ [ 2, 5, 3 ] ], [ [ 2, 1 ] ] ] ]
gap> DefBlock(H,4,1,[[2,5,2]]);
[ [ [ 2 ] ], [ [ [ 2, 5, 2 ] ] ] ]
gap> DefBlock(H,6,1,[[1,0],[1,8,2],[1,16]]);
[ [ [ 2 ] ], 
  [ [ [ 1, 0 ] ], [ [ 1, 8, 2 ] ], [ [ 1, 16 ] ], [ [ 2, 9 ] ], [ [ 2, 1 ] ], 
      [ [ 3, 6 ] ] ] ]
gap> DefBlock(H,6,1,[[1,4,1],[1,12,1],[1,8,3]]);
[ [ [ 2 ] ], 
  [ [ [ 1, 4, 1 ] ], [ [ 1, 12, 1 ] ], [ [ 1, 8, 3 ] ], [ [ 2, 7, 1 ] ], 
      [ [ 2, 5, 3 ] ], [ [ 3, 4 ] ] ] ]
gap> DefBlock(H,6,1,[[1,8,1],[1,4,2],[1,12,2]]);
[ [ [ 2 ] ], 
  [ [ [ 1, 8, 1 ] ], [ [ 1, 4, 2 ] ], [ [ 1, 12, 2 ] ], [ [ 2, 5, 1 ] ], 
      [ [ 2, 3, 2 ] ], [ [ 3, 2 ] ] ] ]
gap> DefBlock(H,10,1,[[1,0],[1,12,1]]);         
[ [ [ 1 ] ], [ [ [ 1, 0 ] ], [ [ 1, 12, 1 ] ], [ [ 2, 3, 2 ] ] ] ]
gap> DefBlock(H,10,1,[[1,4,2],[1,16]]);  
[ [ [ 1 ] ], [ [ [ 1, 4, 2 ] ], [ [ 1, 16 ] ], [ [ 2, 7, 1 ] ] ] ]
gap> DefBlock(H,12,1,[[1,0],[1,16]]);  
[ [ [ 1 ] ], [ [ [ 1, 0 ] ], [ [ 1, 16 ] ], [ [ 2, 5, 2 ] ] ] ]
gap> DefBlock(H,12,1,[[1,4,2],[2,7,2]]);
[ [ [ 1 ] ], [ [ [ 1, 4, 2 ] ], [ [ 2, 7, 2 ] ], [ [ 3, 4 ] ] ] ]
gap> DefBlock(H,12,1,[[1,12,1],[2,3,1]]);
[ [ [ 1 ] ], [ [ [ 1, 12, 1 ] ], [ [ 2, 3, 1 ] ], [ [ 3, 2 ] ] ] ]
gap> DefBlock(H,18,1,[[1,0],[2,9]]);     
[ [ [ 1 ] ], [ [ [ 1, 0 ] ], [ [ 2, 9 ] ], [ [ 3, 4 ] ] ] ]
gap> DefBlock(H,18,1,[[1,16],[2,1]]);
[ [ [ 1 ] ], [ [ [ 1, 16 ] ], [ [ 2, 1 ] ], [ [ 3, 2 ] ] ] ]

#####################################################################

G5
Hecke(G5,[[1,x,x^2],[1,x^4,x^8]])

gap> DefBlock(H,1,1,[[1,0]]);        
[ [ [ 4 ] ], 
  [ [ [ 1, 0 ] ], [ [ 1, 4, 1 ] ], [ [ 1, 8, 1 ] ], [ [ 1, 4, 2 ] ], 
      [ [ 1, 8, 2 ] ], [ [ 1, 12, 1 ] ], [ [ 1, 8, 3 ] ], [ [ 1, 12, 2 ] ], 
      [ [ 1, 16 ] ] ] ]
gap> DefBlock(H,1,1,[[2,1]]);
[ [ [ 4 ] ], 
  [ [ [ 2, 9 ] ], [ [ 2, 7, 1 ] ], [ [ 2, 5, 1 ] ], [ [ 2, 7, 2 ] ], 
      [ [ 2, 5, 2 ] ], [ [ 2, 3, 1 ] ], [ [ 2, 5, 3 ] ], [ [ 2, 3, 2 ] ], 
      [ [ 2, 1 ] ] ] ]
gap> DefBlock(H,2,1,[[1,0],[1,4,2]]);
[ [ [ 6 ] ], 
  [ [ [ 1, 0 ] ], [ [ 1, 4, 1 ] ], [ [ 1, 8, 1 ] ], [ [ 1, 4, 2 ] ], 
      [ [ 1, 8, 2 ] ], [ [ 1, 12, 1 ] ], [ [ 1, 8, 3 ] ], [ [ 1, 12, 2 ] ], 
      [ [ 1, 16 ] ], [ [ 2, 9 ] ], [ [ 2, 7, 1 ] ], [ [ 2, 5, 1 ] ], 
      [ [ 2, 5, 3 ] ], [ [ 2, 3, 2 ] ], [ [ 2, 1 ] ], [ [ 3, 6 ] ] ] ]
gap> DefBlock(H,2,1,[[2,3,1]]);          
[ [ [ 2 ] ], [ [ [ 2, 7, 2 ] ], [ [ 2, 5, 2 ] ], [ [ 2, 3, 1 ] ] ] ]
gap> DefBlock(H,4,1,[[1,0],[1,8,3]]);
[ [ [ 4 ] ], 
  [ [ [ 1, 0 ] ], [ [ 1, 4, 1 ] ], [ [ 1, 8, 1 ] ], [ [ 1, 8, 3 ] ], 
      [ [ 1, 12, 2 ] ], [ [ 1, 16 ] ], [ [ 2, 7, 2 ] ], [ [ 2, 5, 2 ] ], 
      [ [ 2, 3, 1 ] ] ] ]
gap> DefBlock(H,4,1,[[1,4,2]]);      
[ [ [ 2 ] ], [ [ [ 1, 4, 2 ] ], [ [ 1, 8, 2 ] ], [ [ 1, 12, 1 ] ] ] ]
gap> DefBlock(H,4,1,[[2,5,1]]);
[ [ [ 2 ] ], [ [ [ 2, 9 ] ], [ [ 2, 7, 1 ] ], [ [ 2, 5, 1 ] ] ] ]
gap> DefBlock(H,4,1,[[2,1]]);  
[ [ [ 2 ] ], [ [ [ 2, 5, 3 ] ], [ [ 2, 3, 2 ] ], [ [ 2, 1 ] ] ] ]
gap> DefBlock(H,6,1,[[1,0],[1,12,1],[1,12,2]]);
[ [ [ 2 ] ], 
  [ [ [ 1, 0 ] ], [ [ 1, 12, 1 ] ], [ [ 1, 12, 2 ] ], [ [ 2, 9 ] ], 
      [ [ 2, 3, 2 ] ], [ [ 3, 2 ] ] ] ]
gap> DefBlock(H,6,1,[[1,8,1],[1,8,2],[1,8,3]]);  
[ [ [ 2 ] ], 
  [ [ [ 1, 8, 1 ] ], [ [ 1, 8, 2 ] ], [ [ 1, 8, 3 ] ], [ [ 2, 5, 1 ] ], 
      [ [ 2, 5, 3 ] ], [ [ 3, 6 ] ] ] ]
gap> DefBlock(H,6,1,[[1,4,1],[1,4,2],[1,16]]); 
[ [ [ 2 ] ], 
  [ [ [ 1, 4, 1 ] ], [ [ 1, 4, 2 ] ], [ [ 1, 16 ] ], [ [ 2, 7, 1 ] ], 
      [ [ 2, 1 ] ], [ [ 3, 4 ] ] ] ]
gap> DefBlock(H,8,1,[[1,0]]);                    
[ [ [ 1 ] ], [ [ [ 1, 0 ] ], [ [ 1, 8, 1 ] ] ] ]
gap> DefBlock(H,8,1,[[2,1]]);
[ [ [ 1 ] ], [ [ [ 2, 5, 3 ] ], [ [ 2, 1 ] ] ] ]
gap> DefBlock(H,8,1,[[2,5,1]]);
[ [ [ 1 ] ], [ [ [ 2, 9 ] ], [ [ 2, 5, 1 ] ] ] ]
gap> DefBlock(H,8,1,[[1,8,3]]);
[ [ [ 1 ] ], [ [ [ 1, 8, 3 ] ], [ [ 1, 16 ] ] ] ]
gap> DefBlock(H,8,1,[[1,4,2],[2,3,1]]);
[ [ [ 2 ] ], 
  [ [ [ 1, 4, 2 ] ], [ [ 1, 12, 1 ] ], [ [ 2, 7, 2 ] ], [ [ 2, 3, 1 ] ], 
      [ [ 3, 6 ] ] ] ]
gap> DefBlock(H,10,1,[[1,0],[1,8,2],[1,16]]);  
[ [ [ 2 ] ], 
  [ [ [ 1, 0 ] ], [ [ 1, 8, 2 ] ], [ [ 1, 16 ] ], [ [ 2, 9 ] ], [ [ 2, 1 ] ], 
      [ [ 3, 6 ] ] ] ]
gap> DefBlock(H,10,1,[[1,4,1],[1,12,1]]);    
[ [ [ 1 ] ], [ [ [ 1, 4, 1 ] ], [ [ 1, 12, 1 ] ], [ [ 2, 5, 3 ] ] ] ]
gap> DefBlock(H,10,1,[[1,4,2],[1,12,2]]);
[ [ [ 1 ] ], [ [ [ 1, 4, 2 ] ], [ [ 1, 12, 2 ] ], [ [ 2, 5, 1 ] ] ] ]
gap> DefBlock(H,12,1,[[1,0],[1,12,2]]);  
[ [ [ 1 ] ], [ [ [ 1, 0 ] ], [ [ 1, 12, 2 ] ], [ [ 2, 3, 1 ] ] ] ]
gap> DefBlock(H,12,1,[[1,8,1],[1,8,3]]); 
[ [ [ 1 ] ], [ [ [ 1, 8, 1 ] ], [ [ 1, 8, 3 ] ], [ [ 2, 5, 2 ] ] ] ]
gap> DefBlock(H,12,1,[[1,4,1],[1,16]]); 
[ [ [ 1 ] ], [ [ [ 1, 4, 1 ] ], [ [ 1, 16 ] ], [ [ 2, 7, 2 ] ] ] ]
gap> DefBlock(H,14,1,[[1,8,1],[1,4,2]]);
[ [ [ 1 ] ], [ [ [ 1, 8, 1 ] ], [ [ 1, 4, 2 ] ], [ [ 2, 3, 2 ] ] ] ]
gap> DefBlock(H,14,1,[[1,12,1],[1,8,3]]);
[ [ [ 1 ] ], [ [ [ 1, 12, 1 ] ], [ [ 1, 8, 3 ] ], [ [ 2, 7, 1 ] ] ] ]
gap> DefBlock(H,18,1,[[1,0],[1,12,1]]);  
[ [ [ 1 ] ], [ [ [ 1, 0 ] ], [ [ 1, 12, 1 ] ], [ [ 2, 3, 2 ] ] ] ]
gap> DefBlock(H,18,1,[[1,16],[1,4,2]]); 
[ [ [ 1 ] ], [ [ [ 1, 4, 2 ] ], [ [ 1, 16 ] ], [ [ 2, 7, 1 ] ] ] ]
gap> DefBlock(H,18,1,[[1,8,1],[2,5,1]]); 
[ [ [ 1 ] ], [ [ [ 1, 8, 1 ] ], [ [ 2, 5, 1 ] ], [ [ 3, 2 ] ] ] ]
gap> DefBlock(H,18,1,[[1,8,3],[2,5,3]]);
[ [ [ 1 ] ], [ [ [ 1, 8, 3 ] ], [ [ 2, 5, 3 ] ], [ [ 3, 4 ] ] ] ]
gap> DefBlock(H,20,1,[[1,0],[1,16]]);   
[ [ [ 1 ] ], [ [ [ 1, 0 ] ], [ [ 1, 16 ] ], [ [ 2, 5, 2 ] ] ] ]
gap> DefBlock(H,24,1,[[1,12,1],[2,3,1]]);
[ [ [ 1 ] ], [ [ [ 1, 12, 1 ] ], [ [ 2, 3, 1 ] ], [ [ 3, 2 ] ] ] ]
gap> DefBlock(H,24,1,[[1,4,2],[2,7,2]]); 
[ [ [ 1 ] ], [ [ [ 1, 4, 2 ] ], [ [ 2, 7, 2 ] ], [ [ 3, 4 ] ] ] ]
gap> DefBlock(H,30,1,[[1,0],[2,9]]);    
[ [ [ 1 ] ], [ [ [ 1, 0 ] ], [ [ 2, 9 ] ], [ [ 3, 4 ] ] ] ]
gap> DefBlock(H,30,1,[[1,16],[2,1]]);
[ [ [ 1 ] ], [ [ [ 1, 16 ] ], [ [ 2, 1 ] ], [ [ 3, 2 ] ] ] ]

####################################################################

G8
Hecke(G8,[[1,E8^3x,E8^5x,x^2]])

gap> DefBlock(H,1,1,[[1,0],[3,2]]);
[ [ [ 2 ] ], 
  [ [ [ 1, 0 ] ], [ [ 1, 18 ] ], [ [ 3, 8 ] ], [ [ 3, 2 ] ], [ [ 4, 5 ] ] ] ]
gap> DefBlock(H,1,1,[[2,1]]);      
[ [ [ 1 ] ], [ [ [ 2, 1 ] ], [ [ 2, 10 ] ] ] ]
gap> DefBlock(H,1,1,[[2,4]]);
[ [ [ 1 ] ], [ [ [ 2, 4 ] ], [ [ 2, 13 ] ] ] ]
gap> DefBlock(H,2,1,[[1,0],[3,2]]);
[ [ [ 2 ] ], 
  [ [ [ 1, 0 ] ], [ [ 1, 18 ] ], [ [ 3, 8 ] ], [ [ 3, 2 ] ], [ [ 4, 5 ] ] ] ]
gap> DefBlock(H,2,1,[[2,1]]);      
[ [ [ 1 ] ], [ [ [ 2, 1 ] ], [ [ 2, 10 ] ] ] ]
gap> DefBlock(H,2,1,[[2,4]]);      
[ [ [ 1 ] ], [ [ [ 2, 4 ] ], [ [ 2, 13 ] ] ] ]
gap> DefBlock(H,4,1,[[1,0],[2,7,2],[1,18]]);
[ [ [ 2 ] ], 
  [ [ [ 1, 0 ] ], [ [ 1, 18 ] ], [ [ 2, 7, 2 ] ], [ [ 3, 8 ] ], [ [ 3, 2 ] ], 
      [ [ 4, 3 ] ] ] ]
### For x=E(8) and x=E(8)^7, the algebra H is the group algebra.
gap> DefBlock(H,8,3,[[1,0],[2,10]]);   
[ [ [ 2 ] ], 
  [ [ [ 1, 0 ] ], [ [ 1, 12 ] ], [ [ 2, 10 ] ], [ [ 3, 8 ] ], [ [ 3, 4 ] ] ] ]
gap> DefBlock(H,8,3,[[1,6],[2,4]]); 
[ [ [ 2 ] ], 
  [ [ [ 1, 6 ] ], [ [ 1, 18 ] ], [ [ 2, 4 ] ], [ [ 3, 6 ] ], [ [ 3, 2 ] ] ] ]
gap> DefBlock(H,8,3,[[2,1]]);      
[ [ [ 2 ] ], [ [ [ 2, 1 ] ], [ [ 2, 7, 1 ] ], [ [ 2, 7, 2 ] ], [ [ 2, 13 ] ] 
     ] ]
gap> DefBlock(H,8,5,[[1,0],[2,13]]);
[ [ [ 2 ] ], 
  [ [ [ 1, 0 ] ], [ [ 1, 6 ] ], [ [ 2, 13 ] ], [ [ 3, 8 ] ], [ [ 3, 6 ] ] ] ]
gap> DefBlock(H,8,5,[[1,12],[2,1]]); 
[ [ [ 2 ] ], 
  [ [ [ 1, 12 ] ], [ [ 1, 18 ] ], [ [ 2, 1 ] ], [ [ 3, 4 ] ], [ [ 3, 2 ] ] ] ]
gap> DefBlock(H,8,5,[[2,4]]);       
[ [ [ 2 ] ], [ [ [ 2, 4 ] ], [ [ 2, 7, 1 ] ], [ [ 2, 7, 2 ] ], [ [ 2, 10 ] ] 
     ] ]
gap> DefBlock(H,12,1,[[1,0],[1,18]]);        
[ [ [ 1 ] ], [ [ [ 1, 0 ] ], [ [ 1, 18 ] ], [ [ 2, 7, 1 ] ] ] ]
gap> DefBlock(H,24,1,[[1,0],[2,10]]); gap> DefBlock(H,24,17,[[1,0],[2,10]]);
[ [ [ 1 ] ], [ [ [ 1, 0 ] ], [ [ 2, 10 ] ], [ [ 3, 4 ] ] ] ]
gap> DefBlock(H,24,1,[[1,18],[2,4]]); gap> DefBlock(H,24,17,[[1,18],[2,4]]); 
[ [ [ 1 ] ], [ [ [ 1, 18 ] ], [ [ 2, 4 ] ], [ [ 3, 6 ] ] ] ]
gap> DefBlock(H,24,1,[[2,1],[2,13]]); gap> DefBlock(H,24,17,[[2,1],[2,13]]);
[ [ [ 1 ] ], [ [ [ 2, 1 ] ], [ [ 2, 13 ] ], [ [ 4, 3 ] ] ] ]
gap> DefBlock(H,24,7,[[1,0],[2,13]]); gap> DefBlock(H,24,23,[[1,0],[2,13]]);
[ [ [ 1 ] ], [ [ [ 1, 0 ] ], [ [ 2, 13 ] ], [ [ 3, 6 ] ] ] ]
gap> DefBlock(H,24,7,[[1,18],[2,1]]); gap> DefBlock(H,24,23,[[1,18],[2,1]]);                                              
[ [ [ 1 ] ], [ [ [ 1, 18 ] ], [ [ 2, 1 ] ], [ [ 3, 4 ] ] ] ]
gap> DefBlock(H,24,23,[[2,4],[2,10]]); gap> DefBlock(H,24,23,[[2,4],[2,10]]);
[ [ [ 1 ] ], [ [ [ 2, 4 ] ], [ [ 2, 10 ] ], [ [ 4, 3 ] ] ] ]
gap> DefBlock(H,24,5,[[1,0],[1,12]]);  gap> DefBlock(H,24,13,[[1,0],[1,12]]);
[ [ [ 1 ] ], [ [ [ 1, 0 ] ], [ [ 1, 12 ] ], [ [ 2, 4 ] ] ] ]
gap> DefBlock(H,24,5,[[1,6],[1,18]]);  gap> DefBlock(H,24,13,[[1,6],[1,18]]);
[ [ [ 1 ] ], [ [ [ 1, 6 ] ], [ [ 1, 18 ] ], [ [ 2, 10 ] ] ] ]
gap> DefBlock(H,24,5,[[2,1],[2,13]]);  gap> DefBlock(H,24,13,[[2,1],[2,13]]);
[ [ [ 1 ] ], [ [ [ 2, 1 ] ], [ [ 2, 13 ] ], [ [ 4, 5 ] ] ] ]
gap> DefBlock(H,24,11,[[1,0],[1,6]]); gap> DefBlock(H,24,19,[[1,0],[1,6]]); 
[ [ [ 1 ] ], [ [ [ 1, 0 ] ], [ [ 1, 6 ] ], [ [ 2, 1 ] ] ] ]
gap> DefBlock(H,24,11,[[1,12],[1,18]]); gap> DefBlock(H,24,19,[[1,12],[1,18]]);
[ [ [ 1 ] ], [ [ [ 1, 12 ] ], [ [ 1, 18 ] ], [ [ 2, 13 ] ] ] ]
gap> DefBlock(H,24,11,[[2,4],[2,10]]);  gap> DefBlock(H,24,19,[[2,4],[2,10]]);
[ [ [ 1 ] ], [ [ [ 2, 4 ] ], [ [ 2, 10 ] ], [ [ 4, 5 ] ] ] ]

####################################################################

G8
Hecke(G8,[[1,-x,x,x^2]])

gap> DefBlock(H,2,1,[[1,0],[2,4]]);
[ [ [ 4 ] ], 
  [ [ [ 1, 0 ] ], [ [ 1, 6 ] ], [ [ 1, 18 ] ], [ [ 2, 4 ] ], [ [ 2, 7, 2 ] ], 
      [ [ 2, 13 ] ], [ [ 3, 8 ] ], [ [ 3, 6 ] ], [ [ 3, 2 ] ] ] ]
gap> DefBlock(H,2,1,[[2,1]]);      
[ [ [ 2 ] ], [ [ [ 2, 1 ] ], [ [ 2, 7, 1 ] ], [ [ 2, 10 ] ] ] ]
gap> DefBlock(H,6,1,[[1,0],[1,12],[1,18]]);
[ [ [ 2 ] ], 
  [ [ [ 1, 0 ] ], [ [ 1, 12 ] ], [ [ 1, 18 ] ], [ [ 2, 4 ] ], [ [ 2, 13 ] ], 
      [ [ 3, 6 ] ] ] ]
gap> DefBlock(H,8,1,[[1,0],[3,8]]);        
[ [ [ 1 ] ], [ [ [ 1, 0 ] ], [ [ 3, 8 ] ], [ [ 4, 5 ] ] ] ]
gap> DefBlock(H,8,1,[[1,18],[3,2]]);
[ [ [ 1 ] ], [ [ [ 1, 18 ] ], [ [ 3, 2 ] ], [ [ 4, 3 ] ] ] ]
gap> DefBlock(H,12,1,[[1,0],[1,18]]);
[ [ [ 1 ] ], [ [ [ 1, 0 ] ], [ [ 1, 18 ] ], [ [ 2, 7, 1 ] ] ] ]
gap> DefBlock(H,12,1,[[2,1],[2,13]]);
[ [ [ 1 ] ], [ [ [ 2, 1 ] ], [ [ 2, 13 ] ], [ [ 4, 3 ] ] ] ]
gap> DefBlock(H,12,1,[[2,4],[2,10]]);
[ [ [ 1 ] ], [ [ [ 2, 4 ] ], [ [ 2, 10 ] ], [ [ 4, 5 ] ] ] ]

####################################################################

G8
Hecke(G8,[[1,x,x^2,x^3]])

[ [ [ 4 ] ], 
  [ [ [ 1, 0 ] ], [ [ 1, 6 ] ], [ [ 1, 12 ] ], [ [ 1, 18 ] ], [ [ 3, 8 ] ], 
      [ [ 3, 6 ] ], [ [ 3, 4 ] ], [ [ 3, 2 ] ], [ [ 4, 5 ] ] ] ]
gap> DefBlock(H,1,1,[[2,1]]);      
[ [ [ 4 ] ], [ [ [ 2, 1 ] ], [ [ 2, 4 ] ], [ [ 2, 7, 1 ] ], [ [ 2, 7, 2 ] ], 
      [ [ 2, 10 ] ], [ [ 2, 13 ] ] ] ]
gap> DefBlock(H,2,1,[[1,0],[1,6],[2,1]]);
[ [ [ 4 ] ], 
  [ [ [ 1, 0 ] ], [ [ 1, 6 ] ], [ [ 1, 12 ] ], [ [ 1, 18 ] ], [ [ 2, 1 ] ], 
      [ [ 2, 7, 1 ] ], [ [ 2, 7, 2 ] ], [ [ 2, 13 ] ], [ [ 3, 8 ] ], 
      [ [ 3, 6 ] ], [ [ 3, 4 ] ], [ [ 3, 2 ] ], [ [ 4, 3 ] ] ] ]
gap> DefBlock(H,3,1,[[2,4],[2,1]]);      
[ [ [ 2 ] ], 
  [ [ [ 2, 1 ] ], [ [ 2, 4 ] ], [ [ 2, 10 ] ], [ [ 2, 13 ] ], [ [ 4, 3 ] ] ] ]
gap> DefBlock(H,3,1,[[1,0],[3,2]]);
[ [ [ 2 ] ], 
  [ [ [ 1, 0 ] ], [ [ 1, 18 ] ], [ [ 3, 8 ] ], [ [ 3, 2 ] ], [ [ 4, 5 ] ] ] ]
gap> DefBlock(H,6,1,[[1,0],[1,6],[1,12],[1,18]]);
[ [ [ 3 ] ], 
  [ [ [ 1, 0 ] ], [ [ 1, 6 ] ], [ [ 1, 12 ] ], [ [ 1, 18 ] ], [ [ 2, 1 ] ], 
      [ [ 2, 7, 2 ] ], [ [ 2, 13 ] ], [ [ 3, 8 ] ], [ [ 3, 2 ] ], 
      [ [ 4, 3 ] ] ] ]
gap> DefBlock(H,6,1,[[2,4],[2,10]]);              
[ [ [ 1 ] ], [ [ [ 2, 4 ] ], [ [ 2, 10 ] ], [ [ 4, 5 ] ] ] ]
gap> DefBlock(H,10,1,[[1,0],[2,13]]);            
[ [ [ 1 ] ], [ [ [ 1, 0 ] ], [ [ 2, 13 ] ], [ [ 3, 6 ] ] ] ]
gap> DefBlock(H,10,1,[[2,1],[1,18]]);
[ [ [ 1 ] ], [ [ [ 1, 18 ] ], [ [ 2, 1 ] ], [ [ 3, 4 ] ] ] ]
gap> DefBlock(H,12,1,[[1,0],[1,12]]);
[ [ [ 1 ] ], [ [ [ 1, 0 ] ], [ [ 1, 12 ] ], [ [ 2, 4 ] ] ] ]
gap> DefBlock(H,12,1,[[1,6],[1,18]]);
[ [ [ 1 ] ], [ [ [ 1, 6 ] ], [ [ 1, 18 ] ], [ [ 2, 10 ] ] ] ]
gap> DefBlock(H,12,1,[[2,1],[2,13]]); 
[ [ [ 1 ] ], [ [ [ 2, 1 ] ], [ [ 2, 13 ] ], [ [ 4, 5 ] ] ] ]
gap> DefBlock(H,18,1,[[1,0],[1,18]]);
[ [ [ 1 ] ], [ [ [ 1, 0 ] ], [ [ 1, 18 ] ], [ [ 2, 7, 1 ] ] ] ]

####################################################################

G8
Hecke(G8,[[1,x,-x,-x^4]])

gap> DefBlock(H,2,1,[[1,0],[1,6],[2,1]]);
[ [ [ 4 ] ], 
  [ [ [ 1, 0 ] ], [ [ 1, 6 ] ], [ [ 1, 12 ] ], [ [ 1, 18 ] ], [ [ 2, 1 ] ], 
      [ [ 2, 7, 1 ] ], [ [ 2, 7, 2 ] ], [ [ 2, 13 ] ], [ [ 3, 8 ] ], 
      [ [ 3, 6 ] ], [ [ 3, 4 ] ], [ [ 3, 2 ] ], [ [ 4, 3 ] ] ] ]
gap> DefBlock(H,3,1,[[1,0],[1,12],[2,7,2]]);
[ [ [ 3 ] ], 
  [ [ [ 1, 0 ] ], [ [ 1, 12 ] ], [ [ 1, 18 ] ], [ [ 2, 4 ] ], [ [ 2, 7, 1 ] ],
      [ [ 2, 7, 2 ] ], [ [ 2, 10 ] ], [ [ 3, 8 ] ], [ [ 4, 5 ] ] ] ]
gap> DefBlock(H,3,1,[[2,1],[2,13]]);        
[ [ [ 1 ] ], [ [ [ 2, 1 ] ], [ [ 2, 13 ] ], [ [ 4, 3 ] ] ] ]
gap> DefBlock(H,3,1,[[3,2]]);       
[ [ [ 1 ] ], [ [ [ 3, 4 ] ], [ [ 3, 2 ] ] ] ]
gap> DefBlock(H,5,1,[[1,0],[2,10]]);
[ [ [ 1 ] ], [ [ [ 1, 0 ] ], [ [ 2, 10 ] ], [ [ 3, 4 ] ] ] ]
gap> DefBlock(H,5,1,[[1,18],[3,2]]); 
[ [ [ 1 ] ], [ [ [ 1, 18 ] ], [ [ 3, 2 ] ], [ [ 4, 5 ] ] ] ]
gap> DefBlock(H,7,1,[[1,18],[2,4]]);
[ [ [ 1 ] ], [ [ [ 1, 18 ] ], [ [ 2, 4 ] ], [ [ 3, 6 ] ] ] ]
gap> DefBlock(H,8,1,[[1,0]]);       
[ [ [ 1 ] ], [ [ [ 1, 0 ] ], [ [ 1, 18 ] ] ] ]
gap> DefBlock(H,8,1,[[2,1]]);
[ [ [ 1 ] ], [ [ [ 2, 1 ] ], [ [ 2, 10 ] ] ] ]
gap> DefBlock(H,8,1,[[2,4]]);
[ [ [ 1 ] ], [ [ [ 2, 4 ] ], [ [ 2, 13 ] ] ] ]
gap> DefBlock(H,8,1,[[3,2]]);
[ [ [ 1 ] ], [ [ [ 3, 8 ] ], [ [ 3, 2 ] ] ] ]
gap> DefBlock(H,9,1,[[1,6],[1,18]]);
[ [ [ 1 ] ], [ [ [ 1, 6 ] ], [ [ 1, 18 ] ], [ [ 2, 10 ] ] ] ]
gap> DefBlock(H,12,1,[[1,0],[1,18]]);
[ [ [ 1 ] ], [ [ [ 1, 0 ] ], [ [ 1, 18 ] ], [ [ 2, 7, 1 ] ] ] ]
gap> DefBlock(H,12,1,[[2,1],[2,13]]);
[ [ [ 1 ] ], [ [ [ 2, 1 ] ], [ [ 2, 13 ] ], [ [ 4, 5 ] ] ] ]
gap> DefBlock(H,12,1,[[2,4],[2,10]]);
[ [ [ 1 ] ], [ [ [ 2, 4 ] ], [ [ 2, 10 ] ], [ [ 4, 3 ] ] ] ]

####################################################################

G8
Hecke(G8,[[1,x^3,-x^3,-x^4]])

gap> DefBlock(H,2,1,[[1,0],[1,6],[2,1]]);
[ [ [ 4 ] ], 
  [ [ [ 1, 0 ] ], [ [ 1, 6 ] ], [ [ 1, 12 ] ], [ [ 1, 18 ] ], [ [ 2, 1 ] ], 
      [ [ 2, 7, 1 ] ], [ [ 2, 7, 2 ] ], [ [ 2, 13 ] ], [ [ 3, 8 ] ], 
      [ [ 3, 6 ] ], [ [ 3, 4 ] ], [ [ 3, 2 ] ], [ [ 4, 3 ] ] ] ]
gap> DefBlock(H,3,1,[[1,0],[1,18],[2,4]]);  
[ [ [ 3 ] ], 
  [ [ [ 1, 0 ] ], [ [ 1, 6 ] ], [ [ 1, 18 ] ], [ [ 2, 4 ] ], [ [ 2, 7, 1 ] ], 
      [ [ 2, 7, 2 ] ], [ [ 2, 10 ] ], [ [ 3, 2 ] ], [ [ 4, 5 ] ] ] ]
gap> DefBlock(H,3,1,[[2,1],[2,13]]);      
[ [ [ 1 ] ], [ [ [ 2, 1 ] ], [ [ 2, 13 ] ], [ [ 4, 3 ] ] ] ]
gap> DefBlock(H,3,1,[[3,6]]);             
[ [ [ 1 ] ], [ [ [ 3, 8 ] ], [ [ 3, 6 ] ] ] ]
gap> DefBlock(H,5,1,[[1,0],[3,8]]); 
[ [ [ 1 ] ], [ [ [ 1, 0 ] ], [ [ 3, 8 ] ], [ [ 4, 5 ] ] ] ]
gap> DefBlock(H,5,1,[[1,18],[2,4]]);
[ [ [ 1 ] ], [ [ [ 1, 18 ] ], [ [ 2, 4 ] ], [ [ 3, 6 ] ] ] ]
gap> DefBlock(H,7,1,[[1,0],[2,10]]);
[ [ [ 1 ] ], [ [ [ 1, 0 ] ], [ [ 2, 10 ] ], [ [ 3, 4 ] ] ] ]
gap> DefBlock(H,8,1,[[1,0]]);       
[ [ [ 1 ] ], [ [ [ 1, 0 ] ], [ [ 1, 18 ] ] ] ]
gap> DefBlock(H,8,1,[[2,1]]);
[ [ [ 1 ] ], [ [ [ 2, 1 ] ], [ [ 2, 10 ] ] ] ]
gap> DefBlock(H,8,1,[[2,4]]);
[ [ [ 1 ] ], [ [ [ 2, 4 ] ], [ [ 2, 13 ] ] ] ]
gap> DefBlock(H,8,1,[[3,2]]);
[ [ [ 1 ] ], [ [ [ 3, 8 ] ], [ [ 3, 2 ] ] ] ]
gap> DefBlock(H,9,1,[[1,0],[1,12]]);
[ [ [ 1 ] ], [ [ [ 1, 0 ] ], [ [ 1, 12 ] ], [ [ 2, 4 ] ] ] ]
gap> DefBlock(H,12,1,[[1,0],[1,18]]);
[ [ [ 1 ] ], [ [ [ 1, 0 ] ], [ [ 1, 18 ] ], [ [ 2, 7, 1 ] ] ] ]
gap> DefBlock(H,12,1,[[2,1],[2,13]]);
[ [ [ 1 ] ], [ [ [ 2, 1 ] ], [ [ 2, 13 ] ], [ [ 4, 5 ] ] ] ]
gap> DefBlock(H,12,1,[[2,4],[2,10]]);
[ [ [ 1 ] ], [ [ [ 2, 4 ] ], [ [ 2, 10 ] ], [ [ 4, 3 ] ] ] ]

####################################################################

G8
Hecke(G8,[[1,-1,-x,x^5]])

gap> DefBlock(H,1,1,[[1,0],[1,6],[2,1]]);
[ [ [ 4 ] ], 
  [ [ [ 1, 0 ] ], [ [ 1, 6 ] ], [ [ 1, 12 ] ], [ [ 1, 18 ] ], [ [ 2, 1 ] ], 
      [ [ 2, 4 ] ], [ [ 2, 10 ] ], [ [ 2, 13 ] ], [ [ 3, 8 ] ], [ [ 3, 6 ] ], 
      [ [ 3, 4 ] ], [ [ 3, 2 ] ], [ [ 4, 5 ] ] ] ]
gap> DefBlock(H,2,1,[[1,0],[1,6],[2,1]]);
[ [ [ 4 ] ], 
  [ [ [ 1, 0 ] ], [ [ 1, 6 ] ], [ [ 1, 12 ] ], [ [ 1, 18 ] ], [ [ 2, 1 ] ], 
      [ [ 2, 7, 1 ] ], [ [ 2, 7, 2 ] ], [ [ 2, 13 ] ], [ [ 3, 8 ] ], 
      [ [ 3, 6 ] ], [ [ 3, 4 ] ], [ [ 3, 2 ] ], [ [ 4, 3 ] ] ] ]
gap> DefBlock(H,3,1,[[1,0],[1,6],[1,12],[1,18]]);
[ [ [ 3 ] ], 
  [ [ [ 1, 0 ] ], [ [ 1, 6 ] ], [ [ 1, 12 ] ], [ [ 1, 18 ] ], [ [ 2, 4 ] ], 
      [ [ 2, 10 ] ], [ [ 2, 13 ] ], [ [ 3, 8 ] ], [ [ 3, 6 ] ], [ [ 4, 5 ] ] 
     ] ]
gap> DefBlock(H,3,1,[[2,7,1],[2,7,2]]);            
[ [ [ 1 ] ], [ [ [ 2, 7, 1 ] ], [ [ 2, 7, 2 ] ], [ [ 4, 3 ] ] ] ]
gap> DefBlock(H,5,1,[[1,0],[2,1]]);    
[ [ [ 2 ] ], 
  [ [ [ 1, 0 ] ], [ [ 1, 18 ] ], [ [ 2, 1 ] ], [ [ 2, 10 ] ], [ [ 3, 4 ] ] ] ]
gap> DefBlock(H,5,1,[[2,4]]);       
[ [ [ 1 ] ], [ [ [ 2, 4 ] ], [ [ 2, 13 ] ] ] ]
gap> DefBlock(H,5,1,[[3,2]]);
[ [ [ 1 ] ], [ [ [ 3, 8 ] ], [ [ 3, 2 ] ] ] ]
gap> DefBlock(H,10,1,[[1,6],[2,1]]);
[ [ [ 2 ] ], 
  [ [ [ 1, 6 ] ], [ [ 1, 18 ] ], [ [ 2, 1 ] ], [ [ 2, 7, 1 ] ], [ [ 3, 4 ] ] 
     ] ]
gap> DefBlock(H,10,1,[[2,7,2]]);    
[ [ [ 1 ] ], [ [ [ 2, 7, 2 ] ], [ [ 2, 13 ] ] ] ]
gap> DefBlock(H,10,1,[[3,2]]);  
[ [ [ 1 ] ], [ [ [ 3, 6 ] ], [ [ 3, 2 ] ] ] ]
gap> DefBlock(H,6,1,[[1,0],[1,6],[1,12],[1,18]]);
[ [ [ 3 ] ], 
  [ [ [ 1, 0 ] ], [ [ 1, 6 ] ], [ [ 1, 12 ] ], [ [ 1, 18 ] ], [ [ 2, 7, 1 ] ],
      [ [ 2, 7, 2 ] ], [ [ 2, 13 ] ], [ [ 3, 8 ] ], [ [ 3, 6 ] ], 
      [ [ 4, 3 ] ] ] ]
gap> DefBlock(H,6,1,[[2,4],[2,10]]);             
[ [ [ 1 ] ], [ [ [ 2, 4 ] ], [ [ 2, 10 ] ], [ [ 4, 5 ] ] ] ]
gap> DefBlock(H,7,1,[[3,2],[1,18]]);
[ [ [ 1 ] ], [ [ [ 1, 18 ] ], [ [ 3, 2 ] ], [ [ 4, 5 ] ] ] ]
gap> DefBlock(H,9,1,[[2,4],[1,18]]);
[ [ [ 1 ] ], [ [ [ 1, 18 ] ], [ [ 2, 4 ] ], [ [ 3, 6 ] ] ] ]
gap> DefBlock(H,9,1,[[2,1],[2,13]]);
[ [ [ 1 ] ], [ [ [ 2, 1 ] ], [ [ 2, 13 ] ], [ [ 4, 5 ] ] ] ]
gap> DefBlock(H,8,1,[[3,2]]);       
[ [ [ 1 ] ], [ [ [ 3, 4 ] ], [ [ 3, 2 ] ] ] ]
gap> DefBlock(H,8,1,[[1,12]]);
[ [ [ 1 ] ], [ [ [ 1, 12 ] ], [ [ 1, 18 ] ] ] ]
gap> DefBlock(H,8,1,[[2,4]]); 
[ [ [ 1 ] ], [ [ [ 2, 4 ] ], [ [ 2, 7, 1 ] ] ] ]
gap> DefBlock(H,8,1,[[2,7,2]]);
[ [ [ 1 ] ], [ [ [ 2, 7, 2 ] ], [ [ 2, 10 ] ] ] ]
gap> DefBlock(H,12,1,[[1,12],[1,18]]);
[ [ [ 1 ] ], [ [ [ 1, 12 ] ], [ [ 1, 18 ] ], [ [ 2, 13 ] ] ] ]
gap> DefBlock(H,12,1,[[2,4],[2,10]]); 
[ [ [ 1 ] ], [ [ [ 2, 4 ] ], [ [ 2, 10 ] ], [ [ 4, 3 ] ] ] ]
gap> DefBlock(H,12,1,[[2,7,1],[2,7,2]]);
[ [ [ 1 ] ], [ [ [ 2, 7, 1 ] ], [ [ 2, 7, 2 ] ], [ [ 4, 5 ] ] ] ]
gap> DefBlock(H,14,1,[[1,18],[3,2]]);   
[ [ [ 1 ] ], [ [ [ 1, 18 ] ], [ [ 3, 2 ] ], [ [ 4, 3 ] ] ] ]
gap> DefBlock(H,15,1,[[1,18],[1,6]]);
[ [ [ 1 ] ], [ [ [ 1, 6 ] ], [ [ 1, 18 ] ], [ [ 2, 10 ] ] ] ]
gap> DefBlock(H,18,1,[[1,18],[2,7,2]]);
[ [ [ 1 ] ], [ [ [ 1, 18 ] ], [ [ 2, 7, 2 ] ], [ [ 3, 8 ] ] ] ]
gap> DefBlock(H,18,1,[[2,1],[2,13]]);  
[ [ [ 1 ] ], [ [ [ 2, 1 ] ], [ [ 2, 13 ] ], [ [ 4, 3 ] ] ] ]
gap> DefBlock(H,30,1,[[1,18],[1,0]]);  
[ [ [ 1 ] ], [ [ [ 1, 0 ] ], [ [ 1, 18 ] ], [ [ 2, 7, 1 ] ] ] ]

####################################################################

G8
Hecke(G8,[[1,-x^4,x^5,-x^5]])

gap> DefBlock(H,1,1,[[1,0],[1,6],[2,1]]);
[ [ [ 4 ] ], 
  [ [ [ 1, 0 ] ], [ [ 1, 6 ] ], [ [ 1, 12 ] ], [ [ 1, 18 ] ], [ [ 2, 1 ] ], 
      [ [ 2, 7, 1 ] ], [ [ 2, 7, 2 ] ], [ [ 2, 13 ] ], [ [ 3, 8 ] ], 
      [ [ 3, 6 ] ], [ [ 3, 4 ] ], [ [ 3, 2 ] ], [ [ 4, 5 ] ] ] ]
gap> DefBlock(H,3,1,[[1,0],[1,6],[1,12],[1,18]]);
[ [ [ 3 ] ], 
  [ [ [ 1, 0 ] ], [ [ 1, 6 ] ], [ [ 1, 12 ] ], [ [ 1, 18 ] ], [ [ 2, 1 ] ], 
      [ [ 2, 7, 1 ] ], [ [ 2, 7, 2 ] ], [ [ 3, 4 ] ], [ [ 3, 2 ] ], 
      [ [ 4, 5 ] ] ] ]
gap> DefBlock(H,3,1,[[2,4],[2,10]]);             
[ [ [ 1 ] ], [ [ [ 2, 4 ] ], [ [ 2, 10 ] ], [ [ 4, 3 ] ] ] ]
gap> DefBlock(H,5,1,[[1,0],[2,7,1]]);
[ [ [ 2 ] ], 
  [ [ [ 1, 0 ] ], [ [ 1, 12 ] ], [ [ 2, 7, 1 ] ], [ [ 2, 13 ] ], [ [ 3, 6 ] ] 
     ] ]
gap> DefBlock(H,5,1,[[2,1]]);        
[ [ [ 1 ] ], [ [ [ 2, 1 ] ], [ [ 2, 7, 2 ] ] ] ]
gap> DefBlock(H,5,1,[[3,4]]);
[ [ [ 1 ] ], [ [ [ 3, 8 ] ], [ [ 3, 4 ] ] ] ]
gap> DefBlock(H,7,1,[[1,0],[3,8]]);
[ [ [ 1 ] ], [ [ [ 1, 0 ] ], [ [ 3, 8 ] ], [ [ 4, 5 ] ] ] ]
gap> DefBlock(H,8,1,[[1,0]]);      
[ [ [ 1 ] ], [ [ [ 1, 0 ] ], [ [ 1, 6 ] ] ] ]
gap> DefBlock(H,8,1,[[2,4]]);  
[ [ [ 1 ] ], [ [ [ 2, 4 ] ], [ [ 2, 7, 2 ] ] ] ]
gap> DefBlock(H,8,1,[[2,7,1]]);
[ [ [ 1 ] ], [ [ [ 2, 7, 1 ] ], [ [ 2, 10 ] ] ] ]
gap> DefBlock(H,8,1,[[3,6]]);  
[ [ [ 1 ] ], [ [ [ 3, 8 ] ], [ [ 3, 6 ] ] ] ]
gap> DefBlock(H,9,1,[[1,0],[2,7,2]]);
[ [ [ 1 ] ], [ [ [ 1, 0 ] ], [ [ 2, 7, 2 ] ], [ [ 3, 2 ] ] ] ]
gap> DefBlock(H,9,1,[[2,1],[2,13]]); 
[ [ [ 1 ] ], [ [ [ 2, 1 ] ], [ [ 2, 13 ] ], [ [ 4, 5 ] ] ] ]
gap> DefBlock(H,12,1,[[1,0],[1,6]]);    
[ [ [ 1 ] ], [ [ [ 1, 0 ] ], [ [ 1, 6 ] ], [ [ 2, 1 ] ] ] ]
gap> DefBlock(H,12,1,[[2,4],[2,10]]);
[ [ [ 1 ] ], [ [ [ 2, 4 ] ], [ [ 2, 10 ] ], [ [ 4, 5 ] ] ] ]
gap> DefBlock(H,12,1,[[2,7,1],[2,7,2]]);
[ [ [ 1 ] ], [ [ [ 2, 7, 1 ] ], [ [ 2, 7, 2 ] ], [ [ 4, 3 ] ] ] ]
gap> DefBlock(H,15,1,[[1,18],[1,0]]);   
[ [ [ 1 ] ], [ [ [ 1, 0 ] ], [ [ 1, 18 ] ], [ [ 2, 7, 1 ] ] ] ]

####################################################################

G8
Hecke(G8,[[1,-x,-x^4,x^5]])

gap> DefBlock(H,1,1,[[1,0],[1,6],[2,1]]);
[ [ [ 4 ] ], 
  [ [ [ 1, 0 ] ], [ [ 1, 6 ] ], [ [ 1, 12 ] ], [ [ 1, 18 ] ], [ [ 2, 1 ] ], 
      [ [ 2, 4 ] ], [ [ 2, 10 ] ], [ [ 2, 13 ] ], [ [ 3, 8 ] ], [ [ 3, 6 ] ], 
      [ [ 3, 4 ] ], [ [ 3, 2 ] ], [ [ 4, 5 ] ] ] ]

ERRATUM TO THE ChMi PAPER : We have written [[1,0],[1,6],[2,1]] (as above) but it should be:
gap> DefBlock(H,2,1,[[1,0],[1,18],[2,4]]); 
[ [ [ 4 ] ], 
  [ [ [ 1, 0 ] ], [ [ 1, 6 ] ], [ [ 1, 12 ] ], [ [ 1, 18 ] ], [ [ 2, 4 ] ], 
      [ [ 2, 7, 1 ] ], [ [ 2, 7, 2 ] ], [ [ 2, 10 ] ], [ [ 3, 8 ] ], 
      [ [ 3, 6 ] ], [ [ 3, 4 ] ], [ [ 3, 2 ] ], [ [ 4, 3 ] ] ] ]

gap> DefBlock(H,3,1,[[1,0],[1,6],[1,18]]);       
[ [ [ 4 ] ], 
  [ [ [ 1, 0 ] ], [ [ 1, 6 ] ], [ [ 1, 12 ] ], [ [ 1, 18 ] ], [ [ 2, 1 ] ], 
      [ [ 2, 4 ] ], [ [ 2, 10 ] ], [ [ 2, 13 ] ], [ [ 3, 6 ] ], [ [ 3, 4 ] ], 
      [ [ 4, 5 ] ] ] ]
gap> DefBlock(H,5,1,[[1,0],[3,2]]);        
[ [ [ 2 ] ], 
  [ [ [ 1, 0 ] ], [ [ 1, 18 ] ], [ [ 3, 8 ] ], [ [ 3, 2 ] ], [ [ 4, 5 ] ] ] ]
gap> DefBlock(H,5,1,[[2,1]]);      
[ [ [ 1 ] ], [ [ [ 2, 1 ] ], [ [ 2, 10 ] ] ] ]
gap> DefBlock(H,5,1,[[2,4]]);  
[ [ [ 1 ] ], [ [ [ 2, 4 ] ], [ [ 2, 13 ] ] ] ]
gap> DefBlock(H,6,1,[[1,0],[1,6],[1,12],[1,18]]);
[ [ [ 3 ] ], 
  [ [ [ 1, 0 ] ], [ [ 1, 6 ] ], [ [ 1, 12 ] ], [ [ 1, 18 ] ], [ [ 2, 4 ] ], 
      [ [ 2, 7, 1 ] ], [ [ 2, 10 ] ], [ [ 3, 6 ] ], [ [ 3, 4 ] ], 
      [ [ 4, 3 ] ] ] ]
gap> DefBlock(H,6,1,[[2,1],[2,13]]);             
[ [ [ 1 ] ], [ [ [ 2, 1 ] ], [ [ 2, 13 ] ], [ [ 4, 5 ] ] ] ]
gap> DefBlock(H,7,1,[[1,6],[2,13]]);
[ [ [ 1 ] ], [ [ [ 1, 6 ] ], [ [ 2, 13 ] ], [ [ 3, 8 ] ] ] ]
gap> DefBlock(H,7,1,[[1,12],[2,1]]); 
[ [ [ 1 ] ], [ [ [ 1, 12 ] ], [ [ 2, 1 ] ], [ [ 3, 2 ] ] ] ]
gap> DefBlock(H,8,1,[[1,0]]);       
[ [ [ 1 ] ], [ [ [ 1, 0 ] ], [ [ 1, 12 ] ] ] ]
gap> DefBlock(H,8,1,[[1,6]]);
[ [ [ 1 ] ], [ [ [ 1, 6 ] ], [ [ 1, 18 ] ] ] ]
gap> DefBlock(H,8,1,[[3,2]]);
[ [ [ 1 ] ], [ [ [ 3, 6 ] ], [ [ 3, 2 ] ] ] ]
gap> DefBlock(H,8,1,[[3,4]]);
[ [ [ 1 ] ], [ [ [ 3, 8 ] ], [ [ 3, 4 ] ] ] ]
gap> DefBlock(H,8,1,[[2,1]]);
[ [ [ 2 ] ], [ [ [ 2, 1 ] ], [ [ 2, 7, 1 ] ], [ [ 2, 7, 2 ] ], [ [ 2, 13 ] ] 
     ] ]
gap> DefBlock(H,9,1,[[1,0],[2,13]]);
[ [ [ 1 ] ], [ [ [ 1, 0 ] ], [ [ 2, 13 ] ], [ [ 3, 6 ] ] ] ]
gap> DefBlock(H,9,1,[[1,18],[2,1]]); 
[ [ [ 1 ] ], [ [ [ 1, 18 ] ], [ [ 2, 1 ] ], [ [ 3, 4 ] ] ] ]
gap> DefBlock(H,10,1,[[1,18],[2,7,2],[1,0]]);
[ [ [ 2 ] ], 
  [ [ [ 1, 0 ] ], [ [ 1, 18 ] ], [ [ 2, 7, 2 ] ], [ [ 3, 8 ] ], [ [ 3, 2 ] ], 
      [ [ 4, 3 ] ] ] ]
gap> DefBlock(H,12,1,[[1,0],[1,12]]);         
[ [ [ 1 ] ], [ [ [ 1, 0 ] ], [ [ 1, 12 ] ], [ [ 2, 4 ] ] ] ]
gap> DefBlock(H,12,1,[[1,6],[1,18]]);
[ [ [ 1 ] ], [ [ [ 1, 6 ] ], [ [ 1, 18 ] ], [ [ 2, 10 ] ] ] ]
gap> DefBlock(H,12,1,[[2,1],[2,13]]);
[ [ [ 1 ] ], [ [ [ 2, 1 ] ], [ [ 2, 13 ] ], [ [ 4, 5 ] ] ] ]
gap> DefBlock(H,18,1,[[1,6],[1,12]]);
[ [ [ 1 ] ], [ [ [ 1, 6 ] ], [ [ 1, 12 ] ], [ [ 2, 7, 2 ] ] ] ]
gap> DefBlock(H,24,1,[[2,1],[2,13]]);
[ [ [ 1 ] ], [ [ [ 2, 1 ] ], [ [ 2, 13 ] ], [ [ 4, 3 ] ] ] ]
gap> DefBlock(H,30,1,[[1,18],[1,0]]);
[ [ [ 1 ] ], [ [ [ 1, 0 ] ], [ [ 1, 18 ] ], [ [ 2, 7, 1 ] ] ] ]

####################################################################

G9
Hecke(G9,[[1,x^4],[1,x^2,x^4,x^6]])

gap> DefBlock(H,2,1,[[1,0],[2,5]]);
[ [ [ 8 ] ], 
  [ [ [ 1, 0 ] ], [ [ 1, 6 ] ], [ [ 1, 12, 1 ] ], [ [ 1, 18, 1 ] ], 
      [ [ 1, 12, 2 ] ], [ [ 1, 18, 2 ] ], [ [ 1, 24 ] ], [ [ 1, 30 ] ], 
      [ [ 2, 5 ] ], [ [ 2, 10 ] ], [ [ 2, 17 ] ], [ [ 2, 11, 1 ] ], 
      [ [ 2, 11, 2 ] ], [ [ 2, 8 ] ], [ [ 3, 8, 1 ] ], [ [ 3, 6, 1 ] ], 
      [ [ 3, 4 ] ], [ [ 3, 2 ] ], [ [ 3, 12 ] ], [ [ 3, 10 ] ], 
      [ [ 3, 8, 2 ] ], [ [ 3, 6, 2 ] ], [ [ 4, 7 ] ] ] ]
gap> DefBlock(H,2,1,[[2,1]]);      
[ [ [ 4 ] ], [ [ [ 2, 4 ] ], [ [ 2, 7, 1 ] ], [ [ 2, 7, 2 ] ], [ [ 2, 13 ] ], 
      [ [ 2, 1 ] ], [ [ 2, 14 ] ] ] ]
gap> DefBlock(H,3,1,[[1,0],[1,6],[1,12,2],[1,24]]);
[ [ [ 4 ] ], 
  [ [ [ 1, 0 ] ], [ [ 1, 6 ] ], [ [ 1, 18, 1 ] ], [ [ 1, 12, 2 ] ], 
      [ [ 1, 24 ] ], [ [ 1, 30 ] ], [ [ 2, 7, 1 ] ], [ [ 2, 10 ] ], 
      [ [ 2, 13 ] ], [ [ 2, 1 ] ], [ [ 2, 8 ] ], [ [ 3, 4 ] ], [ [ 3, 10 ] ], 
      [ [ 4, 5 ] ] ] ]
gap> DefBlock(H,3,1,[[1,12,1],[1,18,2]]);          
[ [ [ 1 ] ], [ [ [ 1, 12, 1 ] ], [ [ 1, 18, 2 ] ], [ [ 2, 7, 2 ] ] ] ]
gap> DefBlock(H,3,1,[[2,5],[2,4]]);      
[ [ [ 2 ] ], 
  [ [ [ 2, 5 ] ], [ [ 2, 4 ] ], [ [ 2, 14 ] ], [ [ 2, 17 ] ], [ [ 4, 7 ] ] ] ]
gap> DefBlock(H,3,1,[[3,2]]);      
[ [ [ 1 ] ], [ [ [ 3, 8, 1 ] ], [ [ 3, 2 ] ] ] ]
gap> DefBlock(H,3,1,[[3,6,2]]);
[ [ [ 1 ] ], [ [ [ 3, 12 ] ], [ [ 3, 6, 2 ] ] ] ]
gap> DefBlock(H,4,1,[[1,0],[2,14]]);
[ [ [ 4 ] ], 
  [ [ [ 1, 0 ] ], [ [ 1, 12, 1 ] ], [ [ 1, 12, 2 ] ], [ [ 1, 24 ] ], 
      [ [ 2, 14 ] ], [ [ 3, 8, 1 ] ], [ [ 3, 4 ] ], [ [ 3, 12 ] ], 
      [ [ 3, 8, 2 ] ], [ [ 4, 3 ] ] ] ]
gap> DefBlock(H,4,1,[[1,6],[2,4]]); 
[ [ [ 4 ] ], 
  [ [ [ 1, 6 ] ], [ [ 1, 18, 1 ] ], [ [ 1, 18, 2 ] ], [ [ 1, 30 ] ], 
      [ [ 2, 4 ] ], [ [ 3, 6, 1 ] ], [ [ 3, 2 ] ], [ [ 3, 10 ] ], 
      [ [ 3, 6, 2 ] ], [ [ 4, 9 ] ] ] ]
gap> DefBlock(H,4,1,[[2,1]]);       
[ [ [ 2 ] ], 
  [ [ [ 2, 13 ] ], [ [ 2, 1 ] ], [ [ 2, 11, 1 ] ], [ [ 2, 11, 2 ] ] ] ]
gap> DefBlock(H,4,1,[[2,5]]);
[ [ [ 2 ] ], [ [ [ 2, 5 ] ], [ [ 2, 7, 1 ] ], [ [ 2, 7, 2 ] ], [ [ 2, 17 ] ] 
     ] ]
gap> DefBlock(H,5,1,[[1,0],[2,7,2],[1,30]]);
[ [ [ 2 ] ], 
  [ [ [ 1, 0 ] ], [ [ 1, 30 ] ], [ [ 2, 7, 2 ] ], [ [ 3, 2 ] ], [ [ 3, 12 ] ],
      [ [ 4, 5 ] ] ] ]
gap> DefBlock(H,5,1,[[1,24],[2,1]]);
[ [ [ 1 ] ], [ [ [ 1, 24 ] ], [ [ 2, 1 ] ], [ [ 3, 6, 2 ] ] ] ]
gap> DefBlock(H,5,1,[[1,6],[2,13]]);
[ [ [ 1 ] ], [ [ [ 1, 6 ] ], [ [ 2, 13 ] ], [ [ 3, 8, 1 ] ] ] ]
gap> DefBlock(H,7,1,[[1,0],[2,13]]);
[ [ [ 1 ] ], [ [ [ 1, 0 ] ], [ [ 2, 13 ] ], [ [ 3, 6, 1 ] ] ] ]
gap> DefBlock(H,7,1,[[1,30],[2,1]]);
[ [ [ 1 ] ], [ [ [ 1, 30 ] ], [ [ 2, 1 ] ], [ [ 3, 8, 2 ] ] ] ]
gap> DefBlock(H,9,1,[[1,0],[1,18,2]]);
[ [ [ 1 ] ], [ [ [ 1, 0 ] ], [ [ 1, 18, 2 ] ], [ [ 2, 1 ] ] ] ]
gap> DefBlock(H,9,1,[[1,6],[1,24]]);  
[ [ [ 1 ] ], [ [ [ 1, 6 ] ], [ [ 1, 24 ] ], [ [ 2, 7, 2 ] ] ] ]
gap> DefBlock(H,9,1,[[1,12,1],[1,30]]);
[ [ [ 1 ] ], [ [ [ 1, 12, 1 ] ], [ [ 1, 30 ] ], [ [ 2, 13 ] ] ] ]
gap> DefBlock(H,12,1,[[1,0],[1,24],[2,14]]);
[ [ [ 2 ] ], 
  [ [ [ 1, 0 ] ], [ [ 1, 24 ] ], [ [ 2, 14 ] ], [ [ 2, 8 ] ], [ [ 3, 4 ] ], 
      [ [ 4, 9 ] ] ] ]
gap> DefBlock(H,12,1,[[1,6],[1,30],[2,4]]); 
[ [ [ 2 ] ], 
  [ [ [ 1, 6 ] ], [ [ 1, 30 ] ], [ [ 2, 4 ] ], [ [ 2, 10 ] ], [ [ 3, 10 ] ], 
      [ [ 4, 3 ] ] ] ]
gap> DefBlock(H,12,1,[[2,1],[2,13]]);     
[ [ [ 1 ] ], [ [ [ 2, 13 ] ], [ [ 2, 1 ] ], [ [ 4, 7 ] ] ] ]
gap> DefBlock(H,12,1,[[2,5],[2,17]]);
[ [ [ 1 ] ], [ [ [ 2, 5 ] ], [ [ 2, 17 ] ], [ [ 4, 5 ] ] ] ]
gap> DefBlock(H,15,1,[[1,0],[1,30]]);
[ [ [ 1 ] ], [ [ [ 1, 0 ] ], [ [ 1, 30 ] ], [ [ 2, 7, 1 ] ] ] ]
gap> DefBlock(H,20,1,[[1,0],[3,12]]);
[ [ [ 1 ] ], [ [ [ 1, 0 ] ], [ [ 3, 12 ] ], [ [ 4, 3 ] ] ] ]
gap> DefBlock(H,20,1,[[1,30],[3,2]]); 
[ [ [ 1 ] ], [ [ [ 1, 30 ] ], [ [ 3, 2 ] ], [ [ 4, 9 ] ] ] ]
gap> DefBlock(H,24,1,[[1,0],[1,24]]);
[ [ [ 1 ] ], [ [ [ 1, 0 ] ], [ [ 1, 24 ] ], [ [ 2, 4 ] ] ] ]
gap> DefBlock(H,24,1,[[1,6],[1,30]]);
[ [ [ 1 ] ], [ [ [ 1, 6 ] ], [ [ 1, 30 ] ], [ [ 2, 14 ] ] ] ]
gap> DefBlock(H,24,1,[[2,1],[2,17]]);
[ [ [ 1 ] ], [ [ [ 2, 1 ] ], [ [ 2, 17 ] ], [ [ 4, 9 ] ] ] ]
gap> DefBlock(H,24,1,[[2,5],[2,13]]);
[ [ [ 1 ] ], [ [ [ 2, 5 ] ], [ [ 2, 13 ] ], [ [ 4, 3 ] ] ] ]

#################################################################################

G10
Hecke(G10,[[1,-x^2,x^4],[1,x^3,-x^3,x^6]])

gap> DefBlock(H,2,1,[[1,0],[1,6],[1,8]]);        
[ [ [ 8 ] ], 
  [ [ [ 1, 0 ] ], [ [ 1, 6 ] ], [ [ 1, 12 ] ], [ [ 1, 18 ] ], [ [ 1, 8 ] ], 
      [ [ 1, 20 ] ], [ [ 1, 26 ] ], [ [ 1, 16 ] ], [ [ 1, 22 ] ], 
      [ [ 1, 28 ] ], [ [ 1, 34 ] ], [ [ 2, 12 ] ], [ [ 2, 15, 1 ] ], 
      [ [ 2, 21 ] ], [ [ 2, 5 ] ], [ [ 2, 11, 2 ] ], [ [ 2, 14 ] ], 
      [ [ 2, 4 ] ], [ [ 2, 7, 1 ] ], [ [ 2, 13 ] ], [ [ 3, 12, 2 ] ], 
      [ [ 3, 6, 2 ] ], [ [ 3, 12, 1 ] ], [ [ 3, 6, 1 ] ], [ [ 4, 9 ] ], 
      [ [ 4, 7 ] ] ] ]
gap> DefBlock(H,2,1,[[2,1],[2,8]]);      
[ [ [ 4 ] ], 
  [ [ [ 2, 9 ] ], [ [ 2, 15, 2 ] ], [ [ 2, 18 ] ], [ [ 2, 8 ] ], [ [ 2, 11, 1 
             ] ], [ [ 2, 17 ] ], [ [ 2, 1 ] ], [ [ 2, 7, 2 ] ], 
      [ [ 2, 10 ] ], [ [ 4, 3 ] ], [ [ 4, 13 ] ] ] ]
gap> DefBlock(H,2,1,[[3,2]]);            
[ [ [ 2 ] ], [ [ [ 3, 8, 2 ] ], [ [ 3, 8, 1 ] ], [ [ 3, 2 ] ] ] ]
gap> DefBlock(H,2,1,[[3,10,1]]);
[ [ [ 2 ] ], [ [ [ 3, 16 ] ], [ [ 3, 4 ] ], [ [ 3, 10, 1 ] ] ] ]
gap> DefBlock(H,3,1,[[1,0],[1,12],[2,9]]);
[ [ [ 4 ] ], 
  [ [ [ 1, 0 ] ], [ [ 1, 6 ] ], [ [ 1, 12 ] ], [ [ 1, 18 ] ], [ [ 2, 9 ] ], 
      [ [ 2, 15, 1 ] ], [ [ 2, 18 ] ], [ [ 3, 14 ] ], [ [ 3, 8, 1 ] ], 
      [ [ 3, 10, 1 ] ], [ [ 3, 12, 2 ] ], [ [ 4, 3 ] ] ] ]
gap> DefBlock(H,3,1,[[1,16],[1,28],[2,1]]);
[ [ [ 4 ] ], 
  [ [ [ 1, 16 ] ], [ [ 1, 22 ] ], [ [ 1, 28 ] ], [ [ 1, 34 ] ], [ [ 2, 1 ] ], 
      [ [ 2, 7, 1 ] ], [ [ 2, 10 ] ], [ [ 3, 8, 2 ] ], [ [ 3, 10, 2 ] ], 
      [ [ 3, 4 ] ], [ [ 3, 6, 1 ] ], [ [ 4, 13 ] ] ] ]
gap> DefBlock(H,3,1,[[1,8],[2,8]]);       
[ [ [ 4 ] ], 
  [ [ [ 1, 8 ] ], [ [ 1, 14 ] ], [ [ 1, 26 ] ], [ [ 2, 8 ] ], [ [ 2, 11, 2 ] ]
        , [ [ 2, 17 ] ], [ [ 3, 2 ] ], [ [ 3, 16 ] ], [ [ 3, 6, 2 ] ] ] ]
gap> DefBlock(H,3,1,[[2,12]]);     
[ [ [ 2 ] ], [ [ [ 2, 12 ] ], [ [ 2, 15, 2 ] ], [ [ 2, 21 ] ] ] ]
gap> DefBlock(H,3,1,[[2,5]]); 
[ [ [ 2 ] ], [ [ [ 2, 5 ] ], [ [ 2, 11, 1 ] ], [ [ 2, 14 ] ] ] ]
gap> DefBlock(H,3,1,[[2,4]]);
[ [ [ 2 ] ], [ [ [ 2, 4 ] ], [ [ 2, 7, 2 ] ], [ [ 2, 13 ] ] ] ]
gap> DefBlock(H,4,1,[[1,0],[1,18]]);       
[ [ [ 4 ] ], 
  [ [ [ 1, 0 ] ], [ [ 1, 18 ] ], [ [ 1, 8 ] ], [ [ 1, 26 ] ], [ [ 1, 16 ] ], 
      [ [ 1, 34 ] ], [ [ 2, 15, 1 ] ], [ [ 2, 11, 1 ] ], [ [ 2, 7, 1 ] ] ] ]
gap> DefBlock(H,4,1,[[1,6],[1,12]]);
[ [ [ 4 ] ], 
  [ [ [ 1, 6 ] ], [ [ 1, 12 ] ], [ [ 1, 14 ] ], [ [ 1, 20 ] ], [ [ 1, 22 ] ], 
      [ [ 1, 28 ] ], [ [ 2, 15, 2 ] ], [ [ 2, 11, 2 ] ], [ [ 2, 7, 2 ] ] ] ]
gap> DefBlock(H,4,1,[[2,4],[2,10]]);
[ [ [ 4 ] ], 
  [ [ [ 2, 12 ] ], [ [ 2, 18 ] ], [ [ 2, 8 ] ], [ [ 2, 14 ] ], [ [ 2, 4 ] ], 
      [ [ 2, 10 ] ], [ [ 4, 9 ] ], [ [ 4, 5 ] ], [ [ 4, 13 ] ] ] ]
gap> DefBlock(H,4,1,[[2,1],[2,13]]);
[ [ [ 4 ] ], 
  [ [ [ 2, 9 ] ], [ [ 2, 21 ] ], [ [ 2, 5 ] ], [ [ 2, 17 ] ], [ [ 2, 1 ] ], 
      [ [ 2, 13 ] ], [ [ 4, 11 ] ], [ [ 4, 7 ] ], [ [ 4, 3 ] ] ] ]
gap> DefBlock(H,5,1,[[1,8],[1,22]]);
[ [ [ 1 ] ], [ [ [ 1, 8 ] ], [ [ 1, 22 ] ], [ [ 2, 9 ] ] ] ]
gap> DefBlock(H,5,1,[[1,6],[1,26]]);
[ [ [ 1 ] ], [ [ [ 1, 6 ] ], [ [ 1, 26 ] ], [ [ 2, 10 ] ] ] ]
gap> DefBlock(H,5,1,[[1,0],[1,14],[1,34]]);
[ [ [ 2 ] ], 
  [ [ [ 1, 0 ] ], [ [ 1, 14 ] ], [ [ 1, 34 ] ], [ [ 2, 18 ] ], [ [ 2, 1 ] ], 
      [ [ 3, 12, 1 ] ] ] ]
gap> DefBlock(H,7,1,[[1,0],[1,28]]);       
[ [ [ 1 ] ], [ [ [ 1, 0 ] ], [ [ 1, 28 ] ], [ [ 2, 8 ] ] ] ]
gap> DefBlock(H,7,1,[[1,12],[1,34]]);
[ [ [ 1 ] ], [ [ [ 1, 12 ] ], [ [ 1, 34 ] ], [ [ 2, 17 ] ] ] ]
gap> DefBlock(H,8,1,[[1,0],[2,15,2],[1,26]]);
[ [ [ 2 ] ], 
  [ [ [ 1, 0 ] ], [ [ 1, 26 ] ], [ [ 2, 15, 2 ] ], [ [ 2, 7, 1 ] ], 
      [ [ 3, 6, 1 ] ], [ [ 4, 11 ] ] ] ]
gap> DefBlock(H,8,1,[[1,8],[2,7,2],[1,34]]); 
[ [ [ 2 ] ], 
  [ [ [ 1, 8 ] ], [ [ 1, 34 ] ], [ [ 2, 15, 1 ] ], [ [ 2, 7, 2 ] ], 
      [ [ 3, 12, 2 ] ], [ [ 4, 5 ] ] ] ]
gap> DefBlock(H,8,1,[[2,8],[2,18]]);        
[ [ [ 1 ] ], [ [ [ 2, 18 ] ], [ [ 2, 8 ] ], [ [ 4, 7 ] ] ] ]
gap> DefBlock(H,8,1,[[2,5],[2,21]]);
[ [ [ 1 ] ], [ [ [ 2, 21 ] ], [ [ 2, 5 ] ], [ [ 4, 13 ] ] ] ]
gap> DefBlock(H,8,1,[[2,4],[2,14]]);
[ [ [ 1 ] ], [ [ [ 2, 14 ] ], [ [ 2, 4 ] ], [ [ 4, 3 ] ] ] ]
gap> DefBlock(H,8,1,[[2,1],[2,17]]);
[ [ [ 1 ] ], [ [ [ 2, 17 ] ], [ [ 2, 1 ] ], [ [ 4, 9 ] ] ] ]
gap> DefBlock(H,9,1,[[1,0],[3,8,2]]);
[ [ [ 1 ] ], [ [ [ 1, 0 ] ], [ [ 3, 8, 2 ] ], [ [ 4, 3 ] ] ] ]
gap> DefBlock(H,9,1,[[1,34],[3,10,1]]);
[ [ [ 1 ] ], [ [ [ 1, 34 ] ], [ [ 3, 10, 1 ] ], [ [ 4, 13 ] ] ] ]
gap> DefBlock(H,9,1,[[1,26],[2,8]]);   
[ [ [ 1 ] ], [ [ [ 1, 26 ] ], [ [ 2, 8 ] ], [ [ 3, 14 ] ] ] ]
gap> DefBlock(H,9,1,[[1,12],[2,18]]);
[ [ [ 1 ] ], [ [ [ 1, 12 ] ], [ [ 2, 18 ] ], [ [ 3, 16 ] ] ] ]
gap> DefBlock(H,9,1,[[1,8],[2,17]]); 
[ [ [ 1 ] ], [ [ [ 1, 8 ] ], [ [ 2, 17 ] ], [ [ 3, 10, 2 ] ] ] ]
gap> DefBlock(H,9,1,[[1,28],[2,1]]); 
[ [ [ 1 ] ], [ [ [ 1, 28 ] ], [ [ 2, 1 ] ], [ [ 3, 2 ] ] ] ]
gap> DefBlock(H,15,1,[[1,0],[2,18]]);
[ [ [ 1 ] ], [ [ [ 1, 0 ] ], [ [ 2, 18 ] ], [ [ 3, 4 ] ] ] ]
gap> DefBlock(H,15,1,[[1,34],[2,1]]); 
[ [ [ 1 ] ], [ [ [ 1, 34 ] ], [ [ 2, 1 ] ], [ [ 3, 8, 1 ] ] ] ]
gap> DefBlock(H,20,1,[[1,0],[1,34]]);
[ [ [ 1 ] ], [ [ [ 1, 0 ] ], [ [ 1, 34 ] ], [ [ 2, 11, 1 ] ] ] ]
gap> DefBlock(H,20,1,[[2,1],[2,21]]);
[ [ [ 1 ] ], [ [ [ 2, 21 ] ], [ [ 2, 1 ] ], [ [ 4, 11 ] ] ] ]
gap> DefBlock(H,20,1,[[2,4],[2,18]]);
[ [ [ 1 ] ], [ [ [ 2, 18 ] ], [ [ 2, 4 ] ], [ [ 4, 5 ] ] ] ]
gap> DefBlock(H,24,1,[[1,0],[2,15,2]]);
[ [ [ 1 ] ], [ [ [ 1, 0 ] ], [ [ 2, 15, 2 ] ], [ [ 3, 2 ] ] ] ]
gap> DefBlock(H,24,1,[[1,34],[2,7,2]]); 
[ [ [ 1 ] ], [ [ [ 1, 34 ] ], [ [ 2, 7, 2 ] ], [ [ 3, 16 ] ] ] ]
gap> DefBlock(H,24,1,[[1,8],[3,8,2]]); 
[ [ [ 1 ] ], [ [ [ 1, 8 ] ], [ [ 3, 8, 2 ] ], [ [ 4, 11 ] ] ] ]
gap> DefBlock(H,24,1,[[1,26],[3,10,1]]);
[ [ [ 1 ] ], [ [ [ 1, 26 ] ], [ [ 3, 10, 1 ] ], [ [ 4, 5 ] ] ] ]

#################################################################################

G12
Hecke(G12,[[1,x^2]])

gap> DefBlock(H,2,1,[[1,0],[2,4]]);  
[ [ [ 2 ] ], 
  [ [ [ 1, 0 ] ], [ [ 1, 12 ] ], [ [ 2, 4 ] ], [ [ 3, 2 ] ], [ [ 3, 6 ] ] ] ]
gap> DefBlock(H,8,1,[[1,0],[1,12],[2,1]]);
[ [ [ 2 ] ], 
  [ [ [ 1, 0 ] ], [ [ 1, 12 ] ], [ [ 2, 1 ] ], [ [ 3, 2 ] ], [ [ 3, 6 ] ], 
  [ [ 4, 3 ] ] ] ]
gap> DefBlock(H,8,3,[[1,0],[1,12],[2,5]]);
[ [ [ 2 ] ], 
  [ [ [ 1, 0 ] ], [ [ 1, 12 ] ], [ [ 2, 5 ] ], [ [ 3, 2 ] ], [ [ 3, 6 ] ], 
  [ [ 4, 3 ] ] ] ]
gap> DefBlock(H,8,5,[[1,0],[1,12],[2,5]]);
[ [ [ 2 ] ], 
  [ [ [ 1, 0 ] ], [ [ 1, 12 ] ], [ [ 2, 5 ] ], [ [ 3, 2 ] ], [ [ 3, 6 ] ], 
  [ [ 4, 3 ] ] ] ]
gap> DefBlock(H,8,7,[[1,0],[1,12],[2,1]]);
[ [ [ 2 ] ], 
  [ [ [ 1, 0 ] ], [ [ 1, 12 ] ], [ [ 2, 1 ] ], [ [ 3, 2 ] ], [ [ 3, 6 ] ], 
  [ [ 4, 3 ] ] ] ]
gap> DefBlock(H,12,1,[[1,0],[1,12]]);                         
[ [ [ 1 ] ], [ [ [ 1, 0 ] ], [ [ 1, 12 ] ], [ [ 2, 4 ] ] ] ]
gap> DefBlock(H,24,1,[[1,0],[1,12]]);gap> DefBlock(H,24,7,[[1,0],[1,12]]);gap> DefBlock(H,24,17,[[1,0],[1,12]]);gap> DefBlock(H,24,23,[[1,0],[1,12]]);
[ [ [ 1 ] ], [ [ [ 1, 0 ] ], [ [ 1, 12 ] ], [ [ 2, 1 ] ] ] ]
gap> DefBlock(H,24,5,[[1,0],[1,12]]);gap> DefBlock(H,24,11,[[1,0],[1,12]]);gap> DefBlock(H,24,13,[[1,0],[1,12]]);gap> DefBlock(H,24,19,[[1,0],[1,12]]);
[ [ [ 1 ] ], [ [ [ 1, 0 ] ], [ [ 1, 12 ] ], [ [ 2, 5 ] ] ] ]

#################################################################################

G16
Hecke(G16,[[1,x,x^2,x^3,x^4]])

gap> DefBlock(H,1,1,[[1,0],[3,2]]);           
[ [ [ 8 ] ], 
  [ [ [ 1, 0 ] ], [ [ 1, 12 ] ], [ [ 1, 24 ] ], [ [ 1, 36 ] ], [ [ 1, 48 ] ], 
      [ [ 3, 2 ] ], [ [ 3, 6 ] ], [ [ 3, 10, 2 ] ], [ [ 3, 10, 1 ] ], 
      [ [ 3, 14, 1 ] ], [ [ 3, 18, 1 ] ], [ [ 3, 14, 2 ] ], [ [ 3, 18, 2 ] ], 
      [ [ 3, 22 ] ], [ [ 3, 26 ] ], [ [ 4, 20 ] ], [ [ 4, 12 ] ], 
      [ [ 4, 14 ] ], [ [ 4, 6 ] ], [ [ 4, 8 ] ] ] ]
gap> DefBlock(H,1,1,[[2,1],[4,3]]);
[ [ [ 8 ] ], 
  [ [ [ 2, 1 ] ], [ [ 2, 7 ] ], [ [ 2, 13, 1 ] ], [ [ 2, 19, 1 ] ], 
      [ [ 2, 13, 2 ] ], [ [ 2, 19, 2 ] ], [ [ 2, 25, 2 ] ], [ [ 2, 25, 1 ] ], 
      [ [ 2, 31 ] ], [ [ 2, 37 ] ], [ [ 4, 15 ] ], [ [ 4, 17 ] ], 
      [ [ 4, 9 ] ], [ [ 4, 11 ] ], [ [ 4, 3 ] ], [ [ 6, 5 ] ], [ [ 6, 7 ] ], 
      [ [ 6, 9 ] ], [ [ 6, 11 ] ], [ [ 6, 13 ] ] ] ]
gap> DefBlock(H,2,1,[[1,0],[1,12],[2,1]]);
[ [ [ 8 ] ], 
  [ [ [ 1, 0 ] ], [ [ 1, 12 ] ], [ [ 1, 24 ] ], [ [ 1, 36 ] ], [ [ 1, 48 ] ], 
      [ [ 2, 1 ] ], [ [ 2, 13, 1 ] ], [ [ 2, 13, 2 ] ], [ [ 2, 25, 2 ] ], 
      [ [ 2, 25, 1 ] ], [ [ 2, 37 ] ], [ [ 3, 2 ] ], [ [ 3, 6 ] ], 
      [ [ 3, 10, 2 ] ], [ [ 3, 10, 1 ] ], [ [ 3, 18, 1 ] ], [ [ 3, 14, 2 ] ], 
      [ [ 3, 18, 2 ] ], [ [ 3, 22 ] ], [ [ 3, 26 ] ], [ [ 4, 15 ] ], 
      [ [ 4, 3 ] ], [ [ 4, 14 ] ], [ [ 5, 10 ] ], [ [ 6, 7 ] ], [ [ 6, 11 ] ] 
     ] ]
gap> DefBlock(H,2,1,[[2,7],[4,8]]);       
[ [ [ 4 ] ], 
  [ [ [ 2, 7 ] ], [ [ 2, 19, 1 ] ], [ [ 2, 31 ] ], [ [ 4, 9 ] ], [ [ 4, 20 ] ]
        , [ [ 4, 8 ] ], [ [ 6, 5 ] ], [ [ 6, 9 ] ], [ [ 6, 13 ] ] ] ]
gap> DefBlock(H,2,1,[[4,6]]);             
[ [ [ 1 ] ], [ [ [ 4, 17 ] ], [ [ 4, 6 ] ] ] ]
gap> DefBlock(H,2,1,[[4,11]]);
[ [ [ 1 ] ], [ [ [ 4, 11 ] ], [ [ 4, 12 ] ] ] ]
gap> DefBlock(H,3,1,[[1,0],[1,12],[3,2]]);
[ [ [ 4 ] ], 
  [ [ [ 1, 0 ] ], [ [ 1, 12 ] ], [ [ 1, 36 ] ], [ [ 1, 48 ] ], [ [ 3, 2 ] ], 
      [ [ 3, 14, 1 ] ], [ [ 3, 14, 2 ] ], [ [ 3, 26 ] ], [ [ 4, 20 ] ], 
      [ [ 4, 12 ] ], [ [ 4, 6 ] ], [ [ 4, 8 ] ], [ [ 5, 10 ] ] ] ]
gap> DefBlock(H,3,1,[[2,1],[2,7],[2,13,2]]);
[ [ [ 4 ] ], 
  [ [ [ 2, 1 ] ], [ [ 2, 7 ] ], [ [ 2, 19, 1 ] ], [ [ 2, 13, 2 ] ], 
      [ [ 2, 19, 2 ] ], [ [ 2, 25, 1 ] ], [ [ 2, 31 ] ], [ [ 2, 37 ] ], 
      [ [ 4, 15 ] ], [ [ 4, 17 ] ], [ [ 4, 11 ] ], [ [ 4, 3 ] ], [ [ 6, 9 ] ] 
     ] ]
gap> DefBlock(H,3,1,[[2,25,2],[2,13,1]]);
[ [ [ 1 ] ], [ [ [ 2, 13, 1 ] ], [ [ 2, 25, 2 ] ], [ [ 4, 9 ] ] ] ]
gap> DefBlock(H,3,1,[[3,6]]);
[ [ [ 1 ] ], [ [ [ 3, 6 ] ], [ [ 3, 18, 1 ] ] ] ]
gap> DefBlock(H,3,1,[[3,10,2]]);
[ [ [ 1 ] ], [ [ [ 3, 10, 2 ] ], [ [ 3, 22 ] ] ] ]
gap> DefBlock(H,3,1,[[6,5]]);   
[ [ [ 1 ] ], [ [ [ 6, 5 ] ], [ [ 6, 11 ] ] ] ]
gap> DefBlock(H,3,1,[[6,7]]);
[ [ [ 1 ] ], [ [ [ 6, 7 ] ], [ [ 6, 13 ] ] ] ]
gap> DefBlock(H,4,1,[[1,0],[2,7],[3,6]]); 
[ [ [ 4 ] ], 
  [ [ [ 1, 0 ] ], [ [ 1, 48 ] ], [ [ 2, 7 ] ], [ [ 2, 31 ] ], [ [ 3, 6 ] ], 
      [ [ 3, 14, 1 ] ], [ [ 3, 22 ] ], [ [ 4, 14 ] ], [ [ 5, 10 ] ], 
      [ [ 6, 5 ] ], [ [ 6, 13 ] ] ] ]
gap> DefBlock(H,4,1,[[1,12],[2,19,1],[1,36]]);
[ [ [ 2 ] ], 
  [ [ [ 1, 12 ] ], [ [ 1, 36 ] ], [ [ 2, 19, 1 ] ], [ [ 3, 10, 2 ] ], 
      [ [ 3, 18, 1 ] ], [ [ 4, 9 ] ] ] ]
gap> DefBlock(H,4,1,[[2,1],[4,8]]);             
[ [ [ 2 ] ], 
  [ [ [ 2, 1 ] ], [ [ 2, 25, 2 ] ], [ [ 4, 15 ] ], [ [ 4, 8 ] ], [ [ 6, 7 ] ] 
     ] ]
gap> DefBlock(H,4,1,[[3,2],[3,10,1]]);
[ [ [ 2 ] ], 
  [ [ [ 3, 2 ] ], [ [ 3, 10, 1 ] ], [ [ 3, 18, 2 ] ], [ [ 3, 26 ] ], 
      [ [ 6, 9 ] ] ] ]
gap> DefBlock(H,4,1,[[2,13,1],[4,3]]);
[ [ [ 2 ] ], [ [ [ 2, 13, 1 ] ], [ [ 2, 37 ] ], [ [ 4, 3 ] ], [ [ 4, 20 ] ], 
      [ [ 6, 11 ] ] ] ]
gap> DefBlock(H,6,1,[[1,0],[1,12],[1,24],[1,36],[1,48]]);
[ [ [ 4 ] ], 
  [ [ [ 1, 0 ] ], [ [ 1, 12 ] ], [ [ 1, 24 ] ], [ [ 1, 36 ] ], [ [ 1, 48 ] ], 
      [ [ 2, 1 ] ], [ [ 2, 13, 2 ] ], [ [ 2, 25, 1 ] ], [ [ 2, 37 ] ], 
      [ [ 3, 2 ] ], [ [ 3, 14, 2 ] ], [ [ 3, 26 ] ], [ [ 4, 15 ] ], 
      [ [ 4, 3 ] ], [ [ 5, 10 ] ] ] ]
gap> DefBlock(H,6,1,[[2,7],[2,19,2],[2,31]]);              
[ [ [ 2 ] ], [ [ [ 2, 7 ] ], [ [ 2, 19, 2 ] ], [ [ 2, 31 ] ], [ [ 4, 20 ] ], 
      [ [ 4, 8 ] ], [ [ 6, 9 ] ] ] ]
gap> DefBlock(H,6,1,[[2,13,1],[2,25,2]]);
[ [ [ 1 ] ], [ [ [ 2, 13, 1 ] ], [ [ 2, 25, 2 ] ], [ [ 4, 14 ] ] ] ]
gap> DefBlock(H,6,1,[[3,6],[3,18,2]]);   
[ [ [ 1 ] ], [ [ [ 3, 6 ] ], [ [ 3, 18, 2 ] ], [ [ 6, 7 ] ] ] ]
gap> DefBlock(H,6,1,[[3,22],[3,10,1]]);
[ [ [ 1 ] ], [ [ [ 3, 10, 1 ] ], [ [ 3, 22 ] ], [ [ 6, 11 ] ] ] ]
gap> DefBlock(H,7,1,[[1,0],[3,18,2]]); 
[ [ [ 1 ] ], [ [ [ 1, 0 ] ], [ [ 3, 18, 2 ] ], [ [ 4, 6 ] ] ] ]
gap> DefBlock(H,7,1,[[1,48],[3,10,1]]);
[ [ [ 1 ] ], [ [ [ 1, 48 ] ], [ [ 3, 10, 1 ] ], [ [ 4, 12 ] ] ] ]
gap> DefBlock(H,7,1,[[2,1],[4,17]]);   
[ [ [ 1 ] ], [ [ [ 2, 1 ] ], [ [ 4, 17 ] ], [ [ 6, 5 ] ] ] ]
gap> DefBlock(H,7,1,[[2,37],[4,11]]);
[ [ [ 1 ] ], [ [ [ 2, 37 ] ], [ [ 4, 11 ] ], [ [ 6, 13 ] ] ] ]
gap> DefBlock(H,8,1,[[1,0],[2,19,2],[1,48]]);
[ [ [ 2 ] ], 
  [ [ [ 1, 0 ] ], [ [ 1, 48 ] ], [ [ 2, 19, 2 ] ], [ [ 3, 6 ] ], [ [ 3, 22 ] ]
        , [ [ 4, 9 ] ] ] ]
gap> DefBlock(H,8,1,[[1,12],[2,31]]);         
[ [ [ 1 ] ], [ [ [ 1, 12 ] ], [ [ 2, 31 ] ], [ [ 3, 18, 2 ] ] ] ]
gap> DefBlock(H,8,1,[[1,36],[2,7]]); 
[ [ [ 1 ] ], [ [ [ 1, 36 ] ], [ [ 2, 7 ] ], [ [ 3, 10, 1 ] ] ] ]
gap> DefBlock(H,8,1,[[2,1],[4,20]]); 
[ [ [ 1 ] ], [ [ [ 2, 1 ] ], [ [ 4, 20 ] ], [ [ 6, 7 ] ] ] ]
gap> DefBlock(H,8,1,[[2,37],[4,8]]); 
[ [ [ 1 ] ], [ [ [ 2, 37 ] ], [ [ 4, 8 ] ], [ [ 6, 11 ] ] ] ]
gap> DefBlock(H,8,1,[[3,2],[3,18,1]]);
[ [ [ 1 ] ], [ [ [ 3, 2 ] ], [ [ 3, 18, 1 ] ], [ [ 6, 5 ] ] ] ]
gap> DefBlock(H,8,1,[[3,26],[3,10,2]]);
[ [ [ 1 ] ], [ [ [ 3, 10, 2 ] ], [ [ 3, 26 ] ], [ [ 6, 13 ] ] ] ]
gap> DefBlock(H,9,1,[[1,0],[3,26]]);   
[ [ [ 1 ] ], [ [ [ 1, 0 ] ], [ [ 3, 26 ] ], [ [ 4, 12 ] ] ] ]
gap> DefBlock(H,9,1,[[1,48],[3,2]]); 
[ [ [ 1 ] ], [ [ [ 1, 48 ] ], [ [ 3, 2 ] ], [ [ 4, 6 ] ] ] ]
gap> DefBlock(H,9,1,[[2,1],[2,37]]);
[ [ [ 1 ] ], [ [ [ 2, 1 ] ], [ [ 2, 37 ] ], [ [ 4, 9 ] ] ] ]
gap> DefBlock(H,9,1,[[2,7],[2,25,2]]);
[ [ [ 1 ] ], [ [ [ 2, 7 ] ], [ [ 2, 25, 2 ] ], [ [ 4, 11 ] ] ] ]
gap> DefBlock(H,9,1,[[2,31],[2,13,1]]);
[ [ [ 1 ] ], [ [ [ 2, 13, 1 ] ], [ [ 2, 31 ] ], [ [ 4, 17 ] ] ] ]
gap> DefBlock(H,10,1,[[1,0],[2,25,1],[2,25,2]]);
[ [ [ 2 ] ], 
  [ [ [ 1, 0 ] ], [ [ 2, 25, 2 ] ], [ [ 2, 25, 1 ] ], [ [ 3, 10, 2 ] ], 
      [ [ 3, 10, 1 ] ], [ [ 5, 8 ] ] ] ]
gap> DefBlock(H,10,1,[[1,48],[2,13,1],[2,13,2]]);
[ [ [ 2 ] ], 
  [ [ [ 1, 48 ] ], [ [ 2, 13, 1 ] ], [ [ 2, 13, 2 ] ], [ [ 3, 18, 1 ] ], 
      [ [ 3, 18, 2 ] ], [ [ 5, 12 ] ] ] ]
gap> DefBlock(H,10,1,[[1,12],[2,37],[3,2]]);     
[ [ [ 2 ] ], 
  [ [ [ 1, 12 ] ], [ [ 2, 37 ] ], [ [ 3, 2 ] ], [ [ 3, 22 ] ], [ [ 5, 4 ] ], 
      [ [ 6, 7 ] ] ] ]
gap> DefBlock(H,10,1,[[1,36],[2,1],[3,26]]);
[ [ [ 2 ] ], 
  [ [ [ 1, 36 ] ], [ [ 2, 1 ] ], [ [ 3, 6 ] ], [ [ 3, 26 ] ], [ [ 5, 16 ] ], 
      [ [ 6, 11 ] ] ] ]
gap> DefBlock(H,12,1,[[1,0],[1,24],[1,48]]);     
[ [ [ 2 ] ], 
  [ [ [ 1, 0 ] ], [ [ 1, 24 ] ], [ [ 1, 48 ] ], [ [ 2, 7 ] ], [ [ 2, 31 ] ], 
      [ [ 3, 14, 1 ] ] ] ]
gap> DefBlock(H,12,1,[[1,12],[1,36]]);       
[ [ [ 1 ] ], [ [ [ 1, 12 ] ], [ [ 1, 36 ] ], [ [ 2, 19, 2 ] ] ] ]
gap> DefBlock(H,12,1,[[2,1],[2,25,1]]);
[ [ [ 1 ] ], [ [ [ 2, 1 ] ], [ [ 2, 25, 1 ] ], [ [ 4, 8 ] ] ] ]
gap> DefBlock(H,12,1,[[2,37],[2,13,2]]);
[ [ [ 1 ] ], [ [ [ 2, 13, 2 ] ], [ [ 2, 37 ] ], [ [ 4, 20 ] ] ] ]
gap> DefBlock(H,12,1,[[3,2],[3,26]]);   
[ [ [ 1 ] ], [ [ [ 3, 2 ] ], [ [ 3, 26 ] ], [ [ 6, 9 ] ] ] ]
gap> DefBlock(H,14,1,[[2,37],[1,0]]);   
[ [ [ 1 ] ], [ [ [ 1, 0 ] ], [ [ 2, 37 ] ], [ [ 3, 18, 1 ] ] ] ]
gap> DefBlock(H,14,1,[[2,1],[1,48]]);
[ [ [ 1 ] ], [ [ [ 1, 48 ] ], [ [ 2, 1 ] ], [ [ 3, 10, 2 ] ] ] ]
gap> DefBlock(H,15,1,[[4,20],[1,0]]);
[ [ [ 1 ] ], [ [ [ 1, 0 ] ], [ [ 4, 20 ] ], [ [ 5, 12 ] ] ] ]
gap> DefBlock(H,15,1,[[4,12],[1,12]]);
[ [ [ 1 ] ], [ [ [ 1, 12 ] ], [ [ 4, 12 ] ], [ [ 5, 16 ] ] ] ]
gap> DefBlock(H,15,1,[[4,6],[1,36]]); 
[ [ [ 1 ] ], [ [ [ 1, 36 ] ], [ [ 4, 6 ] ], [ [ 5, 4 ] ] ] ]
gap> DefBlock(H,15,1,[[4,8],[1,48]]);
[ [ [ 1 ] ], [ [ [ 1, 48 ] ], [ [ 4, 8 ] ], [ [ 5, 8 ] ] ] ]
gap> DefBlock(H,15,1,[[2,1],[2,31]]);
[ [ [ 1 ] ], [ [ [ 2, 1 ] ], [ [ 2, 31 ] ], [ [ 4, 11 ] ] ] ]
gap> DefBlock(H,15,1,[[2,7],[2,37]]);
[ [ [ 1 ] ], [ [ [ 2, 7 ] ], [ [ 2, 37 ] ], [ [ 4, 17 ] ] ] ]
gap> DefBlock(H,18,1,[[1,0],[1,36]]); 
[ [ [ 1 ] ], [ [ [ 1, 0 ] ], [ [ 1, 36 ] ], [ [ 2, 13, 1 ] ] ] ]
gap> DefBlock(H,18,1,[[1,12],[1,48]]);
[ [ [ 1 ] ], [ [ [ 1, 12 ] ], [ [ 1, 48 ] ], [ [ 2, 25, 2 ] ] ] ]
gap> DefBlock(H,18,1,[[2,1],[2,37]]); 
[ [ [ 1 ] ], [ [ [ 2, 1 ] ], [ [ 2, 37 ] ], [ [ 4, 14 ] ] ] ]
gap> DefBlock(H,20,1,[[1,0],[5,4]]);
[ [ [ 1 ] ], [ [ [ 1, 0 ] ], [ [ 5, 4 ] ], [ [ 6, 5 ] ] ] ]
gap> DefBlock(H,20,1,[[1,48],[5,16]]);
[ [ [ 1 ] ], [ [ [ 1, 48 ] ], [ [ 5, 16 ] ], [ [ 6, 13 ] ] ] ]
gap> DefBlock(H,20,1,[[2,7],[3,22]]); 
[ [ [ 1 ] ], [ [ [ 2, 7 ] ], [ [ 3, 22 ] ], [ [ 5, 12 ] ] ] ]
gap> DefBlock(H,20,1,[[2,31],[3,6]]); 
[ [ [ 1 ] ], [ [ [ 2, 31 ] ], [ [ 3, 6 ] ], [ [ 5, 8 ] ] ] 
gap> DefBlock(H,24,1,[[1,0],[1,48]]);
[ [ [ 1 ] ], [ [ [ 1, 0 ] ], [ [ 1, 48 ] ], [ [ 2, 19, 1 ] ] ] ]
gap> DefBlock(H,30,1,[[1,0],[4,15]]);
[ [ [ 1 ] ], [ [ [ 1, 0 ] ], [ [ 4, 15 ] ], [ [ 5, 16 ] ] ] ]
gap> DefBlock(H,30,1,[[1,48],[4,3]]); 
[ [ [ 1 ] ], [ [ [ 1, 48 ] ], [ [ 4, 3 ] ], [ [ 5, 4 ] ] ] ]
gap> DefBlock(H,30,1,[[2,1],[3,26]]);
[ [ [ 1 ] ], [ [ [ 2, 1 ] ], [ [ 3, 26 ] ], [ [ 5, 12 ] ] ] ]
gap> DefBlock(H,30,1,[[2,37],[3,2]]); 
[ [ [ 1 ] ], [ [ [ 2, 37 ] ], [ [ 3, 2 ] ], [ [ 5, 8 ] ] ] ]

#################################################################################

G20
Hecke(G20,[[1,x,x^2]])

gap> DefBlock(H,1,1,[[1,0],[4,6]]);                               
[ [ [ 4 ] ], 
  [ [ [ 1, 0 ] ], [ [ 1, 20 ] ], [ [ 1, 40 ] ], [ [ 4, 6 ] ], [ [ 4, 8 ] ], 
      [ [ 4, 16 ] ], [ [ 5, 12 ] ], [ [ 5, 8 ] ], [ [ 5, 4 ] ] ] ]
gap> DefBlock(H,1,1,[[2,1],[2,7]]); 
[ [ [ 4 ] ], 
  [ [ [ 2, 21 ] ], [ [ 2, 27 ] ], [ [ 2, 11 ] ], [ [ 2, 17 ] ], [ [ 2, 1 ] ], 
      [ [ 2, 7 ] ], [ [ 4, 3 ] ], [ [ 4, 11 ] ], [ [ 4, 13 ] ] ] ]
gap> DefBlock(H,2,1,[[1,0],[2,1],[2,7]]);
[ [ [ 4 ] ], 
  [ [ [ 1, 0 ] ], [ [ 1, 40 ] ], [ [ 2, 21 ] ], [ [ 2, 27 ] ], [ [ 2, 1 ] ], 
      [ [ 2, 7 ] ], [ [ 3, 12 ] ], [ [ 3, 6 ] ], [ [ 4, 8 ] ], [ [ 5, 12 ] ], 
      [ [ 5, 4 ] ] ] ]
gap> DefBlock(H,2,1,[[4,3]]);            
[ [ [ 1 ] ], [ [ [ 4, 3 ] ], [ [ 4, 16 ] ] ] ]
gap> DefBlock(H,2,1,[[4,6]]);
[ [ [ 1 ] ], [ [ [ 4, 13 ] ], [ [ 4, 6 ] ] ] ]
gap> DefBlock(H,4,1,[[4,11],[1,0],[1,40]]);
[ [ [ 2 ] ], 
  [ [ [ 1, 0 ] ], [ [ 1, 40 ] ], [ [ 4, 11 ] ], [ [ 5, 12 ] ], [ [ 5, 4 ] ], 
      [ [ 6, 9 ] ] ] ]
gap> DefBlock(H,5,1,[[3,6],[1,0],[1,40]]);   
[ [ [ 2 ] ], 
  [ [ [ 1, 0 ] ], [ [ 1, 40 ] ], [ [ 3, 6 ] ], [ [ 4, 6 ] ], [ [ 4, 16 ] ], 
      [ [ 5, 8 ] ] ] ]
gap> DefBlock(H,5,1,[[2,1],[2,11],[2,21]]);
[ [ [ 2 ] ], 
  [ [ [ 2, 21 ] ], [ [ 2, 11 ] ], [ [ 2, 1 ] ], [ [ 4, 3 ] ], [ [ 4, 13 ] ], 
      [ [ 6, 9 ] ] ] ]
gap> DefBlock(H,5,1,[[2,7],[2,27]]);       
[ [ [ 1 ] ], [ [ [ 2, 27 ] ], [ [ 2, 7 ] ], [ [ 4, 11 ] ] ] ]
gap> DefBlock(H,5,2,[[3,12],[1,0],[1,40]]);
[ [ [ 2 ] ], 
  [ [ [ 1, 0 ] ], [ [ 1, 40 ] ], [ [ 3, 12 ] ], [ [ 4, 6 ] ], [ [ 4, 16 ] ], 
      [ [ 5, 8 ] ] ] ]
gap> DefBlock(H,5,2,[[2,7],[2,17],[2,27]]);
[ [ [ 2 ] ], 
  [ [ [ 2, 27 ] ], [ [ 2, 17 ] ], [ [ 2, 7 ] ], [ [ 4, 3 ] ], [ [ 4, 13 ] ], 
      [ [ 6, 9 ] ] ] ]
gap> DefBlock(H,5,2,[[2,1],[2,21]]);       
[ [ [ 1 ] ], [ [ [ 2, 21 ] ], [ [ 2, 1 ] ], [ [ 4, 11 ] ] ] ]
gap> DefBlock(H,5,3,[[3,12],[1,0],[1,40]]);
[ [ [ 2 ] ], 
  [ [ [ 1, 0 ] ], [ [ 1, 40 ] ], [ [ 3, 12 ] ], [ [ 4, 6 ] ], [ [ 4, 16 ] ], 
      [ [ 5, 8 ] ] ] ]
gap> DefBlock(H,5,3,[[2,7],[2,17],[2,27]]);
[ [ [ 2 ] ], 
  [ [ [ 2, 27 ] ], [ [ 2, 17 ] ], [ [ 2, 7 ] ], [ [ 4, 3 ] ], [ [ 4, 13 ] ], 
      [ [ 6, 9 ] ] ] ]
gap> DefBlock(H,5,3,[[2,1],[2,21]]);       
[ [ [ 1 ] ], [ [ [ 2, 21 ] ], [ [ 2, 1 ] ], [ [ 4, 11 ] ] ] ]
gap> DefBlock(H,5,4,[[3,6],[1,0],[1,40]]);   
[ [ [ 2 ] ], 
  [ [ [ 1, 0 ] ], [ [ 1, 40 ] ], [ [ 3, 6 ] ], [ [ 4, 6 ] ], [ [ 4, 16 ] ], 
      [ [ 5, 8 ] ] ] ]
gap> DefBlock(H,5,4,[[2,1],[2,11],[2,21]]);
[ [ [ 2 ] ], 
  [ [ [ 2, 21 ] ], [ [ 2, 11 ] ], [ [ 2, 1 ] ], [ [ 4, 3 ] ], [ [ 4, 13 ] ], 
      [ [ 6, 9 ] ] ] ]
gap> DefBlock(H,5,4,[[2,7],[2,27]]);       
[ [ [ 1 ] ], [ [ [ 2, 27 ] ], [ [ 2, 7 ] ], [ [ 4, 11 ] ] ] ]
gap> DefBlock(H,6,1,[[1,0],[2,21],[2,27]]);
[ [ [ 2 ] ], 
  [ [ [ 1, 0 ] ], [ [ 2, 21 ] ], [ [ 2, 27 ] ], [ [ 3, 2 ] ], [ [ 3, 14 ] ], 
      [ [ 5, 12 ] ] ] ]
gap> DefBlock(H,6,1,[[1,40],[2,1],[2,7]]);  
[ [ [ 2 ] ], 
  [ [ [ 1, 40 ] ], [ [ 2, 1 ] ], [ [ 2, 7 ] ], [ [ 3, 10, 1 ] ], [ [ 3, 10, 2 
             ] ], [ [ 5, 4 ] ] ] ]
gap> DefBlock(H,10,1,[[1,0],[1,20],[1,40]]);
[ [ [ 2 ] ], 
  [ [ [ 1, 0 ] ], [ [ 1, 20 ] ], [ [ 1, 40 ] ], [ [ 2, 27 ] ], [ [ 2, 7 ] ], 
      [ [ 3, 6 ] ] ] ]
gap> DefBlock(H,10,1,[[2,1],[2,21]]);       
[ [ [ 1 ] ], [ [ [ 2, 21 ] ], [ [ 2, 1 ] ], [ [ 4, 8 ] ] ] ]
gap> DefBlock(H,10,3,[[1,0],[1,20],[1,40]]);
[ [ [ 2 ] ], 
  [ [ [ 1, 0 ] ], [ [ 1, 20 ] ], [ [ 1, 40 ] ], [ [ 2, 21 ] ], [ [ 2, 1 ] ], 
      [ [ 3, 12 ] ] ] ]
gap> DefBlock(H,10,3,[[2,7],[2,27]]);       
[ [ [ 1 ] ], [ [ [ 2, 27 ] ], [ [ 2, 7 ] ], [ [ 4, 8 ] ] ] ]
gap> DefBlock(H,10,7,[[1,0],[1,20],[1,40]]);
[ [ [ 2 ] ], 
  [ [ [ 1, 0 ] ], [ [ 1, 20 ] ], [ [ 1, 40 ] ], [ [ 2, 21 ] ], [ [ 2, 1 ] ], 
      [ [ 3, 12 ] ] ] ]
gap> DefBlock(H,10,7,[[2,7],[2,27]]);       
[ [ [ 1 ] ], [ [ [ 2, 27 ] ], [ [ 2, 7 ] ], [ [ 4, 8 ] ] ] ]
gap> DefBlock(H,10,9,[[1,0],[1,20],[1,40]]);
[ [ [ 2 ] ], 
  [ [ [ 1, 0 ] ], [ [ 1, 20 ] ], [ [ 1, 40 ] ], [ [ 2, 27 ] ], [ [ 2, 7 ] ], 
      [ [ 3, 6 ] ] ] ]
gap> DefBlock(H,10,9,[[2,1],[2,21]]);       
[ [ [ 1 ] ], [ [ [ 2, 21 ] ], [ [ 2, 1 ] ], [ [ 4, 8 ] ] ] ]
gap> DefBlock(H,12,1,[[1,0],[5,12]]);       
[ [ [ 1 ] ], [ [ [ 1, 0 ] ], [ [ 5, 12 ] ], [ [ 6, 7 ] ] ] ]
gap> DefBlock(H,12,1,[[1,40],[5,4]]); 
[ [ [ 1 ] ], [ [ [ 1, 40 ] ], [ [ 5, 4 ] ], [ [ 6, 5 ] ] ] ]
gap> DefBlock(H,15,1,[[1,0],[3,2]]); DefBlock(H,15,4,[[1,0],[3,2]]);
[ [ [ 1 ] ], [ [ [ 1, 0 ] ], [ [ 3, 2 ] ], [ [ 4, 6 ] ] ] ]
gap> DefBlock(H,15,1,[[2,7],[4,13]]); DefBlock(H,15,4,[[1,0],[3,2]]);
[ [ [ 1 ] ], [ [ [ 2, 7 ] ], [ [ 4, 13 ] ], [ [ 6, 7 ] ] ] ]
gap> DefBlock(H,15,1,[[2,27],[4,3]]); DefBlock(H,15,4,[[1,0],[3,2]]);
[ [ [ 1 ] ], [ [ [ 2, 27 ] ], [ [ 4, 3 ] ], [ [ 6, 5 ] ] ] ]
gap> DefBlock(H,15,1,[[1,40],[3,10,1]]); DefBlock(H,15,4,[[1,0],[3,2]]);
[ [ [ 1 ] ], [ [ [ 1, 40 ] ], [ [ 3, 10, 1 ] ], [ [ 4, 16 ] ] ] ]
gap> DefBlock(H,15,2,[[1,0],[3,10,2]]); DefBlock(H,15,8,[[1,40],[3,14]]);
[ [ [ 1 ] ], [ [ [ 1, 0 ] ], [ [ 3, 10, 2 ] ], [ [ 4, 6 ] ] ] ]
gap> DefBlock(H,15,2,[[1,40],[3,14]]); DefBlock(H,15,8,[[1,40],[3,14]]);  
[ [ [ 1 ] ], [ [ [ 1, 40 ] ], [ [ 3, 14 ] ], [ [ 4, 16 ] ] ] ]
gap> DefBlock(H,15,2,[[2,1],[4,13]]); DefBlock(H,15,8,[[2,1],[4,13]]);
[ [ [ 1 ] ], [ [ [ 2, 1 ] ], [ [ 4, 13 ] ], [ [ 6, 5 ] ] ] ]
gap> DefBlock(H,15,2,[[2,21],[4,3]]); DefBlock(H,15,8,[[2,1],[4,13]]);
[ [ [ 1 ] ], [ [ [ 2, 21 ] ], [ [ 4, 3 ] ], [ [ 6, 7 ] ] ] ] 
gap> DefBlock(H,15,7,[[1,0],[3,14]]);   DefBlock(H,15,13,[[1,0],[3,14]]);
[ [ [ 1 ] ], [ [ [ 1, 0 ] ], [ [ 3, 14 ] ], [ [ 4, 6 ] ] ] ]
gap> DefBlock(H,15,7,[[1,40],[3,10,2]]); DefBlock(H,15,13,[[1,0],[3,14]]);
[ [ [ 1 ] ], [ [ [ 1, 40 ] ], [ [ 3, 10, 2 ] ], [ [ 4, 16 ] ] ] ]
gap> DefBlock(H,15,7,[[2,1],[4,13]]);   DefBlock(H,15,13,[[1,0],[3,14]]);
[ [ [ 1 ] ], [ [ [ 2, 1 ] ], [ [ 4, 13 ] ], [ [ 6, 7 ] ] ] ]
gap> DefBlock(H,15,7,[[2,21],[4,3]]);  DefBlock(H,15,13,[[1,0],[3,14]]);
[ [ [ 1 ] ], [ [ [ 2, 21 ] ], [ [ 4, 3 ] ], [ [ 6, 5 ] ] ] ]
gap> DefBlock(H,15,11,[[1,0],[3,10,1]]); DefBlock(H,15,14,[[1,0],[3,10,1]]);
[ [ [ 1 ] ], [ [ [ 1, 0 ] ], [ [ 3, 10, 1 ] ], [ [ 4, 6 ] ] ] ]
gap> DefBlock(H,15,11,[[1,40],[3,2]]);   DefBlock(H,15,14,[[1,0],[3,10,1]]);
[ [ [ 1 ] ], [ [ [ 1, 40 ] ], [ [ 3, 2 ] ], [ [ 4, 16 ] ] ] ]
gap> DefBlock(H,15,11,[[2,7],[4,13]]);   DefBlock(H,15,14,[[1,0],[3,10,1]]);
[ [ [ 1 ] ], [ [ [ 2, 7 ] ], [ [ 4, 13 ] ], [ [ 6, 5 ] ] ] ]
gap> DefBlock(H,15,11,[[2,27],[4,3]]);   DefBlock(H,15,14,[[1,0],[3,10,1]]);
[ [ [ 1 ] ], [ [ [ 2, 27 ] ], [ [ 4, 3 ] ], [ [ 6, 7 ] ] ] ]
gap> DefBlock(H,20,1,[[1,0],[1,40]]); DefBlock(H,20,9,[[1,0],[1,40]]); 
DefBlock(H,20,11,[[1,0],[1,40]]); DefBlock(H,20,19,[[1,0],[1,40]]);
[ [ [ 1 ] ], [ [ [ 1, 0 ] ], [ [ 1, 40 ] ], [ [ 2, 17 ] ] ] ]
gap> DefBlock(H,20,3,[[1,0],[1,40]]); DefBlock(H,20,7,[[1,0],[1,40]]);
DefBlock(H,20,13,[[1,0],[1,40]]); DefBlock(H,20,17,[[1,0],[1,40]]);
[ [ [ 1 ] ], [ [ [ 1, 0 ] ], [ [ 1, 40 ] ], [ [ 2, 11 ] ] ] ]
gap> DefBlock(H,30,1,[[1,0],[2,21]]); 
[ [ [ 1 ] ], [ [ [ 1, 0 ] ], [ [ 2, 21 ] ], [ [ 3, 10, 1 ] ] ] ]
gap> DefBlock(H,30,11,[[1,0],[2,21]]);
[ [ [ 1 ] ], [ [ [ 1, 0 ] ], [ [ 2, 21 ] ], [ [ 3, 2 ] ] ] ]
gap> DefBlock(H,30,19,[[1,0],[2,21]]);
[ [ [ 1 ] ], [ [ [ 1, 0 ] ], [ [ 2, 21 ] ], [ [ 3, 10, 1 ] ] ] ]
gap> DefBlock(H,30,29,[[1,0],[2,21]]);
[ [ [ 1 ] ], [ [ [ 1, 0 ] ], [ [ 2, 21 ] ], [ [ 3, 2 ] ] ] ]
gap> DefBlock(H,30,1,[[1,40],[2,1]]); 
[ [ [ 1 ] ], [ [ [ 1, 40 ] ], [ [ 2, 1 ] ], [ [ 3, 2 ] ] ] ]
gap> DefBlock(H,30,11,[[1,40],[2,1]]);
[ [ [ 1 ] ], [ [ [ 1, 40 ] ], [ [ 2, 1 ] ], [ [ 3, 10, 1 ] ] ] ]
gap> DefBlock(H,30,19,[[1,40],[2,1]]);
[ [ [ 1 ] ], [ [ [ 1, 40 ] ], [ [ 2, 1 ] ], [ [ 3, 2 ] ] ] ]
gap> DefBlock(H,30,29,[[1,40],[2,1]]);
[ [ [ 1 ] ], [ [ [ 1, 40 ] ], [ [ 2, 1 ] ], [ [ 3, 10, 1 ] ] ] ]
gap> DefBlock(H,30,7,[[1,0],[2,27]]); 
[ [ [ 1 ] ], [ [ [ 1, 0 ] ], [ [ 2, 27 ] ], [ [ 3, 10, 2 ] ] ] ]
gap> DefBlock(H,30,13,[[1,0],[2,27]]);
[ [ [ 1 ] ], [ [ [ 1, 0 ] ], [ [ 2, 27 ] ], [ [ 3, 10, 2 ] ] ] ]
gap> DefBlock(H,30,17,[[1,0],[2,27]]);
[ [ [ 1 ] ], [ [ [ 1, 0 ] ], [ [ 2, 27 ] ], [ [ 3, 14 ] ] ] ]
gap> DefBlock(H,30,23,[[1,0],[2,27]]);
[ [ [ 1 ] ], [ [ [ 1, 0 ] ], [ [ 2, 27 ] ], [ [ 3, 14 ] ] ] ]
gap> DefBlock(H,30,7,[[1,40],[2,7]]); 
[ [ [ 1 ] ], [ [ [ 1, 40 ] ], [ [ 2, 7 ] ], [ [ 3, 14 ] ] ] ]
gap> DefBlock(H,30,13,[[1,40],[2,7]]);
[ [ [ 1 ] ], [ [ [ 1, 40 ] ], [ [ 2, 7 ] ], [ [ 3, 14 ] ] ] ]
gap> DefBlock(H,30,17,[[1,40],[2,7]]);
[ [ [ 1 ] ], [ [ [ 1, 40 ] ], [ [ 2, 7 ] ], [ [ 3, 10, 2 ] ] ] ]
gap> DefBlock(H,30,23,[[1,40],[2,7]]);
[ [ [ 1 ] ], [ [ [ 1, 40 ] ], [ [ 2, 7 ] ], [ [ 3, 10, 2 ] ] ] ]

#################################################################################

G22
Hecke(G22,[[1,x^2]])

gap> DefBlock(H,2,1,[[1,0],[2,13],[2,1]]);
[ [ [ 4 ] ], 
  [ [ [ 1, 0 ] ], [ [ 1, 30 ] ], [ [ 2, 13 ] ], [ [ 2, 1 ] ], [ [ 3, 2 ] ], 
      [ [ 3, 6 ] ], [ [ 3, 12 ] ], [ [ 3, 16 ] ], [ [ 5, 4 ] ], 
      [ [ 5, 10 ] ], [ [ 6, 7 ] ] ] ]
gap> DefBlock(H,6,1,[[1,0],[1,30],[4,6]]);
[ [ [ 2 ] ], 
  [ [ [ 1, 0 ] ], [ [ 1, 30 ] ], [ [ 4, 6 ] ], [ [ 5, 4 ] ], [ [ 5, 10 ] ], 
      [ [ 6, 7 ] ] ] ]
gap> DefBlock(H,10,1,[[1,0],[1,30],[2,13]]);
[ [ [ 2 ] ], 
[ [ [ 1, 0 ] ], [ [ 1, 30 ] ], [ [ 2, 13 ] ], [ [ 3, 6 ] ], 
[ [ 3, 16 ] ], [ [ 4, 6 ] ] ] ]
gap> DefBlock(H,10,1,[[3,2],[3,12]]);
[ [ [ 1 ] ], 
[ [ [ 3, 2 ] ], [ [ 3, 12 ] ], [ [ 6, 7 ] ] ] ]
gap> DefBlock(H,10,3,[[1,0],[1,30],[2,1]]);
[ [ [ 2 ] ], 
[ [ [ 1, 0 ] ], [ [ 1, 30 ] ], [ [ 2, 1 ] ], [ [ 3, 2 ] ], 
[ [ 3, 12 ] ], [ [ 4, 6 ] ] ] ]
gap> DefBlock(H,10,3,[[3,6],[3,16]]);
[ [ [ 3, 6 ] ], [ [ 3, 16 ] ], [ [ 6, 7 ] ] ] ]
gap> DefBlock(H,10,7,[[1,0],[1,30],[2,1]]);
[ [ [ 2 ] ], 
[ [ [ 1, 0 ] ], [ [ 1, 30 ] ], [ [ 2, 1 ] ], [ [ 3, 2 ] ], 
[ [ 3, 12 ] ], [ [ 4, 6 ] ] ] ]
gap> DefBlock(H,10,7,[[3,6],[3,16]]);
[ [ [ 3, 6 ] ], [ [ 3, 16 ] ], [ [ 6, 7 ] ] ] ]
gap> DefBlock(H,10,9,[[1,0],[1,30],[2,13]]);
[ [ [ 2 ] ], 
[ [ [ 1, 0 ] ], [ [ 1, 30 ] ], [ [ 2, 13 ] ], [ [ 3, 6 ] ], 
[ [ 3, 16 ] ], [ [ 4, 6 ] ] ] ]
gap> DefBlock(H,10,9,[[3,2],[3,12]]);
[ [ [ 1 ] ], 
[ [ [ 3, 2 ] ], [ [ 3, 12 ] ], [ [ 6, 7 ] ] ] ]
gap> DefBlock(H,12,1,[[1,0],[4,3]]); 
[ [ [ 1 ] ], [ [ [ 1, 0 ] ], [ [ 4, 3 ] ], [ [ 5, 4 ] ] ] ]
gap> DefBlock(H,12,1,[[1,30],[4,9]]);
[ [ [ 1 ] ], [ [ [ 1, 30 ] ], [ [ 4, 9 ] ], [ [ 5, 10 ] ] ] ]
gap> DefBlock(H,20,1,[[1,0],[3,12]]); gap> DefBlock(H,20,9,[[1,0],[3,12]]); gap> DefBlock(H,20,11,[[1,0],[3,12]]); gap> DefBlock(H,20,19,[[1,0],[3,12]]);
[ [ [ 1 ] ], 
[ [ [ 1, 0 ] ], [ [ 3, 12 ] ], [ [ 4, 3 ] ] ] ]
gap> DefBlock(H,20,1,[[1,30],[3,2]]); gap> DefBlock(H,20,9,[[1,30],[3,2]]); gap> DefBlock(H,20,11,[[1,30],[3,2]]); gap> DefBlock(H,20,19,[[1,30],[3,2]]);
[ [ [ 1 ] ], 
[ [ [ 1, 30 ] ], [ [ 3, 2 ] ], [ [ 4, 9 ] ] ] ]
gap> DefBlock(H,20,3,[[1,0],[3,16]]); gap> DefBlock(H,20,7,[[1,0],[3,16]]); gap> DefBlock(H,20,13,[[1,0],[3,16]]); gap> DefBlock(H,20,17,[[1,0],[3,16]]);
[ [ [ 1 ] ], 
[ [ [ 1, 0 ] ], [ [ 3, 16 ] ], [ [ 4, 3 ] ] ] ]
gap> DefBlock(H,20,3,[[1,30],[3,6]]); gap> DefBlock(H,20,7,[[1,30],[3,6]]); gap> DefBlock(H,20,13,[[1,30],[3,6]]); gap> DefBlock(H,20,17,[[1,30],[3,6]]);
[ [ [ 1 ] ], 
[ [ [ 1, 30 ] ], [ [ 3, 6 ] ], [ [ 4, 9 ] ] ] ]
gap> DefBlock(H,30,1,[[1,0],[1,30]]); gap> DefBlock(H,30,11,[[1,0],[1,30]]); gap> DefBlock(H,30,19,[[1,0],[1,30]]); gap> DefBlock(H,30,29,[[1,0],[1,30]]);
[ [ [ 1 ] ], 
[ [ [ 1, 0 ] ], [ [ 1, 30 ] ], [ [ 2, 13 ] ] ] ]
gap> DefBlock(H,30,7,[[1,0],[1,30]]); gap> DefBlock(H,30,13,[[1,0],[1,30]]); gap> DefBlock(H,30,17,[[1,0],[1,30]]); gap> DefBlock(H,30,23,[[1,0],[1,30]]);
[ [ [ 1 ] ], 
[ [ [ 1, 0 ] ], [ [ 1, 30 ] ], [ [ 2, 1 ] ] ] ]