degree:9
 order:56
[ 9, 9, 9, 10, 18 ][ 4, 0, 0, 2, 5, 0, 0, 0, 2, 5 ]

minimal polynomial:[ x-9, x-5, x+5, x+9, x^2-5 ]
 Galois type:1

 minimal polynomial of other basis elements:
 x^2-8*x-9
x^6-111*x^4+2555*x^2-10125
x^3-100*x
x^3-8*x^2-180*x

 SITA:
[ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], 
      [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], 
  [ [ 0, 9, 0, 0, 0, 0 ], [ 1, 0, 4, 0, 0, 4 ], [ 0, 4, 0, 5, 0, 0 ], 
      [ 0, 0, 5, 0, 0, 4 ], [ 0, 0, 0, 0, 0, 9 ], [ 0, 2, 0, 2, 5, 0 ] ], 
  [ [ 0, 0, 9, 0, 0, 0 ], [ 0, 4, 0, 5, 0, 0 ], [ 1, 0, 8, 0, 0, 0 ], 
      [ 0, 5, 0, 4, 0, 0 ], [ 0, 0, 0, 0, 9, 0 ], [ 0, 0, 0, 0, 0, 9 ] ], 
  [ [ 0, 0, 0, 9, 0, 0 ], [ 0, 0, 5, 0, 0, 4 ], [ 0, 5, 0, 4, 0, 0 ], 
      [ 1, 0, 4, 0, 0, 4 ], [ 0, 0, 0, 0, 0, 9 ], [ 0, 2, 0, 2, 5, 0 ] ], 
  [ [ 0, 0, 0, 0, 10, 0 ], [ 0, 0, 0, 0, 0, 10 ], [ 0, 0, 0, 0, 10, 0 ], 
      [ 0, 0, 0, 0, 0, 10 ], [ 1, 0, 9, 0, 0, 0 ], [ 0, 5, 0, 5, 0, 0 ] ], 
  [ [ 0, 0, 0, 0, 0, 18 ], [ 0, 4, 0, 4, 10, 0 ], [ 0, 0, 0, 0, 0, 18 ], 
      [ 0, 4, 0, 4, 10, 0 ], [ 0, 9, 0, 9, 0, 0 ], [ 1, 0, 9, 0, 0, 8 ] ] ]


 Q-polynomial