degree:9
 order:40
[ 9, 9, 9, 12 ][ 1, 2, 0, 3, 3, 3 ]

minimal polynomial:[ x-9, x+1, x+3, x^2-4*x-11 ]
 Galois type:1

 minimal polynomial of other basis elements:
 x^5-9*x^4-24*x^3+160*x^2+471*x+297
x^2-8*x-9
x^3-10*x^2-32*x+96

 SITA:
[ [ [ 1, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 1 ] ], 
  [ [ 0, 9, 0, 0, 0 ], [ 1, 5, 1, 2, 0 ], [ 0, 1, 1, 3, 4 ], [ 0, 2, 3, 0, 4 ], [ 0, 0, 3, 3, 3 ] ], 
  [ [ 0, 0, 9, 0, 0 ], [ 0, 1, 1, 3, 4 ], [ 1, 1, 5, 2, 0 ], [ 0, 3, 2, 0, 4 ], [ 0, 3, 0, 3, 3 ] ], 
  [ [ 0, 0, 0, 9, 0 ], [ 0, 2, 3, 0, 4 ], [ 0, 3, 2, 0, 4 ], [ 1, 0, 0, 8, 0 ], [ 0, 3, 3, 0, 3 ] ], 
  [ [ 0, 0, 0, 0, 12 ], [ 0, 0, 4, 4, 4 ], [ 0, 4, 0, 4, 4 ], [ 0, 4, 4, 0, 4 ], [ 1, 3, 3, 3, 2 ] ] ]