degree:3
 order:30
[ 3, 6, 8, 12 ][ 1, 0, 0, 0, 1, 2 ]

minimal polynomial:[ x-3, x-2, x, x+2, x+3 ]

 minimal polynomial of other basis elements:
[ x-6, x-1, x+3 ]
[ x-8, x-2, x+2 ]
[ x-12, x-2, x, x+2, x+12 ]

 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, 3, 0, 0, 0 ], [ 1, 0, 2, 0, 0 ], [ 0, 1, 0, 0, 2 ], 
      [ 0, 0, 0, 0, 3 ], [ 0, 0, 1, 2, 0 ] ], 
  [ [ 0, 0, 6, 0, 0 ], [ 0, 2, 0, 0, 4 ], [ 1, 0, 1, 4, 0 ], 
      [ 0, 0, 3, 3, 0 ], [ 0, 1, 0, 0, 5 ] ], 
  [ [ 0, 0, 0, 8, 0 ], [ 0, 0, 0, 0, 8 ], [ 0, 0, 4, 4, 0 ], 
      [ 1, 0, 3, 4, 0 ], [ 0, 2, 0, 0, 6 ] ], 
  [ [ 0, 0, 0, 0, 12 ], [ 0, 0, 4, 8, 0 ], [ 0, 2, 0, 0, 10 ], 
      [ 0, 3, 0, 0, 9 ], [ 1, 0, 5, 6, 0 ] ] ]