=== |X| = 2
class  0 inv=1 idem=1 H_A=[1, 2, 4, 8, 16, 32, 64] H_B=[1, 2, 0, 0, 0, 0, 0] (exact to n=2) Euler=[1, 0, 0, 0, 0, 0, 0] first_fail=None
class  1 inv=1 idem=0 H_A=[1, 2, 3, 4, 5, 6, 7] H_B=[1, 2, 1, 0, 0, 0, 0] (exact to n=3) Euler=[1, 0, 0, 0, 0, 0, 0] first_fail=None
class  2 inv=0 idem=0 H_A=[1, 2, 1, 1, 1, 1, 1] H_B=[1, 2, 3, 5, 8, 13, 21] (exact to n=6) Euler=[1, 0, 0, 0, 0, 0, 0] first_fail=None
class  3 inv=0 idem=0 H_A=[1, 2, 1, 1, 1, 1, 1] H_B=[1, 2, 3, 5, 8, 13, 21] (exact to n=6) Euler=[1, 0, 0, 0, 0, 0, 0] first_fail=None
class  4 inv=1 idem=0 H_A=[1, 2, 3, 4, 5, 6, 7] H_B=[1, 2, 1, 0, 0, 0, 0] (exact to n=3) Euler=[1, 0, 0, 0, 0, 0, 0] first_fail=None
|X|=2: classes=5 involutive=3 failing(Euler test to weight 6)=0
=== |X| = 3
class  0 inv=1 idem=1 H_A=[1, 3, 9, 27, 81, 243, 729] H_B=[1, 3, 0, 0, 0, 0, 0] (exact to n=2) Euler=[1, 0, 0, 0, 0, 0, 0] first_fail=None
class  1 inv=1 idem=0 H_A=[1, 3, 7, 15, 31, 63, 127] H_B=[1, 3, 2, 0, 0, 0, 0] (exact to n=3) Euler=[1, 0, 0, 0, 0, 0, 0] first_fail=None
class  2 inv=1 idem=0 H_A=[1, 3, 7, 15, 31, 63, 127] H_B=[1, 3, 2, 0, 0, 0, 0] (exact to n=3) Euler=[1, 0, 0, 0, 0, 0, 0] first_fail=None
class  3 inv=1 idem=0 H_A=[1, 3, 6, 10, 15, 21, 28] H_B=[1, 3, 3, 1, 0, 0, 0] (exact to n=4) Euler=[1, 0, 0, 0, 0, 0, 0] first_fail=None
class  4 inv=0 idem=0 H_A=[1, 3, 5, 7, 9, 11, 13] H_B=[1, 3, 4, 4, 3, 1, 0] (exact to n=5) Euler=[1, 0, 0, 0, -1, 0, 0] first_fail=4
class  5 inv=0 idem=0 H_A=[1, 3, 4, 5, 6, 7, 8] H_B=[1, 3, 5, 8, 13, 21, 34] (exact to n=5) Euler=[1, 0, 0, 0, 0, 0, 0] first_fail=None
class  6 inv=0 idem=0 H_A=[1, 3, 4, 5, 6, 7, 8] H_B=[1, 3, 5, 8, 13, 21, 34] (exact to n=5) Euler=[1, 0, 0, 0, 0, 0, 0] first_fail=None
class  7 inv=1 idem=0 H_A=[1, 3, 6, 10, 15, 21, 28] H_B=[1, 3, 3, 1, 0, 0, 0] (exact to n=4) Euler=[1, 0, 0, 0, 0, 0, 0] first_fail=None
class  8 inv=0 idem=0 H_A=[1, 3, 5, 7, 9, 11, 13] H_B=[1, 3, 4, 4, 3, 1, 0] (exact to n=5) Euler=[1, 0, 0, 0, -1, 0, 0] first_fail=4
class  9 inv=0 idem=0 H_A=[1, 3, 3, 4, 5, 6, 7] H_B=[1, 3, 6, 13, 28, 60, 129] (exact to n=5) Euler=[1, 0, 0, 0, 0, 0, 0] first_fail=None
class 10 inv=0 idem=0 H_A=[1, 3, 3, 4, 5, 6, 7] H_B=[1, 3, 6, 13, 28, 60, 129] (exact to n=5) Euler=[1, 0, 0, 0, 0, 0, 0] first_fail=None
class 11 inv=0 idem=0 H_A=[1, 3, 5, 7, 9, 11, 13] H_B=[1, 3, 4, 4, 3, 1, 0] (exact to n=5) Euler=[1, 0, 0, 0, -1, 0, 0] first_fail=4
class 12 inv=0 idem=0 H_A=[1, 3, 5, 6, 6, 6, 6] H_B=[1, 3, 4, 3, 1, 0, 0] (exact to n=5) Euler=[1, 0, 0, 0, 0, 0, -1] first_fail=6
class 13 inv=1 idem=0 H_A=[1, 3, 6, 10, 15, 21, 28] H_B=[1, 3, 3, 1, 0, 0, 0] (exact to n=4) Euler=[1, 0, 0, 0, 0, 0, 0] first_fail=None
class 14 inv=0 idem=0 H_A=[1, 3, 5, 6, 6, 6, 6] H_B=[1, 3, 4, 3, 1, 0, 0] (exact to n=5) Euler=[1, 0, 0, 0, 0, 0, -1] first_fail=6
class 15 inv=0 idem=0 H_A=[1, 3, 3, 4, 5, 6, 7] H_B=[1, 3, 6, 13, 28, 60, 129] (exact to n=5) Euler=[1, 0, 0, 0, 0, 0, 0] first_fail=None
class 16 inv=0 idem=0 H_A=[1, 3, 3, 4, 5, 6, 7] H_B=[1, 3, 6, 13, 28, 60, 129] (exact to n=5) Euler=[1, 0, 0, 0, 0, 0, 0] first_fail=None
class 17 inv=0 idem=0 H_A=[1, 3, 5, 7, 9, 11, 13] H_B=[1, 3, 4, 4, 3, 1, 0] (exact to n=5) Euler=[1, 0, 0, 0, -1, 0, 0] first_fail=4
class 18 inv=0 idem=0 H_A=[1, 3, 4, 5, 6, 7, 8] H_B=[1, 3, 5, 8, 13, 21, 34] (exact to n=5) Euler=[1, 0, 0, 0, 0, 0, 0] first_fail=None
class 19 inv=0 idem=0 H_A=[1, 3, 4, 5, 6, 7, 8] H_B=[1, 3, 5, 8, 13, 21, 34] (exact to n=5) Euler=[1, 0, 0, 0, 0, 0, 0] first_fail=None
class 20 inv=1 idem=0 H_A=[1, 3, 6, 10, 15, 21, 28] H_B=[1, 3, 3, 1, 0, 0, 0] (exact to n=4) Euler=[1, 0, 0, 0, 0, 0, 0] first_fail=None
class 21 inv=0 idem=0 H_A=[1, 3, 5, 6, 6, 6, 6] H_B=[1, 3, 4, 3, 1, 0, 0] (exact to n=5) Euler=[1, 0, 0, 0, 0, 0, -1] first_fail=6
class 22 inv=0 idem=0 H_A=[1, 3, 5, 6, 6, 6, 6] H_B=[1, 3, 4, 3, 1, 0, 0] (exact to n=5) Euler=[1, 0, 0, 0, 0, 0, -1] first_fail=6
class 23 inv=0 idem=0 H_A=[1, 3, 2, 1, 1, 1, 1] H_B=[1, 3, 7, 16, 33, 64, 113] (exact to n=5) Euler=[1, 0, 0, 0, -3, 8, -24] first_fail=4
class 24 inv=0 idem=0 H_A=[1, 3, 2, 1, 1, 1, 1] H_B=[1, 3, 7, 16, 33, 64, 113] (exact to n=5) Euler=[1, 0, 0, 0, -3, 8, -24] first_fail=4
class 25 inv=0 idem=0 H_A=[1, 3, 5, 6, 6, 6, 6] H_B=[1, 3, 4, 3, 1, 0, 0] (exact to n=5) Euler=[1, 0, 0, 0, 0, 0, -1] first_fail=6
class 26 inv=0 idem=0 H_A=[1, 3, 5, 6, 6, 6, 6] H_B=[1, 3, 4, 3, 1, 0, 0] (exact to n=5) Euler=[1, 0, 0, 0, 0, 0, -1] first_fail=6
class 27 inv=0 idem=0 H_A=[1, 3, 2, 1, 1, 1, 1] H_B=[1, 3, 7, 16, 33, 64, 113] (exact to n=5) Euler=[1, 0, 0, 0, -3, 8, -24] first_fail=4
class 28 inv=1 idem=0 H_A=[1, 3, 6, 10, 15, 21, 28] H_B=[1, 3, 3, 1, 0, 0, 0] (exact to n=4) Euler=[1, 0, 0, 0, 0, 0, 0] first_fail=None
|X|=3: classes=29 involutive=8 failing(Euler test to weight 6)=13
