N=4 m=2: spanning vectors=1 (Brauer 1, det-type 0); dim Fix_SO_N=1 (mod p 1); rank on non-trivial words=0 (mod p 0); dim intersection=1 [exact over Q (sympy DomainMatrix over ZZ)]; Catalan=1; equal: True  [0.1s]
N=4 m=3: Fix_SO_N = 0; intersection 0; Catalan=0
N=4 m=4: spanning vectors=4 (Brauer 3, det-type 1); dim Fix_SO_N=4 (mod p 4); rank on non-trivial words=2 (mod p 2); dim intersection=2 [exact over Q (sympy DomainMatrix over ZZ)]; Catalan=2; equal: True  [0.0s]
N=4 m=5: Fix_SO_N = 0; intersection 0; Catalan=0
N=4 m=6: spanning vectors=30 (Brauer 15, det-type 15); dim Fix_SO_N=25 (mod p 25); rank on non-trivial words=20 (mod p 20); dim intersection=5 [exact over Q (sympy DomainMatrix over ZZ)]; Catalan=5; equal: True  [0.0s]
N=5 m=2: spanning vectors=1 (Brauer 1, det-type 0); dim Fix_SO_N=1 (mod p 1); rank on non-trivial words=0 (mod p 0); dim intersection=1 [exact over Q (sympy DomainMatrix over ZZ)]; Catalan=1; equal: True  [0.1s]
N=5 m=3: Fix_SO_N = 0; intersection 0; Catalan=0
N=5 m=4: spanning vectors=3 (Brauer 3, det-type 0); dim Fix_SO_N=3 (mod p 3); rank on non-trivial words=1 (mod p 1); dim intersection=2 [exact over Q (sympy DomainMatrix over ZZ)]; Catalan=2; equal: True  [0.0s]
N=5 m=5: spanning vectors=1 (Brauer 0, det-type 1); dim Fix_SO_N=1 (mod p 1); rank on non-trivial words=1 (mod p 1); dim intersection=0 [exact over Q (sympy DomainMatrix over ZZ)]; Catalan=0; equal: True  [0.0s]
N=5 m=6: spanning vectors=15 (Brauer 15, det-type 0); dim Fix_SO_N=15 (mod p 15); rank on non-trivial words=10 (mod p 10); dim intersection=5 [exact over Q (sympy DomainMatrix over ZZ)]; Catalan=5; equal: True  [0.0s]
N=5 m=7: spanning vectors=21 (Brauer 0, det-type 21); dim Fix_SO_N=15 (mod p 15); rank on non-trivial words=15 (mod p 15); dim intersection=0 [exact over Q (sympy DomainMatrix over ZZ)]; Catalan=0; equal: True  [0.0s]
