CONTROL RUN: F_2 replaced by Z^2
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=4: spanning vectors=4 (Brauer 3, det-type 1); dim Fix_SO_N=4 (mod p 4); rank on non-trivial words=0 (mod p 0); dim intersection=4 [exact over Q (sympy DomainMatrix over ZZ)]; Catalan=2; equal: False  [0.0s]
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=0 (mod p 0); dim intersection=25 [exact over Q (sympy DomainMatrix over ZZ)]; Catalan=5; equal: False  [0.0s]
N=4 m=8: spanning vectors=315 (Brauer 105, det-type 210); dim Fix_SO_N=196 (mod p 196); rank on non-trivial words=0 (mod p 0); dim intersection=196 [exact over Q (sympy DomainMatrix over ZZ)]; Catalan=14; equal: False  [3.2s]
CONTROL RUN: F_2 replaced by Z^2
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=0 (mod p 0); dim intersection=3 [exact over Q (sympy DomainMatrix over ZZ)]; Catalan=2; equal: False  [0.1s]
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=0 (mod p 0); dim intersection=1 [exact over Q (sympy DomainMatrix over ZZ)]; Catalan=0; equal: False  [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=0 (mod p 0); dim intersection=15 [exact over Q (sympy DomainMatrix over ZZ)]; Catalan=5; equal: False  [0.0s]
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=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=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=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  [0.1s]
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]
