q=4: C1 C(U)=U True
 c=(d^0s^1) r=2 field: C2 True (#beta normalizing U=12); C3 torus+ t,v,#centralizing=[(5, 1, 0)] -> True
q=5: C1 C(U)=U True
 c=delta r=2: q=5 mod 8, #V4 classes=1, |N(V)|=12, #beta normalizing V=12 -> C4 True
q=7: C1 C(U)=U True
 c=delta r=2: q=7 mod 8 OBSTRUCTION CASE (p = 7): #V4 classes=2, delta swaps them=True; delta centralizes a Sylow t for odd t|q^2-1: {3: True}
q=8: C1 C(U)=U True
 c=(d^0s^1) r=3 field: C2 True (#beta normalizing U=56); C3 torus- t,v,#centralizing=[(7, 1, 0)] -> True
 c=(d^0s^2) r=3 field: C2 True (#beta normalizing U=56); C3 torus- t,v,#centralizing=[(7, 1, 0)] -> True
q=9: C1 C(U)=U True
 c=(d^0s^1) r=2 field: C2 True (#beta normalizing U=36); C3 torus+ t,v,#centralizing=[(5, 1, 0)] -> True
 c=delta r=2: q=1 mod 8 OBSTRUCTION CASE (p = 3): #V4 classes=2, delta swaps them=True; delta centralizes a Sylow t for odd t|q^2-1: {5: True}
 c=(d^1s^1) r=2 field: C2 True (#beta normalizing U=36); C3 torus+ t,v,#centralizing=[(5, 1, 0)] -> True
q=11: C1 C(U)=U True
 c=delta r=2: q=3 mod 8, #V4 classes=1, |N(V)|=12, #beta normalizing V=12 -> C4 True
q=13: C1 C(U)=U True
 c=delta r=2: q=5 mod 8, #V4 classes=1, |N(V)|=12, #beta normalizing V=12 -> C4 True
q=16: C1 C(U)=U True
 c=(d^0s^2) r=2 field: C2 True (#beta normalizing U=240); C3 torus+ t,v,#centralizing=[(17, 1, 0)] -> True
q=17: C1 C(U)=U True
 c=delta r=2: q=1 mod 8 OBSTRUCTION CASE (p = 17): #V4 classes=2, delta swaps them=True; delta centralizes a Sylow t for odd t|q^2-1: {3: True}
q=19: C1 C(U)=U True
 c=delta r=2: q=3 mod 8, #V4 classes=1, |N(V)|=12, #beta normalizing V=12 -> C4 True
q=23: C1 C(U)=U True
 c=delta r=2: q=7 mod 8 OBSTRUCTION CASE (p = 23): #V4 classes=2, delta swaps them=True; delta centralizes a Sylow t for odd t|q^2-1: {3: True, 11: True}
q=25: C1 C(U)=U True
 c=(d^0s^1) r=2 field: C2 True (#beta normalizing U=300); C3 torus+ t,v,#centralizing=[(13, 1, 0)] -> True
 c=delta r=2: q=1 mod 8 OBSTRUCTION CASE (p = 5): #V4 classes=2, delta swaps them=True; delta centralizes a Sylow t for odd t|q^2-1: {3: True, 13: True}
 c=(d^1s^1) r=2 field: C2 True (#beta normalizing U=300); C3 torus+ t,v,#centralizing=[(13, 1, 0)] -> True
q=27: C1 C(U)=U True
 c=(d^0s^1) r=3 field: C2 True (#beta normalizing U=351); C3 torus+ t,v,#centralizing=[(7, 1, 0)] -> True
 c=(d^0s^2) r=3 field: C2 True (#beta normalizing U=351); C3 torus+ t,v,#centralizing=[(7, 1, 0)] -> True
 c=delta r=2: q=3 mod 8, #V4 classes=1, |N(V)|=12, #beta normalizing V=12 -> C4 True
q=29: C1 C(U)=U True
 c=delta r=2: q=5 mod 8, #V4 classes=1, |N(V)|=12, #beta normalizing V=12 -> C4 True
q=31: C1 C(U)=U True
 c=delta r=2: q=7 mod 8 OBSTRUCTION CASE (p = 31): #V4 classes=2, delta swaps them=True; delta centralizes a Sylow t for odd t|q^2-1: {3: True, 5: True}
q=32: C1 C(U)=U True
 c=(d^0s^1) r=5 field: C2 True (#beta normalizing U=992); C3 torus+ t,v,#centralizing=[(11, 1, 0)] -> True
 c=(d^0s^2) r=5 field: C2 True (#beta normalizing U=992); C3 torus+ t,v,#centralizing=[(11, 1, 0)] -> True
 c=(d^0s^3) r=5 field: C2 True (#beta normalizing U=992); C3 torus+ t,v,#centralizing=[(11, 1, 0)] -> True
 c=(d^0s^4) r=5 field: C2 True (#beta normalizing U=992); C3 torus+ t,v,#centralizing=[(11, 1, 0)] -> True
ALL CHECKS PASSED
