n=5: k(A_n) = 5, p(n) = 7, primes [4099981, 4099961, 4099943, 4099903, 4099897]; S_n table 0.0 s
   degrees = hook length formula: True; S_n column orthogonality mod p: True; row sums: True; top Garner digit 0: True; all 125 a(K,C;L) equal the brute force: True
   perfect matching for every class C: True; max |T(C)| = 3; classes with no vanishing irreducible character: 1
   (0.0 s)
n=6: k(A_n) = 7, p(n) = 11, primes [4099981, 4099961, 4099943, 4099903, 4099897]; S_n table 0.0 s
   degrees = hook length formula: True; S_n column orthogonality mod p: True; row sums: True; top Garner digit 0: True; all 343 a(K,C;L) equal the brute force: True
   perfect matching for every class C: True; max |T(C)| = 3; classes with no vanishing irreducible character: 1
   (0.0 s)
n=7: k(A_n) = 9, p(n) = 15, primes [4099981, 4099961, 4099943, 4099903, 4099897]; S_n table 0.0 s
   degrees = hook length formula: True; S_n column orthogonality mod p: True; row sums: True; top Garner digit 0: True; all 729 a(K,C;L) equal the brute force: True
   perfect matching for every class C: True; max |T(C)| = 3; classes with no vanishing irreducible character: 4
   Theorem C: Lemma 5.3 (equal residues across C+-, halves of K and L): True; rule of Remark 5.7: True; permutation of the proof valid: True
   (0.0 s)
n=8: k(A_n) = 14, p(n) = 22, primes [4099981, 4099961, 4099943, 4099903, 4099897]; S_n table 0.0 s
   degrees = hook length formula: True; S_n column orthogonality mod p: True; row sums: True; top Garner digit 0: True; all 2744 a(K,C;L) equal the brute force: True
   perfect matching for every class C: True; max |T(C)| = 5; classes with no vanishing irreducible character: 1
   (0.0 s)
n=9: k(A_n) = 18, p(n) = 30, primes [4099981, 4099961, 4099943, 4099903, 4099897]; S_n table 0.0 s
   degrees = hook length formula: True; S_n column orthogonality mod p: True; row sums: True; top Garner digit 0: True; all 5832 a(K,C;L) equal the brute force: True
   perfect matching for every class C: True; max |T(C)| = 6; classes with no vanishing irreducible character: 1
   Theorem C: Lemma 5.3 (equal residues across C+-, halves of K and L): True; rule of Remark 5.7: True; permutation of the proof valid: True
   (0.0 s)
n=10: k(A_n) = 24, p(n) = 42, primes [4099981, 4099961, 4099943, 4099903, 4099897]; S_n table 0.0 s
   degrees = hook length formula: True; S_n column orthogonality mod p: True; row sums: True; top Garner digit 0: True; all 13824 a(K,C;L) equal the brute force: True
   perfect matching for every class C: True; max |T(C)| = 6; classes with no vanishing irreducible character: 1
   (0.0 s)
n=11: k(A_n) = 31, p(n) = 56, primes [4099981, 4099961, 4099943, 4099903, 4099897]; S_n table 0.0 s
   degrees = hook length formula: True; S_n column orthogonality mod p: True; row sums: True; top Garner digit 0: True
   perfect matching for every class C: True; max |T(C)| = 8; classes with no vanishing irreducible character: 4
   Theorem C: Lemma 5.3 (equal residues across C+-, halves of K and L): True; rule of Remark 5.7: True; permutation of the proof valid: True
   (0.0 s)
n=12: k(A_n) = 43, p(n) = 77, primes [4099981, 4099961, 4099943, 4099903, 4099897]; S_n table 0.0 s
   degrees = hook length formula: True; S_n column orthogonality mod p: True; row sums: True; top Garner digit 0: True
   perfect matching for every class C: True; max |T(C)| = 10; classes with no vanishing irreducible character: 1
   Theorem B: T(C) = E(mu,n) for the five mu: True; permutation of Remark 4.5 valid: True
   (0.0 s)
n=13: k(A_n) = 55, p(n) = 101, primes [4099981, 4099961, 4099943, 4099903, 4099897]; S_n table 0.0 s
   degrees = hook length formula: True; S_n column orthogonality mod p: True; row sums: True; top Garner digit 0: True
   perfect matching for every class C: True; max |T(C)| = 11; classes with no vanishing irreducible character: 4
   Theorem B: T(C) = E(mu,n) for the five mu: True; permutation of Remark 4.5 valid: True
   Theorem C: Lemma 5.3 (equal residues across C+-, halves of K and L): True; rule of Remark 5.7: True; permutation of the proof valid: True
   (0.0 s)
n=14: k(A_n) = 72, p(n) = 135, primes [4099981, 4099961, 4099943, 4099903, 4099897]; S_n table 0.0 s
   degrees = hook length formula: True; S_n column orthogonality mod p: True; row sums: True; top Garner digit 0: True
   perfect matching for every class C: True; max |T(C)| = 15; classes with no vanishing irreducible character: 1
   Theorem B: T(C) = E(mu,n) for the five mu: True; permutation of Remark 4.5 valid: True
   (0.1 s)
n=15: k(A_n) = 94, p(n) = 176, primes [4099981, 4099961, 4099943, 4099903, 4099897]; S_n table 0.0 s
   degrees = hook length formula: True; S_n column orthogonality mod p: True; row sums: True; top Garner digit 0: True
   perfect matching for every class C: True; max |T(C)| = 19; classes with no vanishing irreducible character: 2
   Theorem B: T(C) = E(mu,n) for the five mu: True; permutation of Remark 4.5 valid: True
   Theorem C: Lemma 5.3 (equal residues across C+-, halves of K and L): True; rule of Remark 5.7: True; permutation of the proof valid: True
   (0.1 s)
n=16: k(A_n) = 123, p(n) = 231, primes [4099981, 4099961, 4099943, 4099903, 4099897]; S_n table 0.0 s
   degrees = hook length formula: True; S_n column orthogonality mod p: True; row sums: True; top Garner digit 0: True
   perfect matching for every class C: True; max |T(C)| = 22; classes with no vanishing irreducible character: 2
   Theorem B: T(C) = E(mu,n) for the five mu: True; permutation of Remark 4.5 valid: True
   (0.2 s)
n=17: k(A_n) = 156, p(n) = 297, primes [4099981, 4099961, 4099943, 4099903, 4099897]; S_n table 0.0 s
   degrees = hook length formula: True; S_n column orthogonality mod p: True; row sums: True; top Garner digit 0: True
   perfect matching for every class C: True; max |T(C)| = 24; classes with no vanishing irreducible character: 1
   Theorem B: T(C) = E(mu,n) for the five mu: True; permutation of Remark 4.5 valid: True
   Theorem C: Lemma 5.3 (equal residues across C+-, halves of K and L): True; rule of Remark 5.7: True; permutation of the proof valid: True
   (0.5 s)
n=18: k(A_n) = 200, p(n) = 385, primes [4099981, 4099961, 4099943, 4099903, 4099897]; S_n table 0.1 s
   degrees = hook length formula: True; S_n column orthogonality mod p: True; row sums: True; top Garner digit 0: True
   perfect matching for every class C: True; max |T(C)| = 34; classes with no vanishing irreducible character: 2
   Theorem B: T(C) = E(mu,n) for the five mu: True; permutation of Remark 4.5 valid: True
   (0.9 s)
n=19: k(A_n) = 254, p(n) = 490, primes [4099981, 4099961, 4099943, 4099903, 4099897]; S_n table 0.1 s
   degrees = hook length formula: True; S_n column orthogonality mod p: True; row sums: True; top Garner digit 0: True
   perfect matching for every class C: True; max |T(C)| = 48; classes with no vanishing irreducible character: 2
   Theorem B: T(C) = E(mu,n) for the five mu: True; permutation of Remark 4.5 valid: True
   Theorem C: Lemma 5.3 (equal residues across C+-, halves of K and L): True; rule of Remark 5.7: True; permutation of the proof valid: True
   (2.0 s)
n=20: k(A_n) = 324, p(n) = 627, primes [4099981, 4099961, 4099943, 4099903, 4099897]; S_n table 0.1 s
   degrees = hook length formula: True; S_n column orthogonality mod p: True; row sums: True; top Garner digit 0: True
   perfect matching for every class C: True; max |T(C)| = 56; classes with no vanishing irreducible character: 3
   Theorem B: T(C) = E(mu,n) for the five mu: True; permutation of Remark 4.5 valid: True
   (3.9 s)
n=21: k(A_n) = 408, p(n) = 792, primes [4099981, 4099961, 4099943, 4099903, 4099897]; S_n table 0.2 s
   degrees = hook length formula: True; S_n column orthogonality mod p: True; row sums: True; top Garner digit 0: True
   perfect matching for every class C: True; max |T(C)| = 58; classes with no vanishing irreducible character: 1
   Theorem B: T(C) = E(mu,n) for the five mu: True; permutation of Remark 4.5 valid: True
   Theorem C: Lemma 5.3 (equal residues across C+-, halves of K and L): True; rule of Remark 5.7: True; permutation of the proof valid: True
   (8.2 s)
n=22: k(A_n) = 513, p(n) = 1002, primes [4099981, 4099961, 4099943, 4099903, 4099897]; S_n table 0.2 s
   degrees = hook length formula: True; S_n column orthogonality mod p: True; row sums: True; top Garner digit 0: True
   perfect matching for every class C: True; max |T(C)| = 77; classes with no vanishing irreducible character: 3
   Theorem B: T(C) = E(mu,n) for the five mu: True; permutation of Remark 4.5 valid: True
   (16.5 s)
n=23: k(A_n) = 641, p(n) = 1255, primes [4099981, 4099961, 4099943, 4099903, 4099897]; S_n table 0.3 s
   degrees = hook length formula: True; S_n column orthogonality mod p: True; row sums: True; top Garner digit 0: True
   perfect matching for every class C: True; max |T(C)| = 101; classes with no vanishing irreducible character: 2
   Theorem B: T(C) = E(mu,n) for the five mu: True; permutation of Remark 4.5 valid: True
   Theorem C: Lemma 5.3 (equal residues across C+-, halves of K and L): True; rule of Remark 5.7: True; permutation of the proof valid: True
   (35.5 s)
n=24: k(A_n) = 804, p(n) = 1575, primes [4099981, 4099961, 4099943, 4099903, 4099897]; S_n table 0.4 s
   degrees = hook length formula: True; S_n column orthogonality mod p: True; row sums: True; top Garner digit 0: True
   perfect matching for every class C: True; max |T(C)| = 121; classes with no vanishing irreducible character: 2
   Theorem B: T(C) = E(mu,n) for the five mu: True; permutation of Remark 4.5 valid: True
   (72.1 s)
summary: n, k(A_n), max |T(C)|, perfect matching for every C
   5 5 3 True
   6 7 3 True
   7 9 3 True
   8 14 5 True
   9 18 6 True
   10 24 6 True
   11 31 8 True
   12 43 10 True
   13 55 11 True
   14 72 15 True
   15 94 19 True
   16 123 22 True
   17 156 24 True
   18 200 34 True
   19 254 48 True
   20 324 56 True
   21 408 58 True
   22 513 77 True
   23 641 101 True
   24 804 121 True
