n=5: 30 words in phi, theta: Veech's factors n/gcd(n,4j(a-b)) equal the factors found by unfolding in the direction D sigma(side): convention (D phi, D theta) = (T, R): 24 words; (T, R^-1): 30 words
n=7: 30 words in phi, theta: Veech's factors n/gcd(n,4j(a-b)) equal the factors found by unfolding in the direction D sigma(side): convention (D phi, D theta) = (T, R): 25 words; (T, R^-1): 30 words
n=9: 30 words in phi, theta: Veech's factors n/gcd(n,4j(a-b)) equal the factors found by unfolding in the direction D sigma(side): convention (D phi, D theta) = (T, R): 20 words; (T, R^-1): 30 words
n=15: 30 words in phi, theta: Veech's factors n/gcd(n,4j(a-b)) equal the factors found by unfolding in the direction D sigma(side): convention (D phi, D theta) = (T, R): 20 words; (T, R^-1): 30 words
n=21: 30 words in phi, theta: Veech's factors n/gcd(n,4j(a-b)) equal the factors found by unfolding in the direction D sigma(side): convention (D phi, D theta) = (T, R): 20 words; (T, R^-1): 30 words
n=25: 30 words in phi, theta: Veech's factors n/gcd(n,4j(a-b)) equal the factors found by unfolding in the direction D sigma(side): convention (D phi, D theta) = (T, R): 17 words; (T, R^-1): 30 words
n=27: 30 words in phi, theta: Veech's factors n/gcd(n,4j(a-b)) equal the factors found by unfolding in the direction D sigma(side): convention (D phi, D theta) = (T, R): 19 words; (T, R^-1): 30 words
n=33: 12 words in phi, theta: Veech's factors n/gcd(n,4j(a-b)) equal the factors found by unfolding in the direction D sigma(side): convention (D phi, D theta) = (T, R): 7 words; (T, R^-1): 12 words
n=35: 12 words in phi, theta: Veech's factors n/gcd(n,4j(a-b)) equal the factors found by unfolding in the direction D sigma(side): convention (D phi, D theta) = (T, R): 9 words; (T, R^-1): 12 words
n=45: 12 words in phi, theta: Veech's factors n/gcd(n,4j(a-b)) equal the factors found by unfolding in the direction D sigma(side): convention (D phi, D theta) = (T, R): 7 words; (T, R^-1): 12 words
total 246 words: agreement for (T, R): 168, for (T, R^-1): 246
patterns from Veech's formulas over all first rows (a,b):
  n=5 (odd): the patterns are exactly d_j = n'/gcd(n',j) for the divisors n' of n: [5, 1]
  n=7 (odd): the patterns are exactly d_j = n'/gcd(n',j) for the divisors n' of n: [7, 1]
  n=9 (odd): the patterns are exactly d_j = n'/gcd(n',j) for the divisors n' of n: [9, 3, 1]
  n=15 (odd): the patterns are exactly d_j = n'/gcd(n',j) for the divisors n' of n: [15, 5, 3, 1]
  n=21 (odd): the patterns are exactly d_j = n'/gcd(n',j) for the divisors n' of n: [21, 7, 3, 1]
  n=25 (odd): the patterns are exactly d_j = n'/gcd(n',j) for the divisors n' of n: [25, 5, 1]
  n=27 (odd): the patterns are exactly d_j = n'/gcd(n',j) for the divisors n' of n: [27, 9, 3, 1]
  n=45 (odd): the patterns are exactly d_j = n'/gcd(n',j) for the divisors n' of n: [45, 15, 9, 5, 3, 1]
  n=6 (even): class of the vertical direction (Sect. 1 of the source: 'even'): [(1, 1), (3, 1)] ; class of the direction of a side ('odd'): [(1,), (3,)]
  n=8 (even): class of the vertical direction (Sect. 1 of the source: 'even'): [(4, 4)] ; class of the direction of a side ('odd'): [(2, 1)]
  n=10 (even): class of the vertical direction (Sect. 1 of the source: 'even'): [(1, 1, 1), (5, 5, 1)] ; class of the direction of a side ('odd'): [(1, 1), (5, 5)]
  n=12 (even): class of the vertical direction (Sect. 1 of the source: 'even'): [(2, 2, 2), (6, 2, 6)] ; class of the direction of a side ('odd'): [(1, 1, 1), (3, 3, 1)]
  these are the factor patterns of Table 4 of the note
ALL CHECKS PASSED
