|A_7| = 2520; 7-cycles 720, subgroups of order 7: 120; 5-cycles 504, subgroups of order 5: 126
left cosets of all these subgroups: 106704
file OWR-14299292-011_A_cert_p7_r2.json: p = 7, r = 2, terms = 1251
  recorded convention: (x o y)(i) = x[y[i]]; coset = z K' = {z o k}
  structural failures (non-permutation, wrong cycle type, odd element, bad coefficient): 0
  terms with K_j of order 7: 525, of order 5: 726, other: 0
  distinct subgroups K_j: 240 (of order 7: 115, of order 5: 125)
  sum_j c_j z_j s_(K_j) = identity of F_2A_7 (recorded product): True  (support size of the sum: 1)
  same sum with the opposite product equals the identity: False  (support size 1193; not required)
  negative control, first coefficient changed: identity? False
  negative control, one term dropped: identity? False
  RESULT PASS
file OWR-14299292-011_A_cert_p7_r3.json: p = 7, r = 3, terms = 1675
  recorded convention: (x o y)(i) = x[y[i]]; coset = z K' = {z o k}
  structural failures (non-permutation, wrong cycle type, odd element, bad coefficient): 0
  terms with K_j of order 7: 706, of order 5: 969, other: 0
  distinct subgroups K_j: 245 (of order 7: 119, of order 5: 126)
  sum_j c_j z_j s_(K_j) = identity of F_3A_7 (recorded product): True  (support size of the sum: 1)
  same sum with the opposite product equals the identity: False  (support size 1631; not required)
  negative control, first coefficient changed: identity? False
  negative control, one term dropped: identity? False
  RESULT PASS
TOTAL PASS
