residual set R(1000000): size 16703, first 12: [45, 117, 153, 245, 261, 333, 369, 405, 477, 549, 585, 605]
certified lines: 16703 (dups 0) by family {'F3': 602, 'F1': 15330, 'F2': 771}
problems: 0 []
residual without certificate: 0 []
certified but not in R: 0 []
  cert 45 ('F3', '1/1|1/1|1/1|1/1')
  cert 245 ('F3', '1/2|1/1|2/1|1/1')
  cert 605 ('F3', '1/1|2/1|1/1|2/3')
  cert 1805 ('F3', '1/1|3/1|1/2|1/3')
  cert 2645 ('F3', '1/1|3/1|1/1|3/5')
  cert 4805 ('F3', '1/5|1/1|5/1|1/1')
  cert 79037 ('F2', '1/1|13/1|6/13')
  cert 84113 ('F3', '1/2|2/1|14/3|3/1')
  cert 280845 ('F3', '1/2|1/2|17/8|1/4')
  cert 983053 ('F2', '17/6|1/4|4/11')
Lambda3 identity: False
Lambda4 identity: False
W3 polynomial invariant under j->j+1: False
W3 polynomial invariant under swap 0<->2: True
Thm3 (I): (1 + 2*I)*(a**2 + a*b + b**2)
Thm3 (II): (-1 - 2*I)*(X**2 - 3*Y**2)
Thm4 Lambda3: d*(A + I*B)
W3 poly == Stoimenow f1^2+f2^2 under stated matching: True
Theorem 3 representation check for primes q=3 mod 4 below 20000: {'I': 570, 'II': 566}, failures []
