all alpha_k = 0: True
beta_1..beta_8 = 4, 2, 4/3, 7/6, 11/10, 414/385, 16868/15939, 102259729/97766928
beta_k (float), k=1..22: 4.000000 2.000000 1.333333 1.166667 1.100000 1.075325 1.058285 1.045954 1.036218 1.030482 1.026264 1.022850 1.019732 1.017507 1.015780 1.014333 1.012933 1.011830 1.010939 1.010177 1.009422 1.008789

moment ratios (lower bounds for (max supp mu)^2):
   m_4/m_2 = 6 = 6.000000
   m_6/m_4 = 58/9 = 6.444444
   m_8/m_6 = 191/29 = 6.586207
   m_10/m_8 = 6342/955 = 6.640838
   m_12/m_10 = 126797/19026 = 6.664407
   m_14/m_12 = 5924902/887579 = 6.675352
   m_14/m_12 - 20/3 = 23126/2662737 > 0 : True;   m_6/m_4 = 58/9 > 6 : True
   sqrt(k_44/k_42) = 2.0995331878  (lower bound for ||QbQ||)

Gauss nodes of mu (top node = Rayleigh-Ritz lower bound for c = ||b||), weight of the top node:
   K= 8: top node 2.585705183949854080731  weight 0.251579202609445111   2nd node 1.83239314197 (weight 0.048588477)
   K=12: top node 2.585826237397453255632  weight 0.251332868897915143   2nd node 1.96106318684 (weight 0.017582947)
   K=16: top node 2.585826605013431672455  weight 0.251331659333049367   2nd node 1.99282334732 (weight 0.0093477743)
   K=20: top node 2.585826606045398206637  weight 0.251331654654623804   2nd node 2.00354602723 (weight 0.0062661954)
   K=22: top node 2.585826606048059403683  weight 0.251331654639346453   2nd node 2.00614591748 (weight 0.0054323191)
Gauss nodes of nu (Jacobi parameters beta_2, beta_3, ...): top node = lower bound for ||QbQ||:
   K= 8: top node 2.092049393338163  weight 0.117223577233
   K=12: top node 2.101020787609935  weight 0.10262044318
   K=16: top node 2.101898527951942  weight 0.100194539448
   K=20: top node 2.101982405820587  weight 0.099855289448
   K=21: top node 2.101986204249692  weight 0.0998359823166

enclosure from m_0..m_44 (file direct_moments_N44.txt), kappa_+ = 49/20 = 2.450000, J = 20:
   z_- = 2.5857947438 < c < z_+ = 2.5860369463
   F'(z_-) <= 3.9998218724,  F'(z_+) >= 3.9506745181
   1/F'(z_-) >= 0.2500111334  <  w  <  1/F'(z_+) <= 0.2531213330
   w > 1/4 certified: True
