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..80: 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 1.008262 1.007805 1.007347 1.006947 1.006605 1.006306 1.006005 1.005734 1.005497 1.005289 1.005078 1.004884 1.004712 1.004559 1.004405 1.004260 1.004130 1.004014 1.003896 1.003784 1.003682 1.003591 1.003498 1.003409 1.003327 1.003253 1.003178 1.003106 1.003038 1.002977 1.002915 1.002854 1.002798 1.002746 1.002693 1.002642 1.002594 1.002549 1.002504 1.002460 1.002417 1.002378 1.002339 1.002301 1.002264 1.002229 1.002195 1.002160 1.002127 1.002097 1.002066 1.002035 1.002006 1.001978 1.001951 1.001923 1.001897 1.001872

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_160/k_158) = 2.1019879808  (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=80: top node 2.585826606048204448632  weight 0.251331654638419315   2nd node 2.01148558627 (weight 0.0031287405)
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=79: top node 2.101990760466022  weight 0.0998095879805

enclosure from m_0..m_160 (file model_moments_N160.txt), kappa_+ = 49/20 = 2.450000, J = 78:
   z_- = 2.58582660604820329650 < c < z_+ = 2.58582660604821205961
   F'(z_-) <= 3.97880641592556663709,  F'(z_+) >= 3.97880641592057655061
   1/F'(z_-) >= 0.25133165463828573967  <  w  <  1/F'(z_+) <= 0.25133165463860095147
   w > 1/4 certified: True
