Second verification run, r2_kstar.py, mp.dps = 50
(1) roots of kappa*(a/b) = 0, tau = 1, b = 1 (secant method on the measured A*_f1/A):
   N=6: a/b = 2.0  |A*_f1| <= 1.07e-49 at six members, A varies (rel. spread 0.0107); lambda = 0.44444444444444444444, lambda of kappa*=0 from (1): 0.44444444444444444444
        at a/b + 0.05: A*_f/Abar_f ranges over [-0.081147501, -0.081147501]
   N=8: a/b = 1.853847304381821014624039  |A*_f1| <= 7.48e-50 at six members, A varies (rel. spread 0.000486); lambda = 0.25278935048914019585, lambda of kappa*=0 from (1): 0.25278935048914019585
        at a/b + 0.05: A*_f/Abar_f ranges over [-0.06410123, -0.064027935]
   N=10: a/b = 1.803919044585109361876021  |A*_f1| <= 6.95e-50 at six members, A varies (rel. spread 2.63e-5); lambda = 0.16275114667576476501, lambda of kappa*=0 from (1): 0.16275114667576476501
        at a/b + 0.05: A*_f/Abar_f ranges over [-0.058031313, -0.058031313]
   N=12: a/b = 1.779969416244837329727708  |A*_f1| <= 7.48e-50 at six members, A varies (rel. spread 1.51e-6); lambda = 0.11340993586391128091, lambda of kappa*=0 from (1): 0.11340993586391128091
        at a/b + 0.05: A*_f/Abar_f ranges over [-0.055122229, -0.055122013]
(2) measured kappa* (one member) against the closed form (1), several (N, tau) and a/b:
   max relative deviation: 1.3e-44
   signs of kappa* (tau = 1) at a/b = 1.7, 1.8, 1.9, 2.0, 2.1:
     N=6: 0.497045, 0.34087, 0.175208, -1.2761e-50, -0.184808
     N=8: 0.263049, 0.0947113, -0.0834482, -0.271464, -0.469362
     N=10: 0.178486, 0.00692501, -0.174537, -0.365922, -0.567248
     N=12: 0.137453, -0.0354234, -0.218236, -0.410998, -0.613723
(3) N = 6, tau = 1: kappa_p and kappa* against the rational expressions in r = a/b:
   max |kappa_p - r(2r+1)/(r+1)^2| = 8.02e-50, max |kappa* + (r-2)(r+1)^2/(2r+1)| and |lambda - r^2/(r+1)^2| = 5.88e-50
(4) constants:
   N=5, tau=1, a=1.5: kappa (k806,a) = 0.58189686469496841287
   N=6, tau=1, a=1.5: kappa_p = 0.96, kappa* = 0.78125, kappa = 0.65, k404 constant = 0.813802083333333
