=== family a=1 b=0.5 N=4 tau=1: lambda=0.2 k^2=0.9375 K=2.80120608467 K'=1.59624222213 h=2.80120608467; real-member validation (closure, tangency, reflection law) worst=8.51e-38
   parity |F(c+w)+F(c-w)|/max(|F|,1) at c=u0=K-Delta+iK': {'A': '1.12e-40', 'Adag': '1.94e-36', 'Apol': '8.44e-36', 'AdualR': '5.99e-36', 'Aped': '1.41e-36', 'Aant': '3.68e-40', 'ApedX': '9.6e-36'}
   parity |F(c+w)+F(c-w)|/max(|F|,1) at c=iK': {'A': '1.87e-39', 'Adag': '2.89e-40', 'Apol': '2.09e-39', 'AdualR': '1.21e-41', 'Aped': '5.4e-40', 'Aant': '2.02e-37', 'ApedX': '2.99e-42'}
   parity |F(c+w)+F(c-w)|/max(|F|,1) at c=u0+2K: {'A': '1.87e-40', 'Adag': '4.23e-36', 'Apol': '4.66e-36', 'AdualR': '1.06e-35', 'Aped': '1.45e-36', 'Aant': '9.25e-41', 'ApedX': '7.09e-36'}
   sign flip |F(u+2iK')+F(u)|: {'A': '0.0', 'Adag': '9.47e-41', 'Apol': '8.82e-39', 'AdualR': '1.28e-41', 'Aped': '1.23e-41', 'Aant': '3.46e-41', 'ApedX': '7.17e-43'}  periodicity h,4K: {'A': '6.33e-41', 'Adag': '1.78e-39', 'Apol': '3.32e-38', 'AdualR': '1.43e-41', 'Aped': '7.16e-41', 'Aant': '1.1e-39', 'ApedX': '8.5e-41'}
   Laurent at u0, r=0.001: A: c-4=1.46e-54,c-3=1.52e-52,c-2=1.01e-48,c-1=1.39e-45,c0=6.47e-41; Adag: c-4=3.5e-41,c-3=1.12e-36,c-2=2.66e-35,c-1=4.0,c0=1.95e-29; Apol: c-4=2.03e-39,c-3=5.83e-35,c-2=1.34e-33,c-1=128.0,c0=7.41e-28; AdualR: c-4=5.28e-43,c-3=6.19e-40,c-2=1.2e-36,c-1=0.0625,c0=2.26e-31; Aped: c-4=1.06e-42,c-3=2.94e-38,c-2=1.03e-36,c-1=0.32,c0=1.41e-30; Aant: c-4=1.49e-53,c-3=1.22e-50,c-2=2.88e-47,c-1=8.55e-45,c0=2.2e-40; ApedX: c-4=2.37e-36,c-3=0.08,c-2=3.0e-30,c-1=0.102,c0=3.69e-24
   Laurent at u0, r=0.0003: A: c-4=6.2e-57,c-3=4.82e-53,c-2=6.31e-50,c-1=5.65e-46,c0=7.18e-41; Adag: c-4=2.41e-41,c-3=1.11e-36,c-2=4.52e-34,c-1=4.0,c0=1.44e-27; Apol: c-4=1.7e-39,c-3=5.82e-35,c-2=2.74e-32,c-1=128.0,c0=1.57e-25; AdualR: c-4=1.53e-43,c-3=1.51e-39,c-2=6.6e-36,c-1=0.0625,c0=7.62e-29; Aped: c-4=1.27e-42,c-3=3.18e-38,c-2=2.13e-36,c-1=0.32,c0=1.3e-28; Aant: c-4=6.72e-56,c-3=2.47e-52,c-2=4.52e-49,c-1=4.31e-45,c0=2.01e-40; ApedX: c-4=2.92e-35,c-3=0.08,c-2=1.04e-28,c-1=0.102,c0=3.05e-21
   Laurent at iK', r=0.001: A: c-4=1.63e-51,c-3=7.25e-46,c-2=1.85e-41,c-1=0.8,c0=3.04e-39; Adag: c-4=1.11e-54,c-3=7.02e-52,c-2=8.65e-48,c-1=3.34e-45,c0=1.16e-40; Apol: c-4=3.58e-50,c-3=5.95e-47,c-2=1.49e-44,c-1=6.5e-41,c0=1.35e-38; AdualR: c-4=1.43e-53,c-3=2.28e-50,c-2=6.03e-48,c-1=2.47e-44,c0=5.19e-42; Aped: c-4=1.09e-51,c-3=1.11e-48,c-2=2.54e-46,c-1=5.19e-43,c0=8.61e-40; Aant: c-4=4.56e-45,c-3=1.64e-40,c-2=4.53e-39,c-1=1.6,c0=3.84e-33; ApedX: c-4=3.91e-57,c-3=2.13e-54,c-2=2.13e-51,c-1=8.88e-49,c0=1.83e-45
   Laurent at iK', r=0.0003: A: c-4=1.19e-52,c-3=4.04e-46,c-2=1.85e-41,c-1=0.8,c0=2.8e-39; Adag: c-4=9.57e-57,c-3=2.72e-53,c-2=1.06e-48,c-1=2.69e-46,c0=1.08e-40; Apol: c-4=1.01e-51,c-3=7.58e-48,c-2=9.86e-45,c-1=8.53e-42,c0=1.13e-37; AdualR: c-4=3.82e-55,c-3=2.98e-51,c-2=3.71e-48,c-1=3.38e-45,c0=4.48e-41; Aped: c-4=2.93e-53,c-3=1.04e-49,c-2=2.78e-46,c-1=2.76e-43,c0=1.72e-39; Aant: c-4=3.32e-45,c-3=1.64e-40,c-2=3.69e-38,c-1=1.6,c0=4.07e-31; ApedX: c-4=2.42e-60,c-3=2.09e-56,c-2=8.22e-53,c-1=6.37e-49,c0=6.2e-46
   residue ratios at u0 vs real-member invariants: Apol/Adag (32.0 + 1.1486057603979e-31j) 32.0 | AdualR/Adag (0.015625 + 3.7536739228255e-37j) 0.015625 | ApedX/AdualR (1.64 - 1.8159706312947e-26j) 1.5997588012673 | Aped/AdualR (5.12 - 1.7823937415993e-33j) 5.12 | Adag/Aant (2.245178378087e+44 - 4.1054586674917e+44j) 2.4996231269802
   grid cells (u/K, Im u/K') with |F| > 1e4: {'A': [], 'Adag': [], 'Apol': [], 'AdualR': [], 'Aped': [], 'Aant': [], 'ApedX': []}
   predicted (Re/K, Im/K'): f1-isotropic coset [('0.5', '1.0'), ('1.5', '1.0'), ('2.5', '1.0'), ('3.5', '1.0')] 
     f2-isotropic coset [('0.5', '1.0'), ('1.5', '1.0'), ('2.5', '1.0'), ('3.5', '1.0')] 
     Jacobi coset [('0.0', '1.0'), ('1.0', '1.0'), ('2.0', '1.0'), ('3.0', '1.0')]
=== family a=1 b=0.5 N=5 tau=1: lambda=0.14862444743721648632 k^2=0.880927338989678 K=2.49625757634 K'=1.62097305603 h=1.99700606107; real-member validation (closure, tangency, reflection law) worst=3.06e-37
   parity |F(c+w)+F(c-w)|/max(|F|,1) at c=u0=K-Delta+iK': {'A': '6.09e-40', 'Adag': '1.44e-35', 'Apol': '1.1e-35', 'AdualR': '2.24e-36', 'Aped': '1.92e-39', 'Aant': '8.34e-39', 'ApedX': '4.64e-36'}
   parity |F(c+w)+F(c-w)|/max(|F|,1) at c=iK': {'A': '1.48e-40', 'Adag': '2.08', 'Apol': '2.08', 'AdualR': '0.193', 'Aped': '1.81', 'Aant': '2.0', 'ApedX': '2.02'}
   parity |F(c+w)+F(c-w)|/max(|F|,1) at c=u0+2K: {'A': '3.39e-40', 'Adag': '1.28e-39', 'Apol': '2.88e-39', 'AdualR': '3.87e-41', 'Aped': '3.6e-36', 'Aant': '3.44e-39', 'ApedX': '2.7e-36'}
   sign flip |F(u+2iK')+F(u)|: {'A': '7.17e-43', 'Adag': '0.0', 'Apol': '6.43e-40', 'AdualR': '1.28e-41', 'Aped': '1.32e-41', 'Aant': '3.63e-41', 'ApedX': '7.4e-41'}  periodicity h,4K: {'A': '2.19e-41', 'Adag': '2.77e-39', 'Apol': '9.69e-39', 'AdualR': '2.87e-41', 'Aped': '1.14e-40', 'Aant': '3.04e-40', 'ApedX': '2.6e-40'}
   Laurent at u0, r=0.001: A: c-4=2.65e-54,c-3=1.7e-50,c-2=6.41e-48,c-1=4.83e-45,c0=2.4e-40; Adag: c-4=3.07e-40,c-3=5.1e-36,c-2=3.3e-35,c-1=6.44,c0=1.05e-28; Apol: c-4=2.56e-39,c-3=3.82e-35,c-2=7.38e-34,c-1=56.1,c0=1.17e-27; AdualR: c-4=5.74e-43,c-3=4.26e-40,c-2=6.27e-37,c-1=0.0615,c0=1.3e-31; Aped: c-4=1.21e-50,c-3=7.02e-50,c-2=2.06e-43,c-1=3.67e-39,c0=1.25e-38; Aant: c-4=1.15e-52,c-3=2.25e-49,c-2=1.62e-46,c-1=1.46e-43,c0=3.83e-39; ApedX: c-4=1.14e-41,c-3=2.26e-37,c-2=3.05e-36,c-1=1.01,c0=5.18e-30
   Laurent at u0, r=0.0003: A: c-4=3.29e-56,c-3=6.33e-53,c-2=7.88e-49,c-1=8.9e-46,c0=2.4e-40; Adag: c-4=5.51e-41,c-3=5.1e-36,c-2=6.45e-34,c-1=6.44,c0=1.23e-26; Apol: c-4=6.39e-40,c-3=3.9e-35,c-2=1.65e-33,c-1=56.1,c0=2.1e-25; AdualR: c-4=4.1e-43,c-3=7.51e-40,c-2=5.64e-36,c-1=0.0615,c0=5.82e-29; Aped: c-4=4.07e-51,c-3=3.06e-48,c-2=8.34e-45,c-1=3.64e-39,c0=5.01e-37; Aant: c-4=8.12e-56,c-3=1.15e-51,c-2=1.18e-47,c-1=6.04e-45,c0=3.72e-39; ApedX: c-4=5.04e-42,c-3=2.18e-37,c-2=1.64e-34,c-1=1.01,c0=9.79e-28
   Laurent at iK', r=0.001: A: c-4=2.13e-51,c-3=9.49e-47,c-2=7.37e-43,c-1=0.356,c0=3.75e-39; Adag: c-4=2.79e-51,c-3=3.37e-48,c-2=7.7e-47,c-1=5.45e-43,c0=10.1; Apol: c-4=7.02e-51,c-3=8.84e-48,c-2=1.01e-44,c-1=1.01e-41,c0=88.3; AdualR: c-4=3.8e-53,c-3=1.27e-50,c-2=1.5e-47,c-1=6.53e-45,c0=0.0967; Aped: c-4=8.29e-52,c-3=4.1e-49,c-2=1.35e-45,c-1=7.93e-43,c0=0.908; Aant: c-4=8.05e-46,c-3=6.28e-42,c-2=1.51,c-1=0.148,c0=2.49; ApedX: c-4=3.87e-52,c-3=6.74e-50,c-2=8.55e-47,c-1=1.11e-43,c0=2.65
   Laurent at iK', r=0.0003: A: c-4=2.89e-53,c-3=1.43e-47,c-2=7.42e-43,c-1=0.356,c0=4.96e-39; Adag: c-4=2.97e-53,c-3=7.17e-51,c-2=1.77e-46,c-1=2.57e-44,c0=10.1; Apol: c-4=1.67e-52,c-3=5.14e-49,c-2=4.83e-45,c-1=8.36e-42,c0=88.3; AdualR: c-4=4.04e-55,c-3=9.68e-52,c-2=1.42e-47,c-1=3.02e-44,c0=0.0967; Aped: c-4=1.26e-53,c-3=5.86e-50,c-2=1.14e-46,c-1=6.1e-43,c0=0.908; Aant: c-4=1.21e-46,c-3=6.29e-42,c-2=1.51,c-1=0.148,c0=2.49; ApedX: c-4=1.76e-54,c-3=4.88e-51,c-2=3.22e-47,c-1=1.48e-43,c0=2.65
   residue ratios at u0 vs real-member invariants: Apol/Adag (8.7226225329274 + 4.0253344085214e-32j) 8.7226225329274 | AdualR/Adag (0.0095558668288412 + 5.3995601812311e-35j) 0.0095558668288412 | ApedX/AdualR (16.401454081882 - 7.8965398931493e-32j) 4.9952671825655 | Aped/AdualR (-5.9659974476944e-38 + 4.850932677349e-43j) 9.7574976920147 | Adag/Aant (-4.3938568043086e+43 + 1.087990902469e+42j) 57.737914790709
   grid cells (u/K, Im u/K') with |F| > 1e4: {'A': [], 'Adag': [], 'Apol': [], 'AdualR': [], 'Aped': [], 'Aant': [], 'ApedX': []}
   predicted (Re/K, Im/K'): f1-isotropic coset [('0.6', '1.0'), ('1.4', '1.0'), ('2.2', '1.0'), ('3.0', '1.0'), ('3.8', '1.0')] 
     f2-isotropic coset [('0.2', '1.0'), ('1.0', '1.0'), ('1.8', '1.0'), ('2.6', '1.0'), ('3.4', '1.0')] 
     Jacobi coset [('0.0', '1.0'), ('0.4', '1.0'), ('0.8', '1.0'), ('1.2', '1.0'), ('1.6', '1.0'), ('2.0', '1.0'), ('2.4', '1.0'), ('2.8', '1.0'), ('3.2', '1.0'), ('3.6', '1.0')]
=== family a=1 b=0.5 N=6 tau=1: lambda=0.11111111111111111111 k^2=0.84375 K=2.3701853443 K'=1.63821383437 h=1.58012356286; real-member validation (closure, tangency, reflection law) worst=2.27e-37
   parity |F(c+w)+F(c-w)|/max(|F|,1) at c=u0=K-Delta+iK': {'A': '6.27e-40', 'Adag': '1.38e-35', 'Apol': '1.31e-35', 'AdualR': '5.96e-36', 'Aped': '2.19e-36', 'Aant': '9.64e-38', 'ApedX': '5.65e-35'}
   parity |F(c+w)+F(c-w)|/max(|F|,1) at c=iK': {'A': '6.02e-40', 'Adag': '3.35e-36', 'Apol': '6.76e-36', 'AdualR': '7.5e-36', 'Aped': '2.19e-36', 'Aant': '1.2e-35', 'ApedX': '2.35e-35'}
   parity |F(c+w)+F(c-w)|/max(|F|,1) at c=u0+2K: {'A': '6.64e-40', 'Adag': '1.12e-35', 'Apol': '1.44e-35', 'AdualR': '8.59e-36', 'Aped': '2.22e-36', 'Aant': '1.44e-37', 'ApedX': '5.06e-35'}
   sign flip |F(u+2iK')+F(u)|: {'A': '1.43e-42', 'Adag': '3.73e-41', 'Apol': '5.97e-40', 'AdualR': '1.62e-41', 'Aped': '2.32e-41', 'Aant': '1.84e-41', 'ApedX': '1.85e-40'}  periodicity h,4K: {'A': '2.68e-41', 'Adag': '2.01e-39', 'Apol': '3.7e-39', 'AdualR': '1.93e-41', 'Aped': '9.43e-41', 'Aant': '7.78e-41', 'ApedX': '3.01e-40'}
   Laurent at u0, r=0.001: A: c-4=8.44e-51,c-3=5.84e-47,c-2=4.8e-42,c-1=0.629,c0=1.84e-39; Adag: c-4=9.59e-41,c-3=5.07e-36,c-2=1.62e-34,c-1=8.49,c0=6.66e-29; Apol: c-4=2.64e-40,c-3=1.3e-35,c-2=9.16e-34,c-1=36.2,c0=6.29e-28; AdualR: c-4=2.84e-43,c-3=2.59e-40,c-2=1.04e-36,c-1=0.0589,c0=4.37e-31; Aped: c-4=1.27e-42,c-3=1.37e-37,c-2=2.71e-36,c-1=0.698,c0=4.06e-31; Aant: c-4=1.19e-44,c-3=4.66e-42,c-2=1.19e-38,c-1=3.92e-38,c0=3.92e-32; ApedX: c-4=1.24e-41,c-3=5.32e-37,c-2=6.57e-35,c-1=0.786,c0=1.03e-29
   Laurent at u0, r=0.0003: A: c-4=1.69e-52,c-3=5.12e-47,c-2=4.79e-42,c-1=0.629,c0=1.87e-38; Adag: c-4=1.26e-40,c-3=4.14e-36,c-2=1.81e-33,c-1=8.49,c0=3.93e-27; Apol: c-4=5.31e-41,c-3=1.01e-35,c-2=8.52e-33,c-1=36.2,c0=5.67e-26; AdualR: c-4=7.32e-44,c-3=1.14e-39,c-2=3.43e-36,c-1=0.0589,c0=5.62e-29; Aped: c-4=2.0e-42,c-3=1.27e-37,c-2=3.75e-37,c-1=0.698,c0=4.25e-29; Aant: c-4=9.87e-45,c-3=4.63e-42,c-2=1.1e-37,c-1=2.42e-37,c0=5.15e-31; ApedX: c-4=6.52e-42,c-3=5.28e-37,c-2=6.07e-34,c-1=0.786,c0=1.03e-27
   Laurent at iK', r=0.001: A: c-4=1.76e-51,c-3=5.74e-46,c-2=4.63e-42,c-1=0.629,c0=6.7e-39; Adag: c-4=3.43e-41,c-3=5.14e-36,c-2=6.21e-35,c-1=8.49,c0=1.16e-29; Apol: c-4=3.65e-40,c-3=1.31e-35,c-2=6.22e-34,c-1=36.2,c0=4.79e-28; AdualR: c-4=3.68e-43,c-3=2.0e-40,c-2=1.06e-36,c-1=0.0589,c0=2.84e-31; Aped: c-4=1.09e-42,c-3=1.35e-37,c-2=2.89e-36,c-1=0.698,c0=5.88e-31; Aant: c-4=4.07e-45,c-3=4.65e-42,c-2=4.08e-39,c-1=2.08e-38,c0=3.44e-33; ApedX: c-4=2.6e-41,c-3=5.58e-37,c-2=5.42e-35,c-1=0.786,c0=3.82e-30
   Laurent at iK', r=0.0003: A: c-4=1.27e-52,c-3=3.18e-46,c-2=4.61e-42,c-1=0.629,c0=2.92e-38; Adag: c-4=1.75e-41,c-3=3.94e-36,c-2=1.39e-33,c-1=8.49,c0=7.89e-27; Apol: c-4=1.3e-40,c-3=9.39e-36,c-2=7.43e-33,c-1=36.2,c0=8.87e-26; AdualR: c-4=2.04e-43,c-3=1.75e-39,c-2=3.65e-36,c-1=0.0589,c0=5.05e-29; Aped: c-4=5.46e-43,c-3=1.19e-37,c-2=3.77e-37,c-1=0.698,c0=1.37e-28; Aant: c-4=2.98e-45,c-3=4.63e-42,c-2=3.31e-38,c-1=8.29e-38,c0=3.64e-31; ApedX: c-4=4.43e-42,c-3=5.08e-37,c-2=6.05e-34,c-1=0.786,c0=1.21e-27
   residue ratios at u0 vs real-member invariants: Apol/Adag (4.2666666666667 - 2.5621191324988e-32j) 4.2666666666667 | AdualR/Adag (0.0069444444444444 + 1.9995199320512e-35j) 0.0069444444444444 | ApedX/AdualR (13.333333333333 + 5.4944023965108e-31j) 13.333333333333 | Aped/AdualR (11.851851851852 - 7.17003341252e-32j) 11.851851851852 | Adag/Aant (-2.1618451969604e+38 + 1.4574141282079e+37j) -6.5787400112733e+38
   grid cells (u/K, Im u/K') with |F| > 1e4: {'A': [], 'Adag': [], 'Apol': [], 'AdualR': [], 'Aped': [], 'Aant': [], 'ApedX': []}
   predicted (Re/K, Im/K'): f1-isotropic coset [('0.0', '1.0'), ('0.6667', '1.0'), ('1.333', '1.0'), ('2.0', '1.0'), ('2.667', '1.0'), ('3.333', '1.0')] 
     f2-isotropic coset [('0.0', '1.0'), ('0.6667', '1.0'), ('1.333', '1.0'), ('2.0', '1.0'), ('2.667', '1.0'), ('3.333', '1.0')] 
     Jacobi coset [('0.0', '1.0'), ('0.6667', '1.0'), ('1.333', '1.0'), ('2.0', '1.0'), ('2.667', '1.0'), ('3.333', '1.0')]
=== family a=1 b=0.8 N=6 tau=1: lambda=0.1975308641975308642 k^2=0.448615384615385 K=1.81282870747 K'=1.90024322883 h=1.20855247164; real-member validation (closure, tangency, reflection law) worst=6.43e-40
   parity |F(c+w)+F(c-w)|/max(|F|,1) at c=u0=K-Delta+iK': {'A': '3.86e-39', 'Adag': '5.12e-36', 'Apol': '5.62e-36', 'AdualR': '9.93e-36', 'Aped': '1.03e-35', 'Aant': '4.01e-37', 'ApedX': '2.01e-35'}
   parity |F(c+w)+F(c-w)|/max(|F|,1) at c=iK': {'A': '1.52e-39', 'Adag': '3.47e-35', 'Apol': '1.9e-35', 'AdualR': '3.23e-36', 'Aped': '1.39e-37', 'Aant': '1.51e-37', 'ApedX': '8.16e-35'}
   parity |F(c+w)+F(c-w)|/max(|F|,1) at c=u0+2K: {'A': '6.59e-39', 'Adag': '3.9e-35', 'Apol': '2.34e-35', 'AdualR': '1.24e-35', 'Aped': '1.02e-35', 'Aant': '1.01e-38', 'ApedX': '6.23e-35'}
   sign flip |F(u+2iK')+F(u)|: {'A': '7.17e-43', 'Adag': '0.0', 'Apol': '0.0', 'AdualR': '0.0', 'Aped': '0.0', 'Aant': '5.74e-42', 'ApedX': '0.0'}  periodicity h,4K: {'A': '4.95e-41', 'Adag': '3.0e-40', 'Apol': '7.46e-40', 'AdualR': '1.15e-40', 'Aped': '2.3e-41', 'Aant': '8.4e-41', 'ApedX': '2.28e-40'}
   Laurent at u0, r=0.001: A: c-4=6.36e-49,c-3=3.89e-48,c-2=3.61e-41,c-1=0.796,c0=6.45e-37; Adag: c-4=1.01e-41,c-3=1.59e-38,c-2=1.5e-35,c-1=1.89,c0=3.33e-29; Apol: c-4=5.27e-41,c-3=8.36e-38,c-2=4.47e-35,c-1=3.51,c0=8.09e-29; AdualR: c-4=1.17e-42,c-3=8.14e-39,c-2=7.42e-36,c-1=0.367,c0=1.33e-30; Aped: c-4=4.16e-42,c-3=2.09e-40,c-2=1.11e-36,c-1=0.688,c0=5.02e-30; Aant: c-4=8.61e-45,c-3=1.33e-40,c-2=8.64e-39,c-1=0.864,c0=5.24e-33; ApedX: c-4=2.91e-41,c-3=4.77e-38,c-2=4.27e-35,c-1=0.697,c0=1.02e-29
   Laurent at u0, r=0.0003: A: c-4=1.46e-49,c-3=3.92e-49,c-2=3.58e-41,c-1=0.796,c0=1.8e-35; Adag: c-4=9.83e-42,c-3=2.26e-37,c-2=7.21e-34,c-1=1.89,c0=7.97e-27; Apol: c-4=6.02e-41,c-3=2.72e-37,c-2=1.68e-33,c-1=3.51,c0=2.06e-26; AdualR: c-4=2.71e-42,c-3=2.15e-38,c-2=1.22e-34,c-1=0.367,c0=7.0e-28; Aped: c-4=5.41e-42,c-3=1.41e-39,c-2=7.93e-36,c-1=0.688,c0=5.03e-29; Aant: c-4=4.84e-45,c-3=1.31e-40,c-2=5.38e-38,c-1=0.864,c0=2.23e-31; ApedX: c-4=4.71e-41,c-3=1.37e-37,c-2=6.17e-34,c-1=0.697,c0=8.38e-27
   Laurent at iK', r=0.001: A: c-4=3.45e-51,c-3=1.06e-47,c-2=1.45e-41,c-1=0.796,c0=9.6e-39; Adag: c-4=9.9e-41,c-3=2.37e-38,c-2=3.71e-35,c-1=1.89,c0=2.73e-29; Apol: c-4=1.21e-40,c-3=2.55e-38,c-2=1.45e-34,c-1=3.51,c0=4.21e-29; AdualR: c-4=2.44e-42,c-3=3.31e-39,c-2=9.75e-36,c-1=0.367,c0=2.09e-30; Aped: c-4=4.57e-42,c-3=7.5e-40,c-2=5.42e-37,c-1=0.688,c0=2.19e-30; Aant: c-4=1.17e-45,c-3=3.13e-41,c-2=1.2e-39,c-1=0.864,c0=1.3e-35; ApedX: c-4=3.16e-42,c-3=1.64e-38,c-2=4.46e-35,c-1=0.697,c0=3.06e-29
   Laurent at iK', r=0.0003: A: c-4=3.69e-53,c-3=4.73e-47,c-2=1.45e-41,c-1=0.796,c0=6.93e-38; Adag: c-4=3.41e-41,c-3=1.35e-37,c-2=7.43e-34,c-1=1.89,c0=5.21e-27; Apol: c-4=1.96e-40,c-3=3.32e-37,c-2=1.29e-33,c-1=3.51,c0=7.65e-27; AdualR: c-4=1.16e-41,c-3=1.4e-38,c-2=4.18e-35,c-1=0.367,c0=4.81e-28; Aped: c-4=4.16e-43,c-3=1.24e-38,c-2=1.58e-35,c-1=0.688,c0=7.58e-29; Aant: c-4=8.94e-47,c-3=3.13e-41,c-2=9.89e-40,c-1=0.864,c0=1.65e-33; ApedX: c-4=4.95e-41,c-3=6.71e-38,c-2=1.02e-33,c-1=0.697,c0=3.55e-27
   residue ratios at u0 vs real-member invariants: Apol/Adag (1.860119047619 + 3.1832940824394e-32j) 1.860119047619 | AdualR/Adag (0.19418074074074 - 4.1848585177574e-33j) 0.19418074074074 | ApedX/AdualR (1.8988715277778 + 2.6883124950223e-32j) 1.8988715277778 | Aped/AdualR (1.8754286694102 + 3.9456421337165e-32j) 1.8754286694102 | Adag/Aant (2.1875 + 1.1234992010873e-33j) 2.1875
   grid cells (u/K, Im u/K') with |F| > 1e4: {'A': [], 'Adag': [], 'Apol': [], 'AdualR': [], 'Aped': [], 'Aant': [], 'ApedX': []}
   predicted (Re/K, Im/K'): f1-isotropic coset [('0.0', '1.0'), ('0.6667', '1.0'), ('1.333', '1.0'), ('2.0', '1.0'), ('2.667', '1.0'), ('3.333', '1.0')] 
     f2-isotropic coset [('0.0', '1.0'), ('0.6667', '1.0'), ('1.333', '1.0'), ('2.0', '1.0'), ('2.667', '1.0'), ('3.333', '1.0')] 
     Jacobi coset [('0.0', '1.0'), ('0.6667', '1.0'), ('1.333', '1.0'), ('2.0', '1.0'), ('2.667', '1.0'), ('3.333', '1.0')]
=== family a=1 b=0.5 N=8 tau=1: lambda=0.066938089231460943459 k^2=0.803805183068982 K=2.26593916424 K'=1.65771018756 h=1.13296958212; real-member validation (closure, tangency, reflection law) worst=1.09e-37
   parity |F(c+w)+F(c-w)|/max(|F|,1) at c=u0=K-Delta+iK': {'A': '7.58e-40', 'Adag': '1.64e-35', 'Apol': '2.55e-36', 'AdualR': '1.34e-35', 'Aped': '9.18e-36', 'Aant': '3.1e-39', 'ApedX': '8.37e-35'}
   parity |F(c+w)+F(c-w)|/max(|F|,1) at c=iK': {'A': '1.66e-39', 'Adag': '2.72e-38', 'Apol': '1.08e-38', 'AdualR': '2.76e-40', 'Aped': '1.74e-39', 'Aant': '2.63e-36', 'ApedX': '7.16e-37'}
   parity |F(c+w)+F(c-w)|/max(|F|,1) at c=u0+2K: {'A': '7.55e-40', 'Adag': '8.36e-36', 'Apol': '1.97e-35', 'AdualR': '3.42e-36', 'Aped': '9.18e-36', 'Aant': '1.11e-38', 'ApedX': '2.27e-35'}
   sign flip |F(u+2iK')+F(u)|: {'A': '2.3e-41', 'Adag': '9.1e-40', 'Apol': '2.3e-39', 'AdualR': '1.18e-41', 'Aped': '6.46e-42', 'Aant': '1.55e-41', 'ApedX': '9.91e-41'}  periodicity h,4K: {'A': '4.64e-41', 'Adag': '3.33e-39', 'Apol': '2.28e-39', 'AdualR': '5.38e-41', 'Aped': '1.87e-40', 'Aant': '7.77e-41', 'ApedX': '1.63e-39'}
   Laurent at u0, r=0.001: A: c-4=4.91e-54,c-3=1.01e-50,c-2=1.7e-48,c-1=1.08e-44,c0=3.84e-40; Adag: c-4=6.52e-40,c-3=4.02e-36,c-2=1.15e-34,c-1=10.7,c0=3.89e-28; Apol: c-4=6.47e-40,c-3=2.67e-36,c-2=3.7e-34,c-1=21.8,c0=4.39e-28; AdualR: c-4=2.75e-43,c-3=3.4e-40,c-2=8.2e-37,c-1=0.052,c0=5.15e-31; Aped: c-4=8.19e-42,c-3=7.8e-38,c-2=9.62e-36,c-1=0.732,c0=6.66e-30; Aant: c-4=6.55e-53,c-3=1.43e-48,c-2=1.95e-47,c-1=3.64e-43,c0=1.78e-39; ApedX: c-4=1.31e-40,c-3=6.58e-37,c-2=2.66e-34,c-1=2.3,c0=1.36e-28
   Laurent at u0, r=0.0003: A: c-4=3.06e-56,c-3=1.63e-52,c-2=6.42e-49,c-1=2.86e-45,c0=3.77e-40; Adag: c-4=1.66e-40,c-3=5.27e-36,c-2=1.83e-33,c-1=10.7,c0=4.56e-26; Apol: c-4=2.28e-40,c-3=3.5e-36,c-2=4.41e-33,c-1=21.8,c0=2.89e-26; AdualR: c-4=4.36e-43,c-3=8.72e-40,c-2=9.65e-36,c-1=0.052,c0=1.14e-29; Aped: c-4=4.49e-42,c-3=7.88e-38,c-2=8.53e-36,c-1=0.732,c0=5.75e-28; Aant: c-4=1.81e-54,c-3=5.5e-51,c-2=1.52e-47,c-1=1.0e-43,c0=1.61e-39; ApedX: c-4=2.24e-40,c-3=4.13e-37,c-2=6.86e-33,c-1=2.3,c0=3.6e-26
   Laurent at iK', r=0.001: A: c-4=3.91e-51,c-3=4.53e-46,c-2=1.04e-41,c-1=0.5,c0=3.6e-39; Adag: c-4=2.6e-51,c-3=8.02e-50,c-2=4.34e-45,c-1=2.5e-42,c0=7.67e-39; Apol: c-4=6.39e-51,c-3=1.63e-48,c-2=2.58e-45,c-1=9.2e-42,c0=3.82e-39; AdualR: c-4=3.43e-53,c-3=2.73e-50,c-2=2.47e-47,c-1=1.74e-45,c0=4.05e-41; Aped: c-4=4.03e-51,c-3=1.42e-48,c-2=8.15e-45,c-1=2.98e-42,c0=3.45e-39; Aant: c-4=5.01e-45,c-3=1.63e-40,c-2=4.96e-39,c-1=0.136,c0=4.25e-33; ApedX: c-4=2.56e-50,c-3=1.64e-47,c-2=6.82e-45,c-1=2.72e-41,c0=1.07e-37
   Laurent at iK', r=0.0003: A: c-4=1.15e-52,c-3=2.52e-46,c-2=1.04e-41,c-1=0.5,c0=1.69e-38; Adag: c-4=1.96e-53,c-3=9.9e-50,c-2=1.46e-46,c-1=3.78e-43,c0=2.0e-39; Apol: c-4=2.31e-53,c-3=7.93e-50,c-2=1.11e-45,c-1=3.95e-42,c0=1.69e-39; AdualR: c-4=2.52e-55,c-3=3.2e-52,c-2=4.14e-48,c-1=1.69e-45,c0=9.09e-41; Aped: c-4=1.14e-52,c-3=4.91e-49,c-2=9.94e-46,c-1=3.71e-42,c0=1.96e-38; Aant: c-4=3.65e-45,c-3=1.63e-40,c-2=4.06e-38,c-1=0.136,c0=4.47e-31; ApedX: c-4=5.93e-53,c-3=6.81e-49,c-2=3.5e-46,c-1=2.92e-42,c0=8.34e-38
   residue ratios at u0 vs real-member invariants: Apol/Adag (2.0401512450509 + 1.7987313769956e-32j) 2.0401512450509 | AdualR/Adag (0.0048596449720546 - 1.8056474812474e-35j) 0.0048596449720546 | ApedX/AdualR (44.273383256197 - 5.8077985673816e-31j) 44.273383256197 | Aped/AdualR (14.068694676624 + 8.8739982962142e-32j) 14.068694676624 | Adag/Aant (2.9416189721548e+43 - 1.9716490414981e+41j) -78.954860400376
   grid cells (u/K, Im u/K') with |F| > 1e4: {'A': [], 'Adag': [], 'Apol': [], 'AdualR': [], 'Aped': [], 'Aant': [], 'ApedX': []}
   predicted (Re/K, Im/K'): f1-isotropic coset [('0.25', '1.0'), ('0.75', '1.0'), ('1.25', '1.0'), ('1.75', '1.0'), ('2.25', '1.0'), ('2.75', '1.0'), ('3.25', '1.0'), ('3.75', '1.0')] 
     f2-isotropic coset [('0.25', '1.0'), ('0.75', '1.0'), ('1.25', '1.0'), ('1.75', '1.0'), ('2.25', '1.0'), ('2.75', '1.0'), ('3.25', '1.0'), ('3.75', '1.0')] 
     Jacobi coset [('0.0', '1.0'), ('0.5', '1.0'), ('1.0', '1.0'), ('1.5', '1.0'), ('2.0', '1.0'), ('2.5', '1.0'), ('3.0', '1.0'), ('3.5', '1.0')]
=== family a=1 b=0.5 N=10 tau=1: lambda=0.044158110477264742525 k^2=0.784648599544518 K=2.22367633065 K'=1.66744729191 h=0.889470532262; real-member validation (closure, tangency, reflection law) worst=2.21e-38
   parity |F(c+w)+F(c-w)|/max(|F|,1) at c=u0=K-Delta+iK': {'A': '1.81e-39', 'Adag': '3.02e-35', 'Apol': '2.36e-35', 'AdualR': '1.19e-35', 'Aped': '1.18e-35', 'Aant': '4.82e-36', 'ApedX': '3.39e-35'}
   parity |F(c+w)+F(c-w)|/max(|F|,1) at c=iK': {'A': '2.08e-40', 'Adag': '1.82e-35', 'Apol': '1.43e-35', 'AdualR': '1.82e-35', 'Aped': '3.9e-36', 'Aant': '2.97e-36', 'ApedX': '1.21e-34'}
   parity |F(c+w)+F(c-w)|/max(|F|,1) at c=u0+2K: {'A': '3.74e-39', 'Adag': '3.28e-35', 'Apol': '5.25e-35', 'AdualR': '3.56e-35', 'Aped': '3.9e-36', 'Aant': '1.11e-37', 'ApedX': '8.19e-35'}
   sign flip |F(u+2iK')+F(u)|: {'A': '2.3e-41', 'Adag': '7.68e-40', 'Apol': '9.32e-40', 'AdualR': '1.16e-41', 'Aped': '4.59e-41', 'Aant': '2.41e-41', 'ApedX': '3.71e-40'}  periodicity h,4K: {'A': '4.66e-41', 'Adag': '3.27e-39', 'Apol': '1.52e-39', 'AdualR': '4.36e-41', 'Aped': '9.4e-41', 'Aant': '8.64e-41', 'ApedX': '2.56e-39'}
   Laurent at u0, r=0.001: A: c-4=2.02e-50,c-3=1.7e-46,c-2=8.9e-42,c-1=0.411,c0=2.36e-38; Adag: c-4=2.61e-40,c-3=2.33e-36,c-2=4.19e-34,c-1=11.2,c0=1.12e-28; Apol: c-4=3.54e-40,c-3=9.9e-37,c-2=4.53e-34,c-1=16.0,c0=2.64e-28; AdualR: c-4=4.24e-43,c-3=5.98e-40,c-2=1.66e-37,c-1=0.0454,c0=8.66e-31; Aped: c-4=1.87e-42,c-3=3.04e-38,c-2=1.82e-36,c-1=0.677,c0=3.81e-30; Aant: c-4=1.78e-44,c-3=7.33e-41,c-2=1.79e-38,c-1=0.15,c0=7.52e-32; ApedX: c-4=1.3e-39,c-3=1.14e-36,c-2=1.27e-33,c-1=4.04,c0=8.61e-28
   Laurent at u0, r=0.0003: A: c-4=8.15e-50,c-3=1.19e-47,c-2=1.02e-41,c-1=0.411,c0=1.01e-35; Adag: c-4=8.62e-40,c-3=1.18e-36,c-2=2.12e-33,c-1=11.2,c0=4.6e-26; Apol: c-4=7.57e-40,c-3=2.4e-36,c-2=4.57e-33,c-1=16.0,c0=4.25e-26; AdualR: c-4=1.17e-42,c-3=2.46e-39,c-2=1.27e-35,c-1=0.0454,c0=3.64e-29; Aped: c-4=4.99e-42,c-3=3.75e-38,c-2=1.51e-35,c-1=0.677,c0=2.3e-28; Aant: c-4=6.65e-45,c-3=3.33e-41,c-2=7.39e-38,c-1=0.15,c0=1.15e-30; ApedX: c-4=4.41e-40,c-3=5.17e-36,c-2=8.38e-33,c-1=4.04,c0=1.62e-26
   Laurent at iK', r=0.001: A: c-4=1.24e-51,c-3=3.74e-46,c-2=9.19e-43,c-1=0.411,c0=2.11e-39; Adag: c-4=2.2e-40,c-3=2.09e-36,c-2=1.1e-34,c-1=11.2,c0=3.07e-28; Apol: c-4=4.53e-40,c-3=8.9e-37,c-2=3.59e-34,c-1=16.0,c0=8.37e-29; AdualR: c-4=8.87e-43,c-3=9.62e-40,c-2=1.34e-37,c-1=0.0454,c0=6.5e-31; Aped: c-4=6.24e-43,c-3=3.65e-38,c-2=4.36e-37,c-1=0.677,c0=1.68e-33; Aant: c-4=6.1e-45,c-3=1.13e-42,c-2=6.2e-39,c-1=0.15,c0=5.19e-33; ApedX: c-4=2.16e-39,c-3=9.16e-37,c-2=1.34e-33,c-1=4.04,c0=1.57e-27
   Laurent at iK', r=0.0003: A: c-4=4.45e-53,c-3=2.07e-46,c-2=9.17e-43,c-1=0.411,c0=4.1e-38; Adag: c-4=9.75e-40,c-3=1.71e-36,c-2=6.01e-33,c-1=11.2,c0=1.13e-25; Apol: c-4=7.9e-40,c-3=2.35e-36,c-2=9.16e-33,c-1=16.0,c0=4.16e-26; AdualR: c-4=8.29e-43,c-3=2.63e-39,c-2=1.71e-35,c-1=0.0454,c0=2.83e-29; Aped: c-4=1.25e-42,c-3=3.85e-38,c-2=4.22e-36,c-1=0.677,c0=7.52e-29; Aant: c-4=4.45e-45,c-3=1.08e-42,c-2=4.95e-38,c-1=0.15,c0=5.46e-31; ApedX: c-4=1.21e-39,c-3=2.97e-36,c-2=1.05e-32,c-1=4.04,c0=1.33e-25
   residue ratios at u0 vs real-member invariants: Apol/Adag (1.4272246466737 + 6.6278899573004e-33j) 1.4272246466737 | AdualR/Adag (0.0040533840631472 + 4.6674528111443e-35j) 0.0040533840631472 | ApedX/AdualR (89.000178423794 - 2.1246370076669e-29j) 89.000178423794 | Aped/AdualR (14.919081997947 - 3.1366192868085e-32j) 14.919081997947 | Adag/Aant (-74.417501017085 + 7.0020303394652e-31j) -74.417501017085
   grid cells (u/K, Im u/K') with |F| > 1e4: {'A': [], 'Adag': [], 'Apol': [], 'AdualR': [], 'Aped': [], 'Aant': [], 'ApedX': []}
   predicted (Re/K, Im/K'): f1-isotropic coset [('0.0', '1.0'), ('0.4', '1.0'), ('0.8', '1.0'), ('1.2', '1.0'), ('1.6', '1.0'), ('2.0', '1.0'), ('2.4', '1.0'), ('2.8', '1.0'), ('3.2', '1.0'), ('3.6', '1.0')] 
     f2-isotropic coset [('0.0', '1.0'), ('0.4', '1.0'), ('0.8', '1.0'), ('1.2', '1.0'), ('1.6', '1.0'), ('2.0', '1.0'), ('2.4', '1.0'), ('2.8', '1.0'), ('3.2', '1.0'), ('3.6', '1.0')] 
     Jacobi coset [('0.0', '1.0'), ('0.4', '1.0'), ('0.8', '1.0'), ('1.2', '1.0'), ('1.6', '1.0'), ('2.0', '1.0'), ('2.4', '1.0'), ('2.8', '1.0'), ('3.2', '1.0'), ('3.6', '1.0')]
=== family a=1 b=0.8 N=7 tau=2: lambda=0.47220180483038746759 k^2=0.682078876537861 K=2.04976282286 K'=1.72452219579 h=2.34258608326; real-member validation (closure, tangency, reflection law) worst=4.49e-38
   parity |F(c+w)+F(c-w)|/max(|F|,1) at c=u0=K-Delta+iK': {'A': '2.09e-39', 'Adag': '4.5e-36', 'Apol': '9.65e-36', 'AdualR': '6.1e-36', 'Aped': '8.26e-39', 'Aant': '5.61e-39', 'ApedX': '3.88e-37'}
   parity |F(c+w)+F(c-w)|/max(|F|,1) at c=iK': {'A': '1.96e-40', 'Adag': '2.14', 'Apol': '2.14', 'AdualR': '2.14', 'Aped': '1.75', 'Aant': '2.04', 'ApedX': '1.99'}
   parity |F(c+w)+F(c-w)|/max(|F|,1) at c=u0+2K: {'A': '5.03e-39', 'Adag': '3.17e-39', 'Apol': '1.5e-38', 'AdualR': '1.58e-39', 'Aped': '1.77e-36', 'Aant': '1.54e-38', 'ApedX': '1.92e-36'}
   sign flip |F(u+2iK')+F(u)|: {'A': '3.59e-42', 'Adag': '1.15e-41', 'Apol': '4.11e-40', 'AdualR': '2.87e-42', 'Aped': '0.0', 'Aant': '1.85e-40', 'ApedX': '2.91e-41'}  periodicity h,4K: {'A': '1.38e-40', 'Adag': '7.37e-40', 'Apol': '6.42e-39', 'AdualR': '1.06e-40', 'Aped': '7.26e-41', 'Aant': '1.5e-39', 'ApedX': '2.08e-40'}
   Laurent at u0, r=0.001: A: c-4=3.06e-53,c-3=6.68e-50,c-2=1.08e-47,c-1=2.98e-45,c0=1.42e-39; Adag: c-4=1.32e-41,c-3=5.84e-38,c-2=6.01e-36,c-1=1.36,c0=6.51e-30; Apol: c-4=2.52e-40,c-3=1.07e-36,c-2=8.61e-35,c-1=11.6,c0=1.29e-28; AdualR: c-4=4.88e-42,c-3=2.15e-39,c-2=4.48e-36,c-1=0.404,c0=3.02e-30; Aped: c-4=1.33e-49,c-3=1.28e-46,c-2=3.54e-43,c-1=2.12e-39,c0=1.32e-37; Aant: c-4=3.26e-52,c-3=8.27e-49,c-2=7.56e-47,c-1=1.14e-43,c0=2.39e-38; ApedX: c-4=8.57e-43,c-3=4.0e-39,c-2=1.06e-37,c-1=1.45,c0=2.86e-31
   Laurent at u0, r=0.0003: A: c-4=2.59e-55,c-3=5.89e-52,c-2=1.09e-48,c-1=6.44e-45,c0=1.55e-39; Adag: c-4=2.08e-42,c-3=3.69e-38,c-2=6.44e-35,c-1=1.36,c0=1.17e-27; Apol: c-4=1.0e-40,c-3=8.42e-37,c-2=8.52e-34,c-1=11.6,c0=2.13e-26; AdualR: c-4=3.18e-42,c-3=8.57e-39,c-2=2.11e-35,c-1=0.404,c0=2.18e-28; Aped: c-4=7.98e-51,c-3=6.29e-47,c-2=5.89e-44,c-1=1.55e-39,c0=9.84e-37; Aant: c-4=3.02e-54,c-3=6.65e-51,c-2=1.81e-47,c-1=1.31e-43,c0=2.54e-38; ApedX: c-4=1.58e-42,c-3=3.28e-39,c-2=3.67e-36,c-1=1.45,c0=3.45e-30
   Laurent at iK', r=0.001: A: c-4=9.09e-52,c-3=1.36e-46,c-2=1.56e-42,c-1=0.499,c0=1.12e-38; Adag: c-4=4.63e-52,c-3=3.95e-49,c-2=1.7e-46,c-1=5.67e-43,c0=3.64; Apol: c-4=1.3e-50,c-3=3.43e-47,c-2=2.34e-44,c-1=3.78e-42,c0=31.2; AdualR: c-4=5.79e-52,c-3=1.69e-49,c-2=2.04e-46,c-1=7.02e-43,c0=1.08; Aped: c-4=1.18e-51,c-3=1.7e-48,c-2=1.33e-45,c-1=1.32e-42,c0=0.878; Aant: c-4=5.79e-46,c-3=6.69e-42,c-2=1.08,c-1=1.51,c0=5.16; ApedX: c-4=7.9e-52,c-3=3.38e-49,c-2=9.88e-46,c-1=9.66e-43,c0=8.43
   Laurent at iK', r=0.0003: A: c-4=5.17e-53,c-3=2.01e-47,c-2=1.55e-42,c-1=0.499,c0=1.69e-38; Adag: c-4=2.86e-54,c-3=2.43e-51,c-2=2.81e-47,c-1=1.45e-43,c0=3.64; Apol: c-4=1.93e-52,c-3=9.31e-49,c-2=4.44e-45,c-1=8.66e-42,c0=31.2; AdualR: c-4=3.08e-54,c-3=2.24e-50,c-2=3.9e-47,c-1=8.19e-45,c0=1.08; Aped: c-4=6.12e-53,c-3=7.25e-50,c-2=4.23e-46,c-1=1.93e-42,c0=0.878; Aant: c-4=8.67e-47,c-3=6.69e-42,c-2=1.08,c-1=1.51,c0=5.16; ApedX: c-4=3.4e-54,c-3=1.95e-50,c-2=3.57e-47,c-1=3.0e-43,c0=8.43
   residue ratios at u0 vs real-member invariants: Apol/Adag (8.5751160345842 + 5.5249774050724e-33j) 8.5751160345842 | AdualR/Adag (0.29803420388682 + 4.9931646742932e-34j) 0.29803420388682 | ApedX/AdualR (-3.6019920289183 + 6.2199748276692e-33j) 0.5749117722319 | Aped/AdualR (-5.2577716243218e-39 + 3.0445088680504e-43j) 0.80976015661604 | Adag/Aant (-1.1914963808285e+43 - 5.4932028359956e+41j) 0.44824741903867
   grid cells (u/K, Im u/K') with |F| > 1e4: {'A': [], 'Adag': [], 'Apol': [], 'AdualR': [], 'Aped': [], 'Aant': [], 'ApedX': []}
   predicted (Re/K, Im/K'): f1-isotropic coset [('0.4286', '1.0'), ('1.0', '1.0'), ('1.571', '1.0'), ('2.143', '1.0'), ('2.714', '1.0'), ('3.286', '1.0'), ('3.857', '1.0')] 
     f2-isotropic coset [('0.1429', '1.0'), ('0.7143', '1.0'), ('1.286', '1.0'), ('1.857', '1.0'), ('2.429', '1.0'), ('3.0', '1.0'), ('3.571', '1.0')] 
     Jacobi coset [('0.0', '1.0'), ('0.2857', '1.0'), ('0.5714', '1.0'), ('0.8571', '1.0'), ('1.143', '1.0'), ('1.429', '1.0'), ('1.714', '1.0'), ('2.0', '1.0'), ('2.286', '1.0'), ('2.571', '1.0'), ('2.857', '1.0'), ('3.143', '1.0'), ('3.429', '1.0'), ('3.714', '1.0')]
=== family a=1 b=0.5 N=12 tau=1: lambda=0.031162988959724260091 k^2=0.774124018233673 K=2.20212560376 K'=1.67291021488 h=0.734041867921; real-member validation (closure, tangency, reflection law) worst=4.5e-38
   parity |F(c+w)+F(c-w)|/max(|F|,1) at c=u0=K-Delta+iK': {'A': '4.35e-40', 'Adag': '4.3e-35', 'Apol': '2.49e-35', 'AdualR': '2.71e-35', 'Aped': '1.9e-35', 'Aant': '4.71e-39', 'ApedX': '5.29e-34'}
   parity |F(c+w)+F(c-w)|/max(|F|,1) at c=iK': {'A': '1.8e-39', 'Adag': '3.36e-37', 'Apol': '1.49e-37', 'AdualR': '3.89e-39', 'Aped': '1.0e-38', 'Aant': '3.67e-36', 'ApedX': '3.7e-35'}
   parity |F(c+w)+F(c-w)|/max(|F|,1) at c=u0+2K: {'A': '1.33e-39', 'Adag': '1.09e-34', 'Apol': '3.2e-35', 'AdualR': '1.8e-35', 'Aped': '1.9e-35', 'Aant': '6.72e-38', 'ApedX': '2.92e-34'}
   sign flip |F(u+2iK')+F(u)|: {'A': '2.3e-41', 'Adag': '1.1e-39', 'Apol': '1.54e-39', 'AdualR': '3.47e-41', 'Aped': '7.89e-42', 'Aant': '5.27e-41', 'ApedX': '4.12e-40'}  periodicity h,4K: {'A': '2.62e-41', 'Adag': '2.27e-39', 'Apol': '6.21e-39', 'AdualR': '2.93e-41', 'Aped': '1.47e-41', 'Aant': '7.03e-41', 'ApedX': '1.75e-39'}
   Laurent at u0, r=0.001: A: c-4=7.65e-54,c-3=2.47e-51,c-2=8.08e-48,c-1=1.74e-44,c0=2.41e-40; Adag: c-4=1.35e-39,c-3=1.55e-36,c-2=7.31e-34,c-1=10.9,c0=1.02e-27; Apol: c-4=1.52e-39,c-3=8.07e-37,c-2=5.47e-34,c-1=12.7,c0=6.22e-28; AdualR: c-4=1.61e-42,c-3=1.8e-39,c-2=7.73e-37,c-1=0.0397,c0=9.49e-31; Aped: c-4=9.19e-42,c-3=1.87e-38,c-2=5.95e-37,c-1=0.608,c0=1.04e-29; Aant: c-4=3.59e-52,c-3=5.94e-48,c-2=1.11e-45,c-1=1.67e-42,c0=1.63e-39; ApedX: c-4=4.29e-39,c-3=4.64e-36,c-2=5.95e-33,c-1=5.43,c0=6.13e-27
   Laurent at u0, r=0.0003: A: c-4=4.63e-56,c-3=5.25e-52,c-2=1.16e-48,c-1=7.22e-45,c0=2.54e-40; Adag: c-4=1.0e-39,c-3=3.21e-36,c-2=1.56e-32,c-1=10.9,c0=1.38e-26; Apol: c-4=8.16e-40,c-3=1.21e-36,c-2=5.37e-33,c-1=12.7,c0=3.18e-26; AdualR: c-4=1.21e-42,c-3=4.37e-39,c-2=1.19e-35,c-1=0.0397,c0=6.8e-30; Aped: c-4=4.76e-42,c-3=4.06e-38,c-2=1.56e-34,c-1=0.608,c0=6.18e-28; Aant: c-4=5.1e-55,c-3=2.8e-50,c-2=5.43e-47,c-1=3.16e-43,c0=1.29e-40; ApedX: c-4=3.84e-40,c-3=4.98e-36,c-2=1.23e-32,c-1=5.43,c0=1.25e-25
   Laurent at iK', r=0.001: A: c-4=1.92e-51,c-3=3.16e-46,c-2=7.31e-42,c-1=0.348,c0=4.89e-39; Adag: c-4=1.46e-50,c-3=1.12e-46,c-2=3.37e-44,c-1=2.75e-41,c0=4.43e-38; Apol: c-4=5.93e-50,c-3=1.83e-47,c-2=2.53e-44,c-1=9.01e-41,c0=3.39e-38; AdualR: c-4=4.54e-53,c-3=4.9e-50,c-2=2.12e-46,c-1=2.97e-43,c0=1.77e-40; Aped: c-4=1.4e-51,c-3=9.71e-49,c-2=3.64e-46,c-1=3.55e-43,c0=2.53e-39; Aant: c-4=7.25e-45,c-3=2.39e-40,c-2=7.19e-39,c-1=0.143,c0=6.12e-33; ApedX: c-4=1.3e-49,c-3=4.16e-46,c-2=2.83e-42,c-1=5.78e-40,c0=1.12e-35
   Laurent at iK', r=0.0003: A: c-4=7.71e-53,c-3=1.76e-46,c-2=7.31e-42,c-1=0.348,c0=1.25e-38; Adag: c-4=1.25e-52,c-3=2.02e-48,c-2=6.18e-45,c-1=4.3e-42,c0=1.99e-38; Apol: c-4=4.67e-52,c-3=1.09e-49,c-2=1.88e-45,c-1=2.83e-42,c0=3.61e-38; AdualR: c-4=1.26e-55,c-3=6.1e-51,c-2=5.51e-48,c-1=1.05e-44,c0=3.87e-41; Aped: c-4=1.53e-53,c-3=9.16e-50,c-2=5.15e-46,c-1=1.46e-42,c0=6.51e-39; Aant: c-4=5.28e-45,c-3=2.39e-40,c-2=5.86e-38,c-1=0.143,c0=6.46e-31; ApedX: c-4=3.33e-50,c-3=4.54e-47,c-2=3.85e-43,c-1=9.65e-40,c0=5.3e-36
   residue ratios at u0 vs real-member invariants: Apol/Adag (1.1685633675157 - 1.4713862226722e-31j) 1.1685633675157 | AdualR/Adag (0.003654085144889 - 2.1625349571727e-36j) 0.003654085144889 | ApedX/AdualR (136.60506311795 - 4.1452792432064e-29j) 136.60506311795 | Aped/AdualR (15.314934855511 - 6.0127392316837e-31j) 15.314934855511 | Adag/Aant (6.5017449807835e+42 + 1.6142885418742e+40j) -76.115818038191
   grid cells (u/K, Im u/K') with |F| > 1e4: {'A': [], 'Adag': [], 'Apol': [], 'AdualR': [], 'Aped': [], 'Aant': [], 'ApedX': []}
   predicted (Re/K, Im/K'): f1-isotropic coset [('0.1667', '1.0'), ('0.5', '1.0'), ('0.8333', '1.0'), ('1.167', '1.0'), ('1.5', '1.0'), ('1.833', '1.0'), ('2.167', '1.0'), ('2.5', '1.0'), ('2.833', '1.0'), ('3.167', '1.0'), ('3.5', '1.0'), ('3.833', '1.0')] 
     f2-isotropic coset [('0.1667', '1.0'), ('0.5', '1.0'), ('0.8333', '1.0'), ('1.167', '1.0'), ('1.5', '1.0'), ('1.833', '1.0'), ('2.167', '1.0'), ('2.5', '1.0'), ('2.833', '1.0'), ('3.167', '1.0'), ('3.5', '1.0'), ('3.833', '1.0')] 
     Jacobi coset [('0.0', '1.0'), ('0.3333', '1.0'), ('0.6667', '1.0'), ('1.0', '1.0'), ('1.333', '1.0'), ('1.667', '1.0'), ('2.0', '1.0'), ('2.333', '1.0'), ('2.667', '1.0'), ('3.0', '1.0'), ('3.333', '1.0'), ('3.667', '1.0')]
