  tail coef magnitude (should be ~0): 1.6225017781747483e-08
(0, 1, 2, 3) rho4 values: [np.float64(0.1027), np.float64(0.1033), np.float64(0.5011), np.float64(0.6333), np.float64(0.7029), np.float64(0.7055)]  max residual M2,M3: 3.624770633470875e-07
  tail coef magnitude (should be ~0): 7.012509283166619e-08
(1, 2, 3, 4) rho4 values: [np.float64(0.156), np.float64(0.1584), np.float64(0.174), np.float64(0.3417), np.float64(0.6293), np.float64(0.6546)]  max residual M2,M3: 1.8564606107869778e-07
  tail coef magnitude (should be ~0): 2.0641276839013452e-08
(0, 1, 5, 9) rho4 values: [np.float64(0.1874), np.float64(0.1874), np.float64(0.6196), np.float64(0.6199), np.float64(0.6947), np.float64(0.6953)]  max residual M2,M3: 4.842200585849789e-08
  tail coef magnitude (should be ~0): 5.323177410825904e-08
(2, 3, 7, 20) rho4 values: [np.float64(0.1626), np.float64(0.1627), np.float64(0.4912), np.float64(0.4974), np.float64(0.6473), np.float64(0.6531)]  max residual M2,M3: 4.1024925990756274e-07
  tail coef magnitude (should be ~0): 1.2663726596504547e-08
(0, 4, 5, 6) rho4 values: [np.float64(0.3692), np.float64(0.4011), np.float64(0.4768), np.float64(0.5689), np.float64(0.6377), np.float64(0.6448)]  max residual M2,M3: 2.278227969220291e-07
--- refined with Newton ---
(0, 1, 2, 3) [np.float64(0.10312), np.float64(0.10312), np.float64(0.56938), np.float64(0.56938), np.float64(0.70756), np.float64(0.70756)] max resid 1.0e-15
(1, 2, 3, 4) [np.float64(0.09837), np.float64(0.09837), np.float64(0.09837), np.float64(0.5172), np.float64(0.5172), np.float64(0.61716)] max resid 2.2e-15
(0, 1, 5, 9) [np.float64(0.18737), np.float64(0.18737), np.float64(0.61973), np.float64(0.61973), np.float64(0.6948), np.float64(0.6948)] max resid 2.8e-15
(2, 3, 7, 20) [np.float64(0.16173), np.float64(0.16173), np.float64(0.50863), np.float64(0.50863), np.float64(0.64117), np.float64(0.64117)] max resid 6.1e-14
