printed e* ('-0.18272', '-0.18098', '769.085', '825.728'): rho_4 = 9.392e-06; all six: ['4.206e-01', '4.206e-01', '9.086e-01', '9.086e-01', '9.392e-06', '9.392e-06']
full double-precision point ('-0.18271900153639156', '-0.1809796744363755', '769.0851161513428', '825.7277931734245'): rho_4 = 2.034e-14 (max residual of M_2, M_3: 1.1e-74)
  Newton step 0: rho_4 = 2.034e-14 at (e3, e4) = (769.0851161513428, 825.7277931734245)
  Newton step 1: rho_4 = 3.377e-24 at (e3, e4) = (769.0851161471728282383531869231, 825.7277931780407876854642832189)
  Newton step 2: rho_4 = 2.008e-44 at (e3, e4) = (769.0851161471728282386914180479, 825.7277931780407876851261872884)
  Newton step 3: rho_4 = 9.638e-65 at (e3, e4) = (769.0851161471728282386914180479, 825.7277931780407876851261872884)
zero of M_4 on the branch: (e3, e4) = (769.085116147172828238691418047906450362, 825.727793178040787685126187288473094146), rho_4 = 9.638e-65
at the 20-digit values (769.08511614717282824, 825.72779317804078769): rho_4 = 8.675e-22
1 + 4 e1 = 0.2691239938
real Jacobian of (Re M_4, Im M_4) in (e3, e4) at the zero: det = 1.200e-24, singular values 3.502e-11 and 3.428e-14
winding number of M_4 (chart y1 = 1) along the tracked branch on the circle of radius 1e-6 about the zero: 1.000000 (branch closes: True; 148 solves; max |arg step| 0.297; max distance ratio 2.10e-09)
total 18.0s
python3 check_k4_real_zero.py  17.90s user 0.06s system 99% cpu 17.982 total
