=== check2: the disk picture (double precision) ===
pi_3 = 5.299916250856350   h = 4.589862111171579

[K1] base points of Z_S (sm = -i):
   w = 0.749770454882877 +3.646997258195222i   |sm+i| = 2.2e-15   |cm| = 1.122462
   w = 1.766638750285456 +1.885729705952335i   |sm+i| = 4.7e-16   |cm| = 1.122462
   w = 2.783507045688093 +3.646997258195658i   |sm+i| = 1.4e-15   |cm| = 1.122462
    base points of Ztilde_S (sm = +i):
   w = 0.133548920259869 +0.942864852976109i   |sm-i| = 2.8e-17   |cm| = 1.122462
   w = 3.399728580311107 +0.942864852976164i   |sm-i| = 1.2e-13   |cm| = 1.122462
   w = 4.416596875713728 +2.704132405219353i   |sm-i| = 2.8e-13   |cm| = 1.122462
   reflection check: Ztilde_S = { conj(w) + P : w in Z_S } with P = pi_3*omega ?
     conj(w)+P reduced = 3.399728580311 +0.942864852976i   min dist to Ztilde_S = 2.0e-13
     conj(w)+P reduced = 4.416596875714 +2.704132405219i   min dist to Ztilde_S = 1.4e-13
     conj(w)+P reduced = 0.133548920260 +0.942864852976i   min dist to Ztilde_S = 1.9e-13

[K2] Blaschke sums (truncated at |k| <= 14) and decay rate
   base 0.749770+3.646997i : sum = 0.518751968094   ratio k=6/5: 2.657994e-02, k=-6/-5: 2.657993e-02   (exp(-2pi/sqrt3) = 2.657993e-02)
   base 1.766639+1.885730i : sum = 0.621024978402   ratio k=6/5: 2.657992e-02, k=-6/-5: 2.657993e-02   (exp(-2pi/sqrt3) = 2.657993e-02)
   base 2.783507+3.646997i : sum = 0.363398901346   ratio k=6/5: 2.657998e-02, k=-6/-5: 2.657993e-02   (exp(-2pi/sqrt3) = 2.657993e-02)
   base 0.133549+0.942865i : sum = 0.564120404241   ratio k=6/5: 2.657994e-02, k=-6/-5: 2.657994e-02   (exp(-2pi/sqrt3) = 2.657993e-02)
   base 3.399729+0.942865i : sum = 0.392605569807   ratio k=6/5: 2.658001e-02, k=-6/-5: 2.657994e-02   (exp(-2pi/sqrt3) = 2.657993e-02)
   base 4.416597+2.704132i : sum = 0.794919411343   ratio k=6/5: 2.657991e-02, k=-6/-5: 2.657994e-02   (exp(-2pi/sqrt3) = 2.657993e-02)
   max |z| in truncated Z: 1.0   min |z|: 0.5541473252510328

[K3] boundedness on a polar grid and near the zeros
   polar grid (39 radii x 240 angles, r <= 0.975): max|F| = 0.915361 at z = 0.5203+0.8246i, max|G| = 0.927964, max|H| = 0.927986, max|F^3+G^3-H^3| = 3.7e-13
   along the gamma-orbit of the point psi^{-1}(0.5 pi_3 + 0.5 i h):
     k= -8  |z| = 0.999999999997  |F| = 0.077404  |G| = 0.101547  |H| = 0.101547  |B| = 0.086327
     k= -6  |z| = 0.999999995674  |F| = 0.077413  |G| = 0.101559  |H| = 0.101559  |B| = 0.086337
     k= -4  |z| = 0.999993876957  |F| = 0.077413  |G| = 0.101559  |H| = 0.101559  |B| = 0.086337
     k= -2  |z| = 0.991370553998  |F| = 0.077413  |G| = 0.101559  |H| = 0.101559  |B| = 0.086337
     k=  0  |z| = 0.719640870293  |F| = 0.077413  |G| = 0.101559  |H| = 0.101559  |B| = 0.086337
     k=  2  |z| = 0.999769662473  |F| = 0.077413  |G| = 0.101559  |H| = 0.101559  |B| = 0.086337
     k=  4  |z| = 0.999999837249  |F| = 0.077413  |G| = 0.101559  |H| = 0.101559  |B| = 0.086337
     k=  6  |z| = 0.999999999885  |F| = 0.077413  |G| = 0.101559  |H| = 0.101559  |B| = 0.086337
     k=  8  |z| = 1.000000000000  |F| = 0.077140  |G| = 0.101182  |H| = 0.101218  |B| = 0.085985
   on circles of radius 1e-3 (in the strip) around the base zeros, and at the zeros' orbit images:
     base 0.749770+3.646997i : max|F| = 0.188527  max|G| = 0.211547  max|H| = 0.188305
     base 1.766639+1.885730i : max|F| = 0.095516  max|G| = 0.107217  max|H| = 0.095516
     base 2.783507+3.646997i : max|F| = 0.188305  max|G| = 0.211547  max|H| = 0.188527
   sup over the grid of |q| = |sm/(sm+i)| off the 1e-3-disks: 81.584901

[K4] boundary identity at zeta = e^{it}
   t = 0.30  Im psi = 4.589862 (0 or h=4.5899)  |Im sm| = 1.2e-13  |Im cm| = 2.0e-15  |B| = 1.000000000000  |Bt| = 1.000000000000  identity err = 2.4e-13
   t = 1.00  Im psi = 4.589862 (0 or h=4.5899)  |Im sm| = 1.0e-04  |Im cm| = 1.0e-04  |B| = 1.000000000000  |Bt| = 1.000000000000  identity err = 1.3e-13
   t = 1.70  Im psi = 4.589862 (0 or h=4.5899)  |Im sm| = 3.7e-14  |Im cm| = 3.3e-13  |B| = 1.000000000000  |Bt| = 1.000000000000  identity err = 4.2e-13
   t = 2.50  Im psi = 4.589862 (0 or h=4.5899)  |Im sm| = 1.8e-13  |Im cm| = 9.1e-14  |B| = 1.000000000000  |Bt| = 1.000000000000  identity err = 2.0e-13
   t = 3.00  Im psi = 4.589862 (0 or h=4.5899)  |Im sm| = 1.6e-13  |Im cm| = 3.3e-13  |B| = 1.000000000000  |Bt| = 1.000000000000  identity err = 2.2e-13
   t = 3.50  Im psi = 0.000000 (0 or h=4.5899)  |Im sm| = 0.0e+00  |Im cm| = 0.0e+00  |B| = 1.000000000000  |Bt| = 1.000000000000  identity err = 7.3e-16
   t = 4.20  Im psi = 0.000000 (0 or h=4.5899)  |Im sm| = 0.0e+00  |Im cm| = 0.0e+00  |B| = 1.000000000000  |Bt| = 1.000000000000  identity err = 5.7e-16
   t = 5.00  Im psi = 0.000000 (0 or h=4.5899)  |Im sm| = 0.0e+00  |Im cm| = 0.0e+00  |B| = 1.000000000000  |Bt| = 1.000000000000  identity err = 3.5e-16
   t = 5.80  Im psi = 0.000000 (0 or h=4.5899)  |Im sm| = 0.0e+00  |Im cm| = 0.0e+00  |B| = 1.000000000000  |Bt| = 1.000000000000  identity err = 4.0e-16
   worst identity error: 4.2e-13

[K5] pseudocontinuation: sm(psi(z)) vs conj(sm(psi(1/conj z))) for |z| > 1
   z = (1.5+0.7j) : Im psi(z) = 5.894911 ; sm(psi(z)) - conj(sm(psi(1/conj z))) = 4.5e-14 ; cm: 2.4e-13
   z = (-2+0.1j) : Im psi(z) = 6.787859 ; sm(psi(z)) - conj(sm(psi(1/conj z))) = 6.3e-13 ; cm: 7.4e-13
   z = (0.3-1.4j) : Im psi(z) = -0.524163 ; sm(psi(z)) - conj(sm(psi(1/conj z))) = 4.0e-16 ; cm: 2.3e-16
   z = (3+3j) : Im psi(z) = 6.389087 ; sm(psi(z)) - conj(sm(psi(1/conj z))) = 6.0e-13 ; cm: 2.0e-13
   z = (-1.2-0.4j) : Im psi(z) = -0.940154 ; sm(psi(z)) - conj(sm(psi(1/conj z))) = 6.3e-16 ; cm: 3.1e-16

DONE check2
