[PASS] residue of psi*w at x0 is affine in mu with a unique zero
[PASS] the zero equals mu* (first printed form)
[PASS] the two printed forms of mu* agree
[PASS] 2 delta^2 - gamma(1+delta^2) = sigma(m'^2 + delta^2)
   eps^-2 coefficient of psi*W: -(m**2*sigma**2 - 2*sigma + 1)/(m**4*sigma**3)
[PASS] A0'(x0) = -m^2(gamma - sigma delta^2)/gamma
[PASS] A0(x0) = -(gamma - sigma delta^2)/sigma
[PASS] (w'/w)(x0) = -m^2 sigma (1+delta^2)/(2 delta^2)
[PASS] w'/w = (2x-1)/(2x(1-x)) for w = (x(1-x))^(-1/2)
[PASS] 2 - mu* = kappa(a, b, lam) under Lemma 4.4(i)
[PASS] Lemma 4.4(i) consistent: a^2 - lam = a''^2 = 1, b^2 - lam = b''^2 = m'^2, a^2 - b^2 = c^2 = m^2
[PASS] converse substitution consistent: gamma + sigma = 1, delta^2 = 1 - m^2 sigma, m'^2 = 1 - m^2
[PASS] mu* = (a^2+b^2)(a^2b^2 - lam(a^2+b^2))/(2a^2b^2(b^2-lam))
[PASS] 2 - mu* = kappa directly in (a, b, lam)
[PASS] printed pieces: gamma - sigma delta^2 = b''^2(a^2b^2 - lam(a^2+b^2))/(a''^2 b^4); m'^2+delta^2 = b''^2(a^2+b^2)/(a''^2b^2); 2 gamma delta^2 m'^2 = 2a^2 b''^6/(a''^4 b^4)
[PASS] DLMF facts used in Section 4.3 (quarter/half-period rules, identity (4.1), residues at iK') -- max error 8.34e-20
[PASS] k=0.6, N=3: principal parts at p-, p+ + 2iK', p- + 2iK' are (-c2,c1), (-c2,-c1), (c2,-c1) -- (c2,c1) at p+ = ((5.1979e-32 - 0.515596j), (-2.74156e-31 + 1.60249j)), max deviation 6.76e-31
[PASS] k=0.6, N=3: residue at p+ vanishes for mu = mu* -- |c1| = 2.59e-31, mu* = -2.50389713035
[PASS] k=0.6, N=3: phi = O(u - iK') at iK' -- |phi(iK' + 1e-8)| = 1.15e-8
[PASS] k=0.6, N=3: S(v) = 0 for mu* at random complex v; S != 0 for mu* + 0.1 -- max |S(mu*)| = 5.38e-30, min |S(mu*+0.1)| = 0.341
[PASS] k=0.6, N=3: phi even, 2K- and 4iK'-periodic, 2iK'-antiperiodic
[PASS] k=0.8, N=4: principal parts at p-, p+ + 2iK', p- + 2iK' are (-c2,c1), (-c2,-c1), (c2,-c1) -- (c2,c1) at p+ = ((1.39347e-63 + 1.31477e-31j), (2.59229e-62 - 2.10363e-31j)), max deviation 3.21e-61
[PASS] k=0.8, N=4: residue at p+ vanishes for mu = mu* -- |c1| = 1.15e-61, mu* = 5.84341411275e-31
[PASS] k=0.8, N=4: phi = O(u - iK') at iK' -- |phi(iK' + 1e-8)| = 5.21e-39
[PASS] k=0.8, N=4: S(v) = 0 for mu* at random complex v; S != 0 for mu* + 0.1 -- max |S(mu*)| = 1.18e-60, min |S(mu*+0.1)| = 0.164
[PASS] k=0.8, N=4: phi even, 2K- and 4iK'-periodic, 2iK'-antiperiodic
[PASS] k=0.45, N=5: principal parts at p-, p+ + 2iK', p- + 2iK' are (-c2,c1), (-c2,-c1), (c2,-c1) -- (c2,c1) at p+ = ((-3.51121e-32 + 0.306851j), (-1.55206e-31 - 0.422409j)), max deviation 4.38e-31
[PASS] k=0.45, N=5: residue at p+ vanishes for mu = mu* -- |c1| = 9.36e-32, mu* = 0.529666939521
[PASS] k=0.45, N=5: phi = O(u - iK') at iK' -- |phi(iK' + 1e-8)| = 4.14e-8
[PASS] k=0.45, N=5: S(v) = 0 for mu* at random complex v; S != 0 for mu* + 0.1 -- max |S(mu*)| = 7.03e-31, min |S(mu*+0.1)| = 0.754
[PASS] k=0.45, N=5: phi even, 2K- and 4iK'-periodic, 2iK'-antiperiodic
[PASS] k=0.9, N=6: principal parts at p-, p+ + 2iK', p- + 2iK' are (-c2,c1), (-c2,-c1), (c2,-c1) -- (c2,c1) at p+ = ((7.57808e-33 + 0.373192j), (1.93436e-31 - 0.333934j)), max deviation 6.11e-31
[PASS] k=0.9, N=6: residue at p+ vanishes for mu = mu* -- |c1| = 1.46e-31, mu* = 1.75754968079
[PASS] k=0.9, N=6: phi = O(u - iK') at iK' -- |phi(iK' + 1e-8)| = 3.42e-8
[PASS] k=0.9, N=6: S(v) = 0 for mu* at random complex v; S != 0 for mu* + 0.1 -- max |S(mu*)| = 5.96e-30, min |S(mu*+0.1)| = 0.16
[PASS] k=0.9, N=6: phi even, 2K- and 4iK'-periodic, 2iK'-antiperiodic
[PASS] k=0.7, N=7: principal parts at p-, p+ + 2iK', p- + 2iK' are (-c2,c1), (-c2,-c1), (c2,-c1) -- (c2,c1) at p+ = ((-2.7592e-32 + 0.672862j), (7.36476e-31 - 0.565721j)), max deviation 1.61e-30
[PASS] k=0.7, N=7: residue at p+ vanishes for mu = mu* -- |c1| = 1.82e-31, mu* = 1.10925775875
[PASS] k=0.7, N=7: phi = O(u - iK') at iK' -- |phi(iK' + 1e-8)| = 1.83e-7
[PASS] k=0.7, N=7: S(v) = 0 for mu* at random complex v; S != 0 for mu* + 0.1 -- max |S(mu*)| = 7.03e-30, min |S(mu*+0.1)| = 0.607
[PASS] k=0.7, N=7: phi even, 2K- and 4iK'-periodic, 2iK'-antiperiodic
[PASS] k=0.97, N=10: principal parts at p-, p+ + 2iK', p- + 2iK' are (-c2,c1), (-c2,-c1), (c2,-c1) -- (c2,c1) at p+ = ((5.48514e-33 + 0.704061j), (-1.664e-31 - 0.394075j)), max deviation 1.31e-30
[PASS] k=0.97, N=10: residue at p+ vanishes for mu = mu* -- |c1| = 5.78e-31, mu* = 6.66793471868
[PASS] k=0.97, N=10: phi = O(u - iK') at iK' -- |phi(iK' + 1e-8)| = 1.56e-7
[PASS] k=0.97, N=10: S(v) = 0 for mu* at random complex v; S != 0 for mu* + 0.1 -- max |S(mu*)| = 3.37e-29, min |S(mu*+0.1)| = 0.0426
[PASS] k=0.97, N=10: phi even, 2K- and 4iK'-periodic, 2iK'-antiperiodic

45 of 45 checks pass; ALL PASS: True  (elapsed 10.3 s)
