=== (a)-(c): parametrisation, side formulas, Proposition 3 and Lemma 6 against reflection-law orbits ===
  max error cn Delta = b/b: 5.5936e-35
  max error a = a dn/cn: 1.0878e-34
  max error contact step 2Delta: 3.3349e-33
  max error vertex formula: 8.2073e-34
  max error sin omega & h1h2=b^2: 1.3896e-33
  max error L formula: 3.6209e-33
  max error lr formula: 2.2373e-34
  max error Lemma 6 summand: 5.3e-31
  max error Prop 3 (mu=0.3): 8.9381e-30
  max error Thm A (kappa=2-mu*): 8.8126e-30

=== (d) Theorem 8: S(v) = sum phi(v + 2 i Delta) at random complex v ===
  a=1.6 b=1.0 N=6 v=(-0.5003 - 1.469j): |S(mu*)| = 9.8228e-40   |S(mu*+0.1)| = 0.38519
  a=1.6 b=1.0 N=6 v=(1.951 - 0.6041j): |S(mu*)| = 2.6172e-40   |S(mu*+0.1)| = 0.25877
  a=1.6 b=1.0 N=6 v=(-0.7895 - 0.919j): |S(mu*)| = 2.9384e-40   |S(mu*+0.1)| = 0.27002
  a=1.6 b=1.0 N=5 v=(0.396 - 1.015j): |S(mu*)| = 8.7848e-41   |S(mu*+0.1)| = 0.16807
  a=1.6 b=1.0 N=5 v=(-2.254 - 0.2012j): |S(mu*)| = 6.0353e-41   |S(mu*+0.1)| = 0.17078
  a=1.6 b=1.0 N=5 v=(0.3725 - 0.977j): |S(mu*)| = 1.2898e-40   |S(mu*+0.1)| = 0.16885
  a=2.0 b=1.0 N=7 v=(0.3193 - 0.4353j): |S(mu*)| = 9.6781e-41   |S(mu*+0.1)| = 0.17194
  a=2.0 b=1.0 N=7 v=(2.748 - 1.226j): |S(mu*)| = 3.8057e-40   |S(mu*+0.1)| = 0.17474
  a=2.0 b=1.0 N=7 v=(2.872 - 0.2636j): |S(mu*)| = 1.8941e-40   |S(mu*+0.1)| = 0.17194
  a=1.0 b=0.35 N=10 v=(0.02361 - 1.056j): |S(mu*)| = 3.8008e-40   |S(mu*+0.1)| = 0.11007
  a=1.0 b=0.35 N=10 v=(1.314 - 0.9301j): |S(mu*)| = 2.4727e-40   |S(mu*+0.1)| = 0.11826
  a=1.0 b=0.35 N=10 v=(-0.9506 - 1.429j): |S(mu*)| = 3.8233e-40   |S(mu*+0.1)| = 0.066306
  a=1.5 b=1.0 N=4 v=(-0.9629 + 1.402j): |S(mu*)| = 0.0   |S(mu*+0.1)| = 0.2645
  a=1.5 b=1.0 N=4 v=(2.873 + 0.7336j): |S(mu*)| = 0.0   |S(mu*+0.1)| = 0.11176
  a=1.5 b=1.0 N=4 v=(-2.979 + 1.321j): |S(mu*)| = 0.0   |S(mu*+0.1)| = 0.14559
  a=1.2 b=1.0 N=9 v=(2.225 + 0.8125j): |S(mu*)| = 8.8944e-40   |S(mu*+0.1)| = 1.077
  a=1.2 b=1.0 N=9 v=(-1.927 - 1.202j): |S(mu*)| = 9.6352e-40   |S(mu*+0.1)| = 1.077
  a=1.2 b=1.0 N=9 v=(-0.5128 + 1.157j): |S(mu*)| = 8.7274e-40   |S(mu*+0.1)| = 1.077

=== (e) Lemma 7: antiperiodicity, holomorphy at iK', principal parts at p+ and p- (contour integrals) ===
  a=1.6 N=6: |phi(u+2iK') + phi(u)| = 2.2414e-41
    |phi(iK' + 1e-3)| = 0.0048738
    |phi(iK' + 1e-6)| = 4.8738e-6
    mu*: Res(p+) = (2.86262e-47 + 1.7063e-41j), Res(p-) = (2.6362e-46 + 1.93879e-41j), c2(p+) = (3.25676e-47 + 0.416667j), c2(p-) = (-1.86279e-47 - 0.416667j), c2(p+)+c2(p-) = 1.394e-47
    mu*+0.1: Res(p+) = (1.14308e-47 + 0.0284831j), Res(p-) = (2.78195e-46 + 0.0284831j), c2(p+) = (-1.75082e-43 + 0.416667j), c2(p-) = (-1.75133e-43 - 0.416667j), c2(p+)+c2(p-) = 3.502e-43
  a=2.0 N=5: |phi(u+2iK') + phi(u)| = 0.0
    |phi(iK' + 1e-3)| = 0.00074052
    |phi(iK' + 1e-6)| = 7.4052e-7
    mu*: Res(p+) = (7.68489e-47 + 6.11835e-42j), Res(p-) = (-1.65472e-46 + 7.12676e-42j), c2(p+) = (1.20624e-47 + 0.180535j), c2(p-) = (-1.45476e-47 - 0.180535j), c2(p+)+c2(p-) = 2.485e-48
    mu*+0.1: Res(p+) = (7.11719e-47 + 0.0119073j), Res(p-) = (-1.74029e-46 + 0.0119073j), c2(p+) = (4.86677e-44 + 0.180535j), c2(p-) = (4.86411e-44 - 0.180535j), c2(p+)+c2(p-) = 9.731e-44

=== (f) Lemma 1 on random polygons: A*_f = sum T_i (1 - s_i s'_i / h_i^2) ===
  max relative error over 200 random polygons: 3.1111e-39
