L = 2*omega_1 (quadrature)      = 5.29991625085634987194106849895
pi_3 = Gamma(1/3)^2/Gamma(2/3)  = 5.29991625085634987194106849895  diff 7.01e-46
B(1/3,1/3)                      = 5.29991625085634987194106849895
h = sqrt(3)/2 * L               = 4.58986211117157862473958251693
0. max relative |P'^2-4P^3+g3| at 4 points with |v|<=3.05: 3.64e-43
1. series(v) vs series(v-lambda), lambda in {L, L w, L w^2, L(1+w)}: max diff 5.92e-47
   control: v vs v-L/2 differ by 0.47658 (must be O(1))
2. |sm'-cm^2| 5.33e-46, |cm'+sm^2| 5.33e-46 (relative), |sm^3+cm^3-1| 3.61e-46 at 5 points; sm(1e-12)=(1.0e-12 + 0.0j), cm(1e-12)-1=(-3.33e-37 + 0.0j)
3. sm(L/3)-1 = 1.75e-46, cm(L/3) = 8.76e-47; at 2L/3: 1-3P' = 1.75e-46 (pole of sm iff 0)
   sm(wu)=w sm(u), cm(wu)=cm(u): 9.43e-46 ; conjugation symmetry: 0
4. max |Im sm|, |Im cm| on Im u = h and Im u = 0 (18 points): 0
   2ih - L(1+2w) = 0.0
5. zeros of sm + i in the strip mod L: 3
   (0.7497704548828558397945 + 3.646997258195469354795j)   |sm+i| 2.1e-46  cm^3 = (1.0 - 1.0j)  |cm| = 1.12246204831
   (1.766638750285449957314 + 1.88572970595221853989j)   |sm+i| 3.9e-47  cm^3 = (1.0 - 1.0j)  |cm| = 1.12246204831
   (2.783507045688044074833 + 3.646997258195469354795j)   |sm+i| 1.0e-46  cm^3 = (1.0 - 1.0j)  |cm| = 1.12246204831
   zeros of sm - i in the strip mod L: 3
   (0.1335489202598691388624 + 0.9428648529761092699448j)   |sm-i| 5.1e-47  cm^3 = (1.0 + 1.0j)
   (3.399728580311030775765 + 0.9428648529761092699448j)   |sm-i| 0.0  cm^3 = (1.0 + 1.0j)
   (4.416596875713624893284 + 2.70413240521936008485j)   |sm-i| 3.9e-47  cm^3 = (1.0 + 1.0j)
   2^(1/6) = 1.12246204831 ; min distance of zeros to the lines: 0.942864852976109
   pairwise |cm_i - cm_j| at Z_S: ['1.94416', '1.94416', '1.94416']
6. argument principle on [0.2,0.2+L]x[0.3,0.3+h]: winding of 1/(sm+i) = -1.00704e-46 (expect 0 = 3 - 3); winding of 1-3P' = -1.27454e-45 (expect 0: 3 zeros = poles of sm, one triple pole)
