OK   A: 1 - 2eps_-(5) - (1+eps_+(5))/(20 pi) > 0   [0.8133338830006983904705276773324035252991752065663615715901343989, 0.8133338830006983904705276773324035252991752065663615715901343989]
OK   C: e^10 >= 8 pi * 65
OK   B: 1 - (1+eps_-)/2 - (1+eps_+)/sqrt(120 pi) > 0   [0.4449872992614430916830356735081370963266025818168218651537278327, 0.4449872992614430916830356735081370963266025818168218651537278327]
OK   loc: 60*lambda(60) <= 0.5708   [0.5681065490517346880776977046692455264971701293003107487560765334, 0.5681065490517346880776977046692455264971701293003107487560765334]
OK   loc: |z-F_m| <= (120/119) lambda(60) < 0.0097   [0.009548009227760246858448700918810849184826388727736315105144130344, 0.009548009227760246858448700918810849184826388727736315105144130344]
OK   index: 60 - pi/4 - lambda(60) > 18 pi
OK   T_m maps Omega to Omega: 20 pi > 60
OK   loc radius * 2 pi m < 1 at m = 10   [0.572967622562678616371801636518056998550869578765501670922321076, 0.572967622562678616371801636518056998550869578765501670922321076]
OK   Rouche m=10: (2 pi m)|E| < (2 pi m)|u-1|   [0.5640733252655948530536627465319654116763513387191944177560719536, 0.5640733252655948530536627465319654116763513387191944177560719536] < [0.9837165046742145656054753659990918132136394259160450802500023387, 0.9837165046742145656054753659990918132136394259160450802500023387]
OK   h'(0.4) > 0
OK   D_m in Omega: 20 pi - 1/(20 pi) > 60 and Im F_m >= ln(40 pi^2)/2 > 1/(20 pi)
OK   ODE m=10: m^2 G(m) > m^2 (half-widths)   [0.3196707845371313698380657832883229899355363131261688199706364207, 0.3196707845371313698380657832883229899355363131261688199706364207] > [0.04626905120478335362364932046588170078240304861877426434629971806, 0.04626905120478335362364932046588170078240304861877426434629971806]
OK   Im F_10 <= 3.0193
OK   Q: |S-1| <= 0.0643 < 0.065   [0.06426351100803334239297850085987015043068124541984882723254176813, 0.06426351100803334239297850085987015043068124541984882723254176813]
OK   per-m rigorous checks for 450 values of m in [10, 1e10]   []
m^2 G(m) at m=10,100,1e4,1e8: ['[0.3196707845371313698380657832883229899355363131261688199706364207, 0.3196707845371313698380657832883229899355363131261688199706364207]', '[0.5665591894004053826282344414807564547597417199643802617360789345, 0.5665591894004053826282344414807564547597417199643802617360789345]', '[0.945652554993940843548418615145769432693865925272206384538805188, 0.945652554993940843548418615145769432693865925272206384538805188]', '[1.678800908354165615493537391681898182399402941253380789190574008, 1.678800908354165615493537391681898182399402941253380789190574008]']
Rouche ratio (2 pi m)|E| / (2 pi m)|u-1| at m=10,100,1e4: ['[0.5734104516752045612358916760601017748814453672189620711034357568, 0.5734104516752045612358916760601017748814453672189620711034357568]', '[0.558139756619956373636972664671922236471881568517461118237619052, 0.558139756619956373636972664671922236471881568517461118237619052]', '[0.5565078897736892135246486643307562730579460925420622868918643372, 0.5565078897736892135246486643307562730579460925420622868918643372]']
[non-rigorous] max |R1+|/eps+ = 0.49937   max |R1-|/eps- = 0.33834 (must be <= 1)
ALL RIGOROUS CHECKS PASSED
