  J2: Lemma 3.5(b),(c) brute force N<=40: violations = [('b', 6, 1), ('b', 10, 1), ('b', 10, 3), ('b', 14, 1), ('b', 14, 3), ('b', 14, 5), ('b', 18, 1), ('b', 18, 5), ('b', 18, 7), ('b', 22, 1), ('b', 22, 3), ('b', 22, 5), ('b', 22, 7), ('b', 22, 9), ('b', 26, 1), ('b', 26, 3), ('b', 26, 5), ('b', 26, 7), ('b', 26, 9), ('b', 26, 11), ('b', 30, 1), ('b', 30, 7), ('b', 30, 11), ('b', 30, 13), ('b', 34, 1), ('b', 34, 3), ('b', 34, 5), ('b', 34, 7), ('b', 34, 9), ('b', 34, 11), ('b', 34, 13), ('b', 34, 15), ('b', 38, 1), ('b', 38, 3), ('b', 38, 5), ('b', 38, 7), ('b', 38, 9), ('b', 38, 11), ('b', 38, 13), ('b', 38, 15), ('b', 38, 17)]
=== a=1.5 b=1 N=3 tau=1 class=odd lambda=0.94337976665279116377 k^2=0.9566666489
  J0: |N h - 4 tau K|=3.37e-80; on_e=1.05e-81; tangency=1.27e-80; reflection=2.11e-81; Jacobi polygon == geometric orbit (either direction): 1.71e-80
  J1: order of d'.d' at t=K+iK': 2.0; at K+iK'+h: 1.0; at K+iK'-h: 1.0; |sn(K+iK'+h) - dn h/(k cn h)| = 6.89e-82; generic t=0.3+0.2i: |d'.d'|=17.0
  J3 growth exponents p (|F| ~ eps^p; -1 simple pole, -2 double, 0 regular, +1 simple zero), class odd:
    at S1: A=1.0 Ap=1.0 Abar1=1.0 Abar2=-1.0 Abarp1=1.0 Abarp2=-1.0 Astar1=3.0 Astar2=1.0 Adag1=-1.0 Adag2=1.0 Adagp1=-1.0 Adagp2=1.0 Apol1=-1.0 Apol2=1.0 AdualR1=-1.0 AdualR2=1.0 AdualP1=-1.0 AdualP2=1.0
    at S2: A=1.0 Ap=1.0 Abar1=-1.0 Abar2=1.0 Abarp1=-1.0 Abarp2=1.0 Astar1=1.0 Astar2=3.0 Adag1=1.0 Adag2=-1.0 Adagp1=1.0 Adagp2=-1.0 Apol1=1.0 Apol2=-1.0 AdualR1=1.0 AdualR2=-1.0 AdualP1=1.0 AdualP2=-1.0
    at PA: A=-1.0 Ap=-1.0 Abar1=-6.75e-10 Abar2=6.75e-10 Abarp1=-6.75e-10 Abarp2=6.75e-10 Astar1=-2.0 Astar2=-2.0 Adag1=6.75e-10 Adag2=-6.75e-10 Adagp1=6.75e-10 Adagp2=-6.75e-10 Apol1=6.75e-10 Apol2=-6.75e-10 AdualR1=6.75e-10 AdualR2=-6.75e-10 AdualP1=6.75e-10 AdualP2=-6.75e-10
  J4 (complex phases, 4 random points, class odd): A'dag1 - kap Adag1: 4.41e-80; A'dag2 - kap Adag2: 2.59e-80; kap1 - kap2 (real axis): 5.27e-82; k605a product const (odd): 7.19e-81; k904a product const (odd): 1.18e-80; k907aR product const (odd): 7.51e-80; k907aP product const (odd): 3.5e-80; k903a product const (odd): 3.28e-80; k604a product const (odd): 5.27e-80; pol product const (odd): 2.81e-79; F(u+h)=F(u): 2.6e-79; F(u+2iK')=-F(u): 3.83e-79; A,A'(u+2K)=same: 4.64e-81; F_1(u+2K)=F_2(u): 2.95e-79
  J5: Res A'dag1/Res Adag1 at S1 = (0.38102496759066543941 + 3.6853070705707918373e-49j) vs real-axis ratio 0.38102496759066543941; Res A at iK' numeric (2.25488474535444e-87 - 1.11024280715477j) closed form (0.0 - 1.11024280715477j)
=== a=1.5 b=1 N=4 tau=1 class=0mod4 lambda=0.69230769230769230769 k^2=0.8024691358
  J0: |N h - 4 tau K|=0.0; on_e=3.16e-81; tangency=1.27e-80; reflection=2.11e-81; Jacobi polygon == geometric orbit (either direction): 2.49e-81
  J1: order of d'.d' at t=K+iK': 2.0; at K+iK'+h: -1.0; at K+iK'-h: -1.0; |sn(K+iK'+h) - dn h/(k cn h)| = 4.35e+80; generic t=0.3+0.2i: |d'.d'|=3.37
  J3 growth exponents p (|F| ~ eps^p; -1 simple pole, -2 double, 0 regular, +1 simple zero), class 0mod4:
    at S1: A=1.0 Ap=-1.0 Abar1=-1.0 Abar2=-1.0 Abarp1=-1.0 Abarp2=-1.0 Astar1=1.0 Astar2=1.0 Adag1=-1.0 Adag2=-1.0 Adagp1=-1.0 Adagp2=-1.0 Apol1=-1.0 Apol2=-1.0 AdualR1=-1.0 AdualR2=-1.0 AdualP1=-1.0 AdualP2=-1.0
    at S2: A=1.0 Ap=-1.0 Abar1=-1.0 Abar2=-1.0 Abarp1=-1.0 Abarp2=-1.0 Astar1=1.0 Astar2=1.0 Adag1=-1.0 Adag2=-1.0 Adagp1=-1.0 Adagp2=-1.0 Apol1=-1.0 Apol2=-1.0 AdualR1=-1.0 AdualR2=-1.0 AdualP1=-1.0 AdualP2=-1.0
    at PA: A=-1.0 Ap=1.0 Abar1=1.0 Abar2=1.0 Abarp1=1.0 Abarp2=1.0 Astar1=-1.0 Astar2=-1.0 Adag1=1.0 Adag2=1.0 Adagp1=1.0 Adagp2=1.0 Apol1=1.0 Apol2=1.0 AdualR1=1.0 AdualR2=1.0 AdualP1=1.0 AdualP2=1.0
  J4 (complex phases, 4 random points, class 0mod4): A'dag1 - kap Adag1: 3.49e-79; A'dag2 - kap Adag2: 3.07e-79; kap1 - kap2 (real axis): 1.05e-81; A*1 - kap* A (even): 3.29e-80; A*2 - A*1 (even): 4.76e-80; F(u+h)=F(u): 1.64e-78; F(u+2iK')=-F(u): 6.33e-79; A,A'(u+2K)=same: 1.42e-80; F_1(u+2K)=F_2(u): 1.24e-78
  J5: Res A'dag1/Res Adag1 at S1 = (0.5 + 9.1948681306423039309e-57j) vs real-axis ratio 0.5; Res A*1/Res A at iK' = (2.0 + 9.9602072132084078151e-74j) vs A*1/A 2.0; Res A at iK' numeric (4.19514661188194e-87 - 2.07692307692308j) closed form (0.0 - 2.07692307692308j)
=== a=1.5 b=1 N=5 tau=1 class=odd lambda=0.49172266873827466865 k^2=0.7109231165
  J0: |N h - 4 tau K|=1.69e-80; on_e=0.0; tangency=1.48e-80; reflection=7.38e-81; Jacobi polygon == geometric orbit (either direction): 1.04e-80
  J1: order of d'.d' at t=K+iK': 2.0; at K+iK'+h: 1.0; at K+iK'-h: 1.0; |sn(K+iK'+h) - dn h/(k cn h)| = 1.03e-80; generic t=0.3+0.2i: |d'.d'|=2.21
  J3 growth exponents p (|F| ~ eps^p; -1 simple pole, -2 double, 0 regular, +1 simple zero), class odd:
    at S1: A=1.0 Ap=1.0 Abar1=1.0 Abar2=-1.0 Abarp1=1.0 Abarp2=-1.0 Astar1=1.0 Astar2=1.0 Adag1=-1.0 Adag2=1.0 Adagp1=-1.0 Adagp2=1.0 Apol1=-1.0 Apol2=1.0 AdualR1=-1.0 AdualR2=1.0 AdualP1=-1.0 AdualP2=1.0
    at S2: A=1.0 Ap=1.0 Abar1=-1.0 Abar2=1.0 Abarp1=-1.0 Abarp2=1.0 Astar1=1.0 Astar2=1.0 Adag1=1.0 Adag2=-1.0 Adagp1=1.0 Adagp2=-1.0 Apol1=1.0 Apol2=-1.0 AdualR1=1.0 AdualR2=-1.0 AdualP1=1.0 AdualP2=-1.0
    at PA: A=-1.0 Ap=-1.0 Abar1=1.56e-9 Abar2=-1.56e-9 Abarp1=1.56e-9 Abarp2=-1.56e-9 Astar1=-2.0 Astar2=-2.0 Adag1=-1.56e-9 Adag2=1.56e-9 Adagp1=-1.56e-9 Adagp2=1.56e-9 Apol1=-1.56e-9 Apol2=1.56e-9 AdualR1=-1.56e-9 AdualR2=1.56e-9 AdualP1=-1.56e-9 AdualP2=1.56e-9
  J4 (complex phases, 4 random points, class odd): A'dag1 - kap Adag1: 5.45e-79; A'dag2 - kap Adag2: 7.35e-80; kap1 - kap2 (real axis): 3.16e-81; k605a product const (odd): 1.83e-80; k904a product const (odd): 2.15e-79; k907aR product const (odd): 4.66e-80; k907aP product const (odd): 4.41e-80; k903a product const (odd): 4.69e-79; k604a product const (odd): 2.06e-79; pol product const (odd): 3.91e-79; F(u+h)=F(u): 8.75e-80; F(u+2iK')=-F(u): 3.75e-79; A,A'(u+2K)=same: 2.51e-80; F_1(u+2K)=F_2(u): 2.15e-79
  J5: Res A'dag1/Res Adag1 at S1 = (0.58189686469496841287 + 1.7392372711191561226e-49j) vs real-axis ratio 0.58189686469496841287; Res A at iK' numeric (1.39587907462322e-85 - 0.929830533866267j) closed form (0.0 - 0.929830533866267j)
=== a=2.2 b=1 N=5 tau=2 class=odd lambda=0.99996038150019675639 k^2=0.9999896828
  J0: |N h - 4 tau K|=6.42e-77; on_e=2.11e-81; tangency=1.12e-77; reflection=2.56e-78; Jacobi polygon == geometric orbit (either direction): 1.12e-77
  J1: order of d'.d' at t=K+iK': 2.0; at K+iK'+h: 1.0; at K+iK'-h: 1.0; |sn(K+iK'+h) - dn h/(k cn h)| = 2.11e-81; generic t=0.3+0.2i: |d'.d'|=2.4e+4
  J3 growth exponents p (|F| ~ eps^p; -1 simple pole, -2 double, 0 regular, +1 simple zero), class odd:
    at S1: A=1.0 Ap=1.0 Abar1=1.0 Abar2=-1.0 Abarp1=1.0 Abarp2=-1.0 Astar1=1.0 Astar2=1.0 Adag1=-1.0 Adag2=1.0 Adagp1=-1.0 Adagp2=1.0 Apol1=-1.0 Apol2=1.0 AdualR1=-1.0 AdualR2=1.0 AdualP1=-1.0 AdualP2=1.0
    at S2: A=1.0 Ap=1.0 Abar1=-1.0 Abar2=1.0 Abarp1=-1.0 Abarp2=1.0 Astar1=1.0 Astar2=1.0 Adag1=1.0 Adag2=-1.0 Adagp1=1.0 Adagp2=-1.0 Apol1=1.0 Apol2=-1.0 AdualR1=1.0 AdualR2=-1.0 AdualP1=1.0 AdualP2=-1.0
    at PA: A=-1.0 Ap=-1.0 Abar1=-5.17e-10 Abar2=5.17e-10 Abarp1=-5.17e-10 Abarp2=5.17e-10 Astar1=-2.0 Astar2=-2.0 Adag1=5.17e-10 Adag2=-5.17e-10 Adagp1=5.17e-10 Adagp2=-5.17e-10 Apol1=5.17e-10 Apol2=-5.17e-10 AdualR1=5.17e-10 AdualR2=-5.17e-10 AdualP1=5.17e-10 AdualP2=-5.17e-10
  J4 (complex phases, 4 random points, class odd): A'dag1 - kap Adag1: 1.21e-76; A'dag2 - kap Adag2: 5.35e-76; kap1 - kap2 (real axis): 1.97e-77; k605a product const (odd): 1.57e-79; k904a product const (odd): 5.23e-78; k907aR product const (odd): 1.22e-76; k907aP product const (odd): 6.17e-75; k903a product const (odd): 5.15e-76; k604a product const (odd): 1.18e-73; pol product const (odd): 2.56e-72; F(u+h)=F(u): 3.38e-72; F(u+2iK')=-F(u): 4.49e-76; A,A'(u+2K)=same: 6.78e-80; F_1(u+2K)=F_2(u): 7.38e-75
  J5: Res A'dag1/Res Adag1 at S1 = (0.41588827887167894705 + 1.5614664266229278451e-48j) vs real-axis ratio 0.41588827887167894705; Res A at iK' numeric (2.54639417784324e-85 - 1.95956308443768j) closed form (0.0 - 1.95956308443768j)
=== a=1.5 b=1 N=6 tau=1 class=2mod4 lambda=0.36 k^2=0.6613756614
  J0: |N h - 4 tau K|=1.69e-80; on_e=1.05e-81; tangency=9.49e-81; reflection=3.16e-81; Jacobi polygon == geometric orbit (either direction): 5.67e-80
  J1: order of d'.d' at t=K+iK': 2.0; at K+iK'+h: 1.0; at K+iK'-h: 1.0; |sn(K+iK'+h) - dn h/(k cn h)| = 4.51e-81; generic t=0.3+0.2i: |d'.d'|=1.86
  J3 growth exponents p (|F| ~ eps^p; -1 simple pole, -2 double, 0 regular, +1 simple zero), class 2mod4:
    at S1: A=-1.0 Ap=1.0 Abar1=-1.0 Abar2=-1.0 Abarp1=-1.0 Abarp2=-1.0 Astar1=-1.0 Astar2=-1.0 Adag1=-1.0 Adag2=-1.0 Adagp1=-1.0 Adagp2=-1.0 Apol1=-1.0 Apol2=-1.0 AdualR1=-1.0 AdualR2=-1.0 AdualP1=-1.0 AdualP2=-1.0
    at S2: A=-1.0 Ap=1.0 Abar1=-1.0 Abar2=-1.0 Abarp1=-1.0 Abarp2=-1.0 Astar1=-1.0 Astar2=-1.0 Adag1=-1.0 Adag2=-1.0 Adagp1=-1.0 Adagp2=-1.0 Apol1=-1.0 Apol2=-1.0 AdualR1=-1.0 AdualR2=-1.0 AdualP1=-1.0 AdualP2=-1.0
    at PA: A=-1.0 Ap=1.0 Abar1=-1.0 Abar2=-1.0 Abarp1=-1.0 Abarp2=-1.0 Astar1=-1.0 Astar2=-1.0 Adag1=-1.0 Adag2=-1.0 Adagp1=-1.0 Adagp2=-1.0 Apol1=-1.0 Apol2=-1.0 AdualR1=-1.0 AdualR2=-1.0 AdualP1=-1.0 AdualP2=-1.0
  J4 (complex phases, 4 random points, class 2mod4): A'dag1 - kap Adag1: 1.01e-78; A'dag2 - kap Adag2: 3.59e-79; kap1 - kap2 (real axis): 0.0; A*1 - kap* A (even): 1.73e-79; A*2 - A*1 (even): 2.93e-79; Abar1 - kap_ped A (2mod4): 5.4e-80; F(u+h)=F(u): 3.75e-79; F(u+2iK')=-F(u): 1.13e-78; A,A'(u+2K)=same: 3.64e-80; F_1(u+2K)=F_2(u): 8.52e-79
  J5: Res A'dag1/Res Adag1 at S1 = (0.65 + 2.1968951642347173863e-49j) vs real-axis ratio 0.65; Res A*1/Res A at iK' = (0.78125 - 4.4705972617227295745e-72j) vs A*1/A 0.78125; Res Abar1/Res A at iK' = (0.96 - 2.2271034024364880798e-49j) vs Abar1/A 0.96; Res A at iK' numeric (6.21696460779009e-85 - 1.6497272501841j) closed form (0.0 - 1.6497272501841j)
=== a=1.5 b=1 N=7 tau=3 class=odd lambda=0.99997186003389348662 k^2=0.9999774885
  J0: |N h - 4 tau K|=3.2e-77; on_e=1.05e-81; tangency=1.38e-77; reflection=3.13e-78; Jacobi polygon == geometric orbit (either direction): 5.35e-77
  J1: order of d'.d' at t=K+iK': 2.0; at K+iK'+h: 1.0; at K+iK'-h: 1.0; |sn(K+iK'+h) - dn h/(k cn h)| = 1.06e-85; generic t=0.3+0.2i: |d'.d'|=3.37e+4
  J3 growth exponents p (|F| ~ eps^p; -1 simple pole, -2 double, 0 regular, +1 simple zero), class odd:
    at S1: A=1.0 Ap=1.0 Abar1=1.0 Abar2=-1.0 Abarp1=1.0 Abarp2=-1.0 Astar1=1.0 Astar2=1.0 Adag1=-1.0 Adag2=1.0 Adagp1=-1.0 Adagp2=1.0 Apol1=-1.0 Apol2=1.0 AdualR1=-1.0 AdualR2=1.0 AdualP1=-1.0 AdualP2=1.0
    at S2: A=1.0 Ap=1.0 Abar1=-1.0 Abar2=1.0 Abarp1=-1.0 Abarp2=1.0 Astar1=1.0 Astar2=1.0 Adag1=1.0 Adag2=-1.0 Adagp1=1.0 Adagp2=-1.0 Apol1=1.0 Apol2=-1.0 AdualR1=1.0 AdualR2=-1.0 AdualP1=1.0 AdualP2=-1.0
    at PA: A=-1.0 Ap=-1.0 Abar1=-6.94e-10 Abar2=6.94e-10 Abarp1=-6.94e-10 Abarp2=6.94e-10 Astar1=-2.0 Astar2=-2.0 Adag1=6.94e-10 Adag2=-6.94e-10 Adagp1=6.94e-10 Adagp2=-6.94e-10 Apol1=6.94e-10 Apol2=-6.94e-10 AdualR1=6.94e-10 AdualR2=-6.94e-10 AdualP1=6.94e-10 AdualP2=-6.94e-10
  J4 (complex phases, 4 random points, class odd): A'dag1 - kap Adag1: 3.08e-77; A'dag2 - kap Adag2: 2.86e-77; kap1 - kap2 (real axis): 5.83e-78; k605a product const (odd): 5.17e-79; k904a product const (odd): 9.31e-78; k907aR product const (odd): 1.68e-76; k907aP product const (odd): 2.74e-74; k903a product const (odd): 2.99e-77; k604a product const (odd): 6.31e-74; pol product const (odd): 4.17e-73; F(u+h)=F(u): 6.86e-75; F(u+2iK')=-F(u): 3.92e-75; A,A'(u+2K)=same: 6.05e-79; F_1(u+2K)=F_2(u): 2.97e-75
  J5: Res A'dag1/Res Adag1 at S1 = (0.30179076896933957933 - 1.080427410739064544e-49j) vs real-axis ratio 0.30179076896933957933; Res A at iK' numeric (-1.33620042265469e-85 - 1.11803084224748j) closed form (0.0 - 1.11803084224748j)
=== a=1.5 b=1 N=8 tau=3 class=0mod4 lambda=0.99112013708084732346 k^2=0.992946219
  J0: |N h - 4 tau K|=4.72e-79; on_e=2.11e-81; tangency=2.49e-79; reflection=3.8e-80; Jacobi polygon == geometric orbit (either direction): 9.44e-80
  J1: order of d'.d' at t=K+iK': 2.0; at K+iK'+h: 1.0; at K+iK'-h: 1.0; |sn(K+iK'+h) - dn h/(k cn h)| = 2.11e-81; generic t=0.3+0.2i: |d'.d'|=107.0
  J3 growth exponents p (|F| ~ eps^p; -1 simple pole, -2 double, 0 regular, +1 simple zero), class 0mod4:
    at S1: A=1.0 Ap=-1.0 Abar1=-1.0 Abar2=-1.0 Abarp1=-1.0 Abarp2=-1.0 Astar1=1.0 Astar2=1.0 Adag1=-1.0 Adag2=-1.0 Adagp1=-1.0 Adagp2=-1.0 Apol1=-1.0 Apol2=-1.0 AdualR1=-1.0 AdualR2=-1.0 AdualP1=-1.0 AdualP2=-1.0
    at S2: A=1.0 Ap=-1.0 Abar1=-1.0 Abar2=-1.0 Abarp1=-1.0 Abarp2=-1.0 Astar1=1.0 Astar2=1.0 Adag1=-1.0 Adag2=-1.0 Adagp1=-1.0 Adagp2=-1.0 Apol1=-1.0 Apol2=-1.0 AdualR1=-1.0 AdualR2=-1.0 AdualP1=-1.0 AdualP2=-1.0
    at PA: A=-1.0 Ap=1.0 Abar1=1.0 Abar2=1.0 Abarp1=1.0 Abarp2=1.0 Astar1=-1.0 Astar2=-1.0 Adag1=1.0 Adag2=1.0 Adagp1=1.0 Adagp2=1.0 Apol1=1.0 Apol2=1.0 AdualR1=1.0 AdualR2=1.0 AdualP1=1.0 AdualP2=1.0
  J4 (complex phases, 4 random points, class 0mod4): A'dag1 - kap Adag1: 1.14e-78; A'dag2 - kap Adag2: 1.37e-78; kap1 - kap2 (real axis): 3.32e-80; A*1 - kap* A (even): 5.25e-78; A*2 - A*1 (even): 1.17e-77; F(u+h)=F(u): 3.89e-77; F(u+2iK')=-F(u): 1.64e-77; A,A'(u+2K)=same: 3.73e-80; F_1(u+2K)=F_2(u): 1.16e-77
  J5: Res A'dag1/Res Adag1 at S1 = (0.32058057839351465445 - 8.1707394264088223515e-49j) vs real-axis ratio 0.32058057839351465445; Res A*1/Res A at iK' = (80.985364642884162863 + 2.0856384219037383335e-70j) vs A*1/A 80.985364642884162863; Res A at iK' numeric (8.15192502678051e-86 - 2.23401090624442j) closed form (0.0 - 2.23401090624442j)
=== a=2.2 b=1 N=10 tau=3 class=2mod4 lambda=0.95353802843150187006 k^2=0.9880451753
  J0: |N h - 4 tau K|=8.77e-79; on_e=3.16e-81; tangency=2.91e-79; reflection=6.22e-80; Jacobi polygon == geometric orbit (either direction): 5.76e-79
  J1: order of d'.d' at t=K+iK': 2.0; at K+iK'+h: 1.0; at K+iK'-h: 1.0; |sn(K+iK'+h) - dn h/(k cn h)| = 8.48e-81; generic t=0.3+0.2i: |d'.d'|=21.9
  J3 growth exponents p (|F| ~ eps^p; -1 simple pole, -2 double, 0 regular, +1 simple zero), class 2mod4:
    at S1: A=-1.0 Ap=1.0 Abar1=-1.0 Abar2=-1.0 Abarp1=-1.0 Abarp2=-1.0 Astar1=-1.0 Astar2=-1.0 Adag1=-1.0 Adag2=-1.0 Adagp1=-1.0 Adagp2=-1.0 Apol1=-1.0 Apol2=-1.0 AdualR1=-1.0 AdualR2=-1.0 AdualP1=-1.0 AdualP2=-1.0
    at S2: A=-1.0 Ap=1.0 Abar1=-1.0 Abar2=-1.0 Abarp1=-1.0 Abarp2=-1.0 Astar1=-1.0 Astar2=-1.0 Adag1=-1.0 Adag2=-1.0 Adagp1=-1.0 Adagp2=-1.0 Apol1=-1.0 Apol2=-1.0 AdualR1=-1.0 AdualR2=-1.0 AdualP1=-1.0 AdualP2=-1.0
    at PA: A=-1.0 Ap=1.0 Abar1=-1.0 Abar2=-1.0 Abarp1=-1.0 Abarp2=-1.0 Astar1=-1.0 Astar2=-1.0 Adag1=-1.0 Adag2=-1.0 Adagp1=-1.0 Adagp2=-1.0 Apol1=-1.0 Apol2=-1.0 AdualR1=-1.0 AdualR2=-1.0 AdualP1=-1.0 AdualP2=-1.0
  J4 (complex phases, 4 random points, class 2mod4): A'dag1 - kap Adag1: 4.07e-79; A'dag2 - kap Adag2: 1.25e-79; kap1 - kap2 (real axis): 3.9e-80; A*1 - kap* A (even): 1.63e-78; A*2 - A*1 (even): 1.6e-78; Abar1 - kap_ped A (2mod4): 4.71e-79; F(u+h)=F(u): 5.95e-78; F(u+2iK')=-F(u): 1.39e-79; A,A'(u+2K)=same: 1.55e-80; F_1(u+2K)=F_2(u): 5.46e-79
  J5: Res A'dag1/Res Adag1 at S1 = (0.46924447331201386715 + 5.0022343676726834514e-48j) vs real-axis ratio 0.46924447331201386715; Res A*1/Res A at iK' = (11.461631460479634347 - 1.3981925511809959515e-71j) vs A*1/A 11.461631460479634347; Res Abar1/Res A at iK' = (0.10221633745069588587 - 2.3384339366124746275e-50j) vs Abar1/A 0.10221633745069588587; Res A at iK' numeric (-3.98967989391572e-86 - 3.85013728895136j) closed form (0.0 - 3.85013728895136j)
=== a=1.5 b=1 N=9 tau=4 class=odd lambda=0.99999940093564412615 k^2=0.9999995207
  J0: |N h - 4 tau K|=7.31e-75; on_e=2.11e-81; tangency=3.89e-75; reflection=5.79e-76; Jacobi polygon == geometric orbit (either direction): 7.17e-76
  J1: order of d'.d' at t=K+iK': 2.0; at K+iK'+h: 1.0; at K+iK'-h: 1.0; |sn(K+iK'+h) - dn h/(k cn h)| = 9.2e-86; generic t=0.3+0.2i: |d'.d'|=1.58e+6
  J3 growth exponents p (|F| ~ eps^p; -1 simple pole, -2 double, 0 regular, +1 simple zero), class odd:
    at S1: A=1.0 Ap=1.0 Abar1=1.0 Abar2=-1.0 Abarp1=1.0 Abarp2=-1.0 Astar1=1.0 Astar2=1.0 Adag1=-1.0 Adag2=1.0 Adagp1=-1.0 Adagp2=1.0 Apol1=-1.0 Apol2=1.0 AdualR1=-1.0 AdualR2=1.0 AdualP1=-1.0 AdualP2=1.0
    at S2: A=1.0 Ap=1.0 Abar1=-1.0 Abar2=1.0 Abarp1=-1.0 Abarp2=1.0 Astar1=1.0 Astar2=1.0 Adag1=1.0 Adag2=-1.0 Adagp1=1.0 Adagp2=-1.0 Apol1=1.0 Apol2=-1.0 AdualR1=1.0 AdualR2=-1.0 AdualP1=1.0 AdualP2=-1.0
    at PA: A=-1.0 Ap=-1.0 Abar1=-6.94e-10 Abar2=6.94e-10 Abarp1=-6.94e-10 Abarp2=6.94e-10 Astar1=-2.0 Astar2=-2.0 Adag1=6.94e-10 Adag2=-6.94e-10 Adagp1=6.94e-10 Adagp2=-6.94e-10 Apol1=6.94e-10 Apol2=-6.94e-10 AdualR1=6.94e-10 AdualR2=-6.94e-10 AdualP1=6.94e-10 AdualP2=-6.94e-10
  J4 (complex phases, 4 random points, class odd): A'dag1 - kap Adag1: 3.73e-75; A'dag2 - kap Adag2: 4.87e-74; kap1 - kap2 (real axis): 1.05e-75; k605a product const (odd): 1.17e-76; k904a product const (odd): 2.17e-75; k907aR product const (odd): 4.37e-73; k907aP product const (odd): 2.98e-70; k903a product const (odd): 4.63e-74; k604a product const (odd): 2.07e-69; pol product const (odd): 3.14e-68; F(u+h)=F(u): 9.74e-69; F(u+2iK')=-F(u): 4.88e-73; A,A'(u+2K)=same: 1.89e-79; F_1(u+2K)=F_2(u): 1.04e-72
  J5: Res A'dag1/Res Adag1 at S1 = (0.30172555693573424719 - 2.389058679778244367e-49j) vs real-axis ratio 0.30172555693573424719; Res A at iK' numeric (3.11980846572237e-85 - 1.1180339217723j) closed form (0.0 - 1.1180339217723j)
=== a=1.5 b=1 N=12 tau=5 class=0mod4 lambda=0.99980723723103774661 k^2=0.9998458136
  J0: |N h - 4 tau K|=4.18e-78; on_e=3.16e-81; tangency=2.1e-78; reflection=3.7e-79; Jacobi polygon == geometric orbit (either direction): 5.27e-77
  J1: order of d'.d' at t=K+iK': 2.0; at K+iK'+h: 1.0; at K+iK'-h: 1.0; |sn(K+iK'+h) - dn h/(k cn h)| = 6.99e-85; generic t=0.3+0.2i: |d'.d'|=4.93e+3
  J3 growth exponents p (|F| ~ eps^p; -1 simple pole, -2 double, 0 regular, +1 simple zero), class 0mod4:
    at S1: A=1.0 Ap=-1.0 Abar1=-1.0 Abar2=-1.0 Abarp1=-1.0 Abarp2=-1.0 Astar1=1.0 Astar2=1.0 Adag1=-1.0 Adag2=-1.0 Adagp1=-1.0 Adagp2=-1.0 Apol1=-1.0 Apol2=-1.0 AdualR1=-1.0 AdualR2=-1.0 AdualP1=-1.0 AdualP2=-1.0
    at S2: A=1.0 Ap=-1.0 Abar1=-1.0 Abar2=-1.0 Abarp1=-1.0 Abarp2=-1.0 Astar1=1.0 Astar2=1.0 Adag1=-1.0 Adag2=-1.0 Adagp1=-1.0 Adagp2=-1.0 Apol1=-1.0 Apol2=-1.0 AdualR1=-1.0 AdualR2=-1.0 AdualP1=-1.0 AdualP2=-1.0
    at PA: A=-1.0 Ap=1.0 Abar1=1.0 Abar2=1.0 Abarp1=1.0 Abarp2=1.0 Astar1=-1.0 Astar2=-1.0 Adag1=1.0 Adag2=1.0 Adagp1=1.0 Adagp2=1.0 Apol1=1.0 Apol2=1.0 AdualR1=1.0 AdualR2=1.0 AdualP1=1.0 AdualP2=1.0
  J4 (complex phases, 4 random points, class 0mod4): A'dag1 - kap Adag1: 3.94e-78; A'dag2 - kap Adag2: 3.74e-78; kap1 - kap2 (real axis): 2.5e-79; A*1 - kap* A (even): 2.71e-75; A*2 - A*1 (even): 2.71e-75; F(u+h)=F(u): 2.62e-74; F(u+2iK')=-F(u): 1.03e-76; A,A'(u+2K)=same: 4.48e-80; F_1(u+2K)=F_2(u): 2.3e-76
  J5: Res A'dag1/Res Adag1 at S1 = (0.30217958413982719155 + 1.7574227989564844279e-49j) vs real-axis ratio 0.30217958413982719155; Res A*1/Res A at iK' = (3746.3421727804353282 + 4.5908014148634879969e-66j) vs A*1/A 3746.3421727804353282; Res A at iK' numeric (-2.25029861175971e-85 - 2.23602484078355j) closed form (0.0 - 2.23602484078355j)
=== a=1.25 b=1 N=14 tau=5 class=2mod4 lambda=0.93802769087663527171 k^2=0.900760517
  J0: |N h - 4 tau K|=6.75e-80; on_e=2.11e-81; tangency=6.75e-80; reflection=8.43e-81; Jacobi polygon == geometric orbit (either direction): 5.74e-80
  J1: order of d'.d' at t=K+iK': 2.0; at K+iK'+h: 1.0; at K+iK'-h: 1.0; |sn(K+iK'+h) - dn h/(k cn h)| = 4.23e-81; generic t=0.3+0.2i: |d'.d'|=15.2
  J3 growth exponents p (|F| ~ eps^p; -1 simple pole, -2 double, 0 regular, +1 simple zero), class 2mod4:
    at S1: A=-1.0 Ap=1.0 Abar1=-1.0 Abar2=-1.0 Abarp1=-1.0 Abarp2=-1.0 Astar1=-1.0 Astar2=-1.0 Adag1=-1.0 Adag2=-1.0 Adagp1=-1.0 Adagp2=-1.0 Apol1=-1.0 Apol2=-1.0 AdualR1=-1.0 AdualR2=-1.0 AdualP1=-1.0 AdualP2=-1.0
    at S2: A=-1.0 Ap=1.0 Abar1=-1.0 Abar2=-1.0 Abarp1=-1.0 Abarp2=-1.0 Astar1=-1.0 Astar2=-1.0 Adag1=-1.0 Adag2=-1.0 Adagp1=-1.0 Adagp2=-1.0 Apol1=-1.0 Apol2=-1.0 AdualR1=-1.0 AdualR2=-1.0 AdualP1=-1.0 AdualP2=-1.0
    at PA: A=-1.0 Ap=1.0 Abar1=-1.0 Abar2=-1.0 Abarp1=-1.0 Abarp2=-1.0 Astar1=-1.0 Astar2=-1.0 Adag1=-1.0 Adag2=-1.0 Adagp1=-1.0 Adagp2=-1.0 Apol1=-1.0 Apol2=-1.0 AdualR1=-1.0 AdualR2=-1.0 AdualP1=-1.0 AdualP2=-1.0
  J4 (complex phases, 4 random points, class 2mod4): A'dag1 - kap Adag1: 1.55e-79; A'dag2 - kap Adag2: 1.83e-79; kap1 - kap2 (real axis): 1.05e-81; A*1 - kap* A (even): 2.01e-79; A*2 - A*1 (even): 3.6e-79; Abar1 - kap_ped A (2mod4): 1.3e-79; F(u+h)=F(u): 4.0e-78; F(u+2iK')=-F(u): 8.02e-79; A,A'(u+2K)=same: 5.56e-80; F_1(u+2K)=F_2(u): 1.87e-78
  J5: Res A'dag1/Res Adag1 at S1 = (0.27877004104143115315 - 1.5603978984469791346e-49j) vs real-axis ratio 0.27877004104143115315; Res A*1/Res A at iK' = (13.130466093839152245 + 1.6028963234858855274e-71j) vs A*1/A 13.130466093839152245; Res Abar1/Res A at iK' = (0.077465386404205910366 + 4.8184069416719372642e-51j) vs Abar1/A 0.077465386404205910366; Res A at iK' numeric (-3.09126472311551e-86 - 1.53071528135495j) closed form (0.0 - 1.53071528135495j)
