# local_checks.py  mp.dps = 60

## family a=1.5 b=1 N=3 tau=1  (N mod 4 = 3)
  at u0 in S1 (t_0 = K+iK'): growth exponent p in |F| ~ eps^p (from eps=1e-6..1e-12 and 1e-12..1e-18); -1 = simple pole, +1 = simple zero, 0 = regular nonzero
    A        p=     1.0      1.0   |F(1e-18)|=2.78e-18
    A'       p=     1.0      1.0   |F(1e-18)|=1.533e-17
    ped1     p=     1.0      1.0   |F(1e-18)|=1.12e-19
    ped2     p=    -1.0     -1.0   |F(1e-18)|=1.886e+17
    ant1     p=     3.0      3.0   |F(1e-18)|=4.099e-53
    ant2     p=     1.0      1.0   |F(1e-18)|=6.9e-17
    ped'1    p=     1.0      1.0   |F(1e-18)|=1.298e-18
    ped'2    p=    -1.0     -1.0   |F(1e-18)|=2.185e+18
    inv1     p=    -1.0     -1.0   |F(1e-18)|=6.373e+17
    inv2     p=     1.0      1.0   |F(1e-18)|=3.786e-19
    inv'1    p=    -1.0     -1.0   |F(1e-18)|=2.428e+17
    inv'2    p=     1.0      1.0   |F(1e-18)|=1.442e-19
    dual1    p=    -1.0     -1.0   |F(1e-18)|=4.317e+17
    dual2    p=     1.0      1.0   |F(1e-18)|=2.564e-19
    dualpw1  p=    -1.0     -1.0   |F(1e-18)|=1.079e+17
    dualpw2  p=     1.0      1.0   |F(1e-18)|=6.411e-20
  at u0 in S2 (t_0 = 3K+iK'): growth exponent p in |F| ~ eps^p (from eps=1e-6..1e-12 and 1e-12..1e-18); -1 = simple pole, +1 = simple zero, 0 = regular nonzero
    A        p=     1.0      1.0   |F(1e-18)|=2.78e-18
    A'       p=     1.0      1.0   |F(1e-18)|=1.533e-17
    ped1     p=    -1.0     -1.0   |F(1e-18)|=1.886e+17
    ped2     p=     1.0      1.0   |F(1e-18)|=1.12e-19
    ant1     p=     1.0      1.0   |F(1e-18)|=6.9e-17
    ant2     p=     3.0      3.0   |F(1e-18)|=4.099e-53
    ped'1    p=    -1.0     -1.0   |F(1e-18)|=2.185e+18
    ped'2    p=     1.0      1.0   |F(1e-18)|=1.298e-18
    inv1     p=     1.0      1.0   |F(1e-18)|=3.786e-19
    inv2     p=    -1.0     -1.0   |F(1e-18)|=6.373e+17
    inv'1    p=     1.0      1.0   |F(1e-18)|=1.442e-19
    inv'2    p=    -1.0     -1.0   |F(1e-18)|=2.428e+17
    dual1    p=     1.0      1.0   |F(1e-18)|=2.564e-19
    dual2    p=    -1.0     -1.0   |F(1e-18)|=4.317e+17
    dualpw1  p=     1.0      1.0   |F(1e-18)|=6.411e-20
    dualpw2  p=    -1.0     -1.0   |F(1e-18)|=1.079e+17
  at u0 in P_A (u_0 = iK'): growth exponent p in |F| ~ eps^p (from eps=1e-6..1e-12 and 1e-12..1e-18); -1 = simple pole, +1 = simple zero, 0 = regular nonzero
    A        p=    -1.0     -1.0   |F(1e-18)|=1.11e+18
    A'       p=    -1.0     -1.0   |F(1e-18)|=6.123e+18
    ped1     p=-8.315e-8 -8.315e-14   |F(1e-18)|=0.1454
    ped2     p=8.315e-8 8.315e-14   |F(1e-18)|=0.1454
    ant1     p=    -2.0     -2.0   |F(1e-18)|=8.48e+36
    ant2     p=    -2.0     -2.0   |F(1e-18)|=8.48e+36
    ped'1    p=-8.315e-8 -8.315e-14   |F(1e-18)|=1.684
    ped'2    p=8.315e-8 8.315e-14   |F(1e-18)|=1.684
    inv1     p=8.315e-8 8.315e-14   |F(1e-18)|=0.4912
    inv2     p=-8.315e-8 -8.315e-14   |F(1e-18)|=0.4912
    inv'1    p=8.315e-8 8.315e-14   |F(1e-18)|=0.1872
    inv'2    p=-8.315e-8 -8.315e-14   |F(1e-18)|=0.1872
    dual1    p=8.315e-8 8.315e-14   |F(1e-18)|=0.3327
    dual2    p=-8.315e-8 -8.315e-14   |F(1e-18)|=0.3327
    dualpw1  p=8.315e-8 8.315e-14   |F(1e-18)|=0.08318
    dualpw2  p=-8.315e-8 -8.315e-14   |F(1e-18)|=0.08318
  k806a: Res(inv'1)/Res(inv1) at S1 = (0.3810249675906654394129723 - 8.305739934710662828609469e-32j)   real-axis inv'1/inv1 = 0.3810249675906654394129723
  Lemma 3.11: Res_(iK') A = (-9.280190608235525786e-21 - 1.1102428071547707223j)   closed form = (0.0 - 1.1102428071547707223j)

## family a=1.5 b=1 N=4 tau=1  (N mod 4 = 0)
  at u0 in S1 (t_0 = K+iK'): growth exponent p in |F| ~ eps^p (from eps=1e-6..1e-12 and 1e-12..1e-18); -1 = simple pole, +1 = simple zero, 0 = regular nonzero
    A        p=     1.0      1.0   |F(1e-18)|=4.0e-18
    A'       p=    -1.0     -1.0   |F(1e-18)|=4.5e+18
    ped1     p=    -1.0     -1.0   |F(1e-18)|=9.586e+17
    ped2     p=    -1.0     -1.0   |F(1e-18)|=9.586e+17
    ant1     p=     1.0      1.0   |F(1e-18)|=8.0e-18
    ant2     p=     1.0      1.0   |F(1e-18)|=8.0e-18
    ped'1    p=    -1.0     -1.0   |F(1e-18)|=2.25e+18
    ped'2    p=    -1.0     -1.0   |F(1e-18)|=2.25e+18
    inv1     p=    -1.0     -1.0   |F(1e-18)|=1.0e+18
    inv2     p=    -1.0     -1.0   |F(1e-18)|=1.0e+18
    inv'1    p=    -1.0     -1.0   |F(1e-18)|=5.0e+17
    inv'2    p=    -1.0     -1.0   |F(1e-18)|=5.0e+17
    dual1    p=    -1.0     -1.0   |F(1e-18)|=4.444e+17
    dual2    p=    -1.0     -1.0   |F(1e-18)|=4.444e+17
    dualpw1  p=    -1.0     -1.0   |F(1e-18)|=2.222e+17
    dualpw2  p=    -1.0     -1.0   |F(1e-18)|=2.222e+17
  at u0 in S2 (t_0 = 3K+iK'): growth exponent p in |F| ~ eps^p (from eps=1e-6..1e-12 and 1e-12..1e-18); -1 = simple pole, +1 = simple zero, 0 = regular nonzero
    A        p=     1.0      1.0   |F(1e-18)|=4.0e-18
    A'       p=    -1.0     -1.0   |F(1e-18)|=4.5e+18
    ped1     p=    -1.0     -1.0   |F(1e-18)|=9.586e+17
    ped2     p=    -1.0     -1.0   |F(1e-18)|=9.586e+17
    ant1     p=     1.0      1.0   |F(1e-18)|=8.0e-18
    ant2     p=     1.0      1.0   |F(1e-18)|=8.0e-18
    ped'1    p=    -1.0     -1.0   |F(1e-18)|=2.25e+18
    ped'2    p=    -1.0     -1.0   |F(1e-18)|=2.25e+18
    inv1     p=    -1.0     -1.0   |F(1e-18)|=1.0e+18
    inv2     p=    -1.0     -1.0   |F(1e-18)|=1.0e+18
    inv'1    p=    -1.0     -1.0   |F(1e-18)|=5.0e+17
    inv'2    p=    -1.0     -1.0   |F(1e-18)|=5.0e+17
    dual1    p=    -1.0     -1.0   |F(1e-18)|=4.444e+17
    dual2    p=    -1.0     -1.0   |F(1e-18)|=4.444e+17
    dualpw1  p=    -1.0     -1.0   |F(1e-18)|=2.222e+17
    dualpw2  p=    -1.0     -1.0   |F(1e-18)|=2.222e+17
  at u0 in P_A (u_0 = iK'): growth exponent p in |F| ~ eps^p (from eps=1e-6..1e-12 and 1e-12..1e-18); -1 = simple pole, +1 = simple zero, 0 = regular nonzero
    A        p=    -1.0     -1.0   |F(1e-18)|=2.077e+18
    A'       p=     1.0      1.0   |F(1e-18)|=8.667e-18
    ped1     p=     1.0      1.0   |F(1e-18)|=1.846e-18
    ped2     p=     1.0      1.0   |F(1e-18)|=1.846e-18
    ant1     p=    -1.0     -1.0   |F(1e-18)|=4.154e+18
    ant2     p=    -1.0     -1.0   |F(1e-18)|=4.154e+18
    ped'1    p=     1.0      1.0   |F(1e-18)|=4.333e-18
    ped'2    p=     1.0      1.0   |F(1e-18)|=4.333e-18
    inv1     p=     1.0      1.0   |F(1e-18)|=1.926e-18
    inv2     p=     1.0      1.0   |F(1e-18)|=1.926e-18
    inv'1    p=     1.0      1.0   |F(1e-18)|=9.63e-19
    inv'2    p=     1.0      1.0   |F(1e-18)|=9.63e-19
    dual1    p=     1.0      1.0   |F(1e-18)|=8.56e-19
    dual2    p=     1.0      1.0   |F(1e-18)|=8.56e-19
    dualpw1  p=     1.0      1.0   |F(1e-18)|=4.28e-19
    dualpw2  p=     1.0      1.0   |F(1e-18)|=4.28e-19
  k806a: Res(inv'1)/Res(inv1) at S1 = (0.5 - 1.777659184551907193476061e-31j)   real-axis inv'1/inv1 = 0.5
  Lemma 3.11: Res_(iK') A = (-1.3376068376068376068e-20 - 2.0769230769230769231j)   closed form = (0.0 - 2.0769230769230769231j)
  even N: Res(ant1)/Res(A) at P_A = (2.0 - 3.708888546527187931149098e-41j)   real-axis ant1/A = 2.0

## family a=1.5 b=1 N=5 tau=1  (N mod 4 = 1)
  at u0 in S1 (t_0 = K+iK'): growth exponent p in |F| ~ eps^p (from eps=1e-6..1e-12 and 1e-12..1e-18); -1 = simple pole, +1 = simple zero, 0 = regular nonzero
    A        p=     1.0      1.0   |F(1e-18)|=1.311e-17
    A'       p=     1.0      1.0   |F(1e-18)|=2.08e-17
    ped1     p=     1.0      1.0   |F(1e-18)|=4.997e-18
    ped2     p=    -1.0     -1.0   |F(1e-18)|=1.418e+18
    ant1     p=     1.0      1.0   |F(1e-18)|=1.564e-16
    ant2     p=     1.0      1.0   |F(1e-18)|=1.283e-16
    ped'1    p=     1.0      1.0   |F(1e-18)|=7.722e-18
    ped'2    p=    -1.0     -1.0   |F(1e-18)|=2.191e+18
    inv1     p=    -1.0     -1.0   |F(1e-18)|=1.33e+18
    inv2     p=     1.0      1.0   |F(1e-18)|=4.687e-18
    inv'1    p=    -1.0     -1.0   |F(1e-18)|=7.738e+17
    inv'2    p=     1.0      1.0   |F(1e-18)|=2.727e-18
    dual1    p=    -1.0     -1.0   |F(1e-18)|=4.328e+17
    dual2    p=     1.0      1.0   |F(1e-18)|=1.525e-18
    dualpw1  p=    -1.0     -1.0   |F(1e-18)|=2.584e+17
    dualpw2  p=     1.0      1.0   |F(1e-18)|=9.108e-19
  at u0 in S2 (t_0 = 3K+iK'): growth exponent p in |F| ~ eps^p (from eps=1e-6..1e-12 and 1e-12..1e-18); -1 = simple pole, +1 = simple zero, 0 = regular nonzero
    A        p=     1.0      1.0   |F(1e-18)|=1.311e-17
    A'       p=     1.0      1.0   |F(1e-18)|=2.08e-17
    ped1     p=    -1.0     -1.0   |F(1e-18)|=1.418e+18
    ped2     p=     1.0      1.0   |F(1e-18)|=4.997e-18
    ant1     p=     1.0      1.0   |F(1e-18)|=1.283e-16
    ant2     p=     1.0      1.0   |F(1e-18)|=1.564e-16
    ped'1    p=    -1.0     -1.0   |F(1e-18)|=2.191e+18
    ped'2    p=     1.0      1.0   |F(1e-18)|=7.722e-18
    inv1     p=     1.0      1.0   |F(1e-18)|=4.687e-18
    inv2     p=    -1.0     -1.0   |F(1e-18)|=1.33e+18
    inv'1    p=     1.0      1.0   |F(1e-18)|=2.727e-18
    inv'2    p=    -1.0     -1.0   |F(1e-18)|=7.738e+17
    dual1    p=     1.0      1.0   |F(1e-18)|=1.525e-18
    dual2    p=    -1.0     -1.0   |F(1e-18)|=4.328e+17
    dualpw1  p=     1.0      1.0   |F(1e-18)|=9.108e-19
    dualpw2  p=    -1.0     -1.0   |F(1e-18)|=2.584e+17
  at u0 in P_A (u_0 = iK'): growth exponent p in |F| ~ eps^p (from eps=1e-6..1e-12 and 1e-12..1e-18); -1 = simple pole, +1 = simple zero, 0 = regular nonzero
    A        p=    -1.0     -1.0   |F(1e-18)|=9.298e+17
    A'       p=    -1.0     -1.0   |F(1e-18)|=1.475e+18
    ped1     p=1.922e-7 1.922e-13   |F(1e-18)|=2.662
    ped2     p=-1.922e-7 -1.922e-13   |F(1e-18)|=2.662
    ant1     p=    -2.0     -2.0   |F(1e-18)|=2.689e+36
    ant2     p=    -2.0     -2.0   |F(1e-18)|=2.689e+36
    ped'1    p=1.922e-7 1.922e-13   |F(1e-18)|=4.113
    ped'2    p=-1.922e-7 -1.922e-13   |F(1e-18)|=4.113
    inv1     p=-1.922e-7 -1.922e-13   |F(1e-18)|=2.496
    inv2     p=1.922e-7 1.922e-13   |F(1e-18)|=2.496
    inv'1    p=-1.922e-7 -1.922e-13   |F(1e-18)|=1.453
    inv'2    p=1.922e-7 1.922e-13   |F(1e-18)|=1.453
    dual1    p=-1.922e-7 -1.922e-13   |F(1e-18)|=0.8125
    dual2    p=1.922e-7 1.922e-13   |F(1e-18)|=0.8125
    dualpw1  p=-1.922e-7 -1.922e-13   |F(1e-18)|=0.4852
    dualpw2  p=1.922e-7 1.922e-13   |F(1e-18)|=0.4852
  k806a: Res(inv'1)/Res(inv1) at S1 = (0.5818968646949684128650963 + 2.625779072320206252344239e-31j)   real-axis inv'1/inv1 = 0.5818968646949684128650963
  Lemma 3.11: Res_(iK') A = (-4.3694594220477522933e-20 - 0.92983053386626694512j)   closed form = (0.0 - 0.92983053386626694512j)

## family a=1.5 b=1 N=6 tau=1  (N mod 4 = 2)
  at u0 in S1 (t_0 = K+iK'): growth exponent p in |F| ~ eps^p (from eps=1e-6..1e-12 and 1e-12..1e-18); -1 = simple pole, +1 = simple zero, 0 = regular nonzero
    A        p=    -1.0     -1.0   |F(1e-18)|=1.65e+18
    A'       p=     1.0      1.0   |F(1e-18)|=1.222e-17
    ped1     p=    -1.0     -1.0   |F(1e-18)|=1.584e+18
    ped2     p=    -1.0     -1.0   |F(1e-18)|=1.584e+18
    ant1     p=    -1.0     -1.0   |F(1e-18)|=1.289e+18
    ant2     p=    -1.0     -1.0   |F(1e-18)|=1.289e+18
    ped'1    p=    -1.0     -1.0   |F(1e-18)|=2.062e+18
    ped'2    p=    -1.0     -1.0   |F(1e-18)|=2.062e+18
    inv1     p=    -1.0     -1.0   |F(1e-18)|=1.528e+18
    inv2     p=    -1.0     -1.0   |F(1e-18)|=1.528e+18
    inv'1    p=    -1.0     -1.0   |F(1e-18)|=9.929e+17
    inv'2    p=    -1.0     -1.0   |F(1e-18)|=9.929e+17
    dual1    p=    -1.0     -1.0   |F(1e-18)|=4.073e+17
    dual2    p=    -1.0     -1.0   |F(1e-18)|=4.073e+17
    dualpw1  p=    -1.0     -1.0   |F(1e-18)|=2.716e+17
    dualpw2  p=    -1.0     -1.0   |F(1e-18)|=2.716e+17
  at u0 in S2 (t_0 = 3K+iK'): growth exponent p in |F| ~ eps^p (from eps=1e-6..1e-12 and 1e-12..1e-18); -1 = simple pole, +1 = simple zero, 0 = regular nonzero
    A        p=    -1.0     -1.0   |F(1e-18)|=1.65e+18
    A'       p=     1.0      1.0   |F(1e-18)|=1.222e-17
    ped1     p=    -1.0     -1.0   |F(1e-18)|=1.584e+18
    ped2     p=    -1.0     -1.0   |F(1e-18)|=1.584e+18
    ant1     p=    -1.0     -1.0   |F(1e-18)|=1.289e+18
    ant2     p=    -1.0     -1.0   |F(1e-18)|=1.289e+18
    ped'1    p=    -1.0     -1.0   |F(1e-18)|=2.062e+18
    ped'2    p=    -1.0     -1.0   |F(1e-18)|=2.062e+18
    inv1     p=    -1.0     -1.0   |F(1e-18)|=1.528e+18
    inv2     p=    -1.0     -1.0   |F(1e-18)|=1.528e+18
    inv'1    p=    -1.0     -1.0   |F(1e-18)|=9.929e+17
    inv'2    p=    -1.0     -1.0   |F(1e-18)|=9.929e+17
    dual1    p=    -1.0     -1.0   |F(1e-18)|=4.073e+17
    dual2    p=    -1.0     -1.0   |F(1e-18)|=4.073e+17
    dualpw1  p=    -1.0     -1.0   |F(1e-18)|=2.716e+17
    dualpw2  p=    -1.0     -1.0   |F(1e-18)|=2.716e+17
  at u0 in P_A (u_0 = iK'): growth exponent p in |F| ~ eps^p (from eps=1e-6..1e-12 and 1e-12..1e-18); -1 = simple pole, +1 = simple zero, 0 = regular nonzero
    A        p=    -1.0     -1.0   |F(1e-18)|=1.65e+18
    A'       p=     1.0      1.0   |F(1e-18)|=1.222e-17
    ped1     p=    -1.0     -1.0   |F(1e-18)|=1.584e+18
    ped2     p=    -1.0     -1.0   |F(1e-18)|=1.584e+18
    ant1     p=    -1.0     -1.0   |F(1e-18)|=1.289e+18
    ant2     p=    -1.0     -1.0   |F(1e-18)|=1.289e+18
    ped'1    p=    -1.0     -1.0   |F(1e-18)|=2.062e+18
    ped'2    p=    -1.0     -1.0   |F(1e-18)|=2.062e+18
    inv1     p=    -1.0     -1.0   |F(1e-18)|=1.528e+18
    inv2     p=    -1.0     -1.0   |F(1e-18)|=1.528e+18
    inv'1    p=    -1.0     -1.0   |F(1e-18)|=9.929e+17
    inv'2    p=    -1.0     -1.0   |F(1e-18)|=9.929e+17
    dual1    p=    -1.0     -1.0   |F(1e-18)|=4.073e+17
    dual2    p=    -1.0     -1.0   |F(1e-18)|=4.073e+17
    dualpw1  p=    -1.0     -1.0   |F(1e-18)|=2.716e+17
    dualpw2  p=    -1.0     -1.0   |F(1e-18)|=2.716e+17
  k806a: Res(inv'1)/Res(inv1) at S1 = (0.65 + 4.093479647998307571891815e-31j)   real-axis inv'1/inv1 = 0.65
  Lemma 3.11: Res_(iK') A = (-2.9866755243632823916e-20 - 1.6497272501841024024j)   closed form = (0.0 - 1.6497272501841024024j)
  even N: Res(ant1)/Res(A) at P_A = (0.78125 - 3.166707306618625773690064e-40j)   real-axis ant1/A = 0.78125
  N=2 mod 4: Res(ped1)/Res(A) at P_A = (0.96 - 7.080991297681269842641718e-41j)   real-axis ped1/A = 0.96   ant1/ped1 = 0.81380208333333333333

## family a=1.5 b=1 N=7 tau=2  (N mod 4 = 3)
  at u0 in S1 (t_0 = K+iK'): growth exponent p in |F| ~ eps^p (from eps=1e-6..1e-12 and 1e-12..1e-18); -1 = simple pole, +1 = simple zero, 0 = regular nonzero
    A        p=     1.0      1.0   |F(1e-18)|=2.144e-17
    A'       p=     1.0      1.0   |F(1e-18)|=6.346e-17
    ped1     p=     1.0      1.0   |F(1e-18)|=2.888e-18
    ped2     p=    -1.0     -1.0   |F(1e-18)|=5.836e+17
    ant1     p=     1.0      1.0   |F(1e-18)|=3.947e-16
    ant2     p=     1.0      1.0   |F(1e-18)|=2.372e-16
    ped'1    p=     1.0      1.0   |F(1e-18)|=1.105e-17
    ped'2    p=    -1.0     -1.0   |F(1e-18)|=2.232e+18
    inv1     p=    -1.0     -1.0   |F(1e-18)|=8.049e+17
    inv2     p=     1.0      1.0   |F(1e-18)|=3.984e-18
    inv'1    p=    -1.0     -1.0   |F(1e-18)|=3.625e+17
    inv'2    p=     1.0      1.0   |F(1e-18)|=1.794e-18
    dual1    p=    -1.0     -1.0   |F(1e-18)|=4.408e+17
    dual2    p=     1.0      1.0   |F(1e-18)|=2.182e-18
    dualpw1  p=    -1.0     -1.0   |F(1e-18)|=1.848e+17
    dualpw2  p=     1.0      1.0   |F(1e-18)|=9.149e-19
  at u0 in S2 (t_0 = 3K+iK'): growth exponent p in |F| ~ eps^p (from eps=1e-6..1e-12 and 1e-12..1e-18); -1 = simple pole, +1 = simple zero, 0 = regular nonzero
    A        p=     1.0      1.0   |F(1e-18)|=2.144e-17
    A'       p=     1.0      1.0   |F(1e-18)|=6.346e-17
    ped1     p=    -1.0     -1.0   |F(1e-18)|=5.836e+17
    ped2     p=     1.0      1.0   |F(1e-18)|=2.888e-18
    ant1     p=     1.0      1.0   |F(1e-18)|=2.372e-16
    ant2     p=     1.0      1.0   |F(1e-18)|=3.947e-16
    ped'1    p=    -1.0     -1.0   |F(1e-18)|=2.232e+18
    ped'2    p=     1.0      1.0   |F(1e-18)|=1.105e-17
    inv1     p=     1.0      1.0   |F(1e-18)|=3.984e-18
    inv2     p=    -1.0     -1.0   |F(1e-18)|=8.049e+17
    inv'1    p=     1.0      1.0   |F(1e-18)|=1.794e-18
    inv'2    p=    -1.0     -1.0   |F(1e-18)|=3.625e+17
    dual1    p=     1.0      1.0   |F(1e-18)|=2.182e-18
    dual2    p=    -1.0     -1.0   |F(1e-18)|=4.408e+17
    dualpw1  p=     1.0      1.0   |F(1e-18)|=9.149e-19
    dualpw2  p=    -1.0     -1.0   |F(1e-18)|=1.848e+17
  at u0 in P_A (u_0 = iK'): growth exponent p in |F| ~ eps^p (from eps=1e-6..1e-12 and 1e-12..1e-18); -1 = simple pole, +1 = simple zero, 0 = regular nonzero
    A        p=    -1.0     -1.0   |F(1e-18)|=1.083e+18
    A'       p=    -1.0     -1.0   |F(1e-18)|=3.206e+18
    ped1     p=2.277e-7 2.277e-13   |F(1e-18)|=1.298
    ped2     p=-2.277e-7 -2.277e-13   |F(1e-18)|=1.298
    ant1     p=    -2.0     -2.0   |F(1e-18)|=3.587e+36
    ant2     p=    -2.0     -2.0   |F(1e-18)|=3.587e+36
    ped'1    p=2.277e-7 2.277e-13   |F(1e-18)|=4.965
    ped'2    p=-2.277e-7 -2.277e-13   |F(1e-18)|=4.965
    inv1     p=-2.277e-7 -2.277e-13   |F(1e-18)|=1.791
    inv2     p=2.277e-7 2.277e-13   |F(1e-18)|=1.791
    inv'1    p=-2.277e-7 -2.277e-13   |F(1e-18)|=0.8066
    inv'2    p=2.277e-7 2.277e-13   |F(1e-18)|=0.8066
    dual1    p=-2.277e-7 -2.277e-13   |F(1e-18)|=0.9808
    dual2    p=2.277e-7 2.277e-13   |F(1e-18)|=0.9808
    dualpw1  p=-2.277e-7 -2.277e-13   |F(1e-18)|=0.4112
    dualpw2  p=2.277e-7 2.277e-13   |F(1e-18)|=0.4112
  k806a: Res(inv'1)/Res(inv1) at S1 = (0.4504273185243418197526557 - 1.022067464892948747950339e-31j)   real-axis inv'1/inv1 = 0.4504273185243418197526557
  Lemma 3.11: Res_(iK') A = (-7.1469018087673991009e-20 - 1.0829715530773554634j)   closed form = (0.0 - 1.0829715530773554634j)

## family a=1.5 b=1 N=8 tau=3  (N mod 4 = 0)
  at u0 in S1 (t_0 = K+iK'): growth exponent p in |F| ~ eps^p (from eps=1e-6..1e-12 and 1e-12..1e-18); -1 = simple pole, +1 = simple zero, 0 = regular nonzero
    A        p=     1.0      1.0   |F(1e-18)|=5.892e-18
    A'       p=    -1.0     -1.0   |F(1e-18)|=3.169e+19
    ped1     p=    -1.0     -1.0   |F(1e-18)|=2.976e+16
    ped2     p=    -1.0     -1.0   |F(1e-18)|=2.976e+16
    ant1     p=     1.0      1.0   |F(1e-18)|=4.771e-16
    ant2     p=     1.0      1.0   |F(1e-18)|=4.771e-16
    ped'1    p=    -1.0     -1.0   |F(1e-18)|=2.161e+18
    ped'2    p=    -1.0     -1.0   |F(1e-18)|=2.161e+18
    inv1     p=    -1.0     -1.0   |F(1e-18)|=5.779e+17
    inv2     p=    -1.0     -1.0   |F(1e-18)|=5.779e+17
    inv'1    p=    -1.0     -1.0   |F(1e-18)|=1.853e+17
    inv'2    p=    -1.0     -1.0   |F(1e-18)|=1.853e+17
    dual1    p=    -1.0     -1.0   |F(1e-18)|=4.269e+17
    dual2    p=    -1.0     -1.0   |F(1e-18)|=4.269e+17
    dualpw1  p=    -1.0     -1.0   |F(1e-18)|=2.654e+16
    dualpw2  p=    -1.0     -1.0   |F(1e-18)|=2.654e+16
  at u0 in S2 (t_0 = 3K+iK'): growth exponent p in |F| ~ eps^p (from eps=1e-6..1e-12 and 1e-12..1e-18); -1 = simple pole, +1 = simple zero, 0 = regular nonzero
    A        p=     1.0      1.0   |F(1e-18)|=5.892e-18
    A'       p=    -1.0     -1.0   |F(1e-18)|=3.169e+19
    ped1     p=    -1.0     -1.0   |F(1e-18)|=2.976e+16
    ped2     p=    -1.0     -1.0   |F(1e-18)|=2.976e+16
    ant1     p=     1.0      1.0   |F(1e-18)|=4.771e-16
    ant2     p=     1.0      1.0   |F(1e-18)|=4.771e-16
    ped'1    p=    -1.0     -1.0   |F(1e-18)|=2.161e+18
    ped'2    p=    -1.0     -1.0   |F(1e-18)|=2.161e+18
    inv1     p=    -1.0     -1.0   |F(1e-18)|=5.779e+17
    inv2     p=    -1.0     -1.0   |F(1e-18)|=5.779e+17
    inv'1    p=    -1.0     -1.0   |F(1e-18)|=1.853e+17
    inv'2    p=    -1.0     -1.0   |F(1e-18)|=1.853e+17
    dual1    p=    -1.0     -1.0   |F(1e-18)|=4.269e+17
    dual2    p=    -1.0     -1.0   |F(1e-18)|=4.269e+17
    dualpw1  p=    -1.0     -1.0   |F(1e-18)|=2.654e+16
    dualpw2  p=    -1.0     -1.0   |F(1e-18)|=2.654e+16
  at u0 in P_A (u_0 = iK'): growth exponent p in |F| ~ eps^p (from eps=1e-6..1e-12 and 1e-12..1e-18); -1 = simple pole, +1 = simple zero, 0 = regular nonzero
    A        p=    -1.0     -1.0   |F(1e-18)|=2.234e+18
    A'       p=     1.0      1.0   |F(1e-18)|=8.359e-17
    ped1     p=     1.0      1.0   |F(1e-18)|=7.848e-20
    ped2     p=     1.0      1.0   |F(1e-18)|=7.848e-20
    ant1     p=    -1.0     -1.0   |F(1e-18)|=1.809e+20
    ant2     p=    -1.0     -1.0   |F(1e-18)|=1.809e+20
    ped'1    p=     1.0      1.0   |F(1e-18)|=5.699e-18
    ped'2    p=     1.0      1.0   |F(1e-18)|=5.699e-18
    inv1     p=     1.0      1.0   |F(1e-18)|=1.524e-18
    inv2     p=     1.0      1.0   |F(1e-18)|=1.524e-18
    inv'1    p=     1.0      1.0   |F(1e-18)|=4.886e-19
    inv'2    p=     1.0      1.0   |F(1e-18)|=4.886e-19
    dual1    p=     1.0      1.0   |F(1e-18)|=1.126e-18
    dual2    p=     1.0      1.0   |F(1e-18)|=1.126e-18
    dualpw1  p=     1.0      1.0   |F(1e-18)|=6.999e-20
    dualpw2  p=     1.0      1.0   |F(1e-18)|=6.999e-20
  k806a: Res(inv'1)/Res(inv1) at S1 = (0.3205805783935146544470259 - 1.451608702026336851150787e-33j)   real-axis inv'1/inv1 = 0.3205805783935146544470259
  Lemma 3.11: Res_(iK') A = (-1.9661934819717425142e-20 - 2.2340109062444157085j)   closed form = (0.0 - 2.2340109062444157085j)
  even N: Res(ant1)/Res(A) at P_A = (80.98536464288416286328343 - 8.576788753780518738527667e-39j)   real-axis ant1/A = 80.98536464288416286328343

## family a=1.5 b=1 N=10 tau=3  (N mod 4 = 2)
  at u0 in S1 (t_0 = K+iK'): growth exponent p in |F| ~ eps^p (from eps=1e-6..1e-12 and 1e-12..1e-18); -1 = simple pole, +1 = simple zero, 0 = regular nonzero
    A        p=    -1.0     -1.0   |F(1e-18)|=2.189e+18
    A'       p=     1.0      1.0   |F(1e-18)|=6.972e-17
    ped1     p=    -1.0     -1.0   |F(1e-18)|=4.458e+17
    ped2     p=    -1.0     -1.0   |F(1e-18)|=4.458e+17
    ant1     p=    -1.0     -1.0   |F(1e-18)|=1.088e+19
    ant2     p=    -1.0     -1.0   |F(1e-18)|=1.088e+19
    ped'1    p=    -1.0     -1.0   |F(1e-18)|=2.218e+18
    ped'2    p=    -1.0     -1.0   |F(1e-18)|=2.218e+18
    inv1     p=    -1.0     -1.0   |F(1e-18)|=7.428e+17
    inv2     p=    -1.0     -1.0   |F(1e-18)|=7.428e+17
    inv'1    p=    -1.0     -1.0   |F(1e-18)|=3.2e+17
    inv'2    p=    -1.0     -1.0   |F(1e-18)|=3.2e+17
    dual1    p=    -1.0     -1.0   |F(1e-18)|=4.381e+17
    dual2    p=    -1.0     -1.0   |F(1e-18)|=4.381e+17
    dualpw1  p=    -1.0     -1.0   |F(1e-18)|=1.658e+17
    dualpw2  p=    -1.0     -1.0   |F(1e-18)|=1.658e+17
  at u0 in S2 (t_0 = 3K+iK'): growth exponent p in |F| ~ eps^p (from eps=1e-6..1e-12 and 1e-12..1e-18); -1 = simple pole, +1 = simple zero, 0 = regular nonzero
    A        p=    -1.0     -1.0   |F(1e-18)|=2.189e+18
    A'       p=     1.0      1.0   |F(1e-18)|=6.972e-17
    ped1     p=    -1.0     -1.0   |F(1e-18)|=4.458e+17
    ped2     p=    -1.0     -1.0   |F(1e-18)|=4.458e+17
    ant1     p=    -1.0     -1.0   |F(1e-18)|=1.088e+19
    ant2     p=    -1.0     -1.0   |F(1e-18)|=1.088e+19
    ped'1    p=    -1.0     -1.0   |F(1e-18)|=2.218e+18
    ped'2    p=    -1.0     -1.0   |F(1e-18)|=2.218e+18
    inv1     p=    -1.0     -1.0   |F(1e-18)|=7.428e+17
    inv2     p=    -1.0     -1.0   |F(1e-18)|=7.428e+17
    inv'1    p=    -1.0     -1.0   |F(1e-18)|=3.2e+17
    inv'2    p=    -1.0     -1.0   |F(1e-18)|=3.2e+17
    dual1    p=    -1.0     -1.0   |F(1e-18)|=4.381e+17
    dual2    p=    -1.0     -1.0   |F(1e-18)|=4.381e+17
    dualpw1  p=    -1.0     -1.0   |F(1e-18)|=1.658e+17
    dualpw2  p=    -1.0     -1.0   |F(1e-18)|=1.658e+17
  at u0 in P_A (u_0 = iK'): growth exponent p in |F| ~ eps^p (from eps=1e-6..1e-12 and 1e-12..1e-18); -1 = simple pole, +1 = simple zero, 0 = regular nonzero
    A        p=    -1.0     -1.0   |F(1e-18)|=2.189e+18
    A'       p=     1.0      1.0   |F(1e-18)|=6.972e-17
    ped1     p=    -1.0     -1.0   |F(1e-18)|=4.458e+17
    ped2     p=    -1.0     -1.0   |F(1e-18)|=4.458e+17
    ant1     p=    -1.0     -1.0   |F(1e-18)|=1.088e+19
    ant2     p=    -1.0     -1.0   |F(1e-18)|=1.088e+19
    ped'1    p=    -1.0     -1.0   |F(1e-18)|=2.218e+18
    ped'2    p=    -1.0     -1.0   |F(1e-18)|=2.218e+18
    inv1     p=    -1.0     -1.0   |F(1e-18)|=7.428e+17
    inv2     p=    -1.0     -1.0   |F(1e-18)|=7.428e+17
    inv'1    p=    -1.0     -1.0   |F(1e-18)|=3.2e+17
    inv'2    p=    -1.0     -1.0   |F(1e-18)|=3.2e+17
    dual1    p=    -1.0     -1.0   |F(1e-18)|=4.381e+17
    dual2    p=    -1.0     -1.0   |F(1e-18)|=4.381e+17
    dualpw1  p=    -1.0     -1.0   |F(1e-18)|=1.658e+17
    dualpw2  p=    -1.0     -1.0   |F(1e-18)|=1.658e+17
  k806a: Res(inv'1)/Res(inv1) at S1 = (0.4307798547953187582434851 + 2.731891548603911159025768e-32j)   real-axis inv'1/inv1 = 0.4307798547953187582434851
  Lemma 3.11: Res_(iK') A = (-6.7208161448582293799e-20 - 2.1887154329799607729j)   closed form = (0.0 - 2.1887154329799607729j)
  even N: Res(ant1)/Res(A) at P_A = (4.971841164208067186453031 - 4.651225789644396281808179e-40j)   real-axis ant1/A = 4.971841164208067186453031
  N=2 mod 4: Res(ped1)/Res(A) at P_A = (0.2036699423618593279665658 + 2.006247762890932752429625e-42j)   real-axis ped1/A = 0.2036699423618593279665658   ant1/ped1 = 24.411266122787145648

## family a=2.2 b=1 N=5 tau=2  (N mod 4 = 1)
  at u0 in S1 (t_0 = K+iK'): growth exponent p in |F| ~ eps^p (from eps=1e-6..1e-12 and 1e-12..1e-18); -1 = simple pole, +1 = simple zero, 0 = regular nonzero
    A        p=     1.0      1.0   |F(1e-18)|=2.361e-18
    A'       p=     1.0      1.0   |F(1e-18)|=4.211e-16
    ped1     p=     1.0      1.0   |F(1e-18)|=8.003e-23
    ped2     p=    -1.0     -1.0   |F(1e-18)|=3.416e+14
    ant1     p=     1.0      1.0   |F(1e-18)|=2.911e-15
    ant2     p=     1.0      1.0   |F(1e-18)|=6.899e-14
    ped'1    p=     1.0      1.0   |F(1e-18)|=1.126e-18
    ped'2    p=    -1.0     -1.0   |F(1e-18)|=4.808e+18
    inv1     p=    -1.0     -1.0   |F(1e-18)|=5.287e+17
    inv2     p=     1.0      1.0   |F(1e-18)|=1.239e-19
    inv'1    p=    -1.0     -1.0   |F(1e-18)|=2.199e+17
    inv'2    p=     1.0      1.0   |F(1e-18)|=5.151e-20
    dual1    p=    -1.0     -1.0   |F(1e-18)|=2.052e+17
    dual2    p=     1.0      1.0   |F(1e-18)|=4.808e-20
    dualpw1  p=    -1.0     -1.0   |F(1e-18)|=3.405e+14
    dualpw2  p=     1.0      1.0   |F(1e-18)|=7.977e-23
  at u0 in S2 (t_0 = 3K+iK'): growth exponent p in |F| ~ eps^p (from eps=1e-6..1e-12 and 1e-12..1e-18); -1 = simple pole, +1 = simple zero, 0 = regular nonzero
    A        p=     1.0      1.0   |F(1e-18)|=2.361e-18
    A'       p=     1.0      1.0   |F(1e-18)|=4.211e-16
    ped1     p=    -1.0     -1.0   |F(1e-18)|=3.416e+14
    ped2     p=     1.0      1.0   |F(1e-18)|=8.003e-23
    ant1     p=     1.0      1.0   |F(1e-18)|=6.899e-14
    ant2     p=     1.0      1.0   |F(1e-18)|=2.911e-15
    ped'1    p=    -1.0     -1.0   |F(1e-18)|=4.808e+18
    ped'2    p=     1.0      1.0   |F(1e-18)|=1.126e-18
    inv1     p=     1.0      1.0   |F(1e-18)|=1.239e-19
    inv2     p=    -1.0     -1.0   |F(1e-18)|=5.287e+17
    inv'1    p=     1.0      1.0   |F(1e-18)|=5.151e-20
    inv'2    p=    -1.0     -1.0   |F(1e-18)|=2.199e+17
    dual1    p=     1.0      1.0   |F(1e-18)|=4.808e-20
    dual2    p=    -1.0     -1.0   |F(1e-18)|=2.052e+17
    dualpw1  p=     1.0      1.0   |F(1e-18)|=7.977e-23
    dualpw2  p=    -1.0     -1.0   |F(1e-18)|=3.405e+14
  at u0 in P_A (u_0 = iK'): growth exponent p in |F| ~ eps^p (from eps=1e-6..1e-12 and 1e-12..1e-18); -1 = simple pole, +1 = simple zero, 0 = regular nonzero
    A        p=    -1.0     -1.0   |F(1e-18)|=1.96e+18
    A'       p=    -1.0     -1.0   |F(1e-18)|=3.495e+20
    ped1     p=-6.37e-8 -6.37e-14   |F(1e-18)|=0.0001653
    ped2     p= 6.37e-8 6.37e-14   |F(1e-18)|=0.0001653
    ant1     p=    -2.0     -2.0   |F(1e-18)|=2.203e+40
    ant2     p=    -2.0     -2.0   |F(1e-18)|=2.203e+40
    ped'1    p=-6.37e-8 -6.37e-14   |F(1e-18)|=2.327
    ped'2    p= 6.37e-8 6.37e-14   |F(1e-18)|=2.327
    inv1     p= 6.37e-8 6.37e-14   |F(1e-18)|=0.2559
    inv2     p=-6.37e-8 -6.37e-14   |F(1e-18)|=0.2559
    inv'1    p= 6.37e-8 6.37e-14   |F(1e-18)|=0.1064
    inv'2    p=-6.37e-8 -6.37e-14   |F(1e-18)|=0.1064
    dual1    p= 6.37e-8 6.37e-14   |F(1e-18)|=0.09934
    dual2    p=-6.37e-8 -6.37e-14   |F(1e-18)|=0.09934
    dualpw1  p= 6.37e-8 6.37e-14   |F(1e-18)|=0.0001648
    dualpw2  p=-6.37e-8 -6.37e-14   |F(1e-18)|=0.0001648
  k806a: Res(inv'1)/Res(inv1) at S1 = (0.4158882788716789470475983 + 1.436522484325571379741313e-31j)   real-axis inv'1/inv1 = 0.4158882788716789470475983
  Lemma 3.11: Res_(iK') A = (-8.1195343585989390062e-21 - 1.9595630844376848644j)   closed form = (0.0 - 1.9595630844376848644j)

## family a=2.2 b=1 N=6 tau=1  (N mod 4 = 2)
  at u0 in S1 (t_0 = K+iK'): growth exponent p in |F| ~ eps^p (from eps=1e-6..1e-12 and 1e-12..1e-18); -1 = simple pole, +1 = simple zero, 0 = regular nonzero
    A        p=    -1.0     -1.0   |F(1e-18)|=2.874e+18
    A'       p=     1.0      1.0   |F(1e-18)|=1.492e-17
    ped1     p=    -1.0     -1.0   |F(1e-18)|=3.334e+18
    ped2     p=    -1.0     -1.0   |F(1e-18)|=3.334e+18
    ant1     p=    -1.0     -1.0   |F(1e-18)|=1.09e+18
    ant2     p=    -1.0     -1.0   |F(1e-18)|=1.09e+18
    ped'1    p=    -1.0     -1.0   |F(1e-18)|=4.598e+18
    ped'2    p=    -1.0     -1.0   |F(1e-18)|=4.598e+18
    inv1     p=    -1.0     -1.0   |F(1e-18)|=2.349e+18
    inv2     p=    -1.0     -1.0   |F(1e-18)|=2.349e+18
    inv'1    p=    -1.0     -1.0   |F(1e-18)|=1.412e+18
    inv'2    p=    -1.0     -1.0   |F(1e-18)|=1.412e+18
    dual1    p=    -1.0     -1.0   |F(1e-18)|=1.963e+17
    dual2    p=    -1.0     -1.0   |F(1e-18)|=1.963e+17
    dualpw1  p=    -1.0     -1.0   |F(1e-18)|=1.204e+17
    dualpw2  p=    -1.0     -1.0   |F(1e-18)|=1.204e+17
  at u0 in S2 (t_0 = 3K+iK'): growth exponent p in |F| ~ eps^p (from eps=1e-6..1e-12 and 1e-12..1e-18); -1 = simple pole, +1 = simple zero, 0 = regular nonzero
    A        p=    -1.0     -1.0   |F(1e-18)|=2.874e+18
    A'       p=     1.0      1.0   |F(1e-18)|=1.492e-17
    ped1     p=    -1.0     -1.0   |F(1e-18)|=3.334e+18
    ped2     p=    -1.0     -1.0   |F(1e-18)|=3.334e+18
    ant1     p=    -1.0     -1.0   |F(1e-18)|=1.09e+18
    ant2     p=    -1.0     -1.0   |F(1e-18)|=1.09e+18
    ped'1    p=    -1.0     -1.0   |F(1e-18)|=4.598e+18
    ped'2    p=    -1.0     -1.0   |F(1e-18)|=4.598e+18
    inv1     p=    -1.0     -1.0   |F(1e-18)|=2.349e+18
    inv2     p=    -1.0     -1.0   |F(1e-18)|=2.349e+18
    inv'1    p=    -1.0     -1.0   |F(1e-18)|=1.412e+18
    inv'2    p=    -1.0     -1.0   |F(1e-18)|=1.412e+18
    dual1    p=    -1.0     -1.0   |F(1e-18)|=1.963e+17
    dual2    p=    -1.0     -1.0   |F(1e-18)|=1.963e+17
    dualpw1  p=    -1.0     -1.0   |F(1e-18)|=1.204e+17
    dualpw2  p=    -1.0     -1.0   |F(1e-18)|=1.204e+17
  at u0 in P_A (u_0 = iK'): growth exponent p in |F| ~ eps^p (from eps=1e-6..1e-12 and 1e-12..1e-18); -1 = simple pole, +1 = simple zero, 0 = regular nonzero
    A        p=    -1.0     -1.0   |F(1e-18)|=2.874e+18
    A'       p=     1.0      1.0   |F(1e-18)|=1.492e-17
    ped1     p=    -1.0     -1.0   |F(1e-18)|=3.334e+18
    ped2     p=    -1.0     -1.0   |F(1e-18)|=3.334e+18
    ant1     p=    -1.0     -1.0   |F(1e-18)|=1.09e+18
    ant2     p=    -1.0     -1.0   |F(1e-18)|=1.09e+18
    ped'1    p=    -1.0     -1.0   |F(1e-18)|=4.598e+18
    ped'2    p=    -1.0     -1.0   |F(1e-18)|=4.598e+18
    inv1     p=    -1.0     -1.0   |F(1e-18)|=2.349e+18
    inv2     p=    -1.0     -1.0   |F(1e-18)|=2.349e+18
    inv'1    p=    -1.0     -1.0   |F(1e-18)|=1.412e+18
    inv'2    p=    -1.0     -1.0   |F(1e-18)|=1.412e+18
    dual1    p=    -1.0     -1.0   |F(1e-18)|=1.963e+17
    dual2    p=    -1.0     -1.0   |F(1e-18)|=1.963e+17
    dualpw1  p=    -1.0     -1.0   |F(1e-18)|=1.204e+17
    dualpw2  p=    -1.0     -1.0   |F(1e-18)|=1.204e+17
  k806a: Res(inv'1)/Res(inv1) at S1 = (0.6011029411764705882352941 + 9.076151829142418801041516e-31j)   real-axis inv'1/inv1 = 0.6011029411764705882352941
  Lemma 3.11: Res_(iK') A = (-3.4317321139768825939e-20 - 2.8735012227844535929j)   closed form = (0.0 - 2.8735012227844535929j)
  even N: Res(ant1)/Res(A) at P_A = (-0.3792592592592592592592593 + 1.260852560221013065678716e-40j)   real-axis ant1/A = -0.3792592592592592592592593
  N=2 mod 4: Res(ped1)/Res(A) at P_A = (1.16015625 - 1.904121333881555263396149e-41j)   real-axis ped1/A = 1.16015625   ant1/ped1 = -0.32690360394064097768

## family a=2.2 b=1 N=14 tau=3  (N mod 4 = 2)
  at u0 in S1 (t_0 = K+iK'): growth exponent p in |F| ~ eps^p (from eps=1e-6..1e-12 and 1e-12..1e-18); -1 = simple pole, +1 = simple zero, 0 = regular nonzero
    A        p=    -1.0     -1.0   |F(1e-18)|=3.384e+18
    A'       p=     1.0      1.0   |F(1e-18)|=1.076e-16
    ped1     p=    -1.0     -1.0   |F(1e-18)|=2.309e+18
    ped2     p=    -1.0     -1.0   |F(1e-18)|=2.309e+18
    ant1     p=    -1.0     -1.0   |F(1e-18)|=1.428e+18
    ant2     p=    -1.0     -1.0   |F(1e-18)|=1.428e+18
    ped'1    p=    -1.0     -1.0   |F(1e-18)|=4.812e+18
    ped'2    p=    -1.0     -1.0   |F(1e-18)|=4.812e+18
    inv1     p=    -1.0     -1.0   |F(1e-18)|=1.468e+18
    inv2     p=    -1.0     -1.0   |F(1e-18)|=1.468e+18
    inv'1    p=    -1.0     -1.0   |F(1e-18)|=7.82e+17
    inv'2    p=    -1.0     -1.0   |F(1e-18)|=7.82e+17
    dual1    p=    -1.0     -1.0   |F(1e-18)|=2.054e+17
    dual2    p=    -1.0     -1.0   |F(1e-18)|=2.054e+17
    dualpw1  p=    -1.0     -1.0   |F(1e-18)|=1.115e+17
    dualpw2  p=    -1.0     -1.0   |F(1e-18)|=1.115e+17
  at u0 in S2 (t_0 = 3K+iK'): growth exponent p in |F| ~ eps^p (from eps=1e-6..1e-12 and 1e-12..1e-18); -1 = simple pole, +1 = simple zero, 0 = regular nonzero
    A        p=    -1.0     -1.0   |F(1e-18)|=3.384e+18
    A'       p=     1.0      1.0   |F(1e-18)|=1.076e-16
    ped1     p=    -1.0     -1.0   |F(1e-18)|=2.309e+18
    ped2     p=    -1.0     -1.0   |F(1e-18)|=2.309e+18
    ant1     p=    -1.0     -1.0   |F(1e-18)|=1.428e+18
    ant2     p=    -1.0     -1.0   |F(1e-18)|=1.428e+18
    ped'1    p=    -1.0     -1.0   |F(1e-18)|=4.812e+18
    ped'2    p=    -1.0     -1.0   |F(1e-18)|=4.812e+18
    inv1     p=    -1.0     -1.0   |F(1e-18)|=1.468e+18
    inv2     p=    -1.0     -1.0   |F(1e-18)|=1.468e+18
    inv'1    p=    -1.0     -1.0   |F(1e-18)|=7.82e+17
    inv'2    p=    -1.0     -1.0   |F(1e-18)|=7.82e+17
    dual1    p=    -1.0     -1.0   |F(1e-18)|=2.054e+17
    dual2    p=    -1.0     -1.0   |F(1e-18)|=2.054e+17
    dualpw1  p=    -1.0     -1.0   |F(1e-18)|=1.115e+17
    dualpw2  p=    -1.0     -1.0   |F(1e-18)|=1.115e+17
  at u0 in P_A (u_0 = iK'): growth exponent p in |F| ~ eps^p (from eps=1e-6..1e-12 and 1e-12..1e-18); -1 = simple pole, +1 = simple zero, 0 = regular nonzero
    A        p=    -1.0     -1.0   |F(1e-18)|=3.384e+18
    A'       p=     1.0      1.0   |F(1e-18)|=1.076e-16
    ped1     p=    -1.0     -1.0   |F(1e-18)|=2.309e+18
    ped2     p=    -1.0     -1.0   |F(1e-18)|=2.309e+18
    ant1     p=    -1.0     -1.0   |F(1e-18)|=1.428e+18
    ant2     p=    -1.0     -1.0   |F(1e-18)|=1.428e+18
    ped'1    p=    -1.0     -1.0   |F(1e-18)|=4.812e+18
    ped'2    p=    -1.0     -1.0   |F(1e-18)|=4.812e+18
    inv1     p=    -1.0     -1.0   |F(1e-18)|=1.468e+18
    inv2     p=    -1.0     -1.0   |F(1e-18)|=1.468e+18
    inv'1    p=    -1.0     -1.0   |F(1e-18)|=7.82e+17
    inv'2    p=    -1.0     -1.0   |F(1e-18)|=7.82e+17
    dual1    p=    -1.0     -1.0   |F(1e-18)|=2.054e+17
    dual2    p=    -1.0     -1.0   |F(1e-18)|=2.054e+17
    dualpw1  p=    -1.0     -1.0   |F(1e-18)|=1.115e+17
    dualpw2  p=    -1.0     -1.0   |F(1e-18)|=1.115e+17
  k806a: Res(inv'1)/Res(inv1) at S1 = (0.5326398992425411038301234 + 7.018207016936363964245453e-32j)   real-axis inv'1/inv1 = 0.5326398992425411038301234
  Lemma 3.11: Res_(iK') A = (-1.8489276111137929829e-19 - 3.3840771248472608686j)   closed form = (0.0 - 3.3840771248472608686j)
  even N: Res(ant1)/Res(A) at P_A = (0.421925183949210502060597 + 5.436435811476439920365435e-40j)   real-axis ant1/A = 0.421925183949210502060597
  N=2 mod 4: Res(ped1)/Res(A) at P_A = (0.6823214046942292620894472 + 6.574132741152950657696696e-41j)   real-axis ped1/A = 0.6823214046942292620894472   ant1/ped1 = 0.61836721088691201243

# done
