N = 6: kappa_a(b) = A_ant/A for a = 1:
   b = 0.05  kappa_a = -193.60975609756097561
   b = 0.1   kappa_a = -46.095238095238095238
   b = 0.15  kappa_a = -19.136950904392764858
   b = 0.2   kappa_a = -9.8181818181818181818
   b = 0.25  kappa_a = -5.5555555555555555556
   b = 0.3   kappa_a = -3.2657004830917874396
   b = 0.35  kappa_a = -1.8992618323925314807
   b = 0.4   kappa_a = -1.0208333333333333333
   b = 0.45  kappa_a = -0.42378432854623330814
   b = 0.5   kappa_a = 3.9526528939278921378e-31   <-- sign change in (0.45, 0.5)
   b = 0.55  kappa_a = 0.31145681413061092205
   b = 0.6   kappa_a = 0.54700854700854700855
   b = 0.65  kappa_a = 0.72948531874511555208
   b = 0.7   kappa_a = 0.87377173091458805745
   b = 0.75  kappa_a = 0.98989898989898989899
   b = 0.8   kappa_a = 1.0848214285714285714
   b = 0.85  kappa_a = 1.163479633339403873
   b = 0.9   kappa_a = 1.2294593444018731375
   b = 0.95  kappa_a = 1.2854124606789051129
   zero of kappa_a near b = 0.5: b = 0.5
N = 10: kappa_a(b) = A_ant/A for a = 1:
   b = 0.05  kappa_a = -197.8825790359920155
   b = 0.1   kappa_a = -48.106006225701869546
   b = 0.15  kappa_a = -20.423533236314259433
   b = 0.2   kappa_a = -10.755658575148015706
   b = 0.25  kappa_a = -6.2909340085152551291
   b = 0.3   kappa_a = -3.8711250364873684352
   b = 0.35  kappa_a = -2.4152246426364896531
   b = 0.4   kappa_a = -1.4721970783814225462
   b = 0.45  kappa_a = -0.82683107411390673883
   b = 0.5   kappa_a = -0.36592224200680896039
   b = 0.55  kappa_a = -0.025330942809971754208
   b = 0.6   kappa_a = 0.23347643610207247786   <-- sign change in (0.55, 0.6)
   b = 0.65  kappa_a = 0.43477525705363976508
   b = 0.7   kappa_a = 0.59447077689348527121
   b = 0.75  kappa_a = 0.72333409314275865573
   b = 0.8   kappa_a = 0.82886795822504354033
   b = 0.85  kappa_a = 0.91642730857391939922
   b = 0.9   kappa_a = 0.98991618826681489459
   b = 0.95  kappa_a = 1.0522346055534982522
N = 14: kappa_a(b) = A_ant/A for a = 1:
   b = 0.05  kappa_a = -198.252458292586076
   b = 0.1   kappa_a = -48.332368771620382144
   b = 0.15  kappa_a = -20.591102269317641439
   b = 0.2   kappa_a = -10.890499271761034902
   b = 0.25  kappa_a = -6.4048755176810634331
   b = 0.3   kappa_a = -3.9706380744722000864
   b = 0.35  kappa_a = -2.5042673712244447118
   b = 0.4   kappa_a = -1.5533785167917749837
   b = 0.45  kappa_a = -0.9019653933368831173
   b = 0.5   kappa_a = -0.43632253359847098469
   b = 0.55  kappa_a = -0.091977677175333728181
   b = 0.6   kappa_a = 0.16983275287799254168   <-- sign change in (0.55, 0.6)
   b = 0.65  kappa_a = 0.37354842239644814121
   b = 0.7   kappa_a = 0.53519520338845418022
   b = 0.75  kappa_a = 0.66563477057513911937
   b = 0.8   kappa_a = 0.77243922111506691742
   b = 0.85  kappa_a = 0.86101746826969207675
   b = 0.9   kappa_a = 0.93531617963650538246
   b = 0.95  kappa_a = 0.99826944823603901063
N = 4 constants (a = 1):
   b = 0.3   A_pol/A^dag = 246.91358024691358       2a^4/b^4 = 246.91358024691358        A_pol/A_dual = 338701.756168605734       (A_pol/A_dual)*b^14/a^6 = 0.0162
   b = 0.5   A_pol/A^dag = 32.0                     2a^4/b^4 = 32.0                      A_pol/A_dual = 2048.0                    (A_pol/A_dual)*b^14/a^6 = 0.125
   b = 0.6   A_pol/A^dag = 15.4320987654320988      2a^4/b^4 = 15.4320987654320988       A_pol/A_dual = 330.763433758404037       (A_pol/A_dual)*b^14/a^6 = 0.2592
   b = 0.8   A_pol/A^dag = 4.8828125                2a^4/b^4 = 4.8828125                 A_pol/A_dual = 18.6264514923095703       (A_pol/A_dual)*b^14/a^6 = 0.8192
   b = 0.95  A_pol/A^dag = 2.45547532630965079      2a^4/b^4 = 2.45547532630965079       A_pol/A_dual = 3.34036514023018615       (A_pol/A_dual)*b^14/a^6 = 1.6290125
