a=2 N=6 tau=1 (N mod 4 = 2)
   pole (j,p,q)=(0, 0, 0): Res A = (1.27431060188881e-83 - 2.51415744421884j) ; kappa(M) = ['(0.7777777777777777777777778 + 1.101518882391235687529408e-67j)', '(0.8588888888888888888888889 + 3.251047717966069407264767e-67j)', '(0.6966666666666666666666667 + 0.07111111111111111111111111j)']
   pole (j,p,q)=(1, 1, 0): Res A = (-1.50664016943625e-82 - 2.51415744421884j) ; kappa(M) = ['(0.7777777777777777777777778 + 1.104779621587211750359366e-67j)', '(0.8588888888888888888888889 - 1.328857067125045957866118e-67j)', '(0.6966666666666666666666667 + 0.07111111111111111111111111j)']
   pole (j,p,q)=(2, 0, 1): Res A = (2.86315395818337e-83 + 2.51415744421884j) ; kappa(M) = ['(0.7777777777777777777777778 + 3.306785982624038944354465e-67j)', '(0.8588888888888888888888889 + 1.661071333906308188518822e-67j)', '(0.6966666666666666666666667 + 0.07111111111111111111111111j)']
   pole (j,p,q)=(3, -1, 1): Res A = (-1.79746749634626e-82 + 2.51415744421884j) ; kappa(M) = ['(0.7777777777777777777777778 - 1.393945536102983242251092e-66j)', '(0.8588888888888888888888889 - 2.218726092449798229891575e-66j)', '(0.6966666666666666666666667 + 0.07111111111111111111111111j)']
   real-axis ratio at u=0.971498: ['0.7777777777777777777777778', '0.8588888888888888888888889', '(0.6966666666666666666666667 + 0.07111111111111111111111111j)']
   kappa0 + kappa2 |Mc|^2 (bilinear |.|^2) = (0.6966666666666666666666667 + 0.07111111111111111111111111j) vs ratio at Mc = (0.6966666666666666666666667 + 0.07111111111111111111111111j)
a=1.3 N=10 tau=3 (N mod 4 = 2)
   pole (j,p,q)=(0, 0, 0): Res A = (-1.48074742461827e-83 - 1.6880862717155j) ; kappa(M) = ['(0.3283381122459400590360604 + 5.047590416184748055979444e-68j)', '(0.2494391083345665261860753 + 1.810102385317203099303827e-67j)', '(0.4072371161573135918860455 - 0.06917172945654665893697323j)']
   pole (j,p,q)=(1, 1, 0): Res A = (2.02753509794245e-83 - 1.6880862717155j) ; kappa(M) = ['(0.3283381122459400590360604 + 2.550006791916777646840754e-68j)', '(0.2494391083345665261860753 - 1.71134011562390826235646e-67j)', '(0.4072371161573135918860455 - 0.06917172945654665893697323j)']
   pole (j,p,q)=(2, 0, 1): Res A = (4.03676502078748e-83 + 1.6880862717155j) ; kappa(M) = ['(0.3283381122459400590360604 - 6.370294772929041927568483e-67j)', '(0.2494391083345665261860753 - 4.947845296170828538277565e-67j)', '(0.4072371161573135918860455 - 0.06917172945654665893697323j)']
   pole (j,p,q)=(3, -1, 1): Res A = (-1.35662715038334e-82 + 1.6880862717155j) ; kappa(M) = ['(0.3283381122459400590360604 - 6.378254370995836985393428e-67j)', '(0.2494391083345665261860753 - 1.484353588851248779839218e-67j)', '(0.4072371161573135918860455 - 0.06917172945654665893697323j)']
   real-axis ratio at u=0.452548: ['0.3283381122459400590360604', '0.2494391083345665261860753', '(0.4072371161573135918860455 - 0.06917172945654665893697323j)']
   kappa0 + kappa2 |Mc|^2 (bilinear |.|^2) = (0.4072371161573135918860455 - 0.06917172945654665893697323j) vs ratio at Mc = (0.4072371161573135918860455 - 0.06917172945654665893697323j)
a=2 N=14 tau=3 (N mod 4 = 2)
   pole (j,p,q)=(0, 0, 0): Res A = (7.9429294009107e-83 - 2.96457200676129j) ; kappa(M) = ['(0.5516127811628294081723053 + 7.366689053075853440724217e-68j)', '(0.584164937118378075221065 - 4.111285888295725902313786e-68j)', '(0.5190606252072807411235457 + 0.02853887645417965330302218j)']
   pole (j,p,q)=(1, 1, 0): Res A = (2.74152893043126e-83 - 2.96457200676129j) ; kappa(M) = ['(0.5516127811628294081723053 + 3.68379031251397364968764e-68j)', '(0.584164937118378075221065 - 4.523810151484097929975324e-68j)', '(0.5190606252072807411235457 + 0.02853887645417965330302218j)']
   pole (j,p,q)=(2, 0, 1): Res A = (6.19310112291397e-83 + 2.96457200676129j) ; kappa(M) = ['(0.5516127811628294081723053 - 9.288995724486359922562622e-67j)', '(0.584164937118378075221065 - 1.566837087792831143976294e-66j)', '(0.5190606252072807411235457 + 0.02853887645417965330302218j)']
   pole (j,p,q)=(3, -1, 1): Res A = (6.79431910185525e-83 + 2.96457200676129j) ; kappa(M) = ['(0.5516127811628294081723053 - 9.309223372680226634785427e-67j)', '(0.584164937118378075221065 - 1.690440920305966256697469e-67j)', '(0.5190606252072807411235457 + 0.02853887645417965330302218j)']
   real-axis ratio at u=1.9528: ['0.5516127811628294081723053', '0.584164937118378075221065', '(0.5190606252072807411235457 + 0.02853887645417965330302218j)']
   kappa0 + kappa2 |Mc|^2 (bilinear |.|^2) = (0.5190606252072807411235457 + 0.02853887645417965330302218j) vs ratio at Mc = (0.5190606252072807411235457 + 0.02853887645417965330302218j)
a=2 N=8 tau=1 (N mod 4 = 0)
   pole (j,p,q)=(0, 0, 0): Res A = (2.57595489347891e-70 - 2.41878714223524j) ; kappa(M) = ['(0.9469175504300234261614225 - 1.872072330044108739174237e-70j)', '(1.0514972257584532484017 - 4.511458414732744735647856e-67j)', '(0.8423378751015936039211449 + 0.09168629069889737840243517j)']
   pole (j,p,q)=(1, 1, 0): Res A = (1.18147918660124e-69 - 2.41878714223524j) ; kappa(M) = ['(0.9469175504300234261614225 - 9.260377513591619648092912e-71j)', '(1.0514972257584532484017 - 8.99245471248569674592861e-67j)', '(0.8423378751015936039211449 + 0.09168629069889737840243517j)']
   pole (j,p,q)=(2, 0, 1): Res A = (4.75585326096906e-70 + 2.41878714223524j) ; kappa(M) = ['(0.9469175504300234261614225 + 1.572151325044520879546956e-70j)', '(1.0514972257584532484017 + 7.389050610137070904619165e-67j)', '(0.8423378751015936039211449 + 0.09168629069889737840243517j)']
   pole (j,p,q)=(3, -1, 1): Res A = (4.0885371044973e-71 + 2.41878714223524j) ; kappa(M) = ['(0.9469175504300234261614225 + 1.600598693343122498896658e-71j)', '(1.0514972257584532484017 + 1.532023093185411860444562e-67j)', '(0.8423378751015936039211449 + 0.09168629069889737840243517j)']
   real-axis ratio at u=0.217309: ['0.9469175504300234261614225', '1.0514972257584532484017', '(0.8423378751015936039211449 + 0.09168629069889737840243517j)']
   kappa0 + kappa2 |Mc|^2 (bilinear |.|^2) = (0.8423378751015936039211449 + 0.09168629069889737840243517j) vs ratio at Mc = (0.8423378751015936039211449 + 0.09168629069889737840243517j)
a=3.5 N=16 tau=3 (N mod 4 = 0)
   pole (j,p,q)=(0, 0, 0): Res A = (-1.59132244353581e-69 - 10.8775217687709j) ; kappa(M) = ['(0.7713945279461530333290427 + 2.154140780231207276224715e-70j)', '(0.7936695984198952275301071 - 1.841984567002372464673472e-69j)', '(0.7491194574724108391279784 + 0.01952882890848630724476873j)']
   pole (j,p,q)=(1, 1, 0): Res A = (-1.02669623153614e-69 - 10.8775217687709j) ; kappa(M) = ['(0.7713945279461530333290427 - 2.505826928246035783175457e-72j)', '(0.7936695984198952275301071 - 2.623693963259770424945632e-68j)', '(0.7491194574724108391279784 + 0.01952882890848630724476873j)']
   pole (j,p,q)=(2, 0, 1): Res A = (-3.00305399491906e-79 + 10.8775217687709j) ; kappa(M) = ['(0.7713945279461530333290427 + 2.341439048518022402240132e-81j)', '(0.7936695984198952275301071 + 5.053853111391842597423815e-68j)', '(0.7491194574724108391279784 + 0.01952882890848630724476873j)']
   pole (j,p,q)=(3, -1, 1): Res A = (-8.84666848632559e-70 + 10.8775217687709j) ; kappa(M) = ['(0.7713945279461530333290427 + 6.025772385953685903865767e-72j)', '(0.7936695984198952275301071 + 8.126045196519115374726722e-68j)', '(0.7491194574724108391279784 + 0.01952882890848630724476873j)']
   real-axis ratio at u=1.60765: ['0.7713945279461530333290427', '0.7936695984198952275301071', '(0.7491194574724108391279784 + 0.01952882890848630724476873j)']
   kappa0 + kappa2 |Mc|^2 (bilinear |.|^2) = (0.7491194574724108391279784 + 0.01952882890848630724476873j) vs ratio at Mc = (0.7491194574724108391279784 + 0.01952882890848630724476873j)
done
