Lemma C check: det[V_R(z); L_Xi] / det[Re S(z); Im S(z)] must be constant in z (z real)
(1, 1) ratio det[V_R;L]/det[ReS;ImS]: [0.17163707 0.17163707 0.17163707 0.17163707 0.17163707] | det[S;Sbar]/((-2i)^a det[ReS;ImS]): [1.+0.j 1.+0.j] | det(V_R Y^T)/det[ReS;ImS]: [-1. -1.]
(1, 2) ratio det[V_R;L]/det[ReS;ImS]: [-0.35471246 -0.35471246 -0.35471246 -0.35471246 -0.35471246] | det[S;Sbar]/((-2i)^a det[ReS;ImS]): [1.-0.j 1.+0.j] | det(V_R Y^T)/det[ReS;ImS]: [-1. -1.]
(1, 3) ratio det[V_R;L]/det[ReS;ImS]: [0.11836746 0.11836746 0.11836746 0.11836746 0.11836746] | det[S;Sbar]/((-2i)^a det[ReS;ImS]): [1.+0.j 1.+0.j] | det(V_R Y^T)/det[ReS;ImS]: [-1. -1.]
(2, 1) ratio det[V_R;L]/det[ReS;ImS]: [-0.25104296 -0.25104296 -0.25104296 -0.25104296 -0.25104296] | det[S;Sbar]/((-2i)^a det[ReS;ImS]): [1.+0.j 1.-0.j] | det(V_R Y^T)/det[ReS;ImS]: [-1. -1.]
(2, 2) ratio det[V_R;L]/det[ReS;ImS]: [0.10279775 0.10279775 0.10279775 0.10279775 0.10279775] | det[S;Sbar]/((-2i)^a det[ReS;ImS]): [1.-0.j 1.+0.j] | det(V_R Y^T)/det[ReS;ImS]: [-1. -1.]
(2, 3) ratio det[V_R;L]/det[ReS;ImS]: [-0.02664997 -0.02664997 -0.02664997 -0.02664997 -0.02664997] | det[S;Sbar]/((-2i)^a det[ReS;ImS]): [1.+0.j 1.-0.j] | det(V_R Y^T)/det[ReS;ImS]: [-1. -1.]
(3, 2) ratio det[V_R;L]/det[ReS;ImS]: [0.00974796 0.00974796 0.00974796 0.00974796 0.00974796] | det[S;Sbar]/((-2i)^a det[ReS;ImS]): [1.-0.j 1.+0.j] | det(V_R Y^T)/det[ReS;ImS]: [1. 1.]
b=1 j=1: det[S;Sbar] = (3.5714411214+0j)  vs  -2i(tau2 conj tau1 - tau1 conj tau2) = (3.5714411214-0j) ; det[ReS;ImS] = -0.8928602804 vs Im(tau1 conj tau2) = -0.8928602804
b=1 j=2: det[ReS;ImS] = -2.6342775589  vs  |det S'|^2 = 2.6342775589
b=2 j=1: det[S;Sbar] = (3732.9520739708-0j)  vs  -2i(tau2 conj tau1 - tau1 conj tau2) = (3732.9520739708-0j) ; det[ReS;ImS] = -933.2380184927 vs Im(tau1 conj tau2) = -933.2380184927
b=2 j=2: det[ReS;ImS] = -132.2201789777  vs  |det S'|^2 = 132.2201789777
b=3 j=1: det[S;Sbar] = (-8070.7986944869+0j)  vs  -2i(tau2 conj tau1 - tau1 conj tau2) = (-8070.7986944869+0j) ; det[ReS;ImS] = 2017.6996736217 vs Im(tau1 conj tau2) = 2017.6996736217
b=3 j=2: det[ReS;ImS] = -1137.9636330909  vs  |det S'|^2 = 1137.9636330909
