Fig. 3

Contour plot of the function \(g_{\nu }(\lambda )\) in the complex \(\lambda \)-plane. a As in Fig. 1, the real and the imaginary part of the function \(g_{\nu }(\lambda )\) vanish on the blue lines and red lines, respectively, and the eigenvalues can be found at the intersection points of blue and red lines. For a real index (for \(\nu =2\) and \(\gamma =5\) as an example), all intersection points are located on the real axis. b For a complex index (exemplarily shown for \(\nu =2+\mathrm {i}\) and \(\gamma =5\)), the geometry of the contour plots appears again more complicated as for real indices.