Towards a more robust algorithm for computing the Kerr quasinormal mode frequencies

Leaver's method has been the standard for computing the quasinormal mode (QNM) frequencies for a Kerr black hole (BH) for a few decades. We start with a spectral variant of Leaver's method introduced by Cook and Zalutskiy [Phys. Rev. D 90, 124021 (2014)], and propose improvements in the form of computing the necessary derivatives analytically, rather than by numerical finite differencing. We also incorporate this derivative information into qnm, a Python package, which finds the QNM frequencies via the spectral variant of Leaver's method. We confine ourselves to first derivatives only