Although finding numerically the quasinormal modes of a nonrotating black hole is a well-studied question , the physics of the problem is often hidden behind complicated numerical procedures aimed at avoiding the direct solution of the spectral system in this case .
In this article , we use the exact analytical solutions of the Regge-Wheeler equation and the Teukolsky radial equation , written in terms of confluent Heun functions .
In both cases , we obtain the quasinormal modes numerically from spectral condition written in terms of the Heun functions .
The frequencies are compared with ones already published by Andersson and other authors .
A new method of studying the branch cuts in the solutions is presented – the epsilon-method .
In particular , we prove that the mode n = 8 is not algebraically special and find its value with more than 6 firm figures of precision for the first time .
The stability of that mode is explored using the \epsilon method , and the results show that this new method provides a natural way of studying the behavior of the modes around the branch cut points .