  We prove that the number of quasinormal modes (QNM) for Schwarzschild and
Schwarzschild-de Sitter black holes in a disc of radius $ r $ is bounded from
below by $ c r^3 $. This shows that the recent upper bound by J\'ez\'equel is
sharp. The argument is an application of a spectral asymptotics result for
non-self-adjoint operators which provides a finer description of QNM and
explains the emergence of a distorted lattice on which they lie. Our
presentation gives a general result about exponentially accurate
Bohr-Sommerfeld quantization rules for one dimensional problems. The
description of QNM allows their accurate evaluation ``deep in the complex"
where numerical methods break down due to pseudospectral effects.
