Overtones of black holes via time-domain integration

We show that the first several overtones could be calculated by the time-domain integration method for asymptotically de Sitter black holes already at the lowest multipole numbers of gravitational and electromagnetic perturbations. This is not possible for asymptotically flat black holes, for which extraction of frequencies with the Prony method is usually possible with reasonable accuracy only for the fundamental mode. The reason for much better efficiency in the de Sitter case is the absence of power-law tails: the quasinormal modes dominate the signal not only at the intermediate stage, but also at asymptotically late times.