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In previous work [1] we proposed an improvement of the WKB-based semianalytictechnique of Iyer and Will for calculation of the quasiormal modes of blackholes by constructing the Pad\'e approximants of the formal series for$\omega^{2}.$ It has been demonstrated that (within the domain ofapplicability) the diagonal Pad\'e transforms $\mathcal{P}_{6}^{6}$ and$\mathcal{P}_{7}^{6}$ are always in a very good agreement with the numericalresults. In this paper we present a further extension of the method. We showthat it is possible to reproduce many known numerical results with a greataccuracy (or even exactly) if the Pad\'e transforms are constructed from theperturbative series of a really high order. In our calculations the orderdepends on the problem but it never exceeds 700. For example, the frequenciesof the gravitational mode $l=2,$ $n=0$ calculated with the aid of the Pad\'eapproximants and within the framework of the continued fractions method agreeto 24 decimal places. The use of such a large number of terms is necessary asthe stabilization of the quasinormal frequencies can be slow. Our resultsreveal some unexpected features of the WKB-based approximations and may shedsome fresh light on the problem of overtones.

Quasinormal modes of black holes. II. Pad\'e summation of the higher-order WKB terms