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