  The oscillation modes of a simple polytropic stellar model are studied. Using
a new numerical approach (based on integration for complex coordinates) to the
problem for the stellar exterior we have computed the eigenfrequencies of the
highly damped w-modes. The results obtained agree well with recent ones of
Leins, Nollert and Soffel (1993) Specifically, we are able to explain why
several modes in this regime of the complex frequency plane could not be
identified within the WKB approach of Kokkotas and Schutz (1992). Furthermore,
we have established that the ``kink'' that was a prominent feature of the
spectra of Kokkotas and Schutz, but did not appear in the results of Leins {\em
et al.}, was a numerical artefact. Using our new numerical code we are also
able to compute, for the first time, several of the slowly damped (p) modes for
the considered stellar models. For very compact stars we find, somewhat
surprisingly, that the damping of these modes does not decrease monotonically
as one proceeds to higher oscillation frequencies. The existence of low-order
modes that damp away much faster than anticipated may have implications for
questions regarding stellar stability and the lifetime of gravitational-wave
sources. The present results illustrate the accuracy and reliability of the
complex-coordinate method and indicate that the method could prove to be of
great use also in problems involving rotating stars. There is no apparent
reason why the complex-coordinate approach should not extend to rotating stars,
whereas it is accepted that all previous methods will fail to do so.
