  Properties of inertial modes of Jupiter are investigated for an n=1
polytropic description of the planet interior. We use the anelastic
approximation to overcome the usual handicap of a severe spherical harmonics
truncation. A powerful iterative solver then allows us to compute the
frequencies of the most promising low-order modes using as many spherical
harmonics as necessary. The induced O(1%) errors of our model are now within
observational limits. A plausible seismological model of Jupiter might thus be
at hand provided the use of a more realistic description of the planet
interior.
