  We calculate the spectrum of inertial oscillation modes in a slowly rotating
superfluid neutron star, including, for the first time, both the effects of
finite temperatures and entrainment between superfluid neutrons and protons. We
work in the Newtonian limit and assume minimal core composition (neutrons,
protons and electrons). We also developed an approximate method that allows one
to calculate the superfluid r-mode analytically. Finally, we derive and analyze
dispersion relations for inertial modes in the superfluid NS matter in the
short wavelength limit.
