  We present complete 2D computations of g modes in distorted polytropic models
of stars performed with the Two-dimensional Oscillation Program (TOP). We
computed low-degree modes (l=1 modes with radial order n=-1...-14, and l=2,3
modes with n=-1...-5 and -16...-20) of a nonrotating model and followed them by
slowly increasing the rotation rate up to 70 % of the Keplerian break-up
velocity. We use these computations to determine the domain of validity of
perturbative methods up to the 3rd order. We study the evolution of the
regularities of the spectrum and show quantitative agreement with the
traditional approximation for not too large values of the ratio of the rotation
rate to the pulsation frequency. We also show the appearance of new types of
modes, called "rosette" modes due to their spatial structure. Thanks to the ray
theory for gravito-inertial waves that we developed, we can associate these
modes with stable periodic rays.
