Linear hydrodynamic growth rates of overstable modes in a perturbed ring for different values of the nonlinearity parameter q describing the satellite perturbation. The wavelengths λ correspond to the uncompressed state of the model ring adopted at times t = lπ∕Ω_L, with non-negative integer l (cf. Eq. (59)). The used parameters are the Pr76-parameters with varyingvalue of β and all growth rates are scaled with Ω = Ω_L. In all panels the growth rates for q = 0, obtained by numerical solution of Eq. (14), are plotted additionally as black solid curves.