Eigenvalues associated with even Hough modes (left), coupling coefficients (middle) and amplification factors (right) as functions of the spin parameter (ν) for n = {−6, −4, −2, 0, 2, 4} (three Rossby modes and three gravity modes). To represent quantities varying over a large range of magnitude and with sign changes, the function f(X) = sign(X)log(1 + |X|) is used. It enforces f(X) ≈ X for X ≪ 1 and f(X) ≈sign(X)log(|X|) with a continuous transition. The peak observed in the right panel corresponds to the equality between the tidal frequency and the characteristic frequency of the Rossby mode of degree n = −2 (at this frequency, , see Lee & Saio 1997).