(a) Contours of the maximum growth rate σ₀ from Eq. (59) in the parameter space for N = 2. Black dashed lines represent the upper limit of the instability from Eq. (61) for different N, and the white dashed line represents f_max from (64) where the maximum growth rate is attained. (b) Contours of σ₀ from Eq. (59) in the parameter space at f = 1. (c) Contours of the first-order term σ₁ in the parameter space for N = 2 and the first branch at m = 1.