this family have spiral patterns with multiple peaks in their $P_m(R)$ functions. The (global) fastest growing mode belongs to the spectrum of $m=2$. That is the bar mode of a two-member unstable family.

The length scale of Clutton-Brock functions has been set to $b=1.5$ for $m=2$ and $b=2$ for other wavenumbers. Changing this length scale slightly displaces the eigenfrequencies although the spectrum maintains its global pattern. Large values of $b$ lead to a better computation accuracy of extensive modes (with smaller pattern speeds), while compact bar modes show a rapid convergence for small values of $b$. Moreover, the suitable value of $b$ differs from one azimuthal wavenumber to another. Finding an optimum length scale that gives the best results for all modes and wavenumbers is an open problem yet to be investigated precisely. For the cored exponential disks with $0.5 \le R_C,R_D\le 2$, working in the range $1\le b\le 2.5$ gives reasonable results.

For $m=2$, I have zoomed out and plotted in Figure \[pic:spectrum-m2-unstable\][*a*]{} the portion of the spectrum that contains growing modes. The first and second modes reported in Table 4 of JH have been shown by circles in the same figure. The most unstable mode (labeled as B1) 