Imaginary part of the frequency of the slow sausage quasimode (solid line) as a function of l/R for k_zR = 1 (top), k_zR = 3 (middle), and k_zR = 5 (bottom) calculated from the dispersion relation obtained through the series method outlined in the previous sections. The modes represented here are the same as those from Fig. 3. The dashed line is the imaginary part of the frequency of the slow sausage quasimode calculated with the thin boundary approximation (42).