Nominal location of ZLK secondary 2:1 and 3:1 resonances (see red dashed lines), determined by fundamental frequencies for different mass ratios at α_m = 1.1 (left panel) and α_m = 40 (right panel). For comparison, the characteristic curves of periodic families associated with ZLK resonance (solid blue lines), the conventional ZLK resonant centers (black stars), and the level curves of octupole-order Hamiltonian (gradient gray curves) are presented as background. It is observed that there is a good correspondence between the nominal location of ZLK secondary resonances and the bifurcation points of periodic orbit families.