Effect of the halo orientation. Physical trajectories and the corresponding Poincaré sections y − v_y with plane x = 0 and v_x> 0 for the orbits listed in Table 1. The orientation is φ = 90.0, the flattening is q_z = 1.25. The orbits with lower velocities, LC1, LF1, HC1, and HF1, previously chaotic, remain chaotic. Regarding the higher velocities, H-orbits HF2 and HC2, which were previously regular, are now chaotic. L-orbits LC2 and LF2, previously regular, remain regular. The predictabilities remain the same for low velocities, but they change towards lower values for the highest velocities (except for LF2).