Trajectories associated to the magenta and brown point in Fig. 3. The time-span for both orbits is 650 years. The plots highlight the precision of the modified FLI method. Small displacements of the initial conditions corresponding to the maximum mFLI value lead to large differences in the orbits: in this scenario, the variation of the initial velocity is about 3 × 10⁻¹² and −3 × 10⁻¹¹ AU day⁻¹ for the magenta and brown trajectories. Both orbits are escaping from L₃.