Possible secular trajectories for the KOI-1257 system seen in the (ω,i) plane (top), and in the (ω,e_in) plane (bottom). The colours are preserved in both pictures, each one corresponding to the same orbital evolution. The trajectories correspond to the level curves of constant energy using the quadrupolar approximation combined with general relativity. The dashed lines define the regions of initial conditions that are compatible with the observational data (Table 6), namely ° (top) and e_in = 0.772 (bottom), while 105° ≤ ω ≤ 177° (Eqs. (8)−(10)).