Possible values of the amplitudes S_j for the inclination terms of planet HIP 41378 f. The frequency of each term is labelled. The amplitude of the zero-frequency term s₅ is not shown. The masses, semi-major axes, and inclinations of all planets are set to their nominal observed values (see Table 1); all inclinations values I_k are assumed to be I_k ⩽ 90°. The unknown longitudes of node Ω_k of the planets in the sky plane are drawn from a uniform random distribution in an interval ΔΩ₀ common for all planets. For a given value of the range ΔΩ₀ (vertical axis), a histogram of each amplitude is built from 10⁶ realisations of the Lagrange-Laplace system (colour scale). A bin is coloured grey if no occurrence is found among our 10⁶ realisations. The scale is the same for all graphs to highlight the disparity of amplitude between the different terms.