Real part of complex SCH of order m = 1 and degree l₃ = 6.806057 corresponding to an ocean basin of angular radius θ₀ = 80° (i.e. = 100°) with Dirichlet boundary conditions (Eq. (C.16)). Left: Function plotted in its coordinate system using the expression given by Eq. (C.19). Middle: Function expanded in SPHs up to the truncation degree L = 6, 8, 16 (from top to bottom) in the same coordinate system using the transition relation of Eq. (F.9). Right: Function expanded in rotated SPHs (α = 120°, β = 60°, γ = 270°) following the relation given by Eq. (F.11). All functions are plotted in polar coordinates, the radial coordinate corresponding to the colatitude of the considered coordinate system, and the angular coordinate to its longitude (in degrees).