Beam window function error modes. Panels a), b) and c) show the first six eigenmodes defined in Eq. (G.11) for respectively the effective auto-beam 100ds1 and 143ds2 and the effective cross-beam 217-1 × 217-2. The first five modes used in the current beam error modelling are shown as solid coloured curves, while the 6th mode (the first one to be ignored) appears as yellow dashes. The grey dashes show the ±1 σ envelope obtained by adding the first five modes in quadrature, while the solid grey curve is the ±1 σ envelope estimated from the simulations (therefore including all eigenmodes). The black dashes show the relative difference between and B_mean(ℓ) defined in Eqs. (G.6) and (G.5), respectively. In panel d), for a selection of effective beams, the coloured symbols show (d_k/d₁)² where d_k is the kth eigenvalue of the diagonal matrix D (Eq. (G.12)), while the coloured dashes show the error made on the quadratic sum of the eigenvalues by truncating it to n_modes: . The vertical dashes show the current n_modes = 5 value.