Relative difference of diagonals for temperature TTTT (top) and polarization EEEE (bottom). In red we plot the relative differences every 25 multipoles until ℓ = 1500 and a few well-chosen ones (at the locations of peaks and troughs of the spectra) up to ℓ = 2000. In gray, the same quantity is plotted for all multipoles for ℓ ∊ [ℓ_cut = 200, ℓ_max,ex = 1000]. We are able to compute the covariance exactly only for a limited number of rows, and it is computationally cheaper for lower multipoles, justifying our choice of full calculation at ℓ < ℓ_max,ex and partial calculation for larger multipoles. This plot shows the agreement between the two approaches and validates our exact calculation.