Truncation errors are negligible. Using the kernel with the largest truncation error as worst case scenario, we plot the beam convolved simulated CMB map used in this test of the Planck 217   GHz channels (left panel, we show a 10° × 10° patch). Middle panel: the difference map between the results obtained with the exact convolution and the compressed convolution with three beam modes. Right panel: compared to the fiducial power spectrum of the input map (dashed line), the power spectrum of the difference map is subdominant by a large margin on all angular scales.