Left: histogram of the distribution of the components of the dipole modulation for 900 unmodulated realizations. The distribution is not normalized. From top to bottom we show δα⁽⁰⁾, Re(δα⁽¹⁾) and Im(δα⁽¹⁾). The three histograms correspond to Planck-like modulation-free simulated data with ℓ_max = 600. The black line corresponds to the measurements in the actual Planck CMB map. Right: the same thing for ℓ_max = 1500.