The Δ²(k) = P(k)k³/(2π²) dimensionless power spectrum of the Millennium run and its complementary pair at z = 0 redshift. The dashed line represents the shot-noise limit. We plot the linear power spectrum with a gray solid line for the different redshifts. The average dimensionless power spectrum of the pair initially matched this linear spectrum. The complementary pair compensates for the fluctuations around the linear input spectrum due to Rayleigh sampling at all scales initially.