  We analyze the angular power spectrum (APS) of the unresolved gamma-ray
background (UGRB) emission and combine it with the measured properties of the
resolved gamma-ray sources of the Fermi-LAT 4FGL catalog. Our goals are to
dissect the composition of the gamma-ray sky and to establish the relevance of
different classes of source populations of active galactic nuclei in
determining the observed size of the UGRB anisotropy, especially at low
energies. We find that, under physical assumptions for the spectral energy
dispersion, i.e. by using the 4FGL catalog data as a prior, two populations are
required to fit APS data, namely flat spectrum radio quasars (FSRQs) at low
energies and BL Lacs (BLLs) at higher energies. The inferred luminosity
functions agree well with the extrapolation of the FSRQ and BLL ones obtained
from the 4FLG catalog. We use these luminosity functions to calculate the UGRB
intensity from blazars, finding a contribution of 20% at 1GeV and 30% above 10
GeV. Finally, bounds on an additional gamma-ray emission due to annihilating
dark matter are derived.
