  The central challenge in 21~cm cosmology is isolating the cosmological signal
from bright foregrounds. Many separation techniques rely on the accurate
knowledge of the sky and the instrumental response, including the antenna
primary beam. For drift-scan telescopes such as the Hydrogen Epoch of
Reionization Array \citep[HERA, ][]{DeBoer2017} that do not move, primary beam
characterization is particularly challenging because standard beam-calibration
routines do not apply \citep{Cornwell2005} and current techniques require
accurate source catalogs at the telescope resolution. We present an extension
of the method from \citet{Pober2012} where they use beam symmetries to create a
network of overlapping source tracks that break the degeneracy between source
flux density and beam response and allow their simultaneous estimation. We fit
the beam response of our instrument using early HERA observations and find that
our results agree well with electromagnetic simulations down to a -20~dB level
in power relative to peak gain for sources with high signal-to-noise ratio. In
addition, we construct a source catalog with 90 sources down to a flux density
of 1.4~Jy at 151~MHz.
