  We calculate the one-body temperature Green's (Matsubara) function of the
unitary Fermi gas via Quantum Monte Carlo, and extract the spectral weight
function $A(p,\omega)$ using the methods of maximum entropy and singular value
decomposition. From $A(p,\omega)$ we determine the quasiparticle spectrum,
which can be accurately parametrized by three functions of temperature: an
effective mass $m^*$, a mean-field potential $U$, and a gap $\Delta$. Below the
critical temperature $T_c=0.15\varepsilon_F$ the results for $m^*$, $U$ and
$\Delta$ can be accurately reproduced using an independent quasiparticle model.
We find evidence of a pseudogap in the fermionic excitation spectrum for
temperatures up to {$T^*\approx 0.20\varepsilon_{F} > T_c$}.
