We calculate the one-body temperature Greens (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 $T_c=0.15varepsilon_F$ 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 {$T^*approx 0.20varepsilon_{F} > T_c$}.
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