  We numerically study the next-to-leading order corrections of the Lorentzian
Engle-Pereira-Rovelli-Livine (EPRL) 4-simplex amplitude in the large-$j$
expansions. We perform large-$j$ expansions of Lorentzian EPRL 4-simplex
amplitudes with two different types of boundary states, the coherent
intertwiners and the coherent spin-network, and numerically compute the
leading-order and the next-to-leading order $O(1/j)$ contributions of these
amplitudes. We also study the dependences of these $O(1/j)$ corrections on the
Barbero-Immirzi parameter $\gamma$. We show that they, as functions of
$\gamma$, stabilize to finite real constants as $\gamma\to\infty$. Lastly, we
obtain the quantum corrections to the Regge action because of the $O(1/j)$
contribution to the spinfoam amplitude.
