The torus one-point diagram in two-dimensional string cosmology

We calculate numerically the torus one-point string diagram in two-dimensional cosmology background by decomposing functions $c=1$ and $c=25$ Liouville CFT into Virasoro conformal blocks integrating over fundamental domain of moduli space. find a remarkably simple result as function outgoing closed energy. This is expected to contribute cosmological wavefunction at order $g_s$, four-point $g_s^2$ through disconnected product sphere three-point diagram.