  We implement the universal wave function overlap (UWFO) method to extract
modular $S$ and $T$ matrices for topological orders in Gutzwiller-projected
parton wave functions (GPWFs). The modular $S$ and $T$ matrices generate a
projective representation of $SL(2,\mathbb{Z})$ on the degenerate-ground-state
Hilbert space on a torus and may fully characterize the 2+1D topological
orders, i.e. the quasi-particle statistics and chiral central charge (up to
$E_8$ bosonic quantum Hall states). We used the variational Monte Carlo method
to computed the $S$ and $T$ matrices of the chiral spin liquid (CSL)
constructed by the GPWF on the square lattice, and confirm that the CSL carries
the same topological order as the $\nu=\frac{1}{2}$ bosonic Laughlin state. We
find that the non-universal exponents in UWFO can be small and direct numerical
computation is able to be applied on relatively large systems. We also discuss
the UWFO method for GPWFs on other Bravais lattices in two and three dimensions
by using the Monte Carlo method. UWFO may be a powerful method to calculate the
topological order in GPWFs.
