  We present a method which allows for the extraction of physical quantities
directly from zero- to ultralow-field nuclear magnetic resonance (ZULF NMR)
data. A numerical density matrix evolution is used to simulate ZULF NMR spectra
of several molecules in order to fit experimental data. The method is utilized
to determine the indirect spin-spin couplings ($J$-couplings) in these, which
is achieved with precision of $10^{-2}$--$10^{-4}$ Hz. The simulated and
measured spectra are compared to earlier research. Agreement and precision
improvement for most of the $J$-coupling estimates are achieved. The
availability of an efficient, flexible fitting method for ZULF NMR enables a
new generation of precision-measurement experiments for spin-dependent
interactions and physics beyond the Standard Model.
