  We compute and compare even- and odd-parity superconducting order parameters
of strontium ruthenate ($\mathrm{Sr}_2\mathrm{RuO}_4$) in the limit of weak
interactions, resulting from a fully microscopic three-dimensional model
including spin-orbit coupling. We find that odd-parity helical and even-parity
$d$-wave order are favored for smaller and larger values of the Hund's coupling
parameter $J$, respectively. Both orders are found compatible with specific
heat data and the recently-reported nuclear magnetic resonance (NMR) Knight
shift drop [A. Pustogow et al. Nature 574, 72 (2019)]. The chiral $p$-wave
order, numerically very competitive with helical order, sharply conflicts with
the NMR experiment.
