We revisit the possibility of redshift evolution in the $M_{rm{BH}}-sigma_*$ relation with a sample of 22 Seyfert 1 galaxies with black holes (BHs) in the mass range $10^{6.3}-10^{8.3}~M_odot$ and redshift range $0.03<z<0.57$ with spectra obtained from spatially resolved Keck/Low-Resolution Imaging Spectrometer observations. Stellar velocity dispersions were measured directly from the Mg Ib region, taking into consideration the effect of Fe II contamination, active galactic nucleus (AGN) dilution, and host-galaxy morphology on our measurements. BH masses are estimated using the H$beta$ line width, and the luminosity at 5100 $overset{lower.5emcirc}{mathrm{A}}$ is estimated from surface brightness decomposition of the AGN from the host galaxy using high-resolution imaging from the Hubble Space Telescope. Additionally, we investigate the use of the [O III]$lambda5007$ emission line width as a surrogate for stellar velocity dispersion, finding better correlation once corrected for Fe II contamination and any possible blueshifted wing components. Our selection criteria allowed us to probe lower-luminosity AGNs and lower-mass BHs in the non-local universe than those measured in previous single-epoch studies. We find that any offset in the $M_{rm{BH}}-sigma_*$ relation up to $zsim0.6$ is consistent with the scatter of local BH masses, and address the sources of biases and uncertainties that contribute to this scatter.
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