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Fig. E.1.

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Posterior distributions for the radial M/LF814W (left) and M/LF160W (right) variation profiles obtained after the burn-in phase of the ADAMET MCMC optimization process for the JAM applied to the stellar kinematics of the nucleus of NGC 4736, measured using the NIRSpec G235H/F170LP observations, are presented. In each triangle plot, the analysis involves four parameters (i, MBH, M / L 2 . 0 $ M/L_{2{{\overset{\prime\prime}{.}}}0} $, and βr), shown as scatter plots for their 2D projected PDF with white indicates maximum likelihood and a CL at 1σ, while black corresponds to a confidence level at 3σ. The top histograms display the 1D projected distributions of the best-fitting model parameters, including the best-fit values (indicated by vertical black lines, corresponding to the highest likelihood within the PDF) and 3σ uncertainty (indicated by either side black dash lines). Insert plots in the top-right of each triangle plot illustrate the agreement by directly comparing the Vrms data with that generated from the best-fit JAM using the radially varying M/LF814W profile (left) and the constant M/LF160W value (right) in the same velocity range. It is evident that the constrained model shows excellent agreement with the data across the NIRSpec FoV.

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