We report on VLA measurements between 1 and 45 GHz of the evolving radio spectral energy distribution (SED) of SN 1986J, made in conjunction with VLBI imaging. The SED of SN 1986J is unique among supernovae, and shows an inversion point and a high-frequency turnover. Both are due to the central component seen in the VLBI images, and both are progressing downward in frequency with time. The optically-thin spectral index of the central component is almost the same as that of the shell. We fit a simple model to the evolving SED consisting of an optically-thin shell and a partly-absorbed central component. The evolution of the SED is consistent with that of a homologously expanding system. Both components are fading, but the shell more rapidly. We conclude that the central component is physically inside the expanding shell, and not a surface hot-spot central only in projection. Our observations are consistent with the central component being due to interaction of the shock with the dense and highly-structured circumstellar medium that resulted from a period of common-envelope evolution of the progenitor. However a young pulsar-wind nebula or emission from an accreting black hole can also not be ruled out at this point.