The NA60 experiment at the CERN SPS has studied low-mass dimuon production in 158A GeV In-In collisions. A significant excess of pairs is observed above the yield expected from neutral meson decays, consistent with a dominant contribution from ππ→ρ→μμ. This paper presents precision results on the mass and transverse momentum spectra of the excess pairs. The space-time averaged rho spectral function associated to the measured mass distribution shows a significant broadening, but essentially no mass shift. The slope parameter Teff extracted from the spectra rises with dimuon mass up to the ρ, followed by a sudden decline above. While the initial rise is consistent with the expectations for radial flow of a hadronic decay source, the decline indicates a transition to an emission source with much smaller flow, possibly of partonic origin.The NA60 experiment at the CERN SPS has studied low-mass dimuon production in 158A GeV In-In collisions. A significant excess of pairs is observed above the yield expected from neutral meson decays, consistent with a dominant contribution from ππ→ρ→μμ.This paper presents precision results on the mass and transverse momentum spectra of the excess pairs. The space-time averaged rho spectral function associated to the measured mass distribution shows a significant broadening, but essentially no mass shift. The slope parameter Teff extracted from the spectra rises with dimuon mass up to the ρ , followed by a sudden decline above. While the initial rise is consistent with the expectations for radial flow of a hadronic decay source, the decline indicates a transition to an emission source with much smaller flow , possibly of partonic origin