  GRB 130427A was extremely bright as a result of occurring at low redshift
whilst the energetics were more typical of high-redshift gamma-ray bursts
(GRBs). We collected well-sampled light curves at 1.4 and 4.8 GHz of GRB
130427A with the Westerbork Synthesis Radio Telescope (WSRT); and we obtained
its most accurate position with the European Very Long Baseline Interferometry
Network (EVN). Our flux density measurements are combined with all the data
available at radio, optical and X-ray frequencies to perform broadband modeling
in the framework of a reverse-forward shock model and a two-component jet
model, and we discuss the implications and limitations of both models. The low
density inferred from the modeling implies that the GRB 130427A progenitor is
either a very low-metallicity Wolf-Rayet star, or a rapidly rotating,
low-metallicity O star. We also find that the fraction of the energy in
electrons is evolving over time, and that the fraction of electrons
participating in a relativistic power-law energy distribution is less than 15%.
We observed intraday variability during the earliest WSRT observations, and the
source sizes inferred from our modeling are consistent with this variability
being due to interstellar scintillation effects. Finally, we present and
discuss our limits on the linear and circular polarization, which are among the
deepest limits of GRB radio polarization to date.
