  We prove a slightly sharper version of a result of Rider and Vir\'ag who
proved that after centering, the logarithm of the absolute value of the
characteristic polynomial of the Ginibre ensemble converges in law to the
Gaussian Free Field on the unit disk with free boundary conditions (and
continued harmonically outside of it). Using their results on the linear
statistics of the Ginibre ensemble, we prove a result that removes the
ambiguity concerning the "constant part" or zero mode of the field.
