Before revision:  To capture intermediate spacings between Ginibre and Poisson, we also compare to numerically generated two-dimensional Coulomb gases at different temperatures, which interpolate between the two. We find a stronger repulsion between nearest neighbours than between next-to-nearest ones, for more than the first half of the observed period.
After revision:  To capture intermediate spacings between Ginibre and Poisson, we also compare to numerically generated two-dimensional Coulomb gas interpolating between these two. A one-parameter fit to a time-moving average reveals a significant increase of repulsion between neighbouring nests, as a function of the observed period.