In this paper, efficient sampling representations of the electromagnetic field, radiated by a centered parabolic antenna over a plane in the near-field region and over the far-field sphere, are presented. They use a. non-redundant number of samples, which remains finite even in the case of an unbounded planar observation domain. This result relies on a proper choice of the phase factor extracted from the field expression and of the coordinates used to parameterize the domain. By making explicit reference to the minimal convex domain enclosing the antenna, the number of needed data can be significantly reduced as compared with that required by modelling the antenna as enclosed in a ball. For the considered observation geometries, precise and fast sampling algorithms of central type have been developed. The reconstruction examples assess the effectiveness of the proposed representations. At last, the stability of the algorithms, with respect to random errors affecting the data, is proved by adding uniformly distributed random errors to the exact samples.