A SITELLE view of M31's central region - I: Calibrations and radial velocity catalogue of nearly 800 emission-line point-like sources

We present a detailed description of the wavelength, astrometric and photometric calibration plan for SITELLE, the imaging Fourier transform spectrometer attached to the Canada-France-Hawaii telescope, based on observations of a red (647 - 685 nm) data cube of the central region (11$' \times 11'$) of the Andromeda galaxy. The first application, presented in this paper, is a radial-velocity catalogue (with uncertainties of $\sim 2 - 6$ km/s) of nearly 800 emission-line point-like sources, including $\sim$ 450 new discoveries. Most of the sources are likely planetary nebulae, although we also detect five novae (having erupted in the first 8 months of 2016) and one new supernova remnant candidate.