International audienceContext: Environmental effects are known to have an important influence on cluster galaxies, but studies at very faint magnitudes (R>21) are almost exclusively based on imaging. We present here a very deep spectroscopic survey of galaxies on the line of sight to the Coma cluster. Aims: After a series of papers based on deep multi-band imaging of the Coma cluster, we explore spectroscopically part of the central regions of Coma, in order to confirm and generalize previous results, concerning in particular the galaxy luminosity function, red sequence, stellar populations and the most likely formation scenario for the Coma cluster. Methods: We have obtained reliable VIMOS redshifts for 715 galaxies in the direction of the...