This work presents a statistical analysis of near-relativistic solar energetic electron event spectra near 1 au. We use measurements of the Solar Electron and Proton Telescope (SEPT) on board STEREO in the energy range of 45-425 keV and utilize the SEPT electron event list containing all electron events observed by STEREO A and STEREO B from 2007 through 2018. We select 781 events with significant signal-to-noise ratios for our analysis and fit the spectra with single or broken-power-law functions of energy. We find 437 events showing broken power laws and 344 events only showing a single power law in the energy range of SEPT. For those events with broken power laws, we find a mean break energy of about 120 keV. We analyze the dependence of the spectral index on the rise times and peak intensities of the events as well as on the presence of relativistic electrons. The results show a relation between the power law spectral index and the rise times of the events with softer spectra belonging to rather impulsive events. Long rise-time events are associated with hard spectra as well as with the presence of higher-energy (>0.7 MeV) electrons. This group of events cannot be explained by a pure flare scenario but suggests an additional acceleration mechanism, involving a prolonged acceleration and/or injection of the particles. A dependence of the spectral index on the longitudinal separation from the parent solar source region was not found. A statistical analysis of the spectral indices during impulsively rising events where the rise times are below 20 minutes is also shown. is also shown.