We investigate the spectrum of a quasi-monoenergetic ensemble of relativistic electrons, especially for the mildly relativistic case, and discuss the effect of inclination of the magnetic field on the emissivity. We apply the exact theoretical description to the spectrum of the radio source Sgr A* which is located at or very close to the dynamical center of our Galaxy. We find that the radio-MIR spectrum can be reproduced well, but that the resulting self-comptonized X-ray flux is much smaller than the observed one.