We present the results of the spectral analysis of the public data of 438 gamma ray bursts (GRBs) detected by the Fermi Gamma ray Burst Monitor (GBM) up to March 2010. For 432 bursts we could fit the time-integrated spectrum. In 318 cases we could reliably constrain the peak energy E-peak(obs) of their vF(v) spectrum by analyzing their time-integrated spectrum between 8 keV and 35 MeV. Eighty percent of these spectra are fitted by a power-law with an exponential cutoff, and the remaining with the Band function. Among these 318 GRBs, 274 belong to the long GRB class and 44 to the short. Long GRBs have a typical peak energy E-peak(obs) similar to 160 keV and low-energy spectral index alpha similar to -0.92. Short GRBs have a harder peak energy (E-peak(obs) similar to 490 keV) and a harder low-energy spectral index (alpha similar to -0.50) than long bursts. For each Fermi GRB we also analyzed the spectrum corresponding to the peak flux of the burst. On average, the peak spectrum has a harder low-energy spectral index than the corresponding time-integrated spectrum for the same burst, but similar E-peak(obs). T he spectral parameters derived in our analysis of Fermi/GBM bursts are globally consistent with those reported in the GRB Cicular Network (GCN) archive after December 2008, while we found systematic differences in the low-energy power-law index for earlier bursts.
