  (Abridged) We have conducted a detailed investigation of the broad-band
spectral properties of the \gamma-ray selected blazars of the Fermi LAT Bright
AGN Sample (LBAS). By combining our accurately estimated Fermi gamma-ray
spectra with Swift, radio, infra-red, optical and other hard X-ray/gamma-ray
data, collected within three months of the LBAS data taking period, we were
able to assemble high-quality and quasi-simultaneous Spectral Energy
Distributions (SED) for 48 LBAS blazars.The SED of these gamma-ray sources is
similar to that of blazars discovered at other wavelengths, clearly showing, in
the usual Log $\nu $ - Log $\nu$ F$_\nu$ representation, the typical broad-band
spectral signatures normally attributed to a combination of low-energy
synchrotron radiation followed by inverse Compton emission of one or more
components. We have used these SEDs to characterize the peak intensity of both
the low and the high-energy components. The results have been used to derive
empirical relationships that estimate the position of the two peaks from the
broad-band colors (i.e. the radio to optical and optical to X-ray spectral
slopes) and from the gamma-ray spectral index. Our data show that the
synchrotron peak frequency $\nu_p^S$ is positioned between 10$^{12.5}$ and
10$^{14.5}$ Hz in broad-lined FSRQs and between $10^{13}$ and $10^{17}$ Hz in
featureless BL Lacertae objects.We find that the gamma-ray spectral slope is
strongly correlated with the synchrotron peak energy and with the X-ray
spectral index, as expected at first order in synchrotron - inverse Compton
scenarios. However, simple homogeneous, one-zone, Synchrotron Self Compton
(SSC) models cannot explain most of our SEDs, especially in the case of FSRQs
and low energy peaked (LBL) BL Lacs. (...)
