The organization of the lipid headgroups in a neutral model membrane is studied by atomistic simulations in the fluid lamellar phase, L-alpha. In particular, we report the results obtained for a fully hydrated 1-stearoyl-2-docosahexaenoyl-sn-glycero-3-phosphocholine lipid bilayer at room temperature. The orientational distribution of the lipid dipole moments with respect to the membrane normal presents a maximum at 70degrees (20degrees above the plane of the interface, pointing toward the water region). We also found another smaller peak at 110degrees (-20degrees with respect to the membrane plane). This preferential orientation of the lipid headgroup dipoles with respect to the bilayer normal obtained at 303 K is qualitatively different from previous calculations at higher temperatures in the fluid lamellar phase, where headgroup dipoles were uniformly distributed with orientations spanning 0degrees-135degrees. Despite their differences, both situations give rise to a similar mean orientation of similar to70degrees, which is in excellent agreement with experiment. The statistics of the main lipid-lipid interactions, the charge density profiles, the electrostatic potential along the bilayer normal, and the polarization of water molecules at the interfacial plane are also analyzed.