Omega Centauri is no longer the only globular cluster known to contain multiple stellar populations, yet it remains the most puzzling. Due to the extreme way in which the multiple stellar population phenomenon manifests in this cluster, it has been suggested that it may be the remnant of a larger stellar system. In this work, we present a spectroscopic investigation of the stellar populations hosted in the globular cluster ω Centauri to shed light on its still puzzling chemical enrichment history. With this aim, we used FLAMES+GIRAFFE@VLT to observe 300 stars distributed along the multimodal red giant branch of this cluster, sampling with good statistics the stellar populations of different metallicities. We determined chemical abundances for Fe, Na, O, and n-capture elements Ba and La. We confirm that ω Centauri exhibits large star-to-star variations in iron with [Fe/H] ranging from ~-2.0 to ~-0.7 dex. Barium and lanthanum abundances of metal-poor stars are correlated with iron, up to [Fe/H] ~-1.5, while they are almost constant (or at least have only a moderate increase) in the more metal-rich populations. There is an extended Na-O anticorrelation for stars with [Fe/H] lsim-1.3 while more metal-rich stars are almost all Na-rich. Sodium was found to mildly increase with iron over the entire metallicity range. Based on data collected at the European Southern Observatory with the VLT-UT2, Paranal, Chile.