Based on ab initio electronic structure calculations, the three-dimensional potential energy functions for the electronic ground state X 2-PI(g) of N3 have been generated and used in beyond Born-Oppenheimer calculations of the rovibronic energy levels by a variational approach accounting for anharmonicity, rotation-vibration, electronic angular momenta, and electron spin coupling effects. The vibronic levels (J = P) for energies up to 4300 cm-1 are given. The few experimentally known vibronic energy differences have been reproduced with an accuracy of better than 10 cm-1. For several vibronic levels also the rovibronic levels are reported. The electron-nuclear motion and anharmonic coupling effects have been analyzed. The strength of the Born-Oppenheimer breakdown depends strongly on the rovibronic symmetry. Like in the isoelectronic CO2+ ion, the anharmonic coupling in the vibronic states occurs mainly within the blocks of Fermi polyads for (2v1 + v2) = constant. In low lying states the anharmonic coupling effects are weaker in N3 than in CO2+. The presence of the Fermi polyad blocks of interacting states strongly alleviates the characterization of the excited rovibronic states in the N3 radical.