The results presented have been obtained in collaboration with P.M. Santini (University of Roma I). We consider the periodic direct spectral problem for the self-focusing NLS equation in a special situation corresponding to a small perturbation of the constant solution. This model is actively used now as a model for generation of the rogue waves in nonlinear medias. We show that in this special situation all ingredients of the theta-functional formulas can be efficiently calculated as explicit power series with respect to the amplitude of the perturbation.