  We present the first self-consistent direct calculation of a spectral
function in the framework of the Functional Renormalization Group. The study is
carried out in the relativistic $O(N)$ model, where the full momentum
dependence of the propagators in the complex plane as well as
momentum-dependent vertices are considered. The analysis is supplemented by a
comparative study of the Euclidean momentum dependence and of the complex
momentum dependence on the level of spectral functions. This work lays the
groundwork for the computation of full spectral functions in more complex
systems.
