  We study the orbital structure of a self-consistent N-body equilibrium
configuration of a barred galaxy constructed from cosmological initial
conditions. The value of its spin parameter L is near the observed value of our
Galaxy L=0.22. We classify the orbits in regular and chaotic using a
combination of two different methods and find 60% of them to be chaotic. We
examine the phase space using projections of the 4D surfaces of section for
test particles as well as for real N-body particles. The real particles are not
uniformly distributed in the whole phase space but they avoid orbits that do
not support the bar. We use frequency analysis for the regular orbits as well
as for the chaotic ones to classify certain types of orbits of our
self-consistent system. We find the main resonant orbits and their statistical
weight in supporting the shape of the bar and we emphasize the role of weakly
chaotic orbits in supporting the boxiness at the end of the bar.
