  In this paper we present for the first time the angular power spectra
$C_\ell(z,z')$ for number counts from relativistic N-body simulations. We use
the relativistic N-body code gevolution with its exact integration of lightlike
geodesics which include all relativistic scalar contributions to the number
counts. We compare our non-perturbative numerical results with the results from
CLASS using the HMCODE approximation for the non-linear matter power spectrum.
We find that this simple description is excellent for both, the density and the
convergence. On the other hand, the current implementation of redshift-space
distortions in Boltzmann codes is not accurate. We also find that the largest
contribution to the unequal-redshift power spectra is the cross-correlation of
the density and the lensing contribution to the number counts, especially for
redshift bins that are far apart. Correlating the number counts with the
convergence map we find that the signal is dominated by the lensing-lensing
term when the convergence field redshift is not higher than the number counts
one, while it is dominated by the density-lensing term in the opposite case. In
the present study, the issue of galaxy bias is deliberately left aside by
considering only unbiased samples of matter particles from the simulations.
