  We study numerically the spectrum of the non-Hermitian effective Hamiltonian
that describes the dipolar interaction of a gas of $N\gg 1$ atoms with the
radiation field. We analyze the interplay between cooperative effects and
disorder for both scalar and vectorial radiation fields. We show that for dense
gases, the resonance width distribution follows, both in the scalar and
vectorial cases, a power law $P(\Gamma) \sim \Gamma^{-4/3}$ that originates
from cooperative effects between more than two atoms. This power law is
different from the $ P(\Gamma) \sim \Gamma^{-1}$ behavior, which has been
considered as a signature of Anderson localization of light in random systems.
We show that in dilute clouds, the center of the energy distribution is
described by Wigner's semicircle law in the scalar and vectorial cases. For
dense gases, this law is replaced in the vectorial case by the Laplace
distribution. Finally, we show that in the scalar case the degree of resonance
overlap increases as a power law of the system size for dilute gases, but
decays exponentially with the system size for dense clouds.
