  We study numerically the properties of (statistically) homogeneous soliton
gas depending on soliton density (proportional to number of solitons per unit
length) and soliton velocities, in the framework of the focusing
one-dimensional Nonlinear Schr{\"o}dinger (NLS) equation. In order to model
such gas we use N-soliton solutions (N-SS) with $N\sim 100$, which we generate
with specific implementation of the dressing method combined with 100-digits
arithmetics. We examine the major statistical characteristics, in particular
the kinetic and potential energies, the kurtosis, the wave-action spectrum and
the probability density function (PDF) of wave intensity.
  We show that in the case of small soliton density the kinetic and potential
energies, as well as the kurtosis, are very well described by the analytical
relations derived without taking into account soliton interactions. With
increasing soliton density and velocities, soliton interactions enhance, and we
observe increasing deviations from these relations leading to increased
absolute values for all of these three characteristics. The wave-action
spectrum is smooth, decays close to exponentially at large wavenumbers and
widens with increasing soliton density and velocities. The PDF of wave
intensity deviates from the exponential (Rayleigh) PDF drastically for rarefied
soliton gas, transforming much closer to it at densities corresponding to
essential interaction between the solitons. Rogue waves emerging in soliton gas
are multi-soliton collisions, and yet some of them have spatial profiles very
similar to those of the Peregrine solutions of different orders. We present
example of three-soliton collision, for which even the temporal behavior of the
maximal amplitude is very well approximated by the Peregrine solution of the
second order.
