  Thermodynamics of the quark-gluon plasma at finite density is studied in the
framework of the Field Correlator Method, where thermodynamical effects of
Polyakov loops and colormagnetic confinement are taken into account. Having
found good agreement with numerical lattice data for zero density, we calculate
pressure $P(T,\,\mu)$ for $0 <\mu< 400$ MeV and $150 <T< 1000$ MeV. For the
first time the explicit intergral form is found in this region,demonstrating
analytic structure in the complex $\mu$ plane. The resulting multiple complex
branch points are found at the Roberge-Weiss values of
$\operatorname{Im}\,\mu$, with $\operatorname{Re}\,\mu$ defined by the values
of Polyakov lines and colormagnetic confinement.
