  We study QCD thermodynamics in presence of two independent imaginary chemical
potentials coupled to two degenerate flavors of staggered quarks. Analytic
continuation is used to determine non-linear susceptibilities, to test the
Hadron Resonance Gas (HRG) model below the zero density critical temperature,
Tc, and to determine the average phase factor of the fermion determinant.
Deviations from HRG predictions, of the order of a few percent, are clearly
visible for temperatures T > 0.95 Tc. The determination of non-linear
susceptibilities, using different interpolating functions for analytic
continuation, gives consistent results and in agreement with Taylor expansion
computations, apart from some systematic effects at or right above Tc. Results
for the average phase factor are compared with the predictions of Chiral
Perturbation Theory; below Tc we are able to distinguish the contribution of
different hadron states, which is positive (i.e. tends to mitigate the sign
problem) in the case of baryons.
