  The first principle lattice QCD methods allow to calculate the thermodynamic
observables at finite temperature and imaginary chemical potential. These can
be compared to the predictions of various phenomenological models. We argue
that Fourier coefficients with respect to imaginary baryochemical potential are
sensitive to modeling of baryonic interactions. As a first application of this
sensitivity, we consider the hadron resonance gas (HRG) model with repulsive
baryonic interactions, which are modeled by means of the excluded volume
correction. The Fourier coefficients of the imaginary part of the net-baryon
density at imaginary baryochemical potential -- corresponding to the fugacity
or virial expansion at real chemical potential -- are calculated within this
model, and compared with the $N_t = 12$ lattice data. The lattice QCD behavior
of the first four Fourier coefficients up to $T \simeq 185$ MeV is described
fairly well by an interacting HRG with a single baryon-baryon eigenvolume
interaction parameter $b \simeq 1$ fm$^3$, while the available lattice data on
the difference $\chi_2^B - \chi_4^B$ of baryon number susceptibilities is
reproduced up to $T \simeq 175$ MeV.
