  We determine the pseudo-critical couplings at imaginary chemical potentials
by high-statistics Monte Carlo simulations of QCD with four degenerate quarks
at non-zero temperature and baryon density by the method of analytic
continuationan. We reveal deviations from the simple quadratic dependence on
the chemical potential visible in earlier works on the same subject. Finally,
we discuss the implications of our findings for the shape of the
pseudo-critical line at real chemical potential, comparing different possible
extrapolations.
