  We investigate the quality of the extrapolation procedure employed in Ref.
[1] to extract the crossover line at real chemical potential from lattice data
at imaginary potential. To this end we employ a functional approach that does
not suffer from the sign problem. We utilize a well-studied combination of
lattice Yang--Mills theory with a truncated set of Dyson--Schwinger equations
in Landau gauge for $2 + 1$ quark flavors. This system predicts a critical
endpoint at moderate temperatures and rather large (real) chemical potential
with a curvature comparable to recent lattice extrapolations. We determine the
light quark condensate and chiral susceptibility at imaginary chemical
potentials and perform an analytic continuation along the lines described in
[1]. We find that the analytically continued crossover line agrees very well
(within one percent) with the explicitly calculated one for chemical potentials
up to about 80 % of the one of the critical end point. The method breaks down
in the region where the chiral susceptibility as a function of the condensate
cannot any longer be well described by a polynomial.

High Energy Physics - Phenomenology;High Energy Physics - Lattice