  We show that the spectrum of the Dirac operator in complex Langevin
simulations of QCD at non-zero chemical potential must behave in a way which is
radically different from the one in simulations with ordinary non-complexified
gauge fields: At low temperatures the small eigenvalues of the Dirac operator
must be inside the quark mass for chemical potentials as large as a third of
the nucleon mass. In particular, in the chiral limit the Dirac eigenvalues of
complex Langevin simulations must accumulate at the origin.
