  We consider the spectrum of transfer matrix eigenvalues associated with
Polyakov loops in lattice QCD at strong coupling. The transfer matrix at finite
density is non-Hermitian, and its eigenvalues become complex as a manifestation
of the sign problem. We show that the symmetry under charge conjugation and
complex conjugation ensures that the eigenvalues are either real or part of a
complex conjugate pair, and the complex pairs lead to damped oscillatory
behavior in Polyakov loop correlation functions, which also appeared in our
previous phenomenological models using complex saddle points. We argue that
this effect should be observable in lattice simulations of QCD at finite
density.
