  We analyze the low-lying spectrum and eigenmodes of lattice Dirac operators
with a twisted mass term. The twist term expels the eigenvalues from a strip in
the complex plane and all eigenmodes obtain a non-vanishing matrix element with
gamma-5. For a twisted Ginsparg-Wilson operator the spectrum is located on two
arcs in the complex plane. Modes due to non-trivial topological charge of the
underlying gauge field have their eigenvalues at the edges of these arcs and
obey a remnant index theorem. For configurations in the confined phase we find
that the twist mainly affects the zero modes, while the bulk of the spectrum is
essentially unchanged.
