  In this paper I investigate the analytic properties of the quark propagator
Dyson-Schwinger equation (DSE) in the Landau gauge. In the quark self-energy,
the combined gluon propagator and quark-gluon vertex is modeled by an effective
interaction (the so-called Maris-Tandy interaction), where the ultraviolet term
is neglected. This renders the loop integrand of the quark self-energy analytic
on the cut-plane -Pi < arg(x) < Pi of the square of the external momentum.
Exploiting the simplicity of the truncation, I study solutions of the quark
propagator in the domain x in [-5.1,0] GeV^2 X i[0,10.2] GeV^2. Because of a
complex conjugation symmetry, this region fully covers the parabolic
integration domain for Bethe-Salpeter equations (BSEs) for bound state masses
of up to 4.5 GeV. Employing a novel numerical technique that is based on highly
parallel computation on graphics processing units (GPUs), I extract more than
6500 poles in this region, which arise as the bare quark mass is varied over a
wide range of closely spaced values. The poles are grouped in 23 individual
'trajectories', that capture the movement of the poles in the complex region as
the bare mass is varied. The raw data of the pole locations and -residues is
provided as supplemental material, which can be used to parametrize solutions
of the complex quark propagator for a wide range of bare mass values and for
large bound state masses. This study is a first step towards an extension of
previous work on the analytic continuation of perturbative one-loop integrals,
with the long-term goal of establishing a framework that allows for the
numerical extraction of the analytic properties of the quark propagator with a
truncation that extends beyond the rainbow by making adequate adjustments in
the contour of the radial integration of the quark self-energy.

High Energy Physics - Phenomenology;Nuclear Theory