  We present evidence for a spatially-dependent systematic error in the first
data release of ${\it Gaia}$ parallaxes based on comparisons to asteroseismic
parallaxes in the ${\it Kepler}$ field, and present a parametrized model of the
angular dependence of these systematics. We report an error of
$0.059^{+0.004}_{-0.004}$mas on scales of 0.3deg, which decreases for larger
scales to become $0.011^{+0.006}_{-0.004}$mas at 8deg. This is consistent with
the $\sim2\%$ zeropoint offset for the whole sample discussed by Huber et al.,
and is compatible with the effect predicted by the ${\it Gaia}$ team. Our
results are robust to dust prescriptions and choices in temperature scales used
to calculate asteroseismic parallaxes. We also do not find evidence for
significant differences in the signal when using red clump versus red giant
stars. Our approach allows us to quantify and map the correlations in an
astrophysically interesting field, resulting in a parametrized model of the
spatial systematics that can be used to construct a covariance matrix for any
work that relies upon TGAS parallaxes.
