  We analyse Gaia EDR3 parallax systematics as a function of magnitude and sky
location using a recently published catalogue of 12,500 asteroseismic red-giant
star distances. We selected ~ 3500 red clump (RC) stars of similar chemical
composition as the optimal subsample for this purpose. We perform a detailed
assessment of systematic uncertainties relevant for parallax offset estimation
based on the asteroseismic distances. Following this assessment, we adopt for
our baseline analysis the asteroseismic parameters measured as in Elsworth et
al. (2020), spectroscopy from APOGEE (DR17), and we further restrict the sample
to low-extinction RC stars with quality astrometric solutions from Gaia EDR3.
We then investigated both the parallax offset relative to the published Gaia
EDR3 parallaxes and the residual parallax offset after correcting Gaia EDR3
parallaxes following Lindegren et al. (2021).
  We find residual parallax offsets very close to zero (-1.6 +/- 0.5 (stat.)
+/- 10 (syst.) muas) for stars fainter than G > 11 mag in the initial Kepler
field. For 17 K2 campaigns in the same magnitude range, the residual parallax
offset is +16.5 +/- 1.7 (stat.) +/- 10 (syst.) muas. At brighter magnitudes (G
<= 11 mag), we find inconsistent residual parallax offsets between the Kepler
field, 17 K2 campaigns, and the TESS southern continuous viewing zone, with
differences of up to 60 muas. This suggests a significant dependence on sky
location at bright magnitudes due to the lack of bright physical pairs
available for determining the parallax offset corrections. Finally, we estimate
the absolute magnitude of the RC and obtain M_Ks^RC = -1.650 +/- 0.025 mag in
the 2MASS Ks-band and M_G^RC = (0.432 +/- 0.004) - (0.821 +/- 0.033) (Teff [K]
- 4800K)/1000K [mag] in the Gaia G-band.
