  We compute the strong coupling constant of Landau gauge QCD in the full
complex momentum plane, both directly and via spectral reconstruction. In
particular, we consider the Taylor coupling given by the product of ghost and
gluon dressing functions. Assuming spectral representations for the latter, we
first show that also the coupling obeys such a representation. The subsequent
spectral reconstruction of the coupling data, obtained from 2+1 flavour lattice
QCD results for the ghost and gluon, is based on a probabilistic inversion of
this representation using Gaussian process regression with analytically
enforced asymptotics. In contradistinction, our direct calculation relies on
earlier reconstruction results for the ghost and gluon spectral functions
themselves, as well as data obtained in functional QCD. Apart from its
relevance for studies of resonances or scattering processes, the calculation
also serves as a non-trivial benchmark of our reconstruction approach. The
results show remarkable agreement, testifying to the reliability of the method.
