  We solve, numerically, the massless spin-2 equations, written in terms of a
gauge based on the properties of conformal geodesics, in a neighbourhood of
spatial infinity using spectral methods in both space and time. This strategy
allows us to compute the solutions to these equations up to the critical sets
where null infinity intersects with spatial infinity. Moreover, we use the
convergence rates of the numerical solutions to read-off their regularity
properties.
