  The standard cosmological model is inherently relativistic, and yet a wide
range of cosmological observations can be predicted accurately from essentially
Newtonian theory. This is not the case on `ultra-large' distance scales, around
the cosmic horizon size, however, where relativistic effects can no longer be
neglected. In this paper, we present a novel suite of 53 fully relativistic
simulations generated using the gevolution code, each covering the full sky out
to $z \approx$ 0.85, and approximately 1930 square degrees out to $z \approx$
3.55. These include a relativistic treatment of massive neutrinos, as well as
the gravitational potential that can be used to exactly calculate observables
on the past light cone. The simulations are divided into two sets, the first
being a set of 39 simulations of the same fiducial cosmology (based on the
Euclid Flagship 2 cosmology) with different realisations of the initial
conditions, and the second which fixes the initial conditions, but varies each
of seven cosmological parameters in turn. Taken together, these simulations
allow us to perform statistical studies and calculate derivatives of any
relativistic observable with respect to cosmological parameters. As an example
application, we compute the cross-correlation between the Doppler magnification
term in the convergence, $\kappa_v$, and the CDM+baryon density contrast,
$\delta_{\rm cb}$, which arises only in a (special) relativistic treatment. We
are able to accurately recover this term as predicted by relativistic
perturbation theory, and study its sample variance and derivatives with respect
to cosmological parameters.
