Numerical calculation of conformally smooth hyperboloidal data

This is the third paper in a series describing a numerical implementation o f the conformal Einstein equation. This paper describes a scheme to calcula te (three-)dimensional data for the conformal field equations from a set of free functions. The actual implementation depends on the topology of the s pacetime. We discuss the implementation and exemplary calculations for data leading to spacetimes with one spherical null infinity (asymptotically Min kowski) and for data leading to spacetimes with two toroidal null infinitie s (asymptotically A3). We also outline the (technical) modifications of the implementation needed to calculate data for spacetimes with two and more s pherical null infinities (asymptotically Schwarzschild and asymptotically m ultiple black holes).