  When modelling an ionised plasma, all spectral synthesis codes need the
thermally averaged free-free Gaunt factor defined over a very wide range of
parameter space in order to produce an accurate prediction for the spectrum.
Until now no data set exists that would meet these needs completely. We have
therefore produced a table of relativistic Gaunt factors over a much wider
range of parameter space than has ever been produced before. We present tables
of the thermally averaged Gaunt factor covering the range log10(gamma^2) = -6
to 10 and log10(u) = -16 to 13 for all atomic numbers Z = 1 through 36. The
data were calculated using the relativistic Bethe-Heitler-Elwert (BHE)
approximation and were subsequently merged with accurate non-relativistic
results in those parts of the parameter space where the BHE approximation is
not valid. These data will be incorporated in the next major release of the
spectral synthesis code Cloudy. We also produced tables of the frequency
integrated Gaunt factor covering the parameter space log10(gamma^2) = -6 to 10
for all values of Z between 1 and 36. All the data presented in this paper are
available online.
