  We present the full Lagrangian and supersymmetry transformation rules for the
gauged D=4, N=4 (half-maximal) supergravity coupled to an arbitrary number of
vector multiplets. Using the embedding tensor formulation, the final results
are universal and valid in arbitrary symplectic frames. We also analyze the
conditions for the critical points of the scalar potential and specify the full
spectrum of the quadratic fluctuations about Minkowski vacua. This allows us
also to exclude the appearance of quadratic divergences in the 1-loop
corrections to the scalar potential for any Minkowski vacuum fully breaking
supersymmetry. We also provide some interesting byproducts of our analysis,
like the field equations and the quadratic constraints for the fermion shifts
characterizing the gauging (also known as T-tensor identities).
