The space of continuous, SL(m, C)-equivariant, m ≥ 2, and translation covariant valuations taking values in the space of real symmetric tensors on C m ∼ = R 2m of rank r ≥ 0 is completely described. The classification involves the moment tensor valuation for r ≥ 1 and is analogous to the known classification of the corresponding tensor valuations that are SL(2m, R)equivariant, although the method of proof cannot be adapted. * AMS 2010 subject classification: Primary 52B45; Secondary 52A40