  In [5], P. Lecomte conjectured the existence of a natural and conformally
invariant quantization. In [7], we gave a proof of this theorem thanks to the
theory of Cartan connections. In this paper, we give an explicit formula for
the natural and conformally invariant quantization of trace-free symbols thanks
to the method used in [7] and to tools already used in [8] in the projective
setting. This formula is extremely similar to the one giving the natural and
projectively invariant quantization in [8].
