  Let $G_{\mathbb{R}}$ be a simple real linear Lie group with maximal compact
subgroup $K_{\mathbb{R}}$ and assume that ${\rm rank}(G_\mathbb{R})={\rm
rank}(K_\mathbb{R})$. In \cite{MPVZ} we proved that for any representation $X$
of Gelfand-Kirillov dimension $\frac{1}{2}\dim(G_{\mathbb{R}}/K_{\mathbb{R}})$,
the polynomial on the dual of a compact Cartan subalgebra given by the
dimension of the Dirac index of members of the coherent family containing $X$
is a linear combination, with integer coefficients, of the multiplicities of
the irreducible components occurring in the associated cycle. In this paper we
compute these coefficients explicitly.
