  Let $G$ be a real reductive group in Harish-Chandra's class. We derive some
consequences of theory of coherent continuation representations to the counting
of irreducible representations of $G$ with a given infinitesimal character and
a given bound of the complex associated variety. When $G$ is a real classical
group (including the real metaplectic group), we investigate the set of special
unipotent representations of $G$ attached to $\check{\mathcal O}$, in the sense
of Arthur and Barbasch-Vogan. Here $\check{\mathcal O}$ is a nilpotent adjoint
orbit in the Langlands dual of $G$ (or the metaplectic dual of $G$ when $G$ is
a real metaplectic group). We give a precise count for the number of special
unipotent representations of $G$ attached to $\check{ \mathcal O}$. We also
reduce the problem of constructing special unipotent representations attached
to $\check{\mathcal O}$ to the case when $\check{\mathcal O}$ is analytically
even (equivalently for a real classical group, has good parity in the sense of
M{\oe}glin). The paper is the first in a series of two papers on the
classification of special unipotent representations of real classical groups.
