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 Oˇ, in the sense of Arthur and Barbasch-Vogan. Here Oˇ 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 Oˇ. We also reduce the problem of constructing special unipotent representations attached to Oˇ to the case when Oˇ is analytically even (equivalently for a real classical group, has good parity in the sense of Mœglin). The paper is the first in a series of two papers on the classification of special unipotent representations of real classical groups
