  Let \Gamma<\PSL(2,\C) be a geometrically finite non-elementary discrete
subgroup, and let its critical exponent \delta\ be greater than 1. We use
representation theory of \PSL(2,\C) to prove an effective bisector counting
theorem for \Gamma, which allows counting the number of points of \Gamma\ in
general expanding regions in \PSL(2,\C) and provides an explicit error term. We
apply this theorem to give power savings in the Apollonian circle packing
problem and related counting problems.
