Eigenvalues of hyperbolic elements in Kleinian groups

Let Γ be a torsion-free Kleinian group, so that M = H/Γ is an orientable hyperbolic 3-manifold. The non-trivial elements of Γ are classified as either parabolic or hyperbolic. If γ ∈ Γ is hyperbolic, then γ has an axis in H which projects to a closed geodesic gγ in M (which depends only on the conjugacy class of γ in Γ). The element γ acts on its axis by translating and possibly rotating around the axis. In terms of eigenvalues, if γ ∈ Γ is hyperbolic, we let