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The winding of a closed oriented geodesic around the cusp of the modularorbifold is computed by the Rademacher symbol, a classical function from thetheory of modular forms. For a general cusped hyperbolic orbifold, we have aprocedure to associate to each cusp a Rademacher symbol. In this paper weconstruct winding numbers related to these Rademacher symbols. In cases wherethe two functions coincide, access to the spectral theory of automorphic formsyields statistical results on the distribution of closed (primitive) orientedgeodesics with respect to their winding.

Windings of prime geodesics