Let X be an arithmetic surface on which G, a finite group, tamely acts. Let Y be the quotient X/G, and let V be a representation of G. Associated to this setup, one can define an L-function and an epsilon constant which turns up in the functional equation of said L-function. In this talk, I will discuss a result which allows one to compute the epsilon constant by looking only at how the representation acts on a finite collection of points of Y under the additional hypothesis that V is in fact an orthogonal representation.