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Given a finite group G, we say that a subset C of G is power-closed if, forevery x in C and y in <x> with <x>=<y>, we have that y lies in C.  In this paper we are interested in finite Cayley digraphs Cay(G,C) over Gwith connection set C, where C is a union of conjugacy classes of G. We showthat each eigenvalue of Cay(G,C) is integral if and only if C is power-closed.This result will follow from a discussion of some more general rationalityconditions on the eigenvalues of Cay(G,C).

Rationality conditions for the eigenvalues of normal finite Cayley graphs