  Taking the d-th distance power of a graph, one adds edges between all pairs
of vertices of that graph whose distance is at most d. It is shown that only
the numbers -3, -2, -1, 0, 1, 2d can be integer eigenvalues of a circuit
distance power. Moreover, their respective multiplicities are determined and
explicit constructions for corresponding eigenspace bases containing only
vectors with entries -1, 0, 1 are given.
