  We examine closed geodesics in the quotient of hyperbolic three space by the
discrete group of isometries SL(2,Z[i]). There is a correspondence between
closed geodesics in the manifold, the complex continued fractions originally
studied by Hurwitz, and binary quadratic forms over the Gaussian integers.
According to this correspondence, a geodesic is called fundamental if the
associated binary quadratic form is. Using techniques from sieve theory,
symbolic dynamics, and the theory of expander graphs, we show the existence of
a compact set in the manifold containing infinitely many fundamental geodesics.
