  We are interested in diagonal perturbations of a periodic Jacobi operator
that introduce embedded eigenvalues in its essential spectrum. Embedding
multiple points in the essential spectrum has been known to be difficult, given
that eigenvalues are destroyed easily by small perturbations. However, given a
finite or countably infinite set of points within an absolutely continuous band
of the original periodic operator (subject only to a very weak non-resonance
condition) we are able to construct a diagonal perturbation that preserves the
essential spectrum and places eigenvalues in all of those points.
