  We consider the coincidence problem for the square lattice that is translated
by an arbitrary vector. General results are obtained about the set of
coincidence isometries and the coincidence site lattices of a shifted square
lattice by identifying the square lattice with the ring of Gaussian integers.
To illustrate them, we calculate the set of coincidence isometries, as well as
generating functions for the number of coincidence site lattices and
coincidence isometries, for specific examples.
