  We study the image of a generalized Dedekind sum relating to the weight zero
Eisenstein series $E_{\chi_1,\chi_2}$. We show that the image is a lattice of
full rank inside a number field determined by the characters $\chi_1$ and
$\chi_2$. We also give a generalization of Knopp's identity for the classical
Dedekind sum.
