  For primitive non-trivial Dirichlet characters $\chi_1$ and $\chi_2$, we
study the weight zero newform Eisenstein series $E_{\chi_1,\chi_2}(z,s)$ at
$s=1$. The holomorphic part of this function has a transformation rule that we
express in finite terms as a generalized Dedekind sum. This gives rise to the
explicit construction (in finite terms) of elements of $H^1(\Gamma_0(N),
\mathbb{C})$. We also give a short proof of the reciprocity formula for this
Dedekind sum.
