  We study a family of functions defined in a very simple way as sums of powers
of binary Hermitian forms with coefficients in the ring of integers of an
Euclidean imaginary quadratic field $K$ with discriminant $d_K$. Using these
functions we construct a nontrivial cocycle belonging to the space of parabolic
cocycles on Euclidean Bianchi groups. We also show that the average value of
these functions is related to the special values of $L(\chi_{d_K},s)$. Using
the properties of these functions we give new and computationally efficient
formulas for computing some special values of $L(\chi_{d_K},s)$.
