  In this work we exploit Jonqui\`{e}re's formula relating the Hurwitz zeta
function to a linear combination of polylogarithmic functions in order to
evaluate the real and imaginary part of $\zeta_{H}(s,ia)$ and its first
derivative with respect to the first argument $s$. In particular, we obtain
expressions for the real and imaginary party of $\zeta_{H}(s,i a)$ and its
derivative for $s=m$ with $m\in\mathbb{Z}\backslash\{1\}$ involving simpler
transcendental functions.
