Singular Series

$$\rho_{2s}(n)={\pi^s\over\Gamma(s)} n^{s-1} \sum_{p, q} \left({S_{p, q}\over q}\right)^{2s} e^{2np\pi i/q},$$

where $S_{p,q}$ is a Gaussian Sum, and $\Gamma(s)$ is the Gamma Function.