We prove that if $\mathcal{L} \subset \mathbb{R}^n$ is a lattice such that $\det(\mathcal{L}') \geq 1$ for all sublattices $\mathcal{L}' \subseteq \mathcal{L}$, then \[ \sum_{\mathbf{y} \in \mathcal{L}} (\|\mathbf{y}\|^2+q)^{-s} \leq \sum_{\mathbf{z} \in \mathbb{Z}^n} (\|\mathbf{z}\|^2+q)^{-s} \] for all $s > n/2$ and all $0 < q \leq (2s-n)/(n+2)$, with equality if and only if $\mathcal{L}$ is isomorphic to $\mathbb{Z}^n$.