 Lattice Eisenstein sum

For a period lattice $\Lambda \subset \mathbb{C}$ and an integer $k>2$, this sum converges absolutely. Pairing $\omega$ and $-\omega$ makes it zero when $k$ is odd. For even weights it supplies the Laurent coefficients of the Weierstrass elliptic function. Scaling the period lattice gives $G_k(a\Lambda )=a^{-k}{G}_k(\Lambda )$.