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convergence of a particular series
I am reading about the construction of the Weierstrass $\wp$-function for an arbitrary lattice in $\mathbb{C}$. If $a, b$ are complex nonzero numbers with $a/b \not\in \mathbb{R}$ and $\Lambda = \{ma + nb: m, n \in \mathbb{Z}\} \subset \mathbb{C}$, why does $$\sum_{\omega \in \Lambda - \{0\}}\frac{1}{|\omega|^{3}}$$ converge?