Independent Zeta

Let $X$ and $Y$ be independent $\text{Zeta}(2)$ random variables. This means that they have PMF $\mathbb{P}[X=k] \propto \dfrac{1}{k^2}$ for all positive integers $k$. This means that the PMF is a constant multiple of $1/k^2$ for each $k$. Find $\text{Cov}(X,Y)$. If it is $+\infty$, enter $123$. If it is $-\infty$, enter $-123$. If it does not exist, enter $12345$.