Let us consider the Riemann Zeta function non-trivial zeros $\rho_{n}=\frac{1}{2} + i\gamma_{n}$. Let us now consider the following sum: $\tau (n)=\sum_{k=1}^{n}\sin(k)\sin(\gamma _{k})$ where: $\gamma _{1}=14.1347251417346\ldots$ $\gamma _{2}=21.0220396387715\ldots$ $\gamma _{3}=25.0108575801456\ldots$ etc This is the plot of $\tau (n)$ for $n$ between 1 and $10^4$: ![Plot 1][1] My question is: does anyone know any articles where this periodicity is investigated? [1]: https://i.sstatic.net/xqpws.png