A sum rule for the critical zeros of $ζ(s)$

The two-parameter series over the critical zeros of the Riemann Zeta function $Re\sum_ρ\frac{x^{(ρ-a)/4a}}{\sqrt{ρ-a}\sinh[\fracπ{2}\sqrt{\frac{ρ-a}{a}}]ζ'(ρ)}$ is evaluated in terms of $ζ(s)$ on the real axis.

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