Explicit approximation of the sum of the reciprocal of the imaginary parts of the zeta zeros

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In this note, we give some explicit upper and lower bounds for the summation $\sum_{0<γ\leq T}\frac{1}γ$, where $γ$ is the imaginary part of nontrivial zeros $ρ=β+iγ$ of $ζ(s)$.
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