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given a sum over the imaginary part of the zeros $ \sum_{t} h(t) $

is this version of the Riemann-Weyl formula correct?

$ \sum _{t} h(t) -2h(i/2)= -2 \sum_{n=1}^{\infty}\Lambda (n)g(\log n)n^{-1/2}+ \frac{1}{2\pi} \int_{-\infty}^{\infty}\mathrm{d}r h(r) \Psi(1/4+ir/2)-g(0)\log\pi $

here $ h(r)=h(-r) $ and $ g(x)=g(-x)$ and are related by a Fourier transform

my question here is if the sum over the IMAGINARY PARTS of the zeros is taken over ALL the complex plane or only the positive imaginary part that lie on the upper complex plane are taken into account

i have tried reading Weil-Guinand explicit formula but it seems there is a facto 2 missing

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