## Numerical evaluation of this series

let be the series $$\sum_{n=0}^{\infty}\Lambda (n) cos(ulogn)$$ her /\(n) is the Mangoldt function.

i know this series is divergent for any value of parameter 'u' , my question is if there is any numerical method to obtain a finite value from this series by truncating upto some finite N

the zeta-regularized value of this series is the Real part of $$1/2 \frac{d}{du}log \zeta (1/2+iu)$$ but i would like to know if there is a method to evaluate it numerically.
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