Let $ \Lambda$ be the von Mangoldt function and $ \chi$ a primitive character mod $ q$ , then we have the explicit formula $ $ \sum_{n \leq X} \Lambda(n) \chi(n) = \delta_{\chi} X – \sum_{ |Im \ \rho| \leq T} \frac{X^{\rho}}{\rho} + O((\frac{X}{T}+1) \log^2(qXT)), $ $ where $ \delta_{\chi}$ is $ 1$ if $ \chi$ is the principal character and $ 0$ otherwise, and $ \rho$ ‘s are the non-trivial zeros of the $ L$ function $ L(s, \chi)$ . From this formula we can easily deduce that $ $ | \sum_{ |Im \ \rho| \leq T} \frac{X^{\rho}}{\rho} | \ll X. $ $ I was wondering does the bound still hold if I put the absolute value inside the sum?, i.e. do we have $ $ \sum_{ |Im \ \rho| \leq T} | \frac{X^{\rho}}{\rho} | \ll X. $ $ My guess is that it is true but I was not sure how to see this. Any comments would be appreciated. Thank you very much.