I have done some search many times on web to find any approximation of $\log|(\zeta'(s))|$ in Dirichlet polynomial but I didn't got it, Probably that $\log(|\zeta'(s)|$ dosn't have a Dirichlet polynomial approximation yield probably for $\log(|\zeta'(\frac{1}{2}+it)|)$ also dosn't have an approximation in Dirichlet polynomial but I do not have complet confidence for that , Now my question here is: What is the approximation of $\log(|\zeta'(\frac{1}{2}+it)|)$ in Dirichlet polynomiall if it is exists ?

**Edit** $s$ is a complex variable ,note that $0<t\leq T$ , $T$ is large enough, I have added this detail because I missed it when I posted the question.

**Related question:**
(Series representation for $\log(|\zeta(\frac{1}{2}+it)|)$)

**Note** The motivation of this question is the mean -value estimate of derivative of Riemann zeta function over non trivial zero of Riemann zeta function