Li's numbers $\{\lambda_n\}$ are defined as $$\lambda_n=\frac{1}{(n-1)!}\frac{d^n}{ds^n} [s^{n-1}\log\xi(s)]_{s=1} $$ for all positive integers $n$. Also $\lambda_n$ is given as a sum over the non trivial zeros of $\zeta(s)$ by $$\lambda_n=\sum_{\rho}\left[1-\left(1-\frac{1}{\rho}\right)^n\right] $$ where $\rho$ are the non trivial zeros of the Riemann zeta function.

My question is:

Are the $\lambda_n$'s absolutely convergent for $n>1$?

An article of Mark W. Coffey "On certian sums over the non trivial zeta zeros" the year being (2010) says in line 1 p.2 that fot $n>1$, $\lambda_n$ is absolutely convergent, while for $\lambda_1$ the sum should be taken over complex conjugate pairs of zeros of increasing imaginary part.

An answer or a reference is desired.