To investigate the relations between Appell / Jensen polynomials and the real-valued function for real $t$
$$\Omega(t) = \xi(1/2+it)/\xi(1/2),$$
where $\xi(s)$ is the Landau Riemann xi function, I need reasonable approximations, say to 3 significant digits, of
$$ Tr_{2n}= \sum_{k=0}^\infty 1/(z_k)^{2n}$$
for $n=1,2,3,4$ where the $z_k$ are the imaginary parts of the nontrivial zeros of the Riemann zeta function above the real axis. (Assume the RH is true, of course.)
I don't have access to Mathematica nor Maple, so help would be appreciated.
Edit (June 5, 2020):
To allay any further doubts about the convergence of $Tr_2$:
Titchmarsh in his classic book On the Theory of the Riemann Zeta Function has, on p. 18, Eqn 2.1.14
$$\Xi(z)= \xi(1/2+iz),$$
and on p. 30 he states that it is an even integral function of order 1, whose exponent of convergence is 1. "Hence $\Xi(z)$ has an infinity of zeros, whose exponent of convergence is 1. The same is true of $\xi(s).$" In his Theory of Functions on p. 249 is
Theorem 8.22: If $r_1, r_2...$ are the moduli of the roots of $f(z)$, then the series $\sum 1/r^{\alpha}$ is convergent if $\alpha > \rho.$
$\rho$ in an earlier paragraph is called the order of the integral function $f(z)$.
The absolute contribution of a zero of $\Omega$, $a+ib$, and its complex conjugate to the sum of the inverse squares of the zeros is $2(a^2-b^2)/(a^2+b^2)^2=2\cos(2\theta)/r^2$ with $\theta=0$ for the real zeros. This is less than $2/r^{\alpha}$ for $0< \alpha < 2$, so the trace of the paired inverse squares, even including any complex zeros if they were to be found, is absolutely convergent