# Is it possible to compute $\Gamma(\rho_k)$ or $\zeta(3+2\omega_k)$, when $\rho_k=\frac{1}{2}+i\omega_k$ is a nontrivial zero of Riemann zeta function?

I believe that I can to use the equation (1) (from reference ), a well known equation involving the Gamma function, Riemann zeta function and the theta function $\psi(x)=\sum_{n=1}^\infty e^{-n^2\pi x}$, for relating $\Gamma(\rho_k)$ and $\zeta(3+2\omega_k)$, where $\rho_k=\frac{1}{2}+i\omega_k$ is a (fixed) nontrivial zero of Riemann zeta function, and is taken $3+2\omega_k=s_k$, as this manner $$\Gamma(\rho_k)\pi^{\frac{-s_k}{2}}\zeta(3+2\omega_k)=\int_{0}^\infty\psi(x)x^{\frac{s_k}{2}}\frac{dx}{x}.$$

Question. Can you compute (I believe that in terms of the given real $\omega_k$) the values $\Gamma(\rho_k)$ or $\zeta(3+2\omega_k)$, when we assume that $\rho_k=\frac{1}{2}+i\omega_k$ is a nontrivial (fixed) zero of Riemann zeta function? Thanks in advance.

I don't know if using the functionals equations my question could be easily answered, or is a difficult question, and I excuse to compute $\Gamma(\rho_k)$ or $\zeta(3+2\omega_k)$, for the case it is difficult compute both values.

References:

• I wish you Math Christmas and a Happy New $\frac{\left(\zeta(2)^2-\zeta(0)\zeta(4)\right)^3}{\zeta(0)^6\zeta(4)\zeta(8)}.$ After the bounty question was answered I will delete this last comment. Thanks – user243301 Dec 24 '15 at 16:16