I have seen the Fourier and Mellin transform for Riemann

$\Xi (t)=\xi ({\frac 12}+it)$

where:

$\xi (s)={\tfrac {1}{2}}s(s-1)\pi ^{{-s/2}}\Gamma \left({\tfrac {1}{2}}s\right)\zeta (s)$

Fourier transform of $\Xi(t)$ is:

$\Xi (t) = \int_{-\infty}^\infty\Phi(u)e^{iut}\,du$

Where:

$\Phi(u) = \sum_{n=1}^\infty (4\pi^2n^4e^{9u/2} - 6n^2\pi e^{5u/2} ) exp(-n^2\pi e^{2u})$

But I had not seen something similar for Fourier or Mellin transform for Riemann $\zeta(s)$ itself.

Is there a "closed form" formula for Fourier or Mellin transform for Riemann $\zeta(s)$ itself ?

Thank you.