Laplace transform of power of zeta function

Question

Let $s$ is the complex variable. I would like to figure out the region of absolutely convergency of the following integral $$ e^{\frac{is}{2}}\int\limits_{\frac{1}{2}-i\infty}^{\frac{1}{2}+i\infty}\Gamma^k(z)\zeta^{2k}(z)\left(\ (2\pi i)^k e^{-is}\right)^{-z}dz $$