How to show that the following function is Schwarz

Question

We know $f(x)$ is in Schwartz space if for given $m,k $ non-negative integers the supremum of $ \left|x^{m } f^{(k)}(x) \right| $ over the real numbers is finite. Let $a $ be positive real and $f(t) = (|\Gamma (a+ i t )| )^2 $ is in Schwarz space.