The inverse mellin transform of the reciprocal of the Archimedean factor of the Zeta function

Question

How to compute the inverse Mellin transform of $\frac{1}{\pi^{-s/2}\Gamma(s/2)}$? Or equivalently, if $*$ denote the multiplicative convolution, what is the convolutional inverse of $e^{-x^2\pi}$? that is, $f$ such that

$$e^{-x^2\pi}*f=\delta(t-1).$$

Thank you.