Inverse of the Riemann zeta function

Question

Is there an inverse function of the Riemann zeta function? A formula for inverse function is \begin{equation} f^{-1}(y) =\sum_{n=1}^\infty \frac{y^{n/3}}{n!}\cdot\lim_{ \theta \to 0} \left(\frac{\mathrm{d}^{\,n-1}}{\mathrm{d} \theta^{\,n-1}} \left(\frac \theta { \sqrt[3]{ \theta - \sin( \theta )} } \right)^n\right). \end{equation} Can this help to evaluate the inverse?
If there isn't an inverse for all the complex numbers, is there a formula for the inverse at a specific interval, for example the critical strip?