This question is related to my question here, I have used The Riemann-Siegle theta function particulary its taylor series arround $t=0$ to check wether Riemann zeta function has an explicite inversion formula near $s=0$ may it exist as a formal power series using lagrange inversion theorem since it is converges for $|t|< \frac12 $ then :
What is the compositional inverse of Riemann zeta function near $s=0$ if it exists?
Note: The motivation of this question is to compute $\zeta^{-1}(\dfrac{-1}{2})$