Calculate calculate $E(\frac{1}{\bar X})$, Var$(\frac{1}{\bar X})$

Question

Consider n i.i.d. observations from a Poisson (λ) distribution.

Suppose $\bar X =\frac1n\sum_{i=1}^n X_i.$

How do I calculate Var$(\frac{1}{\bar X})$ or even $E(\frac{1}{\bar X})$ for that matter.

I know that $E(\frac{1}{\bar X})\ne \frac{1}{E(\bar X)}.$ Hence I'm stuck.