The ARE of the zero-frequency estimator is $\lambda/(e^\lambda-1)$, not a listed option

Let $X_1,X_2,\dots,X_n$ be independent Poisson$(\lambda)$ random variables and $T_1=\frac1n\sum_{i=1}^nI(X_i=0)$, $T_2=e^{-\bar X}$. Then, the asymptotic relative efficiency $\mathrm{ARE}(T_1,T_2)$ is: