Cauchy distribution and Fisher information

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Let $X$ has a Cauchy distribution with p.d.f. $$ f(x,\theta)=\frac{1}{\pi\left\{ 1+\left(x-\theta\right)^{2}\right\} } $$ , $-\infty<x<\infty$, $-\infty<\theta<\infty$.

The characteristic function of this distribution is $$ \phi\left(t\right)=e^{i\theta t-|t|}. $$

Question is : What is the Fisher information contained in $\bar{X}$?

I know that $\phi_{\bar{X}}\left(t\right)=\phi(t)$. It is Qualification exam problem, but what does this question want me to do?