# What does the following distribution look like?

I want to pick $$x+\sqrt{-1}y$$ at random with respect to the hyperbolic measure from the standard domain $$\{z:|z|\geq1,|\mathcal R(z)|\leq\frac12\}$$ for $$SL_2(\mathbb Z)\backslash\mathbb H$$. What does the probability distribution function of $$\frac1{\sqrt y}$$ look like?