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Let $\lambda$ be the lambda modular function on the complex upper half plane. It induces an analytic isomorphism $\lambda:X(2) \longrightarrow \mathbf{P}^1$ and sends $X(2) - Y(2)$ to $\{0,1,\infty\}$

Consider the point $a= \frac{1+i \sqrt{3}}{2}$ in $ \mathbf{P}^1$.

How can I compute the inverse image of $a$ in $X(2)$?

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