Elliptic stabilizers of the modular group
= Elliptic stabilizers of the modular group
For the boundary convention $-1/2<\operatorname{Re}z\leq1/2$, retaining only the right half of the unit circle, the exceptional points are $i$ and $\rho_+=e^{i\pi/3}$. Their stabilizers in $SL_2(\mathbb Z)$ are the cyclic groups generated by $\begin{pmatrix}0&-1\\1&0\end{pmatrix}$ and $\begin{pmatrix}1&-1\\1&0\end{pmatrix}$, of orders four and six. Every other stabilizer is $\{I,-I\}$.