Legend

• H: toggle upper half plane
• Space: toggle transform
• T: τ ↦ τ + 1 (Shift+T to perform inverse)
• R: τ ↦ τ/(1 - τ) (Shift+R to perform inverse)
• S: τ ↦ −1/τ
• W: τ ↦ τ + 1 left action
• Q: τ ↦ τ/(τ + 1) left action
• F: Fricke involution
• I: Reset to identity