(\frac{\theta_0 i}{0}, \frac{\varphi i}{0}+\pi i, \frac{|\beta|}{0} + \pi i)$ and $S(\frac{\theta_0 i}{0}, \frac{\varphi i}{0}+\pi i, \frac{|\beta|}{0} + \pi i)$ the value used for $\Delta_0$ is $\frac{