Two passive two-port networks $\mathbf{P}$ and $\mathbf{Q}$ are connected as shown in the figure. The impedance matrix of network $\mathbf{P}$ is $Z_{\mathbf{P}}=\left[\begin{array}{cc}40 \Omega & 60 \Omega \\ 80 \Omega & 100 \Omega\end{array}\right]$. The admittance matrix of network $\mathbf{Q}$ is $Y_{\mathbf{Q}}=\left[\begin{array}{cc}5 \mathrm{~S} & -2.5 \mathrm{~S} \\ -2.5 \mathrm{~S} & 1 \mathrm{~S}\end{array}\right]$. Let the $\mathrm{ABCD}$ matrix of the two-port network $\mathbf{R}$ in the figure be $\left[\begin{array}{ll}\alpha & \beta \\ \gamma & \delta\end{array}\right]$. The value of $\beta$ in $\Omega$ is ____________(rounded off to $2$ decimal places).
