Absolute stability region
Stable region in red.

Coefficients

\begin{align} \begin{array}{c|ccc} - \frac{\sqrt{6}}{10} + \frac{2}{5} & - \frac{7 \sqrt{6}}{360} + \frac{11}{45} & - \frac{169 \sqrt{6}}{1800} + \frac{37}{225} & - \frac{2}{225} + \frac{\sqrt{6}}{75}\\ \frac{\sqrt{6}}{10} + \frac{2}{5} & \frac{37}{225} + \frac{169 \sqrt{6}}{1800} & \frac{7 \sqrt{6}}{360} + \frac{11}{45} & - \frac{\sqrt{6}}{75} - \frac{2}{225}\\ 1 & - \frac{\sqrt{6}}{36} + \frac{4}{9} & \frac{\sqrt{6}}{36} + \frac{4}{9} & \frac{1}{9}\\ \hline & - \frac{\sqrt{6}}{36} + \frac{4}{9} & \frac{\sqrt{6}}{36} + \frac{4}{9} & \frac{1}{9} \end{array}\end{align}

Properties