\left( \begin{array}{c}\frac{1}{2} \end{array} \right)
 \left( \begin{array}{cccc} i & -1 & \sqrt{2} & 0\\
 -1 & i & 0 & \sqrt{2}\\
 -i & 1 & \sqrt{2} & 0\\
 1 & -i & 0 & \sqrt{2} \end{array} \right)