\[\Psi^{(\mathrm{E})}\left(-\tfrac{1}{2}x\mp\tfrac{\sqrt{3}}{2}y,\pm\tfrac{\sqrt%
{3}}{2}x-\tfrac{1}{2}y,z\right)=\Psi^{(\mathrm{E})}\left(x,y,z\right),\]