\[\Psi_{K}\left(\boldsymbol{{0}}\right)=\frac{2}{K+2}\Gamma\left(\frac{1}{K+2}%
\right)\*\begin{cases}\exp\left(i\dfrac{\pi}{2(K+2)}\right),&K\text{ even,}\\
\cos\left(\dfrac{\pi}{2(K+2)}\right),&K\text{ odd}.\end{cases}\]