v_j=\frac{1}{\sqrt{n}} (1,~ \omega_j,~ \omega_j^2,~ \ldots,~ \omega_j^{n-1})^T,\quad j=0, 1,\ldots, n-1, where \omega_j=\exp \left(\tfrac{2\pi i j}{n}\right) are the n-th roots of unity and i is the imaginary unit.
The corresponding eigenvalues are then given by .