As we know discrete Fourier transform, DFT enjoys four eigenvalues $\{\pm1,\pm i\}$ whose multiplicities depend on the order. So, one may find many eigenvectors corresponded to the eigenvalues.
In some papers in which there is a discussion on eigenvectors of discrete Fourier transform DFT, I face the following sentence: we are usually interested in the real-valued, orthogonal, symmetric eigenvectors of the DFT matrix. What could be the reason for this point of view?