I am coding up parts of Morton's '78 paper "On the eigenvectors of Schur's matrix". These are a cyclic shift of the eigenvectors of the DFT. On pg. 126 he describes the eigenvectors (15), and states they are independent. He counts them as $\sum_{\chi}\sum_{d|q/f} 1 = q$.
The issue I'm having is I iterate over $\chi$ and $d$, and compute not just 1, but possibly 2 or 4 eigenvectors for each pair $(\chi,d)$. I end up with extra eigenvectors which are dependent.
What is the correct parameterization here? I can't quite see how he's counting using the conditions in (15).
