We explore numerically the eigenvalues of the hermitian form$$\sum _{q\le Q}\sum _{amod{}^{*}q}{\left|\sum _{n\le N}{\varphi }_{n}e(na/q)\right|}^2$$when $N={\sum }_{q\le Q}\phi \left(q\right)$. We improve on the existing upper bound, and produce a (conjectural) plot of the asymptotic distribution of its eigenvalues by exploiting fairly extensive computations. The main outcome is that this asymptotic density most probably exists but is not continuous with respect to the Lebesgue measure.