Scottish flag

\begin{align} \text{Spec}\begin{pmatrix} \cos (2\pi /N) & i/2 & 0 & 0 & \cdots & i/2 \\ i/2 & \cos(4\pi / N) & i/2 & 0 & \cdots & 0 \\ 0 & i/2 & \cos(6\pi /N) & i/2 & \ddots & 0 \\ \vdots & \ddots & \ddots & \ddots & \ddots & \vdots \\ 0 & \cdots & 0 & i/2 & \cos(2(N-1)\pi/N) & i/2 \\ i/2 & 0 & \cdots & 0 & i/2 & \cos(2\pi) \end{pmatrix} \end{align}

Scottish flag

\begin{align} \text{Spec}\begin{pmatrix} \cos (2\pi /N) & i/2 & 0 & 0 & \cdots & i/2 \\ i/2 & \cos(4\pi / N) & i/2 & 0 & \cdots & 0 \\ 0 & i/2 & \cos(6\pi /N) & i/2 & \ddots & 0 \\ \vdots & \ddots & \ddots & \ddots & \ddots & \vdots \\ 0 & \cdots & 0 & i/2 & \cos(2(N-1)\pi/N) & i/2 \\ i/2 & 0 & \cdots & 0 & i/2 & \cos(2\pi) \end{pmatrix} \end{align}

Vogel's theorem

$\text{Spec}(\text{Op}_N(\cos(2\pi x) + i \cos (2\pi \xi))+ \delta Q_\omega )$

Probabilistic Weyl-law for Toeplitz operator on complex projective space

$\text{Spec}(T_N(x_1 + i x_2) + \delta Q_\omega )$

Probabilistic Weyl-law for Toeplitz operator on complex projective space with entires of random matrix uniform(0,1).

$\text{Spec}(T_N(x_1 + i x_2) + \delta Q_\omega )$

Pringle operator

$\text{Spec}(T_N(\cos(t) x_1 + \sin(t) x_1^2 + i x_2) + \delta Q_\omega)$ for $t\in [0,2\pi]$