A plot of the truncated wave trace for the Euclidean disk with 650 eigenvalues, which are zeros of Bessel functions. The first spike is at 4, corresponding to bouncing ball modes along the diameter.

Truncated wave trace on the torus with 4486 eigenvalues, which are sums of squares of Integers.

Truncated wave trace on the modular surface using the first 400 embedded eigenvalues, corresponding to Maaß (cusp) forms.