  We study the low frequency spectra of complex Sachdev-Ye-Kitaev (SYK) models
at general densities. The analysis applies also to SU($M$) magnets with random
exchange at large $M$. The spectral densities are computed by numerical
analysis of the saddle point equations on the real frequency ($\omega$) axis at
zero temperature ($T$). The asymptotic low $\omega$ behaviors are found to be
in excellent agreement with the scaling dimensions of irrelevant operators
which perturb the conformally invariant critical states. Of possible
experimental interest is our computation of the universal spin spectral weight
of the SU($M$) magnets at low $\omega$ and $T$: this includes a contribution
from the time reparameterization mode, which is the boundary graviton of the
holographic dual. This analysis is extended to a random $t$-$J$ model in a
companion paper.
