  We present a generalized set of complex rays for a qutrit in terms of
parameter $q=e^{i2\pi/k}$, a $k$-th root of unity. Remarkably, when $k=2,3$,
the set reduces to two well known state-independent contextuality (SIC) sets:
the Yu-Oh set and the Bengtsson-Blanchfield-Cabello set. Based on the
Ramanathan-Horodecki criterion and the violation of a noncontextuality
inequality, we have proven that the sets with $k=3m$ and $k=4$ are SIC, while
the set with $k=5$ is not. Our generalized set of rays will theoretically
enrich the study of SIC proof, and experimentally stimulate the novel
application to quantum information processing.
