  A finite oscillator dictionary which has important applications in sequences
designs and the compressive sensing was introduced by Gurevich, Hadani and
Sochen. In this paper, we first revisit closed formulae of the finite split
oscillator dictionary $\mathfrak{S}^s$ by a simple proof. Then we study the
non-split tori of the group $SL(2,\mathbb{F}_p)$. Finally, An explicit
algorithm for computing the finite non-split oscillator dictionary
$\mathfrak{S}^{ns}$ is described.
