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We consider quantum bosons with contact interactions at the Lowest Landau Level (LLL) of a two-dimensional isotropic harmonic trap. At linear order in the coupling parameter $g$, we construct a large, explicit family of quantum states with energies of the form $E_0+gE_1/4+O(g^2)$, where $E_0$ and $E_1$ are integers. Any superposition of these states evolves periodically with a period of $8\pi/g$ until, at much longer time scales of order $1/g^2$, corrections to the energies of order $g^2$ may become relevant. These quantum states provide a counterpart to the known time-periodic behaviors of the corresponding classical (mean field) theory.