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We state a conjecture for the formulas of the depth 4 low-weight rotationaleigenvectors and their corresponding eigenvalues for the $3^G$ subfactor planaralgebras. We prove the conjecture in the case when $|G|$ is odd. To do so, wefind an action of $G$ on the reduced subfactor planar algebra at $f^{(2)}$,which is obtained from shading the planar algebra of the even half. We alsoshow that this reduced subfactor planar algebra is a Yang-Baxter planaralgebra.

The generator conjecture for $3^G$ subfactor planar algebras