Evans–Gannon-type near-group modular-data conjecture for arbitrary abelian groups

Let $A$ be a finite abelian group, let $G=A\times A$, and let $\langle\langle\cdot,\cdot\rangle\rangle$ be a non-degenerate symmetric bicharacter on $A$. Define $q_1(a_1,a_2)=\langle\langle a_1,a_2\rangle\rangle$ and let the involution be $\theta_1(a_1,a_2)=(a_2,a_1)$. Near-group modular-data conjecture. The modular data of the Drinfeld center of the near-group category for $A$ with multiplicity $|A|$ are the modular data constructed from these data, with $|\Gamma|=|G|+4|U|=|A|(|A|+4)$. This generalizes the odd-group Evans–Gannon conjecture; it is known in some examples, but the general realization remains open.