An impossibility theorem for linear symplectic circle quotients

We prove that when $d>2$, a $d$-dimensional symplectic quotient at the zero level of a unitary circle representation $V$ such that $V^{{\text{Sp}}^1}=\{0\}$ cannot be $\mathbb{Z}$-graded regularly symplectomorphic to the quotient of a unitary representations of a finite group.