The functional-equation conjecture for normal zeta functions of Heisenberg groups

Let $K$ be a number field, let $g$ be the number of primes of $K$ above a rational prime, and let $(\mathbf{e},\mathbf{f})\in\mathbb{N}^g\times\mathbb{N}^g$ satisfy

$$\sum_{i=1}^g e_i f_i=n.$$

Here $W^\vartriangleleft_{\mathbf{e},\mathbf{f}}(X,Y)$ denotes the corresponding local normal zeta-function factor for the Heisenberg group over the number ring of $K$. Functional-equation conjecture. For all primes, one has

$$W^\vartriangleleft_{\mathbf{e}, \mathbf{f}}(X^{-1},Y^{-1}) = (-1)^{3n} X^{\binom{3n}{2}} Y^{5n + \sum_{i=1}^g 2(e_i - 1)f_i} W^\vartriangleleft_{\mathbf{e}, \mathbf{f}}(X,Y).$$

This predicts functional equations for the local normal zeta functions of Heisenberg groups over number rings at every rational prime, extending the known result for all but finitely many primes and the established formulae at unramified and non-split primes. The claim is refuted in the stated generality: such a functional equation at all primes does not hold in general.