Parker's explicit coordinator polynomial conjecture for the cyclotomic lattice of order 15

Let $\zeta_{15}=e^{2\pi i/15}$, and let $h_{15}(x)$ be the coordinator polynomial of the lattice $\mathbb Z[\zeta_{15}]$ with respect to the set of all $15$th roots of unity. Parker's conjecture. The coordinator polynomial is

$$h_{15}(x)=(1+x^8)+7(x+x^7)+28(x^2+x^6)+79(x^3+x^5)+130x^4.$$

The paper proves this explicit formula as part of its computations for cyclotomic polytopes.