Alternating-location conjecture for zeros near the unit circles

Let $G(d;z)$ be the polynomial considered in the paper, let $A_1$ and $A_3$ be the indicated regions containing zeros, and let $\mathcal C_0$ and $\mathcal C_1$ be the corresponding circles, with $\mathcal C_0$ the unit circle. For even $d$, the zeros on $\mathcal C_0$ are those described in the paper's proposition on the zeros of $G(d;z)$.

Alternating-location conjecture. If $d$ is even, all the zeros of $G(d;z)$ in $A_1$ are the zeros on the unit circle $\mathcal C_0$ given in that proposition. If $d$ is odd, the zeros of $G(d;z)$ in $A_1$ alternately lie inside and outside $\mathcal C_0$. Furthermore, the zeros of $G(d;z)$ in $A_3$ are always outside of $\mathcal C_1$.

This conjecture refines the proposed three-group description by specifying how zeros are positioned relative to the two circles. It is stated as an open numerical and geometric prediction, and the supplied text gives no proof or resolution.