Parity formula for the Kepler limit of $p_\lambda$

Let $p=p_\lambda$ be the polynomial family considered in the paper, and let $\gamma(p)$ denote the quantity defined in the preceding observation. Parity formula for $p_\lambda$. For polynomials of the form $p=p_\lambda$, the statements in the preceding observation hold for all $k\geq 5$. In particular, the preceding observation asserts that $\gamma(p)=1$ for odd $k$ and $\gamma(p)=2$ for even $k$. This extends computations carried out for $5\leq k\leq 500$; no proof or resolution is supplied in the given text.