Kawauchi's splitting conjecture for the Conway polynomial of achiral knots

Let $K$ be an achiral knot, and let $C(z)$ denote its Conway polynomial. Kawauchi's conjecture. The polynomial $C(z)$ has the splitting property: there is a polynomial $F(z)$ with integer coefficients such that

$$C(z)=F(z)F(-z).$$

The conjecture concerns an arithmetic constraint on the Conway polynomial of achiral knots. It is refuted by the counterexample given in this paper, although the splitting property holds for quasi-arborescent knots and alternating counterexamples must be quasi-polyhedral.