McLeman's Zassenhaus type conjecture for imaginary quadratic fields

Let $p>3$ be a prime, and let $K$ be an imaginary quadratic field whose class group has $p$-rank two. The Zassenhaus type is the pair $(i,j)$ occurring in the Zassenhaus polynomial $Z_G(t)=t^i+t^j-2t+1$ of the relevant pro-$p$ Galois group $G=\operatorname{Gal}(K^{\operatorname{ur},p}/K)$. McLeman's conjecture. The $p$-class field tower of $K$ is finite if and only if its Zassenhaus type is $(3,3)$. The paper states that it has found counterexamples to this conjecture, so the claim is refuted.