Squared class-number ratio conjecture for pairs of split primes in imaginary quadratic fields

Let $\mathbb{Q}(\sqrt{-d})$ be an imaginary quadratic field and let $C_1$ be the fixed cone. Let $PQ_M(-d)$ count pairs of primes $(p,q)$ less than $M$ that split completely, with $p=N(\gamma_1)$ and $q=N(\gamma_1+\gamma_2)$ for algebraic integers $\gamma_1,\gamma_2$ lying in $C_1$. Let $h(-d)$ be the class number. Imaginary quadratic pair-count conjecture.

$$\lim_{M\rightarrow\infty}\frac{PQ_M(-d_1)}{PQ_M(-d_2)}=\left(\frac{h(-d_2)}{h(-d_1)}\right)^2.$$

The source reports experimental verification for $d<14$ and primes below $500^2$.