Residue ratio conjecture for split primes in imaginary quadratic fields

For imaginary quadratic fields, let $P_M(-d)$ count primes less than $M$ that split completely and whose factors lie in the cone $C_1$. Let $\operatorname{Res}_{s=1}\zeta_{\mathbb{Q}(\sqrt{-d})}(s)$ denote the residue at $s=1$ of the Dedekind zeta function. Imaginary quadratic residue-ratio conjecture.

$$\lim_{M\rightarrow\infty}\frac{P_M(-d_1)}{P_M(-d_2)}=\frac{\sqrt{d_1}\operatorname{Res}_{s=1}\zeta_{\mathbb{Q}(\sqrt{-d_1})}(s)}{\sqrt{d_2}\operatorname{Res}_{s=1}\zeta_{\mathbb{Q}(\sqrt{-d_2})}(s)}.$$

The source presents this as a reformulation of the imaginary quadratic class-number comparison and says it has been tested numerically.