Class-number ratio conjecture for split primes in imaginary quadratic fields

Let $K=\mathbb{Q}(\sqrt{-d})$ be an imaginary quadratic field, and let $C_1$ be the cone whose elements have angle between $\pi/36$ and $2\pi/36$. Let $P_M(-d)$ count primes less than $M$ that split completely in $K$ and whose factors lie in $C_1$, and let $h(-d)$ be the class number. Imaginary quadratic class-number conjecture. For two such fields,

$$\lim_{M\rightarrow\infty}\frac{P_M(-d_1)}{P_M(-d_2)}=\frac{h(-d_2)}{h(-d_1)}.$$

The paper reports numerical verification for all $d<20$ with primes below $1{,}000^2$, with errors below one percent.