Bruinier–Ono integrality conjecture for CM-values of a weak Maass form

Let $p(n)$ be the partition function. For a positive definite integral binary quadratic form $Q(x,y)=ax^2+bxy+cy^2$ of discriminant $-24n+1=b^2-4ac$, with $6\mid a$, $a>0$, and $b\equiv 1\pmod {12}$, let $\alpha_Q$ be the root of $Q(x,1)=0$ in the upper half-plane. Define

$$P_p(z):=-\left(\frac{1}{2\pi i}\frac{d}{dz}+\frac{1}{2\pi y}\right)F_p(z),\qquad z=x+iy,$$

where

$$F_p(z):=\frac{1}{2}\frac{E_2(z)-2E_2(2z)-3E_2(3z)+6E_2(6z)}{\eta(z)^2\eta(2z)^2\eta(3z)^2\eta(6z)^2}.$$

Bruinier and Ono's integrality conjecture. For the Maass form $P_p(z)$ and the CM points $\alpha_Q$ occurring in the formula for $p(n)$, the number

$$(24n-1)P_p(\alpha_Q)$$

is an algebraic integer.