The pole classification conjecture for degenerate Eisenstein series on $E_8$

Let $\mathcal{E}_{P_2}^{E_8}(s,\chi)$ be the Eisenstein series attached to the parabolic $P_2$ of the split group of type $E_8$, where $\chi$ is a Hecke character. For $\operatorname{Re}(s)>0$, the possible poles are classified according to the order of $\chi$.

Pole classification conjecture. For $\operatorname{Re}(s)>0$, if $\chi$ is trivial, then $\mathcal{E}_{P_2}^{E_8}(s,\chi)$ can have a double pole at $s=\frac32,\frac52,\frac72$ and a simple pole at $s=\frac12,\frac92,\frac{11}{2},\frac{13}{2},\frac{17}{2}$. If $\chi$ is nontrivial quadratic, it can have simple poles at $s=\frac12,\frac32,\frac52,\frac72$. If $\chi$ is nontrivial cubic, it can have a simple pole at $s=\frac32$. If the order of $\chi$ exceeds $3$, the Eisenstein series is holomorphic in $\operatorname{Re}(s)>0$.

The preceding results are presented as settling a conjecture of David Ginzburg and Joseph Hundley. Thus this candidate is not an open conjecture in the paper.