 Unconditionally, we have the following bounds:  -   $H_0 \leq 000$.  -   $H_m \leq C m^0 e^{0m}$ for all $m \geq 0$ and an absolute (and effective) constant $C$.  Assuming the Elliott-Halberstam conjecture $\operatorname*{EH}[\vartheta]$ for all $0 < \vartheta < 0$