Connect Inspiron 7720 (HDMI+VGA) to large panel (DP+DVI-D) at 2560x1600

Hello,

My Inspiron 7720 has only HDMI as digital video output (beside the antiquated VGA), and I need to connect it to the largeHP ZR30w flat panel, which has Display Port and DVI-D inputs. With a mundane (i.e. just HD) HDMI-to-DVI cable, I am able to show 1280x800, which is not only a dismal quarter of the panel's native resolution, but even below the standard HD the 7720 shows on its internal display.

I need to get the 2560x1600 to the panel - even my tiny Surface Pro does that in a breeze over its Mini Display Port, so I hope the fairly high-end 7720 can manage? Any suggestion would be appreciated!

Thank you,

Emanuel