The Blade of Harbingers

Source
Sold by at the Sun's Reach Armory of the Isle of Quel'Danas and Anwehu in Shattrath City for 780 Justice points.

This weapon has an intrinsic Haste Rating of +53 which makes the weapon speed no slower than 3.39 on equip and thus the unmodified DPS is actually 138.35 = ((375+563) / 2 / 3.39)