Source : Webster's Revised Unabridged Dictionary (1913)

Arrogantly \Ar"ro*gant*ly\, adv.
   In an arrogant manner; with undue pride or self-importance.

Source : WordNet®

arrogantly
     adv : in an arrogant manner; "in the old days she had been harsh
           and stiff ; afraid of her husband and yet arrogantly
           proud that she had a husband strong and fierce enough
           to make her afraid"