Source : Webster's Revised Unabridged Dictionary (1913)

Quixotically \Quix*ot"ic*al*ly\, adv.
   In a quixotic way.

Source : WordNet®

quixotically
     adv : in a quixotic manner; "sent to jail for two years, he has
           quixotically refused to clear himself by betraying his
           colleagues"