1) a leader of any kind, a guide, ruler, prefect, president, chief, general, commander, sovereign
1a) a "legatus Caesaris", an officer administering a province in the name and with the authority of the Roman emperor
1a1) the governor of a province
1b) a procurator, an officer who was attached to a proconsul or a proprietor and had charge of the imperial revenues
1b1) in causes relating to these revenues he administered justice. In the smaller provinces also, which were so to speak appendages of the greater, he discharged the functions of governor of the province; and such was the relation of the procurator of Judaea to the governor of Syria.
1c) first, leading, chief
1c1) of a principal town as the capital of the region
Part of Speech: noun masculine
From G2233; a leader, that is, chief person (or figuratively place) of a province: - governor, prince, ruler.
These two sites give similar information, with the definition from several dictionaries and statistics on the use of the word.
Perseus Digital Library
University of Chicago's Logion lexicon
Thayer's dictionary plus other information.
From this site's dictionary (in Italian)
Click on the first column to search for that word as a form of the root ἡγεμών; click on the second column to search for that grammatical form of the root ἡγεμών; click on the third column to search for that word and grammatical form; click on the total to search for the root ἡγεμών.