magisterially vs authoritatively

magisterially and authoritatively both are adverbs.

Word	Noun	Adjective	Verb	Adverb
magisterially	No	No	No	Yes
authoritatively	No	No	No	Yes

As adverbs, magisterially and authoritatively are synonyms defined as:

magisterially and authoritatively: in an authoritative and magisterial manner

magisterially (adverb)	authoritatively (adverb)
in an authoritative and magisterial manner	in an authoritative and magisterial manner
in an overbearingly domineering manner; as a dictator