authoritatively vs magisterially

authoritatively and magisterially both are adverbs.

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

As adverbs, authoritatively and magisterially are synonyms defined as:

authoritatively and magisterially: in an authoritative and magisterial manner

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