From royal +‎ -ly.

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royally (comparative more royally, superlative most royally)

1. In a royal manner; in a manner having to do with royalty.

   Unless it was decreed royally, it never got done.

2. (colloquial, idiomatic) Excessively; thoroughly.
   • 1991, Helen Mittermeyer, A Moment in Time, page 32:

     Bahira returned his stare, royally annoyed with herself for letting him affect her.

   • 2025 August 2, Bryan Mena, “Did the Fed just royally screw up?”, in CNN Business‎^[1], archived from the original on 20 August 2025:

     Still, it may be too soon to conclude that the Fed has royally screwed up.