F# min7 (b5)
This is a very nice sounding chord to play, the musical interactivity between the b5 note and the 11th note (that is also the 4th note) forms a Major 7th interval. It's quite beautiful.
Described as a "Modal Chord", min11b5 is the tonic chord of the Locrian Mode.
If you are improvising in the modal key signature of A Dorian, and this chord F# min11b5 is in the progression, then it isn't necessary to suddenly start playing the F# Locrian Mode. Just keep playing melody with A Dorian, it's fine.
The A Dorian Mode is the second mode of the G Major Scale, whilst F# Locrian Mode is seventh mode of the G Major Scale.
So why even think about this? It's about musical distances, musical relationships, and slowly learning how the sounds of these modal chords contribute to the character of a song.