Written out
Every accidental is written in, rather than left to a key signature, so the letters can be read one at a time.
The step pattern
C♯WD♯WE♯WF𝄪HG♯WA♯WB♯HC♯
What is true of it
C♯ Lydian is C♯, D♯, E♯, F𝄪, G♯, A♯ and B♯, and back to C♯.
Its steps are W – W – W – H – W – W – H, where W is a whole step and H a half.
Written correctly it needs 8 alterations, F𝄪 among them. That is what the letters force, and it is also why nobody writes music in this key: the same notes spelled from the other side are easier to read.
On the same tonic, C♯ major differs from it by exactly one note.
Across the first twelve frets of the ukulele its notes fall in 30 places, which is what makes a scale a shape rather than a list.
Chords made only of these notes
C♯majorC♯maj7major seventhD♯majorD♯7dominant seventhG♯majorG♯maj7major seventhA♯mminorA♯m7minor seventh
Found by testing every chord in the catalogue against these 7 sounds, not chosen.