lambertw, all branches

[Gil]

For W (k=-1, a=+3*PI/2),
the result for the real part is tiny, but not 0 — zero as the exact result is according to Wolfram.

Could you check, Albert, what you find with your program(s)?

PS: as you mentioned, with roundings, cos 3pi/2 ≠ 0, though sin 3*pi/2 = exactly 1.

Thanks in advance for your answer.

Regards