# Argument:
# - F, a field object, e.g., F = GF(2^255 - 19)
def find_z_ell2(F):
    ctr = F.gen()
    while True:
        for Z_cand in (F(ctr), F(-ctr)):
            # Z must be a non-square in F.
            if is_square(Z_cand):
                continue
            return Z_cand
        ctr += 1