  Previously we observed that newforms obey a strict bias towards root number
$+1$ in squarefree levels: at least half of the newforms in $S_k(\Gamma_0(N))$
with root number $+1$ for $N$ squarefree, and it is strictly more than half
outside of a few special cases. Subsequently, other authors treated levels
which are cubes of squarefree numbers. Here we treat arbitrary levels, and find
that if the level is not the square of a squarefree number, this strict bias
still holds for any weight. In fact the number of such exceptional levels is
finite for fixed weight, and 0 if $k < 12$. We also investigate some variants
of this question to better understand the exceptional levels.
