  We extend our studies of the TQ equation introduced by Baxter in his 1972
solution of the 8 vertex model with parameter $\eta$ given by
$2L\eta=2m_1K+im_2K'$ from $m_2=0$ to the more general case of complex $\eta.$
We find that there are several different cases depending on the parity of $m_1$
and $m_2$.
