  We classify the combinations of parameters which lead three generations of
quarks and leptons in the framework of magnetized twisted orbifolds on
$T^2/Z_2$, $T^2/Z_3$, $T^2/Z_4$ and $T^2/Z_6$ with allowing nonzero discretized
Wilson line phases and Scherk-Schwarz phases. We also analyze two actual
examples with nonzero phases leading to one-pair Higgs and five-pair Higgses
and discuss the difference from the results without nonzero phases studied
previously.
