Complex Curves

ZV=Table[Table[{Re[Zeta[.1*(5+l*I)]],
Im[Zeta[(.1+.0005m)*(5+l*I)]]},
{l,Range[530]}],{m,Range[5]}];
Table[Graphics[Table[{Hue[l/530],
Line[{ZV[[K,l]],ZV[[K,l+1]]}]},{l,529}],
Axes->True,GridLines->Automatic,ImageSize->500,
GridLinesStyle->LightGray],{K,Range[4]}]