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Mathematics
Polynoms
Roots
Rational functions
Exp, Gauss
Sin, Cos, Tan, Cot, Sec, Csc
Sinh, Cosh, Tanh, Coth, Sech, Csch
ArcSin, ArcCos, ArcTan, ArcCot, ArcSec, ArcCsc
ArcSinh, ArcCosh, ArcTanh, ArcCoth, ArcSech, ArcCsch
Log, ProductLog
PolyLog
Gamma, Reciprocal Gamma
LogGamma, Polygamma's
Riemann Siegel Theta (in 3 different magnifications), Riemann Siegel Z (in 2 different magnifications)
Riemann zeta, Dirichlet eta, Riemann Xi
Eisenstein series
KleinInvariantJ, Modular lambda, Dedekind eta
Theta
Zeros of Riemann zeta function
Because I dont know how to add a mathematica worksheet here, I made a screenprint from the mathematica function I use together with two examples.I designed the color function such that you can see even for values near infinity or zero a slight coloring so you can always identify the phase. I use mathematica 5.0. You are welcome to make further pictures. Be careful not missing blanks when copying it and dont forget to add the coloring function in the picture description! It would be interesting for me, if you let me know about new pictures on my german wikipedia page: Jan Homann (also in english).
There is a very nice version of the function for mathematica 6.0 which you can directly download here [[1]]
the pictures show normally lines as artefacts. To compensate this, expand the picture in the mathematica worksheet by a certain small factor.
