Customize ColorFunction in ComplexPlot

I want to customize the ColorFunction in

ComplexPlot[EllipticTheta[3, w, 0.5], {w, 8},      ColorFunction -> Function[{z}, Hue[Arg[z]/(2 Pi)]],     PlotLegends -> Automatic] 

However, I cannot find any MMA document about the parameters a color function receives. Neither can I print the parameters out to check its range.

By some random typing, I figured out this color function receives at least 8 parameters. And the following code gives the same color (by color, I mean Hue) as MMA’s default

ColorFunction -> Function[{x, y, r, arg, c, d, e, f}, Hue[f*2, 1, 1]] 

However, I still cannot figure out which is the norm. I want to know the meaning and range of these parameters. And most importantly, where ON EARTH can I find it.

There is also a minor issue. After customizing the color function, the colormap legend besides the plot disappeared.

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