Visible domain: ${\displaystyle [-0.7,0.7]\times [-0.7,0.7]}$.

The hue represents the complex argument;

${\displaystyle \operatorname {hue} (z)=\operatorname {arg} (z)}$

The luminance represents the absolute value. After some experimentation, I chose the following luminance mapping:

${\displaystyle \operatorname {luminance} (z)=\operatorname {atan} (\ln(|z|^{0.6}))}$

This yields a value between -pi/2 and +pi/2, which was then affinely transformed into the required [0,1] range. I chose a slowly-growing function in order to avoid the hue getting drowned by black and white too much.

The resulting color map looks like this:

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