What is the shape of the Riemann zeta function in the vicinity of its pole at s=1? Circularly symmetric? It shoots up to infinity, but how quickly? This should be easy to investigate. The questions might be slightly tricky because it is complex-valued.

Magnitude might be an interesting shape to 3D print, a funnel.

Invert the function centered at the pole, transforming it to a pole at infinity.

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