Obviously, it should not be totally green, but the singularities get all the color, and the rest none.
Is there a way I can limit (in a heatmap, not contourf) the values for the color gradient?
Either the range of colormap lookup is determined automatically as the extrema of the data, or you set it manually with colorrange. If there are values exceeding the range, you can either leave them saturated at the extreme color value, or give them a separate color with highclip and lowclip