To finish the drawing, I add more dark tones, and use the eraser to lift out and re-work some lighter areas. Pay extra attention to reflected light - depending on your choice of background, the strength of the light source and the color of your egg, yours may look quite different. Notice how the darkest area is the band of shadow around the side of the egg, just below the widest part - closer to the paper, it brightens a little due to reflected light - and then the very dark area where it touches the surface.
The quality of cast shadow will vary too, with some reflected light from the egg lightening areas, and the edges may be crisp, diffuse or it may have a multiple shadow depending on the light source. So draw what you see!
For an alternative and very useful approach to this exercise, try drawing an egg in white chalk on black paper.