A fan of the eagles who live on the Arconic plant property in Riverdale, Iowa shared this video on Facebook. It's from the Arconic Eaglecam.
"Elfruler" comments about Liberty's egg-laying process in the YouTube description, "She makes a complete circle of the nest cup while she is having contractions before the final push comes at 13:32. We get a glimpse of the egg at 13:32 (look for the arrow in the video)."
By the way, the time reference is recorded within the original video and does not refer to the timing of the uploaded YouTube content.