How to rotate around shifter center precisely in Illustrator?

If I select Rotate tool, I can select center of rotation then and move it. After that I am able to rotate object around that center. But this rotation is imprecise. Suppose I want to rotate for 120 degrees. I can double click on Rotate tool and get Rotate dialog, where I can enter precise value in degrees. But this way I can't use shifted center of rotation because it jumps back to geometric center at the moment I call Rotate dialog.

Is it possible to rotate by precise angle with dialog and have shifted center of rotation.