Where and when was the coronation of Charlemagne as emperor?

Charlemagne’s coronation as emperor took place in 800 in Rome. At that time, there were turbulent times here, representatives of the nobility assembled a conspiracy against Pope Leo 3, he had to flee. Karl promised to help the pope, eventually arrived in Rome and for six months extinguished conflicts between the pope and the nobility. Here Leo 3 held the coronation of Charles. It was a matter of marriage between Charles and Empress Irina, but a palace coup deprived Irina of power. The new emperor refused to recognize the title of Charles and he had to start a war in 806-810. As a result, Emperor Michael 1 recognized Charles as an emperor.