Not answering your question directly, but I wanted to point out that Constantine was not Emperor of the Holy Roman Empire. It sounds like you are under the misconception that the Holy Roman Empire is the name given to the Roman Empire upon being converted to Christianity. However, the Holy Roman Empire is the name of the political entity that ruled much of Germany and Northern Italy from 962 when Otto I was named Emperor of the Romans, until 1806 when Napoleon took Vienna and dissolved the Empire. It was called the "Holy Roman Empire" as it was an attempt at recreating the Roman Empire via the principle of translatio imperii. Though, as Voltaire famously said, the name is a bit of a misnomer, as it was neither Holy, nor Roman, nor an Empire.