The court administrator shall keep a register of all criminal actions, in which the court administrator shall enter:

1. (1) all indictments found in the court, or sent or removed to it for trial, with the time of finding the indictment, or when it was sent or removed; and
2. (2) the time of arraignment, of the demurrer or plea, and of the trial, conviction, or acquittal of the defendant, together with a brief note of all the other proceedings in the action.