James joins a football team and becomes the star.  He scores 4 touchdowns per game and each touchdown is worth 6 points.  There are 15 games in the season.  He also manages to score 2 point conversions 6 times during the season.  The old record was 300 points during the season.  How many points did James beat the old record by?
Please reason step by step, and put your final answer within \boxed{}.
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