The
SQLite date and time functions page[
^] should help you out.
I'm guessing the numbers you have in your database are UNIX epoch with milliseconds - removing the final three digits gives me a recent date and time:
sqlite> select datetime(1378307780519 / 1000, 'unixepoch');
2013-09-04 15:16:20
sqlite> select datetime(1378350490627 / 1000, 'unixepoch');
2013-09-05 03:08:10