You can work it out yourself fairly easily. When the Sun passes through your local meridian (i.e. - noon), your local sidereal time is whatever right ascension the Sun is at. Right now, the Sun is at ~2h54m. To get to 13h00m, you therefore need to wait 13:00-2:54=10:06. That would mean that 13h00m passes overhead at 12:00pm + 10:06 = 10:06pm.
Though that presumes that your local noon, when the Sun is in the middle of the sky, is in fact 12:00pm! Depending on where you are in the timezone this may be incorrect, and you would have to add (or subtract) whatever is the difference.