i.e. it is sometimes even 2 days off.\
According to the calculated Islamic calendar, though, the month of [*Shawwāl*]{} in the year 158h would be running from AD 775 Aug 4 to Sep 1 (according to, e.g., Spuler & Mayr 1961). To convert a Muslim date to a Julian or Gregorian date, the calculated Islamic calendar can be used as a first approximation, but if an accuracy of better than one or two days is needed and/or if the precision or error bar is needed, one should consider the exact time of crescent new moon sighting at the relevant location, which we will do next.\
According to NASA GSFC[^7], new moon was on AD 775 Aug 1 (Julian calendar) at 6:57h UT ($\pm 53$ min), according to Gautschy (2011)[^8], it was at 6:59h UT. According to Gautschy (2014), the crescent new moon can be seen if the lag-time between sunset and moonset and the difference in their azimut are large enough, see Fig. 3, weather permitting. The earliest reported sighting of the crescent (new) moon was 15.4 hours (by naked-eye viewing by Julius Sch- midt, a modern 19th century observer in Greece) after the exact new moon time (Fotheringham 1910, 