# New Year Tables for 5:40:400 Rule

The 5:40:400 leapweek calendar has a leapweek on every year divisible by 5, except those divisible by 40, except those divisible by 400. Its cycle matches the Gregorian cycle, hence its New year repeats every 400 years, with respect to the Gregorian Calendar. The new years can be calculated using two tables each with 20 entries.

Below is such a pair of tables, where the new years match for 2001.

The first table gives the position of 5:40:400 New year relative to the Gregorian New year for the period 2001-2020

Table 1: 2001-2020
```2001: same            2011: 2 days late
2002: 1 day early     2012: 1 day late
2003: 2 days early    2013: 1 day early
2004: 3 days early    2014: 2 days early
2005: 5 days early    2015: 3 days early

2006: 1 day late      2016: 3 days late
2007: same            2017: 1 day late
2008: 1 day early     2018: same
2009: 3 days early    2019: 1 day early
2010: 4 days early    2020: 2 days early
```

The new years for other 20 year periods follow the same pattern, but are displaced by a constant number of days as shown in Table 2.

Table 2: Other 20 year periods
```2021-2040  3 days later
2041-2060  1 day earlier
2061-2080  2 days later
2081-2100  2 days earlier

2101-2120  2 days later
2121-2140  2 days earlier
2141 2160  1 day later
2161-2180  3 days earlier
2181-2200  as 2001-2020

1801-1820  3 days earlier
1821-1840  as 2001-2020
1841-1860  4 days earlier
1861-1880  1 day earlier
1881-1900  5 days earlier

1901-1920  1 day earlier
1921-1940  5 days earlier
1941-1960  2 days earlier
1961-1980  6 days earlier
1981-2000  3 days earlier
```
Examples
```For example 1999:
table 1 year 2019: 1 day early
table 2 1981-2000: 3 days earlier
total: 4 days early (i.e. 28 Dec 1998).

For example 2022:
table 1 year 2002: 1 day early
table 2 2021-2040: 3 days later
total: 2 days late (i.e. 3 Jan 2022).
```

The earliest new year is 1965 (11 days early), which is Monday 21 Dec 1964 and a Solstice day.

The latest new year is 2036 (6 days late) which is Monday 7 Jan 2036.