sage: H = DirichletGroup(5610)
pari: g = idealstar(,5610,2)
Character group
sage: G.order()
pari: g.no
| ||
Order | = | 1280 |
sage: H.invariants()
pari: g.cyc
| ||
Structure | = | \(C_{2}\times C_{2}\times C_{4}\times C_{80}\) |
sage: H.gens()
pari: g.gen
| ||
Generators | = | $\chi_{5610}(1871,\cdot)$, $\chi_{5610}(3367,\cdot)$, $\chi_{5610}(1531,\cdot)$, $\chi_{5610}(3301,\cdot)$ |
First 32 of 1280 characters
Each row describes a character. When available, the columns show the orbit label, order of the character, whether the character is primitive, and several values of the character.
Character | Orbit | Order | Primitive | \(-1\) | \(1\) | \(7\) | \(13\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) | \(47\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{5610}(1,\cdot)\) | 5610.a | 1 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
\(\chi_{5610}(7,\cdot)\) | 5610.ez | 80 | no | \(-1\) | \(1\) | \(e\left(\frac{57}{80}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{9}{40}\right)\) | \(e\left(\frac{1}{16}\right)\) | \(e\left(\frac{27}{80}\right)\) | \(e\left(\frac{31}{80}\right)\) | \(e\left(\frac{27}{80}\right)\) | \(e\left(\frac{53}{80}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{3}{5}\right)\) |
\(\chi_{5610}(13,\cdot)\) | 5610.dn | 20 | no | \(1\) | \(1\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(1\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(i\) | \(e\left(\frac{11}{20}\right)\) |
\(\chi_{5610}(19,\cdot)\) | 5610.eu | 40 | no | \(-1\) | \(1\) | \(e\left(\frac{9}{40}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{19}{40}\right)\) | \(e\left(\frac{27}{40}\right)\) | \(e\left(\frac{39}{40}\right)\) | \(e\left(\frac{21}{40}\right)\) | \(-i\) | \(e\left(\frac{2}{5}\right)\) |
\(\chi_{5610}(23,\cdot)\) | 5610.dj | 16 | no | \(-1\) | \(1\) | \(e\left(\frac{1}{16}\right)\) | \(1\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{13}{16}\right)\) | \(e\left(\frac{3}{16}\right)\) | \(e\left(\frac{7}{16}\right)\) | \(e\left(\frac{11}{16}\right)\) | \(e\left(\frac{13}{16}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(1\) |
\(\chi_{5610}(29,\cdot)\) | 5610.fi | 80 | no | \(-1\) | \(1\) | \(e\left(\frac{27}{80}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{19}{40}\right)\) | \(e\left(\frac{3}{16}\right)\) | \(e\left(\frac{77}{80}\right)\) | \(e\left(\frac{41}{80}\right)\) | \(e\left(\frac{57}{80}\right)\) | \(e\left(\frac{43}{80}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{17}{20}\right)\) |
\(\chi_{5610}(31,\cdot)\) | 5610.fe | 80 | no | \(-1\) | \(1\) | \(e\left(\frac{31}{80}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{27}{40}\right)\) | \(e\left(\frac{7}{16}\right)\) | \(e\left(\frac{41}{80}\right)\) | \(e\left(\frac{53}{80}\right)\) | \(e\left(\frac{61}{80}\right)\) | \(e\left(\frac{79}{80}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{1}{20}\right)\) |
\(\chi_{5610}(37,\cdot)\) | 5610.fa | 80 | no | \(1\) | \(1\) | \(e\left(\frac{27}{80}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{39}{40}\right)\) | \(e\left(\frac{11}{16}\right)\) | \(e\left(\frac{57}{80}\right)\) | \(e\left(\frac{61}{80}\right)\) | \(e\left(\frac{57}{80}\right)\) | \(e\left(\frac{23}{80}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{1}{10}\right)\) |
\(\chi_{5610}(41,\cdot)\) | 5610.ff | 80 | no | \(-1\) | \(1\) | \(e\left(\frac{53}{80}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{21}{40}\right)\) | \(e\left(\frac{13}{16}\right)\) | \(e\left(\frac{43}{80}\right)\) | \(e\left(\frac{79}{80}\right)\) | \(e\left(\frac{23}{80}\right)\) | \(e\left(\frac{77}{80}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{13}{20}\right)\) |
\(\chi_{5610}(43,\cdot)\) | 5610.bz | 8 | no | \(1\) | \(1\) | \(e\left(\frac{5}{8}\right)\) | \(i\) | \(-i\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(1\) | \(i\) |
\(\chi_{5610}(47,\cdot)\) | 5610.dl | 20 | no | \(1\) | \(1\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(1\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(i\) | \(e\left(\frac{3}{20}\right)\) |
\(\chi_{5610}(49,\cdot)\) | 5610.ei | 40 | no | \(1\) | \(1\) | \(e\left(\frac{17}{40}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{27}{40}\right)\) | \(e\left(\frac{31}{40}\right)\) | \(e\left(\frac{27}{40}\right)\) | \(e\left(\frac{13}{40}\right)\) | \(i\) | \(e\left(\frac{1}{5}\right)\) |
\(\chi_{5610}(53,\cdot)\) | 5610.eq | 40 | no | \(1\) | \(1\) | \(e\left(\frac{23}{40}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{23}{40}\right)\) | \(e\left(\frac{19}{40}\right)\) | \(e\left(\frac{33}{40}\right)\) | \(e\left(\frac{37}{40}\right)\) | \(1\) | \(e\left(\frac{11}{20}\right)\) |
\(\chi_{5610}(59,\cdot)\) | 5610.ek | 40 | no | \(-1\) | \(1\) | \(e\left(\frac{31}{40}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{1}{40}\right)\) | \(e\left(\frac{33}{40}\right)\) | \(e\left(\frac{21}{40}\right)\) | \(e\left(\frac{39}{40}\right)\) | \(-i\) | \(e\left(\frac{1}{10}\right)\) |
\(\chi_{5610}(61,\cdot)\) | 5610.fc | 80 | no | \(1\) | \(1\) | \(e\left(\frac{29}{80}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{13}{40}\right)\) | \(e\left(\frac{13}{16}\right)\) | \(e\left(\frac{59}{80}\right)\) | \(e\left(\frac{7}{80}\right)\) | \(e\left(\frac{79}{80}\right)\) | \(e\left(\frac{61}{80}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{19}{20}\right)\) |
\(\chi_{5610}(67,\cdot)\) | 5610.ba | 4 | no | \(-1\) | \(1\) | \(-i\) | \(-i\) | \(-1\) | \(i\) | \(1\) | \(-1\) | \(-i\) | \(-1\) | \(-i\) | \(i\) |
\(\chi_{5610}(71,\cdot)\) | 5610.fd | 80 | no | \(1\) | \(1\) | \(e\left(\frac{39}{80}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{3}{40}\right)\) | \(e\left(\frac{7}{16}\right)\) | \(e\left(\frac{9}{80}\right)\) | \(e\left(\frac{77}{80}\right)\) | \(e\left(\frac{69}{80}\right)\) | \(e\left(\frac{31}{80}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{19}{20}\right)\) |
\(\chi_{5610}(73,\cdot)\) | 5610.ez | 80 | no | \(-1\) | \(1\) | \(e\left(\frac{7}{80}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{39}{40}\right)\) | \(e\left(\frac{15}{16}\right)\) | \(e\left(\frac{37}{80}\right)\) | \(e\left(\frac{1}{80}\right)\) | \(e\left(\frac{37}{80}\right)\) | \(e\left(\frac{43}{80}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{3}{5}\right)\) |
\(\chi_{5610}(79,\cdot)\) | 5610.fh | 80 | no | \(1\) | \(1\) | \(e\left(\frac{1}{80}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{17}{40}\right)\) | \(e\left(\frac{1}{16}\right)\) | \(e\left(\frac{31}{80}\right)\) | \(e\left(\frac{43}{80}\right)\) | \(e\left(\frac{11}{80}\right)\) | \(e\left(\frac{9}{80}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{1}{20}\right)\) |
\(\chi_{5610}(83,\cdot)\) | 5610.en | 40 | no | \(-1\) | \(1\) | \(e\left(\frac{7}{40}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{7}{40}\right)\) | \(e\left(\frac{31}{40}\right)\) | \(e\left(\frac{37}{40}\right)\) | \(e\left(\frac{13}{40}\right)\) | \(-1\) | \(e\left(\frac{19}{20}\right)\) |
\(\chi_{5610}(89,\cdot)\) | 5610.v | 4 | no | \(-1\) | \(1\) | \(-i\) | \(-1\) | \(-1\) | \(i\) | \(i\) | \(-i\) | \(i\) | \(-i\) | \(1\) | \(1\) |
\(\chi_{5610}(91,\cdot)\) | 5610.fe | 80 | no | \(-1\) | \(1\) | \(e\left(\frac{73}{80}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{21}{40}\right)\) | \(e\left(\frac{1}{16}\right)\) | \(e\left(\frac{63}{80}\right)\) | \(e\left(\frac{19}{80}\right)\) | \(e\left(\frac{43}{80}\right)\) | \(e\left(\frac{57}{80}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{3}{20}\right)\) |
\(\chi_{5610}(97,\cdot)\) | 5610.fa | 80 | no | \(1\) | \(1\) | \(e\left(\frac{31}{80}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{27}{40}\right)\) | \(e\left(\frac{15}{16}\right)\) | \(e\left(\frac{21}{80}\right)\) | \(e\left(\frac{73}{80}\right)\) | \(e\left(\frac{21}{80}\right)\) | \(e\left(\frac{59}{80}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{3}{10}\right)\) |
\(\chi_{5610}(101,\cdot)\) | 5610.cl | 10 | no | \(1\) | \(1\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(1\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(-1\) | \(e\left(\frac{3}{10}\right)\) |
\(\chi_{5610}(103,\cdot)\) | 5610.dy | 20 | no | \(-1\) | \(1\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(i\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(i\) | \(e\left(\frac{7}{20}\right)\) |
\(\chi_{5610}(107,\cdot)\) | 5610.fk | 80 | no | \(1\) | \(1\) | \(e\left(\frac{63}{80}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{31}{40}\right)\) | \(e\left(\frac{15}{16}\right)\) | \(e\left(\frac{13}{80}\right)\) | \(e\left(\frac{49}{80}\right)\) | \(e\left(\frac{13}{80}\right)\) | \(e\left(\frac{67}{80}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{2}{5}\right)\) |
\(\chi_{5610}(109,\cdot)\) | 5610.de | 16 | no | \(1\) | \(1\) | \(e\left(\frac{9}{16}\right)\) | \(-i\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{13}{16}\right)\) | \(e\left(\frac{7}{16}\right)\) | \(e\left(\frac{3}{16}\right)\) | \(e\left(\frac{3}{16}\right)\) | \(e\left(\frac{1}{16}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(i\) |
\(\chi_{5610}(113,\cdot)\) | 5610.ey | 80 | no | \(-1\) | \(1\) | \(e\left(\frac{13}{80}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{1}{40}\right)\) | \(e\left(\frac{5}{16}\right)\) | \(e\left(\frac{23}{80}\right)\) | \(e\left(\frac{59}{80}\right)\) | \(e\left(\frac{63}{80}\right)\) | \(e\left(\frac{57}{80}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{2}{5}\right)\) |
\(\chi_{5610}(127,\cdot)\) | 5610.eo | 40 | no | \(1\) | \(1\) | \(e\left(\frac{17}{40}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{37}{40}\right)\) | \(e\left(\frac{1}{40}\right)\) | \(e\left(\frac{27}{40}\right)\) | \(e\left(\frac{23}{40}\right)\) | \(-1\) | \(e\left(\frac{19}{20}\right)\) |
\(\chi_{5610}(131,\cdot)\) | 5610.cy | 16 | no | \(-1\) | \(1\) | \(e\left(\frac{7}{16}\right)\) | \(-i\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{11}{16}\right)\) | \(e\left(\frac{9}{16}\right)\) | \(e\left(\frac{5}{16}\right)\) | \(e\left(\frac{13}{16}\right)\) | \(e\left(\frac{15}{16}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(-i\) |
\(\chi_{5610}(133,\cdot)\) | 5610.cw | 16 | no | \(1\) | \(1\) | \(e\left(\frac{15}{16}\right)\) | \(-1\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{11}{16}\right)\) | \(e\left(\frac{13}{16}\right)\) | \(e\left(\frac{1}{16}\right)\) | \(e\left(\frac{5}{16}\right)\) | \(e\left(\frac{3}{16}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(1\) |
\(\chi_{5610}(137,\cdot)\) | 5610.dw | 20 | no | \(1\) | \(1\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(i\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(-i\) | \(e\left(\frac{19}{20}\right)\) |