sage: H = DirichletGroup(5520)
pari: g = idealstar(,5520,2)
Character group
sage: G.order()
pari: g.no
| ||
Order | = | 1408 |
sage: H.invariants()
pari: g.cyc
| ||
Structure | = | \(C_{2}\times C_{2}\times C_{2}\times C_{4}\times C_{44}\) |
sage: H.gens()
pari: g.gen
| ||
Generators | = | $\chi_{5520}(4831,\cdot)$, $\chi_{5520}(1381,\cdot)$, $\chi_{5520}(1841,\cdot)$, $\chi_{5520}(4417,\cdot)$, $\chi_{5520}(1201,\cdot)$ |
First 32 of 1408 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 | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{5520}(1,\cdot)\) | 5520.a | 1 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
\(\chi_{5520}(7,\cdot)\) | 5520.fp | 44 | no | \(-1\) | \(1\) | \(e\left(\frac{7}{44}\right)\) | \(e\left(\frac{17}{22}\right)\) | \(e\left(\frac{15}{44}\right)\) | \(e\left(\frac{13}{44}\right)\) | \(e\left(\frac{5}{11}\right)\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{15}{22}\right)\) | \(e\left(\frac{39}{44}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{3}{44}\right)\) |
\(\chi_{5520}(11,\cdot)\) | 5520.fz | 44 | no | \(-1\) | \(1\) | \(e\left(\frac{17}{22}\right)\) | \(e\left(\frac{41}{44}\right)\) | \(e\left(\frac{21}{44}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{17}{44}\right)\) | \(e\left(\frac{27}{44}\right)\) | \(e\left(\frac{21}{22}\right)\) | \(e\left(\frac{37}{44}\right)\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{35}{44}\right)\) |
\(\chi_{5520}(13,\cdot)\) | 5520.fj | 44 | no | \(-1\) | \(1\) | \(e\left(\frac{15}{44}\right)\) | \(e\left(\frac{21}{44}\right)\) | \(e\left(\frac{9}{22}\right)\) | \(e\left(\frac{9}{44}\right)\) | \(e\left(\frac{13}{44}\right)\) | \(e\left(\frac{9}{44}\right)\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{19}{22}\right)\) | \(e\left(\frac{3}{22}\right)\) | \(e\left(\frac{2}{11}\right)\) |
\(\chi_{5520}(17,\cdot)\) | 5520.eq | 44 | no | \(-1\) | \(1\) | \(e\left(\frac{13}{44}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{9}{44}\right)\) | \(e\left(\frac{43}{44}\right)\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{41}{44}\right)\) | \(e\left(\frac{7}{22}\right)\) | \(e\left(\frac{15}{44}\right)\) |
\(\chi_{5520}(19,\cdot)\) | 5520.el | 44 | no | \(1\) | \(1\) | \(e\left(\frac{5}{11}\right)\) | \(e\left(\frac{17}{44}\right)\) | \(e\left(\frac{13}{44}\right)\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{43}{44}\right)\) | \(e\left(\frac{23}{44}\right)\) | \(e\left(\frac{13}{22}\right)\) | \(e\left(\frac{25}{44}\right)\) | \(e\left(\frac{15}{22}\right)\) | \(e\left(\frac{7}{44}\right)\) |
\(\chi_{5520}(29,\cdot)\) | 5520.ej | 44 | yes | \(-1\) | \(1\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{27}{44}\right)\) | \(e\left(\frac{9}{44}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{23}{44}\right)\) | \(e\left(\frac{21}{44}\right)\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{19}{44}\right)\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{15}{44}\right)\) |
\(\chi_{5520}(31,\cdot)\) | 5520.ea | 22 | no | \(-1\) | \(1\) | \(e\left(\frac{15}{22}\right)\) | \(e\left(\frac{21}{22}\right)\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{13}{22}\right)\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{3}{22}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{19}{22}\right)\) |
\(\chi_{5520}(37,\cdot)\) | 5520.fh | 44 | no | \(1\) | \(1\) | \(e\left(\frac{39}{44}\right)\) | \(e\left(\frac{37}{44}\right)\) | \(e\left(\frac{19}{22}\right)\) | \(e\left(\frac{41}{44}\right)\) | \(e\left(\frac{25}{44}\right)\) | \(e\left(\frac{19}{44}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{21}{22}\right)\) | \(e\left(\frac{17}{22}\right)\) |
\(\chi_{5520}(41,\cdot)\) | 5520.di | 22 | no | \(-1\) | \(1\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{3}{22}\right)\) | \(e\left(\frac{7}{22}\right)\) | \(e\left(\frac{15}{22}\right)\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{21}{22}\right)\) | \(e\left(\frac{1}{22}\right)\) | \(e\left(\frac{5}{22}\right)\) |
\(\chi_{5520}(43,\cdot)\) | 5520.ff | 44 | no | \(-1\) | \(1\) | \(e\left(\frac{3}{44}\right)\) | \(e\left(\frac{35}{44}\right)\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{15}{44}\right)\) | \(e\left(\frac{7}{44}\right)\) | \(e\left(\frac{15}{44}\right)\) | \(e\left(\frac{19}{22}\right)\) | \(e\left(\frac{17}{22}\right)\) | \(e\left(\frac{5}{22}\right)\) | \(e\left(\frac{3}{22}\right)\) |
\(\chi_{5520}(47,\cdot)\) | 5520.cs | 4 | no | \(-1\) | \(1\) | \(-i\) | \(1\) | \(-i\) | \(-i\) | \(1\) | \(1\) | \(-1\) | \(i\) | \(-1\) | \(i\) |
\(\chi_{5520}(49,\cdot)\) | 5520.dy | 22 | no | \(1\) | \(1\) | \(e\left(\frac{7}{22}\right)\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{15}{22}\right)\) | \(e\left(\frac{13}{22}\right)\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{1}{11}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{17}{22}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{3}{22}\right)\) |
\(\chi_{5520}(53,\cdot)\) | 5520.fa | 44 | yes | \(-1\) | \(1\) | \(e\left(\frac{29}{44}\right)\) | \(e\left(\frac{23}{44}\right)\) | \(e\left(\frac{1}{11}\right)\) | \(e\left(\frac{13}{44}\right)\) | \(e\left(\frac{9}{44}\right)\) | \(e\left(\frac{13}{44}\right)\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{3}{22}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{9}{11}\right)\) |
\(\chi_{5520}(59,\cdot)\) | 5520.fy | 44 | yes | \(1\) | \(1\) | \(e\left(\frac{13}{22}\right)\) | \(e\left(\frac{43}{44}\right)\) | \(e\left(\frac{7}{44}\right)\) | \(e\left(\frac{5}{11}\right)\) | \(e\left(\frac{35}{44}\right)\) | \(e\left(\frac{31}{44}\right)\) | \(e\left(\frac{7}{22}\right)\) | \(e\left(\frac{5}{44}\right)\) | \(e\left(\frac{7}{11}\right)\) | \(e\left(\frac{19}{44}\right)\) |
\(\chi_{5520}(61,\cdot)\) | 5520.en | 44 | no | \(-1\) | \(1\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{31}{44}\right)\) | \(e\left(\frac{3}{44}\right)\) | \(e\left(\frac{9}{22}\right)\) | \(e\left(\frac{37}{44}\right)\) | \(e\left(\frac{7}{44}\right)\) | \(e\left(\frac{7}{11}\right)\) | \(e\left(\frac{43}{44}\right)\) | \(e\left(\frac{17}{22}\right)\) | \(e\left(\frac{27}{44}\right)\) |
\(\chi_{5520}(67,\cdot)\) | 5520.ff | 44 | no | \(-1\) | \(1\) | \(e\left(\frac{21}{44}\right)\) | \(e\left(\frac{25}{44}\right)\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{17}{44}\right)\) | \(e\left(\frac{5}{44}\right)\) | \(e\left(\frac{17}{44}\right)\) | \(e\left(\frac{1}{22}\right)\) | \(e\left(\frac{9}{22}\right)\) | \(e\left(\frac{13}{22}\right)\) | \(e\left(\frac{21}{22}\right)\) |
\(\chi_{5520}(71,\cdot)\) | 5520.eg | 22 | no | \(1\) | \(1\) | \(e\left(\frac{5}{22}\right)\) | \(e\left(\frac{7}{22}\right)\) | \(e\left(\frac{17}{22}\right)\) | \(e\left(\frac{3}{22}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{7}{11}\right)\) | \(e\left(\frac{1}{22}\right)\) | \(e\left(\frac{9}{22}\right)\) | \(e\left(\frac{13}{22}\right)\) | \(e\left(\frac{5}{11}\right)\) |
\(\chi_{5520}(73,\cdot)\) | 5520.fo | 44 | no | \(-1\) | \(1\) | \(e\left(\frac{9}{44}\right)\) | \(e\left(\frac{3}{22}\right)\) | \(e\left(\frac{13}{44}\right)\) | \(e\left(\frac{1}{44}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{1}{11}\right)\) | \(e\left(\frac{3}{44}\right)\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{29}{44}\right)\) |
\(\chi_{5520}(77,\cdot)\) | 5520.ey | 44 | yes | \(1\) | \(1\) | \(e\left(\frac{41}{44}\right)\) | \(e\left(\frac{31}{44}\right)\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{29}{44}\right)\) | \(e\left(\frac{37}{44}\right)\) | \(e\left(\frac{7}{44}\right)\) | \(e\left(\frac{7}{11}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{19}{22}\right)\) |
\(\chi_{5520}(79,\cdot)\) | 5520.dw | 22 | no | \(1\) | \(1\) | \(e\left(\frac{13}{22}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{9}{22}\right)\) | \(e\left(\frac{5}{11}\right)\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{5}{11}\right)\) | \(e\left(\frac{7}{22}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{7}{11}\right)\) | \(e\left(\frac{15}{22}\right)\) |
\(\chi_{5520}(83,\cdot)\) | 5520.fk | 44 | yes | \(1\) | \(1\) | \(e\left(\frac{39}{44}\right)\) | \(e\left(\frac{15}{44}\right)\) | \(e\left(\frac{19}{22}\right)\) | \(e\left(\frac{41}{44}\right)\) | \(e\left(\frac{25}{44}\right)\) | \(e\left(\frac{19}{44}\right)\) | \(e\left(\frac{5}{22}\right)\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{5}{11}\right)\) | \(e\left(\frac{3}{11}\right)\) |
\(\chi_{5520}(89,\cdot)\) | 5520.dm | 22 | no | \(1\) | \(1\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{1}{22}\right)\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{13}{22}\right)\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{1}{11}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{17}{22}\right)\) | \(e\left(\frac{5}{22}\right)\) | \(e\left(\frac{3}{22}\right)\) |
\(\chi_{5520}(91,\cdot)\) | 5520.bg | 4 | no | \(1\) | \(1\) | \(-1\) | \(i\) | \(-i\) | \(-1\) | \(-i\) | \(-i\) | \(-1\) | \(-i\) | \(-1\) | \(i\) |
\(\chi_{5520}(97,\cdot)\) | 5520.fq | 44 | no | \(1\) | \(1\) | \(e\left(\frac{5}{44}\right)\) | \(e\left(\frac{9}{22}\right)\) | \(e\left(\frac{17}{44}\right)\) | \(e\left(\frac{25}{44}\right)\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{7}{22}\right)\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{9}{44}\right)\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{43}{44}\right)\) |
\(\chi_{5520}(101,\cdot)\) | 5520.ga | 44 | no | \(-1\) | \(1\) | \(e\left(\frac{3}{22}\right)\) | \(e\left(\frac{37}{44}\right)\) | \(e\left(\frac{5}{44}\right)\) | \(e\left(\frac{15}{22}\right)\) | \(e\left(\frac{25}{44}\right)\) | \(e\left(\frac{19}{44}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{35}{44}\right)\) | \(e\left(\frac{5}{11}\right)\) | \(e\left(\frac{23}{44}\right)\) |
\(\chi_{5520}(103,\cdot)\) | 5520.fp | 44 | no | \(-1\) | \(1\) | \(e\left(\frac{1}{44}\right)\) | \(e\left(\frac{15}{22}\right)\) | \(e\left(\frac{21}{44}\right)\) | \(e\left(\frac{27}{44}\right)\) | \(e\left(\frac{7}{11}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{21}{22}\right)\) | \(e\left(\frac{37}{44}\right)\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{13}{44}\right)\) |
\(\chi_{5520}(107,\cdot)\) | 5520.fk | 44 | yes | \(1\) | \(1\) | \(e\left(\frac{41}{44}\right)\) | \(e\left(\frac{9}{44}\right)\) | \(e\left(\frac{7}{22}\right)\) | \(e\left(\frac{7}{44}\right)\) | \(e\left(\frac{15}{44}\right)\) | \(e\left(\frac{29}{44}\right)\) | \(e\left(\frac{3}{22}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{4}{11}\right)\) |
\(\chi_{5520}(109,\cdot)\) | 5520.fw | 44 | no | \(-1\) | \(1\) | \(e\left(\frac{1}{22}\right)\) | \(e\left(\frac{27}{44}\right)\) | \(e\left(\frac{9}{44}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{1}{44}\right)\) | \(e\left(\frac{43}{44}\right)\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{41}{44}\right)\) | \(e\left(\frac{7}{22}\right)\) | \(e\left(\frac{37}{44}\right)\) |
\(\chi_{5520}(113,\cdot)\) | 5520.eq | 44 | no | \(-1\) | \(1\) | \(e\left(\frac{43}{44}\right)\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{23}{44}\right)\) | \(e\left(\frac{17}{44}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{7}{11}\right)\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{7}{44}\right)\) | \(e\left(\frac{13}{22}\right)\) | \(e\left(\frac{9}{44}\right)\) |
\(\chi_{5520}(119,\cdot)\) | 5520.dk | 22 | no | \(1\) | \(1\) | \(e\left(\frac{5}{11}\right)\) | \(e\left(\frac{3}{22}\right)\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{13}{22}\right)\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{15}{22}\right)\) | \(e\left(\frac{9}{22}\right)\) |
\(\chi_{5520}(121,\cdot)\) | 5520.dp | 22 | no | \(1\) | \(1\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{19}{22}\right)\) | \(e\left(\frac{21}{22}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{17}{22}\right)\) | \(e\left(\frac{5}{22}\right)\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{15}{22}\right)\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{13}{22}\right)\) |