sage: H = DirichletGroup(2760)
pari: g = idealstar(,2760,2)
Character group
sage: G.order()
pari: g.no
| ||
Order | = | 704 |
sage: H.invariants()
pari: g.cyc
| ||
Structure | = | \(C_{2}\times C_{2}\times C_{2}\times C_{2}\times C_{44}\) |
sage: H.gens()
pari: g.gen
| ||
Generators | = | $\chi_{2760}(2071,\cdot)$, $\chi_{2760}(1381,\cdot)$, $\chi_{2760}(1841,\cdot)$, $\chi_{2760}(1657,\cdot)$, $\chi_{2760}(1201,\cdot)$ |
First 32 of 704 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 | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{2760}(1,\cdot)\) | 2760.a | 1 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
\(\chi_{2760}(7,\cdot)\) | 2760.dj | 44 | no | \(-1\) | \(1\) | \(e\left(\frac{7}{44}\right)\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{37}{44}\right)\) | \(e\left(\frac{13}{44}\right)\) | \(e\left(\frac{21}{22}\right)\) | \(e\left(\frac{1}{22}\right)\) | \(e\left(\frac{15}{22}\right)\) | \(e\left(\frac{17}{44}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{25}{44}\right)\) |
\(\chi_{2760}(11,\cdot)\) | 2760.ca | 22 | no | \(-1\) | \(1\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{5}{22}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{3}{22}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{21}{22}\right)\) | \(e\left(\frac{1}{11}\right)\) | \(e\left(\frac{9}{22}\right)\) | \(e\left(\frac{1}{22}\right)\) |
\(\chi_{2760}(13,\cdot)\) | 2760.dk | 44 | no | \(-1\) | \(1\) | \(e\left(\frac{37}{44}\right)\) | \(e\left(\frac{5}{22}\right)\) | \(e\left(\frac{29}{44}\right)\) | \(e\left(\frac{9}{44}\right)\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{5}{11}\right)\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{27}{44}\right)\) | \(e\left(\frac{7}{11}\right)\) | \(e\left(\frac{41}{44}\right)\) |
\(\chi_{2760}(17,\cdot)\) | 2760.dc | 44 | no | \(-1\) | \(1\) | \(e\left(\frac{13}{44}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{9}{44}\right)\) | \(e\left(\frac{43}{44}\right)\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{41}{44}\right)\) | \(e\left(\frac{7}{22}\right)\) | \(e\left(\frac{15}{44}\right)\) |
\(\chi_{2760}(19,\cdot)\) | 2760.cv | 22 | no | \(1\) | \(1\) | \(e\left(\frac{21}{22}\right)\) | \(e\left(\frac{3}{22}\right)\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{5}{22}\right)\) | \(e\left(\frac{17}{22}\right)\) | \(e\left(\frac{13}{22}\right)\) | \(e\left(\frac{7}{22}\right)\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{10}{11}\right)\) |
\(\chi_{2760}(29,\cdot)\) | 2760.cm | 22 | yes | \(-1\) | \(1\) | \(e\left(\frac{1}{22}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{5}{11}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{17}{22}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{7}{22}\right)\) | \(e\left(\frac{1}{11}\right)\) |
\(\chi_{2760}(31,\cdot)\) | 2760.cu | 22 | no | \(-1\) | \(1\) | \(e\left(\frac{15}{22}\right)\) | \(e\left(\frac{21}{22}\right)\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{13}{22}\right)\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{3}{22}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{19}{22}\right)\) |
\(\chi_{2760}(37,\cdot)\) | 2760.dg | 44 | no | \(1\) | \(1\) | \(e\left(\frac{17}{44}\right)\) | \(e\left(\frac{1}{11}\right)\) | \(e\left(\frac{27}{44}\right)\) | \(e\left(\frac{41}{44}\right)\) | \(e\left(\frac{7}{22}\right)\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{35}{44}\right)\) | \(e\left(\frac{5}{11}\right)\) | \(e\left(\frac{1}{44}\right)\) |
\(\chi_{2760}(41,\cdot)\) | 2760.ch | 22 | no | \(-1\) | \(1\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{9}{22}\right)\) | \(e\left(\frac{7}{11}\right)\) | \(e\left(\frac{7}{22}\right)\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{7}{22}\right)\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{5}{11}\right)\) | \(e\left(\frac{1}{22}\right)\) | \(e\left(\frac{8}{11}\right)\) |
\(\chi_{2760}(43,\cdot)\) | 2760.dl | 44 | no | \(-1\) | \(1\) | \(e\left(\frac{25}{44}\right)\) | \(e\left(\frac{1}{22}\right)\) | \(e\left(\frac{41}{44}\right)\) | \(e\left(\frac{15}{44}\right)\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{1}{11}\right)\) | \(e\left(\frac{19}{22}\right)\) | \(e\left(\frac{1}{44}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{17}{44}\right)\) |
\(\chi_{2760}(47,\cdot)\) | 2760.bu | 4 | no | \(-1\) | \(1\) | \(-i\) | \(1\) | \(-i\) | \(-i\) | \(1\) | \(1\) | \(-1\) | \(i\) | \(-1\) | \(i\) |
\(\chi_{2760}(49,\cdot)\) | 2760.cs | 22 | no | \(1\) | \(1\) | \(e\left(\frac{7}{22}\right)\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{15}{22}\right)\) | \(e\left(\frac{13}{22}\right)\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{1}{11}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{17}{22}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{3}{22}\right)\) |
\(\chi_{2760}(53,\cdot)\) | 2760.dq | 44 | yes | \(-1\) | \(1\) | \(e\left(\frac{7}{44}\right)\) | \(e\left(\frac{17}{22}\right)\) | \(e\left(\frac{37}{44}\right)\) | \(e\left(\frac{13}{44}\right)\) | \(e\left(\frac{21}{22}\right)\) | \(e\left(\frac{1}{22}\right)\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{17}{44}\right)\) | \(e\left(\frac{19}{22}\right)\) | \(e\left(\frac{3}{44}\right)\) |
\(\chi_{2760}(59,\cdot)\) | 2760.ce | 22 | yes | \(1\) | \(1\) | \(e\left(\frac{1}{11}\right)\) | \(e\left(\frac{5}{22}\right)\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{5}{11}\right)\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{5}{11}\right)\) | \(e\left(\frac{7}{22}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{3}{22}\right)\) | \(e\left(\frac{15}{22}\right)\) |
\(\chi_{2760}(61,\cdot)\) | 2760.ct | 22 | no | \(-1\) | \(1\) | \(e\left(\frac{15}{22}\right)\) | \(e\left(\frac{5}{11}\right)\) | \(e\left(\frac{7}{22}\right)\) | \(e\left(\frac{9}{22}\right)\) | \(e\left(\frac{1}{11}\right)\) | \(e\left(\frac{9}{22}\right)\) | \(e\left(\frac{7}{11}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{4}{11}\right)\) |
\(\chi_{2760}(67,\cdot)\) | 2760.dl | 44 | no | \(-1\) | \(1\) | \(e\left(\frac{43}{44}\right)\) | \(e\left(\frac{7}{22}\right)\) | \(e\left(\frac{23}{44}\right)\) | \(e\left(\frac{17}{44}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{7}{11}\right)\) | \(e\left(\frac{1}{22}\right)\) | \(e\left(\frac{7}{44}\right)\) | \(e\left(\frac{1}{11}\right)\) | \(e\left(\frac{31}{44}\right)\) |
\(\chi_{2760}(71,\cdot)\) | 2760.cp | 22 | no | \(1\) | \(1\) | \(e\left(\frac{5}{22}\right)\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{3}{22}\right)\) | \(e\left(\frac{19}{22}\right)\) | \(e\left(\frac{3}{22}\right)\) | \(e\left(\frac{1}{22}\right)\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{13}{22}\right)\) | \(e\left(\frac{21}{22}\right)\) |
\(\chi_{2760}(73,\cdot)\) | 2760.di | 44 | no | \(-1\) | \(1\) | \(e\left(\frac{9}{44}\right)\) | \(e\left(\frac{7}{11}\right)\) | \(e\left(\frac{35}{44}\right)\) | \(e\left(\frac{1}{44}\right)\) | \(e\left(\frac{5}{22}\right)\) | \(e\left(\frac{17}{22}\right)\) | \(e\left(\frac{1}{11}\right)\) | \(e\left(\frac{25}{44}\right)\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{7}{44}\right)\) |
\(\chi_{2760}(77,\cdot)\) | 2760.de | 44 | yes | \(1\) | \(1\) | \(e\left(\frac{19}{44}\right)\) | \(e\left(\frac{5}{11}\right)\) | \(e\left(\frac{3}{44}\right)\) | \(e\left(\frac{29}{44}\right)\) | \(e\left(\frac{1}{11}\right)\) | \(e\left(\frac{9}{22}\right)\) | \(e\left(\frac{7}{11}\right)\) | \(e\left(\frac{21}{44}\right)\) | \(e\left(\frac{17}{22}\right)\) | \(e\left(\frac{27}{44}\right)\) |
\(\chi_{2760}(79,\cdot)\) | 2760.cq | 22 | no | \(1\) | \(1\) | \(e\left(\frac{13}{22}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{9}{22}\right)\) | \(e\left(\frac{5}{11}\right)\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{5}{11}\right)\) | \(e\left(\frac{7}{22}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{7}{11}\right)\) | \(e\left(\frac{15}{22}\right)\) |
\(\chi_{2760}(83,\cdot)\) | 2760.df | 44 | yes | \(1\) | \(1\) | \(e\left(\frac{17}{44}\right)\) | \(e\left(\frac{1}{11}\right)\) | \(e\left(\frac{5}{44}\right)\) | \(e\left(\frac{41}{44}\right)\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{15}{22}\right)\) | \(e\left(\frac{5}{22}\right)\) | \(e\left(\frac{13}{44}\right)\) | \(e\left(\frac{21}{22}\right)\) | \(e\left(\frac{1}{44}\right)\) |
\(\chi_{2760}(89,\cdot)\) | 2760.cd | 22 | no | \(1\) | \(1\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{15}{22}\right)\) | \(e\left(\frac{13}{22}\right)\) | \(e\left(\frac{9}{22}\right)\) | \(e\left(\frac{13}{22}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{5}{22}\right)\) | \(e\left(\frac{7}{11}\right)\) |
\(\chi_{2760}(91,\cdot)\) | 2760.r | 2 | no | \(1\) | \(1\) | \(1\) | \(-1\) | \(-1\) | \(-1\) | \(-1\) | \(-1\) | \(-1\) | \(1\) | \(1\) | \(-1\) |
\(\chi_{2760}(97,\cdot)\) | 2760.dm | 44 | no | \(1\) | \(1\) | \(e\left(\frac{5}{44}\right)\) | \(e\left(\frac{9}{22}\right)\) | \(e\left(\frac{17}{44}\right)\) | \(e\left(\frac{25}{44}\right)\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{7}{22}\right)\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{9}{44}\right)\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{43}{44}\right)\) |
\(\chi_{2760}(101,\cdot)\) | 2760.cc | 22 | no | \(-1\) | \(1\) | \(e\left(\frac{7}{11}\right)\) | \(e\left(\frac{1}{11}\right)\) | \(e\left(\frac{19}{22}\right)\) | \(e\left(\frac{15}{22}\right)\) | \(e\left(\frac{7}{22}\right)\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{1}{22}\right)\) | \(e\left(\frac{21}{22}\right)\) | \(e\left(\frac{17}{22}\right)\) |
\(\chi_{2760}(103,\cdot)\) | 2760.dj | 44 | no | \(-1\) | \(1\) | \(e\left(\frac{1}{44}\right)\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{43}{44}\right)\) | \(e\left(\frac{27}{44}\right)\) | \(e\left(\frac{3}{22}\right)\) | \(e\left(\frac{19}{22}\right)\) | \(e\left(\frac{21}{22}\right)\) | \(e\left(\frac{15}{44}\right)\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{35}{44}\right)\) |
\(\chi_{2760}(107,\cdot)\) | 2760.df | 44 | yes | \(1\) | \(1\) | \(e\left(\frac{19}{44}\right)\) | \(e\left(\frac{5}{11}\right)\) | \(e\left(\frac{3}{44}\right)\) | \(e\left(\frac{7}{44}\right)\) | \(e\left(\frac{1}{11}\right)\) | \(e\left(\frac{9}{22}\right)\) | \(e\left(\frac{3}{22}\right)\) | \(e\left(\frac{43}{44}\right)\) | \(e\left(\frac{17}{22}\right)\) | \(e\left(\frac{27}{44}\right)\) |
\(\chi_{2760}(109,\cdot)\) | 2760.bx | 22 | no | \(-1\) | \(1\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{5}{11}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{5}{22}\right)\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{15}{22}\right)\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{13}{22}\right)\) |
\(\chi_{2760}(113,\cdot)\) | 2760.dc | 44 | no | \(-1\) | \(1\) | \(e\left(\frac{43}{44}\right)\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{23}{44}\right)\) | \(e\left(\frac{17}{44}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{7}{11}\right)\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{7}{44}\right)\) | \(e\left(\frac{13}{22}\right)\) | \(e\left(\frac{9}{44}\right)\) |
\(\chi_{2760}(119,\cdot)\) | 2760.cb | 22 | no | \(1\) | \(1\) | \(e\left(\frac{5}{11}\right)\) | \(e\left(\frac{7}{11}\right)\) | \(e\left(\frac{1}{22}\right)\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{5}{22}\right)\) | \(e\left(\frac{17}{22}\right)\) | \(e\left(\frac{13}{22}\right)\) | \(e\left(\frac{7}{22}\right)\) | \(e\left(\frac{15}{22}\right)\) | \(e\left(\frac{10}{11}\right)\) |
\(\chi_{2760}(121,\cdot)\) | 2760.bw | 11 | no | \(1\) | \(1\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{5}{11}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{1}{11}\right)\) |