sage: H = DirichletGroup(1840)
pari: g = idealstar(,1840,2)
Character group
sage: G.order()
pari: g.no
| ||
Order | = | 704 |
sage: H.invariants()
pari: g.cyc
| ||
Structure | = | \(C_{2}\times C_{2}\times C_{4}\times C_{44}\) |
sage: H.gens()
pari: g.gen
| ||
Generators | = | $\chi_{1840}(1151,\cdot)$, $\chi_{1840}(1381,\cdot)$, $\chi_{1840}(737,\cdot)$, $\chi_{1840}(1201,\cdot)$ |
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 | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(27\) | \(29\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{1840}(1,\cdot)\) | 1840.a | 1 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
\(\chi_{1840}(3,\cdot)\) | 1840.ch | 44 | yes | \(1\) | \(1\) | \(e\left(\frac{7}{11}\right)\) | \(e\left(\frac{25}{44}\right)\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{35}{44}\right)\) | \(e\left(\frac{15}{22}\right)\) | \(e\left(\frac{37}{44}\right)\) | \(e\left(\frac{7}{44}\right)\) | \(e\left(\frac{9}{44}\right)\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{37}{44}\right)\) |
\(\chi_{1840}(7,\cdot)\) | 1840.cq | 44 | no | \(-1\) | \(1\) | \(e\left(\frac{25}{44}\right)\) | \(e\left(\frac{7}{44}\right)\) | \(e\left(\frac{3}{22}\right)\) | \(e\left(\frac{17}{22}\right)\) | \(e\left(\frac{15}{44}\right)\) | \(e\left(\frac{13}{44}\right)\) | \(e\left(\frac{5}{11}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{31}{44}\right)\) | \(e\left(\frac{6}{11}\right)\) |
\(\chi_{1840}(9,\cdot)\) | 1840.bv | 22 | no | \(1\) | \(1\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{3}{22}\right)\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{13}{22}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{15}{22}\right)\) | \(e\left(\frac{7}{22}\right)\) | \(e\left(\frac{9}{22}\right)\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{15}{22}\right)\) |
\(\chi_{1840}(11,\cdot)\) | 1840.cw | 44 | no | \(1\) | \(1\) | \(e\left(\frac{35}{44}\right)\) | \(e\left(\frac{17}{22}\right)\) | \(e\left(\frac{13}{22}\right)\) | \(e\left(\frac{19}{44}\right)\) | \(e\left(\frac{21}{44}\right)\) | \(e\left(\frac{19}{22}\right)\) | \(e\left(\frac{17}{44}\right)\) | \(e\left(\frac{25}{44}\right)\) | \(e\left(\frac{17}{44}\right)\) | \(e\left(\frac{5}{44}\right)\) |
\(\chi_{1840}(13,\cdot)\) | 1840.db | 44 | yes | \(-1\) | \(1\) | \(e\left(\frac{15}{22}\right)\) | \(e\left(\frac{15}{44}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{21}{44}\right)\) | \(e\left(\frac{9}{22}\right)\) | \(e\left(\frac{9}{44}\right)\) | \(e\left(\frac{13}{44}\right)\) | \(e\left(\frac{1}{44}\right)\) | \(e\left(\frac{1}{22}\right)\) | \(e\left(\frac{9}{44}\right)\) |
\(\chi_{1840}(17,\cdot)\) | 1840.ct | 44 | no | \(1\) | \(1\) | \(e\left(\frac{37}{44}\right)\) | \(e\left(\frac{13}{44}\right)\) | \(e\left(\frac{15}{22}\right)\) | \(e\left(\frac{19}{22}\right)\) | \(e\left(\frac{9}{44}\right)\) | \(e\left(\frac{21}{44}\right)\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{3}{22}\right)\) | \(e\left(\frac{23}{44}\right)\) | \(e\left(\frac{5}{22}\right)\) |
\(\chi_{1840}(19,\cdot)\) | 1840.cj | 44 | yes | \(1\) | \(1\) | \(e\left(\frac{7}{44}\right)\) | \(e\left(\frac{5}{11}\right)\) | \(e\left(\frac{7}{22}\right)\) | \(e\left(\frac{17}{44}\right)\) | \(e\left(\frac{13}{44}\right)\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{43}{44}\right)\) | \(e\left(\frac{27}{44}\right)\) | \(e\left(\frac{21}{44}\right)\) | \(e\left(\frac{23}{44}\right)\) |
\(\chi_{1840}(21,\cdot)\) | 1840.cl | 44 | no | \(-1\) | \(1\) | \(e\left(\frac{9}{44}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{9}{22}\right)\) | \(e\left(\frac{25}{44}\right)\) | \(e\left(\frac{1}{44}\right)\) | \(e\left(\frac{3}{22}\right)\) | \(e\left(\frac{27}{44}\right)\) | \(e\left(\frac{41}{44}\right)\) | \(e\left(\frac{27}{44}\right)\) | \(e\left(\frac{17}{44}\right)\) |
\(\chi_{1840}(27,\cdot)\) | 1840.ch | 44 | yes | \(1\) | \(1\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{31}{44}\right)\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{17}{44}\right)\) | \(e\left(\frac{1}{22}\right)\) | \(e\left(\frac{23}{44}\right)\) | \(e\left(\frac{21}{44}\right)\) | \(e\left(\frac{27}{44}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{23}{44}\right)\) |
\(\chi_{1840}(29,\cdot)\) | 1840.ck | 44 | yes | \(1\) | \(1\) | \(e\left(\frac{37}{44}\right)\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{15}{22}\right)\) | \(e\left(\frac{5}{44}\right)\) | \(e\left(\frac{9}{44}\right)\) | \(e\left(\frac{5}{22}\right)\) | \(e\left(\frac{23}{44}\right)\) | \(e\left(\frac{17}{44}\right)\) | \(e\left(\frac{23}{44}\right)\) | \(e\left(\frac{43}{44}\right)\) |
\(\chi_{1840}(31,\cdot)\) | 1840.cc | 22 | no | \(-1\) | \(1\) | \(e\left(\frac{19}{22}\right)\) | \(e\left(\frac{15}{22}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{21}{22}\right)\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{13}{22}\right)\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{13}{22}\right)\) | \(e\left(\frac{10}{11}\right)\) |
\(\chi_{1840}(33,\cdot)\) | 1840.ct | 44 | no | \(1\) | \(1\) | \(e\left(\frac{19}{44}\right)\) | \(e\left(\frac{15}{44}\right)\) | \(e\left(\frac{19}{22}\right)\) | \(e\left(\frac{5}{22}\right)\) | \(e\left(\frac{7}{44}\right)\) | \(e\left(\frac{31}{44}\right)\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{17}{22}\right)\) | \(e\left(\frac{13}{44}\right)\) | \(e\left(\frac{21}{22}\right)\) |
\(\chi_{1840}(37,\cdot)\) | 1840.da | 44 | yes | \(1\) | \(1\) | \(e\left(\frac{17}{22}\right)\) | \(e\left(\frac{39}{44}\right)\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{37}{44}\right)\) | \(e\left(\frac{19}{22}\right)\) | \(e\left(\frac{41}{44}\right)\) | \(e\left(\frac{25}{44}\right)\) | \(e\left(\frac{29}{44}\right)\) | \(e\left(\frac{7}{22}\right)\) | \(e\left(\frac{19}{44}\right)\) |
\(\chi_{1840}(39,\cdot)\) | 1840.bx | 22 | no | \(-1\) | \(1\) | \(e\left(\frac{7}{22}\right)\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{7}{11}\right)\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{1}{11}\right)\) | \(e\left(\frac{1}{22}\right)\) | \(e\left(\frac{5}{11}\right)\) | \(e\left(\frac{5}{22}\right)\) | \(e\left(\frac{21}{22}\right)\) | \(e\left(\frac{1}{22}\right)\) |
\(\chi_{1840}(41,\cdot)\) | 1840.bz | 22 | no | \(1\) | \(1\) | \(e\left(\frac{5}{22}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{5}{11}\right)\) | \(e\left(\frac{9}{22}\right)\) | \(e\left(\frac{3}{22}\right)\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{15}{22}\right)\) | \(e\left(\frac{13}{22}\right)\) | \(e\left(\frac{15}{22}\right)\) | \(e\left(\frac{7}{22}\right)\) |
\(\chi_{1840}(43,\cdot)\) | 1840.cz | 44 | yes | \(-1\) | \(1\) | \(e\left(\frac{3}{22}\right)\) | \(e\left(\frac{3}{44}\right)\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{35}{44}\right)\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{15}{44}\right)\) | \(e\left(\frac{7}{44}\right)\) | \(e\left(\frac{9}{44}\right)\) | \(e\left(\frac{9}{22}\right)\) | \(e\left(\frac{15}{44}\right)\) |
\(\chi_{1840}(47,\cdot)\) | 1840.ba | 4 | no | \(1\) | \(1\) | \(i\) | \(-i\) | \(-1\) | \(-1\) | \(-i\) | \(i\) | \(1\) | \(1\) | \(-i\) | \(-1\) |
\(\chi_{1840}(49,\cdot)\) | 1840.ca | 22 | no | \(1\) | \(1\) | \(e\left(\frac{3}{22}\right)\) | \(e\left(\frac{7}{22}\right)\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{15}{22}\right)\) | \(e\left(\frac{13}{22}\right)\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{5}{11}\right)\) | \(e\left(\frac{9}{22}\right)\) | \(e\left(\frac{1}{11}\right)\) |
\(\chi_{1840}(51,\cdot)\) | 1840.cw | 44 | no | \(1\) | \(1\) | \(e\left(\frac{21}{44}\right)\) | \(e\left(\frac{19}{22}\right)\) | \(e\left(\frac{21}{22}\right)\) | \(e\left(\frac{29}{44}\right)\) | \(e\left(\frac{39}{44}\right)\) | \(e\left(\frac{7}{22}\right)\) | \(e\left(\frac{19}{44}\right)\) | \(e\left(\frac{15}{44}\right)\) | \(e\left(\frac{19}{44}\right)\) | \(e\left(\frac{3}{44}\right)\) |
\(\chi_{1840}(53,\cdot)\) | 1840.cf | 44 | yes | \(1\) | \(1\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{29}{44}\right)\) | \(e\left(\frac{7}{11}\right)\) | \(e\left(\frac{1}{44}\right)\) | \(e\left(\frac{1}{11}\right)\) | \(e\left(\frac{35}{44}\right)\) | \(e\left(\frac{9}{44}\right)\) | \(e\left(\frac{21}{44}\right)\) | \(e\left(\frac{5}{11}\right)\) | \(e\left(\frac{35}{44}\right)\) |
\(\chi_{1840}(57,\cdot)\) | 1840.cm | 44 | no | \(1\) | \(1\) | \(e\left(\frac{35}{44}\right)\) | \(e\left(\frac{1}{44}\right)\) | \(e\left(\frac{13}{22}\right)\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{43}{44}\right)\) | \(e\left(\frac{5}{44}\right)\) | \(e\left(\frac{3}{22}\right)\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{17}{44}\right)\) | \(e\left(\frac{4}{11}\right)\) |
\(\chi_{1840}(59,\cdot)\) | 1840.cx | 44 | yes | \(-1\) | \(1\) | \(e\left(\frac{41}{44}\right)\) | \(e\left(\frac{13}{22}\right)\) | \(e\left(\frac{19}{22}\right)\) | \(e\left(\frac{21}{44}\right)\) | \(e\left(\frac{7}{44}\right)\) | \(e\left(\frac{21}{22}\right)\) | \(e\left(\frac{35}{44}\right)\) | \(e\left(\frac{23}{44}\right)\) | \(e\left(\frac{35}{44}\right)\) | \(e\left(\frac{9}{44}\right)\) |
\(\chi_{1840}(61,\cdot)\) | 1840.cl | 44 | no | \(-1\) | \(1\) | \(e\left(\frac{27}{44}\right)\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{5}{22}\right)\) | \(e\left(\frac{31}{44}\right)\) | \(e\left(\frac{3}{44}\right)\) | \(e\left(\frac{9}{22}\right)\) | \(e\left(\frac{37}{44}\right)\) | \(e\left(\frac{35}{44}\right)\) | \(e\left(\frac{37}{44}\right)\) | \(e\left(\frac{7}{44}\right)\) |
\(\chi_{1840}(63,\cdot)\) | 1840.cp | 44 | no | \(-1\) | \(1\) | \(e\left(\frac{37}{44}\right)\) | \(e\left(\frac{13}{44}\right)\) | \(e\left(\frac{15}{22}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{31}{44}\right)\) | \(e\left(\frac{43}{44}\right)\) | \(e\left(\frac{17}{22}\right)\) | \(e\left(\frac{3}{22}\right)\) | \(e\left(\frac{23}{44}\right)\) | \(e\left(\frac{5}{22}\right)\) |
\(\chi_{1840}(67,\cdot)\) | 1840.cz | 44 | yes | \(-1\) | \(1\) | \(e\left(\frac{21}{22}\right)\) | \(e\left(\frac{21}{44}\right)\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{25}{44}\right)\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{17}{44}\right)\) | \(e\left(\frac{5}{44}\right)\) | \(e\left(\frac{19}{44}\right)\) | \(e\left(\frac{19}{22}\right)\) | \(e\left(\frac{17}{44}\right)\) |
\(\chi_{1840}(71,\cdot)\) | 1840.bt | 22 | no | \(-1\) | \(1\) | \(e\left(\frac{5}{11}\right)\) | \(e\left(\frac{5}{22}\right)\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{17}{22}\right)\) | \(e\left(\frac{7}{11}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{15}{22}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{3}{22}\right)\) |
\(\chi_{1840}(73,\cdot)\) | 1840.cs | 44 | no | \(-1\) | \(1\) | \(e\left(\frac{29}{44}\right)\) | \(e\left(\frac{9}{44}\right)\) | \(e\left(\frac{7}{22}\right)\) | \(e\left(\frac{3}{22}\right)\) | \(e\left(\frac{13}{44}\right)\) | \(e\left(\frac{1}{44}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{19}{22}\right)\) | \(e\left(\frac{43}{44}\right)\) | \(e\left(\frac{3}{11}\right)\) |
\(\chi_{1840}(77,\cdot)\) | 1840.ce | 44 | yes | \(-1\) | \(1\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{41}{44}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{9}{44}\right)\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{7}{44}\right)\) | \(e\left(\frac{37}{44}\right)\) | \(e\left(\frac{13}{44}\right)\) | \(e\left(\frac{1}{11}\right)\) | \(e\left(\frac{29}{44}\right)\) |
\(\chi_{1840}(79,\cdot)\) | 1840.bs | 22 | no | \(1\) | \(1\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{13}{22}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{9}{22}\right)\) | \(e\left(\frac{5}{11}\right)\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{17}{22}\right)\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{5}{11}\right)\) |
\(\chi_{1840}(81,\cdot)\) | 1840.bo | 11 | no | \(1\) | \(1\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{1}{11}\right)\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{7}{11}\right)\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{7}{11}\right)\) | \(e\left(\frac{4}{11}\right)\) |
\(\chi_{1840}(83,\cdot)\) | 1840.cg | 44 | yes | \(-1\) | \(1\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{39}{44}\right)\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{37}{44}\right)\) | \(e\left(\frac{19}{22}\right)\) | \(e\left(\frac{19}{44}\right)\) | \(e\left(\frac{25}{44}\right)\) | \(e\left(\frac{7}{44}\right)\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{41}{44}\right)\) |