sage: H = DirichletGroup(1476)
pari: g = idealstar(,1476,2)
Character group
sage: G.order()
pari: g.no
| ||
Order | = | 480 |
sage: H.invariants()
pari: g.cyc
| ||
Structure | = | \(C_{2}\times C_{2}\times C_{120}\) |
sage: H.gens()
pari: g.gen
| ||
Generators | = | $\chi_{1476}(739,\cdot)$, $\chi_{1476}(821,\cdot)$, $\chi_{1476}(1441,\cdot)$ |
First 32 of 480 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 | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{1476}(1,\cdot)\) | 1476.a | 1 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
\(\chi_{1476}(5,\cdot)\) | 1476.cg | 60 | no | \(-1\) | \(1\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{47}{60}\right)\) | \(e\left(\frac{29}{60}\right)\) | \(e\left(\frac{43}{60}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{41}{60}\right)\) | \(e\left(\frac{1}{15}\right)\) |
\(\chi_{1476}(7,\cdot)\) | 1476.cl | 120 | yes | \(1\) | \(1\) | \(e\left(\frac{47}{60}\right)\) | \(e\left(\frac{23}{120}\right)\) | \(e\left(\frac{11}{120}\right)\) | \(e\left(\frac{67}{120}\right)\) | \(e\left(\frac{7}{40}\right)\) | \(e\left(\frac{11}{40}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{59}{120}\right)\) | \(e\left(\frac{2}{15}\right)\) |
\(\chi_{1476}(11,\cdot)\) | 1476.cj | 120 | yes | \(-1\) | \(1\) | \(e\left(\frac{29}{60}\right)\) | \(e\left(\frac{11}{120}\right)\) | \(e\left(\frac{107}{120}\right)\) | \(e\left(\frac{79}{120}\right)\) | \(e\left(\frac{39}{40}\right)\) | \(e\left(\frac{7}{40}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{83}{120}\right)\) | \(e\left(\frac{14}{15}\right)\) |
\(\chi_{1476}(13,\cdot)\) | 1476.ci | 120 | no | \(-1\) | \(1\) | \(e\left(\frac{43}{60}\right)\) | \(e\left(\frac{67}{120}\right)\) | \(e\left(\frac{79}{120}\right)\) | \(e\left(\frac{83}{120}\right)\) | \(e\left(\frac{23}{40}\right)\) | \(e\left(\frac{39}{40}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{91}{120}\right)\) | \(e\left(\frac{11}{30}\right)\) |
\(\chi_{1476}(17,\cdot)\) | 1476.cb | 40 | no | \(1\) | \(1\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{7}{40}\right)\) | \(e\left(\frac{39}{40}\right)\) | \(e\left(\frac{23}{40}\right)\) | \(e\left(\frac{29}{40}\right)\) | \(e\left(\frac{17}{40}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{11}{40}\right)\) | \(e\left(\frac{1}{10}\right)\) |
\(\chi_{1476}(19,\cdot)\) | 1476.ca | 40 | no | \(1\) | \(1\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{11}{40}\right)\) | \(e\left(\frac{7}{40}\right)\) | \(e\left(\frac{39}{40}\right)\) | \(e\left(\frac{17}{40}\right)\) | \(e\left(\frac{21}{40}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{23}{40}\right)\) | \(e\left(\frac{4}{5}\right)\) |
\(\chi_{1476}(23,\cdot)\) | 1476.bv | 30 | yes | \(1\) | \(1\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{11}{30}\right)\) |
\(\chi_{1476}(25,\cdot)\) | 1476.bx | 30 | no | \(1\) | \(1\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{2}{15}\right)\) |
\(\chi_{1476}(29,\cdot)\) | 1476.ck | 120 | no | \(1\) | \(1\) | \(e\left(\frac{41}{60}\right)\) | \(e\left(\frac{59}{120}\right)\) | \(e\left(\frac{83}{120}\right)\) | \(e\left(\frac{91}{120}\right)\) | \(e\left(\frac{11}{40}\right)\) | \(e\left(\frac{23}{40}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{47}{120}\right)\) | \(e\left(\frac{7}{30}\right)\) |
\(\chi_{1476}(31,\cdot)\) | 1476.bz | 30 | yes | \(-1\) | \(1\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{23}{30}\right)\) |
\(\chi_{1476}(35,\cdot)\) | 1476.cc | 40 | no | \(-1\) | \(1\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{39}{40}\right)\) | \(e\left(\frac{23}{40}\right)\) | \(e\left(\frac{11}{40}\right)\) | \(e\left(\frac{33}{40}\right)\) | \(e\left(\frac{9}{40}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{7}{40}\right)\) | \(e\left(\frac{1}{5}\right)\) |
\(\chi_{1476}(37,\cdot)\) | 1476.n | 5 | no | \(1\) | \(1\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{2}{5}\right)\) |
\(\chi_{1476}(43,\cdot)\) | 1476.ce | 60 | yes | \(-1\) | \(1\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{31}{60}\right)\) | \(e\left(\frac{7}{60}\right)\) | \(e\left(\frac{29}{60}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{13}{60}\right)\) | \(e\left(\frac{1}{30}\right)\) |
\(\chi_{1476}(47,\cdot)\) | 1476.cj | 120 | yes | \(-1\) | \(1\) | \(e\left(\frac{23}{60}\right)\) | \(e\left(\frac{17}{120}\right)\) | \(e\left(\frac{89}{120}\right)\) | \(e\left(\frac{13}{120}\right)\) | \(e\left(\frac{13}{40}\right)\) | \(e\left(\frac{29}{40}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{41}{120}\right)\) | \(e\left(\frac{8}{15}\right)\) |
\(\chi_{1476}(49,\cdot)\) | 1476.cf | 60 | no | \(1\) | \(1\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{23}{60}\right)\) | \(e\left(\frac{11}{60}\right)\) | \(e\left(\frac{7}{60}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{59}{60}\right)\) | \(e\left(\frac{4}{15}\right)\) |
\(\chi_{1476}(53,\cdot)\) | 1476.cb | 40 | no | \(1\) | \(1\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{13}{40}\right)\) | \(e\left(\frac{21}{40}\right)\) | \(e\left(\frac{37}{40}\right)\) | \(e\left(\frac{31}{40}\right)\) | \(e\left(\frac{3}{40}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{9}{40}\right)\) | \(e\left(\frac{9}{10}\right)\) |
\(\chi_{1476}(55,\cdot)\) | 1476.y | 8 | no | \(1\) | \(1\) | \(-i\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(1\) | \(-1\) | \(e\left(\frac{3}{8}\right)\) | \(1\) |
\(\chi_{1476}(59,\cdot)\) | 1476.bu | 30 | yes | \(1\) | \(1\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{11}{30}\right)\) |
\(\chi_{1476}(61,\cdot)\) | 1476.cf | 60 | no | \(1\) | \(1\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{49}{60}\right)\) | \(e\left(\frac{13}{60}\right)\) | \(e\left(\frac{41}{60}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{37}{60}\right)\) | \(e\left(\frac{2}{15}\right)\) |
\(\chi_{1476}(65,\cdot)\) | 1476.ck | 120 | no | \(1\) | \(1\) | \(e\left(\frac{59}{60}\right)\) | \(e\left(\frac{41}{120}\right)\) | \(e\left(\frac{17}{120}\right)\) | \(e\left(\frac{49}{120}\right)\) | \(e\left(\frac{9}{40}\right)\) | \(e\left(\frac{37}{40}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{53}{120}\right)\) | \(e\left(\frac{13}{30}\right)\) |
\(\chi_{1476}(67,\cdot)\) | 1476.cl | 120 | yes | \(1\) | \(1\) | \(e\left(\frac{1}{60}\right)\) | \(e\left(\frac{49}{120}\right)\) | \(e\left(\frac{13}{120}\right)\) | \(e\left(\frac{101}{120}\right)\) | \(e\left(\frac{1}{40}\right)\) | \(e\left(\frac{13}{40}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{37}{120}\right)\) | \(e\left(\frac{1}{15}\right)\) |
\(\chi_{1476}(71,\cdot)\) | 1476.cc | 40 | no | \(-1\) | \(1\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{37}{40}\right)\) | \(e\left(\frac{29}{40}\right)\) | \(e\left(\frac{33}{40}\right)\) | \(e\left(\frac{19}{40}\right)\) | \(e\left(\frac{27}{40}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{21}{40}\right)\) | \(e\left(\frac{3}{5}\right)\) |
\(\chi_{1476}(73,\cdot)\) | 1476.k | 4 | no | \(1\) | \(1\) | \(-1\) | \(-i\) | \(-i\) | \(-i\) | \(i\) | \(i\) | \(1\) | \(1\) | \(-i\) | \(1\) |
\(\chi_{1476}(77,\cdot)\) | 1476.cg | 60 | no | \(-1\) | \(1\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{17}{60}\right)\) | \(e\left(\frac{59}{60}\right)\) | \(e\left(\frac{13}{60}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{11}{60}\right)\) | \(e\left(\frac{1}{15}\right)\) |
\(\chi_{1476}(79,\cdot)\) | 1476.bp | 24 | yes | \(1\) | \(1\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{7}{24}\right)\) | \(e\left(\frac{19}{24}\right)\) | \(e\left(\frac{11}{24}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{19}{24}\right)\) | \(e\left(\frac{1}{3}\right)\) |
\(\chi_{1476}(83,\cdot)\) | 1476.t | 6 | no | \(1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{5}{6}\right)\) |
\(\chi_{1476}(85,\cdot)\) | 1476.bs | 24 | no | \(-1\) | \(1\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{23}{24}\right)\) | \(e\left(\frac{11}{24}\right)\) | \(e\left(\frac{7}{24}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{23}{24}\right)\) | \(e\left(\frac{1}{6}\right)\) |
\(\chi_{1476}(89,\cdot)\) | 1476.cb | 40 | no | \(1\) | \(1\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{1}{40}\right)\) | \(e\left(\frac{17}{40}\right)\) | \(e\left(\frac{9}{40}\right)\) | \(e\left(\frac{27}{40}\right)\) | \(e\left(\frac{31}{40}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{13}{40}\right)\) | \(e\left(\frac{3}{10}\right)\) |
\(\chi_{1476}(91,\cdot)\) | 1476.j | 4 | no | \(-1\) | \(1\) | \(-1\) | \(-i\) | \(-i\) | \(i\) | \(-i\) | \(i\) | \(-1\) | \(1\) | \(i\) | \(-1\) |
\(\chi_{1476}(95,\cdot)\) | 1476.cj | 120 | yes | \(-1\) | \(1\) | \(e\left(\frac{13}{60}\right)\) | \(e\left(\frac{7}{120}\right)\) | \(e\left(\frac{79}{120}\right)\) | \(e\left(\frac{83}{120}\right)\) | \(e\left(\frac{3}{40}\right)\) | \(e\left(\frac{19}{40}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{31}{120}\right)\) | \(e\left(\frac{13}{15}\right)\) |
\(\chi_{1476}(97,\cdot)\) | 1476.ci | 120 | no | \(-1\) | \(1\) | \(e\left(\frac{41}{60}\right)\) | \(e\left(\frac{89}{120}\right)\) | \(e\left(\frac{53}{120}\right)\) | \(e\left(\frac{1}{120}\right)\) | \(e\left(\frac{21}{40}\right)\) | \(e\left(\frac{13}{40}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{17}{120}\right)\) | \(e\left(\frac{7}{30}\right)\) |