sage: H = DirichletGroup(388080)
pari: g = idealstar(,388080,2)
Character group
sage: G.order()
pari: g.no
| ||
Order | = | 80640 |
sage: H.invariants()
pari: g.cyc
| ||
Structure | = | \(C_{2}\times C_{2}\times C_{2}\times C_{2}\times C_{12}\times C_{420}\) |
sage: H.gens()
pari: g.gen
| ||
Generators | = | $\chi_{388080}(48511,\cdot)$, $\chi_{388080}(291061,\cdot)$, $\chi_{388080}(43121,\cdot)$, $\chi_{388080}(77617,\cdot)$, $\chi_{388080}(300961,\cdot)$, $\chi_{388080}(141121,\cdot)$ |
First 32 of 80640 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 | \(-1\) | \(1\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) | \(47\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{388080}(1,\cdot)\) | 388080.a | 1 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
\(\chi_{388080}(13,\cdot)\) | 388080.era | 420 | yes | \(-1\) | \(1\) | \(e\left(\frac{41}{210}\right)\) | \(e\left(\frac{41}{140}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{23}{84}\right)\) | \(e\left(\frac{389}{420}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{59}{70}\right)\) | \(e\left(\frac{53}{210}\right)\) | \(e\left(\frac{23}{42}\right)\) | \(e\left(\frac{341}{420}\right)\) |
\(\chi_{388080}(17,\cdot)\) | 388080.ejx | 420 | no | \(1\) | \(1\) | \(e\left(\frac{41}{140}\right)\) | \(e\left(\frac{307}{420}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{73}{84}\right)\) | \(e\left(\frac{1}{70}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{41}{420}\right)\) | \(e\left(\frac{9}{70}\right)\) | \(e\left(\frac{23}{28}\right)\) | \(e\left(\frac{389}{420}\right)\) |
\(\chi_{388080}(19,\cdot)\) | 388080.cpf | 60 | no | \(-1\) | \(1\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{49}{60}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{31}{60}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(i\) | \(e\left(\frac{17}{30}\right)\) |
\(\chi_{388080}(23,\cdot)\) | 388080.djs | 84 | no | \(-1\) | \(1\) | \(e\left(\frac{23}{84}\right)\) | \(e\left(\frac{73}{84}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{25}{84}\right)\) | \(e\left(\frac{5}{42}\right)\) | \(-1\) | \(e\left(\frac{17}{84}\right)\) | \(e\left(\frac{31}{42}\right)\) | \(e\left(\frac{1}{84}\right)\) | \(e\left(\frac{17}{28}\right)\) |
\(\chi_{388080}(29,\cdot)\) | 388080.eha | 420 | yes | \(1\) | \(1\) | \(e\left(\frac{389}{420}\right)\) | \(e\left(\frac{1}{70}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{5}{42}\right)\) | \(e\left(\frac{13}{420}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{51}{140}\right)\) | \(e\left(\frac{181}{210}\right)\) | \(e\left(\frac{83}{84}\right)\) | \(e\left(\frac{43}{105}\right)\) |
\(\chi_{388080}(31,\cdot)\) | 388080.bty | 30 | no | \(1\) | \(1\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(-1\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{7}{15}\right)\) |
\(\chi_{388080}(37,\cdot)\) | 388080.eeu | 420 | no | \(-1\) | \(1\) | \(e\left(\frac{59}{70}\right)\) | \(e\left(\frac{41}{420}\right)\) | \(e\left(\frac{31}{60}\right)\) | \(e\left(\frac{17}{84}\right)\) | \(e\left(\frac{51}{140}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{59}{210}\right)\) | \(e\left(\frac{37}{70}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{277}{420}\right)\) |
\(\chi_{388080}(41,\cdot)\) | 388080.dzv | 210 | no | \(-1\) | \(1\) | \(e\left(\frac{53}{210}\right)\) | \(e\left(\frac{9}{70}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{31}{42}\right)\) | \(e\left(\frac{181}{210}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{37}{70}\right)\) | \(e\left(\frac{89}{210}\right)\) | \(e\left(\frac{10}{21}\right)\) | \(e\left(\frac{2}{105}\right)\) |
\(\chi_{388080}(43,\cdot)\) | 388080.ddq | 84 | yes | \(-1\) | \(1\) | \(e\left(\frac{23}{42}\right)\) | \(e\left(\frac{23}{28}\right)\) | \(i\) | \(e\left(\frac{1}{84}\right)\) | \(e\left(\frac{83}{84}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{10}{21}\right)\) | \(e\left(\frac{1}{42}\right)\) | \(e\left(\frac{53}{84}\right)\) |
\(\chi_{388080}(47,\cdot)\) | 388080.ekm | 420 | no | \(1\) | \(1\) | \(e\left(\frac{341}{420}\right)\) | \(e\left(\frac{389}{420}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{17}{28}\right)\) | \(e\left(\frac{43}{105}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{277}{420}\right)\) | \(e\left(\frac{2}{105}\right)\) | \(e\left(\frac{53}{84}\right)\) | \(e\left(\frac{383}{420}\right)\) |
\(\chi_{388080}(53,\cdot)\) | 388080.esx | 420 | no | \(1\) | \(1\) | \(e\left(\frac{16}{35}\right)\) | \(e\left(\frac{253}{420}\right)\) | \(e\left(\frac{23}{60}\right)\) | \(e\left(\frac{25}{84}\right)\) | \(e\left(\frac{33}{140}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{86}{105}\right)\) | \(e\left(\frac{13}{35}\right)\) | \(e\left(\frac{13}{14}\right)\) | \(e\left(\frac{101}{420}\right)\) |
\(\chi_{388080}(59,\cdot)\) | 388080.eok | 420 | yes | \(-1\) | \(1\) | \(e\left(\frac{139}{420}\right)\) | \(e\left(\frac{113}{210}\right)\) | \(e\left(\frac{41}{60}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{233}{420}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{23}{420}\right)\) | \(e\left(\frac{191}{210}\right)\) | \(e\left(\frac{37}{84}\right)\) | \(e\left(\frac{103}{105}\right)\) |
\(\chi_{388080}(61,\cdot)\) | 388080.ejb | 420 | no | \(1\) | \(1\) | \(e\left(\frac{53}{420}\right)\) | \(e\left(\frac{68}{105}\right)\) | \(e\left(\frac{7}{60}\right)\) | \(e\left(\frac{11}{14}\right)\) | \(e\left(\frac{391}{420}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{391}{420}\right)\) | \(e\left(\frac{97}{210}\right)\) | \(e\left(\frac{41}{84}\right)\) | \(e\left(\frac{37}{210}\right)\) |
\(\chi_{388080}(67,\cdot)\) | 388080.uh | 12 | no | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(-i\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{5}{12}\right)\) |
\(\chi_{388080}(71,\cdot)\) | 388080.czr | 70 | no | \(1\) | \(1\) | \(e\left(\frac{53}{70}\right)\) | \(e\left(\frac{27}{70}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{3}{35}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{41}{70}\right)\) | \(e\left(\frac{19}{70}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{2}{35}\right)\) |
\(\chi_{388080}(73,\cdot)\) | 388080.elv | 420 | no | \(-1\) | \(1\) | \(e\left(\frac{73}{140}\right)\) | \(e\left(\frac{31}{420}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{61}{84}\right)\) | \(e\left(\frac{53}{70}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{353}{420}\right)\) | \(e\left(\frac{11}{35}\right)\) | \(e\left(\frac{15}{28}\right)\) | \(e\left(\frac{317}{420}\right)\) |
\(\chi_{388080}(79,\cdot)\) | 388080.bzd | 30 | no | \(1\) | \(1\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(1\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{2}{15}\right)\) |
\(\chi_{388080}(83,\cdot)\) | 388080.erp | 420 | yes | \(-1\) | \(1\) | \(e\left(\frac{169}{210}\right)\) | \(e\left(\frac{99}{140}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{19}{84}\right)\) | \(e\left(\frac{31}{420}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{11}{70}\right)\) | \(e\left(\frac{26}{105}\right)\) | \(e\left(\frac{20}{21}\right)\) | \(e\left(\frac{289}{420}\right)\) |
\(\chi_{388080}(89,\cdot)\) | 388080.cju | 42 | no | \(1\) | \(1\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{29}{42}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{17}{21}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{11}{21}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{31}{42}\right)\) |
\(\chi_{388080}(97,\cdot)\) | 388080.cpu | 60 | no | \(1\) | \(1\) | \(e\left(\frac{11}{60}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{13}{60}\right)\) |
\(\chi_{388080}(101,\cdot)\) | 388080.epp | 420 | no | \(-1\) | \(1\) | \(e\left(\frac{407}{420}\right)\) | \(e\left(\frac{209}{210}\right)\) | \(e\left(\frac{53}{60}\right)\) | \(e\left(\frac{5}{21}\right)\) | \(e\left(\frac{19}{420}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{89}{420}\right)\) | \(e\left(\frac{104}{105}\right)\) | \(e\left(\frac{47}{84}\right)\) | \(e\left(\frac{3}{35}\right)\) |
\(\chi_{388080}(103,\cdot)\) | 388080.emd | 420 | no | \(-1\) | \(1\) | \(e\left(\frac{169}{420}\right)\) | \(e\left(\frac{341}{420}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{55}{84}\right)\) | \(e\left(\frac{17}{105}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{313}{420}\right)\) | \(e\left(\frac{131}{210}\right)\) | \(e\left(\frac{61}{84}\right)\) | \(e\left(\frac{89}{140}\right)\) |
\(\chi_{388080}(107,\cdot)\) | 388080.esr | 420 | no | \(1\) | \(1\) | \(e\left(\frac{13}{35}\right)\) | \(e\left(\frac{269}{420}\right)\) | \(e\left(\frac{19}{60}\right)\) | \(e\left(\frac{5}{84}\right)\) | \(e\left(\frac{99}{140}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{131}{210}\right)\) | \(e\left(\frac{43}{70}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{373}{420}\right)\) |
\(\chi_{388080}(109,\cdot)\) | 388080.dmy | 84 | no | \(-1\) | \(1\) | \(e\left(\frac{19}{28}\right)\) | \(e\left(\frac{17}{21}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{4}{21}\right)\) | \(e\left(\frac{25}{28}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{61}{84}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{13}{28}\right)\) | \(e\left(\frac{11}{42}\right)\) |
\(\chi_{388080}(113,\cdot)\) | 388080.enu | 420 | no | \(1\) | \(1\) | \(e\left(\frac{121}{420}\right)\) | \(e\left(\frac{43}{140}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{47}{84}\right)\) | \(e\left(\frac{83}{105}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{29}{140}\right)\) | \(e\left(\frac{59}{210}\right)\) | \(e\left(\frac{73}{84}\right)\) | \(e\left(\frac{233}{420}\right)\) |
\(\chi_{388080}(127,\cdot)\) | 388080.dth | 140 | no | \(-1\) | \(1\) | \(e\left(\frac{111}{140}\right)\) | \(e\left(\frac{9}{140}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{15}{28}\right)\) | \(e\left(\frac{18}{35}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{107}{140}\right)\) | \(e\left(\frac{9}{70}\right)\) | \(e\left(\frac{9}{28}\right)\) | \(e\left(\frac{13}{140}\right)\) |
\(\chi_{388080}(131,\cdot)\) | 388080.dfz | 84 | no | \(1\) | \(1\) | \(e\left(\frac{53}{84}\right)\) | \(e\left(\frac{17}{42}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{11}{42}\right)\) | \(e\left(\frac{13}{84}\right)\) | \(1\) | \(e\left(\frac{83}{84}\right)\) | \(e\left(\frac{17}{21}\right)\) | \(e\left(\frac{79}{84}\right)\) | \(e\left(\frac{3}{14}\right)\) |
\(\chi_{388080}(137,\cdot)\) | 388080.ems | 420 | no | \(1\) | \(1\) | \(e\left(\frac{293}{420}\right)\) | \(e\left(\frac{247}{420}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{29}{84}\right)\) | \(e\left(\frac{113}{210}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{191}{420}\right)\) | \(e\left(\frac{37}{210}\right)\) | \(e\left(\frac{65}{84}\right)\) | \(e\left(\frac{93}{140}\right)\) |
\(\chi_{388080}(139,\cdot)\) | 388080.ehb | 420 | yes | \(-1\) | \(1\) | \(e\left(\frac{169}{420}\right)\) | \(e\left(\frac{51}{70}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{31}{42}\right)\) | \(e\left(\frac{173}{420}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{81}{140}\right)\) | \(e\left(\frac{131}{210}\right)\) | \(e\left(\frac{19}{84}\right)\) | \(e\left(\frac{151}{210}\right)\) |
\(\chi_{388080}(149,\cdot)\) | 388080.eop | 420 | yes | \(1\) | \(1\) | \(e\left(\frac{103}{420}\right)\) | \(e\left(\frac{121}{210}\right)\) | \(e\left(\frac{7}{60}\right)\) | \(e\left(\frac{29}{42}\right)\) | \(e\left(\frac{11}{420}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{151}{420}\right)\) | \(e\left(\frac{137}{210}\right)\) | \(e\left(\frac{25}{84}\right)\) | \(e\left(\frac{22}{35}\right)\) |
\(\chi_{388080}(151,\cdot)\) | 388080.dxv | 210 | no | \(1\) | \(1\) | \(e\left(\frac{104}{105}\right)\) | \(e\left(\frac{137}{210}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{37}{42}\right)\) | \(e\left(\frac{58}{105}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{151}{210}\right)\) | \(e\left(\frac{169}{210}\right)\) | \(e\left(\frac{25}{42}\right)\) | \(e\left(\frac{53}{70}\right)\) |