sage: H = DirichletGroup(9800)
pari: g = idealstar(,9800,2)
Character group
sage: G.order()
pari: g.no
| ||
Order | = | 3360 |
sage: H.invariants()
pari: g.cyc
| ||
Structure | = | \(C_{2}\times C_{2}\times C_{2}\times C_{420}\) |
sage: H.gens()
pari: g.gen
| ||
Generators | = | $\chi_{9800}(7351,\cdot)$, $\chi_{9800}(4901,\cdot)$, $\chi_{9800}(1177,\cdot)$, $\chi_{9800}(5001,\cdot)$ |
First 32 of 3360 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 | \(-1\) | \(1\) | \(3\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(27\) | \(29\) | \(31\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{9800}(1,\cdot)\) | 9800.a | 1 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
\(\chi_{9800}(3,\cdot)\) | 9800.hf | 420 | yes | \(-1\) | \(1\) | \(e\left(\frac{199}{420}\right)\) | \(e\left(\frac{199}{210}\right)\) | \(e\left(\frac{58}{105}\right)\) | \(e\left(\frac{131}{140}\right)\) | \(e\left(\frac{61}{420}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{107}{420}\right)\) | \(e\left(\frac{59}{140}\right)\) | \(e\left(\frac{22}{35}\right)\) | \(e\left(\frac{7}{15}\right)\) |
\(\chi_{9800}(9,\cdot)\) | 9800.gv | 210 | no | \(1\) | \(1\) | \(e\left(\frac{199}{210}\right)\) | \(e\left(\frac{94}{105}\right)\) | \(e\left(\frac{11}{105}\right)\) | \(e\left(\frac{61}{70}\right)\) | \(e\left(\frac{61}{210}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{107}{210}\right)\) | \(e\left(\frac{59}{70}\right)\) | \(e\left(\frac{9}{35}\right)\) | \(e\left(\frac{14}{15}\right)\) |
\(\chi_{9800}(11,\cdot)\) | 9800.go | 210 | yes | \(-1\) | \(1\) | \(e\left(\frac{58}{105}\right)\) | \(e\left(\frac{11}{105}\right)\) | \(e\left(\frac{94}{105}\right)\) | \(e\left(\frac{9}{70}\right)\) | \(e\left(\frac{22}{105}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{103}{210}\right)\) | \(e\left(\frac{23}{35}\right)\) | \(e\left(\frac{17}{70}\right)\) | \(e\left(\frac{17}{30}\right)\) |
\(\chi_{9800}(13,\cdot)\) | 9800.gi | 140 | yes | \(1\) | \(1\) | \(e\left(\frac{131}{140}\right)\) | \(e\left(\frac{61}{70}\right)\) | \(e\left(\frac{9}{70}\right)\) | \(e\left(\frac{67}{140}\right)\) | \(e\left(\frac{139}{140}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{43}{140}\right)\) | \(e\left(\frac{113}{140}\right)\) | \(e\left(\frac{19}{35}\right)\) | \(e\left(\frac{1}{10}\right)\) |
\(\chi_{9800}(17,\cdot)\) | 9800.he | 420 | no | \(1\) | \(1\) | \(e\left(\frac{61}{420}\right)\) | \(e\left(\frac{61}{210}\right)\) | \(e\left(\frac{22}{105}\right)\) | \(e\left(\frac{139}{140}\right)\) | \(e\left(\frac{139}{420}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{323}{420}\right)\) | \(e\left(\frac{61}{140}\right)\) | \(e\left(\frac{1}{70}\right)\) | \(e\left(\frac{11}{30}\right)\) |
\(\chi_{9800}(19,\cdot)\) | 9800.eh | 30 | no | \(1\) | \(1\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{8}{15}\right)\) |
\(\chi_{9800}(23,\cdot)\) | 9800.hi | 420 | no | \(1\) | \(1\) | \(e\left(\frac{107}{420}\right)\) | \(e\left(\frac{107}{210}\right)\) | \(e\left(\frac{103}{210}\right)\) | \(e\left(\frac{43}{140}\right)\) | \(e\left(\frac{323}{420}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{391}{420}\right)\) | \(e\left(\frac{107}{140}\right)\) | \(e\left(\frac{27}{70}\right)\) | \(e\left(\frac{7}{30}\right)\) |
\(\chi_{9800}(27,\cdot)\) | 9800.gk | 140 | yes | \(-1\) | \(1\) | \(e\left(\frac{59}{140}\right)\) | \(e\left(\frac{59}{70}\right)\) | \(e\left(\frac{23}{35}\right)\) | \(e\left(\frac{113}{140}\right)\) | \(e\left(\frac{61}{140}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{107}{140}\right)\) | \(e\left(\frac{37}{140}\right)\) | \(e\left(\frac{31}{35}\right)\) | \(e\left(\frac{2}{5}\right)\) |
\(\chi_{9800}(29,\cdot)\) | 9800.fs | 70 | yes | \(1\) | \(1\) | \(e\left(\frac{22}{35}\right)\) | \(e\left(\frac{9}{35}\right)\) | \(e\left(\frac{17}{70}\right)\) | \(e\left(\frac{19}{35}\right)\) | \(e\left(\frac{1}{70}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{27}{70}\right)\) | \(e\left(\frac{31}{35}\right)\) | \(e\left(\frac{29}{70}\right)\) | \(e\left(\frac{4}{5}\right)\) |
\(\chi_{9800}(31,\cdot)\) | 9800.ef | 30 | no | \(1\) | \(1\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{13}{15}\right)\) |
\(\chi_{9800}(33,\cdot)\) | 9800.he | 420 | no | \(1\) | \(1\) | \(e\left(\frac{11}{420}\right)\) | \(e\left(\frac{11}{210}\right)\) | \(e\left(\frac{47}{105}\right)\) | \(e\left(\frac{9}{140}\right)\) | \(e\left(\frac{149}{420}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{313}{420}\right)\) | \(e\left(\frac{11}{140}\right)\) | \(e\left(\frac{61}{70}\right)\) | \(e\left(\frac{1}{30}\right)\) |
\(\chi_{9800}(37,\cdot)\) | 9800.hj | 420 | yes | \(-1\) | \(1\) | \(e\left(\frac{173}{420}\right)\) | \(e\left(\frac{173}{210}\right)\) | \(e\left(\frac{37}{210}\right)\) | \(e\left(\frac{27}{140}\right)\) | \(e\left(\frac{377}{420}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{379}{420}\right)\) | \(e\left(\frac{33}{140}\right)\) | \(e\left(\frac{4}{35}\right)\) | \(e\left(\frac{14}{15}\right)\) |
\(\chi_{9800}(39,\cdot)\) | 9800.gq | 210 | no | \(-1\) | \(1\) | \(e\left(\frac{43}{105}\right)\) | \(e\left(\frac{86}{105}\right)\) | \(e\left(\frac{143}{210}\right)\) | \(e\left(\frac{29}{70}\right)\) | \(e\left(\frac{29}{210}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{59}{105}\right)\) | \(e\left(\frac{8}{35}\right)\) | \(e\left(\frac{6}{35}\right)\) | \(e\left(\frac{17}{30}\right)\) |
\(\chi_{9800}(41,\cdot)\) | 9800.fm | 70 | no | \(-1\) | \(1\) | \(e\left(\frac{53}{70}\right)\) | \(e\left(\frac{18}{35}\right)\) | \(e\left(\frac{17}{35}\right)\) | \(e\left(\frac{41}{70}\right)\) | \(e\left(\frac{37}{70}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{27}{35}\right)\) | \(e\left(\frac{19}{70}\right)\) | \(e\left(\frac{29}{35}\right)\) | \(e\left(\frac{1}{10}\right)\) |
\(\chi_{9800}(43,\cdot)\) | 9800.dm | 28 | no | \(1\) | \(1\) | \(e\left(\frac{11}{28}\right)\) | \(e\left(\frac{11}{14}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{13}{28}\right)\) | \(e\left(\frac{9}{28}\right)\) | \(-1\) | \(e\left(\frac{5}{28}\right)\) | \(e\left(\frac{5}{28}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(-1\) |
\(\chi_{9800}(47,\cdot)\) | 9800.hg | 420 | no | \(-1\) | \(1\) | \(e\left(\frac{239}{420}\right)\) | \(e\left(\frac{29}{210}\right)\) | \(e\left(\frac{181}{210}\right)\) | \(e\left(\frac{11}{140}\right)\) | \(e\left(\frac{11}{420}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{157}{420}\right)\) | \(e\left(\frac{99}{140}\right)\) | \(e\left(\frac{59}{70}\right)\) | \(e\left(\frac{2}{15}\right)\) |
\(\chi_{9800}(51,\cdot)\) | 9800.ex | 42 | no | \(-1\) | \(1\) | \(e\left(\frac{13}{21}\right)\) | \(e\left(\frac{5}{21}\right)\) | \(e\left(\frac{16}{21}\right)\) | \(e\left(\frac{13}{14}\right)\) | \(e\left(\frac{10}{21}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{42}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{9}{14}\right)\) | \(e\left(\frac{5}{6}\right)\) |
\(\chi_{9800}(53,\cdot)\) | 9800.hj | 420 | yes | \(-1\) | \(1\) | \(e\left(\frac{79}{420}\right)\) | \(e\left(\frac{79}{210}\right)\) | \(e\left(\frac{131}{210}\right)\) | \(e\left(\frac{1}{140}\right)\) | \(e\left(\frac{211}{420}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{377}{420}\right)\) | \(e\left(\frac{79}{140}\right)\) | \(e\left(\frac{17}{35}\right)\) | \(e\left(\frac{7}{15}\right)\) |
\(\chi_{9800}(57,\cdot)\) | 9800.dn | 28 | no | \(-1\) | \(1\) | \(e\left(\frac{17}{28}\right)\) | \(e\left(\frac{3}{14}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{1}{28}\right)\) | \(e\left(\frac{19}{28}\right)\) | \(-1\) | \(e\left(\frac{9}{28}\right)\) | \(e\left(\frac{23}{28}\right)\) | \(e\left(\frac{13}{14}\right)\) | \(1\) |
\(\chi_{9800}(59,\cdot)\) | 9800.gn | 210 | yes | \(1\) | \(1\) | \(e\left(\frac{22}{105}\right)\) | \(e\left(\frac{44}{105}\right)\) | \(e\left(\frac{61}{105}\right)\) | \(e\left(\frac{1}{70}\right)\) | \(e\left(\frac{88}{105}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{101}{105}\right)\) | \(e\left(\frac{22}{35}\right)\) | \(e\left(\frac{33}{70}\right)\) | \(e\left(\frac{4}{15}\right)\) |
\(\chi_{9800}(61,\cdot)\) | 9800.gt | 210 | yes | \(-1\) | \(1\) | \(e\left(\frac{38}{105}\right)\) | \(e\left(\frac{76}{105}\right)\) | \(e\left(\frac{163}{210}\right)\) | \(e\left(\frac{12}{35}\right)\) | \(e\left(\frac{199}{210}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{79}{105}\right)\) | \(e\left(\frac{3}{35}\right)\) | \(e\left(\frac{57}{70}\right)\) | \(e\left(\frac{7}{30}\right)\) |
\(\chi_{9800}(67,\cdot)\) | 9800.fd | 60 | no | \(1\) | \(1\) | \(e\left(\frac{13}{60}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{7}{60}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{59}{60}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{11}{30}\right)\) |
\(\chi_{9800}(69,\cdot)\) | 9800.fh | 70 | yes | \(-1\) | \(1\) | \(e\left(\frac{51}{70}\right)\) | \(e\left(\frac{16}{35}\right)\) | \(e\left(\frac{3}{70}\right)\) | \(e\left(\frac{17}{70}\right)\) | \(e\left(\frac{32}{35}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{13}{70}\right)\) | \(e\left(\frac{13}{70}\right)\) | \(e\left(\frac{1}{70}\right)\) | \(e\left(\frac{7}{10}\right)\) |
\(\chi_{9800}(71,\cdot)\) | 9800.fk | 70 | no | \(-1\) | \(1\) | \(e\left(\frac{19}{70}\right)\) | \(e\left(\frac{19}{35}\right)\) | \(e\left(\frac{67}{70}\right)\) | \(e\left(\frac{9}{35}\right)\) | \(e\left(\frac{3}{35}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{57}{70}\right)\) | \(e\left(\frac{57}{70}\right)\) | \(e\left(\frac{17}{35}\right)\) | \(e\left(\frac{3}{10}\right)\) |
\(\chi_{9800}(73,\cdot)\) | 9800.he | 420 | no | \(1\) | \(1\) | \(e\left(\frac{307}{420}\right)\) | \(e\left(\frac{97}{210}\right)\) | \(e\left(\frac{4}{105}\right)\) | \(e\left(\frac{73}{140}\right)\) | \(e\left(\frac{73}{420}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{221}{420}\right)\) | \(e\left(\frac{27}{140}\right)\) | \(e\left(\frac{67}{70}\right)\) | \(e\left(\frac{17}{30}\right)\) |
\(\chi_{9800}(79,\cdot)\) | 9800.ee | 30 | no | \(-1\) | \(1\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{19}{30}\right)\) |
\(\chi_{9800}(81,\cdot)\) | 9800.ge | 105 | no | \(1\) | \(1\) | \(e\left(\frac{94}{105}\right)\) | \(e\left(\frac{83}{105}\right)\) | \(e\left(\frac{22}{105}\right)\) | \(e\left(\frac{26}{35}\right)\) | \(e\left(\frac{61}{105}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{2}{105}\right)\) | \(e\left(\frac{24}{35}\right)\) | \(e\left(\frac{18}{35}\right)\) | \(e\left(\frac{13}{15}\right)\) |
\(\chi_{9800}(83,\cdot)\) | 9800.gk | 140 | yes | \(-1\) | \(1\) | \(e\left(\frac{37}{140}\right)\) | \(e\left(\frac{37}{70}\right)\) | \(e\left(\frac{34}{35}\right)\) | \(e\left(\frac{59}{140}\right)\) | \(e\left(\frac{43}{140}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{41}{140}\right)\) | \(e\left(\frac{111}{140}\right)\) | \(e\left(\frac{23}{35}\right)\) | \(e\left(\frac{1}{5}\right)\) |
\(\chi_{9800}(87,\cdot)\) | 9800.hg | 420 | no | \(-1\) | \(1\) | \(e\left(\frac{43}{420}\right)\) | \(e\left(\frac{43}{210}\right)\) | \(e\left(\frac{167}{210}\right)\) | \(e\left(\frac{67}{140}\right)\) | \(e\left(\frac{67}{420}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{269}{420}\right)\) | \(e\left(\frac{43}{140}\right)\) | \(e\left(\frac{3}{70}\right)\) | \(e\left(\frac{4}{15}\right)\) |
\(\chi_{9800}(89,\cdot)\) | 9800.gp | 210 | no | \(-1\) | \(1\) | \(e\left(\frac{68}{105}\right)\) | \(e\left(\frac{31}{105}\right)\) | \(e\left(\frac{74}{105}\right)\) | \(e\left(\frac{27}{35}\right)\) | \(e\left(\frac{62}{105}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{23}{210}\right)\) | \(e\left(\frac{33}{35}\right)\) | \(e\left(\frac{16}{35}\right)\) | \(e\left(\frac{7}{30}\right)\) |
\(\chi_{9800}(93,\cdot)\) | 9800.fw | 84 | no | \(-1\) | \(1\) | \(e\left(\frac{79}{84}\right)\) | \(e\left(\frac{37}{42}\right)\) | \(e\left(\frac{5}{42}\right)\) | \(e\left(\frac{1}{28}\right)\) | \(e\left(\frac{43}{84}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{41}{84}\right)\) | \(e\left(\frac{23}{28}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{1}{3}\right)\) |