sage: H = DirichletGroup(8036)
pari: g = idealstar(,8036,2)
Character group
sage: G.order()
pari: g.no
| ||
Order | = | 3360 |
sage: H.invariants()
pari: g.cyc
| ||
Structure | = | \(C_{2}\times C_{2}\times C_{840}\) |
sage: H.gens()
pari: g.gen
| ||
Generators | = | $\chi_{8036}(4019,\cdot)$, $\chi_{8036}(493,\cdot)$, $\chi_{8036}(785,\cdot)$ |
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 | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{8036}(1,\cdot)\) | 8036.a | 1 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
\(\chi_{8036}(3,\cdot)\) | 8036.ee | 168 | yes | \(-1\) | \(1\) | \(e\left(\frac{25}{168}\right)\) | \(e\left(\frac{79}{84}\right)\) | \(e\left(\frac{25}{84}\right)\) | \(e\left(\frac{97}{168}\right)\) | \(e\left(\frac{23}{56}\right)\) | \(e\left(\frac{5}{56}\right)\) | \(e\left(\frac{163}{168}\right)\) | \(e\left(\frac{17}{24}\right)\) | \(e\left(\frac{19}{21}\right)\) | \(e\left(\frac{37}{42}\right)\) |
\(\chi_{8036}(5,\cdot)\) | 8036.eq | 420 | no | \(-1\) | \(1\) | \(e\left(\frac{79}{84}\right)\) | \(e\left(\frac{13}{105}\right)\) | \(e\left(\frac{37}{42}\right)\) | \(e\left(\frac{113}{420}\right)\) | \(e\left(\frac{117}{140}\right)\) | \(e\left(\frac{9}{140}\right)\) | \(e\left(\frac{173}{420}\right)\) | \(e\left(\frac{7}{60}\right)\) | \(e\left(\frac{4}{105}\right)\) | \(e\left(\frac{26}{105}\right)\) |
\(\chi_{8036}(9,\cdot)\) | 8036.dp | 84 | no | \(1\) | \(1\) | \(e\left(\frac{25}{84}\right)\) | \(e\left(\frac{37}{42}\right)\) | \(e\left(\frac{25}{42}\right)\) | \(e\left(\frac{13}{84}\right)\) | \(e\left(\frac{23}{28}\right)\) | \(e\left(\frac{5}{28}\right)\) | \(e\left(\frac{79}{84}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{17}{21}\right)\) | \(e\left(\frac{16}{21}\right)\) |
\(\chi_{8036}(11,\cdot)\) | 8036.ev | 840 | yes | \(1\) | \(1\) | \(e\left(\frac{97}{168}\right)\) | \(e\left(\frac{113}{420}\right)\) | \(e\left(\frac{13}{84}\right)\) | \(e\left(\frac{689}{840}\right)\) | \(e\left(\frac{211}{280}\right)\) | \(e\left(\frac{237}{280}\right)\) | \(e\left(\frac{239}{840}\right)\) | \(e\left(\frac{61}{120}\right)\) | \(e\left(\frac{41}{105}\right)\) | \(e\left(\frac{113}{210}\right)\) |
\(\chi_{8036}(13,\cdot)\) | 8036.em | 280 | no | \(1\) | \(1\) | \(e\left(\frac{23}{56}\right)\) | \(e\left(\frac{117}{140}\right)\) | \(e\left(\frac{23}{28}\right)\) | \(e\left(\frac{211}{280}\right)\) | \(e\left(\frac{267}{280}\right)\) | \(e\left(\frac{69}{280}\right)\) | \(e\left(\frac{61}{280}\right)\) | \(e\left(\frac{19}{40}\right)\) | \(e\left(\frac{53}{70}\right)\) | \(e\left(\frac{47}{70}\right)\) |
\(\chi_{8036}(15,\cdot)\) | 8036.eo | 280 | yes | \(1\) | \(1\) | \(e\left(\frac{5}{56}\right)\) | \(e\left(\frac{9}{140}\right)\) | \(e\left(\frac{5}{28}\right)\) | \(e\left(\frac{237}{280}\right)\) | \(e\left(\frac{69}{280}\right)\) | \(e\left(\frac{43}{280}\right)\) | \(e\left(\frac{107}{280}\right)\) | \(e\left(\frac{33}{40}\right)\) | \(e\left(\frac{33}{35}\right)\) | \(e\left(\frac{9}{70}\right)\) |
\(\chi_{8036}(17,\cdot)\) | 8036.ex | 840 | no | \(1\) | \(1\) | \(e\left(\frac{163}{168}\right)\) | \(e\left(\frac{173}{420}\right)\) | \(e\left(\frac{79}{84}\right)\) | \(e\left(\frac{239}{840}\right)\) | \(e\left(\frac{61}{280}\right)\) | \(e\left(\frac{107}{280}\right)\) | \(e\left(\frac{89}{840}\right)\) | \(e\left(\frac{31}{120}\right)\) | \(e\left(\frac{67}{210}\right)\) | \(e\left(\frac{173}{210}\right)\) |
\(\chi_{8036}(19,\cdot)\) | 8036.dv | 120 | no | \(-1\) | \(1\) | \(e\left(\frac{17}{24}\right)\) | \(e\left(\frac{7}{60}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{61}{120}\right)\) | \(e\left(\frac{19}{40}\right)\) | \(e\left(\frac{33}{40}\right)\) | \(e\left(\frac{31}{120}\right)\) | \(e\left(\frac{83}{120}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{7}{30}\right)\) |
\(\chi_{8036}(23,\cdot)\) | 8036.ej | 210 | yes | \(-1\) | \(1\) | \(e\left(\frac{19}{21}\right)\) | \(e\left(\frac{4}{105}\right)\) | \(e\left(\frac{17}{21}\right)\) | \(e\left(\frac{41}{105}\right)\) | \(e\left(\frac{53}{70}\right)\) | \(e\left(\frac{33}{35}\right)\) | \(e\left(\frac{67}{210}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{59}{210}\right)\) | \(e\left(\frac{8}{105}\right)\) |
\(\chi_{8036}(25,\cdot)\) | 8036.ef | 210 | no | \(1\) | \(1\) | \(e\left(\frac{37}{42}\right)\) | \(e\left(\frac{26}{105}\right)\) | \(e\left(\frac{16}{21}\right)\) | \(e\left(\frac{113}{210}\right)\) | \(e\left(\frac{47}{70}\right)\) | \(e\left(\frac{9}{70}\right)\) | \(e\left(\frac{173}{210}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{8}{105}\right)\) | \(e\left(\frac{52}{105}\right)\) |
\(\chi_{8036}(27,\cdot)\) | 8036.cz | 56 | yes | \(-1\) | \(1\) | \(e\left(\frac{25}{56}\right)\) | \(e\left(\frac{23}{28}\right)\) | \(e\left(\frac{25}{28}\right)\) | \(e\left(\frac{41}{56}\right)\) | \(e\left(\frac{13}{56}\right)\) | \(e\left(\frac{15}{56}\right)\) | \(e\left(\frac{51}{56}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{9}{14}\right)\) |
\(\chi_{8036}(29,\cdot)\) | 8036.en | 280 | no | \(-1\) | \(1\) | \(e\left(\frac{3}{56}\right)\) | \(e\left(\frac{39}{140}\right)\) | \(e\left(\frac{3}{28}\right)\) | \(e\left(\frac{187}{280}\right)\) | \(e\left(\frac{159}{280}\right)\) | \(e\left(\frac{93}{280}\right)\) | \(e\left(\frac{137}{280}\right)\) | \(e\left(\frac{23}{40}\right)\) | \(e\left(\frac{41}{70}\right)\) | \(e\left(\frac{39}{70}\right)\) |
\(\chi_{8036}(31,\cdot)\) | 8036.cj | 30 | no | \(1\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{7}{15}\right)\) |
\(\chi_{8036}(33,\cdot)\) | 8036.eq | 420 | no | \(-1\) | \(1\) | \(e\left(\frac{61}{84}\right)\) | \(e\left(\frac{22}{105}\right)\) | \(e\left(\frac{19}{42}\right)\) | \(e\left(\frac{167}{420}\right)\) | \(e\left(\frac{23}{140}\right)\) | \(e\left(\frac{131}{140}\right)\) | \(e\left(\frac{107}{420}\right)\) | \(e\left(\frac{13}{60}\right)\) | \(e\left(\frac{31}{105}\right)\) | \(e\left(\frac{44}{105}\right)\) |
\(\chi_{8036}(37,\cdot)\) | 8036.ds | 105 | no | \(1\) | \(1\) | \(e\left(\frac{16}{21}\right)\) | \(e\left(\frac{73}{105}\right)\) | \(e\left(\frac{11}{21}\right)\) | \(e\left(\frac{92}{105}\right)\) | \(e\left(\frac{33}{35}\right)\) | \(e\left(\frac{16}{35}\right)\) | \(e\left(\frac{47}{105}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{79}{105}\right)\) | \(e\left(\frac{41}{105}\right)\) |
\(\chi_{8036}(39,\cdot)\) | 8036.et | 420 | yes | \(-1\) | \(1\) | \(e\left(\frac{47}{84}\right)\) | \(e\left(\frac{163}{210}\right)\) | \(e\left(\frac{5}{42}\right)\) | \(e\left(\frac{139}{420}\right)\) | \(e\left(\frac{51}{140}\right)\) | \(e\left(\frac{47}{140}\right)\) | \(e\left(\frac{79}{420}\right)\) | \(e\left(\frac{11}{60}\right)\) | \(e\left(\frac{139}{210}\right)\) | \(e\left(\frac{58}{105}\right)\) |
\(\chi_{8036}(43,\cdot)\) | 8036.dx | 140 | yes | \(-1\) | \(1\) | \(e\left(\frac{11}{28}\right)\) | \(e\left(\frac{31}{70}\right)\) | \(e\left(\frac{11}{14}\right)\) | \(e\left(\frac{23}{140}\right)\) | \(e\left(\frac{121}{140}\right)\) | \(e\left(\frac{117}{140}\right)\) | \(e\left(\frac{3}{140}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{23}{70}\right)\) | \(e\left(\frac{31}{35}\right)\) |
\(\chi_{8036}(45,\cdot)\) | 8036.el | 210 | no | \(-1\) | \(1\) | \(e\left(\frac{5}{21}\right)\) | \(e\left(\frac{1}{210}\right)\) | \(e\left(\frac{10}{21}\right)\) | \(e\left(\frac{89}{210}\right)\) | \(e\left(\frac{23}{35}\right)\) | \(e\left(\frac{17}{70}\right)\) | \(e\left(\frac{37}{105}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{89}{105}\right)\) | \(e\left(\frac{1}{105}\right)\) |
\(\chi_{8036}(47,\cdot)\) | 8036.eu | 840 | yes | \(-1\) | \(1\) | \(e\left(\frac{167}{168}\right)\) | \(e\left(\frac{1}{420}\right)\) | \(e\left(\frac{83}{84}\right)\) | \(e\left(\frac{283}{840}\right)\) | \(e\left(\frac{197}{280}\right)\) | \(e\left(\frac{279}{280}\right)\) | \(e\left(\frac{673}{840}\right)\) | \(e\left(\frac{107}{120}\right)\) | \(e\left(\frac{97}{105}\right)\) | \(e\left(\frac{1}{210}\right)\) |
\(\chi_{8036}(51,\cdot)\) | 8036.eg | 210 | yes | \(-1\) | \(1\) | \(e\left(\frac{5}{42}\right)\) | \(e\left(\frac{37}{105}\right)\) | \(e\left(\frac{5}{21}\right)\) | \(e\left(\frac{181}{210}\right)\) | \(e\left(\frac{22}{35}\right)\) | \(e\left(\frac{33}{70}\right)\) | \(e\left(\frac{8}{105}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{47}{210}\right)\) | \(e\left(\frac{74}{105}\right)\) |
\(\chi_{8036}(53,\cdot)\) | 8036.ew | 840 | no | \(-1\) | \(1\) | \(e\left(\frac{61}{168}\right)\) | \(e\left(\frac{317}{420}\right)\) | \(e\left(\frac{61}{84}\right)\) | \(e\left(\frac{461}{840}\right)\) | \(e\left(\frac{219}{280}\right)\) | \(e\left(\frac{33}{280}\right)\) | \(e\left(\frac{191}{840}\right)\) | \(e\left(\frac{49}{120}\right)\) | \(e\left(\frac{73}{210}\right)\) | \(e\left(\frac{107}{210}\right)\) |
\(\chi_{8036}(55,\cdot)\) | 8036.cz | 56 | yes | \(-1\) | \(1\) | \(e\left(\frac{29}{56}\right)\) | \(e\left(\frac{11}{28}\right)\) | \(e\left(\frac{1}{28}\right)\) | \(e\left(\frac{5}{56}\right)\) | \(e\left(\frac{33}{56}\right)\) | \(e\left(\frac{51}{56}\right)\) | \(e\left(\frac{39}{56}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{11}{14}\right)\) |
\(\chi_{8036}(57,\cdot)\) | 8036.cn | 35 | no | \(1\) | \(1\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{2}{35}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{3}{35}\right)\) | \(e\left(\frac{31}{35}\right)\) | \(e\left(\frac{32}{35}\right)\) | \(e\left(\frac{8}{35}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{6}{35}\right)\) | \(e\left(\frac{4}{35}\right)\) |
\(\chi_{8036}(59,\cdot)\) | 8036.ek | 210 | yes | \(1\) | \(1\) | \(e\left(\frac{17}{21}\right)\) | \(e\left(\frac{163}{210}\right)\) | \(e\left(\frac{13}{21}\right)\) | \(e\left(\frac{17}{210}\right)\) | \(e\left(\frac{43}{70}\right)\) | \(e\left(\frac{41}{70}\right)\) | \(e\left(\frac{197}{210}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{139}{210}\right)\) | \(e\left(\frac{58}{105}\right)\) |
\(\chi_{8036}(61,\cdot)\) | 8036.eq | 420 | no | \(-1\) | \(1\) | \(e\left(\frac{1}{84}\right)\) | \(e\left(\frac{31}{105}\right)\) | \(e\left(\frac{1}{42}\right)\) | \(e\left(\frac{11}{420}\right)\) | \(e\left(\frac{139}{140}\right)\) | \(e\left(\frac{43}{140}\right)\) | \(e\left(\frac{251}{420}\right)\) | \(e\left(\frac{49}{60}\right)\) | \(e\left(\frac{58}{105}\right)\) | \(e\left(\frac{62}{105}\right)\) |
\(\chi_{8036}(65,\cdot)\) | 8036.ew | 840 | no | \(-1\) | \(1\) | \(e\left(\frac{59}{168}\right)\) | \(e\left(\frac{403}{420}\right)\) | \(e\left(\frac{59}{84}\right)\) | \(e\left(\frac{19}{840}\right)\) | \(e\left(\frac{221}{280}\right)\) | \(e\left(\frac{87}{280}\right)\) | \(e\left(\frac{529}{840}\right)\) | \(e\left(\frac{71}{120}\right)\) | \(e\left(\frac{167}{210}\right)\) | \(e\left(\frac{193}{210}\right)\) |
\(\chi_{8036}(67,\cdot)\) | 8036.dw | 120 | no | \(1\) | \(1\) | \(e\left(\frac{13}{24}\right)\) | \(e\left(\frac{41}{60}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{53}{120}\right)\) | \(e\left(\frac{7}{40}\right)\) | \(e\left(\frac{9}{40}\right)\) | \(e\left(\frac{83}{120}\right)\) | \(e\left(\frac{79}{120}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{11}{30}\right)\) |
\(\chi_{8036}(69,\cdot)\) | 8036.em | 280 | no | \(1\) | \(1\) | \(e\left(\frac{3}{56}\right)\) | \(e\left(\frac{137}{140}\right)\) | \(e\left(\frac{3}{28}\right)\) | \(e\left(\frac{271}{280}\right)\) | \(e\left(\frac{47}{280}\right)\) | \(e\left(\frac{9}{280}\right)\) | \(e\left(\frac{81}{280}\right)\) | \(e\left(\frac{39}{40}\right)\) | \(e\left(\frac{13}{70}\right)\) | \(e\left(\frac{67}{70}\right)\) |
\(\chi_{8036}(71,\cdot)\) | 8036.eo | 280 | yes | \(1\) | \(1\) | \(e\left(\frac{39}{56}\right)\) | \(e\left(\frac{31}{140}\right)\) | \(e\left(\frac{11}{28}\right)\) | \(e\left(\frac{23}{280}\right)\) | \(e\left(\frac{191}{280}\right)\) | \(e\left(\frac{257}{280}\right)\) | \(e\left(\frac{73}{280}\right)\) | \(e\left(\frac{27}{40}\right)\) | \(e\left(\frac{32}{35}\right)\) | \(e\left(\frac{31}{70}\right)\) |
\(\chi_{8036}(73,\cdot)\) | 8036.dr | 84 | no | \(-1\) | \(1\) | \(e\left(\frac{53}{84}\right)\) | \(e\left(\frac{1}{21}\right)\) | \(e\left(\frac{11}{42}\right)\) | \(e\left(\frac{83}{84}\right)\) | \(e\left(\frac{23}{28}\right)\) | \(e\left(\frac{19}{28}\right)\) | \(e\left(\frac{23}{84}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{10}{21}\right)\) | \(e\left(\frac{2}{21}\right)\) |
\(\chi_{8036}(75,\cdot)\) | 8036.eu | 840 | yes | \(-1\) | \(1\) | \(e\left(\frac{5}{168}\right)\) | \(e\left(\frac{79}{420}\right)\) | \(e\left(\frac{5}{84}\right)\) | \(e\left(\frac{97}{840}\right)\) | \(e\left(\frac{23}{280}\right)\) | \(e\left(\frac{61}{280}\right)\) | \(e\left(\frac{667}{840}\right)\) | \(e\left(\frac{113}{120}\right)\) | \(e\left(\frac{103}{105}\right)\) | \(e\left(\frac{79}{210}\right)\) |