sage: H = DirichletGroup(29645)
pari: g = idealstar(,29645,2)
Character group
sage: G.order()
pari: g.no
| ||
Order | = | 18480 |
sage: H.invariants()
pari: g.cyc
| ||
Structure | = | \(C_{2}\times C_{2}\times C_{4620}\) |
sage: H.gens()
pari: g.gen
| ||
Generators | = | $\chi_{29645}(23717,\cdot)$, $\chi_{29645}(1816,\cdot)$, $\chi_{29645}(19846,\cdot)$ |
First 32 of 18480 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 | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(12\) | \(13\) | \(16\) | \(17\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{29645}(1,\cdot)\) | 29645.a | 1 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
\(\chi_{29645}(2,\cdot)\) | 29645.hj | 4620 | yes | \(1\) | \(1\) | \(e\left(\frac{1637}{4620}\right)\) | \(e\left(\frac{71}{420}\right)\) | \(e\left(\frac{1637}{2310}\right)\) | \(e\left(\frac{403}{770}\right)\) | \(e\left(\frac{97}{1540}\right)\) | \(e\left(\frac{71}{210}\right)\) | \(e\left(\frac{811}{924}\right)\) | \(e\left(\frac{149}{1540}\right)\) | \(e\left(\frac{482}{1155}\right)\) | \(e\left(\frac{793}{4620}\right)\) |
\(\chi_{29645}(3,\cdot)\) | 29645.fv | 420 | no | \(1\) | \(1\) | \(e\left(\frac{71}{420}\right)\) | \(e\left(\frac{283}{420}\right)\) | \(e\left(\frac{71}{210}\right)\) | \(e\left(\frac{59}{70}\right)\) | \(e\left(\frac{71}{140}\right)\) | \(e\left(\frac{73}{210}\right)\) | \(e\left(\frac{1}{84}\right)\) | \(e\left(\frac{117}{140}\right)\) | \(e\left(\frac{71}{105}\right)\) | \(e\left(\frac{229}{420}\right)\) |
\(\chi_{29645}(4,\cdot)\) | 29645.hc | 2310 | yes | \(1\) | \(1\) | \(e\left(\frac{1637}{2310}\right)\) | \(e\left(\frac{71}{210}\right)\) | \(e\left(\frac{482}{1155}\right)\) | \(e\left(\frac{18}{385}\right)\) | \(e\left(\frac{97}{770}\right)\) | \(e\left(\frac{71}{105}\right)\) | \(e\left(\frac{349}{462}\right)\) | \(e\left(\frac{149}{770}\right)\) | \(e\left(\frac{964}{1155}\right)\) | \(e\left(\frac{793}{2310}\right)\) |
\(\chi_{29645}(6,\cdot)\) | 29645.gm | 770 | no | \(1\) | \(1\) | \(e\left(\frac{403}{770}\right)\) | \(e\left(\frac{59}{70}\right)\) | \(e\left(\frac{18}{385}\right)\) | \(e\left(\frac{141}{385}\right)\) | \(e\left(\frac{439}{770}\right)\) | \(e\left(\frac{24}{35}\right)\) | \(e\left(\frac{137}{154}\right)\) | \(e\left(\frac{359}{385}\right)\) | \(e\left(\frac{36}{385}\right)\) | \(e\left(\frac{276}{385}\right)\) |
\(\chi_{29645}(8,\cdot)\) | 29645.gx | 1540 | yes | \(1\) | \(1\) | \(e\left(\frac{97}{1540}\right)\) | \(e\left(\frac{71}{140}\right)\) | \(e\left(\frac{97}{770}\right)\) | \(e\left(\frac{439}{770}\right)\) | \(e\left(\frac{291}{1540}\right)\) | \(e\left(\frac{1}{70}\right)\) | \(e\left(\frac{195}{308}\right)\) | \(e\left(\frac{447}{1540}\right)\) | \(e\left(\frac{97}{385}\right)\) | \(e\left(\frac{793}{1540}\right)\) |
\(\chi_{29645}(9,\cdot)\) | 29645.fb | 210 | no | \(1\) | \(1\) | \(e\left(\frac{71}{210}\right)\) | \(e\left(\frac{73}{210}\right)\) | \(e\left(\frac{71}{105}\right)\) | \(e\left(\frac{24}{35}\right)\) | \(e\left(\frac{1}{70}\right)\) | \(e\left(\frac{73}{105}\right)\) | \(e\left(\frac{1}{42}\right)\) | \(e\left(\frac{47}{70}\right)\) | \(e\left(\frac{37}{105}\right)\) | \(e\left(\frac{19}{210}\right)\) |
\(\chi_{29645}(12,\cdot)\) | 29645.gr | 924 | yes | \(1\) | \(1\) | \(e\left(\frac{811}{924}\right)\) | \(e\left(\frac{1}{84}\right)\) | \(e\left(\frac{349}{462}\right)\) | \(e\left(\frac{137}{154}\right)\) | \(e\left(\frac{195}{308}\right)\) | \(e\left(\frac{1}{42}\right)\) | \(e\left(\frac{709}{924}\right)\) | \(e\left(\frac{9}{308}\right)\) | \(e\left(\frac{118}{231}\right)\) | \(e\left(\frac{821}{924}\right)\) |
\(\chi_{29645}(13,\cdot)\) | 29645.gw | 1540 | yes | \(-1\) | \(1\) | \(e\left(\frac{149}{1540}\right)\) | \(e\left(\frac{117}{140}\right)\) | \(e\left(\frac{149}{770}\right)\) | \(e\left(\frac{359}{385}\right)\) | \(e\left(\frac{447}{1540}\right)\) | \(e\left(\frac{47}{70}\right)\) | \(e\left(\frac{9}{308}\right)\) | \(e\left(\frac{1409}{1540}\right)\) | \(e\left(\frac{149}{385}\right)\) | \(e\left(\frac{591}{1540}\right)\) |
\(\chi_{29645}(16,\cdot)\) | 29645.gu | 1155 | no | \(1\) | \(1\) | \(e\left(\frac{482}{1155}\right)\) | \(e\left(\frac{71}{105}\right)\) | \(e\left(\frac{964}{1155}\right)\) | \(e\left(\frac{36}{385}\right)\) | \(e\left(\frac{97}{385}\right)\) | \(e\left(\frac{37}{105}\right)\) | \(e\left(\frac{118}{231}\right)\) | \(e\left(\frac{149}{385}\right)\) | \(e\left(\frac{773}{1155}\right)\) | \(e\left(\frac{793}{1155}\right)\) |
\(\chi_{29645}(17,\cdot)\) | 29645.hg | 4620 | yes | \(-1\) | \(1\) | \(e\left(\frac{793}{4620}\right)\) | \(e\left(\frac{229}{420}\right)\) | \(e\left(\frac{793}{2310}\right)\) | \(e\left(\frac{276}{385}\right)\) | \(e\left(\frac{793}{1540}\right)\) | \(e\left(\frac{19}{210}\right)\) | \(e\left(\frac{821}{924}\right)\) | \(e\left(\frac{591}{1540}\right)\) | \(e\left(\frac{793}{1155}\right)\) | \(e\left(\frac{4427}{4620}\right)\) |
\(\chi_{29645}(18,\cdot)\) | 29645.gf | 660 | no | \(1\) | \(1\) | \(e\left(\frac{457}{660}\right)\) | \(e\left(\frac{31}{60}\right)\) | \(e\left(\frac{127}{330}\right)\) | \(e\left(\frac{23}{110}\right)\) | \(e\left(\frac{17}{220}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{119}{132}\right)\) | \(e\left(\frac{169}{220}\right)\) | \(e\left(\frac{127}{165}\right)\) | \(e\left(\frac{173}{660}\right)\) |
\(\chi_{29645}(19,\cdot)\) | 29645.fo | 330 | no | \(1\) | \(1\) | \(e\left(\frac{152}{165}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{139}{165}\right)\) | \(e\left(\frac{36}{55}\right)\) | \(e\left(\frac{42}{55}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{19}{33}\right)\) | \(e\left(\frac{23}{110}\right)\) | \(e\left(\frac{113}{165}\right)\) | \(e\left(\frac{101}{330}\right)\) |
\(\chi_{29645}(23,\cdot)\) | 29645.gs | 924 | yes | \(-1\) | \(1\) | \(e\left(\frac{841}{924}\right)\) | \(e\left(\frac{13}{84}\right)\) | \(e\left(\frac{379}{462}\right)\) | \(e\left(\frac{5}{77}\right)\) | \(e\left(\frac{225}{308}\right)\) | \(e\left(\frac{13}{42}\right)\) | \(e\left(\frac{901}{924}\right)\) | \(e\left(\frac{117}{308}\right)\) | \(e\left(\frac{148}{231}\right)\) | \(e\left(\frac{509}{924}\right)\) |
\(\chi_{29645}(24,\cdot)\) | 29645.hd | 2310 | yes | \(1\) | \(1\) | \(e\left(\frac{268}{1155}\right)\) | \(e\left(\frac{19}{105}\right)\) | \(e\left(\frac{536}{1155}\right)\) | \(e\left(\frac{159}{385}\right)\) | \(e\left(\frac{268}{385}\right)\) | \(e\left(\frac{38}{105}\right)\) | \(e\left(\frac{149}{231}\right)\) | \(e\left(\frac{97}{770}\right)\) | \(e\left(\frac{1072}{1155}\right)\) | \(e\left(\frac{139}{2310}\right)\) |
\(\chi_{29645}(26,\cdot)\) | 29645.hf | 2310 | no | \(-1\) | \(1\) | \(e\left(\frac{521}{1155}\right)\) | \(e\left(\frac{1}{210}\right)\) | \(e\left(\frac{1042}{1155}\right)\) | \(e\left(\frac{351}{770}\right)\) | \(e\left(\frac{136}{385}\right)\) | \(e\left(\frac{1}{105}\right)\) | \(e\left(\frac{419}{462}\right)\) | \(e\left(\frac{9}{770}\right)\) | \(e\left(\frac{929}{1155}\right)\) | \(e\left(\frac{1283}{2310}\right)\) |
\(\chi_{29645}(27,\cdot)\) | 29645.ek | 140 | no | \(1\) | \(1\) | \(e\left(\frac{71}{140}\right)\) | \(e\left(\frac{3}{140}\right)\) | \(e\left(\frac{1}{70}\right)\) | \(e\left(\frac{37}{70}\right)\) | \(e\left(\frac{73}{140}\right)\) | \(e\left(\frac{3}{70}\right)\) | \(e\left(\frac{1}{28}\right)\) | \(e\left(\frac{71}{140}\right)\) | \(e\left(\frac{1}{35}\right)\) | \(e\left(\frac{89}{140}\right)\) |
\(\chi_{29645}(29,\cdot)\) | 29645.gj | 770 | yes | \(-1\) | \(1\) | \(e\left(\frac{307}{385}\right)\) | \(e\left(\frac{37}{70}\right)\) | \(e\left(\frac{229}{385}\right)\) | \(e\left(\frac{251}{770}\right)\) | \(e\left(\frac{151}{385}\right)\) | \(e\left(\frac{2}{35}\right)\) | \(e\left(\frac{19}{154}\right)\) | \(e\left(\frac{97}{385}\right)\) | \(e\left(\frac{73}{385}\right)\) | \(e\left(\frac{303}{385}\right)\) |
\(\chi_{29645}(31,\cdot)\) | 29645.fm | 330 | no | \(-1\) | \(1\) | \(e\left(\frac{19}{165}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{38}{165}\right)\) | \(e\left(\frac{9}{110}\right)\) | \(e\left(\frac{19}{55}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{13}{66}\right)\) | \(e\left(\frac{51}{110}\right)\) | \(e\left(\frac{76}{165}\right)\) | \(e\left(\frac{157}{330}\right)\) |
\(\chi_{29645}(32,\cdot)\) | 29645.gq | 924 | yes | \(1\) | \(1\) | \(e\left(\frac{713}{924}\right)\) | \(e\left(\frac{71}{84}\right)\) | \(e\left(\frac{251}{462}\right)\) | \(e\left(\frac{95}{154}\right)\) | \(e\left(\frac{97}{308}\right)\) | \(e\left(\frac{29}{42}\right)\) | \(e\left(\frac{359}{924}\right)\) | \(e\left(\frac{149}{308}\right)\) | \(e\left(\frac{20}{231}\right)\) | \(e\left(\frac{793}{924}\right)\) |
\(\chi_{29645}(34,\cdot)\) | 29645.ep | 154 | yes | \(-1\) | \(1\) | \(e\left(\frac{81}{154}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{4}{77}\right)\) | \(e\left(\frac{37}{154}\right)\) | \(e\left(\frac{89}{154}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{59}{77}\right)\) | \(e\left(\frac{37}{77}\right)\) | \(e\left(\frac{8}{77}\right)\) | \(e\left(\frac{10}{77}\right)\) |
\(\chi_{29645}(36,\cdot)\) | 29645.ft | 385 | no | \(1\) | \(1\) | \(e\left(\frac{18}{385}\right)\) | \(e\left(\frac{24}{35}\right)\) | \(e\left(\frac{36}{385}\right)\) | \(e\left(\frac{282}{385}\right)\) | \(e\left(\frac{54}{385}\right)\) | \(e\left(\frac{13}{35}\right)\) | \(e\left(\frac{60}{77}\right)\) | \(e\left(\frac{333}{385}\right)\) | \(e\left(\frac{72}{385}\right)\) | \(e\left(\frac{167}{385}\right)\) |
\(\chi_{29645}(37,\cdot)\) | 29645.hh | 4620 | yes | \(-1\) | \(1\) | \(e\left(\frac{2039}{4620}\right)\) | \(e\left(\frac{47}{420}\right)\) | \(e\left(\frac{2039}{2310}\right)\) | \(e\left(\frac{213}{385}\right)\) | \(e\left(\frac{499}{1540}\right)\) | \(e\left(\frac{47}{210}\right)\) | \(e\left(\frac{919}{924}\right)\) | \(e\left(\frac{703}{1540}\right)\) | \(e\left(\frac{884}{1155}\right)\) | \(e\left(\frac{31}{4620}\right)\) |
\(\chi_{29645}(38,\cdot)\) | 29645.hi | 4620 | yes | \(1\) | \(1\) | \(e\left(\frac{1273}{4620}\right)\) | \(e\left(\frac{379}{420}\right)\) | \(e\left(\frac{1273}{2310}\right)\) | \(e\left(\frac{137}{770}\right)\) | \(e\left(\frac{1273}{1540}\right)\) | \(e\left(\frac{169}{210}\right)\) | \(e\left(\frac{419}{924}\right)\) | \(e\left(\frac{471}{1540}\right)\) | \(e\left(\frac{118}{1155}\right)\) | \(e\left(\frac{2207}{4620}\right)\) |
\(\chi_{29645}(39,\cdot)\) | 29645.he | 2310 | yes | \(-1\) | \(1\) | \(e\left(\frac{307}{1155}\right)\) | \(e\left(\frac{107}{210}\right)\) | \(e\left(\frac{614}{1155}\right)\) | \(e\left(\frac{597}{770}\right)\) | \(e\left(\frac{307}{385}\right)\) | \(e\left(\frac{2}{105}\right)\) | \(e\left(\frac{19}{462}\right)\) | \(e\left(\frac{289}{385}\right)\) | \(e\left(\frac{73}{1155}\right)\) | \(e\left(\frac{1073}{1155}\right)\) |
\(\chi_{29645}(41,\cdot)\) | 29645.gm | 770 | no | \(1\) | \(1\) | \(e\left(\frac{381}{770}\right)\) | \(e\left(\frac{53}{70}\right)\) | \(e\left(\frac{381}{385}\right)\) | \(e\left(\frac{97}{385}\right)\) | \(e\left(\frac{373}{770}\right)\) | \(e\left(\frac{18}{35}\right)\) | \(e\left(\frac{115}{154}\right)\) | \(e\left(\frac{348}{385}\right)\) | \(e\left(\frac{377}{385}\right)\) | \(e\left(\frac{67}{385}\right)\) |
\(\chi_{29645}(43,\cdot)\) | 29645.fj | 308 | yes | \(1\) | \(1\) | \(e\left(\frac{213}{308}\right)\) | \(e\left(\frac{11}{28}\right)\) | \(e\left(\frac{59}{154}\right)\) | \(e\left(\frac{13}{154}\right)\) | \(e\left(\frac{23}{308}\right)\) | \(e\left(\frac{11}{14}\right)\) | \(e\left(\frac{239}{308}\right)\) | \(e\left(\frac{283}{308}\right)\) | \(e\left(\frac{59}{77}\right)\) | \(e\left(\frac{141}{308}\right)\) |
\(\chi_{29645}(46,\cdot)\) | 29645.ha | 2310 | no | \(-1\) | \(1\) | \(e\left(\frac{611}{2310}\right)\) | \(e\left(\frac{34}{105}\right)\) | \(e\left(\frac{611}{1155}\right)\) | \(e\left(\frac{453}{770}\right)\) | \(e\left(\frac{611}{770}\right)\) | \(e\left(\frac{68}{105}\right)\) | \(e\left(\frac{197}{231}\right)\) | \(e\left(\frac{367}{770}\right)\) | \(e\left(\frac{67}{1155}\right)\) | \(e\left(\frac{1669}{2310}\right)\) |
\(\chi_{29645}(47,\cdot)\) | 29645.hi | 4620 | yes | \(1\) | \(1\) | \(e\left(\frac{1091}{4620}\right)\) | \(e\left(\frac{113}{420}\right)\) | \(e\left(\frac{1091}{2310}\right)\) | \(e\left(\frac{389}{770}\right)\) | \(e\left(\frac{1091}{1540}\right)\) | \(e\left(\frac{113}{210}\right)\) | \(e\left(\frac{685}{924}\right)\) | \(e\left(\frac{1017}{1540}\right)\) | \(e\left(\frac{1091}{1155}\right)\) | \(e\left(\frac{4069}{4620}\right)\) |
\(\chi_{29645}(48,\cdot)\) | 29645.fd | 220 | no | \(1\) | \(1\) | \(e\left(\frac{129}{220}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{19}{110}\right)\) | \(e\left(\frac{103}{110}\right)\) | \(e\left(\frac{167}{220}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{23}{44}\right)\) | \(e\left(\frac{49}{220}\right)\) | \(e\left(\frac{19}{55}\right)\) | \(e\left(\frac{51}{220}\right)\) |
\(\chi_{29645}(51,\cdot)\) | 29645.ha | 2310 | no | \(-1\) | \(1\) | \(e\left(\frac{787}{2310}\right)\) | \(e\left(\frac{23}{105}\right)\) | \(e\left(\frac{787}{1155}\right)\) | \(e\left(\frac{431}{770}\right)\) | \(e\left(\frac{17}{770}\right)\) | \(e\left(\frac{46}{105}\right)\) | \(e\left(\frac{208}{231}\right)\) | \(e\left(\frac{169}{770}\right)\) | \(e\left(\frac{419}{1155}\right)\) | \(e\left(\frac{1163}{2310}\right)\) |
\(\chi_{29645}(52,\cdot)\) | 29645.hg | 4620 | yes | \(-1\) | \(1\) | \(e\left(\frac{3721}{4620}\right)\) | \(e\left(\frac{73}{420}\right)\) | \(e\left(\frac{1411}{2310}\right)\) | \(e\left(\frac{377}{385}\right)\) | \(e\left(\frac{641}{1540}\right)\) | \(e\left(\frac{73}{210}\right)\) | \(e\left(\frac{725}{924}\right)\) | \(e\left(\frac{167}{1540}\right)\) | \(e\left(\frac{256}{1155}\right)\) | \(e\left(\frac{3359}{4620}\right)\) |