sage: H = DirichletGroup(5415)
pari: g = idealstar(,5415,2)
Character group
sage: G.order()
pari: g.no
| ||
Order | = | 2736 |
sage: H.invariants()
pari: g.cyc
| ||
Structure | = | \(C_{2}\times C_{2}\times C_{684}\) |
sage: H.gens()
pari: g.gen
| ||
Generators | = | $\chi_{5415}(3611,\cdot)$, $\chi_{5415}(2167,\cdot)$, $\chi_{5415}(5056,\cdot)$ |
First 32 of 2736 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 | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(22\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{5415}(1,\cdot)\) | 5415.a | 1 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
\(\chi_{5415}(2,\cdot)\) | 5415.cq | 684 | yes | \(-1\) | \(1\) | \(e\left(\frac{515}{684}\right)\) | \(e\left(\frac{173}{342}\right)\) | \(e\left(\frac{157}{228}\right)\) | \(e\left(\frac{59}{228}\right)\) | \(e\left(\frac{91}{114}\right)\) | \(e\left(\frac{487}{684}\right)\) | \(e\left(\frac{151}{342}\right)\) | \(e\left(\frac{2}{171}\right)\) | \(e\left(\frac{281}{684}\right)\) | \(e\left(\frac{377}{684}\right)\) |
\(\chi_{5415}(4,\cdot)\) | 5415.ck | 342 | no | \(1\) | \(1\) | \(e\left(\frac{173}{342}\right)\) | \(e\left(\frac{2}{171}\right)\) | \(e\left(\frac{43}{114}\right)\) | \(e\left(\frac{59}{114}\right)\) | \(e\left(\frac{34}{57}\right)\) | \(e\left(\frac{145}{342}\right)\) | \(e\left(\frac{151}{171}\right)\) | \(e\left(\frac{4}{171}\right)\) | \(e\left(\frac{281}{342}\right)\) | \(e\left(\frac{35}{342}\right)\) |
\(\chi_{5415}(7,\cdot)\) | 5415.cf | 228 | no | \(-1\) | \(1\) | \(e\left(\frac{157}{228}\right)\) | \(e\left(\frac{43}{114}\right)\) | \(e\left(\frac{3}{76}\right)\) | \(e\left(\frac{5}{76}\right)\) | \(e\left(\frac{14}{19}\right)\) | \(e\left(\frac{11}{228}\right)\) | \(e\left(\frac{83}{114}\right)\) | \(e\left(\frac{43}{57}\right)\) | \(e\left(\frac{85}{228}\right)\) | \(e\left(\frac{97}{228}\right)\) |
\(\chi_{5415}(8,\cdot)\) | 5415.ch | 228 | yes | \(-1\) | \(1\) | \(e\left(\frac{59}{228}\right)\) | \(e\left(\frac{59}{114}\right)\) | \(e\left(\frac{5}{76}\right)\) | \(e\left(\frac{59}{76}\right)\) | \(e\left(\frac{15}{38}\right)\) | \(e\left(\frac{31}{228}\right)\) | \(e\left(\frac{37}{114}\right)\) | \(e\left(\frac{2}{57}\right)\) | \(e\left(\frac{53}{228}\right)\) | \(e\left(\frac{149}{228}\right)\) |
\(\chi_{5415}(11,\cdot)\) | 5415.by | 114 | no | \(-1\) | \(1\) | \(e\left(\frac{91}{114}\right)\) | \(e\left(\frac{34}{57}\right)\) | \(e\left(\frac{14}{19}\right)\) | \(e\left(\frac{15}{38}\right)\) | \(e\left(\frac{35}{38}\right)\) | \(e\left(\frac{7}{57}\right)\) | \(e\left(\frac{61}{114}\right)\) | \(e\left(\frac{11}{57}\right)\) | \(e\left(\frac{103}{114}\right)\) | \(e\left(\frac{41}{57}\right)\) |
\(\chi_{5415}(13,\cdot)\) | 5415.cs | 684 | no | \(1\) | \(1\) | \(e\left(\frac{487}{684}\right)\) | \(e\left(\frac{145}{342}\right)\) | \(e\left(\frac{11}{228}\right)\) | \(e\left(\frac{31}{228}\right)\) | \(e\left(\frac{7}{57}\right)\) | \(e\left(\frac{509}{684}\right)\) | \(e\left(\frac{130}{171}\right)\) | \(e\left(\frac{145}{171}\right)\) | \(e\left(\frac{109}{684}\right)\) | \(e\left(\frac{571}{684}\right)\) |
\(\chi_{5415}(14,\cdot)\) | 5415.cj | 342 | yes | \(1\) | \(1\) | \(e\left(\frac{151}{342}\right)\) | \(e\left(\frac{151}{171}\right)\) | \(e\left(\frac{83}{114}\right)\) | \(e\left(\frac{37}{114}\right)\) | \(e\left(\frac{61}{114}\right)\) | \(e\left(\frac{130}{171}\right)\) | \(e\left(\frac{29}{171}\right)\) | \(e\left(\frac{131}{171}\right)\) | \(e\left(\frac{134}{171}\right)\) | \(e\left(\frac{167}{171}\right)\) |
\(\chi_{5415}(16,\cdot)\) | 5415.ce | 171 | no | \(1\) | \(1\) | \(e\left(\frac{2}{171}\right)\) | \(e\left(\frac{4}{171}\right)\) | \(e\left(\frac{43}{57}\right)\) | \(e\left(\frac{2}{57}\right)\) | \(e\left(\frac{11}{57}\right)\) | \(e\left(\frac{145}{171}\right)\) | \(e\left(\frac{131}{171}\right)\) | \(e\left(\frac{8}{171}\right)\) | \(e\left(\frac{110}{171}\right)\) | \(e\left(\frac{35}{171}\right)\) |
\(\chi_{5415}(17,\cdot)\) | 5415.cr | 684 | yes | \(1\) | \(1\) | \(e\left(\frac{281}{684}\right)\) | \(e\left(\frac{281}{342}\right)\) | \(e\left(\frac{85}{228}\right)\) | \(e\left(\frac{53}{228}\right)\) | \(e\left(\frac{103}{114}\right)\) | \(e\left(\frac{109}{684}\right)\) | \(e\left(\frac{134}{171}\right)\) | \(e\left(\frac{110}{171}\right)\) | \(e\left(\frac{65}{684}\right)\) | \(e\left(\frac{215}{684}\right)\) |
\(\chi_{5415}(22,\cdot)\) | 5415.cs | 684 | no | \(1\) | \(1\) | \(e\left(\frac{377}{684}\right)\) | \(e\left(\frac{35}{342}\right)\) | \(e\left(\frac{97}{228}\right)\) | \(e\left(\frac{149}{228}\right)\) | \(e\left(\frac{41}{57}\right)\) | \(e\left(\frac{571}{684}\right)\) | \(e\left(\frac{167}{171}\right)\) | \(e\left(\frac{35}{171}\right)\) | \(e\left(\frac{215}{684}\right)\) | \(e\left(\frac{185}{684}\right)\) |
\(\chi_{5415}(23,\cdot)\) | 5415.cr | 684 | yes | \(1\) | \(1\) | \(e\left(\frac{463}{684}\right)\) | \(e\left(\frac{121}{342}\right)\) | \(e\left(\frac{179}{228}\right)\) | \(e\left(\frac{7}{228}\right)\) | \(e\left(\frac{5}{114}\right)\) | \(e\left(\frac{479}{684}\right)\) | \(e\left(\frac{79}{171}\right)\) | \(e\left(\frac{121}{171}\right)\) | \(e\left(\frac{499}{684}\right)\) | \(e\left(\frac{493}{684}\right)\) |
\(\chi_{5415}(26,\cdot)\) | 5415.by | 114 | no | \(-1\) | \(1\) | \(e\left(\frac{53}{114}\right)\) | \(e\left(\frac{53}{57}\right)\) | \(e\left(\frac{14}{19}\right)\) | \(e\left(\frac{15}{38}\right)\) | \(e\left(\frac{35}{38}\right)\) | \(e\left(\frac{26}{57}\right)\) | \(e\left(\frac{23}{114}\right)\) | \(e\left(\frac{49}{57}\right)\) | \(e\left(\frac{65}{114}\right)\) | \(e\left(\frac{22}{57}\right)\) |
\(\chi_{5415}(28,\cdot)\) | 5415.bh | 36 | no | \(-1\) | \(1\) | \(e\left(\frac{7}{36}\right)\) | \(e\left(\frac{7}{18}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{17}{36}\right)\) | \(e\left(\frac{11}{18}\right)\) | \(e\left(\frac{7}{9}\right)\) | \(e\left(\frac{7}{36}\right)\) | \(e\left(\frac{19}{36}\right)\) |
\(\chi_{5415}(29,\cdot)\) | 5415.cj | 342 | yes | \(1\) | \(1\) | \(e\left(\frac{17}{342}\right)\) | \(e\left(\frac{17}{171}\right)\) | \(e\left(\frac{109}{114}\right)\) | \(e\left(\frac{17}{114}\right)\) | \(e\left(\frac{65}{114}\right)\) | \(e\left(\frac{146}{171}\right)\) | \(e\left(\frac{1}{171}\right)\) | \(e\left(\frac{34}{171}\right)\) | \(e\left(\frac{40}{171}\right)\) | \(e\left(\frac{106}{171}\right)\) |
\(\chi_{5415}(31,\cdot)\) | 5415.bx | 114 | no | \(-1\) | \(1\) | \(e\left(\frac{101}{114}\right)\) | \(e\left(\frac{44}{57}\right)\) | \(e\left(\frac{17}{19}\right)\) | \(e\left(\frac{25}{38}\right)\) | \(e\left(\frac{7}{19}\right)\) | \(e\left(\frac{55}{114}\right)\) | \(e\left(\frac{89}{114}\right)\) | \(e\left(\frac{31}{57}\right)\) | \(e\left(\frac{13}{57}\right)\) | \(e\left(\frac{29}{114}\right)\) |
\(\chi_{5415}(32,\cdot)\) | 5415.cq | 684 | yes | \(-1\) | \(1\) | \(e\left(\frac{523}{684}\right)\) | \(e\left(\frac{181}{342}\right)\) | \(e\left(\frac{101}{228}\right)\) | \(e\left(\frac{67}{228}\right)\) | \(e\left(\frac{113}{114}\right)\) | \(e\left(\frac{383}{684}\right)\) | \(e\left(\frac{71}{342}\right)\) | \(e\left(\frac{10}{171}\right)\) | \(e\left(\frac{37}{684}\right)\) | \(e\left(\frac{517}{684}\right)\) |
\(\chi_{5415}(34,\cdot)\) | 5415.cm | 342 | no | \(-1\) | \(1\) | \(e\left(\frac{28}{171}\right)\) | \(e\left(\frac{56}{171}\right)\) | \(e\left(\frac{7}{114}\right)\) | \(e\left(\frac{28}{57}\right)\) | \(e\left(\frac{40}{57}\right)\) | \(e\left(\frac{149}{171}\right)\) | \(e\left(\frac{77}{342}\right)\) | \(e\left(\frac{112}{171}\right)\) | \(e\left(\frac{173}{342}\right)\) | \(e\left(\frac{148}{171}\right)\) |
\(\chi_{5415}(37,\cdot)\) | 5415.bt | 76 | no | \(1\) | \(1\) | \(e\left(\frac{29}{76}\right)\) | \(e\left(\frac{29}{38}\right)\) | \(e\left(\frac{75}{76}\right)\) | \(e\left(\frac{11}{76}\right)\) | \(e\left(\frac{8}{19}\right)\) | \(e\left(\frac{3}{76}\right)\) | \(e\left(\frac{7}{19}\right)\) | \(e\left(\frac{10}{19}\right)\) | \(e\left(\frac{75}{76}\right)\) | \(e\left(\frac{61}{76}\right)\) |
\(\chi_{5415}(41,\cdot)\) | 5415.cp | 342 | no | \(1\) | \(1\) | \(e\left(\frac{119}{171}\right)\) | \(e\left(\frac{67}{171}\right)\) | \(e\left(\frac{22}{57}\right)\) | \(e\left(\frac{5}{57}\right)\) | \(e\left(\frac{55}{114}\right)\) | \(e\left(\frac{155}{342}\right)\) | \(e\left(\frac{14}{171}\right)\) | \(e\left(\frac{134}{171}\right)\) | \(e\left(\frac{265}{342}\right)\) | \(e\left(\frac{61}{342}\right)\) |
\(\chi_{5415}(43,\cdot)\) | 5415.ct | 684 | no | \(-1\) | \(1\) | \(e\left(\frac{617}{684}\right)\) | \(e\left(\frac{275}{342}\right)\) | \(e\left(\frac{127}{228}\right)\) | \(e\left(\frac{161}{228}\right)\) | \(e\left(\frac{29}{57}\right)\) | \(e\left(\frac{187}{684}\right)\) | \(e\left(\frac{157}{342}\right)\) | \(e\left(\frac{104}{171}\right)\) | \(e\left(\frac{77}{684}\right)\) | \(e\left(\frac{281}{684}\right)\) |
\(\chi_{5415}(44,\cdot)\) | 5415.cl | 342 | yes | \(-1\) | \(1\) | \(e\left(\frac{52}{171}\right)\) | \(e\left(\frac{104}{171}\right)\) | \(e\left(\frac{13}{114}\right)\) | \(e\left(\frac{52}{57}\right)\) | \(e\left(\frac{59}{114}\right)\) | \(e\left(\frac{187}{342}\right)\) | \(e\left(\frac{143}{342}\right)\) | \(e\left(\frac{37}{171}\right)\) | \(e\left(\frac{124}{171}\right)\) | \(e\left(\frac{281}{342}\right)\) |
\(\chi_{5415}(46,\cdot)\) | 5415.bx | 114 | no | \(-1\) | \(1\) | \(e\left(\frac{49}{114}\right)\) | \(e\left(\frac{49}{57}\right)\) | \(e\left(\frac{9}{19}\right)\) | \(e\left(\frac{11}{38}\right)\) | \(e\left(\frac{16}{19}\right)\) | \(e\left(\frac{47}{114}\right)\) | \(e\left(\frac{103}{114}\right)\) | \(e\left(\frac{41}{57}\right)\) | \(e\left(\frac{8}{57}\right)\) | \(e\left(\frac{31}{114}\right)\) |
\(\chi_{5415}(47,\cdot)\) | 5415.cr | 684 | yes | \(1\) | \(1\) | \(e\left(\frac{565}{684}\right)\) | \(e\left(\frac{223}{342}\right)\) | \(e\left(\frac{149}{228}\right)\) | \(e\left(\frac{109}{228}\right)\) | \(e\left(\frac{29}{114}\right)\) | \(e\left(\frac{521}{684}\right)\) | \(e\left(\frac{82}{171}\right)\) | \(e\left(\frac{52}{171}\right)\) | \(e\left(\frac{637}{684}\right)\) | \(e\left(\frac{55}{684}\right)\) |
\(\chi_{5415}(49,\cdot)\) | 5415.bz | 114 | no | \(1\) | \(1\) | \(e\left(\frac{43}{114}\right)\) | \(e\left(\frac{43}{57}\right)\) | \(e\left(\frac{3}{38}\right)\) | \(e\left(\frac{5}{38}\right)\) | \(e\left(\frac{9}{19}\right)\) | \(e\left(\frac{11}{114}\right)\) | \(e\left(\frac{26}{57}\right)\) | \(e\left(\frac{29}{57}\right)\) | \(e\left(\frac{85}{114}\right)\) | \(e\left(\frac{97}{114}\right)\) |
\(\chi_{5415}(52,\cdot)\) | 5415.cs | 684 | no | \(1\) | \(1\) | \(e\left(\frac{149}{684}\right)\) | \(e\left(\frac{149}{342}\right)\) | \(e\left(\frac{97}{228}\right)\) | \(e\left(\frac{149}{228}\right)\) | \(e\left(\frac{41}{57}\right)\) | \(e\left(\frac{115}{684}\right)\) | \(e\left(\frac{110}{171}\right)\) | \(e\left(\frac{149}{171}\right)\) | \(e\left(\frac{671}{684}\right)\) | \(e\left(\frac{641}{684}\right)\) |
\(\chi_{5415}(53,\cdot)\) | 5415.cq | 684 | yes | \(-1\) | \(1\) | \(e\left(\frac{337}{684}\right)\) | \(e\left(\frac{337}{342}\right)\) | \(e\left(\frac{35}{228}\right)\) | \(e\left(\frac{109}{228}\right)\) | \(e\left(\frac{29}{114}\right)\) | \(e\left(\frac{65}{684}\right)\) | \(e\left(\frac{221}{342}\right)\) | \(e\left(\frac{166}{171}\right)\) | \(e\left(\frac{67}{684}\right)\) | \(e\left(\frac{511}{684}\right)\) |
\(\chi_{5415}(56,\cdot)\) | 5415.bl | 38 | no | \(1\) | \(1\) | \(e\left(\frac{18}{19}\right)\) | \(e\left(\frac{17}{19}\right)\) | \(e\left(\frac{2}{19}\right)\) | \(e\left(\frac{16}{19}\right)\) | \(e\left(\frac{5}{38}\right)\) | \(e\left(\frac{7}{38}\right)\) | \(e\left(\frac{1}{19}\right)\) | \(e\left(\frac{15}{19}\right)\) | \(e\left(\frac{23}{38}\right)\) | \(e\left(\frac{3}{38}\right)\) |
\(\chi_{5415}(58,\cdot)\) | 5415.bu | 76 | no | \(-1\) | \(1\) | \(e\left(\frac{61}{76}\right)\) | \(e\left(\frac{23}{38}\right)\) | \(e\left(\frac{49}{76}\right)\) | \(e\left(\frac{31}{76}\right)\) | \(e\left(\frac{7}{19}\right)\) | \(e\left(\frac{43}{76}\right)\) | \(e\left(\frac{17}{38}\right)\) | \(e\left(\frac{4}{19}\right)\) | \(e\left(\frac{49}{76}\right)\) | \(e\left(\frac{13}{76}\right)\) |
\(\chi_{5415}(59,\cdot)\) | 5415.cj | 342 | yes | \(1\) | \(1\) | \(e\left(\frac{181}{342}\right)\) | \(e\left(\frac{10}{171}\right)\) | \(e\left(\frac{101}{114}\right)\) | \(e\left(\frac{67}{114}\right)\) | \(e\left(\frac{55}{114}\right)\) | \(e\left(\frac{106}{171}\right)\) | \(e\left(\frac{71}{171}\right)\) | \(e\left(\frac{20}{171}\right)\) | \(e\left(\frac{104}{171}\right)\) | \(e\left(\frac{2}{171}\right)\) |
\(\chi_{5415}(61,\cdot)\) | 5415.ce | 171 | no | \(1\) | \(1\) | \(e\left(\frac{46}{171}\right)\) | \(e\left(\frac{92}{171}\right)\) | \(e\left(\frac{20}{57}\right)\) | \(e\left(\frac{46}{57}\right)\) | \(e\left(\frac{25}{57}\right)\) | \(e\left(\frac{86}{171}\right)\) | \(e\left(\frac{106}{171}\right)\) | \(e\left(\frac{13}{171}\right)\) | \(e\left(\frac{136}{171}\right)\) | \(e\left(\frac{121}{171}\right)\) |
\(\chi_{5415}(62,\cdot)\) | 5415.bj | 36 | no | \(1\) | \(1\) | \(e\left(\frac{23}{36}\right)\) | \(e\left(\frac{5}{18}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{7}{36}\right)\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{23}{36}\right)\) | \(e\left(\frac{29}{36}\right)\) |