sage: H = DirichletGroup(8664)
pari: g = idealstar(,8664,2)
Character group
sage: G.order()
pari: g.no
| ||
Order | = | 2736 |
sage: H.invariants()
pari: g.cyc
| ||
Structure | = | \(C_{2}\times C_{2}\times C_{2}\times C_{342}\) |
sage: H.gens()
pari: g.gen
| ||
Generators | = | $\chi_{8664}(2167,\cdot)$, $\chi_{8664}(4333,\cdot)$, $\chi_{8664}(5777,\cdot)$, $\chi_{8664}(8305,\cdot)$ |
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 | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{8664}(1,\cdot)\) | 8664.a | 1 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
\(\chi_{8664}(5,\cdot)\) | 8664.dr | 342 | yes | \(-1\) | \(1\) | \(e\left(\frac{65}{171}\right)\) | \(e\left(\frac{43}{57}\right)\) | \(e\left(\frac{11}{57}\right)\) | \(e\left(\frac{233}{342}\right)\) | \(e\left(\frac{277}{342}\right)\) | \(e\left(\frac{185}{342}\right)\) | \(e\left(\frac{130}{171}\right)\) | \(e\left(\frac{91}{171}\right)\) | \(e\left(\frac{31}{57}\right)\) | \(e\left(\frac{23}{171}\right)\) |
\(\chi_{8664}(7,\cdot)\) | 8664.db | 114 | no | \(-1\) | \(1\) | \(e\left(\frac{43}{57}\right)\) | \(e\left(\frac{11}{38}\right)\) | \(e\left(\frac{9}{38}\right)\) | \(e\left(\frac{17}{57}\right)\) | \(e\left(\frac{7}{57}\right)\) | \(e\left(\frac{61}{114}\right)\) | \(e\left(\frac{29}{57}\right)\) | \(e\left(\frac{26}{57}\right)\) | \(e\left(\frac{15}{38}\right)\) | \(e\left(\frac{5}{114}\right)\) |
\(\chi_{8664}(11,\cdot)\) | 8664.cy | 114 | yes | \(1\) | \(1\) | \(e\left(\frac{11}{57}\right)\) | \(e\left(\frac{9}{38}\right)\) | \(e\left(\frac{35}{38}\right)\) | \(e\left(\frac{71}{114}\right)\) | \(e\left(\frac{103}{114}\right)\) | \(e\left(\frac{31}{57}\right)\) | \(e\left(\frac{22}{57}\right)\) | \(e\left(\frac{4}{57}\right)\) | \(e\left(\frac{33}{38}\right)\) | \(e\left(\frac{49}{114}\right)\) |
\(\chi_{8664}(13,\cdot)\) | 8664.dl | 342 | no | \(-1\) | \(1\) | \(e\left(\frac{233}{342}\right)\) | \(e\left(\frac{17}{57}\right)\) | \(e\left(\frac{71}{114}\right)\) | \(e\left(\frac{170}{171}\right)\) | \(e\left(\frac{70}{171}\right)\) | \(e\left(\frac{77}{171}\right)\) | \(e\left(\frac{62}{171}\right)\) | \(e\left(\frac{146}{171}\right)\) | \(e\left(\frac{55}{114}\right)\) | \(e\left(\frac{335}{342}\right)\) |
\(\chi_{8664}(17,\cdot)\) | 8664.dn | 342 | no | \(-1\) | \(1\) | \(e\left(\frac{277}{342}\right)\) | \(e\left(\frac{7}{57}\right)\) | \(e\left(\frac{103}{114}\right)\) | \(e\left(\frac{70}{171}\right)\) | \(e\left(\frac{289}{342}\right)\) | \(e\left(\frac{335}{342}\right)\) | \(e\left(\frac{106}{171}\right)\) | \(e\left(\frac{251}{342}\right)\) | \(e\left(\frac{13}{57}\right)\) | \(e\left(\frac{319}{342}\right)\) |
\(\chi_{8664}(23,\cdot)\) | 8664.dh | 342 | no | \(1\) | \(1\) | \(e\left(\frac{185}{342}\right)\) | \(e\left(\frac{61}{114}\right)\) | \(e\left(\frac{31}{57}\right)\) | \(e\left(\frac{77}{171}\right)\) | \(e\left(\frac{335}{342}\right)\) | \(e\left(\frac{56}{171}\right)\) | \(e\left(\frac{14}{171}\right)\) | \(e\left(\frac{259}{342}\right)\) | \(e\left(\frac{97}{114}\right)\) | \(e\left(\frac{13}{171}\right)\) |
\(\chi_{8664}(25,\cdot)\) | 8664.dc | 171 | no | \(1\) | \(1\) | \(e\left(\frac{130}{171}\right)\) | \(e\left(\frac{29}{57}\right)\) | \(e\left(\frac{22}{57}\right)\) | \(e\left(\frac{62}{171}\right)\) | \(e\left(\frac{106}{171}\right)\) | \(e\left(\frac{14}{171}\right)\) | \(e\left(\frac{89}{171}\right)\) | \(e\left(\frac{11}{171}\right)\) | \(e\left(\frac{5}{57}\right)\) | \(e\left(\frac{46}{171}\right)\) |
\(\chi_{8664}(29,\cdot)\) | 8664.dp | 342 | yes | \(1\) | \(1\) | \(e\left(\frac{91}{171}\right)\) | \(e\left(\frac{26}{57}\right)\) | \(e\left(\frac{4}{57}\right)\) | \(e\left(\frac{146}{171}\right)\) | \(e\left(\frac{251}{342}\right)\) | \(e\left(\frac{259}{342}\right)\) | \(e\left(\frac{11}{171}\right)\) | \(e\left(\frac{289}{342}\right)\) | \(e\left(\frac{7}{114}\right)\) | \(e\left(\frac{169}{171}\right)\) |
\(\chi_{8664}(31,\cdot)\) | 8664.cz | 114 | no | \(1\) | \(1\) | \(e\left(\frac{31}{57}\right)\) | \(e\left(\frac{15}{38}\right)\) | \(e\left(\frac{33}{38}\right)\) | \(e\left(\frac{55}{114}\right)\) | \(e\left(\frac{13}{57}\right)\) | \(e\left(\frac{97}{114}\right)\) | \(e\left(\frac{5}{57}\right)\) | \(e\left(\frac{7}{114}\right)\) | \(e\left(\frac{18}{19}\right)\) | \(e\left(\frac{107}{114}\right)\) |
\(\chi_{8664}(35,\cdot)\) | 8664.de | 342 | yes | \(1\) | \(1\) | \(e\left(\frac{23}{171}\right)\) | \(e\left(\frac{5}{114}\right)\) | \(e\left(\frac{49}{114}\right)\) | \(e\left(\frac{335}{342}\right)\) | \(e\left(\frac{319}{342}\right)\) | \(e\left(\frac{13}{171}\right)\) | \(e\left(\frac{46}{171}\right)\) | \(e\left(\frac{169}{171}\right)\) | \(e\left(\frac{107}{114}\right)\) | \(e\left(\frac{61}{342}\right)\) |
\(\chi_{8664}(37,\cdot)\) | 8664.ce | 38 | no | \(-1\) | \(1\) | \(e\left(\frac{1}{38}\right)\) | \(e\left(\frac{14}{19}\right)\) | \(e\left(\frac{35}{38}\right)\) | \(e\left(\frac{15}{19}\right)\) | \(e\left(\frac{14}{19}\right)\) | \(e\left(\frac{4}{19}\right)\) | \(e\left(\frac{1}{19}\right)\) | \(e\left(\frac{14}{19}\right)\) | \(e\left(\frac{33}{38}\right)\) | \(e\left(\frac{29}{38}\right)\) |
\(\chi_{8664}(41,\cdot)\) | 8664.dm | 342 | no | \(1\) | \(1\) | \(e\left(\frac{325}{342}\right)\) | \(e\left(\frac{22}{57}\right)\) | \(e\left(\frac{55}{114}\right)\) | \(e\left(\frac{155}{342}\right)\) | \(e\left(\frac{265}{342}\right)\) | \(e\left(\frac{35}{342}\right)\) | \(e\left(\frac{154}{171}\right)\) | \(e\left(\frac{142}{171}\right)\) | \(e\left(\frac{41}{114}\right)\) | \(e\left(\frac{115}{342}\right)\) |
\(\chi_{8664}(43,\cdot)\) | 8664.di | 342 | no | \(-1\) | \(1\) | \(e\left(\frac{265}{342}\right)\) | \(e\left(\frac{35}{114}\right)\) | \(e\left(\frac{29}{57}\right)\) | \(e\left(\frac{179}{342}\right)\) | \(e\left(\frac{62}{171}\right)\) | \(e\left(\frac{239}{342}\right)\) | \(e\left(\frac{94}{171}\right)\) | \(e\left(\frac{29}{342}\right)\) | \(e\left(\frac{65}{114}\right)\) | \(e\left(\frac{14}{171}\right)\) |
\(\chi_{8664}(47,\cdot)\) | 8664.dh | 342 | no | \(1\) | \(1\) | \(e\left(\frac{47}{342}\right)\) | \(e\left(\frac{103}{114}\right)\) | \(e\left(\frac{43}{57}\right)\) | \(e\left(\frac{2}{171}\right)\) | \(e\left(\frac{233}{342}\right)\) | \(e\left(\frac{17}{171}\right)\) | \(e\left(\frac{47}{171}\right)\) | \(e\left(\frac{271}{342}\right)\) | \(e\left(\frac{61}{114}\right)\) | \(e\left(\frac{7}{171}\right)\) |
\(\chi_{8664}(49,\cdot)\) | 8664.cm | 57 | no | \(1\) | \(1\) | \(e\left(\frac{29}{57}\right)\) | \(e\left(\frac{11}{19}\right)\) | \(e\left(\frac{9}{19}\right)\) | \(e\left(\frac{34}{57}\right)\) | \(e\left(\frac{14}{57}\right)\) | \(e\left(\frac{4}{57}\right)\) | \(e\left(\frac{1}{57}\right)\) | \(e\left(\frac{52}{57}\right)\) | \(e\left(\frac{15}{19}\right)\) | \(e\left(\frac{5}{57}\right)\) |
\(\chi_{8664}(53,\cdot)\) | 8664.dp | 342 | yes | \(1\) | \(1\) | \(e\left(\frac{52}{171}\right)\) | \(e\left(\frac{23}{57}\right)\) | \(e\left(\frac{43}{57}\right)\) | \(e\left(\frac{59}{171}\right)\) | \(e\left(\frac{119}{342}\right)\) | \(e\left(\frac{319}{342}\right)\) | \(e\left(\frac{104}{171}\right)\) | \(e\left(\frac{43}{342}\right)\) | \(e\left(\frac{61}{114}\right)\) | \(e\left(\frac{121}{171}\right)\) |
\(\chi_{8664}(55,\cdot)\) | 8664.dd | 342 | no | \(-1\) | \(1\) | \(e\left(\frac{98}{171}\right)\) | \(e\left(\frac{113}{114}\right)\) | \(e\left(\frac{13}{114}\right)\) | \(e\left(\frac{52}{171}\right)\) | \(e\left(\frac{122}{171}\right)\) | \(e\left(\frac{29}{342}\right)\) | \(e\left(\frac{25}{171}\right)\) | \(e\left(\frac{103}{171}\right)\) | \(e\left(\frac{47}{114}\right)\) | \(e\left(\frac{193}{342}\right)\) |
\(\chi_{8664}(59,\cdot)\) | 8664.df | 342 | yes | \(-1\) | \(1\) | \(e\left(\frac{134}{171}\right)\) | \(e\left(\frac{101}{114}\right)\) | \(e\left(\frac{55}{114}\right)\) | \(e\left(\frac{106}{171}\right)\) | \(e\left(\frac{37}{342}\right)\) | \(e\left(\frac{46}{171}\right)\) | \(e\left(\frac{97}{171}\right)\) | \(e\left(\frac{341}{342}\right)\) | \(e\left(\frac{49}{57}\right)\) | \(e\left(\frac{229}{342}\right)\) |
\(\chi_{8664}(61,\cdot)\) | 8664.do | 342 | no | \(1\) | \(1\) | \(e\left(\frac{311}{342}\right)\) | \(e\left(\frac{20}{57}\right)\) | \(e\left(\frac{107}{114}\right)\) | \(e\left(\frac{1}{342}\right)\) | \(e\left(\frac{136}{171}\right)\) | \(e\left(\frac{47}{171}\right)\) | \(e\left(\frac{140}{171}\right)\) | \(e\left(\frac{25}{342}\right)\) | \(e\left(\frac{29}{57}\right)\) | \(e\left(\frac{89}{342}\right)\) |
\(\chi_{8664}(65,\cdot)\) | 8664.cn | 114 | no | \(1\) | \(1\) | \(e\left(\frac{7}{114}\right)\) | \(e\left(\frac{1}{19}\right)\) | \(e\left(\frac{31}{38}\right)\) | \(e\left(\frac{77}{114}\right)\) | \(e\left(\frac{25}{114}\right)\) | \(e\left(\frac{113}{114}\right)\) | \(e\left(\frac{7}{57}\right)\) | \(e\left(\frac{22}{57}\right)\) | \(e\left(\frac{1}{38}\right)\) | \(e\left(\frac{13}{114}\right)\) |
\(\chi_{8664}(67,\cdot)\) | 8664.dj | 342 | no | \(1\) | \(1\) | \(e\left(\frac{335}{342}\right)\) | \(e\left(\frac{55}{114}\right)\) | \(e\left(\frac{13}{57}\right)\) | \(e\left(\frac{47}{171}\right)\) | \(e\left(\frac{130}{171}\right)\) | \(e\left(\frac{115}{342}\right)\) | \(e\left(\frac{164}{171}\right)\) | \(e\left(\frac{149}{171}\right)\) | \(e\left(\frac{47}{57}\right)\) | \(e\left(\frac{79}{171}\right)\) |
\(\chi_{8664}(71,\cdot)\) | 8664.dk | 342 | no | \(-1\) | \(1\) | \(e\left(\frac{31}{342}\right)\) | \(e\left(\frac{17}{114}\right)\) | \(e\left(\frac{32}{57}\right)\) | \(e\left(\frac{341}{342}\right)\) | \(e\left(\frac{241}{342}\right)\) | \(e\left(\frac{124}{171}\right)\) | \(e\left(\frac{31}{171}\right)\) | \(e\left(\frac{73}{171}\right)\) | \(e\left(\frac{28}{57}\right)\) | \(e\left(\frac{41}{171}\right)\) |
\(\chi_{8664}(73,\cdot)\) | 8664.dc | 171 | no | \(1\) | \(1\) | \(e\left(\frac{167}{171}\right)\) | \(e\left(\frac{7}{57}\right)\) | \(e\left(\frac{23}{57}\right)\) | \(e\left(\frac{127}{171}\right)\) | \(e\left(\frac{2}{171}\right)\) | \(e\left(\frac{139}{171}\right)\) | \(e\left(\frac{163}{171}\right)\) | \(e\left(\frac{97}{171}\right)\) | \(e\left(\frac{13}{57}\right)\) | \(e\left(\frac{17}{171}\right)\) |
\(\chi_{8664}(77,\cdot)\) | 8664.bz | 38 | yes | \(-1\) | \(1\) | \(e\left(\frac{18}{19}\right)\) | \(e\left(\frac{10}{19}\right)\) | \(e\left(\frac{3}{19}\right)\) | \(e\left(\frac{35}{38}\right)\) | \(e\left(\frac{1}{38}\right)\) | \(e\left(\frac{3}{38}\right)\) | \(e\left(\frac{17}{19}\right)\) | \(e\left(\frac{10}{19}\right)\) | \(e\left(\frac{5}{19}\right)\) | \(e\left(\frac{9}{19}\right)\) |
\(\chi_{8664}(79,\cdot)\) | 8664.dg | 342 | no | \(1\) | \(1\) | \(e\left(\frac{104}{171}\right)\) | \(e\left(\frac{35}{114}\right)\) | \(e\left(\frac{1}{114}\right)\) | \(e\left(\frac{65}{342}\right)\) | \(e\left(\frac{119}{171}\right)\) | \(e\left(\frac{125}{342}\right)\) | \(e\left(\frac{37}{171}\right)\) | \(e\left(\frac{257}{342}\right)\) | \(e\left(\frac{4}{57}\right)\) | \(e\left(\frac{313}{342}\right)\) |
\(\chi_{8664}(83,\cdot)\) | 8664.cy | 114 | yes | \(1\) | \(1\) | \(e\left(\frac{10}{57}\right)\) | \(e\left(\frac{3}{38}\right)\) | \(e\left(\frac{37}{38}\right)\) | \(e\left(\frac{49}{114}\right)\) | \(e\left(\frac{47}{114}\right)\) | \(e\left(\frac{23}{57}\right)\) | \(e\left(\frac{20}{57}\right)\) | \(e\left(\frac{14}{57}\right)\) | \(e\left(\frac{11}{38}\right)\) | \(e\left(\frac{29}{114}\right)\) |
\(\chi_{8664}(85,\cdot)\) | 8664.do | 342 | no | \(1\) | \(1\) | \(e\left(\frac{65}{342}\right)\) | \(e\left(\frac{50}{57}\right)\) | \(e\left(\frac{11}{114}\right)\) | \(e\left(\frac{31}{342}\right)\) | \(e\left(\frac{112}{171}\right)\) | \(e\left(\frac{89}{171}\right)\) | \(e\left(\frac{65}{171}\right)\) | \(e\left(\frac{91}{342}\right)\) | \(e\left(\frac{44}{57}\right)\) | \(e\left(\frac{23}{342}\right)\) |
\(\chi_{8664}(89,\cdot)\) | 8664.dm | 342 | no | \(1\) | \(1\) | \(e\left(\frac{179}{342}\right)\) | \(e\left(\frac{50}{57}\right)\) | \(e\left(\frac{11}{114}\right)\) | \(e\left(\frac{259}{342}\right)\) | \(e\left(\frac{167}{342}\right)\) | \(e\left(\frac{235}{342}\right)\) | \(e\left(\frac{8}{171}\right)\) | \(e\left(\frac{74}{171}\right)\) | \(e\left(\frac{31}{114}\right)\) | \(e\left(\frac{137}{342}\right)\) |
\(\chi_{8664}(91,\cdot)\) | 8664.dj | 342 | no | \(1\) | \(1\) | \(e\left(\frac{149}{342}\right)\) | \(e\left(\frac{67}{114}\right)\) | \(e\left(\frac{49}{57}\right)\) | \(e\left(\frac{50}{171}\right)\) | \(e\left(\frac{91}{171}\right)\) | \(e\left(\frac{337}{342}\right)\) | \(e\left(\frac{149}{171}\right)\) | \(e\left(\frac{53}{171}\right)\) | \(e\left(\frac{50}{57}\right)\) | \(e\left(\frac{4}{171}\right)\) |
\(\chi_{8664}(97,\cdot)\) | 8664.dq | 342 | no | \(-1\) | \(1\) | \(e\left(\frac{89}{171}\right)\) | \(e\left(\frac{1}{57}\right)\) | \(e\left(\frac{44}{57}\right)\) | \(e\left(\frac{77}{342}\right)\) | \(e\left(\frac{41}{171}\right)\) | \(e\left(\frac{28}{171}\right)\) | \(e\left(\frac{7}{171}\right)\) | \(e\left(\frac{215}{342}\right)\) | \(e\left(\frac{77}{114}\right)\) | \(e\left(\frac{92}{171}\right)\) |
\(\chi_{8664}(101,\cdot)\) | 8664.dr | 342 | yes | \(-1\) | \(1\) | \(e\left(\frac{157}{171}\right)\) | \(e\left(\frac{53}{57}\right)\) | \(e\left(\frac{52}{57}\right)\) | \(e\left(\frac{205}{342}\right)\) | \(e\left(\frac{185}{342}\right)\) | \(e\left(\frac{289}{342}\right)\) | \(e\left(\frac{143}{171}\right)\) | \(e\left(\frac{83}{171}\right)\) | \(e\left(\frac{17}{57}\right)\) | \(e\left(\frac{145}{171}\right)\) |