sage: H = DirichletGroup(8021)
pari: g = idealstar(,8021,2)
Character group
| sage: G.order()
pari: g.no
| ||
| Order | = | 7392 |
| sage: H.invariants()
pari: g.cyc
| ||
| Structure | = | \(C_{4}\times C_{1848}\) |
| sage: H.gens()
pari: g.gen
| ||
| Generators | = | $\chi_{8021}(6788,\cdot)$, $\chi_{8021}(2471,\cdot)$ |
First 32 of 7392 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 | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{8021}(1,\cdot)\) | 8021.a | 1 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(\chi_{8021}(2,\cdot)\) | 8021.ec | 924 | yes | \(-1\) | \(1\) | \(e\left(\frac{425}{924}\right)\) | \(e\left(\frac{13}{462}\right)\) | \(e\left(\frac{425}{462}\right)\) | \(e\left(\frac{241}{308}\right)\) | \(e\left(\frac{41}{84}\right)\) | \(e\left(\frac{535}{924}\right)\) | \(e\left(\frac{117}{308}\right)\) | \(e\left(\frac{13}{231}\right)\) | \(e\left(\frac{8}{33}\right)\) | \(e\left(\frac{731}{924}\right)\) |
| \(\chi_{8021}(3,\cdot)\) | 8021.eh | 1848 | yes | \(-1\) | \(1\) | \(e\left(\frac{13}{462}\right)\) | \(e\left(\frac{619}{1848}\right)\) | \(e\left(\frac{13}{231}\right)\) | \(e\left(\frac{321}{616}\right)\) | \(e\left(\frac{61}{168}\right)\) | \(e\left(\frac{829}{924}\right)\) | \(e\left(\frac{13}{154}\right)\) | \(e\left(\frac{619}{924}\right)\) | \(e\left(\frac{145}{264}\right)\) | \(e\left(\frac{479}{924}\right)\) |
| \(\chi_{8021}(4,\cdot)\) | 8021.ds | 462 | yes | \(1\) | \(1\) | \(e\left(\frac{425}{462}\right)\) | \(e\left(\frac{13}{231}\right)\) | \(e\left(\frac{194}{231}\right)\) | \(e\left(\frac{87}{154}\right)\) | \(e\left(\frac{41}{42}\right)\) | \(e\left(\frac{73}{462}\right)\) | \(e\left(\frac{117}{154}\right)\) | \(e\left(\frac{26}{231}\right)\) | \(e\left(\frac{16}{33}\right)\) | \(e\left(\frac{269}{462}\right)\) |
| \(\chi_{8021}(5,\cdot)\) | 8021.dw | 616 | yes | \(1\) | \(1\) | \(e\left(\frac{241}{308}\right)\) | \(e\left(\frac{321}{616}\right)\) | \(e\left(\frac{87}{154}\right)\) | \(e\left(\frac{15}{616}\right)\) | \(e\left(\frac{17}{56}\right)\) | \(e\left(\frac{19}{77}\right)\) | \(e\left(\frac{107}{308}\right)\) | \(e\left(\frac{13}{308}\right)\) | \(e\left(\frac{71}{88}\right)\) | \(e\left(\frac{101}{154}\right)\) |
| \(\chi_{8021}(6,\cdot)\) | 8021.de | 168 | yes | \(1\) | \(1\) | \(e\left(\frac{41}{84}\right)\) | \(e\left(\frac{61}{168}\right)\) | \(e\left(\frac{41}{42}\right)\) | \(e\left(\frac{17}{56}\right)\) | \(e\left(\frac{143}{168}\right)\) | \(e\left(\frac{10}{21}\right)\) | \(e\left(\frac{13}{28}\right)\) | \(e\left(\frac{61}{84}\right)\) | \(e\left(\frac{19}{24}\right)\) | \(e\left(\frac{13}{42}\right)\) |
| \(\chi_{8021}(7,\cdot)\) | 8021.eb | 924 | yes | \(-1\) | \(1\) | \(e\left(\frac{535}{924}\right)\) | \(e\left(\frac{829}{924}\right)\) | \(e\left(\frac{73}{462}\right)\) | \(e\left(\frac{19}{77}\right)\) | \(e\left(\frac{10}{21}\right)\) | \(e\left(\frac{755}{924}\right)\) | \(e\left(\frac{227}{308}\right)\) | \(e\left(\frac{367}{462}\right)\) | \(e\left(\frac{109}{132}\right)\) | \(e\left(\frac{643}{924}\right)\) |
| \(\chi_{8021}(8,\cdot)\) | 8021.dm | 308 | yes | \(-1\) | \(1\) | \(e\left(\frac{117}{308}\right)\) | \(e\left(\frac{13}{154}\right)\) | \(e\left(\frac{117}{154}\right)\) | \(e\left(\frac{107}{308}\right)\) | \(e\left(\frac{13}{28}\right)\) | \(e\left(\frac{227}{308}\right)\) | \(e\left(\frac{43}{308}\right)\) | \(e\left(\frac{13}{77}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{115}{308}\right)\) |
| \(\chi_{8021}(9,\cdot)\) | 8021.dy | 924 | yes | \(1\) | \(1\) | \(e\left(\frac{13}{231}\right)\) | \(e\left(\frac{619}{924}\right)\) | \(e\left(\frac{26}{231}\right)\) | \(e\left(\frac{13}{308}\right)\) | \(e\left(\frac{61}{84}\right)\) | \(e\left(\frac{367}{462}\right)\) | \(e\left(\frac{13}{77}\right)\) | \(e\left(\frac{157}{462}\right)\) | \(e\left(\frac{13}{132}\right)\) | \(e\left(\frac{17}{462}\right)\) |
| \(\chi_{8021}(10,\cdot)\) | 8021.dk | 264 | yes | \(-1\) | \(1\) | \(e\left(\frac{8}{33}\right)\) | \(e\left(\frac{145}{264}\right)\) | \(e\left(\frac{16}{33}\right)\) | \(e\left(\frac{71}{88}\right)\) | \(e\left(\frac{19}{24}\right)\) | \(e\left(\frac{109}{132}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{13}{132}\right)\) | \(e\left(\frac{13}{264}\right)\) | \(e\left(\frac{59}{132}\right)\) |
| \(\chi_{8021}(11,\cdot)\) | 8021.ea | 924 | yes | \(-1\) | \(1\) | \(e\left(\frac{731}{924}\right)\) | \(e\left(\frac{479}{924}\right)\) | \(e\left(\frac{269}{462}\right)\) | \(e\left(\frac{101}{154}\right)\) | \(e\left(\frac{13}{42}\right)\) | \(e\left(\frac{643}{924}\right)\) | \(e\left(\frac{115}{308}\right)\) | \(e\left(\frac{17}{462}\right)\) | \(e\left(\frac{59}{132}\right)\) | \(e\left(\frac{167}{924}\right)\) |
| \(\chi_{8021}(12,\cdot)\) | 8021.dx | 616 | yes | \(-1\) | \(1\) | \(e\left(\frac{73}{77}\right)\) | \(e\left(\frac{241}{616}\right)\) | \(e\left(\frac{69}{77}\right)\) | \(e\left(\frac{53}{616}\right)\) | \(e\left(\frac{19}{56}\right)\) | \(e\left(\frac{17}{308}\right)\) | \(e\left(\frac{65}{77}\right)\) | \(e\left(\frac{241}{308}\right)\) | \(e\left(\frac{3}{88}\right)\) | \(e\left(\frac{31}{308}\right)\) |
| \(\chi_{8021}(14,\cdot)\) | 8021.dq | 308 | no | \(1\) | \(1\) | \(e\left(\frac{3}{77}\right)\) | \(e\left(\frac{285}{308}\right)\) | \(e\left(\frac{6}{77}\right)\) | \(e\left(\frac{9}{308}\right)\) | \(e\left(\frac{27}{28}\right)\) | \(e\left(\frac{61}{154}\right)\) | \(e\left(\frac{9}{77}\right)\) | \(e\left(\frac{131}{154}\right)\) | \(e\left(\frac{3}{44}\right)\) | \(e\left(\frac{75}{154}\right)\) |
| \(\chi_{8021}(15,\cdot)\) | 8021.cv | 132 | yes | \(-1\) | \(1\) | \(e\left(\frac{107}{132}\right)\) | \(e\left(\frac{113}{132}\right)\) | \(e\left(\frac{41}{66}\right)\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{19}{132}\right)\) | \(e\left(\frac{19}{44}\right)\) | \(e\left(\frac{47}{66}\right)\) | \(e\left(\frac{47}{132}\right)\) | \(e\left(\frac{23}{132}\right)\) |
| \(\chi_{8021}(16,\cdot)\) | 8021.dg | 231 | yes | \(1\) | \(1\) | \(e\left(\frac{194}{231}\right)\) | \(e\left(\frac{26}{231}\right)\) | \(e\left(\frac{157}{231}\right)\) | \(e\left(\frac{10}{77}\right)\) | \(e\left(\frac{20}{21}\right)\) | \(e\left(\frac{73}{231}\right)\) | \(e\left(\frac{40}{77}\right)\) | \(e\left(\frac{52}{231}\right)\) | \(e\left(\frac{32}{33}\right)\) | \(e\left(\frac{38}{231}\right)\) |
| \(\chi_{8021}(17,\cdot)\) | 8021.ee | 1848 | yes | \(-1\) | \(1\) | \(e\left(\frac{13}{231}\right)\) | \(e\left(\frac{545}{1848}\right)\) | \(e\left(\frac{26}{231}\right)\) | \(e\left(\frac{103}{616}\right)\) | \(e\left(\frac{59}{168}\right)\) | \(e\left(\frac{41}{924}\right)\) | \(e\left(\frac{13}{77}\right)\) | \(e\left(\frac{545}{924}\right)\) | \(e\left(\frac{59}{264}\right)\) | \(e\left(\frac{727}{924}\right)\) |
| \(\chi_{8021}(18,\cdot)\) | 8021.dn | 308 | yes | \(-1\) | \(1\) | \(e\left(\frac{159}{308}\right)\) | \(e\left(\frac{215}{308}\right)\) | \(e\left(\frac{5}{154}\right)\) | \(e\left(\frac{127}{154}\right)\) | \(e\left(\frac{3}{14}\right)\) | \(e\left(\frac{115}{308}\right)\) | \(e\left(\frac{169}{308}\right)\) | \(e\left(\frac{61}{154}\right)\) | \(e\left(\frac{15}{44}\right)\) | \(e\left(\frac{255}{308}\right)\) |
| \(\chi_{8021}(19,\cdot)\) | 8021.eb | 924 | yes | \(-1\) | \(1\) | \(e\left(\frac{853}{924}\right)\) | \(e\left(\frac{643}{924}\right)\) | \(e\left(\frac{391}{462}\right)\) | \(e\left(\frac{10}{77}\right)\) | \(e\left(\frac{13}{21}\right)\) | \(e\left(\frac{677}{924}\right)\) | \(e\left(\frac{237}{308}\right)\) | \(e\left(\frac{181}{462}\right)\) | \(e\left(\frac{7}{132}\right)\) | \(e\left(\frac{229}{924}\right)\) |
| \(\chi_{8021}(20,\cdot)\) | 8021.dd | 168 | yes | \(1\) | \(1\) | \(e\left(\frac{59}{84}\right)\) | \(e\left(\frac{97}{168}\right)\) | \(e\left(\frac{17}{42}\right)\) | \(e\left(\frac{33}{56}\right)\) | \(e\left(\frac{47}{168}\right)\) | \(e\left(\frac{17}{42}\right)\) | \(e\left(\frac{3}{28}\right)\) | \(e\left(\frac{13}{84}\right)\) | \(e\left(\frac{7}{24}\right)\) | \(e\left(\frac{5}{21}\right)\) |
| \(\chi_{8021}(21,\cdot)\) | 8021.cc | 56 | yes | \(1\) | \(1\) | \(e\left(\frac{17}{28}\right)\) | \(e\left(\frac{13}{56}\right)\) | \(e\left(\frac{3}{14}\right)\) | \(e\left(\frac{43}{56}\right)\) | \(e\left(\frac{47}{56}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{23}{28}\right)\) | \(e\left(\frac{13}{28}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{3}{14}\right)\) |
| \(\chi_{8021}(22,\cdot)\) | 8021.dy | 924 | yes | \(1\) | \(1\) | \(e\left(\frac{58}{231}\right)\) | \(e\left(\frac{505}{924}\right)\) | \(e\left(\frac{116}{231}\right)\) | \(e\left(\frac{135}{308}\right)\) | \(e\left(\frac{67}{84}\right)\) | \(e\left(\frac{127}{462}\right)\) | \(e\left(\frac{58}{77}\right)\) | \(e\left(\frac{43}{462}\right)\) | \(e\left(\frac{91}{132}\right)\) | \(e\left(\frac{449}{462}\right)\) |
| \(\chi_{8021}(23,\cdot)\) | 8021.ee | 1848 | yes | \(-1\) | \(1\) | \(e\left(\frac{116}{231}\right)\) | \(e\left(\frac{1327}{1848}\right)\) | \(e\left(\frac{1}{231}\right)\) | \(e\left(\frac{1}{616}\right)\) | \(e\left(\frac{37}{168}\right)\) | \(e\left(\frac{739}{924}\right)\) | \(e\left(\frac{39}{77}\right)\) | \(e\left(\frac{403}{924}\right)\) | \(e\left(\frac{133}{264}\right)\) | \(e\left(\frac{641}{924}\right)\) |
| \(\chi_{8021}(24,\cdot)\) | 8021.eg | 1848 | yes | \(1\) | \(1\) | \(e\left(\frac{377}{924}\right)\) | \(e\left(\frac{775}{1848}\right)\) | \(e\left(\frac{377}{462}\right)\) | \(e\left(\frac{535}{616}\right)\) | \(e\left(\frac{139}{168}\right)\) | \(e\left(\frac{293}{462}\right)\) | \(e\left(\frac{69}{308}\right)\) | \(e\left(\frac{775}{924}\right)\) | \(e\left(\frac{73}{264}\right)\) | \(e\left(\frac{206}{231}\right)\) |
| \(\chi_{8021}(25,\cdot)\) | 8021.dl | 308 | yes | \(1\) | \(1\) | \(e\left(\frac{87}{154}\right)\) | \(e\left(\frac{13}{308}\right)\) | \(e\left(\frac{10}{77}\right)\) | \(e\left(\frac{15}{308}\right)\) | \(e\left(\frac{17}{28}\right)\) | \(e\left(\frac{38}{77}\right)\) | \(e\left(\frac{107}{154}\right)\) | \(e\left(\frac{13}{154}\right)\) | \(e\left(\frac{27}{44}\right)\) | \(e\left(\frac{24}{77}\right)\) |
| \(\chi_{8021}(27,\cdot)\) | 8021.du | 616 | no | \(-1\) | \(1\) | \(e\left(\frac{13}{154}\right)\) | \(e\left(\frac{3}{616}\right)\) | \(e\left(\frac{13}{77}\right)\) | \(e\left(\frac{347}{616}\right)\) | \(e\left(\frac{5}{56}\right)\) | \(e\left(\frac{213}{308}\right)\) | \(e\left(\frac{39}{154}\right)\) | \(e\left(\frac{3}{308}\right)\) | \(e\left(\frac{57}{88}\right)\) | \(e\left(\frac{171}{308}\right)\) |
| \(\chi_{8021}(28,\cdot)\) | 8021.ea | 924 | yes | \(-1\) | \(1\) | \(e\left(\frac{461}{924}\right)\) | \(e\left(\frac{881}{924}\right)\) | \(e\left(\frac{461}{462}\right)\) | \(e\left(\frac{125}{154}\right)\) | \(e\left(\frac{19}{42}\right)\) | \(e\left(\frac{901}{924}\right)\) | \(e\left(\frac{153}{308}\right)\) | \(e\left(\frac{419}{462}\right)\) | \(e\left(\frac{41}{132}\right)\) | \(e\left(\frac{257}{924}\right)\) |
| \(\chi_{8021}(29,\cdot)\) | 8021.dh | 264 | yes | \(-1\) | \(1\) | \(e\left(\frac{7}{66}\right)\) | \(e\left(\frac{181}{264}\right)\) | \(e\left(\frac{7}{33}\right)\) | \(e\left(\frac{7}{88}\right)\) | \(e\left(\frac{19}{24}\right)\) | \(e\left(\frac{91}{132}\right)\) | \(e\left(\frac{7}{22}\right)\) | \(e\left(\frac{49}{132}\right)\) | \(e\left(\frac{49}{264}\right)\) | \(e\left(\frac{65}{132}\right)\) |
| \(\chi_{8021}(30,\cdot)\) | 8021.ed | 924 | yes | \(1\) | \(1\) | \(e\left(\frac{125}{462}\right)\) | \(e\left(\frac{817}{924}\right)\) | \(e\left(\frac{125}{231}\right)\) | \(e\left(\frac{101}{308}\right)\) | \(e\left(\frac{13}{84}\right)\) | \(e\left(\frac{167}{231}\right)\) | \(e\left(\frac{125}{154}\right)\) | \(e\left(\frac{355}{462}\right)\) | \(e\left(\frac{79}{132}\right)\) | \(e\left(\frac{223}{231}\right)\) |
| \(\chi_{8021}(31,\cdot)\) | 8021.bw | 44 | yes | \(-1\) | \(1\) | \(e\left(\frac{29}{44}\right)\) | \(e\left(\frac{1}{11}\right)\) | \(e\left(\frac{7}{22}\right)\) | \(e\left(\frac{41}{44}\right)\) | \(-i\) | \(e\left(\frac{7}{44}\right)\) | \(e\left(\frac{43}{44}\right)\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{13}{22}\right)\) | \(e\left(\frac{27}{44}\right)\) |
| \(\chi_{8021}(32,\cdot)\) | 8021.ec | 924 | yes | \(-1\) | \(1\) | \(e\left(\frac{277}{924}\right)\) | \(e\left(\frac{65}{462}\right)\) | \(e\left(\frac{277}{462}\right)\) | \(e\left(\frac{281}{308}\right)\) | \(e\left(\frac{37}{84}\right)\) | \(e\left(\frac{827}{924}\right)\) | \(e\left(\frac{277}{308}\right)\) | \(e\left(\frac{65}{231}\right)\) | \(e\left(\frac{7}{33}\right)\) | \(e\left(\frac{883}{924}\right)\) |
| \(\chi_{8021}(33,\cdot)\) | 8021.ef | 1848 | yes | \(1\) | \(1\) | \(e\left(\frac{757}{924}\right)\) | \(e\left(\frac{1577}{1848}\right)\) | \(e\left(\frac{295}{462}\right)\) | \(e\left(\frac{109}{616}\right)\) | \(e\left(\frac{113}{168}\right)\) | \(e\left(\frac{137}{231}\right)\) | \(e\left(\frac{141}{308}\right)\) | \(e\left(\frac{653}{924}\right)\) | \(e\left(\frac{263}{264}\right)\) | \(e\left(\frac{323}{462}\right)\) |
| \(\chi_{8021}(34,\cdot)\) | 8021.dw | 616 | yes | \(1\) | \(1\) | \(e\left(\frac{159}{308}\right)\) | \(e\left(\frac{199}{616}\right)\) | \(e\left(\frac{5}{154}\right)\) | \(e\left(\frac{585}{616}\right)\) | \(e\left(\frac{47}{56}\right)\) | \(e\left(\frac{48}{77}\right)\) | \(e\left(\frac{169}{308}\right)\) | \(e\left(\frac{199}{308}\right)\) | \(e\left(\frac{41}{88}\right)\) | \(e\left(\frac{89}{154}\right)\) |