sage: H = DirichletGroup(4598)
pari: g = idealstar(,4598,2)
Character group
| sage: G.order()
pari: g.no
| ||
| Order | = | 1980 |
| sage: H.invariants()
pari: g.cyc
| ||
| Structure | = | \(C_{2}\times C_{990}\) |
| sage: H.gens()
pari: g.gen
| ||
| Generators | = | $\chi_{4598}(3269,\cdot)$, $\chi_{4598}(3631,\cdot)$ |
First 32 of 1980 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 | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) | \(25\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{4598}(1,\cdot)\) | 4598.a | 1 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(\chi_{4598}(3,\cdot)\) | 4598.bg | 90 | no | \(-1\) | \(1\) | \(e\left(\frac{71}{90}\right)\) | \(e\left(\frac{34}{45}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{26}{45}\right)\) | \(e\left(\frac{37}{90}\right)\) | \(e\left(\frac{49}{90}\right)\) | \(e\left(\frac{19}{45}\right)\) | \(e\left(\frac{13}{18}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{23}{45}\right)\) |
| \(\chi_{4598}(5,\cdot)\) | 4598.bs | 495 | no | \(1\) | \(1\) | \(e\left(\frac{34}{45}\right)\) | \(e\left(\frac{2}{495}\right)\) | \(e\left(\frac{7}{165}\right)\) | \(e\left(\frac{23}{45}\right)\) | \(e\left(\frac{193}{495}\right)\) | \(e\left(\frac{376}{495}\right)\) | \(e\left(\frac{422}{495}\right)\) | \(e\left(\frac{79}{99}\right)\) | \(e\left(\frac{86}{99}\right)\) | \(e\left(\frac{4}{495}\right)\) |
| \(\chi_{4598}(7,\cdot)\) | 4598.br | 330 | no | \(-1\) | \(1\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{7}{165}\right)\) | \(e\left(\frac{49}{110}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{31}{330}\right)\) | \(e\left(\frac{161}{165}\right)\) | \(e\left(\frac{149}{330}\right)\) | \(e\left(\frac{25}{66}\right)\) | \(e\left(\frac{4}{33}\right)\) | \(e\left(\frac{14}{165}\right)\) |
| \(\chi_{4598}(9,\cdot)\) | 4598.z | 45 | no | \(1\) | \(1\) | \(e\left(\frac{26}{45}\right)\) | \(e\left(\frac{23}{45}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{7}{45}\right)\) | \(e\left(\frac{37}{45}\right)\) | \(e\left(\frac{4}{45}\right)\) | \(e\left(\frac{38}{45}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{1}{45}\right)\) |
| \(\chi_{4598}(13,\cdot)\) | 4598.bu | 990 | no | \(1\) | \(1\) | \(e\left(\frac{37}{90}\right)\) | \(e\left(\frac{193}{495}\right)\) | \(e\left(\frac{31}{330}\right)\) | \(e\left(\frac{37}{45}\right)\) | \(e\left(\frac{62}{495}\right)\) | \(e\left(\frac{793}{990}\right)\) | \(e\left(\frac{761}{990}\right)\) | \(e\left(\frac{50}{99}\right)\) | \(e\left(\frac{82}{99}\right)\) | \(e\left(\frac{386}{495}\right)\) |
| \(\chi_{4598}(15,\cdot)\) | 4598.bt | 990 | no | \(-1\) | \(1\) | \(e\left(\frac{49}{90}\right)\) | \(e\left(\frac{376}{495}\right)\) | \(e\left(\frac{161}{165}\right)\) | \(e\left(\frac{4}{45}\right)\) | \(e\left(\frac{793}{990}\right)\) | \(e\left(\frac{301}{990}\right)\) | \(e\left(\frac{136}{495}\right)\) | \(e\left(\frac{103}{198}\right)\) | \(e\left(\frac{31}{99}\right)\) | \(e\left(\frac{257}{495}\right)\) |
| \(\chi_{4598}(17,\cdot)\) | 4598.bv | 990 | no | \(-1\) | \(1\) | \(e\left(\frac{19}{45}\right)\) | \(e\left(\frac{422}{495}\right)\) | \(e\left(\frac{149}{330}\right)\) | \(e\left(\frac{38}{45}\right)\) | \(e\left(\frac{761}{990}\right)\) | \(e\left(\frac{136}{495}\right)\) | \(e\left(\frac{379}{990}\right)\) | \(e\left(\frac{173}{198}\right)\) | \(e\left(\frac{29}{99}\right)\) | \(e\left(\frac{349}{495}\right)\) |
| \(\chi_{4598}(21,\cdot)\) | 4598.bn | 198 | no | \(1\) | \(1\) | \(e\left(\frac{13}{18}\right)\) | \(e\left(\frac{79}{99}\right)\) | \(e\left(\frac{25}{66}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{50}{99}\right)\) | \(e\left(\frac{103}{198}\right)\) | \(e\left(\frac{173}{198}\right)\) | \(e\left(\frac{10}{99}\right)\) | \(e\left(\frac{56}{99}\right)\) | \(e\left(\frac{59}{99}\right)\) |
| \(\chi_{4598}(23,\cdot)\) | 4598.bh | 99 | no | \(1\) | \(1\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{86}{99}\right)\) | \(e\left(\frac{4}{33}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{82}{99}\right)\) | \(e\left(\frac{31}{99}\right)\) | \(e\left(\frac{29}{99}\right)\) | \(e\left(\frac{56}{99}\right)\) | \(e\left(\frac{76}{99}\right)\) | \(e\left(\frac{73}{99}\right)\) |
| \(\chi_{4598}(25,\cdot)\) | 4598.bs | 495 | no | \(1\) | \(1\) | \(e\left(\frac{23}{45}\right)\) | \(e\left(\frac{4}{495}\right)\) | \(e\left(\frac{14}{165}\right)\) | \(e\left(\frac{1}{45}\right)\) | \(e\left(\frac{386}{495}\right)\) | \(e\left(\frac{257}{495}\right)\) | \(e\left(\frac{349}{495}\right)\) | \(e\left(\frac{59}{99}\right)\) | \(e\left(\frac{73}{99}\right)\) | \(e\left(\frac{8}{495}\right)\) |
| \(\chi_{4598}(27,\cdot)\) | 4598.v | 30 | no | \(-1\) | \(1\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{8}{15}\right)\) |
| \(\chi_{4598}(29,\cdot)\) | 4598.bu | 990 | no | \(1\) | \(1\) | \(e\left(\frac{79}{90}\right)\) | \(e\left(\frac{271}{495}\right)\) | \(e\left(\frac{247}{330}\right)\) | \(e\left(\frac{34}{45}\right)\) | \(e\left(\frac{164}{495}\right)\) | \(e\left(\frac{421}{990}\right)\) | \(e\left(\frac{17}{990}\right)\) | \(e\left(\frac{62}{99}\right)\) | \(e\left(\frac{70}{99}\right)\) | \(e\left(\frac{47}{495}\right)\) |
| \(\chi_{4598}(31,\cdot)\) | 4598.bq | 330 | no | \(-1\) | \(1\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{31}{165}\right)\) | \(e\left(\frac{26}{55}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{43}{330}\right)\) | \(e\left(\frac{271}{330}\right)\) | \(e\left(\frac{106}{165}\right)\) | \(e\left(\frac{7}{66}\right)\) | \(e\left(\frac{13}{33}\right)\) | \(e\left(\frac{62}{165}\right)\) |
| \(\chi_{4598}(35,\cdot)\) | 4598.bv | 990 | no | \(-1\) | \(1\) | \(e\left(\frac{31}{45}\right)\) | \(e\left(\frac{23}{495}\right)\) | \(e\left(\frac{161}{330}\right)\) | \(e\left(\frac{17}{45}\right)\) | \(e\left(\frac{479}{990}\right)\) | \(e\left(\frac{364}{495}\right)\) | \(e\left(\frac{301}{990}\right)\) | \(e\left(\frac{35}{198}\right)\) | \(e\left(\frac{98}{99}\right)\) | \(e\left(\frac{46}{495}\right)\) |
| \(\chi_{4598}(37,\cdot)\) | 4598.bk | 110 | no | \(-1\) | \(1\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{14}{55}\right)\) | \(e\left(\frac{37}{55}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{7}{110}\right)\) | \(e\left(\frac{39}{110}\right)\) | \(e\left(\frac{39}{55}\right)\) | \(e\left(\frac{17}{22}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{28}{55}\right)\) |
| \(\chi_{4598}(39,\cdot)\) | 4598.bi | 110 | no | \(-1\) | \(1\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{8}{55}\right)\) | \(e\left(\frac{3}{110}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{59}{110}\right)\) | \(e\left(\frac{19}{55}\right)\) | \(e\left(\frac{21}{110}\right)\) | \(e\left(\frac{5}{22}\right)\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{16}{55}\right)\) |
| \(\chi_{4598}(41,\cdot)\) | 4598.bu | 990 | no | \(1\) | \(1\) | \(e\left(\frac{71}{90}\right)\) | \(e\left(\frac{14}{495}\right)\) | \(e\left(\frac{263}{330}\right)\) | \(e\left(\frac{26}{45}\right)\) | \(e\left(\frac{361}{495}\right)\) | \(e\left(\frac{809}{990}\right)\) | \(e\left(\frac{463}{990}\right)\) | \(e\left(\frac{58}{99}\right)\) | \(e\left(\frac{8}{99}\right)\) | \(e\left(\frac{28}{495}\right)\) |
| \(\chi_{4598}(43,\cdot)\) | 4598.bm | 198 | no | \(-1\) | \(1\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{4}{99}\right)\) | \(e\left(\frac{61}{66}\right)\) | \(e\left(\frac{1}{9}\right)\) | \(e\left(\frac{79}{198}\right)\) | \(e\left(\frac{59}{99}\right)\) | \(e\left(\frac{5}{198}\right)\) | \(e\left(\frac{95}{198}\right)\) | \(e\left(\frac{68}{99}\right)\) | \(e\left(\frac{8}{99}\right)\) |
| \(\chi_{4598}(45,\cdot)\) | 4598.y | 33 | no | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{17}{33}\right)\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{7}{33}\right)\) | \(e\left(\frac{28}{33}\right)\) | \(e\left(\frac{23}{33}\right)\) | \(e\left(\frac{8}{33}\right)\) | \(e\left(\frac{25}{33}\right)\) | \(e\left(\frac{1}{33}\right)\) |
| \(\chi_{4598}(47,\cdot)\) | 4598.bs | 495 | no | \(1\) | \(1\) | \(e\left(\frac{8}{45}\right)\) | \(e\left(\frac{19}{495}\right)\) | \(e\left(\frac{149}{165}\right)\) | \(e\left(\frac{16}{45}\right)\) | \(e\left(\frac{101}{495}\right)\) | \(e\left(\frac{107}{495}\right)\) | \(e\left(\frac{49}{495}\right)\) | \(e\left(\frac{8}{99}\right)\) | \(e\left(\frac{25}{99}\right)\) | \(e\left(\frac{38}{495}\right)\) |
| \(\chi_{4598}(49,\cdot)\) | 4598.bl | 165 | no | \(1\) | \(1\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{14}{165}\right)\) | \(e\left(\frac{49}{55}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{31}{165}\right)\) | \(e\left(\frac{157}{165}\right)\) | \(e\left(\frac{149}{165}\right)\) | \(e\left(\frac{25}{33}\right)\) | \(e\left(\frac{8}{33}\right)\) | \(e\left(\frac{28}{165}\right)\) |
| \(\chi_{4598}(51,\cdot)\) | 4598.bu | 990 | no | \(1\) | \(1\) | \(e\left(\frac{19}{90}\right)\) | \(e\left(\frac{301}{495}\right)\) | \(e\left(\frac{127}{330}\right)\) | \(e\left(\frac{19}{45}\right)\) | \(e\left(\frac{89}{495}\right)\) | \(e\left(\frac{811}{990}\right)\) | \(e\left(\frac{797}{990}\right)\) | \(e\left(\frac{59}{99}\right)\) | \(e\left(\frac{73}{99}\right)\) | \(e\left(\frac{107}{495}\right)\) |
| \(\chi_{4598}(53,\cdot)\) | 4598.bt | 990 | no | \(-1\) | \(1\) | \(e\left(\frac{67}{90}\right)\) | \(e\left(\frac{43}{495}\right)\) | \(e\left(\frac{68}{165}\right)\) | \(e\left(\frac{22}{45}\right)\) | \(e\left(\frac{379}{990}\right)\) | \(e\left(\frac{823}{990}\right)\) | \(e\left(\frac{163}{495}\right)\) | \(e\left(\frac{31}{198}\right)\) | \(e\left(\frac{67}{99}\right)\) | \(e\left(\frac{86}{495}\right)\) |
| \(\chi_{4598}(59,\cdot)\) | 4598.bt | 990 | no | \(-1\) | \(1\) | \(e\left(\frac{29}{90}\right)\) | \(e\left(\frac{206}{495}\right)\) | \(e\left(\frac{61}{165}\right)\) | \(e\left(\frac{29}{45}\right)\) | \(e\left(\frac{653}{990}\right)\) | \(e\left(\frac{731}{990}\right)\) | \(e\left(\frac{401}{495}\right)\) | \(e\left(\frac{137}{198}\right)\) | \(e\left(\frac{47}{99}\right)\) | \(e\left(\frac{412}{495}\right)\) |
| \(\chi_{4598}(61,\cdot)\) | 4598.bv | 990 | no | \(-1\) | \(1\) | \(e\left(\frac{29}{45}\right)\) | \(e\left(\frac{52}{495}\right)\) | \(e\left(\frac{199}{330}\right)\) | \(e\left(\frac{13}{45}\right)\) | \(e\left(\frac{631}{990}\right)\) | \(e\left(\frac{371}{495}\right)\) | \(e\left(\frac{659}{990}\right)\) | \(e\left(\frac{49}{198}\right)\) | \(e\left(\frac{58}{99}\right)\) | \(e\left(\frac{104}{495}\right)\) |
| \(\chi_{4598}(63,\cdot)\) | 4598.bv | 990 | no | \(-1\) | \(1\) | \(e\left(\frac{23}{45}\right)\) | \(e\left(\frac{274}{495}\right)\) | \(e\left(\frac{103}{330}\right)\) | \(e\left(\frac{1}{45}\right)\) | \(e\left(\frac{907}{990}\right)\) | \(e\left(\frac{32}{495}\right)\) | \(e\left(\frac{293}{990}\right)\) | \(e\left(\frac{163}{198}\right)\) | \(e\left(\frac{1}{99}\right)\) | \(e\left(\frac{53}{495}\right)\) |
| \(\chi_{4598}(65,\cdot)\) | 4598.bd | 66 | no | \(1\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{13}{33}\right)\) | \(e\left(\frac{3}{22}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{17}{33}\right)\) | \(e\left(\frac{37}{66}\right)\) | \(e\left(\frac{41}{66}\right)\) | \(e\left(\frac{10}{33}\right)\) | \(e\left(\frac{23}{33}\right)\) | \(e\left(\frac{26}{33}\right)\) |
| \(\chi_{4598}(67,\cdot)\) | 4598.bo | 198 | no | \(-1\) | \(1\) | \(e\left(\frac{5}{18}\right)\) | \(e\left(\frac{38}{99}\right)\) | \(e\left(\frac{1}{33}\right)\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{107}{198}\right)\) | \(e\left(\frac{131}{198}\right)\) | \(e\left(\frac{98}{99}\right)\) | \(e\left(\frac{61}{198}\right)\) | \(e\left(\frac{52}{99}\right)\) | \(e\left(\frac{76}{99}\right)\) |
| \(\chi_{4598}(69,\cdot)\) | 4598.bq | 330 | no | \(-1\) | \(1\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{103}{165}\right)\) | \(e\left(\frac{3}{55}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{79}{330}\right)\) | \(e\left(\frac{283}{330}\right)\) | \(e\left(\frac{118}{165}\right)\) | \(e\left(\frac{19}{66}\right)\) | \(e\left(\frac{7}{33}\right)\) | \(e\left(\frac{41}{165}\right)\) |
| \(\chi_{4598}(71,\cdot)\) | 4598.bt | 990 | no | \(-1\) | \(1\) | \(e\left(\frac{23}{90}\right)\) | \(e\left(\frac{227}{495}\right)\) | \(e\left(\frac{52}{165}\right)\) | \(e\left(\frac{23}{45}\right)\) | \(e\left(\frac{251}{990}\right)\) | \(e\left(\frac{707}{990}\right)\) | \(e\left(\frac{377}{495}\right)\) | \(e\left(\frac{113}{198}\right)\) | \(e\left(\frac{59}{99}\right)\) | \(e\left(\frac{454}{495}\right)\) |
| \(\chi_{4598}(73,\cdot)\) | 4598.bv | 990 | no | \(-1\) | \(1\) | \(e\left(\frac{22}{45}\right)\) | \(e\left(\frac{221}{495}\right)\) | \(e\left(\frac{227}{330}\right)\) | \(e\left(\frac{44}{45}\right)\) | \(e\left(\frac{83}{990}\right)\) | \(e\left(\frac{463}{495}\right)\) | \(e\left(\frac{697}{990}\right)\) | \(e\left(\frac{35}{198}\right)\) | \(e\left(\frac{98}{99}\right)\) | \(e\left(\frac{442}{495}\right)\) |