sage: H = DirichletGroup(2070)
pari: g = idealstar(,2070,2)
Character group
sage: G.order()
pari: g.no
| ||
Order | = | 528 |
sage: H.invariants()
pari: g.cyc
| ||
Structure | = | \(C_{2}\times C_{2}\times C_{132}\) |
sage: H.gens()
pari: g.gen
| ||
Generators | = | $\chi_{2070}(461,\cdot)$, $\chi_{2070}(1657,\cdot)$, $\chi_{2070}(1891,\cdot)$ |
First 32 of 528 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 | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{2070}(1,\cdot)\) | 2070.a | 1 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
\(\chi_{2070}(7,\cdot)\) | 2070.bs | 132 | no | \(1\) | \(1\) | \(e\left(\frac{43}{132}\right)\) | \(e\left(\frac{29}{66}\right)\) | \(e\left(\frac{23}{132}\right)\) | \(e\left(\frac{13}{44}\right)\) | \(e\left(\frac{5}{11}\right)\) | \(e\left(\frac{47}{66}\right)\) | \(e\left(\frac{17}{33}\right)\) | \(e\left(\frac{17}{44}\right)\) | \(e\left(\frac{23}{33}\right)\) | \(e\left(\frac{97}{132}\right)\) |
\(\chi_{2070}(11,\cdot)\) | 2070.bo | 66 | no | \(1\) | \(1\) | \(e\left(\frac{29}{66}\right)\) | \(e\left(\frac{28}{33}\right)\) | \(e\left(\frac{2}{33}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{3}{22}\right)\) | \(e\left(\frac{35}{66}\right)\) | \(e\left(\frac{26}{33}\right)\) | \(e\left(\frac{13}{22}\right)\) | \(e\left(\frac{49}{66}\right)\) | \(e\left(\frac{47}{66}\right)\) |
\(\chi_{2070}(13,\cdot)\) | 2070.bv | 132 | no | \(-1\) | \(1\) | \(e\left(\frac{23}{132}\right)\) | \(e\left(\frac{2}{33}\right)\) | \(e\left(\frac{109}{132}\right)\) | \(e\left(\frac{9}{44}\right)\) | \(e\left(\frac{1}{22}\right)\) | \(e\left(\frac{19}{66}\right)\) | \(e\left(\frac{16}{33}\right)\) | \(e\left(\frac{5}{44}\right)\) | \(e\left(\frac{10}{33}\right)\) | \(e\left(\frac{101}{132}\right)\) |
\(\chi_{2070}(17,\cdot)\) | 2070.bh | 44 | no | \(-1\) | \(1\) | \(e\left(\frac{13}{44}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{9}{44}\right)\) | \(e\left(\frac{43}{44}\right)\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{41}{44}\right)\) | \(e\left(\frac{7}{22}\right)\) | \(e\left(\frac{15}{44}\right)\) |
\(\chi_{2070}(19,\cdot)\) | 2070.bb | 22 | no | \(-1\) | \(1\) | \(e\left(\frac{5}{11}\right)\) | \(e\left(\frac{3}{22}\right)\) | \(e\left(\frac{1}{22}\right)\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{5}{22}\right)\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{1}{11}\right)\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{10}{11}\right)\) |
\(\chi_{2070}(29,\cdot)\) | 2070.bl | 66 | no | \(-1\) | \(1\) | \(e\left(\frac{47}{66}\right)\) | \(e\left(\frac{35}{66}\right)\) | \(e\left(\frac{19}{66}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{59}{66}\right)\) | \(e\left(\frac{8}{33}\right)\) | \(e\left(\frac{15}{22}\right)\) | \(e\left(\frac{43}{66}\right)\) | \(e\left(\frac{17}{66}\right)\) |
\(\chi_{2070}(31,\cdot)\) | 2070.bg | 33 | no | \(1\) | \(1\) | \(e\left(\frac{17}{33}\right)\) | \(e\left(\frac{26}{33}\right)\) | \(e\left(\frac{16}{33}\right)\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{1}{11}\right)\) | \(e\left(\frac{8}{33}\right)\) | \(e\left(\frac{10}{33}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{31}{33}\right)\) | \(e\left(\frac{23}{33}\right)\) |
\(\chi_{2070}(37,\cdot)\) | 2070.bj | 44 | no | \(1\) | \(1\) | \(e\left(\frac{17}{44}\right)\) | \(e\left(\frac{13}{22}\right)\) | \(e\left(\frac{5}{44}\right)\) | \(e\left(\frac{41}{44}\right)\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{15}{22}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{13}{44}\right)\) | \(e\left(\frac{5}{11}\right)\) | \(e\left(\frac{23}{44}\right)\) |
\(\chi_{2070}(41,\cdot)\) | 2070.bq | 66 | no | \(-1\) | \(1\) | \(e\left(\frac{23}{33}\right)\) | \(e\left(\frac{49}{66}\right)\) | \(e\left(\frac{10}{33}\right)\) | \(e\left(\frac{7}{22}\right)\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{43}{66}\right)\) | \(e\left(\frac{31}{33}\right)\) | \(e\left(\frac{5}{11}\right)\) | \(e\left(\frac{47}{66}\right)\) | \(e\left(\frac{2}{33}\right)\) |
\(\chi_{2070}(43,\cdot)\) | 2070.bs | 132 | no | \(1\) | \(1\) | \(e\left(\frac{97}{132}\right)\) | \(e\left(\frac{47}{66}\right)\) | \(e\left(\frac{101}{132}\right)\) | \(e\left(\frac{15}{44}\right)\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{17}{66}\right)\) | \(e\left(\frac{23}{33}\right)\) | \(e\left(\frac{23}{44}\right)\) | \(e\left(\frac{2}{33}\right)\) | \(e\left(\frac{7}{132}\right)\) |
\(\chi_{2070}(47,\cdot)\) | 2070.x | 12 | no | \(1\) | \(1\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(-i\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(i\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{5}{12}\right)\) |
\(\chi_{2070}(49,\cdot)\) | 2070.bn | 66 | no | \(1\) | \(1\) | \(e\left(\frac{43}{66}\right)\) | \(e\left(\frac{29}{33}\right)\) | \(e\left(\frac{23}{66}\right)\) | \(e\left(\frac{13}{22}\right)\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{14}{33}\right)\) | \(e\left(\frac{1}{33}\right)\) | \(e\left(\frac{17}{22}\right)\) | \(e\left(\frac{13}{33}\right)\) | \(e\left(\frac{31}{66}\right)\) |
\(\chi_{2070}(53,\cdot)\) | 2070.bh | 44 | no | \(-1\) | \(1\) | \(e\left(\frac{7}{44}\right)\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{15}{44}\right)\) | \(e\left(\frac{13}{44}\right)\) | \(e\left(\frac{5}{11}\right)\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{39}{44}\right)\) | \(e\left(\frac{19}{22}\right)\) | \(e\left(\frac{25}{44}\right)\) |
\(\chi_{2070}(59,\cdot)\) | 2070.bl | 66 | no | \(-1\) | \(1\) | \(e\left(\frac{61}{66}\right)\) | \(e\left(\frac{37}{66}\right)\) | \(e\left(\frac{5}{66}\right)\) | \(e\left(\frac{5}{11}\right)\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{19}{66}\right)\) | \(e\left(\frac{16}{33}\right)\) | \(e\left(\frac{19}{22}\right)\) | \(e\left(\frac{53}{66}\right)\) | \(e\left(\frac{1}{66}\right)\) |
\(\chi_{2070}(61,\cdot)\) | 2070.bm | 66 | no | \(-1\) | \(1\) | \(e\left(\frac{23}{66}\right)\) | \(e\left(\frac{41}{66}\right)\) | \(e\left(\frac{5}{33}\right)\) | \(e\left(\frac{9}{22}\right)\) | \(e\left(\frac{13}{22}\right)\) | \(e\left(\frac{19}{33}\right)\) | \(e\left(\frac{32}{33}\right)\) | \(e\left(\frac{5}{22}\right)\) | \(e\left(\frac{20}{33}\right)\) | \(e\left(\frac{35}{66}\right)\) |
\(\chi_{2070}(67,\cdot)\) | 2070.bs | 132 | no | \(1\) | \(1\) | \(e\left(\frac{107}{132}\right)\) | \(e\left(\frac{43}{66}\right)\) | \(e\left(\frac{91}{132}\right)\) | \(e\left(\frac{17}{44}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{31}{66}\right)\) | \(e\left(\frac{7}{33}\right)\) | \(e\left(\frac{29}{44}\right)\) | \(e\left(\frac{25}{33}\right)\) | \(e\left(\frac{5}{132}\right)\) |
\(\chi_{2070}(71,\cdot)\) | 2070.ba | 22 | no | \(-1\) | \(1\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{7}{22}\right)\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{3}{22}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{3}{22}\right)\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{13}{22}\right)\) | \(e\left(\frac{5}{11}\right)\) |
\(\chi_{2070}(73,\cdot)\) | 2070.bi | 44 | no | \(-1\) | \(1\) | \(e\left(\frac{9}{44}\right)\) | \(e\left(\frac{7}{11}\right)\) | \(e\left(\frac{35}{44}\right)\) | \(e\left(\frac{1}{44}\right)\) | \(e\left(\frac{5}{22}\right)\) | \(e\left(\frac{17}{22}\right)\) | \(e\left(\frac{1}{11}\right)\) | \(e\left(\frac{25}{44}\right)\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{7}{44}\right)\) |
\(\chi_{2070}(77,\cdot)\) | 2070.bt | 132 | no | \(1\) | \(1\) | \(e\left(\frac{101}{132}\right)\) | \(e\left(\frac{19}{66}\right)\) | \(e\left(\frac{31}{132}\right)\) | \(e\left(\frac{29}{44}\right)\) | \(e\left(\frac{13}{22}\right)\) | \(e\left(\frac{8}{33}\right)\) | \(e\left(\frac{10}{33}\right)\) | \(e\left(\frac{43}{44}\right)\) | \(e\left(\frac{29}{66}\right)\) | \(e\left(\frac{59}{132}\right)\) |
\(\chi_{2070}(79,\cdot)\) | 2070.bp | 66 | no | \(-1\) | \(1\) | \(e\left(\frac{25}{33}\right)\) | \(e\left(\frac{59}{66}\right)\) | \(e\left(\frac{49}{66}\right)\) | \(e\left(\frac{5}{11}\right)\) | \(e\left(\frac{1}{22}\right)\) | \(e\left(\frac{4}{33}\right)\) | \(e\left(\frac{5}{33}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{32}{33}\right)\) | \(e\left(\frac{28}{33}\right)\) |
\(\chi_{2070}(83,\cdot)\) | 2070.bu | 132 | no | \(-1\) | \(1\) | \(e\left(\frac{73}{132}\right)\) | \(e\left(\frac{25}{33}\right)\) | \(e\left(\frac{125}{132}\right)\) | \(e\left(\frac{41}{44}\right)\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{28}{33}\right)\) | \(e\left(\frac{2}{33}\right)\) | \(e\left(\frac{35}{44}\right)\) | \(e\left(\frac{19}{66}\right)\) | \(e\left(\frac{91}{132}\right)\) |
\(\chi_{2070}(89,\cdot)\) | 2070.z | 22 | no | \(1\) | \(1\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{15}{22}\right)\) | \(e\left(\frac{13}{22}\right)\) | \(e\left(\frac{9}{22}\right)\) | \(e\left(\frac{13}{22}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{5}{22}\right)\) | \(e\left(\frac{7}{11}\right)\) |
\(\chi_{2070}(91,\cdot)\) | 2070.c | 2 | no | \(-1\) | \(1\) | \(-1\) | \(-1\) | \(1\) | \(-1\) | \(-1\) | \(1\) | \(1\) | \(-1\) | \(1\) | \(-1\) |
\(\chi_{2070}(97,\cdot)\) | 2070.bs | 132 | no | \(1\) | \(1\) | \(e\left(\frac{103}{132}\right)\) | \(e\left(\frac{5}{66}\right)\) | \(e\left(\frac{95}{132}\right)\) | \(e\left(\frac{25}{44}\right)\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{65}{66}\right)\) | \(e\left(\frac{20}{33}\right)\) | \(e\left(\frac{9}{44}\right)\) | \(e\left(\frac{29}{33}\right)\) | \(e\left(\frac{85}{132}\right)\) |
\(\chi_{2070}(101,\cdot)\) | 2070.bq | 66 | no | \(-1\) | \(1\) | \(e\left(\frac{10}{33}\right)\) | \(e\left(\frac{17}{66}\right)\) | \(e\left(\frac{23}{33}\right)\) | \(e\left(\frac{15}{22}\right)\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{23}{66}\right)\) | \(e\left(\frac{2}{33}\right)\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{19}{66}\right)\) | \(e\left(\frac{31}{33}\right)\) |
\(\chi_{2070}(103,\cdot)\) | 2070.bs | 132 | no | \(1\) | \(1\) | \(e\left(\frac{113}{132}\right)\) | \(e\left(\frac{1}{66}\right)\) | \(e\left(\frac{85}{132}\right)\) | \(e\left(\frac{27}{44}\right)\) | \(e\left(\frac{7}{11}\right)\) | \(e\left(\frac{13}{66}\right)\) | \(e\left(\frac{4}{33}\right)\) | \(e\left(\frac{15}{44}\right)\) | \(e\left(\frac{19}{33}\right)\) | \(e\left(\frac{83}{132}\right)\) |
\(\chi_{2070}(107,\cdot)\) | 2070.bh | 44 | no | \(-1\) | \(1\) | \(e\left(\frac{41}{44}\right)\) | \(e\left(\frac{5}{11}\right)\) | \(e\left(\frac{25}{44}\right)\) | \(e\left(\frac{7}{44}\right)\) | \(e\left(\frac{1}{11}\right)\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{7}{11}\right)\) | \(e\left(\frac{21}{44}\right)\) | \(e\left(\frac{17}{22}\right)\) | \(e\left(\frac{27}{44}\right)\) |
\(\chi_{2070}(109,\cdot)\) | 2070.bb | 22 | no | \(-1\) | \(1\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{19}{22}\right)\) | \(e\left(\frac{21}{22}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{17}{22}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{1}{11}\right)\) |
\(\chi_{2070}(113,\cdot)\) | 2070.bu | 132 | no | \(-1\) | \(1\) | \(e\left(\frac{41}{132}\right)\) | \(e\left(\frac{5}{33}\right)\) | \(e\left(\frac{25}{132}\right)\) | \(e\left(\frac{17}{44}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{32}{33}\right)\) | \(e\left(\frac{7}{33}\right)\) | \(e\left(\frac{7}{44}\right)\) | \(e\left(\frac{17}{66}\right)\) | \(e\left(\frac{71}{132}\right)\) |
\(\chi_{2070}(119,\cdot)\) | 2070.bl | 66 | no | \(-1\) | \(1\) | \(e\left(\frac{41}{66}\right)\) | \(e\left(\frac{53}{66}\right)\) | \(e\left(\frac{25}{66}\right)\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{29}{66}\right)\) | \(e\left(\frac{14}{33}\right)\) | \(e\left(\frac{7}{22}\right)\) | \(e\left(\frac{1}{66}\right)\) | \(e\left(\frac{5}{66}\right)\) |
\(\chi_{2070}(121,\cdot)\) | 2070.bg | 33 | no | \(1\) | \(1\) | \(e\left(\frac{29}{33}\right)\) | \(e\left(\frac{23}{33}\right)\) | \(e\left(\frac{4}{33}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{2}{33}\right)\) | \(e\left(\frac{19}{33}\right)\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{16}{33}\right)\) | \(e\left(\frac{14}{33}\right)\) |