sage: H = DirichletGroup(3864)
pari: g = idealstar(,3864,2)
Character group
sage: G.order()
pari: g.no
| ||
Order | = | 1056 |
sage: H.invariants()
pari: g.cyc
| ||
Structure | = | \(C_{2}\times C_{2}\times C_{2}\times C_{2}\times C_{66}\) |
sage: H.gens()
pari: g.gen
| ||
Generators | = | $\chi_{3864}(967,\cdot)$, $\chi_{3864}(1933,\cdot)$, $\chi_{3864}(1289,\cdot)$, $\chi_{3864}(2761,\cdot)$, $\chi_{3864}(2857,\cdot)$ |
First 32 of 1056 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 | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(25\) | \(29\) | \(31\) | \(37\) | \(41\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{3864}(1,\cdot)\) | 3864.a | 1 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
\(\chi_{3864}(5,\cdot)\) | 3864.ej | 66 | yes | \(-1\) | \(1\) | \(e\left(\frac{7}{33}\right)\) | \(e\left(\frac{49}{66}\right)\) | \(e\left(\frac{7}{11}\right)\) | \(e\left(\frac{43}{66}\right)\) | \(e\left(\frac{23}{66}\right)\) | \(e\left(\frac{14}{33}\right)\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{7}{66}\right)\) | \(e\left(\frac{4}{33}\right)\) | \(e\left(\frac{6}{11}\right)\) |
\(\chi_{3864}(11,\cdot)\) | 3864.eh | 66 | yes | \(-1\) | \(1\) | \(e\left(\frac{49}{66}\right)\) | \(e\left(\frac{28}{33}\right)\) | \(e\left(\frac{5}{22}\right)\) | \(e\left(\frac{1}{33}\right)\) | \(e\left(\frac{31}{66}\right)\) | \(e\left(\frac{16}{33}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{41}{66}\right)\) | \(e\left(\frac{14}{33}\right)\) | \(e\left(\frac{9}{22}\right)\) |
\(\chi_{3864}(13,\cdot)\) | 3864.cw | 22 | no | \(-1\) | \(1\) | \(e\left(\frac{7}{11}\right)\) | \(e\left(\frac{5}{22}\right)\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{21}{22}\right)\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{21}{22}\right)\) | \(e\left(\frac{7}{22}\right)\) | \(e\left(\frac{19}{22}\right)\) | \(e\left(\frac{3}{22}\right)\) |
\(\chi_{3864}(17,\cdot)\) | 3864.eg | 66 | no | \(-1\) | \(1\) | \(e\left(\frac{43}{66}\right)\) | \(e\left(\frac{1}{33}\right)\) | \(e\left(\frac{21}{22}\right)\) | \(e\left(\frac{59}{66}\right)\) | \(e\left(\frac{20}{33}\right)\) | \(e\left(\frac{10}{33}\right)\) | \(e\left(\frac{5}{22}\right)\) | \(e\left(\frac{5}{66}\right)\) | \(e\left(\frac{1}{66}\right)\) | \(e\left(\frac{9}{11}\right)\) |
\(\chi_{3864}(19,\cdot)\) | 3864.dw | 66 | no | \(-1\) | \(1\) | \(e\left(\frac{23}{66}\right)\) | \(e\left(\frac{31}{66}\right)\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{20}{33}\right)\) | \(e\left(\frac{13}{33}\right)\) | \(e\left(\frac{23}{33}\right)\) | \(e\left(\frac{17}{22}\right)\) | \(e\left(\frac{14}{33}\right)\) | \(e\left(\frac{16}{33}\right)\) | \(e\left(\frac{15}{22}\right)\) |
\(\chi_{3864}(25,\cdot)\) | 3864.ds | 33 | no | \(1\) | \(1\) | \(e\left(\frac{14}{33}\right)\) | \(e\left(\frac{16}{33}\right)\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{10}{33}\right)\) | \(e\left(\frac{23}{33}\right)\) | \(e\left(\frac{28}{33}\right)\) | \(e\left(\frac{7}{11}\right)\) | \(e\left(\frac{7}{33}\right)\) | \(e\left(\frac{8}{33}\right)\) | \(e\left(\frac{1}{11}\right)\) |
\(\chi_{3864}(29,\cdot)\) | 3864.ct | 22 | no | \(-1\) | \(1\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{21}{22}\right)\) | \(e\left(\frac{5}{22}\right)\) | \(e\left(\frac{17}{22}\right)\) | \(e\left(\frac{7}{11}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{15}{22}\right)\) | \(e\left(\frac{7}{22}\right)\) |
\(\chi_{3864}(31,\cdot)\) | 3864.dy | 66 | no | \(1\) | \(1\) | \(e\left(\frac{7}{66}\right)\) | \(e\left(\frac{41}{66}\right)\) | \(e\left(\frac{7}{22}\right)\) | \(e\left(\frac{5}{66}\right)\) | \(e\left(\frac{14}{33}\right)\) | \(e\left(\frac{7}{33}\right)\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{10}{33}\right)\) | \(e\left(\frac{2}{33}\right)\) | \(e\left(\frac{17}{22}\right)\) |
\(\chi_{3864}(37,\cdot)\) | 3864.ev | 66 | no | \(-1\) | \(1\) | \(e\left(\frac{4}{33}\right)\) | \(e\left(\frac{14}{33}\right)\) | \(e\left(\frac{19}{22}\right)\) | \(e\left(\frac{1}{66}\right)\) | \(e\left(\frac{16}{33}\right)\) | \(e\left(\frac{8}{33}\right)\) | \(e\left(\frac{15}{22}\right)\) | \(e\left(\frac{2}{33}\right)\) | \(e\left(\frac{7}{33}\right)\) | \(e\left(\frac{5}{11}\right)\) |
\(\chi_{3864}(41,\cdot)\) | 3864.cz | 22 | no | \(1\) | \(1\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{9}{22}\right)\) | \(e\left(\frac{3}{22}\right)\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{15}{22}\right)\) | \(e\left(\frac{1}{11}\right)\) | \(e\left(\frac{7}{22}\right)\) | \(e\left(\frac{17}{22}\right)\) | \(e\left(\frac{5}{11}\right)\) | \(e\left(\frac{6}{11}\right)\) |
\(\chi_{3864}(43,\cdot)\) | 3864.db | 22 | no | \(1\) | \(1\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{1}{22}\right)\) | \(e\left(\frac{15}{22}\right)\) | \(e\left(\frac{13}{22}\right)\) | \(e\left(\frac{9}{22}\right)\) | \(e\left(\frac{5}{11}\right)\) | \(e\left(\frac{13}{22}\right)\) | \(e\left(\frac{19}{22}\right)\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{8}{11}\right)\) |
\(\chi_{3864}(47,\cdot)\) | 3864.bh | 6 | no | \(-1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
\(\chi_{3864}(53,\cdot)\) | 3864.ea | 66 | yes | \(1\) | \(1\) | \(e\left(\frac{13}{66}\right)\) | \(e\left(\frac{29}{66}\right)\) | \(e\left(\frac{13}{22}\right)\) | \(e\left(\frac{7}{33}\right)\) | \(e\left(\frac{26}{33}\right)\) | \(e\left(\frac{13}{33}\right)\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{28}{33}\right)\) | \(e\left(\frac{32}{33}\right)\) | \(e\left(\frac{19}{22}\right)\) |
\(\chi_{3864}(55,\cdot)\) | 3864.dq | 22 | no | \(1\) | \(1\) | \(e\left(\frac{21}{22}\right)\) | \(e\left(\frac{13}{22}\right)\) | \(e\left(\frac{19}{22}\right)\) | \(e\left(\frac{15}{22}\right)\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{21}{22}\right)\) |
\(\chi_{3864}(59,\cdot)\) | 3864.dv | 66 | yes | \(-1\) | \(1\) | \(e\left(\frac{31}{66}\right)\) | \(e\left(\frac{59}{66}\right)\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{4}{33}\right)\) | \(e\left(\frac{25}{66}\right)\) | \(e\left(\frac{31}{33}\right)\) | \(e\left(\frac{5}{11}\right)\) | \(e\left(\frac{16}{33}\right)\) | \(e\left(\frac{13}{66}\right)\) | \(e\left(\frac{7}{11}\right)\) |
\(\chi_{3864}(61,\cdot)\) | 3864.ed | 66 | no | \(1\) | \(1\) | \(e\left(\frac{29}{66}\right)\) | \(e\left(\frac{26}{33}\right)\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{8}{33}\right)\) | \(e\left(\frac{17}{66}\right)\) | \(e\left(\frac{29}{33}\right)\) | \(e\left(\frac{9}{22}\right)\) | \(e\left(\frac{31}{66}\right)\) | \(e\left(\frac{13}{33}\right)\) | \(e\left(\frac{17}{22}\right)\) |
\(\chi_{3864}(65,\cdot)\) | 3864.et | 66 | no | \(1\) | \(1\) | \(e\left(\frac{28}{33}\right)\) | \(e\left(\frac{32}{33}\right)\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{20}{33}\right)\) | \(e\left(\frac{59}{66}\right)\) | \(e\left(\frac{23}{33}\right)\) | \(e\left(\frac{17}{22}\right)\) | \(e\left(\frac{14}{33}\right)\) | \(e\left(\frac{65}{66}\right)\) | \(e\left(\frac{15}{22}\right)\) |
\(\chi_{3864}(67,\cdot)\) | 3864.en | 66 | no | \(1\) | \(1\) | \(e\left(\frac{14}{33}\right)\) | \(e\left(\frac{65}{66}\right)\) | \(e\left(\frac{17}{22}\right)\) | \(e\left(\frac{53}{66}\right)\) | \(e\left(\frac{13}{66}\right)\) | \(e\left(\frac{28}{33}\right)\) | \(e\left(\frac{3}{22}\right)\) | \(e\left(\frac{47}{66}\right)\) | \(e\left(\frac{8}{33}\right)\) | \(e\left(\frac{1}{11}\right)\) |
\(\chi_{3864}(71,\cdot)\) | 3864.df | 22 | no | \(1\) | \(1\) | \(e\left(\frac{13}{22}\right)\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{3}{22}\right)\) | \(e\left(\frac{19}{22}\right)\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{3}{22}\right)\) | \(e\left(\frac{1}{22}\right)\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{13}{22}\right)\) |
\(\chi_{3864}(73,\cdot)\) | 3864.ef | 66 | no | \(-1\) | \(1\) | \(e\left(\frac{1}{66}\right)\) | \(e\left(\frac{10}{33}\right)\) | \(e\left(\frac{1}{22}\right)\) | \(e\left(\frac{29}{66}\right)\) | \(e\left(\frac{37}{66}\right)\) | \(e\left(\frac{1}{33}\right)\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{17}{66}\right)\) | \(e\left(\frac{5}{33}\right)\) | \(e\left(\frac{15}{22}\right)\) |
\(\chi_{3864}(79,\cdot)\) | 3864.ec | 66 | no | \(1\) | \(1\) | \(e\left(\frac{53}{66}\right)\) | \(e\left(\frac{2}{33}\right)\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{19}{66}\right)\) | \(e\left(\frac{7}{33}\right)\) | \(e\left(\frac{20}{33}\right)\) | \(e\left(\frac{5}{11}\right)\) | \(e\left(\frac{43}{66}\right)\) | \(e\left(\frac{35}{66}\right)\) | \(e\left(\frac{7}{11}\right)\) |
\(\chi_{3864}(83,\cdot)\) | 3864.co | 22 | yes | \(1\) | \(1\) | \(e\left(\frac{5}{11}\right)\) | \(e\left(\frac{1}{11}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{15}{22}\right)\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{5}{11}\right)\) |
\(\chi_{3864}(85,\cdot)\) | 3864.dp | 22 | no | \(1\) | \(1\) | \(e\left(\frac{19}{22}\right)\) | \(e\left(\frac{17}{22}\right)\) | \(e\left(\frac{13}{22}\right)\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{21}{22}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{1}{22}\right)\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{3}{22}\right)\) | \(e\left(\frac{4}{11}\right)\) |
\(\chi_{3864}(89,\cdot)\) | 3864.eg | 66 | no | \(-1\) | \(1\) | \(e\left(\frac{59}{66}\right)\) | \(e\left(\frac{29}{33}\right)\) | \(e\left(\frac{15}{22}\right)\) | \(e\left(\frac{61}{66}\right)\) | \(e\left(\frac{19}{33}\right)\) | \(e\left(\frac{26}{33}\right)\) | \(e\left(\frac{13}{22}\right)\) | \(e\left(\frac{13}{66}\right)\) | \(e\left(\frac{29}{66}\right)\) | \(e\left(\frac{8}{11}\right)\) |
\(\chi_{3864}(95,\cdot)\) | 3864.eb | 66 | no | \(1\) | \(1\) | \(e\left(\frac{37}{66}\right)\) | \(e\left(\frac{7}{33}\right)\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{17}{66}\right)\) | \(e\left(\frac{49}{66}\right)\) | \(e\left(\frac{4}{33}\right)\) | \(e\left(\frac{13}{22}\right)\) | \(e\left(\frac{35}{66}\right)\) | \(e\left(\frac{20}{33}\right)\) | \(e\left(\frac{5}{22}\right)\) |
\(\chi_{3864}(97,\cdot)\) | 3864.cy | 22 | no | \(1\) | \(1\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{9}{22}\right)\) | \(e\left(\frac{3}{22}\right)\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{1}{11}\right)\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{17}{22}\right)\) | \(e\left(\frac{21}{22}\right)\) | \(e\left(\frac{1}{22}\right)\) |
\(\chi_{3864}(101,\cdot)\) | 3864.ee | 66 | yes | \(1\) | \(1\) | \(e\left(\frac{19}{66}\right)\) | \(e\left(\frac{25}{33}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{28}{33}\right)\) | \(e\left(\frac{5}{33}\right)\) | \(e\left(\frac{19}{33}\right)\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{59}{66}\right)\) | \(e\left(\frac{25}{66}\right)\) | \(e\left(\frac{5}{11}\right)\) |
\(\chi_{3864}(103,\cdot)\) | 3864.ew | 66 | no | \(-1\) | \(1\) | \(e\left(\frac{19}{33}\right)\) | \(e\left(\frac{17}{33}\right)\) | \(e\left(\frac{5}{22}\right)\) | \(e\left(\frac{23}{33}\right)\) | \(e\left(\frac{53}{66}\right)\) | \(e\left(\frac{5}{33}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{26}{33}\right)\) | \(e\left(\frac{17}{66}\right)\) | \(e\left(\frac{9}{22}\right)\) |
\(\chi_{3864}(107,\cdot)\) | 3864.eh | 66 | yes | \(-1\) | \(1\) | \(e\left(\frac{29}{66}\right)\) | \(e\left(\frac{26}{33}\right)\) | \(e\left(\frac{7}{22}\right)\) | \(e\left(\frac{8}{33}\right)\) | \(e\left(\frac{17}{66}\right)\) | \(e\left(\frac{29}{33}\right)\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{31}{66}\right)\) | \(e\left(\frac{13}{33}\right)\) | \(e\left(\frac{17}{22}\right)\) |
\(\chi_{3864}(109,\cdot)\) | 3864.ev | 66 | no | \(-1\) | \(1\) | \(e\left(\frac{5}{33}\right)\) | \(e\left(\frac{1}{33}\right)\) | \(e\left(\frac{21}{22}\right)\) | \(e\left(\frac{59}{66}\right)\) | \(e\left(\frac{20}{33}\right)\) | \(e\left(\frac{10}{33}\right)\) | \(e\left(\frac{5}{22}\right)\) | \(e\left(\frac{19}{33}\right)\) | \(e\left(\frac{17}{33}\right)\) | \(e\left(\frac{9}{11}\right)\) |
\(\chi_{3864}(113,\cdot)\) | 3864.cn | 22 | no | \(1\) | \(1\) | \(e\left(\frac{1}{11}\right)\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{7}{11}\right)\) | \(e\left(\frac{19}{22}\right)\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{3}{22}\right)\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{9}{22}\right)\) | \(e\left(\frac{13}{22}\right)\) |