sage: H = DirichletGroup(368)
pari: g = idealstar(,368,2)
Character group
sage: G.order()
pari: g.no
| ||
Order | = | 176 |
sage: H.invariants()
pari: g.cyc
| ||
Structure | = | \(C_{2}\times C_{2}\times C_{44}\) |
sage: H.gens()
pari: g.gen
| ||
Generators | = | $\chi_{368}(47,\cdot)$, $\chi_{368}(277,\cdot)$, $\chi_{368}(97,\cdot)$ |
First 32 of 176 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 | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{368}(1,\cdot)\) | 368.a | 1 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
\(\chi_{368}(3,\cdot)\) | 368.u | 44 | yes | \(-1\) | \(1\) | \(e\left(\frac{17}{44}\right)\) | \(e\left(\frac{21}{44}\right)\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{17}{22}\right)\) | \(e\left(\frac{35}{44}\right)\) | \(e\left(\frac{19}{44}\right)\) | \(e\left(\frac{19}{22}\right)\) | \(e\left(\frac{1}{11}\right)\) | \(e\left(\frac{29}{44}\right)\) | \(e\left(\frac{9}{44}\right)\) |
\(\chi_{368}(5,\cdot)\) | 368.v | 44 | yes | \(-1\) | \(1\) | \(e\left(\frac{21}{44}\right)\) | \(e\left(\frac{13}{44}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{21}{22}\right)\) | \(e\left(\frac{29}{44}\right)\) | \(e\left(\frac{17}{44}\right)\) | \(e\left(\frac{17}{22}\right)\) | \(e\left(\frac{7}{22}\right)\) | \(e\left(\frac{19}{44}\right)\) | \(e\left(\frac{37}{44}\right)\) |
\(\chi_{368}(7,\cdot)\) | 368.n | 22 | no | \(1\) | \(1\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{7}{11}\right)\) | \(e\left(\frac{17}{22}\right)\) | \(e\left(\frac{13}{22}\right)\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{1}{22}\right)\) | \(e\left(\frac{21}{22}\right)\) | \(e\left(\frac{8}{11}\right)\) |
\(\chi_{368}(9,\cdot)\) | 368.t | 22 | no | \(1\) | \(1\) | \(e\left(\frac{17}{22}\right)\) | \(e\left(\frac{21}{22}\right)\) | \(e\left(\frac{7}{11}\right)\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{13}{22}\right)\) | \(e\left(\frac{19}{22}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{7}{22}\right)\) | \(e\left(\frac{9}{22}\right)\) |
\(\chi_{368}(11,\cdot)\) | 368.x | 44 | yes | \(1\) | \(1\) | \(e\left(\frac{35}{44}\right)\) | \(e\left(\frac{29}{44}\right)\) | \(e\left(\frac{17}{22}\right)\) | \(e\left(\frac{13}{22}\right)\) | \(e\left(\frac{19}{44}\right)\) | \(e\left(\frac{21}{44}\right)\) | \(e\left(\frac{5}{11}\right)\) | \(e\left(\frac{19}{22}\right)\) | \(e\left(\frac{17}{44}\right)\) | \(e\left(\frac{25}{44}\right)\) |
\(\chi_{368}(13,\cdot)\) | 368.w | 44 | yes | \(1\) | \(1\) | \(e\left(\frac{19}{44}\right)\) | \(e\left(\frac{17}{44}\right)\) | \(e\left(\frac{13}{22}\right)\) | \(e\left(\frac{19}{22}\right)\) | \(e\left(\frac{21}{44}\right)\) | \(e\left(\frac{7}{44}\right)\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{5}{11}\right)\) | \(e\left(\frac{35}{44}\right)\) | \(e\left(\frac{1}{44}\right)\) |
\(\chi_{368}(15,\cdot)\) | 368.s | 22 | no | \(1\) | \(1\) | \(e\left(\frac{19}{22}\right)\) | \(e\left(\frac{17}{22}\right)\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{5}{11}\right)\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{7}{11}\right)\) | \(e\left(\frac{9}{22}\right)\) | \(e\left(\frac{1}{11}\right)\) | \(e\left(\frac{1}{22}\right)\) |
\(\chi_{368}(17,\cdot)\) | 368.p | 22 | no | \(-1\) | \(1\) | \(e\left(\frac{1}{11}\right)\) | \(e\left(\frac{7}{22}\right)\) | \(e\left(\frac{1}{22}\right)\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{19}{22}\right)\) | \(e\left(\frac{5}{11}\right)\) | \(e\left(\frac{9}{22}\right)\) | \(e\left(\frac{5}{22}\right)\) | \(e\left(\frac{17}{22}\right)\) | \(e\left(\frac{3}{22}\right)\) |
\(\chi_{368}(19,\cdot)\) | 368.x | 44 | yes | \(1\) | \(1\) | \(e\left(\frac{29}{44}\right)\) | \(e\left(\frac{19}{44}\right)\) | \(e\left(\frac{21}{22}\right)\) | \(e\left(\frac{7}{22}\right)\) | \(e\left(\frac{17}{44}\right)\) | \(e\left(\frac{35}{44}\right)\) | \(e\left(\frac{1}{11}\right)\) | \(e\left(\frac{17}{22}\right)\) | \(e\left(\frac{43}{44}\right)\) | \(e\left(\frac{27}{44}\right)\) |
\(\chi_{368}(21,\cdot)\) | 368.v | 44 | yes | \(-1\) | \(1\) | \(e\left(\frac{9}{44}\right)\) | \(e\left(\frac{37}{44}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{9}{22}\right)\) | \(e\left(\frac{25}{44}\right)\) | \(e\left(\frac{1}{44}\right)\) | \(e\left(\frac{1}{22}\right)\) | \(e\left(\frac{3}{22}\right)\) | \(e\left(\frac{27}{44}\right)\) | \(e\left(\frac{41}{44}\right)\) |
\(\chi_{368}(25,\cdot)\) | 368.t | 22 | no | \(1\) | \(1\) | \(e\left(\frac{21}{22}\right)\) | \(e\left(\frac{13}{22}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{7}{22}\right)\) | \(e\left(\frac{17}{22}\right)\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{7}{11}\right)\) | \(e\left(\frac{19}{22}\right)\) | \(e\left(\frac{15}{22}\right)\) |
\(\chi_{368}(27,\cdot)\) | 368.u | 44 | yes | \(-1\) | \(1\) | \(e\left(\frac{7}{44}\right)\) | \(e\left(\frac{19}{44}\right)\) | \(e\left(\frac{5}{11}\right)\) | \(e\left(\frac{7}{22}\right)\) | \(e\left(\frac{17}{44}\right)\) | \(e\left(\frac{13}{44}\right)\) | \(e\left(\frac{13}{22}\right)\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{43}{44}\right)\) | \(e\left(\frac{27}{44}\right)\) |
\(\chi_{368}(29,\cdot)\) | 368.w | 44 | yes | \(1\) | \(1\) | \(e\left(\frac{15}{44}\right)\) | \(e\left(\frac{25}{44}\right)\) | \(e\left(\frac{1}{22}\right)\) | \(e\left(\frac{15}{22}\right)\) | \(e\left(\frac{5}{44}\right)\) | \(e\left(\frac{31}{44}\right)\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{23}{44}\right)\) | \(e\left(\frac{17}{44}\right)\) |
\(\chi_{368}(31,\cdot)\) | 368.r | 22 | no | \(-1\) | \(1\) | \(e\left(\frac{19}{22}\right)\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{15}{22}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{21}{22}\right)\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{3}{22}\right)\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{13}{22}\right)\) | \(e\left(\frac{6}{11}\right)\) |
\(\chi_{368}(33,\cdot)\) | 368.p | 22 | no | \(-1\) | \(1\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{3}{22}\right)\) | \(e\left(\frac{13}{22}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{5}{22}\right)\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{7}{22}\right)\) | \(e\left(\frac{21}{22}\right)\) | \(e\left(\frac{1}{22}\right)\) | \(e\left(\frac{17}{22}\right)\) |
\(\chi_{368}(35,\cdot)\) | 368.u | 44 | yes | \(-1\) | \(1\) | \(e\left(\frac{13}{44}\right)\) | \(e\left(\frac{29}{44}\right)\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{13}{22}\right)\) | \(e\left(\frac{19}{44}\right)\) | \(e\left(\frac{43}{44}\right)\) | \(e\left(\frac{21}{22}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{17}{44}\right)\) | \(e\left(\frac{25}{44}\right)\) |
\(\chi_{368}(37,\cdot)\) | 368.v | 44 | yes | \(-1\) | \(1\) | \(e\left(\frac{1}{44}\right)\) | \(e\left(\frac{9}{44}\right)\) | \(e\left(\frac{7}{11}\right)\) | \(e\left(\frac{1}{22}\right)\) | \(e\left(\frac{37}{44}\right)\) | \(e\left(\frac{5}{44}\right)\) | \(e\left(\frac{5}{22}\right)\) | \(e\left(\frac{15}{22}\right)\) | \(e\left(\frac{3}{44}\right)\) | \(e\left(\frac{29}{44}\right)\) |
\(\chi_{368}(39,\cdot)\) | 368.o | 22 | no | \(-1\) | \(1\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{19}{22}\right)\) | \(e\left(\frac{9}{22}\right)\) | \(e\left(\frac{7}{11}\right)\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{13}{22}\right)\) | \(e\left(\frac{15}{22}\right)\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{5}{11}\right)\) | \(e\left(\frac{5}{22}\right)\) |
\(\chi_{368}(41,\cdot)\) | 368.t | 22 | no | \(1\) | \(1\) | \(e\left(\frac{5}{22}\right)\) | \(e\left(\frac{1}{22}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{5}{11}\right)\) | \(e\left(\frac{9}{22}\right)\) | \(e\left(\frac{3}{22}\right)\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{15}{22}\right)\) | \(e\left(\frac{13}{22}\right)\) |
\(\chi_{368}(43,\cdot)\) | 368.x | 44 | yes | \(1\) | \(1\) | \(e\left(\frac{39}{44}\right)\) | \(e\left(\frac{21}{44}\right)\) | \(e\left(\frac{7}{22}\right)\) | \(e\left(\frac{17}{22}\right)\) | \(e\left(\frac{35}{44}\right)\) | \(e\left(\frac{41}{44}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{13}{22}\right)\) | \(e\left(\frac{29}{44}\right)\) | \(e\left(\frac{9}{44}\right)\) |
\(\chi_{368}(45,\cdot)\) | 368.k | 4 | yes | \(-1\) | \(1\) | \(i\) | \(i\) | \(1\) | \(-1\) | \(i\) | \(i\) | \(-1\) | \(-1\) | \(-i\) | \(i\) |
\(\chi_{368}(47,\cdot)\) | 368.d | 2 | no | \(-1\) | \(1\) | \(-1\) | \(1\) | \(-1\) | \(1\) | \(-1\) | \(1\) | \(-1\) | \(1\) | \(-1\) | \(1\) |
\(\chi_{368}(49,\cdot)\) | 368.m | 11 | no | \(1\) | \(1\) | \(e\left(\frac{7}{11}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{1}{11}\right)\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{5}{11}\right)\) |
\(\chi_{368}(51,\cdot)\) | 368.x | 44 | yes | \(1\) | \(1\) | \(e\left(\frac{21}{44}\right)\) | \(e\left(\frac{35}{44}\right)\) | \(e\left(\frac{19}{22}\right)\) | \(e\left(\frac{21}{22}\right)\) | \(e\left(\frac{29}{44}\right)\) | \(e\left(\frac{39}{44}\right)\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{7}{22}\right)\) | \(e\left(\frac{19}{44}\right)\) | \(e\left(\frac{15}{44}\right)\) |
\(\chi_{368}(53,\cdot)\) | 368.v | 44 | yes | \(-1\) | \(1\) | \(e\left(\frac{25}{44}\right)\) | \(e\left(\frac{5}{44}\right)\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{3}{22}\right)\) | \(e\left(\frac{1}{44}\right)\) | \(e\left(\frac{37}{44}\right)\) | \(e\left(\frac{15}{22}\right)\) | \(e\left(\frac{1}{22}\right)\) | \(e\left(\frac{31}{44}\right)\) | \(e\left(\frac{21}{44}\right)\) |
\(\chi_{368}(55,\cdot)\) | 368.o | 22 | no | \(-1\) | \(1\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{21}{22}\right)\) | \(e\left(\frac{3}{22}\right)\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{1}{11}\right)\) | \(e\left(\frac{19}{22}\right)\) | \(e\left(\frac{5}{22}\right)\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{9}{22}\right)\) |
\(\chi_{368}(57,\cdot)\) | 368.q | 22 | no | \(-1\) | \(1\) | \(e\left(\frac{1}{22}\right)\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{17}{22}\right)\) | \(e\left(\frac{1}{11}\right)\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{5}{22}\right)\) | \(e\left(\frac{21}{22}\right)\) | \(e\left(\frac{19}{22}\right)\) | \(e\left(\frac{7}{11}\right)\) | \(e\left(\frac{9}{11}\right)\) |
\(\chi_{368}(59,\cdot)\) | 368.u | 44 | yes | \(-1\) | \(1\) | \(e\left(\frac{19}{44}\right)\) | \(e\left(\frac{39}{44}\right)\) | \(e\left(\frac{1}{11}\right)\) | \(e\left(\frac{19}{22}\right)\) | \(e\left(\frac{21}{44}\right)\) | \(e\left(\frac{29}{44}\right)\) | \(e\left(\frac{7}{22}\right)\) | \(e\left(\frac{5}{11}\right)\) | \(e\left(\frac{35}{44}\right)\) | \(e\left(\frac{23}{44}\right)\) |
\(\chi_{368}(61,\cdot)\) | 368.v | 44 | yes | \(-1\) | \(1\) | \(e\left(\frac{27}{44}\right)\) | \(e\left(\frac{23}{44}\right)\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{5}{22}\right)\) | \(e\left(\frac{31}{44}\right)\) | \(e\left(\frac{3}{44}\right)\) | \(e\left(\frac{3}{22}\right)\) | \(e\left(\frac{9}{22}\right)\) | \(e\left(\frac{37}{44}\right)\) | \(e\left(\frac{35}{44}\right)\) |
\(\chi_{368}(63,\cdot)\) | 368.s | 22 | no | \(1\) | \(1\) | \(e\left(\frac{13}{22}\right)\) | \(e\left(\frac{7}{22}\right)\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{5}{11}\right)\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{5}{22}\right)\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{3}{22}\right)\) |
\(\chi_{368}(65,\cdot)\) | 368.p | 22 | no | \(-1\) | \(1\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{15}{22}\right)\) | \(e\left(\frac{21}{22}\right)\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{3}{22}\right)\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{13}{22}\right)\) | \(e\left(\frac{17}{22}\right)\) | \(e\left(\frac{5}{22}\right)\) | \(e\left(\frac{19}{22}\right)\) |