sage: H = DirichletGroup(376)
pari: g = idealstar(,376,2)
Character group
sage: G.order()
pari: g.no
| ||
Order | = | 184 |
sage: H.invariants()
pari: g.cyc
| ||
Structure | = | \(C_{2}\times C_{2}\times C_{46}\) |
sage: H.gens()
pari: g.gen
| ||
Generators | = | $\chi_{376}(95,\cdot)$, $\chi_{376}(189,\cdot)$, $\chi_{376}(193,\cdot)$ |
First 32 of 184 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 | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{376}(1,\cdot)\) | 376.a | 1 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
\(\chi_{376}(3,\cdot)\) | 376.l | 46 | yes | \(-1\) | \(1\) | \(e\left(\frac{16}{23}\right)\) | \(e\left(\frac{43}{46}\right)\) | \(e\left(\frac{19}{46}\right)\) | \(e\left(\frac{9}{23}\right)\) | \(e\left(\frac{1}{23}\right)\) | \(e\left(\frac{13}{46}\right)\) | \(e\left(\frac{29}{46}\right)\) | \(e\left(\frac{22}{23}\right)\) | \(e\left(\frac{13}{23}\right)\) | \(e\left(\frac{5}{46}\right)\) |
\(\chi_{376}(5,\cdot)\) | 376.m | 46 | yes | \(-1\) | \(1\) | \(e\left(\frac{43}{46}\right)\) | \(e\left(\frac{12}{23}\right)\) | \(e\left(\frac{16}{23}\right)\) | \(e\left(\frac{20}{23}\right)\) | \(e\left(\frac{15}{23}\right)\) | \(e\left(\frac{17}{23}\right)\) | \(e\left(\frac{21}{46}\right)\) | \(e\left(\frac{8}{23}\right)\) | \(e\left(\frac{11}{23}\right)\) | \(e\left(\frac{29}{46}\right)\) |
\(\chi_{376}(7,\cdot)\) | 376.n | 46 | no | \(-1\) | \(1\) | \(e\left(\frac{19}{46}\right)\) | \(e\left(\frac{16}{23}\right)\) | \(e\left(\frac{35}{46}\right)\) | \(e\left(\frac{19}{23}\right)\) | \(e\left(\frac{17}{46}\right)\) | \(e\left(\frac{15}{23}\right)\) | \(e\left(\frac{5}{46}\right)\) | \(e\left(\frac{3}{23}\right)\) | \(e\left(\frac{37}{46}\right)\) | \(e\left(\frac{4}{23}\right)\) |
\(\chi_{376}(9,\cdot)\) | 376.i | 23 | no | \(1\) | \(1\) | \(e\left(\frac{9}{23}\right)\) | \(e\left(\frac{20}{23}\right)\) | \(e\left(\frac{19}{23}\right)\) | \(e\left(\frac{18}{23}\right)\) | \(e\left(\frac{2}{23}\right)\) | \(e\left(\frac{13}{23}\right)\) | \(e\left(\frac{6}{23}\right)\) | \(e\left(\frac{21}{23}\right)\) | \(e\left(\frac{3}{23}\right)\) | \(e\left(\frac{5}{23}\right)\) |
\(\chi_{376}(11,\cdot)\) | 376.j | 46 | yes | \(1\) | \(1\) | \(e\left(\frac{1}{23}\right)\) | \(e\left(\frac{15}{23}\right)\) | \(e\left(\frac{17}{46}\right)\) | \(e\left(\frac{2}{23}\right)\) | \(e\left(\frac{3}{46}\right)\) | \(e\left(\frac{4}{23}\right)\) | \(e\left(\frac{16}{23}\right)\) | \(e\left(\frac{10}{23}\right)\) | \(e\left(\frac{39}{46}\right)\) | \(e\left(\frac{19}{46}\right)\) |
\(\chi_{376}(13,\cdot)\) | 376.m | 46 | yes | \(-1\) | \(1\) | \(e\left(\frac{13}{46}\right)\) | \(e\left(\frac{17}{23}\right)\) | \(e\left(\frac{15}{23}\right)\) | \(e\left(\frac{13}{23}\right)\) | \(e\left(\frac{4}{23}\right)\) | \(e\left(\frac{3}{23}\right)\) | \(e\left(\frac{1}{46}\right)\) | \(e\left(\frac{19}{23}\right)\) | \(e\left(\frac{6}{23}\right)\) | \(e\left(\frac{43}{46}\right)\) |
\(\chi_{376}(15,\cdot)\) | 376.p | 46 | no | \(1\) | \(1\) | \(e\left(\frac{29}{46}\right)\) | \(e\left(\frac{21}{46}\right)\) | \(e\left(\frac{5}{46}\right)\) | \(e\left(\frac{6}{23}\right)\) | \(e\left(\frac{16}{23}\right)\) | \(e\left(\frac{1}{46}\right)\) | \(e\left(\frac{2}{23}\right)\) | \(e\left(\frac{7}{23}\right)\) | \(e\left(\frac{1}{23}\right)\) | \(e\left(\frac{17}{23}\right)\) |
\(\chi_{376}(17,\cdot)\) | 376.i | 23 | no | \(1\) | \(1\) | \(e\left(\frac{22}{23}\right)\) | \(e\left(\frac{8}{23}\right)\) | \(e\left(\frac{3}{23}\right)\) | \(e\left(\frac{21}{23}\right)\) | \(e\left(\frac{10}{23}\right)\) | \(e\left(\frac{19}{23}\right)\) | \(e\left(\frac{7}{23}\right)\) | \(e\left(\frac{13}{23}\right)\) | \(e\left(\frac{15}{23}\right)\) | \(e\left(\frac{2}{23}\right)\) |
\(\chi_{376}(19,\cdot)\) | 376.j | 46 | yes | \(1\) | \(1\) | \(e\left(\frac{13}{23}\right)\) | \(e\left(\frac{11}{23}\right)\) | \(e\left(\frac{37}{46}\right)\) | \(e\left(\frac{3}{23}\right)\) | \(e\left(\frac{39}{46}\right)\) | \(e\left(\frac{6}{23}\right)\) | \(e\left(\frac{1}{23}\right)\) | \(e\left(\frac{15}{23}\right)\) | \(e\left(\frac{1}{46}\right)\) | \(e\left(\frac{17}{46}\right)\) |
\(\chi_{376}(21,\cdot)\) | 376.o | 46 | yes | \(1\) | \(1\) | \(e\left(\frac{5}{46}\right)\) | \(e\left(\frac{29}{46}\right)\) | \(e\left(\frac{4}{23}\right)\) | \(e\left(\frac{5}{23}\right)\) | \(e\left(\frac{19}{46}\right)\) | \(e\left(\frac{43}{46}\right)\) | \(e\left(\frac{17}{23}\right)\) | \(e\left(\frac{2}{23}\right)\) | \(e\left(\frac{17}{46}\right)\) | \(e\left(\frac{13}{46}\right)\) |
\(\chi_{376}(23,\cdot)\) | 376.p | 46 | no | \(1\) | \(1\) | \(e\left(\frac{31}{46}\right)\) | \(e\left(\frac{5}{46}\right)\) | \(e\left(\frac{45}{46}\right)\) | \(e\left(\frac{8}{23}\right)\) | \(e\left(\frac{6}{23}\right)\) | \(e\left(\frac{9}{46}\right)\) | \(e\left(\frac{18}{23}\right)\) | \(e\left(\frac{17}{23}\right)\) | \(e\left(\frac{9}{23}\right)\) | \(e\left(\frac{15}{23}\right)\) |
\(\chi_{376}(25,\cdot)\) | 376.i | 23 | no | \(1\) | \(1\) | \(e\left(\frac{20}{23}\right)\) | \(e\left(\frac{1}{23}\right)\) | \(e\left(\frac{9}{23}\right)\) | \(e\left(\frac{17}{23}\right)\) | \(e\left(\frac{7}{23}\right)\) | \(e\left(\frac{11}{23}\right)\) | \(e\left(\frac{21}{23}\right)\) | \(e\left(\frac{16}{23}\right)\) | \(e\left(\frac{22}{23}\right)\) | \(e\left(\frac{6}{23}\right)\) |
\(\chi_{376}(27,\cdot)\) | 376.l | 46 | yes | \(-1\) | \(1\) | \(e\left(\frac{2}{23}\right)\) | \(e\left(\frac{37}{46}\right)\) | \(e\left(\frac{11}{46}\right)\) | \(e\left(\frac{4}{23}\right)\) | \(e\left(\frac{3}{23}\right)\) | \(e\left(\frac{39}{46}\right)\) | \(e\left(\frac{41}{46}\right)\) | \(e\left(\frac{20}{23}\right)\) | \(e\left(\frac{16}{23}\right)\) | \(e\left(\frac{15}{46}\right)\) |
\(\chi_{376}(29,\cdot)\) | 376.m | 46 | yes | \(-1\) | \(1\) | \(e\left(\frac{33}{46}\right)\) | \(e\left(\frac{6}{23}\right)\) | \(e\left(\frac{8}{23}\right)\) | \(e\left(\frac{10}{23}\right)\) | \(e\left(\frac{19}{23}\right)\) | \(e\left(\frac{20}{23}\right)\) | \(e\left(\frac{45}{46}\right)\) | \(e\left(\frac{4}{23}\right)\) | \(e\left(\frac{17}{23}\right)\) | \(e\left(\frac{3}{46}\right)\) |
\(\chi_{376}(31,\cdot)\) | 376.p | 46 | no | \(1\) | \(1\) | \(e\left(\frac{37}{46}\right)\) | \(e\left(\frac{3}{46}\right)\) | \(e\left(\frac{27}{46}\right)\) | \(e\left(\frac{14}{23}\right)\) | \(e\left(\frac{22}{23}\right)\) | \(e\left(\frac{33}{46}\right)\) | \(e\left(\frac{20}{23}\right)\) | \(e\left(\frac{1}{23}\right)\) | \(e\left(\frac{10}{23}\right)\) | \(e\left(\frac{9}{23}\right)\) |
\(\chi_{376}(33,\cdot)\) | 376.k | 46 | no | \(-1\) | \(1\) | \(e\left(\frac{17}{23}\right)\) | \(e\left(\frac{27}{46}\right)\) | \(e\left(\frac{18}{23}\right)\) | \(e\left(\frac{11}{23}\right)\) | \(e\left(\frac{5}{46}\right)\) | \(e\left(\frac{21}{46}\right)\) | \(e\left(\frac{15}{46}\right)\) | \(e\left(\frac{9}{23}\right)\) | \(e\left(\frac{19}{46}\right)\) | \(e\left(\frac{12}{23}\right)\) |
\(\chi_{376}(35,\cdot)\) | 376.j | 46 | yes | \(1\) | \(1\) | \(e\left(\frac{8}{23}\right)\) | \(e\left(\frac{5}{23}\right)\) | \(e\left(\frac{21}{46}\right)\) | \(e\left(\frac{16}{23}\right)\) | \(e\left(\frac{1}{46}\right)\) | \(e\left(\frac{9}{23}\right)\) | \(e\left(\frac{13}{23}\right)\) | \(e\left(\frac{11}{23}\right)\) | \(e\left(\frac{13}{46}\right)\) | \(e\left(\frac{37}{46}\right)\) |
\(\chi_{376}(37,\cdot)\) | 376.o | 46 | yes | \(1\) | \(1\) | \(e\left(\frac{35}{46}\right)\) | \(e\left(\frac{19}{46}\right)\) | \(e\left(\frac{5}{23}\right)\) | \(e\left(\frac{12}{23}\right)\) | \(e\left(\frac{41}{46}\right)\) | \(e\left(\frac{25}{46}\right)\) | \(e\left(\frac{4}{23}\right)\) | \(e\left(\frac{14}{23}\right)\) | \(e\left(\frac{27}{46}\right)\) | \(e\left(\frac{45}{46}\right)\) |
\(\chi_{376}(39,\cdot)\) | 376.p | 46 | no | \(1\) | \(1\) | \(e\left(\frac{45}{46}\right)\) | \(e\left(\frac{31}{46}\right)\) | \(e\left(\frac{3}{46}\right)\) | \(e\left(\frac{22}{23}\right)\) | \(e\left(\frac{5}{23}\right)\) | \(e\left(\frac{19}{46}\right)\) | \(e\left(\frac{15}{23}\right)\) | \(e\left(\frac{18}{23}\right)\) | \(e\left(\frac{19}{23}\right)\) | \(e\left(\frac{1}{23}\right)\) |
\(\chi_{376}(41,\cdot)\) | 376.k | 46 | no | \(-1\) | \(1\) | \(e\left(\frac{12}{23}\right)\) | \(e\left(\frac{15}{46}\right)\) | \(e\left(\frac{10}{23}\right)\) | \(e\left(\frac{1}{23}\right)\) | \(e\left(\frac{13}{46}\right)\) | \(e\left(\frac{27}{46}\right)\) | \(e\left(\frac{39}{46}\right)\) | \(e\left(\frac{5}{23}\right)\) | \(e\left(\frac{31}{46}\right)\) | \(e\left(\frac{22}{23}\right)\) |
\(\chi_{376}(43,\cdot)\) | 376.j | 46 | yes | \(1\) | \(1\) | \(e\left(\frac{15}{23}\right)\) | \(e\left(\frac{18}{23}\right)\) | \(e\left(\frac{25}{46}\right)\) | \(e\left(\frac{7}{23}\right)\) | \(e\left(\frac{45}{46}\right)\) | \(e\left(\frac{14}{23}\right)\) | \(e\left(\frac{10}{23}\right)\) | \(e\left(\frac{12}{23}\right)\) | \(e\left(\frac{33}{46}\right)\) | \(e\left(\frac{9}{46}\right)\) |
\(\chi_{376}(45,\cdot)\) | 376.m | 46 | yes | \(-1\) | \(1\) | \(e\left(\frac{15}{46}\right)\) | \(e\left(\frac{9}{23}\right)\) | \(e\left(\frac{12}{23}\right)\) | \(e\left(\frac{15}{23}\right)\) | \(e\left(\frac{17}{23}\right)\) | \(e\left(\frac{7}{23}\right)\) | \(e\left(\frac{33}{46}\right)\) | \(e\left(\frac{6}{23}\right)\) | \(e\left(\frac{14}{23}\right)\) | \(e\left(\frac{39}{46}\right)\) |
\(\chi_{376}(49,\cdot)\) | 376.i | 23 | no | \(1\) | \(1\) | \(e\left(\frac{19}{23}\right)\) | \(e\left(\frac{9}{23}\right)\) | \(e\left(\frac{12}{23}\right)\) | \(e\left(\frac{15}{23}\right)\) | \(e\left(\frac{17}{23}\right)\) | \(e\left(\frac{7}{23}\right)\) | \(e\left(\frac{5}{23}\right)\) | \(e\left(\frac{6}{23}\right)\) | \(e\left(\frac{14}{23}\right)\) | \(e\left(\frac{8}{23}\right)\) |
\(\chi_{376}(51,\cdot)\) | 376.l | 46 | yes | \(-1\) | \(1\) | \(e\left(\frac{15}{23}\right)\) | \(e\left(\frac{13}{46}\right)\) | \(e\left(\frac{25}{46}\right)\) | \(e\left(\frac{7}{23}\right)\) | \(e\left(\frac{11}{23}\right)\) | \(e\left(\frac{5}{46}\right)\) | \(e\left(\frac{43}{46}\right)\) | \(e\left(\frac{12}{23}\right)\) | \(e\left(\frac{5}{23}\right)\) | \(e\left(\frac{9}{46}\right)\) |
\(\chi_{376}(53,\cdot)\) | 376.o | 46 | yes | \(1\) | \(1\) | \(e\left(\frac{1}{46}\right)\) | \(e\left(\frac{15}{46}\right)\) | \(e\left(\frac{10}{23}\right)\) | \(e\left(\frac{1}{23}\right)\) | \(e\left(\frac{13}{46}\right)\) | \(e\left(\frac{27}{46}\right)\) | \(e\left(\frac{8}{23}\right)\) | \(e\left(\frac{5}{23}\right)\) | \(e\left(\frac{31}{46}\right)\) | \(e\left(\frac{21}{46}\right)\) |
\(\chi_{376}(55,\cdot)\) | 376.n | 46 | no | \(-1\) | \(1\) | \(e\left(\frac{45}{46}\right)\) | \(e\left(\frac{4}{23}\right)\) | \(e\left(\frac{3}{46}\right)\) | \(e\left(\frac{22}{23}\right)\) | \(e\left(\frac{33}{46}\right)\) | \(e\left(\frac{21}{23}\right)\) | \(e\left(\frac{7}{46}\right)\) | \(e\left(\frac{18}{23}\right)\) | \(e\left(\frac{15}{46}\right)\) | \(e\left(\frac{1}{23}\right)\) |
\(\chi_{376}(57,\cdot)\) | 376.k | 46 | no | \(-1\) | \(1\) | \(e\left(\frac{6}{23}\right)\) | \(e\left(\frac{19}{46}\right)\) | \(e\left(\frac{5}{23}\right)\) | \(e\left(\frac{12}{23}\right)\) | \(e\left(\frac{41}{46}\right)\) | \(e\left(\frac{25}{46}\right)\) | \(e\left(\frac{31}{46}\right)\) | \(e\left(\frac{14}{23}\right)\) | \(e\left(\frac{27}{46}\right)\) | \(e\left(\frac{11}{23}\right)\) |
\(\chi_{376}(59,\cdot)\) | 376.l | 46 | yes | \(-1\) | \(1\) | \(e\left(\frac{8}{23}\right)\) | \(e\left(\frac{33}{46}\right)\) | \(e\left(\frac{21}{46}\right)\) | \(e\left(\frac{16}{23}\right)\) | \(e\left(\frac{12}{23}\right)\) | \(e\left(\frac{41}{46}\right)\) | \(e\left(\frac{3}{46}\right)\) | \(e\left(\frac{11}{23}\right)\) | \(e\left(\frac{18}{23}\right)\) | \(e\left(\frac{37}{46}\right)\) |
\(\chi_{376}(61,\cdot)\) | 376.o | 46 | yes | \(1\) | \(1\) | \(e\left(\frac{11}{46}\right)\) | \(e\left(\frac{27}{46}\right)\) | \(e\left(\frac{18}{23}\right)\) | \(e\left(\frac{11}{23}\right)\) | \(e\left(\frac{5}{46}\right)\) | \(e\left(\frac{21}{46}\right)\) | \(e\left(\frac{19}{23}\right)\) | \(e\left(\frac{9}{23}\right)\) | \(e\left(\frac{19}{46}\right)\) | \(e\left(\frac{1}{46}\right)\) |
\(\chi_{376}(63,\cdot)\) | 376.n | 46 | no | \(-1\) | \(1\) | \(e\left(\frac{37}{46}\right)\) | \(e\left(\frac{13}{23}\right)\) | \(e\left(\frac{27}{46}\right)\) | \(e\left(\frac{14}{23}\right)\) | \(e\left(\frac{21}{46}\right)\) | \(e\left(\frac{5}{23}\right)\) | \(e\left(\frac{17}{46}\right)\) | \(e\left(\frac{1}{23}\right)\) | \(e\left(\frac{43}{46}\right)\) | \(e\left(\frac{9}{23}\right)\) |
\(\chi_{376}(65,\cdot)\) | 376.i | 23 | no | \(1\) | \(1\) | \(e\left(\frac{5}{23}\right)\) | \(e\left(\frac{6}{23}\right)\) | \(e\left(\frac{8}{23}\right)\) | \(e\left(\frac{10}{23}\right)\) | \(e\left(\frac{19}{23}\right)\) | \(e\left(\frac{20}{23}\right)\) | \(e\left(\frac{11}{23}\right)\) | \(e\left(\frac{4}{23}\right)\) | \(e\left(\frac{17}{23}\right)\) | \(e\left(\frac{13}{23}\right)\) |