sage: H = DirichletGroup(309)
pari: g = idealstar(,309,2)
Character group
sage: G.order()
pari: g.no
| ||
Order | = | 204 |
sage: H.invariants()
pari: g.cyc
| ||
Structure | = | \(C_{2}\times C_{102}\) |
sage: H.gens()
pari: g.gen
| ||
Generators | = | $\chi_{309}(104,\cdot)$, $\chi_{309}(211,\cdot)$ |
First 32 of 204 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 | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{309}(1,\cdot)\) | 309.a | 1 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
\(\chi_{309}(2,\cdot)\) | 309.n | 102 | yes | \(-1\) | \(1\) | \(e\left(\frac{49}{102}\right)\) | \(e\left(\frac{49}{51}\right)\) | \(e\left(\frac{95}{102}\right)\) | \(e\left(\frac{37}{51}\right)\) | \(e\left(\frac{15}{34}\right)\) | \(e\left(\frac{7}{17}\right)\) | \(e\left(\frac{83}{102}\right)\) | \(e\left(\frac{1}{17}\right)\) | \(e\left(\frac{7}{34}\right)\) | \(e\left(\frac{47}{51}\right)\) |
\(\chi_{309}(4,\cdot)\) | 309.m | 51 | no | \(1\) | \(1\) | \(e\left(\frac{49}{51}\right)\) | \(e\left(\frac{47}{51}\right)\) | \(e\left(\frac{44}{51}\right)\) | \(e\left(\frac{23}{51}\right)\) | \(e\left(\frac{15}{17}\right)\) | \(e\left(\frac{14}{17}\right)\) | \(e\left(\frac{32}{51}\right)\) | \(e\left(\frac{2}{17}\right)\) | \(e\left(\frac{7}{17}\right)\) | \(e\left(\frac{43}{51}\right)\) |
\(\chi_{309}(5,\cdot)\) | 309.o | 102 | yes | \(1\) | \(1\) | \(e\left(\frac{95}{102}\right)\) | \(e\left(\frac{44}{51}\right)\) | \(e\left(\frac{26}{51}\right)\) | \(e\left(\frac{2}{51}\right)\) | \(e\left(\frac{27}{34}\right)\) | \(e\left(\frac{15}{34}\right)\) | \(e\left(\frac{5}{51}\right)\) | \(e\left(\frac{12}{17}\right)\) | \(e\left(\frac{33}{34}\right)\) | \(e\left(\frac{37}{51}\right)\) |
\(\chi_{309}(7,\cdot)\) | 309.m | 51 | no | \(1\) | \(1\) | \(e\left(\frac{37}{51}\right)\) | \(e\left(\frac{23}{51}\right)\) | \(e\left(\frac{2}{51}\right)\) | \(e\left(\frac{8}{51}\right)\) | \(e\left(\frac{3}{17}\right)\) | \(e\left(\frac{13}{17}\right)\) | \(e\left(\frac{20}{51}\right)\) | \(e\left(\frac{14}{17}\right)\) | \(e\left(\frac{15}{17}\right)\) | \(e\left(\frac{46}{51}\right)\) |
\(\chi_{309}(8,\cdot)\) | 309.l | 34 | yes | \(-1\) | \(1\) | \(e\left(\frac{15}{34}\right)\) | \(e\left(\frac{15}{17}\right)\) | \(e\left(\frac{27}{34}\right)\) | \(e\left(\frac{3}{17}\right)\) | \(e\left(\frac{11}{34}\right)\) | \(e\left(\frac{4}{17}\right)\) | \(e\left(\frac{15}{34}\right)\) | \(e\left(\frac{3}{17}\right)\) | \(e\left(\frac{21}{34}\right)\) | \(e\left(\frac{13}{17}\right)\) |
\(\chi_{309}(10,\cdot)\) | 309.j | 34 | no | \(-1\) | \(1\) | \(e\left(\frac{7}{17}\right)\) | \(e\left(\frac{14}{17}\right)\) | \(e\left(\frac{15}{34}\right)\) | \(e\left(\frac{13}{17}\right)\) | \(e\left(\frac{4}{17}\right)\) | \(e\left(\frac{29}{34}\right)\) | \(e\left(\frac{31}{34}\right)\) | \(e\left(\frac{13}{17}\right)\) | \(e\left(\frac{3}{17}\right)\) | \(e\left(\frac{11}{17}\right)\) |
\(\chi_{309}(11,\cdot)\) | 309.o | 102 | yes | \(1\) | \(1\) | \(e\left(\frac{83}{102}\right)\) | \(e\left(\frac{32}{51}\right)\) | \(e\left(\frac{5}{51}\right)\) | \(e\left(\frac{20}{51}\right)\) | \(e\left(\frac{15}{34}\right)\) | \(e\left(\frac{31}{34}\right)\) | \(e\left(\frac{50}{51}\right)\) | \(e\left(\frac{1}{17}\right)\) | \(e\left(\frac{7}{34}\right)\) | \(e\left(\frac{13}{51}\right)\) |
\(\chi_{309}(13,\cdot)\) | 309.i | 17 | no | \(1\) | \(1\) | \(e\left(\frac{1}{17}\right)\) | \(e\left(\frac{2}{17}\right)\) | \(e\left(\frac{12}{17}\right)\) | \(e\left(\frac{14}{17}\right)\) | \(e\left(\frac{3}{17}\right)\) | \(e\left(\frac{13}{17}\right)\) | \(e\left(\frac{1}{17}\right)\) | \(e\left(\frac{14}{17}\right)\) | \(e\left(\frac{15}{17}\right)\) | \(e\left(\frac{4}{17}\right)\) |
\(\chi_{309}(14,\cdot)\) | 309.l | 34 | yes | \(-1\) | \(1\) | \(e\left(\frac{7}{34}\right)\) | \(e\left(\frac{7}{17}\right)\) | \(e\left(\frac{33}{34}\right)\) | \(e\left(\frac{15}{17}\right)\) | \(e\left(\frac{21}{34}\right)\) | \(e\left(\frac{3}{17}\right)\) | \(e\left(\frac{7}{34}\right)\) | \(e\left(\frac{15}{17}\right)\) | \(e\left(\frac{3}{34}\right)\) | \(e\left(\frac{14}{17}\right)\) |
\(\chi_{309}(16,\cdot)\) | 309.m | 51 | no | \(1\) | \(1\) | \(e\left(\frac{47}{51}\right)\) | \(e\left(\frac{43}{51}\right)\) | \(e\left(\frac{37}{51}\right)\) | \(e\left(\frac{46}{51}\right)\) | \(e\left(\frac{13}{17}\right)\) | \(e\left(\frac{11}{17}\right)\) | \(e\left(\frac{13}{51}\right)\) | \(e\left(\frac{4}{17}\right)\) | \(e\left(\frac{14}{17}\right)\) | \(e\left(\frac{35}{51}\right)\) |
\(\chi_{309}(17,\cdot)\) | 309.n | 102 | yes | \(-1\) | \(1\) | \(e\left(\frac{71}{102}\right)\) | \(e\left(\frac{20}{51}\right)\) | \(e\left(\frac{19}{102}\right)\) | \(e\left(\frac{38}{51}\right)\) | \(e\left(\frac{3}{34}\right)\) | \(e\left(\frac{15}{17}\right)\) | \(e\left(\frac{37}{102}\right)\) | \(e\left(\frac{7}{17}\right)\) | \(e\left(\frac{15}{34}\right)\) | \(e\left(\frac{40}{51}\right)\) |
\(\chi_{309}(19,\cdot)\) | 309.m | 51 | no | \(1\) | \(1\) | \(e\left(\frac{26}{51}\right)\) | \(e\left(\frac{1}{51}\right)\) | \(e\left(\frac{40}{51}\right)\) | \(e\left(\frac{7}{51}\right)\) | \(e\left(\frac{9}{17}\right)\) | \(e\left(\frac{5}{17}\right)\) | \(e\left(\frac{43}{51}\right)\) | \(e\left(\frac{8}{17}\right)\) | \(e\left(\frac{11}{17}\right)\) | \(e\left(\frac{2}{51}\right)\) |
\(\chi_{309}(20,\cdot)\) | 309.o | 102 | yes | \(1\) | \(1\) | \(e\left(\frac{91}{102}\right)\) | \(e\left(\frac{40}{51}\right)\) | \(e\left(\frac{19}{51}\right)\) | \(e\left(\frac{25}{51}\right)\) | \(e\left(\frac{23}{34}\right)\) | \(e\left(\frac{9}{34}\right)\) | \(e\left(\frac{37}{51}\right)\) | \(e\left(\frac{14}{17}\right)\) | \(e\left(\frac{13}{34}\right)\) | \(e\left(\frac{29}{51}\right)\) |
\(\chi_{309}(22,\cdot)\) | 309.j | 34 | no | \(-1\) | \(1\) | \(e\left(\frac{5}{17}\right)\) | \(e\left(\frac{10}{17}\right)\) | \(e\left(\frac{1}{34}\right)\) | \(e\left(\frac{2}{17}\right)\) | \(e\left(\frac{15}{17}\right)\) | \(e\left(\frac{11}{34}\right)\) | \(e\left(\frac{27}{34}\right)\) | \(e\left(\frac{2}{17}\right)\) | \(e\left(\frac{7}{17}\right)\) | \(e\left(\frac{3}{17}\right)\) |
\(\chi_{309}(23,\cdot)\) | 309.l | 34 | yes | \(-1\) | \(1\) | \(e\left(\frac{29}{34}\right)\) | \(e\left(\frac{12}{17}\right)\) | \(e\left(\frac{25}{34}\right)\) | \(e\left(\frac{16}{17}\right)\) | \(e\left(\frac{19}{34}\right)\) | \(e\left(\frac{10}{17}\right)\) | \(e\left(\frac{29}{34}\right)\) | \(e\left(\frac{16}{17}\right)\) | \(e\left(\frac{27}{34}\right)\) | \(e\left(\frac{7}{17}\right)\) |
\(\chi_{309}(25,\cdot)\) | 309.m | 51 | no | \(1\) | \(1\) | \(e\left(\frac{44}{51}\right)\) | \(e\left(\frac{37}{51}\right)\) | \(e\left(\frac{1}{51}\right)\) | \(e\left(\frac{4}{51}\right)\) | \(e\left(\frac{10}{17}\right)\) | \(e\left(\frac{15}{17}\right)\) | \(e\left(\frac{10}{51}\right)\) | \(e\left(\frac{7}{17}\right)\) | \(e\left(\frac{16}{17}\right)\) | \(e\left(\frac{23}{51}\right)\) |
\(\chi_{309}(26,\cdot)\) | 309.n | 102 | yes | \(-1\) | \(1\) | \(e\left(\frac{55}{102}\right)\) | \(e\left(\frac{4}{51}\right)\) | \(e\left(\frac{65}{102}\right)\) | \(e\left(\frac{28}{51}\right)\) | \(e\left(\frac{21}{34}\right)\) | \(e\left(\frac{3}{17}\right)\) | \(e\left(\frac{89}{102}\right)\) | \(e\left(\frac{15}{17}\right)\) | \(e\left(\frac{3}{34}\right)\) | \(e\left(\frac{8}{51}\right)\) |
\(\chi_{309}(28,\cdot)\) | 309.m | 51 | no | \(1\) | \(1\) | \(e\left(\frac{35}{51}\right)\) | \(e\left(\frac{19}{51}\right)\) | \(e\left(\frac{46}{51}\right)\) | \(e\left(\frac{31}{51}\right)\) | \(e\left(\frac{1}{17}\right)\) | \(e\left(\frac{10}{17}\right)\) | \(e\left(\frac{1}{51}\right)\) | \(e\left(\frac{16}{17}\right)\) | \(e\left(\frac{5}{17}\right)\) | \(e\left(\frac{38}{51}\right)\) |
\(\chi_{309}(29,\cdot)\) | 309.n | 102 | yes | \(-1\) | \(1\) | \(e\left(\frac{61}{102}\right)\) | \(e\left(\frac{10}{51}\right)\) | \(e\left(\frac{35}{102}\right)\) | \(e\left(\frac{19}{51}\right)\) | \(e\left(\frac{27}{34}\right)\) | \(e\left(\frac{16}{17}\right)\) | \(e\left(\frac{95}{102}\right)\) | \(e\left(\frac{12}{17}\right)\) | \(e\left(\frac{33}{34}\right)\) | \(e\left(\frac{20}{51}\right)\) |
\(\chi_{309}(31,\cdot)\) | 309.j | 34 | no | \(-1\) | \(1\) | \(e\left(\frac{10}{17}\right)\) | \(e\left(\frac{3}{17}\right)\) | \(e\left(\frac{19}{34}\right)\) | \(e\left(\frac{4}{17}\right)\) | \(e\left(\frac{13}{17}\right)\) | \(e\left(\frac{5}{34}\right)\) | \(e\left(\frac{3}{34}\right)\) | \(e\left(\frac{4}{17}\right)\) | \(e\left(\frac{14}{17}\right)\) | \(e\left(\frac{6}{17}\right)\) |
\(\chi_{309}(32,\cdot)\) | 309.n | 102 | yes | \(-1\) | \(1\) | \(e\left(\frac{41}{102}\right)\) | \(e\left(\frac{41}{51}\right)\) | \(e\left(\frac{67}{102}\right)\) | \(e\left(\frac{32}{51}\right)\) | \(e\left(\frac{7}{34}\right)\) | \(e\left(\frac{1}{17}\right)\) | \(e\left(\frac{7}{102}\right)\) | \(e\left(\frac{5}{17}\right)\) | \(e\left(\frac{1}{34}\right)\) | \(e\left(\frac{31}{51}\right)\) |
\(\chi_{309}(34,\cdot)\) | 309.i | 17 | no | \(1\) | \(1\) | \(e\left(\frac{3}{17}\right)\) | \(e\left(\frac{6}{17}\right)\) | \(e\left(\frac{2}{17}\right)\) | \(e\left(\frac{8}{17}\right)\) | \(e\left(\frac{9}{17}\right)\) | \(e\left(\frac{5}{17}\right)\) | \(e\left(\frac{3}{17}\right)\) | \(e\left(\frac{8}{17}\right)\) | \(e\left(\frac{11}{17}\right)\) | \(e\left(\frac{12}{17}\right)\) |
\(\chi_{309}(35,\cdot)\) | 309.o | 102 | yes | \(1\) | \(1\) | \(e\left(\frac{67}{102}\right)\) | \(e\left(\frac{16}{51}\right)\) | \(e\left(\frac{28}{51}\right)\) | \(e\left(\frac{10}{51}\right)\) | \(e\left(\frac{33}{34}\right)\) | \(e\left(\frac{7}{34}\right)\) | \(e\left(\frac{25}{51}\right)\) | \(e\left(\frac{9}{17}\right)\) | \(e\left(\frac{29}{34}\right)\) | \(e\left(\frac{32}{51}\right)\) |
\(\chi_{309}(37,\cdot)\) | 309.j | 34 | no | \(-1\) | \(1\) | \(e\left(\frac{2}{17}\right)\) | \(e\left(\frac{4}{17}\right)\) | \(e\left(\frac{31}{34}\right)\) | \(e\left(\frac{11}{17}\right)\) | \(e\left(\frac{6}{17}\right)\) | \(e\left(\frac{1}{34}\right)\) | \(e\left(\frac{21}{34}\right)\) | \(e\left(\frac{11}{17}\right)\) | \(e\left(\frac{13}{17}\right)\) | \(e\left(\frac{8}{17}\right)\) |
\(\chi_{309}(38,\cdot)\) | 309.n | 102 | yes | \(-1\) | \(1\) | \(e\left(\frac{101}{102}\right)\) | \(e\left(\frac{50}{51}\right)\) | \(e\left(\frac{73}{102}\right)\) | \(e\left(\frac{44}{51}\right)\) | \(e\left(\frac{33}{34}\right)\) | \(e\left(\frac{12}{17}\right)\) | \(e\left(\frac{67}{102}\right)\) | \(e\left(\frac{9}{17}\right)\) | \(e\left(\frac{29}{34}\right)\) | \(e\left(\frac{49}{51}\right)\) |
\(\chi_{309}(40,\cdot)\) | 309.p | 102 | no | \(-1\) | \(1\) | \(e\left(\frac{19}{51}\right)\) | \(e\left(\frac{38}{51}\right)\) | \(e\left(\frac{31}{102}\right)\) | \(e\left(\frac{11}{51}\right)\) | \(e\left(\frac{2}{17}\right)\) | \(e\left(\frac{23}{34}\right)\) | \(e\left(\frac{55}{102}\right)\) | \(e\left(\frac{15}{17}\right)\) | \(e\left(\frac{10}{17}\right)\) | \(e\left(\frac{25}{51}\right)\) |
\(\chi_{309}(41,\cdot)\) | 309.n | 102 | yes | \(-1\) | \(1\) | \(e\left(\frac{7}{102}\right)\) | \(e\left(\frac{7}{51}\right)\) | \(e\left(\frac{101}{102}\right)\) | \(e\left(\frac{49}{51}\right)\) | \(e\left(\frac{7}{34}\right)\) | \(e\left(\frac{1}{17}\right)\) | \(e\left(\frac{41}{102}\right)\) | \(e\left(\frac{5}{17}\right)\) | \(e\left(\frac{1}{34}\right)\) | \(e\left(\frac{14}{51}\right)\) |
\(\chi_{309}(43,\cdot)\) | 309.p | 102 | no | \(-1\) | \(1\) | \(e\left(\frac{11}{51}\right)\) | \(e\left(\frac{22}{51}\right)\) | \(e\left(\frac{77}{102}\right)\) | \(e\left(\frac{1}{51}\right)\) | \(e\left(\frac{11}{17}\right)\) | \(e\left(\frac{33}{34}\right)\) | \(e\left(\frac{5}{102}\right)\) | \(e\left(\frac{6}{17}\right)\) | \(e\left(\frac{4}{17}\right)\) | \(e\left(\frac{44}{51}\right)\) |
\(\chi_{309}(44,\cdot)\) | 309.o | 102 | yes | \(1\) | \(1\) | \(e\left(\frac{79}{102}\right)\) | \(e\left(\frac{28}{51}\right)\) | \(e\left(\frac{49}{51}\right)\) | \(e\left(\frac{43}{51}\right)\) | \(e\left(\frac{11}{34}\right)\) | \(e\left(\frac{25}{34}\right)\) | \(e\left(\frac{31}{51}\right)\) | \(e\left(\frac{3}{17}\right)\) | \(e\left(\frac{21}{34}\right)\) | \(e\left(\frac{5}{51}\right)\) |
\(\chi_{309}(46,\cdot)\) | 309.e | 3 | no | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
\(\chi_{309}(47,\cdot)\) | 309.g | 6 | yes | \(1\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) |