sage: H = DirichletGroup(79)
pari: g = idealstar(,79,2)
Character group
sage: G.order()
pari: g.no
| ||
Order | = | 78 |
sage: H.invariants()
pari: g.cyc
| ||
Structure | = | \(C_{78}\) |
sage: H.gens()
pari: g.gen
| ||
Generators | = | $\chi_{79}(3,\cdot)$ |
First 32 of 78 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 | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{79}(1,\cdot)\) | 79.a | 1 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
\(\chi_{79}(2,\cdot)\) | 79.g | 39 | yes | \(1\) | \(1\) | \(e\left(\frac{8}{39}\right)\) | \(e\left(\frac{2}{39}\right)\) | \(e\left(\frac{16}{39}\right)\) | \(e\left(\frac{7}{39}\right)\) | \(e\left(\frac{10}{39}\right)\) | \(e\left(\frac{28}{39}\right)\) | \(e\left(\frac{8}{13}\right)\) | \(e\left(\frac{4}{39}\right)\) | \(e\left(\frac{5}{13}\right)\) | \(e\left(\frac{19}{39}\right)\) |
\(\chi_{79}(3,\cdot)\) | 79.h | 78 | yes | \(-1\) | \(1\) | \(e\left(\frac{2}{39}\right)\) | \(e\left(\frac{1}{78}\right)\) | \(e\left(\frac{4}{39}\right)\) | \(e\left(\frac{31}{39}\right)\) | \(e\left(\frac{5}{78}\right)\) | \(e\left(\frac{53}{78}\right)\) | \(e\left(\frac{2}{13}\right)\) | \(e\left(\frac{1}{39}\right)\) | \(e\left(\frac{11}{13}\right)\) | \(e\left(\frac{34}{39}\right)\) |
\(\chi_{79}(4,\cdot)\) | 79.g | 39 | yes | \(1\) | \(1\) | \(e\left(\frac{16}{39}\right)\) | \(e\left(\frac{4}{39}\right)\) | \(e\left(\frac{32}{39}\right)\) | \(e\left(\frac{14}{39}\right)\) | \(e\left(\frac{20}{39}\right)\) | \(e\left(\frac{17}{39}\right)\) | \(e\left(\frac{3}{13}\right)\) | \(e\left(\frac{8}{39}\right)\) | \(e\left(\frac{10}{13}\right)\) | \(e\left(\frac{38}{39}\right)\) |
\(\chi_{79}(5,\cdot)\) | 79.g | 39 | yes | \(1\) | \(1\) | \(e\left(\frac{7}{39}\right)\) | \(e\left(\frac{31}{39}\right)\) | \(e\left(\frac{14}{39}\right)\) | \(e\left(\frac{11}{39}\right)\) | \(e\left(\frac{38}{39}\right)\) | \(e\left(\frac{5}{39}\right)\) | \(e\left(\frac{7}{13}\right)\) | \(e\left(\frac{23}{39}\right)\) | \(e\left(\frac{6}{13}\right)\) | \(e\left(\frac{2}{39}\right)\) |
\(\chi_{79}(6,\cdot)\) | 79.h | 78 | yes | \(-1\) | \(1\) | \(e\left(\frac{10}{39}\right)\) | \(e\left(\frac{5}{78}\right)\) | \(e\left(\frac{20}{39}\right)\) | \(e\left(\frac{38}{39}\right)\) | \(e\left(\frac{25}{78}\right)\) | \(e\left(\frac{31}{78}\right)\) | \(e\left(\frac{10}{13}\right)\) | \(e\left(\frac{5}{39}\right)\) | \(e\left(\frac{3}{13}\right)\) | \(e\left(\frac{14}{39}\right)\) |
\(\chi_{79}(7,\cdot)\) | 79.h | 78 | yes | \(-1\) | \(1\) | \(e\left(\frac{28}{39}\right)\) | \(e\left(\frac{53}{78}\right)\) | \(e\left(\frac{17}{39}\right)\) | \(e\left(\frac{5}{39}\right)\) | \(e\left(\frac{31}{78}\right)\) | \(e\left(\frac{1}{78}\right)\) | \(e\left(\frac{2}{13}\right)\) | \(e\left(\frac{14}{39}\right)\) | \(e\left(\frac{11}{13}\right)\) | \(e\left(\frac{8}{39}\right)\) |
\(\chi_{79}(8,\cdot)\) | 79.e | 13 | yes | \(1\) | \(1\) | \(e\left(\frac{8}{13}\right)\) | \(e\left(\frac{2}{13}\right)\) | \(e\left(\frac{3}{13}\right)\) | \(e\left(\frac{7}{13}\right)\) | \(e\left(\frac{10}{13}\right)\) | \(e\left(\frac{2}{13}\right)\) | \(e\left(\frac{11}{13}\right)\) | \(e\left(\frac{4}{13}\right)\) | \(e\left(\frac{2}{13}\right)\) | \(e\left(\frac{6}{13}\right)\) |
\(\chi_{79}(9,\cdot)\) | 79.g | 39 | yes | \(1\) | \(1\) | \(e\left(\frac{4}{39}\right)\) | \(e\left(\frac{1}{39}\right)\) | \(e\left(\frac{8}{39}\right)\) | \(e\left(\frac{23}{39}\right)\) | \(e\left(\frac{5}{39}\right)\) | \(e\left(\frac{14}{39}\right)\) | \(e\left(\frac{4}{13}\right)\) | \(e\left(\frac{2}{39}\right)\) | \(e\left(\frac{9}{13}\right)\) | \(e\left(\frac{29}{39}\right)\) |
\(\chi_{79}(10,\cdot)\) | 79.e | 13 | yes | \(1\) | \(1\) | \(e\left(\frac{5}{13}\right)\) | \(e\left(\frac{11}{13}\right)\) | \(e\left(\frac{10}{13}\right)\) | \(e\left(\frac{6}{13}\right)\) | \(e\left(\frac{3}{13}\right)\) | \(e\left(\frac{11}{13}\right)\) | \(e\left(\frac{2}{13}\right)\) | \(e\left(\frac{9}{13}\right)\) | \(e\left(\frac{11}{13}\right)\) | \(e\left(\frac{7}{13}\right)\) |
\(\chi_{79}(11,\cdot)\) | 79.g | 39 | yes | \(1\) | \(1\) | \(e\left(\frac{19}{39}\right)\) | \(e\left(\frac{34}{39}\right)\) | \(e\left(\frac{38}{39}\right)\) | \(e\left(\frac{2}{39}\right)\) | \(e\left(\frac{14}{39}\right)\) | \(e\left(\frac{8}{39}\right)\) | \(e\left(\frac{6}{13}\right)\) | \(e\left(\frac{29}{39}\right)\) | \(e\left(\frac{7}{13}\right)\) | \(e\left(\frac{11}{39}\right)\) |
\(\chi_{79}(12,\cdot)\) | 79.f | 26 | yes | \(-1\) | \(1\) | \(e\left(\frac{6}{13}\right)\) | \(e\left(\frac{3}{26}\right)\) | \(e\left(\frac{12}{13}\right)\) | \(e\left(\frac{2}{13}\right)\) | \(e\left(\frac{15}{26}\right)\) | \(e\left(\frac{3}{26}\right)\) | \(e\left(\frac{5}{13}\right)\) | \(e\left(\frac{3}{13}\right)\) | \(e\left(\frac{8}{13}\right)\) | \(e\left(\frac{11}{13}\right)\) |
\(\chi_{79}(13,\cdot)\) | 79.g | 39 | yes | \(1\) | \(1\) | \(e\left(\frac{29}{39}\right)\) | \(e\left(\frac{17}{39}\right)\) | \(e\left(\frac{19}{39}\right)\) | \(e\left(\frac{1}{39}\right)\) | \(e\left(\frac{7}{39}\right)\) | \(e\left(\frac{4}{39}\right)\) | \(e\left(\frac{3}{13}\right)\) | \(e\left(\frac{34}{39}\right)\) | \(e\left(\frac{10}{13}\right)\) | \(e\left(\frac{25}{39}\right)\) |
\(\chi_{79}(14,\cdot)\) | 79.f | 26 | yes | \(-1\) | \(1\) | \(e\left(\frac{12}{13}\right)\) | \(e\left(\frac{19}{26}\right)\) | \(e\left(\frac{11}{13}\right)\) | \(e\left(\frac{4}{13}\right)\) | \(e\left(\frac{17}{26}\right)\) | \(e\left(\frac{19}{26}\right)\) | \(e\left(\frac{10}{13}\right)\) | \(e\left(\frac{6}{13}\right)\) | \(e\left(\frac{3}{13}\right)\) | \(e\left(\frac{9}{13}\right)\) |
\(\chi_{79}(15,\cdot)\) | 79.f | 26 | yes | \(-1\) | \(1\) | \(e\left(\frac{3}{13}\right)\) | \(e\left(\frac{21}{26}\right)\) | \(e\left(\frac{6}{13}\right)\) | \(e\left(\frac{1}{13}\right)\) | \(e\left(\frac{1}{26}\right)\) | \(e\left(\frac{21}{26}\right)\) | \(e\left(\frac{9}{13}\right)\) | \(e\left(\frac{8}{13}\right)\) | \(e\left(\frac{4}{13}\right)\) | \(e\left(\frac{12}{13}\right)\) |
\(\chi_{79}(16,\cdot)\) | 79.g | 39 | yes | \(1\) | \(1\) | \(e\left(\frac{32}{39}\right)\) | \(e\left(\frac{8}{39}\right)\) | \(e\left(\frac{25}{39}\right)\) | \(e\left(\frac{28}{39}\right)\) | \(e\left(\frac{1}{39}\right)\) | \(e\left(\frac{34}{39}\right)\) | \(e\left(\frac{6}{13}\right)\) | \(e\left(\frac{16}{39}\right)\) | \(e\left(\frac{7}{13}\right)\) | \(e\left(\frac{37}{39}\right)\) |
\(\chi_{79}(17,\cdot)\) | 79.f | 26 | yes | \(-1\) | \(1\) | \(e\left(\frac{1}{13}\right)\) | \(e\left(\frac{7}{26}\right)\) | \(e\left(\frac{2}{13}\right)\) | \(e\left(\frac{9}{13}\right)\) | \(e\left(\frac{9}{26}\right)\) | \(e\left(\frac{7}{26}\right)\) | \(e\left(\frac{3}{13}\right)\) | \(e\left(\frac{7}{13}\right)\) | \(e\left(\frac{10}{13}\right)\) | \(e\left(\frac{4}{13}\right)\) |
\(\chi_{79}(18,\cdot)\) | 79.e | 13 | yes | \(1\) | \(1\) | \(e\left(\frac{4}{13}\right)\) | \(e\left(\frac{1}{13}\right)\) | \(e\left(\frac{8}{13}\right)\) | \(e\left(\frac{10}{13}\right)\) | \(e\left(\frac{5}{13}\right)\) | \(e\left(\frac{1}{13}\right)\) | \(e\left(\frac{12}{13}\right)\) | \(e\left(\frac{2}{13}\right)\) | \(e\left(\frac{1}{13}\right)\) | \(e\left(\frac{3}{13}\right)\) |
\(\chi_{79}(19,\cdot)\) | 79.g | 39 | yes | \(1\) | \(1\) | \(e\left(\frac{25}{39}\right)\) | \(e\left(\frac{16}{39}\right)\) | \(e\left(\frac{11}{39}\right)\) | \(e\left(\frac{17}{39}\right)\) | \(e\left(\frac{2}{39}\right)\) | \(e\left(\frac{29}{39}\right)\) | \(e\left(\frac{12}{13}\right)\) | \(e\left(\frac{32}{39}\right)\) | \(e\left(\frac{1}{13}\right)\) | \(e\left(\frac{35}{39}\right)\) |
\(\chi_{79}(20,\cdot)\) | 79.g | 39 | yes | \(1\) | \(1\) | \(e\left(\frac{23}{39}\right)\) | \(e\left(\frac{35}{39}\right)\) | \(e\left(\frac{7}{39}\right)\) | \(e\left(\frac{25}{39}\right)\) | \(e\left(\frac{19}{39}\right)\) | \(e\left(\frac{22}{39}\right)\) | \(e\left(\frac{10}{13}\right)\) | \(e\left(\frac{31}{39}\right)\) | \(e\left(\frac{3}{13}\right)\) | \(e\left(\frac{1}{39}\right)\) |
\(\chi_{79}(21,\cdot)\) | 79.e | 13 | yes | \(1\) | \(1\) | \(e\left(\frac{10}{13}\right)\) | \(e\left(\frac{9}{13}\right)\) | \(e\left(\frac{7}{13}\right)\) | \(e\left(\frac{12}{13}\right)\) | \(e\left(\frac{6}{13}\right)\) | \(e\left(\frac{9}{13}\right)\) | \(e\left(\frac{4}{13}\right)\) | \(e\left(\frac{5}{13}\right)\) | \(e\left(\frac{9}{13}\right)\) | \(e\left(\frac{1}{13}\right)\) |
\(\chi_{79}(22,\cdot)\) | 79.e | 13 | yes | \(1\) | \(1\) | \(e\left(\frac{9}{13}\right)\) | \(e\left(\frac{12}{13}\right)\) | \(e\left(\frac{5}{13}\right)\) | \(e\left(\frac{3}{13}\right)\) | \(e\left(\frac{8}{13}\right)\) | \(e\left(\frac{12}{13}\right)\) | \(e\left(\frac{1}{13}\right)\) | \(e\left(\frac{11}{13}\right)\) | \(e\left(\frac{12}{13}\right)\) | \(e\left(\frac{10}{13}\right)\) |
\(\chi_{79}(23,\cdot)\) | 79.c | 3 | yes | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
\(\chi_{79}(24,\cdot)\) | 79.d | 6 | yes | \(-1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
\(\chi_{79}(25,\cdot)\) | 79.g | 39 | yes | \(1\) | \(1\) | \(e\left(\frac{14}{39}\right)\) | \(e\left(\frac{23}{39}\right)\) | \(e\left(\frac{28}{39}\right)\) | \(e\left(\frac{22}{39}\right)\) | \(e\left(\frac{37}{39}\right)\) | \(e\left(\frac{10}{39}\right)\) | \(e\left(\frac{1}{13}\right)\) | \(e\left(\frac{7}{39}\right)\) | \(e\left(\frac{12}{13}\right)\) | \(e\left(\frac{4}{39}\right)\) |
\(\chi_{79}(26,\cdot)\) | 79.g | 39 | yes | \(1\) | \(1\) | \(e\left(\frac{37}{39}\right)\) | \(e\left(\frac{19}{39}\right)\) | \(e\left(\frac{35}{39}\right)\) | \(e\left(\frac{8}{39}\right)\) | \(e\left(\frac{17}{39}\right)\) | \(e\left(\frac{32}{39}\right)\) | \(e\left(\frac{11}{13}\right)\) | \(e\left(\frac{38}{39}\right)\) | \(e\left(\frac{2}{13}\right)\) | \(e\left(\frac{5}{39}\right)\) |
\(\chi_{79}(27,\cdot)\) | 79.f | 26 | yes | \(-1\) | \(1\) | \(e\left(\frac{2}{13}\right)\) | \(e\left(\frac{1}{26}\right)\) | \(e\left(\frac{4}{13}\right)\) | \(e\left(\frac{5}{13}\right)\) | \(e\left(\frac{5}{26}\right)\) | \(e\left(\frac{1}{26}\right)\) | \(e\left(\frac{6}{13}\right)\) | \(e\left(\frac{1}{13}\right)\) | \(e\left(\frac{7}{13}\right)\) | \(e\left(\frac{8}{13}\right)\) |
\(\chi_{79}(28,\cdot)\) | 79.h | 78 | yes | \(-1\) | \(1\) | \(e\left(\frac{5}{39}\right)\) | \(e\left(\frac{61}{78}\right)\) | \(e\left(\frac{10}{39}\right)\) | \(e\left(\frac{19}{39}\right)\) | \(e\left(\frac{71}{78}\right)\) | \(e\left(\frac{35}{78}\right)\) | \(e\left(\frac{5}{13}\right)\) | \(e\left(\frac{22}{39}\right)\) | \(e\left(\frac{8}{13}\right)\) | \(e\left(\frac{7}{39}\right)\) |
\(\chi_{79}(29,\cdot)\) | 79.h | 78 | yes | \(-1\) | \(1\) | \(e\left(\frac{22}{39}\right)\) | \(e\left(\frac{11}{78}\right)\) | \(e\left(\frac{5}{39}\right)\) | \(e\left(\frac{29}{39}\right)\) | \(e\left(\frac{55}{78}\right)\) | \(e\left(\frac{37}{78}\right)\) | \(e\left(\frac{9}{13}\right)\) | \(e\left(\frac{11}{39}\right)\) | \(e\left(\frac{4}{13}\right)\) | \(e\left(\frac{23}{39}\right)\) |
\(\chi_{79}(30,\cdot)\) | 79.h | 78 | yes | \(-1\) | \(1\) | \(e\left(\frac{17}{39}\right)\) | \(e\left(\frac{67}{78}\right)\) | \(e\left(\frac{34}{39}\right)\) | \(e\left(\frac{10}{39}\right)\) | \(e\left(\frac{23}{78}\right)\) | \(e\left(\frac{41}{78}\right)\) | \(e\left(\frac{4}{13}\right)\) | \(e\left(\frac{28}{39}\right)\) | \(e\left(\frac{9}{13}\right)\) | \(e\left(\frac{16}{39}\right)\) |
\(\chi_{79}(31,\cdot)\) | 79.g | 39 | yes | \(1\) | \(1\) | \(e\left(\frac{34}{39}\right)\) | \(e\left(\frac{28}{39}\right)\) | \(e\left(\frac{29}{39}\right)\) | \(e\left(\frac{20}{39}\right)\) | \(e\left(\frac{23}{39}\right)\) | \(e\left(\frac{2}{39}\right)\) | \(e\left(\frac{8}{13}\right)\) | \(e\left(\frac{17}{39}\right)\) | \(e\left(\frac{5}{13}\right)\) | \(e\left(\frac{32}{39}\right)\) |
\(\chi_{79}(32,\cdot)\) | 79.g | 39 | yes | \(1\) | \(1\) | \(e\left(\frac{1}{39}\right)\) | \(e\left(\frac{10}{39}\right)\) | \(e\left(\frac{2}{39}\right)\) | \(e\left(\frac{35}{39}\right)\) | \(e\left(\frac{11}{39}\right)\) | \(e\left(\frac{23}{39}\right)\) | \(e\left(\frac{1}{13}\right)\) | \(e\left(\frac{20}{39}\right)\) | \(e\left(\frac{12}{13}\right)\) | \(e\left(\frac{17}{39}\right)\) |