sage: H = DirichletGroup(59)
pari: g = idealstar(,59,2)
Character group
sage: G.order()
pari: g.no
| ||
Order | = | 58 |
sage: H.invariants()
pari: g.cyc
| ||
Structure | = | \(C_{58}\) |
sage: H.gens()
pari: g.gen
| ||
Generators | = | $\chi_{59}(2,\cdot)$ |
First 32 of 58 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 | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{59}(1,\cdot)\) | 59.a | 1 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
\(\chi_{59}(2,\cdot)\) | 59.d | 58 | yes | \(-1\) | \(1\) | \(e\left(\frac{1}{58}\right)\) | \(e\left(\frac{25}{29}\right)\) | \(e\left(\frac{1}{29}\right)\) | \(e\left(\frac{3}{29}\right)\) | \(e\left(\frac{51}{58}\right)\) | \(e\left(\frac{9}{29}\right)\) | \(e\left(\frac{3}{58}\right)\) | \(e\left(\frac{21}{29}\right)\) | \(e\left(\frac{7}{58}\right)\) | \(e\left(\frac{25}{58}\right)\) |
\(\chi_{59}(3,\cdot)\) | 59.c | 29 | yes | \(1\) | \(1\) | \(e\left(\frac{25}{29}\right)\) | \(e\left(\frac{3}{29}\right)\) | \(e\left(\frac{21}{29}\right)\) | \(e\left(\frac{5}{29}\right)\) | \(e\left(\frac{28}{29}\right)\) | \(e\left(\frac{15}{29}\right)\) | \(e\left(\frac{17}{29}\right)\) | \(e\left(\frac{6}{29}\right)\) | \(e\left(\frac{1}{29}\right)\) | \(e\left(\frac{16}{29}\right)\) |
\(\chi_{59}(4,\cdot)\) | 59.c | 29 | yes | \(1\) | \(1\) | \(e\left(\frac{1}{29}\right)\) | \(e\left(\frac{21}{29}\right)\) | \(e\left(\frac{2}{29}\right)\) | \(e\left(\frac{6}{29}\right)\) | \(e\left(\frac{22}{29}\right)\) | \(e\left(\frac{18}{29}\right)\) | \(e\left(\frac{3}{29}\right)\) | \(e\left(\frac{13}{29}\right)\) | \(e\left(\frac{7}{29}\right)\) | \(e\left(\frac{25}{29}\right)\) |
\(\chi_{59}(5,\cdot)\) | 59.c | 29 | yes | \(1\) | \(1\) | \(e\left(\frac{3}{29}\right)\) | \(e\left(\frac{5}{29}\right)\) | \(e\left(\frac{6}{29}\right)\) | \(e\left(\frac{18}{29}\right)\) | \(e\left(\frac{8}{29}\right)\) | \(e\left(\frac{25}{29}\right)\) | \(e\left(\frac{9}{29}\right)\) | \(e\left(\frac{10}{29}\right)\) | \(e\left(\frac{21}{29}\right)\) | \(e\left(\frac{17}{29}\right)\) |
\(\chi_{59}(6,\cdot)\) | 59.d | 58 | yes | \(-1\) | \(1\) | \(e\left(\frac{51}{58}\right)\) | \(e\left(\frac{28}{29}\right)\) | \(e\left(\frac{22}{29}\right)\) | \(e\left(\frac{8}{29}\right)\) | \(e\left(\frac{49}{58}\right)\) | \(e\left(\frac{24}{29}\right)\) | \(e\left(\frac{37}{58}\right)\) | \(e\left(\frac{27}{29}\right)\) | \(e\left(\frac{9}{58}\right)\) | \(e\left(\frac{57}{58}\right)\) |
\(\chi_{59}(7,\cdot)\) | 59.c | 29 | yes | \(1\) | \(1\) | \(e\left(\frac{9}{29}\right)\) | \(e\left(\frac{15}{29}\right)\) | \(e\left(\frac{18}{29}\right)\) | \(e\left(\frac{25}{29}\right)\) | \(e\left(\frac{24}{29}\right)\) | \(e\left(\frac{17}{29}\right)\) | \(e\left(\frac{27}{29}\right)\) | \(e\left(\frac{1}{29}\right)\) | \(e\left(\frac{5}{29}\right)\) | \(e\left(\frac{22}{29}\right)\) |
\(\chi_{59}(8,\cdot)\) | 59.d | 58 | yes | \(-1\) | \(1\) | \(e\left(\frac{3}{58}\right)\) | \(e\left(\frac{17}{29}\right)\) | \(e\left(\frac{3}{29}\right)\) | \(e\left(\frac{9}{29}\right)\) | \(e\left(\frac{37}{58}\right)\) | \(e\left(\frac{27}{29}\right)\) | \(e\left(\frac{9}{58}\right)\) | \(e\left(\frac{5}{29}\right)\) | \(e\left(\frac{21}{58}\right)\) | \(e\left(\frac{17}{58}\right)\) |
\(\chi_{59}(9,\cdot)\) | 59.c | 29 | yes | \(1\) | \(1\) | \(e\left(\frac{21}{29}\right)\) | \(e\left(\frac{6}{29}\right)\) | \(e\left(\frac{13}{29}\right)\) | \(e\left(\frac{10}{29}\right)\) | \(e\left(\frac{27}{29}\right)\) | \(e\left(\frac{1}{29}\right)\) | \(e\left(\frac{5}{29}\right)\) | \(e\left(\frac{12}{29}\right)\) | \(e\left(\frac{2}{29}\right)\) | \(e\left(\frac{3}{29}\right)\) |
\(\chi_{59}(10,\cdot)\) | 59.d | 58 | yes | \(-1\) | \(1\) | \(e\left(\frac{7}{58}\right)\) | \(e\left(\frac{1}{29}\right)\) | \(e\left(\frac{7}{29}\right)\) | \(e\left(\frac{21}{29}\right)\) | \(e\left(\frac{9}{58}\right)\) | \(e\left(\frac{5}{29}\right)\) | \(e\left(\frac{21}{58}\right)\) | \(e\left(\frac{2}{29}\right)\) | \(e\left(\frac{49}{58}\right)\) | \(e\left(\frac{1}{58}\right)\) |
\(\chi_{59}(11,\cdot)\) | 59.d | 58 | yes | \(-1\) | \(1\) | \(e\left(\frac{25}{58}\right)\) | \(e\left(\frac{16}{29}\right)\) | \(e\left(\frac{25}{29}\right)\) | \(e\left(\frac{17}{29}\right)\) | \(e\left(\frac{57}{58}\right)\) | \(e\left(\frac{22}{29}\right)\) | \(e\left(\frac{17}{58}\right)\) | \(e\left(\frac{3}{29}\right)\) | \(e\left(\frac{1}{58}\right)\) | \(e\left(\frac{45}{58}\right)\) |
\(\chi_{59}(12,\cdot)\) | 59.c | 29 | yes | \(1\) | \(1\) | \(e\left(\frac{26}{29}\right)\) | \(e\left(\frac{24}{29}\right)\) | \(e\left(\frac{23}{29}\right)\) | \(e\left(\frac{11}{29}\right)\) | \(e\left(\frac{21}{29}\right)\) | \(e\left(\frac{4}{29}\right)\) | \(e\left(\frac{20}{29}\right)\) | \(e\left(\frac{19}{29}\right)\) | \(e\left(\frac{8}{29}\right)\) | \(e\left(\frac{12}{29}\right)\) |
\(\chi_{59}(13,\cdot)\) | 59.d | 58 | yes | \(-1\) | \(1\) | \(e\left(\frac{45}{58}\right)\) | \(e\left(\frac{23}{29}\right)\) | \(e\left(\frac{16}{29}\right)\) | \(e\left(\frac{19}{29}\right)\) | \(e\left(\frac{33}{58}\right)\) | \(e\left(\frac{28}{29}\right)\) | \(e\left(\frac{19}{58}\right)\) | \(e\left(\frac{17}{29}\right)\) | \(e\left(\frac{25}{58}\right)\) | \(e\left(\frac{23}{58}\right)\) |
\(\chi_{59}(14,\cdot)\) | 59.d | 58 | yes | \(-1\) | \(1\) | \(e\left(\frac{19}{58}\right)\) | \(e\left(\frac{11}{29}\right)\) | \(e\left(\frac{19}{29}\right)\) | \(e\left(\frac{28}{29}\right)\) | \(e\left(\frac{41}{58}\right)\) | \(e\left(\frac{26}{29}\right)\) | \(e\left(\frac{57}{58}\right)\) | \(e\left(\frac{22}{29}\right)\) | \(e\left(\frac{17}{58}\right)\) | \(e\left(\frac{11}{58}\right)\) |
\(\chi_{59}(15,\cdot)\) | 59.c | 29 | yes | \(1\) | \(1\) | \(e\left(\frac{28}{29}\right)\) | \(e\left(\frac{8}{29}\right)\) | \(e\left(\frac{27}{29}\right)\) | \(e\left(\frac{23}{29}\right)\) | \(e\left(\frac{7}{29}\right)\) | \(e\left(\frac{11}{29}\right)\) | \(e\left(\frac{26}{29}\right)\) | \(e\left(\frac{16}{29}\right)\) | \(e\left(\frac{22}{29}\right)\) | \(e\left(\frac{4}{29}\right)\) |
\(\chi_{59}(16,\cdot)\) | 59.c | 29 | yes | \(1\) | \(1\) | \(e\left(\frac{2}{29}\right)\) | \(e\left(\frac{13}{29}\right)\) | \(e\left(\frac{4}{29}\right)\) | \(e\left(\frac{12}{29}\right)\) | \(e\left(\frac{15}{29}\right)\) | \(e\left(\frac{7}{29}\right)\) | \(e\left(\frac{6}{29}\right)\) | \(e\left(\frac{26}{29}\right)\) | \(e\left(\frac{14}{29}\right)\) | \(e\left(\frac{21}{29}\right)\) |
\(\chi_{59}(17,\cdot)\) | 59.c | 29 | yes | \(1\) | \(1\) | \(e\left(\frac{20}{29}\right)\) | \(e\left(\frac{14}{29}\right)\) | \(e\left(\frac{11}{29}\right)\) | \(e\left(\frac{4}{29}\right)\) | \(e\left(\frac{5}{29}\right)\) | \(e\left(\frac{12}{29}\right)\) | \(e\left(\frac{2}{29}\right)\) | \(e\left(\frac{28}{29}\right)\) | \(e\left(\frac{24}{29}\right)\) | \(e\left(\frac{7}{29}\right)\) |
\(\chi_{59}(18,\cdot)\) | 59.d | 58 | yes | \(-1\) | \(1\) | \(e\left(\frac{43}{58}\right)\) | \(e\left(\frac{2}{29}\right)\) | \(e\left(\frac{14}{29}\right)\) | \(e\left(\frac{13}{29}\right)\) | \(e\left(\frac{47}{58}\right)\) | \(e\left(\frac{10}{29}\right)\) | \(e\left(\frac{13}{58}\right)\) | \(e\left(\frac{4}{29}\right)\) | \(e\left(\frac{11}{58}\right)\) | \(e\left(\frac{31}{58}\right)\) |
\(\chi_{59}(19,\cdot)\) | 59.c | 29 | yes | \(1\) | \(1\) | \(e\left(\frac{19}{29}\right)\) | \(e\left(\frac{22}{29}\right)\) | \(e\left(\frac{9}{29}\right)\) | \(e\left(\frac{27}{29}\right)\) | \(e\left(\frac{12}{29}\right)\) | \(e\left(\frac{23}{29}\right)\) | \(e\left(\frac{28}{29}\right)\) | \(e\left(\frac{15}{29}\right)\) | \(e\left(\frac{17}{29}\right)\) | \(e\left(\frac{11}{29}\right)\) |
\(\chi_{59}(20,\cdot)\) | 59.c | 29 | yes | \(1\) | \(1\) | \(e\left(\frac{4}{29}\right)\) | \(e\left(\frac{26}{29}\right)\) | \(e\left(\frac{8}{29}\right)\) | \(e\left(\frac{24}{29}\right)\) | \(e\left(\frac{1}{29}\right)\) | \(e\left(\frac{14}{29}\right)\) | \(e\left(\frac{12}{29}\right)\) | \(e\left(\frac{23}{29}\right)\) | \(e\left(\frac{28}{29}\right)\) | \(e\left(\frac{13}{29}\right)\) |
\(\chi_{59}(21,\cdot)\) | 59.c | 29 | yes | \(1\) | \(1\) | \(e\left(\frac{5}{29}\right)\) | \(e\left(\frac{18}{29}\right)\) | \(e\left(\frac{10}{29}\right)\) | \(e\left(\frac{1}{29}\right)\) | \(e\left(\frac{23}{29}\right)\) | \(e\left(\frac{3}{29}\right)\) | \(e\left(\frac{15}{29}\right)\) | \(e\left(\frac{7}{29}\right)\) | \(e\left(\frac{6}{29}\right)\) | \(e\left(\frac{9}{29}\right)\) |
\(\chi_{59}(22,\cdot)\) | 59.c | 29 | yes | \(1\) | \(1\) | \(e\left(\frac{13}{29}\right)\) | \(e\left(\frac{12}{29}\right)\) | \(e\left(\frac{26}{29}\right)\) | \(e\left(\frac{20}{29}\right)\) | \(e\left(\frac{25}{29}\right)\) | \(e\left(\frac{2}{29}\right)\) | \(e\left(\frac{10}{29}\right)\) | \(e\left(\frac{24}{29}\right)\) | \(e\left(\frac{4}{29}\right)\) | \(e\left(\frac{6}{29}\right)\) |
\(\chi_{59}(23,\cdot)\) | 59.d | 58 | yes | \(-1\) | \(1\) | \(e\left(\frac{15}{58}\right)\) | \(e\left(\frac{27}{29}\right)\) | \(e\left(\frac{15}{29}\right)\) | \(e\left(\frac{16}{29}\right)\) | \(e\left(\frac{11}{58}\right)\) | \(e\left(\frac{19}{29}\right)\) | \(e\left(\frac{45}{58}\right)\) | \(e\left(\frac{25}{29}\right)\) | \(e\left(\frac{47}{58}\right)\) | \(e\left(\frac{27}{58}\right)\) |
\(\chi_{59}(24,\cdot)\) | 59.d | 58 | yes | \(-1\) | \(1\) | \(e\left(\frac{53}{58}\right)\) | \(e\left(\frac{20}{29}\right)\) | \(e\left(\frac{24}{29}\right)\) | \(e\left(\frac{14}{29}\right)\) | \(e\left(\frac{35}{58}\right)\) | \(e\left(\frac{13}{29}\right)\) | \(e\left(\frac{43}{58}\right)\) | \(e\left(\frac{11}{29}\right)\) | \(e\left(\frac{23}{58}\right)\) | \(e\left(\frac{49}{58}\right)\) |
\(\chi_{59}(25,\cdot)\) | 59.c | 29 | yes | \(1\) | \(1\) | \(e\left(\frac{6}{29}\right)\) | \(e\left(\frac{10}{29}\right)\) | \(e\left(\frac{12}{29}\right)\) | \(e\left(\frac{7}{29}\right)\) | \(e\left(\frac{16}{29}\right)\) | \(e\left(\frac{21}{29}\right)\) | \(e\left(\frac{18}{29}\right)\) | \(e\left(\frac{20}{29}\right)\) | \(e\left(\frac{13}{29}\right)\) | \(e\left(\frac{5}{29}\right)\) |
\(\chi_{59}(26,\cdot)\) | 59.c | 29 | yes | \(1\) | \(1\) | \(e\left(\frac{23}{29}\right)\) | \(e\left(\frac{19}{29}\right)\) | \(e\left(\frac{17}{29}\right)\) | \(e\left(\frac{22}{29}\right)\) | \(e\left(\frac{13}{29}\right)\) | \(e\left(\frac{8}{29}\right)\) | \(e\left(\frac{11}{29}\right)\) | \(e\left(\frac{9}{29}\right)\) | \(e\left(\frac{16}{29}\right)\) | \(e\left(\frac{24}{29}\right)\) |
\(\chi_{59}(27,\cdot)\) | 59.c | 29 | yes | \(1\) | \(1\) | \(e\left(\frac{17}{29}\right)\) | \(e\left(\frac{9}{29}\right)\) | \(e\left(\frac{5}{29}\right)\) | \(e\left(\frac{15}{29}\right)\) | \(e\left(\frac{26}{29}\right)\) | \(e\left(\frac{16}{29}\right)\) | \(e\left(\frac{22}{29}\right)\) | \(e\left(\frac{18}{29}\right)\) | \(e\left(\frac{3}{29}\right)\) | \(e\left(\frac{19}{29}\right)\) |
\(\chi_{59}(28,\cdot)\) | 59.c | 29 | yes | \(1\) | \(1\) | \(e\left(\frac{10}{29}\right)\) | \(e\left(\frac{7}{29}\right)\) | \(e\left(\frac{20}{29}\right)\) | \(e\left(\frac{2}{29}\right)\) | \(e\left(\frac{17}{29}\right)\) | \(e\left(\frac{6}{29}\right)\) | \(e\left(\frac{1}{29}\right)\) | \(e\left(\frac{14}{29}\right)\) | \(e\left(\frac{12}{29}\right)\) | \(e\left(\frac{18}{29}\right)\) |
\(\chi_{59}(29,\cdot)\) | 59.c | 29 | yes | \(1\) | \(1\) | \(e\left(\frac{14}{29}\right)\) | \(e\left(\frac{4}{29}\right)\) | \(e\left(\frac{28}{29}\right)\) | \(e\left(\frac{26}{29}\right)\) | \(e\left(\frac{18}{29}\right)\) | \(e\left(\frac{20}{29}\right)\) | \(e\left(\frac{13}{29}\right)\) | \(e\left(\frac{8}{29}\right)\) | \(e\left(\frac{11}{29}\right)\) | \(e\left(\frac{2}{29}\right)\) |
\(\chi_{59}(30,\cdot)\) | 59.d | 58 | yes | \(-1\) | \(1\) | \(e\left(\frac{57}{58}\right)\) | \(e\left(\frac{4}{29}\right)\) | \(e\left(\frac{28}{29}\right)\) | \(e\left(\frac{26}{29}\right)\) | \(e\left(\frac{7}{58}\right)\) | \(e\left(\frac{20}{29}\right)\) | \(e\left(\frac{55}{58}\right)\) | \(e\left(\frac{8}{29}\right)\) | \(e\left(\frac{51}{58}\right)\) | \(e\left(\frac{33}{58}\right)\) |
\(\chi_{59}(31,\cdot)\) | 59.d | 58 | yes | \(-1\) | \(1\) | \(e\left(\frac{49}{58}\right)\) | \(e\left(\frac{7}{29}\right)\) | \(e\left(\frac{20}{29}\right)\) | \(e\left(\frac{2}{29}\right)\) | \(e\left(\frac{5}{58}\right)\) | \(e\left(\frac{6}{29}\right)\) | \(e\left(\frac{31}{58}\right)\) | \(e\left(\frac{14}{29}\right)\) | \(e\left(\frac{53}{58}\right)\) | \(e\left(\frac{7}{58}\right)\) |
\(\chi_{59}(32,\cdot)\) | 59.d | 58 | yes | \(-1\) | \(1\) | \(e\left(\frac{5}{58}\right)\) | \(e\left(\frac{9}{29}\right)\) | \(e\left(\frac{5}{29}\right)\) | \(e\left(\frac{15}{29}\right)\) | \(e\left(\frac{23}{58}\right)\) | \(e\left(\frac{16}{29}\right)\) | \(e\left(\frac{15}{58}\right)\) | \(e\left(\frac{18}{29}\right)\) | \(e\left(\frac{35}{58}\right)\) | \(e\left(\frac{9}{58}\right)\) |