sage: H = DirichletGroup(103)
pari: g = idealstar(,103,2)
Character group
sage: G.order()
pari: g.no
| ||
Order | = | 102 |
sage: H.invariants()
pari: g.cyc
| ||
Structure | = | \(C_{102}\) |
sage: H.gens()
pari: g.gen
| ||
Generators | = | $\chi_{103}(5,\cdot)$ |
First 32 of 102 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 | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{103}(1,\cdot)\) | 103.a | 1 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
\(\chi_{103}(2,\cdot)\) | 103.g | 51 | yes | \(1\) | \(1\) | \(e\left(\frac{50}{51}\right)\) | \(e\left(\frac{14}{17}\right)\) | \(e\left(\frac{49}{51}\right)\) | \(e\left(\frac{22}{51}\right)\) | \(e\left(\frac{41}{51}\right)\) | \(e\left(\frac{37}{51}\right)\) | \(e\left(\frac{16}{17}\right)\) | \(e\left(\frac{11}{17}\right)\) | \(e\left(\frac{7}{17}\right)\) | \(e\left(\frac{16}{51}\right)\) |
\(\chi_{103}(3,\cdot)\) | 103.f | 34 | yes | \(-1\) | \(1\) | \(e\left(\frac{14}{17}\right)\) | \(e\left(\frac{31}{34}\right)\) | \(e\left(\frac{11}{17}\right)\) | \(e\left(\frac{13}{34}\right)\) | \(e\left(\frac{25}{34}\right)\) | \(e\left(\frac{9}{17}\right)\) | \(e\left(\frac{8}{17}\right)\) | \(e\left(\frac{14}{17}\right)\) | \(e\left(\frac{7}{34}\right)\) | \(e\left(\frac{11}{34}\right)\) |
\(\chi_{103}(4,\cdot)\) | 103.g | 51 | yes | \(1\) | \(1\) | \(e\left(\frac{49}{51}\right)\) | \(e\left(\frac{11}{17}\right)\) | \(e\left(\frac{47}{51}\right)\) | \(e\left(\frac{44}{51}\right)\) | \(e\left(\frac{31}{51}\right)\) | \(e\left(\frac{23}{51}\right)\) | \(e\left(\frac{15}{17}\right)\) | \(e\left(\frac{5}{17}\right)\) | \(e\left(\frac{14}{17}\right)\) | \(e\left(\frac{32}{51}\right)\) |
\(\chi_{103}(5,\cdot)\) | 103.h | 102 | yes | \(-1\) | \(1\) | \(e\left(\frac{22}{51}\right)\) | \(e\left(\frac{13}{34}\right)\) | \(e\left(\frac{44}{51}\right)\) | \(e\left(\frac{1}{102}\right)\) | \(e\left(\frac{83}{102}\right)\) | \(e\left(\frac{2}{51}\right)\) | \(e\left(\frac{5}{17}\right)\) | \(e\left(\frac{13}{17}\right)\) | \(e\left(\frac{15}{34}\right)\) | \(e\left(\frac{61}{102}\right)\) |
\(\chi_{103}(6,\cdot)\) | 103.h | 102 | yes | \(-1\) | \(1\) | \(e\left(\frac{41}{51}\right)\) | \(e\left(\frac{25}{34}\right)\) | \(e\left(\frac{31}{51}\right)\) | \(e\left(\frac{83}{102}\right)\) | \(e\left(\frac{55}{102}\right)\) | \(e\left(\frac{13}{51}\right)\) | \(e\left(\frac{7}{17}\right)\) | \(e\left(\frac{8}{17}\right)\) | \(e\left(\frac{21}{34}\right)\) | \(e\left(\frac{65}{102}\right)\) |
\(\chi_{103}(7,\cdot)\) | 103.g | 51 | yes | \(1\) | \(1\) | \(e\left(\frac{37}{51}\right)\) | \(e\left(\frac{9}{17}\right)\) | \(e\left(\frac{23}{51}\right)\) | \(e\left(\frac{2}{51}\right)\) | \(e\left(\frac{13}{51}\right)\) | \(e\left(\frac{8}{51}\right)\) | \(e\left(\frac{3}{17}\right)\) | \(e\left(\frac{1}{17}\right)\) | \(e\left(\frac{13}{17}\right)\) | \(e\left(\frac{20}{51}\right)\) |
\(\chi_{103}(8,\cdot)\) | 103.e | 17 | yes | \(1\) | \(1\) | \(e\left(\frac{16}{17}\right)\) | \(e\left(\frac{8}{17}\right)\) | \(e\left(\frac{15}{17}\right)\) | \(e\left(\frac{5}{17}\right)\) | \(e\left(\frac{7}{17}\right)\) | \(e\left(\frac{3}{17}\right)\) | \(e\left(\frac{14}{17}\right)\) | \(e\left(\frac{16}{17}\right)\) | \(e\left(\frac{4}{17}\right)\) | \(e\left(\frac{16}{17}\right)\) |
\(\chi_{103}(9,\cdot)\) | 103.e | 17 | yes | \(1\) | \(1\) | \(e\left(\frac{11}{17}\right)\) | \(e\left(\frac{14}{17}\right)\) | \(e\left(\frac{5}{17}\right)\) | \(e\left(\frac{13}{17}\right)\) | \(e\left(\frac{8}{17}\right)\) | \(e\left(\frac{1}{17}\right)\) | \(e\left(\frac{16}{17}\right)\) | \(e\left(\frac{11}{17}\right)\) | \(e\left(\frac{7}{17}\right)\) | \(e\left(\frac{11}{17}\right)\) |
\(\chi_{103}(10,\cdot)\) | 103.f | 34 | yes | \(-1\) | \(1\) | \(e\left(\frac{7}{17}\right)\) | \(e\left(\frac{7}{34}\right)\) | \(e\left(\frac{14}{17}\right)\) | \(e\left(\frac{15}{34}\right)\) | \(e\left(\frac{21}{34}\right)\) | \(e\left(\frac{13}{17}\right)\) | \(e\left(\frac{4}{17}\right)\) | \(e\left(\frac{7}{17}\right)\) | \(e\left(\frac{29}{34}\right)\) | \(e\left(\frac{31}{34}\right)\) |
\(\chi_{103}(11,\cdot)\) | 103.h | 102 | yes | \(-1\) | \(1\) | \(e\left(\frac{16}{51}\right)\) | \(e\left(\frac{11}{34}\right)\) | \(e\left(\frac{32}{51}\right)\) | \(e\left(\frac{61}{102}\right)\) | \(e\left(\frac{65}{102}\right)\) | \(e\left(\frac{20}{51}\right)\) | \(e\left(\frac{16}{17}\right)\) | \(e\left(\frac{11}{17}\right)\) | \(e\left(\frac{31}{34}\right)\) | \(e\left(\frac{49}{102}\right)\) |
\(\chi_{103}(12,\cdot)\) | 103.h | 102 | yes | \(-1\) | \(1\) | \(e\left(\frac{40}{51}\right)\) | \(e\left(\frac{19}{34}\right)\) | \(e\left(\frac{29}{51}\right)\) | \(e\left(\frac{25}{102}\right)\) | \(e\left(\frac{35}{102}\right)\) | \(e\left(\frac{50}{51}\right)\) | \(e\left(\frac{6}{17}\right)\) | \(e\left(\frac{2}{17}\right)\) | \(e\left(\frac{1}{34}\right)\) | \(e\left(\frac{97}{102}\right)\) |
\(\chi_{103}(13,\cdot)\) | 103.e | 17 | yes | \(1\) | \(1\) | \(e\left(\frac{1}{17}\right)\) | \(e\left(\frac{9}{17}\right)\) | \(e\left(\frac{2}{17}\right)\) | \(e\left(\frac{12}{17}\right)\) | \(e\left(\frac{10}{17}\right)\) | \(e\left(\frac{14}{17}\right)\) | \(e\left(\frac{3}{17}\right)\) | \(e\left(\frac{1}{17}\right)\) | \(e\left(\frac{13}{17}\right)\) | \(e\left(\frac{1}{17}\right)\) |
\(\chi_{103}(14,\cdot)\) | 103.e | 17 | yes | \(1\) | \(1\) | \(e\left(\frac{12}{17}\right)\) | \(e\left(\frac{6}{17}\right)\) | \(e\left(\frac{7}{17}\right)\) | \(e\left(\frac{8}{17}\right)\) | \(e\left(\frac{1}{17}\right)\) | \(e\left(\frac{15}{17}\right)\) | \(e\left(\frac{2}{17}\right)\) | \(e\left(\frac{12}{17}\right)\) | \(e\left(\frac{3}{17}\right)\) | \(e\left(\frac{12}{17}\right)\) |
\(\chi_{103}(15,\cdot)\) | 103.g | 51 | yes | \(1\) | \(1\) | \(e\left(\frac{13}{51}\right)\) | \(e\left(\frac{5}{17}\right)\) | \(e\left(\frac{26}{51}\right)\) | \(e\left(\frac{20}{51}\right)\) | \(e\left(\frac{28}{51}\right)\) | \(e\left(\frac{29}{51}\right)\) | \(e\left(\frac{13}{17}\right)\) | \(e\left(\frac{10}{17}\right)\) | \(e\left(\frac{11}{17}\right)\) | \(e\left(\frac{47}{51}\right)\) |
\(\chi_{103}(16,\cdot)\) | 103.g | 51 | yes | \(1\) | \(1\) | \(e\left(\frac{47}{51}\right)\) | \(e\left(\frac{5}{17}\right)\) | \(e\left(\frac{43}{51}\right)\) | \(e\left(\frac{37}{51}\right)\) | \(e\left(\frac{11}{51}\right)\) | \(e\left(\frac{46}{51}\right)\) | \(e\left(\frac{13}{17}\right)\) | \(e\left(\frac{10}{17}\right)\) | \(e\left(\frac{11}{17}\right)\) | \(e\left(\frac{13}{51}\right)\) |
\(\chi_{103}(17,\cdot)\) | 103.g | 51 | yes | \(1\) | \(1\) | \(e\left(\frac{10}{51}\right)\) | \(e\left(\frac{13}{17}\right)\) | \(e\left(\frac{20}{51}\right)\) | \(e\left(\frac{35}{51}\right)\) | \(e\left(\frac{49}{51}\right)\) | \(e\left(\frac{38}{51}\right)\) | \(e\left(\frac{10}{17}\right)\) | \(e\left(\frac{9}{17}\right)\) | \(e\left(\frac{15}{17}\right)\) | \(e\left(\frac{44}{51}\right)\) |
\(\chi_{103}(18,\cdot)\) | 103.g | 51 | yes | \(1\) | \(1\) | \(e\left(\frac{32}{51}\right)\) | \(e\left(\frac{11}{17}\right)\) | \(e\left(\frac{13}{51}\right)\) | \(e\left(\frac{10}{51}\right)\) | \(e\left(\frac{14}{51}\right)\) | \(e\left(\frac{40}{51}\right)\) | \(e\left(\frac{15}{17}\right)\) | \(e\left(\frac{5}{17}\right)\) | \(e\left(\frac{14}{17}\right)\) | \(e\left(\frac{49}{51}\right)\) |
\(\chi_{103}(19,\cdot)\) | 103.g | 51 | yes | \(1\) | \(1\) | \(e\left(\frac{26}{51}\right)\) | \(e\left(\frac{10}{17}\right)\) | \(e\left(\frac{1}{51}\right)\) | \(e\left(\frac{40}{51}\right)\) | \(e\left(\frac{5}{51}\right)\) | \(e\left(\frac{7}{51}\right)\) | \(e\left(\frac{9}{17}\right)\) | \(e\left(\frac{3}{17}\right)\) | \(e\left(\frac{5}{17}\right)\) | \(e\left(\frac{43}{51}\right)\) |
\(\chi_{103}(20,\cdot)\) | 103.h | 102 | yes | \(-1\) | \(1\) | \(e\left(\frac{20}{51}\right)\) | \(e\left(\frac{1}{34}\right)\) | \(e\left(\frac{40}{51}\right)\) | \(e\left(\frac{89}{102}\right)\) | \(e\left(\frac{43}{102}\right)\) | \(e\left(\frac{25}{51}\right)\) | \(e\left(\frac{3}{17}\right)\) | \(e\left(\frac{1}{17}\right)\) | \(e\left(\frac{9}{34}\right)\) | \(e\left(\frac{23}{102}\right)\) |
\(\chi_{103}(21,\cdot)\) | 103.h | 102 | yes | \(-1\) | \(1\) | \(e\left(\frac{28}{51}\right)\) | \(e\left(\frac{15}{34}\right)\) | \(e\left(\frac{5}{51}\right)\) | \(e\left(\frac{43}{102}\right)\) | \(e\left(\frac{101}{102}\right)\) | \(e\left(\frac{35}{51}\right)\) | \(e\left(\frac{11}{17}\right)\) | \(e\left(\frac{15}{17}\right)\) | \(e\left(\frac{33}{34}\right)\) | \(e\left(\frac{73}{102}\right)\) |
\(\chi_{103}(22,\cdot)\) | 103.f | 34 | yes | \(-1\) | \(1\) | \(e\left(\frac{5}{17}\right)\) | \(e\left(\frac{5}{34}\right)\) | \(e\left(\frac{10}{17}\right)\) | \(e\left(\frac{1}{34}\right)\) | \(e\left(\frac{15}{34}\right)\) | \(e\left(\frac{2}{17}\right)\) | \(e\left(\frac{15}{17}\right)\) | \(e\left(\frac{5}{17}\right)\) | \(e\left(\frac{11}{34}\right)\) | \(e\left(\frac{27}{34}\right)\) |
\(\chi_{103}(23,\cdot)\) | 103.e | 17 | yes | \(1\) | \(1\) | \(e\left(\frac{6}{17}\right)\) | \(e\left(\frac{3}{17}\right)\) | \(e\left(\frac{12}{17}\right)\) | \(e\left(\frac{4}{17}\right)\) | \(e\left(\frac{9}{17}\right)\) | \(e\left(\frac{16}{17}\right)\) | \(e\left(\frac{1}{17}\right)\) | \(e\left(\frac{6}{17}\right)\) | \(e\left(\frac{10}{17}\right)\) | \(e\left(\frac{6}{17}\right)\) |
\(\chi_{103}(24,\cdot)\) | 103.f | 34 | yes | \(-1\) | \(1\) | \(e\left(\frac{13}{17}\right)\) | \(e\left(\frac{13}{34}\right)\) | \(e\left(\frac{9}{17}\right)\) | \(e\left(\frac{23}{34}\right)\) | \(e\left(\frac{5}{34}\right)\) | \(e\left(\frac{12}{17}\right)\) | \(e\left(\frac{5}{17}\right)\) | \(e\left(\frac{13}{17}\right)\) | \(e\left(\frac{15}{34}\right)\) | \(e\left(\frac{9}{34}\right)\) |
\(\chi_{103}(25,\cdot)\) | 103.g | 51 | yes | \(1\) | \(1\) | \(e\left(\frac{44}{51}\right)\) | \(e\left(\frac{13}{17}\right)\) | \(e\left(\frac{37}{51}\right)\) | \(e\left(\frac{1}{51}\right)\) | \(e\left(\frac{32}{51}\right)\) | \(e\left(\frac{4}{51}\right)\) | \(e\left(\frac{10}{17}\right)\) | \(e\left(\frac{9}{17}\right)\) | \(e\left(\frac{15}{17}\right)\) | \(e\left(\frac{10}{51}\right)\) |
\(\chi_{103}(26,\cdot)\) | 103.g | 51 | yes | \(1\) | \(1\) | \(e\left(\frac{2}{51}\right)\) | \(e\left(\frac{6}{17}\right)\) | \(e\left(\frac{4}{51}\right)\) | \(e\left(\frac{7}{51}\right)\) | \(e\left(\frac{20}{51}\right)\) | \(e\left(\frac{28}{51}\right)\) | \(e\left(\frac{2}{17}\right)\) | \(e\left(\frac{12}{17}\right)\) | \(e\left(\frac{3}{17}\right)\) | \(e\left(\frac{19}{51}\right)\) |
\(\chi_{103}(27,\cdot)\) | 103.f | 34 | yes | \(-1\) | \(1\) | \(e\left(\frac{8}{17}\right)\) | \(e\left(\frac{25}{34}\right)\) | \(e\left(\frac{16}{17}\right)\) | \(e\left(\frac{5}{34}\right)\) | \(e\left(\frac{7}{34}\right)\) | \(e\left(\frac{10}{17}\right)\) | \(e\left(\frac{7}{17}\right)\) | \(e\left(\frac{8}{17}\right)\) | \(e\left(\frac{21}{34}\right)\) | \(e\left(\frac{33}{34}\right)\) |
\(\chi_{103}(28,\cdot)\) | 103.g | 51 | yes | \(1\) | \(1\) | \(e\left(\frac{35}{51}\right)\) | \(e\left(\frac{3}{17}\right)\) | \(e\left(\frac{19}{51}\right)\) | \(e\left(\frac{46}{51}\right)\) | \(e\left(\frac{44}{51}\right)\) | \(e\left(\frac{31}{51}\right)\) | \(e\left(\frac{1}{17}\right)\) | \(e\left(\frac{6}{17}\right)\) | \(e\left(\frac{10}{17}\right)\) | \(e\left(\frac{1}{51}\right)\) |
\(\chi_{103}(29,\cdot)\) | 103.g | 51 | yes | \(1\) | \(1\) | \(e\left(\frac{5}{51}\right)\) | \(e\left(\frac{15}{17}\right)\) | \(e\left(\frac{10}{51}\right)\) | \(e\left(\frac{43}{51}\right)\) | \(e\left(\frac{50}{51}\right)\) | \(e\left(\frac{19}{51}\right)\) | \(e\left(\frac{5}{17}\right)\) | \(e\left(\frac{13}{17}\right)\) | \(e\left(\frac{16}{17}\right)\) | \(e\left(\frac{22}{51}\right)\) |
\(\chi_{103}(30,\cdot)\) | 103.e | 17 | yes | \(1\) | \(1\) | \(e\left(\frac{4}{17}\right)\) | \(e\left(\frac{2}{17}\right)\) | \(e\left(\frac{8}{17}\right)\) | \(e\left(\frac{14}{17}\right)\) | \(e\left(\frac{6}{17}\right)\) | \(e\left(\frac{5}{17}\right)\) | \(e\left(\frac{12}{17}\right)\) | \(e\left(\frac{4}{17}\right)\) | \(e\left(\frac{1}{17}\right)\) | \(e\left(\frac{4}{17}\right)\) |
\(\chi_{103}(31,\cdot)\) | 103.f | 34 | yes | \(-1\) | \(1\) | \(e\left(\frac{10}{17}\right)\) | \(e\left(\frac{27}{34}\right)\) | \(e\left(\frac{3}{17}\right)\) | \(e\left(\frac{19}{34}\right)\) | \(e\left(\frac{13}{34}\right)\) | \(e\left(\frac{4}{17}\right)\) | \(e\left(\frac{13}{17}\right)\) | \(e\left(\frac{10}{17}\right)\) | \(e\left(\frac{5}{34}\right)\) | \(e\left(\frac{3}{34}\right)\) |
\(\chi_{103}(32,\cdot)\) | 103.g | 51 | yes | \(1\) | \(1\) | \(e\left(\frac{46}{51}\right)\) | \(e\left(\frac{2}{17}\right)\) | \(e\left(\frac{41}{51}\right)\) | \(e\left(\frac{8}{51}\right)\) | \(e\left(\frac{1}{51}\right)\) | \(e\left(\frac{32}{51}\right)\) | \(e\left(\frac{12}{17}\right)\) | \(e\left(\frac{4}{17}\right)\) | \(e\left(\frac{1}{17}\right)\) | \(e\left(\frac{29}{51}\right)\) |