Properties

Modulus 79
Structure \(C_{78}\)
Order 78

Learn more about

Show commands for: SageMath / Pari/GP

sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
sage: H = DirichletGroup_conrey(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.

orbit label 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 \(1\) \(1\) \(e\left(\frac{1}{39}\right)\) \(e\left(\frac{10}{39}\right)\) \(e\left(\frac{2}{39}\right)\) \(e\left(\frac{35}{39}\right)\) \(e\left(\frac{11}{39}\right)\) \(e\left(\frac{23}{39}\right)\) \(e\left(\frac{1}{13}\right)\) \(e\left(\frac{20}{39}\right)\) \(e\left(\frac{12}{13}\right)\) \(e\left(\frac{17}{39}\right)\)