Properties

Modulus 139
Structure \(C_{138}\)
Order 138

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(139)
pari: g = idealstar(,139,2)

Character group

sage: G.order()
pari: g.no
Order = 138
sage: H.invariants()
pari: g.cyc
Structure = \(C_{138}\)
sage: H.gens()
pari: g.gen
Generators = $\chi_{139}(2,\cdot)$

First 32 of 138 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
\(\chi_{139}(1,\cdot)\) 139.a 1 No \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{139}(2,\cdot)\) 139.h 138 Yes \(-1\) \(1\) \(e\left(\frac{1}{138}\right)\) \(e\left(\frac{41}{138}\right)\) \(e\left(\frac{1}{69}\right)\) \(e\left(\frac{43}{69}\right)\) \(e\left(\frac{7}{23}\right)\) \(e\left(\frac{25}{69}\right)\) \(e\left(\frac{1}{46}\right)\) \(e\left(\frac{41}{69}\right)\) \(e\left(\frac{29}{46}\right)\) \(e\left(\frac{38}{69}\right)\)
\(\chi_{139}(3,\cdot)\) 139.h 138 Yes \(-1\) \(1\) \(e\left(\frac{41}{138}\right)\) \(e\left(\frac{25}{138}\right)\) \(e\left(\frac{41}{69}\right)\) \(e\left(\frac{38}{69}\right)\) \(e\left(\frac{11}{23}\right)\) \(e\left(\frac{59}{69}\right)\) \(e\left(\frac{41}{46}\right)\) \(e\left(\frac{25}{69}\right)\) \(e\left(\frac{39}{46}\right)\) \(e\left(\frac{40}{69}\right)\)
\(\chi_{139}(4,\cdot)\) 139.g 69 Yes \(1\) \(1\) \(e\left(\frac{1}{69}\right)\) \(e\left(\frac{41}{69}\right)\) \(e\left(\frac{2}{69}\right)\) \(e\left(\frac{17}{69}\right)\) \(e\left(\frac{14}{23}\right)\) \(e\left(\frac{50}{69}\right)\) \(e\left(\frac{1}{23}\right)\) \(e\left(\frac{13}{69}\right)\) \(e\left(\frac{6}{23}\right)\) \(e\left(\frac{7}{69}\right)\)
\(\chi_{139}(5,\cdot)\) 139.g 69 Yes \(1\) \(1\) \(e\left(\frac{43}{69}\right)\) \(e\left(\frac{38}{69}\right)\) \(e\left(\frac{17}{69}\right)\) \(e\left(\frac{41}{69}\right)\) \(e\left(\frac{4}{23}\right)\) \(e\left(\frac{11}{69}\right)\) \(e\left(\frac{20}{23}\right)\) \(e\left(\frac{7}{69}\right)\) \(e\left(\frac{5}{23}\right)\) \(e\left(\frac{25}{69}\right)\)
\(\chi_{139}(6,\cdot)\) 139.e 23 Yes \(1\) \(1\) \(e\left(\frac{7}{23}\right)\) \(e\left(\frac{11}{23}\right)\) \(e\left(\frac{14}{23}\right)\) \(e\left(\frac{4}{23}\right)\) \(e\left(\frac{18}{23}\right)\) \(e\left(\frac{5}{23}\right)\) \(e\left(\frac{21}{23}\right)\) \(e\left(\frac{22}{23}\right)\) \(e\left(\frac{11}{23}\right)\) \(e\left(\frac{3}{23}\right)\)
\(\chi_{139}(7,\cdot)\) 139.g 69 Yes \(1\) \(1\) \(e\left(\frac{25}{69}\right)\) \(e\left(\frac{59}{69}\right)\) \(e\left(\frac{50}{69}\right)\) \(e\left(\frac{11}{69}\right)\) \(e\left(\frac{5}{23}\right)\) \(e\left(\frac{8}{69}\right)\) \(e\left(\frac{2}{23}\right)\) \(e\left(\frac{49}{69}\right)\) \(e\left(\frac{12}{23}\right)\) \(e\left(\frac{37}{69}\right)\)
\(\chi_{139}(8,\cdot)\) 139.f 46 Yes \(-1\) \(1\) \(e\left(\frac{1}{46}\right)\) \(e\left(\frac{41}{46}\right)\) \(e\left(\frac{1}{23}\right)\) \(e\left(\frac{20}{23}\right)\) \(e\left(\frac{21}{23}\right)\) \(e\left(\frac{2}{23}\right)\) \(e\left(\frac{3}{46}\right)\) \(e\left(\frac{18}{23}\right)\) \(e\left(\frac{41}{46}\right)\) \(e\left(\frac{15}{23}\right)\)
\(\chi_{139}(9,\cdot)\) 139.g 69 Yes \(1\) \(1\) \(e\left(\frac{41}{69}\right)\) \(e\left(\frac{25}{69}\right)\) \(e\left(\frac{13}{69}\right)\) \(e\left(\frac{7}{69}\right)\) \(e\left(\frac{22}{23}\right)\) \(e\left(\frac{49}{69}\right)\) \(e\left(\frac{18}{23}\right)\) \(e\left(\frac{50}{69}\right)\) \(e\left(\frac{16}{23}\right)\) \(e\left(\frac{11}{69}\right)\)
\(\chi_{139}(10,\cdot)\) 139.f 46 Yes \(-1\) \(1\) \(e\left(\frac{29}{46}\right)\) \(e\left(\frac{39}{46}\right)\) \(e\left(\frac{6}{23}\right)\) \(e\left(\frac{5}{23}\right)\) \(e\left(\frac{11}{23}\right)\) \(e\left(\frac{12}{23}\right)\) \(e\left(\frac{41}{46}\right)\) \(e\left(\frac{16}{23}\right)\) \(e\left(\frac{39}{46}\right)\) \(e\left(\frac{21}{23}\right)\)
\(\chi_{139}(11,\cdot)\) 139.g 69 Yes \(1\) \(1\) \(e\left(\frac{38}{69}\right)\) \(e\left(\frac{40}{69}\right)\) \(e\left(\frac{7}{69}\right)\) \(e\left(\frac{25}{69}\right)\) \(e\left(\frac{3}{23}\right)\) \(e\left(\frac{37}{69}\right)\) \(e\left(\frac{15}{23}\right)\) \(e\left(\frac{11}{69}\right)\) \(e\left(\frac{21}{23}\right)\) \(e\left(\frac{59}{69}\right)\)
\(\chi_{139}(12,\cdot)\) 139.h 138 Yes \(-1\) \(1\) \(e\left(\frac{43}{138}\right)\) \(e\left(\frac{107}{138}\right)\) \(e\left(\frac{43}{69}\right)\) \(e\left(\frac{55}{69}\right)\) \(e\left(\frac{2}{23}\right)\) \(e\left(\frac{40}{69}\right)\) \(e\left(\frac{43}{46}\right)\) \(e\left(\frac{38}{69}\right)\) \(e\left(\frac{5}{46}\right)\) \(e\left(\frac{47}{69}\right)\)
\(\chi_{139}(13,\cdot)\) 139.g 69 Yes \(1\) \(1\) \(e\left(\frac{32}{69}\right)\) \(e\left(\frac{1}{69}\right)\) \(e\left(\frac{64}{69}\right)\) \(e\left(\frac{61}{69}\right)\) \(e\left(\frac{11}{23}\right)\) \(e\left(\frac{13}{69}\right)\) \(e\left(\frac{9}{23}\right)\) \(e\left(\frac{2}{69}\right)\) \(e\left(\frac{8}{23}\right)\) \(e\left(\frac{17}{69}\right)\)
\(\chi_{139}(14,\cdot)\) 139.f 46 Yes \(-1\) \(1\) \(e\left(\frac{17}{46}\right)\) \(e\left(\frac{7}{46}\right)\) \(e\left(\frac{17}{23}\right)\) \(e\left(\frac{18}{23}\right)\) \(e\left(\frac{12}{23}\right)\) \(e\left(\frac{11}{23}\right)\) \(e\left(\frac{5}{46}\right)\) \(e\left(\frac{7}{23}\right)\) \(e\left(\frac{7}{46}\right)\) \(e\left(\frac{2}{23}\right)\)
\(\chi_{139}(15,\cdot)\) 139.h 138 Yes \(-1\) \(1\) \(e\left(\frac{127}{138}\right)\) \(e\left(\frac{101}{138}\right)\) \(e\left(\frac{58}{69}\right)\) \(e\left(\frac{10}{69}\right)\) \(e\left(\frac{15}{23}\right)\) \(e\left(\frac{1}{69}\right)\) \(e\left(\frac{35}{46}\right)\) \(e\left(\frac{32}{69}\right)\) \(e\left(\frac{3}{46}\right)\) \(e\left(\frac{65}{69}\right)\)
\(\chi_{139}(16,\cdot)\) 139.g 69 Yes \(1\) \(1\) \(e\left(\frac{2}{69}\right)\) \(e\left(\frac{13}{69}\right)\) \(e\left(\frac{4}{69}\right)\) \(e\left(\frac{34}{69}\right)\) \(e\left(\frac{5}{23}\right)\) \(e\left(\frac{31}{69}\right)\) \(e\left(\frac{2}{23}\right)\) \(e\left(\frac{26}{69}\right)\) \(e\left(\frac{12}{23}\right)\) \(e\left(\frac{14}{69}\right)\)
\(\chi_{139}(17,\cdot)\) 139.h 138 Yes \(-1\) \(1\) \(e\left(\frac{107}{138}\right)\) \(e\left(\frac{109}{138}\right)\) \(e\left(\frac{38}{69}\right)\) \(e\left(\frac{47}{69}\right)\) \(e\left(\frac{13}{23}\right)\) \(e\left(\frac{53}{69}\right)\) \(e\left(\frac{15}{46}\right)\) \(e\left(\frac{40}{69}\right)\) \(e\left(\frac{21}{46}\right)\) \(e\left(\frac{64}{69}\right)\)
\(\chi_{139}(18,\cdot)\) 139.h 138 Yes \(-1\) \(1\) \(e\left(\frac{83}{138}\right)\) \(e\left(\frac{91}{138}\right)\) \(e\left(\frac{14}{69}\right)\) \(e\left(\frac{50}{69}\right)\) \(e\left(\frac{6}{23}\right)\) \(e\left(\frac{5}{69}\right)\) \(e\left(\frac{37}{46}\right)\) \(e\left(\frac{22}{69}\right)\) \(e\left(\frac{15}{46}\right)\) \(e\left(\frac{49}{69}\right)\)
\(\chi_{139}(19,\cdot)\) 139.h 138 Yes \(-1\) \(1\) \(e\left(\frac{61}{138}\right)\) \(e\left(\frac{17}{138}\right)\) \(e\left(\frac{61}{69}\right)\) \(e\left(\frac{1}{69}\right)\) \(e\left(\frac{13}{23}\right)\) \(e\left(\frac{7}{69}\right)\) \(e\left(\frac{15}{46}\right)\) \(e\left(\frac{17}{69}\right)\) \(e\left(\frac{21}{46}\right)\) \(e\left(\frac{41}{69}\right)\)
\(\chi_{139}(20,\cdot)\) 139.g 69 Yes \(1\) \(1\) \(e\left(\frac{44}{69}\right)\) \(e\left(\frac{10}{69}\right)\) \(e\left(\frac{19}{69}\right)\) \(e\left(\frac{58}{69}\right)\) \(e\left(\frac{18}{23}\right)\) \(e\left(\frac{61}{69}\right)\) \(e\left(\frac{21}{23}\right)\) \(e\left(\frac{20}{69}\right)\) \(e\left(\frac{11}{23}\right)\) \(e\left(\frac{32}{69}\right)\)
\(\chi_{139}(21,\cdot)\) 139.h 138 Yes \(-1\) \(1\) \(e\left(\frac{91}{138}\right)\) \(e\left(\frac{5}{138}\right)\) \(e\left(\frac{22}{69}\right)\) \(e\left(\frac{49}{69}\right)\) \(e\left(\frac{16}{23}\right)\) \(e\left(\frac{67}{69}\right)\) \(e\left(\frac{45}{46}\right)\) \(e\left(\frac{5}{69}\right)\) \(e\left(\frac{17}{46}\right)\) \(e\left(\frac{8}{69}\right)\)
\(\chi_{139}(22,\cdot)\) 139.h 138 Yes \(-1\) \(1\) \(e\left(\frac{77}{138}\right)\) \(e\left(\frac{121}{138}\right)\) \(e\left(\frac{8}{69}\right)\) \(e\left(\frac{68}{69}\right)\) \(e\left(\frac{10}{23}\right)\) \(e\left(\frac{62}{69}\right)\) \(e\left(\frac{31}{46}\right)\) \(e\left(\frac{52}{69}\right)\) \(e\left(\frac{25}{46}\right)\) \(e\left(\frac{28}{69}\right)\)
\(\chi_{139}(23,\cdot)\) 139.f 46 Yes \(-1\) \(1\) \(e\left(\frac{9}{46}\right)\) \(e\left(\frac{1}{46}\right)\) \(e\left(\frac{9}{23}\right)\) \(e\left(\frac{19}{23}\right)\) \(e\left(\frac{5}{23}\right)\) \(e\left(\frac{18}{23}\right)\) \(e\left(\frac{27}{46}\right)\) \(e\left(\frac{1}{23}\right)\) \(e\left(\frac{1}{46}\right)\) \(e\left(\frac{20}{23}\right)\)
\(\chi_{139}(24,\cdot)\) 139.g 69 Yes \(1\) \(1\) \(e\left(\frac{22}{69}\right)\) \(e\left(\frac{5}{69}\right)\) \(e\left(\frac{44}{69}\right)\) \(e\left(\frac{29}{69}\right)\) \(e\left(\frac{9}{23}\right)\) \(e\left(\frac{65}{69}\right)\) \(e\left(\frac{22}{23}\right)\) \(e\left(\frac{10}{69}\right)\) \(e\left(\frac{17}{23}\right)\) \(e\left(\frac{16}{69}\right)\)
\(\chi_{139}(25,\cdot)\) 139.g 69 Yes \(1\) \(1\) \(e\left(\frac{17}{69}\right)\) \(e\left(\frac{7}{69}\right)\) \(e\left(\frac{34}{69}\right)\) \(e\left(\frac{13}{69}\right)\) \(e\left(\frac{8}{23}\right)\) \(e\left(\frac{22}{69}\right)\) \(e\left(\frac{17}{23}\right)\) \(e\left(\frac{14}{69}\right)\) \(e\left(\frac{10}{23}\right)\) \(e\left(\frac{50}{69}\right)\)
\(\chi_{139}(26,\cdot)\) 139.h 138 Yes \(-1\) \(1\) \(e\left(\frac{65}{138}\right)\) \(e\left(\frac{43}{138}\right)\) \(e\left(\frac{65}{69}\right)\) \(e\left(\frac{35}{69}\right)\) \(e\left(\frac{18}{23}\right)\) \(e\left(\frac{38}{69}\right)\) \(e\left(\frac{19}{46}\right)\) \(e\left(\frac{43}{69}\right)\) \(e\left(\frac{45}{46}\right)\) \(e\left(\frac{55}{69}\right)\)
\(\chi_{139}(27,\cdot)\) 139.f 46 Yes \(-1\) \(1\) \(e\left(\frac{41}{46}\right)\) \(e\left(\frac{25}{46}\right)\) \(e\left(\frac{18}{23}\right)\) \(e\left(\frac{15}{23}\right)\) \(e\left(\frac{10}{23}\right)\) \(e\left(\frac{13}{23}\right)\) \(e\left(\frac{31}{46}\right)\) \(e\left(\frac{2}{23}\right)\) \(e\left(\frac{25}{46}\right)\) \(e\left(\frac{17}{23}\right)\)
\(\chi_{139}(28,\cdot)\) 139.g 69 Yes \(1\) \(1\) \(e\left(\frac{26}{69}\right)\) \(e\left(\frac{31}{69}\right)\) \(e\left(\frac{52}{69}\right)\) \(e\left(\frac{28}{69}\right)\) \(e\left(\frac{19}{23}\right)\) \(e\left(\frac{58}{69}\right)\) \(e\left(\frac{3}{23}\right)\) \(e\left(\frac{62}{69}\right)\) \(e\left(\frac{18}{23}\right)\) \(e\left(\frac{44}{69}\right)\)
\(\chi_{139}(29,\cdot)\) 139.g 69 Yes \(1\) \(1\) \(e\left(\frac{47}{69}\right)\) \(e\left(\frac{64}{69}\right)\) \(e\left(\frac{25}{69}\right)\) \(e\left(\frac{40}{69}\right)\) \(e\left(\frac{14}{23}\right)\) \(e\left(\frac{4}{69}\right)\) \(e\left(\frac{1}{23}\right)\) \(e\left(\frac{59}{69}\right)\) \(e\left(\frac{6}{23}\right)\) \(e\left(\frac{53}{69}\right)\)
\(\chi_{139}(30,\cdot)\) 139.g 69 Yes \(1\) \(1\) \(e\left(\frac{64}{69}\right)\) \(e\left(\frac{2}{69}\right)\) \(e\left(\frac{59}{69}\right)\) \(e\left(\frac{53}{69}\right)\) \(e\left(\frac{22}{23}\right)\) \(e\left(\frac{26}{69}\right)\) \(e\left(\frac{18}{23}\right)\) \(e\left(\frac{4}{69}\right)\) \(e\left(\frac{16}{23}\right)\) \(e\left(\frac{34}{69}\right)\)
\(\chi_{139}(31,\cdot)\) 139.g 69 Yes \(1\) \(1\) \(e\left(\frac{28}{69}\right)\) \(e\left(\frac{44}{69}\right)\) \(e\left(\frac{56}{69}\right)\) \(e\left(\frac{62}{69}\right)\) \(e\left(\frac{1}{23}\right)\) \(e\left(\frac{20}{69}\right)\) \(e\left(\frac{5}{23}\right)\) \(e\left(\frac{19}{69}\right)\) \(e\left(\frac{7}{23}\right)\) \(e\left(\frac{58}{69}\right)\)
\(\chi_{139}(32,\cdot)\) 139.h 138 Yes \(-1\) \(1\) \(e\left(\frac{5}{138}\right)\) \(e\left(\frac{67}{138}\right)\) \(e\left(\frac{5}{69}\right)\) \(e\left(\frac{8}{69}\right)\) \(e\left(\frac{12}{23}\right)\) \(e\left(\frac{56}{69}\right)\) \(e\left(\frac{5}{46}\right)\) \(e\left(\frac{67}{69}\right)\) \(e\left(\frac{7}{46}\right)\) \(e\left(\frac{52}{69}\right)\)