Properties

Modulus 131
Structure \(C_{130}\)
Order 130

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(131)
pari: g = idealstar(,131,2)

Character group

sage: G.order()
pari: g.no
Order = 130
sage: H.invariants()
pari: g.cyc
Structure = \(C_{130}\)
sage: H.gens()
pari: g.gen
Generators = $\chi_{131}(2,\cdot)$

First 32 of 130 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
\(\chi_{131}(1,\cdot)\) 131.a 1 No \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{131}(2,\cdot)\) 131.h 130 Yes \(-1\) \(1\) \(e\left(\frac{1}{130}\right)\) \(e\left(\frac{36}{65}\right)\) \(e\left(\frac{1}{65}\right)\) \(e\left(\frac{23}{65}\right)\) \(e\left(\frac{73}{130}\right)\) \(e\left(\frac{48}{65}\right)\) \(e\left(\frac{3}{130}\right)\) \(e\left(\frac{7}{65}\right)\) \(e\left(\frac{47}{130}\right)\) \(e\left(\frac{28}{65}\right)\)
\(\chi_{131}(3,\cdot)\) 131.g 65 Yes \(1\) \(1\) \(e\left(\frac{36}{65}\right)\) \(e\left(\frac{57}{65}\right)\) \(e\left(\frac{7}{65}\right)\) \(e\left(\frac{31}{65}\right)\) \(e\left(\frac{28}{65}\right)\) \(e\left(\frac{11}{65}\right)\) \(e\left(\frac{43}{65}\right)\) \(e\left(\frac{49}{65}\right)\) \(e\left(\frac{2}{65}\right)\) \(e\left(\frac{1}{65}\right)\)
\(\chi_{131}(4,\cdot)\) 131.g 65 Yes \(1\) \(1\) \(e\left(\frac{1}{65}\right)\) \(e\left(\frac{7}{65}\right)\) \(e\left(\frac{2}{65}\right)\) \(e\left(\frac{46}{65}\right)\) \(e\left(\frac{8}{65}\right)\) \(e\left(\frac{31}{65}\right)\) \(e\left(\frac{3}{65}\right)\) \(e\left(\frac{14}{65}\right)\) \(e\left(\frac{47}{65}\right)\) \(e\left(\frac{56}{65}\right)\)
\(\chi_{131}(5,\cdot)\) 131.g 65 Yes \(1\) \(1\) \(e\left(\frac{23}{65}\right)\) \(e\left(\frac{31}{65}\right)\) \(e\left(\frac{46}{65}\right)\) \(e\left(\frac{18}{65}\right)\) \(e\left(\frac{54}{65}\right)\) \(e\left(\frac{63}{65}\right)\) \(e\left(\frac{4}{65}\right)\) \(e\left(\frac{62}{65}\right)\) \(e\left(\frac{41}{65}\right)\) \(e\left(\frac{53}{65}\right)\)
\(\chi_{131}(6,\cdot)\) 131.h 130 Yes \(-1\) \(1\) \(e\left(\frac{73}{130}\right)\) \(e\left(\frac{28}{65}\right)\) \(e\left(\frac{8}{65}\right)\) \(e\left(\frac{54}{65}\right)\) \(e\left(\frac{129}{130}\right)\) \(e\left(\frac{59}{65}\right)\) \(e\left(\frac{89}{130}\right)\) \(e\left(\frac{56}{65}\right)\) \(e\left(\frac{51}{130}\right)\) \(e\left(\frac{29}{65}\right)\)
\(\chi_{131}(7,\cdot)\) 131.g 65 Yes \(1\) \(1\) \(e\left(\frac{48}{65}\right)\) \(e\left(\frac{11}{65}\right)\) \(e\left(\frac{31}{65}\right)\) \(e\left(\frac{63}{65}\right)\) \(e\left(\frac{59}{65}\right)\) \(e\left(\frac{58}{65}\right)\) \(e\left(\frac{14}{65}\right)\) \(e\left(\frac{22}{65}\right)\) \(e\left(\frac{46}{65}\right)\) \(e\left(\frac{23}{65}\right)\)
\(\chi_{131}(8,\cdot)\) 131.h 130 Yes \(-1\) \(1\) \(e\left(\frac{3}{130}\right)\) \(e\left(\frac{43}{65}\right)\) \(e\left(\frac{3}{65}\right)\) \(e\left(\frac{4}{65}\right)\) \(e\left(\frac{89}{130}\right)\) \(e\left(\frac{14}{65}\right)\) \(e\left(\frac{9}{130}\right)\) \(e\left(\frac{21}{65}\right)\) \(e\left(\frac{11}{130}\right)\) \(e\left(\frac{19}{65}\right)\)
\(\chi_{131}(9,\cdot)\) 131.g 65 Yes \(1\) \(1\) \(e\left(\frac{7}{65}\right)\) \(e\left(\frac{49}{65}\right)\) \(e\left(\frac{14}{65}\right)\) \(e\left(\frac{62}{65}\right)\) \(e\left(\frac{56}{65}\right)\) \(e\left(\frac{22}{65}\right)\) \(e\left(\frac{21}{65}\right)\) \(e\left(\frac{33}{65}\right)\) \(e\left(\frac{4}{65}\right)\) \(e\left(\frac{2}{65}\right)\)
\(\chi_{131}(10,\cdot)\) 131.h 130 Yes \(-1\) \(1\) \(e\left(\frac{47}{130}\right)\) \(e\left(\frac{2}{65}\right)\) \(e\left(\frac{47}{65}\right)\) \(e\left(\frac{41}{65}\right)\) \(e\left(\frac{51}{130}\right)\) \(e\left(\frac{46}{65}\right)\) \(e\left(\frac{11}{130}\right)\) \(e\left(\frac{4}{65}\right)\) \(e\left(\frac{129}{130}\right)\) \(e\left(\frac{16}{65}\right)\)
\(\chi_{131}(11,\cdot)\) 131.g 65 Yes \(1\) \(1\) \(e\left(\frac{28}{65}\right)\) \(e\left(\frac{1}{65}\right)\) \(e\left(\frac{56}{65}\right)\) \(e\left(\frac{53}{65}\right)\) \(e\left(\frac{29}{65}\right)\) \(e\left(\frac{23}{65}\right)\) \(e\left(\frac{19}{65}\right)\) \(e\left(\frac{2}{65}\right)\) \(e\left(\frac{16}{65}\right)\) \(e\left(\frac{8}{65}\right)\)
\(\chi_{131}(12,\cdot)\) 131.g 65 Yes \(1\) \(1\) \(e\left(\frac{37}{65}\right)\) \(e\left(\frac{64}{65}\right)\) \(e\left(\frac{9}{65}\right)\) \(e\left(\frac{12}{65}\right)\) \(e\left(\frac{36}{65}\right)\) \(e\left(\frac{42}{65}\right)\) \(e\left(\frac{46}{65}\right)\) \(e\left(\frac{63}{65}\right)\) \(e\left(\frac{49}{65}\right)\) \(e\left(\frac{57}{65}\right)\)
\(\chi_{131}(13,\cdot)\) 131.g 65 Yes \(1\) \(1\) \(e\left(\frac{9}{65}\right)\) \(e\left(\frac{63}{65}\right)\) \(e\left(\frac{18}{65}\right)\) \(e\left(\frac{24}{65}\right)\) \(e\left(\frac{7}{65}\right)\) \(e\left(\frac{19}{65}\right)\) \(e\left(\frac{27}{65}\right)\) \(e\left(\frac{61}{65}\right)\) \(e\left(\frac{33}{65}\right)\) \(e\left(\frac{49}{65}\right)\)
\(\chi_{131}(14,\cdot)\) 131.h 130 Yes \(-1\) \(1\) \(e\left(\frac{97}{130}\right)\) \(e\left(\frac{47}{65}\right)\) \(e\left(\frac{32}{65}\right)\) \(e\left(\frac{21}{65}\right)\) \(e\left(\frac{61}{130}\right)\) \(e\left(\frac{41}{65}\right)\) \(e\left(\frac{31}{130}\right)\) \(e\left(\frac{29}{65}\right)\) \(e\left(\frac{9}{130}\right)\) \(e\left(\frac{51}{65}\right)\)
\(\chi_{131}(15,\cdot)\) 131.g 65 Yes \(1\) \(1\) \(e\left(\frac{59}{65}\right)\) \(e\left(\frac{23}{65}\right)\) \(e\left(\frac{53}{65}\right)\) \(e\left(\frac{49}{65}\right)\) \(e\left(\frac{17}{65}\right)\) \(e\left(\frac{9}{65}\right)\) \(e\left(\frac{47}{65}\right)\) \(e\left(\frac{46}{65}\right)\) \(e\left(\frac{43}{65}\right)\) \(e\left(\frac{54}{65}\right)\)
\(\chi_{131}(16,\cdot)\) 131.g 65 Yes \(1\) \(1\) \(e\left(\frac{2}{65}\right)\) \(e\left(\frac{14}{65}\right)\) \(e\left(\frac{4}{65}\right)\) \(e\left(\frac{27}{65}\right)\) \(e\left(\frac{16}{65}\right)\) \(e\left(\frac{62}{65}\right)\) \(e\left(\frac{6}{65}\right)\) \(e\left(\frac{28}{65}\right)\) \(e\left(\frac{29}{65}\right)\) \(e\left(\frac{47}{65}\right)\)
\(\chi_{131}(17,\cdot)\) 131.h 130 Yes \(-1\) \(1\) \(e\left(\frac{43}{130}\right)\) \(e\left(\frac{53}{65}\right)\) \(e\left(\frac{43}{65}\right)\) \(e\left(\frac{14}{65}\right)\) \(e\left(\frac{19}{130}\right)\) \(e\left(\frac{49}{65}\right)\) \(e\left(\frac{129}{130}\right)\) \(e\left(\frac{41}{65}\right)\) \(e\left(\frac{71}{130}\right)\) \(e\left(\frac{34}{65}\right)\)
\(\chi_{131}(18,\cdot)\) 131.f 26 Yes \(-1\) \(1\) \(e\left(\frac{3}{26}\right)\) \(e\left(\frac{4}{13}\right)\) \(e\left(\frac{3}{13}\right)\) \(e\left(\frac{4}{13}\right)\) \(e\left(\frac{11}{26}\right)\) \(e\left(\frac{1}{13}\right)\) \(e\left(\frac{9}{26}\right)\) \(e\left(\frac{8}{13}\right)\) \(e\left(\frac{11}{26}\right)\) \(e\left(\frac{6}{13}\right)\)
\(\chi_{131}(19,\cdot)\) 131.f 26 Yes \(-1\) \(1\) \(e\left(\frac{7}{26}\right)\) \(e\left(\frac{5}{13}\right)\) \(e\left(\frac{7}{13}\right)\) \(e\left(\frac{5}{13}\right)\) \(e\left(\frac{17}{26}\right)\) \(e\left(\frac{11}{13}\right)\) \(e\left(\frac{21}{26}\right)\) \(e\left(\frac{10}{13}\right)\) \(e\left(\frac{17}{26}\right)\) \(e\left(\frac{1}{13}\right)\)
\(\chi_{131}(20,\cdot)\) 131.g 65 Yes \(1\) \(1\) \(e\left(\frac{24}{65}\right)\) \(e\left(\frac{38}{65}\right)\) \(e\left(\frac{48}{65}\right)\) \(e\left(\frac{64}{65}\right)\) \(e\left(\frac{62}{65}\right)\) \(e\left(\frac{29}{65}\right)\) \(e\left(\frac{7}{65}\right)\) \(e\left(\frac{11}{65}\right)\) \(e\left(\frac{23}{65}\right)\) \(e\left(\frac{44}{65}\right)\)
\(\chi_{131}(21,\cdot)\) 131.g 65 Yes \(1\) \(1\) \(e\left(\frac{19}{65}\right)\) \(e\left(\frac{3}{65}\right)\) \(e\left(\frac{38}{65}\right)\) \(e\left(\frac{29}{65}\right)\) \(e\left(\frac{22}{65}\right)\) \(e\left(\frac{4}{65}\right)\) \(e\left(\frac{57}{65}\right)\) \(e\left(\frac{6}{65}\right)\) \(e\left(\frac{48}{65}\right)\) \(e\left(\frac{24}{65}\right)\)
\(\chi_{131}(22,\cdot)\) 131.h 130 Yes \(-1\) \(1\) \(e\left(\frac{57}{130}\right)\) \(e\left(\frac{37}{65}\right)\) \(e\left(\frac{57}{65}\right)\) \(e\left(\frac{11}{65}\right)\) \(e\left(\frac{1}{130}\right)\) \(e\left(\frac{6}{65}\right)\) \(e\left(\frac{41}{130}\right)\) \(e\left(\frac{9}{65}\right)\) \(e\left(\frac{79}{130}\right)\) \(e\left(\frac{36}{65}\right)\)
\(\chi_{131}(23,\cdot)\) 131.h 130 Yes \(-1\) \(1\) \(e\left(\frac{23}{130}\right)\) \(e\left(\frac{48}{65}\right)\) \(e\left(\frac{23}{65}\right)\) \(e\left(\frac{9}{65}\right)\) \(e\left(\frac{119}{130}\right)\) \(e\left(\frac{64}{65}\right)\) \(e\left(\frac{69}{130}\right)\) \(e\left(\frac{31}{65}\right)\) \(e\left(\frac{41}{130}\right)\) \(e\left(\frac{59}{65}\right)\)
\(\chi_{131}(24,\cdot)\) 131.f 26 Yes \(-1\) \(1\) \(e\left(\frac{15}{26}\right)\) \(e\left(\frac{7}{13}\right)\) \(e\left(\frac{2}{13}\right)\) \(e\left(\frac{7}{13}\right)\) \(e\left(\frac{3}{26}\right)\) \(e\left(\frac{5}{13}\right)\) \(e\left(\frac{19}{26}\right)\) \(e\left(\frac{1}{13}\right)\) \(e\left(\frac{3}{26}\right)\) \(e\left(\frac{4}{13}\right)\)
\(\chi_{131}(25,\cdot)\) 131.g 65 Yes \(1\) \(1\) \(e\left(\frac{46}{65}\right)\) \(e\left(\frac{62}{65}\right)\) \(e\left(\frac{27}{65}\right)\) \(e\left(\frac{36}{65}\right)\) \(e\left(\frac{43}{65}\right)\) \(e\left(\frac{61}{65}\right)\) \(e\left(\frac{8}{65}\right)\) \(e\left(\frac{59}{65}\right)\) \(e\left(\frac{17}{65}\right)\) \(e\left(\frac{41}{65}\right)\)
\(\chi_{131}(26,\cdot)\) 131.h 130 Yes \(-1\) \(1\) \(e\left(\frac{19}{130}\right)\) \(e\left(\frac{34}{65}\right)\) \(e\left(\frac{19}{65}\right)\) \(e\left(\frac{47}{65}\right)\) \(e\left(\frac{87}{130}\right)\) \(e\left(\frac{2}{65}\right)\) \(e\left(\frac{57}{130}\right)\) \(e\left(\frac{3}{65}\right)\) \(e\left(\frac{113}{130}\right)\) \(e\left(\frac{12}{65}\right)\)
\(\chi_{131}(27,\cdot)\) 131.g 65 Yes \(1\) \(1\) \(e\left(\frac{43}{65}\right)\) \(e\left(\frac{41}{65}\right)\) \(e\left(\frac{21}{65}\right)\) \(e\left(\frac{28}{65}\right)\) \(e\left(\frac{19}{65}\right)\) \(e\left(\frac{33}{65}\right)\) \(e\left(\frac{64}{65}\right)\) \(e\left(\frac{17}{65}\right)\) \(e\left(\frac{6}{65}\right)\) \(e\left(\frac{3}{65}\right)\)
\(\chi_{131}(28,\cdot)\) 131.g 65 Yes \(1\) \(1\) \(e\left(\frac{49}{65}\right)\) \(e\left(\frac{18}{65}\right)\) \(e\left(\frac{33}{65}\right)\) \(e\left(\frac{44}{65}\right)\) \(e\left(\frac{2}{65}\right)\) \(e\left(\frac{24}{65}\right)\) \(e\left(\frac{17}{65}\right)\) \(e\left(\frac{36}{65}\right)\) \(e\left(\frac{28}{65}\right)\) \(e\left(\frac{14}{65}\right)\)
\(\chi_{131}(29,\cdot)\) 131.h 130 Yes \(-1\) \(1\) \(e\left(\frac{51}{130}\right)\) \(e\left(\frac{16}{65}\right)\) \(e\left(\frac{51}{65}\right)\) \(e\left(\frac{3}{65}\right)\) \(e\left(\frac{83}{130}\right)\) \(e\left(\frac{43}{65}\right)\) \(e\left(\frac{23}{130}\right)\) \(e\left(\frac{32}{65}\right)\) \(e\left(\frac{57}{130}\right)\) \(e\left(\frac{63}{65}\right)\)
\(\chi_{131}(30,\cdot)\) 131.h 130 Yes \(-1\) \(1\) \(e\left(\frac{119}{130}\right)\) \(e\left(\frac{59}{65}\right)\) \(e\left(\frac{54}{65}\right)\) \(e\left(\frac{7}{65}\right)\) \(e\left(\frac{107}{130}\right)\) \(e\left(\frac{57}{65}\right)\) \(e\left(\frac{97}{130}\right)\) \(e\left(\frac{53}{65}\right)\) \(e\left(\frac{3}{130}\right)\) \(e\left(\frac{17}{65}\right)\)
\(\chi_{131}(31,\cdot)\) 131.h 130 Yes \(-1\) \(1\) \(e\left(\frac{29}{130}\right)\) \(e\left(\frac{4}{65}\right)\) \(e\left(\frac{29}{65}\right)\) \(e\left(\frac{17}{65}\right)\) \(e\left(\frac{37}{130}\right)\) \(e\left(\frac{27}{65}\right)\) \(e\left(\frac{87}{130}\right)\) \(e\left(\frac{8}{65}\right)\) \(e\left(\frac{63}{130}\right)\) \(e\left(\frac{32}{65}\right)\)
\(\chi_{131}(32,\cdot)\) 131.f 26 Yes \(-1\) \(1\) \(e\left(\frac{1}{26}\right)\) \(e\left(\frac{10}{13}\right)\) \(e\left(\frac{1}{13}\right)\) \(e\left(\frac{10}{13}\right)\) \(e\left(\frac{21}{26}\right)\) \(e\left(\frac{9}{13}\right)\) \(e\left(\frac{3}{26}\right)\) \(e\left(\frac{7}{13}\right)\) \(e\left(\frac{21}{26}\right)\) \(e\left(\frac{2}{13}\right)\)