Properties

Modulus 373
Structure \(C_{372}\)
Order 372

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Show commands for: SageMath / Pari/GP

sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
 
sage: H = DirichletGroup_conrey(373)
 
pari: g = idealstar(,373,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 372
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{372}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{373}(2,\cdot)$

First 32 of 372 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
\(\chi_{373}(1,\cdot)\) 373.a 1 No \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{373}(2,\cdot)\) 373.l 372 Yes \(-1\) \(1\) \(e\left(\frac{1}{372}\right)\) \(e\left(\frac{119}{186}\right)\) \(e\left(\frac{1}{186}\right)\) \(e\left(\frac{169}{372}\right)\) \(e\left(\frac{239}{372}\right)\) \(e\left(\frac{33}{62}\right)\) \(e\left(\frac{1}{124}\right)\) \(e\left(\frac{26}{93}\right)\) \(e\left(\frac{85}{186}\right)\) \(e\left(\frac{245}{372}\right)\)
\(\chi_{373}(3,\cdot)\) 373.k 186 Yes \(1\) \(1\) \(e\left(\frac{119}{186}\right)\) \(e\left(\frac{25}{93}\right)\) \(e\left(\frac{26}{93}\right)\) \(e\left(\frac{23}{186}\right)\) \(e\left(\frac{169}{186}\right)\) \(e\left(\frac{21}{31}\right)\) \(e\left(\frac{57}{62}\right)\) \(e\left(\frac{50}{93}\right)\) \(e\left(\frac{71}{93}\right)\) \(e\left(\frac{139}{186}\right)\)
\(\chi_{373}(4,\cdot)\) 373.k 186 Yes \(1\) \(1\) \(e\left(\frac{1}{186}\right)\) \(e\left(\frac{26}{93}\right)\) \(e\left(\frac{1}{93}\right)\) \(e\left(\frac{169}{186}\right)\) \(e\left(\frac{53}{186}\right)\) \(e\left(\frac{2}{31}\right)\) \(e\left(\frac{1}{62}\right)\) \(e\left(\frac{52}{93}\right)\) \(e\left(\frac{85}{93}\right)\) \(e\left(\frac{59}{186}\right)\)
\(\chi_{373}(5,\cdot)\) 373.l 372 Yes \(-1\) \(1\) \(e\left(\frac{169}{372}\right)\) \(e\left(\frac{23}{186}\right)\) \(e\left(\frac{169}{186}\right)\) \(e\left(\frac{289}{372}\right)\) \(e\left(\frac{215}{372}\right)\) \(e\left(\frac{59}{62}\right)\) \(e\left(\frac{45}{124}\right)\) \(e\left(\frac{23}{93}\right)\) \(e\left(\frac{43}{186}\right)\) \(e\left(\frac{113}{372}\right)\)
\(\chi_{373}(6,\cdot)\) 373.l 372 Yes \(-1\) \(1\) \(e\left(\frac{239}{372}\right)\) \(e\left(\frac{169}{186}\right)\) \(e\left(\frac{53}{186}\right)\) \(e\left(\frac{215}{372}\right)\) \(e\left(\frac{205}{372}\right)\) \(e\left(\frac{13}{62}\right)\) \(e\left(\frac{115}{124}\right)\) \(e\left(\frac{76}{93}\right)\) \(e\left(\frac{41}{186}\right)\) \(e\left(\frac{151}{372}\right)\)
\(\chi_{373}(7,\cdot)\) 373.h 62 Yes \(1\) \(1\) \(e\left(\frac{33}{62}\right)\) \(e\left(\frac{21}{31}\right)\) \(e\left(\frac{2}{31}\right)\) \(e\left(\frac{59}{62}\right)\) \(e\left(\frac{13}{62}\right)\) \(e\left(\frac{12}{31}\right)\) \(e\left(\frac{37}{62}\right)\) \(e\left(\frac{11}{31}\right)\) \(e\left(\frac{15}{31}\right)\) \(e\left(\frac{25}{62}\right)\)
\(\chi_{373}(8,\cdot)\) 373.j 124 Yes \(-1\) \(1\) \(e\left(\frac{1}{124}\right)\) \(e\left(\frac{57}{62}\right)\) \(e\left(\frac{1}{62}\right)\) \(e\left(\frac{45}{124}\right)\) \(e\left(\frac{115}{124}\right)\) \(e\left(\frac{37}{62}\right)\) \(e\left(\frac{3}{124}\right)\) \(e\left(\frac{26}{31}\right)\) \(e\left(\frac{23}{62}\right)\) \(e\left(\frac{121}{124}\right)\)
\(\chi_{373}(9,\cdot)\) 373.i 93 Yes \(1\) \(1\) \(e\left(\frac{26}{93}\right)\) \(e\left(\frac{50}{93}\right)\) \(e\left(\frac{52}{93}\right)\) \(e\left(\frac{23}{93}\right)\) \(e\left(\frac{76}{93}\right)\) \(e\left(\frac{11}{31}\right)\) \(e\left(\frac{26}{31}\right)\) \(e\left(\frac{7}{93}\right)\) \(e\left(\frac{49}{93}\right)\) \(e\left(\frac{46}{93}\right)\)
\(\chi_{373}(10,\cdot)\) 373.k 186 Yes \(1\) \(1\) \(e\left(\frac{85}{186}\right)\) \(e\left(\frac{71}{93}\right)\) \(e\left(\frac{85}{93}\right)\) \(e\left(\frac{43}{186}\right)\) \(e\left(\frac{41}{186}\right)\) \(e\left(\frac{15}{31}\right)\) \(e\left(\frac{23}{62}\right)\) \(e\left(\frac{49}{93}\right)\) \(e\left(\frac{64}{93}\right)\) \(e\left(\frac{179}{186}\right)\)
\(\chi_{373}(11,\cdot)\) 373.l 372 Yes \(-1\) \(1\) \(e\left(\frac{245}{372}\right)\) \(e\left(\frac{139}{186}\right)\) \(e\left(\frac{59}{186}\right)\) \(e\left(\frac{113}{372}\right)\) \(e\left(\frac{151}{372}\right)\) \(e\left(\frac{25}{62}\right)\) \(e\left(\frac{121}{124}\right)\) \(e\left(\frac{46}{93}\right)\) \(e\left(\frac{179}{186}\right)\) \(e\left(\frac{133}{372}\right)\)
\(\chi_{373}(12,\cdot)\) 373.g 31 Yes \(1\) \(1\) \(e\left(\frac{20}{31}\right)\) \(e\left(\frac{17}{31}\right)\) \(e\left(\frac{9}{31}\right)\) \(e\left(\frac{1}{31}\right)\) \(e\left(\frac{6}{31}\right)\) \(e\left(\frac{23}{31}\right)\) \(e\left(\frac{29}{31}\right)\) \(e\left(\frac{3}{31}\right)\) \(e\left(\frac{21}{31}\right)\) \(e\left(\frac{2}{31}\right)\)
\(\chi_{373}(13,\cdot)\) 373.h 62 Yes \(1\) \(1\) \(e\left(\frac{15}{62}\right)\) \(e\left(\frac{18}{31}\right)\) \(e\left(\frac{15}{31}\right)\) \(e\left(\frac{55}{62}\right)\) \(e\left(\frac{51}{62}\right)\) \(e\left(\frac{28}{31}\right)\) \(e\left(\frac{45}{62}\right)\) \(e\left(\frac{5}{31}\right)\) \(e\left(\frac{4}{31}\right)\) \(e\left(\frac{17}{62}\right)\)
\(\chi_{373}(14,\cdot)\) 373.l 372 Yes \(-1\) \(1\) \(e\left(\frac{199}{372}\right)\) \(e\left(\frac{59}{186}\right)\) \(e\left(\frac{13}{186}\right)\) \(e\left(\frac{151}{372}\right)\) \(e\left(\frac{317}{372}\right)\) \(e\left(\frac{57}{62}\right)\) \(e\left(\frac{75}{124}\right)\) \(e\left(\frac{59}{93}\right)\) \(e\left(\frac{175}{186}\right)\) \(e\left(\frac{23}{372}\right)\)
\(\chi_{373}(15,\cdot)\) 373.l 372 Yes \(-1\) \(1\) \(e\left(\frac{35}{372}\right)\) \(e\left(\frac{73}{186}\right)\) \(e\left(\frac{35}{186}\right)\) \(e\left(\frac{335}{372}\right)\) \(e\left(\frac{181}{372}\right)\) \(e\left(\frac{39}{62}\right)\) \(e\left(\frac{35}{124}\right)\) \(e\left(\frac{73}{93}\right)\) \(e\left(\frac{185}{186}\right)\) \(e\left(\frac{19}{372}\right)\)
\(\chi_{373}(16,\cdot)\) 373.i 93 Yes \(1\) \(1\) \(e\left(\frac{1}{93}\right)\) \(e\left(\frac{52}{93}\right)\) \(e\left(\frac{2}{93}\right)\) \(e\left(\frac{76}{93}\right)\) \(e\left(\frac{53}{93}\right)\) \(e\left(\frac{4}{31}\right)\) \(e\left(\frac{1}{31}\right)\) \(e\left(\frac{11}{93}\right)\) \(e\left(\frac{77}{93}\right)\) \(e\left(\frac{59}{93}\right)\)
\(\chi_{373}(17,\cdot)\) 373.h 62 Yes \(1\) \(1\) \(e\left(\frac{21}{62}\right)\) \(e\left(\frac{19}{31}\right)\) \(e\left(\frac{21}{31}\right)\) \(e\left(\frac{15}{62}\right)\) \(e\left(\frac{59}{62}\right)\) \(e\left(\frac{2}{31}\right)\) \(e\left(\frac{1}{62}\right)\) \(e\left(\frac{7}{31}\right)\) \(e\left(\frac{18}{31}\right)\) \(e\left(\frac{61}{62}\right)\)
\(\chi_{373}(18,\cdot)\) 373.j 124 Yes \(-1\) \(1\) \(e\left(\frac{35}{124}\right)\) \(e\left(\frac{11}{62}\right)\) \(e\left(\frac{35}{62}\right)\) \(e\left(\frac{87}{124}\right)\) \(e\left(\frac{57}{124}\right)\) \(e\left(\frac{55}{62}\right)\) \(e\left(\frac{105}{124}\right)\) \(e\left(\frac{11}{31}\right)\) \(e\left(\frac{61}{62}\right)\) \(e\left(\frac{19}{124}\right)\)
\(\chi_{373}(19,\cdot)\) 373.j 124 Yes \(-1\) \(1\) \(e\left(\frac{9}{124}\right)\) \(e\left(\frac{17}{62}\right)\) \(e\left(\frac{9}{62}\right)\) \(e\left(\frac{33}{124}\right)\) \(e\left(\frac{43}{124}\right)\) \(e\left(\frac{23}{62}\right)\) \(e\left(\frac{27}{124}\right)\) \(e\left(\frac{17}{31}\right)\) \(e\left(\frac{21}{62}\right)\) \(e\left(\frac{97}{124}\right)\)
\(\chi_{373}(20,\cdot)\) 373.j 124 Yes \(-1\) \(1\) \(e\left(\frac{57}{124}\right)\) \(e\left(\frac{25}{62}\right)\) \(e\left(\frac{57}{62}\right)\) \(e\left(\frac{85}{124}\right)\) \(e\left(\frac{107}{124}\right)\) \(e\left(\frac{1}{62}\right)\) \(e\left(\frac{47}{124}\right)\) \(e\left(\frac{25}{31}\right)\) \(e\left(\frac{9}{62}\right)\) \(e\left(\frac{77}{124}\right)\)
\(\chi_{373}(21,\cdot)\) 373.i 93 Yes \(1\) \(1\) \(e\left(\frac{16}{93}\right)\) \(e\left(\frac{88}{93}\right)\) \(e\left(\frac{32}{93}\right)\) \(e\left(\frac{7}{93}\right)\) \(e\left(\frac{11}{93}\right)\) \(e\left(\frac{2}{31}\right)\) \(e\left(\frac{16}{31}\right)\) \(e\left(\frac{83}{93}\right)\) \(e\left(\frac{23}{93}\right)\) \(e\left(\frac{14}{93}\right)\)
\(\chi_{373}(22,\cdot)\) 373.h 62 Yes \(1\) \(1\) \(e\left(\frac{41}{62}\right)\) \(e\left(\frac{12}{31}\right)\) \(e\left(\frac{10}{31}\right)\) \(e\left(\frac{47}{62}\right)\) \(e\left(\frac{3}{62}\right)\) \(e\left(\frac{29}{31}\right)\) \(e\left(\frac{61}{62}\right)\) \(e\left(\frac{24}{31}\right)\) \(e\left(\frac{13}{31}\right)\) \(e\left(\frac{1}{62}\right)\)
\(\chi_{373}(23,\cdot)\) 373.j 124 Yes \(-1\) \(1\) \(e\left(\frac{117}{124}\right)\) \(e\left(\frac{35}{62}\right)\) \(e\left(\frac{55}{62}\right)\) \(e\left(\frac{57}{124}\right)\) \(e\left(\frac{63}{124}\right)\) \(e\left(\frac{51}{62}\right)\) \(e\left(\frac{103}{124}\right)\) \(e\left(\frac{4}{31}\right)\) \(e\left(\frac{25}{62}\right)\) \(e\left(\frac{21}{124}\right)\)
\(\chi_{373}(24,\cdot)\) 373.l 372 Yes \(-1\) \(1\) \(e\left(\frac{241}{372}\right)\) \(e\left(\frac{35}{186}\right)\) \(e\left(\frac{55}{186}\right)\) \(e\left(\frac{181}{372}\right)\) \(e\left(\frac{311}{372}\right)\) \(e\left(\frac{17}{62}\right)\) \(e\left(\frac{117}{124}\right)\) \(e\left(\frac{35}{93}\right)\) \(e\left(\frac{25}{186}\right)\) \(e\left(\frac{269}{372}\right)\)
\(\chi_{373}(25,\cdot)\) 373.k 186 Yes \(1\) \(1\) \(e\left(\frac{169}{186}\right)\) \(e\left(\frac{23}{93}\right)\) \(e\left(\frac{76}{93}\right)\) \(e\left(\frac{103}{186}\right)\) \(e\left(\frac{29}{186}\right)\) \(e\left(\frac{28}{31}\right)\) \(e\left(\frac{45}{62}\right)\) \(e\left(\frac{46}{93}\right)\) \(e\left(\frac{43}{93}\right)\) \(e\left(\frac{113}{186}\right)\)
\(\chi_{373}(26,\cdot)\) 373.l 372 Yes \(-1\) \(1\) \(e\left(\frac{91}{372}\right)\) \(e\left(\frac{41}{186}\right)\) \(e\left(\frac{91}{186}\right)\) \(e\left(\frac{127}{372}\right)\) \(e\left(\frac{173}{372}\right)\) \(e\left(\frac{27}{62}\right)\) \(e\left(\frac{91}{124}\right)\) \(e\left(\frac{41}{93}\right)\) \(e\left(\frac{109}{186}\right)\) \(e\left(\frac{347}{372}\right)\)
\(\chi_{373}(27,\cdot)\) 373.h 62 Yes \(1\) \(1\) \(e\left(\frac{57}{62}\right)\) \(e\left(\frac{25}{31}\right)\) \(e\left(\frac{26}{31}\right)\) \(e\left(\frac{23}{62}\right)\) \(e\left(\frac{45}{62}\right)\) \(e\left(\frac{1}{31}\right)\) \(e\left(\frac{47}{62}\right)\) \(e\left(\frac{19}{31}\right)\) \(e\left(\frac{9}{31}\right)\) \(e\left(\frac{15}{62}\right)\)
\(\chi_{373}(28,\cdot)\) 373.i 93 Yes \(1\) \(1\) \(e\left(\frac{50}{93}\right)\) \(e\left(\frac{89}{93}\right)\) \(e\left(\frac{7}{93}\right)\) \(e\left(\frac{80}{93}\right)\) \(e\left(\frac{46}{93}\right)\) \(e\left(\frac{14}{31}\right)\) \(e\left(\frac{19}{31}\right)\) \(e\left(\frac{85}{93}\right)\) \(e\left(\frac{37}{93}\right)\) \(e\left(\frac{67}{93}\right)\)
\(\chi_{373}(29,\cdot)\) 373.i 93 Yes \(1\) \(1\) \(e\left(\frac{71}{93}\right)\) \(e\left(\frac{65}{93}\right)\) \(e\left(\frac{49}{93}\right)\) \(e\left(\frac{2}{93}\right)\) \(e\left(\frac{43}{93}\right)\) \(e\left(\frac{5}{31}\right)\) \(e\left(\frac{9}{31}\right)\) \(e\left(\frac{37}{93}\right)\) \(e\left(\frac{73}{93}\right)\) \(e\left(\frac{4}{93}\right)\)
\(\chi_{373}(30,\cdot)\) 373.g 31 Yes \(1\) \(1\) \(e\left(\frac{3}{31}\right)\) \(e\left(\frac{1}{31}\right)\) \(e\left(\frac{6}{31}\right)\) \(e\left(\frac{11}{31}\right)\) \(e\left(\frac{4}{31}\right)\) \(e\left(\frac{5}{31}\right)\) \(e\left(\frac{9}{31}\right)\) \(e\left(\frac{2}{31}\right)\) \(e\left(\frac{14}{31}\right)\) \(e\left(\frac{22}{31}\right)\)
\(\chi_{373}(31,\cdot)\) 373.h 62 Yes \(1\) \(1\) \(e\left(\frac{53}{62}\right)\) \(e\left(\frac{14}{31}\right)\) \(e\left(\frac{22}{31}\right)\) \(e\left(\frac{29}{62}\right)\) \(e\left(\frac{19}{62}\right)\) \(e\left(\frac{8}{31}\right)\) \(e\left(\frac{35}{62}\right)\) \(e\left(\frac{28}{31}\right)\) \(e\left(\frac{10}{31}\right)\) \(e\left(\frac{27}{62}\right)\)
\(\chi_{373}(32,\cdot)\) 373.l 372 Yes \(-1\) \(1\) \(e\left(\frac{5}{372}\right)\) \(e\left(\frac{37}{186}\right)\) \(e\left(\frac{5}{186}\right)\) \(e\left(\frac{101}{372}\right)\) \(e\left(\frac{79}{372}\right)\) \(e\left(\frac{41}{62}\right)\) \(e\left(\frac{5}{124}\right)\) \(e\left(\frac{37}{93}\right)\) \(e\left(\frac{53}{186}\right)\) \(e\left(\frac{109}{372}\right)\)