Properties

Modulus 167
Structure \(C_{166}\)
Order 166

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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(167)
 
pari: g = idealstar(,167,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 166
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{166}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{167}(5,\cdot)$

First 32 of 166 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
\(\chi_{167}(1,\cdot)\) 167.a 1 No \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{167}(2,\cdot)\) 167.c 83 Yes \(1\) \(1\) \(e\left(\frac{53}{83}\right)\) \(e\left(\frac{54}{83}\right)\) \(e\left(\frac{23}{83}\right)\) \(e\left(\frac{20}{83}\right)\) \(e\left(\frac{24}{83}\right)\) \(e\left(\frac{36}{83}\right)\) \(e\left(\frac{76}{83}\right)\) \(e\left(\frac{25}{83}\right)\) \(e\left(\frac{73}{83}\right)\) \(e\left(\frac{62}{83}\right)\)
\(\chi_{167}(3,\cdot)\) 167.c 83 Yes \(1\) \(1\) \(e\left(\frac{54}{83}\right)\) \(e\left(\frac{19}{83}\right)\) \(e\left(\frac{25}{83}\right)\) \(e\left(\frac{47}{83}\right)\) \(e\left(\frac{73}{83}\right)\) \(e\left(\frac{68}{83}\right)\) \(e\left(\frac{79}{83}\right)\) \(e\left(\frac{38}{83}\right)\) \(e\left(\frac{18}{83}\right)\) \(e\left(\frac{71}{83}\right)\)
\(\chi_{167}(4,\cdot)\) 167.c 83 Yes \(1\) \(1\) \(e\left(\frac{23}{83}\right)\) \(e\left(\frac{25}{83}\right)\) \(e\left(\frac{46}{83}\right)\) \(e\left(\frac{40}{83}\right)\) \(e\left(\frac{48}{83}\right)\) \(e\left(\frac{72}{83}\right)\) \(e\left(\frac{69}{83}\right)\) \(e\left(\frac{50}{83}\right)\) \(e\left(\frac{63}{83}\right)\) \(e\left(\frac{41}{83}\right)\)
\(\chi_{167}(5,\cdot)\) 167.d 166 Yes \(-1\) \(1\) \(e\left(\frac{20}{83}\right)\) \(e\left(\frac{47}{83}\right)\) \(e\left(\frac{40}{83}\right)\) \(e\left(\frac{1}{166}\right)\) \(e\left(\frac{67}{83}\right)\) \(e\left(\frac{59}{83}\right)\) \(e\left(\frac{60}{83}\right)\) \(e\left(\frac{11}{83}\right)\) \(e\left(\frac{41}{166}\right)\) \(e\left(\frac{14}{83}\right)\)
\(\chi_{167}(6,\cdot)\) 167.c 83 Yes \(1\) \(1\) \(e\left(\frac{24}{83}\right)\) \(e\left(\frac{73}{83}\right)\) \(e\left(\frac{48}{83}\right)\) \(e\left(\frac{67}{83}\right)\) \(e\left(\frac{14}{83}\right)\) \(e\left(\frac{21}{83}\right)\) \(e\left(\frac{72}{83}\right)\) \(e\left(\frac{63}{83}\right)\) \(e\left(\frac{8}{83}\right)\) \(e\left(\frac{50}{83}\right)\)
\(\chi_{167}(7,\cdot)\) 167.c 83 Yes \(1\) \(1\) \(e\left(\frac{36}{83}\right)\) \(e\left(\frac{68}{83}\right)\) \(e\left(\frac{72}{83}\right)\) \(e\left(\frac{59}{83}\right)\) \(e\left(\frac{21}{83}\right)\) \(e\left(\frac{73}{83}\right)\) \(e\left(\frac{25}{83}\right)\) \(e\left(\frac{53}{83}\right)\) \(e\left(\frac{12}{83}\right)\) \(e\left(\frac{75}{83}\right)\)
\(\chi_{167}(8,\cdot)\) 167.c 83 Yes \(1\) \(1\) \(e\left(\frac{76}{83}\right)\) \(e\left(\frac{79}{83}\right)\) \(e\left(\frac{69}{83}\right)\) \(e\left(\frac{60}{83}\right)\) \(e\left(\frac{72}{83}\right)\) \(e\left(\frac{25}{83}\right)\) \(e\left(\frac{62}{83}\right)\) \(e\left(\frac{75}{83}\right)\) \(e\left(\frac{53}{83}\right)\) \(e\left(\frac{20}{83}\right)\)
\(\chi_{167}(9,\cdot)\) 167.c 83 Yes \(1\) \(1\) \(e\left(\frac{25}{83}\right)\) \(e\left(\frac{38}{83}\right)\) \(e\left(\frac{50}{83}\right)\) \(e\left(\frac{11}{83}\right)\) \(e\left(\frac{63}{83}\right)\) \(e\left(\frac{53}{83}\right)\) \(e\left(\frac{75}{83}\right)\) \(e\left(\frac{76}{83}\right)\) \(e\left(\frac{36}{83}\right)\) \(e\left(\frac{59}{83}\right)\)
\(\chi_{167}(10,\cdot)\) 167.d 166 Yes \(-1\) \(1\) \(e\left(\frac{73}{83}\right)\) \(e\left(\frac{18}{83}\right)\) \(e\left(\frac{63}{83}\right)\) \(e\left(\frac{41}{166}\right)\) \(e\left(\frac{8}{83}\right)\) \(e\left(\frac{12}{83}\right)\) \(e\left(\frac{53}{83}\right)\) \(e\left(\frac{36}{83}\right)\) \(e\left(\frac{21}{166}\right)\) \(e\left(\frac{76}{83}\right)\)
\(\chi_{167}(11,\cdot)\) 167.c 83 Yes \(1\) \(1\) \(e\left(\frac{62}{83}\right)\) \(e\left(\frac{71}{83}\right)\) \(e\left(\frac{41}{83}\right)\) \(e\left(\frac{14}{83}\right)\) \(e\left(\frac{50}{83}\right)\) \(e\left(\frac{75}{83}\right)\) \(e\left(\frac{20}{83}\right)\) \(e\left(\frac{59}{83}\right)\) \(e\left(\frac{76}{83}\right)\) \(e\left(\frac{60}{83}\right)\)
\(\chi_{167}(12,\cdot)\) 167.c 83 Yes \(1\) \(1\) \(e\left(\frac{77}{83}\right)\) \(e\left(\frac{44}{83}\right)\) \(e\left(\frac{71}{83}\right)\) \(e\left(\frac{4}{83}\right)\) \(e\left(\frac{38}{83}\right)\) \(e\left(\frac{57}{83}\right)\) \(e\left(\frac{65}{83}\right)\) \(e\left(\frac{5}{83}\right)\) \(e\left(\frac{81}{83}\right)\) \(e\left(\frac{29}{83}\right)\)
\(\chi_{167}(13,\cdot)\) 167.d 166 Yes \(-1\) \(1\) \(e\left(\frac{68}{83}\right)\) \(e\left(\frac{27}{83}\right)\) \(e\left(\frac{53}{83}\right)\) \(e\left(\frac{103}{166}\right)\) \(e\left(\frac{12}{83}\right)\) \(e\left(\frac{18}{83}\right)\) \(e\left(\frac{38}{83}\right)\) \(e\left(\frac{54}{83}\right)\) \(e\left(\frac{73}{166}\right)\) \(e\left(\frac{31}{83}\right)\)
\(\chi_{167}(14,\cdot)\) 167.c 83 Yes \(1\) \(1\) \(e\left(\frac{6}{83}\right)\) \(e\left(\frac{39}{83}\right)\) \(e\left(\frac{12}{83}\right)\) \(e\left(\frac{79}{83}\right)\) \(e\left(\frac{45}{83}\right)\) \(e\left(\frac{26}{83}\right)\) \(e\left(\frac{18}{83}\right)\) \(e\left(\frac{78}{83}\right)\) \(e\left(\frac{2}{83}\right)\) \(e\left(\frac{54}{83}\right)\)
\(\chi_{167}(15,\cdot)\) 167.d 166 Yes \(-1\) \(1\) \(e\left(\frac{74}{83}\right)\) \(e\left(\frac{66}{83}\right)\) \(e\left(\frac{65}{83}\right)\) \(e\left(\frac{95}{166}\right)\) \(e\left(\frac{57}{83}\right)\) \(e\left(\frac{44}{83}\right)\) \(e\left(\frac{56}{83}\right)\) \(e\left(\frac{49}{83}\right)\) \(e\left(\frac{77}{166}\right)\) \(e\left(\frac{2}{83}\right)\)
\(\chi_{167}(16,\cdot)\) 167.c 83 Yes \(1\) \(1\) \(e\left(\frac{46}{83}\right)\) \(e\left(\frac{50}{83}\right)\) \(e\left(\frac{9}{83}\right)\) \(e\left(\frac{80}{83}\right)\) \(e\left(\frac{13}{83}\right)\) \(e\left(\frac{61}{83}\right)\) \(e\left(\frac{55}{83}\right)\) \(e\left(\frac{17}{83}\right)\) \(e\left(\frac{43}{83}\right)\) \(e\left(\frac{82}{83}\right)\)
\(\chi_{167}(17,\cdot)\) 167.d 166 Yes \(-1\) \(1\) \(e\left(\frac{64}{83}\right)\) \(e\left(\frac{1}{83}\right)\) \(e\left(\frac{45}{83}\right)\) \(e\left(\frac{53}{166}\right)\) \(e\left(\frac{65}{83}\right)\) \(e\left(\frac{56}{83}\right)\) \(e\left(\frac{26}{83}\right)\) \(e\left(\frac{2}{83}\right)\) \(e\left(\frac{15}{166}\right)\) \(e\left(\frac{78}{83}\right)\)
\(\chi_{167}(18,\cdot)\) 167.c 83 Yes \(1\) \(1\) \(e\left(\frac{78}{83}\right)\) \(e\left(\frac{9}{83}\right)\) \(e\left(\frac{73}{83}\right)\) \(e\left(\frac{31}{83}\right)\) \(e\left(\frac{4}{83}\right)\) \(e\left(\frac{6}{83}\right)\) \(e\left(\frac{68}{83}\right)\) \(e\left(\frac{18}{83}\right)\) \(e\left(\frac{26}{83}\right)\) \(e\left(\frac{38}{83}\right)\)
\(\chi_{167}(19,\cdot)\) 167.c 83 Yes \(1\) \(1\) \(e\left(\frac{81}{83}\right)\) \(e\left(\frac{70}{83}\right)\) \(e\left(\frac{79}{83}\right)\) \(e\left(\frac{29}{83}\right)\) \(e\left(\frac{68}{83}\right)\) \(e\left(\frac{19}{83}\right)\) \(e\left(\frac{77}{83}\right)\) \(e\left(\frac{57}{83}\right)\) \(e\left(\frac{27}{83}\right)\) \(e\left(\frac{65}{83}\right)\)
\(\chi_{167}(20,\cdot)\) 167.d 166 Yes \(-1\) \(1\) \(e\left(\frac{43}{83}\right)\) \(e\left(\frac{72}{83}\right)\) \(e\left(\frac{3}{83}\right)\) \(e\left(\frac{81}{166}\right)\) \(e\left(\frac{32}{83}\right)\) \(e\left(\frac{48}{83}\right)\) \(e\left(\frac{46}{83}\right)\) \(e\left(\frac{61}{83}\right)\) \(e\left(\frac{1}{166}\right)\) \(e\left(\frac{55}{83}\right)\)
\(\chi_{167}(21,\cdot)\) 167.c 83 Yes \(1\) \(1\) \(e\left(\frac{7}{83}\right)\) \(e\left(\frac{4}{83}\right)\) \(e\left(\frac{14}{83}\right)\) \(e\left(\frac{23}{83}\right)\) \(e\left(\frac{11}{83}\right)\) \(e\left(\frac{58}{83}\right)\) \(e\left(\frac{21}{83}\right)\) \(e\left(\frac{8}{83}\right)\) \(e\left(\frac{30}{83}\right)\) \(e\left(\frac{63}{83}\right)\)
\(\chi_{167}(22,\cdot)\) 167.c 83 Yes \(1\) \(1\) \(e\left(\frac{32}{83}\right)\) \(e\left(\frac{42}{83}\right)\) \(e\left(\frac{64}{83}\right)\) \(e\left(\frac{34}{83}\right)\) \(e\left(\frac{74}{83}\right)\) \(e\left(\frac{28}{83}\right)\) \(e\left(\frac{13}{83}\right)\) \(e\left(\frac{1}{83}\right)\) \(e\left(\frac{66}{83}\right)\) \(e\left(\frac{39}{83}\right)\)
\(\chi_{167}(23,\cdot)\) 167.d 166 Yes \(-1\) \(1\) \(e\left(\frac{71}{83}\right)\) \(e\left(\frac{5}{83}\right)\) \(e\left(\frac{59}{83}\right)\) \(e\left(\frac{99}{166}\right)\) \(e\left(\frac{76}{83}\right)\) \(e\left(\frac{31}{83}\right)\) \(e\left(\frac{47}{83}\right)\) \(e\left(\frac{10}{83}\right)\) \(e\left(\frac{75}{166}\right)\) \(e\left(\frac{58}{83}\right)\)
\(\chi_{167}(24,\cdot)\) 167.c 83 Yes \(1\) \(1\) \(e\left(\frac{47}{83}\right)\) \(e\left(\frac{15}{83}\right)\) \(e\left(\frac{11}{83}\right)\) \(e\left(\frac{24}{83}\right)\) \(e\left(\frac{62}{83}\right)\) \(e\left(\frac{10}{83}\right)\) \(e\left(\frac{58}{83}\right)\) \(e\left(\frac{30}{83}\right)\) \(e\left(\frac{71}{83}\right)\) \(e\left(\frac{8}{83}\right)\)
\(\chi_{167}(25,\cdot)\) 167.c 83 Yes \(1\) \(1\) \(e\left(\frac{40}{83}\right)\) \(e\left(\frac{11}{83}\right)\) \(e\left(\frac{80}{83}\right)\) \(e\left(\frac{1}{83}\right)\) \(e\left(\frac{51}{83}\right)\) \(e\left(\frac{35}{83}\right)\) \(e\left(\frac{37}{83}\right)\) \(e\left(\frac{22}{83}\right)\) \(e\left(\frac{41}{83}\right)\) \(e\left(\frac{28}{83}\right)\)
\(\chi_{167}(26,\cdot)\) 167.d 166 Yes \(-1\) \(1\) \(e\left(\frac{38}{83}\right)\) \(e\left(\frac{81}{83}\right)\) \(e\left(\frac{76}{83}\right)\) \(e\left(\frac{143}{166}\right)\) \(e\left(\frac{36}{83}\right)\) \(e\left(\frac{54}{83}\right)\) \(e\left(\frac{31}{83}\right)\) \(e\left(\frac{79}{83}\right)\) \(e\left(\frac{53}{166}\right)\) \(e\left(\frac{10}{83}\right)\)
\(\chi_{167}(27,\cdot)\) 167.c 83 Yes \(1\) \(1\) \(e\left(\frac{79}{83}\right)\) \(e\left(\frac{57}{83}\right)\) \(e\left(\frac{75}{83}\right)\) \(e\left(\frac{58}{83}\right)\) \(e\left(\frac{53}{83}\right)\) \(e\left(\frac{38}{83}\right)\) \(e\left(\frac{71}{83}\right)\) \(e\left(\frac{31}{83}\right)\) \(e\left(\frac{54}{83}\right)\) \(e\left(\frac{47}{83}\right)\)
\(\chi_{167}(28,\cdot)\) 167.c 83 Yes \(1\) \(1\) \(e\left(\frac{59}{83}\right)\) \(e\left(\frac{10}{83}\right)\) \(e\left(\frac{35}{83}\right)\) \(e\left(\frac{16}{83}\right)\) \(e\left(\frac{69}{83}\right)\) \(e\left(\frac{62}{83}\right)\) \(e\left(\frac{11}{83}\right)\) \(e\left(\frac{20}{83}\right)\) \(e\left(\frac{75}{83}\right)\) \(e\left(\frac{33}{83}\right)\)
\(\chi_{167}(29,\cdot)\) 167.c 83 Yes \(1\) \(1\) \(e\left(\frac{12}{83}\right)\) \(e\left(\frac{78}{83}\right)\) \(e\left(\frac{24}{83}\right)\) \(e\left(\frac{75}{83}\right)\) \(e\left(\frac{7}{83}\right)\) \(e\left(\frac{52}{83}\right)\) \(e\left(\frac{36}{83}\right)\) \(e\left(\frac{73}{83}\right)\) \(e\left(\frac{4}{83}\right)\) \(e\left(\frac{25}{83}\right)\)
\(\chi_{167}(30,\cdot)\) 167.d 166 Yes \(-1\) \(1\) \(e\left(\frac{44}{83}\right)\) \(e\left(\frac{37}{83}\right)\) \(e\left(\frac{5}{83}\right)\) \(e\left(\frac{135}{166}\right)\) \(e\left(\frac{81}{83}\right)\) \(e\left(\frac{80}{83}\right)\) \(e\left(\frac{49}{83}\right)\) \(e\left(\frac{74}{83}\right)\) \(e\left(\frac{57}{166}\right)\) \(e\left(\frac{64}{83}\right)\)
\(\chi_{167}(31,\cdot)\) 167.c 83 Yes \(1\) \(1\) \(e\left(\frac{57}{83}\right)\) \(e\left(\frac{80}{83}\right)\) \(e\left(\frac{31}{83}\right)\) \(e\left(\frac{45}{83}\right)\) \(e\left(\frac{54}{83}\right)\) \(e\left(\frac{81}{83}\right)\) \(e\left(\frac{5}{83}\right)\) \(e\left(\frac{77}{83}\right)\) \(e\left(\frac{19}{83}\right)\) \(e\left(\frac{15}{83}\right)\)
\(\chi_{167}(32,\cdot)\) 167.c 83 Yes \(1\) \(1\) \(e\left(\frac{16}{83}\right)\) \(e\left(\frac{21}{83}\right)\) \(e\left(\frac{32}{83}\right)\) \(e\left(\frac{17}{83}\right)\) \(e\left(\frac{37}{83}\right)\) \(e\left(\frac{14}{83}\right)\) \(e\left(\frac{48}{83}\right)\) \(e\left(\frac{42}{83}\right)\) \(e\left(\frac{33}{83}\right)\) \(e\left(\frac{61}{83}\right)\)