Properties

Modulus 173
Structure \(C_{172}\)
Order 172

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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(173)
 
pari: g = idealstar(,173,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 172
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{172}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{173}(2,\cdot)$

First 32 of 172 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
\(\chi_{173}(1,\cdot)\) 173.a 1 No \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{173}(2,\cdot)\) 173.f 172 Yes \(-1\) \(1\) \(e\left(\frac{1}{172}\right)\) \(e\left(\frac{27}{172}\right)\) \(e\left(\frac{1}{86}\right)\) \(e\left(\frac{39}{172}\right)\) \(e\left(\frac{7}{43}\right)\) \(e\left(\frac{95}{172}\right)\) \(e\left(\frac{3}{172}\right)\) \(e\left(\frac{27}{86}\right)\) \(e\left(\frac{10}{43}\right)\) \(e\left(\frac{23}{172}\right)\)
\(\chi_{173}(3,\cdot)\) 173.f 172 Yes \(-1\) \(1\) \(e\left(\frac{27}{172}\right)\) \(e\left(\frac{41}{172}\right)\) \(e\left(\frac{27}{86}\right)\) \(e\left(\frac{21}{172}\right)\) \(e\left(\frac{17}{43}\right)\) \(e\left(\frac{157}{172}\right)\) \(e\left(\frac{81}{172}\right)\) \(e\left(\frac{41}{86}\right)\) \(e\left(\frac{12}{43}\right)\) \(e\left(\frac{105}{172}\right)\)
\(\chi_{173}(4,\cdot)\) 173.e 86 Yes \(1\) \(1\) \(e\left(\frac{1}{86}\right)\) \(e\left(\frac{27}{86}\right)\) \(e\left(\frac{1}{43}\right)\) \(e\left(\frac{39}{86}\right)\) \(e\left(\frac{14}{43}\right)\) \(e\left(\frac{9}{86}\right)\) \(e\left(\frac{3}{86}\right)\) \(e\left(\frac{27}{43}\right)\) \(e\left(\frac{20}{43}\right)\) \(e\left(\frac{23}{86}\right)\)
\(\chi_{173}(5,\cdot)\) 173.f 172 Yes \(-1\) \(1\) \(e\left(\frac{39}{172}\right)\) \(e\left(\frac{21}{172}\right)\) \(e\left(\frac{39}{86}\right)\) \(e\left(\frac{145}{172}\right)\) \(e\left(\frac{15}{43}\right)\) \(e\left(\frac{93}{172}\right)\) \(e\left(\frac{117}{172}\right)\) \(e\left(\frac{21}{86}\right)\) \(e\left(\frac{3}{43}\right)\) \(e\left(\frac{37}{172}\right)\)
\(\chi_{173}(6,\cdot)\) 173.d 43 Yes \(1\) \(1\) \(e\left(\frac{7}{43}\right)\) \(e\left(\frac{17}{43}\right)\) \(e\left(\frac{14}{43}\right)\) \(e\left(\frac{15}{43}\right)\) \(e\left(\frac{24}{43}\right)\) \(e\left(\frac{20}{43}\right)\) \(e\left(\frac{21}{43}\right)\) \(e\left(\frac{34}{43}\right)\) \(e\left(\frac{22}{43}\right)\) \(e\left(\frac{32}{43}\right)\)
\(\chi_{173}(7,\cdot)\) 173.f 172 Yes \(-1\) \(1\) \(e\left(\frac{95}{172}\right)\) \(e\left(\frac{157}{172}\right)\) \(e\left(\frac{9}{86}\right)\) \(e\left(\frac{93}{172}\right)\) \(e\left(\frac{20}{43}\right)\) \(e\left(\frac{81}{172}\right)\) \(e\left(\frac{113}{172}\right)\) \(e\left(\frac{71}{86}\right)\) \(e\left(\frac{4}{43}\right)\) \(e\left(\frac{121}{172}\right)\)
\(\chi_{173}(8,\cdot)\) 173.f 172 Yes \(-1\) \(1\) \(e\left(\frac{3}{172}\right)\) \(e\left(\frac{81}{172}\right)\) \(e\left(\frac{3}{86}\right)\) \(e\left(\frac{117}{172}\right)\) \(e\left(\frac{21}{43}\right)\) \(e\left(\frac{113}{172}\right)\) \(e\left(\frac{9}{172}\right)\) \(e\left(\frac{81}{86}\right)\) \(e\left(\frac{30}{43}\right)\) \(e\left(\frac{69}{172}\right)\)
\(\chi_{173}(9,\cdot)\) 173.e 86 Yes \(1\) \(1\) \(e\left(\frac{27}{86}\right)\) \(e\left(\frac{41}{86}\right)\) \(e\left(\frac{27}{43}\right)\) \(e\left(\frac{21}{86}\right)\) \(e\left(\frac{34}{43}\right)\) \(e\left(\frac{71}{86}\right)\) \(e\left(\frac{81}{86}\right)\) \(e\left(\frac{41}{43}\right)\) \(e\left(\frac{24}{43}\right)\) \(e\left(\frac{19}{86}\right)\)
\(\chi_{173}(10,\cdot)\) 173.d 43 Yes \(1\) \(1\) \(e\left(\frac{10}{43}\right)\) \(e\left(\frac{12}{43}\right)\) \(e\left(\frac{20}{43}\right)\) \(e\left(\frac{3}{43}\right)\) \(e\left(\frac{22}{43}\right)\) \(e\left(\frac{4}{43}\right)\) \(e\left(\frac{30}{43}\right)\) \(e\left(\frac{24}{43}\right)\) \(e\left(\frac{13}{43}\right)\) \(e\left(\frac{15}{43}\right)\)
\(\chi_{173}(11,\cdot)\) 173.f 172 Yes \(-1\) \(1\) \(e\left(\frac{23}{172}\right)\) \(e\left(\frac{105}{172}\right)\) \(e\left(\frac{23}{86}\right)\) \(e\left(\frac{37}{172}\right)\) \(e\left(\frac{32}{43}\right)\) \(e\left(\frac{121}{172}\right)\) \(e\left(\frac{69}{172}\right)\) \(e\left(\frac{19}{86}\right)\) \(e\left(\frac{15}{43}\right)\) \(e\left(\frac{13}{172}\right)\)
\(\chi_{173}(12,\cdot)\) 173.f 172 Yes \(-1\) \(1\) \(e\left(\frac{29}{172}\right)\) \(e\left(\frac{95}{172}\right)\) \(e\left(\frac{29}{86}\right)\) \(e\left(\frac{99}{172}\right)\) \(e\left(\frac{31}{43}\right)\) \(e\left(\frac{3}{172}\right)\) \(e\left(\frac{87}{172}\right)\) \(e\left(\frac{9}{86}\right)\) \(e\left(\frac{32}{43}\right)\) \(e\left(\frac{151}{172}\right)\)
\(\chi_{173}(13,\cdot)\) 173.e 86 Yes \(1\) \(1\) \(e\left(\frac{65}{86}\right)\) \(e\left(\frac{35}{86}\right)\) \(e\left(\frac{22}{43}\right)\) \(e\left(\frac{41}{86}\right)\) \(e\left(\frac{7}{43}\right)\) \(e\left(\frac{69}{86}\right)\) \(e\left(\frac{23}{86}\right)\) \(e\left(\frac{35}{43}\right)\) \(e\left(\frac{10}{43}\right)\) \(e\left(\frac{33}{86}\right)\)
\(\chi_{173}(14,\cdot)\) 173.d 43 Yes \(1\) \(1\) \(e\left(\frac{24}{43}\right)\) \(e\left(\frac{3}{43}\right)\) \(e\left(\frac{5}{43}\right)\) \(e\left(\frac{33}{43}\right)\) \(e\left(\frac{27}{43}\right)\) \(e\left(\frac{1}{43}\right)\) \(e\left(\frac{29}{43}\right)\) \(e\left(\frac{6}{43}\right)\) \(e\left(\frac{14}{43}\right)\) \(e\left(\frac{36}{43}\right)\)
\(\chi_{173}(15,\cdot)\) 173.e 86 Yes \(1\) \(1\) \(e\left(\frac{33}{86}\right)\) \(e\left(\frac{31}{86}\right)\) \(e\left(\frac{33}{43}\right)\) \(e\left(\frac{83}{86}\right)\) \(e\left(\frac{32}{43}\right)\) \(e\left(\frac{39}{86}\right)\) \(e\left(\frac{13}{86}\right)\) \(e\left(\frac{31}{43}\right)\) \(e\left(\frac{15}{43}\right)\) \(e\left(\frac{71}{86}\right)\)
\(\chi_{173}(16,\cdot)\) 173.d 43 Yes \(1\) \(1\) \(e\left(\frac{1}{43}\right)\) \(e\left(\frac{27}{43}\right)\) \(e\left(\frac{2}{43}\right)\) \(e\left(\frac{39}{43}\right)\) \(e\left(\frac{28}{43}\right)\) \(e\left(\frac{9}{43}\right)\) \(e\left(\frac{3}{43}\right)\) \(e\left(\frac{11}{43}\right)\) \(e\left(\frac{40}{43}\right)\) \(e\left(\frac{23}{43}\right)\)
\(\chi_{173}(17,\cdot)\) 173.f 172 Yes \(-1\) \(1\) \(e\left(\frac{73}{172}\right)\) \(e\left(\frac{79}{172}\right)\) \(e\left(\frac{73}{86}\right)\) \(e\left(\frac{95}{172}\right)\) \(e\left(\frac{38}{43}\right)\) \(e\left(\frac{55}{172}\right)\) \(e\left(\frac{47}{172}\right)\) \(e\left(\frac{79}{86}\right)\) \(e\left(\frac{42}{43}\right)\) \(e\left(\frac{131}{172}\right)\)
\(\chi_{173}(18,\cdot)\) 173.f 172 Yes \(-1\) \(1\) \(e\left(\frac{55}{172}\right)\) \(e\left(\frac{109}{172}\right)\) \(e\left(\frac{55}{86}\right)\) \(e\left(\frac{81}{172}\right)\) \(e\left(\frac{41}{43}\right)\) \(e\left(\frac{65}{172}\right)\) \(e\left(\frac{165}{172}\right)\) \(e\left(\frac{23}{86}\right)\) \(e\left(\frac{34}{43}\right)\) \(e\left(\frac{61}{172}\right)\)
\(\chi_{173}(19,\cdot)\) 173.f 172 Yes \(-1\) \(1\) \(e\left(\frac{33}{172}\right)\) \(e\left(\frac{31}{172}\right)\) \(e\left(\frac{33}{86}\right)\) \(e\left(\frac{83}{172}\right)\) \(e\left(\frac{16}{43}\right)\) \(e\left(\frac{39}{172}\right)\) \(e\left(\frac{99}{172}\right)\) \(e\left(\frac{31}{86}\right)\) \(e\left(\frac{29}{43}\right)\) \(e\left(\frac{71}{172}\right)\)
\(\chi_{173}(20,\cdot)\) 173.f 172 Yes \(-1\) \(1\) \(e\left(\frac{41}{172}\right)\) \(e\left(\frac{75}{172}\right)\) \(e\left(\frac{41}{86}\right)\) \(e\left(\frac{51}{172}\right)\) \(e\left(\frac{29}{43}\right)\) \(e\left(\frac{111}{172}\right)\) \(e\left(\frac{123}{172}\right)\) \(e\left(\frac{75}{86}\right)\) \(e\left(\frac{23}{43}\right)\) \(e\left(\frac{83}{172}\right)\)
\(\chi_{173}(21,\cdot)\) 173.e 86 Yes \(1\) \(1\) \(e\left(\frac{61}{86}\right)\) \(e\left(\frac{13}{86}\right)\) \(e\left(\frac{18}{43}\right)\) \(e\left(\frac{57}{86}\right)\) \(e\left(\frac{37}{43}\right)\) \(e\left(\frac{33}{86}\right)\) \(e\left(\frac{11}{86}\right)\) \(e\left(\frac{13}{43}\right)\) \(e\left(\frac{16}{43}\right)\) \(e\left(\frac{27}{86}\right)\)
\(\chi_{173}(22,\cdot)\) 173.d 43 Yes \(1\) \(1\) \(e\left(\frac{6}{43}\right)\) \(e\left(\frac{33}{43}\right)\) \(e\left(\frac{12}{43}\right)\) \(e\left(\frac{19}{43}\right)\) \(e\left(\frac{39}{43}\right)\) \(e\left(\frac{11}{43}\right)\) \(e\left(\frac{18}{43}\right)\) \(e\left(\frac{23}{43}\right)\) \(e\left(\frac{25}{43}\right)\) \(e\left(\frac{9}{43}\right)\)
\(\chi_{173}(23,\cdot)\) 173.d 43 Yes \(1\) \(1\) \(e\left(\frac{5}{43}\right)\) \(e\left(\frac{6}{43}\right)\) \(e\left(\frac{10}{43}\right)\) \(e\left(\frac{23}{43}\right)\) \(e\left(\frac{11}{43}\right)\) \(e\left(\frac{2}{43}\right)\) \(e\left(\frac{15}{43}\right)\) \(e\left(\frac{12}{43}\right)\) \(e\left(\frac{28}{43}\right)\) \(e\left(\frac{29}{43}\right)\)
\(\chi_{173}(24,\cdot)\) 173.e 86 Yes \(1\) \(1\) \(e\left(\frac{15}{86}\right)\) \(e\left(\frac{61}{86}\right)\) \(e\left(\frac{15}{43}\right)\) \(e\left(\frac{69}{86}\right)\) \(e\left(\frac{38}{43}\right)\) \(e\left(\frac{49}{86}\right)\) \(e\left(\frac{45}{86}\right)\) \(e\left(\frac{18}{43}\right)\) \(e\left(\frac{42}{43}\right)\) \(e\left(\frac{1}{86}\right)\)
\(\chi_{173}(25,\cdot)\) 173.e 86 Yes \(1\) \(1\) \(e\left(\frac{39}{86}\right)\) \(e\left(\frac{21}{86}\right)\) \(e\left(\frac{39}{43}\right)\) \(e\left(\frac{59}{86}\right)\) \(e\left(\frac{30}{43}\right)\) \(e\left(\frac{7}{86}\right)\) \(e\left(\frac{31}{86}\right)\) \(e\left(\frac{21}{43}\right)\) \(e\left(\frac{6}{43}\right)\) \(e\left(\frac{37}{86}\right)\)
\(\chi_{173}(26,\cdot)\) 173.f 172 Yes \(-1\) \(1\) \(e\left(\frac{131}{172}\right)\) \(e\left(\frac{97}{172}\right)\) \(e\left(\frac{45}{86}\right)\) \(e\left(\frac{121}{172}\right)\) \(e\left(\frac{14}{43}\right)\) \(e\left(\frac{61}{172}\right)\) \(e\left(\frac{49}{172}\right)\) \(e\left(\frac{11}{86}\right)\) \(e\left(\frac{20}{43}\right)\) \(e\left(\frac{89}{172}\right)\)
\(\chi_{173}(27,\cdot)\) 173.f 172 Yes \(-1\) \(1\) \(e\left(\frac{81}{172}\right)\) \(e\left(\frac{123}{172}\right)\) \(e\left(\frac{81}{86}\right)\) \(e\left(\frac{63}{172}\right)\) \(e\left(\frac{8}{43}\right)\) \(e\left(\frac{127}{172}\right)\) \(e\left(\frac{71}{172}\right)\) \(e\left(\frac{37}{86}\right)\) \(e\left(\frac{36}{43}\right)\) \(e\left(\frac{143}{172}\right)\)
\(\chi_{173}(28,\cdot)\) 173.f 172 Yes \(-1\) \(1\) \(e\left(\frac{97}{172}\right)\) \(e\left(\frac{39}{172}\right)\) \(e\left(\frac{11}{86}\right)\) \(e\left(\frac{171}{172}\right)\) \(e\left(\frac{34}{43}\right)\) \(e\left(\frac{99}{172}\right)\) \(e\left(\frac{119}{172}\right)\) \(e\left(\frac{39}{86}\right)\) \(e\left(\frac{24}{43}\right)\) \(e\left(\frac{167}{172}\right)\)
\(\chi_{173}(29,\cdot)\) 173.d 43 Yes \(1\) \(1\) \(e\left(\frac{36}{43}\right)\) \(e\left(\frac{26}{43}\right)\) \(e\left(\frac{29}{43}\right)\) \(e\left(\frac{28}{43}\right)\) \(e\left(\frac{19}{43}\right)\) \(e\left(\frac{23}{43}\right)\) \(e\left(\frac{22}{43}\right)\) \(e\left(\frac{9}{43}\right)\) \(e\left(\frac{21}{43}\right)\) \(e\left(\frac{11}{43}\right)\)
\(\chi_{173}(30,\cdot)\) 173.f 172 Yes \(-1\) \(1\) \(e\left(\frac{67}{172}\right)\) \(e\left(\frac{89}{172}\right)\) \(e\left(\frac{67}{86}\right)\) \(e\left(\frac{33}{172}\right)\) \(e\left(\frac{39}{43}\right)\) \(e\left(\frac{1}{172}\right)\) \(e\left(\frac{29}{172}\right)\) \(e\left(\frac{3}{86}\right)\) \(e\left(\frac{25}{43}\right)\) \(e\left(\frac{165}{172}\right)\)
\(\chi_{173}(31,\cdot)\) 173.e 86 Yes \(1\) \(1\) \(e\left(\frac{51}{86}\right)\) \(e\left(\frac{1}{86}\right)\) \(e\left(\frac{8}{43}\right)\) \(e\left(\frac{11}{86}\right)\) \(e\left(\frac{26}{43}\right)\) \(e\left(\frac{29}{86}\right)\) \(e\left(\frac{67}{86}\right)\) \(e\left(\frac{1}{43}\right)\) \(e\left(\frac{31}{43}\right)\) \(e\left(\frac{55}{86}\right)\)
\(\chi_{173}(32,\cdot)\) 173.f 172 Yes \(-1\) \(1\) \(e\left(\frac{5}{172}\right)\) \(e\left(\frac{135}{172}\right)\) \(e\left(\frac{5}{86}\right)\) \(e\left(\frac{23}{172}\right)\) \(e\left(\frac{35}{43}\right)\) \(e\left(\frac{131}{172}\right)\) \(e\left(\frac{15}{172}\right)\) \(e\left(\frac{49}{86}\right)\) \(e\left(\frac{7}{43}\right)\) \(e\left(\frac{115}{172}\right)\)