Properties

Modulus $531$
Structure \(C_{174}\times C_{2}\)
Order $348$

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Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(531)
 
pari: g = idealstar(,531,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 348
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{174}\times C_{2}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{531}(119,\cdot)$, $\chi_{531}(415,\cdot)$

First 32 of 348 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.

Character Orbit Order Primitive \(-1\) \(1\) \(2\) \(4\) \(5\) \(7\) \(8\) \(10\) \(11\) \(13\) \(14\) \(16\)
\(\chi_{531}(1,\cdot)\) 531.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{531}(2,\cdot)\) 531.p 174 yes \(1\) \(1\) \(e\left(\frac{16}{87}\right)\) \(e\left(\frac{32}{87}\right)\) \(e\left(\frac{163}{174}\right)\) \(e\left(\frac{85}{87}\right)\) \(e\left(\frac{16}{29}\right)\) \(e\left(\frac{7}{58}\right)\) \(e\left(\frac{52}{87}\right)\) \(e\left(\frac{19}{174}\right)\) \(e\left(\frac{14}{87}\right)\) \(e\left(\frac{64}{87}\right)\)
\(\chi_{531}(4,\cdot)\) 531.m 87 yes \(1\) \(1\) \(e\left(\frac{32}{87}\right)\) \(e\left(\frac{64}{87}\right)\) \(e\left(\frac{76}{87}\right)\) \(e\left(\frac{83}{87}\right)\) \(e\left(\frac{3}{29}\right)\) \(e\left(\frac{7}{29}\right)\) \(e\left(\frac{17}{87}\right)\) \(e\left(\frac{19}{87}\right)\) \(e\left(\frac{28}{87}\right)\) \(e\left(\frac{41}{87}\right)\)
\(\chi_{531}(5,\cdot)\) 531.n 174 yes \(-1\) \(1\) \(e\left(\frac{163}{174}\right)\) \(e\left(\frac{76}{87}\right)\) \(e\left(\frac{137}{174}\right)\) \(e\left(\frac{17}{87}\right)\) \(e\left(\frac{47}{58}\right)\) \(e\left(\frac{21}{29}\right)\) \(e\left(\frac{73}{174}\right)\) \(e\left(\frac{28}{87}\right)\) \(e\left(\frac{23}{174}\right)\) \(e\left(\frac{65}{87}\right)\)
\(\chi_{531}(7,\cdot)\) 531.m 87 yes \(1\) \(1\) \(e\left(\frac{85}{87}\right)\) \(e\left(\frac{83}{87}\right)\) \(e\left(\frac{17}{87}\right)\) \(e\left(\frac{22}{87}\right)\) \(e\left(\frac{27}{29}\right)\) \(e\left(\frac{5}{29}\right)\) \(e\left(\frac{37}{87}\right)\) \(e\left(\frac{26}{87}\right)\) \(e\left(\frac{20}{87}\right)\) \(e\left(\frac{79}{87}\right)\)
\(\chi_{531}(8,\cdot)\) 531.j 58 no \(1\) \(1\) \(e\left(\frac{16}{29}\right)\) \(e\left(\frac{3}{29}\right)\) \(e\left(\frac{47}{58}\right)\) \(e\left(\frac{27}{29}\right)\) \(e\left(\frac{19}{29}\right)\) \(e\left(\frac{21}{58}\right)\) \(e\left(\frac{23}{29}\right)\) \(e\left(\frac{19}{58}\right)\) \(e\left(\frac{14}{29}\right)\) \(e\left(\frac{6}{29}\right)\)
\(\chi_{531}(10,\cdot)\) 531.k 58 no \(-1\) \(1\) \(e\left(\frac{7}{58}\right)\) \(e\left(\frac{7}{29}\right)\) \(e\left(\frac{21}{29}\right)\) \(e\left(\frac{5}{29}\right)\) \(e\left(\frac{21}{58}\right)\) \(e\left(\frac{49}{58}\right)\) \(e\left(\frac{1}{58}\right)\) \(e\left(\frac{25}{58}\right)\) \(e\left(\frac{17}{58}\right)\) \(e\left(\frac{14}{29}\right)\)
\(\chi_{531}(11,\cdot)\) 531.p 174 yes \(1\) \(1\) \(e\left(\frac{52}{87}\right)\) \(e\left(\frac{17}{87}\right)\) \(e\left(\frac{73}{174}\right)\) \(e\left(\frac{37}{87}\right)\) \(e\left(\frac{23}{29}\right)\) \(e\left(\frac{1}{58}\right)\) \(e\left(\frac{82}{87}\right)\) \(e\left(\frac{127}{174}\right)\) \(e\left(\frac{2}{87}\right)\) \(e\left(\frac{34}{87}\right)\)
\(\chi_{531}(13,\cdot)\) 531.o 174 yes \(-1\) \(1\) \(e\left(\frac{19}{174}\right)\) \(e\left(\frac{19}{87}\right)\) \(e\left(\frac{28}{87}\right)\) \(e\left(\frac{26}{87}\right)\) \(e\left(\frac{19}{58}\right)\) \(e\left(\frac{25}{58}\right)\) \(e\left(\frac{127}{174}\right)\) \(e\left(\frac{101}{174}\right)\) \(e\left(\frac{71}{174}\right)\) \(e\left(\frac{38}{87}\right)\)
\(\chi_{531}(14,\cdot)\) 531.p 174 yes \(1\) \(1\) \(e\left(\frac{14}{87}\right)\) \(e\left(\frac{28}{87}\right)\) \(e\left(\frac{23}{174}\right)\) \(e\left(\frac{20}{87}\right)\) \(e\left(\frac{14}{29}\right)\) \(e\left(\frac{17}{58}\right)\) \(e\left(\frac{2}{87}\right)\) \(e\left(\frac{71}{174}\right)\) \(e\left(\frac{34}{87}\right)\) \(e\left(\frac{56}{87}\right)\)
\(\chi_{531}(16,\cdot)\) 531.m 87 yes \(1\) \(1\) \(e\left(\frac{64}{87}\right)\) \(e\left(\frac{41}{87}\right)\) \(e\left(\frac{65}{87}\right)\) \(e\left(\frac{79}{87}\right)\) \(e\left(\frac{6}{29}\right)\) \(e\left(\frac{14}{29}\right)\) \(e\left(\frac{34}{87}\right)\) \(e\left(\frac{38}{87}\right)\) \(e\left(\frac{56}{87}\right)\) \(e\left(\frac{82}{87}\right)\)
\(\chi_{531}(17,\cdot)\) 531.l 58 no \(-1\) \(1\) \(e\left(\frac{11}{58}\right)\) \(e\left(\frac{11}{29}\right)\) \(e\left(\frac{37}{58}\right)\) \(e\left(\frac{12}{29}\right)\) \(e\left(\frac{33}{58}\right)\) \(e\left(\frac{24}{29}\right)\) \(e\left(\frac{43}{58}\right)\) \(e\left(\frac{1}{29}\right)\) \(e\left(\frac{35}{58}\right)\) \(e\left(\frac{22}{29}\right)\)
\(\chi_{531}(19,\cdot)\) 531.i 29 no \(1\) \(1\) \(e\left(\frac{19}{29}\right)\) \(e\left(\frac{9}{29}\right)\) \(e\left(\frac{27}{29}\right)\) \(e\left(\frac{23}{29}\right)\) \(e\left(\frac{28}{29}\right)\) \(e\left(\frac{17}{29}\right)\) \(e\left(\frac{11}{29}\right)\) \(e\left(\frac{14}{29}\right)\) \(e\left(\frac{13}{29}\right)\) \(e\left(\frac{18}{29}\right)\)
\(\chi_{531}(20,\cdot)\) 531.n 174 yes \(-1\) \(1\) \(e\left(\frac{53}{174}\right)\) \(e\left(\frac{53}{87}\right)\) \(e\left(\frac{115}{174}\right)\) \(e\left(\frac{13}{87}\right)\) \(e\left(\frac{53}{58}\right)\) \(e\left(\frac{28}{29}\right)\) \(e\left(\frac{107}{174}\right)\) \(e\left(\frac{47}{87}\right)\) \(e\left(\frac{79}{174}\right)\) \(e\left(\frac{19}{87}\right)\)
\(\chi_{531}(22,\cdot)\) 531.m 87 yes \(1\) \(1\) \(e\left(\frac{68}{87}\right)\) \(e\left(\frac{49}{87}\right)\) \(e\left(\frac{31}{87}\right)\) \(e\left(\frac{35}{87}\right)\) \(e\left(\frac{10}{29}\right)\) \(e\left(\frac{4}{29}\right)\) \(e\left(\frac{47}{87}\right)\) \(e\left(\frac{73}{87}\right)\) \(e\left(\frac{16}{87}\right)\) \(e\left(\frac{11}{87}\right)\)
\(\chi_{531}(23,\cdot)\) 531.p 174 yes \(1\) \(1\) \(e\left(\frac{8}{87}\right)\) \(e\left(\frac{16}{87}\right)\) \(e\left(\frac{125}{174}\right)\) \(e\left(\frac{86}{87}\right)\) \(e\left(\frac{8}{29}\right)\) \(e\left(\frac{47}{58}\right)\) \(e\left(\frac{26}{87}\right)\) \(e\left(\frac{53}{174}\right)\) \(e\left(\frac{7}{87}\right)\) \(e\left(\frac{32}{87}\right)\)
\(\chi_{531}(25,\cdot)\) 531.m 87 yes \(1\) \(1\) \(e\left(\frac{76}{87}\right)\) \(e\left(\frac{65}{87}\right)\) \(e\left(\frac{50}{87}\right)\) \(e\left(\frac{34}{87}\right)\) \(e\left(\frac{18}{29}\right)\) \(e\left(\frac{13}{29}\right)\) \(e\left(\frac{73}{87}\right)\) \(e\left(\frac{56}{87}\right)\) \(e\left(\frac{23}{87}\right)\) \(e\left(\frac{43}{87}\right)\)
\(\chi_{531}(26,\cdot)\) 531.l 58 no \(-1\) \(1\) \(e\left(\frac{17}{58}\right)\) \(e\left(\frac{17}{29}\right)\) \(e\left(\frac{15}{58}\right)\) \(e\left(\frac{8}{29}\right)\) \(e\left(\frac{51}{58}\right)\) \(e\left(\frac{16}{29}\right)\) \(e\left(\frac{19}{58}\right)\) \(e\left(\frac{20}{29}\right)\) \(e\left(\frac{33}{58}\right)\) \(e\left(\frac{5}{29}\right)\)
\(\chi_{531}(28,\cdot)\) 531.i 29 no \(1\) \(1\) \(e\left(\frac{10}{29}\right)\) \(e\left(\frac{20}{29}\right)\) \(e\left(\frac{2}{29}\right)\) \(e\left(\frac{6}{29}\right)\) \(e\left(\frac{1}{29}\right)\) \(e\left(\frac{12}{29}\right)\) \(e\left(\frac{18}{29}\right)\) \(e\left(\frac{15}{29}\right)\) \(e\left(\frac{16}{29}\right)\) \(e\left(\frac{11}{29}\right)\)
\(\chi_{531}(29,\cdot)\) 531.n 174 yes \(-1\) \(1\) \(e\left(\frac{113}{174}\right)\) \(e\left(\frac{26}{87}\right)\) \(e\left(\frac{127}{174}\right)\) \(e\left(\frac{31}{87}\right)\) \(e\left(\frac{55}{58}\right)\) \(e\left(\frac{11}{29}\right)\) \(e\left(\frac{41}{174}\right)\) \(e\left(\frac{5}{87}\right)\) \(e\left(\frac{1}{174}\right)\) \(e\left(\frac{52}{87}\right)\)
\(\chi_{531}(31,\cdot)\) 531.o 174 yes \(-1\) \(1\) \(e\left(\frac{31}{174}\right)\) \(e\left(\frac{31}{87}\right)\) \(e\left(\frac{64}{87}\right)\) \(e\left(\frac{47}{87}\right)\) \(e\left(\frac{31}{58}\right)\) \(e\left(\frac{53}{58}\right)\) \(e\left(\frac{79}{174}\right)\) \(e\left(\frac{119}{174}\right)\) \(e\left(\frac{125}{174}\right)\) \(e\left(\frac{62}{87}\right)\)
\(\chi_{531}(32,\cdot)\) 531.p 174 yes \(1\) \(1\) \(e\left(\frac{80}{87}\right)\) \(e\left(\frac{73}{87}\right)\) \(e\left(\frac{119}{174}\right)\) \(e\left(\frac{77}{87}\right)\) \(e\left(\frac{22}{29}\right)\) \(e\left(\frac{35}{58}\right)\) \(e\left(\frac{86}{87}\right)\) \(e\left(\frac{95}{174}\right)\) \(e\left(\frac{70}{87}\right)\) \(e\left(\frac{59}{87}\right)\)
\(\chi_{531}(34,\cdot)\) 531.o 174 yes \(-1\) \(1\) \(e\left(\frac{65}{174}\right)\) \(e\left(\frac{65}{87}\right)\) \(e\left(\frac{50}{87}\right)\) \(e\left(\frac{34}{87}\right)\) \(e\left(\frac{7}{58}\right)\) \(e\left(\frac{55}{58}\right)\) \(e\left(\frac{59}{174}\right)\) \(e\left(\frac{25}{174}\right)\) \(e\left(\frac{133}{174}\right)\) \(e\left(\frac{43}{87}\right)\)
\(\chi_{531}(35,\cdot)\) 531.l 58 no \(-1\) \(1\) \(e\left(\frac{53}{58}\right)\) \(e\left(\frac{24}{29}\right)\) \(e\left(\frac{57}{58}\right)\) \(e\left(\frac{13}{29}\right)\) \(e\left(\frac{43}{58}\right)\) \(e\left(\frac{26}{29}\right)\) \(e\left(\frac{49}{58}\right)\) \(e\left(\frac{18}{29}\right)\) \(e\left(\frac{21}{58}\right)\) \(e\left(\frac{19}{29}\right)\)
\(\chi_{531}(37,\cdot)\) 531.k 58 no \(-1\) \(1\) \(e\left(\frac{55}{58}\right)\) \(e\left(\frac{26}{29}\right)\) \(e\left(\frac{20}{29}\right)\) \(e\left(\frac{2}{29}\right)\) \(e\left(\frac{49}{58}\right)\) \(e\left(\frac{37}{58}\right)\) \(e\left(\frac{41}{58}\right)\) \(e\left(\frac{39}{58}\right)\) \(e\left(\frac{1}{58}\right)\) \(e\left(\frac{23}{29}\right)\)
\(\chi_{531}(38,\cdot)\) 531.p 174 yes \(1\) \(1\) \(e\left(\frac{73}{87}\right)\) \(e\left(\frac{59}{87}\right)\) \(e\left(\frac{151}{174}\right)\) \(e\left(\frac{67}{87}\right)\) \(e\left(\frac{15}{29}\right)\) \(e\left(\frac{41}{58}\right)\) \(e\left(\frac{85}{87}\right)\) \(e\left(\frac{103}{174}\right)\) \(e\left(\frac{53}{87}\right)\) \(e\left(\frac{31}{87}\right)\)
\(\chi_{531}(40,\cdot)\) 531.o 174 yes \(-1\) \(1\) \(e\left(\frac{85}{174}\right)\) \(e\left(\frac{85}{87}\right)\) \(e\left(\frac{52}{87}\right)\) \(e\left(\frac{11}{87}\right)\) \(e\left(\frac{27}{58}\right)\) \(e\left(\frac{5}{58}\right)\) \(e\left(\frac{37}{174}\right)\) \(e\left(\frac{113}{174}\right)\) \(e\left(\frac{107}{174}\right)\) \(e\left(\frac{83}{87}\right)\)
\(\chi_{531}(41,\cdot)\) 531.n 174 yes \(-1\) \(1\) \(e\left(\frac{13}{174}\right)\) \(e\left(\frac{13}{87}\right)\) \(e\left(\frac{107}{174}\right)\) \(e\left(\frac{59}{87}\right)\) \(e\left(\frac{13}{58}\right)\) \(e\left(\frac{20}{29}\right)\) \(e\left(\frac{151}{174}\right)\) \(e\left(\frac{46}{87}\right)\) \(e\left(\frac{131}{174}\right)\) \(e\left(\frac{26}{87}\right)\)
\(\chi_{531}(43,\cdot)\) 531.o 174 yes \(-1\) \(1\) \(e\left(\frac{41}{174}\right)\) \(e\left(\frac{41}{87}\right)\) \(e\left(\frac{65}{87}\right)\) \(e\left(\frac{79}{87}\right)\) \(e\left(\frac{41}{58}\right)\) \(e\left(\frac{57}{58}\right)\) \(e\left(\frac{155}{174}\right)\) \(e\left(\frac{163}{174}\right)\) \(e\left(\frac{25}{174}\right)\) \(e\left(\frac{82}{87}\right)\)
\(\chi_{531}(44,\cdot)\) 531.j 58 no \(1\) \(1\) \(e\left(\frac{28}{29}\right)\) \(e\left(\frac{27}{29}\right)\) \(e\left(\frac{17}{58}\right)\) \(e\left(\frac{11}{29}\right)\) \(e\left(\frac{26}{29}\right)\) \(e\left(\frac{15}{58}\right)\) \(e\left(\frac{4}{29}\right)\) \(e\left(\frac{55}{58}\right)\) \(e\left(\frac{10}{29}\right)\) \(e\left(\frac{25}{29}\right)\)
\(\chi_{531}(46,\cdot)\) 531.i 29 no \(1\) \(1\) \(e\left(\frac{8}{29}\right)\) \(e\left(\frac{16}{29}\right)\) \(e\left(\frac{19}{29}\right)\) \(e\left(\frac{28}{29}\right)\) \(e\left(\frac{24}{29}\right)\) \(e\left(\frac{27}{29}\right)\) \(e\left(\frac{26}{29}\right)\) \(e\left(\frac{12}{29}\right)\) \(e\left(\frac{7}{29}\right)\) \(e\left(\frac{3}{29}\right)\)
\(\chi_{531}(47,\cdot)\) 531.p 174 yes \(1\) \(1\) \(e\left(\frac{49}{87}\right)\) \(e\left(\frac{11}{87}\right)\) \(e\left(\frac{37}{174}\right)\) \(e\left(\frac{70}{87}\right)\) \(e\left(\frac{20}{29}\right)\) \(e\left(\frac{45}{58}\right)\) \(e\left(\frac{7}{87}\right)\) \(e\left(\frac{31}{174}\right)\) \(e\left(\frac{32}{87}\right)\) \(e\left(\frac{22}{87}\right)\)