Properties

Modulus $668$
Structure \(C_{2}\times C_{166}\)
Order $332$

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Show commands: PariGP / SageMath

sage: H = DirichletGroup(668)
 
pari: g = idealstar(,668,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 332
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{2}\times C_{166}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{668}(335,\cdot)$, $\chi_{668}(5,\cdot)$

First 32 of 332 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 \(-1\) \(1\) \(3\) \(5\) \(7\) \(9\) \(11\) \(13\) \(15\) \(17\) \(19\) \(21\)
\(\chi_{668}(1,\cdot)\) 668.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{668}(3,\cdot)\) 668.g 166 yes \(-1\) \(1\) \(e\left(\frac{121}{166}\right)\) \(e\left(\frac{47}{83}\right)\) \(e\left(\frac{53}{166}\right)\) \(e\left(\frac{38}{83}\right)\) \(e\left(\frac{59}{166}\right)\) \(e\left(\frac{27}{83}\right)\) \(e\left(\frac{49}{166}\right)\) \(e\left(\frac{1}{83}\right)\) \(e\left(\frac{57}{166}\right)\) \(e\left(\frac{4}{83}\right)\)
\(\chi_{668}(5,\cdot)\) 668.f 166 no \(-1\) \(1\) \(e\left(\frac{47}{83}\right)\) \(e\left(\frac{1}{166}\right)\) \(e\left(\frac{59}{83}\right)\) \(e\left(\frac{11}{83}\right)\) \(e\left(\frac{14}{83}\right)\) \(e\left(\frac{103}{166}\right)\) \(e\left(\frac{95}{166}\right)\) \(e\left(\frac{53}{166}\right)\) \(e\left(\frac{29}{83}\right)\) \(e\left(\frac{23}{83}\right)\)
\(\chi_{668}(7,\cdot)\) 668.g 166 yes \(-1\) \(1\) \(e\left(\frac{53}{166}\right)\) \(e\left(\frac{59}{83}\right)\) \(e\left(\frac{63}{166}\right)\) \(e\left(\frac{53}{83}\right)\) \(e\left(\frac{67}{166}\right)\) \(e\left(\frac{18}{83}\right)\) \(e\left(\frac{5}{166}\right)\) \(e\left(\frac{56}{83}\right)\) \(e\left(\frac{121}{166}\right)\) \(e\left(\frac{58}{83}\right)\)
\(\chi_{668}(9,\cdot)\) 668.e 83 no \(1\) \(1\) \(e\left(\frac{38}{83}\right)\) \(e\left(\frac{11}{83}\right)\) \(e\left(\frac{53}{83}\right)\) \(e\left(\frac{76}{83}\right)\) \(e\left(\frac{59}{83}\right)\) \(e\left(\frac{54}{83}\right)\) \(e\left(\frac{49}{83}\right)\) \(e\left(\frac{2}{83}\right)\) \(e\left(\frac{57}{83}\right)\) \(e\left(\frac{8}{83}\right)\)
\(\chi_{668}(11,\cdot)\) 668.g 166 yes \(-1\) \(1\) \(e\left(\frac{59}{166}\right)\) \(e\left(\frac{14}{83}\right)\) \(e\left(\frac{67}{166}\right)\) \(e\left(\frac{59}{83}\right)\) \(e\left(\frac{37}{166}\right)\) \(e\left(\frac{31}{83}\right)\) \(e\left(\frac{87}{166}\right)\) \(e\left(\frac{78}{83}\right)\) \(e\left(\frac{47}{166}\right)\) \(e\left(\frac{63}{83}\right)\)
\(\chi_{668}(13,\cdot)\) 668.f 166 no \(-1\) \(1\) \(e\left(\frac{27}{83}\right)\) \(e\left(\frac{103}{166}\right)\) \(e\left(\frac{18}{83}\right)\) \(e\left(\frac{54}{83}\right)\) \(e\left(\frac{31}{83}\right)\) \(e\left(\frac{151}{166}\right)\) \(e\left(\frac{157}{166}\right)\) \(e\left(\frac{147}{166}\right)\) \(e\left(\frac{82}{83}\right)\) \(e\left(\frac{45}{83}\right)\)
\(\chi_{668}(15,\cdot)\) 668.h 166 yes \(1\) \(1\) \(e\left(\frac{49}{166}\right)\) \(e\left(\frac{95}{166}\right)\) \(e\left(\frac{5}{166}\right)\) \(e\left(\frac{49}{83}\right)\) \(e\left(\frac{87}{166}\right)\) \(e\left(\frac{157}{166}\right)\) \(e\left(\frac{72}{83}\right)\) \(e\left(\frac{55}{166}\right)\) \(e\left(\frac{115}{166}\right)\) \(e\left(\frac{27}{83}\right)\)
\(\chi_{668}(17,\cdot)\) 668.f 166 no \(-1\) \(1\) \(e\left(\frac{1}{83}\right)\) \(e\left(\frac{53}{166}\right)\) \(e\left(\frac{56}{83}\right)\) \(e\left(\frac{2}{83}\right)\) \(e\left(\frac{78}{83}\right)\) \(e\left(\frac{147}{166}\right)\) \(e\left(\frac{55}{166}\right)\) \(e\left(\frac{153}{166}\right)\) \(e\left(\frac{43}{83}\right)\) \(e\left(\frac{57}{83}\right)\)
\(\chi_{668}(19,\cdot)\) 668.g 166 yes \(-1\) \(1\) \(e\left(\frac{57}{166}\right)\) \(e\left(\frac{29}{83}\right)\) \(e\left(\frac{121}{166}\right)\) \(e\left(\frac{57}{83}\right)\) \(e\left(\frac{47}{166}\right)\) \(e\left(\frac{82}{83}\right)\) \(e\left(\frac{115}{166}\right)\) \(e\left(\frac{43}{83}\right)\) \(e\left(\frac{127}{166}\right)\) \(e\left(\frac{6}{83}\right)\)
\(\chi_{668}(21,\cdot)\) 668.e 83 no \(1\) \(1\) \(e\left(\frac{4}{83}\right)\) \(e\left(\frac{23}{83}\right)\) \(e\left(\frac{58}{83}\right)\) \(e\left(\frac{8}{83}\right)\) \(e\left(\frac{63}{83}\right)\) \(e\left(\frac{45}{83}\right)\) \(e\left(\frac{27}{83}\right)\) \(e\left(\frac{57}{83}\right)\) \(e\left(\frac{6}{83}\right)\) \(e\left(\frac{62}{83}\right)\)
\(\chi_{668}(23,\cdot)\) 668.h 166 yes \(1\) \(1\) \(e\left(\frac{93}{166}\right)\) \(e\left(\frac{99}{166}\right)\) \(e\left(\frac{145}{166}\right)\) \(e\left(\frac{10}{83}\right)\) \(e\left(\frac{33}{166}\right)\) \(e\left(\frac{71}{166}\right)\) \(e\left(\frac{13}{83}\right)\) \(e\left(\frac{101}{166}\right)\) \(e\left(\frac{15}{166}\right)\) \(e\left(\frac{36}{83}\right)\)
\(\chi_{668}(25,\cdot)\) 668.e 83 no \(1\) \(1\) \(e\left(\frac{11}{83}\right)\) \(e\left(\frac{1}{83}\right)\) \(e\left(\frac{35}{83}\right)\) \(e\left(\frac{22}{83}\right)\) \(e\left(\frac{28}{83}\right)\) \(e\left(\frac{20}{83}\right)\) \(e\left(\frac{12}{83}\right)\) \(e\left(\frac{53}{83}\right)\) \(e\left(\frac{58}{83}\right)\) \(e\left(\frac{46}{83}\right)\)
\(\chi_{668}(27,\cdot)\) 668.g 166 yes \(-1\) \(1\) \(e\left(\frac{31}{166}\right)\) \(e\left(\frac{58}{83}\right)\) \(e\left(\frac{159}{166}\right)\) \(e\left(\frac{31}{83}\right)\) \(e\left(\frac{11}{166}\right)\) \(e\left(\frac{81}{83}\right)\) \(e\left(\frac{147}{166}\right)\) \(e\left(\frac{3}{83}\right)\) \(e\left(\frac{5}{166}\right)\) \(e\left(\frac{12}{83}\right)\)
\(\chi_{668}(29,\cdot)\) 668.e 83 no \(1\) \(1\) \(e\left(\frac{78}{83}\right)\) \(e\left(\frac{75}{83}\right)\) \(e\left(\frac{52}{83}\right)\) \(e\left(\frac{73}{83}\right)\) \(e\left(\frac{25}{83}\right)\) \(e\left(\frac{6}{83}\right)\) \(e\left(\frac{70}{83}\right)\) \(e\left(\frac{74}{83}\right)\) \(e\left(\frac{34}{83}\right)\) \(e\left(\frac{47}{83}\right)\)
\(\chi_{668}(31,\cdot)\) 668.g 166 yes \(-1\) \(1\) \(e\left(\frac{77}{166}\right)\) \(e\left(\frac{45}{83}\right)\) \(e\left(\frac{79}{166}\right)\) \(e\left(\frac{77}{83}\right)\) \(e\left(\frac{113}{166}\right)\) \(e\left(\frac{70}{83}\right)\) \(e\left(\frac{1}{166}\right)\) \(e\left(\frac{61}{83}\right)\) \(e\left(\frac{157}{166}\right)\) \(e\left(\frac{78}{83}\right)\)
\(\chi_{668}(33,\cdot)\) 668.e 83 no \(1\) \(1\) \(e\left(\frac{7}{83}\right)\) \(e\left(\frac{61}{83}\right)\) \(e\left(\frac{60}{83}\right)\) \(e\left(\frac{14}{83}\right)\) \(e\left(\frac{48}{83}\right)\) \(e\left(\frac{58}{83}\right)\) \(e\left(\frac{68}{83}\right)\) \(e\left(\frac{79}{83}\right)\) \(e\left(\frac{52}{83}\right)\) \(e\left(\frac{67}{83}\right)\)
\(\chi_{668}(35,\cdot)\) 668.h 166 yes \(1\) \(1\) \(e\left(\frac{147}{166}\right)\) \(e\left(\frac{119}{166}\right)\) \(e\left(\frac{15}{166}\right)\) \(e\left(\frac{64}{83}\right)\) \(e\left(\frac{95}{166}\right)\) \(e\left(\frac{139}{166}\right)\) \(e\left(\frac{50}{83}\right)\) \(e\left(\frac{165}{166}\right)\) \(e\left(\frac{13}{166}\right)\) \(e\left(\frac{81}{83}\right)\)
\(\chi_{668}(37,\cdot)\) 668.f 166 no \(-1\) \(1\) \(e\left(\frac{45}{83}\right)\) \(e\left(\frac{61}{166}\right)\) \(e\left(\frac{30}{83}\right)\) \(e\left(\frac{7}{83}\right)\) \(e\left(\frac{24}{83}\right)\) \(e\left(\frac{141}{166}\right)\) \(e\left(\frac{151}{166}\right)\) \(e\left(\frac{79}{166}\right)\) \(e\left(\frac{26}{83}\right)\) \(e\left(\frac{75}{83}\right)\)
\(\chi_{668}(39,\cdot)\) 668.h 166 yes \(1\) \(1\) \(e\left(\frac{9}{166}\right)\) \(e\left(\frac{31}{166}\right)\) \(e\left(\frac{89}{166}\right)\) \(e\left(\frac{9}{83}\right)\) \(e\left(\frac{121}{166}\right)\) \(e\left(\frac{39}{166}\right)\) \(e\left(\frac{20}{83}\right)\) \(e\left(\frac{149}{166}\right)\) \(e\left(\frac{55}{166}\right)\) \(e\left(\frac{49}{83}\right)\)
\(\chi_{668}(41,\cdot)\) 668.f 166 no \(-1\) \(1\) \(e\left(\frac{77}{83}\right)\) \(e\left(\frac{97}{166}\right)\) \(e\left(\frac{79}{83}\right)\) \(e\left(\frac{71}{83}\right)\) \(e\left(\frac{30}{83}\right)\) \(e\left(\frac{31}{166}\right)\) \(e\left(\frac{85}{166}\right)\) \(e\left(\frac{161}{166}\right)\) \(e\left(\frac{74}{83}\right)\) \(e\left(\frac{73}{83}\right)\)
\(\chi_{668}(43,\cdot)\) 668.h 166 yes \(1\) \(1\) \(e\left(\frac{127}{166}\right)\) \(e\left(\frac{87}{166}\right)\) \(e\left(\frac{57}{166}\right)\) \(e\left(\frac{44}{83}\right)\) \(e\left(\frac{29}{166}\right)\) \(e\left(\frac{163}{166}\right)\) \(e\left(\frac{24}{83}\right)\) \(e\left(\frac{129}{166}\right)\) \(e\left(\frac{149}{166}\right)\) \(e\left(\frac{9}{83}\right)\)
\(\chi_{668}(45,\cdot)\) 668.f 166 no \(-1\) \(1\) \(e\left(\frac{2}{83}\right)\) \(e\left(\frac{23}{166}\right)\) \(e\left(\frac{29}{83}\right)\) \(e\left(\frac{4}{83}\right)\) \(e\left(\frac{73}{83}\right)\) \(e\left(\frac{45}{166}\right)\) \(e\left(\frac{27}{166}\right)\) \(e\left(\frac{57}{166}\right)\) \(e\left(\frac{3}{83}\right)\) \(e\left(\frac{31}{83}\right)\)
\(\chi_{668}(47,\cdot)\) 668.g 166 yes \(-1\) \(1\) \(e\left(\frac{41}{166}\right)\) \(e\left(\frac{66}{83}\right)\) \(e\left(\frac{55}{166}\right)\) \(e\left(\frac{41}{83}\right)\) \(e\left(\frac{127}{166}\right)\) \(e\left(\frac{75}{83}\right)\) \(e\left(\frac{7}{166}\right)\) \(e\left(\frac{12}{83}\right)\) \(e\left(\frac{103}{166}\right)\) \(e\left(\frac{48}{83}\right)\)
\(\chi_{668}(49,\cdot)\) 668.e 83 no \(1\) \(1\) \(e\left(\frac{53}{83}\right)\) \(e\left(\frac{35}{83}\right)\) \(e\left(\frac{63}{83}\right)\) \(e\left(\frac{23}{83}\right)\) \(e\left(\frac{67}{83}\right)\) \(e\left(\frac{36}{83}\right)\) \(e\left(\frac{5}{83}\right)\) \(e\left(\frac{29}{83}\right)\) \(e\left(\frac{38}{83}\right)\) \(e\left(\frac{33}{83}\right)\)
\(\chi_{668}(51,\cdot)\) 668.h 166 yes \(1\) \(1\) \(e\left(\frac{123}{166}\right)\) \(e\left(\frac{147}{166}\right)\) \(e\left(\frac{165}{166}\right)\) \(e\left(\frac{40}{83}\right)\) \(e\left(\frac{49}{166}\right)\) \(e\left(\frac{35}{166}\right)\) \(e\left(\frac{52}{83}\right)\) \(e\left(\frac{155}{166}\right)\) \(e\left(\frac{143}{166}\right)\) \(e\left(\frac{61}{83}\right)\)
\(\chi_{668}(53,\cdot)\) 668.f 166 no \(-1\) \(1\) \(e\left(\frac{60}{83}\right)\) \(e\left(\frac{109}{166}\right)\) \(e\left(\frac{40}{83}\right)\) \(e\left(\frac{37}{83}\right)\) \(e\left(\frac{32}{83}\right)\) \(e\left(\frac{105}{166}\right)\) \(e\left(\frac{63}{166}\right)\) \(e\left(\frac{133}{166}\right)\) \(e\left(\frac{7}{83}\right)\) \(e\left(\frac{17}{83}\right)\)
\(\chi_{668}(55,\cdot)\) 668.h 166 yes \(1\) \(1\) \(e\left(\frac{153}{166}\right)\) \(e\left(\frac{29}{166}\right)\) \(e\left(\frac{19}{166}\right)\) \(e\left(\frac{70}{83}\right)\) \(e\left(\frac{65}{166}\right)\) \(e\left(\frac{165}{166}\right)\) \(e\left(\frac{8}{83}\right)\) \(e\left(\frac{43}{166}\right)\) \(e\left(\frac{105}{166}\right)\) \(e\left(\frac{3}{83}\right)\)
\(\chi_{668}(57,\cdot)\) 668.e 83 no \(1\) \(1\) \(e\left(\frac{6}{83}\right)\) \(e\left(\frac{76}{83}\right)\) \(e\left(\frac{4}{83}\right)\) \(e\left(\frac{12}{83}\right)\) \(e\left(\frac{53}{83}\right)\) \(e\left(\frac{26}{83}\right)\) \(e\left(\frac{82}{83}\right)\) \(e\left(\frac{44}{83}\right)\) \(e\left(\frac{9}{83}\right)\) \(e\left(\frac{10}{83}\right)\)
\(\chi_{668}(59,\cdot)\) 668.h 166 yes \(1\) \(1\) \(e\left(\frac{81}{166}\right)\) \(e\left(\frac{113}{166}\right)\) \(e\left(\frac{137}{166}\right)\) \(e\left(\frac{81}{83}\right)\) \(e\left(\frac{93}{166}\right)\) \(e\left(\frac{19}{166}\right)\) \(e\left(\frac{14}{83}\right)\) \(e\left(\frac{13}{166}\right)\) \(e\left(\frac{163}{166}\right)\) \(e\left(\frac{26}{83}\right)\)
\(\chi_{668}(61,\cdot)\) 668.e 83 no \(1\) \(1\) \(e\left(\frac{31}{83}\right)\) \(e\left(\frac{33}{83}\right)\) \(e\left(\frac{76}{83}\right)\) \(e\left(\frac{62}{83}\right)\) \(e\left(\frac{11}{83}\right)\) \(e\left(\frac{79}{83}\right)\) \(e\left(\frac{64}{83}\right)\) \(e\left(\frac{6}{83}\right)\) \(e\left(\frac{5}{83}\right)\) \(e\left(\frac{24}{83}\right)\)
\(\chi_{668}(63,\cdot)\) 668.g 166 yes \(-1\) \(1\) \(e\left(\frac{129}{166}\right)\) \(e\left(\frac{70}{83}\right)\) \(e\left(\frac{3}{166}\right)\) \(e\left(\frac{46}{83}\right)\) \(e\left(\frac{19}{166}\right)\) \(e\left(\frac{72}{83}\right)\) \(e\left(\frac{103}{166}\right)\) \(e\left(\frac{58}{83}\right)\) \(e\left(\frac{69}{166}\right)\) \(e\left(\frac{66}{83}\right)\)
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