Properties

Modulus 6009
Structure \(C_{2002}\times C_{2}\)
Order 4004

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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(6009)
pari: g = idealstar(,6009,2)

Character group

sage: G.order()
pari: g.no
Order = 4004
sage: H.invariants()
pari: g.cyc
Structure = \(C_{2002}\times C_{2}\)
sage: H.gens()
pari: g.gen
Generators = $\chi_{6009}(2008,\cdot)$, $\chi_{6009}(4007,\cdot)$

First 32 of 4004 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 4 5 7 8 10 11 13 14 16
\(\chi_{6009}(1,\cdot)\) 6009.a 1 No \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{6009}(2,\cdot)\) 6009.bb 286 Yes \(1\) \(1\) \(e\left(\frac{56}{143}\right)\) \(e\left(\frac{112}{143}\right)\) \(e\left(\frac{24}{143}\right)\) \(e\left(\frac{41}{286}\right)\) \(e\left(\frac{25}{143}\right)\) \(e\left(\frac{80}{143}\right)\) \(e\left(\frac{32}{143}\right)\) \(e\left(\frac{106}{143}\right)\) \(e\left(\frac{153}{286}\right)\) \(e\left(\frac{81}{143}\right)\)
\(\chi_{6009}(4,\cdot)\) 6009.s 143 No \(1\) \(1\) \(e\left(\frac{112}{143}\right)\) \(e\left(\frac{81}{143}\right)\) \(e\left(\frac{48}{143}\right)\) \(e\left(\frac{41}{143}\right)\) \(e\left(\frac{50}{143}\right)\) \(e\left(\frac{17}{143}\right)\) \(e\left(\frac{64}{143}\right)\) \(e\left(\frac{69}{143}\right)\) \(e\left(\frac{10}{143}\right)\) \(e\left(\frac{19}{143}\right)\)
\(\chi_{6009}(5,\cdot)\) 6009.bf 2002 Yes \(1\) \(1\) \(e\left(\frac{24}{143}\right)\) \(e\left(\frac{48}{143}\right)\) \(e\left(\frac{501}{1001}\right)\) \(e\left(\frac{123}{2002}\right)\) \(e\left(\frac{72}{143}\right)\) \(e\left(\frac{669}{1001}\right)\) \(e\left(\frac{75}{143}\right)\) \(e\left(\frac{747}{1001}\right)\) \(e\left(\frac{459}{2002}\right)\) \(e\left(\frac{96}{143}\right)\)
\(\chi_{6009}(7,\cdot)\) 6009.be 2002 No \(-1\) \(1\) \(e\left(\frac{41}{286}\right)\) \(e\left(\frac{41}{143}\right)\) \(e\left(\frac{123}{2002}\right)\) \(e\left(\frac{1115}{2002}\right)\) \(e\left(\frac{123}{286}\right)\) \(e\left(\frac{205}{1001}\right)\) \(e\left(\frac{3}{286}\right)\) \(e\left(\frac{790}{1001}\right)\) \(e\left(\frac{701}{1001}\right)\) \(e\left(\frac{82}{143}\right)\)
\(\chi_{6009}(8,\cdot)\) 6009.bb 286 Yes \(1\) \(1\) \(e\left(\frac{25}{143}\right)\) \(e\left(\frac{50}{143}\right)\) \(e\left(\frac{72}{143}\right)\) \(e\left(\frac{123}{286}\right)\) \(e\left(\frac{75}{143}\right)\) \(e\left(\frac{97}{143}\right)\) \(e\left(\frac{96}{143}\right)\) \(e\left(\frac{32}{143}\right)\) \(e\left(\frac{173}{286}\right)\) \(e\left(\frac{100}{143}\right)\)
\(\chi_{6009}(10,\cdot)\) 6009.bc 1001 No \(1\) \(1\) \(e\left(\frac{80}{143}\right)\) \(e\left(\frac{17}{143}\right)\) \(e\left(\frac{669}{1001}\right)\) \(e\left(\frac{205}{1001}\right)\) \(e\left(\frac{97}{143}\right)\) \(e\left(\frac{228}{1001}\right)\) \(e\left(\frac{107}{143}\right)\) \(e\left(\frac{488}{1001}\right)\) \(e\left(\frac{765}{1001}\right)\) \(e\left(\frac{34}{143}\right)\)
\(\chi_{6009}(11,\cdot)\) 6009.bb 286 Yes \(1\) \(1\) \(e\left(\frac{32}{143}\right)\) \(e\left(\frac{64}{143}\right)\) \(e\left(\frac{75}{143}\right)\) \(e\left(\frac{3}{286}\right)\) \(e\left(\frac{96}{143}\right)\) \(e\left(\frac{107}{143}\right)\) \(e\left(\frac{100}{143}\right)\) \(e\left(\frac{81}{143}\right)\) \(e\left(\frac{67}{286}\right)\) \(e\left(\frac{128}{143}\right)\)
\(\chi_{6009}(13,\cdot)\) 6009.bc 1001 No \(1\) \(1\) \(e\left(\frac{106}{143}\right)\) \(e\left(\frac{69}{143}\right)\) \(e\left(\frac{747}{1001}\right)\) \(e\left(\frac{790}{1001}\right)\) \(e\left(\frac{32}{143}\right)\) \(e\left(\frac{488}{1001}\right)\) \(e\left(\frac{81}{143}\right)\) \(e\left(\frac{904}{1001}\right)\) \(e\left(\frac{531}{1001}\right)\) \(e\left(\frac{138}{143}\right)\)
\(\chi_{6009}(14,\cdot)\) 6009.bd 2002 Yes \(-1\) \(1\) \(e\left(\frac{153}{286}\right)\) \(e\left(\frac{10}{143}\right)\) \(e\left(\frac{459}{2002}\right)\) \(e\left(\frac{701}{1001}\right)\) \(e\left(\frac{173}{286}\right)\) \(e\left(\frac{765}{1001}\right)\) \(e\left(\frac{67}{286}\right)\) \(e\left(\frac{531}{1001}\right)\) \(e\left(\frac{471}{2002}\right)\) \(e\left(\frac{20}{143}\right)\)
\(\chi_{6009}(16,\cdot)\) 6009.s 143 No \(1\) \(1\) \(e\left(\frac{81}{143}\right)\) \(e\left(\frac{19}{143}\right)\) \(e\left(\frac{96}{143}\right)\) \(e\left(\frac{82}{143}\right)\) \(e\left(\frac{100}{143}\right)\) \(e\left(\frac{34}{143}\right)\) \(e\left(\frac{128}{143}\right)\) \(e\left(\frac{138}{143}\right)\) \(e\left(\frac{20}{143}\right)\) \(e\left(\frac{38}{143}\right)\)
\(\chi_{6009}(17,\cdot)\) 6009.w 182 Yes \(1\) \(1\) \(e\left(\frac{2}{13}\right)\) \(e\left(\frac{4}{13}\right)\) \(e\left(\frac{58}{91}\right)\) \(e\left(\frac{163}{182}\right)\) \(e\left(\frac{6}{13}\right)\) \(e\left(\frac{72}{91}\right)\) \(e\left(\frac{3}{13}\right)\) \(e\left(\frac{20}{91}\right)\) \(e\left(\frac{9}{182}\right)\) \(e\left(\frac{8}{13}\right)\)
\(\chi_{6009}(19,\cdot)\) 6009.bc 1001 No \(1\) \(1\) \(e\left(\frac{42}{143}\right)\) \(e\left(\frac{84}{143}\right)\) \(e\left(\frac{269}{1001}\right)\) \(e\left(\frac{54}{1001}\right)\) \(e\left(\frac{126}{143}\right)\) \(e\left(\frac{563}{1001}\right)\) \(e\left(\frac{24}{143}\right)\) \(e\left(\frac{485}{1001}\right)\) \(e\left(\frac{348}{1001}\right)\) \(e\left(\frac{25}{143}\right)\)
\(\chi_{6009}(20,\cdot)\) 6009.bf 2002 Yes \(1\) \(1\) \(e\left(\frac{136}{143}\right)\) \(e\left(\frac{129}{143}\right)\) \(e\left(\frac{837}{1001}\right)\) \(e\left(\frac{697}{2002}\right)\) \(e\left(\frac{122}{143}\right)\) \(e\left(\frac{788}{1001}\right)\) \(e\left(\frac{139}{143}\right)\) \(e\left(\frac{229}{1001}\right)\) \(e\left(\frac{599}{2002}\right)\) \(e\left(\frac{115}{143}\right)\)
\(\chi_{6009}(22,\cdot)\) 6009.g 13 No \(1\) \(1\) \(e\left(\frac{8}{13}\right)\) \(e\left(\frac{3}{13}\right)\) \(e\left(\frac{9}{13}\right)\) \(e\left(\frac{2}{13}\right)\) \(e\left(\frac{11}{13}\right)\) \(e\left(\frac{4}{13}\right)\) \(e\left(\frac{12}{13}\right)\) \(e\left(\frac{4}{13}\right)\) \(e\left(\frac{10}{13}\right)\) \(e\left(\frac{6}{13}\right)\)
\(\chi_{6009}(23,\cdot)\) 6009.bb 286 Yes \(1\) \(1\) \(e\left(\frac{45}{143}\right)\) \(e\left(\frac{90}{143}\right)\) \(e\left(\frac{101}{143}\right)\) \(e\left(\frac{107}{286}\right)\) \(e\left(\frac{135}{143}\right)\) \(e\left(\frac{3}{143}\right)\) \(e\left(\frac{87}{143}\right)\) \(e\left(\frac{29}{143}\right)\) \(e\left(\frac{197}{286}\right)\) \(e\left(\frac{37}{143}\right)\)
\(\chi_{6009}(25,\cdot)\) 6009.bc 1001 No \(1\) \(1\) \(e\left(\frac{48}{143}\right)\) \(e\left(\frac{96}{143}\right)\) \(e\left(\frac{1}{1001}\right)\) \(e\left(\frac{123}{1001}\right)\) \(e\left(\frac{1}{143}\right)\) \(e\left(\frac{337}{1001}\right)\) \(e\left(\frac{7}{143}\right)\) \(e\left(\frac{493}{1001}\right)\) \(e\left(\frac{459}{1001}\right)\) \(e\left(\frac{49}{143}\right)\)
\(\chi_{6009}(26,\cdot)\) 6009.bf 2002 Yes \(1\) \(1\) \(e\left(\frac{19}{143}\right)\) \(e\left(\frac{38}{143}\right)\) \(e\left(\frac{915}{1001}\right)\) \(e\left(\frac{1867}{2002}\right)\) \(e\left(\frac{57}{143}\right)\) \(e\left(\frac{47}{1001}\right)\) \(e\left(\frac{113}{143}\right)\) \(e\left(\frac{645}{1001}\right)\) \(e\left(\frac{131}{2002}\right)\) \(e\left(\frac{76}{143}\right)\)
\(\chi_{6009}(28,\cdot)\) 6009.be 2002 No \(-1\) \(1\) \(e\left(\frac{265}{286}\right)\) \(e\left(\frac{122}{143}\right)\) \(e\left(\frac{795}{2002}\right)\) \(e\left(\frac{1689}{2002}\right)\) \(e\left(\frac{223}{286}\right)\) \(e\left(\frac{324}{1001}\right)\) \(e\left(\frac{131}{286}\right)\) \(e\left(\frac{272}{1001}\right)\) \(e\left(\frac{771}{1001}\right)\) \(e\left(\frac{101}{143}\right)\)
\(\chi_{6009}(29,\cdot)\) 6009.bf 2002 Yes \(1\) \(1\) \(e\left(\frac{1}{143}\right)\) \(e\left(\frac{2}{143}\right)\) \(e\left(\frac{289}{1001}\right)\) \(e\left(\frac{23}{2002}\right)\) \(e\left(\frac{3}{143}\right)\) \(e\left(\frac{296}{1001}\right)\) \(e\left(\frac{21}{143}\right)\) \(e\left(\frac{335}{1001}\right)\) \(e\left(\frac{37}{2002}\right)\) \(e\left(\frac{4}{143}\right)\)
\(\chi_{6009}(31,\cdot)\) 6009.be 2002 No \(-1\) \(1\) \(e\left(\frac{127}{286}\right)\) \(e\left(\frac{127}{143}\right)\) \(e\left(\frac{1525}{2002}\right)\) \(e\left(\frac{1389}{2002}\right)\) \(e\left(\frac{95}{286}\right)\) \(e\left(\frac{206}{1001}\right)\) \(e\left(\frac{93}{286}\right)\) \(e\left(\frac{37}{1001}\right)\) \(e\left(\frac{138}{1001}\right)\) \(e\left(\frac{111}{143}\right)\)
\(\chi_{6009}(32,\cdot)\) 6009.bb 286 Yes \(1\) \(1\) \(e\left(\frac{137}{143}\right)\) \(e\left(\frac{131}{143}\right)\) \(e\left(\frac{120}{143}\right)\) \(e\left(\frac{205}{286}\right)\) \(e\left(\frac{125}{143}\right)\) \(e\left(\frac{114}{143}\right)\) \(e\left(\frac{17}{143}\right)\) \(e\left(\frac{101}{143}\right)\) \(e\left(\frac{193}{286}\right)\) \(e\left(\frac{119}{143}\right)\)
\(\chi_{6009}(34,\cdot)\) 6009.q 77 No \(1\) \(1\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{62}{77}\right)\) \(e\left(\frac{3}{77}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{27}{77}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{74}{77}\right)\) \(e\left(\frac{45}{77}\right)\) \(e\left(\frac{2}{11}\right)\)
\(\chi_{6009}(35,\cdot)\) 6009.bd 2002 Yes \(-1\) \(1\) \(e\left(\frac{89}{286}\right)\) \(e\left(\frac{89}{143}\right)\) \(e\left(\frac{1125}{2002}\right)\) \(e\left(\frac{619}{1001}\right)\) \(e\left(\frac{267}{286}\right)\) \(e\left(\frac{874}{1001}\right)\) \(e\left(\frac{153}{286}\right)\) \(e\left(\frac{536}{1001}\right)\) \(e\left(\frac{1861}{2002}\right)\) \(e\left(\frac{35}{143}\right)\)
\(\chi_{6009}(37,\cdot)\) 6009.be 2002 No \(-1\) \(1\) \(e\left(\frac{19}{286}\right)\) \(e\left(\frac{19}{143}\right)\) \(e\left(\frac{629}{2002}\right)\) \(e\left(\frac{1291}{2002}\right)\) \(e\left(\frac{57}{286}\right)\) \(e\left(\frac{381}{1001}\right)\) \(e\left(\frac{113}{286}\right)\) \(e\left(\frac{394}{1001}\right)\) \(e\left(\frac{712}{1001}\right)\) \(e\left(\frac{38}{143}\right)\)
\(\chi_{6009}(38,\cdot)\) 6009.bf 2002 Yes \(1\) \(1\) \(e\left(\frac{98}{143}\right)\) \(e\left(\frac{53}{143}\right)\) \(e\left(\frac{437}{1001}\right)\) \(e\left(\frac{395}{2002}\right)\) \(e\left(\frac{8}{143}\right)\) \(e\left(\frac{122}{1001}\right)\) \(e\left(\frac{56}{143}\right)\) \(e\left(\frac{226}{1001}\right)\) \(e\left(\frac{1767}{2002}\right)\) \(e\left(\frac{106}{143}\right)\)
\(\chi_{6009}(40,\cdot)\) 6009.bc 1001 No \(1\) \(1\) \(e\left(\frac{49}{143}\right)\) \(e\left(\frac{98}{143}\right)\) \(e\left(\frac{4}{1001}\right)\) \(e\left(\frac{492}{1001}\right)\) \(e\left(\frac{4}{143}\right)\) \(e\left(\frac{347}{1001}\right)\) \(e\left(\frac{28}{143}\right)\) \(e\left(\frac{971}{1001}\right)\) \(e\left(\frac{835}{1001}\right)\) \(e\left(\frac{53}{143}\right)\)
\(\chi_{6009}(41,\cdot)\) 6009.bf 2002 Yes \(1\) \(1\) \(e\left(\frac{25}{143}\right)\) \(e\left(\frac{50}{143}\right)\) \(e\left(\frac{218}{1001}\right)\) \(e\left(\frac{575}{2002}\right)\) \(e\left(\frac{75}{143}\right)\) \(e\left(\frac{393}{1001}\right)\) \(e\left(\frac{96}{143}\right)\) \(e\left(\frac{367}{1001}\right)\) \(e\left(\frac{925}{2002}\right)\) \(e\left(\frac{100}{143}\right)\)
\(\chi_{6009}(43,\cdot)\) 6009.be 2002 No \(-1\) \(1\) \(e\left(\frac{37}{286}\right)\) \(e\left(\frac{37}{143}\right)\) \(e\left(\frac{1255}{2002}\right)\) \(e\left(\frac{211}{2002}\right)\) \(e\left(\frac{111}{286}\right)\) \(e\left(\frac{757}{1001}\right)\) \(e\left(\frac{205}{286}\right)\) \(e\left(\frac{549}{1001}\right)\) \(e\left(\frac{235}{1001}\right)\) \(e\left(\frac{74}{143}\right)\)
\(\chi_{6009}(44,\cdot)\) 6009.bb 286 Yes \(1\) \(1\) \(e\left(\frac{1}{143}\right)\) \(e\left(\frac{2}{143}\right)\) \(e\left(\frac{123}{143}\right)\) \(e\left(\frac{85}{286}\right)\) \(e\left(\frac{3}{143}\right)\) \(e\left(\frac{124}{143}\right)\) \(e\left(\frac{21}{143}\right)\) \(e\left(\frac{7}{143}\right)\) \(e\left(\frac{87}{286}\right)\) \(e\left(\frac{4}{143}\right)\)
\(\chi_{6009}(46,\cdot)\) 6009.s 143 No \(1\) \(1\) \(e\left(\frac{101}{143}\right)\) \(e\left(\frac{59}{143}\right)\) \(e\left(\frac{125}{143}\right)\) \(e\left(\frac{74}{143}\right)\) \(e\left(\frac{17}{143}\right)\) \(e\left(\frac{83}{143}\right)\) \(e\left(\frac{119}{143}\right)\) \(e\left(\frac{135}{143}\right)\) \(e\left(\frac{32}{143}\right)\) \(e\left(\frac{118}{143}\right)\)
\(\chi_{6009}(47,\cdot)\) 6009.bd 2002 Yes \(-1\) \(1\) \(e\left(\frac{115}{286}\right)\) \(e\left(\frac{115}{143}\right)\) \(e\left(\frac{1775}{2002}\right)\) \(e\left(\frac{554}{1001}\right)\) \(e\left(\frac{59}{286}\right)\) \(e\left(\frac{289}{1001}\right)\) \(e\left(\frac{127}{286}\right)\) \(e\left(\frac{601}{1001}\right)\) \(e\left(\frac{1913}{2002}\right)\) \(e\left(\frac{87}{143}\right)\)