Properties

Modulus 1049
Structure \(C_{1048}\)
Order 1048

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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(1049)
pari: g = idealstar(,1049,2)

Character group

sage: G.order()
pari: g.no
Order = 1048
sage: H.invariants()
pari: g.cyc
Structure = \(C_{1048}\)
sage: H.gens()
pari: g.gen
Generators = $\chi_{1049}(3,\cdot)$

First 32 of 1048 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
\(\chi_{1049}(1,\cdot)\) 1049.a 1 No \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{1049}(2,\cdot)\) 1049.f 262 Yes \(1\) \(1\) \(e\left(\frac{124}{131}\right)\) \(e\left(\frac{149}{262}\right)\) \(e\left(\frac{117}{131}\right)\) \(e\left(\frac{96}{131}\right)\) \(e\left(\frac{135}{262}\right)\) \(e\left(\frac{5}{262}\right)\) \(e\left(\frac{110}{131}\right)\) \(e\left(\frac{18}{131}\right)\) \(e\left(\frac{89}{131}\right)\) \(e\left(\frac{94}{131}\right)\)
\(\chi_{1049}(3,\cdot)\) 1049.h 1048 Yes \(-1\) \(1\) \(e\left(\frac{149}{262}\right)\) \(e\left(\frac{1}{1048}\right)\) \(e\left(\frac{18}{131}\right)\) \(e\left(\frac{49}{524}\right)\) \(e\left(\frac{597}{1048}\right)\) \(e\left(\frac{255}{1048}\right)\) \(e\left(\frac{185}{262}\right)\) \(e\left(\frac{1}{524}\right)\) \(e\left(\frac{347}{524}\right)\) \(e\left(\frac{209}{524}\right)\)
\(\chi_{1049}(4,\cdot)\) 1049.e 131 Yes \(1\) \(1\) \(e\left(\frac{117}{131}\right)\) \(e\left(\frac{18}{131}\right)\) \(e\left(\frac{103}{131}\right)\) \(e\left(\frac{61}{131}\right)\) \(e\left(\frac{4}{131}\right)\) \(e\left(\frac{5}{131}\right)\) \(e\left(\frac{89}{131}\right)\) \(e\left(\frac{36}{131}\right)\) \(e\left(\frac{47}{131}\right)\) \(e\left(\frac{57}{131}\right)\)
\(\chi_{1049}(5,\cdot)\) 1049.g 524 Yes \(1\) \(1\) \(e\left(\frac{96}{131}\right)\) \(e\left(\frac{49}{524}\right)\) \(e\left(\frac{61}{131}\right)\) \(e\left(\frac{43}{262}\right)\) \(e\left(\frac{433}{524}\right)\) \(e\left(\frac{443}{524}\right)\) \(e\left(\frac{26}{131}\right)\) \(e\left(\frac{49}{262}\right)\) \(e\left(\frac{235}{262}\right)\) \(e\left(\frac{23}{262}\right)\)
\(\chi_{1049}(6,\cdot)\) 1049.h 1048 Yes \(-1\) \(1\) \(e\left(\frac{135}{262}\right)\) \(e\left(\frac{597}{1048}\right)\) \(e\left(\frac{4}{131}\right)\) \(e\left(\frac{433}{524}\right)\) \(e\left(\frac{89}{1048}\right)\) \(e\left(\frac{275}{1048}\right)\) \(e\left(\frac{143}{262}\right)\) \(e\left(\frac{73}{524}\right)\) \(e\left(\frac{179}{524}\right)\) \(e\left(\frac{61}{524}\right)\)
\(\chi_{1049}(7,\cdot)\) 1049.h 1048 Yes \(-1\) \(1\) \(e\left(\frac{5}{262}\right)\) \(e\left(\frac{255}{1048}\right)\) \(e\left(\frac{5}{131}\right)\) \(e\left(\frac{443}{524}\right)\) \(e\left(\frac{275}{1048}\right)\) \(e\left(\frac{49}{1048}\right)\) \(e\left(\frac{15}{262}\right)\) \(e\left(\frac{255}{524}\right)\) \(e\left(\frac{453}{524}\right)\) \(e\left(\frac{371}{524}\right)\)
\(\chi_{1049}(8,\cdot)\) 1049.f 262 Yes \(1\) \(1\) \(e\left(\frac{110}{131}\right)\) \(e\left(\frac{185}{262}\right)\) \(e\left(\frac{89}{131}\right)\) \(e\left(\frac{26}{131}\right)\) \(e\left(\frac{143}{262}\right)\) \(e\left(\frac{15}{262}\right)\) \(e\left(\frac{68}{131}\right)\) \(e\left(\frac{54}{131}\right)\) \(e\left(\frac{5}{131}\right)\) \(e\left(\frac{20}{131}\right)\)
\(\chi_{1049}(9,\cdot)\) 1049.g 524 Yes \(1\) \(1\) \(e\left(\frac{18}{131}\right)\) \(e\left(\frac{1}{524}\right)\) \(e\left(\frac{36}{131}\right)\) \(e\left(\frac{49}{262}\right)\) \(e\left(\frac{73}{524}\right)\) \(e\left(\frac{255}{524}\right)\) \(e\left(\frac{54}{131}\right)\) \(e\left(\frac{1}{262}\right)\) \(e\left(\frac{85}{262}\right)\) \(e\left(\frac{209}{262}\right)\)
\(\chi_{1049}(10,\cdot)\) 1049.g 524 Yes \(1\) \(1\) \(e\left(\frac{89}{131}\right)\) \(e\left(\frac{347}{524}\right)\) \(e\left(\frac{47}{131}\right)\) \(e\left(\frac{235}{262}\right)\) \(e\left(\frac{179}{524}\right)\) \(e\left(\frac{453}{524}\right)\) \(e\left(\frac{5}{131}\right)\) \(e\left(\frac{85}{262}\right)\) \(e\left(\frac{151}{262}\right)\) \(e\left(\frac{211}{262}\right)\)
\(\chi_{1049}(11,\cdot)\) 1049.g 524 Yes \(1\) \(1\) \(e\left(\frac{94}{131}\right)\) \(e\left(\frac{209}{524}\right)\) \(e\left(\frac{57}{131}\right)\) \(e\left(\frac{23}{262}\right)\) \(e\left(\frac{61}{524}\right)\) \(e\left(\frac{371}{524}\right)\) \(e\left(\frac{20}{131}\right)\) \(e\left(\frac{209}{262}\right)\) \(e\left(\frac{211}{262}\right)\) \(e\left(\frac{189}{262}\right)\)
\(\chi_{1049}(12,\cdot)\) 1049.h 1048 Yes \(-1\) \(1\) \(e\left(\frac{121}{262}\right)\) \(e\left(\frac{145}{1048}\right)\) \(e\left(\frac{121}{131}\right)\) \(e\left(\frac{293}{524}\right)\) \(e\left(\frac{629}{1048}\right)\) \(e\left(\frac{295}{1048}\right)\) \(e\left(\frac{101}{262}\right)\) \(e\left(\frac{145}{524}\right)\) \(e\left(\frac{11}{524}\right)\) \(e\left(\frac{437}{524}\right)\)
\(\chi_{1049}(13,\cdot)\) 1049.f 262 Yes \(1\) \(1\) \(e\left(\frac{81}{131}\right)\) \(e\left(\frac{35}{262}\right)\) \(e\left(\frac{31}{131}\right)\) \(e\left(\frac{12}{131}\right)\) \(e\left(\frac{197}{262}\right)\) \(e\left(\frac{17}{262}\right)\) \(e\left(\frac{112}{131}\right)\) \(e\left(\frac{35}{131}\right)\) \(e\left(\frac{93}{131}\right)\) \(e\left(\frac{110}{131}\right)\)
\(\chi_{1049}(14,\cdot)\) 1049.h 1048 Yes \(-1\) \(1\) \(e\left(\frac{253}{262}\right)\) \(e\left(\frac{851}{1048}\right)\) \(e\left(\frac{122}{131}\right)\) \(e\left(\frac{303}{524}\right)\) \(e\left(\frac{815}{1048}\right)\) \(e\left(\frac{69}{1048}\right)\) \(e\left(\frac{235}{262}\right)\) \(e\left(\frac{327}{524}\right)\) \(e\left(\frac{285}{524}\right)\) \(e\left(\frac{223}{524}\right)\)
\(\chi_{1049}(15,\cdot)\) 1049.h 1048 Yes \(-1\) \(1\) \(e\left(\frac{79}{262}\right)\) \(e\left(\frac{99}{1048}\right)\) \(e\left(\frac{79}{131}\right)\) \(e\left(\frac{135}{524}\right)\) \(e\left(\frac{415}{1048}\right)\) \(e\left(\frac{93}{1048}\right)\) \(e\left(\frac{237}{262}\right)\) \(e\left(\frac{99}{524}\right)\) \(e\left(\frac{293}{524}\right)\) \(e\left(\frac{255}{524}\right)\)
\(\chi_{1049}(16,\cdot)\) 1049.e 131 Yes \(1\) \(1\) \(e\left(\frac{103}{131}\right)\) \(e\left(\frac{36}{131}\right)\) \(e\left(\frac{75}{131}\right)\) \(e\left(\frac{122}{131}\right)\) \(e\left(\frac{8}{131}\right)\) \(e\left(\frac{10}{131}\right)\) \(e\left(\frac{47}{131}\right)\) \(e\left(\frac{72}{131}\right)\) \(e\left(\frac{94}{131}\right)\) \(e\left(\frac{114}{131}\right)\)
\(\chi_{1049}(17,\cdot)\) 1049.h 1048 Yes \(-1\) \(1\) \(e\left(\frac{133}{262}\right)\) \(e\left(\frac{757}{1048}\right)\) \(e\left(\frac{2}{131}\right)\) \(e\left(\frac{413}{524}\right)\) \(e\left(\frac{241}{1048}\right)\) \(e\left(\frac{203}{1048}\right)\) \(e\left(\frac{137}{262}\right)\) \(e\left(\frac{233}{524}\right)\) \(e\left(\frac{155}{524}\right)\) \(e\left(\frac{489}{524}\right)\)
\(\chi_{1049}(18,\cdot)\) 1049.g 524 Yes \(1\) \(1\) \(e\left(\frac{11}{131}\right)\) \(e\left(\frac{299}{524}\right)\) \(e\left(\frac{22}{131}\right)\) \(e\left(\frac{241}{262}\right)\) \(e\left(\frac{343}{524}\right)\) \(e\left(\frac{265}{524}\right)\) \(e\left(\frac{33}{131}\right)\) \(e\left(\frac{37}{262}\right)\) \(e\left(\frac{1}{262}\right)\) \(e\left(\frac{135}{262}\right)\)
\(\chi_{1049}(19,\cdot)\) 1049.e 131 Yes \(1\) \(1\) \(e\left(\frac{58}{131}\right)\) \(e\left(\frac{19}{131}\right)\) \(e\left(\frac{116}{131}\right)\) \(e\left(\frac{28}{131}\right)\) \(e\left(\frac{77}{131}\right)\) \(e\left(\frac{129}{131}\right)\) \(e\left(\frac{43}{131}\right)\) \(e\left(\frac{38}{131}\right)\) \(e\left(\frac{86}{131}\right)\) \(e\left(\frac{82}{131}\right)\)
\(\chi_{1049}(20,\cdot)\) 1049.g 524 Yes \(1\) \(1\) \(e\left(\frac{82}{131}\right)\) \(e\left(\frac{121}{524}\right)\) \(e\left(\frac{33}{131}\right)\) \(e\left(\frac{165}{262}\right)\) \(e\left(\frac{449}{524}\right)\) \(e\left(\frac{463}{524}\right)\) \(e\left(\frac{115}{131}\right)\) \(e\left(\frac{121}{262}\right)\) \(e\left(\frac{67}{262}\right)\) \(e\left(\frac{137}{262}\right)\)
\(\chi_{1049}(21,\cdot)\) 1049.e 131 Yes \(1\) \(1\) \(e\left(\frac{77}{131}\right)\) \(e\left(\frac{32}{131}\right)\) \(e\left(\frac{23}{131}\right)\) \(e\left(\frac{123}{131}\right)\) \(e\left(\frac{109}{131}\right)\) \(e\left(\frac{38}{131}\right)\) \(e\left(\frac{100}{131}\right)\) \(e\left(\frac{64}{131}\right)\) \(e\left(\frac{69}{131}\right)\) \(e\left(\frac{14}{131}\right)\)
\(\chi_{1049}(22,\cdot)\) 1049.g 524 Yes \(1\) \(1\) \(e\left(\frac{87}{131}\right)\) \(e\left(\frac{507}{524}\right)\) \(e\left(\frac{43}{131}\right)\) \(e\left(\frac{215}{262}\right)\) \(e\left(\frac{331}{524}\right)\) \(e\left(\frac{381}{524}\right)\) \(e\left(\frac{130}{131}\right)\) \(e\left(\frac{245}{262}\right)\) \(e\left(\frac{127}{262}\right)\) \(e\left(\frac{115}{262}\right)\)
\(\chi_{1049}(23,\cdot)\) 1049.h 1048 Yes \(-1\) \(1\) \(e\left(\frac{25}{262}\right)\) \(e\left(\frac{227}{1048}\right)\) \(e\left(\frac{25}{131}\right)\) \(e\left(\frac{119}{524}\right)\) \(e\left(\frac{327}{1048}\right)\) \(e\left(\frac{245}{1048}\right)\) \(e\left(\frac{75}{262}\right)\) \(e\left(\frac{227}{524}\right)\) \(e\left(\frac{169}{524}\right)\) \(e\left(\frac{283}{524}\right)\)
\(\chi_{1049}(24,\cdot)\) 1049.h 1048 Yes \(-1\) \(1\) \(e\left(\frac{107}{262}\right)\) \(e\left(\frac{741}{1048}\right)\) \(e\left(\frac{107}{131}\right)\) \(e\left(\frac{153}{524}\right)\) \(e\left(\frac{121}{1048}\right)\) \(e\left(\frac{315}{1048}\right)\) \(e\left(\frac{59}{262}\right)\) \(e\left(\frac{217}{524}\right)\) \(e\left(\frac{367}{524}\right)\) \(e\left(\frac{289}{524}\right)\)
\(\chi_{1049}(25,\cdot)\) 1049.f 262 Yes \(1\) \(1\) \(e\left(\frac{61}{131}\right)\) \(e\left(\frac{49}{262}\right)\) \(e\left(\frac{122}{131}\right)\) \(e\left(\frac{43}{131}\right)\) \(e\left(\frac{171}{262}\right)\) \(e\left(\frac{181}{262}\right)\) \(e\left(\frac{52}{131}\right)\) \(e\left(\frac{49}{131}\right)\) \(e\left(\frac{104}{131}\right)\) \(e\left(\frac{23}{131}\right)\)
\(\chi_{1049}(26,\cdot)\) 1049.e 131 Yes \(1\) \(1\) \(e\left(\frac{74}{131}\right)\) \(e\left(\frac{92}{131}\right)\) \(e\left(\frac{17}{131}\right)\) \(e\left(\frac{108}{131}\right)\) \(e\left(\frac{35}{131}\right)\) \(e\left(\frac{11}{131}\right)\) \(e\left(\frac{91}{131}\right)\) \(e\left(\frac{53}{131}\right)\) \(e\left(\frac{51}{131}\right)\) \(e\left(\frac{73}{131}\right)\)
\(\chi_{1049}(27,\cdot)\) 1049.h 1048 Yes \(-1\) \(1\) \(e\left(\frac{185}{262}\right)\) \(e\left(\frac{3}{1048}\right)\) \(e\left(\frac{54}{131}\right)\) \(e\left(\frac{147}{524}\right)\) \(e\left(\frac{743}{1048}\right)\) \(e\left(\frac{765}{1048}\right)\) \(e\left(\frac{31}{262}\right)\) \(e\left(\frac{3}{524}\right)\) \(e\left(\frac{517}{524}\right)\) \(e\left(\frac{103}{524}\right)\)
\(\chi_{1049}(28,\cdot)\) 1049.h 1048 Yes \(-1\) \(1\) \(e\left(\frac{239}{262}\right)\) \(e\left(\frac{399}{1048}\right)\) \(e\left(\frac{108}{131}\right)\) \(e\left(\frac{163}{524}\right)\) \(e\left(\frac{307}{1048}\right)\) \(e\left(\frac{89}{1048}\right)\) \(e\left(\frac{193}{262}\right)\) \(e\left(\frac{399}{524}\right)\) \(e\left(\frac{117}{524}\right)\) \(e\left(\frac{75}{524}\right)\)
\(\chi_{1049}(29,\cdot)\) 1049.f 262 Yes \(1\) \(1\) \(e\left(\frac{92}{131}\right)\) \(e\left(\frac{119}{262}\right)\) \(e\left(\frac{53}{131}\right)\) \(e\left(\frac{67}{131}\right)\) \(e\left(\frac{41}{262}\right)\) \(e\left(\frac{215}{262}\right)\) \(e\left(\frac{14}{131}\right)\) \(e\left(\frac{119}{131}\right)\) \(e\left(\frac{28}{131}\right)\) \(e\left(\frac{112}{131}\right)\)
\(\chi_{1049}(30,\cdot)\) 1049.h 1048 Yes \(-1\) \(1\) \(e\left(\frac{65}{262}\right)\) \(e\left(\frac{695}{1048}\right)\) \(e\left(\frac{65}{131}\right)\) \(e\left(\frac{519}{524}\right)\) \(e\left(\frac{955}{1048}\right)\) \(e\left(\frac{113}{1048}\right)\) \(e\left(\frac{195}{262}\right)\) \(e\left(\frac{171}{524}\right)\) \(e\left(\frac{125}{524}\right)\) \(e\left(\frac{107}{524}\right)\)
\(\chi_{1049}(31,\cdot)\) 1049.h 1048 Yes \(-1\) \(1\) \(e\left(\frac{73}{262}\right)\) \(e\left(\frac{841}{1048}\right)\) \(e\left(\frac{73}{131}\right)\) \(e\left(\frac{337}{524}\right)\) \(e\left(\frac{85}{1048}\right)\) \(e\left(\frac{663}{1048}\right)\) \(e\left(\frac{219}{262}\right)\) \(e\left(\frac{317}{524}\right)\) \(e\left(\frac{483}{524}\right)\) \(e\left(\frac{229}{524}\right)\)
\(\chi_{1049}(32,\cdot)\) 1049.f 262 Yes \(1\) \(1\) \(e\left(\frac{96}{131}\right)\) \(e\left(\frac{221}{262}\right)\) \(e\left(\frac{61}{131}\right)\) \(e\left(\frac{87}{131}\right)\) \(e\left(\frac{151}{262}\right)\) \(e\left(\frac{25}{262}\right)\) \(e\left(\frac{26}{131}\right)\) \(e\left(\frac{90}{131}\right)\) \(e\left(\frac{52}{131}\right)\) \(e\left(\frac{77}{131}\right)\)