Properties

Modulus 569
Structure \(C_{568}\)
Order 568

Learn more about

Show commands for: SageMath / Pari/GP

sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
 
sage: H = DirichletGroup_conrey(569)
 
pari: g = idealstar(,569,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 568
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{568}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{569}(3,\cdot)$

First 32 of 568 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
\(\chi_{569}(1,\cdot)\) 569.a 1 No \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{569}(2,\cdot)\) 569.g 284 Yes \(1\) \(1\) \(e\left(\frac{131}{142}\right)\) \(e\left(\frac{255}{284}\right)\) \(e\left(\frac{60}{71}\right)\) \(e\left(\frac{55}{71}\right)\) \(e\left(\frac{233}{284}\right)\) \(e\left(\frac{47}{142}\right)\) \(e\left(\frac{109}{142}\right)\) \(e\left(\frac{113}{142}\right)\) \(e\left(\frac{99}{142}\right)\) \(e\left(\frac{265}{284}\right)\)
\(\chi_{569}(3,\cdot)\) 569.h 568 Yes \(-1\) \(1\) \(e\left(\frac{255}{284}\right)\) \(e\left(\frac{1}{568}\right)\) \(e\left(\frac{113}{142}\right)\) \(e\left(\frac{37}{71}\right)\) \(e\left(\frac{511}{568}\right)\) \(e\left(\frac{111}{284}\right)\) \(e\left(\frac{197}{284}\right)\) \(e\left(\frac{1}{284}\right)\) \(e\left(\frac{119}{284}\right)\) \(e\left(\frac{79}{568}\right)\)
\(\chi_{569}(4,\cdot)\) 569.f 142 Yes \(1\) \(1\) \(e\left(\frac{60}{71}\right)\) \(e\left(\frac{113}{142}\right)\) \(e\left(\frac{49}{71}\right)\) \(e\left(\frac{39}{71}\right)\) \(e\left(\frac{91}{142}\right)\) \(e\left(\frac{47}{71}\right)\) \(e\left(\frac{38}{71}\right)\) \(e\left(\frac{42}{71}\right)\) \(e\left(\frac{28}{71}\right)\) \(e\left(\frac{123}{142}\right)\)
\(\chi_{569}(5,\cdot)\) 569.e 71 Yes \(1\) \(1\) \(e\left(\frac{55}{71}\right)\) \(e\left(\frac{37}{71}\right)\) \(e\left(\frac{39}{71}\right)\) \(e\left(\frac{18}{71}\right)\) \(e\left(\frac{21}{71}\right)\) \(e\left(\frac{49}{71}\right)\) \(e\left(\frac{23}{71}\right)\) \(e\left(\frac{3}{71}\right)\) \(e\left(\frac{2}{71}\right)\) \(e\left(\frac{12}{71}\right)\)
\(\chi_{569}(6,\cdot)\) 569.h 568 Yes \(-1\) \(1\) \(e\left(\frac{233}{284}\right)\) \(e\left(\frac{511}{568}\right)\) \(e\left(\frac{91}{142}\right)\) \(e\left(\frac{21}{71}\right)\) \(e\left(\frac{409}{568}\right)\) \(e\left(\frac{205}{284}\right)\) \(e\left(\frac{131}{284}\right)\) \(e\left(\frac{227}{284}\right)\) \(e\left(\frac{33}{284}\right)\) \(e\left(\frac{41}{568}\right)\)
\(\chi_{569}(7,\cdot)\) 569.g 284 Yes \(1\) \(1\) \(e\left(\frac{47}{142}\right)\) \(e\left(\frac{111}{284}\right)\) \(e\left(\frac{47}{71}\right)\) \(e\left(\frac{49}{71}\right)\) \(e\left(\frac{205}{284}\right)\) \(e\left(\frac{109}{142}\right)\) \(e\left(\frac{141}{142}\right)\) \(e\left(\frac{111}{142}\right)\) \(e\left(\frac{3}{142}\right)\) \(e\left(\frac{249}{284}\right)\)
\(\chi_{569}(8,\cdot)\) 569.g 284 Yes \(1\) \(1\) \(e\left(\frac{109}{142}\right)\) \(e\left(\frac{197}{284}\right)\) \(e\left(\frac{38}{71}\right)\) \(e\left(\frac{23}{71}\right)\) \(e\left(\frac{131}{284}\right)\) \(e\left(\frac{141}{142}\right)\) \(e\left(\frac{43}{142}\right)\) \(e\left(\frac{55}{142}\right)\) \(e\left(\frac{13}{142}\right)\) \(e\left(\frac{227}{284}\right)\)
\(\chi_{569}(9,\cdot)\) 569.g 284 Yes \(1\) \(1\) \(e\left(\frac{113}{142}\right)\) \(e\left(\frac{1}{284}\right)\) \(e\left(\frac{42}{71}\right)\) \(e\left(\frac{3}{71}\right)\) \(e\left(\frac{227}{284}\right)\) \(e\left(\frac{111}{142}\right)\) \(e\left(\frac{55}{142}\right)\) \(e\left(\frac{1}{142}\right)\) \(e\left(\frac{119}{142}\right)\) \(e\left(\frac{79}{284}\right)\)
\(\chi_{569}(10,\cdot)\) 569.g 284 Yes \(1\) \(1\) \(e\left(\frac{99}{142}\right)\) \(e\left(\frac{119}{284}\right)\) \(e\left(\frac{28}{71}\right)\) \(e\left(\frac{2}{71}\right)\) \(e\left(\frac{33}{284}\right)\) \(e\left(\frac{3}{142}\right)\) \(e\left(\frac{13}{142}\right)\) \(e\left(\frac{119}{142}\right)\) \(e\left(\frac{103}{142}\right)\) \(e\left(\frac{29}{284}\right)\)
\(\chi_{569}(11,\cdot)\) 569.h 568 Yes \(-1\) \(1\) \(e\left(\frac{265}{284}\right)\) \(e\left(\frac{79}{568}\right)\) \(e\left(\frac{123}{142}\right)\) \(e\left(\frac{12}{71}\right)\) \(e\left(\frac{41}{568}\right)\) \(e\left(\frac{249}{284}\right)\) \(e\left(\frac{227}{284}\right)\) \(e\left(\frac{79}{284}\right)\) \(e\left(\frac{29}{284}\right)\) \(e\left(\frac{561}{568}\right)\)
\(\chi_{569}(12,\cdot)\) 569.h 568 Yes \(-1\) \(1\) \(e\left(\frac{211}{284}\right)\) \(e\left(\frac{453}{568}\right)\) \(e\left(\frac{69}{142}\right)\) \(e\left(\frac{5}{71}\right)\) \(e\left(\frac{307}{568}\right)\) \(e\left(\frac{15}{284}\right)\) \(e\left(\frac{65}{284}\right)\) \(e\left(\frac{169}{284}\right)\) \(e\left(\frac{231}{284}\right)\) \(e\left(\frac{3}{568}\right)\)
\(\chi_{569}(13,\cdot)\) 569.g 284 Yes \(1\) \(1\) \(e\left(\frac{17}{142}\right)\) \(e\left(\frac{19}{284}\right)\) \(e\left(\frac{17}{71}\right)\) \(e\left(\frac{57}{71}\right)\) \(e\left(\frac{53}{284}\right)\) \(e\left(\frac{121}{142}\right)\) \(e\left(\frac{51}{142}\right)\) \(e\left(\frac{19}{142}\right)\) \(e\left(\frac{131}{142}\right)\) \(e\left(\frac{81}{284}\right)\)
\(\chi_{569}(14,\cdot)\) 569.f 142 Yes \(1\) \(1\) \(e\left(\frac{18}{71}\right)\) \(e\left(\frac{41}{142}\right)\) \(e\left(\frac{36}{71}\right)\) \(e\left(\frac{33}{71}\right)\) \(e\left(\frac{77}{142}\right)\) \(e\left(\frac{7}{71}\right)\) \(e\left(\frac{54}{71}\right)\) \(e\left(\frac{41}{71}\right)\) \(e\left(\frac{51}{71}\right)\) \(e\left(\frac{115}{142}\right)\)
\(\chi_{569}(15,\cdot)\) 569.h 568 Yes \(-1\) \(1\) \(e\left(\frac{191}{284}\right)\) \(e\left(\frac{297}{568}\right)\) \(e\left(\frac{49}{142}\right)\) \(e\left(\frac{55}{71}\right)\) \(e\left(\frac{111}{568}\right)\) \(e\left(\frac{23}{284}\right)\) \(e\left(\frac{5}{284}\right)\) \(e\left(\frac{13}{284}\right)\) \(e\left(\frac{127}{284}\right)\) \(e\left(\frac{175}{568}\right)\)
\(\chi_{569}(16,\cdot)\) 569.e 71 Yes \(1\) \(1\) \(e\left(\frac{49}{71}\right)\) \(e\left(\frac{42}{71}\right)\) \(e\left(\frac{27}{71}\right)\) \(e\left(\frac{7}{71}\right)\) \(e\left(\frac{20}{71}\right)\) \(e\left(\frac{23}{71}\right)\) \(e\left(\frac{5}{71}\right)\) \(e\left(\frac{13}{71}\right)\) \(e\left(\frac{56}{71}\right)\) \(e\left(\frac{52}{71}\right)\)
\(\chi_{569}(17,\cdot)\) 569.g 284 Yes \(1\) \(1\) \(e\left(\frac{133}{142}\right)\) \(e\left(\frac{15}{284}\right)\) \(e\left(\frac{62}{71}\right)\) \(e\left(\frac{45}{71}\right)\) \(e\left(\frac{281}{284}\right)\) \(e\left(\frac{103}{142}\right)\) \(e\left(\frac{115}{142}\right)\) \(e\left(\frac{15}{142}\right)\) \(e\left(\frac{81}{142}\right)\) \(e\left(\frac{49}{284}\right)\)
\(\chi_{569}(18,\cdot)\) 569.e 71 Yes \(1\) \(1\) \(e\left(\frac{51}{71}\right)\) \(e\left(\frac{64}{71}\right)\) \(e\left(\frac{31}{71}\right)\) \(e\left(\frac{58}{71}\right)\) \(e\left(\frac{44}{71}\right)\) \(e\left(\frac{8}{71}\right)\) \(e\left(\frac{11}{71}\right)\) \(e\left(\frac{57}{71}\right)\) \(e\left(\frac{38}{71}\right)\) \(e\left(\frac{15}{71}\right)\)
\(\chi_{569}(19,\cdot)\) 569.h 568 Yes \(-1\) \(1\) \(e\left(\frac{115}{284}\right)\) \(e\left(\frac{329}{568}\right)\) \(e\left(\frac{115}{142}\right)\) \(e\left(\frac{32}{71}\right)\) \(e\left(\frac{559}{568}\right)\) \(e\left(\frac{167}{284}\right)\) \(e\left(\frac{61}{284}\right)\) \(e\left(\frac{45}{284}\right)\) \(e\left(\frac{243}{284}\right)\) \(e\left(\frac{431}{568}\right)\)
\(\chi_{569}(20,\cdot)\) 569.f 142 Yes \(1\) \(1\) \(e\left(\frac{44}{71}\right)\) \(e\left(\frac{45}{142}\right)\) \(e\left(\frac{17}{71}\right)\) \(e\left(\frac{57}{71}\right)\) \(e\left(\frac{133}{142}\right)\) \(e\left(\frac{25}{71}\right)\) \(e\left(\frac{61}{71}\right)\) \(e\left(\frac{45}{71}\right)\) \(e\left(\frac{30}{71}\right)\) \(e\left(\frac{5}{142}\right)\)
\(\chi_{569}(21,\cdot)\) 569.h 568 Yes \(-1\) \(1\) \(e\left(\frac{65}{284}\right)\) \(e\left(\frac{223}{568}\right)\) \(e\left(\frac{65}{142}\right)\) \(e\left(\frac{15}{71}\right)\) \(e\left(\frac{353}{568}\right)\) \(e\left(\frac{45}{284}\right)\) \(e\left(\frac{195}{284}\right)\) \(e\left(\frac{223}{284}\right)\) \(e\left(\frac{125}{284}\right)\) \(e\left(\frac{9}{568}\right)\)
\(\chi_{569}(22,\cdot)\) 569.h 568 Yes \(-1\) \(1\) \(e\left(\frac{243}{284}\right)\) \(e\left(\frac{21}{568}\right)\) \(e\left(\frac{101}{142}\right)\) \(e\left(\frac{67}{71}\right)\) \(e\left(\frac{507}{568}\right)\) \(e\left(\frac{59}{284}\right)\) \(e\left(\frac{161}{284}\right)\) \(e\left(\frac{21}{284}\right)\) \(e\left(\frac{227}{284}\right)\) \(e\left(\frac{523}{568}\right)\)
\(\chi_{569}(23,\cdot)\) 569.h 568 Yes \(-1\) \(1\) \(e\left(\frac{77}{284}\right)\) \(e\left(\frac{487}{568}\right)\) \(e\left(\frac{77}{142}\right)\) \(e\left(\frac{56}{71}\right)\) \(e\left(\frac{73}{568}\right)\) \(e\left(\frac{97}{284}\right)\) \(e\left(\frac{231}{284}\right)\) \(e\left(\frac{203}{284}\right)\) \(e\left(\frac{17}{284}\right)\) \(e\left(\frac{417}{568}\right)\)
\(\chi_{569}(24,\cdot)\) 569.h 568 Yes \(-1\) \(1\) \(e\left(\frac{189}{284}\right)\) \(e\left(\frac{395}{568}\right)\) \(e\left(\frac{47}{142}\right)\) \(e\left(\frac{60}{71}\right)\) \(e\left(\frac{205}{568}\right)\) \(e\left(\frac{109}{284}\right)\) \(e\left(\frac{283}{284}\right)\) \(e\left(\frac{111}{284}\right)\) \(e\left(\frac{145}{284}\right)\) \(e\left(\frac{533}{568}\right)\)
\(\chi_{569}(25,\cdot)\) 569.e 71 Yes \(1\) \(1\) \(e\left(\frac{39}{71}\right)\) \(e\left(\frac{3}{71}\right)\) \(e\left(\frac{7}{71}\right)\) \(e\left(\frac{36}{71}\right)\) \(e\left(\frac{42}{71}\right)\) \(e\left(\frac{27}{71}\right)\) \(e\left(\frac{46}{71}\right)\) \(e\left(\frac{6}{71}\right)\) \(e\left(\frac{4}{71}\right)\) \(e\left(\frac{24}{71}\right)\)
\(\chi_{569}(26,\cdot)\) 569.f 142 Yes \(1\) \(1\) \(e\left(\frac{3}{71}\right)\) \(e\left(\frac{137}{142}\right)\) \(e\left(\frac{6}{71}\right)\) \(e\left(\frac{41}{71}\right)\) \(e\left(\frac{1}{142}\right)\) \(e\left(\frac{13}{71}\right)\) \(e\left(\frac{9}{71}\right)\) \(e\left(\frac{66}{71}\right)\) \(e\left(\frac{44}{71}\right)\) \(e\left(\frac{31}{142}\right)\)
\(\chi_{569}(27,\cdot)\) 569.h 568 Yes \(-1\) \(1\) \(e\left(\frac{197}{284}\right)\) \(e\left(\frac{3}{568}\right)\) \(e\left(\frac{55}{142}\right)\) \(e\left(\frac{40}{71}\right)\) \(e\left(\frac{397}{568}\right)\) \(e\left(\frac{49}{284}\right)\) \(e\left(\frac{23}{284}\right)\) \(e\left(\frac{3}{284}\right)\) \(e\left(\frac{73}{284}\right)\) \(e\left(\frac{237}{568}\right)\)
\(\chi_{569}(28,\cdot)\) 569.g 284 Yes \(1\) \(1\) \(e\left(\frac{25}{142}\right)\) \(e\left(\frac{53}{284}\right)\) \(e\left(\frac{25}{71}\right)\) \(e\left(\frac{17}{71}\right)\) \(e\left(\frac{103}{284}\right)\) \(e\left(\frac{61}{142}\right)\) \(e\left(\frac{75}{142}\right)\) \(e\left(\frac{53}{142}\right)\) \(e\left(\frac{59}{142}\right)\) \(e\left(\frac{211}{284}\right)\)
\(\chi_{569}(29,\cdot)\) 569.h 568 Yes \(-1\) \(1\) \(e\left(\frac{89}{284}\right)\) \(e\left(\frac{467}{568}\right)\) \(e\left(\frac{89}{142}\right)\) \(e\left(\frac{26}{71}\right)\) \(e\left(\frac{77}{568}\right)\) \(e\left(\frac{149}{284}\right)\) \(e\left(\frac{267}{284}\right)\) \(e\left(\frac{183}{284}\right)\) \(e\left(\frac{193}{284}\right)\) \(e\left(\frac{541}{568}\right)\)
\(\chi_{569}(30,\cdot)\) 569.h 568 Yes \(-1\) \(1\) \(e\left(\frac{169}{284}\right)\) \(e\left(\frac{239}{568}\right)\) \(e\left(\frac{27}{142}\right)\) \(e\left(\frac{39}{71}\right)\) \(e\left(\frac{9}{568}\right)\) \(e\left(\frac{117}{284}\right)\) \(e\left(\frac{223}{284}\right)\) \(e\left(\frac{239}{284}\right)\) \(e\left(\frac{41}{284}\right)\) \(e\left(\frac{137}{568}\right)\)
\(\chi_{569}(31,\cdot)\) 569.h 568 Yes \(-1\) \(1\) \(e\left(\frac{61}{284}\right)\) \(e\left(\frac{419}{568}\right)\) \(e\left(\frac{61}{142}\right)\) \(e\left(\frac{25}{71}\right)\) \(e\left(\frac{541}{568}\right)\) \(e\left(\frac{217}{284}\right)\) \(e\left(\frac{183}{284}\right)\) \(e\left(\frac{135}{284}\right)\) \(e\left(\frac{161}{284}\right)\) \(e\left(\frac{157}{568}\right)\)
\(\chi_{569}(32,\cdot)\) 569.g 284 Yes \(1\) \(1\) \(e\left(\frac{87}{142}\right)\) \(e\left(\frac{139}{284}\right)\) \(e\left(\frac{16}{71}\right)\) \(e\left(\frac{62}{71}\right)\) \(e\left(\frac{29}{284}\right)\) \(e\left(\frac{93}{142}\right)\) \(e\left(\frac{119}{142}\right)\) \(e\left(\frac{139}{142}\right)\) \(e\left(\frac{69}{142}\right)\) \(e\left(\frac{189}{284}\right)\)