LMFDB - Dirichlet character orbit 4729.k

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(4729, base_ring=CyclotomicField(1182)) M = H._module chi = DirichletCharacter(H, M([994])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(14,4729)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$4729$
Conductor:	$4729$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$591$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	yes	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)

Related number fields

Field of values:	$\Q(\zeta_{591})$
Fixed field:	Number field defined by a degree 591 polynomial (not computed)

First 31 of 392 characters in Galois orbit

Character	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{4729}(14,\cdot)$	$1$	$1$	$e\left(\frac{83}{197}\right)$	$e\left(\frac{58}{197}\right)$	$e\left(\frac{166}{197}\right)$	$e\left(\frac{524}{591}\right)$	$e\left(\frac{141}{197}\right)$	$e\left(\frac{110}{591}\right)$	$e\left(\frac{52}{197}\right)$	$e\left(\frac{116}{197}\right)$	$e\left(\frac{182}{591}\right)$	$e\left(\frac{136}{197}\right)$
$\chi_{4729}(19,\cdot)$	$1$	$1$	$e\left(\frac{82}{197}\right)$	$e\left(\frac{138}{197}\right)$	$e\left(\frac{164}{197}\right)$	$e\left(\frac{221}{591}\right)$	$e\left(\frac{23}{197}\right)$	$e\left(\frac{581}{591}\right)$	$e\left(\frac{49}{197}\right)$	$e\left(\frac{79}{197}\right)$	$e\left(\frac{467}{591}\right)$	$e\left(\frac{113}{197}\right)$
$\chi_{4729}(21,\cdot)$	$1$	$1$	$e\left(\frac{92}{197}\right)$	$e\left(\frac{126}{197}\right)$	$e\left(\frac{184}{197}\right)$	$e\left(\frac{296}{591}\right)$	$e\left(\frac{21}{197}\right)$	$e\left(\frac{8}{591}\right)$	$e\left(\frac{79}{197}\right)$	$e\left(\frac{55}{197}\right)$	$e\left(\frac{572}{591}\right)$	$e\left(\frac{146}{197}\right)$
$\chi_{4729}(35,\cdot)$	$1$	$1$	$e\left(\frac{50}{197}\right)$	$e\left(\frac{137}{197}\right)$	$e\left(\frac{100}{197}\right)$	$e\left(\frac{178}{591}\right)$	$e\left(\frac{187}{197}\right)$	$e\left(\frac{484}{591}\right)$	$e\left(\frac{150}{197}\right)$	$e\left(\frac{77}{197}\right)$	$e\left(\frac{328}{591}\right)$	$e\left(\frac{165}{197}\right)$
$\chi_{4729}(37,\cdot)$	$1$	$1$	$e\left(\frac{62}{197}\right)$	$e\left(\frac{162}{197}\right)$	$e\left(\frac{124}{197}\right)$	$e\left(\frac{71}{591}\right)$	$e\left(\frac{27}{197}\right)$	$e\left(\frac{545}{591}\right)$	$e\left(\frac{186}{197}\right)$	$e\left(\frac{127}{197}\right)$	$e\left(\frac{257}{591}\right)$	$e\left(\frac{47}{197}\right)$
$\chi_{4729}(40,\cdot)$	$1$	$1$	$e\left(\frac{76}{197}\right)$	$e\left(\frac{27}{197}\right)$	$e\left(\frac{152}{197}\right)$	$e\left(\frac{176}{591}\right)$	$e\left(\frac{103}{197}\right)$	$e\left(\frac{452}{591}\right)$	$e\left(\frac{31}{197}\right)$	$e\left(\frac{54}{197}\right)$	$e\left(\frac{404}{591}\right)$	$e\left(\frac{172}{197}\right)$
$\chi_{4729}(52,\cdot)$	$1$	$1$	$e\left(\frac{116}{197}\right)$	$e\left(\frac{176}{197}\right)$	$e\left(\frac{35}{197}\right)$	$e\left(\frac{476}{591}\right)$	$e\left(\frac{95}{197}\right)$	$e\left(\frac{524}{591}\right)$	$e\left(\frac{151}{197}\right)$	$e\left(\frac{155}{197}\right)$	$e\left(\frac{233}{591}\right)$	$e\left(\frac{107}{197}\right)$
$\chi_{4729}(60,\cdot)$	$1$	$1$	$e\left(\frac{85}{197}\right)$	$e\left(\frac{95}{197}\right)$	$e\left(\frac{170}{197}\right)$	$e\left(\frac{539}{591}\right)$	$e\left(\frac{180}{197}\right)$	$e\left(\frac{350}{591}\right)$	$e\left(\frac{58}{197}\right)$	$e\left(\frac{190}{197}\right)$	$e\left(\frac{203}{591}\right)$	$e\left(\frac{182}{197}\right)$
$\chi_{4729}(67,\cdot)$	$1$	$1$	$e\left(\frac{119}{197}\right)$	$e\left(\frac{133}{197}\right)$	$e\left(\frac{41}{197}\right)$	$e\left(\frac{400}{591}\right)$	$e\left(\frac{55}{197}\right)$	$e\left(\frac{490}{591}\right)$	$e\left(\frac{160}{197}\right)$	$e\left(\frac{69}{197}\right)$	$e\left(\frac{166}{591}\right)$	$e\left(\frac{176}{197}\right)$
$\chi_{4729}(78,\cdot)$	$1$	$1$	$e\left(\frac{125}{197}\right)$	$e\left(\frac{47}{197}\right)$	$e\left(\frac{53}{197}\right)$	$e\left(\frac{248}{591}\right)$	$e\left(\frac{172}{197}\right)$	$e\left(\frac{422}{591}\right)$	$e\left(\frac{178}{197}\right)$	$e\left(\frac{94}{197}\right)$	$e\left(\frac{32}{591}\right)$	$e\left(\frac{117}{197}\right)$
$\chi_{4729}(83,\cdot)$	$1$	$1$	$e\left(\frac{106}{197}\right)$	$e\left(\frac{188}{197}\right)$	$e\left(\frac{15}{197}\right)$	$e\left(\frac{7}{591}\right)$	$e\left(\frac{97}{197}\right)$	$e\left(\frac{112}{591}\right)$	$e\left(\frac{121}{197}\right)$	$e\left(\frac{179}{197}\right)$	$e\left(\frac{325}{591}\right)$	$e\left(\frac{74}{197}\right)$
$\chi_{4729}(90,\cdot)$	$1$	$1$	$e\left(\frac{94}{197}\right)$	$e\left(\frac{163}{197}\right)$	$e\left(\frac{188}{197}\right)$	$e\left(\frac{311}{591}\right)$	$e\left(\frac{60}{197}\right)$	$e\left(\frac{248}{591}\right)$	$e\left(\frac{85}{197}\right)$	$e\left(\frac{129}{197}\right)$	$e\left(\frac{2}{591}\right)$	$e\left(\frac{192}{197}\right)$
$\chi_{4729}(100,\cdot)$	$1$	$1$	$e\left(\frac{43}{197}\right)$	$e\left(\frac{106}{197}\right)$	$e\left(\frac{86}{197}\right)$	$e\left(\frac{421}{591}\right)$	$e\left(\frac{149}{197}\right)$	$e\left(\frac{235}{591}\right)$	$e\left(\frac{129}{197}\right)$	$e\left(\frac{15}{197}\right)$	$e\left(\frac{550}{591}\right)$	$e\left(\frac{4}{197}\right)$
$\chi_{4729}(117,\cdot)$	$1$	$1$	$e\left(\frac{134}{197}\right)$	$e\left(\frac{115}{197}\right)$	$e\left(\frac{71}{197}\right)$	$e\left(\frac{20}{591}\right)$	$e\left(\frac{52}{197}\right)$	$e\left(\frac{320}{591}\right)$	$e\left(\frac{8}{197}\right)$	$e\left(\frac{33}{197}\right)$	$e\left(\frac{422}{591}\right)$	$e\left(\frac{127}{197}\right)$
$\chi_{4729}(118,\cdot)$	$1$	$1$	$e\left(\frac{95}{197}\right)$	$e\left(\frac{83}{197}\right)$	$e\left(\frac{190}{197}\right)$	$e\left(\frac{220}{591}\right)$	$e\left(\frac{178}{197}\right)$	$e\left(\frac{565}{591}\right)$	$e\left(\frac{88}{197}\right)$	$e\left(\frac{166}{197}\right)$	$e\left(\frac{505}{591}\right)$	$e\left(\frac{18}{197}\right)$
$\chi_{4729}(130,\cdot)$	$1$	$1$	$e\left(\frac{83}{197}\right)$	$e\left(\frac{58}{197}\right)$	$e\left(\frac{166}{197}\right)$	$e\left(\frac{130}{591}\right)$	$e\left(\frac{141}{197}\right)$	$e\left(\frac{307}{591}\right)$	$e\left(\frac{52}{197}\right)$	$e\left(\frac{116}{197}\right)$	$e\left(\frac{379}{591}\right)$	$e\left(\frac{136}{197}\right)$
$\chi_{4729}(131,\cdot)$	$1$	$1$	$e\left(\frac{33}{197}\right)$	$e\left(\frac{118}{197}\right)$	$e\left(\frac{66}{197}\right)$	$e\left(\frac{149}{591}\right)$	$e\left(\frac{151}{197}\right)$	$e\left(\frac{20}{591}\right)$	$e\left(\frac{99}{197}\right)$	$e\left(\frac{39}{197}\right)$	$e\left(\frac{248}{591}\right)$	$e\left(\frac{168}{197}\right)$
$\chi_{4729}(135,\cdot)$	$1$	$1$	$e\left(\frac{103}{197}\right)$	$e\left(\frac{34}{197}\right)$	$e\left(\frac{9}{197}\right)$	$e\left(\frac{83}{591}\right)$	$e\left(\frac{137}{197}\right)$	$e\left(\frac{146}{591}\right)$	$e\left(\frac{112}{197}\right)$	$e\left(\frac{68}{197}\right)$	$e\left(\frac{392}{591}\right)$	$e\left(\frac{5}{197}\right)$
$\chi_{4729}(150,\cdot)$	$1$	$1$	$e\left(\frac{52}{197}\right)$	$e\left(\frac{174}{197}\right)$	$e\left(\frac{104}{197}\right)$	$e\left(\frac{193}{591}\right)$	$e\left(\frac{29}{197}\right)$	$e\left(\frac{133}{591}\right)$	$e\left(\frac{156}{197}\right)$	$e\left(\frac{151}{197}\right)$	$e\left(\frac{349}{591}\right)$	$e\left(\frac{14}{197}\right)$
$\chi_{4729}(169,\cdot)$	$1$	$1$	$e\left(\frac{123}{197}\right)$	$e\left(\frac{10}{197}\right)$	$e\left(\frac{49}{197}\right)$	$e\left(\frac{430}{591}\right)$	$e\left(\frac{133}{197}\right)$	$e\left(\frac{379}{591}\right)$	$e\left(\frac{172}{197}\right)$	$e\left(\frac{20}{197}\right)$	$e\left(\frac{208}{591}\right)$	$e\left(\frac{71}{197}\right)$
$\chi_{4729}(177,\cdot)$	$1$	$1$	$e\left(\frac{104}{197}\right)$	$e\left(\frac{151}{197}\right)$	$e\left(\frac{11}{197}\right)$	$e\left(\frac{583}{591}\right)$	$e\left(\frac{58}{197}\right)$	$e\left(\frac{463}{591}\right)$	$e\left(\frac{115}{197}\right)$	$e\left(\frac{105}{197}\right)$	$e\left(\frac{304}{591}\right)$	$e\left(\frac{28}{197}\right)$
$\chi_{4729}(187,\cdot)$	$1$	$1$	$e\left(\frac{49}{197}\right)$	$e\left(\frac{20}{197}\right)$	$e\left(\frac{98}{197}\right)$	$e\left(\frac{269}{591}\right)$	$e\left(\frac{69}{197}\right)$	$e\left(\frac{167}{591}\right)$	$e\left(\frac{147}{197}\right)$	$e\left(\frac{40}{197}\right)$	$e\left(\frac{416}{591}\right)$	$e\left(\frac{142}{197}\right)$
$\chi_{4729}(193,\cdot)$	$1$	$1$	$e\left(\frac{184}{197}\right)$	$e\left(\frac{55}{197}\right)$	$e\left(\frac{171}{197}\right)$	$e\left(\frac{395}{591}\right)$	$e\left(\frac{42}{197}\right)$	$e\left(\frac{410}{591}\right)$	$e\left(\frac{158}{197}\right)$	$e\left(\frac{110}{197}\right)$	$e\left(\frac{356}{591}\right)$	$e\left(\frac{95}{197}\right)$
$\chi_{4729}(195,\cdot)$	$1$	$1$	$e\left(\frac{92}{197}\right)$	$e\left(\frac{126}{197}\right)$	$e\left(\frac{184}{197}\right)$	$e\left(\frac{493}{591}\right)$	$e\left(\frac{21}{197}\right)$	$e\left(\frac{205}{591}\right)$	$e\left(\frac{79}{197}\right)$	$e\left(\frac{55}{197}\right)$	$e\left(\frac{178}{591}\right)$	$e\left(\frac{146}{197}\right)$
$\chi_{4729}(196,\cdot)$	$1$	$1$	$e\left(\frac{166}{197}\right)$	$e\left(\frac{116}{197}\right)$	$e\left(\frac{135}{197}\right)$	$e\left(\frac{457}{591}\right)$	$e\left(\frac{85}{197}\right)$	$e\left(\frac{220}{591}\right)$	$e\left(\frac{104}{197}\right)$	$e\left(\frac{35}{197}\right)$	$e\left(\frac{364}{591}\right)$	$e\left(\frac{75}{197}\right)$
$\chi_{4729}(224,\cdot)$	$1$	$1$	$e\left(\frac{192}{197}\right)$	$e\left(\frac{6}{197}\right)$	$e\left(\frac{187}{197}\right)$	$e\left(\frac{455}{591}\right)$	$e\left(\frac{1}{197}\right)$	$e\left(\frac{188}{591}\right)$	$e\left(\frac{182}{197}\right)$	$e\left(\frac{12}{197}\right)$	$e\left(\frac{440}{591}\right)$	$e\left(\frac{82}{197}\right)$
$\chi_{4729}(225,\cdot)$	$1$	$1$	$e\left(\frac{61}{197}\right)$	$e\left(\frac{45}{197}\right)$	$e\left(\frac{122}{197}\right)$	$e\left(\frac{556}{591}\right)$	$e\left(\frac{106}{197}\right)$	$e\left(\frac{31}{591}\right)$	$e\left(\frac{183}{197}\right)$	$e\left(\frac{90}{197}\right)$	$e\left(\frac{148}{591}\right)$	$e\left(\frac{24}{197}\right)$
$\chi_{4729}(266,\cdot)$	$1$	$1$	$e\left(\frac{165}{197}\right)$	$e\left(\frac{196}{197}\right)$	$e\left(\frac{133}{197}\right)$	$e\left(\frac{154}{591}\right)$	$e\left(\frac{164}{197}\right)$	$e\left(\frac{100}{591}\right)$	$e\left(\frac{101}{197}\right)$	$e\left(\frac{195}{197}\right)$	$e\left(\frac{58}{591}\right)$	$e\left(\frac{52}{197}\right)$
$\chi_{4729}(294,\cdot)$	$1$	$1$	$e\left(\frac{175}{197}\right)$	$e\left(\frac{184}{197}\right)$	$e\left(\frac{153}{197}\right)$	$e\left(\frac{229}{591}\right)$	$e\left(\frac{162}{197}\right)$	$e\left(\frac{118}{591}\right)$	$e\left(\frac{131}{197}\right)$	$e\left(\frac{171}{197}\right)$	$e\left(\frac{163}{591}\right)$	$e\left(\frac{85}{197}\right)$
$\chi_{4729}(304,\cdot)$	$1$	$1$	$e\left(\frac{191}{197}\right)$	$e\left(\frac{86}{197}\right)$	$e\left(\frac{185}{197}\right)$	$e\left(\frac{152}{591}\right)$	$e\left(\frac{80}{197}\right)$	$e\left(\frac{68}{591}\right)$	$e\left(\frac{179}{197}\right)$	$e\left(\frac{172}{197}\right)$	$e\left(\frac{134}{591}\right)$	$e\left(\frac{59}{197}\right)$
$\chi_{4729}(336,\cdot)$	$1$	$1$	$e\left(\frac{4}{197}\right)$	$e\left(\frac{74}{197}\right)$	$e\left(\frac{8}{197}\right)$	$e\left(\frac{227}{591}\right)$	$e\left(\frac{78}{197}\right)$	$e\left(\frac{86}{591}\right)$	$e\left(\frac{12}{197}\right)$	$e\left(\frac{148}{197}\right)$	$e\left(\frac{239}{591}\right)$	$e\left(\frac{92}{197}\right)$

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Character	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\(\chi_{4729}(14,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{83}{197}\right)\)	\(e\left(\frac{58}{197}\right)\)	\(e\left(\frac{166}{197}\right)\)	\(e\left(\frac{524}{591}\right)\)	\(e\left(\frac{141}{197}\right)\)	\(e\left(\frac{110}{591}\right)\)	\(e\left(\frac{52}{197}\right)\)	\(e\left(\frac{116}{197}\right)\)	\(e\left(\frac{182}{591}\right)\)	\(e\left(\frac{136}{197}\right)\)
\(\chi_{4729}(19,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{82}{197}\right)\)	\(e\left(\frac{138}{197}\right)\)	\(e\left(\frac{164}{197}\right)\)	\(e\left(\frac{221}{591}\right)\)	\(e\left(\frac{23}{197}\right)\)	\(e\left(\frac{581}{591}\right)\)	\(e\left(\frac{49}{197}\right)\)	\(e\left(\frac{79}{197}\right)\)	\(e\left(\frac{467}{591}\right)\)	\(e\left(\frac{113}{197}\right)\)
\(\chi_{4729}(21,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{92}{197}\right)\)	\(e\left(\frac{126}{197}\right)\)	\(e\left(\frac{184}{197}\right)\)	\(e\left(\frac{296}{591}\right)\)	\(e\left(\frac{21}{197}\right)\)	\(e\left(\frac{8}{591}\right)\)	\(e\left(\frac{79}{197}\right)\)	\(e\left(\frac{55}{197}\right)\)	\(e\left(\frac{572}{591}\right)\)	\(e\left(\frac{146}{197}\right)\)
\(\chi_{4729}(35,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{50}{197}\right)\)	\(e\left(\frac{137}{197}\right)\)	\(e\left(\frac{100}{197}\right)\)	\(e\left(\frac{178}{591}\right)\)	\(e\left(\frac{187}{197}\right)\)	\(e\left(\frac{484}{591}\right)\)	\(e\left(\frac{150}{197}\right)\)	\(e\left(\frac{77}{197}\right)\)	\(e\left(\frac{328}{591}\right)\)	\(e\left(\frac{165}{197}\right)\)
\(\chi_{4729}(37,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{62}{197}\right)\)	\(e\left(\frac{162}{197}\right)\)	\(e\left(\frac{124}{197}\right)\)	\(e\left(\frac{71}{591}\right)\)	\(e\left(\frac{27}{197}\right)\)	\(e\left(\frac{545}{591}\right)\)	\(e\left(\frac{186}{197}\right)\)	\(e\left(\frac{127}{197}\right)\)	\(e\left(\frac{257}{591}\right)\)	\(e\left(\frac{47}{197}\right)\)
\(\chi_{4729}(40,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{76}{197}\right)\)	\(e\left(\frac{27}{197}\right)\)	\(e\left(\frac{152}{197}\right)\)	\(e\left(\frac{176}{591}\right)\)	\(e\left(\frac{103}{197}\right)\)	\(e\left(\frac{452}{591}\right)\)	\(e\left(\frac{31}{197}\right)\)	\(e\left(\frac{54}{197}\right)\)	\(e\left(\frac{404}{591}\right)\)	\(e\left(\frac{172}{197}\right)\)
\(\chi_{4729}(52,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{116}{197}\right)\)	\(e\left(\frac{176}{197}\right)\)	\(e\left(\frac{35}{197}\right)\)	\(e\left(\frac{476}{591}\right)\)	\(e\left(\frac{95}{197}\right)\)	\(e\left(\frac{524}{591}\right)\)	\(e\left(\frac{151}{197}\right)\)	\(e\left(\frac{155}{197}\right)\)	\(e\left(\frac{233}{591}\right)\)	\(e\left(\frac{107}{197}\right)\)
\(\chi_{4729}(60,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{85}{197}\right)\)	\(e\left(\frac{95}{197}\right)\)	\(e\left(\frac{170}{197}\right)\)	\(e\left(\frac{539}{591}\right)\)	\(e\left(\frac{180}{197}\right)\)	\(e\left(\frac{350}{591}\right)\)	\(e\left(\frac{58}{197}\right)\)	\(e\left(\frac{190}{197}\right)\)	\(e\left(\frac{203}{591}\right)\)	\(e\left(\frac{182}{197}\right)\)
\(\chi_{4729}(67,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{119}{197}\right)\)	\(e\left(\frac{133}{197}\right)\)	\(e\left(\frac{41}{197}\right)\)	\(e\left(\frac{400}{591}\right)\)	\(e\left(\frac{55}{197}\right)\)	\(e\left(\frac{490}{591}\right)\)	\(e\left(\frac{160}{197}\right)\)	\(e\left(\frac{69}{197}\right)\)	\(e\left(\frac{166}{591}\right)\)	\(e\left(\frac{176}{197}\right)\)
\(\chi_{4729}(78,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{125}{197}\right)\)	\(e\left(\frac{47}{197}\right)\)	\(e\left(\frac{53}{197}\right)\)	\(e\left(\frac{248}{591}\right)\)	\(e\left(\frac{172}{197}\right)\)	\(e\left(\frac{422}{591}\right)\)	\(e\left(\frac{178}{197}\right)\)	\(e\left(\frac{94}{197}\right)\)	\(e\left(\frac{32}{591}\right)\)	\(e\left(\frac{117}{197}\right)\)
\(\chi_{4729}(83,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{106}{197}\right)\)	\(e\left(\frac{188}{197}\right)\)	\(e\left(\frac{15}{197}\right)\)	\(e\left(\frac{7}{591}\right)\)	\(e\left(\frac{97}{197}\right)\)	\(e\left(\frac{112}{591}\right)\)	\(e\left(\frac{121}{197}\right)\)	\(e\left(\frac{179}{197}\right)\)	\(e\left(\frac{325}{591}\right)\)	\(e\left(\frac{74}{197}\right)\)
\(\chi_{4729}(90,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{94}{197}\right)\)	\(e\left(\frac{163}{197}\right)\)	\(e\left(\frac{188}{197}\right)\)	\(e\left(\frac{311}{591}\right)\)	\(e\left(\frac{60}{197}\right)\)	\(e\left(\frac{248}{591}\right)\)	\(e\left(\frac{85}{197}\right)\)	\(e\left(\frac{129}{197}\right)\)	\(e\left(\frac{2}{591}\right)\)	\(e\left(\frac{192}{197}\right)\)
\(\chi_{4729}(100,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{197}\right)\)	\(e\left(\frac{106}{197}\right)\)	\(e\left(\frac{86}{197}\right)\)	\(e\left(\frac{421}{591}\right)\)	\(e\left(\frac{149}{197}\right)\)	\(e\left(\frac{235}{591}\right)\)	\(e\left(\frac{129}{197}\right)\)	\(e\left(\frac{15}{197}\right)\)	\(e\left(\frac{550}{591}\right)\)	\(e\left(\frac{4}{197}\right)\)
\(\chi_{4729}(117,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{134}{197}\right)\)	\(e\left(\frac{115}{197}\right)\)	\(e\left(\frac{71}{197}\right)\)	\(e\left(\frac{20}{591}\right)\)	\(e\left(\frac{52}{197}\right)\)	\(e\left(\frac{320}{591}\right)\)	\(e\left(\frac{8}{197}\right)\)	\(e\left(\frac{33}{197}\right)\)	\(e\left(\frac{422}{591}\right)\)	\(e\left(\frac{127}{197}\right)\)
\(\chi_{4729}(118,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{95}{197}\right)\)	\(e\left(\frac{83}{197}\right)\)	\(e\left(\frac{190}{197}\right)\)	\(e\left(\frac{220}{591}\right)\)	\(e\left(\frac{178}{197}\right)\)	\(e\left(\frac{565}{591}\right)\)	\(e\left(\frac{88}{197}\right)\)	\(e\left(\frac{166}{197}\right)\)	\(e\left(\frac{505}{591}\right)\)	\(e\left(\frac{18}{197}\right)\)
\(\chi_{4729}(130,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{83}{197}\right)\)	\(e\left(\frac{58}{197}\right)\)	\(e\left(\frac{166}{197}\right)\)	\(e\left(\frac{130}{591}\right)\)	\(e\left(\frac{141}{197}\right)\)	\(e\left(\frac{307}{591}\right)\)	\(e\left(\frac{52}{197}\right)\)	\(e\left(\frac{116}{197}\right)\)	\(e\left(\frac{379}{591}\right)\)	\(e\left(\frac{136}{197}\right)\)
\(\chi_{4729}(131,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{33}{197}\right)\)	\(e\left(\frac{118}{197}\right)\)	\(e\left(\frac{66}{197}\right)\)	\(e\left(\frac{149}{591}\right)\)	\(e\left(\frac{151}{197}\right)\)	\(e\left(\frac{20}{591}\right)\)	\(e\left(\frac{99}{197}\right)\)	\(e\left(\frac{39}{197}\right)\)	\(e\left(\frac{248}{591}\right)\)	\(e\left(\frac{168}{197}\right)\)
\(\chi_{4729}(135,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{103}{197}\right)\)	\(e\left(\frac{34}{197}\right)\)	\(e\left(\frac{9}{197}\right)\)	\(e\left(\frac{83}{591}\right)\)	\(e\left(\frac{137}{197}\right)\)	\(e\left(\frac{146}{591}\right)\)	\(e\left(\frac{112}{197}\right)\)	\(e\left(\frac{68}{197}\right)\)	\(e\left(\frac{392}{591}\right)\)	\(e\left(\frac{5}{197}\right)\)
\(\chi_{4729}(150,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{52}{197}\right)\)	\(e\left(\frac{174}{197}\right)\)	\(e\left(\frac{104}{197}\right)\)	\(e\left(\frac{193}{591}\right)\)	\(e\left(\frac{29}{197}\right)\)	\(e\left(\frac{133}{591}\right)\)	\(e\left(\frac{156}{197}\right)\)	\(e\left(\frac{151}{197}\right)\)	\(e\left(\frac{349}{591}\right)\)	\(e\left(\frac{14}{197}\right)\)
\(\chi_{4729}(169,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{123}{197}\right)\)	\(e\left(\frac{10}{197}\right)\)	\(e\left(\frac{49}{197}\right)\)	\(e\left(\frac{430}{591}\right)\)	\(e\left(\frac{133}{197}\right)\)	\(e\left(\frac{379}{591}\right)\)	\(e\left(\frac{172}{197}\right)\)	\(e\left(\frac{20}{197}\right)\)	\(e\left(\frac{208}{591}\right)\)	\(e\left(\frac{71}{197}\right)\)
\(\chi_{4729}(177,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{104}{197}\right)\)	\(e\left(\frac{151}{197}\right)\)	\(e\left(\frac{11}{197}\right)\)	\(e\left(\frac{583}{591}\right)\)	\(e\left(\frac{58}{197}\right)\)	\(e\left(\frac{463}{591}\right)\)	\(e\left(\frac{115}{197}\right)\)	\(e\left(\frac{105}{197}\right)\)	\(e\left(\frac{304}{591}\right)\)	\(e\left(\frac{28}{197}\right)\)
\(\chi_{4729}(187,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{49}{197}\right)\)	\(e\left(\frac{20}{197}\right)\)	\(e\left(\frac{98}{197}\right)\)	\(e\left(\frac{269}{591}\right)\)	\(e\left(\frac{69}{197}\right)\)	\(e\left(\frac{167}{591}\right)\)	\(e\left(\frac{147}{197}\right)\)	\(e\left(\frac{40}{197}\right)\)	\(e\left(\frac{416}{591}\right)\)	\(e\left(\frac{142}{197}\right)\)
\(\chi_{4729}(193,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{184}{197}\right)\)	\(e\left(\frac{55}{197}\right)\)	\(e\left(\frac{171}{197}\right)\)	\(e\left(\frac{395}{591}\right)\)	\(e\left(\frac{42}{197}\right)\)	\(e\left(\frac{410}{591}\right)\)	\(e\left(\frac{158}{197}\right)\)	\(e\left(\frac{110}{197}\right)\)	\(e\left(\frac{356}{591}\right)\)	\(e\left(\frac{95}{197}\right)\)
\(\chi_{4729}(195,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{92}{197}\right)\)	\(e\left(\frac{126}{197}\right)\)	\(e\left(\frac{184}{197}\right)\)	\(e\left(\frac{493}{591}\right)\)	\(e\left(\frac{21}{197}\right)\)	\(e\left(\frac{205}{591}\right)\)	\(e\left(\frac{79}{197}\right)\)	\(e\left(\frac{55}{197}\right)\)	\(e\left(\frac{178}{591}\right)\)	\(e\left(\frac{146}{197}\right)\)
\(\chi_{4729}(196,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{166}{197}\right)\)	\(e\left(\frac{116}{197}\right)\)	\(e\left(\frac{135}{197}\right)\)	\(e\left(\frac{457}{591}\right)\)	\(e\left(\frac{85}{197}\right)\)	\(e\left(\frac{220}{591}\right)\)	\(e\left(\frac{104}{197}\right)\)	\(e\left(\frac{35}{197}\right)\)	\(e\left(\frac{364}{591}\right)\)	\(e\left(\frac{75}{197}\right)\)
\(\chi_{4729}(224,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{192}{197}\right)\)	\(e\left(\frac{6}{197}\right)\)	\(e\left(\frac{187}{197}\right)\)	\(e\left(\frac{455}{591}\right)\)	\(e\left(\frac{1}{197}\right)\)	\(e\left(\frac{188}{591}\right)\)	\(e\left(\frac{182}{197}\right)\)	\(e\left(\frac{12}{197}\right)\)	\(e\left(\frac{440}{591}\right)\)	\(e\left(\frac{82}{197}\right)\)
\(\chi_{4729}(225,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{61}{197}\right)\)	\(e\left(\frac{45}{197}\right)\)	\(e\left(\frac{122}{197}\right)\)	\(e\left(\frac{556}{591}\right)\)	\(e\left(\frac{106}{197}\right)\)	\(e\left(\frac{31}{591}\right)\)	\(e\left(\frac{183}{197}\right)\)	\(e\left(\frac{90}{197}\right)\)	\(e\left(\frac{148}{591}\right)\)	\(e\left(\frac{24}{197}\right)\)
\(\chi_{4729}(266,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{165}{197}\right)\)	\(e\left(\frac{196}{197}\right)\)	\(e\left(\frac{133}{197}\right)\)	\(e\left(\frac{154}{591}\right)\)	\(e\left(\frac{164}{197}\right)\)	\(e\left(\frac{100}{591}\right)\)	\(e\left(\frac{101}{197}\right)\)	\(e\left(\frac{195}{197}\right)\)	\(e\left(\frac{58}{591}\right)\)	\(e\left(\frac{52}{197}\right)\)
\(\chi_{4729}(294,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{175}{197}\right)\)	\(e\left(\frac{184}{197}\right)\)	\(e\left(\frac{153}{197}\right)\)	\(e\left(\frac{229}{591}\right)\)	\(e\left(\frac{162}{197}\right)\)	\(e\left(\frac{118}{591}\right)\)	\(e\left(\frac{131}{197}\right)\)	\(e\left(\frac{171}{197}\right)\)	\(e\left(\frac{163}{591}\right)\)	\(e\left(\frac{85}{197}\right)\)
\(\chi_{4729}(304,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{191}{197}\right)\)	\(e\left(\frac{86}{197}\right)\)	\(e\left(\frac{185}{197}\right)\)	\(e\left(\frac{152}{591}\right)\)	\(e\left(\frac{80}{197}\right)\)	\(e\left(\frac{68}{591}\right)\)	\(e\left(\frac{179}{197}\right)\)	\(e\left(\frac{172}{197}\right)\)	\(e\left(\frac{134}{591}\right)\)	\(e\left(\frac{59}{197}\right)\)
\(\chi_{4729}(336,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{197}\right)\)	\(e\left(\frac{74}{197}\right)\)	\(e\left(\frac{8}{197}\right)\)	\(e\left(\frac{227}{591}\right)\)	\(e\left(\frac{78}{197}\right)\)	\(e\left(\frac{86}{591}\right)\)	\(e\left(\frac{12}{197}\right)\)	\(e\left(\frac{148}{197}\right)\)	\(e\left(\frac{239}{591}\right)\)	\(e\left(\frac{92}{197}\right)\)

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First 31 of 392 characters in Galois orbit

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	4729.k
Modulus	$4729$
Conductor	$4729$
Order	$591$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(4729\)
Conductor:	\(4729\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(591\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	yes	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)