LMFDB - Dirichlet character orbit 4729.j

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(4729, base_ring=CyclotomicField(394)) M = H._module chi = DirichletCharacter(H, M([53])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(4,4729)) 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:	$394$	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:	$\Q(\zeta_{197})$
Fixed field:	Number field defined by a degree 394 polynomial (not computed)

First 31 of 196 characters in Galois orbit

Character	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{4729}(4,\cdot)$	$1$	$1$	$e\left(\frac{153}{197}\right)$	$e\left(\frac{171}{197}\right)$	$e\left(\frac{109}{197}\right)$	$e\left(\frac{87}{197}\right)$	$e\left(\frac{127}{197}\right)$	$e\left(\frac{13}{197}\right)$	$e\left(\frac{65}{197}\right)$	$e\left(\frac{145}{197}\right)$	$e\left(\frac{43}{197}\right)$	$e\left(\frac{143}{394}\right)$
$\chi_{4729}(6,\cdot)$	$1$	$1$	$e\left(\frac{162}{197}\right)$	$e\left(\frac{42}{197}\right)$	$e\left(\frac{127}{197}\right)$	$e\left(\frac{11}{197}\right)$	$e\left(\frac{7}{197}\right)$	$e\left(\frac{176}{197}\right)$	$e\left(\frac{92}{197}\right)$	$e\left(\frac{84}{197}\right)$	$e\left(\frac{173}{197}\right)$	$e\left(\frac{163}{394}\right)$
$\chi_{4729}(9,\cdot)$	$1$	$1$	$e\left(\frac{171}{197}\right)$	$e\left(\frac{110}{197}\right)$	$e\left(\frac{145}{197}\right)$	$e\left(\frac{132}{197}\right)$	$e\left(\frac{84}{197}\right)$	$e\left(\frac{142}{197}\right)$	$e\left(\frac{119}{197}\right)$	$e\left(\frac{23}{197}\right)$	$e\left(\frac{106}{197}\right)$	$e\left(\frac{183}{394}\right)$
$\chi_{4729}(64,\cdot)$	$1$	$1$	$e\left(\frac{65}{197}\right)$	$e\left(\frac{119}{197}\right)$	$e\left(\frac{130}{197}\right)$	$e\left(\frac{64}{197}\right)$	$e\left(\frac{184}{197}\right)$	$e\left(\frac{39}{197}\right)$	$e\left(\frac{195}{197}\right)$	$e\left(\frac{41}{197}\right)$	$e\left(\frac{129}{197}\right)$	$e\left(\frac{35}{394}\right)$
$\chi_{4729}(96,\cdot)$	$1$	$1$	$e\left(\frac{74}{197}\right)$	$e\left(\frac{187}{197}\right)$	$e\left(\frac{148}{197}\right)$	$e\left(\frac{185}{197}\right)$	$e\left(\frac{64}{197}\right)$	$e\left(\frac{5}{197}\right)$	$e\left(\frac{25}{197}\right)$	$e\left(\frac{177}{197}\right)$	$e\left(\frac{62}{197}\right)$	$e\left(\frac{55}{394}\right)$
$\chi_{4729}(144,\cdot)$	$1$	$1$	$e\left(\frac{83}{197}\right)$	$e\left(\frac{58}{197}\right)$	$e\left(\frac{166}{197}\right)$	$e\left(\frac{109}{197}\right)$	$e\left(\frac{141}{197}\right)$	$e\left(\frac{168}{197}\right)$	$e\left(\frac{52}{197}\right)$	$e\left(\frac{116}{197}\right)$	$e\left(\frac{192}{197}\right)$	$e\left(\frac{75}{394}\right)$
$\chi_{4729}(197,\cdot)$	$1$	$1$	$e\left(\frac{79}{197}\right)$	$e\left(\frac{181}{197}\right)$	$e\left(\frac{158}{197}\right)$	$e\left(\frac{99}{197}\right)$	$e\left(\frac{63}{197}\right)$	$e\left(\frac{8}{197}\right)$	$e\left(\frac{40}{197}\right)$	$e\left(\frac{165}{197}\right)$	$e\left(\frac{178}{197}\right)$	$e\left(\frac{285}{394}\right)$
$\chi_{4729}(216,\cdot)$	$1$	$1$	$e\left(\frac{92}{197}\right)$	$e\left(\frac{126}{197}\right)$	$e\left(\frac{184}{197}\right)$	$e\left(\frac{33}{197}\right)$	$e\left(\frac{21}{197}\right)$	$e\left(\frac{134}{197}\right)$	$e\left(\frac{79}{197}\right)$	$e\left(\frac{55}{197}\right)$	$e\left(\frac{125}{197}\right)$	$e\left(\frac{95}{394}\right)$
$\chi_{4729}(242,\cdot)$	$1$	$1$	$e\left(\frac{148}{197}\right)$	$e\left(\frac{177}{197}\right)$	$e\left(\frac{99}{197}\right)$	$e\left(\frac{173}{197}\right)$	$e\left(\frac{128}{197}\right)$	$e\left(\frac{10}{197}\right)$	$e\left(\frac{50}{197}\right)$	$e\left(\frac{157}{197}\right)$	$e\left(\frac{124}{197}\right)$	$e\left(\frac{307}{394}\right)$
$\chi_{4729}(254,\cdot)$	$1$	$1$	$e\left(\frac{23}{197}\right)$	$e\left(\frac{130}{197}\right)$	$e\left(\frac{46}{197}\right)$	$e\left(\frac{156}{197}\right)$	$e\left(\frac{153}{197}\right)$	$e\left(\frac{132}{197}\right)$	$e\left(\frac{69}{197}\right)$	$e\left(\frac{63}{197}\right)$	$e\left(\frac{179}{197}\right)$	$e\left(\frac{73}{394}\right)$
$\chi_{4729}(324,\cdot)$	$1$	$1$	$e\left(\frac{101}{197}\right)$	$e\left(\frac{194}{197}\right)$	$e\left(\frac{5}{197}\right)$	$e\left(\frac{154}{197}\right)$	$e\left(\frac{98}{197}\right)$	$e\left(\frac{100}{197}\right)$	$e\left(\frac{106}{197}\right)$	$e\left(\frac{191}{197}\right)$	$e\left(\frac{58}{197}\right)$	$e\left(\frac{115}{394}\right)$
$\chi_{4729}(350,\cdot)$	$1$	$1$	$e\left(\frac{170}{197}\right)$	$e\left(\frac{190}{197}\right)$	$e\left(\frac{143}{197}\right)$	$e\left(\frac{31}{197}\right)$	$e\left(\frac{163}{197}\right)$	$e\left(\frac{102}{197}\right)$	$e\left(\frac{116}{197}\right)$	$e\left(\frac{183}{197}\right)$	$e\left(\frac{4}{197}\right)$	$e\left(\frac{137}{394}\right)$
$\chi_{4729}(355,\cdot)$	$1$	$1$	$e\left(\frac{84}{197}\right)$	$e\left(\frac{175}{197}\right)$	$e\left(\frac{168}{197}\right)$	$e\left(\frac{13}{197}\right)$	$e\left(\frac{62}{197}\right)$	$e\left(\frac{11}{197}\right)$	$e\left(\frac{55}{197}\right)$	$e\left(\frac{153}{197}\right)$	$e\left(\frac{97}{197}\right)$	$e\left(\frac{121}{394}\right)$
$\chi_{4729}(363,\cdot)$	$1$	$1$	$e\left(\frac{157}{197}\right)$	$e\left(\frac{48}{197}\right)$	$e\left(\frac{117}{197}\right)$	$e\left(\frac{97}{197}\right)$	$e\left(\frac{8}{197}\right)$	$e\left(\frac{173}{197}\right)$	$e\left(\frac{77}{197}\right)$	$e\left(\frac{96}{197}\right)$	$e\left(\frac{57}{197}\right)$	$e\left(\frac{327}{394}\right)$
$\chi_{4729}(381,\cdot)$	$1$	$1$	$e\left(\frac{32}{197}\right)$	$e\left(\frac{1}{197}\right)$	$e\left(\frac{64}{197}\right)$	$e\left(\frac{80}{197}\right)$	$e\left(\frac{33}{197}\right)$	$e\left(\frac{98}{197}\right)$	$e\left(\frac{96}{197}\right)$	$e\left(\frac{2}{197}\right)$	$e\left(\frac{112}{197}\right)$	$e\left(\frac{93}{394}\right)$
$\chi_{4729}(413,\cdot)$	$1$	$1$	$e\left(\frac{25}{197}\right)$	$e\left(\frac{167}{197}\right)$	$e\left(\frac{50}{197}\right)$	$e\left(\frac{161}{197}\right)$	$e\left(\frac{192}{197}\right)$	$e\left(\frac{15}{197}\right)$	$e\left(\frac{75}{197}\right)$	$e\left(\frac{137}{197}\right)$	$e\left(\frac{186}{197}\right)$	$e\left(\frac{165}{394}\right)$
$\chi_{4729}(422,\cdot)$	$1$	$1$	$e\left(\frac{121}{197}\right)$	$e\left(\frac{170}{197}\right)$	$e\left(\frac{45}{197}\right)$	$e\left(\frac{7}{197}\right)$	$e\left(\frac{94}{197}\right)$	$e\left(\frac{112}{197}\right)$	$e\left(\frac{166}{197}\right)$	$e\left(\frac{143}{197}\right)$	$e\left(\frac{128}{197}\right)$	$e\left(\frac{247}{394}\right)$
$\chi_{4729}(451,\cdot)$	$1$	$1$	$e\left(\frac{68}{197}\right)$	$e\left(\frac{76}{197}\right)$	$e\left(\frac{136}{197}\right)$	$e\left(\frac{170}{197}\right)$	$e\left(\frac{144}{197}\right)$	$e\left(\frac{159}{197}\right)$	$e\left(\frac{7}{197}\right)$	$e\left(\frac{152}{197}\right)$	$e\left(\frac{41}{197}\right)$	$e\left(\frac{173}{394}\right)$
$\chi_{4729}(454,\cdot)$	$1$	$1$	$e\left(\frac{143}{197}\right)$	$e\left(\frac{183}{197}\right)$	$e\left(\frac{89}{197}\right)$	$e\left(\frac{62}{197}\right)$	$e\left(\frac{129}{197}\right)$	$e\left(\frac{7}{197}\right)$	$e\left(\frac{35}{197}\right)$	$e\left(\frac{169}{197}\right)$	$e\left(\frac{8}{197}\right)$	$e\left(\frac{77}{394}\right)$
$\chi_{4729}(455,\cdot)$	$1$	$1$	$e\left(\frac{13}{197}\right)$	$e\left(\frac{142}{197}\right)$	$e\left(\frac{26}{197}\right)$	$e\left(\frac{131}{197}\right)$	$e\left(\frac{155}{197}\right)$	$e\left(\frac{126}{197}\right)$	$e\left(\frac{39}{197}\right)$	$e\left(\frac{87}{197}\right)$	$e\left(\frac{144}{197}\right)$	$e\left(\frac{7}{394}\right)$
$\chi_{4729}(458,\cdot)$	$1$	$1$	$e\left(\frac{137}{197}\right)$	$e\left(\frac{72}{197}\right)$	$e\left(\frac{77}{197}\right)$	$e\left(\frac{47}{197}\right)$	$e\left(\frac{12}{197}\right)$	$e\left(\frac{161}{197}\right)$	$e\left(\frac{17}{197}\right)$	$e\left(\frac{144}{197}\right)$	$e\left(\frac{184}{197}\right)$	$e\left(\frac{195}{394}\right)$
$\chi_{4729}(475,\cdot)$	$1$	$1$	$e\left(\frac{169}{197}\right)$	$e\left(\frac{73}{197}\right)$	$e\left(\frac{141}{197}\right)$	$e\left(\frac{127}{197}\right)$	$e\left(\frac{45}{197}\right)$	$e\left(\frac{62}{197}\right)$	$e\left(\frac{113}{197}\right)$	$e\left(\frac{146}{197}\right)$	$e\left(\frac{99}{197}\right)$	$e\left(\frac{91}{394}\right)$
$\chi_{4729}(486,\cdot)$	$1$	$1$	$e\left(\frac{110}{197}\right)$	$e\left(\frac{65}{197}\right)$	$e\left(\frac{23}{197}\right)$	$e\left(\frac{78}{197}\right)$	$e\left(\frac{175}{197}\right)$	$e\left(\frac{66}{197}\right)$	$e\left(\frac{133}{197}\right)$	$e\left(\frac{130}{197}\right)$	$e\left(\frac{188}{197}\right)$	$e\left(\frac{135}{394}\right)$
$\chi_{4729}(525,\cdot)$	$1$	$1$	$e\left(\frac{179}{197}\right)$	$e\left(\frac{61}{197}\right)$	$e\left(\frac{161}{197}\right)$	$e\left(\frac{152}{197}\right)$	$e\left(\frac{43}{197}\right)$	$e\left(\frac{68}{197}\right)$	$e\left(\frac{143}{197}\right)$	$e\left(\frac{122}{197}\right)$	$e\left(\frac{134}{197}\right)$	$e\left(\frac{157}{394}\right)$
$\chi_{4729}(607,\cdot)$	$1$	$1$	$e\left(\frac{111}{197}\right)$	$e\left(\frac{182}{197}\right)$	$e\left(\frac{25}{197}\right)$	$e\left(\frac{179}{197}\right)$	$e\left(\frac{96}{197}\right)$	$e\left(\frac{106}{197}\right)$	$e\left(\frac{136}{197}\right)$	$e\left(\frac{167}{197}\right)$	$e\left(\frac{93}{197}\right)$	$e\left(\frac{181}{394}\right)$
$\chi_{4729}(613,\cdot)$	$1$	$1$	$e\left(\frac{61}{197}\right)$	$e\left(\frac{45}{197}\right)$	$e\left(\frac{122}{197}\right)$	$e\left(\frac{54}{197}\right)$	$e\left(\frac{106}{197}\right)$	$e\left(\frac{76}{197}\right)$	$e\left(\frac{183}{197}\right)$	$e\left(\frac{90}{197}\right)$	$e\left(\frac{115}{197}\right)$	$e\left(\frac{245}{394}\right)$
$\chi_{4729}(633,\cdot)$	$1$	$1$	$e\left(\frac{130}{197}\right)$	$e\left(\frac{41}{197}\right)$	$e\left(\frac{63}{197}\right)$	$e\left(\frac{128}{197}\right)$	$e\left(\frac{171}{197}\right)$	$e\left(\frac{78}{197}\right)$	$e\left(\frac{193}{197}\right)$	$e\left(\frac{82}{197}\right)$	$e\left(\frac{61}{197}\right)$	$e\left(\frac{267}{394}\right)$
$\chi_{4729}(634,\cdot)$	$1$	$1$	$e\left(\frac{184}{197}\right)$	$e\left(\frac{55}{197}\right)$	$e\left(\frac{171}{197}\right)$	$e\left(\frac{66}{197}\right)$	$e\left(\frac{42}{197}\right)$	$e\left(\frac{71}{197}\right)$	$e\left(\frac{158}{197}\right)$	$e\left(\frac{110}{197}\right)$	$e\left(\frac{53}{197}\right)$	$e\left(\frac{387}{394}\right)$
$\chi_{4729}(643,\cdot)$	$1$	$1$	$e\left(\frac{117}{197}\right)$	$e\left(\frac{96}{197}\right)$	$e\left(\frac{37}{197}\right)$	$e\left(\frac{194}{197}\right)$	$e\left(\frac{16}{197}\right)$	$e\left(\frac{149}{197}\right)$	$e\left(\frac{154}{197}\right)$	$e\left(\frac{192}{197}\right)$	$e\left(\frac{114}{197}\right)$	$e\left(\frac{63}{394}\right)$
$\chi_{4729}(670,\cdot)$	$1$	$1$	$e\left(\frac{42}{197}\right)$	$e\left(\frac{186}{197}\right)$	$e\left(\frac{84}{197}\right)$	$e\left(\frac{105}{197}\right)$	$e\left(\frac{31}{197}\right)$	$e\left(\frac{104}{197}\right)$	$e\left(\frac{126}{197}\right)$	$e\left(\frac{175}{197}\right)$	$e\left(\frac{147}{197}\right)$	$e\left(\frac{159}{394}\right)$
$\chi_{4729}(681,\cdot)$	$1$	$1$	$e\left(\frac{152}{197}\right)$	$e\left(\frac{54}{197}\right)$	$e\left(\frac{107}{197}\right)$	$e\left(\frac{183}{197}\right)$	$e\left(\frac{9}{197}\right)$	$e\left(\frac{170}{197}\right)$	$e\left(\frac{62}{197}\right)$	$e\left(\frac{108}{197}\right)$	$e\left(\frac{138}{197}\right)$	$e\left(\frac{97}{394}\right)$

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	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\(\chi_{4729}(4,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{153}{197}\right)\)	\(e\left(\frac{171}{197}\right)\)	\(e\left(\frac{109}{197}\right)\)	\(e\left(\frac{87}{197}\right)\)	\(e\left(\frac{127}{197}\right)\)	\(e\left(\frac{13}{197}\right)\)	\(e\left(\frac{65}{197}\right)\)	\(e\left(\frac{145}{197}\right)\)	\(e\left(\frac{43}{197}\right)\)	\(e\left(\frac{143}{394}\right)\)
\(\chi_{4729}(6,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{162}{197}\right)\)	\(e\left(\frac{42}{197}\right)\)	\(e\left(\frac{127}{197}\right)\)	\(e\left(\frac{11}{197}\right)\)	\(e\left(\frac{7}{197}\right)\)	\(e\left(\frac{176}{197}\right)\)	\(e\left(\frac{92}{197}\right)\)	\(e\left(\frac{84}{197}\right)\)	\(e\left(\frac{173}{197}\right)\)	\(e\left(\frac{163}{394}\right)\)
\(\chi_{4729}(9,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{171}{197}\right)\)	\(e\left(\frac{110}{197}\right)\)	\(e\left(\frac{145}{197}\right)\)	\(e\left(\frac{132}{197}\right)\)	\(e\left(\frac{84}{197}\right)\)	\(e\left(\frac{142}{197}\right)\)	\(e\left(\frac{119}{197}\right)\)	\(e\left(\frac{23}{197}\right)\)	\(e\left(\frac{106}{197}\right)\)	\(e\left(\frac{183}{394}\right)\)
\(\chi_{4729}(64,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{65}{197}\right)\)	\(e\left(\frac{119}{197}\right)\)	\(e\left(\frac{130}{197}\right)\)	\(e\left(\frac{64}{197}\right)\)	\(e\left(\frac{184}{197}\right)\)	\(e\left(\frac{39}{197}\right)\)	\(e\left(\frac{195}{197}\right)\)	\(e\left(\frac{41}{197}\right)\)	\(e\left(\frac{129}{197}\right)\)	\(e\left(\frac{35}{394}\right)\)
\(\chi_{4729}(96,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{74}{197}\right)\)	\(e\left(\frac{187}{197}\right)\)	\(e\left(\frac{148}{197}\right)\)	\(e\left(\frac{185}{197}\right)\)	\(e\left(\frac{64}{197}\right)\)	\(e\left(\frac{5}{197}\right)\)	\(e\left(\frac{25}{197}\right)\)	\(e\left(\frac{177}{197}\right)\)	\(e\left(\frac{62}{197}\right)\)	\(e\left(\frac{55}{394}\right)\)
\(\chi_{4729}(144,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{83}{197}\right)\)	\(e\left(\frac{58}{197}\right)\)	\(e\left(\frac{166}{197}\right)\)	\(e\left(\frac{109}{197}\right)\)	\(e\left(\frac{141}{197}\right)\)	\(e\left(\frac{168}{197}\right)\)	\(e\left(\frac{52}{197}\right)\)	\(e\left(\frac{116}{197}\right)\)	\(e\left(\frac{192}{197}\right)\)	\(e\left(\frac{75}{394}\right)\)
\(\chi_{4729}(197,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{79}{197}\right)\)	\(e\left(\frac{181}{197}\right)\)	\(e\left(\frac{158}{197}\right)\)	\(e\left(\frac{99}{197}\right)\)	\(e\left(\frac{63}{197}\right)\)	\(e\left(\frac{8}{197}\right)\)	\(e\left(\frac{40}{197}\right)\)	\(e\left(\frac{165}{197}\right)\)	\(e\left(\frac{178}{197}\right)\)	\(e\left(\frac{285}{394}\right)\)
\(\chi_{4729}(216,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{92}{197}\right)\)	\(e\left(\frac{126}{197}\right)\)	\(e\left(\frac{184}{197}\right)\)	\(e\left(\frac{33}{197}\right)\)	\(e\left(\frac{21}{197}\right)\)	\(e\left(\frac{134}{197}\right)\)	\(e\left(\frac{79}{197}\right)\)	\(e\left(\frac{55}{197}\right)\)	\(e\left(\frac{125}{197}\right)\)	\(e\left(\frac{95}{394}\right)\)
\(\chi_{4729}(242,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{148}{197}\right)\)	\(e\left(\frac{177}{197}\right)\)	\(e\left(\frac{99}{197}\right)\)	\(e\left(\frac{173}{197}\right)\)	\(e\left(\frac{128}{197}\right)\)	\(e\left(\frac{10}{197}\right)\)	\(e\left(\frac{50}{197}\right)\)	\(e\left(\frac{157}{197}\right)\)	\(e\left(\frac{124}{197}\right)\)	\(e\left(\frac{307}{394}\right)\)
\(\chi_{4729}(254,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{197}\right)\)	\(e\left(\frac{130}{197}\right)\)	\(e\left(\frac{46}{197}\right)\)	\(e\left(\frac{156}{197}\right)\)	\(e\left(\frac{153}{197}\right)\)	\(e\left(\frac{132}{197}\right)\)	\(e\left(\frac{69}{197}\right)\)	\(e\left(\frac{63}{197}\right)\)	\(e\left(\frac{179}{197}\right)\)	\(e\left(\frac{73}{394}\right)\)
\(\chi_{4729}(324,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{101}{197}\right)\)	\(e\left(\frac{194}{197}\right)\)	\(e\left(\frac{5}{197}\right)\)	\(e\left(\frac{154}{197}\right)\)	\(e\left(\frac{98}{197}\right)\)	\(e\left(\frac{100}{197}\right)\)	\(e\left(\frac{106}{197}\right)\)	\(e\left(\frac{191}{197}\right)\)	\(e\left(\frac{58}{197}\right)\)	\(e\left(\frac{115}{394}\right)\)
\(\chi_{4729}(350,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{170}{197}\right)\)	\(e\left(\frac{190}{197}\right)\)	\(e\left(\frac{143}{197}\right)\)	\(e\left(\frac{31}{197}\right)\)	\(e\left(\frac{163}{197}\right)\)	\(e\left(\frac{102}{197}\right)\)	\(e\left(\frac{116}{197}\right)\)	\(e\left(\frac{183}{197}\right)\)	\(e\left(\frac{4}{197}\right)\)	\(e\left(\frac{137}{394}\right)\)
\(\chi_{4729}(355,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{84}{197}\right)\)	\(e\left(\frac{175}{197}\right)\)	\(e\left(\frac{168}{197}\right)\)	\(e\left(\frac{13}{197}\right)\)	\(e\left(\frac{62}{197}\right)\)	\(e\left(\frac{11}{197}\right)\)	\(e\left(\frac{55}{197}\right)\)	\(e\left(\frac{153}{197}\right)\)	\(e\left(\frac{97}{197}\right)\)	\(e\left(\frac{121}{394}\right)\)
\(\chi_{4729}(363,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{157}{197}\right)\)	\(e\left(\frac{48}{197}\right)\)	\(e\left(\frac{117}{197}\right)\)	\(e\left(\frac{97}{197}\right)\)	\(e\left(\frac{8}{197}\right)\)	\(e\left(\frac{173}{197}\right)\)	\(e\left(\frac{77}{197}\right)\)	\(e\left(\frac{96}{197}\right)\)	\(e\left(\frac{57}{197}\right)\)	\(e\left(\frac{327}{394}\right)\)
\(\chi_{4729}(381,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{32}{197}\right)\)	\(e\left(\frac{1}{197}\right)\)	\(e\left(\frac{64}{197}\right)\)	\(e\left(\frac{80}{197}\right)\)	\(e\left(\frac{33}{197}\right)\)	\(e\left(\frac{98}{197}\right)\)	\(e\left(\frac{96}{197}\right)\)	\(e\left(\frac{2}{197}\right)\)	\(e\left(\frac{112}{197}\right)\)	\(e\left(\frac{93}{394}\right)\)
\(\chi_{4729}(413,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{25}{197}\right)\)	\(e\left(\frac{167}{197}\right)\)	\(e\left(\frac{50}{197}\right)\)	\(e\left(\frac{161}{197}\right)\)	\(e\left(\frac{192}{197}\right)\)	\(e\left(\frac{15}{197}\right)\)	\(e\left(\frac{75}{197}\right)\)	\(e\left(\frac{137}{197}\right)\)	\(e\left(\frac{186}{197}\right)\)	\(e\left(\frac{165}{394}\right)\)
\(\chi_{4729}(422,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{121}{197}\right)\)	\(e\left(\frac{170}{197}\right)\)	\(e\left(\frac{45}{197}\right)\)	\(e\left(\frac{7}{197}\right)\)	\(e\left(\frac{94}{197}\right)\)	\(e\left(\frac{112}{197}\right)\)	\(e\left(\frac{166}{197}\right)\)	\(e\left(\frac{143}{197}\right)\)	\(e\left(\frac{128}{197}\right)\)	\(e\left(\frac{247}{394}\right)\)
\(\chi_{4729}(451,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{68}{197}\right)\)	\(e\left(\frac{76}{197}\right)\)	\(e\left(\frac{136}{197}\right)\)	\(e\left(\frac{170}{197}\right)\)	\(e\left(\frac{144}{197}\right)\)	\(e\left(\frac{159}{197}\right)\)	\(e\left(\frac{7}{197}\right)\)	\(e\left(\frac{152}{197}\right)\)	\(e\left(\frac{41}{197}\right)\)	\(e\left(\frac{173}{394}\right)\)
\(\chi_{4729}(454,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{143}{197}\right)\)	\(e\left(\frac{183}{197}\right)\)	\(e\left(\frac{89}{197}\right)\)	\(e\left(\frac{62}{197}\right)\)	\(e\left(\frac{129}{197}\right)\)	\(e\left(\frac{7}{197}\right)\)	\(e\left(\frac{35}{197}\right)\)	\(e\left(\frac{169}{197}\right)\)	\(e\left(\frac{8}{197}\right)\)	\(e\left(\frac{77}{394}\right)\)
\(\chi_{4729}(455,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{197}\right)\)	\(e\left(\frac{142}{197}\right)\)	\(e\left(\frac{26}{197}\right)\)	\(e\left(\frac{131}{197}\right)\)	\(e\left(\frac{155}{197}\right)\)	\(e\left(\frac{126}{197}\right)\)	\(e\left(\frac{39}{197}\right)\)	\(e\left(\frac{87}{197}\right)\)	\(e\left(\frac{144}{197}\right)\)	\(e\left(\frac{7}{394}\right)\)
\(\chi_{4729}(458,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{137}{197}\right)\)	\(e\left(\frac{72}{197}\right)\)	\(e\left(\frac{77}{197}\right)\)	\(e\left(\frac{47}{197}\right)\)	\(e\left(\frac{12}{197}\right)\)	\(e\left(\frac{161}{197}\right)\)	\(e\left(\frac{17}{197}\right)\)	\(e\left(\frac{144}{197}\right)\)	\(e\left(\frac{184}{197}\right)\)	\(e\left(\frac{195}{394}\right)\)
\(\chi_{4729}(475,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{169}{197}\right)\)	\(e\left(\frac{73}{197}\right)\)	\(e\left(\frac{141}{197}\right)\)	\(e\left(\frac{127}{197}\right)\)	\(e\left(\frac{45}{197}\right)\)	\(e\left(\frac{62}{197}\right)\)	\(e\left(\frac{113}{197}\right)\)	\(e\left(\frac{146}{197}\right)\)	\(e\left(\frac{99}{197}\right)\)	\(e\left(\frac{91}{394}\right)\)
\(\chi_{4729}(486,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{110}{197}\right)\)	\(e\left(\frac{65}{197}\right)\)	\(e\left(\frac{23}{197}\right)\)	\(e\left(\frac{78}{197}\right)\)	\(e\left(\frac{175}{197}\right)\)	\(e\left(\frac{66}{197}\right)\)	\(e\left(\frac{133}{197}\right)\)	\(e\left(\frac{130}{197}\right)\)	\(e\left(\frac{188}{197}\right)\)	\(e\left(\frac{135}{394}\right)\)
\(\chi_{4729}(525,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{179}{197}\right)\)	\(e\left(\frac{61}{197}\right)\)	\(e\left(\frac{161}{197}\right)\)	\(e\left(\frac{152}{197}\right)\)	\(e\left(\frac{43}{197}\right)\)	\(e\left(\frac{68}{197}\right)\)	\(e\left(\frac{143}{197}\right)\)	\(e\left(\frac{122}{197}\right)\)	\(e\left(\frac{134}{197}\right)\)	\(e\left(\frac{157}{394}\right)\)
\(\chi_{4729}(607,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{111}{197}\right)\)	\(e\left(\frac{182}{197}\right)\)	\(e\left(\frac{25}{197}\right)\)	\(e\left(\frac{179}{197}\right)\)	\(e\left(\frac{96}{197}\right)\)	\(e\left(\frac{106}{197}\right)\)	\(e\left(\frac{136}{197}\right)\)	\(e\left(\frac{167}{197}\right)\)	\(e\left(\frac{93}{197}\right)\)	\(e\left(\frac{181}{394}\right)\)
\(\chi_{4729}(613,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{61}{197}\right)\)	\(e\left(\frac{45}{197}\right)\)	\(e\left(\frac{122}{197}\right)\)	\(e\left(\frac{54}{197}\right)\)	\(e\left(\frac{106}{197}\right)\)	\(e\left(\frac{76}{197}\right)\)	\(e\left(\frac{183}{197}\right)\)	\(e\left(\frac{90}{197}\right)\)	\(e\left(\frac{115}{197}\right)\)	\(e\left(\frac{245}{394}\right)\)
\(\chi_{4729}(633,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{130}{197}\right)\)	\(e\left(\frac{41}{197}\right)\)	\(e\left(\frac{63}{197}\right)\)	\(e\left(\frac{128}{197}\right)\)	\(e\left(\frac{171}{197}\right)\)	\(e\left(\frac{78}{197}\right)\)	\(e\left(\frac{193}{197}\right)\)	\(e\left(\frac{82}{197}\right)\)	\(e\left(\frac{61}{197}\right)\)	\(e\left(\frac{267}{394}\right)\)
\(\chi_{4729}(634,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{184}{197}\right)\)	\(e\left(\frac{55}{197}\right)\)	\(e\left(\frac{171}{197}\right)\)	\(e\left(\frac{66}{197}\right)\)	\(e\left(\frac{42}{197}\right)\)	\(e\left(\frac{71}{197}\right)\)	\(e\left(\frac{158}{197}\right)\)	\(e\left(\frac{110}{197}\right)\)	\(e\left(\frac{53}{197}\right)\)	\(e\left(\frac{387}{394}\right)\)
\(\chi_{4729}(643,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{117}{197}\right)\)	\(e\left(\frac{96}{197}\right)\)	\(e\left(\frac{37}{197}\right)\)	\(e\left(\frac{194}{197}\right)\)	\(e\left(\frac{16}{197}\right)\)	\(e\left(\frac{149}{197}\right)\)	\(e\left(\frac{154}{197}\right)\)	\(e\left(\frac{192}{197}\right)\)	\(e\left(\frac{114}{197}\right)\)	\(e\left(\frac{63}{394}\right)\)
\(\chi_{4729}(670,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{42}{197}\right)\)	\(e\left(\frac{186}{197}\right)\)	\(e\left(\frac{84}{197}\right)\)	\(e\left(\frac{105}{197}\right)\)	\(e\left(\frac{31}{197}\right)\)	\(e\left(\frac{104}{197}\right)\)	\(e\left(\frac{126}{197}\right)\)	\(e\left(\frac{175}{197}\right)\)	\(e\left(\frac{147}{197}\right)\)	\(e\left(\frac{159}{394}\right)\)
\(\chi_{4729}(681,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{152}{197}\right)\)	\(e\left(\frac{54}{197}\right)\)	\(e\left(\frac{107}{197}\right)\)	\(e\left(\frac{183}{197}\right)\)	\(e\left(\frac{9}{197}\right)\)	\(e\left(\frac{170}{197}\right)\)	\(e\left(\frac{62}{197}\right)\)	\(e\left(\frac{108}{197}\right)\)	\(e\left(\frac{138}{197}\right)\)	\(e\left(\frac{97}{394}\right)\)

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First 31 of 196 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.j
Modulus	$4729$
Conductor	$4729$
Order	$394$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(4729\)
Conductor:	\(4729\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(394\)	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)