LMFDB - Dirichlet character orbit 2349.br

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2349, base_ring=CyclotomicField(378)) M = H._module chi = DirichletCharacter(H, M([175,324])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(20,2349)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$2349$
Conductor:	$2349$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$378$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	yes	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	odd	sage:chi.is_odd() pari:zncharisodd(g,chi)

Related number fields

Field of values:	$\Q(\zeta_{189})$
Fixed field:	Number field defined by a degree 378 polynomial (not computed)

First 31 of 108 characters in Galois orbit

Character	$-1$	$1$	$2$	$4$	$5$	$7$	$8$	$10$	$11$	$13$	$14$	$16$
$\chi_{2349}(20,\cdot)$	$-1$	$1$	$e\left(\frac{121}{378}\right)$	$e\left(\frac{121}{189}\right)$	$e\left(\frac{191}{378}\right)$	$e\left(\frac{131}{189}\right)$	$e\left(\frac{121}{126}\right)$	$e\left(\frac{52}{63}\right)$	$e\left(\frac{169}{378}\right)$	$e\left(\frac{25}{189}\right)$	$e\left(\frac{5}{378}\right)$	$e\left(\frac{53}{189}\right)$
$\chi_{2349}(23,\cdot)$	$-1$	$1$	$e\left(\frac{347}{378}\right)$	$e\left(\frac{158}{189}\right)$	$e\left(\frac{151}{378}\right)$	$e\left(\frac{157}{189}\right)$	$e\left(\frac{95}{126}\right)$	$e\left(\frac{20}{63}\right)$	$e\left(\frac{191}{378}\right)$	$e\left(\frac{92}{189}\right)$	$e\left(\frac{283}{378}\right)$	$e\left(\frac{127}{189}\right)$
$\chi_{2349}(65,\cdot)$	$-1$	$1$	$e\left(\frac{1}{378}\right)$	$e\left(\frac{1}{189}\right)$	$e\left(\frac{239}{378}\right)$	$e\left(\frac{62}{189}\right)$	$e\left(\frac{1}{126}\right)$	$e\left(\frac{40}{63}\right)$	$e\left(\frac{67}{378}\right)$	$e\left(\frac{58}{189}\right)$	$e\left(\frac{125}{378}\right)$	$e\left(\frac{2}{189}\right)$
$\chi_{2349}(74,\cdot)$	$-1$	$1$	$e\left(\frac{355}{378}\right)$	$e\left(\frac{166}{189}\right)$	$e\left(\frac{173}{378}\right)$	$e\left(\frac{86}{189}\right)$	$e\left(\frac{103}{126}\right)$	$e\left(\frac{25}{63}\right)$	$e\left(\frac{349}{378}\right)$	$e\left(\frac{178}{189}\right)$	$e\left(\frac{149}{378}\right)$	$e\left(\frac{143}{189}\right)$
$\chi_{2349}(83,\cdot)$	$-1$	$1$	$e\left(\frac{223}{378}\right)$	$e\left(\frac{34}{189}\right)$	$e\left(\frac{377}{378}\right)$	$e\left(\frac{29}{189}\right)$	$e\left(\frac{97}{126}\right)$	$e\left(\frac{37}{63}\right)$	$e\left(\frac{199}{378}\right)$	$e\left(\frac{82}{189}\right)$	$e\left(\frac{281}{378}\right)$	$e\left(\frac{68}{189}\right)$
$\chi_{2349}(110,\cdot)$	$-1$	$1$	$e\left(\frac{151}{378}\right)$	$e\left(\frac{151}{189}\right)$	$e\left(\frac{179}{378}\right)$	$e\left(\frac{101}{189}\right)$	$e\left(\frac{25}{126}\right)$	$e\left(\frac{55}{63}\right)$	$e\left(\frac{289}{378}\right)$	$e\left(\frac{64}{189}\right)$	$e\left(\frac{353}{378}\right)$	$e\left(\frac{113}{189}\right)$
$\chi_{2349}(140,\cdot)$	$-1$	$1$	$e\left(\frac{17}{378}\right)$	$e\left(\frac{17}{189}\right)$	$e\left(\frac{283}{378}\right)$	$e\left(\frac{109}{189}\right)$	$e\left(\frac{17}{126}\right)$	$e\left(\frac{50}{63}\right)$	$e\left(\frac{5}{378}\right)$	$e\left(\frac{41}{189}\right)$	$e\left(\frac{235}{378}\right)$	$e\left(\frac{34}{189}\right)$
$\chi_{2349}(194,\cdot)$	$-1$	$1$	$e\left(\frac{359}{378}\right)$	$e\left(\frac{170}{189}\right)$	$e\left(\frac{373}{378}\right)$	$e\left(\frac{145}{189}\right)$	$e\left(\frac{107}{126}\right)$	$e\left(\frac{59}{63}\right)$	$e\left(\frac{239}{378}\right)$	$e\left(\frac{32}{189}\right)$	$e\left(\frac{271}{378}\right)$	$e\left(\frac{151}{189}\right)$
$\chi_{2349}(227,\cdot)$	$-1$	$1$	$e\left(\frac{325}{378}\right)$	$e\left(\frac{136}{189}\right)$	$e\left(\frac{185}{378}\right)$	$e\left(\frac{116}{189}\right)$	$e\left(\frac{73}{126}\right)$	$e\left(\frac{22}{63}\right)$	$e\left(\frac{229}{378}\right)$	$e\left(\frac{139}{189}\right)$	$e\left(\frac{179}{378}\right)$	$e\left(\frac{83}{189}\right)$
$\chi_{2349}(239,\cdot)$	$-1$	$1$	$e\left(\frac{365}{378}\right)$	$e\left(\frac{176}{189}\right)$	$e\left(\frac{295}{378}\right)$	$e\left(\frac{139}{189}\right)$	$e\left(\frac{113}{126}\right)$	$e\left(\frac{47}{63}\right)$	$e\left(\frac{263}{378}\right)$	$e\left(\frac{2}{189}\right)$	$e\left(\frac{265}{378}\right)$	$e\left(\frac{163}{189}\right)$
$\chi_{2349}(248,\cdot)$	$-1$	$1$	$e\left(\frac{215}{378}\right)$	$e\left(\frac{26}{189}\right)$	$e\left(\frac{355}{378}\right)$	$e\left(\frac{100}{189}\right)$	$e\left(\frac{89}{126}\right)$	$e\left(\frac{32}{63}\right)$	$e\left(\frac{41}{378}\right)$	$e\left(\frac{185}{189}\right)$	$e\left(\frac{37}{378}\right)$	$e\left(\frac{52}{189}\right)$
$\chi_{2349}(257,\cdot)$	$-1$	$1$	$e\left(\frac{335}{378}\right)$	$e\left(\frac{146}{189}\right)$	$e\left(\frac{307}{378}\right)$	$e\left(\frac{169}{189}\right)$	$e\left(\frac{83}{126}\right)$	$e\left(\frac{44}{63}\right)$	$e\left(\frac{143}{378}\right)$	$e\left(\frac{152}{189}\right)$	$e\left(\frac{295}{378}\right)$	$e\left(\frac{103}{189}\right)$
$\chi_{2349}(281,\cdot)$	$-1$	$1$	$e\left(\frac{289}{378}\right)$	$e\left(\frac{100}{189}\right)$	$e\left(\frac{275}{378}\right)$	$e\left(\frac{152}{189}\right)$	$e\left(\frac{37}{126}\right)$	$e\left(\frac{31}{63}\right)$	$e\left(\frac{85}{378}\right)$	$e\left(\frac{130}{189}\right)$	$e\left(\frac{215}{378}\right)$	$e\left(\frac{11}{189}\right)$
$\chi_{2349}(284,\cdot)$	$-1$	$1$	$e\left(\frac{263}{378}\right)$	$e\left(\frac{74}{189}\right)$	$e\left(\frac{109}{378}\right)$	$e\left(\frac{52}{189}\right)$	$e\left(\frac{11}{126}\right)$	$e\left(\frac{62}{63}\right)$	$e\left(\frac{233}{378}\right)$	$e\left(\frac{134}{189}\right)$	$e\left(\frac{367}{378}\right)$	$e\left(\frac{148}{189}\right)$
$\chi_{2349}(326,\cdot)$	$-1$	$1$	$e\left(\frac{169}{378}\right)$	$e\left(\frac{169}{189}\right)$	$e\left(\frac{323}{378}\right)$	$e\left(\frac{83}{189}\right)$	$e\left(\frac{43}{126}\right)$	$e\left(\frac{19}{63}\right)$	$e\left(\frac{361}{378}\right)$	$e\left(\frac{163}{189}\right)$	$e\left(\frac{335}{378}\right)$	$e\left(\frac{149}{189}\right)$
$\chi_{2349}(335,\cdot)$	$-1$	$1$	$e\left(\frac{145}{378}\right)$	$e\left(\frac{145}{189}\right)$	$e\left(\frac{257}{378}\right)$	$e\left(\frac{107}{189}\right)$	$e\left(\frac{19}{126}\right)$	$e\left(\frac{4}{63}\right)$	$e\left(\frac{265}{378}\right)$	$e\left(\frac{94}{189}\right)$	$e\left(\frac{359}{378}\right)$	$e\left(\frac{101}{189}\right)$
$\chi_{2349}(344,\cdot)$	$-1$	$1$	$e\left(\frac{13}{378}\right)$	$e\left(\frac{13}{189}\right)$	$e\left(\frac{83}{378}\right)$	$e\left(\frac{50}{189}\right)$	$e\left(\frac{13}{126}\right)$	$e\left(\frac{16}{63}\right)$	$e\left(\frac{115}{378}\right)$	$e\left(\frac{187}{189}\right)$	$e\left(\frac{113}{378}\right)$	$e\left(\frac{26}{189}\right)$
$\chi_{2349}(371,\cdot)$	$-1$	$1$	$e\left(\frac{319}{378}\right)$	$e\left(\frac{130}{189}\right)$	$e\left(\frac{263}{378}\right)$	$e\left(\frac{122}{189}\right)$	$e\left(\frac{67}{126}\right)$	$e\left(\frac{34}{63}\right)$	$e\left(\frac{205}{378}\right)$	$e\left(\frac{169}{189}\right)$	$e\left(\frac{185}{378}\right)$	$e\left(\frac{71}{189}\right)$
$\chi_{2349}(401,\cdot)$	$-1$	$1$	$e\left(\frac{311}{378}\right)$	$e\left(\frac{122}{189}\right)$	$e\left(\frac{241}{378}\right)$	$e\left(\frac{4}{189}\right)$	$e\left(\frac{59}{126}\right)$	$e\left(\frac{29}{63}\right)$	$e\left(\frac{47}{378}\right)$	$e\left(\frac{83}{189}\right)$	$e\left(\frac{319}{378}\right)$	$e\left(\frac{55}{189}\right)$
$\chi_{2349}(455,\cdot)$	$-1$	$1$	$e\left(\frac{275}{378}\right)$	$e\left(\frac{86}{189}\right)$	$e\left(\frac{331}{378}\right)$	$e\left(\frac{40}{189}\right)$	$e\left(\frac{23}{126}\right)$	$e\left(\frac{38}{63}\right)$	$e\left(\frac{281}{378}\right)$	$e\left(\frac{74}{189}\right)$	$e\left(\frac{355}{378}\right)$	$e\left(\frac{172}{189}\right)$
$\chi_{2349}(488,\cdot)$	$-1$	$1$	$e\left(\frac{115}{378}\right)$	$e\left(\frac{115}{189}\right)$	$e\left(\frac{269}{378}\right)$	$e\left(\frac{137}{189}\right)$	$e\left(\frac{115}{126}\right)$	$e\left(\frac{1}{63}\right)$	$e\left(\frac{145}{378}\right)$	$e\left(\frac{55}{189}\right)$	$e\left(\frac{11}{378}\right)$	$e\left(\frac{41}{189}\right)$
$\chi_{2349}(500,\cdot)$	$-1$	$1$	$e\left(\frac{281}{378}\right)$	$e\left(\frac{92}{189}\right)$	$e\left(\frac{253}{378}\right)$	$e\left(\frac{34}{189}\right)$	$e\left(\frac{29}{126}\right)$	$e\left(\frac{26}{63}\right)$	$e\left(\frac{305}{378}\right)$	$e\left(\frac{44}{189}\right)$	$e\left(\frac{349}{378}\right)$	$e\left(\frac{184}{189}\right)$
$\chi_{2349}(509,\cdot)$	$-1$	$1$	$e\left(\frac{131}{378}\right)$	$e\left(\frac{131}{189}\right)$	$e\left(\frac{313}{378}\right)$	$e\left(\frac{184}{189}\right)$	$e\left(\frac{5}{126}\right)$	$e\left(\frac{11}{63}\right)$	$e\left(\frac{83}{378}\right)$	$e\left(\frac{38}{189}\right)$	$e\left(\frac{121}{378}\right)$	$e\left(\frac{73}{189}\right)$
$\chi_{2349}(518,\cdot)$	$-1$	$1$	$e\left(\frac{251}{378}\right)$	$e\left(\frac{62}{189}\right)$	$e\left(\frac{265}{378}\right)$	$e\left(\frac{64}{189}\right)$	$e\left(\frac{125}{126}\right)$	$e\left(\frac{23}{63}\right)$	$e\left(\frac{185}{378}\right)$	$e\left(\frac{5}{189}\right)$	$e\left(\frac{1}{378}\right)$	$e\left(\frac{124}{189}\right)$
$\chi_{2349}(542,\cdot)$	$-1$	$1$	$e\left(\frac{79}{378}\right)$	$e\left(\frac{79}{189}\right)$	$e\left(\frac{359}{378}\right)$	$e\left(\frac{173}{189}\right)$	$e\left(\frac{79}{126}\right)$	$e\left(\frac{10}{63}\right)$	$e\left(\frac{1}{378}\right)$	$e\left(\frac{46}{189}\right)$	$e\left(\frac{47}{378}\right)$	$e\left(\frac{158}{189}\right)$
$\chi_{2349}(545,\cdot)$	$-1$	$1$	$e\left(\frac{179}{378}\right)$	$e\left(\frac{179}{189}\right)$	$e\left(\frac{67}{378}\right)$	$e\left(\frac{136}{189}\right)$	$e\left(\frac{53}{126}\right)$	$e\left(\frac{41}{63}\right)$	$e\left(\frac{275}{378}\right)$	$e\left(\frac{176}{189}\right)$	$e\left(\frac{73}{378}\right)$	$e\left(\frac{169}{189}\right)$
$\chi_{2349}(587,\cdot)$	$-1$	$1$	$e\left(\frac{337}{378}\right)$	$e\left(\frac{148}{189}\right)$	$e\left(\frac{29}{378}\right)$	$e\left(\frac{104}{189}\right)$	$e\left(\frac{85}{126}\right)$	$e\left(\frac{61}{63}\right)$	$e\left(\frac{277}{378}\right)$	$e\left(\frac{79}{189}\right)$	$e\left(\frac{167}{378}\right)$	$e\left(\frac{107}{189}\right)$
$\chi_{2349}(596,\cdot)$	$-1$	$1$	$e\left(\frac{313}{378}\right)$	$e\left(\frac{124}{189}\right)$	$e\left(\frac{341}{378}\right)$	$e\left(\frac{128}{189}\right)$	$e\left(\frac{61}{126}\right)$	$e\left(\frac{46}{63}\right)$	$e\left(\frac{181}{378}\right)$	$e\left(\frac{10}{189}\right)$	$e\left(\frac{191}{378}\right)$	$e\left(\frac{59}{189}\right)$
$\chi_{2349}(605,\cdot)$	$-1$	$1$	$e\left(\frac{181}{378}\right)$	$e\left(\frac{181}{189}\right)$	$e\left(\frac{167}{378}\right)$	$e\left(\frac{71}{189}\right)$	$e\left(\frac{55}{126}\right)$	$e\left(\frac{58}{63}\right)$	$e\left(\frac{31}{378}\right)$	$e\left(\frac{103}{189}\right)$	$e\left(\frac{323}{378}\right)$	$e\left(\frac{173}{189}\right)$
$\chi_{2349}(632,\cdot)$	$-1$	$1$	$e\left(\frac{109}{378}\right)$	$e\left(\frac{109}{189}\right)$	$e\left(\frac{347}{378}\right)$	$e\left(\frac{143}{189}\right)$	$e\left(\frac{109}{126}\right)$	$e\left(\frac{13}{63}\right)$	$e\left(\frac{121}{378}\right)$	$e\left(\frac{85}{189}\right)$	$e\left(\frac{17}{378}\right)$	$e\left(\frac{29}{189}\right)$
$\chi_{2349}(662,\cdot)$	$-1$	$1$	$e\left(\frac{227}{378}\right)$	$e\left(\frac{38}{189}\right)$	$e\left(\frac{199}{378}\right)$	$e\left(\frac{88}{189}\right)$	$e\left(\frac{101}{126}\right)$	$e\left(\frac{8}{63}\right)$	$e\left(\frac{89}{378}\right)$	$e\left(\frac{125}{189}\right)$	$e\left(\frac{25}{378}\right)$	$e\left(\frac{76}{189}\right)$

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	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(7\)	\(8\)	\(10\)	\(11\)	\(13\)	\(14\)	\(16\)
\(\chi_{2349}(20,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{121}{378}\right)\)	\(e\left(\frac{121}{189}\right)\)	\(e\left(\frac{191}{378}\right)\)	\(e\left(\frac{131}{189}\right)\)	\(e\left(\frac{121}{126}\right)\)	\(e\left(\frac{52}{63}\right)\)	\(e\left(\frac{169}{378}\right)\)	\(e\left(\frac{25}{189}\right)\)	\(e\left(\frac{5}{378}\right)\)	\(e\left(\frac{53}{189}\right)\)
\(\chi_{2349}(23,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{347}{378}\right)\)	\(e\left(\frac{158}{189}\right)\)	\(e\left(\frac{151}{378}\right)\)	\(e\left(\frac{157}{189}\right)\)	\(e\left(\frac{95}{126}\right)\)	\(e\left(\frac{20}{63}\right)\)	\(e\left(\frac{191}{378}\right)\)	\(e\left(\frac{92}{189}\right)\)	\(e\left(\frac{283}{378}\right)\)	\(e\left(\frac{127}{189}\right)\)
\(\chi_{2349}(65,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{378}\right)\)	\(e\left(\frac{1}{189}\right)\)	\(e\left(\frac{239}{378}\right)\)	\(e\left(\frac{62}{189}\right)\)	\(e\left(\frac{1}{126}\right)\)	\(e\left(\frac{40}{63}\right)\)	\(e\left(\frac{67}{378}\right)\)	\(e\left(\frac{58}{189}\right)\)	\(e\left(\frac{125}{378}\right)\)	\(e\left(\frac{2}{189}\right)\)
\(\chi_{2349}(74,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{355}{378}\right)\)	\(e\left(\frac{166}{189}\right)\)	\(e\left(\frac{173}{378}\right)\)	\(e\left(\frac{86}{189}\right)\)	\(e\left(\frac{103}{126}\right)\)	\(e\left(\frac{25}{63}\right)\)	\(e\left(\frac{349}{378}\right)\)	\(e\left(\frac{178}{189}\right)\)	\(e\left(\frac{149}{378}\right)\)	\(e\left(\frac{143}{189}\right)\)
\(\chi_{2349}(83,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{223}{378}\right)\)	\(e\left(\frac{34}{189}\right)\)	\(e\left(\frac{377}{378}\right)\)	\(e\left(\frac{29}{189}\right)\)	\(e\left(\frac{97}{126}\right)\)	\(e\left(\frac{37}{63}\right)\)	\(e\left(\frac{199}{378}\right)\)	\(e\left(\frac{82}{189}\right)\)	\(e\left(\frac{281}{378}\right)\)	\(e\left(\frac{68}{189}\right)\)
\(\chi_{2349}(110,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{151}{378}\right)\)	\(e\left(\frac{151}{189}\right)\)	\(e\left(\frac{179}{378}\right)\)	\(e\left(\frac{101}{189}\right)\)	\(e\left(\frac{25}{126}\right)\)	\(e\left(\frac{55}{63}\right)\)	\(e\left(\frac{289}{378}\right)\)	\(e\left(\frac{64}{189}\right)\)	\(e\left(\frac{353}{378}\right)\)	\(e\left(\frac{113}{189}\right)\)
\(\chi_{2349}(140,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{17}{378}\right)\)	\(e\left(\frac{17}{189}\right)\)	\(e\left(\frac{283}{378}\right)\)	\(e\left(\frac{109}{189}\right)\)	\(e\left(\frac{17}{126}\right)\)	\(e\left(\frac{50}{63}\right)\)	\(e\left(\frac{5}{378}\right)\)	\(e\left(\frac{41}{189}\right)\)	\(e\left(\frac{235}{378}\right)\)	\(e\left(\frac{34}{189}\right)\)
\(\chi_{2349}(194,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{359}{378}\right)\)	\(e\left(\frac{170}{189}\right)\)	\(e\left(\frac{373}{378}\right)\)	\(e\left(\frac{145}{189}\right)\)	\(e\left(\frac{107}{126}\right)\)	\(e\left(\frac{59}{63}\right)\)	\(e\left(\frac{239}{378}\right)\)	\(e\left(\frac{32}{189}\right)\)	\(e\left(\frac{271}{378}\right)\)	\(e\left(\frac{151}{189}\right)\)
\(\chi_{2349}(227,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{325}{378}\right)\)	\(e\left(\frac{136}{189}\right)\)	\(e\left(\frac{185}{378}\right)\)	\(e\left(\frac{116}{189}\right)\)	\(e\left(\frac{73}{126}\right)\)	\(e\left(\frac{22}{63}\right)\)	\(e\left(\frac{229}{378}\right)\)	\(e\left(\frac{139}{189}\right)\)	\(e\left(\frac{179}{378}\right)\)	\(e\left(\frac{83}{189}\right)\)
\(\chi_{2349}(239,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{365}{378}\right)\)	\(e\left(\frac{176}{189}\right)\)	\(e\left(\frac{295}{378}\right)\)	\(e\left(\frac{139}{189}\right)\)	\(e\left(\frac{113}{126}\right)\)	\(e\left(\frac{47}{63}\right)\)	\(e\left(\frac{263}{378}\right)\)	\(e\left(\frac{2}{189}\right)\)	\(e\left(\frac{265}{378}\right)\)	\(e\left(\frac{163}{189}\right)\)
\(\chi_{2349}(248,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{215}{378}\right)\)	\(e\left(\frac{26}{189}\right)\)	\(e\left(\frac{355}{378}\right)\)	\(e\left(\frac{100}{189}\right)\)	\(e\left(\frac{89}{126}\right)\)	\(e\left(\frac{32}{63}\right)\)	\(e\left(\frac{41}{378}\right)\)	\(e\left(\frac{185}{189}\right)\)	\(e\left(\frac{37}{378}\right)\)	\(e\left(\frac{52}{189}\right)\)
\(\chi_{2349}(257,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{335}{378}\right)\)	\(e\left(\frac{146}{189}\right)\)	\(e\left(\frac{307}{378}\right)\)	\(e\left(\frac{169}{189}\right)\)	\(e\left(\frac{83}{126}\right)\)	\(e\left(\frac{44}{63}\right)\)	\(e\left(\frac{143}{378}\right)\)	\(e\left(\frac{152}{189}\right)\)	\(e\left(\frac{295}{378}\right)\)	\(e\left(\frac{103}{189}\right)\)
\(\chi_{2349}(281,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{289}{378}\right)\)	\(e\left(\frac{100}{189}\right)\)	\(e\left(\frac{275}{378}\right)\)	\(e\left(\frac{152}{189}\right)\)	\(e\left(\frac{37}{126}\right)\)	\(e\left(\frac{31}{63}\right)\)	\(e\left(\frac{85}{378}\right)\)	\(e\left(\frac{130}{189}\right)\)	\(e\left(\frac{215}{378}\right)\)	\(e\left(\frac{11}{189}\right)\)
\(\chi_{2349}(284,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{263}{378}\right)\)	\(e\left(\frac{74}{189}\right)\)	\(e\left(\frac{109}{378}\right)\)	\(e\left(\frac{52}{189}\right)\)	\(e\left(\frac{11}{126}\right)\)	\(e\left(\frac{62}{63}\right)\)	\(e\left(\frac{233}{378}\right)\)	\(e\left(\frac{134}{189}\right)\)	\(e\left(\frac{367}{378}\right)\)	\(e\left(\frac{148}{189}\right)\)
\(\chi_{2349}(326,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{169}{378}\right)\)	\(e\left(\frac{169}{189}\right)\)	\(e\left(\frac{323}{378}\right)\)	\(e\left(\frac{83}{189}\right)\)	\(e\left(\frac{43}{126}\right)\)	\(e\left(\frac{19}{63}\right)\)	\(e\left(\frac{361}{378}\right)\)	\(e\left(\frac{163}{189}\right)\)	\(e\left(\frac{335}{378}\right)\)	\(e\left(\frac{149}{189}\right)\)
\(\chi_{2349}(335,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{145}{378}\right)\)	\(e\left(\frac{145}{189}\right)\)	\(e\left(\frac{257}{378}\right)\)	\(e\left(\frac{107}{189}\right)\)	\(e\left(\frac{19}{126}\right)\)	\(e\left(\frac{4}{63}\right)\)	\(e\left(\frac{265}{378}\right)\)	\(e\left(\frac{94}{189}\right)\)	\(e\left(\frac{359}{378}\right)\)	\(e\left(\frac{101}{189}\right)\)
\(\chi_{2349}(344,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{13}{378}\right)\)	\(e\left(\frac{13}{189}\right)\)	\(e\left(\frac{83}{378}\right)\)	\(e\left(\frac{50}{189}\right)\)	\(e\left(\frac{13}{126}\right)\)	\(e\left(\frac{16}{63}\right)\)	\(e\left(\frac{115}{378}\right)\)	\(e\left(\frac{187}{189}\right)\)	\(e\left(\frac{113}{378}\right)\)	\(e\left(\frac{26}{189}\right)\)
\(\chi_{2349}(371,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{319}{378}\right)\)	\(e\left(\frac{130}{189}\right)\)	\(e\left(\frac{263}{378}\right)\)	\(e\left(\frac{122}{189}\right)\)	\(e\left(\frac{67}{126}\right)\)	\(e\left(\frac{34}{63}\right)\)	\(e\left(\frac{205}{378}\right)\)	\(e\left(\frac{169}{189}\right)\)	\(e\left(\frac{185}{378}\right)\)	\(e\left(\frac{71}{189}\right)\)
\(\chi_{2349}(401,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{311}{378}\right)\)	\(e\left(\frac{122}{189}\right)\)	\(e\left(\frac{241}{378}\right)\)	\(e\left(\frac{4}{189}\right)\)	\(e\left(\frac{59}{126}\right)\)	\(e\left(\frac{29}{63}\right)\)	\(e\left(\frac{47}{378}\right)\)	\(e\left(\frac{83}{189}\right)\)	\(e\left(\frac{319}{378}\right)\)	\(e\left(\frac{55}{189}\right)\)
\(\chi_{2349}(455,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{275}{378}\right)\)	\(e\left(\frac{86}{189}\right)\)	\(e\left(\frac{331}{378}\right)\)	\(e\left(\frac{40}{189}\right)\)	\(e\left(\frac{23}{126}\right)\)	\(e\left(\frac{38}{63}\right)\)	\(e\left(\frac{281}{378}\right)\)	\(e\left(\frac{74}{189}\right)\)	\(e\left(\frac{355}{378}\right)\)	\(e\left(\frac{172}{189}\right)\)
\(\chi_{2349}(488,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{115}{378}\right)\)	\(e\left(\frac{115}{189}\right)\)	\(e\left(\frac{269}{378}\right)\)	\(e\left(\frac{137}{189}\right)\)	\(e\left(\frac{115}{126}\right)\)	\(e\left(\frac{1}{63}\right)\)	\(e\left(\frac{145}{378}\right)\)	\(e\left(\frac{55}{189}\right)\)	\(e\left(\frac{11}{378}\right)\)	\(e\left(\frac{41}{189}\right)\)
\(\chi_{2349}(500,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{281}{378}\right)\)	\(e\left(\frac{92}{189}\right)\)	\(e\left(\frac{253}{378}\right)\)	\(e\left(\frac{34}{189}\right)\)	\(e\left(\frac{29}{126}\right)\)	\(e\left(\frac{26}{63}\right)\)	\(e\left(\frac{305}{378}\right)\)	\(e\left(\frac{44}{189}\right)\)	\(e\left(\frac{349}{378}\right)\)	\(e\left(\frac{184}{189}\right)\)
\(\chi_{2349}(509,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{131}{378}\right)\)	\(e\left(\frac{131}{189}\right)\)	\(e\left(\frac{313}{378}\right)\)	\(e\left(\frac{184}{189}\right)\)	\(e\left(\frac{5}{126}\right)\)	\(e\left(\frac{11}{63}\right)\)	\(e\left(\frac{83}{378}\right)\)	\(e\left(\frac{38}{189}\right)\)	\(e\left(\frac{121}{378}\right)\)	\(e\left(\frac{73}{189}\right)\)
\(\chi_{2349}(518,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{251}{378}\right)\)	\(e\left(\frac{62}{189}\right)\)	\(e\left(\frac{265}{378}\right)\)	\(e\left(\frac{64}{189}\right)\)	\(e\left(\frac{125}{126}\right)\)	\(e\left(\frac{23}{63}\right)\)	\(e\left(\frac{185}{378}\right)\)	\(e\left(\frac{5}{189}\right)\)	\(e\left(\frac{1}{378}\right)\)	\(e\left(\frac{124}{189}\right)\)
\(\chi_{2349}(542,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{79}{378}\right)\)	\(e\left(\frac{79}{189}\right)\)	\(e\left(\frac{359}{378}\right)\)	\(e\left(\frac{173}{189}\right)\)	\(e\left(\frac{79}{126}\right)\)	\(e\left(\frac{10}{63}\right)\)	\(e\left(\frac{1}{378}\right)\)	\(e\left(\frac{46}{189}\right)\)	\(e\left(\frac{47}{378}\right)\)	\(e\left(\frac{158}{189}\right)\)
\(\chi_{2349}(545,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{179}{378}\right)\)	\(e\left(\frac{179}{189}\right)\)	\(e\left(\frac{67}{378}\right)\)	\(e\left(\frac{136}{189}\right)\)	\(e\left(\frac{53}{126}\right)\)	\(e\left(\frac{41}{63}\right)\)	\(e\left(\frac{275}{378}\right)\)	\(e\left(\frac{176}{189}\right)\)	\(e\left(\frac{73}{378}\right)\)	\(e\left(\frac{169}{189}\right)\)
\(\chi_{2349}(587,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{337}{378}\right)\)	\(e\left(\frac{148}{189}\right)\)	\(e\left(\frac{29}{378}\right)\)	\(e\left(\frac{104}{189}\right)\)	\(e\left(\frac{85}{126}\right)\)	\(e\left(\frac{61}{63}\right)\)	\(e\left(\frac{277}{378}\right)\)	\(e\left(\frac{79}{189}\right)\)	\(e\left(\frac{167}{378}\right)\)	\(e\left(\frac{107}{189}\right)\)
\(\chi_{2349}(596,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{313}{378}\right)\)	\(e\left(\frac{124}{189}\right)\)	\(e\left(\frac{341}{378}\right)\)	\(e\left(\frac{128}{189}\right)\)	\(e\left(\frac{61}{126}\right)\)	\(e\left(\frac{46}{63}\right)\)	\(e\left(\frac{181}{378}\right)\)	\(e\left(\frac{10}{189}\right)\)	\(e\left(\frac{191}{378}\right)\)	\(e\left(\frac{59}{189}\right)\)
\(\chi_{2349}(605,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{181}{378}\right)\)	\(e\left(\frac{181}{189}\right)\)	\(e\left(\frac{167}{378}\right)\)	\(e\left(\frac{71}{189}\right)\)	\(e\left(\frac{55}{126}\right)\)	\(e\left(\frac{58}{63}\right)\)	\(e\left(\frac{31}{378}\right)\)	\(e\left(\frac{103}{189}\right)\)	\(e\left(\frac{323}{378}\right)\)	\(e\left(\frac{173}{189}\right)\)
\(\chi_{2349}(632,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{109}{378}\right)\)	\(e\left(\frac{109}{189}\right)\)	\(e\left(\frac{347}{378}\right)\)	\(e\left(\frac{143}{189}\right)\)	\(e\left(\frac{109}{126}\right)\)	\(e\left(\frac{13}{63}\right)\)	\(e\left(\frac{121}{378}\right)\)	\(e\left(\frac{85}{189}\right)\)	\(e\left(\frac{17}{378}\right)\)	\(e\left(\frac{29}{189}\right)\)
\(\chi_{2349}(662,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{227}{378}\right)\)	\(e\left(\frac{38}{189}\right)\)	\(e\left(\frac{199}{378}\right)\)	\(e\left(\frac{88}{189}\right)\)	\(e\left(\frac{101}{126}\right)\)	\(e\left(\frac{8}{63}\right)\)	\(e\left(\frac{89}{378}\right)\)	\(e\left(\frac{125}{189}\right)\)	\(e\left(\frac{25}{378}\right)\)	\(e\left(\frac{76}{189}\right)\)

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First 31 of 108 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	2349.br
Modulus	$2349$
Conductor	$2349$
Order	$378$
Real	no
Primitive	yes
Minimal	yes
Parity	odd

Modulus:	\(2349\)
Conductor:	\(2349\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(378\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	yes	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	odd	sage:chi.is_odd() pari:zncharisodd(g,chi)