LMFDB - Dirichlet character orbit 1083.x

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1083, base_ring=CyclotomicField(342)) M = H._module chi = DirichletCharacter(H, M([171,1])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(2,1083)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$1083$
Conductor:	$1083$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$342$	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:	$\Q(\zeta_{171})$
Fixed field:	Number field defined by a degree 342 polynomial (not computed)

First 31 of 108 characters in Galois orbit

Character	$-1$	$1$	$2$	$4$	$5$	$7$	$8$	$10$	$11$	$13$	$14$	$16$
$\chi_{1083}(2,\cdot)$	$1$	$1$	$e\left(\frac{86}{171}\right)$	$e\left(\frac{1}{171}\right)$	$e\left(\frac{61}{342}\right)$	$e\left(\frac{25}{57}\right)$	$e\left(\frac{29}{57}\right)$	$e\left(\frac{233}{342}\right)$	$e\left(\frac{91}{114}\right)$	$e\left(\frac{329}{342}\right)$	$e\left(\frac{161}{171}\right)$	$e\left(\frac{2}{171}\right)$
$\chi_{1083}(14,\cdot)$	$1$	$1$	$e\left(\frac{161}{171}\right)$	$e\left(\frac{151}{171}\right)$	$e\left(\frac{319}{342}\right)$	$e\left(\frac{13}{57}\right)$	$e\left(\frac{47}{57}\right)$	$e\left(\frac{299}{342}\right)$	$e\left(\frac{61}{114}\right)$	$e\left(\frac{89}{342}\right)$	$e\left(\frac{29}{171}\right)$	$e\left(\frac{131}{171}\right)$
$\chi_{1083}(29,\cdot)$	$1$	$1$	$e\left(\frac{94}{171}\right)$	$e\left(\frac{17}{171}\right)$	$e\left(\frac{11}{342}\right)$	$e\left(\frac{26}{57}\right)$	$e\left(\frac{37}{57}\right)$	$e\left(\frac{199}{342}\right)$	$e\left(\frac{65}{114}\right)$	$e\left(\frac{121}{342}\right)$	$e\left(\frac{1}{171}\right)$	$e\left(\frac{34}{171}\right)$
$\chi_{1083}(32,\cdot)$	$1$	$1$	$e\left(\frac{88}{171}\right)$	$e\left(\frac{5}{171}\right)$	$e\left(\frac{305}{342}\right)$	$e\left(\frac{11}{57}\right)$	$e\left(\frac{31}{57}\right)$	$e\left(\frac{139}{342}\right)$	$e\left(\frac{113}{114}\right)$	$e\left(\frac{277}{342}\right)$	$e\left(\frac{121}{171}\right)$	$e\left(\frac{10}{171}\right)$
$\chi_{1083}(41,\cdot)$	$1$	$1$	$e\left(\frac{119}{171}\right)$	$e\left(\frac{67}{171}\right)$	$e\left(\frac{325}{342}\right)$	$e\left(\frac{22}{57}\right)$	$e\left(\frac{5}{57}\right)$	$e\left(\frac{221}{342}\right)$	$e\left(\frac{55}{114}\right)$	$e\left(\frac{155}{342}\right)$	$e\left(\frac{14}{171}\right)$	$e\left(\frac{134}{171}\right)$
$\chi_{1083}(53,\cdot)$	$1$	$1$	$e\left(\frac{127}{171}\right)$	$e\left(\frac{83}{171}\right)$	$e\left(\frac{275}{342}\right)$	$e\left(\frac{23}{57}\right)$	$e\left(\frac{13}{57}\right)$	$e\left(\frac{187}{342}\right)$	$e\left(\frac{29}{114}\right)$	$e\left(\frac{289}{342}\right)$	$e\left(\frac{25}{171}\right)$	$e\left(\frac{166}{171}\right)$
$\chi_{1083}(59,\cdot)$	$1$	$1$	$e\left(\frac{5}{171}\right)$	$e\left(\frac{10}{171}\right)$	$e\left(\frac{97}{342}\right)$	$e\left(\frac{22}{57}\right)$	$e\left(\frac{5}{57}\right)$	$e\left(\frac{107}{342}\right)$	$e\left(\frac{55}{114}\right)$	$e\left(\frac{41}{342}\right)$	$e\left(\frac{71}{171}\right)$	$e\left(\frac{20}{171}\right)$
$\chi_{1083}(71,\cdot)$	$1$	$1$	$e\left(\frac{125}{171}\right)$	$e\left(\frac{79}{171}\right)$	$e\left(\frac{31}{342}\right)$	$e\left(\frac{37}{57}\right)$	$e\left(\frac{11}{57}\right)$	$e\left(\frac{281}{342}\right)$	$e\left(\frac{7}{114}\right)$	$e\left(\frac{341}{342}\right)$	$e\left(\frac{65}{171}\right)$	$e\left(\frac{158}{171}\right)$
$\chi_{1083}(86,\cdot)$	$1$	$1$	$e\left(\frac{112}{171}\right)$	$e\left(\frac{53}{171}\right)$	$e\left(\frac{155}{342}\right)$	$e\left(\frac{14}{57}\right)$	$e\left(\frac{55}{57}\right)$	$e\left(\frac{37}{342}\right)$	$e\left(\frac{35}{114}\right)$	$e\left(\frac{337}{342}\right)$	$e\left(\frac{154}{171}\right)$	$e\left(\frac{106}{171}\right)$
$\chi_{1083}(89,\cdot)$	$1$	$1$	$e\left(\frac{115}{171}\right)$	$e\left(\frac{59}{171}\right)$	$e\left(\frac{179}{342}\right)$	$e\left(\frac{50}{57}\right)$	$e\left(\frac{1}{57}\right)$	$e\left(\frac{67}{342}\right)$	$e\left(\frac{11}{114}\right)$	$e\left(\frac{259}{342}\right)$	$e\left(\frac{94}{171}\right)$	$e\left(\frac{118}{171}\right)$
$\chi_{1083}(98,\cdot)$	$1$	$1$	$e\left(\frac{65}{171}\right)$	$e\left(\frac{130}{171}\right)$	$e\left(\frac{235}{342}\right)$	$e\left(\frac{1}{57}\right)$	$e\left(\frac{8}{57}\right)$	$e\left(\frac{23}{342}\right)$	$e\left(\frac{31}{114}\right)$	$e\left(\frac{191}{342}\right)$	$e\left(\frac{68}{171}\right)$	$e\left(\frac{89}{171}\right)$
$\chi_{1083}(110,\cdot)$	$1$	$1$	$e\left(\frac{82}{171}\right)$	$e\left(\frac{164}{171}\right)$	$e\left(\frac{257}{342}\right)$	$e\left(\frac{53}{57}\right)$	$e\left(\frac{25}{57}\right)$	$e\left(\frac{79}{342}\right)$	$e\left(\frac{47}{114}\right)$	$e\left(\frac{91}{342}\right)$	$e\left(\frac{70}{171}\right)$	$e\left(\frac{157}{171}\right)$
$\chi_{1083}(128,\cdot)$	$1$	$1$	$e\left(\frac{89}{171}\right)$	$e\left(\frac{7}{171}\right)$	$e\left(\frac{85}{342}\right)$	$e\left(\frac{4}{57}\right)$	$e\left(\frac{32}{57}\right)$	$e\left(\frac{263}{342}\right)$	$e\left(\frac{67}{114}\right)$	$e\left(\frac{251}{342}\right)$	$e\left(\frac{101}{171}\right)$	$e\left(\frac{14}{171}\right)$
$\chi_{1083}(143,\cdot)$	$1$	$1$	$e\left(\frac{130}{171}\right)$	$e\left(\frac{89}{171}\right)$	$e\left(\frac{299}{342}\right)$	$e\left(\frac{2}{57}\right)$	$e\left(\frac{16}{57}\right)$	$e\left(\frac{217}{342}\right)$	$e\left(\frac{5}{114}\right)$	$e\left(\frac{211}{342}\right)$	$e\left(\frac{136}{171}\right)$	$e\left(\frac{7}{171}\right)$
$\chi_{1083}(146,\cdot)$	$1$	$1$	$e\left(\frac{142}{171}\right)$	$e\left(\frac{113}{171}\right)$	$e\left(\frac{53}{342}\right)$	$e\left(\frac{32}{57}\right)$	$e\left(\frac{28}{57}\right)$	$e\left(\frac{337}{342}\right)$	$e\left(\frac{23}{114}\right)$	$e\left(\frac{241}{342}\right)$	$e\left(\frac{67}{171}\right)$	$e\left(\frac{55}{171}\right)$
$\chi_{1083}(155,\cdot)$	$1$	$1$	$e\left(\frac{11}{171}\right)$	$e\left(\frac{22}{171}\right)$	$e\left(\frac{145}{342}\right)$	$e\left(\frac{37}{57}\right)$	$e\left(\frac{11}{57}\right)$	$e\left(\frac{167}{342}\right)$	$e\left(\frac{7}{114}\right)$	$e\left(\frac{227}{342}\right)$	$e\left(\frac{122}{171}\right)$	$e\left(\frac{44}{171}\right)$
$\chi_{1083}(167,\cdot)$	$1$	$1$	$e\left(\frac{37}{171}\right)$	$e\left(\frac{74}{171}\right)$	$e\left(\frac{239}{342}\right)$	$e\left(\frac{26}{57}\right)$	$e\left(\frac{37}{57}\right)$	$e\left(\frac{313}{342}\right)$	$e\left(\frac{65}{114}\right)$	$e\left(\frac{235}{342}\right)$	$e\left(\frac{115}{171}\right)$	$e\left(\frac{148}{171}\right)$
$\chi_{1083}(173,\cdot)$	$1$	$1$	$e\left(\frac{14}{171}\right)$	$e\left(\frac{28}{171}\right)$	$e\left(\frac{169}{342}\right)$	$e\left(\frac{16}{57}\right)$	$e\left(\frac{14}{57}\right)$	$e\left(\frac{197}{342}\right)$	$e\left(\frac{97}{114}\right)$	$e\left(\frac{149}{342}\right)$	$e\left(\frac{62}{171}\right)$	$e\left(\frac{56}{171}\right)$
$\chi_{1083}(185,\cdot)$	$1$	$1$	$e\left(\frac{53}{171}\right)$	$e\left(\frac{106}{171}\right)$	$e\left(\frac{139}{342}\right)$	$e\left(\frac{28}{57}\right)$	$e\left(\frac{53}{57}\right)$	$e\left(\frac{245}{342}\right)$	$e\left(\frac{13}{114}\right)$	$e\left(\frac{161}{342}\right)$	$e\left(\frac{137}{171}\right)$	$e\left(\frac{41}{171}\right)$
$\chi_{1083}(200,\cdot)$	$1$	$1$	$e\left(\frac{148}{171}\right)$	$e\left(\frac{125}{171}\right)$	$e\left(\frac{101}{342}\right)$	$e\left(\frac{47}{57}\right)$	$e\left(\frac{34}{57}\right)$	$e\left(\frac{55}{342}\right)$	$e\left(\frac{89}{114}\right)$	$e\left(\frac{85}{342}\right)$	$e\left(\frac{118}{171}\right)$	$e\left(\frac{79}{171}\right)$
$\chi_{1083}(203,\cdot)$	$1$	$1$	$e\left(\frac{169}{171}\right)$	$e\left(\frac{167}{171}\right)$	$e\left(\frac{269}{342}\right)$	$e\left(\frac{14}{57}\right)$	$e\left(\frac{55}{57}\right)$	$e\left(\frac{265}{342}\right)$	$e\left(\frac{35}{114}\right)$	$e\left(\frac{223}{342}\right)$	$e\left(\frac{40}{171}\right)$	$e\left(\frac{163}{171}\right)$
$\chi_{1083}(212,\cdot)$	$1$	$1$	$e\left(\frac{128}{171}\right)$	$e\left(\frac{85}{171}\right)$	$e\left(\frac{55}{342}\right)$	$e\left(\frac{16}{57}\right)$	$e\left(\frac{14}{57}\right)$	$e\left(\frac{311}{342}\right)$	$e\left(\frac{97}{114}\right)$	$e\left(\frac{263}{342}\right)$	$e\left(\frac{5}{171}\right)$	$e\left(\frac{170}{171}\right)$
$\chi_{1083}(224,\cdot)$	$1$	$1$	$e\left(\frac{163}{171}\right)$	$e\left(\frac{155}{171}\right)$	$e\left(\frac{221}{342}\right)$	$e\left(\frac{56}{57}\right)$	$e\left(\frac{49}{57}\right)$	$e\left(\frac{205}{342}\right)$	$e\left(\frac{83}{114}\right)$	$e\left(\frac{37}{342}\right)$	$e\left(\frac{160}{171}\right)$	$e\left(\frac{139}{171}\right)$
$\chi_{1083}(230,\cdot)$	$1$	$1$	$e\left(\frac{104}{171}\right)$	$e\left(\frac{37}{171}\right)$	$e\left(\frac{205}{342}\right)$	$e\left(\frac{13}{57}\right)$	$e\left(\frac{47}{57}\right)$	$e\left(\frac{71}{342}\right)$	$e\left(\frac{61}{114}\right)$	$e\left(\frac{203}{342}\right)$	$e\left(\frac{143}{171}\right)$	$e\left(\frac{74}{171}\right)$
$\chi_{1083}(242,\cdot)$	$1$	$1$	$e\left(\frac{17}{171}\right)$	$e\left(\frac{34}{171}\right)$	$e\left(\frac{193}{342}\right)$	$e\left(\frac{52}{57}\right)$	$e\left(\frac{17}{57}\right)$	$e\left(\frac{227}{342}\right)$	$e\left(\frac{73}{114}\right)$	$e\left(\frac{71}{342}\right)$	$e\left(\frac{2}{171}\right)$	$e\left(\frac{68}{171}\right)$
$\chi_{1083}(257,\cdot)$	$1$	$1$	$e\left(\frac{166}{171}\right)$	$e\left(\frac{161}{171}\right)$	$e\left(\frac{245}{342}\right)$	$e\left(\frac{35}{57}\right)$	$e\left(\frac{52}{57}\right)$	$e\left(\frac{235}{342}\right)$	$e\left(\frac{59}{114}\right)$	$e\left(\frac{301}{342}\right)$	$e\left(\frac{100}{171}\right)$	$e\left(\frac{151}{171}\right)$
$\chi_{1083}(260,\cdot)$	$1$	$1$	$e\left(\frac{25}{171}\right)$	$e\left(\frac{50}{171}\right)$	$e\left(\frac{143}{342}\right)$	$e\left(\frac{53}{57}\right)$	$e\left(\frac{25}{57}\right)$	$e\left(\frac{193}{342}\right)$	$e\left(\frac{47}{114}\right)$	$e\left(\frac{205}{342}\right)$	$e\left(\frac{13}{171}\right)$	$e\left(\frac{100}{171}\right)$
$\chi_{1083}(269,\cdot)$	$1$	$1$	$e\left(\frac{74}{171}\right)$	$e\left(\frac{148}{171}\right)$	$e\left(\frac{307}{342}\right)$	$e\left(\frac{52}{57}\right)$	$e\left(\frac{17}{57}\right)$	$e\left(\frac{113}{342}\right)$	$e\left(\frac{73}{114}\right)$	$e\left(\frac{299}{342}\right)$	$e\left(\frac{59}{171}\right)$	$e\left(\frac{125}{171}\right)$
$\chi_{1083}(281,\cdot)$	$1$	$1$	$e\left(\frac{118}{171}\right)$	$e\left(\frac{65}{171}\right)$	$e\left(\frac{203}{342}\right)$	$e\left(\frac{29}{57}\right)$	$e\left(\frac{4}{57}\right)$	$e\left(\frac{97}{342}\right)$	$e\left(\frac{101}{114}\right)$	$e\left(\frac{181}{342}\right)$	$e\left(\frac{34}{171}\right)$	$e\left(\frac{130}{171}\right)$
$\chi_{1083}(287,\cdot)$	$1$	$1$	$e\left(\frac{23}{171}\right)$	$e\left(\frac{46}{171}\right)$	$e\left(\frac{241}{342}\right)$	$e\left(\frac{10}{57}\right)$	$e\left(\frac{23}{57}\right)$	$e\left(\frac{287}{342}\right)$	$e\left(\frac{25}{114}\right)$	$e\left(\frac{257}{342}\right)$	$e\left(\frac{53}{171}\right)$	$e\left(\frac{92}{171}\right)$
$\chi_{1083}(314,\cdot)$	$1$	$1$	$e\left(\frac{13}{171}\right)$	$e\left(\frac{26}{171}\right)$	$e\left(\frac{47}{342}\right)$	$e\left(\frac{23}{57}\right)$	$e\left(\frac{13}{57}\right)$	$e\left(\frac{73}{342}\right)$	$e\left(\frac{29}{114}\right)$	$e\left(\frac{175}{342}\right)$	$e\left(\frac{82}{171}\right)$	$e\left(\frac{52}{171}\right)$

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	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(7\)	\(8\)	\(10\)	\(11\)	\(13\)	\(14\)	\(16\)
\(\chi_{1083}(2,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{86}{171}\right)\)	\(e\left(\frac{1}{171}\right)\)	\(e\left(\frac{61}{342}\right)\)	\(e\left(\frac{25}{57}\right)\)	\(e\left(\frac{29}{57}\right)\)	\(e\left(\frac{233}{342}\right)\)	\(e\left(\frac{91}{114}\right)\)	\(e\left(\frac{329}{342}\right)\)	\(e\left(\frac{161}{171}\right)\)	\(e\left(\frac{2}{171}\right)\)
\(\chi_{1083}(14,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{161}{171}\right)\)	\(e\left(\frac{151}{171}\right)\)	\(e\left(\frac{319}{342}\right)\)	\(e\left(\frac{13}{57}\right)\)	\(e\left(\frac{47}{57}\right)\)	\(e\left(\frac{299}{342}\right)\)	\(e\left(\frac{61}{114}\right)\)	\(e\left(\frac{89}{342}\right)\)	\(e\left(\frac{29}{171}\right)\)	\(e\left(\frac{131}{171}\right)\)
\(\chi_{1083}(29,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{94}{171}\right)\)	\(e\left(\frac{17}{171}\right)\)	\(e\left(\frac{11}{342}\right)\)	\(e\left(\frac{26}{57}\right)\)	\(e\left(\frac{37}{57}\right)\)	\(e\left(\frac{199}{342}\right)\)	\(e\left(\frac{65}{114}\right)\)	\(e\left(\frac{121}{342}\right)\)	\(e\left(\frac{1}{171}\right)\)	\(e\left(\frac{34}{171}\right)\)
\(\chi_{1083}(32,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{88}{171}\right)\)	\(e\left(\frac{5}{171}\right)\)	\(e\left(\frac{305}{342}\right)\)	\(e\left(\frac{11}{57}\right)\)	\(e\left(\frac{31}{57}\right)\)	\(e\left(\frac{139}{342}\right)\)	\(e\left(\frac{113}{114}\right)\)	\(e\left(\frac{277}{342}\right)\)	\(e\left(\frac{121}{171}\right)\)	\(e\left(\frac{10}{171}\right)\)
\(\chi_{1083}(41,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{119}{171}\right)\)	\(e\left(\frac{67}{171}\right)\)	\(e\left(\frac{325}{342}\right)\)	\(e\left(\frac{22}{57}\right)\)	\(e\left(\frac{5}{57}\right)\)	\(e\left(\frac{221}{342}\right)\)	\(e\left(\frac{55}{114}\right)\)	\(e\left(\frac{155}{342}\right)\)	\(e\left(\frac{14}{171}\right)\)	\(e\left(\frac{134}{171}\right)\)
\(\chi_{1083}(53,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{127}{171}\right)\)	\(e\left(\frac{83}{171}\right)\)	\(e\left(\frac{275}{342}\right)\)	\(e\left(\frac{23}{57}\right)\)	\(e\left(\frac{13}{57}\right)\)	\(e\left(\frac{187}{342}\right)\)	\(e\left(\frac{29}{114}\right)\)	\(e\left(\frac{289}{342}\right)\)	\(e\left(\frac{25}{171}\right)\)	\(e\left(\frac{166}{171}\right)\)
\(\chi_{1083}(59,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{171}\right)\)	\(e\left(\frac{10}{171}\right)\)	\(e\left(\frac{97}{342}\right)\)	\(e\left(\frac{22}{57}\right)\)	\(e\left(\frac{5}{57}\right)\)	\(e\left(\frac{107}{342}\right)\)	\(e\left(\frac{55}{114}\right)\)	\(e\left(\frac{41}{342}\right)\)	\(e\left(\frac{71}{171}\right)\)	\(e\left(\frac{20}{171}\right)\)
\(\chi_{1083}(71,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{125}{171}\right)\)	\(e\left(\frac{79}{171}\right)\)	\(e\left(\frac{31}{342}\right)\)	\(e\left(\frac{37}{57}\right)\)	\(e\left(\frac{11}{57}\right)\)	\(e\left(\frac{281}{342}\right)\)	\(e\left(\frac{7}{114}\right)\)	\(e\left(\frac{341}{342}\right)\)	\(e\left(\frac{65}{171}\right)\)	\(e\left(\frac{158}{171}\right)\)
\(\chi_{1083}(86,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{112}{171}\right)\)	\(e\left(\frac{53}{171}\right)\)	\(e\left(\frac{155}{342}\right)\)	\(e\left(\frac{14}{57}\right)\)	\(e\left(\frac{55}{57}\right)\)	\(e\left(\frac{37}{342}\right)\)	\(e\left(\frac{35}{114}\right)\)	\(e\left(\frac{337}{342}\right)\)	\(e\left(\frac{154}{171}\right)\)	\(e\left(\frac{106}{171}\right)\)
\(\chi_{1083}(89,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{115}{171}\right)\)	\(e\left(\frac{59}{171}\right)\)	\(e\left(\frac{179}{342}\right)\)	\(e\left(\frac{50}{57}\right)\)	\(e\left(\frac{1}{57}\right)\)	\(e\left(\frac{67}{342}\right)\)	\(e\left(\frac{11}{114}\right)\)	\(e\left(\frac{259}{342}\right)\)	\(e\left(\frac{94}{171}\right)\)	\(e\left(\frac{118}{171}\right)\)
\(\chi_{1083}(98,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{65}{171}\right)\)	\(e\left(\frac{130}{171}\right)\)	\(e\left(\frac{235}{342}\right)\)	\(e\left(\frac{1}{57}\right)\)	\(e\left(\frac{8}{57}\right)\)	\(e\left(\frac{23}{342}\right)\)	\(e\left(\frac{31}{114}\right)\)	\(e\left(\frac{191}{342}\right)\)	\(e\left(\frac{68}{171}\right)\)	\(e\left(\frac{89}{171}\right)\)
\(\chi_{1083}(110,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{82}{171}\right)\)	\(e\left(\frac{164}{171}\right)\)	\(e\left(\frac{257}{342}\right)\)	\(e\left(\frac{53}{57}\right)\)	\(e\left(\frac{25}{57}\right)\)	\(e\left(\frac{79}{342}\right)\)	\(e\left(\frac{47}{114}\right)\)	\(e\left(\frac{91}{342}\right)\)	\(e\left(\frac{70}{171}\right)\)	\(e\left(\frac{157}{171}\right)\)
\(\chi_{1083}(128,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{89}{171}\right)\)	\(e\left(\frac{7}{171}\right)\)	\(e\left(\frac{85}{342}\right)\)	\(e\left(\frac{4}{57}\right)\)	\(e\left(\frac{32}{57}\right)\)	\(e\left(\frac{263}{342}\right)\)	\(e\left(\frac{67}{114}\right)\)	\(e\left(\frac{251}{342}\right)\)	\(e\left(\frac{101}{171}\right)\)	\(e\left(\frac{14}{171}\right)\)
\(\chi_{1083}(143,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{130}{171}\right)\)	\(e\left(\frac{89}{171}\right)\)	\(e\left(\frac{299}{342}\right)\)	\(e\left(\frac{2}{57}\right)\)	\(e\left(\frac{16}{57}\right)\)	\(e\left(\frac{217}{342}\right)\)	\(e\left(\frac{5}{114}\right)\)	\(e\left(\frac{211}{342}\right)\)	\(e\left(\frac{136}{171}\right)\)	\(e\left(\frac{7}{171}\right)\)
\(\chi_{1083}(146,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{142}{171}\right)\)	\(e\left(\frac{113}{171}\right)\)	\(e\left(\frac{53}{342}\right)\)	\(e\left(\frac{32}{57}\right)\)	\(e\left(\frac{28}{57}\right)\)	\(e\left(\frac{337}{342}\right)\)	\(e\left(\frac{23}{114}\right)\)	\(e\left(\frac{241}{342}\right)\)	\(e\left(\frac{67}{171}\right)\)	\(e\left(\frac{55}{171}\right)\)
\(\chi_{1083}(155,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{171}\right)\)	\(e\left(\frac{22}{171}\right)\)	\(e\left(\frac{145}{342}\right)\)	\(e\left(\frac{37}{57}\right)\)	\(e\left(\frac{11}{57}\right)\)	\(e\left(\frac{167}{342}\right)\)	\(e\left(\frac{7}{114}\right)\)	\(e\left(\frac{227}{342}\right)\)	\(e\left(\frac{122}{171}\right)\)	\(e\left(\frac{44}{171}\right)\)
\(\chi_{1083}(167,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{171}\right)\)	\(e\left(\frac{74}{171}\right)\)	\(e\left(\frac{239}{342}\right)\)	\(e\left(\frac{26}{57}\right)\)	\(e\left(\frac{37}{57}\right)\)	\(e\left(\frac{313}{342}\right)\)	\(e\left(\frac{65}{114}\right)\)	\(e\left(\frac{235}{342}\right)\)	\(e\left(\frac{115}{171}\right)\)	\(e\left(\frac{148}{171}\right)\)
\(\chi_{1083}(173,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{14}{171}\right)\)	\(e\left(\frac{28}{171}\right)\)	\(e\left(\frac{169}{342}\right)\)	\(e\left(\frac{16}{57}\right)\)	\(e\left(\frac{14}{57}\right)\)	\(e\left(\frac{197}{342}\right)\)	\(e\left(\frac{97}{114}\right)\)	\(e\left(\frac{149}{342}\right)\)	\(e\left(\frac{62}{171}\right)\)	\(e\left(\frac{56}{171}\right)\)
\(\chi_{1083}(185,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{171}\right)\)	\(e\left(\frac{106}{171}\right)\)	\(e\left(\frac{139}{342}\right)\)	\(e\left(\frac{28}{57}\right)\)	\(e\left(\frac{53}{57}\right)\)	\(e\left(\frac{245}{342}\right)\)	\(e\left(\frac{13}{114}\right)\)	\(e\left(\frac{161}{342}\right)\)	\(e\left(\frac{137}{171}\right)\)	\(e\left(\frac{41}{171}\right)\)
\(\chi_{1083}(200,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{148}{171}\right)\)	\(e\left(\frac{125}{171}\right)\)	\(e\left(\frac{101}{342}\right)\)	\(e\left(\frac{47}{57}\right)\)	\(e\left(\frac{34}{57}\right)\)	\(e\left(\frac{55}{342}\right)\)	\(e\left(\frac{89}{114}\right)\)	\(e\left(\frac{85}{342}\right)\)	\(e\left(\frac{118}{171}\right)\)	\(e\left(\frac{79}{171}\right)\)
\(\chi_{1083}(203,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{169}{171}\right)\)	\(e\left(\frac{167}{171}\right)\)	\(e\left(\frac{269}{342}\right)\)	\(e\left(\frac{14}{57}\right)\)	\(e\left(\frac{55}{57}\right)\)	\(e\left(\frac{265}{342}\right)\)	\(e\left(\frac{35}{114}\right)\)	\(e\left(\frac{223}{342}\right)\)	\(e\left(\frac{40}{171}\right)\)	\(e\left(\frac{163}{171}\right)\)
\(\chi_{1083}(212,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{128}{171}\right)\)	\(e\left(\frac{85}{171}\right)\)	\(e\left(\frac{55}{342}\right)\)	\(e\left(\frac{16}{57}\right)\)	\(e\left(\frac{14}{57}\right)\)	\(e\left(\frac{311}{342}\right)\)	\(e\left(\frac{97}{114}\right)\)	\(e\left(\frac{263}{342}\right)\)	\(e\left(\frac{5}{171}\right)\)	\(e\left(\frac{170}{171}\right)\)
\(\chi_{1083}(224,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{163}{171}\right)\)	\(e\left(\frac{155}{171}\right)\)	\(e\left(\frac{221}{342}\right)\)	\(e\left(\frac{56}{57}\right)\)	\(e\left(\frac{49}{57}\right)\)	\(e\left(\frac{205}{342}\right)\)	\(e\left(\frac{83}{114}\right)\)	\(e\left(\frac{37}{342}\right)\)	\(e\left(\frac{160}{171}\right)\)	\(e\left(\frac{139}{171}\right)\)
\(\chi_{1083}(230,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{104}{171}\right)\)	\(e\left(\frac{37}{171}\right)\)	\(e\left(\frac{205}{342}\right)\)	\(e\left(\frac{13}{57}\right)\)	\(e\left(\frac{47}{57}\right)\)	\(e\left(\frac{71}{342}\right)\)	\(e\left(\frac{61}{114}\right)\)	\(e\left(\frac{203}{342}\right)\)	\(e\left(\frac{143}{171}\right)\)	\(e\left(\frac{74}{171}\right)\)
\(\chi_{1083}(242,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{171}\right)\)	\(e\left(\frac{34}{171}\right)\)	\(e\left(\frac{193}{342}\right)\)	\(e\left(\frac{52}{57}\right)\)	\(e\left(\frac{17}{57}\right)\)	\(e\left(\frac{227}{342}\right)\)	\(e\left(\frac{73}{114}\right)\)	\(e\left(\frac{71}{342}\right)\)	\(e\left(\frac{2}{171}\right)\)	\(e\left(\frac{68}{171}\right)\)
\(\chi_{1083}(257,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{166}{171}\right)\)	\(e\left(\frac{161}{171}\right)\)	\(e\left(\frac{245}{342}\right)\)	\(e\left(\frac{35}{57}\right)\)	\(e\left(\frac{52}{57}\right)\)	\(e\left(\frac{235}{342}\right)\)	\(e\left(\frac{59}{114}\right)\)	\(e\left(\frac{301}{342}\right)\)	\(e\left(\frac{100}{171}\right)\)	\(e\left(\frac{151}{171}\right)\)
\(\chi_{1083}(260,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{25}{171}\right)\)	\(e\left(\frac{50}{171}\right)\)	\(e\left(\frac{143}{342}\right)\)	\(e\left(\frac{53}{57}\right)\)	\(e\left(\frac{25}{57}\right)\)	\(e\left(\frac{193}{342}\right)\)	\(e\left(\frac{47}{114}\right)\)	\(e\left(\frac{205}{342}\right)\)	\(e\left(\frac{13}{171}\right)\)	\(e\left(\frac{100}{171}\right)\)
\(\chi_{1083}(269,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{74}{171}\right)\)	\(e\left(\frac{148}{171}\right)\)	\(e\left(\frac{307}{342}\right)\)	\(e\left(\frac{52}{57}\right)\)	\(e\left(\frac{17}{57}\right)\)	\(e\left(\frac{113}{342}\right)\)	\(e\left(\frac{73}{114}\right)\)	\(e\left(\frac{299}{342}\right)\)	\(e\left(\frac{59}{171}\right)\)	\(e\left(\frac{125}{171}\right)\)
\(\chi_{1083}(281,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{118}{171}\right)\)	\(e\left(\frac{65}{171}\right)\)	\(e\left(\frac{203}{342}\right)\)	\(e\left(\frac{29}{57}\right)\)	\(e\left(\frac{4}{57}\right)\)	\(e\left(\frac{97}{342}\right)\)	\(e\left(\frac{101}{114}\right)\)	\(e\left(\frac{181}{342}\right)\)	\(e\left(\frac{34}{171}\right)\)	\(e\left(\frac{130}{171}\right)\)
\(\chi_{1083}(287,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{171}\right)\)	\(e\left(\frac{46}{171}\right)\)	\(e\left(\frac{241}{342}\right)\)	\(e\left(\frac{10}{57}\right)\)	\(e\left(\frac{23}{57}\right)\)	\(e\left(\frac{287}{342}\right)\)	\(e\left(\frac{25}{114}\right)\)	\(e\left(\frac{257}{342}\right)\)	\(e\left(\frac{53}{171}\right)\)	\(e\left(\frac{92}{171}\right)\)
\(\chi_{1083}(314,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{171}\right)\)	\(e\left(\frac{26}{171}\right)\)	\(e\left(\frac{47}{342}\right)\)	\(e\left(\frac{23}{57}\right)\)	\(e\left(\frac{13}{57}\right)\)	\(e\left(\frac{73}{342}\right)\)	\(e\left(\frac{29}{114}\right)\)	\(e\left(\frac{175}{342}\right)\)	\(e\left(\frac{82}{171}\right)\)	\(e\left(\frac{52}{171}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Basic properties

Related number fields

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	1083.x
Modulus	$1083$
Conductor	$1083$
Order	$342$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(1083\)
Conductor:	\(1083\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(342\)	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)