LMFDB - Dirichlet character orbit 1063.j

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comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1063, base_ring=CyclotomicField(354)) M = H._module chi = DirichletCharacter(H, M([313])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(5, 1063)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

magma:// Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1063.5"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$1063$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$1063$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$354$	comment:Order sage:chi.multiplicative_order() gp:charorder(g,chi) magma:Order(chi);
Real:	no	comment:Whether the character is real sage:chi.multiplicative_order() <= 2 gp:charorder(g,chi) <= 2 magma:Order(chi) le 2;
Primitive:	yes	comment:If the character is primitive sage:chi.is_primitive() gp:#znconreyconductor(g,chi)==1 magma:IsPrimitive(chi);
Minimal:	yes
Parity:	odd	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);

Related number fields

Field of values:	$\Q(\zeta_{177})$	comment:Field of values of chi sage:CyclotomicField(chi.multiplicative_order()) gp:nfinit(polcyclo(charorder(g,chi))) magma:CyclotomicField(Order(chi));
Fixed field:	Number field defined by a degree 354 polynomial (not computed)	comment:Fixed field sage:chi.fixed_field()

First 31 of 116 characters in Galois orbit

Character	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{1063}(5,\cdot)$	$-1$	$1$	$e\left(\frac{110}{177}\right)$	$e\left(\frac{313}{354}\right)$	$e\left(\frac{43}{177}\right)$	$e\left(\frac{29}{118}\right)$	$e\left(\frac{179}{354}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{51}{59}\right)$	$e\left(\frac{136}{177}\right)$	$e\left(\frac{307}{354}\right)$	$e\left(\frac{149}{177}\right)$
$\chi_{1063}(27,\cdot)$	$-1$	$1$	$e\left(\frac{170}{177}\right)$	$e\left(\frac{1}{354}\right)$	$e\left(\frac{163}{177}\right)$	$e\left(\frac{77}{118}\right)$	$e\left(\frac{341}{354}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{52}{59}\right)$	$e\left(\frac{1}{177}\right)$	$e\left(\frac{217}{354}\right)$	$e\left(\frac{5}{177}\right)$
$\chi_{1063}(40,\cdot)$	$-1$	$1$	$e\left(\frac{31}{177}\right)$	$e\left(\frac{299}{354}\right)$	$e\left(\frac{62}{177}\right)$	$e\left(\frac{13}{118}\right)$	$e\left(\frac{7}{354}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{31}{59}\right)$	$e\left(\frac{122}{177}\right)$	$e\left(\frac{101}{354}\right)$	$e\left(\frac{79}{177}\right)$
$\chi_{1063}(41,\cdot)$	$-1$	$1$	$e\left(\frac{167}{177}\right)$	$e\left(\frac{229}{354}\right)$	$e\left(\frac{157}{177}\right)$	$e\left(\frac{51}{118}\right)$	$e\left(\frac{209}{354}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{49}{59}\right)$	$e\left(\frac{52}{177}\right)$	$e\left(\frac{133}{354}\right)$	$e\left(\frac{83}{177}\right)$
$\chi_{1063}(42,\cdot)$	$-1$	$1$	$e\left(\frac{109}{177}\right)$	$e\left(\frac{35}{354}\right)$	$e\left(\frac{41}{177}\right)$	$e\left(\frac{99}{118}\right)$	$e\left(\frac{253}{354}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{50}{59}\right)$	$e\left(\frac{35}{177}\right)$	$e\left(\frac{161}{354}\right)$	$e\left(\frac{175}{177}\right)$
$\chi_{1063}(43,\cdot)$	$-1$	$1$	$e\left(\frac{20}{177}\right)$	$e\left(\frac{73}{354}\right)$	$e\left(\frac{40}{177}\right)$	$e\left(\frac{75}{118}\right)$	$e\left(\frac{113}{354}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{20}{59}\right)$	$e\left(\frac{73}{177}\right)$	$e\left(\frac{265}{354}\right)$	$e\left(\frac{11}{177}\right)$
$\chi_{1063}(57,\cdot)$	$-1$	$1$	$e\left(\frac{175}{177}\right)$	$e\left(\frac{329}{354}\right)$	$e\left(\frac{173}{177}\right)$	$e\left(\frac{81}{118}\right)$	$e\left(\frac{325}{354}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{57}{59}\right)$	$e\left(\frac{152}{177}\right)$	$e\left(\frac{239}{354}\right)$	$e\left(\frac{52}{177}\right)$
$\chi_{1063}(59,\cdot)$	$-1$	$1$	$e\left(\frac{149}{177}\right)$	$e\left(\frac{181}{354}\right)$	$e\left(\frac{121}{177}\right)$	$e\left(\frac{13}{118}\right)$	$e\left(\frac{125}{354}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{31}{59}\right)$	$e\left(\frac{4}{177}\right)$	$e\left(\frac{337}{354}\right)$	$e\left(\frac{20}{177}\right)$
$\chi_{1063}(65,\cdot)$	$-1$	$1$	$e\left(\frac{85}{177}\right)$	$e\left(\frac{89}{354}\right)$	$e\left(\frac{170}{177}\right)$	$e\left(\frac{9}{118}\right)$	$e\left(\frac{259}{354}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{26}{59}\right)$	$e\left(\frac{89}{177}\right)$	$e\left(\frac{197}{354}\right)$	$e\left(\frac{91}{177}\right)$
$\chi_{1063}(66,\cdot)$	$-1$	$1$	$e\left(\frac{125}{177}\right)$	$e\left(\frac{235}{354}\right)$	$e\left(\frac{73}{177}\right)$	$e\left(\frac{41}{118}\right)$	$e\left(\frac{131}{354}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{59}\right)$	$e\left(\frac{58}{177}\right)$	$e\left(\frac{19}{354}\right)$	$e\left(\frac{113}{177}\right)$
$\chi_{1063}(85,\cdot)$	$-1$	$1$	$e\left(\frac{134}{177}\right)$	$e\left(\frac{259}{354}\right)$	$e\left(\frac{91}{177}\right)$	$e\left(\frac{1}{118}\right)$	$e\left(\frac{173}{354}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{16}{59}\right)$	$e\left(\frac{82}{177}\right)$	$e\left(\frac{271}{354}\right)$	$e\left(\frac{56}{177}\right)$
$\chi_{1063}(96,\cdot)$	$-1$	$1$	$e\left(\frac{161}{177}\right)$	$e\left(\frac{331}{354}\right)$	$e\left(\frac{145}{177}\right)$	$e\left(\frac{117}{118}\right)$	$e\left(\frac{299}{354}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{43}{59}\right)$	$e\left(\frac{154}{177}\right)$	$e\left(\frac{319}{354}\right)$	$e\left(\frac{62}{177}\right)$
$\chi_{1063}(106,\cdot)$	$-1$	$1$	$e\left(\frac{32}{177}\right)$	$e\left(\frac{223}{354}\right)$	$e\left(\frac{64}{177}\right)$	$e\left(\frac{61}{118}\right)$	$e\left(\frac{287}{354}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{32}{59}\right)$	$e\left(\frac{46}{177}\right)$	$e\left(\frac{247}{354}\right)$	$e\left(\frac{53}{177}\right)$
$\chi_{1063}(107,\cdot)$	$-1$	$1$	$e\left(\frac{113}{177}\right)$	$e\left(\frac{85}{354}\right)$	$e\left(\frac{49}{177}\right)$	$e\left(\frac{55}{118}\right)$	$e\left(\frac{311}{354}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{54}{59}\right)$	$e\left(\frac{85}{177}\right)$	$e\left(\frac{37}{354}\right)$	$e\left(\frac{71}{177}\right)$
$\chi_{1063}(113,\cdot)$	$-1$	$1$	$e\left(\frac{76}{177}\right)$	$e\left(\frac{65}{354}\right)$	$e\left(\frac{152}{177}\right)$	$e\left(\frac{49}{118}\right)$	$e\left(\frac{217}{354}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{17}{59}\right)$	$e\left(\frac{65}{177}\right)$	$e\left(\frac{299}{354}\right)$	$e\left(\frac{148}{177}\right)$
$\chi_{1063}(116,\cdot)$	$-1$	$1$	$e\left(\frac{5}{177}\right)$	$e\left(\frac{151}{354}\right)$	$e\left(\frac{10}{177}\right)$	$e\left(\frac{63}{118}\right)$	$e\left(\frac{161}{354}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{59}\right)$	$e\left(\frac{151}{177}\right)$	$e\left(\frac{199}{354}\right)$	$e\left(\frac{47}{177}\right)$
$\chi_{1063}(124,\cdot)$	$-1$	$1$	$e\left(\frac{4}{177}\right)$	$e\left(\frac{227}{354}\right)$	$e\left(\frac{8}{177}\right)$	$e\left(\frac{15}{118}\right)$	$e\left(\frac{235}{354}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{4}{59}\right)$	$e\left(\frac{50}{177}\right)$	$e\left(\frac{53}{354}\right)$	$e\left(\frac{73}{177}\right)$
$\chi_{1063}(140,\cdot)$	$-1$	$1$	$e\left(\frac{77}{177}\right)$	$e\left(\frac{343}{354}\right)$	$e\left(\frac{154}{177}\right)$	$e\left(\frac{97}{118}\right)$	$e\left(\frac{143}{354}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{18}{59}\right)$	$e\left(\frac{166}{177}\right)$	$e\left(\frac{91}{354}\right)$	$e\left(\frac{122}{177}\right)$
$\chi_{1063}(141,\cdot)$	$-1$	$1$	$e\left(\frac{164}{177}\right)$	$e\left(\frac{103}{354}\right)$	$e\left(\frac{151}{177}\right)$	$e\left(\frac{25}{118}\right)$	$e\left(\frac{77}{354}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{46}{59}\right)$	$e\left(\frac{103}{177}\right)$	$e\left(\frac{49}{354}\right)$	$e\left(\frac{161}{177}\right)$
$\chi_{1063}(147,\cdot)$	$-1$	$1$	$e\left(\frac{155}{177}\right)$	$e\left(\frac{79}{354}\right)$	$e\left(\frac{133}{177}\right)$	$e\left(\frac{65}{118}\right)$	$e\left(\frac{35}{354}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{37}{59}\right)$	$e\left(\frac{79}{177}\right)$	$e\left(\frac{151}{354}\right)$	$e\left(\frac{41}{177}\right)$
$\chi_{1063}(156,\cdot)$	$-1$	$1$	$e\left(\frac{38}{177}\right)$	$e\left(\frac{121}{354}\right)$	$e\left(\frac{76}{177}\right)$	$e\left(\frac{113}{118}\right)$	$e\left(\frac{197}{354}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{38}{59}\right)$	$e\left(\frac{121}{177}\right)$	$e\left(\frac{61}{354}\right)$	$e\left(\frac{74}{177}\right)$
$\chi_{1063}(185,\cdot)$	$-1$	$1$	$e\left(\frac{136}{177}\right)$	$e\left(\frac{107}{354}\right)$	$e\left(\frac{95}{177}\right)$	$e\left(\frac{97}{118}\right)$	$e\left(\frac{25}{354}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{18}{59}\right)$	$e\left(\frac{107}{177}\right)$	$e\left(\frac{209}{354}\right)$	$e\left(\frac{4}{177}\right)$
$\chi_{1063}(190,\cdot)$	$-1$	$1$	$e\left(\frac{143}{177}\right)$	$e\left(\frac{283}{354}\right)$	$e\left(\frac{109}{177}\right)$	$e\left(\frac{79}{118}\right)$	$e\left(\frac{215}{354}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{25}{59}\right)$	$e\left(\frac{106}{177}\right)$	$e\left(\frac{169}{354}\right)$	$e\left(\frac{176}{177}\right)$
$\chi_{1063}(216,\cdot)$	$-1$	$1$	$e\left(\frac{91}{177}\right)$	$e\left(\frac{341}{354}\right)$	$e\left(\frac{5}{177}\right)$	$e\left(\frac{61}{118}\right)$	$e\left(\frac{169}{354}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{32}{59}\right)$	$e\left(\frac{164}{177}\right)$	$e\left(\frac{11}{354}\right)$	$e\left(\frac{112}{177}\right)$
$\chi_{1063}(244,\cdot)$	$-1$	$1$	$e\left(\frac{49}{177}\right)$	$e\left(\frac{347}{354}\right)$	$e\left(\frac{98}{177}\right)$	$e\left(\frac{51}{118}\right)$	$e\left(\frac{91}{354}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{49}{59}\right)$	$e\left(\frac{170}{177}\right)$	$e\left(\frac{251}{354}\right)$	$e\left(\frac{142}{177}\right)$
$\chi_{1063}(254,\cdot)$	$-1$	$1$	$e\left(\frac{101}{177}\right)$	$e\left(\frac{289}{354}\right)$	$e\left(\frac{25}{177}\right)$	$e\left(\frac{69}{118}\right)$	$e\left(\frac{137}{354}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{42}{59}\right)$	$e\left(\frac{112}{177}\right)$	$e\left(\frac{55}{354}\right)$	$e\left(\frac{29}{177}\right)$
$\chi_{1063}(261,\cdot)$	$-1$	$1$	$e\left(\frac{112}{177}\right)$	$e\left(\frac{161}{354}\right)$	$e\left(\frac{47}{177}\right)$	$e\left(\frac{7}{118}\right)$	$e\left(\frac{31}{354}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{53}{59}\right)$	$e\left(\frac{161}{177}\right)$	$e\left(\frac{245}{354}\right)$	$e\left(\frac{97}{177}\right)$
$\chi_{1063}(271,\cdot)$	$-1$	$1$	$e\left(\frac{11}{177}\right)$	$e\left(\frac{49}{354}\right)$	$e\left(\frac{22}{177}\right)$	$e\left(\frac{115}{118}\right)$	$e\left(\frac{71}{354}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{59}\right)$	$e\left(\frac{49}{177}\right)$	$e\left(\frac{13}{354}\right)$	$e\left(\frac{68}{177}\right)$
$\chi_{1063}(277,\cdot)$	$-1$	$1$	$e\left(\frac{40}{177}\right)$	$e\left(\frac{323}{354}\right)$	$e\left(\frac{80}{177}\right)$	$e\left(\frac{91}{118}\right)$	$e\left(\frac{49}{354}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{40}{59}\right)$	$e\left(\frac{146}{177}\right)$	$e\left(\frac{353}{354}\right)$	$e\left(\frac{22}{177}\right)$
$\chi_{1063}(283,\cdot)$	$-1$	$1$	$e\left(\frac{148}{177}\right)$	$e\left(\frac{257}{354}\right)$	$e\left(\frac{119}{177}\right)$	$e\left(\frac{83}{118}\right)$	$e\left(\frac{199}{354}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{30}{59}\right)$	$e\left(\frac{80}{177}\right)$	$e\left(\frac{191}{354}\right)$	$e\left(\frac{46}{177}\right)$
$\chi_{1063}(300,\cdot)$	$-1$	$1$	$e\left(\frac{106}{177}\right)$	$e\left(\frac{263}{354}\right)$	$e\left(\frac{35}{177}\right)$	$e\left(\frac{73}{118}\right)$	$e\left(\frac{121}{354}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{47}{59}\right)$	$e\left(\frac{86}{177}\right)$	$e\left(\frac{77}{354}\right)$	$e\left(\frac{76}{177}\right)$

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	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\(\chi_{1063}(5,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{110}{177}\right)\)	\(e\left(\frac{313}{354}\right)\)	\(e\left(\frac{43}{177}\right)\)	\(e\left(\frac{29}{118}\right)\)	\(e\left(\frac{179}{354}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{51}{59}\right)\)	\(e\left(\frac{136}{177}\right)\)	\(e\left(\frac{307}{354}\right)\)	\(e\left(\frac{149}{177}\right)\)
\(\chi_{1063}(27,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{170}{177}\right)\)	\(e\left(\frac{1}{354}\right)\)	\(e\left(\frac{163}{177}\right)\)	\(e\left(\frac{77}{118}\right)\)	\(e\left(\frac{341}{354}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{52}{59}\right)\)	\(e\left(\frac{1}{177}\right)\)	\(e\left(\frac{217}{354}\right)\)	\(e\left(\frac{5}{177}\right)\)
\(\chi_{1063}(40,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{31}{177}\right)\)	\(e\left(\frac{299}{354}\right)\)	\(e\left(\frac{62}{177}\right)\)	\(e\left(\frac{13}{118}\right)\)	\(e\left(\frac{7}{354}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{31}{59}\right)\)	\(e\left(\frac{122}{177}\right)\)	\(e\left(\frac{101}{354}\right)\)	\(e\left(\frac{79}{177}\right)\)
\(\chi_{1063}(41,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{167}{177}\right)\)	\(e\left(\frac{229}{354}\right)\)	\(e\left(\frac{157}{177}\right)\)	\(e\left(\frac{51}{118}\right)\)	\(e\left(\frac{209}{354}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{49}{59}\right)\)	\(e\left(\frac{52}{177}\right)\)	\(e\left(\frac{133}{354}\right)\)	\(e\left(\frac{83}{177}\right)\)
\(\chi_{1063}(42,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{109}{177}\right)\)	\(e\left(\frac{35}{354}\right)\)	\(e\left(\frac{41}{177}\right)\)	\(e\left(\frac{99}{118}\right)\)	\(e\left(\frac{253}{354}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{50}{59}\right)\)	\(e\left(\frac{35}{177}\right)\)	\(e\left(\frac{161}{354}\right)\)	\(e\left(\frac{175}{177}\right)\)
\(\chi_{1063}(43,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{20}{177}\right)\)	\(e\left(\frac{73}{354}\right)\)	\(e\left(\frac{40}{177}\right)\)	\(e\left(\frac{75}{118}\right)\)	\(e\left(\frac{113}{354}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{20}{59}\right)\)	\(e\left(\frac{73}{177}\right)\)	\(e\left(\frac{265}{354}\right)\)	\(e\left(\frac{11}{177}\right)\)
\(\chi_{1063}(57,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{175}{177}\right)\)	\(e\left(\frac{329}{354}\right)\)	\(e\left(\frac{173}{177}\right)\)	\(e\left(\frac{81}{118}\right)\)	\(e\left(\frac{325}{354}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{57}{59}\right)\)	\(e\left(\frac{152}{177}\right)\)	\(e\left(\frac{239}{354}\right)\)	\(e\left(\frac{52}{177}\right)\)
\(\chi_{1063}(59,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{149}{177}\right)\)	\(e\left(\frac{181}{354}\right)\)	\(e\left(\frac{121}{177}\right)\)	\(e\left(\frac{13}{118}\right)\)	\(e\left(\frac{125}{354}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{31}{59}\right)\)	\(e\left(\frac{4}{177}\right)\)	\(e\left(\frac{337}{354}\right)\)	\(e\left(\frac{20}{177}\right)\)
\(\chi_{1063}(65,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{85}{177}\right)\)	\(e\left(\frac{89}{354}\right)\)	\(e\left(\frac{170}{177}\right)\)	\(e\left(\frac{9}{118}\right)\)	\(e\left(\frac{259}{354}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{26}{59}\right)\)	\(e\left(\frac{89}{177}\right)\)	\(e\left(\frac{197}{354}\right)\)	\(e\left(\frac{91}{177}\right)\)
\(\chi_{1063}(66,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{125}{177}\right)\)	\(e\left(\frac{235}{354}\right)\)	\(e\left(\frac{73}{177}\right)\)	\(e\left(\frac{41}{118}\right)\)	\(e\left(\frac{131}{354}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{7}{59}\right)\)	\(e\left(\frac{58}{177}\right)\)	\(e\left(\frac{19}{354}\right)\)	\(e\left(\frac{113}{177}\right)\)
\(\chi_{1063}(85,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{134}{177}\right)\)	\(e\left(\frac{259}{354}\right)\)	\(e\left(\frac{91}{177}\right)\)	\(e\left(\frac{1}{118}\right)\)	\(e\left(\frac{173}{354}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{16}{59}\right)\)	\(e\left(\frac{82}{177}\right)\)	\(e\left(\frac{271}{354}\right)\)	\(e\left(\frac{56}{177}\right)\)
\(\chi_{1063}(96,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{161}{177}\right)\)	\(e\left(\frac{331}{354}\right)\)	\(e\left(\frac{145}{177}\right)\)	\(e\left(\frac{117}{118}\right)\)	\(e\left(\frac{299}{354}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{43}{59}\right)\)	\(e\left(\frac{154}{177}\right)\)	\(e\left(\frac{319}{354}\right)\)	\(e\left(\frac{62}{177}\right)\)
\(\chi_{1063}(106,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{32}{177}\right)\)	\(e\left(\frac{223}{354}\right)\)	\(e\left(\frac{64}{177}\right)\)	\(e\left(\frac{61}{118}\right)\)	\(e\left(\frac{287}{354}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{32}{59}\right)\)	\(e\left(\frac{46}{177}\right)\)	\(e\left(\frac{247}{354}\right)\)	\(e\left(\frac{53}{177}\right)\)
\(\chi_{1063}(107,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{113}{177}\right)\)	\(e\left(\frac{85}{354}\right)\)	\(e\left(\frac{49}{177}\right)\)	\(e\left(\frac{55}{118}\right)\)	\(e\left(\frac{311}{354}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{54}{59}\right)\)	\(e\left(\frac{85}{177}\right)\)	\(e\left(\frac{37}{354}\right)\)	\(e\left(\frac{71}{177}\right)\)
\(\chi_{1063}(113,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{76}{177}\right)\)	\(e\left(\frac{65}{354}\right)\)	\(e\left(\frac{152}{177}\right)\)	\(e\left(\frac{49}{118}\right)\)	\(e\left(\frac{217}{354}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{17}{59}\right)\)	\(e\left(\frac{65}{177}\right)\)	\(e\left(\frac{299}{354}\right)\)	\(e\left(\frac{148}{177}\right)\)
\(\chi_{1063}(116,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{5}{177}\right)\)	\(e\left(\frac{151}{354}\right)\)	\(e\left(\frac{10}{177}\right)\)	\(e\left(\frac{63}{118}\right)\)	\(e\left(\frac{161}{354}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{59}\right)\)	\(e\left(\frac{151}{177}\right)\)	\(e\left(\frac{199}{354}\right)\)	\(e\left(\frac{47}{177}\right)\)
\(\chi_{1063}(124,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{4}{177}\right)\)	\(e\left(\frac{227}{354}\right)\)	\(e\left(\frac{8}{177}\right)\)	\(e\left(\frac{15}{118}\right)\)	\(e\left(\frac{235}{354}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{4}{59}\right)\)	\(e\left(\frac{50}{177}\right)\)	\(e\left(\frac{53}{354}\right)\)	\(e\left(\frac{73}{177}\right)\)
\(\chi_{1063}(140,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{77}{177}\right)\)	\(e\left(\frac{343}{354}\right)\)	\(e\left(\frac{154}{177}\right)\)	\(e\left(\frac{97}{118}\right)\)	\(e\left(\frac{143}{354}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{18}{59}\right)\)	\(e\left(\frac{166}{177}\right)\)	\(e\left(\frac{91}{354}\right)\)	\(e\left(\frac{122}{177}\right)\)
\(\chi_{1063}(141,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{164}{177}\right)\)	\(e\left(\frac{103}{354}\right)\)	\(e\left(\frac{151}{177}\right)\)	\(e\left(\frac{25}{118}\right)\)	\(e\left(\frac{77}{354}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{46}{59}\right)\)	\(e\left(\frac{103}{177}\right)\)	\(e\left(\frac{49}{354}\right)\)	\(e\left(\frac{161}{177}\right)\)
\(\chi_{1063}(147,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{155}{177}\right)\)	\(e\left(\frac{79}{354}\right)\)	\(e\left(\frac{133}{177}\right)\)	\(e\left(\frac{65}{118}\right)\)	\(e\left(\frac{35}{354}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{37}{59}\right)\)	\(e\left(\frac{79}{177}\right)\)	\(e\left(\frac{151}{354}\right)\)	\(e\left(\frac{41}{177}\right)\)
\(\chi_{1063}(156,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{38}{177}\right)\)	\(e\left(\frac{121}{354}\right)\)	\(e\left(\frac{76}{177}\right)\)	\(e\left(\frac{113}{118}\right)\)	\(e\left(\frac{197}{354}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{38}{59}\right)\)	\(e\left(\frac{121}{177}\right)\)	\(e\left(\frac{61}{354}\right)\)	\(e\left(\frac{74}{177}\right)\)
\(\chi_{1063}(185,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{136}{177}\right)\)	\(e\left(\frac{107}{354}\right)\)	\(e\left(\frac{95}{177}\right)\)	\(e\left(\frac{97}{118}\right)\)	\(e\left(\frac{25}{354}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{18}{59}\right)\)	\(e\left(\frac{107}{177}\right)\)	\(e\left(\frac{209}{354}\right)\)	\(e\left(\frac{4}{177}\right)\)
\(\chi_{1063}(190,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{143}{177}\right)\)	\(e\left(\frac{283}{354}\right)\)	\(e\left(\frac{109}{177}\right)\)	\(e\left(\frac{79}{118}\right)\)	\(e\left(\frac{215}{354}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{25}{59}\right)\)	\(e\left(\frac{106}{177}\right)\)	\(e\left(\frac{169}{354}\right)\)	\(e\left(\frac{176}{177}\right)\)
\(\chi_{1063}(216,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{91}{177}\right)\)	\(e\left(\frac{341}{354}\right)\)	\(e\left(\frac{5}{177}\right)\)	\(e\left(\frac{61}{118}\right)\)	\(e\left(\frac{169}{354}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{32}{59}\right)\)	\(e\left(\frac{164}{177}\right)\)	\(e\left(\frac{11}{354}\right)\)	\(e\left(\frac{112}{177}\right)\)
\(\chi_{1063}(244,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{49}{177}\right)\)	\(e\left(\frac{347}{354}\right)\)	\(e\left(\frac{98}{177}\right)\)	\(e\left(\frac{51}{118}\right)\)	\(e\left(\frac{91}{354}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{49}{59}\right)\)	\(e\left(\frac{170}{177}\right)\)	\(e\left(\frac{251}{354}\right)\)	\(e\left(\frac{142}{177}\right)\)
\(\chi_{1063}(254,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{101}{177}\right)\)	\(e\left(\frac{289}{354}\right)\)	\(e\left(\frac{25}{177}\right)\)	\(e\left(\frac{69}{118}\right)\)	\(e\left(\frac{137}{354}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{42}{59}\right)\)	\(e\left(\frac{112}{177}\right)\)	\(e\left(\frac{55}{354}\right)\)	\(e\left(\frac{29}{177}\right)\)
\(\chi_{1063}(261,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{112}{177}\right)\)	\(e\left(\frac{161}{354}\right)\)	\(e\left(\frac{47}{177}\right)\)	\(e\left(\frac{7}{118}\right)\)	\(e\left(\frac{31}{354}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{53}{59}\right)\)	\(e\left(\frac{161}{177}\right)\)	\(e\left(\frac{245}{354}\right)\)	\(e\left(\frac{97}{177}\right)\)
\(\chi_{1063}(271,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{11}{177}\right)\)	\(e\left(\frac{49}{354}\right)\)	\(e\left(\frac{22}{177}\right)\)	\(e\left(\frac{115}{118}\right)\)	\(e\left(\frac{71}{354}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{59}\right)\)	\(e\left(\frac{49}{177}\right)\)	\(e\left(\frac{13}{354}\right)\)	\(e\left(\frac{68}{177}\right)\)
\(\chi_{1063}(277,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{40}{177}\right)\)	\(e\left(\frac{323}{354}\right)\)	\(e\left(\frac{80}{177}\right)\)	\(e\left(\frac{91}{118}\right)\)	\(e\left(\frac{49}{354}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{40}{59}\right)\)	\(e\left(\frac{146}{177}\right)\)	\(e\left(\frac{353}{354}\right)\)	\(e\left(\frac{22}{177}\right)\)
\(\chi_{1063}(283,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{148}{177}\right)\)	\(e\left(\frac{257}{354}\right)\)	\(e\left(\frac{119}{177}\right)\)	\(e\left(\frac{83}{118}\right)\)	\(e\left(\frac{199}{354}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{30}{59}\right)\)	\(e\left(\frac{80}{177}\right)\)	\(e\left(\frac{191}{354}\right)\)	\(e\left(\frac{46}{177}\right)\)
\(\chi_{1063}(300,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{106}{177}\right)\)	\(e\left(\frac{263}{354}\right)\)	\(e\left(\frac{35}{177}\right)\)	\(e\left(\frac{73}{118}\right)\)	\(e\left(\frac{121}{354}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{47}{59}\right)\)	\(e\left(\frac{86}{177}\right)\)	\(e\left(\frac{77}{354}\right)\)	\(e\left(\frac{76}{177}\right)\)

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First 31 of 116 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	1063.j
Modulus	$1063$
Conductor	$1063$
Order	$354$
Real	no
Primitive	yes
Minimal	yes
Parity	odd

Modulus:	\(1063\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(1063\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(354\)	comment:Order sage:chi.multiplicative_order() gp:charorder(g,chi) magma:Order(chi);
Real:	no	comment:Whether the character is real sage:chi.multiplicative_order() <= 2 gp:charorder(g,chi) <= 2 magma:Order(chi) le 2;
Primitive:	yes	comment:If the character is primitive sage:chi.is_primitive() gp:#znconreyconductor(g,chi)==1 magma:IsPrimitive(chi);
Minimal:	yes
Parity:	odd	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);