LMFDB - Dirichlet character orbit 1063.i

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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([340])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(8, 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("1063.8"); 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:	$177$	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:	even	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 177 polynomial (not computed)	comment:Fixed field sage:chi.fixed_field()

First 31 of 116 characters in Galois orbit

Character	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{1063}(8,\cdot)$	$1$	$1$	$e\left(\frac{98}{177}\right)$	$e\left(\frac{170}{177}\right)$	$e\left(\frac{19}{177}\right)$	$e\left(\frac{51}{59}\right)$	$e\left(\frac{91}{177}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{39}{59}\right)$	$e\left(\frac{163}{177}\right)$	$e\left(\frac{74}{177}\right)$	$e\left(\frac{107}{177}\right)$
$\chi_{1063}(13,\cdot)$	$1$	$1$	$e\left(\frac{152}{177}\right)$	$e\left(\frac{65}{177}\right)$	$e\left(\frac{127}{177}\right)$	$e\left(\frac{49}{59}\right)$	$e\left(\frac{40}{177}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{34}{59}\right)$	$e\left(\frac{130}{177}\right)$	$e\left(\frac{122}{177}\right)$	$e\left(\frac{119}{177}\right)$
$\chi_{1063}(18,\cdot)$	$1$	$1$	$e\left(\frac{28}{177}\right)$	$e\left(\frac{175}{177}\right)$	$e\left(\frac{56}{177}\right)$	$e\left(\frac{23}{59}\right)$	$e\left(\frac{26}{177}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{28}{59}\right)$	$e\left(\frac{173}{177}\right)$	$e\left(\frac{97}{177}\right)$	$e\left(\frac{157}{177}\right)$
$\chi_{1063}(25,\cdot)$	$1$	$1$	$e\left(\frac{43}{177}\right)$	$e\left(\frac{136}{177}\right)$	$e\left(\frac{86}{177}\right)$	$e\left(\frac{29}{59}\right)$	$e\left(\frac{2}{177}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{43}{59}\right)$	$e\left(\frac{95}{177}\right)$	$e\left(\frac{130}{177}\right)$	$e\left(\frac{121}{177}\right)$
$\chi_{1063}(37,\cdot)$	$1$	$1$	$e\left(\frac{26}{177}\right)$	$e\left(\frac{74}{177}\right)$	$e\left(\frac{52}{177}\right)$	$e\left(\frac{34}{59}\right)$	$e\left(\frac{100}{177}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{26}{59}\right)$	$e\left(\frac{148}{177}\right)$	$e\left(\frac{128}{177}\right)$	$e\left(\frac{32}{177}\right)$
$\chi_{1063}(44,\cdot)$	$1$	$1$	$e\left(\frac{160}{177}\right)$	$e\left(\frac{115}{177}\right)$	$e\left(\frac{143}{177}\right)$	$e\left(\frac{5}{59}\right)$	$e\left(\frac{98}{177}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{42}{59}\right)$	$e\left(\frac{53}{177}\right)$	$e\left(\frac{175}{177}\right)$	$e\left(\frac{88}{177}\right)$
$\chi_{1063}(60,\cdot)$	$1$	$1$	$e\left(\frac{173}{177}\right)$	$e\left(\frac{152}{177}\right)$	$e\left(\frac{169}{177}\right)$	$e\left(\frac{22}{59}\right)$	$e\left(\frac{148}{177}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{55}{59}\right)$	$e\left(\frac{127}{177}\right)$	$e\left(\frac{62}{177}\right)$	$e\left(\frac{104}{177}\right)$
$\chi_{1063}(63,\cdot)$	$1$	$1$	$e\left(\frac{74}{177}\right)$	$e\left(\frac{20}{177}\right)$	$e\left(\frac{148}{177}\right)$	$e\left(\frac{6}{59}\right)$	$e\left(\frac{94}{177}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{15}{59}\right)$	$e\left(\frac{40}{177}\right)$	$e\left(\frac{92}{177}\right)$	$e\left(\frac{23}{177}\right)$
$\chi_{1063}(64,\cdot)$	$1$	$1$	$e\left(\frac{19}{177}\right)$	$e\left(\frac{163}{177}\right)$	$e\left(\frac{38}{177}\right)$	$e\left(\frac{43}{59}\right)$	$e\left(\frac{5}{177}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{19}{59}\right)$	$e\left(\frac{149}{177}\right)$	$e\left(\frac{148}{177}\right)$	$e\left(\frac{37}{177}\right)$
$\chi_{1063}(89,\cdot)$	$1$	$1$	$e\left(\frac{47}{177}\right)$	$e\left(\frac{161}{177}\right)$	$e\left(\frac{94}{177}\right)$	$e\left(\frac{7}{59}\right)$	$e\left(\frac{31}{177}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{47}{59}\right)$	$e\left(\frac{145}{177}\right)$	$e\left(\frac{68}{177}\right)$	$e\left(\frac{17}{177}\right)$
$\chi_{1063}(92,\cdot)$	$1$	$1$	$e\left(\frac{104}{177}\right)$	$e\left(\frac{119}{177}\right)$	$e\left(\frac{31}{177}\right)$	$e\left(\frac{18}{59}\right)$	$e\left(\frac{46}{177}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{45}{59}\right)$	$e\left(\frac{61}{177}\right)$	$e\left(\frac{158}{177}\right)$	$e\left(\frac{128}{177}\right)$
$\chi_{1063}(94,\cdot)$	$1$	$1$	$e\left(\frac{22}{177}\right)$	$e\left(\frac{49}{177}\right)$	$e\left(\frac{44}{177}\right)$	$e\left(\frac{56}{59}\right)$	$e\left(\frac{71}{177}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{22}{59}\right)$	$e\left(\frac{98}{177}\right)$	$e\left(\frac{13}{177}\right)$	$e\left(\frac{136}{177}\right)$
$\chi_{1063}(98,\cdot)$	$1$	$1$	$e\left(\frac{13}{177}\right)$	$e\left(\frac{37}{177}\right)$	$e\left(\frac{26}{177}\right)$	$e\left(\frac{17}{59}\right)$	$e\left(\frac{50}{177}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{13}{59}\right)$	$e\left(\frac{74}{177}\right)$	$e\left(\frac{64}{177}\right)$	$e\left(\frac{16}{177}\right)$
$\chi_{1063}(104,\cdot)$	$1$	$1$	$e\left(\frac{73}{177}\right)$	$e\left(\frac{58}{177}\right)$	$e\left(\frac{146}{177}\right)$	$e\left(\frac{41}{59}\right)$	$e\left(\frac{131}{177}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{14}{59}\right)$	$e\left(\frac{116}{177}\right)$	$e\left(\frac{19}{177}\right)$	$e\left(\frac{49}{177}\right)$
$\chi_{1063}(133,\cdot)$	$1$	$1$	$e\left(\frac{79}{177}\right)$	$e\left(\frac{7}{177}\right)$	$e\left(\frac{158}{177}\right)$	$e\left(\frac{8}{59}\right)$	$e\left(\frac{86}{177}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{20}{59}\right)$	$e\left(\frac{14}{177}\right)$	$e\left(\frac{103}{177}\right)$	$e\left(\frac{70}{177}\right)$
$\chi_{1063}(135,\cdot)$	$1$	$1$	$e\left(\frac{103}{177}\right)$	$e\left(\frac{157}{177}\right)$	$e\left(\frac{29}{177}\right)$	$e\left(\frac{53}{59}\right)$	$e\left(\frac{83}{177}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{44}{59}\right)$	$e\left(\frac{137}{177}\right)$	$e\left(\frac{85}{177}\right)$	$e\left(\frac{154}{177}\right)$
$\chi_{1063}(136,\cdot)$	$1$	$1$	$e\left(\frac{122}{177}\right)$	$e\left(\frac{143}{177}\right)$	$e\left(\frac{67}{177}\right)$	$e\left(\frac{37}{59}\right)$	$e\left(\frac{88}{177}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{4}{59}\right)$	$e\left(\frac{109}{177}\right)$	$e\left(\frac{56}{177}\right)$	$e\left(\frac{14}{177}\right)$
$\chi_{1063}(154,\cdot)$	$1$	$1$	$e\left(\frac{29}{177}\right)$	$e\left(\frac{137}{177}\right)$	$e\left(\frac{58}{177}\right)$	$e\left(\frac{47}{59}\right)$	$e\left(\frac{166}{177}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{29}{59}\right)$	$e\left(\frac{97}{177}\right)$	$e\left(\frac{170}{177}\right)$	$e\left(\frac{131}{177}\right)$
$\chi_{1063}(169,\cdot)$	$1$	$1$	$e\left(\frac{127}{177}\right)$	$e\left(\frac{130}{177}\right)$	$e\left(\frac{77}{177}\right)$	$e\left(\frac{39}{59}\right)$	$e\left(\frac{80}{177}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{9}{59}\right)$	$e\left(\frac{83}{177}\right)$	$e\left(\frac{67}{177}\right)$	$e\left(\frac{61}{177}\right)$
$\chi_{1063}(186,\cdot)$	$1$	$1$	$e\left(\frac{146}{177}\right)$	$e\left(\frac{116}{177}\right)$	$e\left(\frac{115}{177}\right)$	$e\left(\frac{23}{59}\right)$	$e\left(\frac{85}{177}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{28}{59}\right)$	$e\left(\frac{55}{177}\right)$	$e\left(\frac{38}{177}\right)$	$e\left(\frac{98}{177}\right)$
$\chi_{1063}(193,\cdot)$	$1$	$1$	$e\left(\frac{80}{177}\right)$	$e\left(\frac{146}{177}\right)$	$e\left(\frac{160}{177}\right)$	$e\left(\frac{32}{59}\right)$	$e\left(\frac{49}{177}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{21}{59}\right)$	$e\left(\frac{115}{177}\right)$	$e\left(\frac{176}{177}\right)$	$e\left(\frac{44}{177}\right)$
$\chi_{1063}(205,\cdot)$	$1$	$1$	$e\left(\frac{100}{177}\right)$	$e\left(\frac{94}{177}\right)$	$e\left(\frac{23}{177}\right)$	$e\left(\frac{40}{59}\right)$	$e\left(\frac{17}{177}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{41}{59}\right)$	$e\left(\frac{11}{177}\right)$	$e\left(\frac{43}{177}\right)$	$e\left(\frac{55}{177}\right)$
$\chi_{1063}(207,\cdot)$	$1$	$1$	$e\left(\frac{34}{177}\right)$	$e\left(\frac{124}{177}\right)$	$e\left(\frac{68}{177}\right)$	$e\left(\frac{49}{59}\right)$	$e\left(\frac{158}{177}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{34}{59}\right)$	$e\left(\frac{71}{177}\right)$	$e\left(\frac{4}{177}\right)$	$e\left(\frac{1}{177}\right)$
$\chi_{1063}(209,\cdot)$	$1$	$1$	$e\left(\frac{95}{177}\right)$	$e\left(\frac{107}{177}\right)$	$e\left(\frac{13}{177}\right)$	$e\left(\frac{38}{59}\right)$	$e\left(\frac{25}{177}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{36}{59}\right)$	$e\left(\frac{37}{177}\right)$	$e\left(\frac{32}{177}\right)$	$e\left(\frac{8}{177}\right)$
$\chi_{1063}(215,\cdot)$	$1$	$1$	$e\left(\frac{130}{177}\right)$	$e\left(\frac{16}{177}\right)$	$e\left(\frac{83}{177}\right)$	$e\left(\frac{52}{59}\right)$	$e\left(\frac{146}{177}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{12}{59}\right)$	$e\left(\frac{32}{177}\right)$	$e\left(\frac{109}{177}\right)$	$e\left(\frac{160}{177}\right)$
$\chi_{1063}(221,\cdot)$	$1$	$1$	$e\left(\frac{176}{177}\right)$	$e\left(\frac{38}{177}\right)$	$e\left(\frac{175}{177}\right)$	$e\left(\frac{35}{59}\right)$	$e\left(\frac{37}{177}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{58}{59}\right)$	$e\left(\frac{76}{177}\right)$	$e\left(\frac{104}{177}\right)$	$e\left(\frac{26}{177}\right)$
$\chi_{1063}(224,\cdot)$	$1$	$1$	$e\left(\frac{65}{177}\right)$	$e\left(\frac{8}{177}\right)$	$e\left(\frac{130}{177}\right)$	$e\left(\frac{26}{59}\right)$	$e\left(\frac{73}{177}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{6}{59}\right)$	$e\left(\frac{16}{177}\right)$	$e\left(\frac{143}{177}\right)$	$e\left(\frac{80}{177}\right)$
$\chi_{1063}(268,\cdot)$	$1$	$1$	$e\left(\frac{107}{177}\right)$	$e\left(\frac{5}{177}\right)$	$e\left(\frac{37}{177}\right)$	$e\left(\frac{31}{59}\right)$	$e\left(\frac{112}{177}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{48}{59}\right)$	$e\left(\frac{10}{177}\right)$	$e\left(\frac{23}{177}\right)$	$e\left(\frac{50}{177}\right)$
$\chi_{1063}(278,\cdot)$	$1$	$1$	$e\left(\frac{92}{177}\right)$	$e\left(\frac{44}{177}\right)$	$e\left(\frac{7}{177}\right)$	$e\left(\frac{25}{59}\right)$	$e\left(\frac{136}{177}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{33}{59}\right)$	$e\left(\frac{88}{177}\right)$	$e\left(\frac{167}{177}\right)$	$e\left(\frac{86}{177}\right)$
$\chi_{1063}(292,\cdot)$	$1$	$1$	$e\left(\frac{121}{177}\right)$	$e\left(\frac{4}{177}\right)$	$e\left(\frac{65}{177}\right)$	$e\left(\frac{13}{59}\right)$	$e\left(\frac{125}{177}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{59}\right)$	$e\left(\frac{8}{177}\right)$	$e\left(\frac{160}{177}\right)$	$e\left(\frac{40}{177}\right)$
$\chi_{1063}(293,\cdot)$	$1$	$1$	$e\left(\frac{139}{177}\right)$	$e\left(\frac{28}{177}\right)$	$e\left(\frac{101}{177}\right)$	$e\left(\frac{32}{59}\right)$	$e\left(\frac{167}{177}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{21}{59}\right)$	$e\left(\frac{56}{177}\right)$	$e\left(\frac{58}{177}\right)$	$e\left(\frac{103}{177}\right)$

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	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\(\chi_{1063}(8,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{98}{177}\right)\)	\(e\left(\frac{170}{177}\right)\)	\(e\left(\frac{19}{177}\right)\)	\(e\left(\frac{51}{59}\right)\)	\(e\left(\frac{91}{177}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{39}{59}\right)\)	\(e\left(\frac{163}{177}\right)\)	\(e\left(\frac{74}{177}\right)\)	\(e\left(\frac{107}{177}\right)\)
\(\chi_{1063}(13,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{152}{177}\right)\)	\(e\left(\frac{65}{177}\right)\)	\(e\left(\frac{127}{177}\right)\)	\(e\left(\frac{49}{59}\right)\)	\(e\left(\frac{40}{177}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{34}{59}\right)\)	\(e\left(\frac{130}{177}\right)\)	\(e\left(\frac{122}{177}\right)\)	\(e\left(\frac{119}{177}\right)\)
\(\chi_{1063}(18,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{28}{177}\right)\)	\(e\left(\frac{175}{177}\right)\)	\(e\left(\frac{56}{177}\right)\)	\(e\left(\frac{23}{59}\right)\)	\(e\left(\frac{26}{177}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{28}{59}\right)\)	\(e\left(\frac{173}{177}\right)\)	\(e\left(\frac{97}{177}\right)\)	\(e\left(\frac{157}{177}\right)\)
\(\chi_{1063}(25,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{177}\right)\)	\(e\left(\frac{136}{177}\right)\)	\(e\left(\frac{86}{177}\right)\)	\(e\left(\frac{29}{59}\right)\)	\(e\left(\frac{2}{177}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{43}{59}\right)\)	\(e\left(\frac{95}{177}\right)\)	\(e\left(\frac{130}{177}\right)\)	\(e\left(\frac{121}{177}\right)\)
\(\chi_{1063}(37,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{26}{177}\right)\)	\(e\left(\frac{74}{177}\right)\)	\(e\left(\frac{52}{177}\right)\)	\(e\left(\frac{34}{59}\right)\)	\(e\left(\frac{100}{177}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{26}{59}\right)\)	\(e\left(\frac{148}{177}\right)\)	\(e\left(\frac{128}{177}\right)\)	\(e\left(\frac{32}{177}\right)\)
\(\chi_{1063}(44,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{160}{177}\right)\)	\(e\left(\frac{115}{177}\right)\)	\(e\left(\frac{143}{177}\right)\)	\(e\left(\frac{5}{59}\right)\)	\(e\left(\frac{98}{177}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{42}{59}\right)\)	\(e\left(\frac{53}{177}\right)\)	\(e\left(\frac{175}{177}\right)\)	\(e\left(\frac{88}{177}\right)\)
\(\chi_{1063}(60,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{173}{177}\right)\)	\(e\left(\frac{152}{177}\right)\)	\(e\left(\frac{169}{177}\right)\)	\(e\left(\frac{22}{59}\right)\)	\(e\left(\frac{148}{177}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{55}{59}\right)\)	\(e\left(\frac{127}{177}\right)\)	\(e\left(\frac{62}{177}\right)\)	\(e\left(\frac{104}{177}\right)\)
\(\chi_{1063}(63,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{74}{177}\right)\)	\(e\left(\frac{20}{177}\right)\)	\(e\left(\frac{148}{177}\right)\)	\(e\left(\frac{6}{59}\right)\)	\(e\left(\frac{94}{177}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{15}{59}\right)\)	\(e\left(\frac{40}{177}\right)\)	\(e\left(\frac{92}{177}\right)\)	\(e\left(\frac{23}{177}\right)\)
\(\chi_{1063}(64,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{177}\right)\)	\(e\left(\frac{163}{177}\right)\)	\(e\left(\frac{38}{177}\right)\)	\(e\left(\frac{43}{59}\right)\)	\(e\left(\frac{5}{177}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{19}{59}\right)\)	\(e\left(\frac{149}{177}\right)\)	\(e\left(\frac{148}{177}\right)\)	\(e\left(\frac{37}{177}\right)\)
\(\chi_{1063}(89,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{177}\right)\)	\(e\left(\frac{161}{177}\right)\)	\(e\left(\frac{94}{177}\right)\)	\(e\left(\frac{7}{59}\right)\)	\(e\left(\frac{31}{177}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{47}{59}\right)\)	\(e\left(\frac{145}{177}\right)\)	\(e\left(\frac{68}{177}\right)\)	\(e\left(\frac{17}{177}\right)\)
\(\chi_{1063}(92,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{104}{177}\right)\)	\(e\left(\frac{119}{177}\right)\)	\(e\left(\frac{31}{177}\right)\)	\(e\left(\frac{18}{59}\right)\)	\(e\left(\frac{46}{177}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{45}{59}\right)\)	\(e\left(\frac{61}{177}\right)\)	\(e\left(\frac{158}{177}\right)\)	\(e\left(\frac{128}{177}\right)\)
\(\chi_{1063}(94,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{22}{177}\right)\)	\(e\left(\frac{49}{177}\right)\)	\(e\left(\frac{44}{177}\right)\)	\(e\left(\frac{56}{59}\right)\)	\(e\left(\frac{71}{177}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{22}{59}\right)\)	\(e\left(\frac{98}{177}\right)\)	\(e\left(\frac{13}{177}\right)\)	\(e\left(\frac{136}{177}\right)\)
\(\chi_{1063}(98,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{177}\right)\)	\(e\left(\frac{37}{177}\right)\)	\(e\left(\frac{26}{177}\right)\)	\(e\left(\frac{17}{59}\right)\)	\(e\left(\frac{50}{177}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{13}{59}\right)\)	\(e\left(\frac{74}{177}\right)\)	\(e\left(\frac{64}{177}\right)\)	\(e\left(\frac{16}{177}\right)\)
\(\chi_{1063}(104,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{73}{177}\right)\)	\(e\left(\frac{58}{177}\right)\)	\(e\left(\frac{146}{177}\right)\)	\(e\left(\frac{41}{59}\right)\)	\(e\left(\frac{131}{177}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{14}{59}\right)\)	\(e\left(\frac{116}{177}\right)\)	\(e\left(\frac{19}{177}\right)\)	\(e\left(\frac{49}{177}\right)\)
\(\chi_{1063}(133,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{79}{177}\right)\)	\(e\left(\frac{7}{177}\right)\)	\(e\left(\frac{158}{177}\right)\)	\(e\left(\frac{8}{59}\right)\)	\(e\left(\frac{86}{177}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{20}{59}\right)\)	\(e\left(\frac{14}{177}\right)\)	\(e\left(\frac{103}{177}\right)\)	\(e\left(\frac{70}{177}\right)\)
\(\chi_{1063}(135,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{103}{177}\right)\)	\(e\left(\frac{157}{177}\right)\)	\(e\left(\frac{29}{177}\right)\)	\(e\left(\frac{53}{59}\right)\)	\(e\left(\frac{83}{177}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{44}{59}\right)\)	\(e\left(\frac{137}{177}\right)\)	\(e\left(\frac{85}{177}\right)\)	\(e\left(\frac{154}{177}\right)\)
\(\chi_{1063}(136,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{122}{177}\right)\)	\(e\left(\frac{143}{177}\right)\)	\(e\left(\frac{67}{177}\right)\)	\(e\left(\frac{37}{59}\right)\)	\(e\left(\frac{88}{177}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{4}{59}\right)\)	\(e\left(\frac{109}{177}\right)\)	\(e\left(\frac{56}{177}\right)\)	\(e\left(\frac{14}{177}\right)\)
\(\chi_{1063}(154,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{177}\right)\)	\(e\left(\frac{137}{177}\right)\)	\(e\left(\frac{58}{177}\right)\)	\(e\left(\frac{47}{59}\right)\)	\(e\left(\frac{166}{177}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{29}{59}\right)\)	\(e\left(\frac{97}{177}\right)\)	\(e\left(\frac{170}{177}\right)\)	\(e\left(\frac{131}{177}\right)\)
\(\chi_{1063}(169,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{127}{177}\right)\)	\(e\left(\frac{130}{177}\right)\)	\(e\left(\frac{77}{177}\right)\)	\(e\left(\frac{39}{59}\right)\)	\(e\left(\frac{80}{177}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{9}{59}\right)\)	\(e\left(\frac{83}{177}\right)\)	\(e\left(\frac{67}{177}\right)\)	\(e\left(\frac{61}{177}\right)\)
\(\chi_{1063}(186,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{146}{177}\right)\)	\(e\left(\frac{116}{177}\right)\)	\(e\left(\frac{115}{177}\right)\)	\(e\left(\frac{23}{59}\right)\)	\(e\left(\frac{85}{177}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{28}{59}\right)\)	\(e\left(\frac{55}{177}\right)\)	\(e\left(\frac{38}{177}\right)\)	\(e\left(\frac{98}{177}\right)\)
\(\chi_{1063}(193,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{80}{177}\right)\)	\(e\left(\frac{146}{177}\right)\)	\(e\left(\frac{160}{177}\right)\)	\(e\left(\frac{32}{59}\right)\)	\(e\left(\frac{49}{177}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{21}{59}\right)\)	\(e\left(\frac{115}{177}\right)\)	\(e\left(\frac{176}{177}\right)\)	\(e\left(\frac{44}{177}\right)\)
\(\chi_{1063}(205,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{100}{177}\right)\)	\(e\left(\frac{94}{177}\right)\)	\(e\left(\frac{23}{177}\right)\)	\(e\left(\frac{40}{59}\right)\)	\(e\left(\frac{17}{177}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{41}{59}\right)\)	\(e\left(\frac{11}{177}\right)\)	\(e\left(\frac{43}{177}\right)\)	\(e\left(\frac{55}{177}\right)\)
\(\chi_{1063}(207,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{34}{177}\right)\)	\(e\left(\frac{124}{177}\right)\)	\(e\left(\frac{68}{177}\right)\)	\(e\left(\frac{49}{59}\right)\)	\(e\left(\frac{158}{177}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{34}{59}\right)\)	\(e\left(\frac{71}{177}\right)\)	\(e\left(\frac{4}{177}\right)\)	\(e\left(\frac{1}{177}\right)\)
\(\chi_{1063}(209,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{95}{177}\right)\)	\(e\left(\frac{107}{177}\right)\)	\(e\left(\frac{13}{177}\right)\)	\(e\left(\frac{38}{59}\right)\)	\(e\left(\frac{25}{177}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{36}{59}\right)\)	\(e\left(\frac{37}{177}\right)\)	\(e\left(\frac{32}{177}\right)\)	\(e\left(\frac{8}{177}\right)\)
\(\chi_{1063}(215,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{130}{177}\right)\)	\(e\left(\frac{16}{177}\right)\)	\(e\left(\frac{83}{177}\right)\)	\(e\left(\frac{52}{59}\right)\)	\(e\left(\frac{146}{177}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{12}{59}\right)\)	\(e\left(\frac{32}{177}\right)\)	\(e\left(\frac{109}{177}\right)\)	\(e\left(\frac{160}{177}\right)\)
\(\chi_{1063}(221,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{176}{177}\right)\)	\(e\left(\frac{38}{177}\right)\)	\(e\left(\frac{175}{177}\right)\)	\(e\left(\frac{35}{59}\right)\)	\(e\left(\frac{37}{177}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{58}{59}\right)\)	\(e\left(\frac{76}{177}\right)\)	\(e\left(\frac{104}{177}\right)\)	\(e\left(\frac{26}{177}\right)\)
\(\chi_{1063}(224,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{65}{177}\right)\)	\(e\left(\frac{8}{177}\right)\)	\(e\left(\frac{130}{177}\right)\)	\(e\left(\frac{26}{59}\right)\)	\(e\left(\frac{73}{177}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{6}{59}\right)\)	\(e\left(\frac{16}{177}\right)\)	\(e\left(\frac{143}{177}\right)\)	\(e\left(\frac{80}{177}\right)\)
\(\chi_{1063}(268,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{107}{177}\right)\)	\(e\left(\frac{5}{177}\right)\)	\(e\left(\frac{37}{177}\right)\)	\(e\left(\frac{31}{59}\right)\)	\(e\left(\frac{112}{177}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{48}{59}\right)\)	\(e\left(\frac{10}{177}\right)\)	\(e\left(\frac{23}{177}\right)\)	\(e\left(\frac{50}{177}\right)\)
\(\chi_{1063}(278,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{92}{177}\right)\)	\(e\left(\frac{44}{177}\right)\)	\(e\left(\frac{7}{177}\right)\)	\(e\left(\frac{25}{59}\right)\)	\(e\left(\frac{136}{177}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{33}{59}\right)\)	\(e\left(\frac{88}{177}\right)\)	\(e\left(\frac{167}{177}\right)\)	\(e\left(\frac{86}{177}\right)\)
\(\chi_{1063}(292,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{121}{177}\right)\)	\(e\left(\frac{4}{177}\right)\)	\(e\left(\frac{65}{177}\right)\)	\(e\left(\frac{13}{59}\right)\)	\(e\left(\frac{125}{177}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{3}{59}\right)\)	\(e\left(\frac{8}{177}\right)\)	\(e\left(\frac{160}{177}\right)\)	\(e\left(\frac{40}{177}\right)\)
\(\chi_{1063}(293,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{139}{177}\right)\)	\(e\left(\frac{28}{177}\right)\)	\(e\left(\frac{101}{177}\right)\)	\(e\left(\frac{32}{59}\right)\)	\(e\left(\frac{167}{177}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{21}{59}\right)\)	\(e\left(\frac{56}{177}\right)\)	\(e\left(\frac{58}{177}\right)\)	\(e\left(\frac{103}{177}\right)\)

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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.i
Modulus	$1063$
Conductor	$1063$
Order	$177$
Real	no
Primitive	yes
Minimal	yes
Parity	even

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:	\(177\)	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:	even	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);