LMFDB - Dirichlet character orbit 1183.cc

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comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1183, base_ring=CyclotomicField(156)) M = H._module chi = DirichletCharacter(H, M([130,9])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(5, 1183)) 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("1183.5"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$1183$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$1183$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$156$	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:	$\Q(\zeta_{156})$	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 156 polynomial (not computed)	comment:Fixed field sage:chi.fixed_field()

First 31 of 48 characters in Galois orbit

Character	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$8$	$9$	$10$	$11$	$12$
$\chi_{1183}(5,\cdot)$	$1$	$1$	$e\left(\frac{113}{156}\right)$	$e\left(\frac{77}{78}\right)$	$e\left(\frac{35}{78}\right)$	$e\left(\frac{107}{156}\right)$	$e\left(\frac{37}{52}\right)$	$e\left(\frac{9}{52}\right)$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{43}{156}\right)$	$e\left(\frac{17}{39}\right)$
$\chi_{1183}(31,\cdot)$	$1$	$1$	$e\left(\frac{73}{156}\right)$	$e\left(\frac{67}{78}\right)$	$e\left(\frac{73}{78}\right)$	$e\left(\frac{7}{156}\right)$	$e\left(\frac{17}{52}\right)$	$e\left(\frac{21}{52}\right)$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{83}{156}\right)$	$e\left(\frac{31}{39}\right)$
$\chi_{1183}(47,\cdot)$	$1$	$1$	$e\left(\frac{11}{156}\right)$	$e\left(\frac{71}{78}\right)$	$e\left(\frac{11}{78}\right)$	$e\left(\frac{125}{156}\right)$	$e\left(\frac{51}{52}\right)$	$e\left(\frac{11}{52}\right)$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{145}{156}\right)$	$e\left(\frac{2}{39}\right)$
$\chi_{1183}(73,\cdot)$	$1$	$1$	$e\left(\frac{103}{156}\right)$	$e\left(\frac{55}{78}\right)$	$e\left(\frac{25}{78}\right)$	$e\left(\frac{121}{156}\right)$	$e\left(\frac{19}{52}\right)$	$e\left(\frac{51}{52}\right)$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{53}{156}\right)$	$e\left(\frac{1}{39}\right)$
$\chi_{1183}(96,\cdot)$	$1$	$1$	$e\left(\frac{77}{156}\right)$	$e\left(\frac{29}{78}\right)$	$e\left(\frac{77}{78}\right)$	$e\left(\frac{95}{156}\right)$	$e\left(\frac{45}{52}\right)$	$e\left(\frac{25}{52}\right)$	$e\left(\frac{29}{39}\right)$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{79}{156}\right)$	$e\left(\frac{14}{39}\right)$
$\chi_{1183}(122,\cdot)$	$1$	$1$	$e\left(\frac{37}{156}\right)$	$e\left(\frac{19}{78}\right)$	$e\left(\frac{37}{78}\right)$	$e\left(\frac{151}{156}\right)$	$e\left(\frac{25}{52}\right)$	$e\left(\frac{37}{52}\right)$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{119}{156}\right)$	$e\left(\frac{28}{39}\right)$
$\chi_{1183}(138,\cdot)$	$1$	$1$	$e\left(\frac{47}{156}\right)$	$e\left(\frac{41}{78}\right)$	$e\left(\frac{47}{78}\right)$	$e\left(\frac{137}{156}\right)$	$e\left(\frac{43}{52}\right)$	$e\left(\frac{47}{52}\right)$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{109}{156}\right)$	$e\left(\frac{5}{39}\right)$
$\chi_{1183}(164,\cdot)$	$1$	$1$	$e\left(\frac{139}{156}\right)$	$e\left(\frac{25}{78}\right)$	$e\left(\frac{61}{78}\right)$	$e\left(\frac{133}{156}\right)$	$e\left(\frac{11}{52}\right)$	$e\left(\frac{35}{52}\right)$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{29}{39}\right)$	$e\left(\frac{17}{156}\right)$	$e\left(\frac{4}{39}\right)$
$\chi_{1183}(187,\cdot)$	$1$	$1$	$e\left(\frac{41}{156}\right)$	$e\left(\frac{59}{78}\right)$	$e\left(\frac{41}{78}\right)$	$e\left(\frac{83}{156}\right)$	$e\left(\frac{1}{52}\right)$	$e\left(\frac{41}{52}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{115}{156}\right)$	$e\left(\frac{11}{39}\right)$
$\chi_{1183}(213,\cdot)$	$1$	$1$	$e\left(\frac{1}{156}\right)$	$e\left(\frac{49}{78}\right)$	$e\left(\frac{1}{78}\right)$	$e\left(\frac{139}{156}\right)$	$e\left(\frac{33}{52}\right)$	$e\left(\frac{1}{52}\right)$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{155}{156}\right)$	$e\left(\frac{25}{39}\right)$
$\chi_{1183}(229,\cdot)$	$1$	$1$	$e\left(\frac{83}{156}\right)$	$e\left(\frac{11}{78}\right)$	$e\left(\frac{5}{78}\right)$	$e\left(\frac{149}{156}\right)$	$e\left(\frac{35}{52}\right)$	$e\left(\frac{31}{52}\right)$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{73}{156}\right)$	$e\left(\frac{8}{39}\right)$
$\chi_{1183}(255,\cdot)$	$1$	$1$	$e\left(\frac{19}{156}\right)$	$e\left(\frac{73}{78}\right)$	$e\left(\frac{19}{78}\right)$	$e\left(\frac{145}{156}\right)$	$e\left(\frac{3}{52}\right)$	$e\left(\frac{19}{52}\right)$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{137}{156}\right)$	$e\left(\frac{7}{39}\right)$
$\chi_{1183}(278,\cdot)$	$1$	$1$	$e\left(\frac{5}{156}\right)$	$e\left(\frac{11}{78}\right)$	$e\left(\frac{5}{78}\right)$	$e\left(\frac{71}{156}\right)$	$e\left(\frac{9}{52}\right)$	$e\left(\frac{5}{52}\right)$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{151}{156}\right)$	$e\left(\frac{8}{39}\right)$
$\chi_{1183}(304,\cdot)$	$1$	$1$	$e\left(\frac{121}{156}\right)$	$e\left(\frac{1}{78}\right)$	$e\left(\frac{43}{78}\right)$	$e\left(\frac{127}{156}\right)$	$e\left(\frac{41}{52}\right)$	$e\left(\frac{17}{52}\right)$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{35}{156}\right)$	$e\left(\frac{22}{39}\right)$
$\chi_{1183}(320,\cdot)$	$1$	$1$	$e\left(\frac{119}{156}\right)$	$e\left(\frac{59}{78}\right)$	$e\left(\frac{41}{78}\right)$	$e\left(\frac{5}{156}\right)$	$e\left(\frac{27}{52}\right)$	$e\left(\frac{15}{52}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{37}{156}\right)$	$e\left(\frac{11}{39}\right)$
$\chi_{1183}(346,\cdot)$	$1$	$1$	$e\left(\frac{55}{156}\right)$	$e\left(\frac{43}{78}\right)$	$e\left(\frac{55}{78}\right)$	$e\left(\frac{1}{156}\right)$	$e\left(\frac{47}{52}\right)$	$e\left(\frac{3}{52}\right)$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{101}{156}\right)$	$e\left(\frac{10}{39}\right)$
$\chi_{1183}(369,\cdot)$	$1$	$1$	$e\left(\frac{125}{156}\right)$	$e\left(\frac{41}{78}\right)$	$e\left(\frac{47}{78}\right)$	$e\left(\frac{59}{156}\right)$	$e\left(\frac{17}{52}\right)$	$e\left(\frac{21}{52}\right)$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{31}{156}\right)$	$e\left(\frac{5}{39}\right)$
$\chi_{1183}(395,\cdot)$	$1$	$1$	$e\left(\frac{85}{156}\right)$	$e\left(\frac{31}{78}\right)$	$e\left(\frac{7}{78}\right)$	$e\left(\frac{115}{156}\right)$	$e\left(\frac{49}{52}\right)$	$e\left(\frac{33}{52}\right)$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{71}{156}\right)$	$e\left(\frac{19}{39}\right)$
$\chi_{1183}(411,\cdot)$	$1$	$1$	$e\left(\frac{155}{156}\right)$	$e\left(\frac{29}{78}\right)$	$e\left(\frac{77}{78}\right)$	$e\left(\frac{17}{156}\right)$	$e\left(\frac{19}{52}\right)$	$e\left(\frac{51}{52}\right)$	$e\left(\frac{29}{39}\right)$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{1}{156}\right)$	$e\left(\frac{14}{39}\right)$
$\chi_{1183}(460,\cdot)$	$1$	$1$	$e\left(\frac{89}{156}\right)$	$e\left(\frac{71}{78}\right)$	$e\left(\frac{11}{78}\right)$	$e\left(\frac{47}{156}\right)$	$e\left(\frac{25}{52}\right)$	$e\left(\frac{37}{52}\right)$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{67}{156}\right)$	$e\left(\frac{2}{39}\right)$
$\chi_{1183}(486,\cdot)$	$1$	$1$	$e\left(\frac{49}{156}\right)$	$e\left(\frac{61}{78}\right)$	$e\left(\frac{49}{78}\right)$	$e\left(\frac{103}{156}\right)$	$e\left(\frac{5}{52}\right)$	$e\left(\frac{49}{52}\right)$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{107}{156}\right)$	$e\left(\frac{16}{39}\right)$
$\chi_{1183}(502,\cdot)$	$1$	$1$	$e\left(\frac{35}{156}\right)$	$e\left(\frac{77}{78}\right)$	$e\left(\frac{35}{78}\right)$	$e\left(\frac{29}{156}\right)$	$e\left(\frac{11}{52}\right)$	$e\left(\frac{35}{52}\right)$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{121}{156}\right)$	$e\left(\frac{17}{39}\right)$
$\chi_{1183}(528,\cdot)$	$1$	$1$	$e\left(\frac{127}{156}\right)$	$e\left(\frac{61}{78}\right)$	$e\left(\frac{49}{78}\right)$	$e\left(\frac{25}{156}\right)$	$e\left(\frac{31}{52}\right)$	$e\left(\frac{23}{52}\right)$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{29}{156}\right)$	$e\left(\frac{16}{39}\right)$
$\chi_{1183}(551,\cdot)$	$1$	$1$	$e\left(\frac{53}{156}\right)$	$e\left(\frac{23}{78}\right)$	$e\left(\frac{53}{78}\right)$	$e\left(\frac{35}{156}\right)$	$e\left(\frac{33}{52}\right)$	$e\left(\frac{1}{52}\right)$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{103}{156}\right)$	$e\left(\frac{38}{39}\right)$
$\chi_{1183}(593,\cdot)$	$1$	$1$	$e\left(\frac{71}{156}\right)$	$e\left(\frac{47}{78}\right)$	$e\left(\frac{71}{78}\right)$	$e\left(\frac{41}{156}\right)$	$e\left(\frac{3}{52}\right)$	$e\left(\frac{19}{52}\right)$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{85}{156}\right)$	$e\left(\frac{20}{39}\right)$
$\chi_{1183}(619,\cdot)$	$1$	$1$	$e\left(\frac{7}{156}\right)$	$e\left(\frac{31}{78}\right)$	$e\left(\frac{7}{78}\right)$	$e\left(\frac{37}{156}\right)$	$e\left(\frac{23}{52}\right)$	$e\left(\frac{7}{52}\right)$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{149}{156}\right)$	$e\left(\frac{19}{39}\right)$
$\chi_{1183}(642,\cdot)$	$1$	$1$	$e\left(\frac{17}{156}\right)$	$e\left(\frac{53}{78}\right)$	$e\left(\frac{17}{78}\right)$	$e\left(\frac{23}{156}\right)$	$e\left(\frac{41}{52}\right)$	$e\left(\frac{17}{52}\right)$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{139}{156}\right)$	$e\left(\frac{35}{39}\right)$
$\chi_{1183}(668,\cdot)$	$1$	$1$	$e\left(\frac{133}{156}\right)$	$e\left(\frac{43}{78}\right)$	$e\left(\frac{55}{78}\right)$	$e\left(\frac{79}{156}\right)$	$e\left(\frac{21}{52}\right)$	$e\left(\frac{29}{52}\right)$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{23}{156}\right)$	$e\left(\frac{10}{39}\right)$
$\chi_{1183}(684,\cdot)$	$1$	$1$	$e\left(\frac{107}{156}\right)$	$e\left(\frac{17}{78}\right)$	$e\left(\frac{29}{78}\right)$	$e\left(\frac{53}{156}\right)$	$e\left(\frac{47}{52}\right)$	$e\left(\frac{3}{52}\right)$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{49}{156}\right)$	$e\left(\frac{23}{39}\right)$
$\chi_{1183}(710,\cdot)$	$1$	$1$	$e\left(\frac{43}{156}\right)$	$e\left(\frac{1}{78}\right)$	$e\left(\frac{43}{78}\right)$	$e\left(\frac{49}{156}\right)$	$e\left(\frac{15}{52}\right)$	$e\left(\frac{43}{52}\right)$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{113}{156}\right)$	$e\left(\frac{22}{39}\right)$
$\chi_{1183}(733,\cdot)$	$1$	$1$	$e\left(\frac{137}{156}\right)$	$e\left(\frac{5}{78}\right)$	$e\left(\frac{59}{78}\right)$	$e\left(\frac{11}{156}\right)$	$e\left(\frac{49}{52}\right)$	$e\left(\frac{33}{52}\right)$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{19}{156}\right)$	$e\left(\frac{32}{39}\right)$

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	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(8\)	\(9\)	\(10\)	\(11\)	\(12\)
\(\chi_{1183}(5,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{113}{156}\right)\)	\(e\left(\frac{77}{78}\right)\)	\(e\left(\frac{35}{78}\right)\)	\(e\left(\frac{107}{156}\right)\)	\(e\left(\frac{37}{52}\right)\)	\(e\left(\frac{9}{52}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{43}{156}\right)\)	\(e\left(\frac{17}{39}\right)\)
\(\chi_{1183}(31,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{73}{156}\right)\)	\(e\left(\frac{67}{78}\right)\)	\(e\left(\frac{73}{78}\right)\)	\(e\left(\frac{7}{156}\right)\)	\(e\left(\frac{17}{52}\right)\)	\(e\left(\frac{21}{52}\right)\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{83}{156}\right)\)	\(e\left(\frac{31}{39}\right)\)
\(\chi_{1183}(47,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{156}\right)\)	\(e\left(\frac{71}{78}\right)\)	\(e\left(\frac{11}{78}\right)\)	\(e\left(\frac{125}{156}\right)\)	\(e\left(\frac{51}{52}\right)\)	\(e\left(\frac{11}{52}\right)\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{34}{39}\right)\)	\(e\left(\frac{145}{156}\right)\)	\(e\left(\frac{2}{39}\right)\)
\(\chi_{1183}(73,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{103}{156}\right)\)	\(e\left(\frac{55}{78}\right)\)	\(e\left(\frac{25}{78}\right)\)	\(e\left(\frac{121}{156}\right)\)	\(e\left(\frac{19}{52}\right)\)	\(e\left(\frac{51}{52}\right)\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{53}{156}\right)\)	\(e\left(\frac{1}{39}\right)\)
\(\chi_{1183}(96,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{77}{156}\right)\)	\(e\left(\frac{29}{78}\right)\)	\(e\left(\frac{77}{78}\right)\)	\(e\left(\frac{95}{156}\right)\)	\(e\left(\frac{45}{52}\right)\)	\(e\left(\frac{25}{52}\right)\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{79}{156}\right)\)	\(e\left(\frac{14}{39}\right)\)
\(\chi_{1183}(122,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{156}\right)\)	\(e\left(\frac{19}{78}\right)\)	\(e\left(\frac{37}{78}\right)\)	\(e\left(\frac{151}{156}\right)\)	\(e\left(\frac{25}{52}\right)\)	\(e\left(\frac{37}{52}\right)\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{119}{156}\right)\)	\(e\left(\frac{28}{39}\right)\)
\(\chi_{1183}(138,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{156}\right)\)	\(e\left(\frac{41}{78}\right)\)	\(e\left(\frac{47}{78}\right)\)	\(e\left(\frac{137}{156}\right)\)	\(e\left(\frac{43}{52}\right)\)	\(e\left(\frac{47}{52}\right)\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{109}{156}\right)\)	\(e\left(\frac{5}{39}\right)\)
\(\chi_{1183}(164,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{139}{156}\right)\)	\(e\left(\frac{25}{78}\right)\)	\(e\left(\frac{61}{78}\right)\)	\(e\left(\frac{133}{156}\right)\)	\(e\left(\frac{11}{52}\right)\)	\(e\left(\frac{35}{52}\right)\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{17}{156}\right)\)	\(e\left(\frac{4}{39}\right)\)
\(\chi_{1183}(187,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{156}\right)\)	\(e\left(\frac{59}{78}\right)\)	\(e\left(\frac{41}{78}\right)\)	\(e\left(\frac{83}{156}\right)\)	\(e\left(\frac{1}{52}\right)\)	\(e\left(\frac{41}{52}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{115}{156}\right)\)	\(e\left(\frac{11}{39}\right)\)
\(\chi_{1183}(213,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{156}\right)\)	\(e\left(\frac{49}{78}\right)\)	\(e\left(\frac{1}{78}\right)\)	\(e\left(\frac{139}{156}\right)\)	\(e\left(\frac{33}{52}\right)\)	\(e\left(\frac{1}{52}\right)\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{155}{156}\right)\)	\(e\left(\frac{25}{39}\right)\)
\(\chi_{1183}(229,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{83}{156}\right)\)	\(e\left(\frac{11}{78}\right)\)	\(e\left(\frac{5}{78}\right)\)	\(e\left(\frac{149}{156}\right)\)	\(e\left(\frac{35}{52}\right)\)	\(e\left(\frac{31}{52}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{73}{156}\right)\)	\(e\left(\frac{8}{39}\right)\)
\(\chi_{1183}(255,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{156}\right)\)	\(e\left(\frac{73}{78}\right)\)	\(e\left(\frac{19}{78}\right)\)	\(e\left(\frac{145}{156}\right)\)	\(e\left(\frac{3}{52}\right)\)	\(e\left(\frac{19}{52}\right)\)	\(e\left(\frac{34}{39}\right)\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{137}{156}\right)\)	\(e\left(\frac{7}{39}\right)\)
\(\chi_{1183}(278,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{156}\right)\)	\(e\left(\frac{11}{78}\right)\)	\(e\left(\frac{5}{78}\right)\)	\(e\left(\frac{71}{156}\right)\)	\(e\left(\frac{9}{52}\right)\)	\(e\left(\frac{5}{52}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{151}{156}\right)\)	\(e\left(\frac{8}{39}\right)\)
\(\chi_{1183}(304,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{121}{156}\right)\)	\(e\left(\frac{1}{78}\right)\)	\(e\left(\frac{43}{78}\right)\)	\(e\left(\frac{127}{156}\right)\)	\(e\left(\frac{41}{52}\right)\)	\(e\left(\frac{17}{52}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{35}{156}\right)\)	\(e\left(\frac{22}{39}\right)\)
\(\chi_{1183}(320,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{119}{156}\right)\)	\(e\left(\frac{59}{78}\right)\)	\(e\left(\frac{41}{78}\right)\)	\(e\left(\frac{5}{156}\right)\)	\(e\left(\frac{27}{52}\right)\)	\(e\left(\frac{15}{52}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{37}{156}\right)\)	\(e\left(\frac{11}{39}\right)\)
\(\chi_{1183}(346,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{55}{156}\right)\)	\(e\left(\frac{43}{78}\right)\)	\(e\left(\frac{55}{78}\right)\)	\(e\left(\frac{1}{156}\right)\)	\(e\left(\frac{47}{52}\right)\)	\(e\left(\frac{3}{52}\right)\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{101}{156}\right)\)	\(e\left(\frac{10}{39}\right)\)
\(\chi_{1183}(369,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{125}{156}\right)\)	\(e\left(\frac{41}{78}\right)\)	\(e\left(\frac{47}{78}\right)\)	\(e\left(\frac{59}{156}\right)\)	\(e\left(\frac{17}{52}\right)\)	\(e\left(\frac{21}{52}\right)\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{31}{156}\right)\)	\(e\left(\frac{5}{39}\right)\)
\(\chi_{1183}(395,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{85}{156}\right)\)	\(e\left(\frac{31}{78}\right)\)	\(e\left(\frac{7}{78}\right)\)	\(e\left(\frac{115}{156}\right)\)	\(e\left(\frac{49}{52}\right)\)	\(e\left(\frac{33}{52}\right)\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{71}{156}\right)\)	\(e\left(\frac{19}{39}\right)\)
\(\chi_{1183}(411,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{155}{156}\right)\)	\(e\left(\frac{29}{78}\right)\)	\(e\left(\frac{77}{78}\right)\)	\(e\left(\frac{17}{156}\right)\)	\(e\left(\frac{19}{52}\right)\)	\(e\left(\frac{51}{52}\right)\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{1}{156}\right)\)	\(e\left(\frac{14}{39}\right)\)
\(\chi_{1183}(460,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{89}{156}\right)\)	\(e\left(\frac{71}{78}\right)\)	\(e\left(\frac{11}{78}\right)\)	\(e\left(\frac{47}{156}\right)\)	\(e\left(\frac{25}{52}\right)\)	\(e\left(\frac{37}{52}\right)\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{34}{39}\right)\)	\(e\left(\frac{67}{156}\right)\)	\(e\left(\frac{2}{39}\right)\)
\(\chi_{1183}(486,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{49}{156}\right)\)	\(e\left(\frac{61}{78}\right)\)	\(e\left(\frac{49}{78}\right)\)	\(e\left(\frac{103}{156}\right)\)	\(e\left(\frac{5}{52}\right)\)	\(e\left(\frac{49}{52}\right)\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{107}{156}\right)\)	\(e\left(\frac{16}{39}\right)\)
\(\chi_{1183}(502,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{35}{156}\right)\)	\(e\left(\frac{77}{78}\right)\)	\(e\left(\frac{35}{78}\right)\)	\(e\left(\frac{29}{156}\right)\)	\(e\left(\frac{11}{52}\right)\)	\(e\left(\frac{35}{52}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{121}{156}\right)\)	\(e\left(\frac{17}{39}\right)\)
\(\chi_{1183}(528,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{127}{156}\right)\)	\(e\left(\frac{61}{78}\right)\)	\(e\left(\frac{49}{78}\right)\)	\(e\left(\frac{25}{156}\right)\)	\(e\left(\frac{31}{52}\right)\)	\(e\left(\frac{23}{52}\right)\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{29}{156}\right)\)	\(e\left(\frac{16}{39}\right)\)
\(\chi_{1183}(551,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{156}\right)\)	\(e\left(\frac{23}{78}\right)\)	\(e\left(\frac{53}{78}\right)\)	\(e\left(\frac{35}{156}\right)\)	\(e\left(\frac{33}{52}\right)\)	\(e\left(\frac{1}{52}\right)\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{103}{156}\right)\)	\(e\left(\frac{38}{39}\right)\)
\(\chi_{1183}(593,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{71}{156}\right)\)	\(e\left(\frac{47}{78}\right)\)	\(e\left(\frac{71}{78}\right)\)	\(e\left(\frac{41}{156}\right)\)	\(e\left(\frac{3}{52}\right)\)	\(e\left(\frac{19}{52}\right)\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{85}{156}\right)\)	\(e\left(\frac{20}{39}\right)\)
\(\chi_{1183}(619,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{156}\right)\)	\(e\left(\frac{31}{78}\right)\)	\(e\left(\frac{7}{78}\right)\)	\(e\left(\frac{37}{156}\right)\)	\(e\left(\frac{23}{52}\right)\)	\(e\left(\frac{7}{52}\right)\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{149}{156}\right)\)	\(e\left(\frac{19}{39}\right)\)
\(\chi_{1183}(642,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{156}\right)\)	\(e\left(\frac{53}{78}\right)\)	\(e\left(\frac{17}{78}\right)\)	\(e\left(\frac{23}{156}\right)\)	\(e\left(\frac{41}{52}\right)\)	\(e\left(\frac{17}{52}\right)\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{139}{156}\right)\)	\(e\left(\frac{35}{39}\right)\)
\(\chi_{1183}(668,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{133}{156}\right)\)	\(e\left(\frac{43}{78}\right)\)	\(e\left(\frac{55}{78}\right)\)	\(e\left(\frac{79}{156}\right)\)	\(e\left(\frac{21}{52}\right)\)	\(e\left(\frac{29}{52}\right)\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{23}{156}\right)\)	\(e\left(\frac{10}{39}\right)\)
\(\chi_{1183}(684,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{107}{156}\right)\)	\(e\left(\frac{17}{78}\right)\)	\(e\left(\frac{29}{78}\right)\)	\(e\left(\frac{53}{156}\right)\)	\(e\left(\frac{47}{52}\right)\)	\(e\left(\frac{3}{52}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{49}{156}\right)\)	\(e\left(\frac{23}{39}\right)\)
\(\chi_{1183}(710,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{156}\right)\)	\(e\left(\frac{1}{78}\right)\)	\(e\left(\frac{43}{78}\right)\)	\(e\left(\frac{49}{156}\right)\)	\(e\left(\frac{15}{52}\right)\)	\(e\left(\frac{43}{52}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{113}{156}\right)\)	\(e\left(\frac{22}{39}\right)\)
\(\chi_{1183}(733,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{137}{156}\right)\)	\(e\left(\frac{5}{78}\right)\)	\(e\left(\frac{59}{78}\right)\)	\(e\left(\frac{11}{156}\right)\)	\(e\left(\frac{49}{52}\right)\)	\(e\left(\frac{33}{52}\right)\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{19}{156}\right)\)	\(e\left(\frac{32}{39}\right)\)

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First 31 of 48 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	1183.cc
Modulus	$1183$
Conductor	$1183$
Order	$156$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(1183\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(1183\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(156\)	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);