LMFDB - Dirichlet character orbit 2166.r

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comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2166, base_ring=CyclotomicField(114)) M = H._module chi = DirichletCharacter(H, M([57,73])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(65, 2166)) 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("2166.65"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$2166$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$1083$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$114$	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:	no, induced from 1083.t	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:	$\Q(\zeta_{57})$	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 114 polynomial (not computed)	comment:Fixed field sage:chi.fixed_field()

First 31 of 36 characters in Galois orbit

Character	$-1$	$1$	$5$	$7$	$11$	$13$	$17$	$23$	$25$	$29$	$31$	$35$
$\chi_{2166}(65,\cdot)$	$1$	$1$	$e\left(\frac{7}{114}\right)$	$e\left(\frac{1}{19}\right)$	$e\left(\frac{31}{38}\right)$	$e\left(\frac{77}{114}\right)$	$e\left(\frac{25}{114}\right)$	$e\left(\frac{113}{114}\right)$	$e\left(\frac{7}{57}\right)$	$e\left(\frac{22}{57}\right)$	$e\left(\frac{1}{38}\right)$	$e\left(\frac{13}{114}\right)$
$\chi_{2166}(107,\cdot)$	$1$	$1$	$e\left(\frac{71}{114}\right)$	$e\left(\frac{2}{19}\right)$	$e\left(\frac{5}{38}\right)$	$e\left(\frac{97}{114}\right)$	$e\left(\frac{107}{114}\right)$	$e\left(\frac{55}{114}\right)$	$e\left(\frac{14}{57}\right)$	$e\left(\frac{44}{57}\right)$	$e\left(\frac{21}{38}\right)$	$e\left(\frac{83}{114}\right)$
$\chi_{2166}(179,\cdot)$	$1$	$1$	$e\left(\frac{13}{114}\right)$	$e\left(\frac{10}{19}\right)$	$e\left(\frac{25}{38}\right)$	$e\left(\frac{29}{114}\right)$	$e\left(\frac{79}{114}\right)$	$e\left(\frac{47}{114}\right)$	$e\left(\frac{13}{57}\right)$	$e\left(\frac{49}{57}\right)$	$e\left(\frac{29}{38}\right)$	$e\left(\frac{73}{114}\right)$
$\chi_{2166}(221,\cdot)$	$1$	$1$	$e\left(\frac{113}{114}\right)$	$e\left(\frac{8}{19}\right)$	$e\left(\frac{1}{38}\right)$	$e\left(\frac{103}{114}\right)$	$e\left(\frac{29}{114}\right)$	$e\left(\frac{49}{114}\right)$	$e\left(\frac{56}{57}\right)$	$e\left(\frac{5}{57}\right)$	$e\left(\frac{27}{38}\right)$	$e\left(\frac{47}{114}\right)$
$\chi_{2166}(335,\cdot)$	$1$	$1$	$e\left(\frac{41}{114}\right)$	$e\left(\frac{14}{19}\right)$	$e\left(\frac{35}{38}\right)$	$e\left(\frac{109}{114}\right)$	$e\left(\frac{65}{114}\right)$	$e\left(\frac{43}{114}\right)$	$e\left(\frac{41}{57}\right)$	$e\left(\frac{23}{57}\right)$	$e\left(\frac{33}{38}\right)$	$e\left(\frac{11}{114}\right)$
$\chi_{2166}(407,\cdot)$	$1$	$1$	$e\left(\frac{25}{114}\right)$	$e\left(\frac{9}{19}\right)$	$e\left(\frac{13}{38}\right)$	$e\left(\frac{47}{114}\right)$	$e\left(\frac{73}{114}\right)$	$e\left(\frac{29}{114}\right)$	$e\left(\frac{25}{57}\right)$	$e\left(\frac{46}{57}\right)$	$e\left(\frac{9}{38}\right)$	$e\left(\frac{79}{114}\right)$
$\chi_{2166}(449,\cdot)$	$1$	$1$	$e\left(\frac{83}{114}\right)$	$e\left(\frac{1}{19}\right)$	$e\left(\frac{31}{38}\right)$	$e\left(\frac{1}{114}\right)$	$e\left(\frac{101}{114}\right)$	$e\left(\frac{37}{114}\right)$	$e\left(\frac{26}{57}\right)$	$e\left(\frac{41}{57}\right)$	$e\left(\frac{1}{38}\right)$	$e\left(\frac{89}{114}\right)$
$\chi_{2166}(521,\cdot)$	$1$	$1$	$e\left(\frac{31}{114}\right)$	$e\left(\frac{18}{19}\right)$	$e\left(\frac{7}{38}\right)$	$e\left(\frac{113}{114}\right)$	$e\left(\frac{13}{114}\right)$	$e\left(\frac{77}{114}\right)$	$e\left(\frac{31}{57}\right)$	$e\left(\frac{16}{57}\right)$	$e\left(\frac{37}{38}\right)$	$e\left(\frac{25}{114}\right)$
$\chi_{2166}(563,\cdot)$	$1$	$1$	$e\left(\frac{11}{114}\right)$	$e\left(\frac{7}{19}\right)$	$e\left(\frac{27}{38}\right)$	$e\left(\frac{7}{114}\right)$	$e\left(\frac{23}{114}\right)$	$e\left(\frac{31}{114}\right)$	$e\left(\frac{11}{57}\right)$	$e\left(\frac{2}{57}\right)$	$e\left(\frac{7}{38}\right)$	$e\left(\frac{53}{114}\right)$
$\chi_{2166}(635,\cdot)$	$1$	$1$	$e\left(\frac{37}{114}\right)$	$e\left(\frac{8}{19}\right)$	$e\left(\frac{1}{38}\right)$	$e\left(\frac{65}{114}\right)$	$e\left(\frac{67}{114}\right)$	$e\left(\frac{11}{114}\right)$	$e\left(\frac{37}{57}\right)$	$e\left(\frac{43}{57}\right)$	$e\left(\frac{27}{38}\right)$	$e\left(\frac{85}{114}\right)$
$\chi_{2166}(677,\cdot)$	$1$	$1$	$e\left(\frac{53}{114}\right)$	$e\left(\frac{13}{19}\right)$	$e\left(\frac{23}{38}\right)$	$e\left(\frac{13}{114}\right)$	$e\left(\frac{59}{114}\right)$	$e\left(\frac{25}{114}\right)$	$e\left(\frac{53}{57}\right)$	$e\left(\frac{20}{57}\right)$	$e\left(\frac{13}{38}\right)$	$e\left(\frac{17}{114}\right)$
$\chi_{2166}(749,\cdot)$	$1$	$1$	$e\left(\frac{43}{114}\right)$	$e\left(\frac{17}{19}\right)$	$e\left(\frac{33}{38}\right)$	$e\left(\frac{17}{114}\right)$	$e\left(\frac{7}{114}\right)$	$e\left(\frac{59}{114}\right)$	$e\left(\frac{43}{57}\right)$	$e\left(\frac{13}{57}\right)$	$e\left(\frac{17}{38}\right)$	$e\left(\frac{31}{114}\right)$
$\chi_{2166}(863,\cdot)$	$1$	$1$	$e\left(\frac{49}{114}\right)$	$e\left(\frac{7}{19}\right)$	$e\left(\frac{27}{38}\right)$	$e\left(\frac{83}{114}\right)$	$e\left(\frac{61}{114}\right)$	$e\left(\frac{107}{114}\right)$	$e\left(\frac{49}{57}\right)$	$e\left(\frac{40}{57}\right)$	$e\left(\frac{7}{38}\right)$	$e\left(\frac{91}{114}\right)$
$\chi_{2166}(905,\cdot)$	$1$	$1$	$e\left(\frac{23}{114}\right)$	$e\left(\frac{6}{19}\right)$	$e\left(\frac{15}{38}\right)$	$e\left(\frac{25}{114}\right)$	$e\left(\frac{17}{114}\right)$	$e\left(\frac{13}{114}\right)$	$e\left(\frac{23}{57}\right)$	$e\left(\frac{56}{57}\right)$	$e\left(\frac{25}{38}\right)$	$e\left(\frac{59}{114}\right)$
$\chi_{2166}(977,\cdot)$	$1$	$1$	$e\left(\frac{55}{114}\right)$	$e\left(\frac{16}{19}\right)$	$e\left(\frac{21}{38}\right)$	$e\left(\frac{35}{114}\right)$	$e\left(\frac{1}{114}\right)$	$e\left(\frac{41}{114}\right)$	$e\left(\frac{55}{57}\right)$	$e\left(\frac{10}{57}\right)$	$e\left(\frac{35}{38}\right)$	$e\left(\frac{37}{114}\right)$
$\chi_{2166}(1019,\cdot)$	$1$	$1$	$e\left(\frac{65}{114}\right)$	$e\left(\frac{12}{19}\right)$	$e\left(\frac{11}{38}\right)$	$e\left(\frac{31}{114}\right)$	$e\left(\frac{53}{114}\right)$	$e\left(\frac{7}{114}\right)$	$e\left(\frac{8}{57}\right)$	$e\left(\frac{17}{57}\right)$	$e\left(\frac{31}{38}\right)$	$e\left(\frac{23}{114}\right)$
$\chi_{2166}(1091,\cdot)$	$1$	$1$	$e\left(\frac{61}{114}\right)$	$e\left(\frac{6}{19}\right)$	$e\left(\frac{15}{38}\right)$	$e\left(\frac{101}{114}\right)$	$e\left(\frac{55}{114}\right)$	$e\left(\frac{89}{114}\right)$	$e\left(\frac{4}{57}\right)$	$e\left(\frac{37}{57}\right)$	$e\left(\frac{25}{38}\right)$	$e\left(\frac{97}{114}\right)$
$\chi_{2166}(1133,\cdot)$	$1$	$1$	$e\left(\frac{107}{114}\right)$	$e\left(\frac{18}{19}\right)$	$e\left(\frac{7}{38}\right)$	$e\left(\frac{37}{114}\right)$	$e\left(\frac{89}{114}\right)$	$e\left(\frac{1}{114}\right)$	$e\left(\frac{50}{57}\right)$	$e\left(\frac{35}{57}\right)$	$e\left(\frac{37}{38}\right)$	$e\left(\frac{101}{114}\right)$
$\chi_{2166}(1205,\cdot)$	$1$	$1$	$e\left(\frac{67}{114}\right)$	$e\left(\frac{15}{19}\right)$	$e\left(\frac{9}{38}\right)$	$e\left(\frac{53}{114}\right)$	$e\left(\frac{109}{114}\right)$	$e\left(\frac{23}{114}\right)$	$e\left(\frac{10}{57}\right)$	$e\left(\frac{7}{57}\right)$	$e\left(\frac{15}{38}\right)$	$e\left(\frac{43}{114}\right)$
$\chi_{2166}(1247,\cdot)$	$1$	$1$	$e\left(\frac{35}{114}\right)$	$e\left(\frac{5}{19}\right)$	$e\left(\frac{3}{38}\right)$	$e\left(\frac{43}{114}\right)$	$e\left(\frac{11}{114}\right)$	$e\left(\frac{109}{114}\right)$	$e\left(\frac{35}{57}\right)$	$e\left(\frac{53}{57}\right)$	$e\left(\frac{5}{38}\right)$	$e\left(\frac{65}{114}\right)$
$\chi_{2166}(1319,\cdot)$	$1$	$1$	$e\left(\frac{73}{114}\right)$	$e\left(\frac{5}{19}\right)$	$e\left(\frac{3}{38}\right)$	$e\left(\frac{5}{114}\right)$	$e\left(\frac{49}{114}\right)$	$e\left(\frac{71}{114}\right)$	$e\left(\frac{16}{57}\right)$	$e\left(\frac{34}{57}\right)$	$e\left(\frac{5}{38}\right)$	$e\left(\frac{103}{114}\right)$
$\chi_{2166}(1361,\cdot)$	$1$	$1$	$e\left(\frac{77}{114}\right)$	$e\left(\frac{11}{19}\right)$	$e\left(\frac{37}{38}\right)$	$e\left(\frac{49}{114}\right)$	$e\left(\frac{47}{114}\right)$	$e\left(\frac{103}{114}\right)$	$e\left(\frac{20}{57}\right)$	$e\left(\frac{14}{57}\right)$	$e\left(\frac{11}{38}\right)$	$e\left(\frac{29}{114}\right)$
$\chi_{2166}(1433,\cdot)$	$1$	$1$	$e\left(\frac{79}{114}\right)$	$e\left(\frac{14}{19}\right)$	$e\left(\frac{35}{38}\right)$	$e\left(\frac{71}{114}\right)$	$e\left(\frac{103}{114}\right)$	$e\left(\frac{5}{114}\right)$	$e\left(\frac{22}{57}\right)$	$e\left(\frac{4}{57}\right)$	$e\left(\frac{33}{38}\right)$	$e\left(\frac{49}{114}\right)$
$\chi_{2166}(1475,\cdot)$	$1$	$1$	$e\left(\frac{5}{114}\right)$	$e\left(\frac{17}{19}\right)$	$e\left(\frac{33}{38}\right)$	$e\left(\frac{55}{114}\right)$	$e\left(\frac{83}{114}\right)$	$e\left(\frac{97}{114}\right)$	$e\left(\frac{5}{57}\right)$	$e\left(\frac{32}{57}\right)$	$e\left(\frac{17}{38}\right)$	$e\left(\frac{107}{114}\right)$
$\chi_{2166}(1547,\cdot)$	$1$	$1$	$e\left(\frac{85}{114}\right)$	$e\left(\frac{4}{19}\right)$	$e\left(\frac{29}{38}\right)$	$e\left(\frac{23}{114}\right)$	$e\left(\frac{43}{114}\right)$	$e\left(\frac{53}{114}\right)$	$e\left(\frac{28}{57}\right)$	$e\left(\frac{31}{57}\right)$	$e\left(\frac{23}{38}\right)$	$e\left(\frac{109}{114}\right)$
$\chi_{2166}(1589,\cdot)$	$1$	$1$	$e\left(\frac{47}{114}\right)$	$e\left(\frac{4}{19}\right)$	$e\left(\frac{29}{38}\right)$	$e\left(\frac{61}{114}\right)$	$e\left(\frac{5}{114}\right)$	$e\left(\frac{91}{114}\right)$	$e\left(\frac{47}{57}\right)$	$e\left(\frac{50}{57}\right)$	$e\left(\frac{23}{38}\right)$	$e\left(\frac{71}{114}\right)$
$\chi_{2166}(1661,\cdot)$	$1$	$1$	$e\left(\frac{91}{114}\right)$	$e\left(\frac{13}{19}\right)$	$e\left(\frac{23}{38}\right)$	$e\left(\frac{89}{114}\right)$	$e\left(\frac{97}{114}\right)$	$e\left(\frac{101}{114}\right)$	$e\left(\frac{34}{57}\right)$	$e\left(\frac{1}{57}\right)$	$e\left(\frac{13}{38}\right)$	$e\left(\frac{55}{114}\right)$
$\chi_{2166}(1703,\cdot)$	$1$	$1$	$e\left(\frac{89}{114}\right)$	$e\left(\frac{10}{19}\right)$	$e\left(\frac{25}{38}\right)$	$e\left(\frac{67}{114}\right)$	$e\left(\frac{41}{114}\right)$	$e\left(\frac{85}{114}\right)$	$e\left(\frac{32}{57}\right)$	$e\left(\frac{11}{57}\right)$	$e\left(\frac{29}{38}\right)$	$e\left(\frac{35}{114}\right)$
$\chi_{2166}(1775,\cdot)$	$1$	$1$	$e\left(\frac{97}{114}\right)$	$e\left(\frac{3}{19}\right)$	$e\left(\frac{17}{38}\right)$	$e\left(\frac{41}{114}\right)$	$e\left(\frac{37}{114}\right)$	$e\left(\frac{35}{114}\right)$	$e\left(\frac{40}{57}\right)$	$e\left(\frac{28}{57}\right)$	$e\left(\frac{3}{38}\right)$	$e\left(\frac{1}{114}\right)$
$\chi_{2166}(1817,\cdot)$	$1$	$1$	$e\left(\frac{17}{114}\right)$	$e\left(\frac{16}{19}\right)$	$e\left(\frac{21}{38}\right)$	$e\left(\frac{73}{114}\right)$	$e\left(\frac{77}{114}\right)$	$e\left(\frac{79}{114}\right)$	$e\left(\frac{17}{57}\right)$	$e\left(\frac{29}{57}\right)$	$e\left(\frac{35}{38}\right)$	$e\left(\frac{113}{114}\right)$
$\chi_{2166}(1889,\cdot)$	$1$	$1$	$e\left(\frac{103}{114}\right)$	$e\left(\frac{12}{19}\right)$	$e\left(\frac{11}{38}\right)$	$e\left(\frac{107}{114}\right)$	$e\left(\frac{91}{114}\right)$	$e\left(\frac{83}{114}\right)$	$e\left(\frac{46}{57}\right)$	$e\left(\frac{55}{57}\right)$	$e\left(\frac{31}{38}\right)$	$e\left(\frac{61}{114}\right)$

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$ over number fields
Genus 2 curves
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Character	\(-1\)	\(1\)	\(5\)	\(7\)	\(11\)	\(13\)	\(17\)	\(23\)	\(25\)	\(29\)	\(31\)	\(35\)
\(\chi_{2166}(65,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{114}\right)\)	\(e\left(\frac{1}{19}\right)\)	\(e\left(\frac{31}{38}\right)\)	\(e\left(\frac{77}{114}\right)\)	\(e\left(\frac{25}{114}\right)\)	\(e\left(\frac{113}{114}\right)\)	\(e\left(\frac{7}{57}\right)\)	\(e\left(\frac{22}{57}\right)\)	\(e\left(\frac{1}{38}\right)\)	\(e\left(\frac{13}{114}\right)\)
\(\chi_{2166}(107,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{71}{114}\right)\)	\(e\left(\frac{2}{19}\right)\)	\(e\left(\frac{5}{38}\right)\)	\(e\left(\frac{97}{114}\right)\)	\(e\left(\frac{107}{114}\right)\)	\(e\left(\frac{55}{114}\right)\)	\(e\left(\frac{14}{57}\right)\)	\(e\left(\frac{44}{57}\right)\)	\(e\left(\frac{21}{38}\right)\)	\(e\left(\frac{83}{114}\right)\)
\(\chi_{2166}(179,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{114}\right)\)	\(e\left(\frac{10}{19}\right)\)	\(e\left(\frac{25}{38}\right)\)	\(e\left(\frac{29}{114}\right)\)	\(e\left(\frac{79}{114}\right)\)	\(e\left(\frac{47}{114}\right)\)	\(e\left(\frac{13}{57}\right)\)	\(e\left(\frac{49}{57}\right)\)	\(e\left(\frac{29}{38}\right)\)	\(e\left(\frac{73}{114}\right)\)
\(\chi_{2166}(221,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{113}{114}\right)\)	\(e\left(\frac{8}{19}\right)\)	\(e\left(\frac{1}{38}\right)\)	\(e\left(\frac{103}{114}\right)\)	\(e\left(\frac{29}{114}\right)\)	\(e\left(\frac{49}{114}\right)\)	\(e\left(\frac{56}{57}\right)\)	\(e\left(\frac{5}{57}\right)\)	\(e\left(\frac{27}{38}\right)\)	\(e\left(\frac{47}{114}\right)\)
\(\chi_{2166}(335,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{114}\right)\)	\(e\left(\frac{14}{19}\right)\)	\(e\left(\frac{35}{38}\right)\)	\(e\left(\frac{109}{114}\right)\)	\(e\left(\frac{65}{114}\right)\)	\(e\left(\frac{43}{114}\right)\)	\(e\left(\frac{41}{57}\right)\)	\(e\left(\frac{23}{57}\right)\)	\(e\left(\frac{33}{38}\right)\)	\(e\left(\frac{11}{114}\right)\)
\(\chi_{2166}(407,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{25}{114}\right)\)	\(e\left(\frac{9}{19}\right)\)	\(e\left(\frac{13}{38}\right)\)	\(e\left(\frac{47}{114}\right)\)	\(e\left(\frac{73}{114}\right)\)	\(e\left(\frac{29}{114}\right)\)	\(e\left(\frac{25}{57}\right)\)	\(e\left(\frac{46}{57}\right)\)	\(e\left(\frac{9}{38}\right)\)	\(e\left(\frac{79}{114}\right)\)
\(\chi_{2166}(449,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{83}{114}\right)\)	\(e\left(\frac{1}{19}\right)\)	\(e\left(\frac{31}{38}\right)\)	\(e\left(\frac{1}{114}\right)\)	\(e\left(\frac{101}{114}\right)\)	\(e\left(\frac{37}{114}\right)\)	\(e\left(\frac{26}{57}\right)\)	\(e\left(\frac{41}{57}\right)\)	\(e\left(\frac{1}{38}\right)\)	\(e\left(\frac{89}{114}\right)\)
\(\chi_{2166}(521,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{114}\right)\)	\(e\left(\frac{18}{19}\right)\)	\(e\left(\frac{7}{38}\right)\)	\(e\left(\frac{113}{114}\right)\)	\(e\left(\frac{13}{114}\right)\)	\(e\left(\frac{77}{114}\right)\)	\(e\left(\frac{31}{57}\right)\)	\(e\left(\frac{16}{57}\right)\)	\(e\left(\frac{37}{38}\right)\)	\(e\left(\frac{25}{114}\right)\)
\(\chi_{2166}(563,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{114}\right)\)	\(e\left(\frac{7}{19}\right)\)	\(e\left(\frac{27}{38}\right)\)	\(e\left(\frac{7}{114}\right)\)	\(e\left(\frac{23}{114}\right)\)	\(e\left(\frac{31}{114}\right)\)	\(e\left(\frac{11}{57}\right)\)	\(e\left(\frac{2}{57}\right)\)	\(e\left(\frac{7}{38}\right)\)	\(e\left(\frac{53}{114}\right)\)
\(\chi_{2166}(635,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{114}\right)\)	\(e\left(\frac{8}{19}\right)\)	\(e\left(\frac{1}{38}\right)\)	\(e\left(\frac{65}{114}\right)\)	\(e\left(\frac{67}{114}\right)\)	\(e\left(\frac{11}{114}\right)\)	\(e\left(\frac{37}{57}\right)\)	\(e\left(\frac{43}{57}\right)\)	\(e\left(\frac{27}{38}\right)\)	\(e\left(\frac{85}{114}\right)\)
\(\chi_{2166}(677,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{114}\right)\)	\(e\left(\frac{13}{19}\right)\)	\(e\left(\frac{23}{38}\right)\)	\(e\left(\frac{13}{114}\right)\)	\(e\left(\frac{59}{114}\right)\)	\(e\left(\frac{25}{114}\right)\)	\(e\left(\frac{53}{57}\right)\)	\(e\left(\frac{20}{57}\right)\)	\(e\left(\frac{13}{38}\right)\)	\(e\left(\frac{17}{114}\right)\)
\(\chi_{2166}(749,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{114}\right)\)	\(e\left(\frac{17}{19}\right)\)	\(e\left(\frac{33}{38}\right)\)	\(e\left(\frac{17}{114}\right)\)	\(e\left(\frac{7}{114}\right)\)	\(e\left(\frac{59}{114}\right)\)	\(e\left(\frac{43}{57}\right)\)	\(e\left(\frac{13}{57}\right)\)	\(e\left(\frac{17}{38}\right)\)	\(e\left(\frac{31}{114}\right)\)
\(\chi_{2166}(863,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{49}{114}\right)\)	\(e\left(\frac{7}{19}\right)\)	\(e\left(\frac{27}{38}\right)\)	\(e\left(\frac{83}{114}\right)\)	\(e\left(\frac{61}{114}\right)\)	\(e\left(\frac{107}{114}\right)\)	\(e\left(\frac{49}{57}\right)\)	\(e\left(\frac{40}{57}\right)\)	\(e\left(\frac{7}{38}\right)\)	\(e\left(\frac{91}{114}\right)\)
\(\chi_{2166}(905,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{114}\right)\)	\(e\left(\frac{6}{19}\right)\)	\(e\left(\frac{15}{38}\right)\)	\(e\left(\frac{25}{114}\right)\)	\(e\left(\frac{17}{114}\right)\)	\(e\left(\frac{13}{114}\right)\)	\(e\left(\frac{23}{57}\right)\)	\(e\left(\frac{56}{57}\right)\)	\(e\left(\frac{25}{38}\right)\)	\(e\left(\frac{59}{114}\right)\)
\(\chi_{2166}(977,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{55}{114}\right)\)	\(e\left(\frac{16}{19}\right)\)	\(e\left(\frac{21}{38}\right)\)	\(e\left(\frac{35}{114}\right)\)	\(e\left(\frac{1}{114}\right)\)	\(e\left(\frac{41}{114}\right)\)	\(e\left(\frac{55}{57}\right)\)	\(e\left(\frac{10}{57}\right)\)	\(e\left(\frac{35}{38}\right)\)	\(e\left(\frac{37}{114}\right)\)
\(\chi_{2166}(1019,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{65}{114}\right)\)	\(e\left(\frac{12}{19}\right)\)	\(e\left(\frac{11}{38}\right)\)	\(e\left(\frac{31}{114}\right)\)	\(e\left(\frac{53}{114}\right)\)	\(e\left(\frac{7}{114}\right)\)	\(e\left(\frac{8}{57}\right)\)	\(e\left(\frac{17}{57}\right)\)	\(e\left(\frac{31}{38}\right)\)	\(e\left(\frac{23}{114}\right)\)
\(\chi_{2166}(1091,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{61}{114}\right)\)	\(e\left(\frac{6}{19}\right)\)	\(e\left(\frac{15}{38}\right)\)	\(e\left(\frac{101}{114}\right)\)	\(e\left(\frac{55}{114}\right)\)	\(e\left(\frac{89}{114}\right)\)	\(e\left(\frac{4}{57}\right)\)	\(e\left(\frac{37}{57}\right)\)	\(e\left(\frac{25}{38}\right)\)	\(e\left(\frac{97}{114}\right)\)
\(\chi_{2166}(1133,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{107}{114}\right)\)	\(e\left(\frac{18}{19}\right)\)	\(e\left(\frac{7}{38}\right)\)	\(e\left(\frac{37}{114}\right)\)	\(e\left(\frac{89}{114}\right)\)	\(e\left(\frac{1}{114}\right)\)	\(e\left(\frac{50}{57}\right)\)	\(e\left(\frac{35}{57}\right)\)	\(e\left(\frac{37}{38}\right)\)	\(e\left(\frac{101}{114}\right)\)
\(\chi_{2166}(1205,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{67}{114}\right)\)	\(e\left(\frac{15}{19}\right)\)	\(e\left(\frac{9}{38}\right)\)	\(e\left(\frac{53}{114}\right)\)	\(e\left(\frac{109}{114}\right)\)	\(e\left(\frac{23}{114}\right)\)	\(e\left(\frac{10}{57}\right)\)	\(e\left(\frac{7}{57}\right)\)	\(e\left(\frac{15}{38}\right)\)	\(e\left(\frac{43}{114}\right)\)
\(\chi_{2166}(1247,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{35}{114}\right)\)	\(e\left(\frac{5}{19}\right)\)	\(e\left(\frac{3}{38}\right)\)	\(e\left(\frac{43}{114}\right)\)	\(e\left(\frac{11}{114}\right)\)	\(e\left(\frac{109}{114}\right)\)	\(e\left(\frac{35}{57}\right)\)	\(e\left(\frac{53}{57}\right)\)	\(e\left(\frac{5}{38}\right)\)	\(e\left(\frac{65}{114}\right)\)
\(\chi_{2166}(1319,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{73}{114}\right)\)	\(e\left(\frac{5}{19}\right)\)	\(e\left(\frac{3}{38}\right)\)	\(e\left(\frac{5}{114}\right)\)	\(e\left(\frac{49}{114}\right)\)	\(e\left(\frac{71}{114}\right)\)	\(e\left(\frac{16}{57}\right)\)	\(e\left(\frac{34}{57}\right)\)	\(e\left(\frac{5}{38}\right)\)	\(e\left(\frac{103}{114}\right)\)
\(\chi_{2166}(1361,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{77}{114}\right)\)	\(e\left(\frac{11}{19}\right)\)	\(e\left(\frac{37}{38}\right)\)	\(e\left(\frac{49}{114}\right)\)	\(e\left(\frac{47}{114}\right)\)	\(e\left(\frac{103}{114}\right)\)	\(e\left(\frac{20}{57}\right)\)	\(e\left(\frac{14}{57}\right)\)	\(e\left(\frac{11}{38}\right)\)	\(e\left(\frac{29}{114}\right)\)
\(\chi_{2166}(1433,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{79}{114}\right)\)	\(e\left(\frac{14}{19}\right)\)	\(e\left(\frac{35}{38}\right)\)	\(e\left(\frac{71}{114}\right)\)	\(e\left(\frac{103}{114}\right)\)	\(e\left(\frac{5}{114}\right)\)	\(e\left(\frac{22}{57}\right)\)	\(e\left(\frac{4}{57}\right)\)	\(e\left(\frac{33}{38}\right)\)	\(e\left(\frac{49}{114}\right)\)
\(\chi_{2166}(1475,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{114}\right)\)	\(e\left(\frac{17}{19}\right)\)	\(e\left(\frac{33}{38}\right)\)	\(e\left(\frac{55}{114}\right)\)	\(e\left(\frac{83}{114}\right)\)	\(e\left(\frac{97}{114}\right)\)	\(e\left(\frac{5}{57}\right)\)	\(e\left(\frac{32}{57}\right)\)	\(e\left(\frac{17}{38}\right)\)	\(e\left(\frac{107}{114}\right)\)
\(\chi_{2166}(1547,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{85}{114}\right)\)	\(e\left(\frac{4}{19}\right)\)	\(e\left(\frac{29}{38}\right)\)	\(e\left(\frac{23}{114}\right)\)	\(e\left(\frac{43}{114}\right)\)	\(e\left(\frac{53}{114}\right)\)	\(e\left(\frac{28}{57}\right)\)	\(e\left(\frac{31}{57}\right)\)	\(e\left(\frac{23}{38}\right)\)	\(e\left(\frac{109}{114}\right)\)
\(\chi_{2166}(1589,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{114}\right)\)	\(e\left(\frac{4}{19}\right)\)	\(e\left(\frac{29}{38}\right)\)	\(e\left(\frac{61}{114}\right)\)	\(e\left(\frac{5}{114}\right)\)	\(e\left(\frac{91}{114}\right)\)	\(e\left(\frac{47}{57}\right)\)	\(e\left(\frac{50}{57}\right)\)	\(e\left(\frac{23}{38}\right)\)	\(e\left(\frac{71}{114}\right)\)
\(\chi_{2166}(1661,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{91}{114}\right)\)	\(e\left(\frac{13}{19}\right)\)	\(e\left(\frac{23}{38}\right)\)	\(e\left(\frac{89}{114}\right)\)	\(e\left(\frac{97}{114}\right)\)	\(e\left(\frac{101}{114}\right)\)	\(e\left(\frac{34}{57}\right)\)	\(e\left(\frac{1}{57}\right)\)	\(e\left(\frac{13}{38}\right)\)	\(e\left(\frac{55}{114}\right)\)
\(\chi_{2166}(1703,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{89}{114}\right)\)	\(e\left(\frac{10}{19}\right)\)	\(e\left(\frac{25}{38}\right)\)	\(e\left(\frac{67}{114}\right)\)	\(e\left(\frac{41}{114}\right)\)	\(e\left(\frac{85}{114}\right)\)	\(e\left(\frac{32}{57}\right)\)	\(e\left(\frac{11}{57}\right)\)	\(e\left(\frac{29}{38}\right)\)	\(e\left(\frac{35}{114}\right)\)
\(\chi_{2166}(1775,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{97}{114}\right)\)	\(e\left(\frac{3}{19}\right)\)	\(e\left(\frac{17}{38}\right)\)	\(e\left(\frac{41}{114}\right)\)	\(e\left(\frac{37}{114}\right)\)	\(e\left(\frac{35}{114}\right)\)	\(e\left(\frac{40}{57}\right)\)	\(e\left(\frac{28}{57}\right)\)	\(e\left(\frac{3}{38}\right)\)	\(e\left(\frac{1}{114}\right)\)
\(\chi_{2166}(1817,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{114}\right)\)	\(e\left(\frac{16}{19}\right)\)	\(e\left(\frac{21}{38}\right)\)	\(e\left(\frac{73}{114}\right)\)	\(e\left(\frac{77}{114}\right)\)	\(e\left(\frac{79}{114}\right)\)	\(e\left(\frac{17}{57}\right)\)	\(e\left(\frac{29}{57}\right)\)	\(e\left(\frac{35}{38}\right)\)	\(e\left(\frac{113}{114}\right)\)
\(\chi_{2166}(1889,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{103}{114}\right)\)	\(e\left(\frac{12}{19}\right)\)	\(e\left(\frac{11}{38}\right)\)	\(e\left(\frac{107}{114}\right)\)	\(e\left(\frac{91}{114}\right)\)	\(e\left(\frac{83}{114}\right)\)	\(e\left(\frac{46}{57}\right)\)	\(e\left(\frac{55}{57}\right)\)	\(e\left(\frac{31}{38}\right)\)	\(e\left(\frac{61}{114}\right)\)

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First 31 of 36 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	2166.r
Modulus	$2166$
Conductor	$1083$
Order	$114$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(2166\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(1083\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(114\)	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:	no, induced from 1083.t	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);