LMFDB - Dirichlet character orbit 553.y

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comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(553, base_ring=CyclotomicField(78)) M = H._module chi = DirichletCharacter(H, M([26,2])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(9, 553)) 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("553.9"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$553$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$553$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$39$	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:	$\Q(\zeta_{39})$
Fixed field:	39.39.12088669642594427834079815641631684897704150233955220736437592661471356964310045748175158745489.2

Characters in Galois orbit

Character	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$8$	$9$	$10$	$11$	$12$
$\chi_{553}(9,\cdot)$	$1$	$1$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{35}{39}\right)$
$\chi_{553}(25,\cdot)$	$1$	$1$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{25}{39}\right)$
$\chi_{553}(72,\cdot)$	$1$	$1$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{11}{39}\right)$
$\chi_{553}(81,\cdot)$	$1$	$1$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{31}{39}\right)$
$\chi_{553}(95,\cdot)$	$1$	$1$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{29}{39}\right)$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{7}{39}\right)$
$\chi_{553}(123,\cdot)$	$1$	$1$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{29}{39}\right)$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{4}{39}\right)$
$\chi_{553}(130,\cdot)$	$1$	$1$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{34}{39}\right)$
$\chi_{553}(163,\cdot)$	$1$	$1$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{32}{39}\right)$
$\chi_{553}(177,\cdot)$	$1$	$1$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{29}{39}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{14}{39}\right)$
$\chi_{553}(184,\cdot)$	$1$	$1$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{2}{39}\right)$
$\chi_{553}(198,\cdot)$	$1$	$1$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{29}{39}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{8}{39}\right)$
$\chi_{553}(200,\cdot)$	$1$	$1$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{29}{39}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{1}{39}\right)$
$\chi_{553}(207,\cdot)$	$1$	$1$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{22}{39}\right)$
$\chi_{553}(268,\cdot)$	$1$	$1$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{5}{39}\right)$
$\chi_{553}(310,\cdot)$	$1$	$1$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{29}{39}\right)$
$\chi_{553}(361,\cdot)$	$1$	$1$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{28}{39}\right)$
$\chi_{553}(366,\cdot)$	$1$	$1$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{17}{39}\right)$
$\chi_{553}(431,\cdot)$	$1$	$1$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{19}{39}\right)$
$\chi_{553}(478,\cdot)$	$1$	$1$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{23}{39}\right)$
$\chi_{553}(485,\cdot)$	$1$	$1$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{20}{39}\right)$
$\chi_{553}(487,\cdot)$	$1$	$1$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{10}{39}\right)$
$\chi_{553}(494,\cdot)$	$1$	$1$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{16}{39}\right)$
$\chi_{553}(506,\cdot)$	$1$	$1$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{38}{39}\right)$
$\chi_{553}(550,\cdot)$	$1$	$1$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{37}{39}\right)$

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	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(8\)	\(9\)	\(10\)	\(11\)	\(12\)
\(\chi_{553}(9,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{35}{39}\right)\)
\(\chi_{553}(25,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{25}{39}\right)\)
\(\chi_{553}(72,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{11}{39}\right)\)
\(\chi_{553}(81,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{31}{39}\right)\)
\(\chi_{553}(95,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{34}{39}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{7}{39}\right)\)
\(\chi_{553}(123,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{34}{39}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{4}{39}\right)\)
\(\chi_{553}(130,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{34}{39}\right)\)
\(\chi_{553}(163,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{32}{39}\right)\)
\(\chi_{553}(177,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{14}{39}\right)\)
\(\chi_{553}(184,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{34}{39}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{2}{39}\right)\)
\(\chi_{553}(198,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{8}{39}\right)\)
\(\chi_{553}(200,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{1}{39}\right)\)
\(\chi_{553}(207,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{22}{39}\right)\)
\(\chi_{553}(268,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{5}{39}\right)\)
\(\chi_{553}(310,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{29}{39}\right)\)
\(\chi_{553}(361,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{28}{39}\right)\)
\(\chi_{553}(366,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{17}{39}\right)\)
\(\chi_{553}(431,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{19}{39}\right)\)
\(\chi_{553}(478,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{34}{39}\right)\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{23}{39}\right)\)
\(\chi_{553}(485,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{34}{39}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{20}{39}\right)\)
\(\chi_{553}(487,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{10}{39}\right)\)
\(\chi_{553}(494,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{16}{39}\right)\)
\(\chi_{553}(506,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{38}{39}\right)\)
\(\chi_{553}(550,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{37}{39}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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Basic properties

Related number fields

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	553.y
Modulus	$553$
Conductor	$553$
Order	$39$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(553\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(553\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(39\)	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);