LMFDB - Dirichlet character orbit 5408.cm

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comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(5408, base_ring=CyclotomicField(78)) M = H._module chi = DirichletCharacter(H, M([0,0,68])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(289, 5408)) 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("5408.289"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$5408$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$169$	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:	no, induced from 169.i	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:	Number field defined by a degree 39 polynomial

Characters in Galois orbit

Character	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$15$	$17$	$19$	$21$	$23$
$\chi_{5408}(289,\cdot)$	$1$	$1$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{5408}(321,\cdot)$	$1$	$1$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{5408}(705,\cdot)$	$1$	$1$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{5408}(737,\cdot)$	$1$	$1$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{5408}(1121,\cdot)$	$1$	$1$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{5408}(1153,\cdot)$	$1$	$1$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{29}{39}\right)$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{5408}(1537,\cdot)$	$1$	$1$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{29}{39}\right)$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{29}{39}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{5408}(1569,\cdot)$	$1$	$1$	$e\left(\frac{29}{39}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{5408}(1953,\cdot)$	$1$	$1$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{29}{39}\right)$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{5408}(1985,\cdot)$	$1$	$1$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{5408}(2369,\cdot)$	$1$	$1$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{5408}(2401,\cdot)$	$1$	$1$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{5408}(2785,\cdot)$	$1$	$1$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{5408}(2817,\cdot)$	$1$	$1$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{5408}(3201,\cdot)$	$1$	$1$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{5408}(3617,\cdot)$	$1$	$1$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{5408}(3649,\cdot)$	$1$	$1$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{5408}(4065,\cdot)$	$1$	$1$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{29}{39}\right)$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{5408}(4449,\cdot)$	$1$	$1$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{5408}(4481,\cdot)$	$1$	$1$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{5408}(4865,\cdot)$	$1$	$1$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{5408}(4897,\cdot)$	$1$	$1$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{5408}(5281,\cdot)$	$1$	$1$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{5408}(5313,\cdot)$	$1$	$1$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{2}{3}\right)$

Overview	Random
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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	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(15\)	\(17\)	\(19\)	\(21\)	\(23\)
\(\chi_{5408}(289,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{5408}(321,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{5408}(705,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{5408}(737,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{5408}(1121,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{5408}(1153,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{5408}(1537,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{5408}(1569,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{5408}(1953,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{34}{39}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{5408}(1985,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{5408}(2369,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{34}{39}\right)\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{5408}(2401,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{5408}(2785,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{34}{39}\right)\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{5408}(2817,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{34}{39}\right)\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{5408}(3201,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{5408}(3617,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{5408}(3649,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{5408}(4065,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{5408}(4449,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{5408}(4481,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{5408}(4865,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{5408}(4897,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{34}{39}\right)\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{34}{39}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{5408}(5281,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{5408}(5313,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{2}{3}\right)\)

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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	5408.cm
Modulus	$5408$
Conductor	$169$
Order	$39$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(5408\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(169\)	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:	no, induced from 169.i	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);