LMFDB - Dirichlet character orbit 12482.g

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(12482, base_ring=CyclotomicField(78)) M = H._module chi = DirichletCharacter(H, M([56])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(31,12482)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$12482$
Conductor:	$79$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$39$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 79.g	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	no
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,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	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$17$	$19$	$21$
$\chi_{12482}(31,\cdot)$	$1$	$1$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{10}{13}\right)$
$\chi_{12482}(439,\cdot)$	$1$	$1$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{8}{13}\right)$
$\chi_{12482}(795,\cdot)$	$1$	$1$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{12}{13}\right)$
$\chi_{12482}(961,\cdot)$	$1$	$1$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{7}{13}\right)$
$\chi_{12482}(1905,\cdot)$	$1$	$1$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{29}{39}\right)$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{5}{13}\right)$
$\chi_{12482}(2465,\cdot)$	$1$	$1$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{1}{13}\right)$
$\chi_{12482}(3209,\cdot)$	$1$	$1$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{5}{13}\right)$
$\chi_{12482}(4153,\cdot)$	$1$	$1$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{4}{13}\right)$
$\chi_{12482}(5491,\cdot)$	$1$	$1$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{3}{13}\right)$
$\chi_{12482}(5771,\cdot)$	$1$	$1$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{7}{13}\right)$
$\chi_{12482}(6845,\cdot)$	$1$	$1$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{3}{13}\right)$
$\chi_{12482}(7051,\cdot)$	$1$	$1$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{6}{13}\right)$
$\chi_{12482}(7925,\cdot)$	$1$	$1$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{11}{13}\right)$
$\chi_{12482}(8683,\cdot)$	$1$	$1$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{29}{39}\right)$	$e\left(\frac{9}{13}\right)$
$\chi_{12482}(9079,\cdot)$	$1$	$1$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{6}{13}\right)$
$\chi_{12482}(9127,\cdot)$	$1$	$1$	$e\left(\frac{29}{39}\right)$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{2}{13}\right)$
$\chi_{12482}(9245,\cdot)$	$1$	$1$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{29}{39}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{10}{13}\right)$
$\chi_{12482}(9275,\cdot)$	$1$	$1$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{11}{13}\right)$
$\chi_{12482}(9595,\cdot)$	$1$	$1$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{12}{13}\right)$
$\chi_{12482}(9743,\cdot)$	$1$	$1$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{4}{13}\right)$
$\chi_{12482}(9767,\cdot)$	$1$	$1$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{29}{39}\right)$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{8}{13}\right)$
$\chi_{12482}(9973,\cdot)$	$1$	$1$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{29}{39}\right)$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{2}{13}\right)$
$\chi_{12482}(12163,\cdot)$	$1$	$1$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{9}{13}\right)$
$\chi_{12482}(12335,\cdot)$	$1$	$1$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{29}{39}\right)$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{1}{13}\right)$

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	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(21\)
\(\chi_{12482}(31,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{10}{13}\right)\)
\(\chi_{12482}(439,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{8}{13}\right)\)
\(\chi_{12482}(795,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{12}{13}\right)\)
\(\chi_{12482}(961,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{34}{39}\right)\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{7}{13}\right)\)
\(\chi_{12482}(1905,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{34}{39}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{5}{13}\right)\)
\(\chi_{12482}(2465,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{34}{39}\right)\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{1}{13}\right)\)
\(\chi_{12482}(3209,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{5}{13}\right)\)
\(\chi_{12482}(4153,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{34}{39}\right)\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{4}{13}\right)\)
\(\chi_{12482}(5491,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{3}{13}\right)\)
\(\chi_{12482}(5771,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{7}{13}\right)\)
\(\chi_{12482}(6845,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{3}{13}\right)\)
\(\chi_{12482}(7051,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{6}{13}\right)\)
\(\chi_{12482}(7925,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{34}{39}\right)\)	\(e\left(\frac{11}{13}\right)\)
\(\chi_{12482}(8683,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{9}{13}\right)\)
\(\chi_{12482}(9079,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{6}{13}\right)\)
\(\chi_{12482}(9127,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{2}{13}\right)\)
\(\chi_{12482}(9245,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{10}{13}\right)\)
\(\chi_{12482}(9275,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{11}{13}\right)\)
\(\chi_{12482}(9595,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{12}{13}\right)\)
\(\chi_{12482}(9743,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{4}{13}\right)\)
\(\chi_{12482}(9767,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{8}{13}\right)\)
\(\chi_{12482}(9973,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{2}{13}\right)\)
\(\chi_{12482}(12163,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{34}{39}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{9}{13}\right)\)
\(\chi_{12482}(12335,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{34}{39}\right)\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{1}{13}\right)\)

Introduction

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Properties

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Basic properties

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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	12482.g
Modulus	$12482$
Conductor	$79$
Order	$39$
Real	no
Primitive	no
Minimal	no
Parity	even

Modulus:	\(12482\)
Conductor:	\(79\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(39\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 79.g	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	no
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)