LMFDB - Dirichlet character orbit 676.q

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(676, base_ring=CyclotomicField(78)) M = H._module chi = DirichletCharacter(H, M([0,46])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(9,676)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$676$
Conductor:	$169$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$39$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 169.i	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
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	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$15$	$17$	$19$	$21$	$23$
$\chi_{676}(9,\cdot)$	$1$	$1$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{29}{39}\right)$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{676}(29,\cdot)$	$1$	$1$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{676}(61,\cdot)$	$1$	$1$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{676}(81,\cdot)$	$1$	$1$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{676}(113,\cdot)$	$1$	$1$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{676}(133,\cdot)$	$1$	$1$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{676}(165,\cdot)$	$1$	$1$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{676}(185,\cdot)$	$1$	$1$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{29}{39}\right)$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{29}{39}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{676}(217,\cdot)$	$1$	$1$	$e\left(\frac{29}{39}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{676}(237,\cdot)$	$1$	$1$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{676}(269,\cdot)$	$1$	$1$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{676}(289,\cdot)$	$1$	$1$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{676}(321,\cdot)$	$1$	$1$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{676}(341,\cdot)$	$1$	$1$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{676}(373,\cdot)$	$1$	$1$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{676}(393,\cdot)$	$1$	$1$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{676}(425,\cdot)$	$1$	$1$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{676}(445,\cdot)$	$1$	$1$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{676}(477,\cdot)$	$1$	$1$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{29}{39}\right)$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{676}(497,\cdot)$	$1$	$1$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{676}(549,\cdot)$	$1$	$1$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{676}(581,\cdot)$	$1$	$1$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{676}(601,\cdot)$	$1$	$1$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{29}{39}\right)$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{676}(633,\cdot)$	$1$	$1$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{2}{3}\right)$

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	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(15\)	\(17\)	\(19\)	\(21\)	\(23\)
\(\chi_{676}(9,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{676}(29,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{676}(61,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{676}(81,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{34}{39}\right)\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{676}(113,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{34}{39}\right)\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{676}(133,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{676}(165,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{34}{39}\right)\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{34}{39}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{676}(185,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{676}(217,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{676}(237,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{676}(269,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{676}(289,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{676}(321,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{676}(341,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{34}{39}\right)\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{676}(373,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{676}(393,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{676}(425,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{676}(445,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{676}(477,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{676}(497,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{676}(549,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{676}(581,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{676}(601,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{34}{39}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{676}(633,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{2}{3}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

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	676.q
Modulus	$676$
Conductor	$169$
Order	$39$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(676\)
Conductor:	\(169\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(39\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 169.i	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)