LMFDB - Dirichlet character orbit 507.q

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(507, base_ring=CyclotomicField(78)) M = H._module chi = DirichletCharacter(H, M([0,2])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(16,507)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$507$
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	$-1$	$1$	$2$	$4$	$5$	$7$	$8$	$10$	$11$	$14$	$16$	$17$
$\chi_{507}(16,\cdot)$	$1$	$1$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{29}{39}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{29}{39}\right)$
$\chi_{507}(55,\cdot)$	$1$	$1$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{32}{39}\right)$
$\chi_{507}(61,\cdot)$	$1$	$1$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{1}{39}\right)$
$\chi_{507}(94,\cdot)$	$1$	$1$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{35}{39}\right)$
$\chi_{507}(100,\cdot)$	$1$	$1$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{28}{39}\right)$
$\chi_{507}(133,\cdot)$	$1$	$1$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{38}{39}\right)$
$\chi_{507}(139,\cdot)$	$1$	$1$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{16}{39}\right)$
$\chi_{507}(172,\cdot)$	$1$	$1$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{2}{39}\right)$
$\chi_{507}(178,\cdot)$	$1$	$1$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{29}{39}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{4}{39}\right)$
$\chi_{507}(211,\cdot)$	$1$	$1$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{5}{39}\right)$
$\chi_{507}(217,\cdot)$	$1$	$1$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{31}{39}\right)$
$\chi_{507}(250,\cdot)$	$1$	$1$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{8}{39}\right)$
$\chi_{507}(256,\cdot)$	$1$	$1$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{19}{39}\right)$
$\chi_{507}(289,\cdot)$	$1$	$1$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{29}{39}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{11}{39}\right)$
$\chi_{507}(295,\cdot)$	$1$	$1$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{7}{39}\right)$
$\chi_{507}(328,\cdot)$	$1$	$1$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{14}{39}\right)$
$\chi_{507}(334,\cdot)$	$1$	$1$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{34}{39}\right)$
$\chi_{507}(367,\cdot)$	$1$	$1$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{17}{39}\right)$
$\chi_{507}(373,\cdot)$	$1$	$1$	$e\left(\frac{29}{39}\right)$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{22}{39}\right)$
$\chi_{507}(406,\cdot)$	$1$	$1$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{20}{39}\right)$
$\chi_{507}(412,\cdot)$	$1$	$1$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{29}{39}\right)$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{10}{39}\right)$
$\chi_{507}(445,\cdot)$	$1$	$1$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{23}{39}\right)$
$\chi_{507}(451,\cdot)$	$1$	$1$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{37}{39}\right)$
$\chi_{507}(490,\cdot)$	$1$	$1$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{29}{39}\right)$	$e\left(\frac{25}{39}\right)$

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	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(7\)	\(8\)	\(10\)	\(11\)	\(14\)	\(16\)	\(17\)
\(\chi_{507}(16,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{29}{39}\right)\)
\(\chi_{507}(55,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{34}{39}\right)\)	\(e\left(\frac{32}{39}\right)\)
\(\chi_{507}(61,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{1}{39}\right)\)
\(\chi_{507}(94,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{35}{39}\right)\)
\(\chi_{507}(100,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{28}{39}\right)\)
\(\chi_{507}(133,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{38}{39}\right)\)
\(\chi_{507}(139,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{16}{39}\right)\)
\(\chi_{507}(172,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{34}{39}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{2}{39}\right)\)
\(\chi_{507}(178,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{4}{39}\right)\)
\(\chi_{507}(211,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{34}{39}\right)\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{5}{39}\right)\)
\(\chi_{507}(217,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{31}{39}\right)\)
\(\chi_{507}(250,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{8}{39}\right)\)
\(\chi_{507}(256,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{19}{39}\right)\)
\(\chi_{507}(289,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{34}{39}\right)\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{11}{39}\right)\)
\(\chi_{507}(295,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{7}{39}\right)\)
\(\chi_{507}(328,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{14}{39}\right)\)
\(\chi_{507}(334,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{34}{39}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{34}{39}\right)\)
\(\chi_{507}(367,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{17}{39}\right)\)
\(\chi_{507}(373,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{22}{39}\right)\)
\(\chi_{507}(406,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{20}{39}\right)\)
\(\chi_{507}(412,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{10}{39}\right)\)
\(\chi_{507}(445,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{23}{39}\right)\)
\(\chi_{507}(451,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{37}{39}\right)\)
\(\chi_{507}(490,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{34}{39}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{25}{39}\right)\)

Introduction

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Groups

Database

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	507.q
Modulus	$507$
Conductor	$169$
Order	$39$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(507\)
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)