LMFDB - Dirichlet character orbit 507.s

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(507, base_ring=CyclotomicField(52)) M = H._module chi = DirichletCharacter(H, M([26,3])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(5,507)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$507$
Conductor:	$507$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$52$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	yes	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:	$\Q(\zeta_{52})$
Fixed field:	Number field defined by a degree 52 polynomial

Characters in Galois orbit

Character	$-1$	$1$	$2$	$4$	$5$	$7$	$8$	$10$	$11$	$14$	$16$	$17$
$\chi_{507}(5,\cdot)$	$1$	$1$	$e\left(\frac{29}{52}\right)$	$e\left(\frac{3}{26}\right)$	$e\left(\frac{1}{52}\right)$	$e\left(\frac{9}{52}\right)$	$e\left(\frac{35}{52}\right)$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{23}{52}\right)$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{12}{13}\right)$
$\chi_{507}(8,\cdot)$	$1$	$1$	$e\left(\frac{27}{52}\right)$	$e\left(\frac{1}{26}\right)$	$e\left(\frac{35}{52}\right)$	$e\left(\frac{3}{52}\right)$	$e\left(\frac{29}{52}\right)$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{25}{52}\right)$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{4}{13}\right)$
$\chi_{507}(44,\cdot)$	$1$	$1$	$e\left(\frac{9}{52}\right)$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{29}{52}\right)$	$e\left(\frac{1}{52}\right)$	$e\left(\frac{27}{52}\right)$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{43}{52}\right)$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{10}{13}\right)$
$\chi_{507}(47,\cdot)$	$1$	$1$	$e\left(\frac{47}{52}\right)$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{7}{52}\right)$	$e\left(\frac{11}{52}\right)$	$e\left(\frac{37}{52}\right)$	$e\left(\frac{1}{26}\right)$	$e\left(\frac{5}{52}\right)$	$e\left(\frac{3}{26}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{6}{13}\right)$
$\chi_{507}(83,\cdot)$	$1$	$1$	$e\left(\frac{41}{52}\right)$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{5}{52}\right)$	$e\left(\frac{45}{52}\right)$	$e\left(\frac{19}{52}\right)$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{11}{52}\right)$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{8}{13}\right)$
$\chi_{507}(86,\cdot)$	$1$	$1$	$e\left(\frac{15}{52}\right)$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{31}{52}\right)$	$e\left(\frac{19}{52}\right)$	$e\left(\frac{45}{52}\right)$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{37}{52}\right)$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{8}{13}\right)$
$\chi_{507}(122,\cdot)$	$1$	$1$	$e\left(\frac{21}{52}\right)$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{33}{52}\right)$	$e\left(\frac{37}{52}\right)$	$e\left(\frac{11}{52}\right)$	$e\left(\frac{1}{26}\right)$	$e\left(\frac{31}{52}\right)$	$e\left(\frac{3}{26}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{6}{13}\right)$
$\chi_{507}(125,\cdot)$	$1$	$1$	$e\left(\frac{35}{52}\right)$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{3}{52}\right)$	$e\left(\frac{27}{52}\right)$	$e\left(\frac{1}{52}\right)$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{17}{52}\right)$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{10}{13}\right)$
$\chi_{507}(161,\cdot)$	$1$	$1$	$e\left(\frac{1}{52}\right)$	$e\left(\frac{1}{26}\right)$	$e\left(\frac{9}{52}\right)$	$e\left(\frac{29}{52}\right)$	$e\left(\frac{3}{52}\right)$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{51}{52}\right)$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{4}{13}\right)$
$\chi_{507}(164,\cdot)$	$1$	$1$	$e\left(\frac{3}{52}\right)$	$e\left(\frac{3}{26}\right)$	$e\left(\frac{27}{52}\right)$	$e\left(\frac{35}{52}\right)$	$e\left(\frac{9}{52}\right)$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{49}{52}\right)$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{12}{13}\right)$
$\chi_{507}(200,\cdot)$	$1$	$1$	$e\left(\frac{33}{52}\right)$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{37}{52}\right)$	$e\left(\frac{21}{52}\right)$	$e\left(\frac{47}{52}\right)$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{19}{52}\right)$	$e\left(\frac{1}{26}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{2}{13}\right)$
$\chi_{507}(203,\cdot)$	$1$	$1$	$e\left(\frac{23}{52}\right)$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{51}{52}\right)$	$e\left(\frac{43}{52}\right)$	$e\left(\frac{17}{52}\right)$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{29}{52}\right)$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{1}{13}\right)$
$\chi_{507}(242,\cdot)$	$1$	$1$	$e\left(\frac{43}{52}\right)$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{23}{52}\right)$	$e\left(\frac{51}{52}\right)$	$e\left(\frac{25}{52}\right)$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{9}{52}\right)$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{3}{13}\right)$
$\chi_{507}(278,\cdot)$	$1$	$1$	$e\left(\frac{45}{52}\right)$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{41}{52}\right)$	$e\left(\frac{5}{52}\right)$	$e\left(\frac{31}{52}\right)$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{7}{52}\right)$	$e\left(\frac{25}{26}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{11}{13}\right)$
$\chi_{507}(281,\cdot)$	$1$	$1$	$e\left(\frac{11}{52}\right)$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{47}{52}\right)$	$e\left(\frac{7}{52}\right)$	$e\left(\frac{33}{52}\right)$	$e\left(\frac{3}{26}\right)$	$e\left(\frac{41}{52}\right)$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{5}{13}\right)$
$\chi_{507}(317,\cdot)$	$1$	$1$	$e\left(\frac{25}{52}\right)$	$e\left(\frac{25}{26}\right)$	$e\left(\frac{17}{52}\right)$	$e\left(\frac{49}{52}\right)$	$e\left(\frac{23}{52}\right)$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{27}{52}\right)$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{9}{13}\right)$
$\chi_{507}(320,\cdot)$	$1$	$1$	$e\left(\frac{31}{52}\right)$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{19}{52}\right)$	$e\left(\frac{15}{52}\right)$	$e\left(\frac{41}{52}\right)$	$e\left(\frac{25}{26}\right)$	$e\left(\frac{21}{52}\right)$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{7}{13}\right)$
$\chi_{507}(356,\cdot)$	$1$	$1$	$e\left(\frac{5}{52}\right)$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{45}{52}\right)$	$e\left(\frac{41}{52}\right)$	$e\left(\frac{15}{52}\right)$	$e\left(\frac{25}{26}\right)$	$e\left(\frac{47}{52}\right)$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{7}{13}\right)$
$\chi_{507}(359,\cdot)$	$1$	$1$	$e\left(\frac{51}{52}\right)$	$e\left(\frac{25}{26}\right)$	$e\left(\frac{43}{52}\right)$	$e\left(\frac{23}{52}\right)$	$e\left(\frac{49}{52}\right)$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{1}{52}\right)$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{9}{13}\right)$
$\chi_{507}(395,\cdot)$	$1$	$1$	$e\left(\frac{37}{52}\right)$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{21}{52}\right)$	$e\left(\frac{33}{52}\right)$	$e\left(\frac{7}{52}\right)$	$e\left(\frac{3}{26}\right)$	$e\left(\frac{15}{52}\right)$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{5}{13}\right)$
$\chi_{507}(398,\cdot)$	$1$	$1$	$e\left(\frac{19}{52}\right)$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{15}{52}\right)$	$e\left(\frac{31}{52}\right)$	$e\left(\frac{5}{52}\right)$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{33}{52}\right)$	$e\left(\frac{25}{26}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{11}{13}\right)$
$\chi_{507}(434,\cdot)$	$1$	$1$	$e\left(\frac{17}{52}\right)$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{49}{52}\right)$	$e\left(\frac{25}{52}\right)$	$e\left(\frac{51}{52}\right)$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{35}{52}\right)$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{3}{13}\right)$
$\chi_{507}(473,\cdot)$	$1$	$1$	$e\left(\frac{49}{52}\right)$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{25}{52}\right)$	$e\left(\frac{17}{52}\right)$	$e\left(\frac{43}{52}\right)$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{3}{52}\right)$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{1}{13}\right)$
$\chi_{507}(476,\cdot)$	$1$	$1$	$e\left(\frac{7}{52}\right)$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{11}{52}\right)$	$e\left(\frac{47}{52}\right)$	$e\left(\frac{21}{52}\right)$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{45}{52}\right)$	$e\left(\frac{1}{26}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{2}{13}\right)$

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	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(7\)	\(8\)	\(10\)	\(11\)	\(14\)	\(16\)	\(17\)
\(\chi_{507}(5,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{52}\right)\)	\(e\left(\frac{3}{26}\right)\)	\(e\left(\frac{1}{52}\right)\)	\(e\left(\frac{9}{52}\right)\)	\(e\left(\frac{35}{52}\right)\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{23}{52}\right)\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{12}{13}\right)\)
\(\chi_{507}(8,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{27}{52}\right)\)	\(e\left(\frac{1}{26}\right)\)	\(e\left(\frac{35}{52}\right)\)	\(e\left(\frac{3}{52}\right)\)	\(e\left(\frac{29}{52}\right)\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{25}{52}\right)\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{4}{13}\right)\)
\(\chi_{507}(44,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{52}\right)\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{29}{52}\right)\)	\(e\left(\frac{1}{52}\right)\)	\(e\left(\frac{27}{52}\right)\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{43}{52}\right)\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{10}{13}\right)\)
\(\chi_{507}(47,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{52}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{7}{52}\right)\)	\(e\left(\frac{11}{52}\right)\)	\(e\left(\frac{37}{52}\right)\)	\(e\left(\frac{1}{26}\right)\)	\(e\left(\frac{5}{52}\right)\)	\(e\left(\frac{3}{26}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{6}{13}\right)\)
\(\chi_{507}(83,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{52}\right)\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{5}{52}\right)\)	\(e\left(\frac{45}{52}\right)\)	\(e\left(\frac{19}{52}\right)\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{11}{52}\right)\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{8}{13}\right)\)
\(\chi_{507}(86,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{15}{52}\right)\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{31}{52}\right)\)	\(e\left(\frac{19}{52}\right)\)	\(e\left(\frac{45}{52}\right)\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{37}{52}\right)\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{8}{13}\right)\)
\(\chi_{507}(122,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{21}{52}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{33}{52}\right)\)	\(e\left(\frac{37}{52}\right)\)	\(e\left(\frac{11}{52}\right)\)	\(e\left(\frac{1}{26}\right)\)	\(e\left(\frac{31}{52}\right)\)	\(e\left(\frac{3}{26}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{6}{13}\right)\)
\(\chi_{507}(125,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{35}{52}\right)\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{3}{52}\right)\)	\(e\left(\frac{27}{52}\right)\)	\(e\left(\frac{1}{52}\right)\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{17}{52}\right)\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{10}{13}\right)\)
\(\chi_{507}(161,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{52}\right)\)	\(e\left(\frac{1}{26}\right)\)	\(e\left(\frac{9}{52}\right)\)	\(e\left(\frac{29}{52}\right)\)	\(e\left(\frac{3}{52}\right)\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{51}{52}\right)\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{4}{13}\right)\)
\(\chi_{507}(164,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{52}\right)\)	\(e\left(\frac{3}{26}\right)\)	\(e\left(\frac{27}{52}\right)\)	\(e\left(\frac{35}{52}\right)\)	\(e\left(\frac{9}{52}\right)\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{49}{52}\right)\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{12}{13}\right)\)
\(\chi_{507}(200,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{33}{52}\right)\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{37}{52}\right)\)	\(e\left(\frac{21}{52}\right)\)	\(e\left(\frac{47}{52}\right)\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{19}{52}\right)\)	\(e\left(\frac{1}{26}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{2}{13}\right)\)
\(\chi_{507}(203,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{52}\right)\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{51}{52}\right)\)	\(e\left(\frac{43}{52}\right)\)	\(e\left(\frac{17}{52}\right)\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{29}{52}\right)\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{1}{13}\right)\)
\(\chi_{507}(242,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{52}\right)\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{23}{52}\right)\)	\(e\left(\frac{51}{52}\right)\)	\(e\left(\frac{25}{52}\right)\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{9}{52}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{3}{13}\right)\)
\(\chi_{507}(278,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{45}{52}\right)\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{41}{52}\right)\)	\(e\left(\frac{5}{52}\right)\)	\(e\left(\frac{31}{52}\right)\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{7}{52}\right)\)	\(e\left(\frac{25}{26}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{11}{13}\right)\)
\(\chi_{507}(281,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{52}\right)\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{47}{52}\right)\)	\(e\left(\frac{7}{52}\right)\)	\(e\left(\frac{33}{52}\right)\)	\(e\left(\frac{3}{26}\right)\)	\(e\left(\frac{41}{52}\right)\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{5}{13}\right)\)
\(\chi_{507}(317,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{25}{52}\right)\)	\(e\left(\frac{25}{26}\right)\)	\(e\left(\frac{17}{52}\right)\)	\(e\left(\frac{49}{52}\right)\)	\(e\left(\frac{23}{52}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{27}{52}\right)\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{9}{13}\right)\)
\(\chi_{507}(320,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{52}\right)\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{19}{52}\right)\)	\(e\left(\frac{15}{52}\right)\)	\(e\left(\frac{41}{52}\right)\)	\(e\left(\frac{25}{26}\right)\)	\(e\left(\frac{21}{52}\right)\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{7}{13}\right)\)
\(\chi_{507}(356,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{52}\right)\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{45}{52}\right)\)	\(e\left(\frac{41}{52}\right)\)	\(e\left(\frac{15}{52}\right)\)	\(e\left(\frac{25}{26}\right)\)	\(e\left(\frac{47}{52}\right)\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{7}{13}\right)\)
\(\chi_{507}(359,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{51}{52}\right)\)	\(e\left(\frac{25}{26}\right)\)	\(e\left(\frac{43}{52}\right)\)	\(e\left(\frac{23}{52}\right)\)	\(e\left(\frac{49}{52}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{1}{52}\right)\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{9}{13}\right)\)
\(\chi_{507}(395,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{52}\right)\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{21}{52}\right)\)	\(e\left(\frac{33}{52}\right)\)	\(e\left(\frac{7}{52}\right)\)	\(e\left(\frac{3}{26}\right)\)	\(e\left(\frac{15}{52}\right)\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{5}{13}\right)\)
\(\chi_{507}(398,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{52}\right)\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{15}{52}\right)\)	\(e\left(\frac{31}{52}\right)\)	\(e\left(\frac{5}{52}\right)\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{33}{52}\right)\)	\(e\left(\frac{25}{26}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{11}{13}\right)\)
\(\chi_{507}(434,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{52}\right)\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{49}{52}\right)\)	\(e\left(\frac{25}{52}\right)\)	\(e\left(\frac{51}{52}\right)\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{35}{52}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{3}{13}\right)\)
\(\chi_{507}(473,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{49}{52}\right)\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{25}{52}\right)\)	\(e\left(\frac{17}{52}\right)\)	\(e\left(\frac{43}{52}\right)\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{3}{52}\right)\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{1}{13}\right)\)
\(\chi_{507}(476,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{52}\right)\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{11}{52}\right)\)	\(e\left(\frac{47}{52}\right)\)	\(e\left(\frac{21}{52}\right)\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{45}{52}\right)\)	\(e\left(\frac{1}{26}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{2}{13}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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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	507.s
Modulus	$507$
Conductor	$507$
Order	$52$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(507\)
Conductor:	\(507\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(52\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	yes	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)