LMFDB - Dirichlet character orbit 539.z

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(539, base_ring=CyclotomicField(70)) M = H._module chi = DirichletCharacter(H, M([45,63])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(6,539)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$539$
Conductor:	$539$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$70$	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:	$\Q(\zeta_{35})$
Fixed field:	Number field defined by a degree 70 polynomial

Characters in Galois orbit

Character	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$8$	$9$	$10$	$12$	$13$
$\chi_{539}(6,\cdot)$	$1$	$1$	$e\left(\frac{43}{70}\right)$	$e\left(\frac{59}{70}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{17}{70}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{59}{70}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{4}{35}\right)$
$\chi_{539}(13,\cdot)$	$1$	$1$	$e\left(\frac{37}{70}\right)$	$e\left(\frac{41}{70}\right)$	$e\left(\frac{2}{35}\right)$	$e\left(\frac{13}{70}\right)$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{41}{70}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{1}{35}\right)$
$\chi_{539}(41,\cdot)$	$1$	$1$	$e\left(\frac{41}{70}\right)$	$e\left(\frac{53}{70}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{39}{70}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{53}{70}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{3}{35}\right)$
$\chi_{539}(62,\cdot)$	$1$	$1$	$e\left(\frac{9}{70}\right)$	$e\left(\frac{27}{70}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{41}{70}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{27}{70}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{22}{35}\right)$
$\chi_{539}(83,\cdot)$	$1$	$1$	$e\left(\frac{33}{70}\right)$	$e\left(\frac{29}{70}\right)$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{57}{70}\right)$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{29}{70}\right)$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{34}{35}\right)$
$\chi_{539}(90,\cdot)$	$1$	$1$	$e\left(\frac{27}{70}\right)$	$e\left(\frac{11}{70}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{53}{70}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{11}{70}\right)$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{31}{35}\right)$
$\chi_{539}(118,\cdot)$	$1$	$1$	$e\left(\frac{31}{70}\right)$	$e\left(\frac{23}{70}\right)$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{9}{70}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{23}{70}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{33}{35}\right)$
$\chi_{539}(139,\cdot)$	$1$	$1$	$e\left(\frac{69}{70}\right)$	$e\left(\frac{67}{70}\right)$	$e\left(\frac{34}{35}\right)$	$e\left(\frac{11}{70}\right)$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{67}{70}\right)$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{17}{35}\right)$
$\chi_{539}(160,\cdot)$	$1$	$1$	$e\left(\frac{23}{70}\right)$	$e\left(\frac{69}{70}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{27}{70}\right)$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{69}{70}\right)$	$e\left(\frac{34}{35}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{29}{35}\right)$
$\chi_{539}(167,\cdot)$	$1$	$1$	$e\left(\frac{17}{70}\right)$	$e\left(\frac{51}{70}\right)$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{23}{70}\right)$	$e\left(\frac{34}{35}\right)$	$e\left(\frac{51}{70}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{26}{35}\right)$
$\chi_{539}(216,\cdot)$	$1$	$1$	$e\left(\frac{59}{70}\right)$	$e\left(\frac{37}{70}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{51}{70}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{37}{70}\right)$	$e\left(\frac{2}{35}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{12}{35}\right)$
$\chi_{539}(237,\cdot)$	$1$	$1$	$e\left(\frac{13}{70}\right)$	$e\left(\frac{39}{70}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{67}{70}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{39}{70}\right)$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{24}{35}\right)$
$\chi_{539}(272,\cdot)$	$1$	$1$	$e\left(\frac{11}{70}\right)$	$e\left(\frac{33}{70}\right)$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{19}{70}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{33}{70}\right)$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{23}{35}\right)$
$\chi_{539}(314,\cdot)$	$1$	$1$	$e\left(\frac{3}{70}\right)$	$e\left(\frac{9}{70}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{37}{70}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{9}{70}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{19}{35}\right)$
$\chi_{539}(321,\cdot)$	$1$	$1$	$e\left(\frac{67}{70}\right)$	$e\left(\frac{61}{70}\right)$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{33}{70}\right)$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{61}{70}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{16}{35}\right)$
$\chi_{539}(349,\cdot)$	$1$	$1$	$e\left(\frac{1}{70}\right)$	$e\left(\frac{3}{70}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{59}{70}\right)$	$e\left(\frac{2}{35}\right)$	$e\left(\frac{3}{70}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{18}{35}\right)$
$\chi_{539}(370,\cdot)$	$1$	$1$	$e\left(\frac{39}{70}\right)$	$e\left(\frac{47}{70}\right)$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{61}{70}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{47}{70}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{2}{35}\right)$
$\chi_{539}(398,\cdot)$	$1$	$1$	$e\left(\frac{57}{70}\right)$	$e\left(\frac{31}{70}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{3}{70}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{31}{70}\right)$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{11}{35}\right)$
$\chi_{539}(426,\cdot)$	$1$	$1$	$e\left(\frac{61}{70}\right)$	$e\left(\frac{43}{70}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{29}{70}\right)$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{43}{70}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{13}{35}\right)$
$\chi_{539}(447,\cdot)$	$1$	$1$	$e\left(\frac{29}{70}\right)$	$e\left(\frac{17}{70}\right)$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{31}{70}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{17}{70}\right)$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{32}{35}\right)$
$\chi_{539}(468,\cdot)$	$1$	$1$	$e\left(\frac{53}{70}\right)$	$e\left(\frac{19}{70}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{47}{70}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{19}{70}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{9}{35}\right)$
$\chi_{539}(475,\cdot)$	$1$	$1$	$e\left(\frac{47}{70}\right)$	$e\left(\frac{1}{70}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{43}{70}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{1}{70}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{6}{35}\right)$
$\chi_{539}(503,\cdot)$	$1$	$1$	$e\left(\frac{51}{70}\right)$	$e\left(\frac{13}{70}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{69}{70}\right)$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{13}{70}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{8}{35}\right)$
$\chi_{539}(524,\cdot)$	$1$	$1$	$e\left(\frac{19}{70}\right)$	$e\left(\frac{57}{70}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{1}{70}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{57}{70}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{27}{35}\right)$

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	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(8\)	\(9\)	\(10\)	\(12\)	\(13\)
\(\chi_{539}(6,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{70}\right)\)	\(e\left(\frac{59}{70}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{17}{70}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{59}{70}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{4}{35}\right)\)
\(\chi_{539}(13,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{70}\right)\)	\(e\left(\frac{41}{70}\right)\)	\(e\left(\frac{2}{35}\right)\)	\(e\left(\frac{13}{70}\right)\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{41}{70}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{1}{35}\right)\)
\(\chi_{539}(41,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{70}\right)\)	\(e\left(\frac{53}{70}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{39}{70}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{53}{70}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{3}{35}\right)\)
\(\chi_{539}(62,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{70}\right)\)	\(e\left(\frac{27}{70}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{41}{70}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{27}{70}\right)\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{22}{35}\right)\)
\(\chi_{539}(83,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{33}{70}\right)\)	\(e\left(\frac{29}{70}\right)\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{57}{70}\right)\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{29}{70}\right)\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{34}{35}\right)\)
\(\chi_{539}(90,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{27}{70}\right)\)	\(e\left(\frac{11}{70}\right)\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{53}{70}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{11}{70}\right)\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{31}{35}\right)\)
\(\chi_{539}(118,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{70}\right)\)	\(e\left(\frac{23}{70}\right)\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{9}{70}\right)\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{23}{70}\right)\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{33}{35}\right)\)
\(\chi_{539}(139,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{69}{70}\right)\)	\(e\left(\frac{67}{70}\right)\)	\(e\left(\frac{34}{35}\right)\)	\(e\left(\frac{11}{70}\right)\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{67}{70}\right)\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{17}{35}\right)\)
\(\chi_{539}(160,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{70}\right)\)	\(e\left(\frac{69}{70}\right)\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{27}{70}\right)\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{69}{70}\right)\)	\(e\left(\frac{34}{35}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{29}{35}\right)\)
\(\chi_{539}(167,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{70}\right)\)	\(e\left(\frac{51}{70}\right)\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{23}{70}\right)\)	\(e\left(\frac{34}{35}\right)\)	\(e\left(\frac{51}{70}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{26}{35}\right)\)
\(\chi_{539}(216,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{70}\right)\)	\(e\left(\frac{37}{70}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{51}{70}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{37}{70}\right)\)	\(e\left(\frac{2}{35}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{12}{35}\right)\)
\(\chi_{539}(237,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{70}\right)\)	\(e\left(\frac{39}{70}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{67}{70}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{39}{70}\right)\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{24}{35}\right)\)
\(\chi_{539}(272,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{70}\right)\)	\(e\left(\frac{33}{70}\right)\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{19}{70}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{33}{70}\right)\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{23}{35}\right)\)
\(\chi_{539}(314,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{70}\right)\)	\(e\left(\frac{9}{70}\right)\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{37}{70}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{9}{70}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{19}{35}\right)\)
\(\chi_{539}(321,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{67}{70}\right)\)	\(e\left(\frac{61}{70}\right)\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{33}{70}\right)\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{61}{70}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{16}{35}\right)\)
\(\chi_{539}(349,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{70}\right)\)	\(e\left(\frac{3}{70}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{59}{70}\right)\)	\(e\left(\frac{2}{35}\right)\)	\(e\left(\frac{3}{70}\right)\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{18}{35}\right)\)
\(\chi_{539}(370,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{39}{70}\right)\)	\(e\left(\frac{47}{70}\right)\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{61}{70}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{47}{70}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{2}{35}\right)\)
\(\chi_{539}(398,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{57}{70}\right)\)	\(e\left(\frac{31}{70}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{3}{70}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{31}{70}\right)\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{11}{35}\right)\)
\(\chi_{539}(426,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{61}{70}\right)\)	\(e\left(\frac{43}{70}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{29}{70}\right)\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{43}{70}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{13}{35}\right)\)
\(\chi_{539}(447,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{70}\right)\)	\(e\left(\frac{17}{70}\right)\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{31}{70}\right)\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{17}{70}\right)\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{32}{35}\right)\)
\(\chi_{539}(468,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{70}\right)\)	\(e\left(\frac{19}{70}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{47}{70}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{19}{70}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{9}{35}\right)\)
\(\chi_{539}(475,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{70}\right)\)	\(e\left(\frac{1}{70}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{43}{70}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{1}{70}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{6}{35}\right)\)
\(\chi_{539}(503,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{51}{70}\right)\)	\(e\left(\frac{13}{70}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{69}{70}\right)\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{13}{70}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{8}{35}\right)\)
\(\chi_{539}(524,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{70}\right)\)	\(e\left(\frac{57}{70}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{1}{70}\right)\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{57}{70}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{27}{35}\right)\)

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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	539.z
Modulus	$539$
Conductor	$539$
Order	$70$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(539\)
Conductor:	\(539\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(70\)	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)