LMFDB - Dirichlet character orbit 3234.ca

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comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(3234, base_ring=CyclotomicField(70)) M = H._module chi = DirichletCharacter(H, M([0,55,7])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(13, 3234)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

magma:// Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("3234.13"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$3234$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$539$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$70$	comment:Order sage:chi.multiplicative_order() gp:charorder(g,chi) magma:Order(chi);
Real:	no	comment:Whether the character is real sage:chi.multiplicative_order() <= 2 gp:charorder(g,chi) <= 2 magma:Order(chi) le 2;
Primitive:	no, induced from 539.z	comment:If the character is primitive sage:chi.is_primitive() gp:#znconreyconductor(g,chi)==1 magma:IsPrimitive(chi);
Minimal:	yes
Parity:	even	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);

Related number fields

Field of values:	$\Q(\zeta_{35})$	comment:Field of values of chi sage:CyclotomicField(chi.multiplicative_order()) gp:nfinit(polcyclo(charorder(g,chi))) magma:CyclotomicField(Order(chi));
Fixed field:	Number field defined by a degree 70 polynomial	comment:Fixed field sage:chi.fixed_field()

Characters in Galois orbit

Character	$-1$	$1$	$5$	$13$	$17$	$19$	$23$	$25$	$29$	$31$	$37$	$41$
$\chi_{3234}(13,\cdot)$	$1$	$1$	$e\left(\frac{13}{70}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{59}{70}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{3}{35}\right)$
$\chi_{3234}(139,\cdot)$	$1$	$1$	$e\left(\frac{11}{70}\right)$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{23}{70}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{16}{35}\right)$
$\chi_{3234}(349,\cdot)$	$1$	$1$	$e\left(\frac{59}{70}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{47}{70}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{19}{35}\right)$
$\chi_{3234}(475,\cdot)$	$1$	$1$	$e\left(\frac{43}{70}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{39}{70}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{2}{35}\right)$	$e\left(\frac{18}{35}\right)$
$\chi_{3234}(601,\cdot)$	$1$	$1$	$e\left(\frac{41}{70}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{3}{70}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{31}{35}\right)$
$\chi_{3234}(811,\cdot)$	$1$	$1$	$e\left(\frac{19}{70}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{27}{70}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{34}{35}\right)$
$\chi_{3234}(853,\cdot)$	$1$	$1$	$e\left(\frac{37}{70}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{2}{35}\right)$	$e\left(\frac{1}{70}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{22}{35}\right)$
$\chi_{3234}(937,\cdot)$	$1$	$1$	$e\left(\frac{3}{70}\right)$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{34}{35}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{19}{70}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{33}{35}\right)$
$\chi_{3234}(1063,\cdot)$	$1$	$1$	$e\left(\frac{1}{70}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{53}{70}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{11}{35}\right)$
$\chi_{3234}(1315,\cdot)$	$1$	$1$	$e\left(\frac{67}{70}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{51}{70}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{2}{35}\right)$
$\chi_{3234}(1399,\cdot)$	$1$	$1$	$e\left(\frac{33}{70}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{69}{70}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{13}{35}\right)$
$\chi_{3234}(1525,\cdot)$	$1$	$1$	$e\left(\frac{31}{70}\right)$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{33}{70}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{34}{35}\right)$	$e\left(\frac{26}{35}\right)$
$\chi_{3234}(1735,\cdot)$	$1$	$1$	$e\left(\frac{9}{70}\right)$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{57}{70}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{29}{35}\right)$
$\chi_{3234}(1777,\cdot)$	$1$	$1$	$e\left(\frac{27}{70}\right)$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{31}{70}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{17}{35}\right)$
$\chi_{3234}(1987,\cdot)$	$1$	$1$	$e\left(\frac{61}{70}\right)$	$e\left(\frac{2}{35}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{13}{70}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{6}{35}\right)$
$\chi_{3234}(2197,\cdot)$	$1$	$1$	$e\left(\frac{39}{70}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{37}{70}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{9}{35}\right)$
$\chi_{3234}(2239,\cdot)$	$1$	$1$	$e\left(\frac{57}{70}\right)$	$e\left(\frac{34}{35}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{11}{70}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{32}{35}\right)$
$\chi_{3234}(2323,\cdot)$	$1$	$1$	$e\left(\frac{23}{70}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{29}{70}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{8}{35}\right)$
$\chi_{3234}(2659,\cdot)$	$1$	$1$	$e\left(\frac{69}{70}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{34}{35}\right)$	$e\left(\frac{17}{70}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{24}{35}\right)$
$\chi_{3234}(2701,\cdot)$	$1$	$1$	$e\left(\frac{17}{70}\right)$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{61}{70}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{12}{35}\right)$
$\chi_{3234}(2785,\cdot)$	$1$	$1$	$e\left(\frac{53}{70}\right)$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{9}{70}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{23}{35}\right)$
$\chi_{3234}(2911,\cdot)$	$1$	$1$	$e\left(\frac{51}{70}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{43}{70}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{1}{35}\right)$
$\chi_{3234}(3121,\cdot)$	$1$	$1$	$e\left(\frac{29}{70}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{2}{35}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{67}{70}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{4}{35}\right)$
$\chi_{3234}(3163,\cdot)$	$1$	$1$	$e\left(\frac{47}{70}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{41}{70}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{27}{35}\right)$

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	\(-1\)	\(1\)	\(5\)	\(13\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)	\(37\)	\(41\)
\(\chi_{3234}(13,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{70}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{59}{70}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{3}{35}\right)\)
\(\chi_{3234}(139,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{70}\right)\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{23}{70}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{16}{35}\right)\)
\(\chi_{3234}(349,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{70}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{47}{70}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{19}{35}\right)\)
\(\chi_{3234}(475,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{70}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{39}{70}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{2}{35}\right)\)	\(e\left(\frac{18}{35}\right)\)
\(\chi_{3234}(601,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{70}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{3}{70}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{31}{35}\right)\)
\(\chi_{3234}(811,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{70}\right)\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{27}{70}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{34}{35}\right)\)
\(\chi_{3234}(853,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{70}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{2}{35}\right)\)	\(e\left(\frac{1}{70}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{22}{35}\right)\)
\(\chi_{3234}(937,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{70}\right)\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{34}{35}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{19}{70}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{33}{35}\right)\)
\(\chi_{3234}(1063,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{70}\right)\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{53}{70}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{11}{35}\right)\)
\(\chi_{3234}(1315,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{67}{70}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{51}{70}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{2}{35}\right)\)
\(\chi_{3234}(1399,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{33}{70}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{69}{70}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{13}{35}\right)\)
\(\chi_{3234}(1525,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{70}\right)\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{33}{70}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{34}{35}\right)\)	\(e\left(\frac{26}{35}\right)\)
\(\chi_{3234}(1735,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{70}\right)\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{57}{70}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{29}{35}\right)\)
\(\chi_{3234}(1777,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{27}{70}\right)\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{31}{70}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{17}{35}\right)\)
\(\chi_{3234}(1987,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{61}{70}\right)\)	\(e\left(\frac{2}{35}\right)\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{13}{70}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{6}{35}\right)\)
\(\chi_{3234}(2197,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{39}{70}\right)\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{37}{70}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{9}{35}\right)\)
\(\chi_{3234}(2239,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{57}{70}\right)\)	\(e\left(\frac{34}{35}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{11}{70}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{32}{35}\right)\)
\(\chi_{3234}(2323,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{70}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{29}{70}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{8}{35}\right)\)
\(\chi_{3234}(2659,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{69}{70}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{34}{35}\right)\)	\(e\left(\frac{17}{70}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{24}{35}\right)\)
\(\chi_{3234}(2701,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{70}\right)\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{61}{70}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{12}{35}\right)\)
\(\chi_{3234}(2785,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{70}\right)\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{9}{70}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{23}{35}\right)\)
\(\chi_{3234}(2911,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{51}{70}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{43}{70}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{1}{35}\right)\)
\(\chi_{3234}(3121,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{70}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{2}{35}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{67}{70}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{4}{35}\right)\)
\(\chi_{3234}(3163,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{70}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{41}{70}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{27}{35}\right)\)

Introduction

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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	3234.ca
Modulus	$3234$
Conductor	$539$
Order	$70$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(3234\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(539\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(70\)	comment:Order sage:chi.multiplicative_order() gp:charorder(g,chi) magma:Order(chi);
Real:	no	comment:Whether the character is real sage:chi.multiplicative_order() <= 2 gp:charorder(g,chi) <= 2 magma:Order(chi) le 2;
Primitive:	no, induced from 539.z	comment:If the character is primitive sage:chi.is_primitive() gp:#znconreyconductor(g,chi)==1 magma:IsPrimitive(chi);
Minimal:	yes
Parity:	even	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);