LMFDB - Dirichlet character orbit 3234.bp

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(3234, base_ring=CyclotomicField(70)) M = H._module chi = DirichletCharacter(H, M([0,40,14])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(169,3234)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$3234$
Conductor:	$539$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$35$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 539.v	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 35 polynomial

Characters in Galois orbit

Character	$-1$	$1$	$5$	$13$	$17$	$19$	$23$	$25$	$29$	$31$	$37$	$41$
$\chi_{3234}(169,\cdot)$	$1$	$1$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{2}{35}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{6}{35}\right)$
$\chi_{3234}(379,\cdot)$	$1$	$1$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{17}{35}\right)$
$\chi_{3234}(421,\cdot)$	$1$	$1$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{29}{35}\right)$
$\chi_{3234}(631,\cdot)$	$1$	$1$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{34}{35}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{34}{35}\right)$	$e\left(\frac{26}{35}\right)$
$\chi_{3234}(757,\cdot)$	$1$	$1$	$e\left(\frac{34}{35}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{13}{35}\right)$
$\chi_{3234}(841,\cdot)$	$1$	$1$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{2}{35}\right)$
$\chi_{3234}(1093,\cdot)$	$1$	$1$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{11}{35}\right)$
$\chi_{3234}(1219,\cdot)$	$1$	$1$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{34}{35}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{33}{35}\right)$
$\chi_{3234}(1303,\cdot)$	$1$	$1$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{2}{35}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{22}{35}\right)$
$\chi_{3234}(1345,\cdot)$	$1$	$1$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{34}{35}\right)$
$\chi_{3234}(1555,\cdot)$	$1$	$1$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{31}{35}\right)$
$\chi_{3234}(1681,\cdot)$	$1$	$1$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{2}{35}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{2}{35}\right)$	$e\left(\frac{18}{35}\right)$
$\chi_{3234}(1807,\cdot)$	$1$	$1$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{19}{35}\right)$
$\chi_{3234}(2017,\cdot)$	$1$	$1$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{16}{35}\right)$
$\chi_{3234}(2143,\cdot)$	$1$	$1$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{3}{35}\right)$
$\chi_{3234}(2227,\cdot)$	$1$	$1$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{27}{35}\right)$
$\chi_{3234}(2269,\cdot)$	$1$	$1$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{2}{35}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{4}{35}\right)$
$\chi_{3234}(2479,\cdot)$	$1$	$1$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{1}{35}\right)$
$\chi_{3234}(2605,\cdot)$	$1$	$1$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{23}{35}\right)$
$\chi_{3234}(2689,\cdot)$	$1$	$1$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{12}{35}\right)$
$\chi_{3234}(2731,\cdot)$	$1$	$1$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{34}{35}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{24}{35}\right)$
$\chi_{3234}(3067,\cdot)$	$1$	$1$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{8}{35}\right)$
$\chi_{3234}(3151,\cdot)$	$1$	$1$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{34}{35}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{32}{35}\right)$
$\chi_{3234}(3193,\cdot)$	$1$	$1$	$e\left(\frac{2}{35}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{9}{35}\right)$

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	\(-1\)	\(1\)	\(5\)	\(13\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)	\(37\)	\(41\)
\(\chi_{3234}(169,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{2}{35}\right)\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{6}{35}\right)\)
\(\chi_{3234}(379,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{17}{35}\right)\)
\(\chi_{3234}(421,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{29}{35}\right)\)
\(\chi_{3234}(631,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{34}{35}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{34}{35}\right)\)	\(e\left(\frac{26}{35}\right)\)
\(\chi_{3234}(757,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{34}{35}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{13}{35}\right)\)
\(\chi_{3234}(841,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{2}{35}\right)\)
\(\chi_{3234}(1093,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{11}{35}\right)\)
\(\chi_{3234}(1219,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{34}{35}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{33}{35}\right)\)
\(\chi_{3234}(1303,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{2}{35}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{22}{35}\right)\)
\(\chi_{3234}(1345,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{34}{35}\right)\)
\(\chi_{3234}(1555,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{31}{35}\right)\)
\(\chi_{3234}(1681,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{2}{35}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{2}{35}\right)\)	\(e\left(\frac{18}{35}\right)\)
\(\chi_{3234}(1807,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{19}{35}\right)\)
\(\chi_{3234}(2017,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{16}{35}\right)\)
\(\chi_{3234}(2143,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{3}{35}\right)\)
\(\chi_{3234}(2227,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{27}{35}\right)\)
\(\chi_{3234}(2269,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{2}{35}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{4}{35}\right)\)
\(\chi_{3234}(2479,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{1}{35}\right)\)
\(\chi_{3234}(2605,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{23}{35}\right)\)
\(\chi_{3234}(2689,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{12}{35}\right)\)
\(\chi_{3234}(2731,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{34}{35}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{24}{35}\right)\)
\(\chi_{3234}(3067,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{8}{35}\right)\)
\(\chi_{3234}(3151,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{34}{35}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{32}{35}\right)\)
\(\chi_{3234}(3193,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{35}\right)\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{9}{35}\right)\)

Introduction

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Varieties

Fields

Representations

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	3234.bp
Modulus	$3234$
Conductor	$539$
Order	$35$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(3234\)
Conductor:	\(539\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(35\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 539.v	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)