LMFDB - Dirichlet character orbit 213.m

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(213, base_ring=CyclotomicField(70)) M = H._module chi = DirichletCharacter(H, M([0,12])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(4,213)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$213$
Conductor:	$71$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$35$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 71.g	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	$-1$	$1$	$2$	$4$	$5$	$7$	$8$	$10$	$11$	$13$	$14$	$16$
$\chi_{213}(4,\cdot)$	$1$	$1$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{2}{35}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{4}{35}\right)$
$\chi_{213}(10,\cdot)$	$1$	$1$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{2}{35}\right)$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{23}{35}\right)$
$\chi_{213}(16,\cdot)$	$1$	$1$	$e\left(\frac{2}{35}\right)$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{8}{35}\right)$
$\chi_{213}(19,\cdot)$	$1$	$1$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{17}{35}\right)$
$\chi_{213}(40,\cdot)$	$1$	$1$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{27}{35}\right)$
$\chi_{213}(43,\cdot)$	$1$	$1$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{16}{35}\right)$
$\chi_{213}(49,\cdot)$	$1$	$1$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{34}{35}\right)$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{24}{35}\right)$
$\chi_{213}(58,\cdot)$	$1$	$1$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{2}{35}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{13}{35}\right)$
$\chi_{213}(64,\cdot)$	$1$	$1$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{2}{35}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{12}{35}\right)$
$\chi_{213}(73,\cdot)$	$1$	$1$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{2}{35}\right)$
$\chi_{213}(79,\cdot)$	$1$	$1$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{34}{35}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{6}{35}\right)$
$\chi_{213}(100,\cdot)$	$1$	$1$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{34}{35}\right)$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{11}{35}\right)$
$\chi_{213}(109,\cdot)$	$1$	$1$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{19}{35}\right)$
$\chi_{213}(121,\cdot)$	$1$	$1$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{9}{35}\right)$
$\chi_{213}(145,\cdot)$	$1$	$1$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{32}{35}\right)$
$\chi_{213}(148,\cdot)$	$1$	$1$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{34}{35}\right)$
$\chi_{213}(151,\cdot)$	$1$	$1$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{34}{35}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{29}{35}\right)$
$\chi_{213}(154,\cdot)$	$1$	$1$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{35}\right)$
$\chi_{213}(157,\cdot)$	$1$	$1$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{18}{35}\right)$
$\chi_{213}(160,\cdot)$	$1$	$1$	$e\left(\frac{34}{35}\right)$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{31}{35}\right)$
$\chi_{213}(166,\cdot)$	$1$	$1$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{35}\right)$
$\chi_{213}(169,\cdot)$	$1$	$1$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{2}{35}\right)$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{26}{35}\right)$
$\chi_{213}(178,\cdot)$	$1$	$1$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{34}{35}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{33}{35}\right)$
$\chi_{213}(202,\cdot)$	$1$	$1$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{34}{35}\right)$	$e\left(\frac{2}{35}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{22}{35}\right)$

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	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(7\)	\(8\)	\(10\)	\(11\)	\(13\)	\(14\)	\(16\)
\(\chi_{213}(4,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{2}{35}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{4}{35}\right)\)
\(\chi_{213}(10,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{2}{35}\right)\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{23}{35}\right)\)
\(\chi_{213}(16,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{35}\right)\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{8}{35}\right)\)
\(\chi_{213}(19,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{17}{35}\right)\)
\(\chi_{213}(40,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{27}{35}\right)\)
\(\chi_{213}(43,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{16}{35}\right)\)
\(\chi_{213}(49,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{34}{35}\right)\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{24}{35}\right)\)
\(\chi_{213}(58,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{2}{35}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{13}{35}\right)\)
\(\chi_{213}(64,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{2}{35}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{12}{35}\right)\)
\(\chi_{213}(73,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{2}{35}\right)\)
\(\chi_{213}(79,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{34}{35}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{6}{35}\right)\)
\(\chi_{213}(100,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{34}{35}\right)\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{11}{35}\right)\)
\(\chi_{213}(109,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{19}{35}\right)\)
\(\chi_{213}(121,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{9}{35}\right)\)
\(\chi_{213}(145,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{32}{35}\right)\)
\(\chi_{213}(148,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{34}{35}\right)\)
\(\chi_{213}(151,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{34}{35}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{29}{35}\right)\)
\(\chi_{213}(154,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{35}\right)\)
\(\chi_{213}(157,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{18}{35}\right)\)
\(\chi_{213}(160,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{34}{35}\right)\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{31}{35}\right)\)
\(\chi_{213}(166,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{35}\right)\)
\(\chi_{213}(169,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{2}{35}\right)\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{26}{35}\right)\)
\(\chi_{213}(178,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{34}{35}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{33}{35}\right)\)
\(\chi_{213}(202,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{34}{35}\right)\)	\(e\left(\frac{2}{35}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{22}{35}\right)\)

Introduction

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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	213.m
Modulus	$213$
Conductor	$71$
Order	$35$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(213\)
Conductor:	\(71\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(35\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 71.g	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)