LMFDB - Dirichlet character orbit 9702.es

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(9702, base_ring=CyclotomicField(70)) M = H._module chi = DirichletCharacter(H, M([35,50,21])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(701,9702)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$9702$
Conductor:	$1617$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$70$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 1617.cc	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	$-1$	$1$	$5$	$13$	$17$	$19$	$23$	$25$	$29$	$31$	$37$	$41$
$\chi_{9702}(701,\cdot)$	$1$	$1$	$e\left(\frac{29}{70}\right)$	$e\left(\frac{61}{70}\right)$	$e\left(\frac{2}{35}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{4}{35}\right)$
$\chi_{9702}(827,\cdot)$	$1$	$1$	$e\left(\frac{3}{70}\right)$	$e\left(\frac{57}{70}\right)$	$e\left(\frac{34}{35}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{33}{35}\right)$
$\chi_{9702}(953,\cdot)$	$1$	$1$	$e\left(\frac{61}{70}\right)$	$e\left(\frac{39}{70}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{6}{35}\right)$
$\chi_{9702}(1205,\cdot)$	$1$	$1$	$e\left(\frac{37}{70}\right)$	$e\left(\frac{3}{70}\right)$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{2}{35}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{22}{35}\right)$
$\chi_{9702}(2087,\cdot)$	$1$	$1$	$e\left(\frac{9}{70}\right)$	$e\left(\frac{31}{70}\right)$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{29}{35}\right)$
$\chi_{9702}(2213,\cdot)$	$1$	$1$	$e\left(\frac{53}{70}\right)$	$e\left(\frac{27}{70}\right)$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{23}{35}\right)$
$\chi_{9702}(2339,\cdot)$	$1$	$1$	$e\left(\frac{41}{70}\right)$	$e\left(\frac{9}{70}\right)$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{31}{35}\right)$
$\chi_{9702}(2591,\cdot)$	$1$	$1$	$e\left(\frac{17}{70}\right)$	$e\left(\frac{43}{70}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{12}{35}\right)$
$\chi_{9702}(3473,\cdot)$	$1$	$1$	$e\left(\frac{59}{70}\right)$	$e\left(\frac{1}{70}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{19}{35}\right)$
$\chi_{9702}(3599,\cdot)$	$1$	$1$	$e\left(\frac{33}{70}\right)$	$e\left(\frac{67}{70}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{13}{35}\right)$
$\chi_{9702}(3977,\cdot)$	$1$	$1$	$e\left(\frac{67}{70}\right)$	$e\left(\frac{13}{70}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{2}{35}\right)$
$\chi_{9702}(4859,\cdot)$	$1$	$1$	$e\left(\frac{39}{70}\right)$	$e\left(\frac{41}{70}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{9}{35}\right)$
$\chi_{9702}(4985,\cdot)$	$1$	$1$	$e\left(\frac{13}{70}\right)$	$e\left(\frac{37}{70}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{3}{35}\right)$
$\chi_{9702}(5111,\cdot)$	$1$	$1$	$e\left(\frac{1}{70}\right)$	$e\left(\frac{19}{70}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{11}{35}\right)$
$\chi_{9702}(5363,\cdot)$	$1$	$1$	$e\left(\frac{47}{70}\right)$	$e\left(\frac{53}{70}\right)$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{27}{35}\right)$
$\chi_{9702}(6245,\cdot)$	$1$	$1$	$e\left(\frac{19}{70}\right)$	$e\left(\frac{11}{70}\right)$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{34}{35}\right)$
$\chi_{9702}(6497,\cdot)$	$1$	$1$	$e\left(\frac{51}{70}\right)$	$e\left(\frac{59}{70}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{1}{35}\right)$
$\chi_{9702}(6749,\cdot)$	$1$	$1$	$e\left(\frac{27}{70}\right)$	$e\left(\frac{23}{70}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{17}{35}\right)$
$\chi_{9702}(7631,\cdot)$	$1$	$1$	$e\left(\frac{69}{70}\right)$	$e\left(\frac{51}{70}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{34}{35}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{24}{35}\right)$
$\chi_{9702}(7757,\cdot)$	$1$	$1$	$e\left(\frac{43}{70}\right)$	$e\left(\frac{47}{70}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{2}{35}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{2}{35}\right)$	$e\left(\frac{18}{35}\right)$
$\chi_{9702}(7883,\cdot)$	$1$	$1$	$e\left(\frac{31}{70}\right)$	$e\left(\frac{29}{70}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{34}{35}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{34}{35}\right)$	$e\left(\frac{26}{35}\right)$
$\chi_{9702}(9143,\cdot)$	$1$	$1$	$e\left(\frac{23}{70}\right)$	$e\left(\frac{17}{70}\right)$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{8}{35}\right)$
$\chi_{9702}(9269,\cdot)$	$1$	$1$	$e\left(\frac{11}{70}\right)$	$e\left(\frac{69}{70}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{16}{35}\right)$
$\chi_{9702}(9521,\cdot)$	$1$	$1$	$e\left(\frac{57}{70}\right)$	$e\left(\frac{33}{70}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{32}{35}\right)$

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	\(-1\)	\(1\)	\(5\)	\(13\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)	\(37\)	\(41\)
\(\chi_{9702}(701,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{70}\right)\)	\(e\left(\frac{61}{70}\right)\)	\(e\left(\frac{2}{35}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{4}{35}\right)\)
\(\chi_{9702}(827,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{70}\right)\)	\(e\left(\frac{57}{70}\right)\)	\(e\left(\frac{34}{35}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{33}{35}\right)\)
\(\chi_{9702}(953,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{61}{70}\right)\)	\(e\left(\frac{39}{70}\right)\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{6}{35}\right)\)
\(\chi_{9702}(1205,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{70}\right)\)	\(e\left(\frac{3}{70}\right)\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{2}{35}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{22}{35}\right)\)
\(\chi_{9702}(2087,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{70}\right)\)	\(e\left(\frac{31}{70}\right)\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{29}{35}\right)\)
\(\chi_{9702}(2213,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{70}\right)\)	\(e\left(\frac{27}{70}\right)\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{23}{35}\right)\)
\(\chi_{9702}(2339,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{70}\right)\)	\(e\left(\frac{9}{70}\right)\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{31}{35}\right)\)
\(\chi_{9702}(2591,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{70}\right)\)	\(e\left(\frac{43}{70}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{12}{35}\right)\)
\(\chi_{9702}(3473,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{70}\right)\)	\(e\left(\frac{1}{70}\right)\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{19}{35}\right)\)
\(\chi_{9702}(3599,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{33}{70}\right)\)	\(e\left(\frac{67}{70}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{13}{35}\right)\)
\(\chi_{9702}(3977,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{67}{70}\right)\)	\(e\left(\frac{13}{70}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{2}{35}\right)\)
\(\chi_{9702}(4859,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{39}{70}\right)\)	\(e\left(\frac{41}{70}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{9}{35}\right)\)
\(\chi_{9702}(4985,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{70}\right)\)	\(e\left(\frac{37}{70}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{3}{35}\right)\)
\(\chi_{9702}(5111,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{70}\right)\)	\(e\left(\frac{19}{70}\right)\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{11}{35}\right)\)
\(\chi_{9702}(5363,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{70}\right)\)	\(e\left(\frac{53}{70}\right)\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{27}{35}\right)\)
\(\chi_{9702}(6245,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{70}\right)\)	\(e\left(\frac{11}{70}\right)\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{34}{35}\right)\)
\(\chi_{9702}(6497,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{51}{70}\right)\)	\(e\left(\frac{59}{70}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{1}{35}\right)\)
\(\chi_{9702}(6749,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{27}{70}\right)\)	\(e\left(\frac{23}{70}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{17}{35}\right)\)
\(\chi_{9702}(7631,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{69}{70}\right)\)	\(e\left(\frac{51}{70}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{34}{35}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{24}{35}\right)\)
\(\chi_{9702}(7757,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{70}\right)\)	\(e\left(\frac{47}{70}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{2}{35}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{2}{35}\right)\)	\(e\left(\frac{18}{35}\right)\)
\(\chi_{9702}(7883,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{70}\right)\)	\(e\left(\frac{29}{70}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{34}{35}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{34}{35}\right)\)	\(e\left(\frac{26}{35}\right)\)
\(\chi_{9702}(9143,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{70}\right)\)	\(e\left(\frac{17}{70}\right)\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{8}{35}\right)\)
\(\chi_{9702}(9269,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{70}\right)\)	\(e\left(\frac{69}{70}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{16}{35}\right)\)
\(\chi_{9702}(9521,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{57}{70}\right)\)	\(e\left(\frac{33}{70}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{32}{35}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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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	9702.es
Modulus	$9702$
Conductor	$1617$
Order	$70$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(9702\)
Conductor:	\(1617\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(70\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 1617.cc	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)