LMFDB - Dirichlet character orbit 9800.fp

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(9800, base_ring=CyclotomicField(70)) M = H._module chi = DirichletCharacter(H, M([35,0,56,55])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(111,9800)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$9800$
Conductor:	$4900$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$70$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 4900.cv	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	no
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	$-1$	$1$	$3$	$9$	$11$	$13$	$17$	$19$	$23$	$27$	$29$	$31$
$\chi_{9800}(111,\cdot)$	$1$	$1$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{51}{70}\right)$	$e\left(\frac{9}{70}\right)$	$e\left(\frac{3}{70}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{11}{70}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{2}{5}\right)$
$\chi_{9800}(671,\cdot)$	$1$	$1$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{47}{70}\right)$	$e\left(\frac{33}{70}\right)$	$e\left(\frac{11}{70}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{17}{70}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{2}{35}\right)$	$e\left(\frac{4}{5}\right)$
$\chi_{9800}(1231,\cdot)$	$1$	$1$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{43}{70}\right)$	$e\left(\frac{57}{70}\right)$	$e\left(\frac{19}{70}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{23}{70}\right)$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{1}{5}\right)$
$\chi_{9800}(1511,\cdot)$	$1$	$1$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{41}{70}\right)$	$e\left(\frac{69}{70}\right)$	$e\left(\frac{23}{70}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{61}{70}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{2}{5}\right)$
$\chi_{9800}(1791,\cdot)$	$1$	$1$	$e\left(\frac{34}{35}\right)$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{39}{70}\right)$	$e\left(\frac{11}{70}\right)$	$e\left(\frac{27}{70}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{29}{70}\right)$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{3}{5}\right)$
$\chi_{9800}(2071,\cdot)$	$1$	$1$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{34}{35}\right)$	$e\left(\frac{37}{70}\right)$	$e\left(\frac{23}{70}\right)$	$e\left(\frac{31}{70}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{67}{70}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{4}{5}\right)$
$\chi_{9800}(2631,\cdot)$	$1$	$1$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{33}{70}\right)$	$e\left(\frac{47}{70}\right)$	$e\left(\frac{39}{70}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{70}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{1}{5}\right)$
$\chi_{9800}(2911,\cdot)$	$1$	$1$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{2}{35}\right)$	$e\left(\frac{31}{70}\right)$	$e\left(\frac{59}{70}\right)$	$e\left(\frac{43}{70}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{41}{70}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{2}{5}\right)$
$\chi_{9800}(3191,\cdot)$	$1$	$1$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{29}{70}\right)$	$e\left(\frac{1}{70}\right)$	$e\left(\frac{47}{70}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{9}{70}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{34}{35}\right)$	$e\left(\frac{3}{5}\right)$
$\chi_{9800}(3471,\cdot)$	$1$	$1$	$e\left(\frac{2}{35}\right)$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{27}{70}\right)$	$e\left(\frac{13}{70}\right)$	$e\left(\frac{51}{70}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{47}{70}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{4}{5}\right)$
$\chi_{9800}(4031,\cdot)$	$1$	$1$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{23}{70}\right)$	$e\left(\frac{37}{70}\right)$	$e\left(\frac{59}{70}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{53}{70}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{1}{5}\right)$
$\chi_{9800}(4591,\cdot)$	$1$	$1$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{19}{70}\right)$	$e\left(\frac{61}{70}\right)$	$e\left(\frac{67}{70}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{59}{70}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{3}{5}\right)$
$\chi_{9800}(4871,\cdot)$	$1$	$1$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{17}{70}\right)$	$e\left(\frac{3}{70}\right)$	$e\left(\frac{1}{70}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{27}{70}\right)$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{4}{5}\right)$
$\chi_{9800}(5431,\cdot)$	$1$	$1$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{13}{70}\right)$	$e\left(\frac{27}{70}\right)$	$e\left(\frac{9}{70}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{33}{70}\right)$	$e\left(\frac{34}{35}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{1}{5}\right)$
$\chi_{9800}(5711,\cdot)$	$1$	$1$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{11}{70}\right)$	$e\left(\frac{39}{70}\right)$	$e\left(\frac{13}{70}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{70}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{2}{5}\right)$
$\chi_{9800}(5991,\cdot)$	$1$	$1$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{9}{70}\right)$	$e\left(\frac{51}{70}\right)$	$e\left(\frac{17}{70}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{39}{70}\right)$	$e\left(\frac{2}{35}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{3}{5}\right)$
$\chi_{9800}(6831,\cdot)$	$1$	$1$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{3}{70}\right)$	$e\left(\frac{17}{70}\right)$	$e\left(\frac{29}{70}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{13}{70}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{1}{5}\right)$
$\chi_{9800}(7111,\cdot)$	$1$	$1$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{1}{70}\right)$	$e\left(\frac{29}{70}\right)$	$e\left(\frac{33}{70}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{51}{70}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{2}{5}\right)$
$\chi_{9800}(7391,\cdot)$	$1$	$1$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{69}{70}\right)$	$e\left(\frac{41}{70}\right)$	$e\left(\frac{37}{70}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{19}{70}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{3}{5}\right)$
$\chi_{9800}(7671,\cdot)$	$1$	$1$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{67}{70}\right)$	$e\left(\frac{53}{70}\right)$	$e\left(\frac{41}{70}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{57}{70}\right)$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{4}{5}\right)$
$\chi_{9800}(8511,\cdot)$	$1$	$1$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{61}{70}\right)$	$e\left(\frac{19}{70}\right)$	$e\left(\frac{53}{70}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{31}{70}\right)$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{2}{5}\right)$
$\chi_{9800}(8791,\cdot)$	$1$	$1$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{59}{70}\right)$	$e\left(\frac{31}{70}\right)$	$e\left(\frac{57}{70}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{69}{70}\right)$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{3}{5}\right)$
$\chi_{9800}(9071,\cdot)$	$1$	$1$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{57}{70}\right)$	$e\left(\frac{43}{70}\right)$	$e\left(\frac{61}{70}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{37}{70}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{4}{5}\right)$
$\chi_{9800}(9631,\cdot)$	$1$	$1$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{53}{70}\right)$	$e\left(\frac{67}{70}\right)$	$e\left(\frac{69}{70}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{43}{70}\right)$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{1}{5}\right)$

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	\(-1\)	\(1\)	\(3\)	\(9\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(27\)	\(29\)	\(31\)
\(\chi_{9800}(111,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{51}{70}\right)\)	\(e\left(\frac{9}{70}\right)\)	\(e\left(\frac{3}{70}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{11}{70}\right)\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{2}{5}\right)\)
\(\chi_{9800}(671,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{47}{70}\right)\)	\(e\left(\frac{33}{70}\right)\)	\(e\left(\frac{11}{70}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{17}{70}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{2}{35}\right)\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{9800}(1231,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{43}{70}\right)\)	\(e\left(\frac{57}{70}\right)\)	\(e\left(\frac{19}{70}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{23}{70}\right)\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{1}{5}\right)\)
\(\chi_{9800}(1511,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{41}{70}\right)\)	\(e\left(\frac{69}{70}\right)\)	\(e\left(\frac{23}{70}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{61}{70}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{2}{5}\right)\)
\(\chi_{9800}(1791,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{34}{35}\right)\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{39}{70}\right)\)	\(e\left(\frac{11}{70}\right)\)	\(e\left(\frac{27}{70}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{29}{70}\right)\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{3}{5}\right)\)
\(\chi_{9800}(2071,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{34}{35}\right)\)	\(e\left(\frac{37}{70}\right)\)	\(e\left(\frac{23}{70}\right)\)	\(e\left(\frac{31}{70}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{67}{70}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{9800}(2631,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{33}{70}\right)\)	\(e\left(\frac{47}{70}\right)\)	\(e\left(\frac{39}{70}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{70}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{1}{5}\right)\)
\(\chi_{9800}(2911,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{2}{35}\right)\)	\(e\left(\frac{31}{70}\right)\)	\(e\left(\frac{59}{70}\right)\)	\(e\left(\frac{43}{70}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{41}{70}\right)\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{2}{5}\right)\)
\(\chi_{9800}(3191,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{29}{70}\right)\)	\(e\left(\frac{1}{70}\right)\)	\(e\left(\frac{47}{70}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{9}{70}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{34}{35}\right)\)	\(e\left(\frac{3}{5}\right)\)
\(\chi_{9800}(3471,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{35}\right)\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{27}{70}\right)\)	\(e\left(\frac{13}{70}\right)\)	\(e\left(\frac{51}{70}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{47}{70}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{9800}(4031,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{23}{70}\right)\)	\(e\left(\frac{37}{70}\right)\)	\(e\left(\frac{59}{70}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{53}{70}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{1}{5}\right)\)
\(\chi_{9800}(4591,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{19}{70}\right)\)	\(e\left(\frac{61}{70}\right)\)	\(e\left(\frac{67}{70}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{59}{70}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{3}{5}\right)\)
\(\chi_{9800}(4871,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{17}{70}\right)\)	\(e\left(\frac{3}{70}\right)\)	\(e\left(\frac{1}{70}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{27}{70}\right)\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{9800}(5431,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{13}{70}\right)\)	\(e\left(\frac{27}{70}\right)\)	\(e\left(\frac{9}{70}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{33}{70}\right)\)	\(e\left(\frac{34}{35}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{1}{5}\right)\)
\(\chi_{9800}(5711,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{11}{70}\right)\)	\(e\left(\frac{39}{70}\right)\)	\(e\left(\frac{13}{70}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{70}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{2}{5}\right)\)
\(\chi_{9800}(5991,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{9}{70}\right)\)	\(e\left(\frac{51}{70}\right)\)	\(e\left(\frac{17}{70}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{39}{70}\right)\)	\(e\left(\frac{2}{35}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{3}{5}\right)\)
\(\chi_{9800}(6831,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{3}{70}\right)\)	\(e\left(\frac{17}{70}\right)\)	\(e\left(\frac{29}{70}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{13}{70}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{1}{5}\right)\)
\(\chi_{9800}(7111,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{1}{70}\right)\)	\(e\left(\frac{29}{70}\right)\)	\(e\left(\frac{33}{70}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{51}{70}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{2}{5}\right)\)
\(\chi_{9800}(7391,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{69}{70}\right)\)	\(e\left(\frac{41}{70}\right)\)	\(e\left(\frac{37}{70}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{19}{70}\right)\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{3}{5}\right)\)
\(\chi_{9800}(7671,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{67}{70}\right)\)	\(e\left(\frac{53}{70}\right)\)	\(e\left(\frac{41}{70}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{57}{70}\right)\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{9800}(8511,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{61}{70}\right)\)	\(e\left(\frac{19}{70}\right)\)	\(e\left(\frac{53}{70}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{31}{70}\right)\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{2}{5}\right)\)
\(\chi_{9800}(8791,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{59}{70}\right)\)	\(e\left(\frac{31}{70}\right)\)	\(e\left(\frac{57}{70}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{69}{70}\right)\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{3}{5}\right)\)
\(\chi_{9800}(9071,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{57}{70}\right)\)	\(e\left(\frac{43}{70}\right)\)	\(e\left(\frac{61}{70}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{37}{70}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{9800}(9631,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{53}{70}\right)\)	\(e\left(\frac{67}{70}\right)\)	\(e\left(\frac{69}{70}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{43}{70}\right)\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{1}{5}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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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	9800.fp
Modulus	$9800$
Conductor	$4900$
Order	$70$
Real	no
Primitive	no
Minimal	no
Parity	even

Modulus:	\(9800\)
Conductor:	\(4900\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(70\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 4900.cv	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	no
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)