LMFDB - Dirichlet character orbit 9800.fy

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(9800, base_ring=CyclotomicField(84)) M = H._module chi = DirichletCharacter(H, M([0,42,21,26])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(157,9800)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$9800$
Conductor:	$1960$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$84$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 1960.dm	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:	$\Q(\zeta_{84})$
Fixed field:	Number field defined by a degree 84 polynomial

Characters in Galois orbit

Character	$-1$	$1$	$3$	$9$	$11$	$13$	$17$	$19$	$23$	$27$	$29$	$31$
$\chi_{9800}(157,\cdot)$	$1$	$1$	$e\left(\frac{47}{84}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{83}{84}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{43}{84}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{9800}(493,\cdot)$	$1$	$1$	$e\left(\frac{65}{84}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{29}{84}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{13}{84}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{9800}(957,\cdot)$	$1$	$1$	$e\left(\frac{55}{84}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{31}{84}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{84}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{9800}(1557,\cdot)$	$1$	$1$	$e\left(\frac{59}{84}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{47}{84}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{79}{84}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{9800}(2357,\cdot)$	$1$	$1$	$e\left(\frac{79}{84}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{43}{84}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{83}{84}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{9800}(2693,\cdot)$	$1$	$1$	$e\left(\frac{73}{84}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{61}{84}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{65}{84}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{9800}(2957,\cdot)$	$1$	$1$	$e\left(\frac{71}{84}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{11}{84}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{31}{84}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{9800}(3293,\cdot)$	$1$	$1$	$e\left(\frac{5}{84}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{41}{84}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{84}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{9800}(3757,\cdot)$	$1$	$1$	$e\left(\frac{19}{84}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{55}{84}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{71}{84}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{9800}(4093,\cdot)$	$1$	$1$	$e\left(\frac{13}{84}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{73}{84}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{53}{84}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{9800}(4357,\cdot)$	$1$	$1$	$e\left(\frac{83}{84}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{59}{84}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{67}{84}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{9800}(4693,\cdot)$	$1$	$1$	$e\left(\frac{17}{84}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{5}{84}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{37}{84}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{9800}(5157,\cdot)$	$1$	$1$	$e\left(\frac{43}{84}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{67}{84}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{59}{84}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{9800}(5493,\cdot)$	$1$	$1$	$e\left(\frac{37}{84}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{1}{84}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{41}{84}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{9800}(5757,\cdot)$	$1$	$1$	$e\left(\frac{11}{84}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{23}{84}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{19}{84}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{9800}(6093,\cdot)$	$1$	$1$	$e\left(\frac{29}{84}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{53}{84}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{73}{84}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{9800}(6557,\cdot)$	$1$	$1$	$e\left(\frac{67}{84}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{79}{84}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{47}{84}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{9800}(6893,\cdot)$	$1$	$1$	$e\left(\frac{61}{84}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{13}{84}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{29}{84}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{9800}(7157,\cdot)$	$1$	$1$	$e\left(\frac{23}{84}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{71}{84}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{55}{84}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{9800}(7493,\cdot)$	$1$	$1$	$e\left(\frac{41}{84}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{17}{84}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{25}{84}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{9800}(8293,\cdot)$	$1$	$1$	$e\left(\frac{1}{84}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{25}{84}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{17}{84}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{9800}(8893,\cdot)$	$1$	$1$	$e\left(\frac{53}{84}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{65}{84}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{61}{84}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{9800}(9357,\cdot)$	$1$	$1$	$e\left(\frac{31}{84}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{19}{84}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{23}{84}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{9800}(9693,\cdot)$	$1$	$1$	$e\left(\frac{25}{84}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{37}{84}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{84}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{5}{6}\right)$

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	\(-1\)	\(1\)	\(3\)	\(9\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(27\)	\(29\)	\(31\)
\(\chi_{9800}(157,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{84}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{83}{84}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{43}{84}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{9800}(493,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{65}{84}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{29}{84}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{13}{84}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{9800}(957,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{55}{84}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{31}{84}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{11}{84}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{9800}(1557,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{84}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{47}{84}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{79}{84}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{9800}(2357,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{79}{84}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{43}{84}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{83}{84}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{9800}(2693,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{73}{84}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{61}{84}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{65}{84}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{9800}(2957,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{71}{84}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{11}{84}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{31}{84}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{9800}(3293,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{84}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{41}{84}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{84}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{9800}(3757,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{84}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{55}{84}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{71}{84}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{9800}(4093,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{84}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{73}{84}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{53}{84}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{9800}(4357,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{83}{84}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{59}{84}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{67}{84}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{9800}(4693,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{84}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{5}{84}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{37}{84}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{9800}(5157,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{84}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{67}{84}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{59}{84}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{9800}(5493,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{84}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{1}{84}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{41}{84}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{9800}(5757,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{84}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{23}{84}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{19}{84}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{9800}(6093,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{84}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{53}{84}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{73}{84}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{9800}(6557,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{67}{84}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{79}{84}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{47}{84}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{9800}(6893,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{61}{84}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{13}{84}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{29}{84}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{9800}(7157,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{84}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{71}{84}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{55}{84}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{9800}(7493,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{84}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{17}{84}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{25}{84}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{9800}(8293,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{84}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{25}{84}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{17}{84}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{9800}(8893,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{84}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{65}{84}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{61}{84}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{9800}(9357,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{84}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{19}{84}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{23}{84}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{9800}(9693,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{25}{84}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{37}{84}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{84}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{5}{6}\right)\)

Introduction

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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	9800.fy
Modulus	$9800$
Conductor	$1960$
Order	$84$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(9800\)
Conductor:	\(1960\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(84\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 1960.dm	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)