LMFDB - Dirichlet character orbit 8820.ja

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(8820, base_ring=CyclotomicField(84)) M = H._module chi = DirichletCharacter(H, M([0,28,63,66])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(13,8820)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$8820$
Conductor:	$2205$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$84$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 2205.ej	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	$-1$	$1$	$11$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$	$43$
$\chi_{8820}(13,\cdot)$	$1$	$1$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{71}{84}\right)$	$e\left(\frac{11}{28}\right)$	$1$	$e\left(\frac{65}{84}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{25}{84}\right)$
$\chi_{8820}(517,\cdot)$	$1$	$1$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{65}{84}\right)$	$e\left(\frac{1}{28}\right)$	$1$	$e\left(\frac{11}{84}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{43}{84}\right)$
$\chi_{8820}(853,\cdot)$	$1$	$1$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{19}{84}\right)$	$e\left(\frac{27}{28}\right)$	$1$	$e\left(\frac{73}{84}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{41}{84}\right)$
$\chi_{8820}(1357,\cdot)$	$1$	$1$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{13}{84}\right)$	$e\left(\frac{17}{28}\right)$	$1$	$e\left(\frac{19}{84}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{59}{84}\right)$
$\chi_{8820}(1777,\cdot)$	$1$	$1$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{29}{84}\right)$	$e\left(\frac{25}{28}\right)$	$1$	$e\left(\frac{23}{84}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{67}{84}\right)$
$\chi_{8820}(2113,\cdot)$	$1$	$1$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{67}{84}\right)$	$e\left(\frac{23}{28}\right)$	$1$	$e\left(\frac{1}{84}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{65}{84}\right)$
$\chi_{8820}(2533,\cdot)$	$1$	$1$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{83}{84}\right)$	$e\left(\frac{3}{28}\right)$	$1$	$e\left(\frac{5}{84}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{73}{84}\right)$
$\chi_{8820}(2617,\cdot)$	$1$	$1$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{61}{84}\right)$	$e\left(\frac{13}{28}\right)$	$1$	$e\left(\frac{31}{84}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{83}{84}\right)$
$\chi_{8820}(3373,\cdot)$	$1$	$1$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{31}{84}\right)$	$e\left(\frac{19}{28}\right)$	$1$	$e\left(\frac{13}{84}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{5}{84}\right)$
$\chi_{8820}(3793,\cdot)$	$1$	$1$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{47}{84}\right)$	$e\left(\frac{27}{28}\right)$	$1$	$e\left(\frac{17}{84}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{13}{84}\right)$
$\chi_{8820}(3877,\cdot)$	$1$	$1$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{25}{84}\right)$	$e\left(\frac{9}{28}\right)$	$1$	$e\left(\frac{43}{84}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{23}{84}\right)$
$\chi_{8820}(4297,\cdot)$	$1$	$1$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{41}{84}\right)$	$e\left(\frac{17}{28}\right)$	$1$	$e\left(\frac{47}{84}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{31}{84}\right)$
$\chi_{8820}(4633,\cdot)$	$1$	$1$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{79}{84}\right)$	$e\left(\frac{15}{28}\right)$	$1$	$e\left(\frac{25}{84}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{29}{84}\right)$
$\chi_{8820}(5053,\cdot)$	$1$	$1$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{11}{84}\right)$	$e\left(\frac{23}{28}\right)$	$1$	$e\left(\frac{29}{84}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{37}{84}\right)$
$\chi_{8820}(5137,\cdot)$	$1$	$1$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{73}{84}\right)$	$e\left(\frac{5}{28}\right)$	$1$	$e\left(\frac{55}{84}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{47}{84}\right)$
$\chi_{8820}(5557,\cdot)$	$1$	$1$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{5}{84}\right)$	$e\left(\frac{13}{28}\right)$	$1$	$e\left(\frac{59}{84}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{55}{84}\right)$
$\chi_{8820}(5893,\cdot)$	$1$	$1$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{43}{84}\right)$	$e\left(\frac{11}{28}\right)$	$1$	$e\left(\frac{37}{84}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{53}{84}\right)$
$\chi_{8820}(6313,\cdot)$	$1$	$1$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{59}{84}\right)$	$e\left(\frac{19}{28}\right)$	$1$	$e\left(\frac{41}{84}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{61}{84}\right)$
$\chi_{8820}(6397,\cdot)$	$1$	$1$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{37}{84}\right)$	$e\left(\frac{1}{28}\right)$	$1$	$e\left(\frac{67}{84}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{71}{84}\right)$
$\chi_{8820}(6817,\cdot)$	$1$	$1$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{53}{84}\right)$	$e\left(\frac{9}{28}\right)$	$1$	$e\left(\frac{71}{84}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{79}{84}\right)$
$\chi_{8820}(7573,\cdot)$	$1$	$1$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{23}{84}\right)$	$e\left(\frac{15}{28}\right)$	$1$	$e\left(\frac{53}{84}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{1}{84}\right)$
$\chi_{8820}(7657,\cdot)$	$1$	$1$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{1}{84}\right)$	$e\left(\frac{25}{28}\right)$	$1$	$e\left(\frac{79}{84}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{11}{84}\right)$
$\chi_{8820}(8077,\cdot)$	$1$	$1$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{17}{84}\right)$	$e\left(\frac{5}{28}\right)$	$1$	$e\left(\frac{83}{84}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{19}{84}\right)$
$\chi_{8820}(8413,\cdot)$	$1$	$1$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{55}{84}\right)$	$e\left(\frac{3}{28}\right)$	$1$	$e\left(\frac{61}{84}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{17}{84}\right)$

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	\(-1\)	\(1\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)	\(43\)
\(\chi_{8820}(13,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{71}{84}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(1\)	\(e\left(\frac{65}{84}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{25}{84}\right)\)
\(\chi_{8820}(517,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{65}{84}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(1\)	\(e\left(\frac{11}{84}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{43}{84}\right)\)
\(\chi_{8820}(853,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{19}{84}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(1\)	\(e\left(\frac{73}{84}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{41}{84}\right)\)
\(\chi_{8820}(1357,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{13}{84}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(1\)	\(e\left(\frac{19}{84}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{59}{84}\right)\)
\(\chi_{8820}(1777,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{29}{84}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(1\)	\(e\left(\frac{23}{84}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{67}{84}\right)\)
\(\chi_{8820}(2113,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{67}{84}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(1\)	\(e\left(\frac{1}{84}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{65}{84}\right)\)
\(\chi_{8820}(2533,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{83}{84}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(1\)	\(e\left(\frac{5}{84}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{73}{84}\right)\)
\(\chi_{8820}(2617,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{61}{84}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(1\)	\(e\left(\frac{31}{84}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{83}{84}\right)\)
\(\chi_{8820}(3373,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{31}{84}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(1\)	\(e\left(\frac{13}{84}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{5}{84}\right)\)
\(\chi_{8820}(3793,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{47}{84}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(1\)	\(e\left(\frac{17}{84}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{13}{84}\right)\)
\(\chi_{8820}(3877,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{25}{84}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(1\)	\(e\left(\frac{43}{84}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{23}{84}\right)\)
\(\chi_{8820}(4297,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{41}{84}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(1\)	\(e\left(\frac{47}{84}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{31}{84}\right)\)
\(\chi_{8820}(4633,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{79}{84}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(1\)	\(e\left(\frac{25}{84}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{29}{84}\right)\)
\(\chi_{8820}(5053,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{11}{84}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(1\)	\(e\left(\frac{29}{84}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{37}{84}\right)\)
\(\chi_{8820}(5137,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{73}{84}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(1\)	\(e\left(\frac{55}{84}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{47}{84}\right)\)
\(\chi_{8820}(5557,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{5}{84}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(1\)	\(e\left(\frac{59}{84}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{55}{84}\right)\)
\(\chi_{8820}(5893,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{43}{84}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(1\)	\(e\left(\frac{37}{84}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{53}{84}\right)\)
\(\chi_{8820}(6313,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{59}{84}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(1\)	\(e\left(\frac{41}{84}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{61}{84}\right)\)
\(\chi_{8820}(6397,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{37}{84}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(1\)	\(e\left(\frac{67}{84}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{71}{84}\right)\)
\(\chi_{8820}(6817,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{53}{84}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(1\)	\(e\left(\frac{71}{84}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{79}{84}\right)\)
\(\chi_{8820}(7573,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{23}{84}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(1\)	\(e\left(\frac{53}{84}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{1}{84}\right)\)
\(\chi_{8820}(7657,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{1}{84}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(1\)	\(e\left(\frac{79}{84}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{11}{84}\right)\)
\(\chi_{8820}(8077,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{17}{84}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(1\)	\(e\left(\frac{83}{84}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{19}{84}\right)\)
\(\chi_{8820}(8413,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{55}{84}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(1\)	\(e\left(\frac{61}{84}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{17}{84}\right)\)

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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	8820.ja
Modulus	$8820$
Conductor	$2205$
Order	$84$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(8820\)
Conductor:	\(2205\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(84\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 2205.ej	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)