LMFDB - Dirichlet character orbit 8820.iy

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(8820, base_ring=CyclotomicField(84)) M = H._module chi = DirichletCharacter(H, M([42,70,63,46])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(383,8820)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$8820$
Conductor:	$8820$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$84$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	yes	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	$-1$	$1$	$11$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$	$43$
$\chi_{8820}(383,\cdot)$	$1$	$1$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{83}{84}\right)$	$e\left(\frac{79}{84}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{61}{84}\right)$	$e\left(\frac{4}{21}\right)$	$1$	$e\left(\frac{23}{84}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{31}{84}\right)$
$\chi_{8820}(887,\cdot)$	$1$	$1$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{17}{84}\right)$	$e\left(\frac{1}{84}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{55}{84}\right)$	$e\left(\frac{16}{21}\right)$	$1$	$e\left(\frac{29}{84}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{61}{84}\right)$
$\chi_{8820}(983,\cdot)$	$1$	$1$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{31}{84}\right)$	$e\left(\frac{71}{84}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{41}{84}\right)$	$e\left(\frac{2}{21}\right)$	$1$	$e\left(\frac{43}{84}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{47}{84}\right)$
$\chi_{8820}(1487,\cdot)$	$1$	$1$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{61}{84}\right)$	$e\left(\frac{53}{84}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{59}{84}\right)$	$e\left(\frac{8}{21}\right)$	$1$	$e\left(\frac{25}{84}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{41}{84}\right)$
$\chi_{8820}(1643,\cdot)$	$1$	$1$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{23}{84}\right)$	$e\left(\frac{31}{84}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{25}{84}\right)$	$e\left(\frac{13}{21}\right)$	$1$	$e\left(\frac{59}{84}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{43}{84}\right)$
$\chi_{8820}(2147,\cdot)$	$1$	$1$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{41}{84}\right)$	$e\left(\frac{37}{84}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{19}{84}\right)$	$e\left(\frac{4}{21}\right)$	$1$	$e\left(\frac{65}{84}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{73}{84}\right)$
$\chi_{8820}(2243,\cdot)$	$1$	$1$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{43}{84}\right)$	$e\left(\frac{47}{84}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{65}{84}\right)$	$e\left(\frac{17}{21}\right)$	$1$	$e\left(\frac{19}{84}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{11}{84}\right)$
$\chi_{8820}(2747,\cdot)$	$1$	$1$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{73}{84}\right)$	$e\left(\frac{29}{84}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{83}{84}\right)$	$e\left(\frac{2}{21}\right)$	$1$	$e\left(\frac{1}{84}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{5}{84}\right)$
$\chi_{8820}(2903,\cdot)$	$1$	$1$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{47}{84}\right)$	$e\left(\frac{67}{84}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{73}{84}\right)$	$e\left(\frac{1}{21}\right)$	$1$	$e\left(\frac{11}{84}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{55}{84}\right)$
$\chi_{8820}(3407,\cdot)$	$1$	$1$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{65}{84}\right)$	$e\left(\frac{73}{84}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{67}{84}\right)$	$e\left(\frac{13}{21}\right)$	$1$	$e\left(\frac{17}{84}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{1}{84}\right)$
$\chi_{8820}(3503,\cdot)$	$1$	$1$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{55}{84}\right)$	$e\left(\frac{23}{84}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{84}\right)$	$e\left(\frac{11}{21}\right)$	$1$	$e\left(\frac{79}{84}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{59}{84}\right)$
$\chi_{8820}(4007,\cdot)$	$1$	$1$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{1}{84}\right)$	$e\left(\frac{5}{84}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{23}{84}\right)$	$e\left(\frac{17}{21}\right)$	$1$	$e\left(\frac{61}{84}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{53}{84}\right)$
$\chi_{8820}(4163,\cdot)$	$1$	$1$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{71}{84}\right)$	$e\left(\frac{19}{84}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{37}{84}\right)$	$e\left(\frac{10}{21}\right)$	$1$	$e\left(\frac{47}{84}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{67}{84}\right)$
$\chi_{8820}(4667,\cdot)$	$1$	$1$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{5}{84}\right)$	$e\left(\frac{25}{84}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{31}{84}\right)$	$e\left(\frac{1}{21}\right)$	$1$	$e\left(\frac{53}{84}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{13}{84}\right)$
$\chi_{8820}(4763,\cdot)$	$1$	$1$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{67}{84}\right)$	$e\left(\frac{83}{84}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{29}{84}\right)$	$e\left(\frac{5}{21}\right)$	$1$	$e\left(\frac{55}{84}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{23}{84}\right)$
$\chi_{8820}(5267,\cdot)$	$1$	$1$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{13}{84}\right)$	$e\left(\frac{65}{84}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{47}{84}\right)$	$e\left(\frac{11}{21}\right)$	$1$	$e\left(\frac{37}{84}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{17}{84}\right)$
$\chi_{8820}(5423,\cdot)$	$1$	$1$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{11}{84}\right)$	$e\left(\frac{55}{84}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{84}\right)$	$e\left(\frac{19}{21}\right)$	$1$	$e\left(\frac{83}{84}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{79}{84}\right)$
$\chi_{8820}(5927,\cdot)$	$1$	$1$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{29}{84}\right)$	$e\left(\frac{61}{84}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{79}{84}\right)$	$e\left(\frac{10}{21}\right)$	$1$	$e\left(\frac{5}{84}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{25}{84}\right)$
$\chi_{8820}(6023,\cdot)$	$1$	$1$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{79}{84}\right)$	$e\left(\frac{59}{84}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{53}{84}\right)$	$e\left(\frac{20}{21}\right)$	$1$	$e\left(\frac{31}{84}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{71}{84}\right)$
$\chi_{8820}(6527,\cdot)$	$1$	$1$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{25}{84}\right)$	$e\left(\frac{41}{84}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{71}{84}\right)$	$e\left(\frac{5}{21}\right)$	$1$	$e\left(\frac{13}{84}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{65}{84}\right)$
$\chi_{8820}(7187,\cdot)$	$1$	$1$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{53}{84}\right)$	$e\left(\frac{13}{84}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{43}{84}\right)$	$e\left(\frac{19}{21}\right)$	$1$	$e\left(\frac{41}{84}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{37}{84}\right)$
$\chi_{8820}(7787,\cdot)$	$1$	$1$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{37}{84}\right)$	$e\left(\frac{17}{84}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{84}\right)$	$e\left(\frac{20}{21}\right)$	$1$	$e\left(\frac{73}{84}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{29}{84}\right)$
$\chi_{8820}(7943,\cdot)$	$1$	$1$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{59}{84}\right)$	$e\left(\frac{43}{84}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{13}{84}\right)$	$e\left(\frac{16}{21}\right)$	$1$	$e\left(\frac{71}{84}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{19}{84}\right)$
$\chi_{8820}(8543,\cdot)$	$1$	$1$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{19}{84}\right)$	$e\left(\frac{11}{84}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{17}{84}\right)$	$e\left(\frac{8}{21}\right)$	$1$	$e\left(\frac{67}{84}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{83}{84}\right)$

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	\(-1\)	\(1\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)	\(43\)
\(\chi_{8820}(383,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{83}{84}\right)\)	\(e\left(\frac{79}{84}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{61}{84}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(1\)	\(e\left(\frac{23}{84}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{31}{84}\right)\)
\(\chi_{8820}(887,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{17}{84}\right)\)	\(e\left(\frac{1}{84}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{55}{84}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(1\)	\(e\left(\frac{29}{84}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{61}{84}\right)\)
\(\chi_{8820}(983,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{31}{84}\right)\)	\(e\left(\frac{71}{84}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{41}{84}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(1\)	\(e\left(\frac{43}{84}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{47}{84}\right)\)
\(\chi_{8820}(1487,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{61}{84}\right)\)	\(e\left(\frac{53}{84}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{59}{84}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(1\)	\(e\left(\frac{25}{84}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{41}{84}\right)\)
\(\chi_{8820}(1643,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{23}{84}\right)\)	\(e\left(\frac{31}{84}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{25}{84}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(1\)	\(e\left(\frac{59}{84}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{43}{84}\right)\)
\(\chi_{8820}(2147,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{41}{84}\right)\)	\(e\left(\frac{37}{84}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{19}{84}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(1\)	\(e\left(\frac{65}{84}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{73}{84}\right)\)
\(\chi_{8820}(2243,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{43}{84}\right)\)	\(e\left(\frac{47}{84}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{65}{84}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(1\)	\(e\left(\frac{19}{84}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{11}{84}\right)\)
\(\chi_{8820}(2747,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{73}{84}\right)\)	\(e\left(\frac{29}{84}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{83}{84}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(1\)	\(e\left(\frac{1}{84}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{5}{84}\right)\)
\(\chi_{8820}(2903,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{47}{84}\right)\)	\(e\left(\frac{67}{84}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{73}{84}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(1\)	\(e\left(\frac{11}{84}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{55}{84}\right)\)
\(\chi_{8820}(3407,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{65}{84}\right)\)	\(e\left(\frac{73}{84}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{67}{84}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(1\)	\(e\left(\frac{17}{84}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{1}{84}\right)\)
\(\chi_{8820}(3503,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{55}{84}\right)\)	\(e\left(\frac{23}{84}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{84}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(1\)	\(e\left(\frac{79}{84}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{59}{84}\right)\)
\(\chi_{8820}(4007,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{1}{84}\right)\)	\(e\left(\frac{5}{84}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{23}{84}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(1\)	\(e\left(\frac{61}{84}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{53}{84}\right)\)
\(\chi_{8820}(4163,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{71}{84}\right)\)	\(e\left(\frac{19}{84}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{37}{84}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(1\)	\(e\left(\frac{47}{84}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{67}{84}\right)\)
\(\chi_{8820}(4667,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{5}{84}\right)\)	\(e\left(\frac{25}{84}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{31}{84}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(1\)	\(e\left(\frac{53}{84}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{13}{84}\right)\)
\(\chi_{8820}(4763,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{67}{84}\right)\)	\(e\left(\frac{83}{84}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{29}{84}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(1\)	\(e\left(\frac{55}{84}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{23}{84}\right)\)
\(\chi_{8820}(5267,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{13}{84}\right)\)	\(e\left(\frac{65}{84}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{47}{84}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(1\)	\(e\left(\frac{37}{84}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{17}{84}\right)\)
\(\chi_{8820}(5423,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{11}{84}\right)\)	\(e\left(\frac{55}{84}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{84}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(1\)	\(e\left(\frac{83}{84}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{79}{84}\right)\)
\(\chi_{8820}(5927,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{29}{84}\right)\)	\(e\left(\frac{61}{84}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{79}{84}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(1\)	\(e\left(\frac{5}{84}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{25}{84}\right)\)
\(\chi_{8820}(6023,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{79}{84}\right)\)	\(e\left(\frac{59}{84}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{53}{84}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(1\)	\(e\left(\frac{31}{84}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{71}{84}\right)\)
\(\chi_{8820}(6527,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{25}{84}\right)\)	\(e\left(\frac{41}{84}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{71}{84}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(1\)	\(e\left(\frac{13}{84}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{65}{84}\right)\)
\(\chi_{8820}(7187,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{53}{84}\right)\)	\(e\left(\frac{13}{84}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{43}{84}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(1\)	\(e\left(\frac{41}{84}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{37}{84}\right)\)
\(\chi_{8820}(7787,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{37}{84}\right)\)	\(e\left(\frac{17}{84}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{84}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(1\)	\(e\left(\frac{73}{84}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{29}{84}\right)\)
\(\chi_{8820}(7943,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{59}{84}\right)\)	\(e\left(\frac{43}{84}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{13}{84}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(1\)	\(e\left(\frac{71}{84}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{19}{84}\right)\)
\(\chi_{8820}(8543,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{19}{84}\right)\)	\(e\left(\frac{11}{84}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{17}{84}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(1\)	\(e\left(\frac{67}{84}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{83}{84}\right)\)

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

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