LMFDB - Dirichlet character orbit 8820.ih

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(8820, base_ring=CyclotomicField(84)) M = H._module chi = DirichletCharacter(H, M([42,28,21,52])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(247,8820)) 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	$-1$	$1$	$11$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$	$43$
$\chi_{8820}(247,\cdot)$	$1$	$1$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{71}{84}\right)$	$e\left(\frac{61}{84}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{37}{84}\right)$	$e\left(\frac{41}{42}\right)$	$-1$	$e\left(\frac{5}{84}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{25}{84}\right)$
$\chi_{8820}(403,\cdot)$	$1$	$1$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{1}{84}\right)$	$e\left(\frac{47}{84}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{23}{84}\right)$	$e\left(\frac{13}{42}\right)$	$-1$	$e\left(\frac{19}{84}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{11}{84}\right)$
$\chi_{8820}(907,\cdot)$	$1$	$1$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{55}{84}\right)$	$e\left(\frac{65}{84}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{84}\right)$	$e\left(\frac{1}{42}\right)$	$-1$	$e\left(\frac{37}{84}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{17}{84}\right)$
$\chi_{8820}(1003,\cdot)$	$1$	$1$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{65}{84}\right)$	$e\left(\frac{31}{84}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{67}{84}\right)$	$e\left(\frac{5}{42}\right)$	$-1$	$e\left(\frac{59}{84}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{43}{84}\right)$
$\chi_{8820}(1507,\cdot)$	$1$	$1$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{47}{84}\right)$	$e\left(\frac{25}{84}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{73}{84}\right)$	$e\left(\frac{23}{42}\right)$	$-1$	$e\left(\frac{53}{84}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{13}{84}\right)$
$\chi_{8820}(1663,\cdot)$	$1$	$1$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{73}{84}\right)$	$e\left(\frac{71}{84}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{83}{84}\right)$	$e\left(\frac{25}{42}\right)$	$-1$	$e\left(\frac{43}{84}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{47}{84}\right)$
$\chi_{8820}(2167,\cdot)$	$1$	$1$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{43}{84}\right)$	$e\left(\frac{5}{84}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{65}{84}\right)$	$e\left(\frac{13}{42}\right)$	$-1$	$e\left(\frac{61}{84}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{53}{84}\right)$
$\chi_{8820}(2263,\cdot)$	$1$	$1$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{41}{84}\right)$	$e\left(\frac{79}{84}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{19}{84}\right)$	$e\left(\frac{29}{42}\right)$	$-1$	$e\left(\frac{23}{84}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{31}{84}\right)$
$\chi_{8820}(2767,\cdot)$	$1$	$1$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{23}{84}\right)$	$e\left(\frac{73}{84}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{25}{84}\right)$	$e\left(\frac{5}{42}\right)$	$-1$	$e\left(\frac{17}{84}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{1}{84}\right)$
$\chi_{8820}(2923,\cdot)$	$1$	$1$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{61}{84}\right)$	$e\left(\frac{11}{84}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{59}{84}\right)$	$e\left(\frac{37}{42}\right)$	$-1$	$e\left(\frac{67}{84}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{83}{84}\right)$
$\chi_{8820}(3427,\cdot)$	$1$	$1$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{31}{84}\right)$	$e\left(\frac{29}{84}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{41}{84}\right)$	$e\left(\frac{25}{42}\right)$	$-1$	$e\left(\frac{1}{84}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{5}{84}\right)$
$\chi_{8820}(3523,\cdot)$	$1$	$1$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{17}{84}\right)$	$e\left(\frac{43}{84}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{55}{84}\right)$	$e\left(\frac{11}{42}\right)$	$-1$	$e\left(\frac{71}{84}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{19}{84}\right)$
$\chi_{8820}(4027,\cdot)$	$1$	$1$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{83}{84}\right)$	$e\left(\frac{37}{84}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{61}{84}\right)$	$e\left(\frac{29}{42}\right)$	$-1$	$e\left(\frac{65}{84}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{73}{84}\right)$
$\chi_{8820}(4687,\cdot)$	$1$	$1$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{19}{84}\right)$	$e\left(\frac{53}{84}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{17}{84}\right)$	$e\left(\frac{37}{42}\right)$	$-1$	$e\left(\frac{25}{84}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{41}{84}\right)$
$\chi_{8820}(5287,\cdot)$	$1$	$1$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{59}{84}\right)$	$e\left(\frac{1}{84}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{13}{84}\right)$	$e\left(\frac{11}{42}\right)$	$-1$	$e\left(\frac{29}{84}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{61}{84}\right)$
$\chi_{8820}(5443,\cdot)$	$1$	$1$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{37}{84}\right)$	$e\left(\frac{59}{84}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{84}\right)$	$e\left(\frac{19}{42}\right)$	$-1$	$e\left(\frac{31}{84}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{71}{84}\right)$
$\chi_{8820}(6043,\cdot)$	$1$	$1$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{53}{84}\right)$	$e\left(\frac{55}{84}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{43}{84}\right)$	$e\left(\frac{17}{42}\right)$	$-1$	$e\left(\frac{83}{84}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{79}{84}\right)$
$\chi_{8820}(6703,\cdot)$	$1$	$1$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{25}{84}\right)$	$e\left(\frac{83}{84}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{71}{84}\right)$	$e\left(\frac{31}{42}\right)$	$-1$	$e\left(\frac{55}{84}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{23}{84}\right)$
$\chi_{8820}(7207,\cdot)$	$1$	$1$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{79}{84}\right)$	$e\left(\frac{17}{84}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{53}{84}\right)$	$e\left(\frac{19}{42}\right)$	$-1$	$e\left(\frac{73}{84}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{29}{84}\right)$
$\chi_{8820}(7303,\cdot)$	$1$	$1$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{29}{84}\right)$	$e\left(\frac{19}{84}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{79}{84}\right)$	$e\left(\frac{41}{42}\right)$	$-1$	$e\left(\frac{47}{84}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{67}{84}\right)$
$\chi_{8820}(7807,\cdot)$	$1$	$1$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{11}{84}\right)$	$e\left(\frac{13}{84}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{84}\right)$	$e\left(\frac{17}{42}\right)$	$-1$	$e\left(\frac{41}{84}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{37}{84}\right)$
$\chi_{8820}(7963,\cdot)$	$1$	$1$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{13}{84}\right)$	$e\left(\frac{23}{84}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{47}{84}\right)$	$e\left(\frac{1}{42}\right)$	$-1$	$e\left(\frac{79}{84}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{59}{84}\right)$
$\chi_{8820}(8467,\cdot)$	$1$	$1$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{67}{84}\right)$	$e\left(\frac{41}{84}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{29}{84}\right)$	$e\left(\frac{31}{42}\right)$	$-1$	$e\left(\frac{13}{84}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{65}{84}\right)$
$\chi_{8820}(8563,\cdot)$	$1$	$1$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{5}{84}\right)$	$e\left(\frac{67}{84}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{31}{84}\right)$	$e\left(\frac{23}{42}\right)$	$-1$	$e\left(\frac{11}{84}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{55}{84}\right)$

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	\(-1\)	\(1\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)	\(43\)
\(\chi_{8820}(247,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{71}{84}\right)\)	\(e\left(\frac{61}{84}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{37}{84}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(-1\)	\(e\left(\frac{5}{84}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{25}{84}\right)\)
\(\chi_{8820}(403,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{1}{84}\right)\)	\(e\left(\frac{47}{84}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{23}{84}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(-1\)	\(e\left(\frac{19}{84}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{11}{84}\right)\)
\(\chi_{8820}(907,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{55}{84}\right)\)	\(e\left(\frac{65}{84}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{84}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(-1\)	\(e\left(\frac{37}{84}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{17}{84}\right)\)
\(\chi_{8820}(1003,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{65}{84}\right)\)	\(e\left(\frac{31}{84}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{67}{84}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(-1\)	\(e\left(\frac{59}{84}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{43}{84}\right)\)
\(\chi_{8820}(1507,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{47}{84}\right)\)	\(e\left(\frac{25}{84}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{73}{84}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(-1\)	\(e\left(\frac{53}{84}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{13}{84}\right)\)
\(\chi_{8820}(1663,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{73}{84}\right)\)	\(e\left(\frac{71}{84}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{83}{84}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(-1\)	\(e\left(\frac{43}{84}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{47}{84}\right)\)
\(\chi_{8820}(2167,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{43}{84}\right)\)	\(e\left(\frac{5}{84}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{65}{84}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(-1\)	\(e\left(\frac{61}{84}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{53}{84}\right)\)
\(\chi_{8820}(2263,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{41}{84}\right)\)	\(e\left(\frac{79}{84}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{19}{84}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(-1\)	\(e\left(\frac{23}{84}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{31}{84}\right)\)
\(\chi_{8820}(2767,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{23}{84}\right)\)	\(e\left(\frac{73}{84}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{25}{84}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(-1\)	\(e\left(\frac{17}{84}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{1}{84}\right)\)
\(\chi_{8820}(2923,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{61}{84}\right)\)	\(e\left(\frac{11}{84}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{59}{84}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(-1\)	\(e\left(\frac{67}{84}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{83}{84}\right)\)
\(\chi_{8820}(3427,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{31}{84}\right)\)	\(e\left(\frac{29}{84}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{41}{84}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(-1\)	\(e\left(\frac{1}{84}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{5}{84}\right)\)
\(\chi_{8820}(3523,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{17}{84}\right)\)	\(e\left(\frac{43}{84}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{55}{84}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(-1\)	\(e\left(\frac{71}{84}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{19}{84}\right)\)
\(\chi_{8820}(4027,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{83}{84}\right)\)	\(e\left(\frac{37}{84}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{61}{84}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(-1\)	\(e\left(\frac{65}{84}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{73}{84}\right)\)
\(\chi_{8820}(4687,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{19}{84}\right)\)	\(e\left(\frac{53}{84}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{17}{84}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(-1\)	\(e\left(\frac{25}{84}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{41}{84}\right)\)
\(\chi_{8820}(5287,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{59}{84}\right)\)	\(e\left(\frac{1}{84}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{13}{84}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(-1\)	\(e\left(\frac{29}{84}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{61}{84}\right)\)
\(\chi_{8820}(5443,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{37}{84}\right)\)	\(e\left(\frac{59}{84}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{84}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(-1\)	\(e\left(\frac{31}{84}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{71}{84}\right)\)
\(\chi_{8820}(6043,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{53}{84}\right)\)	\(e\left(\frac{55}{84}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{43}{84}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(-1\)	\(e\left(\frac{83}{84}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{79}{84}\right)\)
\(\chi_{8820}(6703,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{25}{84}\right)\)	\(e\left(\frac{83}{84}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{71}{84}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(-1\)	\(e\left(\frac{55}{84}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{23}{84}\right)\)
\(\chi_{8820}(7207,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{79}{84}\right)\)	\(e\left(\frac{17}{84}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{53}{84}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(-1\)	\(e\left(\frac{73}{84}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{29}{84}\right)\)
\(\chi_{8820}(7303,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{29}{84}\right)\)	\(e\left(\frac{19}{84}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{79}{84}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(-1\)	\(e\left(\frac{47}{84}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{67}{84}\right)\)
\(\chi_{8820}(7807,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{11}{84}\right)\)	\(e\left(\frac{13}{84}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{84}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(-1\)	\(e\left(\frac{41}{84}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{37}{84}\right)\)
\(\chi_{8820}(7963,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{13}{84}\right)\)	\(e\left(\frac{23}{84}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{47}{84}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(-1\)	\(e\left(\frac{79}{84}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{59}{84}\right)\)
\(\chi_{8820}(8467,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{67}{84}\right)\)	\(e\left(\frac{41}{84}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{29}{84}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(-1\)	\(e\left(\frac{13}{84}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{65}{84}\right)\)
\(\chi_{8820}(8563,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{5}{84}\right)\)	\(e\left(\frac{67}{84}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{31}{84}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(-1\)	\(e\left(\frac{11}{84}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{55}{84}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

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	8820.ih
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)