LMFDB - Dirichlet character orbit 8820.ir

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comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(8820, base_ring=CyclotomicField(84)) M = H._module chi = DirichletCharacter(H, M([42,14,63,18])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(83, 8820)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

magma:// Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("8820.83"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$8820$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$8820$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$84$	comment:Order sage:chi.multiplicative_order() gp:charorder(g,chi) magma:Order(chi);
Real:	no	comment:Whether the character is real sage:chi.multiplicative_order() <= 2 gp:charorder(g,chi) <= 2 magma:Order(chi) le 2;
Primitive:	yes	comment:If the character is primitive sage:chi.is_primitive() gp:#znconreyconductor(g,chi)==1 magma:IsPrimitive(chi);
Minimal:	yes
Parity:	even	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(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	$-1$	$1$	$11$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$	$43$
$\chi_{8820}(83,\cdot)$	$1$	$1$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{55}{84}\right)$	$e\left(\frac{17}{28}\right)$	$-1$	$e\left(\frac{61}{84}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{59}{84}\right)$
$\chi_{8820}(167,\cdot)$	$1$	$1$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{5}{84}\right)$	$e\left(\frac{27}{28}\right)$	$-1$	$e\left(\frac{59}{84}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{13}{84}\right)$
$\chi_{8820}(923,\cdot)$	$1$	$1$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{59}{84}\right)$	$e\left(\frac{5}{28}\right)$	$-1$	$e\left(\frac{41}{84}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{19}{84}\right)$
$\chi_{8820}(1343,\cdot)$	$1$	$1$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{19}{84}\right)$	$e\left(\frac{13}{28}\right)$	$-1$	$e\left(\frac{73}{84}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{83}{84}\right)$
$\chi_{8820}(1427,\cdot)$	$1$	$1$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{53}{84}\right)$	$e\left(\frac{23}{28}\right)$	$-1$	$e\left(\frac{71}{84}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{37}{84}\right)$
$\chi_{8820}(1847,\cdot)$	$1$	$1$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{13}{84}\right)$	$e\left(\frac{3}{28}\right)$	$-1$	$e\left(\frac{19}{84}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{17}{84}\right)$
$\chi_{8820}(2183,\cdot)$	$1$	$1$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{23}{84}\right)$	$e\left(\frac{1}{28}\right)$	$-1$	$e\left(\frac{53}{84}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{43}{84}\right)$
$\chi_{8820}(2603,\cdot)$	$1$	$1$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{67}{84}\right)$	$e\left(\frac{9}{28}\right)$	$-1$	$e\left(\frac{1}{84}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{23}{84}\right)$
$\chi_{8820}(2687,\cdot)$	$1$	$1$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{17}{84}\right)$	$e\left(\frac{19}{28}\right)$	$-1$	$e\left(\frac{83}{84}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{61}{84}\right)$
$\chi_{8820}(3107,\cdot)$	$1$	$1$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{61}{84}\right)$	$e\left(\frac{27}{28}\right)$	$-1$	$e\left(\frac{31}{84}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{41}{84}\right)$
$\chi_{8820}(3443,\cdot)$	$1$	$1$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{71}{84}\right)$	$e\left(\frac{25}{28}\right)$	$-1$	$e\left(\frac{65}{84}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{67}{84}\right)$
$\chi_{8820}(3863,\cdot)$	$1$	$1$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{31}{84}\right)$	$e\left(\frac{5}{28}\right)$	$-1$	$e\left(\frac{13}{84}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{47}{84}\right)$
$\chi_{8820}(3947,\cdot)$	$1$	$1$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{65}{84}\right)$	$e\left(\frac{15}{28}\right)$	$-1$	$e\left(\frac{11}{84}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{1}{84}\right)$
$\chi_{8820}(4367,\cdot)$	$1$	$1$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{25}{84}\right)$	$e\left(\frac{23}{28}\right)$	$-1$	$e\left(\frac{43}{84}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{65}{84}\right)$
$\chi_{8820}(5123,\cdot)$	$1$	$1$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{79}{84}\right)$	$e\left(\frac{1}{28}\right)$	$-1$	$e\left(\frac{25}{84}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{71}{84}\right)$
$\chi_{8820}(5207,\cdot)$	$1$	$1$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{29}{84}\right)$	$e\left(\frac{11}{28}\right)$	$-1$	$e\left(\frac{23}{84}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{25}{84}\right)$
$\chi_{8820}(5627,\cdot)$	$1$	$1$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{73}{84}\right)$	$e\left(\frac{19}{28}\right)$	$-1$	$e\left(\frac{55}{84}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{5}{84}\right)$
$\chi_{8820}(5963,\cdot)$	$1$	$1$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{83}{84}\right)$	$e\left(\frac{17}{28}\right)$	$-1$	$e\left(\frac{5}{84}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{31}{84}\right)$
$\chi_{8820}(6383,\cdot)$	$1$	$1$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{43}{84}\right)$	$e\left(\frac{25}{28}\right)$	$-1$	$e\left(\frac{37}{84}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{11}{84}\right)$
$\chi_{8820}(6887,\cdot)$	$1$	$1$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{37}{84}\right)$	$e\left(\frac{15}{28}\right)$	$-1$	$e\left(\frac{67}{84}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{29}{84}\right)$
$\chi_{8820}(7223,\cdot)$	$1$	$1$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{47}{84}\right)$	$e\left(\frac{13}{28}\right)$	$-1$	$e\left(\frac{17}{84}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{55}{84}\right)$
$\chi_{8820}(7727,\cdot)$	$1$	$1$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{41}{84}\right)$	$e\left(\frac{3}{28}\right)$	$-1$	$e\left(\frac{47}{84}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{73}{84}\right)$
$\chi_{8820}(8147,\cdot)$	$1$	$1$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{1}{84}\right)$	$e\left(\frac{11}{28}\right)$	$-1$	$e\left(\frac{79}{84}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{53}{84}\right)$
$\chi_{8820}(8483,\cdot)$	$1$	$1$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{11}{84}\right)$	$e\left(\frac{9}{28}\right)$	$-1$	$e\left(\frac{29}{84}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{79}{84}\right)$

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	\(-1\)	\(1\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)	\(43\)
\(\chi_{8820}(83,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{55}{84}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(-1\)	\(e\left(\frac{61}{84}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{59}{84}\right)\)
\(\chi_{8820}(167,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{5}{84}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(-1\)	\(e\left(\frac{59}{84}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{13}{84}\right)\)
\(\chi_{8820}(923,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{59}{84}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(-1\)	\(e\left(\frac{41}{84}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{19}{84}\right)\)
\(\chi_{8820}(1343,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{19}{84}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(-1\)	\(e\left(\frac{73}{84}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{83}{84}\right)\)
\(\chi_{8820}(1427,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{53}{84}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(-1\)	\(e\left(\frac{71}{84}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{37}{84}\right)\)
\(\chi_{8820}(1847,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{13}{84}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(-1\)	\(e\left(\frac{19}{84}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{17}{84}\right)\)
\(\chi_{8820}(2183,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{23}{84}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(-1\)	\(e\left(\frac{53}{84}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{43}{84}\right)\)
\(\chi_{8820}(2603,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{67}{84}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(-1\)	\(e\left(\frac{1}{84}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{23}{84}\right)\)
\(\chi_{8820}(2687,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{17}{84}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(-1\)	\(e\left(\frac{83}{84}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{61}{84}\right)\)
\(\chi_{8820}(3107,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{61}{84}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(-1\)	\(e\left(\frac{31}{84}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{41}{84}\right)\)
\(\chi_{8820}(3443,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{71}{84}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(-1\)	\(e\left(\frac{65}{84}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{67}{84}\right)\)
\(\chi_{8820}(3863,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{31}{84}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(-1\)	\(e\left(\frac{13}{84}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{47}{84}\right)\)
\(\chi_{8820}(3947,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{65}{84}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(-1\)	\(e\left(\frac{11}{84}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{1}{84}\right)\)
\(\chi_{8820}(4367,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{25}{84}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(-1\)	\(e\left(\frac{43}{84}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{65}{84}\right)\)
\(\chi_{8820}(5123,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{79}{84}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(-1\)	\(e\left(\frac{25}{84}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{71}{84}\right)\)
\(\chi_{8820}(5207,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{29}{84}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(-1\)	\(e\left(\frac{23}{84}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{25}{84}\right)\)
\(\chi_{8820}(5627,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{73}{84}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(-1\)	\(e\left(\frac{55}{84}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{5}{84}\right)\)
\(\chi_{8820}(5963,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{83}{84}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(-1\)	\(e\left(\frac{5}{84}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{31}{84}\right)\)
\(\chi_{8820}(6383,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{43}{84}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(-1\)	\(e\left(\frac{37}{84}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{11}{84}\right)\)
\(\chi_{8820}(6887,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{37}{84}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(-1\)	\(e\left(\frac{67}{84}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{29}{84}\right)\)
\(\chi_{8820}(7223,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{47}{84}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(-1\)	\(e\left(\frac{17}{84}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{55}{84}\right)\)
\(\chi_{8820}(7727,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{41}{84}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(-1\)	\(e\left(\frac{47}{84}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{73}{84}\right)\)
\(\chi_{8820}(8147,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{1}{84}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(-1\)	\(e\left(\frac{79}{84}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{53}{84}\right)\)
\(\chi_{8820}(8483,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{11}{84}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(-1\)	\(e\left(\frac{29}{84}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{79}{84}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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

Modulus:	\(8820\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(8820\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(84\)	comment:Order sage:chi.multiplicative_order() gp:charorder(g,chi) magma:Order(chi);
Real:	no	comment:Whether the character is real sage:chi.multiplicative_order() <= 2 gp:charorder(g,chi) <= 2 magma:Order(chi) le 2;
Primitive:	yes	comment:If the character is primitive sage:chi.is_primitive() gp:#znconreyconductor(g,chi)==1 magma:IsPrimitive(chi);
Minimal:	yes
Parity:	even	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);