LMFDB - Dirichlet character orbit 2205.eo

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2205, base_ring=CyclotomicField(84)) M = H._module chi = DirichletCharacter(H, M([56,21,2])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(52,2205)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$2205$
Conductor:	$2205$	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	$-1$	$1$	$2$	$4$	$8$	$11$	$13$	$16$	$17$	$19$	$22$	$23$
$\chi_{2205}(52,\cdot)$	$1$	$1$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{73}{84}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{71}{84}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{13}{84}\right)$	$e\left(\frac{83}{84}\right)$
$\chi_{2205}(103,\cdot)$	$1$	$1$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{59}{84}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{1}{84}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{83}{84}\right)$	$e\left(\frac{13}{84}\right)$
$\chi_{2205}(292,\cdot)$	$1$	$1$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{29}{84}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{19}{84}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{65}{84}\right)$	$e\left(\frac{79}{84}\right)$
$\chi_{2205}(367,\cdot)$	$1$	$1$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{13}{84}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{23}{84}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{61}{84}\right)$	$e\left(\frac{47}{84}\right)$
$\chi_{2205}(418,\cdot)$	$1$	$1$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{23}{84}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{73}{84}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{11}{84}\right)$	$e\left(\frac{25}{84}\right)$
$\chi_{2205}(493,\cdot)$	$1$	$1$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{31}{84}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{29}{84}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{55}{84}\right)$	$e\left(\frac{41}{84}\right)$
$\chi_{2205}(682,\cdot)$	$1$	$1$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{37}{84}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{59}{84}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{25}{84}\right)$	$e\left(\frac{11}{84}\right)$
$\chi_{2205}(733,\cdot)$	$1$	$1$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{71}{84}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{61}{84}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{23}{84}\right)$	$e\left(\frac{37}{84}\right)$
$\chi_{2205}(808,\cdot)$	$1$	$1$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{55}{84}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{65}{84}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{19}{84}\right)$	$e\left(\frac{5}{84}\right)$
$\chi_{2205}(922,\cdot)$	$1$	$1$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{41}{84}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{79}{84}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{84}\right)$	$e\left(\frac{19}{84}\right)$
$\chi_{2205}(997,\cdot)$	$1$	$1$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{61}{84}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{11}{84}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{73}{84}\right)$	$e\left(\frac{59}{84}\right)$
$\chi_{2205}(1123,\cdot)$	$1$	$1$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{79}{84}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{17}{84}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{67}{84}\right)$	$e\left(\frac{53}{84}\right)$
$\chi_{2205}(1237,\cdot)$	$1$	$1$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{5}{84}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{67}{84}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{17}{84}\right)$	$e\left(\frac{31}{84}\right)$
$\chi_{2205}(1312,\cdot)$	$1$	$1$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{1}{84}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{47}{84}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{37}{84}\right)$	$e\left(\frac{23}{84}\right)$
$\chi_{2205}(1363,\cdot)$	$1$	$1$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{83}{84}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{37}{84}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{47}{84}\right)$	$e\left(\frac{61}{84}\right)$
$\chi_{2205}(1438,\cdot)$	$1$	$1$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{19}{84}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{53}{84}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{31}{84}\right)$	$e\left(\frac{17}{84}\right)$
$\chi_{2205}(1552,\cdot)$	$1$	$1$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{53}{84}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{55}{84}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{29}{84}\right)$	$e\left(\frac{43}{84}\right)$
$\chi_{2205}(1627,\cdot)$	$1$	$1$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{25}{84}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{83}{84}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{84}\right)$	$e\left(\frac{71}{84}\right)$
$\chi_{2205}(1678,\cdot)$	$1$	$1$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{47}{84}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{25}{84}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{59}{84}\right)$	$e\left(\frac{73}{84}\right)$
$\chi_{2205}(1753,\cdot)$	$1$	$1$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{43}{84}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{5}{84}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{79}{84}\right)$	$e\left(\frac{65}{84}\right)$
$\chi_{2205}(1867,\cdot)$	$1$	$1$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{17}{84}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{43}{84}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{41}{84}\right)$	$e\left(\frac{55}{84}\right)$
$\chi_{2205}(1993,\cdot)$	$1$	$1$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{11}{84}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{13}{84}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{71}{84}\right)$	$e\left(\frac{1}{84}\right)$
$\chi_{2205}(2068,\cdot)$	$1$	$1$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{67}{84}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{41}{84}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{43}{84}\right)$	$e\left(\frac{29}{84}\right)$
$\chi_{2205}(2182,\cdot)$	$1$	$1$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{65}{84}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{31}{84}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{53}{84}\right)$	$e\left(\frac{67}{84}\right)$

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	\(-1\)	\(1\)	\(2\)	\(4\)	\(8\)	\(11\)	\(13\)	\(16\)	\(17\)	\(19\)	\(22\)	\(23\)
\(\chi_{2205}(52,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{73}{84}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{71}{84}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{13}{84}\right)\)	\(e\left(\frac{83}{84}\right)\)
\(\chi_{2205}(103,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{59}{84}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{1}{84}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{83}{84}\right)\)	\(e\left(\frac{13}{84}\right)\)
\(\chi_{2205}(292,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{29}{84}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{19}{84}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{65}{84}\right)\)	\(e\left(\frac{79}{84}\right)\)
\(\chi_{2205}(367,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{13}{84}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{23}{84}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{61}{84}\right)\)	\(e\left(\frac{47}{84}\right)\)
\(\chi_{2205}(418,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{23}{84}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{73}{84}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{11}{84}\right)\)	\(e\left(\frac{25}{84}\right)\)
\(\chi_{2205}(493,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{31}{84}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{29}{84}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{55}{84}\right)\)	\(e\left(\frac{41}{84}\right)\)
\(\chi_{2205}(682,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{37}{84}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{59}{84}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{25}{84}\right)\)	\(e\left(\frac{11}{84}\right)\)
\(\chi_{2205}(733,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{71}{84}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{61}{84}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{23}{84}\right)\)	\(e\left(\frac{37}{84}\right)\)
\(\chi_{2205}(808,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{55}{84}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{65}{84}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{19}{84}\right)\)	\(e\left(\frac{5}{84}\right)\)
\(\chi_{2205}(922,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{41}{84}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{79}{84}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{84}\right)\)	\(e\left(\frac{19}{84}\right)\)
\(\chi_{2205}(997,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{61}{84}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{11}{84}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{73}{84}\right)\)	\(e\left(\frac{59}{84}\right)\)
\(\chi_{2205}(1123,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{79}{84}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{17}{84}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{67}{84}\right)\)	\(e\left(\frac{53}{84}\right)\)
\(\chi_{2205}(1237,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{5}{84}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{67}{84}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{17}{84}\right)\)	\(e\left(\frac{31}{84}\right)\)
\(\chi_{2205}(1312,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{1}{84}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{47}{84}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{37}{84}\right)\)	\(e\left(\frac{23}{84}\right)\)
\(\chi_{2205}(1363,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{83}{84}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{37}{84}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{47}{84}\right)\)	\(e\left(\frac{61}{84}\right)\)
\(\chi_{2205}(1438,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{19}{84}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{53}{84}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{31}{84}\right)\)	\(e\left(\frac{17}{84}\right)\)
\(\chi_{2205}(1552,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{53}{84}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{55}{84}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{29}{84}\right)\)	\(e\left(\frac{43}{84}\right)\)
\(\chi_{2205}(1627,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{25}{84}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{83}{84}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{84}\right)\)	\(e\left(\frac{71}{84}\right)\)
\(\chi_{2205}(1678,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{47}{84}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{25}{84}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{59}{84}\right)\)	\(e\left(\frac{73}{84}\right)\)
\(\chi_{2205}(1753,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{43}{84}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{5}{84}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{79}{84}\right)\)	\(e\left(\frac{65}{84}\right)\)
\(\chi_{2205}(1867,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{17}{84}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{43}{84}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{41}{84}\right)\)	\(e\left(\frac{55}{84}\right)\)
\(\chi_{2205}(1993,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{11}{84}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{13}{84}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{71}{84}\right)\)	\(e\left(\frac{1}{84}\right)\)
\(\chi_{2205}(2068,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{67}{84}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{41}{84}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{43}{84}\right)\)	\(e\left(\frac{29}{84}\right)\)
\(\chi_{2205}(2182,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{65}{84}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{31}{84}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{53}{84}\right)\)	\(e\left(\frac{67}{84}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

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

Modulus:	\(2205\)
Conductor:	\(2205\)	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)