LMFDB - Dirichlet character orbit 2032.cg

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2032, base_ring=CyclotomicField(84)) M = H._module chi = DirichletCharacter(H, M([0,63,52])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(61,2032)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$2032$
Conductor:	$2032$	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	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$17$	$19$	$21$
$\chi_{2032}(61,\cdot)$	$1$	$1$	$e\left(\frac{73}{84}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{71}{84}\right)$	$e\left(\frac{37}{84}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{11}{21}\right)$	$i$	$e\left(\frac{47}{84}\right)$
$\chi_{2032}(117,\cdot)$	$1$	$1$	$e\left(\frac{43}{84}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{5}{84}\right)$	$e\left(\frac{31}{84}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{20}{21}\right)$	$-i$	$e\left(\frac{53}{84}\right)$
$\chi_{2032}(165,\cdot)$	$1$	$1$	$e\left(\frac{83}{84}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{37}{84}\right)$	$e\left(\frac{11}{84}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{1}{21}\right)$	$-i$	$e\left(\frac{73}{84}\right)$
$\chi_{2032}(221,\cdot)$	$1$	$1$	$e\left(\frac{25}{84}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{83}{84}\right)$	$e\left(\frac{61}{84}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{17}{21}\right)$	$i$	$e\left(\frac{23}{84}\right)$
$\chi_{2032}(301,\cdot)$	$1$	$1$	$e\left(\frac{61}{84}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{11}{84}\right)$	$e\left(\frac{1}{84}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{2}{21}\right)$	$i$	$e\left(\frac{83}{84}\right)$
$\chi_{2032}(341,\cdot)$	$1$	$1$	$e\left(\frac{55}{84}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{65}{84}\right)$	$e\left(\frac{67}{84}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{8}{21}\right)$	$-i$	$e\left(\frac{17}{84}\right)$
$\chi_{2032}(533,\cdot)$	$1$	$1$	$e\left(\frac{11}{84}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{13}{84}\right)$	$e\left(\frac{47}{84}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{10}{21}\right)$	$-i$	$e\left(\frac{37}{84}\right)$
$\chi_{2032}(581,\cdot)$	$1$	$1$	$e\left(\frac{71}{84}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{61}{84}\right)$	$e\left(\frac{59}{84}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{13}{21}\right)$	$-i$	$e\left(\frac{25}{84}\right)$
$\chi_{2032}(685,\cdot)$	$1$	$1$	$e\left(\frac{17}{84}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{43}{84}\right)$	$e\left(\frac{65}{84}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{4}{21}\right)$	$i$	$e\left(\frac{19}{84}\right)$
$\chi_{2032}(757,\cdot)$	$1$	$1$	$e\left(\frac{79}{84}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{17}{84}\right)$	$e\left(\frac{55}{84}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{5}{21}\right)$	$-i$	$e\left(\frac{29}{84}\right)$
$\chi_{2032}(965,\cdot)$	$1$	$1$	$e\left(\frac{47}{84}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{25}{84}\right)$	$e\left(\frac{71}{84}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{16}{21}\right)$	$-i$	$e\left(\frac{13}{84}\right)$
$\chi_{2032}(989,\cdot)$	$1$	$1$	$e\left(\frac{65}{84}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{31}{84}\right)$	$e\left(\frac{41}{84}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{19}{21}\right)$	$i$	$e\left(\frac{43}{84}\right)$
$\chi_{2032}(1077,\cdot)$	$1$	$1$	$e\left(\frac{31}{84}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{29}{84}\right)$	$e\left(\frac{79}{84}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{11}{21}\right)$	$-i$	$e\left(\frac{5}{84}\right)$
$\chi_{2032}(1133,\cdot)$	$1$	$1$	$e\left(\frac{1}{84}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{47}{84}\right)$	$e\left(\frac{73}{84}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{20}{21}\right)$	$i$	$e\left(\frac{11}{84}\right)$
$\chi_{2032}(1181,\cdot)$	$1$	$1$	$e\left(\frac{41}{84}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{79}{84}\right)$	$e\left(\frac{53}{84}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{1}{21}\right)$	$i$	$e\left(\frac{31}{84}\right)$
$\chi_{2032}(1237,\cdot)$	$1$	$1$	$e\left(\frac{67}{84}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{41}{84}\right)$	$e\left(\frac{19}{84}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{17}{21}\right)$	$-i$	$e\left(\frac{65}{84}\right)$
$\chi_{2032}(1317,\cdot)$	$1$	$1$	$e\left(\frac{19}{84}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{53}{84}\right)$	$e\left(\frac{43}{84}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{2}{21}\right)$	$-i$	$e\left(\frac{41}{84}\right)$
$\chi_{2032}(1357,\cdot)$	$1$	$1$	$e\left(\frac{13}{84}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{23}{84}\right)$	$e\left(\frac{25}{84}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{8}{21}\right)$	$i$	$e\left(\frac{59}{84}\right)$
$\chi_{2032}(1549,\cdot)$	$1$	$1$	$e\left(\frac{53}{84}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{55}{84}\right)$	$e\left(\frac{5}{84}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{10}{21}\right)$	$i$	$e\left(\frac{79}{84}\right)$
$\chi_{2032}(1597,\cdot)$	$1$	$1$	$e\left(\frac{29}{84}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{19}{84}\right)$	$e\left(\frac{17}{84}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{13}{21}\right)$	$i$	$e\left(\frac{67}{84}\right)$
$\chi_{2032}(1701,\cdot)$	$1$	$1$	$e\left(\frac{59}{84}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{1}{84}\right)$	$e\left(\frac{23}{84}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{4}{21}\right)$	$-i$	$e\left(\frac{61}{84}\right)$
$\chi_{2032}(1773,\cdot)$	$1$	$1$	$e\left(\frac{37}{84}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{59}{84}\right)$	$e\left(\frac{13}{84}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{5}{21}\right)$	$i$	$e\left(\frac{71}{84}\right)$
$\chi_{2032}(1981,\cdot)$	$1$	$1$	$e\left(\frac{5}{84}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{67}{84}\right)$	$e\left(\frac{29}{84}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{16}{21}\right)$	$i$	$e\left(\frac{55}{84}\right)$
$\chi_{2032}(2005,\cdot)$	$1$	$1$	$e\left(\frac{23}{84}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{73}{84}\right)$	$e\left(\frac{83}{84}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{19}{21}\right)$	$-i$	$e\left(\frac{1}{84}\right)$

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	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(21\)
\(\chi_{2032}(61,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{73}{84}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{71}{84}\right)\)	\(e\left(\frac{37}{84}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(i\)	\(e\left(\frac{47}{84}\right)\)
\(\chi_{2032}(117,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{84}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{5}{84}\right)\)	\(e\left(\frac{31}{84}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(-i\)	\(e\left(\frac{53}{84}\right)\)
\(\chi_{2032}(165,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{83}{84}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{37}{84}\right)\)	\(e\left(\frac{11}{84}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(-i\)	\(e\left(\frac{73}{84}\right)\)
\(\chi_{2032}(221,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{25}{84}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{83}{84}\right)\)	\(e\left(\frac{61}{84}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(i\)	\(e\left(\frac{23}{84}\right)\)
\(\chi_{2032}(301,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{61}{84}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{11}{84}\right)\)	\(e\left(\frac{1}{84}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(i\)	\(e\left(\frac{83}{84}\right)\)
\(\chi_{2032}(341,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{55}{84}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{65}{84}\right)\)	\(e\left(\frac{67}{84}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(-i\)	\(e\left(\frac{17}{84}\right)\)
\(\chi_{2032}(533,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{84}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{13}{84}\right)\)	\(e\left(\frac{47}{84}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(-i\)	\(e\left(\frac{37}{84}\right)\)
\(\chi_{2032}(581,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{71}{84}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{61}{84}\right)\)	\(e\left(\frac{59}{84}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(-i\)	\(e\left(\frac{25}{84}\right)\)
\(\chi_{2032}(685,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{84}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{43}{84}\right)\)	\(e\left(\frac{65}{84}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(i\)	\(e\left(\frac{19}{84}\right)\)
\(\chi_{2032}(757,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{79}{84}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{17}{84}\right)\)	\(e\left(\frac{55}{84}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(-i\)	\(e\left(\frac{29}{84}\right)\)
\(\chi_{2032}(965,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{84}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{25}{84}\right)\)	\(e\left(\frac{71}{84}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(-i\)	\(e\left(\frac{13}{84}\right)\)
\(\chi_{2032}(989,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{65}{84}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{31}{84}\right)\)	\(e\left(\frac{41}{84}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(i\)	\(e\left(\frac{43}{84}\right)\)
\(\chi_{2032}(1077,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{84}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{29}{84}\right)\)	\(e\left(\frac{79}{84}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(-i\)	\(e\left(\frac{5}{84}\right)\)
\(\chi_{2032}(1133,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{84}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{47}{84}\right)\)	\(e\left(\frac{73}{84}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(i\)	\(e\left(\frac{11}{84}\right)\)
\(\chi_{2032}(1181,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{84}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{79}{84}\right)\)	\(e\left(\frac{53}{84}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(i\)	\(e\left(\frac{31}{84}\right)\)
\(\chi_{2032}(1237,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{67}{84}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{41}{84}\right)\)	\(e\left(\frac{19}{84}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(-i\)	\(e\left(\frac{65}{84}\right)\)
\(\chi_{2032}(1317,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{84}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{53}{84}\right)\)	\(e\left(\frac{43}{84}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(-i\)	\(e\left(\frac{41}{84}\right)\)
\(\chi_{2032}(1357,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{84}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{23}{84}\right)\)	\(e\left(\frac{25}{84}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(i\)	\(e\left(\frac{59}{84}\right)\)
\(\chi_{2032}(1549,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{84}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{55}{84}\right)\)	\(e\left(\frac{5}{84}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(i\)	\(e\left(\frac{79}{84}\right)\)
\(\chi_{2032}(1597,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{84}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{19}{84}\right)\)	\(e\left(\frac{17}{84}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(i\)	\(e\left(\frac{67}{84}\right)\)
\(\chi_{2032}(1701,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{84}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{1}{84}\right)\)	\(e\left(\frac{23}{84}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(-i\)	\(e\left(\frac{61}{84}\right)\)
\(\chi_{2032}(1773,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{84}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{59}{84}\right)\)	\(e\left(\frac{13}{84}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(i\)	\(e\left(\frac{71}{84}\right)\)
\(\chi_{2032}(1981,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{84}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{67}{84}\right)\)	\(e\left(\frac{29}{84}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(i\)	\(e\left(\frac{55}{84}\right)\)
\(\chi_{2032}(2005,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{84}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{73}{84}\right)\)	\(e\left(\frac{83}{84}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(-i\)	\(e\left(\frac{1}{84}\right)\)

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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	2032.cg
Modulus	$2032$
Conductor	$2032$
Order	$84$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(2032\)
Conductor:	\(2032\)	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)