LMFDB - Dirichlet character orbit 9984.hd

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(9984, base_ring=CyclotomicField(96)) M = H._module chi = DirichletCharacter(H, M([48,33,0,32])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(55,9984)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$9984$
Conductor:	$1664$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$96$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 1664.df	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	no
Parity:	odd	sage:chi.is_odd() pari:zncharisodd(g,chi)

Related number fields

Field of values:	$\Q(\zeta_{96})$
Fixed field:	Number field defined by a degree 96 polynomial

First 31 of 32 characters in Galois orbit

Character	$-1$	$1$	$5$	$7$	$11$	$17$	$19$	$23$	$25$	$29$	$31$	$35$
$\chi_{9984}(55,\cdot)$	$-1$	$1$	$e\left(\frac{11}{32}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{5}{96}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{7}{96}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{59}{96}\right)$	$i$	$e\left(\frac{91}{96}\right)$
$\chi_{9984}(295,\cdot)$	$-1$	$1$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{7}{96}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{29}{96}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{25}{96}\right)$	$-i$	$e\left(\frac{89}{96}\right)$
$\chi_{9984}(679,\cdot)$	$-1$	$1$	$e\left(\frac{25}{32}\right)$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{23}{96}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{13}{96}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{41}{96}\right)$	$-i$	$e\left(\frac{73}{96}\right)$
$\chi_{9984}(919,\cdot)$	$-1$	$1$	$e\left(\frac{23}{32}\right)$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{25}{96}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{35}{96}\right)$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{7}{96}\right)$	$i$	$e\left(\frac{71}{96}\right)$
$\chi_{9984}(1303,\cdot)$	$-1$	$1$	$e\left(\frac{7}{32}\right)$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{41}{96}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{19}{96}\right)$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{23}{96}\right)$	$i$	$e\left(\frac{55}{96}\right)$
$\chi_{9984}(1543,\cdot)$	$-1$	$1$	$e\left(\frac{5}{32}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{43}{96}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{41}{96}\right)$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{85}{96}\right)$	$-i$	$e\left(\frac{53}{96}\right)$
$\chi_{9984}(1927,\cdot)$	$-1$	$1$	$e\left(\frac{21}{32}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{59}{96}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{25}{96}\right)$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{5}{96}\right)$	$-i$	$e\left(\frac{37}{96}\right)$
$\chi_{9984}(2167,\cdot)$	$-1$	$1$	$e\left(\frac{19}{32}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{61}{96}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{47}{96}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{67}{96}\right)$	$i$	$e\left(\frac{35}{96}\right)$
$\chi_{9984}(2551,\cdot)$	$-1$	$1$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{77}{96}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{31}{96}\right)$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{83}{96}\right)$	$i$	$e\left(\frac{19}{96}\right)$
$\chi_{9984}(2791,\cdot)$	$-1$	$1$	$e\left(\frac{1}{32}\right)$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{79}{96}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{53}{96}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{49}{96}\right)$	$-i$	$e\left(\frac{17}{96}\right)$
$\chi_{9984}(3175,\cdot)$	$-1$	$1$	$e\left(\frac{17}{32}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{95}{96}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{37}{96}\right)$	$e\left(\frac{13}{48}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{65}{96}\right)$	$-i$	$e\left(\frac{1}{96}\right)$
$\chi_{9984}(3415,\cdot)$	$-1$	$1$	$e\left(\frac{15}{32}\right)$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{1}{96}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{59}{96}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{31}{96}\right)$	$i$	$e\left(\frac{95}{96}\right)$
$\chi_{9984}(3799,\cdot)$	$-1$	$1$	$e\left(\frac{31}{32}\right)$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{17}{96}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{43}{96}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{47}{96}\right)$	$i$	$e\left(\frac{79}{96}\right)$
$\chi_{9984}(4039,\cdot)$	$-1$	$1$	$e\left(\frac{29}{32}\right)$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{19}{96}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{65}{96}\right)$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{13}{96}\right)$	$-i$	$e\left(\frac{77}{96}\right)$
$\chi_{9984}(4423,\cdot)$	$-1$	$1$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{35}{96}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{49}{96}\right)$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{29}{96}\right)$	$-i$	$e\left(\frac{61}{96}\right)$
$\chi_{9984}(4663,\cdot)$	$-1$	$1$	$e\left(\frac{11}{32}\right)$	$e\left(\frac{13}{48}\right)$	$e\left(\frac{37}{96}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{71}{96}\right)$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{91}{96}\right)$	$i$	$e\left(\frac{59}{96}\right)$
$\chi_{9984}(5047,\cdot)$	$-1$	$1$	$e\left(\frac{27}{32}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{53}{96}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{55}{96}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{11}{96}\right)$	$i$	$e\left(\frac{43}{96}\right)$
$\chi_{9984}(5287,\cdot)$	$-1$	$1$	$e\left(\frac{25}{32}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{55}{96}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{77}{96}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{73}{96}\right)$	$-i$	$e\left(\frac{41}{96}\right)$
$\chi_{9984}(5671,\cdot)$	$-1$	$1$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{71}{96}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{61}{96}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{89}{96}\right)$	$-i$	$e\left(\frac{25}{96}\right)$
$\chi_{9984}(5911,\cdot)$	$-1$	$1$	$e\left(\frac{7}{32}\right)$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{73}{96}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{83}{96}\right)$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{55}{96}\right)$	$i$	$e\left(\frac{23}{96}\right)$
$\chi_{9984}(6295,\cdot)$	$-1$	$1$	$e\left(\frac{23}{32}\right)$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{89}{96}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{67}{96}\right)$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{71}{96}\right)$	$i$	$e\left(\frac{7}{96}\right)$
$\chi_{9984}(6535,\cdot)$	$-1$	$1$	$e\left(\frac{21}{32}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{91}{96}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{89}{96}\right)$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{37}{96}\right)$	$-i$	$e\left(\frac{5}{96}\right)$
$\chi_{9984}(6919,\cdot)$	$-1$	$1$	$e\left(\frac{5}{32}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{11}{96}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{73}{96}\right)$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{53}{96}\right)$	$-i$	$e\left(\frac{85}{96}\right)$
$\chi_{9984}(7159,\cdot)$	$-1$	$1$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{13}{96}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{95}{96}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{19}{96}\right)$	$i$	$e\left(\frac{83}{96}\right)$
$\chi_{9984}(7543,\cdot)$	$-1$	$1$	$e\left(\frac{19}{32}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{29}{96}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{79}{96}\right)$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{35}{96}\right)$	$i$	$e\left(\frac{67}{96}\right)$
$\chi_{9984}(7783,\cdot)$	$-1$	$1$	$e\left(\frac{17}{32}\right)$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{31}{96}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{5}{96}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{1}{96}\right)$	$-i$	$e\left(\frac{65}{96}\right)$
$\chi_{9984}(8167,\cdot)$	$-1$	$1$	$e\left(\frac{1}{32}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{47}{96}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{85}{96}\right)$	$e\left(\frac{13}{48}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{17}{96}\right)$	$-i$	$e\left(\frac{49}{96}\right)$
$\chi_{9984}(8407,\cdot)$	$-1$	$1$	$e\left(\frac{31}{32}\right)$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{49}{96}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{11}{96}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{79}{96}\right)$	$i$	$e\left(\frac{47}{96}\right)$
$\chi_{9984}(8791,\cdot)$	$-1$	$1$	$e\left(\frac{15}{32}\right)$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{65}{96}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{91}{96}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{95}{96}\right)$	$i$	$e\left(\frac{31}{96}\right)$
$\chi_{9984}(9031,\cdot)$	$-1$	$1$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{67}{96}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{17}{96}\right)$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{61}{96}\right)$	$-i$	$e\left(\frac{29}{96}\right)$
$\chi_{9984}(9415,\cdot)$	$-1$	$1$	$e\left(\frac{29}{32}\right)$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{83}{96}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{1}{96}\right)$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{77}{96}\right)$	$-i$	$e\left(\frac{13}{96}\right)$

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	\(-1\)	\(1\)	\(5\)	\(7\)	\(11\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)	\(35\)
\(\chi_{9984}(55,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{11}{32}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{5}{96}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{7}{96}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{59}{96}\right)\)	\(i\)	\(e\left(\frac{91}{96}\right)\)
\(\chi_{9984}(295,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{9}{32}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{7}{96}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{29}{96}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{25}{96}\right)\)	\(-i\)	\(e\left(\frac{89}{96}\right)\)
\(\chi_{9984}(679,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{25}{32}\right)\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{23}{96}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{13}{96}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{41}{96}\right)\)	\(-i\)	\(e\left(\frac{73}{96}\right)\)
\(\chi_{9984}(919,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{23}{32}\right)\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{25}{96}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{35}{96}\right)\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{7}{96}\right)\)	\(i\)	\(e\left(\frac{71}{96}\right)\)
\(\chi_{9984}(1303,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{7}{32}\right)\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{41}{96}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{19}{96}\right)\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{23}{96}\right)\)	\(i\)	\(e\left(\frac{55}{96}\right)\)
\(\chi_{9984}(1543,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{5}{32}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{43}{96}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{41}{96}\right)\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{85}{96}\right)\)	\(-i\)	\(e\left(\frac{53}{96}\right)\)
\(\chi_{9984}(1927,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{21}{32}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{59}{96}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{25}{96}\right)\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{5}{96}\right)\)	\(-i\)	\(e\left(\frac{37}{96}\right)\)
\(\chi_{9984}(2167,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{19}{32}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{61}{96}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{47}{96}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{67}{96}\right)\)	\(i\)	\(e\left(\frac{35}{96}\right)\)
\(\chi_{9984}(2551,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{3}{32}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{77}{96}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{31}{96}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{83}{96}\right)\)	\(i\)	\(e\left(\frac{19}{96}\right)\)
\(\chi_{9984}(2791,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{32}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{79}{96}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{53}{96}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{49}{96}\right)\)	\(-i\)	\(e\left(\frac{17}{96}\right)\)
\(\chi_{9984}(3175,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{17}{32}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{95}{96}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{37}{96}\right)\)	\(e\left(\frac{13}{48}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{65}{96}\right)\)	\(-i\)	\(e\left(\frac{1}{96}\right)\)
\(\chi_{9984}(3415,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{15}{32}\right)\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{1}{96}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{59}{96}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{31}{96}\right)\)	\(i\)	\(e\left(\frac{95}{96}\right)\)
\(\chi_{9984}(3799,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{31}{32}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{17}{96}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{43}{96}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{47}{96}\right)\)	\(i\)	\(e\left(\frac{79}{96}\right)\)
\(\chi_{9984}(4039,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{29}{32}\right)\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{19}{96}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{65}{96}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{13}{96}\right)\)	\(-i\)	\(e\left(\frac{77}{96}\right)\)
\(\chi_{9984}(4423,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{13}{32}\right)\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{35}{96}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{49}{96}\right)\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{29}{96}\right)\)	\(-i\)	\(e\left(\frac{61}{96}\right)\)
\(\chi_{9984}(4663,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{11}{32}\right)\)	\(e\left(\frac{13}{48}\right)\)	\(e\left(\frac{37}{96}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{71}{96}\right)\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{91}{96}\right)\)	\(i\)	\(e\left(\frac{59}{96}\right)\)
\(\chi_{9984}(5047,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{27}{32}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{53}{96}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{55}{96}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{11}{96}\right)\)	\(i\)	\(e\left(\frac{43}{96}\right)\)
\(\chi_{9984}(5287,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{25}{32}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{55}{96}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{77}{96}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{73}{96}\right)\)	\(-i\)	\(e\left(\frac{41}{96}\right)\)
\(\chi_{9984}(5671,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{9}{32}\right)\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{71}{96}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{61}{96}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{89}{96}\right)\)	\(-i\)	\(e\left(\frac{25}{96}\right)\)
\(\chi_{9984}(5911,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{7}{32}\right)\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{73}{96}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{83}{96}\right)\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{55}{96}\right)\)	\(i\)	\(e\left(\frac{23}{96}\right)\)
\(\chi_{9984}(6295,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{23}{32}\right)\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{89}{96}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{67}{96}\right)\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{71}{96}\right)\)	\(i\)	\(e\left(\frac{7}{96}\right)\)
\(\chi_{9984}(6535,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{21}{32}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{91}{96}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{89}{96}\right)\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{37}{96}\right)\)	\(-i\)	\(e\left(\frac{5}{96}\right)\)
\(\chi_{9984}(6919,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{5}{32}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{11}{96}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{73}{96}\right)\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{53}{96}\right)\)	\(-i\)	\(e\left(\frac{85}{96}\right)\)
\(\chi_{9984}(7159,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{3}{32}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{13}{96}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{95}{96}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{19}{96}\right)\)	\(i\)	\(e\left(\frac{83}{96}\right)\)
\(\chi_{9984}(7543,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{19}{32}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{29}{96}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{79}{96}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{35}{96}\right)\)	\(i\)	\(e\left(\frac{67}{96}\right)\)
\(\chi_{9984}(7783,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{17}{32}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{31}{96}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{5}{96}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{1}{96}\right)\)	\(-i\)	\(e\left(\frac{65}{96}\right)\)
\(\chi_{9984}(8167,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{32}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{47}{96}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{85}{96}\right)\)	\(e\left(\frac{13}{48}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{17}{96}\right)\)	\(-i\)	\(e\left(\frac{49}{96}\right)\)
\(\chi_{9984}(8407,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{31}{32}\right)\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{49}{96}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{11}{96}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{79}{96}\right)\)	\(i\)	\(e\left(\frac{47}{96}\right)\)
\(\chi_{9984}(8791,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{15}{32}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{65}{96}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{91}{96}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{95}{96}\right)\)	\(i\)	\(e\left(\frac{31}{96}\right)\)
\(\chi_{9984}(9031,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{13}{32}\right)\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{67}{96}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{17}{96}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{61}{96}\right)\)	\(-i\)	\(e\left(\frac{29}{96}\right)\)
\(\chi_{9984}(9415,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{29}{32}\right)\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{83}{96}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{1}{96}\right)\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{77}{96}\right)\)	\(-i\)	\(e\left(\frac{13}{96}\right)\)

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First 31 of 32 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	9984.hd
Modulus	$9984$
Conductor	$1664$
Order	$96$
Real	no
Primitive	no
Minimal	no
Parity	odd

Modulus:	\(9984\)
Conductor:	\(1664\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(96\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 1664.df	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	no
Parity:	odd	sage:chi.is_odd() pari:zncharisodd(g,chi)