LMFDB - Dirichlet character orbit 3328.dn

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(3328, base_ring=CyclotomicField(96)) M = H._module chi = DirichletCharacter(H, M([48,33,32])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(55,3328)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$3328$
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	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$15$	$17$	$19$	$21$	$23$
$\chi_{3328}(55,\cdot)$	$-1$	$1$	$e\left(\frac{83}{96}\right)$	$e\left(\frac{11}{32}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{5}{96}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{7}{96}\right)$	$e\left(\frac{15}{32}\right)$	$e\left(\frac{31}{48}\right)$
$\chi_{3328}(87,\cdot)$	$-1$	$1$	$e\left(\frac{55}{96}\right)$	$e\left(\frac{15}{32}\right)$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{1}{96}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{59}{96}\right)$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{35}{48}\right)$
$\chi_{3328}(263,\cdot)$	$-1$	$1$	$e\left(\frac{29}{96}\right)$	$e\left(\frac{5}{32}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{11}{96}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{73}{96}\right)$	$e\left(\frac{1}{32}\right)$	$e\left(\frac{1}{48}\right)$
$\chi_{3328}(295,\cdot)$	$-1$	$1$	$e\left(\frac{1}{96}\right)$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{7}{96}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{29}{96}\right)$	$e\left(\frac{21}{32}\right)$	$e\left(\frac{5}{48}\right)$
$\chi_{3328}(471,\cdot)$	$-1$	$1$	$e\left(\frac{71}{96}\right)$	$e\left(\frac{31}{32}\right)$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{17}{96}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{43}{96}\right)$	$e\left(\frac{19}{32}\right)$	$e\left(\frac{19}{48}\right)$
$\chi_{3328}(503,\cdot)$	$-1$	$1$	$e\left(\frac{43}{96}\right)$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{13}{96}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{95}{96}\right)$	$e\left(\frac{7}{32}\right)$	$e\left(\frac{23}{48}\right)$
$\chi_{3328}(679,\cdot)$	$-1$	$1$	$e\left(\frac{17}{96}\right)$	$e\left(\frac{25}{32}\right)$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{23}{96}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{13}{96}\right)$	$e\left(\frac{5}{32}\right)$	$e\left(\frac{37}{48}\right)$
$\chi_{3328}(711,\cdot)$	$-1$	$1$	$e\left(\frac{85}{96}\right)$	$e\left(\frac{29}{32}\right)$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{19}{96}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{65}{96}\right)$	$e\left(\frac{25}{32}\right)$	$e\left(\frac{41}{48}\right)$
$\chi_{3328}(887,\cdot)$	$-1$	$1$	$e\left(\frac{59}{96}\right)$	$e\left(\frac{19}{32}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{29}{96}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{79}{96}\right)$	$e\left(\frac{23}{32}\right)$	$e\left(\frac{7}{48}\right)$
$\chi_{3328}(919,\cdot)$	$-1$	$1$	$e\left(\frac{31}{96}\right)$	$e\left(\frac{23}{32}\right)$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{25}{96}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{35}{96}\right)$	$e\left(\frac{11}{32}\right)$	$e\left(\frac{11}{48}\right)$
$\chi_{3328}(1095,\cdot)$	$-1$	$1$	$e\left(\frac{5}{96}\right)$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{35}{96}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{49}{96}\right)$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{25}{48}\right)$
$\chi_{3328}(1127,\cdot)$	$-1$	$1$	$e\left(\frac{73}{96}\right)$	$e\left(\frac{17}{32}\right)$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{31}{96}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{5}{96}\right)$	$e\left(\frac{29}{32}\right)$	$e\left(\frac{29}{48}\right)$
$\chi_{3328}(1303,\cdot)$	$-1$	$1$	$e\left(\frac{47}{96}\right)$	$e\left(\frac{7}{32}\right)$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{41}{96}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{19}{96}\right)$	$e\left(\frac{27}{32}\right)$	$e\left(\frac{43}{48}\right)$
$\chi_{3328}(1335,\cdot)$	$-1$	$1$	$e\left(\frac{19}{96}\right)$	$e\left(\frac{11}{32}\right)$	$e\left(\frac{13}{48}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{37}{96}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{71}{96}\right)$	$e\left(\frac{15}{32}\right)$	$e\left(\frac{47}{48}\right)$
$\chi_{3328}(1511,\cdot)$	$-1$	$1$	$e\left(\frac{89}{96}\right)$	$e\left(\frac{1}{32}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{47}{96}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{85}{96}\right)$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{13}{48}\right)$
$\chi_{3328}(1543,\cdot)$	$-1$	$1$	$e\left(\frac{61}{96}\right)$	$e\left(\frac{5}{32}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{13}{48}\right)$	$e\left(\frac{43}{96}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{41}{96}\right)$	$e\left(\frac{1}{32}\right)$	$e\left(\frac{17}{48}\right)$
$\chi_{3328}(1719,\cdot)$	$-1$	$1$	$e\left(\frac{35}{96}\right)$	$e\left(\frac{27}{32}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{53}{96}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{55}{96}\right)$	$e\left(\frac{31}{32}\right)$	$e\left(\frac{31}{48}\right)$
$\chi_{3328}(1751,\cdot)$	$-1$	$1$	$e\left(\frac{7}{96}\right)$	$e\left(\frac{31}{32}\right)$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{49}{96}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{11}{96}\right)$	$e\left(\frac{19}{32}\right)$	$e\left(\frac{35}{48}\right)$
$\chi_{3328}(1927,\cdot)$	$-1$	$1$	$e\left(\frac{77}{96}\right)$	$e\left(\frac{21}{32}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{59}{96}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{25}{96}\right)$	$e\left(\frac{17}{32}\right)$	$e\left(\frac{1}{48}\right)$
$\chi_{3328}(1959,\cdot)$	$-1$	$1$	$e\left(\frac{49}{96}\right)$	$e\left(\frac{25}{32}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{55}{96}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{77}{96}\right)$	$e\left(\frac{5}{32}\right)$	$e\left(\frac{5}{48}\right)$
$\chi_{3328}(2135,\cdot)$	$-1$	$1$	$e\left(\frac{23}{96}\right)$	$e\left(\frac{15}{32}\right)$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{65}{96}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{91}{96}\right)$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{19}{48}\right)$
$\chi_{3328}(2167,\cdot)$	$-1$	$1$	$e\left(\frac{91}{96}\right)$	$e\left(\frac{19}{32}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{61}{96}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{47}{96}\right)$	$e\left(\frac{23}{32}\right)$	$e\left(\frac{23}{48}\right)$
$\chi_{3328}(2343,\cdot)$	$-1$	$1$	$e\left(\frac{65}{96}\right)$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{71}{96}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{61}{96}\right)$	$e\left(\frac{21}{32}\right)$	$e\left(\frac{37}{48}\right)$
$\chi_{3328}(2375,\cdot)$	$-1$	$1$	$e\left(\frac{37}{96}\right)$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{67}{96}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{17}{96}\right)$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{41}{48}\right)$
$\chi_{3328}(2551,\cdot)$	$-1$	$1$	$e\left(\frac{11}{96}\right)$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{77}{96}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{31}{96}\right)$	$e\left(\frac{7}{32}\right)$	$e\left(\frac{7}{48}\right)$
$\chi_{3328}(2583,\cdot)$	$-1$	$1$	$e\left(\frac{79}{96}\right)$	$e\left(\frac{7}{32}\right)$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{73}{96}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{83}{96}\right)$	$e\left(\frac{27}{32}\right)$	$e\left(\frac{11}{48}\right)$
$\chi_{3328}(2759,\cdot)$	$-1$	$1$	$e\left(\frac{53}{96}\right)$	$e\left(\frac{29}{32}\right)$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{83}{96}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{1}{96}\right)$	$e\left(\frac{25}{32}\right)$	$e\left(\frac{25}{48}\right)$
$\chi_{3328}(2791,\cdot)$	$-1$	$1$	$e\left(\frac{25}{96}\right)$	$e\left(\frac{1}{32}\right)$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{79}{96}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{53}{96}\right)$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{29}{48}\right)$
$\chi_{3328}(2967,\cdot)$	$-1$	$1$	$e\left(\frac{95}{96}\right)$	$e\left(\frac{23}{32}\right)$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{89}{96}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{67}{96}\right)$	$e\left(\frac{11}{32}\right)$	$e\left(\frac{43}{48}\right)$
$\chi_{3328}(2999,\cdot)$	$-1$	$1$	$e\left(\frac{67}{96}\right)$	$e\left(\frac{27}{32}\right)$	$e\left(\frac{13}{48}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{85}{96}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{23}{96}\right)$	$e\left(\frac{31}{32}\right)$	$e\left(\frac{47}{48}\right)$
$\chi_{3328}(3175,\cdot)$	$-1$	$1$	$e\left(\frac{41}{96}\right)$	$e\left(\frac{17}{32}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{95}{96}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{37}{96}\right)$	$e\left(\frac{29}{32}\right)$	$e\left(\frac{13}{48}\right)$

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	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(15\)	\(17\)	\(19\)	\(21\)	\(23\)
\(\chi_{3328}(55,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{83}{96}\right)\)	\(e\left(\frac{11}{32}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{5}{96}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{7}{96}\right)\)	\(e\left(\frac{15}{32}\right)\)	\(e\left(\frac{31}{48}\right)\)
\(\chi_{3328}(87,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{55}{96}\right)\)	\(e\left(\frac{15}{32}\right)\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{1}{96}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{59}{96}\right)\)	\(e\left(\frac{3}{32}\right)\)	\(e\left(\frac{35}{48}\right)\)
\(\chi_{3328}(263,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{29}{96}\right)\)	\(e\left(\frac{5}{32}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{11}{96}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{73}{96}\right)\)	\(e\left(\frac{1}{32}\right)\)	\(e\left(\frac{1}{48}\right)\)
\(\chi_{3328}(295,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{96}\right)\)	\(e\left(\frac{9}{32}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{7}{96}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{29}{96}\right)\)	\(e\left(\frac{21}{32}\right)\)	\(e\left(\frac{5}{48}\right)\)
\(\chi_{3328}(471,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{71}{96}\right)\)	\(e\left(\frac{31}{32}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{17}{96}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{43}{96}\right)\)	\(e\left(\frac{19}{32}\right)\)	\(e\left(\frac{19}{48}\right)\)
\(\chi_{3328}(503,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{43}{96}\right)\)	\(e\left(\frac{3}{32}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{13}{96}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{95}{96}\right)\)	\(e\left(\frac{7}{32}\right)\)	\(e\left(\frac{23}{48}\right)\)
\(\chi_{3328}(679,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{17}{96}\right)\)	\(e\left(\frac{25}{32}\right)\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{23}{96}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{13}{96}\right)\)	\(e\left(\frac{5}{32}\right)\)	\(e\left(\frac{37}{48}\right)\)
\(\chi_{3328}(711,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{85}{96}\right)\)	\(e\left(\frac{29}{32}\right)\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{19}{96}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{65}{96}\right)\)	\(e\left(\frac{25}{32}\right)\)	\(e\left(\frac{41}{48}\right)\)
\(\chi_{3328}(887,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{59}{96}\right)\)	\(e\left(\frac{19}{32}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{29}{96}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{79}{96}\right)\)	\(e\left(\frac{23}{32}\right)\)	\(e\left(\frac{7}{48}\right)\)
\(\chi_{3328}(919,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{31}{96}\right)\)	\(e\left(\frac{23}{32}\right)\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{25}{96}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{35}{96}\right)\)	\(e\left(\frac{11}{32}\right)\)	\(e\left(\frac{11}{48}\right)\)
\(\chi_{3328}(1095,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{5}{96}\right)\)	\(e\left(\frac{13}{32}\right)\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{35}{96}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{49}{96}\right)\)	\(e\left(\frac{9}{32}\right)\)	\(e\left(\frac{25}{48}\right)\)
\(\chi_{3328}(1127,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{73}{96}\right)\)	\(e\left(\frac{17}{32}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{31}{96}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{5}{96}\right)\)	\(e\left(\frac{29}{32}\right)\)	\(e\left(\frac{29}{48}\right)\)
\(\chi_{3328}(1303,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{47}{96}\right)\)	\(e\left(\frac{7}{32}\right)\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{41}{96}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{19}{96}\right)\)	\(e\left(\frac{27}{32}\right)\)	\(e\left(\frac{43}{48}\right)\)
\(\chi_{3328}(1335,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{19}{96}\right)\)	\(e\left(\frac{11}{32}\right)\)	\(e\left(\frac{13}{48}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{37}{96}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{71}{96}\right)\)	\(e\left(\frac{15}{32}\right)\)	\(e\left(\frac{47}{48}\right)\)
\(\chi_{3328}(1511,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{89}{96}\right)\)	\(e\left(\frac{1}{32}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{47}{96}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{85}{96}\right)\)	\(e\left(\frac{13}{32}\right)\)	\(e\left(\frac{13}{48}\right)\)
\(\chi_{3328}(1543,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{61}{96}\right)\)	\(e\left(\frac{5}{32}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{13}{48}\right)\)	\(e\left(\frac{43}{96}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{41}{96}\right)\)	\(e\left(\frac{1}{32}\right)\)	\(e\left(\frac{17}{48}\right)\)
\(\chi_{3328}(1719,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{35}{96}\right)\)	\(e\left(\frac{27}{32}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{53}{96}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{55}{96}\right)\)	\(e\left(\frac{31}{32}\right)\)	\(e\left(\frac{31}{48}\right)\)
\(\chi_{3328}(1751,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{7}{96}\right)\)	\(e\left(\frac{31}{32}\right)\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{49}{96}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{11}{96}\right)\)	\(e\left(\frac{19}{32}\right)\)	\(e\left(\frac{35}{48}\right)\)
\(\chi_{3328}(1927,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{77}{96}\right)\)	\(e\left(\frac{21}{32}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{59}{96}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{25}{96}\right)\)	\(e\left(\frac{17}{32}\right)\)	\(e\left(\frac{1}{48}\right)\)
\(\chi_{3328}(1959,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{49}{96}\right)\)	\(e\left(\frac{25}{32}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{55}{96}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{77}{96}\right)\)	\(e\left(\frac{5}{32}\right)\)	\(e\left(\frac{5}{48}\right)\)
\(\chi_{3328}(2135,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{23}{96}\right)\)	\(e\left(\frac{15}{32}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{65}{96}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{91}{96}\right)\)	\(e\left(\frac{3}{32}\right)\)	\(e\left(\frac{19}{48}\right)\)
\(\chi_{3328}(2167,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{91}{96}\right)\)	\(e\left(\frac{19}{32}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{61}{96}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{47}{96}\right)\)	\(e\left(\frac{23}{32}\right)\)	\(e\left(\frac{23}{48}\right)\)
\(\chi_{3328}(2343,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{65}{96}\right)\)	\(e\left(\frac{9}{32}\right)\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{71}{96}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{61}{96}\right)\)	\(e\left(\frac{21}{32}\right)\)	\(e\left(\frac{37}{48}\right)\)
\(\chi_{3328}(2375,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{37}{96}\right)\)	\(e\left(\frac{13}{32}\right)\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{67}{96}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{17}{96}\right)\)	\(e\left(\frac{9}{32}\right)\)	\(e\left(\frac{41}{48}\right)\)
\(\chi_{3328}(2551,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{11}{96}\right)\)	\(e\left(\frac{3}{32}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{77}{96}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{31}{96}\right)\)	\(e\left(\frac{7}{32}\right)\)	\(e\left(\frac{7}{48}\right)\)
\(\chi_{3328}(2583,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{79}{96}\right)\)	\(e\left(\frac{7}{32}\right)\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{73}{96}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{83}{96}\right)\)	\(e\left(\frac{27}{32}\right)\)	\(e\left(\frac{11}{48}\right)\)
\(\chi_{3328}(2759,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{53}{96}\right)\)	\(e\left(\frac{29}{32}\right)\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{83}{96}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{1}{96}\right)\)	\(e\left(\frac{25}{32}\right)\)	\(e\left(\frac{25}{48}\right)\)
\(\chi_{3328}(2791,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{25}{96}\right)\)	\(e\left(\frac{1}{32}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{79}{96}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{53}{96}\right)\)	\(e\left(\frac{13}{32}\right)\)	\(e\left(\frac{29}{48}\right)\)
\(\chi_{3328}(2967,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{95}{96}\right)\)	\(e\left(\frac{23}{32}\right)\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{89}{96}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{67}{96}\right)\)	\(e\left(\frac{11}{32}\right)\)	\(e\left(\frac{43}{48}\right)\)
\(\chi_{3328}(2999,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{67}{96}\right)\)	\(e\left(\frac{27}{32}\right)\)	\(e\left(\frac{13}{48}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{85}{96}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{23}{96}\right)\)	\(e\left(\frac{31}{32}\right)\)	\(e\left(\frac{47}{48}\right)\)
\(\chi_{3328}(3175,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{41}{96}\right)\)	\(e\left(\frac{17}{32}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{95}{96}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{37}{96}\right)\)	\(e\left(\frac{29}{32}\right)\)	\(e\left(\frac{13}{48}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Basic properties

Related number fields

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	3328.dn
Modulus	$3328$
Conductor	$1664$
Order	$96$
Real	no
Primitive	no
Minimal	no
Parity	odd

Modulus:	\(3328\)
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)