LMFDB - Dirichlet character orbit 3328.df

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(3328, base_ring=CyclotomicField(64)) M = H._module chi = DirichletCharacter(H, M([0,5,0])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(53,3328)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$3328$
Conductor:	$256$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$64$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 256.m	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:	$\Q(\zeta_{64})$
Fixed field:	Number field defined by a degree 64 polynomial

First 31 of 32 characters in Galois orbit

Character	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$15$	$17$	$19$	$21$	$23$
$\chi_{3328}(53,\cdot)$	$1$	$1$	$e\left(\frac{47}{64}\right)$	$e\left(\frac{5}{64}\right)$	$e\left(\frac{25}{32}\right)$	$e\left(\frac{15}{32}\right)$	$e\left(\frac{41}{64}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{51}{64}\right)$	$e\left(\frac{33}{64}\right)$	$e\left(\frac{3}{32}\right)$
$\chi_{3328}(157,\cdot)$	$1$	$1$	$e\left(\frac{49}{64}\right)$	$e\left(\frac{27}{64}\right)$	$e\left(\frac{7}{32}\right)$	$e\left(\frac{17}{32}\right)$	$e\left(\frac{55}{64}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{45}{64}\right)$	$e\left(\frac{63}{64}\right)$	$e\left(\frac{29}{32}\right)$
$\chi_{3328}(261,\cdot)$	$1$	$1$	$e\left(\frac{35}{64}\right)$	$e\left(\frac{1}{64}\right)$	$e\left(\frac{5}{32}\right)$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{21}{64}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{23}{64}\right)$	$e\left(\frac{45}{64}\right)$	$e\left(\frac{7}{32}\right)$
$\chi_{3328}(365,\cdot)$	$1$	$1$	$e\left(\frac{5}{64}\right)$	$e\left(\frac{55}{64}\right)$	$e\left(\frac{19}{32}\right)$	$e\left(\frac{5}{32}\right)$	$e\left(\frac{3}{64}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{49}{64}\right)$	$e\left(\frac{43}{64}\right)$	$e\left(\frac{1}{32}\right)$
$\chi_{3328}(469,\cdot)$	$1$	$1$	$e\left(\frac{23}{64}\right)$	$e\left(\frac{61}{64}\right)$	$e\left(\frac{17}{32}\right)$	$e\left(\frac{23}{32}\right)$	$e\left(\frac{1}{64}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{59}{64}\right)$	$e\left(\frac{57}{64}\right)$	$e\left(\frac{11}{32}\right)$
$\chi_{3328}(573,\cdot)$	$1$	$1$	$e\left(\frac{25}{64}\right)$	$e\left(\frac{19}{64}\right)$	$e\left(\frac{31}{32}\right)$	$e\left(\frac{25}{32}\right)$	$e\left(\frac{15}{64}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{53}{64}\right)$	$e\left(\frac{23}{64}\right)$	$e\left(\frac{5}{32}\right)$
$\chi_{3328}(677,\cdot)$	$1$	$1$	$e\left(\frac{11}{64}\right)$	$e\left(\frac{57}{64}\right)$	$e\left(\frac{29}{32}\right)$	$e\left(\frac{11}{32}\right)$	$e\left(\frac{45}{64}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{31}{64}\right)$	$e\left(\frac{5}{64}\right)$	$e\left(\frac{15}{32}\right)$
$\chi_{3328}(781,\cdot)$	$1$	$1$	$e\left(\frac{45}{64}\right)$	$e\left(\frac{47}{64}\right)$	$e\left(\frac{11}{32}\right)$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{27}{64}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{57}{64}\right)$	$e\left(\frac{3}{64}\right)$	$e\left(\frac{9}{32}\right)$
$\chi_{3328}(885,\cdot)$	$1$	$1$	$e\left(\frac{63}{64}\right)$	$e\left(\frac{53}{64}\right)$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{31}{32}\right)$	$e\left(\frac{25}{64}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{3}{64}\right)$	$e\left(\frac{17}{64}\right)$	$e\left(\frac{19}{32}\right)$
$\chi_{3328}(989,\cdot)$	$1$	$1$	$e\left(\frac{1}{64}\right)$	$e\left(\frac{11}{64}\right)$	$e\left(\frac{23}{32}\right)$	$e\left(\frac{1}{32}\right)$	$e\left(\frac{39}{64}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{61}{64}\right)$	$e\left(\frac{47}{64}\right)$	$e\left(\frac{13}{32}\right)$
$\chi_{3328}(1093,\cdot)$	$1$	$1$	$e\left(\frac{51}{64}\right)$	$e\left(\frac{49}{64}\right)$	$e\left(\frac{21}{32}\right)$	$e\left(\frac{19}{32}\right)$	$e\left(\frac{5}{64}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{39}{64}\right)$	$e\left(\frac{29}{64}\right)$	$e\left(\frac{23}{32}\right)$
$\chi_{3328}(1197,\cdot)$	$1$	$1$	$e\left(\frac{21}{64}\right)$	$e\left(\frac{39}{64}\right)$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{21}{32}\right)$	$e\left(\frac{51}{64}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{1}{64}\right)$	$e\left(\frac{27}{64}\right)$	$e\left(\frac{17}{32}\right)$
$\chi_{3328}(1301,\cdot)$	$1$	$1$	$e\left(\frac{39}{64}\right)$	$e\left(\frac{45}{64}\right)$	$e\left(\frac{1}{32}\right)$	$e\left(\frac{7}{32}\right)$	$e\left(\frac{49}{64}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{11}{64}\right)$	$e\left(\frac{41}{64}\right)$	$e\left(\frac{27}{32}\right)$
$\chi_{3328}(1405,\cdot)$	$1$	$1$	$e\left(\frac{41}{64}\right)$	$e\left(\frac{3}{64}\right)$	$e\left(\frac{15}{32}\right)$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{63}{64}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{5}{64}\right)$	$e\left(\frac{7}{64}\right)$	$e\left(\frac{21}{32}\right)$
$\chi_{3328}(1509,\cdot)$	$1$	$1$	$e\left(\frac{27}{64}\right)$	$e\left(\frac{41}{64}\right)$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{27}{32}\right)$	$e\left(\frac{29}{64}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{47}{64}\right)$	$e\left(\frac{53}{64}\right)$	$e\left(\frac{31}{32}\right)$
$\chi_{3328}(1613,\cdot)$	$1$	$1$	$e\left(\frac{61}{64}\right)$	$e\left(\frac{31}{64}\right)$	$e\left(\frac{27}{32}\right)$	$e\left(\frac{29}{32}\right)$	$e\left(\frac{11}{64}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{9}{64}\right)$	$e\left(\frac{51}{64}\right)$	$e\left(\frac{25}{32}\right)$
$\chi_{3328}(1717,\cdot)$	$1$	$1$	$e\left(\frac{15}{64}\right)$	$e\left(\frac{37}{64}\right)$	$e\left(\frac{25}{32}\right)$	$e\left(\frac{15}{32}\right)$	$e\left(\frac{9}{64}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{19}{64}\right)$	$e\left(\frac{1}{64}\right)$	$e\left(\frac{3}{32}\right)$
$\chi_{3328}(1821,\cdot)$	$1$	$1$	$e\left(\frac{17}{64}\right)$	$e\left(\frac{59}{64}\right)$	$e\left(\frac{7}{32}\right)$	$e\left(\frac{17}{32}\right)$	$e\left(\frac{23}{64}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{13}{64}\right)$	$e\left(\frac{31}{64}\right)$	$e\left(\frac{29}{32}\right)$
$\chi_{3328}(1925,\cdot)$	$1$	$1$	$e\left(\frac{3}{64}\right)$	$e\left(\frac{33}{64}\right)$	$e\left(\frac{5}{32}\right)$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{53}{64}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{55}{64}\right)$	$e\left(\frac{13}{64}\right)$	$e\left(\frac{7}{32}\right)$
$\chi_{3328}(2029,\cdot)$	$1$	$1$	$e\left(\frac{37}{64}\right)$	$e\left(\frac{23}{64}\right)$	$e\left(\frac{19}{32}\right)$	$e\left(\frac{5}{32}\right)$	$e\left(\frac{35}{64}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{17}{64}\right)$	$e\left(\frac{11}{64}\right)$	$e\left(\frac{1}{32}\right)$
$\chi_{3328}(2133,\cdot)$	$1$	$1$	$e\left(\frac{55}{64}\right)$	$e\left(\frac{29}{64}\right)$	$e\left(\frac{17}{32}\right)$	$e\left(\frac{23}{32}\right)$	$e\left(\frac{33}{64}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{27}{64}\right)$	$e\left(\frac{25}{64}\right)$	$e\left(\frac{11}{32}\right)$
$\chi_{3328}(2237,\cdot)$	$1$	$1$	$e\left(\frac{57}{64}\right)$	$e\left(\frac{51}{64}\right)$	$e\left(\frac{31}{32}\right)$	$e\left(\frac{25}{32}\right)$	$e\left(\frac{47}{64}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{21}{64}\right)$	$e\left(\frac{55}{64}\right)$	$e\left(\frac{5}{32}\right)$
$\chi_{3328}(2341,\cdot)$	$1$	$1$	$e\left(\frac{43}{64}\right)$	$e\left(\frac{25}{64}\right)$	$e\left(\frac{29}{32}\right)$	$e\left(\frac{11}{32}\right)$	$e\left(\frac{13}{64}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{63}{64}\right)$	$e\left(\frac{37}{64}\right)$	$e\left(\frac{15}{32}\right)$
$\chi_{3328}(2445,\cdot)$	$1$	$1$	$e\left(\frac{13}{64}\right)$	$e\left(\frac{15}{64}\right)$	$e\left(\frac{11}{32}\right)$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{59}{64}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{25}{64}\right)$	$e\left(\frac{35}{64}\right)$	$e\left(\frac{9}{32}\right)$
$\chi_{3328}(2549,\cdot)$	$1$	$1$	$e\left(\frac{31}{64}\right)$	$e\left(\frac{21}{64}\right)$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{31}{32}\right)$	$e\left(\frac{57}{64}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{35}{64}\right)$	$e\left(\frac{49}{64}\right)$	$e\left(\frac{19}{32}\right)$
$\chi_{3328}(2653,\cdot)$	$1$	$1$	$e\left(\frac{33}{64}\right)$	$e\left(\frac{43}{64}\right)$	$e\left(\frac{23}{32}\right)$	$e\left(\frac{1}{32}\right)$	$e\left(\frac{7}{64}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{29}{64}\right)$	$e\left(\frac{15}{64}\right)$	$e\left(\frac{13}{32}\right)$
$\chi_{3328}(2757,\cdot)$	$1$	$1$	$e\left(\frac{19}{64}\right)$	$e\left(\frac{17}{64}\right)$	$e\left(\frac{21}{32}\right)$	$e\left(\frac{19}{32}\right)$	$e\left(\frac{37}{64}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{7}{64}\right)$	$e\left(\frac{61}{64}\right)$	$e\left(\frac{23}{32}\right)$
$\chi_{3328}(2861,\cdot)$	$1$	$1$	$e\left(\frac{53}{64}\right)$	$e\left(\frac{7}{64}\right)$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{21}{32}\right)$	$e\left(\frac{19}{64}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{33}{64}\right)$	$e\left(\frac{59}{64}\right)$	$e\left(\frac{17}{32}\right)$
$\chi_{3328}(2965,\cdot)$	$1$	$1$	$e\left(\frac{7}{64}\right)$	$e\left(\frac{13}{64}\right)$	$e\left(\frac{1}{32}\right)$	$e\left(\frac{7}{32}\right)$	$e\left(\frac{17}{64}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{43}{64}\right)$	$e\left(\frac{9}{64}\right)$	$e\left(\frac{27}{32}\right)$
$\chi_{3328}(3069,\cdot)$	$1$	$1$	$e\left(\frac{9}{64}\right)$	$e\left(\frac{35}{64}\right)$	$e\left(\frac{15}{32}\right)$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{31}{64}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{37}{64}\right)$	$e\left(\frac{39}{64}\right)$	$e\left(\frac{21}{32}\right)$
$\chi_{3328}(3173,\cdot)$	$1$	$1$	$e\left(\frac{59}{64}\right)$	$e\left(\frac{9}{64}\right)$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{27}{32}\right)$	$e\left(\frac{61}{64}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{15}{64}\right)$	$e\left(\frac{21}{64}\right)$	$e\left(\frac{31}{32}\right)$

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	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(15\)	\(17\)	\(19\)	\(21\)	\(23\)
\(\chi_{3328}(53,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{64}\right)\)	\(e\left(\frac{5}{64}\right)\)	\(e\left(\frac{25}{32}\right)\)	\(e\left(\frac{15}{32}\right)\)	\(e\left(\frac{41}{64}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{51}{64}\right)\)	\(e\left(\frac{33}{64}\right)\)	\(e\left(\frac{3}{32}\right)\)
\(\chi_{3328}(157,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{49}{64}\right)\)	\(e\left(\frac{27}{64}\right)\)	\(e\left(\frac{7}{32}\right)\)	\(e\left(\frac{17}{32}\right)\)	\(e\left(\frac{55}{64}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{45}{64}\right)\)	\(e\left(\frac{63}{64}\right)\)	\(e\left(\frac{29}{32}\right)\)
\(\chi_{3328}(261,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{35}{64}\right)\)	\(e\left(\frac{1}{64}\right)\)	\(e\left(\frac{5}{32}\right)\)	\(e\left(\frac{3}{32}\right)\)	\(e\left(\frac{21}{64}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{23}{64}\right)\)	\(e\left(\frac{45}{64}\right)\)	\(e\left(\frac{7}{32}\right)\)
\(\chi_{3328}(365,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{64}\right)\)	\(e\left(\frac{55}{64}\right)\)	\(e\left(\frac{19}{32}\right)\)	\(e\left(\frac{5}{32}\right)\)	\(e\left(\frac{3}{64}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{49}{64}\right)\)	\(e\left(\frac{43}{64}\right)\)	\(e\left(\frac{1}{32}\right)\)
\(\chi_{3328}(469,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{64}\right)\)	\(e\left(\frac{61}{64}\right)\)	\(e\left(\frac{17}{32}\right)\)	\(e\left(\frac{23}{32}\right)\)	\(e\left(\frac{1}{64}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{59}{64}\right)\)	\(e\left(\frac{57}{64}\right)\)	\(e\left(\frac{11}{32}\right)\)
\(\chi_{3328}(573,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{25}{64}\right)\)	\(e\left(\frac{19}{64}\right)\)	\(e\left(\frac{31}{32}\right)\)	\(e\left(\frac{25}{32}\right)\)	\(e\left(\frac{15}{64}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{53}{64}\right)\)	\(e\left(\frac{23}{64}\right)\)	\(e\left(\frac{5}{32}\right)\)
\(\chi_{3328}(677,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{64}\right)\)	\(e\left(\frac{57}{64}\right)\)	\(e\left(\frac{29}{32}\right)\)	\(e\left(\frac{11}{32}\right)\)	\(e\left(\frac{45}{64}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{31}{64}\right)\)	\(e\left(\frac{5}{64}\right)\)	\(e\left(\frac{15}{32}\right)\)
\(\chi_{3328}(781,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{45}{64}\right)\)	\(e\left(\frac{47}{64}\right)\)	\(e\left(\frac{11}{32}\right)\)	\(e\left(\frac{13}{32}\right)\)	\(e\left(\frac{27}{64}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{57}{64}\right)\)	\(e\left(\frac{3}{64}\right)\)	\(e\left(\frac{9}{32}\right)\)
\(\chi_{3328}(885,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{63}{64}\right)\)	\(e\left(\frac{53}{64}\right)\)	\(e\left(\frac{9}{32}\right)\)	\(e\left(\frac{31}{32}\right)\)	\(e\left(\frac{25}{64}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{3}{64}\right)\)	\(e\left(\frac{17}{64}\right)\)	\(e\left(\frac{19}{32}\right)\)
\(\chi_{3328}(989,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{64}\right)\)	\(e\left(\frac{11}{64}\right)\)	\(e\left(\frac{23}{32}\right)\)	\(e\left(\frac{1}{32}\right)\)	\(e\left(\frac{39}{64}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{61}{64}\right)\)	\(e\left(\frac{47}{64}\right)\)	\(e\left(\frac{13}{32}\right)\)
\(\chi_{3328}(1093,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{51}{64}\right)\)	\(e\left(\frac{49}{64}\right)\)	\(e\left(\frac{21}{32}\right)\)	\(e\left(\frac{19}{32}\right)\)	\(e\left(\frac{5}{64}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{39}{64}\right)\)	\(e\left(\frac{29}{64}\right)\)	\(e\left(\frac{23}{32}\right)\)
\(\chi_{3328}(1197,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{21}{64}\right)\)	\(e\left(\frac{39}{64}\right)\)	\(e\left(\frac{3}{32}\right)\)	\(e\left(\frac{21}{32}\right)\)	\(e\left(\frac{51}{64}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{1}{64}\right)\)	\(e\left(\frac{27}{64}\right)\)	\(e\left(\frac{17}{32}\right)\)
\(\chi_{3328}(1301,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{39}{64}\right)\)	\(e\left(\frac{45}{64}\right)\)	\(e\left(\frac{1}{32}\right)\)	\(e\left(\frac{7}{32}\right)\)	\(e\left(\frac{49}{64}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{11}{64}\right)\)	\(e\left(\frac{41}{64}\right)\)	\(e\left(\frac{27}{32}\right)\)
\(\chi_{3328}(1405,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{64}\right)\)	\(e\left(\frac{3}{64}\right)\)	\(e\left(\frac{15}{32}\right)\)	\(e\left(\frac{9}{32}\right)\)	\(e\left(\frac{63}{64}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{5}{64}\right)\)	\(e\left(\frac{7}{64}\right)\)	\(e\left(\frac{21}{32}\right)\)
\(\chi_{3328}(1509,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{27}{64}\right)\)	\(e\left(\frac{41}{64}\right)\)	\(e\left(\frac{13}{32}\right)\)	\(e\left(\frac{27}{32}\right)\)	\(e\left(\frac{29}{64}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{47}{64}\right)\)	\(e\left(\frac{53}{64}\right)\)	\(e\left(\frac{31}{32}\right)\)
\(\chi_{3328}(1613,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{61}{64}\right)\)	\(e\left(\frac{31}{64}\right)\)	\(e\left(\frac{27}{32}\right)\)	\(e\left(\frac{29}{32}\right)\)	\(e\left(\frac{11}{64}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{9}{64}\right)\)	\(e\left(\frac{51}{64}\right)\)	\(e\left(\frac{25}{32}\right)\)
\(\chi_{3328}(1717,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{15}{64}\right)\)	\(e\left(\frac{37}{64}\right)\)	\(e\left(\frac{25}{32}\right)\)	\(e\left(\frac{15}{32}\right)\)	\(e\left(\frac{9}{64}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{19}{64}\right)\)	\(e\left(\frac{1}{64}\right)\)	\(e\left(\frac{3}{32}\right)\)
\(\chi_{3328}(1821,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{64}\right)\)	\(e\left(\frac{59}{64}\right)\)	\(e\left(\frac{7}{32}\right)\)	\(e\left(\frac{17}{32}\right)\)	\(e\left(\frac{23}{64}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{13}{64}\right)\)	\(e\left(\frac{31}{64}\right)\)	\(e\left(\frac{29}{32}\right)\)
\(\chi_{3328}(1925,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{64}\right)\)	\(e\left(\frac{33}{64}\right)\)	\(e\left(\frac{5}{32}\right)\)	\(e\left(\frac{3}{32}\right)\)	\(e\left(\frac{53}{64}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{55}{64}\right)\)	\(e\left(\frac{13}{64}\right)\)	\(e\left(\frac{7}{32}\right)\)
\(\chi_{3328}(2029,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{64}\right)\)	\(e\left(\frac{23}{64}\right)\)	\(e\left(\frac{19}{32}\right)\)	\(e\left(\frac{5}{32}\right)\)	\(e\left(\frac{35}{64}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{17}{64}\right)\)	\(e\left(\frac{11}{64}\right)\)	\(e\left(\frac{1}{32}\right)\)
\(\chi_{3328}(2133,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{55}{64}\right)\)	\(e\left(\frac{29}{64}\right)\)	\(e\left(\frac{17}{32}\right)\)	\(e\left(\frac{23}{32}\right)\)	\(e\left(\frac{33}{64}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{27}{64}\right)\)	\(e\left(\frac{25}{64}\right)\)	\(e\left(\frac{11}{32}\right)\)
\(\chi_{3328}(2237,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{57}{64}\right)\)	\(e\left(\frac{51}{64}\right)\)	\(e\left(\frac{31}{32}\right)\)	\(e\left(\frac{25}{32}\right)\)	\(e\left(\frac{47}{64}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{21}{64}\right)\)	\(e\left(\frac{55}{64}\right)\)	\(e\left(\frac{5}{32}\right)\)
\(\chi_{3328}(2341,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{64}\right)\)	\(e\left(\frac{25}{64}\right)\)	\(e\left(\frac{29}{32}\right)\)	\(e\left(\frac{11}{32}\right)\)	\(e\left(\frac{13}{64}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{63}{64}\right)\)	\(e\left(\frac{37}{64}\right)\)	\(e\left(\frac{15}{32}\right)\)
\(\chi_{3328}(2445,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{64}\right)\)	\(e\left(\frac{15}{64}\right)\)	\(e\left(\frac{11}{32}\right)\)	\(e\left(\frac{13}{32}\right)\)	\(e\left(\frac{59}{64}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{25}{64}\right)\)	\(e\left(\frac{35}{64}\right)\)	\(e\left(\frac{9}{32}\right)\)
\(\chi_{3328}(2549,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{64}\right)\)	\(e\left(\frac{21}{64}\right)\)	\(e\left(\frac{9}{32}\right)\)	\(e\left(\frac{31}{32}\right)\)	\(e\left(\frac{57}{64}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{35}{64}\right)\)	\(e\left(\frac{49}{64}\right)\)	\(e\left(\frac{19}{32}\right)\)
\(\chi_{3328}(2653,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{33}{64}\right)\)	\(e\left(\frac{43}{64}\right)\)	\(e\left(\frac{23}{32}\right)\)	\(e\left(\frac{1}{32}\right)\)	\(e\left(\frac{7}{64}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{29}{64}\right)\)	\(e\left(\frac{15}{64}\right)\)	\(e\left(\frac{13}{32}\right)\)
\(\chi_{3328}(2757,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{64}\right)\)	\(e\left(\frac{17}{64}\right)\)	\(e\left(\frac{21}{32}\right)\)	\(e\left(\frac{19}{32}\right)\)	\(e\left(\frac{37}{64}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{7}{64}\right)\)	\(e\left(\frac{61}{64}\right)\)	\(e\left(\frac{23}{32}\right)\)
\(\chi_{3328}(2861,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{64}\right)\)	\(e\left(\frac{7}{64}\right)\)	\(e\left(\frac{3}{32}\right)\)	\(e\left(\frac{21}{32}\right)\)	\(e\left(\frac{19}{64}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{33}{64}\right)\)	\(e\left(\frac{59}{64}\right)\)	\(e\left(\frac{17}{32}\right)\)
\(\chi_{3328}(2965,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{64}\right)\)	\(e\left(\frac{13}{64}\right)\)	\(e\left(\frac{1}{32}\right)\)	\(e\left(\frac{7}{32}\right)\)	\(e\left(\frac{17}{64}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{43}{64}\right)\)	\(e\left(\frac{9}{64}\right)\)	\(e\left(\frac{27}{32}\right)\)
\(\chi_{3328}(3069,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{64}\right)\)	\(e\left(\frac{35}{64}\right)\)	\(e\left(\frac{15}{32}\right)\)	\(e\left(\frac{9}{32}\right)\)	\(e\left(\frac{31}{64}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{37}{64}\right)\)	\(e\left(\frac{39}{64}\right)\)	\(e\left(\frac{21}{32}\right)\)
\(\chi_{3328}(3173,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{64}\right)\)	\(e\left(\frac{9}{64}\right)\)	\(e\left(\frac{13}{32}\right)\)	\(e\left(\frac{27}{32}\right)\)	\(e\left(\frac{61}{64}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{15}{64}\right)\)	\(e\left(\frac{21}{64}\right)\)	\(e\left(\frac{31}{32}\right)\)

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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	3328.df
Modulus	$3328$
Conductor	$256$
Order	$64$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(3328\)
Conductor:	\(256\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(64\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 256.m	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)