LMFDB - Dirichlet character orbit 3328.dd

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(3328, base_ring=CyclotomicField(64)) M = H._module chi = DirichletCharacter(H, M([0,1,48])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(5,3328)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$3328$
Conductor:	$3328$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$64$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	yes	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	odd	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	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$15$	$17$	$19$	$21$	$23$
$\chi_{3328}(5,\cdot)$	$-1$	$1$	$e\left(\frac{35}{64}\right)$	$e\left(\frac{49}{64}\right)$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{37}{64}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{7}{64}\right)$	$e\left(\frac{61}{64}\right)$	$e\left(\frac{23}{32}\right)$
$\chi_{3328}(125,\cdot)$	$-1$	$1$	$e\left(\frac{41}{64}\right)$	$e\left(\frac{19}{64}\right)$	$e\left(\frac{7}{32}\right)$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{47}{64}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{21}{64}\right)$	$e\left(\frac{55}{64}\right)$	$e\left(\frac{5}{32}\right)$
$\chi_{3328}(213,\cdot)$	$-1$	$1$	$e\left(\frac{23}{64}\right)$	$e\left(\frac{45}{64}\right)$	$e\left(\frac{25}{32}\right)$	$e\left(\frac{23}{32}\right)$	$e\left(\frac{17}{64}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{43}{64}\right)$	$e\left(\frac{9}{64}\right)$	$e\left(\frac{27}{32}\right)$
$\chi_{3328}(333,\cdot)$	$-1$	$1$	$e\left(\frac{61}{64}\right)$	$e\left(\frac{47}{64}\right)$	$e\left(\frac{19}{32}\right)$	$e\left(\frac{29}{32}\right)$	$e\left(\frac{59}{64}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{25}{64}\right)$	$e\left(\frac{35}{64}\right)$	$e\left(\frac{9}{32}\right)$
$\chi_{3328}(421,\cdot)$	$-1$	$1$	$e\left(\frac{11}{64}\right)$	$e\left(\frac{41}{64}\right)$	$e\left(\frac{5}{32}\right)$	$e\left(\frac{11}{32}\right)$	$e\left(\frac{61}{64}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{15}{64}\right)$	$e\left(\frac{21}{64}\right)$	$e\left(\frac{31}{32}\right)$
$\chi_{3328}(541,\cdot)$	$-1$	$1$	$e\left(\frac{17}{64}\right)$	$e\left(\frac{11}{64}\right)$	$e\left(\frac{31}{32}\right)$	$e\left(\frac{17}{32}\right)$	$e\left(\frac{7}{64}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{29}{64}\right)$	$e\left(\frac{15}{64}\right)$	$e\left(\frac{13}{32}\right)$
$\chi_{3328}(629,\cdot)$	$-1$	$1$	$e\left(\frac{63}{64}\right)$	$e\left(\frac{37}{64}\right)$	$e\left(\frac{17}{32}\right)$	$e\left(\frac{31}{32}\right)$	$e\left(\frac{41}{64}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{51}{64}\right)$	$e\left(\frac{33}{64}\right)$	$e\left(\frac{3}{32}\right)$
$\chi_{3328}(749,\cdot)$	$-1$	$1$	$e\left(\frac{37}{64}\right)$	$e\left(\frac{39}{64}\right)$	$e\left(\frac{11}{32}\right)$	$e\left(\frac{5}{32}\right)$	$e\left(\frac{19}{64}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{33}{64}\right)$	$e\left(\frac{59}{64}\right)$	$e\left(\frac{17}{32}\right)$
$\chi_{3328}(837,\cdot)$	$-1$	$1$	$e\left(\frac{51}{64}\right)$	$e\left(\frac{33}{64}\right)$	$e\left(\frac{29}{32}\right)$	$e\left(\frac{19}{32}\right)$	$e\left(\frac{21}{64}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{23}{64}\right)$	$e\left(\frac{45}{64}\right)$	$e\left(\frac{7}{32}\right)$
$\chi_{3328}(957,\cdot)$	$-1$	$1$	$e\left(\frac{57}{64}\right)$	$e\left(\frac{3}{64}\right)$	$e\left(\frac{23}{32}\right)$	$e\left(\frac{25}{32}\right)$	$e\left(\frac{31}{64}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{37}{64}\right)$	$e\left(\frac{39}{64}\right)$	$e\left(\frac{21}{32}\right)$
$\chi_{3328}(1045,\cdot)$	$-1$	$1$	$e\left(\frac{39}{64}\right)$	$e\left(\frac{29}{64}\right)$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{7}{32}\right)$	$e\left(\frac{1}{64}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{59}{64}\right)$	$e\left(\frac{57}{64}\right)$	$e\left(\frac{11}{32}\right)$
$\chi_{3328}(1165,\cdot)$	$-1$	$1$	$e\left(\frac{13}{64}\right)$	$e\left(\frac{31}{64}\right)$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{43}{64}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{41}{64}\right)$	$e\left(\frac{19}{64}\right)$	$e\left(\frac{25}{32}\right)$
$\chi_{3328}(1253,\cdot)$	$-1$	$1$	$e\left(\frac{27}{64}\right)$	$e\left(\frac{25}{64}\right)$	$e\left(\frac{21}{32}\right)$	$e\left(\frac{27}{32}\right)$	$e\left(\frac{45}{64}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{31}{64}\right)$	$e\left(\frac{5}{64}\right)$	$e\left(\frac{15}{32}\right)$
$\chi_{3328}(1373,\cdot)$	$-1$	$1$	$e\left(\frac{33}{64}\right)$	$e\left(\frac{59}{64}\right)$	$e\left(\frac{15}{32}\right)$	$e\left(\frac{1}{32}\right)$	$e\left(\frac{55}{64}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{45}{64}\right)$	$e\left(\frac{63}{64}\right)$	$e\left(\frac{29}{32}\right)$
$\chi_{3328}(1461,\cdot)$	$-1$	$1$	$e\left(\frac{15}{64}\right)$	$e\left(\frac{21}{64}\right)$	$e\left(\frac{1}{32}\right)$	$e\left(\frac{15}{32}\right)$	$e\left(\frac{25}{64}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{3}{64}\right)$	$e\left(\frac{17}{64}\right)$	$e\left(\frac{19}{32}\right)$
$\chi_{3328}(1581,\cdot)$	$-1$	$1$	$e\left(\frac{53}{64}\right)$	$e\left(\frac{23}{64}\right)$	$e\left(\frac{27}{32}\right)$	$e\left(\frac{21}{32}\right)$	$e\left(\frac{3}{64}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{49}{64}\right)$	$e\left(\frac{43}{64}\right)$	$e\left(\frac{1}{32}\right)$
$\chi_{3328}(1669,\cdot)$	$-1$	$1$	$e\left(\frac{3}{64}\right)$	$e\left(\frac{17}{64}\right)$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{5}{64}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{39}{64}\right)$	$e\left(\frac{29}{64}\right)$	$e\left(\frac{23}{32}\right)$
$\chi_{3328}(1789,\cdot)$	$-1$	$1$	$e\left(\frac{9}{64}\right)$	$e\left(\frac{51}{64}\right)$	$e\left(\frac{7}{32}\right)$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{15}{64}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{53}{64}\right)$	$e\left(\frac{23}{64}\right)$	$e\left(\frac{5}{32}\right)$
$\chi_{3328}(1877,\cdot)$	$-1$	$1$	$e\left(\frac{55}{64}\right)$	$e\left(\frac{13}{64}\right)$	$e\left(\frac{25}{32}\right)$	$e\left(\frac{23}{32}\right)$	$e\left(\frac{49}{64}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{11}{64}\right)$	$e\left(\frac{41}{64}\right)$	$e\left(\frac{27}{32}\right)$
$\chi_{3328}(1997,\cdot)$	$-1$	$1$	$e\left(\frac{29}{64}\right)$	$e\left(\frac{15}{64}\right)$	$e\left(\frac{19}{32}\right)$	$e\left(\frac{29}{32}\right)$	$e\left(\frac{27}{64}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{57}{64}\right)$	$e\left(\frac{3}{64}\right)$	$e\left(\frac{9}{32}\right)$
$\chi_{3328}(2085,\cdot)$	$-1$	$1$	$e\left(\frac{43}{64}\right)$	$e\left(\frac{9}{64}\right)$	$e\left(\frac{5}{32}\right)$	$e\left(\frac{11}{32}\right)$	$e\left(\frac{29}{64}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{47}{64}\right)$	$e\left(\frac{53}{64}\right)$	$e\left(\frac{31}{32}\right)$
$\chi_{3328}(2205,\cdot)$	$-1$	$1$	$e\left(\frac{49}{64}\right)$	$e\left(\frac{43}{64}\right)$	$e\left(\frac{31}{32}\right)$	$e\left(\frac{17}{32}\right)$	$e\left(\frac{39}{64}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{61}{64}\right)$	$e\left(\frac{47}{64}\right)$	$e\left(\frac{13}{32}\right)$
$\chi_{3328}(2293,\cdot)$	$-1$	$1$	$e\left(\frac{31}{64}\right)$	$e\left(\frac{5}{64}\right)$	$e\left(\frac{17}{32}\right)$	$e\left(\frac{31}{32}\right)$	$e\left(\frac{9}{64}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{19}{64}\right)$	$e\left(\frac{1}{64}\right)$	$e\left(\frac{3}{32}\right)$
$\chi_{3328}(2413,\cdot)$	$-1$	$1$	$e\left(\frac{5}{64}\right)$	$e\left(\frac{7}{64}\right)$	$e\left(\frac{11}{32}\right)$	$e\left(\frac{5}{32}\right)$	$e\left(\frac{51}{64}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{1}{64}\right)$	$e\left(\frac{27}{64}\right)$	$e\left(\frac{17}{32}\right)$
$\chi_{3328}(2501,\cdot)$	$-1$	$1$	$e\left(\frac{19}{64}\right)$	$e\left(\frac{1}{64}\right)$	$e\left(\frac{29}{32}\right)$	$e\left(\frac{19}{32}\right)$	$e\left(\frac{53}{64}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{55}{64}\right)$	$e\left(\frac{13}{64}\right)$	$e\left(\frac{7}{32}\right)$
$\chi_{3328}(2621,\cdot)$	$-1$	$1$	$e\left(\frac{25}{64}\right)$	$e\left(\frac{35}{64}\right)$	$e\left(\frac{23}{32}\right)$	$e\left(\frac{25}{32}\right)$	$e\left(\frac{63}{64}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{5}{64}\right)$	$e\left(\frac{7}{64}\right)$	$e\left(\frac{21}{32}\right)$
$\chi_{3328}(2709,\cdot)$	$-1$	$1$	$e\left(\frac{7}{64}\right)$	$e\left(\frac{61}{64}\right)$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{7}{32}\right)$	$e\left(\frac{33}{64}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{27}{64}\right)$	$e\left(\frac{25}{64}\right)$	$e\left(\frac{11}{32}\right)$
$\chi_{3328}(2829,\cdot)$	$-1$	$1$	$e\left(\frac{45}{64}\right)$	$e\left(\frac{63}{64}\right)$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{11}{64}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{9}{64}\right)$	$e\left(\frac{51}{64}\right)$	$e\left(\frac{25}{32}\right)$
$\chi_{3328}(2917,\cdot)$	$-1$	$1$	$e\left(\frac{59}{64}\right)$	$e\left(\frac{57}{64}\right)$	$e\left(\frac{21}{32}\right)$	$e\left(\frac{27}{32}\right)$	$e\left(\frac{13}{64}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{63}{64}\right)$	$e\left(\frac{37}{64}\right)$	$e\left(\frac{15}{32}\right)$
$\chi_{3328}(3037,\cdot)$	$-1$	$1$	$e\left(\frac{1}{64}\right)$	$e\left(\frac{27}{64}\right)$	$e\left(\frac{15}{32}\right)$	$e\left(\frac{1}{32}\right)$	$e\left(\frac{23}{64}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{13}{64}\right)$	$e\left(\frac{31}{64}\right)$	$e\left(\frac{29}{32}\right)$
$\chi_{3328}(3125,\cdot)$	$-1$	$1$	$e\left(\frac{47}{64}\right)$	$e\left(\frac{53}{64}\right)$	$e\left(\frac{1}{32}\right)$	$e\left(\frac{15}{32}\right)$	$e\left(\frac{57}{64}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{35}{64}\right)$	$e\left(\frac{49}{64}\right)$	$e\left(\frac{19}{32}\right)$

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	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(15\)	\(17\)	\(19\)	\(21\)	\(23\)
\(\chi_{3328}(5,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{35}{64}\right)\)	\(e\left(\frac{49}{64}\right)\)	\(e\left(\frac{13}{32}\right)\)	\(e\left(\frac{3}{32}\right)\)	\(e\left(\frac{37}{64}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{7}{64}\right)\)	\(e\left(\frac{61}{64}\right)\)	\(e\left(\frac{23}{32}\right)\)
\(\chi_{3328}(125,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{41}{64}\right)\)	\(e\left(\frac{19}{64}\right)\)	\(e\left(\frac{7}{32}\right)\)	\(e\left(\frac{9}{32}\right)\)	\(e\left(\frac{47}{64}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{21}{64}\right)\)	\(e\left(\frac{55}{64}\right)\)	\(e\left(\frac{5}{32}\right)\)
\(\chi_{3328}(213,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{23}{64}\right)\)	\(e\left(\frac{45}{64}\right)\)	\(e\left(\frac{25}{32}\right)\)	\(e\left(\frac{23}{32}\right)\)	\(e\left(\frac{17}{64}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{43}{64}\right)\)	\(e\left(\frac{9}{64}\right)\)	\(e\left(\frac{27}{32}\right)\)
\(\chi_{3328}(333,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{61}{64}\right)\)	\(e\left(\frac{47}{64}\right)\)	\(e\left(\frac{19}{32}\right)\)	\(e\left(\frac{29}{32}\right)\)	\(e\left(\frac{59}{64}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{25}{64}\right)\)	\(e\left(\frac{35}{64}\right)\)	\(e\left(\frac{9}{32}\right)\)
\(\chi_{3328}(421,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{11}{64}\right)\)	\(e\left(\frac{41}{64}\right)\)	\(e\left(\frac{5}{32}\right)\)	\(e\left(\frac{11}{32}\right)\)	\(e\left(\frac{61}{64}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{15}{64}\right)\)	\(e\left(\frac{21}{64}\right)\)	\(e\left(\frac{31}{32}\right)\)
\(\chi_{3328}(541,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{17}{64}\right)\)	\(e\left(\frac{11}{64}\right)\)	\(e\left(\frac{31}{32}\right)\)	\(e\left(\frac{17}{32}\right)\)	\(e\left(\frac{7}{64}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{29}{64}\right)\)	\(e\left(\frac{15}{64}\right)\)	\(e\left(\frac{13}{32}\right)\)
\(\chi_{3328}(629,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{63}{64}\right)\)	\(e\left(\frac{37}{64}\right)\)	\(e\left(\frac{17}{32}\right)\)	\(e\left(\frac{31}{32}\right)\)	\(e\left(\frac{41}{64}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{51}{64}\right)\)	\(e\left(\frac{33}{64}\right)\)	\(e\left(\frac{3}{32}\right)\)
\(\chi_{3328}(749,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{37}{64}\right)\)	\(e\left(\frac{39}{64}\right)\)	\(e\left(\frac{11}{32}\right)\)	\(e\left(\frac{5}{32}\right)\)	\(e\left(\frac{19}{64}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{33}{64}\right)\)	\(e\left(\frac{59}{64}\right)\)	\(e\left(\frac{17}{32}\right)\)
\(\chi_{3328}(837,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{51}{64}\right)\)	\(e\left(\frac{33}{64}\right)\)	\(e\left(\frac{29}{32}\right)\)	\(e\left(\frac{19}{32}\right)\)	\(e\left(\frac{21}{64}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{23}{64}\right)\)	\(e\left(\frac{45}{64}\right)\)	\(e\left(\frac{7}{32}\right)\)
\(\chi_{3328}(957,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{57}{64}\right)\)	\(e\left(\frac{3}{64}\right)\)	\(e\left(\frac{23}{32}\right)\)	\(e\left(\frac{25}{32}\right)\)	\(e\left(\frac{31}{64}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{37}{64}\right)\)	\(e\left(\frac{39}{64}\right)\)	\(e\left(\frac{21}{32}\right)\)
\(\chi_{3328}(1045,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{39}{64}\right)\)	\(e\left(\frac{29}{64}\right)\)	\(e\left(\frac{9}{32}\right)\)	\(e\left(\frac{7}{32}\right)\)	\(e\left(\frac{1}{64}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{59}{64}\right)\)	\(e\left(\frac{57}{64}\right)\)	\(e\left(\frac{11}{32}\right)\)
\(\chi_{3328}(1165,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{13}{64}\right)\)	\(e\left(\frac{31}{64}\right)\)	\(e\left(\frac{3}{32}\right)\)	\(e\left(\frac{13}{32}\right)\)	\(e\left(\frac{43}{64}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{41}{64}\right)\)	\(e\left(\frac{19}{64}\right)\)	\(e\left(\frac{25}{32}\right)\)
\(\chi_{3328}(1253,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{27}{64}\right)\)	\(e\left(\frac{25}{64}\right)\)	\(e\left(\frac{21}{32}\right)\)	\(e\left(\frac{27}{32}\right)\)	\(e\left(\frac{45}{64}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{31}{64}\right)\)	\(e\left(\frac{5}{64}\right)\)	\(e\left(\frac{15}{32}\right)\)
\(\chi_{3328}(1373,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{33}{64}\right)\)	\(e\left(\frac{59}{64}\right)\)	\(e\left(\frac{15}{32}\right)\)	\(e\left(\frac{1}{32}\right)\)	\(e\left(\frac{55}{64}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{45}{64}\right)\)	\(e\left(\frac{63}{64}\right)\)	\(e\left(\frac{29}{32}\right)\)
\(\chi_{3328}(1461,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{15}{64}\right)\)	\(e\left(\frac{21}{64}\right)\)	\(e\left(\frac{1}{32}\right)\)	\(e\left(\frac{15}{32}\right)\)	\(e\left(\frac{25}{64}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{3}{64}\right)\)	\(e\left(\frac{17}{64}\right)\)	\(e\left(\frac{19}{32}\right)\)
\(\chi_{3328}(1581,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{53}{64}\right)\)	\(e\left(\frac{23}{64}\right)\)	\(e\left(\frac{27}{32}\right)\)	\(e\left(\frac{21}{32}\right)\)	\(e\left(\frac{3}{64}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{49}{64}\right)\)	\(e\left(\frac{43}{64}\right)\)	\(e\left(\frac{1}{32}\right)\)
\(\chi_{3328}(1669,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{3}{64}\right)\)	\(e\left(\frac{17}{64}\right)\)	\(e\left(\frac{13}{32}\right)\)	\(e\left(\frac{3}{32}\right)\)	\(e\left(\frac{5}{64}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{39}{64}\right)\)	\(e\left(\frac{29}{64}\right)\)	\(e\left(\frac{23}{32}\right)\)
\(\chi_{3328}(1789,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{9}{64}\right)\)	\(e\left(\frac{51}{64}\right)\)	\(e\left(\frac{7}{32}\right)\)	\(e\left(\frac{9}{32}\right)\)	\(e\left(\frac{15}{64}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{53}{64}\right)\)	\(e\left(\frac{23}{64}\right)\)	\(e\left(\frac{5}{32}\right)\)
\(\chi_{3328}(1877,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{55}{64}\right)\)	\(e\left(\frac{13}{64}\right)\)	\(e\left(\frac{25}{32}\right)\)	\(e\left(\frac{23}{32}\right)\)	\(e\left(\frac{49}{64}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{11}{64}\right)\)	\(e\left(\frac{41}{64}\right)\)	\(e\left(\frac{27}{32}\right)\)
\(\chi_{3328}(1997,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{29}{64}\right)\)	\(e\left(\frac{15}{64}\right)\)	\(e\left(\frac{19}{32}\right)\)	\(e\left(\frac{29}{32}\right)\)	\(e\left(\frac{27}{64}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{57}{64}\right)\)	\(e\left(\frac{3}{64}\right)\)	\(e\left(\frac{9}{32}\right)\)
\(\chi_{3328}(2085,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{43}{64}\right)\)	\(e\left(\frac{9}{64}\right)\)	\(e\left(\frac{5}{32}\right)\)	\(e\left(\frac{11}{32}\right)\)	\(e\left(\frac{29}{64}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{47}{64}\right)\)	\(e\left(\frac{53}{64}\right)\)	\(e\left(\frac{31}{32}\right)\)
\(\chi_{3328}(2205,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{49}{64}\right)\)	\(e\left(\frac{43}{64}\right)\)	\(e\left(\frac{31}{32}\right)\)	\(e\left(\frac{17}{32}\right)\)	\(e\left(\frac{39}{64}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{61}{64}\right)\)	\(e\left(\frac{47}{64}\right)\)	\(e\left(\frac{13}{32}\right)\)
\(\chi_{3328}(2293,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{31}{64}\right)\)	\(e\left(\frac{5}{64}\right)\)	\(e\left(\frac{17}{32}\right)\)	\(e\left(\frac{31}{32}\right)\)	\(e\left(\frac{9}{64}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{19}{64}\right)\)	\(e\left(\frac{1}{64}\right)\)	\(e\left(\frac{3}{32}\right)\)
\(\chi_{3328}(2413,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{5}{64}\right)\)	\(e\left(\frac{7}{64}\right)\)	\(e\left(\frac{11}{32}\right)\)	\(e\left(\frac{5}{32}\right)\)	\(e\left(\frac{51}{64}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{1}{64}\right)\)	\(e\left(\frac{27}{64}\right)\)	\(e\left(\frac{17}{32}\right)\)
\(\chi_{3328}(2501,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{19}{64}\right)\)	\(e\left(\frac{1}{64}\right)\)	\(e\left(\frac{29}{32}\right)\)	\(e\left(\frac{19}{32}\right)\)	\(e\left(\frac{53}{64}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{55}{64}\right)\)	\(e\left(\frac{13}{64}\right)\)	\(e\left(\frac{7}{32}\right)\)
\(\chi_{3328}(2621,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{25}{64}\right)\)	\(e\left(\frac{35}{64}\right)\)	\(e\left(\frac{23}{32}\right)\)	\(e\left(\frac{25}{32}\right)\)	\(e\left(\frac{63}{64}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{5}{64}\right)\)	\(e\left(\frac{7}{64}\right)\)	\(e\left(\frac{21}{32}\right)\)
\(\chi_{3328}(2709,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{7}{64}\right)\)	\(e\left(\frac{61}{64}\right)\)	\(e\left(\frac{9}{32}\right)\)	\(e\left(\frac{7}{32}\right)\)	\(e\left(\frac{33}{64}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{27}{64}\right)\)	\(e\left(\frac{25}{64}\right)\)	\(e\left(\frac{11}{32}\right)\)
\(\chi_{3328}(2829,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{45}{64}\right)\)	\(e\left(\frac{63}{64}\right)\)	\(e\left(\frac{3}{32}\right)\)	\(e\left(\frac{13}{32}\right)\)	\(e\left(\frac{11}{64}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{9}{64}\right)\)	\(e\left(\frac{51}{64}\right)\)	\(e\left(\frac{25}{32}\right)\)
\(\chi_{3328}(2917,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{59}{64}\right)\)	\(e\left(\frac{57}{64}\right)\)	\(e\left(\frac{21}{32}\right)\)	\(e\left(\frac{27}{32}\right)\)	\(e\left(\frac{13}{64}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{63}{64}\right)\)	\(e\left(\frac{37}{64}\right)\)	\(e\left(\frac{15}{32}\right)\)
\(\chi_{3328}(3037,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{64}\right)\)	\(e\left(\frac{27}{64}\right)\)	\(e\left(\frac{15}{32}\right)\)	\(e\left(\frac{1}{32}\right)\)	\(e\left(\frac{23}{64}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{13}{64}\right)\)	\(e\left(\frac{31}{64}\right)\)	\(e\left(\frac{29}{32}\right)\)
\(\chi_{3328}(3125,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{47}{64}\right)\)	\(e\left(\frac{53}{64}\right)\)	\(e\left(\frac{1}{32}\right)\)	\(e\left(\frac{15}{32}\right)\)	\(e\left(\frac{57}{64}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{35}{64}\right)\)	\(e\left(\frac{49}{64}\right)\)	\(e\left(\frac{19}{32}\right)\)

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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.dd
Modulus	$3328$
Conductor	$3328$
Order	$64$
Real	no
Primitive	yes
Minimal	yes
Parity	odd

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