LMFDB - Dirichlet character orbit 9984.gi

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(9984, base_ring=CyclotomicField(64)) M = H._module chi = DirichletCharacter(H, M([0,27,0,0])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(157,9984)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$9984$
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	$-1$	$1$	$5$	$7$	$11$	$17$	$19$	$23$	$25$	$29$	$31$	$35$
$\chi_{9984}(157,\cdot)$	$1$	$1$	$e\left(\frac{27}{64}\right)$	$e\left(\frac{7}{32}\right)$	$e\left(\frac{55}{64}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{45}{64}\right)$	$e\left(\frac{29}{32}\right)$	$e\left(\frac{27}{32}\right)$	$e\left(\frac{57}{64}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{41}{64}\right)$
$\chi_{9984}(469,\cdot)$	$1$	$1$	$e\left(\frac{61}{64}\right)$	$e\left(\frac{17}{32}\right)$	$e\left(\frac{1}{64}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{59}{64}\right)$	$e\left(\frac{11}{32}\right)$	$e\left(\frac{29}{32}\right)$	$e\left(\frac{15}{64}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{31}{64}\right)$
$\chi_{9984}(781,\cdot)$	$1$	$1$	$e\left(\frac{47}{64}\right)$	$e\left(\frac{11}{32}\right)$	$e\left(\frac{27}{64}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{57}{64}\right)$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{15}{32}\right)$	$e\left(\frac{21}{64}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{64}\right)$
$\chi_{9984}(1093,\cdot)$	$1$	$1$	$e\left(\frac{49}{64}\right)$	$e\left(\frac{21}{32}\right)$	$e\left(\frac{5}{64}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{39}{64}\right)$	$e\left(\frac{23}{32}\right)$	$e\left(\frac{17}{32}\right)$	$e\left(\frac{11}{64}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{27}{64}\right)$
$\chi_{9984}(1405,\cdot)$	$1$	$1$	$e\left(\frac{3}{64}\right)$	$e\left(\frac{15}{32}\right)$	$e\left(\frac{63}{64}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{5}{64}\right)$	$e\left(\frac{21}{32}\right)$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{49}{64}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{33}{64}\right)$
$\chi_{9984}(1717,\cdot)$	$1$	$1$	$e\left(\frac{37}{64}\right)$	$e\left(\frac{25}{32}\right)$	$e\left(\frac{9}{64}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{19}{64}\right)$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{5}{32}\right)$	$e\left(\frac{7}{64}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{23}{64}\right)$
$\chi_{9984}(2029,\cdot)$	$1$	$1$	$e\left(\frac{23}{64}\right)$	$e\left(\frac{19}{32}\right)$	$e\left(\frac{35}{64}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{17}{64}\right)$	$e\left(\frac{1}{32}\right)$	$e\left(\frac{23}{32}\right)$	$e\left(\frac{13}{64}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{61}{64}\right)$
$\chi_{9984}(2341,\cdot)$	$1$	$1$	$e\left(\frac{25}{64}\right)$	$e\left(\frac{29}{32}\right)$	$e\left(\frac{13}{64}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{63}{64}\right)$	$e\left(\frac{15}{32}\right)$	$e\left(\frac{25}{32}\right)$	$e\left(\frac{3}{64}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{19}{64}\right)$
$\chi_{9984}(2653,\cdot)$	$1$	$1$	$e\left(\frac{43}{64}\right)$	$e\left(\frac{23}{32}\right)$	$e\left(\frac{7}{64}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{29}{64}\right)$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{11}{32}\right)$	$e\left(\frac{41}{64}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{25}{64}\right)$
$\chi_{9984}(2965,\cdot)$	$1$	$1$	$e\left(\frac{13}{64}\right)$	$e\left(\frac{1}{32}\right)$	$e\left(\frac{17}{64}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{43}{64}\right)$	$e\left(\frac{27}{32}\right)$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{63}{64}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{15}{64}\right)$
$\chi_{9984}(3277,\cdot)$	$1$	$1$	$e\left(\frac{63}{64}\right)$	$e\left(\frac{27}{32}\right)$	$e\left(\frac{43}{64}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{41}{64}\right)$	$e\left(\frac{25}{32}\right)$	$e\left(\frac{31}{32}\right)$	$e\left(\frac{5}{64}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{53}{64}\right)$
$\chi_{9984}(3589,\cdot)$	$1$	$1$	$e\left(\frac{1}{64}\right)$	$e\left(\frac{5}{32}\right)$	$e\left(\frac{21}{64}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{23}{64}\right)$	$e\left(\frac{7}{32}\right)$	$e\left(\frac{1}{32}\right)$	$e\left(\frac{59}{64}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{11}{64}\right)$
$\chi_{9984}(3901,\cdot)$	$1$	$1$	$e\left(\frac{19}{64}\right)$	$e\left(\frac{31}{32}\right)$	$e\left(\frac{15}{64}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{53}{64}\right)$	$e\left(\frac{5}{32}\right)$	$e\left(\frac{19}{32}\right)$	$e\left(\frac{33}{64}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{17}{64}\right)$
$\chi_{9984}(4213,\cdot)$	$1$	$1$	$e\left(\frac{53}{64}\right)$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{25}{64}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{3}{64}\right)$	$e\left(\frac{19}{32}\right)$	$e\left(\frac{21}{32}\right)$	$e\left(\frac{55}{64}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{7}{64}\right)$
$\chi_{9984}(4525,\cdot)$	$1$	$1$	$e\left(\frac{39}{64}\right)$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{51}{64}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{1}{64}\right)$	$e\left(\frac{17}{32}\right)$	$e\left(\frac{7}{32}\right)$	$e\left(\frac{61}{64}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{45}{64}\right)$
$\chi_{9984}(4837,\cdot)$	$1$	$1$	$e\left(\frac{41}{64}\right)$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{29}{64}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{47}{64}\right)$	$e\left(\frac{31}{32}\right)$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{51}{64}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{3}{64}\right)$
$\chi_{9984}(5149,\cdot)$	$1$	$1$	$e\left(\frac{59}{64}\right)$	$e\left(\frac{7}{32}\right)$	$e\left(\frac{23}{64}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{13}{64}\right)$	$e\left(\frac{29}{32}\right)$	$e\left(\frac{27}{32}\right)$	$e\left(\frac{25}{64}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{9}{64}\right)$
$\chi_{9984}(5461,\cdot)$	$1$	$1$	$e\left(\frac{29}{64}\right)$	$e\left(\frac{17}{32}\right)$	$e\left(\frac{33}{64}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{27}{64}\right)$	$e\left(\frac{11}{32}\right)$	$e\left(\frac{29}{32}\right)$	$e\left(\frac{47}{64}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{63}{64}\right)$
$\chi_{9984}(5773,\cdot)$	$1$	$1$	$e\left(\frac{15}{64}\right)$	$e\left(\frac{11}{32}\right)$	$e\left(\frac{59}{64}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{25}{64}\right)$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{15}{32}\right)$	$e\left(\frac{53}{64}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{37}{64}\right)$
$\chi_{9984}(6085,\cdot)$	$1$	$1$	$e\left(\frac{17}{64}\right)$	$e\left(\frac{21}{32}\right)$	$e\left(\frac{37}{64}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{7}{64}\right)$	$e\left(\frac{23}{32}\right)$	$e\left(\frac{17}{32}\right)$	$e\left(\frac{43}{64}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{59}{64}\right)$
$\chi_{9984}(6397,\cdot)$	$1$	$1$	$e\left(\frac{35}{64}\right)$	$e\left(\frac{15}{32}\right)$	$e\left(\frac{31}{64}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{37}{64}\right)$	$e\left(\frac{21}{32}\right)$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{17}{64}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{64}\right)$
$\chi_{9984}(6709,\cdot)$	$1$	$1$	$e\left(\frac{5}{64}\right)$	$e\left(\frac{25}{32}\right)$	$e\left(\frac{41}{64}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{51}{64}\right)$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{5}{32}\right)$	$e\left(\frac{39}{64}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{55}{64}\right)$
$\chi_{9984}(7021,\cdot)$	$1$	$1$	$e\left(\frac{55}{64}\right)$	$e\left(\frac{19}{32}\right)$	$e\left(\frac{3}{64}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{49}{64}\right)$	$e\left(\frac{1}{32}\right)$	$e\left(\frac{23}{32}\right)$	$e\left(\frac{45}{64}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{29}{64}\right)$
$\chi_{9984}(7333,\cdot)$	$1$	$1$	$e\left(\frac{57}{64}\right)$	$e\left(\frac{29}{32}\right)$	$e\left(\frac{45}{64}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{31}{64}\right)$	$e\left(\frac{15}{32}\right)$	$e\left(\frac{25}{32}\right)$	$e\left(\frac{35}{64}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{51}{64}\right)$
$\chi_{9984}(7645,\cdot)$	$1$	$1$	$e\left(\frac{11}{64}\right)$	$e\left(\frac{23}{32}\right)$	$e\left(\frac{39}{64}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{61}{64}\right)$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{11}{32}\right)$	$e\left(\frac{9}{64}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{57}{64}\right)$
$\chi_{9984}(7957,\cdot)$	$1$	$1$	$e\left(\frac{45}{64}\right)$	$e\left(\frac{1}{32}\right)$	$e\left(\frac{49}{64}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{11}{64}\right)$	$e\left(\frac{27}{32}\right)$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{31}{64}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{47}{64}\right)$
$\chi_{9984}(8269,\cdot)$	$1$	$1$	$e\left(\frac{31}{64}\right)$	$e\left(\frac{27}{32}\right)$	$e\left(\frac{11}{64}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{9}{64}\right)$	$e\left(\frac{25}{32}\right)$	$e\left(\frac{31}{32}\right)$	$e\left(\frac{37}{64}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{21}{64}\right)$
$\chi_{9984}(8581,\cdot)$	$1$	$1$	$e\left(\frac{33}{64}\right)$	$e\left(\frac{5}{32}\right)$	$e\left(\frac{53}{64}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{55}{64}\right)$	$e\left(\frac{7}{32}\right)$	$e\left(\frac{1}{32}\right)$	$e\left(\frac{27}{64}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{43}{64}\right)$
$\chi_{9984}(8893,\cdot)$	$1$	$1$	$e\left(\frac{51}{64}\right)$	$e\left(\frac{31}{32}\right)$	$e\left(\frac{47}{64}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{21}{64}\right)$	$e\left(\frac{5}{32}\right)$	$e\left(\frac{19}{32}\right)$	$e\left(\frac{1}{64}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{49}{64}\right)$
$\chi_{9984}(9205,\cdot)$	$1$	$1$	$e\left(\frac{21}{64}\right)$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{57}{64}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{35}{64}\right)$	$e\left(\frac{19}{32}\right)$	$e\left(\frac{21}{32}\right)$	$e\left(\frac{23}{64}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{39}{64}\right)$
$\chi_{9984}(9517,\cdot)$	$1$	$1$	$e\left(\frac{7}{64}\right)$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{19}{64}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{33}{64}\right)$	$e\left(\frac{17}{32}\right)$	$e\left(\frac{7}{32}\right)$	$e\left(\frac{29}{64}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{13}{64}\right)$

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	\(-1\)	\(1\)	\(5\)	\(7\)	\(11\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)	\(35\)
\(\chi_{9984}(157,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{27}{64}\right)\)	\(e\left(\frac{7}{32}\right)\)	\(e\left(\frac{55}{64}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{45}{64}\right)\)	\(e\left(\frac{29}{32}\right)\)	\(e\left(\frac{27}{32}\right)\)	\(e\left(\frac{57}{64}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{41}{64}\right)\)
\(\chi_{9984}(469,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{61}{64}\right)\)	\(e\left(\frac{17}{32}\right)\)	\(e\left(\frac{1}{64}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{59}{64}\right)\)	\(e\left(\frac{11}{32}\right)\)	\(e\left(\frac{29}{32}\right)\)	\(e\left(\frac{15}{64}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{31}{64}\right)\)
\(\chi_{9984}(781,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{64}\right)\)	\(e\left(\frac{11}{32}\right)\)	\(e\left(\frac{27}{64}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{57}{64}\right)\)	\(e\left(\frac{9}{32}\right)\)	\(e\left(\frac{15}{32}\right)\)	\(e\left(\frac{21}{64}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{5}{64}\right)\)
\(\chi_{9984}(1093,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{49}{64}\right)\)	\(e\left(\frac{21}{32}\right)\)	\(e\left(\frac{5}{64}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{39}{64}\right)\)	\(e\left(\frac{23}{32}\right)\)	\(e\left(\frac{17}{32}\right)\)	\(e\left(\frac{11}{64}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{27}{64}\right)\)
\(\chi_{9984}(1405,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{64}\right)\)	\(e\left(\frac{15}{32}\right)\)	\(e\left(\frac{63}{64}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{5}{64}\right)\)	\(e\left(\frac{21}{32}\right)\)	\(e\left(\frac{3}{32}\right)\)	\(e\left(\frac{49}{64}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{33}{64}\right)\)
\(\chi_{9984}(1717,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{64}\right)\)	\(e\left(\frac{25}{32}\right)\)	\(e\left(\frac{9}{64}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{19}{64}\right)\)	\(e\left(\frac{3}{32}\right)\)	\(e\left(\frac{5}{32}\right)\)	\(e\left(\frac{7}{64}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{23}{64}\right)\)
\(\chi_{9984}(2029,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{64}\right)\)	\(e\left(\frac{19}{32}\right)\)	\(e\left(\frac{35}{64}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{17}{64}\right)\)	\(e\left(\frac{1}{32}\right)\)	\(e\left(\frac{23}{32}\right)\)	\(e\left(\frac{13}{64}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{61}{64}\right)\)
\(\chi_{9984}(2341,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{25}{64}\right)\)	\(e\left(\frac{29}{32}\right)\)	\(e\left(\frac{13}{64}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{63}{64}\right)\)	\(e\left(\frac{15}{32}\right)\)	\(e\left(\frac{25}{32}\right)\)	\(e\left(\frac{3}{64}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{19}{64}\right)\)
\(\chi_{9984}(2653,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{64}\right)\)	\(e\left(\frac{23}{32}\right)\)	\(e\left(\frac{7}{64}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{29}{64}\right)\)	\(e\left(\frac{13}{32}\right)\)	\(e\left(\frac{11}{32}\right)\)	\(e\left(\frac{41}{64}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{25}{64}\right)\)
\(\chi_{9984}(2965,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{64}\right)\)	\(e\left(\frac{1}{32}\right)\)	\(e\left(\frac{17}{64}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{43}{64}\right)\)	\(e\left(\frac{27}{32}\right)\)	\(e\left(\frac{13}{32}\right)\)	\(e\left(\frac{63}{64}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{15}{64}\right)\)
\(\chi_{9984}(3277,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{63}{64}\right)\)	\(e\left(\frac{27}{32}\right)\)	\(e\left(\frac{43}{64}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{41}{64}\right)\)	\(e\left(\frac{25}{32}\right)\)	\(e\left(\frac{31}{32}\right)\)	\(e\left(\frac{5}{64}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{53}{64}\right)\)
\(\chi_{9984}(3589,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{64}\right)\)	\(e\left(\frac{5}{32}\right)\)	\(e\left(\frac{21}{64}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{23}{64}\right)\)	\(e\left(\frac{7}{32}\right)\)	\(e\left(\frac{1}{32}\right)\)	\(e\left(\frac{59}{64}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{11}{64}\right)\)
\(\chi_{9984}(3901,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{64}\right)\)	\(e\left(\frac{31}{32}\right)\)	\(e\left(\frac{15}{64}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{53}{64}\right)\)	\(e\left(\frac{5}{32}\right)\)	\(e\left(\frac{19}{32}\right)\)	\(e\left(\frac{33}{64}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{17}{64}\right)\)
\(\chi_{9984}(4213,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{64}\right)\)	\(e\left(\frac{9}{32}\right)\)	\(e\left(\frac{25}{64}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{3}{64}\right)\)	\(e\left(\frac{19}{32}\right)\)	\(e\left(\frac{21}{32}\right)\)	\(e\left(\frac{55}{64}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{7}{64}\right)\)
\(\chi_{9984}(4525,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{39}{64}\right)\)	\(e\left(\frac{3}{32}\right)\)	\(e\left(\frac{51}{64}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{1}{64}\right)\)	\(e\left(\frac{17}{32}\right)\)	\(e\left(\frac{7}{32}\right)\)	\(e\left(\frac{61}{64}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{45}{64}\right)\)
\(\chi_{9984}(4837,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{64}\right)\)	\(e\left(\frac{13}{32}\right)\)	\(e\left(\frac{29}{64}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{47}{64}\right)\)	\(e\left(\frac{31}{32}\right)\)	\(e\left(\frac{9}{32}\right)\)	\(e\left(\frac{51}{64}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{3}{64}\right)\)
\(\chi_{9984}(5149,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{64}\right)\)	\(e\left(\frac{7}{32}\right)\)	\(e\left(\frac{23}{64}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{13}{64}\right)\)	\(e\left(\frac{29}{32}\right)\)	\(e\left(\frac{27}{32}\right)\)	\(e\left(\frac{25}{64}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{9}{64}\right)\)
\(\chi_{9984}(5461,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{64}\right)\)	\(e\left(\frac{17}{32}\right)\)	\(e\left(\frac{33}{64}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{27}{64}\right)\)	\(e\left(\frac{11}{32}\right)\)	\(e\left(\frac{29}{32}\right)\)	\(e\left(\frac{47}{64}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{63}{64}\right)\)
\(\chi_{9984}(5773,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{15}{64}\right)\)	\(e\left(\frac{11}{32}\right)\)	\(e\left(\frac{59}{64}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{25}{64}\right)\)	\(e\left(\frac{9}{32}\right)\)	\(e\left(\frac{15}{32}\right)\)	\(e\left(\frac{53}{64}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{37}{64}\right)\)
\(\chi_{9984}(6085,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{64}\right)\)	\(e\left(\frac{21}{32}\right)\)	\(e\left(\frac{37}{64}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{7}{64}\right)\)	\(e\left(\frac{23}{32}\right)\)	\(e\left(\frac{17}{32}\right)\)	\(e\left(\frac{43}{64}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{59}{64}\right)\)
\(\chi_{9984}(6397,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{35}{64}\right)\)	\(e\left(\frac{15}{32}\right)\)	\(e\left(\frac{31}{64}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{37}{64}\right)\)	\(e\left(\frac{21}{32}\right)\)	\(e\left(\frac{3}{32}\right)\)	\(e\left(\frac{17}{64}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{1}{64}\right)\)
\(\chi_{9984}(6709,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{64}\right)\)	\(e\left(\frac{25}{32}\right)\)	\(e\left(\frac{41}{64}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{51}{64}\right)\)	\(e\left(\frac{3}{32}\right)\)	\(e\left(\frac{5}{32}\right)\)	\(e\left(\frac{39}{64}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{55}{64}\right)\)
\(\chi_{9984}(7021,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{55}{64}\right)\)	\(e\left(\frac{19}{32}\right)\)	\(e\left(\frac{3}{64}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{49}{64}\right)\)	\(e\left(\frac{1}{32}\right)\)	\(e\left(\frac{23}{32}\right)\)	\(e\left(\frac{45}{64}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{29}{64}\right)\)
\(\chi_{9984}(7333,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{57}{64}\right)\)	\(e\left(\frac{29}{32}\right)\)	\(e\left(\frac{45}{64}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{31}{64}\right)\)	\(e\left(\frac{15}{32}\right)\)	\(e\left(\frac{25}{32}\right)\)	\(e\left(\frac{35}{64}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{51}{64}\right)\)
\(\chi_{9984}(7645,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{64}\right)\)	\(e\left(\frac{23}{32}\right)\)	\(e\left(\frac{39}{64}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{61}{64}\right)\)	\(e\left(\frac{13}{32}\right)\)	\(e\left(\frac{11}{32}\right)\)	\(e\left(\frac{9}{64}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{57}{64}\right)\)
\(\chi_{9984}(7957,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{45}{64}\right)\)	\(e\left(\frac{1}{32}\right)\)	\(e\left(\frac{49}{64}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{11}{64}\right)\)	\(e\left(\frac{27}{32}\right)\)	\(e\left(\frac{13}{32}\right)\)	\(e\left(\frac{31}{64}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{47}{64}\right)\)
\(\chi_{9984}(8269,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{64}\right)\)	\(e\left(\frac{27}{32}\right)\)	\(e\left(\frac{11}{64}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{9}{64}\right)\)	\(e\left(\frac{25}{32}\right)\)	\(e\left(\frac{31}{32}\right)\)	\(e\left(\frac{37}{64}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{21}{64}\right)\)
\(\chi_{9984}(8581,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{33}{64}\right)\)	\(e\left(\frac{5}{32}\right)\)	\(e\left(\frac{53}{64}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{55}{64}\right)\)	\(e\left(\frac{7}{32}\right)\)	\(e\left(\frac{1}{32}\right)\)	\(e\left(\frac{27}{64}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{43}{64}\right)\)
\(\chi_{9984}(8893,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{51}{64}\right)\)	\(e\left(\frac{31}{32}\right)\)	\(e\left(\frac{47}{64}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{21}{64}\right)\)	\(e\left(\frac{5}{32}\right)\)	\(e\left(\frac{19}{32}\right)\)	\(e\left(\frac{1}{64}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{49}{64}\right)\)
\(\chi_{9984}(9205,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{21}{64}\right)\)	\(e\left(\frac{9}{32}\right)\)	\(e\left(\frac{57}{64}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{35}{64}\right)\)	\(e\left(\frac{19}{32}\right)\)	\(e\left(\frac{21}{32}\right)\)	\(e\left(\frac{23}{64}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{39}{64}\right)\)
\(\chi_{9984}(9517,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{64}\right)\)	\(e\left(\frac{3}{32}\right)\)	\(e\left(\frac{19}{64}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{33}{64}\right)\)	\(e\left(\frac{17}{32}\right)\)	\(e\left(\frac{7}{32}\right)\)	\(e\left(\frac{29}{64}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{13}{64}\right)\)

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	9984.gi
Modulus	$9984$
Conductor	$256$
Order	$64$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(9984\)
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)