LMFDB - Dirichlet character orbit 8352.hb

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(8352, base_ring=CyclotomicField(56)) M = H._module chi = DirichletCharacter(H, M([28,35,28,48])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(107,8352)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$8352$
Conductor:	$2784$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$56$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 2784.eh	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:	$\Q(\zeta_{56})$
Fixed field:	Number field defined by a degree 56 polynomial

Characters in Galois orbit

Character	$-1$	$1$	$5$	$7$	$11$	$13$	$17$	$19$	$23$	$25$	$31$	$35$
$\chi_{8352}(107,\cdot)$	$1$	$1$	$e\left(\frac{55}{56}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{31}{56}\right)$	$e\left(\frac{45}{56}\right)$	$1$	$e\left(\frac{33}{56}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{1}{56}\right)$
$\chi_{8352}(683,\cdot)$	$1$	$1$	$e\left(\frac{15}{56}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{39}{56}\right)$	$e\left(\frac{53}{56}\right)$	$1$	$e\left(\frac{9}{56}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{41}{56}\right)$
$\chi_{8352}(1475,\cdot)$	$1$	$1$	$e\left(\frac{25}{56}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{9}{56}\right)$	$e\left(\frac{51}{56}\right)$	$1$	$e\left(\frac{15}{56}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{31}{56}\right)$
$\chi_{8352}(1619,\cdot)$	$1$	$1$	$e\left(\frac{37}{56}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{29}{56}\right)$	$e\left(\frac{15}{56}\right)$	$1$	$e\left(\frac{11}{56}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{19}{56}\right)$
$\chi_{8352}(1763,\cdot)$	$1$	$1$	$e\left(\frac{33}{56}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{41}{56}\right)$	$e\left(\frac{27}{56}\right)$	$1$	$e\left(\frac{31}{56}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{23}{56}\right)$
$\chi_{8352}(1979,\cdot)$	$1$	$1$	$e\left(\frac{3}{56}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{19}{56}\right)$	$e\left(\frac{33}{56}\right)$	$1$	$e\left(\frac{13}{56}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{53}{56}\right)$
$\chi_{8352}(2195,\cdot)$	$1$	$1$	$e\left(\frac{13}{56}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{45}{56}\right)$	$e\left(\frac{31}{56}\right)$	$1$	$e\left(\frac{19}{56}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{43}{56}\right)$
$\chi_{8352}(2771,\cdot)$	$1$	$1$	$e\left(\frac{29}{56}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{53}{56}\right)$	$e\left(\frac{39}{56}\right)$	$1$	$e\left(\frac{51}{56}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{27}{56}\right)$
$\chi_{8352}(3563,\cdot)$	$1$	$1$	$e\left(\frac{39}{56}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{23}{56}\right)$	$e\left(\frac{37}{56}\right)$	$1$	$e\left(\frac{1}{56}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{17}{56}\right)$
$\chi_{8352}(3707,\cdot)$	$1$	$1$	$e\left(\frac{51}{56}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{43}{56}\right)$	$e\left(\frac{1}{56}\right)$	$1$	$e\left(\frac{53}{56}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{5}{56}\right)$
$\chi_{8352}(3851,\cdot)$	$1$	$1$	$e\left(\frac{47}{56}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{55}{56}\right)$	$e\left(\frac{13}{56}\right)$	$1$	$e\left(\frac{17}{56}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{9}{56}\right)$
$\chi_{8352}(4067,\cdot)$	$1$	$1$	$e\left(\frac{17}{56}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{33}{56}\right)$	$e\left(\frac{19}{56}\right)$	$1$	$e\left(\frac{55}{56}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{39}{56}\right)$
$\chi_{8352}(4283,\cdot)$	$1$	$1$	$e\left(\frac{27}{56}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{3}{56}\right)$	$e\left(\frac{17}{56}\right)$	$1$	$e\left(\frac{5}{56}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{29}{56}\right)$
$\chi_{8352}(4859,\cdot)$	$1$	$1$	$e\left(\frac{43}{56}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{11}{56}\right)$	$e\left(\frac{25}{56}\right)$	$1$	$e\left(\frac{37}{56}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{13}{56}\right)$
$\chi_{8352}(5651,\cdot)$	$1$	$1$	$e\left(\frac{53}{56}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{37}{56}\right)$	$e\left(\frac{23}{56}\right)$	$1$	$e\left(\frac{43}{56}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{3}{56}\right)$
$\chi_{8352}(5795,\cdot)$	$1$	$1$	$e\left(\frac{9}{56}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{1}{56}\right)$	$e\left(\frac{43}{56}\right)$	$1$	$e\left(\frac{39}{56}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{47}{56}\right)$
$\chi_{8352}(5939,\cdot)$	$1$	$1$	$e\left(\frac{5}{56}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{13}{56}\right)$	$e\left(\frac{55}{56}\right)$	$1$	$e\left(\frac{3}{56}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{51}{56}\right)$
$\chi_{8352}(6155,\cdot)$	$1$	$1$	$e\left(\frac{31}{56}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{47}{56}\right)$	$e\left(\frac{5}{56}\right)$	$1$	$e\left(\frac{41}{56}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{25}{56}\right)$
$\chi_{8352}(6371,\cdot)$	$1$	$1$	$e\left(\frac{41}{56}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{17}{56}\right)$	$e\left(\frac{3}{56}\right)$	$1$	$e\left(\frac{47}{56}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{15}{56}\right)$
$\chi_{8352}(6947,\cdot)$	$1$	$1$	$e\left(\frac{1}{56}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{25}{56}\right)$	$e\left(\frac{11}{56}\right)$	$1$	$e\left(\frac{23}{56}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{55}{56}\right)$
$\chi_{8352}(7739,\cdot)$	$1$	$1$	$e\left(\frac{11}{56}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{51}{56}\right)$	$e\left(\frac{9}{56}\right)$	$1$	$e\left(\frac{29}{56}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{45}{56}\right)$
$\chi_{8352}(7883,\cdot)$	$1$	$1$	$e\left(\frac{23}{56}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{15}{56}\right)$	$e\left(\frac{29}{56}\right)$	$1$	$e\left(\frac{25}{56}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{33}{56}\right)$
$\chi_{8352}(8027,\cdot)$	$1$	$1$	$e\left(\frac{19}{56}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{27}{56}\right)$	$e\left(\frac{41}{56}\right)$	$1$	$e\left(\frac{45}{56}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{37}{56}\right)$
$\chi_{8352}(8243,\cdot)$	$1$	$1$	$e\left(\frac{45}{56}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{5}{56}\right)$	$e\left(\frac{47}{56}\right)$	$1$	$e\left(\frac{27}{56}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{11}{56}\right)$

Overview	Random
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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	\(-1\)	\(1\)	\(5\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(25\)	\(31\)	\(35\)
\(\chi_{8352}(107,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{55}{56}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{31}{56}\right)\)	\(e\left(\frac{45}{56}\right)\)	\(1\)	\(e\left(\frac{33}{56}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{1}{56}\right)\)
\(\chi_{8352}(683,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{15}{56}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{39}{56}\right)\)	\(e\left(\frac{53}{56}\right)\)	\(1\)	\(e\left(\frac{9}{56}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{41}{56}\right)\)
\(\chi_{8352}(1475,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{25}{56}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{9}{56}\right)\)	\(e\left(\frac{51}{56}\right)\)	\(1\)	\(e\left(\frac{15}{56}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{31}{56}\right)\)
\(\chi_{8352}(1619,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{56}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{29}{56}\right)\)	\(e\left(\frac{15}{56}\right)\)	\(1\)	\(e\left(\frac{11}{56}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{19}{56}\right)\)
\(\chi_{8352}(1763,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{33}{56}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{41}{56}\right)\)	\(e\left(\frac{27}{56}\right)\)	\(1\)	\(e\left(\frac{31}{56}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{23}{56}\right)\)
\(\chi_{8352}(1979,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{56}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{19}{56}\right)\)	\(e\left(\frac{33}{56}\right)\)	\(1\)	\(e\left(\frac{13}{56}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{53}{56}\right)\)
\(\chi_{8352}(2195,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{56}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{45}{56}\right)\)	\(e\left(\frac{31}{56}\right)\)	\(1\)	\(e\left(\frac{19}{56}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{43}{56}\right)\)
\(\chi_{8352}(2771,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{56}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{53}{56}\right)\)	\(e\left(\frac{39}{56}\right)\)	\(1\)	\(e\left(\frac{51}{56}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{27}{56}\right)\)
\(\chi_{8352}(3563,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{39}{56}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{23}{56}\right)\)	\(e\left(\frac{37}{56}\right)\)	\(1\)	\(e\left(\frac{1}{56}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{17}{56}\right)\)
\(\chi_{8352}(3707,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{51}{56}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{43}{56}\right)\)	\(e\left(\frac{1}{56}\right)\)	\(1\)	\(e\left(\frac{53}{56}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{5}{56}\right)\)
\(\chi_{8352}(3851,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{56}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{55}{56}\right)\)	\(e\left(\frac{13}{56}\right)\)	\(1\)	\(e\left(\frac{17}{56}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{9}{56}\right)\)
\(\chi_{8352}(4067,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{56}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{33}{56}\right)\)	\(e\left(\frac{19}{56}\right)\)	\(1\)	\(e\left(\frac{55}{56}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{39}{56}\right)\)
\(\chi_{8352}(4283,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{27}{56}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{3}{56}\right)\)	\(e\left(\frac{17}{56}\right)\)	\(1\)	\(e\left(\frac{5}{56}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{29}{56}\right)\)
\(\chi_{8352}(4859,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{56}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{11}{56}\right)\)	\(e\left(\frac{25}{56}\right)\)	\(1\)	\(e\left(\frac{37}{56}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{13}{56}\right)\)
\(\chi_{8352}(5651,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{56}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{37}{56}\right)\)	\(e\left(\frac{23}{56}\right)\)	\(1\)	\(e\left(\frac{43}{56}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{3}{56}\right)\)
\(\chi_{8352}(5795,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{56}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{1}{56}\right)\)	\(e\left(\frac{43}{56}\right)\)	\(1\)	\(e\left(\frac{39}{56}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{47}{56}\right)\)
\(\chi_{8352}(5939,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{56}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{13}{56}\right)\)	\(e\left(\frac{55}{56}\right)\)	\(1\)	\(e\left(\frac{3}{56}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{51}{56}\right)\)
\(\chi_{8352}(6155,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{56}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{47}{56}\right)\)	\(e\left(\frac{5}{56}\right)\)	\(1\)	\(e\left(\frac{41}{56}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{25}{56}\right)\)
\(\chi_{8352}(6371,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{56}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{17}{56}\right)\)	\(e\left(\frac{3}{56}\right)\)	\(1\)	\(e\left(\frac{47}{56}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{15}{56}\right)\)
\(\chi_{8352}(6947,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{56}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{25}{56}\right)\)	\(e\left(\frac{11}{56}\right)\)	\(1\)	\(e\left(\frac{23}{56}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{55}{56}\right)\)
\(\chi_{8352}(7739,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{56}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{51}{56}\right)\)	\(e\left(\frac{9}{56}\right)\)	\(1\)	\(e\left(\frac{29}{56}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{45}{56}\right)\)
\(\chi_{8352}(7883,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{56}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{15}{56}\right)\)	\(e\left(\frac{29}{56}\right)\)	\(1\)	\(e\left(\frac{25}{56}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{33}{56}\right)\)
\(\chi_{8352}(8027,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{56}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{27}{56}\right)\)	\(e\left(\frac{41}{56}\right)\)	\(1\)	\(e\left(\frac{45}{56}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{37}{56}\right)\)
\(\chi_{8352}(8243,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{45}{56}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{5}{56}\right)\)	\(e\left(\frac{47}{56}\right)\)	\(1\)	\(e\left(\frac{27}{56}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{11}{56}\right)\)

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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	8352.hb
Modulus	$8352$
Conductor	$2784$
Order	$56$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(8352\)
Conductor:	\(2784\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(56\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 2784.eh	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)