LMFDB - Dirichlet character orbit 8041.dh

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(8041, base_ring=CyclotomicField(56)) M = H._module chi = DirichletCharacter(H, M([28,21,12])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(32,8041)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$8041$
Conductor:	$8041$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$56$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	yes	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	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$12$
$\chi_{8041}(32,\cdot)$	$1$	$1$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{33}{56}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{13}{56}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{43}{56}\right)$	$e\left(\frac{37}{56}\right)$
$\chi_{8041}(604,\cdot)$	$1$	$1$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{43}{56}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{39}{56}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{17}{56}\right)$	$e\left(\frac{55}{56}\right)$
$\chi_{8041}(978,\cdot)$	$1$	$1$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{19}{56}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{55}{56}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{1}{56}\right)$	$e\left(\frac{23}{56}\right)$
$\chi_{8041}(1011,\cdot)$	$1$	$1$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{55}{56}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{3}{56}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{53}{56}\right)$	$e\left(\frac{43}{56}\right)$
$\chi_{8041}(1341,\cdot)$	$1$	$1$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{17}{56}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{5}{56}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{51}{56}\right)$	$e\left(\frac{53}{56}\right)$
$\chi_{8041}(1759,\cdot)$	$1$	$1$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{23}{56}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{43}{56}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{13}{56}\right)$	$e\left(\frac{19}{56}\right)$
$\chi_{8041}(1957,\cdot)$	$1$	$1$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{13}{56}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{17}{56}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{39}{56}\right)$	$e\left(\frac{1}{56}\right)$
$\chi_{8041}(2287,\cdot)$	$1$	$1$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{3}{56}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{47}{56}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{9}{56}\right)$	$e\left(\frac{39}{56}\right)$
$\chi_{8041}(2650,\cdot)$	$1$	$1$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{25}{56}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{37}{56}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{19}{56}\right)$	$e\left(\frac{45}{56}\right)$
$\chi_{8041}(2705,\cdot)$	$1$	$1$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{37}{56}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{1}{56}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{55}{56}\right)$	$e\left(\frac{33}{56}\right)$
$\chi_{8041}(3442,\cdot)$	$1$	$1$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{15}{56}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{11}{56}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{45}{56}\right)$	$e\left(\frac{27}{56}\right)$
$\chi_{8041}(3596,\cdot)$	$1$	$1$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{11}{56}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{23}{56}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{33}{56}\right)$	$e\left(\frac{31}{56}\right)$
$\chi_{8041}(3816,\cdot)$	$1$	$1$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{47}{56}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{27}{56}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{29}{56}\right)$	$e\left(\frac{51}{56}\right)$
$\chi_{8041}(4388,\cdot)$	$1$	$1$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{29}{56}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{25}{56}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{31}{56}\right)$	$e\left(\frac{41}{56}\right)$
$\chi_{8041}(4762,\cdot)$	$1$	$1$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{5}{56}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{41}{56}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{15}{56}\right)$	$e\left(\frac{9}{56}\right)$
$\chi_{8041}(5125,\cdot)$	$1$	$1$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{31}{56}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{19}{56}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{37}{56}\right)$	$e\left(\frac{11}{56}\right)$
$\chi_{8041}(5268,\cdot)$	$1$	$1$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{41}{56}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{45}{56}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{11}{56}\right)$	$e\left(\frac{29}{56}\right)$
$\chi_{8041}(6016,\cdot)$	$1$	$1$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{9}{56}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{29}{56}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{27}{56}\right)$	$e\left(\frac{5}{56}\right)$
$\chi_{8041}(6071,\cdot)$	$1$	$1$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{45}{56}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{33}{56}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{23}{56}\right)$	$e\left(\frac{25}{56}\right)$
$\chi_{8041}(6214,\cdot)$	$1$	$1$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{27}{56}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{31}{56}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{25}{56}\right)$	$e\left(\frac{15}{56}\right)$
$\chi_{8041}(6434,\cdot)$	$1$	$1$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{39}{56}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{51}{56}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{5}{56}\right)$	$e\left(\frac{3}{56}\right)$
$\chi_{8041}(6962,\cdot)$	$1$	$1$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{51}{56}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{15}{56}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{41}{56}\right)$	$e\left(\frac{47}{56}\right)$
$\chi_{8041}(7380,\cdot)$	$1$	$1$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{53}{56}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{9}{56}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{47}{56}\right)$	$e\left(\frac{17}{56}\right)$
$\chi_{8041}(7699,\cdot)$	$1$	$1$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{1}{56}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{53}{56}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{3}{56}\right)$	$e\left(\frac{13}{56}\right)$

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	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(12\)
\(\chi_{8041}(32,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{33}{56}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{13}{56}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{43}{56}\right)\)	\(e\left(\frac{37}{56}\right)\)
\(\chi_{8041}(604,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{43}{56}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{39}{56}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{17}{56}\right)\)	\(e\left(\frac{55}{56}\right)\)
\(\chi_{8041}(978,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{19}{56}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{55}{56}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{1}{56}\right)\)	\(e\left(\frac{23}{56}\right)\)
\(\chi_{8041}(1011,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{55}{56}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{3}{56}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{53}{56}\right)\)	\(e\left(\frac{43}{56}\right)\)
\(\chi_{8041}(1341,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{17}{56}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{5}{56}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{51}{56}\right)\)	\(e\left(\frac{53}{56}\right)\)
\(\chi_{8041}(1759,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{23}{56}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{43}{56}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{13}{56}\right)\)	\(e\left(\frac{19}{56}\right)\)
\(\chi_{8041}(1957,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{13}{56}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{17}{56}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{39}{56}\right)\)	\(e\left(\frac{1}{56}\right)\)
\(\chi_{8041}(2287,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{3}{56}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{47}{56}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{9}{56}\right)\)	\(e\left(\frac{39}{56}\right)\)
\(\chi_{8041}(2650,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{25}{56}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{37}{56}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{19}{56}\right)\)	\(e\left(\frac{45}{56}\right)\)
\(\chi_{8041}(2705,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{37}{56}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{1}{56}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{55}{56}\right)\)	\(e\left(\frac{33}{56}\right)\)
\(\chi_{8041}(3442,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{15}{56}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{11}{56}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{45}{56}\right)\)	\(e\left(\frac{27}{56}\right)\)
\(\chi_{8041}(3596,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{11}{56}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{23}{56}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{33}{56}\right)\)	\(e\left(\frac{31}{56}\right)\)
\(\chi_{8041}(3816,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{47}{56}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{27}{56}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{29}{56}\right)\)	\(e\left(\frac{51}{56}\right)\)
\(\chi_{8041}(4388,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{29}{56}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{25}{56}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{31}{56}\right)\)	\(e\left(\frac{41}{56}\right)\)
\(\chi_{8041}(4762,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{5}{56}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{41}{56}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{15}{56}\right)\)	\(e\left(\frac{9}{56}\right)\)
\(\chi_{8041}(5125,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{31}{56}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{19}{56}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{37}{56}\right)\)	\(e\left(\frac{11}{56}\right)\)
\(\chi_{8041}(5268,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{41}{56}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{45}{56}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{11}{56}\right)\)	\(e\left(\frac{29}{56}\right)\)
\(\chi_{8041}(6016,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{9}{56}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{29}{56}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{27}{56}\right)\)	\(e\left(\frac{5}{56}\right)\)
\(\chi_{8041}(6071,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{45}{56}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{33}{56}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{23}{56}\right)\)	\(e\left(\frac{25}{56}\right)\)
\(\chi_{8041}(6214,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{27}{56}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{31}{56}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{25}{56}\right)\)	\(e\left(\frac{15}{56}\right)\)
\(\chi_{8041}(6434,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{39}{56}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{51}{56}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{5}{56}\right)\)	\(e\left(\frac{3}{56}\right)\)
\(\chi_{8041}(6962,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{51}{56}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{15}{56}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{41}{56}\right)\)	\(e\left(\frac{47}{56}\right)\)
\(\chi_{8041}(7380,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{53}{56}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{9}{56}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{47}{56}\right)\)	\(e\left(\frac{17}{56}\right)\)
\(\chi_{8041}(7699,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{1}{56}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{53}{56}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{3}{56}\right)\)	\(e\left(\frac{13}{56}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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Basic properties

Related number fields

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	8041.dh
Modulus	$8041$
Conductor	$8041$
Order	$56$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(8041\)
Conductor:	\(8041\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(56\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	yes	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)