LMFDB - Dirichlet character orbit 4563.cd

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(4563, base_ring=CyclotomicField(78)) M = H._module chi = DirichletCharacter(H, M([26,18])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(118,4563)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$4563$
Conductor:	$1521$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$39$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 1521.bl	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	no
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)

Related number fields

Field of values:	$\Q(\zeta_{39})$
Fixed field:	Number field defined by a degree 39 polynomial

Characters in Galois orbit

Character	$-1$	$1$	$2$	$4$	$5$	$7$	$8$	$10$	$11$	$14$	$16$	$17$
$\chi_{4563}(118,\cdot)$	$1$	$1$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{29}{39}\right)$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{9}{13}\right)$
$\chi_{4563}(235,\cdot)$	$1$	$1$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{5}{13}\right)$
$\chi_{4563}(469,\cdot)$	$1$	$1$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{10}{13}\right)$
$\chi_{4563}(586,\cdot)$	$1$	$1$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{6}{13}\right)$
$\chi_{4563}(820,\cdot)$	$1$	$1$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{11}{13}\right)$
$\chi_{4563}(937,\cdot)$	$1$	$1$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{7}{13}\right)$
$\chi_{4563}(1171,\cdot)$	$1$	$1$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{12}{13}\right)$
$\chi_{4563}(1288,\cdot)$	$1$	$1$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{8}{13}\right)$
$\chi_{4563}(1639,\cdot)$	$1$	$1$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{9}{13}\right)$
$\chi_{4563}(1873,\cdot)$	$1$	$1$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{1}{13}\right)$
$\chi_{4563}(1990,\cdot)$	$1$	$1$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{29}{39}\right)$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{10}{13}\right)$
$\chi_{4563}(2224,\cdot)$	$1$	$1$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{2}{13}\right)$
$\chi_{4563}(2341,\cdot)$	$1$	$1$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{11}{13}\right)$
$\chi_{4563}(2575,\cdot)$	$1$	$1$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{3}{13}\right)$
$\chi_{4563}(2692,\cdot)$	$1$	$1$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{12}{13}\right)$
$\chi_{4563}(2926,\cdot)$	$1$	$1$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{29}{39}\right)$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{4}{13}\right)$
$\chi_{4563}(3277,\cdot)$	$1$	$1$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{5}{13}\right)$
$\chi_{4563}(3394,\cdot)$	$1$	$1$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{29}{39}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{1}{13}\right)$
$\chi_{4563}(3628,\cdot)$	$1$	$1$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{6}{13}\right)$
$\chi_{4563}(3745,\cdot)$	$1$	$1$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{2}{13}\right)$
$\chi_{4563}(3979,\cdot)$	$1$	$1$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{7}{13}\right)$
$\chi_{4563}(4096,\cdot)$	$1$	$1$	$e\left(\frac{29}{39}\right)$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{3}{13}\right)$
$\chi_{4563}(4330,\cdot)$	$1$	$1$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{29}{39}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{8}{13}\right)$
$\chi_{4563}(4447,\cdot)$	$1$	$1$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{29}{39}\right)$	$e\left(\frac{4}{13}\right)$

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	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(7\)	\(8\)	\(10\)	\(11\)	\(14\)	\(16\)	\(17\)
\(\chi_{4563}(118,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{9}{13}\right)\)
\(\chi_{4563}(235,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{5}{13}\right)\)
\(\chi_{4563}(469,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{10}{13}\right)\)
\(\chi_{4563}(586,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{6}{13}\right)\)
\(\chi_{4563}(820,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{11}{13}\right)\)
\(\chi_{4563}(937,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{7}{13}\right)\)
\(\chi_{4563}(1171,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{12}{13}\right)\)
\(\chi_{4563}(1288,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{8}{13}\right)\)
\(\chi_{4563}(1639,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{9}{13}\right)\)
\(\chi_{4563}(1873,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{1}{13}\right)\)
\(\chi_{4563}(1990,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{10}{13}\right)\)
\(\chi_{4563}(2224,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{34}{39}\right)\)	\(e\left(\frac{2}{13}\right)\)
\(\chi_{4563}(2341,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{34}{39}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{11}{13}\right)\)
\(\chi_{4563}(2575,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{3}{13}\right)\)
\(\chi_{4563}(2692,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{12}{13}\right)\)
\(\chi_{4563}(2926,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{4}{13}\right)\)
\(\chi_{4563}(3277,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{34}{39}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{5}{13}\right)\)
\(\chi_{4563}(3394,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{1}{13}\right)\)
\(\chi_{4563}(3628,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{6}{13}\right)\)
\(\chi_{4563}(3745,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{34}{39}\right)\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{2}{13}\right)\)
\(\chi_{4563}(3979,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{34}{39}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{7}{13}\right)\)
\(\chi_{4563}(4096,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{3}{13}\right)\)
\(\chi_{4563}(4330,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{34}{39}\right)\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{8}{13}\right)\)
\(\chi_{4563}(4447,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{34}{39}\right)\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{4}{13}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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Basic properties

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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	4563.cd
Modulus	$4563$
Conductor	$1521$
Order	$39$
Real	no
Primitive	no
Minimal	no
Parity	even

Modulus:	\(4563\)
Conductor:	\(1521\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(39\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 1521.bl	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	no
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)