LMFDB - Dirichlet character orbit 6017.ba

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from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6017, base_ring=CyclotomicField(78))

M = H._module

chi = DirichletCharacter(H, M([0,68]))

chi.galois_orbit()

[g,chi] = znchar(Mod(199,6017))

order = charorder(g,chi)

[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$6017$
Conductor:	$547$	sage: chi.conductor() pari: znconreyconductor(g,chi)
Order:	$39$	sage: chi.multiplicative_order() pari: charorder(g,chi)
Real:	no
Primitive:	no, induced from 547.j	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:	$\Q(\zeta_{39})$
Fixed field:	Number field defined by a degree 39 polynomial

Characters in Galois orbit

Character	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$12$
$\chi_{6017}(199,\cdot)$	$1$	$1$	$e\left(\frac{34}{39}\right)$	$1$	$e\left(\frac{29}{39}\right)$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{8}{13}\right)$	$1$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{29}{39}\right)$
$\chi_{6017}(419,\cdot)$	$1$	$1$	$e\left(\frac{20}{39}\right)$	$1$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{7}{13}\right)$	$1$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{1}{39}\right)$
$\chi_{6017}(441,\cdot)$	$1$	$1$	$e\left(\frac{37}{39}\right)$	$1$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{11}{13}\right)$	$1$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{35}{39}\right)$
$\chi_{6017}(683,\cdot)$	$1$	$1$	$e\left(\frac{11}{39}\right)$	$1$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{11}{13}\right)$	$1$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{22}{39}\right)$
$\chi_{6017}(1035,\cdot)$	$1$	$1$	$e\left(\frac{17}{39}\right)$	$1$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{4}{13}\right)$	$1$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{34}{39}\right)$
$\chi_{6017}(1068,\cdot)$	$1$	$1$	$e\left(\frac{1}{39}\right)$	$1$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{1}{13}\right)$	$1$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{2}{39}\right)$
$\chi_{6017}(1662,\cdot)$	$1$	$1$	$e\left(\frac{38}{39}\right)$	$1$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{12}{13}\right)$	$1$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{37}{39}\right)$
$\chi_{6017}(1695,\cdot)$	$1$	$1$	$e\left(\frac{14}{39}\right)$	$1$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{1}{13}\right)$	$1$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{28}{39}\right)$
$\chi_{6017}(1937,\cdot)$	$1$	$1$	$e\left(\frac{35}{39}\right)$	$1$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{9}{13}\right)$	$1$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{31}{39}\right)$
$\chi_{6017}(2421,\cdot)$	$1$	$1$	$e\left(\frac{25}{39}\right)$	$1$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{29}{39}\right)$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{12}{13}\right)$	$1$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{11}{39}\right)$
$\chi_{6017}(2652,\cdot)$	$1$	$1$	$e\left(\frac{23}{39}\right)$	$1$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{29}{39}\right)$	$e\left(\frac{10}{13}\right)$	$1$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{7}{39}\right)$
$\chi_{6017}(2916,\cdot)$	$1$	$1$	$e\left(\frac{28}{39}\right)$	$1$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{2}{13}\right)$	$1$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{17}{39}\right)$
$\chi_{6017}(3037,\cdot)$	$1$	$1$	$e\left(\frac{8}{39}\right)$	$1$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{8}{13}\right)$	$1$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{16}{39}\right)$
$\chi_{6017}(3180,\cdot)$	$1$	$1$	$e\left(\frac{22}{39}\right)$	$1$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{9}{13}\right)$	$1$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{5}{39}\right)$
$\chi_{6017}(3378,\cdot)$	$1$	$1$	$e\left(\frac{31}{39}\right)$	$1$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{5}{13}\right)$	$1$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{23}{39}\right)$
$\chi_{6017}(3411,\cdot)$	$1$	$1$	$e\left(\frac{2}{39}\right)$	$1$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{2}{13}\right)$	$1$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{4}{39}\right)$
$\chi_{6017}(3499,\cdot)$	$1$	$1$	$e\left(\frac{29}{39}\right)$	$1$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{29}{39}\right)$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{3}{13}\right)$	$1$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{19}{39}\right)$
$\chi_{6017}(3521,\cdot)$	$1$	$1$	$e\left(\frac{32}{39}\right)$	$1$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{6}{13}\right)$	$1$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{25}{39}\right)$
$\chi_{6017}(3840,\cdot)$	$1$	$1$	$e\left(\frac{5}{39}\right)$	$1$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{5}{13}\right)$	$1$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{10}{39}\right)$
$\chi_{6017}(3950,\cdot)$	$1$	$1$	$e\left(\frac{10}{39}\right)$	$1$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{10}{13}\right)$	$1$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{20}{39}\right)$
$\chi_{6017}(4060,\cdot)$	$1$	$1$	$e\left(\frac{4}{39}\right)$	$1$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{4}{13}\right)$	$1$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{8}{39}\right)$
$\chi_{6017}(4423,\cdot)$	$1$	$1$	$e\left(\frac{19}{39}\right)$	$1$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{6}{13}\right)$	$1$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{38}{39}\right)$
$\chi_{6017}(5248,\cdot)$	$1$	$1$	$e\left(\frac{7}{39}\right)$	$1$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{7}{13}\right)$	$1$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{14}{39}\right)$
$\chi_{6017}(5325,\cdot)$	$1$	$1$	$e\left(\frac{16}{39}\right)$	$1$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{3}{13}\right)$	$1$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{32}{39}\right)$

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 $\F_{q}$

Character	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(12\)
\(\chi_{6017}(199,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{34}{39}\right)\)	\(1\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{34}{39}\right)\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(1\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{29}{39}\right)\)
\(\chi_{6017}(419,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{20}{39}\right)\)	\(1\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(1\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{1}{39}\right)\)
\(\chi_{6017}(441,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{39}\right)\)	\(1\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(1\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{35}{39}\right)\)
\(\chi_{6017}(683,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{39}\right)\)	\(1\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(1\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{22}{39}\right)\)
\(\chi_{6017}(1035,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{39}\right)\)	\(1\)	\(e\left(\frac{34}{39}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(1\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{34}{39}\right)\)
\(\chi_{6017}(1068,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{39}\right)\)	\(1\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(1\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{2}{39}\right)\)
\(\chi_{6017}(1662,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{38}{39}\right)\)	\(1\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(1\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{37}{39}\right)\)
\(\chi_{6017}(1695,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{14}{39}\right)\)	\(1\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(1\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{28}{39}\right)\)
\(\chi_{6017}(1937,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{35}{39}\right)\)	\(1\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(1\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{31}{39}\right)\)
\(\chi_{6017}(2421,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{25}{39}\right)\)	\(1\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(1\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{11}{39}\right)\)
\(\chi_{6017}(2652,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{39}\right)\)	\(1\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(1\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{7}{39}\right)\)
\(\chi_{6017}(2916,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{28}{39}\right)\)	\(1\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(1\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{17}{39}\right)\)
\(\chi_{6017}(3037,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{8}{39}\right)\)	\(1\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(1\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{16}{39}\right)\)
\(\chi_{6017}(3180,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{22}{39}\right)\)	\(1\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(1\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{5}{39}\right)\)
\(\chi_{6017}(3378,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{39}\right)\)	\(1\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{34}{39}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(1\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{23}{39}\right)\)
\(\chi_{6017}(3411,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{39}\right)\)	\(1\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(1\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{4}{39}\right)\)
\(\chi_{6017}(3499,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{39}\right)\)	\(1\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(1\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{19}{39}\right)\)
\(\chi_{6017}(3521,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{32}{39}\right)\)	\(1\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{34}{39}\right)\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(1\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{25}{39}\right)\)
\(\chi_{6017}(3840,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{39}\right)\)	\(1\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(1\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{10}{39}\right)\)
\(\chi_{6017}(3950,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{10}{39}\right)\)	\(1\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(1\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{20}{39}\right)\)
\(\chi_{6017}(4060,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{39}\right)\)	\(1\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(1\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{8}{39}\right)\)
\(\chi_{6017}(4423,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{39}\right)\)	\(1\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(1\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{38}{39}\right)\)
\(\chi_{6017}(5248,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{39}\right)\)	\(1\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(1\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{14}{39}\right)\)
\(\chi_{6017}(5325,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{16}{39}\right)\)	\(1\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(1\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{32}{39}\right)\)

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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	6017.ba
Modulus	$6017$
Conductor	$547$
Order	$39$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(6017\)
Conductor:	\(547\)	sage: chi.conductor() pari: znconreyconductor(g,chi)
Order:	\(39\)	sage: chi.multiplicative_order() pari: charorder(g,chi)
Real:	no
Primitive:	no, induced from 547.j	sage: chi.is_primitive() pari: #znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage: chi.is_odd() pari: zncharisodd(g,chi)