LMFDB - Dirichlet character orbit 547.j

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(547, base_ring=CyclotomicField(78)) M = H._module chi = DirichletCharacter(H, M([10])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(11,547)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$547$
Conductor:	$547$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$39$	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:	$\Q(\zeta_{39})$
Fixed field:	Number field defined by a degree 39 polynomial

Characters in Galois orbit

Character	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{547}(11,\cdot)$	$1$	$1$	$e\left(\frac{5}{39}\right)$	$1$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{5}{13}\right)$	$1$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{38}{39}\right)$
$\chi_{547}(21,\cdot)$	$1$	$1$	$e\left(\frac{38}{39}\right)$	$1$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{12}{13}\right)$	$1$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{8}{39}\right)$
$\chi_{547}(47,\cdot)$	$1$	$1$	$e\left(\frac{19}{39}\right)$	$1$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{6}{13}\right)$	$1$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{4}{39}\right)$
$\chi_{547}(54,\cdot)$	$1$	$1$	$e\left(\frac{14}{39}\right)$	$1$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{1}{13}\right)$	$1$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{5}{39}\right)$
$\chi_{547}(96,\cdot)$	$1$	$1$	$e\left(\frac{31}{39}\right)$	$1$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{5}{13}\right)$	$1$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{25}{39}\right)$
$\chi_{547}(121,\cdot)$	$1$	$1$	$e\left(\frac{10}{39}\right)$	$1$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{10}{13}\right)$	$1$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{37}{39}\right)$
$\chi_{547}(129,\cdot)$	$1$	$1$	$e\left(\frac{2}{39}\right)$	$1$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{2}{13}\right)$	$1$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{23}{39}\right)$
$\chi_{547}(136,\cdot)$	$1$	$1$	$e\left(\frac{11}{39}\right)$	$1$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{11}{13}\right)$	$1$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{29}{39}\right)$
$\chi_{547}(181,\cdot)$	$1$	$1$	$e\left(\frac{28}{39}\right)$	$1$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{2}{13}\right)$	$1$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{10}{39}\right)$
$\chi_{547}(199,\cdot)$	$1$	$1$	$e\left(\frac{34}{39}\right)$	$1$	$e\left(\frac{29}{39}\right)$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{8}{13}\right)$	$1$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{1}{39}\right)$
$\chi_{547}(217,\cdot)$	$1$	$1$	$e\left(\frac{29}{39}\right)$	$1$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{29}{39}\right)$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{3}{13}\right)$	$1$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{2}{39}\right)$
$\chi_{547}(231,\cdot)$	$1$	$1$	$e\left(\frac{4}{39}\right)$	$1$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{4}{13}\right)$	$1$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{7}{39}\right)$
$\chi_{547}(233,\cdot)$	$1$	$1$	$e\left(\frac{25}{39}\right)$	$1$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{29}{39}\right)$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{12}{13}\right)$	$1$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{34}{39}\right)$
$\chi_{547}(239,\cdot)$	$1$	$1$	$e\left(\frac{32}{39}\right)$	$1$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{6}{13}\right)$	$1$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{17}{39}\right)$
$\chi_{547}(296,\cdot)$	$1$	$1$	$e\left(\frac{35}{39}\right)$	$1$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{9}{13}\right)$	$1$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{32}{39}\right)$
$\chi_{547}(302,\cdot)$	$1$	$1$	$e\left(\frac{8}{39}\right)$	$1$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{8}{13}\right)$	$1$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{14}{39}\right)$
$\chi_{547}(325,\cdot)$	$1$	$1$	$e\left(\frac{7}{39}\right)$	$1$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{7}{13}\right)$	$1$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{22}{39}\right)$
$\chi_{547}(402,\cdot)$	$1$	$1$	$e\left(\frac{16}{39}\right)$	$1$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{3}{13}\right)$	$1$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{28}{39}\right)$
$\chi_{547}(419,\cdot)$	$1$	$1$	$e\left(\frac{20}{39}\right)$	$1$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{7}{13}\right)$	$1$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{35}{39}\right)$
$\chi_{547}(441,\cdot)$	$1$	$1$	$e\left(\frac{37}{39}\right)$	$1$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{11}{13}\right)$	$1$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{16}{39}\right)$
$\chi_{547}(445,\cdot)$	$1$	$1$	$e\left(\frac{22}{39}\right)$	$1$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{9}{13}\right)$	$1$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{19}{39}\right)$
$\chi_{547}(464,\cdot)$	$1$	$1$	$e\left(\frac{23}{39}\right)$	$1$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{29}{39}\right)$	$e\left(\frac{10}{13}\right)$	$1$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{11}{39}\right)$
$\chi_{547}(488,\cdot)$	$1$	$1$	$e\left(\frac{17}{39}\right)$	$1$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{4}{13}\right)$	$1$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{20}{39}\right)$
$\chi_{547}(521,\cdot)$	$1$	$1$	$e\left(\frac{1}{39}\right)$	$1$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{1}{13}\right)$	$1$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{31}{39}\right)$

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Elliptic curves over $\Q$
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Higher genus families
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Character	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\(\chi_{547}(11,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{39}\right)\)	\(1\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(1\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{38}{39}\right)\)
\(\chi_{547}(21,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{38}{39}\right)\)	\(1\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(1\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{8}{39}\right)\)
\(\chi_{547}(47,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{39}\right)\)	\(1\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(1\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{4}{39}\right)\)
\(\chi_{547}(54,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{14}{39}\right)\)	\(1\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(1\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{5}{39}\right)\)
\(\chi_{547}(96,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{39}\right)\)	\(1\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{34}{39}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(1\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{25}{39}\right)\)
\(\chi_{547}(121,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{10}{39}\right)\)	\(1\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(1\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{37}{39}\right)\)
\(\chi_{547}(129,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{39}\right)\)	\(1\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(1\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{23}{39}\right)\)
\(\chi_{547}(136,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{39}\right)\)	\(1\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(1\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{29}{39}\right)\)
\(\chi_{547}(181,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{28}{39}\right)\)	\(1\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(1\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{10}{39}\right)\)
\(\chi_{547}(199,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{34}{39}\right)\)	\(1\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{34}{39}\right)\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(1\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{1}{39}\right)\)
\(\chi_{547}(217,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{39}\right)\)	\(1\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(1\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{2}{39}\right)\)
\(\chi_{547}(231,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{39}\right)\)	\(1\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(1\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{7}{39}\right)\)
\(\chi_{547}(233,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{25}{39}\right)\)	\(1\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(1\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{34}{39}\right)\)
\(\chi_{547}(239,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{32}{39}\right)\)	\(1\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{34}{39}\right)\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(1\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{17}{39}\right)\)
\(\chi_{547}(296,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{35}{39}\right)\)	\(1\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(1\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{32}{39}\right)\)
\(\chi_{547}(302,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{8}{39}\right)\)	\(1\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(1\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{14}{39}\right)\)
\(\chi_{547}(325,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{39}\right)\)	\(1\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(1\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{22}{39}\right)\)
\(\chi_{547}(402,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{16}{39}\right)\)	\(1\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(1\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{28}{39}\right)\)
\(\chi_{547}(419,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{20}{39}\right)\)	\(1\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(1\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{35}{39}\right)\)
\(\chi_{547}(441,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{39}\right)\)	\(1\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(1\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{16}{39}\right)\)
\(\chi_{547}(445,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{22}{39}\right)\)	\(1\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(1\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{19}{39}\right)\)
\(\chi_{547}(464,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{39}\right)\)	\(1\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(1\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{11}{39}\right)\)
\(\chi_{547}(488,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{39}\right)\)	\(1\)	\(e\left(\frac{34}{39}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(1\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{20}{39}\right)\)
\(\chi_{547}(521,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{39}\right)\)	\(1\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(1\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{31}{39}\right)\)

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

Modulus:	\(547\)
Conductor:	\(547\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(39\)	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)