LMFDB - Dirichlet character orbit 939.be

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(939, base_ring=CyclotomicField(312)) M = H._module chi = DirichletCharacter(H, M([0,1])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(10,939)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$939$
Conductor:	$313$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$312$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 313.p	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	odd	sage:chi.is_odd() pari:zncharisodd(g,chi)

Related number fields

Field of values:	$\Q(\zeta_{312})$
Fixed field:	Number field defined by a degree 312 polynomial (not computed)

First 31 of 96 characters in Galois orbit

Character	$-1$	$1$	$2$	$4$	$5$	$7$	$8$	$10$	$11$	$13$	$14$	$16$
$\chi_{939}(10,\cdot)$	$-1$	$1$	$e\left(\frac{137}{156}\right)$	$e\left(\frac{59}{78}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{41}{104}\right)$	$e\left(\frac{33}{52}\right)$	$e\left(\frac{1}{312}\right)$	$e\left(\frac{37}{78}\right)$	$e\left(\frac{107}{156}\right)$	$e\left(\frac{85}{312}\right)$	$e\left(\frac{20}{39}\right)$
$\chi_{939}(28,\cdot)$	$-1$	$1$	$e\left(\frac{43}{156}\right)$	$e\left(\frac{43}{78}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{55}{104}\right)$	$e\left(\frac{43}{52}\right)$	$e\left(\frac{47}{312}\right)$	$e\left(\frac{23}{78}\right)$	$e\left(\frac{37}{156}\right)$	$e\left(\frac{251}{312}\right)$	$e\left(\frac{4}{39}\right)$
$\chi_{939}(31,\cdot)$	$-1$	$1$	$e\left(\frac{47}{156}\right)$	$e\left(\frac{47}{78}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{19}{104}\right)$	$e\left(\frac{47}{52}\right)$	$e\left(\frac{211}{312}\right)$	$e\left(\frac{7}{78}\right)$	$e\left(\frac{113}{156}\right)$	$e\left(\frac{151}{312}\right)$	$e\left(\frac{8}{39}\right)$
$\chi_{939}(34,\cdot)$	$-1$	$1$	$e\left(\frac{103}{156}\right)$	$e\left(\frac{25}{78}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{87}{104}\right)$	$e\left(\frac{51}{52}\right)$	$e\left(\frac{167}{312}\right)$	$e\left(\frac{17}{78}\right)$	$e\left(\frac{85}{156}\right)$	$e\left(\frac{155}{312}\right)$	$e\left(\frac{25}{39}\right)$
$\chi_{939}(37,\cdot)$	$-1$	$1$	$e\left(\frac{23}{156}\right)$	$e\left(\frac{23}{78}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{27}{104}\right)$	$e\left(\frac{23}{52}\right)$	$e\left(\frac{163}{312}\right)$	$e\left(\frac{25}{78}\right)$	$e\left(\frac{125}{156}\right)$	$e\left(\frac{127}{312}\right)$	$e\left(\frac{23}{39}\right)$
$\chi_{939}(46,\cdot)$	$-1$	$1$	$e\left(\frac{53}{156}\right)$	$e\left(\frac{53}{78}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{69}{104}\right)$	$e\left(\frac{1}{52}\right)$	$e\left(\frac{301}{312}\right)$	$e\left(\frac{61}{78}\right)$	$e\left(\frac{71}{156}\right)$	$e\left(\frac{1}{312}\right)$	$e\left(\frac{14}{39}\right)$
$\chi_{939}(55,\cdot)$	$-1$	$1$	$e\left(\frac{35}{156}\right)$	$e\left(\frac{35}{78}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{75}{104}\right)$	$e\left(\frac{35}{52}\right)$	$e\left(\frac{187}{312}\right)$	$e\left(\frac{55}{78}\right)$	$e\left(\frac{41}{156}\right)$	$e\left(\frac{295}{312}\right)$	$e\left(\frac{35}{39}\right)$
$\chi_{939}(67,\cdot)$	$-1$	$1$	$e\left(\frac{55}{156}\right)$	$e\left(\frac{55}{78}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{103}{104}\right)$	$e\left(\frac{3}{52}\right)$	$e\left(\frac{71}{312}\right)$	$e\left(\frac{53}{78}\right)$	$e\left(\frac{109}{156}\right)$	$e\left(\frac{107}{312}\right)$	$e\left(\frac{16}{39}\right)$
$\chi_{939}(91,\cdot)$	$-1$	$1$	$e\left(\frac{149}{156}\right)$	$e\left(\frac{71}{78}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{89}{104}\right)$	$e\left(\frac{45}{52}\right)$	$e\left(\frac{25}{312}\right)$	$e\left(\frac{67}{78}\right)$	$e\left(\frac{23}{156}\right)$	$e\left(\frac{253}{312}\right)$	$e\left(\frac{32}{39}\right)$
$\chi_{939}(94,\cdot)$	$-1$	$1$	$e\left(\frac{19}{156}\right)$	$e\left(\frac{19}{78}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{63}{104}\right)$	$e\left(\frac{19}{52}\right)$	$e\left(\frac{311}{312}\right)$	$e\left(\frac{41}{78}\right)$	$e\left(\frac{49}{156}\right)$	$e\left(\frac{227}{312}\right)$	$e\left(\frac{19}{39}\right)$
$\chi_{939}(106,\cdot)$	$-1$	$1$	$e\left(\frac{11}{156}\right)$	$e\left(\frac{11}{78}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{31}{104}\right)$	$e\left(\frac{11}{52}\right)$	$e\left(\frac{295}{312}\right)$	$e\left(\frac{73}{78}\right)$	$e\left(\frac{53}{156}\right)$	$e\left(\frac{115}{312}\right)$	$e\left(\frac{11}{39}\right)$
$\chi_{939}(109,\cdot)$	$-1$	$1$	$e\left(\frac{73}{156}\right)$	$e\left(\frac{73}{78}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{45}{104}\right)$	$e\left(\frac{21}{52}\right)$	$e\left(\frac{29}{312}\right)$	$e\left(\frac{59}{78}\right)$	$e\left(\frac{139}{156}\right)$	$e\left(\frac{281}{312}\right)$	$e\left(\frac{34}{39}\right)$
$\chi_{939}(112,\cdot)$	$-1$	$1$	$e\left(\frac{83}{156}\right)$	$e\left(\frac{5}{78}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{59}{104}\right)$	$e\left(\frac{31}{52}\right)$	$e\left(\frac{283}{312}\right)$	$e\left(\frac{19}{78}\right)$	$e\left(\frac{17}{156}\right)$	$e\left(\frac{31}{312}\right)$	$e\left(\frac{5}{39}\right)$
$\chi_{939}(127,\cdot)$	$-1$	$1$	$e\left(\frac{17}{156}\right)$	$e\left(\frac{17}{78}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{81}{104}\right)$	$e\left(\frac{17}{52}\right)$	$e\left(\frac{73}{312}\right)$	$e\left(\frac{49}{78}\right)$	$e\left(\frac{11}{156}\right)$	$e\left(\frac{277}{312}\right)$	$e\left(\frac{17}{39}\right)$
$\chi_{939}(130,\cdot)$	$-1$	$1$	$e\left(\frac{127}{156}\right)$	$e\left(\frac{49}{78}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{79}{104}\right)$	$e\left(\frac{23}{52}\right)$	$e\left(\frac{215}{312}\right)$	$e\left(\frac{77}{78}\right)$	$e\left(\frac{73}{156}\right)$	$e\left(\frac{179}{312}\right)$	$e\left(\frac{10}{39}\right)$
$\chi_{939}(154,\cdot)$	$-1$	$1$	$e\left(\frac{97}{156}\right)$	$e\left(\frac{19}{78}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{89}{104}\right)$	$e\left(\frac{45}{52}\right)$	$e\left(\frac{233}{312}\right)$	$e\left(\frac{41}{78}\right)$	$e\left(\frac{127}{156}\right)$	$e\left(\frac{149}{312}\right)$	$e\left(\frac{19}{39}\right)$
$\chi_{939}(160,\cdot)$	$-1$	$1$	$e\left(\frac{61}{156}\right)$	$e\left(\frac{61}{78}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{49}{104}\right)$	$e\left(\frac{9}{52}\right)$	$e\left(\frac{161}{312}\right)$	$e\left(\frac{29}{78}\right)$	$e\left(\frac{67}{156}\right)$	$e\left(\frac{269}{312}\right)$	$e\left(\frac{22}{39}\right)$
$\chi_{939}(187,\cdot)$	$-1$	$1$	$e\left(\frac{1}{156}\right)$	$e\left(\frac{1}{78}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{17}{104}\right)$	$e\left(\frac{1}{52}\right)$	$e\left(\frac{41}{312}\right)$	$e\left(\frac{35}{78}\right)$	$e\left(\frac{19}{156}\right)$	$e\left(\frac{53}{312}\right)$	$e\left(\frac{1}{39}\right)$
$\chi_{939}(190,\cdot)$	$-1$	$1$	$e\left(\frac{113}{156}\right)$	$e\left(\frac{35}{78}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{101}{104}\right)$	$e\left(\frac{9}{52}\right)$	$e\left(\frac{109}{312}\right)$	$e\left(\frac{55}{78}\right)$	$e\left(\frac{119}{156}\right)$	$e\left(\frac{217}{312}\right)$	$e\left(\frac{35}{39}\right)$
$\chi_{939}(193,\cdot)$	$-1$	$1$	$e\left(\frac{49}{156}\right)$	$e\left(\frac{49}{78}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{1}{104}\right)$	$e\left(\frac{49}{52}\right)$	$e\left(\frac{137}{312}\right)$	$e\left(\frac{77}{78}\right)$	$e\left(\frac{151}{156}\right)$	$e\left(\frac{101}{312}\right)$	$e\left(\frac{10}{39}\right)$
$\chi_{939}(211,\cdot)$	$-1$	$1$	$e\left(\frac{131}{156}\right)$	$e\left(\frac{53}{78}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{43}{104}\right)$	$e\left(\frac{27}{52}\right)$	$e\left(\frac{67}{312}\right)$	$e\left(\frac{61}{78}\right)$	$e\left(\frac{149}{156}\right)$	$e\left(\frac{79}{312}\right)$	$e\left(\frac{14}{39}\right)$
$\chi_{939}(223,\cdot)$	$-1$	$1$	$e\left(\frac{37}{156}\right)$	$e\left(\frac{37}{78}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{5}{104}\right)$	$e\left(\frac{37}{52}\right)$	$e\left(\frac{269}{312}\right)$	$e\left(\frac{47}{78}\right)$	$e\left(\frac{79}{156}\right)$	$e\left(\frac{89}{312}\right)$	$e\left(\frac{37}{39}\right)$
$\chi_{939}(229,\cdot)$	$-1$	$1$	$e\left(\frac{71}{156}\right)$	$e\left(\frac{71}{78}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{11}{104}\right)$	$e\left(\frac{19}{52}\right)$	$e\left(\frac{259}{312}\right)$	$e\left(\frac{67}{78}\right)$	$e\left(\frac{101}{156}\right)$	$e\left(\frac{175}{312}\right)$	$e\left(\frac{32}{39}\right)$
$\chi_{939}(244,\cdot)$	$-1$	$1$	$e\left(\frac{139}{156}\right)$	$e\left(\frac{61}{78}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{23}{104}\right)$	$e\left(\frac{35}{52}\right)$	$e\left(\frac{239}{312}\right)$	$e\left(\frac{29}{78}\right)$	$e\left(\frac{145}{156}\right)$	$e\left(\frac{35}{312}\right)$	$e\left(\frac{22}{39}\right)$
$\chi_{939}(250,\cdot)$	$-1$	$1$	$e\left(\frac{59}{156}\right)$	$e\left(\frac{59}{78}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{15}{104}\right)$	$e\left(\frac{7}{52}\right)$	$e\left(\frac{79}{312}\right)$	$e\left(\frac{37}{78}\right)$	$e\left(\frac{29}{156}\right)$	$e\left(\frac{163}{312}\right)$	$e\left(\frac{20}{39}\right)$
$\chi_{939}(253,\cdot)$	$-1$	$1$	$e\left(\frac{107}{156}\right)$	$e\left(\frac{29}{78}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{103}{104}\right)$	$e\left(\frac{3}{52}\right)$	$e\left(\frac{175}{312}\right)$	$e\left(\frac{1}{78}\right)$	$e\left(\frac{5}{156}\right)$	$e\left(\frac{211}{312}\right)$	$e\left(\frac{29}{39}\right)$
$\chi_{939}(268,\cdot)$	$-1$	$1$	$e\left(\frac{95}{156}\right)$	$e\left(\frac{17}{78}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{3}{104}\right)$	$e\left(\frac{43}{52}\right)$	$e\left(\frac{307}{312}\right)$	$e\left(\frac{49}{78}\right)$	$e\left(\frac{89}{156}\right)$	$e\left(\frac{199}{312}\right)$	$e\left(\frac{17}{39}\right)$
$\chi_{939}(292,\cdot)$	$-1$	$1$	$e\left(\frac{31}{156}\right)$	$e\left(\frac{31}{78}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{7}{104}\right)$	$e\left(\frac{31}{52}\right)$	$e\left(\frac{23}{312}\right)$	$e\left(\frac{71}{78}\right)$	$e\left(\frac{121}{156}\right)$	$e\left(\frac{83}{312}\right)$	$e\left(\frac{31}{39}\right)$
$\chi_{939}(298,\cdot)$	$-1$	$1$	$e\left(\frac{67}{156}\right)$	$e\left(\frac{67}{78}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{99}{104}\right)$	$e\left(\frac{15}{52}\right)$	$e\left(\frac{251}{312}\right)$	$e\left(\frac{5}{78}\right)$	$e\left(\frac{25}{156}\right)$	$e\left(\frac{119}{312}\right)$	$e\left(\frac{28}{39}\right)$
$\chi_{939}(328,\cdot)$	$-1$	$1$	$e\left(\frac{67}{156}\right)$	$e\left(\frac{67}{78}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{47}{104}\right)$	$e\left(\frac{15}{52}\right)$	$e\left(\frac{95}{312}\right)$	$e\left(\frac{5}{78}\right)$	$e\left(\frac{25}{156}\right)$	$e\left(\frac{275}{312}\right)$	$e\left(\frac{28}{39}\right)$
$\chi_{939}(334,\cdot)$	$-1$	$1$	$e\left(\frac{31}{156}\right)$	$e\left(\frac{31}{78}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{59}{104}\right)$	$e\left(\frac{31}{52}\right)$	$e\left(\frac{179}{312}\right)$	$e\left(\frac{71}{78}\right)$	$e\left(\frac{121}{156}\right)$	$e\left(\frac{239}{312}\right)$	$e\left(\frac{31}{39}\right)$

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 $\F_{q}$
Belyi maps

Character	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(7\)	\(8\)	\(10\)	\(11\)	\(13\)	\(14\)	\(16\)
\(\chi_{939}(10,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{137}{156}\right)\)	\(e\left(\frac{59}{78}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{41}{104}\right)\)	\(e\left(\frac{33}{52}\right)\)	\(e\left(\frac{1}{312}\right)\)	\(e\left(\frac{37}{78}\right)\)	\(e\left(\frac{107}{156}\right)\)	\(e\left(\frac{85}{312}\right)\)	\(e\left(\frac{20}{39}\right)\)
\(\chi_{939}(28,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{43}{156}\right)\)	\(e\left(\frac{43}{78}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{55}{104}\right)\)	\(e\left(\frac{43}{52}\right)\)	\(e\left(\frac{47}{312}\right)\)	\(e\left(\frac{23}{78}\right)\)	\(e\left(\frac{37}{156}\right)\)	\(e\left(\frac{251}{312}\right)\)	\(e\left(\frac{4}{39}\right)\)
\(\chi_{939}(31,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{47}{156}\right)\)	\(e\left(\frac{47}{78}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{19}{104}\right)\)	\(e\left(\frac{47}{52}\right)\)	\(e\left(\frac{211}{312}\right)\)	\(e\left(\frac{7}{78}\right)\)	\(e\left(\frac{113}{156}\right)\)	\(e\left(\frac{151}{312}\right)\)	\(e\left(\frac{8}{39}\right)\)
\(\chi_{939}(34,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{103}{156}\right)\)	\(e\left(\frac{25}{78}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{87}{104}\right)\)	\(e\left(\frac{51}{52}\right)\)	\(e\left(\frac{167}{312}\right)\)	\(e\left(\frac{17}{78}\right)\)	\(e\left(\frac{85}{156}\right)\)	\(e\left(\frac{155}{312}\right)\)	\(e\left(\frac{25}{39}\right)\)
\(\chi_{939}(37,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{23}{156}\right)\)	\(e\left(\frac{23}{78}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{27}{104}\right)\)	\(e\left(\frac{23}{52}\right)\)	\(e\left(\frac{163}{312}\right)\)	\(e\left(\frac{25}{78}\right)\)	\(e\left(\frac{125}{156}\right)\)	\(e\left(\frac{127}{312}\right)\)	\(e\left(\frac{23}{39}\right)\)
\(\chi_{939}(46,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{53}{156}\right)\)	\(e\left(\frac{53}{78}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{69}{104}\right)\)	\(e\left(\frac{1}{52}\right)\)	\(e\left(\frac{301}{312}\right)\)	\(e\left(\frac{61}{78}\right)\)	\(e\left(\frac{71}{156}\right)\)	\(e\left(\frac{1}{312}\right)\)	\(e\left(\frac{14}{39}\right)\)
\(\chi_{939}(55,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{35}{156}\right)\)	\(e\left(\frac{35}{78}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{75}{104}\right)\)	\(e\left(\frac{35}{52}\right)\)	\(e\left(\frac{187}{312}\right)\)	\(e\left(\frac{55}{78}\right)\)	\(e\left(\frac{41}{156}\right)\)	\(e\left(\frac{295}{312}\right)\)	\(e\left(\frac{35}{39}\right)\)
\(\chi_{939}(67,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{55}{156}\right)\)	\(e\left(\frac{55}{78}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{103}{104}\right)\)	\(e\left(\frac{3}{52}\right)\)	\(e\left(\frac{71}{312}\right)\)	\(e\left(\frac{53}{78}\right)\)	\(e\left(\frac{109}{156}\right)\)	\(e\left(\frac{107}{312}\right)\)	\(e\left(\frac{16}{39}\right)\)
\(\chi_{939}(91,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{149}{156}\right)\)	\(e\left(\frac{71}{78}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{89}{104}\right)\)	\(e\left(\frac{45}{52}\right)\)	\(e\left(\frac{25}{312}\right)\)	\(e\left(\frac{67}{78}\right)\)	\(e\left(\frac{23}{156}\right)\)	\(e\left(\frac{253}{312}\right)\)	\(e\left(\frac{32}{39}\right)\)
\(\chi_{939}(94,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{19}{156}\right)\)	\(e\left(\frac{19}{78}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{63}{104}\right)\)	\(e\left(\frac{19}{52}\right)\)	\(e\left(\frac{311}{312}\right)\)	\(e\left(\frac{41}{78}\right)\)	\(e\left(\frac{49}{156}\right)\)	\(e\left(\frac{227}{312}\right)\)	\(e\left(\frac{19}{39}\right)\)
\(\chi_{939}(106,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{11}{156}\right)\)	\(e\left(\frac{11}{78}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{31}{104}\right)\)	\(e\left(\frac{11}{52}\right)\)	\(e\left(\frac{295}{312}\right)\)	\(e\left(\frac{73}{78}\right)\)	\(e\left(\frac{53}{156}\right)\)	\(e\left(\frac{115}{312}\right)\)	\(e\left(\frac{11}{39}\right)\)
\(\chi_{939}(109,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{73}{156}\right)\)	\(e\left(\frac{73}{78}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{45}{104}\right)\)	\(e\left(\frac{21}{52}\right)\)	\(e\left(\frac{29}{312}\right)\)	\(e\left(\frac{59}{78}\right)\)	\(e\left(\frac{139}{156}\right)\)	\(e\left(\frac{281}{312}\right)\)	\(e\left(\frac{34}{39}\right)\)
\(\chi_{939}(112,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{83}{156}\right)\)	\(e\left(\frac{5}{78}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{59}{104}\right)\)	\(e\left(\frac{31}{52}\right)\)	\(e\left(\frac{283}{312}\right)\)	\(e\left(\frac{19}{78}\right)\)	\(e\left(\frac{17}{156}\right)\)	\(e\left(\frac{31}{312}\right)\)	\(e\left(\frac{5}{39}\right)\)
\(\chi_{939}(127,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{17}{156}\right)\)	\(e\left(\frac{17}{78}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{81}{104}\right)\)	\(e\left(\frac{17}{52}\right)\)	\(e\left(\frac{73}{312}\right)\)	\(e\left(\frac{49}{78}\right)\)	\(e\left(\frac{11}{156}\right)\)	\(e\left(\frac{277}{312}\right)\)	\(e\left(\frac{17}{39}\right)\)
\(\chi_{939}(130,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{127}{156}\right)\)	\(e\left(\frac{49}{78}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{79}{104}\right)\)	\(e\left(\frac{23}{52}\right)\)	\(e\left(\frac{215}{312}\right)\)	\(e\left(\frac{77}{78}\right)\)	\(e\left(\frac{73}{156}\right)\)	\(e\left(\frac{179}{312}\right)\)	\(e\left(\frac{10}{39}\right)\)
\(\chi_{939}(154,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{97}{156}\right)\)	\(e\left(\frac{19}{78}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{89}{104}\right)\)	\(e\left(\frac{45}{52}\right)\)	\(e\left(\frac{233}{312}\right)\)	\(e\left(\frac{41}{78}\right)\)	\(e\left(\frac{127}{156}\right)\)	\(e\left(\frac{149}{312}\right)\)	\(e\left(\frac{19}{39}\right)\)
\(\chi_{939}(160,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{61}{156}\right)\)	\(e\left(\frac{61}{78}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{49}{104}\right)\)	\(e\left(\frac{9}{52}\right)\)	\(e\left(\frac{161}{312}\right)\)	\(e\left(\frac{29}{78}\right)\)	\(e\left(\frac{67}{156}\right)\)	\(e\left(\frac{269}{312}\right)\)	\(e\left(\frac{22}{39}\right)\)
\(\chi_{939}(187,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{156}\right)\)	\(e\left(\frac{1}{78}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{17}{104}\right)\)	\(e\left(\frac{1}{52}\right)\)	\(e\left(\frac{41}{312}\right)\)	\(e\left(\frac{35}{78}\right)\)	\(e\left(\frac{19}{156}\right)\)	\(e\left(\frac{53}{312}\right)\)	\(e\left(\frac{1}{39}\right)\)
\(\chi_{939}(190,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{113}{156}\right)\)	\(e\left(\frac{35}{78}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{101}{104}\right)\)	\(e\left(\frac{9}{52}\right)\)	\(e\left(\frac{109}{312}\right)\)	\(e\left(\frac{55}{78}\right)\)	\(e\left(\frac{119}{156}\right)\)	\(e\left(\frac{217}{312}\right)\)	\(e\left(\frac{35}{39}\right)\)
\(\chi_{939}(193,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{49}{156}\right)\)	\(e\left(\frac{49}{78}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{1}{104}\right)\)	\(e\left(\frac{49}{52}\right)\)	\(e\left(\frac{137}{312}\right)\)	\(e\left(\frac{77}{78}\right)\)	\(e\left(\frac{151}{156}\right)\)	\(e\left(\frac{101}{312}\right)\)	\(e\left(\frac{10}{39}\right)\)
\(\chi_{939}(211,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{131}{156}\right)\)	\(e\left(\frac{53}{78}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{43}{104}\right)\)	\(e\left(\frac{27}{52}\right)\)	\(e\left(\frac{67}{312}\right)\)	\(e\left(\frac{61}{78}\right)\)	\(e\left(\frac{149}{156}\right)\)	\(e\left(\frac{79}{312}\right)\)	\(e\left(\frac{14}{39}\right)\)
\(\chi_{939}(223,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{37}{156}\right)\)	\(e\left(\frac{37}{78}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{5}{104}\right)\)	\(e\left(\frac{37}{52}\right)\)	\(e\left(\frac{269}{312}\right)\)	\(e\left(\frac{47}{78}\right)\)	\(e\left(\frac{79}{156}\right)\)	\(e\left(\frac{89}{312}\right)\)	\(e\left(\frac{37}{39}\right)\)
\(\chi_{939}(229,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{71}{156}\right)\)	\(e\left(\frac{71}{78}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{11}{104}\right)\)	\(e\left(\frac{19}{52}\right)\)	\(e\left(\frac{259}{312}\right)\)	\(e\left(\frac{67}{78}\right)\)	\(e\left(\frac{101}{156}\right)\)	\(e\left(\frac{175}{312}\right)\)	\(e\left(\frac{32}{39}\right)\)
\(\chi_{939}(244,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{139}{156}\right)\)	\(e\left(\frac{61}{78}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{23}{104}\right)\)	\(e\left(\frac{35}{52}\right)\)	\(e\left(\frac{239}{312}\right)\)	\(e\left(\frac{29}{78}\right)\)	\(e\left(\frac{145}{156}\right)\)	\(e\left(\frac{35}{312}\right)\)	\(e\left(\frac{22}{39}\right)\)
\(\chi_{939}(250,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{59}{156}\right)\)	\(e\left(\frac{59}{78}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{15}{104}\right)\)	\(e\left(\frac{7}{52}\right)\)	\(e\left(\frac{79}{312}\right)\)	\(e\left(\frac{37}{78}\right)\)	\(e\left(\frac{29}{156}\right)\)	\(e\left(\frac{163}{312}\right)\)	\(e\left(\frac{20}{39}\right)\)
\(\chi_{939}(253,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{107}{156}\right)\)	\(e\left(\frac{29}{78}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{103}{104}\right)\)	\(e\left(\frac{3}{52}\right)\)	\(e\left(\frac{175}{312}\right)\)	\(e\left(\frac{1}{78}\right)\)	\(e\left(\frac{5}{156}\right)\)	\(e\left(\frac{211}{312}\right)\)	\(e\left(\frac{29}{39}\right)\)
\(\chi_{939}(268,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{95}{156}\right)\)	\(e\left(\frac{17}{78}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{3}{104}\right)\)	\(e\left(\frac{43}{52}\right)\)	\(e\left(\frac{307}{312}\right)\)	\(e\left(\frac{49}{78}\right)\)	\(e\left(\frac{89}{156}\right)\)	\(e\left(\frac{199}{312}\right)\)	\(e\left(\frac{17}{39}\right)\)
\(\chi_{939}(292,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{31}{156}\right)\)	\(e\left(\frac{31}{78}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{7}{104}\right)\)	\(e\left(\frac{31}{52}\right)\)	\(e\left(\frac{23}{312}\right)\)	\(e\left(\frac{71}{78}\right)\)	\(e\left(\frac{121}{156}\right)\)	\(e\left(\frac{83}{312}\right)\)	\(e\left(\frac{31}{39}\right)\)
\(\chi_{939}(298,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{67}{156}\right)\)	\(e\left(\frac{67}{78}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{99}{104}\right)\)	\(e\left(\frac{15}{52}\right)\)	\(e\left(\frac{251}{312}\right)\)	\(e\left(\frac{5}{78}\right)\)	\(e\left(\frac{25}{156}\right)\)	\(e\left(\frac{119}{312}\right)\)	\(e\left(\frac{28}{39}\right)\)
\(\chi_{939}(328,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{67}{156}\right)\)	\(e\left(\frac{67}{78}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{47}{104}\right)\)	\(e\left(\frac{15}{52}\right)\)	\(e\left(\frac{95}{312}\right)\)	\(e\left(\frac{5}{78}\right)\)	\(e\left(\frac{25}{156}\right)\)	\(e\left(\frac{275}{312}\right)\)	\(e\left(\frac{28}{39}\right)\)
\(\chi_{939}(334,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{31}{156}\right)\)	\(e\left(\frac{31}{78}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{59}{104}\right)\)	\(e\left(\frac{31}{52}\right)\)	\(e\left(\frac{179}{312}\right)\)	\(e\left(\frac{71}{78}\right)\)	\(e\left(\frac{121}{156}\right)\)	\(e\left(\frac{239}{312}\right)\)	\(e\left(\frac{31}{39}\right)\)

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First 31 of 96 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	939.be
Modulus	$939$
Conductor	$313$
Order	$312$
Real	no
Primitive	no
Minimal	yes
Parity	odd

Modulus:	\(939\)
Conductor:	\(313\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(312\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 313.p	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	odd	sage:chi.is_odd() pari:zncharisodd(g,chi)