LMFDB - Dirichlet character orbit 39326.bb

Show commands: Magma / Pari/GP / SageMath

comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(39326, base_ring=CyclotomicField(156)) M = H._module chi = DirichletCharacter(H, M([26,153])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(451, 39326)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

magma:// Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("39326.451"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$39326$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$371$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$156$	comment:Order sage:chi.multiplicative_order() gp:charorder(g,chi) magma:Order(chi);
Real:	no	comment:Whether the character is real sage:chi.multiplicative_order() <= 2 gp:charorder(g,chi) <= 2 magma:Order(chi) le 2;
Primitive:	no, induced from 371.w	comment:If the character is primitive sage:chi.is_primitive() gp:#znconreyconductor(g,chi)==1 magma:IsPrimitive(chi);
Minimal:	no
Parity:	even	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);

Related number fields

Field of values:	$\Q(\zeta_{156})$	comment:Field of values of chi sage:CyclotomicField(chi.multiplicative_order()) gp:nfinit(polcyclo(charorder(g,chi))) magma:CyclotomicField(Order(chi));
Fixed field:	Number field defined by a degree 156 polynomial (not computed)	comment:Fixed field sage:chi.fixed_field()

First 31 of 48 characters in Galois orbit

Character	$-1$	$1$	$3$	$5$	$9$	$11$	$13$	$15$	$17$	$19$	$23$	$25$
$\chi_{39326}(451,\cdot)$	$1$	$1$	$e\left(\frac{131}{156}\right)$	$e\left(\frac{145}{156}\right)$	$e\left(\frac{53}{78}\right)$	$e\left(\frac{43}{78}\right)$	$e\left(\frac{1}{26}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{19}{156}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{67}{78}\right)$
$\chi_{39326}(985,\cdot)$	$1$	$1$	$e\left(\frac{97}{156}\right)$	$e\left(\frac{155}{156}\right)$	$e\left(\frac{19}{78}\right)$	$e\left(\frac{11}{78}\right)$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{101}{156}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{77}{78}\right)$
$\chi_{39326}(3671,\cdot)$	$1$	$1$	$e\left(\frac{11}{156}\right)$	$e\left(\frac{61}{156}\right)$	$e\left(\frac{11}{78}\right)$	$e\left(\frac{31}{78}\right)$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{79}{156}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{61}{78}\right)$
$\chi_{39326}(4175,\cdot)$	$1$	$1$	$e\left(\frac{137}{156}\right)$	$e\left(\frac{79}{156}\right)$	$e\left(\frac{59}{78}\right)$	$e\left(\frac{67}{78}\right)$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{133}{156}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{78}\right)$
$\chi_{39326}(4609,\cdot)$	$1$	$1$	$e\left(\frac{155}{156}\right)$	$e\left(\frac{37}{156}\right)$	$e\left(\frac{77}{78}\right)$	$e\left(\frac{61}{78}\right)$	$e\left(\frac{25}{26}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{7}{156}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{37}{78}\right)$
$\chi_{39326}(4749,\cdot)$	$1$	$1$	$e\left(\frac{125}{156}\right)$	$e\left(\frac{55}{156}\right)$	$e\left(\frac{47}{78}\right)$	$e\left(\frac{19}{78}\right)$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{61}{156}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{55}{78}\right)$
$\chi_{39326}(6487,\cdot)$	$1$	$1$	$e\left(\frac{151}{156}\right)$	$e\left(\frac{29}{156}\right)$	$e\left(\frac{73}{78}\right)$	$e\left(\frac{71}{78}\right)$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{35}{156}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{29}{78}\right)$
$\chi_{39326}(6627,\cdot)$	$1$	$1$	$e\left(\frac{25}{156}\right)$	$e\left(\frac{11}{156}\right)$	$e\left(\frac{25}{78}\right)$	$e\left(\frac{35}{78}\right)$	$e\left(\frac{25}{26}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{137}{156}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{11}{78}\right)$
$\chi_{39326}(7061,\cdot)$	$1$	$1$	$e\left(\frac{7}{156}\right)$	$e\left(\frac{53}{156}\right)$	$e\left(\frac{7}{78}\right)$	$e\left(\frac{41}{78}\right)$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{107}{156}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{53}{78}\right)$
$\chi_{39326}(7565,\cdot)$	$1$	$1$	$e\left(\frac{37}{156}\right)$	$e\left(\frac{35}{156}\right)$	$e\left(\frac{37}{78}\right)$	$e\left(\frac{5}{78}\right)$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{53}{156}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{35}{78}\right)$
$\chi_{39326}(10251,\cdot)$	$1$	$1$	$e\left(\frac{71}{156}\right)$	$e\left(\frac{25}{156}\right)$	$e\left(\frac{71}{78}\right)$	$e\left(\frac{37}{78}\right)$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{127}{156}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{25}{78}\right)$
$\chi_{39326}(10785,\cdot)$	$1$	$1$	$e\left(\frac{1}{156}\right)$	$e\left(\frac{119}{156}\right)$	$e\left(\frac{1}{78}\right)$	$e\left(\frac{17}{78}\right)$	$e\left(\frac{1}{26}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{149}{156}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{41}{78}\right)$
$\chi_{39326}(11891,\cdot)$	$1$	$1$	$e\left(\frac{145}{156}\right)$	$e\left(\frac{95}{156}\right)$	$e\left(\frac{67}{78}\right)$	$e\left(\frac{47}{78}\right)$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{77}{156}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{17}{78}\right)$
$\chi_{39326}(11973,\cdot)$	$1$	$1$	$e\left(\frac{5}{156}\right)$	$e\left(\frac{127}{156}\right)$	$e\left(\frac{5}{78}\right)$	$e\left(\frac{7}{78}\right)$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{121}{156}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{49}{78}\right)$
$\chi_{39326}(12087,\cdot)$	$1$	$1$	$e\left(\frac{61}{156}\right)$	$e\left(\frac{83}{156}\right)$	$e\left(\frac{61}{78}\right)$	$e\left(\frac{23}{78}\right)$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{41}{156}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{78}\right)$
$\chi_{39326}(13639,\cdot)$	$1$	$1$	$e\left(\frac{95}{156}\right)$	$e\left(\frac{73}{156}\right)$	$e\left(\frac{17}{78}\right)$	$e\left(\frac{55}{78}\right)$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{115}{156}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{73}{78}\right)$
$\chi_{39326}(14383,\cdot)$	$1$	$1$	$e\left(\frac{133}{156}\right)$	$e\left(\frac{71}{156}\right)$	$e\left(\frac{55}{78}\right)$	$e\left(\frac{77}{78}\right)$	$e\left(\frac{3}{26}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{5}{156}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{71}{78}\right)$
$\chi_{39326}(14451,\cdot)$	$1$	$1$	$e\left(\frac{17}{156}\right)$	$e\left(\frac{151}{156}\right)$	$e\left(\frac{17}{78}\right)$	$e\left(\frac{55}{78}\right)$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{37}{156}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{73}{78}\right)$
$\chi_{39326}(14901,\cdot)$	$1$	$1$	$e\left(\frac{127}{156}\right)$	$e\left(\frac{137}{156}\right)$	$e\left(\frac{49}{78}\right)$	$e\left(\frac{53}{78}\right)$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{47}{156}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{59}{78}\right)$
$\chi_{39326}(16117,\cdot)$	$1$	$1$	$e\left(\frac{83}{156}\right)$	$e\left(\frac{49}{156}\right)$	$e\left(\frac{5}{78}\right)$	$e\left(\frac{7}{78}\right)$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{43}{156}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{49}{78}\right)$
$\chi_{39326}(17839,\cdot)$	$1$	$1$	$e\left(\frac{149}{156}\right)$	$e\left(\frac{103}{156}\right)$	$e\left(\frac{71}{78}\right)$	$e\left(\frac{37}{78}\right)$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{49}{156}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{25}{78}\right)$
$\chi_{39326}(18807,\cdot)$	$1$	$1$	$e\left(\frac{49}{156}\right)$	$e\left(\frac{59}{156}\right)$	$e\left(\frac{49}{78}\right)$	$e\left(\frac{53}{78}\right)$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{125}{156}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{59}{78}\right)$
$\chi_{39326}(19325,\cdot)$	$1$	$1$	$e\left(\frac{55}{156}\right)$	$e\left(\frac{149}{156}\right)$	$e\left(\frac{55}{78}\right)$	$e\left(\frac{77}{78}\right)$	$e\left(\frac{3}{26}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{83}{156}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{71}{78}\right)$
$\chi_{39326}(21621,\cdot)$	$1$	$1$	$e\left(\frac{139}{156}\right)$	$e\left(\frac{5}{156}\right)$	$e\left(\frac{61}{78}\right)$	$e\left(\frac{23}{78}\right)$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{119}{156}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{78}\right)$
$\chi_{39326}(21817,\cdot)$	$1$	$1$	$e\left(\frac{67}{156}\right)$	$e\left(\frac{17}{156}\right)$	$e\left(\frac{67}{78}\right)$	$e\left(\frac{47}{78}\right)$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{155}{156}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{17}{78}\right)$
$\chi_{39326}(22923,\cdot)$	$1$	$1$	$e\left(\frac{79}{156}\right)$	$e\left(\frac{41}{156}\right)$	$e\left(\frac{1}{78}\right)$	$e\left(\frac{17}{78}\right)$	$e\left(\frac{1}{26}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{71}{156}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{41}{78}\right)$
$\chi_{39326}(23341,\cdot)$	$1$	$1$	$e\left(\frac{47}{156}\right)$	$e\left(\frac{133}{156}\right)$	$e\left(\frac{47}{78}\right)$	$e\left(\frac{19}{78}\right)$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{139}{156}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{55}{78}\right)$
$\chi_{39326}(23481,\cdot)$	$1$	$1$	$e\left(\frac{77}{156}\right)$	$e\left(\frac{115}{156}\right)$	$e\left(\frac{77}{78}\right)$	$e\left(\frac{61}{78}\right)$	$e\left(\frac{25}{26}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{85}{156}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{37}{78}\right)$
$\chi_{39326}(23915,\cdot)$	$1$	$1$	$e\left(\frac{59}{156}\right)$	$e\left(\frac{1}{156}\right)$	$e\left(\frac{59}{78}\right)$	$e\left(\frac{67}{78}\right)$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{55}{156}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{78}\right)$
$\chi_{39326}(24419,\cdot)$	$1$	$1$	$e\left(\frac{89}{156}\right)$	$e\left(\frac{139}{156}\right)$	$e\left(\frac{11}{78}\right)$	$e\left(\frac{31}{78}\right)$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{1}{156}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{61}{78}\right)$
$\chi_{39326}(26143,\cdot)$	$1$	$1$	$e\left(\frac{115}{156}\right)$	$e\left(\frac{113}{156}\right)$	$e\left(\frac{37}{78}\right)$	$e\left(\frac{5}{78}\right)$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{131}{156}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{35}{78}\right)$

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	\(-1\)	\(1\)	\(3\)	\(5\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(23\)	\(25\)
\(\chi_{39326}(451,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{131}{156}\right)\)	\(e\left(\frac{145}{156}\right)\)	\(e\left(\frac{53}{78}\right)\)	\(e\left(\frac{43}{78}\right)\)	\(e\left(\frac{1}{26}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{19}{156}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{67}{78}\right)\)
\(\chi_{39326}(985,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{97}{156}\right)\)	\(e\left(\frac{155}{156}\right)\)	\(e\left(\frac{19}{78}\right)\)	\(e\left(\frac{11}{78}\right)\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{101}{156}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{77}{78}\right)\)
\(\chi_{39326}(3671,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{156}\right)\)	\(e\left(\frac{61}{156}\right)\)	\(e\left(\frac{11}{78}\right)\)	\(e\left(\frac{31}{78}\right)\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{79}{156}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{61}{78}\right)\)
\(\chi_{39326}(4175,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{137}{156}\right)\)	\(e\left(\frac{79}{156}\right)\)	\(e\left(\frac{59}{78}\right)\)	\(e\left(\frac{67}{78}\right)\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{133}{156}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{78}\right)\)
\(\chi_{39326}(4609,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{155}{156}\right)\)	\(e\left(\frac{37}{156}\right)\)	\(e\left(\frac{77}{78}\right)\)	\(e\left(\frac{61}{78}\right)\)	\(e\left(\frac{25}{26}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{7}{156}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{37}{78}\right)\)
\(\chi_{39326}(4749,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{125}{156}\right)\)	\(e\left(\frac{55}{156}\right)\)	\(e\left(\frac{47}{78}\right)\)	\(e\left(\frac{19}{78}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{61}{156}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{55}{78}\right)\)
\(\chi_{39326}(6487,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{151}{156}\right)\)	\(e\left(\frac{29}{156}\right)\)	\(e\left(\frac{73}{78}\right)\)	\(e\left(\frac{71}{78}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{35}{156}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{29}{78}\right)\)
\(\chi_{39326}(6627,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{25}{156}\right)\)	\(e\left(\frac{11}{156}\right)\)	\(e\left(\frac{25}{78}\right)\)	\(e\left(\frac{35}{78}\right)\)	\(e\left(\frac{25}{26}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{137}{156}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{11}{78}\right)\)
\(\chi_{39326}(7061,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{156}\right)\)	\(e\left(\frac{53}{156}\right)\)	\(e\left(\frac{7}{78}\right)\)	\(e\left(\frac{41}{78}\right)\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{107}{156}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{53}{78}\right)\)
\(\chi_{39326}(7565,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{156}\right)\)	\(e\left(\frac{35}{156}\right)\)	\(e\left(\frac{37}{78}\right)\)	\(e\left(\frac{5}{78}\right)\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{53}{156}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{35}{78}\right)\)
\(\chi_{39326}(10251,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{71}{156}\right)\)	\(e\left(\frac{25}{156}\right)\)	\(e\left(\frac{71}{78}\right)\)	\(e\left(\frac{37}{78}\right)\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{127}{156}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{25}{78}\right)\)
\(\chi_{39326}(10785,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{156}\right)\)	\(e\left(\frac{119}{156}\right)\)	\(e\left(\frac{1}{78}\right)\)	\(e\left(\frac{17}{78}\right)\)	\(e\left(\frac{1}{26}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{149}{156}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{41}{78}\right)\)
\(\chi_{39326}(11891,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{145}{156}\right)\)	\(e\left(\frac{95}{156}\right)\)	\(e\left(\frac{67}{78}\right)\)	\(e\left(\frac{47}{78}\right)\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{77}{156}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{17}{78}\right)\)
\(\chi_{39326}(11973,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{156}\right)\)	\(e\left(\frac{127}{156}\right)\)	\(e\left(\frac{5}{78}\right)\)	\(e\left(\frac{7}{78}\right)\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{121}{156}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{49}{78}\right)\)
\(\chi_{39326}(12087,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{61}{156}\right)\)	\(e\left(\frac{83}{156}\right)\)	\(e\left(\frac{61}{78}\right)\)	\(e\left(\frac{23}{78}\right)\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{41}{156}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{78}\right)\)
\(\chi_{39326}(13639,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{95}{156}\right)\)	\(e\left(\frac{73}{156}\right)\)	\(e\left(\frac{17}{78}\right)\)	\(e\left(\frac{55}{78}\right)\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{115}{156}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{73}{78}\right)\)
\(\chi_{39326}(14383,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{133}{156}\right)\)	\(e\left(\frac{71}{156}\right)\)	\(e\left(\frac{55}{78}\right)\)	\(e\left(\frac{77}{78}\right)\)	\(e\left(\frac{3}{26}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{5}{156}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{71}{78}\right)\)
\(\chi_{39326}(14451,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{156}\right)\)	\(e\left(\frac{151}{156}\right)\)	\(e\left(\frac{17}{78}\right)\)	\(e\left(\frac{55}{78}\right)\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{37}{156}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{73}{78}\right)\)
\(\chi_{39326}(14901,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{127}{156}\right)\)	\(e\left(\frac{137}{156}\right)\)	\(e\left(\frac{49}{78}\right)\)	\(e\left(\frac{53}{78}\right)\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{47}{156}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{59}{78}\right)\)
\(\chi_{39326}(16117,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{83}{156}\right)\)	\(e\left(\frac{49}{156}\right)\)	\(e\left(\frac{5}{78}\right)\)	\(e\left(\frac{7}{78}\right)\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{43}{156}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{49}{78}\right)\)
\(\chi_{39326}(17839,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{149}{156}\right)\)	\(e\left(\frac{103}{156}\right)\)	\(e\left(\frac{71}{78}\right)\)	\(e\left(\frac{37}{78}\right)\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{49}{156}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{25}{78}\right)\)
\(\chi_{39326}(18807,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{49}{156}\right)\)	\(e\left(\frac{59}{156}\right)\)	\(e\left(\frac{49}{78}\right)\)	\(e\left(\frac{53}{78}\right)\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{125}{156}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{59}{78}\right)\)
\(\chi_{39326}(19325,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{55}{156}\right)\)	\(e\left(\frac{149}{156}\right)\)	\(e\left(\frac{55}{78}\right)\)	\(e\left(\frac{77}{78}\right)\)	\(e\left(\frac{3}{26}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{83}{156}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{71}{78}\right)\)
\(\chi_{39326}(21621,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{139}{156}\right)\)	\(e\left(\frac{5}{156}\right)\)	\(e\left(\frac{61}{78}\right)\)	\(e\left(\frac{23}{78}\right)\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{119}{156}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{78}\right)\)
\(\chi_{39326}(21817,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{67}{156}\right)\)	\(e\left(\frac{17}{156}\right)\)	\(e\left(\frac{67}{78}\right)\)	\(e\left(\frac{47}{78}\right)\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{155}{156}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{17}{78}\right)\)
\(\chi_{39326}(22923,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{79}{156}\right)\)	\(e\left(\frac{41}{156}\right)\)	\(e\left(\frac{1}{78}\right)\)	\(e\left(\frac{17}{78}\right)\)	\(e\left(\frac{1}{26}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{71}{156}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{41}{78}\right)\)
\(\chi_{39326}(23341,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{156}\right)\)	\(e\left(\frac{133}{156}\right)\)	\(e\left(\frac{47}{78}\right)\)	\(e\left(\frac{19}{78}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{139}{156}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{55}{78}\right)\)
\(\chi_{39326}(23481,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{77}{156}\right)\)	\(e\left(\frac{115}{156}\right)\)	\(e\left(\frac{77}{78}\right)\)	\(e\left(\frac{61}{78}\right)\)	\(e\left(\frac{25}{26}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{85}{156}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{37}{78}\right)\)
\(\chi_{39326}(23915,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{156}\right)\)	\(e\left(\frac{1}{156}\right)\)	\(e\left(\frac{59}{78}\right)\)	\(e\left(\frac{67}{78}\right)\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{55}{156}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{78}\right)\)
\(\chi_{39326}(24419,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{89}{156}\right)\)	\(e\left(\frac{139}{156}\right)\)	\(e\left(\frac{11}{78}\right)\)	\(e\left(\frac{31}{78}\right)\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{1}{156}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{61}{78}\right)\)
\(\chi_{39326}(26143,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{115}{156}\right)\)	\(e\left(\frac{113}{156}\right)\)	\(e\left(\frac{37}{78}\right)\)	\(e\left(\frac{5}{78}\right)\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{131}{156}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{35}{78}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Basic properties

Related number fields

First 31 of 48 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	39326.bb
Modulus	$39326$
Conductor	$371$
Order	$156$
Real	no
Primitive	no
Minimal	no
Parity	even

Modulus:	\(39326\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(371\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(156\)	comment:Order sage:chi.multiplicative_order() gp:charorder(g,chi) magma:Order(chi);
Real:	no	comment:Whether the character is real sage:chi.multiplicative_order() <= 2 gp:charorder(g,chi) <= 2 magma:Order(chi) le 2;
Primitive:	no, induced from 371.w	comment:If the character is primitive sage:chi.is_primitive() gp:#znconreyconductor(g,chi)==1 magma:IsPrimitive(chi);
Minimal:	no
Parity:	even	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);