LMFDB - Dirichlet character orbit 38115.nv

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comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(38115, base_ring=CyclotomicField(132)) M = H._module chi = DirichletCharacter(H, M([66,33,88,18])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(1187, 38115)) 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("38115.1187"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$38115$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$12705$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$132$	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 12705.gb	comment:If the character is primitive sage:chi.is_primitive() gp:#znconreyconductor(g,chi)==1 magma:IsPrimitive(chi);
Minimal:	yes
Parity:	odd	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);

Related number fields

Field of values:	$\Q(\zeta_{132})$
Fixed field:	Number field defined by a degree 132 polynomial (not computed)

First 31 of 40 characters in Galois orbit

Character	$-1$	$1$	$2$	$4$	$8$	$13$	$16$	$17$	$19$	$23$	$26$	$29$
$\chi_{38115}(1187,\cdot)$	$-1$	$1$	$e\left(\frac{29}{132}\right)$	$e\left(\frac{29}{66}\right)$	$e\left(\frac{29}{44}\right)$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{13}{132}\right)$	$e\left(\frac{5}{33}\right)$	$e\left(\frac{17}{132}\right)$	$e\left(\frac{49}{66}\right)$	$e\left(\frac{7}{22}\right)$
$\chi_{38115}(1682,\cdot)$	$-1$	$1$	$e\left(\frac{97}{132}\right)$	$e\left(\frac{31}{66}\right)$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{39}{44}\right)$	$e\left(\frac{31}{33}\right)$	$e\left(\frac{89}{132}\right)$	$e\left(\frac{19}{33}\right)$	$e\left(\frac{25}{132}\right)$	$e\left(\frac{41}{66}\right)$	$e\left(\frac{9}{22}\right)$
$\chi_{38115}(2573,\cdot)$	$-1$	$1$	$e\left(\frac{83}{132}\right)$	$e\left(\frac{17}{66}\right)$	$e\left(\frac{39}{44}\right)$	$e\left(\frac{37}{44}\right)$	$e\left(\frac{17}{33}\right)$	$e\left(\frac{19}{132}\right)$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{35}{132}\right)$	$e\left(\frac{31}{66}\right)$	$e\left(\frac{17}{22}\right)$
$\chi_{38115}(3068,\cdot)$	$-1$	$1$	$e\left(\frac{19}{132}\right)$	$e\left(\frac{19}{66}\right)$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{19}{33}\right)$	$e\left(\frac{95}{132}\right)$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{43}{132}\right)$	$e\left(\frac{23}{66}\right)$	$e\left(\frac{19}{22}\right)$
$\chi_{38115}(4652,\cdot)$	$-1$	$1$	$e\left(\frac{65}{132}\right)$	$e\left(\frac{65}{66}\right)$	$e\left(\frac{21}{44}\right)$	$e\left(\frac{3}{44}\right)$	$e\left(\frac{32}{33}\right)$	$e\left(\frac{61}{132}\right)$	$e\left(\frac{26}{33}\right)$	$e\left(\frac{29}{132}\right)$	$e\left(\frac{37}{66}\right)$	$e\left(\frac{21}{22}\right)$
$\chi_{38115}(5147,\cdot)$	$-1$	$1$	$e\left(\frac{1}{132}\right)$	$e\left(\frac{1}{66}\right)$	$e\left(\frac{1}{44}\right)$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{5}{132}\right)$	$e\left(\frac{7}{33}\right)$	$e\left(\frac{37}{132}\right)$	$e\left(\frac{29}{66}\right)$	$e\left(\frac{1}{22}\right)$
$\chi_{38115}(6038,\cdot)$	$-1$	$1$	$e\left(\frac{119}{132}\right)$	$e\left(\frac{53}{66}\right)$	$e\left(\frac{31}{44}\right)$	$e\left(\frac{17}{44}\right)$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{67}{132}\right)$	$e\left(\frac{8}{33}\right)$	$e\left(\frac{47}{132}\right)$	$e\left(\frac{19}{66}\right)$	$e\left(\frac{9}{22}\right)$
$\chi_{38115}(8117,\cdot)$	$-1$	$1$	$e\left(\frac{101}{132}\right)$	$e\left(\frac{35}{66}\right)$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{27}{44}\right)$	$e\left(\frac{2}{33}\right)$	$e\left(\frac{109}{132}\right)$	$e\left(\frac{14}{33}\right)$	$e\left(\frac{41}{132}\right)$	$e\left(\frac{25}{66}\right)$	$e\left(\frac{13}{22}\right)$
$\chi_{38115}(8612,\cdot)$	$-1$	$1$	$e\left(\frac{37}{132}\right)$	$e\left(\frac{37}{66}\right)$	$e\left(\frac{37}{44}\right)$	$e\left(\frac{43}{44}\right)$	$e\left(\frac{4}{33}\right)$	$e\left(\frac{53}{132}\right)$	$e\left(\frac{28}{33}\right)$	$e\left(\frac{49}{132}\right)$	$e\left(\frac{17}{66}\right)$	$e\left(\frac{15}{22}\right)$
$\chi_{38115}(9503,\cdot)$	$-1$	$1$	$e\left(\frac{23}{132}\right)$	$e\left(\frac{23}{66}\right)$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{41}{44}\right)$	$e\left(\frac{23}{33}\right)$	$e\left(\frac{115}{132}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{59}{132}\right)$	$e\left(\frac{7}{66}\right)$	$e\left(\frac{1}{22}\right)$
$\chi_{38115}(9998,\cdot)$	$-1$	$1$	$e\left(\frac{91}{132}\right)$	$e\left(\frac{25}{66}\right)$	$e\left(\frac{3}{44}\right)$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{25}{33}\right)$	$e\left(\frac{59}{132}\right)$	$e\left(\frac{10}{33}\right)$	$e\left(\frac{67}{132}\right)$	$e\left(\frac{65}{66}\right)$	$e\left(\frac{3}{22}\right)$
$\chi_{38115}(11582,\cdot)$	$-1$	$1$	$e\left(\frac{5}{132}\right)$	$e\left(\frac{5}{66}\right)$	$e\left(\frac{5}{44}\right)$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{5}{33}\right)$	$e\left(\frac{25}{132}\right)$	$e\left(\frac{2}{33}\right)$	$e\left(\frac{53}{132}\right)$	$e\left(\frac{13}{66}\right)$	$e\left(\frac{5}{22}\right)$
$\chi_{38115}(12077,\cdot)$	$-1$	$1$	$e\left(\frac{73}{132}\right)$	$e\left(\frac{7}{66}\right)$	$e\left(\frac{29}{44}\right)$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{7}{33}\right)$	$e\left(\frac{101}{132}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{61}{132}\right)$	$e\left(\frac{5}{66}\right)$	$e\left(\frac{7}{22}\right)$
$\chi_{38115}(12968,\cdot)$	$-1$	$1$	$e\left(\frac{59}{132}\right)$	$e\left(\frac{59}{66}\right)$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{21}{44}\right)$	$e\left(\frac{26}{33}\right)$	$e\left(\frac{31}{132}\right)$	$e\left(\frac{17}{33}\right)$	$e\left(\frac{71}{132}\right)$	$e\left(\frac{61}{66}\right)$	$e\left(\frac{15}{22}\right)$
$\chi_{38115}(13463,\cdot)$	$-1$	$1$	$e\left(\frac{127}{132}\right)$	$e\left(\frac{61}{66}\right)$	$e\left(\frac{39}{44}\right)$	$e\left(\frac{37}{44}\right)$	$e\left(\frac{28}{33}\right)$	$e\left(\frac{107}{132}\right)$	$e\left(\frac{31}{33}\right)$	$e\left(\frac{79}{132}\right)$	$e\left(\frac{53}{66}\right)$	$e\left(\frac{17}{22}\right)$
$\chi_{38115}(15047,\cdot)$	$-1$	$1$	$e\left(\frac{41}{132}\right)$	$e\left(\frac{41}{66}\right)$	$e\left(\frac{41}{44}\right)$	$e\left(\frac{31}{44}\right)$	$e\left(\frac{8}{33}\right)$	$e\left(\frac{73}{132}\right)$	$e\left(\frac{23}{33}\right)$	$e\left(\frac{65}{132}\right)$	$e\left(\frac{1}{66}\right)$	$e\left(\frac{19}{22}\right)$
$\chi_{38115}(15542,\cdot)$	$-1$	$1$	$e\left(\frac{109}{132}\right)$	$e\left(\frac{43}{66}\right)$	$e\left(\frac{21}{44}\right)$	$e\left(\frac{3}{44}\right)$	$e\left(\frac{10}{33}\right)$	$e\left(\frac{17}{132}\right)$	$e\left(\frac{4}{33}\right)$	$e\left(\frac{73}{132}\right)$	$e\left(\frac{59}{66}\right)$	$e\left(\frac{21}{22}\right)$
$\chi_{38115}(16433,\cdot)$	$-1$	$1$	$e\left(\frac{95}{132}\right)$	$e\left(\frac{29}{66}\right)$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{1}{44}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{79}{132}\right)$	$e\left(\frac{5}{33}\right)$	$e\left(\frac{83}{132}\right)$	$e\left(\frac{49}{66}\right)$	$e\left(\frac{7}{22}\right)$
$\chi_{38115}(16928,\cdot)$	$-1$	$1$	$e\left(\frac{31}{132}\right)$	$e\left(\frac{31}{66}\right)$	$e\left(\frac{31}{44}\right)$	$e\left(\frac{17}{44}\right)$	$e\left(\frac{31}{33}\right)$	$e\left(\frac{23}{132}\right)$	$e\left(\frac{19}{33}\right)$	$e\left(\frac{91}{132}\right)$	$e\left(\frac{41}{66}\right)$	$e\left(\frac{9}{22}\right)$
$\chi_{38115}(19007,\cdot)$	$-1$	$1$	$e\left(\frac{13}{132}\right)$	$e\left(\frac{13}{66}\right)$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{27}{44}\right)$	$e\left(\frac{13}{33}\right)$	$e\left(\frac{65}{132}\right)$	$e\left(\frac{25}{33}\right)$	$e\left(\frac{85}{132}\right)$	$e\left(\frac{47}{66}\right)$	$e\left(\frac{13}{22}\right)$
$\chi_{38115}(19898,\cdot)$	$-1$	$1$	$e\left(\frac{131}{132}\right)$	$e\left(\frac{65}{66}\right)$	$e\left(\frac{43}{44}\right)$	$e\left(\frac{25}{44}\right)$	$e\left(\frac{32}{33}\right)$	$e\left(\frac{127}{132}\right)$	$e\left(\frac{26}{33}\right)$	$e\left(\frac{95}{132}\right)$	$e\left(\frac{37}{66}\right)$	$e\left(\frac{21}{22}\right)$
$\chi_{38115}(20393,\cdot)$	$-1$	$1$	$e\left(\frac{67}{132}\right)$	$e\left(\frac{1}{66}\right)$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{41}{44}\right)$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{71}{132}\right)$	$e\left(\frac{7}{33}\right)$	$e\left(\frac{103}{132}\right)$	$e\left(\frac{29}{66}\right)$	$e\left(\frac{1}{22}\right)$
$\chi_{38115}(21977,\cdot)$	$-1$	$1$	$e\left(\frac{113}{132}\right)$	$e\left(\frac{47}{66}\right)$	$e\left(\frac{25}{44}\right)$	$e\left(\frac{35}{44}\right)$	$e\left(\frac{14}{33}\right)$	$e\left(\frac{37}{132}\right)$	$e\left(\frac{32}{33}\right)$	$e\left(\frac{89}{132}\right)$	$e\left(\frac{43}{66}\right)$	$e\left(\frac{3}{22}\right)$
$\chi_{38115}(22472,\cdot)$	$-1$	$1$	$e\left(\frac{49}{132}\right)$	$e\left(\frac{49}{66}\right)$	$e\left(\frac{5}{44}\right)$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{113}{132}\right)$	$e\left(\frac{13}{33}\right)$	$e\left(\frac{97}{132}\right)$	$e\left(\frac{35}{66}\right)$	$e\left(\frac{5}{22}\right)$
$\chi_{38115}(23363,\cdot)$	$-1$	$1$	$e\left(\frac{35}{132}\right)$	$e\left(\frac{35}{66}\right)$	$e\left(\frac{35}{44}\right)$	$e\left(\frac{5}{44}\right)$	$e\left(\frac{2}{33}\right)$	$e\left(\frac{43}{132}\right)$	$e\left(\frac{14}{33}\right)$	$e\left(\frac{107}{132}\right)$	$e\left(\frac{25}{66}\right)$	$e\left(\frac{13}{22}\right)$
$\chi_{38115}(23858,\cdot)$	$-1$	$1$	$e\left(\frac{103}{132}\right)$	$e\left(\frac{37}{66}\right)$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{21}{44}\right)$	$e\left(\frac{4}{33}\right)$	$e\left(\frac{119}{132}\right)$	$e\left(\frac{28}{33}\right)$	$e\left(\frac{115}{132}\right)$	$e\left(\frac{17}{66}\right)$	$e\left(\frac{15}{22}\right)$
$\chi_{38115}(25442,\cdot)$	$-1$	$1$	$e\left(\frac{17}{132}\right)$	$e\left(\frac{17}{66}\right)$	$e\left(\frac{17}{44}\right)$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{17}{33}\right)$	$e\left(\frac{85}{132}\right)$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{101}{132}\right)$	$e\left(\frac{31}{66}\right)$	$e\left(\frac{17}{22}\right)$
$\chi_{38115}(25937,\cdot)$	$-1$	$1$	$e\left(\frac{85}{132}\right)$	$e\left(\frac{19}{66}\right)$	$e\left(\frac{41}{44}\right)$	$e\left(\frac{31}{44}\right)$	$e\left(\frac{19}{33}\right)$	$e\left(\frac{29}{132}\right)$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{109}{132}\right)$	$e\left(\frac{23}{66}\right)$	$e\left(\frac{19}{22}\right)$
$\chi_{38115}(26828,\cdot)$	$-1$	$1$	$e\left(\frac{71}{132}\right)$	$e\left(\frac{5}{66}\right)$	$e\left(\frac{27}{44}\right)$	$e\left(\frac{29}{44}\right)$	$e\left(\frac{5}{33}\right)$	$e\left(\frac{91}{132}\right)$	$e\left(\frac{2}{33}\right)$	$e\left(\frac{119}{132}\right)$	$e\left(\frac{13}{66}\right)$	$e\left(\frac{5}{22}\right)$
$\chi_{38115}(27323,\cdot)$	$-1$	$1$	$e\left(\frac{7}{132}\right)$	$e\left(\frac{7}{66}\right)$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{1}{44}\right)$	$e\left(\frac{7}{33}\right)$	$e\left(\frac{35}{132}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{127}{132}\right)$	$e\left(\frac{5}{66}\right)$	$e\left(\frac{7}{22}\right)$
$\chi_{38115}(28907,\cdot)$	$-1$	$1$	$e\left(\frac{53}{132}\right)$	$e\left(\frac{53}{66}\right)$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{39}{44}\right)$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{1}{132}\right)$	$e\left(\frac{8}{33}\right)$	$e\left(\frac{113}{132}\right)$	$e\left(\frac{19}{66}\right)$	$e\left(\frac{9}{22}\right)$

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	\(-1\)	\(1\)	\(2\)	\(4\)	\(8\)	\(13\)	\(16\)	\(17\)	\(19\)	\(23\)	\(26\)	\(29\)
\(\chi_{38115}(1187,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{29}{132}\right)\)	\(e\left(\frac{29}{66}\right)\)	\(e\left(\frac{29}{44}\right)\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{13}{132}\right)\)	\(e\left(\frac{5}{33}\right)\)	\(e\left(\frac{17}{132}\right)\)	\(e\left(\frac{49}{66}\right)\)	\(e\left(\frac{7}{22}\right)\)
\(\chi_{38115}(1682,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{97}{132}\right)\)	\(e\left(\frac{31}{66}\right)\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{39}{44}\right)\)	\(e\left(\frac{31}{33}\right)\)	\(e\left(\frac{89}{132}\right)\)	\(e\left(\frac{19}{33}\right)\)	\(e\left(\frac{25}{132}\right)\)	\(e\left(\frac{41}{66}\right)\)	\(e\left(\frac{9}{22}\right)\)
\(\chi_{38115}(2573,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{83}{132}\right)\)	\(e\left(\frac{17}{66}\right)\)	\(e\left(\frac{39}{44}\right)\)	\(e\left(\frac{37}{44}\right)\)	\(e\left(\frac{17}{33}\right)\)	\(e\left(\frac{19}{132}\right)\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{35}{132}\right)\)	\(e\left(\frac{31}{66}\right)\)	\(e\left(\frac{17}{22}\right)\)
\(\chi_{38115}(3068,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{19}{132}\right)\)	\(e\left(\frac{19}{66}\right)\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{19}{33}\right)\)	\(e\left(\frac{95}{132}\right)\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{43}{132}\right)\)	\(e\left(\frac{23}{66}\right)\)	\(e\left(\frac{19}{22}\right)\)
\(\chi_{38115}(4652,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{65}{132}\right)\)	\(e\left(\frac{65}{66}\right)\)	\(e\left(\frac{21}{44}\right)\)	\(e\left(\frac{3}{44}\right)\)	\(e\left(\frac{32}{33}\right)\)	\(e\left(\frac{61}{132}\right)\)	\(e\left(\frac{26}{33}\right)\)	\(e\left(\frac{29}{132}\right)\)	\(e\left(\frac{37}{66}\right)\)	\(e\left(\frac{21}{22}\right)\)
\(\chi_{38115}(5147,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{132}\right)\)	\(e\left(\frac{1}{66}\right)\)	\(e\left(\frac{1}{44}\right)\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{5}{132}\right)\)	\(e\left(\frac{7}{33}\right)\)	\(e\left(\frac{37}{132}\right)\)	\(e\left(\frac{29}{66}\right)\)	\(e\left(\frac{1}{22}\right)\)
\(\chi_{38115}(6038,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{119}{132}\right)\)	\(e\left(\frac{53}{66}\right)\)	\(e\left(\frac{31}{44}\right)\)	\(e\left(\frac{17}{44}\right)\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{67}{132}\right)\)	\(e\left(\frac{8}{33}\right)\)	\(e\left(\frac{47}{132}\right)\)	\(e\left(\frac{19}{66}\right)\)	\(e\left(\frac{9}{22}\right)\)
\(\chi_{38115}(8117,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{101}{132}\right)\)	\(e\left(\frac{35}{66}\right)\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{27}{44}\right)\)	\(e\left(\frac{2}{33}\right)\)	\(e\left(\frac{109}{132}\right)\)	\(e\left(\frac{14}{33}\right)\)	\(e\left(\frac{41}{132}\right)\)	\(e\left(\frac{25}{66}\right)\)	\(e\left(\frac{13}{22}\right)\)
\(\chi_{38115}(8612,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{37}{132}\right)\)	\(e\left(\frac{37}{66}\right)\)	\(e\left(\frac{37}{44}\right)\)	\(e\left(\frac{43}{44}\right)\)	\(e\left(\frac{4}{33}\right)\)	\(e\left(\frac{53}{132}\right)\)	\(e\left(\frac{28}{33}\right)\)	\(e\left(\frac{49}{132}\right)\)	\(e\left(\frac{17}{66}\right)\)	\(e\left(\frac{15}{22}\right)\)
\(\chi_{38115}(9503,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{23}{132}\right)\)	\(e\left(\frac{23}{66}\right)\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{41}{44}\right)\)	\(e\left(\frac{23}{33}\right)\)	\(e\left(\frac{115}{132}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{59}{132}\right)\)	\(e\left(\frac{7}{66}\right)\)	\(e\left(\frac{1}{22}\right)\)
\(\chi_{38115}(9998,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{91}{132}\right)\)	\(e\left(\frac{25}{66}\right)\)	\(e\left(\frac{3}{44}\right)\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{25}{33}\right)\)	\(e\left(\frac{59}{132}\right)\)	\(e\left(\frac{10}{33}\right)\)	\(e\left(\frac{67}{132}\right)\)	\(e\left(\frac{65}{66}\right)\)	\(e\left(\frac{3}{22}\right)\)
\(\chi_{38115}(11582,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{5}{132}\right)\)	\(e\left(\frac{5}{66}\right)\)	\(e\left(\frac{5}{44}\right)\)	\(e\left(\frac{7}{44}\right)\)	\(e\left(\frac{5}{33}\right)\)	\(e\left(\frac{25}{132}\right)\)	\(e\left(\frac{2}{33}\right)\)	\(e\left(\frac{53}{132}\right)\)	\(e\left(\frac{13}{66}\right)\)	\(e\left(\frac{5}{22}\right)\)
\(\chi_{38115}(12077,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{73}{132}\right)\)	\(e\left(\frac{7}{66}\right)\)	\(e\left(\frac{29}{44}\right)\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{7}{33}\right)\)	\(e\left(\frac{101}{132}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{61}{132}\right)\)	\(e\left(\frac{5}{66}\right)\)	\(e\left(\frac{7}{22}\right)\)
\(\chi_{38115}(12968,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{59}{132}\right)\)	\(e\left(\frac{59}{66}\right)\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{21}{44}\right)\)	\(e\left(\frac{26}{33}\right)\)	\(e\left(\frac{31}{132}\right)\)	\(e\left(\frac{17}{33}\right)\)	\(e\left(\frac{71}{132}\right)\)	\(e\left(\frac{61}{66}\right)\)	\(e\left(\frac{15}{22}\right)\)
\(\chi_{38115}(13463,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{127}{132}\right)\)	\(e\left(\frac{61}{66}\right)\)	\(e\left(\frac{39}{44}\right)\)	\(e\left(\frac{37}{44}\right)\)	\(e\left(\frac{28}{33}\right)\)	\(e\left(\frac{107}{132}\right)\)	\(e\left(\frac{31}{33}\right)\)	\(e\left(\frac{79}{132}\right)\)	\(e\left(\frac{53}{66}\right)\)	\(e\left(\frac{17}{22}\right)\)
\(\chi_{38115}(15047,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{41}{132}\right)\)	\(e\left(\frac{41}{66}\right)\)	\(e\left(\frac{41}{44}\right)\)	\(e\left(\frac{31}{44}\right)\)	\(e\left(\frac{8}{33}\right)\)	\(e\left(\frac{73}{132}\right)\)	\(e\left(\frac{23}{33}\right)\)	\(e\left(\frac{65}{132}\right)\)	\(e\left(\frac{1}{66}\right)\)	\(e\left(\frac{19}{22}\right)\)
\(\chi_{38115}(15542,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{109}{132}\right)\)	\(e\left(\frac{43}{66}\right)\)	\(e\left(\frac{21}{44}\right)\)	\(e\left(\frac{3}{44}\right)\)	\(e\left(\frac{10}{33}\right)\)	\(e\left(\frac{17}{132}\right)\)	\(e\left(\frac{4}{33}\right)\)	\(e\left(\frac{73}{132}\right)\)	\(e\left(\frac{59}{66}\right)\)	\(e\left(\frac{21}{22}\right)\)
\(\chi_{38115}(16433,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{95}{132}\right)\)	\(e\left(\frac{29}{66}\right)\)	\(e\left(\frac{7}{44}\right)\)	\(e\left(\frac{1}{44}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{79}{132}\right)\)	\(e\left(\frac{5}{33}\right)\)	\(e\left(\frac{83}{132}\right)\)	\(e\left(\frac{49}{66}\right)\)	\(e\left(\frac{7}{22}\right)\)
\(\chi_{38115}(16928,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{31}{132}\right)\)	\(e\left(\frac{31}{66}\right)\)	\(e\left(\frac{31}{44}\right)\)	\(e\left(\frac{17}{44}\right)\)	\(e\left(\frac{31}{33}\right)\)	\(e\left(\frac{23}{132}\right)\)	\(e\left(\frac{19}{33}\right)\)	\(e\left(\frac{91}{132}\right)\)	\(e\left(\frac{41}{66}\right)\)	\(e\left(\frac{9}{22}\right)\)
\(\chi_{38115}(19007,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{13}{132}\right)\)	\(e\left(\frac{13}{66}\right)\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{27}{44}\right)\)	\(e\left(\frac{13}{33}\right)\)	\(e\left(\frac{65}{132}\right)\)	\(e\left(\frac{25}{33}\right)\)	\(e\left(\frac{85}{132}\right)\)	\(e\left(\frac{47}{66}\right)\)	\(e\left(\frac{13}{22}\right)\)
\(\chi_{38115}(19898,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{131}{132}\right)\)	\(e\left(\frac{65}{66}\right)\)	\(e\left(\frac{43}{44}\right)\)	\(e\left(\frac{25}{44}\right)\)	\(e\left(\frac{32}{33}\right)\)	\(e\left(\frac{127}{132}\right)\)	\(e\left(\frac{26}{33}\right)\)	\(e\left(\frac{95}{132}\right)\)	\(e\left(\frac{37}{66}\right)\)	\(e\left(\frac{21}{22}\right)\)
\(\chi_{38115}(20393,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{67}{132}\right)\)	\(e\left(\frac{1}{66}\right)\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{41}{44}\right)\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{71}{132}\right)\)	\(e\left(\frac{7}{33}\right)\)	\(e\left(\frac{103}{132}\right)\)	\(e\left(\frac{29}{66}\right)\)	\(e\left(\frac{1}{22}\right)\)
\(\chi_{38115}(21977,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{113}{132}\right)\)	\(e\left(\frac{47}{66}\right)\)	\(e\left(\frac{25}{44}\right)\)	\(e\left(\frac{35}{44}\right)\)	\(e\left(\frac{14}{33}\right)\)	\(e\left(\frac{37}{132}\right)\)	\(e\left(\frac{32}{33}\right)\)	\(e\left(\frac{89}{132}\right)\)	\(e\left(\frac{43}{66}\right)\)	\(e\left(\frac{3}{22}\right)\)
\(\chi_{38115}(22472,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{49}{132}\right)\)	\(e\left(\frac{49}{66}\right)\)	\(e\left(\frac{5}{44}\right)\)	\(e\left(\frac{7}{44}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{113}{132}\right)\)	\(e\left(\frac{13}{33}\right)\)	\(e\left(\frac{97}{132}\right)\)	\(e\left(\frac{35}{66}\right)\)	\(e\left(\frac{5}{22}\right)\)
\(\chi_{38115}(23363,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{35}{132}\right)\)	\(e\left(\frac{35}{66}\right)\)	\(e\left(\frac{35}{44}\right)\)	\(e\left(\frac{5}{44}\right)\)	\(e\left(\frac{2}{33}\right)\)	\(e\left(\frac{43}{132}\right)\)	\(e\left(\frac{14}{33}\right)\)	\(e\left(\frac{107}{132}\right)\)	\(e\left(\frac{25}{66}\right)\)	\(e\left(\frac{13}{22}\right)\)
\(\chi_{38115}(23858,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{103}{132}\right)\)	\(e\left(\frac{37}{66}\right)\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{21}{44}\right)\)	\(e\left(\frac{4}{33}\right)\)	\(e\left(\frac{119}{132}\right)\)	\(e\left(\frac{28}{33}\right)\)	\(e\left(\frac{115}{132}\right)\)	\(e\left(\frac{17}{66}\right)\)	\(e\left(\frac{15}{22}\right)\)
\(\chi_{38115}(25442,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{17}{132}\right)\)	\(e\left(\frac{17}{66}\right)\)	\(e\left(\frac{17}{44}\right)\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{17}{33}\right)\)	\(e\left(\frac{85}{132}\right)\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{101}{132}\right)\)	\(e\left(\frac{31}{66}\right)\)	\(e\left(\frac{17}{22}\right)\)
\(\chi_{38115}(25937,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{85}{132}\right)\)	\(e\left(\frac{19}{66}\right)\)	\(e\left(\frac{41}{44}\right)\)	\(e\left(\frac{31}{44}\right)\)	\(e\left(\frac{19}{33}\right)\)	\(e\left(\frac{29}{132}\right)\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{109}{132}\right)\)	\(e\left(\frac{23}{66}\right)\)	\(e\left(\frac{19}{22}\right)\)
\(\chi_{38115}(26828,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{71}{132}\right)\)	\(e\left(\frac{5}{66}\right)\)	\(e\left(\frac{27}{44}\right)\)	\(e\left(\frac{29}{44}\right)\)	\(e\left(\frac{5}{33}\right)\)	\(e\left(\frac{91}{132}\right)\)	\(e\left(\frac{2}{33}\right)\)	\(e\left(\frac{119}{132}\right)\)	\(e\left(\frac{13}{66}\right)\)	\(e\left(\frac{5}{22}\right)\)
\(\chi_{38115}(27323,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{7}{132}\right)\)	\(e\left(\frac{7}{66}\right)\)	\(e\left(\frac{7}{44}\right)\)	\(e\left(\frac{1}{44}\right)\)	\(e\left(\frac{7}{33}\right)\)	\(e\left(\frac{35}{132}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{127}{132}\right)\)	\(e\left(\frac{5}{66}\right)\)	\(e\left(\frac{7}{22}\right)\)
\(\chi_{38115}(28907,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{53}{132}\right)\)	\(e\left(\frac{53}{66}\right)\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{39}{44}\right)\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{1}{132}\right)\)	\(e\left(\frac{8}{33}\right)\)	\(e\left(\frac{113}{132}\right)\)	\(e\left(\frac{19}{66}\right)\)	\(e\left(\frac{9}{22}\right)\)

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First 31 of 40 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	38115.nv
Modulus	$38115$
Conductor	$12705$
Order	$132$
Real	no
Primitive	no
Minimal	yes
Parity	odd

Modulus:	\(38115\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(12705\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(132\)	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 12705.gb	comment:If the character is primitive sage:chi.is_primitive() gp:#znconreyconductor(g,chi)==1 magma:IsPrimitive(chi);
Minimal:	yes
Parity:	odd	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);