LMFDB - Dirichlet character orbit 39195.bpz

Show commands: Magma / Pari/GP / SageMath

comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(39195, base_ring=CyclotomicField(132)) M = H._module chi = DirichletCharacter(H, M([66,99,121,94])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(98, 39195)) 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("39195.98"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$39195$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$13065$	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 13065.pf	comment:If the character is primitive sage:chi.is_primitive() gp:#znconreyconductor(g,chi)==1 magma:IsPrimitive(chi);
Minimal:	yes
Parity:	even	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	$-1$	$1$	$2$	$4$	$7$	$8$	$11$	$14$	$16$	$17$	$19$	$22$
$\chi_{39195}(98,\cdot)$	$1$	$1$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{25}{33}\right)$	$e\left(\frac{7}{33}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{41}{44}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{17}{33}\right)$	$e\left(\frac{29}{44}\right)$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{107}{132}\right)$
$\chi_{39195}(422,\cdot)$	$1$	$1$	$e\left(\frac{14}{33}\right)$	$e\left(\frac{28}{33}\right)$	$e\left(\frac{25}{33}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{27}{44}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{23}{33}\right)$	$e\left(\frac{3}{44}\right)$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{5}{132}\right)$
$\chi_{39195}(2663,\cdot)$	$1$	$1$	$e\left(\frac{10}{33}\right)$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{32}{33}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{7}{33}\right)$	$e\left(\frac{21}{44}\right)$	$e\left(\frac{5}{44}\right)$	$e\left(\frac{79}{132}\right)$
$\chi_{39195}(3932,\cdot)$	$1$	$1$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{7}{33}\right)$	$e\left(\frac{31}{33}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{14}{33}\right)$	$e\left(\frac{31}{44}\right)$	$e\left(\frac{43}{44}\right)$	$e\left(\frac{125}{132}\right)$
$\chi_{39195}(6272,\cdot)$	$1$	$1$	$e\left(\frac{32}{33}\right)$	$e\left(\frac{31}{33}\right)$	$e\left(\frac{10}{33}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{35}{44}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{43}{44}\right)$	$e\left(\frac{27}{44}\right)$	$e\left(\frac{101}{132}\right)$
$\chi_{39195}(6533,\cdot)$	$1$	$1$	$e\left(\frac{5}{33}\right)$	$e\left(\frac{10}{33}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{1}{44}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{5}{44}\right)$	$e\left(\frac{41}{44}\right)$	$e\left(\frac{23}{132}\right)$
$\chi_{39195}(7217,\cdot)$	$1$	$1$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{32}{33}\right)$	$e\left(\frac{5}{33}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{31}{33}\right)$	$e\left(\frac{27}{44}\right)$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{1}{132}\right)$
$\chi_{39195}(8972,\cdot)$	$1$	$1$	$e\left(\frac{31}{33}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{25}{33}\right)$	$e\left(\frac{31}{44}\right)$	$e\left(\frac{43}{44}\right)$	$e\left(\frac{37}{132}\right)$
$\chi_{39195}(9458,\cdot)$	$1$	$1$	$e\left(\frac{2}{33}\right)$	$e\left(\frac{4}{33}\right)$	$e\left(\frac{13}{33}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{29}{44}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{8}{33}\right)$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{1}{44}\right)$	$e\left(\frac{95}{132}\right)$
$\chi_{39195}(10952,\cdot)$	$1$	$1$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{25}{33}\right)$	$e\left(\frac{7}{33}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{17}{33}\right)$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{31}{44}\right)$	$e\left(\frac{41}{132}\right)$
$\chi_{39195}(11438,\cdot)$	$1$	$1$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{32}{33}\right)$	$e\left(\frac{5}{33}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{1}{44}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{31}{33}\right)$	$e\left(\frac{5}{44}\right)$	$e\left(\frac{41}{44}\right)$	$e\left(\frac{67}{132}\right)$
$\chi_{39195}(13067,\cdot)$	$1$	$1$	$e\left(\frac{28}{33}\right)$	$e\left(\frac{23}{33}\right)$	$e\left(\frac{17}{33}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{43}{44}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{13}{33}\right)$	$e\left(\frac{39}{44}\right)$	$e\left(\frac{3}{44}\right)$	$e\left(\frac{109}{132}\right)$
$\chi_{39195}(13193,\cdot)$	$1$	$1$	$e\left(\frac{31}{33}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{37}{44}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{25}{33}\right)$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{21}{44}\right)$	$e\left(\frac{103}{132}\right)$
$\chi_{39195}(13652,\cdot)$	$1$	$1$	$e\left(\frac{13}{33}\right)$	$e\left(\frac{26}{33}\right)$	$e\left(\frac{2}{33}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{19}{33}\right)$	$e\left(\frac{35}{44}\right)$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{73}{132}\right)$
$\chi_{39195}(15308,\cdot)$	$1$	$1$	$e\left(\frac{8}{33}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{19}{33}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{17}{44}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{32}{33}\right)$	$e\left(\frac{41}{44}\right)$	$e\left(\frac{37}{44}\right)$	$e\left(\frac{83}{132}\right)$
$\chi_{39195}(16478,\cdot)$	$1$	$1$	$e\left(\frac{23}{33}\right)$	$e\left(\frac{13}{33}\right)$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{26}{33}\right)$	$e\left(\frac{1}{44}\right)$	$e\left(\frac{17}{44}\right)$	$e\left(\frac{119}{132}\right)$
$\chi_{39195}(16577,\cdot)$	$1$	$1$	$e\left(\frac{7}{33}\right)$	$e\left(\frac{14}{33}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{28}{33}\right)$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{31}{44}\right)$	$e\left(\frac{85}{132}\right)$
$\chi_{39195}(17288,\cdot)$	$1$	$1$	$e\left(\frac{28}{33}\right)$	$e\left(\frac{23}{33}\right)$	$e\left(\frac{17}{33}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{21}{44}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{13}{33}\right)$	$e\left(\frac{17}{44}\right)$	$e\left(\frac{25}{44}\right)$	$e\left(\frac{43}{132}\right)$
$\chi_{39195}(17387,\cdot)$	$1$	$1$	$e\left(\frac{5}{33}\right)$	$e\left(\frac{10}{33}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{27}{44}\right)$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{89}{132}\right)$
$\chi_{39195}(17873,\cdot)$	$1$	$1$	$e\left(\frac{13}{33}\right)$	$e\left(\frac{26}{33}\right)$	$e\left(\frac{2}{33}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{29}{44}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{19}{33}\right)$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{1}{44}\right)$	$e\left(\frac{7}{132}\right)$
$\chi_{39195}(20312,\cdot)$	$1$	$1$	$e\left(\frac{2}{33}\right)$	$e\left(\frac{4}{33}\right)$	$e\left(\frac{13}{33}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{8}{33}\right)$	$e\left(\frac{35}{44}\right)$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{29}{132}\right)$
$\chi_{39195}(20798,\cdot)$	$1$	$1$	$e\left(\frac{7}{33}\right)$	$e\left(\frac{14}{33}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{41}{44}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{28}{33}\right)$	$e\left(\frac{29}{44}\right)$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{19}{132}\right)$
$\chi_{39195}(21257,\cdot)$	$1$	$1$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{2}{33}\right)$	$e\left(\frac{23}{33}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{31}{44}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{4}{33}\right)$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{39}{44}\right)$	$e\left(\frac{97}{132}\right)$
$\chi_{39195}(23597,\cdot)$	$1$	$1$	$e\left(\frac{4}{33}\right)$	$e\left(\frac{8}{33}\right)$	$e\left(\frac{26}{33}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{3}{44}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{35}{44}\right)$	$e\left(\frac{25}{132}\right)$
$\chi_{39195}(24668,\cdot)$	$1$	$1$	$e\left(\frac{26}{33}\right)$	$e\left(\frac{19}{33}\right)$	$e\left(\frac{4}{33}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{25}{44}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{5}{33}\right)$	$e\left(\frac{37}{44}\right)$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{47}{132}\right)$
$\chi_{39195}(24767,\cdot)$	$1$	$1$	$e\left(\frac{25}{33}\right)$	$e\left(\frac{17}{33}\right)$	$e\left(\frac{14}{33}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{27}{44}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{3}{44}\right)$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{49}{132}\right)$
$\chi_{39195}(25478,\cdot)$	$1$	$1$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{2}{33}\right)$	$e\left(\frac{23}{33}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{4}{33}\right)$	$e\left(\frac{1}{44}\right)$	$e\left(\frac{17}{44}\right)$	$e\left(\frac{31}{132}\right)$
$\chi_{39195}(26162,\cdot)$	$1$	$1$	$e\left(\frac{8}{33}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{19}{33}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{39}{44}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{32}{33}\right)$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{17}{132}\right)$
$\chi_{39195}(26522,\cdot)$	$1$	$1$	$e\left(\frac{19}{33}\right)$	$e\left(\frac{5}{33}\right)$	$e\left(\frac{8}{33}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{39}{44}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{10}{33}\right)$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{61}{132}\right)$
$\chi_{39195}(27008,\cdot)$	$1$	$1$	$e\left(\frac{17}{33}\right)$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{28}{33}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{21}{44}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{2}{33}\right)$	$e\left(\frac{17}{44}\right)$	$e\left(\frac{25}{44}\right)$	$e\left(\frac{131}{132}\right)$
$\chi_{39195}(27332,\cdot)$	$1$	$1$	$e\left(\frac{23}{33}\right)$	$e\left(\frac{13}{33}\right)$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{31}{44}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{26}{33}\right)$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{39}{44}\right)$	$e\left(\frac{53}{132}\right)$

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	\(-1\)	\(1\)	\(2\)	\(4\)	\(7\)	\(8\)	\(11\)	\(14\)	\(16\)	\(17\)	\(19\)	\(22\)
\(\chi_{39195}(98,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{25}{33}\right)\)	\(e\left(\frac{7}{33}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{41}{44}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{17}{33}\right)\)	\(e\left(\frac{29}{44}\right)\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{107}{132}\right)\)
\(\chi_{39195}(422,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{14}{33}\right)\)	\(e\left(\frac{28}{33}\right)\)	\(e\left(\frac{25}{33}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{27}{44}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{23}{33}\right)\)	\(e\left(\frac{3}{44}\right)\)	\(e\left(\frac{7}{44}\right)\)	\(e\left(\frac{5}{132}\right)\)
\(\chi_{39195}(2663,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{10}{33}\right)\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{32}{33}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{7}{33}\right)\)	\(e\left(\frac{21}{44}\right)\)	\(e\left(\frac{5}{44}\right)\)	\(e\left(\frac{79}{132}\right)\)
\(\chi_{39195}(3932,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{7}{33}\right)\)	\(e\left(\frac{31}{33}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{14}{33}\right)\)	\(e\left(\frac{31}{44}\right)\)	\(e\left(\frac{43}{44}\right)\)	\(e\left(\frac{125}{132}\right)\)
\(\chi_{39195}(6272,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{32}{33}\right)\)	\(e\left(\frac{31}{33}\right)\)	\(e\left(\frac{10}{33}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{35}{44}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{43}{44}\right)\)	\(e\left(\frac{27}{44}\right)\)	\(e\left(\frac{101}{132}\right)\)
\(\chi_{39195}(6533,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{33}\right)\)	\(e\left(\frac{10}{33}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{1}{44}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{5}{44}\right)\)	\(e\left(\frac{41}{44}\right)\)	\(e\left(\frac{23}{132}\right)\)
\(\chi_{39195}(7217,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{32}{33}\right)\)	\(e\left(\frac{5}{33}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{31}{33}\right)\)	\(e\left(\frac{27}{44}\right)\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{1}{132}\right)\)
\(\chi_{39195}(8972,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{33}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{25}{33}\right)\)	\(e\left(\frac{31}{44}\right)\)	\(e\left(\frac{43}{44}\right)\)	\(e\left(\frac{37}{132}\right)\)
\(\chi_{39195}(9458,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{33}\right)\)	\(e\left(\frac{4}{33}\right)\)	\(e\left(\frac{13}{33}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{29}{44}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{8}{33}\right)\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{1}{44}\right)\)	\(e\left(\frac{95}{132}\right)\)
\(\chi_{39195}(10952,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{25}{33}\right)\)	\(e\left(\frac{7}{33}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{17}{33}\right)\)	\(e\left(\frac{7}{44}\right)\)	\(e\left(\frac{31}{44}\right)\)	\(e\left(\frac{41}{132}\right)\)
\(\chi_{39195}(11438,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{32}{33}\right)\)	\(e\left(\frac{5}{33}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{1}{44}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{31}{33}\right)\)	\(e\left(\frac{5}{44}\right)\)	\(e\left(\frac{41}{44}\right)\)	\(e\left(\frac{67}{132}\right)\)
\(\chi_{39195}(13067,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{28}{33}\right)\)	\(e\left(\frac{23}{33}\right)\)	\(e\left(\frac{17}{33}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{43}{44}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{13}{33}\right)\)	\(e\left(\frac{39}{44}\right)\)	\(e\left(\frac{3}{44}\right)\)	\(e\left(\frac{109}{132}\right)\)
\(\chi_{39195}(13193,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{33}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{37}{44}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{25}{33}\right)\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{21}{44}\right)\)	\(e\left(\frac{103}{132}\right)\)
\(\chi_{39195}(13652,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{33}\right)\)	\(e\left(\frac{26}{33}\right)\)	\(e\left(\frac{2}{33}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{7}{44}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{19}{33}\right)\)	\(e\left(\frac{35}{44}\right)\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{73}{132}\right)\)
\(\chi_{39195}(15308,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{8}{33}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{19}{33}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{17}{44}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{32}{33}\right)\)	\(e\left(\frac{41}{44}\right)\)	\(e\left(\frac{37}{44}\right)\)	\(e\left(\frac{83}{132}\right)\)
\(\chi_{39195}(16478,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{33}\right)\)	\(e\left(\frac{13}{33}\right)\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{26}{33}\right)\)	\(e\left(\frac{1}{44}\right)\)	\(e\left(\frac{17}{44}\right)\)	\(e\left(\frac{119}{132}\right)\)
\(\chi_{39195}(16577,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{33}\right)\)	\(e\left(\frac{14}{33}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{28}{33}\right)\)	\(e\left(\frac{7}{44}\right)\)	\(e\left(\frac{31}{44}\right)\)	\(e\left(\frac{85}{132}\right)\)
\(\chi_{39195}(17288,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{28}{33}\right)\)	\(e\left(\frac{23}{33}\right)\)	\(e\left(\frac{17}{33}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{21}{44}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{13}{33}\right)\)	\(e\left(\frac{17}{44}\right)\)	\(e\left(\frac{25}{44}\right)\)	\(e\left(\frac{43}{132}\right)\)
\(\chi_{39195}(17387,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{33}\right)\)	\(e\left(\frac{10}{33}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{27}{44}\right)\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{89}{132}\right)\)
\(\chi_{39195}(17873,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{33}\right)\)	\(e\left(\frac{26}{33}\right)\)	\(e\left(\frac{2}{33}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{29}{44}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{19}{33}\right)\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{1}{44}\right)\)	\(e\left(\frac{7}{132}\right)\)
\(\chi_{39195}(20312,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{33}\right)\)	\(e\left(\frac{4}{33}\right)\)	\(e\left(\frac{13}{33}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{7}{44}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{8}{33}\right)\)	\(e\left(\frac{35}{44}\right)\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{29}{132}\right)\)
\(\chi_{39195}(20798,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{33}\right)\)	\(e\left(\frac{14}{33}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{41}{44}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{28}{33}\right)\)	\(e\left(\frac{29}{44}\right)\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{19}{132}\right)\)
\(\chi_{39195}(21257,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{2}{33}\right)\)	\(e\left(\frac{23}{33}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{31}{44}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{4}{33}\right)\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{39}{44}\right)\)	\(e\left(\frac{97}{132}\right)\)
\(\chi_{39195}(23597,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{33}\right)\)	\(e\left(\frac{8}{33}\right)\)	\(e\left(\frac{26}{33}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{3}{44}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{35}{44}\right)\)	\(e\left(\frac{25}{132}\right)\)
\(\chi_{39195}(24668,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{26}{33}\right)\)	\(e\left(\frac{19}{33}\right)\)	\(e\left(\frac{4}{33}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{25}{44}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{5}{33}\right)\)	\(e\left(\frac{37}{44}\right)\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{47}{132}\right)\)
\(\chi_{39195}(24767,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{25}{33}\right)\)	\(e\left(\frac{17}{33}\right)\)	\(e\left(\frac{14}{33}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{27}{44}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{3}{44}\right)\)	\(e\left(\frac{7}{44}\right)\)	\(e\left(\frac{49}{132}\right)\)
\(\chi_{39195}(25478,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{2}{33}\right)\)	\(e\left(\frac{23}{33}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{4}{33}\right)\)	\(e\left(\frac{1}{44}\right)\)	\(e\left(\frac{17}{44}\right)\)	\(e\left(\frac{31}{132}\right)\)
\(\chi_{39195}(26162,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{8}{33}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{19}{33}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{39}{44}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{32}{33}\right)\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{17}{132}\right)\)
\(\chi_{39195}(26522,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{33}\right)\)	\(e\left(\frac{5}{33}\right)\)	\(e\left(\frac{8}{33}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{39}{44}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{10}{33}\right)\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{61}{132}\right)\)
\(\chi_{39195}(27008,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{33}\right)\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{28}{33}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{21}{44}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{2}{33}\right)\)	\(e\left(\frac{17}{44}\right)\)	\(e\left(\frac{25}{44}\right)\)	\(e\left(\frac{131}{132}\right)\)
\(\chi_{39195}(27332,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{33}\right)\)	\(e\left(\frac{13}{33}\right)\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{31}{44}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{26}{33}\right)\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{39}{44}\right)\)	\(e\left(\frac{53}{132}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Basic properties

Related number fields

First 31 of 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	39195.bpz
Modulus	$39195$
Conductor	$13065$
Order	$132$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(39195\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(13065\)	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 13065.pf	comment:If the character is primitive sage:chi.is_primitive() gp:#znconreyconductor(g,chi)==1 magma:IsPrimitive(chi);
Minimal:	yes
Parity:	even	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);