LMFDB - Dirichlet character orbit 3312.dp

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comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(3312, base_ring=CyclotomicField(132)) M = H._module chi = DirichletCharacter(H, M([0,33,110,6])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(5, 3312)) 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("3312.5"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$3312$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$3312$	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:	yes	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:	$\Q(\zeta_{132})$	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 132 polynomial (not computed)	comment:Fixed field sage:chi.fixed_field()

First 31 of 40 characters in Galois orbit

Character	$-1$	$1$	$5$	$7$	$11$	$13$	$17$	$19$	$25$	$29$	$31$	$35$
$\chi_{3312}(5,\cdot)$	$1$	$1$	$e\left(\frac{61}{132}\right)$	$e\left(\frac{23}{33}\right)$	$e\left(\frac{65}{132}\right)$	$e\left(\frac{7}{132}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{61}{66}\right)$	$e\left(\frac{53}{132}\right)$	$e\left(\frac{31}{33}\right)$	$e\left(\frac{7}{44}\right)$
$\chi_{3312}(149,\cdot)$	$1$	$1$	$e\left(\frac{109}{132}\right)$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{101}{132}\right)$	$e\left(\frac{19}{132}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{39}{44}\right)$	$e\left(\frac{43}{66}\right)$	$e\left(\frac{125}{132}\right)$	$e\left(\frac{4}{33}\right)$	$e\left(\frac{19}{44}\right)$
$\chi_{3312}(221,\cdot)$	$1$	$1$	$e\left(\frac{115}{132}\right)$	$e\left(\frac{32}{33}\right)$	$e\left(\frac{23}{132}\right)$	$e\left(\frac{37}{132}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{25}{44}\right)$	$e\left(\frac{49}{66}\right)$	$e\left(\frac{35}{132}\right)$	$e\left(\frac{13}{33}\right)$	$e\left(\frac{37}{44}\right)$
$\chi_{3312}(245,\cdot)$	$1$	$1$	$e\left(\frac{113}{132}\right)$	$e\left(\frac{28}{33}\right)$	$e\left(\frac{49}{132}\right)$	$e\left(\frac{119}{132}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{47}{66}\right)$	$e\left(\frac{109}{132}\right)$	$e\left(\frac{32}{33}\right)$	$e\left(\frac{31}{44}\right)$
$\chi_{3312}(293,\cdot)$	$1$	$1$	$e\left(\frac{97}{132}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{125}{132}\right)$	$e\left(\frac{115}{132}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{31}{66}\right)$	$e\left(\frac{41}{132}\right)$	$e\left(\frac{19}{33}\right)$	$e\left(\frac{27}{44}\right)$
$\chi_{3312}(365,\cdot)$	$1$	$1$	$e\left(\frac{19}{132}\right)$	$e\left(\frac{5}{33}\right)$	$e\left(\frac{83}{132}\right)$	$e\left(\frac{13}{132}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{29}{44}\right)$	$e\left(\frac{19}{66}\right)$	$e\left(\frac{23}{132}\right)$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{13}{44}\right)$
$\chi_{3312}(389,\cdot)$	$1$	$1$	$e\left(\frac{89}{132}\right)$	$e\left(\frac{13}{33}\right)$	$e\left(\frac{97}{132}\right)$	$e\left(\frac{47}{132}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{27}{44}\right)$	$e\left(\frac{23}{66}\right)$	$e\left(\frac{73}{132}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{3}{44}\right)$
$\chi_{3312}(605,\cdot)$	$1$	$1$	$e\left(\frac{59}{132}\right)$	$e\left(\frac{19}{33}\right)$	$e\left(\frac{91}{132}\right)$	$e\left(\frac{89}{132}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{59}{66}\right)$	$e\left(\frac{127}{132}\right)$	$e\left(\frac{17}{33}\right)$	$e\left(\frac{1}{44}\right)$
$\chi_{3312}(677,\cdot)$	$1$	$1$	$e\left(\frac{29}{132}\right)$	$e\left(\frac{25}{33}\right)$	$e\left(\frac{85}{132}\right)$	$e\left(\frac{131}{132}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{35}{44}\right)$	$e\left(\frac{29}{66}\right)$	$e\left(\frac{49}{132}\right)$	$e\left(\frac{5}{33}\right)$	$e\left(\frac{43}{44}\right)$
$\chi_{3312}(797,\cdot)$	$1$	$1$	$e\left(\frac{91}{132}\right)$	$e\left(\frac{17}{33}\right)$	$e\left(\frac{71}{132}\right)$	$e\left(\frac{97}{132}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{37}{44}\right)$	$e\left(\frac{25}{66}\right)$	$e\left(\frac{131}{132}\right)$	$e\left(\frac{10}{33}\right)$	$e\left(\frac{9}{44}\right)$
$\chi_{3312}(893,\cdot)$	$1$	$1$	$e\left(\frac{35}{132}\right)$	$e\left(\frac{4}{33}\right)$	$e\left(\frac{7}{132}\right)$	$e\left(\frac{17}{132}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{21}{44}\right)$	$e\left(\frac{35}{66}\right)$	$e\left(\frac{91}{132}\right)$	$e\left(\frac{14}{33}\right)$	$e\left(\frac{17}{44}\right)$
$\chi_{3312}(941,\cdot)$	$1$	$1$	$e\left(\frac{67}{132}\right)$	$e\left(\frac{2}{33}\right)$	$e\left(\frac{119}{132}\right)$	$e\left(\frac{25}{132}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{5}{44}\right)$	$e\left(\frac{1}{66}\right)$	$e\left(\frac{95}{132}\right)$	$e\left(\frac{7}{33}\right)$	$e\left(\frac{25}{44}\right)$
$\chi_{3312}(1109,\cdot)$	$1$	$1$	$e\left(\frac{17}{132}\right)$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{109}{132}\right)$	$e\left(\frac{95}{132}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{17}{66}\right)$	$e\left(\frac{97}{132}\right)$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{7}{44}\right)$
$\chi_{3312}(1157,\cdot)$	$1$	$1$	$e\left(\frac{37}{132}\right)$	$e\left(\frac{8}{33}\right)$	$e\left(\frac{113}{132}\right)$	$e\left(\frac{67}{132}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{31}{44}\right)$	$e\left(\frac{37}{66}\right)$	$e\left(\frac{17}{132}\right)$	$e\left(\frac{28}{33}\right)$	$e\left(\frac{23}{44}\right)$
$\chi_{3312}(1229,\cdot)$	$1$	$1$	$e\left(\frac{7}{132}\right)$	$e\left(\frac{14}{33}\right)$	$e\left(\frac{107}{132}\right)$	$e\left(\frac{109}{132}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{7}{66}\right)$	$e\left(\frac{71}{132}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{21}{44}\right)$
$\chi_{3312}(1253,\cdot)$	$1$	$1$	$e\left(\frac{65}{132}\right)$	$e\left(\frac{31}{33}\right)$	$e\left(\frac{13}{132}\right)$	$e\left(\frac{107}{132}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{39}{44}\right)$	$e\left(\frac{65}{66}\right)$	$e\left(\frac{37}{132}\right)$	$e\left(\frac{26}{33}\right)$	$e\left(\frac{19}{44}\right)$
$\chi_{3312}(1325,\cdot)$	$1$	$1$	$e\left(\frac{71}{132}\right)$	$e\left(\frac{10}{33}\right)$	$e\left(\frac{67}{132}\right)$	$e\left(\frac{125}{132}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{25}{44}\right)$	$e\left(\frac{5}{66}\right)$	$e\left(\frac{79}{132}\right)$	$e\left(\frac{2}{33}\right)$	$e\left(\frac{37}{44}\right)$
$\chi_{3312}(1397,\cdot)$	$1$	$1$	$e\left(\frac{53}{132}\right)$	$e\left(\frac{7}{33}\right)$	$e\left(\frac{37}{132}\right)$	$e\left(\frac{71}{132}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{53}{66}\right)$	$e\left(\frac{85}{132}\right)$	$e\left(\frac{8}{33}\right)$	$e\left(\frac{27}{44}\right)$
$\chi_{3312}(1445,\cdot)$	$1$	$1$	$e\left(\frac{13}{132}\right)$	$e\left(\frac{26}{33}\right)$	$e\left(\frac{29}{132}\right)$	$e\left(\frac{127}{132}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{43}{44}\right)$	$e\left(\frac{13}{66}\right)$	$e\left(\frac{113}{132}\right)$	$e\left(\frac{25}{33}\right)$	$e\left(\frac{39}{44}\right)$
$\chi_{3312}(1469,\cdot)$	$1$	$1$	$e\left(\frac{107}{132}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{127}{132}\right)$	$e\left(\frac{101}{132}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{29}{44}\right)$	$e\left(\frac{41}{66}\right)$	$e\left(\frac{67}{132}\right)$	$e\left(\frac{23}{33}\right)$	$e\left(\frac{13}{44}\right)$
$\chi_{3312}(1661,\cdot)$	$1$	$1$	$e\left(\frac{127}{132}\right)$	$e\left(\frac{23}{33}\right)$	$e\left(\frac{131}{132}\right)$	$e\left(\frac{73}{132}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{41}{44}\right)$	$e\left(\frac{61}{66}\right)$	$e\left(\frac{119}{132}\right)$	$e\left(\frac{31}{33}\right)$	$e\left(\frac{29}{44}\right)$
$\chi_{3312}(1805,\cdot)$	$1$	$1$	$e\left(\frac{43}{132}\right)$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{35}{132}\right)$	$e\left(\frac{85}{132}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{17}{44}\right)$	$e\left(\frac{43}{66}\right)$	$e\left(\frac{59}{132}\right)$	$e\left(\frac{4}{33}\right)$	$e\left(\frac{41}{44}\right)$
$\chi_{3312}(1877,\cdot)$	$1$	$1$	$e\left(\frac{49}{132}\right)$	$e\left(\frac{32}{33}\right)$	$e\left(\frac{89}{132}\right)$	$e\left(\frac{103}{132}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{3}{44}\right)$	$e\left(\frac{49}{66}\right)$	$e\left(\frac{101}{132}\right)$	$e\left(\frac{13}{33}\right)$	$e\left(\frac{15}{44}\right)$
$\chi_{3312}(1901,\cdot)$	$1$	$1$	$e\left(\frac{47}{132}\right)$	$e\left(\frac{28}{33}\right)$	$e\left(\frac{115}{132}\right)$	$e\left(\frac{53}{132}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{37}{44}\right)$	$e\left(\frac{47}{66}\right)$	$e\left(\frac{43}{132}\right)$	$e\left(\frac{32}{33}\right)$	$e\left(\frac{9}{44}\right)$
$\chi_{3312}(1949,\cdot)$	$1$	$1$	$e\left(\frac{31}{132}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{59}{132}\right)$	$e\left(\frac{49}{132}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{1}{44}\right)$	$e\left(\frac{31}{66}\right)$	$e\left(\frac{107}{132}\right)$	$e\left(\frac{19}{33}\right)$	$e\left(\frac{5}{44}\right)$
$\chi_{3312}(2021,\cdot)$	$1$	$1$	$e\left(\frac{85}{132}\right)$	$e\left(\frac{5}{33}\right)$	$e\left(\frac{17}{132}\right)$	$e\left(\frac{79}{132}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{19}{66}\right)$	$e\left(\frac{89}{132}\right)$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{35}{44}\right)$
$\chi_{3312}(2045,\cdot)$	$1$	$1$	$e\left(\frac{23}{132}\right)$	$e\left(\frac{13}{33}\right)$	$e\left(\frac{31}{132}\right)$	$e\left(\frac{113}{132}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{5}{44}\right)$	$e\left(\frac{23}{66}\right)$	$e\left(\frac{7}{132}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{25}{44}\right)$
$\chi_{3312}(2261,\cdot)$	$1$	$1$	$e\left(\frac{125}{132}\right)$	$e\left(\frac{19}{33}\right)$	$e\left(\frac{25}{132}\right)$	$e\left(\frac{23}{132}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{31}{44}\right)$	$e\left(\frac{59}{66}\right)$	$e\left(\frac{61}{132}\right)$	$e\left(\frac{17}{33}\right)$	$e\left(\frac{23}{44}\right)$
$\chi_{3312}(2333,\cdot)$	$1$	$1$	$e\left(\frac{95}{132}\right)$	$e\left(\frac{25}{33}\right)$	$e\left(\frac{19}{132}\right)$	$e\left(\frac{65}{132}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{29}{66}\right)$	$e\left(\frac{115}{132}\right)$	$e\left(\frac{5}{33}\right)$	$e\left(\frac{21}{44}\right)$
$\chi_{3312}(2453,\cdot)$	$1$	$1$	$e\left(\frac{25}{132}\right)$	$e\left(\frac{17}{33}\right)$	$e\left(\frac{5}{132}\right)$	$e\left(\frac{31}{132}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{25}{66}\right)$	$e\left(\frac{65}{132}\right)$	$e\left(\frac{10}{33}\right)$	$e\left(\frac{31}{44}\right)$
$\chi_{3312}(2549,\cdot)$	$1$	$1$	$e\left(\frac{101}{132}\right)$	$e\left(\frac{4}{33}\right)$	$e\left(\frac{73}{132}\right)$	$e\left(\frac{83}{132}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{43}{44}\right)$	$e\left(\frac{35}{66}\right)$	$e\left(\frac{25}{132}\right)$	$e\left(\frac{14}{33}\right)$	$e\left(\frac{39}{44}\right)$

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	\(-1\)	\(1\)	\(5\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(25\)	\(29\)	\(31\)	\(35\)
\(\chi_{3312}(5,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{61}{132}\right)\)	\(e\left(\frac{23}{33}\right)\)	\(e\left(\frac{65}{132}\right)\)	\(e\left(\frac{7}{132}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{61}{66}\right)\)	\(e\left(\frac{53}{132}\right)\)	\(e\left(\frac{31}{33}\right)\)	\(e\left(\frac{7}{44}\right)\)
\(\chi_{3312}(149,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{109}{132}\right)\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{101}{132}\right)\)	\(e\left(\frac{19}{132}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{39}{44}\right)\)	\(e\left(\frac{43}{66}\right)\)	\(e\left(\frac{125}{132}\right)\)	\(e\left(\frac{4}{33}\right)\)	\(e\left(\frac{19}{44}\right)\)
\(\chi_{3312}(221,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{115}{132}\right)\)	\(e\left(\frac{32}{33}\right)\)	\(e\left(\frac{23}{132}\right)\)	\(e\left(\frac{37}{132}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{25}{44}\right)\)	\(e\left(\frac{49}{66}\right)\)	\(e\left(\frac{35}{132}\right)\)	\(e\left(\frac{13}{33}\right)\)	\(e\left(\frac{37}{44}\right)\)
\(\chi_{3312}(245,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{113}{132}\right)\)	\(e\left(\frac{28}{33}\right)\)	\(e\left(\frac{49}{132}\right)\)	\(e\left(\frac{119}{132}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{47}{66}\right)\)	\(e\left(\frac{109}{132}\right)\)	\(e\left(\frac{32}{33}\right)\)	\(e\left(\frac{31}{44}\right)\)
\(\chi_{3312}(293,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{97}{132}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{125}{132}\right)\)	\(e\left(\frac{115}{132}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{31}{66}\right)\)	\(e\left(\frac{41}{132}\right)\)	\(e\left(\frac{19}{33}\right)\)	\(e\left(\frac{27}{44}\right)\)
\(\chi_{3312}(365,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{132}\right)\)	\(e\left(\frac{5}{33}\right)\)	\(e\left(\frac{83}{132}\right)\)	\(e\left(\frac{13}{132}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{29}{44}\right)\)	\(e\left(\frac{19}{66}\right)\)	\(e\left(\frac{23}{132}\right)\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{13}{44}\right)\)
\(\chi_{3312}(389,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{89}{132}\right)\)	\(e\left(\frac{13}{33}\right)\)	\(e\left(\frac{97}{132}\right)\)	\(e\left(\frac{47}{132}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{27}{44}\right)\)	\(e\left(\frac{23}{66}\right)\)	\(e\left(\frac{73}{132}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{3}{44}\right)\)
\(\chi_{3312}(605,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{132}\right)\)	\(e\left(\frac{19}{33}\right)\)	\(e\left(\frac{91}{132}\right)\)	\(e\left(\frac{89}{132}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{59}{66}\right)\)	\(e\left(\frac{127}{132}\right)\)	\(e\left(\frac{17}{33}\right)\)	\(e\left(\frac{1}{44}\right)\)
\(\chi_{3312}(677,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{132}\right)\)	\(e\left(\frac{25}{33}\right)\)	\(e\left(\frac{85}{132}\right)\)	\(e\left(\frac{131}{132}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{35}{44}\right)\)	\(e\left(\frac{29}{66}\right)\)	\(e\left(\frac{49}{132}\right)\)	\(e\left(\frac{5}{33}\right)\)	\(e\left(\frac{43}{44}\right)\)
\(\chi_{3312}(797,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{91}{132}\right)\)	\(e\left(\frac{17}{33}\right)\)	\(e\left(\frac{71}{132}\right)\)	\(e\left(\frac{97}{132}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{37}{44}\right)\)	\(e\left(\frac{25}{66}\right)\)	\(e\left(\frac{131}{132}\right)\)	\(e\left(\frac{10}{33}\right)\)	\(e\left(\frac{9}{44}\right)\)
\(\chi_{3312}(893,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{35}{132}\right)\)	\(e\left(\frac{4}{33}\right)\)	\(e\left(\frac{7}{132}\right)\)	\(e\left(\frac{17}{132}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{21}{44}\right)\)	\(e\left(\frac{35}{66}\right)\)	\(e\left(\frac{91}{132}\right)\)	\(e\left(\frac{14}{33}\right)\)	\(e\left(\frac{17}{44}\right)\)
\(\chi_{3312}(941,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{67}{132}\right)\)	\(e\left(\frac{2}{33}\right)\)	\(e\left(\frac{119}{132}\right)\)	\(e\left(\frac{25}{132}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{5}{44}\right)\)	\(e\left(\frac{1}{66}\right)\)	\(e\left(\frac{95}{132}\right)\)	\(e\left(\frac{7}{33}\right)\)	\(e\left(\frac{25}{44}\right)\)
\(\chi_{3312}(1109,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{132}\right)\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{109}{132}\right)\)	\(e\left(\frac{95}{132}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{17}{66}\right)\)	\(e\left(\frac{97}{132}\right)\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{7}{44}\right)\)
\(\chi_{3312}(1157,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{132}\right)\)	\(e\left(\frac{8}{33}\right)\)	\(e\left(\frac{113}{132}\right)\)	\(e\left(\frac{67}{132}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{31}{44}\right)\)	\(e\left(\frac{37}{66}\right)\)	\(e\left(\frac{17}{132}\right)\)	\(e\left(\frac{28}{33}\right)\)	\(e\left(\frac{23}{44}\right)\)
\(\chi_{3312}(1229,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{132}\right)\)	\(e\left(\frac{14}{33}\right)\)	\(e\left(\frac{107}{132}\right)\)	\(e\left(\frac{109}{132}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{7}{66}\right)\)	\(e\left(\frac{71}{132}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{21}{44}\right)\)
\(\chi_{3312}(1253,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{65}{132}\right)\)	\(e\left(\frac{31}{33}\right)\)	\(e\left(\frac{13}{132}\right)\)	\(e\left(\frac{107}{132}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{39}{44}\right)\)	\(e\left(\frac{65}{66}\right)\)	\(e\left(\frac{37}{132}\right)\)	\(e\left(\frac{26}{33}\right)\)	\(e\left(\frac{19}{44}\right)\)
\(\chi_{3312}(1325,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{71}{132}\right)\)	\(e\left(\frac{10}{33}\right)\)	\(e\left(\frac{67}{132}\right)\)	\(e\left(\frac{125}{132}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{25}{44}\right)\)	\(e\left(\frac{5}{66}\right)\)	\(e\left(\frac{79}{132}\right)\)	\(e\left(\frac{2}{33}\right)\)	\(e\left(\frac{37}{44}\right)\)
\(\chi_{3312}(1397,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{132}\right)\)	\(e\left(\frac{7}{33}\right)\)	\(e\left(\frac{37}{132}\right)\)	\(e\left(\frac{71}{132}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{53}{66}\right)\)	\(e\left(\frac{85}{132}\right)\)	\(e\left(\frac{8}{33}\right)\)	\(e\left(\frac{27}{44}\right)\)
\(\chi_{3312}(1445,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{132}\right)\)	\(e\left(\frac{26}{33}\right)\)	\(e\left(\frac{29}{132}\right)\)	\(e\left(\frac{127}{132}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{43}{44}\right)\)	\(e\left(\frac{13}{66}\right)\)	\(e\left(\frac{113}{132}\right)\)	\(e\left(\frac{25}{33}\right)\)	\(e\left(\frac{39}{44}\right)\)
\(\chi_{3312}(1469,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{107}{132}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{127}{132}\right)\)	\(e\left(\frac{101}{132}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{29}{44}\right)\)	\(e\left(\frac{41}{66}\right)\)	\(e\left(\frac{67}{132}\right)\)	\(e\left(\frac{23}{33}\right)\)	\(e\left(\frac{13}{44}\right)\)
\(\chi_{3312}(1661,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{127}{132}\right)\)	\(e\left(\frac{23}{33}\right)\)	\(e\left(\frac{131}{132}\right)\)	\(e\left(\frac{73}{132}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{41}{44}\right)\)	\(e\left(\frac{61}{66}\right)\)	\(e\left(\frac{119}{132}\right)\)	\(e\left(\frac{31}{33}\right)\)	\(e\left(\frac{29}{44}\right)\)
\(\chi_{3312}(1805,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{132}\right)\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{35}{132}\right)\)	\(e\left(\frac{85}{132}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{17}{44}\right)\)	\(e\left(\frac{43}{66}\right)\)	\(e\left(\frac{59}{132}\right)\)	\(e\left(\frac{4}{33}\right)\)	\(e\left(\frac{41}{44}\right)\)
\(\chi_{3312}(1877,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{49}{132}\right)\)	\(e\left(\frac{32}{33}\right)\)	\(e\left(\frac{89}{132}\right)\)	\(e\left(\frac{103}{132}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{3}{44}\right)\)	\(e\left(\frac{49}{66}\right)\)	\(e\left(\frac{101}{132}\right)\)	\(e\left(\frac{13}{33}\right)\)	\(e\left(\frac{15}{44}\right)\)
\(\chi_{3312}(1901,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{132}\right)\)	\(e\left(\frac{28}{33}\right)\)	\(e\left(\frac{115}{132}\right)\)	\(e\left(\frac{53}{132}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{37}{44}\right)\)	\(e\left(\frac{47}{66}\right)\)	\(e\left(\frac{43}{132}\right)\)	\(e\left(\frac{32}{33}\right)\)	\(e\left(\frac{9}{44}\right)\)
\(\chi_{3312}(1949,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{132}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{59}{132}\right)\)	\(e\left(\frac{49}{132}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{1}{44}\right)\)	\(e\left(\frac{31}{66}\right)\)	\(e\left(\frac{107}{132}\right)\)	\(e\left(\frac{19}{33}\right)\)	\(e\left(\frac{5}{44}\right)\)
\(\chi_{3312}(2021,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{85}{132}\right)\)	\(e\left(\frac{5}{33}\right)\)	\(e\left(\frac{17}{132}\right)\)	\(e\left(\frac{79}{132}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{7}{44}\right)\)	\(e\left(\frac{19}{66}\right)\)	\(e\left(\frac{89}{132}\right)\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{35}{44}\right)\)
\(\chi_{3312}(2045,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{132}\right)\)	\(e\left(\frac{13}{33}\right)\)	\(e\left(\frac{31}{132}\right)\)	\(e\left(\frac{113}{132}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{5}{44}\right)\)	\(e\left(\frac{23}{66}\right)\)	\(e\left(\frac{7}{132}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{25}{44}\right)\)
\(\chi_{3312}(2261,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{125}{132}\right)\)	\(e\left(\frac{19}{33}\right)\)	\(e\left(\frac{25}{132}\right)\)	\(e\left(\frac{23}{132}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{31}{44}\right)\)	\(e\left(\frac{59}{66}\right)\)	\(e\left(\frac{61}{132}\right)\)	\(e\left(\frac{17}{33}\right)\)	\(e\left(\frac{23}{44}\right)\)
\(\chi_{3312}(2333,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{95}{132}\right)\)	\(e\left(\frac{25}{33}\right)\)	\(e\left(\frac{19}{132}\right)\)	\(e\left(\frac{65}{132}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{29}{66}\right)\)	\(e\left(\frac{115}{132}\right)\)	\(e\left(\frac{5}{33}\right)\)	\(e\left(\frac{21}{44}\right)\)
\(\chi_{3312}(2453,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{25}{132}\right)\)	\(e\left(\frac{17}{33}\right)\)	\(e\left(\frac{5}{132}\right)\)	\(e\left(\frac{31}{132}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{25}{66}\right)\)	\(e\left(\frac{65}{132}\right)\)	\(e\left(\frac{10}{33}\right)\)	\(e\left(\frac{31}{44}\right)\)
\(\chi_{3312}(2549,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{101}{132}\right)\)	\(e\left(\frac{4}{33}\right)\)	\(e\left(\frac{73}{132}\right)\)	\(e\left(\frac{83}{132}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{43}{44}\right)\)	\(e\left(\frac{35}{66}\right)\)	\(e\left(\frac{25}{132}\right)\)	\(e\left(\frac{14}{33}\right)\)	\(e\left(\frac{39}{44}\right)\)

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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	3312.dp
Modulus	$3312$
Conductor	$3312$
Order	$132$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(3312\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(3312\)	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:	yes	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);