LMFDB - Dirichlet character orbit 12584.gw

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comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(12584, base_ring=CyclotomicField(330)) M = H._module chi = DirichletCharacter(H, M([165,165,243,220])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(35, 12584)) 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("12584.35"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$12584$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$12584$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$330$	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:	$\Q(\zeta_{165})$
Fixed field:	Number field defined by a degree 330 polynomial (not computed)

First 31 of 80 characters in Galois orbit

Character	$-1$	$1$	$3$	$5$	$7$	$9$	$15$	$17$	$19$	$21$	$23$	$25$
$\chi_{12584}(35,\cdot)$	$1$	$1$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{109}{110}\right)$	$e\left(\frac{163}{165}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{151}{330}\right)$	$e\left(\frac{137}{330}\right)$	$e\left(\frac{149}{330}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{47}{66}\right)$	$e\left(\frac{54}{55}\right)$
$\chi_{12584}(107,\cdot)$	$1$	$1$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{97}{110}\right)$	$e\left(\frac{29}{165}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{203}{330}\right)$	$e\left(\frac{241}{330}\right)$	$e\left(\frac{67}{330}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{61}{66}\right)$	$e\left(\frac{42}{55}\right)$
$\chi_{12584}(139,\cdot)$	$1$	$1$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{63}{110}\right)$	$e\left(\frac{16}{165}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{277}{330}\right)$	$e\left(\frac{59}{330}\right)$	$e\left(\frac{293}{330}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{53}{66}\right)$	$e\left(\frac{8}{55}\right)$
$\chi_{12584}(211,\cdot)$	$1$	$1$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{39}{110}\right)$	$e\left(\frac{23}{165}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{161}{330}\right)$	$e\left(\frac{157}{330}\right)$	$e\left(\frac{19}{330}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{37}{66}\right)$	$e\left(\frac{39}{55}\right)$
$\chi_{12584}(315,\cdot)$	$1$	$1$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{43}{110}\right)$	$e\left(\frac{86}{165}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{107}{330}\right)$	$e\left(\frac{49}{330}\right)$	$e\left(\frac{193}{330}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{25}{66}\right)$	$e\left(\frac{43}{55}\right)$
$\chi_{12584}(347,\cdot)$	$1$	$1$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{21}{110}\right)$	$e\left(\frac{97}{165}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{19}{330}\right)$	$e\left(\frac{203}{330}\right)$	$e\left(\frac{281}{330}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{47}{66}\right)$	$e\left(\frac{21}{55}\right)$
$\chi_{12584}(523,\cdot)$	$1$	$1$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{71}{110}\right)$	$e\left(\frac{32}{165}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{59}{330}\right)$	$e\left(\frac{283}{330}\right)$	$e\left(\frac{91}{330}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{7}{66}\right)$	$e\left(\frac{16}{55}\right)$
$\chi_{12584}(1075,\cdot)$	$1$	$1$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{97}{110}\right)$	$e\left(\frac{139}{165}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{313}{330}\right)$	$e\left(\frac{131}{330}\right)$	$e\left(\frac{287}{330}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{17}{66}\right)$	$e\left(\frac{42}{55}\right)$
$\chi_{12584}(1179,\cdot)$	$1$	$1$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{39}{110}\right)$	$e\left(\frac{133}{165}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{271}{330}\right)$	$e\left(\frac{47}{330}\right)$	$e\left(\frac{239}{330}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{59}{66}\right)$	$e\left(\frac{39}{55}\right)$
$\chi_{12584}(1251,\cdot)$	$1$	$1$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{107}{110}\right)$	$e\left(\frac{104}{165}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{233}{330}\right)$	$e\left(\frac{301}{330}\right)$	$e\left(\frac{7}{330}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{31}{66}\right)$	$e\left(\frac{52}{55}\right)$
$\chi_{12584}(1283,\cdot)$	$1$	$1$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{43}{110}\right)$	$e\left(\frac{31}{165}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{217}{330}\right)$	$e\left(\frac{269}{330}\right)$	$e\left(\frac{83}{330}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{47}{66}\right)$	$e\left(\frac{43}{55}\right)$
$\chi_{12584}(1355,\cdot)$	$1$	$1$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{79}{110}\right)$	$e\left(\frac{158}{165}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{281}{330}\right)$	$e\left(\frac{67}{330}\right)$	$e\left(\frac{109}{330}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{49}{66}\right)$	$e\left(\frac{24}{55}\right)$
$\chi_{12584}(1459,\cdot)$	$1$	$1$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{23}{110}\right)$	$e\left(\frac{101}{165}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{47}{330}\right)$	$e\left(\frac{259}{330}\right)$	$e\left(\frac{313}{330}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{19}{66}\right)$	$e\left(\frac{23}{55}\right)$
$\chi_{12584}(1491,\cdot)$	$1$	$1$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{71}{110}\right)$	$e\left(\frac{142}{165}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{169}{330}\right)$	$e\left(\frac{173}{330}\right)$	$e\left(\frac{311}{330}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{29}{66}\right)$	$e\left(\frac{16}{55}\right)$
$\chi_{12584}(2219,\cdot)$	$1$	$1$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{107}{110}\right)$	$e\left(\frac{49}{165}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{13}{330}\right)$	$e\left(\frac{191}{330}\right)$	$e\left(\frac{227}{330}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{53}{66}\right)$	$e\left(\frac{52}{55}\right)$
$\chi_{12584}(2323,\cdot)$	$1$	$1$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{79}{110}\right)$	$e\left(\frac{103}{165}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{61}{330}\right)$	$e\left(\frac{287}{330}\right)$	$e\left(\frac{329}{330}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{5}{66}\right)$	$e\left(\frac{24}{55}\right)$
$\chi_{12584}(2395,\cdot)$	$1$	$1$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{7}{110}\right)$	$e\left(\frac{14}{165}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{263}{330}\right)$	$e\left(\frac{31}{330}\right)$	$e\left(\frac{277}{330}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{1}{66}\right)$	$e\left(\frac{7}{55}\right)$
$\chi_{12584}(2427,\cdot)$	$1$	$1$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{23}{110}\right)$	$e\left(\frac{46}{165}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{157}{330}\right)$	$e\left(\frac{149}{330}\right)$	$e\left(\frac{203}{330}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{41}{66}\right)$	$e\left(\frac{23}{55}\right)$
$\chi_{12584}(2499,\cdot)$	$1$	$1$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{9}{110}\right)$	$e\left(\frac{128}{165}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{71}{330}\right)$	$e\left(\frac{307}{330}\right)$	$e\left(\frac{199}{330}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{61}{66}\right)$	$e\left(\frac{9}{55}\right)$
$\chi_{12584}(2603,\cdot)$	$1$	$1$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{3}{110}\right)$	$e\left(\frac{116}{165}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{317}{330}\right)$	$e\left(\frac{139}{330}\right)$	$e\left(\frac{103}{330}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{13}{66}\right)$	$e\left(\frac{3}{55}\right)$
$\chi_{12584}(2811,\cdot)$	$1$	$1$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{61}{110}\right)$	$e\left(\frac{122}{165}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{29}{330}\right)$	$e\left(\frac{223}{330}\right)$	$e\left(\frac{151}{330}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{37}{66}\right)$	$e\left(\frac{6}{55}\right)$
$\chi_{12584}(3363,\cdot)$	$1$	$1$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{7}{110}\right)$	$e\left(\frac{124}{165}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{43}{330}\right)$	$e\left(\frac{251}{330}\right)$	$e\left(\frac{167}{330}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{23}{66}\right)$	$e\left(\frac{7}{55}\right)$
$\chi_{12584}(3467,\cdot)$	$1$	$1$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{9}{110}\right)$	$e\left(\frac{73}{165}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{181}{330}\right)$	$e\left(\frac{197}{330}\right)$	$e\left(\frac{89}{330}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{17}{66}\right)$	$e\left(\frac{9}{55}\right)$
$\chi_{12584}(3539,\cdot)$	$1$	$1$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{17}{110}\right)$	$e\left(\frac{89}{165}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{293}{330}\right)$	$e\left(\frac{91}{330}\right)$	$e\left(\frac{217}{330}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{37}{66}\right)$	$e\left(\frac{17}{55}\right)$
$\chi_{12584}(3571,\cdot)$	$1$	$1$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{3}{110}\right)$	$e\left(\frac{61}{165}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{97}{330}\right)$	$e\left(\frac{29}{330}\right)$	$e\left(\frac{323}{330}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{35}{66}\right)$	$e\left(\frac{3}{55}\right)$
$\chi_{12584}(3643,\cdot)$	$1$	$1$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{49}{110}\right)$	$e\left(\frac{98}{165}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{191}{330}\right)$	$e\left(\frac{217}{330}\right)$	$e\left(\frac{289}{330}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{7}{66}\right)$	$e\left(\frac{49}{55}\right)$
$\chi_{12584}(3747,\cdot)$	$1$	$1$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{93}{110}\right)$	$e\left(\frac{131}{165}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{257}{330}\right)$	$e\left(\frac{19}{330}\right)$	$e\left(\frac{223}{330}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{7}{66}\right)$	$e\left(\frac{38}{55}\right)$
$\chi_{12584}(3779,\cdot)$	$1$	$1$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{61}{110}\right)$	$e\left(\frac{67}{165}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{139}{330}\right)$	$e\left(\frac{113}{330}\right)$	$e\left(\frac{41}{330}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{59}{66}\right)$	$e\left(\frac{6}{55}\right)$
$\chi_{12584}(3955,\cdot)$	$1$	$1$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{1}{110}\right)$	$e\left(\frac{2}{165}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{179}{330}\right)$	$e\left(\frac{193}{330}\right)$	$e\left(\frac{181}{330}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{19}{66}\right)$	$e\left(\frac{1}{55}\right)$
$\chi_{12584}(4507,\cdot)$	$1$	$1$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{17}{110}\right)$	$e\left(\frac{34}{165}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{73}{330}\right)$	$e\left(\frac{311}{330}\right)$	$e\left(\frac{107}{330}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{59}{66}\right)$	$e\left(\frac{17}{55}\right)$
$\chi_{12584}(4611,\cdot)$	$1$	$1$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{49}{110}\right)$	$e\left(\frac{43}{165}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{301}{330}\right)$	$e\left(\frac{107}{330}\right)$	$e\left(\frac{179}{330}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{29}{66}\right)$	$e\left(\frac{49}{55}\right)$

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	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(15\)	\(17\)	\(19\)	\(21\)	\(23\)	\(25\)
\(\chi_{12584}(35,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{109}{110}\right)\)	\(e\left(\frac{163}{165}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{151}{330}\right)\)	\(e\left(\frac{137}{330}\right)\)	\(e\left(\frac{149}{330}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{47}{66}\right)\)	\(e\left(\frac{54}{55}\right)\)
\(\chi_{12584}(107,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{97}{110}\right)\)	\(e\left(\frac{29}{165}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{203}{330}\right)\)	\(e\left(\frac{241}{330}\right)\)	\(e\left(\frac{67}{330}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{61}{66}\right)\)	\(e\left(\frac{42}{55}\right)\)
\(\chi_{12584}(139,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{63}{110}\right)\)	\(e\left(\frac{16}{165}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{277}{330}\right)\)	\(e\left(\frac{59}{330}\right)\)	\(e\left(\frac{293}{330}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{53}{66}\right)\)	\(e\left(\frac{8}{55}\right)\)
\(\chi_{12584}(211,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{39}{110}\right)\)	\(e\left(\frac{23}{165}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{161}{330}\right)\)	\(e\left(\frac{157}{330}\right)\)	\(e\left(\frac{19}{330}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{37}{66}\right)\)	\(e\left(\frac{39}{55}\right)\)
\(\chi_{12584}(315,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{43}{110}\right)\)	\(e\left(\frac{86}{165}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{107}{330}\right)\)	\(e\left(\frac{49}{330}\right)\)	\(e\left(\frac{193}{330}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{25}{66}\right)\)	\(e\left(\frac{43}{55}\right)\)
\(\chi_{12584}(347,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{21}{110}\right)\)	\(e\left(\frac{97}{165}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{19}{330}\right)\)	\(e\left(\frac{203}{330}\right)\)	\(e\left(\frac{281}{330}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{47}{66}\right)\)	\(e\left(\frac{21}{55}\right)\)
\(\chi_{12584}(523,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{71}{110}\right)\)	\(e\left(\frac{32}{165}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{59}{330}\right)\)	\(e\left(\frac{283}{330}\right)\)	\(e\left(\frac{91}{330}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{7}{66}\right)\)	\(e\left(\frac{16}{55}\right)\)
\(\chi_{12584}(1075,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{97}{110}\right)\)	\(e\left(\frac{139}{165}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{313}{330}\right)\)	\(e\left(\frac{131}{330}\right)\)	\(e\left(\frac{287}{330}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{17}{66}\right)\)	\(e\left(\frac{42}{55}\right)\)
\(\chi_{12584}(1179,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{39}{110}\right)\)	\(e\left(\frac{133}{165}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{271}{330}\right)\)	\(e\left(\frac{47}{330}\right)\)	\(e\left(\frac{239}{330}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{59}{66}\right)\)	\(e\left(\frac{39}{55}\right)\)
\(\chi_{12584}(1251,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{107}{110}\right)\)	\(e\left(\frac{104}{165}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{233}{330}\right)\)	\(e\left(\frac{301}{330}\right)\)	\(e\left(\frac{7}{330}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{31}{66}\right)\)	\(e\left(\frac{52}{55}\right)\)
\(\chi_{12584}(1283,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{43}{110}\right)\)	\(e\left(\frac{31}{165}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{217}{330}\right)\)	\(e\left(\frac{269}{330}\right)\)	\(e\left(\frac{83}{330}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{47}{66}\right)\)	\(e\left(\frac{43}{55}\right)\)
\(\chi_{12584}(1355,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{79}{110}\right)\)	\(e\left(\frac{158}{165}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{281}{330}\right)\)	\(e\left(\frac{67}{330}\right)\)	\(e\left(\frac{109}{330}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{49}{66}\right)\)	\(e\left(\frac{24}{55}\right)\)
\(\chi_{12584}(1459,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{23}{110}\right)\)	\(e\left(\frac{101}{165}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{47}{330}\right)\)	\(e\left(\frac{259}{330}\right)\)	\(e\left(\frac{313}{330}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{19}{66}\right)\)	\(e\left(\frac{23}{55}\right)\)
\(\chi_{12584}(1491,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{71}{110}\right)\)	\(e\left(\frac{142}{165}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{169}{330}\right)\)	\(e\left(\frac{173}{330}\right)\)	\(e\left(\frac{311}{330}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{29}{66}\right)\)	\(e\left(\frac{16}{55}\right)\)
\(\chi_{12584}(2219,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{107}{110}\right)\)	\(e\left(\frac{49}{165}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{13}{330}\right)\)	\(e\left(\frac{191}{330}\right)\)	\(e\left(\frac{227}{330}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{53}{66}\right)\)	\(e\left(\frac{52}{55}\right)\)
\(\chi_{12584}(2323,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{79}{110}\right)\)	\(e\left(\frac{103}{165}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{61}{330}\right)\)	\(e\left(\frac{287}{330}\right)\)	\(e\left(\frac{329}{330}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{5}{66}\right)\)	\(e\left(\frac{24}{55}\right)\)
\(\chi_{12584}(2395,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{7}{110}\right)\)	\(e\left(\frac{14}{165}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{263}{330}\right)\)	\(e\left(\frac{31}{330}\right)\)	\(e\left(\frac{277}{330}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{1}{66}\right)\)	\(e\left(\frac{7}{55}\right)\)
\(\chi_{12584}(2427,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{23}{110}\right)\)	\(e\left(\frac{46}{165}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{157}{330}\right)\)	\(e\left(\frac{149}{330}\right)\)	\(e\left(\frac{203}{330}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{41}{66}\right)\)	\(e\left(\frac{23}{55}\right)\)
\(\chi_{12584}(2499,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{9}{110}\right)\)	\(e\left(\frac{128}{165}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{71}{330}\right)\)	\(e\left(\frac{307}{330}\right)\)	\(e\left(\frac{199}{330}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{61}{66}\right)\)	\(e\left(\frac{9}{55}\right)\)
\(\chi_{12584}(2603,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{3}{110}\right)\)	\(e\left(\frac{116}{165}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{317}{330}\right)\)	\(e\left(\frac{139}{330}\right)\)	\(e\left(\frac{103}{330}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{13}{66}\right)\)	\(e\left(\frac{3}{55}\right)\)
\(\chi_{12584}(2811,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{61}{110}\right)\)	\(e\left(\frac{122}{165}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{29}{330}\right)\)	\(e\left(\frac{223}{330}\right)\)	\(e\left(\frac{151}{330}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{37}{66}\right)\)	\(e\left(\frac{6}{55}\right)\)
\(\chi_{12584}(3363,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{7}{110}\right)\)	\(e\left(\frac{124}{165}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{43}{330}\right)\)	\(e\left(\frac{251}{330}\right)\)	\(e\left(\frac{167}{330}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{23}{66}\right)\)	\(e\left(\frac{7}{55}\right)\)
\(\chi_{12584}(3467,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{9}{110}\right)\)	\(e\left(\frac{73}{165}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{181}{330}\right)\)	\(e\left(\frac{197}{330}\right)\)	\(e\left(\frac{89}{330}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{17}{66}\right)\)	\(e\left(\frac{9}{55}\right)\)
\(\chi_{12584}(3539,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{17}{110}\right)\)	\(e\left(\frac{89}{165}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{293}{330}\right)\)	\(e\left(\frac{91}{330}\right)\)	\(e\left(\frac{217}{330}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{37}{66}\right)\)	\(e\left(\frac{17}{55}\right)\)
\(\chi_{12584}(3571,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{3}{110}\right)\)	\(e\left(\frac{61}{165}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{97}{330}\right)\)	\(e\left(\frac{29}{330}\right)\)	\(e\left(\frac{323}{330}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{35}{66}\right)\)	\(e\left(\frac{3}{55}\right)\)
\(\chi_{12584}(3643,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{49}{110}\right)\)	\(e\left(\frac{98}{165}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{191}{330}\right)\)	\(e\left(\frac{217}{330}\right)\)	\(e\left(\frac{289}{330}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{7}{66}\right)\)	\(e\left(\frac{49}{55}\right)\)
\(\chi_{12584}(3747,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{93}{110}\right)\)	\(e\left(\frac{131}{165}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{257}{330}\right)\)	\(e\left(\frac{19}{330}\right)\)	\(e\left(\frac{223}{330}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{7}{66}\right)\)	\(e\left(\frac{38}{55}\right)\)
\(\chi_{12584}(3779,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{61}{110}\right)\)	\(e\left(\frac{67}{165}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{139}{330}\right)\)	\(e\left(\frac{113}{330}\right)\)	\(e\left(\frac{41}{330}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{59}{66}\right)\)	\(e\left(\frac{6}{55}\right)\)
\(\chi_{12584}(3955,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{1}{110}\right)\)	\(e\left(\frac{2}{165}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{179}{330}\right)\)	\(e\left(\frac{193}{330}\right)\)	\(e\left(\frac{181}{330}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{19}{66}\right)\)	\(e\left(\frac{1}{55}\right)\)
\(\chi_{12584}(4507,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{17}{110}\right)\)	\(e\left(\frac{34}{165}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{73}{330}\right)\)	\(e\left(\frac{311}{330}\right)\)	\(e\left(\frac{107}{330}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{59}{66}\right)\)	\(e\left(\frac{17}{55}\right)\)
\(\chi_{12584}(4611,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{49}{110}\right)\)	\(e\left(\frac{43}{165}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{301}{330}\right)\)	\(e\left(\frac{107}{330}\right)\)	\(e\left(\frac{179}{330}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{29}{66}\right)\)	\(e\left(\frac{49}{55}\right)\)

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First 31 of 80 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	12584.gw
Modulus	$12584$
Conductor	$12584$
Order	$330$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(12584\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(12584\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(330\)	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);