LMFDB - Dirichlet character orbit 6664.fz

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comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(6664, base_ring=CyclotomicField(336)) M = H._module chi = DirichletCharacter(H, M([168,168,320,147])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(11, 6664)) 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("6664.11"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$6664$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$6664$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$336$	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:	$\Q(\zeta_{336})$	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 336 polynomial (not computed)	comment:Fixed field sage:chi.fixed_field()

First 31 of 96 characters in Galois orbit

Character	$-1$	$1$	$3$	$5$	$9$	$11$	$13$	$15$	$19$	$23$	$25$	$27$
$\chi_{6664}(11,\cdot)$	$1$	$1$	$e\left(\frac{131}{336}\right)$	$e\left(\frac{103}{336}\right)$	$e\left(\frac{131}{168}\right)$	$e\left(\frac{53}{336}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{39}{56}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{85}{336}\right)$	$e\left(\frac{103}{168}\right)$	$e\left(\frac{19}{112}\right)$
$\chi_{6664}(107,\cdot)$	$1$	$1$	$e\left(\frac{121}{336}\right)$	$e\left(\frac{149}{336}\right)$	$e\left(\frac{121}{168}\right)$	$e\left(\frac{31}{336}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{45}{56}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{335}{336}\right)$	$e\left(\frac{149}{168}\right)$	$e\left(\frac{9}{112}\right)$
$\chi_{6664}(163,\cdot)$	$1$	$1$	$e\left(\frac{223}{336}\right)$	$e\left(\frac{83}{336}\right)$	$e\left(\frac{55}{168}\right)$	$e\left(\frac{121}{336}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{51}{56}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{137}{336}\right)$	$e\left(\frac{83}{168}\right)$	$e\left(\frac{111}{112}\right)$
$\chi_{6664}(235,\cdot)$	$1$	$1$	$e\left(\frac{125}{336}\right)$	$e\left(\frac{265}{336}\right)$	$e\left(\frac{125}{168}\right)$	$e\left(\frac{107}{336}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{9}{56}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{235}{336}\right)$	$e\left(\frac{97}{168}\right)$	$e\left(\frac{13}{112}\right)$
$\chi_{6664}(347,\cdot)$	$1$	$1$	$e\left(\frac{311}{336}\right)$	$e\left(\frac{283}{336}\right)$	$e\left(\frac{143}{168}\right)$	$e\left(\frac{113}{336}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{43}{56}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{289}{336}\right)$	$e\left(\frac{115}{168}\right)$	$e\left(\frac{87}{112}\right)$
$\chi_{6664}(403,\cdot)$	$1$	$1$	$e\left(\frac{257}{336}\right)$	$e\left(\frac{61}{336}\right)$	$e\left(\frac{89}{168}\right)$	$e\left(\frac{263}{336}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{53}{56}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{295}{336}\right)$	$e\left(\frac{61}{168}\right)$	$e\left(\frac{33}{112}\right)$
$\chi_{6664}(499,\cdot)$	$1$	$1$	$e\left(\frac{331}{336}\right)$	$e\left(\frac{191}{336}\right)$	$e\left(\frac{163}{168}\right)$	$e\left(\frac{157}{336}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{31}{56}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{125}{336}\right)$	$e\left(\frac{23}{168}\right)$	$e\left(\frac{107}{112}\right)$
$\chi_{6664}(515,\cdot)$	$1$	$1$	$e\left(\frac{233}{336}\right)$	$e\left(\frac{37}{336}\right)$	$e\left(\frac{65}{168}\right)$	$e\left(\frac{143}{336}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{45}{56}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{223}{336}\right)$	$e\left(\frac{37}{168}\right)$	$e\left(\frac{9}{112}\right)$
$\chi_{6664}(555,\cdot)$	$1$	$1$	$e\left(\frac{307}{336}\right)$	$e\left(\frac{167}{336}\right)$	$e\left(\frac{139}{168}\right)$	$e\left(\frac{37}{336}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{23}{56}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{53}{336}\right)$	$e\left(\frac{167}{168}\right)$	$e\left(\frac{83}{112}\right)$
$\chi_{6664}(571,\cdot)$	$1$	$1$	$e\left(\frac{95}{336}\right)$	$e\left(\frac{67}{336}\right)$	$e\left(\frac{95}{168}\right)$	$e\left(\frac{41}{336}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{27}{56}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{313}{336}\right)$	$e\left(\frac{67}{168}\right)$	$e\left(\frac{95}{112}\right)$
$\chi_{6664}(683,\cdot)$	$1$	$1$	$e\left(\frac{197}{336}\right)$	$e\left(\frac{1}{336}\right)$	$e\left(\frac{29}{168}\right)$	$e\left(\frac{131}{336}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{33}{56}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{115}{336}\right)$	$e\left(\frac{1}{168}\right)$	$e\left(\frac{85}{112}\right)$
$\chi_{6664}(779,\cdot)$	$1$	$1$	$e\left(\frac{253}{336}\right)$	$e\left(\frac{281}{336}\right)$	$e\left(\frac{85}{168}\right)$	$e\left(\frac{187}{336}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{33}{56}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{59}{336}\right)$	$e\left(\frac{113}{168}\right)$	$e\left(\frac{29}{112}\right)$
$\chi_{6664}(891,\cdot)$	$1$	$1$	$e\left(\frac{247}{336}\right)$	$e\left(\frac{107}{336}\right)$	$e\left(\frac{79}{168}\right)$	$e\left(\frac{241}{336}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{3}{56}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{209}{336}\right)$	$e\left(\frac{107}{168}\right)$	$e\left(\frac{23}{112}\right)$
$\chi_{6664}(907,\cdot)$	$1$	$1$	$e\left(\frac{107}{336}\right)$	$e\left(\frac{79}{336}\right)$	$e\left(\frac{107}{168}\right)$	$e\left(\frac{269}{336}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{31}{56}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{13}{336}\right)$	$e\left(\frac{79}{168}\right)$	$e\left(\frac{107}{112}\right)$
$\chi_{6664}(947,\cdot)$	$1$	$1$	$e\left(\frac{97}{336}\right)$	$e\left(\frac{125}{336}\right)$	$e\left(\frac{97}{168}\right)$	$e\left(\frac{247}{336}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{37}{56}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{263}{336}\right)$	$e\left(\frac{125}{168}\right)$	$e\left(\frac{97}{112}\right)$
$\chi_{6664}(963,\cdot)$	$1$	$1$	$e\left(\frac{179}{336}\right)$	$e\left(\frac{151}{336}\right)$	$e\left(\frac{11}{168}\right)$	$e\left(\frac{293}{336}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{55}{56}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{229}{336}\right)$	$e\left(\frac{151}{168}\right)$	$e\left(\frac{67}{112}\right)$
$\chi_{6664}(1115,\cdot)$	$1$	$1$	$e\left(\frac{319}{336}\right)$	$e\left(\frac{179}{336}\right)$	$e\left(\frac{151}{168}\right)$	$e\left(\frac{265}{336}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{27}{56}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{89}{336}\right)$	$e\left(\frac{11}{168}\right)$	$e\left(\frac{95}{112}\right)$
$\chi_{6664}(1187,\cdot)$	$1$	$1$	$e\left(\frac{173}{336}\right)$	$e\left(\frac{313}{336}\right)$	$e\left(\frac{5}{168}\right)$	$e\left(\frac{11}{336}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{25}{56}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{43}{336}\right)$	$e\left(\frac{145}{168}\right)$	$e\left(\frac{61}{112}\right)$
$\chi_{6664}(1227,\cdot)$	$1$	$1$	$e\left(\frac{229}{336}\right)$	$e\left(\frac{257}{336}\right)$	$e\left(\frac{61}{168}\right)$	$e\left(\frac{67}{336}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{25}{56}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{323}{336}\right)$	$e\left(\frac{89}{168}\right)$	$e\left(\frac{5}{112}\right)$
$\chi_{6664}(1299,\cdot)$	$1$	$1$	$e\left(\frac{23}{336}\right)$	$e\left(\frac{331}{336}\right)$	$e\left(\frac{23}{168}\right)$	$e\left(\frac{17}{336}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{3}{56}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{97}{336}\right)$	$e\left(\frac{163}{168}\right)$	$e\left(\frac{23}{112}\right)$
$\chi_{6664}(1355,\cdot)$	$1$	$1$	$e\left(\frac{305}{336}\right)$	$e\left(\frac{109}{336}\right)$	$e\left(\frac{137}{168}\right)$	$e\left(\frac{167}{336}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{13}{56}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{103}{336}\right)$	$e\left(\frac{109}{168}\right)$	$e\left(\frac{81}{112}\right)$
$\chi_{6664}(1467,\cdot)$	$1$	$1$	$e\left(\frac{281}{336}\right)$	$e\left(\frac{85}{336}\right)$	$e\left(\frac{113}{168}\right)$	$e\left(\frac{47}{336}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{5}{56}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{31}{336}\right)$	$e\left(\frac{85}{168}\right)$	$e\left(\frac{57}{112}\right)$
$\chi_{6664}(1507,\cdot)$	$1$	$1$	$e\left(\frac{67}{336}\right)$	$e\left(\frac{263}{336}\right)$	$e\left(\frac{67}{168}\right)$	$e\left(\frac{181}{336}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{55}{56}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{5}{336}\right)$	$e\left(\frac{95}{168}\right)$	$e\left(\frac{67}{112}\right)$
$\chi_{6664}(1523,\cdot)$	$1$	$1$	$e\left(\frac{143}{336}\right)$	$e\left(\frac{115}{336}\right)$	$e\left(\frac{143}{168}\right)$	$e\left(\frac{281}{336}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{43}{56}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{121}{336}\right)$	$e\left(\frac{115}{168}\right)$	$e\left(\frac{31}{112}\right)$
$\chi_{6664}(1731,\cdot)$	$1$	$1$	$e\left(\frac{13}{336}\right)$	$e\left(\frac{41}{336}\right)$	$e\left(\frac{13}{168}\right)$	$e\left(\frac{331}{336}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{9}{56}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{11}{336}\right)$	$e\left(\frac{41}{168}\right)$	$e\left(\frac{13}{112}\right)$
$\chi_{6664}(1859,\cdot)$	$1$	$1$	$e\left(\frac{155}{336}\right)$	$e\left(\frac{127}{336}\right)$	$e\left(\frac{155}{168}\right)$	$e\left(\frac{173}{336}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{47}{56}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{157}{336}\right)$	$e\left(\frac{127}{168}\right)$	$e\left(\frac{43}{112}\right)$
$\chi_{6664}(1899,\cdot)$	$1$	$1$	$e\left(\frac{193}{336}\right)$	$e\left(\frac{221}{336}\right)$	$e\left(\frac{25}{168}\right)$	$e\left(\frac{55}{336}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{13}{56}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{215}{336}\right)$	$e\left(\frac{53}{168}\right)$	$e\left(\frac{81}{112}\right)$
$\chi_{6664}(1915,\cdot)$	$1$	$1$	$e\left(\frac{227}{336}\right)$	$e\left(\frac{199}{336}\right)$	$e\left(\frac{59}{168}\right)$	$e\left(\frac{197}{336}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{15}{56}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{37}{336}\right)$	$e\left(\frac{31}{168}\right)$	$e\left(\frac{3}{112}\right)$
$\chi_{6664}(2011,\cdot)$	$1$	$1$	$e\left(\frac{313}{336}\right)$	$e\left(\frac{5}{336}\right)$	$e\left(\frac{145}{168}\right)$	$e\left(\frac{319}{336}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{53}{56}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{239}{336}\right)$	$e\left(\frac{5}{168}\right)$	$e\left(\frac{89}{112}\right)$
$\chi_{6664}(2067,\cdot)$	$1$	$1$	$e\left(\frac{79}{336}\right)$	$e\left(\frac{275}{336}\right)$	$e\left(\frac{79}{168}\right)$	$e\left(\frac{73}{336}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{3}{56}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{41}{336}\right)$	$e\left(\frac{107}{168}\right)$	$e\left(\frac{79}{112}\right)$
$\chi_{6664}(2139,\cdot)$	$1$	$1$	$e\left(\frac{221}{336}\right)$	$e\left(\frac{25}{336}\right)$	$e\left(\frac{53}{168}\right)$	$e\left(\frac{251}{336}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{41}{56}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{187}{336}\right)$	$e\left(\frac{25}{168}\right)$	$e\left(\frac{109}{112}\right)$

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$ over number fields
Genus 2 curves
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Character	\(-1\)	\(1\)	\(3\)	\(5\)	\(9\)	\(11\)	\(13\)	\(15\)	\(19\)	\(23\)	\(25\)	\(27\)
\(\chi_{6664}(11,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{131}{336}\right)\)	\(e\left(\frac{103}{336}\right)\)	\(e\left(\frac{131}{168}\right)\)	\(e\left(\frac{53}{336}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{39}{56}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{85}{336}\right)\)	\(e\left(\frac{103}{168}\right)\)	\(e\left(\frac{19}{112}\right)\)
\(\chi_{6664}(107,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{121}{336}\right)\)	\(e\left(\frac{149}{336}\right)\)	\(e\left(\frac{121}{168}\right)\)	\(e\left(\frac{31}{336}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{45}{56}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{335}{336}\right)\)	\(e\left(\frac{149}{168}\right)\)	\(e\left(\frac{9}{112}\right)\)
\(\chi_{6664}(163,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{223}{336}\right)\)	\(e\left(\frac{83}{336}\right)\)	\(e\left(\frac{55}{168}\right)\)	\(e\left(\frac{121}{336}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{51}{56}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{137}{336}\right)\)	\(e\left(\frac{83}{168}\right)\)	\(e\left(\frac{111}{112}\right)\)
\(\chi_{6664}(235,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{125}{336}\right)\)	\(e\left(\frac{265}{336}\right)\)	\(e\left(\frac{125}{168}\right)\)	\(e\left(\frac{107}{336}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{9}{56}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{235}{336}\right)\)	\(e\left(\frac{97}{168}\right)\)	\(e\left(\frac{13}{112}\right)\)
\(\chi_{6664}(347,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{311}{336}\right)\)	\(e\left(\frac{283}{336}\right)\)	\(e\left(\frac{143}{168}\right)\)	\(e\left(\frac{113}{336}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{43}{56}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{289}{336}\right)\)	\(e\left(\frac{115}{168}\right)\)	\(e\left(\frac{87}{112}\right)\)
\(\chi_{6664}(403,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{257}{336}\right)\)	\(e\left(\frac{61}{336}\right)\)	\(e\left(\frac{89}{168}\right)\)	\(e\left(\frac{263}{336}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{53}{56}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{295}{336}\right)\)	\(e\left(\frac{61}{168}\right)\)	\(e\left(\frac{33}{112}\right)\)
\(\chi_{6664}(499,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{331}{336}\right)\)	\(e\left(\frac{191}{336}\right)\)	\(e\left(\frac{163}{168}\right)\)	\(e\left(\frac{157}{336}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{31}{56}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{125}{336}\right)\)	\(e\left(\frac{23}{168}\right)\)	\(e\left(\frac{107}{112}\right)\)
\(\chi_{6664}(515,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{233}{336}\right)\)	\(e\left(\frac{37}{336}\right)\)	\(e\left(\frac{65}{168}\right)\)	\(e\left(\frac{143}{336}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{45}{56}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{223}{336}\right)\)	\(e\left(\frac{37}{168}\right)\)	\(e\left(\frac{9}{112}\right)\)
\(\chi_{6664}(555,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{307}{336}\right)\)	\(e\left(\frac{167}{336}\right)\)	\(e\left(\frac{139}{168}\right)\)	\(e\left(\frac{37}{336}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{23}{56}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{53}{336}\right)\)	\(e\left(\frac{167}{168}\right)\)	\(e\left(\frac{83}{112}\right)\)
\(\chi_{6664}(571,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{95}{336}\right)\)	\(e\left(\frac{67}{336}\right)\)	\(e\left(\frac{95}{168}\right)\)	\(e\left(\frac{41}{336}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{27}{56}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{313}{336}\right)\)	\(e\left(\frac{67}{168}\right)\)	\(e\left(\frac{95}{112}\right)\)
\(\chi_{6664}(683,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{197}{336}\right)\)	\(e\left(\frac{1}{336}\right)\)	\(e\left(\frac{29}{168}\right)\)	\(e\left(\frac{131}{336}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{33}{56}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{115}{336}\right)\)	\(e\left(\frac{1}{168}\right)\)	\(e\left(\frac{85}{112}\right)\)
\(\chi_{6664}(779,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{253}{336}\right)\)	\(e\left(\frac{281}{336}\right)\)	\(e\left(\frac{85}{168}\right)\)	\(e\left(\frac{187}{336}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{33}{56}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{59}{336}\right)\)	\(e\left(\frac{113}{168}\right)\)	\(e\left(\frac{29}{112}\right)\)
\(\chi_{6664}(891,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{247}{336}\right)\)	\(e\left(\frac{107}{336}\right)\)	\(e\left(\frac{79}{168}\right)\)	\(e\left(\frac{241}{336}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{3}{56}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{209}{336}\right)\)	\(e\left(\frac{107}{168}\right)\)	\(e\left(\frac{23}{112}\right)\)
\(\chi_{6664}(907,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{107}{336}\right)\)	\(e\left(\frac{79}{336}\right)\)	\(e\left(\frac{107}{168}\right)\)	\(e\left(\frac{269}{336}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{31}{56}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{13}{336}\right)\)	\(e\left(\frac{79}{168}\right)\)	\(e\left(\frac{107}{112}\right)\)
\(\chi_{6664}(947,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{97}{336}\right)\)	\(e\left(\frac{125}{336}\right)\)	\(e\left(\frac{97}{168}\right)\)	\(e\left(\frac{247}{336}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{37}{56}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{263}{336}\right)\)	\(e\left(\frac{125}{168}\right)\)	\(e\left(\frac{97}{112}\right)\)
\(\chi_{6664}(963,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{179}{336}\right)\)	\(e\left(\frac{151}{336}\right)\)	\(e\left(\frac{11}{168}\right)\)	\(e\left(\frac{293}{336}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{55}{56}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{229}{336}\right)\)	\(e\left(\frac{151}{168}\right)\)	\(e\left(\frac{67}{112}\right)\)
\(\chi_{6664}(1115,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{319}{336}\right)\)	\(e\left(\frac{179}{336}\right)\)	\(e\left(\frac{151}{168}\right)\)	\(e\left(\frac{265}{336}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{27}{56}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{89}{336}\right)\)	\(e\left(\frac{11}{168}\right)\)	\(e\left(\frac{95}{112}\right)\)
\(\chi_{6664}(1187,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{173}{336}\right)\)	\(e\left(\frac{313}{336}\right)\)	\(e\left(\frac{5}{168}\right)\)	\(e\left(\frac{11}{336}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{25}{56}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{43}{336}\right)\)	\(e\left(\frac{145}{168}\right)\)	\(e\left(\frac{61}{112}\right)\)
\(\chi_{6664}(1227,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{229}{336}\right)\)	\(e\left(\frac{257}{336}\right)\)	\(e\left(\frac{61}{168}\right)\)	\(e\left(\frac{67}{336}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{25}{56}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{323}{336}\right)\)	\(e\left(\frac{89}{168}\right)\)	\(e\left(\frac{5}{112}\right)\)
\(\chi_{6664}(1299,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{336}\right)\)	\(e\left(\frac{331}{336}\right)\)	\(e\left(\frac{23}{168}\right)\)	\(e\left(\frac{17}{336}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{3}{56}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{97}{336}\right)\)	\(e\left(\frac{163}{168}\right)\)	\(e\left(\frac{23}{112}\right)\)
\(\chi_{6664}(1355,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{305}{336}\right)\)	\(e\left(\frac{109}{336}\right)\)	\(e\left(\frac{137}{168}\right)\)	\(e\left(\frac{167}{336}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{13}{56}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{103}{336}\right)\)	\(e\left(\frac{109}{168}\right)\)	\(e\left(\frac{81}{112}\right)\)
\(\chi_{6664}(1467,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{281}{336}\right)\)	\(e\left(\frac{85}{336}\right)\)	\(e\left(\frac{113}{168}\right)\)	\(e\left(\frac{47}{336}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{5}{56}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{31}{336}\right)\)	\(e\left(\frac{85}{168}\right)\)	\(e\left(\frac{57}{112}\right)\)
\(\chi_{6664}(1507,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{67}{336}\right)\)	\(e\left(\frac{263}{336}\right)\)	\(e\left(\frac{67}{168}\right)\)	\(e\left(\frac{181}{336}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{55}{56}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{5}{336}\right)\)	\(e\left(\frac{95}{168}\right)\)	\(e\left(\frac{67}{112}\right)\)
\(\chi_{6664}(1523,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{143}{336}\right)\)	\(e\left(\frac{115}{336}\right)\)	\(e\left(\frac{143}{168}\right)\)	\(e\left(\frac{281}{336}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{43}{56}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{121}{336}\right)\)	\(e\left(\frac{115}{168}\right)\)	\(e\left(\frac{31}{112}\right)\)
\(\chi_{6664}(1731,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{336}\right)\)	\(e\left(\frac{41}{336}\right)\)	\(e\left(\frac{13}{168}\right)\)	\(e\left(\frac{331}{336}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{9}{56}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{11}{336}\right)\)	\(e\left(\frac{41}{168}\right)\)	\(e\left(\frac{13}{112}\right)\)
\(\chi_{6664}(1859,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{155}{336}\right)\)	\(e\left(\frac{127}{336}\right)\)	\(e\left(\frac{155}{168}\right)\)	\(e\left(\frac{173}{336}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{47}{56}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{157}{336}\right)\)	\(e\left(\frac{127}{168}\right)\)	\(e\left(\frac{43}{112}\right)\)
\(\chi_{6664}(1899,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{193}{336}\right)\)	\(e\left(\frac{221}{336}\right)\)	\(e\left(\frac{25}{168}\right)\)	\(e\left(\frac{55}{336}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{13}{56}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{215}{336}\right)\)	\(e\left(\frac{53}{168}\right)\)	\(e\left(\frac{81}{112}\right)\)
\(\chi_{6664}(1915,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{227}{336}\right)\)	\(e\left(\frac{199}{336}\right)\)	\(e\left(\frac{59}{168}\right)\)	\(e\left(\frac{197}{336}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{15}{56}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{37}{336}\right)\)	\(e\left(\frac{31}{168}\right)\)	\(e\left(\frac{3}{112}\right)\)
\(\chi_{6664}(2011,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{313}{336}\right)\)	\(e\left(\frac{5}{336}\right)\)	\(e\left(\frac{145}{168}\right)\)	\(e\left(\frac{319}{336}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{53}{56}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{239}{336}\right)\)	\(e\left(\frac{5}{168}\right)\)	\(e\left(\frac{89}{112}\right)\)
\(\chi_{6664}(2067,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{79}{336}\right)\)	\(e\left(\frac{275}{336}\right)\)	\(e\left(\frac{79}{168}\right)\)	\(e\left(\frac{73}{336}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{3}{56}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{41}{336}\right)\)	\(e\left(\frac{107}{168}\right)\)	\(e\left(\frac{79}{112}\right)\)
\(\chi_{6664}(2139,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{221}{336}\right)\)	\(e\left(\frac{25}{336}\right)\)	\(e\left(\frac{53}{168}\right)\)	\(e\left(\frac{251}{336}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{41}{56}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{187}{336}\right)\)	\(e\left(\frac{25}{168}\right)\)	\(e\left(\frac{109}{112}\right)\)

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First 31 of 96 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	6664.fz
Modulus	$6664$
Conductor	$6664$
Order	$336$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(6664\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(6664\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(336\)	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);