LMFDB - Dirichlet character orbit 6664.fu

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comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(6664, base_ring=CyclotomicField(168)) M = H._module chi = DirichletCharacter(H, M([0,0,8,21])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(9, 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("6664.9"); 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:	$833$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$168$	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 833.bl	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:	$\Q(\zeta_{168})$
Fixed field:	Number field defined by a degree 168 polynomial (not computed)

First 31 of 48 characters in Galois orbit

Character	$-1$	$1$	$3$	$5$	$9$	$11$	$13$	$15$	$19$	$23$	$25$	$27$
$\chi_{6664}(9,\cdot)$	$1$	$1$	$e\left(\frac{29}{168}\right)$	$e\left(\frac{1}{168}\right)$	$e\left(\frac{29}{84}\right)$	$e\left(\frac{131}{168}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{115}{168}\right)$	$e\left(\frac{1}{84}\right)$	$e\left(\frac{29}{56}\right)$
$\chi_{6664}(25,\cdot)$	$1$	$1$	$e\left(\frac{1}{168}\right)$	$e\left(\frac{29}{168}\right)$	$e\left(\frac{1}{84}\right)$	$e\left(\frac{103}{168}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{143}{168}\right)$	$e\left(\frac{29}{84}\right)$	$e\left(\frac{1}{56}\right)$
$\chi_{6664}(121,\cdot)$	$1$	$1$	$e\left(\frac{131}{168}\right)$	$e\left(\frac{103}{168}\right)$	$e\left(\frac{47}{84}\right)$	$e\left(\frac{53}{168}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{85}{168}\right)$	$e\left(\frac{19}{84}\right)$	$e\left(\frac{19}{56}\right)$
$\chi_{6664}(417,\cdot)$	$1$	$1$	$e\left(\frac{85}{168}\right)$	$e\left(\frac{113}{168}\right)$	$e\left(\frac{1}{84}\right)$	$e\left(\frac{19}{168}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{59}{168}\right)$	$e\left(\frac{29}{84}\right)$	$e\left(\frac{29}{56}\right)$
$\chi_{6664}(457,\cdot)$	$1$	$1$	$e\left(\frac{143}{168}\right)$	$e\left(\frac{115}{168}\right)$	$e\left(\frac{59}{84}\right)$	$e\left(\frac{113}{168}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{121}{168}\right)$	$e\left(\frac{31}{84}\right)$	$e\left(\frac{31}{56}\right)$
$\chi_{6664}(529,\cdot)$	$1$	$1$	$e\left(\frac{115}{168}\right)$	$e\left(\frac{143}{168}\right)$	$e\left(\frac{31}{84}\right)$	$e\left(\frac{85}{168}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{149}{168}\right)$	$e\left(\frac{59}{84}\right)$	$e\left(\frac{3}{56}\right)$
$\chi_{6664}(865,\cdot)$	$1$	$1$	$e\left(\frac{79}{168}\right)$	$e\left(\frac{107}{168}\right)$	$e\left(\frac{79}{84}\right)$	$e\left(\frac{73}{168}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{41}{168}\right)$	$e\left(\frac{23}{84}\right)$	$e\left(\frac{23}{56}\right)$
$\chi_{6664}(977,\cdot)$	$1$	$1$	$e\left(\frac{25}{168}\right)$	$e\left(\frac{53}{168}\right)$	$e\left(\frac{25}{84}\right)$	$e\left(\frac{55}{168}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{47}{168}\right)$	$e\left(\frac{53}{84}\right)$	$e\left(\frac{25}{56}\right)$
$\chi_{6664}(1073,\cdot)$	$1$	$1$	$e\left(\frac{11}{168}\right)$	$e\left(\frac{151}{168}\right)$	$e\left(\frac{11}{84}\right)$	$e\left(\frac{125}{168}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{61}{168}\right)$	$e\left(\frac{67}{84}\right)$	$e\left(\frac{11}{56}\right)$
$\chi_{6664}(1369,\cdot)$	$1$	$1$	$e\left(\frac{109}{168}\right)$	$e\left(\frac{137}{168}\right)$	$e\left(\frac{25}{84}\right)$	$e\left(\frac{139}{168}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{131}{168}\right)$	$e\left(\frac{53}{84}\right)$	$e\left(\frac{53}{56}\right)$
$\chi_{6664}(1409,\cdot)$	$1$	$1$	$e\left(\frac{23}{168}\right)$	$e\left(\frac{163}{168}\right)$	$e\left(\frac{23}{84}\right)$	$e\left(\frac{17}{168}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{97}{168}\right)$	$e\left(\frac{79}{84}\right)$	$e\left(\frac{23}{56}\right)$
$\chi_{6664}(1481,\cdot)$	$1$	$1$	$e\left(\frac{139}{168}\right)$	$e\left(\frac{167}{168}\right)$	$e\left(\frac{55}{84}\right)$	$e\left(\frac{37}{168}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{53}{168}\right)$	$e\left(\frac{83}{84}\right)$	$e\left(\frac{27}{56}\right)$
$\chi_{6664}(1521,\cdot)$	$1$	$1$	$e\left(\frac{41}{168}\right)$	$e\left(\frac{13}{168}\right)$	$e\left(\frac{41}{84}\right)$	$e\left(\frac{23}{168}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{151}{168}\right)$	$e\left(\frac{13}{84}\right)$	$e\left(\frac{41}{56}\right)$
$\chi_{6664}(1817,\cdot)$	$1$	$1$	$e\left(\frac{103}{168}\right)$	$e\left(\frac{131}{168}\right)$	$e\left(\frac{19}{84}\right)$	$e\left(\frac{25}{168}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{113}{168}\right)$	$e\left(\frac{47}{84}\right)$	$e\left(\frac{47}{56}\right)$
$\chi_{6664}(1913,\cdot)$	$1$	$1$	$e\left(\frac{125}{168}\right)$	$e\left(\frac{97}{168}\right)$	$e\left(\frac{41}{84}\right)$	$e\left(\frac{107}{168}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{67}{168}\right)$	$e\left(\frac{13}{84}\right)$	$e\left(\frac{13}{56}\right)$
$\chi_{6664}(2025,\cdot)$	$1$	$1$	$e\left(\frac{59}{168}\right)$	$e\left(\frac{31}{168}\right)$	$e\left(\frac{59}{84}\right)$	$e\left(\frac{29}{168}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{37}{168}\right)$	$e\left(\frac{31}{84}\right)$	$e\left(\frac{3}{56}\right)$
$\chi_{6664}(2361,\cdot)$	$1$	$1$	$e\left(\frac{71}{168}\right)$	$e\left(\frac{43}{168}\right)$	$e\left(\frac{71}{84}\right)$	$e\left(\frac{89}{168}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{73}{168}\right)$	$e\left(\frac{43}{84}\right)$	$e\left(\frac{15}{56}\right)$
$\chi_{6664}(2433,\cdot)$	$1$	$1$	$e\left(\frac{163}{168}\right)$	$e\left(\frac{23}{168}\right)$	$e\left(\frac{79}{84}\right)$	$e\left(\frac{157}{168}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{125}{168}\right)$	$e\left(\frac{23}{84}\right)$	$e\left(\frac{51}{56}\right)$
$\chi_{6664}(2473,\cdot)$	$1$	$1$	$e\left(\frac{89}{168}\right)$	$e\left(\frac{61}{168}\right)$	$e\left(\frac{5}{84}\right)$	$e\left(\frac{95}{168}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{127}{168}\right)$	$e\left(\frac{61}{84}\right)$	$e\left(\frac{33}{56}\right)$
$\chi_{6664}(2769,\cdot)$	$1$	$1$	$e\left(\frac{127}{168}\right)$	$e\left(\frac{155}{168}\right)$	$e\left(\frac{43}{84}\right)$	$e\left(\frac{145}{168}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{17}{168}\right)$	$e\left(\frac{71}{84}\right)$	$e\left(\frac{15}{56}\right)$
$\chi_{6664}(2865,\cdot)$	$1$	$1$	$e\left(\frac{5}{168}\right)$	$e\left(\frac{145}{168}\right)$	$e\left(\frac{5}{84}\right)$	$e\left(\frac{11}{168}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{43}{168}\right)$	$e\left(\frac{61}{84}\right)$	$e\left(\frac{5}{56}\right)$
$\chi_{6664}(2881,\cdot)$	$1$	$1$	$e\left(\frac{73}{168}\right)$	$e\left(\frac{101}{168}\right)$	$e\left(\frac{73}{84}\right)$	$e\left(\frac{127}{168}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{23}{168}\right)$	$e\left(\frac{17}{84}\right)$	$e\left(\frac{17}{56}\right)$
$\chi_{6664}(2977,\cdot)$	$1$	$1$	$e\left(\frac{107}{168}\right)$	$e\left(\frac{79}{168}\right)$	$e\left(\frac{23}{84}\right)$	$e\left(\frac{101}{168}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{13}{168}\right)$	$e\left(\frac{79}{84}\right)$	$e\left(\frac{51}{56}\right)$
$\chi_{6664}(3273,\cdot)$	$1$	$1$	$e\left(\frac{157}{168}\right)$	$e\left(\frac{17}{168}\right)$	$e\left(\frac{73}{84}\right)$	$e\left(\frac{43}{168}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{107}{168}\right)$	$e\left(\frac{17}{84}\right)$	$e\left(\frac{45}{56}\right)$
$\chi_{6664}(3385,\cdot)$	$1$	$1$	$e\left(\frac{19}{168}\right)$	$e\left(\frac{47}{168}\right)$	$e\left(\frac{19}{84}\right)$	$e\left(\frac{109}{168}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{29}{168}\right)$	$e\left(\frac{47}{84}\right)$	$e\left(\frac{19}{56}\right)$
$\chi_{6664}(3425,\cdot)$	$1$	$1$	$e\left(\frac{137}{168}\right)$	$e\left(\frac{109}{168}\right)$	$e\left(\frac{53}{84}\right)$	$e\left(\frac{167}{168}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{103}{168}\right)$	$e\left(\frac{25}{84}\right)$	$e\left(\frac{25}{56}\right)$
$\chi_{6664}(3721,\cdot)$	$1$	$1$	$e\left(\frac{151}{168}\right)$	$e\left(\frac{11}{168}\right)$	$e\left(\frac{67}{84}\right)$	$e\left(\frac{97}{168}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{89}{168}\right)$	$e\left(\frac{11}{84}\right)$	$e\left(\frac{39}{56}\right)$
$\chi_{6664}(3817,\cdot)$	$1$	$1$	$e\left(\frac{53}{168}\right)$	$e\left(\frac{25}{168}\right)$	$e\left(\frac{53}{84}\right)$	$e\left(\frac{83}{168}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{19}{168}\right)$	$e\left(\frac{25}{84}\right)$	$e\left(\frac{53}{56}\right)$
$\chi_{6664}(3833,\cdot)$	$1$	$1$	$e\left(\frac{97}{168}\right)$	$e\left(\frac{125}{168}\right)$	$e\left(\frac{13}{84}\right)$	$e\left(\frac{79}{168}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{95}{168}\right)$	$e\left(\frac{41}{84}\right)$	$e\left(\frac{41}{56}\right)$
$\chi_{6664}(3929,\cdot)$	$1$	$1$	$e\left(\frac{155}{168}\right)$	$e\left(\frac{127}{168}\right)$	$e\left(\frac{71}{84}\right)$	$e\left(\frac{5}{168}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{157}{168}\right)$	$e\left(\frac{43}{84}\right)$	$e\left(\frac{43}{56}\right)$
$\chi_{6664}(4225,\cdot)$	$1$	$1$	$e\left(\frac{13}{168}\right)$	$e\left(\frac{41}{168}\right)$	$e\left(\frac{13}{84}\right)$	$e\left(\frac{163}{168}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{11}{168}\right)$	$e\left(\frac{41}{84}\right)$	$e\left(\frac{13}{56}\right)$

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	\(-1\)	\(1\)	\(3\)	\(5\)	\(9\)	\(11\)	\(13\)	\(15\)	\(19\)	\(23\)	\(25\)	\(27\)
\(\chi_{6664}(9,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{168}\right)\)	\(e\left(\frac{1}{168}\right)\)	\(e\left(\frac{29}{84}\right)\)	\(e\left(\frac{131}{168}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{115}{168}\right)\)	\(e\left(\frac{1}{84}\right)\)	\(e\left(\frac{29}{56}\right)\)
\(\chi_{6664}(25,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{168}\right)\)	\(e\left(\frac{29}{168}\right)\)	\(e\left(\frac{1}{84}\right)\)	\(e\left(\frac{103}{168}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{143}{168}\right)\)	\(e\left(\frac{29}{84}\right)\)	\(e\left(\frac{1}{56}\right)\)
\(\chi_{6664}(121,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{131}{168}\right)\)	\(e\left(\frac{103}{168}\right)\)	\(e\left(\frac{47}{84}\right)\)	\(e\left(\frac{53}{168}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{85}{168}\right)\)	\(e\left(\frac{19}{84}\right)\)	\(e\left(\frac{19}{56}\right)\)
\(\chi_{6664}(417,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{85}{168}\right)\)	\(e\left(\frac{113}{168}\right)\)	\(e\left(\frac{1}{84}\right)\)	\(e\left(\frac{19}{168}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{59}{168}\right)\)	\(e\left(\frac{29}{84}\right)\)	\(e\left(\frac{29}{56}\right)\)
\(\chi_{6664}(457,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{143}{168}\right)\)	\(e\left(\frac{115}{168}\right)\)	\(e\left(\frac{59}{84}\right)\)	\(e\left(\frac{113}{168}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{121}{168}\right)\)	\(e\left(\frac{31}{84}\right)\)	\(e\left(\frac{31}{56}\right)\)
\(\chi_{6664}(529,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{115}{168}\right)\)	\(e\left(\frac{143}{168}\right)\)	\(e\left(\frac{31}{84}\right)\)	\(e\left(\frac{85}{168}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{149}{168}\right)\)	\(e\left(\frac{59}{84}\right)\)	\(e\left(\frac{3}{56}\right)\)
\(\chi_{6664}(865,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{79}{168}\right)\)	\(e\left(\frac{107}{168}\right)\)	\(e\left(\frac{79}{84}\right)\)	\(e\left(\frac{73}{168}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{41}{168}\right)\)	\(e\left(\frac{23}{84}\right)\)	\(e\left(\frac{23}{56}\right)\)
\(\chi_{6664}(977,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{25}{168}\right)\)	\(e\left(\frac{53}{168}\right)\)	\(e\left(\frac{25}{84}\right)\)	\(e\left(\frac{55}{168}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{47}{168}\right)\)	\(e\left(\frac{53}{84}\right)\)	\(e\left(\frac{25}{56}\right)\)
\(\chi_{6664}(1073,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{168}\right)\)	\(e\left(\frac{151}{168}\right)\)	\(e\left(\frac{11}{84}\right)\)	\(e\left(\frac{125}{168}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{61}{168}\right)\)	\(e\left(\frac{67}{84}\right)\)	\(e\left(\frac{11}{56}\right)\)
\(\chi_{6664}(1369,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{109}{168}\right)\)	\(e\left(\frac{137}{168}\right)\)	\(e\left(\frac{25}{84}\right)\)	\(e\left(\frac{139}{168}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{131}{168}\right)\)	\(e\left(\frac{53}{84}\right)\)	\(e\left(\frac{53}{56}\right)\)
\(\chi_{6664}(1409,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{168}\right)\)	\(e\left(\frac{163}{168}\right)\)	\(e\left(\frac{23}{84}\right)\)	\(e\left(\frac{17}{168}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{97}{168}\right)\)	\(e\left(\frac{79}{84}\right)\)	\(e\left(\frac{23}{56}\right)\)
\(\chi_{6664}(1481,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{139}{168}\right)\)	\(e\left(\frac{167}{168}\right)\)	\(e\left(\frac{55}{84}\right)\)	\(e\left(\frac{37}{168}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{53}{168}\right)\)	\(e\left(\frac{83}{84}\right)\)	\(e\left(\frac{27}{56}\right)\)
\(\chi_{6664}(1521,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{168}\right)\)	\(e\left(\frac{13}{168}\right)\)	\(e\left(\frac{41}{84}\right)\)	\(e\left(\frac{23}{168}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{151}{168}\right)\)	\(e\left(\frac{13}{84}\right)\)	\(e\left(\frac{41}{56}\right)\)
\(\chi_{6664}(1817,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{103}{168}\right)\)	\(e\left(\frac{131}{168}\right)\)	\(e\left(\frac{19}{84}\right)\)	\(e\left(\frac{25}{168}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{113}{168}\right)\)	\(e\left(\frac{47}{84}\right)\)	\(e\left(\frac{47}{56}\right)\)
\(\chi_{6664}(1913,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{125}{168}\right)\)	\(e\left(\frac{97}{168}\right)\)	\(e\left(\frac{41}{84}\right)\)	\(e\left(\frac{107}{168}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{67}{168}\right)\)	\(e\left(\frac{13}{84}\right)\)	\(e\left(\frac{13}{56}\right)\)
\(\chi_{6664}(2025,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{168}\right)\)	\(e\left(\frac{31}{168}\right)\)	\(e\left(\frac{59}{84}\right)\)	\(e\left(\frac{29}{168}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{37}{168}\right)\)	\(e\left(\frac{31}{84}\right)\)	\(e\left(\frac{3}{56}\right)\)
\(\chi_{6664}(2361,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{71}{168}\right)\)	\(e\left(\frac{43}{168}\right)\)	\(e\left(\frac{71}{84}\right)\)	\(e\left(\frac{89}{168}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{73}{168}\right)\)	\(e\left(\frac{43}{84}\right)\)	\(e\left(\frac{15}{56}\right)\)
\(\chi_{6664}(2433,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{163}{168}\right)\)	\(e\left(\frac{23}{168}\right)\)	\(e\left(\frac{79}{84}\right)\)	\(e\left(\frac{157}{168}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{125}{168}\right)\)	\(e\left(\frac{23}{84}\right)\)	\(e\left(\frac{51}{56}\right)\)
\(\chi_{6664}(2473,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{89}{168}\right)\)	\(e\left(\frac{61}{168}\right)\)	\(e\left(\frac{5}{84}\right)\)	\(e\left(\frac{95}{168}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{127}{168}\right)\)	\(e\left(\frac{61}{84}\right)\)	\(e\left(\frac{33}{56}\right)\)
\(\chi_{6664}(2769,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{127}{168}\right)\)	\(e\left(\frac{155}{168}\right)\)	\(e\left(\frac{43}{84}\right)\)	\(e\left(\frac{145}{168}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{17}{168}\right)\)	\(e\left(\frac{71}{84}\right)\)	\(e\left(\frac{15}{56}\right)\)
\(\chi_{6664}(2865,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{168}\right)\)	\(e\left(\frac{145}{168}\right)\)	\(e\left(\frac{5}{84}\right)\)	\(e\left(\frac{11}{168}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{43}{168}\right)\)	\(e\left(\frac{61}{84}\right)\)	\(e\left(\frac{5}{56}\right)\)
\(\chi_{6664}(2881,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{73}{168}\right)\)	\(e\left(\frac{101}{168}\right)\)	\(e\left(\frac{73}{84}\right)\)	\(e\left(\frac{127}{168}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{23}{168}\right)\)	\(e\left(\frac{17}{84}\right)\)	\(e\left(\frac{17}{56}\right)\)
\(\chi_{6664}(2977,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{107}{168}\right)\)	\(e\left(\frac{79}{168}\right)\)	\(e\left(\frac{23}{84}\right)\)	\(e\left(\frac{101}{168}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{13}{168}\right)\)	\(e\left(\frac{79}{84}\right)\)	\(e\left(\frac{51}{56}\right)\)
\(\chi_{6664}(3273,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{157}{168}\right)\)	\(e\left(\frac{17}{168}\right)\)	\(e\left(\frac{73}{84}\right)\)	\(e\left(\frac{43}{168}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{107}{168}\right)\)	\(e\left(\frac{17}{84}\right)\)	\(e\left(\frac{45}{56}\right)\)
\(\chi_{6664}(3385,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{168}\right)\)	\(e\left(\frac{47}{168}\right)\)	\(e\left(\frac{19}{84}\right)\)	\(e\left(\frac{109}{168}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{29}{168}\right)\)	\(e\left(\frac{47}{84}\right)\)	\(e\left(\frac{19}{56}\right)\)
\(\chi_{6664}(3425,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{137}{168}\right)\)	\(e\left(\frac{109}{168}\right)\)	\(e\left(\frac{53}{84}\right)\)	\(e\left(\frac{167}{168}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{103}{168}\right)\)	\(e\left(\frac{25}{84}\right)\)	\(e\left(\frac{25}{56}\right)\)
\(\chi_{6664}(3721,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{151}{168}\right)\)	\(e\left(\frac{11}{168}\right)\)	\(e\left(\frac{67}{84}\right)\)	\(e\left(\frac{97}{168}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{89}{168}\right)\)	\(e\left(\frac{11}{84}\right)\)	\(e\left(\frac{39}{56}\right)\)
\(\chi_{6664}(3817,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{168}\right)\)	\(e\left(\frac{25}{168}\right)\)	\(e\left(\frac{53}{84}\right)\)	\(e\left(\frac{83}{168}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{19}{168}\right)\)	\(e\left(\frac{25}{84}\right)\)	\(e\left(\frac{53}{56}\right)\)
\(\chi_{6664}(3833,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{97}{168}\right)\)	\(e\left(\frac{125}{168}\right)\)	\(e\left(\frac{13}{84}\right)\)	\(e\left(\frac{79}{168}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{95}{168}\right)\)	\(e\left(\frac{41}{84}\right)\)	\(e\left(\frac{41}{56}\right)\)
\(\chi_{6664}(3929,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{155}{168}\right)\)	\(e\left(\frac{127}{168}\right)\)	\(e\left(\frac{71}{84}\right)\)	\(e\left(\frac{5}{168}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{157}{168}\right)\)	\(e\left(\frac{43}{84}\right)\)	\(e\left(\frac{43}{56}\right)\)
\(\chi_{6664}(4225,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{168}\right)\)	\(e\left(\frac{41}{168}\right)\)	\(e\left(\frac{13}{84}\right)\)	\(e\left(\frac{163}{168}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{11}{168}\right)\)	\(e\left(\frac{41}{84}\right)\)	\(e\left(\frac{13}{56}\right)\)

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First 31 of 48 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.fu
Modulus	$6664$
Conductor	$833$
Order	$168$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(6664\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(833\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(168\)	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 833.bl	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);