LMFDB - Dirichlet character orbit 8640.ie

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comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(8640, base_ring=CyclotomicField(144)) M = H._module chi = DirichletCharacter(H, M([72,117,32,108])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(43, 8640)) 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("8640.43"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$8640$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$8640$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$144$	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:	$\Q(\zeta_{144})$
Fixed field:	Number field defined by a degree 144 polynomial (not computed)

First 31 of 48 characters in Galois orbit

Character	$-1$	$1$	$7$	$11$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$
$\chi_{8640}(43,\cdot)$	$1$	$1$	$e\left(\frac{67}{72}\right)$	$e\left(\frac{65}{144}\right)$	$e\left(\frac{31}{144}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{41}{72}\right)$	$e\left(\frac{95}{144}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{11}{72}\right)$
$\chi_{8640}(67,\cdot)$	$1$	$1$	$e\left(\frac{53}{72}\right)$	$e\left(\frac{31}{144}\right)$	$e\left(\frac{17}{144}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{55}{72}\right)$	$e\left(\frac{1}{144}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{13}{72}\right)$
$\chi_{8640}(283,\cdot)$	$1$	$1$	$e\left(\frac{71}{72}\right)$	$e\left(\frac{13}{144}\right)$	$e\left(\frac{35}{144}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{13}{48}\right)$	$e\left(\frac{37}{72}\right)$	$e\left(\frac{19}{144}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{31}{72}\right)$
$\chi_{8640}(547,\cdot)$	$1$	$1$	$e\left(\frac{61}{72}\right)$	$e\left(\frac{71}{144}\right)$	$e\left(\frac{25}{144}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{47}{72}\right)$	$e\left(\frac{137}{144}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{53}{72}\right)$
$\chi_{8640}(763,\cdot)$	$1$	$1$	$e\left(\frac{7}{72}\right)$	$e\left(\frac{53}{144}\right)$	$e\left(\frac{43}{144}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{29}{72}\right)$	$e\left(\frac{11}{144}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{71}{72}\right)$
$\chi_{8640}(787,\cdot)$	$1$	$1$	$e\left(\frac{65}{72}\right)$	$e\left(\frac{19}{144}\right)$	$e\left(\frac{29}{144}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{43}{72}\right)$	$e\left(\frac{61}{144}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{1}{72}\right)$
$\chi_{8640}(1003,\cdot)$	$1$	$1$	$e\left(\frac{11}{72}\right)$	$e\left(\frac{1}{144}\right)$	$e\left(\frac{47}{144}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{25}{72}\right)$	$e\left(\frac{79}{144}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{19}{72}\right)$
$\chi_{8640}(1267,\cdot)$	$1$	$1$	$e\left(\frac{1}{72}\right)$	$e\left(\frac{59}{144}\right)$	$e\left(\frac{37}{144}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{35}{72}\right)$	$e\left(\frac{53}{144}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{41}{72}\right)$
$\chi_{8640}(1483,\cdot)$	$1$	$1$	$e\left(\frac{19}{72}\right)$	$e\left(\frac{41}{144}\right)$	$e\left(\frac{55}{144}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{17}{72}\right)$	$e\left(\frac{71}{144}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{59}{72}\right)$
$\chi_{8640}(1507,\cdot)$	$1$	$1$	$e\left(\frac{5}{72}\right)$	$e\left(\frac{7}{144}\right)$	$e\left(\frac{41}{144}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{31}{72}\right)$	$e\left(\frac{121}{144}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{61}{72}\right)$
$\chi_{8640}(1723,\cdot)$	$1$	$1$	$e\left(\frac{23}{72}\right)$	$e\left(\frac{133}{144}\right)$	$e\left(\frac{59}{144}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{13}{72}\right)$	$e\left(\frac{139}{144}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{7}{72}\right)$
$\chi_{8640}(1987,\cdot)$	$1$	$1$	$e\left(\frac{13}{72}\right)$	$e\left(\frac{47}{144}\right)$	$e\left(\frac{49}{144}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{23}{72}\right)$	$e\left(\frac{113}{144}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{13}{48}\right)$	$e\left(\frac{29}{72}\right)$
$\chi_{8640}(2203,\cdot)$	$1$	$1$	$e\left(\frac{31}{72}\right)$	$e\left(\frac{29}{144}\right)$	$e\left(\frac{67}{144}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{5}{72}\right)$	$e\left(\frac{131}{144}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{47}{72}\right)$
$\chi_{8640}(2227,\cdot)$	$1$	$1$	$e\left(\frac{17}{72}\right)$	$e\left(\frac{139}{144}\right)$	$e\left(\frac{53}{144}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{19}{72}\right)$	$e\left(\frac{37}{144}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{49}{72}\right)$
$\chi_{8640}(2443,\cdot)$	$1$	$1$	$e\left(\frac{35}{72}\right)$	$e\left(\frac{121}{144}\right)$	$e\left(\frac{71}{144}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{1}{72}\right)$	$e\left(\frac{55}{144}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{67}{72}\right)$
$\chi_{8640}(2707,\cdot)$	$1$	$1$	$e\left(\frac{25}{72}\right)$	$e\left(\frac{35}{144}\right)$	$e\left(\frac{61}{144}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{11}{72}\right)$	$e\left(\frac{29}{144}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{17}{72}\right)$
$\chi_{8640}(2923,\cdot)$	$1$	$1$	$e\left(\frac{43}{72}\right)$	$e\left(\frac{17}{144}\right)$	$e\left(\frac{79}{144}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{65}{72}\right)$	$e\left(\frac{47}{144}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{35}{72}\right)$
$\chi_{8640}(2947,\cdot)$	$1$	$1$	$e\left(\frac{29}{72}\right)$	$e\left(\frac{127}{144}\right)$	$e\left(\frac{65}{144}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{7}{72}\right)$	$e\left(\frac{97}{144}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{37}{72}\right)$
$\chi_{8640}(3163,\cdot)$	$1$	$1$	$e\left(\frac{47}{72}\right)$	$e\left(\frac{109}{144}\right)$	$e\left(\frac{83}{144}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{13}{48}\right)$	$e\left(\frac{61}{72}\right)$	$e\left(\frac{115}{144}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{55}{72}\right)$
$\chi_{8640}(3427,\cdot)$	$1$	$1$	$e\left(\frac{37}{72}\right)$	$e\left(\frac{23}{144}\right)$	$e\left(\frac{73}{144}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{71}{72}\right)$	$e\left(\frac{89}{144}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{5}{72}\right)$
$\chi_{8640}(3643,\cdot)$	$1$	$1$	$e\left(\frac{55}{72}\right)$	$e\left(\frac{5}{144}\right)$	$e\left(\frac{91}{144}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{53}{72}\right)$	$e\left(\frac{107}{144}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{23}{72}\right)$
$\chi_{8640}(3667,\cdot)$	$1$	$1$	$e\left(\frac{41}{72}\right)$	$e\left(\frac{115}{144}\right)$	$e\left(\frac{77}{144}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{67}{72}\right)$	$e\left(\frac{13}{144}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{25}{72}\right)$
$\chi_{8640}(3883,\cdot)$	$1$	$1$	$e\left(\frac{59}{72}\right)$	$e\left(\frac{97}{144}\right)$	$e\left(\frac{95}{144}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{49}{72}\right)$	$e\left(\frac{31}{144}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{43}{72}\right)$
$\chi_{8640}(4147,\cdot)$	$1$	$1$	$e\left(\frac{49}{72}\right)$	$e\left(\frac{11}{144}\right)$	$e\left(\frac{85}{144}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{59}{72}\right)$	$e\left(\frac{5}{144}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{65}{72}\right)$
$\chi_{8640}(4363,\cdot)$	$1$	$1$	$e\left(\frac{67}{72}\right)$	$e\left(\frac{137}{144}\right)$	$e\left(\frac{103}{144}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{41}{72}\right)$	$e\left(\frac{23}{144}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{11}{72}\right)$
$\chi_{8640}(4387,\cdot)$	$1$	$1$	$e\left(\frac{53}{72}\right)$	$e\left(\frac{103}{144}\right)$	$e\left(\frac{89}{144}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{55}{72}\right)$	$e\left(\frac{73}{144}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{13}{72}\right)$
$\chi_{8640}(4603,\cdot)$	$1$	$1$	$e\left(\frac{71}{72}\right)$	$e\left(\frac{85}{144}\right)$	$e\left(\frac{107}{144}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{37}{72}\right)$	$e\left(\frac{91}{144}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{31}{72}\right)$
$\chi_{8640}(4867,\cdot)$	$1$	$1$	$e\left(\frac{61}{72}\right)$	$e\left(\frac{143}{144}\right)$	$e\left(\frac{97}{144}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{47}{72}\right)$	$e\left(\frac{65}{144}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{13}{48}\right)$	$e\left(\frac{53}{72}\right)$
$\chi_{8640}(5083,\cdot)$	$1$	$1$	$e\left(\frac{7}{72}\right)$	$e\left(\frac{125}{144}\right)$	$e\left(\frac{115}{144}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{29}{72}\right)$	$e\left(\frac{83}{144}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{71}{72}\right)$
$\chi_{8640}(5107,\cdot)$	$1$	$1$	$e\left(\frac{65}{72}\right)$	$e\left(\frac{91}{144}\right)$	$e\left(\frac{101}{144}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{43}{72}\right)$	$e\left(\frac{133}{144}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{1}{72}\right)$
$\chi_{8640}(5323,\cdot)$	$1$	$1$	$e\left(\frac{11}{72}\right)$	$e\left(\frac{73}{144}\right)$	$e\left(\frac{119}{144}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{25}{72}\right)$	$e\left(\frac{7}{144}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{19}{72}\right)$

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	\(-1\)	\(1\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)
\(\chi_{8640}(43,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{67}{72}\right)\)	\(e\left(\frac{65}{144}\right)\)	\(e\left(\frac{31}{144}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{41}{72}\right)\)	\(e\left(\frac{95}{144}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{11}{72}\right)\)
\(\chi_{8640}(67,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{72}\right)\)	\(e\left(\frac{31}{144}\right)\)	\(e\left(\frac{17}{144}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{55}{72}\right)\)	\(e\left(\frac{1}{144}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{13}{72}\right)\)
\(\chi_{8640}(283,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{71}{72}\right)\)	\(e\left(\frac{13}{144}\right)\)	\(e\left(\frac{35}{144}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{13}{48}\right)\)	\(e\left(\frac{37}{72}\right)\)	\(e\left(\frac{19}{144}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{31}{72}\right)\)
\(\chi_{8640}(547,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{61}{72}\right)\)	\(e\left(\frac{71}{144}\right)\)	\(e\left(\frac{25}{144}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{47}{72}\right)\)	\(e\left(\frac{137}{144}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{53}{72}\right)\)
\(\chi_{8640}(763,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{72}\right)\)	\(e\left(\frac{53}{144}\right)\)	\(e\left(\frac{43}{144}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{29}{72}\right)\)	\(e\left(\frac{11}{144}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{71}{72}\right)\)
\(\chi_{8640}(787,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{65}{72}\right)\)	\(e\left(\frac{19}{144}\right)\)	\(e\left(\frac{29}{144}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{43}{72}\right)\)	\(e\left(\frac{61}{144}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{1}{72}\right)\)
\(\chi_{8640}(1003,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{72}\right)\)	\(e\left(\frac{1}{144}\right)\)	\(e\left(\frac{47}{144}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{25}{72}\right)\)	\(e\left(\frac{79}{144}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{19}{72}\right)\)
\(\chi_{8640}(1267,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{72}\right)\)	\(e\left(\frac{59}{144}\right)\)	\(e\left(\frac{37}{144}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{35}{72}\right)\)	\(e\left(\frac{53}{144}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{41}{72}\right)\)
\(\chi_{8640}(1483,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{72}\right)\)	\(e\left(\frac{41}{144}\right)\)	\(e\left(\frac{55}{144}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{17}{72}\right)\)	\(e\left(\frac{71}{144}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{59}{72}\right)\)
\(\chi_{8640}(1507,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{72}\right)\)	\(e\left(\frac{7}{144}\right)\)	\(e\left(\frac{41}{144}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{31}{72}\right)\)	\(e\left(\frac{121}{144}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{61}{72}\right)\)
\(\chi_{8640}(1723,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{72}\right)\)	\(e\left(\frac{133}{144}\right)\)	\(e\left(\frac{59}{144}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{13}{72}\right)\)	\(e\left(\frac{139}{144}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{7}{72}\right)\)
\(\chi_{8640}(1987,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{72}\right)\)	\(e\left(\frac{47}{144}\right)\)	\(e\left(\frac{49}{144}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{23}{72}\right)\)	\(e\left(\frac{113}{144}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{13}{48}\right)\)	\(e\left(\frac{29}{72}\right)\)
\(\chi_{8640}(2203,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{72}\right)\)	\(e\left(\frac{29}{144}\right)\)	\(e\left(\frac{67}{144}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{5}{72}\right)\)	\(e\left(\frac{131}{144}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{47}{72}\right)\)
\(\chi_{8640}(2227,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{72}\right)\)	\(e\left(\frac{139}{144}\right)\)	\(e\left(\frac{53}{144}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{19}{72}\right)\)	\(e\left(\frac{37}{144}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{49}{72}\right)\)
\(\chi_{8640}(2443,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{35}{72}\right)\)	\(e\left(\frac{121}{144}\right)\)	\(e\left(\frac{71}{144}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{1}{72}\right)\)	\(e\left(\frac{55}{144}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{67}{72}\right)\)
\(\chi_{8640}(2707,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{25}{72}\right)\)	\(e\left(\frac{35}{144}\right)\)	\(e\left(\frac{61}{144}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{11}{72}\right)\)	\(e\left(\frac{29}{144}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{17}{72}\right)\)
\(\chi_{8640}(2923,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{72}\right)\)	\(e\left(\frac{17}{144}\right)\)	\(e\left(\frac{79}{144}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{65}{72}\right)\)	\(e\left(\frac{47}{144}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{35}{72}\right)\)
\(\chi_{8640}(2947,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{72}\right)\)	\(e\left(\frac{127}{144}\right)\)	\(e\left(\frac{65}{144}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{7}{72}\right)\)	\(e\left(\frac{97}{144}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{37}{72}\right)\)
\(\chi_{8640}(3163,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{72}\right)\)	\(e\left(\frac{109}{144}\right)\)	\(e\left(\frac{83}{144}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{13}{48}\right)\)	\(e\left(\frac{61}{72}\right)\)	\(e\left(\frac{115}{144}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{55}{72}\right)\)
\(\chi_{8640}(3427,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{72}\right)\)	\(e\left(\frac{23}{144}\right)\)	\(e\left(\frac{73}{144}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{71}{72}\right)\)	\(e\left(\frac{89}{144}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{5}{72}\right)\)
\(\chi_{8640}(3643,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{55}{72}\right)\)	\(e\left(\frac{5}{144}\right)\)	\(e\left(\frac{91}{144}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{53}{72}\right)\)	\(e\left(\frac{107}{144}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{23}{72}\right)\)
\(\chi_{8640}(3667,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{72}\right)\)	\(e\left(\frac{115}{144}\right)\)	\(e\left(\frac{77}{144}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{67}{72}\right)\)	\(e\left(\frac{13}{144}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{25}{72}\right)\)
\(\chi_{8640}(3883,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{72}\right)\)	\(e\left(\frac{97}{144}\right)\)	\(e\left(\frac{95}{144}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{49}{72}\right)\)	\(e\left(\frac{31}{144}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{43}{72}\right)\)
\(\chi_{8640}(4147,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{49}{72}\right)\)	\(e\left(\frac{11}{144}\right)\)	\(e\left(\frac{85}{144}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{59}{72}\right)\)	\(e\left(\frac{5}{144}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{65}{72}\right)\)
\(\chi_{8640}(4363,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{67}{72}\right)\)	\(e\left(\frac{137}{144}\right)\)	\(e\left(\frac{103}{144}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{41}{72}\right)\)	\(e\left(\frac{23}{144}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{11}{72}\right)\)
\(\chi_{8640}(4387,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{72}\right)\)	\(e\left(\frac{103}{144}\right)\)	\(e\left(\frac{89}{144}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{55}{72}\right)\)	\(e\left(\frac{73}{144}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{13}{72}\right)\)
\(\chi_{8640}(4603,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{71}{72}\right)\)	\(e\left(\frac{85}{144}\right)\)	\(e\left(\frac{107}{144}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{37}{72}\right)\)	\(e\left(\frac{91}{144}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{31}{72}\right)\)
\(\chi_{8640}(4867,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{61}{72}\right)\)	\(e\left(\frac{143}{144}\right)\)	\(e\left(\frac{97}{144}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{47}{72}\right)\)	\(e\left(\frac{65}{144}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{13}{48}\right)\)	\(e\left(\frac{53}{72}\right)\)
\(\chi_{8640}(5083,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{72}\right)\)	\(e\left(\frac{125}{144}\right)\)	\(e\left(\frac{115}{144}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{29}{72}\right)\)	\(e\left(\frac{83}{144}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{71}{72}\right)\)
\(\chi_{8640}(5107,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{65}{72}\right)\)	\(e\left(\frac{91}{144}\right)\)	\(e\left(\frac{101}{144}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{43}{72}\right)\)	\(e\left(\frac{133}{144}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{1}{72}\right)\)
\(\chi_{8640}(5323,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{72}\right)\)	\(e\left(\frac{73}{144}\right)\)	\(e\left(\frac{119}{144}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{25}{72}\right)\)	\(e\left(\frac{7}{144}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{19}{72}\right)\)

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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	8640.ie
Modulus	$8640$
Conductor	$8640$
Order	$144$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(8640\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(8640\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(144\)	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);