LMFDB - Dirichlet character orbit 5184.cu

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comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(5184, base_ring=CyclotomicField(216)) M = H._module chi = DirichletCharacter(H, M([108,189,44])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(23, 5184)) 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("5184.23"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$5184$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$2592$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$216$	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 2592.ci	comment:If the character is primitive sage:chi.is_primitive() gp:#znconreyconductor(g,chi)==1 magma:IsPrimitive(chi);
Minimal:	no
Parity:	even	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);

Related number fields

Field of values:	$\Q(\zeta_{216})$	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 216 polynomial (not computed)	comment:Fixed field sage:chi.fixed_field()

First 31 of 72 characters in Galois orbit

Character	$-1$	$1$	$5$	$7$	$11$	$13$	$17$	$19$	$23$	$25$	$29$	$31$
$\chi_{5184}(23,\cdot)$	$1$	$1$	$e\left(\frac{121}{216}\right)$	$e\left(\frac{55}{108}\right)$	$e\left(\frac{113}{216}\right)$	$e\left(\frac{163}{216}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{29}{72}\right)$	$e\left(\frac{107}{108}\right)$	$e\left(\frac{13}{108}\right)$	$e\left(\frac{35}{216}\right)$	$e\left(\frac{31}{54}\right)$
$\chi_{5184}(119,\cdot)$	$1$	$1$	$e\left(\frac{53}{216}\right)$	$e\left(\frac{83}{108}\right)$	$e\left(\frac{37}{216}\right)$	$e\left(\frac{191}{216}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{49}{72}\right)$	$e\left(\frac{79}{108}\right)$	$e\left(\frac{53}{108}\right)$	$e\left(\frac{151}{216}\right)$	$e\left(\frac{35}{54}\right)$
$\chi_{5184}(167,\cdot)$	$1$	$1$	$e\left(\frac{199}{216}\right)$	$e\left(\frac{61}{108}\right)$	$e\left(\frac{143}{216}\right)$	$e\left(\frac{61}{216}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{59}{72}\right)$	$e\left(\frac{101}{108}\right)$	$e\left(\frac{91}{108}\right)$	$e\left(\frac{29}{216}\right)$	$e\left(\frac{1}{54}\right)$
$\chi_{5184}(263,\cdot)$	$1$	$1$	$e\left(\frac{59}{216}\right)$	$e\left(\frac{17}{108}\right)$	$e\left(\frac{139}{216}\right)$	$e\left(\frac{17}{216}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{7}{72}\right)$	$e\left(\frac{37}{108}\right)$	$e\left(\frac{59}{108}\right)$	$e\left(\frac{1}{216}\right)$	$e\left(\frac{41}{54}\right)$
$\chi_{5184}(311,\cdot)$	$1$	$1$	$e\left(\frac{61}{216}\right)$	$e\left(\frac{67}{108}\right)$	$e\left(\frac{173}{216}\right)$	$e\left(\frac{175}{216}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{17}{72}\right)$	$e\left(\frac{95}{108}\right)$	$e\left(\frac{61}{108}\right)$	$e\left(\frac{23}{216}\right)$	$e\left(\frac{25}{54}\right)$
$\chi_{5184}(407,\cdot)$	$1$	$1$	$e\left(\frac{65}{216}\right)$	$e\left(\frac{59}{108}\right)$	$e\left(\frac{25}{216}\right)$	$e\left(\frac{59}{216}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{37}{72}\right)$	$e\left(\frac{103}{108}\right)$	$e\left(\frac{65}{108}\right)$	$e\left(\frac{67}{216}\right)$	$e\left(\frac{47}{54}\right)$
$\chi_{5184}(455,\cdot)$	$1$	$1$	$e\left(\frac{139}{216}\right)$	$e\left(\frac{73}{108}\right)$	$e\left(\frac{203}{216}\right)$	$e\left(\frac{73}{216}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{47}{72}\right)$	$e\left(\frac{89}{108}\right)$	$e\left(\frac{31}{108}\right)$	$e\left(\frac{17}{216}\right)$	$e\left(\frac{49}{54}\right)$
$\chi_{5184}(551,\cdot)$	$1$	$1$	$e\left(\frac{71}{216}\right)$	$e\left(\frac{101}{108}\right)$	$e\left(\frac{127}{216}\right)$	$e\left(\frac{101}{216}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{67}{72}\right)$	$e\left(\frac{61}{108}\right)$	$e\left(\frac{71}{108}\right)$	$e\left(\frac{133}{216}\right)$	$e\left(\frac{53}{54}\right)$
$\chi_{5184}(599,\cdot)$	$1$	$1$	$e\left(\frac{1}{216}\right)$	$e\left(\frac{79}{108}\right)$	$e\left(\frac{17}{216}\right)$	$e\left(\frac{187}{216}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{5}{72}\right)$	$e\left(\frac{83}{108}\right)$	$e\left(\frac{1}{108}\right)$	$e\left(\frac{11}{216}\right)$	$e\left(\frac{19}{54}\right)$
$\chi_{5184}(695,\cdot)$	$1$	$1$	$e\left(\frac{77}{216}\right)$	$e\left(\frac{35}{108}\right)$	$e\left(\frac{13}{216}\right)$	$e\left(\frac{143}{216}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{25}{72}\right)$	$e\left(\frac{19}{108}\right)$	$e\left(\frac{77}{108}\right)$	$e\left(\frac{199}{216}\right)$	$e\left(\frac{5}{54}\right)$
$\chi_{5184}(743,\cdot)$	$1$	$1$	$e\left(\frac{79}{216}\right)$	$e\left(\frac{85}{108}\right)$	$e\left(\frac{47}{216}\right)$	$e\left(\frac{85}{216}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{35}{72}\right)$	$e\left(\frac{77}{108}\right)$	$e\left(\frac{79}{108}\right)$	$e\left(\frac{5}{216}\right)$	$e\left(\frac{43}{54}\right)$
$\chi_{5184}(839,\cdot)$	$1$	$1$	$e\left(\frac{83}{216}\right)$	$e\left(\frac{77}{108}\right)$	$e\left(\frac{115}{216}\right)$	$e\left(\frac{185}{216}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{55}{72}\right)$	$e\left(\frac{85}{108}\right)$	$e\left(\frac{83}{108}\right)$	$e\left(\frac{49}{216}\right)$	$e\left(\frac{11}{54}\right)$
$\chi_{5184}(887,\cdot)$	$1$	$1$	$e\left(\frac{157}{216}\right)$	$e\left(\frac{91}{108}\right)$	$e\left(\frac{77}{216}\right)$	$e\left(\frac{199}{216}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{65}{72}\right)$	$e\left(\frac{71}{108}\right)$	$e\left(\frac{49}{108}\right)$	$e\left(\frac{215}{216}\right)$	$e\left(\frac{13}{54}\right)$
$\chi_{5184}(983,\cdot)$	$1$	$1$	$e\left(\frac{89}{216}\right)$	$e\left(\frac{11}{108}\right)$	$e\left(\frac{1}{216}\right)$	$e\left(\frac{11}{216}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{13}{72}\right)$	$e\left(\frac{43}{108}\right)$	$e\left(\frac{89}{108}\right)$	$e\left(\frac{115}{216}\right)$	$e\left(\frac{17}{54}\right)$
$\chi_{5184}(1031,\cdot)$	$1$	$1$	$e\left(\frac{19}{216}\right)$	$e\left(\frac{97}{108}\right)$	$e\left(\frac{107}{216}\right)$	$e\left(\frac{97}{216}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{23}{72}\right)$	$e\left(\frac{65}{108}\right)$	$e\left(\frac{19}{108}\right)$	$e\left(\frac{209}{216}\right)$	$e\left(\frac{37}{54}\right)$
$\chi_{5184}(1127,\cdot)$	$1$	$1$	$e\left(\frac{95}{216}\right)$	$e\left(\frac{53}{108}\right)$	$e\left(\frac{103}{216}\right)$	$e\left(\frac{53}{216}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{43}{72}\right)$	$e\left(\frac{1}{108}\right)$	$e\left(\frac{95}{108}\right)$	$e\left(\frac{181}{216}\right)$	$e\left(\frac{23}{54}\right)$
$\chi_{5184}(1175,\cdot)$	$1$	$1$	$e\left(\frac{97}{216}\right)$	$e\left(\frac{103}{108}\right)$	$e\left(\frac{137}{216}\right)$	$e\left(\frac{211}{216}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{53}{72}\right)$	$e\left(\frac{59}{108}\right)$	$e\left(\frac{97}{108}\right)$	$e\left(\frac{203}{216}\right)$	$e\left(\frac{7}{54}\right)$
$\chi_{5184}(1271,\cdot)$	$1$	$1$	$e\left(\frac{101}{216}\right)$	$e\left(\frac{95}{108}\right)$	$e\left(\frac{205}{216}\right)$	$e\left(\frac{95}{216}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{1}{72}\right)$	$e\left(\frac{67}{108}\right)$	$e\left(\frac{101}{108}\right)$	$e\left(\frac{31}{216}\right)$	$e\left(\frac{29}{54}\right)$
$\chi_{5184}(1319,\cdot)$	$1$	$1$	$e\left(\frac{175}{216}\right)$	$e\left(\frac{1}{108}\right)$	$e\left(\frac{167}{216}\right)$	$e\left(\frac{109}{216}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{11}{72}\right)$	$e\left(\frac{53}{108}\right)$	$e\left(\frac{67}{108}\right)$	$e\left(\frac{197}{216}\right)$	$e\left(\frac{31}{54}\right)$
$\chi_{5184}(1415,\cdot)$	$1$	$1$	$e\left(\frac{107}{216}\right)$	$e\left(\frac{29}{108}\right)$	$e\left(\frac{91}{216}\right)$	$e\left(\frac{137}{216}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{31}{72}\right)$	$e\left(\frac{25}{108}\right)$	$e\left(\frac{107}{108}\right)$	$e\left(\frac{97}{216}\right)$	$e\left(\frac{35}{54}\right)$
$\chi_{5184}(1463,\cdot)$	$1$	$1$	$e\left(\frac{37}{216}\right)$	$e\left(\frac{7}{108}\right)$	$e\left(\frac{197}{216}\right)$	$e\left(\frac{7}{216}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{41}{72}\right)$	$e\left(\frac{47}{108}\right)$	$e\left(\frac{37}{108}\right)$	$e\left(\frac{191}{216}\right)$	$e\left(\frac{1}{54}\right)$
$\chi_{5184}(1559,\cdot)$	$1$	$1$	$e\left(\frac{113}{216}\right)$	$e\left(\frac{71}{108}\right)$	$e\left(\frac{193}{216}\right)$	$e\left(\frac{179}{216}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{61}{72}\right)$	$e\left(\frac{91}{108}\right)$	$e\left(\frac{5}{108}\right)$	$e\left(\frac{163}{216}\right)$	$e\left(\frac{41}{54}\right)$
$\chi_{5184}(1607,\cdot)$	$1$	$1$	$e\left(\frac{115}{216}\right)$	$e\left(\frac{13}{108}\right)$	$e\left(\frac{11}{216}\right)$	$e\left(\frac{121}{216}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{71}{72}\right)$	$e\left(\frac{41}{108}\right)$	$e\left(\frac{7}{108}\right)$	$e\left(\frac{185}{216}\right)$	$e\left(\frac{25}{54}\right)$
$\chi_{5184}(1703,\cdot)$	$1$	$1$	$e\left(\frac{119}{216}\right)$	$e\left(\frac{5}{108}\right)$	$e\left(\frac{79}{216}\right)$	$e\left(\frac{5}{216}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{19}{72}\right)$	$e\left(\frac{49}{108}\right)$	$e\left(\frac{11}{108}\right)$	$e\left(\frac{13}{216}\right)$	$e\left(\frac{47}{54}\right)$
$\chi_{5184}(1751,\cdot)$	$1$	$1$	$e\left(\frac{193}{216}\right)$	$e\left(\frac{19}{108}\right)$	$e\left(\frac{41}{216}\right)$	$e\left(\frac{19}{216}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{29}{72}\right)$	$e\left(\frac{35}{108}\right)$	$e\left(\frac{85}{108}\right)$	$e\left(\frac{179}{216}\right)$	$e\left(\frac{49}{54}\right)$
$\chi_{5184}(1847,\cdot)$	$1$	$1$	$e\left(\frac{125}{216}\right)$	$e\left(\frac{47}{108}\right)$	$e\left(\frac{181}{216}\right)$	$e\left(\frac{47}{216}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{49}{72}\right)$	$e\left(\frac{7}{108}\right)$	$e\left(\frac{17}{108}\right)$	$e\left(\frac{79}{216}\right)$	$e\left(\frac{53}{54}\right)$
$\chi_{5184}(1895,\cdot)$	$1$	$1$	$e\left(\frac{55}{216}\right)$	$e\left(\frac{25}{108}\right)$	$e\left(\frac{71}{216}\right)$	$e\left(\frac{133}{216}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{59}{72}\right)$	$e\left(\frac{29}{108}\right)$	$e\left(\frac{55}{108}\right)$	$e\left(\frac{173}{216}\right)$	$e\left(\frac{19}{54}\right)$
$\chi_{5184}(1991,\cdot)$	$1$	$1$	$e\left(\frac{131}{216}\right)$	$e\left(\frac{89}{108}\right)$	$e\left(\frac{67}{216}\right)$	$e\left(\frac{89}{216}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{7}{72}\right)$	$e\left(\frac{73}{108}\right)$	$e\left(\frac{23}{108}\right)$	$e\left(\frac{145}{216}\right)$	$e\left(\frac{5}{54}\right)$
$\chi_{5184}(2039,\cdot)$	$1$	$1$	$e\left(\frac{133}{216}\right)$	$e\left(\frac{31}{108}\right)$	$e\left(\frac{101}{216}\right)$	$e\left(\frac{31}{216}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{17}{72}\right)$	$e\left(\frac{23}{108}\right)$	$e\left(\frac{25}{108}\right)$	$e\left(\frac{167}{216}\right)$	$e\left(\frac{43}{54}\right)$
$\chi_{5184}(2135,\cdot)$	$1$	$1$	$e\left(\frac{137}{216}\right)$	$e\left(\frac{23}{108}\right)$	$e\left(\frac{169}{216}\right)$	$e\left(\frac{131}{216}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{37}{72}\right)$	$e\left(\frac{31}{108}\right)$	$e\left(\frac{29}{108}\right)$	$e\left(\frac{211}{216}\right)$	$e\left(\frac{11}{54}\right)$
$\chi_{5184}(2183,\cdot)$	$1$	$1$	$e\left(\frac{211}{216}\right)$	$e\left(\frac{37}{108}\right)$	$e\left(\frac{131}{216}\right)$	$e\left(\frac{145}{216}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{47}{72}\right)$	$e\left(\frac{17}{108}\right)$	$e\left(\frac{103}{108}\right)$	$e\left(\frac{161}{216}\right)$	$e\left(\frac{13}{54}\right)$

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Character	\(-1\)	\(1\)	\(5\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)
\(\chi_{5184}(23,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{121}{216}\right)\)	\(e\left(\frac{55}{108}\right)\)	\(e\left(\frac{113}{216}\right)\)	\(e\left(\frac{163}{216}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{29}{72}\right)\)	\(e\left(\frac{107}{108}\right)\)	\(e\left(\frac{13}{108}\right)\)	\(e\left(\frac{35}{216}\right)\)	\(e\left(\frac{31}{54}\right)\)
\(\chi_{5184}(119,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{216}\right)\)	\(e\left(\frac{83}{108}\right)\)	\(e\left(\frac{37}{216}\right)\)	\(e\left(\frac{191}{216}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{49}{72}\right)\)	\(e\left(\frac{79}{108}\right)\)	\(e\left(\frac{53}{108}\right)\)	\(e\left(\frac{151}{216}\right)\)	\(e\left(\frac{35}{54}\right)\)
\(\chi_{5184}(167,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{199}{216}\right)\)	\(e\left(\frac{61}{108}\right)\)	\(e\left(\frac{143}{216}\right)\)	\(e\left(\frac{61}{216}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{59}{72}\right)\)	\(e\left(\frac{101}{108}\right)\)	\(e\left(\frac{91}{108}\right)\)	\(e\left(\frac{29}{216}\right)\)	\(e\left(\frac{1}{54}\right)\)
\(\chi_{5184}(263,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{216}\right)\)	\(e\left(\frac{17}{108}\right)\)	\(e\left(\frac{139}{216}\right)\)	\(e\left(\frac{17}{216}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{7}{72}\right)\)	\(e\left(\frac{37}{108}\right)\)	\(e\left(\frac{59}{108}\right)\)	\(e\left(\frac{1}{216}\right)\)	\(e\left(\frac{41}{54}\right)\)
\(\chi_{5184}(311,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{61}{216}\right)\)	\(e\left(\frac{67}{108}\right)\)	\(e\left(\frac{173}{216}\right)\)	\(e\left(\frac{175}{216}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{17}{72}\right)\)	\(e\left(\frac{95}{108}\right)\)	\(e\left(\frac{61}{108}\right)\)	\(e\left(\frac{23}{216}\right)\)	\(e\left(\frac{25}{54}\right)\)
\(\chi_{5184}(407,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{65}{216}\right)\)	\(e\left(\frac{59}{108}\right)\)	\(e\left(\frac{25}{216}\right)\)	\(e\left(\frac{59}{216}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{37}{72}\right)\)	\(e\left(\frac{103}{108}\right)\)	\(e\left(\frac{65}{108}\right)\)	\(e\left(\frac{67}{216}\right)\)	\(e\left(\frac{47}{54}\right)\)
\(\chi_{5184}(455,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{139}{216}\right)\)	\(e\left(\frac{73}{108}\right)\)	\(e\left(\frac{203}{216}\right)\)	\(e\left(\frac{73}{216}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{47}{72}\right)\)	\(e\left(\frac{89}{108}\right)\)	\(e\left(\frac{31}{108}\right)\)	\(e\left(\frac{17}{216}\right)\)	\(e\left(\frac{49}{54}\right)\)
\(\chi_{5184}(551,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{71}{216}\right)\)	\(e\left(\frac{101}{108}\right)\)	\(e\left(\frac{127}{216}\right)\)	\(e\left(\frac{101}{216}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{67}{72}\right)\)	\(e\left(\frac{61}{108}\right)\)	\(e\left(\frac{71}{108}\right)\)	\(e\left(\frac{133}{216}\right)\)	\(e\left(\frac{53}{54}\right)\)
\(\chi_{5184}(599,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{216}\right)\)	\(e\left(\frac{79}{108}\right)\)	\(e\left(\frac{17}{216}\right)\)	\(e\left(\frac{187}{216}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{5}{72}\right)\)	\(e\left(\frac{83}{108}\right)\)	\(e\left(\frac{1}{108}\right)\)	\(e\left(\frac{11}{216}\right)\)	\(e\left(\frac{19}{54}\right)\)
\(\chi_{5184}(695,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{77}{216}\right)\)	\(e\left(\frac{35}{108}\right)\)	\(e\left(\frac{13}{216}\right)\)	\(e\left(\frac{143}{216}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{25}{72}\right)\)	\(e\left(\frac{19}{108}\right)\)	\(e\left(\frac{77}{108}\right)\)	\(e\left(\frac{199}{216}\right)\)	\(e\left(\frac{5}{54}\right)\)
\(\chi_{5184}(743,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{79}{216}\right)\)	\(e\left(\frac{85}{108}\right)\)	\(e\left(\frac{47}{216}\right)\)	\(e\left(\frac{85}{216}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{35}{72}\right)\)	\(e\left(\frac{77}{108}\right)\)	\(e\left(\frac{79}{108}\right)\)	\(e\left(\frac{5}{216}\right)\)	\(e\left(\frac{43}{54}\right)\)
\(\chi_{5184}(839,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{83}{216}\right)\)	\(e\left(\frac{77}{108}\right)\)	\(e\left(\frac{115}{216}\right)\)	\(e\left(\frac{185}{216}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{55}{72}\right)\)	\(e\left(\frac{85}{108}\right)\)	\(e\left(\frac{83}{108}\right)\)	\(e\left(\frac{49}{216}\right)\)	\(e\left(\frac{11}{54}\right)\)
\(\chi_{5184}(887,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{157}{216}\right)\)	\(e\left(\frac{91}{108}\right)\)	\(e\left(\frac{77}{216}\right)\)	\(e\left(\frac{199}{216}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{65}{72}\right)\)	\(e\left(\frac{71}{108}\right)\)	\(e\left(\frac{49}{108}\right)\)	\(e\left(\frac{215}{216}\right)\)	\(e\left(\frac{13}{54}\right)\)
\(\chi_{5184}(983,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{89}{216}\right)\)	\(e\left(\frac{11}{108}\right)\)	\(e\left(\frac{1}{216}\right)\)	\(e\left(\frac{11}{216}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{13}{72}\right)\)	\(e\left(\frac{43}{108}\right)\)	\(e\left(\frac{89}{108}\right)\)	\(e\left(\frac{115}{216}\right)\)	\(e\left(\frac{17}{54}\right)\)
\(\chi_{5184}(1031,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{216}\right)\)	\(e\left(\frac{97}{108}\right)\)	\(e\left(\frac{107}{216}\right)\)	\(e\left(\frac{97}{216}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{23}{72}\right)\)	\(e\left(\frac{65}{108}\right)\)	\(e\left(\frac{19}{108}\right)\)	\(e\left(\frac{209}{216}\right)\)	\(e\left(\frac{37}{54}\right)\)
\(\chi_{5184}(1127,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{95}{216}\right)\)	\(e\left(\frac{53}{108}\right)\)	\(e\left(\frac{103}{216}\right)\)	\(e\left(\frac{53}{216}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{43}{72}\right)\)	\(e\left(\frac{1}{108}\right)\)	\(e\left(\frac{95}{108}\right)\)	\(e\left(\frac{181}{216}\right)\)	\(e\left(\frac{23}{54}\right)\)
\(\chi_{5184}(1175,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{97}{216}\right)\)	\(e\left(\frac{103}{108}\right)\)	\(e\left(\frac{137}{216}\right)\)	\(e\left(\frac{211}{216}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{53}{72}\right)\)	\(e\left(\frac{59}{108}\right)\)	\(e\left(\frac{97}{108}\right)\)	\(e\left(\frac{203}{216}\right)\)	\(e\left(\frac{7}{54}\right)\)
\(\chi_{5184}(1271,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{101}{216}\right)\)	\(e\left(\frac{95}{108}\right)\)	\(e\left(\frac{205}{216}\right)\)	\(e\left(\frac{95}{216}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{1}{72}\right)\)	\(e\left(\frac{67}{108}\right)\)	\(e\left(\frac{101}{108}\right)\)	\(e\left(\frac{31}{216}\right)\)	\(e\left(\frac{29}{54}\right)\)
\(\chi_{5184}(1319,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{175}{216}\right)\)	\(e\left(\frac{1}{108}\right)\)	\(e\left(\frac{167}{216}\right)\)	\(e\left(\frac{109}{216}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{11}{72}\right)\)	\(e\left(\frac{53}{108}\right)\)	\(e\left(\frac{67}{108}\right)\)	\(e\left(\frac{197}{216}\right)\)	\(e\left(\frac{31}{54}\right)\)
\(\chi_{5184}(1415,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{107}{216}\right)\)	\(e\left(\frac{29}{108}\right)\)	\(e\left(\frac{91}{216}\right)\)	\(e\left(\frac{137}{216}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{31}{72}\right)\)	\(e\left(\frac{25}{108}\right)\)	\(e\left(\frac{107}{108}\right)\)	\(e\left(\frac{97}{216}\right)\)	\(e\left(\frac{35}{54}\right)\)
\(\chi_{5184}(1463,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{216}\right)\)	\(e\left(\frac{7}{108}\right)\)	\(e\left(\frac{197}{216}\right)\)	\(e\left(\frac{7}{216}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{41}{72}\right)\)	\(e\left(\frac{47}{108}\right)\)	\(e\left(\frac{37}{108}\right)\)	\(e\left(\frac{191}{216}\right)\)	\(e\left(\frac{1}{54}\right)\)
\(\chi_{5184}(1559,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{113}{216}\right)\)	\(e\left(\frac{71}{108}\right)\)	\(e\left(\frac{193}{216}\right)\)	\(e\left(\frac{179}{216}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{61}{72}\right)\)	\(e\left(\frac{91}{108}\right)\)	\(e\left(\frac{5}{108}\right)\)	\(e\left(\frac{163}{216}\right)\)	\(e\left(\frac{41}{54}\right)\)
\(\chi_{5184}(1607,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{115}{216}\right)\)	\(e\left(\frac{13}{108}\right)\)	\(e\left(\frac{11}{216}\right)\)	\(e\left(\frac{121}{216}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{71}{72}\right)\)	\(e\left(\frac{41}{108}\right)\)	\(e\left(\frac{7}{108}\right)\)	\(e\left(\frac{185}{216}\right)\)	\(e\left(\frac{25}{54}\right)\)
\(\chi_{5184}(1703,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{119}{216}\right)\)	\(e\left(\frac{5}{108}\right)\)	\(e\left(\frac{79}{216}\right)\)	\(e\left(\frac{5}{216}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{19}{72}\right)\)	\(e\left(\frac{49}{108}\right)\)	\(e\left(\frac{11}{108}\right)\)	\(e\left(\frac{13}{216}\right)\)	\(e\left(\frac{47}{54}\right)\)
\(\chi_{5184}(1751,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{193}{216}\right)\)	\(e\left(\frac{19}{108}\right)\)	\(e\left(\frac{41}{216}\right)\)	\(e\left(\frac{19}{216}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{29}{72}\right)\)	\(e\left(\frac{35}{108}\right)\)	\(e\left(\frac{85}{108}\right)\)	\(e\left(\frac{179}{216}\right)\)	\(e\left(\frac{49}{54}\right)\)
\(\chi_{5184}(1847,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{125}{216}\right)\)	\(e\left(\frac{47}{108}\right)\)	\(e\left(\frac{181}{216}\right)\)	\(e\left(\frac{47}{216}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{49}{72}\right)\)	\(e\left(\frac{7}{108}\right)\)	\(e\left(\frac{17}{108}\right)\)	\(e\left(\frac{79}{216}\right)\)	\(e\left(\frac{53}{54}\right)\)
\(\chi_{5184}(1895,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{55}{216}\right)\)	\(e\left(\frac{25}{108}\right)\)	\(e\left(\frac{71}{216}\right)\)	\(e\left(\frac{133}{216}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{59}{72}\right)\)	\(e\left(\frac{29}{108}\right)\)	\(e\left(\frac{55}{108}\right)\)	\(e\left(\frac{173}{216}\right)\)	\(e\left(\frac{19}{54}\right)\)
\(\chi_{5184}(1991,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{131}{216}\right)\)	\(e\left(\frac{89}{108}\right)\)	\(e\left(\frac{67}{216}\right)\)	\(e\left(\frac{89}{216}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{7}{72}\right)\)	\(e\left(\frac{73}{108}\right)\)	\(e\left(\frac{23}{108}\right)\)	\(e\left(\frac{145}{216}\right)\)	\(e\left(\frac{5}{54}\right)\)
\(\chi_{5184}(2039,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{133}{216}\right)\)	\(e\left(\frac{31}{108}\right)\)	\(e\left(\frac{101}{216}\right)\)	\(e\left(\frac{31}{216}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{17}{72}\right)\)	\(e\left(\frac{23}{108}\right)\)	\(e\left(\frac{25}{108}\right)\)	\(e\left(\frac{167}{216}\right)\)	\(e\left(\frac{43}{54}\right)\)
\(\chi_{5184}(2135,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{137}{216}\right)\)	\(e\left(\frac{23}{108}\right)\)	\(e\left(\frac{169}{216}\right)\)	\(e\left(\frac{131}{216}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{37}{72}\right)\)	\(e\left(\frac{31}{108}\right)\)	\(e\left(\frac{29}{108}\right)\)	\(e\left(\frac{211}{216}\right)\)	\(e\left(\frac{11}{54}\right)\)
\(\chi_{5184}(2183,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{211}{216}\right)\)	\(e\left(\frac{37}{108}\right)\)	\(e\left(\frac{131}{216}\right)\)	\(e\left(\frac{145}{216}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{47}{72}\right)\)	\(e\left(\frac{17}{108}\right)\)	\(e\left(\frac{103}{108}\right)\)	\(e\left(\frac{161}{216}\right)\)	\(e\left(\frac{13}{54}\right)\)

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First 31 of 72 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	5184.cu
Modulus	$5184$
Conductor	$2592$
Order	$216$
Real	no
Primitive	no
Minimal	no
Parity	even

Modulus:	\(5184\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(2592\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(216\)	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 2592.ci	comment:If the character is primitive sage:chi.is_primitive() gp:#znconreyconductor(g,chi)==1 magma:IsPrimitive(chi);
Minimal:	no
Parity:	even	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);