LMFDB - Dirichlet character orbit 5184.cm

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comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(5184, base_ring=CyclotomicField(108)) M = H._module chi = DirichletCharacter(H, M([54,81,14])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(47, 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("5184.47"); 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:	$1296$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$108$	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 1296.bs	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:	$\Q(\zeta_{108})$	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 108 polynomial (not computed)	comment:Fixed field sage:chi.fixed_field()

First 31 of 36 characters in Galois orbit

Character	$-1$	$1$	$5$	$7$	$11$	$13$	$17$	$19$	$23$	$25$	$29$	$31$
$\chi_{5184}(47,\cdot)$	$1$	$1$	$e\left(\frac{79}{108}\right)$	$e\left(\frac{2}{27}\right)$	$e\left(\frac{101}{108}\right)$	$e\left(\frac{31}{108}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{23}{54}\right)$	$e\left(\frac{25}{54}\right)$	$e\left(\frac{5}{108}\right)$	$e\left(\frac{5}{54}\right)$
$\chi_{5184}(239,\cdot)$	$1$	$1$	$e\left(\frac{11}{108}\right)$	$e\left(\frac{16}{27}\right)$	$e\left(\frac{25}{108}\right)$	$e\left(\frac{59}{108}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{49}{54}\right)$	$e\left(\frac{11}{54}\right)$	$e\left(\frac{13}{108}\right)$	$e\left(\frac{13}{54}\right)$
$\chi_{5184}(335,\cdot)$	$1$	$1$	$e\left(\frac{85}{108}\right)$	$e\left(\frac{23}{27}\right)$	$e\left(\frac{95}{108}\right)$	$e\left(\frac{73}{108}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{35}{54}\right)$	$e\left(\frac{31}{54}\right)$	$e\left(\frac{71}{108}\right)$	$e\left(\frac{17}{54}\right)$
$\chi_{5184}(527,\cdot)$	$1$	$1$	$e\left(\frac{89}{108}\right)$	$e\left(\frac{19}{27}\right)$	$e\left(\frac{55}{108}\right)$	$e\left(\frac{65}{108}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{43}{54}\right)$	$e\left(\frac{35}{54}\right)$	$e\left(\frac{7}{108}\right)$	$e\left(\frac{7}{54}\right)$
$\chi_{5184}(623,\cdot)$	$1$	$1$	$e\left(\frac{91}{108}\right)$	$e\left(\frac{17}{27}\right)$	$e\left(\frac{89}{108}\right)$	$e\left(\frac{7}{108}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{47}{54}\right)$	$e\left(\frac{37}{54}\right)$	$e\left(\frac{29}{108}\right)$	$e\left(\frac{29}{54}\right)$
$\chi_{5184}(815,\cdot)$	$1$	$1$	$e\left(\frac{59}{108}\right)$	$e\left(\frac{22}{27}\right)$	$e\left(\frac{85}{108}\right)$	$e\left(\frac{71}{108}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{37}{54}\right)$	$e\left(\frac{5}{54}\right)$	$e\left(\frac{1}{108}\right)$	$e\left(\frac{1}{54}\right)$
$\chi_{5184}(911,\cdot)$	$1$	$1$	$e\left(\frac{97}{108}\right)$	$e\left(\frac{11}{27}\right)$	$e\left(\frac{83}{108}\right)$	$e\left(\frac{49}{108}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{5}{54}\right)$	$e\left(\frac{43}{54}\right)$	$e\left(\frac{95}{108}\right)$	$e\left(\frac{41}{54}\right)$
$\chi_{5184}(1103,\cdot)$	$1$	$1$	$e\left(\frac{29}{108}\right)$	$e\left(\frac{25}{27}\right)$	$e\left(\frac{7}{108}\right)$	$e\left(\frac{77}{108}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{31}{54}\right)$	$e\left(\frac{29}{54}\right)$	$e\left(\frac{103}{108}\right)$	$e\left(\frac{49}{54}\right)$
$\chi_{5184}(1199,\cdot)$	$1$	$1$	$e\left(\frac{103}{108}\right)$	$e\left(\frac{5}{27}\right)$	$e\left(\frac{77}{108}\right)$	$e\left(\frac{91}{108}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{17}{54}\right)$	$e\left(\frac{49}{54}\right)$	$e\left(\frac{53}{108}\right)$	$e\left(\frac{53}{54}\right)$
$\chi_{5184}(1391,\cdot)$	$1$	$1$	$e\left(\frac{107}{108}\right)$	$e\left(\frac{1}{27}\right)$	$e\left(\frac{37}{108}\right)$	$e\left(\frac{83}{108}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{25}{54}\right)$	$e\left(\frac{53}{54}\right)$	$e\left(\frac{97}{108}\right)$	$e\left(\frac{43}{54}\right)$
$\chi_{5184}(1487,\cdot)$	$1$	$1$	$e\left(\frac{1}{108}\right)$	$e\left(\frac{26}{27}\right)$	$e\left(\frac{71}{108}\right)$	$e\left(\frac{25}{108}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{29}{54}\right)$	$e\left(\frac{1}{54}\right)$	$e\left(\frac{11}{108}\right)$	$e\left(\frac{11}{54}\right)$
$\chi_{5184}(1679,\cdot)$	$1$	$1$	$e\left(\frac{77}{108}\right)$	$e\left(\frac{4}{27}\right)$	$e\left(\frac{67}{108}\right)$	$e\left(\frac{89}{108}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{19}{54}\right)$	$e\left(\frac{23}{54}\right)$	$e\left(\frac{91}{108}\right)$	$e\left(\frac{37}{54}\right)$
$\chi_{5184}(1775,\cdot)$	$1$	$1$	$e\left(\frac{7}{108}\right)$	$e\left(\frac{20}{27}\right)$	$e\left(\frac{65}{108}\right)$	$e\left(\frac{67}{108}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{41}{54}\right)$	$e\left(\frac{7}{54}\right)$	$e\left(\frac{77}{108}\right)$	$e\left(\frac{23}{54}\right)$
$\chi_{5184}(1967,\cdot)$	$1$	$1$	$e\left(\frac{47}{108}\right)$	$e\left(\frac{7}{27}\right)$	$e\left(\frac{97}{108}\right)$	$e\left(\frac{95}{108}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{13}{54}\right)$	$e\left(\frac{47}{54}\right)$	$e\left(\frac{85}{108}\right)$	$e\left(\frac{31}{54}\right)$
$\chi_{5184}(2063,\cdot)$	$1$	$1$	$e\left(\frac{13}{108}\right)$	$e\left(\frac{14}{27}\right)$	$e\left(\frac{59}{108}\right)$	$e\left(\frac{1}{108}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{53}{54}\right)$	$e\left(\frac{13}{54}\right)$	$e\left(\frac{35}{108}\right)$	$e\left(\frac{35}{54}\right)$
$\chi_{5184}(2255,\cdot)$	$1$	$1$	$e\left(\frac{17}{108}\right)$	$e\left(\frac{10}{27}\right)$	$e\left(\frac{19}{108}\right)$	$e\left(\frac{101}{108}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{7}{54}\right)$	$e\left(\frac{17}{54}\right)$	$e\left(\frac{79}{108}\right)$	$e\left(\frac{25}{54}\right)$
$\chi_{5184}(2351,\cdot)$	$1$	$1$	$e\left(\frac{19}{108}\right)$	$e\left(\frac{8}{27}\right)$	$e\left(\frac{53}{108}\right)$	$e\left(\frac{43}{108}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{11}{54}\right)$	$e\left(\frac{19}{54}\right)$	$e\left(\frac{101}{108}\right)$	$e\left(\frac{47}{54}\right)$
$\chi_{5184}(2543,\cdot)$	$1$	$1$	$e\left(\frac{95}{108}\right)$	$e\left(\frac{13}{27}\right)$	$e\left(\frac{49}{108}\right)$	$e\left(\frac{107}{108}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{1}{54}\right)$	$e\left(\frac{41}{54}\right)$	$e\left(\frac{73}{108}\right)$	$e\left(\frac{19}{54}\right)$
$\chi_{5184}(2639,\cdot)$	$1$	$1$	$e\left(\frac{25}{108}\right)$	$e\left(\frac{2}{27}\right)$	$e\left(\frac{47}{108}\right)$	$e\left(\frac{85}{108}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{23}{54}\right)$	$e\left(\frac{25}{54}\right)$	$e\left(\frac{59}{108}\right)$	$e\left(\frac{5}{54}\right)$
$\chi_{5184}(2831,\cdot)$	$1$	$1$	$e\left(\frac{65}{108}\right)$	$e\left(\frac{16}{27}\right)$	$e\left(\frac{79}{108}\right)$	$e\left(\frac{5}{108}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{49}{54}\right)$	$e\left(\frac{11}{54}\right)$	$e\left(\frac{67}{108}\right)$	$e\left(\frac{13}{54}\right)$
$\chi_{5184}(2927,\cdot)$	$1$	$1$	$e\left(\frac{31}{108}\right)$	$e\left(\frac{23}{27}\right)$	$e\left(\frac{41}{108}\right)$	$e\left(\frac{19}{108}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{35}{54}\right)$	$e\left(\frac{31}{54}\right)$	$e\left(\frac{17}{108}\right)$	$e\left(\frac{17}{54}\right)$
$\chi_{5184}(3119,\cdot)$	$1$	$1$	$e\left(\frac{35}{108}\right)$	$e\left(\frac{19}{27}\right)$	$e\left(\frac{1}{108}\right)$	$e\left(\frac{11}{108}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{43}{54}\right)$	$e\left(\frac{35}{54}\right)$	$e\left(\frac{61}{108}\right)$	$e\left(\frac{7}{54}\right)$
$\chi_{5184}(3215,\cdot)$	$1$	$1$	$e\left(\frac{37}{108}\right)$	$e\left(\frac{17}{27}\right)$	$e\left(\frac{35}{108}\right)$	$e\left(\frac{61}{108}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{47}{54}\right)$	$e\left(\frac{37}{54}\right)$	$e\left(\frac{83}{108}\right)$	$e\left(\frac{29}{54}\right)$
$\chi_{5184}(3407,\cdot)$	$1$	$1$	$e\left(\frac{5}{108}\right)$	$e\left(\frac{22}{27}\right)$	$e\left(\frac{31}{108}\right)$	$e\left(\frac{17}{108}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{37}{54}\right)$	$e\left(\frac{5}{54}\right)$	$e\left(\frac{55}{108}\right)$	$e\left(\frac{1}{54}\right)$
$\chi_{5184}(3503,\cdot)$	$1$	$1$	$e\left(\frac{43}{108}\right)$	$e\left(\frac{11}{27}\right)$	$e\left(\frac{29}{108}\right)$	$e\left(\frac{103}{108}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{5}{54}\right)$	$e\left(\frac{43}{54}\right)$	$e\left(\frac{41}{108}\right)$	$e\left(\frac{41}{54}\right)$
$\chi_{5184}(3695,\cdot)$	$1$	$1$	$e\left(\frac{83}{108}\right)$	$e\left(\frac{25}{27}\right)$	$e\left(\frac{61}{108}\right)$	$e\left(\frac{23}{108}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{31}{54}\right)$	$e\left(\frac{29}{54}\right)$	$e\left(\frac{49}{108}\right)$	$e\left(\frac{49}{54}\right)$
$\chi_{5184}(3791,\cdot)$	$1$	$1$	$e\left(\frac{49}{108}\right)$	$e\left(\frac{5}{27}\right)$	$e\left(\frac{23}{108}\right)$	$e\left(\frac{37}{108}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{17}{54}\right)$	$e\left(\frac{49}{54}\right)$	$e\left(\frac{107}{108}\right)$	$e\left(\frac{53}{54}\right)$
$\chi_{5184}(3983,\cdot)$	$1$	$1$	$e\left(\frac{53}{108}\right)$	$e\left(\frac{1}{27}\right)$	$e\left(\frac{91}{108}\right)$	$e\left(\frac{29}{108}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{25}{54}\right)$	$e\left(\frac{53}{54}\right)$	$e\left(\frac{43}{108}\right)$	$e\left(\frac{43}{54}\right)$
$\chi_{5184}(4079,\cdot)$	$1$	$1$	$e\left(\frac{55}{108}\right)$	$e\left(\frac{26}{27}\right)$	$e\left(\frac{17}{108}\right)$	$e\left(\frac{79}{108}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{29}{54}\right)$	$e\left(\frac{1}{54}\right)$	$e\left(\frac{65}{108}\right)$	$e\left(\frac{11}{54}\right)$
$\chi_{5184}(4271,\cdot)$	$1$	$1$	$e\left(\frac{23}{108}\right)$	$e\left(\frac{4}{27}\right)$	$e\left(\frac{13}{108}\right)$	$e\left(\frac{35}{108}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{19}{54}\right)$	$e\left(\frac{23}{54}\right)$	$e\left(\frac{37}{108}\right)$	$e\left(\frac{37}{54}\right)$
$\chi_{5184}(4367,\cdot)$	$1$	$1$	$e\left(\frac{61}{108}\right)$	$e\left(\frac{20}{27}\right)$	$e\left(\frac{11}{108}\right)$	$e\left(\frac{13}{108}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{41}{54}\right)$	$e\left(\frac{7}{54}\right)$	$e\left(\frac{23}{108}\right)$	$e\left(\frac{23}{54}\right)$

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	\(-1\)	\(1\)	\(5\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)
\(\chi_{5184}(47,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{79}{108}\right)\)	\(e\left(\frac{2}{27}\right)\)	\(e\left(\frac{101}{108}\right)\)	\(e\left(\frac{31}{108}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{23}{54}\right)\)	\(e\left(\frac{25}{54}\right)\)	\(e\left(\frac{5}{108}\right)\)	\(e\left(\frac{5}{54}\right)\)
\(\chi_{5184}(239,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{108}\right)\)	\(e\left(\frac{16}{27}\right)\)	\(e\left(\frac{25}{108}\right)\)	\(e\left(\frac{59}{108}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{49}{54}\right)\)	\(e\left(\frac{11}{54}\right)\)	\(e\left(\frac{13}{108}\right)\)	\(e\left(\frac{13}{54}\right)\)
\(\chi_{5184}(335,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{85}{108}\right)\)	\(e\left(\frac{23}{27}\right)\)	\(e\left(\frac{95}{108}\right)\)	\(e\left(\frac{73}{108}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{35}{54}\right)\)	\(e\left(\frac{31}{54}\right)\)	\(e\left(\frac{71}{108}\right)\)	\(e\left(\frac{17}{54}\right)\)
\(\chi_{5184}(527,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{89}{108}\right)\)	\(e\left(\frac{19}{27}\right)\)	\(e\left(\frac{55}{108}\right)\)	\(e\left(\frac{65}{108}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{43}{54}\right)\)	\(e\left(\frac{35}{54}\right)\)	\(e\left(\frac{7}{108}\right)\)	\(e\left(\frac{7}{54}\right)\)
\(\chi_{5184}(623,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{91}{108}\right)\)	\(e\left(\frac{17}{27}\right)\)	\(e\left(\frac{89}{108}\right)\)	\(e\left(\frac{7}{108}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{47}{54}\right)\)	\(e\left(\frac{37}{54}\right)\)	\(e\left(\frac{29}{108}\right)\)	\(e\left(\frac{29}{54}\right)\)
\(\chi_{5184}(815,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{108}\right)\)	\(e\left(\frac{22}{27}\right)\)	\(e\left(\frac{85}{108}\right)\)	\(e\left(\frac{71}{108}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{37}{54}\right)\)	\(e\left(\frac{5}{54}\right)\)	\(e\left(\frac{1}{108}\right)\)	\(e\left(\frac{1}{54}\right)\)
\(\chi_{5184}(911,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{97}{108}\right)\)	\(e\left(\frac{11}{27}\right)\)	\(e\left(\frac{83}{108}\right)\)	\(e\left(\frac{49}{108}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{5}{54}\right)\)	\(e\left(\frac{43}{54}\right)\)	\(e\left(\frac{95}{108}\right)\)	\(e\left(\frac{41}{54}\right)\)
\(\chi_{5184}(1103,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{108}\right)\)	\(e\left(\frac{25}{27}\right)\)	\(e\left(\frac{7}{108}\right)\)	\(e\left(\frac{77}{108}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{31}{54}\right)\)	\(e\left(\frac{29}{54}\right)\)	\(e\left(\frac{103}{108}\right)\)	\(e\left(\frac{49}{54}\right)\)
\(\chi_{5184}(1199,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{103}{108}\right)\)	\(e\left(\frac{5}{27}\right)\)	\(e\left(\frac{77}{108}\right)\)	\(e\left(\frac{91}{108}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{17}{54}\right)\)	\(e\left(\frac{49}{54}\right)\)	\(e\left(\frac{53}{108}\right)\)	\(e\left(\frac{53}{54}\right)\)
\(\chi_{5184}(1391,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{107}{108}\right)\)	\(e\left(\frac{1}{27}\right)\)	\(e\left(\frac{37}{108}\right)\)	\(e\left(\frac{83}{108}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{25}{54}\right)\)	\(e\left(\frac{53}{54}\right)\)	\(e\left(\frac{97}{108}\right)\)	\(e\left(\frac{43}{54}\right)\)
\(\chi_{5184}(1487,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{108}\right)\)	\(e\left(\frac{26}{27}\right)\)	\(e\left(\frac{71}{108}\right)\)	\(e\left(\frac{25}{108}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{29}{54}\right)\)	\(e\left(\frac{1}{54}\right)\)	\(e\left(\frac{11}{108}\right)\)	\(e\left(\frac{11}{54}\right)\)
\(\chi_{5184}(1679,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{77}{108}\right)\)	\(e\left(\frac{4}{27}\right)\)	\(e\left(\frac{67}{108}\right)\)	\(e\left(\frac{89}{108}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{19}{54}\right)\)	\(e\left(\frac{23}{54}\right)\)	\(e\left(\frac{91}{108}\right)\)	\(e\left(\frac{37}{54}\right)\)
\(\chi_{5184}(1775,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{108}\right)\)	\(e\left(\frac{20}{27}\right)\)	\(e\left(\frac{65}{108}\right)\)	\(e\left(\frac{67}{108}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{41}{54}\right)\)	\(e\left(\frac{7}{54}\right)\)	\(e\left(\frac{77}{108}\right)\)	\(e\left(\frac{23}{54}\right)\)
\(\chi_{5184}(1967,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{108}\right)\)	\(e\left(\frac{7}{27}\right)\)	\(e\left(\frac{97}{108}\right)\)	\(e\left(\frac{95}{108}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{13}{54}\right)\)	\(e\left(\frac{47}{54}\right)\)	\(e\left(\frac{85}{108}\right)\)	\(e\left(\frac{31}{54}\right)\)
\(\chi_{5184}(2063,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{108}\right)\)	\(e\left(\frac{14}{27}\right)\)	\(e\left(\frac{59}{108}\right)\)	\(e\left(\frac{1}{108}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{53}{54}\right)\)	\(e\left(\frac{13}{54}\right)\)	\(e\left(\frac{35}{108}\right)\)	\(e\left(\frac{35}{54}\right)\)
\(\chi_{5184}(2255,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{108}\right)\)	\(e\left(\frac{10}{27}\right)\)	\(e\left(\frac{19}{108}\right)\)	\(e\left(\frac{101}{108}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{7}{54}\right)\)	\(e\left(\frac{17}{54}\right)\)	\(e\left(\frac{79}{108}\right)\)	\(e\left(\frac{25}{54}\right)\)
\(\chi_{5184}(2351,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{108}\right)\)	\(e\left(\frac{8}{27}\right)\)	\(e\left(\frac{53}{108}\right)\)	\(e\left(\frac{43}{108}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{11}{54}\right)\)	\(e\left(\frac{19}{54}\right)\)	\(e\left(\frac{101}{108}\right)\)	\(e\left(\frac{47}{54}\right)\)
\(\chi_{5184}(2543,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{95}{108}\right)\)	\(e\left(\frac{13}{27}\right)\)	\(e\left(\frac{49}{108}\right)\)	\(e\left(\frac{107}{108}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{1}{54}\right)\)	\(e\left(\frac{41}{54}\right)\)	\(e\left(\frac{73}{108}\right)\)	\(e\left(\frac{19}{54}\right)\)
\(\chi_{5184}(2639,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{25}{108}\right)\)	\(e\left(\frac{2}{27}\right)\)	\(e\left(\frac{47}{108}\right)\)	\(e\left(\frac{85}{108}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{23}{54}\right)\)	\(e\left(\frac{25}{54}\right)\)	\(e\left(\frac{59}{108}\right)\)	\(e\left(\frac{5}{54}\right)\)
\(\chi_{5184}(2831,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{65}{108}\right)\)	\(e\left(\frac{16}{27}\right)\)	\(e\left(\frac{79}{108}\right)\)	\(e\left(\frac{5}{108}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{49}{54}\right)\)	\(e\left(\frac{11}{54}\right)\)	\(e\left(\frac{67}{108}\right)\)	\(e\left(\frac{13}{54}\right)\)
\(\chi_{5184}(2927,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{108}\right)\)	\(e\left(\frac{23}{27}\right)\)	\(e\left(\frac{41}{108}\right)\)	\(e\left(\frac{19}{108}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{35}{54}\right)\)	\(e\left(\frac{31}{54}\right)\)	\(e\left(\frac{17}{108}\right)\)	\(e\left(\frac{17}{54}\right)\)
\(\chi_{5184}(3119,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{35}{108}\right)\)	\(e\left(\frac{19}{27}\right)\)	\(e\left(\frac{1}{108}\right)\)	\(e\left(\frac{11}{108}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{43}{54}\right)\)	\(e\left(\frac{35}{54}\right)\)	\(e\left(\frac{61}{108}\right)\)	\(e\left(\frac{7}{54}\right)\)
\(\chi_{5184}(3215,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{108}\right)\)	\(e\left(\frac{17}{27}\right)\)	\(e\left(\frac{35}{108}\right)\)	\(e\left(\frac{61}{108}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{47}{54}\right)\)	\(e\left(\frac{37}{54}\right)\)	\(e\left(\frac{83}{108}\right)\)	\(e\left(\frac{29}{54}\right)\)
\(\chi_{5184}(3407,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{108}\right)\)	\(e\left(\frac{22}{27}\right)\)	\(e\left(\frac{31}{108}\right)\)	\(e\left(\frac{17}{108}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{37}{54}\right)\)	\(e\left(\frac{5}{54}\right)\)	\(e\left(\frac{55}{108}\right)\)	\(e\left(\frac{1}{54}\right)\)
\(\chi_{5184}(3503,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{108}\right)\)	\(e\left(\frac{11}{27}\right)\)	\(e\left(\frac{29}{108}\right)\)	\(e\left(\frac{103}{108}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{5}{54}\right)\)	\(e\left(\frac{43}{54}\right)\)	\(e\left(\frac{41}{108}\right)\)	\(e\left(\frac{41}{54}\right)\)
\(\chi_{5184}(3695,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{83}{108}\right)\)	\(e\left(\frac{25}{27}\right)\)	\(e\left(\frac{61}{108}\right)\)	\(e\left(\frac{23}{108}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{31}{54}\right)\)	\(e\left(\frac{29}{54}\right)\)	\(e\left(\frac{49}{108}\right)\)	\(e\left(\frac{49}{54}\right)\)
\(\chi_{5184}(3791,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{49}{108}\right)\)	\(e\left(\frac{5}{27}\right)\)	\(e\left(\frac{23}{108}\right)\)	\(e\left(\frac{37}{108}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{17}{54}\right)\)	\(e\left(\frac{49}{54}\right)\)	\(e\left(\frac{107}{108}\right)\)	\(e\left(\frac{53}{54}\right)\)
\(\chi_{5184}(3983,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{108}\right)\)	\(e\left(\frac{1}{27}\right)\)	\(e\left(\frac{91}{108}\right)\)	\(e\left(\frac{29}{108}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{25}{54}\right)\)	\(e\left(\frac{53}{54}\right)\)	\(e\left(\frac{43}{108}\right)\)	\(e\left(\frac{43}{54}\right)\)
\(\chi_{5184}(4079,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{55}{108}\right)\)	\(e\left(\frac{26}{27}\right)\)	\(e\left(\frac{17}{108}\right)\)	\(e\left(\frac{79}{108}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{29}{54}\right)\)	\(e\left(\frac{1}{54}\right)\)	\(e\left(\frac{65}{108}\right)\)	\(e\left(\frac{11}{54}\right)\)
\(\chi_{5184}(4271,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{108}\right)\)	\(e\left(\frac{4}{27}\right)\)	\(e\left(\frac{13}{108}\right)\)	\(e\left(\frac{35}{108}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{19}{54}\right)\)	\(e\left(\frac{23}{54}\right)\)	\(e\left(\frac{37}{108}\right)\)	\(e\left(\frac{37}{54}\right)\)
\(\chi_{5184}(4367,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{61}{108}\right)\)	\(e\left(\frac{20}{27}\right)\)	\(e\left(\frac{11}{108}\right)\)	\(e\left(\frac{13}{108}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{41}{54}\right)\)	\(e\left(\frac{7}{54}\right)\)	\(e\left(\frac{23}{108}\right)\)	\(e\left(\frac{23}{54}\right)\)

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First 31 of 36 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.cm
Modulus	$5184$
Conductor	$1296$
Order	$108$
Real	no
Primitive	no
Minimal	no
Parity	even

Modulus:	\(5184\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(1296\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(108\)	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 1296.bs	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);