LMFDB - Dirichlet character orbit 287.be

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comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(287, base_ring=CyclotomicField(120)) M = H._module chi = DirichletCharacter(H, M([100,81])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(12, 287)) 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("287.12"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$287$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$287$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$120$	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:	$\Q(\zeta_{120})$	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 120 polynomial (not computed)	comment:Fixed field sage:chi.fixed_field()

First 31 of 32 characters in Galois orbit

Character	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$8$	$9$	$10$	$11$	$12$
$\chi_{287}(12,\cdot)$	$1$	$1$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{43}{120}\right)$	$e\left(\frac{47}{120}\right)$
$\chi_{287}(17,\cdot)$	$1$	$1$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{17}{120}\right)$	$e\left(\frac{13}{120}\right)$
$\chi_{287}(19,\cdot)$	$1$	$1$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{1}{120}\right)$	$e\left(\frac{29}{120}\right)$
$\chi_{287}(24,\cdot)$	$1$	$1$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{77}{120}\right)$	$e\left(\frac{73}{120}\right)$
$\chi_{287}(26,\cdot)$	$1$	$1$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{73}{120}\right)$	$e\left(\frac{77}{120}\right)$
$\chi_{287}(47,\cdot)$	$1$	$1$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{49}{120}\right)$	$e\left(\frac{101}{120}\right)$
$\chi_{287}(52,\cdot)$	$1$	$1$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{107}{120}\right)$	$e\left(\frac{103}{120}\right)$
$\chi_{287}(54,\cdot)$	$1$	$1$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{79}{120}\right)$	$e\left(\frac{11}{120}\right)$
$\chi_{287}(75,\cdot)$	$1$	$1$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{91}{120}\right)$	$e\left(\frac{119}{120}\right)$
$\chi_{287}(89,\cdot)$	$1$	$1$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{31}{120}\right)$	$e\left(\frac{59}{120}\right)$
$\chi_{287}(94,\cdot)$	$1$	$1$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{83}{120}\right)$	$e\left(\frac{7}{120}\right)$
$\chi_{287}(101,\cdot)$	$1$	$1$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{41}{120}\right)$	$e\left(\frac{109}{120}\right)$
$\chi_{287}(108,\cdot)$	$1$	$1$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{113}{120}\right)$	$e\left(\frac{37}{120}\right)$
$\chi_{287}(110,\cdot)$	$1$	$1$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{19}{120}\right)$	$e\left(\frac{71}{120}\right)$
$\chi_{287}(117,\cdot)$	$1$	$1$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{109}{120}\right)$	$e\left(\frac{41}{120}\right)$
$\chi_{287}(129,\cdot)$	$1$	$1$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{89}{120}\right)$	$e\left(\frac{61}{120}\right)$
$\chi_{287}(136,\cdot)$	$1$	$1$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{119}{120}\right)$	$e\left(\frac{91}{120}\right)$
$\chi_{287}(138,\cdot)$	$1$	$1$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{13}{120}\right)$	$e\left(\frac{17}{120}\right)$
$\chi_{287}(145,\cdot)$	$1$	$1$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{61}{120}\right)$	$e\left(\frac{89}{120}\right)$
$\chi_{287}(152,\cdot)$	$1$	$1$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{103}{120}\right)$	$e\left(\frac{107}{120}\right)$
$\chi_{287}(157,\cdot)$	$1$	$1$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{11}{120}\right)$	$e\left(\frac{79}{120}\right)$
$\chi_{287}(171,\cdot)$	$1$	$1$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{71}{120}\right)$	$e\left(\frac{19}{120}\right)$
$\chi_{287}(192,\cdot)$	$1$	$1$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{59}{120}\right)$	$e\left(\frac{31}{120}\right)$
$\chi_{287}(194,\cdot)$	$1$	$1$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{7}{120}\right)$	$e\left(\frac{83}{120}\right)$
$\chi_{287}(199,\cdot)$	$1$	$1$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{29}{120}\right)$	$e\left(\frac{1}{120}\right)$
$\chi_{287}(220,\cdot)$	$1$	$1$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{53}{120}\right)$	$e\left(\frac{97}{120}\right)$
$\chi_{287}(222,\cdot)$	$1$	$1$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{97}{120}\right)$	$e\left(\frac{53}{120}\right)$
$\chi_{287}(227,\cdot)$	$1$	$1$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{101}{120}\right)$	$e\left(\frac{49}{120}\right)$
$\chi_{287}(229,\cdot)$	$1$	$1$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{37}{120}\right)$	$e\left(\frac{113}{120}\right)$
$\chi_{287}(234,\cdot)$	$1$	$1$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{23}{120}\right)$	$e\left(\frac{67}{120}\right)$
$\chi_{287}(257,\cdot)$	$1$	$1$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{67}{120}\right)$	$e\left(\frac{23}{120}\right)$

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	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(8\)	\(9\)	\(10\)	\(11\)	\(12\)
\(\chi_{287}(12,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{43}{120}\right)\)	\(e\left(\frac{47}{120}\right)\)
\(\chi_{287}(17,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{17}{120}\right)\)	\(e\left(\frac{13}{120}\right)\)
\(\chi_{287}(19,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{1}{120}\right)\)	\(e\left(\frac{29}{120}\right)\)
\(\chi_{287}(24,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{77}{120}\right)\)	\(e\left(\frac{73}{120}\right)\)
\(\chi_{287}(26,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{73}{120}\right)\)	\(e\left(\frac{77}{120}\right)\)
\(\chi_{287}(47,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{49}{120}\right)\)	\(e\left(\frac{101}{120}\right)\)
\(\chi_{287}(52,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{107}{120}\right)\)	\(e\left(\frac{103}{120}\right)\)
\(\chi_{287}(54,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{79}{120}\right)\)	\(e\left(\frac{11}{120}\right)\)
\(\chi_{287}(75,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{91}{120}\right)\)	\(e\left(\frac{119}{120}\right)\)
\(\chi_{287}(89,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{31}{120}\right)\)	\(e\left(\frac{59}{120}\right)\)
\(\chi_{287}(94,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{83}{120}\right)\)	\(e\left(\frac{7}{120}\right)\)
\(\chi_{287}(101,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{41}{120}\right)\)	\(e\left(\frac{109}{120}\right)\)
\(\chi_{287}(108,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{113}{120}\right)\)	\(e\left(\frac{37}{120}\right)\)
\(\chi_{287}(110,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{19}{120}\right)\)	\(e\left(\frac{71}{120}\right)\)
\(\chi_{287}(117,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{109}{120}\right)\)	\(e\left(\frac{41}{120}\right)\)
\(\chi_{287}(129,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{89}{120}\right)\)	\(e\left(\frac{61}{120}\right)\)
\(\chi_{287}(136,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{119}{120}\right)\)	\(e\left(\frac{91}{120}\right)\)
\(\chi_{287}(138,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{13}{120}\right)\)	\(e\left(\frac{17}{120}\right)\)
\(\chi_{287}(145,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{61}{120}\right)\)	\(e\left(\frac{89}{120}\right)\)
\(\chi_{287}(152,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{103}{120}\right)\)	\(e\left(\frac{107}{120}\right)\)
\(\chi_{287}(157,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{11}{120}\right)\)	\(e\left(\frac{79}{120}\right)\)
\(\chi_{287}(171,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{71}{120}\right)\)	\(e\left(\frac{19}{120}\right)\)
\(\chi_{287}(192,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{59}{120}\right)\)	\(e\left(\frac{31}{120}\right)\)
\(\chi_{287}(194,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{7}{120}\right)\)	\(e\left(\frac{83}{120}\right)\)
\(\chi_{287}(199,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{29}{120}\right)\)	\(e\left(\frac{1}{120}\right)\)
\(\chi_{287}(220,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{53}{120}\right)\)	\(e\left(\frac{97}{120}\right)\)
\(\chi_{287}(222,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{97}{120}\right)\)	\(e\left(\frac{53}{120}\right)\)
\(\chi_{287}(227,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{101}{120}\right)\)	\(e\left(\frac{49}{120}\right)\)
\(\chi_{287}(229,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{37}{120}\right)\)	\(e\left(\frac{113}{120}\right)\)
\(\chi_{287}(234,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{23}{120}\right)\)	\(e\left(\frac{67}{120}\right)\)
\(\chi_{287}(257,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{67}{120}\right)\)	\(e\left(\frac{23}{120}\right)\)

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First 31 of 32 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	287.be
Modulus	$287$
Conductor	$287$
Order	$120$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(287\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(287\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(120\)	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);