LMFDB - Dirichlet character orbit 1476.cl

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comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1476, base_ring=CyclotomicField(120)) M = H._module chi = DirichletCharacter(H, M([60,80,117])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(7, 1476)) 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("1476.7"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$1476$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$1476$	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	$-1$	$1$	$5$	$7$	$11$	$13$	$17$	$19$	$23$	$25$	$29$	$31$
$\chi_{1476}(7,\cdot)$	$1$	$1$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{23}{120}\right)$	$e\left(\frac{11}{120}\right)$	$e\left(\frac{67}{120}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{59}{120}\right)$	$e\left(\frac{2}{15}\right)$
$\chi_{1476}(67,\cdot)$	$1$	$1$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{49}{120}\right)$	$e\left(\frac{13}{120}\right)$	$e\left(\frac{101}{120}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{37}{120}\right)$	$e\left(\frac{1}{15}\right)$
$\chi_{1476}(151,\cdot)$	$1$	$1$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{107}{120}\right)$	$e\left(\frac{119}{120}\right)$	$e\left(\frac{103}{120}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{71}{120}\right)$	$e\left(\frac{8}{15}\right)$
$\chi_{1476}(175,\cdot)$	$1$	$1$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{91}{120}\right)$	$e\left(\frac{7}{120}\right)$	$e\left(\frac{119}{120}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{103}{120}\right)$	$e\left(\frac{4}{15}\right)$
$\chi_{1476}(211,\cdot)$	$1$	$1$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{97}{120}\right)$	$e\left(\frac{109}{120}\right)$	$e\left(\frac{53}{120}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{61}{120}\right)$	$e\left(\frac{13}{15}\right)$
$\chi_{1476}(259,\cdot)$	$1$	$1$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{47}{120}\right)$	$e\left(\frac{59}{120}\right)$	$e\left(\frac{43}{120}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{11}{120}\right)$	$e\left(\frac{8}{15}\right)$
$\chi_{1476}(391,\cdot)$	$1$	$1$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{13}{120}\right)$	$e\left(\frac{1}{120}\right)$	$e\left(\frac{17}{120}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{49}{120}\right)$	$e\left(\frac{7}{15}\right)$
$\chi_{1476}(403,\cdot)$	$1$	$1$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{83}{120}\right)$	$e\left(\frac{71}{120}\right)$	$e\left(\frac{7}{120}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{119}{120}\right)$	$e\left(\frac{2}{15}\right)$
$\chi_{1476}(427,\cdot)$	$1$	$1$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{1}{120}\right)$	$e\left(\frac{37}{120}\right)$	$e\left(\frac{29}{120}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{13}{120}\right)$	$e\left(\frac{4}{15}\right)$
$\chi_{1476}(439,\cdot)$	$1$	$1$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{119}{120}\right)$	$e\left(\frac{83}{120}\right)$	$e\left(\frac{91}{120}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{107}{120}\right)$	$e\left(\frac{11}{15}\right)$
$\chi_{1476}(463,\cdot)$	$1$	$1$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{19}{120}\right)$	$e\left(\frac{103}{120}\right)$	$e\left(\frac{71}{120}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{7}{120}\right)$	$e\left(\frac{1}{15}\right)$
$\chi_{1476}(475,\cdot)$	$1$	$1$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{101}{120}\right)$	$e\left(\frac{17}{120}\right)$	$e\left(\frac{49}{120}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{113}{120}\right)$	$e\left(\frac{14}{15}\right)$
$\chi_{1476}(499,\cdot)$	$1$	$1$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{103}{120}\right)$	$e\left(\frac{91}{120}\right)$	$e\left(\frac{107}{120}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{19}{120}\right)$	$e\left(\frac{7}{15}\right)$
$\chi_{1476}(511,\cdot)$	$1$	$1$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{113}{120}\right)$	$e\left(\frac{101}{120}\right)$	$e\left(\frac{37}{120}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{29}{120}\right)$	$e\left(\frac{2}{15}\right)$
$\chi_{1476}(643,\cdot)$	$1$	$1$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{67}{120}\right)$	$e\left(\frac{79}{120}\right)$	$e\left(\frac{23}{120}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{31}{120}\right)$	$e\left(\frac{13}{15}\right)$
$\chi_{1476}(691,\cdot)$	$1$	$1$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{77}{120}\right)$	$e\left(\frac{89}{120}\right)$	$e\left(\frac{73}{120}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{41}{120}\right)$	$e\left(\frac{8}{15}\right)$
$\chi_{1476}(727,\cdot)$	$1$	$1$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{71}{120}\right)$	$e\left(\frac{107}{120}\right)$	$e\left(\frac{19}{120}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{83}{120}\right)$	$e\left(\frac{14}{15}\right)$
$\chi_{1476}(751,\cdot)$	$1$	$1$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{7}{120}\right)$	$e\left(\frac{19}{120}\right)$	$e\left(\frac{83}{120}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{91}{120}\right)$	$e\left(\frac{13}{15}\right)$
$\chi_{1476}(835,\cdot)$	$1$	$1$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{29}{120}\right)$	$e\left(\frac{113}{120}\right)$	$e\left(\frac{1}{120}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{17}{120}\right)$	$e\left(\frac{11}{15}\right)$
$\chi_{1476}(895,\cdot)$	$1$	$1$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{43}{120}\right)$	$e\left(\frac{31}{120}\right)$	$e\left(\frac{47}{120}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{79}{120}\right)$	$e\left(\frac{7}{15}\right)$
$\chi_{1476}(931,\cdot)$	$1$	$1$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{79}{120}\right)$	$e\left(\frac{43}{120}\right)$	$e\left(\frac{11}{120}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{67}{120}\right)$	$e\left(\frac{1}{15}\right)$
$\chi_{1476}(967,\cdot)$	$1$	$1$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{61}{120}\right)$	$e\left(\frac{97}{120}\right)$	$e\left(\frac{89}{120}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{73}{120}\right)$	$e\left(\frac{4}{15}\right)$
$\chi_{1476}(1003,\cdot)$	$1$	$1$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{73}{120}\right)$	$e\left(\frac{61}{120}\right)$	$e\left(\frac{77}{120}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{109}{120}\right)$	$e\left(\frac{7}{15}\right)$
$\chi_{1476}(1051,\cdot)$	$1$	$1$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{89}{120}\right)$	$e\left(\frac{53}{120}\right)$	$e\left(\frac{61}{120}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{77}{120}\right)$	$e\left(\frac{11}{15}\right)$
$\chi_{1476}(1159,\cdot)$	$1$	$1$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{11}{120}\right)$	$e\left(\frac{47}{120}\right)$	$e\left(\frac{79}{120}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{23}{120}\right)$	$e\left(\frac{14}{15}\right)$
$\chi_{1476}(1183,\cdot)$	$1$	$1$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{37}{120}\right)$	$e\left(\frac{49}{120}\right)$	$e\left(\frac{113}{120}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{1}{120}\right)$	$e\left(\frac{13}{15}\right)$
$\chi_{1476}(1195,\cdot)$	$1$	$1$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{17}{120}\right)$	$e\left(\frac{29}{120}\right)$	$e\left(\frac{13}{120}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{101}{120}\right)$	$e\left(\frac{8}{15}\right)$
$\chi_{1476}(1219,\cdot)$	$1$	$1$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{31}{120}\right)$	$e\left(\frac{67}{120}\right)$	$e\left(\frac{59}{120}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{43}{120}\right)$	$e\left(\frac{4}{15}\right)$
$\chi_{1476}(1327,\cdot)$	$1$	$1$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{109}{120}\right)$	$e\left(\frac{73}{120}\right)$	$e\left(\frac{41}{120}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{97}{120}\right)$	$e\left(\frac{1}{15}\right)$
$\chi_{1476}(1375,\cdot)$	$1$	$1$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{53}{120}\right)$	$e\left(\frac{41}{120}\right)$	$e\left(\frac{97}{120}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{89}{120}\right)$	$e\left(\frac{2}{15}\right)$
$\chi_{1476}(1411,\cdot)$	$1$	$1$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{41}{120}\right)$	$e\left(\frac{77}{120}\right)$	$e\left(\frac{109}{120}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{53}{120}\right)$	$e\left(\frac{14}{15}\right)$

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	\(-1\)	\(1\)	\(5\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)
\(\chi_{1476}(7,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{23}{120}\right)\)	\(e\left(\frac{11}{120}\right)\)	\(e\left(\frac{67}{120}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{59}{120}\right)\)	\(e\left(\frac{2}{15}\right)\)
\(\chi_{1476}(67,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{49}{120}\right)\)	\(e\left(\frac{13}{120}\right)\)	\(e\left(\frac{101}{120}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{37}{120}\right)\)	\(e\left(\frac{1}{15}\right)\)
\(\chi_{1476}(151,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{107}{120}\right)\)	\(e\left(\frac{119}{120}\right)\)	\(e\left(\frac{103}{120}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{71}{120}\right)\)	\(e\left(\frac{8}{15}\right)\)
\(\chi_{1476}(175,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{91}{120}\right)\)	\(e\left(\frac{7}{120}\right)\)	\(e\left(\frac{119}{120}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{103}{120}\right)\)	\(e\left(\frac{4}{15}\right)\)
\(\chi_{1476}(211,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{97}{120}\right)\)	\(e\left(\frac{109}{120}\right)\)	\(e\left(\frac{53}{120}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{61}{120}\right)\)	\(e\left(\frac{13}{15}\right)\)
\(\chi_{1476}(259,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{47}{120}\right)\)	\(e\left(\frac{59}{120}\right)\)	\(e\left(\frac{43}{120}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{11}{120}\right)\)	\(e\left(\frac{8}{15}\right)\)
\(\chi_{1476}(391,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{13}{120}\right)\)	\(e\left(\frac{1}{120}\right)\)	\(e\left(\frac{17}{120}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{49}{120}\right)\)	\(e\left(\frac{7}{15}\right)\)
\(\chi_{1476}(403,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{83}{120}\right)\)	\(e\left(\frac{71}{120}\right)\)	\(e\left(\frac{7}{120}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{119}{120}\right)\)	\(e\left(\frac{2}{15}\right)\)
\(\chi_{1476}(427,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{1}{120}\right)\)	\(e\left(\frac{37}{120}\right)\)	\(e\left(\frac{29}{120}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{13}{120}\right)\)	\(e\left(\frac{4}{15}\right)\)
\(\chi_{1476}(439,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{119}{120}\right)\)	\(e\left(\frac{83}{120}\right)\)	\(e\left(\frac{91}{120}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{107}{120}\right)\)	\(e\left(\frac{11}{15}\right)\)
\(\chi_{1476}(463,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{19}{120}\right)\)	\(e\left(\frac{103}{120}\right)\)	\(e\left(\frac{71}{120}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{7}{120}\right)\)	\(e\left(\frac{1}{15}\right)\)
\(\chi_{1476}(475,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{101}{120}\right)\)	\(e\left(\frac{17}{120}\right)\)	\(e\left(\frac{49}{120}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{113}{120}\right)\)	\(e\left(\frac{14}{15}\right)\)
\(\chi_{1476}(499,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{103}{120}\right)\)	\(e\left(\frac{91}{120}\right)\)	\(e\left(\frac{107}{120}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{19}{120}\right)\)	\(e\left(\frac{7}{15}\right)\)
\(\chi_{1476}(511,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{113}{120}\right)\)	\(e\left(\frac{101}{120}\right)\)	\(e\left(\frac{37}{120}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{29}{120}\right)\)	\(e\left(\frac{2}{15}\right)\)
\(\chi_{1476}(643,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{67}{120}\right)\)	\(e\left(\frac{79}{120}\right)\)	\(e\left(\frac{23}{120}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{31}{120}\right)\)	\(e\left(\frac{13}{15}\right)\)
\(\chi_{1476}(691,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{77}{120}\right)\)	\(e\left(\frac{89}{120}\right)\)	\(e\left(\frac{73}{120}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{41}{120}\right)\)	\(e\left(\frac{8}{15}\right)\)
\(\chi_{1476}(727,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{71}{120}\right)\)	\(e\left(\frac{107}{120}\right)\)	\(e\left(\frac{19}{120}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{83}{120}\right)\)	\(e\left(\frac{14}{15}\right)\)
\(\chi_{1476}(751,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{7}{120}\right)\)	\(e\left(\frac{19}{120}\right)\)	\(e\left(\frac{83}{120}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{91}{120}\right)\)	\(e\left(\frac{13}{15}\right)\)
\(\chi_{1476}(835,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{29}{120}\right)\)	\(e\left(\frac{113}{120}\right)\)	\(e\left(\frac{1}{120}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{17}{120}\right)\)	\(e\left(\frac{11}{15}\right)\)
\(\chi_{1476}(895,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{43}{120}\right)\)	\(e\left(\frac{31}{120}\right)\)	\(e\left(\frac{47}{120}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{79}{120}\right)\)	\(e\left(\frac{7}{15}\right)\)
\(\chi_{1476}(931,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{79}{120}\right)\)	\(e\left(\frac{43}{120}\right)\)	\(e\left(\frac{11}{120}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{67}{120}\right)\)	\(e\left(\frac{1}{15}\right)\)
\(\chi_{1476}(967,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{61}{120}\right)\)	\(e\left(\frac{97}{120}\right)\)	\(e\left(\frac{89}{120}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{73}{120}\right)\)	\(e\left(\frac{4}{15}\right)\)
\(\chi_{1476}(1003,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{73}{120}\right)\)	\(e\left(\frac{61}{120}\right)\)	\(e\left(\frac{77}{120}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{109}{120}\right)\)	\(e\left(\frac{7}{15}\right)\)
\(\chi_{1476}(1051,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{89}{120}\right)\)	\(e\left(\frac{53}{120}\right)\)	\(e\left(\frac{61}{120}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{77}{120}\right)\)	\(e\left(\frac{11}{15}\right)\)
\(\chi_{1476}(1159,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{11}{120}\right)\)	\(e\left(\frac{47}{120}\right)\)	\(e\left(\frac{79}{120}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{23}{120}\right)\)	\(e\left(\frac{14}{15}\right)\)
\(\chi_{1476}(1183,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{37}{120}\right)\)	\(e\left(\frac{49}{120}\right)\)	\(e\left(\frac{113}{120}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{1}{120}\right)\)	\(e\left(\frac{13}{15}\right)\)
\(\chi_{1476}(1195,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{17}{120}\right)\)	\(e\left(\frac{29}{120}\right)\)	\(e\left(\frac{13}{120}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{101}{120}\right)\)	\(e\left(\frac{8}{15}\right)\)
\(\chi_{1476}(1219,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{31}{120}\right)\)	\(e\left(\frac{67}{120}\right)\)	\(e\left(\frac{59}{120}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{43}{120}\right)\)	\(e\left(\frac{4}{15}\right)\)
\(\chi_{1476}(1327,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{109}{120}\right)\)	\(e\left(\frac{73}{120}\right)\)	\(e\left(\frac{41}{120}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{97}{120}\right)\)	\(e\left(\frac{1}{15}\right)\)
\(\chi_{1476}(1375,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{53}{120}\right)\)	\(e\left(\frac{41}{120}\right)\)	\(e\left(\frac{97}{120}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{89}{120}\right)\)	\(e\left(\frac{2}{15}\right)\)
\(\chi_{1476}(1411,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{41}{120}\right)\)	\(e\left(\frac{77}{120}\right)\)	\(e\left(\frac{109}{120}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{53}{120}\right)\)	\(e\left(\frac{14}{15}\right)\)

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Basic properties

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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	1476.cl
Modulus	$1476$
Conductor	$1476$
Order	$120$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(1476\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(1476\)	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);