LMFDB - Dirichlet character orbit 1309.cu

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1309, base_ring=CyclotomicField(120)) M = H._module chi = DirichletCharacter(H, M([40,12,105])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(2,1309)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$1309$
Conductor:	$1309$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$120$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	yes	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	odd	sage:chi.is_odd() pari:zncharisodd(g,chi)

Related number fields

Field of values:	$\Q(\zeta_{120})$
Fixed field:	Number field defined by a degree 120 polynomial (not computed)

First 31 of 32 characters in Galois orbit

Character	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$8$	$9$	$10$	$12$	$13$
$\chi_{1309}(2,\cdot)$	$-1$	$1$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{1}{120}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{53}{120}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{3}{5}\right)$
$\chi_{1309}(128,\cdot)$	$-1$	$1$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{7}{120}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{11}{120}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{1}{5}\right)$
$\chi_{1309}(151,\cdot)$	$-1$	$1$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{53}{120}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{49}{120}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{4}{5}\right)$
$\chi_{1309}(172,\cdot)$	$-1$	$1$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{17}{120}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{61}{120}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{1}{5}\right)$
$\chi_{1309}(270,\cdot)$	$-1$	$1$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{29}{120}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{97}{120}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{2}{5}\right)$
$\chi_{1309}(338,\cdot)$	$-1$	$1$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{13}{120}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{89}{120}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{4}{5}\right)$
$\chi_{1309}(359,\cdot)$	$-1$	$1$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{97}{120}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{101}{120}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{1}{5}\right)$
$\chi_{1309}(382,\cdot)$	$-1$	$1$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{83}{120}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{79}{120}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{4}{5}\right)$
$\chi_{1309}(457,\cdot)$	$-1$	$1$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{109}{120}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{17}{120}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{2}{5}\right)$
$\chi_{1309}(501,\cdot)$	$-1$	$1$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{59}{120}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{7}{120}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{2}{5}\right)$
$\chi_{1309}(508,\cdot)$	$-1$	$1$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{101}{120}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{73}{120}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{3}{5}\right)$
$\chi_{1309}(536,\cdot)$	$-1$	$1$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{23}{120}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{19}{120}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{4}{5}\right)$
$\chi_{1309}(569,\cdot)$	$-1$	$1$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{43}{120}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{119}{120}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{4}{5}\right)$
$\chi_{1309}(655,\cdot)$	$-1$	$1$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{119}{120}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{67}{120}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{2}{5}\right)$
$\chi_{1309}(688,\cdot)$	$-1$	$1$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{19}{120}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{47}{120}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{2}{5}\right)$
$\chi_{1309}(695,\cdot)$	$-1$	$1$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{61}{120}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{113}{120}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{3}{5}\right)$
$\chi_{1309}(723,\cdot)$	$-1$	$1$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{103}{120}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{59}{120}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{4}{5}\right)$
$\chi_{1309}(739,\cdot)$	$-1$	$1$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{11}{120}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{103}{120}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{3}{5}\right)$
$\chi_{1309}(767,\cdot)$	$-1$	$1$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{113}{120}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{109}{120}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{4}{5}\right)$
$\chi_{1309}(842,\cdot)$	$-1$	$1$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{79}{120}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{107}{120}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{2}{5}\right)$
$\chi_{1309}(865,\cdot)$	$-1$	$1$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{77}{120}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{1}{120}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{1}{5}\right)$
$\chi_{1309}(886,\cdot)$	$-1$	$1$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{89}{120}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{37}{120}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{2}{5}\right)$
$\chi_{1309}(893,\cdot)$	$-1$	$1$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{71}{120}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{43}{120}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{3}{5}\right)$
$\chi_{1309}(926,\cdot)$	$-1$	$1$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{91}{120}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{23}{120}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{3}{5}\right)$
$\chi_{1309}(954,\cdot)$	$-1$	$1$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{73}{120}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{29}{120}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{4}{5}\right)$
$\chi_{1309}(1052,\cdot)$	$-1$	$1$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{37}{120}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{41}{120}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{1}{5}\right)$
$\chi_{1309}(1073,\cdot)$	$-1$	$1$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{49}{120}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{77}{120}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{2}{5}\right)$
$\chi_{1309}(1080,\cdot)$	$-1$	$1$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{31}{120}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{83}{120}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{3}{5}\right)$
$\chi_{1309}(1096,\cdot)$	$-1$	$1$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{107}{120}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{31}{120}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{1}{5}\right)$
$\chi_{1309}(1124,\cdot)$	$-1$	$1$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{41}{120}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{13}{120}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{3}{5}\right)$
$\chi_{1309}(1250,\cdot)$	$-1$	$1$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{47}{120}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{91}{120}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{1}{5}\right)$

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	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(8\)	\(9\)	\(10\)	\(12\)	\(13\)
\(\chi_{1309}(2,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{1}{120}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{53}{120}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{3}{5}\right)\)
\(\chi_{1309}(128,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{7}{120}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{11}{120}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{1}{5}\right)\)
\(\chi_{1309}(151,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{53}{120}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{49}{120}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{1309}(172,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{17}{120}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{61}{120}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{1}{5}\right)\)
\(\chi_{1309}(270,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{29}{120}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{97}{120}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{2}{5}\right)\)
\(\chi_{1309}(338,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{13}{120}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{89}{120}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{1309}(359,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{97}{120}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{101}{120}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{1}{5}\right)\)
\(\chi_{1309}(382,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{83}{120}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{79}{120}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{1309}(457,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{109}{120}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{17}{120}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{2}{5}\right)\)
\(\chi_{1309}(501,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{59}{120}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{7}{120}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{2}{5}\right)\)
\(\chi_{1309}(508,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{101}{120}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{73}{120}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{3}{5}\right)\)
\(\chi_{1309}(536,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{23}{120}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{19}{120}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{1309}(569,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{43}{120}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{119}{120}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{1309}(655,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{119}{120}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{67}{120}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{2}{5}\right)\)
\(\chi_{1309}(688,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{19}{120}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{47}{120}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{2}{5}\right)\)
\(\chi_{1309}(695,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{61}{120}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{113}{120}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{3}{5}\right)\)
\(\chi_{1309}(723,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{103}{120}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{59}{120}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{1309}(739,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{11}{120}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{103}{120}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{3}{5}\right)\)
\(\chi_{1309}(767,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{113}{120}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{109}{120}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{1309}(842,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{79}{120}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{107}{120}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{2}{5}\right)\)
\(\chi_{1309}(865,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{77}{120}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{1}{120}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{1}{5}\right)\)
\(\chi_{1309}(886,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{89}{120}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{37}{120}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{2}{5}\right)\)
\(\chi_{1309}(893,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{71}{120}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{43}{120}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{3}{5}\right)\)
\(\chi_{1309}(926,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{91}{120}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{23}{120}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{3}{5}\right)\)
\(\chi_{1309}(954,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{73}{120}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{29}{120}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{1309}(1052,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{37}{120}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{41}{120}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{1}{5}\right)\)
\(\chi_{1309}(1073,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{49}{120}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{77}{120}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{2}{5}\right)\)
\(\chi_{1309}(1080,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{31}{120}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{83}{120}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{3}{5}\right)\)
\(\chi_{1309}(1096,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{107}{120}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{31}{120}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{1}{5}\right)\)
\(\chi_{1309}(1124,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{41}{120}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{13}{120}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{3}{5}\right)\)
\(\chi_{1309}(1250,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{47}{120}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{91}{120}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{1}{5}\right)\)

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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	1309.cu
Modulus	$1309$
Conductor	$1309$
Order	$120$
Real	no
Primitive	yes
Minimal	yes
Parity	odd

Modulus:	\(1309\)
Conductor:	\(1309\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(120\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	yes	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	odd	sage:chi.is_odd() pari:zncharisodd(g,chi)