LMFDB - Dirichlet character orbit 15840.qc

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(15840, base_ring=CyclotomicField(120)) M = H._module chi = DirichletCharacter(H, M([0,75,80,90,108])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(853,15840)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$15840$
Conductor:	$15840$	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:	even	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	$-1$	$1$	$7$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$	$43$
$\chi_{15840}(853,\cdot)$	$1$	$1$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{103}{120}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{41}{120}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{13}{24}\right)$
$\chi_{15840}(877,\cdot)$	$1$	$1$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{101}{120}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{67}{120}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{23}{24}\right)$
$\chi_{15840}(1597,\cdot)$	$1$	$1$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{17}{120}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{79}{120}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{11}{24}\right)$
$\chi_{15840}(2317,\cdot)$	$1$	$1$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{29}{120}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{43}{120}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{23}{24}\right)$
$\chi_{15840}(3253,\cdot)$	$1$	$1$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{71}{120}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{97}{120}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{5}{24}\right)$
$\chi_{15840}(3517,\cdot)$	$1$	$1$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{1}{120}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{47}{120}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{19}{24}\right)$
$\chi_{15840}(3757,\cdot)$	$1$	$1$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{53}{120}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{91}{120}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{23}{24}\right)$
$\chi_{15840}(3973,\cdot)$	$1$	$1$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{107}{120}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{109}{120}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{17}{24}\right)$
$\chi_{15840}(4237,\cdot)$	$1$	$1$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{37}{120}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{59}{120}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{7}{24}\right)$
$\chi_{15840}(4693,\cdot)$	$1$	$1$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{119}{120}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{73}{120}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{5}{24}\right)$
$\chi_{15840}(4957,\cdot)$	$1$	$1$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{49}{120}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{23}{120}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{19}{24}\right)$
$\chi_{15840}(5893,\cdot)$	$1$	$1$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{91}{120}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{77}{120}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{1}{24}\right)$
$\chi_{15840}(6133,\cdot)$	$1$	$1$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{23}{120}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{120}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{5}{24}\right)$
$\chi_{15840}(6397,\cdot)$	$1$	$1$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{73}{120}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{71}{120}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{19}{24}\right)$
$\chi_{15840}(6613,\cdot)$	$1$	$1$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{7}{120}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{89}{120}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{13}{24}\right)$
$\chi_{15840}(7333,\cdot)$	$1$	$1$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{19}{120}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{53}{120}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{1}{24}\right)$
$\chi_{15840}(8773,\cdot)$	$1$	$1$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{43}{120}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{101}{120}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{1}{24}\right)$
$\chi_{15840}(8797,\cdot)$	$1$	$1$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{41}{120}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{120}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{11}{24}\right)$
$\chi_{15840}(9517,\cdot)$	$1$	$1$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{77}{120}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{19}{120}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{23}{24}\right)$
$\chi_{15840}(10237,\cdot)$	$1$	$1$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{89}{120}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{103}{120}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{11}{24}\right)$
$\chi_{15840}(11173,\cdot)$	$1$	$1$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{11}{120}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{37}{120}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{17}{24}\right)$
$\chi_{15840}(11437,\cdot)$	$1$	$1$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{61}{120}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{107}{120}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{7}{24}\right)$
$\chi_{15840}(11677,\cdot)$	$1$	$1$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{113}{120}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{31}{120}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{11}{24}\right)$
$\chi_{15840}(11893,\cdot)$	$1$	$1$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{47}{120}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{49}{120}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{5}{24}\right)$
$\chi_{15840}(12157,\cdot)$	$1$	$1$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{97}{120}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{119}{120}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{19}{24}\right)$
$\chi_{15840}(12613,\cdot)$	$1$	$1$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{59}{120}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{13}{120}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{17}{24}\right)$
$\chi_{15840}(12877,\cdot)$	$1$	$1$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{109}{120}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{83}{120}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{7}{24}\right)$
$\chi_{15840}(13813,\cdot)$	$1$	$1$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{31}{120}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{17}{120}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{13}{24}\right)$
$\chi_{15840}(14053,\cdot)$	$1$	$1$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{83}{120}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{61}{120}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{17}{24}\right)$
$\chi_{15840}(14317,\cdot)$	$1$	$1$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{13}{120}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{120}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{7}{24}\right)$
$\chi_{15840}(14533,\cdot)$	$1$	$1$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{67}{120}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{29}{120}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{1}{24}\right)$

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	\(-1\)	\(1\)	\(7\)	\(13\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)	\(43\)
\(\chi_{15840}(853,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{103}{120}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{41}{120}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{13}{24}\right)\)
\(\chi_{15840}(877,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{101}{120}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{67}{120}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{23}{24}\right)\)
\(\chi_{15840}(1597,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{17}{120}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{79}{120}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{11}{24}\right)\)
\(\chi_{15840}(2317,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{29}{120}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{43}{120}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{23}{24}\right)\)
\(\chi_{15840}(3253,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{71}{120}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{97}{120}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{5}{24}\right)\)
\(\chi_{15840}(3517,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{1}{120}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{47}{120}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{19}{24}\right)\)
\(\chi_{15840}(3757,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{53}{120}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{91}{120}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{23}{24}\right)\)
\(\chi_{15840}(3973,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{107}{120}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{109}{120}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{17}{24}\right)\)
\(\chi_{15840}(4237,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{37}{120}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{59}{120}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{7}{24}\right)\)
\(\chi_{15840}(4693,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{119}{120}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{73}{120}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{5}{24}\right)\)
\(\chi_{15840}(4957,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{49}{120}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{23}{120}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{19}{24}\right)\)
\(\chi_{15840}(5893,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{91}{120}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{77}{120}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{1}{24}\right)\)
\(\chi_{15840}(6133,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{23}{120}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{120}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{5}{24}\right)\)
\(\chi_{15840}(6397,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{73}{120}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{71}{120}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{19}{24}\right)\)
\(\chi_{15840}(6613,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{7}{120}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{89}{120}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{13}{24}\right)\)
\(\chi_{15840}(7333,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{19}{120}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{53}{120}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{1}{24}\right)\)
\(\chi_{15840}(8773,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{43}{120}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{101}{120}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{1}{24}\right)\)
\(\chi_{15840}(8797,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{41}{120}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{120}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{11}{24}\right)\)
\(\chi_{15840}(9517,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{77}{120}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{19}{120}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{23}{24}\right)\)
\(\chi_{15840}(10237,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{89}{120}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{103}{120}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{11}{24}\right)\)
\(\chi_{15840}(11173,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{11}{120}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{37}{120}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{17}{24}\right)\)
\(\chi_{15840}(11437,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{61}{120}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{107}{120}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{7}{24}\right)\)
\(\chi_{15840}(11677,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{113}{120}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{31}{120}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{11}{24}\right)\)
\(\chi_{15840}(11893,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{47}{120}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{49}{120}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{5}{24}\right)\)
\(\chi_{15840}(12157,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{97}{120}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{119}{120}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{19}{24}\right)\)
\(\chi_{15840}(12613,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{59}{120}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{13}{120}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{17}{24}\right)\)
\(\chi_{15840}(12877,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{109}{120}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{83}{120}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{7}{24}\right)\)
\(\chi_{15840}(13813,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{31}{120}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{17}{120}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{13}{24}\right)\)
\(\chi_{15840}(14053,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{83}{120}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{61}{120}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{17}{24}\right)\)
\(\chi_{15840}(14317,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{13}{120}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{120}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{7}{24}\right)\)
\(\chi_{15840}(14533,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{67}{120}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{29}{120}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{1}{24}\right)\)

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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	15840.qc
Modulus	$15840$
Conductor	$15840$
Order	$120$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(15840\)
Conductor:	\(15840\)	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:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)