LMFDB - Dirichlet character orbit 3168.ew

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(3168, base_ring=CyclotomicField(120)) M = H._module chi = DirichletCharacter(H, M([0,45,40,96])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(157,3168)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$3168$
Conductor:	$3168$	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	$-1$	$1$	$5$	$7$	$13$	$17$	$19$	$23$	$25$	$29$	$31$	$35$
$\chi_{3168}(157,\cdot)$	$1$	$1$	$e\left(\frac{29}{120}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{11}{120}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{7}{120}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{37}{40}\right)$
$\chi_{3168}(229,\cdot)$	$1$	$1$	$e\left(\frac{23}{120}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{17}{120}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{109}{120}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{39}{40}\right)$
$\chi_{3168}(301,\cdot)$	$1$	$1$	$e\left(\frac{41}{120}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{119}{120}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{43}{120}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{33}{40}\right)$
$\chi_{3168}(421,\cdot)$	$1$	$1$	$e\left(\frac{79}{120}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{1}{120}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{77}{120}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{7}{40}\right)$
$\chi_{3168}(445,\cdot)$	$1$	$1$	$e\left(\frac{77}{120}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{83}{120}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{31}{120}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{21}{40}\right)$
$\chi_{3168}(493,\cdot)$	$1$	$1$	$e\left(\frac{73}{120}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{7}{120}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{59}{120}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{9}{40}\right)$
$\chi_{3168}(565,\cdot)$	$1$	$1$	$e\left(\frac{91}{120}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{109}{120}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{113}{120}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{3}{40}\right)$
$\chi_{3168}(709,\cdot)$	$1$	$1$	$e\left(\frac{7}{120}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{73}{120}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{101}{120}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{31}{40}\right)$
$\chi_{3168}(949,\cdot)$	$1$	$1$	$e\left(\frac{59}{120}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{101}{120}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{97}{120}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{27}{40}\right)$
$\chi_{3168}(1021,\cdot)$	$1$	$1$	$e\left(\frac{53}{120}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{107}{120}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{79}{120}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{29}{40}\right)$
$\chi_{3168}(1093,\cdot)$	$1$	$1$	$e\left(\frac{71}{120}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{89}{120}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{13}{120}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{23}{40}\right)$
$\chi_{3168}(1213,\cdot)$	$1$	$1$	$e\left(\frac{109}{120}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{91}{120}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{47}{120}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{37}{40}\right)$
$\chi_{3168}(1237,\cdot)$	$1$	$1$	$e\left(\frac{107}{120}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{53}{120}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{1}{120}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{11}{40}\right)$
$\chi_{3168}(1285,\cdot)$	$1$	$1$	$e\left(\frac{103}{120}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{97}{120}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{29}{120}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{39}{40}\right)$
$\chi_{3168}(1357,\cdot)$	$1$	$1$	$e\left(\frac{1}{120}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{79}{120}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{83}{120}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{33}{40}\right)$
$\chi_{3168}(1501,\cdot)$	$1$	$1$	$e\left(\frac{37}{120}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{43}{120}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{71}{120}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{21}{40}\right)$
$\chi_{3168}(1741,\cdot)$	$1$	$1$	$e\left(\frac{89}{120}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{71}{120}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{67}{120}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{17}{40}\right)$
$\chi_{3168}(1813,\cdot)$	$1$	$1$	$e\left(\frac{83}{120}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{77}{120}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{49}{120}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{19}{40}\right)$
$\chi_{3168}(1885,\cdot)$	$1$	$1$	$e\left(\frac{101}{120}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{59}{120}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{103}{120}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{13}{40}\right)$
$\chi_{3168}(2005,\cdot)$	$1$	$1$	$e\left(\frac{19}{120}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{61}{120}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{17}{120}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{27}{40}\right)$
$\chi_{3168}(2029,\cdot)$	$1$	$1$	$e\left(\frac{17}{120}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{23}{120}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{91}{120}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{1}{40}\right)$
$\chi_{3168}(2077,\cdot)$	$1$	$1$	$e\left(\frac{13}{120}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{67}{120}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{119}{120}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{29}{40}\right)$
$\chi_{3168}(2149,\cdot)$	$1$	$1$	$e\left(\frac{31}{120}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{49}{120}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{53}{120}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{23}{40}\right)$
$\chi_{3168}(2293,\cdot)$	$1$	$1$	$e\left(\frac{67}{120}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{13}{120}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{41}{120}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{11}{40}\right)$
$\chi_{3168}(2533,\cdot)$	$1$	$1$	$e\left(\frac{119}{120}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{41}{120}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{37}{120}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{7}{40}\right)$
$\chi_{3168}(2605,\cdot)$	$1$	$1$	$e\left(\frac{113}{120}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{47}{120}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{19}{120}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{9}{40}\right)$
$\chi_{3168}(2677,\cdot)$	$1$	$1$	$e\left(\frac{11}{120}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{29}{120}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{73}{120}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{3}{40}\right)$
$\chi_{3168}(2797,\cdot)$	$1$	$1$	$e\left(\frac{49}{120}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{31}{120}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{107}{120}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{17}{40}\right)$
$\chi_{3168}(2821,\cdot)$	$1$	$1$	$e\left(\frac{47}{120}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{113}{120}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{61}{120}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{31}{40}\right)$
$\chi_{3168}(2869,\cdot)$	$1$	$1$	$e\left(\frac{43}{120}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{37}{120}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{89}{120}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{19}{40}\right)$
$\chi_{3168}(2941,\cdot)$	$1$	$1$	$e\left(\frac{61}{120}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{19}{120}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{23}{120}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{13}{40}\right)$

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	\(-1\)	\(1\)	\(5\)	\(7\)	\(13\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)	\(35\)
\(\chi_{3168}(157,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{120}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{11}{120}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{7}{120}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{37}{40}\right)\)
\(\chi_{3168}(229,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{120}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{17}{120}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{109}{120}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{39}{40}\right)\)
\(\chi_{3168}(301,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{120}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{119}{120}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{43}{120}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{33}{40}\right)\)
\(\chi_{3168}(421,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{79}{120}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{1}{120}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{77}{120}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{7}{40}\right)\)
\(\chi_{3168}(445,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{77}{120}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{83}{120}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{31}{120}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{21}{40}\right)\)
\(\chi_{3168}(493,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{73}{120}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{7}{120}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{59}{120}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{9}{40}\right)\)
\(\chi_{3168}(565,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{91}{120}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{109}{120}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{113}{120}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{3}{40}\right)\)
\(\chi_{3168}(709,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{120}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{73}{120}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{101}{120}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{31}{40}\right)\)
\(\chi_{3168}(949,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{120}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{101}{120}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{97}{120}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{27}{40}\right)\)
\(\chi_{3168}(1021,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{120}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{107}{120}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{79}{120}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{29}{40}\right)\)
\(\chi_{3168}(1093,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{71}{120}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{89}{120}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{13}{120}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{23}{40}\right)\)
\(\chi_{3168}(1213,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{109}{120}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{91}{120}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{47}{120}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{37}{40}\right)\)
\(\chi_{3168}(1237,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{107}{120}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{53}{120}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{1}{120}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{11}{40}\right)\)
\(\chi_{3168}(1285,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{103}{120}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{97}{120}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{29}{120}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{39}{40}\right)\)
\(\chi_{3168}(1357,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{120}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{79}{120}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{83}{120}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{33}{40}\right)\)
\(\chi_{3168}(1501,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{120}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{43}{120}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{71}{120}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{21}{40}\right)\)
\(\chi_{3168}(1741,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{89}{120}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{71}{120}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{67}{120}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{17}{40}\right)\)
\(\chi_{3168}(1813,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{83}{120}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{77}{120}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{49}{120}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{19}{40}\right)\)
\(\chi_{3168}(1885,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{101}{120}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{59}{120}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{103}{120}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{13}{40}\right)\)
\(\chi_{3168}(2005,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{120}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{61}{120}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{17}{120}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{27}{40}\right)\)
\(\chi_{3168}(2029,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{120}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{23}{120}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{91}{120}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{1}{40}\right)\)
\(\chi_{3168}(2077,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{120}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{67}{120}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{119}{120}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{29}{40}\right)\)
\(\chi_{3168}(2149,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{120}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{49}{120}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{53}{120}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{23}{40}\right)\)
\(\chi_{3168}(2293,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{67}{120}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{13}{120}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{41}{120}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{11}{40}\right)\)
\(\chi_{3168}(2533,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{119}{120}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{41}{120}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{37}{120}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{7}{40}\right)\)
\(\chi_{3168}(2605,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{113}{120}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{47}{120}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{19}{120}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{9}{40}\right)\)
\(\chi_{3168}(2677,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{120}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{29}{120}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{73}{120}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{3}{40}\right)\)
\(\chi_{3168}(2797,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{49}{120}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{31}{120}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{107}{120}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{17}{40}\right)\)
\(\chi_{3168}(2821,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{120}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{113}{120}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{61}{120}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{31}{40}\right)\)
\(\chi_{3168}(2869,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{120}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{37}{120}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{89}{120}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{19}{40}\right)\)
\(\chi_{3168}(2941,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{61}{120}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{19}{120}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{23}{120}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{13}{40}\right)\)

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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	3168.ew
Modulus	$3168$
Conductor	$3168$
Order	$120$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(3168\)
Conductor:	\(3168\)	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)