LMFDB - Dirichlet character orbit 6336.fh

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(6336, base_ring=CyclotomicField(80)) M = H._module chi = DirichletCharacter(H, M([40,75,40,64])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(179,6336)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$6336$
Conductor:	$2112$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$80$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 2112.cv	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:	$\Q(\zeta_{80})$
Fixed field:	Number field defined by a degree 80 polynomial

First 31 of 32 characters in Galois orbit

Character	$-1$	$1$	$5$	$7$	$13$	$17$	$19$	$23$	$25$	$29$	$31$	$35$
$\chi_{6336}(179,\cdot)$	$1$	$1$	$e\left(\frac{51}{80}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{69}{80}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{37}{80}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{33}{80}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{9}{80}\right)$
$\chi_{6336}(251,\cdot)$	$1$	$1$	$e\left(\frac{77}{80}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{43}{80}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{59}{80}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{31}{80}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{23}{80}\right)$
$\chi_{6336}(323,\cdot)$	$1$	$1$	$e\left(\frac{39}{80}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{1}{80}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{33}{80}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{77}{80}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{21}{80}\right)$
$\chi_{6336}(467,\cdot)$	$1$	$1$	$e\left(\frac{43}{80}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{77}{80}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{61}{80}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{9}{80}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{17}{80}\right)$
$\chi_{6336}(971,\cdot)$	$1$	$1$	$e\left(\frac{1}{80}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{39}{80}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{7}{80}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{43}{80}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{19}{80}\right)$
$\chi_{6336}(1043,\cdot)$	$1$	$1$	$e\left(\frac{27}{80}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{13}{80}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{29}{80}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{41}{80}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{33}{80}\right)$
$\chi_{6336}(1115,\cdot)$	$1$	$1$	$e\left(\frac{69}{80}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{51}{80}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{3}{80}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{7}{80}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{31}{80}\right)$
$\chi_{6336}(1259,\cdot)$	$1$	$1$	$e\left(\frac{73}{80}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{47}{80}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{31}{80}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{19}{80}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{27}{80}\right)$
$\chi_{6336}(1763,\cdot)$	$1$	$1$	$e\left(\frac{31}{80}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{9}{80}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{57}{80}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{53}{80}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{29}{80}\right)$
$\chi_{6336}(1835,\cdot)$	$1$	$1$	$e\left(\frac{57}{80}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{63}{80}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{79}{80}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{51}{80}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{43}{80}\right)$
$\chi_{6336}(1907,\cdot)$	$1$	$1$	$e\left(\frac{19}{80}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{21}{80}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{53}{80}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{17}{80}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{41}{80}\right)$
$\chi_{6336}(2051,\cdot)$	$1$	$1$	$e\left(\frac{23}{80}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{17}{80}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{1}{80}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{29}{80}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{37}{80}\right)$
$\chi_{6336}(2555,\cdot)$	$1$	$1$	$e\left(\frac{61}{80}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{59}{80}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{27}{80}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{63}{80}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{39}{80}\right)$
$\chi_{6336}(2627,\cdot)$	$1$	$1$	$e\left(\frac{7}{80}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{33}{80}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{49}{80}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{61}{80}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{53}{80}\right)$
$\chi_{6336}(2699,\cdot)$	$1$	$1$	$e\left(\frac{49}{80}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{71}{80}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{23}{80}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{27}{80}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{51}{80}\right)$
$\chi_{6336}(2843,\cdot)$	$1$	$1$	$e\left(\frac{53}{80}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{67}{80}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{51}{80}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{39}{80}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{47}{80}\right)$
$\chi_{6336}(3347,\cdot)$	$1$	$1$	$e\left(\frac{11}{80}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{29}{80}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{77}{80}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{73}{80}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{49}{80}\right)$
$\chi_{6336}(3419,\cdot)$	$1$	$1$	$e\left(\frac{37}{80}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{3}{80}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{19}{80}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{71}{80}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{63}{80}\right)$
$\chi_{6336}(3491,\cdot)$	$1$	$1$	$e\left(\frac{79}{80}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{41}{80}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{73}{80}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{37}{80}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{61}{80}\right)$
$\chi_{6336}(3635,\cdot)$	$1$	$1$	$e\left(\frac{3}{80}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{37}{80}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{21}{80}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{49}{80}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{57}{80}\right)$
$\chi_{6336}(4139,\cdot)$	$1$	$1$	$e\left(\frac{41}{80}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{79}{80}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{47}{80}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{3}{80}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{59}{80}\right)$
$\chi_{6336}(4211,\cdot)$	$1$	$1$	$e\left(\frac{67}{80}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{53}{80}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{69}{80}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{1}{80}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{73}{80}\right)$
$\chi_{6336}(4283,\cdot)$	$1$	$1$	$e\left(\frac{29}{80}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{11}{80}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{43}{80}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{47}{80}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{71}{80}\right)$
$\chi_{6336}(4427,\cdot)$	$1$	$1$	$e\left(\frac{33}{80}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{7}{80}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{71}{80}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{59}{80}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{67}{80}\right)$
$\chi_{6336}(4931,\cdot)$	$1$	$1$	$e\left(\frac{71}{80}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{49}{80}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{17}{80}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{13}{80}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{69}{80}\right)$
$\chi_{6336}(5003,\cdot)$	$1$	$1$	$e\left(\frac{17}{80}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{23}{80}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{39}{80}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{11}{80}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{80}\right)$
$\chi_{6336}(5075,\cdot)$	$1$	$1$	$e\left(\frac{59}{80}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{61}{80}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{13}{80}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{57}{80}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{80}\right)$
$\chi_{6336}(5219,\cdot)$	$1$	$1$	$e\left(\frac{63}{80}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{57}{80}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{41}{80}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{69}{80}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{77}{80}\right)$
$\chi_{6336}(5723,\cdot)$	$1$	$1$	$e\left(\frac{21}{80}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{19}{80}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{67}{80}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{23}{80}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{79}{80}\right)$
$\chi_{6336}(5795,\cdot)$	$1$	$1$	$e\left(\frac{47}{80}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{73}{80}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{9}{80}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{21}{80}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{13}{80}\right)$
$\chi_{6336}(5867,\cdot)$	$1$	$1$	$e\left(\frac{9}{80}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{31}{80}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{63}{80}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{67}{80}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{11}{80}\right)$

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	\(-1\)	\(1\)	\(5\)	\(7\)	\(13\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)	\(35\)
\(\chi_{6336}(179,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{51}{80}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{69}{80}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{37}{80}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{33}{80}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{9}{80}\right)\)
\(\chi_{6336}(251,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{77}{80}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{43}{80}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{59}{80}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{31}{80}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{23}{80}\right)\)
\(\chi_{6336}(323,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{39}{80}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{1}{80}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{33}{80}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{77}{80}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{21}{80}\right)\)
\(\chi_{6336}(467,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{80}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{77}{80}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{61}{80}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{9}{80}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{17}{80}\right)\)
\(\chi_{6336}(971,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{80}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{39}{80}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{7}{80}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{43}{80}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{19}{80}\right)\)
\(\chi_{6336}(1043,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{27}{80}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{13}{80}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{29}{80}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{41}{80}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{33}{80}\right)\)
\(\chi_{6336}(1115,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{69}{80}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{51}{80}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{3}{80}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{7}{80}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{31}{80}\right)\)
\(\chi_{6336}(1259,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{73}{80}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{47}{80}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{31}{80}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{19}{80}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{27}{80}\right)\)
\(\chi_{6336}(1763,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{80}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{9}{80}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{57}{80}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{53}{80}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{29}{80}\right)\)
\(\chi_{6336}(1835,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{57}{80}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{63}{80}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{79}{80}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{51}{80}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{43}{80}\right)\)
\(\chi_{6336}(1907,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{80}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{21}{80}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{53}{80}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{17}{80}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{41}{80}\right)\)
\(\chi_{6336}(2051,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{80}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{17}{80}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{1}{80}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{29}{80}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{37}{80}\right)\)
\(\chi_{6336}(2555,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{61}{80}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{59}{80}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{27}{80}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{63}{80}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{39}{80}\right)\)
\(\chi_{6336}(2627,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{80}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{33}{80}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{49}{80}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{61}{80}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{53}{80}\right)\)
\(\chi_{6336}(2699,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{49}{80}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{71}{80}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{23}{80}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{27}{80}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{51}{80}\right)\)
\(\chi_{6336}(2843,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{80}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{67}{80}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{51}{80}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{39}{80}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{47}{80}\right)\)
\(\chi_{6336}(3347,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{80}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{29}{80}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{77}{80}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{73}{80}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{49}{80}\right)\)
\(\chi_{6336}(3419,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{80}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{3}{80}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{19}{80}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{71}{80}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{63}{80}\right)\)
\(\chi_{6336}(3491,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{79}{80}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{41}{80}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{73}{80}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{37}{80}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{61}{80}\right)\)
\(\chi_{6336}(3635,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{80}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{37}{80}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{21}{80}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{49}{80}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{57}{80}\right)\)
\(\chi_{6336}(4139,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{80}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{79}{80}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{47}{80}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{3}{80}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{59}{80}\right)\)
\(\chi_{6336}(4211,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{67}{80}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{53}{80}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{69}{80}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{1}{80}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{73}{80}\right)\)
\(\chi_{6336}(4283,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{80}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{11}{80}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{43}{80}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{47}{80}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{71}{80}\right)\)
\(\chi_{6336}(4427,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{33}{80}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{7}{80}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{71}{80}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{59}{80}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{67}{80}\right)\)
\(\chi_{6336}(4931,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{71}{80}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{49}{80}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{17}{80}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{13}{80}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{69}{80}\right)\)
\(\chi_{6336}(5003,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{80}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{23}{80}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{39}{80}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{11}{80}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{3}{80}\right)\)
\(\chi_{6336}(5075,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{80}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{61}{80}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{13}{80}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{57}{80}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{1}{80}\right)\)
\(\chi_{6336}(5219,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{63}{80}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{57}{80}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{41}{80}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{69}{80}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{77}{80}\right)\)
\(\chi_{6336}(5723,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{21}{80}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{19}{80}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{67}{80}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{23}{80}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{79}{80}\right)\)
\(\chi_{6336}(5795,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{80}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{73}{80}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{9}{80}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{21}{80}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{13}{80}\right)\)
\(\chi_{6336}(5867,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{80}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{31}{80}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{63}{80}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{67}{80}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{11}{80}\right)\)

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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	6336.fh
Modulus	$6336$
Conductor	$2112$
Order	$80$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(6336\)
Conductor:	\(2112\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(80\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 2112.cv	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)