LMFDB - Dirichlet character orbit 6223.ja

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(6223, base_ring=CyclotomicField(126)) M = H._module chi = DirichletCharacter(H, M([99,94])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(13,6223)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$6223$
Conductor:	$6223$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$126$	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:	$\Q(\zeta_{63})$
Fixed field:	Number field defined by a degree 126 polynomial (not computed)

First 31 of 36 characters in Galois orbit

Character	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$8$	$9$	$10$	$11$	$12$
$\chi_{6223}(13,\cdot)$	$-1$	$1$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{67}{126}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{85}{126}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{4}{63}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{10}{63}\right)$	$e\left(\frac{103}{126}\right)$
$\chi_{6223}(153,\cdot)$	$-1$	$1$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{121}{126}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{67}{126}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{58}{63}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{19}{63}\right)$	$e\left(\frac{13}{126}\right)$
$\chi_{6223}(314,\cdot)$	$-1$	$1$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{97}{126}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{61}{126}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{34}{63}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{22}{63}\right)$	$e\left(\frac{25}{126}\right)$
$\chi_{6223}(496,\cdot)$	$-1$	$1$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{37}{126}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{109}{126}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{37}{63}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{61}{63}\right)$	$e\left(\frac{55}{126}\right)$
$\chi_{6223}(811,\cdot)$	$-1$	$1$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{113}{126}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{23}{126}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{50}{63}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{62}{63}\right)$	$e\left(\frac{59}{126}\right)$
$\chi_{6223}(1161,\cdot)$	$-1$	$1$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{101}{126}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{83}{126}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{38}{63}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{32}{63}\right)$	$e\left(\frac{65}{126}\right)$
$\chi_{6223}(1217,\cdot)$	$-1$	$1$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{89}{126}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{17}{126}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{26}{63}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{63}\right)$	$e\left(\frac{71}{126}\right)$
$\chi_{6223}(1287,\cdot)$	$-1$	$1$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{11}{126}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{29}{126}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{11}{63}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{59}{63}\right)$	$e\left(\frac{47}{126}\right)$
$\chi_{6223}(1693,\cdot)$	$-1$	$1$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{71}{126}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{107}{126}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{8}{63}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{20}{63}\right)$	$e\left(\frac{17}{126}\right)$
$\chi_{6223}(1735,\cdot)$	$-1$	$1$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{125}{126}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{89}{126}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{62}{63}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{29}{63}\right)$	$e\left(\frac{53}{126}\right)$
$\chi_{6223}(1840,\cdot)$	$-1$	$1$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{1}{126}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{37}{126}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{1}{63}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{34}{63}\right)$	$e\left(\frac{73}{126}\right)$
$\chi_{6223}(2029,\cdot)$	$-1$	$1$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{55}{126}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{19}{126}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{55}{63}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{43}{63}\right)$	$e\left(\frac{109}{126}\right)$
$\chi_{6223}(2190,\cdot)$	$-1$	$1$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{73}{126}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{55}{126}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{10}{63}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{25}{63}\right)$	$e\left(\frac{37}{126}\right)$
$\chi_{6223}(2295,\cdot)$	$-1$	$1$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{47}{126}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{101}{126}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{47}{63}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{23}{63}\right)$	$e\left(\frac{29}{126}\right)$
$\chi_{6223}(2575,\cdot)$	$-1$	$1$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{85}{126}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{121}{126}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{22}{63}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{55}{63}\right)$	$e\left(\frac{31}{126}\right)$
$\chi_{6223}(2701,\cdot)$	$-1$	$1$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{65}{126}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{11}{126}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{2}{63}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{63}\right)$	$e\left(\frac{83}{126}\right)$
$\chi_{6223}(2708,\cdot)$	$-1$	$1$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{53}{126}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{71}{126}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{53}{63}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{38}{63}\right)$	$e\left(\frac{89}{126}\right)$
$\chi_{6223}(3296,\cdot)$	$-1$	$1$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{109}{126}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{1}{126}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{46}{63}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{52}{63}\right)$	$e\left(\frac{19}{126}\right)$
$\chi_{6223}(3317,\cdot)$	$-1$	$1$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{115}{126}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{97}{126}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{52}{63}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{4}{63}\right)$	$e\left(\frac{79}{126}\right)$
$\chi_{6223}(3373,\cdot)$	$-1$	$1$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{61}{126}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{115}{126}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{61}{63}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{58}{63}\right)$	$e\left(\frac{43}{126}\right)$
$\chi_{6223}(3499,\cdot)$	$-1$	$1$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{13}{126}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{103}{126}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{13}{63}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{63}\right)$	$e\left(\frac{67}{126}\right)$
$\chi_{6223}(4094,\cdot)$	$-1$	$1$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{43}{126}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{79}{126}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{43}{63}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{13}{63}\right)$	$e\left(\frac{115}{126}\right)$
$\chi_{6223}(4108,\cdot)$	$-1$	$1$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{5}{126}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{59}{126}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{5}{63}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{44}{63}\right)$	$e\left(\frac{113}{126}\right)$
$\chi_{6223}(4136,\cdot)$	$-1$	$1$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{83}{126}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{47}{126}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{20}{63}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{50}{63}\right)$	$e\left(\frac{11}{126}\right)$
$\chi_{6223}(4549,\cdot)$	$-1$	$1$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{103}{126}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{31}{126}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{40}{63}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{37}{63}\right)$	$e\left(\frac{85}{126}\right)$
$\chi_{6223}(4710,\cdot)$	$-1$	$1$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{23}{126}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{95}{126}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{23}{63}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{26}{63}\right)$	$e\left(\frac{41}{126}\right)$
$\chi_{6223}(4787,\cdot)$	$-1$	$1$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{59}{126}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{41}{126}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{59}{63}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{53}{63}\right)$	$e\left(\frac{23}{126}\right)$
$\chi_{6223}(5228,\cdot)$	$-1$	$1$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{17}{126}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{125}{126}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{17}{63}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{63}\right)$	$e\left(\frac{107}{126}\right)$
$\chi_{6223}(5403,\cdot)$	$-1$	$1$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{95}{126}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{113}{126}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{32}{63}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{17}{63}\right)$	$e\left(\frac{5}{126}\right)$
$\chi_{6223}(5543,\cdot)$	$-1$	$1$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{107}{126}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{53}{126}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{44}{63}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{47}{63}\right)$	$e\left(\frac{125}{126}\right)$
$\chi_{6223}(5669,\cdot)$	$-1$	$1$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{31}{126}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{13}{126}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{31}{63}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{46}{63}\right)$	$e\left(\frac{121}{126}\right)$

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	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(8\)	\(9\)	\(10\)	\(11\)	\(12\)
\(\chi_{6223}(13,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{67}{126}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{85}{126}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{4}{63}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{10}{63}\right)\)	\(e\left(\frac{103}{126}\right)\)
\(\chi_{6223}(153,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{121}{126}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{67}{126}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{58}{63}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{19}{63}\right)\)	\(e\left(\frac{13}{126}\right)\)
\(\chi_{6223}(314,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{97}{126}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{61}{126}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{34}{63}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{22}{63}\right)\)	\(e\left(\frac{25}{126}\right)\)
\(\chi_{6223}(496,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{37}{126}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{109}{126}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{37}{63}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{61}{63}\right)\)	\(e\left(\frac{55}{126}\right)\)
\(\chi_{6223}(811,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{113}{126}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{23}{126}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{50}{63}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{62}{63}\right)\)	\(e\left(\frac{59}{126}\right)\)
\(\chi_{6223}(1161,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{101}{126}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{83}{126}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{38}{63}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{32}{63}\right)\)	\(e\left(\frac{65}{126}\right)\)
\(\chi_{6223}(1217,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{89}{126}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{17}{126}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{26}{63}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{63}\right)\)	\(e\left(\frac{71}{126}\right)\)
\(\chi_{6223}(1287,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{11}{126}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{29}{126}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{11}{63}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{59}{63}\right)\)	\(e\left(\frac{47}{126}\right)\)
\(\chi_{6223}(1693,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{71}{126}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{107}{126}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{8}{63}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{20}{63}\right)\)	\(e\left(\frac{17}{126}\right)\)
\(\chi_{6223}(1735,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{125}{126}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{89}{126}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{62}{63}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{29}{63}\right)\)	\(e\left(\frac{53}{126}\right)\)
\(\chi_{6223}(1840,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{1}{126}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{37}{126}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{1}{63}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{34}{63}\right)\)	\(e\left(\frac{73}{126}\right)\)
\(\chi_{6223}(2029,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{55}{126}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{19}{126}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{55}{63}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{43}{63}\right)\)	\(e\left(\frac{109}{126}\right)\)
\(\chi_{6223}(2190,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{73}{126}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{55}{126}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{10}{63}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{25}{63}\right)\)	\(e\left(\frac{37}{126}\right)\)
\(\chi_{6223}(2295,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{47}{126}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{101}{126}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{47}{63}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{23}{63}\right)\)	\(e\left(\frac{29}{126}\right)\)
\(\chi_{6223}(2575,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{85}{126}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{121}{126}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{22}{63}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{55}{63}\right)\)	\(e\left(\frac{31}{126}\right)\)
\(\chi_{6223}(2701,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{65}{126}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{11}{126}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{2}{63}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{63}\right)\)	\(e\left(\frac{83}{126}\right)\)
\(\chi_{6223}(2708,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{53}{126}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{71}{126}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{53}{63}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{38}{63}\right)\)	\(e\left(\frac{89}{126}\right)\)
\(\chi_{6223}(3296,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{109}{126}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{1}{126}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{46}{63}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{52}{63}\right)\)	\(e\left(\frac{19}{126}\right)\)
\(\chi_{6223}(3317,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{115}{126}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{97}{126}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{52}{63}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{4}{63}\right)\)	\(e\left(\frac{79}{126}\right)\)
\(\chi_{6223}(3373,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{61}{126}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{115}{126}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{61}{63}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{58}{63}\right)\)	\(e\left(\frac{43}{126}\right)\)
\(\chi_{6223}(3499,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{13}{126}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{103}{126}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{13}{63}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{63}\right)\)	\(e\left(\frac{67}{126}\right)\)
\(\chi_{6223}(4094,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{43}{126}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{79}{126}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{43}{63}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{13}{63}\right)\)	\(e\left(\frac{115}{126}\right)\)
\(\chi_{6223}(4108,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{5}{126}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{59}{126}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{5}{63}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{44}{63}\right)\)	\(e\left(\frac{113}{126}\right)\)
\(\chi_{6223}(4136,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{83}{126}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{47}{126}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{20}{63}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{50}{63}\right)\)	\(e\left(\frac{11}{126}\right)\)
\(\chi_{6223}(4549,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{103}{126}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{31}{126}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{40}{63}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{37}{63}\right)\)	\(e\left(\frac{85}{126}\right)\)
\(\chi_{6223}(4710,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{23}{126}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{95}{126}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{23}{63}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{26}{63}\right)\)	\(e\left(\frac{41}{126}\right)\)
\(\chi_{6223}(4787,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{59}{126}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{41}{126}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{59}{63}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{53}{63}\right)\)	\(e\left(\frac{23}{126}\right)\)
\(\chi_{6223}(5228,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{17}{126}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{125}{126}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{17}{63}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{11}{63}\right)\)	\(e\left(\frac{107}{126}\right)\)
\(\chi_{6223}(5403,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{95}{126}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{113}{126}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{32}{63}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{17}{63}\right)\)	\(e\left(\frac{5}{126}\right)\)
\(\chi_{6223}(5543,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{107}{126}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{53}{126}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{44}{63}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{47}{63}\right)\)	\(e\left(\frac{125}{126}\right)\)
\(\chi_{6223}(5669,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{31}{126}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{13}{126}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{31}{63}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{46}{63}\right)\)	\(e\left(\frac{121}{126}\right)\)

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First 31 of 36 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	6223.ja
Modulus	$6223$
Conductor	$6223$
Order	$126$
Real	no
Primitive	yes
Minimal	yes
Parity	odd

Modulus:	\(6223\)
Conductor:	\(6223\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(126\)	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)