LMFDB - Dirichlet character orbit 6223.ks

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(6223, base_ring=CyclotomicField(126)) M = H._module chi = DirichletCharacter(H, M([51,40])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(26,6223)) 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	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$8$	$9$	$10$	$11$	$12$
$\chi_{6223}(26,\cdot)$	$-1$	$1$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{13}{126}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{61}{126}\right)$
$\chi_{6223}(187,\cdot)$	$-1$	$1$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{25}{126}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{1}{126}\right)$
$\chi_{6223}(369,\cdot)$	$-1$	$1$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{55}{126}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{103}{126}\right)$
$\chi_{6223}(430,\cdot)$	$-1$	$1$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{59}{126}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{83}{126}\right)$
$\chi_{6223}(465,\cdot)$	$-1$	$1$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{53}{126}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{113}{126}\right)$
$\chi_{6223}(549,\cdot)$	$-1$	$1$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{89}{126}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{59}{126}\right)$
$\chi_{6223}(1312,\cdot)$	$-1$	$1$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{17}{126}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{41}{126}\right)$
$\chi_{6223}(1662,\cdot)$	$-1$	$1$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{41}{126}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{47}{126}\right)$
$\chi_{6223}(1669,\cdot)$	$-1$	$1$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{65}{126}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{53}{126}\right)$
$\chi_{6223}(1713,\cdot)$	$-1$	$1$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{73}{126}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{13}{126}\right)$
$\chi_{6223}(1902,\cdot)$	$-1$	$1$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{109}{126}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{85}{126}\right)$
$\chi_{6223}(2063,\cdot)$	$-1$	$1$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{37}{126}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{67}{126}\right)$
$\chi_{6223}(2448,\cdot)$	$-1$	$1$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{31}{126}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{97}{126}\right)$
$\chi_{6223}(2495,\cdot)$	$-1$	$1$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{125}{126}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{5}{126}\right)$
$\chi_{6223}(2614,\cdot)$	$-1$	$1$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{71}{126}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{23}{126}\right)$
$\chi_{6223}(2866,\cdot)$	$-1$	$1$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{11}{126}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{71}{126}\right)$
$\chi_{6223}(3169,\cdot)$	$-1$	$1$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{19}{126}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{31}{126}\right)$
$\chi_{6223}(3190,\cdot)$	$-1$	$1$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{79}{126}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{109}{126}\right)$
$\chi_{6223}(3244,\cdot)$	$-1$	$1$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{5}{126}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{101}{126}\right)$
$\chi_{6223}(3246,\cdot)$	$-1$	$1$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{43}{126}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{37}{126}\right)$
$\chi_{6223}(3372,\cdot)$	$-1$	$1$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{67}{126}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{43}{126}\right)$
$\chi_{6223}(3692,\cdot)$	$-1$	$1$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{29}{126}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{107}{126}\right)$
$\chi_{6223}(3967,\cdot)$	$-1$	$1$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{115}{126}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{55}{126}\right)$
$\chi_{6223}(4422,\cdot)$	$-1$	$1$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{85}{126}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{79}{126}\right)$
$\chi_{6223}(4924,\cdot)$	$-1$	$1$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{95}{126}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{29}{126}\right)$
$\chi_{6223}(5295,\cdot)$	$-1$	$1$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{23}{126}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{11}{126}\right)$
$\chi_{6223}(5351,\cdot)$	$-1$	$1$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{47}{126}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{17}{126}\right)$
$\chi_{6223}(5505,\cdot)$	$-1$	$1$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{113}{126}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{65}{126}\right)$
$\chi_{6223}(5542,\cdot)$	$-1$	$1$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{121}{126}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{25}{126}\right)$
$\chi_{6223}(5624,\cdot)$	$-1$	$1$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{101}{126}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{125}{126}\right)$
$\chi_{6223}(5736,\cdot)$	$-1$	$1$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{107}{126}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{95}{126}\right)$

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	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(8\)	\(9\)	\(10\)	\(11\)	\(12\)
\(\chi_{6223}(26,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{13}{126}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{61}{126}\right)\)
\(\chi_{6223}(187,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{25}{126}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{1}{126}\right)\)
\(\chi_{6223}(369,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{55}{126}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{103}{126}\right)\)
\(\chi_{6223}(430,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{59}{126}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{83}{126}\right)\)
\(\chi_{6223}(465,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{53}{126}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{113}{126}\right)\)
\(\chi_{6223}(549,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{89}{126}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{59}{126}\right)\)
\(\chi_{6223}(1312,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{17}{126}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{41}{126}\right)\)
\(\chi_{6223}(1662,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{41}{126}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{47}{126}\right)\)
\(\chi_{6223}(1669,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{65}{126}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{53}{126}\right)\)
\(\chi_{6223}(1713,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{73}{126}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{13}{126}\right)\)
\(\chi_{6223}(1902,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{109}{126}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{85}{126}\right)\)
\(\chi_{6223}(2063,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{37}{126}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{67}{126}\right)\)
\(\chi_{6223}(2448,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{31}{126}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{97}{126}\right)\)
\(\chi_{6223}(2495,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{125}{126}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{5}{126}\right)\)
\(\chi_{6223}(2614,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{71}{126}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{23}{126}\right)\)
\(\chi_{6223}(2866,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{11}{126}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{71}{126}\right)\)
\(\chi_{6223}(3169,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{19}{126}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{31}{126}\right)\)
\(\chi_{6223}(3190,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{79}{126}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{109}{126}\right)\)
\(\chi_{6223}(3244,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{5}{126}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{101}{126}\right)\)
\(\chi_{6223}(3246,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{43}{126}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{37}{126}\right)\)
\(\chi_{6223}(3372,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{67}{126}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{43}{126}\right)\)
\(\chi_{6223}(3692,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{29}{126}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{107}{126}\right)\)
\(\chi_{6223}(3967,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{115}{126}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{55}{126}\right)\)
\(\chi_{6223}(4422,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{85}{126}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{79}{126}\right)\)
\(\chi_{6223}(4924,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{95}{126}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{29}{126}\right)\)
\(\chi_{6223}(5295,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{23}{126}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{11}{126}\right)\)
\(\chi_{6223}(5351,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{47}{126}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{17}{126}\right)\)
\(\chi_{6223}(5505,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{113}{126}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{65}{126}\right)\)
\(\chi_{6223}(5542,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{121}{126}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{25}{126}\right)\)
\(\chi_{6223}(5624,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{101}{126}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{125}{126}\right)\)
\(\chi_{6223}(5736,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{107}{126}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{95}{126}\right)\)

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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.ks
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)