LMFDB - Dirichlet character orbit 6223.kh

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(6223, base_ring=CyclotomicField(126)) M = H._module chi = DirichletCharacter(H, M([3,1])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(3,6223)) 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:	even	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	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$8$	$9$	$10$	$11$	$12$
$\chi_{6223}(3,\cdot)$	$1$	$1$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{2}{63}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{4}{63}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{31}{63}\right)$	$e\left(\frac{26}{63}\right)$
$\chi_{6223}(241,\cdot)$	$1$	$1$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{62}{63}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{61}{63}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{16}{63}\right)$	$e\left(\frac{50}{63}\right)$
$\chi_{6223}(243,\cdot)$	$1$	$1$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{10}{63}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{20}{63}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{29}{63}\right)$	$e\left(\frac{4}{63}\right)$
$\chi_{6223}(388,\cdot)$	$1$	$1$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{41}{63}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{19}{63}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{37}{63}\right)$	$e\left(\frac{29}{63}\right)$
$\chi_{6223}(467,\cdot)$	$1$	$1$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{34}{63}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{5}{63}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{23}{63}\right)$	$e\left(\frac{1}{63}\right)$
$\chi_{6223}(1069,\cdot)$	$1$	$1$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{25}{63}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{50}{63}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{41}{63}\right)$	$e\left(\frac{10}{63}\right)$
$\chi_{6223}(1235,\cdot)$	$1$	$1$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{26}{63}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{52}{63}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{25}{63}\right)$	$e\left(\frac{23}{63}\right)$
$\chi_{6223}(1426,\cdot)$	$1$	$1$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{37}{63}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{11}{63}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{38}{63}\right)$	$e\left(\frac{40}{63}\right)$
$\chi_{6223}(1445,\cdot)$	$1$	$1$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{11}{63}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{22}{63}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{13}{63}\right)$	$e\left(\frac{17}{63}\right)$
$\chi_{6223}(1718,\cdot)$	$1$	$1$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{23}{63}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{46}{63}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{10}{63}\right)$	$e\left(\frac{47}{63}\right)$
$\chi_{6223}(1888,\cdot)$	$1$	$1$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{13}{63}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{26}{63}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{44}{63}\right)$	$e\left(\frac{43}{63}\right)$
$\chi_{6223}(1970,\cdot)$	$1$	$1$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{47}{63}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{31}{63}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{4}{63}\right)$	$e\left(\frac{44}{63}\right)$
$\chi_{6223}(2252,\cdot)$	$1$	$1$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{31}{63}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{62}{63}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{8}{63}\right)$	$e\left(\frac{25}{63}\right)$
$\chi_{6223}(2271,\cdot)$	$1$	$1$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{50}{63}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{37}{63}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{19}{63}\right)$	$e\left(\frac{20}{63}\right)$
$\chi_{6223}(2817,\cdot)$	$1$	$1$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{53}{63}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{43}{63}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{34}{63}\right)$	$e\left(\frac{59}{63}\right)$
$\chi_{6223}(2903,\cdot)$	$1$	$1$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{22}{63}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{44}{63}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{26}{63}\right)$	$e\left(\frac{34}{63}\right)$
$\chi_{6223}(3181,\cdot)$	$1$	$1$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{20}{63}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{40}{63}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{58}{63}\right)$	$e\left(\frac{8}{63}\right)$
$\chi_{6223}(3398,\cdot)$	$1$	$1$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{29}{63}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{58}{63}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{40}{63}\right)$	$e\left(\frac{62}{63}\right)$
$\chi_{6223}(3484,\cdot)$	$1$	$1$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{58}{63}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{53}{63}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{17}{63}\right)$	$e\left(\frac{61}{63}\right)$
$\chi_{6223}(3993,\cdot)$	$1$	$1$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{32}{63}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{1}{63}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{55}{63}\right)$	$e\left(\frac{38}{63}\right)$
$\chi_{6223}(3995,\cdot)$	$1$	$1$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{55}{63}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{47}{63}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{2}{63}\right)$	$e\left(\frac{22}{63}\right)$
$\chi_{6223}(4149,\cdot)$	$1$	$1$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{61}{63}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{59}{63}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{32}{63}\right)$	$e\left(\frac{37}{63}\right)$
$\chi_{6223}(4203,\cdot)$	$1$	$1$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{38}{63}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{13}{63}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{22}{63}\right)$	$e\left(\frac{53}{63}\right)$
$\chi_{6223}(4401,\cdot)$	$1$	$1$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{46}{63}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{29}{63}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{20}{63}\right)$	$e\left(\frac{31}{63}\right)$
$\chi_{6223}(4546,\cdot)$	$1$	$1$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{17}{63}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{34}{63}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{43}{63}\right)$	$e\left(\frac{32}{63}\right)$
$\chi_{6223}(4756,\cdot)$	$1$	$1$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{44}{63}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{25}{63}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{52}{63}\right)$	$e\left(\frac{5}{63}\right)$
$\chi_{6223}(4840,\cdot)$	$1$	$1$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{59}{63}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{55}{63}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{1}{63}\right)$	$e\left(\frac{11}{63}\right)$
$\chi_{6223}(5031,\cdot)$	$1$	$1$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{19}{63}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{38}{63}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{11}{63}\right)$	$e\left(\frac{58}{63}\right)$
$\chi_{6223}(5059,\cdot)$	$1$	$1$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{43}{63}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{23}{63}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{5}{63}\right)$	$e\left(\frac{55}{63}\right)$
$\chi_{6223}(5500,\cdot)$	$1$	$1$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{1}{63}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{2}{63}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{47}{63}\right)$	$e\left(\frac{13}{63}\right)$
$\chi_{6223}(5633,\cdot)$	$1$	$1$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{52}{63}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{41}{63}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{50}{63}\right)$	$e\left(\frac{46}{63}\right)$

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	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(8\)	\(9\)	\(10\)	\(11\)	\(12\)
\(\chi_{6223}(3,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{2}{63}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{4}{63}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{31}{63}\right)\)	\(e\left(\frac{26}{63}\right)\)
\(\chi_{6223}(241,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{62}{63}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{61}{63}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{16}{63}\right)\)	\(e\left(\frac{50}{63}\right)\)
\(\chi_{6223}(243,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{10}{63}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{20}{63}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{29}{63}\right)\)	\(e\left(\frac{4}{63}\right)\)
\(\chi_{6223}(388,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{41}{63}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{19}{63}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{37}{63}\right)\)	\(e\left(\frac{29}{63}\right)\)
\(\chi_{6223}(467,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{34}{63}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{5}{63}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{23}{63}\right)\)	\(e\left(\frac{1}{63}\right)\)
\(\chi_{6223}(1069,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{25}{63}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{50}{63}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{41}{63}\right)\)	\(e\left(\frac{10}{63}\right)\)
\(\chi_{6223}(1235,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{26}{63}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{52}{63}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{25}{63}\right)\)	\(e\left(\frac{23}{63}\right)\)
\(\chi_{6223}(1426,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{37}{63}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{11}{63}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{38}{63}\right)\)	\(e\left(\frac{40}{63}\right)\)
\(\chi_{6223}(1445,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{11}{63}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{22}{63}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{13}{63}\right)\)	\(e\left(\frac{17}{63}\right)\)
\(\chi_{6223}(1718,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{23}{63}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{46}{63}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{10}{63}\right)\)	\(e\left(\frac{47}{63}\right)\)
\(\chi_{6223}(1888,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{13}{63}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{26}{63}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{44}{63}\right)\)	\(e\left(\frac{43}{63}\right)\)
\(\chi_{6223}(1970,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{47}{63}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{31}{63}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{4}{63}\right)\)	\(e\left(\frac{44}{63}\right)\)
\(\chi_{6223}(2252,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{31}{63}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{62}{63}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{8}{63}\right)\)	\(e\left(\frac{25}{63}\right)\)
\(\chi_{6223}(2271,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{50}{63}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{37}{63}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{19}{63}\right)\)	\(e\left(\frac{20}{63}\right)\)
\(\chi_{6223}(2817,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{53}{63}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{43}{63}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{34}{63}\right)\)	\(e\left(\frac{59}{63}\right)\)
\(\chi_{6223}(2903,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{22}{63}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{44}{63}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{26}{63}\right)\)	\(e\left(\frac{34}{63}\right)\)
\(\chi_{6223}(3181,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{20}{63}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{40}{63}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{58}{63}\right)\)	\(e\left(\frac{8}{63}\right)\)
\(\chi_{6223}(3398,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{29}{63}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{58}{63}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{40}{63}\right)\)	\(e\left(\frac{62}{63}\right)\)
\(\chi_{6223}(3484,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{58}{63}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{53}{63}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{17}{63}\right)\)	\(e\left(\frac{61}{63}\right)\)
\(\chi_{6223}(3993,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{32}{63}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{1}{63}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{55}{63}\right)\)	\(e\left(\frac{38}{63}\right)\)
\(\chi_{6223}(3995,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{55}{63}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{47}{63}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{2}{63}\right)\)	\(e\left(\frac{22}{63}\right)\)
\(\chi_{6223}(4149,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{61}{63}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{59}{63}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{32}{63}\right)\)	\(e\left(\frac{37}{63}\right)\)
\(\chi_{6223}(4203,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{38}{63}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{13}{63}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{22}{63}\right)\)	\(e\left(\frac{53}{63}\right)\)
\(\chi_{6223}(4401,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{46}{63}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{29}{63}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{20}{63}\right)\)	\(e\left(\frac{31}{63}\right)\)
\(\chi_{6223}(4546,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{17}{63}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{34}{63}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{43}{63}\right)\)	\(e\left(\frac{32}{63}\right)\)
\(\chi_{6223}(4756,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{44}{63}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{25}{63}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{52}{63}\right)\)	\(e\left(\frac{5}{63}\right)\)
\(\chi_{6223}(4840,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{59}{63}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{55}{63}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{1}{63}\right)\)	\(e\left(\frac{11}{63}\right)\)
\(\chi_{6223}(5031,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{19}{63}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{38}{63}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{11}{63}\right)\)	\(e\left(\frac{58}{63}\right)\)
\(\chi_{6223}(5059,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{43}{63}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{23}{63}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{5}{63}\right)\)	\(e\left(\frac{55}{63}\right)\)
\(\chi_{6223}(5500,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{1}{63}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{2}{63}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{47}{63}\right)\)	\(e\left(\frac{13}{63}\right)\)
\(\chi_{6223}(5633,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{52}{63}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{41}{63}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{50}{63}\right)\)	\(e\left(\frac{46}{63}\right)\)

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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.kh
Modulus	$6223$
Conductor	$6223$
Order	$126$
Real	no
Primitive	yes
Minimal	yes
Parity	even

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:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)