LMFDB - Dirichlet character orbit 6223.hw

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(6223, base_ring=CyclotomicField(126)) M = H._module chi = DirichletCharacter(H, M([24,88])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(142,6223)) 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:	$63$	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 63 polynomial

First 31 of 36 characters in Galois orbit

Character	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$8$	$9$	$10$	$11$	$12$
$\chi_{6223}(142,\cdot)$	$1$	$1$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{8}{63}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{23}{63}\right)$
$\chi_{6223}(443,\cdot)$	$1$	$1$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{5}{63}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{38}{63}\right)$
$\chi_{6223}(550,\cdot)$	$1$	$1$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{40}{63}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{52}{63}\right)$
$\chi_{6223}(676,\cdot)$	$1$	$1$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{13}{63}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{61}{63}\right)$
$\chi_{6223}(695,\cdot)$	$1$	$1$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{44}{63}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{32}{63}\right)$
$\chi_{6223}(963,\cdot)$	$1$	$1$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{4}{63}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{43}{63}\right)$
$\chi_{6223}(968,\cdot)$	$1$	$1$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{32}{63}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{29}{63}\right)$
$\chi_{6223}(977,\cdot)$	$1$	$1$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{43}{63}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{37}{63}\right)$
$\chi_{6223}(1178,\cdot)$	$1$	$1$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{47}{63}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{17}{63}\right)$
$\chi_{6223}(1418,\cdot)$	$1$	$1$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{22}{63}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{16}{63}\right)$
$\chi_{6223}(1495,\cdot)$	$1$	$1$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{16}{63}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{46}{63}\right)$
$\chi_{6223}(2025,\cdot)$	$1$	$1$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{62}{63}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{5}{63}\right)$
$\chi_{6223}(2041,\cdot)$	$1$	$1$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{46}{63}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{22}{63}\right)$
$\chi_{6223}(2172,\cdot)$	$1$	$1$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{20}{63}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{26}{63}\right)$
$\chi_{6223}(2410,\cdot)$	$1$	$1$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{23}{63}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{11}{63}\right)$
$\chi_{6223}(2494,\cdot)$	$1$	$1$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{29}{63}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{44}{63}\right)$
$\chi_{6223}(2697,\cdot)$	$1$	$1$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{26}{63}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{59}{63}\right)$
$\chi_{6223}(3259,\cdot)$	$1$	$1$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{58}{63}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{25}{63}\right)$
$\chi_{6223}(3336,\cdot)$	$1$	$1$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{10}{63}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{13}{63}\right)$
$\chi_{6223}(3371,\cdot)$	$1$	$1$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{34}{63}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{19}{63}\right)$
$\chi_{6223}(3574,\cdot)$	$1$	$1$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{1}{63}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{58}{63}\right)$
$\chi_{6223}(3796,\cdot)$	$1$	$1$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{17}{63}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{41}{63}\right)$
$\chi_{6223}(3854,\cdot)$	$1$	$1$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{25}{63}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{1}{63}\right)$
$\chi_{6223}(3880,\cdot)$	$1$	$1$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{2}{63}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{53}{63}\right)$
$\chi_{6223}(4090,\cdot)$	$1$	$1$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{38}{63}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{62}{63}\right)$
$\chi_{6223}(4433,\cdot)$	$1$	$1$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{59}{63}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{20}{63}\right)$
$\chi_{6223}(4643,\cdot)$	$1$	$1$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{53}{63}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{50}{63}\right)$
$\chi_{6223}(4862,\cdot)$	$1$	$1$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{19}{63}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{31}{63}\right)$
$\chi_{6223}(5238,\cdot)$	$1$	$1$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{50}{63}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{2}{63}\right)$
$\chi_{6223}(5345,\cdot)$	$1$	$1$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{52}{63}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{55}{63}\right)$
$\chi_{6223}(5455,\cdot)$	$1$	$1$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{41}{63}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{47}{63}\right)$

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	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(8\)	\(9\)	\(10\)	\(11\)	\(12\)
\(\chi_{6223}(142,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{8}{63}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{23}{63}\right)\)
\(\chi_{6223}(443,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{5}{63}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{38}{63}\right)\)
\(\chi_{6223}(550,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{40}{63}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{52}{63}\right)\)
\(\chi_{6223}(676,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{13}{63}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{61}{63}\right)\)
\(\chi_{6223}(695,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{44}{63}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{32}{63}\right)\)
\(\chi_{6223}(963,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{4}{63}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{43}{63}\right)\)
\(\chi_{6223}(968,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{32}{63}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{29}{63}\right)\)
\(\chi_{6223}(977,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{43}{63}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{37}{63}\right)\)
\(\chi_{6223}(1178,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{47}{63}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{17}{63}\right)\)
\(\chi_{6223}(1418,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{22}{63}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{16}{63}\right)\)
\(\chi_{6223}(1495,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{16}{63}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{46}{63}\right)\)
\(\chi_{6223}(2025,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{62}{63}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{5}{63}\right)\)
\(\chi_{6223}(2041,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{46}{63}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{22}{63}\right)\)
\(\chi_{6223}(2172,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{20}{63}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{26}{63}\right)\)
\(\chi_{6223}(2410,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{23}{63}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{11}{63}\right)\)
\(\chi_{6223}(2494,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{29}{63}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{44}{63}\right)\)
\(\chi_{6223}(2697,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{26}{63}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{59}{63}\right)\)
\(\chi_{6223}(3259,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{58}{63}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{25}{63}\right)\)
\(\chi_{6223}(3336,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{10}{63}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{13}{63}\right)\)
\(\chi_{6223}(3371,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{34}{63}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{19}{63}\right)\)
\(\chi_{6223}(3574,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{1}{63}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{58}{63}\right)\)
\(\chi_{6223}(3796,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{17}{63}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{41}{63}\right)\)
\(\chi_{6223}(3854,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{25}{63}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{1}{63}\right)\)
\(\chi_{6223}(3880,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{2}{63}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{53}{63}\right)\)
\(\chi_{6223}(4090,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{38}{63}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{62}{63}\right)\)
\(\chi_{6223}(4433,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{59}{63}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{20}{63}\right)\)
\(\chi_{6223}(4643,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{53}{63}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{50}{63}\right)\)
\(\chi_{6223}(4862,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{19}{63}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{31}{63}\right)\)
\(\chi_{6223}(5238,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{50}{63}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{2}{63}\right)\)
\(\chi_{6223}(5345,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{52}{63}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{55}{63}\right)\)
\(\chi_{6223}(5455,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{41}{63}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{47}{63}\right)\)

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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.hw
Modulus	$6223$
Conductor	$6223$
Order	$63$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(6223\)
Conductor:	\(6223\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(63\)	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)