LMFDB - Dirichlet character orbit 6223.ii

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(6223, base_ring=CyclotomicField(126)) M = H._module chi = DirichletCharacter(H, M([33,19])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(12,6223)) 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	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$8$	$9$	$10$	$11$	$12$
$\chi_{6223}(12,\cdot)$	$1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{26}{63}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{5}{63}\right)$	$1$	$e\left(\frac{52}{63}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{46}{63}\right)$	$e\left(\frac{47}{63}\right)$
$\chi_{6223}(194,\cdot)$	$1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{29}{63}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{8}{63}\right)$	$1$	$e\left(\frac{58}{63}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{61}{63}\right)$	$e\left(\frac{50}{63}\right)$
$\chi_{6223}(283,\cdot)$	$1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{22}{63}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{43}{63}\right)$	$1$	$e\left(\frac{44}{63}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{5}{63}\right)$	$e\left(\frac{1}{63}\right)$
$\chi_{6223}(355,\cdot)$	$1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{63}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{47}{63}\right)$	$1$	$e\left(\frac{10}{63}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{4}{63}\right)$	$e\left(\frac{26}{63}\right)$
$\chi_{6223}(495,\cdot)$	$1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{59}{63}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{38}{63}\right)$	$1$	$e\left(\frac{55}{63}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{22}{63}\right)$	$e\left(\frac{17}{63}\right)$
$\chi_{6223}(642,\cdot)$	$1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{38}{63}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{17}{63}\right)$	$1$	$e\left(\frac{13}{63}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{43}{63}\right)$	$e\left(\frac{59}{63}\right)$
$\chi_{6223}(649,\cdot)$	$1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{47}{63}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{26}{63}\right)$	$1$	$e\left(\frac{31}{63}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{25}{63}\right)$	$e\left(\frac{5}{63}\right)$
$\chi_{6223}(810,\cdot)$	$1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{44}{63}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{23}{63}\right)$	$1$	$e\left(\frac{25}{63}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{10}{63}\right)$	$e\left(\frac{2}{63}\right)$
$\chi_{6223}(1062,\cdot)$	$1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{32}{63}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{11}{63}\right)$	$1$	$e\left(\frac{1}{63}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{13}{63}\right)$	$e\left(\frac{53}{63}\right)$
$\chi_{6223}(1515,\cdot)$	$1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{16}{63}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{37}{63}\right)$	$1$	$e\left(\frac{32}{63}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{38}{63}\right)$	$e\left(\frac{58}{63}\right)$
$\chi_{6223}(1963,\cdot)$	$1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{31}{63}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{52}{63}\right)$	$1$	$e\left(\frac{62}{63}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{50}{63}\right)$	$e\left(\frac{10}{63}\right)$
$\chi_{6223}(2182,\cdot)$	$1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{23}{63}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{2}{63}\right)$	$1$	$e\left(\frac{46}{63}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{31}{63}\right)$	$e\left(\frac{44}{63}\right)$
$\chi_{6223}(2341,\cdot)$	$1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{43}{63}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{1}{63}\right)$	$1$	$e\left(\frac{23}{63}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{47}{63}\right)$	$e\left(\frac{22}{63}\right)$
$\chi_{6223}(2593,\cdot)$	$1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{37}{63}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{58}{63}\right)$	$1$	$e\left(\frac{11}{63}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{17}{63}\right)$	$e\left(\frac{16}{63}\right)$
$\chi_{6223}(2637,\cdot)$	$1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{20}{63}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{62}{63}\right)$	$1$	$e\left(\frac{40}{63}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{16}{63}\right)$	$e\left(\frac{41}{63}\right)$
$\chi_{6223}(2712,\cdot)$	$1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{19}{63}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{40}{63}\right)$	$1$	$e\left(\frac{38}{63}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{53}{63}\right)$	$e\left(\frac{61}{63}\right)$
$\chi_{6223}(3232,\cdot)$	$1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{50}{63}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{29}{63}\right)$	$1$	$e\left(\frac{37}{63}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{40}{63}\right)$	$e\left(\frac{8}{63}\right)$
$\chi_{6223}(3358,\cdot)$	$1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{63}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{44}{63}\right)$	$1$	$e\left(\frac{4}{63}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{52}{63}\right)$	$e\left(\frac{23}{63}\right)$
$\chi_{6223}(3414,\cdot)$	$1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{11}{63}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{53}{63}\right)$	$1$	$e\left(\frac{22}{63}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{34}{63}\right)$	$e\left(\frac{32}{63}\right)$
$\chi_{6223}(3435,\cdot)$	$1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{17}{63}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{59}{63}\right)$	$1$	$e\left(\frac{34}{63}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{1}{63}\right)$	$e\left(\frac{38}{63}\right)$
$\chi_{6223}(3538,\cdot)$	$1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{25}{63}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{46}{63}\right)$	$1$	$e\left(\frac{50}{63}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{20}{63}\right)$	$e\left(\frac{4}{63}\right)$
$\chi_{6223}(3545,\cdot)$	$1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{40}{63}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{61}{63}\right)$	$1$	$e\left(\frac{17}{63}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{32}{63}\right)$	$e\left(\frac{19}{63}\right)$
$\chi_{6223}(3895,\cdot)$	$1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{55}{63}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{13}{63}\right)$	$1$	$e\left(\frac{47}{63}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{44}{63}\right)$	$e\left(\frac{34}{63}\right)$
$\chi_{6223}(4156,\cdot)$	$1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{41}{63}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{20}{63}\right)$	$1$	$e\left(\frac{19}{63}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{58}{63}\right)$	$e\left(\frac{62}{63}\right)$
$\chi_{6223}(4541,\cdot)$	$1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{53}{63}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{32}{63}\right)$	$1$	$e\left(\frac{43}{63}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{55}{63}\right)$	$e\left(\frac{11}{63}\right)$
$\chi_{6223}(4658,\cdot)$	$1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{10}{63}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{31}{63}\right)$	$1$	$e\left(\frac{20}{63}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{8}{63}\right)$	$e\left(\frac{52}{63}\right)$
$\chi_{6223}(4702,\cdot)$	$1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{8}{63}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{50}{63}\right)$	$1$	$e\left(\frac{16}{63}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{19}{63}\right)$	$e\left(\frac{29}{63}\right)$
$\chi_{6223}(4742,\cdot)$	$1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{63}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{22}{63}\right)$	$1$	$e\left(\frac{2}{63}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{26}{63}\right)$	$e\left(\frac{43}{63}\right)$
$\chi_{6223}(4777,\cdot)$	$1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{13}{63}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{34}{63}\right)$	$1$	$e\left(\frac{26}{63}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{23}{63}\right)$	$e\left(\frac{55}{63}\right)$
$\chi_{6223}(4891,\cdot)$	$1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{62}{63}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{41}{63}\right)$	$1$	$e\left(\frac{61}{63}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{37}{63}\right)$	$e\left(\frac{20}{63}\right)$
$\chi_{6223}(5554,\cdot)$	$1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{61}{63}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{19}{63}\right)$	$1$	$e\left(\frac{59}{63}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{11}{63}\right)$	$e\left(\frac{40}{63}\right)$

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	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(8\)	\(9\)	\(10\)	\(11\)	\(12\)
\(\chi_{6223}(12,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{26}{63}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{5}{63}\right)\)	\(1\)	\(e\left(\frac{52}{63}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{46}{63}\right)\)	\(e\left(\frac{47}{63}\right)\)
\(\chi_{6223}(194,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{29}{63}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{8}{63}\right)\)	\(1\)	\(e\left(\frac{58}{63}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{61}{63}\right)\)	\(e\left(\frac{50}{63}\right)\)
\(\chi_{6223}(283,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{22}{63}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{43}{63}\right)\)	\(1\)	\(e\left(\frac{44}{63}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{5}{63}\right)\)	\(e\left(\frac{1}{63}\right)\)
\(\chi_{6223}(355,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{63}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{47}{63}\right)\)	\(1\)	\(e\left(\frac{10}{63}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{4}{63}\right)\)	\(e\left(\frac{26}{63}\right)\)
\(\chi_{6223}(495,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{59}{63}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{38}{63}\right)\)	\(1\)	\(e\left(\frac{55}{63}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{22}{63}\right)\)	\(e\left(\frac{17}{63}\right)\)
\(\chi_{6223}(642,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{38}{63}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{17}{63}\right)\)	\(1\)	\(e\left(\frac{13}{63}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{43}{63}\right)\)	\(e\left(\frac{59}{63}\right)\)
\(\chi_{6223}(649,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{47}{63}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{26}{63}\right)\)	\(1\)	\(e\left(\frac{31}{63}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{25}{63}\right)\)	\(e\left(\frac{5}{63}\right)\)
\(\chi_{6223}(810,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{44}{63}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{23}{63}\right)\)	\(1\)	\(e\left(\frac{25}{63}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{10}{63}\right)\)	\(e\left(\frac{2}{63}\right)\)
\(\chi_{6223}(1062,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{32}{63}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{11}{63}\right)\)	\(1\)	\(e\left(\frac{1}{63}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{13}{63}\right)\)	\(e\left(\frac{53}{63}\right)\)
\(\chi_{6223}(1515,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{16}{63}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{37}{63}\right)\)	\(1\)	\(e\left(\frac{32}{63}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{38}{63}\right)\)	\(e\left(\frac{58}{63}\right)\)
\(\chi_{6223}(1963,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{31}{63}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{52}{63}\right)\)	\(1\)	\(e\left(\frac{62}{63}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{50}{63}\right)\)	\(e\left(\frac{10}{63}\right)\)
\(\chi_{6223}(2182,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{23}{63}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{2}{63}\right)\)	\(1\)	\(e\left(\frac{46}{63}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{31}{63}\right)\)	\(e\left(\frac{44}{63}\right)\)
\(\chi_{6223}(2341,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{43}{63}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{1}{63}\right)\)	\(1\)	\(e\left(\frac{23}{63}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{47}{63}\right)\)	\(e\left(\frac{22}{63}\right)\)
\(\chi_{6223}(2593,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{37}{63}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{58}{63}\right)\)	\(1\)	\(e\left(\frac{11}{63}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{17}{63}\right)\)	\(e\left(\frac{16}{63}\right)\)
\(\chi_{6223}(2637,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{20}{63}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{62}{63}\right)\)	\(1\)	\(e\left(\frac{40}{63}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{16}{63}\right)\)	\(e\left(\frac{41}{63}\right)\)
\(\chi_{6223}(2712,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{19}{63}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{40}{63}\right)\)	\(1\)	\(e\left(\frac{38}{63}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{53}{63}\right)\)	\(e\left(\frac{61}{63}\right)\)
\(\chi_{6223}(3232,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{50}{63}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{29}{63}\right)\)	\(1\)	\(e\left(\frac{37}{63}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{40}{63}\right)\)	\(e\left(\frac{8}{63}\right)\)
\(\chi_{6223}(3358,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{63}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{44}{63}\right)\)	\(1\)	\(e\left(\frac{4}{63}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{52}{63}\right)\)	\(e\left(\frac{23}{63}\right)\)
\(\chi_{6223}(3414,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{11}{63}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{53}{63}\right)\)	\(1\)	\(e\left(\frac{22}{63}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{34}{63}\right)\)	\(e\left(\frac{32}{63}\right)\)
\(\chi_{6223}(3435,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{17}{63}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{59}{63}\right)\)	\(1\)	\(e\left(\frac{34}{63}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{1}{63}\right)\)	\(e\left(\frac{38}{63}\right)\)
\(\chi_{6223}(3538,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{25}{63}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{46}{63}\right)\)	\(1\)	\(e\left(\frac{50}{63}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{20}{63}\right)\)	\(e\left(\frac{4}{63}\right)\)
\(\chi_{6223}(3545,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{40}{63}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{61}{63}\right)\)	\(1\)	\(e\left(\frac{17}{63}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{32}{63}\right)\)	\(e\left(\frac{19}{63}\right)\)
\(\chi_{6223}(3895,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{55}{63}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{13}{63}\right)\)	\(1\)	\(e\left(\frac{47}{63}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{44}{63}\right)\)	\(e\left(\frac{34}{63}\right)\)
\(\chi_{6223}(4156,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{41}{63}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{20}{63}\right)\)	\(1\)	\(e\left(\frac{19}{63}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{58}{63}\right)\)	\(e\left(\frac{62}{63}\right)\)
\(\chi_{6223}(4541,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{53}{63}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{32}{63}\right)\)	\(1\)	\(e\left(\frac{43}{63}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{55}{63}\right)\)	\(e\left(\frac{11}{63}\right)\)
\(\chi_{6223}(4658,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{10}{63}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{31}{63}\right)\)	\(1\)	\(e\left(\frac{20}{63}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{8}{63}\right)\)	\(e\left(\frac{52}{63}\right)\)
\(\chi_{6223}(4702,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{8}{63}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{50}{63}\right)\)	\(1\)	\(e\left(\frac{16}{63}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{19}{63}\right)\)	\(e\left(\frac{29}{63}\right)\)
\(\chi_{6223}(4742,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{63}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{22}{63}\right)\)	\(1\)	\(e\left(\frac{2}{63}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{26}{63}\right)\)	\(e\left(\frac{43}{63}\right)\)
\(\chi_{6223}(4777,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{13}{63}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{34}{63}\right)\)	\(1\)	\(e\left(\frac{26}{63}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{23}{63}\right)\)	\(e\left(\frac{55}{63}\right)\)
\(\chi_{6223}(4891,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{62}{63}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{41}{63}\right)\)	\(1\)	\(e\left(\frac{61}{63}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{37}{63}\right)\)	\(e\left(\frac{20}{63}\right)\)
\(\chi_{6223}(5554,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{61}{63}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{19}{63}\right)\)	\(1\)	\(e\left(\frac{59}{63}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{11}{63}\right)\)	\(e\left(\frac{40}{63}\right)\)

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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.ii
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)