LMFDB - Dirichlet character orbit 6223.im

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(6223, base_ring=CyclotomicField(126)) M = H._module chi = DirichletCharacter(H, M([114,121])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(23,6223)) 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	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$8$	$9$	$10$	$11$	$12$
$\chi_{6223}(23,\cdot)$	$-1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{109}{126}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{67}{126}\right)$	$1$	$e\left(\frac{46}{63}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{31}{63}\right)$	$e\left(\frac{25}{126}\right)$
$\chi_{6223}(39,\cdot)$	$-1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{71}{126}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{113}{126}\right)$	$1$	$e\left(\frac{8}{63}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{41}{63}\right)$	$e\left(\frac{29}{126}\right)$
$\chi_{6223}(53,\cdot)$	$-1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{126}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{53}{126}\right)$	$1$	$e\left(\frac{11}{63}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{17}{63}\right)$	$e\left(\frac{95}{126}\right)$
$\chi_{6223}(340,\cdot)$	$-1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{83}{126}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{125}{126}\right)$	$1$	$e\left(\frac{20}{63}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{8}{63}\right)$	$e\left(\frac{41}{126}\right)$
$\chi_{6223}(387,\cdot)$	$-1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{97}{126}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{55}{126}\right)$	$1$	$e\left(\frac{34}{63}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{1}{63}\right)$	$e\left(\frac{13}{126}\right)$
$\chi_{6223}(466,\cdot)$	$-1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{47}{126}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{89}{126}\right)$	$1$	$e\left(\frac{47}{63}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{44}{63}\right)$	$e\left(\frac{5}{126}\right)$
$\chi_{6223}(604,\cdot)$	$-1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{43}{126}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{1}{126}\right)$	$1$	$e\left(\frac{43}{63}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{55}{63}\right)$	$e\left(\frac{85}{126}\right)$
$\chi_{6223}(1061,\cdot)$	$-1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{101}{126}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{17}{126}\right)$	$1$	$e\left(\frac{38}{63}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{53}{63}\right)$	$e\left(\frac{59}{126}\right)$
$\chi_{6223}(1199,\cdot)$	$-1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{67}{126}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{25}{126}\right)$	$1$	$e\left(\frac{4}{63}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{52}{63}\right)$	$e\left(\frac{109}{126}\right)$
$\chi_{6223}(1348,\cdot)$	$-1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{89}{126}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{5}{126}\right)$	$1$	$e\left(\frac{26}{63}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{23}{63}\right)$	$e\left(\frac{47}{126}\right)$
$\chi_{6223}(1409,\cdot)$	$-1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{115}{126}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{73}{126}\right)$	$1$	$e\left(\frac{52}{63}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{46}{63}\right)$	$e\left(\frac{31}{126}\right)$
$\chi_{6223}(1579,\cdot)$	$-1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{23}{126}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{65}{126}\right)$	$1$	$e\left(\frac{23}{63}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{47}{63}\right)$	$e\left(\frac{107}{126}\right)$
$\chi_{6223}(1752,\cdot)$	$-1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{73}{126}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{31}{126}\right)$	$1$	$e\left(\frac{10}{63}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{4}{63}\right)$	$e\left(\frac{115}{126}\right)$
$\chi_{6223}(1761,\cdot)$	$-1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{41}{126}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{83}{126}\right)$	$1$	$e\left(\frac{41}{63}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{29}{63}\right)$	$e\left(\frac{125}{126}\right)$
$\chi_{6223}(1894,\cdot)$	$-1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{17}{126}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{59}{126}\right)$	$1$	$e\left(\frac{17}{63}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{32}{63}\right)$	$e\left(\frac{101}{126}\right)$
$\chi_{6223}(1962,\cdot)$	$-1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{37}{126}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{121}{126}\right)$	$1$	$e\left(\frac{37}{63}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{40}{63}\right)$	$e\left(\frac{79}{126}\right)$
$\chi_{6223}(2046,\cdot)$	$-1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{31}{126}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{115}{126}\right)$	$1$	$e\left(\frac{31}{63}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{25}{63}\right)$	$e\left(\frac{73}{126}\right)$
$\chi_{6223}(2377,\cdot)$	$-1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{126}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{47}{126}\right)$	$1$	$e\left(\frac{5}{63}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{2}{63}\right)$	$e\left(\frac{89}{126}\right)$
$\chi_{6223}(3145,\cdot)$	$-1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{103}{126}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{61}{126}\right)$	$1$	$e\left(\frac{40}{63}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{16}{63}\right)$	$e\left(\frac{19}{126}\right)$
$\chi_{6223}(3348,\cdot)$	$-1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{126}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{85}{126}\right)$	$1$	$e\left(\frac{1}{63}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{13}{63}\right)$	$e\left(\frac{43}{126}\right)$
$\chi_{6223}(3385,\cdot)$	$-1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{53}{126}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{95}{126}\right)$	$1$	$e\left(\frac{53}{63}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{59}{63}\right)$	$e\left(\frac{11}{126}\right)$
$\chi_{6223}(3432,\cdot)$	$-1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{79}{126}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{37}{126}\right)$	$1$	$e\left(\frac{16}{63}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{19}{63}\right)$	$e\left(\frac{121}{126}\right)$
$\chi_{6223}(3665,\cdot)$	$-1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{113}{126}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{29}{126}\right)$	$1$	$e\left(\frac{50}{63}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{20}{63}\right)$	$e\left(\frac{71}{126}\right)$
$\chi_{6223}(3670,\cdot)$	$-1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{55}{126}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{13}{126}\right)$	$1$	$e\left(\frac{55}{63}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{22}{63}\right)$	$e\left(\frac{97}{126}\right)$
$\chi_{6223}(3817,\cdot)$	$-1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{13}{126}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{97}{126}\right)$	$1$	$e\left(\frac{13}{63}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{43}{63}\right)$	$e\left(\frac{55}{126}\right)$
$\chi_{6223}(3868,\cdot)$	$-1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{125}{126}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{41}{126}\right)$	$1$	$e\left(\frac{62}{63}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{50}{63}\right)$	$e\left(\frac{83}{126}\right)$
$\chi_{6223}(3903,\cdot)$	$-1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{59}{126}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{101}{126}\right)$	$1$	$e\left(\frac{59}{63}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{11}{63}\right)$	$e\left(\frac{17}{126}\right)$
$\chi_{6223}(3980,\cdot)$	$-1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{65}{126}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{107}{126}\right)$	$1$	$e\left(\frac{2}{63}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{26}{63}\right)$	$e\left(\frac{23}{126}\right)$
$\chi_{6223}(4664,\cdot)$	$-1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{19}{126}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{103}{126}\right)$	$1$	$e\left(\frac{19}{63}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{58}{63}\right)$	$e\left(\frac{61}{126}\right)$
$\chi_{6223}(4874,\cdot)$	$-1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{25}{126}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{109}{126}\right)$	$1$	$e\left(\frac{25}{63}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{10}{63}\right)$	$e\left(\frac{67}{126}\right)$
$\chi_{6223}(5147,\cdot)$	$-1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{121}{126}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{79}{126}\right)$	$1$	$e\left(\frac{58}{63}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{61}{63}\right)$	$e\left(\frac{37}{126}\right)$

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	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(8\)	\(9\)	\(10\)	\(11\)	\(12\)
\(\chi_{6223}(23,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{109}{126}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{67}{126}\right)\)	\(1\)	\(e\left(\frac{46}{63}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{31}{63}\right)\)	\(e\left(\frac{25}{126}\right)\)
\(\chi_{6223}(39,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{71}{126}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{113}{126}\right)\)	\(1\)	\(e\left(\frac{8}{63}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{41}{63}\right)\)	\(e\left(\frac{29}{126}\right)\)
\(\chi_{6223}(53,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{126}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{53}{126}\right)\)	\(1\)	\(e\left(\frac{11}{63}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{17}{63}\right)\)	\(e\left(\frac{95}{126}\right)\)
\(\chi_{6223}(340,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{83}{126}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{125}{126}\right)\)	\(1\)	\(e\left(\frac{20}{63}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{8}{63}\right)\)	\(e\left(\frac{41}{126}\right)\)
\(\chi_{6223}(387,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{97}{126}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{55}{126}\right)\)	\(1\)	\(e\left(\frac{34}{63}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{1}{63}\right)\)	\(e\left(\frac{13}{126}\right)\)
\(\chi_{6223}(466,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{47}{126}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{89}{126}\right)\)	\(1\)	\(e\left(\frac{47}{63}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{44}{63}\right)\)	\(e\left(\frac{5}{126}\right)\)
\(\chi_{6223}(604,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{43}{126}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{1}{126}\right)\)	\(1\)	\(e\left(\frac{43}{63}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{55}{63}\right)\)	\(e\left(\frac{85}{126}\right)\)
\(\chi_{6223}(1061,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{101}{126}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{17}{126}\right)\)	\(1\)	\(e\left(\frac{38}{63}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{53}{63}\right)\)	\(e\left(\frac{59}{126}\right)\)
\(\chi_{6223}(1199,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{67}{126}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{25}{126}\right)\)	\(1\)	\(e\left(\frac{4}{63}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{52}{63}\right)\)	\(e\left(\frac{109}{126}\right)\)
\(\chi_{6223}(1348,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{89}{126}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{5}{126}\right)\)	\(1\)	\(e\left(\frac{26}{63}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{23}{63}\right)\)	\(e\left(\frac{47}{126}\right)\)
\(\chi_{6223}(1409,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{115}{126}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{73}{126}\right)\)	\(1\)	\(e\left(\frac{52}{63}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{46}{63}\right)\)	\(e\left(\frac{31}{126}\right)\)
\(\chi_{6223}(1579,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{23}{126}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{65}{126}\right)\)	\(1\)	\(e\left(\frac{23}{63}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{47}{63}\right)\)	\(e\left(\frac{107}{126}\right)\)
\(\chi_{6223}(1752,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{73}{126}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{31}{126}\right)\)	\(1\)	\(e\left(\frac{10}{63}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{4}{63}\right)\)	\(e\left(\frac{115}{126}\right)\)
\(\chi_{6223}(1761,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{41}{126}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{83}{126}\right)\)	\(1\)	\(e\left(\frac{41}{63}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{29}{63}\right)\)	\(e\left(\frac{125}{126}\right)\)
\(\chi_{6223}(1894,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{17}{126}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{59}{126}\right)\)	\(1\)	\(e\left(\frac{17}{63}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{32}{63}\right)\)	\(e\left(\frac{101}{126}\right)\)
\(\chi_{6223}(1962,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{37}{126}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{121}{126}\right)\)	\(1\)	\(e\left(\frac{37}{63}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{40}{63}\right)\)	\(e\left(\frac{79}{126}\right)\)
\(\chi_{6223}(2046,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{31}{126}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{115}{126}\right)\)	\(1\)	\(e\left(\frac{31}{63}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{25}{63}\right)\)	\(e\left(\frac{73}{126}\right)\)
\(\chi_{6223}(2377,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{126}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{47}{126}\right)\)	\(1\)	\(e\left(\frac{5}{63}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{2}{63}\right)\)	\(e\left(\frac{89}{126}\right)\)
\(\chi_{6223}(3145,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{103}{126}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{61}{126}\right)\)	\(1\)	\(e\left(\frac{40}{63}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{16}{63}\right)\)	\(e\left(\frac{19}{126}\right)\)
\(\chi_{6223}(3348,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{126}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{85}{126}\right)\)	\(1\)	\(e\left(\frac{1}{63}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{13}{63}\right)\)	\(e\left(\frac{43}{126}\right)\)
\(\chi_{6223}(3385,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{53}{126}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{95}{126}\right)\)	\(1\)	\(e\left(\frac{53}{63}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{59}{63}\right)\)	\(e\left(\frac{11}{126}\right)\)
\(\chi_{6223}(3432,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{79}{126}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{37}{126}\right)\)	\(1\)	\(e\left(\frac{16}{63}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{19}{63}\right)\)	\(e\left(\frac{121}{126}\right)\)
\(\chi_{6223}(3665,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{113}{126}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{29}{126}\right)\)	\(1\)	\(e\left(\frac{50}{63}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{20}{63}\right)\)	\(e\left(\frac{71}{126}\right)\)
\(\chi_{6223}(3670,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{55}{126}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{13}{126}\right)\)	\(1\)	\(e\left(\frac{55}{63}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{22}{63}\right)\)	\(e\left(\frac{97}{126}\right)\)
\(\chi_{6223}(3817,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{13}{126}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{97}{126}\right)\)	\(1\)	\(e\left(\frac{13}{63}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{43}{63}\right)\)	\(e\left(\frac{55}{126}\right)\)
\(\chi_{6223}(3868,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{125}{126}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{41}{126}\right)\)	\(1\)	\(e\left(\frac{62}{63}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{50}{63}\right)\)	\(e\left(\frac{83}{126}\right)\)
\(\chi_{6223}(3903,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{59}{126}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{101}{126}\right)\)	\(1\)	\(e\left(\frac{59}{63}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{11}{63}\right)\)	\(e\left(\frac{17}{126}\right)\)
\(\chi_{6223}(3980,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{65}{126}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{107}{126}\right)\)	\(1\)	\(e\left(\frac{2}{63}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{26}{63}\right)\)	\(e\left(\frac{23}{126}\right)\)
\(\chi_{6223}(4664,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{19}{126}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{103}{126}\right)\)	\(1\)	\(e\left(\frac{19}{63}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{58}{63}\right)\)	\(e\left(\frac{61}{126}\right)\)
\(\chi_{6223}(4874,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{25}{126}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{109}{126}\right)\)	\(1\)	\(e\left(\frac{25}{63}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{10}{63}\right)\)	\(e\left(\frac{67}{126}\right)\)
\(\chi_{6223}(5147,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{121}{126}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{79}{126}\right)\)	\(1\)	\(e\left(\frac{58}{63}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{61}{63}\right)\)	\(e\left(\frac{37}{126}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Basic properties

Related number fields

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.im
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)