LMFDB - Dirichlet character orbit 4563.dm

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(4563, base_ring=CyclotomicField(468)) M = H._module chi = DirichletCharacter(H, M([26,3])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(2,4563)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$4563$
Conductor:	$4563$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$468$	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:	$\Q(\zeta_{468})$
Fixed field:	Number field defined by a degree 468 polynomial (not computed)

First 31 of 144 characters in Galois orbit

Character	$-1$	$1$	$2$	$4$	$5$	$7$	$8$	$10$	$11$	$14$	$16$	$17$
$\chi_{4563}(2,\cdot)$	$1$	$1$	$e\left(\frac{29}{468}\right)$	$e\left(\frac{29}{234}\right)$	$e\left(\frac{157}{468}\right)$	$e\left(\frac{269}{468}\right)$	$e\left(\frac{29}{156}\right)$	$e\left(\frac{31}{78}\right)$	$e\left(\frac{179}{468}\right)$	$e\left(\frac{149}{234}\right)$	$e\left(\frac{29}{117}\right)$	$e\left(\frac{10}{13}\right)$
$\chi_{4563}(11,\cdot)$	$1$	$1$	$e\left(\frac{179}{468}\right)$	$e\left(\frac{179}{234}\right)$	$e\left(\frac{259}{468}\right)$	$e\left(\frac{95}{468}\right)$	$e\left(\frac{23}{156}\right)$	$e\left(\frac{73}{78}\right)$	$e\left(\frac{185}{468}\right)$	$e\left(\frac{137}{234}\right)$	$e\left(\frac{62}{117}\right)$	$e\left(\frac{3}{13}\right)$
$\chi_{4563}(32,\cdot)$	$1$	$1$	$e\left(\frac{145}{468}\right)$	$e\left(\frac{145}{234}\right)$	$e\left(\frac{317}{468}\right)$	$e\left(\frac{409}{468}\right)$	$e\left(\frac{145}{156}\right)$	$e\left(\frac{77}{78}\right)$	$e\left(\frac{427}{468}\right)$	$e\left(\frac{43}{234}\right)$	$e\left(\frac{28}{117}\right)$	$e\left(\frac{11}{13}\right)$
$\chi_{4563}(59,\cdot)$	$1$	$1$	$e\left(\frac{235}{468}\right)$	$e\left(\frac{1}{234}\right)$	$e\left(\frac{191}{468}\right)$	$e\left(\frac{211}{468}\right)$	$e\left(\frac{79}{156}\right)$	$e\left(\frac{71}{78}\right)$	$e\left(\frac{337}{468}\right)$	$e\left(\frac{223}{234}\right)$	$e\left(\frac{1}{117}\right)$	$e\left(\frac{12}{13}\right)$
$\chi_{4563}(119,\cdot)$	$1$	$1$	$e\left(\frac{161}{468}\right)$	$e\left(\frac{161}{234}\right)$	$e\left(\frac{97}{468}\right)$	$e\left(\frac{41}{468}\right)$	$e\left(\frac{5}{156}\right)$	$e\left(\frac{43}{78}\right)$	$e\left(\frac{203}{468}\right)$	$e\left(\frac{101}{234}\right)$	$e\left(\frac{44}{117}\right)$	$e\left(\frac{8}{13}\right)$
$\chi_{4563}(128,\cdot)$	$1$	$1$	$e\left(\frac{203}{468}\right)$	$e\left(\frac{203}{234}\right)$	$e\left(\frac{163}{468}\right)$	$e\left(\frac{11}{468}\right)$	$e\left(\frac{47}{156}\right)$	$e\left(\frac{61}{78}\right)$	$e\left(\frac{317}{468}\right)$	$e\left(\frac{107}{234}\right)$	$e\left(\frac{86}{117}\right)$	$e\left(\frac{5}{13}\right)$
$\chi_{4563}(149,\cdot)$	$1$	$1$	$e\left(\frac{241}{468}\right)$	$e\left(\frac{7}{234}\right)$	$e\left(\frac{401}{468}\right)$	$e\left(\frac{73}{468}\right)$	$e\left(\frac{85}{156}\right)$	$e\left(\frac{29}{78}\right)$	$e\left(\frac{19}{468}\right)$	$e\left(\frac{157}{234}\right)$	$e\left(\frac{7}{117}\right)$	$e\left(\frac{6}{13}\right)$
$\chi_{4563}(176,\cdot)$	$1$	$1$	$e\left(\frac{295}{468}\right)$	$e\left(\frac{61}{234}\right)$	$e\left(\frac{419}{468}\right)$	$e\left(\frac{235}{468}\right)$	$e\left(\frac{139}{156}\right)$	$e\left(\frac{41}{78}\right)$	$e\left(\frac{433}{468}\right)$	$e\left(\frac{31}{234}\right)$	$e\left(\frac{61}{117}\right)$	$e\left(\frac{4}{13}\right)$
$\chi_{4563}(236,\cdot)$	$1$	$1$	$e\left(\frac{293}{468}\right)$	$e\left(\frac{59}{234}\right)$	$e\left(\frac{37}{468}\right)$	$e\left(\frac{281}{468}\right)$	$e\left(\frac{137}{156}\right)$	$e\left(\frac{55}{78}\right)$	$e\left(\frac{227}{468}\right)$	$e\left(\frac{53}{234}\right)$	$e\left(\frac{59}{117}\right)$	$e\left(\frac{6}{13}\right)$
$\chi_{4563}(245,\cdot)$	$1$	$1$	$e\left(\frac{227}{468}\right)$	$e\left(\frac{227}{234}\right)$	$e\left(\frac{67}{468}\right)$	$e\left(\frac{395}{468}\right)$	$e\left(\frac{71}{156}\right)$	$e\left(\frac{49}{78}\right)$	$e\left(\frac{449}{468}\right)$	$e\left(\frac{77}{234}\right)$	$e\left(\frac{110}{117}\right)$	$e\left(\frac{7}{13}\right)$
$\chi_{4563}(266,\cdot)$	$1$	$1$	$e\left(\frac{337}{468}\right)$	$e\left(\frac{103}{234}\right)$	$e\left(\frac{17}{468}\right)$	$e\left(\frac{205}{468}\right)$	$e\left(\frac{25}{156}\right)$	$e\left(\frac{59}{78}\right)$	$e\left(\frac{79}{468}\right)$	$e\left(\frac{37}{234}\right)$	$e\left(\frac{103}{117}\right)$	$e\left(\frac{1}{13}\right)$
$\chi_{4563}(293,\cdot)$	$1$	$1$	$e\left(\frac{355}{468}\right)$	$e\left(\frac{121}{234}\right)$	$e\left(\frac{179}{468}\right)$	$e\left(\frac{259}{468}\right)$	$e\left(\frac{43}{156}\right)$	$e\left(\frac{11}{78}\right)$	$e\left(\frac{61}{468}\right)$	$e\left(\frac{73}{234}\right)$	$e\left(\frac{4}{117}\right)$	$e\left(\frac{9}{13}\right)$
$\chi_{4563}(353,\cdot)$	$1$	$1$	$e\left(\frac{425}{468}\right)$	$e\left(\frac{191}{234}\right)$	$e\left(\frac{445}{468}\right)$	$e\left(\frac{53}{468}\right)$	$e\left(\frac{113}{156}\right)$	$e\left(\frac{67}{78}\right)$	$e\left(\frac{251}{468}\right)$	$e\left(\frac{5}{234}\right)$	$e\left(\frac{74}{117}\right)$	$e\left(\frac{4}{13}\right)$
$\chi_{4563}(362,\cdot)$	$1$	$1$	$e\left(\frac{251}{468}\right)$	$e\left(\frac{17}{234}\right)$	$e\left(\frac{439}{468}\right)$	$e\left(\frac{311}{468}\right)$	$e\left(\frac{95}{156}\right)$	$e\left(\frac{37}{78}\right)$	$e\left(\frac{113}{468}\right)$	$e\left(\frac{47}{234}\right)$	$e\left(\frac{17}{117}\right)$	$e\left(\frac{9}{13}\right)$
$\chi_{4563}(383,\cdot)$	$1$	$1$	$e\left(\frac{433}{468}\right)$	$e\left(\frac{199}{234}\right)$	$e\left(\frac{101}{468}\right)$	$e\left(\frac{337}{468}\right)$	$e\left(\frac{121}{156}\right)$	$e\left(\frac{11}{78}\right)$	$e\left(\frac{139}{468}\right)$	$e\left(\frac{151}{234}\right)$	$e\left(\frac{82}{117}\right)$	$e\left(\frac{9}{13}\right)$
$\chi_{4563}(410,\cdot)$	$1$	$1$	$e\left(\frac{415}{468}\right)$	$e\left(\frac{181}{234}\right)$	$e\left(\frac{407}{468}\right)$	$e\left(\frac{283}{468}\right)$	$e\left(\frac{103}{156}\right)$	$e\left(\frac{59}{78}\right)$	$e\left(\frac{157}{468}\right)$	$e\left(\frac{115}{234}\right)$	$e\left(\frac{64}{117}\right)$	$e\left(\frac{1}{13}\right)$
$\chi_{4563}(470,\cdot)$	$1$	$1$	$e\left(\frac{89}{468}\right)$	$e\left(\frac{89}{234}\right)$	$e\left(\frac{385}{468}\right)$	$e\left(\frac{293}{468}\right)$	$e\left(\frac{89}{156}\right)$	$e\left(\frac{1}{78}\right)$	$e\left(\frac{275}{468}\right)$	$e\left(\frac{191}{234}\right)$	$e\left(\frac{89}{117}\right)$	$e\left(\frac{2}{13}\right)$
$\chi_{4563}(479,\cdot)$	$1$	$1$	$e\left(\frac{275}{468}\right)$	$e\left(\frac{41}{234}\right)$	$e\left(\frac{343}{468}\right)$	$e\left(\frac{227}{468}\right)$	$e\left(\frac{119}{156}\right)$	$e\left(\frac{25}{78}\right)$	$e\left(\frac{245}{468}\right)$	$e\left(\frac{17}{234}\right)$	$e\left(\frac{41}{117}\right)$	$e\left(\frac{11}{13}\right)$
$\chi_{4563}(500,\cdot)$	$1$	$1$	$e\left(\frac{61}{468}\right)$	$e\left(\frac{61}{234}\right)$	$e\left(\frac{185}{468}\right)$	$e\left(\frac{1}{468}\right)$	$e\left(\frac{61}{156}\right)$	$e\left(\frac{41}{78}\right)$	$e\left(\frac{199}{468}\right)$	$e\left(\frac{31}{234}\right)$	$e\left(\frac{61}{117}\right)$	$e\left(\frac{4}{13}\right)$
$\chi_{4563}(527,\cdot)$	$1$	$1$	$e\left(\frac{7}{468}\right)$	$e\left(\frac{7}{234}\right)$	$e\left(\frac{167}{468}\right)$	$e\left(\frac{307}{468}\right)$	$e\left(\frac{7}{156}\right)$	$e\left(\frac{29}{78}\right)$	$e\left(\frac{253}{468}\right)$	$e\left(\frac{157}{234}\right)$	$e\left(\frac{7}{117}\right)$	$e\left(\frac{6}{13}\right)$
$\chi_{4563}(617,\cdot)$	$1$	$1$	$e\left(\frac{157}{468}\right)$	$e\left(\frac{157}{234}\right)$	$e\left(\frac{269}{468}\right)$	$e\left(\frac{133}{468}\right)$	$e\left(\frac{1}{156}\right)$	$e\left(\frac{71}{78}\right)$	$e\left(\frac{259}{468}\right)$	$e\left(\frac{145}{234}\right)$	$e\left(\frac{40}{117}\right)$	$e\left(\frac{12}{13}\right)$
$\chi_{4563}(644,\cdot)$	$1$	$1$	$e\left(\frac{67}{468}\right)$	$e\left(\frac{67}{234}\right)$	$e\left(\frac{395}{468}\right)$	$e\left(\frac{331}{468}\right)$	$e\left(\frac{67}{156}\right)$	$e\left(\frac{77}{78}\right)$	$e\left(\frac{349}{468}\right)$	$e\left(\frac{199}{234}\right)$	$e\left(\frac{67}{117}\right)$	$e\left(\frac{11}{13}\right)$
$\chi_{4563}(704,\cdot)$	$1$	$1$	$e\left(\frac{353}{468}\right)$	$e\left(\frac{119}{234}\right)$	$e\left(\frac{265}{468}\right)$	$e\left(\frac{305}{468}\right)$	$e\left(\frac{41}{156}\right)$	$e\left(\frac{25}{78}\right)$	$e\left(\frac{323}{468}\right)$	$e\left(\frac{95}{234}\right)$	$e\left(\frac{2}{117}\right)$	$e\left(\frac{11}{13}\right)$
$\chi_{4563}(713,\cdot)$	$1$	$1$	$e\left(\frac{323}{468}\right)$	$e\left(\frac{89}{234}\right)$	$e\left(\frac{151}{468}\right)$	$e\left(\frac{59}{468}\right)$	$e\left(\frac{11}{156}\right)$	$e\left(\frac{1}{78}\right)$	$e\left(\frac{41}{468}\right)$	$e\left(\frac{191}{234}\right)$	$e\left(\frac{89}{117}\right)$	$e\left(\frac{2}{13}\right)$
$\chi_{4563}(734,\cdot)$	$1$	$1$	$e\left(\frac{253}{468}\right)$	$e\left(\frac{19}{234}\right)$	$e\left(\frac{353}{468}\right)$	$e\left(\frac{265}{468}\right)$	$e\left(\frac{97}{156}\right)$	$e\left(\frac{23}{78}\right)$	$e\left(\frac{319}{468}\right)$	$e\left(\frac{25}{234}\right)$	$e\left(\frac{19}{117}\right)$	$e\left(\frac{7}{13}\right)$
$\chi_{4563}(761,\cdot)$	$1$	$1$	$e\left(\frac{127}{468}\right)$	$e\left(\frac{127}{234}\right)$	$e\left(\frac{155}{468}\right)$	$e\left(\frac{355}{468}\right)$	$e\left(\frac{127}{156}\right)$	$e\left(\frac{47}{78}\right)$	$e\left(\frac{445}{468}\right)$	$e\left(\frac{7}{234}\right)$	$e\left(\frac{10}{117}\right)$	$e\left(\frac{3}{13}\right)$
$\chi_{4563}(821,\cdot)$	$1$	$1$	$e\left(\frac{17}{468}\right)$	$e\left(\frac{17}{234}\right)$	$e\left(\frac{205}{468}\right)$	$e\left(\frac{77}{468}\right)$	$e\left(\frac{17}{156}\right)$	$e\left(\frac{37}{78}\right)$	$e\left(\frac{347}{468}\right)$	$e\left(\frac{47}{234}\right)$	$e\left(\frac{17}{117}\right)$	$e\left(\frac{9}{13}\right)$
$\chi_{4563}(830,\cdot)$	$1$	$1$	$e\left(\frac{347}{468}\right)$	$e\left(\frac{113}{234}\right)$	$e\left(\frac{55}{468}\right)$	$e\left(\frac{443}{468}\right)$	$e\left(\frac{35}{156}\right)$	$e\left(\frac{67}{78}\right)$	$e\left(\frac{173}{468}\right)$	$e\left(\frac{161}{234}\right)$	$e\left(\frac{113}{117}\right)$	$e\left(\frac{4}{13}\right)$
$\chi_{4563}(851,\cdot)$	$1$	$1$	$e\left(\frac{349}{468}\right)$	$e\left(\frac{115}{234}\right)$	$e\left(\frac{437}{468}\right)$	$e\left(\frac{397}{468}\right)$	$e\left(\frac{37}{156}\right)$	$e\left(\frac{53}{78}\right)$	$e\left(\frac{379}{468}\right)$	$e\left(\frac{139}{234}\right)$	$e\left(\frac{115}{117}\right)$	$e\left(\frac{2}{13}\right)$
$\chi_{4563}(878,\cdot)$	$1$	$1$	$e\left(\frac{187}{468}\right)$	$e\left(\frac{187}{234}\right)$	$e\left(\frac{383}{468}\right)$	$e\left(\frac{379}{468}\right)$	$e\left(\frac{31}{156}\right)$	$e\left(\frac{17}{78}\right)$	$e\left(\frac{73}{468}\right)$	$e\left(\frac{49}{234}\right)$	$e\left(\frac{70}{117}\right)$	$e\left(\frac{8}{13}\right)$
$\chi_{4563}(938,\cdot)$	$1$	$1$	$e\left(\frac{149}{468}\right)$	$e\left(\frac{149}{234}\right)$	$e\left(\frac{145}{468}\right)$	$e\left(\frac{317}{468}\right)$	$e\left(\frac{149}{156}\right)$	$e\left(\frac{49}{78}\right)$	$e\left(\frac{371}{468}\right)$	$e\left(\frac{233}{234}\right)$	$e\left(\frac{32}{117}\right)$	$e\left(\frac{7}{13}\right)$

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	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(7\)	\(8\)	\(10\)	\(11\)	\(14\)	\(16\)	\(17\)
\(\chi_{4563}(2,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{468}\right)\)	\(e\left(\frac{29}{234}\right)\)	\(e\left(\frac{157}{468}\right)\)	\(e\left(\frac{269}{468}\right)\)	\(e\left(\frac{29}{156}\right)\)	\(e\left(\frac{31}{78}\right)\)	\(e\left(\frac{179}{468}\right)\)	\(e\left(\frac{149}{234}\right)\)	\(e\left(\frac{29}{117}\right)\)	\(e\left(\frac{10}{13}\right)\)
\(\chi_{4563}(11,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{179}{468}\right)\)	\(e\left(\frac{179}{234}\right)\)	\(e\left(\frac{259}{468}\right)\)	\(e\left(\frac{95}{468}\right)\)	\(e\left(\frac{23}{156}\right)\)	\(e\left(\frac{73}{78}\right)\)	\(e\left(\frac{185}{468}\right)\)	\(e\left(\frac{137}{234}\right)\)	\(e\left(\frac{62}{117}\right)\)	\(e\left(\frac{3}{13}\right)\)
\(\chi_{4563}(32,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{145}{468}\right)\)	\(e\left(\frac{145}{234}\right)\)	\(e\left(\frac{317}{468}\right)\)	\(e\left(\frac{409}{468}\right)\)	\(e\left(\frac{145}{156}\right)\)	\(e\left(\frac{77}{78}\right)\)	\(e\left(\frac{427}{468}\right)\)	\(e\left(\frac{43}{234}\right)\)	\(e\left(\frac{28}{117}\right)\)	\(e\left(\frac{11}{13}\right)\)
\(\chi_{4563}(59,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{235}{468}\right)\)	\(e\left(\frac{1}{234}\right)\)	\(e\left(\frac{191}{468}\right)\)	\(e\left(\frac{211}{468}\right)\)	\(e\left(\frac{79}{156}\right)\)	\(e\left(\frac{71}{78}\right)\)	\(e\left(\frac{337}{468}\right)\)	\(e\left(\frac{223}{234}\right)\)	\(e\left(\frac{1}{117}\right)\)	\(e\left(\frac{12}{13}\right)\)
\(\chi_{4563}(119,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{161}{468}\right)\)	\(e\left(\frac{161}{234}\right)\)	\(e\left(\frac{97}{468}\right)\)	\(e\left(\frac{41}{468}\right)\)	\(e\left(\frac{5}{156}\right)\)	\(e\left(\frac{43}{78}\right)\)	\(e\left(\frac{203}{468}\right)\)	\(e\left(\frac{101}{234}\right)\)	\(e\left(\frac{44}{117}\right)\)	\(e\left(\frac{8}{13}\right)\)
\(\chi_{4563}(128,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{203}{468}\right)\)	\(e\left(\frac{203}{234}\right)\)	\(e\left(\frac{163}{468}\right)\)	\(e\left(\frac{11}{468}\right)\)	\(e\left(\frac{47}{156}\right)\)	\(e\left(\frac{61}{78}\right)\)	\(e\left(\frac{317}{468}\right)\)	\(e\left(\frac{107}{234}\right)\)	\(e\left(\frac{86}{117}\right)\)	\(e\left(\frac{5}{13}\right)\)
\(\chi_{4563}(149,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{241}{468}\right)\)	\(e\left(\frac{7}{234}\right)\)	\(e\left(\frac{401}{468}\right)\)	\(e\left(\frac{73}{468}\right)\)	\(e\left(\frac{85}{156}\right)\)	\(e\left(\frac{29}{78}\right)\)	\(e\left(\frac{19}{468}\right)\)	\(e\left(\frac{157}{234}\right)\)	\(e\left(\frac{7}{117}\right)\)	\(e\left(\frac{6}{13}\right)\)
\(\chi_{4563}(176,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{295}{468}\right)\)	\(e\left(\frac{61}{234}\right)\)	\(e\left(\frac{419}{468}\right)\)	\(e\left(\frac{235}{468}\right)\)	\(e\left(\frac{139}{156}\right)\)	\(e\left(\frac{41}{78}\right)\)	\(e\left(\frac{433}{468}\right)\)	\(e\left(\frac{31}{234}\right)\)	\(e\left(\frac{61}{117}\right)\)	\(e\left(\frac{4}{13}\right)\)
\(\chi_{4563}(236,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{293}{468}\right)\)	\(e\left(\frac{59}{234}\right)\)	\(e\left(\frac{37}{468}\right)\)	\(e\left(\frac{281}{468}\right)\)	\(e\left(\frac{137}{156}\right)\)	\(e\left(\frac{55}{78}\right)\)	\(e\left(\frac{227}{468}\right)\)	\(e\left(\frac{53}{234}\right)\)	\(e\left(\frac{59}{117}\right)\)	\(e\left(\frac{6}{13}\right)\)
\(\chi_{4563}(245,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{227}{468}\right)\)	\(e\left(\frac{227}{234}\right)\)	\(e\left(\frac{67}{468}\right)\)	\(e\left(\frac{395}{468}\right)\)	\(e\left(\frac{71}{156}\right)\)	\(e\left(\frac{49}{78}\right)\)	\(e\left(\frac{449}{468}\right)\)	\(e\left(\frac{77}{234}\right)\)	\(e\left(\frac{110}{117}\right)\)	\(e\left(\frac{7}{13}\right)\)
\(\chi_{4563}(266,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{337}{468}\right)\)	\(e\left(\frac{103}{234}\right)\)	\(e\left(\frac{17}{468}\right)\)	\(e\left(\frac{205}{468}\right)\)	\(e\left(\frac{25}{156}\right)\)	\(e\left(\frac{59}{78}\right)\)	\(e\left(\frac{79}{468}\right)\)	\(e\left(\frac{37}{234}\right)\)	\(e\left(\frac{103}{117}\right)\)	\(e\left(\frac{1}{13}\right)\)
\(\chi_{4563}(293,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{355}{468}\right)\)	\(e\left(\frac{121}{234}\right)\)	\(e\left(\frac{179}{468}\right)\)	\(e\left(\frac{259}{468}\right)\)	\(e\left(\frac{43}{156}\right)\)	\(e\left(\frac{11}{78}\right)\)	\(e\left(\frac{61}{468}\right)\)	\(e\left(\frac{73}{234}\right)\)	\(e\left(\frac{4}{117}\right)\)	\(e\left(\frac{9}{13}\right)\)
\(\chi_{4563}(353,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{425}{468}\right)\)	\(e\left(\frac{191}{234}\right)\)	\(e\left(\frac{445}{468}\right)\)	\(e\left(\frac{53}{468}\right)\)	\(e\left(\frac{113}{156}\right)\)	\(e\left(\frac{67}{78}\right)\)	\(e\left(\frac{251}{468}\right)\)	\(e\left(\frac{5}{234}\right)\)	\(e\left(\frac{74}{117}\right)\)	\(e\left(\frac{4}{13}\right)\)
\(\chi_{4563}(362,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{251}{468}\right)\)	\(e\left(\frac{17}{234}\right)\)	\(e\left(\frac{439}{468}\right)\)	\(e\left(\frac{311}{468}\right)\)	\(e\left(\frac{95}{156}\right)\)	\(e\left(\frac{37}{78}\right)\)	\(e\left(\frac{113}{468}\right)\)	\(e\left(\frac{47}{234}\right)\)	\(e\left(\frac{17}{117}\right)\)	\(e\left(\frac{9}{13}\right)\)
\(\chi_{4563}(383,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{433}{468}\right)\)	\(e\left(\frac{199}{234}\right)\)	\(e\left(\frac{101}{468}\right)\)	\(e\left(\frac{337}{468}\right)\)	\(e\left(\frac{121}{156}\right)\)	\(e\left(\frac{11}{78}\right)\)	\(e\left(\frac{139}{468}\right)\)	\(e\left(\frac{151}{234}\right)\)	\(e\left(\frac{82}{117}\right)\)	\(e\left(\frac{9}{13}\right)\)
\(\chi_{4563}(410,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{415}{468}\right)\)	\(e\left(\frac{181}{234}\right)\)	\(e\left(\frac{407}{468}\right)\)	\(e\left(\frac{283}{468}\right)\)	\(e\left(\frac{103}{156}\right)\)	\(e\left(\frac{59}{78}\right)\)	\(e\left(\frac{157}{468}\right)\)	\(e\left(\frac{115}{234}\right)\)	\(e\left(\frac{64}{117}\right)\)	\(e\left(\frac{1}{13}\right)\)
\(\chi_{4563}(470,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{89}{468}\right)\)	\(e\left(\frac{89}{234}\right)\)	\(e\left(\frac{385}{468}\right)\)	\(e\left(\frac{293}{468}\right)\)	\(e\left(\frac{89}{156}\right)\)	\(e\left(\frac{1}{78}\right)\)	\(e\left(\frac{275}{468}\right)\)	\(e\left(\frac{191}{234}\right)\)	\(e\left(\frac{89}{117}\right)\)	\(e\left(\frac{2}{13}\right)\)
\(\chi_{4563}(479,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{275}{468}\right)\)	\(e\left(\frac{41}{234}\right)\)	\(e\left(\frac{343}{468}\right)\)	\(e\left(\frac{227}{468}\right)\)	\(e\left(\frac{119}{156}\right)\)	\(e\left(\frac{25}{78}\right)\)	\(e\left(\frac{245}{468}\right)\)	\(e\left(\frac{17}{234}\right)\)	\(e\left(\frac{41}{117}\right)\)	\(e\left(\frac{11}{13}\right)\)
\(\chi_{4563}(500,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{61}{468}\right)\)	\(e\left(\frac{61}{234}\right)\)	\(e\left(\frac{185}{468}\right)\)	\(e\left(\frac{1}{468}\right)\)	\(e\left(\frac{61}{156}\right)\)	\(e\left(\frac{41}{78}\right)\)	\(e\left(\frac{199}{468}\right)\)	\(e\left(\frac{31}{234}\right)\)	\(e\left(\frac{61}{117}\right)\)	\(e\left(\frac{4}{13}\right)\)
\(\chi_{4563}(527,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{468}\right)\)	\(e\left(\frac{7}{234}\right)\)	\(e\left(\frac{167}{468}\right)\)	\(e\left(\frac{307}{468}\right)\)	\(e\left(\frac{7}{156}\right)\)	\(e\left(\frac{29}{78}\right)\)	\(e\left(\frac{253}{468}\right)\)	\(e\left(\frac{157}{234}\right)\)	\(e\left(\frac{7}{117}\right)\)	\(e\left(\frac{6}{13}\right)\)
\(\chi_{4563}(617,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{157}{468}\right)\)	\(e\left(\frac{157}{234}\right)\)	\(e\left(\frac{269}{468}\right)\)	\(e\left(\frac{133}{468}\right)\)	\(e\left(\frac{1}{156}\right)\)	\(e\left(\frac{71}{78}\right)\)	\(e\left(\frac{259}{468}\right)\)	\(e\left(\frac{145}{234}\right)\)	\(e\left(\frac{40}{117}\right)\)	\(e\left(\frac{12}{13}\right)\)
\(\chi_{4563}(644,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{67}{468}\right)\)	\(e\left(\frac{67}{234}\right)\)	\(e\left(\frac{395}{468}\right)\)	\(e\left(\frac{331}{468}\right)\)	\(e\left(\frac{67}{156}\right)\)	\(e\left(\frac{77}{78}\right)\)	\(e\left(\frac{349}{468}\right)\)	\(e\left(\frac{199}{234}\right)\)	\(e\left(\frac{67}{117}\right)\)	\(e\left(\frac{11}{13}\right)\)
\(\chi_{4563}(704,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{353}{468}\right)\)	\(e\left(\frac{119}{234}\right)\)	\(e\left(\frac{265}{468}\right)\)	\(e\left(\frac{305}{468}\right)\)	\(e\left(\frac{41}{156}\right)\)	\(e\left(\frac{25}{78}\right)\)	\(e\left(\frac{323}{468}\right)\)	\(e\left(\frac{95}{234}\right)\)	\(e\left(\frac{2}{117}\right)\)	\(e\left(\frac{11}{13}\right)\)
\(\chi_{4563}(713,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{323}{468}\right)\)	\(e\left(\frac{89}{234}\right)\)	\(e\left(\frac{151}{468}\right)\)	\(e\left(\frac{59}{468}\right)\)	\(e\left(\frac{11}{156}\right)\)	\(e\left(\frac{1}{78}\right)\)	\(e\left(\frac{41}{468}\right)\)	\(e\left(\frac{191}{234}\right)\)	\(e\left(\frac{89}{117}\right)\)	\(e\left(\frac{2}{13}\right)\)
\(\chi_{4563}(734,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{253}{468}\right)\)	\(e\left(\frac{19}{234}\right)\)	\(e\left(\frac{353}{468}\right)\)	\(e\left(\frac{265}{468}\right)\)	\(e\left(\frac{97}{156}\right)\)	\(e\left(\frac{23}{78}\right)\)	\(e\left(\frac{319}{468}\right)\)	\(e\left(\frac{25}{234}\right)\)	\(e\left(\frac{19}{117}\right)\)	\(e\left(\frac{7}{13}\right)\)
\(\chi_{4563}(761,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{127}{468}\right)\)	\(e\left(\frac{127}{234}\right)\)	\(e\left(\frac{155}{468}\right)\)	\(e\left(\frac{355}{468}\right)\)	\(e\left(\frac{127}{156}\right)\)	\(e\left(\frac{47}{78}\right)\)	\(e\left(\frac{445}{468}\right)\)	\(e\left(\frac{7}{234}\right)\)	\(e\left(\frac{10}{117}\right)\)	\(e\left(\frac{3}{13}\right)\)
\(\chi_{4563}(821,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{468}\right)\)	\(e\left(\frac{17}{234}\right)\)	\(e\left(\frac{205}{468}\right)\)	\(e\left(\frac{77}{468}\right)\)	\(e\left(\frac{17}{156}\right)\)	\(e\left(\frac{37}{78}\right)\)	\(e\left(\frac{347}{468}\right)\)	\(e\left(\frac{47}{234}\right)\)	\(e\left(\frac{17}{117}\right)\)	\(e\left(\frac{9}{13}\right)\)
\(\chi_{4563}(830,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{347}{468}\right)\)	\(e\left(\frac{113}{234}\right)\)	\(e\left(\frac{55}{468}\right)\)	\(e\left(\frac{443}{468}\right)\)	\(e\left(\frac{35}{156}\right)\)	\(e\left(\frac{67}{78}\right)\)	\(e\left(\frac{173}{468}\right)\)	\(e\left(\frac{161}{234}\right)\)	\(e\left(\frac{113}{117}\right)\)	\(e\left(\frac{4}{13}\right)\)
\(\chi_{4563}(851,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{349}{468}\right)\)	\(e\left(\frac{115}{234}\right)\)	\(e\left(\frac{437}{468}\right)\)	\(e\left(\frac{397}{468}\right)\)	\(e\left(\frac{37}{156}\right)\)	\(e\left(\frac{53}{78}\right)\)	\(e\left(\frac{379}{468}\right)\)	\(e\left(\frac{139}{234}\right)\)	\(e\left(\frac{115}{117}\right)\)	\(e\left(\frac{2}{13}\right)\)
\(\chi_{4563}(878,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{187}{468}\right)\)	\(e\left(\frac{187}{234}\right)\)	\(e\left(\frac{383}{468}\right)\)	\(e\left(\frac{379}{468}\right)\)	\(e\left(\frac{31}{156}\right)\)	\(e\left(\frac{17}{78}\right)\)	\(e\left(\frac{73}{468}\right)\)	\(e\left(\frac{49}{234}\right)\)	\(e\left(\frac{70}{117}\right)\)	\(e\left(\frac{8}{13}\right)\)
\(\chi_{4563}(938,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{149}{468}\right)\)	\(e\left(\frac{149}{234}\right)\)	\(e\left(\frac{145}{468}\right)\)	\(e\left(\frac{317}{468}\right)\)	\(e\left(\frac{149}{156}\right)\)	\(e\left(\frac{49}{78}\right)\)	\(e\left(\frac{371}{468}\right)\)	\(e\left(\frac{233}{234}\right)\)	\(e\left(\frac{32}{117}\right)\)	\(e\left(\frac{7}{13}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Basic properties

Related number fields

First 31 of 144 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	4563.dm
Modulus	$4563$
Conductor	$4563$
Order	$468$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(4563\)
Conductor:	\(4563\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(468\)	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)