LMFDB - Dirichlet character orbit 4563.dh

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(4563, base_ring=CyclotomicField(234)) M = H._module chi = DirichletCharacter(H, M([130,27])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(25,4563)) 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:	$234$	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:	$\Q(\zeta_{117})$
Fixed field:	Number field defined by a degree 234 polynomial (not computed)

First 31 of 72 characters in Galois orbit

Character	$-1$	$1$	$2$	$4$	$5$	$7$	$8$	$10$	$11$	$14$	$16$	$17$
$\chi_{4563}(25,\cdot)$	$1$	$1$	$e\left(\frac{157}{234}\right)$	$e\left(\frac{40}{117}\right)$	$e\left(\frac{191}{234}\right)$	$e\left(\frac{55}{234}\right)$	$e\left(\frac{1}{78}\right)$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{25}{234}\right)$	$e\left(\frac{106}{117}\right)$	$e\left(\frac{80}{117}\right)$	$e\left(\frac{7}{39}\right)$
$\chi_{4563}(103,\cdot)$	$1$	$1$	$e\left(\frac{173}{234}\right)$	$e\left(\frac{56}{117}\right)$	$e\left(\frac{127}{234}\right)$	$e\left(\frac{77}{234}\right)$	$e\left(\frac{17}{78}\right)$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{35}{234}\right)$	$e\left(\frac{8}{117}\right)$	$e\left(\frac{112}{117}\right)$	$e\left(\frac{2}{39}\right)$
$\chi_{4563}(142,\cdot)$	$1$	$1$	$e\left(\frac{181}{234}\right)$	$e\left(\frac{64}{117}\right)$	$e\left(\frac{95}{234}\right)$	$e\left(\frac{205}{234}\right)$	$e\left(\frac{25}{78}\right)$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{157}{234}\right)$	$e\left(\frac{76}{117}\right)$	$e\left(\frac{11}{117}\right)$	$e\left(\frac{19}{39}\right)$
$\chi_{4563}(220,\cdot)$	$1$	$1$	$e\left(\frac{197}{234}\right)$	$e\left(\frac{80}{117}\right)$	$e\left(\frac{31}{234}\right)$	$e\left(\frac{227}{234}\right)$	$e\left(\frac{41}{78}\right)$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{167}{234}\right)$	$e\left(\frac{95}{117}\right)$	$e\left(\frac{43}{117}\right)$	$e\left(\frac{14}{39}\right)$
$\chi_{4563}(259,\cdot)$	$1$	$1$	$e\left(\frac{205}{234}\right)$	$e\left(\frac{88}{117}\right)$	$e\left(\frac{233}{234}\right)$	$e\left(\frac{121}{234}\right)$	$e\left(\frac{49}{78}\right)$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{55}{234}\right)$	$e\left(\frac{46}{117}\right)$	$e\left(\frac{59}{117}\right)$	$e\left(\frac{31}{39}\right)$
$\chi_{4563}(376,\cdot)$	$1$	$1$	$e\left(\frac{229}{234}\right)$	$e\left(\frac{112}{117}\right)$	$e\left(\frac{137}{234}\right)$	$e\left(\frac{37}{234}\right)$	$e\left(\frac{73}{78}\right)$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{187}{234}\right)$	$e\left(\frac{16}{117}\right)$	$e\left(\frac{107}{117}\right)$	$e\left(\frac{4}{39}\right)$
$\chi_{4563}(454,\cdot)$	$1$	$1$	$e\left(\frac{11}{234}\right)$	$e\left(\frac{11}{117}\right)$	$e\left(\frac{73}{234}\right)$	$e\left(\frac{59}{234}\right)$	$e\left(\frac{11}{78}\right)$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{197}{234}\right)$	$e\left(\frac{35}{117}\right)$	$e\left(\frac{22}{117}\right)$	$e\left(\frac{38}{39}\right)$
$\chi_{4563}(493,\cdot)$	$1$	$1$	$e\left(\frac{19}{234}\right)$	$e\left(\frac{19}{117}\right)$	$e\left(\frac{41}{234}\right)$	$e\left(\frac{187}{234}\right)$	$e\left(\frac{19}{78}\right)$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{85}{234}\right)$	$e\left(\frac{103}{117}\right)$	$e\left(\frac{38}{117}\right)$	$e\left(\frac{16}{39}\right)$
$\chi_{4563}(571,\cdot)$	$1$	$1$	$e\left(\frac{35}{234}\right)$	$e\left(\frac{35}{117}\right)$	$e\left(\frac{211}{234}\right)$	$e\left(\frac{209}{234}\right)$	$e\left(\frac{35}{78}\right)$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{95}{234}\right)$	$e\left(\frac{5}{117}\right)$	$e\left(\frac{70}{117}\right)$	$e\left(\frac{11}{39}\right)$
$\chi_{4563}(610,\cdot)$	$1$	$1$	$e\left(\frac{43}{234}\right)$	$e\left(\frac{43}{117}\right)$	$e\left(\frac{179}{234}\right)$	$e\left(\frac{103}{234}\right)$	$e\left(\frac{43}{78}\right)$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{217}{234}\right)$	$e\left(\frac{73}{117}\right)$	$e\left(\frac{86}{117}\right)$	$e\left(\frac{28}{39}\right)$
$\chi_{4563}(688,\cdot)$	$1$	$1$	$e\left(\frac{59}{234}\right)$	$e\left(\frac{59}{117}\right)$	$e\left(\frac{115}{234}\right)$	$e\left(\frac{125}{234}\right)$	$e\left(\frac{59}{78}\right)$	$e\left(\frac{29}{39}\right)$	$e\left(\frac{227}{234}\right)$	$e\left(\frac{92}{117}\right)$	$e\left(\frac{1}{117}\right)$	$e\left(\frac{23}{39}\right)$
$\chi_{4563}(727,\cdot)$	$1$	$1$	$e\left(\frac{67}{234}\right)$	$e\left(\frac{67}{117}\right)$	$e\left(\frac{83}{234}\right)$	$e\left(\frac{19}{234}\right)$	$e\left(\frac{67}{78}\right)$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{115}{234}\right)$	$e\left(\frac{43}{117}\right)$	$e\left(\frac{17}{117}\right)$	$e\left(\frac{1}{39}\right)$
$\chi_{4563}(805,\cdot)$	$1$	$1$	$e\left(\frac{83}{234}\right)$	$e\left(\frac{83}{117}\right)$	$e\left(\frac{19}{234}\right)$	$e\left(\frac{41}{234}\right)$	$e\left(\frac{5}{78}\right)$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{125}{234}\right)$	$e\left(\frac{62}{117}\right)$	$e\left(\frac{49}{117}\right)$	$e\left(\frac{35}{39}\right)$
$\chi_{4563}(922,\cdot)$	$1$	$1$	$e\left(\frac{107}{234}\right)$	$e\left(\frac{107}{117}\right)$	$e\left(\frac{157}{234}\right)$	$e\left(\frac{191}{234}\right)$	$e\left(\frac{29}{78}\right)$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{23}{234}\right)$	$e\left(\frac{32}{117}\right)$	$e\left(\frac{97}{117}\right)$	$e\left(\frac{8}{39}\right)$
$\chi_{4563}(961,\cdot)$	$1$	$1$	$e\left(\frac{115}{234}\right)$	$e\left(\frac{115}{117}\right)$	$e\left(\frac{125}{234}\right)$	$e\left(\frac{85}{234}\right)$	$e\left(\frac{37}{78}\right)$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{145}{234}\right)$	$e\left(\frac{100}{117}\right)$	$e\left(\frac{113}{117}\right)$	$e\left(\frac{25}{39}\right)$
$\chi_{4563}(1039,\cdot)$	$1$	$1$	$e\left(\frac{131}{234}\right)$	$e\left(\frac{14}{117}\right)$	$e\left(\frac{61}{234}\right)$	$e\left(\frac{107}{234}\right)$	$e\left(\frac{53}{78}\right)$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{155}{234}\right)$	$e\left(\frac{2}{117}\right)$	$e\left(\frac{28}{117}\right)$	$e\left(\frac{20}{39}\right)$
$\chi_{4563}(1078,\cdot)$	$1$	$1$	$e\left(\frac{139}{234}\right)$	$e\left(\frac{22}{117}\right)$	$e\left(\frac{29}{234}\right)$	$e\left(\frac{1}{234}\right)$	$e\left(\frac{61}{78}\right)$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{43}{234}\right)$	$e\left(\frac{70}{117}\right)$	$e\left(\frac{44}{117}\right)$	$e\left(\frac{37}{39}\right)$
$\chi_{4563}(1156,\cdot)$	$1$	$1$	$e\left(\frac{155}{234}\right)$	$e\left(\frac{38}{117}\right)$	$e\left(\frac{199}{234}\right)$	$e\left(\frac{23}{234}\right)$	$e\left(\frac{77}{78}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{53}{234}\right)$	$e\left(\frac{89}{117}\right)$	$e\left(\frac{76}{117}\right)$	$e\left(\frac{32}{39}\right)$
$\chi_{4563}(1195,\cdot)$	$1$	$1$	$e\left(\frac{163}{234}\right)$	$e\left(\frac{46}{117}\right)$	$e\left(\frac{167}{234}\right)$	$e\left(\frac{151}{234}\right)$	$e\left(\frac{7}{78}\right)$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{175}{234}\right)$	$e\left(\frac{40}{117}\right)$	$e\left(\frac{92}{117}\right)$	$e\left(\frac{10}{39}\right)$
$\chi_{4563}(1273,\cdot)$	$1$	$1$	$e\left(\frac{179}{234}\right)$	$e\left(\frac{62}{117}\right)$	$e\left(\frac{103}{234}\right)$	$e\left(\frac{173}{234}\right)$	$e\left(\frac{23}{78}\right)$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{185}{234}\right)$	$e\left(\frac{59}{117}\right)$	$e\left(\frac{7}{117}\right)$	$e\left(\frac{5}{39}\right)$
$\chi_{4563}(1312,\cdot)$	$1$	$1$	$e\left(\frac{187}{234}\right)$	$e\left(\frac{70}{117}\right)$	$e\left(\frac{71}{234}\right)$	$e\left(\frac{67}{234}\right)$	$e\left(\frac{31}{78}\right)$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{73}{234}\right)$	$e\left(\frac{10}{117}\right)$	$e\left(\frac{23}{117}\right)$	$e\left(\frac{22}{39}\right)$
$\chi_{4563}(1390,\cdot)$	$1$	$1$	$e\left(\frac{203}{234}\right)$	$e\left(\frac{86}{117}\right)$	$e\left(\frac{7}{234}\right)$	$e\left(\frac{89}{234}\right)$	$e\left(\frac{47}{78}\right)$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{83}{234}\right)$	$e\left(\frac{29}{117}\right)$	$e\left(\frac{55}{117}\right)$	$e\left(\frac{17}{39}\right)$
$\chi_{4563}(1429,\cdot)$	$1$	$1$	$e\left(\frac{211}{234}\right)$	$e\left(\frac{94}{117}\right)$	$e\left(\frac{209}{234}\right)$	$e\left(\frac{217}{234}\right)$	$e\left(\frac{55}{78}\right)$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{205}{234}\right)$	$e\left(\frac{97}{117}\right)$	$e\left(\frac{71}{117}\right)$	$e\left(\frac{34}{39}\right)$
$\chi_{4563}(1507,\cdot)$	$1$	$1$	$e\left(\frac{227}{234}\right)$	$e\left(\frac{110}{117}\right)$	$e\left(\frac{145}{234}\right)$	$e\left(\frac{5}{234}\right)$	$e\left(\frac{71}{78}\right)$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{215}{234}\right)$	$e\left(\frac{116}{117}\right)$	$e\left(\frac{103}{117}\right)$	$e\left(\frac{29}{39}\right)$
$\chi_{4563}(1546,\cdot)$	$1$	$1$	$e\left(\frac{1}{234}\right)$	$e\left(\frac{1}{117}\right)$	$e\left(\frac{113}{234}\right)$	$e\left(\frac{133}{234}\right)$	$e\left(\frac{1}{78}\right)$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{103}{234}\right)$	$e\left(\frac{67}{117}\right)$	$e\left(\frac{2}{117}\right)$	$e\left(\frac{7}{39}\right)$
$\chi_{4563}(1624,\cdot)$	$1$	$1$	$e\left(\frac{17}{234}\right)$	$e\left(\frac{17}{117}\right)$	$e\left(\frac{49}{234}\right)$	$e\left(\frac{155}{234}\right)$	$e\left(\frac{17}{78}\right)$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{113}{234}\right)$	$e\left(\frac{86}{117}\right)$	$e\left(\frac{34}{117}\right)$	$e\left(\frac{2}{39}\right)$
$\chi_{4563}(1663,\cdot)$	$1$	$1$	$e\left(\frac{25}{234}\right)$	$e\left(\frac{25}{117}\right)$	$e\left(\frac{17}{234}\right)$	$e\left(\frac{49}{234}\right)$	$e\left(\frac{25}{78}\right)$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{1}{234}\right)$	$e\left(\frac{37}{117}\right)$	$e\left(\frac{50}{117}\right)$	$e\left(\frac{19}{39}\right)$
$\chi_{4563}(1741,\cdot)$	$1$	$1$	$e\left(\frac{41}{234}\right)$	$e\left(\frac{41}{117}\right)$	$e\left(\frac{187}{234}\right)$	$e\left(\frac{71}{234}\right)$	$e\left(\frac{41}{78}\right)$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{11}{234}\right)$	$e\left(\frac{56}{117}\right)$	$e\left(\frac{82}{117}\right)$	$e\left(\frac{14}{39}\right)$
$\chi_{4563}(1780,\cdot)$	$1$	$1$	$e\left(\frac{49}{234}\right)$	$e\left(\frac{49}{117}\right)$	$e\left(\frac{155}{234}\right)$	$e\left(\frac{199}{234}\right)$	$e\left(\frac{49}{78}\right)$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{133}{234}\right)$	$e\left(\frac{7}{117}\right)$	$e\left(\frac{98}{117}\right)$	$e\left(\frac{31}{39}\right)$
$\chi_{4563}(1897,\cdot)$	$1$	$1$	$e\left(\frac{73}{234}\right)$	$e\left(\frac{73}{117}\right)$	$e\left(\frac{59}{234}\right)$	$e\left(\frac{115}{234}\right)$	$e\left(\frac{73}{78}\right)$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{31}{234}\right)$	$e\left(\frac{94}{117}\right)$	$e\left(\frac{29}{117}\right)$	$e\left(\frac{4}{39}\right)$
$\chi_{4563}(1975,\cdot)$	$1$	$1$	$e\left(\frac{89}{234}\right)$	$e\left(\frac{89}{117}\right)$	$e\left(\frac{229}{234}\right)$	$e\left(\frac{137}{234}\right)$	$e\left(\frac{11}{78}\right)$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{41}{234}\right)$	$e\left(\frac{113}{117}\right)$	$e\left(\frac{61}{117}\right)$	$e\left(\frac{38}{39}\right)$

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	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(7\)	\(8\)	\(10\)	\(11\)	\(14\)	\(16\)	\(17\)
\(\chi_{4563}(25,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{157}{234}\right)\)	\(e\left(\frac{40}{117}\right)\)	\(e\left(\frac{191}{234}\right)\)	\(e\left(\frac{55}{234}\right)\)	\(e\left(\frac{1}{78}\right)\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{25}{234}\right)\)	\(e\left(\frac{106}{117}\right)\)	\(e\left(\frac{80}{117}\right)\)	\(e\left(\frac{7}{39}\right)\)
\(\chi_{4563}(103,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{173}{234}\right)\)	\(e\left(\frac{56}{117}\right)\)	\(e\left(\frac{127}{234}\right)\)	\(e\left(\frac{77}{234}\right)\)	\(e\left(\frac{17}{78}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{35}{234}\right)\)	\(e\left(\frac{8}{117}\right)\)	\(e\left(\frac{112}{117}\right)\)	\(e\left(\frac{2}{39}\right)\)
\(\chi_{4563}(142,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{181}{234}\right)\)	\(e\left(\frac{64}{117}\right)\)	\(e\left(\frac{95}{234}\right)\)	\(e\left(\frac{205}{234}\right)\)	\(e\left(\frac{25}{78}\right)\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{157}{234}\right)\)	\(e\left(\frac{76}{117}\right)\)	\(e\left(\frac{11}{117}\right)\)	\(e\left(\frac{19}{39}\right)\)
\(\chi_{4563}(220,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{197}{234}\right)\)	\(e\left(\frac{80}{117}\right)\)	\(e\left(\frac{31}{234}\right)\)	\(e\left(\frac{227}{234}\right)\)	\(e\left(\frac{41}{78}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{167}{234}\right)\)	\(e\left(\frac{95}{117}\right)\)	\(e\left(\frac{43}{117}\right)\)	\(e\left(\frac{14}{39}\right)\)
\(\chi_{4563}(259,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{205}{234}\right)\)	\(e\left(\frac{88}{117}\right)\)	\(e\left(\frac{233}{234}\right)\)	\(e\left(\frac{121}{234}\right)\)	\(e\left(\frac{49}{78}\right)\)	\(e\left(\frac{34}{39}\right)\)	\(e\left(\frac{55}{234}\right)\)	\(e\left(\frac{46}{117}\right)\)	\(e\left(\frac{59}{117}\right)\)	\(e\left(\frac{31}{39}\right)\)
\(\chi_{4563}(376,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{229}{234}\right)\)	\(e\left(\frac{112}{117}\right)\)	\(e\left(\frac{137}{234}\right)\)	\(e\left(\frac{37}{234}\right)\)	\(e\left(\frac{73}{78}\right)\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{187}{234}\right)\)	\(e\left(\frac{16}{117}\right)\)	\(e\left(\frac{107}{117}\right)\)	\(e\left(\frac{4}{39}\right)\)
\(\chi_{4563}(454,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{234}\right)\)	\(e\left(\frac{11}{117}\right)\)	\(e\left(\frac{73}{234}\right)\)	\(e\left(\frac{59}{234}\right)\)	\(e\left(\frac{11}{78}\right)\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{197}{234}\right)\)	\(e\left(\frac{35}{117}\right)\)	\(e\left(\frac{22}{117}\right)\)	\(e\left(\frac{38}{39}\right)\)
\(\chi_{4563}(493,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{234}\right)\)	\(e\left(\frac{19}{117}\right)\)	\(e\left(\frac{41}{234}\right)\)	\(e\left(\frac{187}{234}\right)\)	\(e\left(\frac{19}{78}\right)\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{85}{234}\right)\)	\(e\left(\frac{103}{117}\right)\)	\(e\left(\frac{38}{117}\right)\)	\(e\left(\frac{16}{39}\right)\)
\(\chi_{4563}(571,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{35}{234}\right)\)	\(e\left(\frac{35}{117}\right)\)	\(e\left(\frac{211}{234}\right)\)	\(e\left(\frac{209}{234}\right)\)	\(e\left(\frac{35}{78}\right)\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{95}{234}\right)\)	\(e\left(\frac{5}{117}\right)\)	\(e\left(\frac{70}{117}\right)\)	\(e\left(\frac{11}{39}\right)\)
\(\chi_{4563}(610,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{234}\right)\)	\(e\left(\frac{43}{117}\right)\)	\(e\left(\frac{179}{234}\right)\)	\(e\left(\frac{103}{234}\right)\)	\(e\left(\frac{43}{78}\right)\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{217}{234}\right)\)	\(e\left(\frac{73}{117}\right)\)	\(e\left(\frac{86}{117}\right)\)	\(e\left(\frac{28}{39}\right)\)
\(\chi_{4563}(688,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{234}\right)\)	\(e\left(\frac{59}{117}\right)\)	\(e\left(\frac{115}{234}\right)\)	\(e\left(\frac{125}{234}\right)\)	\(e\left(\frac{59}{78}\right)\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{227}{234}\right)\)	\(e\left(\frac{92}{117}\right)\)	\(e\left(\frac{1}{117}\right)\)	\(e\left(\frac{23}{39}\right)\)
\(\chi_{4563}(727,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{67}{234}\right)\)	\(e\left(\frac{67}{117}\right)\)	\(e\left(\frac{83}{234}\right)\)	\(e\left(\frac{19}{234}\right)\)	\(e\left(\frac{67}{78}\right)\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{115}{234}\right)\)	\(e\left(\frac{43}{117}\right)\)	\(e\left(\frac{17}{117}\right)\)	\(e\left(\frac{1}{39}\right)\)
\(\chi_{4563}(805,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{83}{234}\right)\)	\(e\left(\frac{83}{117}\right)\)	\(e\left(\frac{19}{234}\right)\)	\(e\left(\frac{41}{234}\right)\)	\(e\left(\frac{5}{78}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{125}{234}\right)\)	\(e\left(\frac{62}{117}\right)\)	\(e\left(\frac{49}{117}\right)\)	\(e\left(\frac{35}{39}\right)\)
\(\chi_{4563}(922,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{107}{234}\right)\)	\(e\left(\frac{107}{117}\right)\)	\(e\left(\frac{157}{234}\right)\)	\(e\left(\frac{191}{234}\right)\)	\(e\left(\frac{29}{78}\right)\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{23}{234}\right)\)	\(e\left(\frac{32}{117}\right)\)	\(e\left(\frac{97}{117}\right)\)	\(e\left(\frac{8}{39}\right)\)
\(\chi_{4563}(961,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{115}{234}\right)\)	\(e\left(\frac{115}{117}\right)\)	\(e\left(\frac{125}{234}\right)\)	\(e\left(\frac{85}{234}\right)\)	\(e\left(\frac{37}{78}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{145}{234}\right)\)	\(e\left(\frac{100}{117}\right)\)	\(e\left(\frac{113}{117}\right)\)	\(e\left(\frac{25}{39}\right)\)
\(\chi_{4563}(1039,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{131}{234}\right)\)	\(e\left(\frac{14}{117}\right)\)	\(e\left(\frac{61}{234}\right)\)	\(e\left(\frac{107}{234}\right)\)	\(e\left(\frac{53}{78}\right)\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{155}{234}\right)\)	\(e\left(\frac{2}{117}\right)\)	\(e\left(\frac{28}{117}\right)\)	\(e\left(\frac{20}{39}\right)\)
\(\chi_{4563}(1078,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{139}{234}\right)\)	\(e\left(\frac{22}{117}\right)\)	\(e\left(\frac{29}{234}\right)\)	\(e\left(\frac{1}{234}\right)\)	\(e\left(\frac{61}{78}\right)\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{43}{234}\right)\)	\(e\left(\frac{70}{117}\right)\)	\(e\left(\frac{44}{117}\right)\)	\(e\left(\frac{37}{39}\right)\)
\(\chi_{4563}(1156,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{155}{234}\right)\)	\(e\left(\frac{38}{117}\right)\)	\(e\left(\frac{199}{234}\right)\)	\(e\left(\frac{23}{234}\right)\)	\(e\left(\frac{77}{78}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{53}{234}\right)\)	\(e\left(\frac{89}{117}\right)\)	\(e\left(\frac{76}{117}\right)\)	\(e\left(\frac{32}{39}\right)\)
\(\chi_{4563}(1195,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{163}{234}\right)\)	\(e\left(\frac{46}{117}\right)\)	\(e\left(\frac{167}{234}\right)\)	\(e\left(\frac{151}{234}\right)\)	\(e\left(\frac{7}{78}\right)\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{175}{234}\right)\)	\(e\left(\frac{40}{117}\right)\)	\(e\left(\frac{92}{117}\right)\)	\(e\left(\frac{10}{39}\right)\)
\(\chi_{4563}(1273,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{179}{234}\right)\)	\(e\left(\frac{62}{117}\right)\)	\(e\left(\frac{103}{234}\right)\)	\(e\left(\frac{173}{234}\right)\)	\(e\left(\frac{23}{78}\right)\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{185}{234}\right)\)	\(e\left(\frac{59}{117}\right)\)	\(e\left(\frac{7}{117}\right)\)	\(e\left(\frac{5}{39}\right)\)
\(\chi_{4563}(1312,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{187}{234}\right)\)	\(e\left(\frac{70}{117}\right)\)	\(e\left(\frac{71}{234}\right)\)	\(e\left(\frac{67}{234}\right)\)	\(e\left(\frac{31}{78}\right)\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{73}{234}\right)\)	\(e\left(\frac{10}{117}\right)\)	\(e\left(\frac{23}{117}\right)\)	\(e\left(\frac{22}{39}\right)\)
\(\chi_{4563}(1390,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{203}{234}\right)\)	\(e\left(\frac{86}{117}\right)\)	\(e\left(\frac{7}{234}\right)\)	\(e\left(\frac{89}{234}\right)\)	\(e\left(\frac{47}{78}\right)\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{83}{234}\right)\)	\(e\left(\frac{29}{117}\right)\)	\(e\left(\frac{55}{117}\right)\)	\(e\left(\frac{17}{39}\right)\)
\(\chi_{4563}(1429,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{211}{234}\right)\)	\(e\left(\frac{94}{117}\right)\)	\(e\left(\frac{209}{234}\right)\)	\(e\left(\frac{217}{234}\right)\)	\(e\left(\frac{55}{78}\right)\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{205}{234}\right)\)	\(e\left(\frac{97}{117}\right)\)	\(e\left(\frac{71}{117}\right)\)	\(e\left(\frac{34}{39}\right)\)
\(\chi_{4563}(1507,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{227}{234}\right)\)	\(e\left(\frac{110}{117}\right)\)	\(e\left(\frac{145}{234}\right)\)	\(e\left(\frac{5}{234}\right)\)	\(e\left(\frac{71}{78}\right)\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{215}{234}\right)\)	\(e\left(\frac{116}{117}\right)\)	\(e\left(\frac{103}{117}\right)\)	\(e\left(\frac{29}{39}\right)\)
\(\chi_{4563}(1546,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{234}\right)\)	\(e\left(\frac{1}{117}\right)\)	\(e\left(\frac{113}{234}\right)\)	\(e\left(\frac{133}{234}\right)\)	\(e\left(\frac{1}{78}\right)\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{103}{234}\right)\)	\(e\left(\frac{67}{117}\right)\)	\(e\left(\frac{2}{117}\right)\)	\(e\left(\frac{7}{39}\right)\)
\(\chi_{4563}(1624,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{234}\right)\)	\(e\left(\frac{17}{117}\right)\)	\(e\left(\frac{49}{234}\right)\)	\(e\left(\frac{155}{234}\right)\)	\(e\left(\frac{17}{78}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{113}{234}\right)\)	\(e\left(\frac{86}{117}\right)\)	\(e\left(\frac{34}{117}\right)\)	\(e\left(\frac{2}{39}\right)\)
\(\chi_{4563}(1663,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{25}{234}\right)\)	\(e\left(\frac{25}{117}\right)\)	\(e\left(\frac{17}{234}\right)\)	\(e\left(\frac{49}{234}\right)\)	\(e\left(\frac{25}{78}\right)\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{1}{234}\right)\)	\(e\left(\frac{37}{117}\right)\)	\(e\left(\frac{50}{117}\right)\)	\(e\left(\frac{19}{39}\right)\)
\(\chi_{4563}(1741,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{234}\right)\)	\(e\left(\frac{41}{117}\right)\)	\(e\left(\frac{187}{234}\right)\)	\(e\left(\frac{71}{234}\right)\)	\(e\left(\frac{41}{78}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{11}{234}\right)\)	\(e\left(\frac{56}{117}\right)\)	\(e\left(\frac{82}{117}\right)\)	\(e\left(\frac{14}{39}\right)\)
\(\chi_{4563}(1780,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{49}{234}\right)\)	\(e\left(\frac{49}{117}\right)\)	\(e\left(\frac{155}{234}\right)\)	\(e\left(\frac{199}{234}\right)\)	\(e\left(\frac{49}{78}\right)\)	\(e\left(\frac{34}{39}\right)\)	\(e\left(\frac{133}{234}\right)\)	\(e\left(\frac{7}{117}\right)\)	\(e\left(\frac{98}{117}\right)\)	\(e\left(\frac{31}{39}\right)\)
\(\chi_{4563}(1897,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{73}{234}\right)\)	\(e\left(\frac{73}{117}\right)\)	\(e\left(\frac{59}{234}\right)\)	\(e\left(\frac{115}{234}\right)\)	\(e\left(\frac{73}{78}\right)\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{31}{234}\right)\)	\(e\left(\frac{94}{117}\right)\)	\(e\left(\frac{29}{117}\right)\)	\(e\left(\frac{4}{39}\right)\)
\(\chi_{4563}(1975,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{89}{234}\right)\)	\(e\left(\frac{89}{117}\right)\)	\(e\left(\frac{229}{234}\right)\)	\(e\left(\frac{137}{234}\right)\)	\(e\left(\frac{11}{78}\right)\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{41}{234}\right)\)	\(e\left(\frac{113}{117}\right)\)	\(e\left(\frac{61}{117}\right)\)	\(e\left(\frac{38}{39}\right)\)

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First 31 of 72 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.dh
Modulus	$4563$
Conductor	$4563$
Order	$234$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(4563\)
Conductor:	\(4563\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(234\)	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)