LMFDB - Dirichlet character orbit 4864.db

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(4864, base_ring=CyclotomicField(288)) M = H._module chi = DirichletCharacter(H, M([144,63,32])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(23,4864)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$4864$
Conductor:	$2432$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$288$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 2432.ct	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	no
Parity:	odd	sage:chi.is_odd() pari:zncharisodd(g,chi)

Related number fields

Field of values:	$\Q(\zeta_{288})$
Fixed field:	Number field defined by a degree 288 polynomial (not computed)

First 31 of 96 characters in Galois orbit

Character	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$17$	$21$	$23$
$\chi_{4864}(23,\cdot)$	$-1$	$1$	$e\left(\frac{173}{288}\right)$	$e\left(\frac{287}{288}\right)$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{29}{144}\right)$	$e\left(\frac{41}{96}\right)$	$e\left(\frac{241}{288}\right)$	$e\left(\frac{43}{72}\right)$	$e\left(\frac{17}{72}\right)$	$e\left(\frac{275}{288}\right)$	$e\left(\frac{113}{144}\right)$
$\chi_{4864}(55,\cdot)$	$-1$	$1$	$e\left(\frac{217}{288}\right)$	$e\left(\frac{67}{288}\right)$	$e\left(\frac{13}{48}\right)$	$e\left(\frac{73}{144}\right)$	$e\left(\frac{37}{96}\right)$	$e\left(\frac{269}{288}\right)$	$e\left(\frac{71}{72}\right)$	$e\left(\frac{13}{72}\right)$	$e\left(\frac{7}{288}\right)$	$e\left(\frac{61}{144}\right)$
$\chi_{4864}(119,\cdot)$	$-1$	$1$	$e\left(\frac{241}{288}\right)$	$e\left(\frac{235}{288}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{97}{144}\right)$	$e\left(\frac{61}{96}\right)$	$e\left(\frac{101}{288}\right)$	$e\left(\frac{47}{72}\right)$	$e\left(\frac{37}{72}\right)$	$e\left(\frac{175}{288}\right)$	$e\left(\frac{85}{144}\right)$
$\chi_{4864}(199,\cdot)$	$-1$	$1$	$e\left(\frac{287}{288}\right)$	$e\left(\frac{5}{288}\right)$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{143}{144}\right)$	$e\left(\frac{83}{96}\right)$	$e\left(\frac{235}{288}\right)$	$e\left(\frac{1}{72}\right)$	$e\left(\frac{59}{72}\right)$	$e\left(\frac{65}{288}\right)$	$e\left(\frac{11}{144}\right)$
$\chi_{4864}(215,\cdot)$	$-1$	$1$	$e\left(\frac{149}{288}\right)$	$e\left(\frac{119}{288}\right)$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{5}{144}\right)$	$e\left(\frac{17}{96}\right)$	$e\left(\frac{121}{288}\right)$	$e\left(\frac{67}{72}\right)$	$e\left(\frac{65}{72}\right)$	$e\left(\frac{107}{288}\right)$	$e\left(\frac{89}{144}\right)$
$\chi_{4864}(263,\cdot)$	$-1$	$1$	$e\left(\frac{247}{288}\right)$	$e\left(\frac{205}{288}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{103}{144}\right)$	$e\left(\frac{43}{96}\right)$	$e\left(\frac{131}{288}\right)$	$e\left(\frac{41}{72}\right)$	$e\left(\frac{43}{72}\right)$	$e\left(\frac{73}{288}\right)$	$e\left(\frac{19}{144}\right)$
$\chi_{4864}(327,\cdot)$	$-1$	$1$	$e\left(\frac{47}{288}\right)$	$e\left(\frac{53}{288}\right)$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{47}{144}\right)$	$e\left(\frac{35}{96}\right)$	$e\left(\frac{187}{288}\right)$	$e\left(\frac{25}{72}\right)$	$e\left(\frac{35}{72}\right)$	$e\left(\frac{113}{288}\right)$	$e\left(\frac{59}{144}\right)$
$\chi_{4864}(359,\cdot)$	$-1$	$1$	$e\left(\frac{91}{288}\right)$	$e\left(\frac{121}{288}\right)$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{91}{144}\right)$	$e\left(\frac{31}{96}\right)$	$e\left(\frac{215}{288}\right)$	$e\left(\frac{53}{72}\right)$	$e\left(\frac{31}{72}\right)$	$e\left(\frac{133}{288}\right)$	$e\left(\frac{7}{144}\right)$
$\chi_{4864}(423,\cdot)$	$-1$	$1$	$e\left(\frac{115}{288}\right)$	$e\left(\frac{1}{288}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{115}{144}\right)$	$e\left(\frac{55}{96}\right)$	$e\left(\frac{47}{288}\right)$	$e\left(\frac{29}{72}\right)$	$e\left(\frac{55}{72}\right)$	$e\left(\frac{13}{288}\right)$	$e\left(\frac{31}{144}\right)$
$\chi_{4864}(503,\cdot)$	$-1$	$1$	$e\left(\frac{161}{288}\right)$	$e\left(\frac{59}{288}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{17}{144}\right)$	$e\left(\frac{77}{96}\right)$	$e\left(\frac{181}{288}\right)$	$e\left(\frac{55}{72}\right)$	$e\left(\frac{5}{72}\right)$	$e\left(\frac{191}{288}\right)$	$e\left(\frac{101}{144}\right)$
$\chi_{4864}(519,\cdot)$	$-1$	$1$	$e\left(\frac{23}{288}\right)$	$e\left(\frac{173}{288}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{23}{144}\right)$	$e\left(\frac{11}{96}\right)$	$e\left(\frac{67}{288}\right)$	$e\left(\frac{49}{72}\right)$	$e\left(\frac{11}{72}\right)$	$e\left(\frac{233}{288}\right)$	$e\left(\frac{35}{144}\right)$
$\chi_{4864}(567,\cdot)$	$-1$	$1$	$e\left(\frac{121}{288}\right)$	$e\left(\frac{259}{288}\right)$	$e\left(\frac{13}{48}\right)$	$e\left(\frac{121}{144}\right)$	$e\left(\frac{37}{96}\right)$	$e\left(\frac{77}{288}\right)$	$e\left(\frac{23}{72}\right)$	$e\left(\frac{61}{72}\right)$	$e\left(\frac{199}{288}\right)$	$e\left(\frac{109}{144}\right)$
$\chi_{4864}(631,\cdot)$	$-1$	$1$	$e\left(\frac{209}{288}\right)$	$e\left(\frac{107}{288}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{65}{144}\right)$	$e\left(\frac{29}{96}\right)$	$e\left(\frac{133}{288}\right)$	$e\left(\frac{7}{72}\right)$	$e\left(\frac{53}{72}\right)$	$e\left(\frac{239}{288}\right)$	$e\left(\frac{5}{144}\right)$
$\chi_{4864}(663,\cdot)$	$-1$	$1$	$e\left(\frac{253}{288}\right)$	$e\left(\frac{175}{288}\right)$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{109}{144}\right)$	$e\left(\frac{25}{96}\right)$	$e\left(\frac{161}{288}\right)$	$e\left(\frac{35}{72}\right)$	$e\left(\frac{49}{72}\right)$	$e\left(\frac{259}{288}\right)$	$e\left(\frac{97}{144}\right)$
$\chi_{4864}(727,\cdot)$	$-1$	$1$	$e\left(\frac{277}{288}\right)$	$e\left(\frac{55}{288}\right)$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{133}{144}\right)$	$e\left(\frac{49}{96}\right)$	$e\left(\frac{281}{288}\right)$	$e\left(\frac{11}{72}\right)$	$e\left(\frac{1}{72}\right)$	$e\left(\frac{139}{288}\right)$	$e\left(\frac{121}{144}\right)$
$\chi_{4864}(807,\cdot)$	$-1$	$1$	$e\left(\frac{35}{288}\right)$	$e\left(\frac{113}{288}\right)$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{35}{144}\right)$	$e\left(\frac{71}{96}\right)$	$e\left(\frac{127}{288}\right)$	$e\left(\frac{37}{72}\right)$	$e\left(\frac{23}{72}\right)$	$e\left(\frac{29}{288}\right)$	$e\left(\frac{47}{144}\right)$
$\chi_{4864}(823,\cdot)$	$-1$	$1$	$e\left(\frac{185}{288}\right)$	$e\left(\frac{227}{288}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{41}{144}\right)$	$e\left(\frac{5}{96}\right)$	$e\left(\frac{13}{288}\right)$	$e\left(\frac{31}{72}\right)$	$e\left(\frac{29}{72}\right)$	$e\left(\frac{71}{288}\right)$	$e\left(\frac{125}{144}\right)$
$\chi_{4864}(871,\cdot)$	$-1$	$1$	$e\left(\frac{283}{288}\right)$	$e\left(\frac{25}{288}\right)$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{139}{144}\right)$	$e\left(\frac{31}{96}\right)$	$e\left(\frac{23}{288}\right)$	$e\left(\frac{5}{72}\right)$	$e\left(\frac{7}{72}\right)$	$e\left(\frac{37}{288}\right)$	$e\left(\frac{55}{144}\right)$
$\chi_{4864}(935,\cdot)$	$-1$	$1$	$e\left(\frac{83}{288}\right)$	$e\left(\frac{161}{288}\right)$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{83}{144}\right)$	$e\left(\frac{23}{96}\right)$	$e\left(\frac{79}{288}\right)$	$e\left(\frac{61}{72}\right)$	$e\left(\frac{71}{72}\right)$	$e\left(\frac{77}{288}\right)$	$e\left(\frac{95}{144}\right)$
$\chi_{4864}(967,\cdot)$	$-1$	$1$	$e\left(\frac{127}{288}\right)$	$e\left(\frac{229}{288}\right)$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{127}{144}\right)$	$e\left(\frac{19}{96}\right)$	$e\left(\frac{107}{288}\right)$	$e\left(\frac{17}{72}\right)$	$e\left(\frac{67}{72}\right)$	$e\left(\frac{97}{288}\right)$	$e\left(\frac{43}{144}\right)$
$\chi_{4864}(1031,\cdot)$	$-1$	$1$	$e\left(\frac{151}{288}\right)$	$e\left(\frac{109}{288}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{7}{144}\right)$	$e\left(\frac{43}{96}\right)$	$e\left(\frac{227}{288}\right)$	$e\left(\frac{65}{72}\right)$	$e\left(\frac{19}{72}\right)$	$e\left(\frac{265}{288}\right)$	$e\left(\frac{67}{144}\right)$
$\chi_{4864}(1111,\cdot)$	$-1$	$1$	$e\left(\frac{197}{288}\right)$	$e\left(\frac{167}{288}\right)$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{53}{144}\right)$	$e\left(\frac{65}{96}\right)$	$e\left(\frac{73}{288}\right)$	$e\left(\frac{19}{72}\right)$	$e\left(\frac{41}{72}\right)$	$e\left(\frac{155}{288}\right)$	$e\left(\frac{137}{144}\right)$
$\chi_{4864}(1127,\cdot)$	$-1$	$1$	$e\left(\frac{59}{288}\right)$	$e\left(\frac{281}{288}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{59}{144}\right)$	$e\left(\frac{95}{96}\right)$	$e\left(\frac{247}{288}\right)$	$e\left(\frac{13}{72}\right)$	$e\left(\frac{47}{72}\right)$	$e\left(\frac{197}{288}\right)$	$e\left(\frac{71}{144}\right)$
$\chi_{4864}(1175,\cdot)$	$-1$	$1$	$e\left(\frac{157}{288}\right)$	$e\left(\frac{79}{288}\right)$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{13}{144}\right)$	$e\left(\frac{25}{96}\right)$	$e\left(\frac{257}{288}\right)$	$e\left(\frac{59}{72}\right)$	$e\left(\frac{25}{72}\right)$	$e\left(\frac{163}{288}\right)$	$e\left(\frac{1}{144}\right)$
$\chi_{4864}(1239,\cdot)$	$-1$	$1$	$e\left(\frac{245}{288}\right)$	$e\left(\frac{215}{288}\right)$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{101}{144}\right)$	$e\left(\frac{17}{96}\right)$	$e\left(\frac{25}{288}\right)$	$e\left(\frac{43}{72}\right)$	$e\left(\frac{17}{72}\right)$	$e\left(\frac{203}{288}\right)$	$e\left(\frac{41}{144}\right)$
$\chi_{4864}(1271,\cdot)$	$-1$	$1$	$e\left(\frac{1}{288}\right)$	$e\left(\frac{283}{288}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{1}{144}\right)$	$e\left(\frac{13}{96}\right)$	$e\left(\frac{53}{288}\right)$	$e\left(\frac{71}{72}\right)$	$e\left(\frac{13}{72}\right)$	$e\left(\frac{223}{288}\right)$	$e\left(\frac{133}{144}\right)$
$\chi_{4864}(1335,\cdot)$	$-1$	$1$	$e\left(\frac{25}{288}\right)$	$e\left(\frac{163}{288}\right)$	$e\left(\frac{13}{48}\right)$	$e\left(\frac{25}{144}\right)$	$e\left(\frac{37}{96}\right)$	$e\left(\frac{173}{288}\right)$	$e\left(\frac{47}{72}\right)$	$e\left(\frac{37}{72}\right)$	$e\left(\frac{103}{288}\right)$	$e\left(\frac{13}{144}\right)$
$\chi_{4864}(1415,\cdot)$	$-1$	$1$	$e\left(\frac{71}{288}\right)$	$e\left(\frac{221}{288}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{71}{144}\right)$	$e\left(\frac{59}{96}\right)$	$e\left(\frac{19}{288}\right)$	$e\left(\frac{1}{72}\right)$	$e\left(\frac{59}{72}\right)$	$e\left(\frac{281}{288}\right)$	$e\left(\frac{83}{144}\right)$
$\chi_{4864}(1431,\cdot)$	$-1$	$1$	$e\left(\frac{221}{288}\right)$	$e\left(\frac{47}{288}\right)$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{77}{144}\right)$	$e\left(\frac{89}{96}\right)$	$e\left(\frac{193}{288}\right)$	$e\left(\frac{67}{72}\right)$	$e\left(\frac{65}{72}\right)$	$e\left(\frac{35}{288}\right)$	$e\left(\frac{17}{144}\right)$
$\chi_{4864}(1479,\cdot)$	$-1$	$1$	$e\left(\frac{31}{288}\right)$	$e\left(\frac{133}{288}\right)$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{31}{144}\right)$	$e\left(\frac{19}{96}\right)$	$e\left(\frac{203}{288}\right)$	$e\left(\frac{41}{72}\right)$	$e\left(\frac{43}{72}\right)$	$e\left(\frac{1}{288}\right)$	$e\left(\frac{91}{144}\right)$
$\chi_{4864}(1543,\cdot)$	$-1$	$1$	$e\left(\frac{119}{288}\right)$	$e\left(\frac{269}{288}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{119}{144}\right)$	$e\left(\frac{11}{96}\right)$	$e\left(\frac{259}{288}\right)$	$e\left(\frac{25}{72}\right)$	$e\left(\frac{35}{72}\right)$	$e\left(\frac{41}{288}\right)$	$e\left(\frac{131}{144}\right)$

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	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(21\)	\(23\)
\(\chi_{4864}(23,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{173}{288}\right)\)	\(e\left(\frac{287}{288}\right)\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{29}{144}\right)\)	\(e\left(\frac{41}{96}\right)\)	\(e\left(\frac{241}{288}\right)\)	\(e\left(\frac{43}{72}\right)\)	\(e\left(\frac{17}{72}\right)\)	\(e\left(\frac{275}{288}\right)\)	\(e\left(\frac{113}{144}\right)\)
\(\chi_{4864}(55,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{217}{288}\right)\)	\(e\left(\frac{67}{288}\right)\)	\(e\left(\frac{13}{48}\right)\)	\(e\left(\frac{73}{144}\right)\)	\(e\left(\frac{37}{96}\right)\)	\(e\left(\frac{269}{288}\right)\)	\(e\left(\frac{71}{72}\right)\)	\(e\left(\frac{13}{72}\right)\)	\(e\left(\frac{7}{288}\right)\)	\(e\left(\frac{61}{144}\right)\)
\(\chi_{4864}(119,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{241}{288}\right)\)	\(e\left(\frac{235}{288}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{97}{144}\right)\)	\(e\left(\frac{61}{96}\right)\)	\(e\left(\frac{101}{288}\right)\)	\(e\left(\frac{47}{72}\right)\)	\(e\left(\frac{37}{72}\right)\)	\(e\left(\frac{175}{288}\right)\)	\(e\left(\frac{85}{144}\right)\)
\(\chi_{4864}(199,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{287}{288}\right)\)	\(e\left(\frac{5}{288}\right)\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{143}{144}\right)\)	\(e\left(\frac{83}{96}\right)\)	\(e\left(\frac{235}{288}\right)\)	\(e\left(\frac{1}{72}\right)\)	\(e\left(\frac{59}{72}\right)\)	\(e\left(\frac{65}{288}\right)\)	\(e\left(\frac{11}{144}\right)\)
\(\chi_{4864}(215,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{149}{288}\right)\)	\(e\left(\frac{119}{288}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{5}{144}\right)\)	\(e\left(\frac{17}{96}\right)\)	\(e\left(\frac{121}{288}\right)\)	\(e\left(\frac{67}{72}\right)\)	\(e\left(\frac{65}{72}\right)\)	\(e\left(\frac{107}{288}\right)\)	\(e\left(\frac{89}{144}\right)\)
\(\chi_{4864}(263,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{247}{288}\right)\)	\(e\left(\frac{205}{288}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{103}{144}\right)\)	\(e\left(\frac{43}{96}\right)\)	\(e\left(\frac{131}{288}\right)\)	\(e\left(\frac{41}{72}\right)\)	\(e\left(\frac{43}{72}\right)\)	\(e\left(\frac{73}{288}\right)\)	\(e\left(\frac{19}{144}\right)\)
\(\chi_{4864}(327,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{47}{288}\right)\)	\(e\left(\frac{53}{288}\right)\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{47}{144}\right)\)	\(e\left(\frac{35}{96}\right)\)	\(e\left(\frac{187}{288}\right)\)	\(e\left(\frac{25}{72}\right)\)	\(e\left(\frac{35}{72}\right)\)	\(e\left(\frac{113}{288}\right)\)	\(e\left(\frac{59}{144}\right)\)
\(\chi_{4864}(359,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{91}{288}\right)\)	\(e\left(\frac{121}{288}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{91}{144}\right)\)	\(e\left(\frac{31}{96}\right)\)	\(e\left(\frac{215}{288}\right)\)	\(e\left(\frac{53}{72}\right)\)	\(e\left(\frac{31}{72}\right)\)	\(e\left(\frac{133}{288}\right)\)	\(e\left(\frac{7}{144}\right)\)
\(\chi_{4864}(423,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{115}{288}\right)\)	\(e\left(\frac{1}{288}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{115}{144}\right)\)	\(e\left(\frac{55}{96}\right)\)	\(e\left(\frac{47}{288}\right)\)	\(e\left(\frac{29}{72}\right)\)	\(e\left(\frac{55}{72}\right)\)	\(e\left(\frac{13}{288}\right)\)	\(e\left(\frac{31}{144}\right)\)
\(\chi_{4864}(503,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{161}{288}\right)\)	\(e\left(\frac{59}{288}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{17}{144}\right)\)	\(e\left(\frac{77}{96}\right)\)	\(e\left(\frac{181}{288}\right)\)	\(e\left(\frac{55}{72}\right)\)	\(e\left(\frac{5}{72}\right)\)	\(e\left(\frac{191}{288}\right)\)	\(e\left(\frac{101}{144}\right)\)
\(\chi_{4864}(519,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{23}{288}\right)\)	\(e\left(\frac{173}{288}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{23}{144}\right)\)	\(e\left(\frac{11}{96}\right)\)	\(e\left(\frac{67}{288}\right)\)	\(e\left(\frac{49}{72}\right)\)	\(e\left(\frac{11}{72}\right)\)	\(e\left(\frac{233}{288}\right)\)	\(e\left(\frac{35}{144}\right)\)
\(\chi_{4864}(567,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{121}{288}\right)\)	\(e\left(\frac{259}{288}\right)\)	\(e\left(\frac{13}{48}\right)\)	\(e\left(\frac{121}{144}\right)\)	\(e\left(\frac{37}{96}\right)\)	\(e\left(\frac{77}{288}\right)\)	\(e\left(\frac{23}{72}\right)\)	\(e\left(\frac{61}{72}\right)\)	\(e\left(\frac{199}{288}\right)\)	\(e\left(\frac{109}{144}\right)\)
\(\chi_{4864}(631,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{209}{288}\right)\)	\(e\left(\frac{107}{288}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{65}{144}\right)\)	\(e\left(\frac{29}{96}\right)\)	\(e\left(\frac{133}{288}\right)\)	\(e\left(\frac{7}{72}\right)\)	\(e\left(\frac{53}{72}\right)\)	\(e\left(\frac{239}{288}\right)\)	\(e\left(\frac{5}{144}\right)\)
\(\chi_{4864}(663,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{253}{288}\right)\)	\(e\left(\frac{175}{288}\right)\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{109}{144}\right)\)	\(e\left(\frac{25}{96}\right)\)	\(e\left(\frac{161}{288}\right)\)	\(e\left(\frac{35}{72}\right)\)	\(e\left(\frac{49}{72}\right)\)	\(e\left(\frac{259}{288}\right)\)	\(e\left(\frac{97}{144}\right)\)
\(\chi_{4864}(727,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{277}{288}\right)\)	\(e\left(\frac{55}{288}\right)\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{133}{144}\right)\)	\(e\left(\frac{49}{96}\right)\)	\(e\left(\frac{281}{288}\right)\)	\(e\left(\frac{11}{72}\right)\)	\(e\left(\frac{1}{72}\right)\)	\(e\left(\frac{139}{288}\right)\)	\(e\left(\frac{121}{144}\right)\)
\(\chi_{4864}(807,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{35}{288}\right)\)	\(e\left(\frac{113}{288}\right)\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{35}{144}\right)\)	\(e\left(\frac{71}{96}\right)\)	\(e\left(\frac{127}{288}\right)\)	\(e\left(\frac{37}{72}\right)\)	\(e\left(\frac{23}{72}\right)\)	\(e\left(\frac{29}{288}\right)\)	\(e\left(\frac{47}{144}\right)\)
\(\chi_{4864}(823,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{185}{288}\right)\)	\(e\left(\frac{227}{288}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{41}{144}\right)\)	\(e\left(\frac{5}{96}\right)\)	\(e\left(\frac{13}{288}\right)\)	\(e\left(\frac{31}{72}\right)\)	\(e\left(\frac{29}{72}\right)\)	\(e\left(\frac{71}{288}\right)\)	\(e\left(\frac{125}{144}\right)\)
\(\chi_{4864}(871,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{283}{288}\right)\)	\(e\left(\frac{25}{288}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{139}{144}\right)\)	\(e\left(\frac{31}{96}\right)\)	\(e\left(\frac{23}{288}\right)\)	\(e\left(\frac{5}{72}\right)\)	\(e\left(\frac{7}{72}\right)\)	\(e\left(\frac{37}{288}\right)\)	\(e\left(\frac{55}{144}\right)\)
\(\chi_{4864}(935,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{83}{288}\right)\)	\(e\left(\frac{161}{288}\right)\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{83}{144}\right)\)	\(e\left(\frac{23}{96}\right)\)	\(e\left(\frac{79}{288}\right)\)	\(e\left(\frac{61}{72}\right)\)	\(e\left(\frac{71}{72}\right)\)	\(e\left(\frac{77}{288}\right)\)	\(e\left(\frac{95}{144}\right)\)
\(\chi_{4864}(967,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{127}{288}\right)\)	\(e\left(\frac{229}{288}\right)\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{127}{144}\right)\)	\(e\left(\frac{19}{96}\right)\)	\(e\left(\frac{107}{288}\right)\)	\(e\left(\frac{17}{72}\right)\)	\(e\left(\frac{67}{72}\right)\)	\(e\left(\frac{97}{288}\right)\)	\(e\left(\frac{43}{144}\right)\)
\(\chi_{4864}(1031,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{151}{288}\right)\)	\(e\left(\frac{109}{288}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{7}{144}\right)\)	\(e\left(\frac{43}{96}\right)\)	\(e\left(\frac{227}{288}\right)\)	\(e\left(\frac{65}{72}\right)\)	\(e\left(\frac{19}{72}\right)\)	\(e\left(\frac{265}{288}\right)\)	\(e\left(\frac{67}{144}\right)\)
\(\chi_{4864}(1111,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{197}{288}\right)\)	\(e\left(\frac{167}{288}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{53}{144}\right)\)	\(e\left(\frac{65}{96}\right)\)	\(e\left(\frac{73}{288}\right)\)	\(e\left(\frac{19}{72}\right)\)	\(e\left(\frac{41}{72}\right)\)	\(e\left(\frac{155}{288}\right)\)	\(e\left(\frac{137}{144}\right)\)
\(\chi_{4864}(1127,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{59}{288}\right)\)	\(e\left(\frac{281}{288}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{59}{144}\right)\)	\(e\left(\frac{95}{96}\right)\)	\(e\left(\frac{247}{288}\right)\)	\(e\left(\frac{13}{72}\right)\)	\(e\left(\frac{47}{72}\right)\)	\(e\left(\frac{197}{288}\right)\)	\(e\left(\frac{71}{144}\right)\)
\(\chi_{4864}(1175,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{157}{288}\right)\)	\(e\left(\frac{79}{288}\right)\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{13}{144}\right)\)	\(e\left(\frac{25}{96}\right)\)	\(e\left(\frac{257}{288}\right)\)	\(e\left(\frac{59}{72}\right)\)	\(e\left(\frac{25}{72}\right)\)	\(e\left(\frac{163}{288}\right)\)	\(e\left(\frac{1}{144}\right)\)
\(\chi_{4864}(1239,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{245}{288}\right)\)	\(e\left(\frac{215}{288}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{101}{144}\right)\)	\(e\left(\frac{17}{96}\right)\)	\(e\left(\frac{25}{288}\right)\)	\(e\left(\frac{43}{72}\right)\)	\(e\left(\frac{17}{72}\right)\)	\(e\left(\frac{203}{288}\right)\)	\(e\left(\frac{41}{144}\right)\)
\(\chi_{4864}(1271,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{288}\right)\)	\(e\left(\frac{283}{288}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{1}{144}\right)\)	\(e\left(\frac{13}{96}\right)\)	\(e\left(\frac{53}{288}\right)\)	\(e\left(\frac{71}{72}\right)\)	\(e\left(\frac{13}{72}\right)\)	\(e\left(\frac{223}{288}\right)\)	\(e\left(\frac{133}{144}\right)\)
\(\chi_{4864}(1335,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{25}{288}\right)\)	\(e\left(\frac{163}{288}\right)\)	\(e\left(\frac{13}{48}\right)\)	\(e\left(\frac{25}{144}\right)\)	\(e\left(\frac{37}{96}\right)\)	\(e\left(\frac{173}{288}\right)\)	\(e\left(\frac{47}{72}\right)\)	\(e\left(\frac{37}{72}\right)\)	\(e\left(\frac{103}{288}\right)\)	\(e\left(\frac{13}{144}\right)\)
\(\chi_{4864}(1415,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{71}{288}\right)\)	\(e\left(\frac{221}{288}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{71}{144}\right)\)	\(e\left(\frac{59}{96}\right)\)	\(e\left(\frac{19}{288}\right)\)	\(e\left(\frac{1}{72}\right)\)	\(e\left(\frac{59}{72}\right)\)	\(e\left(\frac{281}{288}\right)\)	\(e\left(\frac{83}{144}\right)\)
\(\chi_{4864}(1431,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{221}{288}\right)\)	\(e\left(\frac{47}{288}\right)\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{77}{144}\right)\)	\(e\left(\frac{89}{96}\right)\)	\(e\left(\frac{193}{288}\right)\)	\(e\left(\frac{67}{72}\right)\)	\(e\left(\frac{65}{72}\right)\)	\(e\left(\frac{35}{288}\right)\)	\(e\left(\frac{17}{144}\right)\)
\(\chi_{4864}(1479,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{31}{288}\right)\)	\(e\left(\frac{133}{288}\right)\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{31}{144}\right)\)	\(e\left(\frac{19}{96}\right)\)	\(e\left(\frac{203}{288}\right)\)	\(e\left(\frac{41}{72}\right)\)	\(e\left(\frac{43}{72}\right)\)	\(e\left(\frac{1}{288}\right)\)	\(e\left(\frac{91}{144}\right)\)
\(\chi_{4864}(1543,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{119}{288}\right)\)	\(e\left(\frac{269}{288}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{119}{144}\right)\)	\(e\left(\frac{11}{96}\right)\)	\(e\left(\frac{259}{288}\right)\)	\(e\left(\frac{25}{72}\right)\)	\(e\left(\frac{35}{72}\right)\)	\(e\left(\frac{41}{288}\right)\)	\(e\left(\frac{131}{144}\right)\)

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First 31 of 96 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	4864.db
Modulus	$4864$
Conductor	$2432$
Order	$288$
Real	no
Primitive	no
Minimal	no
Parity	odd

Modulus:	\(4864\)
Conductor:	\(2432\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(288\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 2432.ct	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	no
Parity:	odd	sage:chi.is_odd() pari:zncharisodd(g,chi)