LMFDB - Dirichlet character orbit 4998.da

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(4998, base_ring=CyclotomicField(336)) M = H._module chi = DirichletCharacter(H, M([0,88,63])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(61,4998)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$4998$
Conductor:	$833$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$336$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 833.bn	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:	$\Q(\zeta_{336})$
Fixed field:	Number field defined by a degree 336 polynomial (not computed)

First 31 of 96 characters in Galois orbit

Character	$-1$	$1$	$5$	$11$	$13$	$19$	$23$	$25$	$29$	$31$	$37$	$41$
$\chi_{4998}(61,\cdot)$	$1$	$1$	$e\left(\frac{179}{336}\right)$	$e\left(\frac{265}{336}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{257}{336}\right)$	$e\left(\frac{11}{168}\right)$	$e\left(\frac{17}{112}\right)$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{191}{336}\right)$	$e\left(\frac{111}{112}\right)$
$\chi_{4998}(73,\cdot)$	$1$	$1$	$e\left(\frac{37}{336}\right)$	$e\left(\frac{143}{336}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{55}{336}\right)$	$e\left(\frac{37}{168}\right)$	$e\left(\frac{103}{112}\right)$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{169}{336}\right)$	$e\left(\frac{73}{112}\right)$
$\chi_{4998}(199,\cdot)$	$1$	$1$	$e\left(\frac{253}{336}\right)$	$e\left(\frac{215}{336}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{31}{336}\right)$	$e\left(\frac{85}{168}\right)$	$e\left(\frac{111}{112}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{193}{336}\right)$	$e\left(\frac{33}{112}\right)$
$\chi_{4998}(241,\cdot)$	$1$	$1$	$e\left(\frac{241}{336}\right)$	$e\left(\frac{323}{336}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{331}{336}\right)$	$e\left(\frac{73}{168}\right)$	$e\left(\frac{11}{112}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{229}{336}\right)$	$e\left(\frac{85}{112}\right)$
$\chi_{4998}(283,\cdot)$	$1$	$1$	$e\left(\frac{103}{336}\right)$	$e\left(\frac{53}{336}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{253}{336}\right)$	$e\left(\frac{103}{168}\right)$	$e\left(\frac{93}{112}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{307}{336}\right)$	$e\left(\frac{67}{112}\right)$
$\chi_{4998}(367,\cdot)$	$1$	$1$	$e\left(\frac{163}{336}\right)$	$e\left(\frac{185}{336}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{97}{336}\right)$	$e\left(\frac{163}{168}\right)$	$e\left(\frac{33}{112}\right)$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{127}{336}\right)$	$e\left(\frac{31}{112}\right)$
$\chi_{4998}(397,\cdot)$	$1$	$1$	$e\left(\frac{239}{336}\right)$	$e\left(\frac{61}{336}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{101}{336}\right)$	$e\left(\frac{71}{168}\right)$	$e\left(\frac{69}{112}\right)$	$e\left(\frac{13}{48}\right)$	$e\left(\frac{11}{336}\right)$	$e\left(\frac{75}{112}\right)$
$\chi_{4998}(439,\cdot)$	$1$	$1$	$e\left(\frac{89}{336}\right)$	$e\left(\frac{235}{336}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{323}{336}\right)$	$e\left(\frac{89}{168}\right)$	$e\left(\frac{51}{112}\right)$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{125}{336}\right)$	$e\left(\frac{109}{112}\right)$
$\chi_{4998}(481,\cdot)$	$1$	$1$	$e\left(\frac{149}{336}\right)$	$e\left(\frac{31}{336}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{167}{336}\right)$	$e\left(\frac{149}{168}\right)$	$e\left(\frac{103}{112}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{281}{336}\right)$	$e\left(\frac{73}{112}\right)$
$\chi_{4998}(649,\cdot)$	$1$	$1$	$e\left(\frac{305}{336}\right)$	$e\left(\frac{307}{336}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{299}{336}\right)$	$e\left(\frac{137}{168}\right)$	$e\left(\frac{59}{112}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{149}{336}\right)$	$e\left(\frac{69}{112}\right)$
$\chi_{4998}(691,\cdot)$	$1$	$1$	$e\left(\frac{71}{336}\right)$	$e\left(\frac{229}{336}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{269}{336}\right)$	$e\left(\frac{71}{168}\right)$	$e\left(\frac{13}{112}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{179}{336}\right)$	$e\left(\frac{19}{112}\right)$
$\chi_{4998}(703,\cdot)$	$1$	$1$	$e\left(\frac{319}{336}\right)$	$e\left(\frac{125}{336}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{229}{336}\right)$	$e\left(\frac{151}{168}\right)$	$e\left(\frac{101}{112}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{331}{336}\right)$	$e\left(\frac{27}{112}\right)$
$\chi_{4998}(745,\cdot)$	$1$	$1$	$e\left(\frac{265}{336}\right)$	$e\left(\frac{107}{336}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{67}{336}\right)$	$e\left(\frac{97}{168}\right)$	$e\left(\frac{99}{112}\right)$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{157}{336}\right)$	$e\left(\frac{93}{112}\right)$
$\chi_{4998}(775,\cdot)$	$1$	$1$	$e\left(\frac{275}{336}\right)$	$e\left(\frac{73}{336}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{209}{336}\right)$	$e\left(\frac{107}{168}\right)$	$e\left(\frac{33}{112}\right)$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{239}{336}\right)$	$e\left(\frac{31}{112}\right)$
$\chi_{4998}(787,\cdot)$	$1$	$1$	$e\left(\frac{85}{336}\right)$	$e\left(\frac{47}{336}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{199}{336}\right)$	$e\left(\frac{85}{168}\right)$	$e\left(\frac{55}{112}\right)$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{25}{336}\right)$	$e\left(\frac{89}{112}\right)$
$\chi_{4998}(955,\cdot)$	$1$	$1$	$e\left(\frac{289}{336}\right)$	$e\left(\frac{227}{336}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{139}{336}\right)$	$e\left(\frac{121}{168}\right)$	$e\left(\frac{75}{112}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{85}{336}\right)$	$e\left(\frac{101}{112}\right)$
$\chi_{4998}(997,\cdot)$	$1$	$1$	$e\left(\frac{151}{336}\right)$	$e\left(\frac{293}{336}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{61}{336}\right)$	$e\left(\frac{151}{168}\right)$	$e\left(\frac{45}{112}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{163}{336}\right)$	$e\left(\frac{83}{112}\right)$
$\chi_{4998}(1027,\cdot)$	$1$	$1$	$e\left(\frac{299}{336}\right)$	$e\left(\frac{193}{336}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{281}{336}\right)$	$e\left(\frac{131}{168}\right)$	$e\left(\frac{9}{112}\right)$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{167}{336}\right)$	$e\left(\frac{39}{112}\right)$
$\chi_{4998}(1081,\cdot)$	$1$	$1$	$e\left(\frac{211}{336}\right)$	$e\left(\frac{89}{336}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{241}{336}\right)$	$e\left(\frac{43}{168}\right)$	$e\left(\frac{97}{112}\right)$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{319}{336}\right)$	$e\left(\frac{47}{112}\right)$
$\chi_{4998}(1111,\cdot)$	$1$	$1$	$e\left(\frac{335}{336}\right)$	$e\left(\frac{205}{336}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{53}{336}\right)$	$e\left(\frac{167}{168}\right)$	$e\left(\frac{85}{112}\right)$	$e\left(\frac{13}{48}\right)$	$e\left(\frac{59}{336}\right)$	$e\left(\frac{107}{112}\right)$
$\chi_{4998}(1153,\cdot)$	$1$	$1$	$e\left(\frac{185}{336}\right)$	$e\left(\frac{43}{336}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{275}{336}\right)$	$e\left(\frac{17}{168}\right)$	$e\left(\frac{67}{112}\right)$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{173}{336}\right)$	$e\left(\frac{29}{112}\right)$
$\chi_{4998}(1321,\cdot)$	$1$	$1$	$e\left(\frac{173}{336}\right)$	$e\left(\frac{151}{336}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{239}{336}\right)$	$e\left(\frac{5}{168}\right)$	$e\left(\frac{79}{112}\right)$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{209}{336}\right)$	$e\left(\frac{81}{112}\right)$
$\chi_{4998}(1333,\cdot)$	$1$	$1$	$e\left(\frac{139}{336}\right)$	$e\left(\frac{65}{336}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{25}{336}\right)$	$e\left(\frac{139}{168}\right)$	$e\left(\frac{57}{112}\right)$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{199}{336}\right)$	$e\left(\frac{23}{112}\right)$
$\chi_{4998}(1363,\cdot)$	$1$	$1$	$e\left(\frac{65}{336}\right)$	$e\left(\frac{115}{336}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{251}{336}\right)$	$e\left(\frac{65}{168}\right)$	$e\left(\frac{75}{112}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{197}{336}\right)$	$e\left(\frac{101}{112}\right)$
$\chi_{4998}(1405,\cdot)$	$1$	$1$	$e\left(\frac{167}{336}\right)$	$e\left(\frac{37}{336}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{221}{336}\right)$	$e\left(\frac{167}{168}\right)$	$e\left(\frac{29}{112}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{227}{336}\right)$	$e\left(\frac{51}{112}\right)$
$\chi_{4998}(1417,\cdot)$	$1$	$1$	$e\left(\frac{31}{336}\right)$	$e\left(\frac{29}{336}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{37}{336}\right)$	$e\left(\frac{31}{168}\right)$	$e\left(\frac{53}{112}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{187}{336}\right)$	$e\left(\frac{43}{112}\right)$
$\chi_{4998}(1459,\cdot)$	$1$	$1$	$e\left(\frac{313}{336}\right)$	$e\left(\frac{11}{336}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{211}{336}\right)$	$e\left(\frac{145}{168}\right)$	$e\left(\frac{51}{112}\right)$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{13}{336}\right)$	$e\left(\frac{109}{112}\right)$
$\chi_{4998}(1627,\cdot)$	$1$	$1$	$e\left(\frac{13}{336}\right)$	$e\left(\frac{23}{336}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{319}{336}\right)$	$e\left(\frac{13}{168}\right)$	$e\left(\frac{15}{112}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{241}{336}\right)$	$e\left(\frac{65}{112}\right)$
$\chi_{4998}(1669,\cdot)$	$1$	$1$	$e\left(\frac{1}{336}\right)$	$e\left(\frac{131}{336}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{283}{336}\right)$	$e\left(\frac{1}{168}\right)$	$e\left(\frac{27}{112}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{277}{336}\right)$	$e\left(\frac{5}{112}\right)$
$\chi_{4998}(1711,\cdot)$	$1$	$1$	$e\left(\frac{199}{336}\right)$	$e\left(\frac{197}{336}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{205}{336}\right)$	$e\left(\frac{31}{168}\right)$	$e\left(\frac{109}{112}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{19}{336}\right)$	$e\left(\frac{99}{112}\right)$
$\chi_{4998}(1741,\cdot)$	$1$	$1$	$e\left(\frac{59}{336}\right)$	$e\left(\frac{1}{336}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{233}{336}\right)$	$e\left(\frac{59}{168}\right)$	$e\left(\frac{25}{112}\right)$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{215}{336}\right)$	$e\left(\frac{71}{112}\right)$

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	\(-1\)	\(1\)	\(5\)	\(11\)	\(13\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)	\(37\)	\(41\)
\(\chi_{4998}(61,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{179}{336}\right)\)	\(e\left(\frac{265}{336}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{257}{336}\right)\)	\(e\left(\frac{11}{168}\right)\)	\(e\left(\frac{17}{112}\right)\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{191}{336}\right)\)	\(e\left(\frac{111}{112}\right)\)
\(\chi_{4998}(73,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{336}\right)\)	\(e\left(\frac{143}{336}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{55}{336}\right)\)	\(e\left(\frac{37}{168}\right)\)	\(e\left(\frac{103}{112}\right)\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{169}{336}\right)\)	\(e\left(\frac{73}{112}\right)\)
\(\chi_{4998}(199,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{253}{336}\right)\)	\(e\left(\frac{215}{336}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{31}{336}\right)\)	\(e\left(\frac{85}{168}\right)\)	\(e\left(\frac{111}{112}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{193}{336}\right)\)	\(e\left(\frac{33}{112}\right)\)
\(\chi_{4998}(241,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{241}{336}\right)\)	\(e\left(\frac{323}{336}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{331}{336}\right)\)	\(e\left(\frac{73}{168}\right)\)	\(e\left(\frac{11}{112}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{229}{336}\right)\)	\(e\left(\frac{85}{112}\right)\)
\(\chi_{4998}(283,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{103}{336}\right)\)	\(e\left(\frac{53}{336}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{253}{336}\right)\)	\(e\left(\frac{103}{168}\right)\)	\(e\left(\frac{93}{112}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{307}{336}\right)\)	\(e\left(\frac{67}{112}\right)\)
\(\chi_{4998}(367,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{163}{336}\right)\)	\(e\left(\frac{185}{336}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{97}{336}\right)\)	\(e\left(\frac{163}{168}\right)\)	\(e\left(\frac{33}{112}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{127}{336}\right)\)	\(e\left(\frac{31}{112}\right)\)
\(\chi_{4998}(397,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{239}{336}\right)\)	\(e\left(\frac{61}{336}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{101}{336}\right)\)	\(e\left(\frac{71}{168}\right)\)	\(e\left(\frac{69}{112}\right)\)	\(e\left(\frac{13}{48}\right)\)	\(e\left(\frac{11}{336}\right)\)	\(e\left(\frac{75}{112}\right)\)
\(\chi_{4998}(439,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{89}{336}\right)\)	\(e\left(\frac{235}{336}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{323}{336}\right)\)	\(e\left(\frac{89}{168}\right)\)	\(e\left(\frac{51}{112}\right)\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{125}{336}\right)\)	\(e\left(\frac{109}{112}\right)\)
\(\chi_{4998}(481,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{149}{336}\right)\)	\(e\left(\frac{31}{336}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{167}{336}\right)\)	\(e\left(\frac{149}{168}\right)\)	\(e\left(\frac{103}{112}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{281}{336}\right)\)	\(e\left(\frac{73}{112}\right)\)
\(\chi_{4998}(649,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{305}{336}\right)\)	\(e\left(\frac{307}{336}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{299}{336}\right)\)	\(e\left(\frac{137}{168}\right)\)	\(e\left(\frac{59}{112}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{149}{336}\right)\)	\(e\left(\frac{69}{112}\right)\)
\(\chi_{4998}(691,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{71}{336}\right)\)	\(e\left(\frac{229}{336}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{269}{336}\right)\)	\(e\left(\frac{71}{168}\right)\)	\(e\left(\frac{13}{112}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{179}{336}\right)\)	\(e\left(\frac{19}{112}\right)\)
\(\chi_{4998}(703,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{319}{336}\right)\)	\(e\left(\frac{125}{336}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{229}{336}\right)\)	\(e\left(\frac{151}{168}\right)\)	\(e\left(\frac{101}{112}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{331}{336}\right)\)	\(e\left(\frac{27}{112}\right)\)
\(\chi_{4998}(745,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{265}{336}\right)\)	\(e\left(\frac{107}{336}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{67}{336}\right)\)	\(e\left(\frac{97}{168}\right)\)	\(e\left(\frac{99}{112}\right)\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{157}{336}\right)\)	\(e\left(\frac{93}{112}\right)\)
\(\chi_{4998}(775,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{275}{336}\right)\)	\(e\left(\frac{73}{336}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{209}{336}\right)\)	\(e\left(\frac{107}{168}\right)\)	\(e\left(\frac{33}{112}\right)\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{239}{336}\right)\)	\(e\left(\frac{31}{112}\right)\)
\(\chi_{4998}(787,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{85}{336}\right)\)	\(e\left(\frac{47}{336}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{199}{336}\right)\)	\(e\left(\frac{85}{168}\right)\)	\(e\left(\frac{55}{112}\right)\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{25}{336}\right)\)	\(e\left(\frac{89}{112}\right)\)
\(\chi_{4998}(955,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{289}{336}\right)\)	\(e\left(\frac{227}{336}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{139}{336}\right)\)	\(e\left(\frac{121}{168}\right)\)	\(e\left(\frac{75}{112}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{85}{336}\right)\)	\(e\left(\frac{101}{112}\right)\)
\(\chi_{4998}(997,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{151}{336}\right)\)	\(e\left(\frac{293}{336}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{61}{336}\right)\)	\(e\left(\frac{151}{168}\right)\)	\(e\left(\frac{45}{112}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{163}{336}\right)\)	\(e\left(\frac{83}{112}\right)\)
\(\chi_{4998}(1027,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{299}{336}\right)\)	\(e\left(\frac{193}{336}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{281}{336}\right)\)	\(e\left(\frac{131}{168}\right)\)	\(e\left(\frac{9}{112}\right)\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{167}{336}\right)\)	\(e\left(\frac{39}{112}\right)\)
\(\chi_{4998}(1081,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{211}{336}\right)\)	\(e\left(\frac{89}{336}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{241}{336}\right)\)	\(e\left(\frac{43}{168}\right)\)	\(e\left(\frac{97}{112}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{319}{336}\right)\)	\(e\left(\frac{47}{112}\right)\)
\(\chi_{4998}(1111,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{335}{336}\right)\)	\(e\left(\frac{205}{336}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{53}{336}\right)\)	\(e\left(\frac{167}{168}\right)\)	\(e\left(\frac{85}{112}\right)\)	\(e\left(\frac{13}{48}\right)\)	\(e\left(\frac{59}{336}\right)\)	\(e\left(\frac{107}{112}\right)\)
\(\chi_{4998}(1153,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{185}{336}\right)\)	\(e\left(\frac{43}{336}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{275}{336}\right)\)	\(e\left(\frac{17}{168}\right)\)	\(e\left(\frac{67}{112}\right)\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{173}{336}\right)\)	\(e\left(\frac{29}{112}\right)\)
\(\chi_{4998}(1321,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{173}{336}\right)\)	\(e\left(\frac{151}{336}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{239}{336}\right)\)	\(e\left(\frac{5}{168}\right)\)	\(e\left(\frac{79}{112}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{209}{336}\right)\)	\(e\left(\frac{81}{112}\right)\)
\(\chi_{4998}(1333,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{139}{336}\right)\)	\(e\left(\frac{65}{336}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{25}{336}\right)\)	\(e\left(\frac{139}{168}\right)\)	\(e\left(\frac{57}{112}\right)\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{199}{336}\right)\)	\(e\left(\frac{23}{112}\right)\)
\(\chi_{4998}(1363,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{65}{336}\right)\)	\(e\left(\frac{115}{336}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{251}{336}\right)\)	\(e\left(\frac{65}{168}\right)\)	\(e\left(\frac{75}{112}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{197}{336}\right)\)	\(e\left(\frac{101}{112}\right)\)
\(\chi_{4998}(1405,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{167}{336}\right)\)	\(e\left(\frac{37}{336}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{221}{336}\right)\)	\(e\left(\frac{167}{168}\right)\)	\(e\left(\frac{29}{112}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{227}{336}\right)\)	\(e\left(\frac{51}{112}\right)\)
\(\chi_{4998}(1417,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{336}\right)\)	\(e\left(\frac{29}{336}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{37}{336}\right)\)	\(e\left(\frac{31}{168}\right)\)	\(e\left(\frac{53}{112}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{187}{336}\right)\)	\(e\left(\frac{43}{112}\right)\)
\(\chi_{4998}(1459,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{313}{336}\right)\)	\(e\left(\frac{11}{336}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{211}{336}\right)\)	\(e\left(\frac{145}{168}\right)\)	\(e\left(\frac{51}{112}\right)\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{13}{336}\right)\)	\(e\left(\frac{109}{112}\right)\)
\(\chi_{4998}(1627,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{336}\right)\)	\(e\left(\frac{23}{336}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{319}{336}\right)\)	\(e\left(\frac{13}{168}\right)\)	\(e\left(\frac{15}{112}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{241}{336}\right)\)	\(e\left(\frac{65}{112}\right)\)
\(\chi_{4998}(1669,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{336}\right)\)	\(e\left(\frac{131}{336}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{283}{336}\right)\)	\(e\left(\frac{1}{168}\right)\)	\(e\left(\frac{27}{112}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{277}{336}\right)\)	\(e\left(\frac{5}{112}\right)\)
\(\chi_{4998}(1711,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{199}{336}\right)\)	\(e\left(\frac{197}{336}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{205}{336}\right)\)	\(e\left(\frac{31}{168}\right)\)	\(e\left(\frac{109}{112}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{19}{336}\right)\)	\(e\left(\frac{99}{112}\right)\)
\(\chi_{4998}(1741,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{336}\right)\)	\(e\left(\frac{1}{336}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{233}{336}\right)\)	\(e\left(\frac{59}{168}\right)\)	\(e\left(\frac{25}{112}\right)\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{215}{336}\right)\)	\(e\left(\frac{71}{112}\right)\)

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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	4998.da
Modulus	$4998$
Conductor	$833$
Order	$336$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(4998\)
Conductor:	\(833\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(336\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 833.bn	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)