LMFDB - Dirichlet character orbit 9386.dc

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(9386, base_ring=CyclotomicField(228)) M = H._module chi = DirichletCharacter(H, M([133,110])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(141,9386)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$9386$
Conductor:	$4693$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$228$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 4693.dc	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:	$\Q(\zeta_{228})$
Fixed field:	Number field defined by a degree 228 polynomial (not computed)

First 31 of 72 characters in Galois orbit

Character	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$15$	$17$	$21$	$23$	$25$
$\chi_{9386}(141,\cdot)$	$1$	$1$	$e\left(\frac{15}{38}\right)$	$e\left(\frac{41}{228}\right)$	$e\left(\frac{179}{228}\right)$	$e\left(\frac{15}{19}\right)$	$e\left(\frac{67}{228}\right)$	$e\left(\frac{131}{228}\right)$	$e\left(\frac{23}{114}\right)$	$e\left(\frac{41}{228}\right)$	$e\left(\frac{31}{114}\right)$	$e\left(\frac{41}{114}\right)$
$\chi_{9386}(449,\cdot)$	$1$	$1$	$e\left(\frac{13}{38}\right)$	$e\left(\frac{109}{228}\right)$	$e\left(\frac{31}{228}\right)$	$e\left(\frac{13}{19}\right)$	$e\left(\frac{167}{228}\right)$	$e\left(\frac{187}{228}\right)$	$e\left(\frac{25}{114}\right)$	$e\left(\frac{109}{228}\right)$	$e\left(\frac{113}{114}\right)$	$e\left(\frac{109}{114}\right)$
$\chi_{9386}(483,\cdot)$	$1$	$1$	$e\left(\frac{5}{38}\right)$	$e\left(\frac{191}{228}\right)$	$e\left(\frac{161}{228}\right)$	$e\left(\frac{5}{19}\right)$	$e\left(\frac{73}{228}\right)$	$e\left(\frac{221}{228}\right)$	$e\left(\frac{71}{114}\right)$	$e\left(\frac{191}{228}\right)$	$e\left(\frac{61}{114}\right)$	$e\left(\frac{77}{114}\right)$
$\chi_{9386}(487,\cdot)$	$1$	$1$	$e\left(\frac{1}{38}\right)$	$e\left(\frac{175}{228}\right)$	$e\left(\frac{169}{228}\right)$	$e\left(\frac{1}{19}\right)$	$e\left(\frac{197}{228}\right)$	$e\left(\frac{181}{228}\right)$	$e\left(\frac{37}{114}\right)$	$e\left(\frac{175}{228}\right)$	$e\left(\frac{35}{114}\right)$	$e\left(\frac{61}{114}\right)$
$\chi_{9386}(635,\cdot)$	$1$	$1$	$e\left(\frac{9}{38}\right)$	$e\left(\frac{17}{228}\right)$	$e\left(\frac{191}{228}\right)$	$e\left(\frac{9}{19}\right)$	$e\left(\frac{139}{228}\right)$	$e\left(\frac{71}{228}\right)$	$e\left(\frac{29}{114}\right)$	$e\left(\frac{17}{228}\right)$	$e\left(\frac{49}{114}\right)$	$e\left(\frac{17}{114}\right)$
$\chi_{9386}(943,\cdot)$	$1$	$1$	$e\left(\frac{9}{38}\right)$	$e\left(\frac{169}{228}\right)$	$e\left(\frac{115}{228}\right)$	$e\left(\frac{9}{19}\right)$	$e\left(\frac{215}{228}\right)$	$e\left(\frac{223}{228}\right)$	$e\left(\frac{67}{114}\right)$	$e\left(\frac{169}{228}\right)$	$e\left(\frac{11}{114}\right)$	$e\left(\frac{55}{114}\right)$
$\chi_{9386}(977,\cdot)$	$1$	$1$	$e\left(\frac{37}{38}\right)$	$e\left(\frac{167}{228}\right)$	$e\left(\frac{173}{228}\right)$	$e\left(\frac{18}{19}\right)$	$e\left(\frac{145}{228}\right)$	$e\left(\frac{161}{228}\right)$	$e\left(\frac{77}{114}\right)$	$e\left(\frac{167}{228}\right)$	$e\left(\frac{79}{114}\right)$	$e\left(\frac{53}{114}\right)$
$\chi_{9386}(981,\cdot)$	$1$	$1$	$e\left(\frac{35}{38}\right)$	$e\left(\frac{7}{228}\right)$	$e\left(\frac{25}{228}\right)$	$e\left(\frac{16}{19}\right)$	$e\left(\frac{17}{228}\right)$	$e\left(\frac{217}{228}\right)$	$e\left(\frac{79}{114}\right)$	$e\left(\frac{7}{228}\right)$	$e\left(\frac{47}{114}\right)$	$e\left(\frac{7}{114}\right)$
$\chi_{9386}(1129,\cdot)$	$1$	$1$	$e\left(\frac{3}{38}\right)$	$e\left(\frac{221}{228}\right)$	$e\left(\frac{203}{228}\right)$	$e\left(\frac{3}{19}\right)$	$e\left(\frac{211}{228}\right)$	$e\left(\frac{11}{228}\right)$	$e\left(\frac{35}{114}\right)$	$e\left(\frac{221}{228}\right)$	$e\left(\frac{67}{114}\right)$	$e\left(\frac{107}{114}\right)$
$\chi_{9386}(1437,\cdot)$	$1$	$1$	$e\left(\frac{5}{38}\right)$	$e\left(\frac{1}{228}\right)$	$e\left(\frac{199}{228}\right)$	$e\left(\frac{5}{19}\right)$	$e\left(\frac{35}{228}\right)$	$e\left(\frac{31}{228}\right)$	$e\left(\frac{109}{114}\right)$	$e\left(\frac{1}{228}\right)$	$e\left(\frac{23}{114}\right)$	$e\left(\frac{1}{114}\right)$
$\chi_{9386}(1471,\cdot)$	$1$	$1$	$e\left(\frac{31}{38}\right)$	$e\left(\frac{143}{228}\right)$	$e\left(\frac{185}{228}\right)$	$e\left(\frac{12}{19}\right)$	$e\left(\frac{217}{228}\right)$	$e\left(\frac{101}{228}\right)$	$e\left(\frac{83}{114}\right)$	$e\left(\frac{143}{228}\right)$	$e\left(\frac{97}{114}\right)$	$e\left(\frac{29}{114}\right)$
$\chi_{9386}(1475,\cdot)$	$1$	$1$	$e\left(\frac{31}{38}\right)$	$e\left(\frac{67}{228}\right)$	$e\left(\frac{109}{228}\right)$	$e\left(\frac{12}{19}\right)$	$e\left(\frac{65}{228}\right)$	$e\left(\frac{25}{228}\right)$	$e\left(\frac{7}{114}\right)$	$e\left(\frac{67}{228}\right)$	$e\left(\frac{59}{114}\right)$	$e\left(\frac{67}{114}\right)$
$\chi_{9386}(1623,\cdot)$	$1$	$1$	$e\left(\frac{35}{38}\right)$	$e\left(\frac{197}{228}\right)$	$e\left(\frac{215}{228}\right)$	$e\left(\frac{16}{19}\right)$	$e\left(\frac{55}{228}\right)$	$e\left(\frac{179}{228}\right)$	$e\left(\frac{41}{114}\right)$	$e\left(\frac{197}{228}\right)$	$e\left(\frac{85}{114}\right)$	$e\left(\frac{83}{114}\right)$
$\chi_{9386}(1931,\cdot)$	$1$	$1$	$e\left(\frac{1}{38}\right)$	$e\left(\frac{61}{228}\right)$	$e\left(\frac{55}{228}\right)$	$e\left(\frac{1}{19}\right)$	$e\left(\frac{83}{228}\right)$	$e\left(\frac{67}{228}\right)$	$e\left(\frac{37}{114}\right)$	$e\left(\frac{61}{228}\right)$	$e\left(\frac{35}{114}\right)$	$e\left(\frac{61}{114}\right)$
$\chi_{9386}(1965,\cdot)$	$1$	$1$	$e\left(\frac{25}{38}\right)$	$e\left(\frac{119}{228}\right)$	$e\left(\frac{197}{228}\right)$	$e\left(\frac{6}{19}\right)$	$e\left(\frac{61}{228}\right)$	$e\left(\frac{41}{228}\right)$	$e\left(\frac{89}{114}\right)$	$e\left(\frac{119}{228}\right)$	$e\left(\frac{1}{114}\right)$	$e\left(\frac{5}{114}\right)$
$\chi_{9386}(1969,\cdot)$	$1$	$1$	$e\left(\frac{27}{38}\right)$	$e\left(\frac{127}{228}\right)$	$e\left(\frac{193}{228}\right)$	$e\left(\frac{8}{19}\right)$	$e\left(\frac{113}{228}\right)$	$e\left(\frac{61}{228}\right)$	$e\left(\frac{49}{114}\right)$	$e\left(\frac{127}{228}\right)$	$e\left(\frac{71}{114}\right)$	$e\left(\frac{13}{114}\right)$
$\chi_{9386}(2117,\cdot)$	$1$	$1$	$e\left(\frac{29}{38}\right)$	$e\left(\frac{173}{228}\right)$	$e\left(\frac{227}{228}\right)$	$e\left(\frac{10}{19}\right)$	$e\left(\frac{127}{228}\right)$	$e\left(\frac{119}{228}\right)$	$e\left(\frac{47}{114}\right)$	$e\left(\frac{173}{228}\right)$	$e\left(\frac{103}{114}\right)$	$e\left(\frac{59}{114}\right)$
$\chi_{9386}(2425,\cdot)$	$1$	$1$	$e\left(\frac{35}{38}\right)$	$e\left(\frac{121}{228}\right)$	$e\left(\frac{139}{228}\right)$	$e\left(\frac{16}{19}\right)$	$e\left(\frac{131}{228}\right)$	$e\left(\frac{103}{228}\right)$	$e\left(\frac{79}{114}\right)$	$e\left(\frac{121}{228}\right)$	$e\left(\frac{47}{114}\right)$	$e\left(\frac{7}{114}\right)$
$\chi_{9386}(2463,\cdot)$	$1$	$1$	$e\left(\frac{23}{38}\right)$	$e\left(\frac{187}{228}\right)$	$e\left(\frac{49}{228}\right)$	$e\left(\frac{4}{19}\right)$	$e\left(\frac{161}{228}\right)$	$e\left(\frac{97}{228}\right)$	$e\left(\frac{91}{114}\right)$	$e\left(\frac{187}{228}\right)$	$e\left(\frac{83}{114}\right)$	$e\left(\frac{73}{114}\right)$
$\chi_{9386}(2611,\cdot)$	$1$	$1$	$e\left(\frac{23}{38}\right)$	$e\left(\frac{149}{228}\right)$	$e\left(\frac{11}{228}\right)$	$e\left(\frac{4}{19}\right)$	$e\left(\frac{199}{228}\right)$	$e\left(\frac{59}{228}\right)$	$e\left(\frac{53}{114}\right)$	$e\left(\frac{149}{228}\right)$	$e\left(\frac{7}{114}\right)$	$e\left(\frac{35}{114}\right)$
$\chi_{9386}(2919,\cdot)$	$1$	$1$	$e\left(\frac{31}{38}\right)$	$e\left(\frac{181}{228}\right)$	$e\left(\frac{223}{228}\right)$	$e\left(\frac{12}{19}\right)$	$e\left(\frac{179}{228}\right)$	$e\left(\frac{139}{228}\right)$	$e\left(\frac{7}{114}\right)$	$e\left(\frac{181}{228}\right)$	$e\left(\frac{59}{114}\right)$	$e\left(\frac{67}{114}\right)$
$\chi_{9386}(2953,\cdot)$	$1$	$1$	$e\left(\frac{13}{38}\right)$	$e\left(\frac{71}{228}\right)$	$e\left(\frac{221}{228}\right)$	$e\left(\frac{13}{19}\right)$	$e\left(\frac{205}{228}\right)$	$e\left(\frac{149}{228}\right)$	$e\left(\frac{101}{114}\right)$	$e\left(\frac{71}{228}\right)$	$e\left(\frac{37}{114}\right)$	$e\left(\frac{71}{114}\right)$
$\chi_{9386}(3105,\cdot)$	$1$	$1$	$e\left(\frac{17}{38}\right)$	$e\left(\frac{125}{228}\right)$	$e\left(\frac{23}{228}\right)$	$e\left(\frac{17}{19}\right)$	$e\left(\frac{43}{228}\right)$	$e\left(\frac{227}{228}\right)$	$e\left(\frac{59}{114}\right)$	$e\left(\frac{125}{228}\right)$	$e\left(\frac{25}{114}\right)$	$e\left(\frac{11}{114}\right)$
$\chi_{9386}(3413,\cdot)$	$1$	$1$	$e\left(\frac{27}{38}\right)$	$e\left(\frac{13}{228}\right)$	$e\left(\frac{79}{228}\right)$	$e\left(\frac{8}{19}\right)$	$e\left(\frac{227}{228}\right)$	$e\left(\frac{175}{228}\right)$	$e\left(\frac{49}{114}\right)$	$e\left(\frac{13}{228}\right)$	$e\left(\frac{71}{114}\right)$	$e\left(\frac{13}{114}\right)$
$\chi_{9386}(3447,\cdot)$	$1$	$1$	$e\left(\frac{7}{38}\right)$	$e\left(\frac{47}{228}\right)$	$e\left(\frac{5}{228}\right)$	$e\left(\frac{7}{19}\right)$	$e\left(\frac{49}{228}\right)$	$e\left(\frac{89}{228}\right)$	$e\left(\frac{107}{114}\right)$	$e\left(\frac{47}{228}\right)$	$e\left(\frac{55}{114}\right)$	$e\left(\frac{47}{114}\right)$
$\chi_{9386}(3451,\cdot)$	$1$	$1$	$e\left(\frac{15}{38}\right)$	$e\left(\frac{79}{228}\right)$	$e\left(\frac{217}{228}\right)$	$e\left(\frac{15}{19}\right)$	$e\left(\frac{29}{228}\right)$	$e\left(\frac{169}{228}\right)$	$e\left(\frac{61}{114}\right)$	$e\left(\frac{79}{228}\right)$	$e\left(\frac{107}{114}\right)$	$e\left(\frac{79}{114}\right)$
$\chi_{9386}(3599,\cdot)$	$1$	$1$	$e\left(\frac{11}{38}\right)$	$e\left(\frac{101}{228}\right)$	$e\left(\frac{35}{228}\right)$	$e\left(\frac{11}{19}\right)$	$e\left(\frac{115}{228}\right)$	$e\left(\frac{167}{228}\right)$	$e\left(\frac{65}{114}\right)$	$e\left(\frac{101}{228}\right)$	$e\left(\frac{43}{114}\right)$	$e\left(\frac{101}{114}\right)$
$\chi_{9386}(3907,\cdot)$	$1$	$1$	$e\left(\frac{23}{38}\right)$	$e\left(\frac{73}{228}\right)$	$e\left(\frac{163}{228}\right)$	$e\left(\frac{4}{19}\right)$	$e\left(\frac{47}{228}\right)$	$e\left(\frac{211}{228}\right)$	$e\left(\frac{91}{114}\right)$	$e\left(\frac{73}{228}\right)$	$e\left(\frac{83}{114}\right)$	$e\left(\frac{73}{114}\right)$
$\chi_{9386}(3941,\cdot)$	$1$	$1$	$e\left(\frac{1}{38}\right)$	$e\left(\frac{23}{228}\right)$	$e\left(\frac{17}{228}\right)$	$e\left(\frac{1}{19}\right)$	$e\left(\frac{121}{228}\right)$	$e\left(\frac{29}{228}\right)$	$e\left(\frac{113}{114}\right)$	$e\left(\frac{23}{228}\right)$	$e\left(\frac{73}{114}\right)$	$e\left(\frac{23}{114}\right)$
$\chi_{9386}(3945,\cdot)$	$1$	$1$	$e\left(\frac{11}{38}\right)$	$e\left(\frac{139}{228}\right)$	$e\left(\frac{73}{228}\right)$	$e\left(\frac{11}{19}\right)$	$e\left(\frac{77}{228}\right)$	$e\left(\frac{205}{228}\right)$	$e\left(\frac{103}{114}\right)$	$e\left(\frac{139}{228}\right)$	$e\left(\frac{5}{114}\right)$	$e\left(\frac{25}{114}\right)$
$\chi_{9386}(4093,\cdot)$	$1$	$1$	$e\left(\frac{5}{38}\right)$	$e\left(\frac{77}{228}\right)$	$e\left(\frac{47}{228}\right)$	$e\left(\frac{5}{19}\right)$	$e\left(\frac{187}{228}\right)$	$e\left(\frac{107}{228}\right)$	$e\left(\frac{71}{114}\right)$	$e\left(\frac{77}{228}\right)$	$e\left(\frac{61}{114}\right)$	$e\left(\frac{77}{114}\right)$

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	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(15\)	\(17\)	\(21\)	\(23\)	\(25\)
\(\chi_{9386}(141,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{15}{38}\right)\)	\(e\left(\frac{41}{228}\right)\)	\(e\left(\frac{179}{228}\right)\)	\(e\left(\frac{15}{19}\right)\)	\(e\left(\frac{67}{228}\right)\)	\(e\left(\frac{131}{228}\right)\)	\(e\left(\frac{23}{114}\right)\)	\(e\left(\frac{41}{228}\right)\)	\(e\left(\frac{31}{114}\right)\)	\(e\left(\frac{41}{114}\right)\)
\(\chi_{9386}(449,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{38}\right)\)	\(e\left(\frac{109}{228}\right)\)	\(e\left(\frac{31}{228}\right)\)	\(e\left(\frac{13}{19}\right)\)	\(e\left(\frac{167}{228}\right)\)	\(e\left(\frac{187}{228}\right)\)	\(e\left(\frac{25}{114}\right)\)	\(e\left(\frac{109}{228}\right)\)	\(e\left(\frac{113}{114}\right)\)	\(e\left(\frac{109}{114}\right)\)
\(\chi_{9386}(483,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{38}\right)\)	\(e\left(\frac{191}{228}\right)\)	\(e\left(\frac{161}{228}\right)\)	\(e\left(\frac{5}{19}\right)\)	\(e\left(\frac{73}{228}\right)\)	\(e\left(\frac{221}{228}\right)\)	\(e\left(\frac{71}{114}\right)\)	\(e\left(\frac{191}{228}\right)\)	\(e\left(\frac{61}{114}\right)\)	\(e\left(\frac{77}{114}\right)\)
\(\chi_{9386}(487,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{38}\right)\)	\(e\left(\frac{175}{228}\right)\)	\(e\left(\frac{169}{228}\right)\)	\(e\left(\frac{1}{19}\right)\)	\(e\left(\frac{197}{228}\right)\)	\(e\left(\frac{181}{228}\right)\)	\(e\left(\frac{37}{114}\right)\)	\(e\left(\frac{175}{228}\right)\)	\(e\left(\frac{35}{114}\right)\)	\(e\left(\frac{61}{114}\right)\)
\(\chi_{9386}(635,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{38}\right)\)	\(e\left(\frac{17}{228}\right)\)	\(e\left(\frac{191}{228}\right)\)	\(e\left(\frac{9}{19}\right)\)	\(e\left(\frac{139}{228}\right)\)	\(e\left(\frac{71}{228}\right)\)	\(e\left(\frac{29}{114}\right)\)	\(e\left(\frac{17}{228}\right)\)	\(e\left(\frac{49}{114}\right)\)	\(e\left(\frac{17}{114}\right)\)
\(\chi_{9386}(943,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{38}\right)\)	\(e\left(\frac{169}{228}\right)\)	\(e\left(\frac{115}{228}\right)\)	\(e\left(\frac{9}{19}\right)\)	\(e\left(\frac{215}{228}\right)\)	\(e\left(\frac{223}{228}\right)\)	\(e\left(\frac{67}{114}\right)\)	\(e\left(\frac{169}{228}\right)\)	\(e\left(\frac{11}{114}\right)\)	\(e\left(\frac{55}{114}\right)\)
\(\chi_{9386}(977,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{38}\right)\)	\(e\left(\frac{167}{228}\right)\)	\(e\left(\frac{173}{228}\right)\)	\(e\left(\frac{18}{19}\right)\)	\(e\left(\frac{145}{228}\right)\)	\(e\left(\frac{161}{228}\right)\)	\(e\left(\frac{77}{114}\right)\)	\(e\left(\frac{167}{228}\right)\)	\(e\left(\frac{79}{114}\right)\)	\(e\left(\frac{53}{114}\right)\)
\(\chi_{9386}(981,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{35}{38}\right)\)	\(e\left(\frac{7}{228}\right)\)	\(e\left(\frac{25}{228}\right)\)	\(e\left(\frac{16}{19}\right)\)	\(e\left(\frac{17}{228}\right)\)	\(e\left(\frac{217}{228}\right)\)	\(e\left(\frac{79}{114}\right)\)	\(e\left(\frac{7}{228}\right)\)	\(e\left(\frac{47}{114}\right)\)	\(e\left(\frac{7}{114}\right)\)
\(\chi_{9386}(1129,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{38}\right)\)	\(e\left(\frac{221}{228}\right)\)	\(e\left(\frac{203}{228}\right)\)	\(e\left(\frac{3}{19}\right)\)	\(e\left(\frac{211}{228}\right)\)	\(e\left(\frac{11}{228}\right)\)	\(e\left(\frac{35}{114}\right)\)	\(e\left(\frac{221}{228}\right)\)	\(e\left(\frac{67}{114}\right)\)	\(e\left(\frac{107}{114}\right)\)
\(\chi_{9386}(1437,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{38}\right)\)	\(e\left(\frac{1}{228}\right)\)	\(e\left(\frac{199}{228}\right)\)	\(e\left(\frac{5}{19}\right)\)	\(e\left(\frac{35}{228}\right)\)	\(e\left(\frac{31}{228}\right)\)	\(e\left(\frac{109}{114}\right)\)	\(e\left(\frac{1}{228}\right)\)	\(e\left(\frac{23}{114}\right)\)	\(e\left(\frac{1}{114}\right)\)
\(\chi_{9386}(1471,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{38}\right)\)	\(e\left(\frac{143}{228}\right)\)	\(e\left(\frac{185}{228}\right)\)	\(e\left(\frac{12}{19}\right)\)	\(e\left(\frac{217}{228}\right)\)	\(e\left(\frac{101}{228}\right)\)	\(e\left(\frac{83}{114}\right)\)	\(e\left(\frac{143}{228}\right)\)	\(e\left(\frac{97}{114}\right)\)	\(e\left(\frac{29}{114}\right)\)
\(\chi_{9386}(1475,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{38}\right)\)	\(e\left(\frac{67}{228}\right)\)	\(e\left(\frac{109}{228}\right)\)	\(e\left(\frac{12}{19}\right)\)	\(e\left(\frac{65}{228}\right)\)	\(e\left(\frac{25}{228}\right)\)	\(e\left(\frac{7}{114}\right)\)	\(e\left(\frac{67}{228}\right)\)	\(e\left(\frac{59}{114}\right)\)	\(e\left(\frac{67}{114}\right)\)
\(\chi_{9386}(1623,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{35}{38}\right)\)	\(e\left(\frac{197}{228}\right)\)	\(e\left(\frac{215}{228}\right)\)	\(e\left(\frac{16}{19}\right)\)	\(e\left(\frac{55}{228}\right)\)	\(e\left(\frac{179}{228}\right)\)	\(e\left(\frac{41}{114}\right)\)	\(e\left(\frac{197}{228}\right)\)	\(e\left(\frac{85}{114}\right)\)	\(e\left(\frac{83}{114}\right)\)
\(\chi_{9386}(1931,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{38}\right)\)	\(e\left(\frac{61}{228}\right)\)	\(e\left(\frac{55}{228}\right)\)	\(e\left(\frac{1}{19}\right)\)	\(e\left(\frac{83}{228}\right)\)	\(e\left(\frac{67}{228}\right)\)	\(e\left(\frac{37}{114}\right)\)	\(e\left(\frac{61}{228}\right)\)	\(e\left(\frac{35}{114}\right)\)	\(e\left(\frac{61}{114}\right)\)
\(\chi_{9386}(1965,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{25}{38}\right)\)	\(e\left(\frac{119}{228}\right)\)	\(e\left(\frac{197}{228}\right)\)	\(e\left(\frac{6}{19}\right)\)	\(e\left(\frac{61}{228}\right)\)	\(e\left(\frac{41}{228}\right)\)	\(e\left(\frac{89}{114}\right)\)	\(e\left(\frac{119}{228}\right)\)	\(e\left(\frac{1}{114}\right)\)	\(e\left(\frac{5}{114}\right)\)
\(\chi_{9386}(1969,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{27}{38}\right)\)	\(e\left(\frac{127}{228}\right)\)	\(e\left(\frac{193}{228}\right)\)	\(e\left(\frac{8}{19}\right)\)	\(e\left(\frac{113}{228}\right)\)	\(e\left(\frac{61}{228}\right)\)	\(e\left(\frac{49}{114}\right)\)	\(e\left(\frac{127}{228}\right)\)	\(e\left(\frac{71}{114}\right)\)	\(e\left(\frac{13}{114}\right)\)
\(\chi_{9386}(2117,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{38}\right)\)	\(e\left(\frac{173}{228}\right)\)	\(e\left(\frac{227}{228}\right)\)	\(e\left(\frac{10}{19}\right)\)	\(e\left(\frac{127}{228}\right)\)	\(e\left(\frac{119}{228}\right)\)	\(e\left(\frac{47}{114}\right)\)	\(e\left(\frac{173}{228}\right)\)	\(e\left(\frac{103}{114}\right)\)	\(e\left(\frac{59}{114}\right)\)
\(\chi_{9386}(2425,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{35}{38}\right)\)	\(e\left(\frac{121}{228}\right)\)	\(e\left(\frac{139}{228}\right)\)	\(e\left(\frac{16}{19}\right)\)	\(e\left(\frac{131}{228}\right)\)	\(e\left(\frac{103}{228}\right)\)	\(e\left(\frac{79}{114}\right)\)	\(e\left(\frac{121}{228}\right)\)	\(e\left(\frac{47}{114}\right)\)	\(e\left(\frac{7}{114}\right)\)
\(\chi_{9386}(2463,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{38}\right)\)	\(e\left(\frac{187}{228}\right)\)	\(e\left(\frac{49}{228}\right)\)	\(e\left(\frac{4}{19}\right)\)	\(e\left(\frac{161}{228}\right)\)	\(e\left(\frac{97}{228}\right)\)	\(e\left(\frac{91}{114}\right)\)	\(e\left(\frac{187}{228}\right)\)	\(e\left(\frac{83}{114}\right)\)	\(e\left(\frac{73}{114}\right)\)
\(\chi_{9386}(2611,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{38}\right)\)	\(e\left(\frac{149}{228}\right)\)	\(e\left(\frac{11}{228}\right)\)	\(e\left(\frac{4}{19}\right)\)	\(e\left(\frac{199}{228}\right)\)	\(e\left(\frac{59}{228}\right)\)	\(e\left(\frac{53}{114}\right)\)	\(e\left(\frac{149}{228}\right)\)	\(e\left(\frac{7}{114}\right)\)	\(e\left(\frac{35}{114}\right)\)
\(\chi_{9386}(2919,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{38}\right)\)	\(e\left(\frac{181}{228}\right)\)	\(e\left(\frac{223}{228}\right)\)	\(e\left(\frac{12}{19}\right)\)	\(e\left(\frac{179}{228}\right)\)	\(e\left(\frac{139}{228}\right)\)	\(e\left(\frac{7}{114}\right)\)	\(e\left(\frac{181}{228}\right)\)	\(e\left(\frac{59}{114}\right)\)	\(e\left(\frac{67}{114}\right)\)
\(\chi_{9386}(2953,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{38}\right)\)	\(e\left(\frac{71}{228}\right)\)	\(e\left(\frac{221}{228}\right)\)	\(e\left(\frac{13}{19}\right)\)	\(e\left(\frac{205}{228}\right)\)	\(e\left(\frac{149}{228}\right)\)	\(e\left(\frac{101}{114}\right)\)	\(e\left(\frac{71}{228}\right)\)	\(e\left(\frac{37}{114}\right)\)	\(e\left(\frac{71}{114}\right)\)
\(\chi_{9386}(3105,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{38}\right)\)	\(e\left(\frac{125}{228}\right)\)	\(e\left(\frac{23}{228}\right)\)	\(e\left(\frac{17}{19}\right)\)	\(e\left(\frac{43}{228}\right)\)	\(e\left(\frac{227}{228}\right)\)	\(e\left(\frac{59}{114}\right)\)	\(e\left(\frac{125}{228}\right)\)	\(e\left(\frac{25}{114}\right)\)	\(e\left(\frac{11}{114}\right)\)
\(\chi_{9386}(3413,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{27}{38}\right)\)	\(e\left(\frac{13}{228}\right)\)	\(e\left(\frac{79}{228}\right)\)	\(e\left(\frac{8}{19}\right)\)	\(e\left(\frac{227}{228}\right)\)	\(e\left(\frac{175}{228}\right)\)	\(e\left(\frac{49}{114}\right)\)	\(e\left(\frac{13}{228}\right)\)	\(e\left(\frac{71}{114}\right)\)	\(e\left(\frac{13}{114}\right)\)
\(\chi_{9386}(3447,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{38}\right)\)	\(e\left(\frac{47}{228}\right)\)	\(e\left(\frac{5}{228}\right)\)	\(e\left(\frac{7}{19}\right)\)	\(e\left(\frac{49}{228}\right)\)	\(e\left(\frac{89}{228}\right)\)	\(e\left(\frac{107}{114}\right)\)	\(e\left(\frac{47}{228}\right)\)	\(e\left(\frac{55}{114}\right)\)	\(e\left(\frac{47}{114}\right)\)
\(\chi_{9386}(3451,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{15}{38}\right)\)	\(e\left(\frac{79}{228}\right)\)	\(e\left(\frac{217}{228}\right)\)	\(e\left(\frac{15}{19}\right)\)	\(e\left(\frac{29}{228}\right)\)	\(e\left(\frac{169}{228}\right)\)	\(e\left(\frac{61}{114}\right)\)	\(e\left(\frac{79}{228}\right)\)	\(e\left(\frac{107}{114}\right)\)	\(e\left(\frac{79}{114}\right)\)
\(\chi_{9386}(3599,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{38}\right)\)	\(e\left(\frac{101}{228}\right)\)	\(e\left(\frac{35}{228}\right)\)	\(e\left(\frac{11}{19}\right)\)	\(e\left(\frac{115}{228}\right)\)	\(e\left(\frac{167}{228}\right)\)	\(e\left(\frac{65}{114}\right)\)	\(e\left(\frac{101}{228}\right)\)	\(e\left(\frac{43}{114}\right)\)	\(e\left(\frac{101}{114}\right)\)
\(\chi_{9386}(3907,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{38}\right)\)	\(e\left(\frac{73}{228}\right)\)	\(e\left(\frac{163}{228}\right)\)	\(e\left(\frac{4}{19}\right)\)	\(e\left(\frac{47}{228}\right)\)	\(e\left(\frac{211}{228}\right)\)	\(e\left(\frac{91}{114}\right)\)	\(e\left(\frac{73}{228}\right)\)	\(e\left(\frac{83}{114}\right)\)	\(e\left(\frac{73}{114}\right)\)
\(\chi_{9386}(3941,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{38}\right)\)	\(e\left(\frac{23}{228}\right)\)	\(e\left(\frac{17}{228}\right)\)	\(e\left(\frac{1}{19}\right)\)	\(e\left(\frac{121}{228}\right)\)	\(e\left(\frac{29}{228}\right)\)	\(e\left(\frac{113}{114}\right)\)	\(e\left(\frac{23}{228}\right)\)	\(e\left(\frac{73}{114}\right)\)	\(e\left(\frac{23}{114}\right)\)
\(\chi_{9386}(3945,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{38}\right)\)	\(e\left(\frac{139}{228}\right)\)	\(e\left(\frac{73}{228}\right)\)	\(e\left(\frac{11}{19}\right)\)	\(e\left(\frac{77}{228}\right)\)	\(e\left(\frac{205}{228}\right)\)	\(e\left(\frac{103}{114}\right)\)	\(e\left(\frac{139}{228}\right)\)	\(e\left(\frac{5}{114}\right)\)	\(e\left(\frac{25}{114}\right)\)
\(\chi_{9386}(4093,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{38}\right)\)	\(e\left(\frac{77}{228}\right)\)	\(e\left(\frac{47}{228}\right)\)	\(e\left(\frac{5}{19}\right)\)	\(e\left(\frac{187}{228}\right)\)	\(e\left(\frac{107}{228}\right)\)	\(e\left(\frac{71}{114}\right)\)	\(e\left(\frac{77}{228}\right)\)	\(e\left(\frac{61}{114}\right)\)	\(e\left(\frac{77}{114}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Basic properties

Related number fields

First 31 of 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	9386.dc
Modulus	$9386$
Conductor	$4693$
Order	$228$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(9386\)
Conductor:	\(4693\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(228\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 4693.dc	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)