LMFDB - Dirichlet character orbit 9386.dm

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(9386, base_ring=CyclotomicField(684)) M = H._module chi = DirichletCharacter(H, M([171,578])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(21,9386)) 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:	$684$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 4693.dp	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:	$\Q(\zeta_{684})$
Fixed field:	Number field defined by a degree 684 polynomial (not computed)

First 31 of 216 characters in Galois orbit

Character	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$15$	$17$	$21$	$23$	$25$
$\chi_{9386}(21,\cdot)$	$1$	$1$	$e\left(\frac{157}{342}\right)$	$e\left(\frac{203}{684}\right)$	$e\left(\frac{115}{228}\right)$	$e\left(\frac{157}{171}\right)$	$e\left(\frac{215}{228}\right)$	$e\left(\frac{517}{684}\right)$	$e\left(\frac{163}{342}\right)$	$e\left(\frac{659}{684}\right)$	$e\left(\frac{299}{342}\right)$	$e\left(\frac{203}{342}\right)$
$\chi_{9386}(109,\cdot)$	$1$	$1$	$e\left(\frac{91}{342}\right)$	$e\left(\frac{305}{684}\right)$	$e\left(\frac{193}{228}\right)$	$e\left(\frac{91}{171}\right)$	$e\left(\frac{113}{228}\right)$	$e\left(\frac{487}{684}\right)$	$e\left(\frac{223}{342}\right)$	$e\left(\frac{77}{684}\right)$	$e\left(\frac{23}{342}\right)$	$e\left(\frac{305}{342}\right)$
$\chi_{9386}(135,\cdot)$	$1$	$1$	$e\left(\frac{265}{342}\right)$	$e\left(\frac{5}{684}\right)$	$e\left(\frac{205}{228}\right)$	$e\left(\frac{94}{171}\right)$	$e\left(\frac{185}{228}\right)$	$e\left(\frac{535}{684}\right)$	$e\left(\frac{127}{342}\right)$	$e\left(\frac{461}{684}\right)$	$e\left(\frac{191}{342}\right)$	$e\left(\frac{5}{342}\right)$
$\chi_{9386}(203,\cdot)$	$1$	$1$	$e\left(\frac{299}{342}\right)$	$e\left(\frac{367}{684}\right)$	$e\left(\frac{227}{228}\right)$	$e\left(\frac{128}{171}\right)$	$e\left(\frac{127}{228}\right)$	$e\left(\frac{281}{684}\right)$	$e\left(\frac{293}{342}\right)$	$e\left(\frac{595}{684}\right)$	$e\left(\frac{271}{342}\right)$	$e\left(\frac{25}{342}\right)$
$\chi_{9386}(281,\cdot)$	$1$	$1$	$e\left(\frac{143}{342}\right)$	$e\left(\frac{235}{684}\right)$	$e\left(\frac{59}{228}\right)$	$e\left(\frac{143}{171}\right)$	$e\left(\frac{31}{228}\right)$	$e\left(\frac{521}{684}\right)$	$e\left(\frac{155}{342}\right)$	$e\left(\frac{463}{684}\right)$	$e\left(\frac{85}{342}\right)$	$e\left(\frac{235}{342}\right)$
$\chi_{9386}(317,\cdot)$	$1$	$1$	$e\left(\frac{263}{342}\right)$	$e\left(\frac{205}{684}\right)$	$e\left(\frac{197}{228}\right)$	$e\left(\frac{92}{171}\right)$	$e\left(\frac{61}{228}\right)$	$e\left(\frac{47}{684}\right)$	$e\left(\frac{77}{342}\right)$	$e\left(\frac{433}{684}\right)$	$e\left(\frac{307}{342}\right)$	$e\left(\frac{205}{342}\right)$
$\chi_{9386}(395,\cdot)$	$1$	$1$	$e\left(\frac{89}{342}\right)$	$e\left(\frac{505}{684}\right)$	$e\left(\frac{185}{228}\right)$	$e\left(\frac{89}{171}\right)$	$e\left(\frac{217}{228}\right)$	$e\left(\frac{683}{684}\right)$	$e\left(\frac{173}{342}\right)$	$e\left(\frac{49}{684}\right)$	$e\left(\frac{139}{342}\right)$	$e\left(\frac{163}{342}\right)$
$\chi_{9386}(421,\cdot)$	$1$	$1$	$e\left(\frac{205}{342}\right)$	$e\left(\frac{533}{684}\right)$	$e\left(\frac{193}{228}\right)$	$e\left(\frac{34}{171}\right)$	$e\left(\frac{113}{228}\right)$	$e\left(\frac{259}{684}\right)$	$e\left(\frac{337}{342}\right)$	$e\left(\frac{305}{684}\right)$	$e\left(\frac{251}{342}\right)$	$e\left(\frac{191}{342}\right)$
$\chi_{9386}(447,\cdot)$	$1$	$1$	$e\left(\frac{185}{342}\right)$	$e\left(\frac{481}{684}\right)$	$e\left(\frac{113}{228}\right)$	$e\left(\frac{14}{171}\right)$	$e\left(\frac{13}{228}\right)$	$e\left(\frac{167}{684}\right)$	$e\left(\frac{179}{342}\right)$	$e\left(\frac{25}{684}\right)$	$e\left(\frac{43}{342}\right)$	$e\left(\frac{139}{342}\right)$
$\chi_{9386}(489,\cdot)$	$1$	$1$	$e\left(\frac{289}{342}\right)$	$e\left(\frac{683}{684}\right)$	$e\left(\frac{187}{228}\right)$	$e\left(\frac{118}{171}\right)$	$e\left(\frac{191}{228}\right)$	$e\left(\frac{577}{684}\right)$	$e\left(\frac{43}{342}\right)$	$e\left(\frac{455}{684}\right)$	$e\left(\frac{167}{342}\right)$	$e\left(\frac{341}{342}\right)$
$\chi_{9386}(515,\cdot)$	$1$	$1$	$e\left(\frac{283}{342}\right)$	$e\left(\frac{599}{684}\right)$	$e\left(\frac{163}{228}\right)$	$e\left(\frac{112}{171}\right)$	$e\left(\frac{47}{228}\right)$	$e\left(\frac{481}{684}\right)$	$e\left(\frac{235}{342}\right)$	$e\left(\frac{371}{684}\right)$	$e\left(\frac{173}{342}\right)$	$e\left(\frac{257}{342}\right)$
$\chi_{9386}(603,\cdot)$	$1$	$1$	$e\left(\frac{109}{342}\right)$	$e\left(\frac{557}{684}\right)$	$e\left(\frac{37}{228}\right)$	$e\left(\frac{109}{171}\right)$	$e\left(\frac{89}{228}\right)$	$e\left(\frac{91}{684}\right)$	$e\left(\frac{331}{342}\right)$	$e\left(\frac{329}{684}\right)$	$e\left(\frac{5}{342}\right)$	$e\left(\frac{215}{342}\right)$
$\chi_{9386}(629,\cdot)$	$1$	$1$	$e\left(\frac{49}{342}\right)$	$e\left(\frac{401}{684}\right)$	$e\left(\frac{25}{228}\right)$	$e\left(\frac{49}{171}\right)$	$e\left(\frac{17}{228}\right)$	$e\left(\frac{499}{684}\right)$	$e\left(\frac{199}{342}\right)$	$e\left(\frac{173}{684}\right)$	$e\left(\frac{65}{342}\right)$	$e\left(\frac{59}{342}\right)$
$\chi_{9386}(697,\cdot)$	$1$	$1$	$e\left(\frac{29}{342}\right)$	$e\left(\frac{7}{684}\right)$	$e\left(\frac{59}{228}\right)$	$e\left(\frac{29}{171}\right)$	$e\left(\frac{31}{228}\right)$	$e\left(\frac{65}{684}\right)$	$e\left(\frac{41}{342}\right)$	$e\left(\frac{235}{684}\right)$	$e\left(\frac{199}{342}\right)$	$e\left(\frac{7}{342}\right)$
$\chi_{9386}(775,\cdot)$	$1$	$1$	$e\left(\frac{251}{342}\right)$	$e\left(\frac{379}{684}\right)$	$e\left(\frac{35}{228}\right)$	$e\left(\frac{80}{171}\right)$	$e\left(\frac{115}{228}\right)$	$e\left(\frac{197}{684}\right)$	$e\left(\frac{119}{342}\right)$	$e\left(\frac{607}{684}\right)$	$e\left(\frac{319}{342}\right)$	$e\left(\frac{37}{342}\right)$
$\chi_{9386}(801,\cdot)$	$1$	$1$	$e\left(\frac{331}{342}\right)$	$e\left(\frac{587}{684}\right)$	$e\left(\frac{127}{228}\right)$	$e\left(\frac{160}{171}\right)$	$e\left(\frac{59}{228}\right)$	$e\left(\frac{565}{684}\right)$	$e\left(\frac{67}{342}\right)$	$e\left(\frac{359}{684}\right)$	$e\left(\frac{125}{342}\right)$	$e\left(\frac{245}{342}\right)$
$\chi_{9386}(811,\cdot)$	$1$	$1$	$e\left(\frac{335}{342}\right)$	$e\left(\frac{529}{684}\right)$	$e\left(\frac{29}{228}\right)$	$e\left(\frac{164}{171}\right)$	$e\left(\frac{193}{228}\right)$	$e\left(\frac{515}{684}\right)$	$e\left(\frac{167}{342}\right)$	$e\left(\frac{73}{684}\right)$	$e\left(\frac{235}{342}\right)$	$e\left(\frac{187}{342}\right)$
$\chi_{9386}(827,\cdot)$	$1$	$1$	$e\left(\frac{257}{342}\right)$	$e\left(\frac{463}{684}\right)$	$e\left(\frac{59}{228}\right)$	$e\left(\frac{86}{171}\right)$	$e\left(\frac{31}{228}\right)$	$e\left(\frac{293}{684}\right)$	$e\left(\frac{269}{342}\right)$	$e\left(\frac{7}{684}\right)$	$e\left(\frac{313}{342}\right)$	$e\left(\frac{121}{342}\right)$
$\chi_{9386}(889,\cdot)$	$1$	$1$	$e\left(\frac{197}{342}\right)$	$e\left(\frac{649}{684}\right)$	$e\left(\frac{161}{228}\right)$	$e\left(\frac{26}{171}\right)$	$e\left(\frac{73}{228}\right)$	$e\left(\frac{359}{684}\right)$	$e\left(\frac{137}{342}\right)$	$e\left(\frac{193}{684}\right)$	$e\left(\frac{31}{342}\right)$	$e\left(\frac{307}{342}\right)$
$\chi_{9386}(915,\cdot)$	$1$	$1$	$e\left(\frac{61}{342}\right)$	$e\left(\frac{569}{684}\right)$	$e\left(\frac{73}{228}\right)$	$e\left(\frac{61}{171}\right)$	$e\left(\frac{77}{228}\right)$	$e\left(\frac{7}{684}\right)$	$e\left(\frac{157}{342}\right)$	$e\left(\frac{341}{684}\right)$	$e\left(\frac{53}{342}\right)$	$e\left(\frac{227}{342}\right)$
$\chi_{9386}(941,\cdot)$	$1$	$1$	$e\left(\frac{5}{342}\right)$	$e\left(\frac{13}{684}\right)$	$e\left(\frac{77}{228}\right)$	$e\left(\frac{5}{171}\right)$	$e\left(\frac{25}{228}\right)$	$e\left(\frac{23}{684}\right)$	$e\left(\frac{125}{342}\right)$	$e\left(\frac{241}{684}\right)$	$e\left(\frac{223}{342}\right)$	$e\left(\frac{13}{342}\right)$
$\chi_{9386}(983,\cdot)$	$1$	$1$	$e\left(\frac{307}{342}\right)$	$e\left(\frac{251}{684}\right)$	$e\left(\frac{31}{228}\right)$	$e\left(\frac{136}{171}\right)$	$e\left(\frac{167}{228}\right)$	$e\left(\frac{181}{684}\right)$	$e\left(\frac{151}{342}\right)$	$e\left(\frac{23}{684}\right)$	$e\left(\frac{149}{342}\right)$	$e\left(\frac{251}{342}\right)$
$\chi_{9386}(1009,\cdot)$	$1$	$1$	$e\left(\frac{67}{342}\right)$	$e\left(\frac{311}{684}\right)$	$e\left(\frac{211}{228}\right)$	$e\left(\frac{67}{171}\right)$	$e\left(\frac{107}{228}\right)$	$e\left(\frac{445}{684}\right)$	$e\left(\frac{307}{342}\right)$	$e\left(\frac{83}{684}\right)$	$e\left(\frac{47}{342}\right)$	$e\left(\frac{311}{342}\right)$
$\chi_{9386}(1097,\cdot)$	$1$	$1$	$e\left(\frac{127}{342}\right)$	$e\left(\frac{125}{684}\right)$	$e\left(\frac{109}{228}\right)$	$e\left(\frac{127}{171}\right)$	$e\left(\frac{65}{228}\right)$	$e\left(\frac{379}{684}\right)$	$e\left(\frac{97}{342}\right)$	$e\left(\frac{581}{684}\right)$	$e\left(\frac{329}{342}\right)$	$e\left(\frac{125}{342}\right)$
$\chi_{9386}(1123,\cdot)$	$1$	$1$	$e\left(\frac{175}{342}\right)$	$e\left(\frac{113}{684}\right)$	$e\left(\frac{73}{228}\right)$	$e\left(\frac{4}{171}\right)$	$e\left(\frac{77}{228}\right)$	$e\left(\frac{463}{684}\right)$	$e\left(\frac{271}{342}\right)$	$e\left(\frac{569}{684}\right)$	$e\left(\frac{281}{342}\right)$	$e\left(\frac{113}{342}\right)$
$\chi_{9386}(1191,\cdot)$	$1$	$1$	$e\left(\frac{101}{342}\right)$	$e\left(\frac{331}{684}\right)$	$e\left(\frac{119}{228}\right)$	$e\left(\frac{101}{171}\right)$	$e\left(\frac{163}{228}\right)$	$e\left(\frac{533}{684}\right)$	$e\left(\frac{131}{342}\right)$	$e\left(\frac{559}{684}\right)$	$e\left(\frac{127}{342}\right)$	$e\left(\frac{331}{342}\right)$
$\chi_{9386}(1269,\cdot)$	$1$	$1$	$e\left(\frac{17}{342}\right)$	$e\left(\frac{523}{684}\right)$	$e\left(\frac{11}{228}\right)$	$e\left(\frac{17}{171}\right)$	$e\left(\frac{199}{228}\right)$	$e\left(\frac{557}{684}\right)$	$e\left(\frac{83}{342}\right)$	$e\left(\frac{67}{684}\right)$	$e\left(\frac{211}{342}\right)$	$e\left(\frac{181}{342}\right)$
$\chi_{9386}(1295,\cdot)$	$1$	$1$	$e\left(\frac{187}{342}\right)$	$e\left(\frac{623}{684}\right)$	$e\left(\frac{7}{228}\right)$	$e\left(\frac{16}{171}\right)$	$e\left(\frac{23}{228}\right)$	$e\left(\frac{313}{684}\right)$	$e\left(\frac{229}{342}\right)$	$e\left(\frac{395}{684}\right)$	$e\left(\frac{269}{342}\right)$	$e\left(\frac{281}{342}\right)$
$\chi_{9386}(1305,\cdot)$	$1$	$1$	$e\left(\frac{65}{342}\right)$	$e\left(\frac{169}{684}\right)$	$e\left(\frac{89}{228}\right)$	$e\left(\frac{65}{171}\right)$	$e\left(\frac{97}{228}\right)$	$e\left(\frac{299}{684}\right)$	$e\left(\frac{257}{342}\right)$	$e\left(\frac{397}{684}\right)$	$e\left(\frac{163}{342}\right)$	$e\left(\frac{169}{342}\right)$
$\chi_{9386}(1321,\cdot)$	$1$	$1$	$e\left(\frac{77}{342}\right)$	$e\left(\frac{679}{684}\right)$	$e\left(\frac{23}{228}\right)$	$e\left(\frac{77}{171}\right)$	$e\left(\frac{43}{228}\right)$	$e\left(\frac{149}{684}\right)$	$e\left(\frac{215}{342}\right)$	$e\left(\frac{223}{684}\right)$	$e\left(\frac{151}{342}\right)$	$e\left(\frac{337}{342}\right)$
$\chi_{9386}(1383,\cdot)$	$1$	$1$	$e\left(\frac{305}{342}\right)$	$e\left(\frac{109}{684}\right)$	$e\left(\frac{137}{228}\right)$	$e\left(\frac{134}{171}\right)$	$e\left(\frac{157}{228}\right)$	$e\left(\frac{35}{684}\right)$	$e\left(\frac{101}{342}\right)$	$e\left(\frac{337}{684}\right)$	$e\left(\frac{265}{342}\right)$	$e\left(\frac{109}{342}\right)$

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	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(15\)	\(17\)	\(21\)	\(23\)	\(25\)
\(\chi_{9386}(21,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{157}{342}\right)\)	\(e\left(\frac{203}{684}\right)\)	\(e\left(\frac{115}{228}\right)\)	\(e\left(\frac{157}{171}\right)\)	\(e\left(\frac{215}{228}\right)\)	\(e\left(\frac{517}{684}\right)\)	\(e\left(\frac{163}{342}\right)\)	\(e\left(\frac{659}{684}\right)\)	\(e\left(\frac{299}{342}\right)\)	\(e\left(\frac{203}{342}\right)\)
\(\chi_{9386}(109,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{91}{342}\right)\)	\(e\left(\frac{305}{684}\right)\)	\(e\left(\frac{193}{228}\right)\)	\(e\left(\frac{91}{171}\right)\)	\(e\left(\frac{113}{228}\right)\)	\(e\left(\frac{487}{684}\right)\)	\(e\left(\frac{223}{342}\right)\)	\(e\left(\frac{77}{684}\right)\)	\(e\left(\frac{23}{342}\right)\)	\(e\left(\frac{305}{342}\right)\)
\(\chi_{9386}(135,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{265}{342}\right)\)	\(e\left(\frac{5}{684}\right)\)	\(e\left(\frac{205}{228}\right)\)	\(e\left(\frac{94}{171}\right)\)	\(e\left(\frac{185}{228}\right)\)	\(e\left(\frac{535}{684}\right)\)	\(e\left(\frac{127}{342}\right)\)	\(e\left(\frac{461}{684}\right)\)	\(e\left(\frac{191}{342}\right)\)	\(e\left(\frac{5}{342}\right)\)
\(\chi_{9386}(203,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{299}{342}\right)\)	\(e\left(\frac{367}{684}\right)\)	\(e\left(\frac{227}{228}\right)\)	\(e\left(\frac{128}{171}\right)\)	\(e\left(\frac{127}{228}\right)\)	\(e\left(\frac{281}{684}\right)\)	\(e\left(\frac{293}{342}\right)\)	\(e\left(\frac{595}{684}\right)\)	\(e\left(\frac{271}{342}\right)\)	\(e\left(\frac{25}{342}\right)\)
\(\chi_{9386}(281,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{143}{342}\right)\)	\(e\left(\frac{235}{684}\right)\)	\(e\left(\frac{59}{228}\right)\)	\(e\left(\frac{143}{171}\right)\)	\(e\left(\frac{31}{228}\right)\)	\(e\left(\frac{521}{684}\right)\)	\(e\left(\frac{155}{342}\right)\)	\(e\left(\frac{463}{684}\right)\)	\(e\left(\frac{85}{342}\right)\)	\(e\left(\frac{235}{342}\right)\)
\(\chi_{9386}(317,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{263}{342}\right)\)	\(e\left(\frac{205}{684}\right)\)	\(e\left(\frac{197}{228}\right)\)	\(e\left(\frac{92}{171}\right)\)	\(e\left(\frac{61}{228}\right)\)	\(e\left(\frac{47}{684}\right)\)	\(e\left(\frac{77}{342}\right)\)	\(e\left(\frac{433}{684}\right)\)	\(e\left(\frac{307}{342}\right)\)	\(e\left(\frac{205}{342}\right)\)
\(\chi_{9386}(395,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{89}{342}\right)\)	\(e\left(\frac{505}{684}\right)\)	\(e\left(\frac{185}{228}\right)\)	\(e\left(\frac{89}{171}\right)\)	\(e\left(\frac{217}{228}\right)\)	\(e\left(\frac{683}{684}\right)\)	\(e\left(\frac{173}{342}\right)\)	\(e\left(\frac{49}{684}\right)\)	\(e\left(\frac{139}{342}\right)\)	\(e\left(\frac{163}{342}\right)\)
\(\chi_{9386}(421,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{205}{342}\right)\)	\(e\left(\frac{533}{684}\right)\)	\(e\left(\frac{193}{228}\right)\)	\(e\left(\frac{34}{171}\right)\)	\(e\left(\frac{113}{228}\right)\)	\(e\left(\frac{259}{684}\right)\)	\(e\left(\frac{337}{342}\right)\)	\(e\left(\frac{305}{684}\right)\)	\(e\left(\frac{251}{342}\right)\)	\(e\left(\frac{191}{342}\right)\)
\(\chi_{9386}(447,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{185}{342}\right)\)	\(e\left(\frac{481}{684}\right)\)	\(e\left(\frac{113}{228}\right)\)	\(e\left(\frac{14}{171}\right)\)	\(e\left(\frac{13}{228}\right)\)	\(e\left(\frac{167}{684}\right)\)	\(e\left(\frac{179}{342}\right)\)	\(e\left(\frac{25}{684}\right)\)	\(e\left(\frac{43}{342}\right)\)	\(e\left(\frac{139}{342}\right)\)
\(\chi_{9386}(489,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{289}{342}\right)\)	\(e\left(\frac{683}{684}\right)\)	\(e\left(\frac{187}{228}\right)\)	\(e\left(\frac{118}{171}\right)\)	\(e\left(\frac{191}{228}\right)\)	\(e\left(\frac{577}{684}\right)\)	\(e\left(\frac{43}{342}\right)\)	\(e\left(\frac{455}{684}\right)\)	\(e\left(\frac{167}{342}\right)\)	\(e\left(\frac{341}{342}\right)\)
\(\chi_{9386}(515,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{283}{342}\right)\)	\(e\left(\frac{599}{684}\right)\)	\(e\left(\frac{163}{228}\right)\)	\(e\left(\frac{112}{171}\right)\)	\(e\left(\frac{47}{228}\right)\)	\(e\left(\frac{481}{684}\right)\)	\(e\left(\frac{235}{342}\right)\)	\(e\left(\frac{371}{684}\right)\)	\(e\left(\frac{173}{342}\right)\)	\(e\left(\frac{257}{342}\right)\)
\(\chi_{9386}(603,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{109}{342}\right)\)	\(e\left(\frac{557}{684}\right)\)	\(e\left(\frac{37}{228}\right)\)	\(e\left(\frac{109}{171}\right)\)	\(e\left(\frac{89}{228}\right)\)	\(e\left(\frac{91}{684}\right)\)	\(e\left(\frac{331}{342}\right)\)	\(e\left(\frac{329}{684}\right)\)	\(e\left(\frac{5}{342}\right)\)	\(e\left(\frac{215}{342}\right)\)
\(\chi_{9386}(629,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{49}{342}\right)\)	\(e\left(\frac{401}{684}\right)\)	\(e\left(\frac{25}{228}\right)\)	\(e\left(\frac{49}{171}\right)\)	\(e\left(\frac{17}{228}\right)\)	\(e\left(\frac{499}{684}\right)\)	\(e\left(\frac{199}{342}\right)\)	\(e\left(\frac{173}{684}\right)\)	\(e\left(\frac{65}{342}\right)\)	\(e\left(\frac{59}{342}\right)\)
\(\chi_{9386}(697,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{342}\right)\)	\(e\left(\frac{7}{684}\right)\)	\(e\left(\frac{59}{228}\right)\)	\(e\left(\frac{29}{171}\right)\)	\(e\left(\frac{31}{228}\right)\)	\(e\left(\frac{65}{684}\right)\)	\(e\left(\frac{41}{342}\right)\)	\(e\left(\frac{235}{684}\right)\)	\(e\left(\frac{199}{342}\right)\)	\(e\left(\frac{7}{342}\right)\)
\(\chi_{9386}(775,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{251}{342}\right)\)	\(e\left(\frac{379}{684}\right)\)	\(e\left(\frac{35}{228}\right)\)	\(e\left(\frac{80}{171}\right)\)	\(e\left(\frac{115}{228}\right)\)	\(e\left(\frac{197}{684}\right)\)	\(e\left(\frac{119}{342}\right)\)	\(e\left(\frac{607}{684}\right)\)	\(e\left(\frac{319}{342}\right)\)	\(e\left(\frac{37}{342}\right)\)
\(\chi_{9386}(801,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{331}{342}\right)\)	\(e\left(\frac{587}{684}\right)\)	\(e\left(\frac{127}{228}\right)\)	\(e\left(\frac{160}{171}\right)\)	\(e\left(\frac{59}{228}\right)\)	\(e\left(\frac{565}{684}\right)\)	\(e\left(\frac{67}{342}\right)\)	\(e\left(\frac{359}{684}\right)\)	\(e\left(\frac{125}{342}\right)\)	\(e\left(\frac{245}{342}\right)\)
\(\chi_{9386}(811,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{335}{342}\right)\)	\(e\left(\frac{529}{684}\right)\)	\(e\left(\frac{29}{228}\right)\)	\(e\left(\frac{164}{171}\right)\)	\(e\left(\frac{193}{228}\right)\)	\(e\left(\frac{515}{684}\right)\)	\(e\left(\frac{167}{342}\right)\)	\(e\left(\frac{73}{684}\right)\)	\(e\left(\frac{235}{342}\right)\)	\(e\left(\frac{187}{342}\right)\)
\(\chi_{9386}(827,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{257}{342}\right)\)	\(e\left(\frac{463}{684}\right)\)	\(e\left(\frac{59}{228}\right)\)	\(e\left(\frac{86}{171}\right)\)	\(e\left(\frac{31}{228}\right)\)	\(e\left(\frac{293}{684}\right)\)	\(e\left(\frac{269}{342}\right)\)	\(e\left(\frac{7}{684}\right)\)	\(e\left(\frac{313}{342}\right)\)	\(e\left(\frac{121}{342}\right)\)
\(\chi_{9386}(889,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{197}{342}\right)\)	\(e\left(\frac{649}{684}\right)\)	\(e\left(\frac{161}{228}\right)\)	\(e\left(\frac{26}{171}\right)\)	\(e\left(\frac{73}{228}\right)\)	\(e\left(\frac{359}{684}\right)\)	\(e\left(\frac{137}{342}\right)\)	\(e\left(\frac{193}{684}\right)\)	\(e\left(\frac{31}{342}\right)\)	\(e\left(\frac{307}{342}\right)\)
\(\chi_{9386}(915,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{61}{342}\right)\)	\(e\left(\frac{569}{684}\right)\)	\(e\left(\frac{73}{228}\right)\)	\(e\left(\frac{61}{171}\right)\)	\(e\left(\frac{77}{228}\right)\)	\(e\left(\frac{7}{684}\right)\)	\(e\left(\frac{157}{342}\right)\)	\(e\left(\frac{341}{684}\right)\)	\(e\left(\frac{53}{342}\right)\)	\(e\left(\frac{227}{342}\right)\)
\(\chi_{9386}(941,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{342}\right)\)	\(e\left(\frac{13}{684}\right)\)	\(e\left(\frac{77}{228}\right)\)	\(e\left(\frac{5}{171}\right)\)	\(e\left(\frac{25}{228}\right)\)	\(e\left(\frac{23}{684}\right)\)	\(e\left(\frac{125}{342}\right)\)	\(e\left(\frac{241}{684}\right)\)	\(e\left(\frac{223}{342}\right)\)	\(e\left(\frac{13}{342}\right)\)
\(\chi_{9386}(983,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{307}{342}\right)\)	\(e\left(\frac{251}{684}\right)\)	\(e\left(\frac{31}{228}\right)\)	\(e\left(\frac{136}{171}\right)\)	\(e\left(\frac{167}{228}\right)\)	\(e\left(\frac{181}{684}\right)\)	\(e\left(\frac{151}{342}\right)\)	\(e\left(\frac{23}{684}\right)\)	\(e\left(\frac{149}{342}\right)\)	\(e\left(\frac{251}{342}\right)\)
\(\chi_{9386}(1009,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{67}{342}\right)\)	\(e\left(\frac{311}{684}\right)\)	\(e\left(\frac{211}{228}\right)\)	\(e\left(\frac{67}{171}\right)\)	\(e\left(\frac{107}{228}\right)\)	\(e\left(\frac{445}{684}\right)\)	\(e\left(\frac{307}{342}\right)\)	\(e\left(\frac{83}{684}\right)\)	\(e\left(\frac{47}{342}\right)\)	\(e\left(\frac{311}{342}\right)\)
\(\chi_{9386}(1097,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{127}{342}\right)\)	\(e\left(\frac{125}{684}\right)\)	\(e\left(\frac{109}{228}\right)\)	\(e\left(\frac{127}{171}\right)\)	\(e\left(\frac{65}{228}\right)\)	\(e\left(\frac{379}{684}\right)\)	\(e\left(\frac{97}{342}\right)\)	\(e\left(\frac{581}{684}\right)\)	\(e\left(\frac{329}{342}\right)\)	\(e\left(\frac{125}{342}\right)\)
\(\chi_{9386}(1123,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{175}{342}\right)\)	\(e\left(\frac{113}{684}\right)\)	\(e\left(\frac{73}{228}\right)\)	\(e\left(\frac{4}{171}\right)\)	\(e\left(\frac{77}{228}\right)\)	\(e\left(\frac{463}{684}\right)\)	\(e\left(\frac{271}{342}\right)\)	\(e\left(\frac{569}{684}\right)\)	\(e\left(\frac{281}{342}\right)\)	\(e\left(\frac{113}{342}\right)\)
\(\chi_{9386}(1191,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{101}{342}\right)\)	\(e\left(\frac{331}{684}\right)\)	\(e\left(\frac{119}{228}\right)\)	\(e\left(\frac{101}{171}\right)\)	\(e\left(\frac{163}{228}\right)\)	\(e\left(\frac{533}{684}\right)\)	\(e\left(\frac{131}{342}\right)\)	\(e\left(\frac{559}{684}\right)\)	\(e\left(\frac{127}{342}\right)\)	\(e\left(\frac{331}{342}\right)\)
\(\chi_{9386}(1269,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{342}\right)\)	\(e\left(\frac{523}{684}\right)\)	\(e\left(\frac{11}{228}\right)\)	\(e\left(\frac{17}{171}\right)\)	\(e\left(\frac{199}{228}\right)\)	\(e\left(\frac{557}{684}\right)\)	\(e\left(\frac{83}{342}\right)\)	\(e\left(\frac{67}{684}\right)\)	\(e\left(\frac{211}{342}\right)\)	\(e\left(\frac{181}{342}\right)\)
\(\chi_{9386}(1295,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{187}{342}\right)\)	\(e\left(\frac{623}{684}\right)\)	\(e\left(\frac{7}{228}\right)\)	\(e\left(\frac{16}{171}\right)\)	\(e\left(\frac{23}{228}\right)\)	\(e\left(\frac{313}{684}\right)\)	\(e\left(\frac{229}{342}\right)\)	\(e\left(\frac{395}{684}\right)\)	\(e\left(\frac{269}{342}\right)\)	\(e\left(\frac{281}{342}\right)\)
\(\chi_{9386}(1305,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{65}{342}\right)\)	\(e\left(\frac{169}{684}\right)\)	\(e\left(\frac{89}{228}\right)\)	\(e\left(\frac{65}{171}\right)\)	\(e\left(\frac{97}{228}\right)\)	\(e\left(\frac{299}{684}\right)\)	\(e\left(\frac{257}{342}\right)\)	\(e\left(\frac{397}{684}\right)\)	\(e\left(\frac{163}{342}\right)\)	\(e\left(\frac{169}{342}\right)\)
\(\chi_{9386}(1321,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{77}{342}\right)\)	\(e\left(\frac{679}{684}\right)\)	\(e\left(\frac{23}{228}\right)\)	\(e\left(\frac{77}{171}\right)\)	\(e\left(\frac{43}{228}\right)\)	\(e\left(\frac{149}{684}\right)\)	\(e\left(\frac{215}{342}\right)\)	\(e\left(\frac{223}{684}\right)\)	\(e\left(\frac{151}{342}\right)\)	\(e\left(\frac{337}{342}\right)\)
\(\chi_{9386}(1383,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{305}{342}\right)\)	\(e\left(\frac{109}{684}\right)\)	\(e\left(\frac{137}{228}\right)\)	\(e\left(\frac{134}{171}\right)\)	\(e\left(\frac{157}{228}\right)\)	\(e\left(\frac{35}{684}\right)\)	\(e\left(\frac{101}{342}\right)\)	\(e\left(\frac{337}{684}\right)\)	\(e\left(\frac{265}{342}\right)\)	\(e\left(\frac{109}{342}\right)\)

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First 31 of 216 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.dm
Modulus	$9386$
Conductor	$4693$
Order	$684$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(9386\)
Conductor:	\(4693\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(684\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 4693.dp	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)