LMFDB - Dirichlet character orbit 9386.dh

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(9386, base_ring=CyclotomicField(342)) M = H._module chi = DirichletCharacter(H, M([171,122])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(25,9386)) 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:	$342$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 4693.df	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:	$\Q(\zeta_{171})$
Fixed field:	Number field defined by a degree 342 polynomial (not computed)

First 31 of 108 characters in Galois orbit

Character	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$15$	$17$	$21$	$23$	$25$
$\chi_{9386}(25,\cdot)$	$1$	$1$	$e\left(\frac{100}{171}\right)$	$e\left(\frac{89}{342}\right)$	$e\left(\frac{1}{114}\right)$	$e\left(\frac{29}{171}\right)$	$e\left(\frac{101}{114}\right)$	$e\left(\frac{289}{342}\right)$	$e\left(\frac{106}{171}\right)$	$e\left(\frac{203}{342}\right)$	$e\left(\frac{14}{171}\right)$	$e\left(\frac{89}{171}\right)$
$\chi_{9386}(207,\cdot)$	$1$	$1$	$e\left(\frac{56}{171}\right)$	$e\left(\frac{43}{342}\right)$	$e\left(\frac{53}{114}\right)$	$e\left(\frac{112}{171}\right)$	$e\left(\frac{109}{114}\right)$	$e\left(\frac{155}{342}\right)$	$e\left(\frac{32}{171}\right)$	$e\left(\frac{271}{342}\right)$	$e\left(\frac{1}{171}\right)$	$e\left(\frac{43}{171}\right)$
$\chi_{9386}(233,\cdot)$	$1$	$1$	$e\left(\frac{59}{171}\right)$	$e\left(\frac{85}{342}\right)$	$e\left(\frac{65}{114}\right)$	$e\left(\frac{118}{171}\right)$	$e\left(\frac{67}{114}\right)$	$e\left(\frac{203}{342}\right)$	$e\left(\frac{107}{171}\right)$	$e\left(\frac{313}{342}\right)$	$e\left(\frac{169}{171}\right)$	$e\left(\frac{85}{171}\right)$
$\chi_{9386}(441,\cdot)$	$1$	$1$	$e\left(\frac{157}{171}\right)$	$e\left(\frac{203}{342}\right)$	$e\left(\frac{1}{114}\right)$	$e\left(\frac{143}{171}\right)$	$e\left(\frac{101}{114}\right)$	$e\left(\frac{175}{342}\right)$	$e\left(\frac{163}{171}\right)$	$e\left(\frac{317}{342}\right)$	$e\left(\frac{128}{171}\right)$	$e\left(\frac{32}{171}\right)$
$\chi_{9386}(519,\cdot)$	$1$	$1$	$e\left(\frac{64}{171}\right)$	$e\left(\frac{269}{342}\right)$	$e\left(\frac{85}{114}\right)$	$e\left(\frac{128}{171}\right)$	$e\left(\frac{35}{114}\right)$	$e\left(\frac{55}{342}\right)$	$e\left(\frac{61}{171}\right)$	$e\left(\frac{41}{342}\right)$	$e\left(\frac{50}{171}\right)$	$e\left(\frac{98}{171}\right)$
$\chi_{9386}(701,\cdot)$	$1$	$1$	$e\left(\frac{164}{171}\right)$	$e\left(\frac{187}{342}\right)$	$e\left(\frac{29}{114}\right)$	$e\left(\frac{157}{171}\right)$	$e\left(\frac{79}{114}\right)$	$e\left(\frac{173}{342}\right)$	$e\left(\frac{167}{171}\right)$	$e\left(\frac{73}{342}\right)$	$e\left(\frac{64}{171}\right)$	$e\left(\frac{16}{171}\right)$
$\chi_{9386}(727,\cdot)$	$1$	$1$	$e\left(\frac{50}{171}\right)$	$e\left(\frac{301}{342}\right)$	$e\left(\frac{29}{114}\right)$	$e\left(\frac{100}{171}\right)$	$e\left(\frac{79}{114}\right)$	$e\left(\frac{59}{342}\right)$	$e\left(\frac{53}{171}\right)$	$e\left(\frac{187}{342}\right)$	$e\left(\frac{7}{171}\right)$	$e\left(\frac{130}{171}\right)$
$\chi_{9386}(883,\cdot)$	$1$	$1$	$e\left(\frac{52}{171}\right)$	$e\left(\frac{101}{342}\right)$	$e\left(\frac{37}{114}\right)$	$e\left(\frac{104}{171}\right)$	$e\left(\frac{89}{114}\right)$	$e\left(\frac{205}{342}\right)$	$e\left(\frac{103}{171}\right)$	$e\left(\frac{215}{342}\right)$	$e\left(\frac{62}{171}\right)$	$e\left(\frac{101}{171}\right)$
$\chi_{9386}(909,\cdot)$	$1$	$1$	$e\left(\frac{53}{171}\right)$	$e\left(\frac{1}{342}\right)$	$e\left(\frac{41}{114}\right)$	$e\left(\frac{106}{171}\right)$	$e\left(\frac{37}{114}\right)$	$e\left(\frac{107}{342}\right)$	$e\left(\frac{128}{171}\right)$	$e\left(\frac{229}{342}\right)$	$e\left(\frac{4}{171}\right)$	$e\left(\frac{1}{171}\right)$
$\chi_{9386}(935,\cdot)$	$1$	$1$	$e\left(\frac{103}{171}\right)$	$e\left(\frac{131}{342}\right)$	$e\left(\frac{13}{114}\right)$	$e\left(\frac{35}{171}\right)$	$e\left(\frac{59}{114}\right)$	$e\left(\frac{337}{342}\right)$	$e\left(\frac{10}{171}\right)$	$e\left(\frac{245}{342}\right)$	$e\left(\frac{11}{171}\right)$	$e\left(\frac{131}{171}\right)$
$\chi_{9386}(1013,\cdot)$	$1$	$1$	$e\left(\frac{28}{171}\right)$	$e\left(\frac{107}{342}\right)$	$e\left(\frac{55}{114}\right)$	$e\left(\frac{56}{171}\right)$	$e\left(\frac{83}{114}\right)$	$e\left(\frac{163}{342}\right)$	$e\left(\frac{16}{171}\right)$	$e\left(\frac{221}{342}\right)$	$e\left(\frac{86}{171}\right)$	$e\left(\frac{107}{171}\right)$
$\chi_{9386}(1195,\cdot)$	$1$	$1$	$e\left(\frac{101}{171}\right)$	$e\left(\frac{331}{342}\right)$	$e\left(\frac{5}{114}\right)$	$e\left(\frac{31}{171}\right)$	$e\left(\frac{49}{114}\right)$	$e\left(\frac{191}{342}\right)$	$e\left(\frac{131}{171}\right)$	$e\left(\frac{217}{342}\right)$	$e\left(\frac{127}{171}\right)$	$e\left(\frac{160}{171}\right)$
$\chi_{9386}(1221,\cdot)$	$1$	$1$	$e\left(\frac{41}{171}\right)$	$e\left(\frac{175}{342}\right)$	$e\left(\frac{107}{114}\right)$	$e\left(\frac{82}{171}\right)$	$e\left(\frac{91}{114}\right)$	$e\left(\frac{257}{342}\right)$	$e\left(\frac{170}{171}\right)$	$e\left(\frac{61}{342}\right)$	$e\left(\frac{16}{171}\right)$	$e\left(\frac{4}{171}\right)$
$\chi_{9386}(1377,\cdot)$	$1$	$1$	$e\left(\frac{142}{171}\right)$	$e\left(\frac{335}{342}\right)$	$e\left(\frac{55}{114}\right)$	$e\left(\frac{113}{171}\right)$	$e\left(\frac{83}{114}\right)$	$e\left(\frac{277}{342}\right)$	$e\left(\frac{130}{171}\right)$	$e\left(\frac{107}{342}\right)$	$e\left(\frac{143}{171}\right)$	$e\left(\frac{164}{171}\right)$
$\chi_{9386}(1403,\cdot)$	$1$	$1$	$e\left(\frac{125}{171}\right)$	$e\left(\frac{325}{342}\right)$	$e\left(\frac{101}{114}\right)$	$e\left(\frac{79}{171}\right)$	$e\left(\frac{55}{114}\right)$	$e\left(\frac{233}{342}\right)$	$e\left(\frac{47}{171}\right)$	$e\left(\frac{211}{342}\right)$	$e\left(\frac{103}{171}\right)$	$e\left(\frac{154}{171}\right)$
$\chi_{9386}(1429,\cdot)$	$1$	$1$	$e\left(\frac{49}{171}\right)$	$e\left(\frac{59}{342}\right)$	$e\left(\frac{25}{114}\right)$	$e\left(\frac{98}{171}\right)$	$e\left(\frac{17}{114}\right)$	$e\left(\frac{157}{342}\right)$	$e\left(\frac{28}{171}\right)$	$e\left(\frac{173}{342}\right)$	$e\left(\frac{65}{171}\right)$	$e\left(\frac{59}{171}\right)$
$\chi_{9386}(1507,\cdot)$	$1$	$1$	$e\left(\frac{163}{171}\right)$	$e\left(\frac{287}{342}\right)$	$e\left(\frac{25}{114}\right)$	$e\left(\frac{155}{171}\right)$	$e\left(\frac{17}{114}\right)$	$e\left(\frac{271}{342}\right)$	$e\left(\frac{142}{171}\right)$	$e\left(\frac{59}{342}\right)$	$e\left(\frac{122}{171}\right)$	$e\left(\frac{116}{171}\right)$
$\chi_{9386}(1715,\cdot)$	$1$	$1$	$e\left(\frac{32}{171}\right)$	$e\left(\frac{49}{342}\right)$	$e\left(\frac{71}{114}\right)$	$e\left(\frac{64}{171}\right)$	$e\left(\frac{103}{114}\right)$	$e\left(\frac{113}{342}\right)$	$e\left(\frac{116}{171}\right)$	$e\left(\frac{277}{342}\right)$	$e\left(\frac{25}{171}\right)$	$e\left(\frac{49}{171}\right)$
$\chi_{9386}(1871,\cdot)$	$1$	$1$	$e\left(\frac{61}{171}\right)$	$e\left(\frac{227}{342}\right)$	$e\left(\frac{73}{114}\right)$	$e\left(\frac{122}{171}\right)$	$e\left(\frac{77}{114}\right)$	$e\left(\frac{7}{342}\right)$	$e\left(\frac{157}{171}\right)$	$e\left(\frac{341}{342}\right)$	$e\left(\frac{53}{171}\right)$	$e\left(\frac{56}{171}\right)$
$\chi_{9386}(1897,\cdot)$	$1$	$1$	$e\left(\frac{26}{171}\right)$	$e\left(\frac{307}{342}\right)$	$e\left(\frac{47}{114}\right)$	$e\left(\frac{52}{171}\right)$	$e\left(\frac{73}{114}\right)$	$e\left(\frac{17}{342}\right)$	$e\left(\frac{137}{171}\right)$	$e\left(\frac{193}{342}\right)$	$e\left(\frac{31}{171}\right)$	$e\left(\frac{136}{171}\right)$
$\chi_{9386}(1923,\cdot)$	$1$	$1$	$e\left(\frac{166}{171}\right)$	$e\left(\frac{329}{342}\right)$	$e\left(\frac{37}{114}\right)$	$e\left(\frac{161}{171}\right)$	$e\left(\frac{89}{114}\right)$	$e\left(\frac{319}{342}\right)$	$e\left(\frac{46}{171}\right)$	$e\left(\frac{101}{342}\right)$	$e\left(\frac{119}{171}\right)$	$e\left(\frac{158}{171}\right)$
$\chi_{9386}(2001,\cdot)$	$1$	$1$	$e\left(\frac{127}{171}\right)$	$e\left(\frac{125}{342}\right)$	$e\left(\frac{109}{114}\right)$	$e\left(\frac{83}{171}\right)$	$e\left(\frac{65}{114}\right)$	$e\left(\frac{37}{342}\right)$	$e\left(\frac{97}{171}\right)$	$e\left(\frac{239}{342}\right)$	$e\left(\frac{158}{171}\right)$	$e\left(\frac{125}{171}\right)$
$\chi_{9386}(2183,\cdot)$	$1$	$1$	$e\left(\frac{146}{171}\right)$	$e\left(\frac{277}{342}\right)$	$e\left(\frac{71}{114}\right)$	$e\left(\frac{121}{171}\right)$	$e\left(\frac{103}{114}\right)$	$e\left(\frac{227}{342}\right)$	$e\left(\frac{59}{171}\right)$	$e\left(\frac{163}{342}\right)$	$e\left(\frac{82}{171}\right)$	$e\left(\frac{106}{171}\right)$
$\chi_{9386}(2209,\cdot)$	$1$	$1$	$e\left(\frac{23}{171}\right)$	$e\left(\frac{265}{342}\right)$	$e\left(\frac{35}{114}\right)$	$e\left(\frac{46}{171}\right)$	$e\left(\frac{1}{114}\right)$	$e\left(\frac{311}{342}\right)$	$e\left(\frac{62}{171}\right)$	$e\left(\frac{151}{342}\right)$	$e\left(\frac{34}{171}\right)$	$e\left(\frac{94}{171}\right)$
$\chi_{9386}(2365,\cdot)$	$1$	$1$	$e\left(\frac{151}{171}\right)$	$e\left(\frac{119}{342}\right)$	$e\left(\frac{91}{114}\right)$	$e\left(\frac{131}{171}\right)$	$e\left(\frac{71}{114}\right)$	$e\left(\frac{79}{342}\right)$	$e\left(\frac{13}{171}\right)$	$e\left(\frac{233}{342}\right)$	$e\left(\frac{134}{171}\right)$	$e\left(\frac{119}{171}\right)$
$\chi_{9386}(2391,\cdot)$	$1$	$1$	$e\left(\frac{98}{171}\right)$	$e\left(\frac{289}{342}\right)$	$e\left(\frac{107}{114}\right)$	$e\left(\frac{25}{171}\right)$	$e\left(\frac{91}{114}\right)$	$e\left(\frac{143}{342}\right)$	$e\left(\frac{56}{171}\right)$	$e\left(\frac{175}{342}\right)$	$e\left(\frac{130}{171}\right)$	$e\left(\frac{118}{171}\right)$
$\chi_{9386}(2417,\cdot)$	$1$	$1$	$e\left(\frac{112}{171}\right)$	$e\left(\frac{257}{342}\right)$	$e\left(\frac{49}{114}\right)$	$e\left(\frac{53}{171}\right)$	$e\left(\frac{47}{114}\right)$	$e\left(\frac{139}{342}\right)$	$e\left(\frac{64}{171}\right)$	$e\left(\frac{29}{342}\right)$	$e\left(\frac{2}{171}\right)$	$e\left(\frac{86}{171}\right)$
$\chi_{9386}(2495,\cdot)$	$1$	$1$	$e\left(\frac{91}{171}\right)$	$e\left(\frac{305}{342}\right)$	$e\left(\frac{79}{114}\right)$	$e\left(\frac{11}{171}\right)$	$e\left(\frac{113}{114}\right)$	$e\left(\frac{145}{342}\right)$	$e\left(\frac{52}{171}\right)$	$e\left(\frac{77}{342}\right)$	$e\left(\frac{23}{171}\right)$	$e\left(\frac{134}{171}\right)$
$\chi_{9386}(2677,\cdot)$	$1$	$1$	$e\left(\frac{83}{171}\right)$	$e\left(\frac{79}{342}\right)$	$e\left(\frac{47}{114}\right)$	$e\left(\frac{166}{171}\right)$	$e\left(\frac{73}{114}\right)$	$e\left(\frac{245}{342}\right)$	$e\left(\frac{23}{171}\right)$	$e\left(\frac{307}{342}\right)$	$e\left(\frac{145}{171}\right)$	$e\left(\frac{79}{171}\right)$
$\chi_{9386}(2703,\cdot)$	$1$	$1$	$e\left(\frac{14}{171}\right)$	$e\left(\frac{139}{342}\right)$	$e\left(\frac{113}{114}\right)$	$e\left(\frac{28}{171}\right)$	$e\left(\frac{13}{114}\right)$	$e\left(\frac{167}{342}\right)$	$e\left(\frac{8}{171}\right)$	$e\left(\frac{25}{342}\right)$	$e\left(\frac{43}{171}\right)$	$e\left(\frac{139}{171}\right)$
$\chi_{9386}(2859,\cdot)$	$1$	$1$	$e\left(\frac{70}{171}\right)$	$e\left(\frac{11}{342}\right)$	$e\left(\frac{109}{114}\right)$	$e\left(\frac{140}{171}\right)$	$e\left(\frac{65}{114}\right)$	$e\left(\frac{151}{342}\right)$	$e\left(\frac{40}{171}\right)$	$e\left(\frac{125}{342}\right)$	$e\left(\frac{44}{171}\right)$	$e\left(\frac{11}{171}\right)$

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	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(15\)	\(17\)	\(21\)	\(23\)	\(25\)
\(\chi_{9386}(25,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{100}{171}\right)\)	\(e\left(\frac{89}{342}\right)\)	\(e\left(\frac{1}{114}\right)\)	\(e\left(\frac{29}{171}\right)\)	\(e\left(\frac{101}{114}\right)\)	\(e\left(\frac{289}{342}\right)\)	\(e\left(\frac{106}{171}\right)\)	\(e\left(\frac{203}{342}\right)\)	\(e\left(\frac{14}{171}\right)\)	\(e\left(\frac{89}{171}\right)\)
\(\chi_{9386}(207,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{56}{171}\right)\)	\(e\left(\frac{43}{342}\right)\)	\(e\left(\frac{53}{114}\right)\)	\(e\left(\frac{112}{171}\right)\)	\(e\left(\frac{109}{114}\right)\)	\(e\left(\frac{155}{342}\right)\)	\(e\left(\frac{32}{171}\right)\)	\(e\left(\frac{271}{342}\right)\)	\(e\left(\frac{1}{171}\right)\)	\(e\left(\frac{43}{171}\right)\)
\(\chi_{9386}(233,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{171}\right)\)	\(e\left(\frac{85}{342}\right)\)	\(e\left(\frac{65}{114}\right)\)	\(e\left(\frac{118}{171}\right)\)	\(e\left(\frac{67}{114}\right)\)	\(e\left(\frac{203}{342}\right)\)	\(e\left(\frac{107}{171}\right)\)	\(e\left(\frac{313}{342}\right)\)	\(e\left(\frac{169}{171}\right)\)	\(e\left(\frac{85}{171}\right)\)
\(\chi_{9386}(441,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{157}{171}\right)\)	\(e\left(\frac{203}{342}\right)\)	\(e\left(\frac{1}{114}\right)\)	\(e\left(\frac{143}{171}\right)\)	\(e\left(\frac{101}{114}\right)\)	\(e\left(\frac{175}{342}\right)\)	\(e\left(\frac{163}{171}\right)\)	\(e\left(\frac{317}{342}\right)\)	\(e\left(\frac{128}{171}\right)\)	\(e\left(\frac{32}{171}\right)\)
\(\chi_{9386}(519,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{64}{171}\right)\)	\(e\left(\frac{269}{342}\right)\)	\(e\left(\frac{85}{114}\right)\)	\(e\left(\frac{128}{171}\right)\)	\(e\left(\frac{35}{114}\right)\)	\(e\left(\frac{55}{342}\right)\)	\(e\left(\frac{61}{171}\right)\)	\(e\left(\frac{41}{342}\right)\)	\(e\left(\frac{50}{171}\right)\)	\(e\left(\frac{98}{171}\right)\)
\(\chi_{9386}(701,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{164}{171}\right)\)	\(e\left(\frac{187}{342}\right)\)	\(e\left(\frac{29}{114}\right)\)	\(e\left(\frac{157}{171}\right)\)	\(e\left(\frac{79}{114}\right)\)	\(e\left(\frac{173}{342}\right)\)	\(e\left(\frac{167}{171}\right)\)	\(e\left(\frac{73}{342}\right)\)	\(e\left(\frac{64}{171}\right)\)	\(e\left(\frac{16}{171}\right)\)
\(\chi_{9386}(727,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{50}{171}\right)\)	\(e\left(\frac{301}{342}\right)\)	\(e\left(\frac{29}{114}\right)\)	\(e\left(\frac{100}{171}\right)\)	\(e\left(\frac{79}{114}\right)\)	\(e\left(\frac{59}{342}\right)\)	\(e\left(\frac{53}{171}\right)\)	\(e\left(\frac{187}{342}\right)\)	\(e\left(\frac{7}{171}\right)\)	\(e\left(\frac{130}{171}\right)\)
\(\chi_{9386}(883,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{52}{171}\right)\)	\(e\left(\frac{101}{342}\right)\)	\(e\left(\frac{37}{114}\right)\)	\(e\left(\frac{104}{171}\right)\)	\(e\left(\frac{89}{114}\right)\)	\(e\left(\frac{205}{342}\right)\)	\(e\left(\frac{103}{171}\right)\)	\(e\left(\frac{215}{342}\right)\)	\(e\left(\frac{62}{171}\right)\)	\(e\left(\frac{101}{171}\right)\)
\(\chi_{9386}(909,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{171}\right)\)	\(e\left(\frac{1}{342}\right)\)	\(e\left(\frac{41}{114}\right)\)	\(e\left(\frac{106}{171}\right)\)	\(e\left(\frac{37}{114}\right)\)	\(e\left(\frac{107}{342}\right)\)	\(e\left(\frac{128}{171}\right)\)	\(e\left(\frac{229}{342}\right)\)	\(e\left(\frac{4}{171}\right)\)	\(e\left(\frac{1}{171}\right)\)
\(\chi_{9386}(935,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{103}{171}\right)\)	\(e\left(\frac{131}{342}\right)\)	\(e\left(\frac{13}{114}\right)\)	\(e\left(\frac{35}{171}\right)\)	\(e\left(\frac{59}{114}\right)\)	\(e\left(\frac{337}{342}\right)\)	\(e\left(\frac{10}{171}\right)\)	\(e\left(\frac{245}{342}\right)\)	\(e\left(\frac{11}{171}\right)\)	\(e\left(\frac{131}{171}\right)\)
\(\chi_{9386}(1013,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{28}{171}\right)\)	\(e\left(\frac{107}{342}\right)\)	\(e\left(\frac{55}{114}\right)\)	\(e\left(\frac{56}{171}\right)\)	\(e\left(\frac{83}{114}\right)\)	\(e\left(\frac{163}{342}\right)\)	\(e\left(\frac{16}{171}\right)\)	\(e\left(\frac{221}{342}\right)\)	\(e\left(\frac{86}{171}\right)\)	\(e\left(\frac{107}{171}\right)\)
\(\chi_{9386}(1195,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{101}{171}\right)\)	\(e\left(\frac{331}{342}\right)\)	\(e\left(\frac{5}{114}\right)\)	\(e\left(\frac{31}{171}\right)\)	\(e\left(\frac{49}{114}\right)\)	\(e\left(\frac{191}{342}\right)\)	\(e\left(\frac{131}{171}\right)\)	\(e\left(\frac{217}{342}\right)\)	\(e\left(\frac{127}{171}\right)\)	\(e\left(\frac{160}{171}\right)\)
\(\chi_{9386}(1221,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{171}\right)\)	\(e\left(\frac{175}{342}\right)\)	\(e\left(\frac{107}{114}\right)\)	\(e\left(\frac{82}{171}\right)\)	\(e\left(\frac{91}{114}\right)\)	\(e\left(\frac{257}{342}\right)\)	\(e\left(\frac{170}{171}\right)\)	\(e\left(\frac{61}{342}\right)\)	\(e\left(\frac{16}{171}\right)\)	\(e\left(\frac{4}{171}\right)\)
\(\chi_{9386}(1377,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{142}{171}\right)\)	\(e\left(\frac{335}{342}\right)\)	\(e\left(\frac{55}{114}\right)\)	\(e\left(\frac{113}{171}\right)\)	\(e\left(\frac{83}{114}\right)\)	\(e\left(\frac{277}{342}\right)\)	\(e\left(\frac{130}{171}\right)\)	\(e\left(\frac{107}{342}\right)\)	\(e\left(\frac{143}{171}\right)\)	\(e\left(\frac{164}{171}\right)\)
\(\chi_{9386}(1403,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{125}{171}\right)\)	\(e\left(\frac{325}{342}\right)\)	\(e\left(\frac{101}{114}\right)\)	\(e\left(\frac{79}{171}\right)\)	\(e\left(\frac{55}{114}\right)\)	\(e\left(\frac{233}{342}\right)\)	\(e\left(\frac{47}{171}\right)\)	\(e\left(\frac{211}{342}\right)\)	\(e\left(\frac{103}{171}\right)\)	\(e\left(\frac{154}{171}\right)\)
\(\chi_{9386}(1429,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{49}{171}\right)\)	\(e\left(\frac{59}{342}\right)\)	\(e\left(\frac{25}{114}\right)\)	\(e\left(\frac{98}{171}\right)\)	\(e\left(\frac{17}{114}\right)\)	\(e\left(\frac{157}{342}\right)\)	\(e\left(\frac{28}{171}\right)\)	\(e\left(\frac{173}{342}\right)\)	\(e\left(\frac{65}{171}\right)\)	\(e\left(\frac{59}{171}\right)\)
\(\chi_{9386}(1507,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{163}{171}\right)\)	\(e\left(\frac{287}{342}\right)\)	\(e\left(\frac{25}{114}\right)\)	\(e\left(\frac{155}{171}\right)\)	\(e\left(\frac{17}{114}\right)\)	\(e\left(\frac{271}{342}\right)\)	\(e\left(\frac{142}{171}\right)\)	\(e\left(\frac{59}{342}\right)\)	\(e\left(\frac{122}{171}\right)\)	\(e\left(\frac{116}{171}\right)\)
\(\chi_{9386}(1715,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{32}{171}\right)\)	\(e\left(\frac{49}{342}\right)\)	\(e\left(\frac{71}{114}\right)\)	\(e\left(\frac{64}{171}\right)\)	\(e\left(\frac{103}{114}\right)\)	\(e\left(\frac{113}{342}\right)\)	\(e\left(\frac{116}{171}\right)\)	\(e\left(\frac{277}{342}\right)\)	\(e\left(\frac{25}{171}\right)\)	\(e\left(\frac{49}{171}\right)\)
\(\chi_{9386}(1871,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{61}{171}\right)\)	\(e\left(\frac{227}{342}\right)\)	\(e\left(\frac{73}{114}\right)\)	\(e\left(\frac{122}{171}\right)\)	\(e\left(\frac{77}{114}\right)\)	\(e\left(\frac{7}{342}\right)\)	\(e\left(\frac{157}{171}\right)\)	\(e\left(\frac{341}{342}\right)\)	\(e\left(\frac{53}{171}\right)\)	\(e\left(\frac{56}{171}\right)\)
\(\chi_{9386}(1897,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{26}{171}\right)\)	\(e\left(\frac{307}{342}\right)\)	\(e\left(\frac{47}{114}\right)\)	\(e\left(\frac{52}{171}\right)\)	\(e\left(\frac{73}{114}\right)\)	\(e\left(\frac{17}{342}\right)\)	\(e\left(\frac{137}{171}\right)\)	\(e\left(\frac{193}{342}\right)\)	\(e\left(\frac{31}{171}\right)\)	\(e\left(\frac{136}{171}\right)\)
\(\chi_{9386}(1923,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{166}{171}\right)\)	\(e\left(\frac{329}{342}\right)\)	\(e\left(\frac{37}{114}\right)\)	\(e\left(\frac{161}{171}\right)\)	\(e\left(\frac{89}{114}\right)\)	\(e\left(\frac{319}{342}\right)\)	\(e\left(\frac{46}{171}\right)\)	\(e\left(\frac{101}{342}\right)\)	\(e\left(\frac{119}{171}\right)\)	\(e\left(\frac{158}{171}\right)\)
\(\chi_{9386}(2001,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{127}{171}\right)\)	\(e\left(\frac{125}{342}\right)\)	\(e\left(\frac{109}{114}\right)\)	\(e\left(\frac{83}{171}\right)\)	\(e\left(\frac{65}{114}\right)\)	\(e\left(\frac{37}{342}\right)\)	\(e\left(\frac{97}{171}\right)\)	\(e\left(\frac{239}{342}\right)\)	\(e\left(\frac{158}{171}\right)\)	\(e\left(\frac{125}{171}\right)\)
\(\chi_{9386}(2183,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{146}{171}\right)\)	\(e\left(\frac{277}{342}\right)\)	\(e\left(\frac{71}{114}\right)\)	\(e\left(\frac{121}{171}\right)\)	\(e\left(\frac{103}{114}\right)\)	\(e\left(\frac{227}{342}\right)\)	\(e\left(\frac{59}{171}\right)\)	\(e\left(\frac{163}{342}\right)\)	\(e\left(\frac{82}{171}\right)\)	\(e\left(\frac{106}{171}\right)\)
\(\chi_{9386}(2209,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{171}\right)\)	\(e\left(\frac{265}{342}\right)\)	\(e\left(\frac{35}{114}\right)\)	\(e\left(\frac{46}{171}\right)\)	\(e\left(\frac{1}{114}\right)\)	\(e\left(\frac{311}{342}\right)\)	\(e\left(\frac{62}{171}\right)\)	\(e\left(\frac{151}{342}\right)\)	\(e\left(\frac{34}{171}\right)\)	\(e\left(\frac{94}{171}\right)\)
\(\chi_{9386}(2365,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{151}{171}\right)\)	\(e\left(\frac{119}{342}\right)\)	\(e\left(\frac{91}{114}\right)\)	\(e\left(\frac{131}{171}\right)\)	\(e\left(\frac{71}{114}\right)\)	\(e\left(\frac{79}{342}\right)\)	\(e\left(\frac{13}{171}\right)\)	\(e\left(\frac{233}{342}\right)\)	\(e\left(\frac{134}{171}\right)\)	\(e\left(\frac{119}{171}\right)\)
\(\chi_{9386}(2391,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{98}{171}\right)\)	\(e\left(\frac{289}{342}\right)\)	\(e\left(\frac{107}{114}\right)\)	\(e\left(\frac{25}{171}\right)\)	\(e\left(\frac{91}{114}\right)\)	\(e\left(\frac{143}{342}\right)\)	\(e\left(\frac{56}{171}\right)\)	\(e\left(\frac{175}{342}\right)\)	\(e\left(\frac{130}{171}\right)\)	\(e\left(\frac{118}{171}\right)\)
\(\chi_{9386}(2417,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{112}{171}\right)\)	\(e\left(\frac{257}{342}\right)\)	\(e\left(\frac{49}{114}\right)\)	\(e\left(\frac{53}{171}\right)\)	\(e\left(\frac{47}{114}\right)\)	\(e\left(\frac{139}{342}\right)\)	\(e\left(\frac{64}{171}\right)\)	\(e\left(\frac{29}{342}\right)\)	\(e\left(\frac{2}{171}\right)\)	\(e\left(\frac{86}{171}\right)\)
\(\chi_{9386}(2495,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{91}{171}\right)\)	\(e\left(\frac{305}{342}\right)\)	\(e\left(\frac{79}{114}\right)\)	\(e\left(\frac{11}{171}\right)\)	\(e\left(\frac{113}{114}\right)\)	\(e\left(\frac{145}{342}\right)\)	\(e\left(\frac{52}{171}\right)\)	\(e\left(\frac{77}{342}\right)\)	\(e\left(\frac{23}{171}\right)\)	\(e\left(\frac{134}{171}\right)\)
\(\chi_{9386}(2677,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{83}{171}\right)\)	\(e\left(\frac{79}{342}\right)\)	\(e\left(\frac{47}{114}\right)\)	\(e\left(\frac{166}{171}\right)\)	\(e\left(\frac{73}{114}\right)\)	\(e\left(\frac{245}{342}\right)\)	\(e\left(\frac{23}{171}\right)\)	\(e\left(\frac{307}{342}\right)\)	\(e\left(\frac{145}{171}\right)\)	\(e\left(\frac{79}{171}\right)\)
\(\chi_{9386}(2703,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{14}{171}\right)\)	\(e\left(\frac{139}{342}\right)\)	\(e\left(\frac{113}{114}\right)\)	\(e\left(\frac{28}{171}\right)\)	\(e\left(\frac{13}{114}\right)\)	\(e\left(\frac{167}{342}\right)\)	\(e\left(\frac{8}{171}\right)\)	\(e\left(\frac{25}{342}\right)\)	\(e\left(\frac{43}{171}\right)\)	\(e\left(\frac{139}{171}\right)\)
\(\chi_{9386}(2859,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{70}{171}\right)\)	\(e\left(\frac{11}{342}\right)\)	\(e\left(\frac{109}{114}\right)\)	\(e\left(\frac{140}{171}\right)\)	\(e\left(\frac{65}{114}\right)\)	\(e\left(\frac{151}{342}\right)\)	\(e\left(\frac{40}{171}\right)\)	\(e\left(\frac{125}{342}\right)\)	\(e\left(\frac{44}{171}\right)\)	\(e\left(\frac{11}{171}\right)\)

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First 31 of 108 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.dh
Modulus	$9386$
Conductor	$4693$
Order	$342$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(9386\)
Conductor:	\(4693\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(342\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 4693.df	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)