LMFDB - Dirichlet character orbit 8664.de

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(8664, base_ring=CyclotomicField(342)) M = H._module chi = DirichletCharacter(H, M([171,171,171,40])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(35,8664)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$8664$
Conductor:	$8664$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$342$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	yes	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	$-1$	$1$	$5$	$7$	$11$	$13$	$17$	$23$	$25$	$29$	$31$	$35$
$\chi_{8664}(35,\cdot)$	$1$	$1$	$e\left(\frac{23}{171}\right)$	$e\left(\frac{5}{114}\right)$	$e\left(\frac{49}{114}\right)$	$e\left(\frac{335}{342}\right)$	$e\left(\frac{319}{342}\right)$	$e\left(\frac{13}{171}\right)$	$e\left(\frac{46}{171}\right)$	$e\left(\frac{169}{171}\right)$	$e\left(\frac{107}{114}\right)$	$e\left(\frac{61}{342}\right)$
$\chi_{8664}(131,\cdot)$	$1$	$1$	$e\left(\frac{17}{171}\right)$	$e\left(\frac{83}{114}\right)$	$e\left(\frac{61}{114}\right)$	$e\left(\frac{203}{342}\right)$	$e\left(\frac{325}{342}\right)$	$e\left(\frac{136}{171}\right)$	$e\left(\frac{34}{171}\right)$	$e\left(\frac{58}{171}\right)$	$e\left(\frac{89}{114}\right)$	$e\left(\frac{283}{342}\right)$
$\chi_{8664}(251,\cdot)$	$1$	$1$	$e\left(\frac{43}{171}\right)$	$e\left(\frac{49}{114}\right)$	$e\left(\frac{47}{114}\right)$	$e\left(\frac{91}{342}\right)$	$e\left(\frac{299}{342}\right)$	$e\left(\frac{2}{171}\right)$	$e\left(\frac{86}{171}\right)$	$e\left(\frac{26}{171}\right)$	$e\left(\frac{91}{114}\right)$	$e\left(\frac{233}{342}\right)$
$\chi_{8664}(275,\cdot)$	$1$	$1$	$e\left(\frac{163}{171}\right)$	$e\left(\frac{85}{114}\right)$	$e\left(\frac{35}{114}\right)$	$e\left(\frac{337}{342}\right)$	$e\left(\frac{179}{342}\right)$	$e\left(\frac{107}{171}\right)$	$e\left(\frac{155}{171}\right)$	$e\left(\frac{23}{171}\right)$	$e\left(\frac{109}{114}\right)$	$e\left(\frac{239}{342}\right)$
$\chi_{8664}(347,\cdot)$	$1$	$1$	$e\left(\frac{74}{171}\right)$	$e\left(\frac{83}{114}\right)$	$e\left(\frac{61}{114}\right)$	$e\left(\frac{89}{342}\right)$	$e\left(\frac{97}{342}\right)$	$e\left(\frac{79}{171}\right)$	$e\left(\frac{148}{171}\right)$	$e\left(\frac{1}{171}\right)$	$e\left(\frac{89}{114}\right)$	$e\left(\frac{55}{342}\right)$
$\chi_{8664}(443,\cdot)$	$1$	$1$	$e\left(\frac{22}{171}\right)$	$e\left(\frac{37}{114}\right)$	$e\left(\frac{89}{114}\right)$	$e\left(\frac{313}{342}\right)$	$e\left(\frac{149}{342}\right)$	$e\left(\frac{5}{171}\right)$	$e\left(\frac{44}{171}\right)$	$e\left(\frac{65}{171}\right)$	$e\left(\frac{85}{114}\right)$	$e\left(\frac{155}{342}\right)$
$\chi_{8664}(491,\cdot)$	$1$	$1$	$e\left(\frac{41}{171}\right)$	$e\left(\frac{113}{114}\right)$	$e\left(\frac{13}{114}\right)$	$e\left(\frac{47}{342}\right)$	$e\left(\frac{301}{342}\right)$	$e\left(\frac{157}{171}\right)$	$e\left(\frac{82}{171}\right)$	$e\left(\frac{160}{171}\right)$	$e\left(\frac{47}{114}\right)$	$e\left(\frac{79}{342}\right)$
$\chi_{8664}(587,\cdot)$	$1$	$1$	$e\left(\frac{44}{171}\right)$	$e\left(\frac{17}{114}\right)$	$e\left(\frac{7}{114}\right)$	$e\left(\frac{113}{342}\right)$	$e\left(\frac{127}{342}\right)$	$e\left(\frac{10}{171}\right)$	$e\left(\frac{88}{171}\right)$	$e\left(\frac{130}{171}\right)$	$e\left(\frac{113}{114}\right)$	$e\left(\frac{139}{342}\right)$
$\chi_{8664}(707,\cdot)$	$1$	$1$	$e\left(\frac{115}{171}\right)$	$e\left(\frac{25}{114}\right)$	$e\left(\frac{17}{114}\right)$	$e\left(\frac{307}{342}\right)$	$e\left(\frac{227}{342}\right)$	$e\left(\frac{65}{171}\right)$	$e\left(\frac{59}{171}\right)$	$e\left(\frac{161}{171}\right)$	$e\left(\frac{79}{114}\right)$	$e\left(\frac{305}{342}\right)$
$\chi_{8664}(731,\cdot)$	$1$	$1$	$e\left(\frac{100}{171}\right)$	$e\left(\frac{49}{114}\right)$	$e\left(\frac{47}{114}\right)$	$e\left(\frac{319}{342}\right)$	$e\left(\frac{71}{342}\right)$	$e\left(\frac{116}{171}\right)$	$e\left(\frac{29}{171}\right)$	$e\left(\frac{140}{171}\right)$	$e\left(\frac{91}{114}\right)$	$e\left(\frac{5}{342}\right)$
$\chi_{8664}(803,\cdot)$	$1$	$1$	$e\left(\frac{29}{171}\right)$	$e\left(\frac{41}{114}\right)$	$e\left(\frac{37}{114}\right)$	$e\left(\frac{125}{342}\right)$	$e\left(\frac{313}{342}\right)$	$e\left(\frac{61}{171}\right)$	$e\left(\frac{58}{171}\right)$	$e\left(\frac{109}{171}\right)$	$e\left(\frac{11}{114}\right)$	$e\left(\frac{181}{342}\right)$
$\chi_{8664}(899,\cdot)$	$1$	$1$	$e\left(\frac{13}{171}\right)$	$e\left(\frac{97}{114}\right)$	$e\left(\frac{107}{114}\right)$	$e\left(\frac{115}{342}\right)$	$e\left(\frac{329}{342}\right)$	$e\left(\frac{104}{171}\right)$	$e\left(\frac{26}{171}\right)$	$e\left(\frac{155}{171}\right)$	$e\left(\frac{1}{114}\right)$	$e\left(\frac{317}{342}\right)$
$\chi_{8664}(947,\cdot)$	$1$	$1$	$e\left(\frac{59}{171}\right)$	$e\left(\frac{107}{114}\right)$	$e\left(\frac{91}{114}\right)$	$e\left(\frac{101}{342}\right)$	$e\left(\frac{283}{342}\right)$	$e\left(\frac{130}{171}\right)$	$e\left(\frac{118}{171}\right)$	$e\left(\frac{151}{171}\right)$	$e\left(\frac{101}{114}\right)$	$e\left(\frac{97}{342}\right)$
$\chi_{8664}(1043,\cdot)$	$1$	$1$	$e\left(\frac{71}{171}\right)$	$e\left(\frac{65}{114}\right)$	$e\left(\frac{67}{114}\right)$	$e\left(\frac{23}{342}\right)$	$e\left(\frac{271}{342}\right)$	$e\left(\frac{55}{171}\right)$	$e\left(\frac{142}{171}\right)$	$e\left(\frac{31}{171}\right)$	$e\left(\frac{23}{114}\right)$	$e\left(\frac{337}{342}\right)$
$\chi_{8664}(1163,\cdot)$	$1$	$1$	$e\left(\frac{16}{171}\right)$	$e\left(\frac{1}{114}\right)$	$e\left(\frac{101}{114}\right)$	$e\left(\frac{181}{342}\right)$	$e\left(\frac{155}{342}\right)$	$e\left(\frac{128}{171}\right)$	$e\left(\frac{32}{171}\right)$	$e\left(\frac{125}{171}\right)$	$e\left(\frac{67}{114}\right)$	$e\left(\frac{35}{342}\right)$
$\chi_{8664}(1187,\cdot)$	$1$	$1$	$e\left(\frac{37}{171}\right)$	$e\left(\frac{13}{114}\right)$	$e\left(\frac{59}{114}\right)$	$e\left(\frac{301}{342}\right)$	$e\left(\frac{305}{342}\right)$	$e\left(\frac{125}{171}\right)$	$e\left(\frac{74}{171}\right)$	$e\left(\frac{86}{171}\right)$	$e\left(\frac{73}{114}\right)$	$e\left(\frac{113}{342}\right)$
$\chi_{8664}(1259,\cdot)$	$1$	$1$	$e\left(\frac{155}{171}\right)$	$e\left(\frac{113}{114}\right)$	$e\left(\frac{13}{114}\right)$	$e\left(\frac{161}{342}\right)$	$e\left(\frac{187}{342}\right)$	$e\left(\frac{43}{171}\right)$	$e\left(\frac{139}{171}\right)$	$e\left(\frac{46}{171}\right)$	$e\left(\frac{47}{114}\right)$	$e\left(\frac{307}{342}\right)$
$\chi_{8664}(1355,\cdot)$	$1$	$1$	$e\left(\frac{4}{171}\right)$	$e\left(\frac{43}{114}\right)$	$e\left(\frac{11}{114}\right)$	$e\left(\frac{259}{342}\right)$	$e\left(\frac{167}{342}\right)$	$e\left(\frac{32}{171}\right)$	$e\left(\frac{8}{171}\right)$	$e\left(\frac{74}{171}\right)$	$e\left(\frac{31}{114}\right)$	$e\left(\frac{137}{342}\right)$
$\chi_{8664}(1403,\cdot)$	$1$	$1$	$e\left(\frac{77}{171}\right)$	$e\left(\frac{101}{114}\right)$	$e\left(\frac{55}{114}\right)$	$e\left(\frac{155}{342}\right)$	$e\left(\frac{265}{342}\right)$	$e\left(\frac{103}{171}\right)$	$e\left(\frac{154}{171}\right)$	$e\left(\frac{142}{171}\right)$	$e\left(\frac{41}{114}\right)$	$e\left(\frac{115}{342}\right)$
$\chi_{8664}(1499,\cdot)$	$1$	$1$	$e\left(\frac{98}{171}\right)$	$e\left(\frac{113}{114}\right)$	$e\left(\frac{13}{114}\right)$	$e\left(\frac{275}{342}\right)$	$e\left(\frac{73}{342}\right)$	$e\left(\frac{100}{171}\right)$	$e\left(\frac{25}{171}\right)$	$e\left(\frac{103}{171}\right)$	$e\left(\frac{47}{114}\right)$	$e\left(\frac{193}{342}\right)$
$\chi_{8664}(1619,\cdot)$	$1$	$1$	$e\left(\frac{88}{171}\right)$	$e\left(\frac{91}{114}\right)$	$e\left(\frac{71}{114}\right)$	$e\left(\frac{55}{342}\right)$	$e\left(\frac{83}{342}\right)$	$e\left(\frac{20}{171}\right)$	$e\left(\frac{5}{171}\right)$	$e\left(\frac{89}{171}\right)$	$e\left(\frac{55}{114}\right)$	$e\left(\frac{107}{342}\right)$
$\chi_{8664}(1643,\cdot)$	$1$	$1$	$e\left(\frac{145}{171}\right)$	$e\left(\frac{91}{114}\right)$	$e\left(\frac{71}{114}\right)$	$e\left(\frac{283}{342}\right)$	$e\left(\frac{197}{342}\right)$	$e\left(\frac{134}{171}\right)$	$e\left(\frac{119}{171}\right)$	$e\left(\frac{32}{171}\right)$	$e\left(\frac{55}{114}\right)$	$e\left(\frac{221}{342}\right)$
$\chi_{8664}(1715,\cdot)$	$1$	$1$	$e\left(\frac{110}{171}\right)$	$e\left(\frac{71}{114}\right)$	$e\left(\frac{103}{114}\right)$	$e\left(\frac{197}{342}\right)$	$e\left(\frac{61}{342}\right)$	$e\left(\frac{25}{171}\right)$	$e\left(\frac{49}{171}\right)$	$e\left(\frac{154}{171}\right)$	$e\left(\frac{83}{114}\right)$	$e\left(\frac{91}{342}\right)$
$\chi_{8664}(1811,\cdot)$	$1$	$1$	$e\left(\frac{166}{171}\right)$	$e\left(\frac{103}{114}\right)$	$e\left(\frac{29}{114}\right)$	$e\left(\frac{61}{342}\right)$	$e\left(\frac{5}{342}\right)$	$e\left(\frac{131}{171}\right)$	$e\left(\frac{161}{171}\right)$	$e\left(\frac{164}{171}\right)$	$e\left(\frac{61}{114}\right)$	$e\left(\frac{299}{342}\right)$
$\chi_{8664}(1955,\cdot)$	$1$	$1$	$e\left(\frac{125}{171}\right)$	$e\left(\frac{47}{114}\right)$	$e\left(\frac{73}{114}\right)$	$e\left(\frac{185}{342}\right)$	$e\left(\frac{217}{342}\right)$	$e\left(\frac{145}{171}\right)$	$e\left(\frac{79}{171}\right)$	$e\left(\frac{4}{171}\right)$	$e\left(\frac{71}{114}\right)$	$e\left(\frac{49}{342}\right)$
$\chi_{8664}(2075,\cdot)$	$1$	$1$	$e\left(\frac{160}{171}\right)$	$e\left(\frac{67}{114}\right)$	$e\left(\frac{41}{114}\right)$	$e\left(\frac{271}{342}\right)$	$e\left(\frac{11}{342}\right)$	$e\left(\frac{83}{171}\right)$	$e\left(\frac{149}{171}\right)$	$e\left(\frac{53}{171}\right)$	$e\left(\frac{43}{114}\right)$	$e\left(\frac{179}{342}\right)$
$\chi_{8664}(2099,\cdot)$	$1$	$1$	$e\left(\frac{82}{171}\right)$	$e\left(\frac{55}{114}\right)$	$e\left(\frac{83}{114}\right)$	$e\left(\frac{265}{342}\right)$	$e\left(\frac{89}{342}\right)$	$e\left(\frac{143}{171}\right)$	$e\left(\frac{164}{171}\right)$	$e\left(\frac{149}{171}\right)$	$e\left(\frac{37}{114}\right)$	$e\left(\frac{329}{342}\right)$
$\chi_{8664}(2171,\cdot)$	$1$	$1$	$e\left(\frac{65}{171}\right)$	$e\left(\frac{29}{114}\right)$	$e\left(\frac{79}{114}\right)$	$e\left(\frac{233}{342}\right)$	$e\left(\frac{277}{342}\right)$	$e\left(\frac{7}{171}\right)$	$e\left(\frac{130}{171}\right)$	$e\left(\frac{91}{171}\right)$	$e\left(\frac{5}{114}\right)$	$e\left(\frac{217}{342}\right)$
$\chi_{8664}(2267,\cdot)$	$1$	$1$	$e\left(\frac{157}{171}\right)$	$e\left(\frac{49}{114}\right)$	$e\left(\frac{47}{114}\right)$	$e\left(\frac{205}{342}\right)$	$e\left(\frac{185}{342}\right)$	$e\left(\frac{59}{171}\right)$	$e\left(\frac{143}{171}\right)$	$e\left(\frac{83}{171}\right)$	$e\left(\frac{91}{114}\right)$	$e\left(\frac{119}{342}\right)$
$\chi_{8664}(2315,\cdot)$	$1$	$1$	$e\left(\frac{113}{171}\right)$	$e\left(\frac{89}{114}\right)$	$e\left(\frac{97}{114}\right)$	$e\left(\frac{263}{342}\right)$	$e\left(\frac{229}{342}\right)$	$e\left(\frac{49}{171}\right)$	$e\left(\frac{55}{171}\right)$	$e\left(\frac{124}{171}\right)$	$e\left(\frac{35}{114}\right)$	$e\left(\frac{151}{342}\right)$
$\chi_{8664}(2531,\cdot)$	$1$	$1$	$e\left(\frac{61}{171}\right)$	$e\left(\frac{43}{114}\right)$	$e\left(\frac{11}{114}\right)$	$e\left(\frac{145}{342}\right)$	$e\left(\frac{281}{342}\right)$	$e\left(\frac{146}{171}\right)$	$e\left(\frac{122}{171}\right)$	$e\left(\frac{17}{171}\right)$	$e\left(\frac{31}{114}\right)$	$e\left(\frac{251}{342}\right)$

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	\(-1\)	\(1\)	\(5\)	\(7\)	\(11\)	\(13\)	\(17\)	\(23\)	\(25\)	\(29\)	\(31\)	\(35\)
\(\chi_{8664}(35,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{171}\right)\)	\(e\left(\frac{5}{114}\right)\)	\(e\left(\frac{49}{114}\right)\)	\(e\left(\frac{335}{342}\right)\)	\(e\left(\frac{319}{342}\right)\)	\(e\left(\frac{13}{171}\right)\)	\(e\left(\frac{46}{171}\right)\)	\(e\left(\frac{169}{171}\right)\)	\(e\left(\frac{107}{114}\right)\)	\(e\left(\frac{61}{342}\right)\)
\(\chi_{8664}(131,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{171}\right)\)	\(e\left(\frac{83}{114}\right)\)	\(e\left(\frac{61}{114}\right)\)	\(e\left(\frac{203}{342}\right)\)	\(e\left(\frac{325}{342}\right)\)	\(e\left(\frac{136}{171}\right)\)	\(e\left(\frac{34}{171}\right)\)	\(e\left(\frac{58}{171}\right)\)	\(e\left(\frac{89}{114}\right)\)	\(e\left(\frac{283}{342}\right)\)
\(\chi_{8664}(251,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{171}\right)\)	\(e\left(\frac{49}{114}\right)\)	\(e\left(\frac{47}{114}\right)\)	\(e\left(\frac{91}{342}\right)\)	\(e\left(\frac{299}{342}\right)\)	\(e\left(\frac{2}{171}\right)\)	\(e\left(\frac{86}{171}\right)\)	\(e\left(\frac{26}{171}\right)\)	\(e\left(\frac{91}{114}\right)\)	\(e\left(\frac{233}{342}\right)\)
\(\chi_{8664}(275,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{163}{171}\right)\)	\(e\left(\frac{85}{114}\right)\)	\(e\left(\frac{35}{114}\right)\)	\(e\left(\frac{337}{342}\right)\)	\(e\left(\frac{179}{342}\right)\)	\(e\left(\frac{107}{171}\right)\)	\(e\left(\frac{155}{171}\right)\)	\(e\left(\frac{23}{171}\right)\)	\(e\left(\frac{109}{114}\right)\)	\(e\left(\frac{239}{342}\right)\)
\(\chi_{8664}(347,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{74}{171}\right)\)	\(e\left(\frac{83}{114}\right)\)	\(e\left(\frac{61}{114}\right)\)	\(e\left(\frac{89}{342}\right)\)	\(e\left(\frac{97}{342}\right)\)	\(e\left(\frac{79}{171}\right)\)	\(e\left(\frac{148}{171}\right)\)	\(e\left(\frac{1}{171}\right)\)	\(e\left(\frac{89}{114}\right)\)	\(e\left(\frac{55}{342}\right)\)
\(\chi_{8664}(443,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{22}{171}\right)\)	\(e\left(\frac{37}{114}\right)\)	\(e\left(\frac{89}{114}\right)\)	\(e\left(\frac{313}{342}\right)\)	\(e\left(\frac{149}{342}\right)\)	\(e\left(\frac{5}{171}\right)\)	\(e\left(\frac{44}{171}\right)\)	\(e\left(\frac{65}{171}\right)\)	\(e\left(\frac{85}{114}\right)\)	\(e\left(\frac{155}{342}\right)\)
\(\chi_{8664}(491,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{171}\right)\)	\(e\left(\frac{113}{114}\right)\)	\(e\left(\frac{13}{114}\right)\)	\(e\left(\frac{47}{342}\right)\)	\(e\left(\frac{301}{342}\right)\)	\(e\left(\frac{157}{171}\right)\)	\(e\left(\frac{82}{171}\right)\)	\(e\left(\frac{160}{171}\right)\)	\(e\left(\frac{47}{114}\right)\)	\(e\left(\frac{79}{342}\right)\)
\(\chi_{8664}(587,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{44}{171}\right)\)	\(e\left(\frac{17}{114}\right)\)	\(e\left(\frac{7}{114}\right)\)	\(e\left(\frac{113}{342}\right)\)	\(e\left(\frac{127}{342}\right)\)	\(e\left(\frac{10}{171}\right)\)	\(e\left(\frac{88}{171}\right)\)	\(e\left(\frac{130}{171}\right)\)	\(e\left(\frac{113}{114}\right)\)	\(e\left(\frac{139}{342}\right)\)
\(\chi_{8664}(707,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{115}{171}\right)\)	\(e\left(\frac{25}{114}\right)\)	\(e\left(\frac{17}{114}\right)\)	\(e\left(\frac{307}{342}\right)\)	\(e\left(\frac{227}{342}\right)\)	\(e\left(\frac{65}{171}\right)\)	\(e\left(\frac{59}{171}\right)\)	\(e\left(\frac{161}{171}\right)\)	\(e\left(\frac{79}{114}\right)\)	\(e\left(\frac{305}{342}\right)\)
\(\chi_{8664}(731,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{100}{171}\right)\)	\(e\left(\frac{49}{114}\right)\)	\(e\left(\frac{47}{114}\right)\)	\(e\left(\frac{319}{342}\right)\)	\(e\left(\frac{71}{342}\right)\)	\(e\left(\frac{116}{171}\right)\)	\(e\left(\frac{29}{171}\right)\)	\(e\left(\frac{140}{171}\right)\)	\(e\left(\frac{91}{114}\right)\)	\(e\left(\frac{5}{342}\right)\)
\(\chi_{8664}(803,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{171}\right)\)	\(e\left(\frac{41}{114}\right)\)	\(e\left(\frac{37}{114}\right)\)	\(e\left(\frac{125}{342}\right)\)	\(e\left(\frac{313}{342}\right)\)	\(e\left(\frac{61}{171}\right)\)	\(e\left(\frac{58}{171}\right)\)	\(e\left(\frac{109}{171}\right)\)	\(e\left(\frac{11}{114}\right)\)	\(e\left(\frac{181}{342}\right)\)
\(\chi_{8664}(899,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{171}\right)\)	\(e\left(\frac{97}{114}\right)\)	\(e\left(\frac{107}{114}\right)\)	\(e\left(\frac{115}{342}\right)\)	\(e\left(\frac{329}{342}\right)\)	\(e\left(\frac{104}{171}\right)\)	\(e\left(\frac{26}{171}\right)\)	\(e\left(\frac{155}{171}\right)\)	\(e\left(\frac{1}{114}\right)\)	\(e\left(\frac{317}{342}\right)\)
\(\chi_{8664}(947,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{171}\right)\)	\(e\left(\frac{107}{114}\right)\)	\(e\left(\frac{91}{114}\right)\)	\(e\left(\frac{101}{342}\right)\)	\(e\left(\frac{283}{342}\right)\)	\(e\left(\frac{130}{171}\right)\)	\(e\left(\frac{118}{171}\right)\)	\(e\left(\frac{151}{171}\right)\)	\(e\left(\frac{101}{114}\right)\)	\(e\left(\frac{97}{342}\right)\)
\(\chi_{8664}(1043,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{71}{171}\right)\)	\(e\left(\frac{65}{114}\right)\)	\(e\left(\frac{67}{114}\right)\)	\(e\left(\frac{23}{342}\right)\)	\(e\left(\frac{271}{342}\right)\)	\(e\left(\frac{55}{171}\right)\)	\(e\left(\frac{142}{171}\right)\)	\(e\left(\frac{31}{171}\right)\)	\(e\left(\frac{23}{114}\right)\)	\(e\left(\frac{337}{342}\right)\)
\(\chi_{8664}(1163,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{16}{171}\right)\)	\(e\left(\frac{1}{114}\right)\)	\(e\left(\frac{101}{114}\right)\)	\(e\left(\frac{181}{342}\right)\)	\(e\left(\frac{155}{342}\right)\)	\(e\left(\frac{128}{171}\right)\)	\(e\left(\frac{32}{171}\right)\)	\(e\left(\frac{125}{171}\right)\)	\(e\left(\frac{67}{114}\right)\)	\(e\left(\frac{35}{342}\right)\)
\(\chi_{8664}(1187,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{171}\right)\)	\(e\left(\frac{13}{114}\right)\)	\(e\left(\frac{59}{114}\right)\)	\(e\left(\frac{301}{342}\right)\)	\(e\left(\frac{305}{342}\right)\)	\(e\left(\frac{125}{171}\right)\)	\(e\left(\frac{74}{171}\right)\)	\(e\left(\frac{86}{171}\right)\)	\(e\left(\frac{73}{114}\right)\)	\(e\left(\frac{113}{342}\right)\)
\(\chi_{8664}(1259,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{155}{171}\right)\)	\(e\left(\frac{113}{114}\right)\)	\(e\left(\frac{13}{114}\right)\)	\(e\left(\frac{161}{342}\right)\)	\(e\left(\frac{187}{342}\right)\)	\(e\left(\frac{43}{171}\right)\)	\(e\left(\frac{139}{171}\right)\)	\(e\left(\frac{46}{171}\right)\)	\(e\left(\frac{47}{114}\right)\)	\(e\left(\frac{307}{342}\right)\)
\(\chi_{8664}(1355,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{171}\right)\)	\(e\left(\frac{43}{114}\right)\)	\(e\left(\frac{11}{114}\right)\)	\(e\left(\frac{259}{342}\right)\)	\(e\left(\frac{167}{342}\right)\)	\(e\left(\frac{32}{171}\right)\)	\(e\left(\frac{8}{171}\right)\)	\(e\left(\frac{74}{171}\right)\)	\(e\left(\frac{31}{114}\right)\)	\(e\left(\frac{137}{342}\right)\)
\(\chi_{8664}(1403,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{77}{171}\right)\)	\(e\left(\frac{101}{114}\right)\)	\(e\left(\frac{55}{114}\right)\)	\(e\left(\frac{155}{342}\right)\)	\(e\left(\frac{265}{342}\right)\)	\(e\left(\frac{103}{171}\right)\)	\(e\left(\frac{154}{171}\right)\)	\(e\left(\frac{142}{171}\right)\)	\(e\left(\frac{41}{114}\right)\)	\(e\left(\frac{115}{342}\right)\)
\(\chi_{8664}(1499,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{98}{171}\right)\)	\(e\left(\frac{113}{114}\right)\)	\(e\left(\frac{13}{114}\right)\)	\(e\left(\frac{275}{342}\right)\)	\(e\left(\frac{73}{342}\right)\)	\(e\left(\frac{100}{171}\right)\)	\(e\left(\frac{25}{171}\right)\)	\(e\left(\frac{103}{171}\right)\)	\(e\left(\frac{47}{114}\right)\)	\(e\left(\frac{193}{342}\right)\)
\(\chi_{8664}(1619,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{88}{171}\right)\)	\(e\left(\frac{91}{114}\right)\)	\(e\left(\frac{71}{114}\right)\)	\(e\left(\frac{55}{342}\right)\)	\(e\left(\frac{83}{342}\right)\)	\(e\left(\frac{20}{171}\right)\)	\(e\left(\frac{5}{171}\right)\)	\(e\left(\frac{89}{171}\right)\)	\(e\left(\frac{55}{114}\right)\)	\(e\left(\frac{107}{342}\right)\)
\(\chi_{8664}(1643,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{145}{171}\right)\)	\(e\left(\frac{91}{114}\right)\)	\(e\left(\frac{71}{114}\right)\)	\(e\left(\frac{283}{342}\right)\)	\(e\left(\frac{197}{342}\right)\)	\(e\left(\frac{134}{171}\right)\)	\(e\left(\frac{119}{171}\right)\)	\(e\left(\frac{32}{171}\right)\)	\(e\left(\frac{55}{114}\right)\)	\(e\left(\frac{221}{342}\right)\)
\(\chi_{8664}(1715,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{110}{171}\right)\)	\(e\left(\frac{71}{114}\right)\)	\(e\left(\frac{103}{114}\right)\)	\(e\left(\frac{197}{342}\right)\)	\(e\left(\frac{61}{342}\right)\)	\(e\left(\frac{25}{171}\right)\)	\(e\left(\frac{49}{171}\right)\)	\(e\left(\frac{154}{171}\right)\)	\(e\left(\frac{83}{114}\right)\)	\(e\left(\frac{91}{342}\right)\)
\(\chi_{8664}(1811,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{166}{171}\right)\)	\(e\left(\frac{103}{114}\right)\)	\(e\left(\frac{29}{114}\right)\)	\(e\left(\frac{61}{342}\right)\)	\(e\left(\frac{5}{342}\right)\)	\(e\left(\frac{131}{171}\right)\)	\(e\left(\frac{161}{171}\right)\)	\(e\left(\frac{164}{171}\right)\)	\(e\left(\frac{61}{114}\right)\)	\(e\left(\frac{299}{342}\right)\)
\(\chi_{8664}(1955,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{125}{171}\right)\)	\(e\left(\frac{47}{114}\right)\)	\(e\left(\frac{73}{114}\right)\)	\(e\left(\frac{185}{342}\right)\)	\(e\left(\frac{217}{342}\right)\)	\(e\left(\frac{145}{171}\right)\)	\(e\left(\frac{79}{171}\right)\)	\(e\left(\frac{4}{171}\right)\)	\(e\left(\frac{71}{114}\right)\)	\(e\left(\frac{49}{342}\right)\)
\(\chi_{8664}(2075,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{160}{171}\right)\)	\(e\left(\frac{67}{114}\right)\)	\(e\left(\frac{41}{114}\right)\)	\(e\left(\frac{271}{342}\right)\)	\(e\left(\frac{11}{342}\right)\)	\(e\left(\frac{83}{171}\right)\)	\(e\left(\frac{149}{171}\right)\)	\(e\left(\frac{53}{171}\right)\)	\(e\left(\frac{43}{114}\right)\)	\(e\left(\frac{179}{342}\right)\)
\(\chi_{8664}(2099,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{82}{171}\right)\)	\(e\left(\frac{55}{114}\right)\)	\(e\left(\frac{83}{114}\right)\)	\(e\left(\frac{265}{342}\right)\)	\(e\left(\frac{89}{342}\right)\)	\(e\left(\frac{143}{171}\right)\)	\(e\left(\frac{164}{171}\right)\)	\(e\left(\frac{149}{171}\right)\)	\(e\left(\frac{37}{114}\right)\)	\(e\left(\frac{329}{342}\right)\)
\(\chi_{8664}(2171,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{65}{171}\right)\)	\(e\left(\frac{29}{114}\right)\)	\(e\left(\frac{79}{114}\right)\)	\(e\left(\frac{233}{342}\right)\)	\(e\left(\frac{277}{342}\right)\)	\(e\left(\frac{7}{171}\right)\)	\(e\left(\frac{130}{171}\right)\)	\(e\left(\frac{91}{171}\right)\)	\(e\left(\frac{5}{114}\right)\)	\(e\left(\frac{217}{342}\right)\)
\(\chi_{8664}(2267,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{157}{171}\right)\)	\(e\left(\frac{49}{114}\right)\)	\(e\left(\frac{47}{114}\right)\)	\(e\left(\frac{205}{342}\right)\)	\(e\left(\frac{185}{342}\right)\)	\(e\left(\frac{59}{171}\right)\)	\(e\left(\frac{143}{171}\right)\)	\(e\left(\frac{83}{171}\right)\)	\(e\left(\frac{91}{114}\right)\)	\(e\left(\frac{119}{342}\right)\)
\(\chi_{8664}(2315,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{113}{171}\right)\)	\(e\left(\frac{89}{114}\right)\)	\(e\left(\frac{97}{114}\right)\)	\(e\left(\frac{263}{342}\right)\)	\(e\left(\frac{229}{342}\right)\)	\(e\left(\frac{49}{171}\right)\)	\(e\left(\frac{55}{171}\right)\)	\(e\left(\frac{124}{171}\right)\)	\(e\left(\frac{35}{114}\right)\)	\(e\left(\frac{151}{342}\right)\)
\(\chi_{8664}(2531,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{61}{171}\right)\)	\(e\left(\frac{43}{114}\right)\)	\(e\left(\frac{11}{114}\right)\)	\(e\left(\frac{145}{342}\right)\)	\(e\left(\frac{281}{342}\right)\)	\(e\left(\frac{146}{171}\right)\)	\(e\left(\frac{122}{171}\right)\)	\(e\left(\frac{17}{171}\right)\)	\(e\left(\frac{31}{114}\right)\)	\(e\left(\frac{251}{342}\right)\)

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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	8664.de
Modulus	$8664$
Conductor	$8664$
Order	$342$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(8664\)
Conductor:	\(8664\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(342\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	yes	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)