LMFDB - Dirichlet character orbit 8664.dp

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(8664, base_ring=CyclotomicField(342)) M = H._module chi = DirichletCharacter(H, M([0,171,171,17])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(29,8664)) 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	$-1$	$1$	$5$	$7$	$11$	$13$	$17$	$23$	$25$	$29$	$31$	$35$
$\chi_{8664}(29,\cdot)$	$1$	$1$	$e\left(\frac{91}{171}\right)$	$e\left(\frac{26}{57}\right)$	$e\left(\frac{4}{57}\right)$	$e\left(\frac{146}{171}\right)$	$e\left(\frac{251}{342}\right)$	$e\left(\frac{259}{342}\right)$	$e\left(\frac{11}{171}\right)$	$e\left(\frac{289}{342}\right)$	$e\left(\frac{7}{114}\right)$	$e\left(\frac{169}{171}\right)$
$\chi_{8664}(53,\cdot)$	$1$	$1$	$e\left(\frac{52}{171}\right)$	$e\left(\frac{23}{57}\right)$	$e\left(\frac{43}{57}\right)$	$e\left(\frac{59}{171}\right)$	$e\left(\frac{119}{342}\right)$	$e\left(\frac{319}{342}\right)$	$e\left(\frac{104}{171}\right)$	$e\left(\frac{43}{342}\right)$	$e\left(\frac{61}{114}\right)$	$e\left(\frac{121}{171}\right)$
$\chi_{8664}(173,\cdot)$	$1$	$1$	$e\left(\frac{170}{171}\right)$	$e\left(\frac{16}{57}\right)$	$e\left(\frac{20}{57}\right)$	$e\left(\frac{160}{171}\right)$	$e\left(\frac{1}{342}\right)$	$e\left(\frac{155}{342}\right)$	$e\left(\frac{169}{171}\right)$	$e\left(\frac{305}{342}\right)$	$e\left(\frac{35}{114}\right)$	$e\left(\frac{47}{171}\right)$
$\chi_{8664}(269,\cdot)$	$1$	$1$	$e\left(\frac{68}{171}\right)$	$e\left(\frac{52}{57}\right)$	$e\left(\frac{8}{57}\right)$	$e\left(\frac{64}{171}\right)$	$e\left(\frac{103}{342}\right)$	$e\left(\frac{233}{342}\right)$	$e\left(\frac{136}{171}\right)$	$e\left(\frac{293}{342}\right)$	$e\left(\frac{71}{114}\right)$	$e\left(\frac{53}{171}\right)$
$\chi_{8664}(317,\cdot)$	$1$	$1$	$e\left(\frac{94}{171}\right)$	$e\left(\frac{35}{57}\right)$	$e\left(\frac{1}{57}\right)$	$e\left(\frac{8}{171}\right)$	$e\left(\frac{77}{342}\right)$	$e\left(\frac{307}{342}\right)$	$e\left(\frac{17}{171}\right)$	$e\left(\frac{229}{342}\right)$	$e\left(\frac{73}{114}\right)$	$e\left(\frac{28}{171}\right)$
$\chi_{8664}(413,\cdot)$	$1$	$1$	$e\left(\frac{92}{171}\right)$	$e\left(\frac{10}{57}\right)$	$e\left(\frac{41}{57}\right)$	$e\left(\frac{157}{171}\right)$	$e\left(\frac{79}{342}\right)$	$e\left(\frac{275}{342}\right)$	$e\left(\frac{13}{171}\right)$	$e\left(\frac{155}{342}\right)$	$e\left(\frac{29}{114}\right)$	$e\left(\frac{122}{171}\right)$
$\chi_{8664}(485,\cdot)$	$1$	$1$	$e\left(\frac{154}{171}\right)$	$e\left(\frac{44}{57}\right)$	$e\left(\frac{55}{57}\right)$	$e\left(\frac{155}{171}\right)$	$e\left(\frac{17}{342}\right)$	$e\left(\frac{241}{342}\right)$	$e\left(\frac{137}{171}\right)$	$e\left(\frac{55}{342}\right)$	$e\left(\frac{25}{114}\right)$	$e\left(\frac{115}{171}\right)$
$\chi_{8664}(509,\cdot)$	$1$	$1$	$e\left(\frac{151}{171}\right)$	$e\left(\frac{35}{57}\right)$	$e\left(\frac{1}{57}\right)$	$e\left(\frac{122}{171}\right)$	$e\left(\frac{191}{342}\right)$	$e\left(\frac{193}{342}\right)$	$e\left(\frac{131}{171}\right)$	$e\left(\frac{115}{342}\right)$	$e\left(\frac{73}{114}\right)$	$e\left(\frac{85}{171}\right)$
$\chi_{8664}(629,\cdot)$	$1$	$1$	$e\left(\frac{143}{171}\right)$	$e\left(\frac{49}{57}\right)$	$e\left(\frac{47}{57}\right)$	$e\left(\frac{34}{171}\right)$	$e\left(\frac{199}{342}\right)$	$e\left(\frac{65}{342}\right)$	$e\left(\frac{115}{171}\right)$	$e\left(\frac{161}{342}\right)$	$e\left(\frac{11}{114}\right)$	$e\left(\frac{119}{171}\right)$
$\chi_{8664}(725,\cdot)$	$1$	$1$	$e\left(\frac{50}{171}\right)$	$e\left(\frac{55}{57}\right)$	$e\left(\frac{26}{57}\right)$	$e\left(\frac{37}{171}\right)$	$e\left(\frac{121}{342}\right)$	$e\left(\frac{287}{342}\right)$	$e\left(\frac{100}{171}\right)$	$e\left(\frac{311}{342}\right)$	$e\left(\frac{17}{114}\right)$	$e\left(\frac{44}{171}\right)$
$\chi_{8664}(773,\cdot)$	$1$	$1$	$e\left(\frac{103}{171}\right)$	$e\left(\frac{5}{57}\right)$	$e\left(\frac{49}{57}\right)$	$e\left(\frac{107}{171}\right)$	$e\left(\frac{239}{342}\right)$	$e\left(\frac{109}{342}\right)$	$e\left(\frac{35}{171}\right)$	$e\left(\frac{49}{342}\right)$	$e\left(\frac{43}{114}\right)$	$e\left(\frac{118}{171}\right)$
$\chi_{8664}(869,\cdot)$	$1$	$1$	$e\left(\frac{137}{171}\right)$	$e\left(\frac{31}{57}\right)$	$e\left(\frac{53}{57}\right)$	$e\left(\frac{139}{171}\right)$	$e\left(\frac{205}{342}\right)$	$e\left(\frac{311}{342}\right)$	$e\left(\frac{103}{171}\right)$	$e\left(\frac{281}{342}\right)$	$e\left(\frac{107}{114}\right)$	$e\left(\frac{59}{171}\right)$
$\chi_{8664}(941,\cdot)$	$1$	$1$	$e\left(\frac{46}{171}\right)$	$e\left(\frac{5}{57}\right)$	$e\left(\frac{49}{57}\right)$	$e\left(\frac{164}{171}\right)$	$e\left(\frac{125}{342}\right)$	$e\left(\frac{223}{342}\right)$	$e\left(\frac{92}{171}\right)$	$e\left(\frac{163}{342}\right)$	$e\left(\frac{43}{114}\right)$	$e\left(\frac{61}{171}\right)$
$\chi_{8664}(965,\cdot)$	$1$	$1$	$e\left(\frac{79}{171}\right)$	$e\left(\frac{47}{57}\right)$	$e\left(\frac{16}{57}\right)$	$e\left(\frac{14}{171}\right)$	$e\left(\frac{263}{342}\right)$	$e\left(\frac{67}{342}\right)$	$e\left(\frac{158}{171}\right)$	$e\left(\frac{187}{342}\right)$	$e\left(\frac{85}{114}\right)$	$e\left(\frac{49}{171}\right)$
$\chi_{8664}(1085,\cdot)$	$1$	$1$	$e\left(\frac{116}{171}\right)$	$e\left(\frac{25}{57}\right)$	$e\left(\frac{17}{57}\right)$	$e\left(\frac{79}{171}\right)$	$e\left(\frac{55}{342}\right)$	$e\left(\frac{317}{342}\right)$	$e\left(\frac{61}{171}\right)$	$e\left(\frac{17}{342}\right)$	$e\left(\frac{101}{114}\right)$	$e\left(\frac{20}{171}\right)$
$\chi_{8664}(1181,\cdot)$	$1$	$1$	$e\left(\frac{32}{171}\right)$	$e\left(\frac{1}{57}\right)$	$e\left(\frac{44}{57}\right)$	$e\left(\frac{10}{171}\right)$	$e\left(\frac{139}{342}\right)$	$e\left(\frac{341}{342}\right)$	$e\left(\frac{64}{171}\right)$	$e\left(\frac{329}{342}\right)$	$e\left(\frac{77}{114}\right)$	$e\left(\frac{35}{171}\right)$
$\chi_{8664}(1229,\cdot)$	$1$	$1$	$e\left(\frac{112}{171}\right)$	$e\left(\frac{32}{57}\right)$	$e\left(\frac{40}{57}\right)$	$e\left(\frac{35}{171}\right)$	$e\left(\frac{59}{342}\right)$	$e\left(\frac{253}{342}\right)$	$e\left(\frac{53}{171}\right)$	$e\left(\frac{211}{342}\right)$	$e\left(\frac{13}{114}\right)$	$e\left(\frac{37}{171}\right)$
$\chi_{8664}(1325,\cdot)$	$1$	$1$	$e\left(\frac{11}{171}\right)$	$e\left(\frac{52}{57}\right)$	$e\left(\frac{8}{57}\right)$	$e\left(\frac{121}{171}\right)$	$e\left(\frac{331}{342}\right)$	$e\left(\frac{5}{342}\right)$	$e\left(\frac{22}{171}\right)$	$e\left(\frac{65}{342}\right)$	$e\left(\frac{71}{114}\right)$	$e\left(\frac{167}{171}\right)$
$\chi_{8664}(1397,\cdot)$	$1$	$1$	$e\left(\frac{109}{171}\right)$	$e\left(\frac{23}{57}\right)$	$e\left(\frac{43}{57}\right)$	$e\left(\frac{2}{171}\right)$	$e\left(\frac{233}{342}\right)$	$e\left(\frac{205}{342}\right)$	$e\left(\frac{47}{171}\right)$	$e\left(\frac{271}{342}\right)$	$e\left(\frac{61}{114}\right)$	$e\left(\frac{7}{171}\right)$
$\chi_{8664}(1421,\cdot)$	$1$	$1$	$e\left(\frac{7}{171}\right)$	$e\left(\frac{2}{57}\right)$	$e\left(\frac{31}{57}\right)$	$e\left(\frac{77}{171}\right)$	$e\left(\frac{335}{342}\right)$	$e\left(\frac{283}{342}\right)$	$e\left(\frac{14}{171}\right)$	$e\left(\frac{259}{342}\right)$	$e\left(\frac{97}{114}\right)$	$e\left(\frac{13}{171}\right)$
$\chi_{8664}(1541,\cdot)$	$1$	$1$	$e\left(\frac{89}{171}\right)$	$e\left(\frac{1}{57}\right)$	$e\left(\frac{44}{57}\right)$	$e\left(\frac{124}{171}\right)$	$e\left(\frac{253}{342}\right)$	$e\left(\frac{227}{342}\right)$	$e\left(\frac{7}{171}\right)$	$e\left(\frac{215}{342}\right)$	$e\left(\frac{77}{114}\right)$	$e\left(\frac{92}{171}\right)$
$\chi_{8664}(1637,\cdot)$	$1$	$1$	$e\left(\frac{14}{171}\right)$	$e\left(\frac{4}{57}\right)$	$e\left(\frac{5}{57}\right)$	$e\left(\frac{154}{171}\right)$	$e\left(\frac{157}{342}\right)$	$e\left(\frac{53}{342}\right)$	$e\left(\frac{28}{171}\right)$	$e\left(\frac{5}{342}\right)$	$e\left(\frac{23}{114}\right)$	$e\left(\frac{26}{171}\right)$
$\chi_{8664}(1685,\cdot)$	$1$	$1$	$e\left(\frac{121}{171}\right)$	$e\left(\frac{2}{57}\right)$	$e\left(\frac{31}{57}\right)$	$e\left(\frac{134}{171}\right)$	$e\left(\frac{221}{342}\right)$	$e\left(\frac{55}{342}\right)$	$e\left(\frac{71}{171}\right)$	$e\left(\frac{31}{342}\right)$	$e\left(\frac{97}{114}\right)$	$e\left(\frac{127}{171}\right)$
$\chi_{8664}(1781,\cdot)$	$1$	$1$	$e\left(\frac{56}{171}\right)$	$e\left(\frac{16}{57}\right)$	$e\left(\frac{20}{57}\right)$	$e\left(\frac{103}{171}\right)$	$e\left(\frac{115}{342}\right)$	$e\left(\frac{41}{342}\right)$	$e\left(\frac{112}{171}\right)$	$e\left(\frac{191}{342}\right)$	$e\left(\frac{35}{114}\right)$	$e\left(\frac{104}{171}\right)$
$\chi_{8664}(1853,\cdot)$	$1$	$1$	$e\left(\frac{1}{171}\right)$	$e\left(\frac{41}{57}\right)$	$e\left(\frac{37}{57}\right)$	$e\left(\frac{11}{171}\right)$	$e\left(\frac{341}{342}\right)$	$e\left(\frac{187}{342}\right)$	$e\left(\frac{2}{171}\right)$	$e\left(\frac{37}{342}\right)$	$e\left(\frac{79}{114}\right)$	$e\left(\frac{124}{171}\right)$
$\chi_{8664}(1877,\cdot)$	$1$	$1$	$e\left(\frac{106}{171}\right)$	$e\left(\frac{14}{57}\right)$	$e\left(\frac{46}{57}\right)$	$e\left(\frac{140}{171}\right)$	$e\left(\frac{65}{342}\right)$	$e\left(\frac{157}{342}\right)$	$e\left(\frac{41}{171}\right)$	$e\left(\frac{331}{342}\right)$	$e\left(\frac{109}{114}\right)$	$e\left(\frac{148}{171}\right)$
$\chi_{8664}(1997,\cdot)$	$1$	$1$	$e\left(\frac{62}{171}\right)$	$e\left(\frac{34}{57}\right)$	$e\left(\frac{14}{57}\right)$	$e\left(\frac{169}{171}\right)$	$e\left(\frac{109}{342}\right)$	$e\left(\frac{137}{342}\right)$	$e\left(\frac{124}{171}\right)$	$e\left(\frac{71}{342}\right)$	$e\left(\frac{53}{114}\right)$	$e\left(\frac{164}{171}\right)$
$\chi_{8664}(2093,\cdot)$	$1$	$1$	$e\left(\frac{167}{171}\right)$	$e\left(\frac{7}{57}\right)$	$e\left(\frac{23}{57}\right)$	$e\left(\frac{127}{171}\right)$	$e\left(\frac{175}{342}\right)$	$e\left(\frac{107}{342}\right)$	$e\left(\frac{163}{171}\right)$	$e\left(\frac{23}{342}\right)$	$e\left(\frac{83}{114}\right)$	$e\left(\frac{17}{171}\right)$
$\chi_{8664}(2141,\cdot)$	$1$	$1$	$e\left(\frac{130}{171}\right)$	$e\left(\frac{29}{57}\right)$	$e\left(\frac{22}{57}\right)$	$e\left(\frac{62}{171}\right)$	$e\left(\frac{41}{342}\right)$	$e\left(\frac{199}{342}\right)$	$e\left(\frac{89}{171}\right)$	$e\left(\frac{193}{342}\right)$	$e\left(\frac{67}{114}\right)$	$e\left(\frac{46}{171}\right)$
$\chi_{8664}(2237,\cdot)$	$1$	$1$	$e\left(\frac{101}{171}\right)$	$e\left(\frac{37}{57}\right)$	$e\left(\frac{32}{57}\right)$	$e\left(\frac{85}{171}\right)$	$e\left(\frac{241}{342}\right)$	$e\left(\frac{77}{342}\right)$	$e\left(\frac{31}{171}\right)$	$e\left(\frac{317}{342}\right)$	$e\left(\frac{113}{114}\right)$	$e\left(\frac{41}{171}\right)$
$\chi_{8664}(2309,\cdot)$	$1$	$1$	$e\left(\frac{64}{171}\right)$	$e\left(\frac{2}{57}\right)$	$e\left(\frac{31}{57}\right)$	$e\left(\frac{20}{171}\right)$	$e\left(\frac{107}{342}\right)$	$e\left(\frac{169}{342}\right)$	$e\left(\frac{128}{171}\right)$	$e\left(\frac{145}{342}\right)$	$e\left(\frac{97}{114}\right)$	$e\left(\frac{70}{171}\right)$

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	\(-1\)	\(1\)	\(5\)	\(7\)	\(11\)	\(13\)	\(17\)	\(23\)	\(25\)	\(29\)	\(31\)	\(35\)
\(\chi_{8664}(29,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{91}{171}\right)\)	\(e\left(\frac{26}{57}\right)\)	\(e\left(\frac{4}{57}\right)\)	\(e\left(\frac{146}{171}\right)\)	\(e\left(\frac{251}{342}\right)\)	\(e\left(\frac{259}{342}\right)\)	\(e\left(\frac{11}{171}\right)\)	\(e\left(\frac{289}{342}\right)\)	\(e\left(\frac{7}{114}\right)\)	\(e\left(\frac{169}{171}\right)\)
\(\chi_{8664}(53,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{52}{171}\right)\)	\(e\left(\frac{23}{57}\right)\)	\(e\left(\frac{43}{57}\right)\)	\(e\left(\frac{59}{171}\right)\)	\(e\left(\frac{119}{342}\right)\)	\(e\left(\frac{319}{342}\right)\)	\(e\left(\frac{104}{171}\right)\)	\(e\left(\frac{43}{342}\right)\)	\(e\left(\frac{61}{114}\right)\)	\(e\left(\frac{121}{171}\right)\)
\(\chi_{8664}(173,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{170}{171}\right)\)	\(e\left(\frac{16}{57}\right)\)	\(e\left(\frac{20}{57}\right)\)	\(e\left(\frac{160}{171}\right)\)	\(e\left(\frac{1}{342}\right)\)	\(e\left(\frac{155}{342}\right)\)	\(e\left(\frac{169}{171}\right)\)	\(e\left(\frac{305}{342}\right)\)	\(e\left(\frac{35}{114}\right)\)	\(e\left(\frac{47}{171}\right)\)
\(\chi_{8664}(269,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{68}{171}\right)\)	\(e\left(\frac{52}{57}\right)\)	\(e\left(\frac{8}{57}\right)\)	\(e\left(\frac{64}{171}\right)\)	\(e\left(\frac{103}{342}\right)\)	\(e\left(\frac{233}{342}\right)\)	\(e\left(\frac{136}{171}\right)\)	\(e\left(\frac{293}{342}\right)\)	\(e\left(\frac{71}{114}\right)\)	\(e\left(\frac{53}{171}\right)\)
\(\chi_{8664}(317,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{94}{171}\right)\)	\(e\left(\frac{35}{57}\right)\)	\(e\left(\frac{1}{57}\right)\)	\(e\left(\frac{8}{171}\right)\)	\(e\left(\frac{77}{342}\right)\)	\(e\left(\frac{307}{342}\right)\)	\(e\left(\frac{17}{171}\right)\)	\(e\left(\frac{229}{342}\right)\)	\(e\left(\frac{73}{114}\right)\)	\(e\left(\frac{28}{171}\right)\)
\(\chi_{8664}(413,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{92}{171}\right)\)	\(e\left(\frac{10}{57}\right)\)	\(e\left(\frac{41}{57}\right)\)	\(e\left(\frac{157}{171}\right)\)	\(e\left(\frac{79}{342}\right)\)	\(e\left(\frac{275}{342}\right)\)	\(e\left(\frac{13}{171}\right)\)	\(e\left(\frac{155}{342}\right)\)	\(e\left(\frac{29}{114}\right)\)	\(e\left(\frac{122}{171}\right)\)
\(\chi_{8664}(485,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{154}{171}\right)\)	\(e\left(\frac{44}{57}\right)\)	\(e\left(\frac{55}{57}\right)\)	\(e\left(\frac{155}{171}\right)\)	\(e\left(\frac{17}{342}\right)\)	\(e\left(\frac{241}{342}\right)\)	\(e\left(\frac{137}{171}\right)\)	\(e\left(\frac{55}{342}\right)\)	\(e\left(\frac{25}{114}\right)\)	\(e\left(\frac{115}{171}\right)\)
\(\chi_{8664}(509,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{151}{171}\right)\)	\(e\left(\frac{35}{57}\right)\)	\(e\left(\frac{1}{57}\right)\)	\(e\left(\frac{122}{171}\right)\)	\(e\left(\frac{191}{342}\right)\)	\(e\left(\frac{193}{342}\right)\)	\(e\left(\frac{131}{171}\right)\)	\(e\left(\frac{115}{342}\right)\)	\(e\left(\frac{73}{114}\right)\)	\(e\left(\frac{85}{171}\right)\)
\(\chi_{8664}(629,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{143}{171}\right)\)	\(e\left(\frac{49}{57}\right)\)	\(e\left(\frac{47}{57}\right)\)	\(e\left(\frac{34}{171}\right)\)	\(e\left(\frac{199}{342}\right)\)	\(e\left(\frac{65}{342}\right)\)	\(e\left(\frac{115}{171}\right)\)	\(e\left(\frac{161}{342}\right)\)	\(e\left(\frac{11}{114}\right)\)	\(e\left(\frac{119}{171}\right)\)
\(\chi_{8664}(725,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{50}{171}\right)\)	\(e\left(\frac{55}{57}\right)\)	\(e\left(\frac{26}{57}\right)\)	\(e\left(\frac{37}{171}\right)\)	\(e\left(\frac{121}{342}\right)\)	\(e\left(\frac{287}{342}\right)\)	\(e\left(\frac{100}{171}\right)\)	\(e\left(\frac{311}{342}\right)\)	\(e\left(\frac{17}{114}\right)\)	\(e\left(\frac{44}{171}\right)\)
\(\chi_{8664}(773,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{103}{171}\right)\)	\(e\left(\frac{5}{57}\right)\)	\(e\left(\frac{49}{57}\right)\)	\(e\left(\frac{107}{171}\right)\)	\(e\left(\frac{239}{342}\right)\)	\(e\left(\frac{109}{342}\right)\)	\(e\left(\frac{35}{171}\right)\)	\(e\left(\frac{49}{342}\right)\)	\(e\left(\frac{43}{114}\right)\)	\(e\left(\frac{118}{171}\right)\)
\(\chi_{8664}(869,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{137}{171}\right)\)	\(e\left(\frac{31}{57}\right)\)	\(e\left(\frac{53}{57}\right)\)	\(e\left(\frac{139}{171}\right)\)	\(e\left(\frac{205}{342}\right)\)	\(e\left(\frac{311}{342}\right)\)	\(e\left(\frac{103}{171}\right)\)	\(e\left(\frac{281}{342}\right)\)	\(e\left(\frac{107}{114}\right)\)	\(e\left(\frac{59}{171}\right)\)
\(\chi_{8664}(941,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{46}{171}\right)\)	\(e\left(\frac{5}{57}\right)\)	\(e\left(\frac{49}{57}\right)\)	\(e\left(\frac{164}{171}\right)\)	\(e\left(\frac{125}{342}\right)\)	\(e\left(\frac{223}{342}\right)\)	\(e\left(\frac{92}{171}\right)\)	\(e\left(\frac{163}{342}\right)\)	\(e\left(\frac{43}{114}\right)\)	\(e\left(\frac{61}{171}\right)\)
\(\chi_{8664}(965,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{79}{171}\right)\)	\(e\left(\frac{47}{57}\right)\)	\(e\left(\frac{16}{57}\right)\)	\(e\left(\frac{14}{171}\right)\)	\(e\left(\frac{263}{342}\right)\)	\(e\left(\frac{67}{342}\right)\)	\(e\left(\frac{158}{171}\right)\)	\(e\left(\frac{187}{342}\right)\)	\(e\left(\frac{85}{114}\right)\)	\(e\left(\frac{49}{171}\right)\)
\(\chi_{8664}(1085,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{116}{171}\right)\)	\(e\left(\frac{25}{57}\right)\)	\(e\left(\frac{17}{57}\right)\)	\(e\left(\frac{79}{171}\right)\)	\(e\left(\frac{55}{342}\right)\)	\(e\left(\frac{317}{342}\right)\)	\(e\left(\frac{61}{171}\right)\)	\(e\left(\frac{17}{342}\right)\)	\(e\left(\frac{101}{114}\right)\)	\(e\left(\frac{20}{171}\right)\)
\(\chi_{8664}(1181,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{32}{171}\right)\)	\(e\left(\frac{1}{57}\right)\)	\(e\left(\frac{44}{57}\right)\)	\(e\left(\frac{10}{171}\right)\)	\(e\left(\frac{139}{342}\right)\)	\(e\left(\frac{341}{342}\right)\)	\(e\left(\frac{64}{171}\right)\)	\(e\left(\frac{329}{342}\right)\)	\(e\left(\frac{77}{114}\right)\)	\(e\left(\frac{35}{171}\right)\)
\(\chi_{8664}(1229,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{112}{171}\right)\)	\(e\left(\frac{32}{57}\right)\)	\(e\left(\frac{40}{57}\right)\)	\(e\left(\frac{35}{171}\right)\)	\(e\left(\frac{59}{342}\right)\)	\(e\left(\frac{253}{342}\right)\)	\(e\left(\frac{53}{171}\right)\)	\(e\left(\frac{211}{342}\right)\)	\(e\left(\frac{13}{114}\right)\)	\(e\left(\frac{37}{171}\right)\)
\(\chi_{8664}(1325,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{171}\right)\)	\(e\left(\frac{52}{57}\right)\)	\(e\left(\frac{8}{57}\right)\)	\(e\left(\frac{121}{171}\right)\)	\(e\left(\frac{331}{342}\right)\)	\(e\left(\frac{5}{342}\right)\)	\(e\left(\frac{22}{171}\right)\)	\(e\left(\frac{65}{342}\right)\)	\(e\left(\frac{71}{114}\right)\)	\(e\left(\frac{167}{171}\right)\)
\(\chi_{8664}(1397,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{109}{171}\right)\)	\(e\left(\frac{23}{57}\right)\)	\(e\left(\frac{43}{57}\right)\)	\(e\left(\frac{2}{171}\right)\)	\(e\left(\frac{233}{342}\right)\)	\(e\left(\frac{205}{342}\right)\)	\(e\left(\frac{47}{171}\right)\)	\(e\left(\frac{271}{342}\right)\)	\(e\left(\frac{61}{114}\right)\)	\(e\left(\frac{7}{171}\right)\)
\(\chi_{8664}(1421,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{171}\right)\)	\(e\left(\frac{2}{57}\right)\)	\(e\left(\frac{31}{57}\right)\)	\(e\left(\frac{77}{171}\right)\)	\(e\left(\frac{335}{342}\right)\)	\(e\left(\frac{283}{342}\right)\)	\(e\left(\frac{14}{171}\right)\)	\(e\left(\frac{259}{342}\right)\)	\(e\left(\frac{97}{114}\right)\)	\(e\left(\frac{13}{171}\right)\)
\(\chi_{8664}(1541,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{89}{171}\right)\)	\(e\left(\frac{1}{57}\right)\)	\(e\left(\frac{44}{57}\right)\)	\(e\left(\frac{124}{171}\right)\)	\(e\left(\frac{253}{342}\right)\)	\(e\left(\frac{227}{342}\right)\)	\(e\left(\frac{7}{171}\right)\)	\(e\left(\frac{215}{342}\right)\)	\(e\left(\frac{77}{114}\right)\)	\(e\left(\frac{92}{171}\right)\)
\(\chi_{8664}(1637,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{14}{171}\right)\)	\(e\left(\frac{4}{57}\right)\)	\(e\left(\frac{5}{57}\right)\)	\(e\left(\frac{154}{171}\right)\)	\(e\left(\frac{157}{342}\right)\)	\(e\left(\frac{53}{342}\right)\)	\(e\left(\frac{28}{171}\right)\)	\(e\left(\frac{5}{342}\right)\)	\(e\left(\frac{23}{114}\right)\)	\(e\left(\frac{26}{171}\right)\)
\(\chi_{8664}(1685,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{121}{171}\right)\)	\(e\left(\frac{2}{57}\right)\)	\(e\left(\frac{31}{57}\right)\)	\(e\left(\frac{134}{171}\right)\)	\(e\left(\frac{221}{342}\right)\)	\(e\left(\frac{55}{342}\right)\)	\(e\left(\frac{71}{171}\right)\)	\(e\left(\frac{31}{342}\right)\)	\(e\left(\frac{97}{114}\right)\)	\(e\left(\frac{127}{171}\right)\)
\(\chi_{8664}(1781,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{56}{171}\right)\)	\(e\left(\frac{16}{57}\right)\)	\(e\left(\frac{20}{57}\right)\)	\(e\left(\frac{103}{171}\right)\)	\(e\left(\frac{115}{342}\right)\)	\(e\left(\frac{41}{342}\right)\)	\(e\left(\frac{112}{171}\right)\)	\(e\left(\frac{191}{342}\right)\)	\(e\left(\frac{35}{114}\right)\)	\(e\left(\frac{104}{171}\right)\)
\(\chi_{8664}(1853,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{171}\right)\)	\(e\left(\frac{41}{57}\right)\)	\(e\left(\frac{37}{57}\right)\)	\(e\left(\frac{11}{171}\right)\)	\(e\left(\frac{341}{342}\right)\)	\(e\left(\frac{187}{342}\right)\)	\(e\left(\frac{2}{171}\right)\)	\(e\left(\frac{37}{342}\right)\)	\(e\left(\frac{79}{114}\right)\)	\(e\left(\frac{124}{171}\right)\)
\(\chi_{8664}(1877,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{106}{171}\right)\)	\(e\left(\frac{14}{57}\right)\)	\(e\left(\frac{46}{57}\right)\)	\(e\left(\frac{140}{171}\right)\)	\(e\left(\frac{65}{342}\right)\)	\(e\left(\frac{157}{342}\right)\)	\(e\left(\frac{41}{171}\right)\)	\(e\left(\frac{331}{342}\right)\)	\(e\left(\frac{109}{114}\right)\)	\(e\left(\frac{148}{171}\right)\)
\(\chi_{8664}(1997,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{62}{171}\right)\)	\(e\left(\frac{34}{57}\right)\)	\(e\left(\frac{14}{57}\right)\)	\(e\left(\frac{169}{171}\right)\)	\(e\left(\frac{109}{342}\right)\)	\(e\left(\frac{137}{342}\right)\)	\(e\left(\frac{124}{171}\right)\)	\(e\left(\frac{71}{342}\right)\)	\(e\left(\frac{53}{114}\right)\)	\(e\left(\frac{164}{171}\right)\)
\(\chi_{8664}(2093,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{167}{171}\right)\)	\(e\left(\frac{7}{57}\right)\)	\(e\left(\frac{23}{57}\right)\)	\(e\left(\frac{127}{171}\right)\)	\(e\left(\frac{175}{342}\right)\)	\(e\left(\frac{107}{342}\right)\)	\(e\left(\frac{163}{171}\right)\)	\(e\left(\frac{23}{342}\right)\)	\(e\left(\frac{83}{114}\right)\)	\(e\left(\frac{17}{171}\right)\)
\(\chi_{8664}(2141,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{130}{171}\right)\)	\(e\left(\frac{29}{57}\right)\)	\(e\left(\frac{22}{57}\right)\)	\(e\left(\frac{62}{171}\right)\)	\(e\left(\frac{41}{342}\right)\)	\(e\left(\frac{199}{342}\right)\)	\(e\left(\frac{89}{171}\right)\)	\(e\left(\frac{193}{342}\right)\)	\(e\left(\frac{67}{114}\right)\)	\(e\left(\frac{46}{171}\right)\)
\(\chi_{8664}(2237,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{101}{171}\right)\)	\(e\left(\frac{37}{57}\right)\)	\(e\left(\frac{32}{57}\right)\)	\(e\left(\frac{85}{171}\right)\)	\(e\left(\frac{241}{342}\right)\)	\(e\left(\frac{77}{342}\right)\)	\(e\left(\frac{31}{171}\right)\)	\(e\left(\frac{317}{342}\right)\)	\(e\left(\frac{113}{114}\right)\)	\(e\left(\frac{41}{171}\right)\)
\(\chi_{8664}(2309,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{64}{171}\right)\)	\(e\left(\frac{2}{57}\right)\)	\(e\left(\frac{31}{57}\right)\)	\(e\left(\frac{20}{171}\right)\)	\(e\left(\frac{107}{342}\right)\)	\(e\left(\frac{169}{342}\right)\)	\(e\left(\frac{128}{171}\right)\)	\(e\left(\frac{145}{342}\right)\)	\(e\left(\frac{97}{114}\right)\)	\(e\left(\frac{70}{171}\right)\)

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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	8664.dp
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)