LMFDB - Dirichlet character orbit 8712.eq

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(8712, base_ring=CyclotomicField(330)) M = H._module chi = DirichletCharacter(H, M([165,165,110,201])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(139,8712)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$8712$
Conductor:	$8712$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$330$	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:	$\Q(\zeta_{165})$
Fixed field:	Number field defined by a degree 330 polynomial (not computed)

First 31 of 80 characters in Galois orbit

Character	$-1$	$1$	$5$	$7$	$13$	$17$	$19$	$23$	$25$	$29$	$31$	$35$
$\chi_{8712}(139,\cdot)$	$1$	$1$	$e\left(\frac{79}{330}\right)$	$e\left(\frac{16}{165}\right)$	$e\left(\frac{113}{165}\right)$	$e\left(\frac{93}{110}\right)$	$e\left(\frac{61}{110}\right)$	$e\left(\frac{53}{66}\right)$	$e\left(\frac{79}{165}\right)$	$e\left(\frac{31}{165}\right)$	$e\left(\frac{181}{330}\right)$	$e\left(\frac{37}{110}\right)$
$\chi_{8712}(211,\cdot)$	$1$	$1$	$e\left(\frac{7}{330}\right)$	$e\left(\frac{133}{165}\right)$	$e\left(\frac{104}{165}\right)$	$e\left(\frac{89}{110}\right)$	$e\left(\frac{43}{110}\right)$	$e\left(\frac{59}{66}\right)$	$e\left(\frac{7}{165}\right)$	$e\left(\frac{103}{165}\right)$	$e\left(\frac{133}{330}\right)$	$e\left(\frac{91}{110}\right)$
$\chi_{8712}(259,\cdot)$	$1$	$1$	$e\left(\frac{263}{330}\right)$	$e\left(\frac{47}{165}\right)$	$e\left(\frac{136}{165}\right)$	$e\left(\frac{91}{110}\right)$	$e\left(\frac{107}{110}\right)$	$e\left(\frac{1}{66}\right)$	$e\left(\frac{98}{165}\right)$	$e\left(\frac{122}{165}\right)$	$e\left(\frac{47}{330}\right)$	$e\left(\frac{9}{110}\right)$
$\chi_{8712}(283,\cdot)$	$1$	$1$	$e\left(\frac{211}{330}\right)$	$e\left(\frac{49}{165}\right)$	$e\left(\frac{47}{165}\right)$	$e\left(\frac{27}{110}\right)$	$e\left(\frac{39}{110}\right)$	$e\left(\frac{53}{66}\right)$	$e\left(\frac{46}{165}\right)$	$e\left(\frac{64}{165}\right)$	$e\left(\frac{49}{330}\right)$	$e\left(\frac{103}{110}\right)$
$\chi_{8712}(547,\cdot)$	$1$	$1$	$e\left(\frac{311}{330}\right)$	$e\left(\frac{134}{165}\right)$	$e\left(\frac{142}{165}\right)$	$e\left(\frac{57}{110}\right)$	$e\left(\frac{9}{110}\right)$	$e\left(\frac{19}{66}\right)$	$e\left(\frac{146}{165}\right)$	$e\left(\frac{74}{165}\right)$	$e\left(\frac{299}{330}\right)$	$e\left(\frac{83}{110}\right)$
$\chi_{8712}(787,\cdot)$	$1$	$1$	$e\left(\frac{163}{330}\right)$	$e\left(\frac{127}{165}\right)$	$e\left(\frac{41}{165}\right)$	$e\left(\frac{61}{110}\right)$	$e\left(\frac{27}{110}\right)$	$e\left(\frac{35}{66}\right)$	$e\left(\frac{163}{165}\right)$	$e\left(\frac{112}{165}\right)$	$e\left(\frac{127}{330}\right)$	$e\left(\frac{29}{110}\right)$
$\chi_{8712}(931,\cdot)$	$1$	$1$	$e\left(\frac{139}{330}\right)$	$e\left(\frac{1}{165}\right)$	$e\left(\frac{38}{165}\right)$	$e\left(\frac{23}{110}\right)$	$e\left(\frac{21}{110}\right)$	$e\left(\frac{59}{66}\right)$	$e\left(\frac{139}{165}\right)$	$e\left(\frac{136}{165}\right)$	$e\left(\frac{1}{330}\right)$	$e\left(\frac{47}{110}\right)$
$\chi_{8712}(1003,\cdot)$	$1$	$1$	$e\left(\frac{217}{330}\right)$	$e\left(\frac{163}{165}\right)$	$e\left(\frac{89}{165}\right)$	$e\left(\frac{9}{110}\right)$	$e\left(\frac{13}{110}\right)$	$e\left(\frac{47}{66}\right)$	$e\left(\frac{52}{165}\right)$	$e\left(\frac{58}{165}\right)$	$e\left(\frac{163}{330}\right)$	$e\left(\frac{71}{110}\right)$
$\chi_{8712}(1051,\cdot)$	$1$	$1$	$e\left(\frac{113}{330}\right)$	$e\left(\frac{2}{165}\right)$	$e\left(\frac{76}{165}\right)$	$e\left(\frac{101}{110}\right)$	$e\left(\frac{97}{110}\right)$	$e\left(\frac{19}{66}\right)$	$e\left(\frac{113}{165}\right)$	$e\left(\frac{107}{165}\right)$	$e\left(\frac{167}{330}\right)$	$e\left(\frac{39}{110}\right)$
$\chi_{8712}(1075,\cdot)$	$1$	$1$	$e\left(\frac{181}{330}\right)$	$e\left(\frac{139}{165}\right)$	$e\left(\frac{2}{165}\right)$	$e\left(\frac{7}{110}\right)$	$e\left(\frac{59}{110}\right)$	$e\left(\frac{17}{66}\right)$	$e\left(\frac{16}{165}\right)$	$e\left(\frac{94}{165}\right)$	$e\left(\frac{139}{330}\right)$	$e\left(\frac{43}{110}\right)$
$\chi_{8712}(1195,\cdot)$	$1$	$1$	$e\left(\frac{269}{330}\right)$	$e\left(\frac{161}{165}\right)$	$e\left(\frac{13}{165}\right)$	$e\left(\frac{73}{110}\right)$	$e\left(\frac{81}{110}\right)$	$e\left(\frac{61}{66}\right)$	$e\left(\frac{104}{165}\right)$	$e\left(\frac{116}{165}\right)$	$e\left(\frac{161}{330}\right)$	$e\left(\frac{87}{110}\right)$
$\chi_{8712}(1267,\cdot)$	$1$	$1$	$e\left(\frac{287}{330}\right)$	$e\left(\frac{8}{165}\right)$	$e\left(\frac{139}{165}\right)$	$e\left(\frac{19}{110}\right)$	$e\left(\frac{3}{110}\right)$	$e\left(\frac{43}{66}\right)$	$e\left(\frac{122}{165}\right)$	$e\left(\frac{98}{165}\right)$	$e\left(\frac{173}{330}\right)$	$e\left(\frac{101}{110}\right)$
$\chi_{8712}(1339,\cdot)$	$1$	$1$	$e\left(\frac{281}{330}\right)$	$e\left(\frac{59}{165}\right)$	$e\left(\frac{97}{165}\right)$	$e\left(\frac{37}{110}\right)$	$e\left(\frac{29}{110}\right)$	$e\left(\frac{49}{66}\right)$	$e\left(\frac{116}{165}\right)$	$e\left(\frac{104}{165}\right)$	$e\left(\frac{59}{330}\right)$	$e\left(\frac{23}{110}\right)$
$\chi_{8712}(1579,\cdot)$	$1$	$1$	$e\left(\frac{13}{330}\right)$	$e\left(\frac{82}{165}\right)$	$e\left(\frac{146}{165}\right)$	$e\left(\frac{71}{110}\right)$	$e\left(\frac{17}{110}\right)$	$e\left(\frac{53}{66}\right)$	$e\left(\frac{13}{165}\right)$	$e\left(\frac{97}{165}\right)$	$e\left(\frac{247}{330}\right)$	$e\left(\frac{59}{110}\right)$
$\chi_{8712}(1723,\cdot)$	$1$	$1$	$e\left(\frac{199}{330}\right)$	$e\left(\frac{151}{165}\right)$	$e\left(\frac{128}{165}\right)$	$e\left(\frac{63}{110}\right)$	$e\left(\frac{91}{110}\right)$	$e\left(\frac{65}{66}\right)$	$e\left(\frac{34}{165}\right)$	$e\left(\frac{76}{165}\right)$	$e\left(\frac{151}{330}\right)$	$e\left(\frac{57}{110}\right)$
$\chi_{8712}(1795,\cdot)$	$1$	$1$	$e\left(\frac{97}{330}\right)$	$e\left(\frac{28}{165}\right)$	$e\left(\frac{74}{165}\right)$	$e\left(\frac{39}{110}\right)$	$e\left(\frac{93}{110}\right)$	$e\left(\frac{35}{66}\right)$	$e\left(\frac{97}{165}\right)$	$e\left(\frac{13}{165}\right)$	$e\left(\frac{193}{330}\right)$	$e\left(\frac{51}{110}\right)$
$\chi_{8712}(1843,\cdot)$	$1$	$1$	$e\left(\frac{293}{330}\right)$	$e\left(\frac{122}{165}\right)$	$e\left(\frac{16}{165}\right)$	$e\left(\frac{1}{110}\right)$	$e\left(\frac{87}{110}\right)$	$e\left(\frac{37}{66}\right)$	$e\left(\frac{128}{165}\right)$	$e\left(\frac{92}{165}\right)$	$e\left(\frac{287}{330}\right)$	$e\left(\frac{69}{110}\right)$
$\chi_{8712}(1867,\cdot)$	$1$	$1$	$e\left(\frac{151}{330}\right)$	$e\left(\frac{64}{165}\right)$	$e\left(\frac{122}{165}\right)$	$e\left(\frac{97}{110}\right)$	$e\left(\frac{79}{110}\right)$	$e\left(\frac{47}{66}\right)$	$e\left(\frac{151}{165}\right)$	$e\left(\frac{124}{165}\right)$	$e\left(\frac{229}{330}\right)$	$e\left(\frac{93}{110}\right)$
$\chi_{8712}(1987,\cdot)$	$1$	$1$	$e\left(\frac{329}{330}\right)$	$e\left(\frac{146}{165}\right)$	$e\left(\frac{103}{165}\right)$	$e\left(\frac{3}{110}\right)$	$e\left(\frac{41}{110}\right)$	$e\left(\frac{1}{66}\right)$	$e\left(\frac{164}{165}\right)$	$e\left(\frac{56}{165}\right)$	$e\left(\frac{311}{330}\right)$	$e\left(\frac{97}{110}\right)$
$\chi_{8712}(2059,\cdot)$	$1$	$1$	$e\left(\frac{167}{330}\right)$	$e\left(\frac{38}{165}\right)$	$e\left(\frac{124}{165}\right)$	$e\left(\frac{49}{110}\right)$	$e\left(\frac{83}{110}\right)$	$e\left(\frac{31}{66}\right)$	$e\left(\frac{2}{165}\right)$	$e\left(\frac{53}{165}\right)$	$e\left(\frac{203}{330}\right)$	$e\left(\frac{81}{110}\right)$
$\chi_{8712}(2131,\cdot)$	$1$	$1$	$e\left(\frac{251}{330}\right)$	$e\left(\frac{149}{165}\right)$	$e\left(\frac{52}{165}\right)$	$e\left(\frac{17}{110}\right)$	$e\left(\frac{49}{110}\right)$	$e\left(\frac{13}{66}\right)$	$e\left(\frac{86}{165}\right)$	$e\left(\frac{134}{165}\right)$	$e\left(\frac{149}{330}\right)$	$e\left(\frac{73}{110}\right)$
$\chi_{8712}(2371,\cdot)$	$1$	$1$	$e\left(\frac{193}{330}\right)$	$e\left(\frac{37}{165}\right)$	$e\left(\frac{86}{165}\right)$	$e\left(\frac{81}{110}\right)$	$e\left(\frac{7}{110}\right)$	$e\left(\frac{5}{66}\right)$	$e\left(\frac{28}{165}\right)$	$e\left(\frac{82}{165}\right)$	$e\left(\frac{37}{330}\right)$	$e\left(\frac{89}{110}\right)$
$\chi_{8712}(2515,\cdot)$	$1$	$1$	$e\left(\frac{259}{330}\right)$	$e\left(\frac{136}{165}\right)$	$e\left(\frac{53}{165}\right)$	$e\left(\frac{103}{110}\right)$	$e\left(\frac{51}{110}\right)$	$e\left(\frac{5}{66}\right)$	$e\left(\frac{94}{165}\right)$	$e\left(\frac{16}{165}\right)$	$e\left(\frac{301}{330}\right)$	$e\left(\frac{67}{110}\right)$
$\chi_{8712}(2587,\cdot)$	$1$	$1$	$e\left(\frac{307}{330}\right)$	$e\left(\frac{58}{165}\right)$	$e\left(\frac{59}{165}\right)$	$e\left(\frac{69}{110}\right)$	$e\left(\frac{63}{110}\right)$	$e\left(\frac{23}{66}\right)$	$e\left(\frac{142}{165}\right)$	$e\left(\frac{133}{165}\right)$	$e\left(\frac{223}{330}\right)$	$e\left(\frac{31}{110}\right)$
$\chi_{8712}(2779,\cdot)$	$1$	$1$	$e\left(\frac{59}{330}\right)$	$e\left(\frac{131}{165}\right)$	$e\left(\frac{28}{165}\right)$	$e\left(\frac{43}{110}\right)$	$e\left(\frac{1}{110}\right)$	$e\left(\frac{7}{66}\right)$	$e\left(\frac{59}{165}\right)$	$e\left(\frac{161}{165}\right)$	$e\left(\frac{131}{330}\right)$	$e\left(\frac{107}{110}\right)$
$\chi_{8712}(2851,\cdot)$	$1$	$1$	$e\left(\frac{47}{330}\right)$	$e\left(\frac{68}{165}\right)$	$e\left(\frac{109}{165}\right)$	$e\left(\frac{79}{110}\right)$	$e\left(\frac{53}{110}\right)$	$e\left(\frac{19}{66}\right)$	$e\left(\frac{47}{165}\right)$	$e\left(\frac{8}{165}\right)$	$e\left(\frac{233}{330}\right)$	$e\left(\frac{61}{110}\right)$
$\chi_{8712}(2923,\cdot)$	$1$	$1$	$e\left(\frac{221}{330}\right)$	$e\left(\frac{74}{165}\right)$	$e\left(\frac{7}{165}\right)$	$e\left(\frac{107}{110}\right)$	$e\left(\frac{69}{110}\right)$	$e\left(\frac{43}{66}\right)$	$e\left(\frac{56}{165}\right)$	$e\left(\frac{164}{165}\right)$	$e\left(\frac{239}{330}\right)$	$e\left(\frac{13}{110}\right)$
$\chi_{8712}(3163,\cdot)$	$1$	$1$	$e\left(\frac{43}{330}\right)$	$e\left(\frac{157}{165}\right)$	$e\left(\frac{26}{165}\right)$	$e\left(\frac{91}{110}\right)$	$e\left(\frac{107}{110}\right)$	$e\left(\frac{23}{66}\right)$	$e\left(\frac{43}{165}\right)$	$e\left(\frac{67}{165}\right)$	$e\left(\frac{157}{330}\right)$	$e\left(\frac{9}{110}\right)$
$\chi_{8712}(3427,\cdot)$	$1$	$1$	$e\left(\frac{323}{330}\right)$	$e\left(\frac{32}{165}\right)$	$e\left(\frac{61}{165}\right)$	$e\left(\frac{21}{110}\right)$	$e\left(\frac{67}{110}\right)$	$e\left(\frac{7}{66}\right)$	$e\left(\frac{158}{165}\right)$	$e\left(\frac{62}{165}\right)$	$e\left(\frac{197}{330}\right)$	$e\left(\frac{19}{110}\right)$
$\chi_{8712}(3451,\cdot)$	$1$	$1$	$e\left(\frac{91}{330}\right)$	$e\left(\frac{79}{165}\right)$	$e\left(\frac{32}{165}\right)$	$e\left(\frac{57}{110}\right)$	$e\left(\frac{9}{110}\right)$	$e\left(\frac{41}{66}\right)$	$e\left(\frac{91}{165}\right)$	$e\left(\frac{19}{165}\right)$	$e\left(\frac{79}{330}\right)$	$e\left(\frac{83}{110}\right)$
$\chi_{8712}(3571,\cdot)$	$1$	$1$	$e\left(\frac{119}{330}\right)$	$e\left(\frac{116}{165}\right)$	$e\left(\frac{118}{165}\right)$	$e\left(\frac{83}{110}\right)$	$e\left(\frac{71}{110}\right)$	$e\left(\frac{13}{66}\right)$	$e\left(\frac{119}{165}\right)$	$e\left(\frac{101}{165}\right)$	$e\left(\frac{281}{330}\right)$	$e\left(\frac{7}{110}\right)$

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	\(-1\)	\(1\)	\(5\)	\(7\)	\(13\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)	\(35\)
\(\chi_{8712}(139,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{79}{330}\right)\)	\(e\left(\frac{16}{165}\right)\)	\(e\left(\frac{113}{165}\right)\)	\(e\left(\frac{93}{110}\right)\)	\(e\left(\frac{61}{110}\right)\)	\(e\left(\frac{53}{66}\right)\)	\(e\left(\frac{79}{165}\right)\)	\(e\left(\frac{31}{165}\right)\)	\(e\left(\frac{181}{330}\right)\)	\(e\left(\frac{37}{110}\right)\)
\(\chi_{8712}(211,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{330}\right)\)	\(e\left(\frac{133}{165}\right)\)	\(e\left(\frac{104}{165}\right)\)	\(e\left(\frac{89}{110}\right)\)	\(e\left(\frac{43}{110}\right)\)	\(e\left(\frac{59}{66}\right)\)	\(e\left(\frac{7}{165}\right)\)	\(e\left(\frac{103}{165}\right)\)	\(e\left(\frac{133}{330}\right)\)	\(e\left(\frac{91}{110}\right)\)
\(\chi_{8712}(259,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{263}{330}\right)\)	\(e\left(\frac{47}{165}\right)\)	\(e\left(\frac{136}{165}\right)\)	\(e\left(\frac{91}{110}\right)\)	\(e\left(\frac{107}{110}\right)\)	\(e\left(\frac{1}{66}\right)\)	\(e\left(\frac{98}{165}\right)\)	\(e\left(\frac{122}{165}\right)\)	\(e\left(\frac{47}{330}\right)\)	\(e\left(\frac{9}{110}\right)\)
\(\chi_{8712}(283,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{211}{330}\right)\)	\(e\left(\frac{49}{165}\right)\)	\(e\left(\frac{47}{165}\right)\)	\(e\left(\frac{27}{110}\right)\)	\(e\left(\frac{39}{110}\right)\)	\(e\left(\frac{53}{66}\right)\)	\(e\left(\frac{46}{165}\right)\)	\(e\left(\frac{64}{165}\right)\)	\(e\left(\frac{49}{330}\right)\)	\(e\left(\frac{103}{110}\right)\)
\(\chi_{8712}(547,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{311}{330}\right)\)	\(e\left(\frac{134}{165}\right)\)	\(e\left(\frac{142}{165}\right)\)	\(e\left(\frac{57}{110}\right)\)	\(e\left(\frac{9}{110}\right)\)	\(e\left(\frac{19}{66}\right)\)	\(e\left(\frac{146}{165}\right)\)	\(e\left(\frac{74}{165}\right)\)	\(e\left(\frac{299}{330}\right)\)	\(e\left(\frac{83}{110}\right)\)
\(\chi_{8712}(787,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{163}{330}\right)\)	\(e\left(\frac{127}{165}\right)\)	\(e\left(\frac{41}{165}\right)\)	\(e\left(\frac{61}{110}\right)\)	\(e\left(\frac{27}{110}\right)\)	\(e\left(\frac{35}{66}\right)\)	\(e\left(\frac{163}{165}\right)\)	\(e\left(\frac{112}{165}\right)\)	\(e\left(\frac{127}{330}\right)\)	\(e\left(\frac{29}{110}\right)\)
\(\chi_{8712}(931,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{139}{330}\right)\)	\(e\left(\frac{1}{165}\right)\)	\(e\left(\frac{38}{165}\right)\)	\(e\left(\frac{23}{110}\right)\)	\(e\left(\frac{21}{110}\right)\)	\(e\left(\frac{59}{66}\right)\)	\(e\left(\frac{139}{165}\right)\)	\(e\left(\frac{136}{165}\right)\)	\(e\left(\frac{1}{330}\right)\)	\(e\left(\frac{47}{110}\right)\)
\(\chi_{8712}(1003,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{217}{330}\right)\)	\(e\left(\frac{163}{165}\right)\)	\(e\left(\frac{89}{165}\right)\)	\(e\left(\frac{9}{110}\right)\)	\(e\left(\frac{13}{110}\right)\)	\(e\left(\frac{47}{66}\right)\)	\(e\left(\frac{52}{165}\right)\)	\(e\left(\frac{58}{165}\right)\)	\(e\left(\frac{163}{330}\right)\)	\(e\left(\frac{71}{110}\right)\)
\(\chi_{8712}(1051,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{113}{330}\right)\)	\(e\left(\frac{2}{165}\right)\)	\(e\left(\frac{76}{165}\right)\)	\(e\left(\frac{101}{110}\right)\)	\(e\left(\frac{97}{110}\right)\)	\(e\left(\frac{19}{66}\right)\)	\(e\left(\frac{113}{165}\right)\)	\(e\left(\frac{107}{165}\right)\)	\(e\left(\frac{167}{330}\right)\)	\(e\left(\frac{39}{110}\right)\)
\(\chi_{8712}(1075,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{181}{330}\right)\)	\(e\left(\frac{139}{165}\right)\)	\(e\left(\frac{2}{165}\right)\)	\(e\left(\frac{7}{110}\right)\)	\(e\left(\frac{59}{110}\right)\)	\(e\left(\frac{17}{66}\right)\)	\(e\left(\frac{16}{165}\right)\)	\(e\left(\frac{94}{165}\right)\)	\(e\left(\frac{139}{330}\right)\)	\(e\left(\frac{43}{110}\right)\)
\(\chi_{8712}(1195,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{269}{330}\right)\)	\(e\left(\frac{161}{165}\right)\)	\(e\left(\frac{13}{165}\right)\)	\(e\left(\frac{73}{110}\right)\)	\(e\left(\frac{81}{110}\right)\)	\(e\left(\frac{61}{66}\right)\)	\(e\left(\frac{104}{165}\right)\)	\(e\left(\frac{116}{165}\right)\)	\(e\left(\frac{161}{330}\right)\)	\(e\left(\frac{87}{110}\right)\)
\(\chi_{8712}(1267,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{287}{330}\right)\)	\(e\left(\frac{8}{165}\right)\)	\(e\left(\frac{139}{165}\right)\)	\(e\left(\frac{19}{110}\right)\)	\(e\left(\frac{3}{110}\right)\)	\(e\left(\frac{43}{66}\right)\)	\(e\left(\frac{122}{165}\right)\)	\(e\left(\frac{98}{165}\right)\)	\(e\left(\frac{173}{330}\right)\)	\(e\left(\frac{101}{110}\right)\)
\(\chi_{8712}(1339,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{281}{330}\right)\)	\(e\left(\frac{59}{165}\right)\)	\(e\left(\frac{97}{165}\right)\)	\(e\left(\frac{37}{110}\right)\)	\(e\left(\frac{29}{110}\right)\)	\(e\left(\frac{49}{66}\right)\)	\(e\left(\frac{116}{165}\right)\)	\(e\left(\frac{104}{165}\right)\)	\(e\left(\frac{59}{330}\right)\)	\(e\left(\frac{23}{110}\right)\)
\(\chi_{8712}(1579,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{330}\right)\)	\(e\left(\frac{82}{165}\right)\)	\(e\left(\frac{146}{165}\right)\)	\(e\left(\frac{71}{110}\right)\)	\(e\left(\frac{17}{110}\right)\)	\(e\left(\frac{53}{66}\right)\)	\(e\left(\frac{13}{165}\right)\)	\(e\left(\frac{97}{165}\right)\)	\(e\left(\frac{247}{330}\right)\)	\(e\left(\frac{59}{110}\right)\)
\(\chi_{8712}(1723,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{199}{330}\right)\)	\(e\left(\frac{151}{165}\right)\)	\(e\left(\frac{128}{165}\right)\)	\(e\left(\frac{63}{110}\right)\)	\(e\left(\frac{91}{110}\right)\)	\(e\left(\frac{65}{66}\right)\)	\(e\left(\frac{34}{165}\right)\)	\(e\left(\frac{76}{165}\right)\)	\(e\left(\frac{151}{330}\right)\)	\(e\left(\frac{57}{110}\right)\)
\(\chi_{8712}(1795,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{97}{330}\right)\)	\(e\left(\frac{28}{165}\right)\)	\(e\left(\frac{74}{165}\right)\)	\(e\left(\frac{39}{110}\right)\)	\(e\left(\frac{93}{110}\right)\)	\(e\left(\frac{35}{66}\right)\)	\(e\left(\frac{97}{165}\right)\)	\(e\left(\frac{13}{165}\right)\)	\(e\left(\frac{193}{330}\right)\)	\(e\left(\frac{51}{110}\right)\)
\(\chi_{8712}(1843,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{293}{330}\right)\)	\(e\left(\frac{122}{165}\right)\)	\(e\left(\frac{16}{165}\right)\)	\(e\left(\frac{1}{110}\right)\)	\(e\left(\frac{87}{110}\right)\)	\(e\left(\frac{37}{66}\right)\)	\(e\left(\frac{128}{165}\right)\)	\(e\left(\frac{92}{165}\right)\)	\(e\left(\frac{287}{330}\right)\)	\(e\left(\frac{69}{110}\right)\)
\(\chi_{8712}(1867,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{151}{330}\right)\)	\(e\left(\frac{64}{165}\right)\)	\(e\left(\frac{122}{165}\right)\)	\(e\left(\frac{97}{110}\right)\)	\(e\left(\frac{79}{110}\right)\)	\(e\left(\frac{47}{66}\right)\)	\(e\left(\frac{151}{165}\right)\)	\(e\left(\frac{124}{165}\right)\)	\(e\left(\frac{229}{330}\right)\)	\(e\left(\frac{93}{110}\right)\)
\(\chi_{8712}(1987,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{329}{330}\right)\)	\(e\left(\frac{146}{165}\right)\)	\(e\left(\frac{103}{165}\right)\)	\(e\left(\frac{3}{110}\right)\)	\(e\left(\frac{41}{110}\right)\)	\(e\left(\frac{1}{66}\right)\)	\(e\left(\frac{164}{165}\right)\)	\(e\left(\frac{56}{165}\right)\)	\(e\left(\frac{311}{330}\right)\)	\(e\left(\frac{97}{110}\right)\)
\(\chi_{8712}(2059,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{167}{330}\right)\)	\(e\left(\frac{38}{165}\right)\)	\(e\left(\frac{124}{165}\right)\)	\(e\left(\frac{49}{110}\right)\)	\(e\left(\frac{83}{110}\right)\)	\(e\left(\frac{31}{66}\right)\)	\(e\left(\frac{2}{165}\right)\)	\(e\left(\frac{53}{165}\right)\)	\(e\left(\frac{203}{330}\right)\)	\(e\left(\frac{81}{110}\right)\)
\(\chi_{8712}(2131,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{251}{330}\right)\)	\(e\left(\frac{149}{165}\right)\)	\(e\left(\frac{52}{165}\right)\)	\(e\left(\frac{17}{110}\right)\)	\(e\left(\frac{49}{110}\right)\)	\(e\left(\frac{13}{66}\right)\)	\(e\left(\frac{86}{165}\right)\)	\(e\left(\frac{134}{165}\right)\)	\(e\left(\frac{149}{330}\right)\)	\(e\left(\frac{73}{110}\right)\)
\(\chi_{8712}(2371,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{193}{330}\right)\)	\(e\left(\frac{37}{165}\right)\)	\(e\left(\frac{86}{165}\right)\)	\(e\left(\frac{81}{110}\right)\)	\(e\left(\frac{7}{110}\right)\)	\(e\left(\frac{5}{66}\right)\)	\(e\left(\frac{28}{165}\right)\)	\(e\left(\frac{82}{165}\right)\)	\(e\left(\frac{37}{330}\right)\)	\(e\left(\frac{89}{110}\right)\)
\(\chi_{8712}(2515,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{259}{330}\right)\)	\(e\left(\frac{136}{165}\right)\)	\(e\left(\frac{53}{165}\right)\)	\(e\left(\frac{103}{110}\right)\)	\(e\left(\frac{51}{110}\right)\)	\(e\left(\frac{5}{66}\right)\)	\(e\left(\frac{94}{165}\right)\)	\(e\left(\frac{16}{165}\right)\)	\(e\left(\frac{301}{330}\right)\)	\(e\left(\frac{67}{110}\right)\)
\(\chi_{8712}(2587,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{307}{330}\right)\)	\(e\left(\frac{58}{165}\right)\)	\(e\left(\frac{59}{165}\right)\)	\(e\left(\frac{69}{110}\right)\)	\(e\left(\frac{63}{110}\right)\)	\(e\left(\frac{23}{66}\right)\)	\(e\left(\frac{142}{165}\right)\)	\(e\left(\frac{133}{165}\right)\)	\(e\left(\frac{223}{330}\right)\)	\(e\left(\frac{31}{110}\right)\)
\(\chi_{8712}(2779,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{330}\right)\)	\(e\left(\frac{131}{165}\right)\)	\(e\left(\frac{28}{165}\right)\)	\(e\left(\frac{43}{110}\right)\)	\(e\left(\frac{1}{110}\right)\)	\(e\left(\frac{7}{66}\right)\)	\(e\left(\frac{59}{165}\right)\)	\(e\left(\frac{161}{165}\right)\)	\(e\left(\frac{131}{330}\right)\)	\(e\left(\frac{107}{110}\right)\)
\(\chi_{8712}(2851,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{330}\right)\)	\(e\left(\frac{68}{165}\right)\)	\(e\left(\frac{109}{165}\right)\)	\(e\left(\frac{79}{110}\right)\)	\(e\left(\frac{53}{110}\right)\)	\(e\left(\frac{19}{66}\right)\)	\(e\left(\frac{47}{165}\right)\)	\(e\left(\frac{8}{165}\right)\)	\(e\left(\frac{233}{330}\right)\)	\(e\left(\frac{61}{110}\right)\)
\(\chi_{8712}(2923,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{221}{330}\right)\)	\(e\left(\frac{74}{165}\right)\)	\(e\left(\frac{7}{165}\right)\)	\(e\left(\frac{107}{110}\right)\)	\(e\left(\frac{69}{110}\right)\)	\(e\left(\frac{43}{66}\right)\)	\(e\left(\frac{56}{165}\right)\)	\(e\left(\frac{164}{165}\right)\)	\(e\left(\frac{239}{330}\right)\)	\(e\left(\frac{13}{110}\right)\)
\(\chi_{8712}(3163,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{330}\right)\)	\(e\left(\frac{157}{165}\right)\)	\(e\left(\frac{26}{165}\right)\)	\(e\left(\frac{91}{110}\right)\)	\(e\left(\frac{107}{110}\right)\)	\(e\left(\frac{23}{66}\right)\)	\(e\left(\frac{43}{165}\right)\)	\(e\left(\frac{67}{165}\right)\)	\(e\left(\frac{157}{330}\right)\)	\(e\left(\frac{9}{110}\right)\)
\(\chi_{8712}(3427,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{323}{330}\right)\)	\(e\left(\frac{32}{165}\right)\)	\(e\left(\frac{61}{165}\right)\)	\(e\left(\frac{21}{110}\right)\)	\(e\left(\frac{67}{110}\right)\)	\(e\left(\frac{7}{66}\right)\)	\(e\left(\frac{158}{165}\right)\)	\(e\left(\frac{62}{165}\right)\)	\(e\left(\frac{197}{330}\right)\)	\(e\left(\frac{19}{110}\right)\)
\(\chi_{8712}(3451,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{91}{330}\right)\)	\(e\left(\frac{79}{165}\right)\)	\(e\left(\frac{32}{165}\right)\)	\(e\left(\frac{57}{110}\right)\)	\(e\left(\frac{9}{110}\right)\)	\(e\left(\frac{41}{66}\right)\)	\(e\left(\frac{91}{165}\right)\)	\(e\left(\frac{19}{165}\right)\)	\(e\left(\frac{79}{330}\right)\)	\(e\left(\frac{83}{110}\right)\)
\(\chi_{8712}(3571,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{119}{330}\right)\)	\(e\left(\frac{116}{165}\right)\)	\(e\left(\frac{118}{165}\right)\)	\(e\left(\frac{83}{110}\right)\)	\(e\left(\frac{71}{110}\right)\)	\(e\left(\frac{13}{66}\right)\)	\(e\left(\frac{119}{165}\right)\)	\(e\left(\frac{101}{165}\right)\)	\(e\left(\frac{281}{330}\right)\)	\(e\left(\frac{7}{110}\right)\)

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First 31 of 80 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	8712.eq
Modulus	$8712$
Conductor	$8712$
Order	$330$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(8712\)
Conductor:	\(8712\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(330\)	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)