LMFDB - Dirichlet character orbit 8732.bz

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(8732, base_ring=CyclotomicField(174)) M = H._module chi = DirichletCharacter(H, M([87,116,69])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(47,8732)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$8732$
Conductor:	$8732$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$174$	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:	$\Q(\zeta_{87})$
Fixed field:	Number field defined by a degree 174 polynomial (not computed)

First 31 of 56 characters in Galois orbit

Character	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$17$	$19$	$21$
$\chi_{8732}(47,\cdot)$	$1$	$1$	$e\left(\frac{115}{174}\right)$	$e\left(\frac{62}{87}\right)$	$e\left(\frac{169}{174}\right)$	$e\left(\frac{28}{87}\right)$	$e\left(\frac{12}{29}\right)$	$e\left(\frac{31}{174}\right)$	$e\left(\frac{65}{174}\right)$	$e\left(\frac{46}{87}\right)$	$e\left(\frac{157}{174}\right)$	$e\left(\frac{55}{87}\right)$
$\chi_{8732}(195,\cdot)$	$1$	$1$	$e\left(\frac{157}{174}\right)$	$e\left(\frac{68}{87}\right)$	$e\left(\frac{31}{174}\right)$	$e\left(\frac{70}{87}\right)$	$e\left(\frac{1}{29}\right)$	$e\left(\frac{121}{174}\right)$	$e\left(\frac{119}{174}\right)$	$e\left(\frac{28}{87}\right)$	$e\left(\frac{1}{174}\right)$	$e\left(\frac{7}{87}\right)$
$\chi_{8732}(211,\cdot)$	$1$	$1$	$e\left(\frac{89}{174}\right)$	$e\left(\frac{79}{87}\right)$	$e\left(\frac{155}{174}\right)$	$e\left(\frac{2}{87}\right)$	$e\left(\frac{5}{29}\right)$	$e\left(\frac{83}{174}\right)$	$e\left(\frac{73}{174}\right)$	$e\left(\frac{53}{87}\right)$	$e\left(\frac{5}{174}\right)$	$e\left(\frac{35}{87}\right)$
$\chi_{8732}(655,\cdot)$	$1$	$1$	$e\left(\frac{23}{174}\right)$	$e\left(\frac{82}{87}\right)$	$e\left(\frac{173}{174}\right)$	$e\left(\frac{23}{87}\right)$	$e\left(\frac{14}{29}\right)$	$e\left(\frac{41}{174}\right)$	$e\left(\frac{13}{174}\right)$	$e\left(\frac{44}{87}\right)$	$e\left(\frac{101}{174}\right)$	$e\left(\frac{11}{87}\right)$
$\chi_{8732}(935,\cdot)$	$1$	$1$	$e\left(\frac{7}{174}\right)$	$e\left(\frac{59}{87}\right)$	$e\left(\frac{151}{174}\right)$	$e\left(\frac{7}{87}\right)$	$e\left(\frac{3}{29}\right)$	$e\left(\frac{73}{174}\right)$	$e\left(\frac{125}{174}\right)$	$e\left(\frac{55}{87}\right)$	$e\left(\frac{61}{174}\right)$	$e\left(\frac{79}{87}\right)$
$\chi_{8732}(1099,\cdot)$	$1$	$1$	$e\left(\frac{101}{174}\right)$	$e\left(\frac{31}{87}\right)$	$e\left(\frac{41}{174}\right)$	$e\left(\frac{14}{87}\right)$	$e\left(\frac{6}{29}\right)$	$e\left(\frac{59}{174}\right)$	$e\left(\frac{163}{174}\right)$	$e\left(\frac{23}{87}\right)$	$e\left(\frac{35}{174}\right)$	$e\left(\frac{71}{87}\right)$
$\chi_{8732}(1247,\cdot)$	$1$	$1$	$e\left(\frac{131}{174}\right)$	$e\left(\frac{85}{87}\right)$	$e\left(\frac{17}{174}\right)$	$e\left(\frac{44}{87}\right)$	$e\left(\frac{23}{29}\right)$	$e\left(\frac{173}{174}\right)$	$e\left(\frac{127}{174}\right)$	$e\left(\frac{35}{87}\right)$	$e\left(\frac{23}{174}\right)$	$e\left(\frac{74}{87}\right)$
$\chi_{8732}(1395,\cdot)$	$1$	$1$	$e\left(\frac{137}{174}\right)$	$e\left(\frac{61}{87}\right)$	$e\left(\frac{47}{174}\right)$	$e\left(\frac{50}{87}\right)$	$e\left(\frac{9}{29}\right)$	$e\left(\frac{161}{174}\right)$	$e\left(\frac{85}{174}\right)$	$e\left(\frac{20}{87}\right)$	$e\left(\frac{125}{174}\right)$	$e\left(\frac{5}{87}\right)$
$\chi_{8732}(1527,\cdot)$	$1$	$1$	$e\left(\frac{61}{174}\right)$	$e\left(\frac{17}{87}\right)$	$e\left(\frac{73}{174}\right)$	$e\left(\frac{61}{87}\right)$	$e\left(\frac{22}{29}\right)$	$e\left(\frac{139}{174}\right)$	$e\left(\frac{95}{174}\right)$	$e\left(\frac{7}{87}\right)$	$e\left(\frac{109}{174}\right)$	$e\left(\frac{67}{87}\right)$
$\chi_{8732}(1675,\cdot)$	$1$	$1$	$e\left(\frac{133}{174}\right)$	$e\left(\frac{77}{87}\right)$	$e\left(\frac{85}{174}\right)$	$e\left(\frac{46}{87}\right)$	$e\left(\frac{28}{29}\right)$	$e\left(\frac{169}{174}\right)$	$e\left(\frac{113}{174}\right)$	$e\left(\frac{1}{87}\right)$	$e\left(\frac{115}{174}\right)$	$e\left(\frac{22}{87}\right)$
$\chi_{8732}(1691,\cdot)$	$1$	$1$	$e\left(\frac{11}{174}\right)$	$e\left(\frac{43}{87}\right)$	$e\left(\frac{113}{174}\right)$	$e\left(\frac{11}{87}\right)$	$e\left(\frac{13}{29}\right)$	$e\left(\frac{65}{174}\right)$	$e\left(\frac{97}{174}\right)$	$e\left(\frac{74}{87}\right)$	$e\left(\frac{71}{174}\right)$	$e\left(\frac{62}{87}\right)$
$\chi_{8732}(1839,\cdot)$	$1$	$1$	$e\left(\frac{35}{174}\right)$	$e\left(\frac{34}{87}\right)$	$e\left(\frac{59}{174}\right)$	$e\left(\frac{35}{87}\right)$	$e\left(\frac{15}{29}\right)$	$e\left(\frac{17}{174}\right)$	$e\left(\frac{103}{174}\right)$	$e\left(\frac{14}{87}\right)$	$e\left(\frac{131}{174}\right)$	$e\left(\frac{47}{87}\right)$
$\chi_{8732}(1971,\cdot)$	$1$	$1$	$e\left(\frac{91}{174}\right)$	$e\left(\frac{71}{87}\right)$	$e\left(\frac{49}{174}\right)$	$e\left(\frac{4}{87}\right)$	$e\left(\frac{10}{29}\right)$	$e\left(\frac{79}{174}\right)$	$e\left(\frac{59}{174}\right)$	$e\left(\frac{19}{87}\right)$	$e\left(\frac{97}{174}\right)$	$e\left(\frac{70}{87}\right)$
$\chi_{8732}(1987,\cdot)$	$1$	$1$	$e\left(\frac{161}{174}\right)$	$e\left(\frac{52}{87}\right)$	$e\left(\frac{167}{174}\right)$	$e\left(\frac{74}{87}\right)$	$e\left(\frac{11}{29}\right)$	$e\left(\frac{113}{174}\right)$	$e\left(\frac{91}{174}\right)$	$e\left(\frac{47}{87}\right)$	$e\left(\frac{11}{174}\right)$	$e\left(\frac{77}{87}\right)$
$\chi_{8732}(2119,\cdot)$	$1$	$1$	$e\left(\frac{1}{174}\right)$	$e\left(\frac{83}{87}\right)$	$e\left(\frac{121}{174}\right)$	$e\left(\frac{1}{87}\right)$	$e\left(\frac{17}{29}\right)$	$e\left(\frac{85}{174}\right)$	$e\left(\frac{167}{174}\right)$	$e\left(\frac{70}{87}\right)$	$e\left(\frac{133}{174}\right)$	$e\left(\frac{61}{87}\right)$
$\chi_{8732}(2135,\cdot)$	$1$	$1$	$e\left(\frac{125}{174}\right)$	$e\left(\frac{22}{87}\right)$	$e\left(\frac{161}{174}\right)$	$e\left(\frac{38}{87}\right)$	$e\left(\frac{8}{29}\right)$	$e\left(\frac{11}{174}\right)$	$e\left(\frac{169}{174}\right)$	$e\left(\frac{50}{87}\right)$	$e\left(\frac{95}{174}\right)$	$e\left(\frac{56}{87}\right)$
$\chi_{8732}(2415,\cdot)$	$1$	$1$	$e\left(\frac{97}{174}\right)$	$e\left(\frac{47}{87}\right)$	$e\left(\frac{79}{174}\right)$	$e\left(\frac{10}{87}\right)$	$e\left(\frac{25}{29}\right)$	$e\left(\frac{67}{174}\right)$	$e\left(\frac{17}{174}\right)$	$e\left(\frac{4}{87}\right)$	$e\left(\frac{25}{174}\right)$	$e\left(\frac{1}{87}\right)$
$\chi_{8732}(2579,\cdot)$	$1$	$1$	$e\left(\frac{113}{174}\right)$	$e\left(\frac{70}{87}\right)$	$e\left(\frac{101}{174}\right)$	$e\left(\frac{26}{87}\right)$	$e\left(\frac{7}{29}\right)$	$e\left(\frac{35}{174}\right)$	$e\left(\frac{79}{174}\right)$	$e\left(\frac{80}{87}\right)$	$e\left(\frac{65}{174}\right)$	$e\left(\frac{20}{87}\right)$
$\chi_{8732}(2711,\cdot)$	$1$	$1$	$e\left(\frac{163}{174}\right)$	$e\left(\frac{44}{87}\right)$	$e\left(\frac{61}{174}\right)$	$e\left(\frac{76}{87}\right)$	$e\left(\frac{16}{29}\right)$	$e\left(\frac{109}{174}\right)$	$e\left(\frac{77}{174}\right)$	$e\left(\frac{13}{87}\right)$	$e\left(\frac{103}{174}\right)$	$e\left(\frac{25}{87}\right)$
$\chi_{8732}(2727,\cdot)$	$1$	$1$	$e\left(\frac{167}{174}\right)$	$e\left(\frac{28}{87}\right)$	$e\left(\frac{23}{174}\right)$	$e\left(\frac{80}{87}\right)$	$e\left(\frac{26}{29}\right)$	$e\left(\frac{101}{174}\right)$	$e\left(\frac{49}{174}\right)$	$e\left(\frac{32}{87}\right)$	$e\left(\frac{113}{174}\right)$	$e\left(\frac{8}{87}\right)$
$\chi_{8732}(2875,\cdot)$	$1$	$1$	$e\left(\frac{107}{174}\right)$	$e\left(\frac{7}{87}\right)$	$e\left(\frac{71}{174}\right)$	$e\left(\frac{20}{87}\right)$	$e\left(\frac{21}{29}\right)$	$e\left(\frac{47}{174}\right)$	$e\left(\frac{121}{174}\right)$	$e\left(\frac{8}{87}\right)$	$e\left(\frac{137}{174}\right)$	$e\left(\frac{2}{87}\right)$
$\chi_{8732}(3023,\cdot)$	$1$	$1$	$e\left(\frac{95}{174}\right)$	$e\left(\frac{55}{87}\right)$	$e\left(\frac{11}{174}\right)$	$e\left(\frac{8}{87}\right)$	$e\left(\frac{20}{29}\right)$	$e\left(\frac{71}{174}\right)$	$e\left(\frac{31}{174}\right)$	$e\left(\frac{38}{87}\right)$	$e\left(\frac{107}{174}\right)$	$e\left(\frac{53}{87}\right)$
$\chi_{8732}(3171,\cdot)$	$1$	$1$	$e\left(\frac{77}{174}\right)$	$e\left(\frac{40}{87}\right)$	$e\left(\frac{95}{174}\right)$	$e\left(\frac{77}{87}\right)$	$e\left(\frac{4}{29}\right)$	$e\left(\frac{107}{174}\right)$	$e\left(\frac{157}{174}\right)$	$e\left(\frac{83}{87}\right)$	$e\left(\frac{149}{174}\right)$	$e\left(\frac{86}{87}\right)$
$\chi_{8732}(3747,\cdot)$	$1$	$1$	$e\left(\frac{169}{174}\right)$	$e\left(\frac{20}{87}\right)$	$e\left(\frac{91}{174}\right)$	$e\left(\frac{82}{87}\right)$	$e\left(\frac{2}{29}\right)$	$e\left(\frac{97}{174}\right)$	$e\left(\frac{35}{174}\right)$	$e\left(\frac{85}{87}\right)$	$e\left(\frac{31}{174}\right)$	$e\left(\frac{43}{87}\right)$
$\chi_{8732}(4043,\cdot)$	$1$	$1$	$e\left(\frac{13}{174}\right)$	$e\left(\frac{35}{87}\right)$	$e\left(\frac{7}{174}\right)$	$e\left(\frac{13}{87}\right)$	$e\left(\frac{18}{29}\right)$	$e\left(\frac{61}{174}\right)$	$e\left(\frac{83}{174}\right)$	$e\left(\frac{40}{87}\right)$	$e\left(\frac{163}{174}\right)$	$e\left(\frac{10}{87}\right)$
$\chi_{8732}(4059,\cdot)$	$1$	$1$	$e\left(\frac{173}{174}\right)$	$e\left(\frac{4}{87}\right)$	$e\left(\frac{53}{174}\right)$	$e\left(\frac{86}{87}\right)$	$e\left(\frac{12}{29}\right)$	$e\left(\frac{89}{174}\right)$	$e\left(\frac{7}{174}\right)$	$e\left(\frac{17}{87}\right)$	$e\left(\frac{41}{174}\right)$	$e\left(\frac{26}{87}\right)$
$\chi_{8732}(4191,\cdot)$	$1$	$1$	$e\left(\frac{121}{174}\right)$	$e\left(\frac{38}{87}\right)$	$e\left(\frac{25}{174}\right)$	$e\left(\frac{34}{87}\right)$	$e\left(\frac{27}{29}\right)$	$e\left(\frac{19}{174}\right)$	$e\left(\frac{23}{174}\right)$	$e\left(\frac{31}{87}\right)$	$e\left(\frac{85}{174}\right)$	$e\left(\frac{73}{87}\right)$
$\chi_{8732}(4207,\cdot)$	$1$	$1$	$e\left(\frac{41}{174}\right)$	$e\left(\frac{10}{87}\right)$	$e\left(\frac{89}{174}\right)$	$e\left(\frac{41}{87}\right)$	$e\left(\frac{1}{29}\right)$	$e\left(\frac{5}{174}\right)$	$e\left(\frac{61}{174}\right)$	$e\left(\frac{86}{87}\right)$	$e\left(\frac{59}{174}\right)$	$e\left(\frac{65}{87}\right)$
$\chi_{8732}(4339,\cdot)$	$1$	$1$	$e\left(\frac{25}{174}\right)$	$e\left(\frac{74}{87}\right)$	$e\left(\frac{67}{174}\right)$	$e\left(\frac{25}{87}\right)$	$e\left(\frac{19}{29}\right)$	$e\left(\frac{37}{174}\right)$	$e\left(\frac{173}{174}\right)$	$e\left(\frac{10}{87}\right)$	$e\left(\frac{19}{174}\right)$	$e\left(\frac{46}{87}\right)$
$\chi_{8732}(4635,\cdot)$	$1$	$1$	$e\left(\frac{85}{174}\right)$	$e\left(\frac{8}{87}\right)$	$e\left(\frac{19}{174}\right)$	$e\left(\frac{85}{87}\right)$	$e\left(\frac{24}{29}\right)$	$e\left(\frac{91}{174}\right)$	$e\left(\frac{101}{174}\right)$	$e\left(\frac{34}{87}\right)$	$e\left(\frac{169}{174}\right)$	$e\left(\frac{52}{87}\right)$
$\chi_{8732}(4931,\cdot)$	$1$	$1$	$e\left(\frac{31}{174}\right)$	$e\left(\frac{50}{87}\right)$	$e\left(\frac{97}{174}\right)$	$e\left(\frac{31}{87}\right)$	$e\left(\frac{5}{29}\right)$	$e\left(\frac{25}{174}\right)$	$e\left(\frac{131}{174}\right)$	$e\left(\frac{82}{87}\right)$	$e\left(\frac{121}{174}\right)$	$e\left(\frac{64}{87}\right)$

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	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(21\)
\(\chi_{8732}(47,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{115}{174}\right)\)	\(e\left(\frac{62}{87}\right)\)	\(e\left(\frac{169}{174}\right)\)	\(e\left(\frac{28}{87}\right)\)	\(e\left(\frac{12}{29}\right)\)	\(e\left(\frac{31}{174}\right)\)	\(e\left(\frac{65}{174}\right)\)	\(e\left(\frac{46}{87}\right)\)	\(e\left(\frac{157}{174}\right)\)	\(e\left(\frac{55}{87}\right)\)
\(\chi_{8732}(195,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{157}{174}\right)\)	\(e\left(\frac{68}{87}\right)\)	\(e\left(\frac{31}{174}\right)\)	\(e\left(\frac{70}{87}\right)\)	\(e\left(\frac{1}{29}\right)\)	\(e\left(\frac{121}{174}\right)\)	\(e\left(\frac{119}{174}\right)\)	\(e\left(\frac{28}{87}\right)\)	\(e\left(\frac{1}{174}\right)\)	\(e\left(\frac{7}{87}\right)\)
\(\chi_{8732}(211,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{89}{174}\right)\)	\(e\left(\frac{79}{87}\right)\)	\(e\left(\frac{155}{174}\right)\)	\(e\left(\frac{2}{87}\right)\)	\(e\left(\frac{5}{29}\right)\)	\(e\left(\frac{83}{174}\right)\)	\(e\left(\frac{73}{174}\right)\)	\(e\left(\frac{53}{87}\right)\)	\(e\left(\frac{5}{174}\right)\)	\(e\left(\frac{35}{87}\right)\)
\(\chi_{8732}(655,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{174}\right)\)	\(e\left(\frac{82}{87}\right)\)	\(e\left(\frac{173}{174}\right)\)	\(e\left(\frac{23}{87}\right)\)	\(e\left(\frac{14}{29}\right)\)	\(e\left(\frac{41}{174}\right)\)	\(e\left(\frac{13}{174}\right)\)	\(e\left(\frac{44}{87}\right)\)	\(e\left(\frac{101}{174}\right)\)	\(e\left(\frac{11}{87}\right)\)
\(\chi_{8732}(935,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{174}\right)\)	\(e\left(\frac{59}{87}\right)\)	\(e\left(\frac{151}{174}\right)\)	\(e\left(\frac{7}{87}\right)\)	\(e\left(\frac{3}{29}\right)\)	\(e\left(\frac{73}{174}\right)\)	\(e\left(\frac{125}{174}\right)\)	\(e\left(\frac{55}{87}\right)\)	\(e\left(\frac{61}{174}\right)\)	\(e\left(\frac{79}{87}\right)\)
\(\chi_{8732}(1099,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{101}{174}\right)\)	\(e\left(\frac{31}{87}\right)\)	\(e\left(\frac{41}{174}\right)\)	\(e\left(\frac{14}{87}\right)\)	\(e\left(\frac{6}{29}\right)\)	\(e\left(\frac{59}{174}\right)\)	\(e\left(\frac{163}{174}\right)\)	\(e\left(\frac{23}{87}\right)\)	\(e\left(\frac{35}{174}\right)\)	\(e\left(\frac{71}{87}\right)\)
\(\chi_{8732}(1247,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{131}{174}\right)\)	\(e\left(\frac{85}{87}\right)\)	\(e\left(\frac{17}{174}\right)\)	\(e\left(\frac{44}{87}\right)\)	\(e\left(\frac{23}{29}\right)\)	\(e\left(\frac{173}{174}\right)\)	\(e\left(\frac{127}{174}\right)\)	\(e\left(\frac{35}{87}\right)\)	\(e\left(\frac{23}{174}\right)\)	\(e\left(\frac{74}{87}\right)\)
\(\chi_{8732}(1395,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{137}{174}\right)\)	\(e\left(\frac{61}{87}\right)\)	\(e\left(\frac{47}{174}\right)\)	\(e\left(\frac{50}{87}\right)\)	\(e\left(\frac{9}{29}\right)\)	\(e\left(\frac{161}{174}\right)\)	\(e\left(\frac{85}{174}\right)\)	\(e\left(\frac{20}{87}\right)\)	\(e\left(\frac{125}{174}\right)\)	\(e\left(\frac{5}{87}\right)\)
\(\chi_{8732}(1527,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{61}{174}\right)\)	\(e\left(\frac{17}{87}\right)\)	\(e\left(\frac{73}{174}\right)\)	\(e\left(\frac{61}{87}\right)\)	\(e\left(\frac{22}{29}\right)\)	\(e\left(\frac{139}{174}\right)\)	\(e\left(\frac{95}{174}\right)\)	\(e\left(\frac{7}{87}\right)\)	\(e\left(\frac{109}{174}\right)\)	\(e\left(\frac{67}{87}\right)\)
\(\chi_{8732}(1675,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{133}{174}\right)\)	\(e\left(\frac{77}{87}\right)\)	\(e\left(\frac{85}{174}\right)\)	\(e\left(\frac{46}{87}\right)\)	\(e\left(\frac{28}{29}\right)\)	\(e\left(\frac{169}{174}\right)\)	\(e\left(\frac{113}{174}\right)\)	\(e\left(\frac{1}{87}\right)\)	\(e\left(\frac{115}{174}\right)\)	\(e\left(\frac{22}{87}\right)\)
\(\chi_{8732}(1691,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{174}\right)\)	\(e\left(\frac{43}{87}\right)\)	\(e\left(\frac{113}{174}\right)\)	\(e\left(\frac{11}{87}\right)\)	\(e\left(\frac{13}{29}\right)\)	\(e\left(\frac{65}{174}\right)\)	\(e\left(\frac{97}{174}\right)\)	\(e\left(\frac{74}{87}\right)\)	\(e\left(\frac{71}{174}\right)\)	\(e\left(\frac{62}{87}\right)\)
\(\chi_{8732}(1839,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{35}{174}\right)\)	\(e\left(\frac{34}{87}\right)\)	\(e\left(\frac{59}{174}\right)\)	\(e\left(\frac{35}{87}\right)\)	\(e\left(\frac{15}{29}\right)\)	\(e\left(\frac{17}{174}\right)\)	\(e\left(\frac{103}{174}\right)\)	\(e\left(\frac{14}{87}\right)\)	\(e\left(\frac{131}{174}\right)\)	\(e\left(\frac{47}{87}\right)\)
\(\chi_{8732}(1971,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{91}{174}\right)\)	\(e\left(\frac{71}{87}\right)\)	\(e\left(\frac{49}{174}\right)\)	\(e\left(\frac{4}{87}\right)\)	\(e\left(\frac{10}{29}\right)\)	\(e\left(\frac{79}{174}\right)\)	\(e\left(\frac{59}{174}\right)\)	\(e\left(\frac{19}{87}\right)\)	\(e\left(\frac{97}{174}\right)\)	\(e\left(\frac{70}{87}\right)\)
\(\chi_{8732}(1987,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{161}{174}\right)\)	\(e\left(\frac{52}{87}\right)\)	\(e\left(\frac{167}{174}\right)\)	\(e\left(\frac{74}{87}\right)\)	\(e\left(\frac{11}{29}\right)\)	\(e\left(\frac{113}{174}\right)\)	\(e\left(\frac{91}{174}\right)\)	\(e\left(\frac{47}{87}\right)\)	\(e\left(\frac{11}{174}\right)\)	\(e\left(\frac{77}{87}\right)\)
\(\chi_{8732}(2119,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{174}\right)\)	\(e\left(\frac{83}{87}\right)\)	\(e\left(\frac{121}{174}\right)\)	\(e\left(\frac{1}{87}\right)\)	\(e\left(\frac{17}{29}\right)\)	\(e\left(\frac{85}{174}\right)\)	\(e\left(\frac{167}{174}\right)\)	\(e\left(\frac{70}{87}\right)\)	\(e\left(\frac{133}{174}\right)\)	\(e\left(\frac{61}{87}\right)\)
\(\chi_{8732}(2135,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{125}{174}\right)\)	\(e\left(\frac{22}{87}\right)\)	\(e\left(\frac{161}{174}\right)\)	\(e\left(\frac{38}{87}\right)\)	\(e\left(\frac{8}{29}\right)\)	\(e\left(\frac{11}{174}\right)\)	\(e\left(\frac{169}{174}\right)\)	\(e\left(\frac{50}{87}\right)\)	\(e\left(\frac{95}{174}\right)\)	\(e\left(\frac{56}{87}\right)\)
\(\chi_{8732}(2415,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{97}{174}\right)\)	\(e\left(\frac{47}{87}\right)\)	\(e\left(\frac{79}{174}\right)\)	\(e\left(\frac{10}{87}\right)\)	\(e\left(\frac{25}{29}\right)\)	\(e\left(\frac{67}{174}\right)\)	\(e\left(\frac{17}{174}\right)\)	\(e\left(\frac{4}{87}\right)\)	\(e\left(\frac{25}{174}\right)\)	\(e\left(\frac{1}{87}\right)\)
\(\chi_{8732}(2579,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{113}{174}\right)\)	\(e\left(\frac{70}{87}\right)\)	\(e\left(\frac{101}{174}\right)\)	\(e\left(\frac{26}{87}\right)\)	\(e\left(\frac{7}{29}\right)\)	\(e\left(\frac{35}{174}\right)\)	\(e\left(\frac{79}{174}\right)\)	\(e\left(\frac{80}{87}\right)\)	\(e\left(\frac{65}{174}\right)\)	\(e\left(\frac{20}{87}\right)\)
\(\chi_{8732}(2711,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{163}{174}\right)\)	\(e\left(\frac{44}{87}\right)\)	\(e\left(\frac{61}{174}\right)\)	\(e\left(\frac{76}{87}\right)\)	\(e\left(\frac{16}{29}\right)\)	\(e\left(\frac{109}{174}\right)\)	\(e\left(\frac{77}{174}\right)\)	\(e\left(\frac{13}{87}\right)\)	\(e\left(\frac{103}{174}\right)\)	\(e\left(\frac{25}{87}\right)\)
\(\chi_{8732}(2727,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{167}{174}\right)\)	\(e\left(\frac{28}{87}\right)\)	\(e\left(\frac{23}{174}\right)\)	\(e\left(\frac{80}{87}\right)\)	\(e\left(\frac{26}{29}\right)\)	\(e\left(\frac{101}{174}\right)\)	\(e\left(\frac{49}{174}\right)\)	\(e\left(\frac{32}{87}\right)\)	\(e\left(\frac{113}{174}\right)\)	\(e\left(\frac{8}{87}\right)\)
\(\chi_{8732}(2875,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{107}{174}\right)\)	\(e\left(\frac{7}{87}\right)\)	\(e\left(\frac{71}{174}\right)\)	\(e\left(\frac{20}{87}\right)\)	\(e\left(\frac{21}{29}\right)\)	\(e\left(\frac{47}{174}\right)\)	\(e\left(\frac{121}{174}\right)\)	\(e\left(\frac{8}{87}\right)\)	\(e\left(\frac{137}{174}\right)\)	\(e\left(\frac{2}{87}\right)\)
\(\chi_{8732}(3023,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{95}{174}\right)\)	\(e\left(\frac{55}{87}\right)\)	\(e\left(\frac{11}{174}\right)\)	\(e\left(\frac{8}{87}\right)\)	\(e\left(\frac{20}{29}\right)\)	\(e\left(\frac{71}{174}\right)\)	\(e\left(\frac{31}{174}\right)\)	\(e\left(\frac{38}{87}\right)\)	\(e\left(\frac{107}{174}\right)\)	\(e\left(\frac{53}{87}\right)\)
\(\chi_{8732}(3171,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{77}{174}\right)\)	\(e\left(\frac{40}{87}\right)\)	\(e\left(\frac{95}{174}\right)\)	\(e\left(\frac{77}{87}\right)\)	\(e\left(\frac{4}{29}\right)\)	\(e\left(\frac{107}{174}\right)\)	\(e\left(\frac{157}{174}\right)\)	\(e\left(\frac{83}{87}\right)\)	\(e\left(\frac{149}{174}\right)\)	\(e\left(\frac{86}{87}\right)\)
\(\chi_{8732}(3747,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{169}{174}\right)\)	\(e\left(\frac{20}{87}\right)\)	\(e\left(\frac{91}{174}\right)\)	\(e\left(\frac{82}{87}\right)\)	\(e\left(\frac{2}{29}\right)\)	\(e\left(\frac{97}{174}\right)\)	\(e\left(\frac{35}{174}\right)\)	\(e\left(\frac{85}{87}\right)\)	\(e\left(\frac{31}{174}\right)\)	\(e\left(\frac{43}{87}\right)\)
\(\chi_{8732}(4043,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{174}\right)\)	\(e\left(\frac{35}{87}\right)\)	\(e\left(\frac{7}{174}\right)\)	\(e\left(\frac{13}{87}\right)\)	\(e\left(\frac{18}{29}\right)\)	\(e\left(\frac{61}{174}\right)\)	\(e\left(\frac{83}{174}\right)\)	\(e\left(\frac{40}{87}\right)\)	\(e\left(\frac{163}{174}\right)\)	\(e\left(\frac{10}{87}\right)\)
\(\chi_{8732}(4059,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{173}{174}\right)\)	\(e\left(\frac{4}{87}\right)\)	\(e\left(\frac{53}{174}\right)\)	\(e\left(\frac{86}{87}\right)\)	\(e\left(\frac{12}{29}\right)\)	\(e\left(\frac{89}{174}\right)\)	\(e\left(\frac{7}{174}\right)\)	\(e\left(\frac{17}{87}\right)\)	\(e\left(\frac{41}{174}\right)\)	\(e\left(\frac{26}{87}\right)\)
\(\chi_{8732}(4191,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{121}{174}\right)\)	\(e\left(\frac{38}{87}\right)\)	\(e\left(\frac{25}{174}\right)\)	\(e\left(\frac{34}{87}\right)\)	\(e\left(\frac{27}{29}\right)\)	\(e\left(\frac{19}{174}\right)\)	\(e\left(\frac{23}{174}\right)\)	\(e\left(\frac{31}{87}\right)\)	\(e\left(\frac{85}{174}\right)\)	\(e\left(\frac{73}{87}\right)\)
\(\chi_{8732}(4207,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{174}\right)\)	\(e\left(\frac{10}{87}\right)\)	\(e\left(\frac{89}{174}\right)\)	\(e\left(\frac{41}{87}\right)\)	\(e\left(\frac{1}{29}\right)\)	\(e\left(\frac{5}{174}\right)\)	\(e\left(\frac{61}{174}\right)\)	\(e\left(\frac{86}{87}\right)\)	\(e\left(\frac{59}{174}\right)\)	\(e\left(\frac{65}{87}\right)\)
\(\chi_{8732}(4339,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{25}{174}\right)\)	\(e\left(\frac{74}{87}\right)\)	\(e\left(\frac{67}{174}\right)\)	\(e\left(\frac{25}{87}\right)\)	\(e\left(\frac{19}{29}\right)\)	\(e\left(\frac{37}{174}\right)\)	\(e\left(\frac{173}{174}\right)\)	\(e\left(\frac{10}{87}\right)\)	\(e\left(\frac{19}{174}\right)\)	\(e\left(\frac{46}{87}\right)\)
\(\chi_{8732}(4635,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{85}{174}\right)\)	\(e\left(\frac{8}{87}\right)\)	\(e\left(\frac{19}{174}\right)\)	\(e\left(\frac{85}{87}\right)\)	\(e\left(\frac{24}{29}\right)\)	\(e\left(\frac{91}{174}\right)\)	\(e\left(\frac{101}{174}\right)\)	\(e\left(\frac{34}{87}\right)\)	\(e\left(\frac{169}{174}\right)\)	\(e\left(\frac{52}{87}\right)\)
\(\chi_{8732}(4931,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{174}\right)\)	\(e\left(\frac{50}{87}\right)\)	\(e\left(\frac{97}{174}\right)\)	\(e\left(\frac{31}{87}\right)\)	\(e\left(\frac{5}{29}\right)\)	\(e\left(\frac{25}{174}\right)\)	\(e\left(\frac{131}{174}\right)\)	\(e\left(\frac{82}{87}\right)\)	\(e\left(\frac{121}{174}\right)\)	\(e\left(\frac{64}{87}\right)\)

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First 31 of 56 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	8732.bz
Modulus	$8732$
Conductor	$8732$
Order	$174$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(8732\)
Conductor:	\(8732\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(174\)	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)