LMFDB - Dirichlet character orbit 8732.bs

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(8732, base_ring=CyclotomicField(174)) M = H._module chi = DirichletCharacter(H, M([0,116,150])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(121,8732)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$8732$
Conductor:	$2183$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$87$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 2183.w	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 87 polynomial

First 31 of 56 characters in Galois orbit

Character	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$17$	$19$	$21$
$\chi_{8732}(121,\cdot)$	$1$	$1$	$e\left(\frac{38}{87}\right)$	$e\left(\frac{44}{87}\right)$	$e\left(\frac{74}{87}\right)$	$e\left(\frac{76}{87}\right)$	$e\left(\frac{16}{29}\right)$	$e\left(\frac{11}{87}\right)$	$e\left(\frac{82}{87}\right)$	$e\left(\frac{13}{87}\right)$	$e\left(\frac{8}{87}\right)$	$e\left(\frac{25}{87}\right)$
$\chi_{8732}(137,\cdot)$	$1$	$1$	$e\left(\frac{37}{87}\right)$	$e\left(\frac{52}{87}\right)$	$e\left(\frac{40}{87}\right)$	$e\left(\frac{74}{87}\right)$	$e\left(\frac{11}{29}\right)$	$e\left(\frac{13}{87}\right)$	$e\left(\frac{2}{87}\right)$	$e\left(\frac{47}{87}\right)$	$e\left(\frac{49}{87}\right)$	$e\left(\frac{77}{87}\right)$
$\chi_{8732}(285,\cdot)$	$1$	$1$	$e\left(\frac{61}{87}\right)$	$e\left(\frac{34}{87}\right)$	$e\left(\frac{73}{87}\right)$	$e\left(\frac{35}{87}\right)$	$e\left(\frac{15}{29}\right)$	$e\left(\frac{52}{87}\right)$	$e\left(\frac{8}{87}\right)$	$e\left(\frac{14}{87}\right)$	$e\left(\frac{22}{87}\right)$	$e\left(\frac{47}{87}\right)$
$\chi_{8732}(417,\cdot)$	$1$	$1$	$e\left(\frac{5}{87}\right)$	$e\left(\frac{47}{87}\right)$	$e\left(\frac{83}{87}\right)$	$e\left(\frac{10}{87}\right)$	$e\left(\frac{25}{29}\right)$	$e\left(\frac{77}{87}\right)$	$e\left(\frac{52}{87}\right)$	$e\left(\frac{4}{87}\right)$	$e\left(\frac{56}{87}\right)$	$e\left(\frac{1}{87}\right)$
$\chi_{8732}(433,\cdot)$	$1$	$1$	$e\left(\frac{49}{87}\right)$	$e\left(\frac{43}{87}\right)$	$e\left(\frac{13}{87}\right)$	$e\left(\frac{11}{87}\right)$	$e\left(\frac{13}{29}\right)$	$e\left(\frac{76}{87}\right)$	$e\left(\frac{5}{87}\right)$	$e\left(\frac{74}{87}\right)$	$e\left(\frac{79}{87}\right)$	$e\left(\frac{62}{87}\right)$
$\chi_{8732}(713,\cdot)$	$1$	$1$	$e\left(\frac{44}{87}\right)$	$e\left(\frac{83}{87}\right)$	$e\left(\frac{17}{87}\right)$	$e\left(\frac{1}{87}\right)$	$e\left(\frac{17}{29}\right)$	$e\left(\frac{86}{87}\right)$	$e\left(\frac{40}{87}\right)$	$e\left(\frac{70}{87}\right)$	$e\left(\frac{23}{87}\right)$	$e\left(\frac{61}{87}\right)$
$\chi_{8732}(729,\cdot)$	$1$	$1$	$e\left(\frac{25}{87}\right)$	$e\left(\frac{61}{87}\right)$	$e\left(\frac{67}{87}\right)$	$e\left(\frac{50}{87}\right)$	$e\left(\frac{9}{29}\right)$	$e\left(\frac{37}{87}\right)$	$e\left(\frac{86}{87}\right)$	$e\left(\frac{20}{87}\right)$	$e\left(\frac{19}{87}\right)$	$e\left(\frac{5}{87}\right)$
$\chi_{8732}(861,\cdot)$	$1$	$1$	$e\left(\frac{2}{87}\right)$	$e\left(\frac{71}{87}\right)$	$e\left(\frac{68}{87}\right)$	$e\left(\frac{4}{87}\right)$	$e\left(\frac{10}{29}\right)$	$e\left(\frac{83}{87}\right)$	$e\left(\frac{73}{87}\right)$	$e\left(\frac{19}{87}\right)$	$e\left(\frac{5}{87}\right)$	$e\left(\frac{70}{87}\right)$
$\chi_{8732}(877,\cdot)$	$1$	$1$	$e\left(\frac{22}{87}\right)$	$e\left(\frac{85}{87}\right)$	$e\left(\frac{52}{87}\right)$	$e\left(\frac{44}{87}\right)$	$e\left(\frac{23}{29}\right)$	$e\left(\frac{43}{87}\right)$	$e\left(\frac{20}{87}\right)$	$e\left(\frac{35}{87}\right)$	$e\left(\frac{55}{87}\right)$	$e\left(\frac{74}{87}\right)$
$\chi_{8732}(1025,\cdot)$	$1$	$1$	$e\left(\frac{7}{87}\right)$	$e\left(\frac{31}{87}\right)$	$e\left(\frac{64}{87}\right)$	$e\left(\frac{14}{87}\right)$	$e\left(\frac{6}{29}\right)$	$e\left(\frac{73}{87}\right)$	$e\left(\frac{38}{87}\right)$	$e\left(\frac{23}{87}\right)$	$e\left(\frac{61}{87}\right)$	$e\left(\frac{71}{87}\right)$
$\chi_{8732}(1157,\cdot)$	$1$	$1$	$e\left(\frac{23}{87}\right)$	$e\left(\frac{77}{87}\right)$	$e\left(\frac{86}{87}\right)$	$e\left(\frac{46}{87}\right)$	$e\left(\frac{28}{29}\right)$	$e\left(\frac{41}{87}\right)$	$e\left(\frac{13}{87}\right)$	$e\left(\frac{1}{87}\right)$	$e\left(\frac{14}{87}\right)$	$e\left(\frac{22}{87}\right)$
$\chi_{8732}(1305,\cdot)$	$1$	$1$	$e\left(\frac{74}{87}\right)$	$e\left(\frac{17}{87}\right)$	$e\left(\frac{80}{87}\right)$	$e\left(\frac{61}{87}\right)$	$e\left(\frac{22}{29}\right)$	$e\left(\frac{26}{87}\right)$	$e\left(\frac{4}{87}\right)$	$e\left(\frac{7}{87}\right)$	$e\left(\frac{11}{87}\right)$	$e\left(\frac{67}{87}\right)$
$\chi_{8732}(1469,\cdot)$	$1$	$1$	$e\left(\frac{55}{87}\right)$	$e\left(\frac{82}{87}\right)$	$e\left(\frac{43}{87}\right)$	$e\left(\frac{23}{87}\right)$	$e\left(\frac{14}{29}\right)$	$e\left(\frac{64}{87}\right)$	$e\left(\frac{50}{87}\right)$	$e\left(\frac{44}{87}\right)$	$e\left(\frac{7}{87}\right)$	$e\left(\frac{11}{87}\right)$
$\chi_{8732}(1897,\cdot)$	$1$	$1$	$e\left(\frac{47}{87}\right)$	$e\left(\frac{59}{87}\right)$	$e\left(\frac{32}{87}\right)$	$e\left(\frac{7}{87}\right)$	$e\left(\frac{3}{29}\right)$	$e\left(\frac{80}{87}\right)$	$e\left(\frac{19}{87}\right)$	$e\left(\frac{55}{87}\right)$	$e\left(\frac{74}{87}\right)$	$e\left(\frac{79}{87}\right)$
$\chi_{8732}(1913,\cdot)$	$1$	$1$	$e\left(\frac{1}{87}\right)$	$e\left(\frac{79}{87}\right)$	$e\left(\frac{34}{87}\right)$	$e\left(\frac{2}{87}\right)$	$e\left(\frac{5}{29}\right)$	$e\left(\frac{85}{87}\right)$	$e\left(\frac{80}{87}\right)$	$e\left(\frac{53}{87}\right)$	$e\left(\frac{46}{87}\right)$	$e\left(\frac{35}{87}\right)$
$\chi_{8732}(2209,\cdot)$	$1$	$1$	$e\left(\frac{28}{87}\right)$	$e\left(\frac{37}{87}\right)$	$e\left(\frac{82}{87}\right)$	$e\left(\frac{56}{87}\right)$	$e\left(\frac{24}{29}\right)$	$e\left(\frac{31}{87}\right)$	$e\left(\frac{65}{87}\right)$	$e\left(\frac{5}{87}\right)$	$e\left(\frac{70}{87}\right)$	$e\left(\frac{23}{87}\right)$
$\chi_{8732}(2505,\cdot)$	$1$	$1$	$e\left(\frac{85}{87}\right)$	$e\left(\frac{16}{87}\right)$	$e\left(\frac{19}{87}\right)$	$e\left(\frac{83}{87}\right)$	$e\left(\frac{19}{29}\right)$	$e\left(\frac{4}{87}\right)$	$e\left(\frac{14}{87}\right)$	$e\left(\frac{68}{87}\right)$	$e\left(\frac{82}{87}\right)$	$e\left(\frac{17}{87}\right)$
$\chi_{8732}(2637,\cdot)$	$1$	$1$	$e\left(\frac{35}{87}\right)$	$e\left(\frac{68}{87}\right)$	$e\left(\frac{59}{87}\right)$	$e\left(\frac{70}{87}\right)$	$e\left(\frac{1}{29}\right)$	$e\left(\frac{17}{87}\right)$	$e\left(\frac{16}{87}\right)$	$e\left(\frac{28}{87}\right)$	$e\left(\frac{44}{87}\right)$	$e\left(\frac{7}{87}\right)$
$\chi_{8732}(2653,\cdot)$	$1$	$1$	$e\left(\frac{46}{87}\right)$	$e\left(\frac{67}{87}\right)$	$e\left(\frac{85}{87}\right)$	$e\left(\frac{5}{87}\right)$	$e\left(\frac{27}{29}\right)$	$e\left(\frac{82}{87}\right)$	$e\left(\frac{26}{87}\right)$	$e\left(\frac{2}{87}\right)$	$e\left(\frac{28}{87}\right)$	$e\left(\frac{44}{87}\right)$
$\chi_{8732}(2785,\cdot)$	$1$	$1$	$e\left(\frac{14}{87}\right)$	$e\left(\frac{62}{87}\right)$	$e\left(\frac{41}{87}\right)$	$e\left(\frac{28}{87}\right)$	$e\left(\frac{12}{29}\right)$	$e\left(\frac{59}{87}\right)$	$e\left(\frac{76}{87}\right)$	$e\left(\frac{46}{87}\right)$	$e\left(\frac{35}{87}\right)$	$e\left(\frac{55}{87}\right)$
$\chi_{8732}(2801,\cdot)$	$1$	$1$	$e\left(\frac{79}{87}\right)$	$e\left(\frac{64}{87}\right)$	$e\left(\frac{76}{87}\right)$	$e\left(\frac{71}{87}\right)$	$e\left(\frac{18}{29}\right)$	$e\left(\frac{16}{87}\right)$	$e\left(\frac{56}{87}\right)$	$e\left(\frac{11}{87}\right)$	$e\left(\frac{67}{87}\right)$	$e\left(\frac{68}{87}\right)$
$\chi_{8732}(3097,\cdot)$	$1$	$1$	$e\left(\frac{70}{87}\right)$	$e\left(\frac{49}{87}\right)$	$e\left(\frac{31}{87}\right)$	$e\left(\frac{53}{87}\right)$	$e\left(\frac{2}{29}\right)$	$e\left(\frac{34}{87}\right)$	$e\left(\frac{32}{87}\right)$	$e\left(\frac{56}{87}\right)$	$e\left(\frac{1}{87}\right)$	$e\left(\frac{14}{87}\right)$
$\chi_{8732}(3673,\cdot)$	$1$	$1$	$e\left(\frac{53}{87}\right)$	$e\left(\frac{11}{87}\right)$	$e\left(\frac{62}{87}\right)$	$e\left(\frac{19}{87}\right)$	$e\left(\frac{4}{29}\right)$	$e\left(\frac{68}{87}\right)$	$e\left(\frac{64}{87}\right)$	$e\left(\frac{25}{87}\right)$	$e\left(\frac{2}{87}\right)$	$e\left(\frac{28}{87}\right)$
$\chi_{8732}(3821,\cdot)$	$1$	$1$	$e\left(\frac{62}{87}\right)$	$e\left(\frac{26}{87}\right)$	$e\left(\frac{20}{87}\right)$	$e\left(\frac{37}{87}\right)$	$e\left(\frac{20}{29}\right)$	$e\left(\frac{50}{87}\right)$	$e\left(\frac{1}{87}\right)$	$e\left(\frac{67}{87}\right)$	$e\left(\frac{68}{87}\right)$	$e\left(\frac{82}{87}\right)$
$\chi_{8732}(3969,\cdot)$	$1$	$1$	$e\left(\frac{68}{87}\right)$	$e\left(\frac{65}{87}\right)$	$e\left(\frac{50}{87}\right)$	$e\left(\frac{49}{87}\right)$	$e\left(\frac{21}{29}\right)$	$e\left(\frac{38}{87}\right)$	$e\left(\frac{46}{87}\right)$	$e\left(\frac{37}{87}\right)$	$e\left(\frac{83}{87}\right)$	$e\left(\frac{31}{87}\right)$
$\chi_{8732}(4117,\cdot)$	$1$	$1$	$e\left(\frac{11}{87}\right)$	$e\left(\frac{86}{87}\right)$	$e\left(\frac{26}{87}\right)$	$e\left(\frac{22}{87}\right)$	$e\left(\frac{26}{29}\right)$	$e\left(\frac{65}{87}\right)$	$e\left(\frac{10}{87}\right)$	$e\left(\frac{61}{87}\right)$	$e\left(\frac{71}{87}\right)$	$e\left(\frac{37}{87}\right)$
$\chi_{8732}(4133,\cdot)$	$1$	$1$	$e\left(\frac{67}{87}\right)$	$e\left(\frac{73}{87}\right)$	$e\left(\frac{16}{87}\right)$	$e\left(\frac{47}{87}\right)$	$e\left(\frac{16}{29}\right)$	$e\left(\frac{40}{87}\right)$	$e\left(\frac{53}{87}\right)$	$e\left(\frac{71}{87}\right)$	$e\left(\frac{37}{87}\right)$	$e\left(\frac{83}{87}\right)$
$\chi_{8732}(4265,\cdot)$	$1$	$1$	$e\left(\frac{71}{87}\right)$	$e\left(\frac{41}{87}\right)$	$e\left(\frac{65}{87}\right)$	$e\left(\frac{55}{87}\right)$	$e\left(\frac{7}{29}\right)$	$e\left(\frac{32}{87}\right)$	$e\left(\frac{25}{87}\right)$	$e\left(\frac{22}{87}\right)$	$e\left(\frac{47}{87}\right)$	$e\left(\frac{49}{87}\right)$
$\chi_{8732}(4429,\cdot)$	$1$	$1$	$e\left(\frac{34}{87}\right)$	$e\left(\frac{76}{87}\right)$	$e\left(\frac{25}{87}\right)$	$e\left(\frac{68}{87}\right)$	$e\left(\frac{25}{29}\right)$	$e\left(\frac{19}{87}\right)$	$e\left(\frac{23}{87}\right)$	$e\left(\frac{62}{87}\right)$	$e\left(\frac{85}{87}\right)$	$e\left(\frac{59}{87}\right)$
$\chi_{8732}(4709,\cdot)$	$1$	$1$	$e\left(\frac{77}{87}\right)$	$e\left(\frac{80}{87}\right)$	$e\left(\frac{8}{87}\right)$	$e\left(\frac{67}{87}\right)$	$e\left(\frac{8}{29}\right)$	$e\left(\frac{20}{87}\right)$	$e\left(\frac{70}{87}\right)$	$e\left(\frac{79}{87}\right)$	$e\left(\frac{62}{87}\right)$	$e\left(\frac{85}{87}\right)$
$\chi_{8732}(4725,\cdot)$	$1$	$1$	$e\left(\frac{73}{87}\right)$	$e\left(\frac{25}{87}\right)$	$e\left(\frac{46}{87}\right)$	$e\left(\frac{59}{87}\right)$	$e\left(\frac{17}{29}\right)$	$e\left(\frac{28}{87}\right)$	$e\left(\frac{11}{87}\right)$	$e\left(\frac{41}{87}\right)$	$e\left(\frac{52}{87}\right)$	$e\left(\frac{32}{87}\right)$

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	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(21\)
\(\chi_{8732}(121,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{38}{87}\right)\)	\(e\left(\frac{44}{87}\right)\)	\(e\left(\frac{74}{87}\right)\)	\(e\left(\frac{76}{87}\right)\)	\(e\left(\frac{16}{29}\right)\)	\(e\left(\frac{11}{87}\right)\)	\(e\left(\frac{82}{87}\right)\)	\(e\left(\frac{13}{87}\right)\)	\(e\left(\frac{8}{87}\right)\)	\(e\left(\frac{25}{87}\right)\)
\(\chi_{8732}(137,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{87}\right)\)	\(e\left(\frac{52}{87}\right)\)	\(e\left(\frac{40}{87}\right)\)	\(e\left(\frac{74}{87}\right)\)	\(e\left(\frac{11}{29}\right)\)	\(e\left(\frac{13}{87}\right)\)	\(e\left(\frac{2}{87}\right)\)	\(e\left(\frac{47}{87}\right)\)	\(e\left(\frac{49}{87}\right)\)	\(e\left(\frac{77}{87}\right)\)
\(\chi_{8732}(285,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{61}{87}\right)\)	\(e\left(\frac{34}{87}\right)\)	\(e\left(\frac{73}{87}\right)\)	\(e\left(\frac{35}{87}\right)\)	\(e\left(\frac{15}{29}\right)\)	\(e\left(\frac{52}{87}\right)\)	\(e\left(\frac{8}{87}\right)\)	\(e\left(\frac{14}{87}\right)\)	\(e\left(\frac{22}{87}\right)\)	\(e\left(\frac{47}{87}\right)\)
\(\chi_{8732}(417,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{87}\right)\)	\(e\left(\frac{47}{87}\right)\)	\(e\left(\frac{83}{87}\right)\)	\(e\left(\frac{10}{87}\right)\)	\(e\left(\frac{25}{29}\right)\)	\(e\left(\frac{77}{87}\right)\)	\(e\left(\frac{52}{87}\right)\)	\(e\left(\frac{4}{87}\right)\)	\(e\left(\frac{56}{87}\right)\)	\(e\left(\frac{1}{87}\right)\)
\(\chi_{8732}(433,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{49}{87}\right)\)	\(e\left(\frac{43}{87}\right)\)	\(e\left(\frac{13}{87}\right)\)	\(e\left(\frac{11}{87}\right)\)	\(e\left(\frac{13}{29}\right)\)	\(e\left(\frac{76}{87}\right)\)	\(e\left(\frac{5}{87}\right)\)	\(e\left(\frac{74}{87}\right)\)	\(e\left(\frac{79}{87}\right)\)	\(e\left(\frac{62}{87}\right)\)
\(\chi_{8732}(713,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{44}{87}\right)\)	\(e\left(\frac{83}{87}\right)\)	\(e\left(\frac{17}{87}\right)\)	\(e\left(\frac{1}{87}\right)\)	\(e\left(\frac{17}{29}\right)\)	\(e\left(\frac{86}{87}\right)\)	\(e\left(\frac{40}{87}\right)\)	\(e\left(\frac{70}{87}\right)\)	\(e\left(\frac{23}{87}\right)\)	\(e\left(\frac{61}{87}\right)\)
\(\chi_{8732}(729,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{25}{87}\right)\)	\(e\left(\frac{61}{87}\right)\)	\(e\left(\frac{67}{87}\right)\)	\(e\left(\frac{50}{87}\right)\)	\(e\left(\frac{9}{29}\right)\)	\(e\left(\frac{37}{87}\right)\)	\(e\left(\frac{86}{87}\right)\)	\(e\left(\frac{20}{87}\right)\)	\(e\left(\frac{19}{87}\right)\)	\(e\left(\frac{5}{87}\right)\)
\(\chi_{8732}(861,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{87}\right)\)	\(e\left(\frac{71}{87}\right)\)	\(e\left(\frac{68}{87}\right)\)	\(e\left(\frac{4}{87}\right)\)	\(e\left(\frac{10}{29}\right)\)	\(e\left(\frac{83}{87}\right)\)	\(e\left(\frac{73}{87}\right)\)	\(e\left(\frac{19}{87}\right)\)	\(e\left(\frac{5}{87}\right)\)	\(e\left(\frac{70}{87}\right)\)
\(\chi_{8732}(877,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{22}{87}\right)\)	\(e\left(\frac{85}{87}\right)\)	\(e\left(\frac{52}{87}\right)\)	\(e\left(\frac{44}{87}\right)\)	\(e\left(\frac{23}{29}\right)\)	\(e\left(\frac{43}{87}\right)\)	\(e\left(\frac{20}{87}\right)\)	\(e\left(\frac{35}{87}\right)\)	\(e\left(\frac{55}{87}\right)\)	\(e\left(\frac{74}{87}\right)\)
\(\chi_{8732}(1025,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{87}\right)\)	\(e\left(\frac{31}{87}\right)\)	\(e\left(\frac{64}{87}\right)\)	\(e\left(\frac{14}{87}\right)\)	\(e\left(\frac{6}{29}\right)\)	\(e\left(\frac{73}{87}\right)\)	\(e\left(\frac{38}{87}\right)\)	\(e\left(\frac{23}{87}\right)\)	\(e\left(\frac{61}{87}\right)\)	\(e\left(\frac{71}{87}\right)\)
\(\chi_{8732}(1157,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{87}\right)\)	\(e\left(\frac{77}{87}\right)\)	\(e\left(\frac{86}{87}\right)\)	\(e\left(\frac{46}{87}\right)\)	\(e\left(\frac{28}{29}\right)\)	\(e\left(\frac{41}{87}\right)\)	\(e\left(\frac{13}{87}\right)\)	\(e\left(\frac{1}{87}\right)\)	\(e\left(\frac{14}{87}\right)\)	\(e\left(\frac{22}{87}\right)\)
\(\chi_{8732}(1305,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{74}{87}\right)\)	\(e\left(\frac{17}{87}\right)\)	\(e\left(\frac{80}{87}\right)\)	\(e\left(\frac{61}{87}\right)\)	\(e\left(\frac{22}{29}\right)\)	\(e\left(\frac{26}{87}\right)\)	\(e\left(\frac{4}{87}\right)\)	\(e\left(\frac{7}{87}\right)\)	\(e\left(\frac{11}{87}\right)\)	\(e\left(\frac{67}{87}\right)\)
\(\chi_{8732}(1469,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{55}{87}\right)\)	\(e\left(\frac{82}{87}\right)\)	\(e\left(\frac{43}{87}\right)\)	\(e\left(\frac{23}{87}\right)\)	\(e\left(\frac{14}{29}\right)\)	\(e\left(\frac{64}{87}\right)\)	\(e\left(\frac{50}{87}\right)\)	\(e\left(\frac{44}{87}\right)\)	\(e\left(\frac{7}{87}\right)\)	\(e\left(\frac{11}{87}\right)\)
\(\chi_{8732}(1897,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{87}\right)\)	\(e\left(\frac{59}{87}\right)\)	\(e\left(\frac{32}{87}\right)\)	\(e\left(\frac{7}{87}\right)\)	\(e\left(\frac{3}{29}\right)\)	\(e\left(\frac{80}{87}\right)\)	\(e\left(\frac{19}{87}\right)\)	\(e\left(\frac{55}{87}\right)\)	\(e\left(\frac{74}{87}\right)\)	\(e\left(\frac{79}{87}\right)\)
\(\chi_{8732}(1913,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{87}\right)\)	\(e\left(\frac{79}{87}\right)\)	\(e\left(\frac{34}{87}\right)\)	\(e\left(\frac{2}{87}\right)\)	\(e\left(\frac{5}{29}\right)\)	\(e\left(\frac{85}{87}\right)\)	\(e\left(\frac{80}{87}\right)\)	\(e\left(\frac{53}{87}\right)\)	\(e\left(\frac{46}{87}\right)\)	\(e\left(\frac{35}{87}\right)\)
\(\chi_{8732}(2209,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{28}{87}\right)\)	\(e\left(\frac{37}{87}\right)\)	\(e\left(\frac{82}{87}\right)\)	\(e\left(\frac{56}{87}\right)\)	\(e\left(\frac{24}{29}\right)\)	\(e\left(\frac{31}{87}\right)\)	\(e\left(\frac{65}{87}\right)\)	\(e\left(\frac{5}{87}\right)\)	\(e\left(\frac{70}{87}\right)\)	\(e\left(\frac{23}{87}\right)\)
\(\chi_{8732}(2505,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{85}{87}\right)\)	\(e\left(\frac{16}{87}\right)\)	\(e\left(\frac{19}{87}\right)\)	\(e\left(\frac{83}{87}\right)\)	\(e\left(\frac{19}{29}\right)\)	\(e\left(\frac{4}{87}\right)\)	\(e\left(\frac{14}{87}\right)\)	\(e\left(\frac{68}{87}\right)\)	\(e\left(\frac{82}{87}\right)\)	\(e\left(\frac{17}{87}\right)\)
\(\chi_{8732}(2637,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{35}{87}\right)\)	\(e\left(\frac{68}{87}\right)\)	\(e\left(\frac{59}{87}\right)\)	\(e\left(\frac{70}{87}\right)\)	\(e\left(\frac{1}{29}\right)\)	\(e\left(\frac{17}{87}\right)\)	\(e\left(\frac{16}{87}\right)\)	\(e\left(\frac{28}{87}\right)\)	\(e\left(\frac{44}{87}\right)\)	\(e\left(\frac{7}{87}\right)\)
\(\chi_{8732}(2653,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{46}{87}\right)\)	\(e\left(\frac{67}{87}\right)\)	\(e\left(\frac{85}{87}\right)\)	\(e\left(\frac{5}{87}\right)\)	\(e\left(\frac{27}{29}\right)\)	\(e\left(\frac{82}{87}\right)\)	\(e\left(\frac{26}{87}\right)\)	\(e\left(\frac{2}{87}\right)\)	\(e\left(\frac{28}{87}\right)\)	\(e\left(\frac{44}{87}\right)\)
\(\chi_{8732}(2785,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{14}{87}\right)\)	\(e\left(\frac{62}{87}\right)\)	\(e\left(\frac{41}{87}\right)\)	\(e\left(\frac{28}{87}\right)\)	\(e\left(\frac{12}{29}\right)\)	\(e\left(\frac{59}{87}\right)\)	\(e\left(\frac{76}{87}\right)\)	\(e\left(\frac{46}{87}\right)\)	\(e\left(\frac{35}{87}\right)\)	\(e\left(\frac{55}{87}\right)\)
\(\chi_{8732}(2801,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{79}{87}\right)\)	\(e\left(\frac{64}{87}\right)\)	\(e\left(\frac{76}{87}\right)\)	\(e\left(\frac{71}{87}\right)\)	\(e\left(\frac{18}{29}\right)\)	\(e\left(\frac{16}{87}\right)\)	\(e\left(\frac{56}{87}\right)\)	\(e\left(\frac{11}{87}\right)\)	\(e\left(\frac{67}{87}\right)\)	\(e\left(\frac{68}{87}\right)\)
\(\chi_{8732}(3097,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{70}{87}\right)\)	\(e\left(\frac{49}{87}\right)\)	\(e\left(\frac{31}{87}\right)\)	\(e\left(\frac{53}{87}\right)\)	\(e\left(\frac{2}{29}\right)\)	\(e\left(\frac{34}{87}\right)\)	\(e\left(\frac{32}{87}\right)\)	\(e\left(\frac{56}{87}\right)\)	\(e\left(\frac{1}{87}\right)\)	\(e\left(\frac{14}{87}\right)\)
\(\chi_{8732}(3673,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{87}\right)\)	\(e\left(\frac{11}{87}\right)\)	\(e\left(\frac{62}{87}\right)\)	\(e\left(\frac{19}{87}\right)\)	\(e\left(\frac{4}{29}\right)\)	\(e\left(\frac{68}{87}\right)\)	\(e\left(\frac{64}{87}\right)\)	\(e\left(\frac{25}{87}\right)\)	\(e\left(\frac{2}{87}\right)\)	\(e\left(\frac{28}{87}\right)\)
\(\chi_{8732}(3821,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{62}{87}\right)\)	\(e\left(\frac{26}{87}\right)\)	\(e\left(\frac{20}{87}\right)\)	\(e\left(\frac{37}{87}\right)\)	\(e\left(\frac{20}{29}\right)\)	\(e\left(\frac{50}{87}\right)\)	\(e\left(\frac{1}{87}\right)\)	\(e\left(\frac{67}{87}\right)\)	\(e\left(\frac{68}{87}\right)\)	\(e\left(\frac{82}{87}\right)\)
\(\chi_{8732}(3969,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{68}{87}\right)\)	\(e\left(\frac{65}{87}\right)\)	\(e\left(\frac{50}{87}\right)\)	\(e\left(\frac{49}{87}\right)\)	\(e\left(\frac{21}{29}\right)\)	\(e\left(\frac{38}{87}\right)\)	\(e\left(\frac{46}{87}\right)\)	\(e\left(\frac{37}{87}\right)\)	\(e\left(\frac{83}{87}\right)\)	\(e\left(\frac{31}{87}\right)\)
\(\chi_{8732}(4117,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{87}\right)\)	\(e\left(\frac{86}{87}\right)\)	\(e\left(\frac{26}{87}\right)\)	\(e\left(\frac{22}{87}\right)\)	\(e\left(\frac{26}{29}\right)\)	\(e\left(\frac{65}{87}\right)\)	\(e\left(\frac{10}{87}\right)\)	\(e\left(\frac{61}{87}\right)\)	\(e\left(\frac{71}{87}\right)\)	\(e\left(\frac{37}{87}\right)\)
\(\chi_{8732}(4133,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{67}{87}\right)\)	\(e\left(\frac{73}{87}\right)\)	\(e\left(\frac{16}{87}\right)\)	\(e\left(\frac{47}{87}\right)\)	\(e\left(\frac{16}{29}\right)\)	\(e\left(\frac{40}{87}\right)\)	\(e\left(\frac{53}{87}\right)\)	\(e\left(\frac{71}{87}\right)\)	\(e\left(\frac{37}{87}\right)\)	\(e\left(\frac{83}{87}\right)\)
\(\chi_{8732}(4265,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{71}{87}\right)\)	\(e\left(\frac{41}{87}\right)\)	\(e\left(\frac{65}{87}\right)\)	\(e\left(\frac{55}{87}\right)\)	\(e\left(\frac{7}{29}\right)\)	\(e\left(\frac{32}{87}\right)\)	\(e\left(\frac{25}{87}\right)\)	\(e\left(\frac{22}{87}\right)\)	\(e\left(\frac{47}{87}\right)\)	\(e\left(\frac{49}{87}\right)\)
\(\chi_{8732}(4429,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{34}{87}\right)\)	\(e\left(\frac{76}{87}\right)\)	\(e\left(\frac{25}{87}\right)\)	\(e\left(\frac{68}{87}\right)\)	\(e\left(\frac{25}{29}\right)\)	\(e\left(\frac{19}{87}\right)\)	\(e\left(\frac{23}{87}\right)\)	\(e\left(\frac{62}{87}\right)\)	\(e\left(\frac{85}{87}\right)\)	\(e\left(\frac{59}{87}\right)\)
\(\chi_{8732}(4709,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{77}{87}\right)\)	\(e\left(\frac{80}{87}\right)\)	\(e\left(\frac{8}{87}\right)\)	\(e\left(\frac{67}{87}\right)\)	\(e\left(\frac{8}{29}\right)\)	\(e\left(\frac{20}{87}\right)\)	\(e\left(\frac{70}{87}\right)\)	\(e\left(\frac{79}{87}\right)\)	\(e\left(\frac{62}{87}\right)\)	\(e\left(\frac{85}{87}\right)\)
\(\chi_{8732}(4725,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{73}{87}\right)\)	\(e\left(\frac{25}{87}\right)\)	\(e\left(\frac{46}{87}\right)\)	\(e\left(\frac{59}{87}\right)\)	\(e\left(\frac{17}{29}\right)\)	\(e\left(\frac{28}{87}\right)\)	\(e\left(\frac{11}{87}\right)\)	\(e\left(\frac{41}{87}\right)\)	\(e\left(\frac{52}{87}\right)\)	\(e\left(\frac{32}{87}\right)\)

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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.bs
Modulus	$8732$
Conductor	$2183$
Order	$87$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(8732\)
Conductor:	\(2183\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(87\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 2183.w	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)