LMFDB - Dirichlet character orbit 531.m

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(531, base_ring=CyclotomicField(174)) M = H._module chi = DirichletCharacter(H, M([58,6])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(4,531)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$531$
Conductor:	$531$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$87$	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 87 polynomial

First 31 of 56 characters in Galois orbit

Character	$-1$	$1$	$2$	$4$	$5$	$7$	$8$	$10$	$11$	$13$	$14$	$16$
$\chi_{531}(4,\cdot)$	$1$	$1$	$e\left(\frac{32}{87}\right)$	$e\left(\frac{64}{87}\right)$	$e\left(\frac{76}{87}\right)$	$e\left(\frac{83}{87}\right)$	$e\left(\frac{3}{29}\right)$	$e\left(\frac{7}{29}\right)$	$e\left(\frac{17}{87}\right)$	$e\left(\frac{19}{87}\right)$	$e\left(\frac{28}{87}\right)$	$e\left(\frac{41}{87}\right)$
$\chi_{531}(7,\cdot)$	$1$	$1$	$e\left(\frac{85}{87}\right)$	$e\left(\frac{83}{87}\right)$	$e\left(\frac{17}{87}\right)$	$e\left(\frac{22}{87}\right)$	$e\left(\frac{27}{29}\right)$	$e\left(\frac{5}{29}\right)$	$e\left(\frac{37}{87}\right)$	$e\left(\frac{26}{87}\right)$	$e\left(\frac{20}{87}\right)$	$e\left(\frac{79}{87}\right)$
$\chi_{531}(16,\cdot)$	$1$	$1$	$e\left(\frac{64}{87}\right)$	$e\left(\frac{41}{87}\right)$	$e\left(\frac{65}{87}\right)$	$e\left(\frac{79}{87}\right)$	$e\left(\frac{6}{29}\right)$	$e\left(\frac{14}{29}\right)$	$e\left(\frac{34}{87}\right)$	$e\left(\frac{38}{87}\right)$	$e\left(\frac{56}{87}\right)$	$e\left(\frac{82}{87}\right)$
$\chi_{531}(22,\cdot)$	$1$	$1$	$e\left(\frac{68}{87}\right)$	$e\left(\frac{49}{87}\right)$	$e\left(\frac{31}{87}\right)$	$e\left(\frac{35}{87}\right)$	$e\left(\frac{10}{29}\right)$	$e\left(\frac{4}{29}\right)$	$e\left(\frac{47}{87}\right)$	$e\left(\frac{73}{87}\right)$	$e\left(\frac{16}{87}\right)$	$e\left(\frac{11}{87}\right)$
$\chi_{531}(25,\cdot)$	$1$	$1$	$e\left(\frac{76}{87}\right)$	$e\left(\frac{65}{87}\right)$	$e\left(\frac{50}{87}\right)$	$e\left(\frac{34}{87}\right)$	$e\left(\frac{18}{29}\right)$	$e\left(\frac{13}{29}\right)$	$e\left(\frac{73}{87}\right)$	$e\left(\frac{56}{87}\right)$	$e\left(\frac{23}{87}\right)$	$e\left(\frac{43}{87}\right)$
$\chi_{531}(49,\cdot)$	$1$	$1$	$e\left(\frac{83}{87}\right)$	$e\left(\frac{79}{87}\right)$	$e\left(\frac{34}{87}\right)$	$e\left(\frac{44}{87}\right)$	$e\left(\frac{25}{29}\right)$	$e\left(\frac{10}{29}\right)$	$e\left(\frac{74}{87}\right)$	$e\left(\frac{52}{87}\right)$	$e\left(\frac{40}{87}\right)$	$e\left(\frac{71}{87}\right)$
$\chi_{531}(76,\cdot)$	$1$	$1$	$e\left(\frac{2}{87}\right)$	$e\left(\frac{4}{87}\right)$	$e\left(\frac{70}{87}\right)$	$e\left(\frac{65}{87}\right)$	$e\left(\frac{2}{29}\right)$	$e\left(\frac{24}{29}\right)$	$e\left(\frac{50}{87}\right)$	$e\left(\frac{61}{87}\right)$	$e\left(\frac{67}{87}\right)$	$e\left(\frac{8}{87}\right)$
$\chi_{531}(79,\cdot)$	$1$	$1$	$e\left(\frac{70}{87}\right)$	$e\left(\frac{53}{87}\right)$	$e\left(\frac{14}{87}\right)$	$e\left(\frac{13}{87}\right)$	$e\left(\frac{12}{29}\right)$	$e\left(\frac{28}{29}\right)$	$e\left(\frac{10}{87}\right)$	$e\left(\frac{47}{87}\right)$	$e\left(\frac{83}{87}\right)$	$e\left(\frac{19}{87}\right)$
$\chi_{531}(85,\cdot)$	$1$	$1$	$e\left(\frac{11}{87}\right)$	$e\left(\frac{22}{87}\right)$	$e\left(\frac{37}{87}\right)$	$e\left(\frac{53}{87}\right)$	$e\left(\frac{11}{29}\right)$	$e\left(\frac{16}{29}\right)$	$e\left(\frac{14}{87}\right)$	$e\left(\frac{31}{87}\right)$	$e\left(\frac{64}{87}\right)$	$e\left(\frac{44}{87}\right)$
$\chi_{531}(88,\cdot)$	$1$	$1$	$e\left(\frac{13}{87}\right)$	$e\left(\frac{26}{87}\right)$	$e\left(\frac{20}{87}\right)$	$e\left(\frac{31}{87}\right)$	$e\left(\frac{13}{29}\right)$	$e\left(\frac{11}{29}\right)$	$e\left(\frac{64}{87}\right)$	$e\left(\frac{5}{87}\right)$	$e\left(\frac{44}{87}\right)$	$e\left(\frac{52}{87}\right)$
$\chi_{531}(94,\cdot)$	$1$	$1$	$e\left(\frac{65}{87}\right)$	$e\left(\frac{43}{87}\right)$	$e\left(\frac{13}{87}\right)$	$e\left(\frac{68}{87}\right)$	$e\left(\frac{7}{29}\right)$	$e\left(\frac{26}{29}\right)$	$e\left(\frac{59}{87}\right)$	$e\left(\frac{25}{87}\right)$	$e\left(\frac{46}{87}\right)$	$e\left(\frac{86}{87}\right)$
$\chi_{531}(112,\cdot)$	$1$	$1$	$e\left(\frac{62}{87}\right)$	$e\left(\frac{37}{87}\right)$	$e\left(\frac{82}{87}\right)$	$e\left(\frac{14}{87}\right)$	$e\left(\frac{4}{29}\right)$	$e\left(\frac{19}{29}\right)$	$e\left(\frac{71}{87}\right)$	$e\left(\frac{64}{87}\right)$	$e\left(\frac{76}{87}\right)$	$e\left(\frac{74}{87}\right)$
$\chi_{531}(121,\cdot)$	$1$	$1$	$e\left(\frac{17}{87}\right)$	$e\left(\frac{34}{87}\right)$	$e\left(\frac{73}{87}\right)$	$e\left(\frac{74}{87}\right)$	$e\left(\frac{17}{29}\right)$	$e\left(\frac{1}{29}\right)$	$e\left(\frac{77}{87}\right)$	$e\left(\frac{40}{87}\right)$	$e\left(\frac{4}{87}\right)$	$e\left(\frac{68}{87}\right)$
$\chi_{531}(130,\cdot)$	$1$	$1$	$e\left(\frac{20}{87}\right)$	$e\left(\frac{40}{87}\right)$	$e\left(\frac{4}{87}\right)$	$e\left(\frac{41}{87}\right)$	$e\left(\frac{20}{29}\right)$	$e\left(\frac{8}{29}\right)$	$e\left(\frac{65}{87}\right)$	$e\left(\frac{1}{87}\right)$	$e\left(\frac{61}{87}\right)$	$e\left(\frac{80}{87}\right)$
$\chi_{531}(133,\cdot)$	$1$	$1$	$e\left(\frac{55}{87}\right)$	$e\left(\frac{23}{87}\right)$	$e\left(\frac{11}{87}\right)$	$e\left(\frac{4}{87}\right)$	$e\left(\frac{26}{29}\right)$	$e\left(\frac{22}{29}\right)$	$e\left(\frac{70}{87}\right)$	$e\left(\frac{68}{87}\right)$	$e\left(\frac{59}{87}\right)$	$e\left(\frac{46}{87}\right)$
$\chi_{531}(139,\cdot)$	$1$	$1$	$e\left(\frac{44}{87}\right)$	$e\left(\frac{1}{87}\right)$	$e\left(\frac{61}{87}\right)$	$e\left(\frac{38}{87}\right)$	$e\left(\frac{15}{29}\right)$	$e\left(\frac{6}{29}\right)$	$e\left(\frac{56}{87}\right)$	$e\left(\frac{37}{87}\right)$	$e\left(\frac{82}{87}\right)$	$e\left(\frac{2}{87}\right)$
$\chi_{531}(166,\cdot)$	$1$	$1$	$e\left(\frac{23}{87}\right)$	$e\left(\frac{46}{87}\right)$	$e\left(\frac{22}{87}\right)$	$e\left(\frac{8}{87}\right)$	$e\left(\frac{23}{29}\right)$	$e\left(\frac{15}{29}\right)$	$e\left(\frac{53}{87}\right)$	$e\left(\frac{49}{87}\right)$	$e\left(\frac{31}{87}\right)$	$e\left(\frac{5}{87}\right)$
$\chi_{531}(169,\cdot)$	$1$	$1$	$e\left(\frac{19}{87}\right)$	$e\left(\frac{38}{87}\right)$	$e\left(\frac{56}{87}\right)$	$e\left(\frac{52}{87}\right)$	$e\left(\frac{19}{29}\right)$	$e\left(\frac{25}{29}\right)$	$e\left(\frac{40}{87}\right)$	$e\left(\frac{14}{87}\right)$	$e\left(\frac{71}{87}\right)$	$e\left(\frac{76}{87}\right)$
$\chi_{531}(175,\cdot)$	$1$	$1$	$e\left(\frac{74}{87}\right)$	$e\left(\frac{61}{87}\right)$	$e\left(\frac{67}{87}\right)$	$e\left(\frac{56}{87}\right)$	$e\left(\frac{16}{29}\right)$	$e\left(\frac{18}{29}\right)$	$e\left(\frac{23}{87}\right)$	$e\left(\frac{82}{87}\right)$	$e\left(\frac{43}{87}\right)$	$e\left(\frac{35}{87}\right)$
$\chi_{531}(184,\cdot)$	$1$	$1$	$e\left(\frac{56}{87}\right)$	$e\left(\frac{25}{87}\right)$	$e\left(\frac{46}{87}\right)$	$e\left(\frac{80}{87}\right)$	$e\left(\frac{27}{29}\right)$	$e\left(\frac{5}{29}\right)$	$e\left(\frac{8}{87}\right)$	$e\left(\frac{55}{87}\right)$	$e\left(\frac{49}{87}\right)$	$e\left(\frac{50}{87}\right)$
$\chi_{531}(193,\cdot)$	$1$	$1$	$e\left(\frac{35}{87}\right)$	$e\left(\frac{70}{87}\right)$	$e\left(\frac{7}{87}\right)$	$e\left(\frac{50}{87}\right)$	$e\left(\frac{6}{29}\right)$	$e\left(\frac{14}{29}\right)$	$e\left(\frac{5}{87}\right)$	$e\left(\frac{67}{87}\right)$	$e\left(\frac{85}{87}\right)$	$e\left(\frac{53}{87}\right)$
$\chi_{531}(196,\cdot)$	$1$	$1$	$e\left(\frac{28}{87}\right)$	$e\left(\frac{56}{87}\right)$	$e\left(\frac{23}{87}\right)$	$e\left(\frac{40}{87}\right)$	$e\left(\frac{28}{29}\right)$	$e\left(\frac{17}{29}\right)$	$e\left(\frac{4}{87}\right)$	$e\left(\frac{71}{87}\right)$	$e\left(\frac{68}{87}\right)$	$e\left(\frac{25}{87}\right)$
$\chi_{531}(202,\cdot)$	$1$	$1$	$e\left(\frac{47}{87}\right)$	$e\left(\frac{7}{87}\right)$	$e\left(\frac{79}{87}\right)$	$e\left(\frac{5}{87}\right)$	$e\left(\frac{18}{29}\right)$	$e\left(\frac{13}{29}\right)$	$e\left(\frac{44}{87}\right)$	$e\left(\frac{85}{87}\right)$	$e\left(\frac{52}{87}\right)$	$e\left(\frac{14}{87}\right)$
$\chi_{531}(205,\cdot)$	$1$	$1$	$e\left(\frac{1}{87}\right)$	$e\left(\frac{2}{87}\right)$	$e\left(\frac{35}{87}\right)$	$e\left(\frac{76}{87}\right)$	$e\left(\frac{1}{29}\right)$	$e\left(\frac{12}{29}\right)$	$e\left(\frac{25}{87}\right)$	$e\left(\frac{74}{87}\right)$	$e\left(\frac{77}{87}\right)$	$e\left(\frac{4}{87}\right)$
$\chi_{531}(223,\cdot)$	$1$	$1$	$e\left(\frac{82}{87}\right)$	$e\left(\frac{77}{87}\right)$	$e\left(\frac{86}{87}\right)$	$e\left(\frac{55}{87}\right)$	$e\left(\frac{24}{29}\right)$	$e\left(\frac{27}{29}\right)$	$e\left(\frac{49}{87}\right)$	$e\left(\frac{65}{87}\right)$	$e\left(\frac{50}{87}\right)$	$e\left(\frac{67}{87}\right)$
$\chi_{531}(241,\cdot)$	$1$	$1$	$e\left(\frac{67}{87}\right)$	$e\left(\frac{47}{87}\right)$	$e\left(\frac{83}{87}\right)$	$e\left(\frac{46}{87}\right)$	$e\left(\frac{9}{29}\right)$	$e\left(\frac{21}{29}\right)$	$e\left(\frac{22}{87}\right)$	$e\left(\frac{86}{87}\right)$	$e\left(\frac{26}{87}\right)$	$e\left(\frac{7}{87}\right)$
$\chi_{531}(256,\cdot)$	$1$	$1$	$e\left(\frac{41}{87}\right)$	$e\left(\frac{82}{87}\right)$	$e\left(\frac{43}{87}\right)$	$e\left(\frac{71}{87}\right)$	$e\left(\frac{12}{29}\right)$	$e\left(\frac{28}{29}\right)$	$e\left(\frac{68}{87}\right)$	$e\left(\frac{76}{87}\right)$	$e\left(\frac{25}{87}\right)$	$e\left(\frac{77}{87}\right)$
$\chi_{531}(265,\cdot)$	$1$	$1$	$e\left(\frac{71}{87}\right)$	$e\left(\frac{55}{87}\right)$	$e\left(\frac{49}{87}\right)$	$e\left(\frac{2}{87}\right)$	$e\left(\frac{13}{29}\right)$	$e\left(\frac{11}{29}\right)$	$e\left(\frac{35}{87}\right)$	$e\left(\frac{34}{87}\right)$	$e\left(\frac{73}{87}\right)$	$e\left(\frac{23}{87}\right)$
$\chi_{531}(277,\cdot)$	$1$	$1$	$e\left(\frac{79}{87}\right)$	$e\left(\frac{71}{87}\right)$	$e\left(\frac{68}{87}\right)$	$e\left(\frac{1}{87}\right)$	$e\left(\frac{21}{29}\right)$	$e\left(\frac{20}{29}\right)$	$e\left(\frac{61}{87}\right)$	$e\left(\frac{17}{87}\right)$	$e\left(\frac{80}{87}\right)$	$e\left(\frac{55}{87}\right)$
$\chi_{531}(304,\cdot)$	$1$	$1$	$e\left(\frac{34}{87}\right)$	$e\left(\frac{68}{87}\right)$	$e\left(\frac{59}{87}\right)$	$e\left(\frac{61}{87}\right)$	$e\left(\frac{5}{29}\right)$	$e\left(\frac{2}{29}\right)$	$e\left(\frac{67}{87}\right)$	$e\left(\frac{80}{87}\right)$	$e\left(\frac{8}{87}\right)$	$e\left(\frac{49}{87}\right)$
$\chi_{531}(310,\cdot)$	$1$	$1$	$e\left(\frac{26}{87}\right)$	$e\left(\frac{52}{87}\right)$	$e\left(\frac{40}{87}\right)$	$e\left(\frac{62}{87}\right)$	$e\left(\frac{26}{29}\right)$	$e\left(\frac{22}{29}\right)$	$e\left(\frac{41}{87}\right)$	$e\left(\frac{10}{87}\right)$	$e\left(\frac{1}{87}\right)$	$e\left(\frac{17}{87}\right)$

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	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(7\)	\(8\)	\(10\)	\(11\)	\(13\)	\(14\)	\(16\)
\(\chi_{531}(4,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{32}{87}\right)\)	\(e\left(\frac{64}{87}\right)\)	\(e\left(\frac{76}{87}\right)\)	\(e\left(\frac{83}{87}\right)\)	\(e\left(\frac{3}{29}\right)\)	\(e\left(\frac{7}{29}\right)\)	\(e\left(\frac{17}{87}\right)\)	\(e\left(\frac{19}{87}\right)\)	\(e\left(\frac{28}{87}\right)\)	\(e\left(\frac{41}{87}\right)\)
\(\chi_{531}(7,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{85}{87}\right)\)	\(e\left(\frac{83}{87}\right)\)	\(e\left(\frac{17}{87}\right)\)	\(e\left(\frac{22}{87}\right)\)	\(e\left(\frac{27}{29}\right)\)	\(e\left(\frac{5}{29}\right)\)	\(e\left(\frac{37}{87}\right)\)	\(e\left(\frac{26}{87}\right)\)	\(e\left(\frac{20}{87}\right)\)	\(e\left(\frac{79}{87}\right)\)
\(\chi_{531}(16,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{64}{87}\right)\)	\(e\left(\frac{41}{87}\right)\)	\(e\left(\frac{65}{87}\right)\)	\(e\left(\frac{79}{87}\right)\)	\(e\left(\frac{6}{29}\right)\)	\(e\left(\frac{14}{29}\right)\)	\(e\left(\frac{34}{87}\right)\)	\(e\left(\frac{38}{87}\right)\)	\(e\left(\frac{56}{87}\right)\)	\(e\left(\frac{82}{87}\right)\)
\(\chi_{531}(22,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{68}{87}\right)\)	\(e\left(\frac{49}{87}\right)\)	\(e\left(\frac{31}{87}\right)\)	\(e\left(\frac{35}{87}\right)\)	\(e\left(\frac{10}{29}\right)\)	\(e\left(\frac{4}{29}\right)\)	\(e\left(\frac{47}{87}\right)\)	\(e\left(\frac{73}{87}\right)\)	\(e\left(\frac{16}{87}\right)\)	\(e\left(\frac{11}{87}\right)\)
\(\chi_{531}(25,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{76}{87}\right)\)	\(e\left(\frac{65}{87}\right)\)	\(e\left(\frac{50}{87}\right)\)	\(e\left(\frac{34}{87}\right)\)	\(e\left(\frac{18}{29}\right)\)	\(e\left(\frac{13}{29}\right)\)	\(e\left(\frac{73}{87}\right)\)	\(e\left(\frac{56}{87}\right)\)	\(e\left(\frac{23}{87}\right)\)	\(e\left(\frac{43}{87}\right)\)
\(\chi_{531}(49,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{83}{87}\right)\)	\(e\left(\frac{79}{87}\right)\)	\(e\left(\frac{34}{87}\right)\)	\(e\left(\frac{44}{87}\right)\)	\(e\left(\frac{25}{29}\right)\)	\(e\left(\frac{10}{29}\right)\)	\(e\left(\frac{74}{87}\right)\)	\(e\left(\frac{52}{87}\right)\)	\(e\left(\frac{40}{87}\right)\)	\(e\left(\frac{71}{87}\right)\)
\(\chi_{531}(76,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{87}\right)\)	\(e\left(\frac{4}{87}\right)\)	\(e\left(\frac{70}{87}\right)\)	\(e\left(\frac{65}{87}\right)\)	\(e\left(\frac{2}{29}\right)\)	\(e\left(\frac{24}{29}\right)\)	\(e\left(\frac{50}{87}\right)\)	\(e\left(\frac{61}{87}\right)\)	\(e\left(\frac{67}{87}\right)\)	\(e\left(\frac{8}{87}\right)\)
\(\chi_{531}(79,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{70}{87}\right)\)	\(e\left(\frac{53}{87}\right)\)	\(e\left(\frac{14}{87}\right)\)	\(e\left(\frac{13}{87}\right)\)	\(e\left(\frac{12}{29}\right)\)	\(e\left(\frac{28}{29}\right)\)	\(e\left(\frac{10}{87}\right)\)	\(e\left(\frac{47}{87}\right)\)	\(e\left(\frac{83}{87}\right)\)	\(e\left(\frac{19}{87}\right)\)
\(\chi_{531}(85,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{87}\right)\)	\(e\left(\frac{22}{87}\right)\)	\(e\left(\frac{37}{87}\right)\)	\(e\left(\frac{53}{87}\right)\)	\(e\left(\frac{11}{29}\right)\)	\(e\left(\frac{16}{29}\right)\)	\(e\left(\frac{14}{87}\right)\)	\(e\left(\frac{31}{87}\right)\)	\(e\left(\frac{64}{87}\right)\)	\(e\left(\frac{44}{87}\right)\)
\(\chi_{531}(88,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{87}\right)\)	\(e\left(\frac{26}{87}\right)\)	\(e\left(\frac{20}{87}\right)\)	\(e\left(\frac{31}{87}\right)\)	\(e\left(\frac{13}{29}\right)\)	\(e\left(\frac{11}{29}\right)\)	\(e\left(\frac{64}{87}\right)\)	\(e\left(\frac{5}{87}\right)\)	\(e\left(\frac{44}{87}\right)\)	\(e\left(\frac{52}{87}\right)\)
\(\chi_{531}(94,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{65}{87}\right)\)	\(e\left(\frac{43}{87}\right)\)	\(e\left(\frac{13}{87}\right)\)	\(e\left(\frac{68}{87}\right)\)	\(e\left(\frac{7}{29}\right)\)	\(e\left(\frac{26}{29}\right)\)	\(e\left(\frac{59}{87}\right)\)	\(e\left(\frac{25}{87}\right)\)	\(e\left(\frac{46}{87}\right)\)	\(e\left(\frac{86}{87}\right)\)
\(\chi_{531}(112,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{62}{87}\right)\)	\(e\left(\frac{37}{87}\right)\)	\(e\left(\frac{82}{87}\right)\)	\(e\left(\frac{14}{87}\right)\)	\(e\left(\frac{4}{29}\right)\)	\(e\left(\frac{19}{29}\right)\)	\(e\left(\frac{71}{87}\right)\)	\(e\left(\frac{64}{87}\right)\)	\(e\left(\frac{76}{87}\right)\)	\(e\left(\frac{74}{87}\right)\)
\(\chi_{531}(121,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{87}\right)\)	\(e\left(\frac{34}{87}\right)\)	\(e\left(\frac{73}{87}\right)\)	\(e\left(\frac{74}{87}\right)\)	\(e\left(\frac{17}{29}\right)\)	\(e\left(\frac{1}{29}\right)\)	\(e\left(\frac{77}{87}\right)\)	\(e\left(\frac{40}{87}\right)\)	\(e\left(\frac{4}{87}\right)\)	\(e\left(\frac{68}{87}\right)\)
\(\chi_{531}(130,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{20}{87}\right)\)	\(e\left(\frac{40}{87}\right)\)	\(e\left(\frac{4}{87}\right)\)	\(e\left(\frac{41}{87}\right)\)	\(e\left(\frac{20}{29}\right)\)	\(e\left(\frac{8}{29}\right)\)	\(e\left(\frac{65}{87}\right)\)	\(e\left(\frac{1}{87}\right)\)	\(e\left(\frac{61}{87}\right)\)	\(e\left(\frac{80}{87}\right)\)
\(\chi_{531}(133,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{55}{87}\right)\)	\(e\left(\frac{23}{87}\right)\)	\(e\left(\frac{11}{87}\right)\)	\(e\left(\frac{4}{87}\right)\)	\(e\left(\frac{26}{29}\right)\)	\(e\left(\frac{22}{29}\right)\)	\(e\left(\frac{70}{87}\right)\)	\(e\left(\frac{68}{87}\right)\)	\(e\left(\frac{59}{87}\right)\)	\(e\left(\frac{46}{87}\right)\)
\(\chi_{531}(139,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{44}{87}\right)\)	\(e\left(\frac{1}{87}\right)\)	\(e\left(\frac{61}{87}\right)\)	\(e\left(\frac{38}{87}\right)\)	\(e\left(\frac{15}{29}\right)\)	\(e\left(\frac{6}{29}\right)\)	\(e\left(\frac{56}{87}\right)\)	\(e\left(\frac{37}{87}\right)\)	\(e\left(\frac{82}{87}\right)\)	\(e\left(\frac{2}{87}\right)\)
\(\chi_{531}(166,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{87}\right)\)	\(e\left(\frac{46}{87}\right)\)	\(e\left(\frac{22}{87}\right)\)	\(e\left(\frac{8}{87}\right)\)	\(e\left(\frac{23}{29}\right)\)	\(e\left(\frac{15}{29}\right)\)	\(e\left(\frac{53}{87}\right)\)	\(e\left(\frac{49}{87}\right)\)	\(e\left(\frac{31}{87}\right)\)	\(e\left(\frac{5}{87}\right)\)
\(\chi_{531}(169,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{87}\right)\)	\(e\left(\frac{38}{87}\right)\)	\(e\left(\frac{56}{87}\right)\)	\(e\left(\frac{52}{87}\right)\)	\(e\left(\frac{19}{29}\right)\)	\(e\left(\frac{25}{29}\right)\)	\(e\left(\frac{40}{87}\right)\)	\(e\left(\frac{14}{87}\right)\)	\(e\left(\frac{71}{87}\right)\)	\(e\left(\frac{76}{87}\right)\)
\(\chi_{531}(175,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{74}{87}\right)\)	\(e\left(\frac{61}{87}\right)\)	\(e\left(\frac{67}{87}\right)\)	\(e\left(\frac{56}{87}\right)\)	\(e\left(\frac{16}{29}\right)\)	\(e\left(\frac{18}{29}\right)\)	\(e\left(\frac{23}{87}\right)\)	\(e\left(\frac{82}{87}\right)\)	\(e\left(\frac{43}{87}\right)\)	\(e\left(\frac{35}{87}\right)\)
\(\chi_{531}(184,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{56}{87}\right)\)	\(e\left(\frac{25}{87}\right)\)	\(e\left(\frac{46}{87}\right)\)	\(e\left(\frac{80}{87}\right)\)	\(e\left(\frac{27}{29}\right)\)	\(e\left(\frac{5}{29}\right)\)	\(e\left(\frac{8}{87}\right)\)	\(e\left(\frac{55}{87}\right)\)	\(e\left(\frac{49}{87}\right)\)	\(e\left(\frac{50}{87}\right)\)
\(\chi_{531}(193,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{35}{87}\right)\)	\(e\left(\frac{70}{87}\right)\)	\(e\left(\frac{7}{87}\right)\)	\(e\left(\frac{50}{87}\right)\)	\(e\left(\frac{6}{29}\right)\)	\(e\left(\frac{14}{29}\right)\)	\(e\left(\frac{5}{87}\right)\)	\(e\left(\frac{67}{87}\right)\)	\(e\left(\frac{85}{87}\right)\)	\(e\left(\frac{53}{87}\right)\)
\(\chi_{531}(196,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{28}{87}\right)\)	\(e\left(\frac{56}{87}\right)\)	\(e\left(\frac{23}{87}\right)\)	\(e\left(\frac{40}{87}\right)\)	\(e\left(\frac{28}{29}\right)\)	\(e\left(\frac{17}{29}\right)\)	\(e\left(\frac{4}{87}\right)\)	\(e\left(\frac{71}{87}\right)\)	\(e\left(\frac{68}{87}\right)\)	\(e\left(\frac{25}{87}\right)\)
\(\chi_{531}(202,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{87}\right)\)	\(e\left(\frac{7}{87}\right)\)	\(e\left(\frac{79}{87}\right)\)	\(e\left(\frac{5}{87}\right)\)	\(e\left(\frac{18}{29}\right)\)	\(e\left(\frac{13}{29}\right)\)	\(e\left(\frac{44}{87}\right)\)	\(e\left(\frac{85}{87}\right)\)	\(e\left(\frac{52}{87}\right)\)	\(e\left(\frac{14}{87}\right)\)
\(\chi_{531}(205,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{87}\right)\)	\(e\left(\frac{2}{87}\right)\)	\(e\left(\frac{35}{87}\right)\)	\(e\left(\frac{76}{87}\right)\)	\(e\left(\frac{1}{29}\right)\)	\(e\left(\frac{12}{29}\right)\)	\(e\left(\frac{25}{87}\right)\)	\(e\left(\frac{74}{87}\right)\)	\(e\left(\frac{77}{87}\right)\)	\(e\left(\frac{4}{87}\right)\)
\(\chi_{531}(223,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{82}{87}\right)\)	\(e\left(\frac{77}{87}\right)\)	\(e\left(\frac{86}{87}\right)\)	\(e\left(\frac{55}{87}\right)\)	\(e\left(\frac{24}{29}\right)\)	\(e\left(\frac{27}{29}\right)\)	\(e\left(\frac{49}{87}\right)\)	\(e\left(\frac{65}{87}\right)\)	\(e\left(\frac{50}{87}\right)\)	\(e\left(\frac{67}{87}\right)\)
\(\chi_{531}(241,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{67}{87}\right)\)	\(e\left(\frac{47}{87}\right)\)	\(e\left(\frac{83}{87}\right)\)	\(e\left(\frac{46}{87}\right)\)	\(e\left(\frac{9}{29}\right)\)	\(e\left(\frac{21}{29}\right)\)	\(e\left(\frac{22}{87}\right)\)	\(e\left(\frac{86}{87}\right)\)	\(e\left(\frac{26}{87}\right)\)	\(e\left(\frac{7}{87}\right)\)
\(\chi_{531}(256,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{87}\right)\)	\(e\left(\frac{82}{87}\right)\)	\(e\left(\frac{43}{87}\right)\)	\(e\left(\frac{71}{87}\right)\)	\(e\left(\frac{12}{29}\right)\)	\(e\left(\frac{28}{29}\right)\)	\(e\left(\frac{68}{87}\right)\)	\(e\left(\frac{76}{87}\right)\)	\(e\left(\frac{25}{87}\right)\)	\(e\left(\frac{77}{87}\right)\)
\(\chi_{531}(265,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{71}{87}\right)\)	\(e\left(\frac{55}{87}\right)\)	\(e\left(\frac{49}{87}\right)\)	\(e\left(\frac{2}{87}\right)\)	\(e\left(\frac{13}{29}\right)\)	\(e\left(\frac{11}{29}\right)\)	\(e\left(\frac{35}{87}\right)\)	\(e\left(\frac{34}{87}\right)\)	\(e\left(\frac{73}{87}\right)\)	\(e\left(\frac{23}{87}\right)\)
\(\chi_{531}(277,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{79}{87}\right)\)	\(e\left(\frac{71}{87}\right)\)	\(e\left(\frac{68}{87}\right)\)	\(e\left(\frac{1}{87}\right)\)	\(e\left(\frac{21}{29}\right)\)	\(e\left(\frac{20}{29}\right)\)	\(e\left(\frac{61}{87}\right)\)	\(e\left(\frac{17}{87}\right)\)	\(e\left(\frac{80}{87}\right)\)	\(e\left(\frac{55}{87}\right)\)
\(\chi_{531}(304,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{34}{87}\right)\)	\(e\left(\frac{68}{87}\right)\)	\(e\left(\frac{59}{87}\right)\)	\(e\left(\frac{61}{87}\right)\)	\(e\left(\frac{5}{29}\right)\)	\(e\left(\frac{2}{29}\right)\)	\(e\left(\frac{67}{87}\right)\)	\(e\left(\frac{80}{87}\right)\)	\(e\left(\frac{8}{87}\right)\)	\(e\left(\frac{49}{87}\right)\)
\(\chi_{531}(310,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{26}{87}\right)\)	\(e\left(\frac{52}{87}\right)\)	\(e\left(\frac{40}{87}\right)\)	\(e\left(\frac{62}{87}\right)\)	\(e\left(\frac{26}{29}\right)\)	\(e\left(\frac{22}{29}\right)\)	\(e\left(\frac{41}{87}\right)\)	\(e\left(\frac{10}{87}\right)\)	\(e\left(\frac{1}{87}\right)\)	\(e\left(\frac{17}{87}\right)\)

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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	531.m
Modulus	$531$
Conductor	$531$
Order	$87$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(531\)
Conductor:	\(531\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(87\)	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)