LMFDB - Dirichlet character orbit 8732.bt

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(8732, base_ring=CyclotomicField(116)) M = H._module chi = DirichletCharacter(H, M([58,29,100])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(475,8732)) 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:	$116$	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:	$\Q(\zeta_{116})$
Fixed field:	Number field defined by a degree 116 polynomial (not computed)

First 31 of 56 characters in Galois orbit

Character	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$17$	$19$	$21$
$\chi_{8732}(475,\cdot)$	$1$	$1$	$e\left(\frac{3}{29}\right)$	$e\left(\frac{107}{116}\right)$	$e\left(\frac{1}{58}\right)$	$e\left(\frac{6}{29}\right)$	$e\left(\frac{16}{29}\right)$	$e\left(\frac{63}{116}\right)$	$e\left(\frac{3}{116}\right)$	$e\left(\frac{27}{116}\right)$	$e\left(\frac{1}{116}\right)$	$e\left(\frac{7}{58}\right)$
$\chi_{8732}(487,\cdot)$	$1$	$1$	$e\left(\frac{8}{29}\right)$	$e\left(\frac{5}{116}\right)$	$e\left(\frac{51}{58}\right)$	$e\left(\frac{16}{29}\right)$	$e\left(\frac{4}{29}\right)$	$e\left(\frac{81}{116}\right)$	$e\left(\frac{37}{116}\right)$	$e\left(\frac{101}{116}\right)$	$e\left(\frac{51}{116}\right)$	$e\left(\frac{9}{58}\right)$
$\chi_{8732}(635,\cdot)$	$1$	$1$	$e\left(\frac{11}{29}\right)$	$e\left(\frac{25}{116}\right)$	$e\left(\frac{23}{58}\right)$	$e\left(\frac{22}{29}\right)$	$e\left(\frac{20}{29}\right)$	$e\left(\frac{57}{116}\right)$	$e\left(\frac{69}{116}\right)$	$e\left(\frac{41}{116}\right)$	$e\left(\frac{23}{116}\right)$	$e\left(\frac{45}{58}\right)$
$\chi_{8732}(771,\cdot)$	$1$	$1$	$e\left(\frac{21}{29}\right)$	$e\left(\frac{111}{116}\right)$	$e\left(\frac{7}{58}\right)$	$e\left(\frac{13}{29}\right)$	$e\left(\frac{25}{29}\right)$	$e\left(\frac{35}{116}\right)$	$e\left(\frac{79}{116}\right)$	$e\left(\frac{15}{116}\right)$	$e\left(\frac{65}{116}\right)$	$e\left(\frac{49}{58}\right)$
$\chi_{8732}(783,\cdot)$	$1$	$1$	$e\left(\frac{13}{29}\right)$	$e\left(\frac{77}{116}\right)$	$e\left(\frac{43}{58}\right)$	$e\left(\frac{26}{29}\right)$	$e\left(\frac{21}{29}\right)$	$e\left(\frac{41}{116}\right)$	$e\left(\frac{13}{116}\right)$	$e\left(\frac{1}{116}\right)$	$e\left(\frac{43}{116}\right)$	$e\left(\frac{11}{58}\right)$
$\chi_{8732}(931,\cdot)$	$1$	$1$	$e\left(\frac{23}{29}\right)$	$e\left(\frac{105}{116}\right)$	$e\left(\frac{27}{58}\right)$	$e\left(\frac{17}{29}\right)$	$e\left(\frac{26}{29}\right)$	$e\left(\frac{77}{116}\right)$	$e\left(\frac{81}{116}\right)$	$e\left(\frac{33}{116}\right)$	$e\left(\frac{27}{116}\right)$	$e\left(\frac{15}{58}\right)$
$\chi_{8732}(1067,\cdot)$	$1$	$1$	$e\left(\frac{5}{29}\right)$	$e\left(\frac{43}{116}\right)$	$e\left(\frac{21}{58}\right)$	$e\left(\frac{10}{29}\right)$	$e\left(\frac{17}{29}\right)$	$e\left(\frac{47}{116}\right)$	$e\left(\frac{63}{116}\right)$	$e\left(\frac{103}{116}\right)$	$e\left(\frac{21}{116}\right)$	$e\left(\frac{31}{58}\right)$
$\chi_{8732}(1079,\cdot)$	$1$	$1$	$e\left(\frac{14}{29}\right)$	$e\left(\frac{45}{116}\right)$	$e\left(\frac{53}{58}\right)$	$e\left(\frac{28}{29}\right)$	$e\left(\frac{7}{29}\right)$	$e\left(\frac{33}{116}\right)$	$e\left(\frac{101}{116}\right)$	$e\left(\frac{97}{116}\right)$	$e\left(\frac{111}{116}\right)$	$e\left(\frac{23}{58}\right)$
$\chi_{8732}(1215,\cdot)$	$1$	$1$	$e\left(\frac{20}{29}\right)$	$e\left(\frac{27}{116}\right)$	$e\left(\frac{55}{58}\right)$	$e\left(\frac{11}{29}\right)$	$e\left(\frac{10}{29}\right)$	$e\left(\frac{43}{116}\right)$	$e\left(\frac{107}{116}\right)$	$e\left(\frac{35}{116}\right)$	$e\left(\frac{113}{116}\right)$	$e\left(\frac{37}{58}\right)$
$\chi_{8732}(1511,\cdot)$	$1$	$1$	$e\left(\frac{27}{29}\right)$	$e\left(\frac{35}{116}\right)$	$e\left(\frac{9}{58}\right)$	$e\left(\frac{25}{29}\right)$	$e\left(\frac{28}{29}\right)$	$e\left(\frac{103}{116}\right)$	$e\left(\frac{27}{116}\right)$	$e\left(\frac{11}{116}\right)$	$e\left(\frac{9}{116}\right)$	$e\left(\frac{5}{58}\right)$
$\chi_{8732}(1523,\cdot)$	$1$	$1$	$e\left(\frac{16}{29}\right)$	$e\left(\frac{97}{116}\right)$	$e\left(\frac{15}{58}\right)$	$e\left(\frac{3}{29}\right)$	$e\left(\frac{8}{29}\right)$	$e\left(\frac{17}{116}\right)$	$e\left(\frac{45}{116}\right)$	$e\left(\frac{57}{116}\right)$	$e\left(\frac{15}{116}\right)$	$e\left(\frac{47}{58}\right)$
$\chi_{8732}(1659,\cdot)$	$1$	$1$	$e\left(\frac{15}{29}\right)$	$e\left(\frac{71}{116}\right)$	$e\left(\frac{5}{58}\right)$	$e\left(\frac{1}{29}\right)$	$e\left(\frac{22}{29}\right)$	$e\left(\frac{83}{116}\right)$	$e\left(\frac{15}{116}\right)$	$e\left(\frac{19}{116}\right)$	$e\left(\frac{5}{116}\right)$	$e\left(\frac{35}{58}\right)$
$\chi_{8732}(1671,\cdot)$	$1$	$1$	$e\left(\frac{22}{29}\right)$	$e\left(\frac{21}{116}\right)$	$e\left(\frac{17}{58}\right)$	$e\left(\frac{15}{29}\right)$	$e\left(\frac{11}{29}\right)$	$e\left(\frac{85}{116}\right)$	$e\left(\frac{109}{116}\right)$	$e\left(\frac{53}{116}\right)$	$e\left(\frac{75}{116}\right)$	$e\left(\frac{3}{58}\right)$
$\chi_{8732}(1819,\cdot)$	$1$	$1$	$e\left(\frac{1}{29}\right)$	$e\left(\frac{113}{116}\right)$	$e\left(\frac{39}{58}\right)$	$e\left(\frac{2}{29}\right)$	$e\left(\frac{15}{29}\right)$	$e\left(\frac{21}{116}\right)$	$e\left(\frac{1}{116}\right)$	$e\left(\frac{9}{116}\right)$	$e\left(\frac{39}{116}\right)$	$e\left(\frac{41}{58}\right)$
$\chi_{8732}(1967,\cdot)$	$1$	$1$	$e\left(\frac{26}{29}\right)$	$e\left(\frac{9}{116}\right)$	$e\left(\frac{57}{58}\right)$	$e\left(\frac{23}{29}\right)$	$e\left(\frac{13}{29}\right)$	$e\left(\frac{53}{116}\right)$	$e\left(\frac{113}{116}\right)$	$e\left(\frac{89}{116}\right)$	$e\left(\frac{115}{116}\right)$	$e\left(\frac{51}{58}\right)$
$\chi_{8732}(2251,\cdot)$	$1$	$1$	$e\left(\frac{6}{29}\right)$	$e\left(\frac{11}{116}\right)$	$e\left(\frac{31}{58}\right)$	$e\left(\frac{12}{29}\right)$	$e\left(\frac{3}{29}\right)$	$e\left(\frac{39}{116}\right)$	$e\left(\frac{35}{116}\right)$	$e\left(\frac{83}{116}\right)$	$e\left(\frac{89}{116}\right)$	$e\left(\frac{43}{58}\right)$
$\chi_{8732}(2263,\cdot)$	$1$	$1$	$e\left(\frac{18}{29}\right)$	$e\left(\frac{33}{116}\right)$	$e\left(\frac{35}{58}\right)$	$e\left(\frac{7}{29}\right)$	$e\left(\frac{9}{29}\right)$	$e\left(\frac{1}{116}\right)$	$e\left(\frac{105}{116}\right)$	$e\left(\frac{17}{116}\right)$	$e\left(\frac{35}{116}\right)$	$e\left(\frac{13}{58}\right)$
$\chi_{8732}(2411,\cdot)$	$1$	$1$	$e\left(\frac{17}{29}\right)$	$e\left(\frac{65}{116}\right)$	$e\left(\frac{25}{58}\right)$	$e\left(\frac{5}{29}\right)$	$e\left(\frac{23}{29}\right)$	$e\left(\frac{9}{116}\right)$	$e\left(\frac{17}{116}\right)$	$e\left(\frac{37}{116}\right)$	$e\left(\frac{83}{116}\right)$	$e\left(\frac{1}{58}\right)$
$\chi_{8732}(2559,\cdot)$	$1$	$1$	$e\left(\frac{12}{29}\right)$	$e\left(\frac{109}{116}\right)$	$e\left(\frac{33}{58}\right)$	$e\left(\frac{24}{29}\right)$	$e\left(\frac{6}{29}\right)$	$e\left(\frac{49}{116}\right)$	$e\left(\frac{41}{116}\right)$	$e\left(\frac{21}{116}\right)$	$e\left(\frac{91}{116}\right)$	$e\left(\frac{57}{58}\right)$
$\chi_{8732}(2991,\cdot)$	$1$	$1$	$e\left(\frac{2}{29}\right)$	$e\left(\frac{23}{116}\right)$	$e\left(\frac{49}{58}\right)$	$e\left(\frac{4}{29}\right)$	$e\left(\frac{1}{29}\right)$	$e\left(\frac{71}{116}\right)$	$e\left(\frac{31}{116}\right)$	$e\left(\frac{47}{116}\right)$	$e\left(\frac{49}{116}\right)$	$e\left(\frac{53}{58}\right)$
$\chi_{8732}(3003,\cdot)$	$1$	$1$	$e\left(\frac{28}{29}\right)$	$e\left(\frac{61}{116}\right)$	$e\left(\frac{19}{58}\right)$	$e\left(\frac{27}{29}\right)$	$e\left(\frac{14}{29}\right)$	$e\left(\frac{37}{116}\right)$	$e\left(\frac{57}{116}\right)$	$e\left(\frac{49}{116}\right)$	$e\left(\frac{19}{116}\right)$	$e\left(\frac{17}{58}\right)$
$\chi_{8732}(3139,\cdot)$	$1$	$1$	$e\left(\frac{24}{29}\right)$	$e\left(\frac{15}{116}\right)$	$e\left(\frac{37}{58}\right)$	$e\left(\frac{19}{29}\right)$	$e\left(\frac{12}{29}\right)$	$e\left(\frac{11}{116}\right)$	$e\left(\frac{111}{116}\right)$	$e\left(\frac{71}{116}\right)$	$e\left(\frac{37}{116}\right)$	$e\left(\frac{27}{58}\right)$
$\chi_{8732}(3447,\cdot)$	$1$	$1$	$e\left(\frac{10}{29}\right)$	$e\left(\frac{57}{116}\right)$	$e\left(\frac{13}{58}\right)$	$e\left(\frac{20}{29}\right)$	$e\left(\frac{5}{29}\right)$	$e\left(\frac{65}{116}\right)$	$e\left(\frac{97}{116}\right)$	$e\left(\frac{61}{116}\right)$	$e\left(\frac{71}{116}\right)$	$e\left(\frac{33}{58}\right)$
$\chi_{8732}(3743,\cdot)$	$1$	$1$	$e\left(\frac{19}{29}\right)$	$e\left(\frac{1}{116}\right)$	$e\left(\frac{45}{58}\right)$	$e\left(\frac{9}{29}\right)$	$e\left(\frac{24}{29}\right)$	$e\left(\frac{109}{116}\right)$	$e\left(\frac{77}{116}\right)$	$e\left(\frac{113}{116}\right)$	$e\left(\frac{103}{116}\right)$	$e\left(\frac{25}{58}\right)$
$\chi_{8732}(4027,\cdot)$	$1$	$1$	$e\left(\frac{8}{29}\right)$	$e\left(\frac{63}{116}\right)$	$e\left(\frac{51}{58}\right)$	$e\left(\frac{16}{29}\right)$	$e\left(\frac{4}{29}\right)$	$e\left(\frac{23}{116}\right)$	$e\left(\frac{95}{116}\right)$	$e\left(\frac{43}{116}\right)$	$e\left(\frac{109}{116}\right)$	$e\left(\frac{9}{58}\right)$
$\chi_{8732}(4039,\cdot)$	$1$	$1$	$e\left(\frac{9}{29}\right)$	$e\left(\frac{89}{116}\right)$	$e\left(\frac{3}{58}\right)$	$e\left(\frac{18}{29}\right)$	$e\left(\frac{19}{29}\right)$	$e\left(\frac{73}{116}\right)$	$e\left(\frac{9}{116}\right)$	$e\left(\frac{81}{116}\right)$	$e\left(\frac{3}{116}\right)$	$e\left(\frac{21}{58}\right)$
$\chi_{8732}(4175,\cdot)$	$1$	$1$	$e\left(\frac{11}{29}\right)$	$e\left(\frac{83}{116}\right)$	$e\left(\frac{23}{58}\right)$	$e\left(\frac{22}{29}\right)$	$e\left(\frac{20}{29}\right)$	$e\left(\frac{115}{116}\right)$	$e\left(\frac{11}{116}\right)$	$e\left(\frac{99}{116}\right)$	$e\left(\frac{81}{116}\right)$	$e\left(\frac{45}{58}\right)$
$\chi_{8732}(4187,\cdot)$	$1$	$1$	$e\left(\frac{25}{29}\right)$	$e\left(\frac{41}{116}\right)$	$e\left(\frac{47}{58}\right)$	$e\left(\frac{21}{29}\right)$	$e\left(\frac{27}{29}\right)$	$e\left(\frac{61}{116}\right)$	$e\left(\frac{25}{116}\right)$	$e\left(\frac{109}{116}\right)$	$e\left(\frac{47}{116}\right)$	$e\left(\frac{39}{58}\right)$
$\chi_{8732}(4323,\cdot)$	$1$	$1$	$e\left(\frac{13}{29}\right)$	$e\left(\frac{19}{116}\right)$	$e\left(\frac{43}{58}\right)$	$e\left(\frac{26}{29}\right)$	$e\left(\frac{21}{29}\right)$	$e\left(\frac{99}{116}\right)$	$e\left(\frac{71}{116}\right)$	$e\left(\frac{59}{116}\right)$	$e\left(\frac{101}{116}\right)$	$e\left(\frac{11}{58}\right)$
$\chi_{8732}(4335,\cdot)$	$1$	$1$	$e\left(\frac{7}{29}\right)$	$e\left(\frac{37}{116}\right)$	$e\left(\frac{41}{58}\right)$	$e\left(\frac{14}{29}\right)$	$e\left(\frac{18}{29}\right)$	$e\left(\frac{89}{116}\right)$	$e\left(\frac{65}{116}\right)$	$e\left(\frac{5}{116}\right)$	$e\left(\frac{99}{116}\right)$	$e\left(\frac{55}{58}\right)$
$\chi_{8732}(4471,\cdot)$	$1$	$1$	$e\left(\frac{23}{29}\right)$	$e\left(\frac{47}{116}\right)$	$e\left(\frac{27}{58}\right)$	$e\left(\frac{17}{29}\right)$	$e\left(\frac{26}{29}\right)$	$e\left(\frac{19}{116}\right)$	$e\left(\frac{23}{116}\right)$	$e\left(\frac{91}{116}\right)$	$e\left(\frac{85}{116}\right)$	$e\left(\frac{15}{58}\right)$

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	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(21\)
\(\chi_{8732}(475,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{29}\right)\)	\(e\left(\frac{107}{116}\right)\)	\(e\left(\frac{1}{58}\right)\)	\(e\left(\frac{6}{29}\right)\)	\(e\left(\frac{16}{29}\right)\)	\(e\left(\frac{63}{116}\right)\)	\(e\left(\frac{3}{116}\right)\)	\(e\left(\frac{27}{116}\right)\)	\(e\left(\frac{1}{116}\right)\)	\(e\left(\frac{7}{58}\right)\)
\(\chi_{8732}(487,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{8}{29}\right)\)	\(e\left(\frac{5}{116}\right)\)	\(e\left(\frac{51}{58}\right)\)	\(e\left(\frac{16}{29}\right)\)	\(e\left(\frac{4}{29}\right)\)	\(e\left(\frac{81}{116}\right)\)	\(e\left(\frac{37}{116}\right)\)	\(e\left(\frac{101}{116}\right)\)	\(e\left(\frac{51}{116}\right)\)	\(e\left(\frac{9}{58}\right)\)
\(\chi_{8732}(635,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{29}\right)\)	\(e\left(\frac{25}{116}\right)\)	\(e\left(\frac{23}{58}\right)\)	\(e\left(\frac{22}{29}\right)\)	\(e\left(\frac{20}{29}\right)\)	\(e\left(\frac{57}{116}\right)\)	\(e\left(\frac{69}{116}\right)\)	\(e\left(\frac{41}{116}\right)\)	\(e\left(\frac{23}{116}\right)\)	\(e\left(\frac{45}{58}\right)\)
\(\chi_{8732}(771,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{21}{29}\right)\)	\(e\left(\frac{111}{116}\right)\)	\(e\left(\frac{7}{58}\right)\)	\(e\left(\frac{13}{29}\right)\)	\(e\left(\frac{25}{29}\right)\)	\(e\left(\frac{35}{116}\right)\)	\(e\left(\frac{79}{116}\right)\)	\(e\left(\frac{15}{116}\right)\)	\(e\left(\frac{65}{116}\right)\)	\(e\left(\frac{49}{58}\right)\)
\(\chi_{8732}(783,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{29}\right)\)	\(e\left(\frac{77}{116}\right)\)	\(e\left(\frac{43}{58}\right)\)	\(e\left(\frac{26}{29}\right)\)	\(e\left(\frac{21}{29}\right)\)	\(e\left(\frac{41}{116}\right)\)	\(e\left(\frac{13}{116}\right)\)	\(e\left(\frac{1}{116}\right)\)	\(e\left(\frac{43}{116}\right)\)	\(e\left(\frac{11}{58}\right)\)
\(\chi_{8732}(931,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{29}\right)\)	\(e\left(\frac{105}{116}\right)\)	\(e\left(\frac{27}{58}\right)\)	\(e\left(\frac{17}{29}\right)\)	\(e\left(\frac{26}{29}\right)\)	\(e\left(\frac{77}{116}\right)\)	\(e\left(\frac{81}{116}\right)\)	\(e\left(\frac{33}{116}\right)\)	\(e\left(\frac{27}{116}\right)\)	\(e\left(\frac{15}{58}\right)\)
\(\chi_{8732}(1067,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{29}\right)\)	\(e\left(\frac{43}{116}\right)\)	\(e\left(\frac{21}{58}\right)\)	\(e\left(\frac{10}{29}\right)\)	\(e\left(\frac{17}{29}\right)\)	\(e\left(\frac{47}{116}\right)\)	\(e\left(\frac{63}{116}\right)\)	\(e\left(\frac{103}{116}\right)\)	\(e\left(\frac{21}{116}\right)\)	\(e\left(\frac{31}{58}\right)\)
\(\chi_{8732}(1079,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{14}{29}\right)\)	\(e\left(\frac{45}{116}\right)\)	\(e\left(\frac{53}{58}\right)\)	\(e\left(\frac{28}{29}\right)\)	\(e\left(\frac{7}{29}\right)\)	\(e\left(\frac{33}{116}\right)\)	\(e\left(\frac{101}{116}\right)\)	\(e\left(\frac{97}{116}\right)\)	\(e\left(\frac{111}{116}\right)\)	\(e\left(\frac{23}{58}\right)\)
\(\chi_{8732}(1215,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{20}{29}\right)\)	\(e\left(\frac{27}{116}\right)\)	\(e\left(\frac{55}{58}\right)\)	\(e\left(\frac{11}{29}\right)\)	\(e\left(\frac{10}{29}\right)\)	\(e\left(\frac{43}{116}\right)\)	\(e\left(\frac{107}{116}\right)\)	\(e\left(\frac{35}{116}\right)\)	\(e\left(\frac{113}{116}\right)\)	\(e\left(\frac{37}{58}\right)\)
\(\chi_{8732}(1511,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{27}{29}\right)\)	\(e\left(\frac{35}{116}\right)\)	\(e\left(\frac{9}{58}\right)\)	\(e\left(\frac{25}{29}\right)\)	\(e\left(\frac{28}{29}\right)\)	\(e\left(\frac{103}{116}\right)\)	\(e\left(\frac{27}{116}\right)\)	\(e\left(\frac{11}{116}\right)\)	\(e\left(\frac{9}{116}\right)\)	\(e\left(\frac{5}{58}\right)\)
\(\chi_{8732}(1523,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{16}{29}\right)\)	\(e\left(\frac{97}{116}\right)\)	\(e\left(\frac{15}{58}\right)\)	\(e\left(\frac{3}{29}\right)\)	\(e\left(\frac{8}{29}\right)\)	\(e\left(\frac{17}{116}\right)\)	\(e\left(\frac{45}{116}\right)\)	\(e\left(\frac{57}{116}\right)\)	\(e\left(\frac{15}{116}\right)\)	\(e\left(\frac{47}{58}\right)\)
\(\chi_{8732}(1659,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{15}{29}\right)\)	\(e\left(\frac{71}{116}\right)\)	\(e\left(\frac{5}{58}\right)\)	\(e\left(\frac{1}{29}\right)\)	\(e\left(\frac{22}{29}\right)\)	\(e\left(\frac{83}{116}\right)\)	\(e\left(\frac{15}{116}\right)\)	\(e\left(\frac{19}{116}\right)\)	\(e\left(\frac{5}{116}\right)\)	\(e\left(\frac{35}{58}\right)\)
\(\chi_{8732}(1671,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{22}{29}\right)\)	\(e\left(\frac{21}{116}\right)\)	\(e\left(\frac{17}{58}\right)\)	\(e\left(\frac{15}{29}\right)\)	\(e\left(\frac{11}{29}\right)\)	\(e\left(\frac{85}{116}\right)\)	\(e\left(\frac{109}{116}\right)\)	\(e\left(\frac{53}{116}\right)\)	\(e\left(\frac{75}{116}\right)\)	\(e\left(\frac{3}{58}\right)\)
\(\chi_{8732}(1819,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{29}\right)\)	\(e\left(\frac{113}{116}\right)\)	\(e\left(\frac{39}{58}\right)\)	\(e\left(\frac{2}{29}\right)\)	\(e\left(\frac{15}{29}\right)\)	\(e\left(\frac{21}{116}\right)\)	\(e\left(\frac{1}{116}\right)\)	\(e\left(\frac{9}{116}\right)\)	\(e\left(\frac{39}{116}\right)\)	\(e\left(\frac{41}{58}\right)\)
\(\chi_{8732}(1967,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{26}{29}\right)\)	\(e\left(\frac{9}{116}\right)\)	\(e\left(\frac{57}{58}\right)\)	\(e\left(\frac{23}{29}\right)\)	\(e\left(\frac{13}{29}\right)\)	\(e\left(\frac{53}{116}\right)\)	\(e\left(\frac{113}{116}\right)\)	\(e\left(\frac{89}{116}\right)\)	\(e\left(\frac{115}{116}\right)\)	\(e\left(\frac{51}{58}\right)\)
\(\chi_{8732}(2251,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{6}{29}\right)\)	\(e\left(\frac{11}{116}\right)\)	\(e\left(\frac{31}{58}\right)\)	\(e\left(\frac{12}{29}\right)\)	\(e\left(\frac{3}{29}\right)\)	\(e\left(\frac{39}{116}\right)\)	\(e\left(\frac{35}{116}\right)\)	\(e\left(\frac{83}{116}\right)\)	\(e\left(\frac{89}{116}\right)\)	\(e\left(\frac{43}{58}\right)\)
\(\chi_{8732}(2263,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{18}{29}\right)\)	\(e\left(\frac{33}{116}\right)\)	\(e\left(\frac{35}{58}\right)\)	\(e\left(\frac{7}{29}\right)\)	\(e\left(\frac{9}{29}\right)\)	\(e\left(\frac{1}{116}\right)\)	\(e\left(\frac{105}{116}\right)\)	\(e\left(\frac{17}{116}\right)\)	\(e\left(\frac{35}{116}\right)\)	\(e\left(\frac{13}{58}\right)\)
\(\chi_{8732}(2411,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{29}\right)\)	\(e\left(\frac{65}{116}\right)\)	\(e\left(\frac{25}{58}\right)\)	\(e\left(\frac{5}{29}\right)\)	\(e\left(\frac{23}{29}\right)\)	\(e\left(\frac{9}{116}\right)\)	\(e\left(\frac{17}{116}\right)\)	\(e\left(\frac{37}{116}\right)\)	\(e\left(\frac{83}{116}\right)\)	\(e\left(\frac{1}{58}\right)\)
\(\chi_{8732}(2559,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{12}{29}\right)\)	\(e\left(\frac{109}{116}\right)\)	\(e\left(\frac{33}{58}\right)\)	\(e\left(\frac{24}{29}\right)\)	\(e\left(\frac{6}{29}\right)\)	\(e\left(\frac{49}{116}\right)\)	\(e\left(\frac{41}{116}\right)\)	\(e\left(\frac{21}{116}\right)\)	\(e\left(\frac{91}{116}\right)\)	\(e\left(\frac{57}{58}\right)\)
\(\chi_{8732}(2991,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{29}\right)\)	\(e\left(\frac{23}{116}\right)\)	\(e\left(\frac{49}{58}\right)\)	\(e\left(\frac{4}{29}\right)\)	\(e\left(\frac{1}{29}\right)\)	\(e\left(\frac{71}{116}\right)\)	\(e\left(\frac{31}{116}\right)\)	\(e\left(\frac{47}{116}\right)\)	\(e\left(\frac{49}{116}\right)\)	\(e\left(\frac{53}{58}\right)\)
\(\chi_{8732}(3003,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{28}{29}\right)\)	\(e\left(\frac{61}{116}\right)\)	\(e\left(\frac{19}{58}\right)\)	\(e\left(\frac{27}{29}\right)\)	\(e\left(\frac{14}{29}\right)\)	\(e\left(\frac{37}{116}\right)\)	\(e\left(\frac{57}{116}\right)\)	\(e\left(\frac{49}{116}\right)\)	\(e\left(\frac{19}{116}\right)\)	\(e\left(\frac{17}{58}\right)\)
\(\chi_{8732}(3139,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{24}{29}\right)\)	\(e\left(\frac{15}{116}\right)\)	\(e\left(\frac{37}{58}\right)\)	\(e\left(\frac{19}{29}\right)\)	\(e\left(\frac{12}{29}\right)\)	\(e\left(\frac{11}{116}\right)\)	\(e\left(\frac{111}{116}\right)\)	\(e\left(\frac{71}{116}\right)\)	\(e\left(\frac{37}{116}\right)\)	\(e\left(\frac{27}{58}\right)\)
\(\chi_{8732}(3447,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{10}{29}\right)\)	\(e\left(\frac{57}{116}\right)\)	\(e\left(\frac{13}{58}\right)\)	\(e\left(\frac{20}{29}\right)\)	\(e\left(\frac{5}{29}\right)\)	\(e\left(\frac{65}{116}\right)\)	\(e\left(\frac{97}{116}\right)\)	\(e\left(\frac{61}{116}\right)\)	\(e\left(\frac{71}{116}\right)\)	\(e\left(\frac{33}{58}\right)\)
\(\chi_{8732}(3743,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{29}\right)\)	\(e\left(\frac{1}{116}\right)\)	\(e\left(\frac{45}{58}\right)\)	\(e\left(\frac{9}{29}\right)\)	\(e\left(\frac{24}{29}\right)\)	\(e\left(\frac{109}{116}\right)\)	\(e\left(\frac{77}{116}\right)\)	\(e\left(\frac{113}{116}\right)\)	\(e\left(\frac{103}{116}\right)\)	\(e\left(\frac{25}{58}\right)\)
\(\chi_{8732}(4027,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{8}{29}\right)\)	\(e\left(\frac{63}{116}\right)\)	\(e\left(\frac{51}{58}\right)\)	\(e\left(\frac{16}{29}\right)\)	\(e\left(\frac{4}{29}\right)\)	\(e\left(\frac{23}{116}\right)\)	\(e\left(\frac{95}{116}\right)\)	\(e\left(\frac{43}{116}\right)\)	\(e\left(\frac{109}{116}\right)\)	\(e\left(\frac{9}{58}\right)\)
\(\chi_{8732}(4039,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{29}\right)\)	\(e\left(\frac{89}{116}\right)\)	\(e\left(\frac{3}{58}\right)\)	\(e\left(\frac{18}{29}\right)\)	\(e\left(\frac{19}{29}\right)\)	\(e\left(\frac{73}{116}\right)\)	\(e\left(\frac{9}{116}\right)\)	\(e\left(\frac{81}{116}\right)\)	\(e\left(\frac{3}{116}\right)\)	\(e\left(\frac{21}{58}\right)\)
\(\chi_{8732}(4175,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{29}\right)\)	\(e\left(\frac{83}{116}\right)\)	\(e\left(\frac{23}{58}\right)\)	\(e\left(\frac{22}{29}\right)\)	\(e\left(\frac{20}{29}\right)\)	\(e\left(\frac{115}{116}\right)\)	\(e\left(\frac{11}{116}\right)\)	\(e\left(\frac{99}{116}\right)\)	\(e\left(\frac{81}{116}\right)\)	\(e\left(\frac{45}{58}\right)\)
\(\chi_{8732}(4187,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{25}{29}\right)\)	\(e\left(\frac{41}{116}\right)\)	\(e\left(\frac{47}{58}\right)\)	\(e\left(\frac{21}{29}\right)\)	\(e\left(\frac{27}{29}\right)\)	\(e\left(\frac{61}{116}\right)\)	\(e\left(\frac{25}{116}\right)\)	\(e\left(\frac{109}{116}\right)\)	\(e\left(\frac{47}{116}\right)\)	\(e\left(\frac{39}{58}\right)\)
\(\chi_{8732}(4323,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{29}\right)\)	\(e\left(\frac{19}{116}\right)\)	\(e\left(\frac{43}{58}\right)\)	\(e\left(\frac{26}{29}\right)\)	\(e\left(\frac{21}{29}\right)\)	\(e\left(\frac{99}{116}\right)\)	\(e\left(\frac{71}{116}\right)\)	\(e\left(\frac{59}{116}\right)\)	\(e\left(\frac{101}{116}\right)\)	\(e\left(\frac{11}{58}\right)\)
\(\chi_{8732}(4335,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{29}\right)\)	\(e\left(\frac{37}{116}\right)\)	\(e\left(\frac{41}{58}\right)\)	\(e\left(\frac{14}{29}\right)\)	\(e\left(\frac{18}{29}\right)\)	\(e\left(\frac{89}{116}\right)\)	\(e\left(\frac{65}{116}\right)\)	\(e\left(\frac{5}{116}\right)\)	\(e\left(\frac{99}{116}\right)\)	\(e\left(\frac{55}{58}\right)\)
\(\chi_{8732}(4471,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{29}\right)\)	\(e\left(\frac{47}{116}\right)\)	\(e\left(\frac{27}{58}\right)\)	\(e\left(\frac{17}{29}\right)\)	\(e\left(\frac{26}{29}\right)\)	\(e\left(\frac{19}{116}\right)\)	\(e\left(\frac{23}{116}\right)\)	\(e\left(\frac{91}{116}\right)\)	\(e\left(\frac{85}{116}\right)\)	\(e\left(\frac{15}{58}\right)\)

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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.bt
Modulus	$8732$
Conductor	$8732$
Order	$116$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(8732\)
Conductor:	\(8732\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(116\)	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)