LMFDB - Dirichlet character orbit 309680.buo

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(309680, base_ring=CyclotomicField(182)) M = H._module chi = DirichletCharacter(H, M([91,91,0,104,119])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(71,309680)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$309680$
Conductor:	$30968$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$182$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 30968.jj	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	no
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)

Related number fields

Field of values:	$\Q(\zeta_{91})$
Fixed field:	Number field defined by a degree 182 polynomial (not computed)

First 31 of 72 characters in Galois orbit

Character	$-1$	$1$	$3$	$9$	$11$	$13$	$17$	$19$	$23$	$27$	$29$	$31$
$\chi_{309680}(71,\cdot)$	$1$	$1$	$e\left(\frac{41}{182}\right)$	$e\left(\frac{41}{91}\right)$	$e\left(\frac{29}{91}\right)$	$e\left(\frac{107}{182}\right)$	$e\left(\frac{3}{182}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{123}{182}\right)$	$e\left(\frac{89}{91}\right)$	$e\left(\frac{3}{26}\right)$
$\chi_{309680}(2871,\cdot)$	$1$	$1$	$e\left(\frac{85}{182}\right)$	$e\left(\frac{85}{91}\right)$	$e\left(\frac{69}{91}\right)$	$e\left(\frac{173}{182}\right)$	$e\left(\frac{95}{182}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{73}{182}\right)$	$e\left(\frac{58}{91}\right)$	$e\left(\frac{17}{26}\right)$
$\chi_{309680}(3991,\cdot)$	$1$	$1$	$e\left(\frac{97}{182}\right)$	$e\left(\frac{6}{91}\right)$	$e\left(\frac{22}{91}\right)$	$e\left(\frac{9}{182}\right)$	$e\left(\frac{87}{182}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{109}{182}\right)$	$e\left(\frac{33}{91}\right)$	$e\left(\frac{9}{26}\right)$
$\chi_{309680}(6231,\cdot)$	$1$	$1$	$e\left(\frac{37}{182}\right)$	$e\left(\frac{37}{91}\right)$	$e\left(\frac{75}{91}\right)$	$e\left(\frac{101}{182}\right)$	$e\left(\frac{127}{182}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{111}{182}\right)$	$e\left(\frac{67}{91}\right)$	$e\left(\frac{23}{26}\right)$
$\chi_{309680}(17991,\cdot)$	$1$	$1$	$e\left(\frac{9}{182}\right)$	$e\left(\frac{9}{91}\right)$	$e\left(\frac{33}{91}\right)$	$e\left(\frac{59}{182}\right)$	$e\left(\frac{85}{182}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{27}{182}\right)$	$e\left(\frac{4}{91}\right)$	$e\left(\frac{7}{26}\right)$
$\chi_{309680}(20791,\cdot)$	$1$	$1$	$e\left(\frac{81}{182}\right)$	$e\left(\frac{81}{91}\right)$	$e\left(\frac{24}{91}\right)$	$e\left(\frac{167}{182}\right)$	$e\left(\frac{37}{182}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{61}{182}\right)$	$e\left(\frac{36}{91}\right)$	$e\left(\frac{11}{26}\right)$
$\chi_{309680}(28631,\cdot)$	$1$	$1$	$e\left(\frac{109}{182}\right)$	$e\left(\frac{18}{91}\right)$	$e\left(\frac{66}{91}\right)$	$e\left(\frac{27}{182}\right)$	$e\left(\frac{79}{182}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{145}{182}\right)$	$e\left(\frac{8}{91}\right)$	$e\left(\frac{1}{26}\right)$
$\chi_{309680}(33671,\cdot)$	$1$	$1$	$e\left(\frac{23}{182}\right)$	$e\left(\frac{23}{91}\right)$	$e\left(\frac{54}{91}\right)$	$e\left(\frac{171}{182}\right)$	$e\left(\frac{15}{182}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{69}{182}\right)$	$e\left(\frac{81}{91}\right)$	$e\left(\frac{15}{26}\right)$
$\chi_{309680}(39831,\cdot)$	$1$	$1$	$e\left(\frac{173}{182}\right)$	$e\left(\frac{82}{91}\right)$	$e\left(\frac{58}{91}\right)$	$e\left(\frac{123}{182}\right)$	$e\left(\frac{97}{182}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{155}{182}\right)$	$e\left(\frac{87}{91}\right)$	$e\left(\frac{19}{26}\right)$
$\chi_{309680}(43191,\cdot)$	$1$	$1$	$e\left(\frac{181}{182}\right)$	$e\left(\frac{90}{91}\right)$	$e\left(\frac{57}{91}\right)$	$e\left(\frac{135}{182}\right)$	$e\left(\frac{31}{182}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{179}{182}\right)$	$e\left(\frac{40}{91}\right)$	$e\left(\frac{5}{26}\right)$
$\chi_{309680}(44311,\cdot)$	$1$	$1$	$e\left(\frac{67}{182}\right)$	$e\left(\frac{67}{91}\right)$	$e\left(\frac{3}{91}\right)$	$e\left(\frac{55}{182}\right)$	$e\left(\frac{107}{182}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{19}{182}\right)$	$e\left(\frac{50}{91}\right)$	$e\left(\frac{3}{26}\right)$
$\chi_{309680}(47111,\cdot)$	$1$	$1$	$e\left(\frac{111}{182}\right)$	$e\left(\frac{20}{91}\right)$	$e\left(\frac{43}{91}\right)$	$e\left(\frac{121}{182}\right)$	$e\left(\frac{17}{182}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{151}{182}\right)$	$e\left(\frac{19}{91}\right)$	$e\left(\frac{17}{26}\right)$
$\chi_{309680}(48231,\cdot)$	$1$	$1$	$e\left(\frac{123}{182}\right)$	$e\left(\frac{32}{91}\right)$	$e\left(\frac{87}{91}\right)$	$e\left(\frac{139}{182}\right)$	$e\left(\frac{9}{182}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{5}{182}\right)$	$e\left(\frac{85}{91}\right)$	$e\left(\frac{9}{26}\right)$
$\chi_{309680}(65031,\cdot)$	$1$	$1$	$e\left(\frac{107}{182}\right)$	$e\left(\frac{16}{91}\right)$	$e\left(\frac{89}{91}\right)$	$e\left(\frac{115}{182}\right)$	$e\left(\frac{141}{182}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{139}{182}\right)$	$e\left(\frac{88}{91}\right)$	$e\left(\frac{11}{26}\right)$
$\chi_{309680}(71191,\cdot)$	$1$	$1$	$e\left(\frac{47}{182}\right)$	$e\left(\frac{47}{91}\right)$	$e\left(\frac{51}{91}\right)$	$e\left(\frac{25}{182}\right)$	$e\left(\frac{181}{182}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{141}{182}\right)$	$e\left(\frac{31}{91}\right)$	$e\left(\frac{25}{26}\right)$
$\chi_{309680}(72871,\cdot)$	$1$	$1$	$e\left(\frac{135}{182}\right)$	$e\left(\frac{44}{91}\right)$	$e\left(\frac{40}{91}\right)$	$e\left(\frac{157}{182}\right)$	$e\left(\frac{1}{182}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{41}{182}\right)$	$e\left(\frac{60}{91}\right)$	$e\left(\frac{1}{26}\right)$
$\chi_{309680}(75111,\cdot)$	$1$	$1$	$e\left(\frac{131}{182}\right)$	$e\left(\frac{40}{91}\right)$	$e\left(\frac{86}{91}\right)$	$e\left(\frac{151}{182}\right)$	$e\left(\frac{125}{182}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{29}{182}\right)$	$e\left(\frac{38}{91}\right)$	$e\left(\frac{21}{26}\right)$
$\chi_{309680}(84071,\cdot)$	$1$	$1$	$e\left(\frac{17}{182}\right)$	$e\left(\frac{17}{91}\right)$	$e\left(\frac{32}{91}\right)$	$e\left(\frac{71}{182}\right)$	$e\left(\frac{19}{182}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{51}{182}\right)$	$e\left(\frac{48}{91}\right)$	$e\left(\frac{19}{26}\right)$
$\chi_{309680}(87431,\cdot)$	$1$	$1$	$e\left(\frac{25}{182}\right)$	$e\left(\frac{25}{91}\right)$	$e\left(\frac{31}{91}\right)$	$e\left(\frac{83}{182}\right)$	$e\left(\frac{135}{182}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{75}{182}\right)$	$e\left(\frac{1}{91}\right)$	$e\left(\frac{5}{26}\right)$
$\chi_{309680}(88551,\cdot)$	$1$	$1$	$e\left(\frac{93}{182}\right)$	$e\left(\frac{2}{91}\right)$	$e\left(\frac{68}{91}\right)$	$e\left(\frac{3}{182}\right)$	$e\left(\frac{29}{182}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{97}{182}\right)$	$e\left(\frac{11}{91}\right)$	$e\left(\frac{3}{26}\right)$
$\chi_{309680}(91351,\cdot)$	$1$	$1$	$e\left(\frac{137}{182}\right)$	$e\left(\frac{46}{91}\right)$	$e\left(\frac{17}{91}\right)$	$e\left(\frac{69}{182}\right)$	$e\left(\frac{121}{182}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{47}{182}\right)$	$e\left(\frac{71}{91}\right)$	$e\left(\frac{17}{26}\right)$
$\chi_{309680}(92471,\cdot)$	$1$	$1$	$e\left(\frac{149}{182}\right)$	$e\left(\frac{58}{91}\right)$	$e\left(\frac{61}{91}\right)$	$e\left(\frac{87}{182}\right)$	$e\left(\frac{113}{182}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{83}{182}\right)$	$e\left(\frac{46}{91}\right)$	$e\left(\frac{9}{26}\right)$
$\chi_{309680}(94711,\cdot)$	$1$	$1$	$e\left(\frac{89}{182}\right)$	$e\left(\frac{89}{91}\right)$	$e\left(\frac{23}{91}\right)$	$e\left(\frac{179}{182}\right)$	$e\left(\frac{153}{182}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{85}{182}\right)$	$e\left(\frac{80}{91}\right)$	$e\left(\frac{23}{26}\right)$
$\chi_{309680}(106471,\cdot)$	$1$	$1$	$e\left(\frac{61}{182}\right)$	$e\left(\frac{61}{91}\right)$	$e\left(\frac{72}{91}\right)$	$e\left(\frac{137}{182}\right)$	$e\left(\frac{111}{182}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{1}{182}\right)$	$e\left(\frac{17}{91}\right)$	$e\left(\frac{7}{26}\right)$
$\chi_{309680}(115431,\cdot)$	$1$	$1$	$e\left(\frac{73}{182}\right)$	$e\left(\frac{73}{91}\right)$	$e\left(\frac{25}{91}\right)$	$e\left(\frac{155}{182}\right)$	$e\left(\frac{103}{182}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{37}{182}\right)$	$e\left(\frac{83}{91}\right)$	$e\left(\frac{25}{26}\right)$
$\chi_{309680}(119351,\cdot)$	$1$	$1$	$e\left(\frac{157}{182}\right)$	$e\left(\frac{66}{91}\right)$	$e\left(\frac{60}{91}\right)$	$e\left(\frac{99}{182}\right)$	$e\left(\frac{47}{182}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{107}{182}\right)$	$e\left(\frac{90}{91}\right)$	$e\left(\frac{21}{26}\right)$
$\chi_{309680}(122151,\cdot)$	$1$	$1$	$e\left(\frac{75}{182}\right)$	$e\left(\frac{75}{91}\right)$	$e\left(\frac{2}{91}\right)$	$e\left(\frac{67}{182}\right)$	$e\left(\frac{41}{182}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{43}{182}\right)$	$e\left(\frac{3}{91}\right)$	$e\left(\frac{15}{26}\right)$
$\chi_{309680}(128311,\cdot)$	$1$	$1$	$e\left(\frac{43}{182}\right)$	$e\left(\frac{43}{91}\right)$	$e\left(\frac{6}{91}\right)$	$e\left(\frac{19}{182}\right)$	$e\left(\frac{123}{182}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{129}{182}\right)$	$e\left(\frac{9}{91}\right)$	$e\left(\frac{19}{26}\right)$
$\chi_{309680}(131671,\cdot)$	$1$	$1$	$e\left(\frac{51}{182}\right)$	$e\left(\frac{51}{91}\right)$	$e\left(\frac{5}{91}\right)$	$e\left(\frac{31}{182}\right)$	$e\left(\frac{57}{182}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{153}{182}\right)$	$e\left(\frac{53}{91}\right)$	$e\left(\frac{5}{26}\right)$
$\chi_{309680}(135591,\cdot)$	$1$	$1$	$e\left(\frac{163}{182}\right)$	$e\left(\frac{72}{91}\right)$	$e\left(\frac{82}{91}\right)$	$e\left(\frac{17}{182}\right)$	$e\left(\frac{43}{182}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{125}{182}\right)$	$e\left(\frac{32}{91}\right)$	$e\left(\frac{17}{26}\right)$
$\chi_{309680}(138951,\cdot)$	$1$	$1$	$e\left(\frac{115}{182}\right)$	$e\left(\frac{24}{91}\right)$	$e\left(\frac{88}{91}\right)$	$e\left(\frac{127}{182}\right)$	$e\left(\frac{75}{182}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{163}{182}\right)$	$e\left(\frac{41}{91}\right)$	$e\left(\frac{23}{26}\right)$

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	\(-1\)	\(1\)	\(3\)	\(9\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(27\)	\(29\)	\(31\)
\(\chi_{309680}(71,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{182}\right)\)	\(e\left(\frac{41}{91}\right)\)	\(e\left(\frac{29}{91}\right)\)	\(e\left(\frac{107}{182}\right)\)	\(e\left(\frac{3}{182}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{123}{182}\right)\)	\(e\left(\frac{89}{91}\right)\)	\(e\left(\frac{3}{26}\right)\)
\(\chi_{309680}(2871,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{85}{182}\right)\)	\(e\left(\frac{85}{91}\right)\)	\(e\left(\frac{69}{91}\right)\)	\(e\left(\frac{173}{182}\right)\)	\(e\left(\frac{95}{182}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{73}{182}\right)\)	\(e\left(\frac{58}{91}\right)\)	\(e\left(\frac{17}{26}\right)\)
\(\chi_{309680}(3991,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{97}{182}\right)\)	\(e\left(\frac{6}{91}\right)\)	\(e\left(\frac{22}{91}\right)\)	\(e\left(\frac{9}{182}\right)\)	\(e\left(\frac{87}{182}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{109}{182}\right)\)	\(e\left(\frac{33}{91}\right)\)	\(e\left(\frac{9}{26}\right)\)
\(\chi_{309680}(6231,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{182}\right)\)	\(e\left(\frac{37}{91}\right)\)	\(e\left(\frac{75}{91}\right)\)	\(e\left(\frac{101}{182}\right)\)	\(e\left(\frac{127}{182}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{111}{182}\right)\)	\(e\left(\frac{67}{91}\right)\)	\(e\left(\frac{23}{26}\right)\)
\(\chi_{309680}(17991,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{182}\right)\)	\(e\left(\frac{9}{91}\right)\)	\(e\left(\frac{33}{91}\right)\)	\(e\left(\frac{59}{182}\right)\)	\(e\left(\frac{85}{182}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{27}{182}\right)\)	\(e\left(\frac{4}{91}\right)\)	\(e\left(\frac{7}{26}\right)\)
\(\chi_{309680}(20791,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{81}{182}\right)\)	\(e\left(\frac{81}{91}\right)\)	\(e\left(\frac{24}{91}\right)\)	\(e\left(\frac{167}{182}\right)\)	\(e\left(\frac{37}{182}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{61}{182}\right)\)	\(e\left(\frac{36}{91}\right)\)	\(e\left(\frac{11}{26}\right)\)
\(\chi_{309680}(28631,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{109}{182}\right)\)	\(e\left(\frac{18}{91}\right)\)	\(e\left(\frac{66}{91}\right)\)	\(e\left(\frac{27}{182}\right)\)	\(e\left(\frac{79}{182}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{145}{182}\right)\)	\(e\left(\frac{8}{91}\right)\)	\(e\left(\frac{1}{26}\right)\)
\(\chi_{309680}(33671,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{182}\right)\)	\(e\left(\frac{23}{91}\right)\)	\(e\left(\frac{54}{91}\right)\)	\(e\left(\frac{171}{182}\right)\)	\(e\left(\frac{15}{182}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{69}{182}\right)\)	\(e\left(\frac{81}{91}\right)\)	\(e\left(\frac{15}{26}\right)\)
\(\chi_{309680}(39831,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{173}{182}\right)\)	\(e\left(\frac{82}{91}\right)\)	\(e\left(\frac{58}{91}\right)\)	\(e\left(\frac{123}{182}\right)\)	\(e\left(\frac{97}{182}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{155}{182}\right)\)	\(e\left(\frac{87}{91}\right)\)	\(e\left(\frac{19}{26}\right)\)
\(\chi_{309680}(43191,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{181}{182}\right)\)	\(e\left(\frac{90}{91}\right)\)	\(e\left(\frac{57}{91}\right)\)	\(e\left(\frac{135}{182}\right)\)	\(e\left(\frac{31}{182}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{179}{182}\right)\)	\(e\left(\frac{40}{91}\right)\)	\(e\left(\frac{5}{26}\right)\)
\(\chi_{309680}(44311,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{67}{182}\right)\)	\(e\left(\frac{67}{91}\right)\)	\(e\left(\frac{3}{91}\right)\)	\(e\left(\frac{55}{182}\right)\)	\(e\left(\frac{107}{182}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{19}{182}\right)\)	\(e\left(\frac{50}{91}\right)\)	\(e\left(\frac{3}{26}\right)\)
\(\chi_{309680}(47111,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{111}{182}\right)\)	\(e\left(\frac{20}{91}\right)\)	\(e\left(\frac{43}{91}\right)\)	\(e\left(\frac{121}{182}\right)\)	\(e\left(\frac{17}{182}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{151}{182}\right)\)	\(e\left(\frac{19}{91}\right)\)	\(e\left(\frac{17}{26}\right)\)
\(\chi_{309680}(48231,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{123}{182}\right)\)	\(e\left(\frac{32}{91}\right)\)	\(e\left(\frac{87}{91}\right)\)	\(e\left(\frac{139}{182}\right)\)	\(e\left(\frac{9}{182}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{5}{182}\right)\)	\(e\left(\frac{85}{91}\right)\)	\(e\left(\frac{9}{26}\right)\)
\(\chi_{309680}(65031,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{107}{182}\right)\)	\(e\left(\frac{16}{91}\right)\)	\(e\left(\frac{89}{91}\right)\)	\(e\left(\frac{115}{182}\right)\)	\(e\left(\frac{141}{182}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{139}{182}\right)\)	\(e\left(\frac{88}{91}\right)\)	\(e\left(\frac{11}{26}\right)\)
\(\chi_{309680}(71191,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{182}\right)\)	\(e\left(\frac{47}{91}\right)\)	\(e\left(\frac{51}{91}\right)\)	\(e\left(\frac{25}{182}\right)\)	\(e\left(\frac{181}{182}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{141}{182}\right)\)	\(e\left(\frac{31}{91}\right)\)	\(e\left(\frac{25}{26}\right)\)
\(\chi_{309680}(72871,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{135}{182}\right)\)	\(e\left(\frac{44}{91}\right)\)	\(e\left(\frac{40}{91}\right)\)	\(e\left(\frac{157}{182}\right)\)	\(e\left(\frac{1}{182}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{41}{182}\right)\)	\(e\left(\frac{60}{91}\right)\)	\(e\left(\frac{1}{26}\right)\)
\(\chi_{309680}(75111,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{131}{182}\right)\)	\(e\left(\frac{40}{91}\right)\)	\(e\left(\frac{86}{91}\right)\)	\(e\left(\frac{151}{182}\right)\)	\(e\left(\frac{125}{182}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{29}{182}\right)\)	\(e\left(\frac{38}{91}\right)\)	\(e\left(\frac{21}{26}\right)\)
\(\chi_{309680}(84071,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{182}\right)\)	\(e\left(\frac{17}{91}\right)\)	\(e\left(\frac{32}{91}\right)\)	\(e\left(\frac{71}{182}\right)\)	\(e\left(\frac{19}{182}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{51}{182}\right)\)	\(e\left(\frac{48}{91}\right)\)	\(e\left(\frac{19}{26}\right)\)
\(\chi_{309680}(87431,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{25}{182}\right)\)	\(e\left(\frac{25}{91}\right)\)	\(e\left(\frac{31}{91}\right)\)	\(e\left(\frac{83}{182}\right)\)	\(e\left(\frac{135}{182}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{75}{182}\right)\)	\(e\left(\frac{1}{91}\right)\)	\(e\left(\frac{5}{26}\right)\)
\(\chi_{309680}(88551,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{93}{182}\right)\)	\(e\left(\frac{2}{91}\right)\)	\(e\left(\frac{68}{91}\right)\)	\(e\left(\frac{3}{182}\right)\)	\(e\left(\frac{29}{182}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{97}{182}\right)\)	\(e\left(\frac{11}{91}\right)\)	\(e\left(\frac{3}{26}\right)\)
\(\chi_{309680}(91351,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{137}{182}\right)\)	\(e\left(\frac{46}{91}\right)\)	\(e\left(\frac{17}{91}\right)\)	\(e\left(\frac{69}{182}\right)\)	\(e\left(\frac{121}{182}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{47}{182}\right)\)	\(e\left(\frac{71}{91}\right)\)	\(e\left(\frac{17}{26}\right)\)
\(\chi_{309680}(92471,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{149}{182}\right)\)	\(e\left(\frac{58}{91}\right)\)	\(e\left(\frac{61}{91}\right)\)	\(e\left(\frac{87}{182}\right)\)	\(e\left(\frac{113}{182}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{83}{182}\right)\)	\(e\left(\frac{46}{91}\right)\)	\(e\left(\frac{9}{26}\right)\)
\(\chi_{309680}(94711,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{89}{182}\right)\)	\(e\left(\frac{89}{91}\right)\)	\(e\left(\frac{23}{91}\right)\)	\(e\left(\frac{179}{182}\right)\)	\(e\left(\frac{153}{182}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{85}{182}\right)\)	\(e\left(\frac{80}{91}\right)\)	\(e\left(\frac{23}{26}\right)\)
\(\chi_{309680}(106471,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{61}{182}\right)\)	\(e\left(\frac{61}{91}\right)\)	\(e\left(\frac{72}{91}\right)\)	\(e\left(\frac{137}{182}\right)\)	\(e\left(\frac{111}{182}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{1}{182}\right)\)	\(e\left(\frac{17}{91}\right)\)	\(e\left(\frac{7}{26}\right)\)
\(\chi_{309680}(115431,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{73}{182}\right)\)	\(e\left(\frac{73}{91}\right)\)	\(e\left(\frac{25}{91}\right)\)	\(e\left(\frac{155}{182}\right)\)	\(e\left(\frac{103}{182}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{37}{182}\right)\)	\(e\left(\frac{83}{91}\right)\)	\(e\left(\frac{25}{26}\right)\)
\(\chi_{309680}(119351,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{157}{182}\right)\)	\(e\left(\frac{66}{91}\right)\)	\(e\left(\frac{60}{91}\right)\)	\(e\left(\frac{99}{182}\right)\)	\(e\left(\frac{47}{182}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{107}{182}\right)\)	\(e\left(\frac{90}{91}\right)\)	\(e\left(\frac{21}{26}\right)\)
\(\chi_{309680}(122151,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{75}{182}\right)\)	\(e\left(\frac{75}{91}\right)\)	\(e\left(\frac{2}{91}\right)\)	\(e\left(\frac{67}{182}\right)\)	\(e\left(\frac{41}{182}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{43}{182}\right)\)	\(e\left(\frac{3}{91}\right)\)	\(e\left(\frac{15}{26}\right)\)
\(\chi_{309680}(128311,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{182}\right)\)	\(e\left(\frac{43}{91}\right)\)	\(e\left(\frac{6}{91}\right)\)	\(e\left(\frac{19}{182}\right)\)	\(e\left(\frac{123}{182}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{129}{182}\right)\)	\(e\left(\frac{9}{91}\right)\)	\(e\left(\frac{19}{26}\right)\)
\(\chi_{309680}(131671,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{51}{182}\right)\)	\(e\left(\frac{51}{91}\right)\)	\(e\left(\frac{5}{91}\right)\)	\(e\left(\frac{31}{182}\right)\)	\(e\left(\frac{57}{182}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{153}{182}\right)\)	\(e\left(\frac{53}{91}\right)\)	\(e\left(\frac{5}{26}\right)\)
\(\chi_{309680}(135591,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{163}{182}\right)\)	\(e\left(\frac{72}{91}\right)\)	\(e\left(\frac{82}{91}\right)\)	\(e\left(\frac{17}{182}\right)\)	\(e\left(\frac{43}{182}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{125}{182}\right)\)	\(e\left(\frac{32}{91}\right)\)	\(e\left(\frac{17}{26}\right)\)
\(\chi_{309680}(138951,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{115}{182}\right)\)	\(e\left(\frac{24}{91}\right)\)	\(e\left(\frac{88}{91}\right)\)	\(e\left(\frac{127}{182}\right)\)	\(e\left(\frac{75}{182}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{163}{182}\right)\)	\(e\left(\frac{41}{91}\right)\)	\(e\left(\frac{23}{26}\right)\)

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First 31 of 72 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	309680.buo
Modulus	$309680$
Conductor	$30968$
Order	$182$
Real	no
Primitive	no
Minimal	no
Parity	even

Modulus:	\(309680\)
Conductor:	\(30968\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(182\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 30968.jj	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	no
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)