LMFDB - Dirichlet character orbit 2864.r

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2864, base_ring=CyclotomicField(178)) M = H._module chi = DirichletCharacter(H, M([89,0,68])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(15,2864)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$2864$
Conductor:	$716$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$178$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 716.h	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	odd	sage:chi.is_odd() pari:zncharisodd(g,chi)

Related number fields

Field of values:	$\Q(\zeta_{89})$
Fixed field:	Number field defined by a degree 178 polynomial (not computed)

First 31 of 88 characters in Galois orbit

Character	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$17$	$19$	$21$
$\chi_{2864}(15,\cdot)$	$-1$	$1$	$e\left(\frac{135}{178}\right)$	$e\left(\frac{64}{89}\right)$	$e\left(\frac{147}{178}\right)$	$e\left(\frac{46}{89}\right)$	$e\left(\frac{41}{178}\right)$	$e\left(\frac{49}{89}\right)$	$e\left(\frac{85}{178}\right)$	$e\left(\frac{37}{89}\right)$	$e\left(\frac{23}{178}\right)$	$e\left(\frac{52}{89}\right)$
$\chi_{2864}(31,\cdot)$	$-1$	$1$	$e\left(\frac{21}{178}\right)$	$e\left(\frac{6}{89}\right)$	$e\left(\frac{11}{178}\right)$	$e\left(\frac{21}{89}\right)$	$e\left(\frac{129}{178}\right)$	$e\left(\frac{63}{89}\right)$	$e\left(\frac{33}{178}\right)$	$e\left(\frac{73}{89}\right)$	$e\left(\frac{55}{178}\right)$	$e\left(\frac{16}{89}\right)$
$\chi_{2864}(47,\cdot)$	$-1$	$1$	$e\left(\frac{61}{178}\right)$	$e\left(\frac{81}{89}\right)$	$e\left(\frac{15}{178}\right)$	$e\left(\frac{61}{89}\right)$	$e\left(\frac{95}{178}\right)$	$e\left(\frac{5}{89}\right)$	$e\left(\frac{45}{178}\right)$	$e\left(\frac{51}{89}\right)$	$e\left(\frac{75}{178}\right)$	$e\left(\frac{38}{89}\right)$
$\chi_{2864}(95,\cdot)$	$-1$	$1$	$e\left(\frac{177}{178}\right)$	$e\left(\frac{76}{89}\right)$	$e\left(\frac{169}{178}\right)$	$e\left(\frac{88}{89}\right)$	$e\left(\frac{121}{178}\right)$	$e\left(\frac{86}{89}\right)$	$e\left(\frac{151}{178}\right)$	$e\left(\frac{5}{89}\right)$	$e\left(\frac{133}{178}\right)$	$e\left(\frac{84}{89}\right)$
$\chi_{2864}(191,\cdot)$	$-1$	$1$	$e\left(\frac{43}{178}\right)$	$e\left(\frac{25}{89}\right)$	$e\left(\frac{31}{178}\right)$	$e\left(\frac{43}{89}\right)$	$e\left(\frac{137}{178}\right)$	$e\left(\frac{40}{89}\right)$	$e\left(\frac{93}{178}\right)$	$e\left(\frac{52}{89}\right)$	$e\left(\frac{155}{178}\right)$	$e\left(\frac{37}{89}\right)$
$\chi_{2864}(239,\cdot)$	$-1$	$1$	$e\left(\frac{173}{178}\right)$	$e\left(\frac{24}{89}\right)$	$e\left(\frac{133}{178}\right)$	$e\left(\frac{84}{89}\right)$	$e\left(\frac{71}{178}\right)$	$e\left(\frac{74}{89}\right)$	$e\left(\frac{43}{178}\right)$	$e\left(\frac{25}{89}\right)$	$e\left(\frac{131}{178}\right)$	$e\left(\frac{64}{89}\right)$
$\chi_{2864}(255,\cdot)$	$-1$	$1$	$e\left(\frac{85}{178}\right)$	$e\left(\frac{37}{89}\right)$	$e\left(\frac{53}{178}\right)$	$e\left(\frac{85}{89}\right)$	$e\left(\frac{39}{178}\right)$	$e\left(\frac{77}{89}\right)$	$e\left(\frac{159}{178}\right)$	$e\left(\frac{20}{89}\right)$	$e\left(\frac{87}{178}\right)$	$e\left(\frac{69}{89}\right)$
$\chi_{2864}(287,\cdot)$	$-1$	$1$	$e\left(\frac{53}{178}\right)$	$e\left(\frac{66}{89}\right)$	$e\left(\frac{121}{178}\right)$	$e\left(\frac{53}{89}\right)$	$e\left(\frac{173}{178}\right)$	$e\left(\frac{70}{89}\right)$	$e\left(\frac{7}{178}\right)$	$e\left(\frac{2}{89}\right)$	$e\left(\frac{71}{178}\right)$	$e\left(\frac{87}{89}\right)$
$\chi_{2864}(303,\cdot)$	$-1$	$1$	$e\left(\frac{59}{178}\right)$	$e\left(\frac{55}{89}\right)$	$e\left(\frac{175}{178}\right)$	$e\left(\frac{59}{89}\right)$	$e\left(\frac{159}{178}\right)$	$e\left(\frac{88}{89}\right)$	$e\left(\frac{169}{178}\right)$	$e\left(\frac{61}{89}\right)$	$e\left(\frac{163}{178}\right)$	$e\left(\frac{28}{89}\right)$
$\chi_{2864}(335,\cdot)$	$-1$	$1$	$e\left(\frac{73}{178}\right)$	$e\left(\frac{59}{89}\right)$	$e\left(\frac{123}{178}\right)$	$e\left(\frac{73}{89}\right)$	$e\left(\frac{67}{178}\right)$	$e\left(\frac{41}{89}\right)$	$e\left(\frac{13}{178}\right)$	$e\left(\frac{80}{89}\right)$	$e\left(\frac{81}{178}\right)$	$e\left(\frac{9}{89}\right)$
$\chi_{2864}(351,\cdot)$	$-1$	$1$	$e\left(\frac{45}{178}\right)$	$e\left(\frac{51}{89}\right)$	$e\left(\frac{49}{178}\right)$	$e\left(\frac{45}{89}\right)$	$e\left(\frac{73}{178}\right)$	$e\left(\frac{46}{89}\right)$	$e\left(\frac{147}{178}\right)$	$e\left(\frac{42}{89}\right)$	$e\left(\frac{67}{178}\right)$	$e\left(\frac{47}{89}\right)$
$\chi_{2864}(367,\cdot)$	$-1$	$1$	$e\left(\frac{99}{178}\right)$	$e\left(\frac{41}{89}\right)$	$e\left(\frac{1}{178}\right)$	$e\left(\frac{10}{89}\right)$	$e\left(\frac{125}{178}\right)$	$e\left(\frac{30}{89}\right)$	$e\left(\frac{3}{178}\right)$	$e\left(\frac{39}{89}\right)$	$e\left(\frac{5}{178}\right)$	$e\left(\frac{50}{89}\right)$
$\chi_{2864}(383,\cdot)$	$-1$	$1$	$e\left(\frac{171}{178}\right)$	$e\left(\frac{87}{89}\right)$	$e\left(\frac{115}{178}\right)$	$e\left(\frac{82}{89}\right)$	$e\left(\frac{135}{178}\right)$	$e\left(\frac{68}{89}\right)$	$e\left(\frac{167}{178}\right)$	$e\left(\frac{35}{89}\right)$	$e\left(\frac{41}{178}\right)$	$e\left(\frac{54}{89}\right)$
$\chi_{2864}(415,\cdot)$	$-1$	$1$	$e\left(\frac{141}{178}\right)$	$e\left(\frac{53}{89}\right)$	$e\left(\frac{23}{178}\right)$	$e\left(\frac{52}{89}\right)$	$e\left(\frac{27}{178}\right)$	$e\left(\frac{67}{89}\right)$	$e\left(\frac{69}{178}\right)$	$e\left(\frac{7}{89}\right)$	$e\left(\frac{115}{178}\right)$	$e\left(\frac{82}{89}\right)$
$\chi_{2864}(447,\cdot)$	$-1$	$1$	$e\left(\frac{159}{178}\right)$	$e\left(\frac{20}{89}\right)$	$e\left(\frac{7}{178}\right)$	$e\left(\frac{70}{89}\right)$	$e\left(\frac{163}{178}\right)$	$e\left(\frac{32}{89}\right)$	$e\left(\frac{21}{178}\right)$	$e\left(\frac{6}{89}\right)$	$e\left(\frac{35}{178}\right)$	$e\left(\frac{83}{89}\right)$
$\chi_{2864}(479,\cdot)$	$-1$	$1$	$e\left(\frac{125}{178}\right)$	$e\left(\frac{23}{89}\right)$	$e\left(\frac{57}{178}\right)$	$e\left(\frac{36}{89}\right)$	$e\left(\frac{5}{178}\right)$	$e\left(\frac{19}{89}\right)$	$e\left(\frac{171}{178}\right)$	$e\left(\frac{87}{89}\right)$	$e\left(\frac{107}{178}\right)$	$e\left(\frac{2}{89}\right)$
$\chi_{2864}(511,\cdot)$	$-1$	$1$	$e\left(\frac{49}{178}\right)$	$e\left(\frac{14}{89}\right)$	$e\left(\frac{85}{178}\right)$	$e\left(\frac{49}{89}\right)$	$e\left(\frac{123}{178}\right)$	$e\left(\frac{58}{89}\right)$	$e\left(\frac{77}{178}\right)$	$e\left(\frac{22}{89}\right)$	$e\left(\frac{69}{178}\right)$	$e\left(\frac{67}{89}\right)$
$\chi_{2864}(527,\cdot)$	$-1$	$1$	$e\left(\frac{149}{178}\right)$	$e\left(\frac{68}{89}\right)$	$e\left(\frac{95}{178}\right)$	$e\left(\frac{60}{89}\right)$	$e\left(\frac{127}{178}\right)$	$e\left(\frac{2}{89}\right)$	$e\left(\frac{107}{178}\right)$	$e\left(\frac{56}{89}\right)$	$e\left(\frac{119}{178}\right)$	$e\left(\frac{33}{89}\right)$
$\chi_{2864}(559,\cdot)$	$-1$	$1$	$e\left(\frac{37}{178}\right)$	$e\left(\frac{36}{89}\right)$	$e\left(\frac{155}{178}\right)$	$e\left(\frac{37}{89}\right)$	$e\left(\frac{151}{178}\right)$	$e\left(\frac{22}{89}\right)$	$e\left(\frac{109}{178}\right)$	$e\left(\frac{82}{89}\right)$	$e\left(\frac{63}{178}\right)$	$e\left(\frac{7}{89}\right)$
$\chi_{2864}(607,\cdot)$	$-1$	$1$	$e\left(\frac{105}{178}\right)$	$e\left(\frac{30}{89}\right)$	$e\left(\frac{55}{178}\right)$	$e\left(\frac{16}{89}\right)$	$e\left(\frac{111}{178}\right)$	$e\left(\frac{48}{89}\right)$	$e\left(\frac{165}{178}\right)$	$e\left(\frac{9}{89}\right)$	$e\left(\frac{97}{178}\right)$	$e\left(\frac{80}{89}\right)$
$\chi_{2864}(719,\cdot)$	$-1$	$1$	$e\left(\frac{5}{178}\right)$	$e\left(\frac{65}{89}\right)$	$e\left(\frac{45}{178}\right)$	$e\left(\frac{5}{89}\right)$	$e\left(\frac{107}{178}\right)$	$e\left(\frac{15}{89}\right)$	$e\left(\frac{135}{178}\right)$	$e\left(\frac{64}{89}\right)$	$e\left(\frac{47}{178}\right)$	$e\left(\frac{25}{89}\right)$
$\chi_{2864}(735,\cdot)$	$-1$	$1$	$e\left(\frac{47}{178}\right)$	$e\left(\frac{77}{89}\right)$	$e\left(\frac{67}{178}\right)$	$e\left(\frac{47}{89}\right)$	$e\left(\frac{9}{178}\right)$	$e\left(\frac{52}{89}\right)$	$e\left(\frac{23}{178}\right)$	$e\left(\frac{32}{89}\right)$	$e\left(\frac{157}{178}\right)$	$e\left(\frac{57}{89}\right)$
$\chi_{2864}(767,\cdot)$	$-1$	$1$	$e\left(\frac{133}{178}\right)$	$e\left(\frac{38}{89}\right)$	$e\left(\frac{129}{178}\right)$	$e\left(\frac{44}{89}\right)$	$e\left(\frac{105}{178}\right)$	$e\left(\frac{43}{89}\right)$	$e\left(\frac{31}{178}\right)$	$e\left(\frac{47}{89}\right)$	$e\left(\frac{111}{178}\right)$	$e\left(\frac{42}{89}\right)$
$\chi_{2864}(783,\cdot)$	$-1$	$1$	$e\left(\frac{121}{178}\right)$	$e\left(\frac{60}{89}\right)$	$e\left(\frac{21}{178}\right)$	$e\left(\frac{32}{89}\right)$	$e\left(\frac{133}{178}\right)$	$e\left(\frac{7}{89}\right)$	$e\left(\frac{63}{178}\right)$	$e\left(\frac{18}{89}\right)$	$e\left(\frac{105}{178}\right)$	$e\left(\frac{71}{89}\right)$
$\chi_{2864}(799,\cdot)$	$-1$	$1$	$e\left(\frac{11}{178}\right)$	$e\left(\frac{54}{89}\right)$	$e\left(\frac{99}{178}\right)$	$e\left(\frac{11}{89}\right)$	$e\left(\frac{93}{178}\right)$	$e\left(\frac{33}{89}\right)$	$e\left(\frac{119}{178}\right)$	$e\left(\frac{34}{89}\right)$	$e\left(\frac{139}{178}\right)$	$e\left(\frac{55}{89}\right)$
$\chi_{2864}(863,\cdot)$	$-1$	$1$	$e\left(\frac{95}{178}\right)$	$e\left(\frac{78}{89}\right)$	$e\left(\frac{143}{178}\right)$	$e\left(\frac{6}{89}\right)$	$e\left(\frac{75}{178}\right)$	$e\left(\frac{18}{89}\right)$	$e\left(\frac{73}{178}\right)$	$e\left(\frac{59}{89}\right)$	$e\left(\frac{3}{178}\right)$	$e\left(\frac{30}{89}\right)$
$\chi_{2864}(911,\cdot)$	$-1$	$1$	$e\left(\frac{165}{178}\right)$	$e\left(\frac{9}{89}\right)$	$e\left(\frac{61}{178}\right)$	$e\left(\frac{76}{89}\right)$	$e\left(\frac{149}{178}\right)$	$e\left(\frac{50}{89}\right)$	$e\left(\frac{5}{178}\right)$	$e\left(\frac{65}{89}\right)$	$e\left(\frac{127}{178}\right)$	$e\left(\frac{24}{89}\right)$
$\chi_{2864}(943,\cdot)$	$-1$	$1$	$e\left(\frac{81}{178}\right)$	$e\left(\frac{74}{89}\right)$	$e\left(\frac{17}{178}\right)$	$e\left(\frac{81}{89}\right)$	$e\left(\frac{167}{178}\right)$	$e\left(\frac{65}{89}\right)$	$e\left(\frac{51}{178}\right)$	$e\left(\frac{40}{89}\right)$	$e\left(\frac{85}{178}\right)$	$e\left(\frac{49}{89}\right)$
$\chi_{2864}(959,\cdot)$	$-1$	$1$	$e\left(\frac{25}{178}\right)$	$e\left(\frac{58}{89}\right)$	$e\left(\frac{47}{178}\right)$	$e\left(\frac{25}{89}\right)$	$e\left(\frac{1}{178}\right)$	$e\left(\frac{75}{89}\right)$	$e\left(\frac{141}{178}\right)$	$e\left(\frac{53}{89}\right)$	$e\left(\frac{57}{178}\right)$	$e\left(\frac{36}{89}\right)$
$\chi_{2864}(975,\cdot)$	$-1$	$1$	$e\left(\frac{117}{178}\right)$	$e\left(\frac{8}{89}\right)$	$e\left(\frac{163}{178}\right)$	$e\left(\frac{28}{89}\right)$	$e\left(\frac{83}{178}\right)$	$e\left(\frac{84}{89}\right)$	$e\left(\frac{133}{178}\right)$	$e\left(\frac{38}{89}\right)$	$e\left(\frac{103}{178}\right)$	$e\left(\frac{51}{89}\right)$
$\chi_{2864}(1039,\cdot)$	$-1$	$1$	$e\left(\frac{175}{178}\right)$	$e\left(\frac{50}{89}\right)$	$e\left(\frac{151}{178}\right)$	$e\left(\frac{86}{89}\right)$	$e\left(\frac{7}{178}\right)$	$e\left(\frac{80}{89}\right)$	$e\left(\frac{97}{178}\right)$	$e\left(\frac{15}{89}\right)$	$e\left(\frac{43}{178}\right)$	$e\left(\frac{74}{89}\right)$

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	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(21\)
\(\chi_{2864}(15,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{135}{178}\right)\)	\(e\left(\frac{64}{89}\right)\)	\(e\left(\frac{147}{178}\right)\)	\(e\left(\frac{46}{89}\right)\)	\(e\left(\frac{41}{178}\right)\)	\(e\left(\frac{49}{89}\right)\)	\(e\left(\frac{85}{178}\right)\)	\(e\left(\frac{37}{89}\right)\)	\(e\left(\frac{23}{178}\right)\)	\(e\left(\frac{52}{89}\right)\)
\(\chi_{2864}(31,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{21}{178}\right)\)	\(e\left(\frac{6}{89}\right)\)	\(e\left(\frac{11}{178}\right)\)	\(e\left(\frac{21}{89}\right)\)	\(e\left(\frac{129}{178}\right)\)	\(e\left(\frac{63}{89}\right)\)	\(e\left(\frac{33}{178}\right)\)	\(e\left(\frac{73}{89}\right)\)	\(e\left(\frac{55}{178}\right)\)	\(e\left(\frac{16}{89}\right)\)
\(\chi_{2864}(47,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{61}{178}\right)\)	\(e\left(\frac{81}{89}\right)\)	\(e\left(\frac{15}{178}\right)\)	\(e\left(\frac{61}{89}\right)\)	\(e\left(\frac{95}{178}\right)\)	\(e\left(\frac{5}{89}\right)\)	\(e\left(\frac{45}{178}\right)\)	\(e\left(\frac{51}{89}\right)\)	\(e\left(\frac{75}{178}\right)\)	\(e\left(\frac{38}{89}\right)\)
\(\chi_{2864}(95,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{177}{178}\right)\)	\(e\left(\frac{76}{89}\right)\)	\(e\left(\frac{169}{178}\right)\)	\(e\left(\frac{88}{89}\right)\)	\(e\left(\frac{121}{178}\right)\)	\(e\left(\frac{86}{89}\right)\)	\(e\left(\frac{151}{178}\right)\)	\(e\left(\frac{5}{89}\right)\)	\(e\left(\frac{133}{178}\right)\)	\(e\left(\frac{84}{89}\right)\)
\(\chi_{2864}(191,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{43}{178}\right)\)	\(e\left(\frac{25}{89}\right)\)	\(e\left(\frac{31}{178}\right)\)	\(e\left(\frac{43}{89}\right)\)	\(e\left(\frac{137}{178}\right)\)	\(e\left(\frac{40}{89}\right)\)	\(e\left(\frac{93}{178}\right)\)	\(e\left(\frac{52}{89}\right)\)	\(e\left(\frac{155}{178}\right)\)	\(e\left(\frac{37}{89}\right)\)
\(\chi_{2864}(239,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{173}{178}\right)\)	\(e\left(\frac{24}{89}\right)\)	\(e\left(\frac{133}{178}\right)\)	\(e\left(\frac{84}{89}\right)\)	\(e\left(\frac{71}{178}\right)\)	\(e\left(\frac{74}{89}\right)\)	\(e\left(\frac{43}{178}\right)\)	\(e\left(\frac{25}{89}\right)\)	\(e\left(\frac{131}{178}\right)\)	\(e\left(\frac{64}{89}\right)\)
\(\chi_{2864}(255,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{85}{178}\right)\)	\(e\left(\frac{37}{89}\right)\)	\(e\left(\frac{53}{178}\right)\)	\(e\left(\frac{85}{89}\right)\)	\(e\left(\frac{39}{178}\right)\)	\(e\left(\frac{77}{89}\right)\)	\(e\left(\frac{159}{178}\right)\)	\(e\left(\frac{20}{89}\right)\)	\(e\left(\frac{87}{178}\right)\)	\(e\left(\frac{69}{89}\right)\)
\(\chi_{2864}(287,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{53}{178}\right)\)	\(e\left(\frac{66}{89}\right)\)	\(e\left(\frac{121}{178}\right)\)	\(e\left(\frac{53}{89}\right)\)	\(e\left(\frac{173}{178}\right)\)	\(e\left(\frac{70}{89}\right)\)	\(e\left(\frac{7}{178}\right)\)	\(e\left(\frac{2}{89}\right)\)	\(e\left(\frac{71}{178}\right)\)	\(e\left(\frac{87}{89}\right)\)
\(\chi_{2864}(303,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{59}{178}\right)\)	\(e\left(\frac{55}{89}\right)\)	\(e\left(\frac{175}{178}\right)\)	\(e\left(\frac{59}{89}\right)\)	\(e\left(\frac{159}{178}\right)\)	\(e\left(\frac{88}{89}\right)\)	\(e\left(\frac{169}{178}\right)\)	\(e\left(\frac{61}{89}\right)\)	\(e\left(\frac{163}{178}\right)\)	\(e\left(\frac{28}{89}\right)\)
\(\chi_{2864}(335,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{73}{178}\right)\)	\(e\left(\frac{59}{89}\right)\)	\(e\left(\frac{123}{178}\right)\)	\(e\left(\frac{73}{89}\right)\)	\(e\left(\frac{67}{178}\right)\)	\(e\left(\frac{41}{89}\right)\)	\(e\left(\frac{13}{178}\right)\)	\(e\left(\frac{80}{89}\right)\)	\(e\left(\frac{81}{178}\right)\)	\(e\left(\frac{9}{89}\right)\)
\(\chi_{2864}(351,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{45}{178}\right)\)	\(e\left(\frac{51}{89}\right)\)	\(e\left(\frac{49}{178}\right)\)	\(e\left(\frac{45}{89}\right)\)	\(e\left(\frac{73}{178}\right)\)	\(e\left(\frac{46}{89}\right)\)	\(e\left(\frac{147}{178}\right)\)	\(e\left(\frac{42}{89}\right)\)	\(e\left(\frac{67}{178}\right)\)	\(e\left(\frac{47}{89}\right)\)
\(\chi_{2864}(367,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{99}{178}\right)\)	\(e\left(\frac{41}{89}\right)\)	\(e\left(\frac{1}{178}\right)\)	\(e\left(\frac{10}{89}\right)\)	\(e\left(\frac{125}{178}\right)\)	\(e\left(\frac{30}{89}\right)\)	\(e\left(\frac{3}{178}\right)\)	\(e\left(\frac{39}{89}\right)\)	\(e\left(\frac{5}{178}\right)\)	\(e\left(\frac{50}{89}\right)\)
\(\chi_{2864}(383,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{171}{178}\right)\)	\(e\left(\frac{87}{89}\right)\)	\(e\left(\frac{115}{178}\right)\)	\(e\left(\frac{82}{89}\right)\)	\(e\left(\frac{135}{178}\right)\)	\(e\left(\frac{68}{89}\right)\)	\(e\left(\frac{167}{178}\right)\)	\(e\left(\frac{35}{89}\right)\)	\(e\left(\frac{41}{178}\right)\)	\(e\left(\frac{54}{89}\right)\)
\(\chi_{2864}(415,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{141}{178}\right)\)	\(e\left(\frac{53}{89}\right)\)	\(e\left(\frac{23}{178}\right)\)	\(e\left(\frac{52}{89}\right)\)	\(e\left(\frac{27}{178}\right)\)	\(e\left(\frac{67}{89}\right)\)	\(e\left(\frac{69}{178}\right)\)	\(e\left(\frac{7}{89}\right)\)	\(e\left(\frac{115}{178}\right)\)	\(e\left(\frac{82}{89}\right)\)
\(\chi_{2864}(447,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{159}{178}\right)\)	\(e\left(\frac{20}{89}\right)\)	\(e\left(\frac{7}{178}\right)\)	\(e\left(\frac{70}{89}\right)\)	\(e\left(\frac{163}{178}\right)\)	\(e\left(\frac{32}{89}\right)\)	\(e\left(\frac{21}{178}\right)\)	\(e\left(\frac{6}{89}\right)\)	\(e\left(\frac{35}{178}\right)\)	\(e\left(\frac{83}{89}\right)\)
\(\chi_{2864}(479,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{125}{178}\right)\)	\(e\left(\frac{23}{89}\right)\)	\(e\left(\frac{57}{178}\right)\)	\(e\left(\frac{36}{89}\right)\)	\(e\left(\frac{5}{178}\right)\)	\(e\left(\frac{19}{89}\right)\)	\(e\left(\frac{171}{178}\right)\)	\(e\left(\frac{87}{89}\right)\)	\(e\left(\frac{107}{178}\right)\)	\(e\left(\frac{2}{89}\right)\)
\(\chi_{2864}(511,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{49}{178}\right)\)	\(e\left(\frac{14}{89}\right)\)	\(e\left(\frac{85}{178}\right)\)	\(e\left(\frac{49}{89}\right)\)	\(e\left(\frac{123}{178}\right)\)	\(e\left(\frac{58}{89}\right)\)	\(e\left(\frac{77}{178}\right)\)	\(e\left(\frac{22}{89}\right)\)	\(e\left(\frac{69}{178}\right)\)	\(e\left(\frac{67}{89}\right)\)
\(\chi_{2864}(527,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{149}{178}\right)\)	\(e\left(\frac{68}{89}\right)\)	\(e\left(\frac{95}{178}\right)\)	\(e\left(\frac{60}{89}\right)\)	\(e\left(\frac{127}{178}\right)\)	\(e\left(\frac{2}{89}\right)\)	\(e\left(\frac{107}{178}\right)\)	\(e\left(\frac{56}{89}\right)\)	\(e\left(\frac{119}{178}\right)\)	\(e\left(\frac{33}{89}\right)\)
\(\chi_{2864}(559,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{37}{178}\right)\)	\(e\left(\frac{36}{89}\right)\)	\(e\left(\frac{155}{178}\right)\)	\(e\left(\frac{37}{89}\right)\)	\(e\left(\frac{151}{178}\right)\)	\(e\left(\frac{22}{89}\right)\)	\(e\left(\frac{109}{178}\right)\)	\(e\left(\frac{82}{89}\right)\)	\(e\left(\frac{63}{178}\right)\)	\(e\left(\frac{7}{89}\right)\)
\(\chi_{2864}(607,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{105}{178}\right)\)	\(e\left(\frac{30}{89}\right)\)	\(e\left(\frac{55}{178}\right)\)	\(e\left(\frac{16}{89}\right)\)	\(e\left(\frac{111}{178}\right)\)	\(e\left(\frac{48}{89}\right)\)	\(e\left(\frac{165}{178}\right)\)	\(e\left(\frac{9}{89}\right)\)	\(e\left(\frac{97}{178}\right)\)	\(e\left(\frac{80}{89}\right)\)
\(\chi_{2864}(719,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{5}{178}\right)\)	\(e\left(\frac{65}{89}\right)\)	\(e\left(\frac{45}{178}\right)\)	\(e\left(\frac{5}{89}\right)\)	\(e\left(\frac{107}{178}\right)\)	\(e\left(\frac{15}{89}\right)\)	\(e\left(\frac{135}{178}\right)\)	\(e\left(\frac{64}{89}\right)\)	\(e\left(\frac{47}{178}\right)\)	\(e\left(\frac{25}{89}\right)\)
\(\chi_{2864}(735,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{47}{178}\right)\)	\(e\left(\frac{77}{89}\right)\)	\(e\left(\frac{67}{178}\right)\)	\(e\left(\frac{47}{89}\right)\)	\(e\left(\frac{9}{178}\right)\)	\(e\left(\frac{52}{89}\right)\)	\(e\left(\frac{23}{178}\right)\)	\(e\left(\frac{32}{89}\right)\)	\(e\left(\frac{157}{178}\right)\)	\(e\left(\frac{57}{89}\right)\)
\(\chi_{2864}(767,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{133}{178}\right)\)	\(e\left(\frac{38}{89}\right)\)	\(e\left(\frac{129}{178}\right)\)	\(e\left(\frac{44}{89}\right)\)	\(e\left(\frac{105}{178}\right)\)	\(e\left(\frac{43}{89}\right)\)	\(e\left(\frac{31}{178}\right)\)	\(e\left(\frac{47}{89}\right)\)	\(e\left(\frac{111}{178}\right)\)	\(e\left(\frac{42}{89}\right)\)
\(\chi_{2864}(783,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{121}{178}\right)\)	\(e\left(\frac{60}{89}\right)\)	\(e\left(\frac{21}{178}\right)\)	\(e\left(\frac{32}{89}\right)\)	\(e\left(\frac{133}{178}\right)\)	\(e\left(\frac{7}{89}\right)\)	\(e\left(\frac{63}{178}\right)\)	\(e\left(\frac{18}{89}\right)\)	\(e\left(\frac{105}{178}\right)\)	\(e\left(\frac{71}{89}\right)\)
\(\chi_{2864}(799,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{11}{178}\right)\)	\(e\left(\frac{54}{89}\right)\)	\(e\left(\frac{99}{178}\right)\)	\(e\left(\frac{11}{89}\right)\)	\(e\left(\frac{93}{178}\right)\)	\(e\left(\frac{33}{89}\right)\)	\(e\left(\frac{119}{178}\right)\)	\(e\left(\frac{34}{89}\right)\)	\(e\left(\frac{139}{178}\right)\)	\(e\left(\frac{55}{89}\right)\)
\(\chi_{2864}(863,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{95}{178}\right)\)	\(e\left(\frac{78}{89}\right)\)	\(e\left(\frac{143}{178}\right)\)	\(e\left(\frac{6}{89}\right)\)	\(e\left(\frac{75}{178}\right)\)	\(e\left(\frac{18}{89}\right)\)	\(e\left(\frac{73}{178}\right)\)	\(e\left(\frac{59}{89}\right)\)	\(e\left(\frac{3}{178}\right)\)	\(e\left(\frac{30}{89}\right)\)
\(\chi_{2864}(911,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{165}{178}\right)\)	\(e\left(\frac{9}{89}\right)\)	\(e\left(\frac{61}{178}\right)\)	\(e\left(\frac{76}{89}\right)\)	\(e\left(\frac{149}{178}\right)\)	\(e\left(\frac{50}{89}\right)\)	\(e\left(\frac{5}{178}\right)\)	\(e\left(\frac{65}{89}\right)\)	\(e\left(\frac{127}{178}\right)\)	\(e\left(\frac{24}{89}\right)\)
\(\chi_{2864}(943,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{81}{178}\right)\)	\(e\left(\frac{74}{89}\right)\)	\(e\left(\frac{17}{178}\right)\)	\(e\left(\frac{81}{89}\right)\)	\(e\left(\frac{167}{178}\right)\)	\(e\left(\frac{65}{89}\right)\)	\(e\left(\frac{51}{178}\right)\)	\(e\left(\frac{40}{89}\right)\)	\(e\left(\frac{85}{178}\right)\)	\(e\left(\frac{49}{89}\right)\)
\(\chi_{2864}(959,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{25}{178}\right)\)	\(e\left(\frac{58}{89}\right)\)	\(e\left(\frac{47}{178}\right)\)	\(e\left(\frac{25}{89}\right)\)	\(e\left(\frac{1}{178}\right)\)	\(e\left(\frac{75}{89}\right)\)	\(e\left(\frac{141}{178}\right)\)	\(e\left(\frac{53}{89}\right)\)	\(e\left(\frac{57}{178}\right)\)	\(e\left(\frac{36}{89}\right)\)
\(\chi_{2864}(975,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{117}{178}\right)\)	\(e\left(\frac{8}{89}\right)\)	\(e\left(\frac{163}{178}\right)\)	\(e\left(\frac{28}{89}\right)\)	\(e\left(\frac{83}{178}\right)\)	\(e\left(\frac{84}{89}\right)\)	\(e\left(\frac{133}{178}\right)\)	\(e\left(\frac{38}{89}\right)\)	\(e\left(\frac{103}{178}\right)\)	\(e\left(\frac{51}{89}\right)\)
\(\chi_{2864}(1039,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{175}{178}\right)\)	\(e\left(\frac{50}{89}\right)\)	\(e\left(\frac{151}{178}\right)\)	\(e\left(\frac{86}{89}\right)\)	\(e\left(\frac{7}{178}\right)\)	\(e\left(\frac{80}{89}\right)\)	\(e\left(\frac{97}{178}\right)\)	\(e\left(\frac{15}{89}\right)\)	\(e\left(\frac{43}{178}\right)\)	\(e\left(\frac{74}{89}\right)\)

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First 31 of 88 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	2864.r
Modulus	$2864$
Conductor	$716$
Order	$178$
Real	no
Primitive	no
Minimal	yes
Parity	odd

Modulus:	\(2864\)
Conductor:	\(716\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(178\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 716.h	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	odd	sage:chi.is_odd() pari:zncharisodd(g,chi)