LMFDB - Dirichlet character orbit 867.t

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(867, base_ring=CyclotomicField(272)) M = H._module chi = DirichletCharacter(H, M([136,229])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(5,867)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$867$
Conductor:	$867$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$272$	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:	$\Q(\zeta_{272})$
Fixed field:	Number field defined by a degree 272 polynomial (not computed)

First 31 of 128 characters in Galois orbit

Character	$-1$	$1$	$2$	$4$	$5$	$7$	$8$	$10$	$11$	$13$	$14$	$16$
$\chi_{867}(5,\cdot)$	$1$	$1$	$e\left(\frac{63}{136}\right)$	$e\left(\frac{63}{68}\right)$	$e\left(\frac{81}{272}\right)$	$e\left(\frac{135}{272}\right)$	$e\left(\frac{53}{136}\right)$	$e\left(\frac{207}{272}\right)$	$e\left(\frac{235}{272}\right)$	$e\left(\frac{1}{68}\right)$	$e\left(\frac{261}{272}\right)$	$e\left(\frac{29}{34}\right)$
$\chi_{867}(11,\cdot)$	$1$	$1$	$e\left(\frac{77}{136}\right)$	$e\left(\frac{9}{68}\right)$	$e\left(\frac{235}{272}\right)$	$e\left(\frac{29}{272}\right)$	$e\left(\frac{95}{136}\right)$	$e\left(\frac{117}{272}\right)$	$e\left(\frac{121}{272}\right)$	$e\left(\frac{39}{68}\right)$	$e\left(\frac{183}{272}\right)$	$e\left(\frac{9}{34}\right)$
$\chi_{867}(14,\cdot)$	$1$	$1$	$e\left(\frac{67}{136}\right)$	$e\left(\frac{67}{68}\right)$	$e\left(\frac{261}{272}\right)$	$e\left(\frac{163}{272}\right)$	$e\left(\frac{65}{136}\right)$	$e\left(\frac{123}{272}\right)$	$e\left(\frac{183}{272}\right)$	$e\left(\frac{41}{68}\right)$	$e\left(\frac{25}{272}\right)$	$e\left(\frac{33}{34}\right)$
$\chi_{867}(20,\cdot)$	$1$	$1$	$e\left(\frac{123}{136}\right)$	$e\left(\frac{55}{68}\right)$	$e\left(\frac{61}{272}\right)$	$e\left(\frac{11}{272}\right)$	$e\left(\frac{97}{136}\right)$	$e\left(\frac{35}{272}\right)$	$e\left(\frac{271}{272}\right)$	$e\left(\frac{57}{68}\right)$	$e\left(\frac{257}{272}\right)$	$e\left(\frac{21}{34}\right)$
$\chi_{867}(23,\cdot)$	$1$	$1$	$e\left(\frac{37}{136}\right)$	$e\left(\frac{37}{68}\right)$	$e\left(\frac{67}{272}\right)$	$e\left(\frac{21}{272}\right)$	$e\left(\frac{111}{136}\right)$	$e\left(\frac{141}{272}\right)$	$e\left(\frac{97}{272}\right)$	$e\left(\frac{47}{68}\right)$	$e\left(\frac{95}{272}\right)$	$e\left(\frac{3}{34}\right)$
$\chi_{867}(29,\cdot)$	$1$	$1$	$e\left(\frac{111}{136}\right)$	$e\left(\frac{43}{68}\right)$	$e\left(\frac{201}{272}\right)$	$e\left(\frac{63}{272}\right)$	$e\left(\frac{61}{136}\right)$	$e\left(\frac{151}{272}\right)$	$e\left(\frac{19}{272}\right)$	$e\left(\frac{5}{68}\right)$	$e\left(\frac{13}{272}\right)$	$e\left(\frac{9}{34}\right)$
$\chi_{867}(41,\cdot)$	$1$	$1$	$e\left(\frac{129}{136}\right)$	$e\left(\frac{61}{68}\right)$	$e\left(\frac{127}{272}\right)$	$e\left(\frac{121}{272}\right)$	$e\left(\frac{115}{136}\right)$	$e\left(\frac{113}{272}\right)$	$e\left(\frac{261}{272}\right)$	$e\left(\frac{15}{68}\right)$	$e\left(\frac{107}{272}\right)$	$e\left(\frac{27}{34}\right)$
$\chi_{867}(44,\cdot)$	$1$	$1$	$e\left(\frac{1}{136}\right)$	$e\left(\frac{1}{68}\right)$	$e\left(\frac{215}{272}\right)$	$e\left(\frac{177}{272}\right)$	$e\left(\frac{3}{136}\right)$	$e\left(\frac{217}{272}\right)$	$e\left(\frac{157}{272}\right)$	$e\left(\frac{27}{68}\right)$	$e\left(\frac{179}{272}\right)$	$e\left(\frac{1}{34}\right)$
$\chi_{867}(56,\cdot)$	$1$	$1$	$e\left(\frac{127}{136}\right)$	$e\left(\frac{59}{68}\right)$	$e\left(\frac{241}{272}\right)$	$e\left(\frac{39}{272}\right)$	$e\left(\frac{109}{136}\right)$	$e\left(\frac{223}{272}\right)$	$e\left(\frac{219}{272}\right)$	$e\left(\frac{29}{68}\right)$	$e\left(\frac{21}{272}\right)$	$e\left(\frac{25}{34}\right)$
$\chi_{867}(62,\cdot)$	$1$	$1$	$e\left(\frac{69}{136}\right)$	$e\left(\frac{1}{68}\right)$	$e\left(\frac{11}{272}\right)$	$e\left(\frac{109}{272}\right)$	$e\left(\frac{71}{136}\right)$	$e\left(\frac{149}{272}\right)$	$e\left(\frac{89}{272}\right)$	$e\left(\frac{27}{68}\right)$	$e\left(\frac{247}{272}\right)$	$e\left(\frac{1}{34}\right)$
$\chi_{867}(71,\cdot)$	$1$	$1$	$e\left(\frac{3}{136}\right)$	$e\left(\frac{3}{68}\right)$	$e\left(\frac{237}{272}\right)$	$e\left(\frac{123}{272}\right)$	$e\left(\frac{9}{136}\right)$	$e\left(\frac{243}{272}\right)$	$e\left(\frac{63}{272}\right)$	$e\left(\frac{13}{68}\right)$	$e\left(\frac{129}{272}\right)$	$e\left(\frac{3}{34}\right)$
$\chi_{867}(74,\cdot)$	$1$	$1$	$e\left(\frac{45}{136}\right)$	$e\left(\frac{45}{68}\right)$	$e\left(\frac{19}{272}\right)$	$e\left(\frac{213}{272}\right)$	$e\left(\frac{135}{136}\right)$	$e\left(\frac{109}{272}\right)$	$e\left(\frac{129}{272}\right)$	$e\left(\frac{59}{68}\right)$	$e\left(\frac{31}{272}\right)$	$e\left(\frac{11}{34}\right)$
$\chi_{867}(80,\cdot)$	$1$	$1$	$e\left(\frac{47}{136}\right)$	$e\left(\frac{47}{68}\right)$	$e\left(\frac{41}{272}\right)$	$e\left(\frac{159}{272}\right)$	$e\left(\frac{5}{136}\right)$	$e\left(\frac{135}{272}\right)$	$e\left(\frac{35}{272}\right)$	$e\left(\frac{45}{68}\right)$	$e\left(\frac{253}{272}\right)$	$e\left(\frac{13}{34}\right)$
$\chi_{867}(92,\cdot)$	$1$	$1$	$e\left(\frac{97}{136}\right)$	$e\left(\frac{29}{68}\right)$	$e\left(\frac{47}{272}\right)$	$e\left(\frac{169}{272}\right)$	$e\left(\frac{19}{136}\right)$	$e\left(\frac{241}{272}\right)$	$e\left(\frac{133}{272}\right)$	$e\left(\frac{35}{68}\right)$	$e\left(\frac{91}{272}\right)$	$e\left(\frac{29}{34}\right)$
$\chi_{867}(95,\cdot)$	$1$	$1$	$e\left(\frac{33}{136}\right)$	$e\left(\frac{33}{68}\right)$	$e\left(\frac{23}{272}\right)$	$e\left(\frac{129}{272}\right)$	$e\left(\frac{99}{136}\right)$	$e\left(\frac{89}{272}\right)$	$e\left(\frac{13}{272}\right)$	$e\left(\frac{7}{68}\right)$	$e\left(\frac{195}{272}\right)$	$e\left(\frac{33}{34}\right)$
$\chi_{867}(107,\cdot)$	$1$	$1$	$e\left(\frac{55}{136}\right)$	$e\left(\frac{55}{68}\right)$	$e\left(\frac{129}{272}\right)$	$e\left(\frac{215}{272}\right)$	$e\left(\frac{29}{136}\right)$	$e\left(\frac{239}{272}\right)$	$e\left(\frac{203}{272}\right)$	$e\left(\frac{57}{68}\right)$	$e\left(\frac{53}{272}\right)$	$e\left(\frac{21}{34}\right)$
$\chi_{867}(113,\cdot)$	$1$	$1$	$e\left(\frac{61}{136}\right)$	$e\left(\frac{61}{68}\right)$	$e\left(\frac{59}{272}\right)$	$e\left(\frac{189}{272}\right)$	$e\left(\frac{47}{136}\right)$	$e\left(\frac{181}{272}\right)$	$e\left(\frac{57}{272}\right)$	$e\left(\frac{15}{68}\right)$	$e\left(\frac{39}{272}\right)$	$e\left(\frac{27}{34}\right)$
$\chi_{867}(116,\cdot)$	$1$	$1$	$e\left(\frac{35}{136}\right)$	$e\left(\frac{35}{68}\right)$	$e\left(\frac{181}{272}\right)$	$e\left(\frac{211}{272}\right)$	$e\left(\frac{105}{136}\right)$	$e\left(\frac{251}{272}\right)$	$e\left(\frac{55}{272}\right)$	$e\left(\frac{61}{68}\right)$	$e\left(\frac{9}{272}\right)$	$e\left(\frac{1}{34}\right)$
$\chi_{867}(122,\cdot)$	$1$	$1$	$e\left(\frac{19}{136}\right)$	$e\left(\frac{19}{68}\right)$	$e\left(\frac{141}{272}\right)$	$e\left(\frac{235}{272}\right)$	$e\left(\frac{57}{136}\right)$	$e\left(\frac{179}{272}\right)$	$e\left(\frac{127}{272}\right)$	$e\left(\frac{37}{68}\right)$	$e\left(\frac{1}{272}\right)$	$e\left(\frac{19}{34}\right)$
$\chi_{867}(125,\cdot)$	$1$	$1$	$e\left(\frac{53}{136}\right)$	$e\left(\frac{53}{68}\right)$	$e\left(\frac{243}{272}\right)$	$e\left(\frac{133}{272}\right)$	$e\left(\frac{23}{136}\right)$	$e\left(\frac{77}{272}\right)$	$e\left(\frac{161}{272}\right)$	$e\left(\frac{3}{68}\right)$	$e\left(\frac{239}{272}\right)$	$e\left(\frac{19}{34}\right)$
$\chi_{867}(143,\cdot)$	$1$	$1$	$e\left(\frac{65}{136}\right)$	$e\left(\frac{65}{68}\right)$	$e\left(\frac{239}{272}\right)$	$e\left(\frac{217}{272}\right)$	$e\left(\frac{59}{136}\right)$	$e\left(\frac{97}{272}\right)$	$e\left(\frac{5}{272}\right)$	$e\left(\frac{55}{68}\right)$	$e\left(\frac{75}{272}\right)$	$e\left(\frac{31}{34}\right)$
$\chi_{867}(146,\cdot)$	$1$	$1$	$e\left(\frac{65}{136}\right)$	$e\left(\frac{65}{68}\right)$	$e\left(\frac{103}{272}\right)$	$e\left(\frac{81}{272}\right)$	$e\left(\frac{59}{136}\right)$	$e\left(\frac{233}{272}\right)$	$e\left(\frac{141}{272}\right)$	$e\left(\frac{55}{68}\right)$	$e\left(\frac{211}{272}\right)$	$e\left(\frac{31}{34}\right)$
$\chi_{867}(164,\cdot)$	$1$	$1$	$e\left(\frac{53}{136}\right)$	$e\left(\frac{53}{68}\right)$	$e\left(\frac{107}{272}\right)$	$e\left(\frac{269}{272}\right)$	$e\left(\frac{23}{136}\right)$	$e\left(\frac{213}{272}\right)$	$e\left(\frac{25}{272}\right)$	$e\left(\frac{3}{68}\right)$	$e\left(\frac{103}{272}\right)$	$e\left(\frac{19}{34}\right)$
$\chi_{867}(167,\cdot)$	$1$	$1$	$e\left(\frac{19}{136}\right)$	$e\left(\frac{19}{68}\right)$	$e\left(\frac{5}{272}\right)$	$e\left(\frac{99}{272}\right)$	$e\left(\frac{57}{136}\right)$	$e\left(\frac{43}{272}\right)$	$e\left(\frac{263}{272}\right)$	$e\left(\frac{37}{68}\right)$	$e\left(\frac{137}{272}\right)$	$e\left(\frac{19}{34}\right)$
$\chi_{867}(173,\cdot)$	$1$	$1$	$e\left(\frac{35}{136}\right)$	$e\left(\frac{35}{68}\right)$	$e\left(\frac{45}{272}\right)$	$e\left(\frac{75}{272}\right)$	$e\left(\frac{105}{136}\right)$	$e\left(\frac{115}{272}\right)$	$e\left(\frac{191}{272}\right)$	$e\left(\frac{61}{68}\right)$	$e\left(\frac{145}{272}\right)$	$e\left(\frac{1}{34}\right)$
$\chi_{867}(176,\cdot)$	$1$	$1$	$e\left(\frac{61}{136}\right)$	$e\left(\frac{61}{68}\right)$	$e\left(\frac{195}{272}\right)$	$e\left(\frac{53}{272}\right)$	$e\left(\frac{47}{136}\right)$	$e\left(\frac{45}{272}\right)$	$e\left(\frac{193}{272}\right)$	$e\left(\frac{15}{68}\right)$	$e\left(\frac{175}{272}\right)$	$e\left(\frac{27}{34}\right)$
$\chi_{867}(182,\cdot)$	$1$	$1$	$e\left(\frac{55}{136}\right)$	$e\left(\frac{55}{68}\right)$	$e\left(\frac{265}{272}\right)$	$e\left(\frac{79}{272}\right)$	$e\left(\frac{29}{136}\right)$	$e\left(\frac{103}{272}\right)$	$e\left(\frac{67}{272}\right)$	$e\left(\frac{57}{68}\right)$	$e\left(\frac{189}{272}\right)$	$e\left(\frac{21}{34}\right)$
$\chi_{867}(194,\cdot)$	$1$	$1$	$e\left(\frac{33}{136}\right)$	$e\left(\frac{33}{68}\right)$	$e\left(\frac{159}{272}\right)$	$e\left(\frac{265}{272}\right)$	$e\left(\frac{99}{136}\right)$	$e\left(\frac{225}{272}\right)$	$e\left(\frac{149}{272}\right)$	$e\left(\frac{7}{68}\right)$	$e\left(\frac{59}{272}\right)$	$e\left(\frac{33}{34}\right)$
$\chi_{867}(197,\cdot)$	$1$	$1$	$e\left(\frac{97}{136}\right)$	$e\left(\frac{29}{68}\right)$	$e\left(\frac{183}{272}\right)$	$e\left(\frac{33}{272}\right)$	$e\left(\frac{19}{136}\right)$	$e\left(\frac{105}{272}\right)$	$e\left(\frac{269}{272}\right)$	$e\left(\frac{35}{68}\right)$	$e\left(\frac{227}{272}\right)$	$e\left(\frac{29}{34}\right)$
$\chi_{867}(209,\cdot)$	$1$	$1$	$e\left(\frac{47}{136}\right)$	$e\left(\frac{47}{68}\right)$	$e\left(\frac{177}{272}\right)$	$e\left(\frac{23}{272}\right)$	$e\left(\frac{5}{136}\right)$	$e\left(\frac{271}{272}\right)$	$e\left(\frac{171}{272}\right)$	$e\left(\frac{45}{68}\right)$	$e\left(\frac{117}{272}\right)$	$e\left(\frac{13}{34}\right)$
$\chi_{867}(215,\cdot)$	$1$	$1$	$e\left(\frac{45}{136}\right)$	$e\left(\frac{45}{68}\right)$	$e\left(\frac{155}{272}\right)$	$e\left(\frac{77}{272}\right)$	$e\left(\frac{135}{136}\right)$	$e\left(\frac{245}{272}\right)$	$e\left(\frac{265}{272}\right)$	$e\left(\frac{59}{68}\right)$	$e\left(\frac{167}{272}\right)$	$e\left(\frac{11}{34}\right)$

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	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(7\)	\(8\)	\(10\)	\(11\)	\(13\)	\(14\)	\(16\)
\(\chi_{867}(5,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{63}{136}\right)\)	\(e\left(\frac{63}{68}\right)\)	\(e\left(\frac{81}{272}\right)\)	\(e\left(\frac{135}{272}\right)\)	\(e\left(\frac{53}{136}\right)\)	\(e\left(\frac{207}{272}\right)\)	\(e\left(\frac{235}{272}\right)\)	\(e\left(\frac{1}{68}\right)\)	\(e\left(\frac{261}{272}\right)\)	\(e\left(\frac{29}{34}\right)\)
\(\chi_{867}(11,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{77}{136}\right)\)	\(e\left(\frac{9}{68}\right)\)	\(e\left(\frac{235}{272}\right)\)	\(e\left(\frac{29}{272}\right)\)	\(e\left(\frac{95}{136}\right)\)	\(e\left(\frac{117}{272}\right)\)	\(e\left(\frac{121}{272}\right)\)	\(e\left(\frac{39}{68}\right)\)	\(e\left(\frac{183}{272}\right)\)	\(e\left(\frac{9}{34}\right)\)
\(\chi_{867}(14,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{67}{136}\right)\)	\(e\left(\frac{67}{68}\right)\)	\(e\left(\frac{261}{272}\right)\)	\(e\left(\frac{163}{272}\right)\)	\(e\left(\frac{65}{136}\right)\)	\(e\left(\frac{123}{272}\right)\)	\(e\left(\frac{183}{272}\right)\)	\(e\left(\frac{41}{68}\right)\)	\(e\left(\frac{25}{272}\right)\)	\(e\left(\frac{33}{34}\right)\)
\(\chi_{867}(20,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{123}{136}\right)\)	\(e\left(\frac{55}{68}\right)\)	\(e\left(\frac{61}{272}\right)\)	\(e\left(\frac{11}{272}\right)\)	\(e\left(\frac{97}{136}\right)\)	\(e\left(\frac{35}{272}\right)\)	\(e\left(\frac{271}{272}\right)\)	\(e\left(\frac{57}{68}\right)\)	\(e\left(\frac{257}{272}\right)\)	\(e\left(\frac{21}{34}\right)\)
\(\chi_{867}(23,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{136}\right)\)	\(e\left(\frac{37}{68}\right)\)	\(e\left(\frac{67}{272}\right)\)	\(e\left(\frac{21}{272}\right)\)	\(e\left(\frac{111}{136}\right)\)	\(e\left(\frac{141}{272}\right)\)	\(e\left(\frac{97}{272}\right)\)	\(e\left(\frac{47}{68}\right)\)	\(e\left(\frac{95}{272}\right)\)	\(e\left(\frac{3}{34}\right)\)
\(\chi_{867}(29,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{111}{136}\right)\)	\(e\left(\frac{43}{68}\right)\)	\(e\left(\frac{201}{272}\right)\)	\(e\left(\frac{63}{272}\right)\)	\(e\left(\frac{61}{136}\right)\)	\(e\left(\frac{151}{272}\right)\)	\(e\left(\frac{19}{272}\right)\)	\(e\left(\frac{5}{68}\right)\)	\(e\left(\frac{13}{272}\right)\)	\(e\left(\frac{9}{34}\right)\)
\(\chi_{867}(41,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{129}{136}\right)\)	\(e\left(\frac{61}{68}\right)\)	\(e\left(\frac{127}{272}\right)\)	\(e\left(\frac{121}{272}\right)\)	\(e\left(\frac{115}{136}\right)\)	\(e\left(\frac{113}{272}\right)\)	\(e\left(\frac{261}{272}\right)\)	\(e\left(\frac{15}{68}\right)\)	\(e\left(\frac{107}{272}\right)\)	\(e\left(\frac{27}{34}\right)\)
\(\chi_{867}(44,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{136}\right)\)	\(e\left(\frac{1}{68}\right)\)	\(e\left(\frac{215}{272}\right)\)	\(e\left(\frac{177}{272}\right)\)	\(e\left(\frac{3}{136}\right)\)	\(e\left(\frac{217}{272}\right)\)	\(e\left(\frac{157}{272}\right)\)	\(e\left(\frac{27}{68}\right)\)	\(e\left(\frac{179}{272}\right)\)	\(e\left(\frac{1}{34}\right)\)
\(\chi_{867}(56,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{127}{136}\right)\)	\(e\left(\frac{59}{68}\right)\)	\(e\left(\frac{241}{272}\right)\)	\(e\left(\frac{39}{272}\right)\)	\(e\left(\frac{109}{136}\right)\)	\(e\left(\frac{223}{272}\right)\)	\(e\left(\frac{219}{272}\right)\)	\(e\left(\frac{29}{68}\right)\)	\(e\left(\frac{21}{272}\right)\)	\(e\left(\frac{25}{34}\right)\)
\(\chi_{867}(62,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{69}{136}\right)\)	\(e\left(\frac{1}{68}\right)\)	\(e\left(\frac{11}{272}\right)\)	\(e\left(\frac{109}{272}\right)\)	\(e\left(\frac{71}{136}\right)\)	\(e\left(\frac{149}{272}\right)\)	\(e\left(\frac{89}{272}\right)\)	\(e\left(\frac{27}{68}\right)\)	\(e\left(\frac{247}{272}\right)\)	\(e\left(\frac{1}{34}\right)\)
\(\chi_{867}(71,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{136}\right)\)	\(e\left(\frac{3}{68}\right)\)	\(e\left(\frac{237}{272}\right)\)	\(e\left(\frac{123}{272}\right)\)	\(e\left(\frac{9}{136}\right)\)	\(e\left(\frac{243}{272}\right)\)	\(e\left(\frac{63}{272}\right)\)	\(e\left(\frac{13}{68}\right)\)	\(e\left(\frac{129}{272}\right)\)	\(e\left(\frac{3}{34}\right)\)
\(\chi_{867}(74,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{45}{136}\right)\)	\(e\left(\frac{45}{68}\right)\)	\(e\left(\frac{19}{272}\right)\)	\(e\left(\frac{213}{272}\right)\)	\(e\left(\frac{135}{136}\right)\)	\(e\left(\frac{109}{272}\right)\)	\(e\left(\frac{129}{272}\right)\)	\(e\left(\frac{59}{68}\right)\)	\(e\left(\frac{31}{272}\right)\)	\(e\left(\frac{11}{34}\right)\)
\(\chi_{867}(80,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{136}\right)\)	\(e\left(\frac{47}{68}\right)\)	\(e\left(\frac{41}{272}\right)\)	\(e\left(\frac{159}{272}\right)\)	\(e\left(\frac{5}{136}\right)\)	\(e\left(\frac{135}{272}\right)\)	\(e\left(\frac{35}{272}\right)\)	\(e\left(\frac{45}{68}\right)\)	\(e\left(\frac{253}{272}\right)\)	\(e\left(\frac{13}{34}\right)\)
\(\chi_{867}(92,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{97}{136}\right)\)	\(e\left(\frac{29}{68}\right)\)	\(e\left(\frac{47}{272}\right)\)	\(e\left(\frac{169}{272}\right)\)	\(e\left(\frac{19}{136}\right)\)	\(e\left(\frac{241}{272}\right)\)	\(e\left(\frac{133}{272}\right)\)	\(e\left(\frac{35}{68}\right)\)	\(e\left(\frac{91}{272}\right)\)	\(e\left(\frac{29}{34}\right)\)
\(\chi_{867}(95,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{33}{136}\right)\)	\(e\left(\frac{33}{68}\right)\)	\(e\left(\frac{23}{272}\right)\)	\(e\left(\frac{129}{272}\right)\)	\(e\left(\frac{99}{136}\right)\)	\(e\left(\frac{89}{272}\right)\)	\(e\left(\frac{13}{272}\right)\)	\(e\left(\frac{7}{68}\right)\)	\(e\left(\frac{195}{272}\right)\)	\(e\left(\frac{33}{34}\right)\)
\(\chi_{867}(107,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{55}{136}\right)\)	\(e\left(\frac{55}{68}\right)\)	\(e\left(\frac{129}{272}\right)\)	\(e\left(\frac{215}{272}\right)\)	\(e\left(\frac{29}{136}\right)\)	\(e\left(\frac{239}{272}\right)\)	\(e\left(\frac{203}{272}\right)\)	\(e\left(\frac{57}{68}\right)\)	\(e\left(\frac{53}{272}\right)\)	\(e\left(\frac{21}{34}\right)\)
\(\chi_{867}(113,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{61}{136}\right)\)	\(e\left(\frac{61}{68}\right)\)	\(e\left(\frac{59}{272}\right)\)	\(e\left(\frac{189}{272}\right)\)	\(e\left(\frac{47}{136}\right)\)	\(e\left(\frac{181}{272}\right)\)	\(e\left(\frac{57}{272}\right)\)	\(e\left(\frac{15}{68}\right)\)	\(e\left(\frac{39}{272}\right)\)	\(e\left(\frac{27}{34}\right)\)
\(\chi_{867}(116,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{35}{136}\right)\)	\(e\left(\frac{35}{68}\right)\)	\(e\left(\frac{181}{272}\right)\)	\(e\left(\frac{211}{272}\right)\)	\(e\left(\frac{105}{136}\right)\)	\(e\left(\frac{251}{272}\right)\)	\(e\left(\frac{55}{272}\right)\)	\(e\left(\frac{61}{68}\right)\)	\(e\left(\frac{9}{272}\right)\)	\(e\left(\frac{1}{34}\right)\)
\(\chi_{867}(122,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{136}\right)\)	\(e\left(\frac{19}{68}\right)\)	\(e\left(\frac{141}{272}\right)\)	\(e\left(\frac{235}{272}\right)\)	\(e\left(\frac{57}{136}\right)\)	\(e\left(\frac{179}{272}\right)\)	\(e\left(\frac{127}{272}\right)\)	\(e\left(\frac{37}{68}\right)\)	\(e\left(\frac{1}{272}\right)\)	\(e\left(\frac{19}{34}\right)\)
\(\chi_{867}(125,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{136}\right)\)	\(e\left(\frac{53}{68}\right)\)	\(e\left(\frac{243}{272}\right)\)	\(e\left(\frac{133}{272}\right)\)	\(e\left(\frac{23}{136}\right)\)	\(e\left(\frac{77}{272}\right)\)	\(e\left(\frac{161}{272}\right)\)	\(e\left(\frac{3}{68}\right)\)	\(e\left(\frac{239}{272}\right)\)	\(e\left(\frac{19}{34}\right)\)
\(\chi_{867}(143,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{65}{136}\right)\)	\(e\left(\frac{65}{68}\right)\)	\(e\left(\frac{239}{272}\right)\)	\(e\left(\frac{217}{272}\right)\)	\(e\left(\frac{59}{136}\right)\)	\(e\left(\frac{97}{272}\right)\)	\(e\left(\frac{5}{272}\right)\)	\(e\left(\frac{55}{68}\right)\)	\(e\left(\frac{75}{272}\right)\)	\(e\left(\frac{31}{34}\right)\)
\(\chi_{867}(146,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{65}{136}\right)\)	\(e\left(\frac{65}{68}\right)\)	\(e\left(\frac{103}{272}\right)\)	\(e\left(\frac{81}{272}\right)\)	\(e\left(\frac{59}{136}\right)\)	\(e\left(\frac{233}{272}\right)\)	\(e\left(\frac{141}{272}\right)\)	\(e\left(\frac{55}{68}\right)\)	\(e\left(\frac{211}{272}\right)\)	\(e\left(\frac{31}{34}\right)\)
\(\chi_{867}(164,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{136}\right)\)	\(e\left(\frac{53}{68}\right)\)	\(e\left(\frac{107}{272}\right)\)	\(e\left(\frac{269}{272}\right)\)	\(e\left(\frac{23}{136}\right)\)	\(e\left(\frac{213}{272}\right)\)	\(e\left(\frac{25}{272}\right)\)	\(e\left(\frac{3}{68}\right)\)	\(e\left(\frac{103}{272}\right)\)	\(e\left(\frac{19}{34}\right)\)
\(\chi_{867}(167,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{136}\right)\)	\(e\left(\frac{19}{68}\right)\)	\(e\left(\frac{5}{272}\right)\)	\(e\left(\frac{99}{272}\right)\)	\(e\left(\frac{57}{136}\right)\)	\(e\left(\frac{43}{272}\right)\)	\(e\left(\frac{263}{272}\right)\)	\(e\left(\frac{37}{68}\right)\)	\(e\left(\frac{137}{272}\right)\)	\(e\left(\frac{19}{34}\right)\)
\(\chi_{867}(173,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{35}{136}\right)\)	\(e\left(\frac{35}{68}\right)\)	\(e\left(\frac{45}{272}\right)\)	\(e\left(\frac{75}{272}\right)\)	\(e\left(\frac{105}{136}\right)\)	\(e\left(\frac{115}{272}\right)\)	\(e\left(\frac{191}{272}\right)\)	\(e\left(\frac{61}{68}\right)\)	\(e\left(\frac{145}{272}\right)\)	\(e\left(\frac{1}{34}\right)\)
\(\chi_{867}(176,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{61}{136}\right)\)	\(e\left(\frac{61}{68}\right)\)	\(e\left(\frac{195}{272}\right)\)	\(e\left(\frac{53}{272}\right)\)	\(e\left(\frac{47}{136}\right)\)	\(e\left(\frac{45}{272}\right)\)	\(e\left(\frac{193}{272}\right)\)	\(e\left(\frac{15}{68}\right)\)	\(e\left(\frac{175}{272}\right)\)	\(e\left(\frac{27}{34}\right)\)
\(\chi_{867}(182,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{55}{136}\right)\)	\(e\left(\frac{55}{68}\right)\)	\(e\left(\frac{265}{272}\right)\)	\(e\left(\frac{79}{272}\right)\)	\(e\left(\frac{29}{136}\right)\)	\(e\left(\frac{103}{272}\right)\)	\(e\left(\frac{67}{272}\right)\)	\(e\left(\frac{57}{68}\right)\)	\(e\left(\frac{189}{272}\right)\)	\(e\left(\frac{21}{34}\right)\)
\(\chi_{867}(194,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{33}{136}\right)\)	\(e\left(\frac{33}{68}\right)\)	\(e\left(\frac{159}{272}\right)\)	\(e\left(\frac{265}{272}\right)\)	\(e\left(\frac{99}{136}\right)\)	\(e\left(\frac{225}{272}\right)\)	\(e\left(\frac{149}{272}\right)\)	\(e\left(\frac{7}{68}\right)\)	\(e\left(\frac{59}{272}\right)\)	\(e\left(\frac{33}{34}\right)\)
\(\chi_{867}(197,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{97}{136}\right)\)	\(e\left(\frac{29}{68}\right)\)	\(e\left(\frac{183}{272}\right)\)	\(e\left(\frac{33}{272}\right)\)	\(e\left(\frac{19}{136}\right)\)	\(e\left(\frac{105}{272}\right)\)	\(e\left(\frac{269}{272}\right)\)	\(e\left(\frac{35}{68}\right)\)	\(e\left(\frac{227}{272}\right)\)	\(e\left(\frac{29}{34}\right)\)
\(\chi_{867}(209,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{136}\right)\)	\(e\left(\frac{47}{68}\right)\)	\(e\left(\frac{177}{272}\right)\)	\(e\left(\frac{23}{272}\right)\)	\(e\left(\frac{5}{136}\right)\)	\(e\left(\frac{271}{272}\right)\)	\(e\left(\frac{171}{272}\right)\)	\(e\left(\frac{45}{68}\right)\)	\(e\left(\frac{117}{272}\right)\)	\(e\left(\frac{13}{34}\right)\)
\(\chi_{867}(215,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{45}{136}\right)\)	\(e\left(\frac{45}{68}\right)\)	\(e\left(\frac{155}{272}\right)\)	\(e\left(\frac{77}{272}\right)\)	\(e\left(\frac{135}{136}\right)\)	\(e\left(\frac{245}{272}\right)\)	\(e\left(\frac{265}{272}\right)\)	\(e\left(\frac{59}{68}\right)\)	\(e\left(\frac{167}{272}\right)\)	\(e\left(\frac{11}{34}\right)\)

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First 31 of 128 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	867.t
Modulus	$867$
Conductor	$867$
Order	$272$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(867\)
Conductor:	\(867\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(272\)	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)