LMFDB - Dirichlet character orbit 8041.ga

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(8041, base_ring=CyclotomicField(1680)) M = H._module chi = DirichletCharacter(H, M([1512,735,200])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(28,8041)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$8041$
Conductor:	$8041$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$1680$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	yes	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:	$\Q(\zeta_{1680})$
Fixed field:	Number field defined by a degree 1680 polynomial (not computed)

First 31 of 384 characters in Galois orbit

Character	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$12$
$\chi_{8041}(28,\cdot)$	$-1$	$1$	$e\left(\frac{67}{280}\right)$	$e\left(\frac{1271}{1680}\right)$	$e\left(\frac{67}{140}\right)$	$e\left(\frac{1283}{1680}\right)$	$e\left(\frac{239}{240}\right)$	$e\left(\frac{67}{240}\right)$	$e\left(\frac{201}{280}\right)$	$e\left(\frac{431}{840}\right)$	$e\left(\frac{1}{336}\right)$	$e\left(\frac{79}{336}\right)$
$\chi_{8041}(29,\cdot)$	$-1$	$1$	$e\left(\frac{121}{280}\right)$	$e\left(\frac{653}{1680}\right)$	$e\left(\frac{121}{140}\right)$	$e\left(\frac{449}{1680}\right)$	$e\left(\frac{197}{240}\right)$	$e\left(\frac{1}{240}\right)$	$e\left(\frac{83}{280}\right)$	$e\left(\frac{653}{840}\right)$	$e\left(\frac{235}{336}\right)$	$e\left(\frac{85}{336}\right)$
$\chi_{8041}(46,\cdot)$	$-1$	$1$	$e\left(\frac{33}{280}\right)$	$e\left(\frac{1069}{1680}\right)$	$e\left(\frac{33}{140}\right)$	$e\left(\frac{97}{1680}\right)$	$e\left(\frac{181}{240}\right)$	$e\left(\frac{113}{240}\right)$	$e\left(\frac{99}{280}\right)$	$e\left(\frac{229}{840}\right)$	$e\left(\frac{59}{336}\right)$	$e\left(\frac{293}{336}\right)$
$\chi_{8041}(61,\cdot)$	$-1$	$1$	$e\left(\frac{47}{280}\right)$	$e\left(\frac{131}{1680}\right)$	$e\left(\frac{47}{140}\right)$	$e\left(\frac{1343}{1680}\right)$	$e\left(\frac{59}{240}\right)$	$e\left(\frac{127}{240}\right)$	$e\left(\frac{141}{280}\right)$	$e\left(\frac{131}{840}\right)$	$e\left(\frac{325}{336}\right)$	$e\left(\frac{139}{336}\right)$
$\chi_{8041}(62,\cdot)$	$-1$	$1$	$e\left(\frac{11}{280}\right)$	$e\left(\frac{823}{1680}\right)$	$e\left(\frac{11}{140}\right)$	$e\left(\frac{499}{1680}\right)$	$e\left(\frac{127}{240}\right)$	$e\left(\frac{131}{240}\right)$	$e\left(\frac{33}{280}\right)$	$e\left(\frac{823}{840}\right)$	$e\left(\frac{113}{336}\right)$	$e\left(\frac{191}{336}\right)$
$\chi_{8041}(63,\cdot)$	$-1$	$1$	$e\left(\frac{129}{280}\right)$	$e\left(\frac{157}{1680}\right)$	$e\left(\frac{129}{140}\right)$	$e\left(\frac{481}{1680}\right)$	$e\left(\frac{133}{240}\right)$	$e\left(\frac{209}{240}\right)$	$e\left(\frac{107}{280}\right)$	$e\left(\frac{157}{840}\right)$	$e\left(\frac{251}{336}\right)$	$e\left(\frac{5}{336}\right)$
$\chi_{8041}(73,\cdot)$	$-1$	$1$	$e\left(\frac{41}{280}\right)$	$e\left(\frac{293}{1680}\right)$	$e\left(\frac{41}{140}\right)$	$e\left(\frac{1529}{1680}\right)$	$e\left(\frac{77}{240}\right)$	$e\left(\frac{121}{240}\right)$	$e\left(\frac{123}{280}\right)$	$e\left(\frac{293}{840}\right)$	$e\left(\frac{19}{336}\right)$	$e\left(\frac{157}{336}\right)$
$\chi_{8041}(105,\cdot)$	$-1$	$1$	$e\left(\frac{277}{280}\right)$	$e\left(\frac{1201}{1680}\right)$	$e\left(\frac{137}{140}\right)$	$e\left(\frac{373}{1680}\right)$	$e\left(\frac{169}{240}\right)$	$e\left(\frac{197}{240}\right)$	$e\left(\frac{271}{280}\right)$	$e\left(\frac{361}{840}\right)$	$e\left(\frac{71}{336}\right)$	$e\left(\frac{233}{336}\right)$
$\chi_{8041}(112,\cdot)$	$-1$	$1$	$e\left(\frac{183}{280}\right)$	$e\left(\frac{659}{1680}\right)$	$e\left(\frac{43}{140}\right)$	$e\left(\frac{767}{1680}\right)$	$e\left(\frac{11}{240}\right)$	$e\left(\frac{223}{240}\right)$	$e\left(\frac{269}{280}\right)$	$e\left(\frac{659}{840}\right)$	$e\left(\frac{37}{336}\right)$	$e\left(\frac{235}{336}\right)$
$\chi_{8041}(116,\cdot)$	$-1$	$1$	$e\left(\frac{237}{280}\right)$	$e\left(\frac{41}{1680}\right)$	$e\left(\frac{97}{140}\right)$	$e\left(\frac{1613}{1680}\right)$	$e\left(\frac{209}{240}\right)$	$e\left(\frac{157}{240}\right)$	$e\left(\frac{151}{280}\right)$	$e\left(\frac{41}{840}\right)$	$e\left(\frac{271}{336}\right)$	$e\left(\frac{241}{336}\right)$
$\chi_{8041}(184,\cdot)$	$-1$	$1$	$e\left(\frac{149}{280}\right)$	$e\left(\frac{457}{1680}\right)$	$e\left(\frac{9}{140}\right)$	$e\left(\frac{1261}{1680}\right)$	$e\left(\frac{193}{240}\right)$	$e\left(\frac{29}{240}\right)$	$e\left(\frac{167}{280}\right)$	$e\left(\frac{457}{840}\right)$	$e\left(\frac{95}{336}\right)$	$e\left(\frac{113}{336}\right)$
$\chi_{8041}(227,\cdot)$	$-1$	$1$	$e\left(\frac{51}{280}\right)$	$e\left(\frac{1423}{1680}\right)$	$e\left(\frac{51}{140}\right)$	$e\left(\frac{379}{1680}\right)$	$e\left(\frac{7}{240}\right)$	$e\left(\frac{11}{240}\right)$	$e\left(\frac{153}{280}\right)$	$e\left(\frac{583}{840}\right)$	$e\left(\frac{137}{336}\right)$	$e\left(\frac{71}{336}\right)$
$\chi_{8041}(233,\cdot)$	$-1$	$1$	$e\left(\frac{33}{280}\right)$	$e\left(\frac{509}{1680}\right)$	$e\left(\frac{33}{140}\right)$	$e\left(\frac{1217}{1680}\right)$	$e\left(\frac{101}{240}\right)$	$e\left(\frac{193}{240}\right)$	$e\left(\frac{99}{280}\right)$	$e\left(\frac{509}{840}\right)$	$e\left(\frac{283}{336}\right)$	$e\left(\frac{181}{336}\right)$
$\chi_{8041}(244,\cdot)$	$-1$	$1$	$e\left(\frac{163}{280}\right)$	$e\left(\frac{1199}{1680}\right)$	$e\left(\frac{23}{140}\right)$	$e\left(\frac{827}{1680}\right)$	$e\left(\frac{71}{240}\right)$	$e\left(\frac{43}{240}\right)$	$e\left(\frac{209}{280}\right)$	$e\left(\frac{359}{840}\right)$	$e\left(\frac{25}{336}\right)$	$e\left(\frac{295}{336}\right)$
$\chi_{8041}(248,\cdot)$	$-1$	$1$	$e\left(\frac{127}{280}\right)$	$e\left(\frac{211}{1680}\right)$	$e\left(\frac{127}{140}\right)$	$e\left(\frac{1663}{1680}\right)$	$e\left(\frac{139}{240}\right)$	$e\left(\frac{47}{240}\right)$	$e\left(\frac{101}{280}\right)$	$e\left(\frac{211}{840}\right)$	$e\left(\frac{149}{336}\right)$	$e\left(\frac{11}{336}\right)$
$\chi_{8041}(249,\cdot)$	$-1$	$1$	$e\left(\frac{171}{280}\right)$	$e\left(\frac{983}{1680}\right)$	$e\left(\frac{31}{140}\right)$	$e\left(\frac{1139}{1680}\right)$	$e\left(\frac{47}{240}\right)$	$e\left(\frac{211}{240}\right)$	$e\left(\frac{233}{280}\right)$	$e\left(\frac{143}{840}\right)$	$e\left(\frac{97}{336}\right)$	$e\left(\frac{271}{336}\right)$
$\chi_{8041}(261,\cdot)$	$-1$	$1$	$e\left(\frac{19}{280}\right)$	$e\left(\frac{607}{1680}\right)$	$e\left(\frac{19}{140}\right)$	$e\left(\frac{811}{1680}\right)$	$e\left(\frac{103}{240}\right)$	$e\left(\frac{59}{240}\right)$	$e\left(\frac{57}{280}\right)$	$e\left(\frac{607}{840}\right)$	$e\left(\frac{185}{336}\right)$	$e\left(\frac{167}{336}\right)$
$\chi_{8041}(277,\cdot)$	$-1$	$1$	$e\left(\frac{193}{280}\right)$	$e\left(\frac{949}{1680}\right)$	$e\left(\frac{53}{140}\right)$	$e\left(\frac{457}{1680}\right)$	$e\left(\frac{61}{240}\right)$	$e\left(\frac{233}{240}\right)$	$e\left(\frac{19}{280}\right)$	$e\left(\frac{109}{840}\right)$	$e\left(\frac{323}{336}\right)$	$e\left(\frac{317}{336}\right)$
$\chi_{8041}(292,\cdot)$	$-1$	$1$	$e\left(\frac{157}{280}\right)$	$e\left(\frac{1361}{1680}\right)$	$e\left(\frac{17}{140}\right)$	$e\left(\frac{1013}{1680}\right)$	$e\left(\frac{89}{240}\right)$	$e\left(\frac{37}{240}\right)$	$e\left(\frac{191}{280}\right)$	$e\left(\frac{521}{840}\right)$	$e\left(\frac{55}{336}\right)$	$e\left(\frac{313}{336}\right)$
$\chi_{8041}(347,\cdot)$	$-1$	$1$	$e\left(\frac{47}{280}\right)$	$e\left(\frac{1531}{1680}\right)$	$e\left(\frac{47}{140}\right)$	$e\left(\frac{1063}{1680}\right)$	$e\left(\frac{19}{240}\right)$	$e\left(\frac{167}{240}\right)$	$e\left(\frac{141}{280}\right)$	$e\left(\frac{691}{840}\right)$	$e\left(\frac{269}{336}\right)$	$e\left(\frac{83}{336}\right)$
$\chi_{8041}(413,\cdot)$	$-1$	$1$	$e\left(\frac{57}{280}\right)$	$e\left(\frac{1541}{1680}\right)$	$e\left(\frac{57}{140}\right)$	$e\left(\frac{473}{1680}\right)$	$e\left(\frac{29}{240}\right)$	$e\left(\frac{217}{240}\right)$	$e\left(\frac{171}{280}\right)$	$e\left(\frac{701}{840}\right)$	$e\left(\frac{163}{336}\right)$	$e\left(\frac{109}{336}\right)$
$\chi_{8041}(415,\cdot)$	$-1$	$1$	$e\left(\frac{39}{280}\right)$	$e\left(\frac{347}{1680}\right)$	$e\left(\frac{39}{140}\right)$	$e\left(\frac{1031}{1680}\right)$	$e\left(\frac{83}{240}\right)$	$e\left(\frac{199}{240}\right)$	$e\left(\frac{117}{280}\right)$	$e\left(\frac{347}{840}\right)$	$e\left(\frac{253}{336}\right)$	$e\left(\frac{163}{336}\right)$
$\chi_{8041}(420,\cdot)$	$-1$	$1$	$e\left(\frac{113}{280}\right)$	$e\left(\frac{589}{1680}\right)$	$e\left(\frac{113}{140}\right)$	$e\left(\frac{1537}{1680}\right)$	$e\left(\frac{181}{240}\right)$	$e\left(\frac{113}{240}\right)$	$e\left(\frac{59}{280}\right)$	$e\left(\frac{589}{840}\right)$	$e\left(\frac{107}{336}\right)$	$e\left(\frac{53}{336}\right)$
$\chi_{8041}(435,\cdot)$	$-1$	$1$	$e\left(\frac{167}{280}\right)$	$e\left(\frac{1651}{1680}\right)$	$e\left(\frac{27}{140}\right)$	$e\left(\frac{703}{1680}\right)$	$e\left(\frac{139}{240}\right)$	$e\left(\frac{47}{240}\right)$	$e\left(\frac{221}{280}\right)$	$e\left(\frac{811}{840}\right)$	$e\left(\frac{5}{336}\right)$	$e\left(\frac{59}{336}\right)$
$\chi_{8041}(448,\cdot)$	$-1$	$1$	$e\left(\frac{19}{280}\right)$	$e\left(\frac{47}{1680}\right)$	$e\left(\frac{19}{140}\right)$	$e\left(\frac{251}{1680}\right)$	$e\left(\frac{23}{240}\right)$	$e\left(\frac{139}{240}\right)$	$e\left(\frac{57}{280}\right)$	$e\left(\frac{47}{840}\right)$	$e\left(\frac{73}{336}\right)$	$e\left(\frac{55}{336}\right)$
$\chi_{8041}(464,\cdot)$	$-1$	$1$	$e\left(\frac{73}{280}\right)$	$e\left(\frac{1109}{1680}\right)$	$e\left(\frac{73}{140}\right)$	$e\left(\frac{1097}{1680}\right)$	$e\left(\frac{221}{240}\right)$	$e\left(\frac{73}{240}\right)$	$e\left(\frac{219}{280}\right)$	$e\left(\frac{269}{840}\right)$	$e\left(\frac{307}{336}\right)$	$e\left(\frac{61}{336}\right)$
$\chi_{8041}(503,\cdot)$	$-1$	$1$	$e\left(\frac{279}{280}\right)$	$e\left(\frac{1427}{1680}\right)$	$e\left(\frac{139}{140}\right)$	$e\left(\frac{1151}{1680}\right)$	$e\left(\frac{203}{240}\right)$	$e\left(\frac{79}{240}\right)$	$e\left(\frac{277}{280}\right)$	$e\left(\frac{587}{840}\right)$	$e\left(\frac{229}{336}\right)$	$e\left(\frac{283}{336}\right)$
$\chi_{8041}(534,\cdot)$	$-1$	$1$	$e\left(\frac{47}{280}\right)$	$e\left(\frac{971}{1680}\right)$	$e\left(\frac{47}{140}\right)$	$e\left(\frac{503}{1680}\right)$	$e\left(\frac{179}{240}\right)$	$e\left(\frac{7}{240}\right)$	$e\left(\frac{141}{280}\right)$	$e\left(\frac{131}{840}\right)$	$e\left(\frac{157}{336}\right)$	$e\left(\frac{307}{336}\right)$
$\chi_{8041}(585,\cdot)$	$-1$	$1$	$e\left(\frac{183}{280}\right)$	$e\left(\frac{1499}{1680}\right)$	$e\left(\frac{43}{140}\right)$	$e\left(\frac{1607}{1680}\right)$	$e\left(\frac{131}{240}\right)$	$e\left(\frac{103}{240}\right)$	$e\left(\frac{269}{280}\right)$	$e\left(\frac{659}{840}\right)$	$e\left(\frac{205}{336}\right)$	$e\left(\frac{67}{336}\right)$
$\chi_{8041}(589,\cdot)$	$-1$	$1$	$e\left(\frac{27}{280}\right)$	$e\left(\frac{1511}{1680}\right)$	$e\left(\frac{27}{140}\right)$	$e\left(\frac{563}{1680}\right)$	$e\left(\frac{239}{240}\right)$	$e\left(\frac{67}{240}\right)$	$e\left(\frac{81}{280}\right)$	$e\left(\frac{671}{840}\right)$	$e\left(\frac{145}{336}\right)$	$e\left(\frac{31}{336}\right)$
$\chi_{8041}(607,\cdot)$	$-1$	$1$	$e\left(\frac{153}{280}\right)$	$e\left(\frac{349}{1680}\right)$	$e\left(\frac{13}{140}\right)$	$e\left(\frac{577}{1680}\right)$	$e\left(\frac{181}{240}\right)$	$e\left(\frac{113}{240}\right)$	$e\left(\frac{179}{280}\right)$	$e\left(\frac{349}{840}\right)$	$e\left(\frac{299}{336}\right)$	$e\left(\frac{101}{336}\right)$

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	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(12\)
\(\chi_{8041}(28,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{67}{280}\right)\)	\(e\left(\frac{1271}{1680}\right)\)	\(e\left(\frac{67}{140}\right)\)	\(e\left(\frac{1283}{1680}\right)\)	\(e\left(\frac{239}{240}\right)\)	\(e\left(\frac{67}{240}\right)\)	\(e\left(\frac{201}{280}\right)\)	\(e\left(\frac{431}{840}\right)\)	\(e\left(\frac{1}{336}\right)\)	\(e\left(\frac{79}{336}\right)\)
\(\chi_{8041}(29,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{121}{280}\right)\)	\(e\left(\frac{653}{1680}\right)\)	\(e\left(\frac{121}{140}\right)\)	\(e\left(\frac{449}{1680}\right)\)	\(e\left(\frac{197}{240}\right)\)	\(e\left(\frac{1}{240}\right)\)	\(e\left(\frac{83}{280}\right)\)	\(e\left(\frac{653}{840}\right)\)	\(e\left(\frac{235}{336}\right)\)	\(e\left(\frac{85}{336}\right)\)
\(\chi_{8041}(46,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{33}{280}\right)\)	\(e\left(\frac{1069}{1680}\right)\)	\(e\left(\frac{33}{140}\right)\)	\(e\left(\frac{97}{1680}\right)\)	\(e\left(\frac{181}{240}\right)\)	\(e\left(\frac{113}{240}\right)\)	\(e\left(\frac{99}{280}\right)\)	\(e\left(\frac{229}{840}\right)\)	\(e\left(\frac{59}{336}\right)\)	\(e\left(\frac{293}{336}\right)\)
\(\chi_{8041}(61,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{47}{280}\right)\)	\(e\left(\frac{131}{1680}\right)\)	\(e\left(\frac{47}{140}\right)\)	\(e\left(\frac{1343}{1680}\right)\)	\(e\left(\frac{59}{240}\right)\)	\(e\left(\frac{127}{240}\right)\)	\(e\left(\frac{141}{280}\right)\)	\(e\left(\frac{131}{840}\right)\)	\(e\left(\frac{325}{336}\right)\)	\(e\left(\frac{139}{336}\right)\)
\(\chi_{8041}(62,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{11}{280}\right)\)	\(e\left(\frac{823}{1680}\right)\)	\(e\left(\frac{11}{140}\right)\)	\(e\left(\frac{499}{1680}\right)\)	\(e\left(\frac{127}{240}\right)\)	\(e\left(\frac{131}{240}\right)\)	\(e\left(\frac{33}{280}\right)\)	\(e\left(\frac{823}{840}\right)\)	\(e\left(\frac{113}{336}\right)\)	\(e\left(\frac{191}{336}\right)\)
\(\chi_{8041}(63,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{129}{280}\right)\)	\(e\left(\frac{157}{1680}\right)\)	\(e\left(\frac{129}{140}\right)\)	\(e\left(\frac{481}{1680}\right)\)	\(e\left(\frac{133}{240}\right)\)	\(e\left(\frac{209}{240}\right)\)	\(e\left(\frac{107}{280}\right)\)	\(e\left(\frac{157}{840}\right)\)	\(e\left(\frac{251}{336}\right)\)	\(e\left(\frac{5}{336}\right)\)
\(\chi_{8041}(73,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{41}{280}\right)\)	\(e\left(\frac{293}{1680}\right)\)	\(e\left(\frac{41}{140}\right)\)	\(e\left(\frac{1529}{1680}\right)\)	\(e\left(\frac{77}{240}\right)\)	\(e\left(\frac{121}{240}\right)\)	\(e\left(\frac{123}{280}\right)\)	\(e\left(\frac{293}{840}\right)\)	\(e\left(\frac{19}{336}\right)\)	\(e\left(\frac{157}{336}\right)\)
\(\chi_{8041}(105,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{277}{280}\right)\)	\(e\left(\frac{1201}{1680}\right)\)	\(e\left(\frac{137}{140}\right)\)	\(e\left(\frac{373}{1680}\right)\)	\(e\left(\frac{169}{240}\right)\)	\(e\left(\frac{197}{240}\right)\)	\(e\left(\frac{271}{280}\right)\)	\(e\left(\frac{361}{840}\right)\)	\(e\left(\frac{71}{336}\right)\)	\(e\left(\frac{233}{336}\right)\)
\(\chi_{8041}(112,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{183}{280}\right)\)	\(e\left(\frac{659}{1680}\right)\)	\(e\left(\frac{43}{140}\right)\)	\(e\left(\frac{767}{1680}\right)\)	\(e\left(\frac{11}{240}\right)\)	\(e\left(\frac{223}{240}\right)\)	\(e\left(\frac{269}{280}\right)\)	\(e\left(\frac{659}{840}\right)\)	\(e\left(\frac{37}{336}\right)\)	\(e\left(\frac{235}{336}\right)\)
\(\chi_{8041}(116,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{237}{280}\right)\)	\(e\left(\frac{41}{1680}\right)\)	\(e\left(\frac{97}{140}\right)\)	\(e\left(\frac{1613}{1680}\right)\)	\(e\left(\frac{209}{240}\right)\)	\(e\left(\frac{157}{240}\right)\)	\(e\left(\frac{151}{280}\right)\)	\(e\left(\frac{41}{840}\right)\)	\(e\left(\frac{271}{336}\right)\)	\(e\left(\frac{241}{336}\right)\)
\(\chi_{8041}(184,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{149}{280}\right)\)	\(e\left(\frac{457}{1680}\right)\)	\(e\left(\frac{9}{140}\right)\)	\(e\left(\frac{1261}{1680}\right)\)	\(e\left(\frac{193}{240}\right)\)	\(e\left(\frac{29}{240}\right)\)	\(e\left(\frac{167}{280}\right)\)	\(e\left(\frac{457}{840}\right)\)	\(e\left(\frac{95}{336}\right)\)	\(e\left(\frac{113}{336}\right)\)
\(\chi_{8041}(227,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{51}{280}\right)\)	\(e\left(\frac{1423}{1680}\right)\)	\(e\left(\frac{51}{140}\right)\)	\(e\left(\frac{379}{1680}\right)\)	\(e\left(\frac{7}{240}\right)\)	\(e\left(\frac{11}{240}\right)\)	\(e\left(\frac{153}{280}\right)\)	\(e\left(\frac{583}{840}\right)\)	\(e\left(\frac{137}{336}\right)\)	\(e\left(\frac{71}{336}\right)\)
\(\chi_{8041}(233,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{33}{280}\right)\)	\(e\left(\frac{509}{1680}\right)\)	\(e\left(\frac{33}{140}\right)\)	\(e\left(\frac{1217}{1680}\right)\)	\(e\left(\frac{101}{240}\right)\)	\(e\left(\frac{193}{240}\right)\)	\(e\left(\frac{99}{280}\right)\)	\(e\left(\frac{509}{840}\right)\)	\(e\left(\frac{283}{336}\right)\)	\(e\left(\frac{181}{336}\right)\)
\(\chi_{8041}(244,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{163}{280}\right)\)	\(e\left(\frac{1199}{1680}\right)\)	\(e\left(\frac{23}{140}\right)\)	\(e\left(\frac{827}{1680}\right)\)	\(e\left(\frac{71}{240}\right)\)	\(e\left(\frac{43}{240}\right)\)	\(e\left(\frac{209}{280}\right)\)	\(e\left(\frac{359}{840}\right)\)	\(e\left(\frac{25}{336}\right)\)	\(e\left(\frac{295}{336}\right)\)
\(\chi_{8041}(248,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{127}{280}\right)\)	\(e\left(\frac{211}{1680}\right)\)	\(e\left(\frac{127}{140}\right)\)	\(e\left(\frac{1663}{1680}\right)\)	\(e\left(\frac{139}{240}\right)\)	\(e\left(\frac{47}{240}\right)\)	\(e\left(\frac{101}{280}\right)\)	\(e\left(\frac{211}{840}\right)\)	\(e\left(\frac{149}{336}\right)\)	\(e\left(\frac{11}{336}\right)\)
\(\chi_{8041}(249,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{171}{280}\right)\)	\(e\left(\frac{983}{1680}\right)\)	\(e\left(\frac{31}{140}\right)\)	\(e\left(\frac{1139}{1680}\right)\)	\(e\left(\frac{47}{240}\right)\)	\(e\left(\frac{211}{240}\right)\)	\(e\left(\frac{233}{280}\right)\)	\(e\left(\frac{143}{840}\right)\)	\(e\left(\frac{97}{336}\right)\)	\(e\left(\frac{271}{336}\right)\)
\(\chi_{8041}(261,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{19}{280}\right)\)	\(e\left(\frac{607}{1680}\right)\)	\(e\left(\frac{19}{140}\right)\)	\(e\left(\frac{811}{1680}\right)\)	\(e\left(\frac{103}{240}\right)\)	\(e\left(\frac{59}{240}\right)\)	\(e\left(\frac{57}{280}\right)\)	\(e\left(\frac{607}{840}\right)\)	\(e\left(\frac{185}{336}\right)\)	\(e\left(\frac{167}{336}\right)\)
\(\chi_{8041}(277,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{193}{280}\right)\)	\(e\left(\frac{949}{1680}\right)\)	\(e\left(\frac{53}{140}\right)\)	\(e\left(\frac{457}{1680}\right)\)	\(e\left(\frac{61}{240}\right)\)	\(e\left(\frac{233}{240}\right)\)	\(e\left(\frac{19}{280}\right)\)	\(e\left(\frac{109}{840}\right)\)	\(e\left(\frac{323}{336}\right)\)	\(e\left(\frac{317}{336}\right)\)
\(\chi_{8041}(292,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{157}{280}\right)\)	\(e\left(\frac{1361}{1680}\right)\)	\(e\left(\frac{17}{140}\right)\)	\(e\left(\frac{1013}{1680}\right)\)	\(e\left(\frac{89}{240}\right)\)	\(e\left(\frac{37}{240}\right)\)	\(e\left(\frac{191}{280}\right)\)	\(e\left(\frac{521}{840}\right)\)	\(e\left(\frac{55}{336}\right)\)	\(e\left(\frac{313}{336}\right)\)
\(\chi_{8041}(347,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{47}{280}\right)\)	\(e\left(\frac{1531}{1680}\right)\)	\(e\left(\frac{47}{140}\right)\)	\(e\left(\frac{1063}{1680}\right)\)	\(e\left(\frac{19}{240}\right)\)	\(e\left(\frac{167}{240}\right)\)	\(e\left(\frac{141}{280}\right)\)	\(e\left(\frac{691}{840}\right)\)	\(e\left(\frac{269}{336}\right)\)	\(e\left(\frac{83}{336}\right)\)
\(\chi_{8041}(413,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{57}{280}\right)\)	\(e\left(\frac{1541}{1680}\right)\)	\(e\left(\frac{57}{140}\right)\)	\(e\left(\frac{473}{1680}\right)\)	\(e\left(\frac{29}{240}\right)\)	\(e\left(\frac{217}{240}\right)\)	\(e\left(\frac{171}{280}\right)\)	\(e\left(\frac{701}{840}\right)\)	\(e\left(\frac{163}{336}\right)\)	\(e\left(\frac{109}{336}\right)\)
\(\chi_{8041}(415,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{39}{280}\right)\)	\(e\left(\frac{347}{1680}\right)\)	\(e\left(\frac{39}{140}\right)\)	\(e\left(\frac{1031}{1680}\right)\)	\(e\left(\frac{83}{240}\right)\)	\(e\left(\frac{199}{240}\right)\)	\(e\left(\frac{117}{280}\right)\)	\(e\left(\frac{347}{840}\right)\)	\(e\left(\frac{253}{336}\right)\)	\(e\left(\frac{163}{336}\right)\)
\(\chi_{8041}(420,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{113}{280}\right)\)	\(e\left(\frac{589}{1680}\right)\)	\(e\left(\frac{113}{140}\right)\)	\(e\left(\frac{1537}{1680}\right)\)	\(e\left(\frac{181}{240}\right)\)	\(e\left(\frac{113}{240}\right)\)	\(e\left(\frac{59}{280}\right)\)	\(e\left(\frac{589}{840}\right)\)	\(e\left(\frac{107}{336}\right)\)	\(e\left(\frac{53}{336}\right)\)
\(\chi_{8041}(435,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{167}{280}\right)\)	\(e\left(\frac{1651}{1680}\right)\)	\(e\left(\frac{27}{140}\right)\)	\(e\left(\frac{703}{1680}\right)\)	\(e\left(\frac{139}{240}\right)\)	\(e\left(\frac{47}{240}\right)\)	\(e\left(\frac{221}{280}\right)\)	\(e\left(\frac{811}{840}\right)\)	\(e\left(\frac{5}{336}\right)\)	\(e\left(\frac{59}{336}\right)\)
\(\chi_{8041}(448,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{19}{280}\right)\)	\(e\left(\frac{47}{1680}\right)\)	\(e\left(\frac{19}{140}\right)\)	\(e\left(\frac{251}{1680}\right)\)	\(e\left(\frac{23}{240}\right)\)	\(e\left(\frac{139}{240}\right)\)	\(e\left(\frac{57}{280}\right)\)	\(e\left(\frac{47}{840}\right)\)	\(e\left(\frac{73}{336}\right)\)	\(e\left(\frac{55}{336}\right)\)
\(\chi_{8041}(464,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{73}{280}\right)\)	\(e\left(\frac{1109}{1680}\right)\)	\(e\left(\frac{73}{140}\right)\)	\(e\left(\frac{1097}{1680}\right)\)	\(e\left(\frac{221}{240}\right)\)	\(e\left(\frac{73}{240}\right)\)	\(e\left(\frac{219}{280}\right)\)	\(e\left(\frac{269}{840}\right)\)	\(e\left(\frac{307}{336}\right)\)	\(e\left(\frac{61}{336}\right)\)
\(\chi_{8041}(503,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{279}{280}\right)\)	\(e\left(\frac{1427}{1680}\right)\)	\(e\left(\frac{139}{140}\right)\)	\(e\left(\frac{1151}{1680}\right)\)	\(e\left(\frac{203}{240}\right)\)	\(e\left(\frac{79}{240}\right)\)	\(e\left(\frac{277}{280}\right)\)	\(e\left(\frac{587}{840}\right)\)	\(e\left(\frac{229}{336}\right)\)	\(e\left(\frac{283}{336}\right)\)
\(\chi_{8041}(534,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{47}{280}\right)\)	\(e\left(\frac{971}{1680}\right)\)	\(e\left(\frac{47}{140}\right)\)	\(e\left(\frac{503}{1680}\right)\)	\(e\left(\frac{179}{240}\right)\)	\(e\left(\frac{7}{240}\right)\)	\(e\left(\frac{141}{280}\right)\)	\(e\left(\frac{131}{840}\right)\)	\(e\left(\frac{157}{336}\right)\)	\(e\left(\frac{307}{336}\right)\)
\(\chi_{8041}(585,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{183}{280}\right)\)	\(e\left(\frac{1499}{1680}\right)\)	\(e\left(\frac{43}{140}\right)\)	\(e\left(\frac{1607}{1680}\right)\)	\(e\left(\frac{131}{240}\right)\)	\(e\left(\frac{103}{240}\right)\)	\(e\left(\frac{269}{280}\right)\)	\(e\left(\frac{659}{840}\right)\)	\(e\left(\frac{205}{336}\right)\)	\(e\left(\frac{67}{336}\right)\)
\(\chi_{8041}(589,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{27}{280}\right)\)	\(e\left(\frac{1511}{1680}\right)\)	\(e\left(\frac{27}{140}\right)\)	\(e\left(\frac{563}{1680}\right)\)	\(e\left(\frac{239}{240}\right)\)	\(e\left(\frac{67}{240}\right)\)	\(e\left(\frac{81}{280}\right)\)	\(e\left(\frac{671}{840}\right)\)	\(e\left(\frac{145}{336}\right)\)	\(e\left(\frac{31}{336}\right)\)
\(\chi_{8041}(607,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{153}{280}\right)\)	\(e\left(\frac{349}{1680}\right)\)	\(e\left(\frac{13}{140}\right)\)	\(e\left(\frac{577}{1680}\right)\)	\(e\left(\frac{181}{240}\right)\)	\(e\left(\frac{113}{240}\right)\)	\(e\left(\frac{179}{280}\right)\)	\(e\left(\frac{349}{840}\right)\)	\(e\left(\frac{299}{336}\right)\)	\(e\left(\frac{101}{336}\right)\)

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Basic properties

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First 31 of 384 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	8041.ga
Modulus	$8041$
Conductor	$8041$
Order	$1680$
Real	no
Primitive	yes
Minimal	yes
Parity	odd

Modulus:	\(8041\)
Conductor:	\(8041\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(1680\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	yes	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	odd	sage:chi.is_odd() pari:zncharisodd(g,chi)