LMFDB - Dirichlet character orbit 8041.fz

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(8041, base_ring=CyclotomicField(840)) M = H._module chi = DirichletCharacter(H, M([168,105,340])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(26,8041)) 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:	$840$	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:	$\Q(\zeta_{840})$
Fixed field:	Number field defined by a degree 840 polynomial (not computed)

First 31 of 192 characters in Galois orbit

Character	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$12$
$\chi_{8041}(26,\cdot)$	$-1$	$1$	$e\left(\frac{123}{140}\right)$	$e\left(\frac{109}{840}\right)$	$e\left(\frac{53}{70}\right)$	$e\left(\frac{457}{840}\right)$	$e\left(\frac{1}{120}\right)$	$e\left(\frac{113}{120}\right)$	$e\left(\frac{89}{140}\right)$	$e\left(\frac{109}{420}\right)$	$e\left(\frac{71}{168}\right)$	$e\left(\frac{149}{168}\right)$
$\chi_{8041}(104,\cdot)$	$-1$	$1$	$e\left(\frac{41}{140}\right)$	$e\left(\frac{643}{840}\right)$	$e\left(\frac{41}{70}\right)$	$e\left(\frac{199}{840}\right)$	$e\left(\frac{7}{120}\right)$	$e\left(\frac{71}{120}\right)$	$e\left(\frac{123}{140}\right)$	$e\left(\frac{223}{420}\right)$	$e\left(\frac{89}{168}\right)$	$e\left(\frac{59}{168}\right)$
$\chi_{8041}(202,\cdot)$	$-1$	$1$	$e\left(\frac{73}{140}\right)$	$e\left(\frac{199}{840}\right)$	$e\left(\frac{3}{70}\right)$	$e\left(\frac{187}{840}\right)$	$e\left(\frac{91}{120}\right)$	$e\left(\frac{83}{120}\right)$	$e\left(\frac{79}{140}\right)$	$e\left(\frac{199}{420}\right)$	$e\left(\frac{125}{168}\right)$	$e\left(\frac{47}{168}\right)$
$\chi_{8041}(291,\cdot)$	$-1$	$1$	$e\left(\frac{81}{140}\right)$	$e\left(\frac{683}{840}\right)$	$e\left(\frac{11}{70}\right)$	$e\left(\frac{359}{840}\right)$	$e\left(\frac{47}{120}\right)$	$e\left(\frac{31}{120}\right)$	$e\left(\frac{103}{140}\right)$	$e\left(\frac{263}{420}\right)$	$e\left(\frac{1}{168}\right)$	$e\left(\frac{163}{168}\right)$
$\chi_{8041}(372,\cdot)$	$-1$	$1$	$e\left(\frac{9}{140}\right)$	$e\left(\frac{247}{840}\right)$	$e\left(\frac{9}{70}\right)$	$e\left(\frac{211}{840}\right)$	$e\left(\frac{43}{120}\right)$	$e\left(\frac{59}{120}\right)$	$e\left(\frac{27}{140}\right)$	$e\left(\frac{247}{420}\right)$	$e\left(\frac{53}{168}\right)$	$e\left(\frac{71}{168}\right)$
$\chi_{8041}(399,\cdot)$	$-1$	$1$	$e\left(\frac{127}{140}\right)$	$e\left(\frac{281}{840}\right)$	$e\left(\frac{57}{70}\right)$	$e\left(\frac{53}{840}\right)$	$e\left(\frac{29}{120}\right)$	$e\left(\frac{37}{120}\right)$	$e\left(\frac{101}{140}\right)$	$e\left(\frac{281}{420}\right)$	$e\left(\frac{163}{168}\right)$	$e\left(\frac{25}{168}\right)$
$\chi_{8041}(416,\cdot)$	$-1$	$1$	$e\left(\frac{99}{140}\right)$	$e\left(\frac{337}{840}\right)$	$e\left(\frac{29}{70}\right)$	$e\left(\frac{781}{840}\right)$	$e\left(\frac{13}{120}\right)$	$e\left(\frac{29}{120}\right)$	$e\left(\frac{17}{140}\right)$	$e\left(\frac{337}{420}\right)$	$e\left(\frac{107}{168}\right)$	$e\left(\frac{137}{168}\right)$
$\chi_{8041}(433,\cdot)$	$-1$	$1$	$e\left(\frac{83}{140}\right)$	$e\left(\frac{209}{840}\right)$	$e\left(\frac{13}{70}\right)$	$e\left(\frac{437}{840}\right)$	$e\left(\frac{101}{120}\right)$	$e\left(\frac{13}{120}\right)$	$e\left(\frac{109}{140}\right)$	$e\left(\frac{209}{420}\right)$	$e\left(\frac{19}{168}\right)$	$e\left(\frac{73}{168}\right)$
$\chi_{8041}(478,\cdot)$	$-1$	$1$	$e\left(\frac{101}{140}\right)$	$e\left(\frac{563}{840}\right)$	$e\left(\frac{31}{70}\right)$	$e\left(\frac{719}{840}\right)$	$e\left(\frac{47}{120}\right)$	$e\left(\frac{31}{120}\right)$	$e\left(\frac{23}{140}\right)$	$e\left(\frac{143}{420}\right)$	$e\left(\frac{97}{168}\right)$	$e\left(\frac{19}{168}\right)$
$\chi_{8041}(542,\cdot)$	$-1$	$1$	$e\left(\frac{137}{140}\right)$	$e\left(\frac{151}{840}\right)$	$e\left(\frac{67}{70}\right)$	$e\left(\frac{163}{840}\right)$	$e\left(\frac{19}{120}\right)$	$e\left(\frac{107}{120}\right)$	$e\left(\frac{131}{140}\right)$	$e\left(\frac{151}{420}\right)$	$e\left(\frac{29}{168}\right)$	$e\left(\frac{23}{168}\right)$
$\chi_{8041}(587,\cdot)$	$-1$	$1$	$e\left(\frac{23}{140}\right)$	$e\left(\frac{709}{840}\right)$	$e\left(\frac{23}{70}\right)$	$e\left(\frac{337}{840}\right)$	$e\left(\frac{1}{120}\right)$	$e\left(\frac{113}{120}\right)$	$e\left(\frac{69}{140}\right)$	$e\left(\frac{289}{420}\right)$	$e\left(\frac{95}{168}\right)$	$e\left(\frac{29}{168}\right)$
$\chi_{8041}(614,\cdot)$	$-1$	$1$	$e\left(\frac{29}{140}\right)$	$e\left(\frac{827}{840}\right)$	$e\left(\frac{29}{70}\right)$	$e\left(\frac{431}{840}\right)$	$e\left(\frac{23}{120}\right)$	$e\left(\frac{79}{120}\right)$	$e\left(\frac{87}{140}\right)$	$e\left(\frac{407}{420}\right)$	$e\left(\frac{121}{168}\right)$	$e\left(\frac{67}{168}\right)$
$\chi_{8041}(620,\cdot)$	$-1$	$1$	$e\left(\frac{83}{140}\right)$	$e\left(\frac{769}{840}\right)$	$e\left(\frac{13}{70}\right)$	$e\left(\frac{157}{840}\right)$	$e\left(\frac{61}{120}\right)$	$e\left(\frac{53}{120}\right)$	$e\left(\frac{109}{140}\right)$	$e\left(\frac{349}{420}\right)$	$e\left(\frac{131}{168}\right)$	$e\left(\frac{17}{168}\right)$
$\chi_{8041}(621,\cdot)$	$-1$	$1$	$e\left(\frac{51}{140}\right)$	$e\left(\frac{653}{840}\right)$	$e\left(\frac{51}{70}\right)$	$e\left(\frac{449}{840}\right)$	$e\left(\frac{17}{120}\right)$	$e\left(\frac{1}{120}\right)$	$e\left(\frac{13}{140}\right)$	$e\left(\frac{233}{420}\right)$	$e\left(\frac{151}{168}\right)$	$e\left(\frac{85}{168}\right)$
$\chi_{8041}(631,\cdot)$	$-1$	$1$	$e\left(\frac{113}{140}\right)$	$e\left(\frac{379}{840}\right)$	$e\left(\frac{43}{70}\right)$	$e\left(\frac{487}{840}\right)$	$e\left(\frac{31}{120}\right)$	$e\left(\frac{23}{120}\right)$	$e\left(\frac{59}{140}\right)$	$e\left(\frac{379}{420}\right)$	$e\left(\frac{65}{168}\right)$	$e\left(\frac{11}{168}\right)$
$\chi_{8041}(665,\cdot)$	$-1$	$1$	$e\left(\frac{61}{140}\right)$	$e\left(\frac{803}{840}\right)$	$e\left(\frac{61}{70}\right)$	$e\left(\frac{839}{840}\right)$	$e\left(\frac{47}{120}\right)$	$e\left(\frac{31}{120}\right)$	$e\left(\frac{43}{140}\right)$	$e\left(\frac{383}{420}\right)$	$e\left(\frac{73}{168}\right)$	$e\left(\frac{139}{168}\right)$
$\chi_{8041}(757,\cdot)$	$-1$	$1$	$e\left(\frac{39}{140}\right)$	$e\left(\frac{277}{840}\right)$	$e\left(\frac{39}{70}\right)$	$e\left(\frac{121}{840}\right)$	$e\left(\frac{73}{120}\right)$	$e\left(\frac{89}{120}\right)$	$e\left(\frac{117}{140}\right)$	$e\left(\frac{277}{420}\right)$	$e\left(\frac{71}{168}\right)$	$e\left(\frac{149}{168}\right)$
$\chi_{8041}(807,\cdot)$	$-1$	$1$	$e\left(\frac{123}{140}\right)$	$e\left(\frac{809}{840}\right)$	$e\left(\frac{53}{70}\right)$	$e\left(\frac{317}{840}\right)$	$e\left(\frac{101}{120}\right)$	$e\left(\frac{13}{120}\right)$	$e\left(\frac{89}{140}\right)$	$e\left(\frac{389}{420}\right)$	$e\left(\frac{43}{168}\right)$	$e\left(\frac{121}{168}\right)$
$\chi_{8041}(808,\cdot)$	$-1$	$1$	$e\left(\frac{131}{140}\right)$	$e\left(\frac{733}{840}\right)$	$e\left(\frac{61}{70}\right)$	$e\left(\frac{769}{840}\right)$	$e\left(\frac{97}{120}\right)$	$e\left(\frac{41}{120}\right)$	$e\left(\frac{113}{140}\right)$	$e\left(\frac{313}{420}\right)$	$e\left(\frac{143}{168}\right)$	$e\left(\frac{125}{168}\right)$
$\chi_{8041}(933,\cdot)$	$-1$	$1$	$e\left(\frac{129}{140}\right)$	$e\left(\frac{367}{840}\right)$	$e\left(\frac{59}{70}\right)$	$e\left(\frac{691}{840}\right)$	$e\left(\frac{43}{120}\right)$	$e\left(\frac{59}{120}\right)$	$e\left(\frac{107}{140}\right)$	$e\left(\frac{367}{420}\right)$	$e\left(\frac{125}{168}\right)$	$e\left(\frac{47}{168}\right)$
$\chi_{8041}(994,\cdot)$	$-1$	$1$	$e\left(\frac{3}{140}\right)$	$e\left(\frac{689}{840}\right)$	$e\left(\frac{3}{70}\right)$	$e\left(\frac{677}{840}\right)$	$e\left(\frac{101}{120}\right)$	$e\left(\frac{13}{120}\right)$	$e\left(\frac{9}{140}\right)$	$e\left(\frac{269}{420}\right)$	$e\left(\frac{139}{168}\right)$	$e\left(\frac{145}{168}\right)$
$\chi_{8041}(1103,\cdot)$	$-1$	$1$	$e\left(\frac{37}{140}\right)$	$e\left(\frac{751}{840}\right)$	$e\left(\frac{37}{70}\right)$	$e\left(\frac{43}{840}\right)$	$e\left(\frac{19}{120}\right)$	$e\left(\frac{107}{120}\right)$	$e\left(\frac{111}{140}\right)$	$e\left(\frac{331}{420}\right)$	$e\left(\frac{53}{168}\right)$	$e\left(\frac{71}{168}\right)$
$\chi_{8041}(1137,\cdot)$	$-1$	$1$	$e\left(\frac{93}{140}\right)$	$e\left(\frac{359}{840}\right)$	$e\left(\frac{23}{70}\right)$	$e\left(\frac{827}{840}\right)$	$e\left(\frac{11}{120}\right)$	$e\left(\frac{43}{120}\right)$	$e\left(\frac{139}{140}\right)$	$e\left(\frac{359}{420}\right)$	$e\left(\frac{109}{168}\right)$	$e\left(\frac{127}{168}\right)$
$\chi_{8041}(1147,\cdot)$	$-1$	$1$	$e\left(\frac{127}{140}\right)$	$e\left(\frac{1}{840}\right)$	$e\left(\frac{57}{70}\right)$	$e\left(\frac{613}{840}\right)$	$e\left(\frac{109}{120}\right)$	$e\left(\frac{77}{120}\right)$	$e\left(\frac{101}{140}\right)$	$e\left(\frac{1}{420}\right)$	$e\left(\frac{107}{168}\right)$	$e\left(\frac{137}{168}\right)$
$\chi_{8041}(1148,\cdot)$	$-1$	$1$	$e\left(\frac{3}{140}\right)$	$e\left(\frac{829}{840}\right)$	$e\left(\frac{3}{70}\right)$	$e\left(\frac{817}{840}\right)$	$e\left(\frac{1}{120}\right)$	$e\left(\frac{113}{120}\right)$	$e\left(\frac{9}{140}\right)$	$e\left(\frac{409}{420}\right)$	$e\left(\frac{167}{168}\right)$	$e\left(\frac{5}{168}\right)$
$\chi_{8041}(1164,\cdot)$	$-1$	$1$	$e\left(\frac{139}{140}\right)$	$e\left(\frac{377}{840}\right)$	$e\left(\frac{69}{70}\right)$	$e\left(\frac{101}{840}\right)$	$e\left(\frac{53}{120}\right)$	$e\left(\frac{109}{120}\right)$	$e\left(\frac{137}{140}\right)$	$e\left(\frac{377}{420}\right)$	$e\left(\frac{19}{168}\right)$	$e\left(\frac{73}{168}\right)$
$\chi_{8041}(1181,\cdot)$	$-1$	$1$	$e\left(\frac{103}{140}\right)$	$e\left(\frac{89}{840}\right)$	$e\left(\frac{33}{70}\right)$	$e\left(\frac{797}{840}\right)$	$e\left(\frac{101}{120}\right)$	$e\left(\frac{13}{120}\right)$	$e\left(\frac{29}{140}\right)$	$e\left(\frac{89}{420}\right)$	$e\left(\frac{115}{168}\right)$	$e\left(\frac{97}{168}\right)$
$\chi_{8041}(1318,\cdot)$	$-1$	$1$	$e\left(\frac{79}{140}\right)$	$e\left(\frac{37}{840}\right)$	$e\left(\frac{9}{70}\right)$	$e\left(\frac{1}{840}\right)$	$e\left(\frac{73}{120}\right)$	$e\left(\frac{89}{120}\right)$	$e\left(\frac{97}{140}\right)$	$e\left(\frac{37}{420}\right)$	$e\left(\frac{95}{168}\right)$	$e\left(\frac{29}{168}\right)$
$\chi_{8041}(1324,\cdot)$	$-1$	$1$	$e\left(\frac{33}{140}\right)$	$e\left(\frac{439}{840}\right)$	$e\left(\frac{33}{70}\right)$	$e\left(\frac{307}{840}\right)$	$e\left(\frac{91}{120}\right)$	$e\left(\frac{83}{120}\right)$	$e\left(\frac{99}{140}\right)$	$e\left(\frac{19}{420}\right)$	$e\left(\frac{101}{168}\right)$	$e\left(\frac{167}{168}\right)$
$\chi_{8041}(1345,\cdot)$	$-1$	$1$	$e\left(\frac{57}{140}\right)$	$e\left(\frac{491}{840}\right)$	$e\left(\frac{57}{70}\right)$	$e\left(\frac{263}{840}\right)$	$e\left(\frac{119}{120}\right)$	$e\left(\frac{7}{120}\right)$	$e\left(\frac{31}{140}\right)$	$e\left(\frac{71}{420}\right)$	$e\left(\frac{121}{168}\right)$	$e\left(\frac{67}{168}\right)$
$\chi_{8041}(1351,\cdot)$	$-1$	$1$	$e\left(\frac{139}{140}\right)$	$e\left(\frac{97}{840}\right)$	$e\left(\frac{69}{70}\right)$	$e\left(\frac{661}{840}\right)$	$e\left(\frac{13}{120}\right)$	$e\left(\frac{29}{120}\right)$	$e\left(\frac{137}{140}\right)$	$e\left(\frac{97}{420}\right)$	$e\left(\frac{131}{168}\right)$	$e\left(\frac{17}{168}\right)$

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	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(12\)
\(\chi_{8041}(26,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{123}{140}\right)\)	\(e\left(\frac{109}{840}\right)\)	\(e\left(\frac{53}{70}\right)\)	\(e\left(\frac{457}{840}\right)\)	\(e\left(\frac{1}{120}\right)\)	\(e\left(\frac{113}{120}\right)\)	\(e\left(\frac{89}{140}\right)\)	\(e\left(\frac{109}{420}\right)\)	\(e\left(\frac{71}{168}\right)\)	\(e\left(\frac{149}{168}\right)\)
\(\chi_{8041}(104,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{41}{140}\right)\)	\(e\left(\frac{643}{840}\right)\)	\(e\left(\frac{41}{70}\right)\)	\(e\left(\frac{199}{840}\right)\)	\(e\left(\frac{7}{120}\right)\)	\(e\left(\frac{71}{120}\right)\)	\(e\left(\frac{123}{140}\right)\)	\(e\left(\frac{223}{420}\right)\)	\(e\left(\frac{89}{168}\right)\)	\(e\left(\frac{59}{168}\right)\)
\(\chi_{8041}(202,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{73}{140}\right)\)	\(e\left(\frac{199}{840}\right)\)	\(e\left(\frac{3}{70}\right)\)	\(e\left(\frac{187}{840}\right)\)	\(e\left(\frac{91}{120}\right)\)	\(e\left(\frac{83}{120}\right)\)	\(e\left(\frac{79}{140}\right)\)	\(e\left(\frac{199}{420}\right)\)	\(e\left(\frac{125}{168}\right)\)	\(e\left(\frac{47}{168}\right)\)
\(\chi_{8041}(291,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{81}{140}\right)\)	\(e\left(\frac{683}{840}\right)\)	\(e\left(\frac{11}{70}\right)\)	\(e\left(\frac{359}{840}\right)\)	\(e\left(\frac{47}{120}\right)\)	\(e\left(\frac{31}{120}\right)\)	\(e\left(\frac{103}{140}\right)\)	\(e\left(\frac{263}{420}\right)\)	\(e\left(\frac{1}{168}\right)\)	\(e\left(\frac{163}{168}\right)\)
\(\chi_{8041}(372,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{9}{140}\right)\)	\(e\left(\frac{247}{840}\right)\)	\(e\left(\frac{9}{70}\right)\)	\(e\left(\frac{211}{840}\right)\)	\(e\left(\frac{43}{120}\right)\)	\(e\left(\frac{59}{120}\right)\)	\(e\left(\frac{27}{140}\right)\)	\(e\left(\frac{247}{420}\right)\)	\(e\left(\frac{53}{168}\right)\)	\(e\left(\frac{71}{168}\right)\)
\(\chi_{8041}(399,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{127}{140}\right)\)	\(e\left(\frac{281}{840}\right)\)	\(e\left(\frac{57}{70}\right)\)	\(e\left(\frac{53}{840}\right)\)	\(e\left(\frac{29}{120}\right)\)	\(e\left(\frac{37}{120}\right)\)	\(e\left(\frac{101}{140}\right)\)	\(e\left(\frac{281}{420}\right)\)	\(e\left(\frac{163}{168}\right)\)	\(e\left(\frac{25}{168}\right)\)
\(\chi_{8041}(416,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{99}{140}\right)\)	\(e\left(\frac{337}{840}\right)\)	\(e\left(\frac{29}{70}\right)\)	\(e\left(\frac{781}{840}\right)\)	\(e\left(\frac{13}{120}\right)\)	\(e\left(\frac{29}{120}\right)\)	\(e\left(\frac{17}{140}\right)\)	\(e\left(\frac{337}{420}\right)\)	\(e\left(\frac{107}{168}\right)\)	\(e\left(\frac{137}{168}\right)\)
\(\chi_{8041}(433,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{83}{140}\right)\)	\(e\left(\frac{209}{840}\right)\)	\(e\left(\frac{13}{70}\right)\)	\(e\left(\frac{437}{840}\right)\)	\(e\left(\frac{101}{120}\right)\)	\(e\left(\frac{13}{120}\right)\)	\(e\left(\frac{109}{140}\right)\)	\(e\left(\frac{209}{420}\right)\)	\(e\left(\frac{19}{168}\right)\)	\(e\left(\frac{73}{168}\right)\)
\(\chi_{8041}(478,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{101}{140}\right)\)	\(e\left(\frac{563}{840}\right)\)	\(e\left(\frac{31}{70}\right)\)	\(e\left(\frac{719}{840}\right)\)	\(e\left(\frac{47}{120}\right)\)	\(e\left(\frac{31}{120}\right)\)	\(e\left(\frac{23}{140}\right)\)	\(e\left(\frac{143}{420}\right)\)	\(e\left(\frac{97}{168}\right)\)	\(e\left(\frac{19}{168}\right)\)
\(\chi_{8041}(542,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{137}{140}\right)\)	\(e\left(\frac{151}{840}\right)\)	\(e\left(\frac{67}{70}\right)\)	\(e\left(\frac{163}{840}\right)\)	\(e\left(\frac{19}{120}\right)\)	\(e\left(\frac{107}{120}\right)\)	\(e\left(\frac{131}{140}\right)\)	\(e\left(\frac{151}{420}\right)\)	\(e\left(\frac{29}{168}\right)\)	\(e\left(\frac{23}{168}\right)\)
\(\chi_{8041}(587,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{23}{140}\right)\)	\(e\left(\frac{709}{840}\right)\)	\(e\left(\frac{23}{70}\right)\)	\(e\left(\frac{337}{840}\right)\)	\(e\left(\frac{1}{120}\right)\)	\(e\left(\frac{113}{120}\right)\)	\(e\left(\frac{69}{140}\right)\)	\(e\left(\frac{289}{420}\right)\)	\(e\left(\frac{95}{168}\right)\)	\(e\left(\frac{29}{168}\right)\)
\(\chi_{8041}(614,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{29}{140}\right)\)	\(e\left(\frac{827}{840}\right)\)	\(e\left(\frac{29}{70}\right)\)	\(e\left(\frac{431}{840}\right)\)	\(e\left(\frac{23}{120}\right)\)	\(e\left(\frac{79}{120}\right)\)	\(e\left(\frac{87}{140}\right)\)	\(e\left(\frac{407}{420}\right)\)	\(e\left(\frac{121}{168}\right)\)	\(e\left(\frac{67}{168}\right)\)
\(\chi_{8041}(620,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{83}{140}\right)\)	\(e\left(\frac{769}{840}\right)\)	\(e\left(\frac{13}{70}\right)\)	\(e\left(\frac{157}{840}\right)\)	\(e\left(\frac{61}{120}\right)\)	\(e\left(\frac{53}{120}\right)\)	\(e\left(\frac{109}{140}\right)\)	\(e\left(\frac{349}{420}\right)\)	\(e\left(\frac{131}{168}\right)\)	\(e\left(\frac{17}{168}\right)\)
\(\chi_{8041}(621,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{51}{140}\right)\)	\(e\left(\frac{653}{840}\right)\)	\(e\left(\frac{51}{70}\right)\)	\(e\left(\frac{449}{840}\right)\)	\(e\left(\frac{17}{120}\right)\)	\(e\left(\frac{1}{120}\right)\)	\(e\left(\frac{13}{140}\right)\)	\(e\left(\frac{233}{420}\right)\)	\(e\left(\frac{151}{168}\right)\)	\(e\left(\frac{85}{168}\right)\)
\(\chi_{8041}(631,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{113}{140}\right)\)	\(e\left(\frac{379}{840}\right)\)	\(e\left(\frac{43}{70}\right)\)	\(e\left(\frac{487}{840}\right)\)	\(e\left(\frac{31}{120}\right)\)	\(e\left(\frac{23}{120}\right)\)	\(e\left(\frac{59}{140}\right)\)	\(e\left(\frac{379}{420}\right)\)	\(e\left(\frac{65}{168}\right)\)	\(e\left(\frac{11}{168}\right)\)
\(\chi_{8041}(665,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{61}{140}\right)\)	\(e\left(\frac{803}{840}\right)\)	\(e\left(\frac{61}{70}\right)\)	\(e\left(\frac{839}{840}\right)\)	\(e\left(\frac{47}{120}\right)\)	\(e\left(\frac{31}{120}\right)\)	\(e\left(\frac{43}{140}\right)\)	\(e\left(\frac{383}{420}\right)\)	\(e\left(\frac{73}{168}\right)\)	\(e\left(\frac{139}{168}\right)\)
\(\chi_{8041}(757,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{39}{140}\right)\)	\(e\left(\frac{277}{840}\right)\)	\(e\left(\frac{39}{70}\right)\)	\(e\left(\frac{121}{840}\right)\)	\(e\left(\frac{73}{120}\right)\)	\(e\left(\frac{89}{120}\right)\)	\(e\left(\frac{117}{140}\right)\)	\(e\left(\frac{277}{420}\right)\)	\(e\left(\frac{71}{168}\right)\)	\(e\left(\frac{149}{168}\right)\)
\(\chi_{8041}(807,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{123}{140}\right)\)	\(e\left(\frac{809}{840}\right)\)	\(e\left(\frac{53}{70}\right)\)	\(e\left(\frac{317}{840}\right)\)	\(e\left(\frac{101}{120}\right)\)	\(e\left(\frac{13}{120}\right)\)	\(e\left(\frac{89}{140}\right)\)	\(e\left(\frac{389}{420}\right)\)	\(e\left(\frac{43}{168}\right)\)	\(e\left(\frac{121}{168}\right)\)
\(\chi_{8041}(808,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{131}{140}\right)\)	\(e\left(\frac{733}{840}\right)\)	\(e\left(\frac{61}{70}\right)\)	\(e\left(\frac{769}{840}\right)\)	\(e\left(\frac{97}{120}\right)\)	\(e\left(\frac{41}{120}\right)\)	\(e\left(\frac{113}{140}\right)\)	\(e\left(\frac{313}{420}\right)\)	\(e\left(\frac{143}{168}\right)\)	\(e\left(\frac{125}{168}\right)\)
\(\chi_{8041}(933,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{129}{140}\right)\)	\(e\left(\frac{367}{840}\right)\)	\(e\left(\frac{59}{70}\right)\)	\(e\left(\frac{691}{840}\right)\)	\(e\left(\frac{43}{120}\right)\)	\(e\left(\frac{59}{120}\right)\)	\(e\left(\frac{107}{140}\right)\)	\(e\left(\frac{367}{420}\right)\)	\(e\left(\frac{125}{168}\right)\)	\(e\left(\frac{47}{168}\right)\)
\(\chi_{8041}(994,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{3}{140}\right)\)	\(e\left(\frac{689}{840}\right)\)	\(e\left(\frac{3}{70}\right)\)	\(e\left(\frac{677}{840}\right)\)	\(e\left(\frac{101}{120}\right)\)	\(e\left(\frac{13}{120}\right)\)	\(e\left(\frac{9}{140}\right)\)	\(e\left(\frac{269}{420}\right)\)	\(e\left(\frac{139}{168}\right)\)	\(e\left(\frac{145}{168}\right)\)
\(\chi_{8041}(1103,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{37}{140}\right)\)	\(e\left(\frac{751}{840}\right)\)	\(e\left(\frac{37}{70}\right)\)	\(e\left(\frac{43}{840}\right)\)	\(e\left(\frac{19}{120}\right)\)	\(e\left(\frac{107}{120}\right)\)	\(e\left(\frac{111}{140}\right)\)	\(e\left(\frac{331}{420}\right)\)	\(e\left(\frac{53}{168}\right)\)	\(e\left(\frac{71}{168}\right)\)
\(\chi_{8041}(1137,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{93}{140}\right)\)	\(e\left(\frac{359}{840}\right)\)	\(e\left(\frac{23}{70}\right)\)	\(e\left(\frac{827}{840}\right)\)	\(e\left(\frac{11}{120}\right)\)	\(e\left(\frac{43}{120}\right)\)	\(e\left(\frac{139}{140}\right)\)	\(e\left(\frac{359}{420}\right)\)	\(e\left(\frac{109}{168}\right)\)	\(e\left(\frac{127}{168}\right)\)
\(\chi_{8041}(1147,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{127}{140}\right)\)	\(e\left(\frac{1}{840}\right)\)	\(e\left(\frac{57}{70}\right)\)	\(e\left(\frac{613}{840}\right)\)	\(e\left(\frac{109}{120}\right)\)	\(e\left(\frac{77}{120}\right)\)	\(e\left(\frac{101}{140}\right)\)	\(e\left(\frac{1}{420}\right)\)	\(e\left(\frac{107}{168}\right)\)	\(e\left(\frac{137}{168}\right)\)
\(\chi_{8041}(1148,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{3}{140}\right)\)	\(e\left(\frac{829}{840}\right)\)	\(e\left(\frac{3}{70}\right)\)	\(e\left(\frac{817}{840}\right)\)	\(e\left(\frac{1}{120}\right)\)	\(e\left(\frac{113}{120}\right)\)	\(e\left(\frac{9}{140}\right)\)	\(e\left(\frac{409}{420}\right)\)	\(e\left(\frac{167}{168}\right)\)	\(e\left(\frac{5}{168}\right)\)
\(\chi_{8041}(1164,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{139}{140}\right)\)	\(e\left(\frac{377}{840}\right)\)	\(e\left(\frac{69}{70}\right)\)	\(e\left(\frac{101}{840}\right)\)	\(e\left(\frac{53}{120}\right)\)	\(e\left(\frac{109}{120}\right)\)	\(e\left(\frac{137}{140}\right)\)	\(e\left(\frac{377}{420}\right)\)	\(e\left(\frac{19}{168}\right)\)	\(e\left(\frac{73}{168}\right)\)
\(\chi_{8041}(1181,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{103}{140}\right)\)	\(e\left(\frac{89}{840}\right)\)	\(e\left(\frac{33}{70}\right)\)	\(e\left(\frac{797}{840}\right)\)	\(e\left(\frac{101}{120}\right)\)	\(e\left(\frac{13}{120}\right)\)	\(e\left(\frac{29}{140}\right)\)	\(e\left(\frac{89}{420}\right)\)	\(e\left(\frac{115}{168}\right)\)	\(e\left(\frac{97}{168}\right)\)
\(\chi_{8041}(1318,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{79}{140}\right)\)	\(e\left(\frac{37}{840}\right)\)	\(e\left(\frac{9}{70}\right)\)	\(e\left(\frac{1}{840}\right)\)	\(e\left(\frac{73}{120}\right)\)	\(e\left(\frac{89}{120}\right)\)	\(e\left(\frac{97}{140}\right)\)	\(e\left(\frac{37}{420}\right)\)	\(e\left(\frac{95}{168}\right)\)	\(e\left(\frac{29}{168}\right)\)
\(\chi_{8041}(1324,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{33}{140}\right)\)	\(e\left(\frac{439}{840}\right)\)	\(e\left(\frac{33}{70}\right)\)	\(e\left(\frac{307}{840}\right)\)	\(e\left(\frac{91}{120}\right)\)	\(e\left(\frac{83}{120}\right)\)	\(e\left(\frac{99}{140}\right)\)	\(e\left(\frac{19}{420}\right)\)	\(e\left(\frac{101}{168}\right)\)	\(e\left(\frac{167}{168}\right)\)
\(\chi_{8041}(1345,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{57}{140}\right)\)	\(e\left(\frac{491}{840}\right)\)	\(e\left(\frac{57}{70}\right)\)	\(e\left(\frac{263}{840}\right)\)	\(e\left(\frac{119}{120}\right)\)	\(e\left(\frac{7}{120}\right)\)	\(e\left(\frac{31}{140}\right)\)	\(e\left(\frac{71}{420}\right)\)	\(e\left(\frac{121}{168}\right)\)	\(e\left(\frac{67}{168}\right)\)
\(\chi_{8041}(1351,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{139}{140}\right)\)	\(e\left(\frac{97}{840}\right)\)	\(e\left(\frac{69}{70}\right)\)	\(e\left(\frac{661}{840}\right)\)	\(e\left(\frac{13}{120}\right)\)	\(e\left(\frac{29}{120}\right)\)	\(e\left(\frac{137}{140}\right)\)	\(e\left(\frac{97}{420}\right)\)	\(e\left(\frac{131}{168}\right)\)	\(e\left(\frac{17}{168}\right)\)

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First 31 of 192 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.fz
Modulus	$8041$
Conductor	$8041$
Order	$840$
Real	no
Primitive	yes
Minimal	yes
Parity	odd

Modulus:	\(8041\)
Conductor:	\(8041\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(840\)	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)