LMFDB - Dirichlet character orbit 8041.fy

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(8041, base_ring=CyclotomicField(840)) M = H._module chi = DirichletCharacter(H, M([504,105,40])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(9,8041)) 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:	even	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	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$12$
$\chi_{8041}(9,\cdot)$	$1$	$1$	$e\left(\frac{89}{140}\right)$	$e\left(\frac{817}{840}\right)$	$e\left(\frac{19}{70}\right)$	$e\left(\frac{181}{840}\right)$	$e\left(\frac{73}{120}\right)$	$e\left(\frac{29}{120}\right)$	$e\left(\frac{127}{140}\right)$	$e\left(\frac{397}{420}\right)$	$e\left(\frac{143}{168}\right)$	$e\left(\frac{41}{168}\right)$
$\chi_{8041}(15,\cdot)$	$1$	$1$	$e\left(\frac{23}{140}\right)$	$e\left(\frac{499}{840}\right)$	$e\left(\frac{23}{70}\right)$	$e\left(\frac{127}{840}\right)$	$e\left(\frac{91}{120}\right)$	$e\left(\frac{23}{120}\right)$	$e\left(\frac{69}{140}\right)$	$e\left(\frac{79}{420}\right)$	$e\left(\frac{53}{168}\right)$	$e\left(\frac{155}{168}\right)$
$\chi_{8041}(25,\cdot)$	$1$	$1$	$e\left(\frac{97}{140}\right)$	$e\left(\frac{181}{840}\right)$	$e\left(\frac{27}{70}\right)$	$e\left(\frac{73}{840}\right)$	$e\left(\frac{109}{120}\right)$	$e\left(\frac{17}{120}\right)$	$e\left(\frac{11}{140}\right)$	$e\left(\frac{181}{420}\right)$	$e\left(\frac{131}{168}\right)$	$e\left(\frac{101}{168}\right)$
$\chi_{8041}(53,\cdot)$	$1$	$1$	$e\left(\frac{39}{140}\right)$	$e\left(\frac{767}{840}\right)$	$e\left(\frac{39}{70}\right)$	$e\left(\frac{611}{840}\right)$	$e\left(\frac{23}{120}\right)$	$e\left(\frac{19}{120}\right)$	$e\left(\frac{117}{140}\right)$	$e\left(\frac{347}{420}\right)$	$e\left(\frac{1}{168}\right)$	$e\left(\frac{79}{168}\right)$
$\chi_{8041}(60,\cdot)$	$1$	$1$	$e\left(\frac{81}{140}\right)$	$e\left(\frac{193}{840}\right)$	$e\left(\frac{11}{70}\right)$	$e\left(\frac{709}{840}\right)$	$e\left(\frac{97}{120}\right)$	$e\left(\frac{101}{120}\right)$	$e\left(\frac{103}{140}\right)$	$e\left(\frac{193}{420}\right)$	$e\left(\frac{71}{168}\right)$	$e\left(\frac{65}{168}\right)$
$\chi_{8041}(185,\cdot)$	$1$	$1$	$e\left(\frac{59}{140}\right)$	$e\left(\frac{787}{840}\right)$	$e\left(\frac{59}{70}\right)$	$e\left(\frac{271}{840}\right)$	$e\left(\frac{43}{120}\right)$	$e\left(\frac{119}{120}\right)$	$e\left(\frac{37}{140}\right)$	$e\left(\frac{367}{420}\right)$	$e\left(\frac{125}{168}\right)$	$e\left(\frac{131}{168}\right)$
$\chi_{8041}(196,\cdot)$	$1$	$1$	$e\left(\frac{9}{140}\right)$	$e\left(\frac{737}{840}\right)$	$e\left(\frac{9}{70}\right)$	$e\left(\frac{701}{840}\right)$	$e\left(\frac{113}{120}\right)$	$e\left(\frac{109}{120}\right)$	$e\left(\frac{27}{140}\right)$	$e\left(\frac{317}{420}\right)$	$e\left(\frac{151}{168}\right)$	$e\left(\frac{1}{168}\right)$
$\chi_{8041}(212,\cdot)$	$1$	$1$	$e\left(\frac{97}{140}\right)$	$e\left(\frac{461}{840}\right)$	$e\left(\frac{27}{70}\right)$	$e\left(\frac{353}{840}\right)$	$e\left(\frac{29}{120}\right)$	$e\left(\frac{97}{120}\right)$	$e\left(\frac{11}{140}\right)$	$e\left(\frac{41}{420}\right)$	$e\left(\frac{19}{168}\right)$	$e\left(\frac{157}{168}\right)$
$\chi_{8041}(229,\cdot)$	$1$	$1$	$e\left(\frac{29}{140}\right)$	$e\left(\frac{757}{840}\right)$	$e\left(\frac{29}{70}\right)$	$e\left(\frac{361}{840}\right)$	$e\left(\frac{13}{120}\right)$	$e\left(\frac{89}{120}\right)$	$e\left(\frac{87}{140}\right)$	$e\left(\frac{337}{420}\right)$	$e\left(\frac{107}{168}\right)$	$e\left(\frac{53}{168}\right)$
$\chi_{8041}(240,\cdot)$	$1$	$1$	$e\left(\frac{139}{140}\right)$	$e\left(\frac{727}{840}\right)$	$e\left(\frac{69}{70}\right)$	$e\left(\frac{451}{840}\right)$	$e\left(\frac{103}{120}\right)$	$e\left(\frac{59}{120}\right)$	$e\left(\frac{137}{140}\right)$	$e\left(\frac{307}{420}\right)$	$e\left(\frac{89}{168}\right)$	$e\left(\frac{143}{168}\right)$
$\chi_{8041}(246,\cdot)$	$1$	$1$	$e\left(\frac{113}{140}\right)$	$e\left(\frac{29}{840}\right)$	$e\left(\frac{43}{70}\right)$	$e\left(\frac{137}{840}\right)$	$e\left(\frac{101}{120}\right)$	$e\left(\frac{73}{120}\right)$	$e\left(\frac{59}{140}\right)$	$e\left(\frac{29}{420}\right)$	$e\left(\frac{163}{168}\right)$	$e\left(\frac{109}{168}\right)$
$\chi_{8041}(400,\cdot)$	$1$	$1$	$e\left(\frac{73}{140}\right)$	$e\left(\frac{409}{840}\right)$	$e\left(\frac{3}{70}\right)$	$e\left(\frac{397}{840}\right)$	$e\left(\frac{1}{120}\right)$	$e\left(\frac{53}{120}\right)$	$e\left(\frac{79}{140}\right)$	$e\left(\frac{409}{420}\right)$	$e\left(\frac{167}{168}\right)$	$e\left(\frac{89}{168}\right)$
$\chi_{8041}(410,\cdot)$	$1$	$1$	$e\left(\frac{47}{140}\right)$	$e\left(\frac{551}{840}\right)$	$e\left(\frac{47}{70}\right)$	$e\left(\frac{83}{840}\right)$	$e\left(\frac{119}{120}\right)$	$e\left(\frac{67}{120}\right)$	$e\left(\frac{1}{140}\right)$	$e\left(\frac{131}{420}\right)$	$e\left(\frac{73}{168}\right)$	$e\left(\frac{55}{168}\right)$
$\chi_{8041}(427,\cdot)$	$1$	$1$	$e\left(\frac{139}{140}\right)$	$e\left(\frac{167}{840}\right)$	$e\left(\frac{69}{70}\right)$	$e\left(\frac{731}{840}\right)$	$e\left(\frac{23}{120}\right)$	$e\left(\frac{19}{120}\right)$	$e\left(\frac{137}{140}\right)$	$e\left(\frac{167}{420}\right)$	$e\left(\frac{145}{168}\right)$	$e\left(\frac{31}{168}\right)$
$\chi_{8041}(444,\cdot)$	$1$	$1$	$e\left(\frac{43}{140}\right)$	$e\left(\frac{799}{840}\right)$	$e\left(\frac{43}{70}\right)$	$e\left(\frac{67}{840}\right)$	$e\left(\frac{31}{120}\right)$	$e\left(\frac{83}{120}\right)$	$e\left(\frac{129}{140}\right)$	$e\left(\frac{379}{420}\right)$	$e\left(\frac{65}{168}\right)$	$e\left(\frac{95}{168}\right)$
$\chi_{8041}(576,\cdot)$	$1$	$1$	$e\left(\frac{123}{140}\right)$	$e\left(\frac{739}{840}\right)$	$e\left(\frac{53}{70}\right)$	$e\left(\frac{247}{840}\right)$	$e\left(\frac{91}{120}\right)$	$e\left(\frac{23}{120}\right)$	$e\left(\frac{89}{140}\right)$	$e\left(\frac{319}{420}\right)$	$e\left(\frac{29}{168}\right)$	$e\left(\frac{107}{168}\right)$
$\chi_{8041}(597,\cdot)$	$1$	$1$	$e\left(\frac{87}{140}\right)$	$e\left(\frac{311}{840}\right)$	$e\left(\frac{17}{70}\right)$	$e\left(\frac{803}{840}\right)$	$e\left(\frac{119}{120}\right)$	$e\left(\frac{67}{120}\right)$	$e\left(\frac{121}{140}\right)$	$e\left(\frac{311}{420}\right)$	$e\left(\frac{97}{168}\right)$	$e\left(\frac{103}{168}\right)$
$\chi_{8041}(654,\cdot)$	$1$	$1$	$e\left(\frac{61}{140}\right)$	$e\left(\frac{733}{840}\right)$	$e\left(\frac{61}{70}\right)$	$e\left(\frac{769}{840}\right)$	$e\left(\frac{37}{120}\right)$	$e\left(\frac{41}{120}\right)$	$e\left(\frac{43}{140}\right)$	$e\left(\frac{313}{420}\right)$	$e\left(\frac{59}{168}\right)$	$e\left(\frac{125}{168}\right)$
$\chi_{8041}(740,\cdot)$	$1$	$1$	$e\left(\frac{117}{140}\right)$	$e\left(\frac{481}{840}\right)$	$e\left(\frac{47}{70}\right)$	$e\left(\frac{13}{840}\right)$	$e\left(\frac{49}{120}\right)$	$e\left(\frac{77}{120}\right)$	$e\left(\frac{71}{140}\right)$	$e\left(\frac{61}{420}\right)$	$e\left(\frac{143}{168}\right)$	$e\left(\frac{41}{168}\right)$
$\chi_{8041}(746,\cdot)$	$1$	$1$	$e\left(\frac{79}{140}\right)$	$e\left(\frac{667}{840}\right)$	$e\left(\frac{9}{70}\right)$	$e\left(\frac{631}{840}\right)$	$e\left(\frac{43}{120}\right)$	$e\left(\frac{119}{120}\right)$	$e\left(\frac{97}{140}\right)$	$e\left(\frac{247}{420}\right)$	$e\left(\frac{53}{168}\right)$	$e\left(\frac{155}{168}\right)$
$\chi_{8041}(784,\cdot)$	$1$	$1$	$e\left(\frac{67}{140}\right)$	$e\left(\frac{431}{840}\right)$	$e\left(\frac{67}{70}\right)$	$e\left(\frac{443}{840}\right)$	$e\left(\frac{119}{120}\right)$	$e\left(\frac{67}{120}\right)$	$e\left(\frac{61}{140}\right)$	$e\left(\frac{11}{420}\right)$	$e\left(\frac{1}{168}\right)$	$e\left(\frac{79}{168}\right)$
$\chi_{8041}(797,\cdot)$	$1$	$1$	$e\left(\frac{131}{140}\right)$	$e\left(\frac{803}{840}\right)$	$e\left(\frac{61}{70}\right)$	$e\left(\frac{839}{840}\right)$	$e\left(\frac{107}{120}\right)$	$e\left(\frac{31}{120}\right)$	$e\left(\frac{113}{140}\right)$	$e\left(\frac{383}{420}\right)$	$e\left(\frac{157}{168}\right)$	$e\left(\frac{139}{168}\right)$
$\chi_{8041}(841,\cdot)$	$1$	$1$	$e\left(\frac{121}{140}\right)$	$e\left(\frac{653}{840}\right)$	$e\left(\frac{51}{70}\right)$	$e\left(\frac{449}{840}\right)$	$e\left(\frac{77}{120}\right)$	$e\left(\frac{1}{120}\right)$	$e\left(\frac{83}{140}\right)$	$e\left(\frac{233}{420}\right)$	$e\left(\frac{67}{168}\right)$	$e\left(\frac{85}{168}\right)$
$\chi_{8041}(916,\cdot)$	$1$	$1$	$e\left(\frac{87}{140}\right)$	$e\left(\frac{451}{840}\right)$	$e\left(\frac{17}{70}\right)$	$e\left(\frac{103}{840}\right)$	$e\left(\frac{19}{120}\right)$	$e\left(\frac{47}{120}\right)$	$e\left(\frac{121}{140}\right)$	$e\left(\frac{31}{420}\right)$	$e\left(\frac{125}{168}\right)$	$e\left(\frac{131}{168}\right)$
$\chi_{8041}(927,\cdot)$	$1$	$1$	$e\left(\frac{37}{140}\right)$	$e\left(\frac{401}{840}\right)$	$e\left(\frac{37}{70}\right)$	$e\left(\frac{533}{840}\right)$	$e\left(\frac{89}{120}\right)$	$e\left(\frac{37}{120}\right)$	$e\left(\frac{111}{140}\right)$	$e\left(\frac{401}{420}\right)$	$e\left(\frac{151}{168}\right)$	$e\left(\frac{1}{168}\right)$
$\chi_{8041}(960,\cdot)$	$1$	$1$	$e\left(\frac{57}{140}\right)$	$e\left(\frac{421}{840}\right)$	$e\left(\frac{57}{70}\right)$	$e\left(\frac{193}{840}\right)$	$e\left(\frac{109}{120}\right)$	$e\left(\frac{17}{120}\right)$	$e\left(\frac{31}{140}\right)$	$e\left(\frac{1}{420}\right)$	$e\left(\frac{107}{168}\right)$	$e\left(\frac{53}{168}\right)$
$\chi_{8041}(961,\cdot)$	$1$	$1$	$e\left(\frac{93}{140}\right)$	$e\left(\frac{289}{840}\right)$	$e\left(\frac{23}{70}\right)$	$e\left(\frac{757}{840}\right)$	$e\left(\frac{1}{120}\right)$	$e\left(\frac{53}{120}\right)$	$e\left(\frac{139}{140}\right)$	$e\left(\frac{289}{420}\right)$	$e\left(\frac{95}{168}\right)$	$e\left(\frac{113}{168}\right)$
$\chi_{8041}(971,\cdot)$	$1$	$1$	$e\left(\frac{27}{140}\right)$	$e\left(\frac{391}{840}\right)$	$e\left(\frac{27}{70}\right)$	$e\left(\frac{283}{840}\right)$	$e\left(\frac{79}{120}\right)$	$e\left(\frac{107}{120}\right)$	$e\left(\frac{81}{140}\right)$	$e\left(\frac{391}{420}\right)$	$e\left(\frac{89}{168}\right)$	$e\left(\frac{143}{168}\right)$
$\chi_{8041}(977,\cdot)$	$1$	$1$	$e\left(\frac{29}{140}\right)$	$e\left(\frac{197}{840}\right)$	$e\left(\frac{29}{70}\right)$	$e\left(\frac{641}{840}\right)$	$e\left(\frac{53}{120}\right)$	$e\left(\frac{49}{120}\right)$	$e\left(\frac{87}{140}\right)$	$e\left(\frac{197}{420}\right)$	$e\left(\frac{163}{168}\right)$	$e\left(\frac{109}{168}\right)$
$\chi_{8041}(984,\cdot)$	$1$	$1$	$e\left(\frac{31}{140}\right)$	$e\left(\frac{563}{840}\right)$	$e\left(\frac{31}{70}\right)$	$e\left(\frac{719}{840}\right)$	$e\left(\frac{107}{120}\right)$	$e\left(\frac{31}{120}\right)$	$e\left(\frac{93}{140}\right)$	$e\left(\frac{143}{420}\right)$	$e\left(\frac{13}{168}\right)$	$e\left(\frac{19}{168}\right)$
$\chi_{8041}(1131,\cdot)$	$1$	$1$	$e\left(\frac{129}{140}\right)$	$e\left(\frac{577}{840}\right)$	$e\left(\frac{59}{70}\right)$	$e\left(\frac{61}{840}\right)$	$e\left(\frac{73}{120}\right)$	$e\left(\frac{29}{120}\right)$	$e\left(\frac{107}{140}\right)$	$e\left(\frac{157}{420}\right)$	$e\left(\frac{167}{168}\right)$	$e\left(\frac{89}{168}\right)$

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	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(12\)
\(\chi_{8041}(9,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{89}{140}\right)\)	\(e\left(\frac{817}{840}\right)\)	\(e\left(\frac{19}{70}\right)\)	\(e\left(\frac{181}{840}\right)\)	\(e\left(\frac{73}{120}\right)\)	\(e\left(\frac{29}{120}\right)\)	\(e\left(\frac{127}{140}\right)\)	\(e\left(\frac{397}{420}\right)\)	\(e\left(\frac{143}{168}\right)\)	\(e\left(\frac{41}{168}\right)\)
\(\chi_{8041}(15,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{140}\right)\)	\(e\left(\frac{499}{840}\right)\)	\(e\left(\frac{23}{70}\right)\)	\(e\left(\frac{127}{840}\right)\)	\(e\left(\frac{91}{120}\right)\)	\(e\left(\frac{23}{120}\right)\)	\(e\left(\frac{69}{140}\right)\)	\(e\left(\frac{79}{420}\right)\)	\(e\left(\frac{53}{168}\right)\)	\(e\left(\frac{155}{168}\right)\)
\(\chi_{8041}(25,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{97}{140}\right)\)	\(e\left(\frac{181}{840}\right)\)	\(e\left(\frac{27}{70}\right)\)	\(e\left(\frac{73}{840}\right)\)	\(e\left(\frac{109}{120}\right)\)	\(e\left(\frac{17}{120}\right)\)	\(e\left(\frac{11}{140}\right)\)	\(e\left(\frac{181}{420}\right)\)	\(e\left(\frac{131}{168}\right)\)	\(e\left(\frac{101}{168}\right)\)
\(\chi_{8041}(53,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{39}{140}\right)\)	\(e\left(\frac{767}{840}\right)\)	\(e\left(\frac{39}{70}\right)\)	\(e\left(\frac{611}{840}\right)\)	\(e\left(\frac{23}{120}\right)\)	\(e\left(\frac{19}{120}\right)\)	\(e\left(\frac{117}{140}\right)\)	\(e\left(\frac{347}{420}\right)\)	\(e\left(\frac{1}{168}\right)\)	\(e\left(\frac{79}{168}\right)\)
\(\chi_{8041}(60,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{81}{140}\right)\)	\(e\left(\frac{193}{840}\right)\)	\(e\left(\frac{11}{70}\right)\)	\(e\left(\frac{709}{840}\right)\)	\(e\left(\frac{97}{120}\right)\)	\(e\left(\frac{101}{120}\right)\)	\(e\left(\frac{103}{140}\right)\)	\(e\left(\frac{193}{420}\right)\)	\(e\left(\frac{71}{168}\right)\)	\(e\left(\frac{65}{168}\right)\)
\(\chi_{8041}(185,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{140}\right)\)	\(e\left(\frac{787}{840}\right)\)	\(e\left(\frac{59}{70}\right)\)	\(e\left(\frac{271}{840}\right)\)	\(e\left(\frac{43}{120}\right)\)	\(e\left(\frac{119}{120}\right)\)	\(e\left(\frac{37}{140}\right)\)	\(e\left(\frac{367}{420}\right)\)	\(e\left(\frac{125}{168}\right)\)	\(e\left(\frac{131}{168}\right)\)
\(\chi_{8041}(196,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{140}\right)\)	\(e\left(\frac{737}{840}\right)\)	\(e\left(\frac{9}{70}\right)\)	\(e\left(\frac{701}{840}\right)\)	\(e\left(\frac{113}{120}\right)\)	\(e\left(\frac{109}{120}\right)\)	\(e\left(\frac{27}{140}\right)\)	\(e\left(\frac{317}{420}\right)\)	\(e\left(\frac{151}{168}\right)\)	\(e\left(\frac{1}{168}\right)\)
\(\chi_{8041}(212,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{97}{140}\right)\)	\(e\left(\frac{461}{840}\right)\)	\(e\left(\frac{27}{70}\right)\)	\(e\left(\frac{353}{840}\right)\)	\(e\left(\frac{29}{120}\right)\)	\(e\left(\frac{97}{120}\right)\)	\(e\left(\frac{11}{140}\right)\)	\(e\left(\frac{41}{420}\right)\)	\(e\left(\frac{19}{168}\right)\)	\(e\left(\frac{157}{168}\right)\)
\(\chi_{8041}(229,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{140}\right)\)	\(e\left(\frac{757}{840}\right)\)	\(e\left(\frac{29}{70}\right)\)	\(e\left(\frac{361}{840}\right)\)	\(e\left(\frac{13}{120}\right)\)	\(e\left(\frac{89}{120}\right)\)	\(e\left(\frac{87}{140}\right)\)	\(e\left(\frac{337}{420}\right)\)	\(e\left(\frac{107}{168}\right)\)	\(e\left(\frac{53}{168}\right)\)
\(\chi_{8041}(240,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{139}{140}\right)\)	\(e\left(\frac{727}{840}\right)\)	\(e\left(\frac{69}{70}\right)\)	\(e\left(\frac{451}{840}\right)\)	\(e\left(\frac{103}{120}\right)\)	\(e\left(\frac{59}{120}\right)\)	\(e\left(\frac{137}{140}\right)\)	\(e\left(\frac{307}{420}\right)\)	\(e\left(\frac{89}{168}\right)\)	\(e\left(\frac{143}{168}\right)\)
\(\chi_{8041}(246,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{113}{140}\right)\)	\(e\left(\frac{29}{840}\right)\)	\(e\left(\frac{43}{70}\right)\)	\(e\left(\frac{137}{840}\right)\)	\(e\left(\frac{101}{120}\right)\)	\(e\left(\frac{73}{120}\right)\)	\(e\left(\frac{59}{140}\right)\)	\(e\left(\frac{29}{420}\right)\)	\(e\left(\frac{163}{168}\right)\)	\(e\left(\frac{109}{168}\right)\)
\(\chi_{8041}(400,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{73}{140}\right)\)	\(e\left(\frac{409}{840}\right)\)	\(e\left(\frac{3}{70}\right)\)	\(e\left(\frac{397}{840}\right)\)	\(e\left(\frac{1}{120}\right)\)	\(e\left(\frac{53}{120}\right)\)	\(e\left(\frac{79}{140}\right)\)	\(e\left(\frac{409}{420}\right)\)	\(e\left(\frac{167}{168}\right)\)	\(e\left(\frac{89}{168}\right)\)
\(\chi_{8041}(410,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{140}\right)\)	\(e\left(\frac{551}{840}\right)\)	\(e\left(\frac{47}{70}\right)\)	\(e\left(\frac{83}{840}\right)\)	\(e\left(\frac{119}{120}\right)\)	\(e\left(\frac{67}{120}\right)\)	\(e\left(\frac{1}{140}\right)\)	\(e\left(\frac{131}{420}\right)\)	\(e\left(\frac{73}{168}\right)\)	\(e\left(\frac{55}{168}\right)\)
\(\chi_{8041}(427,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{139}{140}\right)\)	\(e\left(\frac{167}{840}\right)\)	\(e\left(\frac{69}{70}\right)\)	\(e\left(\frac{731}{840}\right)\)	\(e\left(\frac{23}{120}\right)\)	\(e\left(\frac{19}{120}\right)\)	\(e\left(\frac{137}{140}\right)\)	\(e\left(\frac{167}{420}\right)\)	\(e\left(\frac{145}{168}\right)\)	\(e\left(\frac{31}{168}\right)\)
\(\chi_{8041}(444,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{140}\right)\)	\(e\left(\frac{799}{840}\right)\)	\(e\left(\frac{43}{70}\right)\)	\(e\left(\frac{67}{840}\right)\)	\(e\left(\frac{31}{120}\right)\)	\(e\left(\frac{83}{120}\right)\)	\(e\left(\frac{129}{140}\right)\)	\(e\left(\frac{379}{420}\right)\)	\(e\left(\frac{65}{168}\right)\)	\(e\left(\frac{95}{168}\right)\)
\(\chi_{8041}(576,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{123}{140}\right)\)	\(e\left(\frac{739}{840}\right)\)	\(e\left(\frac{53}{70}\right)\)	\(e\left(\frac{247}{840}\right)\)	\(e\left(\frac{91}{120}\right)\)	\(e\left(\frac{23}{120}\right)\)	\(e\left(\frac{89}{140}\right)\)	\(e\left(\frac{319}{420}\right)\)	\(e\left(\frac{29}{168}\right)\)	\(e\left(\frac{107}{168}\right)\)
\(\chi_{8041}(597,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{87}{140}\right)\)	\(e\left(\frac{311}{840}\right)\)	\(e\left(\frac{17}{70}\right)\)	\(e\left(\frac{803}{840}\right)\)	\(e\left(\frac{119}{120}\right)\)	\(e\left(\frac{67}{120}\right)\)	\(e\left(\frac{121}{140}\right)\)	\(e\left(\frac{311}{420}\right)\)	\(e\left(\frac{97}{168}\right)\)	\(e\left(\frac{103}{168}\right)\)
\(\chi_{8041}(654,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{61}{140}\right)\)	\(e\left(\frac{733}{840}\right)\)	\(e\left(\frac{61}{70}\right)\)	\(e\left(\frac{769}{840}\right)\)	\(e\left(\frac{37}{120}\right)\)	\(e\left(\frac{41}{120}\right)\)	\(e\left(\frac{43}{140}\right)\)	\(e\left(\frac{313}{420}\right)\)	\(e\left(\frac{59}{168}\right)\)	\(e\left(\frac{125}{168}\right)\)
\(\chi_{8041}(740,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{117}{140}\right)\)	\(e\left(\frac{481}{840}\right)\)	\(e\left(\frac{47}{70}\right)\)	\(e\left(\frac{13}{840}\right)\)	\(e\left(\frac{49}{120}\right)\)	\(e\left(\frac{77}{120}\right)\)	\(e\left(\frac{71}{140}\right)\)	\(e\left(\frac{61}{420}\right)\)	\(e\left(\frac{143}{168}\right)\)	\(e\left(\frac{41}{168}\right)\)
\(\chi_{8041}(746,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{79}{140}\right)\)	\(e\left(\frac{667}{840}\right)\)	\(e\left(\frac{9}{70}\right)\)	\(e\left(\frac{631}{840}\right)\)	\(e\left(\frac{43}{120}\right)\)	\(e\left(\frac{119}{120}\right)\)	\(e\left(\frac{97}{140}\right)\)	\(e\left(\frac{247}{420}\right)\)	\(e\left(\frac{53}{168}\right)\)	\(e\left(\frac{155}{168}\right)\)
\(\chi_{8041}(784,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{67}{140}\right)\)	\(e\left(\frac{431}{840}\right)\)	\(e\left(\frac{67}{70}\right)\)	\(e\left(\frac{443}{840}\right)\)	\(e\left(\frac{119}{120}\right)\)	\(e\left(\frac{67}{120}\right)\)	\(e\left(\frac{61}{140}\right)\)	\(e\left(\frac{11}{420}\right)\)	\(e\left(\frac{1}{168}\right)\)	\(e\left(\frac{79}{168}\right)\)
\(\chi_{8041}(797,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{131}{140}\right)\)	\(e\left(\frac{803}{840}\right)\)	\(e\left(\frac{61}{70}\right)\)	\(e\left(\frac{839}{840}\right)\)	\(e\left(\frac{107}{120}\right)\)	\(e\left(\frac{31}{120}\right)\)	\(e\left(\frac{113}{140}\right)\)	\(e\left(\frac{383}{420}\right)\)	\(e\left(\frac{157}{168}\right)\)	\(e\left(\frac{139}{168}\right)\)
\(\chi_{8041}(841,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{121}{140}\right)\)	\(e\left(\frac{653}{840}\right)\)	\(e\left(\frac{51}{70}\right)\)	\(e\left(\frac{449}{840}\right)\)	\(e\left(\frac{77}{120}\right)\)	\(e\left(\frac{1}{120}\right)\)	\(e\left(\frac{83}{140}\right)\)	\(e\left(\frac{233}{420}\right)\)	\(e\left(\frac{67}{168}\right)\)	\(e\left(\frac{85}{168}\right)\)
\(\chi_{8041}(916,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{87}{140}\right)\)	\(e\left(\frac{451}{840}\right)\)	\(e\left(\frac{17}{70}\right)\)	\(e\left(\frac{103}{840}\right)\)	\(e\left(\frac{19}{120}\right)\)	\(e\left(\frac{47}{120}\right)\)	\(e\left(\frac{121}{140}\right)\)	\(e\left(\frac{31}{420}\right)\)	\(e\left(\frac{125}{168}\right)\)	\(e\left(\frac{131}{168}\right)\)
\(\chi_{8041}(927,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{140}\right)\)	\(e\left(\frac{401}{840}\right)\)	\(e\left(\frac{37}{70}\right)\)	\(e\left(\frac{533}{840}\right)\)	\(e\left(\frac{89}{120}\right)\)	\(e\left(\frac{37}{120}\right)\)	\(e\left(\frac{111}{140}\right)\)	\(e\left(\frac{401}{420}\right)\)	\(e\left(\frac{151}{168}\right)\)	\(e\left(\frac{1}{168}\right)\)
\(\chi_{8041}(960,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{57}{140}\right)\)	\(e\left(\frac{421}{840}\right)\)	\(e\left(\frac{57}{70}\right)\)	\(e\left(\frac{193}{840}\right)\)	\(e\left(\frac{109}{120}\right)\)	\(e\left(\frac{17}{120}\right)\)	\(e\left(\frac{31}{140}\right)\)	\(e\left(\frac{1}{420}\right)\)	\(e\left(\frac{107}{168}\right)\)	\(e\left(\frac{53}{168}\right)\)
\(\chi_{8041}(961,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{93}{140}\right)\)	\(e\left(\frac{289}{840}\right)\)	\(e\left(\frac{23}{70}\right)\)	\(e\left(\frac{757}{840}\right)\)	\(e\left(\frac{1}{120}\right)\)	\(e\left(\frac{53}{120}\right)\)	\(e\left(\frac{139}{140}\right)\)	\(e\left(\frac{289}{420}\right)\)	\(e\left(\frac{95}{168}\right)\)	\(e\left(\frac{113}{168}\right)\)
\(\chi_{8041}(971,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{27}{140}\right)\)	\(e\left(\frac{391}{840}\right)\)	\(e\left(\frac{27}{70}\right)\)	\(e\left(\frac{283}{840}\right)\)	\(e\left(\frac{79}{120}\right)\)	\(e\left(\frac{107}{120}\right)\)	\(e\left(\frac{81}{140}\right)\)	\(e\left(\frac{391}{420}\right)\)	\(e\left(\frac{89}{168}\right)\)	\(e\left(\frac{143}{168}\right)\)
\(\chi_{8041}(977,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{140}\right)\)	\(e\left(\frac{197}{840}\right)\)	\(e\left(\frac{29}{70}\right)\)	\(e\left(\frac{641}{840}\right)\)	\(e\left(\frac{53}{120}\right)\)	\(e\left(\frac{49}{120}\right)\)	\(e\left(\frac{87}{140}\right)\)	\(e\left(\frac{197}{420}\right)\)	\(e\left(\frac{163}{168}\right)\)	\(e\left(\frac{109}{168}\right)\)
\(\chi_{8041}(984,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{140}\right)\)	\(e\left(\frac{563}{840}\right)\)	\(e\left(\frac{31}{70}\right)\)	\(e\left(\frac{719}{840}\right)\)	\(e\left(\frac{107}{120}\right)\)	\(e\left(\frac{31}{120}\right)\)	\(e\left(\frac{93}{140}\right)\)	\(e\left(\frac{143}{420}\right)\)	\(e\left(\frac{13}{168}\right)\)	\(e\left(\frac{19}{168}\right)\)
\(\chi_{8041}(1131,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{129}{140}\right)\)	\(e\left(\frac{577}{840}\right)\)	\(e\left(\frac{59}{70}\right)\)	\(e\left(\frac{61}{840}\right)\)	\(e\left(\frac{73}{120}\right)\)	\(e\left(\frac{29}{120}\right)\)	\(e\left(\frac{107}{140}\right)\)	\(e\left(\frac{157}{420}\right)\)	\(e\left(\frac{167}{168}\right)\)	\(e\left(\frac{89}{168}\right)\)

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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.fy
Modulus	$8041$
Conductor	$8041$
Order	$840$
Real	no
Primitive	yes
Minimal	yes
Parity	even

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:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)