LMFDB - Dirichlet character orbit 5041.l

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(5041, base_ring=CyclotomicField(994)) M = H._module chi = DirichletCharacter(H, M([806])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(20,5041)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$5041$
Conductor:	$5041$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$497$	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:	$\Q(\zeta_{497})$
Fixed field:	Number field defined by a degree 497 polynomial (not computed)

First 31 of 420 characters in Galois orbit

Character	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{5041}(20,\cdot)$	$1$	$1$	$e\left(\frac{269}{497}\right)$	$e\left(\frac{328}{497}\right)$	$e\left(\frac{41}{497}\right)$	$e\left(\frac{50}{71}\right)$	$e\left(\frac{100}{497}\right)$	$e\left(\frac{403}{497}\right)$	$e\left(\frac{310}{497}\right)$	$e\left(\frac{159}{497}\right)$	$e\left(\frac{122}{497}\right)$	$e\left(\frac{5}{7}\right)$
$\chi_{5041}(30,\cdot)$	$1$	$1$	$e\left(\frac{274}{497}\right)$	$e\left(\frac{408}{497}\right)$	$e\left(\frac{51}{497}\right)$	$e\left(\frac{57}{71}\right)$	$e\left(\frac{185}{497}\right)$	$e\left(\frac{174}{497}\right)$	$e\left(\frac{325}{497}\right)$	$e\left(\frac{319}{497}\right)$	$e\left(\frac{176}{497}\right)$	$e\left(\frac{4}{7}\right)$
$\chi_{5041}(32,\cdot)$	$1$	$1$	$e\left(\frac{333}{497}\right)$	$e\left(\frac{358}{497}\right)$	$e\left(\frac{169}{497}\right)$	$e\left(\frac{26}{71}\right)$	$e\left(\frac{194}{497}\right)$	$e\left(\frac{255}{497}\right)$	$e\left(\frac{5}{497}\right)$	$e\left(\frac{219}{497}\right)$	$e\left(\frac{18}{497}\right)$	$e\left(\frac{2}{7}\right)$
$\chi_{5041}(37,\cdot)$	$1$	$1$	$e\left(\frac{285}{497}\right)$	$e\left(\frac{87}{497}\right)$	$e\left(\frac{73}{497}\right)$	$e\left(\frac{44}{71}\right)$	$e\left(\frac{372}{497}\right)$	$e\left(\frac{366}{497}\right)$	$e\left(\frac{358}{497}\right)$	$e\left(\frac{174}{497}\right)$	$e\left(\frac{96}{497}\right)$	$e\left(\frac{6}{7}\right)$
$\chi_{5041}(45,\cdot)$	$1$	$1$	$e\left(\frac{279}{497}\right)$	$e\left(\frac{488}{497}\right)$	$e\left(\frac{61}{497}\right)$	$e\left(\frac{64}{71}\right)$	$e\left(\frac{270}{497}\right)$	$e\left(\frac{442}{497}\right)$	$e\left(\frac{340}{497}\right)$	$e\left(\frac{479}{497}\right)$	$e\left(\frac{230}{497}\right)$	$e\left(\frac{3}{7}\right)$
$\chi_{5041}(48,\cdot)$	$1$	$1$	$e\left(\frac{338}{497}\right)$	$e\left(\frac{438}{497}\right)$	$e\left(\frac{179}{497}\right)$	$e\left(\frac{33}{71}\right)$	$e\left(\frac{279}{497}\right)$	$e\left(\frac{26}{497}\right)$	$e\left(\frac{20}{497}\right)$	$e\left(\frac{379}{497}\right)$	$e\left(\frac{72}{497}\right)$	$e\left(\frac{1}{7}\right)$
$\chi_{5041}(91,\cdot)$	$1$	$1$	$e\left(\frac{311}{497}\right)$	$e\left(\frac{6}{497}\right)$	$e\left(\frac{125}{497}\right)$	$e\left(\frac{52}{71}\right)$	$e\left(\frac{317}{497}\right)$	$e\left(\frac{368}{497}\right)$	$e\left(\frac{436}{497}\right)$	$e\left(\frac{12}{497}\right)$	$e\left(\frac{178}{497}\right)$	$e\left(\frac{5}{7}\right)$
$\chi_{5041}(101,\cdot)$	$1$	$1$	$e\left(\frac{302}{497}\right)$	$e\left(\frac{359}{497}\right)$	$e\left(\frac{107}{497}\right)$	$e\left(\frac{11}{71}\right)$	$e\left(\frac{164}{497}\right)$	$e\left(\frac{482}{497}\right)$	$e\left(\frac{409}{497}\right)$	$e\left(\frac{221}{497}\right)$	$e\left(\frac{379}{497}\right)$	$e\left(\frac{4}{7}\right)$
$\chi_{5041}(103,\cdot)$	$1$	$1$	$e\left(\frac{235}{497}\right)$	$e\left(\frac{281}{497}\right)$	$e\left(\frac{470}{497}\right)$	$e\left(\frac{45}{71}\right)$	$e\left(\frac{19}{497}\right)$	$e\left(\frac{171}{497}\right)$	$e\left(\frac{208}{497}\right)$	$e\left(\frac{65}{497}\right)$	$e\left(\frac{53}{497}\right)$	$e\left(\frac{2}{7}\right)$
$\chi_{5041}(108,\cdot)$	$1$	$1$	$e\left(\frac{348}{497}\right)$	$e\left(\frac{101}{497}\right)$	$e\left(\frac{199}{497}\right)$	$e\left(\frac{47}{71}\right)$	$e\left(\frac{449}{497}\right)$	$e\left(\frac{65}{497}\right)$	$e\left(\frac{50}{497}\right)$	$e\left(\frac{202}{497}\right)$	$e\left(\frac{180}{497}\right)$	$e\left(\frac{6}{7}\right)$
$\chi_{5041}(116,\cdot)$	$1$	$1$	$e\left(\frac{132}{497}\right)$	$e\left(\frac{124}{497}\right)$	$e\left(\frac{264}{497}\right)$	$e\left(\frac{57}{71}\right)$	$e\left(\frac{256}{497}\right)$	$e\left(\frac{316}{497}\right)$	$e\left(\frac{396}{497}\right)$	$e\left(\frac{248}{497}\right)$	$e\left(\frac{34}{497}\right)$	$e\left(\frac{3}{7}\right)$
$\chi_{5041}(119,\cdot)$	$1$	$1$	$e\left(\frac{107}{497}\right)$	$e\left(\frac{221}{497}\right)$	$e\left(\frac{214}{497}\right)$	$e\left(\frac{22}{71}\right)$	$e\left(\frac{328}{497}\right)$	$e\left(\frac{467}{497}\right)$	$e\left(\frac{321}{497}\right)$	$e\left(\frac{442}{497}\right)$	$e\left(\frac{261}{497}\right)$	$e\left(\frac{1}{7}\right)$
$\chi_{5041}(162,\cdot)$	$1$	$1$	$e\left(\frac{353}{497}\right)$	$e\left(\frac{181}{497}\right)$	$e\left(\frac{209}{497}\right)$	$e\left(\frac{54}{71}\right)$	$e\left(\frac{37}{497}\right)$	$e\left(\frac{333}{497}\right)$	$e\left(\frac{65}{497}\right)$	$e\left(\frac{362}{497}\right)$	$e\left(\frac{234}{497}\right)$	$e\left(\frac{5}{7}\right)$
$\chi_{5041}(172,\cdot)$	$1$	$1$	$e\left(\frac{330}{497}\right)$	$e\left(\frac{310}{497}\right)$	$e\left(\frac{163}{497}\right)$	$e\left(\frac{36}{71}\right)$	$e\left(\frac{143}{497}\right)$	$e\left(\frac{293}{497}\right)$	$e\left(\frac{493}{497}\right)$	$e\left(\frac{123}{497}\right)$	$e\left(\frac{85}{497}\right)$	$e\left(\frac{4}{7}\right)$
$\chi_{5041}(174,\cdot)$	$1$	$1$	$e\left(\frac{137}{497}\right)$	$e\left(\frac{204}{497}\right)$	$e\left(\frac{274}{497}\right)$	$e\left(\frac{64}{71}\right)$	$e\left(\frac{341}{497}\right)$	$e\left(\frac{87}{497}\right)$	$e\left(\frac{411}{497}\right)$	$e\left(\frac{408}{497}\right)$	$e\left(\frac{88}{497}\right)$	$e\left(\frac{2}{7}\right)$
$\chi_{5041}(179,\cdot)$	$1$	$1$	$e\left(\frac{411}{497}\right)$	$e\left(\frac{115}{497}\right)$	$e\left(\frac{325}{497}\right)$	$e\left(\frac{50}{71}\right)$	$e\left(\frac{29}{497}\right)$	$e\left(\frac{261}{497}\right)$	$e\left(\frac{239}{497}\right)$	$e\left(\frac{230}{497}\right)$	$e\left(\frac{264}{497}\right)$	$e\left(\frac{6}{7}\right)$
$\chi_{5041}(187,\cdot)$	$1$	$1$	$e\left(\frac{482}{497}\right)$	$e\left(\frac{257}{497}\right)$	$e\left(\frac{467}{497}\right)$	$e\left(\frac{50}{71}\right)$	$e\left(\frac{242}{497}\right)$	$e\left(\frac{190}{497}\right)$	$e\left(\frac{452}{497}\right)$	$e\left(\frac{17}{497}\right)$	$e\left(\frac{335}{497}\right)$	$e\left(\frac{3}{7}\right)$
$\chi_{5041}(190,\cdot)$	$1$	$1$	$e\left(\frac{373}{497}\right)$	$e\left(\frac{4}{497}\right)$	$e\left(\frac{249}{497}\right)$	$e\left(\frac{11}{71}\right)$	$e\left(\frac{377}{497}\right)$	$e\left(\frac{411}{497}\right)$	$e\left(\frac{125}{497}\right)$	$e\left(\frac{8}{497}\right)$	$e\left(\frac{450}{497}\right)$	$e\left(\frac{1}{7}\right)$
$\chi_{5041}(233,\cdot)$	$1$	$1$	$e\left(\frac{395}{497}\right)$	$e\left(\frac{356}{497}\right)$	$e\left(\frac{293}{497}\right)$	$e\left(\frac{56}{71}\right)$	$e\left(\frac{254}{497}\right)$	$e\left(\frac{298}{497}\right)$	$e\left(\frac{191}{497}\right)$	$e\left(\frac{215}{497}\right)$	$e\left(\frac{290}{497}\right)$	$e\left(\frac{5}{7}\right)$
$\chi_{5041}(243,\cdot)$	$1$	$1$	$e\left(\frac{358}{497}\right)$	$e\left(\frac{261}{497}\right)$	$e\left(\frac{219}{497}\right)$	$e\left(\frac{61}{71}\right)$	$e\left(\frac{122}{497}\right)$	$e\left(\frac{104}{497}\right)$	$e\left(\frac{80}{497}\right)$	$e\left(\frac{25}{497}\right)$	$e\left(\frac{288}{497}\right)$	$e\left(\frac{4}{7}\right)$
$\chi_{5041}(245,\cdot)$	$1$	$1$	$e\left(\frac{39}{497}\right)$	$e\left(\frac{127}{497}\right)$	$e\left(\frac{78}{497}\right)$	$e\left(\frac{12}{71}\right)$	$e\left(\frac{166}{497}\right)$	$e\left(\frac{3}{497}\right)$	$e\left(\frac{117}{497}\right)$	$e\left(\frac{254}{497}\right)$	$e\left(\frac{123}{497}\right)$	$e\left(\frac{2}{7}\right)$
$\chi_{5041}(250,\cdot)$	$1$	$1$	$e\left(\frac{474}{497}\right)$	$e\left(\frac{129}{497}\right)$	$e\left(\frac{451}{497}\right)$	$e\left(\frac{53}{71}\right)$	$e\left(\frac{106}{497}\right)$	$e\left(\frac{457}{497}\right)$	$e\left(\frac{428}{497}\right)$	$e\left(\frac{258}{497}\right)$	$e\left(\frac{348}{497}\right)$	$e\left(\frac{6}{7}\right)$
$\chi_{5041}(258,\cdot)$	$1$	$1$	$e\left(\frac{335}{497}\right)$	$e\left(\frac{390}{497}\right)$	$e\left(\frac{173}{497}\right)$	$e\left(\frac{43}{71}\right)$	$e\left(\frac{228}{497}\right)$	$e\left(\frac{64}{497}\right)$	$e\left(\frac{11}{497}\right)$	$e\left(\frac{283}{497}\right)$	$e\left(\frac{139}{497}\right)$	$e\left(\frac{3}{7}\right)$
$\chi_{5041}(304,\cdot)$	$1$	$1$	$e\left(\frac{437}{497}\right)$	$e\left(\frac{34}{497}\right)$	$e\left(\frac{377}{497}\right)$	$e\left(\frac{58}{71}\right)$	$e\left(\frac{471}{497}\right)$	$e\left(\frac{263}{497}\right)$	$e\left(\frac{317}{497}\right)$	$e\left(\frac{68}{497}\right)$	$e\left(\frac{346}{497}\right)$	$e\left(\frac{5}{7}\right)$
$\chi_{5041}(314,\cdot)$	$1$	$1$	$e\left(\frac{386}{497}\right)$	$e\left(\frac{212}{497}\right)$	$e\left(\frac{275}{497}\right)$	$e\left(\frac{15}{71}\right)$	$e\left(\frac{101}{497}\right)$	$e\left(\frac{412}{497}\right)$	$e\left(\frac{164}{497}\right)$	$e\left(\frac{424}{497}\right)$	$e\left(\frac{491}{497}\right)$	$e\left(\frac{4}{7}\right)$
$\chi_{5041}(316,\cdot)$	$1$	$1$	$e\left(\frac{438}{497}\right)$	$e\left(\frac{50}{497}\right)$	$e\left(\frac{379}{497}\right)$	$e\left(\frac{31}{71}\right)$	$e\left(\frac{488}{497}\right)$	$e\left(\frac{416}{497}\right)$	$e\left(\frac{320}{497}\right)$	$e\left(\frac{100}{497}\right)$	$e\left(\frac{158}{497}\right)$	$e\left(\frac{2}{7}\right)$
$\chi_{5041}(321,\cdot)$	$1$	$1$	$e\left(\frac{40}{497}\right)$	$e\left(\frac{143}{497}\right)$	$e\left(\frac{80}{497}\right)$	$e\left(\frac{56}{71}\right)$	$e\left(\frac{183}{497}\right)$	$e\left(\frac{156}{497}\right)$	$e\left(\frac{120}{497}\right)$	$e\left(\frac{286}{497}\right)$	$e\left(\frac{432}{497}\right)$	$e\left(\frac{6}{7}\right)$
$\chi_{5041}(329,\cdot)$	$1$	$1$	$e\left(\frac{188}{497}\right)$	$e\left(\frac{26}{497}\right)$	$e\left(\frac{376}{497}\right)$	$e\left(\frac{36}{71}\right)$	$e\left(\frac{214}{497}\right)$	$e\left(\frac{435}{497}\right)$	$e\left(\frac{67}{497}\right)$	$e\left(\frac{52}{497}\right)$	$e\left(\frac{440}{497}\right)$	$e\left(\frac{3}{7}\right)$
$\chi_{5041}(332,\cdot)$	$1$	$1$	$e\left(\frac{408}{497}\right)$	$e\left(\frac{67}{497}\right)$	$e\left(\frac{319}{497}\right)$	$e\left(\frac{60}{71}\right)$	$e\left(\frac{475}{497}\right)$	$e\left(\frac{299}{497}\right)$	$e\left(\frac{230}{497}\right)$	$e\left(\frac{134}{497}\right)$	$e\left(\frac{331}{497}\right)$	$e\left(\frac{1}{7}\right)$
$\chi_{5041}(375,\cdot)$	$1$	$1$	$e\left(\frac{479}{497}\right)$	$e\left(\frac{209}{497}\right)$	$e\left(\frac{461}{497}\right)$	$e\left(\frac{60}{71}\right)$	$e\left(\frac{191}{497}\right)$	$e\left(\frac{228}{497}\right)$	$e\left(\frac{443}{497}\right)$	$e\left(\frac{418}{497}\right)$	$e\left(\frac{402}{497}\right)$	$e\left(\frac{5}{7}\right)$
$\chi_{5041}(385,\cdot)$	$1$	$1$	$e\left(\frac{414}{497}\right)$	$e\left(\frac{163}{497}\right)$	$e\left(\frac{331}{497}\right)$	$e\left(\frac{40}{71}\right)$	$e\left(\frac{80}{497}\right)$	$e\left(\frac{223}{497}\right)$	$e\left(\frac{248}{497}\right)$	$e\left(\frac{326}{497}\right)$	$e\left(\frac{197}{497}\right)$	$e\left(\frac{4}{7}\right)$

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	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\(\chi_{5041}(20,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{269}{497}\right)\)	\(e\left(\frac{328}{497}\right)\)	\(e\left(\frac{41}{497}\right)\)	\(e\left(\frac{50}{71}\right)\)	\(e\left(\frac{100}{497}\right)\)	\(e\left(\frac{403}{497}\right)\)	\(e\left(\frac{310}{497}\right)\)	\(e\left(\frac{159}{497}\right)\)	\(e\left(\frac{122}{497}\right)\)	\(e\left(\frac{5}{7}\right)\)
\(\chi_{5041}(30,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{274}{497}\right)\)	\(e\left(\frac{408}{497}\right)\)	\(e\left(\frac{51}{497}\right)\)	\(e\left(\frac{57}{71}\right)\)	\(e\left(\frac{185}{497}\right)\)	\(e\left(\frac{174}{497}\right)\)	\(e\left(\frac{325}{497}\right)\)	\(e\left(\frac{319}{497}\right)\)	\(e\left(\frac{176}{497}\right)\)	\(e\left(\frac{4}{7}\right)\)
\(\chi_{5041}(32,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{333}{497}\right)\)	\(e\left(\frac{358}{497}\right)\)	\(e\left(\frac{169}{497}\right)\)	\(e\left(\frac{26}{71}\right)\)	\(e\left(\frac{194}{497}\right)\)	\(e\left(\frac{255}{497}\right)\)	\(e\left(\frac{5}{497}\right)\)	\(e\left(\frac{219}{497}\right)\)	\(e\left(\frac{18}{497}\right)\)	\(e\left(\frac{2}{7}\right)\)
\(\chi_{5041}(37,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{285}{497}\right)\)	\(e\left(\frac{87}{497}\right)\)	\(e\left(\frac{73}{497}\right)\)	\(e\left(\frac{44}{71}\right)\)	\(e\left(\frac{372}{497}\right)\)	\(e\left(\frac{366}{497}\right)\)	\(e\left(\frac{358}{497}\right)\)	\(e\left(\frac{174}{497}\right)\)	\(e\left(\frac{96}{497}\right)\)	\(e\left(\frac{6}{7}\right)\)
\(\chi_{5041}(45,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{279}{497}\right)\)	\(e\left(\frac{488}{497}\right)\)	\(e\left(\frac{61}{497}\right)\)	\(e\left(\frac{64}{71}\right)\)	\(e\left(\frac{270}{497}\right)\)	\(e\left(\frac{442}{497}\right)\)	\(e\left(\frac{340}{497}\right)\)	\(e\left(\frac{479}{497}\right)\)	\(e\left(\frac{230}{497}\right)\)	\(e\left(\frac{3}{7}\right)\)
\(\chi_{5041}(48,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{338}{497}\right)\)	\(e\left(\frac{438}{497}\right)\)	\(e\left(\frac{179}{497}\right)\)	\(e\left(\frac{33}{71}\right)\)	\(e\left(\frac{279}{497}\right)\)	\(e\left(\frac{26}{497}\right)\)	\(e\left(\frac{20}{497}\right)\)	\(e\left(\frac{379}{497}\right)\)	\(e\left(\frac{72}{497}\right)\)	\(e\left(\frac{1}{7}\right)\)
\(\chi_{5041}(91,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{311}{497}\right)\)	\(e\left(\frac{6}{497}\right)\)	\(e\left(\frac{125}{497}\right)\)	\(e\left(\frac{52}{71}\right)\)	\(e\left(\frac{317}{497}\right)\)	\(e\left(\frac{368}{497}\right)\)	\(e\left(\frac{436}{497}\right)\)	\(e\left(\frac{12}{497}\right)\)	\(e\left(\frac{178}{497}\right)\)	\(e\left(\frac{5}{7}\right)\)
\(\chi_{5041}(101,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{302}{497}\right)\)	\(e\left(\frac{359}{497}\right)\)	\(e\left(\frac{107}{497}\right)\)	\(e\left(\frac{11}{71}\right)\)	\(e\left(\frac{164}{497}\right)\)	\(e\left(\frac{482}{497}\right)\)	\(e\left(\frac{409}{497}\right)\)	\(e\left(\frac{221}{497}\right)\)	\(e\left(\frac{379}{497}\right)\)	\(e\left(\frac{4}{7}\right)\)
\(\chi_{5041}(103,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{235}{497}\right)\)	\(e\left(\frac{281}{497}\right)\)	\(e\left(\frac{470}{497}\right)\)	\(e\left(\frac{45}{71}\right)\)	\(e\left(\frac{19}{497}\right)\)	\(e\left(\frac{171}{497}\right)\)	\(e\left(\frac{208}{497}\right)\)	\(e\left(\frac{65}{497}\right)\)	\(e\left(\frac{53}{497}\right)\)	\(e\left(\frac{2}{7}\right)\)
\(\chi_{5041}(108,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{348}{497}\right)\)	\(e\left(\frac{101}{497}\right)\)	\(e\left(\frac{199}{497}\right)\)	\(e\left(\frac{47}{71}\right)\)	\(e\left(\frac{449}{497}\right)\)	\(e\left(\frac{65}{497}\right)\)	\(e\left(\frac{50}{497}\right)\)	\(e\left(\frac{202}{497}\right)\)	\(e\left(\frac{180}{497}\right)\)	\(e\left(\frac{6}{7}\right)\)
\(\chi_{5041}(116,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{132}{497}\right)\)	\(e\left(\frac{124}{497}\right)\)	\(e\left(\frac{264}{497}\right)\)	\(e\left(\frac{57}{71}\right)\)	\(e\left(\frac{256}{497}\right)\)	\(e\left(\frac{316}{497}\right)\)	\(e\left(\frac{396}{497}\right)\)	\(e\left(\frac{248}{497}\right)\)	\(e\left(\frac{34}{497}\right)\)	\(e\left(\frac{3}{7}\right)\)
\(\chi_{5041}(119,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{107}{497}\right)\)	\(e\left(\frac{221}{497}\right)\)	\(e\left(\frac{214}{497}\right)\)	\(e\left(\frac{22}{71}\right)\)	\(e\left(\frac{328}{497}\right)\)	\(e\left(\frac{467}{497}\right)\)	\(e\left(\frac{321}{497}\right)\)	\(e\left(\frac{442}{497}\right)\)	\(e\left(\frac{261}{497}\right)\)	\(e\left(\frac{1}{7}\right)\)
\(\chi_{5041}(162,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{353}{497}\right)\)	\(e\left(\frac{181}{497}\right)\)	\(e\left(\frac{209}{497}\right)\)	\(e\left(\frac{54}{71}\right)\)	\(e\left(\frac{37}{497}\right)\)	\(e\left(\frac{333}{497}\right)\)	\(e\left(\frac{65}{497}\right)\)	\(e\left(\frac{362}{497}\right)\)	\(e\left(\frac{234}{497}\right)\)	\(e\left(\frac{5}{7}\right)\)
\(\chi_{5041}(172,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{330}{497}\right)\)	\(e\left(\frac{310}{497}\right)\)	\(e\left(\frac{163}{497}\right)\)	\(e\left(\frac{36}{71}\right)\)	\(e\left(\frac{143}{497}\right)\)	\(e\left(\frac{293}{497}\right)\)	\(e\left(\frac{493}{497}\right)\)	\(e\left(\frac{123}{497}\right)\)	\(e\left(\frac{85}{497}\right)\)	\(e\left(\frac{4}{7}\right)\)
\(\chi_{5041}(174,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{137}{497}\right)\)	\(e\left(\frac{204}{497}\right)\)	\(e\left(\frac{274}{497}\right)\)	\(e\left(\frac{64}{71}\right)\)	\(e\left(\frac{341}{497}\right)\)	\(e\left(\frac{87}{497}\right)\)	\(e\left(\frac{411}{497}\right)\)	\(e\left(\frac{408}{497}\right)\)	\(e\left(\frac{88}{497}\right)\)	\(e\left(\frac{2}{7}\right)\)
\(\chi_{5041}(179,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{411}{497}\right)\)	\(e\left(\frac{115}{497}\right)\)	\(e\left(\frac{325}{497}\right)\)	\(e\left(\frac{50}{71}\right)\)	\(e\left(\frac{29}{497}\right)\)	\(e\left(\frac{261}{497}\right)\)	\(e\left(\frac{239}{497}\right)\)	\(e\left(\frac{230}{497}\right)\)	\(e\left(\frac{264}{497}\right)\)	\(e\left(\frac{6}{7}\right)\)
\(\chi_{5041}(187,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{482}{497}\right)\)	\(e\left(\frac{257}{497}\right)\)	\(e\left(\frac{467}{497}\right)\)	\(e\left(\frac{50}{71}\right)\)	\(e\left(\frac{242}{497}\right)\)	\(e\left(\frac{190}{497}\right)\)	\(e\left(\frac{452}{497}\right)\)	\(e\left(\frac{17}{497}\right)\)	\(e\left(\frac{335}{497}\right)\)	\(e\left(\frac{3}{7}\right)\)
\(\chi_{5041}(190,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{373}{497}\right)\)	\(e\left(\frac{4}{497}\right)\)	\(e\left(\frac{249}{497}\right)\)	\(e\left(\frac{11}{71}\right)\)	\(e\left(\frac{377}{497}\right)\)	\(e\left(\frac{411}{497}\right)\)	\(e\left(\frac{125}{497}\right)\)	\(e\left(\frac{8}{497}\right)\)	\(e\left(\frac{450}{497}\right)\)	\(e\left(\frac{1}{7}\right)\)
\(\chi_{5041}(233,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{395}{497}\right)\)	\(e\left(\frac{356}{497}\right)\)	\(e\left(\frac{293}{497}\right)\)	\(e\left(\frac{56}{71}\right)\)	\(e\left(\frac{254}{497}\right)\)	\(e\left(\frac{298}{497}\right)\)	\(e\left(\frac{191}{497}\right)\)	\(e\left(\frac{215}{497}\right)\)	\(e\left(\frac{290}{497}\right)\)	\(e\left(\frac{5}{7}\right)\)
\(\chi_{5041}(243,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{358}{497}\right)\)	\(e\left(\frac{261}{497}\right)\)	\(e\left(\frac{219}{497}\right)\)	\(e\left(\frac{61}{71}\right)\)	\(e\left(\frac{122}{497}\right)\)	\(e\left(\frac{104}{497}\right)\)	\(e\left(\frac{80}{497}\right)\)	\(e\left(\frac{25}{497}\right)\)	\(e\left(\frac{288}{497}\right)\)	\(e\left(\frac{4}{7}\right)\)
\(\chi_{5041}(245,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{39}{497}\right)\)	\(e\left(\frac{127}{497}\right)\)	\(e\left(\frac{78}{497}\right)\)	\(e\left(\frac{12}{71}\right)\)	\(e\left(\frac{166}{497}\right)\)	\(e\left(\frac{3}{497}\right)\)	\(e\left(\frac{117}{497}\right)\)	\(e\left(\frac{254}{497}\right)\)	\(e\left(\frac{123}{497}\right)\)	\(e\left(\frac{2}{7}\right)\)
\(\chi_{5041}(250,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{474}{497}\right)\)	\(e\left(\frac{129}{497}\right)\)	\(e\left(\frac{451}{497}\right)\)	\(e\left(\frac{53}{71}\right)\)	\(e\left(\frac{106}{497}\right)\)	\(e\left(\frac{457}{497}\right)\)	\(e\left(\frac{428}{497}\right)\)	\(e\left(\frac{258}{497}\right)\)	\(e\left(\frac{348}{497}\right)\)	\(e\left(\frac{6}{7}\right)\)
\(\chi_{5041}(258,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{335}{497}\right)\)	\(e\left(\frac{390}{497}\right)\)	\(e\left(\frac{173}{497}\right)\)	\(e\left(\frac{43}{71}\right)\)	\(e\left(\frac{228}{497}\right)\)	\(e\left(\frac{64}{497}\right)\)	\(e\left(\frac{11}{497}\right)\)	\(e\left(\frac{283}{497}\right)\)	\(e\left(\frac{139}{497}\right)\)	\(e\left(\frac{3}{7}\right)\)
\(\chi_{5041}(304,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{437}{497}\right)\)	\(e\left(\frac{34}{497}\right)\)	\(e\left(\frac{377}{497}\right)\)	\(e\left(\frac{58}{71}\right)\)	\(e\left(\frac{471}{497}\right)\)	\(e\left(\frac{263}{497}\right)\)	\(e\left(\frac{317}{497}\right)\)	\(e\left(\frac{68}{497}\right)\)	\(e\left(\frac{346}{497}\right)\)	\(e\left(\frac{5}{7}\right)\)
\(\chi_{5041}(314,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{386}{497}\right)\)	\(e\left(\frac{212}{497}\right)\)	\(e\left(\frac{275}{497}\right)\)	\(e\left(\frac{15}{71}\right)\)	\(e\left(\frac{101}{497}\right)\)	\(e\left(\frac{412}{497}\right)\)	\(e\left(\frac{164}{497}\right)\)	\(e\left(\frac{424}{497}\right)\)	\(e\left(\frac{491}{497}\right)\)	\(e\left(\frac{4}{7}\right)\)
\(\chi_{5041}(316,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{438}{497}\right)\)	\(e\left(\frac{50}{497}\right)\)	\(e\left(\frac{379}{497}\right)\)	\(e\left(\frac{31}{71}\right)\)	\(e\left(\frac{488}{497}\right)\)	\(e\left(\frac{416}{497}\right)\)	\(e\left(\frac{320}{497}\right)\)	\(e\left(\frac{100}{497}\right)\)	\(e\left(\frac{158}{497}\right)\)	\(e\left(\frac{2}{7}\right)\)
\(\chi_{5041}(321,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{40}{497}\right)\)	\(e\left(\frac{143}{497}\right)\)	\(e\left(\frac{80}{497}\right)\)	\(e\left(\frac{56}{71}\right)\)	\(e\left(\frac{183}{497}\right)\)	\(e\left(\frac{156}{497}\right)\)	\(e\left(\frac{120}{497}\right)\)	\(e\left(\frac{286}{497}\right)\)	\(e\left(\frac{432}{497}\right)\)	\(e\left(\frac{6}{7}\right)\)
\(\chi_{5041}(329,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{188}{497}\right)\)	\(e\left(\frac{26}{497}\right)\)	\(e\left(\frac{376}{497}\right)\)	\(e\left(\frac{36}{71}\right)\)	\(e\left(\frac{214}{497}\right)\)	\(e\left(\frac{435}{497}\right)\)	\(e\left(\frac{67}{497}\right)\)	\(e\left(\frac{52}{497}\right)\)	\(e\left(\frac{440}{497}\right)\)	\(e\left(\frac{3}{7}\right)\)
\(\chi_{5041}(332,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{408}{497}\right)\)	\(e\left(\frac{67}{497}\right)\)	\(e\left(\frac{319}{497}\right)\)	\(e\left(\frac{60}{71}\right)\)	\(e\left(\frac{475}{497}\right)\)	\(e\left(\frac{299}{497}\right)\)	\(e\left(\frac{230}{497}\right)\)	\(e\left(\frac{134}{497}\right)\)	\(e\left(\frac{331}{497}\right)\)	\(e\left(\frac{1}{7}\right)\)
\(\chi_{5041}(375,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{479}{497}\right)\)	\(e\left(\frac{209}{497}\right)\)	\(e\left(\frac{461}{497}\right)\)	\(e\left(\frac{60}{71}\right)\)	\(e\left(\frac{191}{497}\right)\)	\(e\left(\frac{228}{497}\right)\)	\(e\left(\frac{443}{497}\right)\)	\(e\left(\frac{418}{497}\right)\)	\(e\left(\frac{402}{497}\right)\)	\(e\left(\frac{5}{7}\right)\)
\(\chi_{5041}(385,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{414}{497}\right)\)	\(e\left(\frac{163}{497}\right)\)	\(e\left(\frac{331}{497}\right)\)	\(e\left(\frac{40}{71}\right)\)	\(e\left(\frac{80}{497}\right)\)	\(e\left(\frac{223}{497}\right)\)	\(e\left(\frac{248}{497}\right)\)	\(e\left(\frac{326}{497}\right)\)	\(e\left(\frac{197}{497}\right)\)	\(e\left(\frac{4}{7}\right)\)

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First 31 of 420 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	5041.l
Modulus	$5041$
Conductor	$5041$
Order	$497$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(5041\)
Conductor:	\(5041\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(497\)	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)