LMFDB - Dirichlet character orbit 5041.i

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(5041, base_ring=CyclotomicField(142)) M = H._module chi = DirichletCharacter(H, M([84])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(72,5041)) 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:	$71$	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:	$\Q(\zeta_{71})$
Fixed field:	Number field defined by a degree 71 polynomial

First 31 of 70 characters in Galois orbit

Character	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{5041}(72,\cdot)$	$1$	$1$	$e\left(\frac{49}{71}\right)$	$e\left(\frac{3}{71}\right)$	$e\left(\frac{27}{71}\right)$	$e\left(\frac{40}{71}\right)$	$e\left(\frac{52}{71}\right)$	$e\left(\frac{42}{71}\right)$	$e\left(\frac{5}{71}\right)$	$e\left(\frac{6}{71}\right)$	$e\left(\frac{18}{71}\right)$	$1$
$\chi_{5041}(143,\cdot)$	$1$	$1$	$e\left(\frac{27}{71}\right)$	$e\left(\frac{6}{71}\right)$	$e\left(\frac{54}{71}\right)$	$e\left(\frac{9}{71}\right)$	$e\left(\frac{33}{71}\right)$	$e\left(\frac{13}{71}\right)$	$e\left(\frac{10}{71}\right)$	$e\left(\frac{12}{71}\right)$	$e\left(\frac{36}{71}\right)$	$1$
$\chi_{5041}(214,\cdot)$	$1$	$1$	$e\left(\frac{5}{71}\right)$	$e\left(\frac{9}{71}\right)$	$e\left(\frac{10}{71}\right)$	$e\left(\frac{49}{71}\right)$	$e\left(\frac{14}{71}\right)$	$e\left(\frac{55}{71}\right)$	$e\left(\frac{15}{71}\right)$	$e\left(\frac{18}{71}\right)$	$e\left(\frac{54}{71}\right)$	$1$
$\chi_{5041}(285,\cdot)$	$1$	$1$	$e\left(\frac{54}{71}\right)$	$e\left(\frac{12}{71}\right)$	$e\left(\frac{37}{71}\right)$	$e\left(\frac{18}{71}\right)$	$e\left(\frac{66}{71}\right)$	$e\left(\frac{26}{71}\right)$	$e\left(\frac{20}{71}\right)$	$e\left(\frac{24}{71}\right)$	$e\left(\frac{1}{71}\right)$	$1$
$\chi_{5041}(356,\cdot)$	$1$	$1$	$e\left(\frac{32}{71}\right)$	$e\left(\frac{15}{71}\right)$	$e\left(\frac{64}{71}\right)$	$e\left(\frac{58}{71}\right)$	$e\left(\frac{47}{71}\right)$	$e\left(\frac{68}{71}\right)$	$e\left(\frac{25}{71}\right)$	$e\left(\frac{30}{71}\right)$	$e\left(\frac{19}{71}\right)$	$1$
$\chi_{5041}(427,\cdot)$	$1$	$1$	$e\left(\frac{10}{71}\right)$	$e\left(\frac{18}{71}\right)$	$e\left(\frac{20}{71}\right)$	$e\left(\frac{27}{71}\right)$	$e\left(\frac{28}{71}\right)$	$e\left(\frac{39}{71}\right)$	$e\left(\frac{30}{71}\right)$	$e\left(\frac{36}{71}\right)$	$e\left(\frac{37}{71}\right)$	$1$
$\chi_{5041}(498,\cdot)$	$1$	$1$	$e\left(\frac{59}{71}\right)$	$e\left(\frac{21}{71}\right)$	$e\left(\frac{47}{71}\right)$	$e\left(\frac{67}{71}\right)$	$e\left(\frac{9}{71}\right)$	$e\left(\frac{10}{71}\right)$	$e\left(\frac{35}{71}\right)$	$e\left(\frac{42}{71}\right)$	$e\left(\frac{55}{71}\right)$	$1$
$\chi_{5041}(569,\cdot)$	$1$	$1$	$e\left(\frac{37}{71}\right)$	$e\left(\frac{24}{71}\right)$	$e\left(\frac{3}{71}\right)$	$e\left(\frac{36}{71}\right)$	$e\left(\frac{61}{71}\right)$	$e\left(\frac{52}{71}\right)$	$e\left(\frac{40}{71}\right)$	$e\left(\frac{48}{71}\right)$	$e\left(\frac{2}{71}\right)$	$1$
$\chi_{5041}(640,\cdot)$	$1$	$1$	$e\left(\frac{15}{71}\right)$	$e\left(\frac{27}{71}\right)$	$e\left(\frac{30}{71}\right)$	$e\left(\frac{5}{71}\right)$	$e\left(\frac{42}{71}\right)$	$e\left(\frac{23}{71}\right)$	$e\left(\frac{45}{71}\right)$	$e\left(\frac{54}{71}\right)$	$e\left(\frac{20}{71}\right)$	$1$
$\chi_{5041}(711,\cdot)$	$1$	$1$	$e\left(\frac{64}{71}\right)$	$e\left(\frac{30}{71}\right)$	$e\left(\frac{57}{71}\right)$	$e\left(\frac{45}{71}\right)$	$e\left(\frac{23}{71}\right)$	$e\left(\frac{65}{71}\right)$	$e\left(\frac{50}{71}\right)$	$e\left(\frac{60}{71}\right)$	$e\left(\frac{38}{71}\right)$	$1$
$\chi_{5041}(782,\cdot)$	$1$	$1$	$e\left(\frac{42}{71}\right)$	$e\left(\frac{33}{71}\right)$	$e\left(\frac{13}{71}\right)$	$e\left(\frac{14}{71}\right)$	$e\left(\frac{4}{71}\right)$	$e\left(\frac{36}{71}\right)$	$e\left(\frac{55}{71}\right)$	$e\left(\frac{66}{71}\right)$	$e\left(\frac{56}{71}\right)$	$1$
$\chi_{5041}(853,\cdot)$	$1$	$1$	$e\left(\frac{20}{71}\right)$	$e\left(\frac{36}{71}\right)$	$e\left(\frac{40}{71}\right)$	$e\left(\frac{54}{71}\right)$	$e\left(\frac{56}{71}\right)$	$e\left(\frac{7}{71}\right)$	$e\left(\frac{60}{71}\right)$	$e\left(\frac{1}{71}\right)$	$e\left(\frac{3}{71}\right)$	$1$
$\chi_{5041}(924,\cdot)$	$1$	$1$	$e\left(\frac{69}{71}\right)$	$e\left(\frac{39}{71}\right)$	$e\left(\frac{67}{71}\right)$	$e\left(\frac{23}{71}\right)$	$e\left(\frac{37}{71}\right)$	$e\left(\frac{49}{71}\right)$	$e\left(\frac{65}{71}\right)$	$e\left(\frac{7}{71}\right)$	$e\left(\frac{21}{71}\right)$	$1$
$\chi_{5041}(995,\cdot)$	$1$	$1$	$e\left(\frac{47}{71}\right)$	$e\left(\frac{42}{71}\right)$	$e\left(\frac{23}{71}\right)$	$e\left(\frac{63}{71}\right)$	$e\left(\frac{18}{71}\right)$	$e\left(\frac{20}{71}\right)$	$e\left(\frac{70}{71}\right)$	$e\left(\frac{13}{71}\right)$	$e\left(\frac{39}{71}\right)$	$1$
$\chi_{5041}(1066,\cdot)$	$1$	$1$	$e\left(\frac{25}{71}\right)$	$e\left(\frac{45}{71}\right)$	$e\left(\frac{50}{71}\right)$	$e\left(\frac{32}{71}\right)$	$e\left(\frac{70}{71}\right)$	$e\left(\frac{62}{71}\right)$	$e\left(\frac{4}{71}\right)$	$e\left(\frac{19}{71}\right)$	$e\left(\frac{57}{71}\right)$	$1$
$\chi_{5041}(1137,\cdot)$	$1$	$1$	$e\left(\frac{3}{71}\right)$	$e\left(\frac{48}{71}\right)$	$e\left(\frac{6}{71}\right)$	$e\left(\frac{1}{71}\right)$	$e\left(\frac{51}{71}\right)$	$e\left(\frac{33}{71}\right)$	$e\left(\frac{9}{71}\right)$	$e\left(\frac{25}{71}\right)$	$e\left(\frac{4}{71}\right)$	$1$
$\chi_{5041}(1208,\cdot)$	$1$	$1$	$e\left(\frac{52}{71}\right)$	$e\left(\frac{51}{71}\right)$	$e\left(\frac{33}{71}\right)$	$e\left(\frac{41}{71}\right)$	$e\left(\frac{32}{71}\right)$	$e\left(\frac{4}{71}\right)$	$e\left(\frac{14}{71}\right)$	$e\left(\frac{31}{71}\right)$	$e\left(\frac{22}{71}\right)$	$1$
$\chi_{5041}(1279,\cdot)$	$1$	$1$	$e\left(\frac{30}{71}\right)$	$e\left(\frac{54}{71}\right)$	$e\left(\frac{60}{71}\right)$	$e\left(\frac{10}{71}\right)$	$e\left(\frac{13}{71}\right)$	$e\left(\frac{46}{71}\right)$	$e\left(\frac{19}{71}\right)$	$e\left(\frac{37}{71}\right)$	$e\left(\frac{40}{71}\right)$	$1$
$\chi_{5041}(1350,\cdot)$	$1$	$1$	$e\left(\frac{8}{71}\right)$	$e\left(\frac{57}{71}\right)$	$e\left(\frac{16}{71}\right)$	$e\left(\frac{50}{71}\right)$	$e\left(\frac{65}{71}\right)$	$e\left(\frac{17}{71}\right)$	$e\left(\frac{24}{71}\right)$	$e\left(\frac{43}{71}\right)$	$e\left(\frac{58}{71}\right)$	$1$
$\chi_{5041}(1421,\cdot)$	$1$	$1$	$e\left(\frac{57}{71}\right)$	$e\left(\frac{60}{71}\right)$	$e\left(\frac{43}{71}\right)$	$e\left(\frac{19}{71}\right)$	$e\left(\frac{46}{71}\right)$	$e\left(\frac{59}{71}\right)$	$e\left(\frac{29}{71}\right)$	$e\left(\frac{49}{71}\right)$	$e\left(\frac{5}{71}\right)$	$1$
$\chi_{5041}(1492,\cdot)$	$1$	$1$	$e\left(\frac{35}{71}\right)$	$e\left(\frac{63}{71}\right)$	$e\left(\frac{70}{71}\right)$	$e\left(\frac{59}{71}\right)$	$e\left(\frac{27}{71}\right)$	$e\left(\frac{30}{71}\right)$	$e\left(\frac{34}{71}\right)$	$e\left(\frac{55}{71}\right)$	$e\left(\frac{23}{71}\right)$	$1$
$\chi_{5041}(1563,\cdot)$	$1$	$1$	$e\left(\frac{13}{71}\right)$	$e\left(\frac{66}{71}\right)$	$e\left(\frac{26}{71}\right)$	$e\left(\frac{28}{71}\right)$	$e\left(\frac{8}{71}\right)$	$e\left(\frac{1}{71}\right)$	$e\left(\frac{39}{71}\right)$	$e\left(\frac{61}{71}\right)$	$e\left(\frac{41}{71}\right)$	$1$
$\chi_{5041}(1634,\cdot)$	$1$	$1$	$e\left(\frac{62}{71}\right)$	$e\left(\frac{69}{71}\right)$	$e\left(\frac{53}{71}\right)$	$e\left(\frac{68}{71}\right)$	$e\left(\frac{60}{71}\right)$	$e\left(\frac{43}{71}\right)$	$e\left(\frac{44}{71}\right)$	$e\left(\frac{67}{71}\right)$	$e\left(\frac{59}{71}\right)$	$1$
$\chi_{5041}(1705,\cdot)$	$1$	$1$	$e\left(\frac{40}{71}\right)$	$e\left(\frac{1}{71}\right)$	$e\left(\frac{9}{71}\right)$	$e\left(\frac{37}{71}\right)$	$e\left(\frac{41}{71}\right)$	$e\left(\frac{14}{71}\right)$	$e\left(\frac{49}{71}\right)$	$e\left(\frac{2}{71}\right)$	$e\left(\frac{6}{71}\right)$	$1$
$\chi_{5041}(1776,\cdot)$	$1$	$1$	$e\left(\frac{18}{71}\right)$	$e\left(\frac{4}{71}\right)$	$e\left(\frac{36}{71}\right)$	$e\left(\frac{6}{71}\right)$	$e\left(\frac{22}{71}\right)$	$e\left(\frac{56}{71}\right)$	$e\left(\frac{54}{71}\right)$	$e\left(\frac{8}{71}\right)$	$e\left(\frac{24}{71}\right)$	$1$
$\chi_{5041}(1847,\cdot)$	$1$	$1$	$e\left(\frac{67}{71}\right)$	$e\left(\frac{7}{71}\right)$	$e\left(\frac{63}{71}\right)$	$e\left(\frac{46}{71}\right)$	$e\left(\frac{3}{71}\right)$	$e\left(\frac{27}{71}\right)$	$e\left(\frac{59}{71}\right)$	$e\left(\frac{14}{71}\right)$	$e\left(\frac{42}{71}\right)$	$1$
$\chi_{5041}(1918,\cdot)$	$1$	$1$	$e\left(\frac{45}{71}\right)$	$e\left(\frac{10}{71}\right)$	$e\left(\frac{19}{71}\right)$	$e\left(\frac{15}{71}\right)$	$e\left(\frac{55}{71}\right)$	$e\left(\frac{69}{71}\right)$	$e\left(\frac{64}{71}\right)$	$e\left(\frac{20}{71}\right)$	$e\left(\frac{60}{71}\right)$	$1$
$\chi_{5041}(1989,\cdot)$	$1$	$1$	$e\left(\frac{23}{71}\right)$	$e\left(\frac{13}{71}\right)$	$e\left(\frac{46}{71}\right)$	$e\left(\frac{55}{71}\right)$	$e\left(\frac{36}{71}\right)$	$e\left(\frac{40}{71}\right)$	$e\left(\frac{69}{71}\right)$	$e\left(\frac{26}{71}\right)$	$e\left(\frac{7}{71}\right)$	$1$
$\chi_{5041}(2060,\cdot)$	$1$	$1$	$e\left(\frac{1}{71}\right)$	$e\left(\frac{16}{71}\right)$	$e\left(\frac{2}{71}\right)$	$e\left(\frac{24}{71}\right)$	$e\left(\frac{17}{71}\right)$	$e\left(\frac{11}{71}\right)$	$e\left(\frac{3}{71}\right)$	$e\left(\frac{32}{71}\right)$	$e\left(\frac{25}{71}\right)$	$1$
$\chi_{5041}(2131,\cdot)$	$1$	$1$	$e\left(\frac{50}{71}\right)$	$e\left(\frac{19}{71}\right)$	$e\left(\frac{29}{71}\right)$	$e\left(\frac{64}{71}\right)$	$e\left(\frac{69}{71}\right)$	$e\left(\frac{53}{71}\right)$	$e\left(\frac{8}{71}\right)$	$e\left(\frac{38}{71}\right)$	$e\left(\frac{43}{71}\right)$	$1$
$\chi_{5041}(2202,\cdot)$	$1$	$1$	$e\left(\frac{28}{71}\right)$	$e\left(\frac{22}{71}\right)$	$e\left(\frac{56}{71}\right)$	$e\left(\frac{33}{71}\right)$	$e\left(\frac{50}{71}\right)$	$e\left(\frac{24}{71}\right)$	$e\left(\frac{13}{71}\right)$	$e\left(\frac{44}{71}\right)$	$e\left(\frac{61}{71}\right)$	$1$

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	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\(\chi_{5041}(72,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{49}{71}\right)\)	\(e\left(\frac{3}{71}\right)\)	\(e\left(\frac{27}{71}\right)\)	\(e\left(\frac{40}{71}\right)\)	\(e\left(\frac{52}{71}\right)\)	\(e\left(\frac{42}{71}\right)\)	\(e\left(\frac{5}{71}\right)\)	\(e\left(\frac{6}{71}\right)\)	\(e\left(\frac{18}{71}\right)\)	\(1\)
\(\chi_{5041}(143,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{27}{71}\right)\)	\(e\left(\frac{6}{71}\right)\)	\(e\left(\frac{54}{71}\right)\)	\(e\left(\frac{9}{71}\right)\)	\(e\left(\frac{33}{71}\right)\)	\(e\left(\frac{13}{71}\right)\)	\(e\left(\frac{10}{71}\right)\)	\(e\left(\frac{12}{71}\right)\)	\(e\left(\frac{36}{71}\right)\)	\(1\)
\(\chi_{5041}(214,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{71}\right)\)	\(e\left(\frac{9}{71}\right)\)	\(e\left(\frac{10}{71}\right)\)	\(e\left(\frac{49}{71}\right)\)	\(e\left(\frac{14}{71}\right)\)	\(e\left(\frac{55}{71}\right)\)	\(e\left(\frac{15}{71}\right)\)	\(e\left(\frac{18}{71}\right)\)	\(e\left(\frac{54}{71}\right)\)	\(1\)
\(\chi_{5041}(285,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{54}{71}\right)\)	\(e\left(\frac{12}{71}\right)\)	\(e\left(\frac{37}{71}\right)\)	\(e\left(\frac{18}{71}\right)\)	\(e\left(\frac{66}{71}\right)\)	\(e\left(\frac{26}{71}\right)\)	\(e\left(\frac{20}{71}\right)\)	\(e\left(\frac{24}{71}\right)\)	\(e\left(\frac{1}{71}\right)\)	\(1\)
\(\chi_{5041}(356,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{32}{71}\right)\)	\(e\left(\frac{15}{71}\right)\)	\(e\left(\frac{64}{71}\right)\)	\(e\left(\frac{58}{71}\right)\)	\(e\left(\frac{47}{71}\right)\)	\(e\left(\frac{68}{71}\right)\)	\(e\left(\frac{25}{71}\right)\)	\(e\left(\frac{30}{71}\right)\)	\(e\left(\frac{19}{71}\right)\)	\(1\)
\(\chi_{5041}(427,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{10}{71}\right)\)	\(e\left(\frac{18}{71}\right)\)	\(e\left(\frac{20}{71}\right)\)	\(e\left(\frac{27}{71}\right)\)	\(e\left(\frac{28}{71}\right)\)	\(e\left(\frac{39}{71}\right)\)	\(e\left(\frac{30}{71}\right)\)	\(e\left(\frac{36}{71}\right)\)	\(e\left(\frac{37}{71}\right)\)	\(1\)
\(\chi_{5041}(498,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{71}\right)\)	\(e\left(\frac{21}{71}\right)\)	\(e\left(\frac{47}{71}\right)\)	\(e\left(\frac{67}{71}\right)\)	\(e\left(\frac{9}{71}\right)\)	\(e\left(\frac{10}{71}\right)\)	\(e\left(\frac{35}{71}\right)\)	\(e\left(\frac{42}{71}\right)\)	\(e\left(\frac{55}{71}\right)\)	\(1\)
\(\chi_{5041}(569,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{71}\right)\)	\(e\left(\frac{24}{71}\right)\)	\(e\left(\frac{3}{71}\right)\)	\(e\left(\frac{36}{71}\right)\)	\(e\left(\frac{61}{71}\right)\)	\(e\left(\frac{52}{71}\right)\)	\(e\left(\frac{40}{71}\right)\)	\(e\left(\frac{48}{71}\right)\)	\(e\left(\frac{2}{71}\right)\)	\(1\)
\(\chi_{5041}(640,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{15}{71}\right)\)	\(e\left(\frac{27}{71}\right)\)	\(e\left(\frac{30}{71}\right)\)	\(e\left(\frac{5}{71}\right)\)	\(e\left(\frac{42}{71}\right)\)	\(e\left(\frac{23}{71}\right)\)	\(e\left(\frac{45}{71}\right)\)	\(e\left(\frac{54}{71}\right)\)	\(e\left(\frac{20}{71}\right)\)	\(1\)
\(\chi_{5041}(711,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{64}{71}\right)\)	\(e\left(\frac{30}{71}\right)\)	\(e\left(\frac{57}{71}\right)\)	\(e\left(\frac{45}{71}\right)\)	\(e\left(\frac{23}{71}\right)\)	\(e\left(\frac{65}{71}\right)\)	\(e\left(\frac{50}{71}\right)\)	\(e\left(\frac{60}{71}\right)\)	\(e\left(\frac{38}{71}\right)\)	\(1\)
\(\chi_{5041}(782,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{42}{71}\right)\)	\(e\left(\frac{33}{71}\right)\)	\(e\left(\frac{13}{71}\right)\)	\(e\left(\frac{14}{71}\right)\)	\(e\left(\frac{4}{71}\right)\)	\(e\left(\frac{36}{71}\right)\)	\(e\left(\frac{55}{71}\right)\)	\(e\left(\frac{66}{71}\right)\)	\(e\left(\frac{56}{71}\right)\)	\(1\)
\(\chi_{5041}(853,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{20}{71}\right)\)	\(e\left(\frac{36}{71}\right)\)	\(e\left(\frac{40}{71}\right)\)	\(e\left(\frac{54}{71}\right)\)	\(e\left(\frac{56}{71}\right)\)	\(e\left(\frac{7}{71}\right)\)	\(e\left(\frac{60}{71}\right)\)	\(e\left(\frac{1}{71}\right)\)	\(e\left(\frac{3}{71}\right)\)	\(1\)
\(\chi_{5041}(924,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{69}{71}\right)\)	\(e\left(\frac{39}{71}\right)\)	\(e\left(\frac{67}{71}\right)\)	\(e\left(\frac{23}{71}\right)\)	\(e\left(\frac{37}{71}\right)\)	\(e\left(\frac{49}{71}\right)\)	\(e\left(\frac{65}{71}\right)\)	\(e\left(\frac{7}{71}\right)\)	\(e\left(\frac{21}{71}\right)\)	\(1\)
\(\chi_{5041}(995,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{71}\right)\)	\(e\left(\frac{42}{71}\right)\)	\(e\left(\frac{23}{71}\right)\)	\(e\left(\frac{63}{71}\right)\)	\(e\left(\frac{18}{71}\right)\)	\(e\left(\frac{20}{71}\right)\)	\(e\left(\frac{70}{71}\right)\)	\(e\left(\frac{13}{71}\right)\)	\(e\left(\frac{39}{71}\right)\)	\(1\)
\(\chi_{5041}(1066,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{25}{71}\right)\)	\(e\left(\frac{45}{71}\right)\)	\(e\left(\frac{50}{71}\right)\)	\(e\left(\frac{32}{71}\right)\)	\(e\left(\frac{70}{71}\right)\)	\(e\left(\frac{62}{71}\right)\)	\(e\left(\frac{4}{71}\right)\)	\(e\left(\frac{19}{71}\right)\)	\(e\left(\frac{57}{71}\right)\)	\(1\)
\(\chi_{5041}(1137,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{71}\right)\)	\(e\left(\frac{48}{71}\right)\)	\(e\left(\frac{6}{71}\right)\)	\(e\left(\frac{1}{71}\right)\)	\(e\left(\frac{51}{71}\right)\)	\(e\left(\frac{33}{71}\right)\)	\(e\left(\frac{9}{71}\right)\)	\(e\left(\frac{25}{71}\right)\)	\(e\left(\frac{4}{71}\right)\)	\(1\)
\(\chi_{5041}(1208,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{52}{71}\right)\)	\(e\left(\frac{51}{71}\right)\)	\(e\left(\frac{33}{71}\right)\)	\(e\left(\frac{41}{71}\right)\)	\(e\left(\frac{32}{71}\right)\)	\(e\left(\frac{4}{71}\right)\)	\(e\left(\frac{14}{71}\right)\)	\(e\left(\frac{31}{71}\right)\)	\(e\left(\frac{22}{71}\right)\)	\(1\)
\(\chi_{5041}(1279,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{30}{71}\right)\)	\(e\left(\frac{54}{71}\right)\)	\(e\left(\frac{60}{71}\right)\)	\(e\left(\frac{10}{71}\right)\)	\(e\left(\frac{13}{71}\right)\)	\(e\left(\frac{46}{71}\right)\)	\(e\left(\frac{19}{71}\right)\)	\(e\left(\frac{37}{71}\right)\)	\(e\left(\frac{40}{71}\right)\)	\(1\)
\(\chi_{5041}(1350,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{8}{71}\right)\)	\(e\left(\frac{57}{71}\right)\)	\(e\left(\frac{16}{71}\right)\)	\(e\left(\frac{50}{71}\right)\)	\(e\left(\frac{65}{71}\right)\)	\(e\left(\frac{17}{71}\right)\)	\(e\left(\frac{24}{71}\right)\)	\(e\left(\frac{43}{71}\right)\)	\(e\left(\frac{58}{71}\right)\)	\(1\)
\(\chi_{5041}(1421,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{57}{71}\right)\)	\(e\left(\frac{60}{71}\right)\)	\(e\left(\frac{43}{71}\right)\)	\(e\left(\frac{19}{71}\right)\)	\(e\left(\frac{46}{71}\right)\)	\(e\left(\frac{59}{71}\right)\)	\(e\left(\frac{29}{71}\right)\)	\(e\left(\frac{49}{71}\right)\)	\(e\left(\frac{5}{71}\right)\)	\(1\)
\(\chi_{5041}(1492,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{35}{71}\right)\)	\(e\left(\frac{63}{71}\right)\)	\(e\left(\frac{70}{71}\right)\)	\(e\left(\frac{59}{71}\right)\)	\(e\left(\frac{27}{71}\right)\)	\(e\left(\frac{30}{71}\right)\)	\(e\left(\frac{34}{71}\right)\)	\(e\left(\frac{55}{71}\right)\)	\(e\left(\frac{23}{71}\right)\)	\(1\)
\(\chi_{5041}(1563,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{71}\right)\)	\(e\left(\frac{66}{71}\right)\)	\(e\left(\frac{26}{71}\right)\)	\(e\left(\frac{28}{71}\right)\)	\(e\left(\frac{8}{71}\right)\)	\(e\left(\frac{1}{71}\right)\)	\(e\left(\frac{39}{71}\right)\)	\(e\left(\frac{61}{71}\right)\)	\(e\left(\frac{41}{71}\right)\)	\(1\)
\(\chi_{5041}(1634,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{62}{71}\right)\)	\(e\left(\frac{69}{71}\right)\)	\(e\left(\frac{53}{71}\right)\)	\(e\left(\frac{68}{71}\right)\)	\(e\left(\frac{60}{71}\right)\)	\(e\left(\frac{43}{71}\right)\)	\(e\left(\frac{44}{71}\right)\)	\(e\left(\frac{67}{71}\right)\)	\(e\left(\frac{59}{71}\right)\)	\(1\)
\(\chi_{5041}(1705,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{40}{71}\right)\)	\(e\left(\frac{1}{71}\right)\)	\(e\left(\frac{9}{71}\right)\)	\(e\left(\frac{37}{71}\right)\)	\(e\left(\frac{41}{71}\right)\)	\(e\left(\frac{14}{71}\right)\)	\(e\left(\frac{49}{71}\right)\)	\(e\left(\frac{2}{71}\right)\)	\(e\left(\frac{6}{71}\right)\)	\(1\)
\(\chi_{5041}(1776,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{18}{71}\right)\)	\(e\left(\frac{4}{71}\right)\)	\(e\left(\frac{36}{71}\right)\)	\(e\left(\frac{6}{71}\right)\)	\(e\left(\frac{22}{71}\right)\)	\(e\left(\frac{56}{71}\right)\)	\(e\left(\frac{54}{71}\right)\)	\(e\left(\frac{8}{71}\right)\)	\(e\left(\frac{24}{71}\right)\)	\(1\)
\(\chi_{5041}(1847,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{67}{71}\right)\)	\(e\left(\frac{7}{71}\right)\)	\(e\left(\frac{63}{71}\right)\)	\(e\left(\frac{46}{71}\right)\)	\(e\left(\frac{3}{71}\right)\)	\(e\left(\frac{27}{71}\right)\)	\(e\left(\frac{59}{71}\right)\)	\(e\left(\frac{14}{71}\right)\)	\(e\left(\frac{42}{71}\right)\)	\(1\)
\(\chi_{5041}(1918,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{45}{71}\right)\)	\(e\left(\frac{10}{71}\right)\)	\(e\left(\frac{19}{71}\right)\)	\(e\left(\frac{15}{71}\right)\)	\(e\left(\frac{55}{71}\right)\)	\(e\left(\frac{69}{71}\right)\)	\(e\left(\frac{64}{71}\right)\)	\(e\left(\frac{20}{71}\right)\)	\(e\left(\frac{60}{71}\right)\)	\(1\)
\(\chi_{5041}(1989,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{71}\right)\)	\(e\left(\frac{13}{71}\right)\)	\(e\left(\frac{46}{71}\right)\)	\(e\left(\frac{55}{71}\right)\)	\(e\left(\frac{36}{71}\right)\)	\(e\left(\frac{40}{71}\right)\)	\(e\left(\frac{69}{71}\right)\)	\(e\left(\frac{26}{71}\right)\)	\(e\left(\frac{7}{71}\right)\)	\(1\)
\(\chi_{5041}(2060,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{71}\right)\)	\(e\left(\frac{16}{71}\right)\)	\(e\left(\frac{2}{71}\right)\)	\(e\left(\frac{24}{71}\right)\)	\(e\left(\frac{17}{71}\right)\)	\(e\left(\frac{11}{71}\right)\)	\(e\left(\frac{3}{71}\right)\)	\(e\left(\frac{32}{71}\right)\)	\(e\left(\frac{25}{71}\right)\)	\(1\)
\(\chi_{5041}(2131,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{50}{71}\right)\)	\(e\left(\frac{19}{71}\right)\)	\(e\left(\frac{29}{71}\right)\)	\(e\left(\frac{64}{71}\right)\)	\(e\left(\frac{69}{71}\right)\)	\(e\left(\frac{53}{71}\right)\)	\(e\left(\frac{8}{71}\right)\)	\(e\left(\frac{38}{71}\right)\)	\(e\left(\frac{43}{71}\right)\)	\(1\)
\(\chi_{5041}(2202,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{28}{71}\right)\)	\(e\left(\frac{22}{71}\right)\)	\(e\left(\frac{56}{71}\right)\)	\(e\left(\frac{33}{71}\right)\)	\(e\left(\frac{50}{71}\right)\)	\(e\left(\frac{24}{71}\right)\)	\(e\left(\frac{13}{71}\right)\)	\(e\left(\frac{44}{71}\right)\)	\(e\left(\frac{61}{71}\right)\)	\(1\)

Introduction

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Basic properties

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First 31 of 70 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.i
Modulus	$5041$
Conductor	$5041$
Order	$71$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(5041\)
Conductor:	\(5041\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(71\)	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)