LMFDB - Dirichlet character orbit 8410.w

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(8410, base_ring=CyclotomicField(58)) M = H._module chi = DirichletCharacter(H, M([0,13])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(231,8410)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$8410$
Conductor:	$841$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$58$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 841.h	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:	$\Q(\zeta_{29})$
Fixed field:	Number field defined by a degree 58 polynomial

Characters in Galois orbit

Character	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$17$	$19$	$21$	$23$	$27$
$\chi_{8410}(231,\cdot)$	$1$	$1$	$e\left(\frac{21}{58}\right)$	$e\left(\frac{8}{29}\right)$	$e\left(\frac{21}{29}\right)$	$e\left(\frac{9}{58}\right)$	$e\left(\frac{11}{29}\right)$	$e\left(\frac{7}{58}\right)$	$e\left(\frac{5}{58}\right)$	$e\left(\frac{37}{58}\right)$	$e\left(\frac{6}{29}\right)$	$e\left(\frac{5}{58}\right)$
$\chi_{8410}(521,\cdot)$	$1$	$1$	$e\left(\frac{11}{58}\right)$	$e\left(\frac{18}{29}\right)$	$e\left(\frac{11}{29}\right)$	$e\left(\frac{13}{58}\right)$	$e\left(\frac{3}{29}\right)$	$e\left(\frac{23}{58}\right)$	$e\left(\frac{33}{58}\right)$	$e\left(\frac{47}{58}\right)$	$e\left(\frac{28}{29}\right)$	$e\left(\frac{33}{58}\right)$
$\chi_{8410}(811,\cdot)$	$1$	$1$	$e\left(\frac{1}{58}\right)$	$e\left(\frac{28}{29}\right)$	$e\left(\frac{1}{29}\right)$	$e\left(\frac{17}{58}\right)$	$e\left(\frac{24}{29}\right)$	$e\left(\frac{39}{58}\right)$	$e\left(\frac{3}{58}\right)$	$e\left(\frac{57}{58}\right)$	$e\left(\frac{21}{29}\right)$	$e\left(\frac{3}{58}\right)$
$\chi_{8410}(1101,\cdot)$	$1$	$1$	$e\left(\frac{49}{58}\right)$	$e\left(\frac{9}{29}\right)$	$e\left(\frac{20}{29}\right)$	$e\left(\frac{21}{58}\right)$	$e\left(\frac{16}{29}\right)$	$e\left(\frac{55}{58}\right)$	$e\left(\frac{31}{58}\right)$	$e\left(\frac{9}{58}\right)$	$e\left(\frac{14}{29}\right)$	$e\left(\frac{31}{58}\right)$
$\chi_{8410}(1391,\cdot)$	$1$	$1$	$e\left(\frac{39}{58}\right)$	$e\left(\frac{19}{29}\right)$	$e\left(\frac{10}{29}\right)$	$e\left(\frac{25}{58}\right)$	$e\left(\frac{8}{29}\right)$	$e\left(\frac{13}{58}\right)$	$e\left(\frac{1}{58}\right)$	$e\left(\frac{19}{58}\right)$	$e\left(\frac{7}{29}\right)$	$e\left(\frac{1}{58}\right)$
$\chi_{8410}(1971,\cdot)$	$1$	$1$	$e\left(\frac{19}{58}\right)$	$e\left(\frac{10}{29}\right)$	$e\left(\frac{19}{29}\right)$	$e\left(\frac{33}{58}\right)$	$e\left(\frac{21}{29}\right)$	$e\left(\frac{45}{58}\right)$	$e\left(\frac{57}{58}\right)$	$e\left(\frac{39}{58}\right)$	$e\left(\frac{22}{29}\right)$	$e\left(\frac{57}{58}\right)$
$\chi_{8410}(2261,\cdot)$	$1$	$1$	$e\left(\frac{9}{58}\right)$	$e\left(\frac{20}{29}\right)$	$e\left(\frac{9}{29}\right)$	$e\left(\frac{37}{58}\right)$	$e\left(\frac{13}{29}\right)$	$e\left(\frac{3}{58}\right)$	$e\left(\frac{27}{58}\right)$	$e\left(\frac{49}{58}\right)$	$e\left(\frac{15}{29}\right)$	$e\left(\frac{27}{58}\right)$
$\chi_{8410}(2551,\cdot)$	$1$	$1$	$e\left(\frac{57}{58}\right)$	$e\left(\frac{1}{29}\right)$	$e\left(\frac{28}{29}\right)$	$e\left(\frac{41}{58}\right)$	$e\left(\frac{5}{29}\right)$	$e\left(\frac{19}{58}\right)$	$e\left(\frac{55}{58}\right)$	$e\left(\frac{1}{58}\right)$	$e\left(\frac{8}{29}\right)$	$e\left(\frac{55}{58}\right)$
$\chi_{8410}(2841,\cdot)$	$1$	$1$	$e\left(\frac{47}{58}\right)$	$e\left(\frac{11}{29}\right)$	$e\left(\frac{18}{29}\right)$	$e\left(\frac{45}{58}\right)$	$e\left(\frac{26}{29}\right)$	$e\left(\frac{35}{58}\right)$	$e\left(\frac{25}{58}\right)$	$e\left(\frac{11}{58}\right)$	$e\left(\frac{1}{29}\right)$	$e\left(\frac{25}{58}\right)$
$\chi_{8410}(3131,\cdot)$	$1$	$1$	$e\left(\frac{37}{58}\right)$	$e\left(\frac{21}{29}\right)$	$e\left(\frac{8}{29}\right)$	$e\left(\frac{49}{58}\right)$	$e\left(\frac{18}{29}\right)$	$e\left(\frac{51}{58}\right)$	$e\left(\frac{53}{58}\right)$	$e\left(\frac{21}{58}\right)$	$e\left(\frac{23}{29}\right)$	$e\left(\frac{53}{58}\right)$
$\chi_{8410}(3421,\cdot)$	$1$	$1$	$e\left(\frac{27}{58}\right)$	$e\left(\frac{2}{29}\right)$	$e\left(\frac{27}{29}\right)$	$e\left(\frac{53}{58}\right)$	$e\left(\frac{10}{29}\right)$	$e\left(\frac{9}{58}\right)$	$e\left(\frac{23}{58}\right)$	$e\left(\frac{31}{58}\right)$	$e\left(\frac{16}{29}\right)$	$e\left(\frac{23}{58}\right)$
$\chi_{8410}(3711,\cdot)$	$1$	$1$	$e\left(\frac{17}{58}\right)$	$e\left(\frac{12}{29}\right)$	$e\left(\frac{17}{29}\right)$	$e\left(\frac{57}{58}\right)$	$e\left(\frac{2}{29}\right)$	$e\left(\frac{25}{58}\right)$	$e\left(\frac{51}{58}\right)$	$e\left(\frac{41}{58}\right)$	$e\left(\frac{9}{29}\right)$	$e\left(\frac{51}{58}\right)$
$\chi_{8410}(4001,\cdot)$	$1$	$1$	$e\left(\frac{7}{58}\right)$	$e\left(\frac{22}{29}\right)$	$e\left(\frac{7}{29}\right)$	$e\left(\frac{3}{58}\right)$	$e\left(\frac{23}{29}\right)$	$e\left(\frac{41}{58}\right)$	$e\left(\frac{21}{58}\right)$	$e\left(\frac{51}{58}\right)$	$e\left(\frac{2}{29}\right)$	$e\left(\frac{21}{58}\right)$
$\chi_{8410}(4291,\cdot)$	$1$	$1$	$e\left(\frac{55}{58}\right)$	$e\left(\frac{3}{29}\right)$	$e\left(\frac{26}{29}\right)$	$e\left(\frac{7}{58}\right)$	$e\left(\frac{15}{29}\right)$	$e\left(\frac{57}{58}\right)$	$e\left(\frac{49}{58}\right)$	$e\left(\frac{3}{58}\right)$	$e\left(\frac{24}{29}\right)$	$e\left(\frac{49}{58}\right)$
$\chi_{8410}(4581,\cdot)$	$1$	$1$	$e\left(\frac{45}{58}\right)$	$e\left(\frac{13}{29}\right)$	$e\left(\frac{16}{29}\right)$	$e\left(\frac{11}{58}\right)$	$e\left(\frac{7}{29}\right)$	$e\left(\frac{15}{58}\right)$	$e\left(\frac{19}{58}\right)$	$e\left(\frac{13}{58}\right)$	$e\left(\frac{17}{29}\right)$	$e\left(\frac{19}{58}\right)$
$\chi_{8410}(4871,\cdot)$	$1$	$1$	$e\left(\frac{35}{58}\right)$	$e\left(\frac{23}{29}\right)$	$e\left(\frac{6}{29}\right)$	$e\left(\frac{15}{58}\right)$	$e\left(\frac{28}{29}\right)$	$e\left(\frac{31}{58}\right)$	$e\left(\frac{47}{58}\right)$	$e\left(\frac{23}{58}\right)$	$e\left(\frac{10}{29}\right)$	$e\left(\frac{47}{58}\right)$
$\chi_{8410}(5161,\cdot)$	$1$	$1$	$e\left(\frac{25}{58}\right)$	$e\left(\frac{4}{29}\right)$	$e\left(\frac{25}{29}\right)$	$e\left(\frac{19}{58}\right)$	$e\left(\frac{20}{29}\right)$	$e\left(\frac{47}{58}\right)$	$e\left(\frac{17}{58}\right)$	$e\left(\frac{33}{58}\right)$	$e\left(\frac{3}{29}\right)$	$e\left(\frac{17}{58}\right)$
$\chi_{8410}(5451,\cdot)$	$1$	$1$	$e\left(\frac{15}{58}\right)$	$e\left(\frac{14}{29}\right)$	$e\left(\frac{15}{29}\right)$	$e\left(\frac{23}{58}\right)$	$e\left(\frac{12}{29}\right)$	$e\left(\frac{5}{58}\right)$	$e\left(\frac{45}{58}\right)$	$e\left(\frac{43}{58}\right)$	$e\left(\frac{25}{29}\right)$	$e\left(\frac{45}{58}\right)$
$\chi_{8410}(5741,\cdot)$	$1$	$1$	$e\left(\frac{5}{58}\right)$	$e\left(\frac{24}{29}\right)$	$e\left(\frac{5}{29}\right)$	$e\left(\frac{27}{58}\right)$	$e\left(\frac{4}{29}\right)$	$e\left(\frac{21}{58}\right)$	$e\left(\frac{15}{58}\right)$	$e\left(\frac{53}{58}\right)$	$e\left(\frac{18}{29}\right)$	$e\left(\frac{15}{58}\right)$
$\chi_{8410}(6031,\cdot)$	$1$	$1$	$e\left(\frac{53}{58}\right)$	$e\left(\frac{5}{29}\right)$	$e\left(\frac{24}{29}\right)$	$e\left(\frac{31}{58}\right)$	$e\left(\frac{25}{29}\right)$	$e\left(\frac{37}{58}\right)$	$e\left(\frac{43}{58}\right)$	$e\left(\frac{5}{58}\right)$	$e\left(\frac{11}{29}\right)$	$e\left(\frac{43}{58}\right)$
$\chi_{8410}(6321,\cdot)$	$1$	$1$	$e\left(\frac{43}{58}\right)$	$e\left(\frac{15}{29}\right)$	$e\left(\frac{14}{29}\right)$	$e\left(\frac{35}{58}\right)$	$e\left(\frac{17}{29}\right)$	$e\left(\frac{53}{58}\right)$	$e\left(\frac{13}{58}\right)$	$e\left(\frac{15}{58}\right)$	$e\left(\frac{4}{29}\right)$	$e\left(\frac{13}{58}\right)$
$\chi_{8410}(6611,\cdot)$	$1$	$1$	$e\left(\frac{33}{58}\right)$	$e\left(\frac{25}{29}\right)$	$e\left(\frac{4}{29}\right)$	$e\left(\frac{39}{58}\right)$	$e\left(\frac{9}{29}\right)$	$e\left(\frac{11}{58}\right)$	$e\left(\frac{41}{58}\right)$	$e\left(\frac{25}{58}\right)$	$e\left(\frac{26}{29}\right)$	$e\left(\frac{41}{58}\right)$
$\chi_{8410}(6901,\cdot)$	$1$	$1$	$e\left(\frac{23}{58}\right)$	$e\left(\frac{6}{29}\right)$	$e\left(\frac{23}{29}\right)$	$e\left(\frac{43}{58}\right)$	$e\left(\frac{1}{29}\right)$	$e\left(\frac{27}{58}\right)$	$e\left(\frac{11}{58}\right)$	$e\left(\frac{35}{58}\right)$	$e\left(\frac{19}{29}\right)$	$e\left(\frac{11}{58}\right)$
$\chi_{8410}(7191,\cdot)$	$1$	$1$	$e\left(\frac{13}{58}\right)$	$e\left(\frac{16}{29}\right)$	$e\left(\frac{13}{29}\right)$	$e\left(\frac{47}{58}\right)$	$e\left(\frac{22}{29}\right)$	$e\left(\frac{43}{58}\right)$	$e\left(\frac{39}{58}\right)$	$e\left(\frac{45}{58}\right)$	$e\left(\frac{12}{29}\right)$	$e\left(\frac{39}{58}\right)$
$\chi_{8410}(7481,\cdot)$	$1$	$1$	$e\left(\frac{3}{58}\right)$	$e\left(\frac{26}{29}\right)$	$e\left(\frac{3}{29}\right)$	$e\left(\frac{51}{58}\right)$	$e\left(\frac{14}{29}\right)$	$e\left(\frac{1}{58}\right)$	$e\left(\frac{9}{58}\right)$	$e\left(\frac{55}{58}\right)$	$e\left(\frac{5}{29}\right)$	$e\left(\frac{9}{58}\right)$
$\chi_{8410}(7771,\cdot)$	$1$	$1$	$e\left(\frac{51}{58}\right)$	$e\left(\frac{7}{29}\right)$	$e\left(\frac{22}{29}\right)$	$e\left(\frac{55}{58}\right)$	$e\left(\frac{6}{29}\right)$	$e\left(\frac{17}{58}\right)$	$e\left(\frac{37}{58}\right)$	$e\left(\frac{7}{58}\right)$	$e\left(\frac{27}{29}\right)$	$e\left(\frac{37}{58}\right)$
$\chi_{8410}(8061,\cdot)$	$1$	$1$	$e\left(\frac{41}{58}\right)$	$e\left(\frac{17}{29}\right)$	$e\left(\frac{12}{29}\right)$	$e\left(\frac{1}{58}\right)$	$e\left(\frac{27}{29}\right)$	$e\left(\frac{33}{58}\right)$	$e\left(\frac{7}{58}\right)$	$e\left(\frac{17}{58}\right)$	$e\left(\frac{20}{29}\right)$	$e\left(\frac{7}{58}\right)$
$\chi_{8410}(8351,\cdot)$	$1$	$1$	$e\left(\frac{31}{58}\right)$	$e\left(\frac{27}{29}\right)$	$e\left(\frac{2}{29}\right)$	$e\left(\frac{5}{58}\right)$	$e\left(\frac{19}{29}\right)$	$e\left(\frac{49}{58}\right)$	$e\left(\frac{35}{58}\right)$	$e\left(\frac{27}{58}\right)$	$e\left(\frac{13}{29}\right)$	$e\left(\frac{35}{58}\right)$

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	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(13\)	\(17\)	\(19\)	\(21\)	\(23\)	\(27\)
\(\chi_{8410}(231,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{21}{58}\right)\)	\(e\left(\frac{8}{29}\right)\)	\(e\left(\frac{21}{29}\right)\)	\(e\left(\frac{9}{58}\right)\)	\(e\left(\frac{11}{29}\right)\)	\(e\left(\frac{7}{58}\right)\)	\(e\left(\frac{5}{58}\right)\)	\(e\left(\frac{37}{58}\right)\)	\(e\left(\frac{6}{29}\right)\)	\(e\left(\frac{5}{58}\right)\)
\(\chi_{8410}(521,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{58}\right)\)	\(e\left(\frac{18}{29}\right)\)	\(e\left(\frac{11}{29}\right)\)	\(e\left(\frac{13}{58}\right)\)	\(e\left(\frac{3}{29}\right)\)	\(e\left(\frac{23}{58}\right)\)	\(e\left(\frac{33}{58}\right)\)	\(e\left(\frac{47}{58}\right)\)	\(e\left(\frac{28}{29}\right)\)	\(e\left(\frac{33}{58}\right)\)
\(\chi_{8410}(811,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{58}\right)\)	\(e\left(\frac{28}{29}\right)\)	\(e\left(\frac{1}{29}\right)\)	\(e\left(\frac{17}{58}\right)\)	\(e\left(\frac{24}{29}\right)\)	\(e\left(\frac{39}{58}\right)\)	\(e\left(\frac{3}{58}\right)\)	\(e\left(\frac{57}{58}\right)\)	\(e\left(\frac{21}{29}\right)\)	\(e\left(\frac{3}{58}\right)\)
\(\chi_{8410}(1101,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{49}{58}\right)\)	\(e\left(\frac{9}{29}\right)\)	\(e\left(\frac{20}{29}\right)\)	\(e\left(\frac{21}{58}\right)\)	\(e\left(\frac{16}{29}\right)\)	\(e\left(\frac{55}{58}\right)\)	\(e\left(\frac{31}{58}\right)\)	\(e\left(\frac{9}{58}\right)\)	\(e\left(\frac{14}{29}\right)\)	\(e\left(\frac{31}{58}\right)\)
\(\chi_{8410}(1391,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{39}{58}\right)\)	\(e\left(\frac{19}{29}\right)\)	\(e\left(\frac{10}{29}\right)\)	\(e\left(\frac{25}{58}\right)\)	\(e\left(\frac{8}{29}\right)\)	\(e\left(\frac{13}{58}\right)\)	\(e\left(\frac{1}{58}\right)\)	\(e\left(\frac{19}{58}\right)\)	\(e\left(\frac{7}{29}\right)\)	\(e\left(\frac{1}{58}\right)\)
\(\chi_{8410}(1971,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{58}\right)\)	\(e\left(\frac{10}{29}\right)\)	\(e\left(\frac{19}{29}\right)\)	\(e\left(\frac{33}{58}\right)\)	\(e\left(\frac{21}{29}\right)\)	\(e\left(\frac{45}{58}\right)\)	\(e\left(\frac{57}{58}\right)\)	\(e\left(\frac{39}{58}\right)\)	\(e\left(\frac{22}{29}\right)\)	\(e\left(\frac{57}{58}\right)\)
\(\chi_{8410}(2261,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{58}\right)\)	\(e\left(\frac{20}{29}\right)\)	\(e\left(\frac{9}{29}\right)\)	\(e\left(\frac{37}{58}\right)\)	\(e\left(\frac{13}{29}\right)\)	\(e\left(\frac{3}{58}\right)\)	\(e\left(\frac{27}{58}\right)\)	\(e\left(\frac{49}{58}\right)\)	\(e\left(\frac{15}{29}\right)\)	\(e\left(\frac{27}{58}\right)\)
\(\chi_{8410}(2551,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{57}{58}\right)\)	\(e\left(\frac{1}{29}\right)\)	\(e\left(\frac{28}{29}\right)\)	\(e\left(\frac{41}{58}\right)\)	\(e\left(\frac{5}{29}\right)\)	\(e\left(\frac{19}{58}\right)\)	\(e\left(\frac{55}{58}\right)\)	\(e\left(\frac{1}{58}\right)\)	\(e\left(\frac{8}{29}\right)\)	\(e\left(\frac{55}{58}\right)\)
\(\chi_{8410}(2841,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{58}\right)\)	\(e\left(\frac{11}{29}\right)\)	\(e\left(\frac{18}{29}\right)\)	\(e\left(\frac{45}{58}\right)\)	\(e\left(\frac{26}{29}\right)\)	\(e\left(\frac{35}{58}\right)\)	\(e\left(\frac{25}{58}\right)\)	\(e\left(\frac{11}{58}\right)\)	\(e\left(\frac{1}{29}\right)\)	\(e\left(\frac{25}{58}\right)\)
\(\chi_{8410}(3131,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{58}\right)\)	\(e\left(\frac{21}{29}\right)\)	\(e\left(\frac{8}{29}\right)\)	\(e\left(\frac{49}{58}\right)\)	\(e\left(\frac{18}{29}\right)\)	\(e\left(\frac{51}{58}\right)\)	\(e\left(\frac{53}{58}\right)\)	\(e\left(\frac{21}{58}\right)\)	\(e\left(\frac{23}{29}\right)\)	\(e\left(\frac{53}{58}\right)\)
\(\chi_{8410}(3421,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{27}{58}\right)\)	\(e\left(\frac{2}{29}\right)\)	\(e\left(\frac{27}{29}\right)\)	\(e\left(\frac{53}{58}\right)\)	\(e\left(\frac{10}{29}\right)\)	\(e\left(\frac{9}{58}\right)\)	\(e\left(\frac{23}{58}\right)\)	\(e\left(\frac{31}{58}\right)\)	\(e\left(\frac{16}{29}\right)\)	\(e\left(\frac{23}{58}\right)\)
\(\chi_{8410}(3711,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{58}\right)\)	\(e\left(\frac{12}{29}\right)\)	\(e\left(\frac{17}{29}\right)\)	\(e\left(\frac{57}{58}\right)\)	\(e\left(\frac{2}{29}\right)\)	\(e\left(\frac{25}{58}\right)\)	\(e\left(\frac{51}{58}\right)\)	\(e\left(\frac{41}{58}\right)\)	\(e\left(\frac{9}{29}\right)\)	\(e\left(\frac{51}{58}\right)\)
\(\chi_{8410}(4001,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{58}\right)\)	\(e\left(\frac{22}{29}\right)\)	\(e\left(\frac{7}{29}\right)\)	\(e\left(\frac{3}{58}\right)\)	\(e\left(\frac{23}{29}\right)\)	\(e\left(\frac{41}{58}\right)\)	\(e\left(\frac{21}{58}\right)\)	\(e\left(\frac{51}{58}\right)\)	\(e\left(\frac{2}{29}\right)\)	\(e\left(\frac{21}{58}\right)\)
\(\chi_{8410}(4291,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{55}{58}\right)\)	\(e\left(\frac{3}{29}\right)\)	\(e\left(\frac{26}{29}\right)\)	\(e\left(\frac{7}{58}\right)\)	\(e\left(\frac{15}{29}\right)\)	\(e\left(\frac{57}{58}\right)\)	\(e\left(\frac{49}{58}\right)\)	\(e\left(\frac{3}{58}\right)\)	\(e\left(\frac{24}{29}\right)\)	\(e\left(\frac{49}{58}\right)\)
\(\chi_{8410}(4581,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{45}{58}\right)\)	\(e\left(\frac{13}{29}\right)\)	\(e\left(\frac{16}{29}\right)\)	\(e\left(\frac{11}{58}\right)\)	\(e\left(\frac{7}{29}\right)\)	\(e\left(\frac{15}{58}\right)\)	\(e\left(\frac{19}{58}\right)\)	\(e\left(\frac{13}{58}\right)\)	\(e\left(\frac{17}{29}\right)\)	\(e\left(\frac{19}{58}\right)\)
\(\chi_{8410}(4871,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{35}{58}\right)\)	\(e\left(\frac{23}{29}\right)\)	\(e\left(\frac{6}{29}\right)\)	\(e\left(\frac{15}{58}\right)\)	\(e\left(\frac{28}{29}\right)\)	\(e\left(\frac{31}{58}\right)\)	\(e\left(\frac{47}{58}\right)\)	\(e\left(\frac{23}{58}\right)\)	\(e\left(\frac{10}{29}\right)\)	\(e\left(\frac{47}{58}\right)\)
\(\chi_{8410}(5161,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{25}{58}\right)\)	\(e\left(\frac{4}{29}\right)\)	\(e\left(\frac{25}{29}\right)\)	\(e\left(\frac{19}{58}\right)\)	\(e\left(\frac{20}{29}\right)\)	\(e\left(\frac{47}{58}\right)\)	\(e\left(\frac{17}{58}\right)\)	\(e\left(\frac{33}{58}\right)\)	\(e\left(\frac{3}{29}\right)\)	\(e\left(\frac{17}{58}\right)\)
\(\chi_{8410}(5451,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{15}{58}\right)\)	\(e\left(\frac{14}{29}\right)\)	\(e\left(\frac{15}{29}\right)\)	\(e\left(\frac{23}{58}\right)\)	\(e\left(\frac{12}{29}\right)\)	\(e\left(\frac{5}{58}\right)\)	\(e\left(\frac{45}{58}\right)\)	\(e\left(\frac{43}{58}\right)\)	\(e\left(\frac{25}{29}\right)\)	\(e\left(\frac{45}{58}\right)\)
\(\chi_{8410}(5741,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{58}\right)\)	\(e\left(\frac{24}{29}\right)\)	\(e\left(\frac{5}{29}\right)\)	\(e\left(\frac{27}{58}\right)\)	\(e\left(\frac{4}{29}\right)\)	\(e\left(\frac{21}{58}\right)\)	\(e\left(\frac{15}{58}\right)\)	\(e\left(\frac{53}{58}\right)\)	\(e\left(\frac{18}{29}\right)\)	\(e\left(\frac{15}{58}\right)\)
\(\chi_{8410}(6031,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{58}\right)\)	\(e\left(\frac{5}{29}\right)\)	\(e\left(\frac{24}{29}\right)\)	\(e\left(\frac{31}{58}\right)\)	\(e\left(\frac{25}{29}\right)\)	\(e\left(\frac{37}{58}\right)\)	\(e\left(\frac{43}{58}\right)\)	\(e\left(\frac{5}{58}\right)\)	\(e\left(\frac{11}{29}\right)\)	\(e\left(\frac{43}{58}\right)\)
\(\chi_{8410}(6321,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{58}\right)\)	\(e\left(\frac{15}{29}\right)\)	\(e\left(\frac{14}{29}\right)\)	\(e\left(\frac{35}{58}\right)\)	\(e\left(\frac{17}{29}\right)\)	\(e\left(\frac{53}{58}\right)\)	\(e\left(\frac{13}{58}\right)\)	\(e\left(\frac{15}{58}\right)\)	\(e\left(\frac{4}{29}\right)\)	\(e\left(\frac{13}{58}\right)\)
\(\chi_{8410}(6611,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{33}{58}\right)\)	\(e\left(\frac{25}{29}\right)\)	\(e\left(\frac{4}{29}\right)\)	\(e\left(\frac{39}{58}\right)\)	\(e\left(\frac{9}{29}\right)\)	\(e\left(\frac{11}{58}\right)\)	\(e\left(\frac{41}{58}\right)\)	\(e\left(\frac{25}{58}\right)\)	\(e\left(\frac{26}{29}\right)\)	\(e\left(\frac{41}{58}\right)\)
\(\chi_{8410}(6901,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{58}\right)\)	\(e\left(\frac{6}{29}\right)\)	\(e\left(\frac{23}{29}\right)\)	\(e\left(\frac{43}{58}\right)\)	\(e\left(\frac{1}{29}\right)\)	\(e\left(\frac{27}{58}\right)\)	\(e\left(\frac{11}{58}\right)\)	\(e\left(\frac{35}{58}\right)\)	\(e\left(\frac{19}{29}\right)\)	\(e\left(\frac{11}{58}\right)\)
\(\chi_{8410}(7191,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{58}\right)\)	\(e\left(\frac{16}{29}\right)\)	\(e\left(\frac{13}{29}\right)\)	\(e\left(\frac{47}{58}\right)\)	\(e\left(\frac{22}{29}\right)\)	\(e\left(\frac{43}{58}\right)\)	\(e\left(\frac{39}{58}\right)\)	\(e\left(\frac{45}{58}\right)\)	\(e\left(\frac{12}{29}\right)\)	\(e\left(\frac{39}{58}\right)\)
\(\chi_{8410}(7481,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{58}\right)\)	\(e\left(\frac{26}{29}\right)\)	\(e\left(\frac{3}{29}\right)\)	\(e\left(\frac{51}{58}\right)\)	\(e\left(\frac{14}{29}\right)\)	\(e\left(\frac{1}{58}\right)\)	\(e\left(\frac{9}{58}\right)\)	\(e\left(\frac{55}{58}\right)\)	\(e\left(\frac{5}{29}\right)\)	\(e\left(\frac{9}{58}\right)\)
\(\chi_{8410}(7771,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{51}{58}\right)\)	\(e\left(\frac{7}{29}\right)\)	\(e\left(\frac{22}{29}\right)\)	\(e\left(\frac{55}{58}\right)\)	\(e\left(\frac{6}{29}\right)\)	\(e\left(\frac{17}{58}\right)\)	\(e\left(\frac{37}{58}\right)\)	\(e\left(\frac{7}{58}\right)\)	\(e\left(\frac{27}{29}\right)\)	\(e\left(\frac{37}{58}\right)\)
\(\chi_{8410}(8061,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{58}\right)\)	\(e\left(\frac{17}{29}\right)\)	\(e\left(\frac{12}{29}\right)\)	\(e\left(\frac{1}{58}\right)\)	\(e\left(\frac{27}{29}\right)\)	\(e\left(\frac{33}{58}\right)\)	\(e\left(\frac{7}{58}\right)\)	\(e\left(\frac{17}{58}\right)\)	\(e\left(\frac{20}{29}\right)\)	\(e\left(\frac{7}{58}\right)\)
\(\chi_{8410}(8351,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{58}\right)\)	\(e\left(\frac{27}{29}\right)\)	\(e\left(\frac{2}{29}\right)\)	\(e\left(\frac{5}{58}\right)\)	\(e\left(\frac{19}{29}\right)\)	\(e\left(\frac{49}{58}\right)\)	\(e\left(\frac{35}{58}\right)\)	\(e\left(\frac{27}{58}\right)\)	\(e\left(\frac{13}{29}\right)\)	\(e\left(\frac{35}{58}\right)\)

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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	8410.w
Modulus	$8410$
Conductor	$841$
Order	$58$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(8410\)
Conductor:	\(841\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(58\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 841.h	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)