LMFDB - Dirichlet character orbit 10002.m

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(10002, base_ring=CyclotomicField(98)) M = H._module chi = DirichletCharacter(H, M([0,22])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(13,10002)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$10002$
Conductor:	$1667$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$49$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 1667.g	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:	$\Q(\zeta_{49})$
Fixed field:	Number field defined by a degree 49 polynomial

First 31 of 42 characters in Galois orbit

Character	$-1$	$1$	$5$	$7$	$11$	$13$	$17$	$19$	$23$	$25$	$29$	$31$
$\chi_{10002}(13,\cdot)$	$1$	$1$	$e\left(\frac{4}{49}\right)$	$e\left(\frac{22}{49}\right)$	$e\left(\frac{47}{49}\right)$	$e\left(\frac{47}{49}\right)$	$e\left(\frac{43}{49}\right)$	$e\left(\frac{22}{49}\right)$	$e\left(\frac{11}{49}\right)$	$e\left(\frac{8}{49}\right)$	$e\left(\frac{34}{49}\right)$	$e\left(\frac{31}{49}\right)$
$\chi_{10002}(169,\cdot)$	$1$	$1$	$e\left(\frac{8}{49}\right)$	$e\left(\frac{44}{49}\right)$	$e\left(\frac{45}{49}\right)$	$e\left(\frac{45}{49}\right)$	$e\left(\frac{37}{49}\right)$	$e\left(\frac{44}{49}\right)$	$e\left(\frac{22}{49}\right)$	$e\left(\frac{16}{49}\right)$	$e\left(\frac{19}{49}\right)$	$e\left(\frac{13}{49}\right)$
$\chi_{10002}(181,\cdot)$	$1$	$1$	$e\left(\frac{38}{49}\right)$	$e\left(\frac{13}{49}\right)$	$e\left(\frac{30}{49}\right)$	$e\left(\frac{30}{49}\right)$	$e\left(\frac{41}{49}\right)$	$e\left(\frac{13}{49}\right)$	$e\left(\frac{31}{49}\right)$	$e\left(\frac{27}{49}\right)$	$e\left(\frac{29}{49}\right)$	$e\left(\frac{25}{49}\right)$
$\chi_{10002}(397,\cdot)$	$1$	$1$	$e\left(\frac{25}{49}\right)$	$e\left(\frac{15}{49}\right)$	$e\left(\frac{12}{49}\right)$	$e\left(\frac{12}{49}\right)$	$e\left(\frac{36}{49}\right)$	$e\left(\frac{15}{49}\right)$	$e\left(\frac{32}{49}\right)$	$e\left(\frac{1}{49}\right)$	$e\left(\frac{41}{49}\right)$	$e\left(\frac{10}{49}\right)$
$\chi_{10002}(535,\cdot)$	$1$	$1$	$e\left(\frac{17}{49}\right)$	$e\left(\frac{20}{49}\right)$	$e\left(\frac{16}{49}\right)$	$e\left(\frac{16}{49}\right)$	$e\left(\frac{48}{49}\right)$	$e\left(\frac{20}{49}\right)$	$e\left(\frac{10}{49}\right)$	$e\left(\frac{34}{49}\right)$	$e\left(\frac{22}{49}\right)$	$e\left(\frac{46}{49}\right)$
$\chi_{10002}(583,\cdot)$	$1$	$1$	$e\left(\frac{46}{49}\right)$	$e\left(\frac{8}{49}\right)$	$e\left(\frac{26}{49}\right)$	$e\left(\frac{26}{49}\right)$	$e\left(\frac{29}{49}\right)$	$e\left(\frac{8}{49}\right)$	$e\left(\frac{4}{49}\right)$	$e\left(\frac{43}{49}\right)$	$e\left(\frac{48}{49}\right)$	$e\left(\frac{38}{49}\right)$
$\chi_{10002}(595,\cdot)$	$1$	$1$	$e\left(\frac{9}{49}\right)$	$e\left(\frac{25}{49}\right)$	$e\left(\frac{20}{49}\right)$	$e\left(\frac{20}{49}\right)$	$e\left(\frac{11}{49}\right)$	$e\left(\frac{25}{49}\right)$	$e\left(\frac{37}{49}\right)$	$e\left(\frac{18}{49}\right)$	$e\left(\frac{3}{49}\right)$	$e\left(\frac{33}{49}\right)$
$\chi_{10002}(1219,\cdot)$	$1$	$1$	$e\left(\frac{20}{49}\right)$	$e\left(\frac{12}{49}\right)$	$e\left(\frac{39}{49}\right)$	$e\left(\frac{39}{49}\right)$	$e\left(\frac{19}{49}\right)$	$e\left(\frac{12}{49}\right)$	$e\left(\frac{6}{49}\right)$	$e\left(\frac{40}{49}\right)$	$e\left(\frac{23}{49}\right)$	$e\left(\frac{8}{49}\right)$
$\chi_{10002}(1405,\cdot)$	$1$	$1$	$e\left(\frac{22}{49}\right)$	$e\left(\frac{23}{49}\right)$	$e\left(\frac{38}{49}\right)$	$e\left(\frac{38}{49}\right)$	$e\left(\frac{16}{49}\right)$	$e\left(\frac{23}{49}\right)$	$e\left(\frac{36}{49}\right)$	$e\left(\frac{44}{49}\right)$	$e\left(\frac{40}{49}\right)$	$e\left(\frac{48}{49}\right)$
$\chi_{10002}(1525,\cdot)$	$1$	$1$	$e\left(\frac{39}{49}\right)$	$e\left(\frac{43}{49}\right)$	$e\left(\frac{5}{49}\right)$	$e\left(\frac{5}{49}\right)$	$e\left(\frac{15}{49}\right)$	$e\left(\frac{43}{49}\right)$	$e\left(\frac{46}{49}\right)$	$e\left(\frac{29}{49}\right)$	$e\left(\frac{13}{49}\right)$	$e\left(\frac{45}{49}\right)$
$\chi_{10002}(2035,\cdot)$	$1$	$1$	$e\left(\frac{37}{49}\right)$	$e\left(\frac{32}{49}\right)$	$e\left(\frac{6}{49}\right)$	$e\left(\frac{6}{49}\right)$	$e\left(\frac{18}{49}\right)$	$e\left(\frac{32}{49}\right)$	$e\left(\frac{16}{49}\right)$	$e\left(\frac{25}{49}\right)$	$e\left(\frac{45}{49}\right)$	$e\left(\frac{5}{49}\right)$
$\chi_{10002}(2197,\cdot)$	$1$	$1$	$e\left(\frac{12}{49}\right)$	$e\left(\frac{17}{49}\right)$	$e\left(\frac{43}{49}\right)$	$e\left(\frac{43}{49}\right)$	$e\left(\frac{31}{49}\right)$	$e\left(\frac{17}{49}\right)$	$e\left(\frac{33}{49}\right)$	$e\left(\frac{24}{49}\right)$	$e\left(\frac{4}{49}\right)$	$e\left(\frac{44}{49}\right)$
$\chi_{10002}(2755,\cdot)$	$1$	$1$	$e\left(\frac{27}{49}\right)$	$e\left(\frac{26}{49}\right)$	$e\left(\frac{11}{49}\right)$	$e\left(\frac{11}{49}\right)$	$e\left(\frac{33}{49}\right)$	$e\left(\frac{26}{49}\right)$	$e\left(\frac{13}{49}\right)$	$e\left(\frac{5}{49}\right)$	$e\left(\frac{9}{49}\right)$	$e\left(\frac{1}{49}\right)$
$\chi_{10002}(3517,\cdot)$	$1$	$1$	$e\left(\frac{3}{49}\right)$	$e\left(\frac{41}{49}\right)$	$e\left(\frac{23}{49}\right)$	$e\left(\frac{23}{49}\right)$	$e\left(\frac{20}{49}\right)$	$e\left(\frac{41}{49}\right)$	$e\left(\frac{45}{49}\right)$	$e\left(\frac{6}{49}\right)$	$e\left(\frac{1}{49}\right)$	$e\left(\frac{11}{49}\right)$
$\chi_{10002}(3631,\cdot)$	$1$	$1$	$e\left(\frac{44}{49}\right)$	$e\left(\frac{46}{49}\right)$	$e\left(\frac{27}{49}\right)$	$e\left(\frac{27}{49}\right)$	$e\left(\frac{32}{49}\right)$	$e\left(\frac{46}{49}\right)$	$e\left(\frac{23}{49}\right)$	$e\left(\frac{39}{49}\right)$	$e\left(\frac{31}{49}\right)$	$e\left(\frac{47}{49}\right)$
$\chi_{10002}(3847,\cdot)$	$1$	$1$	$e\left(\frac{45}{49}\right)$	$e\left(\frac{27}{49}\right)$	$e\left(\frac{2}{49}\right)$	$e\left(\frac{2}{49}\right)$	$e\left(\frac{6}{49}\right)$	$e\left(\frac{27}{49}\right)$	$e\left(\frac{38}{49}\right)$	$e\left(\frac{41}{49}\right)$	$e\left(\frac{15}{49}\right)$	$e\left(\frac{18}{49}\right)$
$\chi_{10002}(3955,\cdot)$	$1$	$1$	$e\left(\frac{18}{49}\right)$	$e\left(\frac{1}{49}\right)$	$e\left(\frac{40}{49}\right)$	$e\left(\frac{40}{49}\right)$	$e\left(\frac{22}{49}\right)$	$e\left(\frac{1}{49}\right)$	$e\left(\frac{25}{49}\right)$	$e\left(\frac{36}{49}\right)$	$e\left(\frac{6}{49}\right)$	$e\left(\frac{17}{49}\right)$
$\chi_{10002}(4255,\cdot)$	$1$	$1$	$e\left(\frac{11}{49}\right)$	$e\left(\frac{36}{49}\right)$	$e\left(\frac{19}{49}\right)$	$e\left(\frac{19}{49}\right)$	$e\left(\frac{8}{49}\right)$	$e\left(\frac{36}{49}\right)$	$e\left(\frac{18}{49}\right)$	$e\left(\frac{22}{49}\right)$	$e\left(\frac{20}{49}\right)$	$e\left(\frac{24}{49}\right)$
$\chi_{10002}(5161,\cdot)$	$1$	$1$	$e\left(\frac{29}{49}\right)$	$e\left(\frac{37}{49}\right)$	$e\left(\frac{10}{49}\right)$	$e\left(\frac{10}{49}\right)$	$e\left(\frac{30}{49}\right)$	$e\left(\frac{37}{49}\right)$	$e\left(\frac{43}{49}\right)$	$e\left(\frac{9}{49}\right)$	$e\left(\frac{26}{49}\right)$	$e\left(\frac{41}{49}\right)$
$\chi_{10002}(5305,\cdot)$	$1$	$1$	$e\left(\frac{15}{49}\right)$	$e\left(\frac{9}{49}\right)$	$e\left(\frac{17}{49}\right)$	$e\left(\frac{17}{49}\right)$	$e\left(\frac{2}{49}\right)$	$e\left(\frac{9}{49}\right)$	$e\left(\frac{29}{49}\right)$	$e\left(\frac{30}{49}\right)$	$e\left(\frac{5}{49}\right)$	$e\left(\frac{6}{49}\right)$
$\chi_{10002}(5665,\cdot)$	$1$	$1$	$e\left(\frac{40}{49}\right)$	$e\left(\frac{24}{49}\right)$	$e\left(\frac{29}{49}\right)$	$e\left(\frac{29}{49}\right)$	$e\left(\frac{38}{49}\right)$	$e\left(\frac{24}{49}\right)$	$e\left(\frac{12}{49}\right)$	$e\left(\frac{31}{49}\right)$	$e\left(\frac{46}{49}\right)$	$e\left(\frac{16}{49}\right)$
$\chi_{10002}(5809,\cdot)$	$1$	$1$	$e\left(\frac{31}{49}\right)$	$e\left(\frac{48}{49}\right)$	$e\left(\frac{9}{49}\right)$	$e\left(\frac{9}{49}\right)$	$e\left(\frac{27}{49}\right)$	$e\left(\frac{48}{49}\right)$	$e\left(\frac{24}{49}\right)$	$e\left(\frac{13}{49}\right)$	$e\left(\frac{43}{49}\right)$	$e\left(\frac{32}{49}\right)$
$\chi_{10002}(5845,\cdot)$	$1$	$1$	$e\left(\frac{24}{49}\right)$	$e\left(\frac{34}{49}\right)$	$e\left(\frac{37}{49}\right)$	$e\left(\frac{37}{49}\right)$	$e\left(\frac{13}{49}\right)$	$e\left(\frac{34}{49}\right)$	$e\left(\frac{17}{49}\right)$	$e\left(\frac{48}{49}\right)$	$e\left(\frac{8}{49}\right)$	$e\left(\frac{39}{49}\right)$
$\chi_{10002}(6169,\cdot)$	$1$	$1$	$e\left(\frac{34}{49}\right)$	$e\left(\frac{40}{49}\right)$	$e\left(\frac{32}{49}\right)$	$e\left(\frac{32}{49}\right)$	$e\left(\frac{47}{49}\right)$	$e\left(\frac{40}{49}\right)$	$e\left(\frac{20}{49}\right)$	$e\left(\frac{19}{49}\right)$	$e\left(\frac{44}{49}\right)$	$e\left(\frac{43}{49}\right)$
$\chi_{10002}(6367,\cdot)$	$1$	$1$	$e\left(\frac{23}{49}\right)$	$e\left(\frac{4}{49}\right)$	$e\left(\frac{13}{49}\right)$	$e\left(\frac{13}{49}\right)$	$e\left(\frac{39}{49}\right)$	$e\left(\frac{4}{49}\right)$	$e\left(\frac{2}{49}\right)$	$e\left(\frac{46}{49}\right)$	$e\left(\frac{24}{49}\right)$	$e\left(\frac{19}{49}\right)$
$\chi_{10002}(6451,\cdot)$	$1$	$1$	$e\left(\frac{41}{49}\right)$	$e\left(\frac{5}{49}\right)$	$e\left(\frac{4}{49}\right)$	$e\left(\frac{4}{49}\right)$	$e\left(\frac{12}{49}\right)$	$e\left(\frac{5}{49}\right)$	$e\left(\frac{27}{49}\right)$	$e\left(\frac{33}{49}\right)$	$e\left(\frac{30}{49}\right)$	$e\left(\frac{36}{49}\right)$
$\chi_{10002}(6817,\cdot)$	$1$	$1$	$e\left(\frac{6}{49}\right)$	$e\left(\frac{33}{49}\right)$	$e\left(\frac{46}{49}\right)$	$e\left(\frac{46}{49}\right)$	$e\left(\frac{40}{49}\right)$	$e\left(\frac{33}{49}\right)$	$e\left(\frac{41}{49}\right)$	$e\left(\frac{12}{49}\right)$	$e\left(\frac{2}{49}\right)$	$e\left(\frac{22}{49}\right)$
$\chi_{10002}(7081,\cdot)$	$1$	$1$	$e\left(\frac{33}{49}\right)$	$e\left(\frac{10}{49}\right)$	$e\left(\frac{8}{49}\right)$	$e\left(\frac{8}{49}\right)$	$e\left(\frac{24}{49}\right)$	$e\left(\frac{10}{49}\right)$	$e\left(\frac{5}{49}\right)$	$e\left(\frac{17}{49}\right)$	$e\left(\frac{11}{49}\right)$	$e\left(\frac{23}{49}\right)$
$\chi_{10002}(7195,\cdot)$	$1$	$1$	$e\left(\frac{48}{49}\right)$	$e\left(\frac{19}{49}\right)$	$e\left(\frac{25}{49}\right)$	$e\left(\frac{25}{49}\right)$	$e\left(\frac{26}{49}\right)$	$e\left(\frac{19}{49}\right)$	$e\left(\frac{34}{49}\right)$	$e\left(\frac{47}{49}\right)$	$e\left(\frac{16}{49}\right)$	$e\left(\frac{29}{49}\right)$
$\chi_{10002}(7399,\cdot)$	$1$	$1$	$e\left(\frac{30}{49}\right)$	$e\left(\frac{18}{49}\right)$	$e\left(\frac{34}{49}\right)$	$e\left(\frac{34}{49}\right)$	$e\left(\frac{4}{49}\right)$	$e\left(\frac{18}{49}\right)$	$e\left(\frac{9}{49}\right)$	$e\left(\frac{11}{49}\right)$	$e\left(\frac{10}{49}\right)$	$e\left(\frac{12}{49}\right)$
$\chi_{10002}(7579,\cdot)$	$1$	$1$	$e\left(\frac{1}{49}\right)$	$e\left(\frac{30}{49}\right)$	$e\left(\frac{24}{49}\right)$	$e\left(\frac{24}{49}\right)$	$e\left(\frac{23}{49}\right)$	$e\left(\frac{30}{49}\right)$	$e\left(\frac{15}{49}\right)$	$e\left(\frac{2}{49}\right)$	$e\left(\frac{33}{49}\right)$	$e\left(\frac{20}{49}\right)$

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	\(-1\)	\(1\)	\(5\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)
\(\chi_{10002}(13,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{49}\right)\)	\(e\left(\frac{22}{49}\right)\)	\(e\left(\frac{47}{49}\right)\)	\(e\left(\frac{47}{49}\right)\)	\(e\left(\frac{43}{49}\right)\)	\(e\left(\frac{22}{49}\right)\)	\(e\left(\frac{11}{49}\right)\)	\(e\left(\frac{8}{49}\right)\)	\(e\left(\frac{34}{49}\right)\)	\(e\left(\frac{31}{49}\right)\)
\(\chi_{10002}(169,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{8}{49}\right)\)	\(e\left(\frac{44}{49}\right)\)	\(e\left(\frac{45}{49}\right)\)	\(e\left(\frac{45}{49}\right)\)	\(e\left(\frac{37}{49}\right)\)	\(e\left(\frac{44}{49}\right)\)	\(e\left(\frac{22}{49}\right)\)	\(e\left(\frac{16}{49}\right)\)	\(e\left(\frac{19}{49}\right)\)	\(e\left(\frac{13}{49}\right)\)
\(\chi_{10002}(181,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{38}{49}\right)\)	\(e\left(\frac{13}{49}\right)\)	\(e\left(\frac{30}{49}\right)\)	\(e\left(\frac{30}{49}\right)\)	\(e\left(\frac{41}{49}\right)\)	\(e\left(\frac{13}{49}\right)\)	\(e\left(\frac{31}{49}\right)\)	\(e\left(\frac{27}{49}\right)\)	\(e\left(\frac{29}{49}\right)\)	\(e\left(\frac{25}{49}\right)\)
\(\chi_{10002}(397,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{25}{49}\right)\)	\(e\left(\frac{15}{49}\right)\)	\(e\left(\frac{12}{49}\right)\)	\(e\left(\frac{12}{49}\right)\)	\(e\left(\frac{36}{49}\right)\)	\(e\left(\frac{15}{49}\right)\)	\(e\left(\frac{32}{49}\right)\)	\(e\left(\frac{1}{49}\right)\)	\(e\left(\frac{41}{49}\right)\)	\(e\left(\frac{10}{49}\right)\)
\(\chi_{10002}(535,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{49}\right)\)	\(e\left(\frac{20}{49}\right)\)	\(e\left(\frac{16}{49}\right)\)	\(e\left(\frac{16}{49}\right)\)	\(e\left(\frac{48}{49}\right)\)	\(e\left(\frac{20}{49}\right)\)	\(e\left(\frac{10}{49}\right)\)	\(e\left(\frac{34}{49}\right)\)	\(e\left(\frac{22}{49}\right)\)	\(e\left(\frac{46}{49}\right)\)
\(\chi_{10002}(583,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{46}{49}\right)\)	\(e\left(\frac{8}{49}\right)\)	\(e\left(\frac{26}{49}\right)\)	\(e\left(\frac{26}{49}\right)\)	\(e\left(\frac{29}{49}\right)\)	\(e\left(\frac{8}{49}\right)\)	\(e\left(\frac{4}{49}\right)\)	\(e\left(\frac{43}{49}\right)\)	\(e\left(\frac{48}{49}\right)\)	\(e\left(\frac{38}{49}\right)\)
\(\chi_{10002}(595,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{49}\right)\)	\(e\left(\frac{25}{49}\right)\)	\(e\left(\frac{20}{49}\right)\)	\(e\left(\frac{20}{49}\right)\)	\(e\left(\frac{11}{49}\right)\)	\(e\left(\frac{25}{49}\right)\)	\(e\left(\frac{37}{49}\right)\)	\(e\left(\frac{18}{49}\right)\)	\(e\left(\frac{3}{49}\right)\)	\(e\left(\frac{33}{49}\right)\)
\(\chi_{10002}(1219,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{20}{49}\right)\)	\(e\left(\frac{12}{49}\right)\)	\(e\left(\frac{39}{49}\right)\)	\(e\left(\frac{39}{49}\right)\)	\(e\left(\frac{19}{49}\right)\)	\(e\left(\frac{12}{49}\right)\)	\(e\left(\frac{6}{49}\right)\)	\(e\left(\frac{40}{49}\right)\)	\(e\left(\frac{23}{49}\right)\)	\(e\left(\frac{8}{49}\right)\)
\(\chi_{10002}(1405,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{22}{49}\right)\)	\(e\left(\frac{23}{49}\right)\)	\(e\left(\frac{38}{49}\right)\)	\(e\left(\frac{38}{49}\right)\)	\(e\left(\frac{16}{49}\right)\)	\(e\left(\frac{23}{49}\right)\)	\(e\left(\frac{36}{49}\right)\)	\(e\left(\frac{44}{49}\right)\)	\(e\left(\frac{40}{49}\right)\)	\(e\left(\frac{48}{49}\right)\)
\(\chi_{10002}(1525,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{39}{49}\right)\)	\(e\left(\frac{43}{49}\right)\)	\(e\left(\frac{5}{49}\right)\)	\(e\left(\frac{5}{49}\right)\)	\(e\left(\frac{15}{49}\right)\)	\(e\left(\frac{43}{49}\right)\)	\(e\left(\frac{46}{49}\right)\)	\(e\left(\frac{29}{49}\right)\)	\(e\left(\frac{13}{49}\right)\)	\(e\left(\frac{45}{49}\right)\)
\(\chi_{10002}(2035,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{49}\right)\)	\(e\left(\frac{32}{49}\right)\)	\(e\left(\frac{6}{49}\right)\)	\(e\left(\frac{6}{49}\right)\)	\(e\left(\frac{18}{49}\right)\)	\(e\left(\frac{32}{49}\right)\)	\(e\left(\frac{16}{49}\right)\)	\(e\left(\frac{25}{49}\right)\)	\(e\left(\frac{45}{49}\right)\)	\(e\left(\frac{5}{49}\right)\)
\(\chi_{10002}(2197,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{12}{49}\right)\)	\(e\left(\frac{17}{49}\right)\)	\(e\left(\frac{43}{49}\right)\)	\(e\left(\frac{43}{49}\right)\)	\(e\left(\frac{31}{49}\right)\)	\(e\left(\frac{17}{49}\right)\)	\(e\left(\frac{33}{49}\right)\)	\(e\left(\frac{24}{49}\right)\)	\(e\left(\frac{4}{49}\right)\)	\(e\left(\frac{44}{49}\right)\)
\(\chi_{10002}(2755,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{27}{49}\right)\)	\(e\left(\frac{26}{49}\right)\)	\(e\left(\frac{11}{49}\right)\)	\(e\left(\frac{11}{49}\right)\)	\(e\left(\frac{33}{49}\right)\)	\(e\left(\frac{26}{49}\right)\)	\(e\left(\frac{13}{49}\right)\)	\(e\left(\frac{5}{49}\right)\)	\(e\left(\frac{9}{49}\right)\)	\(e\left(\frac{1}{49}\right)\)
\(\chi_{10002}(3517,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{49}\right)\)	\(e\left(\frac{41}{49}\right)\)	\(e\left(\frac{23}{49}\right)\)	\(e\left(\frac{23}{49}\right)\)	\(e\left(\frac{20}{49}\right)\)	\(e\left(\frac{41}{49}\right)\)	\(e\left(\frac{45}{49}\right)\)	\(e\left(\frac{6}{49}\right)\)	\(e\left(\frac{1}{49}\right)\)	\(e\left(\frac{11}{49}\right)\)
\(\chi_{10002}(3631,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{44}{49}\right)\)	\(e\left(\frac{46}{49}\right)\)	\(e\left(\frac{27}{49}\right)\)	\(e\left(\frac{27}{49}\right)\)	\(e\left(\frac{32}{49}\right)\)	\(e\left(\frac{46}{49}\right)\)	\(e\left(\frac{23}{49}\right)\)	\(e\left(\frac{39}{49}\right)\)	\(e\left(\frac{31}{49}\right)\)	\(e\left(\frac{47}{49}\right)\)
\(\chi_{10002}(3847,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{45}{49}\right)\)	\(e\left(\frac{27}{49}\right)\)	\(e\left(\frac{2}{49}\right)\)	\(e\left(\frac{2}{49}\right)\)	\(e\left(\frac{6}{49}\right)\)	\(e\left(\frac{27}{49}\right)\)	\(e\left(\frac{38}{49}\right)\)	\(e\left(\frac{41}{49}\right)\)	\(e\left(\frac{15}{49}\right)\)	\(e\left(\frac{18}{49}\right)\)
\(\chi_{10002}(3955,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{18}{49}\right)\)	\(e\left(\frac{1}{49}\right)\)	\(e\left(\frac{40}{49}\right)\)	\(e\left(\frac{40}{49}\right)\)	\(e\left(\frac{22}{49}\right)\)	\(e\left(\frac{1}{49}\right)\)	\(e\left(\frac{25}{49}\right)\)	\(e\left(\frac{36}{49}\right)\)	\(e\left(\frac{6}{49}\right)\)	\(e\left(\frac{17}{49}\right)\)
\(\chi_{10002}(4255,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{49}\right)\)	\(e\left(\frac{36}{49}\right)\)	\(e\left(\frac{19}{49}\right)\)	\(e\left(\frac{19}{49}\right)\)	\(e\left(\frac{8}{49}\right)\)	\(e\left(\frac{36}{49}\right)\)	\(e\left(\frac{18}{49}\right)\)	\(e\left(\frac{22}{49}\right)\)	\(e\left(\frac{20}{49}\right)\)	\(e\left(\frac{24}{49}\right)\)
\(\chi_{10002}(5161,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{49}\right)\)	\(e\left(\frac{37}{49}\right)\)	\(e\left(\frac{10}{49}\right)\)	\(e\left(\frac{10}{49}\right)\)	\(e\left(\frac{30}{49}\right)\)	\(e\left(\frac{37}{49}\right)\)	\(e\left(\frac{43}{49}\right)\)	\(e\left(\frac{9}{49}\right)\)	\(e\left(\frac{26}{49}\right)\)	\(e\left(\frac{41}{49}\right)\)
\(\chi_{10002}(5305,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{15}{49}\right)\)	\(e\left(\frac{9}{49}\right)\)	\(e\left(\frac{17}{49}\right)\)	\(e\left(\frac{17}{49}\right)\)	\(e\left(\frac{2}{49}\right)\)	\(e\left(\frac{9}{49}\right)\)	\(e\left(\frac{29}{49}\right)\)	\(e\left(\frac{30}{49}\right)\)	\(e\left(\frac{5}{49}\right)\)	\(e\left(\frac{6}{49}\right)\)
\(\chi_{10002}(5665,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{40}{49}\right)\)	\(e\left(\frac{24}{49}\right)\)	\(e\left(\frac{29}{49}\right)\)	\(e\left(\frac{29}{49}\right)\)	\(e\left(\frac{38}{49}\right)\)	\(e\left(\frac{24}{49}\right)\)	\(e\left(\frac{12}{49}\right)\)	\(e\left(\frac{31}{49}\right)\)	\(e\left(\frac{46}{49}\right)\)	\(e\left(\frac{16}{49}\right)\)
\(\chi_{10002}(5809,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{49}\right)\)	\(e\left(\frac{48}{49}\right)\)	\(e\left(\frac{9}{49}\right)\)	\(e\left(\frac{9}{49}\right)\)	\(e\left(\frac{27}{49}\right)\)	\(e\left(\frac{48}{49}\right)\)	\(e\left(\frac{24}{49}\right)\)	\(e\left(\frac{13}{49}\right)\)	\(e\left(\frac{43}{49}\right)\)	\(e\left(\frac{32}{49}\right)\)
\(\chi_{10002}(5845,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{24}{49}\right)\)	\(e\left(\frac{34}{49}\right)\)	\(e\left(\frac{37}{49}\right)\)	\(e\left(\frac{37}{49}\right)\)	\(e\left(\frac{13}{49}\right)\)	\(e\left(\frac{34}{49}\right)\)	\(e\left(\frac{17}{49}\right)\)	\(e\left(\frac{48}{49}\right)\)	\(e\left(\frac{8}{49}\right)\)	\(e\left(\frac{39}{49}\right)\)
\(\chi_{10002}(6169,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{34}{49}\right)\)	\(e\left(\frac{40}{49}\right)\)	\(e\left(\frac{32}{49}\right)\)	\(e\left(\frac{32}{49}\right)\)	\(e\left(\frac{47}{49}\right)\)	\(e\left(\frac{40}{49}\right)\)	\(e\left(\frac{20}{49}\right)\)	\(e\left(\frac{19}{49}\right)\)	\(e\left(\frac{44}{49}\right)\)	\(e\left(\frac{43}{49}\right)\)
\(\chi_{10002}(6367,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{49}\right)\)	\(e\left(\frac{4}{49}\right)\)	\(e\left(\frac{13}{49}\right)\)	\(e\left(\frac{13}{49}\right)\)	\(e\left(\frac{39}{49}\right)\)	\(e\left(\frac{4}{49}\right)\)	\(e\left(\frac{2}{49}\right)\)	\(e\left(\frac{46}{49}\right)\)	\(e\left(\frac{24}{49}\right)\)	\(e\left(\frac{19}{49}\right)\)
\(\chi_{10002}(6451,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{49}\right)\)	\(e\left(\frac{5}{49}\right)\)	\(e\left(\frac{4}{49}\right)\)	\(e\left(\frac{4}{49}\right)\)	\(e\left(\frac{12}{49}\right)\)	\(e\left(\frac{5}{49}\right)\)	\(e\left(\frac{27}{49}\right)\)	\(e\left(\frac{33}{49}\right)\)	\(e\left(\frac{30}{49}\right)\)	\(e\left(\frac{36}{49}\right)\)
\(\chi_{10002}(6817,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{6}{49}\right)\)	\(e\left(\frac{33}{49}\right)\)	\(e\left(\frac{46}{49}\right)\)	\(e\left(\frac{46}{49}\right)\)	\(e\left(\frac{40}{49}\right)\)	\(e\left(\frac{33}{49}\right)\)	\(e\left(\frac{41}{49}\right)\)	\(e\left(\frac{12}{49}\right)\)	\(e\left(\frac{2}{49}\right)\)	\(e\left(\frac{22}{49}\right)\)
\(\chi_{10002}(7081,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{33}{49}\right)\)	\(e\left(\frac{10}{49}\right)\)	\(e\left(\frac{8}{49}\right)\)	\(e\left(\frac{8}{49}\right)\)	\(e\left(\frac{24}{49}\right)\)	\(e\left(\frac{10}{49}\right)\)	\(e\left(\frac{5}{49}\right)\)	\(e\left(\frac{17}{49}\right)\)	\(e\left(\frac{11}{49}\right)\)	\(e\left(\frac{23}{49}\right)\)
\(\chi_{10002}(7195,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{48}{49}\right)\)	\(e\left(\frac{19}{49}\right)\)	\(e\left(\frac{25}{49}\right)\)	\(e\left(\frac{25}{49}\right)\)	\(e\left(\frac{26}{49}\right)\)	\(e\left(\frac{19}{49}\right)\)	\(e\left(\frac{34}{49}\right)\)	\(e\left(\frac{47}{49}\right)\)	\(e\left(\frac{16}{49}\right)\)	\(e\left(\frac{29}{49}\right)\)
\(\chi_{10002}(7399,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{30}{49}\right)\)	\(e\left(\frac{18}{49}\right)\)	\(e\left(\frac{34}{49}\right)\)	\(e\left(\frac{34}{49}\right)\)	\(e\left(\frac{4}{49}\right)\)	\(e\left(\frac{18}{49}\right)\)	\(e\left(\frac{9}{49}\right)\)	\(e\left(\frac{11}{49}\right)\)	\(e\left(\frac{10}{49}\right)\)	\(e\left(\frac{12}{49}\right)\)
\(\chi_{10002}(7579,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{49}\right)\)	\(e\left(\frac{30}{49}\right)\)	\(e\left(\frac{24}{49}\right)\)	\(e\left(\frac{24}{49}\right)\)	\(e\left(\frac{23}{49}\right)\)	\(e\left(\frac{30}{49}\right)\)	\(e\left(\frac{15}{49}\right)\)	\(e\left(\frac{2}{49}\right)\)	\(e\left(\frac{33}{49}\right)\)	\(e\left(\frac{20}{49}\right)\)

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First 31 of 42 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	10002.m
Modulus	$10002$
Conductor	$1667$
Order	$49$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(10002\)
Conductor:	\(1667\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(49\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 1667.g	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)