LMFDB - Dirichlet character orbit 3503.cr

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(3503, base_ring=CyclotomicField(280)) M = H._module chi = DirichletCharacter(H, M([224,55])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(126,3503)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$3503$
Conductor:	$3503$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$280$	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:	$\Q(\zeta_{280})$
Fixed field:	Number field defined by a degree 280 polynomial (not computed)

First 31 of 96 characters in Galois orbit

Character	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{3503}(126,\cdot)$	$1$	$1$	$e\left(\frac{39}{70}\right)$	$e\left(\frac{279}{280}\right)$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{17}{56}\right)$	$e\left(\frac{31}{56}\right)$	$e\left(\frac{34}{35}\right)$	$e\left(\frac{47}{70}\right)$	$e\left(\frac{139}{140}\right)$	$e\left(\frac{241}{280}\right)$	$e\left(\frac{131}{140}\right)$
$\chi_{3503}(163,\cdot)$	$1$	$1$	$e\left(\frac{47}{70}\right)$	$e\left(\frac{277}{280}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{51}{56}\right)$	$e\left(\frac{37}{56}\right)$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{1}{70}\right)$	$e\left(\frac{137}{140}\right)$	$e\left(\frac{163}{280}\right)$	$e\left(\frac{113}{140}\right)$
$\chi_{3503}(190,\cdot)$	$1$	$1$	$e\left(\frac{13}{70}\right)$	$e\left(\frac{93}{280}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{43}{56}\right)$	$e\left(\frac{29}{56}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{39}{70}\right)$	$e\left(\frac{93}{140}\right)$	$e\left(\frac{267}{280}\right)$	$e\left(\frac{137}{140}\right)$
$\chi_{3503}(252,\cdot)$	$1$	$1$	$e\left(\frac{3}{70}\right)$	$e\left(\frac{253}{280}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{11}{56}\right)$	$e\left(\frac{53}{56}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{9}{70}\right)$	$e\left(\frac{113}{140}\right)$	$e\left(\frac{67}{280}\right)$	$e\left(\frac{37}{140}\right)$
$\chi_{3503}(287,\cdot)$	$1$	$1$	$e\left(\frac{37}{70}\right)$	$e\left(\frac{87}{280}\right)$	$e\left(\frac{2}{35}\right)$	$e\left(\frac{33}{56}\right)$	$e\left(\frac{47}{56}\right)$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{41}{70}\right)$	$e\left(\frac{87}{140}\right)$	$e\left(\frac{33}{280}\right)$	$e\left(\frac{83}{140}\right)$
$\chi_{3503}(314,\cdot)$	$1$	$1$	$e\left(\frac{13}{70}\right)$	$e\left(\frac{163}{280}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{29}{56}\right)$	$e\left(\frac{43}{56}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{39}{70}\right)$	$e\left(\frac{23}{140}\right)$	$e\left(\frac{197}{280}\right)$	$e\left(\frac{67}{140}\right)$
$\chi_{3503}(326,\cdot)$	$1$	$1$	$e\left(\frac{11}{70}\right)$	$e\left(\frac{251}{280}\right)$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{45}{56}\right)$	$e\left(\frac{3}{56}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{33}{70}\right)$	$e\left(\frac{111}{140}\right)$	$e\left(\frac{269}{280}\right)$	$e\left(\frac{19}{140}\right)$
$\chi_{3503}(380,\cdot)$	$1$	$1$	$e\left(\frac{47}{70}\right)$	$e\left(\frac{67}{280}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{37}{56}\right)$	$e\left(\frac{51}{56}\right)$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{1}{70}\right)$	$e\left(\frac{67}{140}\right)$	$e\left(\frac{93}{280}\right)$	$e\left(\frac{43}{140}\right)$
$\chi_{3503}(411,\cdot)$	$1$	$1$	$e\left(\frac{47}{70}\right)$	$e\left(\frac{207}{280}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{9}{56}\right)$	$e\left(\frac{23}{56}\right)$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{1}{70}\right)$	$e\left(\frac{67}{140}\right)$	$e\left(\frac{233}{280}\right)$	$e\left(\frac{43}{140}\right)$
$\chi_{3503}(504,\cdot)$	$1$	$1$	$e\left(\frac{37}{70}\right)$	$e\left(\frac{227}{280}\right)$	$e\left(\frac{2}{35}\right)$	$e\left(\frac{5}{56}\right)$	$e\left(\frac{19}{56}\right)$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{41}{70}\right)$	$e\left(\frac{87}{140}\right)$	$e\left(\frac{173}{280}\right)$	$e\left(\frac{83}{140}\right)$
$\chi_{3503}(529,\cdot)$	$1$	$1$	$e\left(\frac{69}{70}\right)$	$e\left(\frac{149}{280}\right)$	$e\left(\frac{34}{35}\right)$	$e\left(\frac{43}{56}\right)$	$e\left(\frac{29}{56}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{67}{70}\right)$	$e\left(\frac{9}{140}\right)$	$e\left(\frac{211}{280}\right)$	$e\left(\frac{81}{140}\right)$
$\chi_{3503}(543,\cdot)$	$1$	$1$	$e\left(\frac{1}{70}\right)$	$e\left(\frac{131}{280}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{13}{56}\right)$	$e\left(\frac{27}{56}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{3}{70}\right)$	$e\left(\frac{131}{140}\right)$	$e\left(\frac{69}{280}\right)$	$e\left(\frac{59}{140}\right)$
$\chi_{3503}(574,\cdot)$	$1$	$1$	$e\left(\frac{1}{70}\right)$	$e\left(\frac{61}{280}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{27}{56}\right)$	$e\left(\frac{13}{56}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{3}{70}\right)$	$e\left(\frac{61}{140}\right)$	$e\left(\frac{139}{280}\right)$	$e\left(\frac{129}{140}\right)$
$\chi_{3503}(591,\cdot)$	$1$	$1$	$e\left(\frac{59}{70}\right)$	$e\left(\frac{29}{280}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{11}{56}\right)$	$e\left(\frac{53}{56}\right)$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{37}{70}\right)$	$e\left(\frac{29}{140}\right)$	$e\left(\frac{11}{280}\right)$	$e\left(\frac{121}{140}\right)$
$\chi_{3503}(628,\cdot)$	$1$	$1$	$e\left(\frac{47}{70}\right)$	$e\left(\frac{137}{280}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{23}{56}\right)$	$e\left(\frac{9}{56}\right)$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{1}{70}\right)$	$e\left(\frac{137}{140}\right)$	$e\left(\frac{23}{280}\right)$	$e\left(\frac{113}{140}\right)$
$\chi_{3503}(653,\cdot)$	$1$	$1$	$e\left(\frac{69}{70}\right)$	$e\left(\frac{219}{280}\right)$	$e\left(\frac{34}{35}\right)$	$e\left(\frac{29}{56}\right)$	$e\left(\frac{43}{56}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{67}{70}\right)$	$e\left(\frac{79}{140}\right)$	$e\left(\frac{141}{280}\right)$	$e\left(\frac{11}{140}\right)$
$\chi_{3503}(667,\cdot)$	$1$	$1$	$e\left(\frac{51}{70}\right)$	$e\left(\frac{101}{280}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{19}{56}\right)$	$e\left(\frac{5}{56}\right)$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{13}{70}\right)$	$e\left(\frac{101}{140}\right)$	$e\left(\frac{19}{280}\right)$	$e\left(\frac{69}{140}\right)$
$\chi_{3503}(729,\cdot)$	$1$	$1$	$e\left(\frac{31}{70}\right)$	$e\left(\frac{71}{280}\right)$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{25}{56}\right)$	$e\left(\frac{39}{56}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{23}{70}\right)$	$e\left(\frac{71}{140}\right)$	$e\left(\frac{249}{280}\right)$	$e\left(\frac{79}{140}\right)$
$\chi_{3503}(760,\cdot)$	$1$	$1$	$e\left(\frac{11}{70}\right)$	$e\left(\frac{41}{280}\right)$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{31}{56}\right)$	$e\left(\frac{17}{56}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{33}{70}\right)$	$e\left(\frac{41}{140}\right)$	$e\left(\frac{199}{280}\right)$	$e\left(\frac{89}{140}\right)$
$\chi_{3503}(822,\cdot)$	$1$	$1$	$e\left(\frac{11}{70}\right)$	$e\left(\frac{181}{280}\right)$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{3}{56}\right)$	$e\left(\frac{45}{56}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{33}{70}\right)$	$e\left(\frac{41}{140}\right)$	$e\left(\frac{59}{280}\right)$	$e\left(\frac{89}{140}\right)$
$\chi_{3503}(841,\cdot)$	$1$	$1$	$e\left(\frac{33}{70}\right)$	$e\left(\frac{53}{280}\right)$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{51}{56}\right)$	$e\left(\frac{37}{56}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{29}{70}\right)$	$e\left(\frac{53}{140}\right)$	$e\left(\frac{107}{280}\right)$	$e\left(\frac{57}{140}\right)$
$\chi_{3503}(853,\cdot)$	$1$	$1$	$e\left(\frac{31}{70}\right)$	$e\left(\frac{211}{280}\right)$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{53}{56}\right)$	$e\left(\frac{11}{56}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{23}{70}\right)$	$e\left(\frac{71}{140}\right)$	$e\left(\frac{109}{280}\right)$	$e\left(\frac{79}{140}\right)$
$\chi_{3503}(915,\cdot)$	$1$	$1$	$e\left(\frac{51}{70}\right)$	$e\left(\frac{241}{280}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{47}{56}\right)$	$e\left(\frac{33}{56}\right)$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{13}{70}\right)$	$e\left(\frac{101}{140}\right)$	$e\left(\frac{159}{280}\right)$	$e\left(\frac{69}{140}\right)$
$\chi_{3503}(965,\cdot)$	$1$	$1$	$e\left(\frac{23}{70}\right)$	$e\left(\frac{143}{280}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{33}{56}\right)$	$e\left(\frac{47}{56}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{69}{70}\right)$	$e\left(\frac{3}{140}\right)$	$e\left(\frac{257}{280}\right)$	$e\left(\frac{27}{140}\right)$
$\chi_{3503}(1008,\cdot)$	$1$	$1$	$e\left(\frac{1}{70}\right)$	$e\left(\frac{201}{280}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{55}{56}\right)$	$e\left(\frac{41}{56}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{3}{70}\right)$	$e\left(\frac{61}{140}\right)$	$e\left(\frac{279}{280}\right)$	$e\left(\frac{129}{140}\right)$
$\chi_{3503}(1039,\cdot)$	$1$	$1$	$e\left(\frac{1}{70}\right)$	$e\left(\frac{271}{280}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{41}{56}\right)$	$e\left(\frac{55}{56}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{3}{70}\right)$	$e\left(\frac{131}{140}\right)$	$e\left(\frac{209}{280}\right)$	$e\left(\frac{59}{140}\right)$
$\chi_{3503}(1058,\cdot)$	$1$	$1$	$e\left(\frac{33}{70}\right)$	$e\left(\frac{123}{280}\right)$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{37}{56}\right)$	$e\left(\frac{51}{56}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{29}{70}\right)$	$e\left(\frac{123}{140}\right)$	$e\left(\frac{37}{280}\right)$	$e\left(\frac{127}{140}\right)$
$\chi_{3503}(1089,\cdot)$	$1$	$1$	$e\left(\frac{33}{70}\right)$	$e\left(\frac{263}{280}\right)$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{9}{56}\right)$	$e\left(\frac{23}{56}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{29}{70}\right)$	$e\left(\frac{123}{140}\right)$	$e\left(\frac{177}{280}\right)$	$e\left(\frac{127}{140}\right)$
$\chi_{3503}(1155,\cdot)$	$1$	$1$	$e\left(\frac{27}{70}\right)$	$e\left(\frac{247}{280}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{1}{56}\right)$	$e\left(\frac{15}{56}\right)$	$e\left(\frac{2}{35}\right)$	$e\left(\frac{11}{70}\right)$	$e\left(\frac{107}{140}\right)$	$e\left(\frac{113}{280}\right)$	$e\left(\frac{123}{140}\right)$
$\chi_{3503}(1180,\cdot)$	$1$	$1$	$e\left(\frac{19}{70}\right)$	$e\left(\frac{109}{280}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{51}{56}\right)$	$e\left(\frac{37}{56}\right)$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{57}{70}\right)$	$e\left(\frac{109}{140}\right)$	$e\left(\frac{51}{280}\right)$	$e\left(\frac{1}{140}\right)$
$\chi_{3503}(1182,\cdot)$	$1$	$1$	$e\left(\frac{23}{70}\right)$	$e\left(\frac{3}{280}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{5}{56}\right)$	$e\left(\frac{19}{56}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{69}{70}\right)$	$e\left(\frac{3}{140}\right)$	$e\left(\frac{117}{280}\right)$	$e\left(\frac{27}{140}\right)$

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	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\(\chi_{3503}(126,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{39}{70}\right)\)	\(e\left(\frac{279}{280}\right)\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{17}{56}\right)\)	\(e\left(\frac{31}{56}\right)\)	\(e\left(\frac{34}{35}\right)\)	\(e\left(\frac{47}{70}\right)\)	\(e\left(\frac{139}{140}\right)\)	\(e\left(\frac{241}{280}\right)\)	\(e\left(\frac{131}{140}\right)\)
\(\chi_{3503}(163,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{70}\right)\)	\(e\left(\frac{277}{280}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{51}{56}\right)\)	\(e\left(\frac{37}{56}\right)\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{1}{70}\right)\)	\(e\left(\frac{137}{140}\right)\)	\(e\left(\frac{163}{280}\right)\)	\(e\left(\frac{113}{140}\right)\)
\(\chi_{3503}(190,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{70}\right)\)	\(e\left(\frac{93}{280}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{43}{56}\right)\)	\(e\left(\frac{29}{56}\right)\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{39}{70}\right)\)	\(e\left(\frac{93}{140}\right)\)	\(e\left(\frac{267}{280}\right)\)	\(e\left(\frac{137}{140}\right)\)
\(\chi_{3503}(252,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{70}\right)\)	\(e\left(\frac{253}{280}\right)\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{11}{56}\right)\)	\(e\left(\frac{53}{56}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{9}{70}\right)\)	\(e\left(\frac{113}{140}\right)\)	\(e\left(\frac{67}{280}\right)\)	\(e\left(\frac{37}{140}\right)\)
\(\chi_{3503}(287,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{70}\right)\)	\(e\left(\frac{87}{280}\right)\)	\(e\left(\frac{2}{35}\right)\)	\(e\left(\frac{33}{56}\right)\)	\(e\left(\frac{47}{56}\right)\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{41}{70}\right)\)	\(e\left(\frac{87}{140}\right)\)	\(e\left(\frac{33}{280}\right)\)	\(e\left(\frac{83}{140}\right)\)
\(\chi_{3503}(314,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{70}\right)\)	\(e\left(\frac{163}{280}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{29}{56}\right)\)	\(e\left(\frac{43}{56}\right)\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{39}{70}\right)\)	\(e\left(\frac{23}{140}\right)\)	\(e\left(\frac{197}{280}\right)\)	\(e\left(\frac{67}{140}\right)\)
\(\chi_{3503}(326,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{70}\right)\)	\(e\left(\frac{251}{280}\right)\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{45}{56}\right)\)	\(e\left(\frac{3}{56}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{33}{70}\right)\)	\(e\left(\frac{111}{140}\right)\)	\(e\left(\frac{269}{280}\right)\)	\(e\left(\frac{19}{140}\right)\)
\(\chi_{3503}(380,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{70}\right)\)	\(e\left(\frac{67}{280}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{37}{56}\right)\)	\(e\left(\frac{51}{56}\right)\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{1}{70}\right)\)	\(e\left(\frac{67}{140}\right)\)	\(e\left(\frac{93}{280}\right)\)	\(e\left(\frac{43}{140}\right)\)
\(\chi_{3503}(411,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{70}\right)\)	\(e\left(\frac{207}{280}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{9}{56}\right)\)	\(e\left(\frac{23}{56}\right)\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{1}{70}\right)\)	\(e\left(\frac{67}{140}\right)\)	\(e\left(\frac{233}{280}\right)\)	\(e\left(\frac{43}{140}\right)\)
\(\chi_{3503}(504,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{70}\right)\)	\(e\left(\frac{227}{280}\right)\)	\(e\left(\frac{2}{35}\right)\)	\(e\left(\frac{5}{56}\right)\)	\(e\left(\frac{19}{56}\right)\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{41}{70}\right)\)	\(e\left(\frac{87}{140}\right)\)	\(e\left(\frac{173}{280}\right)\)	\(e\left(\frac{83}{140}\right)\)
\(\chi_{3503}(529,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{69}{70}\right)\)	\(e\left(\frac{149}{280}\right)\)	\(e\left(\frac{34}{35}\right)\)	\(e\left(\frac{43}{56}\right)\)	\(e\left(\frac{29}{56}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{67}{70}\right)\)	\(e\left(\frac{9}{140}\right)\)	\(e\left(\frac{211}{280}\right)\)	\(e\left(\frac{81}{140}\right)\)
\(\chi_{3503}(543,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{70}\right)\)	\(e\left(\frac{131}{280}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{13}{56}\right)\)	\(e\left(\frac{27}{56}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{3}{70}\right)\)	\(e\left(\frac{131}{140}\right)\)	\(e\left(\frac{69}{280}\right)\)	\(e\left(\frac{59}{140}\right)\)
\(\chi_{3503}(574,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{70}\right)\)	\(e\left(\frac{61}{280}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{27}{56}\right)\)	\(e\left(\frac{13}{56}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{3}{70}\right)\)	\(e\left(\frac{61}{140}\right)\)	\(e\left(\frac{139}{280}\right)\)	\(e\left(\frac{129}{140}\right)\)
\(\chi_{3503}(591,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{70}\right)\)	\(e\left(\frac{29}{280}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{11}{56}\right)\)	\(e\left(\frac{53}{56}\right)\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{37}{70}\right)\)	\(e\left(\frac{29}{140}\right)\)	\(e\left(\frac{11}{280}\right)\)	\(e\left(\frac{121}{140}\right)\)
\(\chi_{3503}(628,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{70}\right)\)	\(e\left(\frac{137}{280}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{23}{56}\right)\)	\(e\left(\frac{9}{56}\right)\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{1}{70}\right)\)	\(e\left(\frac{137}{140}\right)\)	\(e\left(\frac{23}{280}\right)\)	\(e\left(\frac{113}{140}\right)\)
\(\chi_{3503}(653,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{69}{70}\right)\)	\(e\left(\frac{219}{280}\right)\)	\(e\left(\frac{34}{35}\right)\)	\(e\left(\frac{29}{56}\right)\)	\(e\left(\frac{43}{56}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{67}{70}\right)\)	\(e\left(\frac{79}{140}\right)\)	\(e\left(\frac{141}{280}\right)\)	\(e\left(\frac{11}{140}\right)\)
\(\chi_{3503}(667,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{51}{70}\right)\)	\(e\left(\frac{101}{280}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{19}{56}\right)\)	\(e\left(\frac{5}{56}\right)\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{13}{70}\right)\)	\(e\left(\frac{101}{140}\right)\)	\(e\left(\frac{19}{280}\right)\)	\(e\left(\frac{69}{140}\right)\)
\(\chi_{3503}(729,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{70}\right)\)	\(e\left(\frac{71}{280}\right)\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{25}{56}\right)\)	\(e\left(\frac{39}{56}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{23}{70}\right)\)	\(e\left(\frac{71}{140}\right)\)	\(e\left(\frac{249}{280}\right)\)	\(e\left(\frac{79}{140}\right)\)
\(\chi_{3503}(760,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{70}\right)\)	\(e\left(\frac{41}{280}\right)\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{31}{56}\right)\)	\(e\left(\frac{17}{56}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{33}{70}\right)\)	\(e\left(\frac{41}{140}\right)\)	\(e\left(\frac{199}{280}\right)\)	\(e\left(\frac{89}{140}\right)\)
\(\chi_{3503}(822,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{70}\right)\)	\(e\left(\frac{181}{280}\right)\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{3}{56}\right)\)	\(e\left(\frac{45}{56}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{33}{70}\right)\)	\(e\left(\frac{41}{140}\right)\)	\(e\left(\frac{59}{280}\right)\)	\(e\left(\frac{89}{140}\right)\)
\(\chi_{3503}(841,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{33}{70}\right)\)	\(e\left(\frac{53}{280}\right)\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{51}{56}\right)\)	\(e\left(\frac{37}{56}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{29}{70}\right)\)	\(e\left(\frac{53}{140}\right)\)	\(e\left(\frac{107}{280}\right)\)	\(e\left(\frac{57}{140}\right)\)
\(\chi_{3503}(853,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{70}\right)\)	\(e\left(\frac{211}{280}\right)\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{53}{56}\right)\)	\(e\left(\frac{11}{56}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{23}{70}\right)\)	\(e\left(\frac{71}{140}\right)\)	\(e\left(\frac{109}{280}\right)\)	\(e\left(\frac{79}{140}\right)\)
\(\chi_{3503}(915,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{51}{70}\right)\)	\(e\left(\frac{241}{280}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{47}{56}\right)\)	\(e\left(\frac{33}{56}\right)\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{13}{70}\right)\)	\(e\left(\frac{101}{140}\right)\)	\(e\left(\frac{159}{280}\right)\)	\(e\left(\frac{69}{140}\right)\)
\(\chi_{3503}(965,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{70}\right)\)	\(e\left(\frac{143}{280}\right)\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{33}{56}\right)\)	\(e\left(\frac{47}{56}\right)\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{69}{70}\right)\)	\(e\left(\frac{3}{140}\right)\)	\(e\left(\frac{257}{280}\right)\)	\(e\left(\frac{27}{140}\right)\)
\(\chi_{3503}(1008,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{70}\right)\)	\(e\left(\frac{201}{280}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{55}{56}\right)\)	\(e\left(\frac{41}{56}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{3}{70}\right)\)	\(e\left(\frac{61}{140}\right)\)	\(e\left(\frac{279}{280}\right)\)	\(e\left(\frac{129}{140}\right)\)
\(\chi_{3503}(1039,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{70}\right)\)	\(e\left(\frac{271}{280}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{41}{56}\right)\)	\(e\left(\frac{55}{56}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{3}{70}\right)\)	\(e\left(\frac{131}{140}\right)\)	\(e\left(\frac{209}{280}\right)\)	\(e\left(\frac{59}{140}\right)\)
\(\chi_{3503}(1058,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{33}{70}\right)\)	\(e\left(\frac{123}{280}\right)\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{37}{56}\right)\)	\(e\left(\frac{51}{56}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{29}{70}\right)\)	\(e\left(\frac{123}{140}\right)\)	\(e\left(\frac{37}{280}\right)\)	\(e\left(\frac{127}{140}\right)\)
\(\chi_{3503}(1089,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{33}{70}\right)\)	\(e\left(\frac{263}{280}\right)\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{9}{56}\right)\)	\(e\left(\frac{23}{56}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{29}{70}\right)\)	\(e\left(\frac{123}{140}\right)\)	\(e\left(\frac{177}{280}\right)\)	\(e\left(\frac{127}{140}\right)\)
\(\chi_{3503}(1155,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{27}{70}\right)\)	\(e\left(\frac{247}{280}\right)\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{1}{56}\right)\)	\(e\left(\frac{15}{56}\right)\)	\(e\left(\frac{2}{35}\right)\)	\(e\left(\frac{11}{70}\right)\)	\(e\left(\frac{107}{140}\right)\)	\(e\left(\frac{113}{280}\right)\)	\(e\left(\frac{123}{140}\right)\)
\(\chi_{3503}(1180,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{70}\right)\)	\(e\left(\frac{109}{280}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{51}{56}\right)\)	\(e\left(\frac{37}{56}\right)\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{57}{70}\right)\)	\(e\left(\frac{109}{140}\right)\)	\(e\left(\frac{51}{280}\right)\)	\(e\left(\frac{1}{140}\right)\)
\(\chi_{3503}(1182,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{70}\right)\)	\(e\left(\frac{3}{280}\right)\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{5}{56}\right)\)	\(e\left(\frac{19}{56}\right)\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{69}{70}\right)\)	\(e\left(\frac{3}{140}\right)\)	\(e\left(\frac{117}{280}\right)\)	\(e\left(\frac{27}{140}\right)\)

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First 31 of 96 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	3503.cr
Modulus	$3503$
Conductor	$3503$
Order	$280$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(3503\)
Conductor:	\(3503\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(280\)	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)