LMFDB - Dirichlet character orbit 3503.cx

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(3503, base_ring=CyclotomicField(560)) M = H._module chi = DirichletCharacter(H, M([504,205])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(23,3503)) 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:	$560$	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:	$\Q(\zeta_{560})$
Fixed field:	Number field defined by a degree 560 polynomial (not computed)

First 31 of 192 characters in Galois orbit

Character	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{3503}(23,\cdot)$	$1$	$1$	$e\left(\frac{139}{140}\right)$	$e\left(\frac{149}{560}\right)$	$e\left(\frac{69}{70}\right)$	$e\left(\frac{43}{112}\right)$	$e\left(\frac{29}{112}\right)$	$e\left(\frac{9}{70}\right)$	$e\left(\frac{137}{140}\right)$	$e\left(\frac{149}{280}\right)$	$e\left(\frac{211}{560}\right)$	$e\left(\frac{221}{280}\right)$
$\chi_{3503}(27,\cdot)$	$1$	$1$	$e\left(\frac{101}{140}\right)$	$e\left(\frac{71}{560}\right)$	$e\left(\frac{31}{70}\right)$	$e\left(\frac{25}{112}\right)$	$e\left(\frac{95}{112}\right)$	$e\left(\frac{1}{70}\right)$	$e\left(\frac{23}{140}\right)$	$e\left(\frac{71}{280}\right)$	$e\left(\frac{529}{560}\right)$	$e\left(\frac{79}{280}\right)$
$\chi_{3503}(29,\cdot)$	$1$	$1$	$e\left(\frac{103}{140}\right)$	$e\left(\frac{53}{560}\right)$	$e\left(\frac{33}{70}\right)$	$e\left(\frac{107}{112}\right)$	$e\left(\frac{93}{112}\right)$	$e\left(\frac{53}{70}\right)$	$e\left(\frac{29}{140}\right)$	$e\left(\frac{53}{280}\right)$	$e\left(\frac{387}{560}\right)$	$e\left(\frac{197}{280}\right)$
$\chi_{3503}(46,\cdot)$	$1$	$1$	$e\left(\frac{67}{140}\right)$	$e\left(\frac{97}{560}\right)$	$e\left(\frac{67}{70}\right)$	$e\left(\frac{31}{112}\right)$	$e\left(\frac{73}{112}\right)$	$e\left(\frac{27}{70}\right)$	$e\left(\frac{61}{140}\right)$	$e\left(\frac{97}{280}\right)$	$e\left(\frac{423}{560}\right)$	$e\left(\frac{33}{280}\right)$
$\chi_{3503}(54,\cdot)$	$1$	$1$	$e\left(\frac{29}{140}\right)$	$e\left(\frac{19}{560}\right)$	$e\left(\frac{29}{70}\right)$	$e\left(\frac{13}{112}\right)$	$e\left(\frac{27}{112}\right)$	$e\left(\frac{19}{70}\right)$	$e\left(\frac{87}{140}\right)$	$e\left(\frac{19}{280}\right)$	$e\left(\frac{181}{560}\right)$	$e\left(\frac{171}{280}\right)$
$\chi_{3503}(58,\cdot)$	$1$	$1$	$e\left(\frac{31}{140}\right)$	$e\left(\frac{1}{560}\right)$	$e\left(\frac{31}{70}\right)$	$e\left(\frac{95}{112}\right)$	$e\left(\frac{25}{112}\right)$	$e\left(\frac{1}{70}\right)$	$e\left(\frac{93}{140}\right)$	$e\left(\frac{1}{280}\right)$	$e\left(\frac{39}{560}\right)$	$e\left(\frac{9}{280}\right)$
$\chi_{3503}(89,\cdot)$	$1$	$1$	$e\left(\frac{51}{140}\right)$	$e\left(\frac{521}{560}\right)$	$e\left(\frac{51}{70}\right)$	$e\left(\frac{103}{112}\right)$	$e\left(\frac{33}{112}\right)$	$e\left(\frac{31}{70}\right)$	$e\left(\frac{13}{140}\right)$	$e\left(\frac{241}{280}\right)$	$e\left(\frac{159}{560}\right)$	$e\left(\frac{209}{280}\right)$
$\chi_{3503}(108,\cdot)$	$1$	$1$	$e\left(\frac{97}{140}\right)$	$e\left(\frac{527}{560}\right)$	$e\left(\frac{27}{70}\right)$	$e\left(\frac{1}{112}\right)$	$e\left(\frac{71}{112}\right)$	$e\left(\frac{37}{70}\right)$	$e\left(\frac{11}{140}\right)$	$e\left(\frac{247}{280}\right)$	$e\left(\frac{393}{560}\right)$	$e\left(\frac{263}{280}\right)$
$\chi_{3503}(116,\cdot)$	$1$	$1$	$e\left(\frac{99}{140}\right)$	$e\left(\frac{509}{560}\right)$	$e\left(\frac{29}{70}\right)$	$e\left(\frac{83}{112}\right)$	$e\left(\frac{69}{112}\right)$	$e\left(\frac{19}{70}\right)$	$e\left(\frac{17}{140}\right)$	$e\left(\frac{229}{280}\right)$	$e\left(\frac{251}{560}\right)$	$e\left(\frac{101}{280}\right)$
$\chi_{3503}(147,\cdot)$	$1$	$1$	$e\left(\frac{59}{140}\right)$	$e\left(\frac{29}{560}\right)$	$e\left(\frac{59}{70}\right)$	$e\left(\frac{67}{112}\right)$	$e\left(\frac{53}{112}\right)$	$e\left(\frac{29}{70}\right)$	$e\left(\frac{37}{140}\right)$	$e\left(\frac{29}{280}\right)$	$e\left(\frac{11}{560}\right)$	$e\left(\frac{261}{280}\right)$
$\chi_{3503}(151,\cdot)$	$1$	$1$	$e\left(\frac{41}{140}\right)$	$e\left(\frac{51}{560}\right)$	$e\left(\frac{41}{70}\right)$	$e\left(\frac{29}{112}\right)$	$e\left(\frac{43}{112}\right)$	$e\left(\frac{51}{70}\right)$	$e\left(\frac{123}{140}\right)$	$e\left(\frac{51}{280}\right)$	$e\left(\frac{309}{560}\right)$	$e\left(\frac{179}{280}\right)$
$\chi_{3503}(209,\cdot)$	$1$	$1$	$e\left(\frac{19}{140}\right)$	$e\left(\frac{249}{560}\right)$	$e\left(\frac{19}{70}\right)$	$e\left(\frac{23}{112}\right)$	$e\left(\frac{65}{112}\right)$	$e\left(\frac{39}{70}\right)$	$e\left(\frac{57}{140}\right)$	$e\left(\frac{249}{280}\right)$	$e\left(\frac{191}{560}\right)$	$e\left(\frac{1}{280}\right)$
$\chi_{3503}(232,\cdot)$	$1$	$1$	$e\left(\frac{27}{140}\right)$	$e\left(\frac{457}{560}\right)$	$e\left(\frac{27}{70}\right)$	$e\left(\frac{71}{112}\right)$	$e\left(\frac{1}{112}\right)$	$e\left(\frac{37}{70}\right)$	$e\left(\frac{81}{140}\right)$	$e\left(\frac{177}{280}\right)$	$e\left(\frac{463}{560}\right)$	$e\left(\frac{193}{280}\right)$
$\chi_{3503}(246,\cdot)$	$1$	$1$	$e\left(\frac{93}{140}\right)$	$e\left(\frac{143}{560}\right)$	$e\left(\frac{23}{70}\right)$	$e\left(\frac{33}{112}\right)$	$e\left(\frac{103}{112}\right)$	$e\left(\frac{3}{70}\right)$	$e\left(\frac{139}{140}\right)$	$e\left(\frac{143}{280}\right)$	$e\left(\frac{537}{560}\right)$	$e\left(\frac{167}{280}\right)$
$\chi_{3503}(263,\cdot)$	$1$	$1$	$e\left(\frac{137}{140}\right)$	$e\left(\frac{167}{560}\right)$	$e\left(\frac{67}{70}\right)$	$e\left(\frac{73}{112}\right)$	$e\left(\frac{31}{112}\right)$	$e\left(\frac{27}{70}\right)$	$e\left(\frac{131}{140}\right)$	$e\left(\frac{167}{280}\right)$	$e\left(\frac{353}{560}\right)$	$e\left(\frac{103}{280}\right)$
$\chi_{3503}(271,\cdot)$	$1$	$1$	$e\left(\frac{99}{140}\right)$	$e\left(\frac{369}{560}\right)$	$e\left(\frac{29}{70}\right)$	$e\left(\frac{111}{112}\right)$	$e\left(\frac{41}{112}\right)$	$e\left(\frac{19}{70}\right)$	$e\left(\frac{17}{140}\right)$	$e\left(\frac{89}{280}\right)$	$e\left(\frac{391}{560}\right)$	$e\left(\frac{241}{280}\right)$
$\chi_{3503}(294,\cdot)$	$1$	$1$	$e\left(\frac{127}{140}\right)$	$e\left(\frac{537}{560}\right)$	$e\left(\frac{57}{70}\right)$	$e\left(\frac{55}{112}\right)$	$e\left(\frac{97}{112}\right)$	$e\left(\frac{47}{70}\right)$	$e\left(\frac{101}{140}\right)$	$e\left(\frac{257}{280}\right)$	$e\left(\frac{223}{560}\right)$	$e\left(\frac{73}{280}\right)$
$\chi_{3503}(302,\cdot)$	$1$	$1$	$e\left(\frac{109}{140}\right)$	$e\left(\frac{559}{560}\right)$	$e\left(\frac{39}{70}\right)$	$e\left(\frac{17}{112}\right)$	$e\left(\frac{87}{112}\right)$	$e\left(\frac{69}{70}\right)$	$e\left(\frac{47}{140}\right)$	$e\left(\frac{279}{280}\right)$	$e\left(\frac{521}{560}\right)$	$e\left(\frac{271}{280}\right)$
$\chi_{3503}(306,\cdot)$	$1$	$1$	$e\left(\frac{61}{140}\right)$	$e\left(\frac{151}{560}\right)$	$e\left(\frac{61}{70}\right)$	$e\left(\frac{9}{112}\right)$	$e\left(\frac{79}{112}\right)$	$e\left(\frac{11}{70}\right)$	$e\left(\frac{43}{140}\right)$	$e\left(\frac{151}{280}\right)$	$e\left(\frac{289}{560}\right)$	$e\left(\frac{239}{280}\right)$
$\chi_{3503}(333,\cdot)$	$1$	$1$	$e\left(\frac{139}{140}\right)$	$e\left(\frac{289}{560}\right)$	$e\left(\frac{69}{70}\right)$	$e\left(\frac{15}{112}\right)$	$e\left(\frac{57}{112}\right)$	$e\left(\frac{9}{70}\right)$	$e\left(\frac{137}{140}\right)$	$e\left(\frac{9}{280}\right)$	$e\left(\frac{71}{560}\right)$	$e\left(\frac{81}{280}\right)$
$\chi_{3503}(356,\cdot)$	$1$	$1$	$e\left(\frac{47}{140}\right)$	$e\left(\frac{417}{560}\right)$	$e\left(\frac{47}{70}\right)$	$e\left(\frac{79}{112}\right)$	$e\left(\frac{9}{112}\right)$	$e\left(\frac{67}{70}\right)$	$e\left(\frac{1}{140}\right)$	$e\left(\frac{137}{280}\right)$	$e\left(\frac{23}{560}\right)$	$e\left(\frac{113}{280}\right)$
$\chi_{3503}(368,\cdot)$	$1$	$1$	$e\left(\frac{131}{140}\right)$	$e\left(\frac{501}{560}\right)$	$e\left(\frac{61}{70}\right)$	$e\left(\frac{107}{112}\right)$	$e\left(\frac{93}{112}\right)$	$e\left(\frac{11}{70}\right)$	$e\left(\frac{113}{140}\right)$	$e\left(\frac{221}{280}\right)$	$e\left(\frac{499}{560}\right)$	$e\left(\frac{29}{280}\right)$
$\chi_{3503}(418,\cdot)$	$1$	$1$	$e\left(\frac{87}{140}\right)$	$e\left(\frac{197}{560}\right)$	$e\left(\frac{17}{70}\right)$	$e\left(\frac{11}{112}\right)$	$e\left(\frac{109}{112}\right)$	$e\left(\frac{57}{70}\right)$	$e\left(\frac{121}{140}\right)$	$e\left(\frac{197}{280}\right)$	$e\left(\frac{403}{560}\right)$	$e\left(\frac{93}{280}\right)$
$\chi_{3503}(432,\cdot)$	$1$	$1$	$e\left(\frac{93}{140}\right)$	$e\left(\frac{423}{560}\right)$	$e\left(\frac{23}{70}\right)$	$e\left(\frac{89}{112}\right)$	$e\left(\frac{47}{112}\right)$	$e\left(\frac{3}{70}\right)$	$e\left(\frac{139}{140}\right)$	$e\left(\frac{143}{280}\right)$	$e\left(\frac{257}{560}\right)$	$e\left(\frac{167}{280}\right)$
$\chi_{3503}(449,\cdot)$	$1$	$1$	$e\left(\frac{127}{140}\right)$	$e\left(\frac{117}{560}\right)$	$e\left(\frac{57}{70}\right)$	$e\left(\frac{27}{112}\right)$	$e\left(\frac{13}{112}\right)$	$e\left(\frac{47}{70}\right)$	$e\left(\frac{101}{140}\right)$	$e\left(\frac{117}{280}\right)$	$e\left(\frac{83}{560}\right)$	$e\left(\frac{213}{280}\right)$
$\chi_{3503}(457,\cdot)$	$1$	$1$	$e\left(\frac{69}{140}\right)$	$e\left(\frac{359}{560}\right)$	$e\left(\frac{69}{70}\right)$	$e\left(\frac{57}{112}\right)$	$e\left(\frac{15}{112}\right)$	$e\left(\frac{9}{70}\right)$	$e\left(\frac{67}{140}\right)$	$e\left(\frac{79}{280}\right)$	$e\left(\frac{1}{560}\right)$	$e\left(\frac{151}{280}\right)$
$\chi_{3503}(511,\cdot)$	$1$	$1$	$e\left(\frac{57}{140}\right)$	$e\left(\frac{187}{560}\right)$	$e\left(\frac{57}{70}\right)$	$e\left(\frac{69}{112}\right)$	$e\left(\frac{83}{112}\right)$	$e\left(\frac{47}{70}\right)$	$e\left(\frac{31}{140}\right)$	$e\left(\frac{187}{280}\right)$	$e\left(\frac{13}{560}\right)$	$e\left(\frac{3}{280}\right)$
$\chi_{3503}(519,\cdot)$	$1$	$1$	$e\left(\frac{39}{140}\right)$	$e\left(\frac{489}{560}\right)$	$e\left(\frac{39}{70}\right)$	$e\left(\frac{87}{112}\right)$	$e\left(\frac{17}{112}\right)$	$e\left(\frac{69}{70}\right)$	$e\left(\frac{117}{140}\right)$	$e\left(\frac{209}{280}\right)$	$e\left(\frac{31}{560}\right)$	$e\left(\frac{201}{280}\right)$
$\chi_{3503}(542,\cdot)$	$1$	$1$	$e\left(\frac{27}{140}\right)$	$e\left(\frac{317}{560}\right)$	$e\left(\frac{27}{70}\right)$	$e\left(\frac{99}{112}\right)$	$e\left(\frac{85}{112}\right)$	$e\left(\frac{37}{70}\right)$	$e\left(\frac{81}{140}\right)$	$e\left(\frac{37}{280}\right)$	$e\left(\frac{43}{560}\right)$	$e\left(\frac{53}{280}\right)$
$\chi_{3503}(585,\cdot)$	$1$	$1$	$e\left(\frac{121}{140}\right)$	$e\left(\frac{31}{560}\right)$	$e\left(\frac{51}{70}\right)$	$e\left(\frac{33}{112}\right)$	$e\left(\frac{103}{112}\right)$	$e\left(\frac{31}{70}\right)$	$e\left(\frac{83}{140}\right)$	$e\left(\frac{31}{280}\right)$	$e\left(\frac{89}{560}\right)$	$e\left(\frac{279}{280}\right)$
$\chi_{3503}(604,\cdot)$	$1$	$1$	$e\left(\frac{37}{140}\right)$	$e\left(\frac{507}{560}\right)$	$e\left(\frac{37}{70}\right)$	$e\left(\frac{5}{112}\right)$	$e\left(\frac{19}{112}\right)$	$e\left(\frac{17}{70}\right)$	$e\left(\frac{111}{140}\right)$	$e\left(\frac{227}{280}\right)$	$e\left(\frac{173}{560}\right)$	$e\left(\frac{83}{280}\right)$

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	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\(\chi_{3503}(23,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{139}{140}\right)\)	\(e\left(\frac{149}{560}\right)\)	\(e\left(\frac{69}{70}\right)\)	\(e\left(\frac{43}{112}\right)\)	\(e\left(\frac{29}{112}\right)\)	\(e\left(\frac{9}{70}\right)\)	\(e\left(\frac{137}{140}\right)\)	\(e\left(\frac{149}{280}\right)\)	\(e\left(\frac{211}{560}\right)\)	\(e\left(\frac{221}{280}\right)\)
\(\chi_{3503}(27,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{101}{140}\right)\)	\(e\left(\frac{71}{560}\right)\)	\(e\left(\frac{31}{70}\right)\)	\(e\left(\frac{25}{112}\right)\)	\(e\left(\frac{95}{112}\right)\)	\(e\left(\frac{1}{70}\right)\)	\(e\left(\frac{23}{140}\right)\)	\(e\left(\frac{71}{280}\right)\)	\(e\left(\frac{529}{560}\right)\)	\(e\left(\frac{79}{280}\right)\)
\(\chi_{3503}(29,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{103}{140}\right)\)	\(e\left(\frac{53}{560}\right)\)	\(e\left(\frac{33}{70}\right)\)	\(e\left(\frac{107}{112}\right)\)	\(e\left(\frac{93}{112}\right)\)	\(e\left(\frac{53}{70}\right)\)	\(e\left(\frac{29}{140}\right)\)	\(e\left(\frac{53}{280}\right)\)	\(e\left(\frac{387}{560}\right)\)	\(e\left(\frac{197}{280}\right)\)
\(\chi_{3503}(46,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{67}{140}\right)\)	\(e\left(\frac{97}{560}\right)\)	\(e\left(\frac{67}{70}\right)\)	\(e\left(\frac{31}{112}\right)\)	\(e\left(\frac{73}{112}\right)\)	\(e\left(\frac{27}{70}\right)\)	\(e\left(\frac{61}{140}\right)\)	\(e\left(\frac{97}{280}\right)\)	\(e\left(\frac{423}{560}\right)\)	\(e\left(\frac{33}{280}\right)\)
\(\chi_{3503}(54,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{140}\right)\)	\(e\left(\frac{19}{560}\right)\)	\(e\left(\frac{29}{70}\right)\)	\(e\left(\frac{13}{112}\right)\)	\(e\left(\frac{27}{112}\right)\)	\(e\left(\frac{19}{70}\right)\)	\(e\left(\frac{87}{140}\right)\)	\(e\left(\frac{19}{280}\right)\)	\(e\left(\frac{181}{560}\right)\)	\(e\left(\frac{171}{280}\right)\)
\(\chi_{3503}(58,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{140}\right)\)	\(e\left(\frac{1}{560}\right)\)	\(e\left(\frac{31}{70}\right)\)	\(e\left(\frac{95}{112}\right)\)	\(e\left(\frac{25}{112}\right)\)	\(e\left(\frac{1}{70}\right)\)	\(e\left(\frac{93}{140}\right)\)	\(e\left(\frac{1}{280}\right)\)	\(e\left(\frac{39}{560}\right)\)	\(e\left(\frac{9}{280}\right)\)
\(\chi_{3503}(89,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{51}{140}\right)\)	\(e\left(\frac{521}{560}\right)\)	\(e\left(\frac{51}{70}\right)\)	\(e\left(\frac{103}{112}\right)\)	\(e\left(\frac{33}{112}\right)\)	\(e\left(\frac{31}{70}\right)\)	\(e\left(\frac{13}{140}\right)\)	\(e\left(\frac{241}{280}\right)\)	\(e\left(\frac{159}{560}\right)\)	\(e\left(\frac{209}{280}\right)\)
\(\chi_{3503}(108,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{97}{140}\right)\)	\(e\left(\frac{527}{560}\right)\)	\(e\left(\frac{27}{70}\right)\)	\(e\left(\frac{1}{112}\right)\)	\(e\left(\frac{71}{112}\right)\)	\(e\left(\frac{37}{70}\right)\)	\(e\left(\frac{11}{140}\right)\)	\(e\left(\frac{247}{280}\right)\)	\(e\left(\frac{393}{560}\right)\)	\(e\left(\frac{263}{280}\right)\)
\(\chi_{3503}(116,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{99}{140}\right)\)	\(e\left(\frac{509}{560}\right)\)	\(e\left(\frac{29}{70}\right)\)	\(e\left(\frac{83}{112}\right)\)	\(e\left(\frac{69}{112}\right)\)	\(e\left(\frac{19}{70}\right)\)	\(e\left(\frac{17}{140}\right)\)	\(e\left(\frac{229}{280}\right)\)	\(e\left(\frac{251}{560}\right)\)	\(e\left(\frac{101}{280}\right)\)
\(\chi_{3503}(147,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{140}\right)\)	\(e\left(\frac{29}{560}\right)\)	\(e\left(\frac{59}{70}\right)\)	\(e\left(\frac{67}{112}\right)\)	\(e\left(\frac{53}{112}\right)\)	\(e\left(\frac{29}{70}\right)\)	\(e\left(\frac{37}{140}\right)\)	\(e\left(\frac{29}{280}\right)\)	\(e\left(\frac{11}{560}\right)\)	\(e\left(\frac{261}{280}\right)\)
\(\chi_{3503}(151,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{140}\right)\)	\(e\left(\frac{51}{560}\right)\)	\(e\left(\frac{41}{70}\right)\)	\(e\left(\frac{29}{112}\right)\)	\(e\left(\frac{43}{112}\right)\)	\(e\left(\frac{51}{70}\right)\)	\(e\left(\frac{123}{140}\right)\)	\(e\left(\frac{51}{280}\right)\)	\(e\left(\frac{309}{560}\right)\)	\(e\left(\frac{179}{280}\right)\)
\(\chi_{3503}(209,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{140}\right)\)	\(e\left(\frac{249}{560}\right)\)	\(e\left(\frac{19}{70}\right)\)	\(e\left(\frac{23}{112}\right)\)	\(e\left(\frac{65}{112}\right)\)	\(e\left(\frac{39}{70}\right)\)	\(e\left(\frac{57}{140}\right)\)	\(e\left(\frac{249}{280}\right)\)	\(e\left(\frac{191}{560}\right)\)	\(e\left(\frac{1}{280}\right)\)
\(\chi_{3503}(232,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{27}{140}\right)\)	\(e\left(\frac{457}{560}\right)\)	\(e\left(\frac{27}{70}\right)\)	\(e\left(\frac{71}{112}\right)\)	\(e\left(\frac{1}{112}\right)\)	\(e\left(\frac{37}{70}\right)\)	\(e\left(\frac{81}{140}\right)\)	\(e\left(\frac{177}{280}\right)\)	\(e\left(\frac{463}{560}\right)\)	\(e\left(\frac{193}{280}\right)\)
\(\chi_{3503}(246,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{93}{140}\right)\)	\(e\left(\frac{143}{560}\right)\)	\(e\left(\frac{23}{70}\right)\)	\(e\left(\frac{33}{112}\right)\)	\(e\left(\frac{103}{112}\right)\)	\(e\left(\frac{3}{70}\right)\)	\(e\left(\frac{139}{140}\right)\)	\(e\left(\frac{143}{280}\right)\)	\(e\left(\frac{537}{560}\right)\)	\(e\left(\frac{167}{280}\right)\)
\(\chi_{3503}(263,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{137}{140}\right)\)	\(e\left(\frac{167}{560}\right)\)	\(e\left(\frac{67}{70}\right)\)	\(e\left(\frac{73}{112}\right)\)	\(e\left(\frac{31}{112}\right)\)	\(e\left(\frac{27}{70}\right)\)	\(e\left(\frac{131}{140}\right)\)	\(e\left(\frac{167}{280}\right)\)	\(e\left(\frac{353}{560}\right)\)	\(e\left(\frac{103}{280}\right)\)
\(\chi_{3503}(271,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{99}{140}\right)\)	\(e\left(\frac{369}{560}\right)\)	\(e\left(\frac{29}{70}\right)\)	\(e\left(\frac{111}{112}\right)\)	\(e\left(\frac{41}{112}\right)\)	\(e\left(\frac{19}{70}\right)\)	\(e\left(\frac{17}{140}\right)\)	\(e\left(\frac{89}{280}\right)\)	\(e\left(\frac{391}{560}\right)\)	\(e\left(\frac{241}{280}\right)\)
\(\chi_{3503}(294,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{127}{140}\right)\)	\(e\left(\frac{537}{560}\right)\)	\(e\left(\frac{57}{70}\right)\)	\(e\left(\frac{55}{112}\right)\)	\(e\left(\frac{97}{112}\right)\)	\(e\left(\frac{47}{70}\right)\)	\(e\left(\frac{101}{140}\right)\)	\(e\left(\frac{257}{280}\right)\)	\(e\left(\frac{223}{560}\right)\)	\(e\left(\frac{73}{280}\right)\)
\(\chi_{3503}(302,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{109}{140}\right)\)	\(e\left(\frac{559}{560}\right)\)	\(e\left(\frac{39}{70}\right)\)	\(e\left(\frac{17}{112}\right)\)	\(e\left(\frac{87}{112}\right)\)	\(e\left(\frac{69}{70}\right)\)	\(e\left(\frac{47}{140}\right)\)	\(e\left(\frac{279}{280}\right)\)	\(e\left(\frac{521}{560}\right)\)	\(e\left(\frac{271}{280}\right)\)
\(\chi_{3503}(306,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{61}{140}\right)\)	\(e\left(\frac{151}{560}\right)\)	\(e\left(\frac{61}{70}\right)\)	\(e\left(\frac{9}{112}\right)\)	\(e\left(\frac{79}{112}\right)\)	\(e\left(\frac{11}{70}\right)\)	\(e\left(\frac{43}{140}\right)\)	\(e\left(\frac{151}{280}\right)\)	\(e\left(\frac{289}{560}\right)\)	\(e\left(\frac{239}{280}\right)\)
\(\chi_{3503}(333,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{139}{140}\right)\)	\(e\left(\frac{289}{560}\right)\)	\(e\left(\frac{69}{70}\right)\)	\(e\left(\frac{15}{112}\right)\)	\(e\left(\frac{57}{112}\right)\)	\(e\left(\frac{9}{70}\right)\)	\(e\left(\frac{137}{140}\right)\)	\(e\left(\frac{9}{280}\right)\)	\(e\left(\frac{71}{560}\right)\)	\(e\left(\frac{81}{280}\right)\)
\(\chi_{3503}(356,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{140}\right)\)	\(e\left(\frac{417}{560}\right)\)	\(e\left(\frac{47}{70}\right)\)	\(e\left(\frac{79}{112}\right)\)	\(e\left(\frac{9}{112}\right)\)	\(e\left(\frac{67}{70}\right)\)	\(e\left(\frac{1}{140}\right)\)	\(e\left(\frac{137}{280}\right)\)	\(e\left(\frac{23}{560}\right)\)	\(e\left(\frac{113}{280}\right)\)
\(\chi_{3503}(368,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{131}{140}\right)\)	\(e\left(\frac{501}{560}\right)\)	\(e\left(\frac{61}{70}\right)\)	\(e\left(\frac{107}{112}\right)\)	\(e\left(\frac{93}{112}\right)\)	\(e\left(\frac{11}{70}\right)\)	\(e\left(\frac{113}{140}\right)\)	\(e\left(\frac{221}{280}\right)\)	\(e\left(\frac{499}{560}\right)\)	\(e\left(\frac{29}{280}\right)\)
\(\chi_{3503}(418,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{87}{140}\right)\)	\(e\left(\frac{197}{560}\right)\)	\(e\left(\frac{17}{70}\right)\)	\(e\left(\frac{11}{112}\right)\)	\(e\left(\frac{109}{112}\right)\)	\(e\left(\frac{57}{70}\right)\)	\(e\left(\frac{121}{140}\right)\)	\(e\left(\frac{197}{280}\right)\)	\(e\left(\frac{403}{560}\right)\)	\(e\left(\frac{93}{280}\right)\)
\(\chi_{3503}(432,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{93}{140}\right)\)	\(e\left(\frac{423}{560}\right)\)	\(e\left(\frac{23}{70}\right)\)	\(e\left(\frac{89}{112}\right)\)	\(e\left(\frac{47}{112}\right)\)	\(e\left(\frac{3}{70}\right)\)	\(e\left(\frac{139}{140}\right)\)	\(e\left(\frac{143}{280}\right)\)	\(e\left(\frac{257}{560}\right)\)	\(e\left(\frac{167}{280}\right)\)
\(\chi_{3503}(449,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{127}{140}\right)\)	\(e\left(\frac{117}{560}\right)\)	\(e\left(\frac{57}{70}\right)\)	\(e\left(\frac{27}{112}\right)\)	\(e\left(\frac{13}{112}\right)\)	\(e\left(\frac{47}{70}\right)\)	\(e\left(\frac{101}{140}\right)\)	\(e\left(\frac{117}{280}\right)\)	\(e\left(\frac{83}{560}\right)\)	\(e\left(\frac{213}{280}\right)\)
\(\chi_{3503}(457,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{69}{140}\right)\)	\(e\left(\frac{359}{560}\right)\)	\(e\left(\frac{69}{70}\right)\)	\(e\left(\frac{57}{112}\right)\)	\(e\left(\frac{15}{112}\right)\)	\(e\left(\frac{9}{70}\right)\)	\(e\left(\frac{67}{140}\right)\)	\(e\left(\frac{79}{280}\right)\)	\(e\left(\frac{1}{560}\right)\)	\(e\left(\frac{151}{280}\right)\)
\(\chi_{3503}(511,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{57}{140}\right)\)	\(e\left(\frac{187}{560}\right)\)	\(e\left(\frac{57}{70}\right)\)	\(e\left(\frac{69}{112}\right)\)	\(e\left(\frac{83}{112}\right)\)	\(e\left(\frac{47}{70}\right)\)	\(e\left(\frac{31}{140}\right)\)	\(e\left(\frac{187}{280}\right)\)	\(e\left(\frac{13}{560}\right)\)	\(e\left(\frac{3}{280}\right)\)
\(\chi_{3503}(519,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{39}{140}\right)\)	\(e\left(\frac{489}{560}\right)\)	\(e\left(\frac{39}{70}\right)\)	\(e\left(\frac{87}{112}\right)\)	\(e\left(\frac{17}{112}\right)\)	\(e\left(\frac{69}{70}\right)\)	\(e\left(\frac{117}{140}\right)\)	\(e\left(\frac{209}{280}\right)\)	\(e\left(\frac{31}{560}\right)\)	\(e\left(\frac{201}{280}\right)\)
\(\chi_{3503}(542,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{27}{140}\right)\)	\(e\left(\frac{317}{560}\right)\)	\(e\left(\frac{27}{70}\right)\)	\(e\left(\frac{99}{112}\right)\)	\(e\left(\frac{85}{112}\right)\)	\(e\left(\frac{37}{70}\right)\)	\(e\left(\frac{81}{140}\right)\)	\(e\left(\frac{37}{280}\right)\)	\(e\left(\frac{43}{560}\right)\)	\(e\left(\frac{53}{280}\right)\)
\(\chi_{3503}(585,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{121}{140}\right)\)	\(e\left(\frac{31}{560}\right)\)	\(e\left(\frac{51}{70}\right)\)	\(e\left(\frac{33}{112}\right)\)	\(e\left(\frac{103}{112}\right)\)	\(e\left(\frac{31}{70}\right)\)	\(e\left(\frac{83}{140}\right)\)	\(e\left(\frac{31}{280}\right)\)	\(e\left(\frac{89}{560}\right)\)	\(e\left(\frac{279}{280}\right)\)
\(\chi_{3503}(604,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{140}\right)\)	\(e\left(\frac{507}{560}\right)\)	\(e\left(\frac{37}{70}\right)\)	\(e\left(\frac{5}{112}\right)\)	\(e\left(\frac{19}{112}\right)\)	\(e\left(\frac{17}{70}\right)\)	\(e\left(\frac{111}{140}\right)\)	\(e\left(\frac{227}{280}\right)\)	\(e\left(\frac{173}{560}\right)\)	\(e\left(\frac{83}{280}\right)\)

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First 31 of 192 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.cx
Modulus	$3503$
Conductor	$3503$
Order	$560$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(3503\)
Conductor:	\(3503\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(560\)	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)