LMFDB - Dirichlet character orbit 31433.cl

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(31433, base_ring=CyclotomicField(1204)) M = H._module chi = DirichletCharacter(H, M([903,848])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(4,31433)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$31433$
Conductor:	$31433$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$1204$	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:	$\Q(\zeta_{1204})$
Fixed field:	Number field defined by a degree 1204 polynomial (not computed)

First 28 of 504 characters in Galois orbit

Character	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{31433}(4,\cdot)$	$1$	$1$	$e\left(\frac{269}{602}\right)$	$e\left(\frac{547}{1204}\right)$	$e\left(\frac{269}{301}\right)$	$e\left(\frac{823}{1204}\right)$	$e\left(\frac{155}{172}\right)$	$e\left(\frac{139}{172}\right)$	$e\left(\frac{205}{602}\right)$	$e\left(\frac{547}{602}\right)$	$e\left(\frac{157}{1204}\right)$	$e\left(\frac{177}{1204}\right)$
$\chi_{31433}(21,\cdot)$	$1$	$1$	$e\left(\frac{79}{602}\right)$	$e\left(\frac{1067}{1204}\right)$	$e\left(\frac{79}{301}\right)$	$e\left(\frac{47}{1204}\right)$	$e\left(\frac{3}{172}\right)$	$e\left(\frac{107}{172}\right)$	$e\left(\frac{237}{602}\right)$	$e\left(\frac{465}{602}\right)$	$e\left(\frac{205}{1204}\right)$	$e\left(\frac{1021}{1204}\right)$
$\chi_{31433}(47,\cdot)$	$1$	$1$	$e\left(\frac{479}{602}\right)$	$e\left(\frac{701}{1204}\right)$	$e\left(\frac{178}{301}\right)$	$e\left(\frac{445}{1204}\right)$	$e\left(\frac{65}{172}\right)$	$e\left(\frac{25}{172}\right)$	$e\left(\frac{233}{602}\right)$	$e\left(\frac{99}{602}\right)$	$e\left(\frac{199}{1204}\right)$	$e\left(\frac{163}{1204}\right)$
$\chi_{31433}(64,\cdot)$	$1$	$1$	$e\left(\frac{205}{602}\right)$	$e\left(\frac{437}{1204}\right)$	$e\left(\frac{205}{301}\right)$	$e\left(\frac{61}{1204}\right)$	$e\left(\frac{121}{172}\right)$	$e\left(\frac{73}{172}\right)$	$e\left(\frac{13}{602}\right)$	$e\left(\frac{437}{602}\right)$	$e\left(\frac{471}{1204}\right)$	$e\left(\frac{531}{1204}\right)$
$\chi_{31433}(140,\cdot)$	$1$	$1$	$e\left(\frac{417}{602}\right)$	$e\left(\frac{839}{1204}\right)$	$e\left(\frac{116}{301}\right)$	$e\left(\frac{591}{1204}\right)$	$e\left(\frac{67}{172}\right)$	$e\left(\frac{39}{172}\right)$	$e\left(\frac{47}{602}\right)$	$e\left(\frac{237}{602}\right)$	$e\left(\frac{221}{1204}\right)$	$e\left(\frac{901}{1204}\right)$
$\chi_{31433}(183,\cdot)$	$1$	$1$	$e\left(\frac{165}{602}\right)$	$e\left(\frac{293}{1204}\right)$	$e\left(\frac{165}{301}\right)$	$e\left(\frac{1165}{1204}\right)$	$e\left(\frac{89}{172}\right)$	$e\left(\frac{21}{172}\right)$	$e\left(\frac{495}{602}\right)$	$e\left(\frac{293}{602}\right)$	$e\left(\frac{291}{1204}\right)$	$e\left(\frac{75}{1204}\right)$
$\chi_{31433}(293,\cdot)$	$1$	$1$	$e\left(\frac{421}{602}\right)$	$e\left(\frac{131}{1204}\right)$	$e\left(\frac{120}{301}\right)$	$e\left(\frac{1203}{1204}\right)$	$e\left(\frac{139}{172}\right)$	$e\left(\frac{27}{172}\right)$	$e\left(\frac{59}{602}\right)$	$e\left(\frac{131}{602}\right)$	$e\left(\frac{841}{1204}\right)$	$e\left(\frac{465}{1204}\right)$
$\chi_{31433}(336,\cdot)$	$1$	$1$	$e\left(\frac{15}{602}\right)$	$e\left(\frac{957}{1204}\right)$	$e\left(\frac{15}{301}\right)$	$e\left(\frac{489}{1204}\right)$	$e\left(\frac{141}{172}\right)$	$e\left(\frac{41}{172}\right)$	$e\left(\frac{45}{602}\right)$	$e\left(\frac{355}{602}\right)$	$e\left(\frac{519}{1204}\right)$	$e\left(\frac{171}{1204}\right)$
$\chi_{31433}(446,\cdot)$	$1$	$1$	$e\left(\frac{461}{602}\right)$	$e\left(\frac{275}{1204}\right)$	$e\left(\frac{160}{301}\right)$	$e\left(\frac{99}{1204}\right)$	$e\left(\frac{171}{172}\right)$	$e\left(\frac{79}{172}\right)$	$e\left(\frac{179}{602}\right)$	$e\left(\frac{275}{602}\right)$	$e\left(\frac{1021}{1204}\right)$	$e\left(\frac{921}{1204}\right)$
$\chi_{31433}(489,\cdot)$	$1$	$1$	$e\left(\frac{363}{602}\right)$	$e\left(\frac{765}{1204}\right)$	$e\left(\frac{62}{301}\right)$	$e\left(\frac{757}{1204}\right)$	$e\left(\frac{41}{172}\right)$	$e\left(\frac{29}{172}\right)$	$e\left(\frac{487}{602}\right)$	$e\left(\frac{163}{602}\right)$	$e\left(\frac{279}{1204}\right)$	$e\left(\frac{767}{1204}\right)$
$\chi_{31433}(514,\cdot)$	$1$	$1$	$e\left(\frac{61}{602}\right)$	$e\left(\frac{39}{1204}\right)$	$e\left(\frac{61}{301}\right)$	$e\left(\frac{303}{1204}\right)$	$e\left(\frac{23}{172}\right)$	$e\left(\frac{75}{172}\right)$	$e\left(\frac{183}{602}\right)$	$e\left(\frac{39}{602}\right)$	$e\left(\frac{425}{1204}\right)$	$e\left(\frac{1177}{1204}\right)$
$\chi_{31433}(557,\cdot)$	$1$	$1$	$e\left(\frac{243}{602}\right)$	$e\left(\frac{333}{1204}\right)$	$e\left(\frac{243}{301}\right)$	$e\left(\frac{457}{1204}\right)$	$e\left(\frac{117}{172}\right)$	$e\left(\frac{45}{172}\right)$	$e\left(\frac{127}{602}\right)$	$e\left(\frac{333}{602}\right)$	$e\left(\frac{943}{1204}\right)$	$e\left(\frac{603}{1204}\right)$
$\chi_{31433}(735,\cdot)$	$1$	$1$	$e\left(\frac{227}{602}\right)$	$e\left(\frac{155}{1204}\right)$	$e\left(\frac{227}{301}\right)$	$e\left(\frac{1019}{1204}\right)$	$e\left(\frac{87}{172}\right)$	$e\left(\frac{7}{172}\right)$	$e\left(\frac{79}{602}\right)$	$e\left(\frac{155}{602}\right)$	$e\left(\frac{269}{1204}\right)$	$e\left(\frac{541}{1204}\right)$
$\chi_{31433}(752,\cdot)$	$1$	$1$	$e\left(\frac{415}{602}\right)$	$e\left(\frac{591}{1204}\right)$	$e\left(\frac{114}{301}\right)$	$e\left(\frac{887}{1204}\right)$	$e\left(\frac{31}{172}\right)$	$e\left(\frac{131}{172}\right)$	$e\left(\frac{41}{602}\right)$	$e\left(\frac{591}{602}\right)$	$e\left(\frac{513}{1204}\right)$	$e\left(\frac{517}{1204}\right)$
$\chi_{31433}(778,\cdot)$	$1$	$1$	$e\left(\frac{437}{602}\right)$	$e\left(\frac{309}{1204}\right)$	$e\left(\frac{136}{301}\right)$	$e\left(\frac{641}{1204}\right)$	$e\left(\frac{169}{172}\right)$	$e\left(\frac{65}{172}\right)$	$e\left(\frac{107}{602}\right)$	$e\left(\frac{309}{602}\right)$	$e\left(\frac{311}{1204}\right)$	$e\left(\frac{527}{1204}\right)$
$\chi_{31433}(795,\cdot)$	$1$	$1$	$e\left(\frac{541}{602}\right)$	$e\left(\frac{1165}{1204}\right)$	$e\left(\frac{240}{301}\right)$	$e\left(\frac{901}{1204}\right)$	$e\left(\frac{149}{172}\right)$	$e\left(\frac{97}{172}\right)$	$e\left(\frac{419}{602}\right)$	$e\left(\frac{563}{602}\right)$	$e\left(\frac{779}{1204}\right)$	$e\left(\frac{27}{1204}\right)$
$\chi_{31433}(871,\cdot)$	$1$	$1$	$e\left(\frac{347}{602}\right)$	$e\left(\frac{587}{1204}\right)$	$e\left(\frac{46}{301}\right)$	$e\left(\frac{115}{1204}\right)$	$e\left(\frac{11}{172}\right)$	$e\left(\frac{163}{172}\right)$	$e\left(\frac{439}{602}\right)$	$e\left(\frac{587}{602}\right)$	$e\left(\frac{809}{1204}\right)$	$e\left(\frac{705}{1204}\right)$
$\chi_{31433}(914,\cdot)$	$1$	$1$	$e\left(\frac{95}{602}\right)$	$e\left(\frac{41}{1204}\right)$	$e\left(\frac{95}{301}\right)$	$e\left(\frac{689}{1204}\right)$	$e\left(\frac{33}{172}\right)$	$e\left(\frac{145}{172}\right)$	$e\left(\frac{285}{602}\right)$	$e\left(\frac{41}{602}\right)$	$e\left(\frac{879}{1204}\right)$	$e\left(\frac{1083}{1204}\right)$
$\chi_{31433}(1024,\cdot)$	$1$	$1$	$e\left(\frac{141}{602}\right)$	$e\left(\frac{327}{1204}\right)$	$e\left(\frac{141}{301}\right)$	$e\left(\frac{503}{1204}\right)$	$e\left(\frac{87}{172}\right)$	$e\left(\frac{7}{172}\right)$	$e\left(\frac{423}{602}\right)$	$e\left(\frac{327}{602}\right)$	$e\left(\frac{785}{1204}\right)$	$e\left(\frac{885}{1204}\right)$
$\chi_{31433}(1067,\cdot)$	$1$	$1$	$e\left(\frac{337}{602}\right)$	$e\left(\frac{1153}{1204}\right)$	$e\left(\frac{36}{301}\right)$	$e\left(\frac{993}{1204}\right)$	$e\left(\frac{89}{172}\right)$	$e\left(\frac{21}{172}\right)$	$e\left(\frac{409}{602}\right)$	$e\left(\frac{551}{602}\right)$	$e\left(\frac{463}{1204}\right)$	$e\left(\frac{591}{1204}\right)$
$\chi_{31433}(1177,\cdot)$	$1$	$1$	$e\left(\frac{601}{602}\right)$	$e\left(\frac{779}{1204}\right)$	$e\left(\frac{300}{301}\right)$	$e\left(\frac{1051}{1204}\right)$	$e\left(\frac{111}{172}\right)$	$e\left(\frac{3}{172}\right)$	$e\left(\frac{599}{602}\right)$	$e\left(\frac{177}{602}\right)$	$e\left(\frac{1049}{1204}\right)$	$e\left(\frac{109}{1204}\right)$
$\chi_{31433}(1220,\cdot)$	$1$	$1$	$e\left(\frac{503}{602}\right)$	$e\left(\frac{65}{1204}\right)$	$e\left(\frac{202}{301}\right)$	$e\left(\frac{505}{1204}\right)$	$e\left(\frac{153}{172}\right)$	$e\left(\frac{125}{172}\right)$	$e\left(\frac{305}{602}\right)$	$e\left(\frac{65}{602}\right)$	$e\left(\frac{307}{1204}\right)$	$e\left(\frac{1159}{1204}\right)$
$\chi_{31433}(1245,\cdot)$	$1$	$1$	$e\left(\frac{145}{602}\right)$	$e\left(\frac{823}{1204}\right)$	$e\left(\frac{145}{301}\right)$	$e\left(\frac{1115}{1204}\right)$	$e\left(\frac{159}{172}\right)$	$e\left(\frac{167}{172}\right)$	$e\left(\frac{435}{602}\right)$	$e\left(\frac{221}{602}\right)$	$e\left(\frac{201}{1204}\right)$	$e\left(\frac{449}{1204}\right)$
$\chi_{31433}(1288,\cdot)$	$1$	$1$	$e\left(\frac{327}{602}\right)$	$e\left(\frac{1117}{1204}\right)$	$e\left(\frac{26}{301}\right)$	$e\left(\frac{65}{1204}\right)$	$e\left(\frac{81}{172}\right)$	$e\left(\frac{137}{172}\right)$	$e\left(\frac{379}{602}\right)$	$e\left(\frac{515}{602}\right)$	$e\left(\frac{719}{1204}\right)$	$e\left(\frac{1079}{1204}\right)$
$\chi_{31433}(1466,\cdot)$	$1$	$1$	$e\left(\frac{185}{602}\right)$	$e\left(\frac{967}{1204}\right)$	$e\left(\frac{185}{301}\right)$	$e\left(\frac{11}{1204}\right)$	$e\left(\frac{19}{172}\right)$	$e\left(\frac{47}{172}\right)$	$e\left(\frac{555}{602}\right)$	$e\left(\frac{365}{602}\right)$	$e\left(\frac{381}{1204}\right)$	$e\left(\frac{905}{1204}\right)$
$\chi_{31433}(1483,\cdot)$	$1$	$1$	$e\left(\frac{149}{602}\right)$	$e\left(\frac{115}{1204}\right)$	$e\left(\frac{149}{301}\right)$	$e\left(\frac{523}{1204}\right)$	$e\left(\frac{59}{172}\right)$	$e\left(\frac{155}{172}\right)$	$e\left(\frac{447}{602}\right)$	$e\left(\frac{115}{602}\right)$	$e\left(\frac{821}{1204}\right)$	$e\left(\frac{13}{1204}\right)$
$\chi_{31433}(1509,\cdot)$	$1$	$1$	$e\left(\frac{395}{602}\right)$	$e\left(\frac{1121}{1204}\right)$	$e\left(\frac{94}{301}\right)$	$e\left(\frac{837}{1204}\right)$	$e\left(\frac{101}{172}\right)$	$e\left(\frac{105}{172}\right)$	$e\left(\frac{583}{602}\right)$	$e\left(\frac{519}{602}\right)$	$e\left(\frac{423}{1204}\right)$	$e\left(\frac{891}{1204}\right)$
$\chi_{31433}(1526,\cdot)$	$1$	$1$	$e\left(\frac{275}{602}\right)$	$e\left(\frac{689}{1204}\right)$	$e\left(\frac{275}{301}\right)$	$e\left(\frac{537}{1204}\right)$	$e\left(\frac{5}{172}\right)$	$e\left(\frac{121}{172}\right)$	$e\left(\frac{223}{602}\right)$	$e\left(\frac{87}{602}\right)$	$e\left(\frac{1087}{1204}\right)$	$e\left(\frac{727}{1204}\right)$

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	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\(\chi_{31433}(4,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{269}{602}\right)\)	\(e\left(\frac{547}{1204}\right)\)	\(e\left(\frac{269}{301}\right)\)	\(e\left(\frac{823}{1204}\right)\)	\(e\left(\frac{155}{172}\right)\)	\(e\left(\frac{139}{172}\right)\)	\(e\left(\frac{205}{602}\right)\)	\(e\left(\frac{547}{602}\right)\)	\(e\left(\frac{157}{1204}\right)\)	\(e\left(\frac{177}{1204}\right)\)
\(\chi_{31433}(21,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{79}{602}\right)\)	\(e\left(\frac{1067}{1204}\right)\)	\(e\left(\frac{79}{301}\right)\)	\(e\left(\frac{47}{1204}\right)\)	\(e\left(\frac{3}{172}\right)\)	\(e\left(\frac{107}{172}\right)\)	\(e\left(\frac{237}{602}\right)\)	\(e\left(\frac{465}{602}\right)\)	\(e\left(\frac{205}{1204}\right)\)	\(e\left(\frac{1021}{1204}\right)\)
\(\chi_{31433}(47,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{479}{602}\right)\)	\(e\left(\frac{701}{1204}\right)\)	\(e\left(\frac{178}{301}\right)\)	\(e\left(\frac{445}{1204}\right)\)	\(e\left(\frac{65}{172}\right)\)	\(e\left(\frac{25}{172}\right)\)	\(e\left(\frac{233}{602}\right)\)	\(e\left(\frac{99}{602}\right)\)	\(e\left(\frac{199}{1204}\right)\)	\(e\left(\frac{163}{1204}\right)\)
\(\chi_{31433}(64,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{205}{602}\right)\)	\(e\left(\frac{437}{1204}\right)\)	\(e\left(\frac{205}{301}\right)\)	\(e\left(\frac{61}{1204}\right)\)	\(e\left(\frac{121}{172}\right)\)	\(e\left(\frac{73}{172}\right)\)	\(e\left(\frac{13}{602}\right)\)	\(e\left(\frac{437}{602}\right)\)	\(e\left(\frac{471}{1204}\right)\)	\(e\left(\frac{531}{1204}\right)\)
\(\chi_{31433}(140,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{417}{602}\right)\)	\(e\left(\frac{839}{1204}\right)\)	\(e\left(\frac{116}{301}\right)\)	\(e\left(\frac{591}{1204}\right)\)	\(e\left(\frac{67}{172}\right)\)	\(e\left(\frac{39}{172}\right)\)	\(e\left(\frac{47}{602}\right)\)	\(e\left(\frac{237}{602}\right)\)	\(e\left(\frac{221}{1204}\right)\)	\(e\left(\frac{901}{1204}\right)\)
\(\chi_{31433}(183,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{165}{602}\right)\)	\(e\left(\frac{293}{1204}\right)\)	\(e\left(\frac{165}{301}\right)\)	\(e\left(\frac{1165}{1204}\right)\)	\(e\left(\frac{89}{172}\right)\)	\(e\left(\frac{21}{172}\right)\)	\(e\left(\frac{495}{602}\right)\)	\(e\left(\frac{293}{602}\right)\)	\(e\left(\frac{291}{1204}\right)\)	\(e\left(\frac{75}{1204}\right)\)
\(\chi_{31433}(293,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{421}{602}\right)\)	\(e\left(\frac{131}{1204}\right)\)	\(e\left(\frac{120}{301}\right)\)	\(e\left(\frac{1203}{1204}\right)\)	\(e\left(\frac{139}{172}\right)\)	\(e\left(\frac{27}{172}\right)\)	\(e\left(\frac{59}{602}\right)\)	\(e\left(\frac{131}{602}\right)\)	\(e\left(\frac{841}{1204}\right)\)	\(e\left(\frac{465}{1204}\right)\)
\(\chi_{31433}(336,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{15}{602}\right)\)	\(e\left(\frac{957}{1204}\right)\)	\(e\left(\frac{15}{301}\right)\)	\(e\left(\frac{489}{1204}\right)\)	\(e\left(\frac{141}{172}\right)\)	\(e\left(\frac{41}{172}\right)\)	\(e\left(\frac{45}{602}\right)\)	\(e\left(\frac{355}{602}\right)\)	\(e\left(\frac{519}{1204}\right)\)	\(e\left(\frac{171}{1204}\right)\)
\(\chi_{31433}(446,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{461}{602}\right)\)	\(e\left(\frac{275}{1204}\right)\)	\(e\left(\frac{160}{301}\right)\)	\(e\left(\frac{99}{1204}\right)\)	\(e\left(\frac{171}{172}\right)\)	\(e\left(\frac{79}{172}\right)\)	\(e\left(\frac{179}{602}\right)\)	\(e\left(\frac{275}{602}\right)\)	\(e\left(\frac{1021}{1204}\right)\)	\(e\left(\frac{921}{1204}\right)\)
\(\chi_{31433}(489,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{363}{602}\right)\)	\(e\left(\frac{765}{1204}\right)\)	\(e\left(\frac{62}{301}\right)\)	\(e\left(\frac{757}{1204}\right)\)	\(e\left(\frac{41}{172}\right)\)	\(e\left(\frac{29}{172}\right)\)	\(e\left(\frac{487}{602}\right)\)	\(e\left(\frac{163}{602}\right)\)	\(e\left(\frac{279}{1204}\right)\)	\(e\left(\frac{767}{1204}\right)\)
\(\chi_{31433}(514,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{61}{602}\right)\)	\(e\left(\frac{39}{1204}\right)\)	\(e\left(\frac{61}{301}\right)\)	\(e\left(\frac{303}{1204}\right)\)	\(e\left(\frac{23}{172}\right)\)	\(e\left(\frac{75}{172}\right)\)	\(e\left(\frac{183}{602}\right)\)	\(e\left(\frac{39}{602}\right)\)	\(e\left(\frac{425}{1204}\right)\)	\(e\left(\frac{1177}{1204}\right)\)
\(\chi_{31433}(557,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{243}{602}\right)\)	\(e\left(\frac{333}{1204}\right)\)	\(e\left(\frac{243}{301}\right)\)	\(e\left(\frac{457}{1204}\right)\)	\(e\left(\frac{117}{172}\right)\)	\(e\left(\frac{45}{172}\right)\)	\(e\left(\frac{127}{602}\right)\)	\(e\left(\frac{333}{602}\right)\)	\(e\left(\frac{943}{1204}\right)\)	\(e\left(\frac{603}{1204}\right)\)
\(\chi_{31433}(735,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{227}{602}\right)\)	\(e\left(\frac{155}{1204}\right)\)	\(e\left(\frac{227}{301}\right)\)	\(e\left(\frac{1019}{1204}\right)\)	\(e\left(\frac{87}{172}\right)\)	\(e\left(\frac{7}{172}\right)\)	\(e\left(\frac{79}{602}\right)\)	\(e\left(\frac{155}{602}\right)\)	\(e\left(\frac{269}{1204}\right)\)	\(e\left(\frac{541}{1204}\right)\)
\(\chi_{31433}(752,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{415}{602}\right)\)	\(e\left(\frac{591}{1204}\right)\)	\(e\left(\frac{114}{301}\right)\)	\(e\left(\frac{887}{1204}\right)\)	\(e\left(\frac{31}{172}\right)\)	\(e\left(\frac{131}{172}\right)\)	\(e\left(\frac{41}{602}\right)\)	\(e\left(\frac{591}{602}\right)\)	\(e\left(\frac{513}{1204}\right)\)	\(e\left(\frac{517}{1204}\right)\)
\(\chi_{31433}(778,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{437}{602}\right)\)	\(e\left(\frac{309}{1204}\right)\)	\(e\left(\frac{136}{301}\right)\)	\(e\left(\frac{641}{1204}\right)\)	\(e\left(\frac{169}{172}\right)\)	\(e\left(\frac{65}{172}\right)\)	\(e\left(\frac{107}{602}\right)\)	\(e\left(\frac{309}{602}\right)\)	\(e\left(\frac{311}{1204}\right)\)	\(e\left(\frac{527}{1204}\right)\)
\(\chi_{31433}(795,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{541}{602}\right)\)	\(e\left(\frac{1165}{1204}\right)\)	\(e\left(\frac{240}{301}\right)\)	\(e\left(\frac{901}{1204}\right)\)	\(e\left(\frac{149}{172}\right)\)	\(e\left(\frac{97}{172}\right)\)	\(e\left(\frac{419}{602}\right)\)	\(e\left(\frac{563}{602}\right)\)	\(e\left(\frac{779}{1204}\right)\)	\(e\left(\frac{27}{1204}\right)\)
\(\chi_{31433}(871,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{347}{602}\right)\)	\(e\left(\frac{587}{1204}\right)\)	\(e\left(\frac{46}{301}\right)\)	\(e\left(\frac{115}{1204}\right)\)	\(e\left(\frac{11}{172}\right)\)	\(e\left(\frac{163}{172}\right)\)	\(e\left(\frac{439}{602}\right)\)	\(e\left(\frac{587}{602}\right)\)	\(e\left(\frac{809}{1204}\right)\)	\(e\left(\frac{705}{1204}\right)\)
\(\chi_{31433}(914,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{95}{602}\right)\)	\(e\left(\frac{41}{1204}\right)\)	\(e\left(\frac{95}{301}\right)\)	\(e\left(\frac{689}{1204}\right)\)	\(e\left(\frac{33}{172}\right)\)	\(e\left(\frac{145}{172}\right)\)	\(e\left(\frac{285}{602}\right)\)	\(e\left(\frac{41}{602}\right)\)	\(e\left(\frac{879}{1204}\right)\)	\(e\left(\frac{1083}{1204}\right)\)
\(\chi_{31433}(1024,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{141}{602}\right)\)	\(e\left(\frac{327}{1204}\right)\)	\(e\left(\frac{141}{301}\right)\)	\(e\left(\frac{503}{1204}\right)\)	\(e\left(\frac{87}{172}\right)\)	\(e\left(\frac{7}{172}\right)\)	\(e\left(\frac{423}{602}\right)\)	\(e\left(\frac{327}{602}\right)\)	\(e\left(\frac{785}{1204}\right)\)	\(e\left(\frac{885}{1204}\right)\)
\(\chi_{31433}(1067,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{337}{602}\right)\)	\(e\left(\frac{1153}{1204}\right)\)	\(e\left(\frac{36}{301}\right)\)	\(e\left(\frac{993}{1204}\right)\)	\(e\left(\frac{89}{172}\right)\)	\(e\left(\frac{21}{172}\right)\)	\(e\left(\frac{409}{602}\right)\)	\(e\left(\frac{551}{602}\right)\)	\(e\left(\frac{463}{1204}\right)\)	\(e\left(\frac{591}{1204}\right)\)
\(\chi_{31433}(1177,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{601}{602}\right)\)	\(e\left(\frac{779}{1204}\right)\)	\(e\left(\frac{300}{301}\right)\)	\(e\left(\frac{1051}{1204}\right)\)	\(e\left(\frac{111}{172}\right)\)	\(e\left(\frac{3}{172}\right)\)	\(e\left(\frac{599}{602}\right)\)	\(e\left(\frac{177}{602}\right)\)	\(e\left(\frac{1049}{1204}\right)\)	\(e\left(\frac{109}{1204}\right)\)
\(\chi_{31433}(1220,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{503}{602}\right)\)	\(e\left(\frac{65}{1204}\right)\)	\(e\left(\frac{202}{301}\right)\)	\(e\left(\frac{505}{1204}\right)\)	\(e\left(\frac{153}{172}\right)\)	\(e\left(\frac{125}{172}\right)\)	\(e\left(\frac{305}{602}\right)\)	\(e\left(\frac{65}{602}\right)\)	\(e\left(\frac{307}{1204}\right)\)	\(e\left(\frac{1159}{1204}\right)\)
\(\chi_{31433}(1245,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{145}{602}\right)\)	\(e\left(\frac{823}{1204}\right)\)	\(e\left(\frac{145}{301}\right)\)	\(e\left(\frac{1115}{1204}\right)\)	\(e\left(\frac{159}{172}\right)\)	\(e\left(\frac{167}{172}\right)\)	\(e\left(\frac{435}{602}\right)\)	\(e\left(\frac{221}{602}\right)\)	\(e\left(\frac{201}{1204}\right)\)	\(e\left(\frac{449}{1204}\right)\)
\(\chi_{31433}(1288,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{327}{602}\right)\)	\(e\left(\frac{1117}{1204}\right)\)	\(e\left(\frac{26}{301}\right)\)	\(e\left(\frac{65}{1204}\right)\)	\(e\left(\frac{81}{172}\right)\)	\(e\left(\frac{137}{172}\right)\)	\(e\left(\frac{379}{602}\right)\)	\(e\left(\frac{515}{602}\right)\)	\(e\left(\frac{719}{1204}\right)\)	\(e\left(\frac{1079}{1204}\right)\)
\(\chi_{31433}(1466,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{185}{602}\right)\)	\(e\left(\frac{967}{1204}\right)\)	\(e\left(\frac{185}{301}\right)\)	\(e\left(\frac{11}{1204}\right)\)	\(e\left(\frac{19}{172}\right)\)	\(e\left(\frac{47}{172}\right)\)	\(e\left(\frac{555}{602}\right)\)	\(e\left(\frac{365}{602}\right)\)	\(e\left(\frac{381}{1204}\right)\)	\(e\left(\frac{905}{1204}\right)\)
\(\chi_{31433}(1483,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{149}{602}\right)\)	\(e\left(\frac{115}{1204}\right)\)	\(e\left(\frac{149}{301}\right)\)	\(e\left(\frac{523}{1204}\right)\)	\(e\left(\frac{59}{172}\right)\)	\(e\left(\frac{155}{172}\right)\)	\(e\left(\frac{447}{602}\right)\)	\(e\left(\frac{115}{602}\right)\)	\(e\left(\frac{821}{1204}\right)\)	\(e\left(\frac{13}{1204}\right)\)
\(\chi_{31433}(1509,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{395}{602}\right)\)	\(e\left(\frac{1121}{1204}\right)\)	\(e\left(\frac{94}{301}\right)\)	\(e\left(\frac{837}{1204}\right)\)	\(e\left(\frac{101}{172}\right)\)	\(e\left(\frac{105}{172}\right)\)	\(e\left(\frac{583}{602}\right)\)	\(e\left(\frac{519}{602}\right)\)	\(e\left(\frac{423}{1204}\right)\)	\(e\left(\frac{891}{1204}\right)\)
\(\chi_{31433}(1526,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{275}{602}\right)\)	\(e\left(\frac{689}{1204}\right)\)	\(e\left(\frac{275}{301}\right)\)	\(e\left(\frac{537}{1204}\right)\)	\(e\left(\frac{5}{172}\right)\)	\(e\left(\frac{121}{172}\right)\)	\(e\left(\frac{223}{602}\right)\)	\(e\left(\frac{87}{602}\right)\)	\(e\left(\frac{1087}{1204}\right)\)	\(e\left(\frac{727}{1204}\right)\)

Introduction

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Basic properties

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First 28 of 504 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	31433.cl
Modulus	$31433$
Conductor	$31433$
Order	$1204$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(31433\)
Conductor:	\(31433\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(1204\)	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)