LMFDB - Dirichlet character orbit 640332.bht

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(640332, base_ring=CyclotomicField(1386)) M = H._module chi = DirichletCharacter(H, M([693,847,1254,882])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(23,640332)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$640332$
Conductor:	$640332$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$1386$	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:	$\Q(\zeta_{693})$
Fixed field:	Number field defined by a degree 1386 polynomial (not computed)

First 31 of 360 characters in Galois orbit

Character	$-1$	$1$	$5$	$13$	$17$	$19$	$23$	$25$	$29$	$31$	$37$	$41$
$\chi_{640332}(23,\cdot)$	$1$	$1$	$e\left(\frac{533}{1386}\right)$	$e\left(\frac{13}{693}\right)$	$e\left(\frac{149}{154}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{103}{693}\right)$	$e\left(\frac{533}{693}\right)$	$e\left(\frac{991}{1386}\right)$	$e\left(\frac{155}{198}\right)$	$e\left(\frac{80}{231}\right)$	$e\left(\frac{827}{1386}\right)$
$\chi_{640332}(2531,\cdot)$	$1$	$1$	$e\left(\frac{223}{1386}\right)$	$e\left(\frac{428}{693}\right)$	$e\left(\frac{19}{154}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{86}{693}\right)$	$e\left(\frac{223}{693}\right)$	$e\left(\frac{269}{1386}\right)$	$e\left(\frac{115}{198}\right)$	$e\left(\frac{4}{231}\right)$	$e\left(\frac{307}{1386}\right)$
$\chi_{640332}(2795,\cdot)$	$1$	$1$	$e\left(\frac{305}{1386}\right)$	$e\left(\frac{430}{693}\right)$	$e\left(\frac{113}{154}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{475}{693}\right)$	$e\left(\frac{305}{693}\right)$	$e\left(\frac{1381}{1386}\right)$	$e\left(\frac{17}{198}\right)$	$e\left(\frac{194}{231}\right)$	$e\left(\frac{221}{1386}\right)$
$\chi_{640332}(5303,\cdot)$	$1$	$1$	$e\left(\frac{193}{1386}\right)$	$e\left(\frac{647}{693}\right)$	$e\left(\frac{71}{154}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{62}{693}\right)$	$e\left(\frac{193}{693}\right)$	$e\left(\frac{65}{1386}\right)$	$e\left(\frac{175}{198}\right)$	$e\left(\frac{19}{231}\right)$	$e\left(\frac{1285}{1386}\right)$
$\chi_{640332}(8075,\cdot)$	$1$	$1$	$e\left(\frac{163}{1386}\right)$	$e\left(\frac{173}{693}\right)$	$e\left(\frac{123}{154}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{38}{693}\right)$	$e\left(\frac{163}{693}\right)$	$e\left(\frac{1247}{1386}\right)$	$e\left(\frac{37}{198}\right)$	$e\left(\frac{34}{231}\right)$	$e\left(\frac{877}{1386}\right)$
$\chi_{640332}(8339,\cdot)$	$1$	$1$	$e\left(\frac{1235}{1386}\right)$	$e\left(\frac{571}{693}\right)$	$e\left(\frac{41}{154}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{526}{693}\right)$	$e\left(\frac{542}{693}\right)$	$e\left(\frac{775}{1386}\right)$	$e\left(\frac{137}{198}\right)$	$e\left(\frac{191}{231}\right)$	$e\left(\frac{395}{1386}\right)$
$\chi_{640332}(11111,\cdot)$	$1$	$1$	$e\left(\frac{1007}{1386}\right)$	$e\left(\frac{295}{693}\right)$	$e\left(\frac{5}{154}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{205}{693}\right)$	$e\left(\frac{314}{693}\right)$	$e\left(\frac{1165}{1386}\right)$	$e\left(\frac{197}{198}\right)$	$e\left(\frac{74}{231}\right)$	$e\left(\frac{1175}{1386}\right)$
$\chi_{640332}(13619,\cdot)$	$1$	$1$	$e\left(\frac{103}{1386}\right)$	$e\left(\frac{611}{693}\right)$	$e\left(\frac{73}{154}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{683}{693}\right)$	$e\left(\frac{103}{693}\right)$	$e\left(\frac{839}{1386}\right)$	$e\left(\frac{157}{198}\right)$	$e\left(\frac{64}{231}\right)$	$e\left(\frac{61}{1386}\right)$
$\chi_{640332}(13883,\cdot)$	$1$	$1$	$e\left(\frac{779}{1386}\right)$	$e\left(\frac{19}{693}\right)$	$e\left(\frac{123}{154}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{577}{693}\right)$	$e\left(\frac{86}{693}\right)$	$e\left(\frac{169}{1386}\right)$	$e\left(\frac{59}{198}\right)$	$e\left(\frac{188}{231}\right)$	$e\left(\frac{569}{1386}\right)$
$\chi_{640332}(16391,\cdot)$	$1$	$1$	$e\left(\frac{73}{1386}\right)$	$e\left(\frac{137}{693}\right)$	$e\left(\frac{125}{154}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{659}{693}\right)$	$e\left(\frac{73}{693}\right)$	$e\left(\frac{635}{1386}\right)$	$e\left(\frac{19}{198}\right)$	$e\left(\frac{79}{231}\right)$	$e\left(\frac{1039}{1386}\right)$
$\chi_{640332}(16655,\cdot)$	$1$	$1$	$e\left(\frac{551}{1386}\right)$	$e\left(\frac{436}{693}\right)$	$e\left(\frac{87}{154}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{256}{693}\right)$	$e\left(\frac{551}{693}\right)$	$e\left(\frac{559}{1386}\right)$	$e\left(\frac{119}{198}\right)$	$e\left(\frac{71}{231}\right)$	$e\left(\frac{1349}{1386}\right)$
$\chi_{640332}(19163,\cdot)$	$1$	$1$	$e\left(\frac{43}{1386}\right)$	$e\left(\frac{356}{693}\right)$	$e\left(\frac{23}{154}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{635}{693}\right)$	$e\left(\frac{43}{693}\right)$	$e\left(\frac{431}{1386}\right)$	$e\left(\frac{79}{198}\right)$	$e\left(\frac{94}{231}\right)$	$e\left(\frac{631}{1386}\right)$
$\chi_{640332}(19427,\cdot)$	$1$	$1$	$e\left(\frac{323}{1386}\right)$	$e\left(\frac{160}{693}\right)$	$e\left(\frac{51}{154}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{628}{693}\right)$	$e\left(\frac{323}{693}\right)$	$e\left(\frac{949}{1386}\right)$	$e\left(\frac{179}{198}\right)$	$e\left(\frac{185}{231}\right)$	$e\left(\frac{743}{1386}\right)$
$\chi_{640332}(21935,\cdot)$	$1$	$1$	$e\left(\frac{13}{1386}\right)$	$e\left(\frac{575}{693}\right)$	$e\left(\frac{75}{154}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{611}{693}\right)$	$e\left(\frac{13}{693}\right)$	$e\left(\frac{227}{1386}\right)$	$e\left(\frac{139}{198}\right)$	$e\left(\frac{109}{231}\right)$	$e\left(\frac{223}{1386}\right)$
$\chi_{640332}(22199,\cdot)$	$1$	$1$	$e\left(\frac{95}{1386}\right)$	$e\left(\frac{577}{693}\right)$	$e\left(\frac{15}{154}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{307}{693}\right)$	$e\left(\frac{95}{693}\right)$	$e\left(\frac{1339}{1386}\right)$	$e\left(\frac{41}{198}\right)$	$e\left(\frac{68}{231}\right)$	$e\left(\frac{137}{1386}\right)$
$\chi_{640332}(24707,\cdot)$	$1$	$1$	$e\left(\frac{1369}{1386}\right)$	$e\left(\frac{101}{693}\right)$	$e\left(\frac{127}{154}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{587}{693}\right)$	$e\left(\frac{676}{693}\right)$	$e\left(\frac{23}{1386}\right)$	$e\left(\frac{1}{198}\right)$	$e\left(\frac{124}{231}\right)$	$e\left(\frac{1201}{1386}\right)$
$\chi_{640332}(27479,\cdot)$	$1$	$1$	$e\left(\frac{1339}{1386}\right)$	$e\left(\frac{320}{693}\right)$	$e\left(\frac{25}{154}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{563}{693}\right)$	$e\left(\frac{646}{693}\right)$	$e\left(\frac{1205}{1386}\right)$	$e\left(\frac{61}{198}\right)$	$e\left(\frac{139}{231}\right)$	$e\left(\frac{793}{1386}\right)$
$\chi_{640332}(27743,\cdot)$	$1$	$1$	$e\left(\frac{1025}{1386}\right)$	$e\left(\frac{25}{693}\right)$	$e\left(\frac{97}{154}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{358}{693}\right)$	$e\left(\frac{332}{693}\right)$	$e\left(\frac{733}{1386}\right)$	$e\left(\frac{161}{198}\right)$	$e\left(\frac{65}{231}\right)$	$e\left(\frac{311}{1386}\right)$
$\chi_{640332}(30515,\cdot)$	$1$	$1$	$e\left(\frac{797}{1386}\right)$	$e\left(\frac{442}{693}\right)$	$e\left(\frac{61}{154}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{37}{693}\right)$	$e\left(\frac{104}{693}\right)$	$e\left(\frac{1123}{1386}\right)$	$e\left(\frac{23}{198}\right)$	$e\left(\frac{179}{231}\right)$	$e\left(\frac{1091}{1386}\right)$
$\chi_{640332}(33023,\cdot)$	$1$	$1$	$e\left(\frac{1279}{1386}\right)$	$e\left(\frac{65}{693}\right)$	$e\left(\frac{129}{154}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{515}{693}\right)$	$e\left(\frac{586}{693}\right)$	$e\left(\frac{797}{1386}\right)$	$e\left(\frac{181}{198}\right)$	$e\left(\frac{169}{231}\right)$	$e\left(\frac{1363}{1386}\right)$
$\chi_{640332}(33287,\cdot)$	$1$	$1$	$e\left(\frac{569}{1386}\right)$	$e\left(\frac{166}{693}\right)$	$e\left(\frac{25}{154}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{409}{693}\right)$	$e\left(\frac{569}{693}\right)$	$e\left(\frac{127}{1386}\right)$	$e\left(\frac{83}{198}\right)$	$e\left(\frac{62}{231}\right)$	$e\left(\frac{485}{1386}\right)$
$\chi_{640332}(35795,\cdot)$	$1$	$1$	$e\left(\frac{1249}{1386}\right)$	$e\left(\frac{284}{693}\right)$	$e\left(\frac{27}{154}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{491}{693}\right)$	$e\left(\frac{556}{693}\right)$	$e\left(\frac{593}{1386}\right)$	$e\left(\frac{43}{198}\right)$	$e\left(\frac{184}{231}\right)$	$e\left(\frac{955}{1386}\right)$
$\chi_{640332}(38567,\cdot)$	$1$	$1$	$e\left(\frac{1219}{1386}\right)$	$e\left(\frac{503}{693}\right)$	$e\left(\frac{79}{154}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{467}{693}\right)$	$e\left(\frac{526}{693}\right)$	$e\left(\frac{389}{1386}\right)$	$e\left(\frac{103}{198}\right)$	$e\left(\frac{199}{231}\right)$	$e\left(\frac{547}{1386}\right)$
$\chi_{640332}(38831,\cdot)$	$1$	$1$	$e\left(\frac{113}{1386}\right)$	$e\left(\frac{307}{693}\right)$	$e\left(\frac{107}{154}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{460}{693}\right)$	$e\left(\frac{113}{693}\right)$	$e\left(\frac{907}{1386}\right)$	$e\left(\frac{5}{198}\right)$	$e\left(\frac{59}{231}\right)$	$e\left(\frac{659}{1386}\right)$
$\chi_{640332}(41339,\cdot)$	$1$	$1$	$e\left(\frac{1189}{1386}\right)$	$e\left(\frac{29}{693}\right)$	$e\left(\frac{131}{154}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{443}{693}\right)$	$e\left(\frac{496}{693}\right)$	$e\left(\frac{185}{1386}\right)$	$e\left(\frac{163}{198}\right)$	$e\left(\frac{214}{231}\right)$	$e\left(\frac{139}{1386}\right)$
$\chi_{640332}(41603,\cdot)$	$1$	$1$	$e\left(\frac{1271}{1386}\right)$	$e\left(\frac{31}{693}\right)$	$e\left(\frac{71}{154}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{139}{693}\right)$	$e\left(\frac{578}{693}\right)$	$e\left(\frac{1297}{1386}\right)$	$e\left(\frac{65}{198}\right)$	$e\left(\frac{173}{231}\right)$	$e\left(\frac{53}{1386}\right)$
$\chi_{640332}(44111,\cdot)$	$1$	$1$	$e\left(\frac{1159}{1386}\right)$	$e\left(\frac{248}{693}\right)$	$e\left(\frac{29}{154}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{419}{693}\right)$	$e\left(\frac{466}{693}\right)$	$e\left(\frac{1367}{1386}\right)$	$e\left(\frac{25}{198}\right)$	$e\left(\frac{229}{231}\right)$	$e\left(\frac{1117}{1386}\right)$
$\chi_{640332}(46883,\cdot)$	$1$	$1$	$e\left(\frac{1129}{1386}\right)$	$e\left(\frac{467}{693}\right)$	$e\left(\frac{81}{154}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{395}{693}\right)$	$e\left(\frac{436}{693}\right)$	$e\left(\frac{1163}{1386}\right)$	$e\left(\frac{85}{198}\right)$	$e\left(\frac{13}{231}\right)$	$e\left(\frac{709}{1386}\right)$
$\chi_{640332}(47147,\cdot)$	$1$	$1$	$e\left(\frac{815}{1386}\right)$	$e\left(\frac{172}{693}\right)$	$e\left(\frac{153}{154}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{190}{693}\right)$	$e\left(\frac{122}{693}\right)$	$e\left(\frac{691}{1386}\right)$	$e\left(\frac{185}{198}\right)$	$e\left(\frac{170}{231}\right)$	$e\left(\frac{227}{1386}\right)$
$\chi_{640332}(49919,\cdot)$	$1$	$1$	$e\left(\frac{587}{1386}\right)$	$e\left(\frac{589}{693}\right)$	$e\left(\frac{117}{154}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{562}{693}\right)$	$e\left(\frac{587}{693}\right)$	$e\left(\frac{1081}{1386}\right)$	$e\left(\frac{47}{198}\right)$	$e\left(\frac{53}{231}\right)$	$e\left(\frac{1007}{1386}\right)$
$\chi_{640332}(52427,\cdot)$	$1$	$1$	$e\left(\frac{1069}{1386}\right)$	$e\left(\frac{212}{693}\right)$	$e\left(\frac{31}{154}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{347}{693}\right)$	$e\left(\frac{376}{693}\right)$	$e\left(\frac{755}{1386}\right)$	$e\left(\frac{7}{198}\right)$	$e\left(\frac{43}{231}\right)$	$e\left(\frac{1279}{1386}\right)$

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	\(-1\)	\(1\)	\(5\)	\(13\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)	\(37\)	\(41\)
\(\chi_{640332}(23,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{533}{1386}\right)\)	\(e\left(\frac{13}{693}\right)\)	\(e\left(\frac{149}{154}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{103}{693}\right)\)	\(e\left(\frac{533}{693}\right)\)	\(e\left(\frac{991}{1386}\right)\)	\(e\left(\frac{155}{198}\right)\)	\(e\left(\frac{80}{231}\right)\)	\(e\left(\frac{827}{1386}\right)\)
\(\chi_{640332}(2531,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{223}{1386}\right)\)	\(e\left(\frac{428}{693}\right)\)	\(e\left(\frac{19}{154}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{86}{693}\right)\)	\(e\left(\frac{223}{693}\right)\)	\(e\left(\frac{269}{1386}\right)\)	\(e\left(\frac{115}{198}\right)\)	\(e\left(\frac{4}{231}\right)\)	\(e\left(\frac{307}{1386}\right)\)
\(\chi_{640332}(2795,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{305}{1386}\right)\)	\(e\left(\frac{430}{693}\right)\)	\(e\left(\frac{113}{154}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{475}{693}\right)\)	\(e\left(\frac{305}{693}\right)\)	\(e\left(\frac{1381}{1386}\right)\)	\(e\left(\frac{17}{198}\right)\)	\(e\left(\frac{194}{231}\right)\)	\(e\left(\frac{221}{1386}\right)\)
\(\chi_{640332}(5303,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{193}{1386}\right)\)	\(e\left(\frac{647}{693}\right)\)	\(e\left(\frac{71}{154}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{62}{693}\right)\)	\(e\left(\frac{193}{693}\right)\)	\(e\left(\frac{65}{1386}\right)\)	\(e\left(\frac{175}{198}\right)\)	\(e\left(\frac{19}{231}\right)\)	\(e\left(\frac{1285}{1386}\right)\)
\(\chi_{640332}(8075,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{163}{1386}\right)\)	\(e\left(\frac{173}{693}\right)\)	\(e\left(\frac{123}{154}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{38}{693}\right)\)	\(e\left(\frac{163}{693}\right)\)	\(e\left(\frac{1247}{1386}\right)\)	\(e\left(\frac{37}{198}\right)\)	\(e\left(\frac{34}{231}\right)\)	\(e\left(\frac{877}{1386}\right)\)
\(\chi_{640332}(8339,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1235}{1386}\right)\)	\(e\left(\frac{571}{693}\right)\)	\(e\left(\frac{41}{154}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{526}{693}\right)\)	\(e\left(\frac{542}{693}\right)\)	\(e\left(\frac{775}{1386}\right)\)	\(e\left(\frac{137}{198}\right)\)	\(e\left(\frac{191}{231}\right)\)	\(e\left(\frac{395}{1386}\right)\)
\(\chi_{640332}(11111,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1007}{1386}\right)\)	\(e\left(\frac{295}{693}\right)\)	\(e\left(\frac{5}{154}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{205}{693}\right)\)	\(e\left(\frac{314}{693}\right)\)	\(e\left(\frac{1165}{1386}\right)\)	\(e\left(\frac{197}{198}\right)\)	\(e\left(\frac{74}{231}\right)\)	\(e\left(\frac{1175}{1386}\right)\)
\(\chi_{640332}(13619,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{103}{1386}\right)\)	\(e\left(\frac{611}{693}\right)\)	\(e\left(\frac{73}{154}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{683}{693}\right)\)	\(e\left(\frac{103}{693}\right)\)	\(e\left(\frac{839}{1386}\right)\)	\(e\left(\frac{157}{198}\right)\)	\(e\left(\frac{64}{231}\right)\)	\(e\left(\frac{61}{1386}\right)\)
\(\chi_{640332}(13883,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{779}{1386}\right)\)	\(e\left(\frac{19}{693}\right)\)	\(e\left(\frac{123}{154}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{577}{693}\right)\)	\(e\left(\frac{86}{693}\right)\)	\(e\left(\frac{169}{1386}\right)\)	\(e\left(\frac{59}{198}\right)\)	\(e\left(\frac{188}{231}\right)\)	\(e\left(\frac{569}{1386}\right)\)
\(\chi_{640332}(16391,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{73}{1386}\right)\)	\(e\left(\frac{137}{693}\right)\)	\(e\left(\frac{125}{154}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{659}{693}\right)\)	\(e\left(\frac{73}{693}\right)\)	\(e\left(\frac{635}{1386}\right)\)	\(e\left(\frac{19}{198}\right)\)	\(e\left(\frac{79}{231}\right)\)	\(e\left(\frac{1039}{1386}\right)\)
\(\chi_{640332}(16655,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{551}{1386}\right)\)	\(e\left(\frac{436}{693}\right)\)	\(e\left(\frac{87}{154}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{256}{693}\right)\)	\(e\left(\frac{551}{693}\right)\)	\(e\left(\frac{559}{1386}\right)\)	\(e\left(\frac{119}{198}\right)\)	\(e\left(\frac{71}{231}\right)\)	\(e\left(\frac{1349}{1386}\right)\)
\(\chi_{640332}(19163,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{1386}\right)\)	\(e\left(\frac{356}{693}\right)\)	\(e\left(\frac{23}{154}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{635}{693}\right)\)	\(e\left(\frac{43}{693}\right)\)	\(e\left(\frac{431}{1386}\right)\)	\(e\left(\frac{79}{198}\right)\)	\(e\left(\frac{94}{231}\right)\)	\(e\left(\frac{631}{1386}\right)\)
\(\chi_{640332}(19427,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{323}{1386}\right)\)	\(e\left(\frac{160}{693}\right)\)	\(e\left(\frac{51}{154}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{628}{693}\right)\)	\(e\left(\frac{323}{693}\right)\)	\(e\left(\frac{949}{1386}\right)\)	\(e\left(\frac{179}{198}\right)\)	\(e\left(\frac{185}{231}\right)\)	\(e\left(\frac{743}{1386}\right)\)
\(\chi_{640332}(21935,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{1386}\right)\)	\(e\left(\frac{575}{693}\right)\)	\(e\left(\frac{75}{154}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{611}{693}\right)\)	\(e\left(\frac{13}{693}\right)\)	\(e\left(\frac{227}{1386}\right)\)	\(e\left(\frac{139}{198}\right)\)	\(e\left(\frac{109}{231}\right)\)	\(e\left(\frac{223}{1386}\right)\)
\(\chi_{640332}(22199,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{95}{1386}\right)\)	\(e\left(\frac{577}{693}\right)\)	\(e\left(\frac{15}{154}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{307}{693}\right)\)	\(e\left(\frac{95}{693}\right)\)	\(e\left(\frac{1339}{1386}\right)\)	\(e\left(\frac{41}{198}\right)\)	\(e\left(\frac{68}{231}\right)\)	\(e\left(\frac{137}{1386}\right)\)
\(\chi_{640332}(24707,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1369}{1386}\right)\)	\(e\left(\frac{101}{693}\right)\)	\(e\left(\frac{127}{154}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{587}{693}\right)\)	\(e\left(\frac{676}{693}\right)\)	\(e\left(\frac{23}{1386}\right)\)	\(e\left(\frac{1}{198}\right)\)	\(e\left(\frac{124}{231}\right)\)	\(e\left(\frac{1201}{1386}\right)\)
\(\chi_{640332}(27479,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1339}{1386}\right)\)	\(e\left(\frac{320}{693}\right)\)	\(e\left(\frac{25}{154}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{563}{693}\right)\)	\(e\left(\frac{646}{693}\right)\)	\(e\left(\frac{1205}{1386}\right)\)	\(e\left(\frac{61}{198}\right)\)	\(e\left(\frac{139}{231}\right)\)	\(e\left(\frac{793}{1386}\right)\)
\(\chi_{640332}(27743,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1025}{1386}\right)\)	\(e\left(\frac{25}{693}\right)\)	\(e\left(\frac{97}{154}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{358}{693}\right)\)	\(e\left(\frac{332}{693}\right)\)	\(e\left(\frac{733}{1386}\right)\)	\(e\left(\frac{161}{198}\right)\)	\(e\left(\frac{65}{231}\right)\)	\(e\left(\frac{311}{1386}\right)\)
\(\chi_{640332}(30515,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{797}{1386}\right)\)	\(e\left(\frac{442}{693}\right)\)	\(e\left(\frac{61}{154}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{37}{693}\right)\)	\(e\left(\frac{104}{693}\right)\)	\(e\left(\frac{1123}{1386}\right)\)	\(e\left(\frac{23}{198}\right)\)	\(e\left(\frac{179}{231}\right)\)	\(e\left(\frac{1091}{1386}\right)\)
\(\chi_{640332}(33023,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1279}{1386}\right)\)	\(e\left(\frac{65}{693}\right)\)	\(e\left(\frac{129}{154}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{515}{693}\right)\)	\(e\left(\frac{586}{693}\right)\)	\(e\left(\frac{797}{1386}\right)\)	\(e\left(\frac{181}{198}\right)\)	\(e\left(\frac{169}{231}\right)\)	\(e\left(\frac{1363}{1386}\right)\)
\(\chi_{640332}(33287,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{569}{1386}\right)\)	\(e\left(\frac{166}{693}\right)\)	\(e\left(\frac{25}{154}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{409}{693}\right)\)	\(e\left(\frac{569}{693}\right)\)	\(e\left(\frac{127}{1386}\right)\)	\(e\left(\frac{83}{198}\right)\)	\(e\left(\frac{62}{231}\right)\)	\(e\left(\frac{485}{1386}\right)\)
\(\chi_{640332}(35795,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1249}{1386}\right)\)	\(e\left(\frac{284}{693}\right)\)	\(e\left(\frac{27}{154}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{491}{693}\right)\)	\(e\left(\frac{556}{693}\right)\)	\(e\left(\frac{593}{1386}\right)\)	\(e\left(\frac{43}{198}\right)\)	\(e\left(\frac{184}{231}\right)\)	\(e\left(\frac{955}{1386}\right)\)
\(\chi_{640332}(38567,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1219}{1386}\right)\)	\(e\left(\frac{503}{693}\right)\)	\(e\left(\frac{79}{154}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{467}{693}\right)\)	\(e\left(\frac{526}{693}\right)\)	\(e\left(\frac{389}{1386}\right)\)	\(e\left(\frac{103}{198}\right)\)	\(e\left(\frac{199}{231}\right)\)	\(e\left(\frac{547}{1386}\right)\)
\(\chi_{640332}(38831,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{113}{1386}\right)\)	\(e\left(\frac{307}{693}\right)\)	\(e\left(\frac{107}{154}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{460}{693}\right)\)	\(e\left(\frac{113}{693}\right)\)	\(e\left(\frac{907}{1386}\right)\)	\(e\left(\frac{5}{198}\right)\)	\(e\left(\frac{59}{231}\right)\)	\(e\left(\frac{659}{1386}\right)\)
\(\chi_{640332}(41339,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1189}{1386}\right)\)	\(e\left(\frac{29}{693}\right)\)	\(e\left(\frac{131}{154}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{443}{693}\right)\)	\(e\left(\frac{496}{693}\right)\)	\(e\left(\frac{185}{1386}\right)\)	\(e\left(\frac{163}{198}\right)\)	\(e\left(\frac{214}{231}\right)\)	\(e\left(\frac{139}{1386}\right)\)
\(\chi_{640332}(41603,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1271}{1386}\right)\)	\(e\left(\frac{31}{693}\right)\)	\(e\left(\frac{71}{154}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{139}{693}\right)\)	\(e\left(\frac{578}{693}\right)\)	\(e\left(\frac{1297}{1386}\right)\)	\(e\left(\frac{65}{198}\right)\)	\(e\left(\frac{173}{231}\right)\)	\(e\left(\frac{53}{1386}\right)\)
\(\chi_{640332}(44111,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1159}{1386}\right)\)	\(e\left(\frac{248}{693}\right)\)	\(e\left(\frac{29}{154}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{419}{693}\right)\)	\(e\left(\frac{466}{693}\right)\)	\(e\left(\frac{1367}{1386}\right)\)	\(e\left(\frac{25}{198}\right)\)	\(e\left(\frac{229}{231}\right)\)	\(e\left(\frac{1117}{1386}\right)\)
\(\chi_{640332}(46883,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1129}{1386}\right)\)	\(e\left(\frac{467}{693}\right)\)	\(e\left(\frac{81}{154}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{395}{693}\right)\)	\(e\left(\frac{436}{693}\right)\)	\(e\left(\frac{1163}{1386}\right)\)	\(e\left(\frac{85}{198}\right)\)	\(e\left(\frac{13}{231}\right)\)	\(e\left(\frac{709}{1386}\right)\)
\(\chi_{640332}(47147,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{815}{1386}\right)\)	\(e\left(\frac{172}{693}\right)\)	\(e\left(\frac{153}{154}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{190}{693}\right)\)	\(e\left(\frac{122}{693}\right)\)	\(e\left(\frac{691}{1386}\right)\)	\(e\left(\frac{185}{198}\right)\)	\(e\left(\frac{170}{231}\right)\)	\(e\left(\frac{227}{1386}\right)\)
\(\chi_{640332}(49919,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{587}{1386}\right)\)	\(e\left(\frac{589}{693}\right)\)	\(e\left(\frac{117}{154}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{562}{693}\right)\)	\(e\left(\frac{587}{693}\right)\)	\(e\left(\frac{1081}{1386}\right)\)	\(e\left(\frac{47}{198}\right)\)	\(e\left(\frac{53}{231}\right)\)	\(e\left(\frac{1007}{1386}\right)\)
\(\chi_{640332}(52427,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1069}{1386}\right)\)	\(e\left(\frac{212}{693}\right)\)	\(e\left(\frac{31}{154}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{347}{693}\right)\)	\(e\left(\frac{376}{693}\right)\)	\(e\left(\frac{755}{1386}\right)\)	\(e\left(\frac{7}{198}\right)\)	\(e\left(\frac{43}{231}\right)\)	\(e\left(\frac{1279}{1386}\right)\)

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Basic properties

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First 31 of 360 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	640332.bht
Modulus	$640332$
Conductor	$640332$
Order	$1386$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(640332\)
Conductor:	\(640332\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(1386\)	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)