LMFDB - Dirichlet character orbit 640332.blo

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(640332, base_ring=CyclotomicField(6930)) M = H._module chi = DirichletCharacter(H, M([0,3850,2640,2394])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(25,640332)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$640332$
Conductor:	$160083$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$3465$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 160083.sw	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:	$\Q(\zeta_{3465})$
Fixed field:	Number field defined by a degree 3465 polynomial (not computed)

First 31 of 1440 characters in Galois orbit

Character	$-1$	$1$	$5$	$13$	$17$	$19$	$23$	$25$	$29$	$31$	$37$	$41$
$\chi_{640332}(25,\cdot)$	$1$	$1$	$e\left(\frac{1348}{3465}\right)$	$e\left(\frac{3142}{3465}\right)$	$e\left(\frac{302}{385}\right)$	$e\left(\frac{37}{55}\right)$	$e\left(\frac{533}{693}\right)$	$e\left(\frac{2696}{3465}\right)$	$e\left(\frac{989}{3465}\right)$	$e\left(\frac{241}{495}\right)$	$e\left(\frac{38}{1155}\right)$	$e\left(\frac{361}{3465}\right)$
$\chi_{640332}(625,\cdot)$	$1$	$1$	$e\left(\frac{2696}{3465}\right)$	$e\left(\frac{2819}{3465}\right)$	$e\left(\frac{219}{385}\right)$	$e\left(\frac{19}{55}\right)$	$e\left(\frac{373}{693}\right)$	$e\left(\frac{1927}{3465}\right)$	$e\left(\frac{1978}{3465}\right)$	$e\left(\frac{482}{495}\right)$	$e\left(\frac{76}{1155}\right)$	$e\left(\frac{722}{3465}\right)$
$\chi_{640332}(1285,\cdot)$	$1$	$1$	$e\left(\frac{1711}{3465}\right)$	$e\left(\frac{3109}{3465}\right)$	$e\left(\frac{104}{385}\right)$	$e\left(\frac{4}{55}\right)$	$e\left(\frac{566}{693}\right)$	$e\left(\frac{3422}{3465}\right)$	$e\left(\frac{2903}{3465}\right)$	$e\left(\frac{307}{495}\right)$	$e\left(\frac{1061}{1155}\right)$	$e\left(\frac{1417}{3465}\right)$
$\chi_{640332}(1633,\cdot)$	$1$	$1$	$e\left(\frac{1244}{3465}\right)$	$e\left(\frac{2951}{3465}\right)$	$e\left(\frac{241}{385}\right)$	$e\left(\frac{41}{55}\right)$	$e\left(\frac{241}{693}\right)$	$e\left(\frac{2488}{3465}\right)$	$e\left(\frac{1252}{3465}\right)$	$e\left(\frac{218}{495}\right)$	$e\left(\frac{604}{1155}\right)$	$e\left(\frac{3428}{3465}\right)$
$\chi_{640332}(1885,\cdot)$	$1$	$1$	$e\left(\frac{1007}{3465}\right)$	$e\left(\frac{1283}{3465}\right)$	$e\left(\frac{313}{385}\right)$	$e\left(\frac{48}{55}\right)$	$e\left(\frac{82}{693}\right)$	$e\left(\frac{2014}{3465}\right)$	$e\left(\frac{2551}{3465}\right)$	$e\left(\frac{494}{495}\right)$	$e\left(\frac{1072}{1155}\right)$	$e\left(\frac{3254}{3465}\right)$
$\chi_{640332}(2293,\cdot)$	$1$	$1$	$e\left(\frac{439}{3465}\right)$	$e\left(\frac{1306}{3465}\right)$	$e\left(\frac{276}{385}\right)$	$e\left(\frac{36}{55}\right)$	$e\left(\frac{353}{693}\right)$	$e\left(\frac{878}{3465}\right)$	$e\left(\frac{1322}{3465}\right)$	$e\left(\frac{178}{495}\right)$	$e\left(\frac{254}{1155}\right)$	$e\left(\frac{2413}{3465}\right)$
$\chi_{640332}(2545,\cdot)$	$1$	$1$	$e\left(\frac{3397}{3465}\right)$	$e\left(\frac{808}{3465}\right)$	$e\left(\frac{123}{385}\right)$	$e\left(\frac{28}{55}\right)$	$e\left(\frac{662}{693}\right)$	$e\left(\frac{3329}{3465}\right)$	$e\left(\frac{2171}{3465}\right)$	$e\left(\frac{4}{495}\right)$	$e\left(\frac{992}{1155}\right)$	$e\left(\frac{1339}{3465}\right)$
$\chi_{640332}(2797,\cdot)$	$1$	$1$	$e\left(\frac{1378}{3465}\right)$	$e\left(\frac{3397}{3465}\right)$	$e\left(\frac{327}{385}\right)$	$e\left(\frac{2}{55}\right)$	$e\left(\frac{404}{693}\right)$	$e\left(\frac{2756}{3465}\right)$	$e\left(\frac{2579}{3465}\right)$	$e\left(\frac{181}{495}\right)$	$e\left(\frac{8}{1155}\right)$	$e\left(\frac{76}{3465}\right)$
$\chi_{640332}(4057,\cdot)$	$1$	$1$	$e\left(\frac{3316}{3465}\right)$	$e\left(\frac{1159}{3465}\right)$	$e\left(\frac{94}{385}\right)$	$e\left(\frac{29}{55}\right)$	$e\left(\frac{248}{693}\right)$	$e\left(\frac{3167}{3465}\right)$	$e\left(\frac{1343}{3465}\right)$	$e\left(\frac{67}{495}\right)$	$e\left(\frac{611}{1155}\right)$	$e\left(\frac{1762}{3465}\right)$
$\chi_{640332}(4405,\cdot)$	$1$	$1$	$e\left(\frac{1724}{3465}\right)$	$e\left(\frac{101}{3465}\right)$	$e\left(\frac{256}{385}\right)$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{256}{693}\right)$	$e\left(\frac{3448}{3465}\right)$	$e\left(\frac{2437}{3465}\right)$	$e\left(\frac{248}{495}\right)$	$e\left(\frac{124}{1155}\right)$	$e\left(\frac{2333}{3465}\right)$
$\chi_{640332}(4657,\cdot)$	$1$	$1$	$e\left(\frac{2432}{3465}\right)$	$e\left(\frac{1268}{3465}\right)$	$e\left(\frac{153}{385}\right)$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{538}{693}\right)$	$e\left(\frac{1399}{3465}\right)$	$e\left(\frac{1846}{3465}\right)$	$e\left(\frac{119}{495}\right)$	$e\left(\frac{802}{1155}\right)$	$e\left(\frac{1844}{3465}\right)$
$\chi_{640332}(4909,\cdot)$	$1$	$1$	$e\left(\frac{1943}{3465}\right)$	$e\left(\frac{3002}{3465}\right)$	$e\left(\frac{92}{385}\right)$	$e\left(\frac{12}{55}\right)$	$e\left(\frac{631}{693}\right)$	$e\left(\frac{421}{3465}\right)$	$e\left(\frac{184}{3465}\right)$	$e\left(\frac{206}{495}\right)$	$e\left(\frac{598}{1155}\right)$	$e\left(\frac{3371}{3465}\right)$
$\chi_{640332}(5317,\cdot)$	$1$	$1$	$e\left(\frac{1852}{3465}\right)$	$e\left(\frac{3268}{3465}\right)$	$e\left(\frac{183}{385}\right)$	$e\left(\frac{43}{55}\right)$	$e\left(\frac{29}{693}\right)$	$e\left(\frac{239}{3465}\right)$	$e\left(\frac{3446}{3465}\right)$	$e\left(\frac{124}{495}\right)$	$e\left(\frac{227}{1155}\right)$	$e\left(\frac{424}{3465}\right)$
$\chi_{640332}(6169,\cdot)$	$1$	$1$	$e\left(\frac{1451}{3465}\right)$	$e\left(\frac{899}{3465}\right)$	$e\left(\frac{144}{385}\right)$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{529}{693}\right)$	$e\left(\frac{2902}{3465}\right)$	$e\left(\frac{1828}{3465}\right)$	$e\left(\frac{2}{495}\right)$	$e\left(\frac{166}{1155}\right)$	$e\left(\frac{422}{3465}\right)$
$\chi_{640332}(7177,\cdot)$	$1$	$1$	$e\left(\frac{2204}{3465}\right)$	$e\left(\frac{716}{3465}\right)$	$e\left(\frac{271}{385}\right)$	$e\left(\frac{21}{55}\right)$	$e\left(\frac{271}{693}\right)$	$e\left(\frac{943}{3465}\right)$	$e\left(\frac{157}{3465}\right)$	$e\left(\frac{278}{495}\right)$	$e\left(\frac{799}{1155}\right)$	$e\left(\frac{1238}{3465}\right)$
$\chi_{640332}(7681,\cdot)$	$1$	$1$	$e\left(\frac{1478}{3465}\right)$	$e\left(\frac{782}{3465}\right)$	$e\left(\frac{282}{385}\right)$	$e\left(\frac{32}{55}\right)$	$e\left(\frac{205}{693}\right)$	$e\left(\frac{2956}{3465}\right)$	$e\left(\frac{3259}{3465}\right)$	$e\left(\frac{146}{495}\right)$	$e\left(\frac{1063}{1155}\right)$	$e\left(\frac{2591}{3465}\right)$
$\chi_{640332}(7837,\cdot)$	$1$	$1$	$e\left(\frac{2389}{3465}\right)$	$e\left(\frac{556}{3465}\right)$	$e\left(\frac{361}{385}\right)$	$e\left(\frac{16}{55}\right)$	$e\left(\frac{284}{693}\right)$	$e\left(\frac{1313}{3465}\right)$	$e\left(\frac{722}{3465}\right)$	$e\left(\frac{238}{495}\right)$	$e\left(\frac{614}{1155}\right)$	$e\left(\frac{1213}{3465}\right)$
$\chi_{640332}(8089,\cdot)$	$1$	$1$	$e\left(\frac{307}{3465}\right)$	$e\left(\frac{2263}{3465}\right)$	$e\left(\frac{243}{385}\right)$	$e\left(\frac{3}{55}\right)$	$e\left(\frac{89}{693}\right)$	$e\left(\frac{614}{3465}\right)$	$e\left(\frac{1256}{3465}\right)$	$e\left(\frac{244}{495}\right)$	$e\left(\frac{617}{1155}\right)$	$e\left(\frac{2974}{3465}\right)$
$\chi_{640332}(8341,\cdot)$	$1$	$1$	$e\left(\frac{1438}{3465}\right)$	$e\left(\frac{442}{3465}\right)$	$e\left(\frac{377}{385}\right)$	$e\left(\frac{42}{55}\right)$	$e\left(\frac{146}{693}\right)$	$e\left(\frac{2876}{3465}\right)$	$e\left(\frac{2294}{3465}\right)$	$e\left(\frac{61}{495}\right)$	$e\left(\frac{1103}{1155}\right)$	$e\left(\frac{2971}{3465}\right)$
$\chi_{640332}(8941,\cdot)$	$1$	$1$	$e\left(\frac{2561}{3465}\right)$	$e\left(\frac{3404}{3465}\right)$	$e\left(\frac{299}{385}\right)$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{607}{693}\right)$	$e\left(\frac{1657}{3465}\right)$	$e\left(\frac{1753}{3465}\right)$	$e\left(\frac{257}{495}\right)$	$e\left(\frac{211}{1155}\right)$	$e\left(\frac{272}{3465}\right)$
$\chi_{640332}(9601,\cdot)$	$1$	$1$	$e\left(\frac{3061}{3465}\right)$	$e\left(\frac{724}{3465}\right)$	$e\left(\frac{74}{385}\right)$	$e\left(\frac{24}{55}\right)$	$e\left(\frac{305}{693}\right)$	$e\left(\frac{2657}{3465}\right)$	$e\left(\frac{1688}{3465}\right)$	$e\left(\frac{82}{495}\right)$	$e\left(\frac{866}{1155}\right)$	$e\left(\frac{2452}{3465}\right)$
$\chi_{640332}(10201,\cdot)$	$1$	$1$	$e\left(\frac{1817}{3465}\right)$	$e\left(\frac{1238}{3465}\right)$	$e\left(\frac{218}{385}\right)$	$e\left(\frac{38}{55}\right)$	$e\left(\frac{64}{693}\right)$	$e\left(\frac{169}{3465}\right)$	$e\left(\frac{436}{3465}\right)$	$e\left(\frac{359}{495}\right)$	$e\left(\frac{262}{1155}\right)$	$e\left(\frac{2489}{3465}\right)$
$\chi_{640332}(10453,\cdot)$	$1$	$1$	$e\left(\frac{1013}{3465}\right)$	$e\left(\frac{2027}{3465}\right)$	$e\left(\frac{87}{385}\right)$	$e\left(\frac{52}{55}\right)$	$e\left(\frac{472}{693}\right)$	$e\left(\frac{2026}{3465}\right)$	$e\left(\frac{2869}{3465}\right)$	$e\left(\frac{86}{495}\right)$	$e\left(\frac{373}{1155}\right)$	$e\left(\frac{1811}{3465}\right)$
$\chi_{640332}(10609,\cdot)$	$1$	$1$	$e\left(\frac{3364}{3465}\right)$	$e\left(\frac{181}{3465}\right)$	$e\left(\frac{211}{385}\right)$	$e\left(\frac{6}{55}\right)$	$e\left(\frac{596}{693}\right)$	$e\left(\frac{3263}{3465}\right)$	$e\left(\frac{422}{3465}\right)$	$e\left(\frac{268}{495}\right)$	$e\left(\frac{794}{1155}\right)$	$e\left(\frac{613}{3465}\right)$
$\chi_{640332}(10861,\cdot)$	$1$	$1$	$e\left(\frac{2227}{3465}\right)$	$e\left(\frac{1258}{3465}\right)$	$e\left(\frac{303}{385}\right)$	$e\left(\frac{18}{55}\right)$	$e\left(\frac{149}{693}\right)$	$e\left(\frac{989}{3465}\right)$	$e\left(\frac{2531}{3465}\right)$	$e\left(\frac{364}{495}\right)$	$e\left(\frac{1007}{1155}\right)$	$e\left(\frac{2059}{3465}\right)$
$\chi_{640332}(11113,\cdot)$	$1$	$1$	$e\left(\frac{1468}{3465}\right)$	$e\left(\frac{697}{3465}\right)$	$e\left(\frac{17}{385}\right)$	$e\left(\frac{7}{55}\right)$	$e\left(\frac{17}{693}\right)$	$e\left(\frac{2936}{3465}\right)$	$e\left(\frac{419}{3465}\right)$	$e\left(\frac{1}{495}\right)$	$e\left(\frac{1073}{1155}\right)$	$e\left(\frac{2686}{3465}\right)$
$\chi_{640332}(11713,\cdot)$	$1$	$1$	$e\left(\frac{206}{3465}\right)$	$e\left(\frac{2444}{3465}\right)$	$e\left(\frac{69}{385}\right)$	$e\left(\frac{9}{55}\right)$	$e\left(\frac{685}{693}\right)$	$e\left(\frac{412}{3465}\right)$	$e\left(\frac{1678}{3465}\right)$	$e\left(\frac{17}{495}\right)$	$e\left(\frac{256}{1155}\right)$	$e\left(\frac{122}{3465}\right)$
$\chi_{640332}(12373,\cdot)$	$1$	$1$	$e\left(\frac{1201}{3465}\right)$	$e\left(\frac{2239}{3465}\right)$	$e\left(\frac{64}{385}\right)$	$e\left(\frac{49}{55}\right)$	$e\left(\frac{680}{693}\right)$	$e\left(\frac{2402}{3465}\right)$	$e\left(\frac{128}{3465}\right)$	$e\left(\frac{337}{495}\right)$	$e\left(\frac{416}{1155}\right)$	$e\left(\frac{2797}{3465}\right)$
$\chi_{640332}(12973,\cdot)$	$1$	$1$	$e\left(\frac{3242}{3465}\right)$	$e\left(\frac{1223}{3465}\right)$	$e\left(\frac{58}{385}\right)$	$e\left(\frac{53}{55}\right)$	$e\left(\frac{520}{693}\right)$	$e\left(\frac{3019}{3465}\right)$	$e\left(\frac{3196}{3465}\right)$	$e\left(\frac{479}{495}\right)$	$e\left(\frac{1147}{1155}\right)$	$e\left(\frac{1079}{3465}\right)$
$\chi_{640332}(13225,\cdot)$	$1$	$1$	$e\left(\frac{548}{3465}\right)$	$e\left(\frac{3272}{3465}\right)$	$e\left(\frac{277}{385}\right)$	$e\left(\frac{17}{55}\right)$	$e\left(\frac{46}{693}\right)$	$e\left(\frac{1096}{3465}\right)$	$e\left(\frac{2479}{3465}\right)$	$e\left(\frac{26}{495}\right)$	$e\left(\frac{838}{1155}\right)$	$e\left(\frac{1031}{3465}\right)$
$\chi_{640332}(13381,\cdot)$	$1$	$1$	$e\left(\frac{874}{3465}\right)$	$e\left(\frac{3271}{3465}\right)$	$e\left(\frac{61}{385}\right)$	$e\left(\frac{51}{55}\right)$	$e\left(\frac{215}{693}\right)$	$e\left(\frac{1748}{3465}\right)$	$e\left(\frac{122}{3465}\right)$	$e\left(\frac{298}{495}\right)$	$e\left(\frac{974}{1155}\right)$	$e\left(\frac{13}{3465}\right)$

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	\(-1\)	\(1\)	\(5\)	\(13\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)	\(37\)	\(41\)
\(\chi_{640332}(25,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1348}{3465}\right)\)	\(e\left(\frac{3142}{3465}\right)\)	\(e\left(\frac{302}{385}\right)\)	\(e\left(\frac{37}{55}\right)\)	\(e\left(\frac{533}{693}\right)\)	\(e\left(\frac{2696}{3465}\right)\)	\(e\left(\frac{989}{3465}\right)\)	\(e\left(\frac{241}{495}\right)\)	\(e\left(\frac{38}{1155}\right)\)	\(e\left(\frac{361}{3465}\right)\)
\(\chi_{640332}(625,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2696}{3465}\right)\)	\(e\left(\frac{2819}{3465}\right)\)	\(e\left(\frac{219}{385}\right)\)	\(e\left(\frac{19}{55}\right)\)	\(e\left(\frac{373}{693}\right)\)	\(e\left(\frac{1927}{3465}\right)\)	\(e\left(\frac{1978}{3465}\right)\)	\(e\left(\frac{482}{495}\right)\)	\(e\left(\frac{76}{1155}\right)\)	\(e\left(\frac{722}{3465}\right)\)
\(\chi_{640332}(1285,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1711}{3465}\right)\)	\(e\left(\frac{3109}{3465}\right)\)	\(e\left(\frac{104}{385}\right)\)	\(e\left(\frac{4}{55}\right)\)	\(e\left(\frac{566}{693}\right)\)	\(e\left(\frac{3422}{3465}\right)\)	\(e\left(\frac{2903}{3465}\right)\)	\(e\left(\frac{307}{495}\right)\)	\(e\left(\frac{1061}{1155}\right)\)	\(e\left(\frac{1417}{3465}\right)\)
\(\chi_{640332}(1633,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1244}{3465}\right)\)	\(e\left(\frac{2951}{3465}\right)\)	\(e\left(\frac{241}{385}\right)\)	\(e\left(\frac{41}{55}\right)\)	\(e\left(\frac{241}{693}\right)\)	\(e\left(\frac{2488}{3465}\right)\)	\(e\left(\frac{1252}{3465}\right)\)	\(e\left(\frac{218}{495}\right)\)	\(e\left(\frac{604}{1155}\right)\)	\(e\left(\frac{3428}{3465}\right)\)
\(\chi_{640332}(1885,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1007}{3465}\right)\)	\(e\left(\frac{1283}{3465}\right)\)	\(e\left(\frac{313}{385}\right)\)	\(e\left(\frac{48}{55}\right)\)	\(e\left(\frac{82}{693}\right)\)	\(e\left(\frac{2014}{3465}\right)\)	\(e\left(\frac{2551}{3465}\right)\)	\(e\left(\frac{494}{495}\right)\)	\(e\left(\frac{1072}{1155}\right)\)	\(e\left(\frac{3254}{3465}\right)\)
\(\chi_{640332}(2293,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{439}{3465}\right)\)	\(e\left(\frac{1306}{3465}\right)\)	\(e\left(\frac{276}{385}\right)\)	\(e\left(\frac{36}{55}\right)\)	\(e\left(\frac{353}{693}\right)\)	\(e\left(\frac{878}{3465}\right)\)	\(e\left(\frac{1322}{3465}\right)\)	\(e\left(\frac{178}{495}\right)\)	\(e\left(\frac{254}{1155}\right)\)	\(e\left(\frac{2413}{3465}\right)\)
\(\chi_{640332}(2545,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3397}{3465}\right)\)	\(e\left(\frac{808}{3465}\right)\)	\(e\left(\frac{123}{385}\right)\)	\(e\left(\frac{28}{55}\right)\)	\(e\left(\frac{662}{693}\right)\)	\(e\left(\frac{3329}{3465}\right)\)	\(e\left(\frac{2171}{3465}\right)\)	\(e\left(\frac{4}{495}\right)\)	\(e\left(\frac{992}{1155}\right)\)	\(e\left(\frac{1339}{3465}\right)\)
\(\chi_{640332}(2797,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1378}{3465}\right)\)	\(e\left(\frac{3397}{3465}\right)\)	\(e\left(\frac{327}{385}\right)\)	\(e\left(\frac{2}{55}\right)\)	\(e\left(\frac{404}{693}\right)\)	\(e\left(\frac{2756}{3465}\right)\)	\(e\left(\frac{2579}{3465}\right)\)	\(e\left(\frac{181}{495}\right)\)	\(e\left(\frac{8}{1155}\right)\)	\(e\left(\frac{76}{3465}\right)\)
\(\chi_{640332}(4057,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3316}{3465}\right)\)	\(e\left(\frac{1159}{3465}\right)\)	\(e\left(\frac{94}{385}\right)\)	\(e\left(\frac{29}{55}\right)\)	\(e\left(\frac{248}{693}\right)\)	\(e\left(\frac{3167}{3465}\right)\)	\(e\left(\frac{1343}{3465}\right)\)	\(e\left(\frac{67}{495}\right)\)	\(e\left(\frac{611}{1155}\right)\)	\(e\left(\frac{1762}{3465}\right)\)
\(\chi_{640332}(4405,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1724}{3465}\right)\)	\(e\left(\frac{101}{3465}\right)\)	\(e\left(\frac{256}{385}\right)\)	\(e\left(\frac{31}{55}\right)\)	\(e\left(\frac{256}{693}\right)\)	\(e\left(\frac{3448}{3465}\right)\)	\(e\left(\frac{2437}{3465}\right)\)	\(e\left(\frac{248}{495}\right)\)	\(e\left(\frac{124}{1155}\right)\)	\(e\left(\frac{2333}{3465}\right)\)
\(\chi_{640332}(4657,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2432}{3465}\right)\)	\(e\left(\frac{1268}{3465}\right)\)	\(e\left(\frac{153}{385}\right)\)	\(e\left(\frac{8}{55}\right)\)	\(e\left(\frac{538}{693}\right)\)	\(e\left(\frac{1399}{3465}\right)\)	\(e\left(\frac{1846}{3465}\right)\)	\(e\left(\frac{119}{495}\right)\)	\(e\left(\frac{802}{1155}\right)\)	\(e\left(\frac{1844}{3465}\right)\)
\(\chi_{640332}(4909,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1943}{3465}\right)\)	\(e\left(\frac{3002}{3465}\right)\)	\(e\left(\frac{92}{385}\right)\)	\(e\left(\frac{12}{55}\right)\)	\(e\left(\frac{631}{693}\right)\)	\(e\left(\frac{421}{3465}\right)\)	\(e\left(\frac{184}{3465}\right)\)	\(e\left(\frac{206}{495}\right)\)	\(e\left(\frac{598}{1155}\right)\)	\(e\left(\frac{3371}{3465}\right)\)
\(\chi_{640332}(5317,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1852}{3465}\right)\)	\(e\left(\frac{3268}{3465}\right)\)	\(e\left(\frac{183}{385}\right)\)	\(e\left(\frac{43}{55}\right)\)	\(e\left(\frac{29}{693}\right)\)	\(e\left(\frac{239}{3465}\right)\)	\(e\left(\frac{3446}{3465}\right)\)	\(e\left(\frac{124}{495}\right)\)	\(e\left(\frac{227}{1155}\right)\)	\(e\left(\frac{424}{3465}\right)\)
\(\chi_{640332}(6169,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1451}{3465}\right)\)	\(e\left(\frac{899}{3465}\right)\)	\(e\left(\frac{144}{385}\right)\)	\(e\left(\frac{14}{55}\right)\)	\(e\left(\frac{529}{693}\right)\)	\(e\left(\frac{2902}{3465}\right)\)	\(e\left(\frac{1828}{3465}\right)\)	\(e\left(\frac{2}{495}\right)\)	\(e\left(\frac{166}{1155}\right)\)	\(e\left(\frac{422}{3465}\right)\)
\(\chi_{640332}(7177,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2204}{3465}\right)\)	\(e\left(\frac{716}{3465}\right)\)	\(e\left(\frac{271}{385}\right)\)	\(e\left(\frac{21}{55}\right)\)	\(e\left(\frac{271}{693}\right)\)	\(e\left(\frac{943}{3465}\right)\)	\(e\left(\frac{157}{3465}\right)\)	\(e\left(\frac{278}{495}\right)\)	\(e\left(\frac{799}{1155}\right)\)	\(e\left(\frac{1238}{3465}\right)\)
\(\chi_{640332}(7681,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1478}{3465}\right)\)	\(e\left(\frac{782}{3465}\right)\)	\(e\left(\frac{282}{385}\right)\)	\(e\left(\frac{32}{55}\right)\)	\(e\left(\frac{205}{693}\right)\)	\(e\left(\frac{2956}{3465}\right)\)	\(e\left(\frac{3259}{3465}\right)\)	\(e\left(\frac{146}{495}\right)\)	\(e\left(\frac{1063}{1155}\right)\)	\(e\left(\frac{2591}{3465}\right)\)
\(\chi_{640332}(7837,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2389}{3465}\right)\)	\(e\left(\frac{556}{3465}\right)\)	\(e\left(\frac{361}{385}\right)\)	\(e\left(\frac{16}{55}\right)\)	\(e\left(\frac{284}{693}\right)\)	\(e\left(\frac{1313}{3465}\right)\)	\(e\left(\frac{722}{3465}\right)\)	\(e\left(\frac{238}{495}\right)\)	\(e\left(\frac{614}{1155}\right)\)	\(e\left(\frac{1213}{3465}\right)\)
\(\chi_{640332}(8089,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{307}{3465}\right)\)	\(e\left(\frac{2263}{3465}\right)\)	\(e\left(\frac{243}{385}\right)\)	\(e\left(\frac{3}{55}\right)\)	\(e\left(\frac{89}{693}\right)\)	\(e\left(\frac{614}{3465}\right)\)	\(e\left(\frac{1256}{3465}\right)\)	\(e\left(\frac{244}{495}\right)\)	\(e\left(\frac{617}{1155}\right)\)	\(e\left(\frac{2974}{3465}\right)\)
\(\chi_{640332}(8341,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1438}{3465}\right)\)	\(e\left(\frac{442}{3465}\right)\)	\(e\left(\frac{377}{385}\right)\)	\(e\left(\frac{42}{55}\right)\)	\(e\left(\frac{146}{693}\right)\)	\(e\left(\frac{2876}{3465}\right)\)	\(e\left(\frac{2294}{3465}\right)\)	\(e\left(\frac{61}{495}\right)\)	\(e\left(\frac{1103}{1155}\right)\)	\(e\left(\frac{2971}{3465}\right)\)
\(\chi_{640332}(8941,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2561}{3465}\right)\)	\(e\left(\frac{3404}{3465}\right)\)	\(e\left(\frac{299}{385}\right)\)	\(e\left(\frac{39}{55}\right)\)	\(e\left(\frac{607}{693}\right)\)	\(e\left(\frac{1657}{3465}\right)\)	\(e\left(\frac{1753}{3465}\right)\)	\(e\left(\frac{257}{495}\right)\)	\(e\left(\frac{211}{1155}\right)\)	\(e\left(\frac{272}{3465}\right)\)
\(\chi_{640332}(9601,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3061}{3465}\right)\)	\(e\left(\frac{724}{3465}\right)\)	\(e\left(\frac{74}{385}\right)\)	\(e\left(\frac{24}{55}\right)\)	\(e\left(\frac{305}{693}\right)\)	\(e\left(\frac{2657}{3465}\right)\)	\(e\left(\frac{1688}{3465}\right)\)	\(e\left(\frac{82}{495}\right)\)	\(e\left(\frac{866}{1155}\right)\)	\(e\left(\frac{2452}{3465}\right)\)
\(\chi_{640332}(10201,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1817}{3465}\right)\)	\(e\left(\frac{1238}{3465}\right)\)	\(e\left(\frac{218}{385}\right)\)	\(e\left(\frac{38}{55}\right)\)	\(e\left(\frac{64}{693}\right)\)	\(e\left(\frac{169}{3465}\right)\)	\(e\left(\frac{436}{3465}\right)\)	\(e\left(\frac{359}{495}\right)\)	\(e\left(\frac{262}{1155}\right)\)	\(e\left(\frac{2489}{3465}\right)\)
\(\chi_{640332}(10453,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1013}{3465}\right)\)	\(e\left(\frac{2027}{3465}\right)\)	\(e\left(\frac{87}{385}\right)\)	\(e\left(\frac{52}{55}\right)\)	\(e\left(\frac{472}{693}\right)\)	\(e\left(\frac{2026}{3465}\right)\)	\(e\left(\frac{2869}{3465}\right)\)	\(e\left(\frac{86}{495}\right)\)	\(e\left(\frac{373}{1155}\right)\)	\(e\left(\frac{1811}{3465}\right)\)
\(\chi_{640332}(10609,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3364}{3465}\right)\)	\(e\left(\frac{181}{3465}\right)\)	\(e\left(\frac{211}{385}\right)\)	\(e\left(\frac{6}{55}\right)\)	\(e\left(\frac{596}{693}\right)\)	\(e\left(\frac{3263}{3465}\right)\)	\(e\left(\frac{422}{3465}\right)\)	\(e\left(\frac{268}{495}\right)\)	\(e\left(\frac{794}{1155}\right)\)	\(e\left(\frac{613}{3465}\right)\)
\(\chi_{640332}(10861,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2227}{3465}\right)\)	\(e\left(\frac{1258}{3465}\right)\)	\(e\left(\frac{303}{385}\right)\)	\(e\left(\frac{18}{55}\right)\)	\(e\left(\frac{149}{693}\right)\)	\(e\left(\frac{989}{3465}\right)\)	\(e\left(\frac{2531}{3465}\right)\)	\(e\left(\frac{364}{495}\right)\)	\(e\left(\frac{1007}{1155}\right)\)	\(e\left(\frac{2059}{3465}\right)\)
\(\chi_{640332}(11113,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1468}{3465}\right)\)	\(e\left(\frac{697}{3465}\right)\)	\(e\left(\frac{17}{385}\right)\)	\(e\left(\frac{7}{55}\right)\)	\(e\left(\frac{17}{693}\right)\)	\(e\left(\frac{2936}{3465}\right)\)	\(e\left(\frac{419}{3465}\right)\)	\(e\left(\frac{1}{495}\right)\)	\(e\left(\frac{1073}{1155}\right)\)	\(e\left(\frac{2686}{3465}\right)\)
\(\chi_{640332}(11713,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{206}{3465}\right)\)	\(e\left(\frac{2444}{3465}\right)\)	\(e\left(\frac{69}{385}\right)\)	\(e\left(\frac{9}{55}\right)\)	\(e\left(\frac{685}{693}\right)\)	\(e\left(\frac{412}{3465}\right)\)	\(e\left(\frac{1678}{3465}\right)\)	\(e\left(\frac{17}{495}\right)\)	\(e\left(\frac{256}{1155}\right)\)	\(e\left(\frac{122}{3465}\right)\)
\(\chi_{640332}(12373,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1201}{3465}\right)\)	\(e\left(\frac{2239}{3465}\right)\)	\(e\left(\frac{64}{385}\right)\)	\(e\left(\frac{49}{55}\right)\)	\(e\left(\frac{680}{693}\right)\)	\(e\left(\frac{2402}{3465}\right)\)	\(e\left(\frac{128}{3465}\right)\)	\(e\left(\frac{337}{495}\right)\)	\(e\left(\frac{416}{1155}\right)\)	\(e\left(\frac{2797}{3465}\right)\)
\(\chi_{640332}(12973,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3242}{3465}\right)\)	\(e\left(\frac{1223}{3465}\right)\)	\(e\left(\frac{58}{385}\right)\)	\(e\left(\frac{53}{55}\right)\)	\(e\left(\frac{520}{693}\right)\)	\(e\left(\frac{3019}{3465}\right)\)	\(e\left(\frac{3196}{3465}\right)\)	\(e\left(\frac{479}{495}\right)\)	\(e\left(\frac{1147}{1155}\right)\)	\(e\left(\frac{1079}{3465}\right)\)
\(\chi_{640332}(13225,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{548}{3465}\right)\)	\(e\left(\frac{3272}{3465}\right)\)	\(e\left(\frac{277}{385}\right)\)	\(e\left(\frac{17}{55}\right)\)	\(e\left(\frac{46}{693}\right)\)	\(e\left(\frac{1096}{3465}\right)\)	\(e\left(\frac{2479}{3465}\right)\)	\(e\left(\frac{26}{495}\right)\)	\(e\left(\frac{838}{1155}\right)\)	\(e\left(\frac{1031}{3465}\right)\)
\(\chi_{640332}(13381,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{874}{3465}\right)\)	\(e\left(\frac{3271}{3465}\right)\)	\(e\left(\frac{61}{385}\right)\)	\(e\left(\frac{51}{55}\right)\)	\(e\left(\frac{215}{693}\right)\)	\(e\left(\frac{1748}{3465}\right)\)	\(e\left(\frac{122}{3465}\right)\)	\(e\left(\frac{298}{495}\right)\)	\(e\left(\frac{974}{1155}\right)\)	\(e\left(\frac{13}{3465}\right)\)

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First 31 of 1440 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.blo
Modulus	$640332$
Conductor	$160083$
Order	$3465$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(640332\)
Conductor:	\(160083\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(3465\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 160083.sw	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)