LMFDB - Dirichlet character orbit 40310.fx

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(40310, base_ring=CyclotomicField(1932)) M = H._module chi = DirichletCharacter(H, M([483,828,700])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(7,40310)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$40310$
Conductor:	$20155$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$1932$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 20155.fy	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	odd	sage:chi.is_odd() pari:zncharisodd(g,chi)

Related number fields

Field of values:	$\Q(\zeta_{1932})$
Fixed field:	Number field defined by a degree 1932 polynomial (not computed)

First 24 of 528 characters in Galois orbit

Character	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$17$	$19$	$21$	$23$	$27$
$\chi_{40310}(7,\cdot)$	$-1$	$1$	$e\left(\frac{1445}{1932}\right)$	$e\left(\frac{983}{1932}\right)$	$e\left(\frac{479}{966}\right)$	$e\left(\frac{121}{483}\right)$	$e\left(\frac{1261}{1932}\right)$	$e\left(\frac{5}{276}\right)$	$e\left(\frac{443}{966}\right)$	$e\left(\frac{124}{483}\right)$	$e\left(\frac{67}{644}\right)$	$e\left(\frac{157}{644}\right)$
$\chi_{40310}(83,\cdot)$	$-1$	$1$	$e\left(\frac{683}{1932}\right)$	$e\left(\frac{1565}{1932}\right)$	$e\left(\frac{683}{966}\right)$	$e\left(\frac{229}{483}\right)$	$e\left(\frac{223}{1932}\right)$	$e\left(\frac{95}{276}\right)$	$e\left(\frac{551}{966}\right)$	$e\left(\frac{79}{483}\right)$	$e\left(\frac{353}{644}\right)$	$e\left(\frac{39}{644}\right)$
$\chi_{40310}(107,\cdot)$	$-1$	$1$	$e\left(\frac{41}{1932}\right)$	$e\left(\frac{671}{1932}\right)$	$e\left(\frac{41}{966}\right)$	$e\left(\frac{88}{483}\right)$	$e\left(\frac{961}{1932}\right)$	$e\left(\frac{173}{276}\right)$	$e\left(\frac{893}{966}\right)$	$e\left(\frac{178}{483}\right)$	$e\left(\frac{239}{644}\right)$	$e\left(\frac{41}{644}\right)$
$\chi_{40310}(257,\cdot)$	$-1$	$1$	$e\left(\frac{277}{1932}\right)$	$e\left(\frac{151}{1932}\right)$	$e\left(\frac{277}{966}\right)$	$e\left(\frac{194}{483}\right)$	$e\left(\frac{461}{1932}\right)$	$e\left(\frac{85}{276}\right)$	$e\left(\frac{355}{966}\right)$	$e\left(\frac{107}{483}\right)$	$e\left(\frac{311}{644}\right)$	$e\left(\frac{277}{644}\right)$
$\chi_{40310}(313,\cdot)$	$-1$	$1$	$e\left(\frac{439}{1932}\right)$	$e\left(\frac{1153}{1932}\right)$	$e\left(\frac{439}{966}\right)$	$e\left(\frac{365}{483}\right)$	$e\left(\frac{347}{1932}\right)$	$e\left(\frac{55}{276}\right)$	$e\left(\frac{43}{966}\right)$	$e\left(\frac{398}{483}\right)$	$e\left(\frac{93}{644}\right)$	$e\left(\frac{439}{644}\right)$
$\chi_{40310}(567,\cdot)$	$-1$	$1$	$e\left(\frac{85}{1932}\right)$	$e\left(\frac{967}{1932}\right)$	$e\left(\frac{85}{966}\right)$	$e\left(\frac{206}{483}\right)$	$e\left(\frac{1097}{1932}\right)$	$e\left(\frac{49}{276}\right)$	$e\left(\frac{367}{966}\right)$	$e\left(\frac{263}{483}\right)$	$e\left(\frac{307}{644}\right)$	$e\left(\frac{85}{644}\right)$
$\chi_{40310}(587,\cdot)$	$-1$	$1$	$e\left(\frac{1025}{1932}\right)$	$e\left(\frac{1319}{1932}\right)$	$e\left(\frac{59}{966}\right)$	$e\left(\frac{268}{483}\right)$	$e\left(\frac{841}{1932}\right)$	$e\left(\frac{185}{276}\right)$	$e\left(\frac{107}{966}\right)$	$e\left(\frac{103}{483}\right)$	$e\left(\frac{179}{644}\right)$	$e\left(\frac{381}{644}\right)$
$\chi_{40310}(603,\cdot)$	$-1$	$1$	$e\left(\frac{1811}{1932}\right)$	$e\left(\frac{1601}{1932}\right)$	$e\left(\frac{845}{966}\right)$	$e\left(\frac{400}{483}\right)$	$e\left(\frac{1075}{1932}\right)$	$e\left(\frac{203}{276}\right)$	$e\left(\frac{239}{966}\right)$	$e\left(\frac{370}{483}\right)$	$e\left(\frac{457}{644}\right)$	$e\left(\frac{523}{644}\right)$
$\chi_{40310}(663,\cdot)$	$-1$	$1$	$e\left(\frac{179}{1932}\right)$	$e\left(\frac{809}{1932}\right)$	$e\left(\frac{179}{966}\right)$	$e\left(\frac{19}{483}\right)$	$e\left(\frac{1651}{1932}\right)$	$e\left(\frac{35}{276}\right)$	$e\left(\frac{341}{966}\right)$	$e\left(\frac{247}{483}\right)$	$e\left(\frac{101}{644}\right)$	$e\left(\frac{179}{644}\right)$
$\chi_{40310}(683,\cdot)$	$-1$	$1$	$e\left(\frac{463}{1932}\right)$	$e\left(\frac{85}{1932}\right)$	$e\left(\frac{463}{966}\right)$	$e\left(\frac{122}{483}\right)$	$e\left(\frac{1475}{1932}\right)$	$e\left(\frac{163}{276}\right)$	$e\left(\frac{283}{966}\right)$	$e\left(\frac{137}{483}\right)$	$e\left(\frac{13}{644}\right)$	$e\left(\frac{463}{644}\right)$
$\chi_{40310}(923,\cdot)$	$-1$	$1$	$e\left(\frac{1115}{1932}\right)$	$e\left(\frac{1661}{1932}\right)$	$e\left(\frac{149}{966}\right)$	$e\left(\frac{202}{483}\right)$	$e\left(\frac{1207}{1932}\right)$	$e\left(\frac{107}{276}\right)$	$e\left(\frac{41}{966}\right)$	$e\left(\frac{211}{483}\right)$	$e\left(\frac{201}{644}\right)$	$e\left(\frac{471}{644}\right)$
$\chi_{40310}(977,\cdot)$	$-1$	$1$	$e\left(\frac{1217}{1932}\right)$	$e\left(\frac{503}{1932}\right)$	$e\left(\frac{251}{966}\right)$	$e\left(\frac{256}{483}\right)$	$e\left(\frac{205}{1932}\right)$	$e\left(\frac{221}{276}\right)$	$e\left(\frac{95}{966}\right)$	$e\left(\frac{430}{483}\right)$	$e\left(\frac{183}{644}\right)$	$e\left(\frac{573}{644}\right)$
$\chi_{40310}(993,\cdot)$	$-1$	$1$	$e\left(\frac{1039}{1932}\right)$	$e\left(\frac{1501}{1932}\right)$	$e\left(\frac{73}{966}\right)$	$e\left(\frac{86}{483}\right)$	$e\left(\frac{1499}{1932}\right)$	$e\left(\frac{271}{276}\right)$	$e\left(\frac{247}{966}\right)$	$e\left(\frac{152}{483}\right)$	$e\left(\frac{25}{644}\right)$	$e\left(\frac{395}{644}\right)$
$\chi_{40310}(1093,\cdot)$	$-1$	$1$	$e\left(\frac{307}{1932}\right)$	$e\left(\frac{265}{1932}\right)$	$e\left(\frac{307}{966}\right)$	$e\left(\frac{11}{483}\right)$	$e\left(\frac{1871}{1932}\right)$	$e\left(\frac{151}{276}\right)$	$e\left(\frac{655}{966}\right)$	$e\left(\frac{143}{483}\right)$	$e\left(\frac{533}{644}\right)$	$e\left(\frac{307}{644}\right)$
$\chi_{40310}(1097,\cdot)$	$-1$	$1$	$e\left(\frac{793}{1932}\right)$	$e\left(\frac{1339}{1932}\right)$	$e\left(\frac{793}{966}\right)$	$e\left(\frac{41}{483}\right)$	$e\left(\frac{1529}{1932}\right)$	$e\left(\frac{61}{276}\right)$	$e\left(\frac{685}{966}\right)$	$e\left(\frac{50}{483}\right)$	$e\left(\frac{523}{644}\right)$	$e\left(\frac{149}{644}\right)$
$\chi_{40310}(1147,\cdot)$	$-1$	$1$	$e\left(\frac{1681}{1932}\right)$	$e\left(\frac{463}{1932}\right)$	$e\left(\frac{715}{966}\right)$	$e\left(\frac{227}{483}\right)$	$e\left(\frac{761}{1932}\right)$	$e\left(\frac{193}{276}\right)$	$e\left(\frac{871}{966}\right)$	$e\left(\frac{53}{483}\right)$	$e\left(\frac{139}{644}\right)$	$e\left(\frac{393}{644}\right)$
$\chi_{40310}(1183,\cdot)$	$-1$	$1$	$e\left(\frac{1363}{1932}\right)$	$e\left(\frac{1573}{1932}\right)$	$e\left(\frac{397}{966}\right)$	$e\left(\frac{428}{483}\right)$	$e\left(\frac{1271}{1932}\right)$	$e\left(\frac{211}{276}\right)$	$e\left(\frac{589}{966}\right)$	$e\left(\frac{251}{483}\right)$	$e\left(\frac{233}{644}\right)$	$e\left(\frac{75}{644}\right)$
$\chi_{40310}(1267,\cdot)$	$-1$	$1$	$e\left(\frac{433}{1932}\right)$	$e\left(\frac{1903}{1932}\right)$	$e\left(\frac{433}{966}\right)$	$e\left(\frac{305}{483}\right)$	$e\left(\frac{65}{1932}\right)$	$e\left(\frac{97}{276}\right)$	$e\left(\frac{949}{966}\right)$	$e\left(\frac{101}{483}\right)$	$e\left(\frac{435}{644}\right)$	$e\left(\frac{433}{644}\right)$
$\chi_{40310}(1387,\cdot)$	$-1$	$1$	$e\left(\frac{1661}{1932}\right)$	$e\left(\frac{1031}{1932}\right)$	$e\left(\frac{695}{966}\right)$	$e\left(\frac{349}{483}\right)$	$e\left(\frac{1753}{1932}\right)$	$e\left(\frac{149}{276}\right)$	$e\left(\frac{671}{966}\right)$	$e\left(\frac{190}{483}\right)$	$e\left(\frac{635}{644}\right)$	$e\left(\frac{373}{644}\right)$
$\chi_{40310}(1437,\cdot)$	$-1$	$1$	$e\left(\frac{1121}{1932}\right)$	$e\left(\frac{911}{1932}\right)$	$e\left(\frac{155}{966}\right)$	$e\left(\frac{262}{483}\right)$	$e\left(\frac{1489}{1932}\right)$	$e\left(\frac{65}{276}\right)$	$e\left(\frac{101}{966}\right)$	$e\left(\frac{25}{483}\right)$	$e\left(\frac{503}{644}\right)$	$e\left(\frac{477}{644}\right)$
$\chi_{40310}(1457,\cdot)$	$-1$	$1$	$e\left(\frac{1249}{1932}\right)$	$e\left(\frac{367}{1932}\right)$	$e\left(\frac{283}{966}\right)$	$e\left(\frac{254}{483}\right)$	$e\left(\frac{1709}{1932}\right)$	$e\left(\frac{181}{276}\right)$	$e\left(\frac{415}{966}\right)$	$e\left(\frac{404}{483}\right)$	$e\left(\frac{291}{644}\right)$	$e\left(\frac{605}{644}\right)$
$\chi_{40310}(1473,\cdot)$	$-1$	$1$	$e\left(\frac{131}{1932}\right)$	$e\left(\frac{1013}{1932}\right)$	$e\left(\frac{131}{966}\right)$	$e\left(\frac{22}{483}\right)$	$e\left(\frac{1327}{1932}\right)$	$e\left(\frac{95}{276}\right)$	$e\left(\frac{827}{966}\right)$	$e\left(\frac{286}{483}\right)$	$e\left(\frac{261}{644}\right)$	$e\left(\frac{131}{644}\right)$
$\chi_{40310}(1503,\cdot)$	$-1$	$1$	$e\left(\frac{947}{1932}\right)$	$e\left(\frac{1409}{1932}\right)$	$e\left(\frac{947}{966}\right)$	$e\left(\frac{454}{483}\right)$	$e\left(\frac{1039}{1932}\right)$	$e\left(\frac{179}{276}\right)$	$e\left(\frac{293}{966}\right)$	$e\left(\frac{106}{483}\right)$	$e\left(\frac{117}{644}\right)$	$e\left(\frac{303}{644}\right)$
$\chi_{40310}(1533,\cdot)$	$-1$	$1$	$e\left(\frac{1355}{1932}\right)$	$e\left(\frac{641}{1932}\right)$	$e\left(\frac{389}{966}\right)$	$e\left(\frac{187}{483}\right)$	$e\left(\frac{895}{1932}\right)$	$e\left(\frac{83}{276}\right)$	$e\left(\frac{509}{966}\right)$	$e\left(\frac{16}{483}\right)$	$e\left(\frac{45}{644}\right)$	$e\left(\frac{67}{644}\right)$

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	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(13\)	\(17\)	\(19\)	\(21\)	\(23\)	\(27\)
\(\chi_{40310}(7,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1445}{1932}\right)\)	\(e\left(\frac{983}{1932}\right)\)	\(e\left(\frac{479}{966}\right)\)	\(e\left(\frac{121}{483}\right)\)	\(e\left(\frac{1261}{1932}\right)\)	\(e\left(\frac{5}{276}\right)\)	\(e\left(\frac{443}{966}\right)\)	\(e\left(\frac{124}{483}\right)\)	\(e\left(\frac{67}{644}\right)\)	\(e\left(\frac{157}{644}\right)\)
\(\chi_{40310}(83,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{683}{1932}\right)\)	\(e\left(\frac{1565}{1932}\right)\)	\(e\left(\frac{683}{966}\right)\)	\(e\left(\frac{229}{483}\right)\)	\(e\left(\frac{223}{1932}\right)\)	\(e\left(\frac{95}{276}\right)\)	\(e\left(\frac{551}{966}\right)\)	\(e\left(\frac{79}{483}\right)\)	\(e\left(\frac{353}{644}\right)\)	\(e\left(\frac{39}{644}\right)\)
\(\chi_{40310}(107,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{41}{1932}\right)\)	\(e\left(\frac{671}{1932}\right)\)	\(e\left(\frac{41}{966}\right)\)	\(e\left(\frac{88}{483}\right)\)	\(e\left(\frac{961}{1932}\right)\)	\(e\left(\frac{173}{276}\right)\)	\(e\left(\frac{893}{966}\right)\)	\(e\left(\frac{178}{483}\right)\)	\(e\left(\frac{239}{644}\right)\)	\(e\left(\frac{41}{644}\right)\)
\(\chi_{40310}(257,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{277}{1932}\right)\)	\(e\left(\frac{151}{1932}\right)\)	\(e\left(\frac{277}{966}\right)\)	\(e\left(\frac{194}{483}\right)\)	\(e\left(\frac{461}{1932}\right)\)	\(e\left(\frac{85}{276}\right)\)	\(e\left(\frac{355}{966}\right)\)	\(e\left(\frac{107}{483}\right)\)	\(e\left(\frac{311}{644}\right)\)	\(e\left(\frac{277}{644}\right)\)
\(\chi_{40310}(313,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{439}{1932}\right)\)	\(e\left(\frac{1153}{1932}\right)\)	\(e\left(\frac{439}{966}\right)\)	\(e\left(\frac{365}{483}\right)\)	\(e\left(\frac{347}{1932}\right)\)	\(e\left(\frac{55}{276}\right)\)	\(e\left(\frac{43}{966}\right)\)	\(e\left(\frac{398}{483}\right)\)	\(e\left(\frac{93}{644}\right)\)	\(e\left(\frac{439}{644}\right)\)
\(\chi_{40310}(567,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{85}{1932}\right)\)	\(e\left(\frac{967}{1932}\right)\)	\(e\left(\frac{85}{966}\right)\)	\(e\left(\frac{206}{483}\right)\)	\(e\left(\frac{1097}{1932}\right)\)	\(e\left(\frac{49}{276}\right)\)	\(e\left(\frac{367}{966}\right)\)	\(e\left(\frac{263}{483}\right)\)	\(e\left(\frac{307}{644}\right)\)	\(e\left(\frac{85}{644}\right)\)
\(\chi_{40310}(587,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1025}{1932}\right)\)	\(e\left(\frac{1319}{1932}\right)\)	\(e\left(\frac{59}{966}\right)\)	\(e\left(\frac{268}{483}\right)\)	\(e\left(\frac{841}{1932}\right)\)	\(e\left(\frac{185}{276}\right)\)	\(e\left(\frac{107}{966}\right)\)	\(e\left(\frac{103}{483}\right)\)	\(e\left(\frac{179}{644}\right)\)	\(e\left(\frac{381}{644}\right)\)
\(\chi_{40310}(603,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1811}{1932}\right)\)	\(e\left(\frac{1601}{1932}\right)\)	\(e\left(\frac{845}{966}\right)\)	\(e\left(\frac{400}{483}\right)\)	\(e\left(\frac{1075}{1932}\right)\)	\(e\left(\frac{203}{276}\right)\)	\(e\left(\frac{239}{966}\right)\)	\(e\left(\frac{370}{483}\right)\)	\(e\left(\frac{457}{644}\right)\)	\(e\left(\frac{523}{644}\right)\)
\(\chi_{40310}(663,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{179}{1932}\right)\)	\(e\left(\frac{809}{1932}\right)\)	\(e\left(\frac{179}{966}\right)\)	\(e\left(\frac{19}{483}\right)\)	\(e\left(\frac{1651}{1932}\right)\)	\(e\left(\frac{35}{276}\right)\)	\(e\left(\frac{341}{966}\right)\)	\(e\left(\frac{247}{483}\right)\)	\(e\left(\frac{101}{644}\right)\)	\(e\left(\frac{179}{644}\right)\)
\(\chi_{40310}(683,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{463}{1932}\right)\)	\(e\left(\frac{85}{1932}\right)\)	\(e\left(\frac{463}{966}\right)\)	\(e\left(\frac{122}{483}\right)\)	\(e\left(\frac{1475}{1932}\right)\)	\(e\left(\frac{163}{276}\right)\)	\(e\left(\frac{283}{966}\right)\)	\(e\left(\frac{137}{483}\right)\)	\(e\left(\frac{13}{644}\right)\)	\(e\left(\frac{463}{644}\right)\)
\(\chi_{40310}(923,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1115}{1932}\right)\)	\(e\left(\frac{1661}{1932}\right)\)	\(e\left(\frac{149}{966}\right)\)	\(e\left(\frac{202}{483}\right)\)	\(e\left(\frac{1207}{1932}\right)\)	\(e\left(\frac{107}{276}\right)\)	\(e\left(\frac{41}{966}\right)\)	\(e\left(\frac{211}{483}\right)\)	\(e\left(\frac{201}{644}\right)\)	\(e\left(\frac{471}{644}\right)\)
\(\chi_{40310}(977,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1217}{1932}\right)\)	\(e\left(\frac{503}{1932}\right)\)	\(e\left(\frac{251}{966}\right)\)	\(e\left(\frac{256}{483}\right)\)	\(e\left(\frac{205}{1932}\right)\)	\(e\left(\frac{221}{276}\right)\)	\(e\left(\frac{95}{966}\right)\)	\(e\left(\frac{430}{483}\right)\)	\(e\left(\frac{183}{644}\right)\)	\(e\left(\frac{573}{644}\right)\)
\(\chi_{40310}(993,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1039}{1932}\right)\)	\(e\left(\frac{1501}{1932}\right)\)	\(e\left(\frac{73}{966}\right)\)	\(e\left(\frac{86}{483}\right)\)	\(e\left(\frac{1499}{1932}\right)\)	\(e\left(\frac{271}{276}\right)\)	\(e\left(\frac{247}{966}\right)\)	\(e\left(\frac{152}{483}\right)\)	\(e\left(\frac{25}{644}\right)\)	\(e\left(\frac{395}{644}\right)\)
\(\chi_{40310}(1093,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{307}{1932}\right)\)	\(e\left(\frac{265}{1932}\right)\)	\(e\left(\frac{307}{966}\right)\)	\(e\left(\frac{11}{483}\right)\)	\(e\left(\frac{1871}{1932}\right)\)	\(e\left(\frac{151}{276}\right)\)	\(e\left(\frac{655}{966}\right)\)	\(e\left(\frac{143}{483}\right)\)	\(e\left(\frac{533}{644}\right)\)	\(e\left(\frac{307}{644}\right)\)
\(\chi_{40310}(1097,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{793}{1932}\right)\)	\(e\left(\frac{1339}{1932}\right)\)	\(e\left(\frac{793}{966}\right)\)	\(e\left(\frac{41}{483}\right)\)	\(e\left(\frac{1529}{1932}\right)\)	\(e\left(\frac{61}{276}\right)\)	\(e\left(\frac{685}{966}\right)\)	\(e\left(\frac{50}{483}\right)\)	\(e\left(\frac{523}{644}\right)\)	\(e\left(\frac{149}{644}\right)\)
\(\chi_{40310}(1147,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1681}{1932}\right)\)	\(e\left(\frac{463}{1932}\right)\)	\(e\left(\frac{715}{966}\right)\)	\(e\left(\frac{227}{483}\right)\)	\(e\left(\frac{761}{1932}\right)\)	\(e\left(\frac{193}{276}\right)\)	\(e\left(\frac{871}{966}\right)\)	\(e\left(\frac{53}{483}\right)\)	\(e\left(\frac{139}{644}\right)\)	\(e\left(\frac{393}{644}\right)\)
\(\chi_{40310}(1183,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1363}{1932}\right)\)	\(e\left(\frac{1573}{1932}\right)\)	\(e\left(\frac{397}{966}\right)\)	\(e\left(\frac{428}{483}\right)\)	\(e\left(\frac{1271}{1932}\right)\)	\(e\left(\frac{211}{276}\right)\)	\(e\left(\frac{589}{966}\right)\)	\(e\left(\frac{251}{483}\right)\)	\(e\left(\frac{233}{644}\right)\)	\(e\left(\frac{75}{644}\right)\)
\(\chi_{40310}(1267,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{433}{1932}\right)\)	\(e\left(\frac{1903}{1932}\right)\)	\(e\left(\frac{433}{966}\right)\)	\(e\left(\frac{305}{483}\right)\)	\(e\left(\frac{65}{1932}\right)\)	\(e\left(\frac{97}{276}\right)\)	\(e\left(\frac{949}{966}\right)\)	\(e\left(\frac{101}{483}\right)\)	\(e\left(\frac{435}{644}\right)\)	\(e\left(\frac{433}{644}\right)\)
\(\chi_{40310}(1387,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1661}{1932}\right)\)	\(e\left(\frac{1031}{1932}\right)\)	\(e\left(\frac{695}{966}\right)\)	\(e\left(\frac{349}{483}\right)\)	\(e\left(\frac{1753}{1932}\right)\)	\(e\left(\frac{149}{276}\right)\)	\(e\left(\frac{671}{966}\right)\)	\(e\left(\frac{190}{483}\right)\)	\(e\left(\frac{635}{644}\right)\)	\(e\left(\frac{373}{644}\right)\)
\(\chi_{40310}(1437,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1121}{1932}\right)\)	\(e\left(\frac{911}{1932}\right)\)	\(e\left(\frac{155}{966}\right)\)	\(e\left(\frac{262}{483}\right)\)	\(e\left(\frac{1489}{1932}\right)\)	\(e\left(\frac{65}{276}\right)\)	\(e\left(\frac{101}{966}\right)\)	\(e\left(\frac{25}{483}\right)\)	\(e\left(\frac{503}{644}\right)\)	\(e\left(\frac{477}{644}\right)\)
\(\chi_{40310}(1457,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1249}{1932}\right)\)	\(e\left(\frac{367}{1932}\right)\)	\(e\left(\frac{283}{966}\right)\)	\(e\left(\frac{254}{483}\right)\)	\(e\left(\frac{1709}{1932}\right)\)	\(e\left(\frac{181}{276}\right)\)	\(e\left(\frac{415}{966}\right)\)	\(e\left(\frac{404}{483}\right)\)	\(e\left(\frac{291}{644}\right)\)	\(e\left(\frac{605}{644}\right)\)
\(\chi_{40310}(1473,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{131}{1932}\right)\)	\(e\left(\frac{1013}{1932}\right)\)	\(e\left(\frac{131}{966}\right)\)	\(e\left(\frac{22}{483}\right)\)	\(e\left(\frac{1327}{1932}\right)\)	\(e\left(\frac{95}{276}\right)\)	\(e\left(\frac{827}{966}\right)\)	\(e\left(\frac{286}{483}\right)\)	\(e\left(\frac{261}{644}\right)\)	\(e\left(\frac{131}{644}\right)\)
\(\chi_{40310}(1503,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{947}{1932}\right)\)	\(e\left(\frac{1409}{1932}\right)\)	\(e\left(\frac{947}{966}\right)\)	\(e\left(\frac{454}{483}\right)\)	\(e\left(\frac{1039}{1932}\right)\)	\(e\left(\frac{179}{276}\right)\)	\(e\left(\frac{293}{966}\right)\)	\(e\left(\frac{106}{483}\right)\)	\(e\left(\frac{117}{644}\right)\)	\(e\left(\frac{303}{644}\right)\)
\(\chi_{40310}(1533,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1355}{1932}\right)\)	\(e\left(\frac{641}{1932}\right)\)	\(e\left(\frac{389}{966}\right)\)	\(e\left(\frac{187}{483}\right)\)	\(e\left(\frac{895}{1932}\right)\)	\(e\left(\frac{83}{276}\right)\)	\(e\left(\frac{509}{966}\right)\)	\(e\left(\frac{16}{483}\right)\)	\(e\left(\frac{45}{644}\right)\)	\(e\left(\frac{67}{644}\right)\)

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First 24 of 528 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	40310.fx
Modulus	$40310$
Conductor	$20155$
Order	$1932$
Real	no
Primitive	no
Minimal	yes
Parity	odd

Modulus:	\(40310\)
Conductor:	\(20155\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(1932\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 20155.fy	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	odd	sage:chi.is_odd() pari:zncharisodd(g,chi)