LMFDB - Dirichlet character orbit 40310.fs

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(40310, base_ring=CyclotomicField(1932)) M = H._module chi = DirichletCharacter(H, M([483,207,1120])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(37,40310)) 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.gc	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:	$\Q(\zeta_{1932})$
Fixed field:	Number field defined by a degree 1932 polynomial (not computed)

First 21 of 528 characters in Galois orbit

Character	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$17$	$19$	$21$	$23$	$27$
$\chi_{40310}(37,\cdot)$	$1$	$1$	$e\left(\frac{26}{483}\right)$	$e\left(\frac{1007}{1932}\right)$	$e\left(\frac{52}{483}\right)$	$e\left(\frac{1423}{1932}\right)$	$e\left(\frac{1507}{1932}\right)$	$e\left(\frac{73}{138}\right)$	$e\left(\frac{1597}{1932}\right)$	$e\left(\frac{1111}{1932}\right)$	$e\left(\frac{351}{644}\right)$	$e\left(\frac{26}{161}\right)$
$\chi_{40310}(47,\cdot)$	$1$	$1$	$e\left(\frac{401}{483}\right)$	$e\left(\frac{911}{1932}\right)$	$e\left(\frac{319}{483}\right)$	$e\left(\frac{1531}{1932}\right)$	$e\left(\frac{523}{1932}\right)$	$e\left(\frac{67}{138}\right)$	$e\left(\frac{685}{1932}\right)$	$e\left(\frac{583}{1932}\right)$	$e\left(\frac{503}{644}\right)$	$e\left(\frac{79}{161}\right)$
$\chi_{40310}(193,\cdot)$	$1$	$1$	$e\left(\frac{337}{483}\right)$	$e\left(\frac{1033}{1932}\right)$	$e\left(\frac{191}{483}\right)$	$e\left(\frac{629}{1932}\right)$	$e\left(\frac{1049}{1932}\right)$	$e\left(\frac{89}{138}\right)$	$e\left(\frac{395}{1932}\right)$	$e\left(\frac{449}{1932}\right)$	$e\left(\frac{605}{644}\right)$	$e\left(\frac{15}{161}\right)$
$\chi_{40310}(263,\cdot)$	$1$	$1$	$e\left(\frac{319}{483}\right)$	$e\left(\frac{373}{1932}\right)$	$e\left(\frac{155}{483}\right)$	$e\left(\frac{1613}{1932}\right)$	$e\left(\frac{1529}{1932}\right)$	$e\left(\frac{65}{138}\right)$	$e\left(\frac{887}{1932}\right)$	$e\left(\frac{1649}{1932}\right)$	$e\left(\frac{201}{644}\right)$	$e\left(\frac{158}{161}\right)$
$\chi_{40310}(287,\cdot)$	$1$	$1$	$e\left(\frac{244}{483}\right)$	$e\left(\frac{199}{1932}\right)$	$e\left(\frac{5}{483}\right)$	$e\left(\frac{239}{1932}\right)$	$e\left(\frac{1919}{1932}\right)$	$e\left(\frac{11}{138}\right)$	$e\left(\frac{1649}{1932}\right)$	$e\left(\frac{1175}{1932}\right)$	$e\left(\frac{235}{644}\right)$	$e\left(\frac{83}{161}\right)$
$\chi_{40310}(327,\cdot)$	$1$	$1$	$e\left(\frac{481}{483}\right)$	$e\left(\frac{1483}{1932}\right)$	$e\left(\frac{479}{483}\right)$	$e\left(\frac{1451}{1932}\right)$	$e\left(\frac{107}{1932}\right)$	$e\left(\frac{5}{138}\right)$	$e\left(\frac{1289}{1932}\right)$	$e\left(\frac{1475}{1932}\right)$	$e\left(\frac{295}{644}\right)$	$e\left(\frac{159}{161}\right)$
$\chi_{40310}(483,\cdot)$	$1$	$1$	$e\left(\frac{442}{483}\right)$	$e\left(\frac{697}{1932}\right)$	$e\left(\frac{401}{483}\right)$	$e\left(\frac{41}{1932}\right)$	$e\left(\frac{1469}{1932}\right)$	$e\left(\frac{137}{138}\right)$	$e\left(\frac{1067}{1932}\right)$	$e\left(\frac{533}{1932}\right)$	$e\left(\frac{493}{644}\right)$	$e\left(\frac{120}{161}\right)$
$\chi_{40310}(537,\cdot)$	$1$	$1$	$e\left(\frac{94}{483}\right)$	$e\left(\frac{1783}{1932}\right)$	$e\left(\frac{188}{483}\right)$	$e\left(\frac{1355}{1932}\right)$	$e\left(\frac{767}{1932}\right)$	$e\left(\frac{41}{138}\right)$	$e\left(\frac{1241}{1932}\right)$	$e\left(\frac{227}{1932}\right)$	$e\left(\frac{303}{644}\right)$	$e\left(\frac{94}{161}\right)$
$\chi_{40310}(553,\cdot)$	$1$	$1$	$e\left(\frac{53}{483}\right)$	$e\left(\frac{65}{1932}\right)$	$e\left(\frac{106}{483}\right)$	$e\left(\frac{913}{1932}\right)$	$e\left(\frac{1753}{1932}\right)$	$e\left(\frac{109}{138}\right)$	$e\left(\frac{859}{1932}\right)$	$e\left(\frac{277}{1932}\right)$	$e\left(\frac{313}{644}\right)$	$e\left(\frac{53}{161}\right)$
$\chi_{40310}(607,\cdot)$	$1$	$1$	$e\left(\frac{193}{483}\right)$	$e\left(\frac{583}{1932}\right)$	$e\left(\frac{386}{483}\right)$	$e\left(\frac{1739}{1932}\right)$	$e\left(\frac{59}{1932}\right)$	$e\left(\frac{35}{138}\right)$	$e\left(\frac{1433}{1932}\right)$	$e\left(\frac{1355}{1932}\right)$	$e\left(\frac{271}{644}\right)$	$e\left(\frac{32}{161}\right)$
$\chi_{40310}(623,\cdot)$	$1$	$1$	$e\left(\frac{157}{483}\right)$	$e\left(\frac{229}{1932}\right)$	$e\left(\frac{314}{483}\right)$	$e\left(\frac{809}{1932}\right)$	$e\left(\frac{53}{1932}\right)$	$e\left(\frac{125}{138}\right)$	$e\left(\frac{1451}{1932}\right)$	$e\left(\frac{857}{1932}\right)$	$e\left(\frac{429}{644}\right)$	$e\left(\frac{157}{161}\right)$
$\chi_{40310}(627,\cdot)$	$1$	$1$	$e\left(\frac{289}{483}\right)$	$e\left(\frac{883}{1932}\right)$	$e\left(\frac{95}{483}\right)$	$e\left(\frac{1643}{1932}\right)$	$e\left(\frac{719}{1932}\right)$	$e\left(\frac{71}{138}\right)$	$e\left(\frac{1385}{1932}\right)$	$e\left(\frac{107}{1932}\right)$	$e\left(\frac{279}{644}\right)$	$e\left(\frac{128}{161}\right)$
$\chi_{40310}(677,\cdot)$	$1$	$1$	$e\left(\frac{8}{483}\right)$	$e\left(\frac{347}{1932}\right)$	$e\left(\frac{16}{483}\right)$	$e\left(\frac{475}{1932}\right)$	$e\left(\frac{55}{1932}\right)$	$e\left(\frac{49}{138}\right)$	$e\left(\frac{157}{1932}\right)$	$e\left(\frac{379}{1932}\right)$	$e\left(\frac{591}{644}\right)$	$e\left(\frac{8}{161}\right)$
$\chi_{40310}(773,\cdot)$	$1$	$1$	$e\left(\frac{169}{483}\right)$	$e\left(\frac{25}{1932}\right)$	$e\left(\frac{338}{483}\right)$	$e\left(\frac{797}{1932}\right)$	$e\left(\frac{377}{1932}\right)$	$e\left(\frac{95}{138}\right)$	$e\left(\frac{479}{1932}\right)$	$e\left(\frac{701}{1932}\right)$	$e\left(\frac{269}{644}\right)$	$e\left(\frac{8}{161}\right)$
$\chi_{40310}(843,\cdot)$	$1$	$1$	$e\left(\frac{382}{483}\right)$	$e\left(\frac{1717}{1932}\right)$	$e\left(\frac{281}{483}\right)$	$e\left(\frac{101}{1932}\right)$	$e\left(\frac{1781}{1932}\right)$	$e\left(\frac{11}{138}\right)$	$e\left(\frac{131}{1932}\right)$	$e\left(\frac{1313}{1932}\right)$	$e\left(\frac{5}{644}\right)$	$e\left(\frac{60}{161}\right)$
$\chi_{40310}(917,\cdot)$	$1$	$1$	$e\left(\frac{464}{483}\right)$	$e\left(\frac{323}{1932}\right)$	$e\left(\frac{445}{483}\right)$	$e\left(\frac{19}{1932}\right)$	$e\left(\frac{775}{1932}\right)$	$e\left(\frac{13}{138}\right)$	$e\left(\frac{1861}{1932}\right)$	$e\left(\frac{247}{1932}\right)$	$e\left(\frac{307}{644}\right)$	$e\left(\frac{142}{161}\right)$
$\chi_{40310}(1117,\cdot)$	$1$	$1$	$e\left(\frac{59}{483}\right)$	$e\left(\frac{1895}{1932}\right)$	$e\left(\frac{118}{483}\right)$	$e\left(\frac{907}{1932}\right)$	$e\left(\frac{1915}{1932}\right)$	$e\left(\frac{25}{138}\right)$	$e\left(\frac{373}{1932}\right)$	$e\left(\frac{199}{1932}\right)$	$e\left(\frac{555}{644}\right)$	$e\left(\frac{59}{161}\right)$
$\chi_{40310}(1123,\cdot)$	$1$	$1$	$e\left(\frac{418}{483}\right)$	$e\left(\frac{1105}{1932}\right)$	$e\left(\frac{353}{483}\right)$	$e\left(\frac{65}{1932}\right)$	$e\left(\frac{821}{1932}\right)$	$e\left(\frac{59}{138}\right)$	$e\left(\frac{1079}{1932}\right)$	$e\left(\frac{845}{1932}\right)$	$e\left(\frac{169}{644}\right)$	$e\left(\frac{96}{161}\right)$
$\chi_{40310}(1163,\cdot)$	$1$	$1$	$e\left(\frac{55}{483}\right)$	$e\left(\frac{997}{1932}\right)$	$e\left(\frac{110}{483}\right)$	$e\left(\frac{1877}{1932}\right)$	$e\left(\frac{197}{1932}\right)$	$e\left(\frac{35}{138}\right)$	$e\left(\frac{1019}{1932}\right)$	$e\left(\frac{1217}{1932}\right)$	$e\left(\frac{501}{644}\right)$	$e\left(\frac{55}{161}\right)$
$\chi_{40310}(1403,\cdot)$	$1$	$1$	$e\left(\frac{352}{483}\right)$	$e\left(\frac{1261}{1932}\right)$	$e\left(\frac{221}{483}\right)$	$e\left(\frac{1097}{1932}\right)$	$e\left(\frac{5}{1932}\right)$	$e\left(\frac{17}{138}\right)$	$e\left(\frac{1595}{1932}\right)$	$e\left(\frac{737}{1932}\right)$	$e\left(\frac{405}{644}\right)$	$e\left(\frac{30}{161}\right)$
$\chi_{40310}(1497,\cdot)$	$1$	$1$	$e\left(\frac{338}{483}\right)$	$e\left(\frac{1499}{1932}\right)$	$e\left(\frac{193}{483}\right)$	$e\left(\frac{1111}{1932}\right)$	$e\left(\frac{271}{1932}\right)$	$e\left(\frac{121}{138}\right)$	$e\left(\frac{1441}{1932}\right)$	$e\left(\frac{919}{1932}\right)$	$e\left(\frac{55}{644}\right)$	$e\left(\frac{16}{161}\right)$

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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	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(13\)	\(17\)	\(19\)	\(21\)	\(23\)	\(27\)
\(\chi_{40310}(37,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{26}{483}\right)\)	\(e\left(\frac{1007}{1932}\right)\)	\(e\left(\frac{52}{483}\right)\)	\(e\left(\frac{1423}{1932}\right)\)	\(e\left(\frac{1507}{1932}\right)\)	\(e\left(\frac{73}{138}\right)\)	\(e\left(\frac{1597}{1932}\right)\)	\(e\left(\frac{1111}{1932}\right)\)	\(e\left(\frac{351}{644}\right)\)	\(e\left(\frac{26}{161}\right)\)
\(\chi_{40310}(47,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{401}{483}\right)\)	\(e\left(\frac{911}{1932}\right)\)	\(e\left(\frac{319}{483}\right)\)	\(e\left(\frac{1531}{1932}\right)\)	\(e\left(\frac{523}{1932}\right)\)	\(e\left(\frac{67}{138}\right)\)	\(e\left(\frac{685}{1932}\right)\)	\(e\left(\frac{583}{1932}\right)\)	\(e\left(\frac{503}{644}\right)\)	\(e\left(\frac{79}{161}\right)\)
\(\chi_{40310}(193,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{337}{483}\right)\)	\(e\left(\frac{1033}{1932}\right)\)	\(e\left(\frac{191}{483}\right)\)	\(e\left(\frac{629}{1932}\right)\)	\(e\left(\frac{1049}{1932}\right)\)	\(e\left(\frac{89}{138}\right)\)	\(e\left(\frac{395}{1932}\right)\)	\(e\left(\frac{449}{1932}\right)\)	\(e\left(\frac{605}{644}\right)\)	\(e\left(\frac{15}{161}\right)\)
\(\chi_{40310}(263,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{319}{483}\right)\)	\(e\left(\frac{373}{1932}\right)\)	\(e\left(\frac{155}{483}\right)\)	\(e\left(\frac{1613}{1932}\right)\)	\(e\left(\frac{1529}{1932}\right)\)	\(e\left(\frac{65}{138}\right)\)	\(e\left(\frac{887}{1932}\right)\)	\(e\left(\frac{1649}{1932}\right)\)	\(e\left(\frac{201}{644}\right)\)	\(e\left(\frac{158}{161}\right)\)
\(\chi_{40310}(287,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{244}{483}\right)\)	\(e\left(\frac{199}{1932}\right)\)	\(e\left(\frac{5}{483}\right)\)	\(e\left(\frac{239}{1932}\right)\)	\(e\left(\frac{1919}{1932}\right)\)	\(e\left(\frac{11}{138}\right)\)	\(e\left(\frac{1649}{1932}\right)\)	\(e\left(\frac{1175}{1932}\right)\)	\(e\left(\frac{235}{644}\right)\)	\(e\left(\frac{83}{161}\right)\)
\(\chi_{40310}(327,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{481}{483}\right)\)	\(e\left(\frac{1483}{1932}\right)\)	\(e\left(\frac{479}{483}\right)\)	\(e\left(\frac{1451}{1932}\right)\)	\(e\left(\frac{107}{1932}\right)\)	\(e\left(\frac{5}{138}\right)\)	\(e\left(\frac{1289}{1932}\right)\)	\(e\left(\frac{1475}{1932}\right)\)	\(e\left(\frac{295}{644}\right)\)	\(e\left(\frac{159}{161}\right)\)
\(\chi_{40310}(483,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{442}{483}\right)\)	\(e\left(\frac{697}{1932}\right)\)	\(e\left(\frac{401}{483}\right)\)	\(e\left(\frac{41}{1932}\right)\)	\(e\left(\frac{1469}{1932}\right)\)	\(e\left(\frac{137}{138}\right)\)	\(e\left(\frac{1067}{1932}\right)\)	\(e\left(\frac{533}{1932}\right)\)	\(e\left(\frac{493}{644}\right)\)	\(e\left(\frac{120}{161}\right)\)
\(\chi_{40310}(537,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{94}{483}\right)\)	\(e\left(\frac{1783}{1932}\right)\)	\(e\left(\frac{188}{483}\right)\)	\(e\left(\frac{1355}{1932}\right)\)	\(e\left(\frac{767}{1932}\right)\)	\(e\left(\frac{41}{138}\right)\)	\(e\left(\frac{1241}{1932}\right)\)	\(e\left(\frac{227}{1932}\right)\)	\(e\left(\frac{303}{644}\right)\)	\(e\left(\frac{94}{161}\right)\)
\(\chi_{40310}(553,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{483}\right)\)	\(e\left(\frac{65}{1932}\right)\)	\(e\left(\frac{106}{483}\right)\)	\(e\left(\frac{913}{1932}\right)\)	\(e\left(\frac{1753}{1932}\right)\)	\(e\left(\frac{109}{138}\right)\)	\(e\left(\frac{859}{1932}\right)\)	\(e\left(\frac{277}{1932}\right)\)	\(e\left(\frac{313}{644}\right)\)	\(e\left(\frac{53}{161}\right)\)
\(\chi_{40310}(607,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{193}{483}\right)\)	\(e\left(\frac{583}{1932}\right)\)	\(e\left(\frac{386}{483}\right)\)	\(e\left(\frac{1739}{1932}\right)\)	\(e\left(\frac{59}{1932}\right)\)	\(e\left(\frac{35}{138}\right)\)	\(e\left(\frac{1433}{1932}\right)\)	\(e\left(\frac{1355}{1932}\right)\)	\(e\left(\frac{271}{644}\right)\)	\(e\left(\frac{32}{161}\right)\)
\(\chi_{40310}(623,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{157}{483}\right)\)	\(e\left(\frac{229}{1932}\right)\)	\(e\left(\frac{314}{483}\right)\)	\(e\left(\frac{809}{1932}\right)\)	\(e\left(\frac{53}{1932}\right)\)	\(e\left(\frac{125}{138}\right)\)	\(e\left(\frac{1451}{1932}\right)\)	\(e\left(\frac{857}{1932}\right)\)	\(e\left(\frac{429}{644}\right)\)	\(e\left(\frac{157}{161}\right)\)
\(\chi_{40310}(627,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{289}{483}\right)\)	\(e\left(\frac{883}{1932}\right)\)	\(e\left(\frac{95}{483}\right)\)	\(e\left(\frac{1643}{1932}\right)\)	\(e\left(\frac{719}{1932}\right)\)	\(e\left(\frac{71}{138}\right)\)	\(e\left(\frac{1385}{1932}\right)\)	\(e\left(\frac{107}{1932}\right)\)	\(e\left(\frac{279}{644}\right)\)	\(e\left(\frac{128}{161}\right)\)
\(\chi_{40310}(677,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{8}{483}\right)\)	\(e\left(\frac{347}{1932}\right)\)	\(e\left(\frac{16}{483}\right)\)	\(e\left(\frac{475}{1932}\right)\)	\(e\left(\frac{55}{1932}\right)\)	\(e\left(\frac{49}{138}\right)\)	\(e\left(\frac{157}{1932}\right)\)	\(e\left(\frac{379}{1932}\right)\)	\(e\left(\frac{591}{644}\right)\)	\(e\left(\frac{8}{161}\right)\)
\(\chi_{40310}(773,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{169}{483}\right)\)	\(e\left(\frac{25}{1932}\right)\)	\(e\left(\frac{338}{483}\right)\)	\(e\left(\frac{797}{1932}\right)\)	\(e\left(\frac{377}{1932}\right)\)	\(e\left(\frac{95}{138}\right)\)	\(e\left(\frac{479}{1932}\right)\)	\(e\left(\frac{701}{1932}\right)\)	\(e\left(\frac{269}{644}\right)\)	\(e\left(\frac{8}{161}\right)\)
\(\chi_{40310}(843,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{382}{483}\right)\)	\(e\left(\frac{1717}{1932}\right)\)	\(e\left(\frac{281}{483}\right)\)	\(e\left(\frac{101}{1932}\right)\)	\(e\left(\frac{1781}{1932}\right)\)	\(e\left(\frac{11}{138}\right)\)	\(e\left(\frac{131}{1932}\right)\)	\(e\left(\frac{1313}{1932}\right)\)	\(e\left(\frac{5}{644}\right)\)	\(e\left(\frac{60}{161}\right)\)
\(\chi_{40310}(917,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{464}{483}\right)\)	\(e\left(\frac{323}{1932}\right)\)	\(e\left(\frac{445}{483}\right)\)	\(e\left(\frac{19}{1932}\right)\)	\(e\left(\frac{775}{1932}\right)\)	\(e\left(\frac{13}{138}\right)\)	\(e\left(\frac{1861}{1932}\right)\)	\(e\left(\frac{247}{1932}\right)\)	\(e\left(\frac{307}{644}\right)\)	\(e\left(\frac{142}{161}\right)\)
\(\chi_{40310}(1117,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{483}\right)\)	\(e\left(\frac{1895}{1932}\right)\)	\(e\left(\frac{118}{483}\right)\)	\(e\left(\frac{907}{1932}\right)\)	\(e\left(\frac{1915}{1932}\right)\)	\(e\left(\frac{25}{138}\right)\)	\(e\left(\frac{373}{1932}\right)\)	\(e\left(\frac{199}{1932}\right)\)	\(e\left(\frac{555}{644}\right)\)	\(e\left(\frac{59}{161}\right)\)
\(\chi_{40310}(1123,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{418}{483}\right)\)	\(e\left(\frac{1105}{1932}\right)\)	\(e\left(\frac{353}{483}\right)\)	\(e\left(\frac{65}{1932}\right)\)	\(e\left(\frac{821}{1932}\right)\)	\(e\left(\frac{59}{138}\right)\)	\(e\left(\frac{1079}{1932}\right)\)	\(e\left(\frac{845}{1932}\right)\)	\(e\left(\frac{169}{644}\right)\)	\(e\left(\frac{96}{161}\right)\)
\(\chi_{40310}(1163,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{55}{483}\right)\)	\(e\left(\frac{997}{1932}\right)\)	\(e\left(\frac{110}{483}\right)\)	\(e\left(\frac{1877}{1932}\right)\)	\(e\left(\frac{197}{1932}\right)\)	\(e\left(\frac{35}{138}\right)\)	\(e\left(\frac{1019}{1932}\right)\)	\(e\left(\frac{1217}{1932}\right)\)	\(e\left(\frac{501}{644}\right)\)	\(e\left(\frac{55}{161}\right)\)
\(\chi_{40310}(1403,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{352}{483}\right)\)	\(e\left(\frac{1261}{1932}\right)\)	\(e\left(\frac{221}{483}\right)\)	\(e\left(\frac{1097}{1932}\right)\)	\(e\left(\frac{5}{1932}\right)\)	\(e\left(\frac{17}{138}\right)\)	\(e\left(\frac{1595}{1932}\right)\)	\(e\left(\frac{737}{1932}\right)\)	\(e\left(\frac{405}{644}\right)\)	\(e\left(\frac{30}{161}\right)\)
\(\chi_{40310}(1497,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{338}{483}\right)\)	\(e\left(\frac{1499}{1932}\right)\)	\(e\left(\frac{193}{483}\right)\)	\(e\left(\frac{1111}{1932}\right)\)	\(e\left(\frac{271}{1932}\right)\)	\(e\left(\frac{121}{138}\right)\)	\(e\left(\frac{1441}{1932}\right)\)	\(e\left(\frac{919}{1932}\right)\)	\(e\left(\frac{55}{644}\right)\)	\(e\left(\frac{16}{161}\right)\)

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First 21 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.fs
Modulus	$40310$
Conductor	$20155$
Order	$1932$
Real	no
Primitive	no
Minimal	yes
Parity	even

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.gc	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)