LMFDB - Dirichlet character orbit 40310.ft

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(40310, base_ring=CyclotomicField(1932)) M = H._module chi = DirichletCharacter(H, M([1449,1863,686])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(73,40310)) 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.gd	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 20 of 528 characters in Galois orbit

Character	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$17$	$19$	$21$	$23$	$27$
$\chi_{40310}(73,\cdot)$	$-1$	$1$	$e\left(\frac{304}{483}\right)$	$e\left(\frac{145}{1932}\right)$	$e\left(\frac{125}{483}\right)$	$e\left(\frac{179}{1932}\right)$	$e\left(\frac{641}{1932}\right)$	$e\left(\frac{137}{138}\right)$	$e\left(\frac{1619}{1932}\right)$	$e\left(\frac{1361}{1932}\right)$	$e\left(\frac{79}{644}\right)$	$e\left(\frac{143}{161}\right)$
$\chi_{40310}(363,\cdot)$	$-1$	$1$	$e\left(\frac{199}{483}\right)$	$e\left(\frac{481}{1932}\right)$	$e\left(\frac{398}{483}\right)$	$e\left(\frac{767}{1932}\right)$	$e\left(\frac{221}{1932}\right)$	$e\left(\frac{89}{138}\right)$	$e\left(\frac{947}{1932}\right)$	$e\left(\frac{1277}{1932}\right)$	$e\left(\frac{191}{644}\right)$	$e\left(\frac{38}{161}\right)$
$\chi_{40310}(443,\cdot)$	$-1$	$1$	$e\left(\frac{47}{483}\right)$	$e\left(\frac{1133}{1932}\right)$	$e\left(\frac{94}{483}\right)$	$e\left(\frac{919}{1932}\right)$	$e\left(\frac{625}{1932}\right)$	$e\left(\frac{55}{138}\right)$	$e\left(\frac{379}{1932}\right)$	$e\left(\frac{1321}{1932}\right)$	$e\left(\frac{71}{644}\right)$	$e\left(\frac{47}{161}\right)$
$\chi_{40310}(467,\cdot)$	$-1$	$1$	$e\left(\frac{20}{483}\right)$	$e\left(\frac{143}{1932}\right)$	$e\left(\frac{40}{483}\right)$	$e\left(\frac{1429}{1932}\right)$	$e\left(\frac{379}{1932}\right)$	$e\left(\frac{19}{138}\right)$	$e\left(\frac{1117}{1932}\right)$	$e\left(\frac{223}{1932}\right)$	$e\left(\frac{109}{644}\right)$	$e\left(\frac{20}{161}\right)$
$\chi_{40310}(507,\cdot)$	$-1$	$1$	$e\left(\frac{136}{483}\right)$	$e\left(\frac{103}{1932}\right)$	$e\left(\frac{272}{483}\right)$	$e\left(\frac{1313}{1932}\right)$	$e\left(\frac{935}{1932}\right)$	$e\left(\frac{5}{138}\right)$	$e\left(\frac{737}{1932}\right)$	$e\left(\frac{647}{1932}\right)$	$e\left(\frac{65}{644}\right)$	$e\left(\frac{136}{161}\right)$
$\chi_{40310}(657,\cdot)$	$-1$	$1$	$e\left(\frac{134}{483}\right)$	$e\left(\frac{1103}{1932}\right)$	$e\left(\frac{268}{483}\right)$	$e\left(\frac{349}{1932}\right)$	$e\left(\frac{559}{1932}\right)$	$e\left(\frac{79}{138}\right)$	$e\left(\frac{577}{1932}\right)$	$e\left(\frac{1639}{1932}\right)$	$e\left(\frac{521}{644}\right)$	$e\left(\frac{134}{161}\right)$
$\chi_{40310}(707,\cdot)$	$-1$	$1$	$e\left(\frac{478}{483}\right)$	$e\left(\frac{1051}{1932}\right)$	$e\left(\frac{473}{483}\right)$	$e\left(\frac{5}{1932}\right)$	$e\left(\frac{1475}{1932}\right)$	$e\left(\frac{47}{138}\right)$	$e\left(\frac{1049}{1932}\right)$	$e\left(\frac{1031}{1932}\right)$	$e\left(\frac{13}{644}\right)$	$e\left(\frac{156}{161}\right)$
$\chi_{40310}(717,\cdot)$	$-1$	$1$	$e\left(\frac{320}{483}\right)$	$e\left(\frac{839}{1932}\right)$	$e\left(\frac{157}{483}\right)$	$e\left(\frac{1129}{1932}\right)$	$e\left(\frac{751}{1932}\right)$	$e\left(\frac{97}{138}\right)$	$e\left(\frac{1}{1932}\right)$	$e\left(\frac{187}{1932}\right)$	$e\left(\frac{617}{644}\right)$	$e\left(\frac{159}{161}\right)$
$\chi_{40310}(727,\cdot)$	$-1$	$1$	$e\left(\frac{200}{483}\right)$	$e\left(\frac{947}{1932}\right)$	$e\left(\frac{400}{483}\right)$	$e\left(\frac{1249}{1932}\right)$	$e\left(\frac{1375}{1932}\right)$	$e\left(\frac{121}{138}\right)$	$e\left(\frac{61}{1932}\right)$	$e\left(\frac{1747}{1932}\right)$	$e\left(\frac{285}{644}\right)$	$e\left(\frac{39}{161}\right)$
$\chi_{40310}(793,\cdot)$	$-1$	$1$	$e\left(\frac{176}{483}\right)$	$e\left(\frac{389}{1932}\right)$	$e\left(\frac{352}{483}\right)$	$e\left(\frac{307}{1932}\right)$	$e\left(\frac{1693}{1932}\right)$	$e\left(\frac{43}{138}\right)$	$e\left(\frac{1039}{1932}\right)$	$e\left(\frac{1093}{1932}\right)$	$e\left(\frac{283}{644}\right)$	$e\left(\frac{15}{161}\right)$
$\chi_{40310}(797,\cdot)$	$-1$	$1$	$e\left(\frac{164}{483}\right)$	$e\left(\frac{1559}{1932}\right)$	$e\left(\frac{328}{483}\right)$	$e\left(\frac{1285}{1932}\right)$	$e\left(\frac{403}{1932}\right)$	$e\left(\frac{73}{138}\right)$	$e\left(\frac{1045}{1932}\right)$	$e\left(\frac{283}{1932}\right)$	$e\left(\frac{121}{644}\right)$	$e\left(\frac{3}{161}\right)$
$\chi_{40310}(943,\cdot)$	$-1$	$1$	$e\left(\frac{290}{483}\right)$	$e\left(\frac{1349}{1932}\right)$	$e\left(\frac{97}{483}\right)$	$e\left(\frac{1159}{1932}\right)$	$e\left(\frac{1873}{1932}\right)$	$e\left(\frac{103}{138}\right)$	$e\left(\frac{499}{1932}\right)$	$e\left(\frac{577}{1932}\right)$	$e\left(\frac{51}{644}\right)$	$e\left(\frac{129}{161}\right)$
$\chi_{40310}(1013,\cdot)$	$-1$	$1$	$e\left(\frac{179}{483}\right)$	$e\left(\frac{821}{1932}\right)$	$e\left(\frac{358}{483}\right)$	$e\left(\frac{787}{1932}\right)$	$e\left(\frac{325}{1932}\right)$	$e\left(\frac{1}{138}\right)$	$e\left(\frac{1279}{1932}\right)$	$e\left(\frac{1537}{1932}\right)$	$e\left(\frac{243}{644}\right)$	$e\left(\frac{18}{161}\right)$
$\chi_{40310}(1023,\cdot)$	$-1$	$1$	$e\left(\frac{89}{483}\right)$	$e\left(\frac{1385}{1932}\right)$	$e\left(\frac{178}{483}\right)$	$e\left(\frac{1843}{1932}\right)$	$e\left(\frac{793}{1932}\right)$	$e\left(\frac{19}{138}\right)$	$e\left(\frac{1807}{1932}\right)$	$e\left(\frac{1741}{1932}\right)$	$e\left(\frac{155}{644}\right)$	$e\left(\frac{89}{161}\right)$
$\chi_{40310}(1083,\cdot)$	$-1$	$1$	$e\left(\frac{379}{483}\right)$	$e\left(\frac{1285}{1932}\right)$	$e\left(\frac{275}{483}\right)$	$e\left(\frac{587}{1932}\right)$	$e\left(\frac{1217}{1932}\right)$	$e\left(\frac{53}{138}\right)$	$e\left(\frac{1823}{1932}\right)$	$e\left(\frac{869}{1932}\right)$	$e\left(\frac{367}{644}\right)$	$e\left(\frac{57}{161}\right)$
$\chi_{40310}(1087,\cdot)$	$-1$	$1$	$e\left(\frac{325}{483}\right)$	$e\left(\frac{271}{1932}\right)$	$e\left(\frac{167}{483}\right)$	$e\left(\frac{641}{1932}\right)$	$e\left(\frac{1691}{1932}\right)$	$e\left(\frac{119}{138}\right)$	$e\left(\frac{401}{1932}\right)$	$e\left(\frac{1571}{1932}\right)$	$e\left(\frac{121}{644}\right)$	$e\left(\frac{3}{161}\right)$
$\chi_{40310}(1273,\cdot)$	$-1$	$1$	$e\left(\frac{251}{483}\right)$	$e\left(\frac{1529}{1932}\right)$	$e\left(\frac{19}{483}\right)$	$e\left(\frac{715}{1932}\right)$	$e\left(\frac{337}{1932}\right)$	$e\left(\frac{97}{138}\right)$	$e\left(\frac{1243}{1932}\right)$	$e\left(\frac{601}{1932}\right)$	$e\left(\frac{571}{644}\right)$	$e\left(\frac{90}{161}\right)$
$\chi_{40310}(1307,\cdot)$	$-1$	$1$	$e\left(\frac{326}{483}\right)$	$e\left(\frac{1703}{1932}\right)$	$e\left(\frac{169}{483}\right)$	$e\left(\frac{157}{1932}\right)$	$e\left(\frac{1879}{1932}\right)$	$e\left(\frac{13}{138}\right)$	$e\left(\frac{481}{1932}\right)$	$e\left(\frac{1075}{1932}\right)$	$e\left(\frac{537}{644}\right)$	$e\left(\frac{4}{161}\right)$
$\chi_{40310}(1323,\cdot)$	$-1$	$1$	$e\left(\frac{226}{483}\right)$	$e\left(\frac{505}{1932}\right)$	$e\left(\frac{452}{483}\right)$	$e\left(\frac{1223}{1932}\right)$	$e\left(\frac{1433}{1932}\right)$	$e\left(\frac{125}{138}\right)$	$e\left(\frac{1175}{1932}\right)$	$e\left(\frac{1409}{1932}\right)$	$e\left(\frac{475}{644}\right)$	$e\left(\frac{65}{161}\right)$
$\chi_{40310}(1377,\cdot)$	$-1$	$1$	$e\left(\frac{283}{483}\right)$	$e\left(\frac{19}{1932}\right)$	$e\left(\frac{83}{483}\right)$	$e\left(\frac{1649}{1932}\right)$	$e\left(\frac{1523}{1932}\right)$	$e\left(\frac{17}{138}\right)$	$e\left(\frac{905}{1932}\right)$	$e\left(\frac{1151}{1932}\right)$	$e\left(\frac{37}{644}\right)$	$e\left(\frac{122}{161}\right)$

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	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(13\)	\(17\)	\(19\)	\(21\)	\(23\)	\(27\)
\(\chi_{40310}(73,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{304}{483}\right)\)	\(e\left(\frac{145}{1932}\right)\)	\(e\left(\frac{125}{483}\right)\)	\(e\left(\frac{179}{1932}\right)\)	\(e\left(\frac{641}{1932}\right)\)	\(e\left(\frac{137}{138}\right)\)	\(e\left(\frac{1619}{1932}\right)\)	\(e\left(\frac{1361}{1932}\right)\)	\(e\left(\frac{79}{644}\right)\)	\(e\left(\frac{143}{161}\right)\)
\(\chi_{40310}(363,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{199}{483}\right)\)	\(e\left(\frac{481}{1932}\right)\)	\(e\left(\frac{398}{483}\right)\)	\(e\left(\frac{767}{1932}\right)\)	\(e\left(\frac{221}{1932}\right)\)	\(e\left(\frac{89}{138}\right)\)	\(e\left(\frac{947}{1932}\right)\)	\(e\left(\frac{1277}{1932}\right)\)	\(e\left(\frac{191}{644}\right)\)	\(e\left(\frac{38}{161}\right)\)
\(\chi_{40310}(443,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{47}{483}\right)\)	\(e\left(\frac{1133}{1932}\right)\)	\(e\left(\frac{94}{483}\right)\)	\(e\left(\frac{919}{1932}\right)\)	\(e\left(\frac{625}{1932}\right)\)	\(e\left(\frac{55}{138}\right)\)	\(e\left(\frac{379}{1932}\right)\)	\(e\left(\frac{1321}{1932}\right)\)	\(e\left(\frac{71}{644}\right)\)	\(e\left(\frac{47}{161}\right)\)
\(\chi_{40310}(467,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{20}{483}\right)\)	\(e\left(\frac{143}{1932}\right)\)	\(e\left(\frac{40}{483}\right)\)	\(e\left(\frac{1429}{1932}\right)\)	\(e\left(\frac{379}{1932}\right)\)	\(e\left(\frac{19}{138}\right)\)	\(e\left(\frac{1117}{1932}\right)\)	\(e\left(\frac{223}{1932}\right)\)	\(e\left(\frac{109}{644}\right)\)	\(e\left(\frac{20}{161}\right)\)
\(\chi_{40310}(507,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{136}{483}\right)\)	\(e\left(\frac{103}{1932}\right)\)	\(e\left(\frac{272}{483}\right)\)	\(e\left(\frac{1313}{1932}\right)\)	\(e\left(\frac{935}{1932}\right)\)	\(e\left(\frac{5}{138}\right)\)	\(e\left(\frac{737}{1932}\right)\)	\(e\left(\frac{647}{1932}\right)\)	\(e\left(\frac{65}{644}\right)\)	\(e\left(\frac{136}{161}\right)\)
\(\chi_{40310}(657,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{134}{483}\right)\)	\(e\left(\frac{1103}{1932}\right)\)	\(e\left(\frac{268}{483}\right)\)	\(e\left(\frac{349}{1932}\right)\)	\(e\left(\frac{559}{1932}\right)\)	\(e\left(\frac{79}{138}\right)\)	\(e\left(\frac{577}{1932}\right)\)	\(e\left(\frac{1639}{1932}\right)\)	\(e\left(\frac{521}{644}\right)\)	\(e\left(\frac{134}{161}\right)\)
\(\chi_{40310}(707,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{478}{483}\right)\)	\(e\left(\frac{1051}{1932}\right)\)	\(e\left(\frac{473}{483}\right)\)	\(e\left(\frac{5}{1932}\right)\)	\(e\left(\frac{1475}{1932}\right)\)	\(e\left(\frac{47}{138}\right)\)	\(e\left(\frac{1049}{1932}\right)\)	\(e\left(\frac{1031}{1932}\right)\)	\(e\left(\frac{13}{644}\right)\)	\(e\left(\frac{156}{161}\right)\)
\(\chi_{40310}(717,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{320}{483}\right)\)	\(e\left(\frac{839}{1932}\right)\)	\(e\left(\frac{157}{483}\right)\)	\(e\left(\frac{1129}{1932}\right)\)	\(e\left(\frac{751}{1932}\right)\)	\(e\left(\frac{97}{138}\right)\)	\(e\left(\frac{1}{1932}\right)\)	\(e\left(\frac{187}{1932}\right)\)	\(e\left(\frac{617}{644}\right)\)	\(e\left(\frac{159}{161}\right)\)
\(\chi_{40310}(727,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{200}{483}\right)\)	\(e\left(\frac{947}{1932}\right)\)	\(e\left(\frac{400}{483}\right)\)	\(e\left(\frac{1249}{1932}\right)\)	\(e\left(\frac{1375}{1932}\right)\)	\(e\left(\frac{121}{138}\right)\)	\(e\left(\frac{61}{1932}\right)\)	\(e\left(\frac{1747}{1932}\right)\)	\(e\left(\frac{285}{644}\right)\)	\(e\left(\frac{39}{161}\right)\)
\(\chi_{40310}(793,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{176}{483}\right)\)	\(e\left(\frac{389}{1932}\right)\)	\(e\left(\frac{352}{483}\right)\)	\(e\left(\frac{307}{1932}\right)\)	\(e\left(\frac{1693}{1932}\right)\)	\(e\left(\frac{43}{138}\right)\)	\(e\left(\frac{1039}{1932}\right)\)	\(e\left(\frac{1093}{1932}\right)\)	\(e\left(\frac{283}{644}\right)\)	\(e\left(\frac{15}{161}\right)\)
\(\chi_{40310}(797,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{164}{483}\right)\)	\(e\left(\frac{1559}{1932}\right)\)	\(e\left(\frac{328}{483}\right)\)	\(e\left(\frac{1285}{1932}\right)\)	\(e\left(\frac{403}{1932}\right)\)	\(e\left(\frac{73}{138}\right)\)	\(e\left(\frac{1045}{1932}\right)\)	\(e\left(\frac{283}{1932}\right)\)	\(e\left(\frac{121}{644}\right)\)	\(e\left(\frac{3}{161}\right)\)
\(\chi_{40310}(943,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{290}{483}\right)\)	\(e\left(\frac{1349}{1932}\right)\)	\(e\left(\frac{97}{483}\right)\)	\(e\left(\frac{1159}{1932}\right)\)	\(e\left(\frac{1873}{1932}\right)\)	\(e\left(\frac{103}{138}\right)\)	\(e\left(\frac{499}{1932}\right)\)	\(e\left(\frac{577}{1932}\right)\)	\(e\left(\frac{51}{644}\right)\)	\(e\left(\frac{129}{161}\right)\)
\(\chi_{40310}(1013,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{179}{483}\right)\)	\(e\left(\frac{821}{1932}\right)\)	\(e\left(\frac{358}{483}\right)\)	\(e\left(\frac{787}{1932}\right)\)	\(e\left(\frac{325}{1932}\right)\)	\(e\left(\frac{1}{138}\right)\)	\(e\left(\frac{1279}{1932}\right)\)	\(e\left(\frac{1537}{1932}\right)\)	\(e\left(\frac{243}{644}\right)\)	\(e\left(\frac{18}{161}\right)\)
\(\chi_{40310}(1023,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{89}{483}\right)\)	\(e\left(\frac{1385}{1932}\right)\)	\(e\left(\frac{178}{483}\right)\)	\(e\left(\frac{1843}{1932}\right)\)	\(e\left(\frac{793}{1932}\right)\)	\(e\left(\frac{19}{138}\right)\)	\(e\left(\frac{1807}{1932}\right)\)	\(e\left(\frac{1741}{1932}\right)\)	\(e\left(\frac{155}{644}\right)\)	\(e\left(\frac{89}{161}\right)\)
\(\chi_{40310}(1083,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{379}{483}\right)\)	\(e\left(\frac{1285}{1932}\right)\)	\(e\left(\frac{275}{483}\right)\)	\(e\left(\frac{587}{1932}\right)\)	\(e\left(\frac{1217}{1932}\right)\)	\(e\left(\frac{53}{138}\right)\)	\(e\left(\frac{1823}{1932}\right)\)	\(e\left(\frac{869}{1932}\right)\)	\(e\left(\frac{367}{644}\right)\)	\(e\left(\frac{57}{161}\right)\)
\(\chi_{40310}(1087,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{325}{483}\right)\)	\(e\left(\frac{271}{1932}\right)\)	\(e\left(\frac{167}{483}\right)\)	\(e\left(\frac{641}{1932}\right)\)	\(e\left(\frac{1691}{1932}\right)\)	\(e\left(\frac{119}{138}\right)\)	\(e\left(\frac{401}{1932}\right)\)	\(e\left(\frac{1571}{1932}\right)\)	\(e\left(\frac{121}{644}\right)\)	\(e\left(\frac{3}{161}\right)\)
\(\chi_{40310}(1273,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{251}{483}\right)\)	\(e\left(\frac{1529}{1932}\right)\)	\(e\left(\frac{19}{483}\right)\)	\(e\left(\frac{715}{1932}\right)\)	\(e\left(\frac{337}{1932}\right)\)	\(e\left(\frac{97}{138}\right)\)	\(e\left(\frac{1243}{1932}\right)\)	\(e\left(\frac{601}{1932}\right)\)	\(e\left(\frac{571}{644}\right)\)	\(e\left(\frac{90}{161}\right)\)
\(\chi_{40310}(1307,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{326}{483}\right)\)	\(e\left(\frac{1703}{1932}\right)\)	\(e\left(\frac{169}{483}\right)\)	\(e\left(\frac{157}{1932}\right)\)	\(e\left(\frac{1879}{1932}\right)\)	\(e\left(\frac{13}{138}\right)\)	\(e\left(\frac{481}{1932}\right)\)	\(e\left(\frac{1075}{1932}\right)\)	\(e\left(\frac{537}{644}\right)\)	\(e\left(\frac{4}{161}\right)\)
\(\chi_{40310}(1323,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{226}{483}\right)\)	\(e\left(\frac{505}{1932}\right)\)	\(e\left(\frac{452}{483}\right)\)	\(e\left(\frac{1223}{1932}\right)\)	\(e\left(\frac{1433}{1932}\right)\)	\(e\left(\frac{125}{138}\right)\)	\(e\left(\frac{1175}{1932}\right)\)	\(e\left(\frac{1409}{1932}\right)\)	\(e\left(\frac{475}{644}\right)\)	\(e\left(\frac{65}{161}\right)\)
\(\chi_{40310}(1377,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{283}{483}\right)\)	\(e\left(\frac{19}{1932}\right)\)	\(e\left(\frac{83}{483}\right)\)	\(e\left(\frac{1649}{1932}\right)\)	\(e\left(\frac{1523}{1932}\right)\)	\(e\left(\frac{17}{138}\right)\)	\(e\left(\frac{905}{1932}\right)\)	\(e\left(\frac{1151}{1932}\right)\)	\(e\left(\frac{37}{644}\right)\)	\(e\left(\frac{122}{161}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Basic properties

Related number fields

First 20 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.ft
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.gd	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	odd	sage:chi.is_odd() pari:zncharisodd(g,chi)