LMFDB - Dirichlet character orbit 40310.fy

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(40310, base_ring=CyclotomicField(1932)) M = H._module chi = DirichletCharacter(H, M([1449,1242,896])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(13,40310)) 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.gb	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 19 of 528 characters in Galois orbit

Character	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$17$	$19$	$21$	$23$	$27$
$\chi_{40310}(13,\cdot)$	$-1$	$1$	$e\left(\frac{925}{1932}\right)$	$e\left(\frac{1261}{1932}\right)$	$e\left(\frac{925}{966}\right)$	$e\left(\frac{307}{966}\right)$	$e\left(\frac{971}{1932}\right)$	$e\left(\frac{241}{276}\right)$	$e\left(\frac{278}{483}\right)$	$e\left(\frac{127}{966}\right)$	$e\left(\frac{405}{644}\right)$	$e\left(\frac{281}{644}\right)$
$\chi_{40310}(67,\cdot)$	$-1$	$1$	$e\left(\frac{559}{1932}\right)$	$e\left(\frac{643}{1932}\right)$	$e\left(\frac{559}{966}\right)$	$e\left(\frac{715}{966}\right)$	$e\left(\frac{1157}{1932}\right)$	$e\left(\frac{43}{276}\right)$	$e\left(\frac{380}{483}\right)$	$e\left(\frac{601}{966}\right)$	$e\left(\frac{15}{644}\right)$	$e\left(\frac{559}{644}\right)$
$\chi_{40310}(167,\cdot)$	$-1$	$1$	$e\left(\frac{1627}{1932}\right)$	$e\left(\frac{451}{1932}\right)$	$e\left(\frac{661}{966}\right)$	$e\left(\frac{823}{966}\right)$	$e\left(\frac{1121}{1932}\right)$	$e\left(\frac{19}{276}\right)$	$e\left(\frac{407}{483}\right)$	$e\left(\frac{73}{966}\right)$	$e\left(\frac{319}{644}\right)$	$e\left(\frac{339}{644}\right)$
$\chi_{40310}(283,\cdot)$	$-1$	$1$	$e\left(\frac{857}{1932}\right)$	$e\left(\frac{101}{1932}\right)$	$e\left(\frac{857}{966}\right)$	$e\left(\frac{557}{966}\right)$	$e\left(\frac{1639}{1932}\right)$	$e\left(\frac{257}{276}\right)$	$e\left(\frac{421}{483}\right)$	$e\left(\frac{479}{966}\right)$	$e\left(\frac{417}{644}\right)$	$e\left(\frac{213}{644}\right)$
$\chi_{40310}(303,\cdot)$	$-1$	$1$	$e\left(\frac{1093}{1932}\right)$	$e\left(\frac{1513}{1932}\right)$	$e\left(\frac{127}{966}\right)$	$e\left(\frac{769}{966}\right)$	$e\left(\frac{1139}{1932}\right)$	$e\left(\frac{169}{276}\right)$	$e\left(\frac{152}{483}\right)$	$e\left(\frac{337}{966}\right)$	$e\left(\frac{489}{644}\right)$	$e\left(\frac{449}{644}\right)$
$\chi_{40310}(593,\cdot)$	$-1$	$1$	$e\left(\frac{449}{1932}\right)$	$e\left(\frac{869}{1932}\right)$	$e\left(\frac{449}{966}\right)$	$e\left(\frac{125}{966}\right)$	$e\left(\frac{1783}{1932}\right)$	$e\left(\frac{77}{276}\right)$	$e\left(\frac{313}{483}\right)$	$e\left(\frac{659}{966}\right)$	$e\left(\frac{489}{644}\right)$	$e\left(\frac{449}{644}\right)$
$\chi_{40310}(673,\cdot)$	$-1$	$1$	$e\left(\frac{1349}{1932}\right)$	$e\left(\frac{425}{1932}\right)$	$e\left(\frac{383}{966}\right)$	$e\left(\frac{737}{966}\right)$	$e\left(\frac{1579}{1932}\right)$	$e\left(\frac{125}{276}\right)$	$e\left(\frac{466}{483}\right)$	$e\left(\frac{887}{966}\right)$	$e\left(\frac{65}{644}\right)$	$e\left(\frac{61}{644}\right)$
$\chi_{40310}(817,\cdot)$	$-1$	$1$	$e\left(\frac{1871}{1932}\right)$	$e\left(\frac{863}{1932}\right)$	$e\left(\frac{905}{966}\right)$	$e\left(\frac{551}{966}\right)$	$e\left(\frac{997}{1932}\right)$	$e\left(\frac{59}{276}\right)$	$e\left(\frac{178}{483}\right)$	$e\left(\frac{401}{966}\right)$	$e\left(\frac{579}{644}\right)$	$e\left(\frac{583}{644}\right)$
$\chi_{40310}(847,\cdot)$	$-1$	$1$	$e\left(\frac{1615}{1932}\right)$	$e\left(\frac{19}{1932}\right)$	$e\left(\frac{649}{966}\right)$	$e\left(\frac{583}{966}\right)$	$e\left(\frac{557}{1932}\right)$	$e\left(\frac{103}{276}\right)$	$e\left(\frac{347}{483}\right)$	$e\left(\frac{817}{966}\right)$	$e\left(\frac{359}{644}\right)$	$e\left(\frac{327}{644}\right)$
$\chi_{40310}(863,\cdot)$	$-1$	$1$	$e\left(\frac{1585}{1932}\right)$	$e\left(\frac{1837}{1932}\right)$	$e\left(\frac{619}{966}\right)$	$e\left(\frac{949}{966}\right)$	$e\left(\frac{1079}{1932}\right)$	$e\left(\frac{37}{276}\right)$	$e\left(\frac{197}{483}\right)$	$e\left(\frac{745}{966}\right)$	$e\left(\frac{137}{644}\right)$	$e\left(\frac{297}{644}\right)$
$\chi_{40310}(883,\cdot)$	$-1$	$1$	$e\left(\frac{337}{1932}\right)$	$e\left(\frac{1345}{1932}\right)$	$e\left(\frac{337}{966}\right)$	$e\left(\frac{139}{966}\right)$	$e\left(\frac{383}{1932}\right)$	$e\left(\frac{217}{276}\right)$	$e\left(\frac{236}{483}\right)$	$e\left(\frac{841}{966}\right)$	$e\left(\frac{433}{644}\right)$	$e\left(\frac{337}{644}\right)$
$\chi_{40310}(903,\cdot)$	$-1$	$1$	$e\left(\frac{1565}{1932}\right)$	$e\left(\frac{473}{1932}\right)$	$e\left(\frac{599}{966}\right)$	$e\left(\frac{227}{966}\right)$	$e\left(\frac{139}{1932}\right)$	$e\left(\frac{269}{276}\right)$	$e\left(\frac{97}{483}\right)$	$e\left(\frac{53}{966}\right)$	$e\left(\frac{633}{644}\right)$	$e\left(\frac{277}{644}\right)$
$\chi_{40310}(933,\cdot)$	$-1$	$1$	$e\left(\frac{233}{1932}\right)$	$e\left(\frac{821}{1932}\right)$	$e\left(\frac{233}{966}\right)$	$e\left(\frac{635}{966}\right)$	$e\left(\frac{1291}{1932}\right)$	$e\left(\frac{209}{276}\right)$	$e\left(\frac{199}{483}\right)$	$e\left(\frac{527}{966}\right)$	$e\left(\frac{565}{644}\right)$	$e\left(\frac{233}{644}\right)$
$\chi_{40310}(1137,\cdot)$	$-1$	$1$	$e\left(\frac{1783}{1932}\right)$	$e\left(\frac{271}{1932}\right)$	$e\left(\frac{817}{966}\right)$	$e\left(\frac{79}{966}\right)$	$e\left(\frac{725}{1932}\right)$	$e\left(\frac{31}{276}\right)$	$e\left(\frac{221}{483}\right)$	$e\left(\frac{61}{966}\right)$	$e\left(\frac{443}{644}\right)$	$e\left(\frac{495}{644}\right)$
$\chi_{40310}(1153,\cdot)$	$-1$	$1$	$e\left(\frac{773}{1932}\right)$	$e\left(\frac{941}{1932}\right)$	$e\left(\frac{773}{966}\right)$	$e\left(\frac{809}{966}\right)$	$e\left(\frac{1555}{1932}\right)$	$e\left(\frac{17}{276}\right)$	$e\left(\frac{1}{483}\right)$	$e\left(\frac{857}{966}\right)$	$e\left(\frac{53}{644}\right)$	$e\left(\frac{129}{644}\right)$
$\chi_{40310}(1193,\cdot)$	$-1$	$1$	$e\left(\frac{641}{1932}\right)$	$e\left(\frac{53}{1932}\right)$	$e\left(\frac{641}{966}\right)$	$e\left(\frac{101}{966}\right)$	$e\left(\frac{1147}{1932}\right)$	$e\left(\frac{113}{276}\right)$	$e\left(\frac{307}{483}\right)$	$e\left(\frac{347}{966}\right)$	$e\left(\frac{493}{644}\right)$	$e\left(\frac{641}{644}\right)$
$\chi_{40310}(1397,\cdot)$	$-1$	$1$	$e\left(\frac{1031}{1932}\right)$	$e\left(\frac{1535}{1932}\right)$	$e\left(\frac{65}{966}\right)$	$e\left(\frac{173}{966}\right)$	$e\left(\frac{157}{1932}\right)$	$e\left(\frac{143}{276}\right)$	$e\left(\frac{325}{483}\right)$	$e\left(\frac{317}{966}\right)$	$e\left(\frac{159}{644}\right)$	$e\left(\frac{387}{644}\right)$
$\chi_{40310}(1427,\cdot)$	$-1$	$1$	$e\left(\frac{1139}{1932}\right)$	$e\left(\frac{1559}{1932}\right)$	$e\left(\frac{173}{966}\right)$	$e\left(\frac{401}{966}\right)$	$e\left(\frac{1369}{1932}\right)$	$e\left(\frac{215}{276}\right)$	$e\left(\frac{382}{483}\right)$	$e\left(\frac{383}{966}\right)$	$e\left(\frac{443}{644}\right)$	$e\left(\frac{495}{644}\right)$
$\chi_{40310}(1517,\cdot)$	$-1$	$1$	$e\left(\frac{1567}{1932}\right)$	$e\left(\frac{223}{1932}\right)$	$e\left(\frac{601}{966}\right)$	$e\left(\frac{589}{966}\right)$	$e\left(\frac{233}{1932}\right)$	$e\left(\frac{163}{276}\right)$	$e\left(\frac{107}{483}\right)$	$e\left(\frac{895}{966}\right)$	$e\left(\frac{519}{644}\right)$	$e\left(\frac{279}{644}\right)$

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	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(13\)	\(17\)	\(19\)	\(21\)	\(23\)	\(27\)
\(\chi_{40310}(13,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{925}{1932}\right)\)	\(e\left(\frac{1261}{1932}\right)\)	\(e\left(\frac{925}{966}\right)\)	\(e\left(\frac{307}{966}\right)\)	\(e\left(\frac{971}{1932}\right)\)	\(e\left(\frac{241}{276}\right)\)	\(e\left(\frac{278}{483}\right)\)	\(e\left(\frac{127}{966}\right)\)	\(e\left(\frac{405}{644}\right)\)	\(e\left(\frac{281}{644}\right)\)
\(\chi_{40310}(67,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{559}{1932}\right)\)	\(e\left(\frac{643}{1932}\right)\)	\(e\left(\frac{559}{966}\right)\)	\(e\left(\frac{715}{966}\right)\)	\(e\left(\frac{1157}{1932}\right)\)	\(e\left(\frac{43}{276}\right)\)	\(e\left(\frac{380}{483}\right)\)	\(e\left(\frac{601}{966}\right)\)	\(e\left(\frac{15}{644}\right)\)	\(e\left(\frac{559}{644}\right)\)
\(\chi_{40310}(167,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1627}{1932}\right)\)	\(e\left(\frac{451}{1932}\right)\)	\(e\left(\frac{661}{966}\right)\)	\(e\left(\frac{823}{966}\right)\)	\(e\left(\frac{1121}{1932}\right)\)	\(e\left(\frac{19}{276}\right)\)	\(e\left(\frac{407}{483}\right)\)	\(e\left(\frac{73}{966}\right)\)	\(e\left(\frac{319}{644}\right)\)	\(e\left(\frac{339}{644}\right)\)
\(\chi_{40310}(283,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{857}{1932}\right)\)	\(e\left(\frac{101}{1932}\right)\)	\(e\left(\frac{857}{966}\right)\)	\(e\left(\frac{557}{966}\right)\)	\(e\left(\frac{1639}{1932}\right)\)	\(e\left(\frac{257}{276}\right)\)	\(e\left(\frac{421}{483}\right)\)	\(e\left(\frac{479}{966}\right)\)	\(e\left(\frac{417}{644}\right)\)	\(e\left(\frac{213}{644}\right)\)
\(\chi_{40310}(303,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1093}{1932}\right)\)	\(e\left(\frac{1513}{1932}\right)\)	\(e\left(\frac{127}{966}\right)\)	\(e\left(\frac{769}{966}\right)\)	\(e\left(\frac{1139}{1932}\right)\)	\(e\left(\frac{169}{276}\right)\)	\(e\left(\frac{152}{483}\right)\)	\(e\left(\frac{337}{966}\right)\)	\(e\left(\frac{489}{644}\right)\)	\(e\left(\frac{449}{644}\right)\)
\(\chi_{40310}(593,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{449}{1932}\right)\)	\(e\left(\frac{869}{1932}\right)\)	\(e\left(\frac{449}{966}\right)\)	\(e\left(\frac{125}{966}\right)\)	\(e\left(\frac{1783}{1932}\right)\)	\(e\left(\frac{77}{276}\right)\)	\(e\left(\frac{313}{483}\right)\)	\(e\left(\frac{659}{966}\right)\)	\(e\left(\frac{489}{644}\right)\)	\(e\left(\frac{449}{644}\right)\)
\(\chi_{40310}(673,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1349}{1932}\right)\)	\(e\left(\frac{425}{1932}\right)\)	\(e\left(\frac{383}{966}\right)\)	\(e\left(\frac{737}{966}\right)\)	\(e\left(\frac{1579}{1932}\right)\)	\(e\left(\frac{125}{276}\right)\)	\(e\left(\frac{466}{483}\right)\)	\(e\left(\frac{887}{966}\right)\)	\(e\left(\frac{65}{644}\right)\)	\(e\left(\frac{61}{644}\right)\)
\(\chi_{40310}(817,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1871}{1932}\right)\)	\(e\left(\frac{863}{1932}\right)\)	\(e\left(\frac{905}{966}\right)\)	\(e\left(\frac{551}{966}\right)\)	\(e\left(\frac{997}{1932}\right)\)	\(e\left(\frac{59}{276}\right)\)	\(e\left(\frac{178}{483}\right)\)	\(e\left(\frac{401}{966}\right)\)	\(e\left(\frac{579}{644}\right)\)	\(e\left(\frac{583}{644}\right)\)
\(\chi_{40310}(847,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1615}{1932}\right)\)	\(e\left(\frac{19}{1932}\right)\)	\(e\left(\frac{649}{966}\right)\)	\(e\left(\frac{583}{966}\right)\)	\(e\left(\frac{557}{1932}\right)\)	\(e\left(\frac{103}{276}\right)\)	\(e\left(\frac{347}{483}\right)\)	\(e\left(\frac{817}{966}\right)\)	\(e\left(\frac{359}{644}\right)\)	\(e\left(\frac{327}{644}\right)\)
\(\chi_{40310}(863,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1585}{1932}\right)\)	\(e\left(\frac{1837}{1932}\right)\)	\(e\left(\frac{619}{966}\right)\)	\(e\left(\frac{949}{966}\right)\)	\(e\left(\frac{1079}{1932}\right)\)	\(e\left(\frac{37}{276}\right)\)	\(e\left(\frac{197}{483}\right)\)	\(e\left(\frac{745}{966}\right)\)	\(e\left(\frac{137}{644}\right)\)	\(e\left(\frac{297}{644}\right)\)
\(\chi_{40310}(883,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{337}{1932}\right)\)	\(e\left(\frac{1345}{1932}\right)\)	\(e\left(\frac{337}{966}\right)\)	\(e\left(\frac{139}{966}\right)\)	\(e\left(\frac{383}{1932}\right)\)	\(e\left(\frac{217}{276}\right)\)	\(e\left(\frac{236}{483}\right)\)	\(e\left(\frac{841}{966}\right)\)	\(e\left(\frac{433}{644}\right)\)	\(e\left(\frac{337}{644}\right)\)
\(\chi_{40310}(903,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1565}{1932}\right)\)	\(e\left(\frac{473}{1932}\right)\)	\(e\left(\frac{599}{966}\right)\)	\(e\left(\frac{227}{966}\right)\)	\(e\left(\frac{139}{1932}\right)\)	\(e\left(\frac{269}{276}\right)\)	\(e\left(\frac{97}{483}\right)\)	\(e\left(\frac{53}{966}\right)\)	\(e\left(\frac{633}{644}\right)\)	\(e\left(\frac{277}{644}\right)\)
\(\chi_{40310}(933,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{233}{1932}\right)\)	\(e\left(\frac{821}{1932}\right)\)	\(e\left(\frac{233}{966}\right)\)	\(e\left(\frac{635}{966}\right)\)	\(e\left(\frac{1291}{1932}\right)\)	\(e\left(\frac{209}{276}\right)\)	\(e\left(\frac{199}{483}\right)\)	\(e\left(\frac{527}{966}\right)\)	\(e\left(\frac{565}{644}\right)\)	\(e\left(\frac{233}{644}\right)\)
\(\chi_{40310}(1137,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1783}{1932}\right)\)	\(e\left(\frac{271}{1932}\right)\)	\(e\left(\frac{817}{966}\right)\)	\(e\left(\frac{79}{966}\right)\)	\(e\left(\frac{725}{1932}\right)\)	\(e\left(\frac{31}{276}\right)\)	\(e\left(\frac{221}{483}\right)\)	\(e\left(\frac{61}{966}\right)\)	\(e\left(\frac{443}{644}\right)\)	\(e\left(\frac{495}{644}\right)\)
\(\chi_{40310}(1153,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{773}{1932}\right)\)	\(e\left(\frac{941}{1932}\right)\)	\(e\left(\frac{773}{966}\right)\)	\(e\left(\frac{809}{966}\right)\)	\(e\left(\frac{1555}{1932}\right)\)	\(e\left(\frac{17}{276}\right)\)	\(e\left(\frac{1}{483}\right)\)	\(e\left(\frac{857}{966}\right)\)	\(e\left(\frac{53}{644}\right)\)	\(e\left(\frac{129}{644}\right)\)
\(\chi_{40310}(1193,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{641}{1932}\right)\)	\(e\left(\frac{53}{1932}\right)\)	\(e\left(\frac{641}{966}\right)\)	\(e\left(\frac{101}{966}\right)\)	\(e\left(\frac{1147}{1932}\right)\)	\(e\left(\frac{113}{276}\right)\)	\(e\left(\frac{307}{483}\right)\)	\(e\left(\frac{347}{966}\right)\)	\(e\left(\frac{493}{644}\right)\)	\(e\left(\frac{641}{644}\right)\)
\(\chi_{40310}(1397,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1031}{1932}\right)\)	\(e\left(\frac{1535}{1932}\right)\)	\(e\left(\frac{65}{966}\right)\)	\(e\left(\frac{173}{966}\right)\)	\(e\left(\frac{157}{1932}\right)\)	\(e\left(\frac{143}{276}\right)\)	\(e\left(\frac{325}{483}\right)\)	\(e\left(\frac{317}{966}\right)\)	\(e\left(\frac{159}{644}\right)\)	\(e\left(\frac{387}{644}\right)\)
\(\chi_{40310}(1427,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1139}{1932}\right)\)	\(e\left(\frac{1559}{1932}\right)\)	\(e\left(\frac{173}{966}\right)\)	\(e\left(\frac{401}{966}\right)\)	\(e\left(\frac{1369}{1932}\right)\)	\(e\left(\frac{215}{276}\right)\)	\(e\left(\frac{382}{483}\right)\)	\(e\left(\frac{383}{966}\right)\)	\(e\left(\frac{443}{644}\right)\)	\(e\left(\frac{495}{644}\right)\)
\(\chi_{40310}(1517,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1567}{1932}\right)\)	\(e\left(\frac{223}{1932}\right)\)	\(e\left(\frac{601}{966}\right)\)	\(e\left(\frac{589}{966}\right)\)	\(e\left(\frac{233}{1932}\right)\)	\(e\left(\frac{163}{276}\right)\)	\(e\left(\frac{107}{483}\right)\)	\(e\left(\frac{895}{966}\right)\)	\(e\left(\frac{519}{644}\right)\)	\(e\left(\frac{279}{644}\right)\)

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First 19 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.fy
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.gb	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	odd	sage:chi.is_odd() pari:zncharisodd(g,chi)