LMFDB - Dirichlet character orbit 40310.gc

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(40310, base_ring=CyclotomicField(1932)) M = H._module chi = DirichletCharacter(H, M([1449,345,574])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(3,40310)) 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.fs	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 18 of 528 characters in Galois orbit

Character	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$17$	$19$	$21$	$23$	$27$
$\chi_{40310}(3,\cdot)$	$-1$	$1$	$e\left(\frac{313}{966}\right)$	$e\left(\frac{1445}{1932}\right)$	$e\left(\frac{313}{483}\right)$	$e\left(\frac{85}{1932}\right)$	$e\left(\frac{925}{1932}\right)$	$e\left(\frac{20}{69}\right)$	$e\left(\frac{445}{1932}\right)$	$e\left(\frac{139}{1932}\right)$	$e\left(\frac{543}{644}\right)$	$e\left(\frac{313}{322}\right)$
$\chi_{40310}(243,\cdot)$	$-1$	$1$	$e\left(\frac{599}{966}\right)$	$e\left(\frac{1429}{1932}\right)$	$e\left(\frac{116}{483}\right)$	$e\left(\frac{425}{1932}\right)$	$e\left(\frac{761}{1932}\right)$	$e\left(\frac{31}{69}\right)$	$e\left(\frac{293}{1932}\right)$	$e\left(\frac{695}{1932}\right)$	$e\left(\frac{139}{644}\right)$	$e\left(\frac{277}{322}\right)$
$\chi_{40310}(247,\cdot)$	$-1$	$1$	$e\left(\frac{685}{966}\right)$	$e\left(\frac{215}{1932}\right)$	$e\left(\frac{202}{483}\right)$	$e\left(\frac{1831}{1932}\right)$	$e\left(\frac{151}{1932}\right)$	$e\left(\frac{29}{69}\right)$	$e\left(\frac{835}{1932}\right)$	$e\left(\frac{1585}{1932}\right)$	$e\left(\frac{317}{644}\right)$	$e\left(\frac{41}{322}\right)$
$\chi_{40310}(253,\cdot)$	$-1$	$1$	$e\left(\frac{857}{966}\right)$	$e\left(\frac{685}{1932}\right)$	$e\left(\frac{374}{483}\right)$	$e\left(\frac{1745}{1932}\right)$	$e\left(\frac{1829}{1932}\right)$	$e\left(\frac{25}{69}\right)$	$e\left(\frac{953}{1932}\right)$	$e\left(\frac{467}{1932}\right)$	$e\left(\frac{351}{644}\right)$	$e\left(\frac{213}{322}\right)$
$\chi_{40310}(293,\cdot)$	$-1$	$1$	$e\left(\frac{845}{966}\right)$	$e\left(\frac{1753}{1932}\right)$	$e\left(\frac{362}{483}\right)$	$e\left(\frac{785}{1932}\right)$	$e\left(\frac{701}{1932}\right)$	$e\left(\frac{67}{69}\right)$	$e\left(\frac{473}{1932}\right)$	$e\left(\frac{1511}{1932}\right)$	$e\left(\frac{431}{644}\right)$	$e\left(\frac{201}{322}\right)$
$\chi_{40310}(387,\cdot)$	$-1$	$1$	$e\left(\frac{373}{966}\right)$	$e\left(\frac{935}{1932}\right)$	$e\left(\frac{373}{483}\right)$	$e\left(\frac{55}{1932}\right)$	$e\left(\frac{1735}{1932}\right)$	$e\left(\frac{17}{69}\right)$	$e\left(\frac{1879}{1932}\right)$	$e\left(\frac{1681}{1932}\right)$	$e\left(\frac{465}{644}\right)$	$e\left(\frac{51}{322}\right)$
$\chi_{40310}(543,\cdot)$	$-1$	$1$	$e\left(\frac{773}{966}\right)$	$e\left(\frac{433}{1932}\right)$	$e\left(\frac{290}{483}\right)$	$e\left(\frac{821}{1932}\right)$	$e\left(\frac{1661}{1932}\right)$	$e\left(\frac{43}{69}\right)$	$e\left(\frac{1457}{1932}\right)$	$e\left(\frac{47}{1932}\right)$	$e\left(\frac{267}{644}\right)$	$e\left(\frac{129}{322}\right)$
$\chi_{40310}(577,\cdot)$	$-1$	$1$	$e\left(\frac{173}{966}\right)$	$e\left(\frac{703}{1932}\right)$	$e\left(\frac{173}{483}\right)$	$e\left(\frac{155}{1932}\right)$	$e\left(\frac{323}{1932}\right)$	$e\left(\frac{4}{69}\right)$	$e\left(\frac{1607}{1932}\right)$	$e\left(\frac{1049}{1932}\right)$	$e\left(\frac{81}{644}\right)$	$e\left(\frac{173}{322}\right)$
$\chi_{40310}(617,\cdot)$	$-1$	$1$	$e\left(\frac{269}{966}\right)$	$e\left(\frac{1819}{1932}\right)$	$e\left(\frac{269}{483}\right)$	$e\left(\frac{107}{1932}\right)$	$e\left(\frac{1619}{1932}\right)$	$e\left(\frac{13}{69}\right)$	$e\left(\frac{1583}{1932}\right)$	$e\left(\frac{425}{1932}\right)$	$e\left(\frac{85}{644}\right)$	$e\left(\frac{269}{322}\right)$
$\chi_{40310}(823,\cdot)$	$-1$	$1$	$e\left(\frac{767}{966}\right)$	$e\left(\frac{1}{1932}\right)$	$e\left(\frac{284}{483}\right)$	$e\left(\frac{341}{1932}\right)$	$e\left(\frac{1097}{1932}\right)$	$e\left(\frac{64}{69}\right)$	$e\left(\frac{1217}{1932}\right)$	$e\left(\frac{1535}{1932}\right)$	$e\left(\frac{307}{644}\right)$	$e\left(\frac{123}{322}\right)$
$\chi_{40310}(827,\cdot)$	$-1$	$1$	$e\left(\frac{895}{966}\right)$	$e\left(\frac{1811}{1932}\right)$	$e\left(\frac{412}{483}\right)$	$e\left(\frac{1243}{1932}\right)$	$e\left(\frac{571}{1932}\right)$	$e\left(\frac{53}{69}\right)$	$e\left(\frac{1507}{1932}\right)$	$e\left(\frac{1669}{1932}\right)$	$e\left(\frac{205}{644}\right)$	$e\left(\frac{251}{322}\right)$
$\chi_{40310}(907,\cdot)$	$-1$	$1$	$e\left(\frac{815}{966}\right)$	$e\left(\frac{559}{1932}\right)$	$e\left(\frac{332}{483}\right)$	$e\left(\frac{1283}{1932}\right)$	$e\left(\frac{779}{1932}\right)$	$e\left(\frac{34}{69}\right)$	$e\left(\frac{239}{1932}\right)$	$e\left(\frac{257}{1932}\right)$	$e\left(\frac{309}{644}\right)$	$e\left(\frac{171}{322}\right)$
$\chi_{40310}(1063,\cdot)$	$-1$	$1$	$e\left(\frac{65}{966}\right)$	$e\left(\frac{1621}{1932}\right)$	$e\left(\frac{65}{483}\right)$	$e\left(\frac{209}{1932}\right)$	$e\left(\frac{797}{1932}\right)$	$e\left(\frac{37}{69}\right)$	$e\left(\frac{185}{1932}\right)$	$e\left(\frac{1751}{1932}\right)$	$e\left(\frac{479}{644}\right)$	$e\left(\frac{65}{322}\right)$
$\chi_{40310}(1133,\cdot)$	$-1$	$1$	$e\left(\frac{449}{966}\right)$	$e\left(\frac{289}{1932}\right)$	$e\left(\frac{449}{483}\right)$	$e\left(\frac{17}{1932}\right)$	$e\left(\frac{185}{1932}\right)$	$e\left(\frac{4}{69}\right)$	$e\left(\frac{89}{1932}\right)$	$e\left(\frac{1187}{1932}\right)$	$e\left(\frac{495}{644}\right)$	$e\left(\frac{127}{322}\right)$
$\chi_{40310}(1197,\cdot)$	$-1$	$1$	$e\left(\frac{605}{966}\right)$	$e\left(\frac{895}{1932}\right)$	$e\left(\frac{122}{483}\right)$	$e\left(\frac{1871}{1932}\right)$	$e\left(\frac{359}{1932}\right)$	$e\left(\frac{10}{69}\right)$	$e\left(\frac{1499}{1932}\right)$	$e\left(\frac{173}{1932}\right)$	$e\left(\frac{421}{644}\right)$	$e\left(\frac{283}{322}\right)$
$\chi_{40310}(1353,\cdot)$	$-1$	$1$	$e\left(\frac{121}{966}\right)$	$e\left(\frac{1145}{1932}\right)$	$e\left(\frac{121}{483}\right)$	$e\left(\frac{181}{1932}\right)$	$e\left(\frac{265}{1932}\right)$	$e\left(\frac{2}{69}\right)$	$e\left(\frac{493}{1932}\right)$	$e\left(\frac{1387}{1932}\right)$	$e\left(\frac{535}{644}\right)$	$e\left(\frac{121}{322}\right)$
$\chi_{40310}(1407,\cdot)$	$-1$	$1$	$e\left(\frac{349}{966}\right)$	$e\left(\frac{1139}{1932}\right)$	$e\left(\frac{349}{483}\right)$	$e\left(\frac{67}{1932}\right)$	$e\left(\frac{1411}{1932}\right)$	$e\left(\frac{32}{69}\right)$	$e\left(\frac{919}{1932}\right)$	$e\left(\frac{1837}{1932}\right)$	$e\left(\frac{625}{644}\right)$	$e\left(\frac{27}{322}\right)$
$\chi_{40310}(1547,\cdot)$	$-1$	$1$	$e\left(\frac{499}{966}\right)$	$e\left(\frac{347}{1932}\right)$	$e\left(\frac{16}{483}\right)$	$e\left(\frac{475}{1932}\right)$	$e\left(\frac{55}{1932}\right)$	$e\left(\frac{59}{69}\right)$	$e\left(\frac{1123}{1932}\right)$	$e\left(\frac{1345}{1932}\right)$	$e\left(\frac{269}{644}\right)$	$e\left(\frac{177}{322}\right)$

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	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(13\)	\(17\)	\(19\)	\(21\)	\(23\)	\(27\)
\(\chi_{40310}(3,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{313}{966}\right)\)	\(e\left(\frac{1445}{1932}\right)\)	\(e\left(\frac{313}{483}\right)\)	\(e\left(\frac{85}{1932}\right)\)	\(e\left(\frac{925}{1932}\right)\)	\(e\left(\frac{20}{69}\right)\)	\(e\left(\frac{445}{1932}\right)\)	\(e\left(\frac{139}{1932}\right)\)	\(e\left(\frac{543}{644}\right)\)	\(e\left(\frac{313}{322}\right)\)
\(\chi_{40310}(243,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{599}{966}\right)\)	\(e\left(\frac{1429}{1932}\right)\)	\(e\left(\frac{116}{483}\right)\)	\(e\left(\frac{425}{1932}\right)\)	\(e\left(\frac{761}{1932}\right)\)	\(e\left(\frac{31}{69}\right)\)	\(e\left(\frac{293}{1932}\right)\)	\(e\left(\frac{695}{1932}\right)\)	\(e\left(\frac{139}{644}\right)\)	\(e\left(\frac{277}{322}\right)\)
\(\chi_{40310}(247,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{685}{966}\right)\)	\(e\left(\frac{215}{1932}\right)\)	\(e\left(\frac{202}{483}\right)\)	\(e\left(\frac{1831}{1932}\right)\)	\(e\left(\frac{151}{1932}\right)\)	\(e\left(\frac{29}{69}\right)\)	\(e\left(\frac{835}{1932}\right)\)	\(e\left(\frac{1585}{1932}\right)\)	\(e\left(\frac{317}{644}\right)\)	\(e\left(\frac{41}{322}\right)\)
\(\chi_{40310}(253,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{857}{966}\right)\)	\(e\left(\frac{685}{1932}\right)\)	\(e\left(\frac{374}{483}\right)\)	\(e\left(\frac{1745}{1932}\right)\)	\(e\left(\frac{1829}{1932}\right)\)	\(e\left(\frac{25}{69}\right)\)	\(e\left(\frac{953}{1932}\right)\)	\(e\left(\frac{467}{1932}\right)\)	\(e\left(\frac{351}{644}\right)\)	\(e\left(\frac{213}{322}\right)\)
\(\chi_{40310}(293,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{845}{966}\right)\)	\(e\left(\frac{1753}{1932}\right)\)	\(e\left(\frac{362}{483}\right)\)	\(e\left(\frac{785}{1932}\right)\)	\(e\left(\frac{701}{1932}\right)\)	\(e\left(\frac{67}{69}\right)\)	\(e\left(\frac{473}{1932}\right)\)	\(e\left(\frac{1511}{1932}\right)\)	\(e\left(\frac{431}{644}\right)\)	\(e\left(\frac{201}{322}\right)\)
\(\chi_{40310}(387,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{373}{966}\right)\)	\(e\left(\frac{935}{1932}\right)\)	\(e\left(\frac{373}{483}\right)\)	\(e\left(\frac{55}{1932}\right)\)	\(e\left(\frac{1735}{1932}\right)\)	\(e\left(\frac{17}{69}\right)\)	\(e\left(\frac{1879}{1932}\right)\)	\(e\left(\frac{1681}{1932}\right)\)	\(e\left(\frac{465}{644}\right)\)	\(e\left(\frac{51}{322}\right)\)
\(\chi_{40310}(543,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{773}{966}\right)\)	\(e\left(\frac{433}{1932}\right)\)	\(e\left(\frac{290}{483}\right)\)	\(e\left(\frac{821}{1932}\right)\)	\(e\left(\frac{1661}{1932}\right)\)	\(e\left(\frac{43}{69}\right)\)	\(e\left(\frac{1457}{1932}\right)\)	\(e\left(\frac{47}{1932}\right)\)	\(e\left(\frac{267}{644}\right)\)	\(e\left(\frac{129}{322}\right)\)
\(\chi_{40310}(577,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{173}{966}\right)\)	\(e\left(\frac{703}{1932}\right)\)	\(e\left(\frac{173}{483}\right)\)	\(e\left(\frac{155}{1932}\right)\)	\(e\left(\frac{323}{1932}\right)\)	\(e\left(\frac{4}{69}\right)\)	\(e\left(\frac{1607}{1932}\right)\)	\(e\left(\frac{1049}{1932}\right)\)	\(e\left(\frac{81}{644}\right)\)	\(e\left(\frac{173}{322}\right)\)
\(\chi_{40310}(617,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{269}{966}\right)\)	\(e\left(\frac{1819}{1932}\right)\)	\(e\left(\frac{269}{483}\right)\)	\(e\left(\frac{107}{1932}\right)\)	\(e\left(\frac{1619}{1932}\right)\)	\(e\left(\frac{13}{69}\right)\)	\(e\left(\frac{1583}{1932}\right)\)	\(e\left(\frac{425}{1932}\right)\)	\(e\left(\frac{85}{644}\right)\)	\(e\left(\frac{269}{322}\right)\)
\(\chi_{40310}(823,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{767}{966}\right)\)	\(e\left(\frac{1}{1932}\right)\)	\(e\left(\frac{284}{483}\right)\)	\(e\left(\frac{341}{1932}\right)\)	\(e\left(\frac{1097}{1932}\right)\)	\(e\left(\frac{64}{69}\right)\)	\(e\left(\frac{1217}{1932}\right)\)	\(e\left(\frac{1535}{1932}\right)\)	\(e\left(\frac{307}{644}\right)\)	\(e\left(\frac{123}{322}\right)\)
\(\chi_{40310}(827,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{895}{966}\right)\)	\(e\left(\frac{1811}{1932}\right)\)	\(e\left(\frac{412}{483}\right)\)	\(e\left(\frac{1243}{1932}\right)\)	\(e\left(\frac{571}{1932}\right)\)	\(e\left(\frac{53}{69}\right)\)	\(e\left(\frac{1507}{1932}\right)\)	\(e\left(\frac{1669}{1932}\right)\)	\(e\left(\frac{205}{644}\right)\)	\(e\left(\frac{251}{322}\right)\)
\(\chi_{40310}(907,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{815}{966}\right)\)	\(e\left(\frac{559}{1932}\right)\)	\(e\left(\frac{332}{483}\right)\)	\(e\left(\frac{1283}{1932}\right)\)	\(e\left(\frac{779}{1932}\right)\)	\(e\left(\frac{34}{69}\right)\)	\(e\left(\frac{239}{1932}\right)\)	\(e\left(\frac{257}{1932}\right)\)	\(e\left(\frac{309}{644}\right)\)	\(e\left(\frac{171}{322}\right)\)
\(\chi_{40310}(1063,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{65}{966}\right)\)	\(e\left(\frac{1621}{1932}\right)\)	\(e\left(\frac{65}{483}\right)\)	\(e\left(\frac{209}{1932}\right)\)	\(e\left(\frac{797}{1932}\right)\)	\(e\left(\frac{37}{69}\right)\)	\(e\left(\frac{185}{1932}\right)\)	\(e\left(\frac{1751}{1932}\right)\)	\(e\left(\frac{479}{644}\right)\)	\(e\left(\frac{65}{322}\right)\)
\(\chi_{40310}(1133,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{449}{966}\right)\)	\(e\left(\frac{289}{1932}\right)\)	\(e\left(\frac{449}{483}\right)\)	\(e\left(\frac{17}{1932}\right)\)	\(e\left(\frac{185}{1932}\right)\)	\(e\left(\frac{4}{69}\right)\)	\(e\left(\frac{89}{1932}\right)\)	\(e\left(\frac{1187}{1932}\right)\)	\(e\left(\frac{495}{644}\right)\)	\(e\left(\frac{127}{322}\right)\)
\(\chi_{40310}(1197,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{605}{966}\right)\)	\(e\left(\frac{895}{1932}\right)\)	\(e\left(\frac{122}{483}\right)\)	\(e\left(\frac{1871}{1932}\right)\)	\(e\left(\frac{359}{1932}\right)\)	\(e\left(\frac{10}{69}\right)\)	\(e\left(\frac{1499}{1932}\right)\)	\(e\left(\frac{173}{1932}\right)\)	\(e\left(\frac{421}{644}\right)\)	\(e\left(\frac{283}{322}\right)\)
\(\chi_{40310}(1353,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{121}{966}\right)\)	\(e\left(\frac{1145}{1932}\right)\)	\(e\left(\frac{121}{483}\right)\)	\(e\left(\frac{181}{1932}\right)\)	\(e\left(\frac{265}{1932}\right)\)	\(e\left(\frac{2}{69}\right)\)	\(e\left(\frac{493}{1932}\right)\)	\(e\left(\frac{1387}{1932}\right)\)	\(e\left(\frac{535}{644}\right)\)	\(e\left(\frac{121}{322}\right)\)
\(\chi_{40310}(1407,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{349}{966}\right)\)	\(e\left(\frac{1139}{1932}\right)\)	\(e\left(\frac{349}{483}\right)\)	\(e\left(\frac{67}{1932}\right)\)	\(e\left(\frac{1411}{1932}\right)\)	\(e\left(\frac{32}{69}\right)\)	\(e\left(\frac{919}{1932}\right)\)	\(e\left(\frac{1837}{1932}\right)\)	\(e\left(\frac{625}{644}\right)\)	\(e\left(\frac{27}{322}\right)\)
\(\chi_{40310}(1547,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{499}{966}\right)\)	\(e\left(\frac{347}{1932}\right)\)	\(e\left(\frac{16}{483}\right)\)	\(e\left(\frac{475}{1932}\right)\)	\(e\left(\frac{55}{1932}\right)\)	\(e\left(\frac{59}{69}\right)\)	\(e\left(\frac{1123}{1932}\right)\)	\(e\left(\frac{1345}{1932}\right)\)	\(e\left(\frac{269}{644}\right)\)	\(e\left(\frac{177}{322}\right)\)

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First 18 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.gc
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.fs	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	odd	sage:chi.is_odd() pari:zncharisodd(g,chi)