LMFDB - Dirichlet character orbit 40310.fu

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(40310, base_ring=CyclotomicField(1932)) M = H._module chi = DirichletCharacter(H, M([0,1173,1274])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(21,40310)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$40310$
Conductor:	$4031$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$1932$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 4031.bu	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 18 of 528 characters in Galois orbit

Character	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$17$	$19$	$21$	$23$	$27$
$\chi_{40310}(21,\cdot)$	$1$	$1$	$e\left(\frac{139}{1932}\right)$	$e\left(\frac{124}{483}\right)$	$e\left(\frac{139}{966}\right)$	$e\left(\frac{569}{1932}\right)$	$e\left(\frac{127}{966}\right)$	$e\left(\frac{85}{276}\right)$	$e\left(\frac{1331}{1932}\right)$	$e\left(\frac{635}{1932}\right)$	$e\left(\frac{305}{322}\right)$	$e\left(\frac{139}{644}\right)$
$\chi_{40310}(61,\cdot)$	$1$	$1$	$e\left(\frac{1711}{1932}\right)$	$e\left(\frac{265}{483}\right)$	$e\left(\frac{745}{966}\right)$	$e\left(\frac{1625}{1932}\right)$	$e\left(\frac{361}{966}\right)$	$e\left(\frac{121}{276}\right)$	$e\left(\frac{1859}{1932}\right)$	$e\left(\frac{839}{1932}\right)$	$e\left(\frac{261}{322}\right)$	$e\left(\frac{423}{644}\right)$
$\chi_{40310}(101,\cdot)$	$1$	$1$	$e\left(\frac{467}{1932}\right)$	$e\left(\frac{17}{483}\right)$	$e\left(\frac{467}{966}\right)$	$e\left(\frac{1453}{1932}\right)$	$e\left(\frac{107}{966}\right)$	$e\left(\frac{89}{276}\right)$	$e\left(\frac{163}{1932}\right)$	$e\left(\frac{535}{1932}\right)$	$e\left(\frac{295}{322}\right)$	$e\left(\frac{467}{644}\right)$
$\chi_{40310}(171,\cdot)$	$1$	$1$	$e\left(\frac{1697}{1932}\right)$	$e\left(\frac{461}{483}\right)$	$e\left(\frac{731}{966}\right)$	$e\left(\frac{1387}{1932}\right)$	$e\left(\frac{515}{966}\right)$	$e\left(\frac{35}{276}\right)$	$e\left(\frac{613}{1932}\right)$	$e\left(\frac{1609}{1932}\right)$	$e\left(\frac{177}{322}\right)$	$e\left(\frac{409}{644}\right)$
$\chi_{40310}(211,\cdot)$	$1$	$1$	$e\left(\frac{1525}{1932}\right)$	$e\left(\frac{40}{483}\right)$	$e\left(\frac{559}{966}\right)$	$e\left(\frac{947}{1932}\right)$	$e\left(\frac{337}{966}\right)$	$e\left(\frac{43}{276}\right)$	$e\left(\frac{1037}{1932}\right)$	$e\left(\frac{1685}{1932}\right)$	$e\left(\frac{249}{322}\right)$	$e\left(\frac{237}{644}\right)$
$\chi_{40310}(271,\cdot)$	$1$	$1$	$e\left(\frac{893}{1932}\right)$	$e\left(\frac{470}{483}\right)$	$e\left(\frac{893}{966}\right)$	$e\left(\frac{139}{1932}\right)$	$e\left(\frac{941}{966}\right)$	$e\left(\frac{143}{276}\right)$	$e\left(\frac{1921}{1932}\right)$	$e\left(\frac{841}{1932}\right)$	$e\left(\frac{229}{322}\right)$	$e\left(\frac{249}{644}\right)$
$\chi_{40310}(351,\cdot)$	$1$	$1$	$e\left(\frac{871}{1932}\right)$	$e\left(\frac{433}{483}\right)$	$e\left(\frac{871}{966}\right)$	$e\left(\frac{869}{1932}\right)$	$e\left(\frac{907}{966}\right)$	$e\left(\frac{205}{276}\right)$	$e\left(\frac{515}{1932}\right)$	$e\left(\frac{671}{1932}\right)$	$e\left(\frac{51}{322}\right)$	$e\left(\frac{227}{644}\right)$
$\chi_{40310}(641,\cdot)$	$1$	$1$	$e\left(\frac{451}{1932}\right)$	$e\left(\frac{34}{483}\right)$	$e\left(\frac{451}{966}\right)$	$e\left(\frac{1457}{1932}\right)$	$e\left(\frac{697}{966}\right)$	$e\left(\frac{109}{276}\right)$	$e\left(\frac{1775}{1932}\right)$	$e\left(\frac{587}{1932}\right)$	$e\left(\frac{107}{322}\right)$	$e\left(\frac{451}{644}\right)$
$\chi_{40310}(751,\cdot)$	$1$	$1$	$e\left(\frac{269}{1932}\right)$	$e\left(\frac{167}{483}\right)$	$e\left(\frac{269}{966}\right)$	$e\left(\frac{295}{1932}\right)$	$e\left(\frac{767}{966}\right)$	$e\left(\frac{95}{276}\right)$	$e\left(\frac{1033}{1932}\right)$	$e\left(\frac{937}{1932}\right)$	$e\left(\frac{303}{322}\right)$	$e\left(\frac{269}{644}\right)$
$\chi_{40310}(851,\cdot)$	$1$	$1$	$e\left(\frac{1733}{1932}\right)$	$e\left(\frac{302}{483}\right)$	$e\left(\frac{767}{966}\right)$	$e\left(\frac{895}{1932}\right)$	$e\left(\frac{395}{966}\right)$	$e\left(\frac{59}{276}\right)$	$e\left(\frac{1333}{1932}\right)$	$e\left(\frac{1009}{1932}\right)$	$e\left(\frac{117}{322}\right)$	$e\left(\frac{445}{644}\right)$
$\chi_{40310}(1041,\cdot)$	$1$	$1$	$e\left(\frac{1501}{1932}\right)$	$e\left(\frac{307}{483}\right)$	$e\left(\frac{535}{966}\right)$	$e\left(\frac{1919}{1932}\right)$	$e\left(\frac{739}{966}\right)$	$e\left(\frac{211}{276}\right)$	$e\left(\frac{557}{1932}\right)$	$e\left(\frac{797}{1932}\right)$	$e\left(\frac{289}{322}\right)$	$e\left(\frac{213}{644}\right)$
$\chi_{40310}(1071,\cdot)$	$1$	$1$	$e\left(\frac{1325}{1932}\right)$	$e\left(\frac{11}{483}\right)$	$e\left(\frac{359}{966}\right)$	$e\left(\frac{31}{1932}\right)$	$e\left(\frac{467}{966}\right)$	$e\left(\frac{155}{276}\right)$	$e\left(\frac{901}{1932}\right)$	$e\left(\frac{1369}{1932}\right)$	$e\left(\frac{153}{322}\right)$	$e\left(\frac{37}{644}\right)$
$\chi_{40310}(1081,\cdot)$	$1$	$1$	$e\left(\frac{1301}{1932}\right)$	$e\left(\frac{278}{483}\right)$	$e\left(\frac{335}{966}\right)$	$e\left(\frac{1003}{1932}\right)$	$e\left(\frac{869}{966}\right)$	$e\left(\frac{47}{276}\right)$	$e\left(\frac{421}{1932}\right)$	$e\left(\frac{481}{1932}\right)$	$e\left(\frac{193}{322}\right)$	$e\left(\frac{13}{644}\right)$
$\chi_{40310}(1221,\cdot)$	$1$	$1$	$e\left(\frac{815}{1932}\right)$	$e\left(\frac{251}{483}\right)$	$e\left(\frac{815}{966}\right)$	$e\left(\frac{1849}{1932}\right)$	$e\left(\frac{557}{966}\right)$	$e\left(\frac{137}{276}\right)$	$e\left(\frac{1327}{1932}\right)$	$e\left(\frac{1819}{1932}\right)$	$e\left(\frac{37}{322}\right)$	$e\left(\frac{171}{644}\right)$
$\chi_{40310}(1291,\cdot)$	$1$	$1$	$e\left(\frac{509}{1932}\right)$	$e\left(\frac{395}{483}\right)$	$e\left(\frac{509}{966}\right)$	$e\left(\frac{235}{1932}\right)$	$e\left(\frac{611}{966}\right)$	$e\left(\frac{71}{276}\right)$	$e\left(\frac{37}{1932}\right)$	$e\left(\frac{157}{1932}\right)$	$e\left(\frac{225}{322}\right)$	$e\left(\frac{509}{644}\right)$
$\chi_{40310}(1361,\cdot)$	$1$	$1$	$e\left(\frac{205}{1932}\right)$	$e\left(\frac{235}{483}\right)$	$e\left(\frac{205}{966}\right)$	$e\left(\frac{311}{1932}\right)$	$e\left(\frac{229}{966}\right)$	$e\left(\frac{175}{276}\right)$	$e\left(\frac{1685}{1932}\right)$	$e\left(\frac{1145}{1932}\right)$	$e\left(\frac{195}{322}\right)$	$e\left(\frac{205}{644}\right)$
$\chi_{40310}(1381,\cdot)$	$1$	$1$	$e\left(\frac{1597}{1932}\right)$	$e\left(\frac{205}{483}\right)$	$e\left(\frac{631}{966}\right)$	$e\left(\frac{1895}{1932}\right)$	$e\left(\frac{97}{966}\right)$	$e\left(\frac{91}{276}\right)$	$e\left(\frac{545}{1932}\right)$	$e\left(\frac{485}{1932}\right)$	$e\left(\frac{129}{322}\right)$	$e\left(\frac{309}{644}\right)$
$\chi_{40310}(1411,\cdot)$	$1$	$1$	$e\left(\frac{1243}{1932}\right)$	$e\left(\frac{400}{483}\right)$	$e\left(\frac{277}{966}\right)$	$e\left(\frac{293}{1932}\right)$	$e\left(\frac{955}{966}\right)$	$e\left(\frac{85}{276}\right)$	$e\left(\frac{227}{1932}\right)$	$e\left(\frac{911}{1932}\right)$	$e\left(\frac{75}{322}\right)$	$e\left(\frac{599}{644}\right)$

Overview	Random
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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	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(13\)	\(17\)	\(19\)	\(21\)	\(23\)	\(27\)
\(\chi_{40310}(21,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{139}{1932}\right)\)	\(e\left(\frac{124}{483}\right)\)	\(e\left(\frac{139}{966}\right)\)	\(e\left(\frac{569}{1932}\right)\)	\(e\left(\frac{127}{966}\right)\)	\(e\left(\frac{85}{276}\right)\)	\(e\left(\frac{1331}{1932}\right)\)	\(e\left(\frac{635}{1932}\right)\)	\(e\left(\frac{305}{322}\right)\)	\(e\left(\frac{139}{644}\right)\)
\(\chi_{40310}(61,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1711}{1932}\right)\)	\(e\left(\frac{265}{483}\right)\)	\(e\left(\frac{745}{966}\right)\)	\(e\left(\frac{1625}{1932}\right)\)	\(e\left(\frac{361}{966}\right)\)	\(e\left(\frac{121}{276}\right)\)	\(e\left(\frac{1859}{1932}\right)\)	\(e\left(\frac{839}{1932}\right)\)	\(e\left(\frac{261}{322}\right)\)	\(e\left(\frac{423}{644}\right)\)
\(\chi_{40310}(101,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{467}{1932}\right)\)	\(e\left(\frac{17}{483}\right)\)	\(e\left(\frac{467}{966}\right)\)	\(e\left(\frac{1453}{1932}\right)\)	\(e\left(\frac{107}{966}\right)\)	\(e\left(\frac{89}{276}\right)\)	\(e\left(\frac{163}{1932}\right)\)	\(e\left(\frac{535}{1932}\right)\)	\(e\left(\frac{295}{322}\right)\)	\(e\left(\frac{467}{644}\right)\)
\(\chi_{40310}(171,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1697}{1932}\right)\)	\(e\left(\frac{461}{483}\right)\)	\(e\left(\frac{731}{966}\right)\)	\(e\left(\frac{1387}{1932}\right)\)	\(e\left(\frac{515}{966}\right)\)	\(e\left(\frac{35}{276}\right)\)	\(e\left(\frac{613}{1932}\right)\)	\(e\left(\frac{1609}{1932}\right)\)	\(e\left(\frac{177}{322}\right)\)	\(e\left(\frac{409}{644}\right)\)
\(\chi_{40310}(211,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1525}{1932}\right)\)	\(e\left(\frac{40}{483}\right)\)	\(e\left(\frac{559}{966}\right)\)	\(e\left(\frac{947}{1932}\right)\)	\(e\left(\frac{337}{966}\right)\)	\(e\left(\frac{43}{276}\right)\)	\(e\left(\frac{1037}{1932}\right)\)	\(e\left(\frac{1685}{1932}\right)\)	\(e\left(\frac{249}{322}\right)\)	\(e\left(\frac{237}{644}\right)\)
\(\chi_{40310}(271,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{893}{1932}\right)\)	\(e\left(\frac{470}{483}\right)\)	\(e\left(\frac{893}{966}\right)\)	\(e\left(\frac{139}{1932}\right)\)	\(e\left(\frac{941}{966}\right)\)	\(e\left(\frac{143}{276}\right)\)	\(e\left(\frac{1921}{1932}\right)\)	\(e\left(\frac{841}{1932}\right)\)	\(e\left(\frac{229}{322}\right)\)	\(e\left(\frac{249}{644}\right)\)
\(\chi_{40310}(351,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{871}{1932}\right)\)	\(e\left(\frac{433}{483}\right)\)	\(e\left(\frac{871}{966}\right)\)	\(e\left(\frac{869}{1932}\right)\)	\(e\left(\frac{907}{966}\right)\)	\(e\left(\frac{205}{276}\right)\)	\(e\left(\frac{515}{1932}\right)\)	\(e\left(\frac{671}{1932}\right)\)	\(e\left(\frac{51}{322}\right)\)	\(e\left(\frac{227}{644}\right)\)
\(\chi_{40310}(641,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{451}{1932}\right)\)	\(e\left(\frac{34}{483}\right)\)	\(e\left(\frac{451}{966}\right)\)	\(e\left(\frac{1457}{1932}\right)\)	\(e\left(\frac{697}{966}\right)\)	\(e\left(\frac{109}{276}\right)\)	\(e\left(\frac{1775}{1932}\right)\)	\(e\left(\frac{587}{1932}\right)\)	\(e\left(\frac{107}{322}\right)\)	\(e\left(\frac{451}{644}\right)\)
\(\chi_{40310}(751,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{269}{1932}\right)\)	\(e\left(\frac{167}{483}\right)\)	\(e\left(\frac{269}{966}\right)\)	\(e\left(\frac{295}{1932}\right)\)	\(e\left(\frac{767}{966}\right)\)	\(e\left(\frac{95}{276}\right)\)	\(e\left(\frac{1033}{1932}\right)\)	\(e\left(\frac{937}{1932}\right)\)	\(e\left(\frac{303}{322}\right)\)	\(e\left(\frac{269}{644}\right)\)
\(\chi_{40310}(851,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1733}{1932}\right)\)	\(e\left(\frac{302}{483}\right)\)	\(e\left(\frac{767}{966}\right)\)	\(e\left(\frac{895}{1932}\right)\)	\(e\left(\frac{395}{966}\right)\)	\(e\left(\frac{59}{276}\right)\)	\(e\left(\frac{1333}{1932}\right)\)	\(e\left(\frac{1009}{1932}\right)\)	\(e\left(\frac{117}{322}\right)\)	\(e\left(\frac{445}{644}\right)\)
\(\chi_{40310}(1041,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1501}{1932}\right)\)	\(e\left(\frac{307}{483}\right)\)	\(e\left(\frac{535}{966}\right)\)	\(e\left(\frac{1919}{1932}\right)\)	\(e\left(\frac{739}{966}\right)\)	\(e\left(\frac{211}{276}\right)\)	\(e\left(\frac{557}{1932}\right)\)	\(e\left(\frac{797}{1932}\right)\)	\(e\left(\frac{289}{322}\right)\)	\(e\left(\frac{213}{644}\right)\)
\(\chi_{40310}(1071,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1325}{1932}\right)\)	\(e\left(\frac{11}{483}\right)\)	\(e\left(\frac{359}{966}\right)\)	\(e\left(\frac{31}{1932}\right)\)	\(e\left(\frac{467}{966}\right)\)	\(e\left(\frac{155}{276}\right)\)	\(e\left(\frac{901}{1932}\right)\)	\(e\left(\frac{1369}{1932}\right)\)	\(e\left(\frac{153}{322}\right)\)	\(e\left(\frac{37}{644}\right)\)
\(\chi_{40310}(1081,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1301}{1932}\right)\)	\(e\left(\frac{278}{483}\right)\)	\(e\left(\frac{335}{966}\right)\)	\(e\left(\frac{1003}{1932}\right)\)	\(e\left(\frac{869}{966}\right)\)	\(e\left(\frac{47}{276}\right)\)	\(e\left(\frac{421}{1932}\right)\)	\(e\left(\frac{481}{1932}\right)\)	\(e\left(\frac{193}{322}\right)\)	\(e\left(\frac{13}{644}\right)\)
\(\chi_{40310}(1221,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{815}{1932}\right)\)	\(e\left(\frac{251}{483}\right)\)	\(e\left(\frac{815}{966}\right)\)	\(e\left(\frac{1849}{1932}\right)\)	\(e\left(\frac{557}{966}\right)\)	\(e\left(\frac{137}{276}\right)\)	\(e\left(\frac{1327}{1932}\right)\)	\(e\left(\frac{1819}{1932}\right)\)	\(e\left(\frac{37}{322}\right)\)	\(e\left(\frac{171}{644}\right)\)
\(\chi_{40310}(1291,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{509}{1932}\right)\)	\(e\left(\frac{395}{483}\right)\)	\(e\left(\frac{509}{966}\right)\)	\(e\left(\frac{235}{1932}\right)\)	\(e\left(\frac{611}{966}\right)\)	\(e\left(\frac{71}{276}\right)\)	\(e\left(\frac{37}{1932}\right)\)	\(e\left(\frac{157}{1932}\right)\)	\(e\left(\frac{225}{322}\right)\)	\(e\left(\frac{509}{644}\right)\)
\(\chi_{40310}(1361,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{205}{1932}\right)\)	\(e\left(\frac{235}{483}\right)\)	\(e\left(\frac{205}{966}\right)\)	\(e\left(\frac{311}{1932}\right)\)	\(e\left(\frac{229}{966}\right)\)	\(e\left(\frac{175}{276}\right)\)	\(e\left(\frac{1685}{1932}\right)\)	\(e\left(\frac{1145}{1932}\right)\)	\(e\left(\frac{195}{322}\right)\)	\(e\left(\frac{205}{644}\right)\)
\(\chi_{40310}(1381,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1597}{1932}\right)\)	\(e\left(\frac{205}{483}\right)\)	\(e\left(\frac{631}{966}\right)\)	\(e\left(\frac{1895}{1932}\right)\)	\(e\left(\frac{97}{966}\right)\)	\(e\left(\frac{91}{276}\right)\)	\(e\left(\frac{545}{1932}\right)\)	\(e\left(\frac{485}{1932}\right)\)	\(e\left(\frac{129}{322}\right)\)	\(e\left(\frac{309}{644}\right)\)
\(\chi_{40310}(1411,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1243}{1932}\right)\)	\(e\left(\frac{400}{483}\right)\)	\(e\left(\frac{277}{966}\right)\)	\(e\left(\frac{293}{1932}\right)\)	\(e\left(\frac{955}{966}\right)\)	\(e\left(\frac{85}{276}\right)\)	\(e\left(\frac{227}{1932}\right)\)	\(e\left(\frac{911}{1932}\right)\)	\(e\left(\frac{75}{322}\right)\)	\(e\left(\frac{599}{644}\right)\)

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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.fu
Modulus	$40310$
Conductor	$4031$
Order	$1932$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(40310\)
Conductor:	\(4031\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(1932\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 4031.bu	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)