LMFDB - Dirichlet character orbit 40310.fw

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(40310, base_ring=CyclotomicField(1932)) M = H._module chi = DirichletCharacter(H, M([1449,552,658])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(53,40310)) 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.fz	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	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$17$	$19$	$21$	$23$	$27$
$\chi_{40310}(53,\cdot)$	$1$	$1$	$e\left(\frac{1241}{1932}\right)$	$e\left(\frac{401}{1932}\right)$	$e\left(\frac{275}{966}\right)$	$e\left(\frac{13}{483}\right)$	$e\left(\frac{367}{1932}\right)$	$e\left(\frac{53}{276}\right)$	$e\left(\frac{409}{483}\right)$	$e\left(\frac{821}{966}\right)$	$e\left(\frac{103}{644}\right)$	$e\left(\frac{597}{644}\right)$
$\chi_{40310}(123,\cdot)$	$1$	$1$	$e\left(\frac{157}{1932}\right)$	$e\left(\frac{661}{1932}\right)$	$e\left(\frac{157}{966}\right)$	$e\left(\frac{443}{483}\right)$	$e\left(\frac{1583}{1932}\right)$	$e\left(\frac{97}{276}\right)$	$e\left(\frac{302}{483}\right)$	$e\left(\frac{409}{966}\right)$	$e\left(\frac{67}{644}\right)$	$e\left(\frac{157}{644}\right)$
$\chi_{40310}(197,\cdot)$	$1$	$1$	$e\left(\frac{1055}{1932}\right)$	$e\left(\frac{467}{1932}\right)$	$e\left(\frac{89}{966}\right)$	$e\left(\frac{85}{483}\right)$	$e\left(\frac{1285}{1932}\right)$	$e\left(\frac{251}{276}\right)$	$e\left(\frac{445}{483}\right)$	$e\left(\frac{761}{966}\right)$	$e\left(\frac{401}{644}\right)$	$e\left(\frac{411}{644}\right)$
$\chi_{40310}(227,\cdot)$	$1$	$1$	$e\left(\frac{1255}{1932}\right)$	$e\left(\frac{583}{1932}\right)$	$e\left(\frac{289}{966}\right)$	$e\left(\frac{314}{483}\right)$	$e\left(\frac{1025}{1932}\right)$	$e\left(\frac{139}{276}\right)$	$e\left(\frac{479}{483}\right)$	$e\left(\frac{919}{966}\right)$	$e\left(\frac{593}{644}\right)$	$e\left(\frac{611}{644}\right)$
$\chi_{40310}(297,\cdot)$	$1$	$1$	$e\left(\frac{31}{1932}\right)$	$e\left(\frac{955}{1932}\right)$	$e\left(\frac{31}{966}\right)$	$e\left(\frac{149}{483}\right)$	$e\left(\frac{1457}{1932}\right)$	$e\left(\frac{151}{276}\right)$	$e\left(\frac{155}{483}\right)$	$e\left(\frac{493}{966}\right)$	$e\left(\frac{165}{644}\right)$	$e\left(\frac{31}{644}\right)$
$\chi_{40310}(393,\cdot)$	$1$	$1$	$e\left(\frac{1037}{1932}\right)$	$e\left(\frac{785}{1932}\right)$	$e\left(\frac{71}{966}\right)$	$e\left(\frac{388}{483}\right)$	$e\left(\frac{439}{1932}\right)$	$e\left(\frac{101}{276}\right)$	$e\left(\frac{355}{483}\right)$	$e\left(\frac{911}{966}\right)$	$e\left(\frac{139}{644}\right)$	$e\left(\frac{393}{644}\right)$
$\chi_{40310}(397,\cdot)$	$1$	$1$	$e\left(\frac{1315}{1932}\right)$	$e\left(\frac{811}{1932}\right)$	$e\left(\frac{349}{966}\right)$	$e\left(\frac{431}{483}\right)$	$e\left(\frac{1913}{1932}\right)$	$e\left(\frac{271}{276}\right)$	$e\left(\frac{296}{483}\right)$	$e\left(\frac{97}{966}\right)$	$e\left(\frac{393}{644}\right)$	$e\left(\frac{27}{644}\right)$
$\chi_{40310}(413,\cdot)$	$1$	$1$	$e\left(\frac{941}{1932}\right)$	$e\left(\frac{1193}{1932}\right)$	$e\left(\frac{941}{966}\right)$	$e\left(\frac{394}{483}\right)$	$e\left(\frac{1723}{1932}\right)$	$e\left(\frac{221}{276}\right)$	$e\left(\frac{358}{483}\right)$	$e\left(\frac{101}{966}\right)$	$e\left(\frac{459}{644}\right)$	$e\left(\frac{297}{644}\right)$
$\chi_{40310}(487,\cdot)$	$1$	$1$	$e\left(\frac{47}{1932}\right)$	$e\left(\frac{887}{1932}\right)$	$e\left(\frac{47}{966}\right)$	$e\left(\frac{148}{483}\right)$	$e\left(\frac{277}{1932}\right)$	$e\left(\frac{131}{276}\right)$	$e\left(\frac{235}{483}\right)$	$e\left(\frac{467}{966}\right)$	$e\left(\frac{541}{644}\right)$	$e\left(\frac{47}{644}\right)$
$\chi_{40310}(547,\cdot)$	$1$	$1$	$e\left(\frac{907}{1932}\right)$	$e\left(\frac{1579}{1932}\right)$	$e\left(\frac{907}{966}\right)$	$e\left(\frac{215}{483}\right)$	$e\left(\frac{125}{1932}\right)$	$e\left(\frac{91}{276}\right)$	$e\left(\frac{188}{483}\right)$	$e\left(\frac{277}{966}\right)$	$e\left(\frac{465}{644}\right)$	$e\left(\frac{263}{644}\right)$
$\chi_{40310}(803,\cdot)$	$1$	$1$	$e\left(\frac{1301}{1932}\right)$	$e\left(\frac{629}{1932}\right)$	$e\left(\frac{335}{966}\right)$	$e\left(\frac{130}{483}\right)$	$e\left(\frac{1255}{1932}\right)$	$e\left(\frac{185}{276}\right)$	$e\left(\frac{226}{483}\right)$	$e\left(\frac{965}{966}\right)$	$e\left(\frac{547}{644}\right)$	$e\left(\frac{13}{644}\right)$
$\chi_{40310}(837,\cdot)$	$1$	$1$	$e\left(\frac{1523}{1932}\right)$	$e\left(\frac{1859}{1932}\right)$	$e\left(\frac{557}{966}\right)$	$e\left(\frac{418}{483}\right)$	$e\left(\frac{97}{1932}\right)$	$e\left(\frac{11}{276}\right)$	$e\left(\frac{370}{483}\right)$	$e\left(\frac{725}{966}\right)$	$e\left(\frac{129}{644}\right)$	$e\left(\frac{235}{644}\right)$
$\chi_{40310}(953,\cdot)$	$1$	$1$	$e\left(\frac{1453}{1932}\right)$	$e\left(\frac{949}{1932}\right)$	$e\left(\frac{487}{966}\right)$	$e\left(\frac{362}{483}\right)$	$e\left(\frac{671}{1932}\right)$	$e\left(\frac{133}{276}\right)$	$e\left(\frac{20}{483}\right)$	$e\left(\frac{235}{966}\right)$	$e\left(\frac{255}{644}\right)$	$e\left(\frac{165}{644}\right)$
$\chi_{40310}(1127,\cdot)$	$1$	$1$	$e\left(\frac{655}{1932}\right)$	$e\left(\frac{235}{1932}\right)$	$e\left(\frac{655}{966}\right)$	$e\left(\frac{110}{483}\right)$	$e\left(\frac{1805}{1932}\right)$	$e\left(\frac{199}{276}\right)$	$e\left(\frac{377}{483}\right)$	$e\left(\frac{445}{966}\right)$	$e\left(\frac{17}{644}\right)$	$e\left(\frac{11}{644}\right)$
$\chi_{40310}(1213,\cdot)$	$1$	$1$	$e\left(\frac{1157}{1932}\right)$	$e\left(\frac{1241}{1932}\right)$	$e\left(\frac{191}{966}\right)$	$e\left(\frac{139}{483}\right)$	$e\left(\frac{283}{1932}\right)$	$e\left(\frac{89}{276}\right)$	$e\left(\frac{472}{483}\right)$	$e\left(\frac{233}{966}\right)$	$e\left(\frac{383}{644}\right)$	$e\left(\frac{513}{644}\right)$
$\chi_{40310}(1263,\cdot)$	$1$	$1$	$e\left(\frac{1429}{1932}\right)$	$e\left(\frac{85}{1932}\right)$	$e\left(\frac{463}{966}\right)$	$e\left(\frac{122}{483}\right)$	$e\left(\frac{1475}{1932}\right)$	$e\left(\frac{25}{276}\right)$	$e\left(\frac{383}{483}\right)$	$e\left(\frac{757}{966}\right)$	$e\left(\frac{335}{644}\right)$	$e\left(\frac{141}{644}\right)$
$\chi_{40310}(1283,\cdot)$	$1$	$1$	$e\left(\frac{1697}{1932}\right)$	$e\left(\frac{1361}{1932}\right)$	$e\left(\frac{731}{966}\right)$	$e\left(\frac{226}{483}\right)$	$e\left(\frac{547}{1932}\right)$	$e\left(\frac{173}{276}\right)$	$e\left(\frac{274}{483}\right)$	$e\left(\frac{563}{966}\right)$	$e\left(\frac{515}{644}\right)$	$e\left(\frac{409}{644}\right)$
$\chi_{40310}(1383,\cdot)$	$1$	$1$	$e\left(\frac{1721}{1932}\right)$	$e\left(\frac{293}{1932}\right)$	$e\left(\frac{755}{966}\right)$	$e\left(\frac{466}{483}\right)$	$e\left(\frac{1675}{1932}\right)$	$e\left(\frac{5}{276}\right)$	$e\left(\frac{394}{483}\right)$	$e\left(\frac{41}{966}\right)$	$e\left(\frac{435}{644}\right)$	$e\left(\frac{433}{644}\right)$

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	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(13\)	\(17\)	\(19\)	\(21\)	\(23\)	\(27\)
\(\chi_{40310}(53,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1241}{1932}\right)\)	\(e\left(\frac{401}{1932}\right)\)	\(e\left(\frac{275}{966}\right)\)	\(e\left(\frac{13}{483}\right)\)	\(e\left(\frac{367}{1932}\right)\)	\(e\left(\frac{53}{276}\right)\)	\(e\left(\frac{409}{483}\right)\)	\(e\left(\frac{821}{966}\right)\)	\(e\left(\frac{103}{644}\right)\)	\(e\left(\frac{597}{644}\right)\)
\(\chi_{40310}(123,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{157}{1932}\right)\)	\(e\left(\frac{661}{1932}\right)\)	\(e\left(\frac{157}{966}\right)\)	\(e\left(\frac{443}{483}\right)\)	\(e\left(\frac{1583}{1932}\right)\)	\(e\left(\frac{97}{276}\right)\)	\(e\left(\frac{302}{483}\right)\)	\(e\left(\frac{409}{966}\right)\)	\(e\left(\frac{67}{644}\right)\)	\(e\left(\frac{157}{644}\right)\)
\(\chi_{40310}(197,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1055}{1932}\right)\)	\(e\left(\frac{467}{1932}\right)\)	\(e\left(\frac{89}{966}\right)\)	\(e\left(\frac{85}{483}\right)\)	\(e\left(\frac{1285}{1932}\right)\)	\(e\left(\frac{251}{276}\right)\)	\(e\left(\frac{445}{483}\right)\)	\(e\left(\frac{761}{966}\right)\)	\(e\left(\frac{401}{644}\right)\)	\(e\left(\frac{411}{644}\right)\)
\(\chi_{40310}(227,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1255}{1932}\right)\)	\(e\left(\frac{583}{1932}\right)\)	\(e\left(\frac{289}{966}\right)\)	\(e\left(\frac{314}{483}\right)\)	\(e\left(\frac{1025}{1932}\right)\)	\(e\left(\frac{139}{276}\right)\)	\(e\left(\frac{479}{483}\right)\)	\(e\left(\frac{919}{966}\right)\)	\(e\left(\frac{593}{644}\right)\)	\(e\left(\frac{611}{644}\right)\)
\(\chi_{40310}(297,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{1932}\right)\)	\(e\left(\frac{955}{1932}\right)\)	\(e\left(\frac{31}{966}\right)\)	\(e\left(\frac{149}{483}\right)\)	\(e\left(\frac{1457}{1932}\right)\)	\(e\left(\frac{151}{276}\right)\)	\(e\left(\frac{155}{483}\right)\)	\(e\left(\frac{493}{966}\right)\)	\(e\left(\frac{165}{644}\right)\)	\(e\left(\frac{31}{644}\right)\)
\(\chi_{40310}(393,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1037}{1932}\right)\)	\(e\left(\frac{785}{1932}\right)\)	\(e\left(\frac{71}{966}\right)\)	\(e\left(\frac{388}{483}\right)\)	\(e\left(\frac{439}{1932}\right)\)	\(e\left(\frac{101}{276}\right)\)	\(e\left(\frac{355}{483}\right)\)	\(e\left(\frac{911}{966}\right)\)	\(e\left(\frac{139}{644}\right)\)	\(e\left(\frac{393}{644}\right)\)
\(\chi_{40310}(397,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1315}{1932}\right)\)	\(e\left(\frac{811}{1932}\right)\)	\(e\left(\frac{349}{966}\right)\)	\(e\left(\frac{431}{483}\right)\)	\(e\left(\frac{1913}{1932}\right)\)	\(e\left(\frac{271}{276}\right)\)	\(e\left(\frac{296}{483}\right)\)	\(e\left(\frac{97}{966}\right)\)	\(e\left(\frac{393}{644}\right)\)	\(e\left(\frac{27}{644}\right)\)
\(\chi_{40310}(413,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{941}{1932}\right)\)	\(e\left(\frac{1193}{1932}\right)\)	\(e\left(\frac{941}{966}\right)\)	\(e\left(\frac{394}{483}\right)\)	\(e\left(\frac{1723}{1932}\right)\)	\(e\left(\frac{221}{276}\right)\)	\(e\left(\frac{358}{483}\right)\)	\(e\left(\frac{101}{966}\right)\)	\(e\left(\frac{459}{644}\right)\)	\(e\left(\frac{297}{644}\right)\)
\(\chi_{40310}(487,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{1932}\right)\)	\(e\left(\frac{887}{1932}\right)\)	\(e\left(\frac{47}{966}\right)\)	\(e\left(\frac{148}{483}\right)\)	\(e\left(\frac{277}{1932}\right)\)	\(e\left(\frac{131}{276}\right)\)	\(e\left(\frac{235}{483}\right)\)	\(e\left(\frac{467}{966}\right)\)	\(e\left(\frac{541}{644}\right)\)	\(e\left(\frac{47}{644}\right)\)
\(\chi_{40310}(547,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{907}{1932}\right)\)	\(e\left(\frac{1579}{1932}\right)\)	\(e\left(\frac{907}{966}\right)\)	\(e\left(\frac{215}{483}\right)\)	\(e\left(\frac{125}{1932}\right)\)	\(e\left(\frac{91}{276}\right)\)	\(e\left(\frac{188}{483}\right)\)	\(e\left(\frac{277}{966}\right)\)	\(e\left(\frac{465}{644}\right)\)	\(e\left(\frac{263}{644}\right)\)
\(\chi_{40310}(803,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1301}{1932}\right)\)	\(e\left(\frac{629}{1932}\right)\)	\(e\left(\frac{335}{966}\right)\)	\(e\left(\frac{130}{483}\right)\)	\(e\left(\frac{1255}{1932}\right)\)	\(e\left(\frac{185}{276}\right)\)	\(e\left(\frac{226}{483}\right)\)	\(e\left(\frac{965}{966}\right)\)	\(e\left(\frac{547}{644}\right)\)	\(e\left(\frac{13}{644}\right)\)
\(\chi_{40310}(837,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1523}{1932}\right)\)	\(e\left(\frac{1859}{1932}\right)\)	\(e\left(\frac{557}{966}\right)\)	\(e\left(\frac{418}{483}\right)\)	\(e\left(\frac{97}{1932}\right)\)	\(e\left(\frac{11}{276}\right)\)	\(e\left(\frac{370}{483}\right)\)	\(e\left(\frac{725}{966}\right)\)	\(e\left(\frac{129}{644}\right)\)	\(e\left(\frac{235}{644}\right)\)
\(\chi_{40310}(953,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1453}{1932}\right)\)	\(e\left(\frac{949}{1932}\right)\)	\(e\left(\frac{487}{966}\right)\)	\(e\left(\frac{362}{483}\right)\)	\(e\left(\frac{671}{1932}\right)\)	\(e\left(\frac{133}{276}\right)\)	\(e\left(\frac{20}{483}\right)\)	\(e\left(\frac{235}{966}\right)\)	\(e\left(\frac{255}{644}\right)\)	\(e\left(\frac{165}{644}\right)\)
\(\chi_{40310}(1127,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{655}{1932}\right)\)	\(e\left(\frac{235}{1932}\right)\)	\(e\left(\frac{655}{966}\right)\)	\(e\left(\frac{110}{483}\right)\)	\(e\left(\frac{1805}{1932}\right)\)	\(e\left(\frac{199}{276}\right)\)	\(e\left(\frac{377}{483}\right)\)	\(e\left(\frac{445}{966}\right)\)	\(e\left(\frac{17}{644}\right)\)	\(e\left(\frac{11}{644}\right)\)
\(\chi_{40310}(1213,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1157}{1932}\right)\)	\(e\left(\frac{1241}{1932}\right)\)	\(e\left(\frac{191}{966}\right)\)	\(e\left(\frac{139}{483}\right)\)	\(e\left(\frac{283}{1932}\right)\)	\(e\left(\frac{89}{276}\right)\)	\(e\left(\frac{472}{483}\right)\)	\(e\left(\frac{233}{966}\right)\)	\(e\left(\frac{383}{644}\right)\)	\(e\left(\frac{513}{644}\right)\)
\(\chi_{40310}(1263,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1429}{1932}\right)\)	\(e\left(\frac{85}{1932}\right)\)	\(e\left(\frac{463}{966}\right)\)	\(e\left(\frac{122}{483}\right)\)	\(e\left(\frac{1475}{1932}\right)\)	\(e\left(\frac{25}{276}\right)\)	\(e\left(\frac{383}{483}\right)\)	\(e\left(\frac{757}{966}\right)\)	\(e\left(\frac{335}{644}\right)\)	\(e\left(\frac{141}{644}\right)\)
\(\chi_{40310}(1283,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1697}{1932}\right)\)	\(e\left(\frac{1361}{1932}\right)\)	\(e\left(\frac{731}{966}\right)\)	\(e\left(\frac{226}{483}\right)\)	\(e\left(\frac{547}{1932}\right)\)	\(e\left(\frac{173}{276}\right)\)	\(e\left(\frac{274}{483}\right)\)	\(e\left(\frac{563}{966}\right)\)	\(e\left(\frac{515}{644}\right)\)	\(e\left(\frac{409}{644}\right)\)
\(\chi_{40310}(1383,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1721}{1932}\right)\)	\(e\left(\frac{293}{1932}\right)\)	\(e\left(\frac{755}{966}\right)\)	\(e\left(\frac{466}{483}\right)\)	\(e\left(\frac{1675}{1932}\right)\)	\(e\left(\frac{5}{276}\right)\)	\(e\left(\frac{394}{483}\right)\)	\(e\left(\frac{41}{966}\right)\)	\(e\left(\frac{435}{644}\right)\)	\(e\left(\frac{433}{644}\right)\)

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