LMFDB - Dirichlet character orbit 3151.be

Show commands: Magma / Pari/GP / SageMath

comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(3151, base_ring=CyclotomicField(1496)) M = H._module chi = DirichletCharacter(H, M([1088,11])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(3, 3151)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

magma:// Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("3151.3"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$3151$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$3151$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$1496$	comment:Order sage:chi.multiplicative_order() gp:charorder(g,chi) magma:Order(chi);
Real:	no	comment:Whether the character is real sage:chi.multiplicative_order() <= 2 gp:charorder(g,chi) <= 2 magma:Order(chi) le 2;
Primitive:	yes	comment:If the character is primitive sage:chi.is_primitive() gp:#znconreyconductor(g,chi)==1 magma:IsPrimitive(chi);
Minimal:	yes
Parity:	odd	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);

Related number fields

Field of values:	$\Q(\zeta_{1496})$
Fixed field:	Number field defined by a degree 1496 polynomial (not computed)

First 31 of 640 characters in Galois orbit

Character	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{3151}(3,\cdot)$	$-1$	$1$	$e\left(\frac{395}{748}\right)$	$e\left(\frac{963}{1496}\right)$	$e\left(\frac{21}{374}\right)$	$e\left(\frac{417}{1496}\right)$	$e\left(\frac{257}{1496}\right)$	$e\left(\frac{95}{748}\right)$	$e\left(\frac{437}{748}\right)$	$e\left(\frac{215}{748}\right)$	$e\left(\frac{71}{88}\right)$	$e\left(\frac{331}{748}\right)$
$\chi_{3151}(6,\cdot)$	$-1$	$1$	$e\left(\frac{333}{748}\right)$	$e\left(\frac{257}{1496}\right)$	$e\left(\frac{333}{374}\right)$	$e\left(\frac{1323}{1496}\right)$	$e\left(\frac{923}{1496}\right)$	$e\left(\frac{705}{748}\right)$	$e\left(\frac{251}{748}\right)$	$e\left(\frac{257}{748}\right)$	$e\left(\frac{29}{88}\right)$	$e\left(\frac{173}{748}\right)$
$\chi_{3151}(12,\cdot)$	$-1$	$1$	$e\left(\frac{271}{748}\right)$	$e\left(\frac{1047}{1496}\right)$	$e\left(\frac{271}{374}\right)$	$e\left(\frac{733}{1496}\right)$	$e\left(\frac{93}{1496}\right)$	$e\left(\frac{567}{748}\right)$	$e\left(\frac{65}{748}\right)$	$e\left(\frac{299}{748}\right)$	$e\left(\frac{75}{88}\right)$	$e\left(\frac{15}{748}\right)$
$\chi_{3151}(13,\cdot)$	$-1$	$1$	$e\left(\frac{83}{748}\right)$	$e\left(\frac{547}{1496}\right)$	$e\left(\frac{83}{374}\right)$	$e\left(\frac{633}{1496}\right)$	$e\left(\frac{713}{1496}\right)$	$e\left(\frac{607}{748}\right)$	$e\left(\frac{249}{748}\right)$	$e\left(\frac{547}{748}\right)$	$e\left(\frac{47}{88}\right)$	$e\left(\frac{115}{748}\right)$
$\chi_{3151}(26,\cdot)$	$-1$	$1$	$e\left(\frac{21}{748}\right)$	$e\left(\frac{1337}{1496}\right)$	$e\left(\frac{21}{374}\right)$	$e\left(\frac{43}{1496}\right)$	$e\left(\frac{1379}{1496}\right)$	$e\left(\frac{469}{748}\right)$	$e\left(\frac{63}{748}\right)$	$e\left(\frac{589}{748}\right)$	$e\left(\frac{5}{88}\right)$	$e\left(\frac{705}{748}\right)$
$\chi_{3151}(27,\cdot)$	$-1$	$1$	$e\left(\frac{437}{748}\right)$	$e\left(\frac{1393}{1496}\right)$	$e\left(\frac{63}{374}\right)$	$e\left(\frac{1251}{1496}\right)$	$e\left(\frac{771}{1496}\right)$	$e\left(\frac{285}{748}\right)$	$e\left(\frac{563}{748}\right)$	$e\left(\frac{645}{748}\right)$	$e\left(\frac{37}{88}\right)$	$e\left(\frac{245}{748}\right)$
$\chi_{3151}(29,\cdot)$	$-1$	$1$	$e\left(\frac{245}{748}\right)$	$e\left(\frac{1137}{1496}\right)$	$e\left(\frac{245}{374}\right)$	$e\left(\frac{3}{1496}\right)$	$e\left(\frac{131}{1496}\right)$	$e\left(\frac{485}{748}\right)$	$e\left(\frac{735}{748}\right)$	$e\left(\frac{389}{748}\right)$	$e\left(\frac{29}{88}\right)$	$e\left(\frac{745}{748}\right)$
$\chi_{3151}(31,\cdot)$	$-1$	$1$	$e\left(\frac{683}{748}\right)$	$e\left(\frac{1347}{1496}\right)$	$e\left(\frac{309}{374}\right)$	$e\left(\frac{793}{1496}\right)$	$e\left(\frac{1217}{1496}\right)$	$e\left(\frac{543}{748}\right)$	$e\left(\frac{553}{748}\right)$	$e\left(\frac{599}{748}\right)$	$e\left(\frac{39}{88}\right)$	$e\left(\frac{703}{748}\right)$
$\chi_{3151}(35,\cdot)$	$-1$	$1$	$e\left(\frac{315}{748}\right)$	$e\left(\frac{607}{1496}\right)$	$e\left(\frac{315}{374}\right)$	$e\left(\frac{645}{1496}\right)$	$e\left(\frac{1237}{1496}\right)$	$e\left(\frac{303}{748}\right)$	$e\left(\frac{197}{748}\right)$	$e\left(\frac{607}{748}\right)$	$e\left(\frac{75}{88}\right)$	$e\left(\frac{103}{748}\right)$
$\chi_{3151}(48,\cdot)$	$-1$	$1$	$e\left(\frac{147}{748}\right)$	$e\left(\frac{1131}{1496}\right)$	$e\left(\frac{147}{374}\right)$	$e\left(\frac{1049}{1496}\right)$	$e\left(\frac{1425}{1496}\right)$	$e\left(\frac{291}{748}\right)$	$e\left(\frac{441}{748}\right)$	$e\left(\frac{383}{748}\right)$	$e\left(\frac{79}{88}\right)$	$e\left(\frac{447}{748}\right)$
$\chi_{3151}(52,\cdot)$	$-1$	$1$	$e\left(\frac{707}{748}\right)$	$e\left(\frac{631}{1496}\right)$	$e\left(\frac{333}{374}\right)$	$e\left(\frac{949}{1496}\right)$	$e\left(\frac{549}{1496}\right)$	$e\left(\frac{331}{748}\right)$	$e\left(\frac{625}{748}\right)$	$e\left(\frac{631}{748}\right)$	$e\left(\frac{51}{88}\right)$	$e\left(\frac{547}{748}\right)$
$\chi_{3151}(54,\cdot)$	$-1$	$1$	$e\left(\frac{375}{748}\right)$	$e\left(\frac{687}{1496}\right)$	$e\left(\frac{1}{374}\right)$	$e\left(\frac{661}{1496}\right)$	$e\left(\frac{1437}{1496}\right)$	$e\left(\frac{147}{748}\right)$	$e\left(\frac{377}{748}\right)$	$e\left(\frac{687}{748}\right)$	$e\left(\frac{83}{88}\right)$	$e\left(\frac{87}{748}\right)$
$\chi_{3151}(55,\cdot)$	$-1$	$1$	$e\left(\frac{295}{748}\right)$	$e\left(\frac{1079}{1496}\right)$	$e\left(\frac{295}{374}\right)$	$e\left(\frac{141}{1496}\right)$	$e\left(\frac{173}{1496}\right)$	$e\left(\frac{355}{748}\right)$	$e\left(\frac{137}{748}\right)$	$e\left(\frac{331}{748}\right)$	$e\left(\frac{43}{88}\right)$	$e\left(\frac{607}{748}\right)$
$\chi_{3151}(58,\cdot)$	$-1$	$1$	$e\left(\frac{183}{748}\right)$	$e\left(\frac{431}{1496}\right)$	$e\left(\frac{183}{374}\right)$	$e\left(\frac{909}{1496}\right)$	$e\left(\frac{797}{1496}\right)$	$e\left(\frac{347}{748}\right)$	$e\left(\frac{549}{748}\right)$	$e\left(\frac{431}{748}\right)$	$e\left(\frac{75}{88}\right)$	$e\left(\frac{587}{748}\right)$
$\chi_{3151}(62,\cdot)$	$-1$	$1$	$e\left(\frac{621}{748}\right)$	$e\left(\frac{641}{1496}\right)$	$e\left(\frac{247}{374}\right)$	$e\left(\frac{203}{1496}\right)$	$e\left(\frac{387}{1496}\right)$	$e\left(\frac{405}{748}\right)$	$e\left(\frac{367}{748}\right)$	$e\left(\frac{641}{748}\right)$	$e\left(\frac{85}{88}\right)$	$e\left(\frac{545}{748}\right)$
$\chi_{3151}(71,\cdot)$	$-1$	$1$	$e\left(\frac{719}{748}\right)$	$e\left(\frac{1395}{1496}\right)$	$e\left(\frac{345}{374}\right)$	$e\left(\frac{1401}{1496}\right)$	$e\left(\frac{1337}{1496}\right)$	$e\left(\frac{599}{748}\right)$	$e\left(\frac{661}{748}\right)$	$e\left(\frac{647}{748}\right)$	$e\left(\frac{79}{88}\right)$	$e\left(\frac{95}{748}\right)$
$\chi_{3151}(75,\cdot)$	$-1$	$1$	$e\left(\frac{553}{748}\right)$	$e\left(\frac{301}{1496}\right)$	$e\left(\frac{179}{374}\right)$	$e\left(\frac{135}{1496}\right)$	$e\left(\frac{1407}{1496}\right)$	$e\left(\frac{133}{748}\right)$	$e\left(\frac{163}{748}\right)$	$e\left(\frac{301}{748}\right)$	$e\left(\frac{73}{88}\right)$	$e\left(\frac{613}{748}\right)$
$\chi_{3151}(82,\cdot)$	$-1$	$1$	$e\left(\frac{567}{748}\right)$	$e\left(\frac{195}{1496}\right)$	$e\left(\frac{193}{374}\right)$	$e\left(\frac{1161}{1496}\right)$	$e\left(\frac{1329}{1496}\right)$	$e\left(\frac{695}{748}\right)$	$e\left(\frac{205}{748}\right)$	$e\left(\frac{195}{748}\right)$	$e\left(\frac{47}{88}\right)$	$e\left(\frac{335}{748}\right)$
$\chi_{3151}(85,\cdot)$	$-1$	$1$	$e\left(\frac{27}{748}\right)$	$e\left(\frac{971}{1496}\right)$	$e\left(\frac{27}{374}\right)$	$e\left(\frac{1017}{1496}\right)$	$e\left(\frac{1025}{1496}\right)$	$e\left(\frac{603}{748}\right)$	$e\left(\frac{81}{748}\right)$	$e\left(\frac{223}{748}\right)$	$e\left(\frac{63}{88}\right)$	$e\left(\frac{479}{748}\right)$
$\chi_{3151}(94,\cdot)$	$-1$	$1$	$e\left(\frac{235}{748}\right)$	$e\left(\frac{999}{1496}\right)$	$e\left(\frac{235}{374}\right)$	$e\left(\frac{125}{1496}\right)$	$e\left(\frac{1469}{1496}\right)$	$e\left(\frac{511}{748}\right)$	$e\left(\frac{705}{748}\right)$	$e\left(\frac{251}{748}\right)$	$e\left(\frac{35}{88}\right)$	$e\left(\frac{623}{748}\right)$
$\chi_{3151}(95,\cdot)$	$-1$	$1$	$e\left(\frac{263}{748}\right)$	$e\left(\frac{787}{1496}\right)$	$e\left(\frac{263}{374}\right)$	$e\left(\frac{681}{1496}\right)$	$e\left(\frac{1313}{1496}\right)$	$e\left(\frac{139}{748}\right)$	$e\left(\frac{41}{748}\right)$	$e\left(\frac{39}{748}\right)$	$e\left(\frac{71}{88}\right)$	$e\left(\frac{67}{748}\right)$
$\chi_{3151}(104,\cdot)$	$-1$	$1$	$e\left(\frac{645}{748}\right)$	$e\left(\frac{1421}{1496}\right)$	$e\left(\frac{271}{374}\right)$	$e\left(\frac{359}{1496}\right)$	$e\left(\frac{1215}{1496}\right)$	$e\left(\frac{193}{748}\right)$	$e\left(\frac{439}{748}\right)$	$e\left(\frac{673}{748}\right)$	$e\left(\frac{9}{88}\right)$	$e\left(\frac{389}{748}\right)$
$\chi_{3151}(108,\cdot)$	$-1$	$1$	$e\left(\frac{313}{748}\right)$	$e\left(\frac{1477}{1496}\right)$	$e\left(\frac{313}{374}\right)$	$e\left(\frac{71}{1496}\right)$	$e\left(\frac{607}{1496}\right)$	$e\left(\frac{9}{748}\right)$	$e\left(\frac{191}{748}\right)$	$e\left(\frac{729}{748}\right)$	$e\left(\frac{41}{88}\right)$	$e\left(\frac{677}{748}\right)$
$\chi_{3151}(110,\cdot)$	$-1$	$1$	$e\left(\frac{233}{748}\right)$	$e\left(\frac{373}{1496}\right)$	$e\left(\frac{233}{374}\right)$	$e\left(\frac{1047}{1496}\right)$	$e\left(\frac{839}{1496}\right)$	$e\left(\frac{217}{748}\right)$	$e\left(\frac{699}{748}\right)$	$e\left(\frac{373}{748}\right)$	$e\left(\frac{1}{88}\right)$	$e\left(\frac{449}{748}\right)$
$\chi_{3151}(117,\cdot)$	$-1$	$1$	$e\left(\frac{125}{748}\right)$	$e\left(\frac{977}{1496}\right)$	$e\left(\frac{125}{374}\right)$	$e\left(\frac{1467}{1496}\right)$	$e\left(\frac{1227}{1496}\right)$	$e\left(\frac{49}{748}\right)$	$e\left(\frac{375}{748}\right)$	$e\left(\frac{229}{748}\right)$	$e\left(\frac{13}{88}\right)$	$e\left(\frac{29}{748}\right)$
$\chi_{3151}(124,\cdot)$	$-1$	$1$	$e\left(\frac{559}{748}\right)$	$e\left(\frac{1431}{1496}\right)$	$e\left(\frac{185}{374}\right)$	$e\left(\frac{1109}{1496}\right)$	$e\left(\frac{1053}{1496}\right)$	$e\left(\frac{267}{748}\right)$	$e\left(\frac{181}{748}\right)$	$e\left(\frac{683}{748}\right)$	$e\left(\frac{43}{88}\right)$	$e\left(\frac{387}{748}\right)$
$\chi_{3151}(131,\cdot)$	$-1$	$1$	$e\left(\frac{401}{748}\right)$	$e\left(\frac{597}{1496}\right)$	$e\left(\frac{27}{374}\right)$	$e\left(\frac{1391}{1496}\right)$	$e\left(\frac{1399}{1496}\right)$	$e\left(\frac{229}{748}\right)$	$e\left(\frac{455}{748}\right)$	$e\left(\frac{597}{748}\right)$	$e\left(\frac{41}{88}\right)$	$e\left(\frac{105}{748}\right)$
$\chi_{3151}(140,\cdot)$	$-1$	$1$	$e\left(\frac{191}{748}\right)$	$e\left(\frac{691}{1496}\right)$	$e\left(\frac{191}{374}\right)$	$e\left(\frac{961}{1496}\right)$	$e\left(\frac{1073}{1496}\right)$	$e\left(\frac{27}{748}\right)$	$e\left(\frac{573}{748}\right)$	$e\left(\frac{691}{748}\right)$	$e\left(\frac{79}{88}\right)$	$e\left(\frac{535}{748}\right)$
$\chi_{3151}(142,\cdot)$	$-1$	$1$	$e\left(\frac{657}{748}\right)$	$e\left(\frac{689}{1496}\right)$	$e\left(\frac{283}{374}\right)$	$e\left(\frac{811}{1496}\right)$	$e\left(\frac{507}{1496}\right)$	$e\left(\frac{461}{748}\right)$	$e\left(\frac{475}{748}\right)$	$e\left(\frac{689}{748}\right)$	$e\left(\frac{37}{88}\right)$	$e\left(\frac{685}{748}\right)$
$\chi_{3151}(150,\cdot)$	$-1$	$1$	$e\left(\frac{491}{748}\right)$	$e\left(\frac{1091}{1496}\right)$	$e\left(\frac{117}{374}\right)$	$e\left(\frac{1041}{1496}\right)$	$e\left(\frac{577}{1496}\right)$	$e\left(\frac{743}{748}\right)$	$e\left(\frac{725}{748}\right)$	$e\left(\frac{343}{748}\right)$	$e\left(\frac{31}{88}\right)$	$e\left(\frac{455}{748}\right)$
$\chi_{3151}(163,\cdot)$	$-1$	$1$	$e\left(\frac{565}{748}\right)$	$e\left(\frac{1065}{1496}\right)$	$e\left(\frac{191}{374}\right)$	$e\left(\frac{587}{1496}\right)$	$e\left(\frac{699}{1496}\right)$	$e\left(\frac{401}{748}\right)$	$e\left(\frac{199}{748}\right)$	$e\left(\frac{317}{748}\right)$	$e\left(\frac{13}{88}\right)$	$e\left(\frac{161}{748}\right)$

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	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\(\chi_{3151}(3,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{395}{748}\right)\)	\(e\left(\frac{963}{1496}\right)\)	\(e\left(\frac{21}{374}\right)\)	\(e\left(\frac{417}{1496}\right)\)	\(e\left(\frac{257}{1496}\right)\)	\(e\left(\frac{95}{748}\right)\)	\(e\left(\frac{437}{748}\right)\)	\(e\left(\frac{215}{748}\right)\)	\(e\left(\frac{71}{88}\right)\)	\(e\left(\frac{331}{748}\right)\)
\(\chi_{3151}(6,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{333}{748}\right)\)	\(e\left(\frac{257}{1496}\right)\)	\(e\left(\frac{333}{374}\right)\)	\(e\left(\frac{1323}{1496}\right)\)	\(e\left(\frac{923}{1496}\right)\)	\(e\left(\frac{705}{748}\right)\)	\(e\left(\frac{251}{748}\right)\)	\(e\left(\frac{257}{748}\right)\)	\(e\left(\frac{29}{88}\right)\)	\(e\left(\frac{173}{748}\right)\)
\(\chi_{3151}(12,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{271}{748}\right)\)	\(e\left(\frac{1047}{1496}\right)\)	\(e\left(\frac{271}{374}\right)\)	\(e\left(\frac{733}{1496}\right)\)	\(e\left(\frac{93}{1496}\right)\)	\(e\left(\frac{567}{748}\right)\)	\(e\left(\frac{65}{748}\right)\)	\(e\left(\frac{299}{748}\right)\)	\(e\left(\frac{75}{88}\right)\)	\(e\left(\frac{15}{748}\right)\)
\(\chi_{3151}(13,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{83}{748}\right)\)	\(e\left(\frac{547}{1496}\right)\)	\(e\left(\frac{83}{374}\right)\)	\(e\left(\frac{633}{1496}\right)\)	\(e\left(\frac{713}{1496}\right)\)	\(e\left(\frac{607}{748}\right)\)	\(e\left(\frac{249}{748}\right)\)	\(e\left(\frac{547}{748}\right)\)	\(e\left(\frac{47}{88}\right)\)	\(e\left(\frac{115}{748}\right)\)
\(\chi_{3151}(26,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{21}{748}\right)\)	\(e\left(\frac{1337}{1496}\right)\)	\(e\left(\frac{21}{374}\right)\)	\(e\left(\frac{43}{1496}\right)\)	\(e\left(\frac{1379}{1496}\right)\)	\(e\left(\frac{469}{748}\right)\)	\(e\left(\frac{63}{748}\right)\)	\(e\left(\frac{589}{748}\right)\)	\(e\left(\frac{5}{88}\right)\)	\(e\left(\frac{705}{748}\right)\)
\(\chi_{3151}(27,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{437}{748}\right)\)	\(e\left(\frac{1393}{1496}\right)\)	\(e\left(\frac{63}{374}\right)\)	\(e\left(\frac{1251}{1496}\right)\)	\(e\left(\frac{771}{1496}\right)\)	\(e\left(\frac{285}{748}\right)\)	\(e\left(\frac{563}{748}\right)\)	\(e\left(\frac{645}{748}\right)\)	\(e\left(\frac{37}{88}\right)\)	\(e\left(\frac{245}{748}\right)\)
\(\chi_{3151}(29,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{245}{748}\right)\)	\(e\left(\frac{1137}{1496}\right)\)	\(e\left(\frac{245}{374}\right)\)	\(e\left(\frac{3}{1496}\right)\)	\(e\left(\frac{131}{1496}\right)\)	\(e\left(\frac{485}{748}\right)\)	\(e\left(\frac{735}{748}\right)\)	\(e\left(\frac{389}{748}\right)\)	\(e\left(\frac{29}{88}\right)\)	\(e\left(\frac{745}{748}\right)\)
\(\chi_{3151}(31,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{683}{748}\right)\)	\(e\left(\frac{1347}{1496}\right)\)	\(e\left(\frac{309}{374}\right)\)	\(e\left(\frac{793}{1496}\right)\)	\(e\left(\frac{1217}{1496}\right)\)	\(e\left(\frac{543}{748}\right)\)	\(e\left(\frac{553}{748}\right)\)	\(e\left(\frac{599}{748}\right)\)	\(e\left(\frac{39}{88}\right)\)	\(e\left(\frac{703}{748}\right)\)
\(\chi_{3151}(35,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{315}{748}\right)\)	\(e\left(\frac{607}{1496}\right)\)	\(e\left(\frac{315}{374}\right)\)	\(e\left(\frac{645}{1496}\right)\)	\(e\left(\frac{1237}{1496}\right)\)	\(e\left(\frac{303}{748}\right)\)	\(e\left(\frac{197}{748}\right)\)	\(e\left(\frac{607}{748}\right)\)	\(e\left(\frac{75}{88}\right)\)	\(e\left(\frac{103}{748}\right)\)
\(\chi_{3151}(48,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{147}{748}\right)\)	\(e\left(\frac{1131}{1496}\right)\)	\(e\left(\frac{147}{374}\right)\)	\(e\left(\frac{1049}{1496}\right)\)	\(e\left(\frac{1425}{1496}\right)\)	\(e\left(\frac{291}{748}\right)\)	\(e\left(\frac{441}{748}\right)\)	\(e\left(\frac{383}{748}\right)\)	\(e\left(\frac{79}{88}\right)\)	\(e\left(\frac{447}{748}\right)\)
\(\chi_{3151}(52,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{707}{748}\right)\)	\(e\left(\frac{631}{1496}\right)\)	\(e\left(\frac{333}{374}\right)\)	\(e\left(\frac{949}{1496}\right)\)	\(e\left(\frac{549}{1496}\right)\)	\(e\left(\frac{331}{748}\right)\)	\(e\left(\frac{625}{748}\right)\)	\(e\left(\frac{631}{748}\right)\)	\(e\left(\frac{51}{88}\right)\)	\(e\left(\frac{547}{748}\right)\)
\(\chi_{3151}(54,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{375}{748}\right)\)	\(e\left(\frac{687}{1496}\right)\)	\(e\left(\frac{1}{374}\right)\)	\(e\left(\frac{661}{1496}\right)\)	\(e\left(\frac{1437}{1496}\right)\)	\(e\left(\frac{147}{748}\right)\)	\(e\left(\frac{377}{748}\right)\)	\(e\left(\frac{687}{748}\right)\)	\(e\left(\frac{83}{88}\right)\)	\(e\left(\frac{87}{748}\right)\)
\(\chi_{3151}(55,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{295}{748}\right)\)	\(e\left(\frac{1079}{1496}\right)\)	\(e\left(\frac{295}{374}\right)\)	\(e\left(\frac{141}{1496}\right)\)	\(e\left(\frac{173}{1496}\right)\)	\(e\left(\frac{355}{748}\right)\)	\(e\left(\frac{137}{748}\right)\)	\(e\left(\frac{331}{748}\right)\)	\(e\left(\frac{43}{88}\right)\)	\(e\left(\frac{607}{748}\right)\)
\(\chi_{3151}(58,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{183}{748}\right)\)	\(e\left(\frac{431}{1496}\right)\)	\(e\left(\frac{183}{374}\right)\)	\(e\left(\frac{909}{1496}\right)\)	\(e\left(\frac{797}{1496}\right)\)	\(e\left(\frac{347}{748}\right)\)	\(e\left(\frac{549}{748}\right)\)	\(e\left(\frac{431}{748}\right)\)	\(e\left(\frac{75}{88}\right)\)	\(e\left(\frac{587}{748}\right)\)
\(\chi_{3151}(62,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{621}{748}\right)\)	\(e\left(\frac{641}{1496}\right)\)	\(e\left(\frac{247}{374}\right)\)	\(e\left(\frac{203}{1496}\right)\)	\(e\left(\frac{387}{1496}\right)\)	\(e\left(\frac{405}{748}\right)\)	\(e\left(\frac{367}{748}\right)\)	\(e\left(\frac{641}{748}\right)\)	\(e\left(\frac{85}{88}\right)\)	\(e\left(\frac{545}{748}\right)\)
\(\chi_{3151}(71,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{719}{748}\right)\)	\(e\left(\frac{1395}{1496}\right)\)	\(e\left(\frac{345}{374}\right)\)	\(e\left(\frac{1401}{1496}\right)\)	\(e\left(\frac{1337}{1496}\right)\)	\(e\left(\frac{599}{748}\right)\)	\(e\left(\frac{661}{748}\right)\)	\(e\left(\frac{647}{748}\right)\)	\(e\left(\frac{79}{88}\right)\)	\(e\left(\frac{95}{748}\right)\)
\(\chi_{3151}(75,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{553}{748}\right)\)	\(e\left(\frac{301}{1496}\right)\)	\(e\left(\frac{179}{374}\right)\)	\(e\left(\frac{135}{1496}\right)\)	\(e\left(\frac{1407}{1496}\right)\)	\(e\left(\frac{133}{748}\right)\)	\(e\left(\frac{163}{748}\right)\)	\(e\left(\frac{301}{748}\right)\)	\(e\left(\frac{73}{88}\right)\)	\(e\left(\frac{613}{748}\right)\)
\(\chi_{3151}(82,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{567}{748}\right)\)	\(e\left(\frac{195}{1496}\right)\)	\(e\left(\frac{193}{374}\right)\)	\(e\left(\frac{1161}{1496}\right)\)	\(e\left(\frac{1329}{1496}\right)\)	\(e\left(\frac{695}{748}\right)\)	\(e\left(\frac{205}{748}\right)\)	\(e\left(\frac{195}{748}\right)\)	\(e\left(\frac{47}{88}\right)\)	\(e\left(\frac{335}{748}\right)\)
\(\chi_{3151}(85,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{27}{748}\right)\)	\(e\left(\frac{971}{1496}\right)\)	\(e\left(\frac{27}{374}\right)\)	\(e\left(\frac{1017}{1496}\right)\)	\(e\left(\frac{1025}{1496}\right)\)	\(e\left(\frac{603}{748}\right)\)	\(e\left(\frac{81}{748}\right)\)	\(e\left(\frac{223}{748}\right)\)	\(e\left(\frac{63}{88}\right)\)	\(e\left(\frac{479}{748}\right)\)
\(\chi_{3151}(94,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{235}{748}\right)\)	\(e\left(\frac{999}{1496}\right)\)	\(e\left(\frac{235}{374}\right)\)	\(e\left(\frac{125}{1496}\right)\)	\(e\left(\frac{1469}{1496}\right)\)	\(e\left(\frac{511}{748}\right)\)	\(e\left(\frac{705}{748}\right)\)	\(e\left(\frac{251}{748}\right)\)	\(e\left(\frac{35}{88}\right)\)	\(e\left(\frac{623}{748}\right)\)
\(\chi_{3151}(95,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{263}{748}\right)\)	\(e\left(\frac{787}{1496}\right)\)	\(e\left(\frac{263}{374}\right)\)	\(e\left(\frac{681}{1496}\right)\)	\(e\left(\frac{1313}{1496}\right)\)	\(e\left(\frac{139}{748}\right)\)	\(e\left(\frac{41}{748}\right)\)	\(e\left(\frac{39}{748}\right)\)	\(e\left(\frac{71}{88}\right)\)	\(e\left(\frac{67}{748}\right)\)
\(\chi_{3151}(104,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{645}{748}\right)\)	\(e\left(\frac{1421}{1496}\right)\)	\(e\left(\frac{271}{374}\right)\)	\(e\left(\frac{359}{1496}\right)\)	\(e\left(\frac{1215}{1496}\right)\)	\(e\left(\frac{193}{748}\right)\)	\(e\left(\frac{439}{748}\right)\)	\(e\left(\frac{673}{748}\right)\)	\(e\left(\frac{9}{88}\right)\)	\(e\left(\frac{389}{748}\right)\)
\(\chi_{3151}(108,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{313}{748}\right)\)	\(e\left(\frac{1477}{1496}\right)\)	\(e\left(\frac{313}{374}\right)\)	\(e\left(\frac{71}{1496}\right)\)	\(e\left(\frac{607}{1496}\right)\)	\(e\left(\frac{9}{748}\right)\)	\(e\left(\frac{191}{748}\right)\)	\(e\left(\frac{729}{748}\right)\)	\(e\left(\frac{41}{88}\right)\)	\(e\left(\frac{677}{748}\right)\)
\(\chi_{3151}(110,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{233}{748}\right)\)	\(e\left(\frac{373}{1496}\right)\)	\(e\left(\frac{233}{374}\right)\)	\(e\left(\frac{1047}{1496}\right)\)	\(e\left(\frac{839}{1496}\right)\)	\(e\left(\frac{217}{748}\right)\)	\(e\left(\frac{699}{748}\right)\)	\(e\left(\frac{373}{748}\right)\)	\(e\left(\frac{1}{88}\right)\)	\(e\left(\frac{449}{748}\right)\)
\(\chi_{3151}(117,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{125}{748}\right)\)	\(e\left(\frac{977}{1496}\right)\)	\(e\left(\frac{125}{374}\right)\)	\(e\left(\frac{1467}{1496}\right)\)	\(e\left(\frac{1227}{1496}\right)\)	\(e\left(\frac{49}{748}\right)\)	\(e\left(\frac{375}{748}\right)\)	\(e\left(\frac{229}{748}\right)\)	\(e\left(\frac{13}{88}\right)\)	\(e\left(\frac{29}{748}\right)\)
\(\chi_{3151}(124,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{559}{748}\right)\)	\(e\left(\frac{1431}{1496}\right)\)	\(e\left(\frac{185}{374}\right)\)	\(e\left(\frac{1109}{1496}\right)\)	\(e\left(\frac{1053}{1496}\right)\)	\(e\left(\frac{267}{748}\right)\)	\(e\left(\frac{181}{748}\right)\)	\(e\left(\frac{683}{748}\right)\)	\(e\left(\frac{43}{88}\right)\)	\(e\left(\frac{387}{748}\right)\)
\(\chi_{3151}(131,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{401}{748}\right)\)	\(e\left(\frac{597}{1496}\right)\)	\(e\left(\frac{27}{374}\right)\)	\(e\left(\frac{1391}{1496}\right)\)	\(e\left(\frac{1399}{1496}\right)\)	\(e\left(\frac{229}{748}\right)\)	\(e\left(\frac{455}{748}\right)\)	\(e\left(\frac{597}{748}\right)\)	\(e\left(\frac{41}{88}\right)\)	\(e\left(\frac{105}{748}\right)\)
\(\chi_{3151}(140,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{191}{748}\right)\)	\(e\left(\frac{691}{1496}\right)\)	\(e\left(\frac{191}{374}\right)\)	\(e\left(\frac{961}{1496}\right)\)	\(e\left(\frac{1073}{1496}\right)\)	\(e\left(\frac{27}{748}\right)\)	\(e\left(\frac{573}{748}\right)\)	\(e\left(\frac{691}{748}\right)\)	\(e\left(\frac{79}{88}\right)\)	\(e\left(\frac{535}{748}\right)\)
\(\chi_{3151}(142,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{657}{748}\right)\)	\(e\left(\frac{689}{1496}\right)\)	\(e\left(\frac{283}{374}\right)\)	\(e\left(\frac{811}{1496}\right)\)	\(e\left(\frac{507}{1496}\right)\)	\(e\left(\frac{461}{748}\right)\)	\(e\left(\frac{475}{748}\right)\)	\(e\left(\frac{689}{748}\right)\)	\(e\left(\frac{37}{88}\right)\)	\(e\left(\frac{685}{748}\right)\)
\(\chi_{3151}(150,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{491}{748}\right)\)	\(e\left(\frac{1091}{1496}\right)\)	\(e\left(\frac{117}{374}\right)\)	\(e\left(\frac{1041}{1496}\right)\)	\(e\left(\frac{577}{1496}\right)\)	\(e\left(\frac{743}{748}\right)\)	\(e\left(\frac{725}{748}\right)\)	\(e\left(\frac{343}{748}\right)\)	\(e\left(\frac{31}{88}\right)\)	\(e\left(\frac{455}{748}\right)\)
\(\chi_{3151}(163,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{565}{748}\right)\)	\(e\left(\frac{1065}{1496}\right)\)	\(e\left(\frac{191}{374}\right)\)	\(e\left(\frac{587}{1496}\right)\)	\(e\left(\frac{699}{1496}\right)\)	\(e\left(\frac{401}{748}\right)\)	\(e\left(\frac{199}{748}\right)\)	\(e\left(\frac{317}{748}\right)\)	\(e\left(\frac{13}{88}\right)\)	\(e\left(\frac{161}{748}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Basic properties

Related number fields

First 31 of 640 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	3151.be
Modulus	$3151$
Conductor	$3151$
Order	$1496$
Real	no
Primitive	yes
Minimal	yes
Parity	odd

Modulus:	\(3151\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(3151\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(1496\)	comment:Order sage:chi.multiplicative_order() gp:charorder(g,chi) magma:Order(chi);
Real:	no	comment:Whether the character is real sage:chi.multiplicative_order() <= 2 gp:charorder(g,chi) <= 2 magma:Order(chi) le 2;
Primitive:	yes	comment:If the character is primitive sage:chi.is_primitive() gp:#znconreyconductor(g,chi)==1 magma:IsPrimitive(chi);
Minimal:	yes
Parity:	odd	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);