LMFDB - Dirichlet character orbit 91091.sg

Show commands: Magma / Pari/GP / SageMath

comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(91091, base_ring=CyclotomicField(5460)) M = H._module chi = DirichletCharacter(H, M([3900,1092,4655])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(15, 91091)) 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("91091.15"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$91091$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$91091$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$5460$	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:	$\Q(\zeta_{5460})$	comment:Field of values of chi sage:CyclotomicField(chi.multiplicative_order()) gp:nfinit(polcyclo(charorder(g,chi))) magma:CyclotomicField(Order(chi));
Fixed field:	Number field defined by a degree 5460 polynomial (not computed)	comment:Fixed field sage:chi.fixed_field()

First 19 of 1152 characters in Galois orbit

Character	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$8$	$9$	$10$	$12$	$15$
$\chi_{91091}(15,\cdot)$	$-1$	$1$	$e\left(\frac{3407}{5460}\right)$	$e\left(\frac{44}{1365}\right)$	$e\left(\frac{677}{2730}\right)$	$e\left(\frac{341}{1820}\right)$	$e\left(\frac{3583}{5460}\right)$	$e\left(\frac{1587}{1820}\right)$	$e\left(\frac{88}{1365}\right)$	$e\left(\frac{443}{546}\right)$	$e\left(\frac{51}{182}\right)$	$e\left(\frac{1199}{5460}\right)$
$\chi_{91091}(71,\cdot)$	$-1$	$1$	$e\left(\frac{739}{5460}\right)$	$e\left(\frac{913}{1365}\right)$	$e\left(\frac{739}{2730}\right)$	$e\left(\frac{137}{1820}\right)$	$e\left(\frac{4391}{5460}\right)$	$e\left(\frac{739}{1820}\right)$	$e\left(\frac{461}{1365}\right)$	$e\left(\frac{115}{546}\right)$	$e\left(\frac{171}{182}\right)$	$e\left(\frac{4063}{5460}\right)$
$\chi_{91091}(141,\cdot)$	$-1$	$1$	$e\left(\frac{2801}{5460}\right)$	$e\left(\frac{797}{1365}\right)$	$e\left(\frac{71}{2730}\right)$	$e\left(\frac{603}{1820}\right)$	$e\left(\frac{529}{5460}\right)$	$e\left(\frac{981}{1820}\right)$	$e\left(\frac{229}{1365}\right)$	$e\left(\frac{461}{546}\right)$	$e\left(\frac{111}{182}\right)$	$e\left(\frac{4997}{5460}\right)$
$\chi_{91091}(267,\cdot)$	$-1$	$1$	$e\left(\frac{193}{5460}\right)$	$e\left(\frac{1186}{1365}\right)$	$e\left(\frac{193}{2730}\right)$	$e\left(\frac{319}{1820}\right)$	$e\left(\frac{4937}{5460}\right)$	$e\left(\frac{193}{1820}\right)$	$e\left(\frac{1007}{1365}\right)$	$e\left(\frac{115}{546}\right)$	$e\left(\frac{171}{182}\right)$	$e\left(\frac{241}{5460}\right)$
$\chi_{91091}(323,\cdot)$	$-1$	$1$	$e\left(\frac{3797}{5460}\right)$	$e\left(\frac{1019}{1365}\right)$	$e\left(\frac{1067}{2730}\right)$	$e\left(\frac{731}{1820}\right)$	$e\left(\frac{2413}{5460}\right)$	$e\left(\frac{157}{1820}\right)$	$e\left(\frac{673}{1365}\right)$	$e\left(\frac{53}{546}\right)$	$e\left(\frac{25}{182}\right)$	$e\left(\frac{809}{5460}\right)$
$\chi_{91091}(379,\cdot)$	$-1$	$1$	$e\left(\frac{2039}{5460}\right)$	$e\left(\frac{68}{1365}\right)$	$e\left(\frac{2039}{2730}\right)$	$e\left(\frac{1437}{1820}\right)$	$e\left(\frac{2311}{5460}\right)$	$e\left(\frac{219}{1820}\right)$	$e\left(\frac{136}{1365}\right)$	$e\left(\frac{89}{546}\right)$	$e\left(\frac{145}{182}\right)$	$e\left(\frac{4583}{5460}\right)$
$\chi_{91091}(449,\cdot)$	$-1$	$1$	$e\left(\frac{3541}{5460}\right)$	$e\left(\frac{337}{1365}\right)$	$e\left(\frac{811}{2730}\right)$	$e\left(\frac{223}{1820}\right)$	$e\left(\frac{4889}{5460}\right)$	$e\left(\frac{1721}{1820}\right)$	$e\left(\frac{674}{1365}\right)$	$e\left(\frac{421}{546}\right)$	$e\left(\frac{99}{182}\right)$	$e\left(\frac{2017}{5460}\right)$
$\chi_{91091}(631,\cdot)$	$-1$	$1$	$e\left(\frac{337}{5460}\right)$	$e\left(\frac{34}{1365}\right)$	$e\left(\frac{337}{2730}\right)$	$e\left(\frac{491}{1820}\right)$	$e\left(\frac{473}{5460}\right)$	$e\left(\frac{337}{1820}\right)$	$e\left(\frac{68}{1365}\right)$	$e\left(\frac{181}{546}\right)$	$e\left(\frac{27}{182}\right)$	$e\left(\frac{1609}{5460}\right)$
$\chi_{91091}(652,\cdot)$	$-1$	$1$	$e\left(\frac{3743}{5460}\right)$	$e\left(\frac{86}{1365}\right)$	$e\left(\frac{1013}{2730}\right)$	$e\left(\frac{1349}{1820}\right)$	$e\left(\frac{4087}{5460}\right)$	$e\left(\frac{103}{1820}\right)$	$e\left(\frac{172}{1365}\right)$	$e\left(\frac{233}{546}\right)$	$e\left(\frac{79}{182}\right)$	$e\left(\frac{4391}{5460}\right)$
$\chi_{91091}(708,\cdot)$	$-1$	$1$	$e\left(\frac{487}{5460}\right)$	$e\left(\frac{199}{1365}\right)$	$e\left(\frac{487}{2730}\right)$	$e\left(\frac{1201}{1820}\right)$	$e\left(\frac{1283}{5460}\right)$	$e\left(\frac{487}{1820}\right)$	$e\left(\frac{398}{1365}\right)$	$e\left(\frac{409}{546}\right)$	$e\left(\frac{59}{182}\right)$	$e\left(\frac{4399}{5460}\right)$
$\chi_{91091}(960,\cdot)$	$-1$	$1$	$e\left(\frac{4553}{5460}\right)$	$e\left(\frac{431}{1365}\right)$	$e\left(\frac{1823}{2730}\right)$	$e\left(\frac{1179}{1820}\right)$	$e\left(\frac{817}{5460}\right)$	$e\left(\frac{913}{1820}\right)$	$e\left(\frac{862}{1365}\right)$	$e\left(\frac{263}{546}\right)$	$e\left(\frac{179}{182}\right)$	$e\left(\frac{5261}{5460}\right)$
$\chi_{91091}(1016,\cdot)$	$-1$	$1$	$e\left(\frac{3467}{5460}\right)$	$e\left(\frac{929}{1365}\right)$	$e\left(\frac{737}{2730}\right)$	$e\left(\frac{261}{1820}\right)$	$e\left(\frac{1723}{5460}\right)$	$e\left(\frac{1647}{1820}\right)$	$e\left(\frac{493}{1365}\right)$	$e\left(\frac{425}{546}\right)$	$e\left(\frac{173}{182}\right)$	$e\left(\frac{4499}{5460}\right)$
$\chi_{91091}(1072,\cdot)$	$-1$	$1$	$e\left(\frac{2059}{5460}\right)$	$e\left(\frac{1273}{1365}\right)$	$e\left(\frac{2059}{2730}\right)$	$e\left(\frac{197}{1820}\right)$	$e\left(\frac{1691}{5460}\right)$	$e\left(\frac{239}{1820}\right)$	$e\left(\frac{1181}{1365}\right)$	$e\left(\frac{265}{546}\right)$	$e\left(\frac{125}{182}\right)$	$e\left(\frac{223}{5460}\right)$
$\chi_{91091}(1142,\cdot)$	$-1$	$1$	$e\left(\frac{1181}{5460}\right)$	$e\left(\frac{107}{1365}\right)$	$e\left(\frac{1181}{2730}\right)$	$e\left(\frac{943}{1820}\right)$	$e\left(\frac{1609}{5460}\right)$	$e\left(\frac{1181}{1820}\right)$	$e\left(\frac{214}{1365}\right)$	$e\left(\frac{401}{546}\right)$	$e\left(\frac{93}{182}\right)$	$e\left(\frac{3257}{5460}\right)$
$\chi_{91091}(1268,\cdot)$	$-1$	$1$	$e\left(\frac{2773}{5460}\right)$	$e\left(\frac{1021}{1365}\right)$	$e\left(\frac{43}{2730}\right)$	$e\left(\frac{519}{1820}\right)$	$e\left(\frac{1397}{5460}\right)$	$e\left(\frac{953}{1820}\right)$	$e\left(\frac{677}{1365}\right)$	$e\left(\frac{433}{546}\right)$	$e\left(\frac{139}{182}\right)$	$e\left(\frac{181}{5460}\right)$
$\chi_{91091}(1345,\cdot)$	$-1$	$1$	$e\left(\frac{4603}{5460}\right)$	$e\left(\frac{31}{1365}\right)$	$e\left(\frac{1873}{2730}\right)$	$e\left(\frac{809}{1820}\right)$	$e\left(\frac{4727}{5460}\right)$	$e\left(\frac{963}{1820}\right)$	$e\left(\frac{62}{1365}\right)$	$e\left(\frac{157}{546}\right)$	$e\left(\frac{129}{182}\right)$	$e\left(\frac{2551}{5460}\right)$
$\chi_{91091}(1380,\cdot)$	$-1$	$1$	$e\left(\frac{2099}{5460}\right)$	$e\left(\frac{953}{1365}\right)$	$e\left(\frac{2099}{2730}\right)$	$e\left(\frac{1357}{1820}\right)$	$e\left(\frac{451}{5460}\right)$	$e\left(\frac{279}{1820}\right)$	$e\left(\frac{541}{1365}\right)$	$e\left(\frac{71}{546}\right)$	$e\left(\frac{85}{182}\right)$	$e\left(\frac{2423}{5460}\right)$
$\chi_{91091}(1450,\cdot)$	$-1$	$1$	$e\left(\frac{661}{5460}\right)$	$e\left(\frac{172}{1365}\right)$	$e\left(\frac{661}{2730}\right)$	$e\left(\frac{423}{1820}\right)$	$e\left(\frac{1349}{5460}\right)$	$e\left(\frac{661}{1820}\right)$	$e\left(\frac{344}{1365}\right)$	$e\left(\frac{193}{546}\right)$	$e\left(\frac{67}{182}\right)$	$e\left(\frac{1957}{5460}\right)$
$\chi_{91091}(1527,\cdot)$	$-1$	$1$	$e\left(\frac{3751}{5460}\right)$	$e\left(\frac{22}{1365}\right)$	$e\left(\frac{1021}{2730}\right)$	$e\left(\frac{853}{1820}\right)$	$e\left(\frac{3839}{5460}\right)$	$e\left(\frac{111}{1820}\right)$	$e\left(\frac{44}{1365}\right)$	$e\left(\frac{85}{546}\right)$	$e\left(\frac{71}{182}\right)$	$e\left(\frac{2647}{5460}\right)$

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	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(8\)	\(9\)	\(10\)	\(12\)	\(15\)
\(\chi_{91091}(15,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{3407}{5460}\right)\)	\(e\left(\frac{44}{1365}\right)\)	\(e\left(\frac{677}{2730}\right)\)	\(e\left(\frac{341}{1820}\right)\)	\(e\left(\frac{3583}{5460}\right)\)	\(e\left(\frac{1587}{1820}\right)\)	\(e\left(\frac{88}{1365}\right)\)	\(e\left(\frac{443}{546}\right)\)	\(e\left(\frac{51}{182}\right)\)	\(e\left(\frac{1199}{5460}\right)\)
\(\chi_{91091}(71,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{739}{5460}\right)\)	\(e\left(\frac{913}{1365}\right)\)	\(e\left(\frac{739}{2730}\right)\)	\(e\left(\frac{137}{1820}\right)\)	\(e\left(\frac{4391}{5460}\right)\)	\(e\left(\frac{739}{1820}\right)\)	\(e\left(\frac{461}{1365}\right)\)	\(e\left(\frac{115}{546}\right)\)	\(e\left(\frac{171}{182}\right)\)	\(e\left(\frac{4063}{5460}\right)\)
\(\chi_{91091}(141,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{2801}{5460}\right)\)	\(e\left(\frac{797}{1365}\right)\)	\(e\left(\frac{71}{2730}\right)\)	\(e\left(\frac{603}{1820}\right)\)	\(e\left(\frac{529}{5460}\right)\)	\(e\left(\frac{981}{1820}\right)\)	\(e\left(\frac{229}{1365}\right)\)	\(e\left(\frac{461}{546}\right)\)	\(e\left(\frac{111}{182}\right)\)	\(e\left(\frac{4997}{5460}\right)\)
\(\chi_{91091}(267,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{193}{5460}\right)\)	\(e\left(\frac{1186}{1365}\right)\)	\(e\left(\frac{193}{2730}\right)\)	\(e\left(\frac{319}{1820}\right)\)	\(e\left(\frac{4937}{5460}\right)\)	\(e\left(\frac{193}{1820}\right)\)	\(e\left(\frac{1007}{1365}\right)\)	\(e\left(\frac{115}{546}\right)\)	\(e\left(\frac{171}{182}\right)\)	\(e\left(\frac{241}{5460}\right)\)
\(\chi_{91091}(323,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{3797}{5460}\right)\)	\(e\left(\frac{1019}{1365}\right)\)	\(e\left(\frac{1067}{2730}\right)\)	\(e\left(\frac{731}{1820}\right)\)	\(e\left(\frac{2413}{5460}\right)\)	\(e\left(\frac{157}{1820}\right)\)	\(e\left(\frac{673}{1365}\right)\)	\(e\left(\frac{53}{546}\right)\)	\(e\left(\frac{25}{182}\right)\)	\(e\left(\frac{809}{5460}\right)\)
\(\chi_{91091}(379,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{2039}{5460}\right)\)	\(e\left(\frac{68}{1365}\right)\)	\(e\left(\frac{2039}{2730}\right)\)	\(e\left(\frac{1437}{1820}\right)\)	\(e\left(\frac{2311}{5460}\right)\)	\(e\left(\frac{219}{1820}\right)\)	\(e\left(\frac{136}{1365}\right)\)	\(e\left(\frac{89}{546}\right)\)	\(e\left(\frac{145}{182}\right)\)	\(e\left(\frac{4583}{5460}\right)\)
\(\chi_{91091}(449,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{3541}{5460}\right)\)	\(e\left(\frac{337}{1365}\right)\)	\(e\left(\frac{811}{2730}\right)\)	\(e\left(\frac{223}{1820}\right)\)	\(e\left(\frac{4889}{5460}\right)\)	\(e\left(\frac{1721}{1820}\right)\)	\(e\left(\frac{674}{1365}\right)\)	\(e\left(\frac{421}{546}\right)\)	\(e\left(\frac{99}{182}\right)\)	\(e\left(\frac{2017}{5460}\right)\)
\(\chi_{91091}(631,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{337}{5460}\right)\)	\(e\left(\frac{34}{1365}\right)\)	\(e\left(\frac{337}{2730}\right)\)	\(e\left(\frac{491}{1820}\right)\)	\(e\left(\frac{473}{5460}\right)\)	\(e\left(\frac{337}{1820}\right)\)	\(e\left(\frac{68}{1365}\right)\)	\(e\left(\frac{181}{546}\right)\)	\(e\left(\frac{27}{182}\right)\)	\(e\left(\frac{1609}{5460}\right)\)
\(\chi_{91091}(652,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{3743}{5460}\right)\)	\(e\left(\frac{86}{1365}\right)\)	\(e\left(\frac{1013}{2730}\right)\)	\(e\left(\frac{1349}{1820}\right)\)	\(e\left(\frac{4087}{5460}\right)\)	\(e\left(\frac{103}{1820}\right)\)	\(e\left(\frac{172}{1365}\right)\)	\(e\left(\frac{233}{546}\right)\)	\(e\left(\frac{79}{182}\right)\)	\(e\left(\frac{4391}{5460}\right)\)
\(\chi_{91091}(708,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{487}{5460}\right)\)	\(e\left(\frac{199}{1365}\right)\)	\(e\left(\frac{487}{2730}\right)\)	\(e\left(\frac{1201}{1820}\right)\)	\(e\left(\frac{1283}{5460}\right)\)	\(e\left(\frac{487}{1820}\right)\)	\(e\left(\frac{398}{1365}\right)\)	\(e\left(\frac{409}{546}\right)\)	\(e\left(\frac{59}{182}\right)\)	\(e\left(\frac{4399}{5460}\right)\)
\(\chi_{91091}(960,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{4553}{5460}\right)\)	\(e\left(\frac{431}{1365}\right)\)	\(e\left(\frac{1823}{2730}\right)\)	\(e\left(\frac{1179}{1820}\right)\)	\(e\left(\frac{817}{5460}\right)\)	\(e\left(\frac{913}{1820}\right)\)	\(e\left(\frac{862}{1365}\right)\)	\(e\left(\frac{263}{546}\right)\)	\(e\left(\frac{179}{182}\right)\)	\(e\left(\frac{5261}{5460}\right)\)
\(\chi_{91091}(1016,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{3467}{5460}\right)\)	\(e\left(\frac{929}{1365}\right)\)	\(e\left(\frac{737}{2730}\right)\)	\(e\left(\frac{261}{1820}\right)\)	\(e\left(\frac{1723}{5460}\right)\)	\(e\left(\frac{1647}{1820}\right)\)	\(e\left(\frac{493}{1365}\right)\)	\(e\left(\frac{425}{546}\right)\)	\(e\left(\frac{173}{182}\right)\)	\(e\left(\frac{4499}{5460}\right)\)
\(\chi_{91091}(1072,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{2059}{5460}\right)\)	\(e\left(\frac{1273}{1365}\right)\)	\(e\left(\frac{2059}{2730}\right)\)	\(e\left(\frac{197}{1820}\right)\)	\(e\left(\frac{1691}{5460}\right)\)	\(e\left(\frac{239}{1820}\right)\)	\(e\left(\frac{1181}{1365}\right)\)	\(e\left(\frac{265}{546}\right)\)	\(e\left(\frac{125}{182}\right)\)	\(e\left(\frac{223}{5460}\right)\)
\(\chi_{91091}(1142,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1181}{5460}\right)\)	\(e\left(\frac{107}{1365}\right)\)	\(e\left(\frac{1181}{2730}\right)\)	\(e\left(\frac{943}{1820}\right)\)	\(e\left(\frac{1609}{5460}\right)\)	\(e\left(\frac{1181}{1820}\right)\)	\(e\left(\frac{214}{1365}\right)\)	\(e\left(\frac{401}{546}\right)\)	\(e\left(\frac{93}{182}\right)\)	\(e\left(\frac{3257}{5460}\right)\)
\(\chi_{91091}(1268,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{2773}{5460}\right)\)	\(e\left(\frac{1021}{1365}\right)\)	\(e\left(\frac{43}{2730}\right)\)	\(e\left(\frac{519}{1820}\right)\)	\(e\left(\frac{1397}{5460}\right)\)	\(e\left(\frac{953}{1820}\right)\)	\(e\left(\frac{677}{1365}\right)\)	\(e\left(\frac{433}{546}\right)\)	\(e\left(\frac{139}{182}\right)\)	\(e\left(\frac{181}{5460}\right)\)
\(\chi_{91091}(1345,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{4603}{5460}\right)\)	\(e\left(\frac{31}{1365}\right)\)	\(e\left(\frac{1873}{2730}\right)\)	\(e\left(\frac{809}{1820}\right)\)	\(e\left(\frac{4727}{5460}\right)\)	\(e\left(\frac{963}{1820}\right)\)	\(e\left(\frac{62}{1365}\right)\)	\(e\left(\frac{157}{546}\right)\)	\(e\left(\frac{129}{182}\right)\)	\(e\left(\frac{2551}{5460}\right)\)
\(\chi_{91091}(1380,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{2099}{5460}\right)\)	\(e\left(\frac{953}{1365}\right)\)	\(e\left(\frac{2099}{2730}\right)\)	\(e\left(\frac{1357}{1820}\right)\)	\(e\left(\frac{451}{5460}\right)\)	\(e\left(\frac{279}{1820}\right)\)	\(e\left(\frac{541}{1365}\right)\)	\(e\left(\frac{71}{546}\right)\)	\(e\left(\frac{85}{182}\right)\)	\(e\left(\frac{2423}{5460}\right)\)
\(\chi_{91091}(1450,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{661}{5460}\right)\)	\(e\left(\frac{172}{1365}\right)\)	\(e\left(\frac{661}{2730}\right)\)	\(e\left(\frac{423}{1820}\right)\)	\(e\left(\frac{1349}{5460}\right)\)	\(e\left(\frac{661}{1820}\right)\)	\(e\left(\frac{344}{1365}\right)\)	\(e\left(\frac{193}{546}\right)\)	\(e\left(\frac{67}{182}\right)\)	\(e\left(\frac{1957}{5460}\right)\)
\(\chi_{91091}(1527,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{3751}{5460}\right)\)	\(e\left(\frac{22}{1365}\right)\)	\(e\left(\frac{1021}{2730}\right)\)	\(e\left(\frac{853}{1820}\right)\)	\(e\left(\frac{3839}{5460}\right)\)	\(e\left(\frac{111}{1820}\right)\)	\(e\left(\frac{44}{1365}\right)\)	\(e\left(\frac{85}{546}\right)\)	\(e\left(\frac{71}{182}\right)\)	\(e\left(\frac{2647}{5460}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Basic properties

Related number fields

First 19 of 1152 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	91091.sg
Modulus	$91091$
Conductor	$91091$
Order	$5460$
Real	no
Primitive	yes
Minimal	yes
Parity	odd

Modulus:	\(91091\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(91091\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(5460\)	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);