LMFDB - Dirichlet character orbit 836352.zu

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comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(836352, base_ring=CyclotomicField(31680)) M = H._module chi = DirichletCharacter(H, M([15840,19305,1760,8352])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(83, 836352)) 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("836352.83"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$836352$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$836352$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$31680$	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:	$\Q(\zeta_{31680})$	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 31680 polynomial (not computed)	comment:Fixed field sage:chi.fixed_field()

First 16 of 7680 characters in Galois orbit

Character	$-1$	$1$	$5$	$7$	$13$	$17$	$19$	$23$	$25$	$29$	$31$	$35$
$\chi_{836352}(83,\cdot)$	$-1$	$1$	$e\left(\frac{12553}{31680}\right)$	$e\left(\frac{5197}{15840}\right)$	$e\left(\frac{22567}{31680}\right)$	$e\left(\frac{2149}{2640}\right)$	$e\left(\frac{677}{10560}\right)$	$e\left(\frac{307}{3168}\right)$	$e\left(\frac{12553}{15840}\right)$	$e\left(\frac{15539}{31680}\right)$	$e\left(\frac{629}{3960}\right)$	$e\left(\frac{7649}{10560}\right)$
$\chi_{836352}(227,\cdot)$	$-1$	$1$	$e\left(\frac{16309}{31680}\right)$	$e\left(\frac{1321}{15840}\right)$	$e\left(\frac{11131}{31680}\right)$	$e\left(\frac{817}{2640}\right)$	$e\left(\frac{1121}{10560}\right)$	$e\left(\frac{1399}{3168}\right)$	$e\left(\frac{469}{15840}\right)$	$e\left(\frac{20567}{31680}\right)$	$e\left(\frac{3857}{3960}\right)$	$e\left(\frac{6317}{10560}\right)$
$\chi_{836352}(299,\cdot)$	$-1$	$1$	$e\left(\frac{8467}{31680}\right)$	$e\left(\frac{12703}{15840}\right)$	$e\left(\frac{7933}{31680}\right)$	$e\left(\frac{1831}{2640}\right)$	$e\left(\frac{1223}{10560}\right)$	$e\left(\frac{865}{3168}\right)$	$e\left(\frac{8467}{15840}\right)$	$e\left(\frac{22721}{31680}\right)$	$e\left(\frac{3671}{3960}\right)$	$e\left(\frac{731}{10560}\right)$
$\chi_{836352}(347,\cdot)$	$-1$	$1$	$e\left(\frac{20183}{31680}\right)$	$e\left(\frac{14867}{15840}\right)$	$e\left(\frac{29177}{31680}\right)$	$e\left(\frac{1019}{2640}\right)$	$e\left(\frac{8827}{10560}\right)$	$e\left(\frac{749}{3168}\right)$	$e\left(\frac{4343}{15840}\right)$	$e\left(\frac{8749}{31680}\right)$	$e\left(\frac{3859}{3960}\right)$	$e\left(\frac{6079}{10560}\right)$
$\chi_{836352}(371,\cdot)$	$-1$	$1$	$e\left(\frac{6241}{31680}\right)$	$e\left(\frac{4069}{15840}\right)$	$e\left(\frac{27919}{31680}\right)$	$e\left(\frac{1933}{2640}\right)$	$e\left(\frac{8669}{10560}\right)$	$e\left(\frac{3067}{3168}\right)$	$e\left(\frac{6241}{15840}\right)$	$e\left(\frac{21563}{31680}\right)$	$e\left(\frac{1973}{3960}\right)$	$e\left(\frac{4793}{10560}\right)$
$\chi_{836352}(491,\cdot)$	$-1$	$1$	$e\left(\frac{25379}{31680}\right)$	$e\left(\frac{6671}{15840}\right)$	$e\left(\frac{22061}{31680}\right)$	$e\left(\frac{2567}{2640}\right)$	$e\left(\frac{3031}{10560}\right)$	$e\left(\frac{2705}{3168}\right)$	$e\left(\frac{9539}{15840}\right)$	$e\left(\frac{26737}{31680}\right)$	$e\left(\frac{607}{3960}\right)$	$e\left(\frac{2347}{10560}\right)$
$\chi_{836352}(563,\cdot)$	$-1$	$1$	$e\left(\frac{19697}{31680}\right)$	$e\left(\frac{11573}{15840}\right)$	$e\left(\frac{25343}{31680}\right)$	$e\left(\frac{2621}{2640}\right)$	$e\left(\frac{4333}{10560}\right)$	$e\left(\frac{299}{3168}\right)$	$e\left(\frac{3857}{15840}\right)$	$e\left(\frac{811}{31680}\right)$	$e\left(\frac{2581}{3960}\right)$	$e\left(\frac{3721}{10560}\right)$
$\chi_{836352}(635,\cdot)$	$-1$	$1$	$e\left(\frac{28271}{31680}\right)$	$e\left(\frac{2219}{15840}\right)$	$e\left(\frac{14369}{31680}\right)$	$e\left(\frac{563}{2640}\right)$	$e\left(\frac{7219}{10560}\right)$	$e\left(\frac{2645}{3168}\right)$	$e\left(\frac{12431}{15840}\right)$	$e\left(\frac{17653}{31680}\right)$	$e\left(\frac{3763}{3960}\right)$	$e\left(\frac{343}{10560}\right)$
$\chi_{836352}(875,\cdot)$	$-1$	$1$	$e\left(\frac{27523}{31680}\right)$	$e\left(\frac{10447}{15840}\right)$	$e\left(\frac{18637}{31680}\right)$	$e\left(\frac{1399}{2640}\right)$	$e\left(\frac{6647}{10560}\right)$	$e\left(\frac{49}{3168}\right)$	$e\left(\frac{11683}{15840}\right)$	$e\left(\frac{3089}{31680}\right)$	$e\left(\frac{2399}{3960}\right)$	$e\left(\frac{5579}{10560}\right)$
$\chi_{836352}(1019,\cdot)$	$-1$	$1$	$e\left(\frac{3919}{31680}\right)$	$e\left(\frac{9451}{15840}\right)$	$e\left(\frac{20161}{31680}\right)$	$e\left(\frac{787}{2640}\right)$	$e\left(\frac{9491}{10560}\right)$	$e\left(\frac{565}{3168}\right)$	$e\left(\frac{3919}{15840}\right)$	$e\left(\frac{15317}{31680}\right)$	$e\left(\frac{2027}{3960}\right)$	$e\left(\frac{7607}{10560}\right)$
$\chi_{836352}(1091,\cdot)$	$-1$	$1$	$e\left(\frac{2557}{31680}\right)$	$e\left(\frac{1393}{15840}\right)$	$e\left(\frac{4723}{31680}\right)$	$e\left(\frac{1561}{2640}\right)$	$e\left(\frac{2633}{10560}\right)$	$e\left(\frac{751}{3168}\right)$	$e\left(\frac{2557}{15840}\right)$	$e\left(\frac{28271}{31680}\right)$	$e\left(\frac{401}{3960}\right)$	$e\left(\frac{1781}{10560}\right)$
$\chi_{836352}(1139,\cdot)$	$-1$	$1$	$e\left(\frac{27233}{31680}\right)$	$e\left(\frac{12197}{15840}\right)$	$e\left(\frac{1487}{31680}\right)$	$e\left(\frac{269}{2640}\right)$	$e\left(\frac{6877}{10560}\right)$	$e\left(\frac{2075}{3168}\right)$	$e\left(\frac{11393}{15840}\right)$	$e\left(\frac{4219}{31680}\right)$	$e\left(\frac{1669}{3960}\right)$	$e\left(\frac{6649}{10560}\right)$
$\chi_{836352}(1163,\cdot)$	$-1$	$1$	$e\left(\frac{1051}{31680}\right)$	$e\left(\frac{6439}{15840}\right)$	$e\left(\frac{26869}{31680}\right)$	$e\left(\frac{463}{2640}\right)$	$e\left(\frac{6959}{10560}\right)$	$e\left(\frac{217}{3168}\right)$	$e\left(\frac{1051}{15840}\right)$	$e\left(\frac{17753}{31680}\right)$	$e\left(\frac{3383}{3960}\right)$	$e\left(\frac{4643}{10560}\right)$
$\chi_{836352}(1283,\cdot)$	$-1$	$1$	$e\left(\frac{5069}{31680}\right)$	$e\left(\frac{6881}{15840}\right)$	$e\left(\frac{7331}{31680}\right)$	$e\left(\frac{2537}{2640}\right)$	$e\left(\frac{3481}{10560}\right)$	$e\left(\frac{287}{3168}\right)$	$e\left(\frac{5069}{15840}\right)$	$e\left(\frac{29407}{31680}\right)$	$e\left(\frac{2737}{3960}\right)$	$e\left(\frac{6277}{10560}\right)$
$\chi_{836352}(1355,\cdot)$	$-1$	$1$	$e\left(\frac{5867}{31680}\right)$	$e\left(\frac{8183}{15840}\right)$	$e\left(\frac{30053}{31680}\right)$	$e\left(\frac{2351}{2640}\right)$	$e\left(\frac{8383}{10560}\right)$	$e\left(\frac{1769}{3168}\right)$	$e\left(\frac{5867}{15840}\right)$	$e\left(\frac{14281}{31680}\right)$	$e\left(\frac{3271}{3960}\right)$	$e\left(\frac{7411}{10560}\right)$
$\chi_{836352}(1427,\cdot)$	$-1$	$1$	$e\left(\frac{15161}{31680}\right)$	$e\left(\frac{12509}{15840}\right)$	$e\left(\frac{21239}{31680}\right)$	$e\left(\frac{1733}{2640}\right)$	$e\left(\frac{8149}{10560}\right)$	$e\left(\frac{1379}{3168}\right)$	$e\left(\frac{15161}{15840}\right)$	$e\left(\frac{21763}{31680}\right)$	$e\left(\frac{1213}{3960}\right)$	$e\left(\frac{2833}{10560}\right)$

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Classical	Maass
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Elliptic curves over $\Q$
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Higher genus families
Abelian varieties over $\F_{q}$
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Character	\(-1\)	\(1\)	\(5\)	\(7\)	\(13\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)	\(35\)
\(\chi_{836352}(83,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{12553}{31680}\right)\)	\(e\left(\frac{5197}{15840}\right)\)	\(e\left(\frac{22567}{31680}\right)\)	\(e\left(\frac{2149}{2640}\right)\)	\(e\left(\frac{677}{10560}\right)\)	\(e\left(\frac{307}{3168}\right)\)	\(e\left(\frac{12553}{15840}\right)\)	\(e\left(\frac{15539}{31680}\right)\)	\(e\left(\frac{629}{3960}\right)\)	\(e\left(\frac{7649}{10560}\right)\)
\(\chi_{836352}(227,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{16309}{31680}\right)\)	\(e\left(\frac{1321}{15840}\right)\)	\(e\left(\frac{11131}{31680}\right)\)	\(e\left(\frac{817}{2640}\right)\)	\(e\left(\frac{1121}{10560}\right)\)	\(e\left(\frac{1399}{3168}\right)\)	\(e\left(\frac{469}{15840}\right)\)	\(e\left(\frac{20567}{31680}\right)\)	\(e\left(\frac{3857}{3960}\right)\)	\(e\left(\frac{6317}{10560}\right)\)
\(\chi_{836352}(299,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{8467}{31680}\right)\)	\(e\left(\frac{12703}{15840}\right)\)	\(e\left(\frac{7933}{31680}\right)\)	\(e\left(\frac{1831}{2640}\right)\)	\(e\left(\frac{1223}{10560}\right)\)	\(e\left(\frac{865}{3168}\right)\)	\(e\left(\frac{8467}{15840}\right)\)	\(e\left(\frac{22721}{31680}\right)\)	\(e\left(\frac{3671}{3960}\right)\)	\(e\left(\frac{731}{10560}\right)\)
\(\chi_{836352}(347,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{20183}{31680}\right)\)	\(e\left(\frac{14867}{15840}\right)\)	\(e\left(\frac{29177}{31680}\right)\)	\(e\left(\frac{1019}{2640}\right)\)	\(e\left(\frac{8827}{10560}\right)\)	\(e\left(\frac{749}{3168}\right)\)	\(e\left(\frac{4343}{15840}\right)\)	\(e\left(\frac{8749}{31680}\right)\)	\(e\left(\frac{3859}{3960}\right)\)	\(e\left(\frac{6079}{10560}\right)\)
\(\chi_{836352}(371,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{6241}{31680}\right)\)	\(e\left(\frac{4069}{15840}\right)\)	\(e\left(\frac{27919}{31680}\right)\)	\(e\left(\frac{1933}{2640}\right)\)	\(e\left(\frac{8669}{10560}\right)\)	\(e\left(\frac{3067}{3168}\right)\)	\(e\left(\frac{6241}{15840}\right)\)	\(e\left(\frac{21563}{31680}\right)\)	\(e\left(\frac{1973}{3960}\right)\)	\(e\left(\frac{4793}{10560}\right)\)
\(\chi_{836352}(491,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{25379}{31680}\right)\)	\(e\left(\frac{6671}{15840}\right)\)	\(e\left(\frac{22061}{31680}\right)\)	\(e\left(\frac{2567}{2640}\right)\)	\(e\left(\frac{3031}{10560}\right)\)	\(e\left(\frac{2705}{3168}\right)\)	\(e\left(\frac{9539}{15840}\right)\)	\(e\left(\frac{26737}{31680}\right)\)	\(e\left(\frac{607}{3960}\right)\)	\(e\left(\frac{2347}{10560}\right)\)
\(\chi_{836352}(563,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{19697}{31680}\right)\)	\(e\left(\frac{11573}{15840}\right)\)	\(e\left(\frac{25343}{31680}\right)\)	\(e\left(\frac{2621}{2640}\right)\)	\(e\left(\frac{4333}{10560}\right)\)	\(e\left(\frac{299}{3168}\right)\)	\(e\left(\frac{3857}{15840}\right)\)	\(e\left(\frac{811}{31680}\right)\)	\(e\left(\frac{2581}{3960}\right)\)	\(e\left(\frac{3721}{10560}\right)\)
\(\chi_{836352}(635,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{28271}{31680}\right)\)	\(e\left(\frac{2219}{15840}\right)\)	\(e\left(\frac{14369}{31680}\right)\)	\(e\left(\frac{563}{2640}\right)\)	\(e\left(\frac{7219}{10560}\right)\)	\(e\left(\frac{2645}{3168}\right)\)	\(e\left(\frac{12431}{15840}\right)\)	\(e\left(\frac{17653}{31680}\right)\)	\(e\left(\frac{3763}{3960}\right)\)	\(e\left(\frac{343}{10560}\right)\)
\(\chi_{836352}(875,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{27523}{31680}\right)\)	\(e\left(\frac{10447}{15840}\right)\)	\(e\left(\frac{18637}{31680}\right)\)	\(e\left(\frac{1399}{2640}\right)\)	\(e\left(\frac{6647}{10560}\right)\)	\(e\left(\frac{49}{3168}\right)\)	\(e\left(\frac{11683}{15840}\right)\)	\(e\left(\frac{3089}{31680}\right)\)	\(e\left(\frac{2399}{3960}\right)\)	\(e\left(\frac{5579}{10560}\right)\)
\(\chi_{836352}(1019,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{3919}{31680}\right)\)	\(e\left(\frac{9451}{15840}\right)\)	\(e\left(\frac{20161}{31680}\right)\)	\(e\left(\frac{787}{2640}\right)\)	\(e\left(\frac{9491}{10560}\right)\)	\(e\left(\frac{565}{3168}\right)\)	\(e\left(\frac{3919}{15840}\right)\)	\(e\left(\frac{15317}{31680}\right)\)	\(e\left(\frac{2027}{3960}\right)\)	\(e\left(\frac{7607}{10560}\right)\)
\(\chi_{836352}(1091,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{2557}{31680}\right)\)	\(e\left(\frac{1393}{15840}\right)\)	\(e\left(\frac{4723}{31680}\right)\)	\(e\left(\frac{1561}{2640}\right)\)	\(e\left(\frac{2633}{10560}\right)\)	\(e\left(\frac{751}{3168}\right)\)	\(e\left(\frac{2557}{15840}\right)\)	\(e\left(\frac{28271}{31680}\right)\)	\(e\left(\frac{401}{3960}\right)\)	\(e\left(\frac{1781}{10560}\right)\)
\(\chi_{836352}(1139,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{27233}{31680}\right)\)	\(e\left(\frac{12197}{15840}\right)\)	\(e\left(\frac{1487}{31680}\right)\)	\(e\left(\frac{269}{2640}\right)\)	\(e\left(\frac{6877}{10560}\right)\)	\(e\left(\frac{2075}{3168}\right)\)	\(e\left(\frac{11393}{15840}\right)\)	\(e\left(\frac{4219}{31680}\right)\)	\(e\left(\frac{1669}{3960}\right)\)	\(e\left(\frac{6649}{10560}\right)\)
\(\chi_{836352}(1163,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1051}{31680}\right)\)	\(e\left(\frac{6439}{15840}\right)\)	\(e\left(\frac{26869}{31680}\right)\)	\(e\left(\frac{463}{2640}\right)\)	\(e\left(\frac{6959}{10560}\right)\)	\(e\left(\frac{217}{3168}\right)\)	\(e\left(\frac{1051}{15840}\right)\)	\(e\left(\frac{17753}{31680}\right)\)	\(e\left(\frac{3383}{3960}\right)\)	\(e\left(\frac{4643}{10560}\right)\)
\(\chi_{836352}(1283,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{5069}{31680}\right)\)	\(e\left(\frac{6881}{15840}\right)\)	\(e\left(\frac{7331}{31680}\right)\)	\(e\left(\frac{2537}{2640}\right)\)	\(e\left(\frac{3481}{10560}\right)\)	\(e\left(\frac{287}{3168}\right)\)	\(e\left(\frac{5069}{15840}\right)\)	\(e\left(\frac{29407}{31680}\right)\)	\(e\left(\frac{2737}{3960}\right)\)	\(e\left(\frac{6277}{10560}\right)\)
\(\chi_{836352}(1355,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{5867}{31680}\right)\)	\(e\left(\frac{8183}{15840}\right)\)	\(e\left(\frac{30053}{31680}\right)\)	\(e\left(\frac{2351}{2640}\right)\)	\(e\left(\frac{8383}{10560}\right)\)	\(e\left(\frac{1769}{3168}\right)\)	\(e\left(\frac{5867}{15840}\right)\)	\(e\left(\frac{14281}{31680}\right)\)	\(e\left(\frac{3271}{3960}\right)\)	\(e\left(\frac{7411}{10560}\right)\)
\(\chi_{836352}(1427,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{15161}{31680}\right)\)	\(e\left(\frac{12509}{15840}\right)\)	\(e\left(\frac{21239}{31680}\right)\)	\(e\left(\frac{1733}{2640}\right)\)	\(e\left(\frac{8149}{10560}\right)\)	\(e\left(\frac{1379}{3168}\right)\)	\(e\left(\frac{15161}{15840}\right)\)	\(e\left(\frac{21763}{31680}\right)\)	\(e\left(\frac{1213}{3960}\right)\)	\(e\left(\frac{2833}{10560}\right)\)

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First 16 of 7680 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	836352.zu
Modulus	$836352$
Conductor	$836352$
Order	$31680$
Real	no
Primitive	yes
Minimal	yes
Parity	odd

Modulus:	\(836352\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(836352\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(31680\)	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);