LMFDB - Dirichlet character orbit 15517.p

Show commands: Magma / Pari/GP / SageMath

comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(15517, base_ring=CyclotomicField(7598)) M = H._module chi = DirichletCharacter(H, M([786,29])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(5, 15517)) 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("15517.5"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$15517$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$15517$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$7598$	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:	$\Q(\zeta_{3799})$	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 7598 polynomial (not computed)	comment:Fixed field sage:chi.fixed_field()

First 31 of 3640 characters in Galois orbit

Character	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{15517}(5,\cdot)$	$-1$	$1$	$e\left(\frac{3148}{3799}\right)$	$e\left(\frac{1380}{3799}\right)$	$e\left(\frac{2497}{3799}\right)$	$e\left(\frac{4745}{7598}\right)$	$e\left(\frac{729}{3799}\right)$	$e\left(\frac{1243}{7598}\right)$	$e\left(\frac{1846}{3799}\right)$	$e\left(\frac{2760}{3799}\right)$	$e\left(\frac{3443}{7598}\right)$	$e\left(\frac{835}{3799}\right)$
$\chi_{15517}(7,\cdot)$	$-1$	$1$	$e\left(\frac{2281}{3799}\right)$	$e\left(\frac{2255}{3799}\right)$	$e\left(\frac{763}{3799}\right)$	$e\left(\frac{1243}{7598}\right)$	$e\left(\frac{737}{3799}\right)$	$e\left(\frac{3091}{7598}\right)$	$e\left(\frac{3044}{3799}\right)$	$e\left(\frac{711}{3799}\right)$	$e\left(\frac{5805}{7598}\right)$	$e\left(\frac{3085}{3799}\right)$
$\chi_{15517}(15,\cdot)$	$-1$	$1$	$e\left(\frac{3610}{3799}\right)$	$e\left(\frac{33}{3799}\right)$	$e\left(\frac{3421}{3799}\right)$	$e\left(\frac{7505}{7598}\right)$	$e\left(\frac{3643}{3799}\right)$	$e\left(\frac{5753}{7598}\right)$	$e\left(\frac{3232}{3799}\right)$	$e\left(\frac{66}{3799}\right)$	$e\left(\frac{7127}{7598}\right)$	$e\left(\frac{1713}{3799}\right)$
$\chi_{15517}(19,\cdot)$	$-1$	$1$	$e\left(\frac{3185}{3799}\right)$	$e\left(\frac{3665}{3799}\right)$	$e\left(\frac{2571}{3799}\right)$	$e\left(\frac{723}{7598}\right)$	$e\left(\frac{3051}{3799}\right)$	$e\left(\frac{5765}{7598}\right)$	$e\left(\frac{1957}{3799}\right)$	$e\left(\frac{3531}{3799}\right)$	$e\left(\frac{7093}{7598}\right)$	$e\left(\frac{2369}{3799}\right)$
$\chi_{15517}(20,\cdot)$	$-1$	$1$	$e\left(\frac{1655}{3799}\right)$	$e\left(\frac{2304}{3799}\right)$	$e\left(\frac{3310}{3799}\right)$	$e\left(\frac{2141}{7598}\right)$	$e\left(\frac{160}{3799}\right)$	$e\left(\frac{2769}{7598}\right)$	$e\left(\frac{1166}{3799}\right)$	$e\left(\frac{809}{3799}\right)$	$e\left(\frac{5451}{7598}\right)$	$e\left(\frac{3211}{3799}\right)$
$\chi_{15517}(21,\cdot)$	$-1$	$1$	$e\left(\frac{2743}{3799}\right)$	$e\left(\frac{908}{3799}\right)$	$e\left(\frac{1687}{3799}\right)$	$e\left(\frac{4003}{7598}\right)$	$e\left(\frac{3651}{3799}\right)$	$e\left(\frac{3}{7598}\right)$	$e\left(\frac{631}{3799}\right)$	$e\left(\frac{1816}{3799}\right)$	$e\left(\frac{1891}{7598}\right)$	$e\left(\frac{164}{3799}\right)$
$\chi_{15517}(28,\cdot)$	$-1$	$1$	$e\left(\frac{788}{3799}\right)$	$e\left(\frac{3179}{3799}\right)$	$e\left(\frac{1576}{3799}\right)$	$e\left(\frac{6237}{7598}\right)$	$e\left(\frac{168}{3799}\right)$	$e\left(\frac{4617}{7598}\right)$	$e\left(\frac{2364}{3799}\right)$	$e\left(\frac{2559}{3799}\right)$	$e\left(\frac{215}{7598}\right)$	$e\left(\frac{1662}{3799}\right)$
$\chi_{15517}(29,\cdot)$	$-1$	$1$	$e\left(\frac{2849}{3799}\right)$	$e\left(\frac{1191}{3799}\right)$	$e\left(\frac{1899}{3799}\right)$	$e\left(\frac{5623}{7598}\right)$	$e\left(\frac{241}{3799}\right)$	$e\left(\frac{2485}{7598}\right)$	$e\left(\frac{949}{3799}\right)$	$e\left(\frac{2382}{3799}\right)$	$e\left(\frac{3723}{7598}\right)$	$e\left(\frac{349}{3799}\right)$
$\chi_{15517}(41,\cdot)$	$-1$	$1$	$e\left(\frac{2164}{3799}\right)$	$e\left(\frac{1190}{3799}\right)$	$e\left(\frac{529}{3799}\right)$	$e\left(\frac{3899}{7598}\right)$	$e\left(\frac{3354}{3799}\right)$	$e\left(\frac{3577}{7598}\right)$	$e\left(\frac{2693}{3799}\right)$	$e\left(\frac{2380}{3799}\right)$	$e\left(\frac{629}{7598}\right)$	$e\left(\frac{3060}{3799}\right)$
$\chi_{15517}(45,\cdot)$	$-1$	$1$	$e\left(\frac{273}{3799}\right)$	$e\left(\frac{2485}{3799}\right)$	$e\left(\frac{546}{3799}\right)$	$e\left(\frac{2667}{7598}\right)$	$e\left(\frac{2758}{3799}\right)$	$e\left(\frac{2665}{7598}\right)$	$e\left(\frac{819}{3799}\right)$	$e\left(\frac{1171}{3799}\right)$	$e\left(\frac{3213}{7598}\right)$	$e\left(\frac{2591}{3799}\right)$
$\chi_{15517}(53,\cdot)$	$-1$	$1$	$e\left(\frac{1673}{3799}\right)$	$e\left(\frac{130}{3799}\right)$	$e\left(\frac{3346}{3799}\right)$	$e\left(\frac{7577}{7598}\right)$	$e\left(\frac{1803}{3799}\right)$	$e\left(\frac{6201}{7598}\right)$	$e\left(\frac{1220}{3799}\right)$	$e\left(\frac{260}{3799}\right)$	$e\left(\frac{3325}{7598}\right)$	$e\left(\frac{877}{3799}\right)$
$\chi_{15517}(57,\cdot)$	$-1$	$1$	$e\left(\frac{3647}{3799}\right)$	$e\left(\frac{2318}{3799}\right)$	$e\left(\frac{3495}{3799}\right)$	$e\left(\frac{3483}{7598}\right)$	$e\left(\frac{2166}{3799}\right)$	$e\left(\frac{2677}{7598}\right)$	$e\left(\frac{3343}{3799}\right)$	$e\left(\frac{837}{3799}\right)$	$e\left(\frac{3179}{7598}\right)$	$e\left(\frac{3247}{3799}\right)$
$\chi_{15517}(63,\cdot)$	$-1$	$1$	$e\left(\frac{3205}{3799}\right)$	$e\left(\frac{3360}{3799}\right)$	$e\left(\frac{2611}{3799}\right)$	$e\left(\frac{6763}{7598}\right)$	$e\left(\frac{2766}{3799}\right)$	$e\left(\frac{4513}{7598}\right)$	$e\left(\frac{2017}{3799}\right)$	$e\left(\frac{2921}{3799}\right)$	$e\left(\frac{5575}{7598}\right)$	$e\left(\frac{1042}{3799}\right)$
$\chi_{15517}(71,\cdot)$	$-1$	$1$	$e\left(\frac{3319}{3799}\right)$	$e\left(\frac{3521}{3799}\right)$	$e\left(\frac{2839}{3799}\right)$	$e\left(\frac{3201}{7598}\right)$	$e\left(\frac{3041}{3799}\right)$	$e\left(\frac{3455}{7598}\right)$	$e\left(\frac{2359}{3799}\right)$	$e\left(\frac{3243}{3799}\right)$	$e\left(\frac{2241}{7598}\right)$	$e\left(\frac{1456}{3799}\right)$
$\chi_{15517}(76,\cdot)$	$-1$	$1$	$e\left(\frac{1692}{3799}\right)$	$e\left(\frac{790}{3799}\right)$	$e\left(\frac{3384}{3799}\right)$	$e\left(\frac{5717}{7598}\right)$	$e\left(\frac{2482}{3799}\right)$	$e\left(\frac{7291}{7598}\right)$	$e\left(\frac{1277}{3799}\right)$	$e\left(\frac{1580}{3799}\right)$	$e\left(\frac{1503}{7598}\right)$	$e\left(\frac{946}{3799}\right)$
$\chi_{15517}(79,\cdot)$	$-1$	$1$	$e\left(\frac{2380}{3799}\right)$	$e\left(\frac{1695}{3799}\right)$	$e\left(\frac{961}{3799}\right)$	$e\left(\frac{749}{7598}\right)$	$e\left(\frac{276}{3799}\right)$	$e\left(\frac{6771}{7598}\right)$	$e\left(\frac{3341}{3799}\right)$	$e\left(\frac{3390}{3799}\right)$	$e\left(\frac{5509}{7598}\right)$	$e\left(\frac{1645}{3799}\right)$
$\chi_{15517}(80,\cdot)$	$-1$	$1$	$e\left(\frac{162}{3799}\right)$	$e\left(\frac{3228}{3799}\right)$	$e\left(\frac{324}{3799}\right)$	$e\left(\frac{7135}{7598}\right)$	$e\left(\frac{3390}{3799}\right)$	$e\left(\frac{4295}{7598}\right)$	$e\left(\frac{486}{3799}\right)$	$e\left(\frac{2657}{3799}\right)$	$e\left(\frac{7459}{7598}\right)$	$e\left(\frac{1788}{3799}\right)$
$\chi_{15517}(84,\cdot)$	$-1$	$1$	$e\left(\frac{1250}{3799}\right)$	$e\left(\frac{1832}{3799}\right)$	$e\left(\frac{2500}{3799}\right)$	$e\left(\frac{1399}{7598}\right)$	$e\left(\frac{3082}{3799}\right)$	$e\left(\frac{1529}{7598}\right)$	$e\left(\frac{3750}{3799}\right)$	$e\left(\frac{3664}{3799}\right)$	$e\left(\frac{3899}{7598}\right)$	$e\left(\frac{2540}{3799}\right)$
$\chi_{15517}(85,\cdot)$	$-1$	$1$	$e\left(\frac{3390}{3799}\right)$	$e\left(\frac{3388}{3799}\right)$	$e\left(\frac{2981}{3799}\right)$	$e\left(\frac{1849}{7598}\right)$	$e\left(\frac{2979}{3799}\right)$	$e\left(\frac{4329}{7598}\right)$	$e\left(\frac{2572}{3799}\right)$	$e\left(\frac{2977}{3799}\right)$	$e\left(\frac{1031}{7598}\right)$	$e\left(\frac{1114}{3799}\right)$
$\chi_{15517}(87,\cdot)$	$-1$	$1$	$e\left(\frac{3311}{3799}\right)$	$e\left(\frac{3643}{3799}\right)$	$e\left(\frac{2823}{3799}\right)$	$e\left(\frac{785}{7598}\right)$	$e\left(\frac{3155}{3799}\right)$	$e\left(\frac{6995}{7598}\right)$	$e\left(\frac{2335}{3799}\right)$	$e\left(\frac{3487}{3799}\right)$	$e\left(\frac{7407}{7598}\right)$	$e\left(\frac{1227}{3799}\right)$
$\chi_{15517}(94,\cdot)$	$-1$	$1$	$e\left(\frac{1282}{3799}\right)$	$e\left(\frac{1344}{3799}\right)$	$e\left(\frac{2564}{3799}\right)$	$e\left(\frac{3465}{7598}\right)$	$e\left(\frac{2626}{3799}\right)$	$e\left(\frac{2565}{7598}\right)$	$e\left(\frac{47}{3799}\right)$	$e\left(\frac{2688}{3799}\right)$	$e\left(\frac{6029}{7598}\right)$	$e\left(\frac{3456}{3799}\right)$
$\chi_{15517}(107,\cdot)$	$-1$	$1$	$e\left(\frac{2754}{3799}\right)$	$e\left(\frac{1690}{3799}\right)$	$e\left(\frac{1709}{3799}\right)$	$e\left(\frac{7325}{7598}\right)$	$e\left(\frac{645}{3799}\right)$	$e\left(\frac{4633}{7598}\right)$	$e\left(\frac{664}{3799}\right)$	$e\left(\frac{3380}{3799}\right)$	$e\left(\frac{5235}{7598}\right)$	$e\left(\frac{4}{3799}\right)$
$\chi_{15517}(110,\cdot)$	$-1$	$1$	$e\left(\frac{1690}{3799}\right)$	$e\left(\frac{2720}{3799}\right)$	$e\left(\frac{3380}{3799}\right)$	$e\left(\frac{5113}{7598}\right)$	$e\left(\frac{611}{3799}\right)$	$e\left(\frac{4377}{7598}\right)$	$e\left(\frac{1271}{3799}\right)$	$e\left(\frac{1641}{3799}\right)$	$e\left(\frac{895}{7598}\right)$	$e\left(\frac{3738}{3799}\right)$
$\chi_{15517}(112,\cdot)$	$-1$	$1$	$e\left(\frac{3094}{3799}\right)$	$e\left(\frac{304}{3799}\right)$	$e\left(\frac{2389}{3799}\right)$	$e\left(\frac{3633}{7598}\right)$	$e\left(\frac{3398}{3799}\right)$	$e\left(\frac{6143}{7598}\right)$	$e\left(\frac{1684}{3799}\right)$	$e\left(\frac{608}{3799}\right)$	$e\left(\frac{2223}{7598}\right)$	$e\left(\frac{239}{3799}\right)$
$\chi_{15517}(116,\cdot)$	$-1$	$1$	$e\left(\frac{1356}{3799}\right)$	$e\left(\frac{2115}{3799}\right)$	$e\left(\frac{2712}{3799}\right)$	$e\left(\frac{3019}{7598}\right)$	$e\left(\frac{3471}{3799}\right)$	$e\left(\frac{4011}{7598}\right)$	$e\left(\frac{269}{3799}\right)$	$e\left(\frac{431}{3799}\right)$	$e\left(\frac{5731}{7598}\right)$	$e\left(\frac{2725}{3799}\right)$
$\chi_{15517}(123,\cdot)$	$-1$	$1$	$e\left(\frac{2626}{3799}\right)$	$e\left(\frac{3642}{3799}\right)$	$e\left(\frac{1453}{3799}\right)$	$e\left(\frac{6659}{7598}\right)$	$e\left(\frac{2469}{3799}\right)$	$e\left(\frac{489}{7598}\right)$	$e\left(\frac{280}{3799}\right)$	$e\left(\frac{3485}{3799}\right)$	$e\left(\frac{4313}{7598}\right)$	$e\left(\frac{139}{3799}\right)$
$\chi_{15517}(125,\cdot)$	$-1$	$1$	$e\left(\frac{1846}{3799}\right)$	$e\left(\frac{341}{3799}\right)$	$e\left(\frac{3692}{3799}\right)$	$e\left(\frac{6637}{7598}\right)$	$e\left(\frac{2187}{3799}\right)$	$e\left(\frac{3729}{7598}\right)$	$e\left(\frac{1739}{3799}\right)$	$e\left(\frac{682}{3799}\right)$	$e\left(\frac{2731}{7598}\right)$	$e\left(\frac{2505}{3799}\right)$
$\chi_{15517}(127,\cdot)$	$-1$	$1$	$e\left(\frac{1736}{3799}\right)$	$e\left(\frac{119}{3799}\right)$	$e\left(\frac{3472}{3799}\right)$	$e\left(\frac{3809}{7598}\right)$	$e\left(\frac{1855}{3799}\right)$	$e\left(\frac{3017}{7598}\right)$	$e\left(\frac{1409}{3799}\right)$	$e\left(\frac{238}{3799}\right)$	$e\left(\frac{7281}{7598}\right)$	$e\left(\frac{306}{3799}\right)$
$\chi_{15517}(130,\cdot)$	$-1$	$1$	$e\left(\frac{1405}{3799}\right)$	$e\left(\frac{418}{3799}\right)$	$e\left(\frac{2810}{3799}\right)$	$e\left(\frac{2621}{7598}\right)$	$e\left(\frac{1823}{3799}\right)$	$e\left(\frac{3223}{7598}\right)$	$e\left(\frac{416}{3799}\right)$	$e\left(\frac{836}{3799}\right)$	$e\left(\frac{5431}{7598}\right)$	$e\left(\frac{2703}{3799}\right)$
$\chi_{15517}(134,\cdot)$	$-1$	$1$	$e\left(\frac{30}{3799}\right)$	$e\left(\frac{1442}{3799}\right)$	$e\left(\frac{60}{3799}\right)$	$e\left(\frac{5261}{7598}\right)$	$e\left(\frac{1472}{3799}\right)$	$e\left(\frac{1921}{7598}\right)$	$e\left(\frac{90}{3799}\right)$	$e\left(\frac{2884}{3799}\right)$	$e\left(\frac{5321}{7598}\right)$	$e\left(\frac{3708}{3799}\right)$
$\chi_{15517}(135,\cdot)$	$-1$	$1$	$e\left(\frac{735}{3799}\right)$	$e\left(\frac{1138}{3799}\right)$	$e\left(\frac{1470}{3799}\right)$	$e\left(\frac{5427}{7598}\right)$	$e\left(\frac{1873}{3799}\right)$	$e\left(\frac{7175}{7598}\right)$	$e\left(\frac{2205}{3799}\right)$	$e\left(\frac{2276}{3799}\right)$	$e\left(\frac{6897}{7598}\right)$	$e\left(\frac{3469}{3799}\right)$

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$ over number fields
Genus 2 curves
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Character	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\(\chi_{15517}(5,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{3148}{3799}\right)\)	\(e\left(\frac{1380}{3799}\right)\)	\(e\left(\frac{2497}{3799}\right)\)	\(e\left(\frac{4745}{7598}\right)\)	\(e\left(\frac{729}{3799}\right)\)	\(e\left(\frac{1243}{7598}\right)\)	\(e\left(\frac{1846}{3799}\right)\)	\(e\left(\frac{2760}{3799}\right)\)	\(e\left(\frac{3443}{7598}\right)\)	\(e\left(\frac{835}{3799}\right)\)
\(\chi_{15517}(7,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{2281}{3799}\right)\)	\(e\left(\frac{2255}{3799}\right)\)	\(e\left(\frac{763}{3799}\right)\)	\(e\left(\frac{1243}{7598}\right)\)	\(e\left(\frac{737}{3799}\right)\)	\(e\left(\frac{3091}{7598}\right)\)	\(e\left(\frac{3044}{3799}\right)\)	\(e\left(\frac{711}{3799}\right)\)	\(e\left(\frac{5805}{7598}\right)\)	\(e\left(\frac{3085}{3799}\right)\)
\(\chi_{15517}(15,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{3610}{3799}\right)\)	\(e\left(\frac{33}{3799}\right)\)	\(e\left(\frac{3421}{3799}\right)\)	\(e\left(\frac{7505}{7598}\right)\)	\(e\left(\frac{3643}{3799}\right)\)	\(e\left(\frac{5753}{7598}\right)\)	\(e\left(\frac{3232}{3799}\right)\)	\(e\left(\frac{66}{3799}\right)\)	\(e\left(\frac{7127}{7598}\right)\)	\(e\left(\frac{1713}{3799}\right)\)
\(\chi_{15517}(19,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{3185}{3799}\right)\)	\(e\left(\frac{3665}{3799}\right)\)	\(e\left(\frac{2571}{3799}\right)\)	\(e\left(\frac{723}{7598}\right)\)	\(e\left(\frac{3051}{3799}\right)\)	\(e\left(\frac{5765}{7598}\right)\)	\(e\left(\frac{1957}{3799}\right)\)	\(e\left(\frac{3531}{3799}\right)\)	\(e\left(\frac{7093}{7598}\right)\)	\(e\left(\frac{2369}{3799}\right)\)
\(\chi_{15517}(20,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1655}{3799}\right)\)	\(e\left(\frac{2304}{3799}\right)\)	\(e\left(\frac{3310}{3799}\right)\)	\(e\left(\frac{2141}{7598}\right)\)	\(e\left(\frac{160}{3799}\right)\)	\(e\left(\frac{2769}{7598}\right)\)	\(e\left(\frac{1166}{3799}\right)\)	\(e\left(\frac{809}{3799}\right)\)	\(e\left(\frac{5451}{7598}\right)\)	\(e\left(\frac{3211}{3799}\right)\)
\(\chi_{15517}(21,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{2743}{3799}\right)\)	\(e\left(\frac{908}{3799}\right)\)	\(e\left(\frac{1687}{3799}\right)\)	\(e\left(\frac{4003}{7598}\right)\)	\(e\left(\frac{3651}{3799}\right)\)	\(e\left(\frac{3}{7598}\right)\)	\(e\left(\frac{631}{3799}\right)\)	\(e\left(\frac{1816}{3799}\right)\)	\(e\left(\frac{1891}{7598}\right)\)	\(e\left(\frac{164}{3799}\right)\)
\(\chi_{15517}(28,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{788}{3799}\right)\)	\(e\left(\frac{3179}{3799}\right)\)	\(e\left(\frac{1576}{3799}\right)\)	\(e\left(\frac{6237}{7598}\right)\)	\(e\left(\frac{168}{3799}\right)\)	\(e\left(\frac{4617}{7598}\right)\)	\(e\left(\frac{2364}{3799}\right)\)	\(e\left(\frac{2559}{3799}\right)\)	\(e\left(\frac{215}{7598}\right)\)	\(e\left(\frac{1662}{3799}\right)\)
\(\chi_{15517}(29,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{2849}{3799}\right)\)	\(e\left(\frac{1191}{3799}\right)\)	\(e\left(\frac{1899}{3799}\right)\)	\(e\left(\frac{5623}{7598}\right)\)	\(e\left(\frac{241}{3799}\right)\)	\(e\left(\frac{2485}{7598}\right)\)	\(e\left(\frac{949}{3799}\right)\)	\(e\left(\frac{2382}{3799}\right)\)	\(e\left(\frac{3723}{7598}\right)\)	\(e\left(\frac{349}{3799}\right)\)
\(\chi_{15517}(41,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{2164}{3799}\right)\)	\(e\left(\frac{1190}{3799}\right)\)	\(e\left(\frac{529}{3799}\right)\)	\(e\left(\frac{3899}{7598}\right)\)	\(e\left(\frac{3354}{3799}\right)\)	\(e\left(\frac{3577}{7598}\right)\)	\(e\left(\frac{2693}{3799}\right)\)	\(e\left(\frac{2380}{3799}\right)\)	\(e\left(\frac{629}{7598}\right)\)	\(e\left(\frac{3060}{3799}\right)\)
\(\chi_{15517}(45,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{273}{3799}\right)\)	\(e\left(\frac{2485}{3799}\right)\)	\(e\left(\frac{546}{3799}\right)\)	\(e\left(\frac{2667}{7598}\right)\)	\(e\left(\frac{2758}{3799}\right)\)	\(e\left(\frac{2665}{7598}\right)\)	\(e\left(\frac{819}{3799}\right)\)	\(e\left(\frac{1171}{3799}\right)\)	\(e\left(\frac{3213}{7598}\right)\)	\(e\left(\frac{2591}{3799}\right)\)
\(\chi_{15517}(53,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1673}{3799}\right)\)	\(e\left(\frac{130}{3799}\right)\)	\(e\left(\frac{3346}{3799}\right)\)	\(e\left(\frac{7577}{7598}\right)\)	\(e\left(\frac{1803}{3799}\right)\)	\(e\left(\frac{6201}{7598}\right)\)	\(e\left(\frac{1220}{3799}\right)\)	\(e\left(\frac{260}{3799}\right)\)	\(e\left(\frac{3325}{7598}\right)\)	\(e\left(\frac{877}{3799}\right)\)
\(\chi_{15517}(57,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{3647}{3799}\right)\)	\(e\left(\frac{2318}{3799}\right)\)	\(e\left(\frac{3495}{3799}\right)\)	\(e\left(\frac{3483}{7598}\right)\)	\(e\left(\frac{2166}{3799}\right)\)	\(e\left(\frac{2677}{7598}\right)\)	\(e\left(\frac{3343}{3799}\right)\)	\(e\left(\frac{837}{3799}\right)\)	\(e\left(\frac{3179}{7598}\right)\)	\(e\left(\frac{3247}{3799}\right)\)
\(\chi_{15517}(63,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{3205}{3799}\right)\)	\(e\left(\frac{3360}{3799}\right)\)	\(e\left(\frac{2611}{3799}\right)\)	\(e\left(\frac{6763}{7598}\right)\)	\(e\left(\frac{2766}{3799}\right)\)	\(e\left(\frac{4513}{7598}\right)\)	\(e\left(\frac{2017}{3799}\right)\)	\(e\left(\frac{2921}{3799}\right)\)	\(e\left(\frac{5575}{7598}\right)\)	\(e\left(\frac{1042}{3799}\right)\)
\(\chi_{15517}(71,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{3319}{3799}\right)\)	\(e\left(\frac{3521}{3799}\right)\)	\(e\left(\frac{2839}{3799}\right)\)	\(e\left(\frac{3201}{7598}\right)\)	\(e\left(\frac{3041}{3799}\right)\)	\(e\left(\frac{3455}{7598}\right)\)	\(e\left(\frac{2359}{3799}\right)\)	\(e\left(\frac{3243}{3799}\right)\)	\(e\left(\frac{2241}{7598}\right)\)	\(e\left(\frac{1456}{3799}\right)\)
\(\chi_{15517}(76,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1692}{3799}\right)\)	\(e\left(\frac{790}{3799}\right)\)	\(e\left(\frac{3384}{3799}\right)\)	\(e\left(\frac{5717}{7598}\right)\)	\(e\left(\frac{2482}{3799}\right)\)	\(e\left(\frac{7291}{7598}\right)\)	\(e\left(\frac{1277}{3799}\right)\)	\(e\left(\frac{1580}{3799}\right)\)	\(e\left(\frac{1503}{7598}\right)\)	\(e\left(\frac{946}{3799}\right)\)
\(\chi_{15517}(79,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{2380}{3799}\right)\)	\(e\left(\frac{1695}{3799}\right)\)	\(e\left(\frac{961}{3799}\right)\)	\(e\left(\frac{749}{7598}\right)\)	\(e\left(\frac{276}{3799}\right)\)	\(e\left(\frac{6771}{7598}\right)\)	\(e\left(\frac{3341}{3799}\right)\)	\(e\left(\frac{3390}{3799}\right)\)	\(e\left(\frac{5509}{7598}\right)\)	\(e\left(\frac{1645}{3799}\right)\)
\(\chi_{15517}(80,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{162}{3799}\right)\)	\(e\left(\frac{3228}{3799}\right)\)	\(e\left(\frac{324}{3799}\right)\)	\(e\left(\frac{7135}{7598}\right)\)	\(e\left(\frac{3390}{3799}\right)\)	\(e\left(\frac{4295}{7598}\right)\)	\(e\left(\frac{486}{3799}\right)\)	\(e\left(\frac{2657}{3799}\right)\)	\(e\left(\frac{7459}{7598}\right)\)	\(e\left(\frac{1788}{3799}\right)\)
\(\chi_{15517}(84,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1250}{3799}\right)\)	\(e\left(\frac{1832}{3799}\right)\)	\(e\left(\frac{2500}{3799}\right)\)	\(e\left(\frac{1399}{7598}\right)\)	\(e\left(\frac{3082}{3799}\right)\)	\(e\left(\frac{1529}{7598}\right)\)	\(e\left(\frac{3750}{3799}\right)\)	\(e\left(\frac{3664}{3799}\right)\)	\(e\left(\frac{3899}{7598}\right)\)	\(e\left(\frac{2540}{3799}\right)\)
\(\chi_{15517}(85,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{3390}{3799}\right)\)	\(e\left(\frac{3388}{3799}\right)\)	\(e\left(\frac{2981}{3799}\right)\)	\(e\left(\frac{1849}{7598}\right)\)	\(e\left(\frac{2979}{3799}\right)\)	\(e\left(\frac{4329}{7598}\right)\)	\(e\left(\frac{2572}{3799}\right)\)	\(e\left(\frac{2977}{3799}\right)\)	\(e\left(\frac{1031}{7598}\right)\)	\(e\left(\frac{1114}{3799}\right)\)
\(\chi_{15517}(87,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{3311}{3799}\right)\)	\(e\left(\frac{3643}{3799}\right)\)	\(e\left(\frac{2823}{3799}\right)\)	\(e\left(\frac{785}{7598}\right)\)	\(e\left(\frac{3155}{3799}\right)\)	\(e\left(\frac{6995}{7598}\right)\)	\(e\left(\frac{2335}{3799}\right)\)	\(e\left(\frac{3487}{3799}\right)\)	\(e\left(\frac{7407}{7598}\right)\)	\(e\left(\frac{1227}{3799}\right)\)
\(\chi_{15517}(94,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1282}{3799}\right)\)	\(e\left(\frac{1344}{3799}\right)\)	\(e\left(\frac{2564}{3799}\right)\)	\(e\left(\frac{3465}{7598}\right)\)	\(e\left(\frac{2626}{3799}\right)\)	\(e\left(\frac{2565}{7598}\right)\)	\(e\left(\frac{47}{3799}\right)\)	\(e\left(\frac{2688}{3799}\right)\)	\(e\left(\frac{6029}{7598}\right)\)	\(e\left(\frac{3456}{3799}\right)\)
\(\chi_{15517}(107,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{2754}{3799}\right)\)	\(e\left(\frac{1690}{3799}\right)\)	\(e\left(\frac{1709}{3799}\right)\)	\(e\left(\frac{7325}{7598}\right)\)	\(e\left(\frac{645}{3799}\right)\)	\(e\left(\frac{4633}{7598}\right)\)	\(e\left(\frac{664}{3799}\right)\)	\(e\left(\frac{3380}{3799}\right)\)	\(e\left(\frac{5235}{7598}\right)\)	\(e\left(\frac{4}{3799}\right)\)
\(\chi_{15517}(110,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1690}{3799}\right)\)	\(e\left(\frac{2720}{3799}\right)\)	\(e\left(\frac{3380}{3799}\right)\)	\(e\left(\frac{5113}{7598}\right)\)	\(e\left(\frac{611}{3799}\right)\)	\(e\left(\frac{4377}{7598}\right)\)	\(e\left(\frac{1271}{3799}\right)\)	\(e\left(\frac{1641}{3799}\right)\)	\(e\left(\frac{895}{7598}\right)\)	\(e\left(\frac{3738}{3799}\right)\)
\(\chi_{15517}(112,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{3094}{3799}\right)\)	\(e\left(\frac{304}{3799}\right)\)	\(e\left(\frac{2389}{3799}\right)\)	\(e\left(\frac{3633}{7598}\right)\)	\(e\left(\frac{3398}{3799}\right)\)	\(e\left(\frac{6143}{7598}\right)\)	\(e\left(\frac{1684}{3799}\right)\)	\(e\left(\frac{608}{3799}\right)\)	\(e\left(\frac{2223}{7598}\right)\)	\(e\left(\frac{239}{3799}\right)\)
\(\chi_{15517}(116,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1356}{3799}\right)\)	\(e\left(\frac{2115}{3799}\right)\)	\(e\left(\frac{2712}{3799}\right)\)	\(e\left(\frac{3019}{7598}\right)\)	\(e\left(\frac{3471}{3799}\right)\)	\(e\left(\frac{4011}{7598}\right)\)	\(e\left(\frac{269}{3799}\right)\)	\(e\left(\frac{431}{3799}\right)\)	\(e\left(\frac{5731}{7598}\right)\)	\(e\left(\frac{2725}{3799}\right)\)
\(\chi_{15517}(123,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{2626}{3799}\right)\)	\(e\left(\frac{3642}{3799}\right)\)	\(e\left(\frac{1453}{3799}\right)\)	\(e\left(\frac{6659}{7598}\right)\)	\(e\left(\frac{2469}{3799}\right)\)	\(e\left(\frac{489}{7598}\right)\)	\(e\left(\frac{280}{3799}\right)\)	\(e\left(\frac{3485}{3799}\right)\)	\(e\left(\frac{4313}{7598}\right)\)	\(e\left(\frac{139}{3799}\right)\)
\(\chi_{15517}(125,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1846}{3799}\right)\)	\(e\left(\frac{341}{3799}\right)\)	\(e\left(\frac{3692}{3799}\right)\)	\(e\left(\frac{6637}{7598}\right)\)	\(e\left(\frac{2187}{3799}\right)\)	\(e\left(\frac{3729}{7598}\right)\)	\(e\left(\frac{1739}{3799}\right)\)	\(e\left(\frac{682}{3799}\right)\)	\(e\left(\frac{2731}{7598}\right)\)	\(e\left(\frac{2505}{3799}\right)\)
\(\chi_{15517}(127,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1736}{3799}\right)\)	\(e\left(\frac{119}{3799}\right)\)	\(e\left(\frac{3472}{3799}\right)\)	\(e\left(\frac{3809}{7598}\right)\)	\(e\left(\frac{1855}{3799}\right)\)	\(e\left(\frac{3017}{7598}\right)\)	\(e\left(\frac{1409}{3799}\right)\)	\(e\left(\frac{238}{3799}\right)\)	\(e\left(\frac{7281}{7598}\right)\)	\(e\left(\frac{306}{3799}\right)\)
\(\chi_{15517}(130,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1405}{3799}\right)\)	\(e\left(\frac{418}{3799}\right)\)	\(e\left(\frac{2810}{3799}\right)\)	\(e\left(\frac{2621}{7598}\right)\)	\(e\left(\frac{1823}{3799}\right)\)	\(e\left(\frac{3223}{7598}\right)\)	\(e\left(\frac{416}{3799}\right)\)	\(e\left(\frac{836}{3799}\right)\)	\(e\left(\frac{5431}{7598}\right)\)	\(e\left(\frac{2703}{3799}\right)\)
\(\chi_{15517}(134,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{30}{3799}\right)\)	\(e\left(\frac{1442}{3799}\right)\)	\(e\left(\frac{60}{3799}\right)\)	\(e\left(\frac{5261}{7598}\right)\)	\(e\left(\frac{1472}{3799}\right)\)	\(e\left(\frac{1921}{7598}\right)\)	\(e\left(\frac{90}{3799}\right)\)	\(e\left(\frac{2884}{3799}\right)\)	\(e\left(\frac{5321}{7598}\right)\)	\(e\left(\frac{3708}{3799}\right)\)
\(\chi_{15517}(135,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{735}{3799}\right)\)	\(e\left(\frac{1138}{3799}\right)\)	\(e\left(\frac{1470}{3799}\right)\)	\(e\left(\frac{5427}{7598}\right)\)	\(e\left(\frac{1873}{3799}\right)\)	\(e\left(\frac{7175}{7598}\right)\)	\(e\left(\frac{2205}{3799}\right)\)	\(e\left(\frac{2276}{3799}\right)\)	\(e\left(\frac{6897}{7598}\right)\)	\(e\left(\frac{3469}{3799}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Basic properties

Related number fields

First 31 of 3640 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	15517.p
Modulus	$15517$
Conductor	$15517$
Order	$7598$
Real	no
Primitive	yes
Minimal	yes
Parity	odd

Modulus:	\(15517\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(15517\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(7598\)	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);