LMFDB - Dirichlet character orbit 15517.m

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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([6550,1450])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(3, 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("15517.3"); 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:	$3799$	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:	even	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 3799 polynomial (not computed)	comment:Fixed field sage:chi.fixed_field()

First 31 of 3640 characters in Galois orbit

Character	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{15517}(3,\cdot)$	$1$	$1$	$e\left(\frac{462}{3799}\right)$	$e\left(\frac{2452}{3799}\right)$	$e\left(\frac{924}{3799}\right)$	$e\left(\frac{1380}{3799}\right)$	$e\left(\frac{2914}{3799}\right)$	$e\left(\frac{2255}{3799}\right)$	$e\left(\frac{1386}{3799}\right)$	$e\left(\frac{1105}{3799}\right)$	$e\left(\frac{1842}{3799}\right)$	$e\left(\frac{878}{3799}\right)$
$\chi_{15517}(4,\cdot)$	$1$	$1$	$e\left(\frac{2306}{3799}\right)$	$e\left(\frac{924}{3799}\right)$	$e\left(\frac{813}{3799}\right)$	$e\left(\frac{2497}{3799}\right)$	$e\left(\frac{3230}{3799}\right)$	$e\left(\frac{763}{3799}\right)$	$e\left(\frac{3119}{3799}\right)$	$e\left(\frac{1848}{3799}\right)$	$e\left(\frac{1004}{3799}\right)$	$e\left(\frac{2376}{3799}\right)$
$\chi_{15517}(9,\cdot)$	$1$	$1$	$e\left(\frac{924}{3799}\right)$	$e\left(\frac{1105}{3799}\right)$	$e\left(\frac{1848}{3799}\right)$	$e\left(\frac{2760}{3799}\right)$	$e\left(\frac{2029}{3799}\right)$	$e\left(\frac{711}{3799}\right)$	$e\left(\frac{2772}{3799}\right)$	$e\left(\frac{2210}{3799}\right)$	$e\left(\frac{3684}{3799}\right)$	$e\left(\frac{1756}{3799}\right)$
$\chi_{15517}(12,\cdot)$	$1$	$1$	$e\left(\frac{2768}{3799}\right)$	$e\left(\frac{3376}{3799}\right)$	$e\left(\frac{1737}{3799}\right)$	$e\left(\frac{78}{3799}\right)$	$e\left(\frac{2345}{3799}\right)$	$e\left(\frac{3018}{3799}\right)$	$e\left(\frac{706}{3799}\right)$	$e\left(\frac{2953}{3799}\right)$	$e\left(\frac{2846}{3799}\right)$	$e\left(\frac{3254}{3799}\right)$
$\chi_{15517}(16,\cdot)$	$1$	$1$	$e\left(\frac{813}{3799}\right)$	$e\left(\frac{1848}{3799}\right)$	$e\left(\frac{1626}{3799}\right)$	$e\left(\frac{1195}{3799}\right)$	$e\left(\frac{2661}{3799}\right)$	$e\left(\frac{1526}{3799}\right)$	$e\left(\frac{2439}{3799}\right)$	$e\left(\frac{3696}{3799}\right)$	$e\left(\frac{2008}{3799}\right)$	$e\left(\frac{953}{3799}\right)$
$\chi_{15517}(17,\cdot)$	$1$	$1$	$e\left(\frac{242}{3799}\right)$	$e\left(\frac{2008}{3799}\right)$	$e\left(\frac{484}{3799}\right)$	$e\left(\frac{2351}{3799}\right)$	$e\left(\frac{2250}{3799}\right)$	$e\left(\frac{1543}{3799}\right)$	$e\left(\frac{726}{3799}\right)$	$e\left(\frac{217}{3799}\right)$	$e\left(\frac{2593}{3799}\right)$	$e\left(\frac{279}{3799}\right)$
$\chi_{15517}(22,\cdot)$	$1$	$1$	$e\left(\frac{2341}{3799}\right)$	$e\left(\frac{1340}{3799}\right)$	$e\left(\frac{883}{3799}\right)$	$e\left(\frac{184}{3799}\right)$	$e\left(\frac{3681}{3799}\right)$	$e\left(\frac{1567}{3799}\right)$	$e\left(\frac{3224}{3799}\right)$	$e\left(\frac{2680}{3799}\right)$	$e\left(\frac{2525}{3799}\right)$	$e\left(\frac{2903}{3799}\right)$
$\chi_{15517}(25,\cdot)$	$1$	$1$	$e\left(\frac{2497}{3799}\right)$	$e\left(\frac{2760}{3799}\right)$	$e\left(\frac{1195}{3799}\right)$	$e\left(\frac{946}{3799}\right)$	$e\left(\frac{1458}{3799}\right)$	$e\left(\frac{1243}{3799}\right)$	$e\left(\frac{3692}{3799}\right)$	$e\left(\frac{1721}{3799}\right)$	$e\left(\frac{3443}{3799}\right)$	$e\left(\frac{1670}{3799}\right)$
$\chi_{15517}(26,\cdot)$	$1$	$1$	$e\left(\frac{2056}{3799}\right)$	$e\left(\frac{2837}{3799}\right)$	$e\left(\frac{313}{3799}\right)$	$e\left(\frac{2737}{3799}\right)$	$e\left(\frac{1094}{3799}\right)$	$e\left(\frac{990}{3799}\right)$	$e\left(\frac{2369}{3799}\right)$	$e\left(\frac{1875}{3799}\right)$	$e\left(\frac{994}{3799}\right)$	$e\left(\frac{1868}{3799}\right)$
$\chi_{15517}(27,\cdot)$	$1$	$1$	$e\left(\frac{1386}{3799}\right)$	$e\left(\frac{3557}{3799}\right)$	$e\left(\frac{2772}{3799}\right)$	$e\left(\frac{341}{3799}\right)$	$e\left(\frac{1144}{3799}\right)$	$e\left(\frac{2966}{3799}\right)$	$e\left(\frac{359}{3799}\right)$	$e\left(\frac{3315}{3799}\right)$	$e\left(\frac{1727}{3799}\right)$	$e\left(\frac{2634}{3799}\right)$
$\chi_{15517}(35,\cdot)$	$1$	$1$	$e\left(\frac{1630}{3799}\right)$	$e\left(\frac{3635}{3799}\right)$	$e\left(\frac{3260}{3799}\right)$	$e\left(\frac{2994}{3799}\right)$	$e\left(\frac{1466}{3799}\right)$	$e\left(\frac{2167}{3799}\right)$	$e\left(\frac{1091}{3799}\right)$	$e\left(\frac{3471}{3799}\right)$	$e\left(\frac{825}{3799}\right)$	$e\left(\frac{121}{3799}\right)$
$\chi_{15517}(36,\cdot)$	$1$	$1$	$e\left(\frac{3230}{3799}\right)$	$e\left(\frac{2029}{3799}\right)$	$e\left(\frac{2661}{3799}\right)$	$e\left(\frac{1458}{3799}\right)$	$e\left(\frac{1460}{3799}\right)$	$e\left(\frac{1474}{3799}\right)$	$e\left(\frac{2092}{3799}\right)$	$e\left(\frac{259}{3799}\right)$	$e\left(\frac{889}{3799}\right)$	$e\left(\frac{333}{3799}\right)$
$\chi_{15517}(46,\cdot)$	$1$	$1$	$e\left(\frac{729}{3799}\right)$	$e\left(\frac{3129}{3799}\right)$	$e\left(\frac{1458}{3799}\right)$	$e\left(\frac{3707}{3799}\right)$	$e\left(\frac{59}{3799}\right)$	$e\left(\frac{1116}{3799}\right)$	$e\left(\frac{2187}{3799}\right)$	$e\left(\frac{2459}{3799}\right)$	$e\left(\frac{637}{3799}\right)$	$e\left(\frac{448}{3799}\right)$
$\chi_{15517}(48,\cdot)$	$1$	$1$	$e\left(\frac{1275}{3799}\right)$	$e\left(\frac{501}{3799}\right)$	$e\left(\frac{2550}{3799}\right)$	$e\left(\frac{2575}{3799}\right)$	$e\left(\frac{1776}{3799}\right)$	$e\left(\frac{3781}{3799}\right)$	$e\left(\frac{26}{3799}\right)$	$e\left(\frac{1002}{3799}\right)$	$e\left(\frac{51}{3799}\right)$	$e\left(\frac{1831}{3799}\right)$
$\chi_{15517}(49,\cdot)$	$1$	$1$	$e\left(\frac{763}{3799}\right)$	$e\left(\frac{711}{3799}\right)$	$e\left(\frac{1526}{3799}\right)$	$e\left(\frac{1243}{3799}\right)$	$e\left(\frac{1474}{3799}\right)$	$e\left(\frac{3091}{3799}\right)$	$e\left(\frac{2289}{3799}\right)$	$e\left(\frac{1422}{3799}\right)$	$e\left(\frac{2006}{3799}\right)$	$e\left(\frac{2371}{3799}\right)$
$\chi_{15517}(51,\cdot)$	$1$	$1$	$e\left(\frac{704}{3799}\right)$	$e\left(\frac{661}{3799}\right)$	$e\left(\frac{1408}{3799}\right)$	$e\left(\frac{3731}{3799}\right)$	$e\left(\frac{1365}{3799}\right)$	$e\left(\frac{3798}{3799}\right)$	$e\left(\frac{2112}{3799}\right)$	$e\left(\frac{1322}{3799}\right)$	$e\left(\frac{636}{3799}\right)$	$e\left(\frac{1157}{3799}\right)$
$\chi_{15517}(62,\cdot)$	$1$	$1$	$e\left(\frac{1042}{3799}\right)$	$e\left(\frac{1205}{3799}\right)$	$e\left(\frac{2084}{3799}\right)$	$e\left(\frac{1583}{3799}\right)$	$e\left(\frac{2247}{3799}\right)$	$e\left(\frac{3096}{3799}\right)$	$e\left(\frac{3126}{3799}\right)$	$e\left(\frac{2410}{3799}\right)$	$e\left(\frac{2625}{3799}\right)$	$e\left(\frac{385}{3799}\right)$
$\chi_{15517}(64,\cdot)$	$1$	$1$	$e\left(\frac{3119}{3799}\right)$	$e\left(\frac{2772}{3799}\right)$	$e\left(\frac{2439}{3799}\right)$	$e\left(\frac{3692}{3799}\right)$	$e\left(\frac{2092}{3799}\right)$	$e\left(\frac{2289}{3799}\right)$	$e\left(\frac{1759}{3799}\right)$	$e\left(\frac{1745}{3799}\right)$	$e\left(\frac{3012}{3799}\right)$	$e\left(\frac{3329}{3799}\right)$
$\chi_{15517}(66,\cdot)$	$1$	$1$	$e\left(\frac{2803}{3799}\right)$	$e\left(\frac{3792}{3799}\right)$	$e\left(\frac{1807}{3799}\right)$	$e\left(\frac{1564}{3799}\right)$	$e\left(\frac{2796}{3799}\right)$	$e\left(\frac{23}{3799}\right)$	$e\left(\frac{811}{3799}\right)$	$e\left(\frac{3785}{3799}\right)$	$e\left(\frac{568}{3799}\right)$	$e\left(\frac{3781}{3799}\right)$
$\chi_{15517}(68,\cdot)$	$1$	$1$	$e\left(\frac{2548}{3799}\right)$	$e\left(\frac{2932}{3799}\right)$	$e\left(\frac{1297}{3799}\right)$	$e\left(\frac{1049}{3799}\right)$	$e\left(\frac{1681}{3799}\right)$	$e\left(\frac{2306}{3799}\right)$	$e\left(\frac{46}{3799}\right)$	$e\left(\frac{2065}{3799}\right)$	$e\left(\frac{3597}{3799}\right)$	$e\left(\frac{2655}{3799}\right)$
$\chi_{15517}(74,\cdot)$	$1$	$1$	$e\left(\frac{130}{3799}\right)$	$e\left(\frac{3716}{3799}\right)$	$e\left(\frac{260}{3799}\right)$	$e\left(\frac{635}{3799}\right)$	$e\left(\frac{47}{3799}\right)$	$e\left(\frac{3529}{3799}\right)$	$e\left(\frac{390}{3799}\right)$	$e\left(\frac{3633}{3799}\right)$	$e\left(\frac{765}{3799}\right)$	$e\left(\frac{872}{3799}\right)$
$\chi_{15517}(75,\cdot)$	$1$	$1$	$e\left(\frac{2959}{3799}\right)$	$e\left(\frac{1413}{3799}\right)$	$e\left(\frac{2119}{3799}\right)$	$e\left(\frac{2326}{3799}\right)$	$e\left(\frac{573}{3799}\right)$	$e\left(\frac{3498}{3799}\right)$	$e\left(\frac{1279}{3799}\right)$	$e\left(\frac{2826}{3799}\right)$	$e\left(\frac{1486}{3799}\right)$	$e\left(\frac{2548}{3799}\right)$
$\chi_{15517}(78,\cdot)$	$1$	$1$	$e\left(\frac{2518}{3799}\right)$	$e\left(\frac{1490}{3799}\right)$	$e\left(\frac{1237}{3799}\right)$	$e\left(\frac{318}{3799}\right)$	$e\left(\frac{209}{3799}\right)$	$e\left(\frac{3245}{3799}\right)$	$e\left(\frac{3755}{3799}\right)$	$e\left(\frac{2980}{3799}\right)$	$e\left(\frac{2836}{3799}\right)$	$e\left(\frac{2746}{3799}\right)$
$\chi_{15517}(81,\cdot)$	$1$	$1$	$e\left(\frac{1848}{3799}\right)$	$e\left(\frac{2210}{3799}\right)$	$e\left(\frac{3696}{3799}\right)$	$e\left(\frac{1721}{3799}\right)$	$e\left(\frac{259}{3799}\right)$	$e\left(\frac{1422}{3799}\right)$	$e\left(\frac{1745}{3799}\right)$	$e\left(\frac{621}{3799}\right)$	$e\left(\frac{3569}{3799}\right)$	$e\left(\frac{3512}{3799}\right)$
$\chi_{15517}(86,\cdot)$	$1$	$1$	$e\left(\frac{197}{3799}\right)$	$e\left(\frac{3644}{3799}\right)$	$e\left(\frac{394}{3799}\right)$	$e\left(\frac{3154}{3799}\right)$	$e\left(\frac{42}{3799}\right)$	$e\left(\frac{1052}{3799}\right)$	$e\left(\frac{591}{3799}\right)$	$e\left(\frac{3489}{3799}\right)$	$e\left(\frac{3351}{3799}\right)$	$e\left(\frac{2315}{3799}\right)$
$\chi_{15517}(88,\cdot)$	$1$	$1$	$e\left(\frac{848}{3799}\right)$	$e\left(\frac{2264}{3799}\right)$	$e\left(\frac{1696}{3799}\right)$	$e\left(\frac{2681}{3799}\right)$	$e\left(\frac{3112}{3799}\right)$	$e\left(\frac{2330}{3799}\right)$	$e\left(\frac{2544}{3799}\right)$	$e\left(\frac{729}{3799}\right)$	$e\left(\frac{3529}{3799}\right)$	$e\left(\frac{1480}{3799}\right)$
$\chi_{15517}(95,\cdot)$	$1$	$1$	$e\left(\frac{2534}{3799}\right)$	$e\left(\frac{1246}{3799}\right)$	$e\left(\frac{1269}{3799}\right)$	$e\left(\frac{2734}{3799}\right)$	$e\left(\frac{3780}{3799}\right)$	$e\left(\frac{3504}{3799}\right)$	$e\left(\frac{4}{3799}\right)$	$e\left(\frac{2492}{3799}\right)$	$e\left(\frac{1469}{3799}\right)$	$e\left(\frac{3204}{3799}\right)$
$\chi_{15517}(100,\cdot)$	$1$	$1$	$e\left(\frac{1004}{3799}\right)$	$e\left(\frac{3684}{3799}\right)$	$e\left(\frac{2008}{3799}\right)$	$e\left(\frac{3443}{3799}\right)$	$e\left(\frac{889}{3799}\right)$	$e\left(\frac{2006}{3799}\right)$	$e\left(\frac{3012}{3799}\right)$	$e\left(\frac{3569}{3799}\right)$	$e\left(\frac{648}{3799}\right)$	$e\left(\frac{247}{3799}\right)$
$\chi_{15517}(104,\cdot)$	$1$	$1$	$e\left(\frac{563}{3799}\right)$	$e\left(\frac{3761}{3799}\right)$	$e\left(\frac{1126}{3799}\right)$	$e\left(\frac{1435}{3799}\right)$	$e\left(\frac{525}{3799}\right)$	$e\left(\frac{1753}{3799}\right)$	$e\left(\frac{1689}{3799}\right)$	$e\left(\frac{3723}{3799}\right)$	$e\left(\frac{1998}{3799}\right)$	$e\left(\frac{445}{3799}\right)$
$\chi_{15517}(105,\cdot)$	$1$	$1$	$e\left(\frac{2092}{3799}\right)$	$e\left(\frac{2288}{3799}\right)$	$e\left(\frac{385}{3799}\right)$	$e\left(\frac{575}{3799}\right)$	$e\left(\frac{581}{3799}\right)$	$e\left(\frac{623}{3799}\right)$	$e\left(\frac{2477}{3799}\right)$	$e\left(\frac{777}{3799}\right)$	$e\left(\frac{2667}{3799}\right)$	$e\left(\frac{999}{3799}\right)$
$\chi_{15517}(108,\cdot)$	$1$	$1$	$e\left(\frac{3692}{3799}\right)$	$e\left(\frac{682}{3799}\right)$	$e\left(\frac{3585}{3799}\right)$	$e\left(\frac{2838}{3799}\right)$	$e\left(\frac{575}{3799}\right)$	$e\left(\frac{3729}{3799}\right)$	$e\left(\frac{3478}{3799}\right)$	$e\left(\frac{1364}{3799}\right)$	$e\left(\frac{2731}{3799}\right)$	$e\left(\frac{1211}{3799}\right)$

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	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\(\chi_{15517}(3,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{462}{3799}\right)\)	\(e\left(\frac{2452}{3799}\right)\)	\(e\left(\frac{924}{3799}\right)\)	\(e\left(\frac{1380}{3799}\right)\)	\(e\left(\frac{2914}{3799}\right)\)	\(e\left(\frac{2255}{3799}\right)\)	\(e\left(\frac{1386}{3799}\right)\)	\(e\left(\frac{1105}{3799}\right)\)	\(e\left(\frac{1842}{3799}\right)\)	\(e\left(\frac{878}{3799}\right)\)
\(\chi_{15517}(4,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2306}{3799}\right)\)	\(e\left(\frac{924}{3799}\right)\)	\(e\left(\frac{813}{3799}\right)\)	\(e\left(\frac{2497}{3799}\right)\)	\(e\left(\frac{3230}{3799}\right)\)	\(e\left(\frac{763}{3799}\right)\)	\(e\left(\frac{3119}{3799}\right)\)	\(e\left(\frac{1848}{3799}\right)\)	\(e\left(\frac{1004}{3799}\right)\)	\(e\left(\frac{2376}{3799}\right)\)
\(\chi_{15517}(9,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{924}{3799}\right)\)	\(e\left(\frac{1105}{3799}\right)\)	\(e\left(\frac{1848}{3799}\right)\)	\(e\left(\frac{2760}{3799}\right)\)	\(e\left(\frac{2029}{3799}\right)\)	\(e\left(\frac{711}{3799}\right)\)	\(e\left(\frac{2772}{3799}\right)\)	\(e\left(\frac{2210}{3799}\right)\)	\(e\left(\frac{3684}{3799}\right)\)	\(e\left(\frac{1756}{3799}\right)\)
\(\chi_{15517}(12,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2768}{3799}\right)\)	\(e\left(\frac{3376}{3799}\right)\)	\(e\left(\frac{1737}{3799}\right)\)	\(e\left(\frac{78}{3799}\right)\)	\(e\left(\frac{2345}{3799}\right)\)	\(e\left(\frac{3018}{3799}\right)\)	\(e\left(\frac{706}{3799}\right)\)	\(e\left(\frac{2953}{3799}\right)\)	\(e\left(\frac{2846}{3799}\right)\)	\(e\left(\frac{3254}{3799}\right)\)
\(\chi_{15517}(16,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{813}{3799}\right)\)	\(e\left(\frac{1848}{3799}\right)\)	\(e\left(\frac{1626}{3799}\right)\)	\(e\left(\frac{1195}{3799}\right)\)	\(e\left(\frac{2661}{3799}\right)\)	\(e\left(\frac{1526}{3799}\right)\)	\(e\left(\frac{2439}{3799}\right)\)	\(e\left(\frac{3696}{3799}\right)\)	\(e\left(\frac{2008}{3799}\right)\)	\(e\left(\frac{953}{3799}\right)\)
\(\chi_{15517}(17,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{242}{3799}\right)\)	\(e\left(\frac{2008}{3799}\right)\)	\(e\left(\frac{484}{3799}\right)\)	\(e\left(\frac{2351}{3799}\right)\)	\(e\left(\frac{2250}{3799}\right)\)	\(e\left(\frac{1543}{3799}\right)\)	\(e\left(\frac{726}{3799}\right)\)	\(e\left(\frac{217}{3799}\right)\)	\(e\left(\frac{2593}{3799}\right)\)	\(e\left(\frac{279}{3799}\right)\)
\(\chi_{15517}(22,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2341}{3799}\right)\)	\(e\left(\frac{1340}{3799}\right)\)	\(e\left(\frac{883}{3799}\right)\)	\(e\left(\frac{184}{3799}\right)\)	\(e\left(\frac{3681}{3799}\right)\)	\(e\left(\frac{1567}{3799}\right)\)	\(e\left(\frac{3224}{3799}\right)\)	\(e\left(\frac{2680}{3799}\right)\)	\(e\left(\frac{2525}{3799}\right)\)	\(e\left(\frac{2903}{3799}\right)\)
\(\chi_{15517}(25,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2497}{3799}\right)\)	\(e\left(\frac{2760}{3799}\right)\)	\(e\left(\frac{1195}{3799}\right)\)	\(e\left(\frac{946}{3799}\right)\)	\(e\left(\frac{1458}{3799}\right)\)	\(e\left(\frac{1243}{3799}\right)\)	\(e\left(\frac{3692}{3799}\right)\)	\(e\left(\frac{1721}{3799}\right)\)	\(e\left(\frac{3443}{3799}\right)\)	\(e\left(\frac{1670}{3799}\right)\)
\(\chi_{15517}(26,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2056}{3799}\right)\)	\(e\left(\frac{2837}{3799}\right)\)	\(e\left(\frac{313}{3799}\right)\)	\(e\left(\frac{2737}{3799}\right)\)	\(e\left(\frac{1094}{3799}\right)\)	\(e\left(\frac{990}{3799}\right)\)	\(e\left(\frac{2369}{3799}\right)\)	\(e\left(\frac{1875}{3799}\right)\)	\(e\left(\frac{994}{3799}\right)\)	\(e\left(\frac{1868}{3799}\right)\)
\(\chi_{15517}(27,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1386}{3799}\right)\)	\(e\left(\frac{3557}{3799}\right)\)	\(e\left(\frac{2772}{3799}\right)\)	\(e\left(\frac{341}{3799}\right)\)	\(e\left(\frac{1144}{3799}\right)\)	\(e\left(\frac{2966}{3799}\right)\)	\(e\left(\frac{359}{3799}\right)\)	\(e\left(\frac{3315}{3799}\right)\)	\(e\left(\frac{1727}{3799}\right)\)	\(e\left(\frac{2634}{3799}\right)\)
\(\chi_{15517}(35,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1630}{3799}\right)\)	\(e\left(\frac{3635}{3799}\right)\)	\(e\left(\frac{3260}{3799}\right)\)	\(e\left(\frac{2994}{3799}\right)\)	\(e\left(\frac{1466}{3799}\right)\)	\(e\left(\frac{2167}{3799}\right)\)	\(e\left(\frac{1091}{3799}\right)\)	\(e\left(\frac{3471}{3799}\right)\)	\(e\left(\frac{825}{3799}\right)\)	\(e\left(\frac{121}{3799}\right)\)
\(\chi_{15517}(36,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3230}{3799}\right)\)	\(e\left(\frac{2029}{3799}\right)\)	\(e\left(\frac{2661}{3799}\right)\)	\(e\left(\frac{1458}{3799}\right)\)	\(e\left(\frac{1460}{3799}\right)\)	\(e\left(\frac{1474}{3799}\right)\)	\(e\left(\frac{2092}{3799}\right)\)	\(e\left(\frac{259}{3799}\right)\)	\(e\left(\frac{889}{3799}\right)\)	\(e\left(\frac{333}{3799}\right)\)
\(\chi_{15517}(46,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{729}{3799}\right)\)	\(e\left(\frac{3129}{3799}\right)\)	\(e\left(\frac{1458}{3799}\right)\)	\(e\left(\frac{3707}{3799}\right)\)	\(e\left(\frac{59}{3799}\right)\)	\(e\left(\frac{1116}{3799}\right)\)	\(e\left(\frac{2187}{3799}\right)\)	\(e\left(\frac{2459}{3799}\right)\)	\(e\left(\frac{637}{3799}\right)\)	\(e\left(\frac{448}{3799}\right)\)
\(\chi_{15517}(48,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1275}{3799}\right)\)	\(e\left(\frac{501}{3799}\right)\)	\(e\left(\frac{2550}{3799}\right)\)	\(e\left(\frac{2575}{3799}\right)\)	\(e\left(\frac{1776}{3799}\right)\)	\(e\left(\frac{3781}{3799}\right)\)	\(e\left(\frac{26}{3799}\right)\)	\(e\left(\frac{1002}{3799}\right)\)	\(e\left(\frac{51}{3799}\right)\)	\(e\left(\frac{1831}{3799}\right)\)
\(\chi_{15517}(49,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{763}{3799}\right)\)	\(e\left(\frac{711}{3799}\right)\)	\(e\left(\frac{1526}{3799}\right)\)	\(e\left(\frac{1243}{3799}\right)\)	\(e\left(\frac{1474}{3799}\right)\)	\(e\left(\frac{3091}{3799}\right)\)	\(e\left(\frac{2289}{3799}\right)\)	\(e\left(\frac{1422}{3799}\right)\)	\(e\left(\frac{2006}{3799}\right)\)	\(e\left(\frac{2371}{3799}\right)\)
\(\chi_{15517}(51,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{704}{3799}\right)\)	\(e\left(\frac{661}{3799}\right)\)	\(e\left(\frac{1408}{3799}\right)\)	\(e\left(\frac{3731}{3799}\right)\)	\(e\left(\frac{1365}{3799}\right)\)	\(e\left(\frac{3798}{3799}\right)\)	\(e\left(\frac{2112}{3799}\right)\)	\(e\left(\frac{1322}{3799}\right)\)	\(e\left(\frac{636}{3799}\right)\)	\(e\left(\frac{1157}{3799}\right)\)
\(\chi_{15517}(62,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1042}{3799}\right)\)	\(e\left(\frac{1205}{3799}\right)\)	\(e\left(\frac{2084}{3799}\right)\)	\(e\left(\frac{1583}{3799}\right)\)	\(e\left(\frac{2247}{3799}\right)\)	\(e\left(\frac{3096}{3799}\right)\)	\(e\left(\frac{3126}{3799}\right)\)	\(e\left(\frac{2410}{3799}\right)\)	\(e\left(\frac{2625}{3799}\right)\)	\(e\left(\frac{385}{3799}\right)\)
\(\chi_{15517}(64,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3119}{3799}\right)\)	\(e\left(\frac{2772}{3799}\right)\)	\(e\left(\frac{2439}{3799}\right)\)	\(e\left(\frac{3692}{3799}\right)\)	\(e\left(\frac{2092}{3799}\right)\)	\(e\left(\frac{2289}{3799}\right)\)	\(e\left(\frac{1759}{3799}\right)\)	\(e\left(\frac{1745}{3799}\right)\)	\(e\left(\frac{3012}{3799}\right)\)	\(e\left(\frac{3329}{3799}\right)\)
\(\chi_{15517}(66,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2803}{3799}\right)\)	\(e\left(\frac{3792}{3799}\right)\)	\(e\left(\frac{1807}{3799}\right)\)	\(e\left(\frac{1564}{3799}\right)\)	\(e\left(\frac{2796}{3799}\right)\)	\(e\left(\frac{23}{3799}\right)\)	\(e\left(\frac{811}{3799}\right)\)	\(e\left(\frac{3785}{3799}\right)\)	\(e\left(\frac{568}{3799}\right)\)	\(e\left(\frac{3781}{3799}\right)\)
\(\chi_{15517}(68,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2548}{3799}\right)\)	\(e\left(\frac{2932}{3799}\right)\)	\(e\left(\frac{1297}{3799}\right)\)	\(e\left(\frac{1049}{3799}\right)\)	\(e\left(\frac{1681}{3799}\right)\)	\(e\left(\frac{2306}{3799}\right)\)	\(e\left(\frac{46}{3799}\right)\)	\(e\left(\frac{2065}{3799}\right)\)	\(e\left(\frac{3597}{3799}\right)\)	\(e\left(\frac{2655}{3799}\right)\)
\(\chi_{15517}(74,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{130}{3799}\right)\)	\(e\left(\frac{3716}{3799}\right)\)	\(e\left(\frac{260}{3799}\right)\)	\(e\left(\frac{635}{3799}\right)\)	\(e\left(\frac{47}{3799}\right)\)	\(e\left(\frac{3529}{3799}\right)\)	\(e\left(\frac{390}{3799}\right)\)	\(e\left(\frac{3633}{3799}\right)\)	\(e\left(\frac{765}{3799}\right)\)	\(e\left(\frac{872}{3799}\right)\)
\(\chi_{15517}(75,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2959}{3799}\right)\)	\(e\left(\frac{1413}{3799}\right)\)	\(e\left(\frac{2119}{3799}\right)\)	\(e\left(\frac{2326}{3799}\right)\)	\(e\left(\frac{573}{3799}\right)\)	\(e\left(\frac{3498}{3799}\right)\)	\(e\left(\frac{1279}{3799}\right)\)	\(e\left(\frac{2826}{3799}\right)\)	\(e\left(\frac{1486}{3799}\right)\)	\(e\left(\frac{2548}{3799}\right)\)
\(\chi_{15517}(78,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2518}{3799}\right)\)	\(e\left(\frac{1490}{3799}\right)\)	\(e\left(\frac{1237}{3799}\right)\)	\(e\left(\frac{318}{3799}\right)\)	\(e\left(\frac{209}{3799}\right)\)	\(e\left(\frac{3245}{3799}\right)\)	\(e\left(\frac{3755}{3799}\right)\)	\(e\left(\frac{2980}{3799}\right)\)	\(e\left(\frac{2836}{3799}\right)\)	\(e\left(\frac{2746}{3799}\right)\)
\(\chi_{15517}(81,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1848}{3799}\right)\)	\(e\left(\frac{2210}{3799}\right)\)	\(e\left(\frac{3696}{3799}\right)\)	\(e\left(\frac{1721}{3799}\right)\)	\(e\left(\frac{259}{3799}\right)\)	\(e\left(\frac{1422}{3799}\right)\)	\(e\left(\frac{1745}{3799}\right)\)	\(e\left(\frac{621}{3799}\right)\)	\(e\left(\frac{3569}{3799}\right)\)	\(e\left(\frac{3512}{3799}\right)\)
\(\chi_{15517}(86,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{197}{3799}\right)\)	\(e\left(\frac{3644}{3799}\right)\)	\(e\left(\frac{394}{3799}\right)\)	\(e\left(\frac{3154}{3799}\right)\)	\(e\left(\frac{42}{3799}\right)\)	\(e\left(\frac{1052}{3799}\right)\)	\(e\left(\frac{591}{3799}\right)\)	\(e\left(\frac{3489}{3799}\right)\)	\(e\left(\frac{3351}{3799}\right)\)	\(e\left(\frac{2315}{3799}\right)\)
\(\chi_{15517}(88,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{848}{3799}\right)\)	\(e\left(\frac{2264}{3799}\right)\)	\(e\left(\frac{1696}{3799}\right)\)	\(e\left(\frac{2681}{3799}\right)\)	\(e\left(\frac{3112}{3799}\right)\)	\(e\left(\frac{2330}{3799}\right)\)	\(e\left(\frac{2544}{3799}\right)\)	\(e\left(\frac{729}{3799}\right)\)	\(e\left(\frac{3529}{3799}\right)\)	\(e\left(\frac{1480}{3799}\right)\)
\(\chi_{15517}(95,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2534}{3799}\right)\)	\(e\left(\frac{1246}{3799}\right)\)	\(e\left(\frac{1269}{3799}\right)\)	\(e\left(\frac{2734}{3799}\right)\)	\(e\left(\frac{3780}{3799}\right)\)	\(e\left(\frac{3504}{3799}\right)\)	\(e\left(\frac{4}{3799}\right)\)	\(e\left(\frac{2492}{3799}\right)\)	\(e\left(\frac{1469}{3799}\right)\)	\(e\left(\frac{3204}{3799}\right)\)
\(\chi_{15517}(100,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1004}{3799}\right)\)	\(e\left(\frac{3684}{3799}\right)\)	\(e\left(\frac{2008}{3799}\right)\)	\(e\left(\frac{3443}{3799}\right)\)	\(e\left(\frac{889}{3799}\right)\)	\(e\left(\frac{2006}{3799}\right)\)	\(e\left(\frac{3012}{3799}\right)\)	\(e\left(\frac{3569}{3799}\right)\)	\(e\left(\frac{648}{3799}\right)\)	\(e\left(\frac{247}{3799}\right)\)
\(\chi_{15517}(104,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{563}{3799}\right)\)	\(e\left(\frac{3761}{3799}\right)\)	\(e\left(\frac{1126}{3799}\right)\)	\(e\left(\frac{1435}{3799}\right)\)	\(e\left(\frac{525}{3799}\right)\)	\(e\left(\frac{1753}{3799}\right)\)	\(e\left(\frac{1689}{3799}\right)\)	\(e\left(\frac{3723}{3799}\right)\)	\(e\left(\frac{1998}{3799}\right)\)	\(e\left(\frac{445}{3799}\right)\)
\(\chi_{15517}(105,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2092}{3799}\right)\)	\(e\left(\frac{2288}{3799}\right)\)	\(e\left(\frac{385}{3799}\right)\)	\(e\left(\frac{575}{3799}\right)\)	\(e\left(\frac{581}{3799}\right)\)	\(e\left(\frac{623}{3799}\right)\)	\(e\left(\frac{2477}{3799}\right)\)	\(e\left(\frac{777}{3799}\right)\)	\(e\left(\frac{2667}{3799}\right)\)	\(e\left(\frac{999}{3799}\right)\)
\(\chi_{15517}(108,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3692}{3799}\right)\)	\(e\left(\frac{682}{3799}\right)\)	\(e\left(\frac{3585}{3799}\right)\)	\(e\left(\frac{2838}{3799}\right)\)	\(e\left(\frac{575}{3799}\right)\)	\(e\left(\frac{3729}{3799}\right)\)	\(e\left(\frac{3478}{3799}\right)\)	\(e\left(\frac{1364}{3799}\right)\)	\(e\left(\frac{2731}{3799}\right)\)	\(e\left(\frac{1211}{3799}\right)\)

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Basic properties

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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.m
Modulus	$15517$
Conductor	$15517$
Order	$3799$
Real	no
Primitive	yes
Minimal	yes
Parity	even

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:	\(3799\)	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:	even	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);