LMFDB - Group of Dirichlet characters of modulus 15517

Show commands: Magma / Pari/GP / SageMath

comment:Define the Dirichlet group

sage:G = DirichletGroup(15517)

gp:g = idealstar(,15517,2)

magma:G = FullDirichletGroup(15517);

Character group

Order	=	15196	comment:Order sage:G.order() gp:g.no magma:Order(G);
Structure	=	$C_{2}\times C_{7598}$	comment:Group structure sage:sorted(g.order() for g in G.gens()) gp:g.cyc magma:PrimaryInvariants(G);
Generators	=	$\chi_{15517}(9206,\cdot)$, $\chi_{15517}(9736,\cdot)$	comment:Generators sage:G.gens() gp:g.gen magma:Generators(G);

First 32 of 15196 characters

Each row describes a character. When available, the columns show the orbit label, order of the character, whether the character is primitive, and several values of the character.

Character	Orbit	Order	Primitive	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{15517}(1,\cdot)$	15517.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{15517}(2,\cdot)$	15517.o	7598	yes	$-1$	$1$	$e\left(\frac{6105}{7598}\right)$	$e\left(\frac{462}{3799}\right)$	$e\left(\frac{2306}{3799}\right)$	$e\left(\frac{3148}{3799}\right)$	$e\left(\frac{7029}{7598}\right)$	$e\left(\frac{2281}{3799}\right)$	$e\left(\frac{3119}{7598}\right)$	$e\left(\frac{924}{3799}\right)$	$e\left(\frac{4803}{7598}\right)$	$e\left(\frac{6175}{7598}\right)$
$\chi_{15517}(3,\cdot)$	15517.m	3799	yes	$1$	$1$	$e\left(\frac{462}{3799}\right)$	$e\left(\frac{2452}{3799}\right)$	$e\left(\frac{924}{3799}\right)$	$e\left(\frac{1380}{3799}\right)$	$e\left(\frac{2914}{3799}\right)$	$e\left(\frac{2255}{3799}\right)$	$e\left(\frac{1386}{3799}\right)$	$e\left(\frac{1105}{3799}\right)$	$e\left(\frac{1842}{3799}\right)$	$e\left(\frac{878}{3799}\right)$
$\chi_{15517}(4,\cdot)$	15517.m	3799	yes	$1$	$1$	$e\left(\frac{2306}{3799}\right)$	$e\left(\frac{924}{3799}\right)$	$e\left(\frac{813}{3799}\right)$	$e\left(\frac{2497}{3799}\right)$	$e\left(\frac{3230}{3799}\right)$	$e\left(\frac{763}{3799}\right)$	$e\left(\frac{3119}{3799}\right)$	$e\left(\frac{1848}{3799}\right)$	$e\left(\frac{1004}{3799}\right)$	$e\left(\frac{2376}{3799}\right)$
$\chi_{15517}(5,\cdot)$	15517.p	7598	yes	$-1$	$1$	$e\left(\frac{3148}{3799}\right)$	$e\left(\frac{1380}{3799}\right)$	$e\left(\frac{2497}{3799}\right)$	$e\left(\frac{4745}{7598}\right)$	$e\left(\frac{729}{3799}\right)$	$e\left(\frac{1243}{7598}\right)$	$e\left(\frac{1846}{3799}\right)$	$e\left(\frac{2760}{3799}\right)$	$e\left(\frac{3443}{7598}\right)$	$e\left(\frac{835}{3799}\right)$
$\chi_{15517}(6,\cdot)$	15517.o	7598	yes	$-1$	$1$	$e\left(\frac{7029}{7598}\right)$	$e\left(\frac{2914}{3799}\right)$	$e\left(\frac{3230}{3799}\right)$	$e\left(\frac{729}{3799}\right)$	$e\left(\frac{5259}{7598}\right)$	$e\left(\frac{737}{3799}\right)$	$e\left(\frac{5891}{7598}\right)$	$e\left(\frac{2029}{3799}\right)$	$e\left(\frac{889}{7598}\right)$	$e\left(\frac{333}{7598}\right)$
$\chi_{15517}(7,\cdot)$	15517.p	7598	yes	$-1$	$1$	$e\left(\frac{2281}{3799}\right)$	$e\left(\frac{2255}{3799}\right)$	$e\left(\frac{763}{3799}\right)$	$e\left(\frac{1243}{7598}\right)$	$e\left(\frac{737}{3799}\right)$	$e\left(\frac{3091}{7598}\right)$	$e\left(\frac{3044}{3799}\right)$	$e\left(\frac{711}{3799}\right)$	$e\left(\frac{5805}{7598}\right)$	$e\left(\frac{3085}{3799}\right)$
$\chi_{15517}(8,\cdot)$	15517.o	7598	yes	$-1$	$1$	$e\left(\frac{3119}{7598}\right)$	$e\left(\frac{1386}{3799}\right)$	$e\left(\frac{3119}{3799}\right)$	$e\left(\frac{1846}{3799}\right)$	$e\left(\frac{5891}{7598}\right)$	$e\left(\frac{3044}{3799}\right)$	$e\left(\frac{1759}{7598}\right)$	$e\left(\frac{2772}{3799}\right)$	$e\left(\frac{6811}{7598}\right)$	$e\left(\frac{3329}{7598}\right)$
$\chi_{15517}(9,\cdot)$	15517.m	3799	yes	$1$	$1$	$e\left(\frac{924}{3799}\right)$	$e\left(\frac{1105}{3799}\right)$	$e\left(\frac{1848}{3799}\right)$	$e\left(\frac{2760}{3799}\right)$	$e\left(\frac{2029}{3799}\right)$	$e\left(\frac{711}{3799}\right)$	$e\left(\frac{2772}{3799}\right)$	$e\left(\frac{2210}{3799}\right)$	$e\left(\frac{3684}{3799}\right)$	$e\left(\frac{1756}{3799}\right)$
$\chi_{15517}(10,\cdot)$	15517.n	7598	yes	$1$	$1$	$e\left(\frac{4803}{7598}\right)$	$e\left(\frac{1842}{3799}\right)$	$e\left(\frac{1004}{3799}\right)$	$e\left(\frac{3443}{7598}\right)$	$e\left(\frac{889}{7598}\right)$	$e\left(\frac{5805}{7598}\right)$	$e\left(\frac{6811}{7598}\right)$	$e\left(\frac{3684}{3799}\right)$	$e\left(\frac{324}{3799}\right)$	$e\left(\frac{247}{7598}\right)$
$\chi_{15517}(11,\cdot)$	15517.o	7598	yes	$-1$	$1$	$e\left(\frac{6175}{7598}\right)$	$e\left(\frac{878}{3799}\right)$	$e\left(\frac{2376}{3799}\right)$	$e\left(\frac{835}{3799}\right)$	$e\left(\frac{333}{7598}\right)$	$e\left(\frac{3085}{3799}\right)$	$e\left(\frac{3329}{7598}\right)$	$e\left(\frac{1756}{3799}\right)$	$e\left(\frac{247}{7598}\right)$	$e\left(\frac{7229}{7598}\right)$
$\chi_{15517}(12,\cdot)$	15517.m	3799	yes	$1$	$1$	$e\left(\frac{2768}{3799}\right)$	$e\left(\frac{3376}{3799}\right)$	$e\left(\frac{1737}{3799}\right)$	$e\left(\frac{78}{3799}\right)$	$e\left(\frac{2345}{3799}\right)$	$e\left(\frac{3018}{3799}\right)$	$e\left(\frac{706}{3799}\right)$	$e\left(\frac{2953}{3799}\right)$	$e\left(\frac{2846}{3799}\right)$	$e\left(\frac{3254}{3799}\right)$
$\chi_{15517}(13,\cdot)$	15517.o	7598	yes	$-1$	$1$	$e\left(\frac{5605}{7598}\right)$	$e\left(\frac{2375}{3799}\right)$	$e\left(\frac{1806}{3799}\right)$	$e\left(\frac{3388}{3799}\right)$	$e\left(\frac{2757}{7598}\right)$	$e\left(\frac{2508}{3799}\right)$	$e\left(\frac{1619}{7598}\right)$	$e\left(\frac{951}{3799}\right)$	$e\left(\frac{4783}{7598}\right)$	$e\left(\frac{5159}{7598}\right)$
$\chi_{15517}(14,\cdot)$	15517.n	7598	yes	$1$	$1$	$e\left(\frac{3069}{7598}\right)$	$e\left(\frac{2717}{3799}\right)$	$e\left(\frac{3069}{3799}\right)$	$e\left(\frac{7539}{7598}\right)$	$e\left(\frac{905}{7598}\right)$	$e\left(\frac{55}{7598}\right)$	$e\left(\frac{1609}{7598}\right)$	$e\left(\frac{1635}{3799}\right)$	$e\left(\frac{1505}{3799}\right)$	$e\left(\frac{4747}{7598}\right)$
$\chi_{15517}(15,\cdot)$	15517.p	7598	yes	$-1$	$1$	$e\left(\frac{3610}{3799}\right)$	$e\left(\frac{33}{3799}\right)$	$e\left(\frac{3421}{3799}\right)$	$e\left(\frac{7505}{7598}\right)$	$e\left(\frac{3643}{3799}\right)$	$e\left(\frac{5753}{7598}\right)$	$e\left(\frac{3232}{3799}\right)$	$e\left(\frac{66}{3799}\right)$	$e\left(\frac{7127}{7598}\right)$	$e\left(\frac{1713}{3799}\right)$
$\chi_{15517}(16,\cdot)$	15517.m	3799	yes	$1$	$1$	$e\left(\frac{813}{3799}\right)$	$e\left(\frac{1848}{3799}\right)$	$e\left(\frac{1626}{3799}\right)$	$e\left(\frac{1195}{3799}\right)$	$e\left(\frac{2661}{3799}\right)$	$e\left(\frac{1526}{3799}\right)$	$e\left(\frac{2439}{3799}\right)$	$e\left(\frac{3696}{3799}\right)$	$e\left(\frac{2008}{3799}\right)$	$e\left(\frac{953}{3799}\right)$
$\chi_{15517}(17,\cdot)$	15517.m	3799	yes	$1$	$1$	$e\left(\frac{242}{3799}\right)$	$e\left(\frac{2008}{3799}\right)$	$e\left(\frac{484}{3799}\right)$	$e\left(\frac{2351}{3799}\right)$	$e\left(\frac{2250}{3799}\right)$	$e\left(\frac{1543}{3799}\right)$	$e\left(\frac{726}{3799}\right)$	$e\left(\frac{217}{3799}\right)$	$e\left(\frac{2593}{3799}\right)$	$e\left(\frac{279}{3799}\right)$
$\chi_{15517}(18,\cdot)$	15517.o	7598	yes	$-1$	$1$	$e\left(\frac{355}{7598}\right)$	$e\left(\frac{1567}{3799}\right)$	$e\left(\frac{355}{3799}\right)$	$e\left(\frac{2109}{3799}\right)$	$e\left(\frac{3489}{7598}\right)$	$e\left(\frac{2992}{3799}\right)$	$e\left(\frac{1065}{7598}\right)$	$e\left(\frac{3134}{3799}\right)$	$e\left(\frac{4573}{7598}\right)$	$e\left(\frac{2089}{7598}\right)$
$\chi_{15517}(19,\cdot)$	15517.p	7598	yes	$-1$	$1$	$e\left(\frac{3185}{3799}\right)$	$e\left(\frac{3665}{3799}\right)$	$e\left(\frac{2571}{3799}\right)$	$e\left(\frac{723}{7598}\right)$	$e\left(\frac{3051}{3799}\right)$	$e\left(\frac{5765}{7598}\right)$	$e\left(\frac{1957}{3799}\right)$	$e\left(\frac{3531}{3799}\right)$	$e\left(\frac{7093}{7598}\right)$	$e\left(\frac{2369}{3799}\right)$
$\chi_{15517}(20,\cdot)$	15517.p	7598	yes	$-1$	$1$	$e\left(\frac{1655}{3799}\right)$	$e\left(\frac{2304}{3799}\right)$	$e\left(\frac{3310}{3799}\right)$	$e\left(\frac{2141}{7598}\right)$	$e\left(\frac{160}{3799}\right)$	$e\left(\frac{2769}{7598}\right)$	$e\left(\frac{1166}{3799}\right)$	$e\left(\frac{809}{3799}\right)$	$e\left(\frac{5451}{7598}\right)$	$e\left(\frac{3211}{3799}\right)$
$\chi_{15517}(21,\cdot)$	15517.p	7598	yes	$-1$	$1$	$e\left(\frac{2743}{3799}\right)$	$e\left(\frac{908}{3799}\right)$	$e\left(\frac{1687}{3799}\right)$	$e\left(\frac{4003}{7598}\right)$	$e\left(\frac{3651}{3799}\right)$	$e\left(\frac{3}{7598}\right)$	$e\left(\frac{631}{3799}\right)$	$e\left(\frac{1816}{3799}\right)$	$e\left(\frac{1891}{7598}\right)$	$e\left(\frac{164}{3799}\right)$
$\chi_{15517}(22,\cdot)$	15517.m	3799	yes	$1$	$1$	$e\left(\frac{2341}{3799}\right)$	$e\left(\frac{1340}{3799}\right)$	$e\left(\frac{883}{3799}\right)$	$e\left(\frac{184}{3799}\right)$	$e\left(\frac{3681}{3799}\right)$	$e\left(\frac{1567}{3799}\right)$	$e\left(\frac{3224}{3799}\right)$	$e\left(\frac{2680}{3799}\right)$	$e\left(\frac{2525}{3799}\right)$	$e\left(\frac{2903}{3799}\right)$
$\chi_{15517}(23,\cdot)$	15517.o	7598	yes	$-1$	$1$	$e\left(\frac{2951}{7598}\right)$	$e\left(\frac{2667}{3799}\right)$	$e\left(\frac{2951}{3799}\right)$	$e\left(\frac{559}{3799}\right)$	$e\left(\frac{687}{7598}\right)$	$e\left(\frac{2634}{3799}\right)$	$e\left(\frac{1255}{7598}\right)$	$e\left(\frac{1535}{3799}\right)$	$e\left(\frac{4069}{7598}\right)$	$e\left(\frac{2319}{7598}\right)$
$\chi_{15517}(24,\cdot)$	15517.o	7598	yes	$-1$	$1$	$e\left(\frac{4043}{7598}\right)$	$e\left(\frac{39}{3799}\right)$	$e\left(\frac{244}{3799}\right)$	$e\left(\frac{3226}{3799}\right)$	$e\left(\frac{4121}{7598}\right)$	$e\left(\frac{1500}{3799}\right)$	$e\left(\frac{4531}{7598}\right)$	$e\left(\frac{78}{3799}\right)$	$e\left(\frac{2897}{7598}\right)$	$e\left(\frac{5085}{7598}\right)$
$\chi_{15517}(25,\cdot)$	15517.m	3799	yes	$1$	$1$	$e\left(\frac{2497}{3799}\right)$	$e\left(\frac{2760}{3799}\right)$	$e\left(\frac{1195}{3799}\right)$	$e\left(\frac{946}{3799}\right)$	$e\left(\frac{1458}{3799}\right)$	$e\left(\frac{1243}{3799}\right)$	$e\left(\frac{3692}{3799}\right)$	$e\left(\frac{1721}{3799}\right)$	$e\left(\frac{3443}{3799}\right)$	$e\left(\frac{1670}{3799}\right)$
$\chi_{15517}(26,\cdot)$	15517.m	3799	yes	$1$	$1$	$e\left(\frac{2056}{3799}\right)$	$e\left(\frac{2837}{3799}\right)$	$e\left(\frac{313}{3799}\right)$	$e\left(\frac{2737}{3799}\right)$	$e\left(\frac{1094}{3799}\right)$	$e\left(\frac{990}{3799}\right)$	$e\left(\frac{2369}{3799}\right)$	$e\left(\frac{1875}{3799}\right)$	$e\left(\frac{994}{3799}\right)$	$e\left(\frac{1868}{3799}\right)$
$\chi_{15517}(27,\cdot)$	15517.m	3799	yes	$1$	$1$	$e\left(\frac{1386}{3799}\right)$	$e\left(\frac{3557}{3799}\right)$	$e\left(\frac{2772}{3799}\right)$	$e\left(\frac{341}{3799}\right)$	$e\left(\frac{1144}{3799}\right)$	$e\left(\frac{2966}{3799}\right)$	$e\left(\frac{359}{3799}\right)$	$e\left(\frac{3315}{3799}\right)$	$e\left(\frac{1727}{3799}\right)$	$e\left(\frac{2634}{3799}\right)$
$\chi_{15517}(28,\cdot)$	15517.p	7598	yes	$-1$	$1$	$e\left(\frac{788}{3799}\right)$	$e\left(\frac{3179}{3799}\right)$	$e\left(\frac{1576}{3799}\right)$	$e\left(\frac{6237}{7598}\right)$	$e\left(\frac{168}{3799}\right)$	$e\left(\frac{4617}{7598}\right)$	$e\left(\frac{2364}{3799}\right)$	$e\left(\frac{2559}{3799}\right)$	$e\left(\frac{215}{7598}\right)$	$e\left(\frac{1662}{3799}\right)$
$\chi_{15517}(29,\cdot)$	15517.p	7598	yes	$-1$	$1$	$e\left(\frac{2849}{3799}\right)$	$e\left(\frac{1191}{3799}\right)$	$e\left(\frac{1899}{3799}\right)$	$e\left(\frac{5623}{7598}\right)$	$e\left(\frac{241}{3799}\right)$	$e\left(\frac{2485}{7598}\right)$	$e\left(\frac{949}{3799}\right)$	$e\left(\frac{2382}{3799}\right)$	$e\left(\frac{3723}{7598}\right)$	$e\left(\frac{349}{3799}\right)$
$\chi_{15517}(30,\cdot)$	15517.n	7598	yes	$1$	$1$	$e\left(\frac{5727}{7598}\right)$	$e\left(\frac{495}{3799}\right)$	$e\left(\frac{1928}{3799}\right)$	$e\left(\frac{6203}{7598}\right)$	$e\left(\frac{6717}{7598}\right)$	$e\left(\frac{2717}{7598}\right)$	$e\left(\frac{1985}{7598}\right)$	$e\left(\frac{990}{3799}\right)$	$e\left(\frac{2166}{3799}\right)$	$e\left(\frac{2003}{7598}\right)$
$\chi_{15517}(31,\cdot)$	15517.o	7598	yes	$-1$	$1$	$e\left(\frac{3577}{7598}\right)$	$e\left(\frac{743}{3799}\right)$	$e\left(\frac{3577}{3799}\right)$	$e\left(\frac{2234}{3799}\right)$	$e\left(\frac{5063}{7598}\right)$	$e\left(\frac{815}{3799}\right)$	$e\left(\frac{3133}{7598}\right)$	$e\left(\frac{1486}{3799}\right)$	$e\left(\frac{447}{7598}\right)$	$e\left(\frac{2193}{7598}\right)$
$\chi_{15517}(32,\cdot)$	15517.o	7598	yes	$-1$	$1$	$e\left(\frac{133}{7598}\right)$	$e\left(\frac{2310}{3799}\right)$	$e\left(\frac{133}{3799}\right)$	$e\left(\frac{544}{3799}\right)$	$e\left(\frac{4753}{7598}\right)$	$e\left(\frac{8}{3799}\right)$	$e\left(\frac{399}{7598}\right)$	$e\left(\frac{821}{3799}\right)$	$e\left(\frac{1221}{7598}\right)$	$e\left(\frac{483}{7598}\right)$

Click here to search among the remaining 15164 characters.

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

Modulus	$15517$
Structure	\(C_{2}\times C_{7598}\)
Order	$15196$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\(\chi_{15517}(1,\cdot)\)	15517.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{15517}(2,\cdot)\)	15517.o	7598	yes	\(-1\)	\(1\)	\(e\left(\frac{6105}{7598}\right)\)	\(e\left(\frac{462}{3799}\right)\)	\(e\left(\frac{2306}{3799}\right)\)	\(e\left(\frac{3148}{3799}\right)\)	\(e\left(\frac{7029}{7598}\right)\)	\(e\left(\frac{2281}{3799}\right)\)	\(e\left(\frac{3119}{7598}\right)\)	\(e\left(\frac{924}{3799}\right)\)	\(e\left(\frac{4803}{7598}\right)\)	\(e\left(\frac{6175}{7598}\right)\)
\(\chi_{15517}(3,\cdot)\)	15517.m	3799	yes	\(1\)	\(1\)	\(e\left(\frac{462}{3799}\right)\)	\(e\left(\frac{2452}{3799}\right)\)	\(e\left(\frac{924}{3799}\right)\)	\(e\left(\frac{1380}{3799}\right)\)	\(e\left(\frac{2914}{3799}\right)\)	\(e\left(\frac{2255}{3799}\right)\)	\(e\left(\frac{1386}{3799}\right)\)	\(e\left(\frac{1105}{3799}\right)\)	\(e\left(\frac{1842}{3799}\right)\)	\(e\left(\frac{878}{3799}\right)\)
\(\chi_{15517}(4,\cdot)\)	15517.m	3799	yes	\(1\)	\(1\)	\(e\left(\frac{2306}{3799}\right)\)	\(e\left(\frac{924}{3799}\right)\)	\(e\left(\frac{813}{3799}\right)\)	\(e\left(\frac{2497}{3799}\right)\)	\(e\left(\frac{3230}{3799}\right)\)	\(e\left(\frac{763}{3799}\right)\)	\(e\left(\frac{3119}{3799}\right)\)	\(e\left(\frac{1848}{3799}\right)\)	\(e\left(\frac{1004}{3799}\right)\)	\(e\left(\frac{2376}{3799}\right)\)
\(\chi_{15517}(5,\cdot)\)	15517.p	7598	yes	\(-1\)	\(1\)	\(e\left(\frac{3148}{3799}\right)\)	\(e\left(\frac{1380}{3799}\right)\)	\(e\left(\frac{2497}{3799}\right)\)	\(e\left(\frac{4745}{7598}\right)\)	\(e\left(\frac{729}{3799}\right)\)	\(e\left(\frac{1243}{7598}\right)\)	\(e\left(\frac{1846}{3799}\right)\)	\(e\left(\frac{2760}{3799}\right)\)	\(e\left(\frac{3443}{7598}\right)\)	\(e\left(\frac{835}{3799}\right)\)
\(\chi_{15517}(6,\cdot)\)	15517.o	7598	yes	\(-1\)	\(1\)	\(e\left(\frac{7029}{7598}\right)\)	\(e\left(\frac{2914}{3799}\right)\)	\(e\left(\frac{3230}{3799}\right)\)	\(e\left(\frac{729}{3799}\right)\)	\(e\left(\frac{5259}{7598}\right)\)	\(e\left(\frac{737}{3799}\right)\)	\(e\left(\frac{5891}{7598}\right)\)	\(e\left(\frac{2029}{3799}\right)\)	\(e\left(\frac{889}{7598}\right)\)	\(e\left(\frac{333}{7598}\right)\)
\(\chi_{15517}(7,\cdot)\)	15517.p	7598	yes	\(-1\)	\(1\)	\(e\left(\frac{2281}{3799}\right)\)	\(e\left(\frac{2255}{3799}\right)\)	\(e\left(\frac{763}{3799}\right)\)	\(e\left(\frac{1243}{7598}\right)\)	\(e\left(\frac{737}{3799}\right)\)	\(e\left(\frac{3091}{7598}\right)\)	\(e\left(\frac{3044}{3799}\right)\)	\(e\left(\frac{711}{3799}\right)\)	\(e\left(\frac{5805}{7598}\right)\)	\(e\left(\frac{3085}{3799}\right)\)
\(\chi_{15517}(8,\cdot)\)	15517.o	7598	yes	\(-1\)	\(1\)	\(e\left(\frac{3119}{7598}\right)\)	\(e\left(\frac{1386}{3799}\right)\)	\(e\left(\frac{3119}{3799}\right)\)	\(e\left(\frac{1846}{3799}\right)\)	\(e\left(\frac{5891}{7598}\right)\)	\(e\left(\frac{3044}{3799}\right)\)	\(e\left(\frac{1759}{7598}\right)\)	\(e\left(\frac{2772}{3799}\right)\)	\(e\left(\frac{6811}{7598}\right)\)	\(e\left(\frac{3329}{7598}\right)\)
\(\chi_{15517}(9,\cdot)\)	15517.m	3799	yes	\(1\)	\(1\)	\(e\left(\frac{924}{3799}\right)\)	\(e\left(\frac{1105}{3799}\right)\)	\(e\left(\frac{1848}{3799}\right)\)	\(e\left(\frac{2760}{3799}\right)\)	\(e\left(\frac{2029}{3799}\right)\)	\(e\left(\frac{711}{3799}\right)\)	\(e\left(\frac{2772}{3799}\right)\)	\(e\left(\frac{2210}{3799}\right)\)	\(e\left(\frac{3684}{3799}\right)\)	\(e\left(\frac{1756}{3799}\right)\)
\(\chi_{15517}(10,\cdot)\)	15517.n	7598	yes	\(1\)	\(1\)	\(e\left(\frac{4803}{7598}\right)\)	\(e\left(\frac{1842}{3799}\right)\)	\(e\left(\frac{1004}{3799}\right)\)	\(e\left(\frac{3443}{7598}\right)\)	\(e\left(\frac{889}{7598}\right)\)	\(e\left(\frac{5805}{7598}\right)\)	\(e\left(\frac{6811}{7598}\right)\)	\(e\left(\frac{3684}{3799}\right)\)	\(e\left(\frac{324}{3799}\right)\)	\(e\left(\frac{247}{7598}\right)\)
\(\chi_{15517}(11,\cdot)\)	15517.o	7598	yes	\(-1\)	\(1\)	\(e\left(\frac{6175}{7598}\right)\)	\(e\left(\frac{878}{3799}\right)\)	\(e\left(\frac{2376}{3799}\right)\)	\(e\left(\frac{835}{3799}\right)\)	\(e\left(\frac{333}{7598}\right)\)	\(e\left(\frac{3085}{3799}\right)\)	\(e\left(\frac{3329}{7598}\right)\)	\(e\left(\frac{1756}{3799}\right)\)	\(e\left(\frac{247}{7598}\right)\)	\(e\left(\frac{7229}{7598}\right)\)
\(\chi_{15517}(12,\cdot)\)	15517.m	3799	yes	\(1\)	\(1\)	\(e\left(\frac{2768}{3799}\right)\)	\(e\left(\frac{3376}{3799}\right)\)	\(e\left(\frac{1737}{3799}\right)\)	\(e\left(\frac{78}{3799}\right)\)	\(e\left(\frac{2345}{3799}\right)\)	\(e\left(\frac{3018}{3799}\right)\)	\(e\left(\frac{706}{3799}\right)\)	\(e\left(\frac{2953}{3799}\right)\)	\(e\left(\frac{2846}{3799}\right)\)	\(e\left(\frac{3254}{3799}\right)\)
\(\chi_{15517}(13,\cdot)\)	15517.o	7598	yes	\(-1\)	\(1\)	\(e\left(\frac{5605}{7598}\right)\)	\(e\left(\frac{2375}{3799}\right)\)	\(e\left(\frac{1806}{3799}\right)\)	\(e\left(\frac{3388}{3799}\right)\)	\(e\left(\frac{2757}{7598}\right)\)	\(e\left(\frac{2508}{3799}\right)\)	\(e\left(\frac{1619}{7598}\right)\)	\(e\left(\frac{951}{3799}\right)\)	\(e\left(\frac{4783}{7598}\right)\)	\(e\left(\frac{5159}{7598}\right)\)
\(\chi_{15517}(14,\cdot)\)	15517.n	7598	yes	\(1\)	\(1\)	\(e\left(\frac{3069}{7598}\right)\)	\(e\left(\frac{2717}{3799}\right)\)	\(e\left(\frac{3069}{3799}\right)\)	\(e\left(\frac{7539}{7598}\right)\)	\(e\left(\frac{905}{7598}\right)\)	\(e\left(\frac{55}{7598}\right)\)	\(e\left(\frac{1609}{7598}\right)\)	\(e\left(\frac{1635}{3799}\right)\)	\(e\left(\frac{1505}{3799}\right)\)	\(e\left(\frac{4747}{7598}\right)\)
\(\chi_{15517}(15,\cdot)\)	15517.p	7598	yes	\(-1\)	\(1\)	\(e\left(\frac{3610}{3799}\right)\)	\(e\left(\frac{33}{3799}\right)\)	\(e\left(\frac{3421}{3799}\right)\)	\(e\left(\frac{7505}{7598}\right)\)	\(e\left(\frac{3643}{3799}\right)\)	\(e\left(\frac{5753}{7598}\right)\)	\(e\left(\frac{3232}{3799}\right)\)	\(e\left(\frac{66}{3799}\right)\)	\(e\left(\frac{7127}{7598}\right)\)	\(e\left(\frac{1713}{3799}\right)\)
\(\chi_{15517}(16,\cdot)\)	15517.m	3799	yes	\(1\)	\(1\)	\(e\left(\frac{813}{3799}\right)\)	\(e\left(\frac{1848}{3799}\right)\)	\(e\left(\frac{1626}{3799}\right)\)	\(e\left(\frac{1195}{3799}\right)\)	\(e\left(\frac{2661}{3799}\right)\)	\(e\left(\frac{1526}{3799}\right)\)	\(e\left(\frac{2439}{3799}\right)\)	\(e\left(\frac{3696}{3799}\right)\)	\(e\left(\frac{2008}{3799}\right)\)	\(e\left(\frac{953}{3799}\right)\)
\(\chi_{15517}(17,\cdot)\)	15517.m	3799	yes	\(1\)	\(1\)	\(e\left(\frac{242}{3799}\right)\)	\(e\left(\frac{2008}{3799}\right)\)	\(e\left(\frac{484}{3799}\right)\)	\(e\left(\frac{2351}{3799}\right)\)	\(e\left(\frac{2250}{3799}\right)\)	\(e\left(\frac{1543}{3799}\right)\)	\(e\left(\frac{726}{3799}\right)\)	\(e\left(\frac{217}{3799}\right)\)	\(e\left(\frac{2593}{3799}\right)\)	\(e\left(\frac{279}{3799}\right)\)
\(\chi_{15517}(18,\cdot)\)	15517.o	7598	yes	\(-1\)	\(1\)	\(e\left(\frac{355}{7598}\right)\)	\(e\left(\frac{1567}{3799}\right)\)	\(e\left(\frac{355}{3799}\right)\)	\(e\left(\frac{2109}{3799}\right)\)	\(e\left(\frac{3489}{7598}\right)\)	\(e\left(\frac{2992}{3799}\right)\)	\(e\left(\frac{1065}{7598}\right)\)	\(e\left(\frac{3134}{3799}\right)\)	\(e\left(\frac{4573}{7598}\right)\)	\(e\left(\frac{2089}{7598}\right)\)
\(\chi_{15517}(19,\cdot)\)	15517.p	7598	yes	\(-1\)	\(1\)	\(e\left(\frac{3185}{3799}\right)\)	\(e\left(\frac{3665}{3799}\right)\)	\(e\left(\frac{2571}{3799}\right)\)	\(e\left(\frac{723}{7598}\right)\)	\(e\left(\frac{3051}{3799}\right)\)	\(e\left(\frac{5765}{7598}\right)\)	\(e\left(\frac{1957}{3799}\right)\)	\(e\left(\frac{3531}{3799}\right)\)	\(e\left(\frac{7093}{7598}\right)\)	\(e\left(\frac{2369}{3799}\right)\)
\(\chi_{15517}(20,\cdot)\)	15517.p	7598	yes	\(-1\)	\(1\)	\(e\left(\frac{1655}{3799}\right)\)	\(e\left(\frac{2304}{3799}\right)\)	\(e\left(\frac{3310}{3799}\right)\)	\(e\left(\frac{2141}{7598}\right)\)	\(e\left(\frac{160}{3799}\right)\)	\(e\left(\frac{2769}{7598}\right)\)	\(e\left(\frac{1166}{3799}\right)\)	\(e\left(\frac{809}{3799}\right)\)	\(e\left(\frac{5451}{7598}\right)\)	\(e\left(\frac{3211}{3799}\right)\)
\(\chi_{15517}(21,\cdot)\)	15517.p	7598	yes	\(-1\)	\(1\)	\(e\left(\frac{2743}{3799}\right)\)	\(e\left(\frac{908}{3799}\right)\)	\(e\left(\frac{1687}{3799}\right)\)	\(e\left(\frac{4003}{7598}\right)\)	\(e\left(\frac{3651}{3799}\right)\)	\(e\left(\frac{3}{7598}\right)\)	\(e\left(\frac{631}{3799}\right)\)	\(e\left(\frac{1816}{3799}\right)\)	\(e\left(\frac{1891}{7598}\right)\)	\(e\left(\frac{164}{3799}\right)\)
\(\chi_{15517}(22,\cdot)\)	15517.m	3799	yes	\(1\)	\(1\)	\(e\left(\frac{2341}{3799}\right)\)	\(e\left(\frac{1340}{3799}\right)\)	\(e\left(\frac{883}{3799}\right)\)	\(e\left(\frac{184}{3799}\right)\)	\(e\left(\frac{3681}{3799}\right)\)	\(e\left(\frac{1567}{3799}\right)\)	\(e\left(\frac{3224}{3799}\right)\)	\(e\left(\frac{2680}{3799}\right)\)	\(e\left(\frac{2525}{3799}\right)\)	\(e\left(\frac{2903}{3799}\right)\)
\(\chi_{15517}(23,\cdot)\)	15517.o	7598	yes	\(-1\)	\(1\)	\(e\left(\frac{2951}{7598}\right)\)	\(e\left(\frac{2667}{3799}\right)\)	\(e\left(\frac{2951}{3799}\right)\)	\(e\left(\frac{559}{3799}\right)\)	\(e\left(\frac{687}{7598}\right)\)	\(e\left(\frac{2634}{3799}\right)\)	\(e\left(\frac{1255}{7598}\right)\)	\(e\left(\frac{1535}{3799}\right)\)	\(e\left(\frac{4069}{7598}\right)\)	\(e\left(\frac{2319}{7598}\right)\)
\(\chi_{15517}(24,\cdot)\)	15517.o	7598	yes	\(-1\)	\(1\)	\(e\left(\frac{4043}{7598}\right)\)	\(e\left(\frac{39}{3799}\right)\)	\(e\left(\frac{244}{3799}\right)\)	\(e\left(\frac{3226}{3799}\right)\)	\(e\left(\frac{4121}{7598}\right)\)	\(e\left(\frac{1500}{3799}\right)\)	\(e\left(\frac{4531}{7598}\right)\)	\(e\left(\frac{78}{3799}\right)\)	\(e\left(\frac{2897}{7598}\right)\)	\(e\left(\frac{5085}{7598}\right)\)
\(\chi_{15517}(25,\cdot)\)	15517.m	3799	yes	\(1\)	\(1\)	\(e\left(\frac{2497}{3799}\right)\)	\(e\left(\frac{2760}{3799}\right)\)	\(e\left(\frac{1195}{3799}\right)\)	\(e\left(\frac{946}{3799}\right)\)	\(e\left(\frac{1458}{3799}\right)\)	\(e\left(\frac{1243}{3799}\right)\)	\(e\left(\frac{3692}{3799}\right)\)	\(e\left(\frac{1721}{3799}\right)\)	\(e\left(\frac{3443}{3799}\right)\)	\(e\left(\frac{1670}{3799}\right)\)
\(\chi_{15517}(26,\cdot)\)	15517.m	3799	yes	\(1\)	\(1\)	\(e\left(\frac{2056}{3799}\right)\)	\(e\left(\frac{2837}{3799}\right)\)	\(e\left(\frac{313}{3799}\right)\)	\(e\left(\frac{2737}{3799}\right)\)	\(e\left(\frac{1094}{3799}\right)\)	\(e\left(\frac{990}{3799}\right)\)	\(e\left(\frac{2369}{3799}\right)\)	\(e\left(\frac{1875}{3799}\right)\)	\(e\left(\frac{994}{3799}\right)\)	\(e\left(\frac{1868}{3799}\right)\)
\(\chi_{15517}(27,\cdot)\)	15517.m	3799	yes	\(1\)	\(1\)	\(e\left(\frac{1386}{3799}\right)\)	\(e\left(\frac{3557}{3799}\right)\)	\(e\left(\frac{2772}{3799}\right)\)	\(e\left(\frac{341}{3799}\right)\)	\(e\left(\frac{1144}{3799}\right)\)	\(e\left(\frac{2966}{3799}\right)\)	\(e\left(\frac{359}{3799}\right)\)	\(e\left(\frac{3315}{3799}\right)\)	\(e\left(\frac{1727}{3799}\right)\)	\(e\left(\frac{2634}{3799}\right)\)
\(\chi_{15517}(28,\cdot)\)	15517.p	7598	yes	\(-1\)	\(1\)	\(e\left(\frac{788}{3799}\right)\)	\(e\left(\frac{3179}{3799}\right)\)	\(e\left(\frac{1576}{3799}\right)\)	\(e\left(\frac{6237}{7598}\right)\)	\(e\left(\frac{168}{3799}\right)\)	\(e\left(\frac{4617}{7598}\right)\)	\(e\left(\frac{2364}{3799}\right)\)	\(e\left(\frac{2559}{3799}\right)\)	\(e\left(\frac{215}{7598}\right)\)	\(e\left(\frac{1662}{3799}\right)\)
\(\chi_{15517}(29,\cdot)\)	15517.p	7598	yes	\(-1\)	\(1\)	\(e\left(\frac{2849}{3799}\right)\)	\(e\left(\frac{1191}{3799}\right)\)	\(e\left(\frac{1899}{3799}\right)\)	\(e\left(\frac{5623}{7598}\right)\)	\(e\left(\frac{241}{3799}\right)\)	\(e\left(\frac{2485}{7598}\right)\)	\(e\left(\frac{949}{3799}\right)\)	\(e\left(\frac{2382}{3799}\right)\)	\(e\left(\frac{3723}{7598}\right)\)	\(e\left(\frac{349}{3799}\right)\)
\(\chi_{15517}(30,\cdot)\)	15517.n	7598	yes	\(1\)	\(1\)	\(e\left(\frac{5727}{7598}\right)\)	\(e\left(\frac{495}{3799}\right)\)	\(e\left(\frac{1928}{3799}\right)\)	\(e\left(\frac{6203}{7598}\right)\)	\(e\left(\frac{6717}{7598}\right)\)	\(e\left(\frac{2717}{7598}\right)\)	\(e\left(\frac{1985}{7598}\right)\)	\(e\left(\frac{990}{3799}\right)\)	\(e\left(\frac{2166}{3799}\right)\)	\(e\left(\frac{2003}{7598}\right)\)
\(\chi_{15517}(31,\cdot)\)	15517.o	7598	yes	\(-1\)	\(1\)	\(e\left(\frac{3577}{7598}\right)\)	\(e\left(\frac{743}{3799}\right)\)	\(e\left(\frac{3577}{3799}\right)\)	\(e\left(\frac{2234}{3799}\right)\)	\(e\left(\frac{5063}{7598}\right)\)	\(e\left(\frac{815}{3799}\right)\)	\(e\left(\frac{3133}{7598}\right)\)	\(e\left(\frac{1486}{3799}\right)\)	\(e\left(\frac{447}{7598}\right)\)	\(e\left(\frac{2193}{7598}\right)\)
\(\chi_{15517}(32,\cdot)\)	15517.o	7598	yes	\(-1\)	\(1\)	\(e\left(\frac{133}{7598}\right)\)	\(e\left(\frac{2310}{3799}\right)\)	\(e\left(\frac{133}{3799}\right)\)	\(e\left(\frac{544}{3799}\right)\)	\(e\left(\frac{4753}{7598}\right)\)	\(e\left(\frac{8}{3799}\right)\)	\(e\left(\frac{399}{7598}\right)\)	\(e\left(\frac{821}{3799}\right)\)	\(e\left(\frac{1221}{7598}\right)\)	\(e\left(\frac{483}{7598}\right)\)

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This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.