LMFDB - Group of Dirichlet characters of modulus 937024

Show commands: Magma / Pari/GP / SageMath

comment:Define the Dirichlet group

sage:G = DirichletGroup(937024)

gp:g = idealstar(,937024,2)

magma:G := FullDirichletGroup(937024);

Character group

Order	=	425920	comment:Order sage:G.order() gp:g.no magma:Order(G);
Structure	=	$C_{2}\times C_{2}\times C_{106480}$	comment:Group structure sage:sorted(g.order() for g in G.gens()) gp:g.cyc magma:PrimaryInvariants(AbelianGroup(G));
Generators	=	$\chi_{937024}(439231,\cdot)$, $\chi_{937024}(58565,\cdot)$, $\chi_{937024}(688129,\cdot)$	comment:Generators sage:G.gens() gp:g.gen magma:Generators(G);

First 32 of 425920 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	$-1$	$1$	$3$	$5$	$7$	$9$	$13$	$15$	$17$	$19$	$21$	$23$
$\chi_{937024}(1,\cdot)$	937024.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{937024}(3,\cdot)$	937024.fb	9680	no	$-1$	$1$	$e\left(\frac{567}{880}\right)$	$e\left(\frac{7991}{9680}\right)$	$e\left(\frac{799}{4840}\right)$	$e\left(\frac{127}{440}\right)$	$e\left(\frac{8089}{9680}\right)$	$e\left(\frac{1137}{2420}\right)$	$e\left(\frac{1229}{2420}\right)$	$e\left(\frac{5897}{9680}\right)$	$e\left(\frac{1567}{1936}\right)$	$e\left(\frac{905}{968}\right)$
$\chi_{937024}(5,\cdot)$	937024.ga	106480	yes	$1$	$1$	$e\left(\frac{7991}{9680}\right)$	$e\left(\frac{103263}{106480}\right)$	$e\left(\frac{36667}{53240}\right)$	$e\left(\frac{3151}{4840}\right)$	$e\left(\frac{9137}{106480}\right)$	$e\left(\frac{21171}{26620}\right)$	$e\left(\frac{17977}{26620}\right)$	$e\left(\frac{67561}{106480}\right)$	$e\left(\frac{10951}{21296}\right)$	$e\left(\frac{8445}{10648}\right)$
$\chi_{937024}(7,\cdot)$	937024.fw	53240	no	$1$	$1$	$e\left(\frac{799}{4840}\right)$	$e\left(\frac{36667}{53240}\right)$	$e\left(\frac{16103}{26620}\right)$	$e\left(\frac{799}{2420}\right)$	$e\left(\frac{53153}{53240}\right)$	$e\left(\frac{5682}{6655}\right)$	$e\left(\frac{5864}{6655}\right)$	$e\left(\frac{26909}{53240}\right)$	$e\left(\frac{8199}{10648}\right)$	$e\left(\frac{1087}{5324}\right)$
$\chi_{937024}(9,\cdot)$	937024.eq	4840	no	$1$	$1$	$e\left(\frac{127}{440}\right)$	$e\left(\frac{3151}{4840}\right)$	$e\left(\frac{799}{2420}\right)$	$e\left(\frac{127}{220}\right)$	$e\left(\frac{3249}{4840}\right)$	$e\left(\frac{1137}{1210}\right)$	$e\left(\frac{19}{1210}\right)$	$e\left(\frac{1057}{4840}\right)$	$e\left(\frac{599}{968}\right)$	$e\left(\frac{421}{484}\right)$
$\chi_{937024}(13,\cdot)$	937024.gc	106480	yes	$-1$	$1$	$e\left(\frac{8089}{9680}\right)$	$e\left(\frac{9137}{106480}\right)$	$e\left(\frac{53153}{53240}\right)$	$e\left(\frac{3249}{4840}\right)$	$e\left(\frac{46023}{106480}\right)$	$e\left(\frac{24529}{26620}\right)$	$e\left(\frac{18313}{26620}\right)$	$e\left(\frac{60079}{106480}\right)$	$e\left(\frac{17761}{21296}\right)$	$e\left(\frac{7955}{10648}\right)$
$\chi_{937024}(15,\cdot)$	937024.fu	26620	no	$-1$	$1$	$e\left(\frac{1137}{2420}\right)$	$e\left(\frac{21171}{26620}\right)$	$e\left(\frac{5682}{6655}\right)$	$e\left(\frac{1137}{1210}\right)$	$e\left(\frac{24529}{26620}\right)$	$e\left(\frac{3529}{13310}\right)$	$e\left(\frac{1219}{6655}\right)$	$e\left(\frac{6487}{26620}\right)$	$e\left(\frac{1723}{5324}\right)$	$e\left(\frac{969}{1331}\right)$
$\chi_{937024}(17,\cdot)$	937024.ft	26620	no	$-1$	$1$	$e\left(\frac{1229}{2420}\right)$	$e\left(\frac{17977}{26620}\right)$	$e\left(\frac{5864}{6655}\right)$	$e\left(\frac{19}{1210}\right)$	$e\left(\frac{18313}{26620}\right)$	$e\left(\frac{1219}{6655}\right)$	$e\left(\frac{4711}{13310}\right)$	$e\left(\frac{21169}{26620}\right)$	$e\left(\frac{2071}{5324}\right)$	$e\left(\frac{2083}{2662}\right)$
$\chi_{937024}(19,\cdot)$	937024.gd	106480	yes	$1$	$1$	$e\left(\frac{5897}{9680}\right)$	$e\left(\frac{67561}{106480}\right)$	$e\left(\frac{26909}{53240}\right)$	$e\left(\frac{1057}{4840}\right)$	$e\left(\frac{60079}{106480}\right)$	$e\left(\frac{6487}{26620}\right)$	$e\left(\frac{21169}{26620}\right)$	$e\left(\frac{16447}{106480}\right)$	$e\left(\frac{2441}{21296}\right)$	$e\left(\frac{7783}{10648}\right)$
$\chi_{937024}(21,\cdot)$	937024.fp	21296	yes	$-1$	$1$	$e\left(\frac{1567}{1936}\right)$	$e\left(\frac{10951}{21296}\right)$	$e\left(\frac{8199}{10648}\right)$	$e\left(\frac{599}{968}\right)$	$e\left(\frac{17761}{21296}\right)$	$e\left(\frac{1723}{5324}\right)$	$e\left(\frac{2071}{5324}\right)$	$e\left(\frac{2441}{21296}\right)$	$e\left(\frac{12339}{21296}\right)$	$e\left(\frac{1481}{10648}\right)$
$\chi_{937024}(23,\cdot)$	937024.fe	10648	no	$-1$	$1$	$e\left(\frac{905}{968}\right)$	$e\left(\frac{8445}{10648}\right)$	$e\left(\frac{1087}{5324}\right)$	$e\left(\frac{421}{484}\right)$	$e\left(\frac{7955}{10648}\right)$	$e\left(\frac{969}{1331}\right)$	$e\left(\frac{2083}{2662}\right)$	$e\left(\frac{7783}{10648}\right)$	$e\left(\frac{1481}{10648}\right)$	$e\left(\frac{4721}{5324}\right)$
$\chi_{937024}(25,\cdot)$	937024.fz	53240	no	$1$	$1$	$e\left(\frac{3151}{4840}\right)$	$e\left(\frac{50023}{53240}\right)$	$e\left(\frac{10047}{26620}\right)$	$e\left(\frac{731}{2420}\right)$	$e\left(\frac{9137}{53240}\right)$	$e\left(\frac{7861}{13310}\right)$	$e\left(\frac{4667}{13310}\right)$	$e\left(\frac{14321}{53240}\right)$	$e\left(\frac{303}{10648}\right)$	$e\left(\frac{3121}{5324}\right)$
$\chi_{937024}(27,\cdot)$	937024.fb	9680	no	$-1$	$1$	$e\left(\frac{821}{880}\right)$	$e\left(\frac{4613}{9680}\right)$	$e\left(\frac{2397}{4840}\right)$	$e\left(\frac{381}{440}\right)$	$e\left(\frac{4907}{9680}\right)$	$e\left(\frac{991}{2420}\right)$	$e\left(\frac{1267}{2420}\right)$	$e\left(\frac{8011}{9680}\right)$	$e\left(\frac{829}{1936}\right)$	$e\left(\frac{779}{968}\right)$
$\chi_{937024}(29,\cdot)$	937024.gc	106480	yes	$-1$	$1$	$e\left(\frac{573}{9680}\right)$	$e\left(\frac{32229}{106480}\right)$	$e\left(\frac{21101}{53240}\right)$	$e\left(\frac{573}{4840}\right)$	$e\left(\frac{17971}{106480}\right)$	$e\left(\frac{9633}{26620}\right)$	$e\left(\frac{841}{26620}\right)$	$e\left(\frac{103083}{106480}\right)$	$e\left(\frac{9701}{21296}\right)$	$e\left(\frac{6815}{10648}\right)$
$\chi_{937024}(31,\cdot)$	937024.fn	13310	no	$-1$	$1$	$e\left(\frac{514}{605}\right)$	$e\left(\frac{10159}{13310}\right)$	$e\left(\frac{11107}{13310}\right)$	$e\left(\frac{423}{605}\right)$	$e\left(\frac{381}{13310}\right)$	$e\left(\frac{8157}{13310}\right)$	$e\left(\frac{2382}{6655}\right)$	$e\left(\frac{5219}{6655}\right)$	$e\left(\frac{1821}{2662}\right)$	$e\left(\frac{2183}{2662}\right)$
$\chi_{937024}(35,\cdot)$	937024.gd	106480	yes	$1$	$1$	$e\left(\frac{9589}{9680}\right)$	$e\left(\frac{70117}{106480}\right)$	$e\left(\frac{15633}{53240}\right)$	$e\left(\frac{4749}{4840}\right)$	$e\left(\frac{8963}{106480}\right)$	$e\left(\frac{17279}{26620}\right)$	$e\left(\frac{14813}{26620}\right)$	$e\left(\frac{14899}{106480}\right)$	$e\left(\frac{6053}{21296}\right)$	$e\left(\frac{10619}{10648}\right)$
$\chi_{937024}(37,\cdot)$	937024.ga	106480	yes	$1$	$1$	$e\left(\frac{9423}{9680}\right)$	$e\left(\frac{27559}{106480}\right)$	$e\left(\frac{17291}{53240}\right)$	$e\left(\frac{4583}{4840}\right)$	$e\left(\frac{90201}{106480}\right)$	$e\left(\frac{6183}{26620}\right)$	$e\left(\frac{5601}{26620}\right)$	$e\left(\frac{96913}{106480}\right)$	$e\left(\frac{6351}{21296}\right)$	$e\left(\frac{317}{10648}\right)$
$\chi_{937024}(39,\cdot)$	937024.fw	53240	no	$1$	$1$	$e\left(\frac{2323}{4840}\right)$	$e\left(\frac{48519}{53240}\right)$	$e\left(\frac{4351}{26620}\right)$	$e\left(\frac{2323}{2420}\right)$	$e\left(\frac{14261}{53240}\right)$	$e\left(\frac{2604}{6655}\right)$	$e\left(\frac{1303}{6655}\right)$	$e\left(\frac{9233}{53240}\right)$	$e\left(\frac{6851}{10648}\right)$	$e\left(\frac{3631}{5324}\right)$
$\chi_{937024}(41,\cdot)$	937024.fx	53240	no	$-1$	$1$	$e\left(\frac{2641}{4840}\right)$	$e\left(\frac{43713}{53240}\right)$	$e\left(\frac{17867}{26620}\right)$	$e\left(\frac{221}{2420}\right)$	$e\left(\frac{38387}{53240}\right)$	$e\left(\frac{4881}{13310}\right)$	$e\left(\frac{811}{6655}\right)$	$e\left(\frac{53011}{53240}\right)$	$e\left(\frac{2309}{10648}\right)$	$e\left(\frac{3735}{5324}\right)$
$\chi_{937024}(43,\cdot)$	937024.fo	21296	yes	$1$	$1$	$e\left(\frac{1671}{1936}\right)$	$e\left(\frac{2311}{21296}\right)$	$e\left(\frac{9347}{10648}\right)$	$e\left(\frac{703}{968}\right)$	$e\left(\frac{12081}{21296}\right)$	$e\left(\frac{5173}{5324}\right)$	$e\left(\frac{2635}{5324}\right)$	$e\left(\frac{625}{21296}\right)$	$e\left(\frac{15779}{21296}\right)$	$e\left(\frac{10013}{10648}\right)$
$\chi_{937024}(45,\cdot)$	937024.fr	21296	yes	$1$	$1$	$e\left(\frac{221}{1936}\right)$	$e\left(\frac{13221}{21296}\right)$	$e\left(\frac{201}{10648}\right)$	$e\left(\frac{221}{968}\right)$	$e\left(\frac{16123}{21296}\right)$	$e\left(\frac{3913}{5324}\right)$	$e\left(\frac{3679}{5324}\right)$	$e\left(\frac{18163}{21296}\right)$	$e\left(\frac{2833}{21296}\right)$	$e\left(\frac{7059}{10648}\right)$
$\chi_{937024}(47,\cdot)$	937024.fu	26620	no	$-1$	$1$	$e\left(\frac{1523}{2420}\right)$	$e\left(\frac{589}{26620}\right)$	$e\left(\frac{5788}{6655}\right)$	$e\left(\frac{313}{1210}\right)$	$e\left(\frac{5551}{26620}\right)$	$e\left(\frac{8671}{13310}\right)$	$e\left(\frac{6086}{6655}\right)$	$e\left(\frac{14453}{26620}\right)$	$e\left(\frac{2657}{5324}\right)$	$e\left(\frac{609}{1331}\right)$
$\chi_{937024}(49,\cdot)$	937024.fv	26620	no	$1$	$1$	$e\left(\frac{799}{2420}\right)$	$e\left(\frac{10047}{26620}\right)$	$e\left(\frac{2793}{13310}\right)$	$e\left(\frac{799}{1210}\right)$	$e\left(\frac{26533}{26620}\right)$	$e\left(\frac{4709}{6655}\right)$	$e\left(\frac{5073}{6655}\right)$	$e\left(\frac{289}{26620}\right)$	$e\left(\frac{2875}{5324}\right)$	$e\left(\frac{1087}{2662}\right)$
$\chi_{937024}(51,\cdot)$	937024.gd	106480	yes	$1$	$1$	$e\left(\frac{1473}{9680}\right)$	$e\left(\frac{53329}{106480}\right)$	$e\left(\frac{2461}{53240}\right)$	$e\left(\frac{1473}{4840}\right)$	$e\left(\frac{55751}{106480}\right)$	$e\left(\frac{17383}{26620}\right)$	$e\left(\frac{22941}{26620}\right)$	$e\left(\frac{43063}{106480}\right)$	$e\left(\frac{4225}{21296}\right)$	$e\left(\frac{7639}{10648}\right)$
$\chi_{937024}(53,\cdot)$	937024.ga	106480	yes	$1$	$1$	$e\left(\frac{179}{9680}\right)$	$e\left(\frac{35307}{106480}\right)$	$e\left(\frac{3023}{53240}\right)$	$e\left(\frac{179}{4840}\right)$	$e\left(\frac{77893}{106480}\right)$	$e\left(\frac{9319}{26620}\right)$	$e\left(\frac{873}{26620}\right)$	$e\left(\frac{47229}{106480}\right)$	$e\left(\frac{1603}{21296}\right)$	$e\left(\frac{5881}{10648}\right)$
$\chi_{937024}(57,\cdot)$	937024.fx	53240	no	$-1$	$1$	$e\left(\frac{1227}{4840}\right)$	$e\left(\frac{24491}{53240}\right)$	$e\left(\frac{17849}{26620}\right)$	$e\left(\frac{1227}{2420}\right)$	$e\left(\frac{21289}{53240}\right)$	$e\left(\frac{9497}{13310}\right)$	$e\left(\frac{2017}{6655}\right)$	$e\left(\frac{40657}{53240}\right)$	$e\left(\frac{9839}{10648}\right)$	$e\left(\frac{3545}{5324}\right)$
$\chi_{937024}(59,\cdot)$	937024.gb	106480	yes	$-1$	$1$	$e\left(\frac{6543}{9680}\right)$	$e\left(\frac{22959}{106480}\right)$	$e\left(\frac{10631}{53240}\right)$	$e\left(\frac{1703}{4840}\right)$	$e\left(\frac{72881}{106480}\right)$	$e\left(\frac{23733}{26620}\right)$	$e\left(\frac{19581}{26620}\right)$	$e\left(\frac{77953}{106480}\right)$	$e\left(\frac{18647}{21296}\right)$	$e\left(\frac{4553}{10648}\right)$
$\chi_{937024}(61,\cdot)$	937024.gc	106480	yes	$-1$	$1$	$e\left(\frac{2341}{9680}\right)$	$e\left(\frac{52813}{106480}\right)$	$e\left(\frac{33357}{53240}\right)$	$e\left(\frac{2341}{4840}\right)$	$e\left(\frac{83067}{106480}\right)$	$e\left(\frac{19641}{26620}\right)$	$e\left(\frac{8977}{26620}\right)$	$e\left(\frac{14131}{106480}\right)$	$e\left(\frac{18493}{21296}\right)$	$e\left(\frac{9591}{10648}\right)$
$\chi_{937024}(63,\cdot)$	937024.fj	13310	no	$1$	$1$	$e\left(\frac{549}{1210}\right)$	$e\left(\frac{2261}{6655}\right)$	$e\left(\frac{6223}{6655}\right)$	$e\left(\frac{549}{605}\right)$	$e\left(\frac{8913}{13310}\right)$	$e\left(\frac{10561}{13310}\right)$	$e\left(\frac{11937}{13310}\right)$	$e\left(\frac{4817}{6655}\right)$	$e\left(\frac{1035}{2662}\right)$	$e\left(\frac{197}{2662}\right)$
$\chi_{937024}(65,\cdot)$	937024.eo	2662	no	$-1$	$1$	$e\left(\frac{80}{121}\right)$	$e\left(\frac{74}{1331}\right)$	$e\left(\frac{1829}{2662}\right)$	$e\left(\frac{39}{121}\right)$	$e\left(\frac{1379}{2662}\right)$	$e\left(\frac{954}{1331}\right)$	$e\left(\frac{967}{2662}\right)$	$e\left(\frac{529}{2662}\right)$	$e\left(\frac{927}{2662}\right)$	$e\left(\frac{719}{1331}\right)$
$\chi_{937024}(67,\cdot)$	937024.fq	21296	yes	$-1$	$1$	$e\left(\frac{73}{1936}\right)$	$e\left(\frac{15129}{21296}\right)$	$e\left(\frac{857}{10648}\right)$	$e\left(\frac{73}{968}\right)$	$e\left(\frac{15159}{21296}\right)$	$e\left(\frac{3983}{5324}\right)$	$e\left(\frac{959}{5324}\right)$	$e\left(\frac{8759}{21296}\right)$	$e\left(\frac{2517}{21296}\right)$	$e\left(\frac{7371}{10648}\right)$
$\chi_{937024}(69,\cdot)$	937024.ga	106480	yes	$1$	$1$	$e\left(\frac{5607}{9680}\right)$	$e\left(\frac{65871}{106480}\right)$	$e\left(\frac{19659}{53240}\right)$	$e\left(\frac{767}{4840}\right)$	$e\left(\frac{62049}{106480}\right)$	$e\left(\frac{5267}{26620}\right)$	$e\left(\frac{7729}{26620}\right)$	$e\left(\frac{36217}{106480}\right)$	$e\left(\frac{20199}{21296}\right)$	$e\left(\frac{8749}{10648}\right)$

Click here to search among the remaining 425888 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	$937024$
Structure	\(C_{2}\times C_{2}\times C_{106480}\)
Order	$425920$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(13\)	\(15\)	\(17\)	\(19\)	\(21\)	\(23\)
\(\chi_{937024}(1,\cdot)\)	937024.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{937024}(3,\cdot)\)	937024.fb	9680	no	\(-1\)	\(1\)	\(e\left(\frac{567}{880}\right)\)	\(e\left(\frac{7991}{9680}\right)\)	\(e\left(\frac{799}{4840}\right)\)	\(e\left(\frac{127}{440}\right)\)	\(e\left(\frac{8089}{9680}\right)\)	\(e\left(\frac{1137}{2420}\right)\)	\(e\left(\frac{1229}{2420}\right)\)	\(e\left(\frac{5897}{9680}\right)\)	\(e\left(\frac{1567}{1936}\right)\)	\(e\left(\frac{905}{968}\right)\)
\(\chi_{937024}(5,\cdot)\)	937024.ga	106480	yes	\(1\)	\(1\)	\(e\left(\frac{7991}{9680}\right)\)	\(e\left(\frac{103263}{106480}\right)\)	\(e\left(\frac{36667}{53240}\right)\)	\(e\left(\frac{3151}{4840}\right)\)	\(e\left(\frac{9137}{106480}\right)\)	\(e\left(\frac{21171}{26620}\right)\)	\(e\left(\frac{17977}{26620}\right)\)	\(e\left(\frac{67561}{106480}\right)\)	\(e\left(\frac{10951}{21296}\right)\)	\(e\left(\frac{8445}{10648}\right)\)
\(\chi_{937024}(7,\cdot)\)	937024.fw	53240	no	\(1\)	\(1\)	\(e\left(\frac{799}{4840}\right)\)	\(e\left(\frac{36667}{53240}\right)\)	\(e\left(\frac{16103}{26620}\right)\)	\(e\left(\frac{799}{2420}\right)\)	\(e\left(\frac{53153}{53240}\right)\)	\(e\left(\frac{5682}{6655}\right)\)	\(e\left(\frac{5864}{6655}\right)\)	\(e\left(\frac{26909}{53240}\right)\)	\(e\left(\frac{8199}{10648}\right)\)	\(e\left(\frac{1087}{5324}\right)\)
\(\chi_{937024}(9,\cdot)\)	937024.eq	4840	no	\(1\)	\(1\)	\(e\left(\frac{127}{440}\right)\)	\(e\left(\frac{3151}{4840}\right)\)	\(e\left(\frac{799}{2420}\right)\)	\(e\left(\frac{127}{220}\right)\)	\(e\left(\frac{3249}{4840}\right)\)	\(e\left(\frac{1137}{1210}\right)\)	\(e\left(\frac{19}{1210}\right)\)	\(e\left(\frac{1057}{4840}\right)\)	\(e\left(\frac{599}{968}\right)\)	\(e\left(\frac{421}{484}\right)\)
\(\chi_{937024}(13,\cdot)\)	937024.gc	106480	yes	\(-1\)	\(1\)	\(e\left(\frac{8089}{9680}\right)\)	\(e\left(\frac{9137}{106480}\right)\)	\(e\left(\frac{53153}{53240}\right)\)	\(e\left(\frac{3249}{4840}\right)\)	\(e\left(\frac{46023}{106480}\right)\)	\(e\left(\frac{24529}{26620}\right)\)	\(e\left(\frac{18313}{26620}\right)\)	\(e\left(\frac{60079}{106480}\right)\)	\(e\left(\frac{17761}{21296}\right)\)	\(e\left(\frac{7955}{10648}\right)\)
\(\chi_{937024}(15,\cdot)\)	937024.fu	26620	no	\(-1\)	\(1\)	\(e\left(\frac{1137}{2420}\right)\)	\(e\left(\frac{21171}{26620}\right)\)	\(e\left(\frac{5682}{6655}\right)\)	\(e\left(\frac{1137}{1210}\right)\)	\(e\left(\frac{24529}{26620}\right)\)	\(e\left(\frac{3529}{13310}\right)\)	\(e\left(\frac{1219}{6655}\right)\)	\(e\left(\frac{6487}{26620}\right)\)	\(e\left(\frac{1723}{5324}\right)\)	\(e\left(\frac{969}{1331}\right)\)
\(\chi_{937024}(17,\cdot)\)	937024.ft	26620	no	\(-1\)	\(1\)	\(e\left(\frac{1229}{2420}\right)\)	\(e\left(\frac{17977}{26620}\right)\)	\(e\left(\frac{5864}{6655}\right)\)	\(e\left(\frac{19}{1210}\right)\)	\(e\left(\frac{18313}{26620}\right)\)	\(e\left(\frac{1219}{6655}\right)\)	\(e\left(\frac{4711}{13310}\right)\)	\(e\left(\frac{21169}{26620}\right)\)	\(e\left(\frac{2071}{5324}\right)\)	\(e\left(\frac{2083}{2662}\right)\)
\(\chi_{937024}(19,\cdot)\)	937024.gd	106480	yes	\(1\)	\(1\)	\(e\left(\frac{5897}{9680}\right)\)	\(e\left(\frac{67561}{106480}\right)\)	\(e\left(\frac{26909}{53240}\right)\)	\(e\left(\frac{1057}{4840}\right)\)	\(e\left(\frac{60079}{106480}\right)\)	\(e\left(\frac{6487}{26620}\right)\)	\(e\left(\frac{21169}{26620}\right)\)	\(e\left(\frac{16447}{106480}\right)\)	\(e\left(\frac{2441}{21296}\right)\)	\(e\left(\frac{7783}{10648}\right)\)
\(\chi_{937024}(21,\cdot)\)	937024.fp	21296	yes	\(-1\)	\(1\)	\(e\left(\frac{1567}{1936}\right)\)	\(e\left(\frac{10951}{21296}\right)\)	\(e\left(\frac{8199}{10648}\right)\)	\(e\left(\frac{599}{968}\right)\)	\(e\left(\frac{17761}{21296}\right)\)	\(e\left(\frac{1723}{5324}\right)\)	\(e\left(\frac{2071}{5324}\right)\)	\(e\left(\frac{2441}{21296}\right)\)	\(e\left(\frac{12339}{21296}\right)\)	\(e\left(\frac{1481}{10648}\right)\)
\(\chi_{937024}(23,\cdot)\)	937024.fe	10648	no	\(-1\)	\(1\)	\(e\left(\frac{905}{968}\right)\)	\(e\left(\frac{8445}{10648}\right)\)	\(e\left(\frac{1087}{5324}\right)\)	\(e\left(\frac{421}{484}\right)\)	\(e\left(\frac{7955}{10648}\right)\)	\(e\left(\frac{969}{1331}\right)\)	\(e\left(\frac{2083}{2662}\right)\)	\(e\left(\frac{7783}{10648}\right)\)	\(e\left(\frac{1481}{10648}\right)\)	\(e\left(\frac{4721}{5324}\right)\)
\(\chi_{937024}(25,\cdot)\)	937024.fz	53240	no	\(1\)	\(1\)	\(e\left(\frac{3151}{4840}\right)\)	\(e\left(\frac{50023}{53240}\right)\)	\(e\left(\frac{10047}{26620}\right)\)	\(e\left(\frac{731}{2420}\right)\)	\(e\left(\frac{9137}{53240}\right)\)	\(e\left(\frac{7861}{13310}\right)\)	\(e\left(\frac{4667}{13310}\right)\)	\(e\left(\frac{14321}{53240}\right)\)	\(e\left(\frac{303}{10648}\right)\)	\(e\left(\frac{3121}{5324}\right)\)
\(\chi_{937024}(27,\cdot)\)	937024.fb	9680	no	\(-1\)	\(1\)	\(e\left(\frac{821}{880}\right)\)	\(e\left(\frac{4613}{9680}\right)\)	\(e\left(\frac{2397}{4840}\right)\)	\(e\left(\frac{381}{440}\right)\)	\(e\left(\frac{4907}{9680}\right)\)	\(e\left(\frac{991}{2420}\right)\)	\(e\left(\frac{1267}{2420}\right)\)	\(e\left(\frac{8011}{9680}\right)\)	\(e\left(\frac{829}{1936}\right)\)	\(e\left(\frac{779}{968}\right)\)
\(\chi_{937024}(29,\cdot)\)	937024.gc	106480	yes	\(-1\)	\(1\)	\(e\left(\frac{573}{9680}\right)\)	\(e\left(\frac{32229}{106480}\right)\)	\(e\left(\frac{21101}{53240}\right)\)	\(e\left(\frac{573}{4840}\right)\)	\(e\left(\frac{17971}{106480}\right)\)	\(e\left(\frac{9633}{26620}\right)\)	\(e\left(\frac{841}{26620}\right)\)	\(e\left(\frac{103083}{106480}\right)\)	\(e\left(\frac{9701}{21296}\right)\)	\(e\left(\frac{6815}{10648}\right)\)
\(\chi_{937024}(31,\cdot)\)	937024.fn	13310	no	\(-1\)	\(1\)	\(e\left(\frac{514}{605}\right)\)	\(e\left(\frac{10159}{13310}\right)\)	\(e\left(\frac{11107}{13310}\right)\)	\(e\left(\frac{423}{605}\right)\)	\(e\left(\frac{381}{13310}\right)\)	\(e\left(\frac{8157}{13310}\right)\)	\(e\left(\frac{2382}{6655}\right)\)	\(e\left(\frac{5219}{6655}\right)\)	\(e\left(\frac{1821}{2662}\right)\)	\(e\left(\frac{2183}{2662}\right)\)
\(\chi_{937024}(35,\cdot)\)	937024.gd	106480	yes	\(1\)	\(1\)	\(e\left(\frac{9589}{9680}\right)\)	\(e\left(\frac{70117}{106480}\right)\)	\(e\left(\frac{15633}{53240}\right)\)	\(e\left(\frac{4749}{4840}\right)\)	\(e\left(\frac{8963}{106480}\right)\)	\(e\left(\frac{17279}{26620}\right)\)	\(e\left(\frac{14813}{26620}\right)\)	\(e\left(\frac{14899}{106480}\right)\)	\(e\left(\frac{6053}{21296}\right)\)	\(e\left(\frac{10619}{10648}\right)\)
\(\chi_{937024}(37,\cdot)\)	937024.ga	106480	yes	\(1\)	\(1\)	\(e\left(\frac{9423}{9680}\right)\)	\(e\left(\frac{27559}{106480}\right)\)	\(e\left(\frac{17291}{53240}\right)\)	\(e\left(\frac{4583}{4840}\right)\)	\(e\left(\frac{90201}{106480}\right)\)	\(e\left(\frac{6183}{26620}\right)\)	\(e\left(\frac{5601}{26620}\right)\)	\(e\left(\frac{96913}{106480}\right)\)	\(e\left(\frac{6351}{21296}\right)\)	\(e\left(\frac{317}{10648}\right)\)
\(\chi_{937024}(39,\cdot)\)	937024.fw	53240	no	\(1\)	\(1\)	\(e\left(\frac{2323}{4840}\right)\)	\(e\left(\frac{48519}{53240}\right)\)	\(e\left(\frac{4351}{26620}\right)\)	\(e\left(\frac{2323}{2420}\right)\)	\(e\left(\frac{14261}{53240}\right)\)	\(e\left(\frac{2604}{6655}\right)\)	\(e\left(\frac{1303}{6655}\right)\)	\(e\left(\frac{9233}{53240}\right)\)	\(e\left(\frac{6851}{10648}\right)\)	\(e\left(\frac{3631}{5324}\right)\)
\(\chi_{937024}(41,\cdot)\)	937024.fx	53240	no	\(-1\)	\(1\)	\(e\left(\frac{2641}{4840}\right)\)	\(e\left(\frac{43713}{53240}\right)\)	\(e\left(\frac{17867}{26620}\right)\)	\(e\left(\frac{221}{2420}\right)\)	\(e\left(\frac{38387}{53240}\right)\)	\(e\left(\frac{4881}{13310}\right)\)	\(e\left(\frac{811}{6655}\right)\)	\(e\left(\frac{53011}{53240}\right)\)	\(e\left(\frac{2309}{10648}\right)\)	\(e\left(\frac{3735}{5324}\right)\)
\(\chi_{937024}(43,\cdot)\)	937024.fo	21296	yes	\(1\)	\(1\)	\(e\left(\frac{1671}{1936}\right)\)	\(e\left(\frac{2311}{21296}\right)\)	\(e\left(\frac{9347}{10648}\right)\)	\(e\left(\frac{703}{968}\right)\)	\(e\left(\frac{12081}{21296}\right)\)	\(e\left(\frac{5173}{5324}\right)\)	\(e\left(\frac{2635}{5324}\right)\)	\(e\left(\frac{625}{21296}\right)\)	\(e\left(\frac{15779}{21296}\right)\)	\(e\left(\frac{10013}{10648}\right)\)
\(\chi_{937024}(45,\cdot)\)	937024.fr	21296	yes	\(1\)	\(1\)	\(e\left(\frac{221}{1936}\right)\)	\(e\left(\frac{13221}{21296}\right)\)	\(e\left(\frac{201}{10648}\right)\)	\(e\left(\frac{221}{968}\right)\)	\(e\left(\frac{16123}{21296}\right)\)	\(e\left(\frac{3913}{5324}\right)\)	\(e\left(\frac{3679}{5324}\right)\)	\(e\left(\frac{18163}{21296}\right)\)	\(e\left(\frac{2833}{21296}\right)\)	\(e\left(\frac{7059}{10648}\right)\)
\(\chi_{937024}(47,\cdot)\)	937024.fu	26620	no	\(-1\)	\(1\)	\(e\left(\frac{1523}{2420}\right)\)	\(e\left(\frac{589}{26620}\right)\)	\(e\left(\frac{5788}{6655}\right)\)	\(e\left(\frac{313}{1210}\right)\)	\(e\left(\frac{5551}{26620}\right)\)	\(e\left(\frac{8671}{13310}\right)\)	\(e\left(\frac{6086}{6655}\right)\)	\(e\left(\frac{14453}{26620}\right)\)	\(e\left(\frac{2657}{5324}\right)\)	\(e\left(\frac{609}{1331}\right)\)
\(\chi_{937024}(49,\cdot)\)	937024.fv	26620	no	\(1\)	\(1\)	\(e\left(\frac{799}{2420}\right)\)	\(e\left(\frac{10047}{26620}\right)\)	\(e\left(\frac{2793}{13310}\right)\)	\(e\left(\frac{799}{1210}\right)\)	\(e\left(\frac{26533}{26620}\right)\)	\(e\left(\frac{4709}{6655}\right)\)	\(e\left(\frac{5073}{6655}\right)\)	\(e\left(\frac{289}{26620}\right)\)	\(e\left(\frac{2875}{5324}\right)\)	\(e\left(\frac{1087}{2662}\right)\)
\(\chi_{937024}(51,\cdot)\)	937024.gd	106480	yes	\(1\)	\(1\)	\(e\left(\frac{1473}{9680}\right)\)	\(e\left(\frac{53329}{106480}\right)\)	\(e\left(\frac{2461}{53240}\right)\)	\(e\left(\frac{1473}{4840}\right)\)	\(e\left(\frac{55751}{106480}\right)\)	\(e\left(\frac{17383}{26620}\right)\)	\(e\left(\frac{22941}{26620}\right)\)	\(e\left(\frac{43063}{106480}\right)\)	\(e\left(\frac{4225}{21296}\right)\)	\(e\left(\frac{7639}{10648}\right)\)
\(\chi_{937024}(53,\cdot)\)	937024.ga	106480	yes	\(1\)	\(1\)	\(e\left(\frac{179}{9680}\right)\)	\(e\left(\frac{35307}{106480}\right)\)	\(e\left(\frac{3023}{53240}\right)\)	\(e\left(\frac{179}{4840}\right)\)	\(e\left(\frac{77893}{106480}\right)\)	\(e\left(\frac{9319}{26620}\right)\)	\(e\left(\frac{873}{26620}\right)\)	\(e\left(\frac{47229}{106480}\right)\)	\(e\left(\frac{1603}{21296}\right)\)	\(e\left(\frac{5881}{10648}\right)\)
\(\chi_{937024}(57,\cdot)\)	937024.fx	53240	no	\(-1\)	\(1\)	\(e\left(\frac{1227}{4840}\right)\)	\(e\left(\frac{24491}{53240}\right)\)	\(e\left(\frac{17849}{26620}\right)\)	\(e\left(\frac{1227}{2420}\right)\)	\(e\left(\frac{21289}{53240}\right)\)	\(e\left(\frac{9497}{13310}\right)\)	\(e\left(\frac{2017}{6655}\right)\)	\(e\left(\frac{40657}{53240}\right)\)	\(e\left(\frac{9839}{10648}\right)\)	\(e\left(\frac{3545}{5324}\right)\)
\(\chi_{937024}(59,\cdot)\)	937024.gb	106480	yes	\(-1\)	\(1\)	\(e\left(\frac{6543}{9680}\right)\)	\(e\left(\frac{22959}{106480}\right)\)	\(e\left(\frac{10631}{53240}\right)\)	\(e\left(\frac{1703}{4840}\right)\)	\(e\left(\frac{72881}{106480}\right)\)	\(e\left(\frac{23733}{26620}\right)\)	\(e\left(\frac{19581}{26620}\right)\)	\(e\left(\frac{77953}{106480}\right)\)	\(e\left(\frac{18647}{21296}\right)\)	\(e\left(\frac{4553}{10648}\right)\)
\(\chi_{937024}(61,\cdot)\)	937024.gc	106480	yes	\(-1\)	\(1\)	\(e\left(\frac{2341}{9680}\right)\)	\(e\left(\frac{52813}{106480}\right)\)	\(e\left(\frac{33357}{53240}\right)\)	\(e\left(\frac{2341}{4840}\right)\)	\(e\left(\frac{83067}{106480}\right)\)	\(e\left(\frac{19641}{26620}\right)\)	\(e\left(\frac{8977}{26620}\right)\)	\(e\left(\frac{14131}{106480}\right)\)	\(e\left(\frac{18493}{21296}\right)\)	\(e\left(\frac{9591}{10648}\right)\)
\(\chi_{937024}(63,\cdot)\)	937024.fj	13310	no	\(1\)	\(1\)	\(e\left(\frac{549}{1210}\right)\)	\(e\left(\frac{2261}{6655}\right)\)	\(e\left(\frac{6223}{6655}\right)\)	\(e\left(\frac{549}{605}\right)\)	\(e\left(\frac{8913}{13310}\right)\)	\(e\left(\frac{10561}{13310}\right)\)	\(e\left(\frac{11937}{13310}\right)\)	\(e\left(\frac{4817}{6655}\right)\)	\(e\left(\frac{1035}{2662}\right)\)	\(e\left(\frac{197}{2662}\right)\)
\(\chi_{937024}(65,\cdot)\)	937024.eo	2662	no	\(-1\)	\(1\)	\(e\left(\frac{80}{121}\right)\)	\(e\left(\frac{74}{1331}\right)\)	\(e\left(\frac{1829}{2662}\right)\)	\(e\left(\frac{39}{121}\right)\)	\(e\left(\frac{1379}{2662}\right)\)	\(e\left(\frac{954}{1331}\right)\)	\(e\left(\frac{967}{2662}\right)\)	\(e\left(\frac{529}{2662}\right)\)	\(e\left(\frac{927}{2662}\right)\)	\(e\left(\frac{719}{1331}\right)\)
\(\chi_{937024}(67,\cdot)\)	937024.fq	21296	yes	\(-1\)	\(1\)	\(e\left(\frac{73}{1936}\right)\)	\(e\left(\frac{15129}{21296}\right)\)	\(e\left(\frac{857}{10648}\right)\)	\(e\left(\frac{73}{968}\right)\)	\(e\left(\frac{15159}{21296}\right)\)	\(e\left(\frac{3983}{5324}\right)\)	\(e\left(\frac{959}{5324}\right)\)	\(e\left(\frac{8759}{21296}\right)\)	\(e\left(\frac{2517}{21296}\right)\)	\(e\left(\frac{7371}{10648}\right)\)
\(\chi_{937024}(69,\cdot)\)	937024.ga	106480	yes	\(1\)	\(1\)	\(e\left(\frac{5607}{9680}\right)\)	\(e\left(\frac{65871}{106480}\right)\)	\(e\left(\frac{19659}{53240}\right)\)	\(e\left(\frac{767}{4840}\right)\)	\(e\left(\frac{62049}{106480}\right)\)	\(e\left(\frac{5267}{26620}\right)\)	\(e\left(\frac{7729}{26620}\right)\)	\(e\left(\frac{36217}{106480}\right)\)	\(e\left(\frac{20199}{21296}\right)\)	\(e\left(\frac{8749}{10648}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Downloads

Learn more

Character group

First 32 of 425920 characters

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