LMFDB - Group of Dirichlet characters of modulus 10063

Show commands: PariGP / SageMath

sage: H = DirichletGroup(10063)

pari: g = idealstar(,10063,2)

Character group

sage: G.order() pari: g.no
Order	=	9688
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{4844}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{10063}(9717,\cdot)$, $\chi_{10063}(349,\cdot)$

First 32 of 9688 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	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{10063}(1,\cdot)$	10063.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{10063}(2,\cdot)$	10063.x	4844	yes	$1$	$1$	$e\left(\frac{187}{4844}\right)$	$e\left(\frac{2993}{4844}\right)$	$e\left(\frac{187}{2422}\right)$	$e\left(\frac{710}{1211}\right)$	$e\left(\frac{795}{1211}\right)$	$e\left(\frac{639}{2422}\right)$	$e\left(\frac{561}{4844}\right)$	$e\left(\frac{571}{2422}\right)$	$e\left(\frac{3027}{4844}\right)$	$e\left(\frac{3289}{4844}\right)$
$\chi_{10063}(3,\cdot)$	10063.w	4844	yes	$-1$	$1$	$e\left(\frac{2993}{4844}\right)$	$e\left(\frac{3233}{4844}\right)$	$e\left(\frac{571}{2422}\right)$	$e\left(\frac{1493}{2422}\right)$	$e\left(\frac{691}{2422}\right)$	$e\left(\frac{124}{1211}\right)$	$e\left(\frac{4135}{4844}\right)$	$e\left(\frac{811}{2422}\right)$	$e\left(\frac{1135}{4844}\right)$	$e\left(\frac{4629}{4844}\right)$
$\chi_{10063}(4,\cdot)$	10063.t	2422	yes	$1$	$1$	$e\left(\frac{187}{2422}\right)$	$e\left(\frac{571}{2422}\right)$	$e\left(\frac{187}{1211}\right)$	$e\left(\frac{209}{1211}\right)$	$e\left(\frac{379}{1211}\right)$	$e\left(\frac{639}{1211}\right)$	$e\left(\frac{561}{2422}\right)$	$e\left(\frac{571}{1211}\right)$	$e\left(\frac{605}{2422}\right)$	$e\left(\frac{867}{2422}\right)$
$\chi_{10063}(5,\cdot)$	10063.v	2422	yes	$-1$	$1$	$e\left(\frac{710}{1211}\right)$	$e\left(\frac{1493}{2422}\right)$	$e\left(\frac{209}{1211}\right)$	$e\left(\frac{111}{2422}\right)$	$e\left(\frac{491}{2422}\right)$	$e\left(\frac{1927}{2422}\right)$	$e\left(\frac{919}{1211}\right)$	$e\left(\frac{282}{1211}\right)$	$e\left(\frac{1531}{2422}\right)$	$e\left(\frac{969}{2422}\right)$
$\chi_{10063}(6,\cdot)$	10063.v	2422	yes	$-1$	$1$	$e\left(\frac{795}{1211}\right)$	$e\left(\frac{691}{2422}\right)$	$e\left(\frac{379}{1211}\right)$	$e\left(\frac{491}{2422}\right)$	$e\left(\frac{2281}{2422}\right)$	$e\left(\frac{887}{2422}\right)$	$e\left(\frac{1174}{1211}\right)$	$e\left(\frac{691}{1211}\right)$	$e\left(\frac{2081}{2422}\right)$	$e\left(\frac{1537}{2422}\right)$
$\chi_{10063}(7,\cdot)$	10063.u	2422	yes	$-1$	$1$	$e\left(\frac{639}{2422}\right)$	$e\left(\frac{124}{1211}\right)$	$e\left(\frac{639}{1211}\right)$	$e\left(\frac{1927}{2422}\right)$	$e\left(\frac{887}{2422}\right)$	$e\left(\frac{1291}{2422}\right)$	$e\left(\frac{1917}{2422}\right)$	$e\left(\frac{248}{1211}\right)$	$e\left(\frac{72}{1211}\right)$	$e\left(\frac{1096}{1211}\right)$
$\chi_{10063}(8,\cdot)$	10063.x	4844	yes	$1$	$1$	$e\left(\frac{561}{4844}\right)$	$e\left(\frac{4135}{4844}\right)$	$e\left(\frac{561}{2422}\right)$	$e\left(\frac{919}{1211}\right)$	$e\left(\frac{1174}{1211}\right)$	$e\left(\frac{1917}{2422}\right)$	$e\left(\frac{1683}{4844}\right)$	$e\left(\frac{1713}{2422}\right)$	$e\left(\frac{4237}{4844}\right)$	$e\left(\frac{179}{4844}\right)$
$\chi_{10063}(9,\cdot)$	10063.t	2422	yes	$1$	$1$	$e\left(\frac{571}{2422}\right)$	$e\left(\frac{811}{2422}\right)$	$e\left(\frac{571}{1211}\right)$	$e\left(\frac{282}{1211}\right)$	$e\left(\frac{691}{1211}\right)$	$e\left(\frac{248}{1211}\right)$	$e\left(\frac{1713}{2422}\right)$	$e\left(\frac{811}{1211}\right)$	$e\left(\frac{1135}{2422}\right)$	$e\left(\frac{2207}{2422}\right)$
$\chi_{10063}(10,\cdot)$	10063.w	4844	yes	$-1$	$1$	$e\left(\frac{3027}{4844}\right)$	$e\left(\frac{1135}{4844}\right)$	$e\left(\frac{605}{2422}\right)$	$e\left(\frac{1531}{2422}\right)$	$e\left(\frac{2081}{2422}\right)$	$e\left(\frac{72}{1211}\right)$	$e\left(\frac{4237}{4844}\right)$	$e\left(\frac{1135}{2422}\right)$	$e\left(\frac{1245}{4844}\right)$	$e\left(\frac{383}{4844}\right)$
$\chi_{10063}(11,\cdot)$	10063.w	4844	yes	$-1$	$1$	$e\left(\frac{3289}{4844}\right)$	$e\left(\frac{4629}{4844}\right)$	$e\left(\frac{867}{2422}\right)$	$e\left(\frac{969}{2422}\right)$	$e\left(\frac{1537}{2422}\right)$	$e\left(\frac{1096}{1211}\right)$	$e\left(\frac{179}{4844}\right)$	$e\left(\frac{2207}{2422}\right)$	$e\left(\frac{383}{4844}\right)$	$e\left(\frac{717}{4844}\right)$
$\chi_{10063}(12,\cdot)$	10063.r	692	yes	$-1$	$1$	$e\left(\frac{481}{692}\right)$	$e\left(\frac{625}{692}\right)$	$e\left(\frac{135}{346}\right)$	$e\left(\frac{273}{346}\right)$	$e\left(\frac{207}{346}\right)$	$e\left(\frac{109}{173}\right)$	$e\left(\frac{59}{692}\right)$	$e\left(\frac{279}{346}\right)$	$e\left(\frac{335}{692}\right)$	$e\left(\frac{217}{692}\right)$
$\chi_{10063}(13,\cdot)$	10063.t	2422	yes	$1$	$1$	$e\left(\frac{801}{2422}\right)$	$e\left(\frac{1863}{2422}\right)$	$e\left(\frac{801}{1211}\right)$	$e\left(\frac{824}{1211}\right)$	$e\left(\frac{121}{1211}\right)$	$e\left(\frac{613}{1211}\right)$	$e\left(\frac{2403}{2422}\right)$	$e\left(\frac{652}{1211}\right)$	$e\left(\frac{27}{2422}\right)$	$e\left(\frac{411}{2422}\right)$
$\chi_{10063}(14,\cdot)$	10063.w	4844	yes	$-1$	$1$	$e\left(\frac{1465}{4844}\right)$	$e\left(\frac{3489}{4844}\right)$	$e\left(\frac{1465}{2422}\right)$	$e\left(\frac{925}{2422}\right)$	$e\left(\frac{55}{2422}\right)$	$e\left(\frac{965}{1211}\right)$	$e\left(\frac{4395}{4844}\right)$	$e\left(\frac{1067}{2422}\right)$	$e\left(\frac{3315}{4844}\right)$	$e\left(\frac{2829}{4844}\right)$
$\chi_{10063}(15,\cdot)$	10063.x	4844	yes	$1$	$1$	$e\left(\frac{989}{4844}\right)$	$e\left(\frac{1375}{4844}\right)$	$e\left(\frac{989}{2422}\right)$	$e\left(\frac{802}{1211}\right)$	$e\left(\frac{591}{1211}\right)$	$e\left(\frac{2175}{2422}\right)$	$e\left(\frac{2967}{4844}\right)$	$e\left(\frac{1375}{2422}\right)$	$e\left(\frac{4197}{4844}\right)$	$e\left(\frac{1723}{4844}\right)$
$\chi_{10063}(16,\cdot)$	10063.s	1211	yes	$1$	$1$	$e\left(\frac{187}{1211}\right)$	$e\left(\frac{571}{1211}\right)$	$e\left(\frac{374}{1211}\right)$	$e\left(\frac{418}{1211}\right)$	$e\left(\frac{758}{1211}\right)$	$e\left(\frac{67}{1211}\right)$	$e\left(\frac{561}{1211}\right)$	$e\left(\frac{1142}{1211}\right)$	$e\left(\frac{605}{1211}\right)$	$e\left(\frac{867}{1211}\right)$
$\chi_{10063}(17,\cdot)$	10063.q	692	yes	$1$	$1$	$e\left(\frac{193}{692}\right)$	$e\left(\frac{99}{692}\right)$	$e\left(\frac{193}{346}\right)$	$e\left(\frac{1}{173}\right)$	$e\left(\frac{73}{173}\right)$	$e\left(\frac{295}{346}\right)$	$e\left(\frac{579}{692}\right)$	$e\left(\frac{99}{346}\right)$	$e\left(\frac{197}{692}\right)$	$e\left(\frac{423}{692}\right)$
$\chi_{10063}(18,\cdot)$	10063.x	4844	yes	$1$	$1$	$e\left(\frac{1329}{4844}\right)$	$e\left(\frac{4615}{4844}\right)$	$e\left(\frac{1329}{2422}\right)$	$e\left(\frac{992}{1211}\right)$	$e\left(\frac{275}{1211}\right)$	$e\left(\frac{1135}{2422}\right)$	$e\left(\frac{3987}{4844}\right)$	$e\left(\frac{2193}{2422}\right)$	$e\left(\frac{453}{4844}\right)$	$e\left(\frac{2859}{4844}\right)$
$\chi_{10063}(19,\cdot)$	10063.x	4844	yes	$1$	$1$	$e\left(\frac{3587}{4844}\right)$	$e\left(\frac{1485}{4844}\right)$	$e\left(\frac{1165}{2422}\right)$	$e\left(\frac{188}{1211}\right)$	$e\left(\frac{57}{1211}\right)$	$e\left(\frac{2349}{2422}\right)$	$e\left(\frac{1073}{4844}\right)$	$e\left(\frac{1485}{2422}\right)$	$e\left(\frac{4339}{4844}\right)$	$e\left(\frac{117}{4844}\right)$
$\chi_{10063}(20,\cdot)$	10063.u	2422	yes	$-1$	$1$	$e\left(\frac{1607}{2422}\right)$	$e\left(\frac{1032}{1211}\right)$	$e\left(\frac{396}{1211}\right)$	$e\left(\frac{529}{2422}\right)$	$e\left(\frac{1249}{2422}\right)$	$e\left(\frac{783}{2422}\right)$	$e\left(\frac{2399}{2422}\right)$	$e\left(\frac{853}{1211}\right)$	$e\left(\frac{1068}{1211}\right)$	$e\left(\frac{918}{1211}\right)$
$\chi_{10063}(21,\cdot)$	10063.x	4844	yes	$1$	$1$	$e\left(\frac{4271}{4844}\right)$	$e\left(\frac{3729}{4844}\right)$	$e\left(\frac{1849}{2422}\right)$	$e\left(\frac{499}{1211}\right)$	$e\left(\frac{789}{1211}\right)$	$e\left(\frac{1539}{2422}\right)$	$e\left(\frac{3125}{4844}\right)$	$e\left(\frac{1307}{2422}\right)$	$e\left(\frac{1423}{4844}\right)$	$e\left(\frac{4169}{4844}\right)$
$\chi_{10063}(22,\cdot)$	10063.v	2422	yes	$-1$	$1$	$e\left(\frac{869}{1211}\right)$	$e\left(\frac{1389}{2422}\right)$	$e\left(\frac{527}{1211}\right)$	$e\left(\frac{2389}{2422}\right)$	$e\left(\frac{705}{2422}\right)$	$e\left(\frac{409}{2422}\right)$	$e\left(\frac{185}{1211}\right)$	$e\left(\frac{178}{1211}\right)$	$e\left(\frac{1705}{2422}\right)$	$e\left(\frac{2003}{2422}\right)$
$\chi_{10063}(23,\cdot)$	10063.u	2422	yes	$-1$	$1$	$e\left(\frac{2367}{2422}\right)$	$e\left(\frac{664}{1211}\right)$	$e\left(\frac{1156}{1211}\right)$	$e\left(\frac{1373}{2422}\right)$	$e\left(\frac{1273}{2422}\right)$	$e\left(\frac{1405}{2422}\right)$	$e\left(\frac{2257}{2422}\right)$	$e\left(\frac{117}{1211}\right)$	$e\left(\frac{659}{1211}\right)$	$e\left(\frac{478}{1211}\right)$
$\chi_{10063}(24,\cdot)$	10063.u	2422	yes	$-1$	$1$	$e\left(\frac{1777}{2422}\right)$	$e\left(\frac{631}{1211}\right)$	$e\left(\frac{566}{1211}\right)$	$e\left(\frac{909}{2422}\right)$	$e\left(\frac{617}{2422}\right)$	$e\left(\frac{2165}{2422}\right)$	$e\left(\frac{487}{2422}\right)$	$e\left(\frac{51}{1211}\right)$	$e\left(\frac{132}{1211}\right)$	$e\left(\frac{1202}{1211}\right)$
$\chi_{10063}(25,\cdot)$	10063.s	1211	yes	$1$	$1$	$e\left(\frac{209}{1211}\right)$	$e\left(\frac{282}{1211}\right)$	$e\left(\frac{418}{1211}\right)$	$e\left(\frac{111}{1211}\right)$	$e\left(\frac{491}{1211}\right)$	$e\left(\frac{716}{1211}\right)$	$e\left(\frac{627}{1211}\right)$	$e\left(\frac{564}{1211}\right)$	$e\left(\frac{320}{1211}\right)$	$e\left(\frac{969}{1211}\right)$
$\chi_{10063}(26,\cdot)$	10063.x	4844	yes	$1$	$1$	$e\left(\frac{1789}{4844}\right)$	$e\left(\frac{1875}{4844}\right)$	$e\left(\frac{1789}{2422}\right)$	$e\left(\frac{323}{1211}\right)$	$e\left(\frac{916}{1211}\right)$	$e\left(\frac{1865}{2422}\right)$	$e\left(\frac{523}{4844}\right)$	$e\left(\frac{1875}{2422}\right)$	$e\left(\frac{3081}{4844}\right)$	$e\left(\frac{4111}{4844}\right)$
$\chi_{10063}(27,\cdot)$	10063.w	4844	yes	$-1$	$1$	$e\left(\frac{4135}{4844}\right)$	$e\left(\frac{11}{4844}\right)$	$e\left(\frac{1713}{2422}\right)$	$e\left(\frac{2057}{2422}\right)$	$e\left(\frac{2073}{2422}\right)$	$e\left(\frac{372}{1211}\right)$	$e\left(\frac{2717}{4844}\right)$	$e\left(\frac{11}{2422}\right)$	$e\left(\frac{3405}{4844}\right)$	$e\left(\frac{4199}{4844}\right)$
$\chi_{10063}(28,\cdot)$	10063.n	346	yes	$-1$	$1$	$e\left(\frac{59}{173}\right)$	$e\left(\frac{117}{346}\right)$	$e\left(\frac{118}{173}\right)$	$e\left(\frac{335}{346}\right)$	$e\left(\frac{235}{346}\right)$	$e\left(\frac{21}{346}\right)$	$e\left(\frac{4}{173}\right)$	$e\left(\frac{117}{173}\right)$	$e\left(\frac{107}{346}\right)$	$e\left(\frac{91}{346}\right)$
$\chi_{10063}(30,\cdot)$	10063.m	173	no	$1$	$1$	$e\left(\frac{42}{173}\right)$	$e\left(\frac{156}{173}\right)$	$e\left(\frac{84}{173}\right)$	$e\left(\frac{43}{173}\right)$	$e\left(\frac{25}{173}\right)$	$e\left(\frac{28}{173}\right)$	$e\left(\frac{126}{173}\right)$	$e\left(\frac{139}{173}\right)$	$e\left(\frac{85}{173}\right)$	$e\left(\frac{6}{173}\right)$
$\chi_{10063}(31,\cdot)$	10063.w	4844	yes	$-1$	$1$	$e\left(\frac{929}{4844}\right)$	$e\left(\frac{4365}{4844}\right)$	$e\left(\frac{929}{2422}\right)$	$e\left(\frac{41}{2422}\right)$	$e\left(\frac{225}{2422}\right)$	$e\left(\frac{645}{1211}\right)$	$e\left(\frac{2787}{4844}\right)$	$e\left(\frac{1943}{2422}\right)$	$e\left(\frac{1011}{4844}\right)$	$e\left(\frac{1665}{4844}\right)$
$\chi_{10063}(32,\cdot)$	10063.x	4844	yes	$1$	$1$	$e\left(\frac{935}{4844}\right)$	$e\left(\frac{433}{4844}\right)$	$e\left(\frac{935}{2422}\right)$	$e\left(\frac{1128}{1211}\right)$	$e\left(\frac{342}{1211}\right)$	$e\left(\frac{773}{2422}\right)$	$e\left(\frac{2805}{4844}\right)$	$e\left(\frac{433}{2422}\right)$	$e\left(\frac{603}{4844}\right)$	$e\left(\frac{1913}{4844}\right)$
$\chi_{10063}(33,\cdot)$	10063.t	2422	yes	$1$	$1$	$e\left(\frac{719}{2422}\right)$	$e\left(\frac{1509}{2422}\right)$	$e\left(\frac{719}{1211}\right)$	$e\left(\frac{20}{1211}\right)$	$e\left(\frac{1114}{1211}\right)$	$e\left(\frac{9}{1211}\right)$	$e\left(\frac{2157}{2422}\right)$	$e\left(\frac{298}{1211}\right)$	$e\left(\frac{759}{2422}\right)$	$e\left(\frac{251}{2422}\right)$

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Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Modulus	$10063$
Structure	\(C_{2}\times C_{4844}\)
Order	$9688$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\(\chi_{10063}(1,\cdot)\)	10063.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{10063}(2,\cdot)\)	10063.x	4844	yes	\(1\)	\(1\)	\(e\left(\frac{187}{4844}\right)\)	\(e\left(\frac{2993}{4844}\right)\)	\(e\left(\frac{187}{2422}\right)\)	\(e\left(\frac{710}{1211}\right)\)	\(e\left(\frac{795}{1211}\right)\)	\(e\left(\frac{639}{2422}\right)\)	\(e\left(\frac{561}{4844}\right)\)	\(e\left(\frac{571}{2422}\right)\)	\(e\left(\frac{3027}{4844}\right)\)	\(e\left(\frac{3289}{4844}\right)\)
\(\chi_{10063}(3,\cdot)\)	10063.w	4844	yes	\(-1\)	\(1\)	\(e\left(\frac{2993}{4844}\right)\)	\(e\left(\frac{3233}{4844}\right)\)	\(e\left(\frac{571}{2422}\right)\)	\(e\left(\frac{1493}{2422}\right)\)	\(e\left(\frac{691}{2422}\right)\)	\(e\left(\frac{124}{1211}\right)\)	\(e\left(\frac{4135}{4844}\right)\)	\(e\left(\frac{811}{2422}\right)\)	\(e\left(\frac{1135}{4844}\right)\)	\(e\left(\frac{4629}{4844}\right)\)
\(\chi_{10063}(4,\cdot)\)	10063.t	2422	yes	\(1\)	\(1\)	\(e\left(\frac{187}{2422}\right)\)	\(e\left(\frac{571}{2422}\right)\)	\(e\left(\frac{187}{1211}\right)\)	\(e\left(\frac{209}{1211}\right)\)	\(e\left(\frac{379}{1211}\right)\)	\(e\left(\frac{639}{1211}\right)\)	\(e\left(\frac{561}{2422}\right)\)	\(e\left(\frac{571}{1211}\right)\)	\(e\left(\frac{605}{2422}\right)\)	\(e\left(\frac{867}{2422}\right)\)
\(\chi_{10063}(5,\cdot)\)	10063.v	2422	yes	\(-1\)	\(1\)	\(e\left(\frac{710}{1211}\right)\)	\(e\left(\frac{1493}{2422}\right)\)	\(e\left(\frac{209}{1211}\right)\)	\(e\left(\frac{111}{2422}\right)\)	\(e\left(\frac{491}{2422}\right)\)	\(e\left(\frac{1927}{2422}\right)\)	\(e\left(\frac{919}{1211}\right)\)	\(e\left(\frac{282}{1211}\right)\)	\(e\left(\frac{1531}{2422}\right)\)	\(e\left(\frac{969}{2422}\right)\)
\(\chi_{10063}(6,\cdot)\)	10063.v	2422	yes	\(-1\)	\(1\)	\(e\left(\frac{795}{1211}\right)\)	\(e\left(\frac{691}{2422}\right)\)	\(e\left(\frac{379}{1211}\right)\)	\(e\left(\frac{491}{2422}\right)\)	\(e\left(\frac{2281}{2422}\right)\)	\(e\left(\frac{887}{2422}\right)\)	\(e\left(\frac{1174}{1211}\right)\)	\(e\left(\frac{691}{1211}\right)\)	\(e\left(\frac{2081}{2422}\right)\)	\(e\left(\frac{1537}{2422}\right)\)
\(\chi_{10063}(7,\cdot)\)	10063.u	2422	yes	\(-1\)	\(1\)	\(e\left(\frac{639}{2422}\right)\)	\(e\left(\frac{124}{1211}\right)\)	\(e\left(\frac{639}{1211}\right)\)	\(e\left(\frac{1927}{2422}\right)\)	\(e\left(\frac{887}{2422}\right)\)	\(e\left(\frac{1291}{2422}\right)\)	\(e\left(\frac{1917}{2422}\right)\)	\(e\left(\frac{248}{1211}\right)\)	\(e\left(\frac{72}{1211}\right)\)	\(e\left(\frac{1096}{1211}\right)\)
\(\chi_{10063}(8,\cdot)\)	10063.x	4844	yes	\(1\)	\(1\)	\(e\left(\frac{561}{4844}\right)\)	\(e\left(\frac{4135}{4844}\right)\)	\(e\left(\frac{561}{2422}\right)\)	\(e\left(\frac{919}{1211}\right)\)	\(e\left(\frac{1174}{1211}\right)\)	\(e\left(\frac{1917}{2422}\right)\)	\(e\left(\frac{1683}{4844}\right)\)	\(e\left(\frac{1713}{2422}\right)\)	\(e\left(\frac{4237}{4844}\right)\)	\(e\left(\frac{179}{4844}\right)\)
\(\chi_{10063}(9,\cdot)\)	10063.t	2422	yes	\(1\)	\(1\)	\(e\left(\frac{571}{2422}\right)\)	\(e\left(\frac{811}{2422}\right)\)	\(e\left(\frac{571}{1211}\right)\)	\(e\left(\frac{282}{1211}\right)\)	\(e\left(\frac{691}{1211}\right)\)	\(e\left(\frac{248}{1211}\right)\)	\(e\left(\frac{1713}{2422}\right)\)	\(e\left(\frac{811}{1211}\right)\)	\(e\left(\frac{1135}{2422}\right)\)	\(e\left(\frac{2207}{2422}\right)\)
\(\chi_{10063}(10,\cdot)\)	10063.w	4844	yes	\(-1\)	\(1\)	\(e\left(\frac{3027}{4844}\right)\)	\(e\left(\frac{1135}{4844}\right)\)	\(e\left(\frac{605}{2422}\right)\)	\(e\left(\frac{1531}{2422}\right)\)	\(e\left(\frac{2081}{2422}\right)\)	\(e\left(\frac{72}{1211}\right)\)	\(e\left(\frac{4237}{4844}\right)\)	\(e\left(\frac{1135}{2422}\right)\)	\(e\left(\frac{1245}{4844}\right)\)	\(e\left(\frac{383}{4844}\right)\)
\(\chi_{10063}(11,\cdot)\)	10063.w	4844	yes	\(-1\)	\(1\)	\(e\left(\frac{3289}{4844}\right)\)	\(e\left(\frac{4629}{4844}\right)\)	\(e\left(\frac{867}{2422}\right)\)	\(e\left(\frac{969}{2422}\right)\)	\(e\left(\frac{1537}{2422}\right)\)	\(e\left(\frac{1096}{1211}\right)\)	\(e\left(\frac{179}{4844}\right)\)	\(e\left(\frac{2207}{2422}\right)\)	\(e\left(\frac{383}{4844}\right)\)	\(e\left(\frac{717}{4844}\right)\)
\(\chi_{10063}(12,\cdot)\)	10063.r	692	yes	\(-1\)	\(1\)	\(e\left(\frac{481}{692}\right)\)	\(e\left(\frac{625}{692}\right)\)	\(e\left(\frac{135}{346}\right)\)	\(e\left(\frac{273}{346}\right)\)	\(e\left(\frac{207}{346}\right)\)	\(e\left(\frac{109}{173}\right)\)	\(e\left(\frac{59}{692}\right)\)	\(e\left(\frac{279}{346}\right)\)	\(e\left(\frac{335}{692}\right)\)	\(e\left(\frac{217}{692}\right)\)
\(\chi_{10063}(13,\cdot)\)	10063.t	2422	yes	\(1\)	\(1\)	\(e\left(\frac{801}{2422}\right)\)	\(e\left(\frac{1863}{2422}\right)\)	\(e\left(\frac{801}{1211}\right)\)	\(e\left(\frac{824}{1211}\right)\)	\(e\left(\frac{121}{1211}\right)\)	\(e\left(\frac{613}{1211}\right)\)	\(e\left(\frac{2403}{2422}\right)\)	\(e\left(\frac{652}{1211}\right)\)	\(e\left(\frac{27}{2422}\right)\)	\(e\left(\frac{411}{2422}\right)\)
\(\chi_{10063}(14,\cdot)\)	10063.w	4844	yes	\(-1\)	\(1\)	\(e\left(\frac{1465}{4844}\right)\)	\(e\left(\frac{3489}{4844}\right)\)	\(e\left(\frac{1465}{2422}\right)\)	\(e\left(\frac{925}{2422}\right)\)	\(e\left(\frac{55}{2422}\right)\)	\(e\left(\frac{965}{1211}\right)\)	\(e\left(\frac{4395}{4844}\right)\)	\(e\left(\frac{1067}{2422}\right)\)	\(e\left(\frac{3315}{4844}\right)\)	\(e\left(\frac{2829}{4844}\right)\)
\(\chi_{10063}(15,\cdot)\)	10063.x	4844	yes	\(1\)	\(1\)	\(e\left(\frac{989}{4844}\right)\)	\(e\left(\frac{1375}{4844}\right)\)	\(e\left(\frac{989}{2422}\right)\)	\(e\left(\frac{802}{1211}\right)\)	\(e\left(\frac{591}{1211}\right)\)	\(e\left(\frac{2175}{2422}\right)\)	\(e\left(\frac{2967}{4844}\right)\)	\(e\left(\frac{1375}{2422}\right)\)	\(e\left(\frac{4197}{4844}\right)\)	\(e\left(\frac{1723}{4844}\right)\)
\(\chi_{10063}(16,\cdot)\)	10063.s	1211	yes	\(1\)	\(1\)	\(e\left(\frac{187}{1211}\right)\)	\(e\left(\frac{571}{1211}\right)\)	\(e\left(\frac{374}{1211}\right)\)	\(e\left(\frac{418}{1211}\right)\)	\(e\left(\frac{758}{1211}\right)\)	\(e\left(\frac{67}{1211}\right)\)	\(e\left(\frac{561}{1211}\right)\)	\(e\left(\frac{1142}{1211}\right)\)	\(e\left(\frac{605}{1211}\right)\)	\(e\left(\frac{867}{1211}\right)\)
\(\chi_{10063}(17,\cdot)\)	10063.q	692	yes	\(1\)	\(1\)	\(e\left(\frac{193}{692}\right)\)	\(e\left(\frac{99}{692}\right)\)	\(e\left(\frac{193}{346}\right)\)	\(e\left(\frac{1}{173}\right)\)	\(e\left(\frac{73}{173}\right)\)	\(e\left(\frac{295}{346}\right)\)	\(e\left(\frac{579}{692}\right)\)	\(e\left(\frac{99}{346}\right)\)	\(e\left(\frac{197}{692}\right)\)	\(e\left(\frac{423}{692}\right)\)
\(\chi_{10063}(18,\cdot)\)	10063.x	4844	yes	\(1\)	\(1\)	\(e\left(\frac{1329}{4844}\right)\)	\(e\left(\frac{4615}{4844}\right)\)	\(e\left(\frac{1329}{2422}\right)\)	\(e\left(\frac{992}{1211}\right)\)	\(e\left(\frac{275}{1211}\right)\)	\(e\left(\frac{1135}{2422}\right)\)	\(e\left(\frac{3987}{4844}\right)\)	\(e\left(\frac{2193}{2422}\right)\)	\(e\left(\frac{453}{4844}\right)\)	\(e\left(\frac{2859}{4844}\right)\)
\(\chi_{10063}(19,\cdot)\)	10063.x	4844	yes	\(1\)	\(1\)	\(e\left(\frac{3587}{4844}\right)\)	\(e\left(\frac{1485}{4844}\right)\)	\(e\left(\frac{1165}{2422}\right)\)	\(e\left(\frac{188}{1211}\right)\)	\(e\left(\frac{57}{1211}\right)\)	\(e\left(\frac{2349}{2422}\right)\)	\(e\left(\frac{1073}{4844}\right)\)	\(e\left(\frac{1485}{2422}\right)\)	\(e\left(\frac{4339}{4844}\right)\)	\(e\left(\frac{117}{4844}\right)\)
\(\chi_{10063}(20,\cdot)\)	10063.u	2422	yes	\(-1\)	\(1\)	\(e\left(\frac{1607}{2422}\right)\)	\(e\left(\frac{1032}{1211}\right)\)	\(e\left(\frac{396}{1211}\right)\)	\(e\left(\frac{529}{2422}\right)\)	\(e\left(\frac{1249}{2422}\right)\)	\(e\left(\frac{783}{2422}\right)\)	\(e\left(\frac{2399}{2422}\right)\)	\(e\left(\frac{853}{1211}\right)\)	\(e\left(\frac{1068}{1211}\right)\)	\(e\left(\frac{918}{1211}\right)\)
\(\chi_{10063}(21,\cdot)\)	10063.x	4844	yes	\(1\)	\(1\)	\(e\left(\frac{4271}{4844}\right)\)	\(e\left(\frac{3729}{4844}\right)\)	\(e\left(\frac{1849}{2422}\right)\)	\(e\left(\frac{499}{1211}\right)\)	\(e\left(\frac{789}{1211}\right)\)	\(e\left(\frac{1539}{2422}\right)\)	\(e\left(\frac{3125}{4844}\right)\)	\(e\left(\frac{1307}{2422}\right)\)	\(e\left(\frac{1423}{4844}\right)\)	\(e\left(\frac{4169}{4844}\right)\)
\(\chi_{10063}(22,\cdot)\)	10063.v	2422	yes	\(-1\)	\(1\)	\(e\left(\frac{869}{1211}\right)\)	\(e\left(\frac{1389}{2422}\right)\)	\(e\left(\frac{527}{1211}\right)\)	\(e\left(\frac{2389}{2422}\right)\)	\(e\left(\frac{705}{2422}\right)\)	\(e\left(\frac{409}{2422}\right)\)	\(e\left(\frac{185}{1211}\right)\)	\(e\left(\frac{178}{1211}\right)\)	\(e\left(\frac{1705}{2422}\right)\)	\(e\left(\frac{2003}{2422}\right)\)
\(\chi_{10063}(23,\cdot)\)	10063.u	2422	yes	\(-1\)	\(1\)	\(e\left(\frac{2367}{2422}\right)\)	\(e\left(\frac{664}{1211}\right)\)	\(e\left(\frac{1156}{1211}\right)\)	\(e\left(\frac{1373}{2422}\right)\)	\(e\left(\frac{1273}{2422}\right)\)	\(e\left(\frac{1405}{2422}\right)\)	\(e\left(\frac{2257}{2422}\right)\)	\(e\left(\frac{117}{1211}\right)\)	\(e\left(\frac{659}{1211}\right)\)	\(e\left(\frac{478}{1211}\right)\)
\(\chi_{10063}(24,\cdot)\)	10063.u	2422	yes	\(-1\)	\(1\)	\(e\left(\frac{1777}{2422}\right)\)	\(e\left(\frac{631}{1211}\right)\)	\(e\left(\frac{566}{1211}\right)\)	\(e\left(\frac{909}{2422}\right)\)	\(e\left(\frac{617}{2422}\right)\)	\(e\left(\frac{2165}{2422}\right)\)	\(e\left(\frac{487}{2422}\right)\)	\(e\left(\frac{51}{1211}\right)\)	\(e\left(\frac{132}{1211}\right)\)	\(e\left(\frac{1202}{1211}\right)\)
\(\chi_{10063}(25,\cdot)\)	10063.s	1211	yes	\(1\)	\(1\)	\(e\left(\frac{209}{1211}\right)\)	\(e\left(\frac{282}{1211}\right)\)	\(e\left(\frac{418}{1211}\right)\)	\(e\left(\frac{111}{1211}\right)\)	\(e\left(\frac{491}{1211}\right)\)	\(e\left(\frac{716}{1211}\right)\)	\(e\left(\frac{627}{1211}\right)\)	\(e\left(\frac{564}{1211}\right)\)	\(e\left(\frac{320}{1211}\right)\)	\(e\left(\frac{969}{1211}\right)\)
\(\chi_{10063}(26,\cdot)\)	10063.x	4844	yes	\(1\)	\(1\)	\(e\left(\frac{1789}{4844}\right)\)	\(e\left(\frac{1875}{4844}\right)\)	\(e\left(\frac{1789}{2422}\right)\)	\(e\left(\frac{323}{1211}\right)\)	\(e\left(\frac{916}{1211}\right)\)	\(e\left(\frac{1865}{2422}\right)\)	\(e\left(\frac{523}{4844}\right)\)	\(e\left(\frac{1875}{2422}\right)\)	\(e\left(\frac{3081}{4844}\right)\)	\(e\left(\frac{4111}{4844}\right)\)
\(\chi_{10063}(27,\cdot)\)	10063.w	4844	yes	\(-1\)	\(1\)	\(e\left(\frac{4135}{4844}\right)\)	\(e\left(\frac{11}{4844}\right)\)	\(e\left(\frac{1713}{2422}\right)\)	\(e\left(\frac{2057}{2422}\right)\)	\(e\left(\frac{2073}{2422}\right)\)	\(e\left(\frac{372}{1211}\right)\)	\(e\left(\frac{2717}{4844}\right)\)	\(e\left(\frac{11}{2422}\right)\)	\(e\left(\frac{3405}{4844}\right)\)	\(e\left(\frac{4199}{4844}\right)\)
\(\chi_{10063}(28,\cdot)\)	10063.n	346	yes	\(-1\)	\(1\)	\(e\left(\frac{59}{173}\right)\)	\(e\left(\frac{117}{346}\right)\)	\(e\left(\frac{118}{173}\right)\)	\(e\left(\frac{335}{346}\right)\)	\(e\left(\frac{235}{346}\right)\)	\(e\left(\frac{21}{346}\right)\)	\(e\left(\frac{4}{173}\right)\)	\(e\left(\frac{117}{173}\right)\)	\(e\left(\frac{107}{346}\right)\)	\(e\left(\frac{91}{346}\right)\)
\(\chi_{10063}(30,\cdot)\)	10063.m	173	no	\(1\)	\(1\)	\(e\left(\frac{42}{173}\right)\)	\(e\left(\frac{156}{173}\right)\)	\(e\left(\frac{84}{173}\right)\)	\(e\left(\frac{43}{173}\right)\)	\(e\left(\frac{25}{173}\right)\)	\(e\left(\frac{28}{173}\right)\)	\(e\left(\frac{126}{173}\right)\)	\(e\left(\frac{139}{173}\right)\)	\(e\left(\frac{85}{173}\right)\)	\(e\left(\frac{6}{173}\right)\)
\(\chi_{10063}(31,\cdot)\)	10063.w	4844	yes	\(-1\)	\(1\)	\(e\left(\frac{929}{4844}\right)\)	\(e\left(\frac{4365}{4844}\right)\)	\(e\left(\frac{929}{2422}\right)\)	\(e\left(\frac{41}{2422}\right)\)	\(e\left(\frac{225}{2422}\right)\)	\(e\left(\frac{645}{1211}\right)\)	\(e\left(\frac{2787}{4844}\right)\)	\(e\left(\frac{1943}{2422}\right)\)	\(e\left(\frac{1011}{4844}\right)\)	\(e\left(\frac{1665}{4844}\right)\)
\(\chi_{10063}(32,\cdot)\)	10063.x	4844	yes	\(1\)	\(1\)	\(e\left(\frac{935}{4844}\right)\)	\(e\left(\frac{433}{4844}\right)\)	\(e\left(\frac{935}{2422}\right)\)	\(e\left(\frac{1128}{1211}\right)\)	\(e\left(\frac{342}{1211}\right)\)	\(e\left(\frac{773}{2422}\right)\)	\(e\left(\frac{2805}{4844}\right)\)	\(e\left(\frac{433}{2422}\right)\)	\(e\left(\frac{603}{4844}\right)\)	\(e\left(\frac{1913}{4844}\right)\)
\(\chi_{10063}(33,\cdot)\)	10063.t	2422	yes	\(1\)	\(1\)	\(e\left(\frac{719}{2422}\right)\)	\(e\left(\frac{1509}{2422}\right)\)	\(e\left(\frac{719}{1211}\right)\)	\(e\left(\frac{20}{1211}\right)\)	\(e\left(\frac{1114}{1211}\right)\)	\(e\left(\frac{9}{1211}\right)\)	\(e\left(\frac{2157}{2422}\right)\)	\(e\left(\frac{298}{1211}\right)\)	\(e\left(\frac{759}{2422}\right)\)	\(e\left(\frac{251}{2422}\right)\)

Introduction

L-functions

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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.