LMFDB - Group of Dirichlet characters of modulus 8014

Show commands: PariGP / SageMath

sage: H = DirichletGroup(8014)

pari: g = idealstar(,8014,2)

Character group

sage: G.order() pari: g.no
Order	=	4006
sage: H.invariants() pari: g.cyc
Structure	=	$C_{4006}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{8014}(5,\cdot)$

First 32 of 4006 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	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$17$	$19$	$21$
$\chi_{8014}(1,\cdot)$	8014.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{8014}(3,\cdot)$	8014.c	2003	no	$1$	$1$	$e\left(\frac{670}{2003}\right)$	$e\left(\frac{847}{2003}\right)$	$e\left(\frac{1729}{2003}\right)$	$e\left(\frac{1340}{2003}\right)$	$e\left(\frac{833}{2003}\right)$	$e\left(\frac{1237}{2003}\right)$	$e\left(\frac{1517}{2003}\right)$	$e\left(\frac{1372}{2003}\right)$	$e\left(\frac{692}{2003}\right)$	$e\left(\frac{396}{2003}\right)$
$\chi_{8014}(5,\cdot)$	8014.d	4006	no	$-1$	$1$	$e\left(\frac{847}{2003}\right)$	$e\left(\frac{1}{4006}\right)$	$e\left(\frac{688}{2003}\right)$	$e\left(\frac{1694}{2003}\right)$	$e\left(\frac{1855}{4006}\right)$	$e\left(\frac{359}{2003}\right)$	$e\left(\frac{1695}{4006}\right)$	$e\left(\frac{581}{4006}\right)$	$e\left(\frac{3645}{4006}\right)$	$e\left(\frac{1535}{2003}\right)$
$\chi_{8014}(7,\cdot)$	8014.c	2003	no	$1$	$1$	$e\left(\frac{1729}{2003}\right)$	$e\left(\frac{688}{2003}\right)$	$e\left(\frac{1272}{2003}\right)$	$e\left(\frac{1455}{2003}\right)$	$e\left(\frac{329}{2003}\right)$	$e\left(\frac{1246}{2003}\right)$	$e\left(\frac{414}{2003}\right)$	$e\left(\frac{1131}{2003}\right)$	$e\left(\frac{4}{2003}\right)$	$e\left(\frac{998}{2003}\right)$
$\chi_{8014}(9,\cdot)$	8014.c	2003	no	$1$	$1$	$e\left(\frac{1340}{2003}\right)$	$e\left(\frac{1694}{2003}\right)$	$e\left(\frac{1455}{2003}\right)$	$e\left(\frac{677}{2003}\right)$	$e\left(\frac{1666}{2003}\right)$	$e\left(\frac{471}{2003}\right)$	$e\left(\frac{1031}{2003}\right)$	$e\left(\frac{741}{2003}\right)$	$e\left(\frac{1384}{2003}\right)$	$e\left(\frac{792}{2003}\right)$
$\chi_{8014}(11,\cdot)$	8014.d	4006	no	$-1$	$1$	$e\left(\frac{833}{2003}\right)$	$e\left(\frac{1855}{4006}\right)$	$e\left(\frac{329}{2003}\right)$	$e\left(\frac{1666}{2003}\right)$	$e\left(\frac{3877}{4006}\right)$	$e\left(\frac{949}{2003}\right)$	$e\left(\frac{3521}{4006}\right)$	$e\left(\frac{141}{4006}\right)$	$e\left(\frac{3353}{4006}\right)$	$e\left(\frac{1162}{2003}\right)$
$\chi_{8014}(13,\cdot)$	8014.c	2003	no	$1$	$1$	$e\left(\frac{1237}{2003}\right)$	$e\left(\frac{359}{2003}\right)$	$e\left(\frac{1246}{2003}\right)$	$e\left(\frac{471}{2003}\right)$	$e\left(\frac{949}{2003}\right)$	$e\left(\frac{1378}{2003}\right)$	$e\left(\frac{1596}{2003}\right)$	$e\left(\frac{267}{2003}\right)$	$e\left(\frac{596}{2003}\right)$	$e\left(\frac{480}{2003}\right)$
$\chi_{8014}(15,\cdot)$	8014.d	4006	no	$-1$	$1$	$e\left(\frac{1517}{2003}\right)$	$e\left(\frac{1695}{4006}\right)$	$e\left(\frac{414}{2003}\right)$	$e\left(\frac{1031}{2003}\right)$	$e\left(\frac{3521}{4006}\right)$	$e\left(\frac{1596}{2003}\right)$	$e\left(\frac{723}{4006}\right)$	$e\left(\frac{3325}{4006}\right)$	$e\left(\frac{1023}{4006}\right)$	$e\left(\frac{1931}{2003}\right)$
$\chi_{8014}(17,\cdot)$	8014.d	4006	no	$-1$	$1$	$e\left(\frac{1372}{2003}\right)$	$e\left(\frac{581}{4006}\right)$	$e\left(\frac{1131}{2003}\right)$	$e\left(\frac{741}{2003}\right)$	$e\left(\frac{141}{4006}\right)$	$e\left(\frac{267}{2003}\right)$	$e\left(\frac{3325}{4006}\right)$	$e\left(\frac{1057}{4006}\right)$	$e\left(\frac{2577}{4006}\right)$	$e\left(\frac{500}{2003}\right)$
$\chi_{8014}(19,\cdot)$	8014.d	4006	no	$-1$	$1$	$e\left(\frac{692}{2003}\right)$	$e\left(\frac{3645}{4006}\right)$	$e\left(\frac{4}{2003}\right)$	$e\left(\frac{1384}{2003}\right)$	$e\left(\frac{3353}{4006}\right)$	$e\left(\frac{596}{2003}\right)$	$e\left(\frac{1023}{4006}\right)$	$e\left(\frac{2577}{4006}\right)$	$e\left(\frac{2129}{4006}\right)$	$e\left(\frac{696}{2003}\right)$
$\chi_{8014}(21,\cdot)$	8014.c	2003	no	$1$	$1$	$e\left(\frac{396}{2003}\right)$	$e\left(\frac{1535}{2003}\right)$	$e\left(\frac{998}{2003}\right)$	$e\left(\frac{792}{2003}\right)$	$e\left(\frac{1162}{2003}\right)$	$e\left(\frac{480}{2003}\right)$	$e\left(\frac{1931}{2003}\right)$	$e\left(\frac{500}{2003}\right)$	$e\left(\frac{696}{2003}\right)$	$e\left(\frac{1394}{2003}\right)$
$\chi_{8014}(23,\cdot)$	8014.c	2003	no	$1$	$1$	$e\left(\frac{1360}{2003}\right)$	$e\left(\frac{942}{2003}\right)$	$e\left(\frac{251}{2003}\right)$	$e\left(\frac{717}{2003}\right)$	$e\left(\frac{794}{2003}\right)$	$e\left(\frac{1345}{2003}\right)$	$e\left(\frac{299}{2003}\right)$	$e\left(\frac{483}{2003}\right)$	$e\left(\frac{448}{2003}\right)$	$e\left(\frac{1611}{2003}\right)$
$\chi_{8014}(25,\cdot)$	8014.c	2003	no	$1$	$1$	$e\left(\frac{1694}{2003}\right)$	$e\left(\frac{1}{2003}\right)$	$e\left(\frac{1376}{2003}\right)$	$e\left(\frac{1385}{2003}\right)$	$e\left(\frac{1855}{2003}\right)$	$e\left(\frac{718}{2003}\right)$	$e\left(\frac{1695}{2003}\right)$	$e\left(\frac{581}{2003}\right)$	$e\left(\frac{1642}{2003}\right)$	$e\left(\frac{1067}{2003}\right)$
$\chi_{8014}(27,\cdot)$	8014.c	2003	no	$1$	$1$	$e\left(\frac{7}{2003}\right)$	$e\left(\frac{538}{2003}\right)$	$e\left(\frac{1181}{2003}\right)$	$e\left(\frac{14}{2003}\right)$	$e\left(\frac{496}{2003}\right)$	$e\left(\frac{1708}{2003}\right)$	$e\left(\frac{545}{2003}\right)$	$e\left(\frac{110}{2003}\right)$	$e\left(\frac{73}{2003}\right)$	$e\left(\frac{1188}{2003}\right)$
$\chi_{8014}(29,\cdot)$	8014.c	2003	no	$1$	$1$	$e\left(\frac{1383}{2003}\right)$	$e\left(\frac{1279}{2003}\right)$	$e\left(\frac{1270}{2003}\right)$	$e\left(\frac{763}{2003}\right)$	$e\left(\frac{993}{2003}\right)$	$e\left(\frac{948}{2003}\right)$	$e\left(\frac{659}{2003}\right)$	$e\left(\frac{1989}{2003}\right)$	$e\left(\frac{974}{2003}\right)$	$e\left(\frac{650}{2003}\right)$
$\chi_{8014}(31,\cdot)$	8014.d	4006	no	$-1$	$1$	$e\left(\frac{1842}{2003}\right)$	$e\left(\frac{1291}{4006}\right)$	$e\left(\frac{879}{2003}\right)$	$e\left(\frac{1681}{2003}\right)$	$e\left(\frac{3223}{4006}\right)$	$e\left(\frac{776}{2003}\right)$	$e\left(\frac{969}{4006}\right)$	$e\left(\frac{949}{4006}\right)$	$e\left(\frac{2651}{4006}\right)$	$e\left(\frac{718}{2003}\right)$
$\chi_{8014}(33,\cdot)$	8014.d	4006	no	$-1$	$1$	$e\left(\frac{1503}{2003}\right)$	$e\left(\frac{3549}{4006}\right)$	$e\left(\frac{55}{2003}\right)$	$e\left(\frac{1003}{2003}\right)$	$e\left(\frac{1537}{4006}\right)$	$e\left(\frac{183}{2003}\right)$	$e\left(\frac{2549}{4006}\right)$	$e\left(\frac{2885}{4006}\right)$	$e\left(\frac{731}{4006}\right)$	$e\left(\frac{1558}{2003}\right)$
$\chi_{8014}(35,\cdot)$	8014.d	4006	no	$-1$	$1$	$e\left(\frac{573}{2003}\right)$	$e\left(\frac{1377}{4006}\right)$	$e\left(\frac{1960}{2003}\right)$	$e\left(\frac{1146}{2003}\right)$	$e\left(\frac{2513}{4006}\right)$	$e\left(\frac{1605}{2003}\right)$	$e\left(\frac{2523}{4006}\right)$	$e\left(\frac{2843}{4006}\right)$	$e\left(\frac{3653}{4006}\right)$	$e\left(\frac{530}{2003}\right)$
$\chi_{8014}(37,\cdot)$	8014.c	2003	no	$1$	$1$	$e\left(\frac{1952}{2003}\right)$	$e\left(\frac{1517}{2003}\right)$	$e\left(\frac{266}{2003}\right)$	$e\left(\frac{1901}{2003}\right)$	$e\left(\frac{1823}{2003}\right)$	$e\left(\frac{1577}{2003}\right)$	$e\left(\frac{1466}{2003}\right)$	$e\left(\frac{57}{2003}\right)$	$e\left(\frac{1185}{2003}\right)$	$e\left(\frac{215}{2003}\right)$
$\chi_{8014}(39,\cdot)$	8014.c	2003	no	$1$	$1$	$e\left(\frac{1907}{2003}\right)$	$e\left(\frac{1206}{2003}\right)$	$e\left(\frac{972}{2003}\right)$	$e\left(\frac{1811}{2003}\right)$	$e\left(\frac{1782}{2003}\right)$	$e\left(\frac{612}{2003}\right)$	$e\left(\frac{1110}{2003}\right)$	$e\left(\frac{1639}{2003}\right)$	$e\left(\frac{1288}{2003}\right)$	$e\left(\frac{876}{2003}\right)$
$\chi_{8014}(41,\cdot)$	8014.d	4006	no	$-1$	$1$	$e\left(\frac{1944}{2003}\right)$	$e\left(\frac{3235}{4006}\right)$	$e\left(\frac{347}{2003}\right)$	$e\left(\frac{1885}{2003}\right)$	$e\left(\frac{3943}{4006}\right)$	$e\left(\frac{1628}{2003}\right)$	$e\left(\frac{3117}{4006}\right)$	$e\left(\frac{721}{4006}\right)$	$e\left(\frac{1917}{4006}\right)$	$e\left(\frac{288}{2003}\right)$
$\chi_{8014}(43,\cdot)$	8014.c	2003	no	$1$	$1$	$e\left(\frac{1808}{2003}\right)$	$e\left(\frac{1323}{2003}\right)$	$e\left(\frac{1724}{2003}\right)$	$e\left(\frac{1613}{2003}\right)$	$e\left(\frac{490}{2003}\right)$	$e\left(\frac{492}{2003}\right)$	$e\left(\frac{1128}{2003}\right)$	$e\left(\frac{1514}{2003}\right)$	$e\left(\frac{1114}{2003}\right)$	$e\left(\frac{1529}{2003}\right)$
$\chi_{8014}(45,\cdot)$	8014.d	4006	no	$-1$	$1$	$e\left(\frac{184}{2003}\right)$	$e\left(\frac{3389}{4006}\right)$	$e\left(\frac{140}{2003}\right)$	$e\left(\frac{368}{2003}\right)$	$e\left(\frac{1181}{4006}\right)$	$e\left(\frac{830}{2003}\right)$	$e\left(\frac{3757}{4006}\right)$	$e\left(\frac{2063}{4006}\right)$	$e\left(\frac{2407}{4006}\right)$	$e\left(\frac{324}{2003}\right)$
$\chi_{8014}(47,\cdot)$	8014.d	4006	no	$-1$	$1$	$e\left(\frac{1331}{2003}\right)$	$e\left(\frac{2863}{4006}\right)$	$e\left(\frac{795}{2003}\right)$	$e\left(\frac{659}{2003}\right)$	$e\left(\frac{2915}{4006}\right)$	$e\left(\frac{278}{2003}\right)$	$e\left(\frac{1519}{4006}\right)$	$e\left(\frac{913}{4006}\right)$	$e\left(\frac{5}{4006}\right)$	$e\left(\frac{123}{2003}\right)$
$\chi_{8014}(49,\cdot)$	8014.c	2003	no	$1$	$1$	$e\left(\frac{1455}{2003}\right)$	$e\left(\frac{1376}{2003}\right)$	$e\left(\frac{541}{2003}\right)$	$e\left(\frac{907}{2003}\right)$	$e\left(\frac{658}{2003}\right)$	$e\left(\frac{489}{2003}\right)$	$e\left(\frac{828}{2003}\right)$	$e\left(\frac{259}{2003}\right)$	$e\left(\frac{8}{2003}\right)$	$e\left(\frac{1996}{2003}\right)$
$\chi_{8014}(51,\cdot)$	8014.d	4006	no	$-1$	$1$	$e\left(\frac{39}{2003}\right)$	$e\left(\frac{2275}{4006}\right)$	$e\left(\frac{857}{2003}\right)$	$e\left(\frac{78}{2003}\right)$	$e\left(\frac{1807}{4006}\right)$	$e\left(\frac{1504}{2003}\right)$	$e\left(\frac{2353}{4006}\right)$	$e\left(\frac{3801}{4006}\right)$	$e\left(\frac{3961}{4006}\right)$	$e\left(\frac{896}{2003}\right)$
$\chi_{8014}(53,\cdot)$	8014.d	4006	no	$-1$	$1$	$e\left(\frac{830}{2003}\right)$	$e\left(\frac{3683}{4006}\right)$	$e\left(\frac{109}{2003}\right)$	$e\left(\frac{1660}{2003}\right)$	$e\left(\frac{1735}{4006}\right)$	$e\left(\frac{217}{2003}\right)$	$e\left(\frac{1337}{4006}\right)$	$e\left(\frac{619}{4006}\right)$	$e\left(\frac{429}{4006}\right)$	$e\left(\frac{939}{2003}\right)$
$\chi_{8014}(55,\cdot)$	8014.c	2003	no	$1$	$1$	$e\left(\frac{1680}{2003}\right)$	$e\left(\frac{928}{2003}\right)$	$e\left(\frac{1017}{2003}\right)$	$e\left(\frac{1357}{2003}\right)$	$e\left(\frac{863}{2003}\right)$	$e\left(\frac{1308}{2003}\right)$	$e\left(\frac{605}{2003}\right)$	$e\left(\frac{361}{2003}\right)$	$e\left(\frac{1496}{2003}\right)$	$e\left(\frac{694}{2003}\right)$
$\chi_{8014}(57,\cdot)$	8014.d	4006	no	$-1$	$1$	$e\left(\frac{1362}{2003}\right)$	$e\left(\frac{1333}{4006}\right)$	$e\left(\frac{1733}{2003}\right)$	$e\left(\frac{721}{2003}\right)$	$e\left(\frac{1013}{4006}\right)$	$e\left(\frac{1833}{2003}\right)$	$e\left(\frac{51}{4006}\right)$	$e\left(\frac{1315}{4006}\right)$	$e\left(\frac{3513}{4006}\right)$	$e\left(\frac{1092}{2003}\right)$
$\chi_{8014}(59,\cdot)$	8014.c	2003	no	$1$	$1$	$e\left(\frac{601}{2003}\right)$	$e\left(\frac{1839}{2003}\right)$	$e\left(\frac{675}{2003}\right)$	$e\left(\frac{1202}{2003}\right)$	$e\left(\frac{236}{2003}\right)$	$e\left(\frac{425}{2003}\right)$	$e\left(\frac{437}{2003}\right)$	$e\left(\frac{860}{2003}\right)$	$e\left(\frac{1117}{2003}\right)$	$e\left(\frac{1276}{2003}\right)$
$\chi_{8014}(61,\cdot)$	8014.c	2003	no	$1$	$1$	$e\left(\frac{1755}{2003}\right)$	$e\left(\frac{111}{2003}\right)$	$e\left(\frac{508}{2003}\right)$	$e\left(\frac{1507}{2003}\right)$	$e\left(\frac{1599}{2003}\right)$	$e\left(\frac{1581}{2003}\right)$	$e\left(\frac{1866}{2003}\right)$	$e\left(\frac{395}{2003}\right)$	$e\left(\frac{1992}{2003}\right)$	$e\left(\frac{260}{2003}\right)$
$\chi_{8014}(63,\cdot)$	8014.c	2003	no	$1$	$1$	$e\left(\frac{1066}{2003}\right)$	$e\left(\frac{379}{2003}\right)$	$e\left(\frac{724}{2003}\right)$	$e\left(\frac{129}{2003}\right)$	$e\left(\frac{1995}{2003}\right)$	$e\left(\frac{1717}{2003}\right)$	$e\left(\frac{1445}{2003}\right)$	$e\left(\frac{1872}{2003}\right)$	$e\left(\frac{1388}{2003}\right)$	$e\left(\frac{1790}{2003}\right)$

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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	$8014$
Structure	\(C_{4006}\)
Order	$4006$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(21\)
\(\chi_{8014}(1,\cdot)\)	8014.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{8014}(3,\cdot)\)	8014.c	2003	no	\(1\)	\(1\)	\(e\left(\frac{670}{2003}\right)\)	\(e\left(\frac{847}{2003}\right)\)	\(e\left(\frac{1729}{2003}\right)\)	\(e\left(\frac{1340}{2003}\right)\)	\(e\left(\frac{833}{2003}\right)\)	\(e\left(\frac{1237}{2003}\right)\)	\(e\left(\frac{1517}{2003}\right)\)	\(e\left(\frac{1372}{2003}\right)\)	\(e\left(\frac{692}{2003}\right)\)	\(e\left(\frac{396}{2003}\right)\)
\(\chi_{8014}(5,\cdot)\)	8014.d	4006	no	\(-1\)	\(1\)	\(e\left(\frac{847}{2003}\right)\)	\(e\left(\frac{1}{4006}\right)\)	\(e\left(\frac{688}{2003}\right)\)	\(e\left(\frac{1694}{2003}\right)\)	\(e\left(\frac{1855}{4006}\right)\)	\(e\left(\frac{359}{2003}\right)\)	\(e\left(\frac{1695}{4006}\right)\)	\(e\left(\frac{581}{4006}\right)\)	\(e\left(\frac{3645}{4006}\right)\)	\(e\left(\frac{1535}{2003}\right)\)
\(\chi_{8014}(7,\cdot)\)	8014.c	2003	no	\(1\)	\(1\)	\(e\left(\frac{1729}{2003}\right)\)	\(e\left(\frac{688}{2003}\right)\)	\(e\left(\frac{1272}{2003}\right)\)	\(e\left(\frac{1455}{2003}\right)\)	\(e\left(\frac{329}{2003}\right)\)	\(e\left(\frac{1246}{2003}\right)\)	\(e\left(\frac{414}{2003}\right)\)	\(e\left(\frac{1131}{2003}\right)\)	\(e\left(\frac{4}{2003}\right)\)	\(e\left(\frac{998}{2003}\right)\)
\(\chi_{8014}(9,\cdot)\)	8014.c	2003	no	\(1\)	\(1\)	\(e\left(\frac{1340}{2003}\right)\)	\(e\left(\frac{1694}{2003}\right)\)	\(e\left(\frac{1455}{2003}\right)\)	\(e\left(\frac{677}{2003}\right)\)	\(e\left(\frac{1666}{2003}\right)\)	\(e\left(\frac{471}{2003}\right)\)	\(e\left(\frac{1031}{2003}\right)\)	\(e\left(\frac{741}{2003}\right)\)	\(e\left(\frac{1384}{2003}\right)\)	\(e\left(\frac{792}{2003}\right)\)
\(\chi_{8014}(11,\cdot)\)	8014.d	4006	no	\(-1\)	\(1\)	\(e\left(\frac{833}{2003}\right)\)	\(e\left(\frac{1855}{4006}\right)\)	\(e\left(\frac{329}{2003}\right)\)	\(e\left(\frac{1666}{2003}\right)\)	\(e\left(\frac{3877}{4006}\right)\)	\(e\left(\frac{949}{2003}\right)\)	\(e\left(\frac{3521}{4006}\right)\)	\(e\left(\frac{141}{4006}\right)\)	\(e\left(\frac{3353}{4006}\right)\)	\(e\left(\frac{1162}{2003}\right)\)
\(\chi_{8014}(13,\cdot)\)	8014.c	2003	no	\(1\)	\(1\)	\(e\left(\frac{1237}{2003}\right)\)	\(e\left(\frac{359}{2003}\right)\)	\(e\left(\frac{1246}{2003}\right)\)	\(e\left(\frac{471}{2003}\right)\)	\(e\left(\frac{949}{2003}\right)\)	\(e\left(\frac{1378}{2003}\right)\)	\(e\left(\frac{1596}{2003}\right)\)	\(e\left(\frac{267}{2003}\right)\)	\(e\left(\frac{596}{2003}\right)\)	\(e\left(\frac{480}{2003}\right)\)
\(\chi_{8014}(15,\cdot)\)	8014.d	4006	no	\(-1\)	\(1\)	\(e\left(\frac{1517}{2003}\right)\)	\(e\left(\frac{1695}{4006}\right)\)	\(e\left(\frac{414}{2003}\right)\)	\(e\left(\frac{1031}{2003}\right)\)	\(e\left(\frac{3521}{4006}\right)\)	\(e\left(\frac{1596}{2003}\right)\)	\(e\left(\frac{723}{4006}\right)\)	\(e\left(\frac{3325}{4006}\right)\)	\(e\left(\frac{1023}{4006}\right)\)	\(e\left(\frac{1931}{2003}\right)\)
\(\chi_{8014}(17,\cdot)\)	8014.d	4006	no	\(-1\)	\(1\)	\(e\left(\frac{1372}{2003}\right)\)	\(e\left(\frac{581}{4006}\right)\)	\(e\left(\frac{1131}{2003}\right)\)	\(e\left(\frac{741}{2003}\right)\)	\(e\left(\frac{141}{4006}\right)\)	\(e\left(\frac{267}{2003}\right)\)	\(e\left(\frac{3325}{4006}\right)\)	\(e\left(\frac{1057}{4006}\right)\)	\(e\left(\frac{2577}{4006}\right)\)	\(e\left(\frac{500}{2003}\right)\)
\(\chi_{8014}(19,\cdot)\)	8014.d	4006	no	\(-1\)	\(1\)	\(e\left(\frac{692}{2003}\right)\)	\(e\left(\frac{3645}{4006}\right)\)	\(e\left(\frac{4}{2003}\right)\)	\(e\left(\frac{1384}{2003}\right)\)	\(e\left(\frac{3353}{4006}\right)\)	\(e\left(\frac{596}{2003}\right)\)	\(e\left(\frac{1023}{4006}\right)\)	\(e\left(\frac{2577}{4006}\right)\)	\(e\left(\frac{2129}{4006}\right)\)	\(e\left(\frac{696}{2003}\right)\)
\(\chi_{8014}(21,\cdot)\)	8014.c	2003	no	\(1\)	\(1\)	\(e\left(\frac{396}{2003}\right)\)	\(e\left(\frac{1535}{2003}\right)\)	\(e\left(\frac{998}{2003}\right)\)	\(e\left(\frac{792}{2003}\right)\)	\(e\left(\frac{1162}{2003}\right)\)	\(e\left(\frac{480}{2003}\right)\)	\(e\left(\frac{1931}{2003}\right)\)	\(e\left(\frac{500}{2003}\right)\)	\(e\left(\frac{696}{2003}\right)\)	\(e\left(\frac{1394}{2003}\right)\)
\(\chi_{8014}(23,\cdot)\)	8014.c	2003	no	\(1\)	\(1\)	\(e\left(\frac{1360}{2003}\right)\)	\(e\left(\frac{942}{2003}\right)\)	\(e\left(\frac{251}{2003}\right)\)	\(e\left(\frac{717}{2003}\right)\)	\(e\left(\frac{794}{2003}\right)\)	\(e\left(\frac{1345}{2003}\right)\)	\(e\left(\frac{299}{2003}\right)\)	\(e\left(\frac{483}{2003}\right)\)	\(e\left(\frac{448}{2003}\right)\)	\(e\left(\frac{1611}{2003}\right)\)
\(\chi_{8014}(25,\cdot)\)	8014.c	2003	no	\(1\)	\(1\)	\(e\left(\frac{1694}{2003}\right)\)	\(e\left(\frac{1}{2003}\right)\)	\(e\left(\frac{1376}{2003}\right)\)	\(e\left(\frac{1385}{2003}\right)\)	\(e\left(\frac{1855}{2003}\right)\)	\(e\left(\frac{718}{2003}\right)\)	\(e\left(\frac{1695}{2003}\right)\)	\(e\left(\frac{581}{2003}\right)\)	\(e\left(\frac{1642}{2003}\right)\)	\(e\left(\frac{1067}{2003}\right)\)
\(\chi_{8014}(27,\cdot)\)	8014.c	2003	no	\(1\)	\(1\)	\(e\left(\frac{7}{2003}\right)\)	\(e\left(\frac{538}{2003}\right)\)	\(e\left(\frac{1181}{2003}\right)\)	\(e\left(\frac{14}{2003}\right)\)	\(e\left(\frac{496}{2003}\right)\)	\(e\left(\frac{1708}{2003}\right)\)	\(e\left(\frac{545}{2003}\right)\)	\(e\left(\frac{110}{2003}\right)\)	\(e\left(\frac{73}{2003}\right)\)	\(e\left(\frac{1188}{2003}\right)\)
\(\chi_{8014}(29,\cdot)\)	8014.c	2003	no	\(1\)	\(1\)	\(e\left(\frac{1383}{2003}\right)\)	\(e\left(\frac{1279}{2003}\right)\)	\(e\left(\frac{1270}{2003}\right)\)	\(e\left(\frac{763}{2003}\right)\)	\(e\left(\frac{993}{2003}\right)\)	\(e\left(\frac{948}{2003}\right)\)	\(e\left(\frac{659}{2003}\right)\)	\(e\left(\frac{1989}{2003}\right)\)	\(e\left(\frac{974}{2003}\right)\)	\(e\left(\frac{650}{2003}\right)\)
\(\chi_{8014}(31,\cdot)\)	8014.d	4006	no	\(-1\)	\(1\)	\(e\left(\frac{1842}{2003}\right)\)	\(e\left(\frac{1291}{4006}\right)\)	\(e\left(\frac{879}{2003}\right)\)	\(e\left(\frac{1681}{2003}\right)\)	\(e\left(\frac{3223}{4006}\right)\)	\(e\left(\frac{776}{2003}\right)\)	\(e\left(\frac{969}{4006}\right)\)	\(e\left(\frac{949}{4006}\right)\)	\(e\left(\frac{2651}{4006}\right)\)	\(e\left(\frac{718}{2003}\right)\)
\(\chi_{8014}(33,\cdot)\)	8014.d	4006	no	\(-1\)	\(1\)	\(e\left(\frac{1503}{2003}\right)\)	\(e\left(\frac{3549}{4006}\right)\)	\(e\left(\frac{55}{2003}\right)\)	\(e\left(\frac{1003}{2003}\right)\)	\(e\left(\frac{1537}{4006}\right)\)	\(e\left(\frac{183}{2003}\right)\)	\(e\left(\frac{2549}{4006}\right)\)	\(e\left(\frac{2885}{4006}\right)\)	\(e\left(\frac{731}{4006}\right)\)	\(e\left(\frac{1558}{2003}\right)\)
\(\chi_{8014}(35,\cdot)\)	8014.d	4006	no	\(-1\)	\(1\)	\(e\left(\frac{573}{2003}\right)\)	\(e\left(\frac{1377}{4006}\right)\)	\(e\left(\frac{1960}{2003}\right)\)	\(e\left(\frac{1146}{2003}\right)\)	\(e\left(\frac{2513}{4006}\right)\)	\(e\left(\frac{1605}{2003}\right)\)	\(e\left(\frac{2523}{4006}\right)\)	\(e\left(\frac{2843}{4006}\right)\)	\(e\left(\frac{3653}{4006}\right)\)	\(e\left(\frac{530}{2003}\right)\)
\(\chi_{8014}(37,\cdot)\)	8014.c	2003	no	\(1\)	\(1\)	\(e\left(\frac{1952}{2003}\right)\)	\(e\left(\frac{1517}{2003}\right)\)	\(e\left(\frac{266}{2003}\right)\)	\(e\left(\frac{1901}{2003}\right)\)	\(e\left(\frac{1823}{2003}\right)\)	\(e\left(\frac{1577}{2003}\right)\)	\(e\left(\frac{1466}{2003}\right)\)	\(e\left(\frac{57}{2003}\right)\)	\(e\left(\frac{1185}{2003}\right)\)	\(e\left(\frac{215}{2003}\right)\)
\(\chi_{8014}(39,\cdot)\)	8014.c	2003	no	\(1\)	\(1\)	\(e\left(\frac{1907}{2003}\right)\)	\(e\left(\frac{1206}{2003}\right)\)	\(e\left(\frac{972}{2003}\right)\)	\(e\left(\frac{1811}{2003}\right)\)	\(e\left(\frac{1782}{2003}\right)\)	\(e\left(\frac{612}{2003}\right)\)	\(e\left(\frac{1110}{2003}\right)\)	\(e\left(\frac{1639}{2003}\right)\)	\(e\left(\frac{1288}{2003}\right)\)	\(e\left(\frac{876}{2003}\right)\)
\(\chi_{8014}(41,\cdot)\)	8014.d	4006	no	\(-1\)	\(1\)	\(e\left(\frac{1944}{2003}\right)\)	\(e\left(\frac{3235}{4006}\right)\)	\(e\left(\frac{347}{2003}\right)\)	\(e\left(\frac{1885}{2003}\right)\)	\(e\left(\frac{3943}{4006}\right)\)	\(e\left(\frac{1628}{2003}\right)\)	\(e\left(\frac{3117}{4006}\right)\)	\(e\left(\frac{721}{4006}\right)\)	\(e\left(\frac{1917}{4006}\right)\)	\(e\left(\frac{288}{2003}\right)\)
\(\chi_{8014}(43,\cdot)\)	8014.c	2003	no	\(1\)	\(1\)	\(e\left(\frac{1808}{2003}\right)\)	\(e\left(\frac{1323}{2003}\right)\)	\(e\left(\frac{1724}{2003}\right)\)	\(e\left(\frac{1613}{2003}\right)\)	\(e\left(\frac{490}{2003}\right)\)	\(e\left(\frac{492}{2003}\right)\)	\(e\left(\frac{1128}{2003}\right)\)	\(e\left(\frac{1514}{2003}\right)\)	\(e\left(\frac{1114}{2003}\right)\)	\(e\left(\frac{1529}{2003}\right)\)
\(\chi_{8014}(45,\cdot)\)	8014.d	4006	no	\(-1\)	\(1\)	\(e\left(\frac{184}{2003}\right)\)	\(e\left(\frac{3389}{4006}\right)\)	\(e\left(\frac{140}{2003}\right)\)	\(e\left(\frac{368}{2003}\right)\)	\(e\left(\frac{1181}{4006}\right)\)	\(e\left(\frac{830}{2003}\right)\)	\(e\left(\frac{3757}{4006}\right)\)	\(e\left(\frac{2063}{4006}\right)\)	\(e\left(\frac{2407}{4006}\right)\)	\(e\left(\frac{324}{2003}\right)\)
\(\chi_{8014}(47,\cdot)\)	8014.d	4006	no	\(-1\)	\(1\)	\(e\left(\frac{1331}{2003}\right)\)	\(e\left(\frac{2863}{4006}\right)\)	\(e\left(\frac{795}{2003}\right)\)	\(e\left(\frac{659}{2003}\right)\)	\(e\left(\frac{2915}{4006}\right)\)	\(e\left(\frac{278}{2003}\right)\)	\(e\left(\frac{1519}{4006}\right)\)	\(e\left(\frac{913}{4006}\right)\)	\(e\left(\frac{5}{4006}\right)\)	\(e\left(\frac{123}{2003}\right)\)
\(\chi_{8014}(49,\cdot)\)	8014.c	2003	no	\(1\)	\(1\)	\(e\left(\frac{1455}{2003}\right)\)	\(e\left(\frac{1376}{2003}\right)\)	\(e\left(\frac{541}{2003}\right)\)	\(e\left(\frac{907}{2003}\right)\)	\(e\left(\frac{658}{2003}\right)\)	\(e\left(\frac{489}{2003}\right)\)	\(e\left(\frac{828}{2003}\right)\)	\(e\left(\frac{259}{2003}\right)\)	\(e\left(\frac{8}{2003}\right)\)	\(e\left(\frac{1996}{2003}\right)\)
\(\chi_{8014}(51,\cdot)\)	8014.d	4006	no	\(-1\)	\(1\)	\(e\left(\frac{39}{2003}\right)\)	\(e\left(\frac{2275}{4006}\right)\)	\(e\left(\frac{857}{2003}\right)\)	\(e\left(\frac{78}{2003}\right)\)	\(e\left(\frac{1807}{4006}\right)\)	\(e\left(\frac{1504}{2003}\right)\)	\(e\left(\frac{2353}{4006}\right)\)	\(e\left(\frac{3801}{4006}\right)\)	\(e\left(\frac{3961}{4006}\right)\)	\(e\left(\frac{896}{2003}\right)\)
\(\chi_{8014}(53,\cdot)\)	8014.d	4006	no	\(-1\)	\(1\)	\(e\left(\frac{830}{2003}\right)\)	\(e\left(\frac{3683}{4006}\right)\)	\(e\left(\frac{109}{2003}\right)\)	\(e\left(\frac{1660}{2003}\right)\)	\(e\left(\frac{1735}{4006}\right)\)	\(e\left(\frac{217}{2003}\right)\)	\(e\left(\frac{1337}{4006}\right)\)	\(e\left(\frac{619}{4006}\right)\)	\(e\left(\frac{429}{4006}\right)\)	\(e\left(\frac{939}{2003}\right)\)
\(\chi_{8014}(55,\cdot)\)	8014.c	2003	no	\(1\)	\(1\)	\(e\left(\frac{1680}{2003}\right)\)	\(e\left(\frac{928}{2003}\right)\)	\(e\left(\frac{1017}{2003}\right)\)	\(e\left(\frac{1357}{2003}\right)\)	\(e\left(\frac{863}{2003}\right)\)	\(e\left(\frac{1308}{2003}\right)\)	\(e\left(\frac{605}{2003}\right)\)	\(e\left(\frac{361}{2003}\right)\)	\(e\left(\frac{1496}{2003}\right)\)	\(e\left(\frac{694}{2003}\right)\)
\(\chi_{8014}(57,\cdot)\)	8014.d	4006	no	\(-1\)	\(1\)	\(e\left(\frac{1362}{2003}\right)\)	\(e\left(\frac{1333}{4006}\right)\)	\(e\left(\frac{1733}{2003}\right)\)	\(e\left(\frac{721}{2003}\right)\)	\(e\left(\frac{1013}{4006}\right)\)	\(e\left(\frac{1833}{2003}\right)\)	\(e\left(\frac{51}{4006}\right)\)	\(e\left(\frac{1315}{4006}\right)\)	\(e\left(\frac{3513}{4006}\right)\)	\(e\left(\frac{1092}{2003}\right)\)
\(\chi_{8014}(59,\cdot)\)	8014.c	2003	no	\(1\)	\(1\)	\(e\left(\frac{601}{2003}\right)\)	\(e\left(\frac{1839}{2003}\right)\)	\(e\left(\frac{675}{2003}\right)\)	\(e\left(\frac{1202}{2003}\right)\)	\(e\left(\frac{236}{2003}\right)\)	\(e\left(\frac{425}{2003}\right)\)	\(e\left(\frac{437}{2003}\right)\)	\(e\left(\frac{860}{2003}\right)\)	\(e\left(\frac{1117}{2003}\right)\)	\(e\left(\frac{1276}{2003}\right)\)
\(\chi_{8014}(61,\cdot)\)	8014.c	2003	no	\(1\)	\(1\)	\(e\left(\frac{1755}{2003}\right)\)	\(e\left(\frac{111}{2003}\right)\)	\(e\left(\frac{508}{2003}\right)\)	\(e\left(\frac{1507}{2003}\right)\)	\(e\left(\frac{1599}{2003}\right)\)	\(e\left(\frac{1581}{2003}\right)\)	\(e\left(\frac{1866}{2003}\right)\)	\(e\left(\frac{395}{2003}\right)\)	\(e\left(\frac{1992}{2003}\right)\)	\(e\left(\frac{260}{2003}\right)\)
\(\chi_{8014}(63,\cdot)\)	8014.c	2003	no	\(1\)	\(1\)	\(e\left(\frac{1066}{2003}\right)\)	\(e\left(\frac{379}{2003}\right)\)	\(e\left(\frac{724}{2003}\right)\)	\(e\left(\frac{129}{2003}\right)\)	\(e\left(\frac{1995}{2003}\right)\)	\(e\left(\frac{1717}{2003}\right)\)	\(e\left(\frac{1445}{2003}\right)\)	\(e\left(\frac{1872}{2003}\right)\)	\(e\left(\frac{1388}{2003}\right)\)	\(e\left(\frac{1790}{2003}\right)\)

Introduction

L-functions

Modular forms

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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.