LMFDB - Group of Dirichlet characters of modulus 4007

Show commands: PariGP / SageMath

sage: H = DirichletGroup(4007)

pari: g = idealstar(,4007,2)

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	=	$\chi_{4007}(5,\cdot)$

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	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{4007}(1,\cdot)$	4007.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{4007}(2,\cdot)$	4007.c	2003	yes	$1$	$1$	$e\left(\frac{1929}{2003}\right)$	$e\left(\frac{1440}{2003}\right)$	$e\left(\frac{1855}{2003}\right)$	$e\left(\frac{1940}{2003}\right)$	$e\left(\frac{1366}{2003}\right)$	$e\left(\frac{1444}{2003}\right)$	$e\left(\frac{1781}{2003}\right)$	$e\left(\frac{877}{2003}\right)$	$e\left(\frac{1866}{2003}\right)$	$e\left(\frac{1312}{2003}\right)$
$\chi_{4007}(3,\cdot)$	4007.c	2003	yes	$1$	$1$	$e\left(\frac{1440}{2003}\right)$	$e\left(\frac{670}{2003}\right)$	$e\left(\frac{877}{2003}\right)$	$e\left(\frac{847}{2003}\right)$	$e\left(\frac{107}{2003}\right)$	$e\left(\frac{1729}{2003}\right)$	$e\left(\frac{314}{2003}\right)$	$e\left(\frac{1340}{2003}\right)$	$e\left(\frac{284}{2003}\right)$	$e\left(\frac{833}{2003}\right)$
$\chi_{4007}(4,\cdot)$	4007.c	2003	yes	$1$	$1$	$e\left(\frac{1855}{2003}\right)$	$e\left(\frac{877}{2003}\right)$	$e\left(\frac{1707}{2003}\right)$	$e\left(\frac{1877}{2003}\right)$	$e\left(\frac{729}{2003}\right)$	$e\left(\frac{885}{2003}\right)$	$e\left(\frac{1559}{2003}\right)$	$e\left(\frac{1754}{2003}\right)$	$e\left(\frac{1729}{2003}\right)$	$e\left(\frac{621}{2003}\right)$
$\chi_{4007}(5,\cdot)$	4007.d	4006	yes	$-1$	$1$	$e\left(\frac{1940}{2003}\right)$	$e\left(\frac{847}{2003}\right)$	$e\left(\frac{1877}{2003}\right)$	$e\left(\frac{1}{4006}\right)$	$e\left(\frac{784}{2003}\right)$	$e\left(\frac{688}{2003}\right)$	$e\left(\frac{1814}{2003}\right)$	$e\left(\frac{1694}{2003}\right)$	$e\left(\frac{3881}{4006}\right)$	$e\left(\frac{1855}{4006}\right)$
$\chi_{4007}(6,\cdot)$	4007.c	2003	yes	$1$	$1$	$e\left(\frac{1366}{2003}\right)$	$e\left(\frac{107}{2003}\right)$	$e\left(\frac{729}{2003}\right)$	$e\left(\frac{784}{2003}\right)$	$e\left(\frac{1473}{2003}\right)$	$e\left(\frac{1170}{2003}\right)$	$e\left(\frac{92}{2003}\right)$	$e\left(\frac{214}{2003}\right)$	$e\left(\frac{147}{2003}\right)$	$e\left(\frac{142}{2003}\right)$
$\chi_{4007}(7,\cdot)$	4007.c	2003	yes	$1$	$1$	$e\left(\frac{1444}{2003}\right)$	$e\left(\frac{1729}{2003}\right)$	$e\left(\frac{885}{2003}\right)$	$e\left(\frac{688}{2003}\right)$	$e\left(\frac{1170}{2003}\right)$	$e\left(\frac{1272}{2003}\right)$	$e\left(\frac{326}{2003}\right)$	$e\left(\frac{1455}{2003}\right)$	$e\left(\frac{129}{2003}\right)$	$e\left(\frac{329}{2003}\right)$
$\chi_{4007}(8,\cdot)$	4007.c	2003	yes	$1$	$1$	$e\left(\frac{1781}{2003}\right)$	$e\left(\frac{314}{2003}\right)$	$e\left(\frac{1559}{2003}\right)$	$e\left(\frac{1814}{2003}\right)$	$e\left(\frac{92}{2003}\right)$	$e\left(\frac{326}{2003}\right)$	$e\left(\frac{1337}{2003}\right)$	$e\left(\frac{628}{2003}\right)$	$e\left(\frac{1592}{2003}\right)$	$e\left(\frac{1933}{2003}\right)$
$\chi_{4007}(9,\cdot)$	4007.c	2003	yes	$1$	$1$	$e\left(\frac{877}{2003}\right)$	$e\left(\frac{1340}{2003}\right)$	$e\left(\frac{1754}{2003}\right)$	$e\left(\frac{1694}{2003}\right)$	$e\left(\frac{214}{2003}\right)$	$e\left(\frac{1455}{2003}\right)$	$e\left(\frac{628}{2003}\right)$	$e\left(\frac{677}{2003}\right)$	$e\left(\frac{568}{2003}\right)$	$e\left(\frac{1666}{2003}\right)$
$\chi_{4007}(10,\cdot)$	4007.d	4006	yes	$-1$	$1$	$e\left(\frac{1866}{2003}\right)$	$e\left(\frac{284}{2003}\right)$	$e\left(\frac{1729}{2003}\right)$	$e\left(\frac{3881}{4006}\right)$	$e\left(\frac{147}{2003}\right)$	$e\left(\frac{129}{2003}\right)$	$e\left(\frac{1592}{2003}\right)$	$e\left(\frac{568}{2003}\right)$	$e\left(\frac{3607}{4006}\right)$	$e\left(\frac{473}{4006}\right)$
$\chi_{4007}(11,\cdot)$	4007.d	4006	yes	$-1$	$1$	$e\left(\frac{1312}{2003}\right)$	$e\left(\frac{833}{2003}\right)$	$e\left(\frac{621}{2003}\right)$	$e\left(\frac{1855}{4006}\right)$	$e\left(\frac{142}{2003}\right)$	$e\left(\frac{329}{2003}\right)$	$e\left(\frac{1933}{2003}\right)$	$e\left(\frac{1666}{2003}\right)$	$e\left(\frac{473}{4006}\right)$	$e\left(\frac{3877}{4006}\right)$
$\chi_{4007}(12,\cdot)$	4007.c	2003	yes	$1$	$1$	$e\left(\frac{1292}{2003}\right)$	$e\left(\frac{1547}{2003}\right)$	$e\left(\frac{581}{2003}\right)$	$e\left(\frac{721}{2003}\right)$	$e\left(\frac{836}{2003}\right)$	$e\left(\frac{611}{2003}\right)$	$e\left(\frac{1873}{2003}\right)$	$e\left(\frac{1091}{2003}\right)$	$e\left(\frac{10}{2003}\right)$	$e\left(\frac{1454}{2003}\right)$
$\chi_{4007}(13,\cdot)$	4007.c	2003	yes	$1$	$1$	$e\left(\frac{835}{2003}\right)$	$e\left(\frac{1237}{2003}\right)$	$e\left(\frac{1670}{2003}\right)$	$e\left(\frac{359}{2003}\right)$	$e\left(\frac{69}{2003}\right)$	$e\left(\frac{1246}{2003}\right)$	$e\left(\frac{502}{2003}\right)$	$e\left(\frac{471}{2003}\right)$	$e\left(\frac{1194}{2003}\right)$	$e\left(\frac{949}{2003}\right)$
$\chi_{4007}(14,\cdot)$	4007.c	2003	yes	$1$	$1$	$e\left(\frac{1370}{2003}\right)$	$e\left(\frac{1166}{2003}\right)$	$e\left(\frac{737}{2003}\right)$	$e\left(\frac{625}{2003}\right)$	$e\left(\frac{533}{2003}\right)$	$e\left(\frac{713}{2003}\right)$	$e\left(\frac{104}{2003}\right)$	$e\left(\frac{329}{2003}\right)$	$e\left(\frac{1995}{2003}\right)$	$e\left(\frac{1641}{2003}\right)$
$\chi_{4007}(15,\cdot)$	4007.d	4006	yes	$-1$	$1$	$e\left(\frac{1377}{2003}\right)$	$e\left(\frac{1517}{2003}\right)$	$e\left(\frac{751}{2003}\right)$	$e\left(\frac{1695}{4006}\right)$	$e\left(\frac{891}{2003}\right)$	$e\left(\frac{414}{2003}\right)$	$e\left(\frac{125}{2003}\right)$	$e\left(\frac{1031}{2003}\right)$	$e\left(\frac{443}{4006}\right)$	$e\left(\frac{3521}{4006}\right)$
$\chi_{4007}(16,\cdot)$	4007.c	2003	yes	$1$	$1$	$e\left(\frac{1707}{2003}\right)$	$e\left(\frac{1754}{2003}\right)$	$e\left(\frac{1411}{2003}\right)$	$e\left(\frac{1751}{2003}\right)$	$e\left(\frac{1458}{2003}\right)$	$e\left(\frac{1770}{2003}\right)$	$e\left(\frac{1115}{2003}\right)$	$e\left(\frac{1505}{2003}\right)$	$e\left(\frac{1455}{2003}\right)$	$e\left(\frac{1242}{2003}\right)$
$\chi_{4007}(17,\cdot)$	4007.d	4006	yes	$-1$	$1$	$e\left(\frac{1454}{2003}\right)$	$e\left(\frac{1372}{2003}\right)$	$e\left(\frac{905}{2003}\right)$	$e\left(\frac{581}{4006}\right)$	$e\left(\frac{823}{2003}\right)$	$e\left(\frac{1131}{2003}\right)$	$e\left(\frac{356}{2003}\right)$	$e\left(\frac{741}{2003}\right)$	$e\left(\frac{3489}{4006}\right)$	$e\left(\frac{141}{4006}\right)$
$\chi_{4007}(18,\cdot)$	4007.c	2003	yes	$1$	$1$	$e\left(\frac{803}{2003}\right)$	$e\left(\frac{777}{2003}\right)$	$e\left(\frac{1606}{2003}\right)$	$e\left(\frac{1631}{2003}\right)$	$e\left(\frac{1580}{2003}\right)$	$e\left(\frac{896}{2003}\right)$	$e\left(\frac{406}{2003}\right)$	$e\left(\frac{1554}{2003}\right)$	$e\left(\frac{431}{2003}\right)$	$e\left(\frac{975}{2003}\right)$
$\chi_{4007}(19,\cdot)$	4007.d	4006	yes	$-1$	$1$	$e\left(\frac{710}{2003}\right)$	$e\left(\frac{692}{2003}\right)$	$e\left(\frac{1420}{2003}\right)$	$e\left(\frac{3645}{4006}\right)$	$e\left(\frac{1402}{2003}\right)$	$e\left(\frac{4}{2003}\right)$	$e\left(\frac{127}{2003}\right)$	$e\left(\frac{1384}{2003}\right)$	$e\left(\frac{1059}{4006}\right)$	$e\left(\frac{3353}{4006}\right)$
$\chi_{4007}(20,\cdot)$	4007.d	4006	yes	$-1$	$1$	$e\left(\frac{1792}{2003}\right)$	$e\left(\frac{1724}{2003}\right)$	$e\left(\frac{1581}{2003}\right)$	$e\left(\frac{3755}{4006}\right)$	$e\left(\frac{1513}{2003}\right)$	$e\left(\frac{1573}{2003}\right)$	$e\left(\frac{1370}{2003}\right)$	$e\left(\frac{1445}{2003}\right)$	$e\left(\frac{3333}{4006}\right)$	$e\left(\frac{3097}{4006}\right)$
$\chi_{4007}(21,\cdot)$	4007.c	2003	yes	$1$	$1$	$e\left(\frac{881}{2003}\right)$	$e\left(\frac{396}{2003}\right)$	$e\left(\frac{1762}{2003}\right)$	$e\left(\frac{1535}{2003}\right)$	$e\left(\frac{1277}{2003}\right)$	$e\left(\frac{998}{2003}\right)$	$e\left(\frac{640}{2003}\right)$	$e\left(\frac{792}{2003}\right)$	$e\left(\frac{413}{2003}\right)$	$e\left(\frac{1162}{2003}\right)$
$\chi_{4007}(22,\cdot)$	4007.d	4006	yes	$-1$	$1$	$e\left(\frac{1238}{2003}\right)$	$e\left(\frac{270}{2003}\right)$	$e\left(\frac{473}{2003}\right)$	$e\left(\frac{1729}{4006}\right)$	$e\left(\frac{1508}{2003}\right)$	$e\left(\frac{1773}{2003}\right)$	$e\left(\frac{1711}{2003}\right)$	$e\left(\frac{540}{2003}\right)$	$e\left(\frac{199}{4006}\right)$	$e\left(\frac{2495}{4006}\right)$
$\chi_{4007}(23,\cdot)$	4007.c	2003	yes	$1$	$1$	$e\left(\frac{1488}{2003}\right)$	$e\left(\frac{1360}{2003}\right)$	$e\left(\frac{973}{2003}\right)$	$e\left(\frac{942}{2003}\right)$	$e\left(\frac{845}{2003}\right)$	$e\left(\frac{251}{2003}\right)$	$e\left(\frac{458}{2003}\right)$	$e\left(\frac{717}{2003}\right)$	$e\left(\frac{427}{2003}\right)$	$e\left(\frac{794}{2003}\right)$
$\chi_{4007}(24,\cdot)$	4007.c	2003	yes	$1$	$1$	$e\left(\frac{1218}{2003}\right)$	$e\left(\frac{984}{2003}\right)$	$e\left(\frac{433}{2003}\right)$	$e\left(\frac{658}{2003}\right)$	$e\left(\frac{199}{2003}\right)$	$e\left(\frac{52}{2003}\right)$	$e\left(\frac{1651}{2003}\right)$	$e\left(\frac{1968}{2003}\right)$	$e\left(\frac{1876}{2003}\right)$	$e\left(\frac{763}{2003}\right)$
$\chi_{4007}(25,\cdot)$	4007.c	2003	yes	$1$	$1$	$e\left(\frac{1877}{2003}\right)$	$e\left(\frac{1694}{2003}\right)$	$e\left(\frac{1751}{2003}\right)$	$e\left(\frac{1}{2003}\right)$	$e\left(\frac{1568}{2003}\right)$	$e\left(\frac{1376}{2003}\right)$	$e\left(\frac{1625}{2003}\right)$	$e\left(\frac{1385}{2003}\right)$	$e\left(\frac{1878}{2003}\right)$	$e\left(\frac{1855}{2003}\right)$
$\chi_{4007}(26,\cdot)$	4007.c	2003	yes	$1$	$1$	$e\left(\frac{761}{2003}\right)$	$e\left(\frac{674}{2003}\right)$	$e\left(\frac{1522}{2003}\right)$	$e\left(\frac{296}{2003}\right)$	$e\left(\frac{1435}{2003}\right)$	$e\left(\frac{687}{2003}\right)$	$e\left(\frac{280}{2003}\right)$	$e\left(\frac{1348}{2003}\right)$	$e\left(\frac{1057}{2003}\right)$	$e\left(\frac{258}{2003}\right)$
$\chi_{4007}(27,\cdot)$	4007.c	2003	yes	$1$	$1$	$e\left(\frac{314}{2003}\right)$	$e\left(\frac{7}{2003}\right)$	$e\left(\frac{628}{2003}\right)$	$e\left(\frac{538}{2003}\right)$	$e\left(\frac{321}{2003}\right)$	$e\left(\frac{1181}{2003}\right)$	$e\left(\frac{942}{2003}\right)$	$e\left(\frac{14}{2003}\right)$	$e\left(\frac{852}{2003}\right)$	$e\left(\frac{496}{2003}\right)$
$\chi_{4007}(28,\cdot)$	4007.c	2003	yes	$1$	$1$	$e\left(\frac{1296}{2003}\right)$	$e\left(\frac{603}{2003}\right)$	$e\left(\frac{589}{2003}\right)$	$e\left(\frac{562}{2003}\right)$	$e\left(\frac{1899}{2003}\right)$	$e\left(\frac{154}{2003}\right)$	$e\left(\frac{1885}{2003}\right)$	$e\left(\frac{1206}{2003}\right)$	$e\left(\frac{1858}{2003}\right)$	$e\left(\frac{950}{2003}\right)$
$\chi_{4007}(29,\cdot)$	4007.c	2003	yes	$1$	$1$	$e\left(\frac{1089}{2003}\right)$	$e\left(\frac{1383}{2003}\right)$	$e\left(\frac{175}{2003}\right)$	$e\left(\frac{1279}{2003}\right)$	$e\left(\frac{469}{2003}\right)$	$e\left(\frac{1270}{2003}\right)$	$e\left(\frac{1264}{2003}\right)$	$e\left(\frac{763}{2003}\right)$	$e\left(\frac{365}{2003}\right)$	$e\left(\frac{993}{2003}\right)$
$\chi_{4007}(30,\cdot)$	4007.d	4006	yes	$-1$	$1$	$e\left(\frac{1303}{2003}\right)$	$e\left(\frac{954}{2003}\right)$	$e\left(\frac{603}{2003}\right)$	$e\left(\frac{1569}{4006}\right)$	$e\left(\frac{254}{2003}\right)$	$e\left(\frac{1858}{2003}\right)$	$e\left(\frac{1906}{2003}\right)$	$e\left(\frac{1908}{2003}\right)$	$e\left(\frac{169}{4006}\right)$	$e\left(\frac{2139}{4006}\right)$
$\chi_{4007}(31,\cdot)$	4007.d	4006	yes	$-1$	$1$	$e\left(\frac{790}{2003}\right)$	$e\left(\frac{1842}{2003}\right)$	$e\left(\frac{1580}{2003}\right)$	$e\left(\frac{1291}{4006}\right)$	$e\left(\frac{629}{2003}\right)$	$e\left(\frac{879}{2003}\right)$	$e\left(\frac{367}{2003}\right)$	$e\left(\frac{1681}{2003}\right)$	$e\left(\frac{2871}{4006}\right)$	$e\left(\frac{3223}{4006}\right)$
$\chi_{4007}(32,\cdot)$	4007.c	2003	yes	$1$	$1$	$e\left(\frac{1633}{2003}\right)$	$e\left(\frac{1191}{2003}\right)$	$e\left(\frac{1263}{2003}\right)$	$e\left(\frac{1688}{2003}\right)$	$e\left(\frac{821}{2003}\right)$	$e\left(\frac{1211}{2003}\right)$	$e\left(\frac{893}{2003}\right)$	$e\left(\frac{379}{2003}\right)$	$e\left(\frac{1318}{2003}\right)$	$e\left(\frac{551}{2003}\right)$

Click here to search among the remaining 3974 characters.

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	$4007$
Structure	\(C_{4006}\)
Order	$4006$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\(\chi_{4007}(1,\cdot)\)	4007.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{4007}(2,\cdot)\)	4007.c	2003	yes	\(1\)	\(1\)	\(e\left(\frac{1929}{2003}\right)\)	\(e\left(\frac{1440}{2003}\right)\)	\(e\left(\frac{1855}{2003}\right)\)	\(e\left(\frac{1940}{2003}\right)\)	\(e\left(\frac{1366}{2003}\right)\)	\(e\left(\frac{1444}{2003}\right)\)	\(e\left(\frac{1781}{2003}\right)\)	\(e\left(\frac{877}{2003}\right)\)	\(e\left(\frac{1866}{2003}\right)\)	\(e\left(\frac{1312}{2003}\right)\)
\(\chi_{4007}(3,\cdot)\)	4007.c	2003	yes	\(1\)	\(1\)	\(e\left(\frac{1440}{2003}\right)\)	\(e\left(\frac{670}{2003}\right)\)	\(e\left(\frac{877}{2003}\right)\)	\(e\left(\frac{847}{2003}\right)\)	\(e\left(\frac{107}{2003}\right)\)	\(e\left(\frac{1729}{2003}\right)\)	\(e\left(\frac{314}{2003}\right)\)	\(e\left(\frac{1340}{2003}\right)\)	\(e\left(\frac{284}{2003}\right)\)	\(e\left(\frac{833}{2003}\right)\)
\(\chi_{4007}(4,\cdot)\)	4007.c	2003	yes	\(1\)	\(1\)	\(e\left(\frac{1855}{2003}\right)\)	\(e\left(\frac{877}{2003}\right)\)	\(e\left(\frac{1707}{2003}\right)\)	\(e\left(\frac{1877}{2003}\right)\)	\(e\left(\frac{729}{2003}\right)\)	\(e\left(\frac{885}{2003}\right)\)	\(e\left(\frac{1559}{2003}\right)\)	\(e\left(\frac{1754}{2003}\right)\)	\(e\left(\frac{1729}{2003}\right)\)	\(e\left(\frac{621}{2003}\right)\)
\(\chi_{4007}(5,\cdot)\)	4007.d	4006	yes	\(-1\)	\(1\)	\(e\left(\frac{1940}{2003}\right)\)	\(e\left(\frac{847}{2003}\right)\)	\(e\left(\frac{1877}{2003}\right)\)	\(e\left(\frac{1}{4006}\right)\)	\(e\left(\frac{784}{2003}\right)\)	\(e\left(\frac{688}{2003}\right)\)	\(e\left(\frac{1814}{2003}\right)\)	\(e\left(\frac{1694}{2003}\right)\)	\(e\left(\frac{3881}{4006}\right)\)	\(e\left(\frac{1855}{4006}\right)\)
\(\chi_{4007}(6,\cdot)\)	4007.c	2003	yes	\(1\)	\(1\)	\(e\left(\frac{1366}{2003}\right)\)	\(e\left(\frac{107}{2003}\right)\)	\(e\left(\frac{729}{2003}\right)\)	\(e\left(\frac{784}{2003}\right)\)	\(e\left(\frac{1473}{2003}\right)\)	\(e\left(\frac{1170}{2003}\right)\)	\(e\left(\frac{92}{2003}\right)\)	\(e\left(\frac{214}{2003}\right)\)	\(e\left(\frac{147}{2003}\right)\)	\(e\left(\frac{142}{2003}\right)\)
\(\chi_{4007}(7,\cdot)\)	4007.c	2003	yes	\(1\)	\(1\)	\(e\left(\frac{1444}{2003}\right)\)	\(e\left(\frac{1729}{2003}\right)\)	\(e\left(\frac{885}{2003}\right)\)	\(e\left(\frac{688}{2003}\right)\)	\(e\left(\frac{1170}{2003}\right)\)	\(e\left(\frac{1272}{2003}\right)\)	\(e\left(\frac{326}{2003}\right)\)	\(e\left(\frac{1455}{2003}\right)\)	\(e\left(\frac{129}{2003}\right)\)	\(e\left(\frac{329}{2003}\right)\)
\(\chi_{4007}(8,\cdot)\)	4007.c	2003	yes	\(1\)	\(1\)	\(e\left(\frac{1781}{2003}\right)\)	\(e\left(\frac{314}{2003}\right)\)	\(e\left(\frac{1559}{2003}\right)\)	\(e\left(\frac{1814}{2003}\right)\)	\(e\left(\frac{92}{2003}\right)\)	\(e\left(\frac{326}{2003}\right)\)	\(e\left(\frac{1337}{2003}\right)\)	\(e\left(\frac{628}{2003}\right)\)	\(e\left(\frac{1592}{2003}\right)\)	\(e\left(\frac{1933}{2003}\right)\)
\(\chi_{4007}(9,\cdot)\)	4007.c	2003	yes	\(1\)	\(1\)	\(e\left(\frac{877}{2003}\right)\)	\(e\left(\frac{1340}{2003}\right)\)	\(e\left(\frac{1754}{2003}\right)\)	\(e\left(\frac{1694}{2003}\right)\)	\(e\left(\frac{214}{2003}\right)\)	\(e\left(\frac{1455}{2003}\right)\)	\(e\left(\frac{628}{2003}\right)\)	\(e\left(\frac{677}{2003}\right)\)	\(e\left(\frac{568}{2003}\right)\)	\(e\left(\frac{1666}{2003}\right)\)
\(\chi_{4007}(10,\cdot)\)	4007.d	4006	yes	\(-1\)	\(1\)	\(e\left(\frac{1866}{2003}\right)\)	\(e\left(\frac{284}{2003}\right)\)	\(e\left(\frac{1729}{2003}\right)\)	\(e\left(\frac{3881}{4006}\right)\)	\(e\left(\frac{147}{2003}\right)\)	\(e\left(\frac{129}{2003}\right)\)	\(e\left(\frac{1592}{2003}\right)\)	\(e\left(\frac{568}{2003}\right)\)	\(e\left(\frac{3607}{4006}\right)\)	\(e\left(\frac{473}{4006}\right)\)
\(\chi_{4007}(11,\cdot)\)	4007.d	4006	yes	\(-1\)	\(1\)	\(e\left(\frac{1312}{2003}\right)\)	\(e\left(\frac{833}{2003}\right)\)	\(e\left(\frac{621}{2003}\right)\)	\(e\left(\frac{1855}{4006}\right)\)	\(e\left(\frac{142}{2003}\right)\)	\(e\left(\frac{329}{2003}\right)\)	\(e\left(\frac{1933}{2003}\right)\)	\(e\left(\frac{1666}{2003}\right)\)	\(e\left(\frac{473}{4006}\right)\)	\(e\left(\frac{3877}{4006}\right)\)
\(\chi_{4007}(12,\cdot)\)	4007.c	2003	yes	\(1\)	\(1\)	\(e\left(\frac{1292}{2003}\right)\)	\(e\left(\frac{1547}{2003}\right)\)	\(e\left(\frac{581}{2003}\right)\)	\(e\left(\frac{721}{2003}\right)\)	\(e\left(\frac{836}{2003}\right)\)	\(e\left(\frac{611}{2003}\right)\)	\(e\left(\frac{1873}{2003}\right)\)	\(e\left(\frac{1091}{2003}\right)\)	\(e\left(\frac{10}{2003}\right)\)	\(e\left(\frac{1454}{2003}\right)\)
\(\chi_{4007}(13,\cdot)\)	4007.c	2003	yes	\(1\)	\(1\)	\(e\left(\frac{835}{2003}\right)\)	\(e\left(\frac{1237}{2003}\right)\)	\(e\left(\frac{1670}{2003}\right)\)	\(e\left(\frac{359}{2003}\right)\)	\(e\left(\frac{69}{2003}\right)\)	\(e\left(\frac{1246}{2003}\right)\)	\(e\left(\frac{502}{2003}\right)\)	\(e\left(\frac{471}{2003}\right)\)	\(e\left(\frac{1194}{2003}\right)\)	\(e\left(\frac{949}{2003}\right)\)
\(\chi_{4007}(14,\cdot)\)	4007.c	2003	yes	\(1\)	\(1\)	\(e\left(\frac{1370}{2003}\right)\)	\(e\left(\frac{1166}{2003}\right)\)	\(e\left(\frac{737}{2003}\right)\)	\(e\left(\frac{625}{2003}\right)\)	\(e\left(\frac{533}{2003}\right)\)	\(e\left(\frac{713}{2003}\right)\)	\(e\left(\frac{104}{2003}\right)\)	\(e\left(\frac{329}{2003}\right)\)	\(e\left(\frac{1995}{2003}\right)\)	\(e\left(\frac{1641}{2003}\right)\)
\(\chi_{4007}(15,\cdot)\)	4007.d	4006	yes	\(-1\)	\(1\)	\(e\left(\frac{1377}{2003}\right)\)	\(e\left(\frac{1517}{2003}\right)\)	\(e\left(\frac{751}{2003}\right)\)	\(e\left(\frac{1695}{4006}\right)\)	\(e\left(\frac{891}{2003}\right)\)	\(e\left(\frac{414}{2003}\right)\)	\(e\left(\frac{125}{2003}\right)\)	\(e\left(\frac{1031}{2003}\right)\)	\(e\left(\frac{443}{4006}\right)\)	\(e\left(\frac{3521}{4006}\right)\)
\(\chi_{4007}(16,\cdot)\)	4007.c	2003	yes	\(1\)	\(1\)	\(e\left(\frac{1707}{2003}\right)\)	\(e\left(\frac{1754}{2003}\right)\)	\(e\left(\frac{1411}{2003}\right)\)	\(e\left(\frac{1751}{2003}\right)\)	\(e\left(\frac{1458}{2003}\right)\)	\(e\left(\frac{1770}{2003}\right)\)	\(e\left(\frac{1115}{2003}\right)\)	\(e\left(\frac{1505}{2003}\right)\)	\(e\left(\frac{1455}{2003}\right)\)	\(e\left(\frac{1242}{2003}\right)\)
\(\chi_{4007}(17,\cdot)\)	4007.d	4006	yes	\(-1\)	\(1\)	\(e\left(\frac{1454}{2003}\right)\)	\(e\left(\frac{1372}{2003}\right)\)	\(e\left(\frac{905}{2003}\right)\)	\(e\left(\frac{581}{4006}\right)\)	\(e\left(\frac{823}{2003}\right)\)	\(e\left(\frac{1131}{2003}\right)\)	\(e\left(\frac{356}{2003}\right)\)	\(e\left(\frac{741}{2003}\right)\)	\(e\left(\frac{3489}{4006}\right)\)	\(e\left(\frac{141}{4006}\right)\)
\(\chi_{4007}(18,\cdot)\)	4007.c	2003	yes	\(1\)	\(1\)	\(e\left(\frac{803}{2003}\right)\)	\(e\left(\frac{777}{2003}\right)\)	\(e\left(\frac{1606}{2003}\right)\)	\(e\left(\frac{1631}{2003}\right)\)	\(e\left(\frac{1580}{2003}\right)\)	\(e\left(\frac{896}{2003}\right)\)	\(e\left(\frac{406}{2003}\right)\)	\(e\left(\frac{1554}{2003}\right)\)	\(e\left(\frac{431}{2003}\right)\)	\(e\left(\frac{975}{2003}\right)\)
\(\chi_{4007}(19,\cdot)\)	4007.d	4006	yes	\(-1\)	\(1\)	\(e\left(\frac{710}{2003}\right)\)	\(e\left(\frac{692}{2003}\right)\)	\(e\left(\frac{1420}{2003}\right)\)	\(e\left(\frac{3645}{4006}\right)\)	\(e\left(\frac{1402}{2003}\right)\)	\(e\left(\frac{4}{2003}\right)\)	\(e\left(\frac{127}{2003}\right)\)	\(e\left(\frac{1384}{2003}\right)\)	\(e\left(\frac{1059}{4006}\right)\)	\(e\left(\frac{3353}{4006}\right)\)
\(\chi_{4007}(20,\cdot)\)	4007.d	4006	yes	\(-1\)	\(1\)	\(e\left(\frac{1792}{2003}\right)\)	\(e\left(\frac{1724}{2003}\right)\)	\(e\left(\frac{1581}{2003}\right)\)	\(e\left(\frac{3755}{4006}\right)\)	\(e\left(\frac{1513}{2003}\right)\)	\(e\left(\frac{1573}{2003}\right)\)	\(e\left(\frac{1370}{2003}\right)\)	\(e\left(\frac{1445}{2003}\right)\)	\(e\left(\frac{3333}{4006}\right)\)	\(e\left(\frac{3097}{4006}\right)\)
\(\chi_{4007}(21,\cdot)\)	4007.c	2003	yes	\(1\)	\(1\)	\(e\left(\frac{881}{2003}\right)\)	\(e\left(\frac{396}{2003}\right)\)	\(e\left(\frac{1762}{2003}\right)\)	\(e\left(\frac{1535}{2003}\right)\)	\(e\left(\frac{1277}{2003}\right)\)	\(e\left(\frac{998}{2003}\right)\)	\(e\left(\frac{640}{2003}\right)\)	\(e\left(\frac{792}{2003}\right)\)	\(e\left(\frac{413}{2003}\right)\)	\(e\left(\frac{1162}{2003}\right)\)
\(\chi_{4007}(22,\cdot)\)	4007.d	4006	yes	\(-1\)	\(1\)	\(e\left(\frac{1238}{2003}\right)\)	\(e\left(\frac{270}{2003}\right)\)	\(e\left(\frac{473}{2003}\right)\)	\(e\left(\frac{1729}{4006}\right)\)	\(e\left(\frac{1508}{2003}\right)\)	\(e\left(\frac{1773}{2003}\right)\)	\(e\left(\frac{1711}{2003}\right)\)	\(e\left(\frac{540}{2003}\right)\)	\(e\left(\frac{199}{4006}\right)\)	\(e\left(\frac{2495}{4006}\right)\)
\(\chi_{4007}(23,\cdot)\)	4007.c	2003	yes	\(1\)	\(1\)	\(e\left(\frac{1488}{2003}\right)\)	\(e\left(\frac{1360}{2003}\right)\)	\(e\left(\frac{973}{2003}\right)\)	\(e\left(\frac{942}{2003}\right)\)	\(e\left(\frac{845}{2003}\right)\)	\(e\left(\frac{251}{2003}\right)\)	\(e\left(\frac{458}{2003}\right)\)	\(e\left(\frac{717}{2003}\right)\)	\(e\left(\frac{427}{2003}\right)\)	\(e\left(\frac{794}{2003}\right)\)
\(\chi_{4007}(24,\cdot)\)	4007.c	2003	yes	\(1\)	\(1\)	\(e\left(\frac{1218}{2003}\right)\)	\(e\left(\frac{984}{2003}\right)\)	\(e\left(\frac{433}{2003}\right)\)	\(e\left(\frac{658}{2003}\right)\)	\(e\left(\frac{199}{2003}\right)\)	\(e\left(\frac{52}{2003}\right)\)	\(e\left(\frac{1651}{2003}\right)\)	\(e\left(\frac{1968}{2003}\right)\)	\(e\left(\frac{1876}{2003}\right)\)	\(e\left(\frac{763}{2003}\right)\)
\(\chi_{4007}(25,\cdot)\)	4007.c	2003	yes	\(1\)	\(1\)	\(e\left(\frac{1877}{2003}\right)\)	\(e\left(\frac{1694}{2003}\right)\)	\(e\left(\frac{1751}{2003}\right)\)	\(e\left(\frac{1}{2003}\right)\)	\(e\left(\frac{1568}{2003}\right)\)	\(e\left(\frac{1376}{2003}\right)\)	\(e\left(\frac{1625}{2003}\right)\)	\(e\left(\frac{1385}{2003}\right)\)	\(e\left(\frac{1878}{2003}\right)\)	\(e\left(\frac{1855}{2003}\right)\)
\(\chi_{4007}(26,\cdot)\)	4007.c	2003	yes	\(1\)	\(1\)	\(e\left(\frac{761}{2003}\right)\)	\(e\left(\frac{674}{2003}\right)\)	\(e\left(\frac{1522}{2003}\right)\)	\(e\left(\frac{296}{2003}\right)\)	\(e\left(\frac{1435}{2003}\right)\)	\(e\left(\frac{687}{2003}\right)\)	\(e\left(\frac{280}{2003}\right)\)	\(e\left(\frac{1348}{2003}\right)\)	\(e\left(\frac{1057}{2003}\right)\)	\(e\left(\frac{258}{2003}\right)\)
\(\chi_{4007}(27,\cdot)\)	4007.c	2003	yes	\(1\)	\(1\)	\(e\left(\frac{314}{2003}\right)\)	\(e\left(\frac{7}{2003}\right)\)	\(e\left(\frac{628}{2003}\right)\)	\(e\left(\frac{538}{2003}\right)\)	\(e\left(\frac{321}{2003}\right)\)	\(e\left(\frac{1181}{2003}\right)\)	\(e\left(\frac{942}{2003}\right)\)	\(e\left(\frac{14}{2003}\right)\)	\(e\left(\frac{852}{2003}\right)\)	\(e\left(\frac{496}{2003}\right)\)
\(\chi_{4007}(28,\cdot)\)	4007.c	2003	yes	\(1\)	\(1\)	\(e\left(\frac{1296}{2003}\right)\)	\(e\left(\frac{603}{2003}\right)\)	\(e\left(\frac{589}{2003}\right)\)	\(e\left(\frac{562}{2003}\right)\)	\(e\left(\frac{1899}{2003}\right)\)	\(e\left(\frac{154}{2003}\right)\)	\(e\left(\frac{1885}{2003}\right)\)	\(e\left(\frac{1206}{2003}\right)\)	\(e\left(\frac{1858}{2003}\right)\)	\(e\left(\frac{950}{2003}\right)\)
\(\chi_{4007}(29,\cdot)\)	4007.c	2003	yes	\(1\)	\(1\)	\(e\left(\frac{1089}{2003}\right)\)	\(e\left(\frac{1383}{2003}\right)\)	\(e\left(\frac{175}{2003}\right)\)	\(e\left(\frac{1279}{2003}\right)\)	\(e\left(\frac{469}{2003}\right)\)	\(e\left(\frac{1270}{2003}\right)\)	\(e\left(\frac{1264}{2003}\right)\)	\(e\left(\frac{763}{2003}\right)\)	\(e\left(\frac{365}{2003}\right)\)	\(e\left(\frac{993}{2003}\right)\)
\(\chi_{4007}(30,\cdot)\)	4007.d	4006	yes	\(-1\)	\(1\)	\(e\left(\frac{1303}{2003}\right)\)	\(e\left(\frac{954}{2003}\right)\)	\(e\left(\frac{603}{2003}\right)\)	\(e\left(\frac{1569}{4006}\right)\)	\(e\left(\frac{254}{2003}\right)\)	\(e\left(\frac{1858}{2003}\right)\)	\(e\left(\frac{1906}{2003}\right)\)	\(e\left(\frac{1908}{2003}\right)\)	\(e\left(\frac{169}{4006}\right)\)	\(e\left(\frac{2139}{4006}\right)\)
\(\chi_{4007}(31,\cdot)\)	4007.d	4006	yes	\(-1\)	\(1\)	\(e\left(\frac{790}{2003}\right)\)	\(e\left(\frac{1842}{2003}\right)\)	\(e\left(\frac{1580}{2003}\right)\)	\(e\left(\frac{1291}{4006}\right)\)	\(e\left(\frac{629}{2003}\right)\)	\(e\left(\frac{879}{2003}\right)\)	\(e\left(\frac{367}{2003}\right)\)	\(e\left(\frac{1681}{2003}\right)\)	\(e\left(\frac{2871}{4006}\right)\)	\(e\left(\frac{3223}{4006}\right)\)
\(\chi_{4007}(32,\cdot)\)	4007.c	2003	yes	\(1\)	\(1\)	\(e\left(\frac{1633}{2003}\right)\)	\(e\left(\frac{1191}{2003}\right)\)	\(e\left(\frac{1263}{2003}\right)\)	\(e\left(\frac{1688}{2003}\right)\)	\(e\left(\frac{821}{2003}\right)\)	\(e\left(\frac{1211}{2003}\right)\)	\(e\left(\frac{893}{2003}\right)\)	\(e\left(\frac{379}{2003}\right)\)	\(e\left(\frac{1318}{2003}\right)\)	\(e\left(\frac{551}{2003}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Learn more

Character group

First 32 of 4006 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.