LMFDB - Group of Dirichlet characters of modulus 8038

Show commands: PariGP / SageMath

sage: H = DirichletGroup(8038)

pari: g = idealstar(,8038,2)

Character group

sage: G.order() pari: g.no
Order	=	4018
sage: H.invariants() pari: g.cyc
Structure	=	$C_{4018}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{8038}(4021,\cdot)$

First 32 of 4018 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	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$17$	$19$	$21$
$\chi_{8038}(1,\cdot)$	8038.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{8038}(3,\cdot)$	8038.f	49	no	$1$	$1$	$e\left(\frac{48}{49}\right)$	$e\left(\frac{3}{49}\right)$	$e\left(\frac{48}{49}\right)$	$e\left(\frac{47}{49}\right)$	$e\left(\frac{4}{49}\right)$	$e\left(\frac{23}{49}\right)$	$e\left(\frac{2}{49}\right)$	$e\left(\frac{5}{49}\right)$	$e\left(\frac{47}{49}\right)$	$e\left(\frac{47}{49}\right)$
$\chi_{8038}(5,\cdot)$	8038.k	2009	no	$1$	$1$	$e\left(\frac{3}{49}\right)$	$e\left(\frac{1395}{2009}\right)$	$e\left(\frac{1348}{2009}\right)$	$e\left(\frac{6}{49}\right)$	$e\left(\frac{1419}{2009}\right)$	$e\left(\frac{1973}{2009}\right)$	$e\left(\frac{1518}{2009}\right)$	$e\left(\frac{316}{2009}\right)$	$e\left(\frac{148}{2009}\right)$	$e\left(\frac{1471}{2009}\right)$
$\chi_{8038}(7,\cdot)$	8038.l	4018	no	$-1$	$1$	$e\left(\frac{48}{49}\right)$	$e\left(\frac{1348}{2009}\right)$	$e\left(\frac{1731}{4018}\right)$	$e\left(\frac{47}{49}\right)$	$e\left(\frac{3317}{4018}\right)$	$e\left(\frac{73}{4018}\right)$	$e\left(\frac{1307}{2009}\right)$	$e\left(\frac{1145}{4018}\right)$	$e\left(\frac{408}{2009}\right)$	$e\left(\frac{1649}{4018}\right)$
$\chi_{8038}(9,\cdot)$	8038.f	49	no	$1$	$1$	$e\left(\frac{47}{49}\right)$	$e\left(\frac{6}{49}\right)$	$e\left(\frac{47}{49}\right)$	$e\left(\frac{45}{49}\right)$	$e\left(\frac{8}{49}\right)$	$e\left(\frac{46}{49}\right)$	$e\left(\frac{4}{49}\right)$	$e\left(\frac{10}{49}\right)$	$e\left(\frac{45}{49}\right)$	$e\left(\frac{45}{49}\right)$
$\chi_{8038}(11,\cdot)$	8038.l	4018	no	$-1$	$1$	$e\left(\frac{4}{49}\right)$	$e\left(\frac{1419}{2009}\right)$	$e\left(\frac{3317}{4018}\right)$	$e\left(\frac{8}{49}\right)$	$e\left(\frac{3833}{4018}\right)$	$e\left(\frac{1521}{4018}\right)$	$e\left(\frac{1583}{2009}\right)$	$e\left(\frac{2721}{4018}\right)$	$e\left(\frac{1896}{2009}\right)$	$e\left(\frac{3645}{4018}\right)$
$\chi_{8038}(13,\cdot)$	8038.l	4018	no	$-1$	$1$	$e\left(\frac{23}{49}\right)$	$e\left(\frac{1973}{2009}\right)$	$e\left(\frac{73}{4018}\right)$	$e\left(\frac{46}{49}\right)$	$e\left(\frac{1521}{4018}\right)$	$e\left(\frac{2633}{4018}\right)$	$e\left(\frac{907}{2009}\right)$	$e\left(\frac{1889}{4018}\right)$	$e\left(\frac{1396}{2009}\right)$	$e\left(\frac{1959}{4018}\right)$
$\chi_{8038}(15,\cdot)$	8038.k	2009	no	$1$	$1$	$e\left(\frac{2}{49}\right)$	$e\left(\frac{1518}{2009}\right)$	$e\left(\frac{1307}{2009}\right)$	$e\left(\frac{4}{49}\right)$	$e\left(\frac{1583}{2009}\right)$	$e\left(\frac{907}{2009}\right)$	$e\left(\frac{1600}{2009}\right)$	$e\left(\frac{521}{2009}\right)$	$e\left(\frac{66}{2009}\right)$	$e\left(\frac{1389}{2009}\right)$
$\chi_{8038}(17,\cdot)$	8038.l	4018	no	$-1$	$1$	$e\left(\frac{5}{49}\right)$	$e\left(\frac{316}{2009}\right)$	$e\left(\frac{1145}{4018}\right)$	$e\left(\frac{10}{49}\right)$	$e\left(\frac{2721}{4018}\right)$	$e\left(\frac{1889}{4018}\right)$	$e\left(\frac{521}{2009}\right)$	$e\left(\frac{1723}{4018}\right)$	$e\left(\frac{1586}{2009}\right)$	$e\left(\frac{1555}{4018}\right)$
$\chi_{8038}(19,\cdot)$	8038.k	2009	no	$1$	$1$	$e\left(\frac{47}{49}\right)$	$e\left(\frac{148}{2009}\right)$	$e\left(\frac{408}{2009}\right)$	$e\left(\frac{45}{49}\right)$	$e\left(\frac{1896}{2009}\right)$	$e\left(\frac{1396}{2009}\right)$	$e\left(\frac{66}{2009}\right)$	$e\left(\frac{1586}{2009}\right)$	$e\left(\frac{1404}{2009}\right)$	$e\left(\frac{326}{2009}\right)$
$\chi_{8038}(21,\cdot)$	8038.l	4018	no	$-1$	$1$	$e\left(\frac{47}{49}\right)$	$e\left(\frac{1471}{2009}\right)$	$e\left(\frac{1649}{4018}\right)$	$e\left(\frac{45}{49}\right)$	$e\left(\frac{3645}{4018}\right)$	$e\left(\frac{1959}{4018}\right)$	$e\left(\frac{1389}{2009}\right)$	$e\left(\frac{1555}{4018}\right)$	$e\left(\frac{326}{2009}\right)$	$e\left(\frac{1485}{4018}\right)$
$\chi_{8038}(23,\cdot)$	8038.k	2009	no	$1$	$1$	$e\left(\frac{31}{49}\right)$	$e\left(\frac{401}{2009}\right)$	$e\left(\frac{291}{2009}\right)$	$e\left(\frac{13}{49}\right)$	$e\left(\frac{1825}{2009}\right)$	$e\left(\frac{1882}{2009}\right)$	$e\left(\frac{1672}{2009}\right)$	$e\left(\frac{1338}{2009}\right)$	$e\left(\frac{1415}{2009}\right)$	$e\left(\frac{1562}{2009}\right)$
$\chi_{8038}(25,\cdot)$	8038.k	2009	no	$1$	$1$	$e\left(\frac{6}{49}\right)$	$e\left(\frac{781}{2009}\right)$	$e\left(\frac{687}{2009}\right)$	$e\left(\frac{12}{49}\right)$	$e\left(\frac{829}{2009}\right)$	$e\left(\frac{1937}{2009}\right)$	$e\left(\frac{1027}{2009}\right)$	$e\left(\frac{632}{2009}\right)$	$e\left(\frac{296}{2009}\right)$	$e\left(\frac{933}{2009}\right)$
$\chi_{8038}(27,\cdot)$	8038.f	49	no	$1$	$1$	$e\left(\frac{46}{49}\right)$	$e\left(\frac{9}{49}\right)$	$e\left(\frac{46}{49}\right)$	$e\left(\frac{43}{49}\right)$	$e\left(\frac{12}{49}\right)$	$e\left(\frac{20}{49}\right)$	$e\left(\frac{6}{49}\right)$	$e\left(\frac{15}{49}\right)$	$e\left(\frac{43}{49}\right)$	$e\left(\frac{43}{49}\right)$
$\chi_{8038}(29,\cdot)$	8038.l	4018	no	$-1$	$1$	$e\left(\frac{36}{49}\right)$	$e\left(\frac{1403}{2009}\right)$	$e\left(\frac{2903}{4018}\right)$	$e\left(\frac{23}{49}\right)$	$e\left(\frac{491}{4018}\right)$	$e\left(\frac{459}{4018}\right)$	$e\left(\frac{870}{2009}\right)$	$e\left(\frac{4007}{4018}\right)$	$e\left(\frac{61}{2009}\right)$	$e\left(\frac{1837}{4018}\right)$
$\chi_{8038}(31,\cdot)$	8038.l	4018	no	$-1$	$1$	$e\left(\frac{39}{49}\right)$	$e\left(\frac{1671}{2009}\right)$	$e\left(\frac{797}{4018}\right)$	$e\left(\frac{29}{49}\right)$	$e\left(\frac{3231}{4018}\right)$	$e\left(\frac{1171}{4018}\right)$	$e\left(\frac{1261}{2009}\right)$	$e\left(\frac{3561}{4018}\right)$	$e\left(\frac{160}{2009}\right)$	$e\left(\frac{3995}{4018}\right)$
$\chi_{8038}(33,\cdot)$	8038.l	4018	no	$-1$	$1$	$e\left(\frac{3}{49}\right)$	$e\left(\frac{1542}{2009}\right)$	$e\left(\frac{3235}{4018}\right)$	$e\left(\frac{6}{49}\right)$	$e\left(\frac{143}{4018}\right)$	$e\left(\frac{3407}{4018}\right)$	$e\left(\frac{1665}{2009}\right)$	$e\left(\frac{3131}{4018}\right)$	$e\left(\frac{1814}{2009}\right)$	$e\left(\frac{3481}{4018}\right)$
$\chi_{8038}(35,\cdot)$	8038.l	4018	no	$-1$	$1$	$e\left(\frac{2}{49}\right)$	$e\left(\frac{734}{2009}\right)$	$e\left(\frac{409}{4018}\right)$	$e\left(\frac{4}{49}\right)$	$e\left(\frac{2137}{4018}\right)$	$e\left(\frac{1}{4018}\right)$	$e\left(\frac{816}{2009}\right)$	$e\left(\frac{1777}{4018}\right)$	$e\left(\frac{556}{2009}\right)$	$e\left(\frac{573}{4018}\right)$
$\chi_{8038}(37,\cdot)$	8038.l	4018	no	$-1$	$1$	$e\left(\frac{9}{49}\right)$	$e\left(\frac{1245}{2009}\right)$	$e\left(\frac{3335}{4018}\right)$	$e\left(\frac{18}{49}\right)$	$e\left(\frac{135}{4018}\right)$	$e\left(\frac{519}{4018}\right)$	$e\left(\frac{1614}{2009}\right)$	$e\left(\frac{2141}{4018}\right)$	$e\left(\frac{1277}{2009}\right)$	$e\left(\frac{55}{4018}\right)$
$\chi_{8038}(39,\cdot)$	8038.l	4018	no	$-1$	$1$	$e\left(\frac{22}{49}\right)$	$e\left(\frac{87}{2009}\right)$	$e\left(\frac{4009}{4018}\right)$	$e\left(\frac{44}{49}\right)$	$e\left(\frac{1849}{4018}\right)$	$e\left(\frac{501}{4018}\right)$	$e\left(\frac{989}{2009}\right)$	$e\left(\frac{2299}{4018}\right)$	$e\left(\frac{1314}{2009}\right)$	$e\left(\frac{1795}{4018}\right)$
$\chi_{8038}(41,\cdot)$	8038.i	287	no	$1$	$1$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{132}{287}\right)$	$e\left(\frac{201}{287}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{225}{287}\right)$	$e\left(\frac{4}{287}\right)$	$e\left(\frac{214}{287}\right)$	$e\left(\frac{220}{287}\right)$	$e\left(\frac{143}{287}\right)$	$e\left(\frac{283}{287}\right)$
$\chi_{8038}(43,\cdot)$	8038.k	2009	no	$1$	$1$	$e\left(\frac{39}{49}\right)$	$e\left(\frac{397}{2009}\right)$	$e\left(\frac{1746}{2009}\right)$	$e\left(\frac{29}{49}\right)$	$e\left(\frac{905}{2009}\right)$	$e\left(\frac{1247}{2009}\right)$	$e\left(\frac{1996}{2009}\right)$	$e\left(\frac{2001}{2009}\right)$	$e\left(\frac{454}{2009}\right)$	$e\left(\frac{1336}{2009}\right)$
$\chi_{8038}(45,\cdot)$	8038.k	2009	no	$1$	$1$	$e\left(\frac{1}{49}\right)$	$e\left(\frac{1641}{2009}\right)$	$e\left(\frac{1266}{2009}\right)$	$e\left(\frac{2}{49}\right)$	$e\left(\frac{1747}{2009}\right)$	$e\left(\frac{1850}{2009}\right)$	$e\left(\frac{1682}{2009}\right)$	$e\left(\frac{726}{2009}\right)$	$e\left(\frac{1993}{2009}\right)$	$e\left(\frac{1307}{2009}\right)$
$\chi_{8038}(47,\cdot)$	8038.l	4018	no	$-1$	$1$	$e\left(\frac{4}{49}\right)$	$e\left(\frac{1615}{2009}\right)$	$e\left(\frac{1357}{4018}\right)$	$e\left(\frac{8}{49}\right)$	$e\left(\frac{1579}{4018}\right)$	$e\left(\frac{3481}{4018}\right)$	$e\left(\frac{1779}{2009}\right)$	$e\left(\frac{2035}{4018}\right)$	$e\left(\frac{769}{2009}\right)$	$e\left(\frac{1685}{4018}\right)$
$\chi_{8038}(49,\cdot)$	8038.k	2009	no	$1$	$1$	$e\left(\frac{47}{49}\right)$	$e\left(\frac{687}{2009}\right)$	$e\left(\frac{1731}{2009}\right)$	$e\left(\frac{45}{49}\right)$	$e\left(\frac{1308}{2009}\right)$	$e\left(\frac{73}{2009}\right)$	$e\left(\frac{605}{2009}\right)$	$e\left(\frac{1145}{2009}\right)$	$e\left(\frac{816}{2009}\right)$	$e\left(\frac{1649}{2009}\right)$
$\chi_{8038}(51,\cdot)$	8038.l	4018	no	$-1$	$1$	$e\left(\frac{4}{49}\right)$	$e\left(\frac{439}{2009}\right)$	$e\left(\frac{1063}{4018}\right)$	$e\left(\frac{8}{49}\right)$	$e\left(\frac{3049}{4018}\right)$	$e\left(\frac{3775}{4018}\right)$	$e\left(\frac{603}{2009}\right)$	$e\left(\frac{2133}{4018}\right)$	$e\left(\frac{1504}{2009}\right)$	$e\left(\frac{1391}{4018}\right)$
$\chi_{8038}(53,\cdot)$	8038.k	2009	no	$1$	$1$	$e\left(\frac{24}{49}\right)$	$e\left(\frac{1311}{2009}\right)$	$e\left(\frac{1768}{2009}\right)$	$e\left(\frac{48}{49}\right)$	$e\left(\frac{180}{2009}\right)$	$e\left(\frac{692}{2009}\right)$	$e\left(\frac{286}{2009}\right)$	$e\left(\frac{176}{2009}\right)$	$e\left(\frac{57}{2009}\right)$	$e\left(\frac{743}{2009}\right)$
$\chi_{8038}(55,\cdot)$	8038.j	574	no	$-1$	$1$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{115}{287}\right)$	$e\left(\frac{285}{574}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{379}{574}\right)$	$e\left(\frac{207}{574}\right)$	$e\left(\frac{156}{287}\right)$	$e\left(\frac{479}{574}\right)$	$e\left(\frac{5}{287}\right)$	$e\left(\frac{367}{574}\right)$
$\chi_{8038}(57,\cdot)$	8038.k	2009	no	$1$	$1$	$e\left(\frac{46}{49}\right)$	$e\left(\frac{271}{2009}\right)$	$e\left(\frac{367}{2009}\right)$	$e\left(\frac{43}{49}\right)$	$e\left(\frac{51}{2009}\right)$	$e\left(\frac{330}{2009}\right)$	$e\left(\frac{148}{2009}\right)$	$e\left(\frac{1791}{2009}\right)$	$e\left(\frac{1322}{2009}\right)$	$e\left(\frac{244}{2009}\right)$
$\chi_{8038}(59,\cdot)$	8038.l	4018	no	$-1$	$1$	$e\left(\frac{18}{49}\right)$	$e\left(\frac{236}{2009}\right)$	$e\left(\frac{3093}{4018}\right)$	$e\left(\frac{36}{49}\right)$	$e\left(\frac{2083}{4018}\right)$	$e\left(\frac{597}{4018}\right)$	$e\left(\frac{974}{2009}\right)$	$e\left(\frac{117}{4018}\right)$	$e\left(\frac{447}{2009}\right)$	$e\left(\frac{551}{4018}\right)$
$\chi_{8038}(61,\cdot)$	8038.l	4018	no	$-1$	$1$	$e\left(\frac{8}{49}\right)$	$e\left(\frac{1417}{2009}\right)$	$e\left(\frac{2763}{4018}\right)$	$e\left(\frac{16}{49}\right)$	$e\left(\frac{2913}{4018}\right)$	$e\left(\frac{2895}{4018}\right)$	$e\left(\frac{1745}{2009}\right)$	$e\left(\frac{1375}{4018}\right)$	$e\left(\frac{411}{2009}\right)$	$e\left(\frac{3419}{4018}\right)$
$\chi_{8038}(63,\cdot)$	8038.l	4018	no	$-1$	$1$	$e\left(\frac{46}{49}\right)$	$e\left(\frac{1594}{2009}\right)$	$e\left(\frac{1567}{4018}\right)$	$e\left(\frac{43}{49}\right)$	$e\left(\frac{3973}{4018}\right)$	$e\left(\frac{3845}{4018}\right)$	$e\left(\frac{1471}{2009}\right)$	$e\left(\frac{1965}{4018}\right)$	$e\left(\frac{244}{2009}\right)$	$e\left(\frac{1321}{4018}\right)$

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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	$8038$
Structure	\(C_{4018}\)
Order	$4018$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(21\)
\(\chi_{8038}(1,\cdot)\)	8038.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{8038}(3,\cdot)\)	8038.f	49	no	\(1\)	\(1\)	\(e\left(\frac{48}{49}\right)\)	\(e\left(\frac{3}{49}\right)\)	\(e\left(\frac{48}{49}\right)\)	\(e\left(\frac{47}{49}\right)\)	\(e\left(\frac{4}{49}\right)\)	\(e\left(\frac{23}{49}\right)\)	\(e\left(\frac{2}{49}\right)\)	\(e\left(\frac{5}{49}\right)\)	\(e\left(\frac{47}{49}\right)\)	\(e\left(\frac{47}{49}\right)\)
\(\chi_{8038}(5,\cdot)\)	8038.k	2009	no	\(1\)	\(1\)	\(e\left(\frac{3}{49}\right)\)	\(e\left(\frac{1395}{2009}\right)\)	\(e\left(\frac{1348}{2009}\right)\)	\(e\left(\frac{6}{49}\right)\)	\(e\left(\frac{1419}{2009}\right)\)	\(e\left(\frac{1973}{2009}\right)\)	\(e\left(\frac{1518}{2009}\right)\)	\(e\left(\frac{316}{2009}\right)\)	\(e\left(\frac{148}{2009}\right)\)	\(e\left(\frac{1471}{2009}\right)\)
\(\chi_{8038}(7,\cdot)\)	8038.l	4018	no	\(-1\)	\(1\)	\(e\left(\frac{48}{49}\right)\)	\(e\left(\frac{1348}{2009}\right)\)	\(e\left(\frac{1731}{4018}\right)\)	\(e\left(\frac{47}{49}\right)\)	\(e\left(\frac{3317}{4018}\right)\)	\(e\left(\frac{73}{4018}\right)\)	\(e\left(\frac{1307}{2009}\right)\)	\(e\left(\frac{1145}{4018}\right)\)	\(e\left(\frac{408}{2009}\right)\)	\(e\left(\frac{1649}{4018}\right)\)
\(\chi_{8038}(9,\cdot)\)	8038.f	49	no	\(1\)	\(1\)	\(e\left(\frac{47}{49}\right)\)	\(e\left(\frac{6}{49}\right)\)	\(e\left(\frac{47}{49}\right)\)	\(e\left(\frac{45}{49}\right)\)	\(e\left(\frac{8}{49}\right)\)	\(e\left(\frac{46}{49}\right)\)	\(e\left(\frac{4}{49}\right)\)	\(e\left(\frac{10}{49}\right)\)	\(e\left(\frac{45}{49}\right)\)	\(e\left(\frac{45}{49}\right)\)
\(\chi_{8038}(11,\cdot)\)	8038.l	4018	no	\(-1\)	\(1\)	\(e\left(\frac{4}{49}\right)\)	\(e\left(\frac{1419}{2009}\right)\)	\(e\left(\frac{3317}{4018}\right)\)	\(e\left(\frac{8}{49}\right)\)	\(e\left(\frac{3833}{4018}\right)\)	\(e\left(\frac{1521}{4018}\right)\)	\(e\left(\frac{1583}{2009}\right)\)	\(e\left(\frac{2721}{4018}\right)\)	\(e\left(\frac{1896}{2009}\right)\)	\(e\left(\frac{3645}{4018}\right)\)
\(\chi_{8038}(13,\cdot)\)	8038.l	4018	no	\(-1\)	\(1\)	\(e\left(\frac{23}{49}\right)\)	\(e\left(\frac{1973}{2009}\right)\)	\(e\left(\frac{73}{4018}\right)\)	\(e\left(\frac{46}{49}\right)\)	\(e\left(\frac{1521}{4018}\right)\)	\(e\left(\frac{2633}{4018}\right)\)	\(e\left(\frac{907}{2009}\right)\)	\(e\left(\frac{1889}{4018}\right)\)	\(e\left(\frac{1396}{2009}\right)\)	\(e\left(\frac{1959}{4018}\right)\)
\(\chi_{8038}(15,\cdot)\)	8038.k	2009	no	\(1\)	\(1\)	\(e\left(\frac{2}{49}\right)\)	\(e\left(\frac{1518}{2009}\right)\)	\(e\left(\frac{1307}{2009}\right)\)	\(e\left(\frac{4}{49}\right)\)	\(e\left(\frac{1583}{2009}\right)\)	\(e\left(\frac{907}{2009}\right)\)	\(e\left(\frac{1600}{2009}\right)\)	\(e\left(\frac{521}{2009}\right)\)	\(e\left(\frac{66}{2009}\right)\)	\(e\left(\frac{1389}{2009}\right)\)
\(\chi_{8038}(17,\cdot)\)	8038.l	4018	no	\(-1\)	\(1\)	\(e\left(\frac{5}{49}\right)\)	\(e\left(\frac{316}{2009}\right)\)	\(e\left(\frac{1145}{4018}\right)\)	\(e\left(\frac{10}{49}\right)\)	\(e\left(\frac{2721}{4018}\right)\)	\(e\left(\frac{1889}{4018}\right)\)	\(e\left(\frac{521}{2009}\right)\)	\(e\left(\frac{1723}{4018}\right)\)	\(e\left(\frac{1586}{2009}\right)\)	\(e\left(\frac{1555}{4018}\right)\)
\(\chi_{8038}(19,\cdot)\)	8038.k	2009	no	\(1\)	\(1\)	\(e\left(\frac{47}{49}\right)\)	\(e\left(\frac{148}{2009}\right)\)	\(e\left(\frac{408}{2009}\right)\)	\(e\left(\frac{45}{49}\right)\)	\(e\left(\frac{1896}{2009}\right)\)	\(e\left(\frac{1396}{2009}\right)\)	\(e\left(\frac{66}{2009}\right)\)	\(e\left(\frac{1586}{2009}\right)\)	\(e\left(\frac{1404}{2009}\right)\)	\(e\left(\frac{326}{2009}\right)\)
\(\chi_{8038}(21,\cdot)\)	8038.l	4018	no	\(-1\)	\(1\)	\(e\left(\frac{47}{49}\right)\)	\(e\left(\frac{1471}{2009}\right)\)	\(e\left(\frac{1649}{4018}\right)\)	\(e\left(\frac{45}{49}\right)\)	\(e\left(\frac{3645}{4018}\right)\)	\(e\left(\frac{1959}{4018}\right)\)	\(e\left(\frac{1389}{2009}\right)\)	\(e\left(\frac{1555}{4018}\right)\)	\(e\left(\frac{326}{2009}\right)\)	\(e\left(\frac{1485}{4018}\right)\)
\(\chi_{8038}(23,\cdot)\)	8038.k	2009	no	\(1\)	\(1\)	\(e\left(\frac{31}{49}\right)\)	\(e\left(\frac{401}{2009}\right)\)	\(e\left(\frac{291}{2009}\right)\)	\(e\left(\frac{13}{49}\right)\)	\(e\left(\frac{1825}{2009}\right)\)	\(e\left(\frac{1882}{2009}\right)\)	\(e\left(\frac{1672}{2009}\right)\)	\(e\left(\frac{1338}{2009}\right)\)	\(e\left(\frac{1415}{2009}\right)\)	\(e\left(\frac{1562}{2009}\right)\)
\(\chi_{8038}(25,\cdot)\)	8038.k	2009	no	\(1\)	\(1\)	\(e\left(\frac{6}{49}\right)\)	\(e\left(\frac{781}{2009}\right)\)	\(e\left(\frac{687}{2009}\right)\)	\(e\left(\frac{12}{49}\right)\)	\(e\left(\frac{829}{2009}\right)\)	\(e\left(\frac{1937}{2009}\right)\)	\(e\left(\frac{1027}{2009}\right)\)	\(e\left(\frac{632}{2009}\right)\)	\(e\left(\frac{296}{2009}\right)\)	\(e\left(\frac{933}{2009}\right)\)
\(\chi_{8038}(27,\cdot)\)	8038.f	49	no	\(1\)	\(1\)	\(e\left(\frac{46}{49}\right)\)	\(e\left(\frac{9}{49}\right)\)	\(e\left(\frac{46}{49}\right)\)	\(e\left(\frac{43}{49}\right)\)	\(e\left(\frac{12}{49}\right)\)	\(e\left(\frac{20}{49}\right)\)	\(e\left(\frac{6}{49}\right)\)	\(e\left(\frac{15}{49}\right)\)	\(e\left(\frac{43}{49}\right)\)	\(e\left(\frac{43}{49}\right)\)
\(\chi_{8038}(29,\cdot)\)	8038.l	4018	no	\(-1\)	\(1\)	\(e\left(\frac{36}{49}\right)\)	\(e\left(\frac{1403}{2009}\right)\)	\(e\left(\frac{2903}{4018}\right)\)	\(e\left(\frac{23}{49}\right)\)	\(e\left(\frac{491}{4018}\right)\)	\(e\left(\frac{459}{4018}\right)\)	\(e\left(\frac{870}{2009}\right)\)	\(e\left(\frac{4007}{4018}\right)\)	\(e\left(\frac{61}{2009}\right)\)	\(e\left(\frac{1837}{4018}\right)\)
\(\chi_{8038}(31,\cdot)\)	8038.l	4018	no	\(-1\)	\(1\)	\(e\left(\frac{39}{49}\right)\)	\(e\left(\frac{1671}{2009}\right)\)	\(e\left(\frac{797}{4018}\right)\)	\(e\left(\frac{29}{49}\right)\)	\(e\left(\frac{3231}{4018}\right)\)	\(e\left(\frac{1171}{4018}\right)\)	\(e\left(\frac{1261}{2009}\right)\)	\(e\left(\frac{3561}{4018}\right)\)	\(e\left(\frac{160}{2009}\right)\)	\(e\left(\frac{3995}{4018}\right)\)
\(\chi_{8038}(33,\cdot)\)	8038.l	4018	no	\(-1\)	\(1\)	\(e\left(\frac{3}{49}\right)\)	\(e\left(\frac{1542}{2009}\right)\)	\(e\left(\frac{3235}{4018}\right)\)	\(e\left(\frac{6}{49}\right)\)	\(e\left(\frac{143}{4018}\right)\)	\(e\left(\frac{3407}{4018}\right)\)	\(e\left(\frac{1665}{2009}\right)\)	\(e\left(\frac{3131}{4018}\right)\)	\(e\left(\frac{1814}{2009}\right)\)	\(e\left(\frac{3481}{4018}\right)\)
\(\chi_{8038}(35,\cdot)\)	8038.l	4018	no	\(-1\)	\(1\)	\(e\left(\frac{2}{49}\right)\)	\(e\left(\frac{734}{2009}\right)\)	\(e\left(\frac{409}{4018}\right)\)	\(e\left(\frac{4}{49}\right)\)	\(e\left(\frac{2137}{4018}\right)\)	\(e\left(\frac{1}{4018}\right)\)	\(e\left(\frac{816}{2009}\right)\)	\(e\left(\frac{1777}{4018}\right)\)	\(e\left(\frac{556}{2009}\right)\)	\(e\left(\frac{573}{4018}\right)\)
\(\chi_{8038}(37,\cdot)\)	8038.l	4018	no	\(-1\)	\(1\)	\(e\left(\frac{9}{49}\right)\)	\(e\left(\frac{1245}{2009}\right)\)	\(e\left(\frac{3335}{4018}\right)\)	\(e\left(\frac{18}{49}\right)\)	\(e\left(\frac{135}{4018}\right)\)	\(e\left(\frac{519}{4018}\right)\)	\(e\left(\frac{1614}{2009}\right)\)	\(e\left(\frac{2141}{4018}\right)\)	\(e\left(\frac{1277}{2009}\right)\)	\(e\left(\frac{55}{4018}\right)\)
\(\chi_{8038}(39,\cdot)\)	8038.l	4018	no	\(-1\)	\(1\)	\(e\left(\frac{22}{49}\right)\)	\(e\left(\frac{87}{2009}\right)\)	\(e\left(\frac{4009}{4018}\right)\)	\(e\left(\frac{44}{49}\right)\)	\(e\left(\frac{1849}{4018}\right)\)	\(e\left(\frac{501}{4018}\right)\)	\(e\left(\frac{989}{2009}\right)\)	\(e\left(\frac{2299}{4018}\right)\)	\(e\left(\frac{1314}{2009}\right)\)	\(e\left(\frac{1795}{4018}\right)\)
\(\chi_{8038}(41,\cdot)\)	8038.i	287	no	\(1\)	\(1\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{132}{287}\right)\)	\(e\left(\frac{201}{287}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{225}{287}\right)\)	\(e\left(\frac{4}{287}\right)\)	\(e\left(\frac{214}{287}\right)\)	\(e\left(\frac{220}{287}\right)\)	\(e\left(\frac{143}{287}\right)\)	\(e\left(\frac{283}{287}\right)\)
\(\chi_{8038}(43,\cdot)\)	8038.k	2009	no	\(1\)	\(1\)	\(e\left(\frac{39}{49}\right)\)	\(e\left(\frac{397}{2009}\right)\)	\(e\left(\frac{1746}{2009}\right)\)	\(e\left(\frac{29}{49}\right)\)	\(e\left(\frac{905}{2009}\right)\)	\(e\left(\frac{1247}{2009}\right)\)	\(e\left(\frac{1996}{2009}\right)\)	\(e\left(\frac{2001}{2009}\right)\)	\(e\left(\frac{454}{2009}\right)\)	\(e\left(\frac{1336}{2009}\right)\)
\(\chi_{8038}(45,\cdot)\)	8038.k	2009	no	\(1\)	\(1\)	\(e\left(\frac{1}{49}\right)\)	\(e\left(\frac{1641}{2009}\right)\)	\(e\left(\frac{1266}{2009}\right)\)	\(e\left(\frac{2}{49}\right)\)	\(e\left(\frac{1747}{2009}\right)\)	\(e\left(\frac{1850}{2009}\right)\)	\(e\left(\frac{1682}{2009}\right)\)	\(e\left(\frac{726}{2009}\right)\)	\(e\left(\frac{1993}{2009}\right)\)	\(e\left(\frac{1307}{2009}\right)\)
\(\chi_{8038}(47,\cdot)\)	8038.l	4018	no	\(-1\)	\(1\)	\(e\left(\frac{4}{49}\right)\)	\(e\left(\frac{1615}{2009}\right)\)	\(e\left(\frac{1357}{4018}\right)\)	\(e\left(\frac{8}{49}\right)\)	\(e\left(\frac{1579}{4018}\right)\)	\(e\left(\frac{3481}{4018}\right)\)	\(e\left(\frac{1779}{2009}\right)\)	\(e\left(\frac{2035}{4018}\right)\)	\(e\left(\frac{769}{2009}\right)\)	\(e\left(\frac{1685}{4018}\right)\)
\(\chi_{8038}(49,\cdot)\)	8038.k	2009	no	\(1\)	\(1\)	\(e\left(\frac{47}{49}\right)\)	\(e\left(\frac{687}{2009}\right)\)	\(e\left(\frac{1731}{2009}\right)\)	\(e\left(\frac{45}{49}\right)\)	\(e\left(\frac{1308}{2009}\right)\)	\(e\left(\frac{73}{2009}\right)\)	\(e\left(\frac{605}{2009}\right)\)	\(e\left(\frac{1145}{2009}\right)\)	\(e\left(\frac{816}{2009}\right)\)	\(e\left(\frac{1649}{2009}\right)\)
\(\chi_{8038}(51,\cdot)\)	8038.l	4018	no	\(-1\)	\(1\)	\(e\left(\frac{4}{49}\right)\)	\(e\left(\frac{439}{2009}\right)\)	\(e\left(\frac{1063}{4018}\right)\)	\(e\left(\frac{8}{49}\right)\)	\(e\left(\frac{3049}{4018}\right)\)	\(e\left(\frac{3775}{4018}\right)\)	\(e\left(\frac{603}{2009}\right)\)	\(e\left(\frac{2133}{4018}\right)\)	\(e\left(\frac{1504}{2009}\right)\)	\(e\left(\frac{1391}{4018}\right)\)
\(\chi_{8038}(53,\cdot)\)	8038.k	2009	no	\(1\)	\(1\)	\(e\left(\frac{24}{49}\right)\)	\(e\left(\frac{1311}{2009}\right)\)	\(e\left(\frac{1768}{2009}\right)\)	\(e\left(\frac{48}{49}\right)\)	\(e\left(\frac{180}{2009}\right)\)	\(e\left(\frac{692}{2009}\right)\)	\(e\left(\frac{286}{2009}\right)\)	\(e\left(\frac{176}{2009}\right)\)	\(e\left(\frac{57}{2009}\right)\)	\(e\left(\frac{743}{2009}\right)\)
\(\chi_{8038}(55,\cdot)\)	8038.j	574	no	\(-1\)	\(1\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{115}{287}\right)\)	\(e\left(\frac{285}{574}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{379}{574}\right)\)	\(e\left(\frac{207}{574}\right)\)	\(e\left(\frac{156}{287}\right)\)	\(e\left(\frac{479}{574}\right)\)	\(e\left(\frac{5}{287}\right)\)	\(e\left(\frac{367}{574}\right)\)
\(\chi_{8038}(57,\cdot)\)	8038.k	2009	no	\(1\)	\(1\)	\(e\left(\frac{46}{49}\right)\)	\(e\left(\frac{271}{2009}\right)\)	\(e\left(\frac{367}{2009}\right)\)	\(e\left(\frac{43}{49}\right)\)	\(e\left(\frac{51}{2009}\right)\)	\(e\left(\frac{330}{2009}\right)\)	\(e\left(\frac{148}{2009}\right)\)	\(e\left(\frac{1791}{2009}\right)\)	\(e\left(\frac{1322}{2009}\right)\)	\(e\left(\frac{244}{2009}\right)\)
\(\chi_{8038}(59,\cdot)\)	8038.l	4018	no	\(-1\)	\(1\)	\(e\left(\frac{18}{49}\right)\)	\(e\left(\frac{236}{2009}\right)\)	\(e\left(\frac{3093}{4018}\right)\)	\(e\left(\frac{36}{49}\right)\)	\(e\left(\frac{2083}{4018}\right)\)	\(e\left(\frac{597}{4018}\right)\)	\(e\left(\frac{974}{2009}\right)\)	\(e\left(\frac{117}{4018}\right)\)	\(e\left(\frac{447}{2009}\right)\)	\(e\left(\frac{551}{4018}\right)\)
\(\chi_{8038}(61,\cdot)\)	8038.l	4018	no	\(-1\)	\(1\)	\(e\left(\frac{8}{49}\right)\)	\(e\left(\frac{1417}{2009}\right)\)	\(e\left(\frac{2763}{4018}\right)\)	\(e\left(\frac{16}{49}\right)\)	\(e\left(\frac{2913}{4018}\right)\)	\(e\left(\frac{2895}{4018}\right)\)	\(e\left(\frac{1745}{2009}\right)\)	\(e\left(\frac{1375}{4018}\right)\)	\(e\left(\frac{411}{2009}\right)\)	\(e\left(\frac{3419}{4018}\right)\)
\(\chi_{8038}(63,\cdot)\)	8038.l	4018	no	\(-1\)	\(1\)	\(e\left(\frac{46}{49}\right)\)	\(e\left(\frac{1594}{2009}\right)\)	\(e\left(\frac{1567}{4018}\right)\)	\(e\left(\frac{43}{49}\right)\)	\(e\left(\frac{3973}{4018}\right)\)	\(e\left(\frac{3845}{4018}\right)\)	\(e\left(\frac{1471}{2009}\right)\)	\(e\left(\frac{1965}{4018}\right)\)	\(e\left(\frac{244}{2009}\right)\)	\(e\left(\frac{1321}{4018}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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Character group

First 32 of 4018 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.