LMFDB - Group of Dirichlet characters of modulus 4019

Show commands: PariGP / SageMath

sage: H = DirichletGroup(4019)

pari: g = idealstar(,4019,2)

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	=	$\chi_{4019}(2,\cdot)$

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	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{4019}(1,\cdot)$	4019.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{4019}(2,\cdot)$	4019.l	4018	yes	$-1$	$1$	$e\left(\frac{1}{4018}\right)$	$e\left(\frac{37}{49}\right)$	$e\left(\frac{1}{2009}\right)$	$e\left(\frac{398}{2009}\right)$	$e\left(\frac{3035}{4018}\right)$	$e\left(\frac{3769}{4018}\right)$	$e\left(\frac{3}{4018}\right)$	$e\left(\frac{25}{49}\right)$	$e\left(\frac{797}{4018}\right)$	$e\left(\frac{261}{4018}\right)$
$\chi_{4019}(3,\cdot)$	4019.f	49	yes	$1$	$1$	$e\left(\frac{37}{49}\right)$	$e\left(\frac{48}{49}\right)$	$e\left(\frac{25}{49}\right)$	$e\left(\frac{3}{49}\right)$	$e\left(\frac{36}{49}\right)$	$e\left(\frac{48}{49}\right)$	$e\left(\frac{13}{49}\right)$	$e\left(\frac{47}{49}\right)$	$e\left(\frac{40}{49}\right)$	$e\left(\frac{4}{49}\right)$
$\chi_{4019}(4,\cdot)$	4019.k	2009	yes	$1$	$1$	$e\left(\frac{1}{2009}\right)$	$e\left(\frac{25}{49}\right)$	$e\left(\frac{2}{2009}\right)$	$e\left(\frac{796}{2009}\right)$	$e\left(\frac{1026}{2009}\right)$	$e\left(\frac{1760}{2009}\right)$	$e\left(\frac{3}{2009}\right)$	$e\left(\frac{1}{49}\right)$	$e\left(\frac{797}{2009}\right)$	$e\left(\frac{261}{2009}\right)$
$\chi_{4019}(5,\cdot)$	4019.k	2009	yes	$1$	$1$	$e\left(\frac{398}{2009}\right)$	$e\left(\frac{3}{49}\right)$	$e\left(\frac{796}{2009}\right)$	$e\left(\frac{1395}{2009}\right)$	$e\left(\frac{521}{2009}\right)$	$e\left(\frac{1348}{2009}\right)$	$e\left(\frac{1194}{2009}\right)$	$e\left(\frac{6}{49}\right)$	$e\left(\frac{1793}{2009}\right)$	$e\left(\frac{1419}{2009}\right)$
$\chi_{4019}(6,\cdot)$	4019.l	4018	yes	$-1$	$1$	$e\left(\frac{3035}{4018}\right)$	$e\left(\frac{36}{49}\right)$	$e\left(\frac{1026}{2009}\right)$	$e\left(\frac{521}{2009}\right)$	$e\left(\frac{1969}{4018}\right)$	$e\left(\frac{3687}{4018}\right)$	$e\left(\frac{1069}{4018}\right)$	$e\left(\frac{23}{49}\right)$	$e\left(\frac{59}{4018}\right)$	$e\left(\frac{589}{4018}\right)$
$\chi_{4019}(7,\cdot)$	4019.l	4018	yes	$-1$	$1$	$e\left(\frac{3769}{4018}\right)$	$e\left(\frac{48}{49}\right)$	$e\left(\frac{1760}{2009}\right)$	$e\left(\frac{1348}{2009}\right)$	$e\left(\frac{3687}{4018}\right)$	$e\left(\frac{1731}{4018}\right)$	$e\left(\frac{3271}{4018}\right)$	$e\left(\frac{47}{49}\right)$	$e\left(\frac{2447}{4018}\right)$	$e\left(\frac{3317}{4018}\right)$
$\chi_{4019}(8,\cdot)$	4019.l	4018	yes	$-1$	$1$	$e\left(\frac{3}{4018}\right)$	$e\left(\frac{13}{49}\right)$	$e\left(\frac{3}{2009}\right)$	$e\left(\frac{1194}{2009}\right)$	$e\left(\frac{1069}{4018}\right)$	$e\left(\frac{3271}{4018}\right)$	$e\left(\frac{9}{4018}\right)$	$e\left(\frac{26}{49}\right)$	$e\left(\frac{2391}{4018}\right)$	$e\left(\frac{783}{4018}\right)$
$\chi_{4019}(9,\cdot)$	4019.f	49	yes	$1$	$1$	$e\left(\frac{25}{49}\right)$	$e\left(\frac{47}{49}\right)$	$e\left(\frac{1}{49}\right)$	$e\left(\frac{6}{49}\right)$	$e\left(\frac{23}{49}\right)$	$e\left(\frac{47}{49}\right)$	$e\left(\frac{26}{49}\right)$	$e\left(\frac{45}{49}\right)$	$e\left(\frac{31}{49}\right)$	$e\left(\frac{8}{49}\right)$
$\chi_{4019}(10,\cdot)$	4019.l	4018	yes	$-1$	$1$	$e\left(\frac{797}{4018}\right)$	$e\left(\frac{40}{49}\right)$	$e\left(\frac{797}{2009}\right)$	$e\left(\frac{1793}{2009}\right)$	$e\left(\frac{59}{4018}\right)$	$e\left(\frac{2447}{4018}\right)$	$e\left(\frac{2391}{4018}\right)$	$e\left(\frac{31}{49}\right)$	$e\left(\frac{365}{4018}\right)$	$e\left(\frac{3099}{4018}\right)$
$\chi_{4019}(11,\cdot)$	4019.l	4018	yes	$-1$	$1$	$e\left(\frac{261}{4018}\right)$	$e\left(\frac{4}{49}\right)$	$e\left(\frac{261}{2009}\right)$	$e\left(\frac{1419}{2009}\right)$	$e\left(\frac{589}{4018}\right)$	$e\left(\frac{3317}{4018}\right)$	$e\left(\frac{783}{4018}\right)$	$e\left(\frac{8}{49}\right)$	$e\left(\frac{3099}{4018}\right)$	$e\left(\frac{3833}{4018}\right)$
$\chi_{4019}(12,\cdot)$	4019.k	2009	yes	$1$	$1$	$e\left(\frac{1518}{2009}\right)$	$e\left(\frac{24}{49}\right)$	$e\left(\frac{1027}{2009}\right)$	$e\left(\frac{919}{2009}\right)$	$e\left(\frac{493}{2009}\right)$	$e\left(\frac{1719}{2009}\right)$	$e\left(\frac{536}{2009}\right)$	$e\left(\frac{48}{49}\right)$	$e\left(\frac{428}{2009}\right)$	$e\left(\frac{425}{2009}\right)$
$\chi_{4019}(13,\cdot)$	4019.l	4018	yes	$-1$	$1$	$e\left(\frac{1807}{4018}\right)$	$e\left(\frac{23}{49}\right)$	$e\left(\frac{1807}{2009}\right)$	$e\left(\frac{1973}{2009}\right)$	$e\left(\frac{3693}{4018}\right)$	$e\left(\frac{73}{4018}\right)$	$e\left(\frac{1403}{4018}\right)$	$e\left(\frac{46}{49}\right)$	$e\left(\frac{1735}{4018}\right)$	$e\left(\frac{1521}{4018}\right)$
$\chi_{4019}(14,\cdot)$	4019.k	2009	yes	$1$	$1$	$e\left(\frac{1885}{2009}\right)$	$e\left(\frac{36}{49}\right)$	$e\left(\frac{1761}{2009}\right)$	$e\left(\frac{1746}{2009}\right)$	$e\left(\frac{1352}{2009}\right)$	$e\left(\frac{741}{2009}\right)$	$e\left(\frac{1637}{2009}\right)$	$e\left(\frac{23}{49}\right)$	$e\left(\frac{1622}{2009}\right)$	$e\left(\frac{1789}{2009}\right)$
$\chi_{4019}(15,\cdot)$	4019.k	2009	yes	$1$	$1$	$e\left(\frac{1915}{2009}\right)$	$e\left(\frac{2}{49}\right)$	$e\left(\frac{1821}{2009}\right)$	$e\left(\frac{1518}{2009}\right)$	$e\left(\frac{1997}{2009}\right)$	$e\left(\frac{1307}{2009}\right)$	$e\left(\frac{1727}{2009}\right)$	$e\left(\frac{4}{49}\right)$	$e\left(\frac{1424}{2009}\right)$	$e\left(\frac{1583}{2009}\right)$
$\chi_{4019}(16,\cdot)$	4019.k	2009	yes	$1$	$1$	$e\left(\frac{2}{2009}\right)$	$e\left(\frac{1}{49}\right)$	$e\left(\frac{4}{2009}\right)$	$e\left(\frac{1592}{2009}\right)$	$e\left(\frac{43}{2009}\right)$	$e\left(\frac{1511}{2009}\right)$	$e\left(\frac{6}{2009}\right)$	$e\left(\frac{2}{49}\right)$	$e\left(\frac{1594}{2009}\right)$	$e\left(\frac{522}{2009}\right)$
$\chi_{4019}(17,\cdot)$	4019.l	4018	yes	$-1$	$1$	$e\left(\frac{657}{4018}\right)$	$e\left(\frac{5}{49}\right)$	$e\left(\frac{657}{2009}\right)$	$e\left(\frac{316}{2009}\right)$	$e\left(\frac{1067}{4018}\right)$	$e\left(\frac{1145}{4018}\right)$	$e\left(\frac{1971}{4018}\right)$	$e\left(\frac{10}{49}\right)$	$e\left(\frac{1289}{4018}\right)$	$e\left(\frac{2721}{4018}\right)$
$\chi_{4019}(18,\cdot)$	4019.j	574	yes	$-1$	$1$	$e\left(\frac{293}{574}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{6}{287}\right)$	$e\left(\frac{92}{287}\right)$	$e\left(\frac{129}{574}\right)$	$e\left(\frac{515}{574}\right)$	$e\left(\frac{305}{574}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{477}{574}\right)$	$e\left(\frac{131}{574}\right)$
$\chi_{4019}(19,\cdot)$	4019.k	2009	yes	$1$	$1$	$e\left(\frac{192}{2009}\right)$	$e\left(\frac{47}{49}\right)$	$e\left(\frac{384}{2009}\right)$	$e\left(\frac{148}{2009}\right)$	$e\left(\frac{110}{2009}\right)$	$e\left(\frac{408}{2009}\right)$	$e\left(\frac{576}{2009}\right)$	$e\left(\frac{45}{49}\right)$	$e\left(\frac{340}{2009}\right)$	$e\left(\frac{1896}{2009}\right)$
$\chi_{4019}(20,\cdot)$	4019.i	287	yes	$1$	$1$	$e\left(\frac{57}{287}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{114}{287}\right)$	$e\left(\frac{26}{287}\right)$	$e\left(\frac{221}{287}\right)$	$e\left(\frac{157}{287}\right)$	$e\left(\frac{171}{287}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{83}{287}\right)$	$e\left(\frac{240}{287}\right)$
$\chi_{4019}(21,\cdot)$	4019.l	4018	yes	$-1$	$1$	$e\left(\frac{2785}{4018}\right)$	$e\left(\frac{47}{49}\right)$	$e\left(\frac{776}{2009}\right)$	$e\left(\frac{1471}{2009}\right)$	$e\left(\frac{2621}{4018}\right)$	$e\left(\frac{1649}{4018}\right)$	$e\left(\frac{319}{4018}\right)$	$e\left(\frac{45}{49}\right)$	$e\left(\frac{1709}{4018}\right)$	$e\left(\frac{3645}{4018}\right)$
$\chi_{4019}(22,\cdot)$	4019.k	2009	yes	$1$	$1$	$e\left(\frac{131}{2009}\right)$	$e\left(\frac{41}{49}\right)$	$e\left(\frac{262}{2009}\right)$	$e\left(\frac{1817}{2009}\right)$	$e\left(\frac{1812}{2009}\right)$	$e\left(\frac{1534}{2009}\right)$	$e\left(\frac{393}{2009}\right)$	$e\left(\frac{33}{49}\right)$	$e\left(\frac{1948}{2009}\right)$	$e\left(\frac{38}{2009}\right)$
$\chi_{4019}(23,\cdot)$	4019.k	2009	yes	$1$	$1$	$e\left(\frac{846}{2009}\right)$	$e\left(\frac{31}{49}\right)$	$e\left(\frac{1692}{2009}\right)$	$e\left(\frac{401}{2009}\right)$	$e\left(\frac{108}{2009}\right)$	$e\left(\frac{291}{2009}\right)$	$e\left(\frac{529}{2009}\right)$	$e\left(\frac{13}{49}\right)$	$e\left(\frac{1247}{2009}\right)$	$e\left(\frac{1825}{2009}\right)$
$\chi_{4019}(24,\cdot)$	4019.l	4018	yes	$-1$	$1$	$e\left(\frac{3037}{4018}\right)$	$e\left(\frac{12}{49}\right)$	$e\left(\frac{1028}{2009}\right)$	$e\left(\frac{1317}{2009}\right)$	$e\left(\frac{3}{4018}\right)$	$e\left(\frac{3189}{4018}\right)$	$e\left(\frac{1075}{4018}\right)$	$e\left(\frac{24}{49}\right)$	$e\left(\frac{1653}{4018}\right)$	$e\left(\frac{1111}{4018}\right)$
$\chi_{4019}(25,\cdot)$	4019.k	2009	yes	$1$	$1$	$e\left(\frac{796}{2009}\right)$	$e\left(\frac{6}{49}\right)$	$e\left(\frac{1592}{2009}\right)$	$e\left(\frac{781}{2009}\right)$	$e\left(\frac{1042}{2009}\right)$	$e\left(\frac{687}{2009}\right)$	$e\left(\frac{379}{2009}\right)$	$e\left(\frac{12}{49}\right)$	$e\left(\frac{1577}{2009}\right)$	$e\left(\frac{829}{2009}\right)$
$\chi_{4019}(26,\cdot)$	4019.k	2009	yes	$1$	$1$	$e\left(\frac{904}{2009}\right)$	$e\left(\frac{11}{49}\right)$	$e\left(\frac{1808}{2009}\right)$	$e\left(\frac{362}{2009}\right)$	$e\left(\frac{1355}{2009}\right)$	$e\left(\frac{1921}{2009}\right)$	$e\left(\frac{703}{2009}\right)$	$e\left(\frac{22}{49}\right)$	$e\left(\frac{1266}{2009}\right)$	$e\left(\frac{891}{2009}\right)$
$\chi_{4019}(27,\cdot)$	4019.f	49	yes	$1$	$1$	$e\left(\frac{13}{49}\right)$	$e\left(\frac{46}{49}\right)$	$e\left(\frac{26}{49}\right)$	$e\left(\frac{9}{49}\right)$	$e\left(\frac{10}{49}\right)$	$e\left(\frac{46}{49}\right)$	$e\left(\frac{39}{49}\right)$	$e\left(\frac{43}{49}\right)$	$e\left(\frac{22}{49}\right)$	$e\left(\frac{12}{49}\right)$
$\chi_{4019}(28,\cdot)$	4019.l	4018	yes	$-1$	$1$	$e\left(\frac{3771}{4018}\right)$	$e\left(\frac{24}{49}\right)$	$e\left(\frac{1762}{2009}\right)$	$e\left(\frac{135}{2009}\right)$	$e\left(\frac{1721}{4018}\right)$	$e\left(\frac{1233}{4018}\right)$	$e\left(\frac{3277}{4018}\right)$	$e\left(\frac{48}{49}\right)$	$e\left(\frac{23}{4018}\right)$	$e\left(\frac{3839}{4018}\right)$
$\chi_{4019}(29,\cdot)$	4019.l	4018	yes	$-1$	$1$	$e\left(\frac{1957}{4018}\right)$	$e\left(\frac{36}{49}\right)$	$e\left(\frac{1957}{2009}\right)$	$e\left(\frac{1403}{2009}\right)$	$e\left(\frac{891}{4018}\right)$	$e\left(\frac{2903}{4018}\right)$	$e\left(\frac{1853}{4018}\right)$	$e\left(\frac{23}{49}\right)$	$e\left(\frac{745}{4018}\right)$	$e\left(\frac{491}{4018}\right)$
$\chi_{4019}(30,\cdot)$	4019.l	4018	yes	$-1$	$1$	$e\left(\frac{3831}{4018}\right)$	$e\left(\frac{39}{49}\right)$	$e\left(\frac{1822}{2009}\right)$	$e\left(\frac{1916}{2009}\right)$	$e\left(\frac{3011}{4018}\right)$	$e\left(\frac{2365}{4018}\right)$	$e\left(\frac{3457}{4018}\right)$	$e\left(\frac{29}{49}\right)$	$e\left(\frac{3645}{4018}\right)$	$e\left(\frac{3427}{4018}\right)$
$\chi_{4019}(31,\cdot)$	4019.l	4018	yes	$-1$	$1$	$e\left(\frac{1675}{4018}\right)$	$e\left(\frac{39}{49}\right)$	$e\left(\frac{1675}{2009}\right)$	$e\left(\frac{1671}{2009}\right)$	$e\left(\frac{855}{4018}\right)$	$e\left(\frac{797}{4018}\right)$	$e\left(\frac{1007}{4018}\right)$	$e\left(\frac{29}{49}\right)$	$e\left(\frac{999}{4018}\right)$	$e\left(\frac{3231}{4018}\right)$
$\chi_{4019}(32,\cdot)$	4019.l	4018	yes	$-1$	$1$	$e\left(\frac{5}{4018}\right)$	$e\left(\frac{38}{49}\right)$	$e\left(\frac{5}{2009}\right)$	$e\left(\frac{1990}{2009}\right)$	$e\left(\frac{3121}{4018}\right)$	$e\left(\frac{2773}{4018}\right)$	$e\left(\frac{15}{4018}\right)$	$e\left(\frac{27}{49}\right)$	$e\left(\frac{3985}{4018}\right)$	$e\left(\frac{1305}{4018}\right)$

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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	$4019$
Structure	\(C_{4018}\)
Order	$4018$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\(\chi_{4019}(1,\cdot)\)	4019.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{4019}(2,\cdot)\)	4019.l	4018	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{4018}\right)\)	\(e\left(\frac{37}{49}\right)\)	\(e\left(\frac{1}{2009}\right)\)	\(e\left(\frac{398}{2009}\right)\)	\(e\left(\frac{3035}{4018}\right)\)	\(e\left(\frac{3769}{4018}\right)\)	\(e\left(\frac{3}{4018}\right)\)	\(e\left(\frac{25}{49}\right)\)	\(e\left(\frac{797}{4018}\right)\)	\(e\left(\frac{261}{4018}\right)\)
\(\chi_{4019}(3,\cdot)\)	4019.f	49	yes	\(1\)	\(1\)	\(e\left(\frac{37}{49}\right)\)	\(e\left(\frac{48}{49}\right)\)	\(e\left(\frac{25}{49}\right)\)	\(e\left(\frac{3}{49}\right)\)	\(e\left(\frac{36}{49}\right)\)	\(e\left(\frac{48}{49}\right)\)	\(e\left(\frac{13}{49}\right)\)	\(e\left(\frac{47}{49}\right)\)	\(e\left(\frac{40}{49}\right)\)	\(e\left(\frac{4}{49}\right)\)
\(\chi_{4019}(4,\cdot)\)	4019.k	2009	yes	\(1\)	\(1\)	\(e\left(\frac{1}{2009}\right)\)	\(e\left(\frac{25}{49}\right)\)	\(e\left(\frac{2}{2009}\right)\)	\(e\left(\frac{796}{2009}\right)\)	\(e\left(\frac{1026}{2009}\right)\)	\(e\left(\frac{1760}{2009}\right)\)	\(e\left(\frac{3}{2009}\right)\)	\(e\left(\frac{1}{49}\right)\)	\(e\left(\frac{797}{2009}\right)\)	\(e\left(\frac{261}{2009}\right)\)
\(\chi_{4019}(5,\cdot)\)	4019.k	2009	yes	\(1\)	\(1\)	\(e\left(\frac{398}{2009}\right)\)	\(e\left(\frac{3}{49}\right)\)	\(e\left(\frac{796}{2009}\right)\)	\(e\left(\frac{1395}{2009}\right)\)	\(e\left(\frac{521}{2009}\right)\)	\(e\left(\frac{1348}{2009}\right)\)	\(e\left(\frac{1194}{2009}\right)\)	\(e\left(\frac{6}{49}\right)\)	\(e\left(\frac{1793}{2009}\right)\)	\(e\left(\frac{1419}{2009}\right)\)
\(\chi_{4019}(6,\cdot)\)	4019.l	4018	yes	\(-1\)	\(1\)	\(e\left(\frac{3035}{4018}\right)\)	\(e\left(\frac{36}{49}\right)\)	\(e\left(\frac{1026}{2009}\right)\)	\(e\left(\frac{521}{2009}\right)\)	\(e\left(\frac{1969}{4018}\right)\)	\(e\left(\frac{3687}{4018}\right)\)	\(e\left(\frac{1069}{4018}\right)\)	\(e\left(\frac{23}{49}\right)\)	\(e\left(\frac{59}{4018}\right)\)	\(e\left(\frac{589}{4018}\right)\)
\(\chi_{4019}(7,\cdot)\)	4019.l	4018	yes	\(-1\)	\(1\)	\(e\left(\frac{3769}{4018}\right)\)	\(e\left(\frac{48}{49}\right)\)	\(e\left(\frac{1760}{2009}\right)\)	\(e\left(\frac{1348}{2009}\right)\)	\(e\left(\frac{3687}{4018}\right)\)	\(e\left(\frac{1731}{4018}\right)\)	\(e\left(\frac{3271}{4018}\right)\)	\(e\left(\frac{47}{49}\right)\)	\(e\left(\frac{2447}{4018}\right)\)	\(e\left(\frac{3317}{4018}\right)\)
\(\chi_{4019}(8,\cdot)\)	4019.l	4018	yes	\(-1\)	\(1\)	\(e\left(\frac{3}{4018}\right)\)	\(e\left(\frac{13}{49}\right)\)	\(e\left(\frac{3}{2009}\right)\)	\(e\left(\frac{1194}{2009}\right)\)	\(e\left(\frac{1069}{4018}\right)\)	\(e\left(\frac{3271}{4018}\right)\)	\(e\left(\frac{9}{4018}\right)\)	\(e\left(\frac{26}{49}\right)\)	\(e\left(\frac{2391}{4018}\right)\)	\(e\left(\frac{783}{4018}\right)\)
\(\chi_{4019}(9,\cdot)\)	4019.f	49	yes	\(1\)	\(1\)	\(e\left(\frac{25}{49}\right)\)	\(e\left(\frac{47}{49}\right)\)	\(e\left(\frac{1}{49}\right)\)	\(e\left(\frac{6}{49}\right)\)	\(e\left(\frac{23}{49}\right)\)	\(e\left(\frac{47}{49}\right)\)	\(e\left(\frac{26}{49}\right)\)	\(e\left(\frac{45}{49}\right)\)	\(e\left(\frac{31}{49}\right)\)	\(e\left(\frac{8}{49}\right)\)
\(\chi_{4019}(10,\cdot)\)	4019.l	4018	yes	\(-1\)	\(1\)	\(e\left(\frac{797}{4018}\right)\)	\(e\left(\frac{40}{49}\right)\)	\(e\left(\frac{797}{2009}\right)\)	\(e\left(\frac{1793}{2009}\right)\)	\(e\left(\frac{59}{4018}\right)\)	\(e\left(\frac{2447}{4018}\right)\)	\(e\left(\frac{2391}{4018}\right)\)	\(e\left(\frac{31}{49}\right)\)	\(e\left(\frac{365}{4018}\right)\)	\(e\left(\frac{3099}{4018}\right)\)
\(\chi_{4019}(11,\cdot)\)	4019.l	4018	yes	\(-1\)	\(1\)	\(e\left(\frac{261}{4018}\right)\)	\(e\left(\frac{4}{49}\right)\)	\(e\left(\frac{261}{2009}\right)\)	\(e\left(\frac{1419}{2009}\right)\)	\(e\left(\frac{589}{4018}\right)\)	\(e\left(\frac{3317}{4018}\right)\)	\(e\left(\frac{783}{4018}\right)\)	\(e\left(\frac{8}{49}\right)\)	\(e\left(\frac{3099}{4018}\right)\)	\(e\left(\frac{3833}{4018}\right)\)
\(\chi_{4019}(12,\cdot)\)	4019.k	2009	yes	\(1\)	\(1\)	\(e\left(\frac{1518}{2009}\right)\)	\(e\left(\frac{24}{49}\right)\)	\(e\left(\frac{1027}{2009}\right)\)	\(e\left(\frac{919}{2009}\right)\)	\(e\left(\frac{493}{2009}\right)\)	\(e\left(\frac{1719}{2009}\right)\)	\(e\left(\frac{536}{2009}\right)\)	\(e\left(\frac{48}{49}\right)\)	\(e\left(\frac{428}{2009}\right)\)	\(e\left(\frac{425}{2009}\right)\)
\(\chi_{4019}(13,\cdot)\)	4019.l	4018	yes	\(-1\)	\(1\)	\(e\left(\frac{1807}{4018}\right)\)	\(e\left(\frac{23}{49}\right)\)	\(e\left(\frac{1807}{2009}\right)\)	\(e\left(\frac{1973}{2009}\right)\)	\(e\left(\frac{3693}{4018}\right)\)	\(e\left(\frac{73}{4018}\right)\)	\(e\left(\frac{1403}{4018}\right)\)	\(e\left(\frac{46}{49}\right)\)	\(e\left(\frac{1735}{4018}\right)\)	\(e\left(\frac{1521}{4018}\right)\)
\(\chi_{4019}(14,\cdot)\)	4019.k	2009	yes	\(1\)	\(1\)	\(e\left(\frac{1885}{2009}\right)\)	\(e\left(\frac{36}{49}\right)\)	\(e\left(\frac{1761}{2009}\right)\)	\(e\left(\frac{1746}{2009}\right)\)	\(e\left(\frac{1352}{2009}\right)\)	\(e\left(\frac{741}{2009}\right)\)	\(e\left(\frac{1637}{2009}\right)\)	\(e\left(\frac{23}{49}\right)\)	\(e\left(\frac{1622}{2009}\right)\)	\(e\left(\frac{1789}{2009}\right)\)
\(\chi_{4019}(15,\cdot)\)	4019.k	2009	yes	\(1\)	\(1\)	\(e\left(\frac{1915}{2009}\right)\)	\(e\left(\frac{2}{49}\right)\)	\(e\left(\frac{1821}{2009}\right)\)	\(e\left(\frac{1518}{2009}\right)\)	\(e\left(\frac{1997}{2009}\right)\)	\(e\left(\frac{1307}{2009}\right)\)	\(e\left(\frac{1727}{2009}\right)\)	\(e\left(\frac{4}{49}\right)\)	\(e\left(\frac{1424}{2009}\right)\)	\(e\left(\frac{1583}{2009}\right)\)
\(\chi_{4019}(16,\cdot)\)	4019.k	2009	yes	\(1\)	\(1\)	\(e\left(\frac{2}{2009}\right)\)	\(e\left(\frac{1}{49}\right)\)	\(e\left(\frac{4}{2009}\right)\)	\(e\left(\frac{1592}{2009}\right)\)	\(e\left(\frac{43}{2009}\right)\)	\(e\left(\frac{1511}{2009}\right)\)	\(e\left(\frac{6}{2009}\right)\)	\(e\left(\frac{2}{49}\right)\)	\(e\left(\frac{1594}{2009}\right)\)	\(e\left(\frac{522}{2009}\right)\)
\(\chi_{4019}(17,\cdot)\)	4019.l	4018	yes	\(-1\)	\(1\)	\(e\left(\frac{657}{4018}\right)\)	\(e\left(\frac{5}{49}\right)\)	\(e\left(\frac{657}{2009}\right)\)	\(e\left(\frac{316}{2009}\right)\)	\(e\left(\frac{1067}{4018}\right)\)	\(e\left(\frac{1145}{4018}\right)\)	\(e\left(\frac{1971}{4018}\right)\)	\(e\left(\frac{10}{49}\right)\)	\(e\left(\frac{1289}{4018}\right)\)	\(e\left(\frac{2721}{4018}\right)\)
\(\chi_{4019}(18,\cdot)\)	4019.j	574	yes	\(-1\)	\(1\)	\(e\left(\frac{293}{574}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{6}{287}\right)\)	\(e\left(\frac{92}{287}\right)\)	\(e\left(\frac{129}{574}\right)\)	\(e\left(\frac{515}{574}\right)\)	\(e\left(\frac{305}{574}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{477}{574}\right)\)	\(e\left(\frac{131}{574}\right)\)
\(\chi_{4019}(19,\cdot)\)	4019.k	2009	yes	\(1\)	\(1\)	\(e\left(\frac{192}{2009}\right)\)	\(e\left(\frac{47}{49}\right)\)	\(e\left(\frac{384}{2009}\right)\)	\(e\left(\frac{148}{2009}\right)\)	\(e\left(\frac{110}{2009}\right)\)	\(e\left(\frac{408}{2009}\right)\)	\(e\left(\frac{576}{2009}\right)\)	\(e\left(\frac{45}{49}\right)\)	\(e\left(\frac{340}{2009}\right)\)	\(e\left(\frac{1896}{2009}\right)\)
\(\chi_{4019}(20,\cdot)\)	4019.i	287	yes	\(1\)	\(1\)	\(e\left(\frac{57}{287}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{114}{287}\right)\)	\(e\left(\frac{26}{287}\right)\)	\(e\left(\frac{221}{287}\right)\)	\(e\left(\frac{157}{287}\right)\)	\(e\left(\frac{171}{287}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{83}{287}\right)\)	\(e\left(\frac{240}{287}\right)\)
\(\chi_{4019}(21,\cdot)\)	4019.l	4018	yes	\(-1\)	\(1\)	\(e\left(\frac{2785}{4018}\right)\)	\(e\left(\frac{47}{49}\right)\)	\(e\left(\frac{776}{2009}\right)\)	\(e\left(\frac{1471}{2009}\right)\)	\(e\left(\frac{2621}{4018}\right)\)	\(e\left(\frac{1649}{4018}\right)\)	\(e\left(\frac{319}{4018}\right)\)	\(e\left(\frac{45}{49}\right)\)	\(e\left(\frac{1709}{4018}\right)\)	\(e\left(\frac{3645}{4018}\right)\)
\(\chi_{4019}(22,\cdot)\)	4019.k	2009	yes	\(1\)	\(1\)	\(e\left(\frac{131}{2009}\right)\)	\(e\left(\frac{41}{49}\right)\)	\(e\left(\frac{262}{2009}\right)\)	\(e\left(\frac{1817}{2009}\right)\)	\(e\left(\frac{1812}{2009}\right)\)	\(e\left(\frac{1534}{2009}\right)\)	\(e\left(\frac{393}{2009}\right)\)	\(e\left(\frac{33}{49}\right)\)	\(e\left(\frac{1948}{2009}\right)\)	\(e\left(\frac{38}{2009}\right)\)
\(\chi_{4019}(23,\cdot)\)	4019.k	2009	yes	\(1\)	\(1\)	\(e\left(\frac{846}{2009}\right)\)	\(e\left(\frac{31}{49}\right)\)	\(e\left(\frac{1692}{2009}\right)\)	\(e\left(\frac{401}{2009}\right)\)	\(e\left(\frac{108}{2009}\right)\)	\(e\left(\frac{291}{2009}\right)\)	\(e\left(\frac{529}{2009}\right)\)	\(e\left(\frac{13}{49}\right)\)	\(e\left(\frac{1247}{2009}\right)\)	\(e\left(\frac{1825}{2009}\right)\)
\(\chi_{4019}(24,\cdot)\)	4019.l	4018	yes	\(-1\)	\(1\)	\(e\left(\frac{3037}{4018}\right)\)	\(e\left(\frac{12}{49}\right)\)	\(e\left(\frac{1028}{2009}\right)\)	\(e\left(\frac{1317}{2009}\right)\)	\(e\left(\frac{3}{4018}\right)\)	\(e\left(\frac{3189}{4018}\right)\)	\(e\left(\frac{1075}{4018}\right)\)	\(e\left(\frac{24}{49}\right)\)	\(e\left(\frac{1653}{4018}\right)\)	\(e\left(\frac{1111}{4018}\right)\)
\(\chi_{4019}(25,\cdot)\)	4019.k	2009	yes	\(1\)	\(1\)	\(e\left(\frac{796}{2009}\right)\)	\(e\left(\frac{6}{49}\right)\)	\(e\left(\frac{1592}{2009}\right)\)	\(e\left(\frac{781}{2009}\right)\)	\(e\left(\frac{1042}{2009}\right)\)	\(e\left(\frac{687}{2009}\right)\)	\(e\left(\frac{379}{2009}\right)\)	\(e\left(\frac{12}{49}\right)\)	\(e\left(\frac{1577}{2009}\right)\)	\(e\left(\frac{829}{2009}\right)\)
\(\chi_{4019}(26,\cdot)\)	4019.k	2009	yes	\(1\)	\(1\)	\(e\left(\frac{904}{2009}\right)\)	\(e\left(\frac{11}{49}\right)\)	\(e\left(\frac{1808}{2009}\right)\)	\(e\left(\frac{362}{2009}\right)\)	\(e\left(\frac{1355}{2009}\right)\)	\(e\left(\frac{1921}{2009}\right)\)	\(e\left(\frac{703}{2009}\right)\)	\(e\left(\frac{22}{49}\right)\)	\(e\left(\frac{1266}{2009}\right)\)	\(e\left(\frac{891}{2009}\right)\)
\(\chi_{4019}(27,\cdot)\)	4019.f	49	yes	\(1\)	\(1\)	\(e\left(\frac{13}{49}\right)\)	\(e\left(\frac{46}{49}\right)\)	\(e\left(\frac{26}{49}\right)\)	\(e\left(\frac{9}{49}\right)\)	\(e\left(\frac{10}{49}\right)\)	\(e\left(\frac{46}{49}\right)\)	\(e\left(\frac{39}{49}\right)\)	\(e\left(\frac{43}{49}\right)\)	\(e\left(\frac{22}{49}\right)\)	\(e\left(\frac{12}{49}\right)\)
\(\chi_{4019}(28,\cdot)\)	4019.l	4018	yes	\(-1\)	\(1\)	\(e\left(\frac{3771}{4018}\right)\)	\(e\left(\frac{24}{49}\right)\)	\(e\left(\frac{1762}{2009}\right)\)	\(e\left(\frac{135}{2009}\right)\)	\(e\left(\frac{1721}{4018}\right)\)	\(e\left(\frac{1233}{4018}\right)\)	\(e\left(\frac{3277}{4018}\right)\)	\(e\left(\frac{48}{49}\right)\)	\(e\left(\frac{23}{4018}\right)\)	\(e\left(\frac{3839}{4018}\right)\)
\(\chi_{4019}(29,\cdot)\)	4019.l	4018	yes	\(-1\)	\(1\)	\(e\left(\frac{1957}{4018}\right)\)	\(e\left(\frac{36}{49}\right)\)	\(e\left(\frac{1957}{2009}\right)\)	\(e\left(\frac{1403}{2009}\right)\)	\(e\left(\frac{891}{4018}\right)\)	\(e\left(\frac{2903}{4018}\right)\)	\(e\left(\frac{1853}{4018}\right)\)	\(e\left(\frac{23}{49}\right)\)	\(e\left(\frac{745}{4018}\right)\)	\(e\left(\frac{491}{4018}\right)\)
\(\chi_{4019}(30,\cdot)\)	4019.l	4018	yes	\(-1\)	\(1\)	\(e\left(\frac{3831}{4018}\right)\)	\(e\left(\frac{39}{49}\right)\)	\(e\left(\frac{1822}{2009}\right)\)	\(e\left(\frac{1916}{2009}\right)\)	\(e\left(\frac{3011}{4018}\right)\)	\(e\left(\frac{2365}{4018}\right)\)	\(e\left(\frac{3457}{4018}\right)\)	\(e\left(\frac{29}{49}\right)\)	\(e\left(\frac{3645}{4018}\right)\)	\(e\left(\frac{3427}{4018}\right)\)
\(\chi_{4019}(31,\cdot)\)	4019.l	4018	yes	\(-1\)	\(1\)	\(e\left(\frac{1675}{4018}\right)\)	\(e\left(\frac{39}{49}\right)\)	\(e\left(\frac{1675}{2009}\right)\)	\(e\left(\frac{1671}{2009}\right)\)	\(e\left(\frac{855}{4018}\right)\)	\(e\left(\frac{797}{4018}\right)\)	\(e\left(\frac{1007}{4018}\right)\)	\(e\left(\frac{29}{49}\right)\)	\(e\left(\frac{999}{4018}\right)\)	\(e\left(\frac{3231}{4018}\right)\)
\(\chi_{4019}(32,\cdot)\)	4019.l	4018	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{4018}\right)\)	\(e\left(\frac{38}{49}\right)\)	\(e\left(\frac{5}{2009}\right)\)	\(e\left(\frac{1990}{2009}\right)\)	\(e\left(\frac{3121}{4018}\right)\)	\(e\left(\frac{2773}{4018}\right)\)	\(e\left(\frac{15}{4018}\right)\)	\(e\left(\frac{27}{49}\right)\)	\(e\left(\frac{3985}{4018}\right)\)	\(e\left(\frac{1305}{4018}\right)\)

Introduction

L-functions

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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.