LMFDB - Group of Dirichlet characters of modulus 20000

Show commands: PariGP / SageMath

sage: H = DirichletGroup(20000)

pari: g = idealstar(,20000,2)

Character group

sage: G.order() pari: g.no
Order	=	8000
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{4}\times C_{1000}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{20000}(18751,\cdot)$, $\chi_{20000}(2501,\cdot)$, $\chi_{20000}(9377,\cdot)$

First 32 of 8000 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	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$17$	$19$	$21$	$23$	$27$
$\chi_{20000}(1,\cdot)$	20000.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{20000}(3,\cdot)$	20000.eg	1000	yes	$1$	$1$	$e\left(\frac{523}{1000}\right)$	$e\left(\frac{1}{25}\right)$	$e\left(\frac{23}{500}\right)$	$e\left(\frac{239}{1000}\right)$	$e\left(\frac{371}{1000}\right)$	$e\left(\frac{261}{500}\right)$	$e\left(\frac{577}{1000}\right)$	$e\left(\frac{563}{1000}\right)$	$e\left(\frac{123}{125}\right)$	$e\left(\frac{569}{1000}\right)$
$\chi_{20000}(7,\cdot)$	20000.cv	100	no	$1$	$1$	$e\left(\frac{1}{25}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{2}{25}\right)$	$e\left(\frac{47}{100}\right)$	$e\left(\frac{29}{50}\right)$	$e\left(\frac{81}{100}\right)$	$e\left(\frac{71}{100}\right)$	$e\left(\frac{49}{100}\right)$	$e\left(\frac{7}{100}\right)$	$e\left(\frac{3}{25}\right)$
$\chi_{20000}(9,\cdot)$	20000.do	500	no	$1$	$1$	$e\left(\frac{23}{500}\right)$	$e\left(\frac{2}{25}\right)$	$e\left(\frac{23}{250}\right)$	$e\left(\frac{239}{500}\right)$	$e\left(\frac{371}{500}\right)$	$e\left(\frac{11}{250}\right)$	$e\left(\frac{77}{500}\right)$	$e\left(\frac{63}{500}\right)$	$e\left(\frac{121}{125}\right)$	$e\left(\frac{69}{500}\right)$
$\chi_{20000}(11,\cdot)$	20000.ec	1000	yes	$-1$	$1$	$e\left(\frac{239}{1000}\right)$	$e\left(\frac{47}{100}\right)$	$e\left(\frac{239}{500}\right)$	$e\left(\frac{777}{1000}\right)$	$e\left(\frac{703}{1000}\right)$	$e\left(\frac{49}{250}\right)$	$e\left(\frac{811}{1000}\right)$	$e\left(\frac{709}{1000}\right)$	$e\left(\frac{281}{500}\right)$	$e\left(\frac{717}{1000}\right)$
$\chi_{20000}(13,\cdot)$	20000.eh	1000	yes	$-1$	$1$	$e\left(\frac{371}{1000}\right)$	$e\left(\frac{29}{50}\right)$	$e\left(\frac{371}{500}\right)$	$e\left(\frac{703}{1000}\right)$	$e\left(\frac{767}{1000}\right)$	$e\left(\frac{297}{500}\right)$	$e\left(\frac{329}{1000}\right)$	$e\left(\frac{951}{1000}\right)$	$e\left(\frac{17}{250}\right)$	$e\left(\frac{113}{1000}\right)$
$\chi_{20000}(17,\cdot)$	20000.dx	500	no	$-1$	$1$	$e\left(\frac{261}{500}\right)$	$e\left(\frac{81}{100}\right)$	$e\left(\frac{11}{250}\right)$	$e\left(\frac{49}{250}\right)$	$e\left(\frac{297}{500}\right)$	$e\left(\frac{429}{500}\right)$	$e\left(\frac{16}{125}\right)$	$e\left(\frac{83}{250}\right)$	$e\left(\frac{63}{500}\right)$	$e\left(\frac{283}{500}\right)$
$\chi_{20000}(19,\cdot)$	20000.ee	1000	yes	$-1$	$1$	$e\left(\frac{577}{1000}\right)$	$e\left(\frac{71}{100}\right)$	$e\left(\frac{77}{500}\right)$	$e\left(\frac{811}{1000}\right)$	$e\left(\frac{329}{1000}\right)$	$e\left(\frac{16}{125}\right)$	$e\left(\frac{73}{1000}\right)$	$e\left(\frac{287}{1000}\right)$	$e\left(\frac{33}{500}\right)$	$e\left(\frac{731}{1000}\right)$
$\chi_{20000}(21,\cdot)$	20000.ed	1000	yes	$1$	$1$	$e\left(\frac{563}{1000}\right)$	$e\left(\frac{49}{100}\right)$	$e\left(\frac{63}{500}\right)$	$e\left(\frac{709}{1000}\right)$	$e\left(\frac{951}{1000}\right)$	$e\left(\frac{83}{250}\right)$	$e\left(\frac{287}{1000}\right)$	$e\left(\frac{53}{1000}\right)$	$e\left(\frac{27}{500}\right)$	$e\left(\frac{689}{1000}\right)$
$\chi_{20000}(23,\cdot)$	20000.ds	500	no	$1$	$1$	$e\left(\frac{123}{125}\right)$	$e\left(\frac{7}{100}\right)$	$e\left(\frac{121}{125}\right)$	$e\left(\frac{281}{500}\right)$	$e\left(\frac{17}{250}\right)$	$e\left(\frac{63}{500}\right)$	$e\left(\frac{33}{500}\right)$	$e\left(\frac{27}{500}\right)$	$e\left(\frac{261}{500}\right)$	$e\left(\frac{119}{125}\right)$
$\chi_{20000}(27,\cdot)$	20000.eg	1000	yes	$1$	$1$	$e\left(\frac{569}{1000}\right)$	$e\left(\frac{3}{25}\right)$	$e\left(\frac{69}{500}\right)$	$e\left(\frac{717}{1000}\right)$	$e\left(\frac{113}{1000}\right)$	$e\left(\frac{283}{500}\right)$	$e\left(\frac{731}{1000}\right)$	$e\left(\frac{689}{1000}\right)$	$e\left(\frac{119}{125}\right)$	$e\left(\frac{707}{1000}\right)$
$\chi_{20000}(29,\cdot)$	20000.ef	1000	yes	$1$	$1$	$e\left(\frac{793}{1000}\right)$	$e\left(\frac{89}{100}\right)$	$e\left(\frac{293}{500}\right)$	$e\left(\frac{99}{1000}\right)$	$e\left(\frac{661}{1000}\right)$	$e\left(\frac{69}{125}\right)$	$e\left(\frac{57}{1000}\right)$	$e\left(\frac{683}{1000}\right)$	$e\left(\frac{447}{500}\right)$	$e\left(\frac{379}{1000}\right)$
$\chi_{20000}(31,\cdot)$	20000.di	250	no	$-1$	$1$	$e\left(\frac{193}{250}\right)$	$e\left(\frac{3}{50}\right)$	$e\left(\frac{68}{125}\right)$	$e\left(\frac{49}{250}\right)$	$e\left(\frac{43}{125}\right)$	$e\left(\frac{76}{125}\right)$	$e\left(\frac{157}{250}\right)$	$e\left(\frac{104}{125}\right)$	$e\left(\frac{219}{250}\right)$	$e\left(\frac{79}{250}\right)$
$\chi_{20000}(33,\cdot)$	20000.du	500	no	$-1$	$1$	$e\left(\frac{381}{500}\right)$	$e\left(\frac{51}{100}\right)$	$e\left(\frac{131}{250}\right)$	$e\left(\frac{2}{125}\right)$	$e\left(\frac{37}{500}\right)$	$e\left(\frac{359}{500}\right)$	$e\left(\frac{97}{250}\right)$	$e\left(\frac{34}{125}\right)$	$e\left(\frac{273}{500}\right)$	$e\left(\frac{143}{500}\right)$
$\chi_{20000}(37,\cdot)$	20000.eh	1000	yes	$-1$	$1$	$e\left(\frac{781}{1000}\right)$	$e\left(\frac{19}{50}\right)$	$e\left(\frac{281}{500}\right)$	$e\left(\frac{833}{1000}\right)$	$e\left(\frac{337}{1000}\right)$	$e\left(\frac{167}{500}\right)$	$e\left(\frac{919}{1000}\right)$	$e\left(\frac{161}{1000}\right)$	$e\left(\frac{87}{250}\right)$	$e\left(\frac{343}{1000}\right)$
$\chi_{20000}(39,\cdot)$	20000.dp	500	no	$-1$	$1$	$e\left(\frac{447}{500}\right)$	$e\left(\frac{31}{50}\right)$	$e\left(\frac{197}{250}\right)$	$e\left(\frac{471}{500}\right)$	$e\left(\frac{69}{500}\right)$	$e\left(\frac{29}{250}\right)$	$e\left(\frac{453}{500}\right)$	$e\left(\frac{257}{500}\right)$	$e\left(\frac{13}{250}\right)$	$e\left(\frac{341}{500}\right)$
$\chi_{20000}(41,\cdot)$	20000.dy	500	no	$1$	$1$	$e\left(\frac{333}{500}\right)$	$e\left(\frac{9}{50}\right)$	$e\left(\frac{83}{250}\right)$	$e\left(\frac{319}{500}\right)$	$e\left(\frac{241}{500}\right)$	$e\left(\frac{28}{125}\right)$	$e\left(\frac{17}{500}\right)$	$e\left(\frac{423}{500}\right)$	$e\left(\frac{107}{250}\right)$	$e\left(\frac{499}{500}\right)$
$\chi_{20000}(43,\cdot)$	20000.dg	200	no	$1$	$1$	$e\left(\frac{21}{200}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{21}{100}\right)$	$e\left(\frac{53}{200}\right)$	$e\left(\frac{117}{200}\right)$	$e\left(\frac{97}{100}\right)$	$e\left(\frac{179}{200}\right)$	$e\left(\frac{1}{200}\right)$	$e\left(\frac{17}{50}\right)$	$e\left(\frac{63}{200}\right)$
$\chi_{20000}(47,\cdot)$	20000.dv	500	no	$1$	$1$	$e\left(\frac{379}{500}\right)$	$e\left(\frac{59}{100}\right)$	$e\left(\frac{129}{250}\right)$	$e\left(\frac{43}{125}\right)$	$e\left(\frac{233}{500}\right)$	$e\left(\frac{281}{500}\right)$	$e\left(\frac{23}{250}\right)$	$e\left(\frac{87}{250}\right)$	$e\left(\frac{57}{500}\right)$	$e\left(\frac{137}{500}\right)$
$\chi_{20000}(49,\cdot)$	20000.cj	50	no	$1$	$1$	$e\left(\frac{2}{25}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{4}{25}\right)$	$e\left(\frac{47}{50}\right)$	$e\left(\frac{4}{25}\right)$	$e\left(\frac{31}{50}\right)$	$e\left(\frac{21}{50}\right)$	$e\left(\frac{49}{50}\right)$	$e\left(\frac{7}{50}\right)$	$e\left(\frac{6}{25}\right)$
$\chi_{20000}(51,\cdot)$	20000.dc	200	no	$-1$	$1$	$e\left(\frac{9}{200}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{9}{100}\right)$	$e\left(\frac{87}{200}\right)$	$e\left(\frac{193}{200}\right)$	$e\left(\frac{19}{50}\right)$	$e\left(\frac{141}{200}\right)$	$e\left(\frac{179}{200}\right)$	$e\left(\frac{11}{100}\right)$	$e\left(\frac{27}{200}\right)$
$\chi_{20000}(53,\cdot)$	20000.eb	1000	yes	$-1$	$1$	$e\left(\frac{413}{1000}\right)$	$e\left(\frac{6}{25}\right)$	$e\left(\frac{413}{500}\right)$	$e\left(\frac{509}{1000}\right)$	$e\left(\frac{401}{1000}\right)$	$e\left(\frac{241}{500}\right)$	$e\left(\frac{187}{1000}\right)$	$e\left(\frac{653}{1000}\right)$	$e\left(\frac{13}{125}\right)$	$e\left(\frac{239}{1000}\right)$
$\chi_{20000}(57,\cdot)$	20000.bv	20	no	$-1$	$1$	$e\left(\frac{1}{10}\right)$	$-i$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{3}{10}\right)$
$\chi_{20000}(59,\cdot)$	20000.ee	1000	yes	$-1$	$1$	$e\left(\frac{551}{1000}\right)$	$e\left(\frac{73}{100}\right)$	$e\left(\frac{51}{500}\right)$	$e\left(\frac{693}{1000}\right)$	$e\left(\frac{127}{1000}\right)$	$e\left(\frac{108}{125}\right)$	$e\left(\frac{399}{1000}\right)$	$e\left(\frac{281}{1000}\right)$	$e\left(\frac{379}{500}\right)$	$e\left(\frac{653}{1000}\right)$
$\chi_{20000}(61,\cdot)$	20000.ed	1000	yes	$1$	$1$	$e\left(\frac{709}{1000}\right)$	$e\left(\frac{7}{100}\right)$	$e\left(\frac{209}{500}\right)$	$e\left(\frac{987}{1000}\right)$	$e\left(\frac{393}{1000}\right)$	$e\left(\frac{69}{250}\right)$	$e\left(\frac{841}{1000}\right)$	$e\left(\frac{779}{1000}\right)$	$e\left(\frac{161}{500}\right)$	$e\left(\frac{127}{1000}\right)$
$\chi_{20000}(63,\cdot)$	20000.dw	500	no	$1$	$1$	$e\left(\frac{43}{500}\right)$	$e\left(\frac{53}{100}\right)$	$e\left(\frac{43}{250}\right)$	$e\left(\frac{237}{250}\right)$	$e\left(\frac{161}{500}\right)$	$e\left(\frac{427}{500}\right)$	$e\left(\frac{108}{125}\right)$	$e\left(\frac{77}{125}\right)$	$e\left(\frac{19}{500}\right)$	$e\left(\frac{129}{500}\right)$
$\chi_{20000}(67,\cdot)$	20000.ea	1000	yes	$1$	$1$	$e\left(\frac{407}{1000}\right)$	$e\left(\frac{43}{50}\right)$	$e\left(\frac{407}{500}\right)$	$e\left(\frac{751}{1000}\right)$	$e\left(\frac{239}{1000}\right)$	$e\left(\frac{499}{500}\right)$	$e\left(\frac{993}{1000}\right)$	$e\left(\frac{267}{1000}\right)$	$e\left(\frac{239}{250}\right)$	$e\left(\frac{221}{1000}\right)$
$\chi_{20000}(69,\cdot)$	20000.ef	1000	yes	$1$	$1$	$e\left(\frac{507}{1000}\right)$	$e\left(\frac{11}{100}\right)$	$e\left(\frac{7}{500}\right)$	$e\left(\frac{801}{1000}\right)$	$e\left(\frac{439}{1000}\right)$	$e\left(\frac{81}{125}\right)$	$e\left(\frac{643}{1000}\right)$	$e\left(\frac{617}{1000}\right)$	$e\left(\frac{253}{500}\right)$	$e\left(\frac{521}{1000}\right)$
$\chi_{20000}(71,\cdot)$	20000.dz	500	no	$-1$	$1$	$e\left(\frac{229}{500}\right)$	$e\left(\frac{21}{25}\right)$	$e\left(\frac{229}{250}\right)$	$e\left(\frac{347}{500}\right)$	$e\left(\frac{183}{500}\right)$	$e\left(\frac{14}{125}\right)$	$e\left(\frac{321}{500}\right)$	$e\left(\frac{149}{500}\right)$	$e\left(\frac{58}{125}\right)$	$e\left(\frac{187}{500}\right)$
$\chi_{20000}(73,\cdot)$	20000.dq	500	no	$-1$	$1$	$e\left(\frac{131}{250}\right)$	$e\left(\frac{77}{100}\right)$	$e\left(\frac{6}{125}\right)$	$e\left(\frac{391}{500}\right)$	$e\left(\frac{37}{250}\right)$	$e\left(\frac{343}{500}\right)$	$e\left(\frac{263}{500}\right)$	$e\left(\frac{147}{500}\right)$	$e\left(\frac{171}{500}\right)$	$e\left(\frac{143}{250}\right)$
$\chi_{20000}(77,\cdot)$	20000.eb	1000	yes	$-1$	$1$	$e\left(\frac{279}{1000}\right)$	$e\left(\frac{23}{25}\right)$	$e\left(\frac{279}{500}\right)$	$e\left(\frac{247}{1000}\right)$	$e\left(\frac{283}{1000}\right)$	$e\left(\frac{3}{500}\right)$	$e\left(\frac{521}{1000}\right)$	$e\left(\frac{199}{1000}\right)$	$e\left(\frac{79}{125}\right)$	$e\left(\frac{837}{1000}\right)$
$\chi_{20000}(79,\cdot)$	20000.dl	250	no	$-1$	$1$	$e\left(\frac{37}{250}\right)$	$e\left(\frac{1}{25}\right)$	$e\left(\frac{37}{125}\right)$	$e\left(\frac{108}{125}\right)$	$e\left(\frac{62}{125}\right)$	$e\left(\frac{193}{250}\right)$	$e\left(\frac{119}{125}\right)$	$e\left(\frac{47}{250}\right)$	$e\left(\frac{123}{125}\right)$	$e\left(\frac{111}{250}\right)$

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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	$20000$
Structure	\(C_{2}\times C_{4}\times C_{1000}\)
Order	$8000$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(13\)	\(17\)	\(19\)	\(21\)	\(23\)	\(27\)
\(\chi_{20000}(1,\cdot)\)	20000.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{20000}(3,\cdot)\)	20000.eg	1000	yes	\(1\)	\(1\)	\(e\left(\frac{523}{1000}\right)\)	\(e\left(\frac{1}{25}\right)\)	\(e\left(\frac{23}{500}\right)\)	\(e\left(\frac{239}{1000}\right)\)	\(e\left(\frac{371}{1000}\right)\)	\(e\left(\frac{261}{500}\right)\)	\(e\left(\frac{577}{1000}\right)\)	\(e\left(\frac{563}{1000}\right)\)	\(e\left(\frac{123}{125}\right)\)	\(e\left(\frac{569}{1000}\right)\)
\(\chi_{20000}(7,\cdot)\)	20000.cv	100	no	\(1\)	\(1\)	\(e\left(\frac{1}{25}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{2}{25}\right)\)	\(e\left(\frac{47}{100}\right)\)	\(e\left(\frac{29}{50}\right)\)	\(e\left(\frac{81}{100}\right)\)	\(e\left(\frac{71}{100}\right)\)	\(e\left(\frac{49}{100}\right)\)	\(e\left(\frac{7}{100}\right)\)	\(e\left(\frac{3}{25}\right)\)
\(\chi_{20000}(9,\cdot)\)	20000.do	500	no	\(1\)	\(1\)	\(e\left(\frac{23}{500}\right)\)	\(e\left(\frac{2}{25}\right)\)	\(e\left(\frac{23}{250}\right)\)	\(e\left(\frac{239}{500}\right)\)	\(e\left(\frac{371}{500}\right)\)	\(e\left(\frac{11}{250}\right)\)	\(e\left(\frac{77}{500}\right)\)	\(e\left(\frac{63}{500}\right)\)	\(e\left(\frac{121}{125}\right)\)	\(e\left(\frac{69}{500}\right)\)
\(\chi_{20000}(11,\cdot)\)	20000.ec	1000	yes	\(-1\)	\(1\)	\(e\left(\frac{239}{1000}\right)\)	\(e\left(\frac{47}{100}\right)\)	\(e\left(\frac{239}{500}\right)\)	\(e\left(\frac{777}{1000}\right)\)	\(e\left(\frac{703}{1000}\right)\)	\(e\left(\frac{49}{250}\right)\)	\(e\left(\frac{811}{1000}\right)\)	\(e\left(\frac{709}{1000}\right)\)	\(e\left(\frac{281}{500}\right)\)	\(e\left(\frac{717}{1000}\right)\)
\(\chi_{20000}(13,\cdot)\)	20000.eh	1000	yes	\(-1\)	\(1\)	\(e\left(\frac{371}{1000}\right)\)	\(e\left(\frac{29}{50}\right)\)	\(e\left(\frac{371}{500}\right)\)	\(e\left(\frac{703}{1000}\right)\)	\(e\left(\frac{767}{1000}\right)\)	\(e\left(\frac{297}{500}\right)\)	\(e\left(\frac{329}{1000}\right)\)	\(e\left(\frac{951}{1000}\right)\)	\(e\left(\frac{17}{250}\right)\)	\(e\left(\frac{113}{1000}\right)\)
\(\chi_{20000}(17,\cdot)\)	20000.dx	500	no	\(-1\)	\(1\)	\(e\left(\frac{261}{500}\right)\)	\(e\left(\frac{81}{100}\right)\)	\(e\left(\frac{11}{250}\right)\)	\(e\left(\frac{49}{250}\right)\)	\(e\left(\frac{297}{500}\right)\)	\(e\left(\frac{429}{500}\right)\)	\(e\left(\frac{16}{125}\right)\)	\(e\left(\frac{83}{250}\right)\)	\(e\left(\frac{63}{500}\right)\)	\(e\left(\frac{283}{500}\right)\)
\(\chi_{20000}(19,\cdot)\)	20000.ee	1000	yes	\(-1\)	\(1\)	\(e\left(\frac{577}{1000}\right)\)	\(e\left(\frac{71}{100}\right)\)	\(e\left(\frac{77}{500}\right)\)	\(e\left(\frac{811}{1000}\right)\)	\(e\left(\frac{329}{1000}\right)\)	\(e\left(\frac{16}{125}\right)\)	\(e\left(\frac{73}{1000}\right)\)	\(e\left(\frac{287}{1000}\right)\)	\(e\left(\frac{33}{500}\right)\)	\(e\left(\frac{731}{1000}\right)\)
\(\chi_{20000}(21,\cdot)\)	20000.ed	1000	yes	\(1\)	\(1\)	\(e\left(\frac{563}{1000}\right)\)	\(e\left(\frac{49}{100}\right)\)	\(e\left(\frac{63}{500}\right)\)	\(e\left(\frac{709}{1000}\right)\)	\(e\left(\frac{951}{1000}\right)\)	\(e\left(\frac{83}{250}\right)\)	\(e\left(\frac{287}{1000}\right)\)	\(e\left(\frac{53}{1000}\right)\)	\(e\left(\frac{27}{500}\right)\)	\(e\left(\frac{689}{1000}\right)\)
\(\chi_{20000}(23,\cdot)\)	20000.ds	500	no	\(1\)	\(1\)	\(e\left(\frac{123}{125}\right)\)	\(e\left(\frac{7}{100}\right)\)	\(e\left(\frac{121}{125}\right)\)	\(e\left(\frac{281}{500}\right)\)	\(e\left(\frac{17}{250}\right)\)	\(e\left(\frac{63}{500}\right)\)	\(e\left(\frac{33}{500}\right)\)	\(e\left(\frac{27}{500}\right)\)	\(e\left(\frac{261}{500}\right)\)	\(e\left(\frac{119}{125}\right)\)
\(\chi_{20000}(27,\cdot)\)	20000.eg	1000	yes	\(1\)	\(1\)	\(e\left(\frac{569}{1000}\right)\)	\(e\left(\frac{3}{25}\right)\)	\(e\left(\frac{69}{500}\right)\)	\(e\left(\frac{717}{1000}\right)\)	\(e\left(\frac{113}{1000}\right)\)	\(e\left(\frac{283}{500}\right)\)	\(e\left(\frac{731}{1000}\right)\)	\(e\left(\frac{689}{1000}\right)\)	\(e\left(\frac{119}{125}\right)\)	\(e\left(\frac{707}{1000}\right)\)
\(\chi_{20000}(29,\cdot)\)	20000.ef	1000	yes	\(1\)	\(1\)	\(e\left(\frac{793}{1000}\right)\)	\(e\left(\frac{89}{100}\right)\)	\(e\left(\frac{293}{500}\right)\)	\(e\left(\frac{99}{1000}\right)\)	\(e\left(\frac{661}{1000}\right)\)	\(e\left(\frac{69}{125}\right)\)	\(e\left(\frac{57}{1000}\right)\)	\(e\left(\frac{683}{1000}\right)\)	\(e\left(\frac{447}{500}\right)\)	\(e\left(\frac{379}{1000}\right)\)
\(\chi_{20000}(31,\cdot)\)	20000.di	250	no	\(-1\)	\(1\)	\(e\left(\frac{193}{250}\right)\)	\(e\left(\frac{3}{50}\right)\)	\(e\left(\frac{68}{125}\right)\)	\(e\left(\frac{49}{250}\right)\)	\(e\left(\frac{43}{125}\right)\)	\(e\left(\frac{76}{125}\right)\)	\(e\left(\frac{157}{250}\right)\)	\(e\left(\frac{104}{125}\right)\)	\(e\left(\frac{219}{250}\right)\)	\(e\left(\frac{79}{250}\right)\)
\(\chi_{20000}(33,\cdot)\)	20000.du	500	no	\(-1\)	\(1\)	\(e\left(\frac{381}{500}\right)\)	\(e\left(\frac{51}{100}\right)\)	\(e\left(\frac{131}{250}\right)\)	\(e\left(\frac{2}{125}\right)\)	\(e\left(\frac{37}{500}\right)\)	\(e\left(\frac{359}{500}\right)\)	\(e\left(\frac{97}{250}\right)\)	\(e\left(\frac{34}{125}\right)\)	\(e\left(\frac{273}{500}\right)\)	\(e\left(\frac{143}{500}\right)\)
\(\chi_{20000}(37,\cdot)\)	20000.eh	1000	yes	\(-1\)	\(1\)	\(e\left(\frac{781}{1000}\right)\)	\(e\left(\frac{19}{50}\right)\)	\(e\left(\frac{281}{500}\right)\)	\(e\left(\frac{833}{1000}\right)\)	\(e\left(\frac{337}{1000}\right)\)	\(e\left(\frac{167}{500}\right)\)	\(e\left(\frac{919}{1000}\right)\)	\(e\left(\frac{161}{1000}\right)\)	\(e\left(\frac{87}{250}\right)\)	\(e\left(\frac{343}{1000}\right)\)
\(\chi_{20000}(39,\cdot)\)	20000.dp	500	no	\(-1\)	\(1\)	\(e\left(\frac{447}{500}\right)\)	\(e\left(\frac{31}{50}\right)\)	\(e\left(\frac{197}{250}\right)\)	\(e\left(\frac{471}{500}\right)\)	\(e\left(\frac{69}{500}\right)\)	\(e\left(\frac{29}{250}\right)\)	\(e\left(\frac{453}{500}\right)\)	\(e\left(\frac{257}{500}\right)\)	\(e\left(\frac{13}{250}\right)\)	\(e\left(\frac{341}{500}\right)\)
\(\chi_{20000}(41,\cdot)\)	20000.dy	500	no	\(1\)	\(1\)	\(e\left(\frac{333}{500}\right)\)	\(e\left(\frac{9}{50}\right)\)	\(e\left(\frac{83}{250}\right)\)	\(e\left(\frac{319}{500}\right)\)	\(e\left(\frac{241}{500}\right)\)	\(e\left(\frac{28}{125}\right)\)	\(e\left(\frac{17}{500}\right)\)	\(e\left(\frac{423}{500}\right)\)	\(e\left(\frac{107}{250}\right)\)	\(e\left(\frac{499}{500}\right)\)
\(\chi_{20000}(43,\cdot)\)	20000.dg	200	no	\(1\)	\(1\)	\(e\left(\frac{21}{200}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{21}{100}\right)\)	\(e\left(\frac{53}{200}\right)\)	\(e\left(\frac{117}{200}\right)\)	\(e\left(\frac{97}{100}\right)\)	\(e\left(\frac{179}{200}\right)\)	\(e\left(\frac{1}{200}\right)\)	\(e\left(\frac{17}{50}\right)\)	\(e\left(\frac{63}{200}\right)\)
\(\chi_{20000}(47,\cdot)\)	20000.dv	500	no	\(1\)	\(1\)	\(e\left(\frac{379}{500}\right)\)	\(e\left(\frac{59}{100}\right)\)	\(e\left(\frac{129}{250}\right)\)	\(e\left(\frac{43}{125}\right)\)	\(e\left(\frac{233}{500}\right)\)	\(e\left(\frac{281}{500}\right)\)	\(e\left(\frac{23}{250}\right)\)	\(e\left(\frac{87}{250}\right)\)	\(e\left(\frac{57}{500}\right)\)	\(e\left(\frac{137}{500}\right)\)
\(\chi_{20000}(49,\cdot)\)	20000.cj	50	no	\(1\)	\(1\)	\(e\left(\frac{2}{25}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{4}{25}\right)\)	\(e\left(\frac{47}{50}\right)\)	\(e\left(\frac{4}{25}\right)\)	\(e\left(\frac{31}{50}\right)\)	\(e\left(\frac{21}{50}\right)\)	\(e\left(\frac{49}{50}\right)\)	\(e\left(\frac{7}{50}\right)\)	\(e\left(\frac{6}{25}\right)\)
\(\chi_{20000}(51,\cdot)\)	20000.dc	200	no	\(-1\)	\(1\)	\(e\left(\frac{9}{200}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{9}{100}\right)\)	\(e\left(\frac{87}{200}\right)\)	\(e\left(\frac{193}{200}\right)\)	\(e\left(\frac{19}{50}\right)\)	\(e\left(\frac{141}{200}\right)\)	\(e\left(\frac{179}{200}\right)\)	\(e\left(\frac{11}{100}\right)\)	\(e\left(\frac{27}{200}\right)\)
\(\chi_{20000}(53,\cdot)\)	20000.eb	1000	yes	\(-1\)	\(1\)	\(e\left(\frac{413}{1000}\right)\)	\(e\left(\frac{6}{25}\right)\)	\(e\left(\frac{413}{500}\right)\)	\(e\left(\frac{509}{1000}\right)\)	\(e\left(\frac{401}{1000}\right)\)	\(e\left(\frac{241}{500}\right)\)	\(e\left(\frac{187}{1000}\right)\)	\(e\left(\frac{653}{1000}\right)\)	\(e\left(\frac{13}{125}\right)\)	\(e\left(\frac{239}{1000}\right)\)
\(\chi_{20000}(57,\cdot)\)	20000.bv	20	no	\(-1\)	\(1\)	\(e\left(\frac{1}{10}\right)\)	\(-i\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)
\(\chi_{20000}(59,\cdot)\)	20000.ee	1000	yes	\(-1\)	\(1\)	\(e\left(\frac{551}{1000}\right)\)	\(e\left(\frac{73}{100}\right)\)	\(e\left(\frac{51}{500}\right)\)	\(e\left(\frac{693}{1000}\right)\)	\(e\left(\frac{127}{1000}\right)\)	\(e\left(\frac{108}{125}\right)\)	\(e\left(\frac{399}{1000}\right)\)	\(e\left(\frac{281}{1000}\right)\)	\(e\left(\frac{379}{500}\right)\)	\(e\left(\frac{653}{1000}\right)\)
\(\chi_{20000}(61,\cdot)\)	20000.ed	1000	yes	\(1\)	\(1\)	\(e\left(\frac{709}{1000}\right)\)	\(e\left(\frac{7}{100}\right)\)	\(e\left(\frac{209}{500}\right)\)	\(e\left(\frac{987}{1000}\right)\)	\(e\left(\frac{393}{1000}\right)\)	\(e\left(\frac{69}{250}\right)\)	\(e\left(\frac{841}{1000}\right)\)	\(e\left(\frac{779}{1000}\right)\)	\(e\left(\frac{161}{500}\right)\)	\(e\left(\frac{127}{1000}\right)\)
\(\chi_{20000}(63,\cdot)\)	20000.dw	500	no	\(1\)	\(1\)	\(e\left(\frac{43}{500}\right)\)	\(e\left(\frac{53}{100}\right)\)	\(e\left(\frac{43}{250}\right)\)	\(e\left(\frac{237}{250}\right)\)	\(e\left(\frac{161}{500}\right)\)	\(e\left(\frac{427}{500}\right)\)	\(e\left(\frac{108}{125}\right)\)	\(e\left(\frac{77}{125}\right)\)	\(e\left(\frac{19}{500}\right)\)	\(e\left(\frac{129}{500}\right)\)
\(\chi_{20000}(67,\cdot)\)	20000.ea	1000	yes	\(1\)	\(1\)	\(e\left(\frac{407}{1000}\right)\)	\(e\left(\frac{43}{50}\right)\)	\(e\left(\frac{407}{500}\right)\)	\(e\left(\frac{751}{1000}\right)\)	\(e\left(\frac{239}{1000}\right)\)	\(e\left(\frac{499}{500}\right)\)	\(e\left(\frac{993}{1000}\right)\)	\(e\left(\frac{267}{1000}\right)\)	\(e\left(\frac{239}{250}\right)\)	\(e\left(\frac{221}{1000}\right)\)
\(\chi_{20000}(69,\cdot)\)	20000.ef	1000	yes	\(1\)	\(1\)	\(e\left(\frac{507}{1000}\right)\)	\(e\left(\frac{11}{100}\right)\)	\(e\left(\frac{7}{500}\right)\)	\(e\left(\frac{801}{1000}\right)\)	\(e\left(\frac{439}{1000}\right)\)	\(e\left(\frac{81}{125}\right)\)	\(e\left(\frac{643}{1000}\right)\)	\(e\left(\frac{617}{1000}\right)\)	\(e\left(\frac{253}{500}\right)\)	\(e\left(\frac{521}{1000}\right)\)
\(\chi_{20000}(71,\cdot)\)	20000.dz	500	no	\(-1\)	\(1\)	\(e\left(\frac{229}{500}\right)\)	\(e\left(\frac{21}{25}\right)\)	\(e\left(\frac{229}{250}\right)\)	\(e\left(\frac{347}{500}\right)\)	\(e\left(\frac{183}{500}\right)\)	\(e\left(\frac{14}{125}\right)\)	\(e\left(\frac{321}{500}\right)\)	\(e\left(\frac{149}{500}\right)\)	\(e\left(\frac{58}{125}\right)\)	\(e\left(\frac{187}{500}\right)\)
\(\chi_{20000}(73,\cdot)\)	20000.dq	500	no	\(-1\)	\(1\)	\(e\left(\frac{131}{250}\right)\)	\(e\left(\frac{77}{100}\right)\)	\(e\left(\frac{6}{125}\right)\)	\(e\left(\frac{391}{500}\right)\)	\(e\left(\frac{37}{250}\right)\)	\(e\left(\frac{343}{500}\right)\)	\(e\left(\frac{263}{500}\right)\)	\(e\left(\frac{147}{500}\right)\)	\(e\left(\frac{171}{500}\right)\)	\(e\left(\frac{143}{250}\right)\)
\(\chi_{20000}(77,\cdot)\)	20000.eb	1000	yes	\(-1\)	\(1\)	\(e\left(\frac{279}{1000}\right)\)	\(e\left(\frac{23}{25}\right)\)	\(e\left(\frac{279}{500}\right)\)	\(e\left(\frac{247}{1000}\right)\)	\(e\left(\frac{283}{1000}\right)\)	\(e\left(\frac{3}{500}\right)\)	\(e\left(\frac{521}{1000}\right)\)	\(e\left(\frac{199}{1000}\right)\)	\(e\left(\frac{79}{125}\right)\)	\(e\left(\frac{837}{1000}\right)\)
\(\chi_{20000}(79,\cdot)\)	20000.dl	250	no	\(-1\)	\(1\)	\(e\left(\frac{37}{250}\right)\)	\(e\left(\frac{1}{25}\right)\)	\(e\left(\frac{37}{125}\right)\)	\(e\left(\frac{108}{125}\right)\)	\(e\left(\frac{62}{125}\right)\)	\(e\left(\frac{193}{250}\right)\)	\(e\left(\frac{119}{125}\right)\)	\(e\left(\frac{47}{250}\right)\)	\(e\left(\frac{123}{125}\right)\)	\(e\left(\frac{111}{250}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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Character group

First 32 of 8000 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.