LMFDB - Group of Dirichlet characters of modulus 8020

Show commands: PariGP / SageMath

sage: H = DirichletGroup(8020)

pari: g = idealstar(,8020,2)

Character group

sage: G.order() pari: g.no
Order	=	3200
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{4}\times C_{400}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{8020}(4011,\cdot)$, $\chi_{8020}(6417,\cdot)$, $\chi_{8020}(7221,\cdot)$

First 32 of 3200 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	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$17$	$19$	$21$	$23$	$27$
$\chi_{8020}(1,\cdot)$	8020.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{8020}(3,\cdot)$	8020.dw	400	yes	$-1$	$1$	$e\left(\frac{301}{400}\right)$	$e\left(\frac{81}{200}\right)$	$e\left(\frac{101}{200}\right)$	$e\left(\frac{197}{200}\right)$	$e\left(\frac{19}{400}\right)$	$e\left(\frac{283}{400}\right)$	$e\left(\frac{163}{400}\right)$	$e\left(\frac{63}{400}\right)$	$e\left(\frac{191}{400}\right)$	$e\left(\frac{103}{400}\right)$
$\chi_{8020}(7,\cdot)$	8020.ds	200	yes	$1$	$1$	$e\left(\frac{81}{200}\right)$	$e\left(\frac{9}{25}\right)$	$e\left(\frac{81}{100}\right)$	$e\left(\frac{57}{100}\right)$	$e\left(\frac{39}{200}\right)$	$e\left(\frac{123}{200}\right)$	$e\left(\frac{53}{200}\right)$	$e\left(\frac{153}{200}\right)$	$e\left(\frac{71}{200}\right)$	$e\left(\frac{43}{200}\right)$
$\chi_{8020}(9,\cdot)$	8020.dp	200	no	$1$	$1$	$e\left(\frac{101}{200}\right)$	$e\left(\frac{81}{100}\right)$	$e\left(\frac{1}{100}\right)$	$e\left(\frac{97}{100}\right)$	$e\left(\frac{19}{200}\right)$	$e\left(\frac{83}{200}\right)$	$e\left(\frac{163}{200}\right)$	$e\left(\frac{63}{200}\right)$	$e\left(\frac{191}{200}\right)$	$e\left(\frac{103}{200}\right)$
$\chi_{8020}(11,\cdot)$	8020.dr	200	no	$-1$	$1$	$e\left(\frac{197}{200}\right)$	$e\left(\frac{57}{100}\right)$	$e\left(\frac{97}{100}\right)$	$e\left(\frac{59}{100}\right)$	$e\left(\frac{143}{200}\right)$	$e\left(\frac{151}{200}\right)$	$e\left(\frac{111}{200}\right)$	$e\left(\frac{111}{200}\right)$	$e\left(\frac{127}{200}\right)$	$e\left(\frac{191}{200}\right)$
$\chi_{8020}(13,\cdot)$	8020.dz	400	no	$1$	$1$	$e\left(\frac{19}{400}\right)$	$e\left(\frac{39}{200}\right)$	$e\left(\frac{19}{200}\right)$	$e\left(\frac{143}{200}\right)$	$e\left(\frac{261}{400}\right)$	$e\left(\frac{77}{400}\right)$	$e\left(\frac{197}{400}\right)$	$e\left(\frac{97}{400}\right)$	$e\left(\frac{129}{400}\right)$	$e\left(\frac{57}{400}\right)$
$\chi_{8020}(17,\cdot)$	8020.dy	400	no	$1$	$1$	$e\left(\frac{283}{400}\right)$	$e\left(\frac{123}{200}\right)$	$e\left(\frac{83}{200}\right)$	$e\left(\frac{151}{200}\right)$	$e\left(\frac{77}{400}\right)$	$e\left(\frac{389}{400}\right)$	$e\left(\frac{229}{400}\right)$	$e\left(\frac{129}{400}\right)$	$e\left(\frac{153}{400}\right)$	$e\left(\frac{49}{400}\right)$
$\chi_{8020}(19,\cdot)$	8020.ed	400	yes	$1$	$1$	$e\left(\frac{163}{400}\right)$	$e\left(\frac{53}{200}\right)$	$e\left(\frac{163}{200}\right)$	$e\left(\frac{111}{200}\right)$	$e\left(\frac{197}{400}\right)$	$e\left(\frac{229}{400}\right)$	$e\left(\frac{369}{400}\right)$	$e\left(\frac{269}{400}\right)$	$e\left(\frac{233}{400}\right)$	$e\left(\frac{89}{400}\right)$
$\chi_{8020}(21,\cdot)$	8020.eb	400	no	$-1$	$1$	$e\left(\frac{63}{400}\right)$	$e\left(\frac{153}{200}\right)$	$e\left(\frac{63}{200}\right)$	$e\left(\frac{111}{200}\right)$	$e\left(\frac{97}{400}\right)$	$e\left(\frac{129}{400}\right)$	$e\left(\frac{269}{400}\right)$	$e\left(\frac{369}{400}\right)$	$e\left(\frac{333}{400}\right)$	$e\left(\frac{189}{400}\right)$
$\chi_{8020}(23,\cdot)$	8020.dx	400	yes	$-1$	$1$	$e\left(\frac{191}{400}\right)$	$e\left(\frac{71}{200}\right)$	$e\left(\frac{191}{200}\right)$	$e\left(\frac{127}{200}\right)$	$e\left(\frac{129}{400}\right)$	$e\left(\frac{153}{400}\right)$	$e\left(\frac{233}{400}\right)$	$e\left(\frac{333}{400}\right)$	$e\left(\frac{181}{400}\right)$	$e\left(\frac{173}{400}\right)$
$\chi_{8020}(27,\cdot)$	8020.dw	400	yes	$-1$	$1$	$e\left(\frac{103}{400}\right)$	$e\left(\frac{43}{200}\right)$	$e\left(\frac{103}{200}\right)$	$e\left(\frac{191}{200}\right)$	$e\left(\frac{57}{400}\right)$	$e\left(\frac{49}{400}\right)$	$e\left(\frac{89}{400}\right)$	$e\left(\frac{189}{400}\right)$	$e\left(\frac{173}{400}\right)$	$e\left(\frac{309}{400}\right)$
$\chi_{8020}(29,\cdot)$	8020.be	10	no	$1$	$1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{5}\right)$
$\chi_{8020}(31,\cdot)$	8020.ec	400	no	$1$	$1$	$e\left(\frac{307}{400}\right)$	$e\left(\frac{17}{200}\right)$	$e\left(\frac{107}{200}\right)$	$e\left(\frac{79}{200}\right)$	$e\left(\frac{133}{400}\right)$	$e\left(\frac{181}{400}\right)$	$e\left(\frac{41}{400}\right)$	$e\left(\frac{341}{400}\right)$	$e\left(\frac{137}{400}\right)$	$e\left(\frac{121}{400}\right)$
$\chi_{8020}(33,\cdot)$	8020.cz	80	no	$1$	$1$	$e\left(\frac{59}{80}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{61}{80}\right)$	$e\left(\frac{37}{80}\right)$	$e\left(\frac{77}{80}\right)$	$e\left(\frac{57}{80}\right)$	$e\left(\frac{9}{80}\right)$	$e\left(\frac{17}{80}\right)$
$\chi_{8020}(37,\cdot)$	8020.dz	400	no	$1$	$1$	$e\left(\frac{133}{400}\right)$	$e\left(\frac{73}{200}\right)$	$e\left(\frac{133}{200}\right)$	$e\left(\frac{1}{200}\right)$	$e\left(\frac{227}{400}\right)$	$e\left(\frac{139}{400}\right)$	$e\left(\frac{179}{400}\right)$	$e\left(\frac{279}{400}\right)$	$e\left(\frac{103}{400}\right)$	$e\left(\frac{399}{400}\right)$
$\chi_{8020}(39,\cdot)$	8020.bd	10	yes	$-1$	$1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{2}{5}\right)$
$\chi_{8020}(41,\cdot)$	8020.cq	50	no	$1$	$1$	$e\left(\frac{41}{50}\right)$	$e\left(\frac{21}{25}\right)$	$e\left(\frac{16}{25}\right)$	$e\left(\frac{2}{25}\right)$	$e\left(\frac{29}{50}\right)$	$e\left(\frac{3}{50}\right)$	$e\left(\frac{33}{50}\right)$	$e\left(\frac{33}{50}\right)$	$e\left(\frac{31}{50}\right)$	$e\left(\frac{23}{50}\right)$
$\chi_{8020}(43,\cdot)$	8020.dt	200	yes	$1$	$1$	$e\left(\frac{93}{200}\right)$	$e\left(\frac{29}{50}\right)$	$e\left(\frac{93}{100}\right)$	$e\left(\frac{21}{100}\right)$	$e\left(\frac{67}{200}\right)$	$e\left(\frac{119}{200}\right)$	$e\left(\frac{109}{200}\right)$	$e\left(\frac{9}{200}\right)$	$e\left(\frac{163}{200}\right)$	$e\left(\frac{79}{200}\right)$
$\chi_{8020}(47,\cdot)$	8020.dt	200	yes	$1$	$1$	$e\left(\frac{159}{200}\right)$	$e\left(\frac{27}{50}\right)$	$e\left(\frac{59}{100}\right)$	$e\left(\frac{23}{100}\right)$	$e\left(\frac{121}{200}\right)$	$e\left(\frac{197}{200}\right)$	$e\left(\frac{167}{200}\right)$	$e\left(\frac{67}{200}\right)$	$e\left(\frac{169}{200}\right)$	$e\left(\frac{77}{200}\right)$
$\chi_{8020}(49,\cdot)$	8020.dd	100	no	$1$	$1$	$e\left(\frac{81}{100}\right)$	$e\left(\frac{18}{25}\right)$	$e\left(\frac{31}{50}\right)$	$e\left(\frac{7}{50}\right)$	$e\left(\frac{39}{100}\right)$	$e\left(\frac{23}{100}\right)$	$e\left(\frac{53}{100}\right)$	$e\left(\frac{53}{100}\right)$	$e\left(\frac{71}{100}\right)$	$e\left(\frac{43}{100}\right)$
$\chi_{8020}(51,\cdot)$	8020.cp	50	no	$-1$	$1$	$e\left(\frac{23}{50}\right)$	$e\left(\frac{1}{50}\right)$	$e\left(\frac{23}{25}\right)$	$e\left(\frac{37}{50}\right)$	$e\left(\frac{6}{25}\right)$	$e\left(\frac{17}{25}\right)$	$e\left(\frac{49}{50}\right)$	$e\left(\frac{12}{25}\right)$	$e\left(\frac{43}{50}\right)$	$e\left(\frac{19}{50}\right)$
$\chi_{8020}(53,\cdot)$	8020.dy	400	no	$1$	$1$	$e\left(\frac{313}{400}\right)$	$e\left(\frac{153}{200}\right)$	$e\left(\frac{113}{200}\right)$	$e\left(\frac{61}{200}\right)$	$e\left(\frac{47}{400}\right)$	$e\left(\frac{279}{400}\right)$	$e\left(\frac{119}{400}\right)$	$e\left(\frac{219}{400}\right)$	$e\left(\frac{83}{400}\right)$	$e\left(\frac{139}{400}\right)$
$\chi_{8020}(57,\cdot)$	8020.dn	100	no	$-1$	$1$	$e\left(\frac{4}{25}\right)$	$e\left(\frac{67}{100}\right)$	$e\left(\frac{8}{25}\right)$	$e\left(\frac{27}{50}\right)$	$e\left(\frac{27}{50}\right)$	$e\left(\frac{7}{25}\right)$	$e\left(\frac{33}{100}\right)$	$e\left(\frac{83}{100}\right)$	$e\left(\frac{3}{50}\right)$	$e\left(\frac{12}{25}\right)$
$\chi_{8020}(59,\cdot)$	8020.ed	400	yes	$1$	$1$	$e\left(\frac{391}{400}\right)$	$e\left(\frac{121}{200}\right)$	$e\left(\frac{191}{200}\right)$	$e\left(\frac{27}{200}\right)$	$e\left(\frac{129}{400}\right)$	$e\left(\frac{353}{400}\right)$	$e\left(\frac{333}{400}\right)$	$e\left(\frac{233}{400}\right)$	$e\left(\frac{181}{400}\right)$	$e\left(\frac{373}{400}\right)$
$\chi_{8020}(61,\cdot)$	8020.eb	400	no	$-1$	$1$	$e\left(\frac{283}{400}\right)$	$e\left(\frac{173}{200}\right)$	$e\left(\frac{83}{200}\right)$	$e\left(\frac{51}{200}\right)$	$e\left(\frac{277}{400}\right)$	$e\left(\frac{389}{400}\right)$	$e\left(\frac{129}{400}\right)$	$e\left(\frac{229}{400}\right)$	$e\left(\frac{353}{400}\right)$	$e\left(\frac{49}{400}\right)$
$\chi_{8020}(63,\cdot)$	8020.di	100	yes	$1$	$1$	$e\left(\frac{91}{100}\right)$	$e\left(\frac{17}{100}\right)$	$e\left(\frac{41}{50}\right)$	$e\left(\frac{27}{50}\right)$	$e\left(\frac{29}{100}\right)$	$e\left(\frac{3}{100}\right)$	$e\left(\frac{2}{25}\right)$	$e\left(\frac{2}{25}\right)$	$e\left(\frac{31}{100}\right)$	$e\left(\frac{73}{100}\right)$
$\chi_{8020}(67,\cdot)$	8020.dx	400	yes	$-1$	$1$	$e\left(\frac{73}{400}\right)$	$e\left(\frac{113}{200}\right)$	$e\left(\frac{73}{200}\right)$	$e\left(\frac{81}{200}\right)$	$e\left(\frac{87}{400}\right)$	$e\left(\frac{159}{400}\right)$	$e\left(\frac{399}{400}\right)$	$e\left(\frac{299}{400}\right)$	$e\left(\frac{243}{400}\right)$	$e\left(\frac{219}{400}\right)$
$\chi_{8020}(69,\cdot)$	8020.dd	100	no	$1$	$1$	$e\left(\frac{23}{100}\right)$	$e\left(\frac{19}{25}\right)$	$e\left(\frac{23}{50}\right)$	$e\left(\frac{31}{50}\right)$	$e\left(\frac{37}{100}\right)$	$e\left(\frac{9}{100}\right)$	$e\left(\frac{99}{100}\right)$	$e\left(\frac{99}{100}\right)$	$e\left(\frac{93}{100}\right)$	$e\left(\frac{69}{100}\right)$
$\chi_{8020}(71,\cdot)$	8020.ec	400	no	$1$	$1$	$e\left(\frac{269}{400}\right)$	$e\left(\frac{39}{200}\right)$	$e\left(\frac{69}{200}\right)$	$e\left(\frac{193}{200}\right)$	$e\left(\frac{11}{400}\right)$	$e\left(\frac{27}{400}\right)$	$e\left(\frac{247}{400}\right)$	$e\left(\frac{347}{400}\right)$	$e\left(\frac{279}{400}\right)$	$e\left(\frac{7}{400}\right)$
$\chi_{8020}(73,\cdot)$	8020.dv	200	no	$-1$	$1$	$e\left(\frac{153}{200}\right)$	$e\left(\frac{17}{25}\right)$	$e\left(\frac{53}{100}\right)$	$e\left(\frac{91}{100}\right)$	$e\left(\frac{107}{200}\right)$	$e\left(\frac{199}{200}\right)$	$e\left(\frac{89}{200}\right)$	$e\left(\frac{89}{200}\right)$	$e\left(\frac{23}{200}\right)$	$e\left(\frac{59}{200}\right)$
$\chi_{8020}(77,\cdot)$	8020.dl	100	no	$-1$	$1$	$e\left(\frac{39}{100}\right)$	$e\left(\frac{93}{100}\right)$	$e\left(\frac{39}{50}\right)$	$e\left(\frac{4}{25}\right)$	$e\left(\frac{91}{100}\right)$	$e\left(\frac{37}{100}\right)$	$e\left(\frac{41}{50}\right)$	$e\left(\frac{8}{25}\right)$	$e\left(\frac{99}{100}\right)$	$e\left(\frac{17}{100}\right)$
$\chi_{8020}(79,\cdot)$	8020.ed	400	yes	$1$	$1$	$e\left(\frac{179}{400}\right)$	$e\left(\frac{149}{200}\right)$	$e\left(\frac{179}{200}\right)$	$e\left(\frac{63}{200}\right)$	$e\left(\frac{101}{400}\right)$	$e\left(\frac{357}{400}\right)$	$e\left(\frac{177}{400}\right)$	$e\left(\frac{77}{400}\right)$	$e\left(\frac{89}{400}\right)$	$e\left(\frac{137}{400}\right)$

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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	$8020$
Structure	\(C_{2}\times C_{4}\times C_{400}\)
Order	$3200$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(13\)	\(17\)	\(19\)	\(21\)	\(23\)	\(27\)
\(\chi_{8020}(1,\cdot)\)	8020.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{8020}(3,\cdot)\)	8020.dw	400	yes	\(-1\)	\(1\)	\(e\left(\frac{301}{400}\right)\)	\(e\left(\frac{81}{200}\right)\)	\(e\left(\frac{101}{200}\right)\)	\(e\left(\frac{197}{200}\right)\)	\(e\left(\frac{19}{400}\right)\)	\(e\left(\frac{283}{400}\right)\)	\(e\left(\frac{163}{400}\right)\)	\(e\left(\frac{63}{400}\right)\)	\(e\left(\frac{191}{400}\right)\)	\(e\left(\frac{103}{400}\right)\)
\(\chi_{8020}(7,\cdot)\)	8020.ds	200	yes	\(1\)	\(1\)	\(e\left(\frac{81}{200}\right)\)	\(e\left(\frac{9}{25}\right)\)	\(e\left(\frac{81}{100}\right)\)	\(e\left(\frac{57}{100}\right)\)	\(e\left(\frac{39}{200}\right)\)	\(e\left(\frac{123}{200}\right)\)	\(e\left(\frac{53}{200}\right)\)	\(e\left(\frac{153}{200}\right)\)	\(e\left(\frac{71}{200}\right)\)	\(e\left(\frac{43}{200}\right)\)
\(\chi_{8020}(9,\cdot)\)	8020.dp	200	no	\(1\)	\(1\)	\(e\left(\frac{101}{200}\right)\)	\(e\left(\frac{81}{100}\right)\)	\(e\left(\frac{1}{100}\right)\)	\(e\left(\frac{97}{100}\right)\)	\(e\left(\frac{19}{200}\right)\)	\(e\left(\frac{83}{200}\right)\)	\(e\left(\frac{163}{200}\right)\)	\(e\left(\frac{63}{200}\right)\)	\(e\left(\frac{191}{200}\right)\)	\(e\left(\frac{103}{200}\right)\)
\(\chi_{8020}(11,\cdot)\)	8020.dr	200	no	\(-1\)	\(1\)	\(e\left(\frac{197}{200}\right)\)	\(e\left(\frac{57}{100}\right)\)	\(e\left(\frac{97}{100}\right)\)	\(e\left(\frac{59}{100}\right)\)	\(e\left(\frac{143}{200}\right)\)	\(e\left(\frac{151}{200}\right)\)	\(e\left(\frac{111}{200}\right)\)	\(e\left(\frac{111}{200}\right)\)	\(e\left(\frac{127}{200}\right)\)	\(e\left(\frac{191}{200}\right)\)
\(\chi_{8020}(13,\cdot)\)	8020.dz	400	no	\(1\)	\(1\)	\(e\left(\frac{19}{400}\right)\)	\(e\left(\frac{39}{200}\right)\)	\(e\left(\frac{19}{200}\right)\)	\(e\left(\frac{143}{200}\right)\)	\(e\left(\frac{261}{400}\right)\)	\(e\left(\frac{77}{400}\right)\)	\(e\left(\frac{197}{400}\right)\)	\(e\left(\frac{97}{400}\right)\)	\(e\left(\frac{129}{400}\right)\)	\(e\left(\frac{57}{400}\right)\)
\(\chi_{8020}(17,\cdot)\)	8020.dy	400	no	\(1\)	\(1\)	\(e\left(\frac{283}{400}\right)\)	\(e\left(\frac{123}{200}\right)\)	\(e\left(\frac{83}{200}\right)\)	\(e\left(\frac{151}{200}\right)\)	\(e\left(\frac{77}{400}\right)\)	\(e\left(\frac{389}{400}\right)\)	\(e\left(\frac{229}{400}\right)\)	\(e\left(\frac{129}{400}\right)\)	\(e\left(\frac{153}{400}\right)\)	\(e\left(\frac{49}{400}\right)\)
\(\chi_{8020}(19,\cdot)\)	8020.ed	400	yes	\(1\)	\(1\)	\(e\left(\frac{163}{400}\right)\)	\(e\left(\frac{53}{200}\right)\)	\(e\left(\frac{163}{200}\right)\)	\(e\left(\frac{111}{200}\right)\)	\(e\left(\frac{197}{400}\right)\)	\(e\left(\frac{229}{400}\right)\)	\(e\left(\frac{369}{400}\right)\)	\(e\left(\frac{269}{400}\right)\)	\(e\left(\frac{233}{400}\right)\)	\(e\left(\frac{89}{400}\right)\)
\(\chi_{8020}(21,\cdot)\)	8020.eb	400	no	\(-1\)	\(1\)	\(e\left(\frac{63}{400}\right)\)	\(e\left(\frac{153}{200}\right)\)	\(e\left(\frac{63}{200}\right)\)	\(e\left(\frac{111}{200}\right)\)	\(e\left(\frac{97}{400}\right)\)	\(e\left(\frac{129}{400}\right)\)	\(e\left(\frac{269}{400}\right)\)	\(e\left(\frac{369}{400}\right)\)	\(e\left(\frac{333}{400}\right)\)	\(e\left(\frac{189}{400}\right)\)
\(\chi_{8020}(23,\cdot)\)	8020.dx	400	yes	\(-1\)	\(1\)	\(e\left(\frac{191}{400}\right)\)	\(e\left(\frac{71}{200}\right)\)	\(e\left(\frac{191}{200}\right)\)	\(e\left(\frac{127}{200}\right)\)	\(e\left(\frac{129}{400}\right)\)	\(e\left(\frac{153}{400}\right)\)	\(e\left(\frac{233}{400}\right)\)	\(e\left(\frac{333}{400}\right)\)	\(e\left(\frac{181}{400}\right)\)	\(e\left(\frac{173}{400}\right)\)
\(\chi_{8020}(27,\cdot)\)	8020.dw	400	yes	\(-1\)	\(1\)	\(e\left(\frac{103}{400}\right)\)	\(e\left(\frac{43}{200}\right)\)	\(e\left(\frac{103}{200}\right)\)	\(e\left(\frac{191}{200}\right)\)	\(e\left(\frac{57}{400}\right)\)	\(e\left(\frac{49}{400}\right)\)	\(e\left(\frac{89}{400}\right)\)	\(e\left(\frac{189}{400}\right)\)	\(e\left(\frac{173}{400}\right)\)	\(e\left(\frac{309}{400}\right)\)
\(\chi_{8020}(29,\cdot)\)	8020.be	10	no	\(1\)	\(1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)
\(\chi_{8020}(31,\cdot)\)	8020.ec	400	no	\(1\)	\(1\)	\(e\left(\frac{307}{400}\right)\)	\(e\left(\frac{17}{200}\right)\)	\(e\left(\frac{107}{200}\right)\)	\(e\left(\frac{79}{200}\right)\)	\(e\left(\frac{133}{400}\right)\)	\(e\left(\frac{181}{400}\right)\)	\(e\left(\frac{41}{400}\right)\)	\(e\left(\frac{341}{400}\right)\)	\(e\left(\frac{137}{400}\right)\)	\(e\left(\frac{121}{400}\right)\)
\(\chi_{8020}(33,\cdot)\)	8020.cz	80	no	\(1\)	\(1\)	\(e\left(\frac{59}{80}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{61}{80}\right)\)	\(e\left(\frac{37}{80}\right)\)	\(e\left(\frac{77}{80}\right)\)	\(e\left(\frac{57}{80}\right)\)	\(e\left(\frac{9}{80}\right)\)	\(e\left(\frac{17}{80}\right)\)
\(\chi_{8020}(37,\cdot)\)	8020.dz	400	no	\(1\)	\(1\)	\(e\left(\frac{133}{400}\right)\)	\(e\left(\frac{73}{200}\right)\)	\(e\left(\frac{133}{200}\right)\)	\(e\left(\frac{1}{200}\right)\)	\(e\left(\frac{227}{400}\right)\)	\(e\left(\frac{139}{400}\right)\)	\(e\left(\frac{179}{400}\right)\)	\(e\left(\frac{279}{400}\right)\)	\(e\left(\frac{103}{400}\right)\)	\(e\left(\frac{399}{400}\right)\)
\(\chi_{8020}(39,\cdot)\)	8020.bd	10	yes	\(-1\)	\(1\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)
\(\chi_{8020}(41,\cdot)\)	8020.cq	50	no	\(1\)	\(1\)	\(e\left(\frac{41}{50}\right)\)	\(e\left(\frac{21}{25}\right)\)	\(e\left(\frac{16}{25}\right)\)	\(e\left(\frac{2}{25}\right)\)	\(e\left(\frac{29}{50}\right)\)	\(e\left(\frac{3}{50}\right)\)	\(e\left(\frac{33}{50}\right)\)	\(e\left(\frac{33}{50}\right)\)	\(e\left(\frac{31}{50}\right)\)	\(e\left(\frac{23}{50}\right)\)
\(\chi_{8020}(43,\cdot)\)	8020.dt	200	yes	\(1\)	\(1\)	\(e\left(\frac{93}{200}\right)\)	\(e\left(\frac{29}{50}\right)\)	\(e\left(\frac{93}{100}\right)\)	\(e\left(\frac{21}{100}\right)\)	\(e\left(\frac{67}{200}\right)\)	\(e\left(\frac{119}{200}\right)\)	\(e\left(\frac{109}{200}\right)\)	\(e\left(\frac{9}{200}\right)\)	\(e\left(\frac{163}{200}\right)\)	\(e\left(\frac{79}{200}\right)\)
\(\chi_{8020}(47,\cdot)\)	8020.dt	200	yes	\(1\)	\(1\)	\(e\left(\frac{159}{200}\right)\)	\(e\left(\frac{27}{50}\right)\)	\(e\left(\frac{59}{100}\right)\)	\(e\left(\frac{23}{100}\right)\)	\(e\left(\frac{121}{200}\right)\)	\(e\left(\frac{197}{200}\right)\)	\(e\left(\frac{167}{200}\right)\)	\(e\left(\frac{67}{200}\right)\)	\(e\left(\frac{169}{200}\right)\)	\(e\left(\frac{77}{200}\right)\)
\(\chi_{8020}(49,\cdot)\)	8020.dd	100	no	\(1\)	\(1\)	\(e\left(\frac{81}{100}\right)\)	\(e\left(\frac{18}{25}\right)\)	\(e\left(\frac{31}{50}\right)\)	\(e\left(\frac{7}{50}\right)\)	\(e\left(\frac{39}{100}\right)\)	\(e\left(\frac{23}{100}\right)\)	\(e\left(\frac{53}{100}\right)\)	\(e\left(\frac{53}{100}\right)\)	\(e\left(\frac{71}{100}\right)\)	\(e\left(\frac{43}{100}\right)\)
\(\chi_{8020}(51,\cdot)\)	8020.cp	50	no	\(-1\)	\(1\)	\(e\left(\frac{23}{50}\right)\)	\(e\left(\frac{1}{50}\right)\)	\(e\left(\frac{23}{25}\right)\)	\(e\left(\frac{37}{50}\right)\)	\(e\left(\frac{6}{25}\right)\)	\(e\left(\frac{17}{25}\right)\)	\(e\left(\frac{49}{50}\right)\)	\(e\left(\frac{12}{25}\right)\)	\(e\left(\frac{43}{50}\right)\)	\(e\left(\frac{19}{50}\right)\)
\(\chi_{8020}(53,\cdot)\)	8020.dy	400	no	\(1\)	\(1\)	\(e\left(\frac{313}{400}\right)\)	\(e\left(\frac{153}{200}\right)\)	\(e\left(\frac{113}{200}\right)\)	\(e\left(\frac{61}{200}\right)\)	\(e\left(\frac{47}{400}\right)\)	\(e\left(\frac{279}{400}\right)\)	\(e\left(\frac{119}{400}\right)\)	\(e\left(\frac{219}{400}\right)\)	\(e\left(\frac{83}{400}\right)\)	\(e\left(\frac{139}{400}\right)\)
\(\chi_{8020}(57,\cdot)\)	8020.dn	100	no	\(-1\)	\(1\)	\(e\left(\frac{4}{25}\right)\)	\(e\left(\frac{67}{100}\right)\)	\(e\left(\frac{8}{25}\right)\)	\(e\left(\frac{27}{50}\right)\)	\(e\left(\frac{27}{50}\right)\)	\(e\left(\frac{7}{25}\right)\)	\(e\left(\frac{33}{100}\right)\)	\(e\left(\frac{83}{100}\right)\)	\(e\left(\frac{3}{50}\right)\)	\(e\left(\frac{12}{25}\right)\)
\(\chi_{8020}(59,\cdot)\)	8020.ed	400	yes	\(1\)	\(1\)	\(e\left(\frac{391}{400}\right)\)	\(e\left(\frac{121}{200}\right)\)	\(e\left(\frac{191}{200}\right)\)	\(e\left(\frac{27}{200}\right)\)	\(e\left(\frac{129}{400}\right)\)	\(e\left(\frac{353}{400}\right)\)	\(e\left(\frac{333}{400}\right)\)	\(e\left(\frac{233}{400}\right)\)	\(e\left(\frac{181}{400}\right)\)	\(e\left(\frac{373}{400}\right)\)
\(\chi_{8020}(61,\cdot)\)	8020.eb	400	no	\(-1\)	\(1\)	\(e\left(\frac{283}{400}\right)\)	\(e\left(\frac{173}{200}\right)\)	\(e\left(\frac{83}{200}\right)\)	\(e\left(\frac{51}{200}\right)\)	\(e\left(\frac{277}{400}\right)\)	\(e\left(\frac{389}{400}\right)\)	\(e\left(\frac{129}{400}\right)\)	\(e\left(\frac{229}{400}\right)\)	\(e\left(\frac{353}{400}\right)\)	\(e\left(\frac{49}{400}\right)\)
\(\chi_{8020}(63,\cdot)\)	8020.di	100	yes	\(1\)	\(1\)	\(e\left(\frac{91}{100}\right)\)	\(e\left(\frac{17}{100}\right)\)	\(e\left(\frac{41}{50}\right)\)	\(e\left(\frac{27}{50}\right)\)	\(e\left(\frac{29}{100}\right)\)	\(e\left(\frac{3}{100}\right)\)	\(e\left(\frac{2}{25}\right)\)	\(e\left(\frac{2}{25}\right)\)	\(e\left(\frac{31}{100}\right)\)	\(e\left(\frac{73}{100}\right)\)
\(\chi_{8020}(67,\cdot)\)	8020.dx	400	yes	\(-1\)	\(1\)	\(e\left(\frac{73}{400}\right)\)	\(e\left(\frac{113}{200}\right)\)	\(e\left(\frac{73}{200}\right)\)	\(e\left(\frac{81}{200}\right)\)	\(e\left(\frac{87}{400}\right)\)	\(e\left(\frac{159}{400}\right)\)	\(e\left(\frac{399}{400}\right)\)	\(e\left(\frac{299}{400}\right)\)	\(e\left(\frac{243}{400}\right)\)	\(e\left(\frac{219}{400}\right)\)
\(\chi_{8020}(69,\cdot)\)	8020.dd	100	no	\(1\)	\(1\)	\(e\left(\frac{23}{100}\right)\)	\(e\left(\frac{19}{25}\right)\)	\(e\left(\frac{23}{50}\right)\)	\(e\left(\frac{31}{50}\right)\)	\(e\left(\frac{37}{100}\right)\)	\(e\left(\frac{9}{100}\right)\)	\(e\left(\frac{99}{100}\right)\)	\(e\left(\frac{99}{100}\right)\)	\(e\left(\frac{93}{100}\right)\)	\(e\left(\frac{69}{100}\right)\)
\(\chi_{8020}(71,\cdot)\)	8020.ec	400	no	\(1\)	\(1\)	\(e\left(\frac{269}{400}\right)\)	\(e\left(\frac{39}{200}\right)\)	\(e\left(\frac{69}{200}\right)\)	\(e\left(\frac{193}{200}\right)\)	\(e\left(\frac{11}{400}\right)\)	\(e\left(\frac{27}{400}\right)\)	\(e\left(\frac{247}{400}\right)\)	\(e\left(\frac{347}{400}\right)\)	\(e\left(\frac{279}{400}\right)\)	\(e\left(\frac{7}{400}\right)\)
\(\chi_{8020}(73,\cdot)\)	8020.dv	200	no	\(-1\)	\(1\)	\(e\left(\frac{153}{200}\right)\)	\(e\left(\frac{17}{25}\right)\)	\(e\left(\frac{53}{100}\right)\)	\(e\left(\frac{91}{100}\right)\)	\(e\left(\frac{107}{200}\right)\)	\(e\left(\frac{199}{200}\right)\)	\(e\left(\frac{89}{200}\right)\)	\(e\left(\frac{89}{200}\right)\)	\(e\left(\frac{23}{200}\right)\)	\(e\left(\frac{59}{200}\right)\)
\(\chi_{8020}(77,\cdot)\)	8020.dl	100	no	\(-1\)	\(1\)	\(e\left(\frac{39}{100}\right)\)	\(e\left(\frac{93}{100}\right)\)	\(e\left(\frac{39}{50}\right)\)	\(e\left(\frac{4}{25}\right)\)	\(e\left(\frac{91}{100}\right)\)	\(e\left(\frac{37}{100}\right)\)	\(e\left(\frac{41}{50}\right)\)	\(e\left(\frac{8}{25}\right)\)	\(e\left(\frac{99}{100}\right)\)	\(e\left(\frac{17}{100}\right)\)
\(\chi_{8020}(79,\cdot)\)	8020.ed	400	yes	\(1\)	\(1\)	\(e\left(\frac{179}{400}\right)\)	\(e\left(\frac{149}{200}\right)\)	\(e\left(\frac{179}{200}\right)\)	\(e\left(\frac{63}{200}\right)\)	\(e\left(\frac{101}{400}\right)\)	\(e\left(\frac{357}{400}\right)\)	\(e\left(\frac{177}{400}\right)\)	\(e\left(\frac{77}{400}\right)\)	\(e\left(\frac{89}{400}\right)\)	\(e\left(\frac{137}{400}\right)\)

Introduction

L-functions

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This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.