LMFDB - Group of Dirichlet characters of modulus 8032

Show commands: PariGP / SageMath

sage: H = DirichletGroup(8032)

pari: g = idealstar(,8032,2)

Character group

sage: G.order() pari: g.no
Order	=	4000
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{1000}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{8032}(6527,\cdot)$, $\chi_{8032}(3013,\cdot)$, $\chi_{8032}(257,\cdot)$

First 32 of 4000 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	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$17$	$19$	$21$
$\chi_{8032}(1,\cdot)$	8032.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{8032}(3,\cdot)$	8032.ci	1000	yes	$-1$	$1$	$e\left(\frac{649}{1000}\right)$	$e\left(\frac{139}{200}\right)$	$e\left(\frac{61}{500}\right)$	$e\left(\frac{149}{500}\right)$	$e\left(\frac{879}{1000}\right)$	$e\left(\frac{273}{1000}\right)$	$e\left(\frac{43}{125}\right)$	$e\left(\frac{59}{250}\right)$	$e\left(\frac{557}{1000}\right)$	$e\left(\frac{771}{1000}\right)$
$\chi_{8032}(5,\cdot)$	8032.bv	200	yes	$1$	$1$	$e\left(\frac{139}{200}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{21}{100}\right)$	$e\left(\frac{39}{100}\right)$	$e\left(\frac{69}{200}\right)$	$e\left(\frac{103}{200}\right)$	$e\left(\frac{21}{50}\right)$	$e\left(\frac{49}{50}\right)$	$e\left(\frac{127}{200}\right)$	$e\left(\frac{181}{200}\right)$
$\chi_{8032}(7,\cdot)$	8032.cf	500	no	$-1$	$1$	$e\left(\frac{61}{500}\right)$	$e\left(\frac{21}{100}\right)$	$e\left(\frac{2}{125}\right)$	$e\left(\frac{61}{250}\right)$	$e\left(\frac{31}{500}\right)$	$e\left(\frac{147}{500}\right)$	$e\left(\frac{83}{250}\right)$	$e\left(\frac{51}{125}\right)$	$e\left(\frac{473}{500}\right)$	$e\left(\frac{69}{500}\right)$
$\chi_{8032}(9,\cdot)$	8032.cg	500	no	$1$	$1$	$e\left(\frac{149}{500}\right)$	$e\left(\frac{39}{100}\right)$	$e\left(\frac{61}{250}\right)$	$e\left(\frac{149}{250}\right)$	$e\left(\frac{379}{500}\right)$	$e\left(\frac{273}{500}\right)$	$e\left(\frac{86}{125}\right)$	$e\left(\frac{59}{125}\right)$	$e\left(\frac{57}{500}\right)$	$e\left(\frac{271}{500}\right)$
$\chi_{8032}(11,\cdot)$	8032.cj	1000	yes	$1$	$1$	$e\left(\frac{879}{1000}\right)$	$e\left(\frac{69}{200}\right)$	$e\left(\frac{31}{500}\right)$	$e\left(\frac{379}{500}\right)$	$e\left(\frac{709}{1000}\right)$	$e\left(\frac{983}{1000}\right)$	$e\left(\frac{28}{125}\right)$	$e\left(\frac{239}{250}\right)$	$e\left(\frac{447}{1000}\right)$	$e\left(\frac{941}{1000}\right)$
$\chi_{8032}(13,\cdot)$	8032.ck	1000	yes	$1$	$1$	$e\left(\frac{273}{1000}\right)$	$e\left(\frac{103}{200}\right)$	$e\left(\frac{147}{500}\right)$	$e\left(\frac{273}{500}\right)$	$e\left(\frac{983}{1000}\right)$	$e\left(\frac{621}{1000}\right)$	$e\left(\frac{197}{250}\right)$	$e\left(\frac{93}{250}\right)$	$e\left(\frac{789}{1000}\right)$	$e\left(\frac{567}{1000}\right)$
$\chi_{8032}(15,\cdot)$	8032.cb	250	no	$-1$	$1$	$e\left(\frac{43}{125}\right)$	$e\left(\frac{21}{50}\right)$	$e\left(\frac{83}{250}\right)$	$e\left(\frac{86}{125}\right)$	$e\left(\frac{28}{125}\right)$	$e\left(\frac{197}{250}\right)$	$e\left(\frac{191}{250}\right)$	$e\left(\frac{27}{125}\right)$	$e\left(\frac{24}{125}\right)$	$e\left(\frac{169}{250}\right)$
$\chi_{8032}(17,\cdot)$	8032.cc	250	no	$1$	$1$	$e\left(\frac{59}{250}\right)$	$e\left(\frac{49}{50}\right)$	$e\left(\frac{51}{125}\right)$	$e\left(\frac{59}{125}\right)$	$e\left(\frac{239}{250}\right)$	$e\left(\frac{93}{250}\right)$	$e\left(\frac{27}{125}\right)$	$e\left(\frac{113}{125}\right)$	$e\left(\frac{187}{250}\right)$	$e\left(\frac{161}{250}\right)$
$\chi_{8032}(19,\cdot)$	8032.cj	1000	yes	$1$	$1$	$e\left(\frac{557}{1000}\right)$	$e\left(\frac{127}{200}\right)$	$e\left(\frac{473}{500}\right)$	$e\left(\frac{57}{500}\right)$	$e\left(\frac{447}{1000}\right)$	$e\left(\frac{789}{1000}\right)$	$e\left(\frac{24}{125}\right)$	$e\left(\frac{187}{250}\right)$	$e\left(\frac{901}{1000}\right)$	$e\left(\frac{503}{1000}\right)$
$\chi_{8032}(21,\cdot)$	8032.ck	1000	yes	$1$	$1$	$e\left(\frac{771}{1000}\right)$	$e\left(\frac{181}{200}\right)$	$e\left(\frac{69}{500}\right)$	$e\left(\frac{271}{500}\right)$	$e\left(\frac{941}{1000}\right)$	$e\left(\frac{567}{1000}\right)$	$e\left(\frac{169}{250}\right)$	$e\left(\frac{161}{250}\right)$	$e\left(\frac{503}{1000}\right)$	$e\left(\frac{909}{1000}\right)$
$\chi_{8032}(23,\cdot)$	8032.cf	500	no	$-1$	$1$	$e\left(\frac{143}{500}\right)$	$e\left(\frac{23}{100}\right)$	$e\left(\frac{101}{125}\right)$	$e\left(\frac{143}{250}\right)$	$e\left(\frac{253}{500}\right)$	$e\left(\frac{361}{500}\right)$	$e\left(\frac{129}{250}\right)$	$e\left(\frac{13}{125}\right)$	$e\left(\frac{199}{500}\right)$	$e\left(\frac{47}{500}\right)$
$\chi_{8032}(25,\cdot)$	8032.bo	100	no	$1$	$1$	$e\left(\frac{39}{100}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{21}{50}\right)$	$e\left(\frac{39}{50}\right)$	$e\left(\frac{69}{100}\right)$	$e\left(\frac{3}{100}\right)$	$e\left(\frac{21}{25}\right)$	$e\left(\frac{24}{25}\right)$	$e\left(\frac{27}{100}\right)$	$e\left(\frac{81}{100}\right)$
$\chi_{8032}(27,\cdot)$	8032.ci	1000	yes	$-1$	$1$	$e\left(\frac{947}{1000}\right)$	$e\left(\frac{17}{200}\right)$	$e\left(\frac{183}{500}\right)$	$e\left(\frac{447}{500}\right)$	$e\left(\frac{637}{1000}\right)$	$e\left(\frac{819}{1000}\right)$	$e\left(\frac{4}{125}\right)$	$e\left(\frac{177}{250}\right)$	$e\left(\frac{671}{1000}\right)$	$e\left(\frac{313}{1000}\right)$
$\chi_{8032}(29,\cdot)$	8032.cl	1000	yes	$-1$	$1$	$e\left(\frac{437}{1000}\right)$	$e\left(\frac{107}{200}\right)$	$e\left(\frac{43}{500}\right)$	$e\left(\frac{437}{500}\right)$	$e\left(\frac{927}{1000}\right)$	$e\left(\frac{49}{1000}\right)$	$e\left(\frac{243}{250}\right)$	$e\left(\frac{17}{250}\right)$	$e\left(\frac{741}{1000}\right)$	$e\left(\frac{523}{1000}\right)$
$\chi_{8032}(31,\cdot)$	8032.bz	250	no	$-1$	$1$	$e\left(\frac{101}{250}\right)$	$e\left(\frac{18}{25}\right)$	$e\left(\frac{3}{250}\right)$	$e\left(\frac{101}{125}\right)$	$e\left(\frac{121}{250}\right)$	$e\left(\frac{51}{125}\right)$	$e\left(\frac{31}{250}\right)$	$e\left(\frac{7}{125}\right)$	$e\left(\frac{193}{250}\right)$	$e\left(\frac{52}{125}\right)$
$\chi_{8032}(33,\cdot)$	8032.bx	250	no	$-1$	$1$	$e\left(\frac{66}{125}\right)$	$e\left(\frac{1}{25}\right)$	$e\left(\frac{23}{125}\right)$	$e\left(\frac{7}{125}\right)$	$e\left(\frac{147}{250}\right)$	$e\left(\frac{32}{125}\right)$	$e\left(\frac{71}{125}\right)$	$e\left(\frac{24}{125}\right)$	$e\left(\frac{1}{250}\right)$	$e\left(\frac{89}{125}\right)$
$\chi_{8032}(35,\cdot)$	8032.ci	1000	yes	$-1$	$1$	$e\left(\frac{817}{1000}\right)$	$e\left(\frac{187}{200}\right)$	$e\left(\frac{113}{500}\right)$	$e\left(\frac{317}{500}\right)$	$e\left(\frac{407}{1000}\right)$	$e\left(\frac{809}{1000}\right)$	$e\left(\frac{94}{125}\right)$	$e\left(\frac{97}{250}\right)$	$e\left(\frac{581}{1000}\right)$	$e\left(\frac{43}{1000}\right)$
$\chi_{8032}(37,\cdot)$	8032.cl	1000	yes	$-1$	$1$	$e\left(\frac{623}{1000}\right)$	$e\left(\frac{153}{200}\right)$	$e\left(\frac{297}{500}\right)$	$e\left(\frac{123}{500}\right)$	$e\left(\frac{333}{1000}\right)$	$e\left(\frac{571}{1000}\right)$	$e\left(\frac{97}{250}\right)$	$e\left(\frac{193}{250}\right)$	$e\left(\frac{839}{1000}\right)$	$e\left(\frac{217}{1000}\right)$
$\chi_{8032}(39,\cdot)$	8032.cf	500	no	$-1$	$1$	$e\left(\frac{461}{500}\right)$	$e\left(\frac{21}{100}\right)$	$e\left(\frac{52}{125}\right)$	$e\left(\frac{211}{250}\right)$	$e\left(\frac{431}{500}\right)$	$e\left(\frac{447}{500}\right)$	$e\left(\frac{33}{250}\right)$	$e\left(\frac{76}{125}\right)$	$e\left(\frac{173}{500}\right)$	$e\left(\frac{169}{500}\right)$
$\chi_{8032}(41,\cdot)$	8032.cg	500	no	$1$	$1$	$e\left(\frac{253}{500}\right)$	$e\left(\frac{83}{100}\right)$	$e\left(\frac{117}{250}\right)$	$e\left(\frac{3}{250}\right)$	$e\left(\frac{63}{500}\right)$	$e\left(\frac{81}{500}\right)$	$e\left(\frac{42}{125}\right)$	$e\left(\frac{23}{125}\right)$	$e\left(\frac{429}{500}\right)$	$e\left(\frac{487}{500}\right)$
$\chi_{8032}(43,\cdot)$	8032.cj	1000	yes	$1$	$1$	$e\left(\frac{183}{1000}\right)$	$e\left(\frac{13}{200}\right)$	$e\left(\frac{387}{500}\right)$	$e\left(\frac{183}{500}\right)$	$e\left(\frac{93}{1000}\right)$	$e\left(\frac{191}{1000}\right)$	$e\left(\frac{31}{125}\right)$	$e\left(\frac{153}{250}\right)$	$e\left(\frac{919}{1000}\right)$	$e\left(\frac{957}{1000}\right)$
$\chi_{8032}(45,\cdot)$	8032.ck	1000	yes	$1$	$1$	$e\left(\frac{993}{1000}\right)$	$e\left(\frac{23}{200}\right)$	$e\left(\frac{227}{500}\right)$	$e\left(\frac{493}{500}\right)$	$e\left(\frac{103}{1000}\right)$	$e\left(\frac{61}{1000}\right)$	$e\left(\frac{27}{250}\right)$	$e\left(\frac{113}{250}\right)$	$e\left(\frac{749}{1000}\right)$	$e\left(\frac{447}{1000}\right)$
$\chi_{8032}(47,\cdot)$	8032.bk	50	no	$1$	$1$	$e\left(\frac{21}{25}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{50}\right)$	$e\left(\frac{17}{25}\right)$	$e\left(\frac{7}{50}\right)$	$e\left(\frac{9}{50}\right)$	$e\left(\frac{27}{50}\right)$	$e\left(\frac{19}{25}\right)$	$e\left(\frac{31}{50}\right)$	$e\left(\frac{43}{50}\right)$
$\chi_{8032}(49,\cdot)$	8032.cc	250	no	$1$	$1$	$e\left(\frac{61}{250}\right)$	$e\left(\frac{21}{50}\right)$	$e\left(\frac{4}{125}\right)$	$e\left(\frac{61}{125}\right)$	$e\left(\frac{31}{250}\right)$	$e\left(\frac{147}{250}\right)$	$e\left(\frac{83}{125}\right)$	$e\left(\frac{102}{125}\right)$	$e\left(\frac{223}{250}\right)$	$e\left(\frac{69}{250}\right)$
$\chi_{8032}(51,\cdot)$	8032.bu	200	yes	$-1$	$1$	$e\left(\frac{177}{200}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{53}{100}\right)$	$e\left(\frac{77}{100}\right)$	$e\left(\frac{167}{200}\right)$	$e\left(\frac{129}{200}\right)$	$e\left(\frac{14}{25}\right)$	$e\left(\frac{7}{50}\right)$	$e\left(\frac{61}{200}\right)$	$e\left(\frac{83}{200}\right)$
$\chi_{8032}(53,\cdot)$	8032.cl	1000	yes	$-1$	$1$	$e\left(\frac{467}{1000}\right)$	$e\left(\frac{37}{200}\right)$	$e\left(\frac{213}{500}\right)$	$e\left(\frac{467}{500}\right)$	$e\left(\frac{57}{1000}\right)$	$e\left(\frac{359}{1000}\right)$	$e\left(\frac{163}{250}\right)$	$e\left(\frac{247}{250}\right)$	$e\left(\frac{531}{1000}\right)$	$e\left(\frac{893}{1000}\right)$
$\chi_{8032}(55,\cdot)$	8032.ch	500	no	$1$	$1$	$e\left(\frac{287}{500}\right)$	$e\left(\frac{7}{100}\right)$	$e\left(\frac{34}{125}\right)$	$e\left(\frac{37}{250}\right)$	$e\left(\frac{27}{500}\right)$	$e\left(\frac{249}{500}\right)$	$e\left(\frac{161}{250}\right)$	$e\left(\frac{117}{125}\right)$	$e\left(\frac{41}{500}\right)$	$e\left(\frac{423}{500}\right)$
$\chi_{8032}(57,\cdot)$	8032.ce	500	no	$-1$	$1$	$e\left(\frac{103}{500}\right)$	$e\left(\frac{33}{100}\right)$	$e\left(\frac{17}{250}\right)$	$e\left(\frac{103}{250}\right)$	$e\left(\frac{163}{500}\right)$	$e\left(\frac{31}{500}\right)$	$e\left(\frac{67}{125}\right)$	$e\left(\frac{123}{125}\right)$	$e\left(\frac{229}{500}\right)$	$e\left(\frac{137}{500}\right)$
$\chi_{8032}(59,\cdot)$	8032.cj	1000	yes	$1$	$1$	$e\left(\frac{139}{1000}\right)$	$e\left(\frac{129}{200}\right)$	$e\left(\frac{171}{500}\right)$	$e\left(\frac{139}{500}\right)$	$e\left(\frac{169}{1000}\right)$	$e\left(\frac{3}{1000}\right)$	$e\left(\frac{98}{125}\right)$	$e\left(\frac{149}{250}\right)$	$e\left(\frac{627}{1000}\right)$	$e\left(\frac{481}{1000}\right)$
$\chi_{8032}(61,\cdot)$	8032.cl	1000	yes	$-1$	$1$	$e\left(\frac{917}{1000}\right)$	$e\left(\frac{187}{200}\right)$	$e\left(\frac{263}{500}\right)$	$e\left(\frac{417}{500}\right)$	$e\left(\frac{7}{1000}\right)$	$e\left(\frac{9}{1000}\right)$	$e\left(\frac{213}{250}\right)$	$e\left(\frac{197}{250}\right)$	$e\left(\frac{381}{1000}\right)$	$e\left(\frac{443}{1000}\right)$
$\chi_{8032}(63,\cdot)$	8032.bj	50	no	$-1$	$1$	$e\left(\frac{21}{50}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{13}{50}\right)$	$e\left(\frac{21}{25}\right)$	$e\left(\frac{41}{50}\right)$	$e\left(\frac{21}{25}\right)$	$e\left(\frac{1}{50}\right)$	$e\left(\frac{22}{25}\right)$	$e\left(\frac{3}{50}\right)$	$e\left(\frac{17}{25}\right)$

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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	$8032$
Structure	\(C_{2}\times C_{2}\times C_{1000}\)
Order	$4000$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(21\)
\(\chi_{8032}(1,\cdot)\)	8032.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{8032}(3,\cdot)\)	8032.ci	1000	yes	\(-1\)	\(1\)	\(e\left(\frac{649}{1000}\right)\)	\(e\left(\frac{139}{200}\right)\)	\(e\left(\frac{61}{500}\right)\)	\(e\left(\frac{149}{500}\right)\)	\(e\left(\frac{879}{1000}\right)\)	\(e\left(\frac{273}{1000}\right)\)	\(e\left(\frac{43}{125}\right)\)	\(e\left(\frac{59}{250}\right)\)	\(e\left(\frac{557}{1000}\right)\)	\(e\left(\frac{771}{1000}\right)\)
\(\chi_{8032}(5,\cdot)\)	8032.bv	200	yes	\(1\)	\(1\)	\(e\left(\frac{139}{200}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{21}{100}\right)\)	\(e\left(\frac{39}{100}\right)\)	\(e\left(\frac{69}{200}\right)\)	\(e\left(\frac{103}{200}\right)\)	\(e\left(\frac{21}{50}\right)\)	\(e\left(\frac{49}{50}\right)\)	\(e\left(\frac{127}{200}\right)\)	\(e\left(\frac{181}{200}\right)\)
\(\chi_{8032}(7,\cdot)\)	8032.cf	500	no	\(-1\)	\(1\)	\(e\left(\frac{61}{500}\right)\)	\(e\left(\frac{21}{100}\right)\)	\(e\left(\frac{2}{125}\right)\)	\(e\left(\frac{61}{250}\right)\)	\(e\left(\frac{31}{500}\right)\)	\(e\left(\frac{147}{500}\right)\)	\(e\left(\frac{83}{250}\right)\)	\(e\left(\frac{51}{125}\right)\)	\(e\left(\frac{473}{500}\right)\)	\(e\left(\frac{69}{500}\right)\)
\(\chi_{8032}(9,\cdot)\)	8032.cg	500	no	\(1\)	\(1\)	\(e\left(\frac{149}{500}\right)\)	\(e\left(\frac{39}{100}\right)\)	\(e\left(\frac{61}{250}\right)\)	\(e\left(\frac{149}{250}\right)\)	\(e\left(\frac{379}{500}\right)\)	\(e\left(\frac{273}{500}\right)\)	\(e\left(\frac{86}{125}\right)\)	\(e\left(\frac{59}{125}\right)\)	\(e\left(\frac{57}{500}\right)\)	\(e\left(\frac{271}{500}\right)\)
\(\chi_{8032}(11,\cdot)\)	8032.cj	1000	yes	\(1\)	\(1\)	\(e\left(\frac{879}{1000}\right)\)	\(e\left(\frac{69}{200}\right)\)	\(e\left(\frac{31}{500}\right)\)	\(e\left(\frac{379}{500}\right)\)	\(e\left(\frac{709}{1000}\right)\)	\(e\left(\frac{983}{1000}\right)\)	\(e\left(\frac{28}{125}\right)\)	\(e\left(\frac{239}{250}\right)\)	\(e\left(\frac{447}{1000}\right)\)	\(e\left(\frac{941}{1000}\right)\)
\(\chi_{8032}(13,\cdot)\)	8032.ck	1000	yes	\(1\)	\(1\)	\(e\left(\frac{273}{1000}\right)\)	\(e\left(\frac{103}{200}\right)\)	\(e\left(\frac{147}{500}\right)\)	\(e\left(\frac{273}{500}\right)\)	\(e\left(\frac{983}{1000}\right)\)	\(e\left(\frac{621}{1000}\right)\)	\(e\left(\frac{197}{250}\right)\)	\(e\left(\frac{93}{250}\right)\)	\(e\left(\frac{789}{1000}\right)\)	\(e\left(\frac{567}{1000}\right)\)
\(\chi_{8032}(15,\cdot)\)	8032.cb	250	no	\(-1\)	\(1\)	\(e\left(\frac{43}{125}\right)\)	\(e\left(\frac{21}{50}\right)\)	\(e\left(\frac{83}{250}\right)\)	\(e\left(\frac{86}{125}\right)\)	\(e\left(\frac{28}{125}\right)\)	\(e\left(\frac{197}{250}\right)\)	\(e\left(\frac{191}{250}\right)\)	\(e\left(\frac{27}{125}\right)\)	\(e\left(\frac{24}{125}\right)\)	\(e\left(\frac{169}{250}\right)\)
\(\chi_{8032}(17,\cdot)\)	8032.cc	250	no	\(1\)	\(1\)	\(e\left(\frac{59}{250}\right)\)	\(e\left(\frac{49}{50}\right)\)	\(e\left(\frac{51}{125}\right)\)	\(e\left(\frac{59}{125}\right)\)	\(e\left(\frac{239}{250}\right)\)	\(e\left(\frac{93}{250}\right)\)	\(e\left(\frac{27}{125}\right)\)	\(e\left(\frac{113}{125}\right)\)	\(e\left(\frac{187}{250}\right)\)	\(e\left(\frac{161}{250}\right)\)
\(\chi_{8032}(19,\cdot)\)	8032.cj	1000	yes	\(1\)	\(1\)	\(e\left(\frac{557}{1000}\right)\)	\(e\left(\frac{127}{200}\right)\)	\(e\left(\frac{473}{500}\right)\)	\(e\left(\frac{57}{500}\right)\)	\(e\left(\frac{447}{1000}\right)\)	\(e\left(\frac{789}{1000}\right)\)	\(e\left(\frac{24}{125}\right)\)	\(e\left(\frac{187}{250}\right)\)	\(e\left(\frac{901}{1000}\right)\)	\(e\left(\frac{503}{1000}\right)\)
\(\chi_{8032}(21,\cdot)\)	8032.ck	1000	yes	\(1\)	\(1\)	\(e\left(\frac{771}{1000}\right)\)	\(e\left(\frac{181}{200}\right)\)	\(e\left(\frac{69}{500}\right)\)	\(e\left(\frac{271}{500}\right)\)	\(e\left(\frac{941}{1000}\right)\)	\(e\left(\frac{567}{1000}\right)\)	\(e\left(\frac{169}{250}\right)\)	\(e\left(\frac{161}{250}\right)\)	\(e\left(\frac{503}{1000}\right)\)	\(e\left(\frac{909}{1000}\right)\)
\(\chi_{8032}(23,\cdot)\)	8032.cf	500	no	\(-1\)	\(1\)	\(e\left(\frac{143}{500}\right)\)	\(e\left(\frac{23}{100}\right)\)	\(e\left(\frac{101}{125}\right)\)	\(e\left(\frac{143}{250}\right)\)	\(e\left(\frac{253}{500}\right)\)	\(e\left(\frac{361}{500}\right)\)	\(e\left(\frac{129}{250}\right)\)	\(e\left(\frac{13}{125}\right)\)	\(e\left(\frac{199}{500}\right)\)	\(e\left(\frac{47}{500}\right)\)
\(\chi_{8032}(25,\cdot)\)	8032.bo	100	no	\(1\)	\(1\)	\(e\left(\frac{39}{100}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{21}{50}\right)\)	\(e\left(\frac{39}{50}\right)\)	\(e\left(\frac{69}{100}\right)\)	\(e\left(\frac{3}{100}\right)\)	\(e\left(\frac{21}{25}\right)\)	\(e\left(\frac{24}{25}\right)\)	\(e\left(\frac{27}{100}\right)\)	\(e\left(\frac{81}{100}\right)\)
\(\chi_{8032}(27,\cdot)\)	8032.ci	1000	yes	\(-1\)	\(1\)	\(e\left(\frac{947}{1000}\right)\)	\(e\left(\frac{17}{200}\right)\)	\(e\left(\frac{183}{500}\right)\)	\(e\left(\frac{447}{500}\right)\)	\(e\left(\frac{637}{1000}\right)\)	\(e\left(\frac{819}{1000}\right)\)	\(e\left(\frac{4}{125}\right)\)	\(e\left(\frac{177}{250}\right)\)	\(e\left(\frac{671}{1000}\right)\)	\(e\left(\frac{313}{1000}\right)\)
\(\chi_{8032}(29,\cdot)\)	8032.cl	1000	yes	\(-1\)	\(1\)	\(e\left(\frac{437}{1000}\right)\)	\(e\left(\frac{107}{200}\right)\)	\(e\left(\frac{43}{500}\right)\)	\(e\left(\frac{437}{500}\right)\)	\(e\left(\frac{927}{1000}\right)\)	\(e\left(\frac{49}{1000}\right)\)	\(e\left(\frac{243}{250}\right)\)	\(e\left(\frac{17}{250}\right)\)	\(e\left(\frac{741}{1000}\right)\)	\(e\left(\frac{523}{1000}\right)\)
\(\chi_{8032}(31,\cdot)\)	8032.bz	250	no	\(-1\)	\(1\)	\(e\left(\frac{101}{250}\right)\)	\(e\left(\frac{18}{25}\right)\)	\(e\left(\frac{3}{250}\right)\)	\(e\left(\frac{101}{125}\right)\)	\(e\left(\frac{121}{250}\right)\)	\(e\left(\frac{51}{125}\right)\)	\(e\left(\frac{31}{250}\right)\)	\(e\left(\frac{7}{125}\right)\)	\(e\left(\frac{193}{250}\right)\)	\(e\left(\frac{52}{125}\right)\)
\(\chi_{8032}(33,\cdot)\)	8032.bx	250	no	\(-1\)	\(1\)	\(e\left(\frac{66}{125}\right)\)	\(e\left(\frac{1}{25}\right)\)	\(e\left(\frac{23}{125}\right)\)	\(e\left(\frac{7}{125}\right)\)	\(e\left(\frac{147}{250}\right)\)	\(e\left(\frac{32}{125}\right)\)	\(e\left(\frac{71}{125}\right)\)	\(e\left(\frac{24}{125}\right)\)	\(e\left(\frac{1}{250}\right)\)	\(e\left(\frac{89}{125}\right)\)
\(\chi_{8032}(35,\cdot)\)	8032.ci	1000	yes	\(-1\)	\(1\)	\(e\left(\frac{817}{1000}\right)\)	\(e\left(\frac{187}{200}\right)\)	\(e\left(\frac{113}{500}\right)\)	\(e\left(\frac{317}{500}\right)\)	\(e\left(\frac{407}{1000}\right)\)	\(e\left(\frac{809}{1000}\right)\)	\(e\left(\frac{94}{125}\right)\)	\(e\left(\frac{97}{250}\right)\)	\(e\left(\frac{581}{1000}\right)\)	\(e\left(\frac{43}{1000}\right)\)
\(\chi_{8032}(37,\cdot)\)	8032.cl	1000	yes	\(-1\)	\(1\)	\(e\left(\frac{623}{1000}\right)\)	\(e\left(\frac{153}{200}\right)\)	\(e\left(\frac{297}{500}\right)\)	\(e\left(\frac{123}{500}\right)\)	\(e\left(\frac{333}{1000}\right)\)	\(e\left(\frac{571}{1000}\right)\)	\(e\left(\frac{97}{250}\right)\)	\(e\left(\frac{193}{250}\right)\)	\(e\left(\frac{839}{1000}\right)\)	\(e\left(\frac{217}{1000}\right)\)
\(\chi_{8032}(39,\cdot)\)	8032.cf	500	no	\(-1\)	\(1\)	\(e\left(\frac{461}{500}\right)\)	\(e\left(\frac{21}{100}\right)\)	\(e\left(\frac{52}{125}\right)\)	\(e\left(\frac{211}{250}\right)\)	\(e\left(\frac{431}{500}\right)\)	\(e\left(\frac{447}{500}\right)\)	\(e\left(\frac{33}{250}\right)\)	\(e\left(\frac{76}{125}\right)\)	\(e\left(\frac{173}{500}\right)\)	\(e\left(\frac{169}{500}\right)\)
\(\chi_{8032}(41,\cdot)\)	8032.cg	500	no	\(1\)	\(1\)	\(e\left(\frac{253}{500}\right)\)	\(e\left(\frac{83}{100}\right)\)	\(e\left(\frac{117}{250}\right)\)	\(e\left(\frac{3}{250}\right)\)	\(e\left(\frac{63}{500}\right)\)	\(e\left(\frac{81}{500}\right)\)	\(e\left(\frac{42}{125}\right)\)	\(e\left(\frac{23}{125}\right)\)	\(e\left(\frac{429}{500}\right)\)	\(e\left(\frac{487}{500}\right)\)
\(\chi_{8032}(43,\cdot)\)	8032.cj	1000	yes	\(1\)	\(1\)	\(e\left(\frac{183}{1000}\right)\)	\(e\left(\frac{13}{200}\right)\)	\(e\left(\frac{387}{500}\right)\)	\(e\left(\frac{183}{500}\right)\)	\(e\left(\frac{93}{1000}\right)\)	\(e\left(\frac{191}{1000}\right)\)	\(e\left(\frac{31}{125}\right)\)	\(e\left(\frac{153}{250}\right)\)	\(e\left(\frac{919}{1000}\right)\)	\(e\left(\frac{957}{1000}\right)\)
\(\chi_{8032}(45,\cdot)\)	8032.ck	1000	yes	\(1\)	\(1\)	\(e\left(\frac{993}{1000}\right)\)	\(e\left(\frac{23}{200}\right)\)	\(e\left(\frac{227}{500}\right)\)	\(e\left(\frac{493}{500}\right)\)	\(e\left(\frac{103}{1000}\right)\)	\(e\left(\frac{61}{1000}\right)\)	\(e\left(\frac{27}{250}\right)\)	\(e\left(\frac{113}{250}\right)\)	\(e\left(\frac{749}{1000}\right)\)	\(e\left(\frac{447}{1000}\right)\)
\(\chi_{8032}(47,\cdot)\)	8032.bk	50	no	\(1\)	\(1\)	\(e\left(\frac{21}{25}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{1}{50}\right)\)	\(e\left(\frac{17}{25}\right)\)	\(e\left(\frac{7}{50}\right)\)	\(e\left(\frac{9}{50}\right)\)	\(e\left(\frac{27}{50}\right)\)	\(e\left(\frac{19}{25}\right)\)	\(e\left(\frac{31}{50}\right)\)	\(e\left(\frac{43}{50}\right)\)
\(\chi_{8032}(49,\cdot)\)	8032.cc	250	no	\(1\)	\(1\)	\(e\left(\frac{61}{250}\right)\)	\(e\left(\frac{21}{50}\right)\)	\(e\left(\frac{4}{125}\right)\)	\(e\left(\frac{61}{125}\right)\)	\(e\left(\frac{31}{250}\right)\)	\(e\left(\frac{147}{250}\right)\)	\(e\left(\frac{83}{125}\right)\)	\(e\left(\frac{102}{125}\right)\)	\(e\left(\frac{223}{250}\right)\)	\(e\left(\frac{69}{250}\right)\)
\(\chi_{8032}(51,\cdot)\)	8032.bu	200	yes	\(-1\)	\(1\)	\(e\left(\frac{177}{200}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{53}{100}\right)\)	\(e\left(\frac{77}{100}\right)\)	\(e\left(\frac{167}{200}\right)\)	\(e\left(\frac{129}{200}\right)\)	\(e\left(\frac{14}{25}\right)\)	\(e\left(\frac{7}{50}\right)\)	\(e\left(\frac{61}{200}\right)\)	\(e\left(\frac{83}{200}\right)\)
\(\chi_{8032}(53,\cdot)\)	8032.cl	1000	yes	\(-1\)	\(1\)	\(e\left(\frac{467}{1000}\right)\)	\(e\left(\frac{37}{200}\right)\)	\(e\left(\frac{213}{500}\right)\)	\(e\left(\frac{467}{500}\right)\)	\(e\left(\frac{57}{1000}\right)\)	\(e\left(\frac{359}{1000}\right)\)	\(e\left(\frac{163}{250}\right)\)	\(e\left(\frac{247}{250}\right)\)	\(e\left(\frac{531}{1000}\right)\)	\(e\left(\frac{893}{1000}\right)\)
\(\chi_{8032}(55,\cdot)\)	8032.ch	500	no	\(1\)	\(1\)	\(e\left(\frac{287}{500}\right)\)	\(e\left(\frac{7}{100}\right)\)	\(e\left(\frac{34}{125}\right)\)	\(e\left(\frac{37}{250}\right)\)	\(e\left(\frac{27}{500}\right)\)	\(e\left(\frac{249}{500}\right)\)	\(e\left(\frac{161}{250}\right)\)	\(e\left(\frac{117}{125}\right)\)	\(e\left(\frac{41}{500}\right)\)	\(e\left(\frac{423}{500}\right)\)
\(\chi_{8032}(57,\cdot)\)	8032.ce	500	no	\(-1\)	\(1\)	\(e\left(\frac{103}{500}\right)\)	\(e\left(\frac{33}{100}\right)\)	\(e\left(\frac{17}{250}\right)\)	\(e\left(\frac{103}{250}\right)\)	\(e\left(\frac{163}{500}\right)\)	\(e\left(\frac{31}{500}\right)\)	\(e\left(\frac{67}{125}\right)\)	\(e\left(\frac{123}{125}\right)\)	\(e\left(\frac{229}{500}\right)\)	\(e\left(\frac{137}{500}\right)\)
\(\chi_{8032}(59,\cdot)\)	8032.cj	1000	yes	\(1\)	\(1\)	\(e\left(\frac{139}{1000}\right)\)	\(e\left(\frac{129}{200}\right)\)	\(e\left(\frac{171}{500}\right)\)	\(e\left(\frac{139}{500}\right)\)	\(e\left(\frac{169}{1000}\right)\)	\(e\left(\frac{3}{1000}\right)\)	\(e\left(\frac{98}{125}\right)\)	\(e\left(\frac{149}{250}\right)\)	\(e\left(\frac{627}{1000}\right)\)	\(e\left(\frac{481}{1000}\right)\)
\(\chi_{8032}(61,\cdot)\)	8032.cl	1000	yes	\(-1\)	\(1\)	\(e\left(\frac{917}{1000}\right)\)	\(e\left(\frac{187}{200}\right)\)	\(e\left(\frac{263}{500}\right)\)	\(e\left(\frac{417}{500}\right)\)	\(e\left(\frac{7}{1000}\right)\)	\(e\left(\frac{9}{1000}\right)\)	\(e\left(\frac{213}{250}\right)\)	\(e\left(\frac{197}{250}\right)\)	\(e\left(\frac{381}{1000}\right)\)	\(e\left(\frac{443}{1000}\right)\)
\(\chi_{8032}(63,\cdot)\)	8032.bj	50	no	\(-1\)	\(1\)	\(e\left(\frac{21}{50}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{13}{50}\right)\)	\(e\left(\frac{21}{25}\right)\)	\(e\left(\frac{41}{50}\right)\)	\(e\left(\frac{21}{25}\right)\)	\(e\left(\frac{1}{50}\right)\)	\(e\left(\frac{22}{25}\right)\)	\(e\left(\frac{3}{50}\right)\)	\(e\left(\frac{17}{25}\right)\)

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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.