LMFDB - Group of Dirichlet characters of modulus 5290

Show commands: PariGP / SageMath

sage: H = DirichletGroup(5290)

pari: g = idealstar(,5290,2)

Character group

sage: G.order() pari: g.no
Order	=	2024
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{1012}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{5290}(2117,\cdot)$, $\chi_{5290}(2121,\cdot)$

First 32 of 2024 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	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$17$	$19$	$21$	$27$	$29$
$\chi_{5290}(1,\cdot)$	5290.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{5290}(3,\cdot)$	5290.x	1012	no	$-1$	$1$	$e\left(\frac{765}{1012}\right)$	$e\left(\frac{839}{1012}\right)$	$e\left(\frac{259}{506}\right)$	$e\left(\frac{50}{253}\right)$	$e\left(\frac{261}{1012}\right)$	$e\left(\frac{675}{1012}\right)$	$e\left(\frac{141}{506}\right)$	$e\left(\frac{148}{253}\right)$	$e\left(\frac{271}{1012}\right)$	$e\left(\frac{123}{506}\right)$
$\chi_{5290}(7,\cdot)$	5290.w	1012	no	$1$	$1$	$e\left(\frac{839}{1012}\right)$	$e\left(\frac{139}{1012}\right)$	$e\left(\frac{333}{506}\right)$	$e\left(\frac{237}{506}\right)$	$e\left(\frac{191}{1012}\right)$	$e\left(\frac{651}{1012}\right)$	$e\left(\frac{181}{253}\right)$	$e\left(\frac{489}{506}\right)$	$e\left(\frac{493}{1012}\right)$	$e\left(\frac{375}{506}\right)$
$\chi_{5290}(9,\cdot)$	5290.t	506	no	$1$	$1$	$e\left(\frac{259}{506}\right)$	$e\left(\frac{333}{506}\right)$	$e\left(\frac{6}{253}\right)$	$e\left(\frac{100}{253}\right)$	$e\left(\frac{261}{506}\right)$	$e\left(\frac{169}{506}\right)$	$e\left(\frac{141}{253}\right)$	$e\left(\frac{43}{253}\right)$	$e\left(\frac{271}{506}\right)$	$e\left(\frac{123}{253}\right)$
$\chi_{5290}(11,\cdot)$	5290.v	506	no	$-1$	$1$	$e\left(\frac{50}{253}\right)$	$e\left(\frac{237}{506}\right)$	$e\left(\frac{100}{253}\right)$	$e\left(\frac{213}{506}\right)$	$e\left(\frac{151}{253}\right)$	$e\left(\frac{371}{506}\right)$	$e\left(\frac{399}{506}\right)$	$e\left(\frac{337}{506}\right)$	$e\left(\frac{150}{253}\right)$	$e\left(\frac{26}{253}\right)$
$\chi_{5290}(13,\cdot)$	5290.x	1012	no	$-1$	$1$	$e\left(\frac{261}{1012}\right)$	$e\left(\frac{191}{1012}\right)$	$e\left(\frac{261}{506}\right)$	$e\left(\frac{151}{253}\right)$	$e\left(\frac{601}{1012}\right)$	$e\left(\frac{647}{1012}\right)$	$e\left(\frac{441}{506}\right)$	$e\left(\frac{113}{253}\right)$	$e\left(\frac{783}{1012}\right)$	$e\left(\frac{417}{506}\right)$
$\chi_{5290}(17,\cdot)$	5290.w	1012	no	$1$	$1$	$e\left(\frac{675}{1012}\right)$	$e\left(\frac{651}{1012}\right)$	$e\left(\frac{169}{506}\right)$	$e\left(\frac{371}{506}\right)$	$e\left(\frac{647}{1012}\right)$	$e\left(\frac{923}{1012}\right)$	$e\left(\frac{25}{253}\right)$	$e\left(\frac{157}{506}\right)$	$e\left(\frac{1}{1012}\right)$	$e\left(\frac{49}{506}\right)$
$\chi_{5290}(19,\cdot)$	5290.u	506	no	$-1$	$1$	$e\left(\frac{141}{506}\right)$	$e\left(\frac{181}{253}\right)$	$e\left(\frac{141}{253}\right)$	$e\left(\frac{399}{506}\right)$	$e\left(\frac{441}{506}\right)$	$e\left(\frac{25}{253}\right)$	$e\left(\frac{49}{506}\right)$	$e\left(\frac{503}{506}\right)$	$e\left(\frac{423}{506}\right)$	$e\left(\frac{234}{253}\right)$
$\chi_{5290}(21,\cdot)$	5290.v	506	no	$-1$	$1$	$e\left(\frac{148}{253}\right)$	$e\left(\frac{489}{506}\right)$	$e\left(\frac{43}{253}\right)$	$e\left(\frac{337}{506}\right)$	$e\left(\frac{113}{253}\right)$	$e\left(\frac{157}{506}\right)$	$e\left(\frac{503}{506}\right)$	$e\left(\frac{279}{506}\right)$	$e\left(\frac{191}{253}\right)$	$e\left(\frac{249}{253}\right)$
$\chi_{5290}(27,\cdot)$	5290.x	1012	no	$-1$	$1$	$e\left(\frac{271}{1012}\right)$	$e\left(\frac{493}{1012}\right)$	$e\left(\frac{271}{506}\right)$	$e\left(\frac{150}{253}\right)$	$e\left(\frac{783}{1012}\right)$	$e\left(\frac{1}{1012}\right)$	$e\left(\frac{423}{506}\right)$	$e\left(\frac{191}{253}\right)$	$e\left(\frac{813}{1012}\right)$	$e\left(\frac{369}{506}\right)$
$\chi_{5290}(29,\cdot)$	5290.t	506	no	$1$	$1$	$e\left(\frac{123}{506}\right)$	$e\left(\frac{375}{506}\right)$	$e\left(\frac{123}{253}\right)$	$e\left(\frac{26}{253}\right)$	$e\left(\frac{417}{506}\right)$	$e\left(\frac{49}{506}\right)$	$e\left(\frac{234}{253}\right)$	$e\left(\frac{249}{253}\right)$	$e\left(\frac{369}{506}\right)$	$e\left(\frac{118}{253}\right)$
$\chi_{5290}(31,\cdot)$	5290.s	253	no	$1$	$1$	$e\left(\frac{103}{253}\right)$	$e\left(\frac{24}{253}\right)$	$e\left(\frac{206}{253}\right)$	$e\left(\frac{60}{253}\right)$	$e\left(\frac{53}{253}\right)$	$e\left(\frac{76}{253}\right)$	$e\left(\frac{34}{253}\right)$	$e\left(\frac{127}{253}\right)$	$e\left(\frac{56}{253}\right)$	$e\left(\frac{175}{253}\right)$
$\chi_{5290}(33,\cdot)$	5290.w	1012	no	$1$	$1$	$e\left(\frac{965}{1012}\right)$	$e\left(\frac{301}{1012}\right)$	$e\left(\frac{459}{506}\right)$	$e\left(\frac{313}{506}\right)$	$e\left(\frac{865}{1012}\right)$	$e\left(\frac{405}{1012}\right)$	$e\left(\frac{17}{253}\right)$	$e\left(\frac{127}{506}\right)$	$e\left(\frac{871}{1012}\right)$	$e\left(\frac{175}{506}\right)$
$\chi_{5290}(37,\cdot)$	5290.w	1012	no	$1$	$1$	$e\left(\frac{551}{1012}\right)$	$e\left(\frac{347}{1012}\right)$	$e\left(\frac{45}{506}\right)$	$e\left(\frac{497}{506}\right)$	$e\left(\frac{819}{1012}\right)$	$e\left(\frac{635}{1012}\right)$	$e\left(\frac{86}{253}\right)$	$e\left(\frac{449}{506}\right)$	$e\left(\frac{641}{1012}\right)$	$e\left(\frac{37}{506}\right)$
$\chi_{5290}(39,\cdot)$	5290.t	506	no	$1$	$1$	$e\left(\frac{7}{506}\right)$	$e\left(\frac{9}{506}\right)$	$e\left(\frac{7}{253}\right)$	$e\left(\frac{201}{253}\right)$	$e\left(\frac{431}{506}\right)$	$e\left(\frac{155}{506}\right)$	$e\left(\frac{38}{253}\right)$	$e\left(\frac{8}{253}\right)$	$e\left(\frac{21}{506}\right)$	$e\left(\frac{17}{253}\right)$
$\chi_{5290}(41,\cdot)$	5290.s	253	no	$1$	$1$	$e\left(\frac{162}{253}\right)$	$e\left(\frac{136}{253}\right)$	$e\left(\frac{71}{253}\right)$	$e\left(\frac{87}{253}\right)$	$e\left(\frac{216}{253}\right)$	$e\left(\frac{9}{253}\right)$	$e\left(\frac{24}{253}\right)$	$e\left(\frac{45}{253}\right)$	$e\left(\frac{233}{253}\right)$	$e\left(\frac{64}{253}\right)$
$\chi_{5290}(43,\cdot)$	5290.w	1012	no	$1$	$1$	$e\left(\frac{105}{1012}\right)$	$e\left(\frac{641}{1012}\right)$	$e\left(\frac{105}{506}\right)$	$e\left(\frac{485}{506}\right)$	$e\left(\frac{393}{1012}\right)$	$e\left(\frac{301}{1012}\right)$	$e\left(\frac{32}{253}\right)$	$e\left(\frac{373}{506}\right)$	$e\left(\frac{315}{1012}\right)$	$e\left(\frac{255}{506}\right)$
$\chi_{5290}(47,\cdot)$	5290.q	92	no	$-1$	$1$	$e\left(\frac{65}{92}\right)$	$e\left(\frac{31}{92}\right)$	$e\left(\frac{19}{46}\right)$	$e\left(\frac{5}{23}\right)$	$e\left(\frac{33}{92}\right)$	$e\left(\frac{79}{92}\right)$	$e\left(\frac{21}{46}\right)$	$e\left(\frac{1}{23}\right)$	$e\left(\frac{11}{92}\right)$	$e\left(\frac{33}{46}\right)$
$\chi_{5290}(49,\cdot)$	5290.t	506	no	$1$	$1$	$e\left(\frac{333}{506}\right)$	$e\left(\frac{139}{506}\right)$	$e\left(\frac{80}{253}\right)$	$e\left(\frac{237}{253}\right)$	$e\left(\frac{191}{506}\right)$	$e\left(\frac{145}{506}\right)$	$e\left(\frac{109}{253}\right)$	$e\left(\frac{236}{253}\right)$	$e\left(\frac{493}{506}\right)$	$e\left(\frac{122}{253}\right)$
$\chi_{5290}(51,\cdot)$	5290.v	506	no	$-1$	$1$	$e\left(\frac{107}{253}\right)$	$e\left(\frac{239}{506}\right)$	$e\left(\frac{214}{253}\right)$	$e\left(\frac{471}{506}\right)$	$e\left(\frac{227}{253}\right)$	$e\left(\frac{293}{506}\right)$	$e\left(\frac{191}{506}\right)$	$e\left(\frac{453}{506}\right)$	$e\left(\frac{68}{253}\right)$	$e\left(\frac{86}{253}\right)$
$\chi_{5290}(53,\cdot)$	5290.w	1012	no	$1$	$1$	$e\left(\frac{905}{1012}\right)$	$e\left(\frac{513}{1012}\right)$	$e\left(\frac{399}{506}\right)$	$e\left(\frac{325}{506}\right)$	$e\left(\frac{785}{1012}\right)$	$e\left(\frac{233}{1012}\right)$	$e\left(\frac{71}{253}\right)$	$e\left(\frac{203}{506}\right)$	$e\left(\frac{691}{1012}\right)$	$e\left(\frac{463}{506}\right)$
$\chi_{5290}(57,\cdot)$	5290.w	1012	no	$1$	$1$	$e\left(\frac{35}{1012}\right)$	$e\left(\frac{551}{1012}\right)$	$e\left(\frac{35}{506}\right)$	$e\left(\frac{499}{506}\right)$	$e\left(\frac{131}{1012}\right)$	$e\left(\frac{775}{1012}\right)$	$e\left(\frac{95}{253}\right)$	$e\left(\frac{293}{506}\right)$	$e\left(\frac{105}{1012}\right)$	$e\left(\frac{85}{506}\right)$
$\chi_{5290}(59,\cdot)$	5290.t	506	no	$1$	$1$	$e\left(\frac{411}{506}\right)$	$e\left(\frac{167}{506}\right)$	$e\left(\frac{158}{253}\right)$	$e\left(\frac{19}{253}\right)$	$e\left(\frac{295}{506}\right)$	$e\left(\frac{65}{506}\right)$	$e\left(\frac{171}{253}\right)$	$e\left(\frac{36}{253}\right)$	$e\left(\frac{221}{506}\right)$	$e\left(\frac{203}{253}\right)$
$\chi_{5290}(61,\cdot)$	5290.v	506	no	$-1$	$1$	$e\left(\frac{169}{253}\right)$	$e\left(\frac{37}{506}\right)$	$e\left(\frac{85}{253}\right)$	$e\left(\frac{219}{506}\right)$	$e\left(\frac{141}{253}\right)$	$e\left(\frac{75}{506}\right)$	$e\left(\frac{453}{506}\right)$	$e\left(\frac{375}{506}\right)$	$e\left(\frac{1}{253}\right)$	$e\left(\frac{98}{253}\right)$
$\chi_{5290}(63,\cdot)$	5290.m	44	no	$1$	$1$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{35}{44}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{31}{44}\right)$	$e\left(\frac{43}{44}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{1}{44}\right)$	$e\left(\frac{5}{22}\right)$
$\chi_{5290}(67,\cdot)$	5290.w	1012	no	$1$	$1$	$e\left(\frac{867}{1012}\right)$	$e\left(\frac{175}{1012}\right)$	$e\left(\frac{361}{506}\right)$	$e\left(\frac{29}{506}\right)$	$e\left(\frac{903}{1012}\right)$	$e\left(\frac{259}{1012}\right)$	$e\left(\frac{4}{253}\right)$	$e\left(\frac{15}{506}\right)$	$e\left(\frac{577}{1012}\right)$	$e\left(\frac{443}{506}\right)$
$\chi_{5290}(71,\cdot)$	5290.s	253	no	$1$	$1$	$e\left(\frac{137}{253}\right)$	$e\left(\frac{140}{253}\right)$	$e\left(\frac{21}{253}\right)$	$e\left(\frac{97}{253}\right)$	$e\left(\frac{14}{253}\right)$	$e\left(\frac{106}{253}\right)$	$e\left(\frac{114}{253}\right)$	$e\left(\frac{24}{253}\right)$	$e\left(\frac{158}{253}\right)$	$e\left(\frac{51}{253}\right)$
$\chi_{5290}(73,\cdot)$	5290.x	1012	no	$-1$	$1$	$e\left(\frac{513}{1012}\right)$	$e\left(\frac{515}{1012}\right)$	$e\left(\frac{7}{506}\right)$	$e\left(\frac{227}{253}\right)$	$e\left(\frac{937}{1012}\right)$	$e\left(\frac{155}{1012}\right)$	$e\left(\frac{291}{506}\right)$	$e\left(\frac{4}{253}\right)$	$e\left(\frac{527}{1012}\right)$	$e\left(\frac{17}{506}\right)$
$\chi_{5290}(77,\cdot)$	5290.x	1012	no	$-1$	$1$	$e\left(\frac{27}{1012}\right)$	$e\left(\frac{613}{1012}\right)$	$e\left(\frac{27}{506}\right)$	$e\left(\frac{225}{253}\right)$	$e\left(\frac{795}{1012}\right)$	$e\left(\frac{381}{1012}\right)$	$e\left(\frac{255}{506}\right)$	$e\left(\frac{160}{253}\right)$	$e\left(\frac{81}{1012}\right)$	$e\left(\frac{427}{506}\right)$
$\chi_{5290}(79,\cdot)$	5290.u	506	no	$-1$	$1$	$e\left(\frac{455}{506}\right)$	$e\left(\frac{166}{253}\right)$	$e\left(\frac{202}{253}\right)$	$e\left(\frac{71}{506}\right)$	$e\left(\frac{185}{506}\right)$	$e\left(\frac{104}{253}\right)$	$e\left(\frac{133}{506}\right)$	$e\left(\frac{281}{506}\right)$	$e\left(\frac{353}{506}\right)$	$e\left(\frac{93}{253}\right)$
$\chi_{5290}(81,\cdot)$	5290.s	253	no	$1$	$1$	$e\left(\frac{6}{253}\right)$	$e\left(\frac{80}{253}\right)$	$e\left(\frac{12}{253}\right)$	$e\left(\frac{200}{253}\right)$	$e\left(\frac{8}{253}\right)$	$e\left(\frac{169}{253}\right)$	$e\left(\frac{29}{253}\right)$	$e\left(\frac{86}{253}\right)$	$e\left(\frac{18}{253}\right)$	$e\left(\frac{246}{253}\right)$
$\chi_{5290}(83,\cdot)$	5290.w	1012	no	$1$	$1$	$e\left(\frac{837}{1012}\right)$	$e\left(\frac{281}{1012}\right)$	$e\left(\frac{331}{506}\right)$	$e\left(\frac{35}{506}\right)$	$e\left(\frac{357}{1012}\right)$	$e\left(\frac{173}{1012}\right)$	$e\left(\frac{31}{253}\right)$	$e\left(\frac{53}{506}\right)$	$e\left(\frac{487}{1012}\right)$	$e\left(\frac{81}{506}\right)$

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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	$5290$
Structure	\(C_{2}\times C_{1012}\)
Order	$2024$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(13\)	\(17\)	\(19\)	\(21\)	\(27\)	\(29\)
\(\chi_{5290}(1,\cdot)\)	5290.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{5290}(3,\cdot)\)	5290.x	1012	no	\(-1\)	\(1\)	\(e\left(\frac{765}{1012}\right)\)	\(e\left(\frac{839}{1012}\right)\)	\(e\left(\frac{259}{506}\right)\)	\(e\left(\frac{50}{253}\right)\)	\(e\left(\frac{261}{1012}\right)\)	\(e\left(\frac{675}{1012}\right)\)	\(e\left(\frac{141}{506}\right)\)	\(e\left(\frac{148}{253}\right)\)	\(e\left(\frac{271}{1012}\right)\)	\(e\left(\frac{123}{506}\right)\)
\(\chi_{5290}(7,\cdot)\)	5290.w	1012	no	\(1\)	\(1\)	\(e\left(\frac{839}{1012}\right)\)	\(e\left(\frac{139}{1012}\right)\)	\(e\left(\frac{333}{506}\right)\)	\(e\left(\frac{237}{506}\right)\)	\(e\left(\frac{191}{1012}\right)\)	\(e\left(\frac{651}{1012}\right)\)	\(e\left(\frac{181}{253}\right)\)	\(e\left(\frac{489}{506}\right)\)	\(e\left(\frac{493}{1012}\right)\)	\(e\left(\frac{375}{506}\right)\)
\(\chi_{5290}(9,\cdot)\)	5290.t	506	no	\(1\)	\(1\)	\(e\left(\frac{259}{506}\right)\)	\(e\left(\frac{333}{506}\right)\)	\(e\left(\frac{6}{253}\right)\)	\(e\left(\frac{100}{253}\right)\)	\(e\left(\frac{261}{506}\right)\)	\(e\left(\frac{169}{506}\right)\)	\(e\left(\frac{141}{253}\right)\)	\(e\left(\frac{43}{253}\right)\)	\(e\left(\frac{271}{506}\right)\)	\(e\left(\frac{123}{253}\right)\)
\(\chi_{5290}(11,\cdot)\)	5290.v	506	no	\(-1\)	\(1\)	\(e\left(\frac{50}{253}\right)\)	\(e\left(\frac{237}{506}\right)\)	\(e\left(\frac{100}{253}\right)\)	\(e\left(\frac{213}{506}\right)\)	\(e\left(\frac{151}{253}\right)\)	\(e\left(\frac{371}{506}\right)\)	\(e\left(\frac{399}{506}\right)\)	\(e\left(\frac{337}{506}\right)\)	\(e\left(\frac{150}{253}\right)\)	\(e\left(\frac{26}{253}\right)\)
\(\chi_{5290}(13,\cdot)\)	5290.x	1012	no	\(-1\)	\(1\)	\(e\left(\frac{261}{1012}\right)\)	\(e\left(\frac{191}{1012}\right)\)	\(e\left(\frac{261}{506}\right)\)	\(e\left(\frac{151}{253}\right)\)	\(e\left(\frac{601}{1012}\right)\)	\(e\left(\frac{647}{1012}\right)\)	\(e\left(\frac{441}{506}\right)\)	\(e\left(\frac{113}{253}\right)\)	\(e\left(\frac{783}{1012}\right)\)	\(e\left(\frac{417}{506}\right)\)
\(\chi_{5290}(17,\cdot)\)	5290.w	1012	no	\(1\)	\(1\)	\(e\left(\frac{675}{1012}\right)\)	\(e\left(\frac{651}{1012}\right)\)	\(e\left(\frac{169}{506}\right)\)	\(e\left(\frac{371}{506}\right)\)	\(e\left(\frac{647}{1012}\right)\)	\(e\left(\frac{923}{1012}\right)\)	\(e\left(\frac{25}{253}\right)\)	\(e\left(\frac{157}{506}\right)\)	\(e\left(\frac{1}{1012}\right)\)	\(e\left(\frac{49}{506}\right)\)
\(\chi_{5290}(19,\cdot)\)	5290.u	506	no	\(-1\)	\(1\)	\(e\left(\frac{141}{506}\right)\)	\(e\left(\frac{181}{253}\right)\)	\(e\left(\frac{141}{253}\right)\)	\(e\left(\frac{399}{506}\right)\)	\(e\left(\frac{441}{506}\right)\)	\(e\left(\frac{25}{253}\right)\)	\(e\left(\frac{49}{506}\right)\)	\(e\left(\frac{503}{506}\right)\)	\(e\left(\frac{423}{506}\right)\)	\(e\left(\frac{234}{253}\right)\)
\(\chi_{5290}(21,\cdot)\)	5290.v	506	no	\(-1\)	\(1\)	\(e\left(\frac{148}{253}\right)\)	\(e\left(\frac{489}{506}\right)\)	\(e\left(\frac{43}{253}\right)\)	\(e\left(\frac{337}{506}\right)\)	\(e\left(\frac{113}{253}\right)\)	\(e\left(\frac{157}{506}\right)\)	\(e\left(\frac{503}{506}\right)\)	\(e\left(\frac{279}{506}\right)\)	\(e\left(\frac{191}{253}\right)\)	\(e\left(\frac{249}{253}\right)\)
\(\chi_{5290}(27,\cdot)\)	5290.x	1012	no	\(-1\)	\(1\)	\(e\left(\frac{271}{1012}\right)\)	\(e\left(\frac{493}{1012}\right)\)	\(e\left(\frac{271}{506}\right)\)	\(e\left(\frac{150}{253}\right)\)	\(e\left(\frac{783}{1012}\right)\)	\(e\left(\frac{1}{1012}\right)\)	\(e\left(\frac{423}{506}\right)\)	\(e\left(\frac{191}{253}\right)\)	\(e\left(\frac{813}{1012}\right)\)	\(e\left(\frac{369}{506}\right)\)
\(\chi_{5290}(29,\cdot)\)	5290.t	506	no	\(1\)	\(1\)	\(e\left(\frac{123}{506}\right)\)	\(e\left(\frac{375}{506}\right)\)	\(e\left(\frac{123}{253}\right)\)	\(e\left(\frac{26}{253}\right)\)	\(e\left(\frac{417}{506}\right)\)	\(e\left(\frac{49}{506}\right)\)	\(e\left(\frac{234}{253}\right)\)	\(e\left(\frac{249}{253}\right)\)	\(e\left(\frac{369}{506}\right)\)	\(e\left(\frac{118}{253}\right)\)
\(\chi_{5290}(31,\cdot)\)	5290.s	253	no	\(1\)	\(1\)	\(e\left(\frac{103}{253}\right)\)	\(e\left(\frac{24}{253}\right)\)	\(e\left(\frac{206}{253}\right)\)	\(e\left(\frac{60}{253}\right)\)	\(e\left(\frac{53}{253}\right)\)	\(e\left(\frac{76}{253}\right)\)	\(e\left(\frac{34}{253}\right)\)	\(e\left(\frac{127}{253}\right)\)	\(e\left(\frac{56}{253}\right)\)	\(e\left(\frac{175}{253}\right)\)
\(\chi_{5290}(33,\cdot)\)	5290.w	1012	no	\(1\)	\(1\)	\(e\left(\frac{965}{1012}\right)\)	\(e\left(\frac{301}{1012}\right)\)	\(e\left(\frac{459}{506}\right)\)	\(e\left(\frac{313}{506}\right)\)	\(e\left(\frac{865}{1012}\right)\)	\(e\left(\frac{405}{1012}\right)\)	\(e\left(\frac{17}{253}\right)\)	\(e\left(\frac{127}{506}\right)\)	\(e\left(\frac{871}{1012}\right)\)	\(e\left(\frac{175}{506}\right)\)
\(\chi_{5290}(37,\cdot)\)	5290.w	1012	no	\(1\)	\(1\)	\(e\left(\frac{551}{1012}\right)\)	\(e\left(\frac{347}{1012}\right)\)	\(e\left(\frac{45}{506}\right)\)	\(e\left(\frac{497}{506}\right)\)	\(e\left(\frac{819}{1012}\right)\)	\(e\left(\frac{635}{1012}\right)\)	\(e\left(\frac{86}{253}\right)\)	\(e\left(\frac{449}{506}\right)\)	\(e\left(\frac{641}{1012}\right)\)	\(e\left(\frac{37}{506}\right)\)
\(\chi_{5290}(39,\cdot)\)	5290.t	506	no	\(1\)	\(1\)	\(e\left(\frac{7}{506}\right)\)	\(e\left(\frac{9}{506}\right)\)	\(e\left(\frac{7}{253}\right)\)	\(e\left(\frac{201}{253}\right)\)	\(e\left(\frac{431}{506}\right)\)	\(e\left(\frac{155}{506}\right)\)	\(e\left(\frac{38}{253}\right)\)	\(e\left(\frac{8}{253}\right)\)	\(e\left(\frac{21}{506}\right)\)	\(e\left(\frac{17}{253}\right)\)
\(\chi_{5290}(41,\cdot)\)	5290.s	253	no	\(1\)	\(1\)	\(e\left(\frac{162}{253}\right)\)	\(e\left(\frac{136}{253}\right)\)	\(e\left(\frac{71}{253}\right)\)	\(e\left(\frac{87}{253}\right)\)	\(e\left(\frac{216}{253}\right)\)	\(e\left(\frac{9}{253}\right)\)	\(e\left(\frac{24}{253}\right)\)	\(e\left(\frac{45}{253}\right)\)	\(e\left(\frac{233}{253}\right)\)	\(e\left(\frac{64}{253}\right)\)
\(\chi_{5290}(43,\cdot)\)	5290.w	1012	no	\(1\)	\(1\)	\(e\left(\frac{105}{1012}\right)\)	\(e\left(\frac{641}{1012}\right)\)	\(e\left(\frac{105}{506}\right)\)	\(e\left(\frac{485}{506}\right)\)	\(e\left(\frac{393}{1012}\right)\)	\(e\left(\frac{301}{1012}\right)\)	\(e\left(\frac{32}{253}\right)\)	\(e\left(\frac{373}{506}\right)\)	\(e\left(\frac{315}{1012}\right)\)	\(e\left(\frac{255}{506}\right)\)
\(\chi_{5290}(47,\cdot)\)	5290.q	92	no	\(-1\)	\(1\)	\(e\left(\frac{65}{92}\right)\)	\(e\left(\frac{31}{92}\right)\)	\(e\left(\frac{19}{46}\right)\)	\(e\left(\frac{5}{23}\right)\)	\(e\left(\frac{33}{92}\right)\)	\(e\left(\frac{79}{92}\right)\)	\(e\left(\frac{21}{46}\right)\)	\(e\left(\frac{1}{23}\right)\)	\(e\left(\frac{11}{92}\right)\)	\(e\left(\frac{33}{46}\right)\)
\(\chi_{5290}(49,\cdot)\)	5290.t	506	no	\(1\)	\(1\)	\(e\left(\frac{333}{506}\right)\)	\(e\left(\frac{139}{506}\right)\)	\(e\left(\frac{80}{253}\right)\)	\(e\left(\frac{237}{253}\right)\)	\(e\left(\frac{191}{506}\right)\)	\(e\left(\frac{145}{506}\right)\)	\(e\left(\frac{109}{253}\right)\)	\(e\left(\frac{236}{253}\right)\)	\(e\left(\frac{493}{506}\right)\)	\(e\left(\frac{122}{253}\right)\)
\(\chi_{5290}(51,\cdot)\)	5290.v	506	no	\(-1\)	\(1\)	\(e\left(\frac{107}{253}\right)\)	\(e\left(\frac{239}{506}\right)\)	\(e\left(\frac{214}{253}\right)\)	\(e\left(\frac{471}{506}\right)\)	\(e\left(\frac{227}{253}\right)\)	\(e\left(\frac{293}{506}\right)\)	\(e\left(\frac{191}{506}\right)\)	\(e\left(\frac{453}{506}\right)\)	\(e\left(\frac{68}{253}\right)\)	\(e\left(\frac{86}{253}\right)\)
\(\chi_{5290}(53,\cdot)\)	5290.w	1012	no	\(1\)	\(1\)	\(e\left(\frac{905}{1012}\right)\)	\(e\left(\frac{513}{1012}\right)\)	\(e\left(\frac{399}{506}\right)\)	\(e\left(\frac{325}{506}\right)\)	\(e\left(\frac{785}{1012}\right)\)	\(e\left(\frac{233}{1012}\right)\)	\(e\left(\frac{71}{253}\right)\)	\(e\left(\frac{203}{506}\right)\)	\(e\left(\frac{691}{1012}\right)\)	\(e\left(\frac{463}{506}\right)\)
\(\chi_{5290}(57,\cdot)\)	5290.w	1012	no	\(1\)	\(1\)	\(e\left(\frac{35}{1012}\right)\)	\(e\left(\frac{551}{1012}\right)\)	\(e\left(\frac{35}{506}\right)\)	\(e\left(\frac{499}{506}\right)\)	\(e\left(\frac{131}{1012}\right)\)	\(e\left(\frac{775}{1012}\right)\)	\(e\left(\frac{95}{253}\right)\)	\(e\left(\frac{293}{506}\right)\)	\(e\left(\frac{105}{1012}\right)\)	\(e\left(\frac{85}{506}\right)\)
\(\chi_{5290}(59,\cdot)\)	5290.t	506	no	\(1\)	\(1\)	\(e\left(\frac{411}{506}\right)\)	\(e\left(\frac{167}{506}\right)\)	\(e\left(\frac{158}{253}\right)\)	\(e\left(\frac{19}{253}\right)\)	\(e\left(\frac{295}{506}\right)\)	\(e\left(\frac{65}{506}\right)\)	\(e\left(\frac{171}{253}\right)\)	\(e\left(\frac{36}{253}\right)\)	\(e\left(\frac{221}{506}\right)\)	\(e\left(\frac{203}{253}\right)\)
\(\chi_{5290}(61,\cdot)\)	5290.v	506	no	\(-1\)	\(1\)	\(e\left(\frac{169}{253}\right)\)	\(e\left(\frac{37}{506}\right)\)	\(e\left(\frac{85}{253}\right)\)	\(e\left(\frac{219}{506}\right)\)	\(e\left(\frac{141}{253}\right)\)	\(e\left(\frac{75}{506}\right)\)	\(e\left(\frac{453}{506}\right)\)	\(e\left(\frac{375}{506}\right)\)	\(e\left(\frac{1}{253}\right)\)	\(e\left(\frac{98}{253}\right)\)
\(\chi_{5290}(63,\cdot)\)	5290.m	44	no	\(1\)	\(1\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{35}{44}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{31}{44}\right)\)	\(e\left(\frac{43}{44}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{1}{44}\right)\)	\(e\left(\frac{5}{22}\right)\)
\(\chi_{5290}(67,\cdot)\)	5290.w	1012	no	\(1\)	\(1\)	\(e\left(\frac{867}{1012}\right)\)	\(e\left(\frac{175}{1012}\right)\)	\(e\left(\frac{361}{506}\right)\)	\(e\left(\frac{29}{506}\right)\)	\(e\left(\frac{903}{1012}\right)\)	\(e\left(\frac{259}{1012}\right)\)	\(e\left(\frac{4}{253}\right)\)	\(e\left(\frac{15}{506}\right)\)	\(e\left(\frac{577}{1012}\right)\)	\(e\left(\frac{443}{506}\right)\)
\(\chi_{5290}(71,\cdot)\)	5290.s	253	no	\(1\)	\(1\)	\(e\left(\frac{137}{253}\right)\)	\(e\left(\frac{140}{253}\right)\)	\(e\left(\frac{21}{253}\right)\)	\(e\left(\frac{97}{253}\right)\)	\(e\left(\frac{14}{253}\right)\)	\(e\left(\frac{106}{253}\right)\)	\(e\left(\frac{114}{253}\right)\)	\(e\left(\frac{24}{253}\right)\)	\(e\left(\frac{158}{253}\right)\)	\(e\left(\frac{51}{253}\right)\)
\(\chi_{5290}(73,\cdot)\)	5290.x	1012	no	\(-1\)	\(1\)	\(e\left(\frac{513}{1012}\right)\)	\(e\left(\frac{515}{1012}\right)\)	\(e\left(\frac{7}{506}\right)\)	\(e\left(\frac{227}{253}\right)\)	\(e\left(\frac{937}{1012}\right)\)	\(e\left(\frac{155}{1012}\right)\)	\(e\left(\frac{291}{506}\right)\)	\(e\left(\frac{4}{253}\right)\)	\(e\left(\frac{527}{1012}\right)\)	\(e\left(\frac{17}{506}\right)\)
\(\chi_{5290}(77,\cdot)\)	5290.x	1012	no	\(-1\)	\(1\)	\(e\left(\frac{27}{1012}\right)\)	\(e\left(\frac{613}{1012}\right)\)	\(e\left(\frac{27}{506}\right)\)	\(e\left(\frac{225}{253}\right)\)	\(e\left(\frac{795}{1012}\right)\)	\(e\left(\frac{381}{1012}\right)\)	\(e\left(\frac{255}{506}\right)\)	\(e\left(\frac{160}{253}\right)\)	\(e\left(\frac{81}{1012}\right)\)	\(e\left(\frac{427}{506}\right)\)
\(\chi_{5290}(79,\cdot)\)	5290.u	506	no	\(-1\)	\(1\)	\(e\left(\frac{455}{506}\right)\)	\(e\left(\frac{166}{253}\right)\)	\(e\left(\frac{202}{253}\right)\)	\(e\left(\frac{71}{506}\right)\)	\(e\left(\frac{185}{506}\right)\)	\(e\left(\frac{104}{253}\right)\)	\(e\left(\frac{133}{506}\right)\)	\(e\left(\frac{281}{506}\right)\)	\(e\left(\frac{353}{506}\right)\)	\(e\left(\frac{93}{253}\right)\)
\(\chi_{5290}(81,\cdot)\)	5290.s	253	no	\(1\)	\(1\)	\(e\left(\frac{6}{253}\right)\)	\(e\left(\frac{80}{253}\right)\)	\(e\left(\frac{12}{253}\right)\)	\(e\left(\frac{200}{253}\right)\)	\(e\left(\frac{8}{253}\right)\)	\(e\left(\frac{169}{253}\right)\)	\(e\left(\frac{29}{253}\right)\)	\(e\left(\frac{86}{253}\right)\)	\(e\left(\frac{18}{253}\right)\)	\(e\left(\frac{246}{253}\right)\)
\(\chi_{5290}(83,\cdot)\)	5290.w	1012	no	\(1\)	\(1\)	\(e\left(\frac{837}{1012}\right)\)	\(e\left(\frac{281}{1012}\right)\)	\(e\left(\frac{331}{506}\right)\)	\(e\left(\frac{35}{506}\right)\)	\(e\left(\frac{357}{1012}\right)\)	\(e\left(\frac{173}{1012}\right)\)	\(e\left(\frac{31}{253}\right)\)	\(e\left(\frac{53}{506}\right)\)	\(e\left(\frac{487}{1012}\right)\)	\(e\left(\frac{81}{506}\right)\)

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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.