LMFDB - Group of Dirichlet characters of modulus 90000

Show commands: PariGP / SageMath

sage: H = DirichletGroup(90000)

pari: g = idealstar(,90000,2)

Character group

sage: G.order() pari: g.no
Order	=	24000
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{4}\times C_{1500}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{90000}(78751,\cdot)$, $\chi_{90000}(22501,\cdot)$, $\chi_{90000}(10001,\cdot)$, $\chi_{90000}(29377,\cdot)$

First 32 of 24000 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	$-1$	$1$	$7$	$11$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$
$\chi_{90000}(1,\cdot)$	90000.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{90000}(7,\cdot)$	90000.jg	300	no	$1$	$1$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{29}{75}\right)$	$e\left(\frac{199}{300}\right)$	$e\left(\frac{81}{100}\right)$	$e\left(\frac{23}{50}\right)$	$e\left(\frac{271}{300}\right)$	$e\left(\frac{23}{75}\right)$	$e\left(\frac{59}{150}\right)$	$e\left(\frac{63}{100}\right)$	$e\left(\frac{1}{75}\right)$
$\chi_{90000}(11,\cdot)$	90000.mf	1500	yes	$1$	$1$	$e\left(\frac{29}{75}\right)$	$e\left(\frac{103}{1500}\right)$	$e\left(\frac{617}{1500}\right)$	$e\left(\frac{49}{250}\right)$	$e\left(\frac{93}{500}\right)$	$e\left(\frac{109}{750}\right)$	$e\left(\frac{211}{1500}\right)$	$e\left(\frac{397}{750}\right)$	$e\left(\frac{229}{500}\right)$	$e\left(\frac{83}{375}\right)$
$\chi_{90000}(13,\cdot)$	90000.ls	1500	yes	$-1$	$1$	$e\left(\frac{199}{300}\right)$	$e\left(\frac{617}{1500}\right)$	$e\left(\frac{419}{750}\right)$	$e\left(\frac{47}{500}\right)$	$e\left(\frac{227}{500}\right)$	$e\left(\frac{1477}{1500}\right)$	$e\left(\frac{929}{1500}\right)$	$e\left(\frac{4}{375}\right)$	$e\left(\frac{53}{250}\right)$	$e\left(\frac{299}{750}\right)$
$\chi_{90000}(17,\cdot)$	90000.kp	500	no	$1$	$1$	$e\left(\frac{81}{100}\right)$	$e\left(\frac{49}{250}\right)$	$e\left(\frac{47}{500}\right)$	$e\left(\frac{179}{500}\right)$	$e\left(\frac{157}{250}\right)$	$e\left(\frac{313}{500}\right)$	$e\left(\frac{69}{125}\right)$	$e\left(\frac{76}{125}\right)$	$e\left(\frac{417}{500}\right)$	$e\left(\frac{181}{250}\right)$
$\chi_{90000}(19,\cdot)$	90000.ku	500	no	$-1$	$1$	$e\left(\frac{23}{50}\right)$	$e\left(\frac{93}{500}\right)$	$e\left(\frac{227}{500}\right)$	$e\left(\frac{157}{250}\right)$	$e\left(\frac{99}{500}\right)$	$e\left(\frac{79}{250}\right)$	$e\left(\frac{341}{500}\right)$	$e\left(\frac{157}{250}\right)$	$e\left(\frac{397}{500}\right)$	$e\left(\frac{71}{250}\right)$
$\chi_{90000}(23,\cdot)$	90000.ma	1500	no	$-1$	$1$	$e\left(\frac{271}{300}\right)$	$e\left(\frac{109}{750}\right)$	$e\left(\frac{1477}{1500}\right)$	$e\left(\frac{313}{500}\right)$	$e\left(\frac{79}{250}\right)$	$e\left(\frac{283}{1500}\right)$	$e\left(\frac{733}{750}\right)$	$e\left(\frac{407}{750}\right)$	$e\left(\frac{49}{500}\right)$	$e\left(\frac{71}{750}\right)$
$\chi_{90000}(29,\cdot)$	90000.ln	1500	yes	$-1$	$1$	$e\left(\frac{23}{75}\right)$	$e\left(\frac{211}{1500}\right)$	$e\left(\frac{929}{1500}\right)$	$e\left(\frac{69}{125}\right)$	$e\left(\frac{341}{500}\right)$	$e\left(\frac{733}{750}\right)$	$e\left(\frac{1357}{1500}\right)$	$e\left(\frac{332}{375}\right)$	$e\left(\frac{173}{500}\right)$	$e\left(\frac{221}{375}\right)$
$\chi_{90000}(31,\cdot)$	90000.li	750	no	$-1$	$1$	$e\left(\frac{59}{150}\right)$	$e\left(\frac{397}{750}\right)$	$e\left(\frac{4}{375}\right)$	$e\left(\frac{76}{125}\right)$	$e\left(\frac{157}{250}\right)$	$e\left(\frac{407}{750}\right)$	$e\left(\frac{332}{375}\right)$	$e\left(\frac{581}{750}\right)$	$e\left(\frac{73}{125}\right)$	$e\left(\frac{334}{375}\right)$
$\chi_{90000}(37,\cdot)$	90000.kh	500	no	$-1$	$1$	$e\left(\frac{63}{100}\right)$	$e\left(\frac{229}{500}\right)$	$e\left(\frac{53}{250}\right)$	$e\left(\frac{417}{500}\right)$	$e\left(\frac{397}{500}\right)$	$e\left(\frac{49}{500}\right)$	$e\left(\frac{173}{500}\right)$	$e\left(\frac{73}{125}\right)$	$e\left(\frac{183}{250}\right)$	$e\left(\frac{113}{250}\right)$
$\chi_{90000}(41,\cdot)$	90000.le	750	no	$-1$	$1$	$e\left(\frac{1}{75}\right)$	$e\left(\frac{83}{375}\right)$	$e\left(\frac{299}{750}\right)$	$e\left(\frac{181}{250}\right)$	$e\left(\frac{71}{250}\right)$	$e\left(\frac{71}{750}\right)$	$e\left(\frac{221}{375}\right)$	$e\left(\frac{334}{375}\right)$	$e\left(\frac{113}{250}\right)$	$e\left(\frac{29}{750}\right)$
$\chi_{90000}(43,\cdot)$	90000.jr	300	no	$1$	$1$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{17}{300}\right)$	$e\left(\frac{22}{75}\right)$	$e\left(\frac{47}{100}\right)$	$e\left(\frac{27}{100}\right)$	$e\left(\frac{127}{300}\right)$	$e\left(\frac{179}{300}\right)$	$e\left(\frac{83}{150}\right)$	$e\left(\frac{14}{25}\right)$	$e\left(\frac{149}{150}\right)$
$\chi_{90000}(47,\cdot)$	90000.lr	1500	no	$-1$	$1$	$e\left(\frac{77}{300}\right)$	$e\left(\frac{4}{375}\right)$	$e\left(\frac{449}{1500}\right)$	$e\left(\frac{31}{500}\right)$	$e\left(\frac{74}{125}\right)$	$e\left(\frac{1421}{1500}\right)$	$e\left(\frac{223}{375}\right)$	$e\left(\frac{109}{750}\right)$	$e\left(\frac{413}{500}\right)$	$e\left(\frac{277}{750}\right)$
$\chi_{90000}(49,\cdot)$	90000.hx	150	no	$1$	$1$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{58}{75}\right)$	$e\left(\frac{49}{150}\right)$	$e\left(\frac{31}{50}\right)$	$e\left(\frac{23}{25}\right)$	$e\left(\frac{121}{150}\right)$	$e\left(\frac{46}{75}\right)$	$e\left(\frac{59}{75}\right)$	$e\left(\frac{13}{50}\right)$	$e\left(\frac{2}{75}\right)$
$\chi_{90000}(53,\cdot)$	90000.kl	500	no	$1$	$1$	$e\left(\frac{49}{100}\right)$	$e\left(\frac{67}{500}\right)$	$e\left(\frac{97}{125}\right)$	$e\left(\frac{241}{500}\right)$	$e\left(\frac{281}{500}\right)$	$e\left(\frac{177}{500}\right)$	$e\left(\frac{79}{500}\right)$	$e\left(\frac{29}{125}\right)$	$e\left(\frac{92}{125}\right)$	$e\left(\frac{37}{125}\right)$
$\chi_{90000}(59,\cdot)$	90000.ll	1500	yes	$1$	$1$	$e\left(\frac{47}{150}\right)$	$e\left(\frac{227}{1500}\right)$	$e\left(\frac{1003}{1500}\right)$	$e\left(\frac{108}{125}\right)$	$e\left(\frac{137}{500}\right)$	$e\left(\frac{253}{375}\right)$	$e\left(\frac{1499}{1500}\right)$	$e\left(\frac{23}{750}\right)$	$e\left(\frac{211}{500}\right)$	$e\left(\frac{172}{375}\right)$
$\chi_{90000}(61,\cdot)$	90000.mg	1500	yes	$1$	$1$	$e\left(\frac{73}{150}\right)$	$e\left(\frac{793}{1500}\right)$	$e\left(\frac{527}{1500}\right)$	$e\left(\frac{97}{125}\right)$	$e\left(\frac{233}{500}\right)$	$e\left(\frac{679}{750}\right)$	$e\left(\frac{991}{1500}\right)$	$e\left(\frac{41}{375}\right)$	$e\left(\frac{399}{500}\right)$	$e\left(\frac{721}{750}\right)$
$\chi_{90000}(67,\cdot)$	90000.lt	1500	yes	$1$	$1$	$e\left(\frac{283}{300}\right)$	$e\left(\frac{1439}{1500}\right)$	$e\left(\frac{199}{375}\right)$	$e\left(\frac{249}{500}\right)$	$e\left(\frac{309}{500}\right)$	$e\left(\frac{1309}{1500}\right)$	$e\left(\frac{1193}{1500}\right)$	$e\left(\frac{311}{750}\right)$	$e\left(\frac{38}{125}\right)$	$e\left(\frac{233}{750}\right)$
$\chi_{90000}(71,\cdot)$	90000.im	250	no	$1$	$1$	$e\left(\frac{17}{50}\right)$	$e\left(\frac{111}{250}\right)$	$e\left(\frac{29}{250}\right)$	$e\left(\frac{153}{250}\right)$	$e\left(\frac{49}{125}\right)$	$e\left(\frac{58}{125}\right)$	$e\left(\frac{16}{125}\right)$	$e\left(\frac{153}{250}\right)$	$e\left(\frac{119}{250}\right)$	$e\left(\frac{109}{250}\right)$
$\chi_{90000}(73,\cdot)$	90000.kn	500	no	$-1$	$1$	$e\left(\frac{27}{100}\right)$	$e\left(\frac{133}{250}\right)$	$e\left(\frac{199}{500}\right)$	$e\left(\frac{343}{500}\right)$	$e\left(\frac{97}{125}\right)$	$e\left(\frac{421}{500}\right)$	$e\left(\frac{98}{125}\right)$	$e\left(\frac{117}{125}\right)$	$e\left(\frac{489}{500}\right)$	$e\left(\frac{76}{125}\right)$
$\chi_{90000}(77,\cdot)$	90000.lw	1500	yes	$1$	$1$	$e\left(\frac{1}{300}\right)$	$e\left(\frac{683}{1500}\right)$	$e\left(\frac{28}{375}\right)$	$e\left(\frac{3}{500}\right)$	$e\left(\frac{323}{500}\right)$	$e\left(\frac{73}{1500}\right)$	$e\left(\frac{671}{1500}\right)$	$e\left(\frac{346}{375}\right)$	$e\left(\frac{11}{125}\right)$	$e\left(\frac{88}{375}\right)$
$\chi_{90000}(79,\cdot)$	90000.la	750	no	$-1$	$1$	$e\left(\frac{53}{75}\right)$	$e\left(\frac{23}{750}\right)$	$e\left(\frac{247}{750}\right)$	$e\left(\frac{193}{250}\right)$	$e\left(\frac{113}{250}\right)$	$e\left(\frac{119}{375}\right)$	$e\left(\frac{313}{375}\right)$	$e\left(\frac{79}{750}\right)$	$e\left(\frac{39}{250}\right)$	$e\left(\frac{281}{375}\right)$
$\chi_{90000}(83,\cdot)$	90000.lx	1500	yes	$-1$	$1$	$e\left(\frac{113}{300}\right)$	$e\left(\frac{1129}{1500}\right)$	$e\left(\frac{103}{750}\right)$	$e\left(\frac{289}{500}\right)$	$e\left(\frac{449}{500}\right)$	$e\left(\frac{449}{1500}\right)$	$e\left(\frac{223}{1500}\right)$	$e\left(\frac{121}{750}\right)$	$e\left(\frac{161}{250}\right)$	$e\left(\frac{269}{375}\right)$
$\chi_{90000}(89,\cdot)$	90000.ir	250	no	$-1$	$1$	$e\left(\frac{1}{50}\right)$	$e\left(\frac{29}{125}\right)$	$e\left(\frac{56}{125}\right)$	$e\left(\frac{67}{125}\right)$	$e\left(\frac{219}{250}\right)$	$e\left(\frac{99}{125}\right)$	$e\left(\frac{23}{125}\right)$	$e\left(\frac{67}{125}\right)$	$e\left(\frac{66}{125}\right)$	$e\left(\frac{227}{250}\right)$
$\chi_{90000}(91,\cdot)$	90000.ka	500	no	$-1$	$1$	$e\left(\frac{7}{25}\right)$	$e\left(\frac{399}{500}\right)$	$e\left(\frac{111}{500}\right)$	$e\left(\frac{113}{125}\right)$	$e\left(\frac{457}{500}\right)$	$e\left(\frac{111}{125}\right)$	$e\left(\frac{463}{500}\right)$	$e\left(\frac{101}{250}\right)$	$e\left(\frac{421}{500}\right)$	$e\left(\frac{103}{250}\right)$
$\chi_{90000}(97,\cdot)$	90000.lo	1500	no	$-1$	$1$	$e\left(\frac{167}{300}\right)$	$e\left(\frac{184}{375}\right)$	$e\left(\frac{29}{1500}\right)$	$e\left(\frac{301}{500}\right)$	$e\left(\frac{183}{250}\right)$	$e\left(\frac{1241}{1500}\right)$	$e\left(\frac{641}{750}\right)$	$e\left(\frac{257}{375}\right)$	$e\left(\frac{373}{500}\right)$	$e\left(\frac{371}{375}\right)$
$\chi_{90000}(101,\cdot)$	90000.ja	300	no	$-1$	$1$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{161}{300}\right)$	$e\left(\frac{229}{300}\right)$	$e\left(\frac{13}{50}\right)$	$e\left(\frac{91}{100}\right)$	$e\left(\frac{4}{75}\right)$	$e\left(\frac{107}{300}\right)$	$e\left(\frac{7}{75}\right)$	$e\left(\frac{73}{100}\right)$	$e\left(\frac{46}{75}\right)$
$\chi_{90000}(103,\cdot)$	90000.lp	1500	no	$1$	$1$	$e\left(\frac{7}{300}\right)$	$e\left(\frac{89}{375}\right)$	$e\left(\frac{709}{1500}\right)$	$e\left(\frac{471}{500}\right)$	$e\left(\frac{43}{250}\right)$	$e\left(\frac{961}{1500}\right)$	$e\left(\frac{368}{375}\right)$	$e\left(\frac{269}{750}\right)$	$e\left(\frac{33}{500}\right)$	$e\left(\frac{316}{375}\right)$
$\chi_{90000}(107,\cdot)$	90000.hn	100	no	$-1$	$1$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{13}{100}\right)$	$e\left(\frac{41}{50}\right)$	$e\left(\frac{99}{100}\right)$	$e\left(\frac{59}{100}\right)$	$e\left(\frac{53}{100}\right)$	$e\left(\frac{31}{100}\right)$	$e\left(\frac{37}{50}\right)$	$e\left(\frac{1}{50}\right)$	$e\left(\frac{18}{25}\right)$
$\chi_{90000}(109,\cdot)$	90000.ks	500	no	$1$	$1$	$e\left(\frac{22}{25}\right)$	$e\left(\frac{79}{500}\right)$	$e\left(\frac{131}{500}\right)$	$e\left(\frac{171}{250}\right)$	$e\left(\frac{197}{500}\right)$	$e\left(\frac{6}{125}\right)$	$e\left(\frac{373}{500}\right)$	$e\left(\frac{23}{125}\right)$	$e\left(\frac{141}{500}\right)$	$e\left(\frac{63}{250}\right)$
$\chi_{90000}(113,\cdot)$	90000.mb	1500	no	$1$	$1$	$e\left(\frac{169}{300}\right)$	$e\left(\frac{301}{750}\right)$	$e\left(\frac{1003}{1500}\right)$	$e\left(\frac{57}{500}\right)$	$e\left(\frac{131}{250}\right)$	$e\left(\frac{637}{1500}\right)$	$e\left(\frac{281}{375}\right)$	$e\left(\frac{199}{375}\right)$	$e\left(\frac{211}{500}\right)$	$e\left(\frac{719}{750}\right)$
$\chi_{90000}(119,\cdot)$	90000.lc	750	no	$1$	$1$	$e\left(\frac{32}{75}\right)$	$e\left(\frac{437}{750}\right)$	$e\left(\frac{284}{375}\right)$	$e\left(\frac{21}{125}\right)$	$e\left(\frac{11}{125}\right)$	$e\left(\frac{397}{750}\right)$	$e\left(\frac{322}{375}\right)$	$e\left(\frac{1}{750}\right)$	$e\left(\frac{58}{125}\right)$	$e\left(\frac{553}{750}\right)$

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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	$90000$
Structure	\(C_{2}\times C_{2}\times C_{4}\times C_{1500}\)
Order	$24000$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)
\(\chi_{90000}(1,\cdot)\)	90000.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{90000}(7,\cdot)\)	90000.jg	300	no	\(1\)	\(1\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{29}{75}\right)\)	\(e\left(\frac{199}{300}\right)\)	\(e\left(\frac{81}{100}\right)\)	\(e\left(\frac{23}{50}\right)\)	\(e\left(\frac{271}{300}\right)\)	\(e\left(\frac{23}{75}\right)\)	\(e\left(\frac{59}{150}\right)\)	\(e\left(\frac{63}{100}\right)\)	\(e\left(\frac{1}{75}\right)\)
\(\chi_{90000}(11,\cdot)\)	90000.mf	1500	yes	\(1\)	\(1\)	\(e\left(\frac{29}{75}\right)\)	\(e\left(\frac{103}{1500}\right)\)	\(e\left(\frac{617}{1500}\right)\)	\(e\left(\frac{49}{250}\right)\)	\(e\left(\frac{93}{500}\right)\)	\(e\left(\frac{109}{750}\right)\)	\(e\left(\frac{211}{1500}\right)\)	\(e\left(\frac{397}{750}\right)\)	\(e\left(\frac{229}{500}\right)\)	\(e\left(\frac{83}{375}\right)\)
\(\chi_{90000}(13,\cdot)\)	90000.ls	1500	yes	\(-1\)	\(1\)	\(e\left(\frac{199}{300}\right)\)	\(e\left(\frac{617}{1500}\right)\)	\(e\left(\frac{419}{750}\right)\)	\(e\left(\frac{47}{500}\right)\)	\(e\left(\frac{227}{500}\right)\)	\(e\left(\frac{1477}{1500}\right)\)	\(e\left(\frac{929}{1500}\right)\)	\(e\left(\frac{4}{375}\right)\)	\(e\left(\frac{53}{250}\right)\)	\(e\left(\frac{299}{750}\right)\)
\(\chi_{90000}(17,\cdot)\)	90000.kp	500	no	\(1\)	\(1\)	\(e\left(\frac{81}{100}\right)\)	\(e\left(\frac{49}{250}\right)\)	\(e\left(\frac{47}{500}\right)\)	\(e\left(\frac{179}{500}\right)\)	\(e\left(\frac{157}{250}\right)\)	\(e\left(\frac{313}{500}\right)\)	\(e\left(\frac{69}{125}\right)\)	\(e\left(\frac{76}{125}\right)\)	\(e\left(\frac{417}{500}\right)\)	\(e\left(\frac{181}{250}\right)\)
\(\chi_{90000}(19,\cdot)\)	90000.ku	500	no	\(-1\)	\(1\)	\(e\left(\frac{23}{50}\right)\)	\(e\left(\frac{93}{500}\right)\)	\(e\left(\frac{227}{500}\right)\)	\(e\left(\frac{157}{250}\right)\)	\(e\left(\frac{99}{500}\right)\)	\(e\left(\frac{79}{250}\right)\)	\(e\left(\frac{341}{500}\right)\)	\(e\left(\frac{157}{250}\right)\)	\(e\left(\frac{397}{500}\right)\)	\(e\left(\frac{71}{250}\right)\)
\(\chi_{90000}(23,\cdot)\)	90000.ma	1500	no	\(-1\)	\(1\)	\(e\left(\frac{271}{300}\right)\)	\(e\left(\frac{109}{750}\right)\)	\(e\left(\frac{1477}{1500}\right)\)	\(e\left(\frac{313}{500}\right)\)	\(e\left(\frac{79}{250}\right)\)	\(e\left(\frac{283}{1500}\right)\)	\(e\left(\frac{733}{750}\right)\)	\(e\left(\frac{407}{750}\right)\)	\(e\left(\frac{49}{500}\right)\)	\(e\left(\frac{71}{750}\right)\)
\(\chi_{90000}(29,\cdot)\)	90000.ln	1500	yes	\(-1\)	\(1\)	\(e\left(\frac{23}{75}\right)\)	\(e\left(\frac{211}{1500}\right)\)	\(e\left(\frac{929}{1500}\right)\)	\(e\left(\frac{69}{125}\right)\)	\(e\left(\frac{341}{500}\right)\)	\(e\left(\frac{733}{750}\right)\)	\(e\left(\frac{1357}{1500}\right)\)	\(e\left(\frac{332}{375}\right)\)	\(e\left(\frac{173}{500}\right)\)	\(e\left(\frac{221}{375}\right)\)
\(\chi_{90000}(31,\cdot)\)	90000.li	750	no	\(-1\)	\(1\)	\(e\left(\frac{59}{150}\right)\)	\(e\left(\frac{397}{750}\right)\)	\(e\left(\frac{4}{375}\right)\)	\(e\left(\frac{76}{125}\right)\)	\(e\left(\frac{157}{250}\right)\)	\(e\left(\frac{407}{750}\right)\)	\(e\left(\frac{332}{375}\right)\)	\(e\left(\frac{581}{750}\right)\)	\(e\left(\frac{73}{125}\right)\)	\(e\left(\frac{334}{375}\right)\)
\(\chi_{90000}(37,\cdot)\)	90000.kh	500	no	\(-1\)	\(1\)	\(e\left(\frac{63}{100}\right)\)	\(e\left(\frac{229}{500}\right)\)	\(e\left(\frac{53}{250}\right)\)	\(e\left(\frac{417}{500}\right)\)	\(e\left(\frac{397}{500}\right)\)	\(e\left(\frac{49}{500}\right)\)	\(e\left(\frac{173}{500}\right)\)	\(e\left(\frac{73}{125}\right)\)	\(e\left(\frac{183}{250}\right)\)	\(e\left(\frac{113}{250}\right)\)
\(\chi_{90000}(41,\cdot)\)	90000.le	750	no	\(-1\)	\(1\)	\(e\left(\frac{1}{75}\right)\)	\(e\left(\frac{83}{375}\right)\)	\(e\left(\frac{299}{750}\right)\)	\(e\left(\frac{181}{250}\right)\)	\(e\left(\frac{71}{250}\right)\)	\(e\left(\frac{71}{750}\right)\)	\(e\left(\frac{221}{375}\right)\)	\(e\left(\frac{334}{375}\right)\)	\(e\left(\frac{113}{250}\right)\)	\(e\left(\frac{29}{750}\right)\)
\(\chi_{90000}(43,\cdot)\)	90000.jr	300	no	\(1\)	\(1\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{17}{300}\right)\)	\(e\left(\frac{22}{75}\right)\)	\(e\left(\frac{47}{100}\right)\)	\(e\left(\frac{27}{100}\right)\)	\(e\left(\frac{127}{300}\right)\)	\(e\left(\frac{179}{300}\right)\)	\(e\left(\frac{83}{150}\right)\)	\(e\left(\frac{14}{25}\right)\)	\(e\left(\frac{149}{150}\right)\)
\(\chi_{90000}(47,\cdot)\)	90000.lr	1500	no	\(-1\)	\(1\)	\(e\left(\frac{77}{300}\right)\)	\(e\left(\frac{4}{375}\right)\)	\(e\left(\frac{449}{1500}\right)\)	\(e\left(\frac{31}{500}\right)\)	\(e\left(\frac{74}{125}\right)\)	\(e\left(\frac{1421}{1500}\right)\)	\(e\left(\frac{223}{375}\right)\)	\(e\left(\frac{109}{750}\right)\)	\(e\left(\frac{413}{500}\right)\)	\(e\left(\frac{277}{750}\right)\)
\(\chi_{90000}(49,\cdot)\)	90000.hx	150	no	\(1\)	\(1\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{58}{75}\right)\)	\(e\left(\frac{49}{150}\right)\)	\(e\left(\frac{31}{50}\right)\)	\(e\left(\frac{23}{25}\right)\)	\(e\left(\frac{121}{150}\right)\)	\(e\left(\frac{46}{75}\right)\)	\(e\left(\frac{59}{75}\right)\)	\(e\left(\frac{13}{50}\right)\)	\(e\left(\frac{2}{75}\right)\)
\(\chi_{90000}(53,\cdot)\)	90000.kl	500	no	\(1\)	\(1\)	\(e\left(\frac{49}{100}\right)\)	\(e\left(\frac{67}{500}\right)\)	\(e\left(\frac{97}{125}\right)\)	\(e\left(\frac{241}{500}\right)\)	\(e\left(\frac{281}{500}\right)\)	\(e\left(\frac{177}{500}\right)\)	\(e\left(\frac{79}{500}\right)\)	\(e\left(\frac{29}{125}\right)\)	\(e\left(\frac{92}{125}\right)\)	\(e\left(\frac{37}{125}\right)\)
\(\chi_{90000}(59,\cdot)\)	90000.ll	1500	yes	\(1\)	\(1\)	\(e\left(\frac{47}{150}\right)\)	\(e\left(\frac{227}{1500}\right)\)	\(e\left(\frac{1003}{1500}\right)\)	\(e\left(\frac{108}{125}\right)\)	\(e\left(\frac{137}{500}\right)\)	\(e\left(\frac{253}{375}\right)\)	\(e\left(\frac{1499}{1500}\right)\)	\(e\left(\frac{23}{750}\right)\)	\(e\left(\frac{211}{500}\right)\)	\(e\left(\frac{172}{375}\right)\)
\(\chi_{90000}(61,\cdot)\)	90000.mg	1500	yes	\(1\)	\(1\)	\(e\left(\frac{73}{150}\right)\)	\(e\left(\frac{793}{1500}\right)\)	\(e\left(\frac{527}{1500}\right)\)	\(e\left(\frac{97}{125}\right)\)	\(e\left(\frac{233}{500}\right)\)	\(e\left(\frac{679}{750}\right)\)	\(e\left(\frac{991}{1500}\right)\)	\(e\left(\frac{41}{375}\right)\)	\(e\left(\frac{399}{500}\right)\)	\(e\left(\frac{721}{750}\right)\)
\(\chi_{90000}(67,\cdot)\)	90000.lt	1500	yes	\(1\)	\(1\)	\(e\left(\frac{283}{300}\right)\)	\(e\left(\frac{1439}{1500}\right)\)	\(e\left(\frac{199}{375}\right)\)	\(e\left(\frac{249}{500}\right)\)	\(e\left(\frac{309}{500}\right)\)	\(e\left(\frac{1309}{1500}\right)\)	\(e\left(\frac{1193}{1500}\right)\)	\(e\left(\frac{311}{750}\right)\)	\(e\left(\frac{38}{125}\right)\)	\(e\left(\frac{233}{750}\right)\)
\(\chi_{90000}(71,\cdot)\)	90000.im	250	no	\(1\)	\(1\)	\(e\left(\frac{17}{50}\right)\)	\(e\left(\frac{111}{250}\right)\)	\(e\left(\frac{29}{250}\right)\)	\(e\left(\frac{153}{250}\right)\)	\(e\left(\frac{49}{125}\right)\)	\(e\left(\frac{58}{125}\right)\)	\(e\left(\frac{16}{125}\right)\)	\(e\left(\frac{153}{250}\right)\)	\(e\left(\frac{119}{250}\right)\)	\(e\left(\frac{109}{250}\right)\)
\(\chi_{90000}(73,\cdot)\)	90000.kn	500	no	\(-1\)	\(1\)	\(e\left(\frac{27}{100}\right)\)	\(e\left(\frac{133}{250}\right)\)	\(e\left(\frac{199}{500}\right)\)	\(e\left(\frac{343}{500}\right)\)	\(e\left(\frac{97}{125}\right)\)	\(e\left(\frac{421}{500}\right)\)	\(e\left(\frac{98}{125}\right)\)	\(e\left(\frac{117}{125}\right)\)	\(e\left(\frac{489}{500}\right)\)	\(e\left(\frac{76}{125}\right)\)
\(\chi_{90000}(77,\cdot)\)	90000.lw	1500	yes	\(1\)	\(1\)	\(e\left(\frac{1}{300}\right)\)	\(e\left(\frac{683}{1500}\right)\)	\(e\left(\frac{28}{375}\right)\)	\(e\left(\frac{3}{500}\right)\)	\(e\left(\frac{323}{500}\right)\)	\(e\left(\frac{73}{1500}\right)\)	\(e\left(\frac{671}{1500}\right)\)	\(e\left(\frac{346}{375}\right)\)	\(e\left(\frac{11}{125}\right)\)	\(e\left(\frac{88}{375}\right)\)
\(\chi_{90000}(79,\cdot)\)	90000.la	750	no	\(-1\)	\(1\)	\(e\left(\frac{53}{75}\right)\)	\(e\left(\frac{23}{750}\right)\)	\(e\left(\frac{247}{750}\right)\)	\(e\left(\frac{193}{250}\right)\)	\(e\left(\frac{113}{250}\right)\)	\(e\left(\frac{119}{375}\right)\)	\(e\left(\frac{313}{375}\right)\)	\(e\left(\frac{79}{750}\right)\)	\(e\left(\frac{39}{250}\right)\)	\(e\left(\frac{281}{375}\right)\)
\(\chi_{90000}(83,\cdot)\)	90000.lx	1500	yes	\(-1\)	\(1\)	\(e\left(\frac{113}{300}\right)\)	\(e\left(\frac{1129}{1500}\right)\)	\(e\left(\frac{103}{750}\right)\)	\(e\left(\frac{289}{500}\right)\)	\(e\left(\frac{449}{500}\right)\)	\(e\left(\frac{449}{1500}\right)\)	\(e\left(\frac{223}{1500}\right)\)	\(e\left(\frac{121}{750}\right)\)	\(e\left(\frac{161}{250}\right)\)	\(e\left(\frac{269}{375}\right)\)
\(\chi_{90000}(89,\cdot)\)	90000.ir	250	no	\(-1\)	\(1\)	\(e\left(\frac{1}{50}\right)\)	\(e\left(\frac{29}{125}\right)\)	\(e\left(\frac{56}{125}\right)\)	\(e\left(\frac{67}{125}\right)\)	\(e\left(\frac{219}{250}\right)\)	\(e\left(\frac{99}{125}\right)\)	\(e\left(\frac{23}{125}\right)\)	\(e\left(\frac{67}{125}\right)\)	\(e\left(\frac{66}{125}\right)\)	\(e\left(\frac{227}{250}\right)\)
\(\chi_{90000}(91,\cdot)\)	90000.ka	500	no	\(-1\)	\(1\)	\(e\left(\frac{7}{25}\right)\)	\(e\left(\frac{399}{500}\right)\)	\(e\left(\frac{111}{500}\right)\)	\(e\left(\frac{113}{125}\right)\)	\(e\left(\frac{457}{500}\right)\)	\(e\left(\frac{111}{125}\right)\)	\(e\left(\frac{463}{500}\right)\)	\(e\left(\frac{101}{250}\right)\)	\(e\left(\frac{421}{500}\right)\)	\(e\left(\frac{103}{250}\right)\)
\(\chi_{90000}(97,\cdot)\)	90000.lo	1500	no	\(-1\)	\(1\)	\(e\left(\frac{167}{300}\right)\)	\(e\left(\frac{184}{375}\right)\)	\(e\left(\frac{29}{1500}\right)\)	\(e\left(\frac{301}{500}\right)\)	\(e\left(\frac{183}{250}\right)\)	\(e\left(\frac{1241}{1500}\right)\)	\(e\left(\frac{641}{750}\right)\)	\(e\left(\frac{257}{375}\right)\)	\(e\left(\frac{373}{500}\right)\)	\(e\left(\frac{371}{375}\right)\)
\(\chi_{90000}(101,\cdot)\)	90000.ja	300	no	\(-1\)	\(1\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{161}{300}\right)\)	\(e\left(\frac{229}{300}\right)\)	\(e\left(\frac{13}{50}\right)\)	\(e\left(\frac{91}{100}\right)\)	\(e\left(\frac{4}{75}\right)\)	\(e\left(\frac{107}{300}\right)\)	\(e\left(\frac{7}{75}\right)\)	\(e\left(\frac{73}{100}\right)\)	\(e\left(\frac{46}{75}\right)\)
\(\chi_{90000}(103,\cdot)\)	90000.lp	1500	no	\(1\)	\(1\)	\(e\left(\frac{7}{300}\right)\)	\(e\left(\frac{89}{375}\right)\)	\(e\left(\frac{709}{1500}\right)\)	\(e\left(\frac{471}{500}\right)\)	\(e\left(\frac{43}{250}\right)\)	\(e\left(\frac{961}{1500}\right)\)	\(e\left(\frac{368}{375}\right)\)	\(e\left(\frac{269}{750}\right)\)	\(e\left(\frac{33}{500}\right)\)	\(e\left(\frac{316}{375}\right)\)
\(\chi_{90000}(107,\cdot)\)	90000.hn	100	no	\(-1\)	\(1\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{13}{100}\right)\)	\(e\left(\frac{41}{50}\right)\)	\(e\left(\frac{99}{100}\right)\)	\(e\left(\frac{59}{100}\right)\)	\(e\left(\frac{53}{100}\right)\)	\(e\left(\frac{31}{100}\right)\)	\(e\left(\frac{37}{50}\right)\)	\(e\left(\frac{1}{50}\right)\)	\(e\left(\frac{18}{25}\right)\)
\(\chi_{90000}(109,\cdot)\)	90000.ks	500	no	\(1\)	\(1\)	\(e\left(\frac{22}{25}\right)\)	\(e\left(\frac{79}{500}\right)\)	\(e\left(\frac{131}{500}\right)\)	\(e\left(\frac{171}{250}\right)\)	\(e\left(\frac{197}{500}\right)\)	\(e\left(\frac{6}{125}\right)\)	\(e\left(\frac{373}{500}\right)\)	\(e\left(\frac{23}{125}\right)\)	\(e\left(\frac{141}{500}\right)\)	\(e\left(\frac{63}{250}\right)\)
\(\chi_{90000}(113,\cdot)\)	90000.mb	1500	no	\(1\)	\(1\)	\(e\left(\frac{169}{300}\right)\)	\(e\left(\frac{301}{750}\right)\)	\(e\left(\frac{1003}{1500}\right)\)	\(e\left(\frac{57}{500}\right)\)	\(e\left(\frac{131}{250}\right)\)	\(e\left(\frac{637}{1500}\right)\)	\(e\left(\frac{281}{375}\right)\)	\(e\left(\frac{199}{375}\right)\)	\(e\left(\frac{211}{500}\right)\)	\(e\left(\frac{719}{750}\right)\)
\(\chi_{90000}(119,\cdot)\)	90000.lc	750	no	\(1\)	\(1\)	\(e\left(\frac{32}{75}\right)\)	\(e\left(\frac{437}{750}\right)\)	\(e\left(\frac{284}{375}\right)\)	\(e\left(\frac{21}{125}\right)\)	\(e\left(\frac{11}{125}\right)\)	\(e\left(\frac{397}{750}\right)\)	\(e\left(\frac{322}{375}\right)\)	\(e\left(\frac{1}{750}\right)\)	\(e\left(\frac{58}{125}\right)\)	\(e\left(\frac{553}{750}\right)\)

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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.