LMFDB - Group of Dirichlet characters of modulus 980000

Show commands: PariGP / SageMath

sage: H = DirichletGroup(980000)

pari: g = idealstar(,980000,2)

Character group

sage: G.order() pari: g.no
Order	=	336000
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{4}\times C_{21000}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{980000}(918751,\cdot)$, $\chi_{980000}(122501,\cdot)$, $\chi_{980000}(89377,\cdot)$, $\chi_{980000}(740001,\cdot)$

First 32 of 336000 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	$-1$	$1$	$3$	$9$	$11$	$13$	$17$	$19$	$23$	$27$	$29$	$31$
$\chi_{980000}(1,\cdot)$	980000.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{980000}(3,\cdot)$	980000.bhw	21000	yes	$-1$	$1$	$e\left(\frac{11483}{21000}\right)$	$e\left(\frac{983}{10500}\right)$	$e\left(\frac{4019}{21000}\right)$	$e\left(\frac{1097}{7000}\right)$	$e\left(\frac{1231}{10500}\right)$	$e\left(\frac{1231}{3000}\right)$	$e\left(\frac{2333}{2625}\right)$	$e\left(\frac{4483}{7000}\right)$	$e\left(\frac{1551}{7000}\right)$	$e\left(\frac{352}{375}\right)$
$\chi_{980000}(9,\cdot)$	980000.bht	10500	no	$1$	$1$	$e\left(\frac{983}{10500}\right)$	$e\left(\frac{983}{5250}\right)$	$e\left(\frac{4019}{10500}\right)$	$e\left(\frac{1097}{3500}\right)$	$e\left(\frac{1231}{5250}\right)$	$e\left(\frac{1231}{1500}\right)$	$e\left(\frac{2041}{2625}\right)$	$e\left(\frac{983}{3500}\right)$	$e\left(\frac{1551}{3500}\right)$	$e\left(\frac{329}{375}\right)$
$\chi_{980000}(11,\cdot)$	980000.bia	21000	yes	$-1$	$1$	$e\left(\frac{4019}{21000}\right)$	$e\left(\frac{4019}{10500}\right)$	$e\left(\frac{18317}{21000}\right)$	$e\left(\frac{921}{7000}\right)$	$e\left(\frac{29}{5250}\right)$	$e\left(\frac{433}{3000}\right)$	$e\left(\frac{7901}{10500}\right)$	$e\left(\frac{4019}{7000}\right)$	$e\left(\frac{1693}{7000}\right)$	$e\left(\frac{647}{750}\right)$
$\chi_{980000}(13,\cdot)$	980000.bgj	7000	yes	$1$	$1$	$e\left(\frac{1097}{7000}\right)$	$e\left(\frac{1097}{3500}\right)$	$e\left(\frac{921}{7000}\right)$	$e\left(\frac{4869}{7000}\right)$	$e\left(\frac{829}{3500}\right)$	$e\left(\frac{829}{1000}\right)$	$e\left(\frac{1619}{1750}\right)$	$e\left(\frac{3291}{7000}\right)$	$e\left(\frac{5627}{7000}\right)$	$e\left(\frac{211}{250}\right)$
$\chi_{980000}(17,\cdot)$	980000.bhp	10500	no	$1$	$1$	$e\left(\frac{1231}{10500}\right)$	$e\left(\frac{1231}{5250}\right)$	$e\left(\frac{29}{5250}\right)$	$e\left(\frac{829}{3500}\right)$	$e\left(\frac{7759}{10500}\right)$	$e\left(\frac{721}{750}\right)$	$e\left(\frac{7823}{10500}\right)$	$e\left(\frac{1231}{3500}\right)$	$e\left(\frac{233}{875}\right)$	$e\left(\frac{581}{750}\right)$
$\chi_{980000}(19,\cdot)$	980000.bdw	3000	no	$1$	$1$	$e\left(\frac{1231}{3000}\right)$	$e\left(\frac{1231}{1500}\right)$	$e\left(\frac{433}{3000}\right)$	$e\left(\frac{829}{1000}\right)$	$e\left(\frac{721}{750}\right)$	$e\left(\frac{719}{3000}\right)$	$e\left(\frac{1099}{1500}\right)$	$e\left(\frac{231}{1000}\right)$	$e\left(\frac{57}{1000}\right)$	$e\left(\frac{173}{375}\right)$
$\chi_{980000}(23,\cdot)$	980000.bhd	10500	no	$1$	$1$	$e\left(\frac{2333}{2625}\right)$	$e\left(\frac{2041}{2625}\right)$	$e\left(\frac{7901}{10500}\right)$	$e\left(\frac{1619}{1750}\right)$	$e\left(\frac{7823}{10500}\right)$	$e\left(\frac{1099}{1500}\right)$	$e\left(\frac{9481}{10500}\right)$	$e\left(\frac{583}{875}\right)$	$e\left(\frac{629}{3500}\right)$	$e\left(\frac{157}{750}\right)$
$\chi_{980000}(27,\cdot)$	980000.bgl	7000	yes	$-1$	$1$	$e\left(\frac{4483}{7000}\right)$	$e\left(\frac{983}{3500}\right)$	$e\left(\frac{4019}{7000}\right)$	$e\left(\frac{3291}{7000}\right)$	$e\left(\frac{1231}{3500}\right)$	$e\left(\frac{231}{1000}\right)$	$e\left(\frac{583}{875}\right)$	$e\left(\frac{6449}{7000}\right)$	$e\left(\frac{4653}{7000}\right)$	$e\left(\frac{102}{125}\right)$
$\chi_{980000}(29,\cdot)$	980000.bgn	7000	yes	$1$	$1$	$e\left(\frac{1551}{7000}\right)$	$e\left(\frac{1551}{3500}\right)$	$e\left(\frac{1693}{7000}\right)$	$e\left(\frac{5627}{7000}\right)$	$e\left(\frac{233}{875}\right)$	$e\left(\frac{57}{1000}\right)$	$e\left(\frac{629}{3500}\right)$	$e\left(\frac{4653}{7000}\right)$	$e\left(\frac{2291}{7000}\right)$	$e\left(\frac{69}{125}\right)$
$\chi_{980000}(31,\cdot)$	980000.ye	750	no	$1$	$1$	$e\left(\frac{352}{375}\right)$	$e\left(\frac{329}{375}\right)$	$e\left(\frac{647}{750}\right)$	$e\left(\frac{211}{250}\right)$	$e\left(\frac{581}{750}\right)$	$e\left(\frac{173}{375}\right)$	$e\left(\frac{157}{750}\right)$	$e\left(\frac{102}{125}\right)$	$e\left(\frac{69}{125}\right)$	$e\left(\frac{103}{375}\right)$
$\chi_{980000}(33,\cdot)$	980000.bhm	10500	no	$1$	$1$	$e\left(\frac{7751}{10500}\right)$	$e\left(\frac{2501}{5250}\right)$	$e\left(\frac{167}{2625}\right)$	$e\left(\frac{1009}{3500}\right)$	$e\left(\frac{1289}{10500}\right)$	$e\left(\frac{208}{375}\right)$	$e\left(\frac{6733}{10500}\right)$	$e\left(\frac{751}{3500}\right)$	$e\left(\frac{811}{1750}\right)$	$e\left(\frac{601}{750}\right)$
$\chi_{980000}(37,\cdot)$	980000.bhz	21000	yes	$-1$	$1$	$e\left(\frac{11401}{21000}\right)$	$e\left(\frac{901}{10500}\right)$	$e\left(\frac{6493}{21000}\right)$	$e\left(\frac{3359}{7000}\right)$	$e\left(\frac{4007}{10500}\right)$	$e\left(\frac{1757}{3000}\right)$	$e\left(\frac{1577}{5250}\right)$	$e\left(\frac{4401}{7000}\right)$	$e\left(\frac{4797}{7000}\right)$	$e\left(\frac{344}{375}\right)$
$\chi_{980000}(39,\cdot)$	980000.bhu	10500	no	$-1$	$1$	$e\left(\frac{7387}{10500}\right)$	$e\left(\frac{2137}{5250}\right)$	$e\left(\frac{3391}{10500}\right)$	$e\left(\frac{2983}{3500}\right)$	$e\left(\frac{1859}{5250}\right)$	$e\left(\frac{359}{1500}\right)$	$e\left(\frac{4273}{5250}\right)$	$e\left(\frac{387}{3500}\right)$	$e\left(\frac{89}{3500}\right)$	$e\left(\frac{587}{750}\right)$
$\chi_{980000}(41,\cdot)$	980000.beh	3500	no	$-1$	$1$	$e\left(\frac{81}{3500}\right)$	$e\left(\frac{81}{1750}\right)$	$e\left(\frac{3233}{3500}\right)$	$e\left(\frac{937}{3500}\right)$	$e\left(\frac{267}{1750}\right)$	$e\left(\frac{267}{500}\right)$	$e\left(\frac{1749}{1750}\right)$	$e\left(\frac{243}{3500}\right)$	$e\left(\frac{3271}{3500}\right)$	$e\left(\frac{181}{250}\right)$
$\chi_{980000}(43,\cdot)$	980000.bao	1400	no	$1$	$1$	$e\left(\frac{347}{1400}\right)$	$e\left(\frac{347}{700}\right)$	$e\left(\frac{1371}{1400}\right)$	$e\left(\frac{419}{1400}\right)$	$e\left(\frac{379}{700}\right)$	$e\left(\frac{179}{200}\right)$	$e\left(\frac{269}{350}\right)$	$e\left(\frac{1041}{1400}\right)$	$e\left(\frac{877}{1400}\right)$	$e\left(\frac{11}{50}\right)$
$\chi_{980000}(47,\cdot)$	980000.bhn	10500	no	$-1$	$1$	$e\left(\frac{9209}{10500}\right)$	$e\left(\frac{3959}{5250}\right)$	$e\left(\frac{278}{2625}\right)$	$e\left(\frac{1381}{3500}\right)$	$e\left(\frac{5651}{10500}\right)$	$e\left(\frac{97}{375}\right)$	$e\left(\frac{6697}{10500}\right)$	$e\left(\frac{2209}{3500}\right)$	$e\left(\frac{62}{875}\right)$	$e\left(\frac{242}{375}\right)$
$\chi_{980000}(51,\cdot)$	980000.bfj	4200	no	$-1$	$1$	$e\left(\frac{2789}{4200}\right)$	$e\left(\frac{689}{2100}\right)$	$e\left(\frac{827}{4200}\right)$	$e\left(\frac{551}{1400}\right)$	$e\left(\frac{899}{1050}\right)$	$e\left(\frac{223}{600}\right)$	$e\left(\frac{1331}{2100}\right)$	$e\left(\frac{1389}{1400}\right)$	$e\left(\frac{683}{1400}\right)$	$e\left(\frac{107}{150}\right)$
$\chi_{980000}(53,\cdot)$	980000.bik	21000	yes	$-1$	$1$	$e\left(\frac{13673}{21000}\right)$	$e\left(\frac{3173}{10500}\right)$	$e\left(\frac{689}{21000}\right)$	$e\left(\frac{1807}{7000}\right)$	$e\left(\frac{4561}{10500}\right)$	$e\left(\frac{1561}{3000}\right)$	$e\left(\frac{398}{2625}\right)$	$e\left(\frac{6673}{7000}\right)$	$e\left(\frac{481}{7000}\right)$	$e\left(\frac{337}{375}\right)$
$\chi_{980000}(57,\cdot)$	980000.op	140	no	$-1$	$1$	$e\left(\frac{67}{70}\right)$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{47}{140}\right)$	$e\left(\frac{69}{70}\right)$	$e\left(\frac{11}{140}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{87}{140}\right)$	$e\left(\frac{61}{70}\right)$	$e\left(\frac{39}{140}\right)$	$e\left(\frac{2}{5}\right)$
$\chi_{980000}(59,\cdot)$	980000.bie	21000	yes	$1$	$1$	$e\left(\frac{18071}{21000}\right)$	$e\left(\frac{7571}{10500}\right)$	$e\left(\frac{1553}{21000}\right)$	$e\left(\frac{2389}{7000}\right)$	$e\left(\frac{3161}{5250}\right)$	$e\left(\frac{697}{3000}\right)$	$e\left(\frac{5459}{10500}\right)$	$e\left(\frac{4071}{7000}\right)$	$e\left(\frac{2537}{7000}\right)$	$e\left(\frac{199}{375}\right)$
$\chi_{980000}(61,\cdot)$	980000.bic	21000	yes	$-1$	$1$	$e\left(\frac{20389}{21000}\right)$	$e\left(\frac{9889}{10500}\right)$	$e\left(\frac{9727}{21000}\right)$	$e\left(\frac{251}{7000}\right)$	$e\left(\frac{2162}{2625}\right)$	$e\left(\frac{23}{3000}\right)$	$e\left(\frac{2881}{10500}\right)$	$e\left(\frac{6389}{7000}\right)$	$e\left(\frac{4083}{7000}\right)$	$e\left(\frac{457}{750}\right)$
$\chi_{980000}(67,\cdot)$	980000.bds	3000	no	$1$	$1$	$e\left(\frac{221}{3000}\right)$	$e\left(\frac{221}{1500}\right)$	$e\left(\frac{1253}{3000}\right)$	$e\left(\frac{239}{1000}\right)$	$e\left(\frac{997}{1500}\right)$	$e\left(\frac{979}{3000}\right)$	$e\left(\frac{217}{750}\right)$	$e\left(\frac{221}{1000}\right)$	$e\left(\frac{337}{1000}\right)$	$e\left(\frac{311}{750}\right)$
$\chi_{980000}(69,\cdot)$	980000.bgm	7000	yes	$-1$	$1$	$e\left(\frac{3049}{7000}\right)$	$e\left(\frac{3049}{3500}\right)$	$e\left(\frac{6607}{7000}\right)$	$e\left(\frac{573}{7000}\right)$	$e\left(\frac{1509}{1750}\right)$	$e\left(\frac{143}{1000}\right)$	$e\left(\frac{2771}{3500}\right)$	$e\left(\frac{2147}{7000}\right)$	$e\left(\frac{2809}{7000}\right)$	$e\left(\frac{37}{250}\right)$
$\chi_{980000}(71,\cdot)$	980000.bef	3500	no	$-1$	$1$	$e\left(\frac{103}{3500}\right)$	$e\left(\frac{103}{1750}\right)$	$e\left(\frac{1929}{3500}\right)$	$e\left(\frac{781}{3500}\right)$	$e\left(\frac{348}{875}\right)$	$e\left(\frac{321}{500}\right)$	$e\left(\frac{156}{875}\right)$	$e\left(\frac{309}{3500}\right)$	$e\left(\frac{573}{3500}\right)$	$e\left(\frac{153}{250}\right)$
$\chi_{980000}(73,\cdot)$	980000.bhf	10500	no	$1$	$1$	$e\left(\frac{1063}{2625}\right)$	$e\left(\frac{2126}{2625}\right)$	$e\left(\frac{211}{10500}\right)$	$e\left(\frac{192}{875}\right)$	$e\left(\frac{7453}{10500}\right)$	$e\left(\frac{539}{1500}\right)$	$e\left(\frac{8591}{10500}\right)$	$e\left(\frac{188}{875}\right)$	$e\left(\frac{1369}{3500}\right)$	$e\left(\frac{77}{750}\right)$
$\chi_{980000}(79,\cdot)$	980000.yl	750	no	$-1$	$1$	$e\left(\frac{361}{750}\right)$	$e\left(\frac{361}{375}\right)$	$e\left(\frac{74}{375}\right)$	$e\left(\frac{62}{125}\right)$	$e\left(\frac{79}{750}\right)$	$e\left(\frac{232}{375}\right)$	$e\left(\frac{244}{375}\right)$	$e\left(\frac{111}{250}\right)$	$e\left(\frac{167}{250}\right)$	$e\left(\frac{79}{750}\right)$
$\chi_{980000}(81,\cdot)$	980000.bgc	5250	no	$1$	$1$	$e\left(\frac{983}{5250}\right)$	$e\left(\frac{983}{2625}\right)$	$e\left(\frac{4019}{5250}\right)$	$e\left(\frac{1097}{1750}\right)$	$e\left(\frac{1231}{2625}\right)$	$e\left(\frac{481}{750}\right)$	$e\left(\frac{1457}{2625}\right)$	$e\left(\frac{983}{1750}\right)$	$e\left(\frac{1551}{1750}\right)$	$e\left(\frac{283}{375}\right)$
$\chi_{980000}(83,\cdot)$	980000.bgl	7000	yes	$-1$	$1$	$e\left(\frac{2389}{7000}\right)$	$e\left(\frac{2389}{3500}\right)$	$e\left(\frac{5477}{7000}\right)$	$e\left(\frac{5253}{7000}\right)$	$e\left(\frac{3273}{3500}\right)$	$e\left(\frac{273}{1000}\right)$	$e\left(\frac{314}{875}\right)$	$e\left(\frac{167}{7000}\right)$	$e\left(\frac{1499}{7000}\right)$	$e\left(\frac{41}{125}\right)$
$\chi_{980000}(87,\cdot)$	980000.bhe	10500	no	$-1$	$1$	$e\left(\frac{2017}{2625}\right)$	$e\left(\frac{1409}{2625}\right)$	$e\left(\frac{4549}{10500}\right)$	$e\left(\frac{1681}{1750}\right)$	$e\left(\frac{4027}{10500}\right)$	$e\left(\frac{701}{1500}\right)$	$e\left(\frac{719}{10500}\right)$	$e\left(\frac{267}{875}\right)$	$e\left(\frac{1921}{3500}\right)$	$e\left(\frac{184}{375}\right)$
$\chi_{980000}(89,\cdot)$	980000.bhs	10500	no	$-1$	$1$	$e\left(\frac{2327}{10500}\right)$	$e\left(\frac{2327}{5250}\right)$	$e\left(\frac{4061}{10500}\right)$	$e\left(\frac{2693}{3500}\right)$	$e\left(\frac{1907}{2625}\right)$	$e\left(\frac{439}{1500}\right)$	$e\left(\frac{1579}{2625}\right)$	$e\left(\frac{2327}{3500}\right)$	$e\left(\frac{2769}{3500}\right)$	$e\left(\frac{277}{750}\right)$
$\chi_{980000}(93,\cdot)$	980000.bfr	4200	no	$-1$	$1$	$e\left(\frac{2039}{4200}\right)$	$e\left(\frac{2039}{2100}\right)$	$e\left(\frac{227}{4200}\right)$	$e\left(\frac{1}{1400}\right)$	$e\left(\frac{1873}{2100}\right)$	$e\left(\frac{523}{600}\right)$	$e\left(\frac{103}{1050}\right)$	$e\left(\frac{639}{1400}\right)$	$e\left(\frac{1083}{1400}\right)$	$e\left(\frac{16}{75}\right)$

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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	$980000$
Structure	\(C_{2}\times C_{2}\times C_{4}\times C_{21000}\)
Order	$336000$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(9\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(27\)	\(29\)	\(31\)
\(\chi_{980000}(1,\cdot)\)	980000.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{980000}(3,\cdot)\)	980000.bhw	21000	yes	\(-1\)	\(1\)	\(e\left(\frac{11483}{21000}\right)\)	\(e\left(\frac{983}{10500}\right)\)	\(e\left(\frac{4019}{21000}\right)\)	\(e\left(\frac{1097}{7000}\right)\)	\(e\left(\frac{1231}{10500}\right)\)	\(e\left(\frac{1231}{3000}\right)\)	\(e\left(\frac{2333}{2625}\right)\)	\(e\left(\frac{4483}{7000}\right)\)	\(e\left(\frac{1551}{7000}\right)\)	\(e\left(\frac{352}{375}\right)\)
\(\chi_{980000}(9,\cdot)\)	980000.bht	10500	no	\(1\)	\(1\)	\(e\left(\frac{983}{10500}\right)\)	\(e\left(\frac{983}{5250}\right)\)	\(e\left(\frac{4019}{10500}\right)\)	\(e\left(\frac{1097}{3500}\right)\)	\(e\left(\frac{1231}{5250}\right)\)	\(e\left(\frac{1231}{1500}\right)\)	\(e\left(\frac{2041}{2625}\right)\)	\(e\left(\frac{983}{3500}\right)\)	\(e\left(\frac{1551}{3500}\right)\)	\(e\left(\frac{329}{375}\right)\)
\(\chi_{980000}(11,\cdot)\)	980000.bia	21000	yes	\(-1\)	\(1\)	\(e\left(\frac{4019}{21000}\right)\)	\(e\left(\frac{4019}{10500}\right)\)	\(e\left(\frac{18317}{21000}\right)\)	\(e\left(\frac{921}{7000}\right)\)	\(e\left(\frac{29}{5250}\right)\)	\(e\left(\frac{433}{3000}\right)\)	\(e\left(\frac{7901}{10500}\right)\)	\(e\left(\frac{4019}{7000}\right)\)	\(e\left(\frac{1693}{7000}\right)\)	\(e\left(\frac{647}{750}\right)\)
\(\chi_{980000}(13,\cdot)\)	980000.bgj	7000	yes	\(1\)	\(1\)	\(e\left(\frac{1097}{7000}\right)\)	\(e\left(\frac{1097}{3500}\right)\)	\(e\left(\frac{921}{7000}\right)\)	\(e\left(\frac{4869}{7000}\right)\)	\(e\left(\frac{829}{3500}\right)\)	\(e\left(\frac{829}{1000}\right)\)	\(e\left(\frac{1619}{1750}\right)\)	\(e\left(\frac{3291}{7000}\right)\)	\(e\left(\frac{5627}{7000}\right)\)	\(e\left(\frac{211}{250}\right)\)
\(\chi_{980000}(17,\cdot)\)	980000.bhp	10500	no	\(1\)	\(1\)	\(e\left(\frac{1231}{10500}\right)\)	\(e\left(\frac{1231}{5250}\right)\)	\(e\left(\frac{29}{5250}\right)\)	\(e\left(\frac{829}{3500}\right)\)	\(e\left(\frac{7759}{10500}\right)\)	\(e\left(\frac{721}{750}\right)\)	\(e\left(\frac{7823}{10500}\right)\)	\(e\left(\frac{1231}{3500}\right)\)	\(e\left(\frac{233}{875}\right)\)	\(e\left(\frac{581}{750}\right)\)
\(\chi_{980000}(19,\cdot)\)	980000.bdw	3000	no	\(1\)	\(1\)	\(e\left(\frac{1231}{3000}\right)\)	\(e\left(\frac{1231}{1500}\right)\)	\(e\left(\frac{433}{3000}\right)\)	\(e\left(\frac{829}{1000}\right)\)	\(e\left(\frac{721}{750}\right)\)	\(e\left(\frac{719}{3000}\right)\)	\(e\left(\frac{1099}{1500}\right)\)	\(e\left(\frac{231}{1000}\right)\)	\(e\left(\frac{57}{1000}\right)\)	\(e\left(\frac{173}{375}\right)\)
\(\chi_{980000}(23,\cdot)\)	980000.bhd	10500	no	\(1\)	\(1\)	\(e\left(\frac{2333}{2625}\right)\)	\(e\left(\frac{2041}{2625}\right)\)	\(e\left(\frac{7901}{10500}\right)\)	\(e\left(\frac{1619}{1750}\right)\)	\(e\left(\frac{7823}{10500}\right)\)	\(e\left(\frac{1099}{1500}\right)\)	\(e\left(\frac{9481}{10500}\right)\)	\(e\left(\frac{583}{875}\right)\)	\(e\left(\frac{629}{3500}\right)\)	\(e\left(\frac{157}{750}\right)\)
\(\chi_{980000}(27,\cdot)\)	980000.bgl	7000	yes	\(-1\)	\(1\)	\(e\left(\frac{4483}{7000}\right)\)	\(e\left(\frac{983}{3500}\right)\)	\(e\left(\frac{4019}{7000}\right)\)	\(e\left(\frac{3291}{7000}\right)\)	\(e\left(\frac{1231}{3500}\right)\)	\(e\left(\frac{231}{1000}\right)\)	\(e\left(\frac{583}{875}\right)\)	\(e\left(\frac{6449}{7000}\right)\)	\(e\left(\frac{4653}{7000}\right)\)	\(e\left(\frac{102}{125}\right)\)
\(\chi_{980000}(29,\cdot)\)	980000.bgn	7000	yes	\(1\)	\(1\)	\(e\left(\frac{1551}{7000}\right)\)	\(e\left(\frac{1551}{3500}\right)\)	\(e\left(\frac{1693}{7000}\right)\)	\(e\left(\frac{5627}{7000}\right)\)	\(e\left(\frac{233}{875}\right)\)	\(e\left(\frac{57}{1000}\right)\)	\(e\left(\frac{629}{3500}\right)\)	\(e\left(\frac{4653}{7000}\right)\)	\(e\left(\frac{2291}{7000}\right)\)	\(e\left(\frac{69}{125}\right)\)
\(\chi_{980000}(31,\cdot)\)	980000.ye	750	no	\(1\)	\(1\)	\(e\left(\frac{352}{375}\right)\)	\(e\left(\frac{329}{375}\right)\)	\(e\left(\frac{647}{750}\right)\)	\(e\left(\frac{211}{250}\right)\)	\(e\left(\frac{581}{750}\right)\)	\(e\left(\frac{173}{375}\right)\)	\(e\left(\frac{157}{750}\right)\)	\(e\left(\frac{102}{125}\right)\)	\(e\left(\frac{69}{125}\right)\)	\(e\left(\frac{103}{375}\right)\)
\(\chi_{980000}(33,\cdot)\)	980000.bhm	10500	no	\(1\)	\(1\)	\(e\left(\frac{7751}{10500}\right)\)	\(e\left(\frac{2501}{5250}\right)\)	\(e\left(\frac{167}{2625}\right)\)	\(e\left(\frac{1009}{3500}\right)\)	\(e\left(\frac{1289}{10500}\right)\)	\(e\left(\frac{208}{375}\right)\)	\(e\left(\frac{6733}{10500}\right)\)	\(e\left(\frac{751}{3500}\right)\)	\(e\left(\frac{811}{1750}\right)\)	\(e\left(\frac{601}{750}\right)\)
\(\chi_{980000}(37,\cdot)\)	980000.bhz	21000	yes	\(-1\)	\(1\)	\(e\left(\frac{11401}{21000}\right)\)	\(e\left(\frac{901}{10500}\right)\)	\(e\left(\frac{6493}{21000}\right)\)	\(e\left(\frac{3359}{7000}\right)\)	\(e\left(\frac{4007}{10500}\right)\)	\(e\left(\frac{1757}{3000}\right)\)	\(e\left(\frac{1577}{5250}\right)\)	\(e\left(\frac{4401}{7000}\right)\)	\(e\left(\frac{4797}{7000}\right)\)	\(e\left(\frac{344}{375}\right)\)
\(\chi_{980000}(39,\cdot)\)	980000.bhu	10500	no	\(-1\)	\(1\)	\(e\left(\frac{7387}{10500}\right)\)	\(e\left(\frac{2137}{5250}\right)\)	\(e\left(\frac{3391}{10500}\right)\)	\(e\left(\frac{2983}{3500}\right)\)	\(e\left(\frac{1859}{5250}\right)\)	\(e\left(\frac{359}{1500}\right)\)	\(e\left(\frac{4273}{5250}\right)\)	\(e\left(\frac{387}{3500}\right)\)	\(e\left(\frac{89}{3500}\right)\)	\(e\left(\frac{587}{750}\right)\)
\(\chi_{980000}(41,\cdot)\)	980000.beh	3500	no	\(-1\)	\(1\)	\(e\left(\frac{81}{3500}\right)\)	\(e\left(\frac{81}{1750}\right)\)	\(e\left(\frac{3233}{3500}\right)\)	\(e\left(\frac{937}{3500}\right)\)	\(e\left(\frac{267}{1750}\right)\)	\(e\left(\frac{267}{500}\right)\)	\(e\left(\frac{1749}{1750}\right)\)	\(e\left(\frac{243}{3500}\right)\)	\(e\left(\frac{3271}{3500}\right)\)	\(e\left(\frac{181}{250}\right)\)
\(\chi_{980000}(43,\cdot)\)	980000.bao	1400	no	\(1\)	\(1\)	\(e\left(\frac{347}{1400}\right)\)	\(e\left(\frac{347}{700}\right)\)	\(e\left(\frac{1371}{1400}\right)\)	\(e\left(\frac{419}{1400}\right)\)	\(e\left(\frac{379}{700}\right)\)	\(e\left(\frac{179}{200}\right)\)	\(e\left(\frac{269}{350}\right)\)	\(e\left(\frac{1041}{1400}\right)\)	\(e\left(\frac{877}{1400}\right)\)	\(e\left(\frac{11}{50}\right)\)
\(\chi_{980000}(47,\cdot)\)	980000.bhn	10500	no	\(-1\)	\(1\)	\(e\left(\frac{9209}{10500}\right)\)	\(e\left(\frac{3959}{5250}\right)\)	\(e\left(\frac{278}{2625}\right)\)	\(e\left(\frac{1381}{3500}\right)\)	\(e\left(\frac{5651}{10500}\right)\)	\(e\left(\frac{97}{375}\right)\)	\(e\left(\frac{6697}{10500}\right)\)	\(e\left(\frac{2209}{3500}\right)\)	\(e\left(\frac{62}{875}\right)\)	\(e\left(\frac{242}{375}\right)\)
\(\chi_{980000}(51,\cdot)\)	980000.bfj	4200	no	\(-1\)	\(1\)	\(e\left(\frac{2789}{4200}\right)\)	\(e\left(\frac{689}{2100}\right)\)	\(e\left(\frac{827}{4200}\right)\)	\(e\left(\frac{551}{1400}\right)\)	\(e\left(\frac{899}{1050}\right)\)	\(e\left(\frac{223}{600}\right)\)	\(e\left(\frac{1331}{2100}\right)\)	\(e\left(\frac{1389}{1400}\right)\)	\(e\left(\frac{683}{1400}\right)\)	\(e\left(\frac{107}{150}\right)\)
\(\chi_{980000}(53,\cdot)\)	980000.bik	21000	yes	\(-1\)	\(1\)	\(e\left(\frac{13673}{21000}\right)\)	\(e\left(\frac{3173}{10500}\right)\)	\(e\left(\frac{689}{21000}\right)\)	\(e\left(\frac{1807}{7000}\right)\)	\(e\left(\frac{4561}{10500}\right)\)	\(e\left(\frac{1561}{3000}\right)\)	\(e\left(\frac{398}{2625}\right)\)	\(e\left(\frac{6673}{7000}\right)\)	\(e\left(\frac{481}{7000}\right)\)	\(e\left(\frac{337}{375}\right)\)
\(\chi_{980000}(57,\cdot)\)	980000.op	140	no	\(-1\)	\(1\)	\(e\left(\frac{67}{70}\right)\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{47}{140}\right)\)	\(e\left(\frac{69}{70}\right)\)	\(e\left(\frac{11}{140}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{87}{140}\right)\)	\(e\left(\frac{61}{70}\right)\)	\(e\left(\frac{39}{140}\right)\)	\(e\left(\frac{2}{5}\right)\)
\(\chi_{980000}(59,\cdot)\)	980000.bie	21000	yes	\(1\)	\(1\)	\(e\left(\frac{18071}{21000}\right)\)	\(e\left(\frac{7571}{10500}\right)\)	\(e\left(\frac{1553}{21000}\right)\)	\(e\left(\frac{2389}{7000}\right)\)	\(e\left(\frac{3161}{5250}\right)\)	\(e\left(\frac{697}{3000}\right)\)	\(e\left(\frac{5459}{10500}\right)\)	\(e\left(\frac{4071}{7000}\right)\)	\(e\left(\frac{2537}{7000}\right)\)	\(e\left(\frac{199}{375}\right)\)
\(\chi_{980000}(61,\cdot)\)	980000.bic	21000	yes	\(-1\)	\(1\)	\(e\left(\frac{20389}{21000}\right)\)	\(e\left(\frac{9889}{10500}\right)\)	\(e\left(\frac{9727}{21000}\right)\)	\(e\left(\frac{251}{7000}\right)\)	\(e\left(\frac{2162}{2625}\right)\)	\(e\left(\frac{23}{3000}\right)\)	\(e\left(\frac{2881}{10500}\right)\)	\(e\left(\frac{6389}{7000}\right)\)	\(e\left(\frac{4083}{7000}\right)\)	\(e\left(\frac{457}{750}\right)\)
\(\chi_{980000}(67,\cdot)\)	980000.bds	3000	no	\(1\)	\(1\)	\(e\left(\frac{221}{3000}\right)\)	\(e\left(\frac{221}{1500}\right)\)	\(e\left(\frac{1253}{3000}\right)\)	\(e\left(\frac{239}{1000}\right)\)	\(e\left(\frac{997}{1500}\right)\)	\(e\left(\frac{979}{3000}\right)\)	\(e\left(\frac{217}{750}\right)\)	\(e\left(\frac{221}{1000}\right)\)	\(e\left(\frac{337}{1000}\right)\)	\(e\left(\frac{311}{750}\right)\)
\(\chi_{980000}(69,\cdot)\)	980000.bgm	7000	yes	\(-1\)	\(1\)	\(e\left(\frac{3049}{7000}\right)\)	\(e\left(\frac{3049}{3500}\right)\)	\(e\left(\frac{6607}{7000}\right)\)	\(e\left(\frac{573}{7000}\right)\)	\(e\left(\frac{1509}{1750}\right)\)	\(e\left(\frac{143}{1000}\right)\)	\(e\left(\frac{2771}{3500}\right)\)	\(e\left(\frac{2147}{7000}\right)\)	\(e\left(\frac{2809}{7000}\right)\)	\(e\left(\frac{37}{250}\right)\)
\(\chi_{980000}(71,\cdot)\)	980000.bef	3500	no	\(-1\)	\(1\)	\(e\left(\frac{103}{3500}\right)\)	\(e\left(\frac{103}{1750}\right)\)	\(e\left(\frac{1929}{3500}\right)\)	\(e\left(\frac{781}{3500}\right)\)	\(e\left(\frac{348}{875}\right)\)	\(e\left(\frac{321}{500}\right)\)	\(e\left(\frac{156}{875}\right)\)	\(e\left(\frac{309}{3500}\right)\)	\(e\left(\frac{573}{3500}\right)\)	\(e\left(\frac{153}{250}\right)\)
\(\chi_{980000}(73,\cdot)\)	980000.bhf	10500	no	\(1\)	\(1\)	\(e\left(\frac{1063}{2625}\right)\)	\(e\left(\frac{2126}{2625}\right)\)	\(e\left(\frac{211}{10500}\right)\)	\(e\left(\frac{192}{875}\right)\)	\(e\left(\frac{7453}{10500}\right)\)	\(e\left(\frac{539}{1500}\right)\)	\(e\left(\frac{8591}{10500}\right)\)	\(e\left(\frac{188}{875}\right)\)	\(e\left(\frac{1369}{3500}\right)\)	\(e\left(\frac{77}{750}\right)\)
\(\chi_{980000}(79,\cdot)\)	980000.yl	750	no	\(-1\)	\(1\)	\(e\left(\frac{361}{750}\right)\)	\(e\left(\frac{361}{375}\right)\)	\(e\left(\frac{74}{375}\right)\)	\(e\left(\frac{62}{125}\right)\)	\(e\left(\frac{79}{750}\right)\)	\(e\left(\frac{232}{375}\right)\)	\(e\left(\frac{244}{375}\right)\)	\(e\left(\frac{111}{250}\right)\)	\(e\left(\frac{167}{250}\right)\)	\(e\left(\frac{79}{750}\right)\)
\(\chi_{980000}(81,\cdot)\)	980000.bgc	5250	no	\(1\)	\(1\)	\(e\left(\frac{983}{5250}\right)\)	\(e\left(\frac{983}{2625}\right)\)	\(e\left(\frac{4019}{5250}\right)\)	\(e\left(\frac{1097}{1750}\right)\)	\(e\left(\frac{1231}{2625}\right)\)	\(e\left(\frac{481}{750}\right)\)	\(e\left(\frac{1457}{2625}\right)\)	\(e\left(\frac{983}{1750}\right)\)	\(e\left(\frac{1551}{1750}\right)\)	\(e\left(\frac{283}{375}\right)\)
\(\chi_{980000}(83,\cdot)\)	980000.bgl	7000	yes	\(-1\)	\(1\)	\(e\left(\frac{2389}{7000}\right)\)	\(e\left(\frac{2389}{3500}\right)\)	\(e\left(\frac{5477}{7000}\right)\)	\(e\left(\frac{5253}{7000}\right)\)	\(e\left(\frac{3273}{3500}\right)\)	\(e\left(\frac{273}{1000}\right)\)	\(e\left(\frac{314}{875}\right)\)	\(e\left(\frac{167}{7000}\right)\)	\(e\left(\frac{1499}{7000}\right)\)	\(e\left(\frac{41}{125}\right)\)
\(\chi_{980000}(87,\cdot)\)	980000.bhe	10500	no	\(-1\)	\(1\)	\(e\left(\frac{2017}{2625}\right)\)	\(e\left(\frac{1409}{2625}\right)\)	\(e\left(\frac{4549}{10500}\right)\)	\(e\left(\frac{1681}{1750}\right)\)	\(e\left(\frac{4027}{10500}\right)\)	\(e\left(\frac{701}{1500}\right)\)	\(e\left(\frac{719}{10500}\right)\)	\(e\left(\frac{267}{875}\right)\)	\(e\left(\frac{1921}{3500}\right)\)	\(e\left(\frac{184}{375}\right)\)
\(\chi_{980000}(89,\cdot)\)	980000.bhs	10500	no	\(-1\)	\(1\)	\(e\left(\frac{2327}{10500}\right)\)	\(e\left(\frac{2327}{5250}\right)\)	\(e\left(\frac{4061}{10500}\right)\)	\(e\left(\frac{2693}{3500}\right)\)	\(e\left(\frac{1907}{2625}\right)\)	\(e\left(\frac{439}{1500}\right)\)	\(e\left(\frac{1579}{2625}\right)\)	\(e\left(\frac{2327}{3500}\right)\)	\(e\left(\frac{2769}{3500}\right)\)	\(e\left(\frac{277}{750}\right)\)
\(\chi_{980000}(93,\cdot)\)	980000.bfr	4200	no	\(-1\)	\(1\)	\(e\left(\frac{2039}{4200}\right)\)	\(e\left(\frac{2039}{2100}\right)\)	\(e\left(\frac{227}{4200}\right)\)	\(e\left(\frac{1}{1400}\right)\)	\(e\left(\frac{1873}{2100}\right)\)	\(e\left(\frac{523}{600}\right)\)	\(e\left(\frac{103}{1050}\right)\)	\(e\left(\frac{639}{1400}\right)\)	\(e\left(\frac{1083}{1400}\right)\)	\(e\left(\frac{16}{75}\right)\)

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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.