LMFDB - Group of Dirichlet characters of modulus 416000

Show commands: Magma / Pari/GP / SageMath

comment:Define the Dirichlet group

sage:G = DirichletGroup(416000)

gp:g = idealstar(,416000,2)

magma:G = FullDirichletGroup(416000);

Character group

Order	=	153600	comment:Order sage:G.order() gp:g.no magma:Order(G);
Structure	=	$C_{2}\times C_{4}\times C_{4}\times C_{4800}$	comment:Group structure sage:sorted(g.order() for g in G.gens()) gp:g.cyc magma:PrimaryInvariants(G);
Generators	=	$\chi_{416000}(74751,\cdot)$, $\chi_{416000}(266501,\cdot)$, $\chi_{416000}(389377,\cdot)$, $\chi_{416000}(64001,\cdot)$	comment:Generators sage:G.gens() gp:g.gen magma:Generators(G);

First 32 of 153600 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	$-1$	$1$	$3$	$7$	$9$	$11$	$17$	$19$	$21$	$23$	$27$	$29$
$\chi_{416000}(1,\cdot)$	416000.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{416000}(3,\cdot)$	416000.btd	4800	yes	$1$	$1$	$e\left(\frac{2227}{4800}\right)$	$e\left(\frac{281}{480}\right)$	$e\left(\frac{2227}{2400}\right)$	$e\left(\frac{3061}{4800}\right)$	$e\left(\frac{107}{1200}\right)$	$e\left(\frac{23}{4800}\right)$	$e\left(\frac{79}{1600}\right)$	$e\left(\frac{1583}{2400}\right)$	$e\left(\frac{627}{1600}\right)$	$e\left(\frac{4507}{4800}\right)$
$\chi_{416000}(7,\cdot)$	416000.bkk	480	no	$-1$	$1$	$e\left(\frac{281}{480}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{41}{240}\right)$	$e\left(\frac{383}{480}\right)$	$e\left(\frac{31}{120}\right)$	$e\left(\frac{469}{480}\right)$	$e\left(\frac{157}{160}\right)$	$e\left(\frac{49}{240}\right)$	$e\left(\frac{121}{160}\right)$	$e\left(\frac{281}{480}\right)$
$\chi_{416000}(9,\cdot)$	416000.brt	2400	no	$1$	$1$	$e\left(\frac{2227}{2400}\right)$	$e\left(\frac{41}{240}\right)$	$e\left(\frac{1027}{1200}\right)$	$e\left(\frac{661}{2400}\right)$	$e\left(\frac{107}{600}\right)$	$e\left(\frac{23}{2400}\right)$	$e\left(\frac{79}{800}\right)$	$e\left(\frac{383}{1200}\right)$	$e\left(\frac{627}{800}\right)$	$e\left(\frac{2107}{2400}\right)$
$\chi_{416000}(11,\cdot)$	416000.bsz	4800	yes	$1$	$1$	$e\left(\frac{3061}{4800}\right)$	$e\left(\frac{383}{480}\right)$	$e\left(\frac{661}{2400}\right)$	$e\left(\frac{1123}{4800}\right)$	$e\left(\frac{1001}{1200}\right)$	$e\left(\frac{3089}{4800}\right)$	$e\left(\frac{697}{1600}\right)$	$e\left(\frac{1169}{2400}\right)$	$e\left(\frac{1461}{1600}\right)$	$e\left(\frac{3901}{4800}\right)$
$\chi_{416000}(17,\cdot)$	416000.bpr	1200	no	$-1$	$1$	$e\left(\frac{107}{1200}\right)$	$e\left(\frac{31}{120}\right)$	$e\left(\frac{107}{600}\right)$	$e\left(\frac{1001}{1200}\right)$	$e\left(\frac{131}{150}\right)$	$e\left(\frac{43}{1200}\right)$	$e\left(\frac{139}{400}\right)$	$e\left(\frac{253}{600}\right)$	$e\left(\frac{107}{400}\right)$	$e\left(\frac{887}{1200}\right)$
$\chi_{416000}(19,\cdot)$	416000.buc	4800	yes	$1$	$1$	$e\left(\frac{23}{4800}\right)$	$e\left(\frac{469}{480}\right)$	$e\left(\frac{23}{2400}\right)$	$e\left(\frac{3089}{4800}\right)$	$e\left(\frac{43}{1200}\right)$	$e\left(\frac{427}{4800}\right)$	$e\left(\frac{1571}{1600}\right)$	$e\left(\frac{667}{2400}\right)$	$e\left(\frac{23}{1600}\right)$	$e\left(\frac{143}{4800}\right)$
$\chi_{416000}(21,\cdot)$	416000.brr	1600	yes	$-1$	$1$	$e\left(\frac{79}{1600}\right)$	$e\left(\frac{157}{160}\right)$	$e\left(\frac{79}{800}\right)$	$e\left(\frac{697}{1600}\right)$	$e\left(\frac{139}{400}\right)$	$e\left(\frac{1571}{1600}\right)$	$e\left(\frac{49}{1600}\right)$	$e\left(\frac{691}{800}\right)$	$e\left(\frac{237}{1600}\right)$	$e\left(\frac{839}{1600}\right)$
$\chi_{416000}(23,\cdot)$	416000.bsf	2400	no	$1$	$1$	$e\left(\frac{1583}{2400}\right)$	$e\left(\frac{49}{240}\right)$	$e\left(\frac{383}{1200}\right)$	$e\left(\frac{1169}{2400}\right)$	$e\left(\frac{253}{600}\right)$	$e\left(\frac{667}{2400}\right)$	$e\left(\frac{691}{800}\right)$	$e\left(\frac{607}{1200}\right)$	$e\left(\frac{783}{800}\right)$	$e\left(\frac{1103}{2400}\right)$
$\chi_{416000}(27,\cdot)$	416000.brn	1600	no	$1$	$1$	$e\left(\frac{627}{1600}\right)$	$e\left(\frac{121}{160}\right)$	$e\left(\frac{627}{800}\right)$	$e\left(\frac{1461}{1600}\right)$	$e\left(\frac{107}{400}\right)$	$e\left(\frac{23}{1600}\right)$	$e\left(\frac{237}{1600}\right)$	$e\left(\frac{783}{800}\right)$	$e\left(\frac{281}{1600}\right)$	$e\left(\frac{1307}{1600}\right)$
$\chi_{416000}(29,\cdot)$	416000.bth	4800	yes	$1$	$1$	$e\left(\frac{4507}{4800}\right)$	$e\left(\frac{281}{480}\right)$	$e\left(\frac{2107}{2400}\right)$	$e\left(\frac{3901}{4800}\right)$	$e\left(\frac{887}{1200}\right)$	$e\left(\frac{143}{4800}\right)$	$e\left(\frac{839}{1600}\right)$	$e\left(\frac{1103}{2400}\right)$	$e\left(\frac{1307}{1600}\right)$	$e\left(\frac{787}{4800}\right)$
$\chi_{416000}(31,\cdot)$	416000.bdn	200	no	$1$	$1$	$e\left(\frac{47}{200}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{47}{100}\right)$	$e\left(\frac{171}{200}\right)$	$e\left(\frac{1}{25}\right)$	$e\left(\frac{153}{200}\right)$	$e\left(\frac{7}{200}\right)$	$e\left(\frac{63}{100}\right)$	$e\left(\frac{141}{200}\right)$	$e\left(\frac{27}{200}\right)$
$\chi_{416000}(33,\cdot)$	416000.blw	600	no	$1$	$1$	$e\left(\frac{61}{600}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{61}{300}\right)$	$e\left(\frac{523}{600}\right)$	$e\left(\frac{277}{300}\right)$	$e\left(\frac{389}{600}\right)$	$e\left(\frac{97}{200}\right)$	$e\left(\frac{11}{75}\right)$	$e\left(\frac{61}{200}\right)$	$e\left(\frac{451}{600}\right)$
$\chi_{416000}(37,\cdot)$	416000.btk	4800	yes	$1$	$1$	$e\left(\frac{169}{4800}\right)$	$e\left(\frac{467}{480}\right)$	$e\left(\frac{169}{2400}\right)$	$e\left(\frac{1567}{4800}\right)$	$e\left(\frac{329}{1200}\right)$	$e\left(\frac{581}{4800}\right)$	$e\left(\frac{13}{1600}\right)$	$e\left(\frac{701}{2400}\right)$	$e\left(\frac{169}{1600}\right)$	$e\left(\frac{1729}{4800}\right)$
$\chi_{416000}(41,\cdot)$	416000.bsb	2400	no	$-1$	$1$	$e\left(\frac{767}{2400}\right)$	$e\left(\frac{1}{240}\right)$	$e\left(\frac{767}{1200}\right)$	$e\left(\frac{881}{2400}\right)$	$e\left(\frac{247}{600}\right)$	$e\left(\frac{1483}{2400}\right)$	$e\left(\frac{259}{800}\right)$	$e\left(\frac{43}{1200}\right)$	$e\left(\frac{767}{800}\right)$	$e\left(\frac{1847}{2400}\right)$
$\chi_{416000}(43,\cdot)$	416000.bod	960	no	$1$	$1$	$e\left(\frac{169}{960}\right)$	$e\left(\frac{59}{96}\right)$	$e\left(\frac{169}{480}\right)$	$e\left(\frac{847}{960}\right)$	$e\left(\frac{89}{240}\right)$	$e\left(\frac{341}{960}\right)$	$e\left(\frac{253}{320}\right)$	$e\left(\frac{461}{480}\right)$	$e\left(\frac{169}{320}\right)$	$e\left(\frac{769}{960}\right)$
$\chi_{416000}(47,\cdot)$	416000.bjc	400	no	$-1$	$1$	$e\left(\frac{141}{400}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{141}{200}\right)$	$e\left(\frac{163}{400}\right)$	$e\left(\frac{14}{25}\right)$	$e\left(\frac{9}{400}\right)$	$e\left(\frac{371}{400}\right)$	$e\left(\frac{139}{200}\right)$	$e\left(\frac{23}{400}\right)$	$e\left(\frac{281}{400}\right)$
$\chi_{416000}(49,\cdot)$	416000.bev	240	no	$1$	$1$	$e\left(\frac{41}{240}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{41}{120}\right)$	$e\left(\frac{143}{240}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{229}{240}\right)$	$e\left(\frac{77}{80}\right)$	$e\left(\frac{49}{120}\right)$	$e\left(\frac{41}{80}\right)$	$e\left(\frac{41}{240}\right)$
$\chi_{416000}(51,\cdot)$	416000.bih	320	no	$-1$	$1$	$e\left(\frac{177}{320}\right)$	$e\left(\frac{27}{32}\right)$	$e\left(\frac{17}{160}\right)$	$e\left(\frac{151}{320}\right)$	$e\left(\frac{77}{80}\right)$	$e\left(\frac{13}{320}\right)$	$e\left(\frac{127}{320}\right)$	$e\left(\frac{13}{160}\right)$	$e\left(\frac{211}{320}\right)$	$e\left(\frac{217}{320}\right)$
$\chi_{416000}(53,\cdot)$	416000.bqr	1600	no	$-1$	$1$	$e\left(\frac{679}{1600}\right)$	$e\left(\frac{117}{160}\right)$	$e\left(\frac{679}{800}\right)$	$e\left(\frac{897}{1600}\right)$	$e\left(\frac{39}{400}\right)$	$e\left(\frac{1371}{1600}\right)$	$e\left(\frac{249}{1600}\right)$	$e\left(\frac{691}{800}\right)$	$e\left(\frac{437}{1600}\right)$	$e\left(\frac{239}{1600}\right)$
$\chi_{416000}(57,\cdot)$	416000.nr	32	no	$1$	$1$	$e\left(\frac{15}{32}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{1}{32}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{31}{32}\right)$
$\chi_{416000}(59,\cdot)$	416000.buc	4800	yes	$1$	$1$	$e\left(\frac{4049}{4800}\right)$	$e\left(\frac{67}{480}\right)$	$e\left(\frac{1649}{2400}\right)$	$e\left(\frac{1607}{4800}\right)$	$e\left(\frac{109}{1200}\right)$	$e\left(\frac{1501}{4800}\right)$	$e\left(\frac{1573}{1600}\right)$	$e\left(\frac{2221}{2400}\right)$	$e\left(\frac{849}{1600}\right)$	$e\left(\frac{2009}{4800}\right)$
$\chi_{416000}(61,\cdot)$	416000.bts	4800	yes	$1$	$1$	$e\left(\frac{4691}{4800}\right)$	$e\left(\frac{433}{480}\right)$	$e\left(\frac{2291}{2400}\right)$	$e\left(\frac{2213}{4800}\right)$	$e\left(\frac{631}{1200}\right)$	$e\left(\frac{1159}{4800}\right)$	$e\left(\frac{1407}{1600}\right)$	$e\left(\frac{439}{2400}\right)$	$e\left(\frac{1491}{1600}\right)$	$e\left(\frac{4331}{4800}\right)$
$\chi_{416000}(63,\cdot)$	416000.bfs	300	no	$-1$	$1$	$e\left(\frac{77}{150}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{2}{75}\right)$	$e\left(\frac{11}{150}\right)$	$e\left(\frac{131}{300}\right)$	$e\left(\frac{74}{75}\right)$	$e\left(\frac{2}{25}\right)$	$e\left(\frac{157}{300}\right)$	$e\left(\frac{27}{50}\right)$	$e\left(\frac{139}{300}\right)$
$\chi_{416000}(67,\cdot)$	416000.btl	4800	yes	$-1$	$1$	$e\left(\frac{3043}{4800}\right)$	$e\left(\frac{209}{480}\right)$	$e\left(\frac{643}{2400}\right)$	$e\left(\frac{3349}{4800}\right)$	$e\left(\frac{1163}{1200}\right)$	$e\left(\frac{2807}{4800}\right)$	$e\left(\frac{111}{1600}\right)$	$e\left(\frac{1247}{2400}\right)$	$e\left(\frac{1443}{1600}\right)$	$e\left(\frac{1963}{4800}\right)$
$\chi_{416000}(69,\cdot)$	416000.btj	4800	yes	$1$	$1$	$e\left(\frac{593}{4800}\right)$	$e\left(\frac{379}{480}\right)$	$e\left(\frac{593}{2400}\right)$	$e\left(\frac{599}{4800}\right)$	$e\left(\frac{613}{1200}\right)$	$e\left(\frac{1357}{4800}\right)$	$e\left(\frac{1461}{1600}\right)$	$e\left(\frac{397}{2400}\right)$	$e\left(\frac{593}{1600}\right)$	$e\left(\frac{1913}{4800}\right)$
$\chi_{416000}(71,\cdot)$	416000.bsa	2400	no	$1$	$1$	$e\left(\frac{1021}{2400}\right)$	$e\left(\frac{83}{240}\right)$	$e\left(\frac{1021}{1200}\right)$	$e\left(\frac{1603}{2400}\right)$	$e\left(\frac{461}{600}\right)$	$e\left(\frac{2129}{2400}\right)$	$e\left(\frac{617}{800}\right)$	$e\left(\frac{809}{1200}\right)$	$e\left(\frac{221}{800}\right)$	$e\left(\frac{661}{2400}\right)$
$\chi_{416000}(73,\cdot)$	416000.bmy	800	no	$1$	$1$	$e\left(\frac{721}{800}\right)$	$e\left(\frac{43}{80}\right)$	$e\left(\frac{321}{400}\right)$	$e\left(\frac{503}{800}\right)$	$e\left(\frac{111}{200}\right)$	$e\left(\frac{29}{800}\right)$	$e\left(\frac{351}{800}\right)$	$e\left(\frac{209}{400}\right)$	$e\left(\frac{563}{800}\right)$	$e\left(\frac{161}{800}\right)$
$\chi_{416000}(77,\cdot)$	416000.brm	1600	yes	$-1$	$1$	$e\left(\frac{357}{1600}\right)$	$e\left(\frac{31}{160}\right)$	$e\left(\frac{357}{800}\right)$	$e\left(\frac{51}{1600}\right)$	$e\left(\frac{37}{400}\right)$	$e\left(\frac{993}{1600}\right)$	$e\left(\frac{667}{1600}\right)$	$e\left(\frac{553}{800}\right)$	$e\left(\frac{1071}{1600}\right)$	$e\left(\frac{637}{1600}\right)$
$\chi_{416000}(79,\cdot)$	416000.bjh	400	no	$-1$	$1$	$e\left(\frac{271}{400}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{71}{200}\right)$	$e\left(\frac{353}{400}\right)$	$e\left(\frac{61}{100}\right)$	$e\left(\frac{379}{400}\right)$	$e\left(\frac{1}{400}\right)$	$e\left(\frac{59}{200}\right)$	$e\left(\frac{13}{400}\right)$	$e\left(\frac{311}{400}\right)$
$\chi_{416000}(81,\cdot)$	416000.bpk	1200	no	$1$	$1$	$e\left(\frac{1027}{1200}\right)$	$e\left(\frac{41}{120}\right)$	$e\left(\frac{427}{600}\right)$	$e\left(\frac{661}{1200}\right)$	$e\left(\frac{107}{300}\right)$	$e\left(\frac{23}{1200}\right)$	$e\left(\frac{79}{400}\right)$	$e\left(\frac{383}{600}\right)$	$e\left(\frac{227}{400}\right)$	$e\left(\frac{907}{1200}\right)$
$\chi_{416000}(83,\cdot)$	416000.brd	1600	yes	$-1$	$1$	$e\left(\frac{1341}{1600}\right)$	$e\left(\frac{63}{160}\right)$	$e\left(\frac{541}{800}\right)$	$e\left(\frac{363}{1600}\right)$	$e\left(\frac{381}{400}\right)$	$e\left(\frac{9}{1600}\right)$	$e\left(\frac{371}{1600}\right)$	$e\left(\frac{689}{800}\right)$	$e\left(\frac{823}{1600}\right)$	$e\left(\frac{981}{1600}\right)$

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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 $\F_{q}$
Belyi maps

Modulus	$416000$
Structure	\(C_{2}\times C_{4}\times C_{4}\times C_{4800}\)
Order	$153600$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(17\)	\(19\)	\(21\)	\(23\)	\(27\)	\(29\)
\(\chi_{416000}(1,\cdot)\)	416000.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{416000}(3,\cdot)\)	416000.btd	4800	yes	\(1\)	\(1\)	\(e\left(\frac{2227}{4800}\right)\)	\(e\left(\frac{281}{480}\right)\)	\(e\left(\frac{2227}{2400}\right)\)	\(e\left(\frac{3061}{4800}\right)\)	\(e\left(\frac{107}{1200}\right)\)	\(e\left(\frac{23}{4800}\right)\)	\(e\left(\frac{79}{1600}\right)\)	\(e\left(\frac{1583}{2400}\right)\)	\(e\left(\frac{627}{1600}\right)\)	\(e\left(\frac{4507}{4800}\right)\)
\(\chi_{416000}(7,\cdot)\)	416000.bkk	480	no	\(-1\)	\(1\)	\(e\left(\frac{281}{480}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{41}{240}\right)\)	\(e\left(\frac{383}{480}\right)\)	\(e\left(\frac{31}{120}\right)\)	\(e\left(\frac{469}{480}\right)\)	\(e\left(\frac{157}{160}\right)\)	\(e\left(\frac{49}{240}\right)\)	\(e\left(\frac{121}{160}\right)\)	\(e\left(\frac{281}{480}\right)\)
\(\chi_{416000}(9,\cdot)\)	416000.brt	2400	no	\(1\)	\(1\)	\(e\left(\frac{2227}{2400}\right)\)	\(e\left(\frac{41}{240}\right)\)	\(e\left(\frac{1027}{1200}\right)\)	\(e\left(\frac{661}{2400}\right)\)	\(e\left(\frac{107}{600}\right)\)	\(e\left(\frac{23}{2400}\right)\)	\(e\left(\frac{79}{800}\right)\)	\(e\left(\frac{383}{1200}\right)\)	\(e\left(\frac{627}{800}\right)\)	\(e\left(\frac{2107}{2400}\right)\)
\(\chi_{416000}(11,\cdot)\)	416000.bsz	4800	yes	\(1\)	\(1\)	\(e\left(\frac{3061}{4800}\right)\)	\(e\left(\frac{383}{480}\right)\)	\(e\left(\frac{661}{2400}\right)\)	\(e\left(\frac{1123}{4800}\right)\)	\(e\left(\frac{1001}{1200}\right)\)	\(e\left(\frac{3089}{4800}\right)\)	\(e\left(\frac{697}{1600}\right)\)	\(e\left(\frac{1169}{2400}\right)\)	\(e\left(\frac{1461}{1600}\right)\)	\(e\left(\frac{3901}{4800}\right)\)
\(\chi_{416000}(17,\cdot)\)	416000.bpr	1200	no	\(-1\)	\(1\)	\(e\left(\frac{107}{1200}\right)\)	\(e\left(\frac{31}{120}\right)\)	\(e\left(\frac{107}{600}\right)\)	\(e\left(\frac{1001}{1200}\right)\)	\(e\left(\frac{131}{150}\right)\)	\(e\left(\frac{43}{1200}\right)\)	\(e\left(\frac{139}{400}\right)\)	\(e\left(\frac{253}{600}\right)\)	\(e\left(\frac{107}{400}\right)\)	\(e\left(\frac{887}{1200}\right)\)
\(\chi_{416000}(19,\cdot)\)	416000.buc	4800	yes	\(1\)	\(1\)	\(e\left(\frac{23}{4800}\right)\)	\(e\left(\frac{469}{480}\right)\)	\(e\left(\frac{23}{2400}\right)\)	\(e\left(\frac{3089}{4800}\right)\)	\(e\left(\frac{43}{1200}\right)\)	\(e\left(\frac{427}{4800}\right)\)	\(e\left(\frac{1571}{1600}\right)\)	\(e\left(\frac{667}{2400}\right)\)	\(e\left(\frac{23}{1600}\right)\)	\(e\left(\frac{143}{4800}\right)\)
\(\chi_{416000}(21,\cdot)\)	416000.brr	1600	yes	\(-1\)	\(1\)	\(e\left(\frac{79}{1600}\right)\)	\(e\left(\frac{157}{160}\right)\)	\(e\left(\frac{79}{800}\right)\)	\(e\left(\frac{697}{1600}\right)\)	\(e\left(\frac{139}{400}\right)\)	\(e\left(\frac{1571}{1600}\right)\)	\(e\left(\frac{49}{1600}\right)\)	\(e\left(\frac{691}{800}\right)\)	\(e\left(\frac{237}{1600}\right)\)	\(e\left(\frac{839}{1600}\right)\)
\(\chi_{416000}(23,\cdot)\)	416000.bsf	2400	no	\(1\)	\(1\)	\(e\left(\frac{1583}{2400}\right)\)	\(e\left(\frac{49}{240}\right)\)	\(e\left(\frac{383}{1200}\right)\)	\(e\left(\frac{1169}{2400}\right)\)	\(e\left(\frac{253}{600}\right)\)	\(e\left(\frac{667}{2400}\right)\)	\(e\left(\frac{691}{800}\right)\)	\(e\left(\frac{607}{1200}\right)\)	\(e\left(\frac{783}{800}\right)\)	\(e\left(\frac{1103}{2400}\right)\)
\(\chi_{416000}(27,\cdot)\)	416000.brn	1600	no	\(1\)	\(1\)	\(e\left(\frac{627}{1600}\right)\)	\(e\left(\frac{121}{160}\right)\)	\(e\left(\frac{627}{800}\right)\)	\(e\left(\frac{1461}{1600}\right)\)	\(e\left(\frac{107}{400}\right)\)	\(e\left(\frac{23}{1600}\right)\)	\(e\left(\frac{237}{1600}\right)\)	\(e\left(\frac{783}{800}\right)\)	\(e\left(\frac{281}{1600}\right)\)	\(e\left(\frac{1307}{1600}\right)\)
\(\chi_{416000}(29,\cdot)\)	416000.bth	4800	yes	\(1\)	\(1\)	\(e\left(\frac{4507}{4800}\right)\)	\(e\left(\frac{281}{480}\right)\)	\(e\left(\frac{2107}{2400}\right)\)	\(e\left(\frac{3901}{4800}\right)\)	\(e\left(\frac{887}{1200}\right)\)	\(e\left(\frac{143}{4800}\right)\)	\(e\left(\frac{839}{1600}\right)\)	\(e\left(\frac{1103}{2400}\right)\)	\(e\left(\frac{1307}{1600}\right)\)	\(e\left(\frac{787}{4800}\right)\)
\(\chi_{416000}(31,\cdot)\)	416000.bdn	200	no	\(1\)	\(1\)	\(e\left(\frac{47}{200}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{47}{100}\right)\)	\(e\left(\frac{171}{200}\right)\)	\(e\left(\frac{1}{25}\right)\)	\(e\left(\frac{153}{200}\right)\)	\(e\left(\frac{7}{200}\right)\)	\(e\left(\frac{63}{100}\right)\)	\(e\left(\frac{141}{200}\right)\)	\(e\left(\frac{27}{200}\right)\)
\(\chi_{416000}(33,\cdot)\)	416000.blw	600	no	\(1\)	\(1\)	\(e\left(\frac{61}{600}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{61}{300}\right)\)	\(e\left(\frac{523}{600}\right)\)	\(e\left(\frac{277}{300}\right)\)	\(e\left(\frac{389}{600}\right)\)	\(e\left(\frac{97}{200}\right)\)	\(e\left(\frac{11}{75}\right)\)	\(e\left(\frac{61}{200}\right)\)	\(e\left(\frac{451}{600}\right)\)
\(\chi_{416000}(37,\cdot)\)	416000.btk	4800	yes	\(1\)	\(1\)	\(e\left(\frac{169}{4800}\right)\)	\(e\left(\frac{467}{480}\right)\)	\(e\left(\frac{169}{2400}\right)\)	\(e\left(\frac{1567}{4800}\right)\)	\(e\left(\frac{329}{1200}\right)\)	\(e\left(\frac{581}{4800}\right)\)	\(e\left(\frac{13}{1600}\right)\)	\(e\left(\frac{701}{2400}\right)\)	\(e\left(\frac{169}{1600}\right)\)	\(e\left(\frac{1729}{4800}\right)\)
\(\chi_{416000}(41,\cdot)\)	416000.bsb	2400	no	\(-1\)	\(1\)	\(e\left(\frac{767}{2400}\right)\)	\(e\left(\frac{1}{240}\right)\)	\(e\left(\frac{767}{1200}\right)\)	\(e\left(\frac{881}{2400}\right)\)	\(e\left(\frac{247}{600}\right)\)	\(e\left(\frac{1483}{2400}\right)\)	\(e\left(\frac{259}{800}\right)\)	\(e\left(\frac{43}{1200}\right)\)	\(e\left(\frac{767}{800}\right)\)	\(e\left(\frac{1847}{2400}\right)\)
\(\chi_{416000}(43,\cdot)\)	416000.bod	960	no	\(1\)	\(1\)	\(e\left(\frac{169}{960}\right)\)	\(e\left(\frac{59}{96}\right)\)	\(e\left(\frac{169}{480}\right)\)	\(e\left(\frac{847}{960}\right)\)	\(e\left(\frac{89}{240}\right)\)	\(e\left(\frac{341}{960}\right)\)	\(e\left(\frac{253}{320}\right)\)	\(e\left(\frac{461}{480}\right)\)	\(e\left(\frac{169}{320}\right)\)	\(e\left(\frac{769}{960}\right)\)
\(\chi_{416000}(47,\cdot)\)	416000.bjc	400	no	\(-1\)	\(1\)	\(e\left(\frac{141}{400}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{141}{200}\right)\)	\(e\left(\frac{163}{400}\right)\)	\(e\left(\frac{14}{25}\right)\)	\(e\left(\frac{9}{400}\right)\)	\(e\left(\frac{371}{400}\right)\)	\(e\left(\frac{139}{200}\right)\)	\(e\left(\frac{23}{400}\right)\)	\(e\left(\frac{281}{400}\right)\)
\(\chi_{416000}(49,\cdot)\)	416000.bev	240	no	\(1\)	\(1\)	\(e\left(\frac{41}{240}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{41}{120}\right)\)	\(e\left(\frac{143}{240}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{229}{240}\right)\)	\(e\left(\frac{77}{80}\right)\)	\(e\left(\frac{49}{120}\right)\)	\(e\left(\frac{41}{80}\right)\)	\(e\left(\frac{41}{240}\right)\)
\(\chi_{416000}(51,\cdot)\)	416000.bih	320	no	\(-1\)	\(1\)	\(e\left(\frac{177}{320}\right)\)	\(e\left(\frac{27}{32}\right)\)	\(e\left(\frac{17}{160}\right)\)	\(e\left(\frac{151}{320}\right)\)	\(e\left(\frac{77}{80}\right)\)	\(e\left(\frac{13}{320}\right)\)	\(e\left(\frac{127}{320}\right)\)	\(e\left(\frac{13}{160}\right)\)	\(e\left(\frac{211}{320}\right)\)	\(e\left(\frac{217}{320}\right)\)
\(\chi_{416000}(53,\cdot)\)	416000.bqr	1600	no	\(-1\)	\(1\)	\(e\left(\frac{679}{1600}\right)\)	\(e\left(\frac{117}{160}\right)\)	\(e\left(\frac{679}{800}\right)\)	\(e\left(\frac{897}{1600}\right)\)	\(e\left(\frac{39}{400}\right)\)	\(e\left(\frac{1371}{1600}\right)\)	\(e\left(\frac{249}{1600}\right)\)	\(e\left(\frac{691}{800}\right)\)	\(e\left(\frac{437}{1600}\right)\)	\(e\left(\frac{239}{1600}\right)\)
\(\chi_{416000}(57,\cdot)\)	416000.nr	32	no	\(1\)	\(1\)	\(e\left(\frac{15}{32}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{9}{32}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{3}{32}\right)\)	\(e\left(\frac{1}{32}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{13}{32}\right)\)	\(e\left(\frac{31}{32}\right)\)
\(\chi_{416000}(59,\cdot)\)	416000.buc	4800	yes	\(1\)	\(1\)	\(e\left(\frac{4049}{4800}\right)\)	\(e\left(\frac{67}{480}\right)\)	\(e\left(\frac{1649}{2400}\right)\)	\(e\left(\frac{1607}{4800}\right)\)	\(e\left(\frac{109}{1200}\right)\)	\(e\left(\frac{1501}{4800}\right)\)	\(e\left(\frac{1573}{1600}\right)\)	\(e\left(\frac{2221}{2400}\right)\)	\(e\left(\frac{849}{1600}\right)\)	\(e\left(\frac{2009}{4800}\right)\)
\(\chi_{416000}(61,\cdot)\)	416000.bts	4800	yes	\(1\)	\(1\)	\(e\left(\frac{4691}{4800}\right)\)	\(e\left(\frac{433}{480}\right)\)	\(e\left(\frac{2291}{2400}\right)\)	\(e\left(\frac{2213}{4800}\right)\)	\(e\left(\frac{631}{1200}\right)\)	\(e\left(\frac{1159}{4800}\right)\)	\(e\left(\frac{1407}{1600}\right)\)	\(e\left(\frac{439}{2400}\right)\)	\(e\left(\frac{1491}{1600}\right)\)	\(e\left(\frac{4331}{4800}\right)\)
\(\chi_{416000}(63,\cdot)\)	416000.bfs	300	no	\(-1\)	\(1\)	\(e\left(\frac{77}{150}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{2}{75}\right)\)	\(e\left(\frac{11}{150}\right)\)	\(e\left(\frac{131}{300}\right)\)	\(e\left(\frac{74}{75}\right)\)	\(e\left(\frac{2}{25}\right)\)	\(e\left(\frac{157}{300}\right)\)	\(e\left(\frac{27}{50}\right)\)	\(e\left(\frac{139}{300}\right)\)
\(\chi_{416000}(67,\cdot)\)	416000.btl	4800	yes	\(-1\)	\(1\)	\(e\left(\frac{3043}{4800}\right)\)	\(e\left(\frac{209}{480}\right)\)	\(e\left(\frac{643}{2400}\right)\)	\(e\left(\frac{3349}{4800}\right)\)	\(e\left(\frac{1163}{1200}\right)\)	\(e\left(\frac{2807}{4800}\right)\)	\(e\left(\frac{111}{1600}\right)\)	\(e\left(\frac{1247}{2400}\right)\)	\(e\left(\frac{1443}{1600}\right)\)	\(e\left(\frac{1963}{4800}\right)\)
\(\chi_{416000}(69,\cdot)\)	416000.btj	4800	yes	\(1\)	\(1\)	\(e\left(\frac{593}{4800}\right)\)	\(e\left(\frac{379}{480}\right)\)	\(e\left(\frac{593}{2400}\right)\)	\(e\left(\frac{599}{4800}\right)\)	\(e\left(\frac{613}{1200}\right)\)	\(e\left(\frac{1357}{4800}\right)\)	\(e\left(\frac{1461}{1600}\right)\)	\(e\left(\frac{397}{2400}\right)\)	\(e\left(\frac{593}{1600}\right)\)	\(e\left(\frac{1913}{4800}\right)\)
\(\chi_{416000}(71,\cdot)\)	416000.bsa	2400	no	\(1\)	\(1\)	\(e\left(\frac{1021}{2400}\right)\)	\(e\left(\frac{83}{240}\right)\)	\(e\left(\frac{1021}{1200}\right)\)	\(e\left(\frac{1603}{2400}\right)\)	\(e\left(\frac{461}{600}\right)\)	\(e\left(\frac{2129}{2400}\right)\)	\(e\left(\frac{617}{800}\right)\)	\(e\left(\frac{809}{1200}\right)\)	\(e\left(\frac{221}{800}\right)\)	\(e\left(\frac{661}{2400}\right)\)
\(\chi_{416000}(73,\cdot)\)	416000.bmy	800	no	\(1\)	\(1\)	\(e\left(\frac{721}{800}\right)\)	\(e\left(\frac{43}{80}\right)\)	\(e\left(\frac{321}{400}\right)\)	\(e\left(\frac{503}{800}\right)\)	\(e\left(\frac{111}{200}\right)\)	\(e\left(\frac{29}{800}\right)\)	\(e\left(\frac{351}{800}\right)\)	\(e\left(\frac{209}{400}\right)\)	\(e\left(\frac{563}{800}\right)\)	\(e\left(\frac{161}{800}\right)\)
\(\chi_{416000}(77,\cdot)\)	416000.brm	1600	yes	\(-1\)	\(1\)	\(e\left(\frac{357}{1600}\right)\)	\(e\left(\frac{31}{160}\right)\)	\(e\left(\frac{357}{800}\right)\)	\(e\left(\frac{51}{1600}\right)\)	\(e\left(\frac{37}{400}\right)\)	\(e\left(\frac{993}{1600}\right)\)	\(e\left(\frac{667}{1600}\right)\)	\(e\left(\frac{553}{800}\right)\)	\(e\left(\frac{1071}{1600}\right)\)	\(e\left(\frac{637}{1600}\right)\)
\(\chi_{416000}(79,\cdot)\)	416000.bjh	400	no	\(-1\)	\(1\)	\(e\left(\frac{271}{400}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{71}{200}\right)\)	\(e\left(\frac{353}{400}\right)\)	\(e\left(\frac{61}{100}\right)\)	\(e\left(\frac{379}{400}\right)\)	\(e\left(\frac{1}{400}\right)\)	\(e\left(\frac{59}{200}\right)\)	\(e\left(\frac{13}{400}\right)\)	\(e\left(\frac{311}{400}\right)\)
\(\chi_{416000}(81,\cdot)\)	416000.bpk	1200	no	\(1\)	\(1\)	\(e\left(\frac{1027}{1200}\right)\)	\(e\left(\frac{41}{120}\right)\)	\(e\left(\frac{427}{600}\right)\)	\(e\left(\frac{661}{1200}\right)\)	\(e\left(\frac{107}{300}\right)\)	\(e\left(\frac{23}{1200}\right)\)	\(e\left(\frac{79}{400}\right)\)	\(e\left(\frac{383}{600}\right)\)	\(e\left(\frac{227}{400}\right)\)	\(e\left(\frac{907}{1200}\right)\)
\(\chi_{416000}(83,\cdot)\)	416000.brd	1600	yes	\(-1\)	\(1\)	\(e\left(\frac{1341}{1600}\right)\)	\(e\left(\frac{63}{160}\right)\)	\(e\left(\frac{541}{800}\right)\)	\(e\left(\frac{363}{1600}\right)\)	\(e\left(\frac{381}{400}\right)\)	\(e\left(\frac{9}{1600}\right)\)	\(e\left(\frac{371}{1600}\right)\)	\(e\left(\frac{689}{800}\right)\)	\(e\left(\frac{823}{1600}\right)\)	\(e\left(\frac{981}{1600}\right)\)

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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.