LMFDB - Group of Dirichlet characters of modulus 409600

Show commands: Magma / Pari/GP / SageMath

comment:Define the Dirichlet group

sage:G = DirichletGroup(409600)

gp:g = idealstar(,409600,2)

magma:G = FullDirichletGroup(409600);

Character group

Order	=	163840	comment:Order sage:G.order() gp:g.no magma:Order(G);
Structure	=	$C_{2}\times C_{4}\times C_{20480}$	comment:Group structure sage:sorted(g.order() for g in G.gens()) gp:g.cyc magma:PrimaryInvariants(G);
Generators	=	$\chi_{409600}(49151,\cdot)$, $\chi_{409600}(311301,\cdot)$, $\chi_{409600}(229377,\cdot)$	comment:Generators sage:G.gens() gp:g.gen magma:Generators(G);

First 32 of 163840 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	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$17$	$19$	$21$	$23$	$27$
$\chi_{409600}(1,\cdot)$	409600.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{409600}(3,\cdot)$	409600.hk	20480	yes	$1$	$1$	$e\left(\frac{14061}{20480}\right)$	$e\left(\frac{1359}{2048}\right)$	$e\left(\frac{3821}{10240}\right)$	$e\left(\frac{14363}{20480}\right)$	$e\left(\frac{2017}{20480}\right)$	$e\left(\frac{2281}{5120}\right)$	$e\left(\frac{10169}{20480}\right)$	$e\left(\frac{7171}{20480}\right)$	$e\left(\frac{5129}{10240}\right)$	$e\left(\frac{1223}{20480}\right)$
$\chi_{409600}(7,\cdot)$	409600.gc	2048	no	$1$	$1$	$e\left(\frac{1359}{2048}\right)$	$e\left(\frac{217}{1024}\right)$	$e\left(\frac{335}{1024}\right)$	$e\left(\frac{1801}{2048}\right)$	$e\left(\frac{75}{2048}\right)$	$e\left(\frac{35}{512}\right)$	$e\left(\frac{915}{2048}\right)$	$e\left(\frac{1793}{2048}\right)$	$e\left(\frac{3}{1024}\right)$	$e\left(\frac{2029}{2048}\right)$
$\chi_{409600}(9,\cdot)$	409600.he	10240	no	$1$	$1$	$e\left(\frac{3821}{10240}\right)$	$e\left(\frac{335}{1024}\right)$	$e\left(\frac{3821}{5120}\right)$	$e\left(\frac{4123}{10240}\right)$	$e\left(\frac{2017}{10240}\right)$	$e\left(\frac{2281}{2560}\right)$	$e\left(\frac{10169}{10240}\right)$	$e\left(\frac{7171}{10240}\right)$	$e\left(\frac{9}{5120}\right)$	$e\left(\frac{1223}{10240}\right)$
$\chi_{409600}(11,\cdot)$	409600.hm	20480	yes	$-1$	$1$	$e\left(\frac{14363}{20480}\right)$	$e\left(\frac{1801}{2048}\right)$	$e\left(\frac{4123}{10240}\right)$	$e\left(\frac{17949}{20480}\right)$	$e\left(\frac{1351}{20480}\right)$	$e\left(\frac{4223}{5120}\right)$	$e\left(\frac{9007}{20480}\right)$	$e\left(\frac{11893}{20480}\right)$	$e\left(\frac{9567}{10240}\right)$	$e\left(\frac{2129}{20480}\right)$
$\chi_{409600}(13,\cdot)$	409600.hl	20480	yes	$-1$	$1$	$e\left(\frac{2017}{20480}\right)$	$e\left(\frac{75}{2048}\right)$	$e\left(\frac{2017}{10240}\right)$	$e\left(\frac{1351}{20480}\right)$	$e\left(\frac{2469}{20480}\right)$	$e\left(\frac{3277}{5120}\right)$	$e\left(\frac{5853}{20480}\right)$	$e\left(\frac{2767}{20480}\right)$	$e\left(\frac{1133}{10240}\right)$	$e\left(\frac{6051}{20480}\right)$
$\chi_{409600}(17,\cdot)$	409600.hb	5120	no	$-1$	$1$	$e\left(\frac{2281}{5120}\right)$	$e\left(\frac{35}{512}\right)$	$e\left(\frac{2281}{2560}\right)$	$e\left(\frac{4223}{5120}\right)$	$e\left(\frac{3277}{5120}\right)$	$e\left(\frac{1141}{1280}\right)$	$e\left(\frac{709}{5120}\right)$	$e\left(\frac{2631}{5120}\right)$	$e\left(\frac{1109}{2560}\right)$	$e\left(\frac{1723}{5120}\right)$
$\chi_{409600}(19,\cdot)$	409600.hn	20480	yes	$-1$	$1$	$e\left(\frac{10169}{20480}\right)$	$e\left(\frac{915}{2048}\right)$	$e\left(\frac{10169}{10240}\right)$	$e\left(\frac{9007}{20480}\right)$	$e\left(\frac{5853}{20480}\right)$	$e\left(\frac{709}{5120}\right)$	$e\left(\frac{18261}{20480}\right)$	$e\left(\frac{19319}{20480}\right)$	$e\left(\frac{5221}{10240}\right)$	$e\left(\frac{10027}{20480}\right)$
$\chi_{409600}(21,\cdot)$	409600.ho	20480	yes	$1$	$1$	$e\left(\frac{7171}{20480}\right)$	$e\left(\frac{1793}{2048}\right)$	$e\left(\frac{7171}{10240}\right)$	$e\left(\frac{11893}{20480}\right)$	$e\left(\frac{2767}{20480}\right)$	$e\left(\frac{2631}{5120}\right)$	$e\left(\frac{19319}{20480}\right)$	$e\left(\frac{4621}{20480}\right)$	$e\left(\frac{5159}{10240}\right)$	$e\left(\frac{1033}{20480}\right)$
$\chi_{409600}(23,\cdot)$	409600.hd	10240	no	$1$	$1$	$e\left(\frac{5129}{10240}\right)$	$e\left(\frac{3}{1024}\right)$	$e\left(\frac{9}{5120}\right)$	$e\left(\frac{9567}{10240}\right)$	$e\left(\frac{1133}{10240}\right)$	$e\left(\frac{1109}{2560}\right)$	$e\left(\frac{5221}{10240}\right)$	$e\left(\frac{5159}{10240}\right)$	$e\left(\frac{2421}{5120}\right)$	$e\left(\frac{5147}{10240}\right)$
$\chi_{409600}(27,\cdot)$	409600.hk	20480	yes	$1$	$1$	$e\left(\frac{1223}{20480}\right)$	$e\left(\frac{2029}{2048}\right)$	$e\left(\frac{1223}{10240}\right)$	$e\left(\frac{2129}{20480}\right)$	$e\left(\frac{6051}{20480}\right)$	$e\left(\frac{1723}{5120}\right)$	$e\left(\frac{10027}{20480}\right)$	$e\left(\frac{1033}{20480}\right)$	$e\left(\frac{5147}{10240}\right)$	$e\left(\frac{3669}{20480}\right)$
$\chi_{409600}(29,\cdot)$	409600.hp	20480	yes	$1$	$1$	$e\left(\frac{661}{20480}\right)$	$e\left(\frac{1159}{2048}\right)$	$e\left(\frac{661}{10240}\right)$	$e\left(\frac{8883}{20480}\right)$	$e\left(\frac{9257}{20480}\right)$	$e\left(\frac{4721}{5120}\right)$	$e\left(\frac{19649}{20480}\right)$	$e\left(\frac{12251}{20480}\right)$	$e\left(\frac{7569}{10240}\right)$	$e\left(\frac{1983}{20480}\right)$
$\chi_{409600}(31,\cdot)$	409600.gg	2560	no	$-1$	$1$	$e\left(\frac{383}{2560}\right)$	$e\left(\frac{85}{256}\right)$	$e\left(\frac{383}{1280}\right)$	$e\left(\frac{89}{2560}\right)$	$e\left(\frac{571}{2560}\right)$	$e\left(\frac{403}{640}\right)$	$e\left(\frac{2307}{2560}\right)$	$e\left(\frac{1233}{2560}\right)$	$e\left(\frac{1267}{1280}\right)$	$e\left(\frac{1149}{2560}\right)$
$\chi_{409600}(33,\cdot)$	409600.gl	2560	no	$-1$	$1$	$e\left(\frac{993}{2560}\right)$	$e\left(\frac{139}{256}\right)$	$e\left(\frac{993}{1280}\right)$	$e\left(\frac{1479}{2560}\right)$	$e\left(\frac{421}{2560}\right)$	$e\left(\frac{173}{640}\right)$	$e\left(\frac{2397}{2560}\right)$	$e\left(\frac{2383}{2560}\right)$	$e\left(\frac{557}{1280}\right)$	$e\left(\frac{419}{2560}\right)$
$\chi_{409600}(37,\cdot)$	409600.hl	20480	yes	$-1$	$1$	$e\left(\frac{9367}{20480}\right)$	$e\left(\frac{989}{2048}\right)$	$e\left(\frac{9367}{10240}\right)$	$e\left(\frac{16641}{20480}\right)$	$e\left(\frac{12979}{20480}\right)$	$e\left(\frac{587}{5120}\right)$	$e\left(\frac{8123}{20480}\right)$	$e\left(\frac{19257}{20480}\right)$	$e\left(\frac{9643}{10240}\right)$	$e\left(\frac{7621}{20480}\right)$
$\chi_{409600}(39,\cdot)$	409600.hf	10240	no	$-1$	$1$	$e\left(\frac{8039}{10240}\right)$	$e\left(\frac{717}{1024}\right)$	$e\left(\frac{2919}{5120}\right)$	$e\left(\frac{7857}{10240}\right)$	$e\left(\frac{2243}{10240}\right)$	$e\left(\frac{219}{2560}\right)$	$e\left(\frac{8011}{10240}\right)$	$e\left(\frac{4969}{10240}\right)$	$e\left(\frac{3131}{5120}\right)$	$e\left(\frac{3637}{10240}\right)$
$\chi_{409600}(41,\cdot)$	409600.hg	10240	no	$1$	$1$	$e\left(\frac{3921}{10240}\right)$	$e\left(\frac{539}{1024}\right)$	$e\left(\frac{3921}{5120}\right)$	$e\left(\frac{2903}{10240}\right)$	$e\left(\frac{8917}{10240}\right)$	$e\left(\frac{1661}{2560}\right)$	$e\left(\frac{7309}{10240}\right)$	$e\left(\frac{9311}{10240}\right)$	$e\left(\frac{3869}{5120}\right)$	$e\left(\frac{1523}{10240}\right)$
$\chi_{409600}(43,\cdot)$	409600.gn	4096	no	$1$	$1$	$e\left(\frac{2007}{4096}\right)$	$e\left(\frac{1553}{2048}\right)$	$e\left(\frac{2007}{2048}\right)$	$e\left(\frac{1985}{4096}\right)$	$e\left(\frac{2803}{4096}\right)$	$e\left(\frac{651}{1024}\right)$	$e\left(\frac{3579}{4096}\right)$	$e\left(\frac{1017}{4096}\right)$	$e\left(\frac{2027}{2048}\right)$	$e\left(\frac{1925}{4096}\right)$
$\chi_{409600}(47,\cdot)$	409600.gv	5120	no	$1$	$1$	$e\left(\frac{229}{5120}\right)$	$e\left(\frac{119}{512}\right)$	$e\left(\frac{229}{2560}\right)$	$e\left(\frac{4067}{5120}\right)$	$e\left(\frac{3513}{5120}\right)$	$e\left(\frac{449}{1280}\right)$	$e\left(\frac{3281}{5120}\right)$	$e\left(\frac{1419}{5120}\right)$	$e\left(\frac{801}{2560}\right)$	$e\left(\frac{687}{5120}\right)$
$\chi_{409600}(49,\cdot)$	409600.fk	1024	no	$1$	$1$	$e\left(\frac{335}{1024}\right)$	$e\left(\frac{217}{512}\right)$	$e\left(\frac{335}{512}\right)$	$e\left(\frac{777}{1024}\right)$	$e\left(\frac{75}{1024}\right)$	$e\left(\frac{35}{256}\right)$	$e\left(\frac{915}{1024}\right)$	$e\left(\frac{769}{1024}\right)$	$e\left(\frac{3}{512}\right)$	$e\left(\frac{1005}{1024}\right)$
$\chi_{409600}(51,\cdot)$	409600.gq	4096	no	$-1$	$1$	$e\left(\frac{541}{4096}\right)$	$e\left(\frac{1499}{2048}\right)$	$e\left(\frac{541}{2048}\right)$	$e\left(\frac{2155}{4096}\right)$	$e\left(\frac{3025}{4096}\right)$	$e\left(\frac{345}{1024}\right)$	$e\left(\frac{2601}{4096}\right)$	$e\left(\frac{3539}{4096}\right)$	$e\left(\frac{1913}{2048}\right)$	$e\left(\frac{1623}{4096}\right)$
$\chi_{409600}(53,\cdot)$	409600.hr	20480	yes	$-1$	$1$	$e\left(\frac{17131}{20480}\right)$	$e\left(\frac{1529}{2048}\right)$	$e\left(\frac{6891}{10240}\right)$	$e\left(\frac{16333}{20480}\right)$	$e\left(\frac{14167}{20480}\right)$	$e\left(\frac{1551}{5120}\right)$	$e\left(\frac{20159}{20480}\right)$	$e\left(\frac{11941}{20480}\right)$	$e\left(\frac{9199}{10240}\right)$	$e\left(\frac{10433}{20480}\right)$
$\chi_{409600}(57,\cdot)$	409600.fx	2048	no	$-1$	$1$	$e\left(\frac{375}{2048}\right)$	$e\left(\frac{113}{1024}\right)$	$e\left(\frac{375}{1024}\right)$	$e\left(\frac{289}{2048}\right)$	$e\left(\frac{787}{2048}\right)$	$e\left(\frac{299}{512}\right)$	$e\left(\frac{795}{2048}\right)$	$e\left(\frac{601}{2048}\right)$	$e\left(\frac{11}{1024}\right)$	$e\left(\frac{1125}{2048}\right)$
$\chi_{409600}(59,\cdot)$	409600.hn	20480	yes	$-1$	$1$	$e\left(\frac{1887}{20480}\right)$	$e\left(\frac{373}{2048}\right)$	$e\left(\frac{1887}{10240}\right)$	$e\left(\frac{6521}{20480}\right)$	$e\left(\frac{19099}{20480}\right)$	$e\left(\frac{627}{5120}\right)$	$e\left(\frac{10083}{20480}\right)$	$e\left(\frac{5617}{20480}\right)$	$e\left(\frac{2003}{10240}\right)$	$e\left(\frac{5661}{20480}\right)$
$\chi_{409600}(61,\cdot)$	409600.ho	20480	yes	$1$	$1$	$e\left(\frac{4413}{20480}\right)$	$e\left(\frac{703}{2048}\right)$	$e\left(\frac{4413}{10240}\right)$	$e\left(\frac{13899}{20480}\right)$	$e\left(\frac{6001}{20480}\right)$	$e\left(\frac{2553}{5120}\right)$	$e\left(\frac{19657}{20480}\right)$	$e\left(\frac{11443}{20480}\right)$	$e\left(\frac{8217}{10240}\right)$	$e\left(\frac{13239}{20480}\right)$
$\chi_{409600}(63,\cdot)$	409600.fo	1280	no	$1$	$1$	$e\left(\frac{47}{1280}\right)$	$e\left(\frac{69}{128}\right)$	$e\left(\frac{47}{640}\right)$	$e\left(\frac{361}{1280}\right)$	$e\left(\frac{299}{1280}\right)$	$e\left(\frac{307}{320}\right)$	$e\left(\frac{563}{1280}\right)$	$e\left(\frac{737}{1280}\right)$	$e\left(\frac{3}{640}\right)$	$e\left(\frac{141}{1280}\right)$
$\chi_{409600}(67,\cdot)$	409600.hq	20480	yes	$1$	$1$	$e\left(\frac{13469}{20480}\right)$	$e\left(\frac{1503}{2048}\right)$	$e\left(\frac{3229}{10240}\right)$	$e\left(\frac{9707}{20480}\right)$	$e\left(\frac{18513}{20480}\right)$	$e\left(\frac{729}{5120}\right)$	$e\left(\frac{16041}{20480}\right)$	$e\left(\frac{8019}{20480}\right)$	$e\left(\frac{4601}{10240}\right)$	$e\left(\frac{19927}{20480}\right)$
$\chi_{409600}(69,\cdot)$	409600.hp	20480	yes	$1$	$1$	$e\left(\frac{3839}{20480}\right)$	$e\left(\frac{1365}{2048}\right)$	$e\left(\frac{3839}{10240}\right)$	$e\left(\frac{13017}{20480}\right)$	$e\left(\frac{4283}{20480}\right)$	$e\left(\frac{4499}{5120}\right)$	$e\left(\frac{131}{20480}\right)$	$e\left(\frac{17489}{20480}\right)$	$e\left(\frac{9971}{10240}\right)$	$e\left(\frac{11517}{20480}\right)$
$\chi_{409600}(71,\cdot)$	409600.hh	10240	no	$-1$	$1$	$e\left(\frac{8643}{10240}\right)$	$e\left(\frac{65}{1024}\right)$	$e\left(\frac{3523}{5120}\right)$	$e\left(\frac{9909}{10240}\right)$	$e\left(\frac{911}{10240}\right)$	$e\left(\frac{263}{2560}\right)$	$e\left(\frac{567}{10240}\right)$	$e\left(\frac{9293}{10240}\right)$	$e\left(\frac{4327}{5120}\right)$	$e\left(\frac{5449}{10240}\right)$
$\chi_{409600}(73,\cdot)$	409600.hi	10240	no	$-1$	$1$	$e\left(\frac{5429}{10240}\right)$	$e\left(\frac{615}{1024}\right)$	$e\left(\frac{309}{5120}\right)$	$e\left(\frac{787}{10240}\right)$	$e\left(\frac{6473}{10240}\right)$	$e\left(\frac{529}{2560}\right)$	$e\left(\frac{1761}{10240}\right)$	$e\left(\frac{1339}{10240}\right)$	$e\left(\frac{3761}{5120}\right)$	$e\left(\frac{6047}{10240}\right)$
$\chi_{409600}(77,\cdot)$	409600.hr	20480	yes	$-1$	$1$	$e\left(\frac{7473}{20480}\right)$	$e\left(\frac{187}{2048}\right)$	$e\left(\frac{7473}{10240}\right)$	$e\left(\frac{15479}{20480}\right)$	$e\left(\frac{2101}{20480}\right)$	$e\left(\frac{4573}{5120}\right)$	$e\left(\frac{18157}{20480}\right)$	$e\left(\frac{9343}{20480}\right)$	$e\left(\frac{9597}{10240}\right)$	$e\left(\frac{1939}{20480}\right)$
$\chi_{409600}(79,\cdot)$	409600.gz	5120	no	$-1$	$1$	$e\left(\frac{2179}{5120}\right)$	$e\left(\frac{129}{512}\right)$	$e\left(\frac{2179}{2560}\right)$	$e\left(\frac{2037}{5120}\right)$	$e\left(\frac{4943}{5120}\right)$	$e\left(\frac{839}{1280}\right)$	$e\left(\frac{5111}{5120}\right)$	$e\left(\frac{3469}{5120}\right)$	$e\left(\frac{1191}{2560}\right)$	$e\left(\frac{1417}{5120}\right)$

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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	$409600$
Structure	\(C_{2}\times C_{4}\times C_{20480}\)
Order	$163840$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(13\)	\(17\)	\(19\)	\(21\)	\(23\)	\(27\)
\(\chi_{409600}(1,\cdot)\)	409600.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{409600}(3,\cdot)\)	409600.hk	20480	yes	\(1\)	\(1\)	\(e\left(\frac{14061}{20480}\right)\)	\(e\left(\frac{1359}{2048}\right)\)	\(e\left(\frac{3821}{10240}\right)\)	\(e\left(\frac{14363}{20480}\right)\)	\(e\left(\frac{2017}{20480}\right)\)	\(e\left(\frac{2281}{5120}\right)\)	\(e\left(\frac{10169}{20480}\right)\)	\(e\left(\frac{7171}{20480}\right)\)	\(e\left(\frac{5129}{10240}\right)\)	\(e\left(\frac{1223}{20480}\right)\)
\(\chi_{409600}(7,\cdot)\)	409600.gc	2048	no	\(1\)	\(1\)	\(e\left(\frac{1359}{2048}\right)\)	\(e\left(\frac{217}{1024}\right)\)	\(e\left(\frac{335}{1024}\right)\)	\(e\left(\frac{1801}{2048}\right)\)	\(e\left(\frac{75}{2048}\right)\)	\(e\left(\frac{35}{512}\right)\)	\(e\left(\frac{915}{2048}\right)\)	\(e\left(\frac{1793}{2048}\right)\)	\(e\left(\frac{3}{1024}\right)\)	\(e\left(\frac{2029}{2048}\right)\)
\(\chi_{409600}(9,\cdot)\)	409600.he	10240	no	\(1\)	\(1\)	\(e\left(\frac{3821}{10240}\right)\)	\(e\left(\frac{335}{1024}\right)\)	\(e\left(\frac{3821}{5120}\right)\)	\(e\left(\frac{4123}{10240}\right)\)	\(e\left(\frac{2017}{10240}\right)\)	\(e\left(\frac{2281}{2560}\right)\)	\(e\left(\frac{10169}{10240}\right)\)	\(e\left(\frac{7171}{10240}\right)\)	\(e\left(\frac{9}{5120}\right)\)	\(e\left(\frac{1223}{10240}\right)\)
\(\chi_{409600}(11,\cdot)\)	409600.hm	20480	yes	\(-1\)	\(1\)	\(e\left(\frac{14363}{20480}\right)\)	\(e\left(\frac{1801}{2048}\right)\)	\(e\left(\frac{4123}{10240}\right)\)	\(e\left(\frac{17949}{20480}\right)\)	\(e\left(\frac{1351}{20480}\right)\)	\(e\left(\frac{4223}{5120}\right)\)	\(e\left(\frac{9007}{20480}\right)\)	\(e\left(\frac{11893}{20480}\right)\)	\(e\left(\frac{9567}{10240}\right)\)	\(e\left(\frac{2129}{20480}\right)\)
\(\chi_{409600}(13,\cdot)\)	409600.hl	20480	yes	\(-1\)	\(1\)	\(e\left(\frac{2017}{20480}\right)\)	\(e\left(\frac{75}{2048}\right)\)	\(e\left(\frac{2017}{10240}\right)\)	\(e\left(\frac{1351}{20480}\right)\)	\(e\left(\frac{2469}{20480}\right)\)	\(e\left(\frac{3277}{5120}\right)\)	\(e\left(\frac{5853}{20480}\right)\)	\(e\left(\frac{2767}{20480}\right)\)	\(e\left(\frac{1133}{10240}\right)\)	\(e\left(\frac{6051}{20480}\right)\)
\(\chi_{409600}(17,\cdot)\)	409600.hb	5120	no	\(-1\)	\(1\)	\(e\left(\frac{2281}{5120}\right)\)	\(e\left(\frac{35}{512}\right)\)	\(e\left(\frac{2281}{2560}\right)\)	\(e\left(\frac{4223}{5120}\right)\)	\(e\left(\frac{3277}{5120}\right)\)	\(e\left(\frac{1141}{1280}\right)\)	\(e\left(\frac{709}{5120}\right)\)	\(e\left(\frac{2631}{5120}\right)\)	\(e\left(\frac{1109}{2560}\right)\)	\(e\left(\frac{1723}{5120}\right)\)
\(\chi_{409600}(19,\cdot)\)	409600.hn	20480	yes	\(-1\)	\(1\)	\(e\left(\frac{10169}{20480}\right)\)	\(e\left(\frac{915}{2048}\right)\)	\(e\left(\frac{10169}{10240}\right)\)	\(e\left(\frac{9007}{20480}\right)\)	\(e\left(\frac{5853}{20480}\right)\)	\(e\left(\frac{709}{5120}\right)\)	\(e\left(\frac{18261}{20480}\right)\)	\(e\left(\frac{19319}{20480}\right)\)	\(e\left(\frac{5221}{10240}\right)\)	\(e\left(\frac{10027}{20480}\right)\)
\(\chi_{409600}(21,\cdot)\)	409600.ho	20480	yes	\(1\)	\(1\)	\(e\left(\frac{7171}{20480}\right)\)	\(e\left(\frac{1793}{2048}\right)\)	\(e\left(\frac{7171}{10240}\right)\)	\(e\left(\frac{11893}{20480}\right)\)	\(e\left(\frac{2767}{20480}\right)\)	\(e\left(\frac{2631}{5120}\right)\)	\(e\left(\frac{19319}{20480}\right)\)	\(e\left(\frac{4621}{20480}\right)\)	\(e\left(\frac{5159}{10240}\right)\)	\(e\left(\frac{1033}{20480}\right)\)
\(\chi_{409600}(23,\cdot)\)	409600.hd	10240	no	\(1\)	\(1\)	\(e\left(\frac{5129}{10240}\right)\)	\(e\left(\frac{3}{1024}\right)\)	\(e\left(\frac{9}{5120}\right)\)	\(e\left(\frac{9567}{10240}\right)\)	\(e\left(\frac{1133}{10240}\right)\)	\(e\left(\frac{1109}{2560}\right)\)	\(e\left(\frac{5221}{10240}\right)\)	\(e\left(\frac{5159}{10240}\right)\)	\(e\left(\frac{2421}{5120}\right)\)	\(e\left(\frac{5147}{10240}\right)\)
\(\chi_{409600}(27,\cdot)\)	409600.hk	20480	yes	\(1\)	\(1\)	\(e\left(\frac{1223}{20480}\right)\)	\(e\left(\frac{2029}{2048}\right)\)	\(e\left(\frac{1223}{10240}\right)\)	\(e\left(\frac{2129}{20480}\right)\)	\(e\left(\frac{6051}{20480}\right)\)	\(e\left(\frac{1723}{5120}\right)\)	\(e\left(\frac{10027}{20480}\right)\)	\(e\left(\frac{1033}{20480}\right)\)	\(e\left(\frac{5147}{10240}\right)\)	\(e\left(\frac{3669}{20480}\right)\)
\(\chi_{409600}(29,\cdot)\)	409600.hp	20480	yes	\(1\)	\(1\)	\(e\left(\frac{661}{20480}\right)\)	\(e\left(\frac{1159}{2048}\right)\)	\(e\left(\frac{661}{10240}\right)\)	\(e\left(\frac{8883}{20480}\right)\)	\(e\left(\frac{9257}{20480}\right)\)	\(e\left(\frac{4721}{5120}\right)\)	\(e\left(\frac{19649}{20480}\right)\)	\(e\left(\frac{12251}{20480}\right)\)	\(e\left(\frac{7569}{10240}\right)\)	\(e\left(\frac{1983}{20480}\right)\)
\(\chi_{409600}(31,\cdot)\)	409600.gg	2560	no	\(-1\)	\(1\)	\(e\left(\frac{383}{2560}\right)\)	\(e\left(\frac{85}{256}\right)\)	\(e\left(\frac{383}{1280}\right)\)	\(e\left(\frac{89}{2560}\right)\)	\(e\left(\frac{571}{2560}\right)\)	\(e\left(\frac{403}{640}\right)\)	\(e\left(\frac{2307}{2560}\right)\)	\(e\left(\frac{1233}{2560}\right)\)	\(e\left(\frac{1267}{1280}\right)\)	\(e\left(\frac{1149}{2560}\right)\)
\(\chi_{409600}(33,\cdot)\)	409600.gl	2560	no	\(-1\)	\(1\)	\(e\left(\frac{993}{2560}\right)\)	\(e\left(\frac{139}{256}\right)\)	\(e\left(\frac{993}{1280}\right)\)	\(e\left(\frac{1479}{2560}\right)\)	\(e\left(\frac{421}{2560}\right)\)	\(e\left(\frac{173}{640}\right)\)	\(e\left(\frac{2397}{2560}\right)\)	\(e\left(\frac{2383}{2560}\right)\)	\(e\left(\frac{557}{1280}\right)\)	\(e\left(\frac{419}{2560}\right)\)
\(\chi_{409600}(37,\cdot)\)	409600.hl	20480	yes	\(-1\)	\(1\)	\(e\left(\frac{9367}{20480}\right)\)	\(e\left(\frac{989}{2048}\right)\)	\(e\left(\frac{9367}{10240}\right)\)	\(e\left(\frac{16641}{20480}\right)\)	\(e\left(\frac{12979}{20480}\right)\)	\(e\left(\frac{587}{5120}\right)\)	\(e\left(\frac{8123}{20480}\right)\)	\(e\left(\frac{19257}{20480}\right)\)	\(e\left(\frac{9643}{10240}\right)\)	\(e\left(\frac{7621}{20480}\right)\)
\(\chi_{409600}(39,\cdot)\)	409600.hf	10240	no	\(-1\)	\(1\)	\(e\left(\frac{8039}{10240}\right)\)	\(e\left(\frac{717}{1024}\right)\)	\(e\left(\frac{2919}{5120}\right)\)	\(e\left(\frac{7857}{10240}\right)\)	\(e\left(\frac{2243}{10240}\right)\)	\(e\left(\frac{219}{2560}\right)\)	\(e\left(\frac{8011}{10240}\right)\)	\(e\left(\frac{4969}{10240}\right)\)	\(e\left(\frac{3131}{5120}\right)\)	\(e\left(\frac{3637}{10240}\right)\)
\(\chi_{409600}(41,\cdot)\)	409600.hg	10240	no	\(1\)	\(1\)	\(e\left(\frac{3921}{10240}\right)\)	\(e\left(\frac{539}{1024}\right)\)	\(e\left(\frac{3921}{5120}\right)\)	\(e\left(\frac{2903}{10240}\right)\)	\(e\left(\frac{8917}{10240}\right)\)	\(e\left(\frac{1661}{2560}\right)\)	\(e\left(\frac{7309}{10240}\right)\)	\(e\left(\frac{9311}{10240}\right)\)	\(e\left(\frac{3869}{5120}\right)\)	\(e\left(\frac{1523}{10240}\right)\)
\(\chi_{409600}(43,\cdot)\)	409600.gn	4096	no	\(1\)	\(1\)	\(e\left(\frac{2007}{4096}\right)\)	\(e\left(\frac{1553}{2048}\right)\)	\(e\left(\frac{2007}{2048}\right)\)	\(e\left(\frac{1985}{4096}\right)\)	\(e\left(\frac{2803}{4096}\right)\)	\(e\left(\frac{651}{1024}\right)\)	\(e\left(\frac{3579}{4096}\right)\)	\(e\left(\frac{1017}{4096}\right)\)	\(e\left(\frac{2027}{2048}\right)\)	\(e\left(\frac{1925}{4096}\right)\)
\(\chi_{409600}(47,\cdot)\)	409600.gv	5120	no	\(1\)	\(1\)	\(e\left(\frac{229}{5120}\right)\)	\(e\left(\frac{119}{512}\right)\)	\(e\left(\frac{229}{2560}\right)\)	\(e\left(\frac{4067}{5120}\right)\)	\(e\left(\frac{3513}{5120}\right)\)	\(e\left(\frac{449}{1280}\right)\)	\(e\left(\frac{3281}{5120}\right)\)	\(e\left(\frac{1419}{5120}\right)\)	\(e\left(\frac{801}{2560}\right)\)	\(e\left(\frac{687}{5120}\right)\)
\(\chi_{409600}(49,\cdot)\)	409600.fk	1024	no	\(1\)	\(1\)	\(e\left(\frac{335}{1024}\right)\)	\(e\left(\frac{217}{512}\right)\)	\(e\left(\frac{335}{512}\right)\)	\(e\left(\frac{777}{1024}\right)\)	\(e\left(\frac{75}{1024}\right)\)	\(e\left(\frac{35}{256}\right)\)	\(e\left(\frac{915}{1024}\right)\)	\(e\left(\frac{769}{1024}\right)\)	\(e\left(\frac{3}{512}\right)\)	\(e\left(\frac{1005}{1024}\right)\)
\(\chi_{409600}(51,\cdot)\)	409600.gq	4096	no	\(-1\)	\(1\)	\(e\left(\frac{541}{4096}\right)\)	\(e\left(\frac{1499}{2048}\right)\)	\(e\left(\frac{541}{2048}\right)\)	\(e\left(\frac{2155}{4096}\right)\)	\(e\left(\frac{3025}{4096}\right)\)	\(e\left(\frac{345}{1024}\right)\)	\(e\left(\frac{2601}{4096}\right)\)	\(e\left(\frac{3539}{4096}\right)\)	\(e\left(\frac{1913}{2048}\right)\)	\(e\left(\frac{1623}{4096}\right)\)
\(\chi_{409600}(53,\cdot)\)	409600.hr	20480	yes	\(-1\)	\(1\)	\(e\left(\frac{17131}{20480}\right)\)	\(e\left(\frac{1529}{2048}\right)\)	\(e\left(\frac{6891}{10240}\right)\)	\(e\left(\frac{16333}{20480}\right)\)	\(e\left(\frac{14167}{20480}\right)\)	\(e\left(\frac{1551}{5120}\right)\)	\(e\left(\frac{20159}{20480}\right)\)	\(e\left(\frac{11941}{20480}\right)\)	\(e\left(\frac{9199}{10240}\right)\)	\(e\left(\frac{10433}{20480}\right)\)
\(\chi_{409600}(57,\cdot)\)	409600.fx	2048	no	\(-1\)	\(1\)	\(e\left(\frac{375}{2048}\right)\)	\(e\left(\frac{113}{1024}\right)\)	\(e\left(\frac{375}{1024}\right)\)	\(e\left(\frac{289}{2048}\right)\)	\(e\left(\frac{787}{2048}\right)\)	\(e\left(\frac{299}{512}\right)\)	\(e\left(\frac{795}{2048}\right)\)	\(e\left(\frac{601}{2048}\right)\)	\(e\left(\frac{11}{1024}\right)\)	\(e\left(\frac{1125}{2048}\right)\)
\(\chi_{409600}(59,\cdot)\)	409600.hn	20480	yes	\(-1\)	\(1\)	\(e\left(\frac{1887}{20480}\right)\)	\(e\left(\frac{373}{2048}\right)\)	\(e\left(\frac{1887}{10240}\right)\)	\(e\left(\frac{6521}{20480}\right)\)	\(e\left(\frac{19099}{20480}\right)\)	\(e\left(\frac{627}{5120}\right)\)	\(e\left(\frac{10083}{20480}\right)\)	\(e\left(\frac{5617}{20480}\right)\)	\(e\left(\frac{2003}{10240}\right)\)	\(e\left(\frac{5661}{20480}\right)\)
\(\chi_{409600}(61,\cdot)\)	409600.ho	20480	yes	\(1\)	\(1\)	\(e\left(\frac{4413}{20480}\right)\)	\(e\left(\frac{703}{2048}\right)\)	\(e\left(\frac{4413}{10240}\right)\)	\(e\left(\frac{13899}{20480}\right)\)	\(e\left(\frac{6001}{20480}\right)\)	\(e\left(\frac{2553}{5120}\right)\)	\(e\left(\frac{19657}{20480}\right)\)	\(e\left(\frac{11443}{20480}\right)\)	\(e\left(\frac{8217}{10240}\right)\)	\(e\left(\frac{13239}{20480}\right)\)
\(\chi_{409600}(63,\cdot)\)	409600.fo	1280	no	\(1\)	\(1\)	\(e\left(\frac{47}{1280}\right)\)	\(e\left(\frac{69}{128}\right)\)	\(e\left(\frac{47}{640}\right)\)	\(e\left(\frac{361}{1280}\right)\)	\(e\left(\frac{299}{1280}\right)\)	\(e\left(\frac{307}{320}\right)\)	\(e\left(\frac{563}{1280}\right)\)	\(e\left(\frac{737}{1280}\right)\)	\(e\left(\frac{3}{640}\right)\)	\(e\left(\frac{141}{1280}\right)\)
\(\chi_{409600}(67,\cdot)\)	409600.hq	20480	yes	\(1\)	\(1\)	\(e\left(\frac{13469}{20480}\right)\)	\(e\left(\frac{1503}{2048}\right)\)	\(e\left(\frac{3229}{10240}\right)\)	\(e\left(\frac{9707}{20480}\right)\)	\(e\left(\frac{18513}{20480}\right)\)	\(e\left(\frac{729}{5120}\right)\)	\(e\left(\frac{16041}{20480}\right)\)	\(e\left(\frac{8019}{20480}\right)\)	\(e\left(\frac{4601}{10240}\right)\)	\(e\left(\frac{19927}{20480}\right)\)
\(\chi_{409600}(69,\cdot)\)	409600.hp	20480	yes	\(1\)	\(1\)	\(e\left(\frac{3839}{20480}\right)\)	\(e\left(\frac{1365}{2048}\right)\)	\(e\left(\frac{3839}{10240}\right)\)	\(e\left(\frac{13017}{20480}\right)\)	\(e\left(\frac{4283}{20480}\right)\)	\(e\left(\frac{4499}{5120}\right)\)	\(e\left(\frac{131}{20480}\right)\)	\(e\left(\frac{17489}{20480}\right)\)	\(e\left(\frac{9971}{10240}\right)\)	\(e\left(\frac{11517}{20480}\right)\)
\(\chi_{409600}(71,\cdot)\)	409600.hh	10240	no	\(-1\)	\(1\)	\(e\left(\frac{8643}{10240}\right)\)	\(e\left(\frac{65}{1024}\right)\)	\(e\left(\frac{3523}{5120}\right)\)	\(e\left(\frac{9909}{10240}\right)\)	\(e\left(\frac{911}{10240}\right)\)	\(e\left(\frac{263}{2560}\right)\)	\(e\left(\frac{567}{10240}\right)\)	\(e\left(\frac{9293}{10240}\right)\)	\(e\left(\frac{4327}{5120}\right)\)	\(e\left(\frac{5449}{10240}\right)\)
\(\chi_{409600}(73,\cdot)\)	409600.hi	10240	no	\(-1\)	\(1\)	\(e\left(\frac{5429}{10240}\right)\)	\(e\left(\frac{615}{1024}\right)\)	\(e\left(\frac{309}{5120}\right)\)	\(e\left(\frac{787}{10240}\right)\)	\(e\left(\frac{6473}{10240}\right)\)	\(e\left(\frac{529}{2560}\right)\)	\(e\left(\frac{1761}{10240}\right)\)	\(e\left(\frac{1339}{10240}\right)\)	\(e\left(\frac{3761}{5120}\right)\)	\(e\left(\frac{6047}{10240}\right)\)
\(\chi_{409600}(77,\cdot)\)	409600.hr	20480	yes	\(-1\)	\(1\)	\(e\left(\frac{7473}{20480}\right)\)	\(e\left(\frac{187}{2048}\right)\)	\(e\left(\frac{7473}{10240}\right)\)	\(e\left(\frac{15479}{20480}\right)\)	\(e\left(\frac{2101}{20480}\right)\)	\(e\left(\frac{4573}{5120}\right)\)	\(e\left(\frac{18157}{20480}\right)\)	\(e\left(\frac{9343}{20480}\right)\)	\(e\left(\frac{9597}{10240}\right)\)	\(e\left(\frac{1939}{20480}\right)\)
\(\chi_{409600}(79,\cdot)\)	409600.gz	5120	no	\(-1\)	\(1\)	\(e\left(\frac{2179}{5120}\right)\)	\(e\left(\frac{129}{512}\right)\)	\(e\left(\frac{2179}{2560}\right)\)	\(e\left(\frac{2037}{5120}\right)\)	\(e\left(\frac{4943}{5120}\right)\)	\(e\left(\frac{839}{1280}\right)\)	\(e\left(\frac{5111}{5120}\right)\)	\(e\left(\frac{3469}{5120}\right)\)	\(e\left(\frac{1191}{2560}\right)\)	\(e\left(\frac{1417}{5120}\right)\)

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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.