LMFDB - Group of Dirichlet characters of modulus 164025

sage:H = DirichletGroup(164025)

pari:g = idealstar(,164025,2)

Character group

sage:G.order() pari:g.no
Order	=	87480
sage:H.invariants() pari:g.cyc
Structure	=	$C_{2}\times C_{43740}$
sage:H.gens() pari:g.gen
Generators	=	$\chi_{164025}(59051,\cdot)$, $\chi_{164025}(104977,\cdot)$

First 32 of 87480 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	$-1$	$1$	$2$	$4$	$7$	$8$	$11$	$13$	$14$	$16$	$17$	$19$
$\chi_{164025}(1,\cdot)$	164025.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{164025}(2,\cdot)$	164025.dq	43740	yes	$1$	$1$	$e\left(\frac{2197}{43740}\right)$	$e\left(\frac{2197}{21870}\right)$	$e\left(\frac{5891}{8748}\right)$	$e\left(\frac{2197}{14580}\right)$	$e\left(\frac{14051}{21870}\right)$	$e\left(\frac{25433}{43740}\right)$	$e\left(\frac{7913}{10935}\right)$	$e\left(\frac{2197}{10935}\right)$	$e\left(\frac{4727}{14580}\right)$	$e\left(\frac{7091}{7290}\right)$
$\chi_{164025}(4,\cdot)$	164025.dp	21870	yes	$1$	$1$	$e\left(\frac{2197}{21870}\right)$	$e\left(\frac{2197}{10935}\right)$	$e\left(\frac{1517}{4374}\right)$	$e\left(\frac{2197}{7290}\right)$	$e\left(\frac{3116}{10935}\right)$	$e\left(\frac{3563}{21870}\right)$	$e\left(\frac{4891}{10935}\right)$	$e\left(\frac{4394}{10935}\right)$	$e\left(\frac{4727}{7290}\right)$	$e\left(\frac{3446}{3645}\right)$
$\chi_{164025}(7,\cdot)$	164025.di	8748	no	$-1$	$1$	$e\left(\frac{5891}{8748}\right)$	$e\left(\frac{1517}{4374}\right)$	$e\left(\frac{3563}{8748}\right)$	$e\left(\frac{59}{2916}\right)$	$e\left(\frac{590}{2187}\right)$	$e\left(\frac{1849}{8748}\right)$	$e\left(\frac{353}{4374}\right)$	$e\left(\frac{1517}{2187}\right)$	$e\left(\frac{2593}{2916}\right)$	$e\left(\frac{211}{1458}\right)$
$\chi_{164025}(8,\cdot)$	164025.dm	14580	no	$1$	$1$	$e\left(\frac{2197}{14580}\right)$	$e\left(\frac{2197}{7290}\right)$	$e\left(\frac{59}{2916}\right)$	$e\left(\frac{2197}{4860}\right)$	$e\left(\frac{6761}{7290}\right)$	$e\left(\frac{10853}{14580}\right)$	$e\left(\frac{623}{3645}\right)$	$e\left(\frac{2197}{3645}\right)$	$e\left(\frac{4727}{4860}\right)$	$e\left(\frac{2231}{2430}\right)$
$\chi_{164025}(11,\cdot)$	164025.do	21870	yes	$-1$	$1$	$e\left(\frac{14051}{21870}\right)$	$e\left(\frac{3116}{10935}\right)$	$e\left(\frac{590}{2187}\right)$	$e\left(\frac{6761}{7290}\right)$	$e\left(\frac{7271}{21870}\right)$	$e\left(\frac{1367}{10935}\right)$	$e\left(\frac{19951}{21870}\right)$	$e\left(\frac{6232}{10935}\right)$	$e\left(\frac{6331}{7290}\right)$	$e\left(\frac{1123}{3645}\right)$
$\chi_{164025}(13,\cdot)$	164025.dr	43740	yes	$-1$	$1$	$e\left(\frac{25433}{43740}\right)$	$e\left(\frac{3563}{21870}\right)$	$e\left(\frac{1849}{8748}\right)$	$e\left(\frac{10853}{14580}\right)$	$e\left(\frac{1367}{10935}\right)$	$e\left(\frac{6067}{43740}\right)$	$e\left(\frac{17339}{21870}\right)$	$e\left(\frac{3563}{10935}\right)$	$e\left(\frac{7603}{14580}\right)$	$e\left(\frac{6589}{7290}\right)$
$\chi_{164025}(14,\cdot)$	164025.dn	21870	yes	$-1$	$1$	$e\left(\frac{7913}{10935}\right)$	$e\left(\frac{4891}{10935}\right)$	$e\left(\frac{353}{4374}\right)$	$e\left(\frac{623}{3645}\right)$	$e\left(\frac{19951}{21870}\right)$	$e\left(\frac{17339}{21870}\right)$	$e\left(\frac{17591}{21870}\right)$	$e\left(\frac{9782}{10935}\right)$	$e\left(\frac{778}{3645}\right)$	$e\left(\frac{428}{3645}\right)$
$\chi_{164025}(16,\cdot)$	164025.dk	10935	yes	$1$	$1$	$e\left(\frac{2197}{10935}\right)$	$e\left(\frac{4394}{10935}\right)$	$e\left(\frac{1517}{2187}\right)$	$e\left(\frac{2197}{3645}\right)$	$e\left(\frac{6232}{10935}\right)$	$e\left(\frac{3563}{10935}\right)$	$e\left(\frac{9782}{10935}\right)$	$e\left(\frac{8788}{10935}\right)$	$e\left(\frac{1082}{3645}\right)$	$e\left(\frac{3247}{3645}\right)$
$\chi_{164025}(17,\cdot)$	164025.dm	14580	no	$1$	$1$	$e\left(\frac{4727}{14580}\right)$	$e\left(\frac{4727}{7290}\right)$	$e\left(\frac{2593}{2916}\right)$	$e\left(\frac{4727}{4860}\right)$	$e\left(\frac{6331}{7290}\right)$	$e\left(\frac{7603}{14580}\right)$	$e\left(\frac{778}{3645}\right)$	$e\left(\frac{1082}{3645}\right)$	$e\left(\frac{3397}{4860}\right)$	$e\left(\frac{241}{2430}\right)$
$\chi_{164025}(19,\cdot)$	164025.df	7290	no	$1$	$1$	$e\left(\frac{7091}{7290}\right)$	$e\left(\frac{3446}{3645}\right)$	$e\left(\frac{211}{1458}\right)$	$e\left(\frac{2231}{2430}\right)$	$e\left(\frac{1123}{3645}\right)$	$e\left(\frac{6589}{7290}\right)$	$e\left(\frac{428}{3645}\right)$	$e\left(\frac{3247}{3645}\right)$	$e\left(\frac{241}{2430}\right)$	$e\left(\frac{388}{1215}\right)$
$\chi_{164025}(22,\cdot)$	164025.dr	43740	yes	$-1$	$1$	$e\left(\frac{30299}{43740}\right)$	$e\left(\frac{8429}{21870}\right)$	$e\left(\frac{8251}{8748}\right)$	$e\left(\frac{1139}{14580}\right)$	$e\left(\frac{10661}{10935}\right)$	$e\left(\frac{30901}{43740}\right)$	$e\left(\frac{13907}{21870}\right)$	$e\left(\frac{8429}{10935}\right)$	$e\left(\frac{2809}{14580}\right)$	$e\left(\frac{2047}{7290}\right)$
$\chi_{164025}(23,\cdot)$	164025.dq	43740	yes	$1$	$1$	$e\left(\frac{32807}{43740}\right)$	$e\left(\frac{10937}{21870}\right)$	$e\left(\frac{2053}{8748}\right)$	$e\left(\frac{3647}{14580}\right)$	$e\left(\frac{21181}{21870}\right)$	$e\left(\frac{42703}{43740}\right)$	$e\left(\frac{10768}{10935}\right)$	$e\left(\frac{2}{10935}\right)$	$e\left(\frac{1237}{14580}\right)$	$e\left(\frac{3751}{7290}\right)$
$\chi_{164025}(26,\cdot)$	164025.cd	486	no	$-1$	$1$	$e\left(\frac{307}{486}\right)$	$e\left(\frac{64}{243}\right)$	$e\left(\frac{215}{243}\right)$	$e\left(\frac{145}{162}\right)$	$e\left(\frac{373}{486}\right)$	$e\left(\frac{175}{243}\right)$	$e\left(\frac{251}{486}\right)$	$e\left(\frac{128}{243}\right)$	$e\left(\frac{137}{162}\right)$	$e\left(\frac{71}{81}\right)$
$\chi_{164025}(28,\cdot)$	164025.de	4860	no	$-1$	$1$	$e\left(\frac{3761}{4860}\right)$	$e\left(\frac{1331}{2430}\right)$	$e\left(\frac{733}{972}\right)$	$e\left(\frac{521}{1620}\right)$	$e\left(\frac{674}{1215}\right)$	$e\left(\frac{1819}{4860}\right)$	$e\left(\frac{1283}{2430}\right)$	$e\left(\frac{116}{1215}\right)$	$e\left(\frac{871}{1620}\right)$	$e\left(\frac{73}{810}\right)$
$\chi_{164025}(29,\cdot)$	164025.dn	21870	yes	$-1$	$1$	$e\left(\frac{4021}{10935}\right)$	$e\left(\frac{8042}{10935}\right)$	$e\left(\frac{1375}{4374}\right)$	$e\left(\frac{376}{3645}\right)$	$e\left(\frac{3107}{21870}\right)$	$e\left(\frac{7393}{21870}\right)$	$e\left(\frac{14917}{21870}\right)$	$e\left(\frac{5149}{10935}\right)$	$e\left(\frac{2921}{3645}\right)$	$e\left(\frac{3406}{3645}\right)$
$\chi_{164025}(31,\cdot)$	164025.dk	10935	yes	$1$	$1$	$e\left(\frac{10094}{10935}\right)$	$e\left(\frac{9253}{10935}\right)$	$e\left(\frac{1672}{2187}\right)$	$e\left(\frac{2804}{3645}\right)$	$e\left(\frac{10829}{10935}\right)$	$e\left(\frac{4126}{10935}\right)$	$e\left(\frac{7519}{10935}\right)$	$e\left(\frac{7571}{10935}\right)$	$e\left(\frac{2899}{3645}\right)$	$e\left(\frac{1979}{3645}\right)$
$\chi_{164025}(32,\cdot)$	164025.dj	8748	no	$1$	$1$	$e\left(\frac{2197}{8748}\right)$	$e\left(\frac{2197}{4374}\right)$	$e\left(\frac{3211}{8748}\right)$	$e\left(\frac{2197}{2916}\right)$	$e\left(\frac{929}{4374}\right)$	$e\left(\frac{7937}{8748}\right)$	$e\left(\frac{1352}{2187}\right)$	$e\left(\frac{10}{2187}\right)$	$e\left(\frac{1811}{2916}\right)$	$e\left(\frac{1259}{1458}\right)$
$\chi_{164025}(34,\cdot)$	164025.dp	21870	yes	$1$	$1$	$e\left(\frac{8189}{21870}\right)$	$e\left(\frac{8189}{10935}\right)$	$e\left(\frac{2461}{4374}\right)$	$e\left(\frac{899}{7290}\right)$	$e\left(\frac{5587}{10935}\right)$	$e\left(\frac{2251}{21870}\right)$	$e\left(\frac{10247}{10935}\right)$	$e\left(\frac{5443}{10935}\right)$	$e\left(\frac{169}{7290}\right)$	$e\left(\frac{262}{3645}\right)$
$\chi_{164025}(37,\cdot)$	164025.dl	14580	no	$-1$	$1$	$e\left(\frac{13901}{14580}\right)$	$e\left(\frac{6611}{7290}\right)$	$e\left(\frac{1753}{2916}\right)$	$e\left(\frac{4181}{4860}\right)$	$e\left(\frac{1229}{3645}\right)$	$e\left(\frac{319}{14580}\right)$	$e\left(\frac{4043}{7290}\right)$	$e\left(\frac{2966}{3645}\right)$	$e\left(\frac{2251}{4860}\right)$	$e\left(\frac{463}{2430}\right)$
$\chi_{164025}(38,\cdot)$	164025.dq	43740	yes	$1$	$1$	$e\left(\frac{1003}{43740}\right)$	$e\left(\frac{1003}{21870}\right)$	$e\left(\frac{7157}{8748}\right)$	$e\left(\frac{1003}{14580}\right)$	$e\left(\frac{20789}{21870}\right)$	$e\left(\frac{21227}{43740}\right)$	$e\left(\frac{9197}{10935}\right)$	$e\left(\frac{1003}{10935}\right)$	$e\left(\frac{6173}{14580}\right)$	$e\left(\frac{2129}{7290}\right)$
$\chi_{164025}(41,\cdot)$	164025.do	21870	yes	$-1$	$1$	$e\left(\frac{3019}{21870}\right)$	$e\left(\frac{3019}{10935}\right)$	$e\left(\frac{559}{2187}\right)$	$e\left(\frac{3019}{7290}\right)$	$e\left(\frac{19429}{21870}\right)$	$e\left(\frac{7378}{10935}\right)$	$e\left(\frac{8609}{21870}\right)$	$e\left(\frac{6038}{10935}\right)$	$e\left(\frac{6479}{7290}\right)$	$e\left(\frac{3272}{3645}\right)$
$\chi_{164025}(43,\cdot)$	164025.di	8748	no	$-1$	$1$	$e\left(\frac{2609}{8748}\right)$	$e\left(\frac{2609}{4374}\right)$	$e\left(\frac{785}{8748}\right)$	$e\left(\frac{2609}{2916}\right)$	$e\left(\frac{575}{2187}\right)$	$e\left(\frac{4267}{8748}\right)$	$e\left(\frac{1697}{4374}\right)$	$e\left(\frac{422}{2187}\right)$	$e\left(\frac{1483}{2916}\right)$	$e\left(\frac{1225}{1458}\right)$
$\chi_{164025}(44,\cdot)$	164025.dh	7290	no	$-1$	$1$	$e\left(\frac{2708}{3645}\right)$	$e\left(\frac{1771}{3645}\right)$	$e\left(\frac{899}{1458}\right)$	$e\left(\frac{278}{1215}\right)$	$e\left(\frac{4501}{7290}\right)$	$e\left(\frac{2099}{7290}\right)$	$e\left(\frac{2621}{7290}\right)$	$e\left(\frac{3542}{3645}\right)$	$e\left(\frac{628}{1215}\right)$	$e\left(\frac{308}{1215}\right)$
$\chi_{164025}(46,\cdot)$	164025.cz	3645	no	$1$	$1$	$e\left(\frac{2917}{3645}\right)$	$e\left(\frac{2189}{3645}\right)$	$e\left(\frac{662}{729}\right)$	$e\left(\frac{487}{1215}\right)$	$e\left(\frac{2227}{3645}\right)$	$e\left(\frac{2033}{3645}\right)$	$e\left(\frac{2582}{3645}\right)$	$e\left(\frac{733}{3645}\right)$	$e\left(\frac{497}{1215}\right)$	$e\left(\frac{592}{1215}\right)$
$\chi_{164025}(47,\cdot)$	164025.dq	43740	yes	$1$	$1$	$e\left(\frac{41029}{43740}\right)$	$e\left(\frac{19159}{21870}\right)$	$e\left(\frac{2303}{8748}\right)$	$e\left(\frac{11869}{14580}\right)$	$e\left(\frac{20867}{21870}\right)$	$e\left(\frac{11441}{43740}\right)$	$e\left(\frac{2201}{10935}\right)$	$e\left(\frac{8224}{10935}\right)$	$e\left(\frac{9059}{14580}\right)$	$e\left(\frac{2117}{7290}\right)$
$\chi_{164025}(49,\cdot)$	164025.da	4374	no	$1$	$1$	$e\left(\frac{1517}{4374}\right)$	$e\left(\frac{1517}{2187}\right)$	$e\left(\frac{3563}{4374}\right)$	$e\left(\frac{59}{1458}\right)$	$e\left(\frac{1180}{2187}\right)$	$e\left(\frac{1849}{4374}\right)$	$e\left(\frac{353}{2187}\right)$	$e\left(\frac{847}{2187}\right)$	$e\left(\frac{1135}{1458}\right)$	$e\left(\frac{211}{729}\right)$
$\chi_{164025}(52,\cdot)$	164025.dr	43740	yes	$-1$	$1$	$e\left(\frac{29827}{43740}\right)$	$e\left(\frac{7957}{21870}\right)$	$e\left(\frac{4883}{8748}\right)$	$e\left(\frac{667}{14580}\right)$	$e\left(\frac{4483}{10935}\right)$	$e\left(\frac{13193}{43740}\right)$	$e\left(\frac{5251}{21870}\right)$	$e\left(\frac{7957}{10935}\right)$	$e\left(\frac{2477}{14580}\right)$	$e\left(\frac{6191}{7290}\right)$
$\chi_{164025}(53,\cdot)$	164025.dd	4860	no	$1$	$1$	$e\left(\frac{3251}{4860}\right)$	$e\left(\frac{821}{2430}\right)$	$e\left(\frac{397}{972}\right)$	$e\left(\frac{11}{1620}\right)$	$e\left(\frac{2083}{2430}\right)$	$e\left(\frac{2599}{4860}\right)$	$e\left(\frac{94}{1215}\right)$	$e\left(\frac{821}{1215}\right)$	$e\left(\frac{121}{1620}\right)$	$e\left(\frac{583}{810}\right)$
$\chi_{164025}(56,\cdot)$	164025.do	21870	yes	$-1$	$1$	$e\left(\frac{18023}{21870}\right)$	$e\left(\frac{7088}{10935}\right)$	$e\left(\frac{935}{2187}\right)$	$e\left(\frac{3443}{7290}\right)$	$e\left(\frac{4313}{21870}\right)$	$e\left(\frac{10451}{10935}\right)$	$e\left(\frac{5503}{21870}\right)$	$e\left(\frac{3241}{10935}\right)$	$e\left(\frac{6283}{7290}\right)$	$e\left(\frac{229}{3645}\right)$
$\chi_{164025}(58,\cdot)$	164025.dr	43740	yes	$-1$	$1$	$e\left(\frac{18281}{43740}\right)$	$e\left(\frac{18281}{21870}\right)$	$e\left(\frac{8641}{8748}\right)$	$e\left(\frac{3701}{14580}\right)$	$e\left(\frac{8579}{10935}\right)$	$e\left(\frac{40219}{43740}\right)$	$e\left(\frac{8873}{21870}\right)$	$e\left(\frac{7346}{10935}\right)$	$e\left(\frac{1831}{14580}\right)$	$e\left(\frac{6613}{7290}\right)$
$\chi_{164025}(59,\cdot)$	164025.dn	21870	yes	$-1$	$1$	$e\left(\frac{3977}{10935}\right)$	$e\left(\frac{7954}{10935}\right)$	$e\left(\frac{2897}{4374}\right)$	$e\left(\frac{332}{3645}\right)$	$e\left(\frac{19999}{21870}\right)$	$e\left(\frac{9281}{21870}\right)$	$e\left(\frac{569}{21870}\right)$	$e\left(\frac{4973}{10935}\right)$	$e\left(\frac{1222}{3645}\right)$	$e\left(\frac{2387}{3645}\right)$

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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	$164025$
Structure	\(C_{2}\times C_{43740}\)
Order	$87480$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(4\)	\(7\)	\(8\)	\(11\)	\(13\)	\(14\)	\(16\)	\(17\)	\(19\)
\(\chi_{164025}(1,\cdot)\)	164025.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{164025}(2,\cdot)\)	164025.dq	43740	yes	\(1\)	\(1\)	\(e\left(\frac{2197}{43740}\right)\)	\(e\left(\frac{2197}{21870}\right)\)	\(e\left(\frac{5891}{8748}\right)\)	\(e\left(\frac{2197}{14580}\right)\)	\(e\left(\frac{14051}{21870}\right)\)	\(e\left(\frac{25433}{43740}\right)\)	\(e\left(\frac{7913}{10935}\right)\)	\(e\left(\frac{2197}{10935}\right)\)	\(e\left(\frac{4727}{14580}\right)\)	\(e\left(\frac{7091}{7290}\right)\)
\(\chi_{164025}(4,\cdot)\)	164025.dp	21870	yes	\(1\)	\(1\)	\(e\left(\frac{2197}{21870}\right)\)	\(e\left(\frac{2197}{10935}\right)\)	\(e\left(\frac{1517}{4374}\right)\)	\(e\left(\frac{2197}{7290}\right)\)	\(e\left(\frac{3116}{10935}\right)\)	\(e\left(\frac{3563}{21870}\right)\)	\(e\left(\frac{4891}{10935}\right)\)	\(e\left(\frac{4394}{10935}\right)\)	\(e\left(\frac{4727}{7290}\right)\)	\(e\left(\frac{3446}{3645}\right)\)
\(\chi_{164025}(7,\cdot)\)	164025.di	8748	no	\(-1\)	\(1\)	\(e\left(\frac{5891}{8748}\right)\)	\(e\left(\frac{1517}{4374}\right)\)	\(e\left(\frac{3563}{8748}\right)\)	\(e\left(\frac{59}{2916}\right)\)	\(e\left(\frac{590}{2187}\right)\)	\(e\left(\frac{1849}{8748}\right)\)	\(e\left(\frac{353}{4374}\right)\)	\(e\left(\frac{1517}{2187}\right)\)	\(e\left(\frac{2593}{2916}\right)\)	\(e\left(\frac{211}{1458}\right)\)
\(\chi_{164025}(8,\cdot)\)	164025.dm	14580	no	\(1\)	\(1\)	\(e\left(\frac{2197}{14580}\right)\)	\(e\left(\frac{2197}{7290}\right)\)	\(e\left(\frac{59}{2916}\right)\)	\(e\left(\frac{2197}{4860}\right)\)	\(e\left(\frac{6761}{7290}\right)\)	\(e\left(\frac{10853}{14580}\right)\)	\(e\left(\frac{623}{3645}\right)\)	\(e\left(\frac{2197}{3645}\right)\)	\(e\left(\frac{4727}{4860}\right)\)	\(e\left(\frac{2231}{2430}\right)\)
\(\chi_{164025}(11,\cdot)\)	164025.do	21870	yes	\(-1\)	\(1\)	\(e\left(\frac{14051}{21870}\right)\)	\(e\left(\frac{3116}{10935}\right)\)	\(e\left(\frac{590}{2187}\right)\)	\(e\left(\frac{6761}{7290}\right)\)	\(e\left(\frac{7271}{21870}\right)\)	\(e\left(\frac{1367}{10935}\right)\)	\(e\left(\frac{19951}{21870}\right)\)	\(e\left(\frac{6232}{10935}\right)\)	\(e\left(\frac{6331}{7290}\right)\)	\(e\left(\frac{1123}{3645}\right)\)
\(\chi_{164025}(13,\cdot)\)	164025.dr	43740	yes	\(-1\)	\(1\)	\(e\left(\frac{25433}{43740}\right)\)	\(e\left(\frac{3563}{21870}\right)\)	\(e\left(\frac{1849}{8748}\right)\)	\(e\left(\frac{10853}{14580}\right)\)	\(e\left(\frac{1367}{10935}\right)\)	\(e\left(\frac{6067}{43740}\right)\)	\(e\left(\frac{17339}{21870}\right)\)	\(e\left(\frac{3563}{10935}\right)\)	\(e\left(\frac{7603}{14580}\right)\)	\(e\left(\frac{6589}{7290}\right)\)
\(\chi_{164025}(14,\cdot)\)	164025.dn	21870	yes	\(-1\)	\(1\)	\(e\left(\frac{7913}{10935}\right)\)	\(e\left(\frac{4891}{10935}\right)\)	\(e\left(\frac{353}{4374}\right)\)	\(e\left(\frac{623}{3645}\right)\)	\(e\left(\frac{19951}{21870}\right)\)	\(e\left(\frac{17339}{21870}\right)\)	\(e\left(\frac{17591}{21870}\right)\)	\(e\left(\frac{9782}{10935}\right)\)	\(e\left(\frac{778}{3645}\right)\)	\(e\left(\frac{428}{3645}\right)\)
\(\chi_{164025}(16,\cdot)\)	164025.dk	10935	yes	\(1\)	\(1\)	\(e\left(\frac{2197}{10935}\right)\)	\(e\left(\frac{4394}{10935}\right)\)	\(e\left(\frac{1517}{2187}\right)\)	\(e\left(\frac{2197}{3645}\right)\)	\(e\left(\frac{6232}{10935}\right)\)	\(e\left(\frac{3563}{10935}\right)\)	\(e\left(\frac{9782}{10935}\right)\)	\(e\left(\frac{8788}{10935}\right)\)	\(e\left(\frac{1082}{3645}\right)\)	\(e\left(\frac{3247}{3645}\right)\)
\(\chi_{164025}(17,\cdot)\)	164025.dm	14580	no	\(1\)	\(1\)	\(e\left(\frac{4727}{14580}\right)\)	\(e\left(\frac{4727}{7290}\right)\)	\(e\left(\frac{2593}{2916}\right)\)	\(e\left(\frac{4727}{4860}\right)\)	\(e\left(\frac{6331}{7290}\right)\)	\(e\left(\frac{7603}{14580}\right)\)	\(e\left(\frac{778}{3645}\right)\)	\(e\left(\frac{1082}{3645}\right)\)	\(e\left(\frac{3397}{4860}\right)\)	\(e\left(\frac{241}{2430}\right)\)
\(\chi_{164025}(19,\cdot)\)	164025.df	7290	no	\(1\)	\(1\)	\(e\left(\frac{7091}{7290}\right)\)	\(e\left(\frac{3446}{3645}\right)\)	\(e\left(\frac{211}{1458}\right)\)	\(e\left(\frac{2231}{2430}\right)\)	\(e\left(\frac{1123}{3645}\right)\)	\(e\left(\frac{6589}{7290}\right)\)	\(e\left(\frac{428}{3645}\right)\)	\(e\left(\frac{3247}{3645}\right)\)	\(e\left(\frac{241}{2430}\right)\)	\(e\left(\frac{388}{1215}\right)\)
\(\chi_{164025}(22,\cdot)\)	164025.dr	43740	yes	\(-1\)	\(1\)	\(e\left(\frac{30299}{43740}\right)\)	\(e\left(\frac{8429}{21870}\right)\)	\(e\left(\frac{8251}{8748}\right)\)	\(e\left(\frac{1139}{14580}\right)\)	\(e\left(\frac{10661}{10935}\right)\)	\(e\left(\frac{30901}{43740}\right)\)	\(e\left(\frac{13907}{21870}\right)\)	\(e\left(\frac{8429}{10935}\right)\)	\(e\left(\frac{2809}{14580}\right)\)	\(e\left(\frac{2047}{7290}\right)\)
\(\chi_{164025}(23,\cdot)\)	164025.dq	43740	yes	\(1\)	\(1\)	\(e\left(\frac{32807}{43740}\right)\)	\(e\left(\frac{10937}{21870}\right)\)	\(e\left(\frac{2053}{8748}\right)\)	\(e\left(\frac{3647}{14580}\right)\)	\(e\left(\frac{21181}{21870}\right)\)	\(e\left(\frac{42703}{43740}\right)\)	\(e\left(\frac{10768}{10935}\right)\)	\(e\left(\frac{2}{10935}\right)\)	\(e\left(\frac{1237}{14580}\right)\)	\(e\left(\frac{3751}{7290}\right)\)
\(\chi_{164025}(26,\cdot)\)	164025.cd	486	no	\(-1\)	\(1\)	\(e\left(\frac{307}{486}\right)\)	\(e\left(\frac{64}{243}\right)\)	\(e\left(\frac{215}{243}\right)\)	\(e\left(\frac{145}{162}\right)\)	\(e\left(\frac{373}{486}\right)\)	\(e\left(\frac{175}{243}\right)\)	\(e\left(\frac{251}{486}\right)\)	\(e\left(\frac{128}{243}\right)\)	\(e\left(\frac{137}{162}\right)\)	\(e\left(\frac{71}{81}\right)\)
\(\chi_{164025}(28,\cdot)\)	164025.de	4860	no	\(-1\)	\(1\)	\(e\left(\frac{3761}{4860}\right)\)	\(e\left(\frac{1331}{2430}\right)\)	\(e\left(\frac{733}{972}\right)\)	\(e\left(\frac{521}{1620}\right)\)	\(e\left(\frac{674}{1215}\right)\)	\(e\left(\frac{1819}{4860}\right)\)	\(e\left(\frac{1283}{2430}\right)\)	\(e\left(\frac{116}{1215}\right)\)	\(e\left(\frac{871}{1620}\right)\)	\(e\left(\frac{73}{810}\right)\)
\(\chi_{164025}(29,\cdot)\)	164025.dn	21870	yes	\(-1\)	\(1\)	\(e\left(\frac{4021}{10935}\right)\)	\(e\left(\frac{8042}{10935}\right)\)	\(e\left(\frac{1375}{4374}\right)\)	\(e\left(\frac{376}{3645}\right)\)	\(e\left(\frac{3107}{21870}\right)\)	\(e\left(\frac{7393}{21870}\right)\)	\(e\left(\frac{14917}{21870}\right)\)	\(e\left(\frac{5149}{10935}\right)\)	\(e\left(\frac{2921}{3645}\right)\)	\(e\left(\frac{3406}{3645}\right)\)
\(\chi_{164025}(31,\cdot)\)	164025.dk	10935	yes	\(1\)	\(1\)	\(e\left(\frac{10094}{10935}\right)\)	\(e\left(\frac{9253}{10935}\right)\)	\(e\left(\frac{1672}{2187}\right)\)	\(e\left(\frac{2804}{3645}\right)\)	\(e\left(\frac{10829}{10935}\right)\)	\(e\left(\frac{4126}{10935}\right)\)	\(e\left(\frac{7519}{10935}\right)\)	\(e\left(\frac{7571}{10935}\right)\)	\(e\left(\frac{2899}{3645}\right)\)	\(e\left(\frac{1979}{3645}\right)\)
\(\chi_{164025}(32,\cdot)\)	164025.dj	8748	no	\(1\)	\(1\)	\(e\left(\frac{2197}{8748}\right)\)	\(e\left(\frac{2197}{4374}\right)\)	\(e\left(\frac{3211}{8748}\right)\)	\(e\left(\frac{2197}{2916}\right)\)	\(e\left(\frac{929}{4374}\right)\)	\(e\left(\frac{7937}{8748}\right)\)	\(e\left(\frac{1352}{2187}\right)\)	\(e\left(\frac{10}{2187}\right)\)	\(e\left(\frac{1811}{2916}\right)\)	\(e\left(\frac{1259}{1458}\right)\)
\(\chi_{164025}(34,\cdot)\)	164025.dp	21870	yes	\(1\)	\(1\)	\(e\left(\frac{8189}{21870}\right)\)	\(e\left(\frac{8189}{10935}\right)\)	\(e\left(\frac{2461}{4374}\right)\)	\(e\left(\frac{899}{7290}\right)\)	\(e\left(\frac{5587}{10935}\right)\)	\(e\left(\frac{2251}{21870}\right)\)	\(e\left(\frac{10247}{10935}\right)\)	\(e\left(\frac{5443}{10935}\right)\)	\(e\left(\frac{169}{7290}\right)\)	\(e\left(\frac{262}{3645}\right)\)
\(\chi_{164025}(37,\cdot)\)	164025.dl	14580	no	\(-1\)	\(1\)	\(e\left(\frac{13901}{14580}\right)\)	\(e\left(\frac{6611}{7290}\right)\)	\(e\left(\frac{1753}{2916}\right)\)	\(e\left(\frac{4181}{4860}\right)\)	\(e\left(\frac{1229}{3645}\right)\)	\(e\left(\frac{319}{14580}\right)\)	\(e\left(\frac{4043}{7290}\right)\)	\(e\left(\frac{2966}{3645}\right)\)	\(e\left(\frac{2251}{4860}\right)\)	\(e\left(\frac{463}{2430}\right)\)
\(\chi_{164025}(38,\cdot)\)	164025.dq	43740	yes	\(1\)	\(1\)	\(e\left(\frac{1003}{43740}\right)\)	\(e\left(\frac{1003}{21870}\right)\)	\(e\left(\frac{7157}{8748}\right)\)	\(e\left(\frac{1003}{14580}\right)\)	\(e\left(\frac{20789}{21870}\right)\)	\(e\left(\frac{21227}{43740}\right)\)	\(e\left(\frac{9197}{10935}\right)\)	\(e\left(\frac{1003}{10935}\right)\)	\(e\left(\frac{6173}{14580}\right)\)	\(e\left(\frac{2129}{7290}\right)\)
\(\chi_{164025}(41,\cdot)\)	164025.do	21870	yes	\(-1\)	\(1\)	\(e\left(\frac{3019}{21870}\right)\)	\(e\left(\frac{3019}{10935}\right)\)	\(e\left(\frac{559}{2187}\right)\)	\(e\left(\frac{3019}{7290}\right)\)	\(e\left(\frac{19429}{21870}\right)\)	\(e\left(\frac{7378}{10935}\right)\)	\(e\left(\frac{8609}{21870}\right)\)	\(e\left(\frac{6038}{10935}\right)\)	\(e\left(\frac{6479}{7290}\right)\)	\(e\left(\frac{3272}{3645}\right)\)
\(\chi_{164025}(43,\cdot)\)	164025.di	8748	no	\(-1\)	\(1\)	\(e\left(\frac{2609}{8748}\right)\)	\(e\left(\frac{2609}{4374}\right)\)	\(e\left(\frac{785}{8748}\right)\)	\(e\left(\frac{2609}{2916}\right)\)	\(e\left(\frac{575}{2187}\right)\)	\(e\left(\frac{4267}{8748}\right)\)	\(e\left(\frac{1697}{4374}\right)\)	\(e\left(\frac{422}{2187}\right)\)	\(e\left(\frac{1483}{2916}\right)\)	\(e\left(\frac{1225}{1458}\right)\)
\(\chi_{164025}(44,\cdot)\)	164025.dh	7290	no	\(-1\)	\(1\)	\(e\left(\frac{2708}{3645}\right)\)	\(e\left(\frac{1771}{3645}\right)\)	\(e\left(\frac{899}{1458}\right)\)	\(e\left(\frac{278}{1215}\right)\)	\(e\left(\frac{4501}{7290}\right)\)	\(e\left(\frac{2099}{7290}\right)\)	\(e\left(\frac{2621}{7290}\right)\)	\(e\left(\frac{3542}{3645}\right)\)	\(e\left(\frac{628}{1215}\right)\)	\(e\left(\frac{308}{1215}\right)\)
\(\chi_{164025}(46,\cdot)\)	164025.cz	3645	no	\(1\)	\(1\)	\(e\left(\frac{2917}{3645}\right)\)	\(e\left(\frac{2189}{3645}\right)\)	\(e\left(\frac{662}{729}\right)\)	\(e\left(\frac{487}{1215}\right)\)	\(e\left(\frac{2227}{3645}\right)\)	\(e\left(\frac{2033}{3645}\right)\)	\(e\left(\frac{2582}{3645}\right)\)	\(e\left(\frac{733}{3645}\right)\)	\(e\left(\frac{497}{1215}\right)\)	\(e\left(\frac{592}{1215}\right)\)
\(\chi_{164025}(47,\cdot)\)	164025.dq	43740	yes	\(1\)	\(1\)	\(e\left(\frac{41029}{43740}\right)\)	\(e\left(\frac{19159}{21870}\right)\)	\(e\left(\frac{2303}{8748}\right)\)	\(e\left(\frac{11869}{14580}\right)\)	\(e\left(\frac{20867}{21870}\right)\)	\(e\left(\frac{11441}{43740}\right)\)	\(e\left(\frac{2201}{10935}\right)\)	\(e\left(\frac{8224}{10935}\right)\)	\(e\left(\frac{9059}{14580}\right)\)	\(e\left(\frac{2117}{7290}\right)\)
\(\chi_{164025}(49,\cdot)\)	164025.da	4374	no	\(1\)	\(1\)	\(e\left(\frac{1517}{4374}\right)\)	\(e\left(\frac{1517}{2187}\right)\)	\(e\left(\frac{3563}{4374}\right)\)	\(e\left(\frac{59}{1458}\right)\)	\(e\left(\frac{1180}{2187}\right)\)	\(e\left(\frac{1849}{4374}\right)\)	\(e\left(\frac{353}{2187}\right)\)	\(e\left(\frac{847}{2187}\right)\)	\(e\left(\frac{1135}{1458}\right)\)	\(e\left(\frac{211}{729}\right)\)
\(\chi_{164025}(52,\cdot)\)	164025.dr	43740	yes	\(-1\)	\(1\)	\(e\left(\frac{29827}{43740}\right)\)	\(e\left(\frac{7957}{21870}\right)\)	\(e\left(\frac{4883}{8748}\right)\)	\(e\left(\frac{667}{14580}\right)\)	\(e\left(\frac{4483}{10935}\right)\)	\(e\left(\frac{13193}{43740}\right)\)	\(e\left(\frac{5251}{21870}\right)\)	\(e\left(\frac{7957}{10935}\right)\)	\(e\left(\frac{2477}{14580}\right)\)	\(e\left(\frac{6191}{7290}\right)\)
\(\chi_{164025}(53,\cdot)\)	164025.dd	4860	no	\(1\)	\(1\)	\(e\left(\frac{3251}{4860}\right)\)	\(e\left(\frac{821}{2430}\right)\)	\(e\left(\frac{397}{972}\right)\)	\(e\left(\frac{11}{1620}\right)\)	\(e\left(\frac{2083}{2430}\right)\)	\(e\left(\frac{2599}{4860}\right)\)	\(e\left(\frac{94}{1215}\right)\)	\(e\left(\frac{821}{1215}\right)\)	\(e\left(\frac{121}{1620}\right)\)	\(e\left(\frac{583}{810}\right)\)
\(\chi_{164025}(56,\cdot)\)	164025.do	21870	yes	\(-1\)	\(1\)	\(e\left(\frac{18023}{21870}\right)\)	\(e\left(\frac{7088}{10935}\right)\)	\(e\left(\frac{935}{2187}\right)\)	\(e\left(\frac{3443}{7290}\right)\)	\(e\left(\frac{4313}{21870}\right)\)	\(e\left(\frac{10451}{10935}\right)\)	\(e\left(\frac{5503}{21870}\right)\)	\(e\left(\frac{3241}{10935}\right)\)	\(e\left(\frac{6283}{7290}\right)\)	\(e\left(\frac{229}{3645}\right)\)
\(\chi_{164025}(58,\cdot)\)	164025.dr	43740	yes	\(-1\)	\(1\)	\(e\left(\frac{18281}{43740}\right)\)	\(e\left(\frac{18281}{21870}\right)\)	\(e\left(\frac{8641}{8748}\right)\)	\(e\left(\frac{3701}{14580}\right)\)	\(e\left(\frac{8579}{10935}\right)\)	\(e\left(\frac{40219}{43740}\right)\)	\(e\left(\frac{8873}{21870}\right)\)	\(e\left(\frac{7346}{10935}\right)\)	\(e\left(\frac{1831}{14580}\right)\)	\(e\left(\frac{6613}{7290}\right)\)
\(\chi_{164025}(59,\cdot)\)	164025.dn	21870	yes	\(-1\)	\(1\)	\(e\left(\frac{3977}{10935}\right)\)	\(e\left(\frac{7954}{10935}\right)\)	\(e\left(\frac{2897}{4374}\right)\)	\(e\left(\frac{332}{3645}\right)\)	\(e\left(\frac{19999}{21870}\right)\)	\(e\left(\frac{9281}{21870}\right)\)	\(e\left(\frac{569}{21870}\right)\)	\(e\left(\frac{4973}{10935}\right)\)	\(e\left(\frac{1222}{3645}\right)\)	\(e\left(\frac{2387}{3645}\right)\)

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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.