LMFDB - Group of Dirichlet characters of modulus 836352

Show commands: Magma / Pari/GP / SageMath

comment:Define the Dirichlet group

sage:G = DirichletGroup(836352)

gp:g = idealstar(,836352,2)

magma:G = FullDirichletGroup(836352);

Character group

Order	=	253440	comment:Order sage:G.order() gp:g.no magma:Order(G);
Structure	=	$C_{2}\times C_{2}\times C_{2}\times C_{31680}$	comment:Group structure sage:sorted(g.order() for g in G.gens()) gp:g.cyc magma:PrimaryInvariants(G);
Generators	=	$\chi_{836352}(137215,\cdot)$, $\chi_{836352}(561925,\cdot)$, $\chi_{836352}(123905,\cdot)$, $\chi_{836352}(781057,\cdot)$	comment:Generators sage:G.gens() gp:g.gen magma:Generators(G);

First 32 of 253440 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	$-1$	$1$	$5$	$7$	$13$	$17$	$19$	$23$	$25$	$29$	$31$	$35$
$\chi_{836352}(1,\cdot)$	836352.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{836352}(5,\cdot)$	836352.zs	31680	yes	$-1$	$1$	$e\left(\frac{5903}{31680}\right)$	$e\left(\frac{4907}{15840}\right)$	$e\left(\frac{28577}{31680}\right)$	$e\left(\frac{1499}{2640}\right)$	$e\left(\frac{5587}{10560}\right)$	$e\left(\frac{1157}{3168}\right)$	$e\left(\frac{5903}{15840}\right)$	$e\left(\frac{20149}{31680}\right)$	$e\left(\frac{2119}{3960}\right)$	$e\left(\frac{5239}{10560}\right)$
$\chi_{836352}(7,\cdot)$	836352.zi	15840	no	$1$	$1$	$e\left(\frac{4907}{15840}\right)$	$e\left(\frac{5783}{7920}\right)$	$e\left(\frac{13973}{15840}\right)$	$e\left(\frac{1091}{1320}\right)$	$e\left(\frac{223}{5280}\right)$	$e\left(\frac{1457}{1584}\right)$	$e\left(\frac{4907}{7920}\right)$	$e\left(\frac{3001}{15840}\right)$	$e\left(\frac{1}{1980}\right)$	$e\left(\frac{211}{5280}\right)$
$\chi_{836352}(13,\cdot)$	836352.zo	31680	yes	$-1$	$1$	$e\left(\frac{28577}{31680}\right)$	$e\left(\frac{13973}{15840}\right)$	$e\left(\frac{25583}{31680}\right)$	$e\left(\frac{581}{2640}\right)$	$e\left(\frac{4573}{10560}\right)$	$e\left(\frac{1403}{3168}\right)$	$e\left(\frac{12737}{15840}\right)$	$e\left(\frac{12091}{31680}\right)$	$e\left(\frac{2881}{3960}\right)$	$e\left(\frac{8281}{10560}\right)$
$\chi_{836352}(17,\cdot)$	836352.ws	2640	no	$1$	$1$	$e\left(\frac{1499}{2640}\right)$	$e\left(\frac{1091}{1320}\right)$	$e\left(\frac{581}{2640}\right)$	$e\left(\frac{127}{220}\right)$	$e\left(\frac{31}{880}\right)$	$e\left(\frac{125}{264}\right)$	$e\left(\frac{179}{1320}\right)$	$e\left(\frac{577}{2640}\right)$	$e\left(\frac{157}{330}\right)$	$e\left(\frac{347}{880}\right)$
$\chi_{836352}(19,\cdot)$	836352.yy	10560	no	$1$	$1$	$e\left(\frac{5587}{10560}\right)$	$e\left(\frac{223}{5280}\right)$	$e\left(\frac{4573}{10560}\right)$	$e\left(\frac{31}{880}\right)$	$e\left(\frac{1383}{3520}\right)$	$e\left(\frac{721}{1056}\right)$	$e\left(\frac{307}{5280}\right)$	$e\left(\frac{7361}{10560}\right)$	$e\left(\frac{791}{1320}\right)$	$e\left(\frac{2011}{3520}\right)$
$\chi_{836352}(23,\cdot)$	836352.xe	3168	no	$1$	$1$	$e\left(\frac{1157}{3168}\right)$	$e\left(\frac{1457}{1584}\right)$	$e\left(\frac{1403}{3168}\right)$	$e\left(\frac{125}{264}\right)$	$e\left(\frac{721}{1056}\right)$	$e\left(\frac{1315}{1584}\right)$	$e\left(\frac{1157}{1584}\right)$	$e\left(\frac{1063}{3168}\right)$	$e\left(\frac{79}{396}\right)$	$e\left(\frac{301}{1056}\right)$
$\chi_{836352}(25,\cdot)$	836352.zj	15840	no	$1$	$1$	$e\left(\frac{5903}{15840}\right)$	$e\left(\frac{4907}{7920}\right)$	$e\left(\frac{12737}{15840}\right)$	$e\left(\frac{179}{1320}\right)$	$e\left(\frac{307}{5280}\right)$	$e\left(\frac{1157}{1584}\right)$	$e\left(\frac{5903}{7920}\right)$	$e\left(\frac{4309}{15840}\right)$	$e\left(\frac{139}{1980}\right)$	$e\left(\frac{5239}{5280}\right)$
$\chi_{836352}(29,\cdot)$	836352.zr	31680	yes	$1$	$1$	$e\left(\frac{20149}{31680}\right)$	$e\left(\frac{3001}{15840}\right)$	$e\left(\frac{12091}{31680}\right)$	$e\left(\frac{577}{2640}\right)$	$e\left(\frac{7361}{10560}\right)$	$e\left(\frac{1063}{3168}\right)$	$e\left(\frac{4309}{15840}\right)$	$e\left(\frac{2327}{31680}\right)$	$e\left(\frac{3077}{3960}\right)$	$e\left(\frac{8717}{10560}\right)$
$\chi_{836352}(31,\cdot)$	836352.xz	3960	no	$-1$	$1$	$e\left(\frac{2119}{3960}\right)$	$e\left(\frac{1}{1980}\right)$	$e\left(\frac{2881}{3960}\right)$	$e\left(\frac{157}{330}\right)$	$e\left(\frac{791}{1320}\right)$	$e\left(\frac{79}{396}\right)$	$e\left(\frac{139}{1980}\right)$	$e\left(\frac{3077}{3960}\right)$	$e\left(\frac{949}{990}\right)$	$e\left(\frac{707}{1320}\right)$
$\chi_{836352}(35,\cdot)$	836352.zb	10560	no	$-1$	$1$	$e\left(\frac{5239}{10560}\right)$	$e\left(\frac{211}{5280}\right)$	$e\left(\frac{8281}{10560}\right)$	$e\left(\frac{347}{880}\right)$	$e\left(\frac{2011}{3520}\right)$	$e\left(\frac{301}{1056}\right)$	$e\left(\frac{5239}{5280}\right)$	$e\left(\frac{8717}{10560}\right)$	$e\left(\frac{707}{1320}\right)$	$e\left(\frac{1887}{3520}\right)$
$\chi_{836352}(37,\cdot)$	836352.yz	10560	no	$1$	$1$	$e\left(\frac{3293}{10560}\right)$	$e\left(\frac{4817}{5280}\right)$	$e\left(\frac{6227}{10560}\right)$	$e\left(\frac{569}{880}\right)$	$e\left(\frac{2377}{3520}\right)$	$e\left(\frac{911}{1056}\right)$	$e\left(\frac{3293}{5280}\right)$	$e\left(\frac{9199}{10560}\right)$	$e\left(\frac{829}{1320}\right)$	$e\left(\frac{789}{3520}\right)$
$\chi_{836352}(41,\cdot)$	836352.zk	15840	no	$1$	$1$	$e\left(\frac{2593}{15840}\right)$	$e\left(\frac{2077}{7920}\right)$	$e\left(\frac{3247}{15840}\right)$	$e\left(\frac{709}{1320}\right)$	$e\left(\frac{5117}{5280}\right)$	$e\left(\frac{931}{1584}\right)$	$e\left(\frac{2593}{7920}\right)$	$e\left(\frac{10379}{15840}\right)$	$e\left(\frac{1229}{1980}\right)$	$e\left(\frac{2249}{5280}\right)$
$\chi_{836352}(43,\cdot)$	836352.yk	6336	yes	$1$	$1$	$e\left(\frac{5591}{6336}\right)$	$e\left(\frac{563}{3168}\right)$	$e\left(\frac{3353}{6336}\right)$	$e\left(\frac{83}{528}\right)$	$e\left(\frac{2011}{2112}\right)$	$e\left(\frac{625}{3168}\right)$	$e\left(\frac{2423}{3168}\right)$	$e\left(\frac{2029}{6336}\right)$	$e\left(\frac{91}{792}\right)$	$e\left(\frac{127}{2112}\right)$
$\chi_{836352}(47,\cdot)$	836352.yv	7920	no	$1$	$1$	$e\left(\frac{4429}{7920}\right)$	$e\left(\frac{3301}{3960}\right)$	$e\left(\frac{3211}{7920}\right)$	$e\left(\frac{487}{660}\right)$	$e\left(\frac{2441}{2640}\right)$	$e\left(\frac{607}{792}\right)$	$e\left(\frac{469}{3960}\right)$	$e\left(\frac{767}{7920}\right)$	$e\left(\frac{196}{495}\right)$	$e\left(\frac{1037}{2640}\right)$
$\chi_{836352}(49,\cdot)$	836352.ys	7920	no	$1$	$1$	$e\left(\frac{4907}{7920}\right)$	$e\left(\frac{1823}{3960}\right)$	$e\left(\frac{6053}{7920}\right)$	$e\left(\frac{431}{660}\right)$	$e\left(\frac{223}{2640}\right)$	$e\left(\frac{665}{792}\right)$	$e\left(\frac{947}{3960}\right)$	$e\left(\frac{3001}{7920}\right)$	$e\left(\frac{1}{990}\right)$	$e\left(\frac{211}{2640}\right)$
$\chi_{836352}(53,\cdot)$	836352.xl	3520	no	$-1$	$1$	$e\left(\frac{3123}{3520}\right)$	$e\left(\frac{927}{1760}\right)$	$e\left(\frac{3517}{3520}\right)$	$e\left(\frac{797}{880}\right)$	$e\left(\frac{2741}{3520}\right)$	$e\left(\frac{17}{352}\right)$	$e\left(\frac{1363}{1760}\right)$	$e\left(\frac{1729}{3520}\right)$	$e\left(\frac{219}{440}\right)$	$e\left(\frac{1457}{3520}\right)$
$\chi_{836352}(59,\cdot)$	836352.zp	31680	yes	$1$	$1$	$e\left(\frac{5759}{31680}\right)$	$e\left(\frac{10091}{15840}\right)$	$e\left(\frac{2801}{31680}\right)$	$e\left(\frac{2267}{2640}\right)$	$e\left(\frac{931}{10560}\right)$	$e\left(\frac{2021}{3168}\right)$	$e\left(\frac{5759}{15840}\right)$	$e\left(\frac{28357}{31680}\right)$	$e\left(\frac{787}{3960}\right)$	$e\left(\frac{8647}{10560}\right)$
$\chi_{836352}(61,\cdot)$	836352.zo	31680	yes	$-1$	$1$	$e\left(\frac{2173}{31680}\right)$	$e\left(\frac{2017}{15840}\right)$	$e\left(\frac{4627}{31680}\right)$	$e\left(\frac{529}{2640}\right)$	$e\left(\frac{7817}{10560}\right)$	$e\left(\frac{943}{3168}\right)$	$e\left(\frac{2173}{15840}\right)$	$e\left(\frac{7919}{31680}\right)$	$e\left(\frac{1469}{3960}\right)$	$e\left(\frac{2069}{10560}\right)$
$\chi_{836352}(65,\cdot)$	836352.qp	396	no	$1$	$1$	$e\left(\frac{35}{396}\right)$	$e\left(\frac{19}{99}\right)$	$e\left(\frac{281}{396}\right)$	$e\left(\frac{26}{33}\right)$	$e\left(\frac{127}{132}\right)$	$e\left(\frac{80}{99}\right)$	$e\left(\frac{35}{198}\right)$	$e\left(\frac{7}{396}\right)$	$e\left(\frac{26}{99}\right)$	$e\left(\frac{37}{132}\right)$
$\chi_{836352}(67,\cdot)$	836352.yn	6336	yes	$-1$	$1$	$e\left(\frac{1849}{6336}\right)$	$e\left(\frac{2989}{3168}\right)$	$e\left(\frac{5239}{6336}\right)$	$e\left(\frac{277}{528}\right)$	$e\left(\frac{1301}{2112}\right)$	$e\left(\frac{575}{3168}\right)$	$e\left(\frac{1849}{3168}\right)$	$e\left(\frac{5795}{6336}\right)$	$e\left(\frac{749}{792}\right)$	$e\left(\frac{497}{2112}\right)$
$\chi_{836352}(71,\cdot)$	836352.yf	5280	no	$1$	$1$	$e\left(\frac{4273}{5280}\right)$	$e\left(\frac{2317}{2640}\right)$	$e\left(\frac{367}{5280}\right)$	$e\left(\frac{329}{440}\right)$	$e\left(\frac{1357}{1760}\right)$	$e\left(\frac{91}{528}\right)$	$e\left(\frac{1633}{2640}\right)$	$e\left(\frac{1739}{5280}\right)$	$e\left(\frac{599}{660}\right)$	$e\left(\frac{1209}{1760}\right)$
$\chi_{836352}(73,\cdot)$	836352.ye	5280	no	$-1$	$1$	$e\left(\frac{359}{5280}\right)$	$e\left(\frac{1211}{2640}\right)$	$e\left(\frac{5081}{5280}\right)$	$e\left(\frac{47}{440}\right)$	$e\left(\frac{571}{1760}\right)$	$e\left(\frac{365}{528}\right)$	$e\left(\frac{359}{2640}\right)$	$e\left(\frac{877}{5280}\right)$	$e\left(\frac{7}{660}\right)$	$e\left(\frac{927}{1760}\right)$
$\chi_{836352}(79,\cdot)$	836352.yq	7920	no	$1$	$1$	$e\left(\frac{1363}{7920}\right)$	$e\left(\frac{487}{3960}\right)$	$e\left(\frac{2197}{7920}\right)$	$e\left(\frac{229}{660}\right)$	$e\left(\frac{2087}{2640}\right)$	$e\left(\frac{61}{792}\right)$	$e\left(\frac{1363}{3960}\right)$	$e\left(\frac{6569}{7920}\right)$	$e\left(\frac{82}{495}\right)$	$e\left(\frac{779}{2640}\right)$
$\chi_{836352}(83,\cdot)$	836352.zu	31680	yes	$-1$	$1$	$e\left(\frac{12553}{31680}\right)$	$e\left(\frac{5197}{15840}\right)$	$e\left(\frac{22567}{31680}\right)$	$e\left(\frac{2149}{2640}\right)$	$e\left(\frac{677}{10560}\right)$	$e\left(\frac{307}{3168}\right)$	$e\left(\frac{12553}{15840}\right)$	$e\left(\frac{15539}{31680}\right)$	$e\left(\frac{629}{3960}\right)$	$e\left(\frac{7649}{10560}\right)$
$\chi_{836352}(85,\cdot)$	836352.zo	31680	yes	$-1$	$1$	$e\left(\frac{23891}{31680}\right)$	$e\left(\frac{2159}{15840}\right)$	$e\left(\frac{3869}{31680}\right)$	$e\left(\frac{383}{2640}\right)$	$e\left(\frac{5959}{10560}\right)$	$e\left(\frac{2657}{3168}\right)$	$e\left(\frac{8051}{15840}\right)$	$e\left(\frac{27073}{31680}\right)$	$e\left(\frac{43}{3960}\right)$	$e\left(\frac{9403}{10560}\right)$
$\chi_{836352}(89,\cdot)$	836352.um	1056	no	$-1$	$1$	$e\left(\frac{1033}{1056}\right)$	$e\left(\frac{157}{528}\right)$	$e\left(\frac{151}{1056}\right)$	$e\left(\frac{9}{88}\right)$	$e\left(\frac{85}{352}\right)$	$e\left(\frac{503}{528}\right)$	$e\left(\frac{505}{528}\right)$	$e\left(\frac{563}{1056}\right)$	$e\left(\frac{65}{132}\right)$	$e\left(\frac{97}{352}\right)$
$\chi_{836352}(91,\cdot)$	836352.zc	10560	no	$-1$	$1$	$e\left(\frac{2237}{10560}\right)$	$e\left(\frac{3233}{5280}\right)$	$e\left(\frac{7283}{10560}\right)$	$e\left(\frac{41}{880}\right)$	$e\left(\frac{1673}{3520}\right)$	$e\left(\frac{383}{1056}\right)$	$e\left(\frac{2237}{5280}\right)$	$e\left(\frac{6031}{10560}\right)$	$e\left(\frac{961}{1320}\right)$	$e\left(\frac{2901}{3520}\right)$
$\chi_{836352}(95,\cdot)$	836352.xw	3960	no	$-1$	$1$	$e\left(\frac{2833}{3960}\right)$	$e\left(\frac{697}{1980}\right)$	$e\left(\frac{1327}{3960}\right)$	$e\left(\frac{199}{330}\right)$	$e\left(\frac{1217}{1320}\right)$	$e\left(\frac{19}{396}\right)$	$e\left(\frac{853}{1980}\right)$	$e\left(\frac{1319}{3960}\right)$	$e\left(\frac{133}{990}\right)$	$e\left(\frac{89}{1320}\right)$
$\chi_{836352}(97,\cdot)$	836352.xx	3960	no	$1$	$1$	$e\left(\frac{3779}{3960}\right)$	$e\left(\frac{191}{1980}\right)$	$e\left(\frac{821}{3960}\right)$	$e\left(\frac{287}{330}\right)$	$e\left(\frac{271}{1320}\right)$	$e\left(\frac{41}{396}\right)$	$e\left(\frac{1799}{1980}\right)$	$e\left(\frac{2617}{3960}\right)$	$e\left(\frac{292}{495}\right)$	$e\left(\frac{67}{1320}\right)$
$\chi_{836352}(101,\cdot)$	836352.zr	31680	yes	$1$	$1$	$e\left(\frac{6727}{31680}\right)$	$e\left(\frac{15283}{15840}\right)$	$e\left(\frac{73}{31680}\right)$	$e\left(\frac{331}{2640}\right)$	$e\left(\frac{7883}{10560}\right)$	$e\left(\frac{1933}{3168}\right)$	$e\left(\frac{6727}{15840}\right)$	$e\left(\frac{29501}{31680}\right)$	$e\left(\frac{1271}{3960}\right)$	$e\left(\frac{1871}{10560}\right)$
$\chi_{836352}(103,\cdot)$	836352.zm	15840	no	$-1$	$1$	$e\left(\frac{7807}{15840}\right)$	$e\left(\frac{163}{7920}\right)$	$e\left(\frac{3313}{15840}\right)$	$e\left(\frac{1171}{1320}\right)$	$e\left(\frac{563}{5280}\right)$	$e\left(\frac{205}{1584}\right)$	$e\left(\frac{7807}{7920}\right)$	$e\left(\frac{15461}{15840}\right)$	$e\left(\frac{1361}{1980}\right)$	$e\left(\frac{2711}{5280}\right)$

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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	$836352$
Structure	\(C_{2}\times C_{2}\times C_{2}\times C_{31680}\)
Order	$253440$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(5\)	\(7\)	\(13\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)	\(35\)
\(\chi_{836352}(1,\cdot)\)	836352.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{836352}(5,\cdot)\)	836352.zs	31680	yes	\(-1\)	\(1\)	\(e\left(\frac{5903}{31680}\right)\)	\(e\left(\frac{4907}{15840}\right)\)	\(e\left(\frac{28577}{31680}\right)\)	\(e\left(\frac{1499}{2640}\right)\)	\(e\left(\frac{5587}{10560}\right)\)	\(e\left(\frac{1157}{3168}\right)\)	\(e\left(\frac{5903}{15840}\right)\)	\(e\left(\frac{20149}{31680}\right)\)	\(e\left(\frac{2119}{3960}\right)\)	\(e\left(\frac{5239}{10560}\right)\)
\(\chi_{836352}(7,\cdot)\)	836352.zi	15840	no	\(1\)	\(1\)	\(e\left(\frac{4907}{15840}\right)\)	\(e\left(\frac{5783}{7920}\right)\)	\(e\left(\frac{13973}{15840}\right)\)	\(e\left(\frac{1091}{1320}\right)\)	\(e\left(\frac{223}{5280}\right)\)	\(e\left(\frac{1457}{1584}\right)\)	\(e\left(\frac{4907}{7920}\right)\)	\(e\left(\frac{3001}{15840}\right)\)	\(e\left(\frac{1}{1980}\right)\)	\(e\left(\frac{211}{5280}\right)\)
\(\chi_{836352}(13,\cdot)\)	836352.zo	31680	yes	\(-1\)	\(1\)	\(e\left(\frac{28577}{31680}\right)\)	\(e\left(\frac{13973}{15840}\right)\)	\(e\left(\frac{25583}{31680}\right)\)	\(e\left(\frac{581}{2640}\right)\)	\(e\left(\frac{4573}{10560}\right)\)	\(e\left(\frac{1403}{3168}\right)\)	\(e\left(\frac{12737}{15840}\right)\)	\(e\left(\frac{12091}{31680}\right)\)	\(e\left(\frac{2881}{3960}\right)\)	\(e\left(\frac{8281}{10560}\right)\)
\(\chi_{836352}(17,\cdot)\)	836352.ws	2640	no	\(1\)	\(1\)	\(e\left(\frac{1499}{2640}\right)\)	\(e\left(\frac{1091}{1320}\right)\)	\(e\left(\frac{581}{2640}\right)\)	\(e\left(\frac{127}{220}\right)\)	\(e\left(\frac{31}{880}\right)\)	\(e\left(\frac{125}{264}\right)\)	\(e\left(\frac{179}{1320}\right)\)	\(e\left(\frac{577}{2640}\right)\)	\(e\left(\frac{157}{330}\right)\)	\(e\left(\frac{347}{880}\right)\)
\(\chi_{836352}(19,\cdot)\)	836352.yy	10560	no	\(1\)	\(1\)	\(e\left(\frac{5587}{10560}\right)\)	\(e\left(\frac{223}{5280}\right)\)	\(e\left(\frac{4573}{10560}\right)\)	\(e\left(\frac{31}{880}\right)\)	\(e\left(\frac{1383}{3520}\right)\)	\(e\left(\frac{721}{1056}\right)\)	\(e\left(\frac{307}{5280}\right)\)	\(e\left(\frac{7361}{10560}\right)\)	\(e\left(\frac{791}{1320}\right)\)	\(e\left(\frac{2011}{3520}\right)\)
\(\chi_{836352}(23,\cdot)\)	836352.xe	3168	no	\(1\)	\(1\)	\(e\left(\frac{1157}{3168}\right)\)	\(e\left(\frac{1457}{1584}\right)\)	\(e\left(\frac{1403}{3168}\right)\)	\(e\left(\frac{125}{264}\right)\)	\(e\left(\frac{721}{1056}\right)\)	\(e\left(\frac{1315}{1584}\right)\)	\(e\left(\frac{1157}{1584}\right)\)	\(e\left(\frac{1063}{3168}\right)\)	\(e\left(\frac{79}{396}\right)\)	\(e\left(\frac{301}{1056}\right)\)
\(\chi_{836352}(25,\cdot)\)	836352.zj	15840	no	\(1\)	\(1\)	\(e\left(\frac{5903}{15840}\right)\)	\(e\left(\frac{4907}{7920}\right)\)	\(e\left(\frac{12737}{15840}\right)\)	\(e\left(\frac{179}{1320}\right)\)	\(e\left(\frac{307}{5280}\right)\)	\(e\left(\frac{1157}{1584}\right)\)	\(e\left(\frac{5903}{7920}\right)\)	\(e\left(\frac{4309}{15840}\right)\)	\(e\left(\frac{139}{1980}\right)\)	\(e\left(\frac{5239}{5280}\right)\)
\(\chi_{836352}(29,\cdot)\)	836352.zr	31680	yes	\(1\)	\(1\)	\(e\left(\frac{20149}{31680}\right)\)	\(e\left(\frac{3001}{15840}\right)\)	\(e\left(\frac{12091}{31680}\right)\)	\(e\left(\frac{577}{2640}\right)\)	\(e\left(\frac{7361}{10560}\right)\)	\(e\left(\frac{1063}{3168}\right)\)	\(e\left(\frac{4309}{15840}\right)\)	\(e\left(\frac{2327}{31680}\right)\)	\(e\left(\frac{3077}{3960}\right)\)	\(e\left(\frac{8717}{10560}\right)\)
\(\chi_{836352}(31,\cdot)\)	836352.xz	3960	no	\(-1\)	\(1\)	\(e\left(\frac{2119}{3960}\right)\)	\(e\left(\frac{1}{1980}\right)\)	\(e\left(\frac{2881}{3960}\right)\)	\(e\left(\frac{157}{330}\right)\)	\(e\left(\frac{791}{1320}\right)\)	\(e\left(\frac{79}{396}\right)\)	\(e\left(\frac{139}{1980}\right)\)	\(e\left(\frac{3077}{3960}\right)\)	\(e\left(\frac{949}{990}\right)\)	\(e\left(\frac{707}{1320}\right)\)
\(\chi_{836352}(35,\cdot)\)	836352.zb	10560	no	\(-1\)	\(1\)	\(e\left(\frac{5239}{10560}\right)\)	\(e\left(\frac{211}{5280}\right)\)	\(e\left(\frac{8281}{10560}\right)\)	\(e\left(\frac{347}{880}\right)\)	\(e\left(\frac{2011}{3520}\right)\)	\(e\left(\frac{301}{1056}\right)\)	\(e\left(\frac{5239}{5280}\right)\)	\(e\left(\frac{8717}{10560}\right)\)	\(e\left(\frac{707}{1320}\right)\)	\(e\left(\frac{1887}{3520}\right)\)
\(\chi_{836352}(37,\cdot)\)	836352.yz	10560	no	\(1\)	\(1\)	\(e\left(\frac{3293}{10560}\right)\)	\(e\left(\frac{4817}{5280}\right)\)	\(e\left(\frac{6227}{10560}\right)\)	\(e\left(\frac{569}{880}\right)\)	\(e\left(\frac{2377}{3520}\right)\)	\(e\left(\frac{911}{1056}\right)\)	\(e\left(\frac{3293}{5280}\right)\)	\(e\left(\frac{9199}{10560}\right)\)	\(e\left(\frac{829}{1320}\right)\)	\(e\left(\frac{789}{3520}\right)\)
\(\chi_{836352}(41,\cdot)\)	836352.zk	15840	no	\(1\)	\(1\)	\(e\left(\frac{2593}{15840}\right)\)	\(e\left(\frac{2077}{7920}\right)\)	\(e\left(\frac{3247}{15840}\right)\)	\(e\left(\frac{709}{1320}\right)\)	\(e\left(\frac{5117}{5280}\right)\)	\(e\left(\frac{931}{1584}\right)\)	\(e\left(\frac{2593}{7920}\right)\)	\(e\left(\frac{10379}{15840}\right)\)	\(e\left(\frac{1229}{1980}\right)\)	\(e\left(\frac{2249}{5280}\right)\)
\(\chi_{836352}(43,\cdot)\)	836352.yk	6336	yes	\(1\)	\(1\)	\(e\left(\frac{5591}{6336}\right)\)	\(e\left(\frac{563}{3168}\right)\)	\(e\left(\frac{3353}{6336}\right)\)	\(e\left(\frac{83}{528}\right)\)	\(e\left(\frac{2011}{2112}\right)\)	\(e\left(\frac{625}{3168}\right)\)	\(e\left(\frac{2423}{3168}\right)\)	\(e\left(\frac{2029}{6336}\right)\)	\(e\left(\frac{91}{792}\right)\)	\(e\left(\frac{127}{2112}\right)\)
\(\chi_{836352}(47,\cdot)\)	836352.yv	7920	no	\(1\)	\(1\)	\(e\left(\frac{4429}{7920}\right)\)	\(e\left(\frac{3301}{3960}\right)\)	\(e\left(\frac{3211}{7920}\right)\)	\(e\left(\frac{487}{660}\right)\)	\(e\left(\frac{2441}{2640}\right)\)	\(e\left(\frac{607}{792}\right)\)	\(e\left(\frac{469}{3960}\right)\)	\(e\left(\frac{767}{7920}\right)\)	\(e\left(\frac{196}{495}\right)\)	\(e\left(\frac{1037}{2640}\right)\)
\(\chi_{836352}(49,\cdot)\)	836352.ys	7920	no	\(1\)	\(1\)	\(e\left(\frac{4907}{7920}\right)\)	\(e\left(\frac{1823}{3960}\right)\)	\(e\left(\frac{6053}{7920}\right)\)	\(e\left(\frac{431}{660}\right)\)	\(e\left(\frac{223}{2640}\right)\)	\(e\left(\frac{665}{792}\right)\)	\(e\left(\frac{947}{3960}\right)\)	\(e\left(\frac{3001}{7920}\right)\)	\(e\left(\frac{1}{990}\right)\)	\(e\left(\frac{211}{2640}\right)\)
\(\chi_{836352}(53,\cdot)\)	836352.xl	3520	no	\(-1\)	\(1\)	\(e\left(\frac{3123}{3520}\right)\)	\(e\left(\frac{927}{1760}\right)\)	\(e\left(\frac{3517}{3520}\right)\)	\(e\left(\frac{797}{880}\right)\)	\(e\left(\frac{2741}{3520}\right)\)	\(e\left(\frac{17}{352}\right)\)	\(e\left(\frac{1363}{1760}\right)\)	\(e\left(\frac{1729}{3520}\right)\)	\(e\left(\frac{219}{440}\right)\)	\(e\left(\frac{1457}{3520}\right)\)
\(\chi_{836352}(59,\cdot)\)	836352.zp	31680	yes	\(1\)	\(1\)	\(e\left(\frac{5759}{31680}\right)\)	\(e\left(\frac{10091}{15840}\right)\)	\(e\left(\frac{2801}{31680}\right)\)	\(e\left(\frac{2267}{2640}\right)\)	\(e\left(\frac{931}{10560}\right)\)	\(e\left(\frac{2021}{3168}\right)\)	\(e\left(\frac{5759}{15840}\right)\)	\(e\left(\frac{28357}{31680}\right)\)	\(e\left(\frac{787}{3960}\right)\)	\(e\left(\frac{8647}{10560}\right)\)
\(\chi_{836352}(61,\cdot)\)	836352.zo	31680	yes	\(-1\)	\(1\)	\(e\left(\frac{2173}{31680}\right)\)	\(e\left(\frac{2017}{15840}\right)\)	\(e\left(\frac{4627}{31680}\right)\)	\(e\left(\frac{529}{2640}\right)\)	\(e\left(\frac{7817}{10560}\right)\)	\(e\left(\frac{943}{3168}\right)\)	\(e\left(\frac{2173}{15840}\right)\)	\(e\left(\frac{7919}{31680}\right)\)	\(e\left(\frac{1469}{3960}\right)\)	\(e\left(\frac{2069}{10560}\right)\)
\(\chi_{836352}(65,\cdot)\)	836352.qp	396	no	\(1\)	\(1\)	\(e\left(\frac{35}{396}\right)\)	\(e\left(\frac{19}{99}\right)\)	\(e\left(\frac{281}{396}\right)\)	\(e\left(\frac{26}{33}\right)\)	\(e\left(\frac{127}{132}\right)\)	\(e\left(\frac{80}{99}\right)\)	\(e\left(\frac{35}{198}\right)\)	\(e\left(\frac{7}{396}\right)\)	\(e\left(\frac{26}{99}\right)\)	\(e\left(\frac{37}{132}\right)\)
\(\chi_{836352}(67,\cdot)\)	836352.yn	6336	yes	\(-1\)	\(1\)	\(e\left(\frac{1849}{6336}\right)\)	\(e\left(\frac{2989}{3168}\right)\)	\(e\left(\frac{5239}{6336}\right)\)	\(e\left(\frac{277}{528}\right)\)	\(e\left(\frac{1301}{2112}\right)\)	\(e\left(\frac{575}{3168}\right)\)	\(e\left(\frac{1849}{3168}\right)\)	\(e\left(\frac{5795}{6336}\right)\)	\(e\left(\frac{749}{792}\right)\)	\(e\left(\frac{497}{2112}\right)\)
\(\chi_{836352}(71,\cdot)\)	836352.yf	5280	no	\(1\)	\(1\)	\(e\left(\frac{4273}{5280}\right)\)	\(e\left(\frac{2317}{2640}\right)\)	\(e\left(\frac{367}{5280}\right)\)	\(e\left(\frac{329}{440}\right)\)	\(e\left(\frac{1357}{1760}\right)\)	\(e\left(\frac{91}{528}\right)\)	\(e\left(\frac{1633}{2640}\right)\)	\(e\left(\frac{1739}{5280}\right)\)	\(e\left(\frac{599}{660}\right)\)	\(e\left(\frac{1209}{1760}\right)\)
\(\chi_{836352}(73,\cdot)\)	836352.ye	5280	no	\(-1\)	\(1\)	\(e\left(\frac{359}{5280}\right)\)	\(e\left(\frac{1211}{2640}\right)\)	\(e\left(\frac{5081}{5280}\right)\)	\(e\left(\frac{47}{440}\right)\)	\(e\left(\frac{571}{1760}\right)\)	\(e\left(\frac{365}{528}\right)\)	\(e\left(\frac{359}{2640}\right)\)	\(e\left(\frac{877}{5280}\right)\)	\(e\left(\frac{7}{660}\right)\)	\(e\left(\frac{927}{1760}\right)\)
\(\chi_{836352}(79,\cdot)\)	836352.yq	7920	no	\(1\)	\(1\)	\(e\left(\frac{1363}{7920}\right)\)	\(e\left(\frac{487}{3960}\right)\)	\(e\left(\frac{2197}{7920}\right)\)	\(e\left(\frac{229}{660}\right)\)	\(e\left(\frac{2087}{2640}\right)\)	\(e\left(\frac{61}{792}\right)\)	\(e\left(\frac{1363}{3960}\right)\)	\(e\left(\frac{6569}{7920}\right)\)	\(e\left(\frac{82}{495}\right)\)	\(e\left(\frac{779}{2640}\right)\)
\(\chi_{836352}(83,\cdot)\)	836352.zu	31680	yes	\(-1\)	\(1\)	\(e\left(\frac{12553}{31680}\right)\)	\(e\left(\frac{5197}{15840}\right)\)	\(e\left(\frac{22567}{31680}\right)\)	\(e\left(\frac{2149}{2640}\right)\)	\(e\left(\frac{677}{10560}\right)\)	\(e\left(\frac{307}{3168}\right)\)	\(e\left(\frac{12553}{15840}\right)\)	\(e\left(\frac{15539}{31680}\right)\)	\(e\left(\frac{629}{3960}\right)\)	\(e\left(\frac{7649}{10560}\right)\)
\(\chi_{836352}(85,\cdot)\)	836352.zo	31680	yes	\(-1\)	\(1\)	\(e\left(\frac{23891}{31680}\right)\)	\(e\left(\frac{2159}{15840}\right)\)	\(e\left(\frac{3869}{31680}\right)\)	\(e\left(\frac{383}{2640}\right)\)	\(e\left(\frac{5959}{10560}\right)\)	\(e\left(\frac{2657}{3168}\right)\)	\(e\left(\frac{8051}{15840}\right)\)	\(e\left(\frac{27073}{31680}\right)\)	\(e\left(\frac{43}{3960}\right)\)	\(e\left(\frac{9403}{10560}\right)\)
\(\chi_{836352}(89,\cdot)\)	836352.um	1056	no	\(-1\)	\(1\)	\(e\left(\frac{1033}{1056}\right)\)	\(e\left(\frac{157}{528}\right)\)	\(e\left(\frac{151}{1056}\right)\)	\(e\left(\frac{9}{88}\right)\)	\(e\left(\frac{85}{352}\right)\)	\(e\left(\frac{503}{528}\right)\)	\(e\left(\frac{505}{528}\right)\)	\(e\left(\frac{563}{1056}\right)\)	\(e\left(\frac{65}{132}\right)\)	\(e\left(\frac{97}{352}\right)\)
\(\chi_{836352}(91,\cdot)\)	836352.zc	10560	no	\(-1\)	\(1\)	\(e\left(\frac{2237}{10560}\right)\)	\(e\left(\frac{3233}{5280}\right)\)	\(e\left(\frac{7283}{10560}\right)\)	\(e\left(\frac{41}{880}\right)\)	\(e\left(\frac{1673}{3520}\right)\)	\(e\left(\frac{383}{1056}\right)\)	\(e\left(\frac{2237}{5280}\right)\)	\(e\left(\frac{6031}{10560}\right)\)	\(e\left(\frac{961}{1320}\right)\)	\(e\left(\frac{2901}{3520}\right)\)
\(\chi_{836352}(95,\cdot)\)	836352.xw	3960	no	\(-1\)	\(1\)	\(e\left(\frac{2833}{3960}\right)\)	\(e\left(\frac{697}{1980}\right)\)	\(e\left(\frac{1327}{3960}\right)\)	\(e\left(\frac{199}{330}\right)\)	\(e\left(\frac{1217}{1320}\right)\)	\(e\left(\frac{19}{396}\right)\)	\(e\left(\frac{853}{1980}\right)\)	\(e\left(\frac{1319}{3960}\right)\)	\(e\left(\frac{133}{990}\right)\)	\(e\left(\frac{89}{1320}\right)\)
\(\chi_{836352}(97,\cdot)\)	836352.xx	3960	no	\(1\)	\(1\)	\(e\left(\frac{3779}{3960}\right)\)	\(e\left(\frac{191}{1980}\right)\)	\(e\left(\frac{821}{3960}\right)\)	\(e\left(\frac{287}{330}\right)\)	\(e\left(\frac{271}{1320}\right)\)	\(e\left(\frac{41}{396}\right)\)	\(e\left(\frac{1799}{1980}\right)\)	\(e\left(\frac{2617}{3960}\right)\)	\(e\left(\frac{292}{495}\right)\)	\(e\left(\frac{67}{1320}\right)\)
\(\chi_{836352}(101,\cdot)\)	836352.zr	31680	yes	\(1\)	\(1\)	\(e\left(\frac{6727}{31680}\right)\)	\(e\left(\frac{15283}{15840}\right)\)	\(e\left(\frac{73}{31680}\right)\)	\(e\left(\frac{331}{2640}\right)\)	\(e\left(\frac{7883}{10560}\right)\)	\(e\left(\frac{1933}{3168}\right)\)	\(e\left(\frac{6727}{15840}\right)\)	\(e\left(\frac{29501}{31680}\right)\)	\(e\left(\frac{1271}{3960}\right)\)	\(e\left(\frac{1871}{10560}\right)\)
\(\chi_{836352}(103,\cdot)\)	836352.zm	15840	no	\(-1\)	\(1\)	\(e\left(\frac{7807}{15840}\right)\)	\(e\left(\frac{163}{7920}\right)\)	\(e\left(\frac{3313}{15840}\right)\)	\(e\left(\frac{1171}{1320}\right)\)	\(e\left(\frac{563}{5280}\right)\)	\(e\left(\frac{205}{1584}\right)\)	\(e\left(\frac{7807}{7920}\right)\)	\(e\left(\frac{15461}{15840}\right)\)	\(e\left(\frac{1361}{1980}\right)\)	\(e\left(\frac{2711}{5280}\right)\)

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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.