LMFDB - Group of Dirichlet characters of modulus 10037

Show commands: PariGP / SageMath

sage: H = DirichletGroup(10037)

pari: g = idealstar(,10037,2)

Character group

sage: G.order() pari: g.no
Order	=	10036
sage: H.invariants() pari: g.cyc
Structure	=	$C_{10036}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{10037}(2,\cdot)$

First 32 of 10036 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	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{10037}(1,\cdot)$	10037.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{10037}(2,\cdot)$	10037.l	10036	yes	$-1$	$1$	$e\left(\frac{1}{10036}\right)$	$e\left(\frac{237}{772}\right)$	$e\left(\frac{1}{5018}\right)$	$e\left(\frac{4861}{10036}\right)$	$e\left(\frac{1541}{5018}\right)$	$e\left(\frac{5585}{10036}\right)$	$e\left(\frac{3}{10036}\right)$	$e\left(\frac{237}{386}\right)$	$e\left(\frac{187}{386}\right)$	$e\left(\frac{1708}{2509}\right)$
$\chi_{10037}(3,\cdot)$	10037.i	772	yes	$-1$	$1$	$e\left(\frac{237}{772}\right)$	$e\left(\frac{657}{772}\right)$	$e\left(\frac{237}{386}\right)$	$e\left(\frac{233}{772}\right)$	$e\left(\frac{61}{386}\right)$	$e\left(\frac{437}{772}\right)$	$e\left(\frac{711}{772}\right)$	$e\left(\frac{271}{386}\right)$	$e\left(\frac{235}{386}\right)$	$e\left(\frac{75}{193}\right)$
$\chi_{10037}(4,\cdot)$	10037.k	5018	yes	$1$	$1$	$e\left(\frac{1}{5018}\right)$	$e\left(\frac{237}{386}\right)$	$e\left(\frac{1}{2509}\right)$	$e\left(\frac{4861}{5018}\right)$	$e\left(\frac{1541}{2509}\right)$	$e\left(\frac{567}{5018}\right)$	$e\left(\frac{3}{5018}\right)$	$e\left(\frac{44}{193}\right)$	$e\left(\frac{187}{193}\right)$	$e\left(\frac{907}{2509}\right)$
$\chi_{10037}(5,\cdot)$	10037.l	10036	yes	$-1$	$1$	$e\left(\frac{4861}{10036}\right)$	$e\left(\frac{233}{772}\right)$	$e\left(\frac{4861}{5018}\right)$	$e\left(\frac{4577}{10036}\right)$	$e\left(\frac{3945}{5018}\right)$	$e\left(\frac{1305}{10036}\right)$	$e\left(\frac{4547}{10036}\right)$	$e\left(\frac{233}{386}\right)$	$e\left(\frac{363}{386}\right)$	$e\left(\frac{307}{2509}\right)$
$\chi_{10037}(6,\cdot)$	10037.k	5018	yes	$1$	$1$	$e\left(\frac{1541}{5018}\right)$	$e\left(\frac{61}{386}\right)$	$e\left(\frac{1541}{2509}\right)$	$e\left(\frac{3945}{5018}\right)$	$e\left(\frac{1167}{2509}\right)$	$e\left(\frac{615}{5018}\right)$	$e\left(\frac{4623}{5018}\right)$	$e\left(\frac{61}{193}\right)$	$e\left(\frac{18}{193}\right)$	$e\left(\frac{174}{2509}\right)$
$\chi_{10037}(7,\cdot)$	10037.l	10036	yes	$-1$	$1$	$e\left(\frac{5585}{10036}\right)$	$e\left(\frac{437}{772}\right)$	$e\left(\frac{567}{5018}\right)$	$e\left(\frac{1305}{10036}\right)$	$e\left(\frac{615}{5018}\right)$	$e\left(\frac{337}{10036}\right)$	$e\left(\frac{6719}{10036}\right)$	$e\left(\frac{51}{386}\right)$	$e\left(\frac{265}{386}\right)$	$e\left(\frac{2471}{2509}\right)$
$\chi_{10037}(8,\cdot)$	10037.l	10036	yes	$-1$	$1$	$e\left(\frac{3}{10036}\right)$	$e\left(\frac{711}{772}\right)$	$e\left(\frac{3}{5018}\right)$	$e\left(\frac{4547}{10036}\right)$	$e\left(\frac{4623}{5018}\right)$	$e\left(\frac{6719}{10036}\right)$	$e\left(\frac{9}{10036}\right)$	$e\left(\frac{325}{386}\right)$	$e\left(\frac{175}{386}\right)$	$e\left(\frac{106}{2509}\right)$
$\chi_{10037}(9,\cdot)$	10037.h	386	yes	$1$	$1$	$e\left(\frac{237}{386}\right)$	$e\left(\frac{271}{386}\right)$	$e\left(\frac{44}{193}\right)$	$e\left(\frac{233}{386}\right)$	$e\left(\frac{61}{193}\right)$	$e\left(\frac{51}{386}\right)$	$e\left(\frac{325}{386}\right)$	$e\left(\frac{78}{193}\right)$	$e\left(\frac{42}{193}\right)$	$e\left(\frac{150}{193}\right)$
$\chi_{10037}(10,\cdot)$	10037.h	386	yes	$1$	$1$	$e\left(\frac{187}{386}\right)$	$e\left(\frac{235}{386}\right)$	$e\left(\frac{187}{193}\right)$	$e\left(\frac{363}{386}\right)$	$e\left(\frac{18}{193}\right)$	$e\left(\frac{265}{386}\right)$	$e\left(\frac{175}{386}\right)$	$e\left(\frac{42}{193}\right)$	$e\left(\frac{82}{193}\right)$	$e\left(\frac{155}{193}\right)$
$\chi_{10037}(11,\cdot)$	10037.j	2509	yes	$1$	$1$	$e\left(\frac{1708}{2509}\right)$	$e\left(\frac{75}{193}\right)$	$e\left(\frac{907}{2509}\right)$	$e\left(\frac{307}{2509}\right)$	$e\left(\frac{174}{2509}\right)$	$e\left(\frac{2471}{2509}\right)$	$e\left(\frac{106}{2509}\right)$	$e\left(\frac{150}{193}\right)$	$e\left(\frac{155}{193}\right)$	$e\left(\frac{2206}{2509}\right)$
$\chi_{10037}(12,\cdot)$	10037.l	10036	yes	$-1$	$1$	$e\left(\frac{3083}{10036}\right)$	$e\left(\frac{359}{772}\right)$	$e\left(\frac{3083}{5018}\right)$	$e\left(\frac{2715}{10036}\right)$	$e\left(\frac{3875}{5018}\right)$	$e\left(\frac{6815}{10036}\right)$	$e\left(\frac{9249}{10036}\right)$	$e\left(\frac{359}{386}\right)$	$e\left(\frac{223}{386}\right)$	$e\left(\frac{1882}{2509}\right)$
$\chi_{10037}(13,\cdot)$	10037.k	5018	yes	$1$	$1$	$e\left(\frac{3509}{5018}\right)$	$e\left(\frac{189}{386}\right)$	$e\left(\frac{1000}{2509}\right)$	$e\left(\frac{1067}{5018}\right)$	$e\left(\frac{474}{2509}\right)$	$e\left(\frac{2475}{5018}\right)$	$e\left(\frac{491}{5018}\right)$	$e\left(\frac{189}{193}\right)$	$e\left(\frac{176}{193}\right)$	$e\left(\frac{1251}{2509}\right)$
$\chi_{10037}(14,\cdot)$	10037.k	5018	yes	$1$	$1$	$e\left(\frac{2793}{5018}\right)$	$e\left(\frac{337}{386}\right)$	$e\left(\frac{284}{2509}\right)$	$e\left(\frac{3083}{5018}\right)$	$e\left(\frac{1078}{2509}\right)$	$e\left(\frac{2961}{5018}\right)$	$e\left(\frac{3361}{5018}\right)$	$e\left(\frac{144}{193}\right)$	$e\left(\frac{33}{193}\right)$	$e\left(\frac{1670}{2509}\right)$
$\chi_{10037}(15,\cdot)$	10037.k	5018	yes	$1$	$1$	$e\left(\frac{3971}{5018}\right)$	$e\left(\frac{59}{386}\right)$	$e\left(\frac{1462}{2509}\right)$	$e\left(\frac{3803}{5018}\right)$	$e\left(\frac{2369}{2509}\right)$	$e\left(\frac{3493}{5018}\right)$	$e\left(\frac{1877}{5018}\right)$	$e\left(\frac{59}{193}\right)$	$e\left(\frac{106}{193}\right)$	$e\left(\frac{1282}{2509}\right)$
$\chi_{10037}(16,\cdot)$	10037.j	2509	yes	$1$	$1$	$e\left(\frac{1}{2509}\right)$	$e\left(\frac{44}{193}\right)$	$e\left(\frac{2}{2509}\right)$	$e\left(\frac{2352}{2509}\right)$	$e\left(\frac{573}{2509}\right)$	$e\left(\frac{567}{2509}\right)$	$e\left(\frac{3}{2509}\right)$	$e\left(\frac{88}{193}\right)$	$e\left(\frac{181}{193}\right)$	$e\left(\frac{1814}{2509}\right)$
$\chi_{10037}(17,\cdot)$	10037.l	10036	yes	$-1$	$1$	$e\left(\frac{4845}{10036}\right)$	$e\left(\frac{301}{772}\right)$	$e\left(\frac{4845}{5018}\right)$	$e\left(\frac{7089}{10036}\right)$	$e\left(\frac{4379}{5018}\right)$	$e\left(\frac{2269}{10036}\right)$	$e\left(\frac{4499}{10036}\right)$	$e\left(\frac{301}{386}\right)$	$e\left(\frac{73}{386}\right)$	$e\left(\frac{578}{2509}\right)$
$\chi_{10037}(18,\cdot)$	10037.l	10036	yes	$-1$	$1$	$e\left(\frac{6163}{10036}\right)$	$e\left(\frac{7}{772}\right)$	$e\left(\frac{1145}{5018}\right)$	$e\left(\frac{883}{10036}\right)$	$e\left(\frac{3127}{5018}\right)$	$e\left(\frac{6911}{10036}\right)$	$e\left(\frac{8453}{10036}\right)$	$e\left(\frac{7}{386}\right)$	$e\left(\frac{271}{386}\right)$	$e\left(\frac{1149}{2509}\right)$
$\chi_{10037}(19,\cdot)$	10037.k	5018	yes	$1$	$1$	$e\left(\frac{4999}{5018}\right)$	$e\left(\frac{129}{386}\right)$	$e\left(\frac{2490}{2509}\right)$	$e\left(\frac{2983}{5018}\right)$	$e\left(\frac{829}{2509}\right)$	$e\left(\frac{4281}{5018}\right)$	$e\left(\frac{4961}{5018}\right)$	$e\left(\frac{129}{193}\right)$	$e\left(\frac{114}{193}\right)$	$e\left(\frac{330}{2509}\right)$
$\chi_{10037}(20,\cdot)$	10037.l	10036	yes	$-1$	$1$	$e\left(\frac{4863}{10036}\right)$	$e\left(\frac{707}{772}\right)$	$e\left(\frac{4863}{5018}\right)$	$e\left(\frac{4263}{10036}\right)$	$e\left(\frac{2009}{5018}\right)$	$e\left(\frac{2439}{10036}\right)$	$e\left(\frac{4553}{10036}\right)$	$e\left(\frac{321}{386}\right)$	$e\left(\frac{351}{386}\right)$	$e\left(\frac{1214}{2509}\right)$
$\chi_{10037}(21,\cdot)$	10037.k	5018	yes	$1$	$1$	$e\left(\frac{4333}{5018}\right)$	$e\left(\frac{161}{386}\right)$	$e\left(\frac{1824}{2509}\right)$	$e\left(\frac{2167}{5018}\right)$	$e\left(\frac{704}{2509}\right)$	$e\left(\frac{3009}{5018}\right)$	$e\left(\frac{2963}{5018}\right)$	$e\left(\frac{161}{193}\right)$	$e\left(\frac{57}{193}\right)$	$e\left(\frac{937}{2509}\right)$
$\chi_{10037}(22,\cdot)$	10037.l	10036	yes	$-1$	$1$	$e\left(\frac{6833}{10036}\right)$	$e\left(\frac{537}{772}\right)$	$e\left(\frac{1815}{5018}\right)$	$e\left(\frac{6089}{10036}\right)$	$e\left(\frac{1889}{5018}\right)$	$e\left(\frac{5433}{10036}\right)$	$e\left(\frac{427}{10036}\right)$	$e\left(\frac{151}{386}\right)$	$e\left(\frac{111}{386}\right)$	$e\left(\frac{1405}{2509}\right)$
$\chi_{10037}(23,\cdot)$	10037.k	5018	yes	$1$	$1$	$e\left(\frac{3915}{5018}\right)$	$e\left(\frac{297}{386}\right)$	$e\left(\frac{1406}{2509}\right)$	$e\left(\frac{2559}{5018}\right)$	$e\left(\frac{1379}{2509}\right)$	$e\left(\frac{1849}{5018}\right)$	$e\left(\frac{1709}{5018}\right)$	$e\left(\frac{104}{193}\right)$	$e\left(\frac{56}{193}\right)$	$e\left(\frac{670}{2509}\right)$
$\chi_{10037}(24,\cdot)$	10037.j	2509	yes	$1$	$1$	$e\left(\frac{771}{2509}\right)$	$e\left(\frac{149}{193}\right)$	$e\left(\frac{1542}{2509}\right)$	$e\left(\frac{1894}{2509}\right)$	$e\left(\frac{199}{2509}\right)$	$e\left(\frac{591}{2509}\right)$	$e\left(\frac{2313}{2509}\right)$	$e\left(\frac{105}{193}\right)$	$e\left(\frac{12}{193}\right)$	$e\left(\frac{1081}{2509}\right)$
$\chi_{10037}(25,\cdot)$	10037.k	5018	yes	$1$	$1$	$e\left(\frac{4861}{5018}\right)$	$e\left(\frac{233}{386}\right)$	$e\left(\frac{2352}{2509}\right)$	$e\left(\frac{4577}{5018}\right)$	$e\left(\frac{1436}{2509}\right)$	$e\left(\frac{1305}{5018}\right)$	$e\left(\frac{4547}{5018}\right)$	$e\left(\frac{40}{193}\right)$	$e\left(\frac{170}{193}\right)$	$e\left(\frac{614}{2509}\right)$
$\chi_{10037}(26,\cdot)$	10037.l	10036	yes	$-1$	$1$	$e\left(\frac{7019}{10036}\right)$	$e\left(\frac{615}{772}\right)$	$e\left(\frac{2001}{5018}\right)$	$e\left(\frac{6995}{10036}\right)$	$e\left(\frac{2489}{5018}\right)$	$e\left(\frac{499}{10036}\right)$	$e\left(\frac{985}{10036}\right)$	$e\left(\frac{229}{386}\right)$	$e\left(\frac{153}{386}\right)$	$e\left(\frac{450}{2509}\right)$
$\chi_{10037}(27,\cdot)$	10037.i	772	yes	$-1$	$1$	$e\left(\frac{711}{772}\right)$	$e\left(\frac{427}{772}\right)$	$e\left(\frac{325}{386}\right)$	$e\left(\frac{699}{772}\right)$	$e\left(\frac{183}{386}\right)$	$e\left(\frac{539}{772}\right)$	$e\left(\frac{589}{772}\right)$	$e\left(\frac{41}{386}\right)$	$e\left(\frac{319}{386}\right)$	$e\left(\frac{32}{193}\right)$
$\chi_{10037}(28,\cdot)$	10037.l	10036	yes	$-1$	$1$	$e\left(\frac{5587}{10036}\right)$	$e\left(\frac{139}{772}\right)$	$e\left(\frac{569}{5018}\right)$	$e\left(\frac{991}{10036}\right)$	$e\left(\frac{3697}{5018}\right)$	$e\left(\frac{1471}{10036}\right)$	$e\left(\frac{6725}{10036}\right)$	$e\left(\frac{139}{386}\right)$	$e\left(\frac{253}{386}\right)$	$e\left(\frac{869}{2509}\right)$
$\chi_{10037}(29,\cdot)$	10037.l	10036	yes	$-1$	$1$	$e\left(\frac{9323}{10036}\right)$	$e\left(\frac{87}{772}\right)$	$e\left(\frac{4305}{5018}\right)$	$e\left(\frac{6563}{10036}\right)$	$e\left(\frac{209}{5018}\right)$	$e\left(\frac{2187}{10036}\right)$	$e\left(\frac{7897}{10036}\right)$	$e\left(\frac{87}{386}\right)$	$e\left(\frac{225}{386}\right)$	$e\left(\frac{1570}{2509}\right)$
$\chi_{10037}(30,\cdot)$	10037.i	772	yes	$-1$	$1$	$e\left(\frac{611}{772}\right)$	$e\left(\frac{355}{772}\right)$	$e\left(\frac{225}{386}\right)$	$e\left(\frac{187}{772}\right)$	$e\left(\frac{97}{386}\right)$	$e\left(\frac{195}{772}\right)$	$e\left(\frac{289}{772}\right)$	$e\left(\frac{355}{386}\right)$	$e\left(\frac{13}{386}\right)$	$e\left(\frac{37}{193}\right)$
$\chi_{10037}(31,\cdot)$	10037.l	10036	yes	$-1$	$1$	$e\left(\frac{3295}{10036}\right)$	$e\left(\frac{423}{772}\right)$	$e\left(\frac{3295}{5018}\right)$	$e\left(\frac{9575}{10036}\right)$	$e\left(\frac{4397}{5018}\right)$	$e\left(\frac{6587}{10036}\right)$	$e\left(\frac{9885}{10036}\right)$	$e\left(\frac{37}{386}\right)$	$e\left(\frac{109}{386}\right)$	$e\left(\frac{173}{2509}\right)$
$\chi_{10037}(32,\cdot)$	10037.l	10036	yes	$-1$	$1$	$e\left(\frac{5}{10036}\right)$	$e\left(\frac{413}{772}\right)$	$e\left(\frac{5}{5018}\right)$	$e\left(\frac{4233}{10036}\right)$	$e\left(\frac{2687}{5018}\right)$	$e\left(\frac{7853}{10036}\right)$	$e\left(\frac{15}{10036}\right)$	$e\left(\frac{27}{386}\right)$	$e\left(\frac{163}{386}\right)$	$e\left(\frac{1013}{2509}\right)$

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Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Modulus	$10037$
Structure	\(C_{10036}\)
Order	$10036$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\(\chi_{10037}(1,\cdot)\)	10037.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{10037}(2,\cdot)\)	10037.l	10036	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{10036}\right)\)	\(e\left(\frac{237}{772}\right)\)	\(e\left(\frac{1}{5018}\right)\)	\(e\left(\frac{4861}{10036}\right)\)	\(e\left(\frac{1541}{5018}\right)\)	\(e\left(\frac{5585}{10036}\right)\)	\(e\left(\frac{3}{10036}\right)\)	\(e\left(\frac{237}{386}\right)\)	\(e\left(\frac{187}{386}\right)\)	\(e\left(\frac{1708}{2509}\right)\)
\(\chi_{10037}(3,\cdot)\)	10037.i	772	yes	\(-1\)	\(1\)	\(e\left(\frac{237}{772}\right)\)	\(e\left(\frac{657}{772}\right)\)	\(e\left(\frac{237}{386}\right)\)	\(e\left(\frac{233}{772}\right)\)	\(e\left(\frac{61}{386}\right)\)	\(e\left(\frac{437}{772}\right)\)	\(e\left(\frac{711}{772}\right)\)	\(e\left(\frac{271}{386}\right)\)	\(e\left(\frac{235}{386}\right)\)	\(e\left(\frac{75}{193}\right)\)
\(\chi_{10037}(4,\cdot)\)	10037.k	5018	yes	\(1\)	\(1\)	\(e\left(\frac{1}{5018}\right)\)	\(e\left(\frac{237}{386}\right)\)	\(e\left(\frac{1}{2509}\right)\)	\(e\left(\frac{4861}{5018}\right)\)	\(e\left(\frac{1541}{2509}\right)\)	\(e\left(\frac{567}{5018}\right)\)	\(e\left(\frac{3}{5018}\right)\)	\(e\left(\frac{44}{193}\right)\)	\(e\left(\frac{187}{193}\right)\)	\(e\left(\frac{907}{2509}\right)\)
\(\chi_{10037}(5,\cdot)\)	10037.l	10036	yes	\(-1\)	\(1\)	\(e\left(\frac{4861}{10036}\right)\)	\(e\left(\frac{233}{772}\right)\)	\(e\left(\frac{4861}{5018}\right)\)	\(e\left(\frac{4577}{10036}\right)\)	\(e\left(\frac{3945}{5018}\right)\)	\(e\left(\frac{1305}{10036}\right)\)	\(e\left(\frac{4547}{10036}\right)\)	\(e\left(\frac{233}{386}\right)\)	\(e\left(\frac{363}{386}\right)\)	\(e\left(\frac{307}{2509}\right)\)
\(\chi_{10037}(6,\cdot)\)	10037.k	5018	yes	\(1\)	\(1\)	\(e\left(\frac{1541}{5018}\right)\)	\(e\left(\frac{61}{386}\right)\)	\(e\left(\frac{1541}{2509}\right)\)	\(e\left(\frac{3945}{5018}\right)\)	\(e\left(\frac{1167}{2509}\right)\)	\(e\left(\frac{615}{5018}\right)\)	\(e\left(\frac{4623}{5018}\right)\)	\(e\left(\frac{61}{193}\right)\)	\(e\left(\frac{18}{193}\right)\)	\(e\left(\frac{174}{2509}\right)\)
\(\chi_{10037}(7,\cdot)\)	10037.l	10036	yes	\(-1\)	\(1\)	\(e\left(\frac{5585}{10036}\right)\)	\(e\left(\frac{437}{772}\right)\)	\(e\left(\frac{567}{5018}\right)\)	\(e\left(\frac{1305}{10036}\right)\)	\(e\left(\frac{615}{5018}\right)\)	\(e\left(\frac{337}{10036}\right)\)	\(e\left(\frac{6719}{10036}\right)\)	\(e\left(\frac{51}{386}\right)\)	\(e\left(\frac{265}{386}\right)\)	\(e\left(\frac{2471}{2509}\right)\)
\(\chi_{10037}(8,\cdot)\)	10037.l	10036	yes	\(-1\)	\(1\)	\(e\left(\frac{3}{10036}\right)\)	\(e\left(\frac{711}{772}\right)\)	\(e\left(\frac{3}{5018}\right)\)	\(e\left(\frac{4547}{10036}\right)\)	\(e\left(\frac{4623}{5018}\right)\)	\(e\left(\frac{6719}{10036}\right)\)	\(e\left(\frac{9}{10036}\right)\)	\(e\left(\frac{325}{386}\right)\)	\(e\left(\frac{175}{386}\right)\)	\(e\left(\frac{106}{2509}\right)\)
\(\chi_{10037}(9,\cdot)\)	10037.h	386	yes	\(1\)	\(1\)	\(e\left(\frac{237}{386}\right)\)	\(e\left(\frac{271}{386}\right)\)	\(e\left(\frac{44}{193}\right)\)	\(e\left(\frac{233}{386}\right)\)	\(e\left(\frac{61}{193}\right)\)	\(e\left(\frac{51}{386}\right)\)	\(e\left(\frac{325}{386}\right)\)	\(e\left(\frac{78}{193}\right)\)	\(e\left(\frac{42}{193}\right)\)	\(e\left(\frac{150}{193}\right)\)
\(\chi_{10037}(10,\cdot)\)	10037.h	386	yes	\(1\)	\(1\)	\(e\left(\frac{187}{386}\right)\)	\(e\left(\frac{235}{386}\right)\)	\(e\left(\frac{187}{193}\right)\)	\(e\left(\frac{363}{386}\right)\)	\(e\left(\frac{18}{193}\right)\)	\(e\left(\frac{265}{386}\right)\)	\(e\left(\frac{175}{386}\right)\)	\(e\left(\frac{42}{193}\right)\)	\(e\left(\frac{82}{193}\right)\)	\(e\left(\frac{155}{193}\right)\)
\(\chi_{10037}(11,\cdot)\)	10037.j	2509	yes	\(1\)	\(1\)	\(e\left(\frac{1708}{2509}\right)\)	\(e\left(\frac{75}{193}\right)\)	\(e\left(\frac{907}{2509}\right)\)	\(e\left(\frac{307}{2509}\right)\)	\(e\left(\frac{174}{2509}\right)\)	\(e\left(\frac{2471}{2509}\right)\)	\(e\left(\frac{106}{2509}\right)\)	\(e\left(\frac{150}{193}\right)\)	\(e\left(\frac{155}{193}\right)\)	\(e\left(\frac{2206}{2509}\right)\)
\(\chi_{10037}(12,\cdot)\)	10037.l	10036	yes	\(-1\)	\(1\)	\(e\left(\frac{3083}{10036}\right)\)	\(e\left(\frac{359}{772}\right)\)	\(e\left(\frac{3083}{5018}\right)\)	\(e\left(\frac{2715}{10036}\right)\)	\(e\left(\frac{3875}{5018}\right)\)	\(e\left(\frac{6815}{10036}\right)\)	\(e\left(\frac{9249}{10036}\right)\)	\(e\left(\frac{359}{386}\right)\)	\(e\left(\frac{223}{386}\right)\)	\(e\left(\frac{1882}{2509}\right)\)
\(\chi_{10037}(13,\cdot)\)	10037.k	5018	yes	\(1\)	\(1\)	\(e\left(\frac{3509}{5018}\right)\)	\(e\left(\frac{189}{386}\right)\)	\(e\left(\frac{1000}{2509}\right)\)	\(e\left(\frac{1067}{5018}\right)\)	\(e\left(\frac{474}{2509}\right)\)	\(e\left(\frac{2475}{5018}\right)\)	\(e\left(\frac{491}{5018}\right)\)	\(e\left(\frac{189}{193}\right)\)	\(e\left(\frac{176}{193}\right)\)	\(e\left(\frac{1251}{2509}\right)\)
\(\chi_{10037}(14,\cdot)\)	10037.k	5018	yes	\(1\)	\(1\)	\(e\left(\frac{2793}{5018}\right)\)	\(e\left(\frac{337}{386}\right)\)	\(e\left(\frac{284}{2509}\right)\)	\(e\left(\frac{3083}{5018}\right)\)	\(e\left(\frac{1078}{2509}\right)\)	\(e\left(\frac{2961}{5018}\right)\)	\(e\left(\frac{3361}{5018}\right)\)	\(e\left(\frac{144}{193}\right)\)	\(e\left(\frac{33}{193}\right)\)	\(e\left(\frac{1670}{2509}\right)\)
\(\chi_{10037}(15,\cdot)\)	10037.k	5018	yes	\(1\)	\(1\)	\(e\left(\frac{3971}{5018}\right)\)	\(e\left(\frac{59}{386}\right)\)	\(e\left(\frac{1462}{2509}\right)\)	\(e\left(\frac{3803}{5018}\right)\)	\(e\left(\frac{2369}{2509}\right)\)	\(e\left(\frac{3493}{5018}\right)\)	\(e\left(\frac{1877}{5018}\right)\)	\(e\left(\frac{59}{193}\right)\)	\(e\left(\frac{106}{193}\right)\)	\(e\left(\frac{1282}{2509}\right)\)
\(\chi_{10037}(16,\cdot)\)	10037.j	2509	yes	\(1\)	\(1\)	\(e\left(\frac{1}{2509}\right)\)	\(e\left(\frac{44}{193}\right)\)	\(e\left(\frac{2}{2509}\right)\)	\(e\left(\frac{2352}{2509}\right)\)	\(e\left(\frac{573}{2509}\right)\)	\(e\left(\frac{567}{2509}\right)\)	\(e\left(\frac{3}{2509}\right)\)	\(e\left(\frac{88}{193}\right)\)	\(e\left(\frac{181}{193}\right)\)	\(e\left(\frac{1814}{2509}\right)\)
\(\chi_{10037}(17,\cdot)\)	10037.l	10036	yes	\(-1\)	\(1\)	\(e\left(\frac{4845}{10036}\right)\)	\(e\left(\frac{301}{772}\right)\)	\(e\left(\frac{4845}{5018}\right)\)	\(e\left(\frac{7089}{10036}\right)\)	\(e\left(\frac{4379}{5018}\right)\)	\(e\left(\frac{2269}{10036}\right)\)	\(e\left(\frac{4499}{10036}\right)\)	\(e\left(\frac{301}{386}\right)\)	\(e\left(\frac{73}{386}\right)\)	\(e\left(\frac{578}{2509}\right)\)
\(\chi_{10037}(18,\cdot)\)	10037.l	10036	yes	\(-1\)	\(1\)	\(e\left(\frac{6163}{10036}\right)\)	\(e\left(\frac{7}{772}\right)\)	\(e\left(\frac{1145}{5018}\right)\)	\(e\left(\frac{883}{10036}\right)\)	\(e\left(\frac{3127}{5018}\right)\)	\(e\left(\frac{6911}{10036}\right)\)	\(e\left(\frac{8453}{10036}\right)\)	\(e\left(\frac{7}{386}\right)\)	\(e\left(\frac{271}{386}\right)\)	\(e\left(\frac{1149}{2509}\right)\)
\(\chi_{10037}(19,\cdot)\)	10037.k	5018	yes	\(1\)	\(1\)	\(e\left(\frac{4999}{5018}\right)\)	\(e\left(\frac{129}{386}\right)\)	\(e\left(\frac{2490}{2509}\right)\)	\(e\left(\frac{2983}{5018}\right)\)	\(e\left(\frac{829}{2509}\right)\)	\(e\left(\frac{4281}{5018}\right)\)	\(e\left(\frac{4961}{5018}\right)\)	\(e\left(\frac{129}{193}\right)\)	\(e\left(\frac{114}{193}\right)\)	\(e\left(\frac{330}{2509}\right)\)
\(\chi_{10037}(20,\cdot)\)	10037.l	10036	yes	\(-1\)	\(1\)	\(e\left(\frac{4863}{10036}\right)\)	\(e\left(\frac{707}{772}\right)\)	\(e\left(\frac{4863}{5018}\right)\)	\(e\left(\frac{4263}{10036}\right)\)	\(e\left(\frac{2009}{5018}\right)\)	\(e\left(\frac{2439}{10036}\right)\)	\(e\left(\frac{4553}{10036}\right)\)	\(e\left(\frac{321}{386}\right)\)	\(e\left(\frac{351}{386}\right)\)	\(e\left(\frac{1214}{2509}\right)\)
\(\chi_{10037}(21,\cdot)\)	10037.k	5018	yes	\(1\)	\(1\)	\(e\left(\frac{4333}{5018}\right)\)	\(e\left(\frac{161}{386}\right)\)	\(e\left(\frac{1824}{2509}\right)\)	\(e\left(\frac{2167}{5018}\right)\)	\(e\left(\frac{704}{2509}\right)\)	\(e\left(\frac{3009}{5018}\right)\)	\(e\left(\frac{2963}{5018}\right)\)	\(e\left(\frac{161}{193}\right)\)	\(e\left(\frac{57}{193}\right)\)	\(e\left(\frac{937}{2509}\right)\)
\(\chi_{10037}(22,\cdot)\)	10037.l	10036	yes	\(-1\)	\(1\)	\(e\left(\frac{6833}{10036}\right)\)	\(e\left(\frac{537}{772}\right)\)	\(e\left(\frac{1815}{5018}\right)\)	\(e\left(\frac{6089}{10036}\right)\)	\(e\left(\frac{1889}{5018}\right)\)	\(e\left(\frac{5433}{10036}\right)\)	\(e\left(\frac{427}{10036}\right)\)	\(e\left(\frac{151}{386}\right)\)	\(e\left(\frac{111}{386}\right)\)	\(e\left(\frac{1405}{2509}\right)\)
\(\chi_{10037}(23,\cdot)\)	10037.k	5018	yes	\(1\)	\(1\)	\(e\left(\frac{3915}{5018}\right)\)	\(e\left(\frac{297}{386}\right)\)	\(e\left(\frac{1406}{2509}\right)\)	\(e\left(\frac{2559}{5018}\right)\)	\(e\left(\frac{1379}{2509}\right)\)	\(e\left(\frac{1849}{5018}\right)\)	\(e\left(\frac{1709}{5018}\right)\)	\(e\left(\frac{104}{193}\right)\)	\(e\left(\frac{56}{193}\right)\)	\(e\left(\frac{670}{2509}\right)\)
\(\chi_{10037}(24,\cdot)\)	10037.j	2509	yes	\(1\)	\(1\)	\(e\left(\frac{771}{2509}\right)\)	\(e\left(\frac{149}{193}\right)\)	\(e\left(\frac{1542}{2509}\right)\)	\(e\left(\frac{1894}{2509}\right)\)	\(e\left(\frac{199}{2509}\right)\)	\(e\left(\frac{591}{2509}\right)\)	\(e\left(\frac{2313}{2509}\right)\)	\(e\left(\frac{105}{193}\right)\)	\(e\left(\frac{12}{193}\right)\)	\(e\left(\frac{1081}{2509}\right)\)
\(\chi_{10037}(25,\cdot)\)	10037.k	5018	yes	\(1\)	\(1\)	\(e\left(\frac{4861}{5018}\right)\)	\(e\left(\frac{233}{386}\right)\)	\(e\left(\frac{2352}{2509}\right)\)	\(e\left(\frac{4577}{5018}\right)\)	\(e\left(\frac{1436}{2509}\right)\)	\(e\left(\frac{1305}{5018}\right)\)	\(e\left(\frac{4547}{5018}\right)\)	\(e\left(\frac{40}{193}\right)\)	\(e\left(\frac{170}{193}\right)\)	\(e\left(\frac{614}{2509}\right)\)
\(\chi_{10037}(26,\cdot)\)	10037.l	10036	yes	\(-1\)	\(1\)	\(e\left(\frac{7019}{10036}\right)\)	\(e\left(\frac{615}{772}\right)\)	\(e\left(\frac{2001}{5018}\right)\)	\(e\left(\frac{6995}{10036}\right)\)	\(e\left(\frac{2489}{5018}\right)\)	\(e\left(\frac{499}{10036}\right)\)	\(e\left(\frac{985}{10036}\right)\)	\(e\left(\frac{229}{386}\right)\)	\(e\left(\frac{153}{386}\right)\)	\(e\left(\frac{450}{2509}\right)\)
\(\chi_{10037}(27,\cdot)\)	10037.i	772	yes	\(-1\)	\(1\)	\(e\left(\frac{711}{772}\right)\)	\(e\left(\frac{427}{772}\right)\)	\(e\left(\frac{325}{386}\right)\)	\(e\left(\frac{699}{772}\right)\)	\(e\left(\frac{183}{386}\right)\)	\(e\left(\frac{539}{772}\right)\)	\(e\left(\frac{589}{772}\right)\)	\(e\left(\frac{41}{386}\right)\)	\(e\left(\frac{319}{386}\right)\)	\(e\left(\frac{32}{193}\right)\)
\(\chi_{10037}(28,\cdot)\)	10037.l	10036	yes	\(-1\)	\(1\)	\(e\left(\frac{5587}{10036}\right)\)	\(e\left(\frac{139}{772}\right)\)	\(e\left(\frac{569}{5018}\right)\)	\(e\left(\frac{991}{10036}\right)\)	\(e\left(\frac{3697}{5018}\right)\)	\(e\left(\frac{1471}{10036}\right)\)	\(e\left(\frac{6725}{10036}\right)\)	\(e\left(\frac{139}{386}\right)\)	\(e\left(\frac{253}{386}\right)\)	\(e\left(\frac{869}{2509}\right)\)
\(\chi_{10037}(29,\cdot)\)	10037.l	10036	yes	\(-1\)	\(1\)	\(e\left(\frac{9323}{10036}\right)\)	\(e\left(\frac{87}{772}\right)\)	\(e\left(\frac{4305}{5018}\right)\)	\(e\left(\frac{6563}{10036}\right)\)	\(e\left(\frac{209}{5018}\right)\)	\(e\left(\frac{2187}{10036}\right)\)	\(e\left(\frac{7897}{10036}\right)\)	\(e\left(\frac{87}{386}\right)\)	\(e\left(\frac{225}{386}\right)\)	\(e\left(\frac{1570}{2509}\right)\)
\(\chi_{10037}(30,\cdot)\)	10037.i	772	yes	\(-1\)	\(1\)	\(e\left(\frac{611}{772}\right)\)	\(e\left(\frac{355}{772}\right)\)	\(e\left(\frac{225}{386}\right)\)	\(e\left(\frac{187}{772}\right)\)	\(e\left(\frac{97}{386}\right)\)	\(e\left(\frac{195}{772}\right)\)	\(e\left(\frac{289}{772}\right)\)	\(e\left(\frac{355}{386}\right)\)	\(e\left(\frac{13}{386}\right)\)	\(e\left(\frac{37}{193}\right)\)
\(\chi_{10037}(31,\cdot)\)	10037.l	10036	yes	\(-1\)	\(1\)	\(e\left(\frac{3295}{10036}\right)\)	\(e\left(\frac{423}{772}\right)\)	\(e\left(\frac{3295}{5018}\right)\)	\(e\left(\frac{9575}{10036}\right)\)	\(e\left(\frac{4397}{5018}\right)\)	\(e\left(\frac{6587}{10036}\right)\)	\(e\left(\frac{9885}{10036}\right)\)	\(e\left(\frac{37}{386}\right)\)	\(e\left(\frac{109}{386}\right)\)	\(e\left(\frac{173}{2509}\right)\)
\(\chi_{10037}(32,\cdot)\)	10037.l	10036	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{10036}\right)\)	\(e\left(\frac{413}{772}\right)\)	\(e\left(\frac{5}{5018}\right)\)	\(e\left(\frac{4233}{10036}\right)\)	\(e\left(\frac{2687}{5018}\right)\)	\(e\left(\frac{7853}{10036}\right)\)	\(e\left(\frac{15}{10036}\right)\)	\(e\left(\frac{27}{386}\right)\)	\(e\left(\frac{163}{386}\right)\)	\(e\left(\frac{1013}{2509}\right)\)

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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.