LMFDB - Group of Dirichlet characters of modulus 20627

Show commands: PariGP / SageMath

sage: H = DirichletGroup(20627)

pari: g = idealstar(,20627,2)

Character group

sage: G.order() pari: g.no
Order	=	20626
sage: H.invariants() pari: g.cyc
Structure	=	$C_{20626}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{20627}(2,\cdot)$

First 32 of 20626 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	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{20627}(1,\cdot)$	20627.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{20627}(2,\cdot)$	20627.d	20626	yes	$-1$	$1$	$e\left(\frac{1}{20626}\right)$	$e\left(\frac{6751}{10313}\right)$	$e\left(\frac{1}{10313}\right)$	$e\left(\frac{19543}{20626}\right)$	$e\left(\frac{13503}{20626}\right)$	$e\left(\frac{9248}{10313}\right)$	$e\left(\frac{3}{20626}\right)$	$e\left(\frac{3189}{10313}\right)$	$e\left(\frac{9772}{10313}\right)$	$e\left(\frac{572}{10313}\right)$
$\chi_{20627}(3,\cdot)$	20627.c	10313	yes	$1$	$1$	$e\left(\frac{6751}{10313}\right)$	$e\left(\frac{5708}{10313}\right)$	$e\left(\frac{3189}{10313}\right)$	$e\left(\frac{584}{10313}\right)$	$e\left(\frac{2146}{10313}\right)$	$e\left(\frac{7005}{10313}\right)$	$e\left(\frac{9940}{10313}\right)$	$e\left(\frac{1103}{10313}\right)$	$e\left(\frac{7335}{10313}\right)$	$e\left(\frac{9020}{10313}\right)$
$\chi_{20627}(4,\cdot)$	20627.c	10313	yes	$1$	$1$	$e\left(\frac{1}{10313}\right)$	$e\left(\frac{3189}{10313}\right)$	$e\left(\frac{2}{10313}\right)$	$e\left(\frac{9230}{10313}\right)$	$e\left(\frac{3190}{10313}\right)$	$e\left(\frac{8183}{10313}\right)$	$e\left(\frac{3}{10313}\right)$	$e\left(\frac{6378}{10313}\right)$	$e\left(\frac{9231}{10313}\right)$	$e\left(\frac{1144}{10313}\right)$
$\chi_{20627}(5,\cdot)$	20627.d	20626	yes	$-1$	$1$	$e\left(\frac{19543}{20626}\right)$	$e\left(\frac{584}{10313}\right)$	$e\left(\frac{9230}{10313}\right)$	$e\left(\frac{17833}{20626}\right)$	$e\left(\frac{85}{20626}\right)$	$e\left(\frac{8652}{10313}\right)$	$e\left(\frac{17377}{20626}\right)$	$e\left(\frac{1168}{10313}\right)$	$e\left(\frac{8375}{10313}\right)$	$e\left(\frac{9617}{10313}\right)$
$\chi_{20627}(6,\cdot)$	20627.d	20626	yes	$-1$	$1$	$e\left(\frac{13503}{20626}\right)$	$e\left(\frac{2146}{10313}\right)$	$e\left(\frac{3190}{10313}\right)$	$e\left(\frac{85}{20626}\right)$	$e\left(\frac{17795}{20626}\right)$	$e\left(\frac{5940}{10313}\right)$	$e\left(\frac{19883}{20626}\right)$	$e\left(\frac{4292}{10313}\right)$	$e\left(\frac{6794}{10313}\right)$	$e\left(\frac{9592}{10313}\right)$
$\chi_{20627}(7,\cdot)$	20627.c	10313	yes	$1$	$1$	$e\left(\frac{9248}{10313}\right)$	$e\left(\frac{7005}{10313}\right)$	$e\left(\frac{8183}{10313}\right)$	$e\left(\frac{8652}{10313}\right)$	$e\left(\frac{5940}{10313}\right)$	$e\left(\frac{9903}{10313}\right)$	$e\left(\frac{7118}{10313}\right)$	$e\left(\frac{3697}{10313}\right)$	$e\left(\frac{7587}{10313}\right)$	$e\left(\frac{8887}{10313}\right)$
$\chi_{20627}(8,\cdot)$	20627.d	20626	yes	$-1$	$1$	$e\left(\frac{3}{20626}\right)$	$e\left(\frac{9940}{10313}\right)$	$e\left(\frac{3}{10313}\right)$	$e\left(\frac{17377}{20626}\right)$	$e\left(\frac{19883}{20626}\right)$	$e\left(\frac{7118}{10313}\right)$	$e\left(\frac{9}{20626}\right)$	$e\left(\frac{9567}{10313}\right)$	$e\left(\frac{8690}{10313}\right)$	$e\left(\frac{1716}{10313}\right)$
$\chi_{20627}(9,\cdot)$	20627.c	10313	yes	$1$	$1$	$e\left(\frac{3189}{10313}\right)$	$e\left(\frac{1103}{10313}\right)$	$e\left(\frac{6378}{10313}\right)$	$e\left(\frac{1168}{10313}\right)$	$e\left(\frac{4292}{10313}\right)$	$e\left(\frac{3697}{10313}\right)$	$e\left(\frac{9567}{10313}\right)$	$e\left(\frac{2206}{10313}\right)$	$e\left(\frac{4357}{10313}\right)$	$e\left(\frac{7727}{10313}\right)$
$\chi_{20627}(10,\cdot)$	20627.c	10313	yes	$1$	$1$	$e\left(\frac{9772}{10313}\right)$	$e\left(\frac{7335}{10313}\right)$	$e\left(\frac{9231}{10313}\right)$	$e\left(\frac{8375}{10313}\right)$	$e\left(\frac{6794}{10313}\right)$	$e\left(\frac{7587}{10313}\right)$	$e\left(\frac{8690}{10313}\right)$	$e\left(\frac{4357}{10313}\right)$	$e\left(\frac{7834}{10313}\right)$	$e\left(\frac{10189}{10313}\right)$
$\chi_{20627}(11,\cdot)$	20627.c	10313	yes	$1$	$1$	$e\left(\frac{572}{10313}\right)$	$e\left(\frac{9020}{10313}\right)$	$e\left(\frac{1144}{10313}\right)$	$e\left(\frac{9617}{10313}\right)$	$e\left(\frac{9592}{10313}\right)$	$e\left(\frac{8887}{10313}\right)$	$e\left(\frac{1716}{10313}\right)$	$e\left(\frac{7727}{10313}\right)$	$e\left(\frac{10189}{10313}\right)$	$e\left(\frac{4649}{10313}\right)$
$\chi_{20627}(12,\cdot)$	20627.c	10313	yes	$1$	$1$	$e\left(\frac{6752}{10313}\right)$	$e\left(\frac{8897}{10313}\right)$	$e\left(\frac{3191}{10313}\right)$	$e\left(\frac{9814}{10313}\right)$	$e\left(\frac{5336}{10313}\right)$	$e\left(\frac{4875}{10313}\right)$	$e\left(\frac{9943}{10313}\right)$	$e\left(\frac{7481}{10313}\right)$	$e\left(\frac{6253}{10313}\right)$	$e\left(\frac{10164}{10313}\right)$
$\chi_{20627}(13,\cdot)$	20627.c	10313	yes	$1$	$1$	$e\left(\frac{10100}{10313}\right)$	$e\left(\frac{1401}{10313}\right)$	$e\left(\frac{9887}{10313}\right)$	$e\left(\frac{3793}{10313}\right)$	$e\left(\frac{1188}{10313}\right)$	$e\left(\frac{10231}{10313}\right)$	$e\left(\frac{9674}{10313}\right)$	$e\left(\frac{2802}{10313}\right)$	$e\left(\frac{3580}{10313}\right)$	$e\left(\frac{3840}{10313}\right)$
$\chi_{20627}(14,\cdot)$	20627.d	20626	yes	$-1$	$1$	$e\left(\frac{18497}{20626}\right)$	$e\left(\frac{3443}{10313}\right)$	$e\left(\frac{8184}{10313}\right)$	$e\left(\frac{16221}{20626}\right)$	$e\left(\frac{4757}{20626}\right)$	$e\left(\frac{8838}{10313}\right)$	$e\left(\frac{14239}{20626}\right)$	$e\left(\frac{6886}{10313}\right)$	$e\left(\frac{7046}{10313}\right)$	$e\left(\frac{9459}{10313}\right)$
$\chi_{20627}(15,\cdot)$	20627.d	20626	yes	$-1$	$1$	$e\left(\frac{12419}{20626}\right)$	$e\left(\frac{6292}{10313}\right)$	$e\left(\frac{2106}{10313}\right)$	$e\left(\frac{19001}{20626}\right)$	$e\left(\frac{4377}{20626}\right)$	$e\left(\frac{5344}{10313}\right)$	$e\left(\frac{16631}{20626}\right)$	$e\left(\frac{2271}{10313}\right)$	$e\left(\frac{5397}{10313}\right)$	$e\left(\frac{8324}{10313}\right)$
$\chi_{20627}(16,\cdot)$	20627.c	10313	yes	$1$	$1$	$e\left(\frac{2}{10313}\right)$	$e\left(\frac{6378}{10313}\right)$	$e\left(\frac{4}{10313}\right)$	$e\left(\frac{8147}{10313}\right)$	$e\left(\frac{6380}{10313}\right)$	$e\left(\frac{6053}{10313}\right)$	$e\left(\frac{6}{10313}\right)$	$e\left(\frac{2443}{10313}\right)$	$e\left(\frac{8149}{10313}\right)$	$e\left(\frac{2288}{10313}\right)$
$\chi_{20627}(17,\cdot)$	20627.d	20626	yes	$-1$	$1$	$e\left(\frac{13949}{20626}\right)$	$e\left(\frac{1696}{10313}\right)$	$e\left(\frac{3636}{10313}\right)$	$e\left(\frac{12091}{20626}\right)$	$e\left(\frac{17341}{20626}\right)$	$e\left(\frac{5348}{10313}\right)$	$e\left(\frac{595}{20626}\right)$	$e\left(\frac{3392}{10313}\right)$	$e\left(\frac{2707}{10313}\right)$	$e\left(\frac{6879}{10313}\right)$
$\chi_{20627}(18,\cdot)$	20627.d	20626	yes	$-1$	$1$	$e\left(\frac{6379}{20626}\right)$	$e\left(\frac{7854}{10313}\right)$	$e\left(\frac{6379}{10313}\right)$	$e\left(\frac{1253}{20626}\right)$	$e\left(\frac{1461}{20626}\right)$	$e\left(\frac{2632}{10313}\right)$	$e\left(\frac{19137}{20626}\right)$	$e\left(\frac{5395}{10313}\right)$	$e\left(\frac{3816}{10313}\right)$	$e\left(\frac{8299}{10313}\right)$
$\chi_{20627}(19,\cdot)$	20627.c	10313	yes	$1$	$1$	$e\left(\frac{5983}{10313}\right)$	$e\left(\frac{737}{10313}\right)$	$e\left(\frac{1653}{10313}\right)$	$e\left(\frac{7288}{10313}\right)$	$e\left(\frac{6720}{10313}\right)$	$e\left(\frac{3078}{10313}\right)$	$e\left(\frac{7636}{10313}\right)$	$e\left(\frac{1474}{10313}\right)$	$e\left(\frac{2958}{10313}\right)$	$e\left(\frac{7033}{10313}\right)$
$\chi_{20627}(20,\cdot)$	20627.d	20626	yes	$-1$	$1$	$e\left(\frac{19545}{20626}\right)$	$e\left(\frac{3773}{10313}\right)$	$e\left(\frac{9232}{10313}\right)$	$e\left(\frac{15667}{20626}\right)$	$e\left(\frac{6465}{20626}\right)$	$e\left(\frac{6522}{10313}\right)$	$e\left(\frac{17383}{20626}\right)$	$e\left(\frac{7546}{10313}\right)$	$e\left(\frac{7293}{10313}\right)$	$e\left(\frac{448}{10313}\right)$
$\chi_{20627}(21,\cdot)$	20627.c	10313	yes	$1$	$1$	$e\left(\frac{5686}{10313}\right)$	$e\left(\frac{2400}{10313}\right)$	$e\left(\frac{1059}{10313}\right)$	$e\left(\frac{9236}{10313}\right)$	$e\left(\frac{8086}{10313}\right)$	$e\left(\frac{6595}{10313}\right)$	$e\left(\frac{6745}{10313}\right)$	$e\left(\frac{4800}{10313}\right)$	$e\left(\frac{4609}{10313}\right)$	$e\left(\frac{7594}{10313}\right)$
$\chi_{20627}(22,\cdot)$	20627.d	20626	yes	$-1$	$1$	$e\left(\frac{1145}{20626}\right)$	$e\left(\frac{5458}{10313}\right)$	$e\left(\frac{1145}{10313}\right)$	$e\left(\frac{18151}{20626}\right)$	$e\left(\frac{12061}{20626}\right)$	$e\left(\frac{7822}{10313}\right)$	$e\left(\frac{3435}{20626}\right)$	$e\left(\frac{603}{10313}\right)$	$e\left(\frac{9648}{10313}\right)$	$e\left(\frac{5221}{10313}\right)$
$\chi_{20627}(23,\cdot)$	20627.c	10313	yes	$1$	$1$	$e\left(\frac{1888}{10313}\right)$	$e\left(\frac{8353}{10313}\right)$	$e\left(\frac{3776}{10313}\right)$	$e\left(\frac{7583}{10313}\right)$	$e\left(\frac{10241}{10313}\right)$	$e\left(\frac{630}{10313}\right)$	$e\left(\frac{5664}{10313}\right)$	$e\left(\frac{6393}{10313}\right)$	$e\left(\frac{9471}{10313}\right)$	$e\left(\frac{4455}{10313}\right)$
$\chi_{20627}(24,\cdot)$	20627.d	20626	yes	$-1$	$1$	$e\left(\frac{13505}{20626}\right)$	$e\left(\frac{5335}{10313}\right)$	$e\left(\frac{3192}{10313}\right)$	$e\left(\frac{18545}{20626}\right)$	$e\left(\frac{3549}{20626}\right)$	$e\left(\frac{3810}{10313}\right)$	$e\left(\frac{19889}{20626}\right)$	$e\left(\frac{357}{10313}\right)$	$e\left(\frac{5712}{10313}\right)$	$e\left(\frac{423}{10313}\right)$
$\chi_{20627}(25,\cdot)$	20627.c	10313	yes	$1$	$1$	$e\left(\frac{9230}{10313}\right)$	$e\left(\frac{1168}{10313}\right)$	$e\left(\frac{8147}{10313}\right)$	$e\left(\frac{7520}{10313}\right)$	$e\left(\frac{85}{10313}\right)$	$e\left(\frac{6991}{10313}\right)$	$e\left(\frac{7064}{10313}\right)$	$e\left(\frac{2336}{10313}\right)$	$e\left(\frac{6437}{10313}\right)$	$e\left(\frac{8921}{10313}\right)$
$\chi_{20627}(26,\cdot)$	20627.d	20626	yes	$-1$	$1$	$e\left(\frac{20201}{20626}\right)$	$e\left(\frac{8152}{10313}\right)$	$e\left(\frac{9888}{10313}\right)$	$e\left(\frac{6503}{20626}\right)$	$e\left(\frac{15879}{20626}\right)$	$e\left(\frac{9166}{10313}\right)$	$e\left(\frac{19351}{20626}\right)$	$e\left(\frac{5991}{10313}\right)$	$e\left(\frac{3039}{10313}\right)$	$e\left(\frac{4412}{10313}\right)$
$\chi_{20627}(27,\cdot)$	20627.c	10313	yes	$1$	$1$	$e\left(\frac{9940}{10313}\right)$	$e\left(\frac{6811}{10313}\right)$	$e\left(\frac{9567}{10313}\right)$	$e\left(\frac{1752}{10313}\right)$	$e\left(\frac{6438}{10313}\right)$	$e\left(\frac{389}{10313}\right)$	$e\left(\frac{9194}{10313}\right)$	$e\left(\frac{3309}{10313}\right)$	$e\left(\frac{1379}{10313}\right)$	$e\left(\frac{6434}{10313}\right)$
$\chi_{20627}(28,\cdot)$	20627.c	10313	yes	$1$	$1$	$e\left(\frac{9249}{10313}\right)$	$e\left(\frac{10194}{10313}\right)$	$e\left(\frac{8185}{10313}\right)$	$e\left(\frac{7569}{10313}\right)$	$e\left(\frac{9130}{10313}\right)$	$e\left(\frac{7773}{10313}\right)$	$e\left(\frac{7121}{10313}\right)$	$e\left(\frac{10075}{10313}\right)$	$e\left(\frac{6505}{10313}\right)$	$e\left(\frac{10031}{10313}\right)$
$\chi_{20627}(29,\cdot)$	20627.d	20626	yes	$-1$	$1$	$e\left(\frac{20247}{20626}\right)$	$e\left(\frac{9308}{10313}\right)$	$e\left(\frac{9934}{10313}\right)$	$e\left(\frac{18563}{20626}\right)$	$e\left(\frac{18237}{20626}\right)$	$e\left(\frac{1428}{10313}\right)$	$e\left(\frac{19489}{20626}\right)$	$e\left(\frac{8303}{10313}\right)$	$e\left(\frac{9092}{10313}\right)$	$e\left(\frac{10098}{10313}\right)$
$\chi_{20627}(30,\cdot)$	20627.c	10313	yes	$1$	$1$	$e\left(\frac{6210}{10313}\right)$	$e\left(\frac{2730}{10313}\right)$	$e\left(\frac{2107}{10313}\right)$	$e\left(\frac{8959}{10313}\right)$	$e\left(\frac{8940}{10313}\right)$	$e\left(\frac{4279}{10313}\right)$	$e\left(\frac{8317}{10313}\right)$	$e\left(\frac{5460}{10313}\right)$	$e\left(\frac{4856}{10313}\right)$	$e\left(\frac{8896}{10313}\right)$
$\chi_{20627}(31,\cdot)$	20627.c	10313	yes	$1$	$1$	$e\left(\frac{7532}{10313}\right)$	$e\left(\frac{571}{10313}\right)$	$e\left(\frac{4751}{10313}\right)$	$e\left(\frac{427}{10313}\right)$	$e\left(\frac{8103}{10313}\right)$	$e\left(\frac{3868}{10313}\right)$	$e\left(\frac{1970}{10313}\right)$	$e\left(\frac{1142}{10313}\right)$	$e\left(\frac{7959}{10313}\right)$	$e\left(\frac{5253}{10313}\right)$
$\chi_{20627}(32,\cdot)$	20627.d	20626	yes	$-1$	$1$	$e\left(\frac{5}{20626}\right)$	$e\left(\frac{2816}{10313}\right)$	$e\left(\frac{5}{10313}\right)$	$e\left(\frac{15211}{20626}\right)$	$e\left(\frac{5637}{20626}\right)$	$e\left(\frac{4988}{10313}\right)$	$e\left(\frac{15}{20626}\right)$	$e\left(\frac{5632}{10313}\right)$	$e\left(\frac{7608}{10313}\right)$	$e\left(\frac{2860}{10313}\right)$

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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	$20627$
Structure	\(C_{20626}\)
Order	$20626$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\(\chi_{20627}(1,\cdot)\)	20627.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{20627}(2,\cdot)\)	20627.d	20626	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{20626}\right)\)	\(e\left(\frac{6751}{10313}\right)\)	\(e\left(\frac{1}{10313}\right)\)	\(e\left(\frac{19543}{20626}\right)\)	\(e\left(\frac{13503}{20626}\right)\)	\(e\left(\frac{9248}{10313}\right)\)	\(e\left(\frac{3}{20626}\right)\)	\(e\left(\frac{3189}{10313}\right)\)	\(e\left(\frac{9772}{10313}\right)\)	\(e\left(\frac{572}{10313}\right)\)
\(\chi_{20627}(3,\cdot)\)	20627.c	10313	yes	\(1\)	\(1\)	\(e\left(\frac{6751}{10313}\right)\)	\(e\left(\frac{5708}{10313}\right)\)	\(e\left(\frac{3189}{10313}\right)\)	\(e\left(\frac{584}{10313}\right)\)	\(e\left(\frac{2146}{10313}\right)\)	\(e\left(\frac{7005}{10313}\right)\)	\(e\left(\frac{9940}{10313}\right)\)	\(e\left(\frac{1103}{10313}\right)\)	\(e\left(\frac{7335}{10313}\right)\)	\(e\left(\frac{9020}{10313}\right)\)
\(\chi_{20627}(4,\cdot)\)	20627.c	10313	yes	\(1\)	\(1\)	\(e\left(\frac{1}{10313}\right)\)	\(e\left(\frac{3189}{10313}\right)\)	\(e\left(\frac{2}{10313}\right)\)	\(e\left(\frac{9230}{10313}\right)\)	\(e\left(\frac{3190}{10313}\right)\)	\(e\left(\frac{8183}{10313}\right)\)	\(e\left(\frac{3}{10313}\right)\)	\(e\left(\frac{6378}{10313}\right)\)	\(e\left(\frac{9231}{10313}\right)\)	\(e\left(\frac{1144}{10313}\right)\)
\(\chi_{20627}(5,\cdot)\)	20627.d	20626	yes	\(-1\)	\(1\)	\(e\left(\frac{19543}{20626}\right)\)	\(e\left(\frac{584}{10313}\right)\)	\(e\left(\frac{9230}{10313}\right)\)	\(e\left(\frac{17833}{20626}\right)\)	\(e\left(\frac{85}{20626}\right)\)	\(e\left(\frac{8652}{10313}\right)\)	\(e\left(\frac{17377}{20626}\right)\)	\(e\left(\frac{1168}{10313}\right)\)	\(e\left(\frac{8375}{10313}\right)\)	\(e\left(\frac{9617}{10313}\right)\)
\(\chi_{20627}(6,\cdot)\)	20627.d	20626	yes	\(-1\)	\(1\)	\(e\left(\frac{13503}{20626}\right)\)	\(e\left(\frac{2146}{10313}\right)\)	\(e\left(\frac{3190}{10313}\right)\)	\(e\left(\frac{85}{20626}\right)\)	\(e\left(\frac{17795}{20626}\right)\)	\(e\left(\frac{5940}{10313}\right)\)	\(e\left(\frac{19883}{20626}\right)\)	\(e\left(\frac{4292}{10313}\right)\)	\(e\left(\frac{6794}{10313}\right)\)	\(e\left(\frac{9592}{10313}\right)\)
\(\chi_{20627}(7,\cdot)\)	20627.c	10313	yes	\(1\)	\(1\)	\(e\left(\frac{9248}{10313}\right)\)	\(e\left(\frac{7005}{10313}\right)\)	\(e\left(\frac{8183}{10313}\right)\)	\(e\left(\frac{8652}{10313}\right)\)	\(e\left(\frac{5940}{10313}\right)\)	\(e\left(\frac{9903}{10313}\right)\)	\(e\left(\frac{7118}{10313}\right)\)	\(e\left(\frac{3697}{10313}\right)\)	\(e\left(\frac{7587}{10313}\right)\)	\(e\left(\frac{8887}{10313}\right)\)
\(\chi_{20627}(8,\cdot)\)	20627.d	20626	yes	\(-1\)	\(1\)	\(e\left(\frac{3}{20626}\right)\)	\(e\left(\frac{9940}{10313}\right)\)	\(e\left(\frac{3}{10313}\right)\)	\(e\left(\frac{17377}{20626}\right)\)	\(e\left(\frac{19883}{20626}\right)\)	\(e\left(\frac{7118}{10313}\right)\)	\(e\left(\frac{9}{20626}\right)\)	\(e\left(\frac{9567}{10313}\right)\)	\(e\left(\frac{8690}{10313}\right)\)	\(e\left(\frac{1716}{10313}\right)\)
\(\chi_{20627}(9,\cdot)\)	20627.c	10313	yes	\(1\)	\(1\)	\(e\left(\frac{3189}{10313}\right)\)	\(e\left(\frac{1103}{10313}\right)\)	\(e\left(\frac{6378}{10313}\right)\)	\(e\left(\frac{1168}{10313}\right)\)	\(e\left(\frac{4292}{10313}\right)\)	\(e\left(\frac{3697}{10313}\right)\)	\(e\left(\frac{9567}{10313}\right)\)	\(e\left(\frac{2206}{10313}\right)\)	\(e\left(\frac{4357}{10313}\right)\)	\(e\left(\frac{7727}{10313}\right)\)
\(\chi_{20627}(10,\cdot)\)	20627.c	10313	yes	\(1\)	\(1\)	\(e\left(\frac{9772}{10313}\right)\)	\(e\left(\frac{7335}{10313}\right)\)	\(e\left(\frac{9231}{10313}\right)\)	\(e\left(\frac{8375}{10313}\right)\)	\(e\left(\frac{6794}{10313}\right)\)	\(e\left(\frac{7587}{10313}\right)\)	\(e\left(\frac{8690}{10313}\right)\)	\(e\left(\frac{4357}{10313}\right)\)	\(e\left(\frac{7834}{10313}\right)\)	\(e\left(\frac{10189}{10313}\right)\)
\(\chi_{20627}(11,\cdot)\)	20627.c	10313	yes	\(1\)	\(1\)	\(e\left(\frac{572}{10313}\right)\)	\(e\left(\frac{9020}{10313}\right)\)	\(e\left(\frac{1144}{10313}\right)\)	\(e\left(\frac{9617}{10313}\right)\)	\(e\left(\frac{9592}{10313}\right)\)	\(e\left(\frac{8887}{10313}\right)\)	\(e\left(\frac{1716}{10313}\right)\)	\(e\left(\frac{7727}{10313}\right)\)	\(e\left(\frac{10189}{10313}\right)\)	\(e\left(\frac{4649}{10313}\right)\)
\(\chi_{20627}(12,\cdot)\)	20627.c	10313	yes	\(1\)	\(1\)	\(e\left(\frac{6752}{10313}\right)\)	\(e\left(\frac{8897}{10313}\right)\)	\(e\left(\frac{3191}{10313}\right)\)	\(e\left(\frac{9814}{10313}\right)\)	\(e\left(\frac{5336}{10313}\right)\)	\(e\left(\frac{4875}{10313}\right)\)	\(e\left(\frac{9943}{10313}\right)\)	\(e\left(\frac{7481}{10313}\right)\)	\(e\left(\frac{6253}{10313}\right)\)	\(e\left(\frac{10164}{10313}\right)\)
\(\chi_{20627}(13,\cdot)\)	20627.c	10313	yes	\(1\)	\(1\)	\(e\left(\frac{10100}{10313}\right)\)	\(e\left(\frac{1401}{10313}\right)\)	\(e\left(\frac{9887}{10313}\right)\)	\(e\left(\frac{3793}{10313}\right)\)	\(e\left(\frac{1188}{10313}\right)\)	\(e\left(\frac{10231}{10313}\right)\)	\(e\left(\frac{9674}{10313}\right)\)	\(e\left(\frac{2802}{10313}\right)\)	\(e\left(\frac{3580}{10313}\right)\)	\(e\left(\frac{3840}{10313}\right)\)
\(\chi_{20627}(14,\cdot)\)	20627.d	20626	yes	\(-1\)	\(1\)	\(e\left(\frac{18497}{20626}\right)\)	\(e\left(\frac{3443}{10313}\right)\)	\(e\left(\frac{8184}{10313}\right)\)	\(e\left(\frac{16221}{20626}\right)\)	\(e\left(\frac{4757}{20626}\right)\)	\(e\left(\frac{8838}{10313}\right)\)	\(e\left(\frac{14239}{20626}\right)\)	\(e\left(\frac{6886}{10313}\right)\)	\(e\left(\frac{7046}{10313}\right)\)	\(e\left(\frac{9459}{10313}\right)\)
\(\chi_{20627}(15,\cdot)\)	20627.d	20626	yes	\(-1\)	\(1\)	\(e\left(\frac{12419}{20626}\right)\)	\(e\left(\frac{6292}{10313}\right)\)	\(e\left(\frac{2106}{10313}\right)\)	\(e\left(\frac{19001}{20626}\right)\)	\(e\left(\frac{4377}{20626}\right)\)	\(e\left(\frac{5344}{10313}\right)\)	\(e\left(\frac{16631}{20626}\right)\)	\(e\left(\frac{2271}{10313}\right)\)	\(e\left(\frac{5397}{10313}\right)\)	\(e\left(\frac{8324}{10313}\right)\)
\(\chi_{20627}(16,\cdot)\)	20627.c	10313	yes	\(1\)	\(1\)	\(e\left(\frac{2}{10313}\right)\)	\(e\left(\frac{6378}{10313}\right)\)	\(e\left(\frac{4}{10313}\right)\)	\(e\left(\frac{8147}{10313}\right)\)	\(e\left(\frac{6380}{10313}\right)\)	\(e\left(\frac{6053}{10313}\right)\)	\(e\left(\frac{6}{10313}\right)\)	\(e\left(\frac{2443}{10313}\right)\)	\(e\left(\frac{8149}{10313}\right)\)	\(e\left(\frac{2288}{10313}\right)\)
\(\chi_{20627}(17,\cdot)\)	20627.d	20626	yes	\(-1\)	\(1\)	\(e\left(\frac{13949}{20626}\right)\)	\(e\left(\frac{1696}{10313}\right)\)	\(e\left(\frac{3636}{10313}\right)\)	\(e\left(\frac{12091}{20626}\right)\)	\(e\left(\frac{17341}{20626}\right)\)	\(e\left(\frac{5348}{10313}\right)\)	\(e\left(\frac{595}{20626}\right)\)	\(e\left(\frac{3392}{10313}\right)\)	\(e\left(\frac{2707}{10313}\right)\)	\(e\left(\frac{6879}{10313}\right)\)
\(\chi_{20627}(18,\cdot)\)	20627.d	20626	yes	\(-1\)	\(1\)	\(e\left(\frac{6379}{20626}\right)\)	\(e\left(\frac{7854}{10313}\right)\)	\(e\left(\frac{6379}{10313}\right)\)	\(e\left(\frac{1253}{20626}\right)\)	\(e\left(\frac{1461}{20626}\right)\)	\(e\left(\frac{2632}{10313}\right)\)	\(e\left(\frac{19137}{20626}\right)\)	\(e\left(\frac{5395}{10313}\right)\)	\(e\left(\frac{3816}{10313}\right)\)	\(e\left(\frac{8299}{10313}\right)\)
\(\chi_{20627}(19,\cdot)\)	20627.c	10313	yes	\(1\)	\(1\)	\(e\left(\frac{5983}{10313}\right)\)	\(e\left(\frac{737}{10313}\right)\)	\(e\left(\frac{1653}{10313}\right)\)	\(e\left(\frac{7288}{10313}\right)\)	\(e\left(\frac{6720}{10313}\right)\)	\(e\left(\frac{3078}{10313}\right)\)	\(e\left(\frac{7636}{10313}\right)\)	\(e\left(\frac{1474}{10313}\right)\)	\(e\left(\frac{2958}{10313}\right)\)	\(e\left(\frac{7033}{10313}\right)\)
\(\chi_{20627}(20,\cdot)\)	20627.d	20626	yes	\(-1\)	\(1\)	\(e\left(\frac{19545}{20626}\right)\)	\(e\left(\frac{3773}{10313}\right)\)	\(e\left(\frac{9232}{10313}\right)\)	\(e\left(\frac{15667}{20626}\right)\)	\(e\left(\frac{6465}{20626}\right)\)	\(e\left(\frac{6522}{10313}\right)\)	\(e\left(\frac{17383}{20626}\right)\)	\(e\left(\frac{7546}{10313}\right)\)	\(e\left(\frac{7293}{10313}\right)\)	\(e\left(\frac{448}{10313}\right)\)
\(\chi_{20627}(21,\cdot)\)	20627.c	10313	yes	\(1\)	\(1\)	\(e\left(\frac{5686}{10313}\right)\)	\(e\left(\frac{2400}{10313}\right)\)	\(e\left(\frac{1059}{10313}\right)\)	\(e\left(\frac{9236}{10313}\right)\)	\(e\left(\frac{8086}{10313}\right)\)	\(e\left(\frac{6595}{10313}\right)\)	\(e\left(\frac{6745}{10313}\right)\)	\(e\left(\frac{4800}{10313}\right)\)	\(e\left(\frac{4609}{10313}\right)\)	\(e\left(\frac{7594}{10313}\right)\)
\(\chi_{20627}(22,\cdot)\)	20627.d	20626	yes	\(-1\)	\(1\)	\(e\left(\frac{1145}{20626}\right)\)	\(e\left(\frac{5458}{10313}\right)\)	\(e\left(\frac{1145}{10313}\right)\)	\(e\left(\frac{18151}{20626}\right)\)	\(e\left(\frac{12061}{20626}\right)\)	\(e\left(\frac{7822}{10313}\right)\)	\(e\left(\frac{3435}{20626}\right)\)	\(e\left(\frac{603}{10313}\right)\)	\(e\left(\frac{9648}{10313}\right)\)	\(e\left(\frac{5221}{10313}\right)\)
\(\chi_{20627}(23,\cdot)\)	20627.c	10313	yes	\(1\)	\(1\)	\(e\left(\frac{1888}{10313}\right)\)	\(e\left(\frac{8353}{10313}\right)\)	\(e\left(\frac{3776}{10313}\right)\)	\(e\left(\frac{7583}{10313}\right)\)	\(e\left(\frac{10241}{10313}\right)\)	\(e\left(\frac{630}{10313}\right)\)	\(e\left(\frac{5664}{10313}\right)\)	\(e\left(\frac{6393}{10313}\right)\)	\(e\left(\frac{9471}{10313}\right)\)	\(e\left(\frac{4455}{10313}\right)\)
\(\chi_{20627}(24,\cdot)\)	20627.d	20626	yes	\(-1\)	\(1\)	\(e\left(\frac{13505}{20626}\right)\)	\(e\left(\frac{5335}{10313}\right)\)	\(e\left(\frac{3192}{10313}\right)\)	\(e\left(\frac{18545}{20626}\right)\)	\(e\left(\frac{3549}{20626}\right)\)	\(e\left(\frac{3810}{10313}\right)\)	\(e\left(\frac{19889}{20626}\right)\)	\(e\left(\frac{357}{10313}\right)\)	\(e\left(\frac{5712}{10313}\right)\)	\(e\left(\frac{423}{10313}\right)\)
\(\chi_{20627}(25,\cdot)\)	20627.c	10313	yes	\(1\)	\(1\)	\(e\left(\frac{9230}{10313}\right)\)	\(e\left(\frac{1168}{10313}\right)\)	\(e\left(\frac{8147}{10313}\right)\)	\(e\left(\frac{7520}{10313}\right)\)	\(e\left(\frac{85}{10313}\right)\)	\(e\left(\frac{6991}{10313}\right)\)	\(e\left(\frac{7064}{10313}\right)\)	\(e\left(\frac{2336}{10313}\right)\)	\(e\left(\frac{6437}{10313}\right)\)	\(e\left(\frac{8921}{10313}\right)\)
\(\chi_{20627}(26,\cdot)\)	20627.d	20626	yes	\(-1\)	\(1\)	\(e\left(\frac{20201}{20626}\right)\)	\(e\left(\frac{8152}{10313}\right)\)	\(e\left(\frac{9888}{10313}\right)\)	\(e\left(\frac{6503}{20626}\right)\)	\(e\left(\frac{15879}{20626}\right)\)	\(e\left(\frac{9166}{10313}\right)\)	\(e\left(\frac{19351}{20626}\right)\)	\(e\left(\frac{5991}{10313}\right)\)	\(e\left(\frac{3039}{10313}\right)\)	\(e\left(\frac{4412}{10313}\right)\)
\(\chi_{20627}(27,\cdot)\)	20627.c	10313	yes	\(1\)	\(1\)	\(e\left(\frac{9940}{10313}\right)\)	\(e\left(\frac{6811}{10313}\right)\)	\(e\left(\frac{9567}{10313}\right)\)	\(e\left(\frac{1752}{10313}\right)\)	\(e\left(\frac{6438}{10313}\right)\)	\(e\left(\frac{389}{10313}\right)\)	\(e\left(\frac{9194}{10313}\right)\)	\(e\left(\frac{3309}{10313}\right)\)	\(e\left(\frac{1379}{10313}\right)\)	\(e\left(\frac{6434}{10313}\right)\)
\(\chi_{20627}(28,\cdot)\)	20627.c	10313	yes	\(1\)	\(1\)	\(e\left(\frac{9249}{10313}\right)\)	\(e\left(\frac{10194}{10313}\right)\)	\(e\left(\frac{8185}{10313}\right)\)	\(e\left(\frac{7569}{10313}\right)\)	\(e\left(\frac{9130}{10313}\right)\)	\(e\left(\frac{7773}{10313}\right)\)	\(e\left(\frac{7121}{10313}\right)\)	\(e\left(\frac{10075}{10313}\right)\)	\(e\left(\frac{6505}{10313}\right)\)	\(e\left(\frac{10031}{10313}\right)\)
\(\chi_{20627}(29,\cdot)\)	20627.d	20626	yes	\(-1\)	\(1\)	\(e\left(\frac{20247}{20626}\right)\)	\(e\left(\frac{9308}{10313}\right)\)	\(e\left(\frac{9934}{10313}\right)\)	\(e\left(\frac{18563}{20626}\right)\)	\(e\left(\frac{18237}{20626}\right)\)	\(e\left(\frac{1428}{10313}\right)\)	\(e\left(\frac{19489}{20626}\right)\)	\(e\left(\frac{8303}{10313}\right)\)	\(e\left(\frac{9092}{10313}\right)\)	\(e\left(\frac{10098}{10313}\right)\)
\(\chi_{20627}(30,\cdot)\)	20627.c	10313	yes	\(1\)	\(1\)	\(e\left(\frac{6210}{10313}\right)\)	\(e\left(\frac{2730}{10313}\right)\)	\(e\left(\frac{2107}{10313}\right)\)	\(e\left(\frac{8959}{10313}\right)\)	\(e\left(\frac{8940}{10313}\right)\)	\(e\left(\frac{4279}{10313}\right)\)	\(e\left(\frac{8317}{10313}\right)\)	\(e\left(\frac{5460}{10313}\right)\)	\(e\left(\frac{4856}{10313}\right)\)	\(e\left(\frac{8896}{10313}\right)\)
\(\chi_{20627}(31,\cdot)\)	20627.c	10313	yes	\(1\)	\(1\)	\(e\left(\frac{7532}{10313}\right)\)	\(e\left(\frac{571}{10313}\right)\)	\(e\left(\frac{4751}{10313}\right)\)	\(e\left(\frac{427}{10313}\right)\)	\(e\left(\frac{8103}{10313}\right)\)	\(e\left(\frac{3868}{10313}\right)\)	\(e\left(\frac{1970}{10313}\right)\)	\(e\left(\frac{1142}{10313}\right)\)	\(e\left(\frac{7959}{10313}\right)\)	\(e\left(\frac{5253}{10313}\right)\)
\(\chi_{20627}(32,\cdot)\)	20627.d	20626	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{20626}\right)\)	\(e\left(\frac{2816}{10313}\right)\)	\(e\left(\frac{5}{10313}\right)\)	\(e\left(\frac{15211}{20626}\right)\)	\(e\left(\frac{5637}{20626}\right)\)	\(e\left(\frac{4988}{10313}\right)\)	\(e\left(\frac{15}{20626}\right)\)	\(e\left(\frac{5632}{10313}\right)\)	\(e\left(\frac{7608}{10313}\right)\)	\(e\left(\frac{2860}{10313}\right)\)

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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.