LMFDB - Group of Dirichlet characters of modulus 27746

Show commands: PariGP / SageMath

sage: H = DirichletGroup(27746)

pari: g = idealstar(,27746,2)

Character group

sage: G.order() pari: g.no
Order	=	13872
sage: H.invariants() pari: g.cyc
Structure	=	$C_{13872}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{27746}(5,\cdot)$

First 32 of 13872 characters

Each row describes a character. When available, the columns show the orbit label, order of the character, whether the character is primitive, and several values of the character.

Character	Orbit	Order	Primitive	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$17$	$19$	$21$
$\chi_{27746}(1,\cdot)$	27746.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{27746}(3,\cdot)$	27746.ba	3468	no	$1$	$1$	$e\left(\frac{562}{867}\right)$	$e\left(\frac{1019}{3468}\right)$	$e\left(\frac{229}{1156}\right)$	$e\left(\frac{257}{867}\right)$	$e\left(\frac{2933}{3468}\right)$	$e\left(\frac{235}{3468}\right)$	$e\left(\frac{1089}{1156}\right)$	$e\left(\frac{429}{578}\right)$	$e\left(\frac{2335}{3468}\right)$	$e\left(\frac{2935}{3468}\right)$
$\chi_{27746}(5,\cdot)$	27746.bd	13872	no	$-1$	$1$	$e\left(\frac{1019}{3468}\right)$	$e\left(\frac{1}{13872}\right)$	$e\left(\frac{4327}{4624}\right)$	$e\left(\frac{1019}{1734}\right)$	$e\left(\frac{8695}{13872}\right)$	$e\left(\frac{2825}{13872}\right)$	$e\left(\frac{1359}{4624}\right)$	$e\left(\frac{1271}{2312}\right)$	$e\left(\frac{8885}{13872}\right)$	$e\left(\frac{3185}{13872}\right)$
$\chi_{27746}(7,\cdot)$	27746.bb	4624	no	$-1$	$1$	$e\left(\frac{229}{1156}\right)$	$e\left(\frac{4327}{4624}\right)$	$e\left(\frac{1059}{4624}\right)$	$e\left(\frac{229}{578}\right)$	$e\left(\frac{2401}{4624}\right)$	$e\left(\frac{2543}{4624}\right)$	$e\left(\frac{619}{4624}\right)$	$e\left(\frac{419}{2312}\right)$	$e\left(\frac{1459}{4624}\right)$	$e\left(\frac{1975}{4624}\right)$
$\chi_{27746}(9,\cdot)$	27746.y	1734	no	$1$	$1$	$e\left(\frac{257}{867}\right)$	$e\left(\frac{1019}{1734}\right)$	$e\left(\frac{229}{578}\right)$	$e\left(\frac{514}{867}\right)$	$e\left(\frac{1199}{1734}\right)$	$e\left(\frac{235}{1734}\right)$	$e\left(\frac{511}{578}\right)$	$e\left(\frac{140}{289}\right)$	$e\left(\frac{601}{1734}\right)$	$e\left(\frac{1201}{1734}\right)$
$\chi_{27746}(11,\cdot)$	27746.bd	13872	no	$-1$	$1$	$e\left(\frac{2933}{3468}\right)$	$e\left(\frac{8695}{13872}\right)$	$e\left(\frac{2401}{4624}\right)$	$e\left(\frac{1199}{1734}\right)$	$e\left(\frac{625}{13872}\right)$	$e\left(\frac{9935}{13872}\right)$	$e\left(\frac{2185}{4624}\right)$	$e\left(\frac{2297}{2312}\right)$	$e\left(\frac{1907}{13872}\right)$	$e\left(\frac{5063}{13872}\right)$
$\chi_{27746}(13,\cdot)$	27746.bd	13872	no	$-1$	$1$	$e\left(\frac{235}{3468}\right)$	$e\left(\frac{2825}{13872}\right)$	$e\left(\frac{2543}{4624}\right)$	$e\left(\frac{235}{1734}\right)$	$e\left(\frac{9935}{13872}\right)$	$e\left(\frac{4225}{13872}\right)$	$e\left(\frac{1255}{4624}\right)$	$e\left(\frac{39}{2312}\right)$	$e\left(\frac{5677}{13872}\right)$	$e\left(\frac{8569}{13872}\right)$
$\chi_{27746}(15,\cdot)$	27746.bb	4624	no	$-1$	$1$	$e\left(\frac{1089}{1156}\right)$	$e\left(\frac{1359}{4624}\right)$	$e\left(\frac{619}{4624}\right)$	$e\left(\frac{511}{578}\right)$	$e\left(\frac{2185}{4624}\right)$	$e\left(\frac{1255}{4624}\right)$	$e\left(\frac{1091}{4624}\right)$	$e\left(\frac{675}{2312}\right)$	$e\left(\frac{1451}{4624}\right)$	$e\left(\frac{351}{4624}\right)$
$\chi_{27746}(17,\cdot)$	27746.z	2312	no	$1$	$1$	$e\left(\frac{429}{578}\right)$	$e\left(\frac{1271}{2312}\right)$	$e\left(\frac{419}{2312}\right)$	$e\left(\frac{140}{289}\right)$	$e\left(\frac{2297}{2312}\right)$	$e\left(\frac{39}{2312}\right)$	$e\left(\frac{675}{2312}\right)$	$e\left(\frac{371}{1156}\right)$	$e\left(\frac{1027}{2312}\right)$	$e\left(\frac{2135}{2312}\right)$
$\chi_{27746}(19,\cdot)$	27746.bd	13872	no	$-1$	$1$	$e\left(\frac{2335}{3468}\right)$	$e\left(\frac{8885}{13872}\right)$	$e\left(\frac{1459}{4624}\right)$	$e\left(\frac{601}{1734}\right)$	$e\left(\frac{1907}{13872}\right)$	$e\left(\frac{5677}{13872}\right)$	$e\left(\frac{1451}{4624}\right)$	$e\left(\frac{1027}{2312}\right)$	$e\left(\frac{11545}{13872}\right)$	$e\left(\frac{13717}{13872}\right)$
$\chi_{27746}(21,\cdot)$	27746.bd	13872	no	$-1$	$1$	$e\left(\frac{2935}{3468}\right)$	$e\left(\frac{3185}{13872}\right)$	$e\left(\frac{1975}{4624}\right)$	$e\left(\frac{1201}{1734}\right)$	$e\left(\frac{5063}{13872}\right)$	$e\left(\frac{8569}{13872}\right)$	$e\left(\frac{351}{4624}\right)$	$e\left(\frac{2135}{2312}\right)$	$e\left(\frac{13717}{13872}\right)$	$e\left(\frac{3793}{13872}\right)$
$\chi_{27746}(23,\cdot)$	27746.s	289	no	$1$	$1$	$e\left(\frac{167}{289}\right)$	$e\left(\frac{73}{289}\right)$	$e\left(\frac{271}{289}\right)$	$e\left(\frac{45}{289}\right)$	$e\left(\frac{91}{289}\right)$	$e\left(\frac{168}{289}\right)$	$e\left(\frac{240}{289}\right)$	$e\left(\frac{84}{289}\right)$	$e\left(\frac{89}{289}\right)$	$e\left(\frac{149}{289}\right)$
$\chi_{27746}(25,\cdot)$	27746.bc	6936	no	$1$	$1$	$e\left(\frac{1019}{1734}\right)$	$e\left(\frac{1}{6936}\right)$	$e\left(\frac{2015}{2312}\right)$	$e\left(\frac{152}{867}\right)$	$e\left(\frac{1759}{6936}\right)$	$e\left(\frac{2825}{6936}\right)$	$e\left(\frac{1359}{2312}\right)$	$e\left(\frac{115}{1156}\right)$	$e\left(\frac{1949}{6936}\right)$	$e\left(\frac{3185}{6936}\right)$
$\chi_{27746}(27,\cdot)$	27746.x	1156	no	$1$	$1$	$e\left(\frac{273}{289}\right)$	$e\left(\frac{1019}{1156}\right)$	$e\left(\frac{687}{1156}\right)$	$e\left(\frac{257}{289}\right)$	$e\left(\frac{621}{1156}\right)$	$e\left(\frac{235}{1156}\right)$	$e\left(\frac{955}{1156}\right)$	$e\left(\frac{131}{578}\right)$	$e\left(\frac{23}{1156}\right)$	$e\left(\frac{623}{1156}\right)$
$\chi_{27746}(29,\cdot)$	27746.bb	4624	no	$-1$	$1$	$e\left(\frac{985}{1156}\right)$	$e\left(\frac{35}{4624}\right)$	$e\left(\frac{1183}{4624}\right)$	$e\left(\frac{407}{578}\right)$	$e\left(\frac{3765}{4624}\right)$	$e\left(\frac{1771}{4624}\right)$	$e\left(\frac{3975}{4624}\right)$	$e\left(\frac{1671}{2312}\right)$	$e\left(\frac{1167}{4624}\right)$	$e\left(\frac{499}{4624}\right)$
$\chi_{27746}(31,\cdot)$	27746.x	1156	no	$1$	$1$	$e\left(\frac{128}{289}\right)$	$e\left(\frac{807}{1156}\right)$	$e\left(\frac{1151}{1156}\right)$	$e\left(\frac{256}{289}\right)$	$e\left(\frac{1101}{1156}\right)$	$e\left(\frac{143}{1156}\right)$	$e\left(\frac{163}{1156}\right)$	$e\left(\frac{397}{578}\right)$	$e\left(\frac{683}{1156}\right)$	$e\left(\frac{507}{1156}\right)$
$\chi_{27746}(33,\cdot)$	27746.bb	4624	no	$-1$	$1$	$e\left(\frac{571}{1156}\right)$	$e\left(\frac{4257}{4624}\right)$	$e\left(\frac{3317}{4624}\right)$	$e\left(\frac{571}{578}\right)$	$e\left(\frac{4119}{4624}\right)$	$e\left(\frac{3625}{4624}\right)$	$e\left(\frac{1917}{4624}\right)$	$e\left(\frac{1701}{2312}\right)$	$e\left(\frac{3749}{4624}\right)$	$e\left(\frac{977}{4624}\right)$
$\chi_{27746}(35,\cdot)$	27746.bc	6936	no	$1$	$1$	$e\left(\frac{853}{1734}\right)$	$e\left(\frac{6491}{6936}\right)$	$e\left(\frac{381}{2312}\right)$	$e\left(\frac{853}{867}\right)$	$e\left(\frac{1013}{6936}\right)$	$e\left(\frac{5227}{6936}\right)$	$e\left(\frac{989}{2312}\right)$	$e\left(\frac{845}{1156}\right)$	$e\left(\frac{6631}{6936}\right)$	$e\left(\frac{4555}{6936}\right)$
$\chi_{27746}(37,\cdot)$	27746.bd	13872	no	$-1$	$1$	$e\left(\frac{649}{3468}\right)$	$e\left(\frac{13631}{13872}\right)$	$e\left(\frac{2217}{4624}\right)$	$e\left(\frac{649}{1734}\right)$	$e\left(\frac{13049}{13872}\right)$	$e\left(\frac{12775}{13872}\right)$	$e\left(\frac{785}{4624}\right)$	$e\left(\frac{1185}{2312}\right)$	$e\left(\frac{8875}{13872}\right)$	$e\left(\frac{9247}{13872}\right)$
$\chi_{27746}(39,\cdot)$	27746.bd	13872	no	$-1$	$1$	$e\left(\frac{2483}{3468}\right)$	$e\left(\frac{6901}{13872}\right)$	$e\left(\frac{3459}{4624}\right)$	$e\left(\frac{749}{1734}\right)$	$e\left(\frac{7795}{13872}\right)$	$e\left(\frac{5165}{13872}\right)$	$e\left(\frac{987}{4624}\right)$	$e\left(\frac{1755}{2312}\right)$	$e\left(\frac{1145}{13872}\right)$	$e\left(\frac{6437}{13872}\right)$
$\chi_{27746}(41,\cdot)$	27746.bd	13872	no	$-1$	$1$	$e\left(\frac{311}{3468}\right)$	$e\left(\frac{1525}{13872}\right)$	$e\left(\frac{227}{4624}\right)$	$e\left(\frac{311}{1734}\right)$	$e\left(\frac{12115}{13872}\right)$	$e\left(\frac{7805}{13872}\right)$	$e\left(\frac{923}{4624}\right)$	$e\left(\frac{819}{2312}\right)$	$e\left(\frac{10553}{13872}\right)$	$e\left(\frac{1925}{13872}\right)$
$\chi_{27746}(43,\cdot)$	27746.bd	13872	no	$-1$	$1$	$e\left(\frac{1567}{3468}\right)$	$e\left(\frac{12713}{13872}\right)$	$e\left(\frac{2047}{4624}\right)$	$e\left(\frac{1567}{1734}\right)$	$e\left(\frac{7439}{13872}\right)$	$e\left(\frac{13489}{13872}\right)$	$e\left(\frac{1703}{4624}\right)$	$e\left(\frac{1967}{2312}\right)$	$e\left(\frac{9181}{13872}\right)$	$e\left(\frac{12409}{13872}\right)$
$\chi_{27746}(45,\cdot)$	27746.bd	13872	no	$-1$	$1$	$e\left(\frac{2047}{3468}\right)$	$e\left(\frac{8153}{13872}\right)$	$e\left(\frac{1535}{4624}\right)$	$e\left(\frac{313}{1734}\right)$	$e\left(\frac{4415}{13872}\right)$	$e\left(\frac{4705}{13872}\right)$	$e\left(\frac{823}{4624}\right)$	$e\left(\frac{79}{2312}\right)$	$e\left(\frac{13693}{13872}\right)$	$e\left(\frac{12793}{13872}\right)$
$\chi_{27746}(47,\cdot)$	27746.ba	3468	no	$1$	$1$	$e\left(\frac{328}{867}\right)$	$e\left(\frac{2375}{3468}\right)$	$e\left(\frac{941}{1156}\right)$	$e\left(\frac{656}{867}\right)$	$e\left(\frac{2153}{3468}\right)$	$e\left(\frac{2263}{3468}\right)$	$e\left(\frac{73}{1156}\right)$	$e\left(\frac{309}{578}\right)$	$e\left(\frac{2563}{3468}\right)$	$e\left(\frac{667}{3468}\right)$
$\chi_{27746}(49,\cdot)$	27746.z	2312	no	$1$	$1$	$e\left(\frac{229}{578}\right)$	$e\left(\frac{2015}{2312}\right)$	$e\left(\frac{1059}{2312}\right)$	$e\left(\frac{229}{289}\right)$	$e\left(\frac{89}{2312}\right)$	$e\left(\frac{231}{2312}\right)$	$e\left(\frac{619}{2312}\right)$	$e\left(\frac{419}{1156}\right)$	$e\left(\frac{1459}{2312}\right)$	$e\left(\frac{1975}{2312}\right)$
$\chi_{27746}(51,\cdot)$	27746.bc	6936	no	$1$	$1$	$e\left(\frac{677}{1734}\right)$	$e\left(\frac{5851}{6936}\right)$	$e\left(\frac{877}{2312}\right)$	$e\left(\frac{677}{867}\right)$	$e\left(\frac{5821}{6936}\right)$	$e\left(\frac{587}{6936}\right)$	$e\left(\frac{541}{2312}\right)$	$e\left(\frac{73}{1156}\right)$	$e\left(\frac{815}{6936}\right)$	$e\left(\frac{5339}{6936}\right)$
$\chi_{27746}(53,\cdot)$	27746.z	2312	no	$1$	$1$	$e\left(\frac{171}{578}\right)$	$e\left(\frac{1699}{2312}\right)$	$e\left(\frac{551}{2312}\right)$	$e\left(\frac{171}{289}\right)$	$e\left(\frac{1437}{2312}\right)$	$e\left(\frac{2275}{2312}\right)$	$e\left(\frac{71}{2312}\right)$	$e\left(\frac{63}{1156}\right)$	$e\left(\frac{567}{2312}\right)$	$e\left(\frac{1235}{2312}\right)$
$\chi_{27746}(55,\cdot)$	27746.y	1734	no	$1$	$1$	$e\left(\frac{121}{867}\right)$	$e\left(\frac{1087}{1734}\right)$	$e\left(\frac{263}{578}\right)$	$e\left(\frac{242}{867}\right)$	$e\left(\frac{1165}{1734}\right)$	$e\left(\frac{1595}{1734}\right)$	$e\left(\frac{443}{578}\right)$	$e\left(\frac{157}{289}\right)$	$e\left(\frac{1349}{1734}\right)$	$e\left(\frac{1031}{1734}\right)$
$\chi_{27746}(57,\cdot)$	27746.bd	13872	no	$-1$	$1$	$e\left(\frac{1115}{3468}\right)$	$e\left(\frac{12961}{13872}\right)$	$e\left(\frac{2375}{4624}\right)$	$e\left(\frac{1115}{1734}\right)$	$e\left(\frac{13639}{13872}\right)$	$e\left(\frac{6617}{13872}\right)$	$e\left(\frac{1183}{4624}\right)$	$e\left(\frac{431}{2312}\right)$	$e\left(\frac{7013}{13872}\right)$	$e\left(\frac{11585}{13872}\right)$
$\chi_{27746}(59,\cdot)$	27746.bb	4624	no	$-1$	$1$	$e\left(\frac{553}{1156}\right)$	$e\left(\frac{2983}{4624}\right)$	$e\left(\frac{947}{4624}\right)$	$e\left(\frac{553}{578}\right)$	$e\left(\frac{1169}{4624}\right)$	$e\left(\frac{2047}{4624}\right)$	$e\left(\frac{571}{4624}\right)$	$e\left(\frac{1451}{2312}\right)$	$e\left(\frac{3811}{4624}\right)$	$e\left(\frac{3159}{4624}\right)$
$\chi_{27746}(61,\cdot)$	27746.bd	13872	no	$-1$	$1$	$e\left(\frac{2555}{3468}\right)$	$e\left(\frac{6217}{13872}\right)$	$e\left(\frac{3151}{4624}\right)$	$e\left(\frac{821}{1734}\right)$	$e\left(\frac{11503}{13872}\right)$	$e\left(\frac{1073}{13872}\right)$	$e\left(\frac{855}{4624}\right)$	$e\left(\frac{1703}{2312}\right)$	$e\left(\frac{13613}{13872}\right)$	$e\left(\frac{5801}{13872}\right)$
$\chi_{27746}(63,\cdot)$	27746.bd	13872	no	$-1$	$1$	$e\left(\frac{1715}{3468}\right)$	$e\left(\frac{7261}{13872}\right)$	$e\left(\frac{2891}{4624}\right)$	$e\left(\frac{1715}{1734}\right)$	$e\left(\frac{2923}{13872}\right)$	$e\left(\frac{9509}{13872}\right)$	$e\left(\frac{83}{4624}\right)$	$e\left(\frac{1539}{2312}\right)$	$e\left(\frac{9185}{13872}\right)$	$e\left(\frac{1661}{13872}\right)$

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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	$27746$
Structure	\(C_{13872}\)
Order	$13872$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(21\)
\(\chi_{27746}(1,\cdot)\)	27746.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{27746}(3,\cdot)\)	27746.ba	3468	no	\(1\)	\(1\)	\(e\left(\frac{562}{867}\right)\)	\(e\left(\frac{1019}{3468}\right)\)	\(e\left(\frac{229}{1156}\right)\)	\(e\left(\frac{257}{867}\right)\)	\(e\left(\frac{2933}{3468}\right)\)	\(e\left(\frac{235}{3468}\right)\)	\(e\left(\frac{1089}{1156}\right)\)	\(e\left(\frac{429}{578}\right)\)	\(e\left(\frac{2335}{3468}\right)\)	\(e\left(\frac{2935}{3468}\right)\)
\(\chi_{27746}(5,\cdot)\)	27746.bd	13872	no	\(-1\)	\(1\)	\(e\left(\frac{1019}{3468}\right)\)	\(e\left(\frac{1}{13872}\right)\)	\(e\left(\frac{4327}{4624}\right)\)	\(e\left(\frac{1019}{1734}\right)\)	\(e\left(\frac{8695}{13872}\right)\)	\(e\left(\frac{2825}{13872}\right)\)	\(e\left(\frac{1359}{4624}\right)\)	\(e\left(\frac{1271}{2312}\right)\)	\(e\left(\frac{8885}{13872}\right)\)	\(e\left(\frac{3185}{13872}\right)\)
\(\chi_{27746}(7,\cdot)\)	27746.bb	4624	no	\(-1\)	\(1\)	\(e\left(\frac{229}{1156}\right)\)	\(e\left(\frac{4327}{4624}\right)\)	\(e\left(\frac{1059}{4624}\right)\)	\(e\left(\frac{229}{578}\right)\)	\(e\left(\frac{2401}{4624}\right)\)	\(e\left(\frac{2543}{4624}\right)\)	\(e\left(\frac{619}{4624}\right)\)	\(e\left(\frac{419}{2312}\right)\)	\(e\left(\frac{1459}{4624}\right)\)	\(e\left(\frac{1975}{4624}\right)\)
\(\chi_{27746}(9,\cdot)\)	27746.y	1734	no	\(1\)	\(1\)	\(e\left(\frac{257}{867}\right)\)	\(e\left(\frac{1019}{1734}\right)\)	\(e\left(\frac{229}{578}\right)\)	\(e\left(\frac{514}{867}\right)\)	\(e\left(\frac{1199}{1734}\right)\)	\(e\left(\frac{235}{1734}\right)\)	\(e\left(\frac{511}{578}\right)\)	\(e\left(\frac{140}{289}\right)\)	\(e\left(\frac{601}{1734}\right)\)	\(e\left(\frac{1201}{1734}\right)\)
\(\chi_{27746}(11,\cdot)\)	27746.bd	13872	no	\(-1\)	\(1\)	\(e\left(\frac{2933}{3468}\right)\)	\(e\left(\frac{8695}{13872}\right)\)	\(e\left(\frac{2401}{4624}\right)\)	\(e\left(\frac{1199}{1734}\right)\)	\(e\left(\frac{625}{13872}\right)\)	\(e\left(\frac{9935}{13872}\right)\)	\(e\left(\frac{2185}{4624}\right)\)	\(e\left(\frac{2297}{2312}\right)\)	\(e\left(\frac{1907}{13872}\right)\)	\(e\left(\frac{5063}{13872}\right)\)
\(\chi_{27746}(13,\cdot)\)	27746.bd	13872	no	\(-1\)	\(1\)	\(e\left(\frac{235}{3468}\right)\)	\(e\left(\frac{2825}{13872}\right)\)	\(e\left(\frac{2543}{4624}\right)\)	\(e\left(\frac{235}{1734}\right)\)	\(e\left(\frac{9935}{13872}\right)\)	\(e\left(\frac{4225}{13872}\right)\)	\(e\left(\frac{1255}{4624}\right)\)	\(e\left(\frac{39}{2312}\right)\)	\(e\left(\frac{5677}{13872}\right)\)	\(e\left(\frac{8569}{13872}\right)\)
\(\chi_{27746}(15,\cdot)\)	27746.bb	4624	no	\(-1\)	\(1\)	\(e\left(\frac{1089}{1156}\right)\)	\(e\left(\frac{1359}{4624}\right)\)	\(e\left(\frac{619}{4624}\right)\)	\(e\left(\frac{511}{578}\right)\)	\(e\left(\frac{2185}{4624}\right)\)	\(e\left(\frac{1255}{4624}\right)\)	\(e\left(\frac{1091}{4624}\right)\)	\(e\left(\frac{675}{2312}\right)\)	\(e\left(\frac{1451}{4624}\right)\)	\(e\left(\frac{351}{4624}\right)\)
\(\chi_{27746}(17,\cdot)\)	27746.z	2312	no	\(1\)	\(1\)	\(e\left(\frac{429}{578}\right)\)	\(e\left(\frac{1271}{2312}\right)\)	\(e\left(\frac{419}{2312}\right)\)	\(e\left(\frac{140}{289}\right)\)	\(e\left(\frac{2297}{2312}\right)\)	\(e\left(\frac{39}{2312}\right)\)	\(e\left(\frac{675}{2312}\right)\)	\(e\left(\frac{371}{1156}\right)\)	\(e\left(\frac{1027}{2312}\right)\)	\(e\left(\frac{2135}{2312}\right)\)
\(\chi_{27746}(19,\cdot)\)	27746.bd	13872	no	\(-1\)	\(1\)	\(e\left(\frac{2335}{3468}\right)\)	\(e\left(\frac{8885}{13872}\right)\)	\(e\left(\frac{1459}{4624}\right)\)	\(e\left(\frac{601}{1734}\right)\)	\(e\left(\frac{1907}{13872}\right)\)	\(e\left(\frac{5677}{13872}\right)\)	\(e\left(\frac{1451}{4624}\right)\)	\(e\left(\frac{1027}{2312}\right)\)	\(e\left(\frac{11545}{13872}\right)\)	\(e\left(\frac{13717}{13872}\right)\)
\(\chi_{27746}(21,\cdot)\)	27746.bd	13872	no	\(-1\)	\(1\)	\(e\left(\frac{2935}{3468}\right)\)	\(e\left(\frac{3185}{13872}\right)\)	\(e\left(\frac{1975}{4624}\right)\)	\(e\left(\frac{1201}{1734}\right)\)	\(e\left(\frac{5063}{13872}\right)\)	\(e\left(\frac{8569}{13872}\right)\)	\(e\left(\frac{351}{4624}\right)\)	\(e\left(\frac{2135}{2312}\right)\)	\(e\left(\frac{13717}{13872}\right)\)	\(e\left(\frac{3793}{13872}\right)\)
\(\chi_{27746}(23,\cdot)\)	27746.s	289	no	\(1\)	\(1\)	\(e\left(\frac{167}{289}\right)\)	\(e\left(\frac{73}{289}\right)\)	\(e\left(\frac{271}{289}\right)\)	\(e\left(\frac{45}{289}\right)\)	\(e\left(\frac{91}{289}\right)\)	\(e\left(\frac{168}{289}\right)\)	\(e\left(\frac{240}{289}\right)\)	\(e\left(\frac{84}{289}\right)\)	\(e\left(\frac{89}{289}\right)\)	\(e\left(\frac{149}{289}\right)\)
\(\chi_{27746}(25,\cdot)\)	27746.bc	6936	no	\(1\)	\(1\)	\(e\left(\frac{1019}{1734}\right)\)	\(e\left(\frac{1}{6936}\right)\)	\(e\left(\frac{2015}{2312}\right)\)	\(e\left(\frac{152}{867}\right)\)	\(e\left(\frac{1759}{6936}\right)\)	\(e\left(\frac{2825}{6936}\right)\)	\(e\left(\frac{1359}{2312}\right)\)	\(e\left(\frac{115}{1156}\right)\)	\(e\left(\frac{1949}{6936}\right)\)	\(e\left(\frac{3185}{6936}\right)\)
\(\chi_{27746}(27,\cdot)\)	27746.x	1156	no	\(1\)	\(1\)	\(e\left(\frac{273}{289}\right)\)	\(e\left(\frac{1019}{1156}\right)\)	\(e\left(\frac{687}{1156}\right)\)	\(e\left(\frac{257}{289}\right)\)	\(e\left(\frac{621}{1156}\right)\)	\(e\left(\frac{235}{1156}\right)\)	\(e\left(\frac{955}{1156}\right)\)	\(e\left(\frac{131}{578}\right)\)	\(e\left(\frac{23}{1156}\right)\)	\(e\left(\frac{623}{1156}\right)\)
\(\chi_{27746}(29,\cdot)\)	27746.bb	4624	no	\(-1\)	\(1\)	\(e\left(\frac{985}{1156}\right)\)	\(e\left(\frac{35}{4624}\right)\)	\(e\left(\frac{1183}{4624}\right)\)	\(e\left(\frac{407}{578}\right)\)	\(e\left(\frac{3765}{4624}\right)\)	\(e\left(\frac{1771}{4624}\right)\)	\(e\left(\frac{3975}{4624}\right)\)	\(e\left(\frac{1671}{2312}\right)\)	\(e\left(\frac{1167}{4624}\right)\)	\(e\left(\frac{499}{4624}\right)\)
\(\chi_{27746}(31,\cdot)\)	27746.x	1156	no	\(1\)	\(1\)	\(e\left(\frac{128}{289}\right)\)	\(e\left(\frac{807}{1156}\right)\)	\(e\left(\frac{1151}{1156}\right)\)	\(e\left(\frac{256}{289}\right)\)	\(e\left(\frac{1101}{1156}\right)\)	\(e\left(\frac{143}{1156}\right)\)	\(e\left(\frac{163}{1156}\right)\)	\(e\left(\frac{397}{578}\right)\)	\(e\left(\frac{683}{1156}\right)\)	\(e\left(\frac{507}{1156}\right)\)
\(\chi_{27746}(33,\cdot)\)	27746.bb	4624	no	\(-1\)	\(1\)	\(e\left(\frac{571}{1156}\right)\)	\(e\left(\frac{4257}{4624}\right)\)	\(e\left(\frac{3317}{4624}\right)\)	\(e\left(\frac{571}{578}\right)\)	\(e\left(\frac{4119}{4624}\right)\)	\(e\left(\frac{3625}{4624}\right)\)	\(e\left(\frac{1917}{4624}\right)\)	\(e\left(\frac{1701}{2312}\right)\)	\(e\left(\frac{3749}{4624}\right)\)	\(e\left(\frac{977}{4624}\right)\)
\(\chi_{27746}(35,\cdot)\)	27746.bc	6936	no	\(1\)	\(1\)	\(e\left(\frac{853}{1734}\right)\)	\(e\left(\frac{6491}{6936}\right)\)	\(e\left(\frac{381}{2312}\right)\)	\(e\left(\frac{853}{867}\right)\)	\(e\left(\frac{1013}{6936}\right)\)	\(e\left(\frac{5227}{6936}\right)\)	\(e\left(\frac{989}{2312}\right)\)	\(e\left(\frac{845}{1156}\right)\)	\(e\left(\frac{6631}{6936}\right)\)	\(e\left(\frac{4555}{6936}\right)\)
\(\chi_{27746}(37,\cdot)\)	27746.bd	13872	no	\(-1\)	\(1\)	\(e\left(\frac{649}{3468}\right)\)	\(e\left(\frac{13631}{13872}\right)\)	\(e\left(\frac{2217}{4624}\right)\)	\(e\left(\frac{649}{1734}\right)\)	\(e\left(\frac{13049}{13872}\right)\)	\(e\left(\frac{12775}{13872}\right)\)	\(e\left(\frac{785}{4624}\right)\)	\(e\left(\frac{1185}{2312}\right)\)	\(e\left(\frac{8875}{13872}\right)\)	\(e\left(\frac{9247}{13872}\right)\)
\(\chi_{27746}(39,\cdot)\)	27746.bd	13872	no	\(-1\)	\(1\)	\(e\left(\frac{2483}{3468}\right)\)	\(e\left(\frac{6901}{13872}\right)\)	\(e\left(\frac{3459}{4624}\right)\)	\(e\left(\frac{749}{1734}\right)\)	\(e\left(\frac{7795}{13872}\right)\)	\(e\left(\frac{5165}{13872}\right)\)	\(e\left(\frac{987}{4624}\right)\)	\(e\left(\frac{1755}{2312}\right)\)	\(e\left(\frac{1145}{13872}\right)\)	\(e\left(\frac{6437}{13872}\right)\)
\(\chi_{27746}(41,\cdot)\)	27746.bd	13872	no	\(-1\)	\(1\)	\(e\left(\frac{311}{3468}\right)\)	\(e\left(\frac{1525}{13872}\right)\)	\(e\left(\frac{227}{4624}\right)\)	\(e\left(\frac{311}{1734}\right)\)	\(e\left(\frac{12115}{13872}\right)\)	\(e\left(\frac{7805}{13872}\right)\)	\(e\left(\frac{923}{4624}\right)\)	\(e\left(\frac{819}{2312}\right)\)	\(e\left(\frac{10553}{13872}\right)\)	\(e\left(\frac{1925}{13872}\right)\)
\(\chi_{27746}(43,\cdot)\)	27746.bd	13872	no	\(-1\)	\(1\)	\(e\left(\frac{1567}{3468}\right)\)	\(e\left(\frac{12713}{13872}\right)\)	\(e\left(\frac{2047}{4624}\right)\)	\(e\left(\frac{1567}{1734}\right)\)	\(e\left(\frac{7439}{13872}\right)\)	\(e\left(\frac{13489}{13872}\right)\)	\(e\left(\frac{1703}{4624}\right)\)	\(e\left(\frac{1967}{2312}\right)\)	\(e\left(\frac{9181}{13872}\right)\)	\(e\left(\frac{12409}{13872}\right)\)
\(\chi_{27746}(45,\cdot)\)	27746.bd	13872	no	\(-1\)	\(1\)	\(e\left(\frac{2047}{3468}\right)\)	\(e\left(\frac{8153}{13872}\right)\)	\(e\left(\frac{1535}{4624}\right)\)	\(e\left(\frac{313}{1734}\right)\)	\(e\left(\frac{4415}{13872}\right)\)	\(e\left(\frac{4705}{13872}\right)\)	\(e\left(\frac{823}{4624}\right)\)	\(e\left(\frac{79}{2312}\right)\)	\(e\left(\frac{13693}{13872}\right)\)	\(e\left(\frac{12793}{13872}\right)\)
\(\chi_{27746}(47,\cdot)\)	27746.ba	3468	no	\(1\)	\(1\)	\(e\left(\frac{328}{867}\right)\)	\(e\left(\frac{2375}{3468}\right)\)	\(e\left(\frac{941}{1156}\right)\)	\(e\left(\frac{656}{867}\right)\)	\(e\left(\frac{2153}{3468}\right)\)	\(e\left(\frac{2263}{3468}\right)\)	\(e\left(\frac{73}{1156}\right)\)	\(e\left(\frac{309}{578}\right)\)	\(e\left(\frac{2563}{3468}\right)\)	\(e\left(\frac{667}{3468}\right)\)
\(\chi_{27746}(49,\cdot)\)	27746.z	2312	no	\(1\)	\(1\)	\(e\left(\frac{229}{578}\right)\)	\(e\left(\frac{2015}{2312}\right)\)	\(e\left(\frac{1059}{2312}\right)\)	\(e\left(\frac{229}{289}\right)\)	\(e\left(\frac{89}{2312}\right)\)	\(e\left(\frac{231}{2312}\right)\)	\(e\left(\frac{619}{2312}\right)\)	\(e\left(\frac{419}{1156}\right)\)	\(e\left(\frac{1459}{2312}\right)\)	\(e\left(\frac{1975}{2312}\right)\)
\(\chi_{27746}(51,\cdot)\)	27746.bc	6936	no	\(1\)	\(1\)	\(e\left(\frac{677}{1734}\right)\)	\(e\left(\frac{5851}{6936}\right)\)	\(e\left(\frac{877}{2312}\right)\)	\(e\left(\frac{677}{867}\right)\)	\(e\left(\frac{5821}{6936}\right)\)	\(e\left(\frac{587}{6936}\right)\)	\(e\left(\frac{541}{2312}\right)\)	\(e\left(\frac{73}{1156}\right)\)	\(e\left(\frac{815}{6936}\right)\)	\(e\left(\frac{5339}{6936}\right)\)
\(\chi_{27746}(53,\cdot)\)	27746.z	2312	no	\(1\)	\(1\)	\(e\left(\frac{171}{578}\right)\)	\(e\left(\frac{1699}{2312}\right)\)	\(e\left(\frac{551}{2312}\right)\)	\(e\left(\frac{171}{289}\right)\)	\(e\left(\frac{1437}{2312}\right)\)	\(e\left(\frac{2275}{2312}\right)\)	\(e\left(\frac{71}{2312}\right)\)	\(e\left(\frac{63}{1156}\right)\)	\(e\left(\frac{567}{2312}\right)\)	\(e\left(\frac{1235}{2312}\right)\)
\(\chi_{27746}(55,\cdot)\)	27746.y	1734	no	\(1\)	\(1\)	\(e\left(\frac{121}{867}\right)\)	\(e\left(\frac{1087}{1734}\right)\)	\(e\left(\frac{263}{578}\right)\)	\(e\left(\frac{242}{867}\right)\)	\(e\left(\frac{1165}{1734}\right)\)	\(e\left(\frac{1595}{1734}\right)\)	\(e\left(\frac{443}{578}\right)\)	\(e\left(\frac{157}{289}\right)\)	\(e\left(\frac{1349}{1734}\right)\)	\(e\left(\frac{1031}{1734}\right)\)
\(\chi_{27746}(57,\cdot)\)	27746.bd	13872	no	\(-1\)	\(1\)	\(e\left(\frac{1115}{3468}\right)\)	\(e\left(\frac{12961}{13872}\right)\)	\(e\left(\frac{2375}{4624}\right)\)	\(e\left(\frac{1115}{1734}\right)\)	\(e\left(\frac{13639}{13872}\right)\)	\(e\left(\frac{6617}{13872}\right)\)	\(e\left(\frac{1183}{4624}\right)\)	\(e\left(\frac{431}{2312}\right)\)	\(e\left(\frac{7013}{13872}\right)\)	\(e\left(\frac{11585}{13872}\right)\)
\(\chi_{27746}(59,\cdot)\)	27746.bb	4624	no	\(-1\)	\(1\)	\(e\left(\frac{553}{1156}\right)\)	\(e\left(\frac{2983}{4624}\right)\)	\(e\left(\frac{947}{4624}\right)\)	\(e\left(\frac{553}{578}\right)\)	\(e\left(\frac{1169}{4624}\right)\)	\(e\left(\frac{2047}{4624}\right)\)	\(e\left(\frac{571}{4624}\right)\)	\(e\left(\frac{1451}{2312}\right)\)	\(e\left(\frac{3811}{4624}\right)\)	\(e\left(\frac{3159}{4624}\right)\)
\(\chi_{27746}(61,\cdot)\)	27746.bd	13872	no	\(-1\)	\(1\)	\(e\left(\frac{2555}{3468}\right)\)	\(e\left(\frac{6217}{13872}\right)\)	\(e\left(\frac{3151}{4624}\right)\)	\(e\left(\frac{821}{1734}\right)\)	\(e\left(\frac{11503}{13872}\right)\)	\(e\left(\frac{1073}{13872}\right)\)	\(e\left(\frac{855}{4624}\right)\)	\(e\left(\frac{1703}{2312}\right)\)	\(e\left(\frac{13613}{13872}\right)\)	\(e\left(\frac{5801}{13872}\right)\)
\(\chi_{27746}(63,\cdot)\)	27746.bd	13872	no	\(-1\)	\(1\)	\(e\left(\frac{1715}{3468}\right)\)	\(e\left(\frac{7261}{13872}\right)\)	\(e\left(\frac{2891}{4624}\right)\)	\(e\left(\frac{1715}{1734}\right)\)	\(e\left(\frac{2923}{13872}\right)\)	\(e\left(\frac{9509}{13872}\right)\)	\(e\left(\frac{83}{4624}\right)\)	\(e\left(\frac{1539}{2312}\right)\)	\(e\left(\frac{9185}{13872}\right)\)	\(e\left(\frac{1661}{13872}\right)\)

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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.