LMFDB - Group of Dirichlet characters of modulus 16384

Show commands: PariGP / SageMath

sage: H = DirichletGroup(16384)

pari: g = idealstar(,16384,2)

Character group

sage: G.order() pari: g.no
Order	=	8192
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{4096}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{16384}(16383,\cdot)$, $\chi_{16384}(5,\cdot)$

First 32 of 8192 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	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$17$	$19$	$21$
$\chi_{16384}(1,\cdot)$	16384.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{16384}(3,\cdot)$	16384.z	4096	yes	$-1$	$1$	$e\left(\frac{969}{4096}\right)$	$e\left(\frac{1699}{4096}\right)$	$e\left(\frac{1871}{2048}\right)$	$e\left(\frac{969}{2048}\right)$	$e\left(\frac{415}{4096}\right)$	$e\left(\frac{1837}{4096}\right)$	$e\left(\frac{667}{1024}\right)$	$e\left(\frac{917}{1024}\right)$	$e\left(\frac{805}{4096}\right)$	$e\left(\frac{615}{4096}\right)$
$\chi_{16384}(5,\cdot)$	16384.y	4096	yes	$1$	$1$	$e\left(\frac{1699}{4096}\right)$	$e\left(\frac{1}{4096}\right)$	$e\left(\frac{1893}{2048}\right)$	$e\left(\frac{1699}{2048}\right)$	$e\left(\frac{3285}{4096}\right)$	$e\left(\frac{2031}{4096}\right)$	$e\left(\frac{425}{1024}\right)$	$e\left(\frac{103}{1024}\right)$	$e\left(\frac{2967}{4096}\right)$	$e\left(\frac{1389}{4096}\right)$
$\chi_{16384}(7,\cdot)$	16384.x	2048	no	$-1$	$1$	$e\left(\frac{1871}{2048}\right)$	$e\left(\frac{1893}{2048}\right)$	$e\left(\frac{985}{1024}\right)$	$e\left(\frac{847}{1024}\right)$	$e\left(\frac{1801}{2048}\right)$	$e\left(\frac{587}{2048}\right)$	$e\left(\frac{429}{512}\right)$	$e\left(\frac{419}{512}\right)$	$e\left(\frac{1939}{2048}\right)$	$e\left(\frac{1793}{2048}\right)$
$\chi_{16384}(9,\cdot)$	16384.w	2048	no	$1$	$1$	$e\left(\frac{969}{2048}\right)$	$e\left(\frac{1699}{2048}\right)$	$e\left(\frac{847}{1024}\right)$	$e\left(\frac{969}{1024}\right)$	$e\left(\frac{415}{2048}\right)$	$e\left(\frac{1837}{2048}\right)$	$e\left(\frac{155}{512}\right)$	$e\left(\frac{405}{512}\right)$	$e\left(\frac{805}{2048}\right)$	$e\left(\frac{615}{2048}\right)$
$\chi_{16384}(11,\cdot)$	16384.z	4096	yes	$-1$	$1$	$e\left(\frac{415}{4096}\right)$	$e\left(\frac{3285}{4096}\right)$	$e\left(\frac{1801}{2048}\right)$	$e\left(\frac{415}{2048}\right)$	$e\left(\frac{313}{4096}\right)$	$e\left(\frac{3547}{4096}\right)$	$e\left(\frac{925}{1024}\right)$	$e\left(\frac{435}{1024}\right)$	$e\left(\frac{163}{4096}\right)$	$e\left(\frac{4017}{4096}\right)$
$\chi_{16384}(13,\cdot)$	16384.y	4096	yes	$1$	$1$	$e\left(\frac{1837}{4096}\right)$	$e\left(\frac{2031}{4096}\right)$	$e\left(\frac{587}{2048}\right)$	$e\left(\frac{1837}{2048}\right)$	$e\left(\frac{3547}{4096}\right)$	$e\left(\frac{289}{4096}\right)$	$e\left(\frac{967}{1024}\right)$	$e\left(\frac{297}{1024}\right)$	$e\left(\frac{761}{4096}\right)$	$e\left(\frac{3011}{4096}\right)$
$\chi_{16384}(15,\cdot)$	16384.v	1024	no	$-1$	$1$	$e\left(\frac{667}{1024}\right)$	$e\left(\frac{425}{1024}\right)$	$e\left(\frac{429}{512}\right)$	$e\left(\frac{155}{512}\right)$	$e\left(\frac{925}{1024}\right)$	$e\left(\frac{967}{1024}\right)$	$e\left(\frac{17}{256}\right)$	$e\left(\frac{255}{256}\right)$	$e\left(\frac{943}{1024}\right)$	$e\left(\frac{501}{1024}\right)$
$\chi_{16384}(17,\cdot)$	16384.u	1024	no	$1$	$1$	$e\left(\frac{917}{1024}\right)$	$e\left(\frac{103}{1024}\right)$	$e\left(\frac{419}{512}\right)$	$e\left(\frac{405}{512}\right)$	$e\left(\frac{435}{1024}\right)$	$e\left(\frac{297}{1024}\right)$	$e\left(\frac{255}{256}\right)$	$e\left(\frac{113}{256}\right)$	$e\left(\frac{449}{1024}\right)$	$e\left(\frac{731}{1024}\right)$
$\chi_{16384}(19,\cdot)$	16384.z	4096	yes	$-1$	$1$	$e\left(\frac{805}{4096}\right)$	$e\left(\frac{2967}{4096}\right)$	$e\left(\frac{1939}{2048}\right)$	$e\left(\frac{805}{2048}\right)$	$e\left(\frac{163}{4096}\right)$	$e\left(\frac{761}{4096}\right)$	$e\left(\frac{943}{1024}\right)$	$e\left(\frac{449}{1024}\right)$	$e\left(\frac{2833}{4096}\right)$	$e\left(\frac{587}{4096}\right)$
$\chi_{16384}(21,\cdot)$	16384.y	4096	yes	$1$	$1$	$e\left(\frac{615}{4096}\right)$	$e\left(\frac{1389}{4096}\right)$	$e\left(\frac{1793}{2048}\right)$	$e\left(\frac{615}{2048}\right)$	$e\left(\frac{4017}{4096}\right)$	$e\left(\frac{3011}{4096}\right)$	$e\left(\frac{501}{1024}\right)$	$e\left(\frac{731}{1024}\right)$	$e\left(\frac{587}{4096}\right)$	$e\left(\frac{105}{4096}\right)$
$\chi_{16384}(23,\cdot)$	16384.x	2048	no	$-1$	$1$	$e\left(\frac{1333}{2048}\right)$	$e\left(\frac{1607}{2048}\right)$	$e\left(\frac{259}{1024}\right)$	$e\left(\frac{309}{1024}\right)$	$e\left(\frac{275}{2048}\right)$	$e\left(\frac{1353}{2048}\right)$	$e\left(\frac{223}{512}\right)$	$e\left(\frac{145}{512}\right)$	$e\left(\frac{1249}{2048}\right)$	$e\left(\frac{1851}{2048}\right)$
$\chi_{16384}(25,\cdot)$	16384.w	2048	no	$1$	$1$	$e\left(\frac{1699}{2048}\right)$	$e\left(\frac{1}{2048}\right)$	$e\left(\frac{869}{1024}\right)$	$e\left(\frac{675}{1024}\right)$	$e\left(\frac{1237}{2048}\right)$	$e\left(\frac{2031}{2048}\right)$	$e\left(\frac{425}{512}\right)$	$e\left(\frac{103}{512}\right)$	$e\left(\frac{919}{2048}\right)$	$e\left(\frac{1389}{2048}\right)$
$\chi_{16384}(27,\cdot)$	16384.z	4096	yes	$-1$	$1$	$e\left(\frac{2907}{4096}\right)$	$e\left(\frac{1001}{4096}\right)$	$e\left(\frac{1517}{2048}\right)$	$e\left(\frac{859}{2048}\right)$	$e\left(\frac{1245}{4096}\right)$	$e\left(\frac{1415}{4096}\right)$	$e\left(\frac{977}{1024}\right)$	$e\left(\frac{703}{1024}\right)$	$e\left(\frac{2415}{4096}\right)$	$e\left(\frac{1845}{4096}\right)$
$\chi_{16384}(29,\cdot)$	16384.y	4096	yes	$1$	$1$	$e\left(\frac{1361}{4096}\right)$	$e\left(\frac{1915}{4096}\right)$	$e\left(\frac{135}{2048}\right)$	$e\left(\frac{1361}{2048}\right)$	$e\left(\frac{3415}{4096}\right)$	$e\left(\frac{2261}{4096}\right)$	$e\left(\frac{819}{1024}\right)$	$e\left(\frac{637}{1024}\right)$	$e\left(\frac{653}{4096}\right)$	$e\left(\frac{1631}{4096}\right)$
$\chi_{16384}(31,\cdot)$	16384.t	512	no	$-1$	$1$	$e\left(\frac{179}{512}\right)$	$e\left(\frac{433}{512}\right)$	$e\left(\frac{85}{256}\right)$	$e\left(\frac{179}{256}\right)$	$e\left(\frac{325}{512}\right)$	$e\left(\frac{319}{512}\right)$	$e\left(\frac{25}{128}\right)$	$e\left(\frac{55}{128}\right)$	$e\left(\frac{359}{512}\right)$	$e\left(\frac{349}{512}\right)$
$\chi_{16384}(33,\cdot)$	16384.s	512	no	$1$	$1$	$e\left(\frac{173}{512}\right)$	$e\left(\frac{111}{512}\right)$	$e\left(\frac{203}{256}\right)$	$e\left(\frac{173}{256}\right)$	$e\left(\frac{91}{512}\right)$	$e\left(\frac{161}{512}\right)$	$e\left(\frac{71}{128}\right)$	$e\left(\frac{41}{128}\right)$	$e\left(\frac{121}{512}\right)$	$e\left(\frac{67}{512}\right)$
$\chi_{16384}(35,\cdot)$	16384.z	4096	yes	$-1$	$1$	$e\left(\frac{1345}{4096}\right)$	$e\left(\frac{3787}{4096}\right)$	$e\left(\frac{1815}{2048}\right)$	$e\left(\frac{1345}{2048}\right)$	$e\left(\frac{2791}{4096}\right)$	$e\left(\frac{3205}{4096}\right)$	$e\left(\frac{259}{1024}\right)$	$e\left(\frac{941}{1024}\right)$	$e\left(\frac{2749}{4096}\right)$	$e\left(\frac{879}{4096}\right)$
$\chi_{16384}(37,\cdot)$	16384.y	4096	yes	$1$	$1$	$e\left(\frac{1259}{4096}\right)$	$e\left(\frac{1305}{4096}\right)$	$e\left(\frac{477}{2048}\right)$	$e\left(\frac{1259}{2048}\right)$	$e\left(\frac{2509}{4096}\right)$	$e\left(\frac{343}{4096}\right)$	$e\left(\frac{641}{1024}\right)$	$e\left(\frac{271}{1024}\right)$	$e\left(\frac{1215}{4096}\right)$	$e\left(\frac{2213}{4096}\right)$
$\chi_{16384}(39,\cdot)$	16384.x	2048	no	$-1$	$1$	$e\left(\frac{1403}{2048}\right)$	$e\left(\frac{1865}{2048}\right)$	$e\left(\frac{205}{1024}\right)$	$e\left(\frac{379}{1024}\right)$	$e\left(\frac{1981}{2048}\right)$	$e\left(\frac{1063}{2048}\right)$	$e\left(\frac{305}{512}\right)$	$e\left(\frac{95}{512}\right)$	$e\left(\frac{783}{2048}\right)$	$e\left(\frac{1813}{2048}\right)$
$\chi_{16384}(41,\cdot)$	16384.w	2048	no	$1$	$1$	$e\left(\frac{2013}{2048}\right)$	$e\left(\frac{1919}{2048}\right)$	$e\left(\frac{539}{1024}\right)$	$e\left(\frac{989}{1024}\right)$	$e\left(\frac{171}{2048}\right)$	$e\left(\frac{145}{2048}\right)$	$e\left(\frac{471}{512}\right)$	$e\left(\frac{25}{512}\right)$	$e\left(\frac{233}{2048}\right)$	$e\left(\frac{1043}{2048}\right)$
$\chi_{16384}(43,\cdot)$	16384.z	4096	yes	$-1$	$1$	$e\left(\frac{983}{4096}\right)$	$e\left(\frac{3389}{4096}\right)$	$e\left(\frac{17}{2048}\right)$	$e\left(\frac{983}{2048}\right)$	$e\left(\frac{1985}{4096}\right)$	$e\left(\frac{1779}{4096}\right)$	$e\left(\frac{69}{1024}\right)$	$e\left(\frac{907}{1024}\right)$	$e\left(\frac{1531}{4096}\right)$	$e\left(\frac{1017}{4096}\right)$
$\chi_{16384}(45,\cdot)$	16384.y	4096	yes	$1$	$1$	$e\left(\frac{3637}{4096}\right)$	$e\left(\frac{3399}{4096}\right)$	$e\left(\frac{1539}{2048}\right)$	$e\left(\frac{1589}{2048}\right)$	$e\left(\frac{19}{4096}\right)$	$e\left(\frac{1609}{4096}\right)$	$e\left(\frac{735}{1024}\right)$	$e\left(\frac{913}{1024}\right)$	$e\left(\frac{481}{4096}\right)$	$e\left(\frac{2619}{4096}\right)$
$\chi_{16384}(47,\cdot)$	16384.v	1024	no	$-1$	$1$	$e\left(\frac{97}{1024}\right)$	$e\left(\frac{811}{1024}\right)$	$e\left(\frac{503}{512}\right)$	$e\left(\frac{97}{512}\right)$	$e\left(\frac{199}{1024}\right)$	$e\left(\frac{549}{1024}\right)$	$e\left(\frac{227}{256}\right)$	$e\left(\frac{77}{256}\right)$	$e\left(\frac{349}{1024}\right)$	$e\left(\frac{79}{1024}\right)$
$\chi_{16384}(49,\cdot)$	16384.u	1024	no	$1$	$1$	$e\left(\frac{847}{1024}\right)$	$e\left(\frac{869}{1024}\right)$	$e\left(\frac{473}{512}\right)$	$e\left(\frac{335}{512}\right)$	$e\left(\frac{777}{1024}\right)$	$e\left(\frac{587}{1024}\right)$	$e\left(\frac{173}{256}\right)$	$e\left(\frac{163}{256}\right)$	$e\left(\frac{915}{1024}\right)$	$e\left(\frac{769}{1024}\right)$
$\chi_{16384}(51,\cdot)$	16384.z	4096	yes	$-1$	$1$	$e\left(\frac{541}{4096}\right)$	$e\left(\frac{2111}{4096}\right)$	$e\left(\frac{1499}{2048}\right)$	$e\left(\frac{541}{2048}\right)$	$e\left(\frac{2155}{4096}\right)$	$e\left(\frac{3025}{4096}\right)$	$e\left(\frac{663}{1024}\right)$	$e\left(\frac{345}{1024}\right)$	$e\left(\frac{2601}{4096}\right)$	$e\left(\frac{3539}{4096}\right)$
$\chi_{16384}(53,\cdot)$	16384.y	4096	yes	$1$	$1$	$e\left(\frac{1583}{4096}\right)$	$e\left(\frac{1797}{4096}\right)$	$e\left(\frac{2041}{2048}\right)$	$e\left(\frac{1583}{2048}\right)$	$e\left(\frac{809}{4096}\right)$	$e\left(\frac{171}{4096}\right)$	$e\left(\frac{845}{1024}\right)$	$e\left(\frac{771}{1024}\right)$	$e\left(\frac{2803}{4096}\right)$	$e\left(\frac{1569}{4096}\right)$
$\chi_{16384}(55,\cdot)$	16384.x	2048	no	$-1$	$1$	$e\left(\frac{1057}{2048}\right)$	$e\left(\frac{1643}{2048}\right)$	$e\left(\frac{823}{1024}\right)$	$e\left(\frac{33}{1024}\right)$	$e\left(\frac{1799}{2048}\right)$	$e\left(\frac{741}{2048}\right)$	$e\left(\frac{163}{512}\right)$	$e\left(\frac{269}{512}\right)$	$e\left(\frac{1565}{2048}\right)$	$e\left(\frac{655}{2048}\right)$
$\chi_{16384}(57,\cdot)$	16384.w	2048	no	$1$	$1$	$e\left(\frac{887}{2048}\right)$	$e\left(\frac{285}{2048}\right)$	$e\left(\frac{881}{1024}\right)$	$e\left(\frac{887}{1024}\right)$	$e\left(\frac{289}{2048}\right)$	$e\left(\frac{1299}{2048}\right)$	$e\left(\frac{293}{512}\right)$	$e\left(\frac{171}{512}\right)$	$e\left(\frac{1819}{2048}\right)$	$e\left(\frac{601}{2048}\right)$
$\chi_{16384}(59,\cdot)$	16384.z	4096	yes	$-1$	$1$	$e\left(\frac{787}{4096}\right)$	$e\left(\frac{209}{4096}\right)$	$e\left(\frac{1397}{2048}\right)$	$e\left(\frac{787}{2048}\right)$	$e\left(\frac{485}{4096}\right)$	$e\left(\frac{2591}{4096}\right)$	$e\left(\frac{249}{1024}\right)$	$e\left(\frac{23}{1024}\right)$	$e\left(\frac{3655}{4096}\right)$	$e\left(\frac{3581}{4096}\right)$
$\chi_{16384}(61,\cdot)$	16384.y	4096	yes	$1$	$1$	$e\left(\frac{2521}{4096}\right)$	$e\left(\frac{339}{4096}\right)$	$e\left(\frac{703}{2048}\right)$	$e\left(\frac{473}{2048}\right)$	$e\left(\frac{3599}{4096}\right)$	$e\left(\frac{381}{4096}\right)$	$e\left(\frac{715}{1024}\right)$	$e\left(\frac{101}{1024}\right)$	$e\left(\frac{2293}{4096}\right)$	$e\left(\frac{3927}{4096}\right)$
$\chi_{16384}(63,\cdot)$	16384.r	256	no	$-1$	$1$	$e\left(\frac{99}{256}\right)$	$e\left(\frac{193}{256}\right)$	$e\left(\frac{101}{128}\right)$	$e\left(\frac{99}{128}\right)$	$e\left(\frac{21}{256}\right)$	$e\left(\frac{47}{256}\right)$	$e\left(\frac{9}{64}\right)$	$e\left(\frac{39}{64}\right)$	$e\left(\frac{87}{256}\right)$	$e\left(\frac{45}{256}\right)$

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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	$16384$
Structure	\(C_{2}\times C_{4096}\)
Order	$8192$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(21\)
\(\chi_{16384}(1,\cdot)\)	16384.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{16384}(3,\cdot)\)	16384.z	4096	yes	\(-1\)	\(1\)	\(e\left(\frac{969}{4096}\right)\)	\(e\left(\frac{1699}{4096}\right)\)	\(e\left(\frac{1871}{2048}\right)\)	\(e\left(\frac{969}{2048}\right)\)	\(e\left(\frac{415}{4096}\right)\)	\(e\left(\frac{1837}{4096}\right)\)	\(e\left(\frac{667}{1024}\right)\)	\(e\left(\frac{917}{1024}\right)\)	\(e\left(\frac{805}{4096}\right)\)	\(e\left(\frac{615}{4096}\right)\)
\(\chi_{16384}(5,\cdot)\)	16384.y	4096	yes	\(1\)	\(1\)	\(e\left(\frac{1699}{4096}\right)\)	\(e\left(\frac{1}{4096}\right)\)	\(e\left(\frac{1893}{2048}\right)\)	\(e\left(\frac{1699}{2048}\right)\)	\(e\left(\frac{3285}{4096}\right)\)	\(e\left(\frac{2031}{4096}\right)\)	\(e\left(\frac{425}{1024}\right)\)	\(e\left(\frac{103}{1024}\right)\)	\(e\left(\frac{2967}{4096}\right)\)	\(e\left(\frac{1389}{4096}\right)\)
\(\chi_{16384}(7,\cdot)\)	16384.x	2048	no	\(-1\)	\(1\)	\(e\left(\frac{1871}{2048}\right)\)	\(e\left(\frac{1893}{2048}\right)\)	\(e\left(\frac{985}{1024}\right)\)	\(e\left(\frac{847}{1024}\right)\)	\(e\left(\frac{1801}{2048}\right)\)	\(e\left(\frac{587}{2048}\right)\)	\(e\left(\frac{429}{512}\right)\)	\(e\left(\frac{419}{512}\right)\)	\(e\left(\frac{1939}{2048}\right)\)	\(e\left(\frac{1793}{2048}\right)\)
\(\chi_{16384}(9,\cdot)\)	16384.w	2048	no	\(1\)	\(1\)	\(e\left(\frac{969}{2048}\right)\)	\(e\left(\frac{1699}{2048}\right)\)	\(e\left(\frac{847}{1024}\right)\)	\(e\left(\frac{969}{1024}\right)\)	\(e\left(\frac{415}{2048}\right)\)	\(e\left(\frac{1837}{2048}\right)\)	\(e\left(\frac{155}{512}\right)\)	\(e\left(\frac{405}{512}\right)\)	\(e\left(\frac{805}{2048}\right)\)	\(e\left(\frac{615}{2048}\right)\)
\(\chi_{16384}(11,\cdot)\)	16384.z	4096	yes	\(-1\)	\(1\)	\(e\left(\frac{415}{4096}\right)\)	\(e\left(\frac{3285}{4096}\right)\)	\(e\left(\frac{1801}{2048}\right)\)	\(e\left(\frac{415}{2048}\right)\)	\(e\left(\frac{313}{4096}\right)\)	\(e\left(\frac{3547}{4096}\right)\)	\(e\left(\frac{925}{1024}\right)\)	\(e\left(\frac{435}{1024}\right)\)	\(e\left(\frac{163}{4096}\right)\)	\(e\left(\frac{4017}{4096}\right)\)
\(\chi_{16384}(13,\cdot)\)	16384.y	4096	yes	\(1\)	\(1\)	\(e\left(\frac{1837}{4096}\right)\)	\(e\left(\frac{2031}{4096}\right)\)	\(e\left(\frac{587}{2048}\right)\)	\(e\left(\frac{1837}{2048}\right)\)	\(e\left(\frac{3547}{4096}\right)\)	\(e\left(\frac{289}{4096}\right)\)	\(e\left(\frac{967}{1024}\right)\)	\(e\left(\frac{297}{1024}\right)\)	\(e\left(\frac{761}{4096}\right)\)	\(e\left(\frac{3011}{4096}\right)\)
\(\chi_{16384}(15,\cdot)\)	16384.v	1024	no	\(-1\)	\(1\)	\(e\left(\frac{667}{1024}\right)\)	\(e\left(\frac{425}{1024}\right)\)	\(e\left(\frac{429}{512}\right)\)	\(e\left(\frac{155}{512}\right)\)	\(e\left(\frac{925}{1024}\right)\)	\(e\left(\frac{967}{1024}\right)\)	\(e\left(\frac{17}{256}\right)\)	\(e\left(\frac{255}{256}\right)\)	\(e\left(\frac{943}{1024}\right)\)	\(e\left(\frac{501}{1024}\right)\)
\(\chi_{16384}(17,\cdot)\)	16384.u	1024	no	\(1\)	\(1\)	\(e\left(\frac{917}{1024}\right)\)	\(e\left(\frac{103}{1024}\right)\)	\(e\left(\frac{419}{512}\right)\)	\(e\left(\frac{405}{512}\right)\)	\(e\left(\frac{435}{1024}\right)\)	\(e\left(\frac{297}{1024}\right)\)	\(e\left(\frac{255}{256}\right)\)	\(e\left(\frac{113}{256}\right)\)	\(e\left(\frac{449}{1024}\right)\)	\(e\left(\frac{731}{1024}\right)\)
\(\chi_{16384}(19,\cdot)\)	16384.z	4096	yes	\(-1\)	\(1\)	\(e\left(\frac{805}{4096}\right)\)	\(e\left(\frac{2967}{4096}\right)\)	\(e\left(\frac{1939}{2048}\right)\)	\(e\left(\frac{805}{2048}\right)\)	\(e\left(\frac{163}{4096}\right)\)	\(e\left(\frac{761}{4096}\right)\)	\(e\left(\frac{943}{1024}\right)\)	\(e\left(\frac{449}{1024}\right)\)	\(e\left(\frac{2833}{4096}\right)\)	\(e\left(\frac{587}{4096}\right)\)
\(\chi_{16384}(21,\cdot)\)	16384.y	4096	yes	\(1\)	\(1\)	\(e\left(\frac{615}{4096}\right)\)	\(e\left(\frac{1389}{4096}\right)\)	\(e\left(\frac{1793}{2048}\right)\)	\(e\left(\frac{615}{2048}\right)\)	\(e\left(\frac{4017}{4096}\right)\)	\(e\left(\frac{3011}{4096}\right)\)	\(e\left(\frac{501}{1024}\right)\)	\(e\left(\frac{731}{1024}\right)\)	\(e\left(\frac{587}{4096}\right)\)	\(e\left(\frac{105}{4096}\right)\)
\(\chi_{16384}(23,\cdot)\)	16384.x	2048	no	\(-1\)	\(1\)	\(e\left(\frac{1333}{2048}\right)\)	\(e\left(\frac{1607}{2048}\right)\)	\(e\left(\frac{259}{1024}\right)\)	\(e\left(\frac{309}{1024}\right)\)	\(e\left(\frac{275}{2048}\right)\)	\(e\left(\frac{1353}{2048}\right)\)	\(e\left(\frac{223}{512}\right)\)	\(e\left(\frac{145}{512}\right)\)	\(e\left(\frac{1249}{2048}\right)\)	\(e\left(\frac{1851}{2048}\right)\)
\(\chi_{16384}(25,\cdot)\)	16384.w	2048	no	\(1\)	\(1\)	\(e\left(\frac{1699}{2048}\right)\)	\(e\left(\frac{1}{2048}\right)\)	\(e\left(\frac{869}{1024}\right)\)	\(e\left(\frac{675}{1024}\right)\)	\(e\left(\frac{1237}{2048}\right)\)	\(e\left(\frac{2031}{2048}\right)\)	\(e\left(\frac{425}{512}\right)\)	\(e\left(\frac{103}{512}\right)\)	\(e\left(\frac{919}{2048}\right)\)	\(e\left(\frac{1389}{2048}\right)\)
\(\chi_{16384}(27,\cdot)\)	16384.z	4096	yes	\(-1\)	\(1\)	\(e\left(\frac{2907}{4096}\right)\)	\(e\left(\frac{1001}{4096}\right)\)	\(e\left(\frac{1517}{2048}\right)\)	\(e\left(\frac{859}{2048}\right)\)	\(e\left(\frac{1245}{4096}\right)\)	\(e\left(\frac{1415}{4096}\right)\)	\(e\left(\frac{977}{1024}\right)\)	\(e\left(\frac{703}{1024}\right)\)	\(e\left(\frac{2415}{4096}\right)\)	\(e\left(\frac{1845}{4096}\right)\)
\(\chi_{16384}(29,\cdot)\)	16384.y	4096	yes	\(1\)	\(1\)	\(e\left(\frac{1361}{4096}\right)\)	\(e\left(\frac{1915}{4096}\right)\)	\(e\left(\frac{135}{2048}\right)\)	\(e\left(\frac{1361}{2048}\right)\)	\(e\left(\frac{3415}{4096}\right)\)	\(e\left(\frac{2261}{4096}\right)\)	\(e\left(\frac{819}{1024}\right)\)	\(e\left(\frac{637}{1024}\right)\)	\(e\left(\frac{653}{4096}\right)\)	\(e\left(\frac{1631}{4096}\right)\)
\(\chi_{16384}(31,\cdot)\)	16384.t	512	no	\(-1\)	\(1\)	\(e\left(\frac{179}{512}\right)\)	\(e\left(\frac{433}{512}\right)\)	\(e\left(\frac{85}{256}\right)\)	\(e\left(\frac{179}{256}\right)\)	\(e\left(\frac{325}{512}\right)\)	\(e\left(\frac{319}{512}\right)\)	\(e\left(\frac{25}{128}\right)\)	\(e\left(\frac{55}{128}\right)\)	\(e\left(\frac{359}{512}\right)\)	\(e\left(\frac{349}{512}\right)\)
\(\chi_{16384}(33,\cdot)\)	16384.s	512	no	\(1\)	\(1\)	\(e\left(\frac{173}{512}\right)\)	\(e\left(\frac{111}{512}\right)\)	\(e\left(\frac{203}{256}\right)\)	\(e\left(\frac{173}{256}\right)\)	\(e\left(\frac{91}{512}\right)\)	\(e\left(\frac{161}{512}\right)\)	\(e\left(\frac{71}{128}\right)\)	\(e\left(\frac{41}{128}\right)\)	\(e\left(\frac{121}{512}\right)\)	\(e\left(\frac{67}{512}\right)\)
\(\chi_{16384}(35,\cdot)\)	16384.z	4096	yes	\(-1\)	\(1\)	\(e\left(\frac{1345}{4096}\right)\)	\(e\left(\frac{3787}{4096}\right)\)	\(e\left(\frac{1815}{2048}\right)\)	\(e\left(\frac{1345}{2048}\right)\)	\(e\left(\frac{2791}{4096}\right)\)	\(e\left(\frac{3205}{4096}\right)\)	\(e\left(\frac{259}{1024}\right)\)	\(e\left(\frac{941}{1024}\right)\)	\(e\left(\frac{2749}{4096}\right)\)	\(e\left(\frac{879}{4096}\right)\)
\(\chi_{16384}(37,\cdot)\)	16384.y	4096	yes	\(1\)	\(1\)	\(e\left(\frac{1259}{4096}\right)\)	\(e\left(\frac{1305}{4096}\right)\)	\(e\left(\frac{477}{2048}\right)\)	\(e\left(\frac{1259}{2048}\right)\)	\(e\left(\frac{2509}{4096}\right)\)	\(e\left(\frac{343}{4096}\right)\)	\(e\left(\frac{641}{1024}\right)\)	\(e\left(\frac{271}{1024}\right)\)	\(e\left(\frac{1215}{4096}\right)\)	\(e\left(\frac{2213}{4096}\right)\)
\(\chi_{16384}(39,\cdot)\)	16384.x	2048	no	\(-1\)	\(1\)	\(e\left(\frac{1403}{2048}\right)\)	\(e\left(\frac{1865}{2048}\right)\)	\(e\left(\frac{205}{1024}\right)\)	\(e\left(\frac{379}{1024}\right)\)	\(e\left(\frac{1981}{2048}\right)\)	\(e\left(\frac{1063}{2048}\right)\)	\(e\left(\frac{305}{512}\right)\)	\(e\left(\frac{95}{512}\right)\)	\(e\left(\frac{783}{2048}\right)\)	\(e\left(\frac{1813}{2048}\right)\)
\(\chi_{16384}(41,\cdot)\)	16384.w	2048	no	\(1\)	\(1\)	\(e\left(\frac{2013}{2048}\right)\)	\(e\left(\frac{1919}{2048}\right)\)	\(e\left(\frac{539}{1024}\right)\)	\(e\left(\frac{989}{1024}\right)\)	\(e\left(\frac{171}{2048}\right)\)	\(e\left(\frac{145}{2048}\right)\)	\(e\left(\frac{471}{512}\right)\)	\(e\left(\frac{25}{512}\right)\)	\(e\left(\frac{233}{2048}\right)\)	\(e\left(\frac{1043}{2048}\right)\)
\(\chi_{16384}(43,\cdot)\)	16384.z	4096	yes	\(-1\)	\(1\)	\(e\left(\frac{983}{4096}\right)\)	\(e\left(\frac{3389}{4096}\right)\)	\(e\left(\frac{17}{2048}\right)\)	\(e\left(\frac{983}{2048}\right)\)	\(e\left(\frac{1985}{4096}\right)\)	\(e\left(\frac{1779}{4096}\right)\)	\(e\left(\frac{69}{1024}\right)\)	\(e\left(\frac{907}{1024}\right)\)	\(e\left(\frac{1531}{4096}\right)\)	\(e\left(\frac{1017}{4096}\right)\)
\(\chi_{16384}(45,\cdot)\)	16384.y	4096	yes	\(1\)	\(1\)	\(e\left(\frac{3637}{4096}\right)\)	\(e\left(\frac{3399}{4096}\right)\)	\(e\left(\frac{1539}{2048}\right)\)	\(e\left(\frac{1589}{2048}\right)\)	\(e\left(\frac{19}{4096}\right)\)	\(e\left(\frac{1609}{4096}\right)\)	\(e\left(\frac{735}{1024}\right)\)	\(e\left(\frac{913}{1024}\right)\)	\(e\left(\frac{481}{4096}\right)\)	\(e\left(\frac{2619}{4096}\right)\)
\(\chi_{16384}(47,\cdot)\)	16384.v	1024	no	\(-1\)	\(1\)	\(e\left(\frac{97}{1024}\right)\)	\(e\left(\frac{811}{1024}\right)\)	\(e\left(\frac{503}{512}\right)\)	\(e\left(\frac{97}{512}\right)\)	\(e\left(\frac{199}{1024}\right)\)	\(e\left(\frac{549}{1024}\right)\)	\(e\left(\frac{227}{256}\right)\)	\(e\left(\frac{77}{256}\right)\)	\(e\left(\frac{349}{1024}\right)\)	\(e\left(\frac{79}{1024}\right)\)
\(\chi_{16384}(49,\cdot)\)	16384.u	1024	no	\(1\)	\(1\)	\(e\left(\frac{847}{1024}\right)\)	\(e\left(\frac{869}{1024}\right)\)	\(e\left(\frac{473}{512}\right)\)	\(e\left(\frac{335}{512}\right)\)	\(e\left(\frac{777}{1024}\right)\)	\(e\left(\frac{587}{1024}\right)\)	\(e\left(\frac{173}{256}\right)\)	\(e\left(\frac{163}{256}\right)\)	\(e\left(\frac{915}{1024}\right)\)	\(e\left(\frac{769}{1024}\right)\)
\(\chi_{16384}(51,\cdot)\)	16384.z	4096	yes	\(-1\)	\(1\)	\(e\left(\frac{541}{4096}\right)\)	\(e\left(\frac{2111}{4096}\right)\)	\(e\left(\frac{1499}{2048}\right)\)	\(e\left(\frac{541}{2048}\right)\)	\(e\left(\frac{2155}{4096}\right)\)	\(e\left(\frac{3025}{4096}\right)\)	\(e\left(\frac{663}{1024}\right)\)	\(e\left(\frac{345}{1024}\right)\)	\(e\left(\frac{2601}{4096}\right)\)	\(e\left(\frac{3539}{4096}\right)\)
\(\chi_{16384}(53,\cdot)\)	16384.y	4096	yes	\(1\)	\(1\)	\(e\left(\frac{1583}{4096}\right)\)	\(e\left(\frac{1797}{4096}\right)\)	\(e\left(\frac{2041}{2048}\right)\)	\(e\left(\frac{1583}{2048}\right)\)	\(e\left(\frac{809}{4096}\right)\)	\(e\left(\frac{171}{4096}\right)\)	\(e\left(\frac{845}{1024}\right)\)	\(e\left(\frac{771}{1024}\right)\)	\(e\left(\frac{2803}{4096}\right)\)	\(e\left(\frac{1569}{4096}\right)\)
\(\chi_{16384}(55,\cdot)\)	16384.x	2048	no	\(-1\)	\(1\)	\(e\left(\frac{1057}{2048}\right)\)	\(e\left(\frac{1643}{2048}\right)\)	\(e\left(\frac{823}{1024}\right)\)	\(e\left(\frac{33}{1024}\right)\)	\(e\left(\frac{1799}{2048}\right)\)	\(e\left(\frac{741}{2048}\right)\)	\(e\left(\frac{163}{512}\right)\)	\(e\left(\frac{269}{512}\right)\)	\(e\left(\frac{1565}{2048}\right)\)	\(e\left(\frac{655}{2048}\right)\)
\(\chi_{16384}(57,\cdot)\)	16384.w	2048	no	\(1\)	\(1\)	\(e\left(\frac{887}{2048}\right)\)	\(e\left(\frac{285}{2048}\right)\)	\(e\left(\frac{881}{1024}\right)\)	\(e\left(\frac{887}{1024}\right)\)	\(e\left(\frac{289}{2048}\right)\)	\(e\left(\frac{1299}{2048}\right)\)	\(e\left(\frac{293}{512}\right)\)	\(e\left(\frac{171}{512}\right)\)	\(e\left(\frac{1819}{2048}\right)\)	\(e\left(\frac{601}{2048}\right)\)
\(\chi_{16384}(59,\cdot)\)	16384.z	4096	yes	\(-1\)	\(1\)	\(e\left(\frac{787}{4096}\right)\)	\(e\left(\frac{209}{4096}\right)\)	\(e\left(\frac{1397}{2048}\right)\)	\(e\left(\frac{787}{2048}\right)\)	\(e\left(\frac{485}{4096}\right)\)	\(e\left(\frac{2591}{4096}\right)\)	\(e\left(\frac{249}{1024}\right)\)	\(e\left(\frac{23}{1024}\right)\)	\(e\left(\frac{3655}{4096}\right)\)	\(e\left(\frac{3581}{4096}\right)\)
\(\chi_{16384}(61,\cdot)\)	16384.y	4096	yes	\(1\)	\(1\)	\(e\left(\frac{2521}{4096}\right)\)	\(e\left(\frac{339}{4096}\right)\)	\(e\left(\frac{703}{2048}\right)\)	\(e\left(\frac{473}{2048}\right)\)	\(e\left(\frac{3599}{4096}\right)\)	\(e\left(\frac{381}{4096}\right)\)	\(e\left(\frac{715}{1024}\right)\)	\(e\left(\frac{101}{1024}\right)\)	\(e\left(\frac{2293}{4096}\right)\)	\(e\left(\frac{3927}{4096}\right)\)
\(\chi_{16384}(63,\cdot)\)	16384.r	256	no	\(-1\)	\(1\)	\(e\left(\frac{99}{256}\right)\)	\(e\left(\frac{193}{256}\right)\)	\(e\left(\frac{101}{128}\right)\)	\(e\left(\frac{99}{128}\right)\)	\(e\left(\frac{21}{256}\right)\)	\(e\left(\frac{47}{256}\right)\)	\(e\left(\frac{9}{64}\right)\)	\(e\left(\frac{39}{64}\right)\)	\(e\left(\frac{87}{256}\right)\)	\(e\left(\frac{45}{256}\right)\)

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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.