LMFDB - Group of Dirichlet characters of modulus 36864

Show commands: PariGP / SageMath

sage: H = DirichletGroup(36864)

pari: g = idealstar(,36864,2)

Character group

sage: G.order() pari: g.no
Order	=	12288
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{3072}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{36864}(8191,\cdot)$, $\chi_{36864}(20485,\cdot)$, $\chi_{36864}(4097,\cdot)$

First 32 of 12288 characters

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

Character	Orbit	Order	Primitive	$-1$	$1$	$5$	$7$	$11$	$13$	$17$	$19$	$23$	$25$	$29$	$31$
$\chi_{36864}(1,\cdot)$	36864.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{36864}(5,\cdot)$	36864.dj	3072	yes	$-1$	$1$	$e\left(\frac{515}{3072}\right)$	$e\left(\frac{47}{1536}\right)$	$e\left(\frac{127}{3072}\right)$	$e\left(\frac{1997}{3072}\right)$	$e\left(\frac{231}{256}\right)$	$e\left(\frac{919}{1024}\right)$	$e\left(\frac{469}{1536}\right)$	$e\left(\frac{515}{1536}\right)$	$e\left(\frac{2161}{3072}\right)$	$e\left(\frac{19}{384}\right)$
$\chi_{36864}(7,\cdot)$	36864.dd	1536	no	$-1$	$1$	$e\left(\frac{47}{1536}\right)$	$e\left(\frac{11}{768}\right)$	$e\left(\frac{1051}{1536}\right)$	$e\left(\frac{737}{1536}\right)$	$e\left(\frac{35}{128}\right)$	$e\left(\frac{147}{512}\right)$	$e\left(\frac{649}{768}\right)$	$e\left(\frac{47}{768}\right)$	$e\left(\frac{1429}{1536}\right)$	$e\left(\frac{31}{192}\right)$
$\chi_{36864}(11,\cdot)$	36864.dh	3072	yes	$1$	$1$	$e\left(\frac{127}{3072}\right)$	$e\left(\frac{1051}{1536}\right)$	$e\left(\frac{2987}{3072}\right)$	$e\left(\frac{2449}{3072}\right)$	$e\left(\frac{51}{256}\right)$	$e\left(\frac{675}{1024}\right)$	$e\left(\frac{1337}{1536}\right)$	$e\left(\frac{127}{1536}\right)$	$e\left(\frac{1541}{3072}\right)$	$e\left(\frac{143}{384}\right)$
$\chi_{36864}(13,\cdot)$	36864.di	3072	yes	$1$	$1$	$e\left(\frac{1997}{3072}\right)$	$e\left(\frac{737}{1536}\right)$	$e\left(\frac{2449}{3072}\right)$	$e\left(\frac{2915}{3072}\right)$	$e\left(\frac{41}{256}\right)$	$e\left(\frac{761}{1024}\right)$	$e\left(\frac{475}{1536}\right)$	$e\left(\frac{461}{1536}\right)$	$e\left(\frac{1663}{3072}\right)$	$e\left(\frac{61}{384}\right)$
$\chi_{36864}(17,\cdot)$	36864.ci	256	no	$-1$	$1$	$e\left(\frac{231}{256}\right)$	$e\left(\frac{35}{128}\right)$	$e\left(\frac{51}{256}\right)$	$e\left(\frac{41}{256}\right)$	$e\left(\frac{17}{64}\right)$	$e\left(\frac{193}{256}\right)$	$e\left(\frac{81}{128}\right)$	$e\left(\frac{103}{128}\right)$	$e\left(\frac{253}{256}\right)$	$e\left(\frac{23}{32}\right)$
$\chi_{36864}(19,\cdot)$	36864.db	1024	no	$-1$	$1$	$e\left(\frac{919}{1024}\right)$	$e\left(\frac{147}{512}\right)$	$e\left(\frac{675}{1024}\right)$	$e\left(\frac{761}{1024}\right)$	$e\left(\frac{193}{256}\right)$	$e\left(\frac{273}{1024}\right)$	$e\left(\frac{481}{512}\right)$	$e\left(\frac{407}{512}\right)$	$e\left(\frac{653}{1024}\right)$	$e\left(\frac{39}{128}\right)$
$\chi_{36864}(23,\cdot)$	36864.df	1536	no	$1$	$1$	$e\left(\frac{469}{1536}\right)$	$e\left(\frac{649}{768}\right)$	$e\left(\frac{1337}{1536}\right)$	$e\left(\frac{475}{1536}\right)$	$e\left(\frac{81}{128}\right)$	$e\left(\frac{481}{512}\right)$	$e\left(\frac{275}{768}\right)$	$e\left(\frac{469}{768}\right)$	$e\left(\frac{599}{1536}\right)$	$e\left(\frac{101}{192}\right)$
$\chi_{36864}(25,\cdot)$	36864.dc	1536	no	$1$	$1$	$e\left(\frac{515}{1536}\right)$	$e\left(\frac{47}{768}\right)$	$e\left(\frac{127}{1536}\right)$	$e\left(\frac{461}{1536}\right)$	$e\left(\frac{103}{128}\right)$	$e\left(\frac{407}{512}\right)$	$e\left(\frac{469}{768}\right)$	$e\left(\frac{515}{768}\right)$	$e\left(\frac{625}{1536}\right)$	$e\left(\frac{19}{192}\right)$
$\chi_{36864}(29,\cdot)$	36864.dj	3072	yes	$-1$	$1$	$e\left(\frac{2161}{3072}\right)$	$e\left(\frac{1429}{1536}\right)$	$e\left(\frac{1541}{3072}\right)$	$e\left(\frac{1663}{3072}\right)$	$e\left(\frac{253}{256}\right)$	$e\left(\frac{653}{1024}\right)$	$e\left(\frac{599}{1536}\right)$	$e\left(\frac{625}{1536}\right)$	$e\left(\frac{1355}{3072}\right)$	$e\left(\frac{161}{384}\right)$
$\chi_{36864}(31,\cdot)$	36864.cp	384	no	$-1$	$1$	$e\left(\frac{19}{384}\right)$	$e\left(\frac{31}{192}\right)$	$e\left(\frac{143}{384}\right)$	$e\left(\frac{61}{384}\right)$	$e\left(\frac{23}{32}\right)$	$e\left(\frac{39}{128}\right)$	$e\left(\frac{101}{192}\right)$	$e\left(\frac{19}{192}\right)$	$e\left(\frac{161}{384}\right)$	$e\left(\frac{11}{48}\right)$
$\chi_{36864}(35,\cdot)$	36864.da	1024	no	$1$	$1$	$e\left(\frac{203}{1024}\right)$	$e\left(\frac{23}{512}\right)$	$e\left(\frac{743}{1024}\right)$	$e\left(\frac{133}{1024}\right)$	$e\left(\frac{45}{256}\right)$	$e\left(\frac{189}{1024}\right)$	$e\left(\frac{77}{512}\right)$	$e\left(\frac{203}{512}\right)$	$e\left(\frac{649}{1024}\right)$	$e\left(\frac{27}{128}\right)$
$\chi_{36864}(37,\cdot)$	36864.cz	1024	no	$1$	$1$	$e\left(\frac{281}{1024}\right)$	$e\left(\frac{477}{512}\right)$	$e\left(\frac{461}{1024}\right)$	$e\left(\frac{343}{1024}\right)$	$e\left(\frac{15}{256}\right)$	$e\left(\frac{191}{1024}\right)$	$e\left(\frac{495}{512}\right)$	$e\left(\frac{281}{512}\right)$	$e\left(\frac{515}{1024}\right)$	$e\left(\frac{73}{128}\right)$
$\chi_{36864}(41,\cdot)$	36864.de	1536	no	$-1$	$1$	$e\left(\frac{1405}{1536}\right)$	$e\left(\frac{337}{768}\right)$	$e\left(\frac{257}{1536}\right)$	$e\left(\frac{1459}{1536}\right)$	$e\left(\frac{89}{128}\right)$	$e\left(\frac{233}{512}\right)$	$e\left(\frac{299}{768}\right)$	$e\left(\frac{637}{768}\right)$	$e\left(\frac{527}{1536}\right)$	$e\left(\frac{173}{192}\right)$
$\chi_{36864}(43,\cdot)$	36864.dg	3072	yes	$-1$	$1$	$e\left(\frac{1975}{3072}\right)$	$e\left(\frac{307}{1536}\right)$	$e\left(\frac{323}{3072}\right)$	$e\left(\frac{217}{3072}\right)$	$e\left(\frac{139}{256}\right)$	$e\left(\frac{1019}{1024}\right)$	$e\left(\frac{1217}{1536}\right)$	$e\left(\frac{439}{1536}\right)$	$e\left(\frac{1517}{3072}\right)$	$e\left(\frac{71}{384}\right)$
$\chi_{36864}(47,\cdot)$	36864.cu	768	no	$1$	$1$	$e\left(\frac{1}{768}\right)$	$e\left(\frac{37}{384}\right)$	$e\left(\frac{341}{768}\right)$	$e\left(\frac{367}{768}\right)$	$e\left(\frac{45}{64}\right)$	$e\left(\frac{221}{256}\right)$	$e\left(\frac{71}{384}\right)$	$e\left(\frac{1}{384}\right)$	$e\left(\frac{635}{768}\right)$	$e\left(\frac{65}{96}\right)$
$\chi_{36864}(49,\cdot)$	36864.cx	768	no	$1$	$1$	$e\left(\frac{47}{768}\right)$	$e\left(\frac{11}{384}\right)$	$e\left(\frac{283}{768}\right)$	$e\left(\frac{737}{768}\right)$	$e\left(\frac{35}{64}\right)$	$e\left(\frac{147}{256}\right)$	$e\left(\frac{265}{384}\right)$	$e\left(\frac{47}{384}\right)$	$e\left(\frac{661}{768}\right)$	$e\left(\frac{31}{96}\right)$
$\chi_{36864}(53,\cdot)$	36864.cy	1024	no	$-1$	$1$	$e\left(\frac{261}{1024}\right)$	$e\left(\frac{505}{512}\right)$	$e\left(\frac{297}{1024}\right)$	$e\left(\frac{171}{1024}\right)$	$e\left(\frac{131}{256}\right)$	$e\left(\frac{755}{1024}\right)$	$e\left(\frac{355}{512}\right)$	$e\left(\frac{261}{512}\right)$	$e\left(\frac{103}{1024}\right)$	$e\left(\frac{117}{128}\right)$
$\chi_{36864}(55,\cdot)$	36864.cq	512	no	$-1$	$1$	$e\left(\frac{107}{512}\right)$	$e\left(\frac{183}{256}\right)$	$e\left(\frac{7}{512}\right)$	$e\left(\frac{229}{512}\right)$	$e\left(\frac{13}{128}\right)$	$e\left(\frac{285}{512}\right)$	$e\left(\frac{45}{256}\right)$	$e\left(\frac{107}{256}\right)$	$e\left(\frac{105}{512}\right)$	$e\left(\frac{27}{64}\right)$
$\chi_{36864}(59,\cdot)$	36864.dh	3072	yes	$1$	$1$	$e\left(\frac{1139}{3072}\right)$	$e\left(\frac{863}{1536}\right)$	$e\left(\frac{2479}{3072}\right)$	$e\left(\frac{605}{3072}\right)$	$e\left(\frac{151}{256}\right)$	$e\left(\frac{71}{1024}\right)$	$e\left(\frac{997}{1536}\right)$	$e\left(\frac{1139}{1536}\right)$	$e\left(\frac{2113}{3072}\right)$	$e\left(\frac{67}{384}\right)$
$\chi_{36864}(61,\cdot)$	36864.di	3072	yes	$1$	$1$	$e\left(\frac{2041}{3072}\right)$	$e\left(\frac{61}{1536}\right)$	$e\left(\frac{557}{3072}\right)$	$e\left(\frac{2167}{3072}\right)$	$e\left(\frac{101}{256}\right)$	$e\left(\frac{245}{1024}\right)$	$e\left(\frac{527}{1536}\right)$	$e\left(\frac{505}{1536}\right)$	$e\left(\frac{1955}{3072}\right)$	$e\left(\frac{41}{384}\right)$
$\chi_{36864}(65,\cdot)$	36864.cf	192	no	$-1$	$1$	$e\left(\frac{157}{192}\right)$	$e\left(\frac{49}{96}\right)$	$e\left(\frac{161}{192}\right)$	$e\left(\frac{115}{192}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{41}{64}\right)$	$e\left(\frac{59}{96}\right)$	$e\left(\frac{61}{96}\right)$	$e\left(\frac{47}{192}\right)$	$e\left(\frac{5}{24}\right)$
$\chi_{36864}(67,\cdot)$	36864.dg	3072	yes	$-1$	$1$	$e\left(\frac{2009}{3072}\right)$	$e\left(\frac{1181}{1536}\right)$	$e\left(\frac{397}{3072}\right)$	$e\left(\frac{2711}{3072}\right)$	$e\left(\frac{197}{256}\right)$	$e\left(\frac{853}{1024}\right)$	$e\left(\frac{559}{1536}\right)$	$e\left(\frac{473}{1536}\right)$	$e\left(\frac{67}{3072}\right)$	$e\left(\frac{73}{384}\right)$
$\chi_{36864}(71,\cdot)$	36864.cs	512	no	$1$	$1$	$e\left(\frac{173}{512}\right)$	$e\left(\frac{193}{256}\right)$	$e\left(\frac{241}{512}\right)$	$e\left(\frac{387}{512}\right)$	$e\left(\frac{91}{128}\right)$	$e\left(\frac{267}{512}\right)$	$e\left(\frac{251}{256}\right)$	$e\left(\frac{173}{256}\right)$	$e\left(\frac{31}{512}\right)$	$e\left(\frac{61}{64}\right)$
$\chi_{36864}(73,\cdot)$	36864.cr	512	no	$1$	$1$	$e\left(\frac{219}{512}\right)$	$e\left(\frac{103}{256}\right)$	$e\left(\frac{55}{512}\right)$	$e\left(\frac{373}{512}\right)$	$e\left(\frac{29}{128}\right)$	$e\left(\frac{45}{512}\right)$	$e\left(\frac{189}{256}\right)$	$e\left(\frac{219}{256}\right)$	$e\left(\frac{57}{512}\right)$	$e\left(\frac{43}{64}\right)$
$\chi_{36864}(77,\cdot)$	36864.dj	3072	yes	$-1$	$1$	$e\left(\frac{221}{3072}\right)$	$e\left(\frac{1073}{1536}\right)$	$e\left(\frac{2017}{3072}\right)$	$e\left(\frac{851}{3072}\right)$	$e\left(\frac{121}{256}\right)$	$e\left(\frac{969}{1024}\right)$	$e\left(\frac{1099}{1536}\right)$	$e\left(\frac{221}{1536}\right)$	$e\left(\frac{1327}{3072}\right)$	$e\left(\frac{205}{384}\right)$
$\chi_{36864}(79,\cdot)$	36864.cv	768	no	$-1$	$1$	$e\left(\frac{199}{768}\right)$	$e\left(\frac{67}{384}\right)$	$e\left(\frac{275}{768}\right)$	$e\left(\frac{457}{768}\right)$	$e\left(\frac{27}{64}\right)$	$e\left(\frac{75}{256}\right)$	$e\left(\frac{113}{384}\right)$	$e\left(\frac{199}{384}\right)$	$e\left(\frac{413}{768}\right)$	$e\left(\frac{71}{96}\right)$
$\chi_{36864}(83,\cdot)$	36864.dh	3072	yes	$1$	$1$	$e\left(\frac{949}{3072}\right)$	$e\left(\frac{1129}{1536}\right)$	$e\left(\frac{2969}{3072}\right)$	$e\left(\frac{763}{3072}\right)$	$e\left(\frac{113}{256}\right)$	$e\left(\frac{577}{1024}\right)$	$e\left(\frac{1331}{1536}\right)$	$e\left(\frac{949}{1536}\right)$	$e\left(\frac{2807}{3072}\right)$	$e\left(\frac{101}{384}\right)$
$\chi_{36864}(85,\cdot)$	36864.di	3072	yes	$1$	$1$	$e\left(\frac{215}{3072}\right)$	$e\left(\frac{467}{1536}\right)$	$e\left(\frac{739}{3072}\right)$	$e\left(\frac{2489}{3072}\right)$	$e\left(\frac{43}{256}\right)$	$e\left(\frac{667}{1024}\right)$	$e\left(\frac{1441}{1536}\right)$	$e\left(\frac{215}{1536}\right)$	$e\left(\frac{2125}{3072}\right)$	$e\left(\frac{295}{384}\right)$
$\chi_{36864}(89,\cdot)$	36864.ct	512	no	$-1$	$1$	$e\left(\frac{441}{512}\right)$	$e\left(\frac{253}{256}\right)$	$e\left(\frac{237}{512}\right)$	$e\left(\frac{439}{512}\right)$	$e\left(\frac{47}{128}\right)$	$e\left(\frac{31}{512}\right)$	$e\left(\frac{207}{256}\right)$	$e\left(\frac{185}{256}\right)$	$e\left(\frac{227}{512}\right)$	$e\left(\frac{41}{64}\right)$
$\chi_{36864}(91,\cdot)$	36864.db	1024	no	$-1$	$1$	$e\left(\frac{697}{1024}\right)$	$e\left(\frac{253}{512}\right)$	$e\left(\frac{493}{1024}\right)$	$e\left(\frac{439}{1024}\right)$	$e\left(\frac{111}{256}\right)$	$e\left(\frac{31}{1024}\right)$	$e\left(\frac{79}{512}\right)$	$e\left(\frac{185}{512}\right)$	$e\left(\frac{483}{1024}\right)$	$e\left(\frac{41}{128}\right)$
$\chi_{36864}(95,\cdot)$	36864.cn	384	no	$1$	$1$	$e\left(\frac{25}{384}\right)$	$e\left(\frac{61}{192}\right)$	$e\left(\frac{269}{384}\right)$	$e\left(\frac{151}{384}\right)$	$e\left(\frac{21}{32}\right)$	$e\left(\frac{21}{128}\right)$	$e\left(\frac{47}{192}\right)$	$e\left(\frac{25}{192}\right)$	$e\left(\frac{131}{384}\right)$	$e\left(\frac{17}{48}\right)$

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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	$36864$
Structure	\(C_{2}\times C_{2}\times C_{3072}\)
Order	$12288$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(5\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)
\(\chi_{36864}(1,\cdot)\)	36864.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{36864}(5,\cdot)\)	36864.dj	3072	yes	\(-1\)	\(1\)	\(e\left(\frac{515}{3072}\right)\)	\(e\left(\frac{47}{1536}\right)\)	\(e\left(\frac{127}{3072}\right)\)	\(e\left(\frac{1997}{3072}\right)\)	\(e\left(\frac{231}{256}\right)\)	\(e\left(\frac{919}{1024}\right)\)	\(e\left(\frac{469}{1536}\right)\)	\(e\left(\frac{515}{1536}\right)\)	\(e\left(\frac{2161}{3072}\right)\)	\(e\left(\frac{19}{384}\right)\)
\(\chi_{36864}(7,\cdot)\)	36864.dd	1536	no	\(-1\)	\(1\)	\(e\left(\frac{47}{1536}\right)\)	\(e\left(\frac{11}{768}\right)\)	\(e\left(\frac{1051}{1536}\right)\)	\(e\left(\frac{737}{1536}\right)\)	\(e\left(\frac{35}{128}\right)\)	\(e\left(\frac{147}{512}\right)\)	\(e\left(\frac{649}{768}\right)\)	\(e\left(\frac{47}{768}\right)\)	\(e\left(\frac{1429}{1536}\right)\)	\(e\left(\frac{31}{192}\right)\)
\(\chi_{36864}(11,\cdot)\)	36864.dh	3072	yes	\(1\)	\(1\)	\(e\left(\frac{127}{3072}\right)\)	\(e\left(\frac{1051}{1536}\right)\)	\(e\left(\frac{2987}{3072}\right)\)	\(e\left(\frac{2449}{3072}\right)\)	\(e\left(\frac{51}{256}\right)\)	\(e\left(\frac{675}{1024}\right)\)	\(e\left(\frac{1337}{1536}\right)\)	\(e\left(\frac{127}{1536}\right)\)	\(e\left(\frac{1541}{3072}\right)\)	\(e\left(\frac{143}{384}\right)\)
\(\chi_{36864}(13,\cdot)\)	36864.di	3072	yes	\(1\)	\(1\)	\(e\left(\frac{1997}{3072}\right)\)	\(e\left(\frac{737}{1536}\right)\)	\(e\left(\frac{2449}{3072}\right)\)	\(e\left(\frac{2915}{3072}\right)\)	\(e\left(\frac{41}{256}\right)\)	\(e\left(\frac{761}{1024}\right)\)	\(e\left(\frac{475}{1536}\right)\)	\(e\left(\frac{461}{1536}\right)\)	\(e\left(\frac{1663}{3072}\right)\)	\(e\left(\frac{61}{384}\right)\)
\(\chi_{36864}(17,\cdot)\)	36864.ci	256	no	\(-1\)	\(1\)	\(e\left(\frac{231}{256}\right)\)	\(e\left(\frac{35}{128}\right)\)	\(e\left(\frac{51}{256}\right)\)	\(e\left(\frac{41}{256}\right)\)	\(e\left(\frac{17}{64}\right)\)	\(e\left(\frac{193}{256}\right)\)	\(e\left(\frac{81}{128}\right)\)	\(e\left(\frac{103}{128}\right)\)	\(e\left(\frac{253}{256}\right)\)	\(e\left(\frac{23}{32}\right)\)
\(\chi_{36864}(19,\cdot)\)	36864.db	1024	no	\(-1\)	\(1\)	\(e\left(\frac{919}{1024}\right)\)	\(e\left(\frac{147}{512}\right)\)	\(e\left(\frac{675}{1024}\right)\)	\(e\left(\frac{761}{1024}\right)\)	\(e\left(\frac{193}{256}\right)\)	\(e\left(\frac{273}{1024}\right)\)	\(e\left(\frac{481}{512}\right)\)	\(e\left(\frac{407}{512}\right)\)	\(e\left(\frac{653}{1024}\right)\)	\(e\left(\frac{39}{128}\right)\)
\(\chi_{36864}(23,\cdot)\)	36864.df	1536	no	\(1\)	\(1\)	\(e\left(\frac{469}{1536}\right)\)	\(e\left(\frac{649}{768}\right)\)	\(e\left(\frac{1337}{1536}\right)\)	\(e\left(\frac{475}{1536}\right)\)	\(e\left(\frac{81}{128}\right)\)	\(e\left(\frac{481}{512}\right)\)	\(e\left(\frac{275}{768}\right)\)	\(e\left(\frac{469}{768}\right)\)	\(e\left(\frac{599}{1536}\right)\)	\(e\left(\frac{101}{192}\right)\)
\(\chi_{36864}(25,\cdot)\)	36864.dc	1536	no	\(1\)	\(1\)	\(e\left(\frac{515}{1536}\right)\)	\(e\left(\frac{47}{768}\right)\)	\(e\left(\frac{127}{1536}\right)\)	\(e\left(\frac{461}{1536}\right)\)	\(e\left(\frac{103}{128}\right)\)	\(e\left(\frac{407}{512}\right)\)	\(e\left(\frac{469}{768}\right)\)	\(e\left(\frac{515}{768}\right)\)	\(e\left(\frac{625}{1536}\right)\)	\(e\left(\frac{19}{192}\right)\)
\(\chi_{36864}(29,\cdot)\)	36864.dj	3072	yes	\(-1\)	\(1\)	\(e\left(\frac{2161}{3072}\right)\)	\(e\left(\frac{1429}{1536}\right)\)	\(e\left(\frac{1541}{3072}\right)\)	\(e\left(\frac{1663}{3072}\right)\)	\(e\left(\frac{253}{256}\right)\)	\(e\left(\frac{653}{1024}\right)\)	\(e\left(\frac{599}{1536}\right)\)	\(e\left(\frac{625}{1536}\right)\)	\(e\left(\frac{1355}{3072}\right)\)	\(e\left(\frac{161}{384}\right)\)
\(\chi_{36864}(31,\cdot)\)	36864.cp	384	no	\(-1\)	\(1\)	\(e\left(\frac{19}{384}\right)\)	\(e\left(\frac{31}{192}\right)\)	\(e\left(\frac{143}{384}\right)\)	\(e\left(\frac{61}{384}\right)\)	\(e\left(\frac{23}{32}\right)\)	\(e\left(\frac{39}{128}\right)\)	\(e\left(\frac{101}{192}\right)\)	\(e\left(\frac{19}{192}\right)\)	\(e\left(\frac{161}{384}\right)\)	\(e\left(\frac{11}{48}\right)\)
\(\chi_{36864}(35,\cdot)\)	36864.da	1024	no	\(1\)	\(1\)	\(e\left(\frac{203}{1024}\right)\)	\(e\left(\frac{23}{512}\right)\)	\(e\left(\frac{743}{1024}\right)\)	\(e\left(\frac{133}{1024}\right)\)	\(e\left(\frac{45}{256}\right)\)	\(e\left(\frac{189}{1024}\right)\)	\(e\left(\frac{77}{512}\right)\)	\(e\left(\frac{203}{512}\right)\)	\(e\left(\frac{649}{1024}\right)\)	\(e\left(\frac{27}{128}\right)\)
\(\chi_{36864}(37,\cdot)\)	36864.cz	1024	no	\(1\)	\(1\)	\(e\left(\frac{281}{1024}\right)\)	\(e\left(\frac{477}{512}\right)\)	\(e\left(\frac{461}{1024}\right)\)	\(e\left(\frac{343}{1024}\right)\)	\(e\left(\frac{15}{256}\right)\)	\(e\left(\frac{191}{1024}\right)\)	\(e\left(\frac{495}{512}\right)\)	\(e\left(\frac{281}{512}\right)\)	\(e\left(\frac{515}{1024}\right)\)	\(e\left(\frac{73}{128}\right)\)
\(\chi_{36864}(41,\cdot)\)	36864.de	1536	no	\(-1\)	\(1\)	\(e\left(\frac{1405}{1536}\right)\)	\(e\left(\frac{337}{768}\right)\)	\(e\left(\frac{257}{1536}\right)\)	\(e\left(\frac{1459}{1536}\right)\)	\(e\left(\frac{89}{128}\right)\)	\(e\left(\frac{233}{512}\right)\)	\(e\left(\frac{299}{768}\right)\)	\(e\left(\frac{637}{768}\right)\)	\(e\left(\frac{527}{1536}\right)\)	\(e\left(\frac{173}{192}\right)\)
\(\chi_{36864}(43,\cdot)\)	36864.dg	3072	yes	\(-1\)	\(1\)	\(e\left(\frac{1975}{3072}\right)\)	\(e\left(\frac{307}{1536}\right)\)	\(e\left(\frac{323}{3072}\right)\)	\(e\left(\frac{217}{3072}\right)\)	\(e\left(\frac{139}{256}\right)\)	\(e\left(\frac{1019}{1024}\right)\)	\(e\left(\frac{1217}{1536}\right)\)	\(e\left(\frac{439}{1536}\right)\)	\(e\left(\frac{1517}{3072}\right)\)	\(e\left(\frac{71}{384}\right)\)
\(\chi_{36864}(47,\cdot)\)	36864.cu	768	no	\(1\)	\(1\)	\(e\left(\frac{1}{768}\right)\)	\(e\left(\frac{37}{384}\right)\)	\(e\left(\frac{341}{768}\right)\)	\(e\left(\frac{367}{768}\right)\)	\(e\left(\frac{45}{64}\right)\)	\(e\left(\frac{221}{256}\right)\)	\(e\left(\frac{71}{384}\right)\)	\(e\left(\frac{1}{384}\right)\)	\(e\left(\frac{635}{768}\right)\)	\(e\left(\frac{65}{96}\right)\)
\(\chi_{36864}(49,\cdot)\)	36864.cx	768	no	\(1\)	\(1\)	\(e\left(\frac{47}{768}\right)\)	\(e\left(\frac{11}{384}\right)\)	\(e\left(\frac{283}{768}\right)\)	\(e\left(\frac{737}{768}\right)\)	\(e\left(\frac{35}{64}\right)\)	\(e\left(\frac{147}{256}\right)\)	\(e\left(\frac{265}{384}\right)\)	\(e\left(\frac{47}{384}\right)\)	\(e\left(\frac{661}{768}\right)\)	\(e\left(\frac{31}{96}\right)\)
\(\chi_{36864}(53,\cdot)\)	36864.cy	1024	no	\(-1\)	\(1\)	\(e\left(\frac{261}{1024}\right)\)	\(e\left(\frac{505}{512}\right)\)	\(e\left(\frac{297}{1024}\right)\)	\(e\left(\frac{171}{1024}\right)\)	\(e\left(\frac{131}{256}\right)\)	\(e\left(\frac{755}{1024}\right)\)	\(e\left(\frac{355}{512}\right)\)	\(e\left(\frac{261}{512}\right)\)	\(e\left(\frac{103}{1024}\right)\)	\(e\left(\frac{117}{128}\right)\)
\(\chi_{36864}(55,\cdot)\)	36864.cq	512	no	\(-1\)	\(1\)	\(e\left(\frac{107}{512}\right)\)	\(e\left(\frac{183}{256}\right)\)	\(e\left(\frac{7}{512}\right)\)	\(e\left(\frac{229}{512}\right)\)	\(e\left(\frac{13}{128}\right)\)	\(e\left(\frac{285}{512}\right)\)	\(e\left(\frac{45}{256}\right)\)	\(e\left(\frac{107}{256}\right)\)	\(e\left(\frac{105}{512}\right)\)	\(e\left(\frac{27}{64}\right)\)
\(\chi_{36864}(59,\cdot)\)	36864.dh	3072	yes	\(1\)	\(1\)	\(e\left(\frac{1139}{3072}\right)\)	\(e\left(\frac{863}{1536}\right)\)	\(e\left(\frac{2479}{3072}\right)\)	\(e\left(\frac{605}{3072}\right)\)	\(e\left(\frac{151}{256}\right)\)	\(e\left(\frac{71}{1024}\right)\)	\(e\left(\frac{997}{1536}\right)\)	\(e\left(\frac{1139}{1536}\right)\)	\(e\left(\frac{2113}{3072}\right)\)	\(e\left(\frac{67}{384}\right)\)
\(\chi_{36864}(61,\cdot)\)	36864.di	3072	yes	\(1\)	\(1\)	\(e\left(\frac{2041}{3072}\right)\)	\(e\left(\frac{61}{1536}\right)\)	\(e\left(\frac{557}{3072}\right)\)	\(e\left(\frac{2167}{3072}\right)\)	\(e\left(\frac{101}{256}\right)\)	\(e\left(\frac{245}{1024}\right)\)	\(e\left(\frac{527}{1536}\right)\)	\(e\left(\frac{505}{1536}\right)\)	\(e\left(\frac{1955}{3072}\right)\)	\(e\left(\frac{41}{384}\right)\)
\(\chi_{36864}(65,\cdot)\)	36864.cf	192	no	\(-1\)	\(1\)	\(e\left(\frac{157}{192}\right)\)	\(e\left(\frac{49}{96}\right)\)	\(e\left(\frac{161}{192}\right)\)	\(e\left(\frac{115}{192}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{41}{64}\right)\)	\(e\left(\frac{59}{96}\right)\)	\(e\left(\frac{61}{96}\right)\)	\(e\left(\frac{47}{192}\right)\)	\(e\left(\frac{5}{24}\right)\)
\(\chi_{36864}(67,\cdot)\)	36864.dg	3072	yes	\(-1\)	\(1\)	\(e\left(\frac{2009}{3072}\right)\)	\(e\left(\frac{1181}{1536}\right)\)	\(e\left(\frac{397}{3072}\right)\)	\(e\left(\frac{2711}{3072}\right)\)	\(e\left(\frac{197}{256}\right)\)	\(e\left(\frac{853}{1024}\right)\)	\(e\left(\frac{559}{1536}\right)\)	\(e\left(\frac{473}{1536}\right)\)	\(e\left(\frac{67}{3072}\right)\)	\(e\left(\frac{73}{384}\right)\)
\(\chi_{36864}(71,\cdot)\)	36864.cs	512	no	\(1\)	\(1\)	\(e\left(\frac{173}{512}\right)\)	\(e\left(\frac{193}{256}\right)\)	\(e\left(\frac{241}{512}\right)\)	\(e\left(\frac{387}{512}\right)\)	\(e\left(\frac{91}{128}\right)\)	\(e\left(\frac{267}{512}\right)\)	\(e\left(\frac{251}{256}\right)\)	\(e\left(\frac{173}{256}\right)\)	\(e\left(\frac{31}{512}\right)\)	\(e\left(\frac{61}{64}\right)\)
\(\chi_{36864}(73,\cdot)\)	36864.cr	512	no	\(1\)	\(1\)	\(e\left(\frac{219}{512}\right)\)	\(e\left(\frac{103}{256}\right)\)	\(e\left(\frac{55}{512}\right)\)	\(e\left(\frac{373}{512}\right)\)	\(e\left(\frac{29}{128}\right)\)	\(e\left(\frac{45}{512}\right)\)	\(e\left(\frac{189}{256}\right)\)	\(e\left(\frac{219}{256}\right)\)	\(e\left(\frac{57}{512}\right)\)	\(e\left(\frac{43}{64}\right)\)
\(\chi_{36864}(77,\cdot)\)	36864.dj	3072	yes	\(-1\)	\(1\)	\(e\left(\frac{221}{3072}\right)\)	\(e\left(\frac{1073}{1536}\right)\)	\(e\left(\frac{2017}{3072}\right)\)	\(e\left(\frac{851}{3072}\right)\)	\(e\left(\frac{121}{256}\right)\)	\(e\left(\frac{969}{1024}\right)\)	\(e\left(\frac{1099}{1536}\right)\)	\(e\left(\frac{221}{1536}\right)\)	\(e\left(\frac{1327}{3072}\right)\)	\(e\left(\frac{205}{384}\right)\)
\(\chi_{36864}(79,\cdot)\)	36864.cv	768	no	\(-1\)	\(1\)	\(e\left(\frac{199}{768}\right)\)	\(e\left(\frac{67}{384}\right)\)	\(e\left(\frac{275}{768}\right)\)	\(e\left(\frac{457}{768}\right)\)	\(e\left(\frac{27}{64}\right)\)	\(e\left(\frac{75}{256}\right)\)	\(e\left(\frac{113}{384}\right)\)	\(e\left(\frac{199}{384}\right)\)	\(e\left(\frac{413}{768}\right)\)	\(e\left(\frac{71}{96}\right)\)
\(\chi_{36864}(83,\cdot)\)	36864.dh	3072	yes	\(1\)	\(1\)	\(e\left(\frac{949}{3072}\right)\)	\(e\left(\frac{1129}{1536}\right)\)	\(e\left(\frac{2969}{3072}\right)\)	\(e\left(\frac{763}{3072}\right)\)	\(e\left(\frac{113}{256}\right)\)	\(e\left(\frac{577}{1024}\right)\)	\(e\left(\frac{1331}{1536}\right)\)	\(e\left(\frac{949}{1536}\right)\)	\(e\left(\frac{2807}{3072}\right)\)	\(e\left(\frac{101}{384}\right)\)
\(\chi_{36864}(85,\cdot)\)	36864.di	3072	yes	\(1\)	\(1\)	\(e\left(\frac{215}{3072}\right)\)	\(e\left(\frac{467}{1536}\right)\)	\(e\left(\frac{739}{3072}\right)\)	\(e\left(\frac{2489}{3072}\right)\)	\(e\left(\frac{43}{256}\right)\)	\(e\left(\frac{667}{1024}\right)\)	\(e\left(\frac{1441}{1536}\right)\)	\(e\left(\frac{215}{1536}\right)\)	\(e\left(\frac{2125}{3072}\right)\)	\(e\left(\frac{295}{384}\right)\)
\(\chi_{36864}(89,\cdot)\)	36864.ct	512	no	\(-1\)	\(1\)	\(e\left(\frac{441}{512}\right)\)	\(e\left(\frac{253}{256}\right)\)	\(e\left(\frac{237}{512}\right)\)	\(e\left(\frac{439}{512}\right)\)	\(e\left(\frac{47}{128}\right)\)	\(e\left(\frac{31}{512}\right)\)	\(e\left(\frac{207}{256}\right)\)	\(e\left(\frac{185}{256}\right)\)	\(e\left(\frac{227}{512}\right)\)	\(e\left(\frac{41}{64}\right)\)
\(\chi_{36864}(91,\cdot)\)	36864.db	1024	no	\(-1\)	\(1\)	\(e\left(\frac{697}{1024}\right)\)	\(e\left(\frac{253}{512}\right)\)	\(e\left(\frac{493}{1024}\right)\)	\(e\left(\frac{439}{1024}\right)\)	\(e\left(\frac{111}{256}\right)\)	\(e\left(\frac{31}{1024}\right)\)	\(e\left(\frac{79}{512}\right)\)	\(e\left(\frac{185}{512}\right)\)	\(e\left(\frac{483}{1024}\right)\)	\(e\left(\frac{41}{128}\right)\)
\(\chi_{36864}(95,\cdot)\)	36864.cn	384	no	\(1\)	\(1\)	\(e\left(\frac{25}{384}\right)\)	\(e\left(\frac{61}{192}\right)\)	\(e\left(\frac{269}{384}\right)\)	\(e\left(\frac{151}{384}\right)\)	\(e\left(\frac{21}{32}\right)\)	\(e\left(\frac{21}{128}\right)\)	\(e\left(\frac{47}{192}\right)\)	\(e\left(\frac{25}{192}\right)\)	\(e\left(\frac{131}{384}\right)\)	\(e\left(\frac{17}{48}\right)\)

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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.