LMFDB - Group of Dirichlet characters of modulus 221184

Show commands: Magma / Pari/GP / SageMath

comment:Define the Dirichlet group

sage:G = DirichletGroup(221184)

gp:g = idealstar(,221184,2)

magma:G := FullDirichletGroup(221184);

Character group

Order	=	73728	comment:Order sage:G.order() gp:g.no magma:Order(G);
Structure	=	$C_{2}\times C_{2}\times C_{18432}$	comment:Group structure sage:sorted(g.order() for g in G.gens()) gp:g.cyc magma:PrimaryInvariants(AbelianGroup(G));
Generators	=	$\chi_{221184}(81919,\cdot)$, $\chi_{221184}(57349,\cdot)$, $\chi_{221184}(40961,\cdot)$	comment:Generators sage:G.gens() gp:g.gen magma:Generators(G);

First 32 of 73728 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	$-1$	$1$	$5$	$7$	$11$	$13$	$17$	$19$	$23$	$25$	$29$	$31$
$\chi_{221184}(1,\cdot)$	221184.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{221184}(5,\cdot)$	221184.fl	18432	yes	$-1$	$1$	$e\left(\frac{7177}{18432}\right)$	$e\left(\frac{2701}{9216}\right)$	$e\left(\frac{3965}{18432}\right)$	$e\left(\frac{3943}{18432}\right)$	$e\left(\frac{565}{1536}\right)$	$e\left(\frac{4805}{6144}\right)$	$e\left(\frac{5759}{9216}\right)$	$e\left(\frac{7177}{9216}\right)$	$e\left(\frac{3923}{18432}\right)$	$e\left(\frac{569}{2304}\right)$
$\chi_{221184}(7,\cdot)$	221184.fj	9216	no	$-1$	$1$	$e\left(\frac{2701}{9216}\right)$	$e\left(\frac{2977}{4608}\right)$	$e\left(\frac{7505}{9216}\right)$	$e\left(\frac{6307}{9216}\right)$	$e\left(\frac{745}{768}\right)$	$e\left(\frac{185}{3072}\right)$	$e\left(\frac{3611}{4608}\right)$	$e\left(\frac{2701}{4608}\right)$	$e\left(\frac{191}{9216}\right)$	$e\left(\frac{1085}{1152}\right)$
$\chi_{221184}(11,\cdot)$	221184.fn	18432	yes	$1$	$1$	$e\left(\frac{3965}{18432}\right)$	$e\left(\frac{7505}{9216}\right)$	$e\left(\frac{769}{18432}\right)$	$e\left(\frac{9395}{18432}\right)$	$e\left(\frac{1049}{1536}\right)$	$e\left(\frac{1513}{6144}\right)$	$e\left(\frac{6571}{9216}\right)$	$e\left(\frac{3965}{9216}\right)$	$e\left(\frac{7183}{18432}\right)$	$e\left(\frac{493}{2304}\right)$
$\chi_{221184}(13,\cdot)$	221184.fk	18432	yes	$1$	$1$	$e\left(\frac{3943}{18432}\right)$	$e\left(\frac{6307}{9216}\right)$	$e\left(\frac{9395}{18432}\right)$	$e\left(\frac{12841}{18432}\right)$	$e\left(\frac{379}{1536}\right)$	$e\left(\frac{4331}{6144}\right)$	$e\left(\frac{1937}{9216}\right)$	$e\left(\frac{3943}{9216}\right)$	$e\left(\frac{10109}{18432}\right)$	$e\left(\frac{311}{2304}\right)$
$\chi_{221184}(17,\cdot)$	221184.ek	1536	no	$-1$	$1$	$e\left(\frac{565}{1536}\right)$	$e\left(\frac{745}{768}\right)$	$e\left(\frac{1049}{1536}\right)$	$e\left(\frac{379}{1536}\right)$	$e\left(\frac{49}{128}\right)$	$e\left(\frac{449}{512}\right)$	$e\left(\frac{563}{768}\right)$	$e\left(\frac{565}{768}\right)$	$e\left(\frac{119}{1536}\right)$	$e\left(\frac{101}{192}\right)$
$\chi_{221184}(19,\cdot)$	221184.fe	6144	no	$-1$	$1$	$e\left(\frac{4805}{6144}\right)$	$e\left(\frac{185}{3072}\right)$	$e\left(\frac{1513}{6144}\right)$	$e\left(\frac{4331}{6144}\right)$	$e\left(\frac{449}{512}\right)$	$e\left(\frac{1809}{2048}\right)$	$e\left(\frac{163}{3072}\right)$	$e\left(\frac{1733}{3072}\right)$	$e\left(\frac{6055}{6144}\right)$	$e\left(\frac{181}{768}\right)$
$\chi_{221184}(23,\cdot)$	221184.fi	9216	no	$1$	$1$	$e\left(\frac{5759}{9216}\right)$	$e\left(\frac{3611}{4608}\right)$	$e\left(\frac{6571}{9216}\right)$	$e\left(\frac{1937}{9216}\right)$	$e\left(\frac{563}{768}\right)$	$e\left(\frac{163}{3072}\right)$	$e\left(\frac{313}{4608}\right)$	$e\left(\frac{1151}{4608}\right)$	$e\left(\frac{8197}{9216}\right)$	$e\left(\frac{1039}{1152}\right)$
$\chi_{221184}(25,\cdot)$	221184.fh	9216	no	$1$	$1$	$e\left(\frac{7177}{9216}\right)$	$e\left(\frac{2701}{4608}\right)$	$e\left(\frac{3965}{9216}\right)$	$e\left(\frac{3943}{9216}\right)$	$e\left(\frac{565}{768}\right)$	$e\left(\frac{1733}{3072}\right)$	$e\left(\frac{1151}{4608}\right)$	$e\left(\frac{2569}{4608}\right)$	$e\left(\frac{3923}{9216}\right)$	$e\left(\frac{569}{1152}\right)$
$\chi_{221184}(29,\cdot)$	221184.fl	18432	yes	$-1$	$1$	$e\left(\frac{3923}{18432}\right)$	$e\left(\frac{191}{9216}\right)$	$e\left(\frac{7183}{18432}\right)$	$e\left(\frac{10109}{18432}\right)$	$e\left(\frac{119}{1536}\right)$	$e\left(\frac{6055}{6144}\right)$	$e\left(\frac{8197}{9216}\right)$	$e\left(\frac{3923}{9216}\right)$	$e\left(\frac{12769}{18432}\right)$	$e\left(\frac{355}{2304}\right)$
$\chi_{221184}(31,\cdot)$	221184.es	2304	no	$-1$	$1$	$e\left(\frac{569}{2304}\right)$	$e\left(\frac{1085}{1152}\right)$	$e\left(\frac{493}{2304}\right)$	$e\left(\frac{311}{2304}\right)$	$e\left(\frac{101}{192}\right)$	$e\left(\frac{181}{768}\right)$	$e\left(\frac{1039}{1152}\right)$	$e\left(\frac{569}{1152}\right)$	$e\left(\frac{355}{2304}\right)$	$e\left(\frac{217}{288}\right)$
$\chi_{221184}(35,\cdot)$	221184.fc	6144	no	$1$	$1$	$e\left(\frac{4193}{6144}\right)$	$e\left(\frac{2885}{3072}\right)$	$e\left(\frac{181}{6144}\right)$	$e\left(\frac{5519}{6144}\right)$	$e\left(\frac{173}{512}\right)$	$e\left(\frac{1725}{2048}\right)$	$e\left(\frac{1255}{3072}\right)$	$e\left(\frac{1121}{3072}\right)$	$e\left(\frac{1435}{6144}\right)$	$e\left(\frac{145}{768}\right)$
$\chi_{221184}(37,\cdot)$	221184.ff	6144	no	$1$	$1$	$e\left(\frac{1867}{6144}\right)$	$e\left(\frac{2455}{3072}\right)$	$e\left(\frac{3431}{6144}\right)$	$e\left(\frac{5125}{6144}\right)$	$e\left(\frac{271}{512}\right)$	$e\left(\frac{1215}{2048}\right)$	$e\left(\frac{1997}{3072}\right)$	$e\left(\frac{1867}{3072}\right)$	$e\left(\frac{3593}{6144}\right)$	$e\left(\frac{731}{768}\right)$
$\chi_{221184}(41,\cdot)$	221184.fg	9216	no	$-1$	$1$	$e\left(\frac{5495}{9216}\right)$	$e\left(\frac{755}{4608}\right)$	$e\left(\frac{4099}{9216}\right)$	$e\left(\frac{6425}{9216}\right)$	$e\left(\frac{203}{768}\right)$	$e\left(\frac{1723}{3072}\right)$	$e\left(\frac{2305}{4608}\right)$	$e\left(\frac{887}{4608}\right)$	$e\left(\frac{6445}{9216}\right)$	$e\left(\frac{583}{1152}\right)$
$\chi_{221184}(43,\cdot)$	221184.fm	18432	yes	$-1$	$1$	$e\left(\frac{14117}{18432}\right)$	$e\left(\frac{665}{9216}\right)$	$e\left(\frac{6601}{18432}\right)$	$e\left(\frac{11915}{18432}\right)$	$e\left(\frac{161}{1536}\right)$	$e\left(\frac{5617}{6144}\right)$	$e\left(\frac{3907}{9216}\right)$	$e\left(\frac{4901}{9216}\right)$	$e\left(\frac{2503}{18432}\right)$	$e\left(\frac{277}{2304}\right)$
$\chi_{221184}(47,\cdot)$	221184.fb	4608	no	$1$	$1$	$e\left(\frac{2435}{4608}\right)$	$e\left(\frac{1583}{2304}\right)$	$e\left(\frac{4351}{4608}\right)$	$e\left(\frac{845}{4608}\right)$	$e\left(\frac{167}{384}\right)$	$e\left(\frac{1303}{1536}\right)$	$e\left(\frac{1621}{2304}\right)$	$e\left(\frac{131}{2304}\right)$	$e\left(\frac{3313}{4608}\right)$	$e\left(\frac{115}{576}\right)$
$\chi_{221184}(49,\cdot)$	221184.ey	4608	no	$1$	$1$	$e\left(\frac{2701}{4608}\right)$	$e\left(\frac{673}{2304}\right)$	$e\left(\frac{2897}{4608}\right)$	$e\left(\frac{1699}{4608}\right)$	$e\left(\frac{361}{384}\right)$	$e\left(\frac{185}{1536}\right)$	$e\left(\frac{1307}{2304}\right)$	$e\left(\frac{397}{2304}\right)$	$e\left(\frac{191}{4608}\right)$	$e\left(\frac{509}{576}\right)$
$\chi_{221184}(53,\cdot)$	221184.ep	2048	no	$-1$	$1$	$e\left(\frac{773}{2048}\right)$	$e\left(\frac{1017}{1024}\right)$	$e\left(\frac{1833}{2048}\right)$	$e\left(\frac{171}{2048}\right)$	$e\left(\frac{3}{512}\right)$	$e\left(\frac{755}{2048}\right)$	$e\left(\frac{611}{1024}\right)$	$e\left(\frac{773}{1024}\right)$	$e\left(\frac{1639}{2048}\right)$	$e\left(\frac{117}{256}\right)$
$\chi_{221184}(55,\cdot)$	221184.ed	1024	no	$-1$	$1$	$e\left(\frac{619}{1024}\right)$	$e\left(\frac{55}{512}\right)$	$e\left(\frac{263}{1024}\right)$	$e\left(\frac{741}{1024}\right)$	$e\left(\frac{13}{256}\right)$	$e\left(\frac{29}{1024}\right)$	$e\left(\frac{173}{512}\right)$	$e\left(\frac{107}{512}\right)$	$e\left(\frac{617}{1024}\right)$	$e\left(\frac{59}{128}\right)$
$\chi_{221184}(59,\cdot)$	221184.fn	18432	yes	$1$	$1$	$e\left(\frac{9049}{18432}\right)$	$e\left(\frac{2845}{9216}\right)$	$e\left(\frac{6413}{18432}\right)$	$e\left(\frac{8983}{18432}\right)$	$e\left(\frac{325}{1536}\right)$	$e\left(\frac{3797}{6144}\right)$	$e\left(\frac{5039}{9216}\right)$	$e\left(\frac{9049}{9216}\right)$	$e\left(\frac{12995}{18432}\right)$	$e\left(\frac{1289}{2304}\right)$
$\chi_{221184}(61,\cdot)$	221184.fk	18432	yes	$1$	$1$	$e\left(\frac{11243}{18432}\right)$	$e\left(\frac{8375}{9216}\right)$	$e\left(\frac{5767}{18432}\right)$	$e\left(\frac{5477}{18432}\right)$	$e\left(\frac{815}{1536}\right)$	$e\left(\frac{4831}{6144}\right)$	$e\left(\frac{7213}{9216}\right)$	$e\left(\frac{2027}{9216}\right)$	$e\left(\frac{16105}{18432}\right)$	$e\left(\frac{379}{2304}\right)$
$\chi_{221184}(65,\cdot)$	221184.ef	1152	no	$-1$	$1$	$e\left(\frac{695}{1152}\right)$	$e\left(\frac{563}{576}\right)$	$e\left(\frac{835}{1152}\right)$	$e\left(\frac{1049}{1152}\right)$	$e\left(\frac{59}{96}\right)$	$e\left(\frac{187}{384}\right)$	$e\left(\frac{481}{576}\right)$	$e\left(\frac{119}{576}\right)$	$e\left(\frac{877}{1152}\right)$	$e\left(\frac{55}{144}\right)$
$\chi_{221184}(67,\cdot)$	221184.fm	18432	yes	$-1$	$1$	$e\left(\frac{3979}{18432}\right)$	$e\left(\frac{5335}{9216}\right)$	$e\left(\frac{7847}{18432}\right)$	$e\left(\frac{12229}{18432}\right)$	$e\left(\frac{79}{1536}\right)$	$e\left(\frac{6143}{6144}\right)$	$e\left(\frac{9101}{9216}\right)$	$e\left(\frac{3979}{9216}\right)$	$e\left(\frac{5321}{18432}\right)$	$e\left(\frac{923}{2304}\right)$
$\chi_{221184}(71,\cdot)$	221184.ev	3072	no	$1$	$1$	$e\left(\frac{263}{3072}\right)$	$e\left(\frac{1475}{1536}\right)$	$e\left(\frac{211}{3072}\right)$	$e\left(\frac{137}{3072}\right)$	$e\left(\frac{27}{256}\right)$	$e\left(\frac{11}{1024}\right)$	$e\left(\frac{241}{1536}\right)$	$e\left(\frac{263}{1536}\right)$	$e\left(\frac{1885}{3072}\right)$	$e\left(\frac{151}{384}\right)$
$\chi_{221184}(73,\cdot)$	221184.ew	3072	no	$1$	$1$	$e\left(\frac{1681}{3072}\right)$	$e\left(\frac{565}{1536}\right)$	$e\left(\frac{677}{3072}\right)$	$e\left(\frac{2143}{3072}\right)$	$e\left(\frac{29}{256}\right)$	$e\left(\frac{557}{1024}\right)$	$e\left(\frac{1079}{1536}\right)$	$e\left(\frac{145}{1536}\right)$	$e\left(\frac{683}{3072}\right)$	$e\left(\frac{65}{384}\right)$
$\chi_{221184}(77,\cdot)$	221184.fl	18432	yes	$-1$	$1$	$e\left(\frac{9367}{18432}\right)$	$e\left(\frac{4243}{9216}\right)$	$e\left(\frac{15779}{18432}\right)$	$e\left(\frac{3577}{18432}\right)$	$e\left(\frac{1003}{1536}\right)$	$e\left(\frac{1883}{6144}\right)$	$e\left(\frac{4577}{9216}\right)$	$e\left(\frac{151}{9216}\right)$	$e\left(\frac{7565}{18432}\right)$	$e\left(\frac{359}{2304}\right)$
$\chi_{221184}(79,\cdot)$	221184.ez	4608	no	$-1$	$1$	$e\left(\frac{1109}{4608}\right)$	$e\left(\frac{2057}{2304}\right)$	$e\left(\frac{1465}{4608}\right)$	$e\left(\frac{2651}{4608}\right)$	$e\left(\frac{17}{384}\right)$	$e\left(\frac{865}{1536}\right)$	$e\left(\frac{787}{2304}\right)$	$e\left(\frac{1109}{2304}\right)$	$e\left(\frac{4567}{4608}\right)$	$e\left(\frac{37}{576}\right)$
$\chi_{221184}(83,\cdot)$	221184.fn	18432	yes	$1$	$1$	$e\left(\frac{287}{18432}\right)$	$e\left(\frac{6203}{9216}\right)$	$e\left(\frac{16075}{18432}\right)$	$e\left(\frac{16625}{18432}\right)$	$e\left(\frac{1235}{1536}\right)$	$e\left(\frac{1219}{6144}\right)$	$e\left(\frac{3481}{9216}\right)$	$e\left(\frac{287}{9216}\right)$	$e\left(\frac{17125}{18432}\right)$	$e\left(\frac{751}{2304}\right)$
$\chi_{221184}(85,\cdot)$	221184.fk	18432	yes	$1$	$1$	$e\left(\frac{13957}{18432}\right)$	$e\left(\frac{2425}{9216}\right)$	$e\left(\frac{16553}{18432}\right)$	$e\left(\frac{8491}{18432}\right)$	$e\left(\frac{1153}{1536}\right)$	$e\left(\frac{4049}{6144}\right)$	$e\left(\frac{3299}{9216}\right)$	$e\left(\frac{4741}{9216}\right)$	$e\left(\frac{5351}{18432}\right)$	$e\left(\frac{1781}{2304}\right)$
$\chi_{221184}(89,\cdot)$	221184.ex	3072	no	$-1$	$1$	$e\left(\frac{1579}{3072}\right)$	$e\left(\frac{1015}{1536}\right)$	$e\left(\frac{455}{3072}\right)$	$e\left(\frac{2341}{3072}\right)$	$e\left(\frac{239}{256}\right)$	$e\left(\frac{543}{1024}\right)$	$e\left(\frac{749}{1536}\right)$	$e\left(\frac{43}{1536}\right)$	$e\left(\frac{1961}{3072}\right)$	$e\left(\frac{59}{384}\right)$
$\chi_{221184}(91,\cdot)$	221184.fe	6144	no	$-1$	$1$	$e\left(\frac{3115}{6144}\right)$	$e\left(\frac{1015}{3072}\right)$	$e\left(\frac{1991}{6144}\right)$	$e\left(\frac{2341}{6144}\right)$	$e\left(\frac{111}{512}\right)$	$e\left(\frac{1567}{2048}\right)$	$e\left(\frac{3053}{3072}\right)$	$e\left(\frac{43}{3072}\right)$	$e\left(\frac{3497}{6144}\right)$	$e\left(\frac{59}{768}\right)$
$\chi_{221184}(95,\cdot)$	221184.eq	2304	no	$1$	$1$	$e\left(\frac{395}{2304}\right)$	$e\left(\frac{407}{1152}\right)$	$e\left(\frac{1063}{2304}\right)$	$e\left(\frac{2117}{2304}\right)$	$e\left(\frac{47}{192}\right)$	$e\left(\frac{511}{768}\right)$	$e\left(\frac{781}{1152}\right)$	$e\left(\frac{395}{1152}\right)$	$e\left(\frac{457}{2304}\right)$	$e\left(\frac{139}{288}\right)$

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Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$ over number fields
Genus 2 curves
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Modulus	$221184$
Structure	\(C_{2}\times C_{2}\times C_{18432}\)
Order	$73728$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(5\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)
\(\chi_{221184}(1,\cdot)\)	221184.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{221184}(5,\cdot)\)	221184.fl	18432	yes	\(-1\)	\(1\)	\(e\left(\frac{7177}{18432}\right)\)	\(e\left(\frac{2701}{9216}\right)\)	\(e\left(\frac{3965}{18432}\right)\)	\(e\left(\frac{3943}{18432}\right)\)	\(e\left(\frac{565}{1536}\right)\)	\(e\left(\frac{4805}{6144}\right)\)	\(e\left(\frac{5759}{9216}\right)\)	\(e\left(\frac{7177}{9216}\right)\)	\(e\left(\frac{3923}{18432}\right)\)	\(e\left(\frac{569}{2304}\right)\)
\(\chi_{221184}(7,\cdot)\)	221184.fj	9216	no	\(-1\)	\(1\)	\(e\left(\frac{2701}{9216}\right)\)	\(e\left(\frac{2977}{4608}\right)\)	\(e\left(\frac{7505}{9216}\right)\)	\(e\left(\frac{6307}{9216}\right)\)	\(e\left(\frac{745}{768}\right)\)	\(e\left(\frac{185}{3072}\right)\)	\(e\left(\frac{3611}{4608}\right)\)	\(e\left(\frac{2701}{4608}\right)\)	\(e\left(\frac{191}{9216}\right)\)	\(e\left(\frac{1085}{1152}\right)\)
\(\chi_{221184}(11,\cdot)\)	221184.fn	18432	yes	\(1\)	\(1\)	\(e\left(\frac{3965}{18432}\right)\)	\(e\left(\frac{7505}{9216}\right)\)	\(e\left(\frac{769}{18432}\right)\)	\(e\left(\frac{9395}{18432}\right)\)	\(e\left(\frac{1049}{1536}\right)\)	\(e\left(\frac{1513}{6144}\right)\)	\(e\left(\frac{6571}{9216}\right)\)	\(e\left(\frac{3965}{9216}\right)\)	\(e\left(\frac{7183}{18432}\right)\)	\(e\left(\frac{493}{2304}\right)\)
\(\chi_{221184}(13,\cdot)\)	221184.fk	18432	yes	\(1\)	\(1\)	\(e\left(\frac{3943}{18432}\right)\)	\(e\left(\frac{6307}{9216}\right)\)	\(e\left(\frac{9395}{18432}\right)\)	\(e\left(\frac{12841}{18432}\right)\)	\(e\left(\frac{379}{1536}\right)\)	\(e\left(\frac{4331}{6144}\right)\)	\(e\left(\frac{1937}{9216}\right)\)	\(e\left(\frac{3943}{9216}\right)\)	\(e\left(\frac{10109}{18432}\right)\)	\(e\left(\frac{311}{2304}\right)\)
\(\chi_{221184}(17,\cdot)\)	221184.ek	1536	no	\(-1\)	\(1\)	\(e\left(\frac{565}{1536}\right)\)	\(e\left(\frac{745}{768}\right)\)	\(e\left(\frac{1049}{1536}\right)\)	\(e\left(\frac{379}{1536}\right)\)	\(e\left(\frac{49}{128}\right)\)	\(e\left(\frac{449}{512}\right)\)	\(e\left(\frac{563}{768}\right)\)	\(e\left(\frac{565}{768}\right)\)	\(e\left(\frac{119}{1536}\right)\)	\(e\left(\frac{101}{192}\right)\)
\(\chi_{221184}(19,\cdot)\)	221184.fe	6144	no	\(-1\)	\(1\)	\(e\left(\frac{4805}{6144}\right)\)	\(e\left(\frac{185}{3072}\right)\)	\(e\left(\frac{1513}{6144}\right)\)	\(e\left(\frac{4331}{6144}\right)\)	\(e\left(\frac{449}{512}\right)\)	\(e\left(\frac{1809}{2048}\right)\)	\(e\left(\frac{163}{3072}\right)\)	\(e\left(\frac{1733}{3072}\right)\)	\(e\left(\frac{6055}{6144}\right)\)	\(e\left(\frac{181}{768}\right)\)
\(\chi_{221184}(23,\cdot)\)	221184.fi	9216	no	\(1\)	\(1\)	\(e\left(\frac{5759}{9216}\right)\)	\(e\left(\frac{3611}{4608}\right)\)	\(e\left(\frac{6571}{9216}\right)\)	\(e\left(\frac{1937}{9216}\right)\)	\(e\left(\frac{563}{768}\right)\)	\(e\left(\frac{163}{3072}\right)\)	\(e\left(\frac{313}{4608}\right)\)	\(e\left(\frac{1151}{4608}\right)\)	\(e\left(\frac{8197}{9216}\right)\)	\(e\left(\frac{1039}{1152}\right)\)
\(\chi_{221184}(25,\cdot)\)	221184.fh	9216	no	\(1\)	\(1\)	\(e\left(\frac{7177}{9216}\right)\)	\(e\left(\frac{2701}{4608}\right)\)	\(e\left(\frac{3965}{9216}\right)\)	\(e\left(\frac{3943}{9216}\right)\)	\(e\left(\frac{565}{768}\right)\)	\(e\left(\frac{1733}{3072}\right)\)	\(e\left(\frac{1151}{4608}\right)\)	\(e\left(\frac{2569}{4608}\right)\)	\(e\left(\frac{3923}{9216}\right)\)	\(e\left(\frac{569}{1152}\right)\)
\(\chi_{221184}(29,\cdot)\)	221184.fl	18432	yes	\(-1\)	\(1\)	\(e\left(\frac{3923}{18432}\right)\)	\(e\left(\frac{191}{9216}\right)\)	\(e\left(\frac{7183}{18432}\right)\)	\(e\left(\frac{10109}{18432}\right)\)	\(e\left(\frac{119}{1536}\right)\)	\(e\left(\frac{6055}{6144}\right)\)	\(e\left(\frac{8197}{9216}\right)\)	\(e\left(\frac{3923}{9216}\right)\)	\(e\left(\frac{12769}{18432}\right)\)	\(e\left(\frac{355}{2304}\right)\)
\(\chi_{221184}(31,\cdot)\)	221184.es	2304	no	\(-1\)	\(1\)	\(e\left(\frac{569}{2304}\right)\)	\(e\left(\frac{1085}{1152}\right)\)	\(e\left(\frac{493}{2304}\right)\)	\(e\left(\frac{311}{2304}\right)\)	\(e\left(\frac{101}{192}\right)\)	\(e\left(\frac{181}{768}\right)\)	\(e\left(\frac{1039}{1152}\right)\)	\(e\left(\frac{569}{1152}\right)\)	\(e\left(\frac{355}{2304}\right)\)	\(e\left(\frac{217}{288}\right)\)
\(\chi_{221184}(35,\cdot)\)	221184.fc	6144	no	\(1\)	\(1\)	\(e\left(\frac{4193}{6144}\right)\)	\(e\left(\frac{2885}{3072}\right)\)	\(e\left(\frac{181}{6144}\right)\)	\(e\left(\frac{5519}{6144}\right)\)	\(e\left(\frac{173}{512}\right)\)	\(e\left(\frac{1725}{2048}\right)\)	\(e\left(\frac{1255}{3072}\right)\)	\(e\left(\frac{1121}{3072}\right)\)	\(e\left(\frac{1435}{6144}\right)\)	\(e\left(\frac{145}{768}\right)\)
\(\chi_{221184}(37,\cdot)\)	221184.ff	6144	no	\(1\)	\(1\)	\(e\left(\frac{1867}{6144}\right)\)	\(e\left(\frac{2455}{3072}\right)\)	\(e\left(\frac{3431}{6144}\right)\)	\(e\left(\frac{5125}{6144}\right)\)	\(e\left(\frac{271}{512}\right)\)	\(e\left(\frac{1215}{2048}\right)\)	\(e\left(\frac{1997}{3072}\right)\)	\(e\left(\frac{1867}{3072}\right)\)	\(e\left(\frac{3593}{6144}\right)\)	\(e\left(\frac{731}{768}\right)\)
\(\chi_{221184}(41,\cdot)\)	221184.fg	9216	no	\(-1\)	\(1\)	\(e\left(\frac{5495}{9216}\right)\)	\(e\left(\frac{755}{4608}\right)\)	\(e\left(\frac{4099}{9216}\right)\)	\(e\left(\frac{6425}{9216}\right)\)	\(e\left(\frac{203}{768}\right)\)	\(e\left(\frac{1723}{3072}\right)\)	\(e\left(\frac{2305}{4608}\right)\)	\(e\left(\frac{887}{4608}\right)\)	\(e\left(\frac{6445}{9216}\right)\)	\(e\left(\frac{583}{1152}\right)\)
\(\chi_{221184}(43,\cdot)\)	221184.fm	18432	yes	\(-1\)	\(1\)	\(e\left(\frac{14117}{18432}\right)\)	\(e\left(\frac{665}{9216}\right)\)	\(e\left(\frac{6601}{18432}\right)\)	\(e\left(\frac{11915}{18432}\right)\)	\(e\left(\frac{161}{1536}\right)\)	\(e\left(\frac{5617}{6144}\right)\)	\(e\left(\frac{3907}{9216}\right)\)	\(e\left(\frac{4901}{9216}\right)\)	\(e\left(\frac{2503}{18432}\right)\)	\(e\left(\frac{277}{2304}\right)\)
\(\chi_{221184}(47,\cdot)\)	221184.fb	4608	no	\(1\)	\(1\)	\(e\left(\frac{2435}{4608}\right)\)	\(e\left(\frac{1583}{2304}\right)\)	\(e\left(\frac{4351}{4608}\right)\)	\(e\left(\frac{845}{4608}\right)\)	\(e\left(\frac{167}{384}\right)\)	\(e\left(\frac{1303}{1536}\right)\)	\(e\left(\frac{1621}{2304}\right)\)	\(e\left(\frac{131}{2304}\right)\)	\(e\left(\frac{3313}{4608}\right)\)	\(e\left(\frac{115}{576}\right)\)
\(\chi_{221184}(49,\cdot)\)	221184.ey	4608	no	\(1\)	\(1\)	\(e\left(\frac{2701}{4608}\right)\)	\(e\left(\frac{673}{2304}\right)\)	\(e\left(\frac{2897}{4608}\right)\)	\(e\left(\frac{1699}{4608}\right)\)	\(e\left(\frac{361}{384}\right)\)	\(e\left(\frac{185}{1536}\right)\)	\(e\left(\frac{1307}{2304}\right)\)	\(e\left(\frac{397}{2304}\right)\)	\(e\left(\frac{191}{4608}\right)\)	\(e\left(\frac{509}{576}\right)\)
\(\chi_{221184}(53,\cdot)\)	221184.ep	2048	no	\(-1\)	\(1\)	\(e\left(\frac{773}{2048}\right)\)	\(e\left(\frac{1017}{1024}\right)\)	\(e\left(\frac{1833}{2048}\right)\)	\(e\left(\frac{171}{2048}\right)\)	\(e\left(\frac{3}{512}\right)\)	\(e\left(\frac{755}{2048}\right)\)	\(e\left(\frac{611}{1024}\right)\)	\(e\left(\frac{773}{1024}\right)\)	\(e\left(\frac{1639}{2048}\right)\)	\(e\left(\frac{117}{256}\right)\)
\(\chi_{221184}(55,\cdot)\)	221184.ed	1024	no	\(-1\)	\(1\)	\(e\left(\frac{619}{1024}\right)\)	\(e\left(\frac{55}{512}\right)\)	\(e\left(\frac{263}{1024}\right)\)	\(e\left(\frac{741}{1024}\right)\)	\(e\left(\frac{13}{256}\right)\)	\(e\left(\frac{29}{1024}\right)\)	\(e\left(\frac{173}{512}\right)\)	\(e\left(\frac{107}{512}\right)\)	\(e\left(\frac{617}{1024}\right)\)	\(e\left(\frac{59}{128}\right)\)
\(\chi_{221184}(59,\cdot)\)	221184.fn	18432	yes	\(1\)	\(1\)	\(e\left(\frac{9049}{18432}\right)\)	\(e\left(\frac{2845}{9216}\right)\)	\(e\left(\frac{6413}{18432}\right)\)	\(e\left(\frac{8983}{18432}\right)\)	\(e\left(\frac{325}{1536}\right)\)	\(e\left(\frac{3797}{6144}\right)\)	\(e\left(\frac{5039}{9216}\right)\)	\(e\left(\frac{9049}{9216}\right)\)	\(e\left(\frac{12995}{18432}\right)\)	\(e\left(\frac{1289}{2304}\right)\)
\(\chi_{221184}(61,\cdot)\)	221184.fk	18432	yes	\(1\)	\(1\)	\(e\left(\frac{11243}{18432}\right)\)	\(e\left(\frac{8375}{9216}\right)\)	\(e\left(\frac{5767}{18432}\right)\)	\(e\left(\frac{5477}{18432}\right)\)	\(e\left(\frac{815}{1536}\right)\)	\(e\left(\frac{4831}{6144}\right)\)	\(e\left(\frac{7213}{9216}\right)\)	\(e\left(\frac{2027}{9216}\right)\)	\(e\left(\frac{16105}{18432}\right)\)	\(e\left(\frac{379}{2304}\right)\)
\(\chi_{221184}(65,\cdot)\)	221184.ef	1152	no	\(-1\)	\(1\)	\(e\left(\frac{695}{1152}\right)\)	\(e\left(\frac{563}{576}\right)\)	\(e\left(\frac{835}{1152}\right)\)	\(e\left(\frac{1049}{1152}\right)\)	\(e\left(\frac{59}{96}\right)\)	\(e\left(\frac{187}{384}\right)\)	\(e\left(\frac{481}{576}\right)\)	\(e\left(\frac{119}{576}\right)\)	\(e\left(\frac{877}{1152}\right)\)	\(e\left(\frac{55}{144}\right)\)
\(\chi_{221184}(67,\cdot)\)	221184.fm	18432	yes	\(-1\)	\(1\)	\(e\left(\frac{3979}{18432}\right)\)	\(e\left(\frac{5335}{9216}\right)\)	\(e\left(\frac{7847}{18432}\right)\)	\(e\left(\frac{12229}{18432}\right)\)	\(e\left(\frac{79}{1536}\right)\)	\(e\left(\frac{6143}{6144}\right)\)	\(e\left(\frac{9101}{9216}\right)\)	\(e\left(\frac{3979}{9216}\right)\)	\(e\left(\frac{5321}{18432}\right)\)	\(e\left(\frac{923}{2304}\right)\)
\(\chi_{221184}(71,\cdot)\)	221184.ev	3072	no	\(1\)	\(1\)	\(e\left(\frac{263}{3072}\right)\)	\(e\left(\frac{1475}{1536}\right)\)	\(e\left(\frac{211}{3072}\right)\)	\(e\left(\frac{137}{3072}\right)\)	\(e\left(\frac{27}{256}\right)\)	\(e\left(\frac{11}{1024}\right)\)	\(e\left(\frac{241}{1536}\right)\)	\(e\left(\frac{263}{1536}\right)\)	\(e\left(\frac{1885}{3072}\right)\)	\(e\left(\frac{151}{384}\right)\)
\(\chi_{221184}(73,\cdot)\)	221184.ew	3072	no	\(1\)	\(1\)	\(e\left(\frac{1681}{3072}\right)\)	\(e\left(\frac{565}{1536}\right)\)	\(e\left(\frac{677}{3072}\right)\)	\(e\left(\frac{2143}{3072}\right)\)	\(e\left(\frac{29}{256}\right)\)	\(e\left(\frac{557}{1024}\right)\)	\(e\left(\frac{1079}{1536}\right)\)	\(e\left(\frac{145}{1536}\right)\)	\(e\left(\frac{683}{3072}\right)\)	\(e\left(\frac{65}{384}\right)\)
\(\chi_{221184}(77,\cdot)\)	221184.fl	18432	yes	\(-1\)	\(1\)	\(e\left(\frac{9367}{18432}\right)\)	\(e\left(\frac{4243}{9216}\right)\)	\(e\left(\frac{15779}{18432}\right)\)	\(e\left(\frac{3577}{18432}\right)\)	\(e\left(\frac{1003}{1536}\right)\)	\(e\left(\frac{1883}{6144}\right)\)	\(e\left(\frac{4577}{9216}\right)\)	\(e\left(\frac{151}{9216}\right)\)	\(e\left(\frac{7565}{18432}\right)\)	\(e\left(\frac{359}{2304}\right)\)
\(\chi_{221184}(79,\cdot)\)	221184.ez	4608	no	\(-1\)	\(1\)	\(e\left(\frac{1109}{4608}\right)\)	\(e\left(\frac{2057}{2304}\right)\)	\(e\left(\frac{1465}{4608}\right)\)	\(e\left(\frac{2651}{4608}\right)\)	\(e\left(\frac{17}{384}\right)\)	\(e\left(\frac{865}{1536}\right)\)	\(e\left(\frac{787}{2304}\right)\)	\(e\left(\frac{1109}{2304}\right)\)	\(e\left(\frac{4567}{4608}\right)\)	\(e\left(\frac{37}{576}\right)\)
\(\chi_{221184}(83,\cdot)\)	221184.fn	18432	yes	\(1\)	\(1\)	\(e\left(\frac{287}{18432}\right)\)	\(e\left(\frac{6203}{9216}\right)\)	\(e\left(\frac{16075}{18432}\right)\)	\(e\left(\frac{16625}{18432}\right)\)	\(e\left(\frac{1235}{1536}\right)\)	\(e\left(\frac{1219}{6144}\right)\)	\(e\left(\frac{3481}{9216}\right)\)	\(e\left(\frac{287}{9216}\right)\)	\(e\left(\frac{17125}{18432}\right)\)	\(e\left(\frac{751}{2304}\right)\)
\(\chi_{221184}(85,\cdot)\)	221184.fk	18432	yes	\(1\)	\(1\)	\(e\left(\frac{13957}{18432}\right)\)	\(e\left(\frac{2425}{9216}\right)\)	\(e\left(\frac{16553}{18432}\right)\)	\(e\left(\frac{8491}{18432}\right)\)	\(e\left(\frac{1153}{1536}\right)\)	\(e\left(\frac{4049}{6144}\right)\)	\(e\left(\frac{3299}{9216}\right)\)	\(e\left(\frac{4741}{9216}\right)\)	\(e\left(\frac{5351}{18432}\right)\)	\(e\left(\frac{1781}{2304}\right)\)
\(\chi_{221184}(89,\cdot)\)	221184.ex	3072	no	\(-1\)	\(1\)	\(e\left(\frac{1579}{3072}\right)\)	\(e\left(\frac{1015}{1536}\right)\)	\(e\left(\frac{455}{3072}\right)\)	\(e\left(\frac{2341}{3072}\right)\)	\(e\left(\frac{239}{256}\right)\)	\(e\left(\frac{543}{1024}\right)\)	\(e\left(\frac{749}{1536}\right)\)	\(e\left(\frac{43}{1536}\right)\)	\(e\left(\frac{1961}{3072}\right)\)	\(e\left(\frac{59}{384}\right)\)
\(\chi_{221184}(91,\cdot)\)	221184.fe	6144	no	\(-1\)	\(1\)	\(e\left(\frac{3115}{6144}\right)\)	\(e\left(\frac{1015}{3072}\right)\)	\(e\left(\frac{1991}{6144}\right)\)	\(e\left(\frac{2341}{6144}\right)\)	\(e\left(\frac{111}{512}\right)\)	\(e\left(\frac{1567}{2048}\right)\)	\(e\left(\frac{3053}{3072}\right)\)	\(e\left(\frac{43}{3072}\right)\)	\(e\left(\frac{3497}{6144}\right)\)	\(e\left(\frac{59}{768}\right)\)
\(\chi_{221184}(95,\cdot)\)	221184.eq	2304	no	\(1\)	\(1\)	\(e\left(\frac{395}{2304}\right)\)	\(e\left(\frac{407}{1152}\right)\)	\(e\left(\frac{1063}{2304}\right)\)	\(e\left(\frac{2117}{2304}\right)\)	\(e\left(\frac{47}{192}\right)\)	\(e\left(\frac{511}{768}\right)\)	\(e\left(\frac{781}{1152}\right)\)	\(e\left(\frac{395}{1152}\right)\)	\(e\left(\frac{457}{2304}\right)\)	\(e\left(\frac{139}{288}\right)\)

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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.