LMFDB - Group of Dirichlet characters of modulus 43904

Show commands: PariGP / SageMath

sage: H = DirichletGroup(43904)

pari: g = idealstar(,43904,2)

Character group

sage: G.order() pari: g.no
Order	=	18816
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{4704}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{43904}(17151,\cdot)$, $\chi_{43904}(9605,\cdot)$, $\chi_{43904}(17153,\cdot)$

First 32 of 18816 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	$-1$	$1$	$3$	$5$	$9$	$11$	$13$	$15$	$17$	$19$	$23$	$25$
$\chi_{43904}(1,\cdot)$	43904.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{43904}(3,\cdot)$	43904.fk	4704	yes	$1$	$1$	$e\left(\frac{3691}{4704}\right)$	$e\left(\frac{905}{4704}\right)$	$e\left(\frac{1339}{2352}\right)$	$e\left(\frac{829}{4704}\right)$	$e\left(\frac{589}{1568}\right)$	$e\left(\frac{383}{392}\right)$	$e\left(\frac{835}{1176}\right)$	$e\left(\frac{47}{96}\right)$	$e\left(\frac{871}{2352}\right)$	$e\left(\frac{905}{2352}\right)$
$\chi_{43904}(5,\cdot)$	43904.fl	4704	yes	$-1$	$1$	$e\left(\frac{905}{4704}\right)$	$e\left(\frac{4195}{4704}\right)$	$e\left(\frac{905}{2352}\right)$	$e\left(\frac{815}{4704}\right)$	$e\left(\frac{911}{1568}\right)$	$e\left(\frac{33}{392}\right)$	$e\left(\frac{401}{1176}\right)$	$e\left(\frac{85}{96}\right)$	$e\left(\frac{1445}{2352}\right)$	$e\left(\frac{1843}{2352}\right)$
$\chi_{43904}(9,\cdot)$	43904.fh	2352	no	$1$	$1$	$e\left(\frac{1339}{2352}\right)$	$e\left(\frac{905}{2352}\right)$	$e\left(\frac{163}{1176}\right)$	$e\left(\frac{829}{2352}\right)$	$e\left(\frac{589}{784}\right)$	$e\left(\frac{187}{196}\right)$	$e\left(\frac{247}{588}\right)$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{871}{1176}\right)$	$e\left(\frac{905}{1176}\right)$
$\chi_{43904}(11,\cdot)$	43904.fm	4704	yes	$-1$	$1$	$e\left(\frac{829}{4704}\right)$	$e\left(\frac{815}{4704}\right)$	$e\left(\frac{829}{2352}\right)$	$e\left(\frac{2059}{4704}\right)$	$e\left(\frac{747}{1568}\right)$	$e\left(\frac{137}{392}\right)$	$e\left(\frac{73}{1176}\right)$	$e\left(\frac{89}{96}\right)$	$e\left(\frac{1681}{2352}\right)$	$e\left(\frac{815}{2352}\right)$
$\chi_{43904}(13,\cdot)$	43904.ff	1568	yes	$-1$	$1$	$e\left(\frac{589}{1568}\right)$	$e\left(\frac{911}{1568}\right)$	$e\left(\frac{589}{784}\right)$	$e\left(\frac{747}{1568}\right)$	$e\left(\frac{481}{1568}\right)$	$e\left(\frac{375}{392}\right)$	$e\left(\frac{141}{392}\right)$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{425}{784}\right)$	$e\left(\frac{127}{784}\right)$
$\chi_{43904}(15,\cdot)$	43904.ek	392	no	$-1$	$1$	$e\left(\frac{383}{392}\right)$	$e\left(\frac{33}{392}\right)$	$e\left(\frac{187}{196}\right)$	$e\left(\frac{137}{392}\right)$	$e\left(\frac{375}{392}\right)$	$e\left(\frac{3}{49}\right)$	$e\left(\frac{5}{98}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{193}{196}\right)$	$e\left(\frac{33}{196}\right)$
$\chi_{43904}(17,\cdot)$	43904.ey	1176	no	$-1$	$1$	$e\left(\frac{835}{1176}\right)$	$e\left(\frac{401}{1176}\right)$	$e\left(\frac{247}{588}\right)$	$e\left(\frac{73}{1176}\right)$	$e\left(\frac{141}{392}\right)$	$e\left(\frac{5}{98}\right)$	$e\left(\frac{92}{147}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{115}{588}\right)$	$e\left(\frac{401}{588}\right)$
$\chi_{43904}(19,\cdot)$	43904.cw	96	no	$1$	$1$	$e\left(\frac{47}{96}\right)$	$e\left(\frac{85}{96}\right)$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{89}{96}\right)$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{19}{96}\right)$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{37}{48}\right)$
$\chi_{43904}(23,\cdot)$	43904.fj	2352	no	$-1$	$1$	$e\left(\frac{871}{2352}\right)$	$e\left(\frac{1445}{2352}\right)$	$e\left(\frac{871}{1176}\right)$	$e\left(\frac{1681}{2352}\right)$	$e\left(\frac{425}{784}\right)$	$e\left(\frac{193}{196}\right)$	$e\left(\frac{115}{588}\right)$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{127}{1176}\right)$	$e\left(\frac{269}{1176}\right)$
$\chi_{43904}(25,\cdot)$	43904.fh	2352	no	$1$	$1$	$e\left(\frac{905}{2352}\right)$	$e\left(\frac{1843}{2352}\right)$	$e\left(\frac{905}{1176}\right)$	$e\left(\frac{815}{2352}\right)$	$e\left(\frac{127}{784}\right)$	$e\left(\frac{33}{196}\right)$	$e\left(\frac{401}{588}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{269}{1176}\right)$	$e\left(\frac{667}{1176}\right)$
$\chi_{43904}(27,\cdot)$	43904.fe	1568	yes	$1$	$1$	$e\left(\frac{555}{1568}\right)$	$e\left(\frac{905}{1568}\right)$	$e\left(\frac{555}{784}\right)$	$e\left(\frac{829}{1568}\right)$	$e\left(\frac{199}{1568}\right)$	$e\left(\frac{365}{392}\right)$	$e\left(\frac{51}{392}\right)$	$e\left(\frac{15}{32}\right)$	$e\left(\frac{87}{784}\right)$	$e\left(\frac{121}{784}\right)$
$\chi_{43904}(29,\cdot)$	43904.fd	1568	yes	$1$	$1$	$e\left(\frac{481}{1568}\right)$	$e\left(\frac{523}{1568}\right)$	$e\left(\frac{481}{784}\right)$	$e\left(\frac{39}{1568}\right)$	$e\left(\frac{1061}{1568}\right)$	$e\left(\frac{251}{392}\right)$	$e\left(\frac{5}{392}\right)$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{781}{784}\right)$	$e\left(\frac{523}{784}\right)$
$\chi_{43904}(31,\cdot)$	43904.ct	84	no	$1$	$1$	$e\left(\frac{59}{84}\right)$	$e\left(\frac{31}{84}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{71}{84}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{31}{42}\right)$
$\chi_{43904}(33,\cdot)$	43904.en	588	no	$-1$	$1$	$e\left(\frac{565}{588}\right)$	$e\left(\frac{215}{588}\right)$	$e\left(\frac{271}{294}\right)$	$e\left(\frac{361}{588}\right)$	$e\left(\frac{167}{196}\right)$	$e\left(\frac{16}{49}\right)$	$e\left(\frac{227}{294}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{25}{294}\right)$	$e\left(\frac{215}{294}\right)$
$\chi_{43904}(37,\cdot)$	43904.fn	4704	yes	$1$	$1$	$e\left(\frac{2801}{4704}\right)$	$e\left(\frac{379}{4704}\right)$	$e\left(\frac{449}{2352}\right)$	$e\left(\frac{3575}{4704}\right)$	$e\left(\frac{711}{1568}\right)$	$e\left(\frac{265}{392}\right)$	$e\left(\frac{197}{1176}\right)$	$e\left(\frac{61}{96}\right)$	$e\left(\frac{509}{2352}\right)$	$e\left(\frac{379}{2352}\right)$
$\chi_{43904}(39,\cdot)$	43904.fj	2352	no	$-1$	$1$	$e\left(\frac{377}{2352}\right)$	$e\left(\frac{1819}{2352}\right)$	$e\left(\frac{377}{1176}\right)$	$e\left(\frac{1535}{2352}\right)$	$e\left(\frac{535}{784}\right)$	$e\left(\frac{183}{196}\right)$	$e\left(\frac{41}{588}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{1073}{1176}\right)$	$e\left(\frac{643}{1176}\right)$
$\chi_{43904}(41,\cdot)$	43904.eu	784	no	$-1$	$1$	$e\left(\frac{341}{784}\right)$	$e\left(\frac{775}{784}\right)$	$e\left(\frac{341}{392}\right)$	$e\left(\frac{123}{784}\right)$	$e\left(\frac{361}{784}\right)$	$e\left(\frac{83}{196}\right)$	$e\left(\frac{159}{196}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{81}{392}\right)$	$e\left(\frac{383}{392}\right)$
$\chi_{43904}(43,\cdot)$	43904.fc	1568	yes	$-1$	$1$	$e\left(\frac{375}{1568}\right)$	$e\left(\frac{781}{1568}\right)$	$e\left(\frac{375}{784}\right)$	$e\left(\frac{1217}{1568}\right)$	$e\left(\frac{643}{1568}\right)$	$e\left(\frac{289}{392}\right)$	$e\left(\frac{347}{392}\right)$	$e\left(\frac{11}{32}\right)$	$e\left(\frac{419}{784}\right)$	$e\left(\frac{781}{784}\right)$
$\chi_{43904}(45,\cdot)$	43904.fl	4704	yes	$-1$	$1$	$e\left(\frac{3583}{4704}\right)$	$e\left(\frac{1301}{4704}\right)$	$e\left(\frac{1231}{2352}\right)$	$e\left(\frac{2473}{4704}\right)$	$e\left(\frac{521}{1568}\right)$	$e\left(\frac{15}{392}\right)$	$e\left(\frac{895}{1176}\right)$	$e\left(\frac{83}{96}\right)$	$e\left(\frac{835}{2352}\right)$	$e\left(\frac{1301}{2352}\right)$
$\chi_{43904}(47,\cdot)$	43904.fb	1176	no	$1$	$1$	$e\left(\frac{419}{1176}\right)$	$e\left(\frac{685}{1176}\right)$	$e\left(\frac{419}{588}\right)$	$e\left(\frac{569}{1176}\right)$	$e\left(\frac{17}{392}\right)$	$e\left(\frac{46}{49}\right)$	$e\left(\frac{115}{147}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{401}{588}\right)$	$e\left(\frac{97}{588}\right)$
$\chi_{43904}(51,\cdot)$	43904.fm	4704	yes	$-1$	$1$	$e\left(\frac{2327}{4704}\right)$	$e\left(\frac{2509}{4704}\right)$	$e\left(\frac{2327}{2352}\right)$	$e\left(\frac{1121}{4704}\right)$	$e\left(\frac{1153}{1568}\right)$	$e\left(\frac{11}{392}\right)$	$e\left(\frac{395}{1176}\right)$	$e\left(\frac{43}{96}\right)$	$e\left(\frac{1331}{2352}\right)$	$e\left(\frac{157}{2352}\right)$
$\chi_{43904}(53,\cdot)$	43904.fn	4704	yes	$1$	$1$	$e\left(\frac{2365}{4704}\right)$	$e\left(\frac{671}{4704}\right)$	$e\left(\frac{13}{2352}\right)$	$e\left(\frac{1675}{4704}\right)$	$e\left(\frac{59}{1568}\right)$	$e\left(\frac{253}{392}\right)$	$e\left(\frac{265}{1176}\right)$	$e\left(\frac{89}{96}\right)$	$e\left(\frac{1801}{2352}\right)$	$e\left(\frac{671}{2352}\right)$
$\chi_{43904}(55,\cdot)$	43904.ew	784	no	$1$	$1$	$e\left(\frac{289}{784}\right)$	$e\left(\frac{51}{784}\right)$	$e\left(\frac{289}{392}\right)$	$e\left(\frac{479}{784}\right)$	$e\left(\frac{45}{784}\right)$	$e\left(\frac{85}{196}\right)$	$e\left(\frac{79}{196}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{129}{392}\right)$	$e\left(\frac{51}{392}\right)$
$\chi_{43904}(57,\cdot)$	43904.ex	784	no	$1$	$1$	$e\left(\frac{215}{784}\right)$	$e\left(\frac{61}{784}\right)$	$e\left(\frac{215}{392}\right)$	$e\left(\frac{81}{784}\right)$	$e\left(\frac{515}{784}\right)$	$e\left(\frac{69}{196}\right)$	$e\left(\frac{131}{196}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{235}{392}\right)$	$e\left(\frac{61}{392}\right)$
$\chi_{43904}(59,\cdot)$	43904.fk	4704	yes	$1$	$1$	$e\left(\frac{649}{4704}\right)$	$e\left(\frac{3827}{4704}\right)$	$e\left(\frac{649}{2352}\right)$	$e\left(\frac{4015}{4704}\right)$	$e\left(\frac{895}{1568}\right)$	$e\left(\frac{373}{392}\right)$	$e\left(\frac{1153}{1176}\right)$	$e\left(\frac{53}{96}\right)$	$e\left(\frac{445}{2352}\right)$	$e\left(\frac{1475}{2352}\right)$
$\chi_{43904}(61,\cdot)$	43904.fl	4704	yes	$-1$	$1$	$e\left(\frac{3179}{4704}\right)$	$e\left(\frac{2521}{4704}\right)$	$e\left(\frac{827}{2352}\right)$	$e\left(\frac{2525}{4704}\right)$	$e\left(\frac{1341}{1568}\right)$	$e\left(\frac{83}{392}\right)$	$e\left(\frac{1163}{1176}\right)$	$e\left(\frac{79}{96}\right)$	$e\left(\frac{47}{2352}\right)$	$e\left(\frac{169}{2352}\right)$
$\chi_{43904}(65,\cdot)$	43904.ec	294	no	$1$	$1$	$e\left(\frac{167}{294}\right)$	$e\left(\frac{139}{294}\right)$	$e\left(\frac{20}{147}\right)$	$e\left(\frac{191}{294}\right)$	$e\left(\frac{87}{98}\right)$	$e\left(\frac{2}{49}\right)$	$e\left(\frac{103}{147}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{23}{147}\right)$	$e\left(\frac{139}{147}\right)$
$\chi_{43904}(67,\cdot)$	43904.es	672	no	$-1$	$1$	$e\left(\frac{445}{672}\right)$	$e\left(\frac{431}{672}\right)$	$e\left(\frac{109}{336}\right)$	$e\left(\frac{139}{672}\right)$	$e\left(\frac{107}{224}\right)$	$e\left(\frac{17}{56}\right)$	$e\left(\frac{25}{168}\right)$	$e\left(\frac{47}{96}\right)$	$e\left(\frac{97}{336}\right)$	$e\left(\frac{95}{336}\right)$
$\chi_{43904}(69,\cdot)$	43904.ff	1568	yes	$-1$	$1$	$e\left(\frac{243}{1568}\right)$	$e\left(\frac{1265}{1568}\right)$	$e\left(\frac{243}{784}\right)$	$e\left(\frac{1397}{1568}\right)$	$e\left(\frac{1439}{1568}\right)$	$e\left(\frac{377}{392}\right)$	$e\left(\frac{355}{392}\right)$	$e\left(\frac{23}{32}\right)$	$e\left(\frac{375}{784}\right)$	$e\left(\frac{481}{784}\right)$
$\chi_{43904}(71,\cdot)$	43904.ev	784	no	$-1$	$1$	$e\left(\frac{127}{784}\right)$	$e\left(\frac{253}{784}\right)$	$e\left(\frac{127}{392}\right)$	$e\left(\frac{201}{784}\right)$	$e\left(\frac{131}{784}\right)$	$e\left(\frac{95}{196}\right)$	$e\left(\frac{71}{196}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{271}{392}\right)$	$e\left(\frac{253}{392}\right)$
$\chi_{43904}(73,\cdot)$	43904.fi	2352	no	$-1$	$1$	$e\left(\frac{779}{2352}\right)$	$e\left(\frac{1129}{2352}\right)$	$e\left(\frac{779}{1176}\right)$	$e\left(\frac{773}{2352}\right)$	$e\left(\frac{701}{784}\right)$	$e\left(\frac{159}{196}\right)$	$e\left(\frac{569}{588}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{815}{1176}\right)$	$e\left(\frac{1129}{1176}\right)$

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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	$43904$
Structure	\(C_{2}\times C_{2}\times C_{4704}\)
Order	$18816$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(5\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(23\)	\(25\)
\(\chi_{43904}(1,\cdot)\)	43904.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{43904}(3,\cdot)\)	43904.fk	4704	yes	\(1\)	\(1\)	\(e\left(\frac{3691}{4704}\right)\)	\(e\left(\frac{905}{4704}\right)\)	\(e\left(\frac{1339}{2352}\right)\)	\(e\left(\frac{829}{4704}\right)\)	\(e\left(\frac{589}{1568}\right)\)	\(e\left(\frac{383}{392}\right)\)	\(e\left(\frac{835}{1176}\right)\)	\(e\left(\frac{47}{96}\right)\)	\(e\left(\frac{871}{2352}\right)\)	\(e\left(\frac{905}{2352}\right)\)
\(\chi_{43904}(5,\cdot)\)	43904.fl	4704	yes	\(-1\)	\(1\)	\(e\left(\frac{905}{4704}\right)\)	\(e\left(\frac{4195}{4704}\right)\)	\(e\left(\frac{905}{2352}\right)\)	\(e\left(\frac{815}{4704}\right)\)	\(e\left(\frac{911}{1568}\right)\)	\(e\left(\frac{33}{392}\right)\)	\(e\left(\frac{401}{1176}\right)\)	\(e\left(\frac{85}{96}\right)\)	\(e\left(\frac{1445}{2352}\right)\)	\(e\left(\frac{1843}{2352}\right)\)
\(\chi_{43904}(9,\cdot)\)	43904.fh	2352	no	\(1\)	\(1\)	\(e\left(\frac{1339}{2352}\right)\)	\(e\left(\frac{905}{2352}\right)\)	\(e\left(\frac{163}{1176}\right)\)	\(e\left(\frac{829}{2352}\right)\)	\(e\left(\frac{589}{784}\right)\)	\(e\left(\frac{187}{196}\right)\)	\(e\left(\frac{247}{588}\right)\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{871}{1176}\right)\)	\(e\left(\frac{905}{1176}\right)\)
\(\chi_{43904}(11,\cdot)\)	43904.fm	4704	yes	\(-1\)	\(1\)	\(e\left(\frac{829}{4704}\right)\)	\(e\left(\frac{815}{4704}\right)\)	\(e\left(\frac{829}{2352}\right)\)	\(e\left(\frac{2059}{4704}\right)\)	\(e\left(\frac{747}{1568}\right)\)	\(e\left(\frac{137}{392}\right)\)	\(e\left(\frac{73}{1176}\right)\)	\(e\left(\frac{89}{96}\right)\)	\(e\left(\frac{1681}{2352}\right)\)	\(e\left(\frac{815}{2352}\right)\)
\(\chi_{43904}(13,\cdot)\)	43904.ff	1568	yes	\(-1\)	\(1\)	\(e\left(\frac{589}{1568}\right)\)	\(e\left(\frac{911}{1568}\right)\)	\(e\left(\frac{589}{784}\right)\)	\(e\left(\frac{747}{1568}\right)\)	\(e\left(\frac{481}{1568}\right)\)	\(e\left(\frac{375}{392}\right)\)	\(e\left(\frac{141}{392}\right)\)	\(e\left(\frac{9}{32}\right)\)	\(e\left(\frac{425}{784}\right)\)	\(e\left(\frac{127}{784}\right)\)
\(\chi_{43904}(15,\cdot)\)	43904.ek	392	no	\(-1\)	\(1\)	\(e\left(\frac{383}{392}\right)\)	\(e\left(\frac{33}{392}\right)\)	\(e\left(\frac{187}{196}\right)\)	\(e\left(\frac{137}{392}\right)\)	\(e\left(\frac{375}{392}\right)\)	\(e\left(\frac{3}{49}\right)\)	\(e\left(\frac{5}{98}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{193}{196}\right)\)	\(e\left(\frac{33}{196}\right)\)
\(\chi_{43904}(17,\cdot)\)	43904.ey	1176	no	\(-1\)	\(1\)	\(e\left(\frac{835}{1176}\right)\)	\(e\left(\frac{401}{1176}\right)\)	\(e\left(\frac{247}{588}\right)\)	\(e\left(\frac{73}{1176}\right)\)	\(e\left(\frac{141}{392}\right)\)	\(e\left(\frac{5}{98}\right)\)	\(e\left(\frac{92}{147}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{115}{588}\right)\)	\(e\left(\frac{401}{588}\right)\)
\(\chi_{43904}(19,\cdot)\)	43904.cw	96	no	\(1\)	\(1\)	\(e\left(\frac{47}{96}\right)\)	\(e\left(\frac{85}{96}\right)\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{89}{96}\right)\)	\(e\left(\frac{9}{32}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{19}{96}\right)\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{37}{48}\right)\)
\(\chi_{43904}(23,\cdot)\)	43904.fj	2352	no	\(-1\)	\(1\)	\(e\left(\frac{871}{2352}\right)\)	\(e\left(\frac{1445}{2352}\right)\)	\(e\left(\frac{871}{1176}\right)\)	\(e\left(\frac{1681}{2352}\right)\)	\(e\left(\frac{425}{784}\right)\)	\(e\left(\frac{193}{196}\right)\)	\(e\left(\frac{115}{588}\right)\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{127}{1176}\right)\)	\(e\left(\frac{269}{1176}\right)\)
\(\chi_{43904}(25,\cdot)\)	43904.fh	2352	no	\(1\)	\(1\)	\(e\left(\frac{905}{2352}\right)\)	\(e\left(\frac{1843}{2352}\right)\)	\(e\left(\frac{905}{1176}\right)\)	\(e\left(\frac{815}{2352}\right)\)	\(e\left(\frac{127}{784}\right)\)	\(e\left(\frac{33}{196}\right)\)	\(e\left(\frac{401}{588}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{269}{1176}\right)\)	\(e\left(\frac{667}{1176}\right)\)
\(\chi_{43904}(27,\cdot)\)	43904.fe	1568	yes	\(1\)	\(1\)	\(e\left(\frac{555}{1568}\right)\)	\(e\left(\frac{905}{1568}\right)\)	\(e\left(\frac{555}{784}\right)\)	\(e\left(\frac{829}{1568}\right)\)	\(e\left(\frac{199}{1568}\right)\)	\(e\left(\frac{365}{392}\right)\)	\(e\left(\frac{51}{392}\right)\)	\(e\left(\frac{15}{32}\right)\)	\(e\left(\frac{87}{784}\right)\)	\(e\left(\frac{121}{784}\right)\)
\(\chi_{43904}(29,\cdot)\)	43904.fd	1568	yes	\(1\)	\(1\)	\(e\left(\frac{481}{1568}\right)\)	\(e\left(\frac{523}{1568}\right)\)	\(e\left(\frac{481}{784}\right)\)	\(e\left(\frac{39}{1568}\right)\)	\(e\left(\frac{1061}{1568}\right)\)	\(e\left(\frac{251}{392}\right)\)	\(e\left(\frac{5}{392}\right)\)	\(e\left(\frac{13}{32}\right)\)	\(e\left(\frac{781}{784}\right)\)	\(e\left(\frac{523}{784}\right)\)
\(\chi_{43904}(31,\cdot)\)	43904.ct	84	no	\(1\)	\(1\)	\(e\left(\frac{59}{84}\right)\)	\(e\left(\frac{31}{84}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{71}{84}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{31}{42}\right)\)
\(\chi_{43904}(33,\cdot)\)	43904.en	588	no	\(-1\)	\(1\)	\(e\left(\frac{565}{588}\right)\)	\(e\left(\frac{215}{588}\right)\)	\(e\left(\frac{271}{294}\right)\)	\(e\left(\frac{361}{588}\right)\)	\(e\left(\frac{167}{196}\right)\)	\(e\left(\frac{16}{49}\right)\)	\(e\left(\frac{227}{294}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{25}{294}\right)\)	\(e\left(\frac{215}{294}\right)\)
\(\chi_{43904}(37,\cdot)\)	43904.fn	4704	yes	\(1\)	\(1\)	\(e\left(\frac{2801}{4704}\right)\)	\(e\left(\frac{379}{4704}\right)\)	\(e\left(\frac{449}{2352}\right)\)	\(e\left(\frac{3575}{4704}\right)\)	\(e\left(\frac{711}{1568}\right)\)	\(e\left(\frac{265}{392}\right)\)	\(e\left(\frac{197}{1176}\right)\)	\(e\left(\frac{61}{96}\right)\)	\(e\left(\frac{509}{2352}\right)\)	\(e\left(\frac{379}{2352}\right)\)
\(\chi_{43904}(39,\cdot)\)	43904.fj	2352	no	\(-1\)	\(1\)	\(e\left(\frac{377}{2352}\right)\)	\(e\left(\frac{1819}{2352}\right)\)	\(e\left(\frac{377}{1176}\right)\)	\(e\left(\frac{1535}{2352}\right)\)	\(e\left(\frac{535}{784}\right)\)	\(e\left(\frac{183}{196}\right)\)	\(e\left(\frac{41}{588}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{1073}{1176}\right)\)	\(e\left(\frac{643}{1176}\right)\)
\(\chi_{43904}(41,\cdot)\)	43904.eu	784	no	\(-1\)	\(1\)	\(e\left(\frac{341}{784}\right)\)	\(e\left(\frac{775}{784}\right)\)	\(e\left(\frac{341}{392}\right)\)	\(e\left(\frac{123}{784}\right)\)	\(e\left(\frac{361}{784}\right)\)	\(e\left(\frac{83}{196}\right)\)	\(e\left(\frac{159}{196}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{81}{392}\right)\)	\(e\left(\frac{383}{392}\right)\)
\(\chi_{43904}(43,\cdot)\)	43904.fc	1568	yes	\(-1\)	\(1\)	\(e\left(\frac{375}{1568}\right)\)	\(e\left(\frac{781}{1568}\right)\)	\(e\left(\frac{375}{784}\right)\)	\(e\left(\frac{1217}{1568}\right)\)	\(e\left(\frac{643}{1568}\right)\)	\(e\left(\frac{289}{392}\right)\)	\(e\left(\frac{347}{392}\right)\)	\(e\left(\frac{11}{32}\right)\)	\(e\left(\frac{419}{784}\right)\)	\(e\left(\frac{781}{784}\right)\)
\(\chi_{43904}(45,\cdot)\)	43904.fl	4704	yes	\(-1\)	\(1\)	\(e\left(\frac{3583}{4704}\right)\)	\(e\left(\frac{1301}{4704}\right)\)	\(e\left(\frac{1231}{2352}\right)\)	\(e\left(\frac{2473}{4704}\right)\)	\(e\left(\frac{521}{1568}\right)\)	\(e\left(\frac{15}{392}\right)\)	\(e\left(\frac{895}{1176}\right)\)	\(e\left(\frac{83}{96}\right)\)	\(e\left(\frac{835}{2352}\right)\)	\(e\left(\frac{1301}{2352}\right)\)
\(\chi_{43904}(47,\cdot)\)	43904.fb	1176	no	\(1\)	\(1\)	\(e\left(\frac{419}{1176}\right)\)	\(e\left(\frac{685}{1176}\right)\)	\(e\left(\frac{419}{588}\right)\)	\(e\left(\frac{569}{1176}\right)\)	\(e\left(\frac{17}{392}\right)\)	\(e\left(\frac{46}{49}\right)\)	\(e\left(\frac{115}{147}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{401}{588}\right)\)	\(e\left(\frac{97}{588}\right)\)
\(\chi_{43904}(51,\cdot)\)	43904.fm	4704	yes	\(-1\)	\(1\)	\(e\left(\frac{2327}{4704}\right)\)	\(e\left(\frac{2509}{4704}\right)\)	\(e\left(\frac{2327}{2352}\right)\)	\(e\left(\frac{1121}{4704}\right)\)	\(e\left(\frac{1153}{1568}\right)\)	\(e\left(\frac{11}{392}\right)\)	\(e\left(\frac{395}{1176}\right)\)	\(e\left(\frac{43}{96}\right)\)	\(e\left(\frac{1331}{2352}\right)\)	\(e\left(\frac{157}{2352}\right)\)
\(\chi_{43904}(53,\cdot)\)	43904.fn	4704	yes	\(1\)	\(1\)	\(e\left(\frac{2365}{4704}\right)\)	\(e\left(\frac{671}{4704}\right)\)	\(e\left(\frac{13}{2352}\right)\)	\(e\left(\frac{1675}{4704}\right)\)	\(e\left(\frac{59}{1568}\right)\)	\(e\left(\frac{253}{392}\right)\)	\(e\left(\frac{265}{1176}\right)\)	\(e\left(\frac{89}{96}\right)\)	\(e\left(\frac{1801}{2352}\right)\)	\(e\left(\frac{671}{2352}\right)\)
\(\chi_{43904}(55,\cdot)\)	43904.ew	784	no	\(1\)	\(1\)	\(e\left(\frac{289}{784}\right)\)	\(e\left(\frac{51}{784}\right)\)	\(e\left(\frac{289}{392}\right)\)	\(e\left(\frac{479}{784}\right)\)	\(e\left(\frac{45}{784}\right)\)	\(e\left(\frac{85}{196}\right)\)	\(e\left(\frac{79}{196}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{129}{392}\right)\)	\(e\left(\frac{51}{392}\right)\)
\(\chi_{43904}(57,\cdot)\)	43904.ex	784	no	\(1\)	\(1\)	\(e\left(\frac{215}{784}\right)\)	\(e\left(\frac{61}{784}\right)\)	\(e\left(\frac{215}{392}\right)\)	\(e\left(\frac{81}{784}\right)\)	\(e\left(\frac{515}{784}\right)\)	\(e\left(\frac{69}{196}\right)\)	\(e\left(\frac{131}{196}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{235}{392}\right)\)	\(e\left(\frac{61}{392}\right)\)
\(\chi_{43904}(59,\cdot)\)	43904.fk	4704	yes	\(1\)	\(1\)	\(e\left(\frac{649}{4704}\right)\)	\(e\left(\frac{3827}{4704}\right)\)	\(e\left(\frac{649}{2352}\right)\)	\(e\left(\frac{4015}{4704}\right)\)	\(e\left(\frac{895}{1568}\right)\)	\(e\left(\frac{373}{392}\right)\)	\(e\left(\frac{1153}{1176}\right)\)	\(e\left(\frac{53}{96}\right)\)	\(e\left(\frac{445}{2352}\right)\)	\(e\left(\frac{1475}{2352}\right)\)
\(\chi_{43904}(61,\cdot)\)	43904.fl	4704	yes	\(-1\)	\(1\)	\(e\left(\frac{3179}{4704}\right)\)	\(e\left(\frac{2521}{4704}\right)\)	\(e\left(\frac{827}{2352}\right)\)	\(e\left(\frac{2525}{4704}\right)\)	\(e\left(\frac{1341}{1568}\right)\)	\(e\left(\frac{83}{392}\right)\)	\(e\left(\frac{1163}{1176}\right)\)	\(e\left(\frac{79}{96}\right)\)	\(e\left(\frac{47}{2352}\right)\)	\(e\left(\frac{169}{2352}\right)\)
\(\chi_{43904}(65,\cdot)\)	43904.ec	294	no	\(1\)	\(1\)	\(e\left(\frac{167}{294}\right)\)	\(e\left(\frac{139}{294}\right)\)	\(e\left(\frac{20}{147}\right)\)	\(e\left(\frac{191}{294}\right)\)	\(e\left(\frac{87}{98}\right)\)	\(e\left(\frac{2}{49}\right)\)	\(e\left(\frac{103}{147}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{23}{147}\right)\)	\(e\left(\frac{139}{147}\right)\)
\(\chi_{43904}(67,\cdot)\)	43904.es	672	no	\(-1\)	\(1\)	\(e\left(\frac{445}{672}\right)\)	\(e\left(\frac{431}{672}\right)\)	\(e\left(\frac{109}{336}\right)\)	\(e\left(\frac{139}{672}\right)\)	\(e\left(\frac{107}{224}\right)\)	\(e\left(\frac{17}{56}\right)\)	\(e\left(\frac{25}{168}\right)\)	\(e\left(\frac{47}{96}\right)\)	\(e\left(\frac{97}{336}\right)\)	\(e\left(\frac{95}{336}\right)\)
\(\chi_{43904}(69,\cdot)\)	43904.ff	1568	yes	\(-1\)	\(1\)	\(e\left(\frac{243}{1568}\right)\)	\(e\left(\frac{1265}{1568}\right)\)	\(e\left(\frac{243}{784}\right)\)	\(e\left(\frac{1397}{1568}\right)\)	\(e\left(\frac{1439}{1568}\right)\)	\(e\left(\frac{377}{392}\right)\)	\(e\left(\frac{355}{392}\right)\)	\(e\left(\frac{23}{32}\right)\)	\(e\left(\frac{375}{784}\right)\)	\(e\left(\frac{481}{784}\right)\)
\(\chi_{43904}(71,\cdot)\)	43904.ev	784	no	\(-1\)	\(1\)	\(e\left(\frac{127}{784}\right)\)	\(e\left(\frac{253}{784}\right)\)	\(e\left(\frac{127}{392}\right)\)	\(e\left(\frac{201}{784}\right)\)	\(e\left(\frac{131}{784}\right)\)	\(e\left(\frac{95}{196}\right)\)	\(e\left(\frac{71}{196}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{271}{392}\right)\)	\(e\left(\frac{253}{392}\right)\)
\(\chi_{43904}(73,\cdot)\)	43904.fi	2352	no	\(-1\)	\(1\)	\(e\left(\frac{779}{2352}\right)\)	\(e\left(\frac{1129}{2352}\right)\)	\(e\left(\frac{779}{1176}\right)\)	\(e\left(\frac{773}{2352}\right)\)	\(e\left(\frac{701}{784}\right)\)	\(e\left(\frac{159}{196}\right)\)	\(e\left(\frac{569}{588}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{815}{1176}\right)\)	\(e\left(\frac{1129}{1176}\right)\)

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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.