LMFDB - Group of Dirichlet characters of modulus 3584

Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(3584)

pari: g = idealstar(,3584,2)

Character group

sage: G.order() pari: g.no
Order	=	1536
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{384}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{3584}(1023,\cdot)$, $\chi_{3584}(1541,\cdot)$, $\chi_{3584}(1025,\cdot)$

First 32 of 1536 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	$-1$	$1$	$3$	$5$	$9$	$11$	$13$	$15$	$17$	$19$	$23$	$25$
$\chi_{3584}(1,\cdot)$	3584.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{3584}(3,\cdot)$	3584.ck	384	yes	$1$	$1$	$e\left(\frac{91}{384}\right)$	$e\left(\frac{41}{384}\right)$	$e\left(\frac{91}{192}\right)$	$e\left(\frac{157}{384}\right)$	$e\left(\frac{109}{128}\right)$	$e\left(\frac{11}{32}\right)$	$e\left(\frac{79}{96}\right)$	$e\left(\frac{239}{384}\right)$	$e\left(\frac{127}{192}\right)$	$e\left(\frac{41}{192}\right)$
$\chi_{3584}(5,\cdot)$	3584.ci	384	yes	$-1$	$1$	$e\left(\frac{41}{384}\right)$	$e\left(\frac{67}{384}\right)$	$e\left(\frac{41}{192}\right)$	$e\left(\frac{383}{384}\right)$	$e\left(\frac{47}{128}\right)$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{5}{96}\right)$	$e\left(\frac{133}{384}\right)$	$e\left(\frac{149}{192}\right)$	$e\left(\frac{67}{192}\right)$
$\chi_{3584}(9,\cdot)$	3584.cf	192	no	$1$	$1$	$e\left(\frac{91}{192}\right)$	$e\left(\frac{41}{192}\right)$	$e\left(\frac{91}{96}\right)$	$e\left(\frac{157}{192}\right)$	$e\left(\frac{45}{64}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{47}{192}\right)$	$e\left(\frac{31}{96}\right)$	$e\left(\frac{41}{96}\right)$
$\chi_{3584}(11,\cdot)$	3584.cj	384	yes	$-1$	$1$	$e\left(\frac{157}{384}\right)$	$e\left(\frac{383}{384}\right)$	$e\left(\frac{157}{192}\right)$	$e\left(\frac{235}{384}\right)$	$e\left(\frac{91}{128}\right)$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{25}{96}\right)$	$e\left(\frac{41}{384}\right)$	$e\left(\frac{25}{192}\right)$	$e\left(\frac{191}{192}\right)$
$\chi_{3584}(13,\cdot)$	3584.cd	128	yes	$-1$	$1$	$e\left(\frac{109}{128}\right)$	$e\left(\frac{47}{128}\right)$	$e\left(\frac{45}{64}\right)$	$e\left(\frac{91}{128}\right)$	$e\left(\frac{97}{128}\right)$	$e\left(\frac{7}{32}\right)$	$e\left(\frac{25}{32}\right)$	$e\left(\frac{57}{128}\right)$	$e\left(\frac{9}{64}\right)$	$e\left(\frac{47}{64}\right)$
$\chi_{3584}(15,\cdot)$	3584.bl	32	no	$-1$	$1$	$e\left(\frac{11}{32}\right)$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{7}{32}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{31}{32}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{9}{16}\right)$
$\chi_{3584}(17,\cdot)$	3584.bz	96	no	$-1$	$1$	$e\left(\frac{79}{96}\right)$	$e\left(\frac{5}{96}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{25}{96}\right)$	$e\left(\frac{25}{32}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{83}{96}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{5}{48}\right)$
$\chi_{3584}(19,\cdot)$	3584.ck	384	yes	$1$	$1$	$e\left(\frac{239}{384}\right)$	$e\left(\frac{133}{384}\right)$	$e\left(\frac{47}{192}\right)$	$e\left(\frac{41}{384}\right)$	$e\left(\frac{57}{128}\right)$	$e\left(\frac{31}{32}\right)$	$e\left(\frac{83}{96}\right)$	$e\left(\frac{307}{384}\right)$	$e\left(\frac{131}{192}\right)$	$e\left(\frac{133}{192}\right)$
$\chi_{3584}(23,\cdot)$	3584.ch	192	no	$-1$	$1$	$e\left(\frac{127}{192}\right)$	$e\left(\frac{149}{192}\right)$	$e\left(\frac{31}{96}\right)$	$e\left(\frac{25}{192}\right)$	$e\left(\frac{9}{64}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{131}{192}\right)$	$e\left(\frac{67}{96}\right)$	$e\left(\frac{53}{96}\right)$
$\chi_{3584}(25,\cdot)$	3584.cf	192	no	$1$	$1$	$e\left(\frac{41}{192}\right)$	$e\left(\frac{67}{192}\right)$	$e\left(\frac{41}{96}\right)$	$e\left(\frac{191}{192}\right)$	$e\left(\frac{47}{64}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{133}{192}\right)$	$e\left(\frac{53}{96}\right)$	$e\left(\frac{67}{96}\right)$
$\chi_{3584}(27,\cdot)$	3584.cb	128	yes	$1$	$1$	$e\left(\frac{91}{128}\right)$	$e\left(\frac{41}{128}\right)$	$e\left(\frac{27}{64}\right)$	$e\left(\frac{29}{128}\right)$	$e\left(\frac{71}{128}\right)$	$e\left(\frac{1}{32}\right)$	$e\left(\frac{15}{32}\right)$	$e\left(\frac{111}{128}\right)$	$e\left(\frac{63}{64}\right)$	$e\left(\frac{41}{64}\right)$
$\chi_{3584}(29,\cdot)$	3584.ca	128	no	$1$	$1$	$e\left(\frac{81}{128}\right)$	$e\left(\frac{123}{128}\right)$	$e\left(\frac{17}{64}\right)$	$e\left(\frac{87}{128}\right)$	$e\left(\frac{85}{128}\right)$	$e\left(\frac{19}{32}\right)$	$e\left(\frac{29}{32}\right)$	$e\left(\frac{13}{128}\right)$	$e\left(\frac{29}{64}\right)$	$e\left(\frac{59}{64}\right)$
$\chi_{3584}(31,\cdot)$	3584.bq	48	no	$1$	$1$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{7}{16}\right)$	$-i$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{19}{24}\right)$
$\chi_{3584}(33,\cdot)$	3584.bo	48	no	$-1$	$1$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{9}{16}\right)$	$-i$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{5}{24}\right)$
$\chi_{3584}(37,\cdot)$	3584.cl	384	yes	$1$	$1$	$e\left(\frac{65}{384}\right)$	$e\left(\frac{331}{384}\right)$	$e\left(\frac{65}{192}\right)$	$e\left(\frac{359}{384}\right)$	$e\left(\frac{87}{128}\right)$	$e\left(\frac{1}{32}\right)$	$e\left(\frac{77}{96}\right)$	$e\left(\frac{61}{384}\right)$	$e\left(\frac{77}{192}\right)$	$e\left(\frac{139}{192}\right)$
$\chi_{3584}(39,\cdot)$	3584.ch	192	no	$-1$	$1$	$e\left(\frac{17}{192}\right)$	$e\left(\frac{91}{192}\right)$	$e\left(\frac{17}{96}\right)$	$e\left(\frac{23}{192}\right)$	$e\left(\frac{39}{64}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{13}{192}\right)$	$e\left(\frac{77}{96}\right)$	$e\left(\frac{91}{96}\right)$
$\chi_{3584}(41,\cdot)$	3584.bt	64	no	$-1$	$1$	$e\left(\frac{61}{64}\right)$	$e\left(\frac{31}{64}\right)$	$e\left(\frac{29}{32}\right)$	$e\left(\frac{43}{64}\right)$	$e\left(\frac{49}{64}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{9}{64}\right)$	$e\left(\frac{25}{32}\right)$	$e\left(\frac{31}{32}\right)$
$\chi_{3584}(43,\cdot)$	3584.cc	128	no	$-1$	$1$	$e\left(\frac{23}{128}\right)$	$e\left(\frac{61}{128}\right)$	$e\left(\frac{23}{64}\right)$	$e\left(\frac{1}{128}\right)$	$e\left(\frac{115}{128}\right)$	$e\left(\frac{21}{32}\right)$	$e\left(\frac{11}{32}\right)$	$e\left(\frac{59}{128}\right)$	$e\left(\frac{11}{64}\right)$	$e\left(\frac{61}{64}\right)$
$\chi_{3584}(45,\cdot)$	3584.ci	384	yes	$-1$	$1$	$e\left(\frac{223}{384}\right)$	$e\left(\frac{149}{384}\right)$	$e\left(\frac{31}{192}\right)$	$e\left(\frac{313}{384}\right)$	$e\left(\frac{9}{128}\right)$	$e\left(\frac{31}{32}\right)$	$e\left(\frac{67}{96}\right)$	$e\left(\frac{227}{384}\right)$	$e\left(\frac{19}{192}\right)$	$e\left(\frac{149}{192}\right)$
$\chi_{3584}(47,\cdot)$	3584.bx	96	no	$1$	$1$	$e\left(\frac{35}{96}\right)$	$e\left(\frac{49}{96}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{5}{96}\right)$	$e\left(\frac{21}{32}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{55}{96}\right)$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{1}{48}\right)$
$\chi_{3584}(51,\cdot)$	3584.cj	384	yes	$-1$	$1$	$e\left(\frac{23}{384}\right)$	$e\left(\frac{61}{384}\right)$	$e\left(\frac{23}{192}\right)$	$e\left(\frac{257}{384}\right)$	$e\left(\frac{81}{128}\right)$	$e\left(\frac{7}{32}\right)$	$e\left(\frac{11}{96}\right)$	$e\left(\frac{187}{384}\right)$	$e\left(\frac{11}{192}\right)$	$e\left(\frac{61}{192}\right)$
$\chi_{3584}(53,\cdot)$	3584.cl	384	yes	$1$	$1$	$e\left(\frac{13}{384}\right)$	$e\left(\frac{143}{384}\right)$	$e\left(\frac{13}{192}\right)$	$e\left(\frac{379}{384}\right)$	$e\left(\frac{43}{128}\right)$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{73}{96}\right)$	$e\left(\frac{89}{384}\right)$	$e\left(\frac{169}{192}\right)$	$e\left(\frac{143}{192}\right)$
$\chi_{3584}(55,\cdot)$	3584.bv	64	no	$1$	$1$	$e\left(\frac{33}{64}\right)$	$e\left(\frac{11}{64}\right)$	$e\left(\frac{1}{32}\right)$	$e\left(\frac{39}{64}\right)$	$e\left(\frac{5}{64}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{29}{64}\right)$	$e\left(\frac{29}{32}\right)$	$e\left(\frac{11}{32}\right)$
$\chi_{3584}(57,\cdot)$	3584.bs	64	no	$1$	$1$	$e\left(\frac{55}{64}\right)$	$e\left(\frac{29}{64}\right)$	$e\left(\frac{23}{32}\right)$	$e\left(\frac{33}{64}\right)$	$e\left(\frac{19}{64}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{27}{64}\right)$	$e\left(\frac{11}{32}\right)$	$e\left(\frac{29}{32}\right)$
$\chi_{3584}(59,\cdot)$	3584.ck	384	yes	$1$	$1$	$e\left(\frac{313}{384}\right)$	$e\left(\frac{179}{384}\right)$	$e\left(\frac{121}{192}\right)$	$e\left(\frac{367}{384}\right)$	$e\left(\frac{95}{128}\right)$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{85}{96}\right)$	$e\left(\frac{341}{384}\right)$	$e\left(\frac{133}{192}\right)$	$e\left(\frac{179}{192}\right)$
$\chi_{3584}(61,\cdot)$	3584.ci	384	yes	$-1$	$1$	$e\left(\frac{203}{384}\right)$	$e\left(\frac{313}{384}\right)$	$e\left(\frac{11}{192}\right)$	$e\left(\frac{173}{384}\right)$	$e\left(\frac{61}{128}\right)$	$e\left(\frac{11}{32}\right)$	$e\left(\frac{95}{96}\right)$	$e\left(\frac{31}{384}\right)$	$e\left(\frac{143}{192}\right)$	$e\left(\frac{121}{192}\right)$
$\chi_{3584}(65,\cdot)$	3584.bh	24	no	$1$	$1$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{1}{8}\right)$	$-1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{12}\right)$
$\chi_{3584}(67,\cdot)$	3584.cj	384	yes	$-1$	$1$	$e\left(\frac{235}{384}\right)$	$e\left(\frac{89}{384}\right)$	$e\left(\frac{43}{192}\right)$	$e\left(\frac{205}{384}\right)$	$e\left(\frac{93}{128}\right)$	$e\left(\frac{27}{32}\right)$	$e\left(\frac{79}{96}\right)$	$e\left(\frac{191}{384}\right)$	$e\left(\frac{79}{192}\right)$	$e\left(\frac{89}{192}\right)$
$\chi_{3584}(69,\cdot)$	3584.cd	128	yes	$-1$	$1$	$e\left(\frac{115}{128}\right)$	$e\left(\frac{113}{128}\right)$	$e\left(\frac{51}{64}\right)$	$e\left(\frac{69}{128}\right)$	$e\left(\frac{127}{128}\right)$	$e\left(\frac{25}{32}\right)$	$e\left(\frac{7}{32}\right)$	$e\left(\frac{39}{128}\right)$	$e\left(\frac{23}{64}\right)$	$e\left(\frac{49}{64}\right)$
$\chi_{3584}(71,\cdot)$	3584.bu	64	no	$-1$	$1$	$e\left(\frac{7}{64}\right)$	$e\left(\frac{45}{64}\right)$	$e\left(\frac{7}{32}\right)$	$e\left(\frac{17}{64}\right)$	$e\left(\frac{3}{64}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{43}{64}\right)$	$e\left(\frac{11}{32}\right)$	$e\left(\frac{13}{32}\right)$
$\chi_{3584}(73,\cdot)$	3584.ce	192	no	$-1$	$1$	$e\left(\frac{179}{192}\right)$	$e\left(\frac{49}{192}\right)$	$e\left(\frac{83}{96}\right)$	$e\left(\frac{101}{192}\right)$	$e\left(\frac{21}{64}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{103}{192}\right)$	$e\left(\frac{23}{96}\right)$	$e\left(\frac{49}{96}\right)$

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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	$3584$
Structure	\(C_{2}\times C_{2}\times C_{384}\)
Order	$1536$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(5\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(23\)	\(25\)
\(\chi_{3584}(1,\cdot)\)	3584.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{3584}(3,\cdot)\)	3584.ck	384	yes	\(1\)	\(1\)	\(e\left(\frac{91}{384}\right)\)	\(e\left(\frac{41}{384}\right)\)	\(e\left(\frac{91}{192}\right)\)	\(e\left(\frac{157}{384}\right)\)	\(e\left(\frac{109}{128}\right)\)	\(e\left(\frac{11}{32}\right)\)	\(e\left(\frac{79}{96}\right)\)	\(e\left(\frac{239}{384}\right)\)	\(e\left(\frac{127}{192}\right)\)	\(e\left(\frac{41}{192}\right)\)
\(\chi_{3584}(5,\cdot)\)	3584.ci	384	yes	\(-1\)	\(1\)	\(e\left(\frac{41}{384}\right)\)	\(e\left(\frac{67}{384}\right)\)	\(e\left(\frac{41}{192}\right)\)	\(e\left(\frac{383}{384}\right)\)	\(e\left(\frac{47}{128}\right)\)	\(e\left(\frac{9}{32}\right)\)	\(e\left(\frac{5}{96}\right)\)	\(e\left(\frac{133}{384}\right)\)	\(e\left(\frac{149}{192}\right)\)	\(e\left(\frac{67}{192}\right)\)
\(\chi_{3584}(9,\cdot)\)	3584.cf	192	no	\(1\)	\(1\)	\(e\left(\frac{91}{192}\right)\)	\(e\left(\frac{41}{192}\right)\)	\(e\left(\frac{91}{96}\right)\)	\(e\left(\frac{157}{192}\right)\)	\(e\left(\frac{45}{64}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{47}{192}\right)\)	\(e\left(\frac{31}{96}\right)\)	\(e\left(\frac{41}{96}\right)\)
\(\chi_{3584}(11,\cdot)\)	3584.cj	384	yes	\(-1\)	\(1\)	\(e\left(\frac{157}{384}\right)\)	\(e\left(\frac{383}{384}\right)\)	\(e\left(\frac{157}{192}\right)\)	\(e\left(\frac{235}{384}\right)\)	\(e\left(\frac{91}{128}\right)\)	\(e\left(\frac{13}{32}\right)\)	\(e\left(\frac{25}{96}\right)\)	\(e\left(\frac{41}{384}\right)\)	\(e\left(\frac{25}{192}\right)\)	\(e\left(\frac{191}{192}\right)\)
\(\chi_{3584}(13,\cdot)\)	3584.cd	128	yes	\(-1\)	\(1\)	\(e\left(\frac{109}{128}\right)\)	\(e\left(\frac{47}{128}\right)\)	\(e\left(\frac{45}{64}\right)\)	\(e\left(\frac{91}{128}\right)\)	\(e\left(\frac{97}{128}\right)\)	\(e\left(\frac{7}{32}\right)\)	\(e\left(\frac{25}{32}\right)\)	\(e\left(\frac{57}{128}\right)\)	\(e\left(\frac{9}{64}\right)\)	\(e\left(\frac{47}{64}\right)\)
\(\chi_{3584}(15,\cdot)\)	3584.bl	32	no	\(-1\)	\(1\)	\(e\left(\frac{11}{32}\right)\)	\(e\left(\frac{9}{32}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{13}{32}\right)\)	\(e\left(\frac{7}{32}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{31}{32}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)
\(\chi_{3584}(17,\cdot)\)	3584.bz	96	no	\(-1\)	\(1\)	\(e\left(\frac{79}{96}\right)\)	\(e\left(\frac{5}{96}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{25}{96}\right)\)	\(e\left(\frac{25}{32}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{83}{96}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{5}{48}\right)\)
\(\chi_{3584}(19,\cdot)\)	3584.ck	384	yes	\(1\)	\(1\)	\(e\left(\frac{239}{384}\right)\)	\(e\left(\frac{133}{384}\right)\)	\(e\left(\frac{47}{192}\right)\)	\(e\left(\frac{41}{384}\right)\)	\(e\left(\frac{57}{128}\right)\)	\(e\left(\frac{31}{32}\right)\)	\(e\left(\frac{83}{96}\right)\)	\(e\left(\frac{307}{384}\right)\)	\(e\left(\frac{131}{192}\right)\)	\(e\left(\frac{133}{192}\right)\)
\(\chi_{3584}(23,\cdot)\)	3584.ch	192	no	\(-1\)	\(1\)	\(e\left(\frac{127}{192}\right)\)	\(e\left(\frac{149}{192}\right)\)	\(e\left(\frac{31}{96}\right)\)	\(e\left(\frac{25}{192}\right)\)	\(e\left(\frac{9}{64}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{131}{192}\right)\)	\(e\left(\frac{67}{96}\right)\)	\(e\left(\frac{53}{96}\right)\)
\(\chi_{3584}(25,\cdot)\)	3584.cf	192	no	\(1\)	\(1\)	\(e\left(\frac{41}{192}\right)\)	\(e\left(\frac{67}{192}\right)\)	\(e\left(\frac{41}{96}\right)\)	\(e\left(\frac{191}{192}\right)\)	\(e\left(\frac{47}{64}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{133}{192}\right)\)	\(e\left(\frac{53}{96}\right)\)	\(e\left(\frac{67}{96}\right)\)
\(\chi_{3584}(27,\cdot)\)	3584.cb	128	yes	\(1\)	\(1\)	\(e\left(\frac{91}{128}\right)\)	\(e\left(\frac{41}{128}\right)\)	\(e\left(\frac{27}{64}\right)\)	\(e\left(\frac{29}{128}\right)\)	\(e\left(\frac{71}{128}\right)\)	\(e\left(\frac{1}{32}\right)\)	\(e\left(\frac{15}{32}\right)\)	\(e\left(\frac{111}{128}\right)\)	\(e\left(\frac{63}{64}\right)\)	\(e\left(\frac{41}{64}\right)\)
\(\chi_{3584}(29,\cdot)\)	3584.ca	128	no	\(1\)	\(1\)	\(e\left(\frac{81}{128}\right)\)	\(e\left(\frac{123}{128}\right)\)	\(e\left(\frac{17}{64}\right)\)	\(e\left(\frac{87}{128}\right)\)	\(e\left(\frac{85}{128}\right)\)	\(e\left(\frac{19}{32}\right)\)	\(e\left(\frac{29}{32}\right)\)	\(e\left(\frac{13}{128}\right)\)	\(e\left(\frac{29}{64}\right)\)	\(e\left(\frac{59}{64}\right)\)
\(\chi_{3584}(31,\cdot)\)	3584.bq	48	no	\(1\)	\(1\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(-i\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{19}{24}\right)\)
\(\chi_{3584}(33,\cdot)\)	3584.bo	48	no	\(-1\)	\(1\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(-i\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{5}{24}\right)\)
\(\chi_{3584}(37,\cdot)\)	3584.cl	384	yes	\(1\)	\(1\)	\(e\left(\frac{65}{384}\right)\)	\(e\left(\frac{331}{384}\right)\)	\(e\left(\frac{65}{192}\right)\)	\(e\left(\frac{359}{384}\right)\)	\(e\left(\frac{87}{128}\right)\)	\(e\left(\frac{1}{32}\right)\)	\(e\left(\frac{77}{96}\right)\)	\(e\left(\frac{61}{384}\right)\)	\(e\left(\frac{77}{192}\right)\)	\(e\left(\frac{139}{192}\right)\)
\(\chi_{3584}(39,\cdot)\)	3584.ch	192	no	\(-1\)	\(1\)	\(e\left(\frac{17}{192}\right)\)	\(e\left(\frac{91}{192}\right)\)	\(e\left(\frac{17}{96}\right)\)	\(e\left(\frac{23}{192}\right)\)	\(e\left(\frac{39}{64}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{13}{192}\right)\)	\(e\left(\frac{77}{96}\right)\)	\(e\left(\frac{91}{96}\right)\)
\(\chi_{3584}(41,\cdot)\)	3584.bt	64	no	\(-1\)	\(1\)	\(e\left(\frac{61}{64}\right)\)	\(e\left(\frac{31}{64}\right)\)	\(e\left(\frac{29}{32}\right)\)	\(e\left(\frac{43}{64}\right)\)	\(e\left(\frac{49}{64}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{9}{64}\right)\)	\(e\left(\frac{25}{32}\right)\)	\(e\left(\frac{31}{32}\right)\)
\(\chi_{3584}(43,\cdot)\)	3584.cc	128	no	\(-1\)	\(1\)	\(e\left(\frac{23}{128}\right)\)	\(e\left(\frac{61}{128}\right)\)	\(e\left(\frac{23}{64}\right)\)	\(e\left(\frac{1}{128}\right)\)	\(e\left(\frac{115}{128}\right)\)	\(e\left(\frac{21}{32}\right)\)	\(e\left(\frac{11}{32}\right)\)	\(e\left(\frac{59}{128}\right)\)	\(e\left(\frac{11}{64}\right)\)	\(e\left(\frac{61}{64}\right)\)
\(\chi_{3584}(45,\cdot)\)	3584.ci	384	yes	\(-1\)	\(1\)	\(e\left(\frac{223}{384}\right)\)	\(e\left(\frac{149}{384}\right)\)	\(e\left(\frac{31}{192}\right)\)	\(e\left(\frac{313}{384}\right)\)	\(e\left(\frac{9}{128}\right)\)	\(e\left(\frac{31}{32}\right)\)	\(e\left(\frac{67}{96}\right)\)	\(e\left(\frac{227}{384}\right)\)	\(e\left(\frac{19}{192}\right)\)	\(e\left(\frac{149}{192}\right)\)
\(\chi_{3584}(47,\cdot)\)	3584.bx	96	no	\(1\)	\(1\)	\(e\left(\frac{35}{96}\right)\)	\(e\left(\frac{49}{96}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{5}{96}\right)\)	\(e\left(\frac{21}{32}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{55}{96}\right)\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{1}{48}\right)\)
\(\chi_{3584}(51,\cdot)\)	3584.cj	384	yes	\(-1\)	\(1\)	\(e\left(\frac{23}{384}\right)\)	\(e\left(\frac{61}{384}\right)\)	\(e\left(\frac{23}{192}\right)\)	\(e\left(\frac{257}{384}\right)\)	\(e\left(\frac{81}{128}\right)\)	\(e\left(\frac{7}{32}\right)\)	\(e\left(\frac{11}{96}\right)\)	\(e\left(\frac{187}{384}\right)\)	\(e\left(\frac{11}{192}\right)\)	\(e\left(\frac{61}{192}\right)\)
\(\chi_{3584}(53,\cdot)\)	3584.cl	384	yes	\(1\)	\(1\)	\(e\left(\frac{13}{384}\right)\)	\(e\left(\frac{143}{384}\right)\)	\(e\left(\frac{13}{192}\right)\)	\(e\left(\frac{379}{384}\right)\)	\(e\left(\frac{43}{128}\right)\)	\(e\left(\frac{13}{32}\right)\)	\(e\left(\frac{73}{96}\right)\)	\(e\left(\frac{89}{384}\right)\)	\(e\left(\frac{169}{192}\right)\)	\(e\left(\frac{143}{192}\right)\)
\(\chi_{3584}(55,\cdot)\)	3584.bv	64	no	\(1\)	\(1\)	\(e\left(\frac{33}{64}\right)\)	\(e\left(\frac{11}{64}\right)\)	\(e\left(\frac{1}{32}\right)\)	\(e\left(\frac{39}{64}\right)\)	\(e\left(\frac{5}{64}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{29}{64}\right)\)	\(e\left(\frac{29}{32}\right)\)	\(e\left(\frac{11}{32}\right)\)
\(\chi_{3584}(57,\cdot)\)	3584.bs	64	no	\(1\)	\(1\)	\(e\left(\frac{55}{64}\right)\)	\(e\left(\frac{29}{64}\right)\)	\(e\left(\frac{23}{32}\right)\)	\(e\left(\frac{33}{64}\right)\)	\(e\left(\frac{19}{64}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{27}{64}\right)\)	\(e\left(\frac{11}{32}\right)\)	\(e\left(\frac{29}{32}\right)\)
\(\chi_{3584}(59,\cdot)\)	3584.ck	384	yes	\(1\)	\(1\)	\(e\left(\frac{313}{384}\right)\)	\(e\left(\frac{179}{384}\right)\)	\(e\left(\frac{121}{192}\right)\)	\(e\left(\frac{367}{384}\right)\)	\(e\left(\frac{95}{128}\right)\)	\(e\left(\frac{9}{32}\right)\)	\(e\left(\frac{85}{96}\right)\)	\(e\left(\frac{341}{384}\right)\)	\(e\left(\frac{133}{192}\right)\)	\(e\left(\frac{179}{192}\right)\)
\(\chi_{3584}(61,\cdot)\)	3584.ci	384	yes	\(-1\)	\(1\)	\(e\left(\frac{203}{384}\right)\)	\(e\left(\frac{313}{384}\right)\)	\(e\left(\frac{11}{192}\right)\)	\(e\left(\frac{173}{384}\right)\)	\(e\left(\frac{61}{128}\right)\)	\(e\left(\frac{11}{32}\right)\)	\(e\left(\frac{95}{96}\right)\)	\(e\left(\frac{31}{384}\right)\)	\(e\left(\frac{143}{192}\right)\)	\(e\left(\frac{121}{192}\right)\)
\(\chi_{3584}(65,\cdot)\)	3584.bh	24	no	\(1\)	\(1\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)
\(\chi_{3584}(67,\cdot)\)	3584.cj	384	yes	\(-1\)	\(1\)	\(e\left(\frac{235}{384}\right)\)	\(e\left(\frac{89}{384}\right)\)	\(e\left(\frac{43}{192}\right)\)	\(e\left(\frac{205}{384}\right)\)	\(e\left(\frac{93}{128}\right)\)	\(e\left(\frac{27}{32}\right)\)	\(e\left(\frac{79}{96}\right)\)	\(e\left(\frac{191}{384}\right)\)	\(e\left(\frac{79}{192}\right)\)	\(e\left(\frac{89}{192}\right)\)
\(\chi_{3584}(69,\cdot)\)	3584.cd	128	yes	\(-1\)	\(1\)	\(e\left(\frac{115}{128}\right)\)	\(e\left(\frac{113}{128}\right)\)	\(e\left(\frac{51}{64}\right)\)	\(e\left(\frac{69}{128}\right)\)	\(e\left(\frac{127}{128}\right)\)	\(e\left(\frac{25}{32}\right)\)	\(e\left(\frac{7}{32}\right)\)	\(e\left(\frac{39}{128}\right)\)	\(e\left(\frac{23}{64}\right)\)	\(e\left(\frac{49}{64}\right)\)
\(\chi_{3584}(71,\cdot)\)	3584.bu	64	no	\(-1\)	\(1\)	\(e\left(\frac{7}{64}\right)\)	\(e\left(\frac{45}{64}\right)\)	\(e\left(\frac{7}{32}\right)\)	\(e\left(\frac{17}{64}\right)\)	\(e\left(\frac{3}{64}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{43}{64}\right)\)	\(e\left(\frac{11}{32}\right)\)	\(e\left(\frac{13}{32}\right)\)
\(\chi_{3584}(73,\cdot)\)	3584.ce	192	no	\(-1\)	\(1\)	\(e\left(\frac{179}{192}\right)\)	\(e\left(\frac{49}{192}\right)\)	\(e\left(\frac{83}{96}\right)\)	\(e\left(\frac{101}{192}\right)\)	\(e\left(\frac{21}{64}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{103}{192}\right)\)	\(e\left(\frac{23}{96}\right)\)	\(e\left(\frac{49}{96}\right)\)

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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.