LMFDB - Group of Dirichlet characters of modulus 4864

sage:H = DirichletGroup(4864)

pari:g = idealstar(,4864,2)

Character group

sage:G.order() pari:g.no
Order	=	2304
sage:H.invariants() pari:g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{576}$
sage:H.gens() pari:g.gen
Generators	=	$\chi_{4864}(3839,\cdot)$, $\chi_{4864}(2053,\cdot)$, $\chi_{4864}(4353,\cdot)$

First 32 of 2304 characters

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

Character	Orbit	Order	Primitive	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$17$	$21$	$23$
$\chi_{4864}(1,\cdot)$	4864.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{4864}(3,\cdot)$	4864.dd	576	yes	$1$	$1$	$e\left(\frac{17}{576}\right)$	$e\left(\frac{59}{576}\right)$	$e\left(\frac{29}{96}\right)$	$e\left(\frac{17}{288}\right)$	$e\left(\frac{125}{192}\right)$	$e\left(\frac{181}{576}\right)$	$e\left(\frac{19}{144}\right)$	$e\left(\frac{77}{144}\right)$	$e\left(\frac{191}{576}\right)$	$e\left(\frac{173}{288}\right)$
$\chi_{4864}(5,\cdot)$	4864.dc	576	yes	$1$	$1$	$e\left(\frac{59}{576}\right)$	$e\left(\frac{137}{576}\right)$	$e\left(\frac{47}{96}\right)$	$e\left(\frac{59}{288}\right)$	$e\left(\frac{191}{192}\right)$	$e\left(\frac{103}{576}\right)$	$e\left(\frac{49}{144}\right)$	$e\left(\frac{47}{144}\right)$	$e\left(\frac{341}{576}\right)$	$e\left(\frac{287}{288}\right)$
$\chi_{4864}(7,\cdot)$	4864.cm	96	no	$-1$	$1$	$e\left(\frac{29}{96}\right)$	$e\left(\frac{47}{96}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{25}{32}\right)$	$e\left(\frac{1}{96}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{35}{96}\right)$	$e\left(\frac{17}{48}\right)$
$\chi_{4864}(9,\cdot)$	4864.da	288	no	$1$	$1$	$e\left(\frac{17}{288}\right)$	$e\left(\frac{59}{288}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{17}{144}\right)$	$e\left(\frac{29}{96}\right)$	$e\left(\frac{181}{288}\right)$	$e\left(\frac{19}{72}\right)$	$e\left(\frac{5}{72}\right)$	$e\left(\frac{191}{288}\right)$	$e\left(\frac{29}{144}\right)$
$\chi_{4864}(11,\cdot)$	4864.cv	192	yes	$-1$	$1$	$e\left(\frac{125}{192}\right)$	$e\left(\frac{191}{192}\right)$	$e\left(\frac{25}{32}\right)$	$e\left(\frac{29}{96}\right)$	$e\left(\frac{25}{64}\right)$	$e\left(\frac{145}{192}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{83}{192}\right)$	$e\left(\frac{41}{96}\right)$
$\chi_{4864}(13,\cdot)$	4864.de	576	yes	$-1$	$1$	$e\left(\frac{181}{576}\right)$	$e\left(\frac{103}{576}\right)$	$e\left(\frac{1}{96}\right)$	$e\left(\frac{181}{288}\right)$	$e\left(\frac{145}{192}\right)$	$e\left(\frac{521}{576}\right)$	$e\left(\frac{71}{144}\right)$	$e\left(\frac{49}{144}\right)$	$e\left(\frac{187}{576}\right)$	$e\left(\frac{241}{288}\right)$
$\chi_{4864}(15,\cdot)$	4864.ct	144	no	$1$	$1$	$e\left(\frac{19}{144}\right)$	$e\left(\frac{49}{144}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{19}{72}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{71}{144}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{133}{144}\right)$	$e\left(\frac{43}{72}\right)$
$\chi_{4864}(17,\cdot)$	4864.cs	144	no	$1$	$1$	$e\left(\frac{77}{144}\right)$	$e\left(\frac{47}{144}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{5}{72}\right)$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{49}{144}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{35}{144}\right)$	$e\left(\frac{17}{72}\right)$
$\chi_{4864}(21,\cdot)$	4864.de	576	yes	$-1$	$1$	$e\left(\frac{191}{576}\right)$	$e\left(\frac{341}{576}\right)$	$e\left(\frac{35}{96}\right)$	$e\left(\frac{191}{288}\right)$	$e\left(\frac{83}{192}\right)$	$e\left(\frac{187}{576}\right)$	$e\left(\frac{133}{144}\right)$	$e\left(\frac{35}{144}\right)$	$e\left(\frac{401}{576}\right)$	$e\left(\frac{275}{288}\right)$
$\chi_{4864}(23,\cdot)$	4864.db	288	no	$-1$	$1$	$e\left(\frac{173}{288}\right)$	$e\left(\frac{287}{288}\right)$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{29}{144}\right)$	$e\left(\frac{41}{96}\right)$	$e\left(\frac{241}{288}\right)$	$e\left(\frac{43}{72}\right)$	$e\left(\frac{17}{72}\right)$	$e\left(\frac{275}{288}\right)$	$e\left(\frac{113}{144}\right)$
$\chi_{4864}(25,\cdot)$	4864.da	288	no	$1$	$1$	$e\left(\frac{59}{288}\right)$	$e\left(\frac{137}{288}\right)$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{59}{144}\right)$	$e\left(\frac{95}{96}\right)$	$e\left(\frac{103}{288}\right)$	$e\left(\frac{49}{72}\right)$	$e\left(\frac{47}{72}\right)$	$e\left(\frac{53}{288}\right)$	$e\left(\frac{143}{144}\right)$
$\chi_{4864}(27,\cdot)$	4864.cw	192	yes	$1$	$1$	$e\left(\frac{17}{192}\right)$	$e\left(\frac{59}{192}\right)$	$e\left(\frac{29}{32}\right)$	$e\left(\frac{17}{96}\right)$	$e\left(\frac{61}{64}\right)$	$e\left(\frac{181}{192}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{191}{192}\right)$	$e\left(\frac{77}{96}\right)$
$\chi_{4864}(29,\cdot)$	4864.de	576	yes	$-1$	$1$	$e\left(\frac{313}{576}\right)$	$e\left(\frac{19}{576}\right)$	$e\left(\frac{85}{96}\right)$	$e\left(\frac{25}{288}\right)$	$e\left(\frac{133}{192}\right)$	$e\left(\frac{29}{576}\right)$	$e\left(\frac{83}{144}\right)$	$e\left(\frac{37}{144}\right)$	$e\left(\frac{247}{576}\right)$	$e\left(\frac{229}{288}\right)$
$\chi_{4864}(31,\cdot)$	4864.br	24	no	$1$	$1$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{11}{24}\right)$	$-i$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{11}{12}\right)$
$\chi_{4864}(33,\cdot)$	4864.cl	72	no	$-1$	$1$	$e\left(\frac{49}{72}\right)$	$e\left(\frac{7}{72}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{5}{72}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{55}{72}\right)$	$e\left(\frac{1}{36}\right)$
$\chi_{4864}(35,\cdot)$	4864.df	576	yes	$-1$	$1$	$e\left(\frac{233}{576}\right)$	$e\left(\frac{419}{576}\right)$	$e\left(\frac{53}{96}\right)$	$e\left(\frac{233}{288}\right)$	$e\left(\frac{149}{192}\right)$	$e\left(\frac{109}{576}\right)$	$e\left(\frac{19}{144}\right)$	$e\left(\frac{5}{144}\right)$	$e\left(\frac{551}{576}\right)$	$e\left(\frac{101}{288}\right)$
$\chi_{4864}(37,\cdot)$	4864.ch	64	yes	$-1$	$1$	$e\left(\frac{11}{64}\right)$	$e\left(\frac{25}{64}\right)$	$e\left(\frac{29}{32}\right)$	$e\left(\frac{11}{32}\right)$	$e\left(\frac{13}{64}\right)$	$e\left(\frac{55}{64}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{5}{64}\right)$	$e\left(\frac{15}{32}\right)$
$\chi_{4864}(39,\cdot)$	4864.bu	32	no	$-1$	$1$	$e\left(\frac{11}{32}\right)$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{7}{32}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{21}{32}\right)$	$e\left(\frac{7}{16}\right)$
$\chi_{4864}(41,\cdot)$	4864.cy	288	no	$-1$	$1$	$e\left(\frac{85}{288}\right)$	$e\left(\frac{151}{288}\right)$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{85}{144}\right)$	$e\left(\frac{1}{96}\right)$	$e\left(\frac{41}{288}\right)$	$e\left(\frac{59}{72}\right)$	$e\left(\frac{25}{72}\right)$	$e\left(\frac{91}{288}\right)$	$e\left(\frac{1}{144}\right)$
$\chi_{4864}(43,\cdot)$	4864.df	576	yes	$-1$	$1$	$e\left(\frac{239}{576}\right)$	$e\left(\frac{101}{576}\right)$	$e\left(\frac{35}{96}\right)$	$e\left(\frac{239}{288}\right)$	$e\left(\frac{35}{192}\right)$	$e\left(\frac{139}{576}\right)$	$e\left(\frac{85}{144}\right)$	$e\left(\frac{83}{144}\right)$	$e\left(\frac{449}{576}\right)$	$e\left(\frac{179}{288}\right)$
$\chi_{4864}(45,\cdot)$	4864.cx	192	yes	$1$	$1$	$e\left(\frac{31}{192}\right)$	$e\left(\frac{85}{192}\right)$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{31}{96}\right)$	$e\left(\frac{19}{64}\right)$	$e\left(\frac{155}{192}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{49}{192}\right)$	$e\left(\frac{19}{96}\right)$
$\chi_{4864}(47,\cdot)$	4864.cq	144	no	$-1$	$1$	$e\left(\frac{49}{144}\right)$	$e\left(\frac{115}{144}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{49}{72}\right)$	$e\left(\frac{13}{48}\right)$	$e\left(\frac{77}{144}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{55}{144}\right)$	$e\left(\frac{1}{72}\right)$
$\chi_{4864}(49,\cdot)$	4864.cb	48	no	$1$	$1$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{17}{24}\right)$
$\chi_{4864}(51,\cdot)$	4864.dd	576	yes	$1$	$1$	$e\left(\frac{325}{576}\right)$	$e\left(\frac{247}{576}\right)$	$e\left(\frac{1}{96}\right)$	$e\left(\frac{37}{288}\right)$	$e\left(\frac{97}{192}\right)$	$e\left(\frac{377}{576}\right)$	$e\left(\frac{143}{144}\right)$	$e\left(\frac{49}{144}\right)$	$e\left(\frac{331}{576}\right)$	$e\left(\frac{241}{288}\right)$
$\chi_{4864}(53,\cdot)$	4864.de	576	yes	$-1$	$1$	$e\left(\frac{391}{576}\right)$	$e\left(\frac{493}{576}\right)$	$e\left(\frac{43}{96}\right)$	$e\left(\frac{103}{288}\right)$	$e\left(\frac{187}{192}\right)$	$e\left(\frac{419}{576}\right)$	$e\left(\frac{77}{144}\right)$	$e\left(\frac{43}{144}\right)$	$e\left(\frac{73}{576}\right)$	$e\left(\frac{91}{288}\right)$
$\chi_{4864}(55,\cdot)$	4864.db	288	no	$-1$	$1$	$e\left(\frac{217}{288}\right)$	$e\left(\frac{67}{288}\right)$	$e\left(\frac{13}{48}\right)$	$e\left(\frac{73}{144}\right)$	$e\left(\frac{37}{96}\right)$	$e\left(\frac{269}{288}\right)$	$e\left(\frac{71}{72}\right)$	$e\left(\frac{13}{72}\right)$	$e\left(\frac{7}{288}\right)$	$e\left(\frac{61}{144}\right)$
$\chi_{4864}(59,\cdot)$	4864.dd	576	yes	$1$	$1$	$e\left(\frac{299}{576}\right)$	$e\left(\frac{89}{576}\right)$	$e\left(\frac{47}{96}\right)$	$e\left(\frac{11}{288}\right)$	$e\left(\frac{143}{192}\right)$	$e\left(\frac{439}{576}\right)$	$e\left(\frac{97}{144}\right)$	$e\left(\frac{143}{144}\right)$	$e\left(\frac{5}{576}\right)$	$e\left(\frac{95}{288}\right)$
$\chi_{4864}(61,\cdot)$	4864.dc	576	yes	$1$	$1$	$e\left(\frac{481}{576}\right)$	$e\left(\frac{43}{576}\right)$	$e\left(\frac{61}{96}\right)$	$e\left(\frac{193}{288}\right)$	$e\left(\frac{109}{192}\right)$	$e\left(\frac{293}{576}\right)$	$e\left(\frac{131}{144}\right)$	$e\left(\frac{61}{144}\right)$	$e\left(\frac{271}{576}\right)$	$e\left(\frac{109}{288}\right)$
$\chi_{4864}(63,\cdot)$	4864.bx	36	no	$-1$	$1$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{5}{9}\right)$
$\chi_{4864}(65,\cdot)$	4864.ba	12	no	$-1$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{12}\right)$	$-1$	$e\left(\frac{5}{6}\right)$	$-i$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{4864}(67,\cdot)$	4864.dd	576	yes	$1$	$1$	$e\left(\frac{385}{576}\right)$	$e\left(\frac{523}{576}\right)$	$e\left(\frac{13}{96}\right)$	$e\left(\frac{97}{288}\right)$	$e\left(\frac{109}{192}\right)$	$e\left(\frac{101}{576}\right)$	$e\left(\frac{83}{144}\right)$	$e\left(\frac{109}{144}\right)$	$e\left(\frac{463}{576}\right)$	$e\left(\frac{157}{288}\right)$

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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 $\F_{q}$
Belyi maps

Modulus	$4864$
Structure	\(C_{2}\times C_{2}\times C_{576}\)
Order	$2304$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(21\)	\(23\)
\(\chi_{4864}(1,\cdot)\)	4864.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{4864}(3,\cdot)\)	4864.dd	576	yes	\(1\)	\(1\)	\(e\left(\frac{17}{576}\right)\)	\(e\left(\frac{59}{576}\right)\)	\(e\left(\frac{29}{96}\right)\)	\(e\left(\frac{17}{288}\right)\)	\(e\left(\frac{125}{192}\right)\)	\(e\left(\frac{181}{576}\right)\)	\(e\left(\frac{19}{144}\right)\)	\(e\left(\frac{77}{144}\right)\)	\(e\left(\frac{191}{576}\right)\)	\(e\left(\frac{173}{288}\right)\)
\(\chi_{4864}(5,\cdot)\)	4864.dc	576	yes	\(1\)	\(1\)	\(e\left(\frac{59}{576}\right)\)	\(e\left(\frac{137}{576}\right)\)	\(e\left(\frac{47}{96}\right)\)	\(e\left(\frac{59}{288}\right)\)	\(e\left(\frac{191}{192}\right)\)	\(e\left(\frac{103}{576}\right)\)	\(e\left(\frac{49}{144}\right)\)	\(e\left(\frac{47}{144}\right)\)	\(e\left(\frac{341}{576}\right)\)	\(e\left(\frac{287}{288}\right)\)
\(\chi_{4864}(7,\cdot)\)	4864.cm	96	no	\(-1\)	\(1\)	\(e\left(\frac{29}{96}\right)\)	\(e\left(\frac{47}{96}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{25}{32}\right)\)	\(e\left(\frac{1}{96}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{35}{96}\right)\)	\(e\left(\frac{17}{48}\right)\)
\(\chi_{4864}(9,\cdot)\)	4864.da	288	no	\(1\)	\(1\)	\(e\left(\frac{17}{288}\right)\)	\(e\left(\frac{59}{288}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{17}{144}\right)\)	\(e\left(\frac{29}{96}\right)\)	\(e\left(\frac{181}{288}\right)\)	\(e\left(\frac{19}{72}\right)\)	\(e\left(\frac{5}{72}\right)\)	\(e\left(\frac{191}{288}\right)\)	\(e\left(\frac{29}{144}\right)\)
\(\chi_{4864}(11,\cdot)\)	4864.cv	192	yes	\(-1\)	\(1\)	\(e\left(\frac{125}{192}\right)\)	\(e\left(\frac{191}{192}\right)\)	\(e\left(\frac{25}{32}\right)\)	\(e\left(\frac{29}{96}\right)\)	\(e\left(\frac{25}{64}\right)\)	\(e\left(\frac{145}{192}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{83}{192}\right)\)	\(e\left(\frac{41}{96}\right)\)
\(\chi_{4864}(13,\cdot)\)	4864.de	576	yes	\(-1\)	\(1\)	\(e\left(\frac{181}{576}\right)\)	\(e\left(\frac{103}{576}\right)\)	\(e\left(\frac{1}{96}\right)\)	\(e\left(\frac{181}{288}\right)\)	\(e\left(\frac{145}{192}\right)\)	\(e\left(\frac{521}{576}\right)\)	\(e\left(\frac{71}{144}\right)\)	\(e\left(\frac{49}{144}\right)\)	\(e\left(\frac{187}{576}\right)\)	\(e\left(\frac{241}{288}\right)\)
\(\chi_{4864}(15,\cdot)\)	4864.ct	144	no	\(1\)	\(1\)	\(e\left(\frac{19}{144}\right)\)	\(e\left(\frac{49}{144}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{19}{72}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{71}{144}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{133}{144}\right)\)	\(e\left(\frac{43}{72}\right)\)
\(\chi_{4864}(17,\cdot)\)	4864.cs	144	no	\(1\)	\(1\)	\(e\left(\frac{77}{144}\right)\)	\(e\left(\frac{47}{144}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{5}{72}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{49}{144}\right)\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{35}{144}\right)\)	\(e\left(\frac{17}{72}\right)\)
\(\chi_{4864}(21,\cdot)\)	4864.de	576	yes	\(-1\)	\(1\)	\(e\left(\frac{191}{576}\right)\)	\(e\left(\frac{341}{576}\right)\)	\(e\left(\frac{35}{96}\right)\)	\(e\left(\frac{191}{288}\right)\)	\(e\left(\frac{83}{192}\right)\)	\(e\left(\frac{187}{576}\right)\)	\(e\left(\frac{133}{144}\right)\)	\(e\left(\frac{35}{144}\right)\)	\(e\left(\frac{401}{576}\right)\)	\(e\left(\frac{275}{288}\right)\)
\(\chi_{4864}(23,\cdot)\)	4864.db	288	no	\(-1\)	\(1\)	\(e\left(\frac{173}{288}\right)\)	\(e\left(\frac{287}{288}\right)\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{29}{144}\right)\)	\(e\left(\frac{41}{96}\right)\)	\(e\left(\frac{241}{288}\right)\)	\(e\left(\frac{43}{72}\right)\)	\(e\left(\frac{17}{72}\right)\)	\(e\left(\frac{275}{288}\right)\)	\(e\left(\frac{113}{144}\right)\)
\(\chi_{4864}(25,\cdot)\)	4864.da	288	no	\(1\)	\(1\)	\(e\left(\frac{59}{288}\right)\)	\(e\left(\frac{137}{288}\right)\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{59}{144}\right)\)	\(e\left(\frac{95}{96}\right)\)	\(e\left(\frac{103}{288}\right)\)	\(e\left(\frac{49}{72}\right)\)	\(e\left(\frac{47}{72}\right)\)	\(e\left(\frac{53}{288}\right)\)	\(e\left(\frac{143}{144}\right)\)
\(\chi_{4864}(27,\cdot)\)	4864.cw	192	yes	\(1\)	\(1\)	\(e\left(\frac{17}{192}\right)\)	\(e\left(\frac{59}{192}\right)\)	\(e\left(\frac{29}{32}\right)\)	\(e\left(\frac{17}{96}\right)\)	\(e\left(\frac{61}{64}\right)\)	\(e\left(\frac{181}{192}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{191}{192}\right)\)	\(e\left(\frac{77}{96}\right)\)
\(\chi_{4864}(29,\cdot)\)	4864.de	576	yes	\(-1\)	\(1\)	\(e\left(\frac{313}{576}\right)\)	\(e\left(\frac{19}{576}\right)\)	\(e\left(\frac{85}{96}\right)\)	\(e\left(\frac{25}{288}\right)\)	\(e\left(\frac{133}{192}\right)\)	\(e\left(\frac{29}{576}\right)\)	\(e\left(\frac{83}{144}\right)\)	\(e\left(\frac{37}{144}\right)\)	\(e\left(\frac{247}{576}\right)\)	\(e\left(\frac{229}{288}\right)\)
\(\chi_{4864}(31,\cdot)\)	4864.br	24	no	\(1\)	\(1\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(-i\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{11}{12}\right)\)
\(\chi_{4864}(33,\cdot)\)	4864.cl	72	no	\(-1\)	\(1\)	\(e\left(\frac{49}{72}\right)\)	\(e\left(\frac{7}{72}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{5}{72}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{55}{72}\right)\)	\(e\left(\frac{1}{36}\right)\)
\(\chi_{4864}(35,\cdot)\)	4864.df	576	yes	\(-1\)	\(1\)	\(e\left(\frac{233}{576}\right)\)	\(e\left(\frac{419}{576}\right)\)	\(e\left(\frac{53}{96}\right)\)	\(e\left(\frac{233}{288}\right)\)	\(e\left(\frac{149}{192}\right)\)	\(e\left(\frac{109}{576}\right)\)	\(e\left(\frac{19}{144}\right)\)	\(e\left(\frac{5}{144}\right)\)	\(e\left(\frac{551}{576}\right)\)	\(e\left(\frac{101}{288}\right)\)
\(\chi_{4864}(37,\cdot)\)	4864.ch	64	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{64}\right)\)	\(e\left(\frac{25}{64}\right)\)	\(e\left(\frac{29}{32}\right)\)	\(e\left(\frac{11}{32}\right)\)	\(e\left(\frac{13}{64}\right)\)	\(e\left(\frac{55}{64}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{5}{64}\right)\)	\(e\left(\frac{15}{32}\right)\)
\(\chi_{4864}(39,\cdot)\)	4864.bu	32	no	\(-1\)	\(1\)	\(e\left(\frac{11}{32}\right)\)	\(e\left(\frac{9}{32}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{13}{32}\right)\)	\(e\left(\frac{7}{32}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{21}{32}\right)\)	\(e\left(\frac{7}{16}\right)\)
\(\chi_{4864}(41,\cdot)\)	4864.cy	288	no	\(-1\)	\(1\)	\(e\left(\frac{85}{288}\right)\)	\(e\left(\frac{151}{288}\right)\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{85}{144}\right)\)	\(e\left(\frac{1}{96}\right)\)	\(e\left(\frac{41}{288}\right)\)	\(e\left(\frac{59}{72}\right)\)	\(e\left(\frac{25}{72}\right)\)	\(e\left(\frac{91}{288}\right)\)	\(e\left(\frac{1}{144}\right)\)
\(\chi_{4864}(43,\cdot)\)	4864.df	576	yes	\(-1\)	\(1\)	\(e\left(\frac{239}{576}\right)\)	\(e\left(\frac{101}{576}\right)\)	\(e\left(\frac{35}{96}\right)\)	\(e\left(\frac{239}{288}\right)\)	\(e\left(\frac{35}{192}\right)\)	\(e\left(\frac{139}{576}\right)\)	\(e\left(\frac{85}{144}\right)\)	\(e\left(\frac{83}{144}\right)\)	\(e\left(\frac{449}{576}\right)\)	\(e\left(\frac{179}{288}\right)\)
\(\chi_{4864}(45,\cdot)\)	4864.cx	192	yes	\(1\)	\(1\)	\(e\left(\frac{31}{192}\right)\)	\(e\left(\frac{85}{192}\right)\)	\(e\left(\frac{3}{32}\right)\)	\(e\left(\frac{31}{96}\right)\)	\(e\left(\frac{19}{64}\right)\)	\(e\left(\frac{155}{192}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{49}{192}\right)\)	\(e\left(\frac{19}{96}\right)\)
\(\chi_{4864}(47,\cdot)\)	4864.cq	144	no	\(-1\)	\(1\)	\(e\left(\frac{49}{144}\right)\)	\(e\left(\frac{115}{144}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{49}{72}\right)\)	\(e\left(\frac{13}{48}\right)\)	\(e\left(\frac{77}{144}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{55}{144}\right)\)	\(e\left(\frac{1}{72}\right)\)
\(\chi_{4864}(49,\cdot)\)	4864.cb	48	no	\(1\)	\(1\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{17}{24}\right)\)
\(\chi_{4864}(51,\cdot)\)	4864.dd	576	yes	\(1\)	\(1\)	\(e\left(\frac{325}{576}\right)\)	\(e\left(\frac{247}{576}\right)\)	\(e\left(\frac{1}{96}\right)\)	\(e\left(\frac{37}{288}\right)\)	\(e\left(\frac{97}{192}\right)\)	\(e\left(\frac{377}{576}\right)\)	\(e\left(\frac{143}{144}\right)\)	\(e\left(\frac{49}{144}\right)\)	\(e\left(\frac{331}{576}\right)\)	\(e\left(\frac{241}{288}\right)\)
\(\chi_{4864}(53,\cdot)\)	4864.de	576	yes	\(-1\)	\(1\)	\(e\left(\frac{391}{576}\right)\)	\(e\left(\frac{493}{576}\right)\)	\(e\left(\frac{43}{96}\right)\)	\(e\left(\frac{103}{288}\right)\)	\(e\left(\frac{187}{192}\right)\)	\(e\left(\frac{419}{576}\right)\)	\(e\left(\frac{77}{144}\right)\)	\(e\left(\frac{43}{144}\right)\)	\(e\left(\frac{73}{576}\right)\)	\(e\left(\frac{91}{288}\right)\)
\(\chi_{4864}(55,\cdot)\)	4864.db	288	no	\(-1\)	\(1\)	\(e\left(\frac{217}{288}\right)\)	\(e\left(\frac{67}{288}\right)\)	\(e\left(\frac{13}{48}\right)\)	\(e\left(\frac{73}{144}\right)\)	\(e\left(\frac{37}{96}\right)\)	\(e\left(\frac{269}{288}\right)\)	\(e\left(\frac{71}{72}\right)\)	\(e\left(\frac{13}{72}\right)\)	\(e\left(\frac{7}{288}\right)\)	\(e\left(\frac{61}{144}\right)\)
\(\chi_{4864}(59,\cdot)\)	4864.dd	576	yes	\(1\)	\(1\)	\(e\left(\frac{299}{576}\right)\)	\(e\left(\frac{89}{576}\right)\)	\(e\left(\frac{47}{96}\right)\)	\(e\left(\frac{11}{288}\right)\)	\(e\left(\frac{143}{192}\right)\)	\(e\left(\frac{439}{576}\right)\)	\(e\left(\frac{97}{144}\right)\)	\(e\left(\frac{143}{144}\right)\)	\(e\left(\frac{5}{576}\right)\)	\(e\left(\frac{95}{288}\right)\)
\(\chi_{4864}(61,\cdot)\)	4864.dc	576	yes	\(1\)	\(1\)	\(e\left(\frac{481}{576}\right)\)	\(e\left(\frac{43}{576}\right)\)	\(e\left(\frac{61}{96}\right)\)	\(e\left(\frac{193}{288}\right)\)	\(e\left(\frac{109}{192}\right)\)	\(e\left(\frac{293}{576}\right)\)	\(e\left(\frac{131}{144}\right)\)	\(e\left(\frac{61}{144}\right)\)	\(e\left(\frac{271}{576}\right)\)	\(e\left(\frac{109}{288}\right)\)
\(\chi_{4864}(63,\cdot)\)	4864.bx	36	no	\(-1\)	\(1\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{5}{9}\right)\)
\(\chi_{4864}(65,\cdot)\)	4864.ba	12	no	\(-1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)	\(-i\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{4864}(67,\cdot)\)	4864.dd	576	yes	\(1\)	\(1\)	\(e\left(\frac{385}{576}\right)\)	\(e\left(\frac{523}{576}\right)\)	\(e\left(\frac{13}{96}\right)\)	\(e\left(\frac{97}{288}\right)\)	\(e\left(\frac{109}{192}\right)\)	\(e\left(\frac{101}{576}\right)\)	\(e\left(\frac{83}{144}\right)\)	\(e\left(\frac{109}{144}\right)\)	\(e\left(\frac{463}{576}\right)\)	\(e\left(\frac{157}{288}\right)\)

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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.