LMFDB - Group of Dirichlet characters of modulus 5712

sage:H = DirichletGroup(5712)

pari:g = idealstar(,5712,2)

Character group

sage:G.order() pari:g.no
Order	=	1536
sage:H.invariants() pari:g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{2}\times C_{4}\times C_{48}$
sage:H.gens() pari:g.gen
Generators	=	$\chi_{5712}(2143,\cdot)$, $\chi_{5712}(1429,\cdot)$, $\chi_{5712}(3809,\cdot)$, $\chi_{5712}(3265,\cdot)$, $\chi_{5712}(2689,\cdot)$

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	$-1$	$1$	$5$	$11$	$13$	$19$	$23$	$25$	$29$	$31$	$37$	$41$
$\chi_{5712}(1,\cdot)$	5712.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{5712}(5,\cdot)$	5712.jy	48	yes	$-1$	$1$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{13}{48}\right)$	$-1$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{15}{16}\right)$
$\chi_{5712}(11,\cdot)$	5712.jw	48	yes	$-1$	$1$	$e\left(\frac{13}{48}\right)$	$e\left(\frac{47}{48}\right)$	$-1$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{13}{16}\right)$
$\chi_{5712}(13,\cdot)$	5712.bi	4	no	$-1$	$1$	$-1$	$-1$	$-i$	$i$	$i$	$1$	$-1$	$-i$	$1$	$-i$
$\chi_{5712}(19,\cdot)$	5712.jn	24	no	$1$	$1$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{17}{24}\right)$	$i$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{5}{8}\right)$
$\chi_{5712}(23,\cdot)$	5712.kt	48	no	$-1$	$1$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{19}{48}\right)$	$i$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{13}{48}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{13}{16}\right)$
$\chi_{5712}(25,\cdot)$	5712.jt	24	no	$1$	$1$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{13}{24}\right)$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{7}{8}\right)$
$\chi_{5712}(29,\cdot)$	5712.hl	16	no	$1$	$1$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{15}{16}\right)$	$-1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{15}{16}\right)$
$\chi_{5712}(31,\cdot)$	5712.ke	48	no	$-1$	$1$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{5}{48}\right)$	$-i$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{13}{48}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{11}{16}\right)$
$\chi_{5712}(37,\cdot)$	5712.kz	48	no	$-1$	$1$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{1}{48}\right)$	$1$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{3}{16}\right)$
$\chi_{5712}(41,\cdot)$	5712.ie	16	no	$-1$	$1$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{13}{16}\right)$	$-i$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{9}{16}\right)$
$\chi_{5712}(43,\cdot)$	5712.fe	8	no	$-1$	$1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{8}\right)$	$i$	$1$	$e\left(\frac{7}{8}\right)$	$-i$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{7}{8}\right)$
$\chi_{5712}(47,\cdot)$	5712.gd	12	no	$-1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{12}\right)$	$-1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{6}\right)$	$-i$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{11}{12}\right)$	$-i$
$\chi_{5712}(53,\cdot)$	5712.jd	24	yes	$-1$	$1$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{13}{24}\right)$	$i$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{5}{8}\right)$
$\chi_{5712}(55,\cdot)$	5712.cs	4	no	$1$	$1$	$-i$	$i$	$1$	$1$	$-i$	$-1$	$i$	$-i$	$i$	$-i$
$\chi_{5712}(59,\cdot)$	5712.jl	24	yes	$-1$	$1$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{7}{24}\right)$	$-i$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{3}{8}\right)$
$\chi_{5712}(61,\cdot)$	5712.jz	48	no	$1$	$1$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{19}{48}\right)$	$-1$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{1}{16}\right)$
$\chi_{5712}(65,\cdot)$	5712.km	48	no	$1$	$1$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{37}{48}\right)$	$i$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{11}{16}\right)$
$\chi_{5712}(67,\cdot)$	5712.gp	12	no	$-1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{12}\right)$	$i$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$-i$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{12}\right)$	$1$
$\chi_{5712}(71,\cdot)$	5712.hs	16	no	$-1$	$1$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{15}{16}\right)$	$-i$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{3}{16}\right)$
$\chi_{5712}(73,\cdot)$	5712.kl	48	no	$1$	$1$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{17}{48}\right)$	$i$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{15}{16}\right)$
$\chi_{5712}(79,\cdot)$	5712.kk	48	no	$1$	$1$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{43}{48}\right)$	$-i$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{13}{16}\right)$
$\chi_{5712}(83,\cdot)$	5712.ex	8	yes	$-1$	$1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{3}{8}\right)$	$i$	$-1$	$e\left(\frac{1}{8}\right)$	$i$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{5}{8}\right)$
$\chi_{5712}(89,\cdot)$	5712.ha	12	no	$1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{7}{12}\right)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{6}\right)$	$-i$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{11}{12}\right)$	$i$
$\chi_{5712}(95,\cdot)$	5712.kg	48	no	$-1$	$1$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{47}{48}\right)$	$-i$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{9}{16}\right)$
$\chi_{5712}(97,\cdot)$	5712.hx	16	no	$1$	$1$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{11}{16}\right)$	$-i$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{7}{16}\right)$
$\chi_{5712}(101,\cdot)$	5712.go	12	yes	$1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{11}{12}\right)$	$i$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$-i$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{12}\right)$	$1$
$\chi_{5712}(103,\cdot)$	5712.di	6	no	$1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$-1$
$\chi_{5712}(107,\cdot)$	5712.kw	48	yes	$-1$	$1$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{37}{48}\right)$	$1$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{7}{16}\right)$
$\chi_{5712}(109,\cdot)$	5712.kz	48	no	$-1$	$1$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{11}{48}\right)$	$1$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{1}{16}\right)$
$\chi_{5712}(113,\cdot)$	5712.hz	16	no	$1$	$1$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{9}{16}\right)$	$-i$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{5}{16}\right)$
$\chi_{5712}(115,\cdot)$	5712.hc	12	no	$1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$-i$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{3}\right)$	$-i$

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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	$5712$
Structure	\(C_{2}\times C_{2}\times C_{2}\times C_{4}\times C_{48}\)
Order	$1536$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(5\)	\(11\)	\(13\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)	\(37\)	\(41\)
\(\chi_{5712}(1,\cdot)\)	5712.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{5712}(5,\cdot)\)	5712.jy	48	yes	\(-1\)	\(1\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{13}{48}\right)\)	\(-1\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{15}{16}\right)\)
\(\chi_{5712}(11,\cdot)\)	5712.jw	48	yes	\(-1\)	\(1\)	\(e\left(\frac{13}{48}\right)\)	\(e\left(\frac{47}{48}\right)\)	\(-1\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{13}{16}\right)\)
\(\chi_{5712}(13,\cdot)\)	5712.bi	4	no	\(-1\)	\(1\)	\(-1\)	\(-1\)	\(-i\)	\(i\)	\(i\)	\(1\)	\(-1\)	\(-i\)	\(1\)	\(-i\)
\(\chi_{5712}(19,\cdot)\)	5712.jn	24	no	\(1\)	\(1\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(i\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{5}{8}\right)\)
\(\chi_{5712}(23,\cdot)\)	5712.kt	48	no	\(-1\)	\(1\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(i\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{13}{48}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{13}{16}\right)\)
\(\chi_{5712}(25,\cdot)\)	5712.jt	24	no	\(1\)	\(1\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{5712}(29,\cdot)\)	5712.hl	16	no	\(1\)	\(1\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(-1\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)
\(\chi_{5712}(31,\cdot)\)	5712.ke	48	no	\(-1\)	\(1\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(-i\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{13}{48}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{11}{16}\right)\)
\(\chi_{5712}(37,\cdot)\)	5712.kz	48	no	\(-1\)	\(1\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{1}{48}\right)\)	\(1\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{3}{16}\right)\)
\(\chi_{5712}(41,\cdot)\)	5712.ie	16	no	\(-1\)	\(1\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(-i\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)
\(\chi_{5712}(43,\cdot)\)	5712.fe	8	no	\(-1\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(i\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(-i\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{5712}(47,\cdot)\)	5712.gd	12	no	\(-1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(-1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-i\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(-i\)
\(\chi_{5712}(53,\cdot)\)	5712.jd	24	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(i\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{5}{8}\right)\)
\(\chi_{5712}(55,\cdot)\)	5712.cs	4	no	\(1\)	\(1\)	\(-i\)	\(i\)	\(1\)	\(1\)	\(-i\)	\(-1\)	\(i\)	\(-i\)	\(i\)	\(-i\)
\(\chi_{5712}(59,\cdot)\)	5712.jl	24	yes	\(-1\)	\(1\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(-i\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{3}{8}\right)\)
\(\chi_{5712}(61,\cdot)\)	5712.jz	48	no	\(1\)	\(1\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(-1\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{1}{16}\right)\)
\(\chi_{5712}(65,\cdot)\)	5712.km	48	no	\(1\)	\(1\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(i\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{11}{16}\right)\)
\(\chi_{5712}(67,\cdot)\)	5712.gp	12	no	\(-1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(i\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-i\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(1\)
\(\chi_{5712}(71,\cdot)\)	5712.hs	16	no	\(-1\)	\(1\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(-i\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)
\(\chi_{5712}(73,\cdot)\)	5712.kl	48	no	\(1\)	\(1\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{17}{48}\right)\)	\(i\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{15}{16}\right)\)
\(\chi_{5712}(79,\cdot)\)	5712.kk	48	no	\(1\)	\(1\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{43}{48}\right)\)	\(-i\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{13}{16}\right)\)
\(\chi_{5712}(83,\cdot)\)	5712.ex	8	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(i\)	\(-1\)	\(e\left(\frac{1}{8}\right)\)	\(i\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)
\(\chi_{5712}(89,\cdot)\)	5712.ha	12	no	\(1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-i\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(i\)
\(\chi_{5712}(95,\cdot)\)	5712.kg	48	no	\(-1\)	\(1\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{47}{48}\right)\)	\(-i\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{9}{16}\right)\)
\(\chi_{5712}(97,\cdot)\)	5712.hx	16	no	\(1\)	\(1\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(-i\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)
\(\chi_{5712}(101,\cdot)\)	5712.go	12	yes	\(1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(i\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-i\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(1\)
\(\chi_{5712}(103,\cdot)\)	5712.di	6	no	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)
\(\chi_{5712}(107,\cdot)\)	5712.kw	48	yes	\(-1\)	\(1\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(1\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{7}{16}\right)\)
\(\chi_{5712}(109,\cdot)\)	5712.kz	48	no	\(-1\)	\(1\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{11}{48}\right)\)	\(1\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{1}{16}\right)\)
\(\chi_{5712}(113,\cdot)\)	5712.hz	16	no	\(1\)	\(1\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(-i\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)
\(\chi_{5712}(115,\cdot)\)	5712.hc	12	no	\(1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-i\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-i\)

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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.