LMFDB - Group of Dirichlet characters of modulus 7616

sage:H = DirichletGroup(7616)

pari:g = idealstar(,7616,2)

Character group

sage:G.order() pari:g.no
Order	=	3072
sage:H.invariants() pari:g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{16}\times C_{48}$
sage:H.gens() pari:g.gen
Generators	=	$\chi_{7616}(5951,\cdot)$, $\chi_{7616}(3333,\cdot)$, $\chi_{7616}(3265,\cdot)$, $\chi_{7616}(2689,\cdot)$

First 32 of 3072 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	$-1$	$1$	$3$	$5$	$9$	$11$	$13$	$15$	$19$	$23$	$25$	$27$
$\chi_{7616}(1,\cdot)$	7616.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{7616}(3,\cdot)$	7616.kt	48	yes	$-1$	$1$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{8}\right)$
$\chi_{7616}(5,\cdot)$	7616.kp	48	yes	$1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{7}{12}\right)$	$1$
$\chi_{7616}(9,\cdot)$	7616.iu	24	no	$1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{8}\right)$	$i$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{1}{3}\right)$	$-i$
$\chi_{7616}(11,\cdot)$	7616.nw	48	yes	$1$	$1$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{8}\right)$
$\chi_{7616}(13,\cdot)$	7616.hg	16	yes	$-1$	$1$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{9}{16}\right)$	$i$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{11}{16}\right)$
$\chi_{7616}(15,\cdot)$	7616.db	8	no	$-1$	$1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{1}{8}\right)$	$i$	$e\left(\frac{3}{8}\right)$	$i$	$-i$	$-1$	$e\left(\frac{5}{8}\right)$	$i$	$e\left(\frac{7}{8}\right)$
$\chi_{7616}(19,\cdot)$	7616.la	48	yes	$1$	$1$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{9}{16}\right)$	$-1$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{9}{16}\right)$
$\chi_{7616}(23,\cdot)$	7616.ml	48	no	$1$	$1$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{3}{16}\right)$
$\chi_{7616}(25,\cdot)$	7616.iq	24	no	$1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{8}\right)$	$i$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{1}{6}\right)$	$1$
$\chi_{7616}(27,\cdot)$	7616.ii	16	yes	$-1$	$1$	$e\left(\frac{7}{8}\right)$	$1$	$-i$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{3}{16}\right)$	$1$	$e\left(\frac{5}{8}\right)$
$\chi_{7616}(29,\cdot)$	7616.gk	16	no	$-1$	$1$	$e\left(\frac{7}{8}\right)$	$-i$	$-i$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{13}{16}\right)$	$-1$	$e\left(\frac{5}{8}\right)$
$\chi_{7616}(31,\cdot)$	7616.lx	48	no	$-1$	$1$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{29}{48}\right)$	$i$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{13}{48}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{3}{16}\right)$
$\chi_{7616}(33,\cdot)$	7616.cb	6	no	$-1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$-1$
$\chi_{7616}(37,\cdot)$	7616.ns	48	yes	$-1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{1}{12}\right)$	$i$
$\chi_{7616}(39,\cdot)$	7616.mb	48	no	$1$	$1$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{13}{48}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{9}{16}\right)$
$\chi_{7616}(41,\cdot)$	7616.hn	16	no	$1$	$1$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{5}{8}\right)$	$i$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{7}{16}\right)$
$\chi_{7616}(43,\cdot)$	7616.fv	16	no	$-1$	$1$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{11}{16}\right)$	$-1$	$e\left(\frac{15}{16}\right)$	$-i$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{3}{16}\right)$
$\chi_{7616}(45,\cdot)$	7616.nr	48	yes	$1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{11}{12}\right)$	$-i$
$\chi_{7616}(47,\cdot)$	7616.ew	12	no	$1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$-i$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{3}\right)$	$-1$
$\chi_{7616}(53,\cdot)$	7616.lf	48	yes	$1$	$1$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{3}{16}\right)$	$-1$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{7}{16}\right)$
$\chi_{7616}(55,\cdot)$	7616.cw	8	no	$1$	$1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{8}\right)$	$-i$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{1}{8}\right)$	$-1$	$e\left(\frac{1}{8}\right)$	$1$	$i$	$e\left(\frac{5}{8}\right)$
$\chi_{7616}(57,\cdot)$	7616.gb	16	no	$-1$	$1$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{1}{8}\right)$	$-1$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{7}{16}\right)$
$\chi_{7616}(59,\cdot)$	7616.lb	48	yes	$1$	$1$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{15}{16}\right)$	$-1$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{7}{16}\right)$
$\chi_{7616}(61,\cdot)$	7616.nr	48	yes	$1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{7}{12}\right)$	$-i$
$\chi_{7616}(65,\cdot)$	7616.mj	48	no	$-1$	$1$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{13}{48}\right)$	$i$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{11}{16}\right)$
$\chi_{7616}(67,\cdot)$	7616.mp	48	yes	$-1$	$1$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{13}{16}\right)$	$i$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{11}{16}\right)$
$\chi_{7616}(69,\cdot)$	7616.hr	16	no	$-1$	$1$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{7}{16}\right)$	$i$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{1}{16}\right)$
$\chi_{7616}(71,\cdot)$	7616.hb	16	no	$1$	$1$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{3}{8}\right)$	$-i$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{16}\right)$
$\chi_{7616}(73,\cdot)$	7616.my	48	no	$1$	$1$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{13}{48}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{13}{16}\right)$
$\chi_{7616}(75,\cdot)$	7616.mx	48	yes	$-1$	$1$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{8}\right)$
$\chi_{7616}(79,\cdot)$	7616.kw	48	no	$1$	$1$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{7}{48}\right)$	$-1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{1}{16}\right)$

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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	$7616$
Structure	\(C_{2}\times C_{2}\times C_{16}\times C_{48}\)
Order	$3072$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(5\)	\(9\)	\(11\)	\(13\)	\(15\)	\(19\)	\(23\)	\(25\)	\(27\)
\(\chi_{7616}(1,\cdot)\)	7616.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{7616}(3,\cdot)\)	7616.kt	48	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{7616}(5,\cdot)\)	7616.kp	48	yes	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(1\)
\(\chi_{7616}(9,\cdot)\)	7616.iu	24	no	\(1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(i\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-i\)
\(\chi_{7616}(11,\cdot)\)	7616.nw	48	yes	\(1\)	\(1\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{8}\right)\)
\(\chi_{7616}(13,\cdot)\)	7616.hg	16	yes	\(-1\)	\(1\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(i\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{11}{16}\right)\)
\(\chi_{7616}(15,\cdot)\)	7616.db	8	no	\(-1\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(i\)	\(e\left(\frac{3}{8}\right)\)	\(i\)	\(-i\)	\(-1\)	\(e\left(\frac{5}{8}\right)\)	\(i\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{7616}(19,\cdot)\)	7616.la	48	yes	\(1\)	\(1\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(-1\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{9}{16}\right)\)
\(\chi_{7616}(23,\cdot)\)	7616.ml	48	no	\(1\)	\(1\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{3}{16}\right)\)
\(\chi_{7616}(25,\cdot)\)	7616.iq	24	no	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(i\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(1\)
\(\chi_{7616}(27,\cdot)\)	7616.ii	16	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(1\)	\(-i\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(1\)	\(e\left(\frac{5}{8}\right)\)
\(\chi_{7616}(29,\cdot)\)	7616.gk	16	no	\(-1\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(-i\)	\(-i\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(-1\)	\(e\left(\frac{5}{8}\right)\)
\(\chi_{7616}(31,\cdot)\)	7616.lx	48	no	\(-1\)	\(1\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(i\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{13}{48}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{3}{16}\right)\)
\(\chi_{7616}(33,\cdot)\)	7616.cb	6	no	\(-1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)
\(\chi_{7616}(37,\cdot)\)	7616.ns	48	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(i\)
\(\chi_{7616}(39,\cdot)\)	7616.mb	48	no	\(1\)	\(1\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{13}{48}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{9}{16}\right)\)
\(\chi_{7616}(41,\cdot)\)	7616.hn	16	no	\(1\)	\(1\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(i\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{7}{16}\right)\)
\(\chi_{7616}(43,\cdot)\)	7616.fv	16	no	\(-1\)	\(1\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(-1\)	\(e\left(\frac{15}{16}\right)\)	\(-i\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{3}{16}\right)\)
\(\chi_{7616}(45,\cdot)\)	7616.nr	48	yes	\(1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(-i\)
\(\chi_{7616}(47,\cdot)\)	7616.ew	12	no	\(1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-i\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)
\(\chi_{7616}(53,\cdot)\)	7616.lf	48	yes	\(1\)	\(1\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(-1\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{7}{16}\right)\)
\(\chi_{7616}(55,\cdot)\)	7616.cw	8	no	\(1\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(-i\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(-1\)	\(e\left(\frac{1}{8}\right)\)	\(1\)	\(i\)	\(e\left(\frac{5}{8}\right)\)
\(\chi_{7616}(57,\cdot)\)	7616.gb	16	no	\(-1\)	\(1\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(-1\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{7}{16}\right)\)
\(\chi_{7616}(59,\cdot)\)	7616.lb	48	yes	\(1\)	\(1\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(-1\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{7}{16}\right)\)
\(\chi_{7616}(61,\cdot)\)	7616.nr	48	yes	\(1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(-i\)
\(\chi_{7616}(65,\cdot)\)	7616.mj	48	no	\(-1\)	\(1\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{13}{48}\right)\)	\(i\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{11}{16}\right)\)
\(\chi_{7616}(67,\cdot)\)	7616.mp	48	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(i\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{11}{16}\right)\)
\(\chi_{7616}(69,\cdot)\)	7616.hr	16	no	\(-1\)	\(1\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(i\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{1}{16}\right)\)
\(\chi_{7616}(71,\cdot)\)	7616.hb	16	no	\(1\)	\(1\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(-i\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{5}{16}\right)\)
\(\chi_{7616}(73,\cdot)\)	7616.my	48	no	\(1\)	\(1\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{13}{48}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{13}{16}\right)\)
\(\chi_{7616}(75,\cdot)\)	7616.mx	48	yes	\(-1\)	\(1\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{7616}(79,\cdot)\)	7616.kw	48	no	\(1\)	\(1\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(-1\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{1}{16}\right)\)

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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.