LMFDB - Group of Dirichlet characters of modulus 8512

Show commands: PariGP / SageMath

sage: H = DirichletGroup(8512)

pari: g = idealstar(,8512,2)

Character group

sage: G.order() pari: g.no
Order	=	3456
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{6}\times C_{144}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{8512}(5055,\cdot)$, $\chi_{8512}(6917,\cdot)$, $\chi_{8512}(7297,\cdot)$, $\chi_{8512}(3137,\cdot)$

First 32 of 3456 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	$-1$	$1$	$3$	$5$	$9$	$11$	$13$	$15$	$17$	$23$	$25$	$27$
$\chi_{8512}(1,\cdot)$	8512.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{8512}(3,\cdot)$	8512.mf	144	yes	$-1$	$1$	$e\left(\frac{89}{144}\right)$	$e\left(\frac{83}{144}\right)$	$e\left(\frac{17}{72}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{133}{144}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{65}{72}\right)$	$e\left(\frac{11}{72}\right)$	$e\left(\frac{41}{48}\right)$
$\chi_{8512}(5,\cdot)$	8512.lq	144	yes	$-1$	$1$	$e\left(\frac{83}{144}\right)$	$e\left(\frac{65}{144}\right)$	$e\left(\frac{11}{72}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{127}{144}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{23}{72}\right)$	$e\left(\frac{65}{72}\right)$	$e\left(\frac{35}{48}\right)$
$\chi_{8512}(9,\cdot)$	8512.lj	72	no	$1$	$1$	$e\left(\frac{17}{72}\right)$	$e\left(\frac{11}{72}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{61}{72}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{17}{24}\right)$
$\chi_{8512}(11,\cdot)$	8512.jk	48	yes	$-1$	$1$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{5}{16}\right)$
$\chi_{8512}(13,\cdot)$	8512.mb	144	yes	$1$	$1$	$e\left(\frac{133}{144}\right)$	$e\left(\frac{127}{144}\right)$	$e\left(\frac{61}{72}\right)$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{137}{144}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{49}{72}\right)$	$e\left(\frac{55}{72}\right)$	$e\left(\frac{37}{48}\right)$
$\chi_{8512}(15,\cdot)$	8512.it	36	no	$1$	$1$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{7}{12}\right)$
$\chi_{8512}(17,\cdot)$	8512.il	36	no	$-1$	$1$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{11}{12}\right)$
$\chi_{8512}(23,\cdot)$	8512.kp	72	no	$-1$	$1$	$e\left(\frac{65}{72}\right)$	$e\left(\frac{23}{72}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{49}{72}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{17}{24}\right)$
$\chi_{8512}(25,\cdot)$	8512.kq	72	no	$1$	$1$	$e\left(\frac{11}{72}\right)$	$e\left(\frac{65}{72}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{55}{72}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{11}{24}\right)$
$\chi_{8512}(27,\cdot)$	8512.kk	48	yes	$-1$	$1$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{9}{16}\right)$
$\chi_{8512}(29,\cdot)$	8512.lv	144	no	$-1$	$1$	$e\left(\frac{49}{144}\right)$	$e\left(\frac{115}{144}\right)$	$e\left(\frac{49}{72}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{5}{144}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{37}{72}\right)$	$e\left(\frac{43}{72}\right)$	$e\left(\frac{1}{48}\right)$
$\chi_{8512}(31,\cdot)$	8512.dd	6	no	$-1$	$1$	$1$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$-1$	$e\left(\frac{1}{3}\right)$	$1$
$\chi_{8512}(33,\cdot)$	8512.fn	18	no	$1$	$1$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{7}{9}\right)$	$-1$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{8512}(37,\cdot)$	8512.jp	48	yes	$-1$	$1$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{15}{16}\right)$	$-i$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{9}{16}\right)$
$\chi_{8512}(39,\cdot)$	8512.ig	24	no	$-1$	$1$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{7}{8}\right)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{8}\right)$
$\chi_{8512}(41,\cdot)$	8512.kw	72	no	$1$	$1$	$e\left(\frac{37}{72}\right)$	$e\left(\frac{67}{72}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{17}{72}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{13}{24}\right)$
$\chi_{8512}(43,\cdot)$	8512.lo	144	no	$-1$	$1$	$e\left(\frac{71}{144}\right)$	$e\left(\frac{5}{144}\right)$	$e\left(\frac{71}{72}\right)$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{91}{144}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{47}{72}\right)$	$e\left(\frac{5}{72}\right)$	$e\left(\frac{23}{48}\right)$
$\chi_{8512}(45,\cdot)$	8512.jm	48	yes	$-1$	$1$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{5}{12}\right)$	$-i$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{7}{16}\right)$
$\chi_{8512}(47,\cdot)$	8512.jd	36	no	$1$	$1$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{1}{12}\right)$
$\chi_{8512}(51,\cdot)$	8512.ll	144	yes	$1$	$1$	$e\left(\frac{37}{144}\right)$	$e\left(\frac{7}{144}\right)$	$e\left(\frac{37}{72}\right)$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{65}{144}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{61}{72}\right)$	$e\left(\frac{7}{72}\right)$	$e\left(\frac{37}{48}\right)$
$\chi_{8512}(53,\cdot)$	8512.ls	144	yes	$-1$	$1$	$e\left(\frac{79}{144}\right)$	$e\left(\frac{61}{144}\right)$	$e\left(\frac{7}{72}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{107}{144}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{67}{72}\right)$	$e\left(\frac{61}{72}\right)$	$e\left(\frac{31}{48}\right)$
$\chi_{8512}(55,\cdot)$	8512.kr	72	no	$1$	$1$	$e\left(\frac{25}{72}\right)$	$e\left(\frac{55}{72}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{65}{72}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{1}{24}\right)$
$\chi_{8512}(59,\cdot)$	8512.mf	144	yes	$-1$	$1$	$e\left(\frac{83}{144}\right)$	$e\left(\frac{113}{144}\right)$	$e\left(\frac{11}{72}\right)$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{103}{144}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{59}{72}\right)$	$e\left(\frac{41}{72}\right)$	$e\left(\frac{35}{48}\right)$
$\chi_{8512}(61,\cdot)$	8512.mg	144	yes	$-1$	$1$	$e\left(\frac{121}{144}\right)$	$e\left(\frac{19}{144}\right)$	$e\left(\frac{49}{72}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{125}{144}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{37}{72}\right)$	$e\left(\frac{19}{72}\right)$	$e\left(\frac{25}{48}\right)$
$\chi_{8512}(65,\cdot)$	8512.bd	6	no	$-1$	$1$	$-1$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$	$1$	$1$	$e\left(\frac{2}{3}\right)$	$-1$
$\chi_{8512}(67,\cdot)$	8512.md	144	yes	$1$	$1$	$e\left(\frac{1}{144}\right)$	$e\left(\frac{91}{144}\right)$	$e\left(\frac{1}{72}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{77}{144}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{25}{72}\right)$	$e\left(\frac{19}{72}\right)$	$e\left(\frac{1}{48}\right)$
$\chi_{8512}(69,\cdot)$	8512.ji	48	yes	$1$	$1$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{9}{16}\right)$
$\chi_{8512}(71,\cdot)$	8512.kv	72	no	$1$	$1$	$e\left(\frac{31}{72}\right)$	$e\left(\frac{61}{72}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{23}{72}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{7}{24}\right)$
$\chi_{8512}(73,\cdot)$	8512.ko	72	no	$-1$	$1$	$e\left(\frac{13}{72}\right)$	$e\left(\frac{55}{72}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{17}{72}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{13}{24}\right)$
$\chi_{8512}(75,\cdot)$	8512.js	48	yes	$-1$	$1$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{11}{16}\right)$	$i$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{5}{16}\right)$
$\chi_{8512}(79,\cdot)$	8512.ip	36	no	$1$	$1$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{17}{18}\right)$	$-i$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{11}{12}\right)$

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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	$8512$
Structure	\(C_{2}\times C_{2}\times C_{6}\times C_{144}\)
Order	$3456$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(5\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(23\)	\(25\)	\(27\)
\(\chi_{8512}(1,\cdot)\)	8512.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{8512}(3,\cdot)\)	8512.mf	144	yes	\(-1\)	\(1\)	\(e\left(\frac{89}{144}\right)\)	\(e\left(\frac{83}{144}\right)\)	\(e\left(\frac{17}{72}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{133}{144}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{65}{72}\right)\)	\(e\left(\frac{11}{72}\right)\)	\(e\left(\frac{41}{48}\right)\)
\(\chi_{8512}(5,\cdot)\)	8512.lq	144	yes	\(-1\)	\(1\)	\(e\left(\frac{83}{144}\right)\)	\(e\left(\frac{65}{144}\right)\)	\(e\left(\frac{11}{72}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{127}{144}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{23}{72}\right)\)	\(e\left(\frac{65}{72}\right)\)	\(e\left(\frac{35}{48}\right)\)
\(\chi_{8512}(9,\cdot)\)	8512.lj	72	no	\(1\)	\(1\)	\(e\left(\frac{17}{72}\right)\)	\(e\left(\frac{11}{72}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{61}{72}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{17}{24}\right)\)
\(\chi_{8512}(11,\cdot)\)	8512.jk	48	yes	\(-1\)	\(1\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{5}{16}\right)\)
\(\chi_{8512}(13,\cdot)\)	8512.mb	144	yes	\(1\)	\(1\)	\(e\left(\frac{133}{144}\right)\)	\(e\left(\frac{127}{144}\right)\)	\(e\left(\frac{61}{72}\right)\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{137}{144}\right)\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{49}{72}\right)\)	\(e\left(\frac{55}{72}\right)\)	\(e\left(\frac{37}{48}\right)\)
\(\chi_{8512}(15,\cdot)\)	8512.it	36	no	\(1\)	\(1\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{7}{12}\right)\)
\(\chi_{8512}(17,\cdot)\)	8512.il	36	no	\(-1\)	\(1\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{11}{12}\right)\)
\(\chi_{8512}(23,\cdot)\)	8512.kp	72	no	\(-1\)	\(1\)	\(e\left(\frac{65}{72}\right)\)	\(e\left(\frac{23}{72}\right)\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{49}{72}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{17}{24}\right)\)
\(\chi_{8512}(25,\cdot)\)	8512.kq	72	no	\(1\)	\(1\)	\(e\left(\frac{11}{72}\right)\)	\(e\left(\frac{65}{72}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{55}{72}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{11}{24}\right)\)
\(\chi_{8512}(27,\cdot)\)	8512.kk	48	yes	\(-1\)	\(1\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{9}{16}\right)\)
\(\chi_{8512}(29,\cdot)\)	8512.lv	144	no	\(-1\)	\(1\)	\(e\left(\frac{49}{144}\right)\)	\(e\left(\frac{115}{144}\right)\)	\(e\left(\frac{49}{72}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{5}{144}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{37}{72}\right)\)	\(e\left(\frac{43}{72}\right)\)	\(e\left(\frac{1}{48}\right)\)
\(\chi_{8512}(31,\cdot)\)	8512.dd	6	no	\(-1\)	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(1\)
\(\chi_{8512}(33,\cdot)\)	8512.fn	18	no	\(1\)	\(1\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(-1\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{8512}(37,\cdot)\)	8512.jp	48	yes	\(-1\)	\(1\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(-i\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{9}{16}\right)\)
\(\chi_{8512}(39,\cdot)\)	8512.ig	24	no	\(-1\)	\(1\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{8}\right)\)
\(\chi_{8512}(41,\cdot)\)	8512.kw	72	no	\(1\)	\(1\)	\(e\left(\frac{37}{72}\right)\)	\(e\left(\frac{67}{72}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{17}{72}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{13}{24}\right)\)
\(\chi_{8512}(43,\cdot)\)	8512.lo	144	no	\(-1\)	\(1\)	\(e\left(\frac{71}{144}\right)\)	\(e\left(\frac{5}{144}\right)\)	\(e\left(\frac{71}{72}\right)\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{91}{144}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{47}{72}\right)\)	\(e\left(\frac{5}{72}\right)\)	\(e\left(\frac{23}{48}\right)\)
\(\chi_{8512}(45,\cdot)\)	8512.jm	48	yes	\(-1\)	\(1\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(-i\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{7}{16}\right)\)
\(\chi_{8512}(47,\cdot)\)	8512.jd	36	no	\(1\)	\(1\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{1}{12}\right)\)
\(\chi_{8512}(51,\cdot)\)	8512.ll	144	yes	\(1\)	\(1\)	\(e\left(\frac{37}{144}\right)\)	\(e\left(\frac{7}{144}\right)\)	\(e\left(\frac{37}{72}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{65}{144}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{61}{72}\right)\)	\(e\left(\frac{7}{72}\right)\)	\(e\left(\frac{37}{48}\right)\)
\(\chi_{8512}(53,\cdot)\)	8512.ls	144	yes	\(-1\)	\(1\)	\(e\left(\frac{79}{144}\right)\)	\(e\left(\frac{61}{144}\right)\)	\(e\left(\frac{7}{72}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{107}{144}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{67}{72}\right)\)	\(e\left(\frac{61}{72}\right)\)	\(e\left(\frac{31}{48}\right)\)
\(\chi_{8512}(55,\cdot)\)	8512.kr	72	no	\(1\)	\(1\)	\(e\left(\frac{25}{72}\right)\)	\(e\left(\frac{55}{72}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{65}{72}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{1}{24}\right)\)
\(\chi_{8512}(59,\cdot)\)	8512.mf	144	yes	\(-1\)	\(1\)	\(e\left(\frac{83}{144}\right)\)	\(e\left(\frac{113}{144}\right)\)	\(e\left(\frac{11}{72}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{103}{144}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{59}{72}\right)\)	\(e\left(\frac{41}{72}\right)\)	\(e\left(\frac{35}{48}\right)\)
\(\chi_{8512}(61,\cdot)\)	8512.mg	144	yes	\(-1\)	\(1\)	\(e\left(\frac{121}{144}\right)\)	\(e\left(\frac{19}{144}\right)\)	\(e\left(\frac{49}{72}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{125}{144}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{37}{72}\right)\)	\(e\left(\frac{19}{72}\right)\)	\(e\left(\frac{25}{48}\right)\)
\(\chi_{8512}(65,\cdot)\)	8512.bd	6	no	\(-1\)	\(1\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)
\(\chi_{8512}(67,\cdot)\)	8512.md	144	yes	\(1\)	\(1\)	\(e\left(\frac{1}{144}\right)\)	\(e\left(\frac{91}{144}\right)\)	\(e\left(\frac{1}{72}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{77}{144}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{25}{72}\right)\)	\(e\left(\frac{19}{72}\right)\)	\(e\left(\frac{1}{48}\right)\)
\(\chi_{8512}(69,\cdot)\)	8512.ji	48	yes	\(1\)	\(1\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{9}{16}\right)\)
\(\chi_{8512}(71,\cdot)\)	8512.kv	72	no	\(1\)	\(1\)	\(e\left(\frac{31}{72}\right)\)	\(e\left(\frac{61}{72}\right)\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{23}{72}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{7}{24}\right)\)
\(\chi_{8512}(73,\cdot)\)	8512.ko	72	no	\(-1\)	\(1\)	\(e\left(\frac{13}{72}\right)\)	\(e\left(\frac{55}{72}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{17}{72}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{13}{24}\right)\)
\(\chi_{8512}(75,\cdot)\)	8512.js	48	yes	\(-1\)	\(1\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(i\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{5}{16}\right)\)
\(\chi_{8512}(79,\cdot)\)	8512.ip	36	no	\(1\)	\(1\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(-i\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{11}{12}\right)\)

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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.