LMFDB - Group of Dirichlet characters of modulus 4284

Show commands: PariGP / SageMath

sage: H = DirichletGroup(4284)

pari: g = idealstar(,4284,2)

Character group

sage: G.order() pari: g.no
Order	=	1152
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{6}\times C_{48}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{4284}(2143,\cdot)$, $\chi_{4284}(3809,\cdot)$, $\chi_{4284}(1837,\cdot)$, $\chi_{4284}(1261,\cdot)$

First 32 of 1152 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	$-1$	$1$	$5$	$11$	$13$	$19$	$23$	$25$	$29$	$31$	$37$	$41$
$\chi_{4284}(1,\cdot)$	4284.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{4284}(5,\cdot)$	4284.gp	48	no	$-1$	$1$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{5}{48}\right)$
$\chi_{4284}(11,\cdot)$	4284.hp	48	yes	$-1$	$1$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{31}{48}\right)$
$\chi_{4284}(13,\cdot)$	4284.et	12	no	$-1$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{12}\right)$	$i$	$e\left(\frac{11}{12}\right)$
$\chi_{4284}(19,\cdot)$	4284.gk	24	no	$1$	$1$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{23}{24}\right)$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{1}{8}\right)$
$\chi_{4284}(23,\cdot)$	4284.hp	48	yes	$-1$	$1$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{23}{48}\right)$
$\chi_{4284}(25,\cdot)$	4284.fw	24	no	$1$	$1$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{5}{24}\right)$
$\chi_{4284}(29,\cdot)$	4284.hf	48	no	$1$	$1$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{37}{48}\right)$
$\chi_{4284}(31,\cdot)$	4284.hb	48	yes	$-1$	$1$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{17}{48}\right)$
$\chi_{4284}(37,\cdot)$	4284.hi	48	no	$-1$	$1$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{37}{48}\right)$	$i$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{11}{16}\right)$
$\chi_{4284}(41,\cdot)$	4284.hl	48	no	$-1$	$1$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{11}{48}\right)$
$\chi_{4284}(43,\cdot)$	4284.ga	24	no	$-1$	$1$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{5}{6}\right)$	$i$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{17}{24}\right)$
$\chi_{4284}(47,\cdot)$	4284.ep	12	yes	$-1$	$1$	$i$	$-i$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$-i$	$-1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{12}\right)$
$\chi_{4284}(53,\cdot)$	4284.fg	24	no	$-1$	$1$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{7}{24}\right)$	$-1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{1}{8}\right)$
$\chi_{4284}(55,\cdot)$	4284.v	4	no	$1$	$1$	$i$	$-i$	$-1$	$-1$	$-i$	$-1$	$-i$	$-i$	$-i$	$-i$
$\chi_{4284}(59,\cdot)$	4284.fn	24	yes	$-1$	$1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{3}{8}\right)$	$i$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{13}{24}\right)$
$\chi_{4284}(61,\cdot)$	4284.hm	48	no	$1$	$1$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{43}{48}\right)$
$\chi_{4284}(65,\cdot)$	4284.hn	48	no	$1$	$1$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{1}{48}\right)$
$\chi_{4284}(67,\cdot)$	4284.bg	6	yes	$-1$	$1$	$-1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{4284}(71,\cdot)$	4284.fe	16	no	$-1$	$1$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{7}{16}\right)$	$i$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{3}{16}\right)$
$\chi_{4284}(73,\cdot)$	4284.hg	48	no	$1$	$1$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{41}{48}\right)$	$-i$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{15}{16}\right)$
$\chi_{4284}(79,\cdot)$	4284.gq	48	yes	$1$	$1$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{7}{48}\right)$
$\chi_{4284}(83,\cdot)$	4284.fm	24	yes	$-1$	$1$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{1}{3}\right)$	$i$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{11}{24}\right)$
$\chi_{4284}(89,\cdot)$	4284.ds	12	no	$1$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{12}\right)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{6}\right)$	$i$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{12}\right)$	$i$
$\chi_{4284}(95,\cdot)$	4284.ha	48	yes	$-1$	$1$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{13}{48}\right)$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{11}{48}\right)$
$\chi_{4284}(97,\cdot)$	4284.hh	48	no	$1$	$1$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{37}{48}\right)$
$\chi_{4284}(101,\cdot)$	4284.co	6	no	$1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{4284}(103,\cdot)$	4284.cy	6	no	$1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{4284}(107,\cdot)$	4284.gu	48	no	$-1$	$1$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{25}{48}\right)$	$i$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{15}{16}\right)$
$\chi_{4284}(109,\cdot)$	4284.hi	48	no	$-1$	$1$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{23}{48}\right)$	$-i$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{9}{16}\right)$
$\chi_{4284}(113,\cdot)$	4284.hf	48	no	$1$	$1$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{47}{48}\right)$
$\chi_{4284}(115,\cdot)$	4284.er	12	yes	$1$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{12}\right)$	$i$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{7}{12}\right)$

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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	$4284$
Structure	\(C_{2}\times C_{2}\times C_{6}\times C_{48}\)
Order	$1152$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(5\)	\(11\)	\(13\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)	\(37\)	\(41\)
\(\chi_{4284}(1,\cdot)\)	4284.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{4284}(5,\cdot)\)	4284.gp	48	no	\(-1\)	\(1\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{5}{48}\right)\)
\(\chi_{4284}(11,\cdot)\)	4284.hp	48	yes	\(-1\)	\(1\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{31}{48}\right)\)
\(\chi_{4284}(13,\cdot)\)	4284.et	12	no	\(-1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(i\)	\(e\left(\frac{11}{12}\right)\)
\(\chi_{4284}(19,\cdot)\)	4284.gk	24	no	\(1\)	\(1\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{1}{8}\right)\)
\(\chi_{4284}(23,\cdot)\)	4284.hp	48	yes	\(-1\)	\(1\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{23}{48}\right)\)
\(\chi_{4284}(25,\cdot)\)	4284.fw	24	no	\(1\)	\(1\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{5}{24}\right)\)
\(\chi_{4284}(29,\cdot)\)	4284.hf	48	no	\(1\)	\(1\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{37}{48}\right)\)
\(\chi_{4284}(31,\cdot)\)	4284.hb	48	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{17}{48}\right)\)
\(\chi_{4284}(37,\cdot)\)	4284.hi	48	no	\(-1\)	\(1\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(i\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{11}{16}\right)\)
\(\chi_{4284}(41,\cdot)\)	4284.hl	48	no	\(-1\)	\(1\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{11}{48}\right)\)
\(\chi_{4284}(43,\cdot)\)	4284.ga	24	no	\(-1\)	\(1\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(i\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{17}{24}\right)\)
\(\chi_{4284}(47,\cdot)\)	4284.ep	12	yes	\(-1\)	\(1\)	\(i\)	\(-i\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-i\)	\(-1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)
\(\chi_{4284}(53,\cdot)\)	4284.fg	24	no	\(-1\)	\(1\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(-1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{1}{8}\right)\)
\(\chi_{4284}(55,\cdot)\)	4284.v	4	no	\(1\)	\(1\)	\(i\)	\(-i\)	\(-1\)	\(-1\)	\(-i\)	\(-1\)	\(-i\)	\(-i\)	\(-i\)	\(-i\)
\(\chi_{4284}(59,\cdot)\)	4284.fn	24	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(i\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{13}{24}\right)\)
\(\chi_{4284}(61,\cdot)\)	4284.hm	48	no	\(1\)	\(1\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{43}{48}\right)\)
\(\chi_{4284}(65,\cdot)\)	4284.hn	48	no	\(1\)	\(1\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{1}{48}\right)\)
\(\chi_{4284}(67,\cdot)\)	4284.bg	6	yes	\(-1\)	\(1\)	\(-1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{4284}(71,\cdot)\)	4284.fe	16	no	\(-1\)	\(1\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(i\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)
\(\chi_{4284}(73,\cdot)\)	4284.hg	48	no	\(1\)	\(1\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(-i\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{15}{16}\right)\)
\(\chi_{4284}(79,\cdot)\)	4284.gq	48	yes	\(1\)	\(1\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{7}{48}\right)\)
\(\chi_{4284}(83,\cdot)\)	4284.fm	24	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(i\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{11}{24}\right)\)
\(\chi_{4284}(89,\cdot)\)	4284.ds	12	no	\(1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(i\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(i\)
\(\chi_{4284}(95,\cdot)\)	4284.ha	48	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{13}{48}\right)\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{11}{48}\right)\)
\(\chi_{4284}(97,\cdot)\)	4284.hh	48	no	\(1\)	\(1\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{37}{48}\right)\)
\(\chi_{4284}(101,\cdot)\)	4284.co	6	no	\(1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{4284}(103,\cdot)\)	4284.cy	6	no	\(1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{4284}(107,\cdot)\)	4284.gu	48	no	\(-1\)	\(1\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{25}{48}\right)\)	\(i\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{15}{16}\right)\)
\(\chi_{4284}(109,\cdot)\)	4284.hi	48	no	\(-1\)	\(1\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(-i\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{9}{16}\right)\)
\(\chi_{4284}(113,\cdot)\)	4284.hf	48	no	\(1\)	\(1\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{47}{48}\right)\)
\(\chi_{4284}(115,\cdot)\)	4284.er	12	yes	\(1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(i\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)

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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.