LMFDB - Group of Dirichlet characters of modulus 1547

Show commands: PariGP / SageMath

sage: H = DirichletGroup(1547)

pari: g = idealstar(,1547,2)

Character group

sage: G.order() pari: g.no
Order	=	1152
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{12}\times C_{48}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{1547}(885,\cdot)$, $\chi_{1547}(834,\cdot)$, $\chi_{1547}(547,\cdot)$

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	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$8$	$9$	$10$	$11$	$12$
$\chi_{1547}(1,\cdot)$	1547.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{1547}(2,\cdot)$	1547.fq	24	yes	$-1$	$1$	$1$	$e\left(\frac{13}{24}\right)$	$1$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{13}{24}\right)$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{13}{24}\right)$
$\chi_{1547}(3,\cdot)$	1547.gf	48	yes	$1$	$1$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{31}{48}\right)$
$\chi_{1547}(4,\cdot)$	1547.ec	12	yes	$1$	$1$	$1$	$e\left(\frac{1}{12}\right)$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{12}\right)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{12}\right)$
$\chi_{1547}(5,\cdot)$	1547.gl	48	yes	$-1$	$1$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{13}{48}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{35}{48}\right)$
$\chi_{1547}(6,\cdot)$	1547.gg	48	yes	$-1$	$1$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{3}{16}\right)$
$\chi_{1547}(8,\cdot)$	1547.ch	8	no	$-1$	$1$	$1$	$e\left(\frac{5}{8}\right)$	$1$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{5}{8}\right)$	$1$	$i$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{5}{8}\right)$
$\chi_{1547}(9,\cdot)$	1547.fb	24	yes	$1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{5}{24}\right)$	$i$	$i$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{7}{24}\right)$
$\chi_{1547}(10,\cdot)$	1547.gs	48	yes	$1$	$1$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{13}{48}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{13}{48}\right)$
$\chi_{1547}(11,\cdot)$	1547.go	48	yes	$1$	$1$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{25}{48}\right)$
$\chi_{1547}(12,\cdot)$	1547.gu	48	yes	$1$	$1$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{13}{48}\right)$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{35}{48}\right)$
$\chi_{1547}(15,\cdot)$	1547.ep	24	no	$-1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{1}{24}\right)$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{3}{8}\right)$
$\chi_{1547}(16,\cdot)$	1547.bz	6	yes	$1$	$1$	$1$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{1547}(18,\cdot)$	1547.cx	12	no	$-1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{12}\right)$	$-i$	$i$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{1547}(19,\cdot)$	1547.eo	24	yes	$1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{17}{24}\right)$	$1$	$-i$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{24}\right)$
$\chi_{1547}(20,\cdot)$	1547.gg	48	yes	$-1$	$1$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{13}{16}\right)$
$\chi_{1547}(22,\cdot)$	1547.gx	48	no	$-1$	$1$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{1}{16}\right)$
$\chi_{1547}(23,\cdot)$	1547.fy	48	yes	$-1$	$1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{29}{48}\right)$	$i$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{41}{48}\right)$
$\chi_{1547}(24,\cdot)$	1547.gj	48	yes	$-1$	$1$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{13}{48}\right)$
$\chi_{1547}(25,\cdot)$	1547.fh	24	yes	$1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{7}{8}\right)$	$-i$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{11}{24}\right)$
$\chi_{1547}(27,\cdot)$	1547.el	16	no	$1$	$1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{11}{16}\right)$	$i$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{15}{16}\right)$
$\chi_{1547}(29,\cdot)$	1547.gx	48	no	$-1$	$1$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{9}{16}\right)$
$\chi_{1547}(30,\cdot)$	1547.cl	12	yes	$1$	$1$	$e\left(\frac{1}{3}\right)$	$i$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{7}{12}\right)$	$1$	$-1$	$-i$	$i$	$e\left(\frac{11}{12}\right)$
$\chi_{1547}(31,\cdot)$	1547.gl	48	yes	$-1$	$1$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{31}{48}\right)$
$\chi_{1547}(32,\cdot)$	1547.fq	24	yes	$-1$	$1$	$1$	$e\left(\frac{17}{24}\right)$	$1$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{17}{24}\right)$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{17}{24}\right)$
$\chi_{1547}(33,\cdot)$	1547.dv	12	yes	$1$	$1$	$e\left(\frac{7}{12}\right)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{7}{12}\right)$	$-i$	$1$	$-1$	$i$	$e\left(\frac{1}{6}\right)$
$\chi_{1547}(36,\cdot)$	1547.ez	24	no	$1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{7}{24}\right)$	$i$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{3}{8}\right)$
$\chi_{1547}(37,\cdot)$	1547.fv	48	yes	$1$	$1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{35}{48}\right)$	$i$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{47}{48}\right)$
$\chi_{1547}(38,\cdot)$	1547.cp	12	yes	$-1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{12}\right)$	$i$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{7}{12}\right)$
$\chi_{1547}(40,\cdot)$	1547.gd	48	no	$1$	$1$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{17}{48}\right)$
$\chi_{1547}(41,\cdot)$	1547.gg	48	yes	$-1$	$1$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{15}{16}\right)$
$\chi_{1547}(43,\cdot)$	1547.ez	24	no	$1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{17}{24}\right)$	$-i$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{5}{8}\right)$

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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	$1547$
Structure	\(C_{2}\times C_{12}\times C_{48}\)
Order	$1152$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(8\)	\(9\)	\(10\)	\(11\)	\(12\)
\(\chi_{1547}(1,\cdot)\)	1547.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{1547}(2,\cdot)\)	1547.fq	24	yes	\(-1\)	\(1\)	\(1\)	\(e\left(\frac{13}{24}\right)\)	\(1\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{13}{24}\right)\)
\(\chi_{1547}(3,\cdot)\)	1547.gf	48	yes	\(1\)	\(1\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{31}{48}\right)\)
\(\chi_{1547}(4,\cdot)\)	1547.ec	12	yes	\(1\)	\(1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)
\(\chi_{1547}(5,\cdot)\)	1547.gl	48	yes	\(-1\)	\(1\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{13}{48}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{35}{48}\right)\)
\(\chi_{1547}(6,\cdot)\)	1547.gg	48	yes	\(-1\)	\(1\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{3}{16}\right)\)
\(\chi_{1547}(8,\cdot)\)	1547.ch	8	no	\(-1\)	\(1\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(1\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(1\)	\(i\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)
\(\chi_{1547}(9,\cdot)\)	1547.fb	24	yes	\(1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(i\)	\(i\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{7}{24}\right)\)
\(\chi_{1547}(10,\cdot)\)	1547.gs	48	yes	\(1\)	\(1\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{13}{48}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{13}{48}\right)\)
\(\chi_{1547}(11,\cdot)\)	1547.go	48	yes	\(1\)	\(1\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{25}{48}\right)\)
\(\chi_{1547}(12,\cdot)\)	1547.gu	48	yes	\(1\)	\(1\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{13}{48}\right)\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{35}{48}\right)\)
\(\chi_{1547}(15,\cdot)\)	1547.ep	24	no	\(-1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{3}{8}\right)\)
\(\chi_{1547}(16,\cdot)\)	1547.bz	6	yes	\(1\)	\(1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{1547}(18,\cdot)\)	1547.cx	12	no	\(-1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(-i\)	\(i\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{1547}(19,\cdot)\)	1547.eo	24	yes	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(1\)	\(-i\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{1}{24}\right)\)
\(\chi_{1547}(20,\cdot)\)	1547.gg	48	yes	\(-1\)	\(1\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{13}{16}\right)\)
\(\chi_{1547}(22,\cdot)\)	1547.gx	48	no	\(-1\)	\(1\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{1}{16}\right)\)
\(\chi_{1547}(23,\cdot)\)	1547.fy	48	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(i\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{41}{48}\right)\)
\(\chi_{1547}(24,\cdot)\)	1547.gj	48	yes	\(-1\)	\(1\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{13}{48}\right)\)
\(\chi_{1547}(25,\cdot)\)	1547.fh	24	yes	\(1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(-i\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{11}{24}\right)\)
\(\chi_{1547}(27,\cdot)\)	1547.el	16	no	\(1\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(i\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)
\(\chi_{1547}(29,\cdot)\)	1547.gx	48	no	\(-1\)	\(1\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{9}{16}\right)\)
\(\chi_{1547}(30,\cdot)\)	1547.cl	12	yes	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(i\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(1\)	\(-1\)	\(-i\)	\(i\)	\(e\left(\frac{11}{12}\right)\)
\(\chi_{1547}(31,\cdot)\)	1547.gl	48	yes	\(-1\)	\(1\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{31}{48}\right)\)
\(\chi_{1547}(32,\cdot)\)	1547.fq	24	yes	\(-1\)	\(1\)	\(1\)	\(e\left(\frac{17}{24}\right)\)	\(1\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{17}{24}\right)\)
\(\chi_{1547}(33,\cdot)\)	1547.dv	12	yes	\(1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(-i\)	\(1\)	\(-1\)	\(i\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{1547}(36,\cdot)\)	1547.ez	24	no	\(1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(i\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{3}{8}\right)\)
\(\chi_{1547}(37,\cdot)\)	1547.fv	48	yes	\(1\)	\(1\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(i\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{47}{48}\right)\)
\(\chi_{1547}(38,\cdot)\)	1547.cp	12	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(i\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)
\(\chi_{1547}(40,\cdot)\)	1547.gd	48	no	\(1\)	\(1\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{17}{48}\right)\)
\(\chi_{1547}(41,\cdot)\)	1547.gg	48	yes	\(-1\)	\(1\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{15}{16}\right)\)
\(\chi_{1547}(43,\cdot)\)	1547.ez	24	no	\(1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(-i\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{5}{8}\right)\)

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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.