LMFDB - Group of Dirichlet characters of modulus 1785

Show commands: PariGP / SageMath

sage: H = DirichletGroup(1785)

pari: g = idealstar(,1785,2)

Character group

sage: G.order() pari: g.no
Order	=	768
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{4}\times C_{48}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{1785}(596,\cdot)$, $\chi_{1785}(1072,\cdot)$, $\chi_{1785}(766,\cdot)$, $\chi_{1785}(1261,\cdot)$

First 32 of 768 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	$-1$	$1$	$2$	$4$	$8$	$11$	$13$	$16$	$19$	$22$	$23$	$26$
$\chi_{1785}(1,\cdot)$	1785.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{1785}(2,\cdot)$	1785.ei	24	yes	$1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{23}{24}\right)$	$i$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{11}{12}\right)$
$\chi_{1785}(4,\cdot)$	1785.cv	12	no	$1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{11}{12}\right)$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$i$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{1785}(8,\cdot)$	1785.cq	8	no	$1$	$1$	$1$	$1$	$1$	$e\left(\frac{7}{8}\right)$	$-i$	$1$	$i$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{1}{8}\right)$	$-i$
$\chi_{1785}(11,\cdot)$	1785.ff	48	no	$1$	$1$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{11}{48}\right)$	$-i$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{17}{24}\right)$
$\chi_{1785}(13,\cdot)$	1785.bc	4	no	$1$	$1$	$i$	$-1$	$-i$	$-i$	$-i$	$1$	$-1$	$1$	$1$	$1$
$\chi_{1785}(16,\cdot)$	1785.bu	6	no	$1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{1785}(19,\cdot)$	1785.ep	24	no	$-1$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{6}\right)$	$i$	$e\left(\frac{11}{24}\right)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{11}{12}\right)$
$\chi_{1785}(22,\cdot)$	1785.ee	16	no	$1$	$1$	$e\left(\frac{5}{8}\right)$	$i$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{3}{16}\right)$	$1$	$-1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{5}{8}\right)$
$\chi_{1785}(23,\cdot)$	1785.fk	48	yes	$-1$	$1$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{19}{48}\right)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{1}{24}\right)$
$\chi_{1785}(26,\cdot)$	1785.es	24	no	$1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$	$-i$	$e\left(\frac{17}{24}\right)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{11}{12}\right)$
$\chi_{1785}(29,\cdot)$	1785.dy	16	no	$1$	$1$	$e\left(\frac{3}{8}\right)$	$-i$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{3}{16}\right)$	$-i$	$-1$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{1}{8}\right)$
$\chi_{1785}(31,\cdot)$	1785.fi	48	no	$1$	$1$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{29}{48}\right)$	$-i$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{23}{24}\right)$
$\chi_{1785}(32,\cdot)$	1785.ei	24	yes	$1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{19}{24}\right)$	$i$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{7}{12}\right)$
$\chi_{1785}(37,\cdot)$	1785.fn	48	no	$1$	$1$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{37}{48}\right)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{19}{24}\right)$
$\chi_{1785}(38,\cdot)$	1785.dg	12	yes	$-1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{6}\right)$	$i$	$e\left(\frac{5}{12}\right)$	$-i$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{1785}(41,\cdot)$	1785.dw	16	no	$-1$	$1$	$e\left(\frac{1}{8}\right)$	$i$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{5}{16}\right)$	$i$	$-1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{3}{8}\right)$
$\chi_{1785}(43,\cdot)$	1785.cf	8	no	$-1$	$1$	$-1$	$1$	$-1$	$e\left(\frac{7}{8}\right)$	$-i$	$1$	$i$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{8}\right)$	$i$
$\chi_{1785}(44,\cdot)$	1785.fh	48	yes	$1$	$1$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{7}{48}\right)$	$i$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{13}{24}\right)$
$\chi_{1785}(46,\cdot)$	1785.fe	48	no	$-1$	$1$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{17}{48}\right)$	$i$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{23}{24}\right)$
$\chi_{1785}(47,\cdot)$	1785.dg	12	yes	$-1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$	$-i$	$e\left(\frac{7}{12}\right)$	$i$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{1785}(52,\cdot)$	1785.cz	12	no	$1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$	$-i$	$e\left(\frac{2}{3}\right)$	$i$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$i$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{1785}(53,\cdot)$	1785.ex	24	yes	$1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{7}{24}\right)$	$-i$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{7}{12}\right)$
$\chi_{1785}(58,\cdot)$	1785.fn	48	no	$1$	$1$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{7}{48}\right)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{1}{24}\right)$
$\chi_{1785}(59,\cdot)$	1785.en	24	yes	$1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{6}\right)$	$i$	$e\left(\frac{13}{24}\right)$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{7}{12}\right)$
$\chi_{1785}(61,\cdot)$	1785.fi	48	no	$1$	$1$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{31}{48}\right)$	$i$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{13}{24}\right)$
$\chi_{1785}(62,\cdot)$	1785.eg	16	yes	$1$	$1$	$e\left(\frac{7}{8}\right)$	$-i$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{9}{16}\right)$	$1$	$-1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{7}{8}\right)$
$\chi_{1785}(64,\cdot)$	1785.bl	4	no	$1$	$1$	$1$	$1$	$1$	$-i$	$-1$	$1$	$-1$	$-i$	$i$	$-1$
$\chi_{1785}(67,\cdot)$	1785.dm	12	no	$-1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$	$-i$	$e\left(\frac{1}{6}\right)$	$-i$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$-i$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{1785}(71,\cdot)$	1785.ea	16	no	$1$	$1$	$e\left(\frac{3}{8}\right)$	$-i$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{15}{16}\right)$	$i$	$-1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{5}{8}\right)$
$\chi_{1785}(73,\cdot)$	1785.fm	48	no	$-1$	$1$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{41}{48}\right)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{13}{48}\right)$	$e\left(\frac{11}{24}\right)$
$\chi_{1785}(74,\cdot)$	1785.fh	48	yes	$1$	$1$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{35}{48}\right)$	$i$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{17}{24}\right)$

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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	$1785$
Structure	\(C_{2}\times C_{2}\times C_{4}\times C_{48}\)
Order	$768$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(4\)	\(8\)	\(11\)	\(13\)	\(16\)	\(19\)	\(22\)	\(23\)	\(26\)
\(\chi_{1785}(1,\cdot)\)	1785.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{1785}(2,\cdot)\)	1785.ei	24	yes	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{23}{24}\right)\)	\(i\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{11}{12}\right)\)
\(\chi_{1785}(4,\cdot)\)	1785.cv	12	no	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(i\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{1785}(8,\cdot)\)	1785.cq	8	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(-i\)	\(1\)	\(i\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(-i\)
\(\chi_{1785}(11,\cdot)\)	1785.ff	48	no	\(1\)	\(1\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{11}{48}\right)\)	\(-i\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{17}{24}\right)\)
\(\chi_{1785}(13,\cdot)\)	1785.bc	4	no	\(1\)	\(1\)	\(i\)	\(-1\)	\(-i\)	\(-i\)	\(-i\)	\(1\)	\(-1\)	\(1\)	\(1\)	\(1\)
\(\chi_{1785}(16,\cdot)\)	1785.bu	6	no	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{1785}(19,\cdot)\)	1785.ep	24	no	\(-1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(i\)	\(e\left(\frac{11}{24}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{11}{12}\right)\)
\(\chi_{1785}(22,\cdot)\)	1785.ee	16	no	\(1\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(i\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(1\)	\(-1\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)
\(\chi_{1785}(23,\cdot)\)	1785.fk	48	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{1}{24}\right)\)
\(\chi_{1785}(26,\cdot)\)	1785.es	24	no	\(1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-i\)	\(e\left(\frac{17}{24}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{11}{12}\right)\)
\(\chi_{1785}(29,\cdot)\)	1785.dy	16	no	\(1\)	\(1\)	\(e\left(\frac{3}{8}\right)\)	\(-i\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(-i\)	\(-1\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)
\(\chi_{1785}(31,\cdot)\)	1785.fi	48	no	\(1\)	\(1\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(-i\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{23}{24}\right)\)
\(\chi_{1785}(32,\cdot)\)	1785.ei	24	yes	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{19}{24}\right)\)	\(i\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{7}{12}\right)\)
\(\chi_{1785}(37,\cdot)\)	1785.fn	48	no	\(1\)	\(1\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{19}{24}\right)\)
\(\chi_{1785}(38,\cdot)\)	1785.dg	12	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(i\)	\(e\left(\frac{5}{12}\right)\)	\(-i\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{1785}(41,\cdot)\)	1785.dw	16	no	\(-1\)	\(1\)	\(e\left(\frac{1}{8}\right)\)	\(i\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(i\)	\(-1\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)
\(\chi_{1785}(43,\cdot)\)	1785.cf	8	no	\(-1\)	\(1\)	\(-1\)	\(1\)	\(-1\)	\(e\left(\frac{7}{8}\right)\)	\(-i\)	\(1\)	\(i\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(i\)
\(\chi_{1785}(44,\cdot)\)	1785.fh	48	yes	\(1\)	\(1\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(i\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{13}{24}\right)\)
\(\chi_{1785}(46,\cdot)\)	1785.fe	48	no	\(-1\)	\(1\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{17}{48}\right)\)	\(i\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{23}{24}\right)\)
\(\chi_{1785}(47,\cdot)\)	1785.dg	12	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-i\)	\(e\left(\frac{7}{12}\right)\)	\(i\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{1785}(52,\cdot)\)	1785.cz	12	no	\(1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-i\)	\(e\left(\frac{2}{3}\right)\)	\(i\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(i\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{1785}(53,\cdot)\)	1785.ex	24	yes	\(1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(e\left(\frac{7}{24}\right)\)	\(-i\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{7}{12}\right)\)
\(\chi_{1785}(58,\cdot)\)	1785.fn	48	no	\(1\)	\(1\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{1}{24}\right)\)
\(\chi_{1785}(59,\cdot)\)	1785.en	24	yes	\(1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(i\)	\(e\left(\frac{13}{24}\right)\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{7}{12}\right)\)
\(\chi_{1785}(61,\cdot)\)	1785.fi	48	no	\(1\)	\(1\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(i\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{13}{24}\right)\)
\(\chi_{1785}(62,\cdot)\)	1785.eg	16	yes	\(1\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(-i\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(1\)	\(-1\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{1785}(64,\cdot)\)	1785.bl	4	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(-i\)	\(-1\)	\(1\)	\(-1\)	\(-i\)	\(i\)	\(-1\)
\(\chi_{1785}(67,\cdot)\)	1785.dm	12	no	\(-1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-i\)	\(e\left(\frac{1}{6}\right)\)	\(-i\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-i\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{1785}(71,\cdot)\)	1785.ea	16	no	\(1\)	\(1\)	\(e\left(\frac{3}{8}\right)\)	\(-i\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(i\)	\(-1\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)
\(\chi_{1785}(73,\cdot)\)	1785.fm	48	no	\(-1\)	\(1\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{13}{48}\right)\)	\(e\left(\frac{11}{24}\right)\)
\(\chi_{1785}(74,\cdot)\)	1785.fh	48	yes	\(1\)	\(1\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(i\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{17}{24}\right)\)

Introduction

L-functions

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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.