LMFDB - Group of Dirichlet characters of modulus 832

sage:H = DirichletGroup(832)

pari:g = idealstar(,832,2)

Character group

sage:G.order() pari:g.no
Order	=	384
sage:H.invariants() pari:g.cyc
Structure	=	$C_{2}\times C_{4}\times C_{48}$
sage:H.gens() pari:g.gen
Generators	=	$\chi_{832}(703,\cdot)$, $\chi_{832}(261,\cdot)$, $\chi_{832}(769,\cdot)$

First 32 of 384 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	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$15$	$17$	$19$	$21$	$23$
$\chi_{832}(1,\cdot)$	832.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{832}(3,\cdot)$	832.cr	48	yes	$-1$	$1$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{11}{24}\right)$
$\chi_{832}(5,\cdot)$	832.cd	16	yes	$-1$	$1$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{9}{16}\right)$	$1$	$i$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{3}{8}\right)$
$\chi_{832}(7,\cdot)$	832.ck	24	no	$1$	$1$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{12}\right)$
$\chi_{832}(9,\cdot)$	832.ci	24	no	$1$	$1$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{11}{12}\right)$
$\chi_{832}(11,\cdot)$	832.cn	48	yes	$1$	$1$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{17}{24}\right)$
$\chi_{832}(15,\cdot)$	832.bs	12	no	$1$	$1$	$e\left(\frac{7}{12}\right)$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{5}{6}\right)$
$\chi_{832}(17,\cdot)$	832.bp	12	no	$1$	$1$	$e\left(\frac{11}{12}\right)$	$i$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{12}\right)$	$i$	$e\left(\frac{1}{6}\right)$
$\chi_{832}(19,\cdot)$	832.cn	48	yes	$1$	$1$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{19}{24}\right)$
$\chi_{832}(21,\cdot)$	832.bx	16	yes	$-1$	$1$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{13}{16}\right)$	$-1$	$i$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{7}{8}\right)$
$\chi_{832}(23,\cdot)$	832.cj	24	no	$-1$	$1$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{1}{12}\right)$
$\chi_{832}(25,\cdot)$	832.bg	8	no	$1$	$1$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{5}{8}\right)$	$-i$	$-i$	$e\left(\frac{1}{8}\right)$	$1$	$-1$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{8}\right)$	$-i$
$\chi_{832}(27,\cdot)$	832.ca	16	no	$-1$	$1$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{5}{16}\right)$	$-i$	$-i$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{3}{8}\right)$
$\chi_{832}(29,\cdot)$	832.cp	48	yes	$1$	$1$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{23}{24}\right)$
$\chi_{832}(31,\cdot)$	832.u	4	no	$1$	$1$	$1$	$i$	$-i$	$1$	$i$	$i$	$-1$	$-i$	$-i$	$1$
$\chi_{832}(33,\cdot)$	832.bv	12	no	$-1$	$1$	$e\left(\frac{1}{6}\right)$	$-i$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{12}\right)$	$i$	$e\left(\frac{1}{6}\right)$
$\chi_{832}(35,\cdot)$	832.cr	48	yes	$-1$	$1$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{19}{24}\right)$
$\chi_{832}(37,\cdot)$	832.cs	48	yes	$-1$	$1$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{17}{24}\right)$
$\chi_{832}(41,\cdot)$	832.ce	24	no	$-1$	$1$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{1}{12}\right)$
$\chi_{832}(43,\cdot)$	832.co	48	yes	$-1$	$1$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{13}{24}\right)$
$\chi_{832}(45,\cdot)$	832.cs	48	yes	$-1$	$1$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{7}{24}\right)$
$\chi_{832}(47,\cdot)$	832.s	4	no	$1$	$1$	$-i$	$1$	$-i$	$-1$	$1$	$-i$	$-1$	$1$	$-1$	$-1$
$\chi_{832}(49,\cdot)$	832.bp	12	no	$1$	$1$	$e\left(\frac{1}{12}\right)$	$-i$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{11}{12}\right)$	$-i$	$e\left(\frac{5}{6}\right)$
$\chi_{832}(51,\cdot)$	832.bz	16	yes	$-1$	$1$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{11}{16}\right)$	$-i$	$i$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{5}{8}\right)$
$\chi_{832}(53,\cdot)$	832.by	16	no	$1$	$1$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{9}{16}\right)$	$i$	$-i$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{3}{8}\right)$
$\chi_{832}(55,\cdot)$	832.cg	24	no	$-1$	$1$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{1}{12}\right)$
$\chi_{832}(57,\cdot)$	832.bc	8	no	$-1$	$1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{3}{8}\right)$	$-1$	$-i$	$e\left(\frac{3}{8}\right)$	$i$	$1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{3}{8}\right)$	$i$
$\chi_{832}(59,\cdot)$	832.cn	48	yes	$1$	$1$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{13}{24}\right)$
$\chi_{832}(61,\cdot)$	832.cp	48	yes	$1$	$1$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{7}{24}\right)$
$\chi_{832}(63,\cdot)$	832.bu	12	no	$1$	$1$	$e\left(\frac{5}{6}\right)$	$i$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{12}\right)$	$-i$	$e\left(\frac{1}{3}\right)$
$\chi_{832}(67,\cdot)$	832.cn	48	yes	$1$	$1$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{23}{24}\right)$
$\chi_{832}(69,\cdot)$	832.cq	48	yes	$1$	$1$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{13}{48}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{13}{24}\right)$

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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 $\F_{q}$
Belyi maps

Modulus	$832$
Structure	\(C_{2}\times C_{4}\times C_{48}\)
Order	$384$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(15\)	\(17\)	\(19\)	\(21\)	\(23\)
\(\chi_{832}(1,\cdot)\)	832.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{832}(3,\cdot)\)	832.cr	48	yes	\(-1\)	\(1\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{11}{24}\right)\)
\(\chi_{832}(5,\cdot)\)	832.cd	16	yes	\(-1\)	\(1\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(1\)	\(i\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)
\(\chi_{832}(7,\cdot)\)	832.ck	24	no	\(1\)	\(1\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{5}{12}\right)\)
\(\chi_{832}(9,\cdot)\)	832.ci	24	no	\(1\)	\(1\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{11}{12}\right)\)
\(\chi_{832}(11,\cdot)\)	832.cn	48	yes	\(1\)	\(1\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{17}{24}\right)\)
\(\chi_{832}(15,\cdot)\)	832.bs	12	no	\(1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{832}(17,\cdot)\)	832.bp	12	no	\(1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(i\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(i\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{832}(19,\cdot)\)	832.cn	48	yes	\(1\)	\(1\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{19}{24}\right)\)
\(\chi_{832}(21,\cdot)\)	832.bx	16	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(-1\)	\(i\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{832}(23,\cdot)\)	832.cj	24	no	\(-1\)	\(1\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{1}{12}\right)\)
\(\chi_{832}(25,\cdot)\)	832.bg	8	no	\(1\)	\(1\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(-i\)	\(-i\)	\(e\left(\frac{1}{8}\right)\)	\(1\)	\(-1\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(-i\)
\(\chi_{832}(27,\cdot)\)	832.ca	16	no	\(-1\)	\(1\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(-i\)	\(-i\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)
\(\chi_{832}(29,\cdot)\)	832.cp	48	yes	\(1\)	\(1\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{23}{24}\right)\)
\(\chi_{832}(31,\cdot)\)	832.u	4	no	\(1\)	\(1\)	\(1\)	\(i\)	\(-i\)	\(1\)	\(i\)	\(i\)	\(-1\)	\(-i\)	\(-i\)	\(1\)
\(\chi_{832}(33,\cdot)\)	832.bv	12	no	\(-1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(-i\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(i\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{832}(35,\cdot)\)	832.cr	48	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{19}{24}\right)\)
\(\chi_{832}(37,\cdot)\)	832.cs	48	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{17}{24}\right)\)
\(\chi_{832}(41,\cdot)\)	832.ce	24	no	\(-1\)	\(1\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{1}{12}\right)\)
\(\chi_{832}(43,\cdot)\)	832.co	48	yes	\(-1\)	\(1\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{13}{24}\right)\)
\(\chi_{832}(45,\cdot)\)	832.cs	48	yes	\(-1\)	\(1\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{7}{24}\right)\)
\(\chi_{832}(47,\cdot)\)	832.s	4	no	\(1\)	\(1\)	\(-i\)	\(1\)	\(-i\)	\(-1\)	\(1\)	\(-i\)	\(-1\)	\(1\)	\(-1\)	\(-1\)
\(\chi_{832}(49,\cdot)\)	832.bp	12	no	\(1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(-i\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(-i\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{832}(51,\cdot)\)	832.bz	16	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(-i\)	\(i\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)
\(\chi_{832}(53,\cdot)\)	832.by	16	no	\(1\)	\(1\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(i\)	\(-i\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)
\(\chi_{832}(55,\cdot)\)	832.cg	24	no	\(-1\)	\(1\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{1}{12}\right)\)
\(\chi_{832}(57,\cdot)\)	832.bc	8	no	\(-1\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(-1\)	\(-i\)	\(e\left(\frac{3}{8}\right)\)	\(i\)	\(1\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(i\)
\(\chi_{832}(59,\cdot)\)	832.cn	48	yes	\(1\)	\(1\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{13}{24}\right)\)
\(\chi_{832}(61,\cdot)\)	832.cp	48	yes	\(1\)	\(1\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{7}{24}\right)\)
\(\chi_{832}(63,\cdot)\)	832.bu	12	no	\(1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(i\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(-i\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{832}(67,\cdot)\)	832.cn	48	yes	\(1\)	\(1\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{23}{24}\right)\)
\(\chi_{832}(69,\cdot)\)	832.cq	48	yes	\(1\)	\(1\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{13}{48}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{13}{24}\right)\)

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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.