LMFDB - Group of Dirichlet characters of modulus 97

Show commands: PariGP / SageMath

sage: H = DirichletGroup(97)

pari: g = idealstar(,97,2)

Character group

sage: G.order() pari: g.no
Order	=	96
sage: H.invariants() pari: g.cyc
Structure	=	$C_{96}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{97}(5,\cdot)$

First 32 of 96 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	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{97}(1,\cdot)$	97.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{97}(2,\cdot)$	97.k	48	yes	$1$	$1$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{11}{24}\right)$
$\chi_{97}(3,\cdot)$	97.k	48	yes	$1$	$1$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{17}{24}\right)$
$\chi_{97}(4,\cdot)$	97.i	24	yes	$1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{23}{24}\right)$	$i$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{11}{12}\right)$
$\chi_{97}(5,\cdot)$	97.l	96	yes	$-1$	$1$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{1}{96}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{31}{96}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{35}{96}\right)$	$e\left(\frac{43}{48}\right)$
$\chi_{97}(6,\cdot)$	97.g	12	yes	$1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{12}\right)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{97}(7,\cdot)$	97.l	96	yes	$-1$	$1$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{31}{96}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{96}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{29}{96}\right)$	$e\left(\frac{37}{48}\right)$
$\chi_{97}(8,\cdot)$	97.h	16	yes	$1$	$1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{3}{8}\right)$	$i$	$e\left(\frac{1}{16}\right)$	$-1$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{3}{8}\right)$	$-i$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{3}{8}\right)$
$\chi_{97}(9,\cdot)$	97.i	24	yes	$1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{24}\right)$	$-i$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{5}{12}\right)$
$\chi_{97}(10,\cdot)$	97.l	96	yes	$-1$	$1$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{35}{96}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{29}{96}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{73}{96}\right)$	$e\left(\frac{17}{48}\right)$
$\chi_{97}(11,\cdot)$	97.k	48	yes	$1$	$1$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{1}{24}\right)$
$\chi_{97}(12,\cdot)$	97.h	16	yes	$1$	$1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{8}\right)$	$-i$	$e\left(\frac{7}{16}\right)$	$-1$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{5}{8}\right)$	$i$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{5}{8}\right)$
$\chi_{97}(13,\cdot)$	97.l	96	yes	$-1$	$1$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{25}{96}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{7}{96}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{11}{96}\right)$	$e\left(\frac{19}{48}\right)$
$\chi_{97}(14,\cdot)$	97.l	96	yes	$-1$	$1$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{65}{96}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{95}{96}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{67}{96}\right)$	$e\left(\frac{11}{48}\right)$
$\chi_{97}(15,\cdot)$	97.l	96	yes	$-1$	$1$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{71}{96}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{89}{96}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{85}{96}\right)$	$e\left(\frac{29}{48}\right)$
$\chi_{97}(16,\cdot)$	97.g	12	yes	$1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{12}\right)$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{97}(17,\cdot)$	97.l	96	yes	$-1$	$1$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{89}{96}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{71}{96}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{43}{96}\right)$	$e\left(\frac{35}{48}\right)$
$\chi_{97}(18,\cdot)$	97.h	16	yes	$1$	$1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{7}{8}\right)$	$i$	$e\left(\frac{13}{16}\right)$	$-1$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{7}{8}\right)$	$-i$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{7}{8}\right)$
$\chi_{97}(19,\cdot)$	97.j	32	yes	$-1$	$1$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{27}{32}\right)$	$-i$	$e\left(\frac{5}{32}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{17}{32}\right)$	$e\left(\frac{9}{16}\right)$
$\chi_{97}(20,\cdot)$	97.j	32	yes	$-1$	$1$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{23}{32}\right)$	$-i$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{5}{32}\right)$	$e\left(\frac{13}{16}\right)$
$\chi_{97}(21,\cdot)$	97.l	96	yes	$-1$	$1$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{5}{96}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{59}{96}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{79}{96}\right)$	$e\left(\frac{23}{48}\right)$
$\chi_{97}(22,\cdot)$	97.d	4	yes	$1$	$1$	$-1$	$-1$	$1$	$i$	$1$	$-i$	$-1$	$1$	$-i$	$-1$
$\chi_{97}(23,\cdot)$	97.l	96	yes	$-1$	$1$	$e\left(\frac{13}{48}\right)$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{77}{96}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{83}{96}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{7}{96}\right)$	$e\left(\frac{47}{48}\right)$
$\chi_{97}(24,\cdot)$	97.i	24	yes	$1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{13}{24}\right)$	$-i$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{1}{12}\right)$
$\chi_{97}(25,\cdot)$	97.k	48	yes	$1$	$1$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{19}{24}\right)$
$\chi_{97}(26,\cdot)$	97.l	96	yes	$-1$	$1$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{59}{96}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{96}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{49}{96}\right)$	$e\left(\frac{41}{48}\right)$
$\chi_{97}(27,\cdot)$	97.h	16	yes	$1$	$1$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{8}\right)$	$-i$	$e\left(\frac{3}{16}\right)$	$-1$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{1}{8}\right)$	$i$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{1}{8}\right)$
$\chi_{97}(28,\cdot)$	97.j	32	yes	$-1$	$1$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{1}{32}\right)$	$i$	$e\left(\frac{31}{32}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{11}{16}\right)$
$\chi_{97}(29,\cdot)$	97.l	96	yes	$-1$	$1$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{13}{96}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{19}{96}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{71}{96}\right)$	$e\left(\frac{31}{48}\right)$
$\chi_{97}(30,\cdot)$	97.j	32	yes	$-1$	$1$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{3}{32}\right)$	$-i$	$e\left(\frac{29}{32}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{1}{16}\right)$
$\chi_{97}(31,\cdot)$	97.k	48	yes	$1$	$1$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{5}{24}\right)$
$\chi_{97}(32,\cdot)$	97.k	48	yes	$1$	$1$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{7}{24}\right)$

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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	$97$
Structure	\(C_{96}\)
Order	$96$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\(\chi_{97}(1,\cdot)\)	97.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{97}(2,\cdot)\)	97.k	48	yes	\(1\)	\(1\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{11}{24}\right)\)
\(\chi_{97}(3,\cdot)\)	97.k	48	yes	\(1\)	\(1\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{17}{24}\right)\)
\(\chi_{97}(4,\cdot)\)	97.i	24	yes	\(1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(i\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{11}{12}\right)\)
\(\chi_{97}(5,\cdot)\)	97.l	96	yes	\(-1\)	\(1\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{1}{96}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{31}{96}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{35}{96}\right)\)	\(e\left(\frac{43}{48}\right)\)
\(\chi_{97}(6,\cdot)\)	97.g	12	yes	\(1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{97}(7,\cdot)\)	97.l	96	yes	\(-1\)	\(1\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{31}{96}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{96}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{29}{96}\right)\)	\(e\left(\frac{37}{48}\right)\)
\(\chi_{97}(8,\cdot)\)	97.h	16	yes	\(1\)	\(1\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(i\)	\(e\left(\frac{1}{16}\right)\)	\(-1\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(-i\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)
\(\chi_{97}(9,\cdot)\)	97.i	24	yes	\(1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(-i\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{5}{12}\right)\)
\(\chi_{97}(10,\cdot)\)	97.l	96	yes	\(-1\)	\(1\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{35}{96}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{29}{96}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{73}{96}\right)\)	\(e\left(\frac{17}{48}\right)\)
\(\chi_{97}(11,\cdot)\)	97.k	48	yes	\(1\)	\(1\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{1}{24}\right)\)
\(\chi_{97}(12,\cdot)\)	97.h	16	yes	\(1\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(-i\)	\(e\left(\frac{7}{16}\right)\)	\(-1\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(i\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)
\(\chi_{97}(13,\cdot)\)	97.l	96	yes	\(-1\)	\(1\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{25}{96}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{7}{96}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{11}{96}\right)\)	\(e\left(\frac{19}{48}\right)\)
\(\chi_{97}(14,\cdot)\)	97.l	96	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{65}{96}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{95}{96}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{67}{96}\right)\)	\(e\left(\frac{11}{48}\right)\)
\(\chi_{97}(15,\cdot)\)	97.l	96	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{71}{96}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{89}{96}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{85}{96}\right)\)	\(e\left(\frac{29}{48}\right)\)
\(\chi_{97}(16,\cdot)\)	97.g	12	yes	\(1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{97}(17,\cdot)\)	97.l	96	yes	\(-1\)	\(1\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{89}{96}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{71}{96}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{43}{96}\right)\)	\(e\left(\frac{35}{48}\right)\)
\(\chi_{97}(18,\cdot)\)	97.h	16	yes	\(1\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(i\)	\(e\left(\frac{13}{16}\right)\)	\(-1\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(-i\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{97}(19,\cdot)\)	97.j	32	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{27}{32}\right)\)	\(-i\)	\(e\left(\frac{5}{32}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{17}{32}\right)\)	\(e\left(\frac{9}{16}\right)\)
\(\chi_{97}(20,\cdot)\)	97.j	32	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{23}{32}\right)\)	\(-i\)	\(e\left(\frac{9}{32}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{5}{32}\right)\)	\(e\left(\frac{13}{16}\right)\)
\(\chi_{97}(21,\cdot)\)	97.l	96	yes	\(-1\)	\(1\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{5}{96}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{59}{96}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{79}{96}\right)\)	\(e\left(\frac{23}{48}\right)\)
\(\chi_{97}(22,\cdot)\)	97.d	4	yes	\(1\)	\(1\)	\(-1\)	\(-1\)	\(1\)	\(i\)	\(1\)	\(-i\)	\(-1\)	\(1\)	\(-i\)	\(-1\)
\(\chi_{97}(23,\cdot)\)	97.l	96	yes	\(-1\)	\(1\)	\(e\left(\frac{13}{48}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{77}{96}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{83}{96}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{7}{96}\right)\)	\(e\left(\frac{47}{48}\right)\)
\(\chi_{97}(24,\cdot)\)	97.i	24	yes	\(1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(-i\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{1}{12}\right)\)
\(\chi_{97}(25,\cdot)\)	97.k	48	yes	\(1\)	\(1\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{19}{24}\right)\)
\(\chi_{97}(26,\cdot)\)	97.l	96	yes	\(-1\)	\(1\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{59}{96}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{96}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{49}{96}\right)\)	\(e\left(\frac{41}{48}\right)\)
\(\chi_{97}(27,\cdot)\)	97.h	16	yes	\(1\)	\(1\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(-i\)	\(e\left(\frac{3}{16}\right)\)	\(-1\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(i\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)
\(\chi_{97}(28,\cdot)\)	97.j	32	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{1}{32}\right)\)	\(i\)	\(e\left(\frac{31}{32}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{3}{32}\right)\)	\(e\left(\frac{11}{16}\right)\)
\(\chi_{97}(29,\cdot)\)	97.l	96	yes	\(-1\)	\(1\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{13}{96}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{19}{96}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{71}{96}\right)\)	\(e\left(\frac{31}{48}\right)\)
\(\chi_{97}(30,\cdot)\)	97.j	32	yes	\(-1\)	\(1\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{3}{32}\right)\)	\(-i\)	\(e\left(\frac{29}{32}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{9}{32}\right)\)	\(e\left(\frac{1}{16}\right)\)
\(\chi_{97}(31,\cdot)\)	97.k	48	yes	\(1\)	\(1\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{5}{24}\right)\)
\(\chi_{97}(32,\cdot)\)	97.k	48	yes	\(1\)	\(1\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{7}{24}\right)\)

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L-functions

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First 32 of 96 characters

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.