LMFDB - Group of Dirichlet characters of modulus 980

Show commands: PariGP / SageMath

sage: H = DirichletGroup(980)

pari: g = idealstar(,980,2)

Character group

sage: G.order() pari: g.no
Order	=	336
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{84}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{980}(491,\cdot)$, $\chi_{980}(197,\cdot)$, $\chi_{980}(101,\cdot)$

First 32 of 336 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	$-1$	$1$	$3$	$9$	$11$	$13$	$17$	$19$	$23$	$27$	$29$	$31$
$\chi_{980}(1,\cdot)$	980.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{980}(3,\cdot)$	980.bt	84	yes	$-1$	$1$	$e\left(\frac{65}{84}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{29}{84}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{55}{84}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{980}(9,\cdot)$	980.bn	42	no	$1$	$1$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{980}(11,\cdot)$	980.bm	42	no	$-1$	$1$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{980}(13,\cdot)$	980.bi	28	no	$1$	$1$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{11}{28}\right)$	$1$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{9}{14}\right)$	$-1$
$\chi_{980}(17,\cdot)$	980.bu	84	no	$1$	$1$	$e\left(\frac{29}{84}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{11}{84}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{31}{84}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{980}(19,\cdot)$	980.s	6	no	$1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$1$	$e\left(\frac{1}{3}\right)$
$\chi_{980}(23,\cdot)$	980.bs	84	yes	$1$	$1$	$e\left(\frac{55}{84}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{31}{84}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{11}{84}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{980}(27,\cdot)$	980.bj	28	yes	$-1$	$1$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{1}{28}\right)$	$-1$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{11}{14}\right)$	$1$
$\chi_{980}(29,\cdot)$	980.bd	14	no	$1$	$1$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{3}{14}\right)$	$1$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{5}{7}\right)$	$1$
$\chi_{980}(31,\cdot)$	980.o	6	no	$1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$1$	$1$	$e\left(\frac{2}{3}\right)$
$\chi_{980}(33,\cdot)$	980.bu	84	no	$1$	$1$	$e\left(\frac{19}{84}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{13}{84}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{29}{84}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{980}(37,\cdot)$	980.bv	84	no	$-1$	$1$	$e\left(\frac{43}{84}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{25}{84}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{59}{84}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{980}(39,\cdot)$	980.bq	42	yes	$-1$	$1$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{980}(41,\cdot)$	980.bc	14	no	$-1$	$1$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{13}{14}\right)$	$-1$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{3}{7}\right)$	$-1$
$\chi_{980}(43,\cdot)$	980.bk	28	yes	$1$	$1$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{9}{28}\right)$	$1$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{1}{14}\right)$	$-1$
$\chi_{980}(47,\cdot)$	980.bt	84	yes	$-1$	$1$	$e\left(\frac{31}{84}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{19}{84}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{65}{84}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{980}(51,\cdot)$	980.bm	42	no	$-1$	$1$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{980}(53,\cdot)$	980.bv	84	no	$-1$	$1$	$e\left(\frac{41}{84}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{59}{84}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{25}{84}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{980}(57,\cdot)$	980.bh	28	no	$-1$	$1$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{19}{28}\right)$	$-1$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{13}{14}\right)$	$1$
$\chi_{980}(59,\cdot)$	980.bl	42	yes	$1$	$1$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{980}(61,\cdot)$	980.bo	42	no	$-1$	$1$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{980}(67,\cdot)$	980.x	12	no	$1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$-i$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{12}\right)$	$-i$	$-1$	$e\left(\frac{1}{6}\right)$
$\chi_{980}(69,\cdot)$	980.z	14	no	$-1$	$1$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{5}{7}\right)$	$-1$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{5}{7}\right)$	$-1$
$\chi_{980}(71,\cdot)$	980.be	14	no	$-1$	$1$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{2}{7}\right)$	$-1$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{2}{7}\right)$	$-1$
$\chi_{980}(73,\cdot)$	980.bu	84	no	$1$	$1$	$e\left(\frac{11}{84}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{65}{84}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{61}{84}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{980}(79,\cdot)$	980.p	6	no	$-1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$1$	$e\left(\frac{5}{6}\right)$
$\chi_{980}(81,\cdot)$	980.bg	21	no	$1$	$1$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{980}(83,\cdot)$	980.bj	28	yes	$-1$	$1$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{3}{28}\right)$	$-1$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{5}{14}\right)$	$1$
$\chi_{980}(87,\cdot)$	980.bt	84	yes	$-1$	$1$	$e\left(\frac{59}{84}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{47}{84}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{37}{84}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{980}(89,\cdot)$	980.br	42	no	$-1$	$1$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{980}(93,\cdot)$	980.bv	84	no	$-1$	$1$	$e\left(\frac{37}{84}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{43}{84}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{41}{84}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{1}{3}\right)$

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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	$980$
Structure	\(C_{2}\times C_{2}\times C_{84}\)
Order	$336$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(9\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(27\)	\(29\)	\(31\)
\(\chi_{980}(1,\cdot)\)	980.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{980}(3,\cdot)\)	980.bt	84	yes	\(-1\)	\(1\)	\(e\left(\frac{65}{84}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{29}{84}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{55}{84}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{980}(9,\cdot)\)	980.bn	42	no	\(1\)	\(1\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{980}(11,\cdot)\)	980.bm	42	no	\(-1\)	\(1\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{980}(13,\cdot)\)	980.bi	28	no	\(1\)	\(1\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(1\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(-1\)
\(\chi_{980}(17,\cdot)\)	980.bu	84	no	\(1\)	\(1\)	\(e\left(\frac{29}{84}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{11}{84}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{31}{84}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{980}(19,\cdot)\)	980.s	6	no	\(1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{980}(23,\cdot)\)	980.bs	84	yes	\(1\)	\(1\)	\(e\left(\frac{55}{84}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{31}{84}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{11}{84}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{980}(27,\cdot)\)	980.bj	28	yes	\(-1\)	\(1\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(-1\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(1\)
\(\chi_{980}(29,\cdot)\)	980.bd	14	no	\(1\)	\(1\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(1\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(1\)
\(\chi_{980}(31,\cdot)\)	980.o	6	no	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{980}(33,\cdot)\)	980.bu	84	no	\(1\)	\(1\)	\(e\left(\frac{19}{84}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{13}{84}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{29}{84}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{980}(37,\cdot)\)	980.bv	84	no	\(-1\)	\(1\)	\(e\left(\frac{43}{84}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{25}{84}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{59}{84}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{980}(39,\cdot)\)	980.bq	42	yes	\(-1\)	\(1\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{980}(41,\cdot)\)	980.bc	14	no	\(-1\)	\(1\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(-1\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(-1\)
\(\chi_{980}(43,\cdot)\)	980.bk	28	yes	\(1\)	\(1\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(1\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(-1\)
\(\chi_{980}(47,\cdot)\)	980.bt	84	yes	\(-1\)	\(1\)	\(e\left(\frac{31}{84}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{19}{84}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{65}{84}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{980}(51,\cdot)\)	980.bm	42	no	\(-1\)	\(1\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{980}(53,\cdot)\)	980.bv	84	no	\(-1\)	\(1\)	\(e\left(\frac{41}{84}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{59}{84}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{25}{84}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{980}(57,\cdot)\)	980.bh	28	no	\(-1\)	\(1\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(-1\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(1\)
\(\chi_{980}(59,\cdot)\)	980.bl	42	yes	\(1\)	\(1\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{980}(61,\cdot)\)	980.bo	42	no	\(-1\)	\(1\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{980}(67,\cdot)\)	980.x	12	no	\(1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-i\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(-i\)	\(-1\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{980}(69,\cdot)\)	980.z	14	no	\(-1\)	\(1\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(-1\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(-1\)
\(\chi_{980}(71,\cdot)\)	980.be	14	no	\(-1\)	\(1\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(-1\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(-1\)
\(\chi_{980}(73,\cdot)\)	980.bu	84	no	\(1\)	\(1\)	\(e\left(\frac{11}{84}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{65}{84}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{61}{84}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{980}(79,\cdot)\)	980.p	6	no	\(-1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{980}(81,\cdot)\)	980.bg	21	no	\(1\)	\(1\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{980}(83,\cdot)\)	980.bj	28	yes	\(-1\)	\(1\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(-1\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(1\)
\(\chi_{980}(87,\cdot)\)	980.bt	84	yes	\(-1\)	\(1\)	\(e\left(\frac{59}{84}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{47}{84}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{37}{84}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{980}(89,\cdot)\)	980.br	42	no	\(-1\)	\(1\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{980}(93,\cdot)\)	980.bv	84	no	\(-1\)	\(1\)	\(e\left(\frac{37}{84}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{43}{84}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{41}{84}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{1}{3}\right)\)

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.