LMFDB - Group of Dirichlet characters of modulus 609

Show commands: PariGP / SageMath

sage: H = DirichletGroup(609)

pari: g = idealstar(,609,2)

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	=	$\chi_{609}(407,\cdot)$, $\chi_{609}(262,\cdot)$, $\chi_{609}(379,\cdot)$

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	$-1$	$1$	$2$	$4$	$5$	$8$	$10$	$11$	$13$	$16$	$17$	$19$
$\chi_{609}(1,\cdot)$	609.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{609}(2,\cdot)$	609.bv	84	yes	$1$	$1$	$e\left(\frac{17}{84}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{13}{84}\right)$	$e\left(\frac{61}{84}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{83}{84}\right)$
$\chi_{609}(4,\cdot)$	609.bn	42	no	$1$	$1$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{41}{42}\right)$
$\chi_{609}(5,\cdot)$	609.br	42	yes	$1$	$1$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{21}\right)$
$\chi_{609}(8,\cdot)$	609.bi	28	no	$1$	$1$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{3}{7}\right)$	$-i$	$e\left(\frac{27}{28}\right)$
$\chi_{609}(10,\cdot)$	609.bu	84	no	$1$	$1$	$e\left(\frac{13}{84}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{5}{84}\right)$	$e\left(\frac{17}{84}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{19}{84}\right)$
$\chi_{609}(11,\cdot)$	609.bv	84	yes	$1$	$1$	$e\left(\frac{61}{84}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{17}{84}\right)$	$e\left(\frac{41}{84}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{31}{84}\right)$
$\chi_{609}(13,\cdot)$	609.bf	14	no	$-1$	$1$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{4}{7}\right)$	$1$	$e\left(\frac{2}{7}\right)$
$\chi_{609}(16,\cdot)$	609.bg	21	no	$1$	$1$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{20}{21}\right)$
$\chi_{609}(17,\cdot)$	609.y	12	yes	$-1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$-i$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{11}{12}\right)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{7}{12}\right)$
$\chi_{609}(19,\cdot)$	609.bu	84	no	$1$	$1$	$e\left(\frac{83}{84}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{19}{84}\right)$	$e\left(\frac{31}{84}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{84}\right)$
$\chi_{609}(20,\cdot)$	609.bd	14	yes	$1$	$1$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{3}{7}\right)$	$1$	$e\left(\frac{3}{14}\right)$
$\chi_{609}(22,\cdot)$	609.bc	14	no	$1$	$1$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{5}{7}\right)$	$-1$	$e\left(\frac{5}{14}\right)$
$\chi_{609}(23,\cdot)$	609.bl	42	yes	$-1$	$1$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{21}\right)$
$\chi_{609}(25,\cdot)$	609.bg	21	no	$1$	$1$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{10}{21}\right)$
$\chi_{609}(26,\cdot)$	609.bs	84	yes	$-1$	$1$	$e\left(\frac{71}{84}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{37}{84}\right)$	$e\left(\frac{67}{84}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{23}{84}\right)$
$\chi_{609}(31,\cdot)$	609.bu	84	no	$1$	$1$	$e\left(\frac{31}{84}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{83}{84}\right)$	$e\left(\frac{47}{84}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{13}{84}\right)$
$\chi_{609}(32,\cdot)$	609.bv	84	yes	$1$	$1$	$e\left(\frac{1}{84}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{65}{84}\right)$	$e\left(\frac{53}{84}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{79}{84}\right)$
$\chi_{609}(34,\cdot)$	609.bf	14	no	$-1$	$1$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{1}{7}\right)$	$1$	$e\left(\frac{4}{7}\right)$
$\chi_{609}(37,\cdot)$	609.bt	84	no	$-1$	$1$	$e\left(\frac{65}{84}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{67}{84}\right)$	$e\left(\frac{1}{84}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{53}{84}\right)$
$\chi_{609}(38,\cdot)$	609.br	42	yes	$1$	$1$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{21}\right)$
$\chi_{609}(40,\cdot)$	609.bu	84	no	$1$	$1$	$e\left(\frac{47}{84}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{31}{84}\right)$	$e\left(\frac{55}{84}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{17}{84}\right)$
$\chi_{609}(41,\cdot)$	609.k	4	yes	$-1$	$1$	$-i$	$-1$	$-1$	$i$	$i$	$-i$	$1$	$1$	$i$	$-i$
$\chi_{609}(43,\cdot)$	609.bk	28	no	$-1$	$1$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{6}{7}\right)$	$-i$	$e\left(\frac{5}{28}\right)$
$\chi_{609}(44,\cdot)$	609.bv	84	yes	$1$	$1$	$e\left(\frac{11}{84}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{43}{84}\right)$	$e\left(\frac{79}{84}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{29}{84}\right)$
$\chi_{609}(46,\cdot)$	609.x	12	no	$-1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$i$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{12}\right)$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{12}\right)$
$\chi_{609}(47,\cdot)$	609.bs	84	yes	$-1$	$1$	$e\left(\frac{47}{84}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{73}{84}\right)$	$e\left(\frac{55}{84}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{59}{84}\right)$
$\chi_{609}(50,\cdot)$	609.bi	28	no	$1$	$1$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{3}{7}\right)$	$i$	$e\left(\frac{13}{28}\right)$
$\chi_{609}(52,\cdot)$	609.bq	42	no	$-1$	$1$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{42}\right)$
$\chi_{609}(53,\cdot)$	609.bl	42	yes	$-1$	$1$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{19}{21}\right)$
$\chi_{609}(55,\cdot)$	609.bh	28	no	$1$	$1$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{5}{7}\right)$	$-i$	$e\left(\frac{17}{28}\right)$
$\chi_{609}(59,\cdot)$	609.q	6	no	$1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$

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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	$609$
Structure	\(C_{2}\times C_{2}\times C_{84}\)
Order	$336$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(8\)	\(10\)	\(11\)	\(13\)	\(16\)	\(17\)	\(19\)
\(\chi_{609}(1,\cdot)\)	609.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{609}(2,\cdot)\)	609.bv	84	yes	\(1\)	\(1\)	\(e\left(\frac{17}{84}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{13}{84}\right)\)	\(e\left(\frac{61}{84}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{83}{84}\right)\)
\(\chi_{609}(4,\cdot)\)	609.bn	42	no	\(1\)	\(1\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{41}{42}\right)\)
\(\chi_{609}(5,\cdot)\)	609.br	42	yes	\(1\)	\(1\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{21}\right)\)
\(\chi_{609}(8,\cdot)\)	609.bi	28	no	\(1\)	\(1\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(-i\)	\(e\left(\frac{27}{28}\right)\)
\(\chi_{609}(10,\cdot)\)	609.bu	84	no	\(1\)	\(1\)	\(e\left(\frac{13}{84}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{5}{84}\right)\)	\(e\left(\frac{17}{84}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{19}{84}\right)\)
\(\chi_{609}(11,\cdot)\)	609.bv	84	yes	\(1\)	\(1\)	\(e\left(\frac{61}{84}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{17}{84}\right)\)	\(e\left(\frac{41}{84}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{31}{84}\right)\)
\(\chi_{609}(13,\cdot)\)	609.bf	14	no	\(-1\)	\(1\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(1\)	\(e\left(\frac{2}{7}\right)\)
\(\chi_{609}(16,\cdot)\)	609.bg	21	no	\(1\)	\(1\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{20}{21}\right)\)
\(\chi_{609}(17,\cdot)\)	609.y	12	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-i\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)
\(\chi_{609}(19,\cdot)\)	609.bu	84	no	\(1\)	\(1\)	\(e\left(\frac{83}{84}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{19}{84}\right)\)	\(e\left(\frac{31}{84}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{84}\right)\)
\(\chi_{609}(20,\cdot)\)	609.bd	14	yes	\(1\)	\(1\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(1\)	\(e\left(\frac{3}{14}\right)\)
\(\chi_{609}(22,\cdot)\)	609.bc	14	no	\(1\)	\(1\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(-1\)	\(e\left(\frac{5}{14}\right)\)
\(\chi_{609}(23,\cdot)\)	609.bl	42	yes	\(-1\)	\(1\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{21}\right)\)
\(\chi_{609}(25,\cdot)\)	609.bg	21	no	\(1\)	\(1\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{10}{21}\right)\)
\(\chi_{609}(26,\cdot)\)	609.bs	84	yes	\(-1\)	\(1\)	\(e\left(\frac{71}{84}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{37}{84}\right)\)	\(e\left(\frac{67}{84}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{23}{84}\right)\)
\(\chi_{609}(31,\cdot)\)	609.bu	84	no	\(1\)	\(1\)	\(e\left(\frac{31}{84}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{83}{84}\right)\)	\(e\left(\frac{47}{84}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{13}{84}\right)\)
\(\chi_{609}(32,\cdot)\)	609.bv	84	yes	\(1\)	\(1\)	\(e\left(\frac{1}{84}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{65}{84}\right)\)	\(e\left(\frac{53}{84}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{79}{84}\right)\)
\(\chi_{609}(34,\cdot)\)	609.bf	14	no	\(-1\)	\(1\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(1\)	\(e\left(\frac{4}{7}\right)\)
\(\chi_{609}(37,\cdot)\)	609.bt	84	no	\(-1\)	\(1\)	\(e\left(\frac{65}{84}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{67}{84}\right)\)	\(e\left(\frac{1}{84}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{53}{84}\right)\)
\(\chi_{609}(38,\cdot)\)	609.br	42	yes	\(1\)	\(1\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{21}\right)\)
\(\chi_{609}(40,\cdot)\)	609.bu	84	no	\(1\)	\(1\)	\(e\left(\frac{47}{84}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{31}{84}\right)\)	\(e\left(\frac{55}{84}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{17}{84}\right)\)
\(\chi_{609}(41,\cdot)\)	609.k	4	yes	\(-1\)	\(1\)	\(-i\)	\(-1\)	\(-1\)	\(i\)	\(i\)	\(-i\)	\(1\)	\(1\)	\(i\)	\(-i\)
\(\chi_{609}(43,\cdot)\)	609.bk	28	no	\(-1\)	\(1\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(-i\)	\(e\left(\frac{5}{28}\right)\)
\(\chi_{609}(44,\cdot)\)	609.bv	84	yes	\(1\)	\(1\)	\(e\left(\frac{11}{84}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{43}{84}\right)\)	\(e\left(\frac{79}{84}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{29}{84}\right)\)
\(\chi_{609}(46,\cdot)\)	609.x	12	no	\(-1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(i\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)
\(\chi_{609}(47,\cdot)\)	609.bs	84	yes	\(-1\)	\(1\)	\(e\left(\frac{47}{84}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{73}{84}\right)\)	\(e\left(\frac{55}{84}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{59}{84}\right)\)
\(\chi_{609}(50,\cdot)\)	609.bi	28	no	\(1\)	\(1\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(i\)	\(e\left(\frac{13}{28}\right)\)
\(\chi_{609}(52,\cdot)\)	609.bq	42	no	\(-1\)	\(1\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{11}{42}\right)\)
\(\chi_{609}(53,\cdot)\)	609.bl	42	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{19}{21}\right)\)
\(\chi_{609}(55,\cdot)\)	609.bh	28	no	\(1\)	\(1\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(-i\)	\(e\left(\frac{17}{28}\right)\)
\(\chi_{609}(59,\cdot)\)	609.q	6	no	\(1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)

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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.