LMFDB - Group of Dirichlet characters of modulus 608

Show commands: PariGP / SageMath

sage: H = DirichletGroup(608)

pari: g = idealstar(,608,2)

Character group

sage: G.order() pari: g.no
Order	=	288
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{72}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{608}(191,\cdot)$, $\chi_{608}(229,\cdot)$, $\chi_{608}(97,\cdot)$

First 32 of 288 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	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$17$	$21$	$23$
$\chi_{608}(1,\cdot)$	608.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{608}(3,\cdot)$	608.bt	72	yes	$1$	$1$	$e\left(\frac{1}{72}\right)$	$e\left(\frac{67}{72}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{17}{72}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{43}{72}\right)$	$e\left(\frac{7}{36}\right)$
$\chi_{608}(5,\cdot)$	608.bs	72	yes	$1$	$1$	$e\left(\frac{67}{72}\right)$	$e\left(\frac{25}{72}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{23}{72}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{37}{72}\right)$	$e\left(\frac{19}{36}\right)$
$\chi_{608}(7,\cdot)$	608.bc	12	no	$-1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{7}{12}\right)$	$1$	$e\left(\frac{1}{6}\right)$	$-i$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{608}(9,\cdot)$	608.bq	36	no	$1$	$1$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{7}{18}\right)$
$\chi_{608}(11,\cdot)$	608.bk	24	yes	$-1$	$1$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{7}{24}\right)$	$-i$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{7}{12}\right)$
$\chi_{608}(13,\cdot)$	608.bv	72	yes	$-1$	$1$	$e\left(\frac{17}{72}\right)$	$e\left(\frac{23}{72}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{37}{72}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{47}{72}\right)$	$e\left(\frac{29}{36}\right)$
$\chi_{608}(15,\cdot)$	608.bh	18	no	$1$	$1$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{13}{18}\right)$
$\chi_{608}(17,\cdot)$	608.bf	18	no	$1$	$1$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{1}{9}\right)$
$\chi_{608}(21,\cdot)$	608.bv	72	yes	$-1$	$1$	$e\left(\frac{43}{72}\right)$	$e\left(\frac{37}{72}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{47}{72}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{13}{72}\right)$	$e\left(\frac{31}{36}\right)$
$\chi_{608}(23,\cdot)$	608.bp	36	no	$-1$	$1$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{2}{9}\right)$
$\chi_{608}(25,\cdot)$	608.bq	36	no	$1$	$1$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{1}{18}\right)$
$\chi_{608}(27,\cdot)$	608.bn	24	yes	$1$	$1$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{19}{24}\right)$	$-i$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{7}{12}\right)$
$\chi_{608}(29,\cdot)$	608.bv	72	yes	$-1$	$1$	$e\left(\frac{29}{72}\right)$	$e\left(\frac{35}{72}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{25}{72}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{59}{72}\right)$	$e\left(\frac{5}{36}\right)$
$\chi_{608}(31,\cdot)$	608.n	6	no	$1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{608}(33,\cdot)$	608.bd	18	no	$-1$	$1$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{7}{9}\right)$
$\chi_{608}(35,\cdot)$	608.bu	72	yes	$-1$	$1$	$e\left(\frac{37}{72}\right)$	$e\left(\frac{67}{72}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{53}{72}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{7}{72}\right)$	$e\left(\frac{7}{36}\right)$
$\chi_{608}(37,\cdot)$	608.w	8	yes	$-1$	$1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{1}{8}\right)$	$i$	$-i$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{3}{8}\right)$	$1$	$-1$	$e\left(\frac{1}{8}\right)$	$-i$
$\chi_{608}(39,\cdot)$	608.l	4	no	$-1$	$1$	$i$	$i$	$1$	$-1$	$-i$	$-i$	$-1$	$1$	$i$	$1$
$\chi_{608}(41,\cdot)$	608.br	36	no	$-1$	$1$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{17}{18}\right)$
$\chi_{608}(43,\cdot)$	608.bu	72	yes	$-1$	$1$	$e\left(\frac{67}{72}\right)$	$e\left(\frac{61}{72}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{59}{72}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{1}{72}\right)$	$e\left(\frac{1}{36}\right)$
$\chi_{608}(45,\cdot)$	608.bm	24	yes	$1$	$1$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{5}{24}\right)$	$-i$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{11}{12}\right)$
$\chi_{608}(47,\cdot)$	608.bg	18	no	$-1$	$1$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{7}{18}\right)$
$\chi_{608}(49,\cdot)$	608.t	6	no	$1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{608}(51,\cdot)$	608.bt	72	yes	$1$	$1$	$e\left(\frac{53}{72}\right)$	$e\left(\frac{23}{72}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{37}{72}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{47}{72}\right)$	$e\left(\frac{11}{36}\right)$
$\chi_{608}(53,\cdot)$	608.bv	72	yes	$-1$	$1$	$e\left(\frac{59}{72}\right)$	$e\left(\frac{29}{72}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{31}{72}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{53}{72}\right)$	$e\left(\frac{35}{36}\right)$
$\chi_{608}(55,\cdot)$	608.bp	36	no	$-1$	$1$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{1}{9}\right)$
$\chi_{608}(59,\cdot)$	608.bt	72	yes	$1$	$1$	$e\left(\frac{43}{72}\right)$	$e\left(\frac{1}{72}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{11}{72}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{49}{72}\right)$	$e\left(\frac{13}{36}\right)$
$\chi_{608}(61,\cdot)$	608.bs	72	yes	$1$	$1$	$e\left(\frac{41}{72}\right)$	$e\left(\frac{11}{72}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{13}{72}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{71}{72}\right)$	$e\left(\frac{17}{36}\right)$
$\chi_{608}(63,\cdot)$	608.bj	18	no	$-1$	$1$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{1}{18}\right)$
$\chi_{608}(65,\cdot)$	608.r	6	no	$-1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{608}(67,\cdot)$	608.bt	72	yes	$1$	$1$	$e\left(\frac{65}{72}\right)$	$e\left(\frac{35}{72}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{25}{72}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{59}{72}\right)$	$e\left(\frac{23}{36}\right)$

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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	$608$
Structure	\(C_{2}\times C_{2}\times C_{72}\)
Order	$288$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(21\)	\(23\)
\(\chi_{608}(1,\cdot)\)	608.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{608}(3,\cdot)\)	608.bt	72	yes	\(1\)	\(1\)	\(e\left(\frac{1}{72}\right)\)	\(e\left(\frac{67}{72}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{17}{72}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{43}{72}\right)\)	\(e\left(\frac{7}{36}\right)\)
\(\chi_{608}(5,\cdot)\)	608.bs	72	yes	\(1\)	\(1\)	\(e\left(\frac{67}{72}\right)\)	\(e\left(\frac{25}{72}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{23}{72}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{37}{72}\right)\)	\(e\left(\frac{19}{36}\right)\)
\(\chi_{608}(7,\cdot)\)	608.bc	12	no	\(-1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(-i\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{608}(9,\cdot)\)	608.bq	36	no	\(1\)	\(1\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{7}{18}\right)\)
\(\chi_{608}(11,\cdot)\)	608.bk	24	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(-i\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{7}{12}\right)\)
\(\chi_{608}(13,\cdot)\)	608.bv	72	yes	\(-1\)	\(1\)	\(e\left(\frac{17}{72}\right)\)	\(e\left(\frac{23}{72}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{37}{72}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{47}{72}\right)\)	\(e\left(\frac{29}{36}\right)\)
\(\chi_{608}(15,\cdot)\)	608.bh	18	no	\(1\)	\(1\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{13}{18}\right)\)
\(\chi_{608}(17,\cdot)\)	608.bf	18	no	\(1\)	\(1\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{1}{9}\right)\)
\(\chi_{608}(21,\cdot)\)	608.bv	72	yes	\(-1\)	\(1\)	\(e\left(\frac{43}{72}\right)\)	\(e\left(\frac{37}{72}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{47}{72}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{13}{72}\right)\)	\(e\left(\frac{31}{36}\right)\)
\(\chi_{608}(23,\cdot)\)	608.bp	36	no	\(-1\)	\(1\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{2}{9}\right)\)
\(\chi_{608}(25,\cdot)\)	608.bq	36	no	\(1\)	\(1\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{1}{18}\right)\)
\(\chi_{608}(27,\cdot)\)	608.bn	24	yes	\(1\)	\(1\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(-i\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{7}{12}\right)\)
\(\chi_{608}(29,\cdot)\)	608.bv	72	yes	\(-1\)	\(1\)	\(e\left(\frac{29}{72}\right)\)	\(e\left(\frac{35}{72}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{25}{72}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{59}{72}\right)\)	\(e\left(\frac{5}{36}\right)\)
\(\chi_{608}(31,\cdot)\)	608.n	6	no	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{608}(33,\cdot)\)	608.bd	18	no	\(-1\)	\(1\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{7}{9}\right)\)
\(\chi_{608}(35,\cdot)\)	608.bu	72	yes	\(-1\)	\(1\)	\(e\left(\frac{37}{72}\right)\)	\(e\left(\frac{67}{72}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{53}{72}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{7}{72}\right)\)	\(e\left(\frac{7}{36}\right)\)
\(\chi_{608}(37,\cdot)\)	608.w	8	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(i\)	\(-i\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(1\)	\(-1\)	\(e\left(\frac{1}{8}\right)\)	\(-i\)
\(\chi_{608}(39,\cdot)\)	608.l	4	no	\(-1\)	\(1\)	\(i\)	\(i\)	\(1\)	\(-1\)	\(-i\)	\(-i\)	\(-1\)	\(1\)	\(i\)	\(1\)
\(\chi_{608}(41,\cdot)\)	608.br	36	no	\(-1\)	\(1\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{17}{18}\right)\)
\(\chi_{608}(43,\cdot)\)	608.bu	72	yes	\(-1\)	\(1\)	\(e\left(\frac{67}{72}\right)\)	\(e\left(\frac{61}{72}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{59}{72}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{1}{72}\right)\)	\(e\left(\frac{1}{36}\right)\)
\(\chi_{608}(45,\cdot)\)	608.bm	24	yes	\(1\)	\(1\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(-i\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{11}{12}\right)\)
\(\chi_{608}(47,\cdot)\)	608.bg	18	no	\(-1\)	\(1\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{7}{18}\right)\)
\(\chi_{608}(49,\cdot)\)	608.t	6	no	\(1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{608}(51,\cdot)\)	608.bt	72	yes	\(1\)	\(1\)	\(e\left(\frac{53}{72}\right)\)	\(e\left(\frac{23}{72}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{37}{72}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{47}{72}\right)\)	\(e\left(\frac{11}{36}\right)\)
\(\chi_{608}(53,\cdot)\)	608.bv	72	yes	\(-1\)	\(1\)	\(e\left(\frac{59}{72}\right)\)	\(e\left(\frac{29}{72}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{31}{72}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{53}{72}\right)\)	\(e\left(\frac{35}{36}\right)\)
\(\chi_{608}(55,\cdot)\)	608.bp	36	no	\(-1\)	\(1\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{1}{9}\right)\)
\(\chi_{608}(59,\cdot)\)	608.bt	72	yes	\(1\)	\(1\)	\(e\left(\frac{43}{72}\right)\)	\(e\left(\frac{1}{72}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{11}{72}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{49}{72}\right)\)	\(e\left(\frac{13}{36}\right)\)
\(\chi_{608}(61,\cdot)\)	608.bs	72	yes	\(1\)	\(1\)	\(e\left(\frac{41}{72}\right)\)	\(e\left(\frac{11}{72}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{13}{72}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{71}{72}\right)\)	\(e\left(\frac{17}{36}\right)\)
\(\chi_{608}(63,\cdot)\)	608.bj	18	no	\(-1\)	\(1\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{1}{18}\right)\)
\(\chi_{608}(65,\cdot)\)	608.r	6	no	\(-1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{608}(67,\cdot)\)	608.bt	72	yes	\(1\)	\(1\)	\(e\left(\frac{65}{72}\right)\)	\(e\left(\frac{35}{72}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{25}{72}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{59}{72}\right)\)	\(e\left(\frac{23}{36}\right)\)

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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.