LMFDB - Group of Dirichlet characters of modulus 736

Show commands: PariGP / SageMath

sage: H = DirichletGroup(736)

pari: g = idealstar(,736,2)

Character group

sage: G.order() pari: g.no
Order	=	352
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{88}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{736}(415,\cdot)$, $\chi_{736}(645,\cdot)$, $\chi_{736}(97,\cdot)$

First 32 of 352 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	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$17$	$19$	$21$
$\chi_{736}(1,\cdot)$	736.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{736}(3,\cdot)$	736.bd	88	yes	$-1$	$1$	$e\left(\frac{23}{88}\right)$	$e\left(\frac{9}{88}\right)$	$e\left(\frac{3}{44}\right)$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{81}{88}\right)$	$e\left(\frac{71}{88}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{3}{88}\right)$	$e\left(\frac{29}{88}\right)$
$\chi_{736}(5,\cdot)$	736.bc	88	yes	$-1$	$1$	$e\left(\frac{9}{88}\right)$	$e\left(\frac{15}{88}\right)$	$e\left(\frac{5}{44}\right)$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{3}{88}\right)$	$e\left(\frac{45}{88}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{49}{88}\right)$	$e\left(\frac{19}{88}\right)$
$\chi_{736}(7,\cdot)$	736.bb	44	no	$1$	$1$	$e\left(\frac{3}{44}\right)$	$e\left(\frac{5}{44}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{37}{44}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{21}{44}\right)$
$\chi_{736}(9,\cdot)$	736.ba	44	no	$1$	$1$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{37}{44}\right)$	$e\left(\frac{27}{44}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{3}{44}\right)$	$e\left(\frac{29}{44}\right)$
$\chi_{736}(11,\cdot)$	736.be	88	yes	$1$	$1$	$e\left(\frac{81}{88}\right)$	$e\left(\frac{3}{88}\right)$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{37}{44}\right)$	$e\left(\frac{27}{88}\right)$	$e\left(\frac{9}{88}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{1}{88}\right)$	$e\left(\frac{39}{88}\right)$
$\chi_{736}(13,\cdot)$	736.bf	88	yes	$1$	$1$	$e\left(\frac{71}{88}\right)$	$e\left(\frac{45}{88}\right)$	$e\left(\frac{37}{44}\right)$	$e\left(\frac{27}{44}\right)$	$e\left(\frac{9}{88}\right)$	$e\left(\frac{3}{88}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{59}{88}\right)$	$e\left(\frac{57}{88}\right)$
$\chi_{736}(15,\cdot)$	736.r	22	no	$1$	$1$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{6}{11}\right)$
$\chi_{736}(17,\cdot)$	736.u	22	no	$-1$	$1$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{7}{11}\right)$
$\chi_{736}(19,\cdot)$	736.be	88	yes	$1$	$1$	$e\left(\frac{3}{88}\right)$	$e\left(\frac{49}{88}\right)$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{3}{44}\right)$	$e\left(\frac{1}{88}\right)$	$e\left(\frac{59}{88}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{75}{88}\right)$	$e\left(\frac{21}{88}\right)$
$\chi_{736}(21,\cdot)$	736.bc	88	yes	$-1$	$1$	$e\left(\frac{29}{88}\right)$	$e\left(\frac{19}{88}\right)$	$e\left(\frac{21}{44}\right)$	$e\left(\frac{29}{44}\right)$	$e\left(\frac{39}{88}\right)$	$e\left(\frac{57}{88}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{21}{88}\right)$	$e\left(\frac{71}{88}\right)$
$\chi_{736}(25,\cdot)$	736.ba	44	no	$1$	$1$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{3}{44}\right)$	$e\left(\frac{1}{44}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{5}{44}\right)$	$e\left(\frac{19}{44}\right)$
$\chi_{736}(27,\cdot)$	736.bd	88	yes	$-1$	$1$	$e\left(\frac{69}{88}\right)$	$e\left(\frac{27}{88}\right)$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{25}{44}\right)$	$e\left(\frac{67}{88}\right)$	$e\left(\frac{37}{88}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{9}{88}\right)$	$e\left(\frac{87}{88}\right)$
$\chi_{736}(29,\cdot)$	736.bf	88	yes	$1$	$1$	$e\left(\frac{19}{88}\right)$	$e\left(\frac{17}{88}\right)$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{21}{88}\right)$	$e\left(\frac{7}{88}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{79}{88}\right)$	$e\left(\frac{45}{88}\right)$
$\chi_{736}(31,\cdot)$	736.v	22	no	$-1$	$1$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{6}{11}\right)$
$\chi_{736}(33,\cdot)$	736.t	22	no	$-1$	$1$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{17}{22}\right)$
$\chi_{736}(35,\cdot)$	736.bd	88	yes	$-1$	$1$	$e\left(\frac{15}{88}\right)$	$e\left(\frac{25}{88}\right)$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{49}{88}\right)$	$e\left(\frac{31}{88}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{67}{88}\right)$	$e\left(\frac{61}{88}\right)$
$\chi_{736}(37,\cdot)$	736.bc	88	yes	$-1$	$1$	$e\left(\frac{57}{88}\right)$	$e\left(\frac{7}{88}\right)$	$e\left(\frac{17}{44}\right)$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{19}{88}\right)$	$e\left(\frac{21}{88}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{17}{88}\right)$	$e\left(\frac{3}{88}\right)$
$\chi_{736}(39,\cdot)$	736.y	44	no	$-1$	$1$	$e\left(\frac{3}{44}\right)$	$e\left(\frac{27}{44}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{1}{44}\right)$	$e\left(\frac{37}{44}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{31}{44}\right)$	$e\left(\frac{43}{44}\right)$
$\chi_{736}(41,\cdot)$	736.ba	44	no	$1$	$1$	$e\left(\frac{43}{44}\right)$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{29}{44}\right)$	$e\left(\frac{39}{44}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{37}{44}\right)$
$\chi_{736}(43,\cdot)$	736.be	88	yes	$1$	$1$	$e\left(\frac{1}{88}\right)$	$e\left(\frac{75}{88}\right)$	$e\left(\frac{3}{44}\right)$	$e\left(\frac{1}{44}\right)$	$e\left(\frac{59}{88}\right)$	$e\left(\frac{49}{88}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{25}{88}\right)$	$e\left(\frac{7}{88}\right)$
$\chi_{736}(45,\cdot)$	736.p	8	yes	$-1$	$1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{3}{8}\right)$	$i$	$i$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{1}{8}\right)$	$1$	$1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{7}{8}\right)$
$\chi_{736}(47,\cdot)$	736.g	2	no	$-1$	$1$	$1$	$-1$	$-1$	$1$	$1$	$-1$	$-1$	$1$	$1$	$-1$
$\chi_{736}(49,\cdot)$	736.x	22	no	$1$	$1$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{21}{22}\right)$
$\chi_{736}(51,\cdot)$	736.be	88	yes	$1$	$1$	$e\left(\frac{75}{88}\right)$	$e\left(\frac{81}{88}\right)$	$e\left(\frac{5}{44}\right)$	$e\left(\frac{31}{44}\right)$	$e\left(\frac{25}{88}\right)$	$e\left(\frac{67}{88}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{27}{88}\right)$	$e\left(\frac{85}{88}\right)$
$\chi_{736}(53,\cdot)$	736.bc	88	yes	$-1$	$1$	$e\left(\frac{61}{88}\right)$	$e\left(\frac{43}{88}\right)$	$e\left(\frac{29}{44}\right)$	$e\left(\frac{17}{44}\right)$	$e\left(\frac{79}{88}\right)$	$e\left(\frac{41}{88}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{29}{88}\right)$	$e\left(\frac{31}{88}\right)$
$\chi_{736}(55,\cdot)$	736.y	44	no	$-1$	$1$	$e\left(\frac{1}{44}\right)$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{27}{44}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{25}{44}\right)$	$e\left(\frac{29}{44}\right)$
$\chi_{736}(57,\cdot)$	736.z	44	no	$-1$	$1$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{29}{44}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{41}{44}\right)$	$e\left(\frac{21}{44}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{39}{44}\right)$	$e\left(\frac{25}{44}\right)$
$\chi_{736}(59,\cdot)$	736.bd	88	yes	$-1$	$1$	$e\left(\frac{5}{88}\right)$	$e\left(\frac{67}{88}\right)$	$e\left(\frac{37}{44}\right)$	$e\left(\frac{5}{44}\right)$	$e\left(\frac{75}{88}\right)$	$e\left(\frac{69}{88}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{81}{88}\right)$	$e\left(\frac{79}{88}\right)$
$\chi_{736}(61,\cdot)$	736.bc	88	yes	$-1$	$1$	$e\left(\frac{43}{88}\right)$	$e\left(\frac{13}{88}\right)$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{43}{44}\right)$	$e\left(\frac{73}{88}\right)$	$e\left(\frac{39}{88}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{19}{88}\right)$	$e\left(\frac{81}{88}\right)$
$\chi_{736}(63,\cdot)$	736.w	22	no	$1$	$1$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{3}{22}\right)$
$\chi_{736}(65,\cdot)$	736.t	22	no	$-1$	$1$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{19}{22}\right)$

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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	$736$
Structure	\(C_{2}\times C_{2}\times C_{88}\)
Order	$352$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(21\)
\(\chi_{736}(1,\cdot)\)	736.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{736}(3,\cdot)\)	736.bd	88	yes	\(-1\)	\(1\)	\(e\left(\frac{23}{88}\right)\)	\(e\left(\frac{9}{88}\right)\)	\(e\left(\frac{3}{44}\right)\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{81}{88}\right)\)	\(e\left(\frac{71}{88}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{3}{88}\right)\)	\(e\left(\frac{29}{88}\right)\)
\(\chi_{736}(5,\cdot)\)	736.bc	88	yes	\(-1\)	\(1\)	\(e\left(\frac{9}{88}\right)\)	\(e\left(\frac{15}{88}\right)\)	\(e\left(\frac{5}{44}\right)\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{3}{88}\right)\)	\(e\left(\frac{45}{88}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{49}{88}\right)\)	\(e\left(\frac{19}{88}\right)\)
\(\chi_{736}(7,\cdot)\)	736.bb	44	no	\(1\)	\(1\)	\(e\left(\frac{3}{44}\right)\)	\(e\left(\frac{5}{44}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{37}{44}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{21}{44}\right)\)
\(\chi_{736}(9,\cdot)\)	736.ba	44	no	\(1\)	\(1\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{37}{44}\right)\)	\(e\left(\frac{27}{44}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{3}{44}\right)\)	\(e\left(\frac{29}{44}\right)\)
\(\chi_{736}(11,\cdot)\)	736.be	88	yes	\(1\)	\(1\)	\(e\left(\frac{81}{88}\right)\)	\(e\left(\frac{3}{88}\right)\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{37}{44}\right)\)	\(e\left(\frac{27}{88}\right)\)	\(e\left(\frac{9}{88}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{1}{88}\right)\)	\(e\left(\frac{39}{88}\right)\)
\(\chi_{736}(13,\cdot)\)	736.bf	88	yes	\(1\)	\(1\)	\(e\left(\frac{71}{88}\right)\)	\(e\left(\frac{45}{88}\right)\)	\(e\left(\frac{37}{44}\right)\)	\(e\left(\frac{27}{44}\right)\)	\(e\left(\frac{9}{88}\right)\)	\(e\left(\frac{3}{88}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{59}{88}\right)\)	\(e\left(\frac{57}{88}\right)\)
\(\chi_{736}(15,\cdot)\)	736.r	22	no	\(1\)	\(1\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{6}{11}\right)\)
\(\chi_{736}(17,\cdot)\)	736.u	22	no	\(-1\)	\(1\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{7}{11}\right)\)
\(\chi_{736}(19,\cdot)\)	736.be	88	yes	\(1\)	\(1\)	\(e\left(\frac{3}{88}\right)\)	\(e\left(\frac{49}{88}\right)\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{3}{44}\right)\)	\(e\left(\frac{1}{88}\right)\)	\(e\left(\frac{59}{88}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{75}{88}\right)\)	\(e\left(\frac{21}{88}\right)\)
\(\chi_{736}(21,\cdot)\)	736.bc	88	yes	\(-1\)	\(1\)	\(e\left(\frac{29}{88}\right)\)	\(e\left(\frac{19}{88}\right)\)	\(e\left(\frac{21}{44}\right)\)	\(e\left(\frac{29}{44}\right)\)	\(e\left(\frac{39}{88}\right)\)	\(e\left(\frac{57}{88}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{21}{88}\right)\)	\(e\left(\frac{71}{88}\right)\)
\(\chi_{736}(25,\cdot)\)	736.ba	44	no	\(1\)	\(1\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{3}{44}\right)\)	\(e\left(\frac{1}{44}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{5}{44}\right)\)	\(e\left(\frac{19}{44}\right)\)
\(\chi_{736}(27,\cdot)\)	736.bd	88	yes	\(-1\)	\(1\)	\(e\left(\frac{69}{88}\right)\)	\(e\left(\frac{27}{88}\right)\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{25}{44}\right)\)	\(e\left(\frac{67}{88}\right)\)	\(e\left(\frac{37}{88}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{9}{88}\right)\)	\(e\left(\frac{87}{88}\right)\)
\(\chi_{736}(29,\cdot)\)	736.bf	88	yes	\(1\)	\(1\)	\(e\left(\frac{19}{88}\right)\)	\(e\left(\frac{17}{88}\right)\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{21}{88}\right)\)	\(e\left(\frac{7}{88}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{79}{88}\right)\)	\(e\left(\frac{45}{88}\right)\)
\(\chi_{736}(31,\cdot)\)	736.v	22	no	\(-1\)	\(1\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{6}{11}\right)\)
\(\chi_{736}(33,\cdot)\)	736.t	22	no	\(-1\)	\(1\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{17}{22}\right)\)
\(\chi_{736}(35,\cdot)\)	736.bd	88	yes	\(-1\)	\(1\)	\(e\left(\frac{15}{88}\right)\)	\(e\left(\frac{25}{88}\right)\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{49}{88}\right)\)	\(e\left(\frac{31}{88}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{67}{88}\right)\)	\(e\left(\frac{61}{88}\right)\)
\(\chi_{736}(37,\cdot)\)	736.bc	88	yes	\(-1\)	\(1\)	\(e\left(\frac{57}{88}\right)\)	\(e\left(\frac{7}{88}\right)\)	\(e\left(\frac{17}{44}\right)\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{19}{88}\right)\)	\(e\left(\frac{21}{88}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{17}{88}\right)\)	\(e\left(\frac{3}{88}\right)\)
\(\chi_{736}(39,\cdot)\)	736.y	44	no	\(-1\)	\(1\)	\(e\left(\frac{3}{44}\right)\)	\(e\left(\frac{27}{44}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{1}{44}\right)\)	\(e\left(\frac{37}{44}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{31}{44}\right)\)	\(e\left(\frac{43}{44}\right)\)
\(\chi_{736}(41,\cdot)\)	736.ba	44	no	\(1\)	\(1\)	\(e\left(\frac{43}{44}\right)\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{29}{44}\right)\)	\(e\left(\frac{39}{44}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{37}{44}\right)\)
\(\chi_{736}(43,\cdot)\)	736.be	88	yes	\(1\)	\(1\)	\(e\left(\frac{1}{88}\right)\)	\(e\left(\frac{75}{88}\right)\)	\(e\left(\frac{3}{44}\right)\)	\(e\left(\frac{1}{44}\right)\)	\(e\left(\frac{59}{88}\right)\)	\(e\left(\frac{49}{88}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{25}{88}\right)\)	\(e\left(\frac{7}{88}\right)\)
\(\chi_{736}(45,\cdot)\)	736.p	8	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(i\)	\(i\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(1\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{736}(47,\cdot)\)	736.g	2	no	\(-1\)	\(1\)	\(1\)	\(-1\)	\(-1\)	\(1\)	\(1\)	\(-1\)	\(-1\)	\(1\)	\(1\)	\(-1\)
\(\chi_{736}(49,\cdot)\)	736.x	22	no	\(1\)	\(1\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{21}{22}\right)\)
\(\chi_{736}(51,\cdot)\)	736.be	88	yes	\(1\)	\(1\)	\(e\left(\frac{75}{88}\right)\)	\(e\left(\frac{81}{88}\right)\)	\(e\left(\frac{5}{44}\right)\)	\(e\left(\frac{31}{44}\right)\)	\(e\left(\frac{25}{88}\right)\)	\(e\left(\frac{67}{88}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{27}{88}\right)\)	\(e\left(\frac{85}{88}\right)\)
\(\chi_{736}(53,\cdot)\)	736.bc	88	yes	\(-1\)	\(1\)	\(e\left(\frac{61}{88}\right)\)	\(e\left(\frac{43}{88}\right)\)	\(e\left(\frac{29}{44}\right)\)	\(e\left(\frac{17}{44}\right)\)	\(e\left(\frac{79}{88}\right)\)	\(e\left(\frac{41}{88}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{29}{88}\right)\)	\(e\left(\frac{31}{88}\right)\)
\(\chi_{736}(55,\cdot)\)	736.y	44	no	\(-1\)	\(1\)	\(e\left(\frac{1}{44}\right)\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{27}{44}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{25}{44}\right)\)	\(e\left(\frac{29}{44}\right)\)
\(\chi_{736}(57,\cdot)\)	736.z	44	no	\(-1\)	\(1\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{29}{44}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{41}{44}\right)\)	\(e\left(\frac{21}{44}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{39}{44}\right)\)	\(e\left(\frac{25}{44}\right)\)
\(\chi_{736}(59,\cdot)\)	736.bd	88	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{88}\right)\)	\(e\left(\frac{67}{88}\right)\)	\(e\left(\frac{37}{44}\right)\)	\(e\left(\frac{5}{44}\right)\)	\(e\left(\frac{75}{88}\right)\)	\(e\left(\frac{69}{88}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{81}{88}\right)\)	\(e\left(\frac{79}{88}\right)\)
\(\chi_{736}(61,\cdot)\)	736.bc	88	yes	\(-1\)	\(1\)	\(e\left(\frac{43}{88}\right)\)	\(e\left(\frac{13}{88}\right)\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{43}{44}\right)\)	\(e\left(\frac{73}{88}\right)\)	\(e\left(\frac{39}{88}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{19}{88}\right)\)	\(e\left(\frac{81}{88}\right)\)
\(\chi_{736}(63,\cdot)\)	736.w	22	no	\(1\)	\(1\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{3}{22}\right)\)
\(\chi_{736}(65,\cdot)\)	736.t	22	no	\(-1\)	\(1\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{19}{22}\right)\)

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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.