LMFDB - Group of Dirichlet characters of modulus 640

Show commands: PariGP / SageMath

sage: H = DirichletGroup(640)

pari: g = idealstar(,640,2)

Character group

sage: G.order() pari: g.no
Order	=	256
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{4}\times C_{32}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{640}(511,\cdot)$, $\chi_{640}(261,\cdot)$, $\chi_{640}(257,\cdot)$

First 32 of 256 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	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$17$	$19$	$21$	$23$	$27$
$\chi_{640}(1,\cdot)$	640.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{640}(3,\cdot)$	640.bl	32	yes	$1$	$1$	$e\left(\frac{1}{32}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{15}{32}\right)$	$e\left(\frac{21}{32}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{5}{32}\right)$	$e\left(\frac{7}{32}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{3}{32}\right)$
$\chi_{640}(7,\cdot)$	640.bj	16	no	$1$	$1$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{7}{16}\right)$	$1$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{9}{16}\right)$
$\chi_{640}(9,\cdot)$	640.bf	16	no	$1$	$1$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{5}{16}\right)$	$-i$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{3}{16}\right)$
$\chi_{640}(11,\cdot)$	640.bp	32	no	$-1$	$1$	$e\left(\frac{15}{32}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{27}{32}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{19}{32}\right)$	$e\left(\frac{17}{32}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{13}{32}\right)$
$\chi_{640}(13,\cdot)$	640.bk	32	yes	$-1$	$1$	$e\left(\frac{21}{32}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{27}{32}\right)$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{31}{32}\right)$
$\chi_{640}(17,\cdot)$	640.bb	8	no	$-1$	$1$	$e\left(\frac{3}{8}\right)$	$1$	$-i$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{7}{8}\right)$	$-i$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{3}{8}\right)$	$1$	$e\left(\frac{1}{8}\right)$
$\chi_{640}(19,\cdot)$	640.bn	32	yes	$-1$	$1$	$e\left(\frac{5}{32}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{19}{32}\right)$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{1}{32}\right)$	$e\left(\frac{11}{32}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{15}{32}\right)$
$\chi_{640}(21,\cdot)$	640.bm	32	no	$1$	$1$	$e\left(\frac{7}{32}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{17}{32}\right)$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{11}{32}\right)$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{21}{32}\right)$
$\chi_{640}(23,\cdot)$	640.bj	16	no	$1$	$1$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{13}{16}\right)$	$1$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{3}{16}\right)$
$\chi_{640}(27,\cdot)$	640.bl	32	yes	$1$	$1$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{31}{32}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{15}{32}\right)$	$e\left(\frac{21}{32}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{9}{32}\right)$
$\chi_{640}(29,\cdot)$	640.bo	32	yes	$1$	$1$	$e\left(\frac{1}{32}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{23}{32}\right)$	$e\left(\frac{5}{32}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{31}{32}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{3}{32}\right)$
$\chi_{640}(31,\cdot)$	640.r	4	no	$-1$	$1$	$i$	$1$	$-1$	$-i$	$-i$	$1$	$i$	$i$	$1$	$-i$
$\chi_{640}(33,\cdot)$	640.i	4	no	$-1$	$1$	$-1$	$i$	$1$	$-i$	$-1$	$-i$	$-i$	$-i$	$-i$	$-1$
$\chi_{640}(37,\cdot)$	640.bk	32	yes	$-1$	$1$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{15}{32}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{15}{32}\right)$	$e\left(\frac{5}{32}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{9}{32}\right)$
$\chi_{640}(39,\cdot)$	640.bh	16	no	$-1$	$1$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{15}{16}\right)$	$i$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{1}{16}\right)$
$\chi_{640}(41,\cdot)$	640.be	16	no	$1$	$1$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{1}{16}\right)$	$i$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{7}{16}\right)$
$\chi_{640}(43,\cdot)$	640.br	32	yes	$1$	$1$	$e\left(\frac{15}{32}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{17}{32}\right)$	$e\left(\frac{27}{32}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{27}{32}\right)$	$e\left(\frac{25}{32}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{13}{32}\right)$
$\chi_{640}(47,\cdot)$	640.u	8	no	$1$	$1$	$e\left(\frac{3}{8}\right)$	$-1$	$-i$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{3}{8}\right)$	$-i$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{7}{8}\right)$	$-1$	$e\left(\frac{1}{8}\right)$
$\chi_{640}(49,\cdot)$	640.z	8	no	$1$	$1$	$e\left(\frac{3}{8}\right)$	$-i$	$-i$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{7}{8}\right)$	$1$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{8}\right)$	$i$	$e\left(\frac{1}{8}\right)$
$\chi_{640}(51,\cdot)$	640.bp	32	no	$-1$	$1$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{27}{32}\right)$	$e\left(\frac{17}{32}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{25}{32}\right)$	$e\left(\frac{19}{32}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{7}{32}\right)$
$\chi_{640}(53,\cdot)$	640.bq	32	yes	$-1$	$1$	$e\left(\frac{23}{32}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{19}{32}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{1}{32}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{5}{32}\right)$
$\chi_{640}(57,\cdot)$	640.bi	16	no	$-1$	$1$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{15}{16}\right)$	$1$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{9}{16}\right)$
$\chi_{640}(59,\cdot)$	640.bn	32	yes	$-1$	$1$	$e\left(\frac{19}{32}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{21}{32}\right)$	$e\left(\frac{15}{32}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{23}{32}\right)$	$e\left(\frac{29}{32}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{25}{32}\right)$
$\chi_{640}(61,\cdot)$	640.bm	32	no	$1$	$1$	$e\left(\frac{25}{32}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{15}{32}\right)$	$e\left(\frac{29}{32}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{21}{32}\right)$	$e\left(\frac{23}{32}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{11}{32}\right)$
$\chi_{640}(63,\cdot)$	640.o	4	no	$1$	$1$	$i$	$i$	$-1$	$1$	$-i$	$-i$	$-1$	$-1$	$-i$	$-i$
$\chi_{640}(67,\cdot)$	640.br	32	yes	$1$	$1$	$e\left(\frac{1}{32}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{31}{32}\right)$	$e\left(\frac{21}{32}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{21}{32}\right)$	$e\left(\frac{23}{32}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{3}{32}\right)$
$\chi_{640}(69,\cdot)$	640.bo	32	yes	$1$	$1$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{5}{32}\right)$	$e\left(\frac{15}{32}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{7}{32}\right)$	$e\left(\frac{29}{32}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{9}{32}\right)$
$\chi_{640}(71,\cdot)$	640.bg	16	no	$-1$	$1$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{3}{16}\right)$	$-i$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{13}{16}\right)$
$\chi_{640}(73,\cdot)$	640.bi	16	no	$-1$	$1$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{9}{16}\right)$	$1$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{15}{16}\right)$
$\chi_{640}(77,\cdot)$	640.bq	32	yes	$-1$	$1$	$e\left(\frac{21}{32}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{11}{32}\right)$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{25}{32}\right)$	$e\left(\frac{19}{32}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{31}{32}\right)$
$\chi_{640}(79,\cdot)$	640.y	8	no	$-1$	$1$	$e\left(\frac{7}{8}\right)$	$i$	$-i$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{7}{8}\right)$	$1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{1}{8}\right)$	$-i$	$e\left(\frac{5}{8}\right)$

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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	$640$
Structure	\(C_{2}\times C_{4}\times C_{32}\)
Order	$256$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(13\)	\(17\)	\(19\)	\(21\)	\(23\)	\(27\)
\(\chi_{640}(1,\cdot)\)	640.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{640}(3,\cdot)\)	640.bl	32	yes	\(1\)	\(1\)	\(e\left(\frac{1}{32}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{15}{32}\right)\)	\(e\left(\frac{21}{32}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{5}{32}\right)\)	\(e\left(\frac{7}{32}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{3}{32}\right)\)
\(\chi_{640}(7,\cdot)\)	640.bj	16	no	\(1\)	\(1\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(1\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{9}{16}\right)\)
\(\chi_{640}(9,\cdot)\)	640.bf	16	no	\(1\)	\(1\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(-i\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{3}{16}\right)\)
\(\chi_{640}(11,\cdot)\)	640.bp	32	no	\(-1\)	\(1\)	\(e\left(\frac{15}{32}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{9}{32}\right)\)	\(e\left(\frac{27}{32}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{19}{32}\right)\)	\(e\left(\frac{17}{32}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{13}{32}\right)\)
\(\chi_{640}(13,\cdot)\)	640.bk	32	yes	\(-1\)	\(1\)	\(e\left(\frac{21}{32}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{27}{32}\right)\)	\(e\left(\frac{9}{32}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{9}{32}\right)\)	\(e\left(\frac{3}{32}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{31}{32}\right)\)
\(\chi_{640}(17,\cdot)\)	640.bb	8	no	\(-1\)	\(1\)	\(e\left(\frac{3}{8}\right)\)	\(1\)	\(-i\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(-i\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(1\)	\(e\left(\frac{1}{8}\right)\)
\(\chi_{640}(19,\cdot)\)	640.bn	32	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{32}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{19}{32}\right)\)	\(e\left(\frac{9}{32}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{1}{32}\right)\)	\(e\left(\frac{11}{32}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{15}{32}\right)\)
\(\chi_{640}(21,\cdot)\)	640.bm	32	no	\(1\)	\(1\)	\(e\left(\frac{7}{32}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{17}{32}\right)\)	\(e\left(\frac{3}{32}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{11}{32}\right)\)	\(e\left(\frac{9}{32}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{21}{32}\right)\)
\(\chi_{640}(23,\cdot)\)	640.bj	16	no	\(1\)	\(1\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(1\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{3}{16}\right)\)
\(\chi_{640}(27,\cdot)\)	640.bl	32	yes	\(1\)	\(1\)	\(e\left(\frac{3}{32}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{13}{32}\right)\)	\(e\left(\frac{31}{32}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{15}{32}\right)\)	\(e\left(\frac{21}{32}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{9}{32}\right)\)
\(\chi_{640}(29,\cdot)\)	640.bo	32	yes	\(1\)	\(1\)	\(e\left(\frac{1}{32}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{23}{32}\right)\)	\(e\left(\frac{5}{32}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{13}{32}\right)\)	\(e\left(\frac{31}{32}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{3}{32}\right)\)
\(\chi_{640}(31,\cdot)\)	640.r	4	no	\(-1\)	\(1\)	\(i\)	\(1\)	\(-1\)	\(-i\)	\(-i\)	\(1\)	\(i\)	\(i\)	\(1\)	\(-i\)
\(\chi_{640}(33,\cdot)\)	640.i	4	no	\(-1\)	\(1\)	\(-1\)	\(i\)	\(1\)	\(-i\)	\(-1\)	\(-i\)	\(-i\)	\(-i\)	\(-i\)	\(-1\)
\(\chi_{640}(37,\cdot)\)	640.bk	32	yes	\(-1\)	\(1\)	\(e\left(\frac{3}{32}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{13}{32}\right)\)	\(e\left(\frac{15}{32}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{15}{32}\right)\)	\(e\left(\frac{5}{32}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{9}{32}\right)\)
\(\chi_{640}(39,\cdot)\)	640.bh	16	no	\(-1\)	\(1\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(i\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{1}{16}\right)\)
\(\chi_{640}(41,\cdot)\)	640.be	16	no	\(1\)	\(1\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(i\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{7}{16}\right)\)
\(\chi_{640}(43,\cdot)\)	640.br	32	yes	\(1\)	\(1\)	\(e\left(\frac{15}{32}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{17}{32}\right)\)	\(e\left(\frac{27}{32}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{27}{32}\right)\)	\(e\left(\frac{25}{32}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{13}{32}\right)\)
\(\chi_{640}(47,\cdot)\)	640.u	8	no	\(1\)	\(1\)	\(e\left(\frac{3}{8}\right)\)	\(-1\)	\(-i\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(-i\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(-1\)	\(e\left(\frac{1}{8}\right)\)
\(\chi_{640}(49,\cdot)\)	640.z	8	no	\(1\)	\(1\)	\(e\left(\frac{3}{8}\right)\)	\(-i\)	\(-i\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(1\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(i\)	\(e\left(\frac{1}{8}\right)\)
\(\chi_{640}(51,\cdot)\)	640.bp	32	no	\(-1\)	\(1\)	\(e\left(\frac{13}{32}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{27}{32}\right)\)	\(e\left(\frac{17}{32}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{25}{32}\right)\)	\(e\left(\frac{19}{32}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{7}{32}\right)\)
\(\chi_{640}(53,\cdot)\)	640.bq	32	yes	\(-1\)	\(1\)	\(e\left(\frac{23}{32}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{9}{32}\right)\)	\(e\left(\frac{19}{32}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{3}{32}\right)\)	\(e\left(\frac{1}{32}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{5}{32}\right)\)
\(\chi_{640}(57,\cdot)\)	640.bi	16	no	\(-1\)	\(1\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(1\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{9}{16}\right)\)
\(\chi_{640}(59,\cdot)\)	640.bn	32	yes	\(-1\)	\(1\)	\(e\left(\frac{19}{32}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{21}{32}\right)\)	\(e\left(\frac{15}{32}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{23}{32}\right)\)	\(e\left(\frac{29}{32}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{25}{32}\right)\)
\(\chi_{640}(61,\cdot)\)	640.bm	32	no	\(1\)	\(1\)	\(e\left(\frac{25}{32}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{15}{32}\right)\)	\(e\left(\frac{29}{32}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{21}{32}\right)\)	\(e\left(\frac{23}{32}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{11}{32}\right)\)
\(\chi_{640}(63,\cdot)\)	640.o	4	no	\(1\)	\(1\)	\(i\)	\(i\)	\(-1\)	\(1\)	\(-i\)	\(-i\)	\(-1\)	\(-1\)	\(-i\)	\(-i\)
\(\chi_{640}(67,\cdot)\)	640.br	32	yes	\(1\)	\(1\)	\(e\left(\frac{1}{32}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{31}{32}\right)\)	\(e\left(\frac{21}{32}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{21}{32}\right)\)	\(e\left(\frac{23}{32}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{3}{32}\right)\)
\(\chi_{640}(69,\cdot)\)	640.bo	32	yes	\(1\)	\(1\)	\(e\left(\frac{3}{32}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{5}{32}\right)\)	\(e\left(\frac{15}{32}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{7}{32}\right)\)	\(e\left(\frac{29}{32}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{9}{32}\right)\)
\(\chi_{640}(71,\cdot)\)	640.bg	16	no	\(-1\)	\(1\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(-i\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{13}{16}\right)\)
\(\chi_{640}(73,\cdot)\)	640.bi	16	no	\(-1\)	\(1\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(1\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{15}{16}\right)\)
\(\chi_{640}(77,\cdot)\)	640.bq	32	yes	\(-1\)	\(1\)	\(e\left(\frac{21}{32}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{11}{32}\right)\)	\(e\left(\frac{9}{32}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{25}{32}\right)\)	\(e\left(\frac{19}{32}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{31}{32}\right)\)
\(\chi_{640}(79,\cdot)\)	640.y	8	no	\(-1\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(i\)	\(-i\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(-i\)	\(e\left(\frac{5}{8}\right)\)

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L-functions

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Character group

First 32 of 256 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.