LMFDB - Group of Dirichlet characters of modulus 1280

sage:H = DirichletGroup(1280)

pari:g = idealstar(,1280,2)

Character group

sage:G.order() pari:g.no
Order	=	512
sage:H.invariants() pari:g.cyc
Structure	=	$C_{2}\times C_{4}\times C_{64}$
sage:H.gens() pari:g.gen
Generators	=	$\chi_{1280}(511,\cdot)$, $\chi_{1280}(261,\cdot)$, $\chi_{1280}(257,\cdot)$

First 32 of 512 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	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$17$	$19$	$21$	$23$	$27$
$\chi_{1280}(1,\cdot)$	1280.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{1280}(3,\cdot)$	1280.bt	64	yes	$1$	$1$	$e\left(\frac{57}{64}\right)$	$e\left(\frac{23}{32}\right)$	$e\left(\frac{25}{32}\right)$	$e\left(\frac{63}{64}\right)$	$e\left(\frac{61}{64}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{37}{64}\right)$	$e\left(\frac{39}{64}\right)$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{43}{64}\right)$
$\chi_{1280}(7,\cdot)$	1280.bl	32	no	$1$	$1$	$e\left(\frac{23}{32}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{25}{32}\right)$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{19}{32}\right)$	$e\left(\frac{1}{32}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{5}{32}\right)$
$\chi_{1280}(9,\cdot)$	1280.bo	32	no	$1$	$1$	$e\left(\frac{25}{32}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{31}{32}\right)$	$e\left(\frac{29}{32}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{5}{32}\right)$	$e\left(\frac{7}{32}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{11}{32}\right)$
$\chi_{1280}(11,\cdot)$	1280.bx	64	no	$-1$	$1$	$e\left(\frac{63}{64}\right)$	$e\left(\frac{25}{32}\right)$	$e\left(\frac{31}{32}\right)$	$e\left(\frac{25}{64}\right)$	$e\left(\frac{27}{64}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{3}{64}\right)$	$e\left(\frac{49}{64}\right)$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{61}{64}\right)$
$\chi_{1280}(13,\cdot)$	1280.bz	64	yes	$-1$	$1$	$e\left(\frac{61}{64}\right)$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{29}{32}\right)$	$e\left(\frac{27}{64}\right)$	$e\left(\frac{49}{64}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{25}{64}\right)$	$e\left(\frac{3}{64}\right)$	$e\left(\frac{17}{32}\right)$	$e\left(\frac{55}{64}\right)$
$\chi_{1280}(17,\cdot)$	1280.bc	16	no	$-1$	$1$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{5}{16}\right)$	$-1$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{3}{16}\right)$
$\chi_{1280}(19,\cdot)$	1280.bu	64	yes	$-1$	$1$	$e\left(\frac{37}{64}\right)$	$e\left(\frac{19}{32}\right)$	$e\left(\frac{5}{32}\right)$	$e\left(\frac{3}{64}\right)$	$e\left(\frac{25}{64}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{49}{64}\right)$	$e\left(\frac{11}{64}\right)$	$e\left(\frac{1}{32}\right)$	$e\left(\frac{47}{64}\right)$
$\chi_{1280}(21,\cdot)$	1280.bv	64	no	$1$	$1$	$e\left(\frac{39}{64}\right)$	$e\left(\frac{1}{32}\right)$	$e\left(\frac{7}{32}\right)$	$e\left(\frac{49}{64}\right)$	$e\left(\frac{3}{64}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{11}{64}\right)$	$e\left(\frac{41}{64}\right)$	$e\left(\frac{27}{32}\right)$	$e\left(\frac{53}{64}\right)$
$\chi_{1280}(23,\cdot)$	1280.bl	32	no	$1$	$1$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{17}{32}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{1}{32}\right)$	$e\left(\frac{27}{32}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{7}{32}\right)$
$\chi_{1280}(27,\cdot)$	1280.bt	64	yes	$1$	$1$	$e\left(\frac{43}{64}\right)$	$e\left(\frac{5}{32}\right)$	$e\left(\frac{11}{32}\right)$	$e\left(\frac{61}{64}\right)$	$e\left(\frac{55}{64}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{47}{64}\right)$	$e\left(\frac{53}{64}\right)$	$e\left(\frac{7}{32}\right)$	$e\left(\frac{1}{64}\right)$
$\chi_{1280}(29,\cdot)$	1280.bw	64	yes	$1$	$1$	$e\left(\frac{49}{64}\right)$	$e\left(\frac{23}{32}\right)$	$e\left(\frac{17}{32}\right)$	$e\left(\frac{23}{64}\right)$	$e\left(\frac{53}{64}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{13}{64}\right)$	$e\left(\frac{31}{64}\right)$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{19}{64}\right)$
$\chi_{1280}(31,\cdot)$	1280.w	8	no	$-1$	$1$	$e\left(\frac{7}{8}\right)$	$-i$	$-i$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{7}{8}\right)$	$-1$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{5}{8}\right)$	$i$	$e\left(\frac{5}{8}\right)$
$\chi_{1280}(33,\cdot)$	1280.v	8	no	$-1$	$1$	$e\left(\frac{7}{8}\right)$	$-1$	$-i$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{3}{8}\right)$	$i$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{3}{8}\right)$	$-1$	$e\left(\frac{5}{8}\right)$
$\chi_{1280}(37,\cdot)$	1280.bz	64	yes	$-1$	$1$	$e\left(\frac{27}{64}\right)$	$e\left(\frac{5}{32}\right)$	$e\left(\frac{27}{32}\right)$	$e\left(\frac{13}{64}\right)$	$e\left(\frac{7}{64}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{31}{64}\right)$	$e\left(\frac{37}{64}\right)$	$e\left(\frac{7}{32}\right)$	$e\left(\frac{17}{64}\right)$
$\chi_{1280}(39,\cdot)$	1280.bn	32	no	$-1$	$1$	$e\left(\frac{27}{32}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{23}{32}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{31}{32}\right)$	$e\left(\frac{21}{32}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{17}{32}\right)$
$\chi_{1280}(41,\cdot)$	1280.bm	32	no	$1$	$1$	$e\left(\frac{29}{32}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{11}{32}\right)$	$e\left(\frac{17}{32}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{19}{32}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{23}{32}\right)$
$\chi_{1280}(43,\cdot)$	1280.by	64	yes	$1$	$1$	$e\left(\frac{7}{64}\right)$	$e\left(\frac{25}{32}\right)$	$e\left(\frac{7}{32}\right)$	$e\left(\frac{33}{64}\right)$	$e\left(\frac{3}{64}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{59}{64}\right)$	$e\left(\frac{57}{64}\right)$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{21}{64}\right)$
$\chi_{1280}(47,\cdot)$	1280.bd	16	no	$1$	$1$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{1}{16}\right)$	$-1$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{15}{16}\right)$
$\chi_{1280}(49,\cdot)$	1280.bf	16	no	$1$	$1$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{3}{16}\right)$	$i$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{16}\right)$
$\chi_{1280}(51,\cdot)$	1280.bx	64	no	$-1$	$1$	$e\left(\frac{61}{64}\right)$	$e\left(\frac{11}{32}\right)$	$e\left(\frac{29}{32}\right)$	$e\left(\frac{11}{64}\right)$	$e\left(\frac{17}{64}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{9}{64}\right)$	$e\left(\frac{19}{64}\right)$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{55}{64}\right)$
$\chi_{1280}(53,\cdot)$	1280.bs	64	yes	$-1$	$1$	$e\left(\frac{63}{64}\right)$	$e\left(\frac{17}{32}\right)$	$e\left(\frac{31}{32}\right)$	$e\left(\frac{41}{64}\right)$	$e\left(\frac{59}{64}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{19}{64}\right)$	$e\left(\frac{33}{64}\right)$	$e\left(\frac{11}{32}\right)$	$e\left(\frac{61}{64}\right)$
$\chi_{1280}(57,\cdot)$	1280.bk	32	no	$-1$	$1$	$e\left(\frac{15}{32}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{1}{32}\right)$	$e\left(\frac{11}{32}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{11}{32}\right)$	$e\left(\frac{25}{32}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{13}{32}\right)$
$\chi_{1280}(59,\cdot)$	1280.bu	64	yes	$-1$	$1$	$e\left(\frac{19}{64}\right)$	$e\left(\frac{21}{32}\right)$	$e\left(\frac{19}{32}\right)$	$e\left(\frac{5}{64}\right)$	$e\left(\frac{63}{64}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{39}{64}\right)$	$e\left(\frac{61}{64}\right)$	$e\left(\frac{23}{32}\right)$	$e\left(\frac{57}{64}\right)$
$\chi_{1280}(61,\cdot)$	1280.bv	64	no	$1$	$1$	$e\left(\frac{25}{64}\right)$	$e\left(\frac{31}{32}\right)$	$e\left(\frac{25}{32}\right)$	$e\left(\frac{15}{64}\right)$	$e\left(\frac{61}{64}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{53}{64}\right)$	$e\left(\frac{23}{64}\right)$	$e\left(\frac{5}{32}\right)$	$e\left(\frac{11}{64}\right)$
$\chi_{1280}(63,\cdot)$	1280.j	4	no	$1$	$1$	$-1$	$-i$	$1$	$-i$	$1$	$-i$	$-i$	$i$	$i$	$-1$
$\chi_{1280}(67,\cdot)$	1280.by	64	yes	$1$	$1$	$e\left(\frac{9}{64}\right)$	$e\left(\frac{23}{32}\right)$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{15}{64}\right)$	$e\left(\frac{13}{64}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{21}{64}\right)$	$e\left(\frac{55}{64}\right)$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{27}{64}\right)$
$\chi_{1280}(69,\cdot)$	1280.bw	64	yes	$1$	$1$	$e\left(\frac{19}{64}\right)$	$e\left(\frac{5}{32}\right)$	$e\left(\frac{19}{32}\right)$	$e\left(\frac{5}{64}\right)$	$e\left(\frac{31}{64}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{39}{64}\right)$	$e\left(\frac{29}{64}\right)$	$e\left(\frac{7}{32}\right)$	$e\left(\frac{57}{64}\right)$
$\chi_{1280}(71,\cdot)$	1280.bp	32	no	$-1$	$1$	$e\left(\frac{23}{32}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{1}{32}\right)$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{27}{32}\right)$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{5}{32}\right)$
$\chi_{1280}(73,\cdot)$	1280.bk	32	no	$-1$	$1$	$e\left(\frac{25}{32}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{23}{32}\right)$	$e\left(\frac{29}{32}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{29}{32}\right)$	$e\left(\frac{31}{32}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{11}{32}\right)$
$\chi_{1280}(77,\cdot)$	1280.bs	64	yes	$-1$	$1$	$e\left(\frac{45}{64}\right)$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{11}{64}\right)$	$e\left(\frac{33}{64}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{41}{64}\right)$	$e\left(\frac{51}{64}\right)$	$e\left(\frac{17}{32}\right)$	$e\left(\frac{7}{64}\right)$
$\chi_{1280}(79,\cdot)$	1280.bh	16	no	$-1$	$1$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{11}{16}\right)$	$i$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{5}{16}\right)$

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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 $\F_{q}$
Belyi maps

Modulus	$1280$
Structure	\(C_{2}\times C_{4}\times C_{64}\)
Order	$512$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(13\)	\(17\)	\(19\)	\(21\)	\(23\)	\(27\)
\(\chi_{1280}(1,\cdot)\)	1280.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{1280}(3,\cdot)\)	1280.bt	64	yes	\(1\)	\(1\)	\(e\left(\frac{57}{64}\right)\)	\(e\left(\frac{23}{32}\right)\)	\(e\left(\frac{25}{32}\right)\)	\(e\left(\frac{63}{64}\right)\)	\(e\left(\frac{61}{64}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{37}{64}\right)\)	\(e\left(\frac{39}{64}\right)\)	\(e\left(\frac{13}{32}\right)\)	\(e\left(\frac{43}{64}\right)\)
\(\chi_{1280}(7,\cdot)\)	1280.bl	32	no	\(1\)	\(1\)	\(e\left(\frac{23}{32}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{25}{32}\right)\)	\(e\left(\frac{3}{32}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{19}{32}\right)\)	\(e\left(\frac{1}{32}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{5}{32}\right)\)
\(\chi_{1280}(9,\cdot)\)	1280.bo	32	no	\(1\)	\(1\)	\(e\left(\frac{25}{32}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{31}{32}\right)\)	\(e\left(\frac{29}{32}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{5}{32}\right)\)	\(e\left(\frac{7}{32}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{11}{32}\right)\)
\(\chi_{1280}(11,\cdot)\)	1280.bx	64	no	\(-1\)	\(1\)	\(e\left(\frac{63}{64}\right)\)	\(e\left(\frac{25}{32}\right)\)	\(e\left(\frac{31}{32}\right)\)	\(e\left(\frac{25}{64}\right)\)	\(e\left(\frac{27}{64}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{3}{64}\right)\)	\(e\left(\frac{49}{64}\right)\)	\(e\left(\frac{3}{32}\right)\)	\(e\left(\frac{61}{64}\right)\)
\(\chi_{1280}(13,\cdot)\)	1280.bz	64	yes	\(-1\)	\(1\)	\(e\left(\frac{61}{64}\right)\)	\(e\left(\frac{3}{32}\right)\)	\(e\left(\frac{29}{32}\right)\)	\(e\left(\frac{27}{64}\right)\)	\(e\left(\frac{49}{64}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{25}{64}\right)\)	\(e\left(\frac{3}{64}\right)\)	\(e\left(\frac{17}{32}\right)\)	\(e\left(\frac{55}{64}\right)\)
\(\chi_{1280}(17,\cdot)\)	1280.bc	16	no	\(-1\)	\(1\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(-1\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{3}{16}\right)\)
\(\chi_{1280}(19,\cdot)\)	1280.bu	64	yes	\(-1\)	\(1\)	\(e\left(\frac{37}{64}\right)\)	\(e\left(\frac{19}{32}\right)\)	\(e\left(\frac{5}{32}\right)\)	\(e\left(\frac{3}{64}\right)\)	\(e\left(\frac{25}{64}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{49}{64}\right)\)	\(e\left(\frac{11}{64}\right)\)	\(e\left(\frac{1}{32}\right)\)	\(e\left(\frac{47}{64}\right)\)
\(\chi_{1280}(21,\cdot)\)	1280.bv	64	no	\(1\)	\(1\)	\(e\left(\frac{39}{64}\right)\)	\(e\left(\frac{1}{32}\right)\)	\(e\left(\frac{7}{32}\right)\)	\(e\left(\frac{49}{64}\right)\)	\(e\left(\frac{3}{64}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{11}{64}\right)\)	\(e\left(\frac{41}{64}\right)\)	\(e\left(\frac{27}{32}\right)\)	\(e\left(\frac{53}{64}\right)\)
\(\chi_{1280}(23,\cdot)\)	1280.bl	32	no	\(1\)	\(1\)	\(e\left(\frac{13}{32}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{3}{32}\right)\)	\(e\left(\frac{17}{32}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{1}{32}\right)\)	\(e\left(\frac{27}{32}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{7}{32}\right)\)
\(\chi_{1280}(27,\cdot)\)	1280.bt	64	yes	\(1\)	\(1\)	\(e\left(\frac{43}{64}\right)\)	\(e\left(\frac{5}{32}\right)\)	\(e\left(\frac{11}{32}\right)\)	\(e\left(\frac{61}{64}\right)\)	\(e\left(\frac{55}{64}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{47}{64}\right)\)	\(e\left(\frac{53}{64}\right)\)	\(e\left(\frac{7}{32}\right)\)	\(e\left(\frac{1}{64}\right)\)
\(\chi_{1280}(29,\cdot)\)	1280.bw	64	yes	\(1\)	\(1\)	\(e\left(\frac{49}{64}\right)\)	\(e\left(\frac{23}{32}\right)\)	\(e\left(\frac{17}{32}\right)\)	\(e\left(\frac{23}{64}\right)\)	\(e\left(\frac{53}{64}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{13}{64}\right)\)	\(e\left(\frac{31}{64}\right)\)	\(e\left(\frac{13}{32}\right)\)	\(e\left(\frac{19}{64}\right)\)
\(\chi_{1280}(31,\cdot)\)	1280.w	8	no	\(-1\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(-i\)	\(-i\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(-1\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(i\)	\(e\left(\frac{5}{8}\right)\)
\(\chi_{1280}(33,\cdot)\)	1280.v	8	no	\(-1\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(-1\)	\(-i\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(i\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(-1\)	\(e\left(\frac{5}{8}\right)\)
\(\chi_{1280}(37,\cdot)\)	1280.bz	64	yes	\(-1\)	\(1\)	\(e\left(\frac{27}{64}\right)\)	\(e\left(\frac{5}{32}\right)\)	\(e\left(\frac{27}{32}\right)\)	\(e\left(\frac{13}{64}\right)\)	\(e\left(\frac{7}{64}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{31}{64}\right)\)	\(e\left(\frac{37}{64}\right)\)	\(e\left(\frac{7}{32}\right)\)	\(e\left(\frac{17}{64}\right)\)
\(\chi_{1280}(39,\cdot)\)	1280.bn	32	no	\(-1\)	\(1\)	\(e\left(\frac{27}{32}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{13}{32}\right)\)	\(e\left(\frac{23}{32}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{31}{32}\right)\)	\(e\left(\frac{21}{32}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{17}{32}\right)\)
\(\chi_{1280}(41,\cdot)\)	1280.bm	32	no	\(1\)	\(1\)	\(e\left(\frac{29}{32}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{11}{32}\right)\)	\(e\left(\frac{17}{32}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{9}{32}\right)\)	\(e\left(\frac{19}{32}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{23}{32}\right)\)
\(\chi_{1280}(43,\cdot)\)	1280.by	64	yes	\(1\)	\(1\)	\(e\left(\frac{7}{64}\right)\)	\(e\left(\frac{25}{32}\right)\)	\(e\left(\frac{7}{32}\right)\)	\(e\left(\frac{33}{64}\right)\)	\(e\left(\frac{3}{64}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{59}{64}\right)\)	\(e\left(\frac{57}{64}\right)\)	\(e\left(\frac{3}{32}\right)\)	\(e\left(\frac{21}{64}\right)\)
\(\chi_{1280}(47,\cdot)\)	1280.bd	16	no	\(1\)	\(1\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(-1\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{15}{16}\right)\)
\(\chi_{1280}(49,\cdot)\)	1280.bf	16	no	\(1\)	\(1\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(i\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{5}{16}\right)\)
\(\chi_{1280}(51,\cdot)\)	1280.bx	64	no	\(-1\)	\(1\)	\(e\left(\frac{61}{64}\right)\)	\(e\left(\frac{11}{32}\right)\)	\(e\left(\frac{29}{32}\right)\)	\(e\left(\frac{11}{64}\right)\)	\(e\left(\frac{17}{64}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{9}{64}\right)\)	\(e\left(\frac{19}{64}\right)\)	\(e\left(\frac{9}{32}\right)\)	\(e\left(\frac{55}{64}\right)\)
\(\chi_{1280}(53,\cdot)\)	1280.bs	64	yes	\(-1\)	\(1\)	\(e\left(\frac{63}{64}\right)\)	\(e\left(\frac{17}{32}\right)\)	\(e\left(\frac{31}{32}\right)\)	\(e\left(\frac{41}{64}\right)\)	\(e\left(\frac{59}{64}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{19}{64}\right)\)	\(e\left(\frac{33}{64}\right)\)	\(e\left(\frac{11}{32}\right)\)	\(e\left(\frac{61}{64}\right)\)
\(\chi_{1280}(57,\cdot)\)	1280.bk	32	no	\(-1\)	\(1\)	\(e\left(\frac{15}{32}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{1}{32}\right)\)	\(e\left(\frac{11}{32}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{11}{32}\right)\)	\(e\left(\frac{25}{32}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{13}{32}\right)\)
\(\chi_{1280}(59,\cdot)\)	1280.bu	64	yes	\(-1\)	\(1\)	\(e\left(\frac{19}{64}\right)\)	\(e\left(\frac{21}{32}\right)\)	\(e\left(\frac{19}{32}\right)\)	\(e\left(\frac{5}{64}\right)\)	\(e\left(\frac{63}{64}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{39}{64}\right)\)	\(e\left(\frac{61}{64}\right)\)	\(e\left(\frac{23}{32}\right)\)	\(e\left(\frac{57}{64}\right)\)
\(\chi_{1280}(61,\cdot)\)	1280.bv	64	no	\(1\)	\(1\)	\(e\left(\frac{25}{64}\right)\)	\(e\left(\frac{31}{32}\right)\)	\(e\left(\frac{25}{32}\right)\)	\(e\left(\frac{15}{64}\right)\)	\(e\left(\frac{61}{64}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{53}{64}\right)\)	\(e\left(\frac{23}{64}\right)\)	\(e\left(\frac{5}{32}\right)\)	\(e\left(\frac{11}{64}\right)\)
\(\chi_{1280}(63,\cdot)\)	1280.j	4	no	\(1\)	\(1\)	\(-1\)	\(-i\)	\(1\)	\(-i\)	\(1\)	\(-i\)	\(-i\)	\(i\)	\(i\)	\(-1\)
\(\chi_{1280}(67,\cdot)\)	1280.by	64	yes	\(1\)	\(1\)	\(e\left(\frac{9}{64}\right)\)	\(e\left(\frac{23}{32}\right)\)	\(e\left(\frac{9}{32}\right)\)	\(e\left(\frac{15}{64}\right)\)	\(e\left(\frac{13}{64}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{21}{64}\right)\)	\(e\left(\frac{55}{64}\right)\)	\(e\left(\frac{13}{32}\right)\)	\(e\left(\frac{27}{64}\right)\)
\(\chi_{1280}(69,\cdot)\)	1280.bw	64	yes	\(1\)	\(1\)	\(e\left(\frac{19}{64}\right)\)	\(e\left(\frac{5}{32}\right)\)	\(e\left(\frac{19}{32}\right)\)	\(e\left(\frac{5}{64}\right)\)	\(e\left(\frac{31}{64}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{39}{64}\right)\)	\(e\left(\frac{29}{64}\right)\)	\(e\left(\frac{7}{32}\right)\)	\(e\left(\frac{57}{64}\right)\)
\(\chi_{1280}(71,\cdot)\)	1280.bp	32	no	\(-1\)	\(1\)	\(e\left(\frac{23}{32}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{1}{32}\right)\)	\(e\left(\frac{3}{32}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{27}{32}\right)\)	\(e\left(\frac{9}{32}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{5}{32}\right)\)
\(\chi_{1280}(73,\cdot)\)	1280.bk	32	no	\(-1\)	\(1\)	\(e\left(\frac{25}{32}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{23}{32}\right)\)	\(e\left(\frac{29}{32}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{29}{32}\right)\)	\(e\left(\frac{31}{32}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{11}{32}\right)\)
\(\chi_{1280}(77,\cdot)\)	1280.bs	64	yes	\(-1\)	\(1\)	\(e\left(\frac{45}{64}\right)\)	\(e\left(\frac{3}{32}\right)\)	\(e\left(\frac{13}{32}\right)\)	\(e\left(\frac{11}{64}\right)\)	\(e\left(\frac{33}{64}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{41}{64}\right)\)	\(e\left(\frac{51}{64}\right)\)	\(e\left(\frac{17}{32}\right)\)	\(e\left(\frac{7}{64}\right)\)
\(\chi_{1280}(79,\cdot)\)	1280.bh	16	no	\(-1\)	\(1\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(i\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{5}{16}\right)\)

Introduction

L-functions

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Character group

First 32 of 512 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.