LMFDB - Group of Dirichlet characters of modulus 2720

sage:H = DirichletGroup(2720)

pari:g = idealstar(,2720,2)

Character group

sage:G.order() pari:g.no
Order	=	1024
sage:H.invariants() pari:g.cyc
Structure	=	$C_{2}\times C_{4}\times C_{8}\times C_{16}$
sage:H.gens() pari:g.gen
Generators	=	$\chi_{2720}(511,\cdot)$, $\chi_{2720}(1701,\cdot)$, $\chi_{2720}(2177,\cdot)$, $\chi_{2720}(1601,\cdot)$

First 32 of 1024 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	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$19$	$21$	$23$	$27$	$29$
$\chi_{2720}(1,\cdot)$	2720.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{2720}(3,\cdot)$	2720.gz	16	yes	$-1$	$1$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{1}{8}\right)$	$-1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{7}{16}\right)$
$\chi_{2720}(7,\cdot)$	2720.hc	16	no	$-1$	$1$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{9}{16}\right)$	$i$	$e\left(\frac{3}{8}\right)$	$-1$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{3}{16}\right)$
$\chi_{2720}(9,\cdot)$	2720.fl	8	no	$1$	$1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{3}{8}\right)$	$-i$	$e\left(\frac{5}{8}\right)$	$i$	$1$	$i$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{7}{8}\right)$
$\chi_{2720}(11,\cdot)$	2720.ij	16	no	$1$	$1$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{1}{8}\right)$	$1$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{9}{16}\right)$
$\chi_{2720}(13,\cdot)$	2720.ew	8	yes	$-1$	$1$	$e\left(\frac{1}{8}\right)$	$i$	$i$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{3}{8}\right)$	$i$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{3}{8}\right)$
$\chi_{2720}(19,\cdot)$	2720.db	8	yes	$-1$	$1$	$-1$	$e\left(\frac{3}{8}\right)$	$1$	$1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{3}{8}\right)$	$-1$	$1$
$\chi_{2720}(21,\cdot)$	2720.dj	8	no	$1$	$1$	$e\left(\frac{5}{8}\right)$	$-1$	$i$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{1}{8}\right)$	$1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{8}\right)$
$\chi_{2720}(23,\cdot)$	2720.ih	16	no	$-1$	$1$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{13}{16}\right)$	$i$	$e\left(\frac{3}{8}\right)$	$1$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{15}{16}\right)$
$\chi_{2720}(27,\cdot)$	2720.gz	16	yes	$-1$	$1$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{3}{8}\right)$	$-1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{5}{16}\right)$
$\chi_{2720}(29,\cdot)$	2720.ip	16	yes	$-1$	$1$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{3}{8}\right)$	$1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{11}{16}\right)$
$\chi_{2720}(31,\cdot)$	2720.hl	16	no	$1$	$1$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{7}{16}\right)$	$i$	$e\left(\frac{3}{8}\right)$	$-i$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{5}{16}\right)$
$\chi_{2720}(33,\cdot)$	2720.bl	4	no	$-1$	$1$	$-i$	$i$	$-1$	$-1$	$i$	$-1$	$1$	$-i$	$i$	$1$
$\chi_{2720}(37,\cdot)$	2720.hr	16	yes	$1$	$1$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{7}{8}\right)$	$i$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{11}{16}\right)$
$\chi_{2720}(39,\cdot)$	2720.gs	16	no	$1$	$1$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{15}{16}\right)$	$-1$	$e\left(\frac{5}{8}\right)$	$1$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{13}{16}\right)$
$\chi_{2720}(41,\cdot)$	2720.iw	16	no	$-1$	$1$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{9}{16}\right)$	$1$	$e\left(\frac{7}{8}\right)$	$1$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{3}{16}\right)$
$\chi_{2720}(43,\cdot)$	2720.dm	8	yes	$1$	$1$	$-i$	$e\left(\frac{7}{8}\right)$	$-1$	$-1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{3}{8}\right)$	$i$	$1$
$\chi_{2720}(47,\cdot)$	2720.cj	4	no	$1$	$1$	$1$	$-1$	$1$	$-i$	$i$	$1$	$-1$	$1$	$1$	$i$
$\chi_{2720}(49,\cdot)$	2720.ef	8	no	$1$	$1$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{5}{8}\right)$	$-i$	$e\left(\frac{1}{8}\right)$	$-1$	$-i$	$1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{3}{8}\right)$
$\chi_{2720}(53,\cdot)$	2720.gg	8	yes	$-1$	$1$	$1$	$e\left(\frac{5}{8}\right)$	$1$	$i$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{1}{8}\right)$	$1$	$-i$
$\chi_{2720}(57,\cdot)$	2720.he	16	no	$1$	$1$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{13}{16}\right)$	$i$	$e\left(\frac{3}{8}\right)$	$-1$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{7}{16}\right)$
$\chi_{2720}(59,\cdot)$	2720.ge	8	yes	$-1$	$1$	$1$	$e\left(\frac{1}{8}\right)$	$1$	$-1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{1}{8}\right)$	$1$	$-1$
$\chi_{2720}(61,\cdot)$	2720.hh	16	no	$-1$	$1$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{3}{8}\right)$	$i$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{9}{16}\right)$
$\chi_{2720}(63,\cdot)$	2720.go	16	no	$-1$	$1$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{3}{16}\right)$	$-1$	$e\left(\frac{3}{8}\right)$	$-i$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{1}{16}\right)$
$\chi_{2720}(67,\cdot)$	2720.gc	8	yes	$1$	$1$	$e\left(\frac{7}{8}\right)$	$1$	$-i$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{7}{8}\right)$	$1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{1}{8}\right)$
$\chi_{2720}(69,\cdot)$	2720.fd	8	no	$1$	$1$	$e\left(\frac{7}{8}\right)$	$-i$	$-i$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{8}\right)$	$i$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{3}{8}\right)$
$\chi_{2720}(71,\cdot)$	2720.ix	16	no	$1$	$1$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{3}{16}\right)$	$1$	$e\left(\frac{1}{8}\right)$	$1$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{9}{16}\right)$
$\chi_{2720}(73,\cdot)$	2720.he	16	no	$1$	$1$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{15}{16}\right)$	$-i$	$e\left(\frac{1}{8}\right)$	$-1$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{13}{16}\right)$
$\chi_{2720}(77,\cdot)$	2720.cy	8	yes	$-1$	$1$	$-1$	$e\left(\frac{3}{8}\right)$	$1$	$i$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{7}{8}\right)$	$-1$	$-i$
$\chi_{2720}(79,\cdot)$	2720.ia	16	no	$1$	$1$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{1}{16}\right)$	$-i$	$e\left(\frac{1}{8}\right)$	$-i$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{3}{16}\right)$
$\chi_{2720}(81,\cdot)$	2720.bq	4	no	$1$	$1$	$-i$	$-i$	$-1$	$i$	$-1$	$1$	$-1$	$-i$	$i$	$-i$
$\chi_{2720}(83,\cdot)$	2720.dn	8	yes	$1$	$1$	$-i$	$e\left(\frac{1}{8}\right)$	$-1$	$-1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{8}\right)$	$i$	$1$

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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	$2720$
Structure	\(C_{2}\times C_{4}\times C_{8}\times C_{16}\)
Order	$1024$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(13\)	\(19\)	\(21\)	\(23\)	\(27\)	\(29\)
\(\chi_{2720}(1,\cdot)\)	2720.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{2720}(3,\cdot)\)	2720.gz	16	yes	\(-1\)	\(1\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(-1\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)
\(\chi_{2720}(7,\cdot)\)	2720.hc	16	no	\(-1\)	\(1\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(i\)	\(e\left(\frac{3}{8}\right)\)	\(-1\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)
\(\chi_{2720}(9,\cdot)\)	2720.fl	8	no	\(1\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(-i\)	\(e\left(\frac{5}{8}\right)\)	\(i\)	\(1\)	\(i\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{2720}(11,\cdot)\)	2720.ij	16	no	\(1\)	\(1\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(1\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)
\(\chi_{2720}(13,\cdot)\)	2720.ew	8	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{8}\right)\)	\(i\)	\(i\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(i\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)
\(\chi_{2720}(19,\cdot)\)	2720.db	8	yes	\(-1\)	\(1\)	\(-1\)	\(e\left(\frac{3}{8}\right)\)	\(1\)	\(1\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(-1\)	\(1\)
\(\chi_{2720}(21,\cdot)\)	2720.dj	8	no	\(1\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(-1\)	\(i\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)
\(\chi_{2720}(23,\cdot)\)	2720.ih	16	no	\(-1\)	\(1\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(i\)	\(e\left(\frac{3}{8}\right)\)	\(1\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)
\(\chi_{2720}(27,\cdot)\)	2720.gz	16	yes	\(-1\)	\(1\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(-1\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)
\(\chi_{2720}(29,\cdot)\)	2720.ip	16	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)
\(\chi_{2720}(31,\cdot)\)	2720.hl	16	no	\(1\)	\(1\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(i\)	\(e\left(\frac{3}{8}\right)\)	\(-i\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)
\(\chi_{2720}(33,\cdot)\)	2720.bl	4	no	\(-1\)	\(1\)	\(-i\)	\(i\)	\(-1\)	\(-1\)	\(i\)	\(-1\)	\(1\)	\(-i\)	\(i\)	\(1\)
\(\chi_{2720}(37,\cdot)\)	2720.hr	16	yes	\(1\)	\(1\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(i\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)
\(\chi_{2720}(39,\cdot)\)	2720.gs	16	no	\(1\)	\(1\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(-1\)	\(e\left(\frac{5}{8}\right)\)	\(1\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)
\(\chi_{2720}(41,\cdot)\)	2720.iw	16	no	\(-1\)	\(1\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(1\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)
\(\chi_{2720}(43,\cdot)\)	2720.dm	8	yes	\(1\)	\(1\)	\(-i\)	\(e\left(\frac{7}{8}\right)\)	\(-1\)	\(-1\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(i\)	\(1\)
\(\chi_{2720}(47,\cdot)\)	2720.cj	4	no	\(1\)	\(1\)	\(1\)	\(-1\)	\(1\)	\(-i\)	\(i\)	\(1\)	\(-1\)	\(1\)	\(1\)	\(i\)
\(\chi_{2720}(49,\cdot)\)	2720.ef	8	no	\(1\)	\(1\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(-i\)	\(e\left(\frac{1}{8}\right)\)	\(-1\)	\(-i\)	\(1\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)
\(\chi_{2720}(53,\cdot)\)	2720.gg	8	yes	\(-1\)	\(1\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(1\)	\(i\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(1\)	\(-i\)
\(\chi_{2720}(57,\cdot)\)	2720.he	16	no	\(1\)	\(1\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(i\)	\(e\left(\frac{3}{8}\right)\)	\(-1\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)
\(\chi_{2720}(59,\cdot)\)	2720.ge	8	yes	\(-1\)	\(1\)	\(1\)	\(e\left(\frac{1}{8}\right)\)	\(1\)	\(-1\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(1\)	\(-1\)
\(\chi_{2720}(61,\cdot)\)	2720.hh	16	no	\(-1\)	\(1\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(i\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)
\(\chi_{2720}(63,\cdot)\)	2720.go	16	no	\(-1\)	\(1\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(-1\)	\(e\left(\frac{3}{8}\right)\)	\(-i\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)
\(\chi_{2720}(67,\cdot)\)	2720.gc	8	yes	\(1\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(1\)	\(-i\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)
\(\chi_{2720}(69,\cdot)\)	2720.fd	8	no	\(1\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(-i\)	\(-i\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(i\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)
\(\chi_{2720}(71,\cdot)\)	2720.ix	16	no	\(1\)	\(1\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(1\)	\(e\left(\frac{1}{8}\right)\)	\(1\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)
\(\chi_{2720}(73,\cdot)\)	2720.he	16	no	\(1\)	\(1\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(-i\)	\(e\left(\frac{1}{8}\right)\)	\(-1\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)
\(\chi_{2720}(77,\cdot)\)	2720.cy	8	yes	\(-1\)	\(1\)	\(-1\)	\(e\left(\frac{3}{8}\right)\)	\(1\)	\(i\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(-1\)	\(-i\)
\(\chi_{2720}(79,\cdot)\)	2720.ia	16	no	\(1\)	\(1\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(-i\)	\(e\left(\frac{1}{8}\right)\)	\(-i\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)
\(\chi_{2720}(81,\cdot)\)	2720.bq	4	no	\(1\)	\(1\)	\(-i\)	\(-i\)	\(-1\)	\(i\)	\(-1\)	\(1\)	\(-1\)	\(-i\)	\(i\)	\(-i\)
\(\chi_{2720}(83,\cdot)\)	2720.dn	8	yes	\(1\)	\(1\)	\(-i\)	\(e\left(\frac{1}{8}\right)\)	\(-1\)	\(-1\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(i\)	\(1\)

Introduction

L-functions

Modular forms

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Fields

Representations

Groups

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Properties

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Character group

First 32 of 1024 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.