LMFDB - Group of Dirichlet characters of modulus 4080

Show commands: PariGP / SageMath

sage: H = DirichletGroup(4080)

pari: g = idealstar(,4080,2)

Character group

sage: G.order() pari: g.no
Order	=	1024
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{4}\times C_{4}\times C_{16}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{4080}(511,\cdot)$, $\chi_{4080}(3061,\cdot)$, $\chi_{4080}(1361,\cdot)$, $\chi_{4080}(817,\cdot)$, $\chi_{4080}(241,\cdot)$

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	$-1$	$1$	$7$	$11$	$13$	$19$	$23$	$29$	$31$	$37$	$41$	$43$
$\chi_{4080}(1,\cdot)$	4080.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{4080}(7,\cdot)$	4080.jz	16	no	$-1$	$1$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{13}{16}\right)$	$1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{1}{8}\right)$
$\chi_{4080}(11,\cdot)$	4080.il	16	no	$-1$	$1$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{5}{16}\right)$	$-1$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{5}{8}\right)$
$\chi_{4080}(13,\cdot)$	4080.er	4	no	$-1$	$1$	$1$	$-1$	$-1$	$i$	$-1$	$1$	$i$	$-i$	$i$	$-1$
$\chi_{4080}(19,\cdot)$	4080.hd	8	no	$-1$	$1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{3}{8}\right)$	$i$	$1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{1}{8}\right)$	$-1$
$\chi_{4080}(23,\cdot)$	4080.ia	16	no	$1$	$1$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{1}{16}\right)$	$-1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{1}{8}\right)$
$\chi_{4080}(29,\cdot)$	4080.ke	16	yes	$1$	$1$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{15}{16}\right)$	$1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{7}{8}\right)$
$\chi_{4080}(31,\cdot)$	4080.jh	16	no	$1$	$1$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{7}{16}\right)$	$i$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{5}{8}\right)$
$\chi_{4080}(37,\cdot)$	4080.ir	16	no	$1$	$1$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{11}{16}\right)$	$-i$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{1}{8}\right)$
$\chi_{4080}(41,\cdot)$	4080.ji	16	no	$1$	$1$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{13}{16}\right)$	$i$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{7}{8}\right)$
$\chi_{4080}(43,\cdot)$	4080.fp	8	no	$1$	$1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{5}{8}\right)$	$-1$	$-1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{7}{8}\right)$	$i$
$\chi_{4080}(47,\cdot)$	4080.bl	4	no	$-1$	$1$	$-1$	$-i$	$-i$	$-1$	$-1$	$i$	$-i$	$-1$	$i$	$-i$
$\chi_{4080}(49,\cdot)$	4080.hs	8	no	$1$	$1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{5}{8}\right)$	$1$	$i$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{1}{8}\right)$	$i$
$\chi_{4080}(53,\cdot)$	4080.fq	8	yes	$1$	$1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{7}{8}\right)$	$-1$	$-1$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{8}\right)$	$i$
$\chi_{4080}(59,\cdot)$	4080.he	8	yes	$1$	$1$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{5}{8}\right)$	$-i$	$1$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{7}{8}\right)$	$-1$
$\chi_{4080}(61,\cdot)$	4080.ka	16	no	$-1$	$1$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{1}{16}\right)$	$1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{1}{8}\right)$
$\chi_{4080}(67,\cdot)$	4080.dt	4	no	$1$	$1$	$-i$	$-i$	$1$	$i$	$i$	$i$	$1$	$-1$	$1$	$1$
$\chi_{4080}(71,\cdot)$	4080.iy	16	no	$-1$	$1$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{15}{16}\right)$	$-i$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{1}{8}\right)$
$\chi_{4080}(73,\cdot)$	4080.kl	16	no	$1$	$1$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{11}{16}\right)$	$1$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{3}{8}\right)$
$\chi_{4080}(77,\cdot)$	4080.fq	8	yes	$1$	$1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{1}{8}\right)$	$-1$	$-1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{3}{8}\right)$	$-i$
$\chi_{4080}(79,\cdot)$	4080.ja	16	no	$1$	$1$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{9}{16}\right)$	$i$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{7}{8}\right)$
$\chi_{4080}(83,\cdot)$	4080.hm	8	yes	$-1$	$1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{3}{8}\right)$	$1$	$-1$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{1}{8}\right)$	$i$
$\chi_{4080}(89,\cdot)$	4080.dx	4	no	$-1$	$1$	$-i$	$i$	$1$	$1$	$i$	$-i$	$-i$	$-i$	$-i$	$-1$
$\chi_{4080}(91,\cdot)$	4080.ii	16	no	$1$	$1$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{5}{16}\right)$	$-1$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{5}{8}\right)$
$\chi_{4080}(97,\cdot)$	4080.jw	16	no	$1$	$1$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{11}{16}\right)$	$1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{3}{8}\right)$
$\chi_{4080}(101,\cdot)$	4080.ey	4	no	$-1$	$1$	$1$	$i$	$-i$	$-i$	$-1$	$-i$	$-1$	$-i$	$-1$	$i$
$\chi_{4080}(103,\cdot)$	4080.ec	4	no	$1$	$1$	$i$	$1$	$-i$	$-1$	$-i$	$1$	$-1$	$i$	$1$	$i$
$\chi_{4080}(107,\cdot)$	4080.iv	16	yes	$1$	$1$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{7}{16}\right)$	$-i$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{1}{8}\right)$
$\chi_{4080}(109,\cdot)$	4080.ik	16	no	$-1$	$1$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{9}{16}\right)$	$-1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{5}{8}\right)$
$\chi_{4080}(113,\cdot)$	4080.kk	16	no	$-1$	$1$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{9}{16}\right)$	$1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{1}{8}\right)$
$\chi_{4080}(121,\cdot)$	4080.ho	8	no	$1$	$1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{5}{8}\right)$	$1$	$-i$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{5}{8}\right)$	$i$
$\chi_{4080}(127,\cdot)$	4080.gp	8	no	$1$	$1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{7}{8}\right)$	$i$	$-i$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{7}{8}\right)$	$-1$

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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 $\F_{q}$

Modulus	$4080$
Structure	\(C_{2}\times C_{2}\times C_{4}\times C_{4}\times C_{16}\)
Order	$1024$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(7\)	\(11\)	\(13\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)	\(43\)
\(\chi_{4080}(1,\cdot)\)	4080.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{4080}(7,\cdot)\)	4080.jz	16	no	\(-1\)	\(1\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(1\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)
\(\chi_{4080}(11,\cdot)\)	4080.il	16	no	\(-1\)	\(1\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(-1\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)
\(\chi_{4080}(13,\cdot)\)	4080.er	4	no	\(-1\)	\(1\)	\(1\)	\(-1\)	\(-1\)	\(i\)	\(-1\)	\(1\)	\(i\)	\(-i\)	\(i\)	\(-1\)
\(\chi_{4080}(19,\cdot)\)	4080.hd	8	no	\(-1\)	\(1\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(i\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(-1\)
\(\chi_{4080}(23,\cdot)\)	4080.ia	16	no	\(1\)	\(1\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(-1\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)
\(\chi_{4080}(29,\cdot)\)	4080.ke	16	yes	\(1\)	\(1\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{4080}(31,\cdot)\)	4080.jh	16	no	\(1\)	\(1\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(i\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)
\(\chi_{4080}(37,\cdot)\)	4080.ir	16	no	\(1\)	\(1\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(-i\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)
\(\chi_{4080}(41,\cdot)\)	4080.ji	16	no	\(1\)	\(1\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(i\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{4080}(43,\cdot)\)	4080.fp	8	no	\(1\)	\(1\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(-1\)	\(-1\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(i\)
\(\chi_{4080}(47,\cdot)\)	4080.bl	4	no	\(-1\)	\(1\)	\(-1\)	\(-i\)	\(-i\)	\(-1\)	\(-1\)	\(i\)	\(-i\)	\(-1\)	\(i\)	\(-i\)
\(\chi_{4080}(49,\cdot)\)	4080.hs	8	no	\(1\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(1\)	\(i\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(i\)
\(\chi_{4080}(53,\cdot)\)	4080.fq	8	yes	\(1\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(-1\)	\(-1\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(i\)
\(\chi_{4080}(59,\cdot)\)	4080.he	8	yes	\(1\)	\(1\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(-i\)	\(1\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(-1\)
\(\chi_{4080}(61,\cdot)\)	4080.ka	16	no	\(-1\)	\(1\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)
\(\chi_{4080}(67,\cdot)\)	4080.dt	4	no	\(1\)	\(1\)	\(-i\)	\(-i\)	\(1\)	\(i\)	\(i\)	\(i\)	\(1\)	\(-1\)	\(1\)	\(1\)
\(\chi_{4080}(71,\cdot)\)	4080.iy	16	no	\(-1\)	\(1\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(-i\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)
\(\chi_{4080}(73,\cdot)\)	4080.kl	16	no	\(1\)	\(1\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(1\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)
\(\chi_{4080}(77,\cdot)\)	4080.fq	8	yes	\(1\)	\(1\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(-1\)	\(-1\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(-i\)
\(\chi_{4080}(79,\cdot)\)	4080.ja	16	no	\(1\)	\(1\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(i\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{4080}(83,\cdot)\)	4080.hm	8	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(1\)	\(-1\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(i\)
\(\chi_{4080}(89,\cdot)\)	4080.dx	4	no	\(-1\)	\(1\)	\(-i\)	\(i\)	\(1\)	\(1\)	\(i\)	\(-i\)	\(-i\)	\(-i\)	\(-i\)	\(-1\)
\(\chi_{4080}(91,\cdot)\)	4080.ii	16	no	\(1\)	\(1\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(-1\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)
\(\chi_{4080}(97,\cdot)\)	4080.jw	16	no	\(1\)	\(1\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)
\(\chi_{4080}(101,\cdot)\)	4080.ey	4	no	\(-1\)	\(1\)	\(1\)	\(i\)	\(-i\)	\(-i\)	\(-1\)	\(-i\)	\(-1\)	\(-i\)	\(-1\)	\(i\)
\(\chi_{4080}(103,\cdot)\)	4080.ec	4	no	\(1\)	\(1\)	\(i\)	\(1\)	\(-i\)	\(-1\)	\(-i\)	\(1\)	\(-1\)	\(i\)	\(1\)	\(i\)
\(\chi_{4080}(107,\cdot)\)	4080.iv	16	yes	\(1\)	\(1\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(-i\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)
\(\chi_{4080}(109,\cdot)\)	4080.ik	16	no	\(-1\)	\(1\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(-1\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)
\(\chi_{4080}(113,\cdot)\)	4080.kk	16	no	\(-1\)	\(1\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)
\(\chi_{4080}(121,\cdot)\)	4080.ho	8	no	\(1\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(1\)	\(-i\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(i\)
\(\chi_{4080}(127,\cdot)\)	4080.gp	8	no	\(1\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(i\)	\(-i\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(-1\)

Introduction

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.