LMFDB - Group of Dirichlet characters of modulus 408

sage:H = DirichletGroup(408)

pari:g = idealstar(,408,2)

Character group

sage:G.order() pari:g.no
Order	=	128
sage:H.invariants() pari:g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{2}\times C_{16}$
sage:H.gens() pari:g.gen
Generators	=	$\chi_{408}(103,\cdot)$, $\chi_{408}(205,\cdot)$, $\chi_{408}(137,\cdot)$, $\chi_{408}(241,\cdot)$

First 32 of 128 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	$-1$	$1$	$5$	$7$	$11$	$13$	$19$	$23$	$25$	$29$	$31$	$35$
$\chi_{408}(1,\cdot)$	408.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{408}(5,\cdot)$	408.bm	16	yes	$1$	$1$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{3}{16}\right)$	$-i$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{13}{16}\right)$	$1$
$\chi_{408}(7,\cdot)$	408.bi	16	no	$1$	$1$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{5}{16}\right)$	$-i$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{11}{16}\right)$	$-1$
$\chi_{408}(11,\cdot)$	408.bg	16	yes	$-1$	$1$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{9}{16}\right)$	$i$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{7}{16}\right)$	$-1$
$\chi_{408}(13,\cdot)$	408.s	4	no	$1$	$1$	$-i$	$-i$	$i$	$-1$	$1$	$-i$	$-1$	$-i$	$i$	$-1$
$\chi_{408}(19,\cdot)$	408.bf	8	no	$-1$	$1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{1}{8}\right)$	$1$	$i$	$e\left(\frac{5}{8}\right)$	$-i$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{3}{8}\right)$	$1$
$\chi_{408}(23,\cdot)$	408.bn	16	no	$-1$	$1$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{9}{16}\right)$	$-i$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{15}{16}\right)$	$1$
$\chi_{408}(25,\cdot)$	408.ba	8	no	$1$	$1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{3}{8}\right)$	$-1$	$-i$	$e\left(\frac{3}{8}\right)$	$i$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{5}{8}\right)$	$1$
$\chi_{408}(29,\cdot)$	408.bm	16	yes	$1$	$1$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{11}{16}\right)$	$-i$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{5}{16}\right)$	$1$
$\chi_{408}(31,\cdot)$	408.bi	16	no	$1$	$1$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{7}{16}\right)$	$i$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{9}{16}\right)$	$-1$
$\chi_{408}(35,\cdot)$	408.j	2	no	$1$	$1$	$1$	$-1$	$-1$	$-1$	$1$	$1$	$1$	$1$	$-1$	$-1$
$\chi_{408}(37,\cdot)$	408.bj	16	no	$-1$	$1$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{15}{16}\right)$	$-i$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{9}{16}\right)$	$-1$
$\chi_{408}(41,\cdot)$	408.bh	16	no	$1$	$1$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{5}{16}\right)$	$-i$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{3}{16}\right)$	$-1$
$\chi_{408}(43,\cdot)$	408.bf	8	no	$-1$	$1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{7}{8}\right)$	$1$	$-i$	$e\left(\frac{3}{8}\right)$	$i$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{5}{8}\right)$	$1$
$\chi_{408}(47,\cdot)$	408.x	4	no	$1$	$1$	$-i$	$i$	$-i$	$1$	$1$	$-i$	$-1$	$-i$	$-i$	$1$
$\chi_{408}(49,\cdot)$	408.ba	8	no	$1$	$1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{5}{8}\right)$	$-1$	$i$	$e\left(\frac{5}{8}\right)$	$-i$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{3}{8}\right)$	$1$
$\chi_{408}(53,\cdot)$	408.be	8	yes	$-1$	$1$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{1}{8}\right)$	$1$	$-i$	$e\left(\frac{5}{8}\right)$	$-i$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{7}{8}\right)$	$1$
$\chi_{408}(55,\cdot)$	408.w	4	no	$-1$	$1$	$-i$	$-i$	$-i$	$1$	$1$	$-i$	$-1$	$-i$	$i$	$-1$
$\chi_{408}(59,\cdot)$	408.bd	8	yes	$1$	$1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{7}{8}\right)$	$1$	$-i$	$e\left(\frac{3}{8}\right)$	$i$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{1}{8}\right)$	$-1$
$\chi_{408}(61,\cdot)$	408.bj	16	no	$-1$	$1$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{13}{16}\right)$	$i$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{11}{16}\right)$	$-1$
$\chi_{408}(65,\cdot)$	408.bh	16	no	$1$	$1$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{7}{16}\right)$	$i$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{1}{16}\right)$	$-1$
$\chi_{408}(67,\cdot)$	408.n	2	no	$-1$	$1$	$1$	$1$	$-1$	$-1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{408}(71,\cdot)$	408.bn	16	no	$-1$	$1$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{7}{16}\right)$	$i$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{1}{16}\right)$	$1$
$\chi_{408}(73,\cdot)$	408.bk	16	no	$-1$	$1$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{3}{16}\right)$	$i$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{13}{16}\right)$	$1$
$\chi_{408}(77,\cdot)$	408.be	8	yes	$-1$	$1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{7}{8}\right)$	$1$	$i$	$e\left(\frac{3}{8}\right)$	$i$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{1}{8}\right)$	$1$
$\chi_{408}(79,\cdot)$	408.bi	16	no	$1$	$1$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{9}{16}\right)$	$-i$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{7}{16}\right)$	$-1$
$\chi_{408}(83,\cdot)$	408.bd	8	yes	$1$	$1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{1}{8}\right)$	$1$	$i$	$e\left(\frac{5}{8}\right)$	$-i$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{7}{8}\right)$	$-1$
$\chi_{408}(89,\cdot)$	408.u	4	no	$-1$	$1$	$i$	$i$	$-i$	$1$	$-1$	$-i$	$-1$	$i$	$-i$	$-1$
$\chi_{408}(91,\cdot)$	408.bl	16	no	$1$	$1$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{9}{16}\right)$	$i$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{15}{16}\right)$	$1$
$\chi_{408}(95,\cdot)$	408.bn	16	no	$-1$	$1$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{5}{16}\right)$	$-i$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{3}{16}\right)$	$1$
$\chi_{408}(97,\cdot)$	408.bk	16	no	$-1$	$1$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{11}{16}\right)$	$i$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{5}{16}\right)$	$1$
$\chi_{408}(101,\cdot)$	408.b	2	yes	$-1$	$1$	$-1$	$-1$	$-1$	$-1$	$-1$	$1$	$1$	$-1$	$-1$	$1$

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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	$408$
Structure	\(C_{2}\times C_{2}\times C_{2}\times C_{16}\)
Order	$128$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(5\)	\(7\)	\(11\)	\(13\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)	\(35\)
\(\chi_{408}(1,\cdot)\)	408.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{408}(5,\cdot)\)	408.bm	16	yes	\(1\)	\(1\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(-i\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(1\)
\(\chi_{408}(7,\cdot)\)	408.bi	16	no	\(1\)	\(1\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(-i\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(-1\)
\(\chi_{408}(11,\cdot)\)	408.bg	16	yes	\(-1\)	\(1\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(i\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(-1\)
\(\chi_{408}(13,\cdot)\)	408.s	4	no	\(1\)	\(1\)	\(-i\)	\(-i\)	\(i\)	\(-1\)	\(1\)	\(-i\)	\(-1\)	\(-i\)	\(i\)	\(-1\)
\(\chi_{408}(19,\cdot)\)	408.bf	8	no	\(-1\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(1\)	\(i\)	\(e\left(\frac{5}{8}\right)\)	\(-i\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(1\)
\(\chi_{408}(23,\cdot)\)	408.bn	16	no	\(-1\)	\(1\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(-i\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(1\)
\(\chi_{408}(25,\cdot)\)	408.ba	8	no	\(1\)	\(1\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(-1\)	\(-i\)	\(e\left(\frac{3}{8}\right)\)	\(i\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(1\)
\(\chi_{408}(29,\cdot)\)	408.bm	16	yes	\(1\)	\(1\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(-i\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(1\)
\(\chi_{408}(31,\cdot)\)	408.bi	16	no	\(1\)	\(1\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(i\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(-1\)
\(\chi_{408}(35,\cdot)\)	408.j	2	no	\(1\)	\(1\)	\(1\)	\(-1\)	\(-1\)	\(-1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(-1\)	\(-1\)
\(\chi_{408}(37,\cdot)\)	408.bj	16	no	\(-1\)	\(1\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(-i\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(-1\)
\(\chi_{408}(41,\cdot)\)	408.bh	16	no	\(1\)	\(1\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(-i\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(-1\)
\(\chi_{408}(43,\cdot)\)	408.bf	8	no	\(-1\)	\(1\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(1\)	\(-i\)	\(e\left(\frac{3}{8}\right)\)	\(i\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(1\)
\(\chi_{408}(47,\cdot)\)	408.x	4	no	\(1\)	\(1\)	\(-i\)	\(i\)	\(-i\)	\(1\)	\(1\)	\(-i\)	\(-1\)	\(-i\)	\(-i\)	\(1\)
\(\chi_{408}(49,\cdot)\)	408.ba	8	no	\(1\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(-1\)	\(i\)	\(e\left(\frac{5}{8}\right)\)	\(-i\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(1\)
\(\chi_{408}(53,\cdot)\)	408.be	8	yes	\(-1\)	\(1\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(1\)	\(-i\)	\(e\left(\frac{5}{8}\right)\)	\(-i\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(1\)
\(\chi_{408}(55,\cdot)\)	408.w	4	no	\(-1\)	\(1\)	\(-i\)	\(-i\)	\(-i\)	\(1\)	\(1\)	\(-i\)	\(-1\)	\(-i\)	\(i\)	\(-1\)
\(\chi_{408}(59,\cdot)\)	408.bd	8	yes	\(1\)	\(1\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(1\)	\(-i\)	\(e\left(\frac{3}{8}\right)\)	\(i\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(-1\)
\(\chi_{408}(61,\cdot)\)	408.bj	16	no	\(-1\)	\(1\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(i\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(-1\)
\(\chi_{408}(65,\cdot)\)	408.bh	16	no	\(1\)	\(1\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(i\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(-1\)
\(\chi_{408}(67,\cdot)\)	408.n	2	no	\(-1\)	\(1\)	\(1\)	\(1\)	\(-1\)	\(-1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{408}(71,\cdot)\)	408.bn	16	no	\(-1\)	\(1\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(i\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(1\)
\(\chi_{408}(73,\cdot)\)	408.bk	16	no	\(-1\)	\(1\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(i\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(1\)
\(\chi_{408}(77,\cdot)\)	408.be	8	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(1\)	\(i\)	\(e\left(\frac{3}{8}\right)\)	\(i\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(1\)
\(\chi_{408}(79,\cdot)\)	408.bi	16	no	\(1\)	\(1\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(-i\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(-1\)
\(\chi_{408}(83,\cdot)\)	408.bd	8	yes	\(1\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(1\)	\(i\)	\(e\left(\frac{5}{8}\right)\)	\(-i\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(-1\)
\(\chi_{408}(89,\cdot)\)	408.u	4	no	\(-1\)	\(1\)	\(i\)	\(i\)	\(-i\)	\(1\)	\(-1\)	\(-i\)	\(-1\)	\(i\)	\(-i\)	\(-1\)
\(\chi_{408}(91,\cdot)\)	408.bl	16	no	\(1\)	\(1\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(i\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(1\)
\(\chi_{408}(95,\cdot)\)	408.bn	16	no	\(-1\)	\(1\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(-i\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(1\)
\(\chi_{408}(97,\cdot)\)	408.bk	16	no	\(-1\)	\(1\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(i\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(1\)
\(\chi_{408}(101,\cdot)\)	408.b	2	yes	\(-1\)	\(1\)	\(-1\)	\(-1\)	\(-1\)	\(-1\)	\(-1\)	\(1\)	\(1\)	\(-1\)	\(-1\)	\(1\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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Character group

First 32 of 128 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.