LMFDB - Group of Dirichlet characters of modulus 85

sage:H = DirichletGroup(85)

pari:g = idealstar(,85,2)

Character group

sage:G.order() pari:g.no
Order	=	64
sage:H.invariants() pari:g.cyc
Structure	=	$C_{4}\times C_{16}$
sage:H.gens() pari:g.gen
Generators	=	$\chi_{85}(52,\cdot)$, $\chi_{85}(71,\cdot)$

First 32 of 64 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	$-1$	$1$	$2$	$3$	$4$	$6$	$7$	$8$	$9$	$11$	$12$	$13$
$\chi_{85}(1,\cdot)$	85.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{85}(2,\cdot)$	85.k	8	yes	$-1$	$1$	$-1$	$e\left(\frac{5}{8}\right)$	$1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{7}{8}\right)$	$-1$	$i$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{5}{8}\right)$	$i$
$\chi_{85}(3,\cdot)$	85.o	16	yes	$1$	$1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{5}{16}\right)$	$i$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{9}{16}\right)$	$-1$
$\chi_{85}(4,\cdot)$	85.j	4	yes	$1$	$1$	$1$	$i$	$1$	$i$	$-i$	$1$	$-1$	$i$	$i$	$-1$
$\chi_{85}(6,\cdot)$	85.q	16	no	$-1$	$1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{15}{16}\right)$	$i$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{3}{16}\right)$	$-i$
$\chi_{85}(7,\cdot)$	85.o	16	yes	$1$	$1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{7}{16}\right)$	$-i$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{3}{16}\right)$	$-1$
$\chi_{85}(8,\cdot)$	85.k	8	yes	$-1$	$1$	$-1$	$e\left(\frac{7}{8}\right)$	$1$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{5}{8}\right)$	$-1$	$-i$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{7}{8}\right)$	$-i$
$\chi_{85}(9,\cdot)$	85.m	8	yes	$1$	$1$	$i$	$e\left(\frac{5}{8}\right)$	$-1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{7}{8}\right)$	$-i$	$i$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{1}{8}\right)$	$1$
$\chi_{85}(11,\cdot)$	85.q	16	no	$-1$	$1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{7}{16}\right)$	$i$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{11}{16}\right)$	$-i$
$\chi_{85}(12,\cdot)$	85.r	16	yes	$1$	$1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{9}{16}\right)$	$i$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{13}{16}\right)$	$1$
$\chi_{85}(13,\cdot)$	85.f	4	yes	$-1$	$1$	$i$	$-1$	$-1$	$-i$	$-1$	$-i$	$1$	$-i$	$1$	$i$
$\chi_{85}(14,\cdot)$	85.p	16	yes	$-1$	$1$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{16}\right)$	$-i$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{13}{16}\right)$	$-i$
$\chi_{85}(16,\cdot)$	85.d	2	no	$1$	$1$	$1$	$-1$	$1$	$-1$	$-1$	$1$	$1$	$-1$	$-1$	$1$
$\chi_{85}(18,\cdot)$	85.h	4	no	$-1$	$1$	$-i$	$i$	$-1$	$1$	$-i$	$i$	$-1$	$1$	$-i$	$i$
$\chi_{85}(19,\cdot)$	85.m	8	yes	$1$	$1$	$-i$	$e\left(\frac{3}{8}\right)$	$-1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{1}{8}\right)$	$i$	$-i$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{7}{8}\right)$	$1$
$\chi_{85}(21,\cdot)$	85.e	4	no	$1$	$1$	$-1$	$-i$	$1$	$i$	$i$	$-1$	$-1$	$i$	$-i$	$1$
$\chi_{85}(22,\cdot)$	85.r	16	yes	$1$	$1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{1}{16}\right)$	$i$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{5}{16}\right)$	$1$
$\chi_{85}(23,\cdot)$	85.r	16	yes	$1$	$1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{3}{16}\right)$	$-i$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{15}{16}\right)$	$1$
$\chi_{85}(24,\cdot)$	85.p	16	yes	$-1$	$1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{3}{16}\right)$	$i$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{7}{16}\right)$	$i$
$\chi_{85}(26,\cdot)$	85.l	8	no	$1$	$1$	$-i$	$e\left(\frac{1}{8}\right)$	$-1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{3}{8}\right)$	$i$	$i$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{8}\right)$	$-1$
$\chi_{85}(27,\cdot)$	85.o	16	yes	$1$	$1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{15}{16}\right)$	$-i$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{11}{16}\right)$	$-1$
$\chi_{85}(28,\cdot)$	85.r	16	yes	$1$	$1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{11}{16}\right)$	$-i$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{7}{16}\right)$	$1$
$\chi_{85}(29,\cdot)$	85.p	16	yes	$-1$	$1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{16}\right)$	$-i$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{1}{16}\right)$	$-i$
$\chi_{85}(31,\cdot)$	85.q	16	no	$-1$	$1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{9}{16}\right)$	$-i$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{5}{16}\right)$	$i$
$\chi_{85}(32,\cdot)$	85.k	8	yes	$-1$	$1$	$-1$	$e\left(\frac{1}{8}\right)$	$1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{3}{8}\right)$	$-1$	$i$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{1}{8}\right)$	$i$
$\chi_{85}(33,\cdot)$	85.g	4	yes	$-1$	$1$	$-i$	$-i$	$-1$	$-1$	$i$	$i$	$-1$	$-1$	$i$	$i$
$\chi_{85}(36,\cdot)$	85.l	8	no	$1$	$1$	$i$	$e\left(\frac{7}{8}\right)$	$-1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{5}{8}\right)$	$-i$	$-i$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{3}{8}\right)$	$-1$
$\chi_{85}(37,\cdot)$	85.r	16	yes	$1$	$1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{13}{16}\right)$	$i$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{1}{16}\right)$	$1$
$\chi_{85}(38,\cdot)$	85.i	4	yes	$-1$	$1$	$i$	$1$	$-1$	$i$	$1$	$-i$	$1$	$i$	$-1$	$i$
$\chi_{85}(39,\cdot)$	85.p	16	yes	$-1$	$1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{13}{16}\right)$	$-i$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{9}{16}\right)$	$-i$
$\chi_{85}(41,\cdot)$	85.q	16	no	$-1$	$1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{11}{16}\right)$	$i$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{15}{16}\right)$	$-i$
$\chi_{85}(42,\cdot)$	85.n	8	yes	$-1$	$1$	$1$	$e\left(\frac{3}{8}\right)$	$1$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{8}\right)$	$1$	$-i$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{3}{8}\right)$	$i$

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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	$85$
Structure	\(C_{4}\times C_{16}\)
Order	$64$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(6\)	\(7\)	\(8\)	\(9\)	\(11\)	\(12\)	\(13\)
\(\chi_{85}(1,\cdot)\)	85.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{85}(2,\cdot)\)	85.k	8	yes	\(-1\)	\(1\)	\(-1\)	\(e\left(\frac{5}{8}\right)\)	\(1\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(-1\)	\(i\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(i\)
\(\chi_{85}(3,\cdot)\)	85.o	16	yes	\(1\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(i\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(-1\)
\(\chi_{85}(4,\cdot)\)	85.j	4	yes	\(1\)	\(1\)	\(1\)	\(i\)	\(1\)	\(i\)	\(-i\)	\(1\)	\(-1\)	\(i\)	\(i\)	\(-1\)
\(\chi_{85}(6,\cdot)\)	85.q	16	no	\(-1\)	\(1\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(i\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(-i\)
\(\chi_{85}(7,\cdot)\)	85.o	16	yes	\(1\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(-i\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(-1\)
\(\chi_{85}(8,\cdot)\)	85.k	8	yes	\(-1\)	\(1\)	\(-1\)	\(e\left(\frac{7}{8}\right)\)	\(1\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(-1\)	\(-i\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(-i\)
\(\chi_{85}(9,\cdot)\)	85.m	8	yes	\(1\)	\(1\)	\(i\)	\(e\left(\frac{5}{8}\right)\)	\(-1\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(-i\)	\(i\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(1\)
\(\chi_{85}(11,\cdot)\)	85.q	16	no	\(-1\)	\(1\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(i\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(-i\)
\(\chi_{85}(12,\cdot)\)	85.r	16	yes	\(1\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(i\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(1\)
\(\chi_{85}(13,\cdot)\)	85.f	4	yes	\(-1\)	\(1\)	\(i\)	\(-1\)	\(-1\)	\(-i\)	\(-1\)	\(-i\)	\(1\)	\(-i\)	\(1\)	\(i\)
\(\chi_{85}(14,\cdot)\)	85.p	16	yes	\(-1\)	\(1\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(-i\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(-i\)
\(\chi_{85}(16,\cdot)\)	85.d	2	no	\(1\)	\(1\)	\(1\)	\(-1\)	\(1\)	\(-1\)	\(-1\)	\(1\)	\(1\)	\(-1\)	\(-1\)	\(1\)
\(\chi_{85}(18,\cdot)\)	85.h	4	no	\(-1\)	\(1\)	\(-i\)	\(i\)	\(-1\)	\(1\)	\(-i\)	\(i\)	\(-1\)	\(1\)	\(-i\)	\(i\)
\(\chi_{85}(19,\cdot)\)	85.m	8	yes	\(1\)	\(1\)	\(-i\)	\(e\left(\frac{3}{8}\right)\)	\(-1\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(i\)	\(-i\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(1\)
\(\chi_{85}(21,\cdot)\)	85.e	4	no	\(1\)	\(1\)	\(-1\)	\(-i\)	\(1\)	\(i\)	\(i\)	\(-1\)	\(-1\)	\(i\)	\(-i\)	\(1\)
\(\chi_{85}(22,\cdot)\)	85.r	16	yes	\(1\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(i\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(1\)
\(\chi_{85}(23,\cdot)\)	85.r	16	yes	\(1\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(-i\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(1\)
\(\chi_{85}(24,\cdot)\)	85.p	16	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(i\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(i\)
\(\chi_{85}(26,\cdot)\)	85.l	8	no	\(1\)	\(1\)	\(-i\)	\(e\left(\frac{1}{8}\right)\)	\(-1\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(i\)	\(i\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(-1\)
\(\chi_{85}(27,\cdot)\)	85.o	16	yes	\(1\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(-i\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(-1\)
\(\chi_{85}(28,\cdot)\)	85.r	16	yes	\(1\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(-i\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(1\)
\(\chi_{85}(29,\cdot)\)	85.p	16	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(-i\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(-i\)
\(\chi_{85}(31,\cdot)\)	85.q	16	no	\(-1\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(-i\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(i\)
\(\chi_{85}(32,\cdot)\)	85.k	8	yes	\(-1\)	\(1\)	\(-1\)	\(e\left(\frac{1}{8}\right)\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(-1\)	\(i\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(i\)
\(\chi_{85}(33,\cdot)\)	85.g	4	yes	\(-1\)	\(1\)	\(-i\)	\(-i\)	\(-1\)	\(-1\)	\(i\)	\(i\)	\(-1\)	\(-1\)	\(i\)	\(i\)
\(\chi_{85}(36,\cdot)\)	85.l	8	no	\(1\)	\(1\)	\(i\)	\(e\left(\frac{7}{8}\right)\)	\(-1\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(-i\)	\(-i\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(-1\)
\(\chi_{85}(37,\cdot)\)	85.r	16	yes	\(1\)	\(1\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(i\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(1\)
\(\chi_{85}(38,\cdot)\)	85.i	4	yes	\(-1\)	\(1\)	\(i\)	\(1\)	\(-1\)	\(i\)	\(1\)	\(-i\)	\(1\)	\(i\)	\(-1\)	\(i\)
\(\chi_{85}(39,\cdot)\)	85.p	16	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(-i\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(-i\)
\(\chi_{85}(41,\cdot)\)	85.q	16	no	\(-1\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(i\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(-i\)
\(\chi_{85}(42,\cdot)\)	85.n	8	yes	\(-1\)	\(1\)	\(1\)	\(e\left(\frac{3}{8}\right)\)	\(1\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(1\)	\(-i\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(i\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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Character group

First 32 of 64 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.