LMFDB - Group of Dirichlet characters of modulus 400

Show commands: PariGP / SageMath

sage: H = DirichletGroup(400)

pari: g = idealstar(,400,2)

Character group

sage: G.order() pari: g.no
Order	=	160
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{4}\times C_{20}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{400}(351,\cdot)$, $\chi_{400}(101,\cdot)$, $\chi_{400}(177,\cdot)$

First 32 of 160 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	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$17$	$19$	$21$	$23$	$27$
$\chi_{400}(1,\cdot)$	400.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{400}(3,\cdot)$	400.bd	20	yes	$1$	$1$	$e\left(\frac{1}{5}\right)$	$-i$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{3}{5}\right)$
$\chi_{400}(7,\cdot)$	400.o	4	no	$1$	$1$	$-i$	$-i$	$-1$	$1$	$i$	$i$	$-1$	$-1$	$i$	$i$
$\chi_{400}(9,\cdot)$	400.w	10	no	$1$	$1$	$e\left(\frac{2}{5}\right)$	$-1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{5}\right)$
$\chi_{400}(11,\cdot)$	400.bk	20	yes	$-1$	$1$	$e\left(\frac{17}{20}\right)$	$1$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{11}{20}\right)$
$\chi_{400}(13,\cdot)$	400.bn	20	yes	$-1$	$1$	$e\left(\frac{9}{10}\right)$	$i$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{7}{10}\right)$
$\chi_{400}(17,\cdot)$	400.bg	20	no	$-1$	$1$	$e\left(\frac{11}{20}\right)$	$i$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{13}{20}\right)$
$\chi_{400}(19,\cdot)$	400.bf	20	yes	$-1$	$1$	$e\left(\frac{1}{20}\right)$	$-1$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{3}{20}\right)$
$\chi_{400}(21,\cdot)$	400.be	20	yes	$1$	$1$	$e\left(\frac{19}{20}\right)$	$-1$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{17}{20}\right)$
$\chi_{400}(23,\cdot)$	400.bh	20	no	$1$	$1$	$e\left(\frac{17}{20}\right)$	$i$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{11}{20}\right)$
$\chi_{400}(27,\cdot)$	400.bd	20	yes	$1$	$1$	$e\left(\frac{3}{5}\right)$	$i$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{4}{5}\right)$
$\chi_{400}(29,\cdot)$	400.bl	20	yes	$1$	$1$	$e\left(\frac{19}{20}\right)$	$1$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{17}{20}\right)$
$\chi_{400}(31,\cdot)$	400.z	10	no	$-1$	$1$	$e\left(\frac{3}{10}\right)$	$-1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{9}{10}\right)$
$\chi_{400}(33,\cdot)$	400.bg	20	no	$-1$	$1$	$e\left(\frac{1}{20}\right)$	$-i$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{3}{20}\right)$
$\chi_{400}(37,\cdot)$	400.bn	20	yes	$-1$	$1$	$e\left(\frac{9}{10}\right)$	$-i$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{7}{10}\right)$
$\chi_{400}(39,\cdot)$	400.ba	10	no	$-1$	$1$	$e\left(\frac{1}{10}\right)$	$1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{10}\right)$
$\chi_{400}(41,\cdot)$	400.bb	10	no	$1$	$1$	$e\left(\frac{9}{10}\right)$	$1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{7}{10}\right)$
$\chi_{400}(43,\cdot)$	400.j	4	no	$1$	$1$	$-1$	$-i$	$1$	$-i$	$1$	$-i$	$-i$	$i$	$i$	$-1$
$\chi_{400}(47,\cdot)$	400.bi	20	no	$1$	$1$	$e\left(\frac{9}{20}\right)$	$-i$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{7}{20}\right)$
$\chi_{400}(49,\cdot)$	400.c	2	no	$1$	$1$	$-1$	$-1$	$1$	$1$	$-1$	$-1$	$1$	$1$	$-1$	$-1$
$\chi_{400}(51,\cdot)$	400.r	4	no	$-1$	$1$	$-i$	$1$	$-1$	$i$	$i$	$1$	$-i$	$-i$	$1$	$i$
$\chi_{400}(53,\cdot)$	400.bc	20	yes	$-1$	$1$	$e\left(\frac{1}{5}\right)$	$i$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{3}{5}\right)$
$\chi_{400}(57,\cdot)$	400.m	4	no	$-1$	$1$	$i$	$i$	$-1$	$-1$	$i$	$i$	$1$	$-1$	$-i$	$-i$
$\chi_{400}(59,\cdot)$	400.bf	20	yes	$-1$	$1$	$e\left(\frac{3}{20}\right)$	$-1$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{9}{20}\right)$
$\chi_{400}(61,\cdot)$	400.be	20	yes	$1$	$1$	$e\left(\frac{17}{20}\right)$	$-1$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{11}{20}\right)$
$\chi_{400}(63,\cdot)$	400.bi	20	no	$1$	$1$	$e\left(\frac{3}{20}\right)$	$i$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{9}{20}\right)$
$\chi_{400}(67,\cdot)$	400.bm	20	yes	$1$	$1$	$e\left(\frac{3}{10}\right)$	$i$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{9}{10}\right)$
$\chi_{400}(69,\cdot)$	400.bl	20	yes	$1$	$1$	$e\left(\frac{1}{20}\right)$	$1$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{20}\right)$
$\chi_{400}(71,\cdot)$	400.v	10	no	$-1$	$1$	$e\left(\frac{1}{5}\right)$	$-1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{3}{5}\right)$
$\chi_{400}(73,\cdot)$	400.bj	20	no	$-1$	$1$	$e\left(\frac{7}{20}\right)$	$-i$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{1}{20}\right)$
$\chi_{400}(77,\cdot)$	400.bc	20	yes	$-1$	$1$	$e\left(\frac{3}{5}\right)$	$-i$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{4}{5}\right)$
$\chi_{400}(79,\cdot)$	400.x	10	no	$-1$	$1$	$e\left(\frac{1}{5}\right)$	$1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{5}\right)$

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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 $\F_{q}$

Modulus	$400$
Structure	\(C_{2}\times C_{4}\times C_{20}\)
Order	$160$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(13\)	\(17\)	\(19\)	\(21\)	\(23\)	\(27\)
\(\chi_{400}(1,\cdot)\)	400.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{400}(3,\cdot)\)	400.bd	20	yes	\(1\)	\(1\)	\(e\left(\frac{1}{5}\right)\)	\(-i\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{3}{5}\right)\)
\(\chi_{400}(7,\cdot)\)	400.o	4	no	\(1\)	\(1\)	\(-i\)	\(-i\)	\(-1\)	\(1\)	\(i\)	\(i\)	\(-1\)	\(-1\)	\(i\)	\(i\)
\(\chi_{400}(9,\cdot)\)	400.w	10	no	\(1\)	\(1\)	\(e\left(\frac{2}{5}\right)\)	\(-1\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)
\(\chi_{400}(11,\cdot)\)	400.bk	20	yes	\(-1\)	\(1\)	\(e\left(\frac{17}{20}\right)\)	\(1\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{11}{20}\right)\)
\(\chi_{400}(13,\cdot)\)	400.bn	20	yes	\(-1\)	\(1\)	\(e\left(\frac{9}{10}\right)\)	\(i\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)
\(\chi_{400}(17,\cdot)\)	400.bg	20	no	\(-1\)	\(1\)	\(e\left(\frac{11}{20}\right)\)	\(i\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{13}{20}\right)\)
\(\chi_{400}(19,\cdot)\)	400.bf	20	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{20}\right)\)	\(-1\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{3}{20}\right)\)
\(\chi_{400}(21,\cdot)\)	400.be	20	yes	\(1\)	\(1\)	\(e\left(\frac{19}{20}\right)\)	\(-1\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{17}{20}\right)\)
\(\chi_{400}(23,\cdot)\)	400.bh	20	no	\(1\)	\(1\)	\(e\left(\frac{17}{20}\right)\)	\(i\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{11}{20}\right)\)
\(\chi_{400}(27,\cdot)\)	400.bd	20	yes	\(1\)	\(1\)	\(e\left(\frac{3}{5}\right)\)	\(i\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{400}(29,\cdot)\)	400.bl	20	yes	\(1\)	\(1\)	\(e\left(\frac{19}{20}\right)\)	\(1\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{17}{20}\right)\)
\(\chi_{400}(31,\cdot)\)	400.z	10	no	\(-1\)	\(1\)	\(e\left(\frac{3}{10}\right)\)	\(-1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)
\(\chi_{400}(33,\cdot)\)	400.bg	20	no	\(-1\)	\(1\)	\(e\left(\frac{1}{20}\right)\)	\(-i\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{3}{20}\right)\)
\(\chi_{400}(37,\cdot)\)	400.bn	20	yes	\(-1\)	\(1\)	\(e\left(\frac{9}{10}\right)\)	\(-i\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)
\(\chi_{400}(39,\cdot)\)	400.ba	10	no	\(-1\)	\(1\)	\(e\left(\frac{1}{10}\right)\)	\(1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)
\(\chi_{400}(41,\cdot)\)	400.bb	10	no	\(1\)	\(1\)	\(e\left(\frac{9}{10}\right)\)	\(1\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)
\(\chi_{400}(43,\cdot)\)	400.j	4	no	\(1\)	\(1\)	\(-1\)	\(-i\)	\(1\)	\(-i\)	\(1\)	\(-i\)	\(-i\)	\(i\)	\(i\)	\(-1\)
\(\chi_{400}(47,\cdot)\)	400.bi	20	no	\(1\)	\(1\)	\(e\left(\frac{9}{20}\right)\)	\(-i\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{7}{20}\right)\)
\(\chi_{400}(49,\cdot)\)	400.c	2	no	\(1\)	\(1\)	\(-1\)	\(-1\)	\(1\)	\(1\)	\(-1\)	\(-1\)	\(1\)	\(1\)	\(-1\)	\(-1\)
\(\chi_{400}(51,\cdot)\)	400.r	4	no	\(-1\)	\(1\)	\(-i\)	\(1\)	\(-1\)	\(i\)	\(i\)	\(1\)	\(-i\)	\(-i\)	\(1\)	\(i\)
\(\chi_{400}(53,\cdot)\)	400.bc	20	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{5}\right)\)	\(i\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{3}{5}\right)\)
\(\chi_{400}(57,\cdot)\)	400.m	4	no	\(-1\)	\(1\)	\(i\)	\(i\)	\(-1\)	\(-1\)	\(i\)	\(i\)	\(1\)	\(-1\)	\(-i\)	\(-i\)
\(\chi_{400}(59,\cdot)\)	400.bf	20	yes	\(-1\)	\(1\)	\(e\left(\frac{3}{20}\right)\)	\(-1\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{9}{20}\right)\)
\(\chi_{400}(61,\cdot)\)	400.be	20	yes	\(1\)	\(1\)	\(e\left(\frac{17}{20}\right)\)	\(-1\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{11}{20}\right)\)
\(\chi_{400}(63,\cdot)\)	400.bi	20	no	\(1\)	\(1\)	\(e\left(\frac{3}{20}\right)\)	\(i\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{9}{20}\right)\)
\(\chi_{400}(67,\cdot)\)	400.bm	20	yes	\(1\)	\(1\)	\(e\left(\frac{3}{10}\right)\)	\(i\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)
\(\chi_{400}(69,\cdot)\)	400.bl	20	yes	\(1\)	\(1\)	\(e\left(\frac{1}{20}\right)\)	\(1\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{20}\right)\)
\(\chi_{400}(71,\cdot)\)	400.v	10	no	\(-1\)	\(1\)	\(e\left(\frac{1}{5}\right)\)	\(-1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)
\(\chi_{400}(73,\cdot)\)	400.bj	20	no	\(-1\)	\(1\)	\(e\left(\frac{7}{20}\right)\)	\(-i\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{1}{20}\right)\)
\(\chi_{400}(77,\cdot)\)	400.bc	20	yes	\(-1\)	\(1\)	\(e\left(\frac{3}{5}\right)\)	\(-i\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{400}(79,\cdot)\)	400.x	10	no	\(-1\)	\(1\)	\(e\left(\frac{1}{5}\right)\)	\(1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)

Introduction

L-functions

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Character group

First 32 of 160 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.